LMFDB - Embedded newform 2394.2.cq.b.1205.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2394,2,Mod(449,2394)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2394.449"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2394, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.cq (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1205.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2394.1205
Dual form			2394.2.cq.b.449.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.72474 - 1.57313i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +(-2.72474 + 1.57313i) q^{10} -1.09638i q^{11} +(3.00000 - 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.05051 - 1.18386i) q^{17} +(-0.500000 - 4.33013i) q^{19} +3.14626i q^{20} +(-0.949490 - 0.548188i) q^{22} +(0.550510 - 0.317837i) q^{23} +(2.44949 + 4.24264i) q^{25} -3.46410i q^{26} +(-0.500000 - 0.866025i) q^{28} +(-3.67423 - 6.36396i) q^{29} +3.46410i q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.05051 + 1.18386i) q^{34} +(-2.72474 - 1.57313i) q^{35} +2.51059i q^{37} +(-4.00000 - 1.73205i) q^{38} +(2.72474 + 1.57313i) q^{40} +(-3.94949 + 6.84072i) q^{41} +(3.22474 - 5.58542i) q^{43} +(-0.949490 + 0.548188i) q^{44} -0.635674i q^{46} +(-6.12372 + 3.53553i) q^{47} +1.00000 q^{49} +4.89898 q^{50} +(-3.00000 - 1.73205i) q^{52} +(-1.22474 - 2.12132i) q^{53} +(-1.72474 + 2.98735i) q^{55} -1.00000 q^{56} -7.34847 q^{58} +(0.550510 - 0.953512i) q^{59} +(-1.55051 - 2.68556i) q^{61} +(3.00000 + 1.73205i) q^{62} +1.00000 q^{64} -10.8990 q^{65} +(-8.02270 + 4.63191i) q^{67} +2.36773i q^{68} +(-2.72474 + 1.57313i) q^{70} +(-5.89898 + 10.2173i) q^{73} +(2.17423 + 1.25529i) q^{74} +(-3.50000 + 2.59808i) q^{76} -1.09638i q^{77} +(-6.00000 - 3.46410i) q^{79} +(2.72474 - 1.57313i) q^{80} +(3.94949 + 6.84072i) q^{82} +5.65685i q^{83} +(3.72474 + 6.45145i) q^{85} +(-3.22474 - 5.58542i) q^{86} +1.09638i q^{88} +(-0.949490 - 1.64456i) q^{89} +(3.00000 - 1.73205i) q^{91} +(-0.550510 - 0.317837i) q^{92} +7.07107i q^{94} +(-5.44949 + 12.5851i) q^{95} +(-7.34847 - 4.24264i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 6 q^{10} + 12 q^{13} + 2 q^{14} - 2 q^{16} - 18 q^{17} - 2 q^{19} + 6 q^{22} + 12 q^{23} - 2 q^{28} + 2 q^{32} - 18 q^{34} - 6 q^{35} - 16 q^{38}+ \cdots + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 6 * q^5 + 4 * q^7 - 4 * q^8 - 6 * q^10 + 12 * q^13 + 2 * q^14 - 2 * q^16 - 18 * q^17 - 2 * q^19 + 6 * q^22 + 12 * q^23 - 2 * q^28 + 2 * q^32 - 18 * q^34 - 6 * q^35 - 16 * q^38 + 6 * q^40 - 6 * q^41 + 8 * q^43 + 6 * q^44 + 4 * q^49 - 12 * q^52 - 2 * q^55 - 4 * q^56 + 12 * q^59 - 16 * q^61 + 12 * q^62 + 4 * q^64 - 24 * q^65 + 12 * q^67 - 6 * q^70 - 4 * q^73 - 6 * q^74 - 14 * q^76 - 24 * q^79 + 6 * q^80 + 6 * q^82 + 10 * q^85 - 8 * q^86 + 6 * q^89 + 12 * q^91 - 12 * q^92 - 12 * q^95 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	−2.72474	−	1.57313i	−1.21854	−	0.703526i	−0.253937	−	0.967221i	$-0.581726\pi$
$5$	−2.72474	−	1.57313i	−1.21854	−	0.703526i	−0.964606	+	0.263695i	$0.915059\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.72474	+	1.57313i	−0.861640	+	0.497468i
$11$		−	1.09638i		−	0.330570i	−0.986246	−	0.165285i	$-0.947146\pi$
$11$		−	1.09638i		−	0.330570i	0.986246	−	0.165285i	$-0.0528544\pi$
$12$		0			0
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	−0.0225039	−	0.999747i	$-0.507164\pi$
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	0.854554	+	0.519362i	$0.173830\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.05051	−	1.18386i	−0.497322	−	0.287129i	0.230285	−	0.973123i	$-0.426034\pi$
$17$	−2.05051	−	1.18386i	−0.497322	−	0.287129i	−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$20$			3.14626i			0.703526i
$21$		0			0
$22$	−0.949490	−	0.548188i	−0.202432	−	0.116874i
$23$	0.550510	−	0.317837i	0.114789	−	0.0662736i	−0.441506	−	0.897258i	$-0.645556\pi$
$23$	0.550510	−	0.317837i	0.114789	−	0.0662736i	0.556295	+	0.830985i	$0.312222\pi$
$24$		0			0
$25$	2.44949	+	4.24264i	0.489898	+	0.848528i
$26$		−	3.46410i		−	0.679366i
$27$		0			0
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	−3.67423	−	6.36396i	−0.682288	−	1.18176i	−0.974281	−	0.225337i	$-0.927652\pi$
$29$	−3.67423	−	6.36396i	−0.682288	−	1.18176i	0.291993	−	0.956421i	$-0.405682\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−2.05051	+	1.18386i	−0.351660	+	0.203031i
$35$	−2.72474	−	1.57313i	−0.460566	−	0.265908i
$36$		0			0
$37$			2.51059i			0.412738i	0.978474	+	0.206369i	$0.0661648\pi$
$37$			2.51059i			0.412738i	−0.978474	+	0.206369i	$0.933835\pi$
$38$	−4.00000	−	1.73205i	−0.648886	−	0.280976i
$39$		0			0
$40$	2.72474	+	1.57313i	0.430820	+	0.248734i
$41$	−3.94949	+	6.84072i	−0.616807	+	1.06834i	0.373258	+	0.927728i	$0.378241\pi$
$41$	−3.94949	+	6.84072i	−0.616807	+	1.06834i	−0.990065	+	0.140613i	$0.955093\pi$
$42$		0			0
$43$	3.22474	−	5.58542i	0.491769	−	0.851769i	−0.508186	−	0.861247i	$-0.669684\pi$
$43$	3.22474	−	5.58542i	0.491769	−	0.851769i	0.999955	+	0.00947842i	$0.00301712\pi$
$44$	−0.949490	+	0.548188i	−0.143141	+	0.0826425i
$45$		0			0
$46$		−	0.635674i		−	0.0937251i
$47$	−6.12372	+	3.53553i	−0.893237	+	0.515711i	−0.875000	−	0.484123i	$-0.839139\pi$
$47$	−6.12372	+	3.53553i	−0.893237	+	0.515711i	−0.0182371	+	0.999834i	$0.505805\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	4.89898			0.692820
$51$		0			0
$52$	−3.00000	−	1.73205i	−0.416025	−	0.240192i
$53$	−1.22474	−	2.12132i	−0.168232	−	0.291386i	0.769567	−	0.638567i	$-0.220472\pi$
$53$	−1.22474	−	2.12132i	−0.168232	−	0.291386i	−0.937798	+	0.347181i	$0.887139\pi$
$54$		0			0
$55$	−1.72474	+	2.98735i	−0.232565	+	0.402814i
$56$	−1.00000			−0.133631
$57$		0			0
$58$	−7.34847			−0.964901
$59$	0.550510	−	0.953512i	0.0716703	−	0.124137i	−0.827963	−	0.560783i	$-0.810500\pi$
$59$	0.550510	−	0.953512i	0.0716703	−	0.124137i	0.899633	+	0.436646i	$0.143834\pi$
$60$		0			0
$61$	−1.55051	−	2.68556i	−0.198522	−	0.343851i	0.749527	−	0.661974i	$-0.230281\pi$
$61$	−1.55051	−	2.68556i	−0.198522	−	0.343851i	−0.948050	+	0.318123i	$0.896948\pi$
$62$	3.00000	+	1.73205i	0.381000	+	0.219971i
$63$		0			0
$64$	1.00000			0.125000
$65$	−10.8990			−1.35185
$66$		0			0
$67$	−8.02270	+	4.63191i	−0.980129	+	0.565878i	−0.902309	−	0.431090i	$-0.858129\pi$
$67$	−8.02270	+	4.63191i	−0.980129	+	0.565878i	−0.0778201	+	0.996967i	$0.524796\pi$
$68$			2.36773i			0.287129i
$69$		0			0
$70$	−2.72474	+	1.57313i	−0.325669	+	0.188025i
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$		0			0
$73$	−5.89898	+	10.2173i	−0.690423	+	1.19585i	0.281276	+	0.959627i	$0.409242\pi$
$73$	−5.89898	+	10.2173i	−0.690423	+	1.19585i	−0.971699	+	0.236221i	$0.924091\pi$
$74$	2.17423	+	1.25529i	0.252750	+	0.145925i
$75$		0			0
$76$	−3.50000	+	2.59808i	−0.401478	+	0.298020i
$77$		−	1.09638i		−	0.124944i
$78$		0			0
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	0.122936	−	0.992415i	$-0.460769\pi$
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	−0.797988	+	0.602673i	$0.794102\pi$
$80$	2.72474	−	1.57313i	0.304636	−	0.175882i
$81$		0			0
$82$	3.94949	+	6.84072i	0.436148	+	0.755431i
$83$			5.65685i			0.620920i	0.950586	+	0.310460i	$0.100483\pi$
$83$			5.65685i			0.620920i	−0.950586	+	0.310460i	$0.899517\pi$
$84$		0			0
$85$	3.72474	+	6.45145i	0.404005	+	0.699758i
$86$	−3.22474	−	5.58542i	−0.347733	−	0.602292i
$87$		0			0
$88$			1.09638i			0.116874i
$89$	−0.949490	−	1.64456i	−0.100646	−	0.174323i	0.811305	−	0.584623i	$-0.198758\pi$
$89$	−0.949490	−	1.64456i	−0.100646	−	0.174323i	−0.911951	+	0.410299i	$0.865424\pi$
$90$		0			0
$91$	3.00000	−	1.73205i	0.314485	−	0.181568i
$92$	−0.550510	−	0.317837i	−0.0573947	−	0.0331368i
$93$		0			0
$94$			7.07107i			0.729325i
$95$	−5.44949	+	12.5851i	−0.559106	+	1.29120i
$96$		0			0
$97$	−7.34847	−	4.24264i	−0.746124	−	0.430775i	0.0781677	−	0.996940i	$-0.475093\pi$
$97$	−7.34847	−	4.24264i	−0.746124	−	0.430775i	−0.824292	+	0.566165i	$0.808426\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$		0			0
$100$	2.44949	−	4.24264i	0.244949	−	0.424264i
$101$	−9.27526	+	5.35507i	−0.922922	+	0.532849i	−0.884566	−	0.466415i	$-0.845545\pi$
$101$	−9.27526	+	5.35507i	−0.922922	+	0.532849i	−0.0383562	+	0.999264i	$0.512212\pi$
$102$		0			0
$103$			0.953512i			0.0939523i	0.998896	+	0.0469762i	$0.0149585\pi$
$103$			0.953512i			0.0939523i	−0.998896	+	0.0469762i	$0.985042\pi$
$104$	−3.00000	+	1.73205i	−0.294174	+	0.169842i
$105$		0			0
$106$	−2.44949			−0.237915
$107$	−1.10102			−0.106440			−0.0532198	−	0.998583i	$-0.516948\pi$
$107$	−1.10102			−0.106440			−0.0532198	+	0.998583i	$0.516948\pi$
$108$		0			0
$109$	12.5227	+	7.22999i	1.19946	+	0.692507i	0.960434	−	0.278507i	$-0.0898395\pi$
$109$	12.5227	+	7.22999i	1.19946	+	0.692507i	0.239023	+	0.971014i	$0.423173\pi$
$110$	1.72474	+	2.98735i	0.164448	+	0.284832i
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	4.89898			0.460857			0.230429	−	0.973089i	$-0.425987\pi$
$113$	4.89898			0.460857			0.230429	+	0.973089i	$0.425987\pi$
$114$		0			0
$115$	−2.00000			−0.186501
$116$	−3.67423	+	6.36396i	−0.341144	+	0.590879i
$117$		0			0
$118$	−0.550510	−	0.953512i	−0.0506786	−	0.0877779i
$119$	−2.05051	−	1.18386i	−0.187970	−	0.108525i
$120$		0			0
$121$	9.79796			0.890724
$122$	−3.10102			−0.280753
$123$		0			0
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$			0.317837i			0.0284282i
$126$		0			0
$127$	0.674235	−	0.389270i	0.0598286	−	0.0345421i	−0.469787	−	0.882780i	$-0.655669\pi$
$127$	0.674235	−	0.389270i	0.0598286	−	0.0345421i	0.529616	+	0.848238i	$0.322336\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−5.44949	+	9.43879i	−0.477952	+	0.827837i
$131$	−10.2247	−	5.90326i	−0.893340	−	0.515770i	−0.0183066	−	0.999832i	$-0.505827\pi$
$131$	−10.2247	−	5.90326i	−0.893340	−	0.515770i	−0.875034	+	0.484062i	$0.839161\pi$
$132$		0			0
$133$	−0.500000	−	4.33013i	−0.0433555	−	0.375470i
$134$			9.26382i			0.800272i
$135$		0			0
$136$	2.05051	+	1.18386i	0.175830	+	0.101515i
$137$	−6.12372	+	3.53553i	−0.523185	+	0.302061i	−0.738237	−	0.674542i	$-0.764341\pi$
$137$	−6.12372	+	3.53553i	−0.523185	+	0.302061i	0.215052	+	0.976603i	$0.431008\pi$
$138$		0			0
$139$	−10.9495	−	18.9651i	−0.928724	−	1.60860i	−0.785460	−	0.618912i	$-0.787574\pi$
$139$	−10.9495	−	18.9651i	−0.928724	−	1.60860i	−0.143263	−	0.989685i	$-0.545760\pi$
$140$			3.14626i			0.265908i
$141$		0			0
$142$		0			0
$143$	−1.89898	−	3.28913i	−0.158801	−	0.275051i
$144$		0			0
$145$			23.1202i			1.92003i
$146$	5.89898	+	10.2173i	0.488203	+	0.845592i
$147$		0			0
$148$	2.17423	−	1.25529i	0.178721	−	0.103185i
$149$	−4.22474	−	2.43916i	−0.346105	−	0.199824i	0.316864	−	0.948471i	$-0.397370\pi$
$149$	−4.22474	−	2.43916i	−0.346105	−	0.199824i	−0.662968	+	0.748648i	$0.730704\pi$
$150$		0			0
$151$			15.4135i			1.25433i	0.778886	+	0.627166i	$0.215785\pi$
$151$			15.4135i			1.25433i	−0.778886	+	0.627166i	$0.784215\pi$
$152$	0.500000	+	4.33013i	0.0405554	+	0.351220i
$153$		0			0
$154$	−0.949490	−	0.548188i	−0.0765121	−	0.0441743i
$155$	5.44949	−	9.43879i	0.437714	−	0.758142i
$156$		0			0
$157$	−8.34847	+	14.4600i	−0.666280	+	1.15403i	0.312656	+	0.949866i	$0.398781\pi$
$157$	−8.34847	+	14.4600i	−0.666280	+	1.15403i	−0.978936	+	0.204165i	$0.934552\pi$
$158$	−6.00000	+	3.46410i	−0.477334	+	0.275589i
$159$		0			0
$160$		−	3.14626i		−	0.248734i
$161$	0.550510	−	0.317837i	0.0433863	−	0.0250491i
$162$		0			0
$163$	18.8990			1.48028			0.740141	−	0.672452i	$-0.234759\pi$
$163$	18.8990			1.48028			0.740141	+	0.672452i	$0.234759\pi$
$164$	7.89898			0.616807
$165$		0			0
$166$	4.89898	+	2.82843i	0.380235	+	0.219529i
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	0.726293	−	0.687386i	$-0.241242\pi$
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	−0.958440	+	0.285295i	$0.907908\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	7.44949			0.571350
$171$		0			0
$172$	−6.44949			−0.491769
$173$	7.34847	−	12.7279i	0.558694	−	0.967686i	−0.438912	−	0.898530i	$-0.644636\pi$
$173$	7.34847	−	12.7279i	0.558694	−	0.967686i	0.997606	−	0.0691560i	$-0.0220306\pi$
$174$		0			0
$175$	2.44949	+	4.24264i	0.185164	+	0.320713i
$176$	0.949490	+	0.548188i	0.0715705	+	0.0413212i
$177$		0			0
$178$	−1.89898			−0.142335
$179$	18.7980			1.40503			0.702513	−	0.711671i	$-0.252061\pi$
$179$	18.7980			1.40503			0.702513	+	0.711671i	$0.252061\pi$
$180$		0			0
$181$	−7.34847	+	4.24264i	−0.546207	+	0.315353i	−0.747591	−	0.664159i	$-0.768790\pi$
$181$	−7.34847	+	4.24264i	−0.546207	+	0.315353i	0.201384	+	0.979512i	$0.435456\pi$
$182$		−	3.46410i		−	0.256776i
$183$		0			0
$184$	−0.550510	+	0.317837i	−0.0405842	+	0.0234313i
$185$	3.94949	−	6.84072i	0.290372	−	0.502940i
$186$		0			0
$187$	−1.29796	+	2.24813i	−0.0949162	+	0.164400i
$188$	6.12372	+	3.53553i	0.446619	+	0.257855i
$189$		0			0
$190$	8.17423	+	11.0119i	0.593021	+	0.798889i
$191$		−	7.84961i		−	0.567978i	−0.958828	−	0.283989i	$-0.908342\pi$
$191$		−	7.84961i		−	0.567978i	0.958828	−	0.283989i	$-0.0916579\pi$
$192$		0			0
$193$	−8.84847	−	5.10867i	−0.636927	−	0.367730i	0.146503	−	0.989210i	$-0.453198\pi$
$193$	−8.84847	−	5.10867i	−0.636927	−	0.367730i	−0.783430	+	0.621480i	$0.786532\pi$
$194$	−7.34847	+	4.24264i	−0.527589	+	0.304604i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$		−	19.7990i		−	1.41062i	−0.708899	−	0.705310i	$-0.750808\pi$
$197$		−	19.7990i		−	1.41062i	0.708899	−	0.705310i	$-0.249192\pi$
$198$		0			0
$199$	−0.449490	−	0.778539i	−0.0318635	−	0.0551892i	0.849654	−	0.527341i	$-0.176811\pi$
$199$	−0.449490	−	0.778539i	−0.0318635	−	0.0551892i	−0.881517	+	0.472152i	$0.843478\pi$
$200$	−2.44949	−	4.24264i	−0.173205	−	0.300000i
$201$		0			0
$202$			10.7101i			0.753563i
$203$	−3.67423	−	6.36396i	−0.257881	−	0.446663i
$204$		0			0
$205$	21.5227	−	12.4261i	1.50321	−	0.867879i
$206$	0.825765	+	0.476756i	0.0575338	+	0.0332172i
$207$		0			0
$208$			3.46410i			0.240192i
$209$	−4.74745	+	0.548188i	−0.328388	+	0.0379190i
$210$		0			0
$211$	1.34847	+	0.778539i	0.0928325	+	0.0535968i	0.545698	−	0.837982i	$-0.316265\pi$
$211$	1.34847	+	0.778539i	0.0928325	+	0.0535968i	−0.452865	+	0.891579i	$0.649598\pi$
$212$	−1.22474	+	2.12132i	−0.0841158	+	0.145693i
$213$		0			0
$214$	−0.550510	+	0.953512i	−0.0376321	+	0.0651807i
$215$	−17.5732	+	10.1459i	−1.19848	+	0.691945i
$216$		0			0
$217$			3.46410i			0.235159i
$218$	12.5227	−	7.22999i	0.848145	−	0.489676i
$219$		0			0
$220$	3.44949			0.232565
$221$	−8.20204			−0.551729
$222$		0			0
$223$	−16.8712	−	9.74058i	−1.12978	−	0.652277i	−0.185898	−	0.982569i	$-0.559520\pi$
$223$	−16.8712	−	9.74058i	−1.12978	−	0.652277i	−0.943879	+	0.330292i	$0.892853\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	2.44949	−	4.24264i	0.162938	−	0.282216i
$227$	−8.44949			−0.560812			−0.280406	−	0.959881i	$-0.590469\pi$
$227$	−8.44949			−0.560812			−0.280406	+	0.959881i	$0.590469\pi$
$228$		0			0
$229$	−11.3485			−0.749928			−0.374964	−	0.927039i	$-0.622345\pi$
$229$	−11.3485			−0.749928			−0.374964	+	0.927039i	$0.622345\pi$
$230$	−1.00000	+	1.73205i	−0.0659380	+	0.114208i
$231$		0			0
$232$	3.67423	+	6.36396i	0.241225	+	0.417815i
$233$	13.1010	+	7.56388i	0.858276	+	0.495526i	0.863435	−	0.504461i	$-0.168309\pi$
$233$	13.1010	+	7.56388i	0.858276	+	0.495526i	−0.00515833	+	0.999987i	$0.501642\pi$
$234$		0			0
$235$	22.2474			1.45126
$236$	−1.10102			−0.0716703
$237$		0			0
$238$	−2.05051	+	1.18386i	−0.132915	+	0.0767384i
$239$		−	12.2672i		−	0.793501i	−0.917927	−	0.396750i	$-0.870138\pi$
$239$		−	12.2672i		−	0.793501i	0.917927	−	0.396750i	$-0.129862\pi$
$240$		0			0
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	−0.0609515	−	0.998141i	$-0.519414\pi$
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	0.833939	+	0.551856i	$0.186080\pi$
$242$	4.89898	−	8.48528i	0.314918	−	0.545455i
$243$		0			0
$244$	−1.55051	+	2.68556i	−0.0992612	+	0.171926i
$245$	−2.72474	−	1.57313i	−0.174078	−	0.100504i
$246$		0			0
$247$	−9.00000	−	12.1244i	−0.572656	−	0.771454i
$248$		−	3.46410i		−	0.219971i
$249$		0			0
$250$	0.275255	+	0.158919i	0.0174087	+	0.0100509i
$251$	7.22474	−	4.17121i	0.456022	−	0.263284i	−0.254348	−	0.967113i	$-0.581861\pi$
$251$	7.22474	−	4.17121i	0.456022	−	0.263284i	0.710370	+	0.703828i	$0.248528\pi$
$252$		0			0
$253$	−0.348469	−	0.603566i	−0.0219081	−	0.0379459i
$254$		−	0.778539i		−	0.0488499i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	−0.888110	−	0.459631i	$-0.847982\pi$
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	0.0460033	−	0.998941i	$-0.485352\pi$
$258$		0			0
$259$			2.51059i			0.156000i
$260$	5.44949	+	9.43879i	0.337963	+	0.585369i
$261$		0			0
$262$	−10.2247	+	5.90326i	−0.631687	+	0.364705i
$263$	−7.37628	−	4.25869i	−0.454841	−	0.262602i	0.255032	−	0.966933i	$-0.417914\pi$
$263$	−7.37628	−	4.25869i	−0.454841	−	0.262602i	−0.709872	+	0.704330i	$0.751247\pi$
$264$		0			0
$265$			7.70674i			0.473421i
$266$	−4.00000	−	1.73205i	−0.245256	−	0.106199i
$267$		0			0
$268$	8.02270	+	4.63191i	0.490065	+	0.282939i
$269$	5.72474	−	9.91555i	0.349044	−	0.604562i	−0.637036	−	0.770834i	$-0.719840\pi$
$269$	5.72474	−	9.91555i	0.349044	−	0.604562i	0.986080	+	0.166272i	$0.0531731\pi$
$270$		0			0
$271$	−2.62372	+	4.54442i	−0.159380	+	0.276054i	−0.934645	−	0.355582i	$-0.884283\pi$
$271$	−2.62372	+	4.54442i	−0.159380	+	0.276054i	0.775265	+	0.631636i	$0.217616\pi$
$272$	2.05051	−	1.18386i	0.124330	−	0.0717822i
$273$		0			0
$274$			7.07107i			0.427179i
$275$	4.65153	−	2.68556i	0.280498	−	0.161946i
$276$		0			0
$277$	12.3485			0.741948			0.370974	−	0.928643i	$-0.379024\pi$
$277$	12.3485			0.741948			0.370974	+	0.928643i	$0.379024\pi$
$278$	−21.8990			−1.31341
$279$		0			0
$280$	2.72474	+	1.57313i	0.162835	+	0.0940126i
$281$	−2.87628	−	4.98186i	−0.171584	−	0.297193i	0.767390	−	0.641181i	$-0.221555\pi$
$281$	−2.87628	−	4.98186i	−0.171584	−	0.297193i	−0.938974	+	0.343988i	$0.888222\pi$
$282$		0			0
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	−0.850782	−	0.525519i	$-0.823871\pi$
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	0.880504	+	0.474039i	$0.157204\pi$
$284$		0			0
$285$		0			0
$286$	−3.79796			−0.224578
$287$	−3.94949	+	6.84072i	−0.233131	+	0.403795i
$288$		0			0
$289$	−5.69694	−	9.86739i	−0.335114	−	0.580435i
$290$	20.0227	+	11.5601i	1.17577	+	0.678833i
$291$		0			0
$292$	11.7980			0.690423
$293$	2.75255			0.160806			0.0804029	−	0.996762i	$-0.474379\pi$
$293$	2.75255			0.160806			0.0804029	+	0.996762i	$0.474379\pi$
$294$		0			0
$295$	−3.00000	+	1.73205i	−0.174667	+	0.100844i
$296$		−	2.51059i		−	0.145925i
$297$		0			0
$298$	−4.22474	+	2.43916i	−0.244733	+	0.141297i
$299$	1.10102	−	1.90702i	0.0636737	−	0.110286i
$300$		0			0
$301$	3.22474	−	5.58542i	0.185871	−	0.321938i
$302$	13.3485	+	7.70674i	0.768118	+	0.443473i
$303$		0			0
$304$	4.00000	+	1.73205i	0.229416	+	0.0993399i
$305$			9.75663i			0.558663i
$306$		0			0
$307$	−12.0000	−	6.92820i	−0.684876	−	0.395413i	0.116814	−	0.993154i	$-0.462732\pi$
$307$	−12.0000	−	6.92820i	−0.684876	−	0.395413i	−0.801690	+	0.597740i	$0.796065\pi$
$308$	−0.949490	+	0.548188i	−0.0541022	+	0.0312359i
$309$		0			0
$310$	−5.44949	−	9.43879i	−0.309510	−	0.536087i
$311$		−	25.9487i		−	1.47141i	−0.677300	−	0.735707i	$-0.736850\pi$
$311$		−	25.9487i		−	1.47141i	0.677300	−	0.735707i	$-0.263150\pi$
$312$		0			0
$313$	−6.44949	−	11.1708i	−0.364547	−	0.631413i	0.624157	−	0.781299i	$-0.285443\pi$
$313$	−6.44949	−	11.1708i	−0.364547	−	0.631413i	−0.988703	+	0.149886i	$0.952109\pi$
$314$	8.34847	+	14.4600i	0.471131	+	0.816023i
$315$		0			0
$316$			6.92820i			0.389742i
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	−6.97730	+	4.02834i	−0.390654	+	0.225544i
$320$	−2.72474	−	1.57313i	−0.152318	−	0.0879408i
$321$		0			0
$322$		−	0.635674i		−	0.0354248i
$323$	−4.10102	+	9.47090i	−0.228187	+	0.526975i
$324$		0			0
$325$	14.6969	+	8.48528i	0.815239	+	0.470679i
$326$	9.44949	−	16.3670i	0.523359	−	0.906484i
$327$		0			0
$328$	3.94949	−	6.84072i	0.218074	−	0.377715i
$329$	−6.12372	+	3.53553i	−0.337612	+	0.194920i
$330$		0			0
$331$		−	33.9411i		−	1.86557i	−0.360429	−	0.932786i	$-0.617370\pi$
$331$		−	33.9411i		−	1.86557i	0.360429	−	0.932786i	$-0.382630\pi$
$332$	4.89898	−	2.82843i	0.268866	−	0.155230i
$333$		0			0
$334$	−6.00000			−0.328305
$335$	29.1464			1.59244
$336$		0			0
$337$	0.303062	+	0.174973i	0.0165088	+	0.00953137i	0.508232	−	0.861220i	$-0.330299\pi$
$337$	0.303062	+	0.174973i	0.0165088	+	0.00953137i	−0.491723	+	0.870752i	$0.663633\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	3.72474	−	6.45145i	0.202003	−	0.349879i
$341$	3.79796			0.205671
$342$		0			0
$343$	1.00000			0.0539949
$344$	−3.22474	+	5.58542i	−0.173867	+	0.301146i
$345$		0			0
$346$	−7.34847	−	12.7279i	−0.395056	−	0.684257i
$347$	11.1464	+	6.43539i	0.598372	+	0.345470i	0.768401	−	0.639969i	$-0.221053\pi$
$347$	11.1464	+	6.43539i	0.598372	+	0.345470i	−0.170029	+	0.985439i	$0.554386\pi$
$348$		0			0
$349$	27.3485			1.46393			0.731965	−	0.681342i	$-0.238603\pi$
$349$	27.3485			1.46393			0.731965	+	0.681342i	$0.238603\pi$
$350$	4.89898			0.261861
$351$		0			0
$352$	0.949490	−	0.548188i	0.0506080	−	0.0292185i
$353$			23.1523i			1.23227i	0.787639	+	0.616137i	$0.211303\pi$
$353$			23.1523i			1.23227i	−0.787639	+	0.616137i	$0.788697\pi$
$354$		0			0
$355$		0			0
$356$	−0.949490	+	1.64456i	−0.0503229	+	0.0871617i
$357$		0			0
$358$	9.39898	−	16.2795i	0.496752	−	0.860399i
$359$	26.4495	+	15.2706i	1.39595	+	0.805952i	0.993965	−	0.109694i	$-0.0349870\pi$
$359$	26.4495	+	15.2706i	1.39595	+	0.805952i	0.401985	+	0.915646i	$0.368320\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$			8.48528i			0.445976i
$363$		0			0
$364$	−3.00000	−	1.73205i	−0.157243	−	0.0907841i
$365$	32.1464	−	18.5597i	1.68262	−	0.971462i
$366$		0			0
$367$	−3.17423	−	5.49794i	−0.165694	−	0.286990i	0.771208	−	0.636584i	$-0.219653\pi$
$367$	−3.17423	−	5.49794i	−0.165694	−	0.286990i	−0.936901	+	0.349594i	$0.886320\pi$
$368$			0.635674i			0.0331368i
$369$		0			0
$370$	−3.94949	−	6.84072i	−0.205324	−	0.355632i
$371$	−1.22474	−	2.12132i	−0.0635856	−	0.110133i
$372$		0			0
$373$		−	4.06767i		−	0.210616i	−0.994440	−	0.105308i	$-0.966417\pi$
$373$		−	4.06767i		−	0.210616i	0.994440	−	0.105308i	$-0.0335828\pi$
$374$	1.29796	+	2.24813i	0.0671159	+	0.116248i
$375$		0			0
$376$	6.12372	−	3.53553i	0.315807	−	0.182331i
$377$	−22.0454	−	12.7279i	−1.13540	−	0.655521i
$378$		0			0
$379$			6.92820i			0.355878i	0.984042	+	0.177939i	$0.0569430\pi$
$379$			6.92820i			0.355878i	−0.984042	+	0.177939i	$0.943057\pi$
$380$	13.6237	−	1.57313i	0.698882	−	0.0807000i
$381$		0			0
$382$	−6.79796	−	3.92480i	−0.347814	−	0.200810i
$383$	10.8990	−	18.8776i	0.556912	−	0.964600i	−0.440840	−	0.897586i	$-0.645319\pi$
$383$	10.8990	−	18.8776i	0.556912	−	0.964600i	0.997752	−	0.0670140i	$-0.0213472\pi$
$384$		0			0
$385$	−1.72474	+	2.98735i	−0.0879011	+	0.152249i
$386$	−8.84847	+	5.10867i	−0.450375	+	0.260024i
$387$		0			0
$388$			8.48528i			0.430775i
$389$	−20.4495	+	11.8065i	−1.03683	+	0.598614i	−0.918934	−	0.394412i	$-0.870948\pi$
$389$	−20.4495	+	11.8065i	−1.03683	+	0.598614i	−0.117896	+	0.993026i	$0.537615\pi$
$390$		0			0
$391$	−1.50510			−0.0761163
$392$	−1.00000			−0.0505076
$393$		0			0
$394$	−17.1464	−	9.89949i	−0.863825	−	0.498729i
$395$	10.8990	+	18.8776i	0.548387	+	0.949834i
$396$		0			0
$397$	2.67423	−	4.63191i	0.134216	−	0.232469i	−0.791082	−	0.611711i	$-0.790482\pi$
$397$	2.67423	−	4.63191i	0.134216	−	0.232469i	0.925298	+	0.379242i	$0.123815\pi$
$398$	−0.898979			−0.0450618
$399$		0			0
$400$	−4.89898			−0.244949
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$		0			0
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	9.27526	+	5.35507i	0.461461	+	0.266425i
$405$		0			0
$406$	−7.34847			−0.364698
$407$	2.75255			0.136439
$408$		0			0
$409$	26.6969	−	15.4135i	1.32008	−	0.762148i	0.336338	−	0.941741i	$-0.390812\pi$
$409$	26.6969	−	15.4135i	1.32008	−	0.762148i	0.983741	+	0.179594i	$0.0574783\pi$
$410$		−	24.8523i		−	1.22737i
$411$		0			0
$412$	0.825765	−	0.476756i	0.0406825	−	0.0234881i
$413$	0.550510	−	0.953512i	0.0270888	−	0.0469192i
$414$		0			0
$415$	8.89898	−	15.4135i	0.436834	−	0.756618i
$416$	3.00000	+	1.73205i	0.147087	+	0.0849208i
$417$		0			0
$418$	−1.89898	+	4.38551i	−0.0928821	+	0.214502i
$419$			20.6417i			1.00842i	0.863582	+	0.504208i	$0.168215\pi$
$419$			20.6417i			1.00842i	−0.863582	+	0.504208i	$0.831785\pi$
$420$		0			0
$421$	−19.8712	−	11.4726i	−0.968462	−	0.559142i	−0.0696948	−	0.997568i	$-0.522203\pi$
$421$	−19.8712	−	11.4726i	−0.968462	−	0.559142i	−0.898767	+	0.438427i	$0.855536\pi$
$422$	1.34847	−	0.778539i	0.0656425	−	0.0378987i
$423$		0			0
$424$	1.22474	+	2.12132i	0.0594789	+	0.103020i
$425$		−	11.5994i		−	0.562655i
$426$		0			0
$427$	−1.55051	−	2.68556i	−0.0750345	−	0.129963i
$428$	0.550510	+	0.953512i	0.0266099	+	0.0460897i
$429$		0			0
$430$			20.2918i			0.978557i
$431$	17.1742	+	29.7466i	0.827254	+	1.43285i	0.900185	+	0.435509i	$0.143431\pi$
$431$	17.1742	+	29.7466i	0.827254	+	1.43285i	−0.0729308	+	0.997337i	$0.523235\pi$
$432$		0			0
$433$	32.6969	−	18.8776i	1.57131	−	0.907199i	0.575306	−	0.817938i	$-0.304883\pi$
$433$	32.6969	−	18.8776i	1.57131	−	0.907199i	0.996008	−	0.0892608i	$-0.0284505\pi$
$434$	3.00000	+	1.73205i	0.144005	+	0.0831411i
$435$		0			0
$436$		−	14.4600i		−	0.692507i
$437$	−1.65153	−	2.22486i	−0.0790034	−	0.106430i
$438$		0			0
$439$	−30.5227	−	17.6223i	−1.45677	−	0.841066i	−0.457918	−	0.888994i	$-0.651405\pi$
$439$	−30.5227	−	17.6223i	−1.45677	−	0.841066i	−0.998851	+	0.0479282i	$0.984738\pi$
$440$	1.72474	−	2.98735i	0.0822240	−	0.142416i
$441$		0			0
$442$	−4.10102	+	7.10318i	−0.195066	+	0.337864i
$443$	−24.4949	+	14.1421i	−1.16379	+	0.671913i	−0.952209	−	0.305448i	$-0.901194\pi$
$443$	−24.4949	+	14.1421i	−1.16379	+	0.671913i	−0.211579	+	0.977361i	$0.567861\pi$
$444$		0			0
$445$			5.97469i			0.283228i
$446$	−16.8712	+	9.74058i	−0.798873	+	0.461230i
$447$		0			0
$448$	1.00000			0.0472456
$449$	22.8990			1.08067			0.540335	−	0.841450i	$-0.318298\pi$
$449$	22.8990			1.08067			0.540335	+	0.841450i	$0.318298\pi$
$450$		0			0
$451$	7.50000	+	4.33013i	0.353161	+	0.203898i
$452$	−2.44949	−	4.24264i	−0.115214	−	0.199557i
$453$		0			0
$454$	−4.22474	+	7.31747i	−0.198277	+	0.343426i
$455$	−10.8990			−0.510952
$456$		0			0
$457$	24.5959			1.15055			0.575274	−	0.817961i	$-0.304895\pi$
$457$	24.5959			1.15055			0.575274	+	0.817961i	$0.304895\pi$
$458$	−5.67423	+	9.82806i	−0.265140	+	0.459235i
$459$		0			0
$460$	1.00000	+	1.73205i	0.0466252	+	0.0807573i
$461$	−2.42168	−	1.39816i	−0.112789	−	0.0651188i	0.442544	−	0.896747i	$-0.354076\pi$
$461$	−2.42168	−	1.39816i	−0.112789	−	0.0651188i	−0.555333	+	0.831628i	$0.687409\pi$
$462$		0			0
$463$	−14.0454			−0.652745			−0.326373	−	0.945241i	$-0.605826\pi$
$463$	−14.0454			−0.652745			−0.326373	+	0.945241i	$0.605826\pi$
$464$	7.34847			0.341144
$465$		0			0
$466$	13.1010	−	7.56388i	0.606893	−	0.350390i
$467$			37.2624i			1.72430i	0.506656	+	0.862148i	$0.330881\pi$
$467$			37.2624i			1.72430i	−0.506656	+	0.862148i	$0.669119\pi$
$468$		0			0
$469$	−8.02270	+	4.63191i	−0.370454	+	0.213882i
$470$	11.1237	−	19.2669i	0.513099	−	0.888714i
$471$		0			0
$472$	−0.550510	+	0.953512i	−0.0253393	+	0.0438889i
$473$	−6.12372	−	3.53553i	−0.281569	−	0.162564i
$474$		0			0
$475$	17.1464	−	12.7279i	0.786732	−	0.583997i
$476$			2.36773i			0.108525i
$477$		0			0
$478$	−10.6237	−	6.13361i	−0.485918	−	0.280545i
$479$	−23.4495	+	13.5386i	−1.07143	+	0.618593i	−0.928573	−	0.371150i	$-0.878964\pi$
$479$	−23.4495	+	13.5386i	−1.07143	+	0.618593i	−0.142861	+	0.989743i	$0.545630\pi$
$480$		0			0
$481$	4.34847	+	7.53177i	0.198273	+	0.343419i
$482$		−	13.8564i		−	0.631142i
$483$		0			0
$484$	−4.89898	−	8.48528i	−0.222681	−	0.385695i
$485$	13.3485	+	23.1202i	0.606123	+	1.04984i
$486$		0			0
$487$		−	1.12848i		−	0.0511365i	−0.999673	−	0.0255683i	$-0.991860\pi$
$487$		−	1.12848i		−	0.0511365i	0.999673	−	0.0255683i	$-0.00813952\pi$
$488$	1.55051	+	2.68556i	0.0701883	+	0.121570i
$489$		0			0
$490$	−2.72474	+	1.57313i	−0.123091	+	0.0710669i
$491$	−7.74745	−	4.47299i	−0.349637	−	0.201863i	0.314888	−	0.949129i	$-0.398033\pi$
$491$	−7.74745	−	4.47299i	−0.349637	−	0.201863i	−0.664526	+	0.747266i	$0.731366\pi$
$492$		0			0
$493$			17.3992i			0.783619i
$494$	−15.0000	+	1.73205i	−0.674882	+	0.0779287i
$495$		0			0
$496$	−3.00000	−	1.73205i	−0.134704	−	0.0777714i
$497$		0			0
$498$		0			0
$499$	1.57321	−	2.72489i	0.0704267	−	0.121983i	−0.828662	−	0.559750i	$-0.810897\pi$
$499$	1.57321	−	2.72489i	0.0704267	−	0.121983i	0.899088	+	0.437767i	$0.144231\pi$
$500$	0.275255	−	0.158919i	0.0123098	−	0.00710706i
$501$		0			0
$502$		−	8.34242i		−	0.372340i
$503$	−10.4722	+	6.04612i	−0.466932	+	0.269583i	−0.714955	−	0.699171i	$-0.753553\pi$
$503$	−10.4722	+	6.04612i	−0.466932	+	0.269583i	0.248023	+	0.968754i	$0.420219\pi$
$504$		0			0
$505$	33.6969			1.49949
$506$	−0.696938			−0.0309827
$507$		0			0
$508$	−0.674235	−	0.389270i	−0.0299143	−	0.0172710i
$509$	5.17423	+	8.96204i	0.229344	+	0.397235i	0.957614	−	0.288055i	$-0.0930086\pi$
$509$	5.17423	+	8.96204i	0.229344	+	0.397235i	−0.728270	+	0.685290i	$0.759675\pi$
$510$		0			0
$511$	−5.89898	+	10.2173i	−0.260955	+	0.451988i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−27.0000			−1.19092
$515$	1.50000	−	2.59808i	0.0660979	−	0.114485i
$516$		0			0
$517$	3.87628	+	6.71391i	0.170478	+	0.295277i
$518$	2.17423	+	1.25529i	0.0955304	+	0.0551545i
$519$		0			0
$520$	10.8990			0.477952
$521$	−9.79796			−0.429256			−0.214628	−	0.976696i	$-0.568854\pi$
$521$	−9.79796			−0.429256			−0.214628	+	0.976696i	$0.568854\pi$
$522$		0			0
$523$	−4.80306	+	2.77305i	−0.210023	+	0.121257i	−0.601322	−	0.799007i	$-0.705359\pi$
$523$	−4.80306	+	2.77305i	−0.210023	+	0.121257i	0.391299	+	0.920264i	$0.372026\pi$
$524$			11.8065i			0.515770i
$525$		0			0
$526$	−7.37628	+	4.25869i	−0.321621	+	0.185688i
$527$	4.10102	−	7.10318i	0.178643	−	0.309419i
$528$		0			0
$529$	−11.2980	+	19.5686i	−0.491216	+	0.850810i
$530$	6.67423	+	3.85337i	0.289910	+	0.167380i
$531$		0			0
$532$	−3.50000	+	2.59808i	−0.151744	+	0.112641i
$533$			27.3629i			1.18522i
$534$		0			0
$535$	3.00000	+	1.73205i	0.129701	+	0.0748831i
$536$	8.02270	−	4.63191i	0.346528	−	0.200068i
$537$		0			0
$538$	−5.72474	−	9.91555i	−0.246811	−	0.427490i
$539$		−	1.09638i		−	0.0472243i
$540$		0			0
$541$	−15.7247	−	27.2361i	−0.676060	−	1.17097i	−0.976158	−	0.217061i	$-0.930353\pi$
$541$	−15.7247	−	27.2361i	−0.676060	−	1.17097i	0.300098	−	0.953908i	$-0.402980\pi$
$542$	2.62372	+	4.54442i	0.112699	+	0.195200i
$543$		0			0
$544$		−	2.36773i		−	0.101515i
$545$	−22.7474	−	39.3997i	−0.974394	−	1.68770i
$546$		0			0
$547$	−6.30306	+	3.63907i	−0.269499	+	0.155596i	−0.628660	−	0.777680i	$-0.716396\pi$
$547$	−6.30306	+	3.63907i	−0.269499	+	0.155596i	0.359161	+	0.933276i	$0.383063\pi$
$548$	6.12372	+	3.53553i	0.261593	+	0.151031i
$549$		0			0
$550$		−	5.37113i		−	0.229026i
$551$	−25.7196	+	19.0919i	−1.09569	+	0.813342i
$552$		0			0
$553$	−6.00000	−	3.46410i	−0.255146	−	0.147309i
$554$	6.17423	−	10.6941i	0.262318	−	0.454348i
$555$		0			0
$556$	−10.9495	+	18.9651i	−0.464362	+	0.804298i
$557$	9.55051	−	5.51399i	0.404668	−	0.233635i	−0.283828	−	0.958875i	$-0.591605\pi$
$557$	9.55051	−	5.51399i	0.404668	−	0.233635i	0.688496	+	0.725240i	$0.258271\pi$
$558$		0			0
$559$		−	22.3417i		−	0.944953i
$560$	2.72474	−	1.57313i	0.115141	−	0.0664770i
$561$		0			0
$562$	−5.75255			−0.242657
$563$	35.1464			1.48125			0.740623	−	0.671921i	$-0.234531\pi$
$563$	35.1464			1.48125			0.740623	+	0.671921i	$0.234531\pi$
$564$		0			0
$565$	−13.3485	−	7.70674i	−0.561574	−	0.324225i
$566$	−0.500000	−	0.866025i	−0.0210166	−	0.0364018i
$567$		0			0
$568$		0			0
$569$	35.3939			1.48379			0.741894	−	0.670517i	$-0.233928\pi$
$569$	35.3939			1.48379			0.741894	+	0.670517i	$0.233928\pi$
$570$		0			0
$571$	−24.9444			−1.04389			−0.521945	−	0.852979i	$-0.674793\pi$
$571$	−24.9444			−1.04389			−0.521945	+	0.852979i	$0.674793\pi$
$572$	−1.89898	+	3.28913i	−0.0794003	+	0.137525i
$573$		0			0
$574$	3.94949	+	6.84072i	0.164849	+	0.285526i
$575$	2.69694	+	1.55708i	0.112470	+	0.0649346i
$576$		0			0
$577$	−11.3485			−0.472443			−0.236221	−	0.971699i	$-0.575909\pi$
$577$	−11.3485			−0.472443			−0.236221	+	0.971699i	$0.575909\pi$
$578$	−11.3939			−0.473923
$579$		0			0
$580$	20.0227	−	11.5601i	0.831398	−	0.480008i
$581$			5.65685i			0.234686i
$582$		0			0
$583$	−2.32577	+	1.34278i	−0.0963234	+	0.0556123i
$584$	5.89898	−	10.2173i	0.244102	−	0.422796i
$585$		0			0
$586$	1.37628	−	2.38378i	0.0568534	−	0.0984730i
$587$	−6.55051	−	3.78194i	−0.270368	−	0.156097i	0.358687	−	0.933458i	$-0.383225\pi$
$587$	−6.55051	−	3.78194i	−0.270368	−	0.156097i	−0.629055	+	0.777361i	$0.716558\pi$
$588$		0			0
$589$	15.0000	−	1.73205i	0.618064	−	0.0713679i
$590$			3.46410i			0.142615i
$591$		0			0
$592$	−2.17423	−	1.25529i	−0.0893605	−	0.0515923i
$593$	−18.9495	+	10.9405i	−0.778162	+	0.449272i	−0.835779	−	0.549067i	$-0.814983\pi$
$593$	−18.9495	+	10.9405i	−0.778162	+	0.449272i	0.0576163	+	0.998339i	$0.481650\pi$
$594$		0			0
$595$	3.72474	+	6.45145i	0.152700	+	0.264484i
$596$			4.87832i			0.199824i
$597$		0			0
$598$	−1.10102	−	1.90702i	−0.0450241	−	0.0779840i
$599$	−1.92679	−	3.33729i	−0.0787263	−	0.136358i	0.823974	−	0.566627i	$-0.191752\pi$
$599$	−1.92679	−	3.33729i	−0.0787263	−	0.136358i	−0.902701	+	0.430269i	$0.858419\pi$
$600$		0			0
$601$		−	38.5337i		−	1.57182i	−0.618339	−	0.785911i	$-0.712194\pi$
$601$		−	38.5337i		−	1.57182i	0.618339	−	0.785911i	$-0.287806\pi$
$602$	−3.22474	−	5.58542i	−0.131431	−	0.227645i
$603$		0			0
$604$	13.3485	−	7.70674i	0.543142	−	0.313583i
$605$	−26.6969	−	15.4135i	−1.08538	−	0.626647i
$606$		0			0
$607$			36.1981i			1.46924i	0.678481	+	0.734618i	$0.262638\pi$
$607$			36.1981i			1.46924i	−0.678481	+	0.734618i	$0.737362\pi$
$608$	3.50000	−	2.59808i	0.141944	−	0.105366i
$609$		0			0
$610$	8.44949	+	4.87832i	0.342110	+	0.197517i
$611$	−12.2474	+	21.2132i	−0.495479	+	0.858194i
$612$		0			0
$613$	5.52270	−	9.56560i	0.223060	−	0.386351i	−0.732676	−	0.680578i	$-0.761729\pi$
$613$	5.52270	−	9.56560i	0.223060	−	0.386351i	0.955736	+	0.294227i	$0.0950621\pi$
$614$	−12.0000	+	6.92820i	−0.484281	+	0.279600i
$615$		0			0
$616$			1.09638i			0.0441743i
$617$	17.2702	−	9.97093i	0.695270	−	0.401414i	−0.110313	−	0.993897i	$-0.535185\pi$
$617$	17.2702	−	9.97093i	0.695270	−	0.401414i	0.805583	+	0.592482i	$0.201852\pi$
$618$		0			0
$619$	6.89898			0.277293			0.138647	−	0.990342i	$-0.455725\pi$
$619$	6.89898			0.277293			0.138647	+	0.990342i	$0.455725\pi$
$620$	−10.8990			−0.437714
$621$		0			0
$622$	−22.4722	−	12.9743i	−0.901053	−	0.520223i
$623$	−0.949490	−	1.64456i	−0.0380405	−	0.0658881i
$624$		0			0
$625$	12.7474	−	22.0792i	0.509898	−	0.883169i
$626$	−12.8990			−0.515547
$627$		0			0
$628$	16.6969			0.666280
$629$	2.97219	−	5.14799i	0.118509	−	0.205264i
$630$		0			0
$631$	−5.77526	−	10.0030i	−0.229909	−	0.398215i	0.727872	−	0.685713i	$-0.240510\pi$
$631$	−5.77526	−	10.0030i	−0.229909	−	0.398215i	−0.957781	+	0.287499i	$0.907176\pi$
$632$	6.00000	+	3.46410i	0.238667	+	0.137795i
$633$		0			0
$634$	12.0000			0.476581
$635$	−2.44949			−0.0972050
$636$		0			0
$637$	3.00000	−	1.73205i	0.118864	−	0.0686264i
$638$			8.05669i			0.318967i
$639$		0			0
$640$	−2.72474	+	1.57313i	−0.107705	+	0.0621835i
$641$	8.02270	−	13.8957i	0.316878	−	0.548848i	−0.662957	−	0.748657i	$-0.730699\pi$
$641$	8.02270	−	13.8957i	0.316878	−	0.548848i	0.979835	+	0.199809i	$0.0640322\pi$
$642$		0			0
$643$	22.5454	−	39.0498i	0.889104	−	1.53997i	0.0481678	−	0.998839i	$-0.484662\pi$
$643$	22.5454	−	39.0498i	0.889104	−	1.53997i	0.840936	−	0.541134i	$-0.182005\pi$
$644$	−0.550510	−	0.317837i	−0.0216931	−	0.0125245i
$645$		0			0
$646$	6.15153	+	8.28704i	0.242029	+	0.326049i
$647$		−	17.8133i		−	0.700314i	−0.936691	−	0.350157i	$-0.886128\pi$
$647$		−	17.8133i		−	0.700314i	0.936691	−	0.350157i	$-0.113872\pi$
$648$		0			0
$649$	−1.04541	−	0.603566i	−0.0410358	−	0.0236921i
$650$	14.6969	−	8.48528i	0.576461	−	0.332820i
$651$		0			0
$652$	−9.44949	−	16.3670i	−0.370071	−	0.640981i
$653$		−	42.9192i		−	1.67956i	−0.542928	−	0.839779i	$-0.682684\pi$
$653$		−	42.9192i		−	1.67956i	0.542928	−	0.839779i	$-0.317316\pi$
$654$		0			0
$655$	18.5732	+	32.1698i	0.725716	+	1.25698i
$656$	−3.94949	−	6.84072i	−0.154202	−	0.267085i
$657$		0			0
$658$			7.07107i			0.275659i
$659$	5.29796	+	9.17633i	0.206379	+	0.357459i	0.950571	−	0.310506i	$-0.100499\pi$
$659$	5.29796	+	9.17633i	0.206379	+	0.357459i	−0.744192	+	0.667966i	$0.767165\pi$
$660$		0			0
$661$	−19.0454	+	10.9959i	−0.740781	+	0.427690i	−0.822353	−	0.568978i	$-0.807339\pi$
$661$	−19.0454	+	10.9959i	−0.740781	+	0.427690i	0.0815725	+	0.996667i	$0.474006\pi$
$662$	−29.3939	−	16.9706i	−1.14243	−	0.659580i
$663$		0			0
$664$		−	5.65685i		−	0.219529i
$665$	−5.44949	+	12.5851i	−0.211322	+	0.488028i
$666$		0			0
$667$	−4.04541	−	2.33562i	−0.156639	−	0.0904355i
$668$	−3.00000	+	5.19615i	−0.116073	+	0.201045i
$669$		0			0
$670$	14.5732	−	25.2415i	0.563012	−	0.975166i
$671$	−2.94439	+	1.69994i	−0.113667	+	0.0656256i
$672$		0			0
$673$		−	48.3224i		−	1.86269i	−0.364133	−	0.931347i	$-0.618635\pi$
$673$		−	48.3224i		−	1.86269i	0.364133	−	0.931347i	$-0.381365\pi$
$674$	0.303062	−	0.174973i	0.0116735	−	0.00673970i
$675$		0			0
$676$	1.00000			0.0384615
$677$	29.4495			1.13184			0.565918	−	0.824462i	$-0.308522\pi$
$677$	29.4495			1.13184			0.565918	+	0.824462i	$0.308522\pi$
$678$		0			0
$679$	−7.34847	−	4.24264i	−0.282008	−	0.162818i
$680$	−3.72474	−	6.45145i	−0.142837	−	0.247402i
$681$		0			0
$682$	1.89898	−	3.28913i	0.0727157	−	0.125947i
$683$	5.20204			0.199051			0.0995253	−	0.995035i	$-0.468268\pi$
$683$	5.20204			0.199051			0.0995253	+	0.995035i	$0.468268\pi$
$684$		0			0
$685$	22.2474			0.850031
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	3.22474	+	5.58542i	0.122942	+	0.212942i
$689$	−7.34847	−	4.24264i	−0.279954	−	0.161632i
$690$		0			0
$691$	−21.6969			−0.825390			−0.412695	−	0.910869i	$-0.635413\pi$
$691$	−21.6969			−0.825390			−0.412695	+	0.910869i	$0.635413\pi$
$692$	−14.6969			−0.558694
$693$		0			0
$694$	11.1464	−	6.43539i	0.423113	−	0.244284i
$695$			68.9000i			2.61353i
$696$		0			0
$697$	16.1969	−	9.35131i	0.613503	−	0.354206i
$698$	13.6742	−	23.6845i	0.517577	−	0.896470i
$699$		0			0
$700$	2.44949	−	4.24264i	0.0925820	−	0.160357i
$701$	18.4268	+	10.6387i	0.695970	+	0.401819i	0.805845	−	0.592127i	$-0.201712\pi$
$701$	18.4268	+	10.6387i	0.695970	+	0.401819i	−0.109875	+	0.993945i	$0.535045\pi$
$702$		0			0
$703$	10.8712	−	1.25529i	0.410014	−	0.0473443i
$704$		−	1.09638i		−	0.0413212i
$705$		0			0
$706$	20.0505	+	11.5762i	0.754611	+	0.435675i
$707$	−9.27526	+	5.35507i	−0.348832	+	0.201398i
$708$		0			0
$709$	−18.9722	−	32.8608i	−0.712516	−	1.23411i	−0.963910	−	0.266229i	$-0.914222\pi$
$709$	−18.9722	−	32.8608i	−0.712516	−	1.23411i	0.251394	−	0.967885i	$-0.419111\pi$
$710$		0			0
$711$		0			0
$712$	0.949490	+	1.64456i	0.0355836	+	0.0616327i
$713$	1.10102	+	1.90702i	0.0412335	+	0.0714186i
$714$		0			0
$715$			11.9494i			0.446882i
$716$	−9.39898	−	16.2795i	−0.351256	−	0.608394i
$717$		0			0
$718$	26.4495	−	15.2706i	0.987086	−	0.569894i
$719$	−2.87628	−	1.66062i	−0.107267	−	0.0619306i	0.445407	−	0.895328i	$-0.353059\pi$
$719$	−2.87628	−	1.66062i	−0.107267	−	0.0619306i	−0.552674	+	0.833398i	$0.686392\pi$
$720$		0			0
$721$			0.953512i			0.0355106i
$722$	−5.50000	+	18.1865i	−0.204689	+	0.676833i
$723$		0			0
$724$	7.34847	+	4.24264i	0.273104	+	0.157676i
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	20.2753	−	35.1178i	0.751968	−	1.30245i	−0.194900	−	0.980823i	$-0.562438\pi$
$727$	20.2753	−	35.1178i	0.751968	−	1.30245i	0.946868	−	0.321623i	$-0.104228\pi$
$728$	−3.00000	+	1.73205i	−0.111187	+	0.0641941i
$729$		0			0
$730$		−	37.1195i		−	1.37385i
$731$	−13.2247	+	7.63531i	−0.489135	+	0.282402i
$732$		0			0
$733$	38.7423			1.43098			0.715491	−	0.698622i	$-0.246203\pi$
$733$	38.7423			1.43098			0.715491	+	0.698622i	$0.246203\pi$
$734$	−6.34847			−0.234326
$735$		0			0
$736$	0.550510	+	0.317837i	0.0202921	+	0.0117156i
$737$	5.07832	+	8.79590i	0.187062	+	0.324001i
$738$		0			0
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	−0.883832	−	0.467804i	$-0.845045\pi$
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	0.847046	+	0.531519i	$0.178379\pi$
$740$	−7.89898			−0.290372
$741$		0			0
$742$	−2.44949			−0.0899236
$743$	−25.8712	+	44.8102i	−0.949121	+	1.64393i	−0.201840	+	0.979419i	$0.564692\pi$
$743$	−25.8712	+	44.8102i	−0.949121	+	1.64393i	−0.747281	+	0.664508i	$0.768641\pi$
$744$		0			0
$745$	7.67423	+	13.2922i	0.281162	+	0.486987i
$746$	−3.52270	−	2.03383i	−0.128975	−	0.0744640i
$747$		0			0
$748$	2.59592			0.0949162
$749$	−1.10102			−0.0402304
$750$		0			0
$751$	−19.6515	+	11.3458i	−0.717095	+	0.414015i	−0.813682	−	0.581310i	$-0.802540\pi$
$751$	−19.6515	+	11.3458i	−0.717095	+	0.414015i	0.0965878	+	0.995324i	$0.469207\pi$
$752$		−	7.07107i		−	0.257855i
$753$		0			0
$754$	−22.0454	+	12.7279i	−0.802846	+	0.463524i
$755$	24.2474	−	41.9978i	0.882455	−	1.52846i
$756$		0			0
$757$	9.07321	−	15.7153i	0.329772	−	0.571181i	−0.652695	−	0.757621i	$-0.726362\pi$
$757$	9.07321	−	15.7153i	0.329772	−	0.571181i	0.982466	+	0.186440i	$0.0596949\pi$
$758$	6.00000	+	3.46410i	0.217930	+	0.125822i
$759$		0			0
$760$	5.44949	−	12.5851i	0.197674	−	0.456508i
$761$			29.5556i			1.07139i	0.844411	+	0.535695i	$0.179950\pi$
$761$			29.5556i			1.07139i	−0.844411	+	0.535695i	$0.820050\pi$
$762$		0			0
$763$	12.5227	+	7.22999i	0.453352	+	0.261743i
$764$	−6.79796	+	3.92480i	−0.245942	+	0.141994i
$765$		0			0
$766$	−10.8990	−	18.8776i	−0.393796	−	0.682075i
$767$		−	3.81405i		−	0.137717i
$768$		0			0
$769$	16.0227	+	27.7521i	0.577793	+	1.00077i	0.995732	+	0.0922923i	$0.0294194\pi$
$769$	16.0227	+	27.7521i	0.577793	+	1.00077i	−0.417938	+	0.908475i	$0.637247\pi$
$770$	1.72474	+	2.98735i	0.0621555	+	0.107656i
$771$		0			0
$772$			10.2173i			0.367730i
$773$	−20.1742	−	34.9428i	−0.725617	−	1.25681i	−0.958720	−	0.284353i	$-0.908221\pi$
$773$	−20.1742	−	34.9428i	−0.725617	−	1.25681i	0.233103	−	0.972452i	$-0.425112\pi$
$774$		0			0
$775$	−14.6969	+	8.48528i	−0.527930	+	0.304800i
$776$	7.34847	+	4.24264i	0.263795	+	0.152302i
$777$		0			0
$778$			23.6130i			0.846568i
$779$	31.5959	+	13.6814i	1.13204	+	0.490188i
$780$		0			0
$781$		0			0
$782$	−0.752551	+	1.30346i	−0.0269112	+	0.0466115i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	45.4949	−	26.2665i	1.62378	−	0.937491i
$786$		0			0
$787$		−	3.63907i		−	0.129719i	−0.997894	−	0.0648595i	$-0.979340\pi$
$787$		−	3.63907i		−	0.129719i	0.997894	−	0.0648595i	$-0.0206599\pi$
$788$	−17.1464	+	9.89949i	−0.610816	+	0.352655i
$789$		0			0
$790$	21.7980			0.775537
$791$	4.89898			0.174188
$792$		0			0
$793$	−9.30306	−	5.37113i	−0.330361	−	0.190734i
$794$	−2.67423	−	4.63191i	−0.0949050	−	0.164380i
$795$		0			0
$796$	−0.449490	+	0.778539i	−0.0159317	+	0.0275946i
$797$	10.8434			0.384092			0.192046	−	0.981386i	$-0.438488\pi$
$797$	10.8434			0.384092			0.192046	+	0.981386i	$0.438488\pi$
$798$		0			0
$799$	16.7423			0.592302
$800$	−2.44949	+	4.24264i	−0.0866025	+	0.150000i
$801$		0			0
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$	11.2020	+	6.46750i	0.395311	+	0.228233i
$804$		0			0
$805$	−2.00000			−0.0704907
$806$	12.0000			0.422682
$807$		0			0
$808$	9.27526	−	5.35507i	0.326302	−	0.188391i
$809$		−	4.38551i		−	0.154186i	−0.997024	−	0.0770931i	$-0.975436\pi$
$809$		−	4.38551i		−	0.154186i	0.997024	−	0.0770931i	$-0.0245639\pi$
$810$		0			0
$811$	−4.19694	+	2.42310i	−0.147374	+	0.0850867i	−0.571874	−	0.820341i	$-0.693783\pi$
$811$	−4.19694	+	2.42310i	−0.147374	+	0.0850867i	0.424500	+	0.905428i	$0.360450\pi$
$812$	−3.67423	+	6.36396i	−0.128940	+	0.223331i
$813$		0			0
$814$	1.37628	−	2.38378i	0.0482384	−	0.0835514i
$815$	−51.4949	−	29.7306i	−1.80379	−	1.04142i
$816$		0			0
$817$	−25.7980	−	11.1708i	−0.902556	−	0.390818i
$818$		−	30.8270i		−	1.07784i
$819$		0			0
$820$	−21.5227	−	12.4261i	−0.751605	−	0.433940i
$821$	40.2929	−	23.2631i	1.40623	−	0.811887i	0.411208	−	0.911541i	$-0.365107\pi$
$821$	40.2929	−	23.2631i	1.40623	−	0.811887i	0.995022	+	0.0996539i	$0.0317736\pi$
$822$		0			0
$823$	−15.4495	−	26.7593i	−0.538535	−	0.932771i	−0.998983	−	0.0450838i	$-0.985645\pi$
$823$	−15.4495	−	26.7593i	−0.538535	−	0.932771i	0.460448	−	0.887687i	$-0.347689\pi$
$824$		−	0.953512i		−	0.0332172i
$825$		0			0
$826$	−0.550510	−	0.953512i	−0.0191547	−	0.0331769i
$827$	27.0959	+	46.9315i	0.942217	+	1.63197i	0.761229	+	0.648483i	$0.224596\pi$
$827$	27.0959	+	46.9315i	0.942217	+	1.63197i	0.180988	+	0.983485i	$0.442070\pi$
$828$		0			0
$829$			22.6916i			0.788113i	0.919086	+	0.394056i	$0.128929\pi$
$829$			22.6916i			0.788113i	−0.919086	+	0.394056i	$0.871071\pi$
$830$	−8.89898	−	15.4135i	−0.308888	−	0.535010i
$831$		0			0
$832$	3.00000	−	1.73205i	0.104006	−	0.0600481i
$833$	−2.05051	−	1.18386i	−0.0710460	−	0.0410184i
$834$		0			0
$835$			18.8776i			0.653286i
$836$	2.84847	+	3.83732i	0.0985164	+	0.132716i
$837$		0			0
$838$	17.8763	+	10.3209i	0.617526	+	0.356529i
$839$	−17.5732	+	30.4377i	−0.606695	+	1.05083i	0.385086	+	0.922880i	$0.374172\pi$
$839$	−17.5732	+	30.4377i	−0.606695	+	1.05083i	−0.991781	+	0.127946i	$0.959162\pi$
$840$		0			0
$841$	−12.5000	+	21.6506i	−0.431034	+	0.746574i
$842$	−19.8712	+	11.4726i	−0.684806	+	0.395373i
$843$		0			0
$844$		−	1.55708i		−	0.0535968i
$845$	2.72474	−	1.57313i	0.0937341	−	0.0541174i
$846$		0			0
$847$	9.79796			0.336662
$848$	2.44949			0.0841158
$849$		0			0
$850$	−10.0454	−	5.79972i	−0.344555	−	0.198929i
$851$	0.797959	+	1.38211i	0.0273537	+	0.0473780i
$852$		0			0
$853$	−13.5505	+	23.4702i	−0.463961	+	0.803603i	−0.999154	−	0.0411262i	$-0.986905\pi$
$853$	−13.5505	+	23.4702i	−0.463961	+	0.803603i	0.535193	+	0.844730i	$0.320239\pi$
$854$	−3.10102			−0.106115
$855$		0			0
$856$	1.10102			0.0376321
$857$	2.29796	−	3.98018i	0.0784968	−	0.135960i	−0.824105	−	0.566437i	$-0.808321\pi$
$857$	2.29796	−	3.98018i	0.0784968	−	0.135960i	0.902602	+	0.430477i	$0.141655\pi$
$858$		0			0
$859$	15.7474	+	27.2754i	0.537296	+	0.930624i	0.999048	+	0.0436151i	$0.0138875\pi$
$859$	15.7474	+	27.2754i	0.537296	+	0.930624i	−0.461752	+	0.887009i	$0.652779\pi$
$860$	17.5732	+	10.1459i	0.599242	+	0.345972i
$861$		0			0
$862$	34.3485			1.16991
$863$	−25.0454			−0.852556			−0.426278	−	0.904592i	$-0.640175\pi$
$863$	−25.0454			−0.852556			−0.426278	+	0.904592i	$0.640175\pi$
$864$		0			0
$865$	−40.0454	+	23.1202i	−1.36158	+	0.786111i
$866$		−	37.7552i		−	1.28297i
$867$		0			0
$868$	3.00000	−	1.73205i	0.101827	−	0.0587896i
$869$	−3.79796	+	6.57826i	−0.128837	+	0.223152i
$870$		0			0
$871$	−16.0454	+	27.7915i	−0.543678	+	0.941678i
$872$	−12.5227	−	7.22999i	−0.424072	−	0.244838i
$873$		0			0
$874$	−2.75255	+	0.317837i	−0.0931064	+	0.0107510i
$875$			0.317837i			0.0107449i
$876$		0			0
$877$	−44.0908	−	25.4558i	−1.48884	−	0.859583i	−0.488922	−	0.872327i	$-0.662610\pi$
$877$	−44.0908	−	25.4558i	−1.48884	−	0.859583i	−0.999919	+	0.0127446i	$0.995943\pi$
$878$	−30.5227	+	17.6223i	−1.03009	+	0.594724i
$879$		0			0
$880$	−1.72474	−	2.98735i	−0.0581411	−	0.100703i
$881$		−	49.5938i		−	1.67086i	−0.549599	−	0.835429i	$-0.685219\pi$
$881$		−	49.5938i		−	1.67086i	0.549599	−	0.835429i	$-0.314781\pi$
$882$		0			0
$883$	−1.00000	−	1.73205i	−0.0336527	−	0.0582882i	0.848709	−	0.528861i	$-0.177381\pi$
$883$	−1.00000	−	1.73205i	−0.0336527	−	0.0582882i	−0.882361	+	0.470573i	$0.844047\pi$
$884$	4.10102	+	7.10318i	0.137932	+	0.238906i
$885$		0			0
$886$			28.2843i			0.950229i
$887$	−24.7980	−	42.9513i	−0.832634	−	1.44216i	−0.895942	−	0.444170i	$-0.853499\pi$
$887$	−24.7980	−	42.9513i	−0.832634	−	1.44216i	0.0633084	−	0.997994i	$-0.479835\pi$
$888$		0			0
$889$	0.674235	−	0.389270i	0.0226131	−	0.0130557i
$890$	5.17423	+	2.98735i	0.173441	+	0.100136i
$891$		0			0
$892$			19.4812i			0.652277i
$893$	18.3712	+	24.7487i	0.614768	+	0.828185i
$894$		0			0
$895$	−51.2196	−	29.5717i	−1.71208	−	0.988472i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$		0			0
$898$	11.4495	−	19.8311i	0.382074	−	0.661772i
$899$	22.0454	−	12.7279i	0.735256	−	0.424500i
$900$		0			0
$901$			5.79972i			0.193217i
$902$	7.50000	−	4.33013i	0.249723	−	0.144177i
$903$		0			0
$904$	−4.89898			−0.162938
$905$	26.6969			0.887436
$906$		0			0
$907$	−13.0454	−	7.53177i	−0.433166	−	0.250088i	0.267529	−	0.963550i	$-0.413793\pi$
$907$	−13.0454	−	7.53177i	−0.433166	−	0.250088i	−0.700694	+	0.713462i	$0.747126\pi$
$908$	4.22474	+	7.31747i	0.140203	+	0.242839i
$909$		0			0
$910$	−5.44949	+	9.43879i	−0.180649	+	0.312893i
$911$	−52.8434			−1.75078			−0.875389	−	0.483418i	$-0.839395\pi$
$911$	−52.8434			−1.75078			−0.875389	+	0.483418i	$0.839395\pi$
$912$		0			0
$913$	6.20204			0.205258
$914$	12.2980	−	21.3007i	0.406780	−	0.704564i
$915$		0			0
$916$	5.67423	+	9.82806i	0.187482	+	0.324728i
$917$	−10.2247	−	5.90326i	−0.337651	−	0.194943i
$918$		0			0
$919$	−24.9444			−0.822839			−0.411420	−	0.911446i	$-0.634967\pi$
$919$	−24.9444			−0.822839			−0.411420	+	0.911446i	$0.634967\pi$
$920$	2.00000			0.0659380
$921$		0			0
$922$	−2.42168	+	1.39816i	−0.0797539	+	0.0460459i
$923$		0			0
$924$		0			0
$925$	−10.6515	+	6.14966i	−0.350220	+	0.202200i
$926$	−7.02270	+	12.1637i	−0.230780	+	0.399723i
$927$		0			0
$928$	3.67423	−	6.36396i	0.120613	−	0.208907i
$929$	24.3434	+	14.0546i	0.798680	+	0.461118i	0.843009	−	0.537899i	$-0.180782\pi$
$929$	24.3434	+	14.0546i	0.798680	+	0.461118i	−0.0443294	+	0.999017i	$0.514115\pi$
$930$		0			0
$931$	−0.500000	−	4.33013i	−0.0163868	−	0.141914i
$932$		−	15.1278i		−	0.495526i
$933$		0			0
$934$	32.2702	+	18.6312i	1.05591	+	0.609631i
$935$	7.07321	−	4.08372i	0.231319	−	0.133552i
$936$		0			0
$937$	−0.573214	−	0.992836i	−0.0187261	−	0.0324345i	0.856511	−	0.516130i	$-0.172628\pi$
$937$	−0.573214	−	0.992836i	−0.0187261	−	0.0324345i	−0.875237	+	0.483695i	$0.839294\pi$
$938$			9.26382i			0.302474i
$939$		0			0
$940$	−11.1237	−	19.2669i	−0.362816	−	0.628416i
$941$	−17.4217	−	30.1752i	−0.567931	−	0.983685i	−0.996770	−	0.0803042i	$-0.974411\pi$
$941$	−17.4217	−	30.1752i	−0.567931	−	0.983685i	0.428840	−	0.903381i	$-0.358922\pi$
$942$		0			0
$943$			5.02118i			0.163512i
$944$	0.550510	+	0.953512i	0.0179176	+	0.0310342i
$945$		0			0
$946$	−6.12372	+	3.53553i	−0.199099	+	0.114950i
$947$	17.6010	+	10.1620i	0.571956	+	0.330219i	0.757930	−	0.652336i	$-0.226211\pi$
$947$	17.6010	+	10.1620i	0.571956	+	0.330219i	−0.185974	+	0.982555i	$0.559544\pi$
$948$		0			0
$949$			40.8693i			1.32667i
$950$	−2.44949	−	21.2132i	−0.0794719	−	0.688247i
$951$		0			0
$952$	2.05051	+	1.18386i	0.0664574	+	0.0383692i
$953$	4.89898	−	8.48528i	0.158694	−	0.274865i	−0.775704	−	0.631097i	$-0.782605\pi$
$953$	4.89898	−	8.48528i	0.158694	−	0.274865i	0.934398	+	0.356231i	$0.115938\pi$
$954$		0			0
$955$	−12.3485	+	21.3882i	−0.399587	+	0.692105i
$956$	−10.6237	+	6.13361i	−0.343596	+	0.198375i
$957$		0			0
$958$			27.0771i			0.874823i
$959$	−6.12372	+	3.53553i	−0.197745	+	0.114168i
$960$		0			0
$961$	19.0000			0.612903
$962$	8.69694			0.280401
$963$		0			0
$964$	−12.0000	−	6.92820i	−0.386494	−	0.223142i
$965$	16.0732	+	27.8396i	0.517415	+	0.896189i
$966$		0			0
$967$	−17.0454	+	29.5235i	−0.548143	+	0.949412i	0.450258	+	0.892898i	$0.351332\pi$
$967$	−17.0454	+	29.5235i	−0.548143	+	0.949412i	−0.998402	+	0.0565139i	$0.982001\pi$
$968$	−9.79796			−0.314918
$969$		0			0
$970$	26.6969			0.857187
$971$	−17.5732	+	30.4377i	−0.563951	+	0.976792i	0.433195	+	0.901300i	$0.357386\pi$
$971$	−17.5732	+	30.4377i	−0.563951	+	0.976792i	−0.997146	+	0.0754921i	$0.975947\pi$
$972$		0			0
$973$	−10.9495	−	18.9651i	−0.351025	−	0.607992i
$974$	−0.977296	−	0.564242i	−0.0313146	−	0.0180795i
$975$		0			0
$976$	3.10102			0.0992612
$977$	−1.34847			−0.0431414			−0.0215707	−	0.999767i	$-0.506867\pi$
$977$	−1.34847			−0.0431414			−0.0215707	+	0.999767i	$0.506867\pi$
$978$		0			0
$979$	−1.80306	+	1.04100i	−0.0576261	+	0.0332704i
$980$			3.14626i			0.100504i
$981$		0			0
$982$	−7.74745	+	4.47299i	−0.247231	+	0.142739i
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$		0			0
$985$	−31.1464	+	53.9472i	−0.992408	+	1.71890i
$986$	15.0681	+	8.69958i	0.479866	+	0.277051i
$987$		0			0
$988$	−6.00000	+	13.8564i	−0.190885	+	0.440831i
$989$		−	4.09978i		−	0.130365i
$990$		0			0
$991$	−44.0908	−	25.4558i	−1.40059	−	0.808632i	−0.406138	−	0.913812i	$-0.633125\pi$
$991$	−44.0908	−	25.4558i	−1.40059	−	0.808632i	−0.994453	+	0.105180i	$0.966458\pi$
$992$	−3.00000	+	1.73205i	−0.0952501	+	0.0549927i
$993$		0			0
$994$		0			0
$995$			2.82843i			0.0896672i
$996$		0			0
$997$	16.3258	+	28.2771i	0.517042	+	0.895543i	0.999804	+	0.0197917i	$0.00630031\pi$
$997$	16.3258	+	28.2771i	0.517042	+	0.895543i	−0.482762	+	0.875752i	$0.660366\pi$
$998$	−1.57321	−	2.72489i	−0.0497992	−	0.0862548i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.cq.b.1205.1	yes	4
3.2	odd	2		2394.2.cq.a.1205.2	yes	4
19.12	odd	6		2394.2.cq.a.449.2	✓	4
57.50	even	6	inner	2394.2.cq.b.449.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2394.2.cq.a.449.2	✓	4	19.12	odd	6
2394.2.cq.a.1205.2	yes	4	3.2	odd	2
2394.2.cq.b.449.1	yes	4	57.50	even	6	inner
2394.2.cq.b.1205.1	yes	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.cq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.72474 - 1.57313i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +(-2.72474 + 1.57313i) q^{10} -1.09638i q^{11} +(3.00000 - 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.05051 - 1.18386i) q^{17} +(-0.500000 - 4.33013i) q^{19} +3.14626i q^{20} +(-0.949490 - 0.548188i) q^{22} +(0.550510 - 0.317837i) q^{23} +(2.44949 + 4.24264i) q^{25} -3.46410i q^{26} +(-0.500000 - 0.866025i) q^{28} +(-3.67423 - 6.36396i) q^{29} +3.46410i q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.05051 + 1.18386i) q^{34} +(-2.72474 - 1.57313i) q^{35} +2.51059i q^{37} +(-4.00000 - 1.73205i) q^{38} +(2.72474 + 1.57313i) q^{40} +(-3.94949 + 6.84072i) q^{41} +(3.22474 - 5.58542i) q^{43} +(-0.949490 + 0.548188i) q^{44} -0.635674i q^{46} +(-6.12372 + 3.53553i) q^{47} +1.00000 q^{49} +4.89898 q^{50} +(-3.00000 - 1.73205i) q^{52} +(-1.22474 - 2.12132i) q^{53} +(-1.72474 + 2.98735i) q^{55} -1.00000 q^{56} -7.34847 q^{58} +(0.550510 - 0.953512i) q^{59} +(-1.55051 - 2.68556i) q^{61} +(3.00000 + 1.73205i) q^{62} +1.00000 q^{64} -10.8990 q^{65} +(-8.02270 + 4.63191i) q^{67} +2.36773i q^{68} +(-2.72474 + 1.57313i) q^{70} +(-5.89898 + 10.2173i) q^{73} +(2.17423 + 1.25529i) q^{74} +(-3.50000 + 2.59808i) q^{76} -1.09638i q^{77} +(-6.00000 - 3.46410i) q^{79} +(2.72474 - 1.57313i) q^{80} +(3.94949 + 6.84072i) q^{82} +5.65685i q^{83} +(3.72474 + 6.45145i) q^{85} +(-3.22474 - 5.58542i) q^{86} +1.09638i q^{88} +(-0.949490 - 1.64456i) q^{89} +(3.00000 - 1.73205i) q^{91} +(-0.550510 - 0.317837i) q^{92} +7.07107i q^{94} +(-5.44949 + 12.5851i) q^{95} +(-7.34847 - 4.24264i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 6 q^{10} + 12 q^{13} + 2 q^{14} - 2 q^{16} - 18 q^{17} - 2 q^{19} + 6 q^{22} + 12 q^{23} - 2 q^{28} + 2 q^{32} - 18 q^{34} - 6 q^{35} - 16 q^{38}+ \cdots + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 6 * q^5 + 4 * q^7 - 4 * q^8 - 6 * q^10 + 12 * q^13 + 2 * q^14 - 2 * q^16 - 18 * q^17 - 2 * q^19 + 6 * q^22 + 12 * q^23 - 2 * q^28 + 2 * q^32 - 18 * q^34 - 6 * q^35 - 16 * q^38 + 6 * q^40 - 6 * q^41 + 8 * q^43 + 6 * q^44 + 4 * q^49 - 12 * q^52 - 2 * q^55 - 4 * q^56 + 12 * q^59 - 16 * q^61 + 12 * q^62 + 4 * q^64 - 24 * q^65 + 12 * q^67 - 6 * q^70 - 4 * q^73 - 6 * q^74 - 14 * q^76 - 24 * q^79 + 6 * q^80 + 6 * q^82 + 10 * q^85 - 8 * q^86 + 6 * q^89 + 12 * q^91 - 12 * q^92 - 12 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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