LMFDB - Embedded newform 2106.2.e.bg.703.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2106,2,Mod(703,2106)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2106, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("2106.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2106 = 2 \cdot 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2106.e (of order $3$, degree $2$, not 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:	$16.8164946657$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			703.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2106.703
Dual form			2106.2.e.bg.1405.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.366025 + 0.633975i) q^{5} +(1.86603 - 3.23205i) q^{7} -1.00000 q^{8} +0.732051 q^{10} +(-1.86603 + 3.23205i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.86603 - 3.23205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.46410 q^{17} +6.46410 q^{19} +(0.366025 - 0.633975i) q^{20} +(1.86603 + 3.23205i) q^{22} +(2.09808 + 3.63397i) q^{23} +(2.23205 - 3.86603i) q^{25} +1.00000 q^{26} -3.73205 q^{28} +(1.23205 - 2.13397i) q^{29} +(2.73205 + 4.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.73205 - 3.00000i) q^{34} +2.73205 q^{35} -9.46410 q^{37} +(3.23205 - 5.59808i) q^{38} +(-0.366025 - 0.633975i) q^{40} +(-3.63397 - 6.29423i) q^{41} +(4.46410 - 7.73205i) q^{43} +3.73205 q^{44} +4.19615 q^{46} +(-2.26795 + 3.92820i) q^{47} +(-3.46410 - 6.00000i) q^{49} +(-2.23205 - 3.86603i) q^{50} +(0.500000 - 0.866025i) q^{52} +12.4641 q^{53} -2.73205 q^{55} +(-1.86603 + 3.23205i) q^{56} +(-1.23205 - 2.13397i) q^{58} +(-2.86603 - 4.96410i) q^{59} +(0.598076 - 1.03590i) q^{61} +5.46410 q^{62} +1.00000 q^{64} +(-0.366025 + 0.633975i) q^{65} +(-7.19615 - 12.4641i) q^{67} +(-1.73205 - 3.00000i) q^{68} +(1.36603 - 2.36603i) q^{70} +8.46410 q^{71} +5.46410 q^{73} +(-4.73205 + 8.19615i) q^{74} +(-3.23205 - 5.59808i) q^{76} +(6.96410 + 12.0622i) q^{77} +(-2.09808 + 3.63397i) q^{79} -0.732051 q^{80} -7.26795 q^{82} +(0.866025 - 1.50000i) q^{83} +(1.26795 + 2.19615i) q^{85} +(-4.46410 - 7.73205i) q^{86} +(1.86603 - 3.23205i) q^{88} +8.19615 q^{89} +3.73205 q^{91} +(2.09808 - 3.63397i) q^{92} +(2.26795 + 3.92820i) q^{94} +(2.36603 + 4.09808i) q^{95} +(-3.36603 + 5.83013i) q^{97} -6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 4 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} - 2 q^{16} + 12 q^{19} - 2 q^{20} + 4 q^{22} - 2 q^{23} + 2 q^{25} + 4 q^{26} - 8 q^{28} - 2 q^{29} + 4 q^{31}+ \cdots - 10 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 4 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 - 2 * q^16 + 12 * q^19 - 2 * q^20 + 4 * q^22 - 2 * q^23 + 2 * q^25 + 4 * q^26 - 8 * q^28 - 2 * q^29 + 4 * q^31 + 2 * q^32 + 4 * q^35 - 24 * q^37 + 6 * q^38 + 2 * q^40 - 18 * q^41 + 4 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 2 * q^50 + 2 * q^52 + 36 * q^53 - 4 * q^55 - 4 * q^56 + 2 * q^58 - 8 * q^59 - 8 * q^61 + 8 * q^62 + 4 * q^64 + 2 * q^65 - 8 * q^67 + 2 * q^70 + 20 * q^71 + 8 * q^73 - 12 * q^74 - 6 * q^76 + 14 * q^77 + 2 * q^79 + 4 * q^80 - 36 * q^82 + 12 * q^85 - 4 * q^86 + 4 * q^88 + 12 * q^89 + 8 * q^91 - 2 * q^92 + 16 * q^94 + 6 * q^95 - 10 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2106\mathbb{Z}\right)^\times$.

$n$	$1379$	$1783$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	0.366025	+	0.633975i	0.163692	+	0.283522i	0.936190	−	0.351495i	$-0.114326\pi$
$5$	0.366025	+	0.633975i	0.163692	+	0.283522i	−0.772498	+	0.635017i	$0.780993\pi$
$6$		0			0
$7$	1.86603	−	3.23205i	0.705291	−	1.22160i	−0.261295	−	0.965259i	$-0.584150\pi$
$7$	1.86603	−	3.23205i	0.705291	−	1.22160i	0.966586	−	0.256341i	$-0.0825171\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.732051			0.231495
$11$	−1.86603	+	3.23205i	−0.562628	+	0.974500i	0.434638	+	0.900605i	$0.356876\pi$
$11$	−1.86603	+	3.23205i	−0.562628	+	0.974500i	−0.997266	+	0.0738948i	$0.976457\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−1.86603	−	3.23205i	−0.498716	−	0.863802i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.46410			0.840168			0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410			0.840168			0.420084	+	0.907485i	$0.362001\pi$
$18$		0			0
$19$	6.46410			1.48297			0.741483	−	0.670971i	$-0.234123\pi$
$19$	6.46410			1.48297			0.741483	+	0.670971i	$0.234123\pi$
$20$	0.366025	−	0.633975i	0.0818458	−	0.141761i
$21$		0			0
$22$	1.86603	+	3.23205i	0.397838	+	0.689076i
$23$	2.09808	+	3.63397i	0.437479	+	0.757736i	0.997494	−	0.0707462i	$-0.0225381\pi$
$23$	2.09808	+	3.63397i	0.437479	+	0.757736i	−0.560015	+	0.828482i	$0.689205\pi$
$24$		0			0
$25$	2.23205	−	3.86603i	0.446410	−	0.773205i
$26$	1.00000			0.196116
$27$		0			0
$28$	−3.73205			−0.705291
$29$	1.23205	−	2.13397i	0.228786	−	0.396269i	−0.728663	−	0.684873i	$-0.759858\pi$
$29$	1.23205	−	2.13397i	0.228786	−	0.396269i	0.957449	+	0.288604i	$0.0931910\pi$
$30$		0			0
$31$	2.73205	+	4.73205i	0.490691	+	0.849901i	0.999943	−	0.0107162i	$-0.00341113\pi$
$31$	2.73205	+	4.73205i	0.490691	+	0.849901i	−0.509252	+	0.860618i	$0.670078\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.73205	−	3.00000i	0.297044	−	0.514496i
$35$	2.73205			0.461801
$36$		0			0
$37$	−9.46410			−1.55589			−0.777944	−	0.628333i	$-0.783737\pi$
$37$	−9.46410			−1.55589			−0.777944	+	0.628333i	$0.783737\pi$
$38$	3.23205	−	5.59808i	0.524308	−	0.908128i
$39$		0			0
$40$	−0.366025	−	0.633975i	−0.0578737	−	0.100240i
$41$	−3.63397	−	6.29423i	−0.567531	−	0.982993i	−0.996809	−	0.0798208i	$-0.974565\pi$
$41$	−3.63397	−	6.29423i	−0.567531	−	0.982993i	0.429278	−	0.903173i	$-0.358768\pi$
$42$		0			0
$43$	4.46410	−	7.73205i	0.680769	−	1.17913i	−0.293977	−	0.955812i	$-0.594979\pi$
$43$	4.46410	−	7.73205i	0.680769	−	1.17913i	0.974746	−	0.223314i	$-0.0716876\pi$
$44$	3.73205			0.562628
$45$		0			0
$46$	4.19615			0.618689
$47$	−2.26795	+	3.92820i	−0.330814	+	0.572987i	−0.982672	−	0.185354i	$-0.940657\pi$
$47$	−2.26795	+	3.92820i	−0.330814	+	0.572987i	0.651857	+	0.758342i	$0.273990\pi$
$48$		0			0
$49$	−3.46410	−	6.00000i	−0.494872	−	0.857143i
$50$	−2.23205	−	3.86603i	−0.315660	−	0.546739i
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	12.4641			1.71208			0.856038	−	0.516913i	$-0.172919\pi$
$53$	12.4641			1.71208			0.856038	+	0.516913i	$0.172919\pi$
$54$		0			0
$55$	−2.73205			−0.368390
$56$	−1.86603	+	3.23205i	−0.249358	+	0.431901i
$57$		0			0
$58$	−1.23205	−	2.13397i	−0.161776	−	0.280205i
$59$	−2.86603	−	4.96410i	−0.373125	−	0.646271i	0.616920	−	0.787026i	$-0.288380\pi$
$59$	−2.86603	−	4.96410i	−0.373125	−	0.646271i	−0.990044	+	0.140755i	$0.955047\pi$
$60$		0			0
$61$	0.598076	−	1.03590i	0.0765758	−	0.132633i	−0.825195	−	0.564848i	$-0.808935\pi$
$61$	0.598076	−	1.03590i	0.0765758	−	0.132633i	0.901770	+	0.432215i	$0.142268\pi$
$62$	5.46410			0.693942
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.366025	+	0.633975i	−0.0453999	+	0.0786349i
$66$		0			0
$67$	−7.19615	−	12.4641i	−0.879150	−	1.52273i	−0.852275	−	0.523094i	$-0.824778\pi$
$67$	−7.19615	−	12.4641i	−0.879150	−	1.52273i	−0.0268747	−	0.999639i	$-0.508556\pi$
$68$	−1.73205	−	3.00000i	−0.210042	−	0.363803i
$69$		0			0
$70$	1.36603	−	2.36603i	0.163271	−	0.282794i
$71$	8.46410			1.00450			0.502252	−	0.864721i	$-0.332505\pi$
$71$	8.46410			1.00450			0.502252	+	0.864721i	$0.332505\pi$
$72$		0			0
$73$	5.46410			0.639525			0.319762	−	0.947498i	$-0.396397\pi$
$73$	5.46410			0.639525			0.319762	+	0.947498i	$0.396397\pi$
$74$	−4.73205	+	8.19615i	−0.550090	+	0.952783i
$75$		0			0
$76$	−3.23205	−	5.59808i	−0.370742	−	0.642143i
$77$	6.96410	+	12.0622i	0.793633	+	1.37461i
$78$		0			0
$79$	−2.09808	+	3.63397i	−0.236052	+	0.408854i	−0.959578	−	0.281443i	$-0.909187\pi$
$79$	−2.09808	+	3.63397i	−0.236052	+	0.408854i	0.723526	+	0.690297i	$0.242520\pi$
$80$	−0.732051			−0.0818458
$81$		0			0
$82$	−7.26795			−0.802611
$83$	0.866025	−	1.50000i	0.0950586	−	0.164646i	−0.814574	−	0.580059i	$-0.803029\pi$
$83$	0.866025	−	1.50000i	0.0950586	−	0.164646i	0.909633	+	0.415413i	$0.136363\pi$
$84$		0			0
$85$	1.26795	+	2.19615i	0.137528	+	0.238206i
$86$	−4.46410	−	7.73205i	−0.481376	−	0.833768i
$87$		0			0
$88$	1.86603	−	3.23205i	0.198919	−	0.344538i
$89$	8.19615			0.868790			0.434395	−	0.900722i	$-0.356962\pi$
$89$	8.19615			0.868790			0.434395	+	0.900722i	$0.356962\pi$
$90$		0			0
$91$	3.73205			0.391225
$92$	2.09808	−	3.63397i	0.218740	−	0.378868i
$93$		0			0
$94$	2.26795	+	3.92820i	0.233921	+	0.405163i
$95$	2.36603	+	4.09808i	0.242749	+	0.420454i
$96$		0			0
$97$	−3.36603	+	5.83013i	−0.341768	+	0.591960i	−0.984761	−	0.173912i	$-0.944359\pi$
$97$	−3.36603	+	5.83013i	−0.341768	+	0.591960i	0.642993	+	0.765872i	$0.277692\pi$
$98$	−6.92820			−0.699854
$99$		0			0
$100$	−4.46410			−0.446410
$101$	−7.23205	+	12.5263i	−0.719616	+	1.24641i	0.241536	+	0.970392i	$0.422349\pi$
$101$	−7.23205	+	12.5263i	−0.719616	+	1.24641i	−0.961152	+	0.276020i	$0.910985\pi$
$102$		0			0
$103$	−8.46410	−	14.6603i	−0.833993	−	1.44452i	−0.894848	−	0.446371i	$-0.852716\pi$
$103$	−8.46410	−	14.6603i	−0.833993	−	1.44452i	0.0608552	−	0.998147i	$-0.480617\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$		0			0
$106$	6.23205	−	10.7942i	0.605310	−	1.04843i
$107$	−13.6603			−1.32059			−0.660293	−	0.751008i	$-0.729568\pi$
$107$	−13.6603			−1.32059			−0.660293	+	0.751008i	$0.729568\pi$
$108$		0			0
$109$	6.19615			0.593484			0.296742	−	0.954958i	$-0.404100\pi$
$109$	6.19615			0.593484			0.296742	+	0.954958i	$0.404100\pi$
$110$	−1.36603	+	2.36603i	−0.130245	+	0.225592i
$111$		0			0
$112$	1.86603	+	3.23205i	0.176323	+	0.305400i
$113$	4.86603	+	8.42820i	0.457757	+	0.792859i	0.998842	−	0.0481093i	$-0.0153196\pi$
$113$	4.86603	+	8.42820i	0.457757	+	0.792859i	−0.541085	+	0.840968i	$0.681986\pi$
$114$		0			0
$115$	−1.53590	+	2.66025i	−0.143223	+	0.248070i
$116$	−2.46410			−0.228786
$117$		0			0
$118$	−5.73205			−0.527678
$119$	6.46410	−	11.1962i	0.592563	−	1.02635i
$120$		0			0
$121$	−1.46410	−	2.53590i	−0.133100	−	0.230536i
$122$	−0.598076	−	1.03590i	−0.0541473	−	0.0937858i
$123$		0			0
$124$	2.73205	−	4.73205i	0.245345	−	0.424951i
$125$	6.92820			0.619677
$126$		0			0
$127$	16.9282			1.50214			0.751068	−	0.660225i	$-0.229539\pi$
$127$	16.9282			1.50214			0.751068	+	0.660225i	$0.229539\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	0.366025	+	0.633975i	0.0321026	+	0.0556033i
$131$	−8.46410	−	14.6603i	−0.739512	−	1.28087i	−0.952715	−	0.303864i	$-0.901723\pi$
$131$	−8.46410	−	14.6603i	−0.739512	−	1.28087i	0.213203	−	0.977008i	$-0.431610\pi$
$132$		0			0
$133$	12.0622	−	20.8923i	1.04592	−	1.81159i
$134$	−14.3923			−1.24331
$135$		0			0
$136$	−3.46410			−0.297044
$137$	−8.66025	+	15.0000i	−0.739895	+	1.28154i	0.212647	+	0.977129i	$0.431792\pi$
$137$	−8.66025	+	15.0000i	−0.739895	+	1.28154i	−0.952542	+	0.304407i	$0.901542\pi$
$138$		0			0
$139$	−3.90192	−	6.75833i	−0.330957	−	0.573234i	0.651743	−	0.758440i	$-0.274038\pi$
$139$	−3.90192	−	6.75833i	−0.330957	−	0.573234i	−0.982700	+	0.185206i	$0.940705\pi$
$140$	−1.36603	−	2.36603i	−0.115450	−	0.199966i
$141$		0			0
$142$	4.23205	−	7.33013i	0.355146	−	0.615131i
$143$	−3.73205			−0.312090
$144$		0			0
$145$	1.80385			0.149801
$146$	2.73205	−	4.73205i	0.226106	−	0.391627i
$147$		0			0
$148$	4.73205	+	8.19615i	0.388972	+	0.673720i
$149$	−0.169873	−	0.294229i	−0.0139165	−	0.0241041i	0.858983	−	0.512004i	$-0.171097\pi$
$149$	−0.169873	−	0.294229i	−0.0139165	−	0.0241041i	−0.872900	+	0.487900i	$0.837763\pi$
$150$		0			0
$151$	4.79423	−	8.30385i	0.390149	−	0.675758i	−0.602320	−	0.798255i	$-0.705757\pi$
$151$	4.79423	−	8.30385i	0.390149	−	0.675758i	0.992469	+	0.122497i	$0.0390902\pi$
$152$	−6.46410			−0.524308
$153$		0			0
$154$	13.9282			1.12237
$155$	−2.00000	+	3.46410i	−0.160644	+	0.278243i
$156$		0			0
$157$	4.13397	+	7.16025i	0.329927	+	0.571450i	0.982497	−	0.186278i	$-0.0596425\pi$
$157$	4.13397	+	7.16025i	0.329927	+	0.571450i	−0.652570	+	0.757728i	$0.726309\pi$
$158$	2.09808	+	3.63397i	0.166914	+	0.289103i
$159$		0			0
$160$	−0.366025	+	0.633975i	−0.0289368	+	0.0501201i
$161$	15.6603			1.23420
$162$		0			0
$163$	13.3205			1.04334			0.521671	−	0.853147i	$-0.325309\pi$
$163$	13.3205			1.04334			0.521671	+	0.853147i	$0.325309\pi$
$164$	−3.63397	+	6.29423i	−0.283766	+	0.491497i
$165$		0			0
$166$	−0.866025	−	1.50000i	−0.0672166	−	0.116423i
$167$	3.69615	+	6.40192i	0.286017	+	0.495396i	0.972855	−	0.231414i	$-0.0743353\pi$
$167$	3.69615	+	6.40192i	0.286017	+	0.495396i	−0.686838	+	0.726810i	$0.741002\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	2.53590			0.194495
$171$		0			0
$172$	−8.92820			−0.680769
$173$	11.5000	−	19.9186i	0.874329	−	1.51438i	0.0168528	−	0.999858i	$-0.494635\pi$
$173$	11.5000	−	19.9186i	0.874329	−	1.51438i	0.857476	−	0.514524i	$-0.172031\pi$
$174$		0			0
$175$	−8.33013	−	14.4282i	−0.629698	−	1.09067i
$176$	−1.86603	−	3.23205i	−0.140657	−	0.243625i
$177$		0			0
$178$	4.09808	−	7.09808i	0.307164	−	0.532023i
$179$	6.92820			0.517838			0.258919	−	0.965899i	$-0.416634\pi$
$179$	6.92820			0.517838			0.258919	+	0.965899i	$0.416634\pi$
$180$		0			0
$181$	−15.5885			−1.15868			−0.579340	−	0.815086i	$-0.696690\pi$
$181$	−15.5885			−1.15868			−0.579340	+	0.815086i	$0.696690\pi$
$182$	1.86603	−	3.23205i	0.138319	−	0.239576i
$183$		0			0
$184$	−2.09808	−	3.63397i	−0.154672	−	0.267900i
$185$	−3.46410	−	6.00000i	−0.254686	−	0.441129i
$186$		0			0
$187$	−6.46410	+	11.1962i	−0.472702	+	0.818744i
$188$	4.53590			0.330814
$189$		0			0
$190$	4.73205			0.343299
$191$	2.46410	−	4.26795i	0.178296	−	0.308818i	−0.763001	−	0.646397i	$-0.776275\pi$
$191$	2.46410	−	4.26795i	0.178296	−	0.308818i	0.941297	+	0.337579i	$0.109608\pi$
$192$		0			0
$193$	0.0980762	+	0.169873i	0.00705968	+	0.0122277i	0.869534	−	0.493874i	$-0.164419\pi$
$193$	0.0980762	+	0.169873i	0.00705968	+	0.0122277i	−0.862474	+	0.506101i	$0.831086\pi$
$194$	3.36603	+	5.83013i	0.241667	+	0.418579i
$195$		0			0
$196$	−3.46410	+	6.00000i	−0.247436	+	0.428571i
$197$	−10.3923			−0.740421			−0.370211	−	0.928948i	$-0.620714\pi$
$197$	−10.3923			−0.740421			−0.370211	+	0.928948i	$0.620714\pi$
$198$		0			0
$199$	0.392305			0.0278098			0.0139049	−	0.999903i	$-0.495574\pi$
$199$	0.392305			0.0278098			0.0139049	+	0.999903i	$0.495574\pi$
$200$	−2.23205	+	3.86603i	−0.157830	+	0.273369i
$201$		0			0
$202$	7.23205	+	12.5263i	0.508845	+	0.881346i
$203$	−4.59808	−	7.96410i	−0.322722	−	0.558970i
$204$		0			0
$205$	2.66025	−	4.60770i	0.185800	−	0.321815i
$206$	−16.9282			−1.17944
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	−12.0622	+	20.8923i	−0.834358	+	1.44515i
$210$		0			0
$211$	−4.16987	−	7.22243i	−0.287066	−	0.497213i	0.686042	−	0.727562i	$-0.259347\pi$
$211$	−4.16987	−	7.22243i	−0.287066	−	0.497213i	−0.973108	+	0.230349i	$0.926013\pi$
$212$	−6.23205	−	10.7942i	−0.428019	−	0.741351i
$213$		0			0
$214$	−6.83013	+	11.8301i	−0.466898	+	0.808691i
$215$	6.53590			0.445745
$216$		0			0
$217$	20.3923			1.38432
$218$	3.09808	−	5.36603i	0.209828	−	0.363433i
$219$		0			0
$220$	1.36603	+	2.36603i	0.0920974	+	0.159517i
$221$	1.73205	+	3.00000i	0.116510	+	0.201802i
$222$		0			0
$223$	−8.59808	+	14.8923i	−0.575770	+	0.997262i	0.420188	+	0.907437i	$0.361964\pi$
$223$	−8.59808	+	14.8923i	−0.575770	+	0.997262i	−0.995958	+	0.0898253i	$0.971369\pi$
$224$	3.73205			0.249358
$225$		0			0
$226$	9.73205			0.647366
$227$	−4.33013	+	7.50000i	−0.287401	+	0.497792i	−0.973189	−	0.230009i	$-0.926124\pi$
$227$	−4.33013	+	7.50000i	−0.287401	+	0.497792i	0.685788	+	0.727801i	$0.259458\pi$
$228$		0			0
$229$	1.73205	+	3.00000i	0.114457	+	0.198246i	0.917563	−	0.397591i	$-0.130154\pi$
$229$	1.73205	+	3.00000i	0.114457	+	0.198246i	−0.803105	+	0.595837i	$0.796820\pi$
$230$	1.53590	+	2.66025i	0.101274	+	0.175412i
$231$		0			0
$232$	−1.23205	+	2.13397i	−0.0808881	+	0.140102i
$233$	−4.80385			−0.314711			−0.157355	−	0.987542i	$-0.550297\pi$
$233$	−4.80385			−0.314711			−0.157355	+	0.987542i	$0.550297\pi$
$234$		0			0
$235$	−3.32051			−0.216606
$236$	−2.86603	+	4.96410i	−0.186562	+	0.323135i
$237$		0			0
$238$	−6.46410	−	11.1962i	−0.419005	−	0.725739i
$239$	2.42820	+	4.20577i	0.157067	+	0.272049i	0.933810	−	0.357770i	$-0.116463\pi$
$239$	2.42820	+	4.20577i	0.157067	+	0.272049i	−0.776742	+	0.629818i	$0.783129\pi$
$240$		0			0
$241$	2.36603	−	4.09808i	0.152409	−	0.263980i	−0.779704	−	0.626149i	$-0.784630\pi$
$241$	2.36603	−	4.09808i	0.152409	−	0.263980i	0.932113	+	0.362169i	$0.117964\pi$
$242$	−2.92820			−0.188232
$243$		0			0
$244$	−1.19615			−0.0765758
$245$	2.53590	−	4.39230i	0.162013	−	0.280614i
$246$		0			0
$247$	3.23205	+	5.59808i	0.205650	+	0.356197i
$248$	−2.73205	−	4.73205i	−0.173485	−	0.300486i
$249$		0			0
$250$	3.46410	−	6.00000i	0.219089	−	0.379473i
$251$	2.19615			0.138620			0.0693100	−	0.997595i	$-0.477920\pi$
$251$	2.19615			0.138620			0.0693100	+	0.997595i	$0.477920\pi$
$252$		0			0
$253$	−15.6603			−0.984552
$254$	8.46410	−	14.6603i	0.531085	−	0.919866i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.2583	+	24.6962i	0.889410	+	1.54050i	0.840574	+	0.541697i	$0.182218\pi$
$257$	14.2583	+	24.6962i	0.889410	+	1.54050i	0.0488363	+	0.998807i	$0.484449\pi$
$258$		0			0
$259$	−17.6603	+	30.5885i	−1.09735	+	1.90067i
$260$	0.732051			0.0453999
$261$		0			0
$262$	−16.9282			−1.04583
$263$	−6.16987	+	10.6865i	−0.380451	+	0.658960i	−0.991127	−	0.132921i	$-0.957564\pi$
$263$	−6.16987	+	10.6865i	−0.380451	+	0.658960i	0.610676	+	0.791881i	$0.290898\pi$
$264$		0			0
$265$	4.56218	+	7.90192i	0.280252	+	0.485411i
$266$	−12.0622	−	20.8923i	−0.739580	−	1.28099i
$267$		0			0
$268$	−7.19615	+	12.4641i	−0.439575	+	0.761366i
$269$	−21.4641			−1.30869			−0.654345	−	0.756196i	$-0.727055\pi$
$269$	−21.4641			−1.30869			−0.654345	+	0.756196i	$0.727055\pi$
$270$		0			0
$271$	15.1962			0.923101			0.461550	−	0.887114i	$-0.347293\pi$
$271$	15.1962			0.923101			0.461550	+	0.887114i	$0.347293\pi$
$272$	−1.73205	+	3.00000i	−0.105021	+	0.181902i
$273$		0			0
$274$	8.66025	+	15.0000i	0.523185	+	0.906183i
$275$	8.33013	+	14.4282i	0.502326	+	0.870053i
$276$		0			0
$277$	0.401924	−	0.696152i	0.0241493	−	0.0418277i	−0.853698	−	0.520768i	$-0.825646\pi$
$277$	0.401924	−	0.696152i	0.0241493	−	0.0418277i	0.877847	+	0.478940i	$0.158979\pi$
$278$	−7.80385			−0.468044
$279$		0			0
$280$	−2.73205			−0.163271
$281$	−9.19615	+	15.9282i	−0.548596	+	0.950197i	0.449775	+	0.893142i	$0.351504\pi$
$281$	−9.19615	+	15.9282i	−0.548596	+	0.950197i	−0.998371	+	0.0570548i	$0.981829\pi$
$282$		0			0
$283$	1.92820	+	3.33975i	0.114620	+	0.198527i	0.917628	−	0.397441i	$-0.130102\pi$
$283$	1.92820	+	3.33975i	0.114620	+	0.198527i	−0.803008	+	0.595968i	$0.796768\pi$
$284$	−4.23205	−	7.33013i	−0.251126	−	0.434963i
$285$		0			0
$286$	−1.86603	+	3.23205i	−0.110340	+	0.191115i
$287$	−27.1244			−1.60110
$288$		0			0
$289$	−5.00000			−0.294118
$290$	0.901924	−	1.56218i	0.0529628	−	0.0917342i
$291$		0			0
$292$	−2.73205	−	4.73205i	−0.159881	−	0.276922i
$293$	−14.3923	−	24.9282i	−0.840807	−	1.45632i	−0.889213	−	0.457493i	$-0.848747\pi$
$293$	−14.3923	−	24.9282i	−0.840807	−	1.45632i	0.0484056	−	0.998828i	$-0.484586\pi$
$294$		0			0
$295$	2.09808	−	3.63397i	0.122155	−	0.211578i
$296$	9.46410			0.550090
$297$		0			0
$298$	−0.339746			−0.0196810
$299$	−2.09808	+	3.63397i	−0.121335	+	0.210158i
$300$		0			0
$301$	−16.6603	−	28.8564i	−0.960281	−	1.66326i
$302$	−4.79423	−	8.30385i	−0.275877	−	0.477833i
$303$		0			0
$304$	−3.23205	+	5.59808i	−0.185371	+	0.321072i
$305$	0.875644			0.0501392
$306$		0			0
$307$	−25.7128			−1.46751			−0.733754	−	0.679415i	$-0.762233\pi$
$307$	−25.7128			−1.46751			−0.733754	+	0.679415i	$0.762233\pi$
$308$	6.96410	−	12.0622i	0.396817	−	0.687306i
$309$		0			0
$310$	2.00000	+	3.46410i	0.113592	+	0.196748i
$311$	−12.1244	−	21.0000i	−0.687509	−	1.19080i	−0.972641	−	0.232313i	$-0.925371\pi$
$311$	−12.1244	−	21.0000i	−0.687509	−	1.19080i	0.285132	−	0.958488i	$-0.407963\pi$
$312$		0			0
$313$	−9.89230	+	17.1340i	−0.559146	+	0.968470i	0.438422	+	0.898769i	$0.355538\pi$
$313$	−9.89230	+	17.1340i	−0.559146	+	0.968470i	−0.997568	+	0.0697002i	$0.977796\pi$
$314$	8.26795			0.466587
$315$		0			0
$316$	4.19615			0.236052
$317$	−11.0263	+	19.0981i	−0.619298	+	1.07265i	0.370317	+	0.928906i	$0.379249\pi$
$317$	−11.0263	+	19.0981i	−0.619298	+	1.07265i	−0.989614	+	0.143749i	$0.954084\pi$
$318$		0			0
$319$	4.59808	+	7.96410i	0.257443	+	0.445904i
$320$	0.366025	+	0.633975i	0.0204614	+	0.0354403i
$321$		0			0
$322$	7.83013	−	13.5622i	0.436356	−	0.755791i
$323$	22.3923			1.24594
$324$		0			0
$325$	4.46410			0.247624
$326$	6.66025	−	11.5359i	0.368877	−	0.638914i
$327$		0			0
$328$	3.63397	+	6.29423i	0.200653	+	0.347541i
$329$	8.46410	+	14.6603i	0.466641	+	0.808246i
$330$		0			0
$331$	−0.660254	+	1.14359i	−0.0362908	+	0.0628576i	−0.883600	−	0.468242i	$-0.844888\pi$
$331$	−0.660254	+	1.14359i	−0.0362908	+	0.0628576i	0.847310	+	0.531099i	$0.178221\pi$
$332$	−1.73205			−0.0950586
$333$		0			0
$334$	7.39230			0.404489
$335$	5.26795	−	9.12436i	0.287819	−	0.498517i
$336$		0			0
$337$	5.46410	+	9.46410i	0.297649	+	0.515542i	0.975598	−	0.219567i	$-0.0704643\pi$
$337$	5.46410	+	9.46410i	0.297649	+	0.515542i	−0.677949	+	0.735109i	$0.737131\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	1.26795	−	2.19615i	0.0687642	−	0.119103i
$341$	−20.3923			−1.10431
$342$		0			0
$343$	0.267949			0.0144679
$344$	−4.46410	+	7.73205i	−0.240688	+	0.416884i
$345$		0			0
$346$	−11.5000	−	19.9186i	−0.618244	−	1.07083i
$347$	9.63397	+	16.6865i	0.517179	+	0.895780i	0.999801	+	0.0199514i	$0.00635113\pi$
$347$	9.63397	+	16.6865i	0.517179	+	0.895780i	−0.482622	+	0.875829i	$0.660316\pi$
$348$		0			0
$349$	0.0717968	−	0.124356i	0.00384319	−	0.00665661i	−0.864097	−	0.503325i	$-0.832110\pi$
$349$	0.0717968	−	0.124356i	0.00384319	−	0.00665661i	0.867941	+	0.496668i	$0.165443\pi$
$350$	−16.6603			−0.890528
$351$		0			0
$352$	−3.73205			−0.198919
$353$	−13.2942	+	23.0263i	−0.707580	+	1.22557i	0.258172	+	0.966099i	$0.416880\pi$
$353$	−13.2942	+	23.0263i	−0.707580	+	1.22557i	−0.965752	+	0.259466i	$0.916453\pi$
$354$		0			0
$355$	3.09808	+	5.36603i	0.164429	+	0.284799i
$356$	−4.09808	−	7.09808i	−0.217198	−	0.376197i
$357$		0			0
$358$	3.46410	−	6.00000i	0.183083	−	0.317110i
$359$	31.8564			1.68132			0.840658	−	0.541566i	$-0.182168\pi$
$359$	31.8564			1.68132			0.840658	+	0.541566i	$0.182168\pi$
$360$		0			0
$361$	22.7846			1.19919
$362$	−7.79423	+	13.5000i	−0.409656	+	0.709544i
$363$		0			0
$364$	−1.86603	−	3.23205i	−0.0978063	−	0.169405i
$365$	2.00000	+	3.46410i	0.104685	+	0.181319i
$366$		0			0
$367$	−13.2942	+	23.0263i	−0.693953	+	1.20196i	0.276579	+	0.960991i	$0.410799\pi$
$367$	−13.2942	+	23.0263i	−0.693953	+	1.20196i	−0.970532	+	0.240971i	$0.922534\pi$
$368$	−4.19615			−0.218740
$369$		0			0
$370$	−6.92820			−0.360180
$371$	23.2583	−	40.2846i	1.20751	−	2.09147i
$372$		0			0
$373$	17.5263	+	30.3564i	0.907476	+	1.57180i	0.817558	+	0.575846i	$0.195327\pi$
$373$	17.5263	+	30.3564i	0.907476	+	1.57180i	0.0899182	+	0.995949i	$0.471339\pi$
$374$	6.46410	+	11.1962i	0.334251	+	0.578939i
$375$		0			0
$376$	2.26795	−	3.92820i	0.116961	−	0.202582i
$377$	2.46410			0.126908
$378$		0			0
$379$	−29.2487			−1.50241			−0.751203	−	0.660072i	$-0.770526\pi$
$379$	−29.2487			−1.50241			−0.751203	+	0.660072i	$0.770526\pi$
$380$	2.36603	−	4.09808i	0.121375	−	0.210227i
$381$		0			0
$382$	−2.46410	−	4.26795i	−0.126074	−	0.218367i
$383$	6.69615	+	11.5981i	0.342157	+	0.592634i	0.984833	−	0.173504i	$-0.0555091\pi$
$383$	6.69615	+	11.5981i	0.342157	+	0.592634i	−0.642676	+	0.766138i	$0.722176\pi$
$384$		0			0
$385$	−5.09808	+	8.83013i	−0.259822	+	0.450025i
$386$	0.196152			0.00998390
$387$		0			0
$388$	6.73205			0.341768
$389$	9.92820	−	17.1962i	0.503380	−	0.871880i	−0.496612	−	0.867972i	$-0.665423\pi$
$389$	9.92820	−	17.1962i	0.503380	−	0.871880i	0.999992	−	0.00390716i	$-0.00124369\pi$
$390$		0			0
$391$	7.26795	+	12.5885i	0.367556	+	0.636626i
$392$	3.46410	+	6.00000i	0.174964	+	0.303046i
$393$		0			0
$394$	−5.19615	+	9.00000i	−0.261778	+	0.453413i
$395$	−3.07180			−0.154559
$396$		0			0
$397$	7.32051			0.367406			0.183703	−	0.982982i	$-0.441192\pi$
$397$	7.32051			0.367406			0.183703	+	0.982982i	$0.441192\pi$
$398$	0.196152	−	0.339746i	0.00983223	−	0.0170299i
$399$		0			0
$400$	2.23205	+	3.86603i	0.111603	+	0.193301i
$401$	14.4904	+	25.0981i	0.723615	+	1.25334i	0.959542	+	0.281567i	$0.0908542\pi$
$401$	14.4904	+	25.0981i	0.723615	+	1.25334i	−0.235926	+	0.971771i	$0.575812\pi$
$402$		0			0
$403$	−2.73205	+	4.73205i	−0.136093	+	0.235720i
$404$	14.4641			0.719616
$405$		0			0
$406$	−9.19615			−0.456397
$407$	17.6603	−	30.5885i	0.875386	−	1.51621i
$408$		0			0
$409$	10.4641	+	18.1244i	0.517417	+	0.896192i	0.999795	+	0.0202290i	$0.00643953\pi$
$409$	10.4641	+	18.1244i	0.517417	+	0.896192i	−0.482379	+	0.875963i	$0.660227\pi$
$410$	−2.66025	−	4.60770i	−0.131381	−	0.227558i
$411$		0			0
$412$	−8.46410	+	14.6603i	−0.416996	+	0.722259i
$413$	−21.3923			−1.05265
$414$		0			0
$415$	1.26795			0.0622412
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	12.0622	+	20.8923i	0.589980	+	1.02188i
$419$	4.43782	+	7.68653i	0.216802	+	0.375512i	0.953828	−	0.300352i	$-0.0971041\pi$
$419$	4.43782	+	7.68653i	0.216802	+	0.375512i	−0.737027	+	0.675864i	$0.763771\pi$
$420$		0			0
$421$	−7.02628	+	12.1699i	−0.342440	+	0.593123i	−0.984885	−	0.173208i	$-0.944587\pi$
$421$	−7.02628	+	12.1699i	−0.342440	+	0.593123i	0.642445	+	0.766332i	$0.277920\pi$
$422$	−8.33975			−0.405972
$423$		0			0
$424$	−12.4641			−0.605310
$425$	7.73205	−	13.3923i	0.375060	−	0.649622i
$426$		0			0
$427$	−2.23205	−	3.86603i	−0.108017	−	0.187090i
$428$	6.83013	+	11.8301i	0.330147	+	0.571831i
$429$		0			0
$430$	3.26795	−	5.66025i	0.157595	−	0.272962i
$431$	33.2487			1.60153			0.800767	−	0.598976i	$-0.204425\pi$
$431$	33.2487			1.60153			0.800767	+	0.598976i	$0.204425\pi$
$432$		0			0
$433$	17.3923			0.835821			0.417910	−	0.908488i	$-0.362763\pi$
$433$	17.3923			0.835821			0.417910	+	0.908488i	$0.362763\pi$
$434$	10.1962	−	17.6603i	0.489431	−	0.847719i
$435$		0			0
$436$	−3.09808	−	5.36603i	−0.148371	−	0.256986i
$437$	13.5622	+	23.4904i	0.648767	+	1.12370i
$438$		0			0
$439$	4.19615	−	7.26795i	0.200271	−	0.346880i	−0.748344	−	0.663310i	$-0.769151\pi$
$439$	4.19615	−	7.26795i	0.200271	−	0.346880i	0.948616	+	0.316430i	$0.102484\pi$
$440$	2.73205			0.130245
$441$		0			0
$442$	3.46410			0.164771
$443$	−4.73205	+	8.19615i	−0.224827	+	0.389411i	−0.956267	−	0.292494i	$-0.905515\pi$
$443$	−4.73205	+	8.19615i	−0.224827	+	0.389411i	0.731441	+	0.681905i	$0.238848\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	8.59808	+	14.8923i	0.407131	+	0.705171i
$447$		0			0
$448$	1.86603	−	3.23205i	0.0881614	−	0.152700i
$449$	−36.7846			−1.73597			−0.867987	−	0.496588i	$-0.834586\pi$
$449$	−36.7846			−1.73597			−0.867987	+	0.496588i	$0.834586\pi$
$450$		0			0
$451$	27.1244			1.27724
$452$	4.86603	−	8.42820i	0.228879	−	0.396429i
$453$		0			0
$454$	4.33013	+	7.50000i	0.203223	+	0.351992i
$455$	1.36603	+	2.36603i	0.0640403	+	0.110921i
$456$		0			0
$457$	−7.02628	+	12.1699i	−0.328675	+	0.569283i	−0.982249	−	0.187580i	$-0.939936\pi$
$457$	−7.02628	+	12.1699i	−0.328675	+	0.569283i	0.653574	+	0.756863i	$0.273269\pi$
$458$	3.46410			0.161867
$459$		0			0
$460$	3.07180			0.143223
$461$	−1.90192	+	3.29423i	−0.0885814	+	0.153428i	−0.906912	−	0.421321i	$-0.861567\pi$
$461$	−1.90192	+	3.29423i	−0.0885814	+	0.153428i	0.818330	+	0.574748i	$0.194900\pi$
$462$		0			0
$463$	13.8660	+	24.0167i	0.644409	+	1.11615i	0.984438	+	0.175734i	$0.0562298\pi$
$463$	13.8660	+	24.0167i	0.644409	+	1.11615i	−0.340029	+	0.940415i	$0.610437\pi$
$464$	1.23205	+	2.13397i	0.0571965	+	0.0990673i
$465$		0			0
$466$	−2.40192	+	4.16025i	−0.111267	+	0.192720i
$467$	−9.26795			−0.428870			−0.214435	−	0.976738i	$-0.568791\pi$
$467$	−9.26795			−0.428870			−0.214435	+	0.976738i	$0.568791\pi$
$468$		0			0
$469$	−53.7128			−2.48023
$470$	−1.66025	+	2.87564i	−0.0765818	+	0.132644i
$471$		0			0
$472$	2.86603	+	4.96410i	0.131920	+	0.228491i
$473$	16.6603	+	28.8564i	0.766039	+	1.32682i
$474$		0			0
$475$	14.4282	−	24.9904i	0.662011	−	1.14664i
$476$	−12.9282			−0.592563
$477$		0			0
$478$	4.85641			0.222127
$479$	4.16025	−	7.20577i	0.190087	−	0.329240i	−0.755192	−	0.655504i	$-0.772456\pi$
$479$	4.16025	−	7.20577i	0.190087	−	0.329240i	0.945279	+	0.326264i	$0.105790\pi$
$480$		0			0
$481$	−4.73205	−	8.19615i	−0.215763	−	0.373712i
$482$	−2.36603	−	4.09808i	−0.107770	−	0.186662i
$483$		0			0
$484$	−1.46410	+	2.53590i	−0.0665501	+	0.115268i
$485$	−4.92820			−0.223778
$486$		0			0
$487$	−34.3731			−1.55759			−0.778796	−	0.627277i	$-0.784169\pi$
$487$	−34.3731			−1.55759			−0.778796	+	0.627277i	$0.784169\pi$
$488$	−0.598076	+	1.03590i	−0.0270736	+	0.0468929i
$489$		0			0
$490$	−2.53590	−	4.39230i	−0.114560	−	0.198424i
$491$	−13.1244	−	22.7321i	−0.592294	−	1.02588i	−0.993923	−	0.110081i	$-0.964889\pi$
$491$	−13.1244	−	22.7321i	−0.592294	−	1.02588i	0.401629	−	0.915803i	$-0.368444\pi$
$492$		0			0
$493$	4.26795	−	7.39230i	0.192219	−	0.332933i
$494$	6.46410			0.290834
$495$		0			0
$496$	−5.46410			−0.245345
$497$	15.7942	−	27.3564i	0.708468	−	1.22710i
$498$		0			0
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	−0.997532	−	0.0702185i	$-0.977630\pi$
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	0.437955	−	0.898997i	$-0.355703\pi$
$500$	−3.46410	−	6.00000i	−0.154919	−	0.268328i
$501$		0			0
$502$	1.09808	−	1.90192i	0.0490095	−	0.0848870i
$503$	−31.8038			−1.41806			−0.709032	−	0.705177i	$-0.750868\pi$
$503$	−31.8038			−1.41806			−0.709032	+	0.705177i	$0.750868\pi$
$504$		0			0
$505$	−10.5885			−0.471180
$506$	−7.83013	+	13.5622i	−0.348092	+	0.602912i
$507$		0			0
$508$	−8.46410	−	14.6603i	−0.375534	−	0.650444i
$509$	−6.53590	−	11.3205i	−0.289699	−	0.501773i	0.684039	−	0.729445i	$-0.260222\pi$
$509$	−6.53590	−	11.3205i	−0.289699	−	0.501773i	−0.973738	+	0.227673i	$0.926888\pi$
$510$		0			0
$511$	10.1962	−	17.6603i	0.451051	−	0.781244i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	28.5167			1.25782
$515$	6.19615	−	10.7321i	0.273035	−	0.472911i
$516$		0			0
$517$	−8.46410	−	14.6603i	−0.372251	−	0.644757i
$518$	17.6603	+	30.5885i	0.775947	+	1.34398i
$519$		0			0
$520$	0.366025	−	0.633975i	0.0160513	−	0.0278016i
$521$	−2.66025			−0.116548			−0.0582739	−	0.998301i	$-0.518560\pi$
$521$	−2.66025			−0.116548			−0.0582739	+	0.998301i	$0.518560\pi$
$522$		0			0
$523$	32.4449			1.41871			0.709357	−	0.704849i	$-0.248985\pi$
$523$	32.4449			1.41871			0.709357	+	0.704849i	$0.248985\pi$
$524$	−8.46410	+	14.6603i	−0.369756	+	0.640436i
$525$		0			0
$526$	6.16987	+	10.6865i	0.269019	+	0.465955i
$527$	9.46410	+	16.3923i	0.412263	+	0.714060i
$528$		0			0
$529$	2.69615	−	4.66987i	0.117224	−	0.203038i
$530$	9.12436			0.396337
$531$		0			0
$532$	−24.1244			−1.04592
$533$	3.63397	−	6.29423i	0.157405	−	0.272633i
$534$		0			0
$535$	−5.00000	−	8.66025i	−0.216169	−	0.374415i
$536$	7.19615	+	12.4641i	0.310826	+	0.538367i
$537$		0			0
$538$	−10.7321	+	18.5885i	−0.462692	+	0.801405i
$539$	25.8564			1.11371
$540$		0			0
$541$	−8.05256			−0.346207			−0.173103	−	0.984904i	$-0.555379\pi$
$541$	−8.05256			−0.346207			−0.173103	+	0.984904i	$0.555379\pi$
$542$	7.59808	−	13.1603i	0.326365	−	0.565281i
$543$		0			0
$544$	1.73205	+	3.00000i	0.0742611	+	0.128624i
$545$	2.26795	+	3.92820i	0.0971483	+	0.168266i
$546$		0			0
$547$	−2.12436	+	3.67949i	−0.0908309	+	0.157324i	−0.907861	−	0.419271i	$-0.862286\pi$
$547$	−2.12436	+	3.67949i	−0.0908309	+	0.157324i	0.817030	+	0.576595i	$0.195619\pi$
$548$	17.3205			0.739895
$549$		0			0
$550$	16.6603			0.710396
$551$	7.96410	−	13.7942i	0.339282	−	0.587654i
$552$		0			0
$553$	7.83013	+	13.5622i	0.332971	+	0.576722i
$554$	−0.401924	−	0.696152i	−0.0170761	−	0.0295767i
$555$		0			0
$556$	−3.90192	+	6.75833i	−0.165478	+	0.286617i
$557$	1.85641			0.0786585			0.0393292	−	0.999226i	$-0.487478\pi$
$557$	1.85641			0.0786585			0.0393292	+	0.999226i	$0.487478\pi$
$558$		0			0
$559$	8.92820			0.377623
$560$	−1.36603	+	2.36603i	−0.0577251	+	0.0999828i
$561$		0			0
$562$	9.19615	+	15.9282i	0.387916	+	0.671891i
$563$	−21.6865	−	37.5622i	−0.913978	−	1.58306i	−0.808390	−	0.588647i	$-0.799661\pi$
$563$	−21.6865	−	37.5622i	−0.913978	−	1.58306i	−0.105588	−	0.994410i	$-0.533673\pi$
$564$		0			0
$565$	−3.56218	+	6.16987i	−0.149862	+	0.259569i
$566$	3.85641			0.162097
$567$		0			0
$568$	−8.46410			−0.355146
$569$	2.80385	−	4.85641i	0.117543	−	0.203591i	−0.801250	−	0.598329i	$-0.795831\pi$
$569$	2.80385	−	4.85641i	0.117543	−	0.203591i	0.918794	+	0.394738i	$0.129165\pi$
$570$		0			0
$571$	5.83013	+	10.0981i	0.243983	+	0.422591i	0.961845	−	0.273594i	$-0.0882125\pi$
$571$	5.83013	+	10.0981i	0.243983	+	0.422591i	−0.717862	+	0.696185i	$0.754879\pi$
$572$	1.86603	+	3.23205i	0.0780224	+	0.135139i
$573$		0			0
$574$	−13.5622	+	23.4904i	−0.566074	+	0.980470i
$575$	18.7321			0.781181
$576$		0			0
$577$	−42.9282			−1.78712			−0.893562	−	0.448939i	$-0.851802\pi$
$577$	−42.9282			−1.78712			−0.893562	+	0.448939i	$0.851802\pi$
$578$	−2.50000	+	4.33013i	−0.103986	+	0.180110i
$579$		0			0
$580$	−0.901924	−	1.56218i	−0.0374503	−	0.0648659i
$581$	−3.23205	−	5.59808i	−0.134088	−	0.232247i
$582$		0			0
$583$	−23.2583	+	40.2846i	−0.963262	+	1.66842i
$584$	−5.46410			−0.226106
$585$		0			0
$586$	−28.7846			−1.18908
$587$	−2.80385	+	4.85641i	−0.115727	+	0.200445i	−0.918070	−	0.396418i	$-0.870253\pi$
$587$	−2.80385	+	4.85641i	−0.115727	+	0.200445i	0.802343	+	0.596863i	$0.203586\pi$
$588$		0			0
$589$	17.6603	+	30.5885i	0.727678	+	1.26038i
$590$	−2.09808	−	3.63397i	−0.0863764	−	0.149608i
$591$		0			0
$592$	4.73205	−	8.19615i	0.194486	−	0.336860i
$593$	13.1244			0.538953			0.269476	−	0.963007i	$-0.413149\pi$
$593$	13.1244			0.538953			0.269476	+	0.963007i	$0.413149\pi$
$594$		0			0
$595$	9.46410			0.387990
$596$	−0.169873	+	0.294229i	−0.00695827	+	0.0120521i
$597$		0			0
$598$	2.09808	+	3.63397i	0.0857967	+	0.148604i
$599$	−19.7583	−	34.2224i	−0.807303	−	1.39829i	−0.914725	−	0.404077i	$-0.867593\pi$
$599$	−19.7583	−	34.2224i	−0.807303	−	1.39829i	0.107421	−	0.994214i	$-0.465741\pi$
$600$		0			0
$601$	0.303848	−	0.526279i	0.0123942	−	0.0214674i	−0.859762	−	0.510695i	$-0.829388\pi$
$601$	0.303848	−	0.526279i	0.0123942	−	0.0214674i	0.872156	+	0.489228i	$0.162721\pi$
$602$	−33.3205			−1.35804
$603$		0			0
$604$	−9.58846			−0.390149
$605$	1.07180	−	1.85641i	0.0435747	−	0.0754737i
$606$		0			0
$607$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$607$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$608$	3.23205	+	5.59808i	0.131077	+	0.227032i
$609$		0			0
$610$	0.437822	−	0.758330i	0.0177269	−	0.0307039i
$611$	−4.53590			−0.183503
$612$		0			0
$613$	38.9282			1.57230			0.786148	−	0.618039i	$-0.212073\pi$
$613$	38.9282			1.57230			0.786148	+	0.618039i	$0.212073\pi$
$614$	−12.8564	+	22.2679i	−0.518842	+	0.898661i
$615$		0			0
$616$	−6.96410	−	12.0622i	−0.280592	−	0.485999i
$617$	−21.3660	−	37.0070i	−0.860164	−	1.48985i	−0.871770	−	0.489915i	$-0.837028\pi$
$617$	−21.3660	−	37.0070i	−0.860164	−	1.48985i	0.0116066	−	0.999933i	$-0.496305\pi$
$618$		0			0
$619$	2.03590	−	3.52628i	0.0818297	−	0.141733i	−0.822206	−	0.569190i	$-0.807257\pi$
$619$	2.03590	−	3.52628i	0.0818297	−	0.141733i	0.904036	+	0.427457i	$0.140590\pi$
$620$	4.00000			0.160644
$621$		0			0
$622$	−24.2487			−0.972285
$623$	15.2942	−	26.4904i	0.612750	−	1.06131i
$624$		0			0
$625$	−8.62436	−	14.9378i	−0.344974	−	0.597513i
$626$	9.89230	+	17.1340i	0.395376	+	0.684811i
$627$		0			0
$628$	4.13397	−	7.16025i	0.164964	−	0.285725i
$629$	−32.7846			−1.30721
$630$		0			0
$631$	−26.8038			−1.06704			−0.533522	−	0.845786i	$-0.679132\pi$
$631$	−26.8038			−1.06704			−0.533522	+	0.845786i	$0.679132\pi$
$632$	2.09808	−	3.63397i	0.0834570	−	0.144552i
$633$		0			0
$634$	11.0263	+	19.0981i	0.437909	+	0.758482i
$635$	6.19615	+	10.7321i	0.245887	+	0.425888i
$636$		0			0
$637$	3.46410	−	6.00000i	0.137253	−	0.237729i
$638$	9.19615			0.364079
$639$		0			0
$640$	0.732051			0.0289368
$641$	−5.66987	+	9.82051i	−0.223947	+	0.387887i	−0.956003	−	0.293357i	$-0.905227\pi$
$641$	−5.66987	+	9.82051i	−0.223947	+	0.387887i	0.732056	+	0.681244i	$0.238561\pi$
$642$		0			0
$643$	1.42820	+	2.47372i	0.0563228	+	0.0975540i	0.892812	−	0.450429i	$-0.148729\pi$
$643$	1.42820	+	2.47372i	0.0563228	+	0.0975540i	−0.836489	+	0.547983i	$0.815396\pi$
$644$	−7.83013	−	13.5622i	−0.308550	−	0.534425i
$645$		0			0
$646$	11.1962	−	19.3923i	0.440507	−	0.762980i
$647$	16.4449			0.646514			0.323257	−	0.946311i	$-0.395222\pi$
$647$	16.4449			0.646514			0.323257	+	0.946311i	$0.395222\pi$
$648$		0			0
$649$	21.3923			0.839721
$650$	2.23205	−	3.86603i	0.0875482	−	0.151638i
$651$		0			0
$652$	−6.66025	−	11.5359i	−0.260836	−	0.451781i
$653$	−12.9282	−	22.3923i	−0.505920	−	0.876279i	−0.999977	−	0.00684901i	$-0.997820\pi$
$653$	−12.9282	−	22.3923i	−0.505920	−	0.876279i	0.494057	−	0.869430i	$-0.335513\pi$
$654$		0			0
$655$	6.19615	−	10.7321i	0.242104	−	0.419336i
$656$	7.26795			0.283766
$657$		0			0
$658$	16.9282			0.659930
$659$	8.53590	−	14.7846i	0.332511	−	0.575927i	−0.650492	−	0.759513i	$-0.725437\pi$
$659$	8.53590	−	14.7846i	0.332511	−	0.575927i	0.983004	+	0.183586i	$0.0587707\pi$
$660$		0			0
$661$	−12.5359	−	21.7128i	−0.487590	−	0.844531i	0.512308	−	0.858802i	$-0.328791\pi$
$661$	−12.5359	−	21.7128i	−0.487590	−	0.844531i	−0.999898	+	0.0142711i	$0.995457\pi$
$662$	0.660254	+	1.14359i	0.0256615	+	0.0444470i
$663$		0			0
$664$	−0.866025	+	1.50000i	−0.0336083	+	0.0582113i
$665$	17.6603			0.684835
$666$		0			0
$667$	10.3397			0.400357
$668$	3.69615	−	6.40192i	0.143008	−	0.247698i
$669$		0			0
$670$	−5.26795	−	9.12436i	−0.203519	−	0.352505i
$671$	2.23205	+	3.86603i	0.0861674	+	0.149246i
$672$		0			0
$673$	−15.1603	+	26.2583i	−0.584385	+	1.01218i	0.410567	+	0.911830i	$0.365331\pi$
$673$	−15.1603	+	26.2583i	−0.584385	+	1.01218i	−0.994952	+	0.100354i	$0.968003\pi$
$674$	10.9282			0.420939
$675$		0			0
$676$	1.00000			0.0384615
$677$	−13.6244	+	23.5981i	−0.523627	+	0.906948i	0.475995	+	0.879448i	$0.342088\pi$
$677$	−13.6244	+	23.5981i	−0.523627	+	0.906948i	−0.999622	+	0.0274999i	$0.991245\pi$
$678$		0			0
$679$	12.5622	+	21.7583i	0.482092	+	0.835008i
$680$	−1.26795	−	2.19615i	−0.0486236	−	0.0842186i
$681$		0			0
$682$	−10.1962	+	17.6603i	−0.390431	+	0.676246i
$683$	−33.3205			−1.27497			−0.637487	−	0.770461i	$-0.720026\pi$
$683$	−33.3205			−1.27497			−0.637487	+	0.770461i	$0.720026\pi$
$684$		0			0
$685$	−12.6795			−0.484458
$686$	0.133975	−	0.232051i	0.00511517	−	0.00885974i
$687$		0			0
$688$	4.46410	+	7.73205i	0.170192	+	0.294782i
$689$	6.23205	+	10.7942i	0.237422	+	0.411227i
$690$		0			0
$691$	−20.6962	+	35.8468i	−0.787319	+	1.36368i	0.140285	+	0.990111i	$0.455198\pi$
$691$	−20.6962	+	35.8468i	−0.787319	+	1.36368i	−0.927604	+	0.373565i	$0.878135\pi$
$692$	−23.0000			−0.874329
$693$		0			0
$694$	19.2679			0.731401
$695$	2.85641	−	4.94744i	0.108350	−	0.187667i
$696$		0			0
$697$	−12.5885	−	21.8038i	−0.476822	−	0.825880i
$698$	−0.0717968	−	0.124356i	−0.00271755	−	0.00470693i
$699$		0			0
$700$	−8.33013	+	14.4282i	−0.314849	+	0.545335i
$701$	27.9282			1.05483			0.527417	−	0.849607i	$-0.323161\pi$
$701$	27.9282			1.05483			0.527417	+	0.849607i	$0.323161\pi$
$702$		0			0
$703$	−61.1769			−2.30733
$704$	−1.86603	+	3.23205i	−0.0703285	+	0.121812i
$705$		0			0
$706$	13.2942	+	23.0263i	0.500335	+	0.866605i
$707$	26.9904	+	46.7487i	1.01508	+	1.75817i
$708$		0			0
$709$	20.9282	−	36.2487i	0.785975	−	1.36135i	−0.142440	−	0.989803i	$-0.545495\pi$
$709$	20.9282	−	36.2487i	0.785975	−	1.36135i	0.928415	−	0.371545i	$-0.121172\pi$
$710$	6.19615			0.232537
$711$		0			0
$712$	−8.19615			−0.307164
$713$	−11.4641	+	19.8564i	−0.429334	+	0.743628i
$714$		0			0
$715$	−1.36603	−	2.36603i	−0.0510865	−	0.0884843i
$716$	−3.46410	−	6.00000i	−0.129460	−	0.224231i
$717$		0			0
$718$	15.9282	−	27.5885i	0.594435	−	1.02959i
$719$	2.05256			0.0765475			0.0382738	−	0.999267i	$-0.487814\pi$
$719$	2.05256			0.0765475			0.0382738	+	0.999267i	$0.487814\pi$
$720$		0			0
$721$	−63.1769			−2.35283
$722$	11.3923	−	19.7321i	0.423978	−	0.734351i
$723$		0			0
$724$	7.79423	+	13.5000i	0.289670	+	0.501724i
$725$	−5.50000	−	9.52628i	−0.204265	−	0.353797i
$726$		0			0
$727$	5.85641	−	10.1436i	0.217202	−	0.376205i	−0.736749	−	0.676166i	$-0.763640\pi$
$727$	5.85641	−	10.1436i	0.217202	−	0.376205i	0.953952	+	0.299961i	$0.0969736\pi$
$728$	−3.73205			−0.138319
$729$		0			0
$730$	4.00000			0.148047
$731$	15.4641	−	26.7846i	0.571960	−	0.990665i
$732$		0			0
$733$	13.0263	+	22.5622i	0.481137	+	0.833353i	0.999766	−	0.0216463i	$-0.00689077\pi$
$733$	13.0263	+	22.5622i	0.481137	+	0.833353i	−0.518629	+	0.854999i	$0.673557\pi$
$734$	13.2942	+	23.0263i	0.490699	+	0.849915i
$735$		0			0
$736$	−2.09808	+	3.63397i	−0.0773361	+	0.133950i
$737$	53.7128			1.97854
$738$		0			0
$739$	12.4641			0.458499			0.229250	−	0.973368i	$-0.426373\pi$
$739$	12.4641			0.458499			0.229250	+	0.973368i	$0.426373\pi$
$740$	−3.46410	+	6.00000i	−0.127343	+	0.220564i
$741$		0			0
$742$	−23.2583	−	40.2846i	−0.853840	−	1.47889i
$743$	−20.1603	−	34.9186i	−0.739608	−	1.28104i	−0.952672	−	0.304000i	$-0.901678\pi$
$743$	−20.1603	−	34.9186i	−0.739608	−	1.28104i	0.213064	−	0.977038i	$-0.431656\pi$
$744$		0			0
$745$	0.124356	−	0.215390i	0.00455604	−	0.00789129i
$746$	35.0526			1.28337
$747$		0			0
$748$	12.9282			0.472702
$749$	−25.4904	+	44.1506i	−0.931398	+	1.61323i
$750$		0			0
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	0.755510	−	0.655137i	$-0.227389\pi$
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	−0.945120	+	0.326722i	$0.894056\pi$
$752$	−2.26795	−	3.92820i	−0.0827036	−	0.143247i
$753$		0			0
$754$	1.23205	−	2.13397i	0.0448686	−	0.0777148i
$755$	7.01924			0.255456
$756$		0			0
$757$	−34.2679			−1.24549			−0.622745	−	0.782425i	$-0.713983\pi$
$757$	−34.2679			−1.24549			−0.622745	+	0.782425i	$0.713983\pi$
$758$	−14.6244	+	25.3301i	−0.531181	+	0.920032i
$759$		0			0
$760$	−2.36603	−	4.09808i	−0.0858248	−	0.148653i
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$		0			0
$763$	11.5622	−	20.0263i	0.418579	−	0.725000i
$764$	−4.92820			−0.178296
$765$		0			0
$766$	13.3923			0.483884
$767$	2.86603	−	4.96410i	0.103486	−	0.179243i
$768$		0			0
$769$	22.0526	+	38.1962i	0.795236	+	1.37739i	0.922689	+	0.385544i	$0.125986\pi$
$769$	22.0526	+	38.1962i	0.795236	+	1.37739i	−0.127454	+	0.991845i	$0.540680\pi$
$770$	5.09808	+	8.83013i	0.183722	+	0.318216i
$771$		0			0
$772$	0.0980762	−	0.169873i	0.00352984	−	0.00611386i
$773$	−40.1051			−1.44248			−0.721240	−	0.692685i	$-0.756428\pi$
$773$	−40.1051			−1.44248			−0.721240	+	0.692685i	$0.756428\pi$
$774$		0			0
$775$	24.3923			0.876197
$776$	3.36603	−	5.83013i	0.120833	−	0.209289i
$777$		0			0
$778$	−9.92820	−	17.1962i	−0.355943	−	0.616512i
$779$	−23.4904	−	40.6865i	−0.841630	−	1.45775i
$780$		0			0
$781$	−15.7942	+	27.3564i	−0.565162	+	0.978889i
$782$	14.5359			0.519803
$783$		0			0
$784$	6.92820			0.247436
$785$	−3.02628	+	5.24167i	−0.108013	+	0.187083i
$786$		0			0
$787$	10.3038	+	17.8468i	0.367292	+	0.636169i	0.989141	−	0.146968i	$-0.0469515\pi$
$787$	10.3038	+	17.8468i	0.367292	+	0.636169i	−0.621849	+	0.783137i	$0.713618\pi$
$788$	5.19615	+	9.00000i	0.185105	+	0.320612i
$789$		0			0
$790$	−1.53590	+	2.66025i	−0.0546448	+	0.0946476i
$791$	36.3205			1.29141
$792$		0			0
$793$	1.19615			0.0424766
$794$	3.66025	−	6.33975i	0.129898	−	0.224989i
$795$		0			0
$796$	−0.196152	−	0.339746i	−0.00695244	−	0.0120420i
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	0.999687	−	0.0249984i	$-0.00795805\pi$
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	−0.521493	+	0.853256i	$0.674625\pi$
$798$		0			0
$799$	−7.85641	+	13.6077i	−0.277940	+	0.481406i
$800$	4.46410			0.157830
$801$		0			0
$802$	28.9808			1.02335
$803$	−10.1962	+	17.6603i	−0.359814	+	0.623217i
$804$		0			0
$805$	5.73205	+	9.92820i	0.202028	+	0.349923i
$806$	2.73205	+	4.73205i	0.0962324	+	0.166679i
$807$		0			0
$808$	7.23205	−	12.5263i	0.254423	−	0.440673i
$809$	−25.9808			−0.913435			−0.456717	−	0.889612i	$-0.650975\pi$
$809$	−25.9808			−0.913435			−0.456717	+	0.889612i	$0.650975\pi$
$810$		0			0
$811$	48.8564			1.71558			0.857790	−	0.514000i	$-0.171837\pi$
$811$	48.8564			1.71558			0.857790	+	0.514000i	$0.171837\pi$
$812$	−4.59808	+	7.96410i	−0.161361	+	0.279485i
$813$		0			0
$814$	−17.6603	−	30.5885i	−0.618992	−	1.07212i
$815$	4.87564	+	8.44486i	0.170786	+	0.295811i
$816$		0			0
$817$	28.8564	−	49.9808i	1.00956	−	1.74861i
$818$	20.9282			0.731737
$819$		0			0
$820$	−5.32051			−0.185800
$821$	−14.0000	+	24.2487i	−0.488603	+	0.846286i	−0.999914	−	0.0131101i	$-0.995827\pi$
$821$	−14.0000	+	24.2487i	−0.488603	+	0.846286i	0.511311	+	0.859396i	$0.329160\pi$
$822$		0			0
$823$	8.66025	+	15.0000i	0.301877	+	0.522867i	0.976561	−	0.215240i	$-0.0690533\pi$
$823$	8.66025	+	15.0000i	0.301877	+	0.522867i	−0.674684	+	0.738107i	$0.735720\pi$
$824$	8.46410	+	14.6603i	0.294861	+	0.510714i
$825$		0			0
$826$	−10.6962	+	18.5263i	−0.372167	+	0.644612i
$827$	−53.5692			−1.86278			−0.931392	−	0.364017i	$-0.881405\pi$
$827$	−53.5692			−1.86278			−0.931392	+	0.364017i	$0.881405\pi$
$828$		0			0
$829$	24.9090			0.865124			0.432562	−	0.901604i	$-0.357610\pi$
$829$	24.9090			0.865124			0.432562	+	0.901604i	$0.357610\pi$
$830$	0.633975	−	1.09808i	0.0220056	−	0.0381148i
$831$		0			0
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	−12.0000	−	20.7846i	−0.415775	−	0.720144i
$834$		0			0
$835$	−2.70577	+	4.68653i	−0.0936371	+	0.162184i
$836$	24.1244			0.834358
$837$		0			0
$838$	8.87564			0.306604
$839$	7.58846	−	13.1436i	0.261983	−	0.453767i	−0.704786	−	0.709420i	$-0.748957\pi$
$839$	7.58846	−	13.1436i	0.261983	−	0.453767i	0.966769	+	0.255653i	$0.0822903\pi$
$840$		0			0
$841$	11.4641	+	19.8564i	0.395314	+	0.684704i
$842$	7.02628	+	12.1699i	0.242142	+	0.419402i
$843$		0			0
$844$	−4.16987	+	7.22243i	−0.143533	+	0.248606i
$845$	−0.732051			−0.0251833
$846$		0			0
$847$	−10.9282			−0.375498
$848$	−6.23205	+	10.7942i	−0.214010	+	0.370675i
$849$		0			0
$850$	−7.73205	−	13.3923i	−0.265207	−	0.459352i
$851$	−19.8564	−	34.3923i	−0.680669	−	1.17895i
$852$		0			0
$853$	13.1699	−	22.8109i	0.450928	−	0.781030i	−0.547516	−	0.836795i	$-0.684426\pi$
$853$	13.1699	−	22.8109i	0.450928	−	0.781030i	0.998444	+	0.0557652i	$0.0177598\pi$
$854$	−4.46410			−0.152758
$855$		0			0
$856$	13.6603			0.466898
$857$	−5.79423	+	10.0359i	−0.197927	+	0.342820i	−0.947856	−	0.318698i	$-0.896754\pi$
$857$	−5.79423	+	10.0359i	−0.197927	+	0.342820i	0.749929	+	0.661518i	$0.230088\pi$
$858$		0			0
$859$	−9.02628	−	15.6340i	−0.307973	−	0.533424i	0.669946	−	0.742410i	$-0.266317\pi$
$859$	−9.02628	−	15.6340i	−0.307973	−	0.533424i	−0.977919	+	0.208985i	$0.932984\pi$
$860$	−3.26795	−	5.66025i	−0.111436	−	0.193013i
$861$		0			0
$862$	16.6244	−	28.7942i	0.566228	−	0.980735i
$863$	−16.7128			−0.568911			−0.284455	−	0.958689i	$-0.591813\pi$
$863$	−16.7128			−0.568911			−0.284455	+	0.958689i	$0.591813\pi$
$864$		0			0
$865$	16.8372			0.572481
$866$	8.69615	−	15.0622i	0.295507	−	0.511834i
$867$		0			0
$868$	−10.1962	−	17.6603i	−0.346080	−	0.599428i
$869$	−7.83013	−	13.5622i	−0.265619	−	0.460065i
$870$		0			0
$871$	7.19615	−	12.4641i	0.243832	−	0.422330i
$872$	−6.19615			−0.209828
$873$		0			0
$874$	27.1244			0.917495
$875$	12.9282	−	22.3923i	0.437053	−	0.756998i
$876$		0			0
$877$	−16.6865	−	28.9019i	−0.563464	−	0.975949i	−0.997191	−	0.0749041i	$-0.976135\pi$
$877$	−16.6865	−	28.9019i	−0.563464	−	0.975949i	0.433727	−	0.901045i	$-0.357198\pi$
$878$	−4.19615	−	7.26795i	−0.141613	−	0.245281i
$879$		0			0
$880$	1.36603	−	2.36603i	0.0460487	−	0.0797587i
$881$	−43.8564			−1.47756			−0.738780	−	0.673947i	$-0.764598\pi$
$881$	−43.8564			−1.47756			−0.738780	+	0.673947i	$0.764598\pi$
$882$		0			0
$883$	44.9808			1.51372			0.756862	−	0.653575i	$-0.226732\pi$
$883$	44.9808			1.51372			0.756862	+	0.653575i	$0.226732\pi$
$884$	1.73205	−	3.00000i	0.0582552	−	0.100901i
$885$		0			0
$886$	4.73205	+	8.19615i	0.158976	+	0.275355i
$887$	−24.4904	−	42.4186i	−0.822307	−	1.42428i	−0.903961	−	0.427616i	$-0.859354\pi$
$887$	−24.4904	−	42.4186i	−0.822307	−	1.42428i	0.0816540	−	0.996661i	$-0.473980\pi$
$888$		0			0
$889$	31.5885	−	54.7128i	1.05944	−	1.83501i
$890$	6.00000			0.201120
$891$		0			0
$892$	17.1962			0.575770
$893$	−14.6603	+	25.3923i	−0.490587	+	0.849721i
$894$		0			0
$895$	2.53590	+	4.39230i	0.0847657	+	0.146819i
$896$	−1.86603	−	3.23205i	−0.0623395	−	0.107975i
$897$		0			0
$898$	−18.3923	+	31.8564i	−0.613759	+	1.06306i
$899$	13.4641			0.449053
$900$		0			0
$901$	43.1769			1.43843
$902$	13.5622	−	23.4904i	0.451571	−	0.782144i
$903$		0			0
$904$	−4.86603	−	8.42820i	−0.161842	−	0.280318i
$905$	−5.70577	−	9.88269i	−0.189666	−	0.328512i
$906$		0			0
$907$	20.3205	−	35.1962i	0.674731	−	1.16867i	−0.301816	−	0.953366i	$-0.597593\pi$
$907$	20.3205	−	35.1962i	0.674731	−	1.16867i	0.976547	−	0.215303i	$-0.0690739\pi$
$908$	8.66025			0.287401
$909$		0			0
$910$	2.73205			0.0905666
$911$	−2.87564	+	4.98076i	−0.0952743	+	0.165020i	−0.909723	−	0.415216i	$-0.863706\pi$
$911$	−2.87564	+	4.98076i	−0.0952743	+	0.165020i	0.814449	+	0.580236i	$0.197040\pi$
$912$		0			0
$913$	3.23205	+	5.59808i	0.106965	+	0.185269i
$914$	7.02628	+	12.1699i	0.232409	+	0.402544i
$915$		0			0
$916$	1.73205	−	3.00000i	0.0572286	−	0.0991228i
$917$	−63.1769			−2.08629
$918$		0			0
$919$	22.6410			0.746858			0.373429	−	0.927659i	$-0.378182\pi$
$919$	22.6410			0.746858			0.373429	+	0.927659i	$0.378182\pi$
$920$	1.53590	−	2.66025i	0.0506371	−	0.0877060i
$921$		0			0
$922$	1.90192	+	3.29423i	0.0626365	+	0.108490i
$923$	4.23205	+	7.33013i	0.139300	+	0.241274i
$924$		0			0
$925$	−21.1244	+	36.5885i	−0.694565	+	1.20302i
$926$	27.7321			0.911332
$927$		0			0
$928$	2.46410			0.0808881
$929$	−4.26795	+	7.39230i	−0.140027	+	0.242534i	−0.927507	−	0.373807i	$-0.878052\pi$
$929$	−4.26795	+	7.39230i	−0.140027	+	0.242534i	0.787480	+	0.616341i	$0.211386\pi$
$930$		0			0
$931$	−22.3923	−	38.7846i	−0.733878	−	1.27111i
$932$	2.40192	+	4.16025i	0.0786776	+	0.136274i
$933$		0			0
$934$	−4.63397	+	8.02628i	−0.151628	+	0.262628i
$935$	−9.46410			−0.309509
$936$		0			0
$937$	−45.9615			−1.50150			−0.750749	−	0.660588i	$-0.770307\pi$
$937$	−45.9615			−1.50150			−0.750749	+	0.660588i	$0.770307\pi$
$938$	−26.8564	+	46.5167i	−0.876893	+	1.51882i
$939$		0			0
$940$	1.66025	+	2.87564i	0.0541515	+	0.0937932i
$941$	−17.7321	−	30.7128i	−0.578048	−	1.00121i	−0.995703	−	0.0926033i	$-0.970481\pi$
$941$	−17.7321	−	30.7128i	−0.578048	−	1.00121i	0.417655	−	0.908606i	$-0.362852\pi$
$942$		0			0
$943$	15.2487	−	26.4115i	0.496566	−	0.860078i
$944$	5.73205			0.186562
$945$		0			0
$946$	33.3205			1.08334
$947$	3.80385	−	6.58846i	0.123608	−	0.214096i	−0.797580	−	0.603214i	$-0.793887\pi$
$947$	3.80385	−	6.58846i	0.123608	−	0.214096i	0.921188	+	0.389117i	$0.127220\pi$
$948$		0			0
$949$	2.73205	+	4.73205i	0.0886861	+	0.153609i
$950$	−14.4282	−	24.9904i	−0.468113	−	0.810795i
$951$		0			0
$952$	−6.46410	+	11.1962i	−0.209503	+	0.362869i
$953$	−11.7128			−0.379415			−0.189708	−	0.981841i	$-0.560754\pi$
$953$	−11.7128			−0.379415			−0.189708	+	0.981841i	$0.560754\pi$
$954$		0			0
$955$	3.60770			0.116742
$956$	2.42820	−	4.20577i	0.0785337	−	0.136024i
$957$		0			0
$958$	−4.16025	−	7.20577i	−0.134412	−	0.232808i
$959$	32.3205	+	55.9808i	1.04368	+	1.80771i
$960$		0			0
$961$	0.571797	−	0.990381i	0.0184451	−	0.0319478i
$962$	−9.46410			−0.305135
$963$		0			0
$964$	−4.73205			−0.152409
$965$	−0.0717968	+	0.124356i	−0.00231122	+	0.00400315i
$966$		0			0
$967$	−24.3827	−	42.2321i	−0.784094	−	1.35809i	−0.929539	−	0.368725i	$-0.879794\pi$
$967$	−24.3827	−	42.2321i	−0.784094	−	1.35809i	0.145444	−	0.989366i	$-0.453539\pi$
$968$	1.46410	+	2.53590i	0.0470580	+	0.0815069i
$969$		0			0
$970$	−2.46410	+	4.26795i	−0.0791175	+	0.137036i
$971$	−46.3013			−1.48588			−0.742939	−	0.669359i	$-0.766569\pi$
$971$	−46.3013			−1.48588			−0.742939	+	0.669359i	$0.766569\pi$
$972$		0			0
$973$	−29.1244			−0.933684
$974$	−17.1865	+	29.7679i	−0.550692	+	0.953827i
$975$		0			0
$976$	0.598076	+	1.03590i	0.0191440	+	0.0331583i
$977$	−4.22243	−	7.31347i	−0.135088	−	0.233979i	0.790543	−	0.612406i	$-0.209798\pi$
$977$	−4.22243	−	7.31347i	−0.135088	−	0.233979i	−0.925631	+	0.378428i	$0.876465\pi$
$978$		0			0
$979$	−15.2942	+	26.4904i	−0.488806	+	0.846636i
$980$	−5.07180			−0.162013
$981$		0			0
$982$	−26.2487			−0.837630
$983$	18.3038	−	31.7032i	0.583802	−	1.01117i	−0.411222	−	0.911535i	$-0.634898\pi$
$983$	18.3038	−	31.7032i	0.583802	−	1.01117i	0.995024	−	0.0996394i	$-0.0317689\pi$
$984$		0			0
$985$	−3.80385	−	6.58846i	−0.121201	−	0.209926i
$986$	−4.26795	−	7.39230i	−0.135919	−	0.235419i
$987$		0			0
$988$	3.23205	−	5.59808i	0.102825	−	0.178099i
$989$	37.4641			1.19129
$990$		0			0
$991$	9.80385			0.311429			0.155715	−	0.987802i	$-0.450232\pi$
$991$	9.80385			0.311429			0.155715	+	0.987802i	$0.450232\pi$
$992$	−2.73205	+	4.73205i	−0.0867427	+	0.150243i
$993$		0			0
$994$	−15.7942	−	27.3564i	−0.500963	−	0.867693i
$995$	0.143594	+	0.248711i	0.00455222	+	0.00788468i
$996$		0			0
$997$	19.7224	−	34.1603i	0.624616	−	1.08187i	−0.363999	−	0.931399i	$-0.618589\pi$
$997$	19.7224	−	34.1603i	0.624616	−	1.08187i	0.988615	−	0.150467i	$-0.0480777\pi$
$998$	−25.0000			−0.791361
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2106.2.e.bg.703.2		4
3.2	odd	2		2106.2.e.be.703.1		4
9.2	odd	6		2106.2.a.l.1.2	yes	2
9.4	even	3	inner	2106.2.e.bg.1405.2		4
9.5	odd	6		2106.2.e.be.1405.1		4
9.7	even	3		2106.2.a.j.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2106.2.a.j.1.1	✓	2	9.7	even	3
2106.2.a.l.1.2	yes	2	9.2	odd	6
2106.2.e.be.703.1		4	3.2	odd	2
2106.2.e.be.1405.1		4	9.5	odd	6
2106.2.e.bg.703.2		4	1.1	even	1	trivial
2106.2.e.bg.1405.2		4	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2106.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.366025 + 0.633975i) q^{5} +(1.86603 - 3.23205i) q^{7} -1.00000 q^{8} +0.732051 q^{10} +(-1.86603 + 3.23205i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.86603 - 3.23205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.46410 q^{17} +6.46410 q^{19} +(0.366025 - 0.633975i) q^{20} +(1.86603 + 3.23205i) q^{22} +(2.09808 + 3.63397i) q^{23} +(2.23205 - 3.86603i) q^{25} +1.00000 q^{26} -3.73205 q^{28} +(1.23205 - 2.13397i) q^{29} +(2.73205 + 4.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.73205 - 3.00000i) q^{34} +2.73205 q^{35} -9.46410 q^{37} +(3.23205 - 5.59808i) q^{38} +(-0.366025 - 0.633975i) q^{40} +(-3.63397 - 6.29423i) q^{41} +(4.46410 - 7.73205i) q^{43} +3.73205 q^{44} +4.19615 q^{46} +(-2.26795 + 3.92820i) q^{47} +(-3.46410 - 6.00000i) q^{49} +(-2.23205 - 3.86603i) q^{50} +(0.500000 - 0.866025i) q^{52} +12.4641 q^{53} -2.73205 q^{55} +(-1.86603 + 3.23205i) q^{56} +(-1.23205 - 2.13397i) q^{58} +(-2.86603 - 4.96410i) q^{59} +(0.598076 - 1.03590i) q^{61} +5.46410 q^{62} +1.00000 q^{64} +(-0.366025 + 0.633975i) q^{65} +(-7.19615 - 12.4641i) q^{67} +(-1.73205 - 3.00000i) q^{68} +(1.36603 - 2.36603i) q^{70} +8.46410 q^{71} +5.46410 q^{73} +(-4.73205 + 8.19615i) q^{74} +(-3.23205 - 5.59808i) q^{76} +(6.96410 + 12.0622i) q^{77} +(-2.09808 + 3.63397i) q^{79} -0.732051 q^{80} -7.26795 q^{82} +(0.866025 - 1.50000i) q^{83} +(1.26795 + 2.19615i) q^{85} +(-4.46410 - 7.73205i) q^{86} +(1.86603 - 3.23205i) q^{88} +8.19615 q^{89} +3.73205 q^{91} +(2.09808 - 3.63397i) q^{92} +(2.26795 + 3.92820i) q^{94} +(2.36603 + 4.09808i) q^{95} +(-3.36603 + 5.83013i) q^{97} -6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 4 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} - 2 q^{16} + 12 q^{19} - 2 q^{20} + 4 q^{22} - 2 q^{23} + 2 q^{25} + 4 q^{26} - 8 q^{28} - 2 q^{29} + 4 q^{31}+ \cdots - 10 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 4 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 - 2 * q^16 + 12 * q^19 - 2 * q^20 + 4 * q^22 - 2 * q^23 + 2 * q^25 + 4 * q^26 - 8 * q^28 - 2 * q^29 + 4 * q^31 + 2 * q^32 + 4 * q^35 - 24 * q^37 + 6 * q^38 + 2 * q^40 - 18 * q^41 + 4 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 2 * q^50 + 2 * q^52 + 36 * q^53 - 4 * q^55 - 4 * q^56 + 2 * q^58 - 8 * q^59 - 8 * q^61 + 8 * q^62 + 4 * q^64 + 2 * q^65 - 8 * q^67 + 2 * q^70 + 20 * q^71 + 8 * q^73 - 12 * q^74 - 6 * q^76 + 14 * q^77 + 2 * q^79 + 4 * q^80 - 36 * q^82 + 12 * q^85 - 4 * q^86 + 4 * q^88 + 12 * q^89 + 8 * q^91 - 2 * q^92 + 16 * q^94 + 6 * q^95 - 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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