LMFDB - Embedded newform 1386.2.bk.b.703.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.8
Root			$0.500000 - 3.32851i$ of defining polynomial
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.b.901.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.13257 - 1.23124i) q^{5} +(0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.13257 - 1.23124i) q^{5} +(0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +(1.23124 - 2.13257i) q^{10} +(2.32803 - 2.36226i) q^{11} +1.32035 q^{13} +(-0.420444 - 2.61213i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.23739 + 3.87528i) q^{17} +(2.21589 + 3.83803i) q^{19} -2.46248i q^{20} +(0.834997 - 3.20979i) q^{22} +(-4.14497 - 7.17931i) q^{23} +(0.531907 - 0.921289i) q^{25} +(1.14346 - 0.660177i) q^{26} +(-1.67018 - 2.05195i) q^{28} -1.44409i q^{29} +(2.34801 + 1.35562i) q^{31} +(-0.866025 - 0.500000i) q^{32} +4.47479i q^{34} +(-1.03534 - 6.43232i) q^{35} +(2.46563 + 4.27060i) q^{37} +(3.83803 + 2.21589i) q^{38} +(-1.23124 - 2.13257i) q^{40} -8.18233 q^{41} +9.63797i q^{43} +(-0.881768 - 3.19726i) q^{44} +(-7.17931 - 4.14497i) q^{46} +(0.664664 - 0.383744i) q^{47} +(-5.22546 - 4.65774i) q^{49} -1.06381i q^{50} +(0.660177 - 1.14346i) q^{52} +(-0.945971 + 1.63847i) q^{53} +(2.05616 - 7.90406i) q^{55} +(-2.47239 - 0.941950i) q^{56} +(-0.722047 - 1.25062i) q^{58} +(-6.74444 - 3.89390i) q^{59} +(2.23943 + 3.87880i) q^{61} +2.71125 q^{62} -1.00000 q^{64} +(2.81575 - 1.62567i) q^{65} +(0.861844 - 1.49276i) q^{67} +(2.23739 + 3.87528i) q^{68} +(-4.11279 - 5.05289i) q^{70} +10.3771 q^{71} +(5.58622 - 9.67562i) q^{73} +(4.27060 + 2.46563i) q^{74} +4.43177 q^{76} +(-3.64757 - 7.98093i) q^{77} +(-2.53630 + 1.46433i) q^{79} +(-2.13257 - 1.23124i) q^{80} +(-7.08611 + 4.09116i) q^{82} +10.1118 q^{83} +11.0191i q^{85} +(4.81898 + 8.34672i) q^{86} +(-2.36226 - 2.32803i) q^{88} +(10.9590 - 6.32720i) q^{89} +(1.24371 - 3.26444i) q^{91} -8.28995 q^{92} +(0.383744 - 0.664664i) q^{94} +(9.45107 + 5.45658i) q^{95} +1.37808i q^{97} +(-6.85425 - 1.42099i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7	$ 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7} - 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} + 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} - 8 q^{35} + 14 q^{37} + 12 q^{38} + 2 q^{40} + 32 q^{41} - 4 q^{44} - 18 q^{46} + 24 q^{47} - 6 q^{49} + 14 q^{55} - 4 q^{56} - 28 q^{61} - 8 q^{62} - 16 q^{64} + 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} + 44 q^{73} + 24 q^{74} + 20 q^{76} + 52 q^{77} + 30 q^{79} + 12 q^{80} - 12 q^{82} + 8 q^{83} + 12 q^{86} - 2 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} - 14 q^{94} + 72 q^{95} - 40 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7 - 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 + 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 - 8 * q^35 + 14 * q^37 + 12 * q^38 + 2 * q^40 + 32 * q^41 - 4 * q^44 - 18 * q^46 + 24 * q^47 - 6 * q^49 + 14 * q^55 - 4 * q^56 - 28 * q^61 - 8 * q^62 - 16 * q^64 + 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 + 44 * q^73 + 24 * q^74 + 20 * q^76 + 52 * q^77 + 30 * q^79 + 12 * q^80 - 12 * q^82 + 8 * q^83 + 12 * q^86 - 2 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 - 14 * q^94 + 72 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.13257	−	1.23124i	0.953715	−	0.550628i	0.0594819	−	0.998229i	$-0.481055\pi$
$5$	2.13257	−	1.23124i	0.953715	−	0.550628i	0.894233	+	0.447602i	$0.147722\pi$
$6$		0			0
$7$	0.941950	−	2.47239i	0.356024	−	0.934477i
$7$	0.941950	−	2.47239i	0.356024	−	0.934477i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.23124	−	2.13257i	0.389352	−	0.674378i
$11$	2.32803	−	2.36226i	0.701926	−	0.712250i
$11$	2.32803	−	2.36226i	0.701926	−	0.712250i
$12$		0			0
$13$	1.32035			0.366201			0.183100	−	0.983094i	$-0.441387\pi$
$13$	1.32035			0.366201			0.183100	+	0.983094i	$0.441387\pi$
$14$	−0.420444	−	2.61213i	−0.112369	−	0.698121i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.23739	+	3.87528i	−0.542647	+	0.939893i	0.456103	+	0.889927i	$0.349245\pi$
$17$	−2.23739	+	3.87528i	−0.542647	+	0.939893i	−0.998751	+	0.0499662i	$0.984089\pi$
$18$		0			0
$19$	2.21589	+	3.83803i	0.508359	+	0.880504i	0.999953	+	0.00967966i	$0.00308118\pi$
$19$	2.21589	+	3.83803i	0.508359	+	0.880504i	−0.491594	+	0.870825i	$0.663585\pi$
$20$		−	2.46248i		−	0.550628i
$21$		0			0
$22$	0.834997	−	3.20979i	0.178022	−	0.684330i
$23$	−4.14497	−	7.17931i	−0.864287	−	1.49699i	−0.867754	−	0.496995i	$-0.834437\pi$
$23$	−4.14497	−	7.17931i	−0.864287	−	1.49699i	0.00346670	−	0.999994i	$-0.498897\pi$
$24$		0			0
$25$	0.531907	−	0.921289i	0.106381	−	0.184258i
$26$	1.14346	−	0.660177i	0.224251	−	0.129471i
$27$		0			0
$28$	−1.67018	−	2.05195i	−0.315635	−	0.387782i
$29$		−	1.44409i		−	0.268162i	−0.990970	−	0.134081i	$-0.957192\pi$
$29$		−	1.44409i		−	0.268162i	0.990970	−	0.134081i	$-0.0428082\pi$
$30$		0			0
$31$	2.34801	+	1.35562i	0.421715	+	0.243477i	0.695811	−	0.718225i	$-0.255045\pi$
$31$	2.34801	+	1.35562i	0.421715	+	0.243477i	−0.274096	+	0.961702i	$0.588379\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			4.47479i			0.767419i
$35$	−1.03534	−	6.43232i	−0.175004	−	1.08726i
$36$		0			0
$37$	2.46563	+	4.27060i	0.405347	+	0.702082i	0.994362	−	0.106040i	$-0.0338172\pi$
$37$	2.46563	+	4.27060i	0.405347	+	0.702082i	−0.589014	+	0.808122i	$0.700484\pi$
$38$	3.83803	+	2.21589i	0.622611	+	0.359464i
$39$		0			0
$40$	−1.23124	−	2.13257i	−0.194676	−	0.337189i
$41$	−8.18233			−1.27787			−0.638933	−	0.769263i	$-0.720624\pi$
$41$	−8.18233			−1.27787			−0.638933	+	0.769263i	$0.720624\pi$
$42$		0			0
$43$			9.63797i			1.46978i	0.678188	+	0.734888i	$0.262765\pi$
$43$			9.63797i			1.46978i	−0.678188	+	0.734888i	$0.737235\pi$
$44$	−0.881768	−	3.19726i	−0.132932	−	0.482005i
$45$		0			0
$46$	−7.17931	−	4.14497i	−1.05853	−	0.611143i
$47$	0.664664	−	0.383744i	0.0969512	−	0.0559748i	−0.450741	−	0.892655i	$-0.648840\pi$
$47$	0.664664	−	0.383744i	0.0969512	−	0.0559748i	0.547692	+	0.836680i	$0.315507\pi$
$48$		0			0
$49$	−5.22546	−	4.65774i	−0.746494	−	0.665392i
$50$		−	1.06381i		−	0.150446i
$51$		0			0
$52$	0.660177	−	1.14346i	0.0915501	−	0.158569i
$53$	−0.945971	+	1.63847i	−0.129939	+	0.225061i	−0.923653	−	0.383230i	$-0.874812\pi$
$53$	−0.945971	+	1.63847i	−0.129939	+	0.225061i	0.793714	+	0.608292i	$0.208145\pi$
$54$		0			0
$55$	2.05616	−	7.90406i	0.277253	−	1.06578i
$56$	−2.47239	−	0.941950i	−0.330388	−	0.125873i
$57$		0			0
$58$	−0.722047	−	1.25062i	−0.0948095	−	0.164215i
$59$	−6.74444	−	3.89390i	−0.878051	−	0.506943i	−0.00803571	−	0.999968i	$-0.502558\pi$
$59$	−6.74444	−	3.89390i	−0.878051	−	0.506943i	−0.870015	+	0.493025i	$0.835891\pi$
$60$		0			0
$61$	2.23943	+	3.87880i	0.286729	+	0.496630i	0.973027	−	0.230691i	$-0.0740986\pi$
$61$	2.23943	+	3.87880i	0.286729	+	0.496630i	−0.686298	+	0.727321i	$0.740765\pi$
$62$	2.71125			0.344329
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.81575	−	1.62567i	0.349251	−	0.201640i
$66$		0			0
$67$	0.861844	−	1.49276i	0.105291	−	0.182369i	−0.808566	−	0.588405i	$-0.799756\pi$
$67$	0.861844	−	1.49276i	0.105291	−	0.182369i	0.913857	+	0.406036i	$0.133089\pi$
$68$	2.23739	+	3.87528i	0.271324	+	0.469946i
$69$		0			0
$70$	−4.11279	−	5.05289i	−0.491572	−	0.603935i
$71$	10.3771			1.23153			0.615766	−	0.787929i	$-0.288847\pi$
$71$	10.3771			1.23153			0.615766	+	0.787929i	$0.288847\pi$
$72$		0			0
$73$	5.58622	−	9.67562i	0.653818	−	1.13245i	−0.328371	−	0.944549i	$-0.606500\pi$
$73$	5.58622	−	9.67562i	0.653818	−	1.13245i	0.982189	−	0.187897i	$-0.0601670\pi$
$74$	4.27060	+	2.46563i	0.496447	+	0.286624i
$75$		0			0
$76$	4.43177			0.508359
$77$	−3.64757	−	7.98093i	−0.415679	−	0.909512i
$78$		0			0
$79$	−2.53630	+	1.46433i	−0.285356	+	0.164750i	−0.635846	−	0.771816i	$-0.719349\pi$
$79$	−2.53630	+	1.46433i	−0.285356	+	0.164750i	0.350490	+	0.936567i	$0.386015\pi$
$80$	−2.13257	−	1.23124i	−0.238429	−	0.137657i
$81$		0			0
$82$	−7.08611	+	4.09116i	−0.782529	+	0.451794i
$83$	10.1118			1.10991			0.554957	−	0.831879i	$-0.312735\pi$
$83$	10.1118			1.10991			0.554957	+	0.831879i	$0.312735\pi$
$84$		0			0
$85$			11.0191i			1.19519i
$86$	4.81898	+	8.34672i	0.519644	+	0.900050i
$87$		0			0
$88$	−2.36226	−	2.32803i	−0.251818	−	0.248168i
$89$	10.9590	−	6.32720i	1.16165	−	0.670682i	0.209955	−	0.977711i	$-0.432668\pi$
$89$	10.9590	−	6.32720i	1.16165	−	0.670682i	0.951700	+	0.307029i	$0.0993350\pi$
$90$		0			0
$91$	1.24371	−	3.26444i	0.130376	−	0.342206i
$92$	−8.28995			−0.864287
$93$		0			0
$94$	0.383744	−	0.664664i	0.0395801	−	0.0685548i
$95$	9.45107	+	5.45658i	0.969660	+	0.559833i
$96$		0			0
$97$			1.37808i			0.139923i	0.997550	+	0.0699613i	$0.0222876\pi$
$97$			1.37808i			0.139923i	−0.997550	+	0.0699613i	$0.977712\pi$
$98$	−6.85425	−	1.42099i	−0.692384	−	0.143542i
$99$		0			0
$100$	−0.531907	−	0.921289i	−0.0531907	−	0.0921289i
$101$	−3.78361	+	6.55341i	−0.376483	+	0.652089i	−0.990548	−	0.137167i	$-0.956200\pi$
$101$	−3.78361	+	6.55341i	−0.376483	+	0.652089i	0.614064	+	0.789256i	$0.289534\pi$
$102$		0			0
$103$	14.2858	−	8.24790i	1.40762	−	0.812690i	0.412461	−	0.910975i	$-0.364669\pi$
$103$	14.2858	−	8.24790i	1.40762	−	0.812690i	0.995158	+	0.0982855i	$0.0313358\pi$
$104$		−	1.32035i		−	0.129471i
$105$		0			0
$106$			1.89194i			0.183762i
$107$	−4.99579	+	2.88432i	−0.482961	+	0.278838i	−0.721650	−	0.692258i	$-0.756616\pi$
$107$	−4.99579	+	2.88432i	−0.482961	+	0.278838i	0.238689	+	0.971096i	$0.423282\pi$
$108$		0			0
$109$	−7.47550	−	4.31598i	−0.716023	−	0.413396i	0.0972641	−	0.995259i	$-0.468991\pi$
$109$	−7.47550	−	4.31598i	−0.716023	−	0.413396i	−0.813287	+	0.581862i	$0.802324\pi$
$110$	−2.17134	−	7.87320i	−0.207029	−	0.750680i
$111$		0			0
$112$	−2.61213	+	0.420444i	−0.246823	+	0.0397283i
$113$	−17.4933			−1.64563			−0.822817	−	0.568306i	$-0.807599\pi$
$113$	−17.4933			−1.64563			−0.822817	+	0.568306i	$0.807599\pi$
$114$		0			0
$115$	−17.6789	−	10.2069i	−1.64857	−	0.951800i
$116$	−1.25062	−	0.722047i	−0.116117	−	0.0670404i
$117$		0			0
$118$	−7.78781			−0.716926
$119$	7.47370	+	9.18203i	0.685113	+	0.841716i
$120$		0			0
$121$	−0.160590	−	10.9988i	−0.0145991	−	0.999893i
$122$	3.87880	+	2.23943i	0.351170	+	0.202748i
$123$		0			0
$124$	2.34801	−	1.35562i	0.210858	−	0.121739i
$125$			9.69279i			0.866949i
$126$		0			0
$127$			12.0959i			1.07333i	0.843794	+	0.536667i	$0.180317\pi$
$127$			12.0959i			1.07333i	−0.843794	+	0.536667i	$0.819683\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.62567	−	2.81575i	0.142581	−	0.246958i
$131$	8.62077	+	14.9316i	0.753200	+	1.30458i	0.946264	+	0.323394i	$0.104824\pi$
$131$	8.62077	+	14.9316i	0.753200	+	1.30458i	−0.193064	+	0.981186i	$0.561843\pi$
$132$		0			0
$133$	11.5764	−	1.86331i	1.00380	−	0.161570i
$134$		−	1.72369i		−	0.148904i
$135$		0			0
$136$	3.87528	+	2.23739i	0.332302	+	0.191855i
$137$	1.25479	−	2.17335i	0.107204	−	0.185682i	−0.807433	−	0.589960i	$-0.799144\pi$
$137$	1.25479	−	2.17335i	0.107204	−	0.185682i	0.914636	+	0.404277i	$0.132477\pi$
$138$		0			0
$139$	−19.9532			−1.69241			−0.846206	−	0.532856i	$-0.821119\pi$
$139$	−19.9532			−1.69241			−0.846206	+	0.532856i	$0.821119\pi$
$140$	−6.08822	−	2.31953i	−0.514549	−	0.196036i
$141$		0			0
$142$	8.98681	−	5.18854i	0.754156	−	0.435412i
$143$	3.07382	−	3.11903i	0.257046	−	0.260826i
$144$		0			0
$145$	−1.77803	−	3.07963i	−0.147657	−	0.255750i
$146$		−	11.1724i		−	0.924638i
$147$		0			0
$148$	4.93126			0.405347
$149$	−8.46998	+	4.89014i	−0.693888	+	0.400616i	−0.805067	−	0.593184i	$-0.797871\pi$
$149$	−8.46998	+	4.89014i	−0.693888	+	0.400616i	0.111179	+	0.993800i	$0.464537\pi$
$150$		0			0
$151$	−2.31521	−	1.33669i	−0.188409	−	0.108778i	0.402829	−	0.915275i	$-0.368027\pi$
$151$	−2.31521	−	1.33669i	−0.188409	−	0.108778i	−0.591237	+	0.806498i	$0.701360\pi$
$152$	3.83803	−	2.21589i	0.311305	−	0.179732i
$153$		0			0
$154$	−7.14935	−	5.08791i	−0.576111	−	0.409995i
$155$	6.67640			0.536261
$156$		0			0
$157$	13.7131	+	7.91724i	1.09442	+	0.631865i	0.934750	−	0.355306i	$-0.115623\pi$
$157$	13.7131	+	7.91724i	1.09442	+	0.631865i	0.159671	+	0.987170i	$0.448957\pi$
$158$	−1.46433	+	2.53630i	−0.116496	+	0.201777i
$159$		0			0
$160$	−2.46248			−0.194676
$161$	−21.6544	+	3.48546i	−1.70661	+	0.274693i
$162$		0			0
$163$	10.1807	+	17.6336i	0.797418	+	1.38117i	0.921293	+	0.388870i	$0.127135\pi$
$163$	10.1807	+	17.6336i	0.797418	+	1.38117i	−0.123875	+	0.992298i	$0.539532\pi$
$164$	−4.09116	+	7.08611i	−0.319466	+	0.553332i
$165$		0			0
$166$	8.75707	−	5.05590i	0.679680	−	0.392414i
$167$	16.1119			1.24678			0.623389	−	0.781912i	$-0.285755\pi$
$167$	16.1119			1.24678			0.623389	+	0.781912i	$0.285755\pi$
$168$		0			0
$169$	−11.2567			−0.865897
$170$	5.50954	+	9.54280i	0.422562	+	0.731899i
$171$		0			0
$172$	8.34672	+	4.81898i	0.636432	+	0.367444i
$173$	−3.62347	−	6.27604i	−0.275487	−	0.477158i	0.694771	−	0.719231i	$-0.255506\pi$
$173$	−3.62347	−	6.27604i	−0.275487	−	0.477158i	−0.970258	+	0.242073i	$0.922173\pi$
$174$		0			0
$175$	−1.77676	−	2.18289i	−0.134310	−	0.165011i
$176$	−3.20979	−	0.834997i	−0.241947	−	0.0629403i
$177$		0			0
$178$	6.32720	−	10.9590i	0.474244	−	0.821414i
$179$	5.80078	−	10.0472i	0.433571	−	0.750966i	−0.563607	−	0.826043i	$-0.690587\pi$
$179$	5.80078	−	10.0472i	0.433571	−	0.750966i	0.997178	+	0.0750767i	$0.0239202\pi$
$180$		0			0
$181$			7.74423i			0.575624i	0.957687	+	0.287812i	$0.0929279\pi$
$181$			7.74423i			0.575624i	−0.957687	+	0.287812i	$0.907072\pi$
$182$	−0.555136	−	3.44894i	−0.0411494	−	0.255652i
$183$		0			0
$184$	−7.17931	+	4.14497i	−0.529265	+	0.305572i
$185$	10.5163	+	6.07157i	0.773172	+	0.446391i
$186$		0			0
$187$	3.94572	+	14.3071i	0.288540	+	1.04624i
$188$		−	0.767488i		−	0.0559748i
$189$		0			0
$190$	10.9132			0.791724
$191$	−10.6157	−	18.3869i	−0.768125	−	1.33043i	−0.938579	−	0.345065i	$-0.887857\pi$
$191$	−10.6157	−	18.3869i	−0.768125	−	1.33043i	0.170454	−	0.985366i	$-0.445477\pi$
$192$		0			0
$193$	3.04258	+	1.75664i	0.219010	+	0.126445i	0.605492	−	0.795852i	$-0.292976\pi$
$193$	3.04258	+	1.75664i	0.219010	+	0.126445i	−0.386482	+	0.922297i	$0.626310\pi$
$194$	0.689039	+	1.19345i	0.0494701	+	0.0856847i
$195$		0			0
$196$	−6.64645	+	2.19651i	−0.474747	+	0.156894i
$197$		−	21.9715i		−	1.56540i	−0.622397	−	0.782702i	$-0.713841\pi$
$197$		−	21.9715i		−	1.56540i	0.622397	−	0.782702i	$-0.286159\pi$
$198$		0			0
$199$	1.24863	+	0.720899i	0.0885133	+	0.0511032i	0.543603	−	0.839342i	$-0.317060\pi$
$199$	1.24863	+	0.720899i	0.0885133	+	0.0511032i	−0.455090	+	0.890445i	$0.650393\pi$
$200$	−0.921289	−	0.531907i	−0.0651450	−	0.0376115i
$201$		0			0
$202$			7.56722i			0.532428i
$203$	−3.57037	−	1.36026i	−0.250591	−	0.0954719i
$204$		0			0
$205$	−17.4494	+	10.0744i	−1.21872	+	0.703628i
$206$	8.24790	−	14.2858i	0.574658	−	0.995337i
$207$		0			0
$208$	−0.660177	−	1.14346i	−0.0457751	−	0.0792847i
$209$	14.2251	+	3.70052i	0.983970	+	0.255970i
$210$		0			0
$211$		−	0.163763i		−	0.0112739i	−0.999984	−	0.00563697i	$-0.998206\pi$
$211$		−	0.163763i		−	0.0112739i	0.999984	−	0.00563697i	$-0.00179431\pi$
$212$	0.945971	+	1.63847i	0.0649695	+	0.112531i
$213$		0			0
$214$	−2.88432	+	4.99579i	−0.197168	+	0.341505i
$215$	11.8667	+	20.5537i	0.809299	+	1.40175i
$216$		0			0
$217$	5.56334	−	4.52828i	0.377664	−	0.307399i
$218$	−8.63196			−0.584630
$219$		0			0
$220$	−5.81703	−	5.73272i	−0.392184	−	0.386500i
$221$	−2.95415	+	5.11674i	−0.198718	+	0.344189i
$222$		0			0
$223$			27.3847i			1.83382i	0.399099	+	0.916908i	$0.369323\pi$
$223$			27.3847i			1.83382i	−0.399099	+	0.916908i	$0.630677\pi$
$224$	−2.05195	+	1.67018i	−0.137102	+	0.111594i
$225$		0			0
$226$	−15.1497	+	8.74667i	−1.00774	+	0.581820i
$227$	1.95128	−	3.37971i	0.129511	−	0.224319i	−0.793976	−	0.607949i	$-0.791993\pi$
$227$	1.95128	−	3.37971i	0.129511	−	0.224319i	0.923487	+	0.383629i	$0.125326\pi$
$228$		0			0
$229$	−4.36524	+	2.52028i	−0.288463	+	0.166544i	−0.637249	−	0.770658i	$-0.719928\pi$
$229$	−4.36524	+	2.52028i	−0.288463	+	0.166544i	0.348785	+	0.937203i	$0.386594\pi$
$230$	−20.4138			−1.34605
$231$		0			0
$232$	−1.44409			−0.0948095
$233$	−18.3993	+	10.6229i	−1.20538	+	0.695927i	−0.961747	−	0.273940i	$-0.911673\pi$
$233$	−18.3993	+	10.6229i	−1.20538	+	0.695927i	−0.243634	+	0.969867i	$0.578340\pi$
$234$		0			0
$235$	0.944962	−	1.63672i	0.0616425	−	0.106768i
$236$	−6.74444	+	3.89390i	−0.439026	+	0.253471i
$237$		0			0
$238$	11.0634	+	4.21502i	0.717136	+	0.273219i
$239$		−	5.64110i		−	0.364893i	−0.983216	−	0.182446i	$-0.941598\pi$
$239$		−	5.64110i		−	0.364893i	0.983216	−	0.182446i	$-0.0584016\pi$
$240$		0			0
$241$	−3.88733	+	6.73305i	−0.250405	+	0.433714i	−0.963637	−	0.267213i	$-0.913897\pi$
$241$	−3.88733	+	6.73305i	−0.250405	+	0.433714i	0.713232	+	0.700928i	$0.247230\pi$
$242$	−5.63849	−	9.44497i	−0.362456	−	0.607146i
$243$		0			0
$244$	4.47886			0.286729
$245$	−16.8785	−	3.49917i	−1.07833	−	0.223553i
$246$		0			0
$247$	2.92576	+	5.06756i	0.186162	+	0.322441i
$248$	1.35562	−	2.34801i	0.0860822	−	0.149099i
$249$		0			0
$250$	4.84639	+	8.39420i	0.306513	+	0.530896i
$251$			22.5045i			1.42047i	0.703963	+	0.710236i	$0.251412\pi$
$251$			22.5045i			1.42047i	−0.703963	+	0.710236i	$0.748588\pi$
$252$		0			0
$253$	−26.6090	−	6.92208i	−1.67290	−	0.435188i
$254$	6.04793	+	10.4753i	0.379481	+	0.657281i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.61175	+	1.50789i	−0.162916	+	0.0940597i	−0.579241	−	0.815156i	$-0.696651\pi$
$257$	−2.61175	+	1.50789i	−0.162916	+	0.0940597i	0.416325	+	0.909216i	$0.363318\pi$
$258$		0			0
$259$	12.8811	−	2.07332i	0.800393	−	0.128830i
$260$		−	3.25135i		−	0.201640i
$261$		0			0
$262$	14.9316	+	8.62077i	0.922478	+	0.532593i
$263$	24.4063	+	14.0910i	1.50496	+	0.868887i	0.999983	+	0.00575106i	$0.00183063\pi$
$263$	24.4063	+	14.0910i	1.50496	+	0.868887i	0.504972	+	0.863136i	$0.331503\pi$
$264$		0			0
$265$			4.65887i			0.286192i
$266$	9.09378	−	7.40187i	0.557575	−	0.453837i
$267$		0			0
$268$	−0.861844	−	1.49276i	−0.0526455	−	0.0911847i
$269$	0.523552	+	0.302273i	0.0319215	+	0.0184299i	0.515876	−	0.856663i	$-0.327467\pi$
$269$	0.523552	+	0.302273i	0.0319215	+	0.0184299i	−0.483954	+	0.875093i	$0.660800\pi$
$270$		0			0
$271$	9.89654	+	17.1413i	0.601172	+	1.04126i	0.992644	+	0.121071i	$0.0386327\pi$
$271$	9.89654	+	17.1413i	0.601172	+	1.04126i	−0.391472	+	0.920190i	$0.628034\pi$
$272$	4.47479			0.271324
$273$		0			0
$274$		−	2.50957i		−	0.151609i
$275$	−0.938037	−	3.40129i	−0.0565657	−	0.205105i
$276$		0			0
$277$	−1.87448	−	1.08223i	−0.112626	−	0.0650249i	0.442629	−	0.896705i	$-0.354046\pi$
$277$	−1.87448	−	1.08223i	−0.112626	−	0.0650249i	−0.555255	+	0.831680i	$0.687379\pi$
$278$	−17.2800	+	9.97662i	−1.03639	+	0.598358i
$279$		0			0
$280$	−6.43232	+	1.03534i	−0.384405	+	0.0618732i
$281$			29.4916i			1.75932i	0.475601	+	0.879661i	$0.342231\pi$
$281$			29.4916i			1.75932i	−0.475601	+	0.879661i	$0.657769\pi$
$282$		0			0
$283$	14.1940	−	24.5847i	0.843745	−	1.46141i	−0.0429613	−	0.999077i	$-0.513679\pi$
$283$	14.1940	−	24.5847i	0.843745	−	1.46141i	0.886707	−	0.462333i	$-0.152987\pi$
$284$	5.18854	−	8.98681i	0.307883	−	0.533269i
$285$		0			0
$286$	1.10249	−	4.23807i	0.0651918	−	0.250602i
$287$	−7.70734	+	20.2299i	−0.454950	+	1.19414i
$288$		0			0
$289$	−1.51185	−	2.61860i	−0.0889324	−	0.154036i
$290$	−3.07963	−	1.77803i	−0.180842	−	0.104409i
$291$		0			0
$292$	−5.58622	−	9.67562i	−0.326909	−	0.566223i
$293$	9.39403			0.548805			0.274403	−	0.961615i	$-0.411520\pi$
$293$	9.39403			0.548805			0.274403	+	0.961615i	$0.411520\pi$
$294$		0			0
$295$	−19.1773			−1.11655
$296$	4.27060	−	2.46563i	0.248224	−	0.143312i
$297$		0			0
$298$	−4.89014	+	8.46998i	−0.283278	+	0.490653i
$299$	−5.47284	−	9.47923i	−0.316502	−	0.548198i
$300$		0			0
$301$	23.8288	+	9.07848i	1.37347	+	0.523275i
$302$	−2.67337			−0.153835
$303$		0			0
$304$	2.21589	−	3.83803i	0.127090	−	0.220126i
$305$	9.55148	+	5.51455i	0.546916	+	0.315762i
$306$		0			0
$307$	26.9732			1.53944			0.769722	−	0.638380i	$-0.220395\pi$
$307$	26.9732			1.53944			0.769722	+	0.638380i	$0.220395\pi$
$308$	−8.73547	−	0.831582i	−0.497750	−	0.0473838i
$309$		0			0
$310$	5.78193	−	3.33820i	0.328392	−	0.189597i
$311$	−0.108539	−	0.0626652i	−0.00615470	−	0.00355342i	0.496919	−	0.867797i	$-0.334464\pi$
$311$	−0.108539	−	0.0626652i	−0.00615470	−	0.00355342i	−0.503074	+	0.864243i	$0.667798\pi$
$312$		0			0
$313$	−6.69427	+	3.86494i	−0.378382	+	0.218459i	−0.677114	−	0.735878i	$-0.736770\pi$
$313$	−6.69427	+	3.86494i	−0.378382	+	0.218459i	0.298732	+	0.954337i	$0.403436\pi$
$314$	15.8345			0.893591
$315$		0			0
$316$			2.92867i			0.164750i
$317$	12.1901	+	21.1139i	0.684665	+	1.18587i	0.973542	+	0.228508i	$0.0733848\pi$
$317$	12.1901	+	21.1139i	0.684665	+	1.18587i	−0.288877	+	0.957366i	$0.593282\pi$
$318$		0			0
$319$	−3.41133	−	3.36189i	−0.190998	−	0.188230i
$320$	−2.13257	+	1.23124i	−0.119214	+	0.0688284i
$321$		0			0
$322$	−17.0106	+	13.8457i	−0.947961	+	0.771591i
$323$	−19.8312			−1.10344
$324$		0			0
$325$	0.702305	−	1.21643i	0.0389569	−	0.0674753i
$326$	17.6336	+	10.1807i	0.976633	+	0.563859i
$327$		0			0
$328$			8.18233i			0.451794i
$329$	−0.322686	−	2.00478i	−0.0177902	−	0.110527i
$330$		0			0
$331$	10.7266	+	18.5790i	0.589588	+	1.02120i	0.994286	+	0.106746i	$0.0340432\pi$
$331$	10.7266	+	18.5790i	0.589588	+	1.02120i	−0.404698	+	0.914450i	$0.632623\pi$
$332$	5.05590	−	8.75707i	0.277478	−	0.480607i
$333$		0			0
$334$	13.9533	−	8.05596i	0.763493	−	0.440803i
$335$		−	4.24455i		−	0.231905i
$336$		0			0
$337$		−	30.0086i		−	1.63467i	−0.576163	−	0.817335i	$-0.695451\pi$
$337$		−	30.0086i		−	1.63467i	0.576163	−	0.817335i	$-0.304549\pi$
$338$	−9.74856	+	5.62833i	−0.530252	+	0.306141i
$339$		0			0
$340$	9.54280	+	5.50954i	0.517531	+	0.298797i
$341$	8.66857	−	2.39069i	0.469429	−	0.129463i
$342$		0			0
$343$	−16.4379	+	8.53204i	−0.887563	+	0.460687i
$344$	9.63797			0.519644
$345$		0			0
$346$	−6.27604	−	3.62347i	−0.337402	−	0.194799i
$347$	−29.9073	−	17.2670i	−1.60551	−	0.926942i	−0.990358	−	0.138533i	$-0.955761\pi$
$347$	−29.9073	−	17.2670i	−1.60551	−	0.926942i	−0.615152	−	0.788408i	$-0.710906\pi$
$348$		0			0
$349$	4.77961			0.255847			0.127923	−	0.991784i	$-0.459169\pi$
$349$	4.77961			0.255847			0.127923	+	0.991784i	$0.459169\pi$
$350$	−2.63016	−	1.00206i	−0.140588	−	0.0535623i
$351$		0			0
$352$	−3.19726	+	0.881768i	−0.170415	+	0.0469984i
$353$	−11.7581	−	6.78853i	−0.625819	−	0.361317i	0.153312	−	0.988178i	$-0.451006\pi$
$353$	−11.7581	−	6.78853i	−0.625819	−	0.361317i	−0.779131	+	0.626861i	$0.784339\pi$
$354$		0			0
$355$	22.1298	−	12.7767i	1.17453	−	0.678115i
$356$		−	12.6544i		−	0.670682i
$357$		0			0
$358$		−	11.6016i		−	0.613161i
$359$	−1.49631	+	0.863893i	−0.0789720	+	0.0455945i	−0.538966	−	0.842328i	$-0.681185\pi$
$359$	−1.49631	+	0.863893i	−0.0789720	+	0.0455945i	0.459994	+	0.887922i	$0.347852\pi$
$360$		0			0
$361$	−0.320313	+	0.554798i	−0.0168586	+	0.0291999i
$362$	3.87212	+	6.70670i	0.203514	+	0.352496i
$363$		0			0
$364$	−2.20523	−	2.70930i	−0.115586	−	0.142006i
$365$		−	27.5119i		−	1.44004i
$366$		0			0
$367$	−22.0716	−	12.7430i	−1.15213	−	0.665182i	−0.202724	−	0.979236i	$-0.564979\pi$
$367$	−22.0716	−	12.7430i	−1.15213	−	0.665182i	−0.949405	+	0.314054i	$0.898313\pi$
$368$	−4.14497	+	7.17931i	−0.216072	+	0.374247i
$369$		0			0
$370$	12.1431			0.631292
$371$	3.15988	+	3.88217i	0.164053	+	0.201552i
$372$		0			0
$373$	−28.8675	+	16.6667i	−1.49470	+	0.862968i	−0.999982	−	0.00608223i	$-0.998064\pi$
$373$	−28.8675	+	16.6667i	−1.49470	+	0.862968i	−0.494723	+	0.869051i	$0.664731\pi$
$374$	10.5706	+	10.4174i	0.546594	+	0.538672i
$375$		0			0
$376$	−0.383744	−	0.664664i	−0.0197901	−	0.0342774i
$377$		−	1.90672i		−	0.0982010i
$378$		0			0
$379$	−19.2656			−0.989610			−0.494805	−	0.869004i	$-0.664760\pi$
$379$	−19.2656			−0.989610			−0.494805	+	0.869004i	$0.664760\pi$
$380$	9.45107	−	5.45658i	0.484830	−	0.279917i
$381$		0			0
$382$	−18.3869	−	10.6157i	−0.940757	−	0.543146i
$383$	−4.46444	+	2.57755i	−0.228122	+	0.131706i	−0.609705	−	0.792628i	$-0.708712\pi$
$383$	−4.46444	+	2.57755i	−0.228122	+	0.131706i	0.381583	+	0.924334i	$0.375379\pi$
$384$		0			0
$385$	−17.6051	−	12.5289i	−0.897241	−	0.638531i
$386$	3.51327			0.178821
$387$		0			0
$388$	1.19345	+	0.689039i	0.0605882	+	0.0349806i
$389$	−2.58228	+	4.47264i	−0.130927	+	0.226772i	−0.924034	−	0.382310i	$-0.875129\pi$
$389$	−2.58228	+	4.47264i	−0.130927	+	0.226772i	0.793107	+	0.609082i	$0.208462\pi$
$390$		0			0
$391$	37.0957			1.87601
$392$	−4.65774	+	5.22546i	−0.235251	+	0.263926i
$393$		0			0
$394$	−10.9857	−	19.0279i	−0.553454	−	0.958610i
$395$	−3.60589	+	6.24559i	−0.181432	+	0.314250i
$396$		0			0
$397$	5.49312	−	3.17146i	0.275692	−	0.159171i	−0.355780	−	0.934570i	$-0.615785\pi$
$397$	5.49312	−	3.17146i	0.275692	−	0.159171i	0.631472	+	0.775399i	$0.282451\pi$
$398$	1.44180			0.0722708
$399$		0			0
$400$	−1.06381			−0.0531907
$401$	11.0008	+	19.0539i	0.549351	+	0.951504i	0.998319	+	0.0579565i	$0.0184585\pi$
$401$	11.0008	+	19.0539i	0.549351	+	0.951504i	−0.448968	+	0.893548i	$0.648208\pi$
$402$		0			0
$403$	3.10021	+	1.78991i	0.154432	+	0.0891615i
$404$	3.78361	+	6.55341i	0.188242	+	0.326044i
$405$		0			0
$406$	−3.77216	+	0.607162i	−0.187209	+	0.0301329i
$407$	15.8283	+	4.11759i	0.784582	+	0.204101i
$408$		0			0
$409$	7.05947	−	12.2274i	0.349068	−	0.604604i	−0.637016	−	0.770851i	$-0.719831\pi$
$409$	7.05947	−	12.2274i	0.349068	−	0.604604i	0.986084	+	0.166247i	$0.0531648\pi$
$410$	−10.0744	+	17.4494i	−0.497540	+	0.861764i
$411$		0			0
$412$		−	16.4958i		−	0.812690i
$413$	−15.9802	+	13.0070i	−0.786333	+	0.640035i
$414$		0			0
$415$	21.5641	−	12.4500i	1.05854	−	0.611149i
$416$	−1.14346	−	0.660177i	−0.0560628	−	0.0323679i
$417$		0			0
$418$	14.1695	−	3.90780i	0.693055	−	0.191137i
$419$			22.7760i			1.11268i	0.830955	+	0.556340i	$0.187795\pi$
$419$			22.7760i			1.11268i	−0.830955	+	0.556340i	$0.812205\pi$
$420$		0			0
$421$	−6.80960			−0.331880			−0.165940	−	0.986136i	$-0.553066\pi$
$421$	−6.80960			−0.331880			−0.165940	+	0.986136i	$0.553066\pi$
$422$	−0.0818817	−	0.141823i	−0.00398594	−	0.00690385i
$423$		0			0
$424$	1.63847	+	0.945971i	0.0795711	+	0.0459404i
$425$	2.38017	+	4.12257i	0.115455	+	0.199974i
$426$		0			0
$427$	11.6994	−	1.88311i	0.566172	−	0.0911301i
$428$			5.76864i			0.278838i
$429$		0			0
$430$	20.5537	+	11.8667i	0.991185	+	0.572261i
$431$	−26.7290	−	15.4320i	−1.28749	−	0.743334i	−0.309286	−	0.950969i	$-0.600090\pi$
$431$	−26.7290	−	15.4320i	−1.28749	−	0.743334i	−0.978206	+	0.207635i	$0.933423\pi$
$432$		0			0
$433$		−	32.2967i		−	1.55208i	−0.630683	−	0.776040i	$-0.717225\pi$
$433$		−	32.2967i		−	1.55208i	0.630683	−	0.776040i	$-0.282775\pi$
$434$	2.55386	−	6.70327i	0.122589	−	0.321767i
$435$		0			0
$436$	−7.47550	+	4.31598i	−0.358012	+	0.206698i
$437$	18.3696	−	31.8171i	0.878737	−	1.52202i
$438$		0			0
$439$	−14.3357	−	24.8302i	−0.684208	−	1.18508i	−0.973685	−	0.227898i	$-0.926815\pi$
$439$	−14.3357	−	24.8302i	−0.684208	−	1.18508i	0.289478	−	0.957185i	$-0.406518\pi$
$440$	−7.90406	−	2.05616i	−0.376811	−	0.0980238i
$441$		0			0
$442$			5.90830i			0.281029i
$443$	17.4908	+	30.2949i	0.831013	+	1.43936i	0.897236	+	0.441552i	$0.145572\pi$
$443$	17.4908	+	30.2949i	0.831013	+	1.43936i	−0.0662231	+	0.997805i	$0.521095\pi$
$444$		0			0
$445$	15.5806	−	26.9864i	0.738592	−	1.27928i
$446$	13.6924	+	23.7159i	0.648352	+	1.12298i
$447$		0			0
$448$	−0.941950	+	2.47239i	−0.0445029	+	0.116810i
$449$	3.57926			0.168916			0.0844579	−	0.996427i	$-0.473084\pi$
$449$	3.57926			0.168916			0.0844579	+	0.996427i	$0.473084\pi$
$450$		0			0
$451$	−19.0487	+	19.3288i	−0.896967	+	0.910159i
$452$	−8.74667	+	15.1497i	−0.411409	+	0.712581i
$453$		0			0
$454$		−	3.90255i		−	0.183156i
$455$	−1.36701	−	8.49295i	−0.0640865	−	0.398156i
$456$		0			0
$457$	−17.6664	+	10.1997i	−0.826398	+	0.477121i	−0.852618	−	0.522535i	$-0.824986\pi$
$457$	−17.6664	+	10.1997i	−0.826398	+	0.477121i	0.0262200	+	0.999656i	$0.491653\pi$
$458$	−2.52028	+	4.36524i	−0.117765	+	0.203974i
$459$		0			0
$460$	−17.6789	+	10.2069i	−0.824283	+	0.475900i
$461$	13.9967			0.651892			0.325946	−	0.945388i	$-0.394317\pi$
$461$	13.9967			0.651892			0.325946	+	0.945388i	$0.394317\pi$
$462$		0			0
$463$	33.6499			1.56384			0.781922	−	0.623376i	$-0.214239\pi$
$463$	33.6499			1.56384			0.781922	+	0.623376i	$0.214239\pi$
$464$	−1.25062	+	0.722047i	−0.0580587	+	0.0335202i
$465$		0			0
$466$	−10.6229	+	18.3993i	−0.492095	+	0.852333i
$467$	−7.87190	+	4.54484i	−0.364268	+	0.210310i	−0.670951	−	0.741501i	$-0.734114\pi$
$467$	−7.87190	+	4.54484i	−0.364268	+	0.210310i	0.306683	+	0.951812i	$0.400781\pi$
$468$		0			0
$469$	−2.87887	−	3.53692i	−0.132934	−	0.163320i
$470$		−	1.88992i		−	0.0871757i
$471$		0			0
$472$	−3.89390	+	6.74444i	−0.179231	+	0.310438i
$473$	22.7674	+	22.4374i	1.04685	+	1.03167i
$474$		0			0
$475$	4.71458			0.216320
$476$	11.6887	−	1.88140i	0.535752	−	0.0862338i
$477$		0			0
$478$	−2.82055	−	4.88534i	−0.129009	−	0.223450i
$479$	19.7827	−	34.2647i	0.903897	−	1.56560i	0.0815054	−	0.996673i	$-0.474027\pi$
$479$	19.7827	−	34.2647i	0.903897	−	1.56560i	0.822391	−	0.568922i	$-0.192639\pi$
$480$		0			0
$481$	3.25551	+	5.63871i	0.148438	+	0.257103i
$482$			7.77466i			0.354126i
$483$		0			0
$484$	−9.60556	−	5.36034i	−0.436616	−	0.243652i
$485$	1.69674	+	2.93885i	0.0770452	+	0.133446i
$486$		0			0
$487$	1.60461	−	2.77927i	0.0727120	−	0.125941i	−0.827377	−	0.561647i	$-0.810168\pi$
$487$	1.60461	−	2.77927i	0.0727120	−	0.125941i	0.900089	+	0.435706i	$0.143501\pi$
$488$	3.87880	−	2.23943i	0.175585	−	0.101374i
$489$		0			0
$490$	−16.3668	+	5.40887i	−0.739375	+	0.244348i
$491$		−	19.0209i		−	0.858401i	−0.903209	−	0.429200i	$-0.858795\pi$
$491$		−	19.0209i		−	0.858401i	0.903209	−	0.429200i	$-0.141205\pi$
$492$		0			0
$493$	5.59627	+	3.23101i	0.252043	+	0.145517i
$494$	5.06756	+	2.92576i	0.228000	+	0.131636i
$495$		0			0
$496$		−	2.71125i		−	0.121739i
$497$	9.77468	−	25.6562i	0.438454	−	1.15084i
$498$		0			0
$499$	−12.8041	−	22.1774i	−0.573190	−	0.992795i	−0.996236	−	0.0866862i	$-0.972372\pi$
$499$	−12.8041	−	22.1774i	−0.573190	−	0.992795i	0.423045	−	0.906108i	$-0.360961\pi$
$500$	8.39420	+	4.84639i	0.375400	+	0.216737i
$501$		0			0
$502$	11.2523	+	19.4895i	0.502213	+	0.869858i
$503$	−2.73335			−0.121874			−0.0609370	−	0.998142i	$-0.519409\pi$
$503$	−2.73335			−0.121874			−0.0609370	+	0.998142i	$0.519409\pi$
$504$		0			0
$505$			18.6341i			0.829209i
$506$	−26.5051	+	7.30981i	−1.17830	+	0.324961i
$507$		0			0
$508$	10.4753	+	6.04793i	0.464768	+	0.268334i
$509$	14.5574	−	8.40471i	0.645245	−	0.372532i	−0.141387	−	0.989954i	$-0.545156\pi$
$509$	14.5574	−	8.40471i	0.645245	−	0.372532i	0.786632	+	0.617422i	$0.211823\pi$
$510$		0			0
$511$	−18.6600	−	22.9253i	−0.825470	−	1.01415i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−1.50789	+	2.61175i	−0.0665103	+	0.115199i
$515$	20.3103	−	35.1785i	0.894979	−	1.55015i
$516$		0			0
$517$	0.640850	−	2.46348i	0.0281845	−	0.108344i
$518$	10.1187	−	8.23610i	0.444590	−	0.361874i
$519$		0			0
$520$	−1.62567	−	2.81575i	−0.0712905	−	0.123479i
$521$	−30.8004	−	17.7826i	−1.34939	−	0.779071i	−0.361227	−	0.932478i	$-0.617642\pi$
$521$	−30.8004	−	17.7826i	−1.34939	−	0.779071i	−0.988163	+	0.153407i	$0.950976\pi$
$522$		0			0
$523$	−1.90926	−	3.30694i	−0.0834863	−	0.144603i	0.821259	−	0.570556i	$-0.193272\pi$
$523$	−1.90926	−	3.30694i	−0.0834863	−	0.144603i	−0.904745	+	0.425953i	$0.859939\pi$
$524$	17.2415			0.753200
$525$		0			0
$526$	28.1819			1.22879
$527$	−10.5068	+	6.06613i	−0.457685	+	0.264245i
$528$		0			0
$529$	−22.8616	+	39.5975i	−0.993984	+	1.72163i
$530$	2.32943	+	4.03470i	0.101184	+	0.175256i
$531$		0			0
$532$	4.17451	−	10.9571i	0.180988	−	0.475050i
$533$	−10.8036			−0.467955
$534$		0			0
$535$	−7.10258	+	12.3020i	−0.307071	+	0.531863i
$536$	−1.49276	−	0.861844i	−0.0644773	−	0.0372260i
$537$		0			0
$538$	0.604546			0.0260638
$539$	−23.1678	+	1.50058i	−0.997909	+	0.0646346i
$540$		0			0
$541$	21.5152	−	12.4218i	0.925011	−	0.534055i	0.0397805	−	0.999208i	$-0.487334\pi$
$541$	21.5152	−	12.4218i	0.925011	−	0.534055i	0.885230	+	0.465153i	$0.154001\pi$
$542$	17.1413	+	9.89654i	0.736283	+	0.425093i
$543$		0			0
$544$	3.87528	−	2.23739i	0.166151	−	0.0959274i
$545$	−21.2560			−0.910509
$546$		0			0
$547$		−	44.4066i		−	1.89869i	−0.314237	−	0.949345i	$-0.601749\pi$
$547$		−	44.4066i		−	1.89869i	0.314237	−	0.949345i	$-0.398251\pi$
$548$	−1.25479	−	2.17335i	−0.0536018	−	0.0928411i
$549$		0			0
$550$	−2.51301	−	2.47658i	−0.107155	−	0.105602i
$551$	5.54248	−	3.19995i	0.236118	−	0.136323i
$552$		0			0
$553$	1.23134	+	7.65006i	0.0523620	+	0.325314i
$554$	−2.16446			−0.0919590
$555$		0			0
$556$	−9.97662	+	17.2800i	−0.423103	+	0.732836i
$557$	−23.9736	−	13.8412i	−1.01579	−	0.586469i	−0.102911	−	0.994691i	$-0.532816\pi$
$557$	−23.9736	−	13.8412i	−1.01579	−	0.586469i	−0.912883	+	0.408222i	$0.866149\pi$
$558$		0			0
$559$			12.7255i			0.538233i
$560$	−5.05289	+	4.11279i	−0.213523	+	0.173797i
$561$		0			0
$562$	14.7458	+	25.5405i	0.622014	+	1.07736i
$563$	5.51765	−	9.55686i	0.232541	−	0.402773i	−0.726014	−	0.687680i	$-0.758629\pi$
$563$	5.51765	−	9.55686i	0.232541	−	0.402773i	0.958555	+	0.284907i	$0.0919626\pi$
$564$		0			0
$565$	−37.3058	+	21.5385i	−1.56947	+	0.906132i
$566$		−	28.3880i		−	1.19324i
$567$		0			0
$568$		−	10.3771i		−	0.435412i
$569$	−35.2007	+	20.3231i	−1.47569	+	0.851989i	−0.999624	−	0.0274209i	$-0.991271\pi$
$569$	−35.2007	+	20.3231i	−1.47569	+	0.851989i	−0.476065	+	0.879410i	$0.657937\pi$
$570$		0			0
$571$	15.3762	+	8.87748i	0.643476	+	0.371511i	0.785952	−	0.618287i	$-0.212173\pi$
$571$	15.3762	+	8.87748i	0.643476	+	0.371511i	−0.142476	+	0.989798i	$0.545506\pi$
$572$	−1.16425	−	4.22152i	−0.0486796	−	0.176511i
$573$		0			0
$574$	3.44022	+	21.3733i	0.143592	+	0.892105i
$575$	−8.81895			−0.367776
$576$		0			0
$577$	−1.50303	−	0.867773i	−0.0625718	−	0.0361259i	0.468388	−	0.883523i	$-0.344835\pi$
$577$	−1.50303	−	0.867773i	−0.0625718	−	0.0361259i	−0.530960	+	0.847397i	$0.678168\pi$
$578$	−2.61860	−	1.51185i	−0.108920	−	0.0628847i
$579$		0			0
$580$	−3.55606			−0.147657
$581$	9.52480	−	25.0003i	0.395155	−	1.03719i
$582$		0			0
$583$	1.66825	+	6.04903i	0.0690920	+	0.250525i
$584$	−9.67562	−	5.58622i	−0.400380	−	0.231159i
$585$		0			0
$586$	8.13547	−	4.69702i	0.336073	−	0.194032i
$587$		−	0.837774i		−	0.0345786i	−0.999851	−	0.0172893i	$-0.994496\pi$
$587$		−	0.837774i		−	0.0345786i	0.999851	−	0.0172893i	$-0.00550363\pi$
$588$		0			0
$589$			12.0156i			0.495096i
$590$	−16.6081	+	9.58866i	−0.683743	+	0.394759i
$591$		0			0
$592$	2.46563	−	4.27060i	0.101337	−	0.175521i
$593$	13.0100	+	22.5339i	0.534255	+	0.925357i	0.999199	+	0.0400166i	$0.0127411\pi$
$593$	13.0100	+	22.5339i	0.534255	+	0.925357i	−0.464944	+	0.885340i	$0.653926\pi$
$594$		0			0
$595$	27.2435	+	10.3794i	1.11687	+	0.425514i
$596$			9.78029i			0.400616i
$597$		0			0
$598$	−9.47923	−	5.47284i	−0.387635	−	0.223801i
$599$	5.62081	−	9.73552i	0.229660	−	0.397783i	−0.728047	−	0.685527i	$-0.759572\pi$
$599$	5.62081	−	9.73552i	0.229660	−	0.397783i	0.957707	+	0.287744i	$0.0929053\pi$
$600$		0			0
$601$	−11.4274			−0.466134			−0.233067	−	0.972461i	$-0.574876\pi$
$601$	−11.4274			−0.466134			−0.233067	+	0.972461i	$0.574876\pi$
$602$	25.1756	−	4.05223i	1.02608	−	0.165157i
$603$		0			0
$604$	−2.31521	+	1.33669i	−0.0942045	+	0.0543890i
$605$	−13.8847	−	23.2581i	−0.564492	−	0.945574i
$606$		0			0
$607$	−5.09027	−	8.81661i	−0.206608	−	0.357855i	0.744036	−	0.668139i	$-0.232909\pi$
$607$	−5.09027	−	8.81661i	−0.206608	−	0.357855i	−0.950644	+	0.310284i	$0.899576\pi$
$608$		−	4.43177i		−	0.179732i
$609$		0			0
$610$	11.0291			0.446555
$611$	0.877592	−	0.506678i	0.0355036	−	0.0204980i
$612$		0			0
$613$	−21.6335	−	12.4901i	−0.873770	−	0.504471i	−0.00517055	−	0.999987i	$-0.501646\pi$
$613$	−21.6335	−	12.4901i	−0.873770	−	0.504471i	−0.868599	+	0.495515i	$0.834979\pi$
$614$	23.3595	−	13.4866i	0.942713	−	0.544275i
$615$		0			0
$616$	−7.98093	+	3.64757i	−0.321561	+	0.146965i
$617$	28.5114			1.14783			0.573914	−	0.818916i	$-0.305424\pi$
$617$	28.5114			1.14783			0.573914	+	0.818916i	$0.305424\pi$
$618$		0			0
$619$	−21.1014	−	12.1829i	−0.848137	−	0.489672i	0.0118852	−	0.999929i	$-0.496217\pi$
$619$	−21.1014	−	12.1829i	−0.848137	−	0.489672i	−0.860022	+	0.510258i	$0.829550\pi$
$620$	3.33820	−	5.78193i	0.134065	−	0.232208i
$621$		0			0
$622$	−0.125330			−0.00502529
$623$	−5.32047	−	33.0549i	−0.213160	−	1.32432i
$624$		0			0
$625$	14.5937	+	25.2770i	0.583747	+	1.01108i
$626$	−3.86494	+	6.69427i	−0.154474	+	0.267557i
$627$		0			0
$628$	13.7131	−	7.91724i	0.547211	−	0.315932i
$629$	−22.0663			−0.879843
$630$		0			0
$631$	−18.2463			−0.726374			−0.363187	−	0.931716i	$-0.618311\pi$
$631$	−18.2463			−0.726374			−0.363187	+	0.931716i	$0.618311\pi$
$632$	1.46433	+	2.53630i	0.0582481	+	0.100889i
$633$		0			0
$634$	21.1139	+	12.1901i	0.838540	+	0.484131i
$635$	14.8929	+	25.7953i	0.591008	+	1.02366i
$636$		0			0
$637$	−6.89946	−	6.14987i	−0.273367	−	0.243667i
$638$	−4.63525	−	1.20582i	−0.183511	−	0.0477387i
$639$		0			0
$640$	−1.23124	+	2.13257i	−0.0486691	+	0.0842973i
$641$	−9.69935	+	16.7998i	−0.383101	+	0.663551i	−0.991504	−	0.130078i	$-0.958477\pi$
$641$	−9.69935	+	16.7998i	−0.383101	+	0.663551i	0.608403	+	0.793628i	$0.291811\pi$
$642$		0			0
$643$			11.3901i			0.449182i	0.974453	+	0.224591i	$0.0721047\pi$
$643$			11.3901i			0.449182i	−0.974453	+	0.224591i	$0.927895\pi$
$644$	−7.80871	+	20.4960i	−0.307706	+	0.807656i
$645$		0			0
$646$	−17.1744	+	9.91562i	−0.675716	+	0.390125i
$647$	−14.8745	−	8.58781i	−0.584778	−	0.337621i	0.178252	−	0.983985i	$-0.442956\pi$
$647$	−14.8745	−	8.58781i	−0.584778	−	0.337621i	−0.763030	+	0.646363i	$0.776289\pi$
$648$		0			0
$649$	−24.8997	+	6.86704i	−0.977397	+	0.269555i
$650$		−	1.40461i		−	0.0550934i
$651$		0			0
$652$	20.3615			0.797418
$653$	−16.1982	−	28.0561i	−0.633884	−	1.09792i	−0.986750	−	0.162246i	$-0.948126\pi$
$653$	−16.1982	−	28.0561i	−0.633884	−	1.09792i	0.352866	−	0.935674i	$-0.385207\pi$
$654$		0			0
$655$	36.7688	+	21.2285i	1.43668	+	0.829465i
$656$	4.09116	+	7.08611i	0.159733	+	0.276666i
$657$		0			0
$658$	−1.28184	−	1.57485i	−0.0499714	−	0.0613939i
$659$		−	8.52103i		−	0.331932i	−0.986131	−	0.165966i	$-0.946926\pi$
$659$		−	8.52103i		−	0.331932i	0.986131	−	0.165966i	$-0.0530742\pi$
$660$		0			0
$661$	34.1086	+	19.6926i	1.32667	+	0.765953i	0.984783	−	0.173788i	$-0.0556009\pi$
$661$	34.1086	+	19.6926i	1.32667	+	0.765953i	0.341886	+	0.939741i	$0.388934\pi$
$662$	18.5790	+	10.7266i	0.722095	+	0.416902i
$663$		0			0
$664$		−	10.1118i		−	0.392414i
$665$	22.3933	−	18.2270i	0.868373	−	0.706811i
$666$		0			0
$667$	−10.3676	+	5.98574i	−0.401435	+	0.231769i
$668$	8.05596	−	13.9533i	0.311695	−	0.539871i
$669$		0			0
$670$	−2.12228	−	3.67589i	−0.0819906	−	0.142012i
$671$	14.3762	+	3.73983i	0.554987	+	0.144375i
$672$		0			0
$673$		−	23.4185i		−	0.902716i	−0.892343	−	0.451358i	$-0.850940\pi$
$673$		−	23.4185i		−	0.902716i	0.892343	−	0.451358i	$-0.149060\pi$
$674$	−15.0043	−	25.9882i	−0.577943	−	1.00103i
$675$		0			0
$676$	−5.62833	+	9.74856i	−0.216474	+	0.374944i
$677$	14.8410	+	25.7054i	0.570388	+	0.987940i	0.996526	+	0.0832822i	$0.0265403\pi$
$677$	14.8410	+	25.7054i	0.570388	+	0.987940i	−0.426138	+	0.904658i	$0.640126\pi$
$678$		0			0
$679$	3.40715	+	1.29808i	0.130754	+	0.0498157i
$680$	11.0191			0.422562
$681$		0			0
$682$	6.31186	−	6.40469i	0.241693	−	0.245248i
$683$	14.4728	−	25.0677i	0.553787	−	0.959188i	−0.444209	−	0.895923i	$-0.646515\pi$
$683$	14.4728	−	25.0677i	0.553787	−	0.959188i	0.997997	−	0.0632649i	$-0.0201513\pi$
$684$		0			0
$685$		−	6.17977i		−	0.236117i
$686$	−9.96961	+	15.6079i	−0.380642	+	0.595913i
$687$		0			0
$688$	8.34672	−	4.81898i	0.318216	−	0.183722i
$689$	−1.24902	+	2.16336i	−0.0475838	+	0.0824175i
$690$		0			0
$691$	24.2055	−	13.9750i	0.920820	−	0.531636i	0.0369236	−	0.999318i	$-0.488244\pi$
$691$	24.2055	−	13.9750i	0.920820	−	0.531636i	0.883897	+	0.467682i	$0.154911\pi$
$692$	−7.24694			−0.275487
$693$		0			0
$694$	−34.5340			−1.31089
$695$	−42.5517	+	24.5672i	−1.61408	+	0.931888i
$696$		0			0
$697$	18.3071	−	31.7088i	0.693430	−	1.20106i
$698$	4.13927	−	2.38981i	0.156674	−	0.0904555i
$699$		0			0
$700$	−2.77882	+	0.447274i	−0.105029	+	0.0169054i
$701$			13.2062i			0.498793i	0.968401	+	0.249397i	$0.0802323\pi$
$701$			13.2062i			0.498793i	−0.968401	+	0.249397i	$0.919768\pi$
$702$		0			0
$703$	−10.9271	+	18.9263i	−0.412124	+	0.713820i
$704$	−2.32803	+	2.36226i	−0.0877408	+	0.0890312i
$705$		0			0
$706$	−13.5771			−0.510979
$707$	12.6386	+	15.5276i	0.475325	+	0.583974i
$708$		0			0
$709$	−7.39039	−	12.8005i	−0.277552	−	0.480734i	0.693224	−	0.720722i	$-0.256190\pi$
$709$	−7.39039	−	12.8005i	−0.277552	−	0.480734i	−0.970776	+	0.239988i	$0.922856\pi$
$710$	12.7767	−	22.1298i	0.479500	−	0.830518i
$711$		0			0
$712$	−6.32720	−	10.9590i	−0.237122	−	0.410707i
$713$		−	22.4761i		−	0.841737i
$714$		0			0
$715$	2.71487	−	10.4362i	0.101530	−	0.390290i
$716$	−5.80078	−	10.0472i	−0.216785	−	0.375483i
$717$		0			0
$718$	−0.863893	+	1.49631i	−0.0322402	+	0.0558416i
$719$	−3.21343	+	1.85527i	−0.119841	+	0.0691900i	−0.558722	−	0.829355i	$-0.688708\pi$
$719$	−3.21343	+	1.85527i	−0.119841	+	0.0691900i	0.438881	+	0.898545i	$0.355375\pi$
$720$		0			0
$721$	−6.93557	−	43.0892i	−0.258294	−	1.60472i
$722$			0.640626i			0.0238416i
$723$		0			0
$724$	6.70670	+	3.87212i	0.249253	+	0.143906i
$725$	−1.33043	−	0.768123i	−0.0494109	−	0.0285274i
$726$		0			0
$727$			16.9392i			0.628241i	0.949383	+	0.314120i	$0.101710\pi$
$727$			16.9392i			0.628241i	−0.949383	+	0.314120i	$0.898290\pi$
$728$	−3.26444	−	1.24371i	−0.120988	−	0.0460949i
$729$		0			0
$730$	−13.7560	−	23.8260i	−0.509131	−	0.881841i
$731$	−37.3498	−	21.5639i	−1.38143	−	0.797570i
$732$		0			0
$733$	5.69951	+	9.87183i	0.210516	+	0.364624i	0.951876	−	0.306483i	$-0.0991523\pi$
$733$	5.69951	+	9.87183i	0.210516	+	0.364624i	−0.741360	+	0.671107i	$0.765819\pi$
$734$	−25.4861			−0.940709
$735$		0			0
$736$			8.28995i			0.305572i
$737$	−1.51989	−	5.51108i	−0.0559860	−	0.203003i
$738$		0			0
$739$	−4.89454	−	2.82586i	−0.180049	−	0.103951i	0.407267	−	0.913309i	$-0.366482\pi$
$739$	−4.89454	−	2.82586i	−0.180049	−	0.103951i	−0.587315	+	0.809358i	$0.699815\pi$
$740$	10.5163	−	6.07157i	0.386586	−	0.223195i
$741$		0			0
$742$	4.67762	+	1.78211i	0.171721	+	0.0654235i
$743$		−	2.21080i		−	0.0811065i	−0.999177	−	0.0405533i	$-0.987088\pi$
$743$		−	2.21080i		−	0.0811065i	0.999177	−	0.0405533i	$-0.0129120\pi$
$744$		0			0
$745$	−12.0419	+	20.8572i	−0.441181	+	0.764147i
$746$	−16.6667	+	28.8675i	−0.610211	+	1.05692i
$747$		0			0
$748$	14.3631	+	3.73643i	0.525168	+	0.136618i
$749$	2.42539	+	15.0684i	0.0886219	+	0.550589i
$750$		0			0
$751$	−2.93707	−	5.08715i	−0.107175	−	0.185633i	0.807450	−	0.589936i	$-0.200847\pi$
$751$	−2.93707	−	5.08715i	−0.107175	−	0.185633i	−0.914625	+	0.404304i	$0.867514\pi$
$752$	−0.664664	−	0.383744i	−0.0242378	−	0.0139937i
$753$		0			0
$754$	−0.953359	−	1.65127i	−0.0347193	−	0.0601356i
$755$	−6.58313			−0.239585
$756$		0			0
$757$	15.3568			0.558152			0.279076	−	0.960269i	$-0.409972\pi$
$757$	15.3568			0.558152			0.279076	+	0.960269i	$0.409972\pi$
$758$	−16.6845	+	9.63282i	−0.606010	+	0.349880i
$759$		0			0
$760$	5.45658	−	9.45107i	0.197931	−	0.342827i
$761$	−11.2463	−	19.4792i	−0.407680	−	0.706122i	0.586950	−	0.809623i	$-0.300329\pi$
$761$	−11.2463	−	19.4792i	−0.407680	−	0.706122i	−0.994629	+	0.103501i	$0.966995\pi$
$762$		0			0
$763$	−17.7124	+	14.4169i	−0.641230	+	0.521928i
$764$	−21.2314			−0.768125
$765$		0			0
$766$	−2.57755	+	4.46444i	−0.0931305	+	0.161307i
$767$	−8.90505	−	5.14133i	−0.321543	−	0.185643i
$768$		0			0
$769$	−39.6302			−1.42910			−0.714551	−	0.699583i	$-0.753369\pi$
$769$	−39.6302			−1.42910			−0.714551	+	0.699583i	$0.753369\pi$
$770$	−21.5109	−	2.04775i	−0.775200	−	0.0737959i
$771$		0			0
$772$	3.04258	−	1.75664i	0.109505	−	0.0632227i
$773$	13.6011	+	7.85260i	0.489198	+	0.282438i	0.724242	−	0.689546i	$-0.242190\pi$
$773$	13.6011	+	7.85260i	0.489198	+	0.282438i	−0.235044	+	0.971985i	$0.575523\pi$
$774$		0			0
$775$	2.49784	−	1.44213i	0.0897252	−	0.0518029i
$776$	1.37808			0.0494701
$777$		0			0
$778$			5.16455i			0.185158i
$779$	−18.1311	−	31.4040i	−0.649615	−	1.12517i
$780$		0			0
$781$	24.1581	−	24.5134i	0.864444	−	0.877158i
$782$	32.1259	−	18.5479i	1.14882	−	0.663270i
$783$		0			0
$784$	−1.42099	+	6.85425i	−0.0507497	+	0.244795i
$785$	38.9921			1.39169
$786$		0			0
$787$	20.6611	−	35.7861i	0.736488	−	1.27563i	−0.217579	−	0.976043i	$-0.569816\pi$
$787$	20.6611	−	35.7861i	0.736488	−	1.27563i	0.954067	−	0.299592i	$-0.0968506\pi$
$788$	−19.0279	−	10.9857i	−0.677840	−	0.391351i
$789$		0			0
$790$			7.21179i			0.256584i
$791$	−16.4778	+	43.2504i	−0.585885	+	1.53781i
$792$		0			0
$793$	2.95684	+	5.12140i	0.105000	+	0.181866i
$794$	3.17146	−	5.49312i	0.112551	−	0.194944i
$795$		0			0
$796$	1.24863	−	0.720899i	0.0442567	−	0.0255516i
$797$		−	20.2076i		−	0.715789i	−0.933762	−	0.357894i	$-0.883495\pi$
$797$		−	20.2076i		−	0.715789i	0.933762	−	0.357894i	$-0.116505\pi$
$798$		0			0
$799$			3.43434i			0.121498i
$800$	−0.921289	+	0.531907i	−0.0325725	+	0.0188057i
$801$		0			0
$802$	19.0539	+	11.0008i	0.672815	+	0.388450i
$803$	−9.85151	−	35.7212i	−0.347652	−	1.26057i
$804$		0			0
$805$	−41.8882	+	34.0948i	−1.47636	+	1.20168i
$806$	3.57981			0.126093
$807$		0			0
$808$	6.55341	+	3.78361i	0.230548	+	0.133107i
$809$	−29.2043	−	16.8611i	−1.02677	−	0.592805i	−0.110711	−	0.993853i	$-0.535313\pi$
$809$	−29.2043	−	16.8611i	−1.02677	−	0.592805i	−0.916057	+	0.401048i	$0.868646\pi$
$810$		0			0
$811$	9.84154			0.345583			0.172792	−	0.984958i	$-0.444721\pi$
$811$	9.84154			0.345583			0.172792	+	0.984958i	$0.444721\pi$
$812$	−2.96321	+	2.41190i	−0.103988	+	0.0846411i
$813$		0			0
$814$	15.7665	−	4.34823i	0.552617	−	0.152405i
$815$	43.4223	+	25.0699i	1.52102	+	0.878160i
$816$		0			0
$817$	−36.9908	+	21.3566i	−1.29414	+	0.747175i
$818$		−	14.1189i		−	0.493657i
$819$		0			0
$820$			20.1488i			0.703628i
$821$	−7.61984	+	4.39932i	−0.265934	+	0.153537i	−0.627039	−	0.778988i	$-0.715733\pi$
$821$	−7.61984	+	4.39932i	−0.265934	+	0.153537i	0.361104	+	0.932525i	$0.382400\pi$
$822$		0			0
$823$	16.4438	−	28.4815i	0.573195	−	0.992802i	−0.423041	−	0.906111i	$-0.639037\pi$
$823$	16.4438	−	28.4815i	0.573195	−	0.992802i	0.996235	−	0.0866913i	$-0.0276294\pi$
$824$	−8.24790	−	14.2858i	−0.287329	−	0.497669i
$825$		0			0
$826$	−7.33572	+	19.2545i	−0.255242	+	0.669951i
$827$			43.5923i			1.51585i	0.652339	+	0.757927i	$0.273788\pi$
$827$			43.5923i			1.51585i	−0.652339	+	0.757927i	$0.726212\pi$
$828$		0			0
$829$	−27.4160	−	15.8286i	−0.952198	−	0.549752i	−0.0584348	−	0.998291i	$-0.518611\pi$
$829$	−27.4160	−	15.8286i	−0.952198	−	0.549752i	−0.893763	+	0.448540i	$0.851944\pi$
$830$	12.4500	−	21.5641i	0.432147	−	0.748501i
$831$		0			0
$832$	−1.32035			−0.0457751
$833$	29.7414	−	9.82892i	1.03048	−	0.340552i
$834$		0			0
$835$	34.3598	−	19.8377i	1.18907	−	0.686511i
$836$	10.3173	−	10.4690i	0.356831	−	0.362079i
$837$		0			0
$838$	11.3880	+	19.7246i	0.393392	+	0.681375i
$839$		−	33.1104i		−	1.14310i	−0.820568	−	0.571549i	$-0.806343\pi$
$839$		−	33.1104i		−	1.14310i	0.820568	−	0.571549i	$-0.193657\pi$
$840$		0			0
$841$	26.9146			0.928089
$842$	−5.89729	+	3.40480i	−0.203234	+	0.117337i
$843$		0			0
$844$	−0.141823	−	0.0818817i	−0.00488176	−	0.00281848i
$845$	−24.0056	+	13.8597i	−0.825819	+	0.476787i
$846$		0			0
$847$	−27.3447	−	9.96330i	−0.939575	−	0.342343i
$848$	1.89194			0.0649695
$849$		0			0
$850$	4.12257	+	2.38017i	0.141403	+	0.0816391i
$851$	20.4400	−	35.4030i	0.700673	−	1.21360i
$852$		0			0
$853$	−32.8121			−1.12347			−0.561733	−	0.827318i	$-0.689865\pi$
$853$	−32.8121			−1.12347			−0.561733	+	0.827318i	$0.689865\pi$
$854$	9.19039	−	7.48050i	0.314489	−	0.255977i
$855$		0			0
$856$	2.88432	+	4.99579i	0.0985840	+	0.170753i
$857$	5.83813	−	10.1119i	0.199427	−	0.345417i	−0.748916	−	0.662665i	$-0.769425\pi$
$857$	5.83813	−	10.1119i	0.199427	−	0.345417i	0.948343	+	0.317248i	$0.102759\pi$
$858$		0			0
$859$	−35.2623	+	20.3587i	−1.20314	+	0.694631i	−0.961251	−	0.275674i	$-0.911099\pi$
$859$	−35.2623	+	20.3587i	−1.20314	+	0.694631i	−0.241885	+	0.970305i	$0.577766\pi$
$860$	23.7333			0.809299
$861$		0			0
$862$	−30.8640			−1.05123
$863$	−9.04438	−	15.6653i	−0.307874	−	0.533254i	0.670023	−	0.742341i	$-0.266284\pi$
$863$	−9.04438	−	15.6653i	−0.307874	−	0.533254i	−0.977897	+	0.209087i	$0.932951\pi$
$864$		0			0
$865$	−15.4546	−	8.92273i	−0.525473	−	0.303382i
$866$	−16.1483	−	27.9698i	−0.548743	−	0.950451i
$867$		0			0
$868$	−1.13993	−	7.08214i	−0.0386917	−	0.240383i
$869$	−2.44543	+	9.40042i	−0.0829555	+	0.318887i
$870$		0			0
$871$	1.13794	−	1.97097i	0.0385576	−	0.0667838i
$872$	−4.31598	+	7.47550i	−0.146158	+	0.253152i
$873$		0			0
$874$		−	36.7392i		−	1.24272i
$875$	23.9644	+	9.13012i	0.810144	+	0.308654i
$876$		0			0
$877$	−5.73392	+	3.31048i	−0.193621	+	0.111787i	−0.593676	−	0.804704i	$-0.702324\pi$
$877$	−5.73392	+	3.31048i	−0.193621	+	0.111787i	0.400056	+	0.916491i	$0.368991\pi$
$878$	−24.8302	−	14.3357i	−0.837980	−	0.483808i
$879$		0			0
$880$	−7.87320	+	2.17134i	−0.265405	+	0.0731958i
$881$			16.5800i			0.558594i	0.960205	+	0.279297i	$0.0901014\pi$
$881$			16.5800i			0.558594i	−0.960205	+	0.279297i	$0.909899\pi$
$882$		0			0
$883$	44.3526			1.49258			0.746292	−	0.665619i	$-0.231832\pi$
$883$	44.3526			1.49258			0.746292	+	0.665619i	$0.231832\pi$
$884$	2.95415	+	5.11674i	0.0993589	+	0.172095i
$885$		0			0
$886$	30.2949	+	17.4908i	1.01778	+	0.587615i
$887$	16.2919	+	28.2184i	0.547028	+	0.947480i	0.998476	+	0.0551831i	$0.0175742\pi$
$887$	16.2919	+	28.2184i	0.547028	+	0.947480i	−0.451448	+	0.892297i	$0.649092\pi$
$888$		0			0
$889$	29.9057	+	11.3937i	1.00301	+	0.382132i
$890$		−	31.1612i		−	1.04453i
$891$		0			0
$892$	23.7159	+	13.6924i	0.794065	+	0.458454i
$893$	2.94564	+	1.70067i	0.0985721	+	0.0569106i
$894$		0			0
$895$		−	28.5686i		−	0.954944i
$896$	0.420444	+	2.61213i	0.0140461	+	0.0872652i
$897$		0			0
$898$	3.09973	−	1.78963i	0.103439	−	0.0597207i
$899$	1.95765	−	3.39075i	0.0652913	−	0.113088i
$900$		0			0
$901$	−4.23302	−	7.33180i	−0.141022	−	0.244258i
$902$	−6.83222	+	26.2636i	−0.227488	+	0.874482i
$903$		0			0
$904$			17.4933i			0.581820i
$905$	9.53501	+	16.5151i	0.316955	+	0.548981i
$906$		0			0
$907$	20.5472	−	35.5887i	0.682257	−	1.18170i	−0.292033	−	0.956408i	$-0.594332\pi$
$907$	20.5472	−	35.5887i	0.682257	−	1.18170i	0.974290	−	0.225296i	$-0.0723350\pi$
$908$	−1.95128	−	3.37971i	−0.0647554	−	0.112160i
$909$		0			0
$910$	−5.43034	−	6.67160i	−0.180014	−	0.221161i
$911$	−28.2471			−0.935868			−0.467934	−	0.883764i	$-0.655001\pi$
$911$	−28.2471			−0.935868			−0.467934	+	0.883764i	$0.655001\pi$
$912$		0			0
$913$	23.5405	−	23.8867i	0.779077	−	0.790535i
$914$	−10.1997	+	17.6664i	−0.337375	+	0.584351i
$915$		0			0
$916$			5.04055i			0.166544i
$917$	45.0371	−	7.24911i	1.48726	−	0.239387i
$918$		0			0
$919$	−33.8721	+	19.5561i	−1.11734	+	0.645095i	−0.940720	−	0.339184i	$-0.889849\pi$
$919$	−33.8721	+	19.5561i	−1.11734	+	0.645095i	−0.176618	+	0.984280i	$0.556516\pi$
$920$	−10.2069	+	17.6789i	−0.336512	+	0.582856i
$921$		0			0
$922$	12.1215	−	6.99836i	0.399201	−	0.230479i
$923$	13.7014			0.450988
$924$		0			0
$925$	5.24594			0.172486
$926$	29.1417	−	16.8250i	0.957655	−	0.552903i
$927$		0			0
$928$	−0.722047	+	1.25062i	−0.0237024	+	0.0410537i
$929$	−21.3559	+	12.3298i	−0.700665	+	0.404529i	−0.807595	−	0.589737i	$-0.799231\pi$
$929$	−21.3559	+	12.3298i	−0.700665	+	0.404529i	0.106930	+	0.994267i	$0.465898\pi$
$930$		0			0
$931$	6.29751	−	30.3765i	0.206393	−	0.995550i
$932$			21.2457i			0.695927i
$933$		0			0
$934$	−4.54484	+	7.87190i	−0.148712	+	0.257576i
$935$	26.0300	+	25.6527i	0.851271	+	0.838933i
$936$		0			0
$937$	−10.7483			−0.351133			−0.175566	−	0.984468i	$-0.556176\pi$
$937$	−10.7483			−0.351133			−0.175566	+	0.984468i	$0.556176\pi$
$938$	−4.26164	−	1.62363i	−0.139147	−	0.0530133i
$939$		0			0
$940$	−0.944962	−	1.63672i	−0.0308213	−	0.0533840i
$941$	16.9368	−	29.3354i	0.552125	−	0.956308i	−0.445996	−	0.895035i	$-0.647151\pi$
$941$	16.9368	−	29.3354i	0.552125	−	0.956308i	0.998121	−	0.0612732i	$-0.0195161\pi$
$942$		0			0
$943$	33.9155	+	58.7434i	1.10444	+	1.91295i
$944$			7.78781i			0.253471i
$945$		0			0
$946$	30.9359	+	8.04768i	1.00581	+	0.261652i
$947$	10.3859	+	17.9889i	0.337497	+	0.584562i	0.983961	−	0.178382i	$-0.0570863\pi$
$947$	10.3859	+	17.9889i	0.337497	+	0.584562i	−0.646464	+	0.762944i	$0.723753\pi$
$948$		0			0
$949$	7.37579	−	12.7753i	0.239428	−	0.414702i
$950$	4.08295	−	2.35729i	0.132468	−	0.0764806i
$951$		0			0
$952$	9.18203	−	7.47370i	0.297591	−	0.242224i
$953$			1.28486i			0.0416205i	0.999783	+	0.0208103i	$0.00662459\pi$
$953$			1.28486i			0.0416205i	−0.999783	+	0.0208103i	$0.993375\pi$
$954$		0			0
$955$	−45.2774	−	26.1409i	−1.46514	−	0.845901i
$956$	−4.88534	−	2.82055i	−0.158003	−	0.0912232i
$957$		0			0
$958$		−	39.5655i		−	1.27830i
$959$	−4.19144	−	5.14952i	−0.135349	−	0.166287i
$960$		0			0
$961$	−11.8246	−	20.4807i	−0.381438	−	0.660669i
$962$	5.63871	+	3.25551i	0.181799	+	0.104962i
$963$		0			0
$964$	3.88733	+	6.73305i	0.125203	+	0.216857i
$965$	8.65137			0.278497
$966$		0			0
$967$		−	44.2584i		−	1.42325i	−0.702558	−	0.711627i	$-0.747959\pi$
$967$		−	44.2584i		−	1.42325i	0.702558	−	0.711627i	$-0.252041\pi$
$968$	−10.9988	+	0.160590i	−0.353516	+	0.00516157i
$969$		0			0
$970$	2.93885	+	1.69674i	0.0943607	+	0.0544792i
$971$	34.5497	−	19.9473i	1.10875	−	0.640138i	0.170246	−	0.985402i	$-0.445544\pi$
$971$	34.5497	−	19.9473i	1.10875	−	0.640138i	0.938506	+	0.345263i	$0.112210\pi$
$972$		0			0
$973$	−18.7949	+	49.3323i	−0.602538	+	1.58152i
$974$		−	3.20923i		−	0.102830i
$975$		0			0
$976$	2.23943	−	3.87880i	0.0716823	−	0.124157i
$977$	−0.803424	+	1.39157i	−0.0257038	+	0.0445203i	−0.878591	−	0.477575i	$-0.841516\pi$
$977$	−0.803424	+	1.39157i	−0.0257038	+	0.0445203i	0.852887	+	0.522095i	$0.174849\pi$
$978$		0			0
$979$	10.5664	−	40.6180i	0.337703	−	1.29816i
$980$	−11.4696	+	12.8676i	−0.366383	+	0.411040i
$981$		0			0
$982$	−9.51044	−	16.4726i	−0.303490	−	0.525661i
$983$	−0.981757	−	0.566818i	−0.0313132	−	0.0180787i	0.484262	−	0.874923i	$-0.339088\pi$
$983$	−0.981757	−	0.566818i	−0.0313132	−	0.0180787i	−0.515575	+	0.856845i	$0.672422\pi$
$984$		0			0
$985$	−27.0522	−	46.8558i	−0.861954	−	1.49295i
$986$	6.46201			0.205792
$987$		0			0
$988$	5.85152			0.186162
$989$	69.1939	−	39.9491i	2.20024	−	1.27031i
$990$		0			0
$991$	2.64334	−	4.57840i	0.0839684	−	0.145438i	−0.820983	−	0.570953i	$-0.806574\pi$
$991$	2.64334	−	4.57840i	0.0839684	−	0.145438i	0.904951	+	0.425515i	$0.139907\pi$
$992$	−1.35562	−	2.34801i	−0.0430411	−	0.0745494i
$993$		0			0
$994$	−4.36298	−	27.1063i	−0.138385	−	0.859759i
$995$	3.55040			0.112555
$996$		0			0
$997$	0.545190	−	0.944297i	0.0172663	−	0.0299062i	−0.857263	−	0.514879i	$-0.827837\pi$
$997$	0.545190	−	0.944297i	0.0172663	−	0.0299062i	0.874529	+	0.484972i	$0.161170\pi$
$998$	−22.1774	−	12.8041i	−0.702012	−	0.405307i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.b.703.8		16
3.2	odd	2		462.2.p.b.241.1	yes	16
7.5	odd	6		1386.2.bk.a.901.4		16
11.10	odd	2		1386.2.bk.a.703.4		16
21.5	even	6		462.2.p.a.439.5	yes	16
21.11	odd	6		3234.2.e.b.2155.2		16
21.17	even	6		3234.2.e.a.2155.7		16
33.32	even	2		462.2.p.a.241.5	✓	16
77.54	even	6	inner	1386.2.bk.b.901.8		16
231.32	even	6		3234.2.e.a.2155.10		16
231.131	odd	6		462.2.p.b.439.1	yes	16
231.164	odd	6		3234.2.e.b.2155.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.5	✓	16	33.32	even	2
462.2.p.a.439.5	yes	16	21.5	even	6
462.2.p.b.241.1	yes	16	3.2	odd	2
462.2.p.b.439.1	yes	16	231.131	odd	6
1386.2.bk.a.703.4		16	11.10	odd	2
1386.2.bk.a.901.4		16	7.5	odd	6
1386.2.bk.b.703.8		16	1.1	even	1	trivial
1386.2.bk.b.901.8		16	77.54	even	6	inner
3234.2.e.a.2155.7		16	21.17	even	6
3234.2.e.a.2155.10		16	231.32	even	6
3234.2.e.b.2155.2		16	21.11	odd	6
3234.2.e.b.2155.15		16	231.164	odd	6

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.13257 - 1.23124i) q^{5} +(0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.13257 - 1.23124i) q^{5} +(0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +(1.23124 - 2.13257i) q^{10} +(2.32803 - 2.36226i) q^{11} +1.32035 q^{13} +(-0.420444 - 2.61213i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.23739 + 3.87528i) q^{17} +(2.21589 + 3.83803i) q^{19} -2.46248i q^{20} +(0.834997 - 3.20979i) q^{22} +(-4.14497 - 7.17931i) q^{23} +(0.531907 - 0.921289i) q^{25} +(1.14346 - 0.660177i) q^{26} +(-1.67018 - 2.05195i) q^{28} -1.44409i q^{29} +(2.34801 + 1.35562i) q^{31} +(-0.866025 - 0.500000i) q^{32} +4.47479i q^{34} +(-1.03534 - 6.43232i) q^{35} +(2.46563 + 4.27060i) q^{37} +(3.83803 + 2.21589i) q^{38} +(-1.23124 - 2.13257i) q^{40} -8.18233 q^{41} +9.63797i q^{43} +(-0.881768 - 3.19726i) q^{44} +(-7.17931 - 4.14497i) q^{46} +(0.664664 - 0.383744i) q^{47} +(-5.22546 - 4.65774i) q^{49} -1.06381i q^{50} +(0.660177 - 1.14346i) q^{52} +(-0.945971 + 1.63847i) q^{53} +(2.05616 - 7.90406i) q^{55} +(-2.47239 - 0.941950i) q^{56} +(-0.722047 - 1.25062i) q^{58} +(-6.74444 - 3.89390i) q^{59} +(2.23943 + 3.87880i) q^{61} +2.71125 q^{62} -1.00000 q^{64} +(2.81575 - 1.62567i) q^{65} +(0.861844 - 1.49276i) q^{67} +(2.23739 + 3.87528i) q^{68} +(-4.11279 - 5.05289i) q^{70} +10.3771 q^{71} +(5.58622 - 9.67562i) q^{73} +(4.27060 + 2.46563i) q^{74} +4.43177 q^{76} +(-3.64757 - 7.98093i) q^{77} +(-2.53630 + 1.46433i) q^{79} +(-2.13257 - 1.23124i) q^{80} +(-7.08611 + 4.09116i) q^{82} +10.1118 q^{83} +11.0191i q^{85} +(4.81898 + 8.34672i) q^{86} +(-2.36226 - 2.32803i) q^{88} +(10.9590 - 6.32720i) q^{89} +(1.24371 - 3.26444i) q^{91} -8.28995 q^{92} +(0.383744 - 0.664664i) q^{94} +(9.45107 + 5.45658i) q^{95} +1.37808i q^{97} +(-6.85425 - 1.42099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7	\( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7} - 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} + 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} - 8 q^{35} + 14 q^{37} + 12 q^{38} + 2 q^{40} + 32 q^{41} - 4 q^{44} - 18 q^{46} + 24 q^{47} - 6 q^{49} + 14 q^{55} - 4 q^{56} - 28 q^{61} - 8 q^{62} - 16 q^{64} + 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} + 44 q^{73} + 24 q^{74} + 20 q^{76} + 52 q^{77} + 30 q^{79} + 12 q^{80} - 12 q^{82} + 8 q^{83} + 12 q^{86} - 2 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} - 14 q^{94} + 72 q^{95} - 40 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7 - 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 + 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 - 8 * q^35 + 14 * q^37 + 12 * q^38 + 2 * q^40 + 32 * q^41 - 4 * q^44 - 18 * q^46 + 24 * q^47 - 6 * q^49 + 14 * q^55 - 4 * q^56 - 28 * q^61 - 8 * q^62 - 16 * q^64 + 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 + 44 * q^73 + 24 * q^74 + 20 * q^76 + 52 * q^77 + 30 * q^79 + 12 * q^80 - 12 * q^82 + 8 * q^83 + 12 * q^86 - 2 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 - 14 * q^94 + 72 * q^95 - 40 * q^98

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