LMFDB - Embedded newform 1386.2.bk.a.901.4

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			901.4
Root			$0.500000 + 3.32851i$ of defining polynomial
Character	$\chi$	$=$	1386.901
Dual form			1386.2.bk.a.703.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.13257 + 1.23124i) q^{5} +(-0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.13257 + 1.23124i) q^{5} +(-0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +(-1.23124 - 2.13257i) q^{10} +(0.881768 + 3.19726i) q^{11} -1.32035 q^{13} +(-0.420444 + 2.61213i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.23739 + 3.87528i) q^{17} +(-2.21589 + 3.83803i) q^{19} +2.46248i q^{20} +(0.834997 - 3.20979i) q^{22} +(-4.14497 + 7.17931i) q^{23} +(0.531907 + 0.921289i) q^{25} +(1.14346 + 0.660177i) q^{26} +(1.67018 - 2.05195i) q^{28} -1.44409i q^{29} +(2.34801 - 1.35562i) q^{31} +(0.866025 - 0.500000i) q^{32} -4.47479i q^{34} +(1.03534 - 6.43232i) q^{35} +(2.46563 - 4.27060i) q^{37} +(3.83803 - 2.21589i) q^{38} +(1.23124 - 2.13257i) q^{40} +8.18233 q^{41} +9.63797i q^{43} +(-2.32803 + 2.36226i) q^{44} +(7.17931 - 4.14497i) q^{46} +(0.664664 + 0.383744i) q^{47} +(-5.22546 + 4.65774i) q^{49} -1.06381i q^{50} +(-0.660177 - 1.14346i) q^{52} +(-0.945971 - 1.63847i) q^{53} +(-2.05616 + 7.90406i) q^{55} +(-2.47239 + 0.941950i) q^{56} +(-0.722047 + 1.25062i) q^{58} +(-6.74444 + 3.89390i) q^{59} +(-2.23943 + 3.87880i) q^{61} -2.71125 q^{62} -1.00000 q^{64} +(-2.81575 - 1.62567i) q^{65} +(0.861844 + 1.49276i) q^{67} +(-2.23739 + 3.87528i) q^{68} +(-4.11279 + 5.05289i) q^{70} +10.3771 q^{71} +(-5.58622 - 9.67562i) q^{73} +(-4.27060 + 2.46563i) q^{74} -4.43177 q^{76} +(7.07431 - 5.19174i) q^{77} +(2.53630 + 1.46433i) q^{79} +(-2.13257 + 1.23124i) q^{80} +(-7.08611 - 4.09116i) q^{82} -10.1118 q^{83} +11.0191i q^{85} +(4.81898 - 8.34672i) q^{86} +(3.19726 - 0.881768i) q^{88} +(10.9590 + 6.32720i) q^{89} +(1.24371 + 3.26444i) q^{91} -8.28995 q^{92} +(-0.383744 - 0.664664i) q^{94} +(-9.45107 + 5.45658i) q^{95} -1.37808i q^{97} +(6.85425 - 1.42099i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 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 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * 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 $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.894233	−	0.447602i	$-0.147722\pi$
$5$	2.13257	+	1.23124i	0.953715	+	0.550628i	0.0594819	+	0.998229i	$0.481055\pi$
$6$		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
$11$	0.881768	+	3.19726i	0.265863	+	0.964011i
$11$	0.881768	+	3.19726i	0.265863	+	0.964011i
$12$		0			0
$13$	−1.32035			−0.366201			−0.183100	−	0.983094i	$-0.558613\pi$
$13$	−1.32035			−0.366201			−0.183100	+	0.983094i	$0.558613\pi$
$14$	−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	0.998751	+	0.0499662i	$0.0159113\pi$
$17$	2.23739	+	3.87528i	0.542647	+	0.939893i	−0.456103	+	0.889927i	$0.650755\pi$
$18$		0			0
$19$	−2.21589	+	3.83803i	−0.508359	+	0.880504i	0.491594	+	0.870825i	$0.336415\pi$
$19$	−2.21589	+	3.83803i	−0.508359	+	0.880504i	−0.999953	+	0.00967966i	$0.996919\pi$
$20$			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	0.00346670	+	0.999994i	$0.498897\pi$
$23$	−4.14497	+	7.17931i	−0.864287	+	1.49699i	−0.867754	+	0.496995i	$0.834437\pi$
$24$		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	−0.274096	−	0.961702i	$-0.588379\pi$
$31$	2.34801	−	1.35562i	0.421715	−	0.243477i	0.695811	+	0.718225i	$0.255045\pi$
$32$	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	−0.589014	−	0.808122i	$-0.700484\pi$
$37$	2.46563	−	4.27060i	0.405347	−	0.702082i	0.994362	+	0.106040i	$0.0338172\pi$
$38$	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	$-0.279376\pi$
$41$	8.18233			1.27787			0.638933	+	0.769263i	$0.279376\pi$
$42$		0			0
$43$			9.63797i			1.46978i	0.678188	+	0.734888i	$0.262765\pi$
$43$			9.63797i			1.46978i	−0.678188	+	0.734888i	$0.737235\pi$
$44$	−2.32803	+	2.36226i	−0.350963	+	0.356125i
$45$		0			0
$46$	7.17931	−	4.14497i	1.05853	−	0.611143i
$47$	0.664664	+	0.383744i	0.0969512	+	0.0559748i	0.547692	−	0.836680i	$-0.315507\pi$
$47$	0.664664	+	0.383744i	0.0969512	+	0.0559748i	−0.450741	+	0.892655i	$0.648840\pi$
$48$		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	0.793714	−	0.608292i	$-0.208145\pi$
$53$	−0.945971	−	1.63847i	−0.129939	−	0.225061i	−0.923653	+	0.383230i	$0.874812\pi$
$54$		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	−0.870015	−	0.493025i	$-0.835891\pi$
$59$	−6.74444	+	3.89390i	−0.878051	+	0.506943i	−0.00803571	+	0.999968i	$0.502558\pi$
$60$		0			0
$61$	−2.23943	+	3.87880i	−0.286729	+	0.496630i	−0.973027	−	0.230691i	$-0.925901\pi$
$61$	−2.23943	+	3.87880i	−0.286729	+	0.496630i	0.686298	+	0.727321i	$0.259235\pi$
$62$	−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	0.913857	−	0.406036i	$-0.133089\pi$
$67$	0.861844	+	1.49276i	0.105291	+	0.182369i	−0.808566	+	0.588405i	$0.799756\pi$
$68$	−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	−0.982189	−	0.187897i	$-0.939833\pi$
$73$	−5.58622	−	9.67562i	−0.653818	−	1.13245i	0.328371	−	0.944549i	$-0.393500\pi$
$74$	−4.27060	+	2.46563i	−0.496447	+	0.286624i
$75$		0			0
$76$	−4.43177			−0.508359
$77$	7.07431	−	5.19174i	0.806192	−	0.591654i
$78$		0			0
$79$	2.53630	+	1.46433i	0.285356	+	0.164750i	0.635846	−	0.771816i	$-0.280651\pi$
$79$	2.53630	+	1.46433i	0.285356	+	0.164750i	−0.350490	+	0.936567i	$0.613985\pi$
$80$	−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	$-0.687265\pi$
$83$	−10.1118			−1.10991			−0.554957	+	0.831879i	$0.687265\pi$
$84$		0			0
$85$			11.0191i			1.19519i
$86$	4.81898	−	8.34672i	0.519644	−	0.900050i
$87$		0			0
$88$	3.19726	−	0.881768i	0.340829	−	0.0939968i
$89$	10.9590	+	6.32720i	1.16165	+	0.670682i	0.951700	−	0.307029i	$-0.0993350\pi$
$89$	10.9590	+	6.32720i	1.16165	+	0.670682i	0.209955	+	0.977711i	$0.432668\pi$
$90$		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	$-0.977712\pi$
$97$		−	1.37808i		−	0.139923i	0.997550	−	0.0699613i	$-0.0222876\pi$
$98$	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	$-0.0437998\pi$
$101$	3.78361	+	6.55341i	0.376483	+	0.652089i	−0.614064	+	0.789256i	$0.710466\pi$
$102$		0			0
$103$	14.2858	+	8.24790i	1.40762	+	0.812690i	0.995158	−	0.0982855i	$-0.0313358\pi$
$103$	14.2858	+	8.24790i	1.40762	+	0.812690i	0.412461	+	0.910975i	$0.364669\pi$
$104$			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	$-0.243384\pi$
$107$	4.99579	+	2.88432i	0.482961	+	0.278838i	−0.238689	+	0.971096i	$0.576718\pi$
$108$		0			0
$109$	7.47550	−	4.31598i	0.716023	−	0.413396i	−0.0972641	−	0.995259i	$-0.531009\pi$
$109$	7.47550	−	4.31598i	0.716023	−	0.413396i	0.813287	+	0.581862i	$0.197676\pi$
$110$	5.73272	−	5.81703i	0.546593	−	0.554632i
$111$		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
$121$	−9.44497	+	5.63849i	−0.858634	+	0.512590i
$122$	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	0.193064	+	0.981186i	$0.438157\pi$
$131$	−8.62077	+	14.9316i	−0.753200	+	1.30458i	−0.946264	+	0.323394i	$0.895176\pi$
$132$		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	0.914636	−	0.404277i	$-0.132477\pi$
$137$	1.25479	+	2.17335i	0.107204	+	0.185682i	−0.807433	+	0.589960i	$0.799144\pi$
$138$		0			0
$139$	19.9532			1.69241			0.846206	−	0.532856i	$-0.178881\pi$
$139$	19.9532			1.69241			0.846206	+	0.532856i	$0.178881\pi$
$140$	6.08822	−	2.31953i	0.514549	−	0.196036i
$141$		0			0
$142$	−8.98681	−	5.18854i	−0.754156	−	0.435412i
$143$	−1.16425	−	4.22152i	−0.0973592	−	0.353021i
$144$		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	$-0.202129\pi$
$149$	8.46998	+	4.89014i	0.693888	+	0.400616i	−0.111179	+	0.993800i	$0.535463\pi$
$150$		0			0
$151$	2.31521	−	1.33669i	0.188409	−	0.108778i	−0.402829	−	0.915275i	$-0.631973\pi$
$151$	2.31521	−	1.33669i	0.188409	−	0.108778i	0.591237	+	0.806498i	$0.298640\pi$
$152$	3.83803	+	2.21589i	0.311305	+	0.179732i
$153$		0			0
$154$	−8.72240	+	0.959023i	−0.702871	+	0.0772803i
$155$	6.67640			0.536261
$156$		0			0
$157$	13.7131	−	7.91724i	1.09442	−	0.631865i	0.159671	−	0.987170i	$-0.448957\pi$
$157$	13.7131	−	7.91724i	1.09442	−	0.631865i	0.934750	+	0.355306i	$0.115623\pi$
$158$	−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	−0.123875	−	0.992298i	$-0.539532\pi$
$163$	10.1807	−	17.6336i	0.797418	−	1.38117i	0.921293	−	0.388870i	$-0.127135\pi$
$164$	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	$-0.714245\pi$
$167$	−16.1119			−1.24678			−0.623389	+	0.781912i	$0.714245\pi$
$168$		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	$-0.744494\pi$
$173$	3.62347	−	6.27604i	0.275487	−	0.477158i	0.970258	+	0.242073i	$0.0778274\pi$
$174$		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	0.997178	−	0.0750767i	$-0.0239202\pi$
$179$	5.80078	+	10.0472i	0.433571	+	0.750966i	−0.563607	+	0.826043i	$0.690587\pi$
$180$		0			0
$181$		−	7.74423i		−	0.575624i	−0.957687	−	0.287812i	$-0.907072\pi$
$181$		−	7.74423i		−	0.575624i	0.957687	−	0.287812i	$-0.0929279\pi$
$182$	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
$187$	−10.4174	+	10.5706i	−0.761797	+	0.773001i
$188$			0.767488i			0.0559748i
$189$		0			0
$190$	10.9132			0.791724
$191$	−10.6157	+	18.3869i	−0.768125	+	1.33043i	0.170454	+	0.985366i	$0.445477\pi$
$191$	−10.6157	+	18.3869i	−0.768125	+	1.33043i	−0.938579	+	0.345065i	$0.887857\pi$
$192$		0			0
$193$	−3.04258	+	1.75664i	−0.219010	+	0.126445i	−0.605492	−	0.795852i	$-0.707024\pi$
$193$	−3.04258	+	1.75664i	−0.219010	+	0.126445i	0.386482	+	0.922297i	$0.373690\pi$
$194$	−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	−0.455090	−	0.890445i	$-0.650393\pi$
$199$	1.24863	−	0.720899i	0.0885133	−	0.0511032i	0.543603	+	0.839342i	$0.317060\pi$
$200$	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
$220$	−7.87320	+	2.17134i	−0.530811	+	0.146392i
$221$	−2.95415	−	5.11674i	−0.198718	−	0.344189i
$222$		0			0
$223$		−	27.3847i		−	1.83382i	−0.399099	−	0.916908i	$-0.630677\pi$
$223$		−	27.3847i		−	1.83382i	0.399099	−	0.916908i	$-0.369323\pi$
$224$	−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	$-0.208007\pi$
$227$	−1.95128	−	3.37971i	−0.129511	−	0.224319i	−0.923487	+	0.383629i	$0.874674\pi$
$228$		0			0
$229$	−4.36524	−	2.52028i	−0.288463	−	0.166544i	0.348785	−	0.937203i	$-0.386594\pi$
$229$	−4.36524	−	2.52028i	−0.288463	−	0.166544i	−0.637249	+	0.770658i	$0.719928\pi$
$230$	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	$-0.0883271\pi$
$233$	18.3993	+	10.6229i	1.20538	+	0.695927i	0.243634	+	0.969867i	$0.421660\pi$
$234$		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	$-0.0861029\pi$
$241$	3.88733	+	6.73305i	0.250405	+	0.433714i	−0.713232	+	0.700928i	$0.752770\pi$
$242$	10.9988	−	0.160590i	0.707031	−	0.0103231i
$243$		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	$-0.748588\pi$
$251$		−	22.5045i		−	1.42047i	0.703963	−	0.710236i	$-0.251412\pi$
$252$		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	0.416325	−	0.909216i	$-0.363318\pi$
$257$	−2.61175	−	1.50789i	−0.162916	−	0.0940597i	−0.579241	+	0.815156i	$0.696651\pi$
$258$		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	−0.504972	+	0.863136i	$0.668497\pi$
$263$	−24.4063	+	14.0910i	−1.50496	+	0.868887i	−0.999983	+	0.00575106i	$0.998169\pi$
$264$		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	−0.483954	−	0.875093i	$-0.660800\pi$
$269$	0.523552	−	0.302273i	0.0319215	−	0.0184299i	0.515876	+	0.856663i	$0.327467\pi$
$270$		0			0
$271$	−9.89654	+	17.1413i	−0.601172	+	1.04126i	0.391472	+	0.920190i	$0.371966\pi$
$271$	−9.89654	+	17.1413i	−0.601172	+	1.04126i	−0.992644	+	0.121071i	$0.961367\pi$
$272$	−4.47479			−0.271324
$273$		0			0
$274$		−	2.50957i		−	0.151609i
$275$	−2.47658	+	2.51301i	−0.149344	+	0.151540i
$276$		0			0
$277$	1.87448	−	1.08223i	0.112626	−	0.0650249i	−0.442629	−	0.896705i	$-0.645954\pi$
$277$	1.87448	−	1.08223i	0.112626	−	0.0650249i	0.555255	+	0.831680i	$0.312621\pi$
$278$	−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	−0.886707	−	0.462333i	$-0.847013\pi$
$283$	−14.1940	−	24.5847i	−0.843745	−	1.46141i	0.0429613	−	0.999077i	$-0.486321\pi$
$284$	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	$-0.588480\pi$
$293$	−9.39403			−0.548805			−0.274403	+	0.961615i	$0.588480\pi$
$294$		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	$-0.779605\pi$
$307$	−26.9732			−1.53944			−0.769722	+	0.638380i	$0.779605\pi$
$308$	8.03333	+	3.53066i	0.457742	+	0.201178i
$309$		0			0
$310$	−5.78193	−	3.33820i	−0.328392	−	0.189597i
$311$	−0.108539	+	0.0626652i	−0.00615470	+	0.00355342i	−0.503074	−	0.864243i	$-0.667798\pi$
$311$	−0.108539	+	0.0626652i	−0.00615470	+	0.00355342i	0.496919	+	0.867797i	$0.334464\pi$
$312$		0			0
$313$	−6.69427	−	3.86494i	−0.378382	−	0.218459i	0.298732	−	0.954337i	$-0.403436\pi$
$313$	−6.69427	−	3.86494i	−0.378382	−	0.218459i	−0.677114	+	0.735878i	$0.736770\pi$
$314$	−15.8345			−0.893591
$315$		0			0
$316$			2.92867i			0.164750i
$317$	12.1901	−	21.1139i	0.684665	−	1.18587i	−0.288877	−	0.957366i	$-0.593282\pi$
$317$	12.1901	−	21.1139i	0.684665	−	1.18587i	0.973542	−	0.228508i	$-0.0733848\pi$
$318$		0			0
$319$	4.61715	−	1.27336i	0.258511	−	0.0712943i
$320$	−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	−0.404698	−	0.914450i	$-0.632623\pi$
$331$	10.7266	−	18.5790i	0.589588	−	1.02120i	0.994286	−	0.106746i	$-0.0340432\pi$
$332$	−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
$341$	6.40469	+	6.31186i	0.346833	+	0.341806i
$342$		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	0.615152	−	0.788408i	$-0.289094\pi$
$347$	29.9073	−	17.2670i	1.60551	−	0.926942i	0.990358	−	0.138533i	$-0.0442389\pi$
$348$		0			0
$349$	−4.77961			−0.255847			−0.127923	−	0.991784i	$-0.540831\pi$
$349$	−4.77961			−0.255847			−0.127923	+	0.991784i	$0.540831\pi$
$350$	−2.63016	+	1.00206i	−0.140588	+	0.0535623i
$351$		0			0
$352$	2.36226	+	2.32803i	0.125909	+	0.124084i
$353$	−11.7581	+	6.78853i	−0.625819	+	0.361317i	−0.779131	−	0.626861i	$-0.784339\pi$
$353$	−11.7581	+	6.78853i	−0.625819	+	0.361317i	0.153312	+	0.988178i	$0.451006\pi$
$354$		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	$-0.318815\pi$
$359$	1.49631	+	0.863893i	0.0789720	+	0.0455945i	−0.459994	+	0.887922i	$0.652148\pi$
$360$		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	−0.949405	−	0.314054i	$-0.898313\pi$
$367$	−22.0716	+	12.7430i	−1.15213	+	0.665182i	−0.202724	+	0.979236i	$0.564979\pi$
$368$	−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	$-0.00193605\pi$
$373$	28.8675	+	16.6667i	1.49470	+	0.862968i	0.494723	+	0.869051i	$0.335269\pi$
$374$	14.3071	−	3.94572i	0.739801	−	0.204029i
$375$		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	0.381583	−	0.924334i	$-0.375379\pi$
$383$	−4.46444	−	2.57755i	−0.228122	−	0.131706i	−0.609705	+	0.792628i	$0.708712\pi$
$384$		0			0
$385$	21.4787	−	2.36158i	1.09466	−	0.120357i
$386$	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	0.793107	−	0.609082i	$-0.208462\pi$
$389$	−2.58228	−	4.47264i	−0.130927	−	0.226772i	−0.924034	+	0.382310i	$0.875129\pi$
$390$		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	0.631472	−	0.775399i	$-0.282451\pi$
$397$	5.49312	+	3.17146i	0.275692	+	0.159171i	−0.355780	+	0.934570i	$0.615785\pi$
$398$	−1.44180			−0.0722708
$399$		0			0
$400$	−1.06381			−0.0531907
$401$	11.0008	−	19.0539i	0.549351	−	0.951504i	−0.448968	−	0.893548i	$-0.648208\pi$
$401$	11.0008	−	19.0539i	0.549351	−	0.951504i	0.998319	−	0.0579565i	$-0.0184585\pi$
$402$		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	$-0.280169\pi$
$409$	−7.05947	−	12.2274i	−0.349068	−	0.604604i	−0.986084	+	0.166247i	$0.946835\pi$
$410$	−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
$418$	10.4690	+	10.3173i	0.512057	+	0.504635i
$419$		−	22.7760i		−	1.11268i	−0.830955	−	0.556340i	$-0.812205\pi$
$419$		−	22.7760i		−	1.11268i	0.830955	−	0.556340i	$-0.187795\pi$
$420$		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	$-0.399910\pi$
$431$	26.7290	−	15.4320i	1.28749	−	0.743334i	0.978206	+	0.207635i	$0.0665767\pi$
$432$		0			0
$433$			32.2967i			1.55208i	0.630683	+	0.776040i	$0.282775\pi$
$433$			32.2967i			1.55208i	−0.630683	+	0.776040i	$0.717225\pi$
$434$	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	−0.289478	−	0.957185i	$-0.593482\pi$
$439$	14.3357	−	24.8302i	0.684208	−	1.18508i	0.973685	−	0.227898i	$-0.0731851\pi$
$440$	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	−0.0662231	−	0.997805i	$-0.521095\pi$
$443$	17.4908	−	30.2949i	0.831013	−	1.43936i	0.897236	−	0.441552i	$-0.145572\pi$
$444$		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
$451$	7.21492	+	26.1611i	0.339737	+	1.23188i
$452$	−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	$-0.175014\pi$
$457$	17.6664	+	10.1997i	0.826398	+	0.477121i	−0.0262200	+	0.999656i	$0.508347\pi$
$458$	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	$-0.605683\pi$
$461$	−13.9967			−0.651892			−0.325946	+	0.945388i	$0.605683\pi$
$462$		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	0.306683	−	0.951812i	$-0.400781\pi$
$467$	−7.87190	−	4.54484i	−0.364268	−	0.210310i	−0.670951	+	0.741501i	$0.734114\pi$
$468$		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
$473$	−30.8151	+	8.49845i	−1.41688	+	0.390759i
$474$		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	−0.822391	−	0.568922i	$-0.807361\pi$
$479$	−19.7827	−	34.2647i	−0.903897	−	1.56560i	−0.0815054	−	0.996673i	$-0.525973\pi$
$480$		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	0.900089	−	0.435706i	$-0.143501\pi$
$487$	1.60461	+	2.77927i	0.0727120	+	0.125941i	−0.827377	+	0.561647i	$0.810168\pi$
$488$	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	0.423045	+	0.906108i	$0.360961\pi$
$499$	−12.8041	+	22.1774i	−0.573190	+	0.992795i	−0.996236	+	0.0866862i	$0.972372\pi$
$500$	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	$-0.480591\pi$
$503$	2.73335			0.121874			0.0609370	+	0.998142i	$0.480591\pi$
$504$		0			0
$505$			18.6341i			0.829209i
$506$	19.5831	+	19.2992i	0.870573	+	0.857955i
$507$		0			0
$508$	−10.4753	+	6.04793i	−0.464768	+	0.268334i
$509$	14.5574	+	8.40471i	0.645245	+	0.372532i	0.786632	−	0.617422i	$-0.211823\pi$
$509$	14.5574	+	8.40471i	0.645245	+	0.372532i	−0.141387	+	0.989954i	$0.545156\pi$
$510$		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	−0.988163	−	0.153407i	$-0.950976\pi$
$521$	−30.8004	+	17.7826i	−1.34939	+	0.779071i	−0.361227	+	0.932478i	$0.617642\pi$
$522$		0			0
$523$	1.90926	−	3.30694i	0.0834863	−	0.144603i	−0.821259	−	0.570556i	$-0.806728\pi$
$523$	1.90926	−	3.30694i	0.0834863	−	0.144603i	0.904745	+	0.425953i	$0.140061\pi$
$524$	−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
$539$	−19.4997	−	12.6001i	−0.839910	−	0.542726i
$540$		0			0
$541$	−21.5152	−	12.4218i	−0.925011	−	0.534055i	−0.0397805	−	0.999208i	$-0.512666\pi$
$541$	−21.5152	−	12.4218i	−0.925011	−	0.534055i	−0.885230	+	0.465153i	$0.845999\pi$
$542$	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
$550$	3.40129	−	0.938037i	0.145031	−	0.0399980i
$551$	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	$-0.467184\pi$
$557$	23.9736	−	13.8412i	1.01579	−	0.586469i	0.912883	+	0.408222i	$0.133851\pi$
$558$		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	$-0.241371\pi$
$563$	−5.51765	−	9.55686i	−0.232541	−	0.402773i	−0.958555	+	0.284907i	$0.908037\pi$
$564$		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	$-0.00872944\pi$
$569$	35.2007	+	20.3231i	1.47569	+	0.851989i	0.476065	+	0.879410i	$0.342063\pi$
$570$		0			0
$571$	−15.3762	+	8.87748i	−0.643476	+	0.371511i	−0.785952	−	0.618287i	$-0.787827\pi$
$571$	−15.3762	+	8.87748i	−0.643476	+	0.371511i	0.142476	+	0.989798i	$0.454494\pi$
$572$	3.07382	−	3.11903i	0.128523	−	0.130413i
$573$		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	−0.530960	−	0.847397i	$-0.678168\pi$
$577$	−1.50303	+	0.867773i	−0.0625718	+	0.0361259i	0.468388	+	0.883523i	$0.344835\pi$
$578$	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
$583$	4.40449	−	4.46927i	0.182415	−	0.185098i
$584$	−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	$0.00550363\pi$
$587$			0.837774i			0.0345786i	−0.999851	+	0.0172893i	$0.994496\pi$
$588$		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	0.464944	+	0.885340i	$0.346074\pi$
$593$	−13.0100	+	22.5339i	−0.534255	+	0.925357i	−0.999199	+	0.0400166i	$0.987259\pi$
$594$		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	0.957707	−	0.287744i	$-0.0929053\pi$
$599$	5.62081	+	9.73552i	0.229660	+	0.397783i	−0.728047	+	0.685527i	$0.759572\pi$
$600$		0			0
$601$	11.4274			0.466134			0.233067	−	0.972461i	$-0.425124\pi$
$601$	11.4274			0.466134			0.233067	+	0.972461i	$0.425124\pi$
$602$	−25.1756	−	4.05223i	−1.02608	−	0.165157i
$603$		0			0
$604$	2.31521	+	1.33669i	0.0942045	+	0.0543890i
$605$	−27.0844	+	0.395451i	−1.10114	+	0.0160774i
$606$		0			0
$607$	5.09027	−	8.81661i	0.206608	−	0.357855i	−0.744036	−	0.668139i	$-0.767091\pi$
$607$	5.09027	−	8.81661i	0.206608	−	0.357855i	0.950644	+	0.310284i	$0.100424\pi$
$608$			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	$-0.498354\pi$
$613$	21.6335	−	12.4901i	0.873770	−	0.504471i	0.868599	+	0.495515i	$0.165021\pi$
$614$	23.3595	+	13.4866i	0.942713	+	0.544275i
$615$		0			0
$616$	−5.19174	−	7.07431i	−0.209181	−	0.285032i
$617$	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	−0.860022	−	0.510258i	$-0.829550\pi$
$619$	−21.1014	+	12.1829i	−0.848137	+	0.489672i	0.0118852	+	0.999929i	$0.496217\pi$
$620$	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	0.608403	−	0.793628i	$-0.291811\pi$
$641$	−9.69935	−	16.7998i	−0.383101	−	0.663551i	−0.991504	+	0.130078i	$0.958477\pi$
$642$		0			0
$643$		−	11.3901i		−	0.449182i	−0.974453	−	0.224591i	$-0.927895\pi$
$643$		−	11.3901i		−	0.449182i	0.974453	−	0.224591i	$-0.0721047\pi$
$644$	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	−0.763030	−	0.646363i	$-0.776289\pi$
$647$	−14.8745	+	8.58781i	−0.584778	+	0.337621i	0.178252	+	0.983985i	$0.442956\pi$
$648$		0			0
$649$	−18.3969	−	18.1302i	−0.722140	−	0.711673i
$650$			1.40461i			0.0550934i
$651$		0			0
$652$	20.3615			0.797418
$653$	−16.1982	+	28.0561i	−0.633884	+	1.09792i	0.352866	+	0.935674i	$0.385207\pi$
$653$	−16.1982	+	28.0561i	−0.633884	+	1.09792i	−0.986750	+	0.162246i	$0.948126\pi$
$654$		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	0.341886	−	0.939741i	$-0.388934\pi$
$661$	34.1086	−	19.6926i	1.32667	−	0.765953i	0.984783	+	0.173788i	$0.0556009\pi$
$662$	−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	0.426138	+	0.904658i	$0.359874\pi$
$677$	−14.8410	+	25.7054i	−0.570388	+	0.987940i	−0.996526	+	0.0832822i	$0.973460\pi$
$678$		0			0
$679$	−3.40715	+	1.29808i	−0.130754	+	0.0498157i
$680$	11.0191			0.422562
$681$		0			0
$682$	−2.39069	−	8.66857i	−0.0915444	−	0.331937i
$683$	14.4728	+	25.0677i	0.553787	+	0.959188i	0.997997	+	0.0632649i	$0.0201513\pi$
$683$	14.4728	+	25.0677i	0.553787	+	0.959188i	−0.444209	+	0.895923i	$0.646515\pi$
$684$		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	0.883897	−	0.467682i	$-0.154911\pi$
$691$	24.2055	+	13.9750i	0.920820	+	0.531636i	0.0369236	+	0.999318i	$0.488244\pi$
$692$	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
$704$	−0.881768	−	3.19726i	−0.0332329	−	0.120501i
$705$		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	−0.970776	−	0.239988i	$-0.922856\pi$
$709$	−7.39039	+	12.8005i	−0.277552	+	0.480734i	0.693224	+	0.720722i	$0.256190\pi$
$710$	−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	0.438881	−	0.898545i	$-0.355375\pi$
$719$	−3.21343	−	1.85527i	−0.119841	−	0.0691900i	−0.558722	+	0.829355i	$0.688708\pi$
$720$		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	$-0.898290\pi$
$727$		−	16.9392i		−	0.628241i	0.949383	−	0.314120i	$-0.101710\pi$
$728$	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	$-0.900848\pi$
$733$	−5.69951	+	9.87183i	−0.210516	+	0.364624i	0.741360	+	0.671107i	$0.234181\pi$
$734$	25.4861			0.940709
$735$		0			0
$736$			8.28995i			0.305572i
$737$	−4.01279	+	4.07181i	−0.147813	+	0.149987i
$738$		0			0
$739$	4.89454	−	2.82586i	0.180049	−	0.103951i	−0.407267	−	0.913309i	$-0.633518\pi$
$739$	4.89454	−	2.82586i	0.180049	−	0.103951i	0.587315	+	0.809358i	$0.300185\pi$
$740$	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	−0.914625	−	0.404304i	$-0.867514\pi$
$751$	−2.93707	+	5.08715i	−0.107175	+	0.185633i	0.807450	+	0.589936i	$0.200847\pi$
$752$	−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	$-0.699671\pi$
$761$	11.2463	−	19.4792i	0.407680	−	0.706122i	0.994629	+	0.103501i	$0.0330047\pi$
$762$		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	$-0.246631\pi$
$769$	39.6302			1.42910			0.714551	+	0.699583i	$0.246631\pi$
$770$	−19.7819	−	8.69419i	−0.712891	−	0.313317i
$771$		0			0
$772$	−3.04258	−	1.75664i	−0.109505	−	0.0632227i
$773$	13.6011	−	7.85260i	0.489198	−	0.282438i	−0.235044	−	0.971985i	$-0.575523\pi$
$773$	13.6011	−	7.85260i	0.489198	−	0.282438i	0.724242	+	0.689546i	$0.242190\pi$
$774$		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
$781$	9.15017	+	33.1782i	0.327419	+	1.18721i
$782$	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	−0.954067	−	0.299592i	$-0.903149\pi$
$787$	−20.6611	−	35.7861i	−0.736488	−	1.27563i	0.217579	−	0.976043i	$-0.430184\pi$
$788$	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	$0.116505\pi$
$797$			20.2076i			0.715789i	−0.933762	+	0.357894i	$0.883495\pi$
$798$		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
$803$	26.0097	−	26.3923i	0.917864	−	0.931363i
$804$		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	$-0.464687\pi$
$809$	29.2043	−	16.8611i	1.02677	−	0.592805i	0.916057	+	0.401048i	$0.131354\pi$
$810$		0			0
$811$	−9.84154			−0.345583			−0.172792	−	0.984958i	$-0.555279\pi$
$811$	−9.84154			−0.345583			−0.172792	+	0.984958i	$0.555279\pi$
$812$	−2.96321	−	2.41190i	−0.103988	−	0.0846411i
$813$		0			0
$814$	−11.6490	−	11.4801i	−0.408296	−	0.402378i
$815$	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	$-0.284267\pi$
$821$	7.61984	+	4.39932i	0.265934	+	0.153537i	−0.361104	+	0.932525i	$0.617600\pi$
$822$		0			0
$823$	16.4438	+	28.4815i	0.573195	+	0.992802i	0.996235	+	0.0866913i	$0.0276294\pi$
$823$	16.4438	+	28.4815i	0.573195	+	0.992802i	−0.423041	+	0.906111i	$0.639037\pi$
$824$	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	−0.893763	−	0.448540i	$-0.851944\pi$
$829$	−27.4160	+	15.8286i	−0.952198	+	0.549752i	−0.0584348	+	0.998291i	$0.518611\pi$
$830$	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
$836$	−3.90780	−	14.1695i	−0.135154	−	0.490064i
$837$		0			0
$838$	−11.3880	+	19.7246i	−0.393392	+	0.681375i
$839$			33.1104i			1.14310i	0.820568	+	0.571549i	$0.193657\pi$
$839$			33.1104i			1.14310i	−0.820568	+	0.571549i	$0.806343\pi$
$840$		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
$847$	22.8373	+	18.0405i	0.784697	+	0.619879i
$848$	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	$-0.310135\pi$
$853$	32.8121			1.12347			0.561733	+	0.827318i	$0.310135\pi$
$854$	−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	$-0.230575\pi$
$857$	−5.83813	−	10.1119i	−0.199427	−	0.345417i	−0.948343	+	0.317248i	$0.897241\pi$
$858$		0			0
$859$	−35.2623	−	20.3587i	−1.20314	−	0.694631i	−0.241885	−	0.970305i	$-0.577766\pi$
$859$	−35.2623	−	20.3587i	−1.20314	−	0.694631i	−0.961251	+	0.275674i	$0.911099\pi$
$860$	−23.7333			−0.809299
$861$		0			0
$862$	−30.8640			−1.05123
$863$	−9.04438	+	15.6653i	−0.307874	+	0.533254i	−0.977897	−	0.209087i	$-0.932951\pi$
$863$	−9.04438	+	15.6653i	−0.307874	+	0.533254i	0.670023	+	0.742341i	$0.266284\pi$
$864$		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	$-0.297676\pi$
$877$	5.73392	+	3.31048i	0.193621	+	0.111787i	−0.400056	+	0.916491i	$0.631009\pi$
$878$	−24.8302	+	14.3357i	−0.837980	+	0.483808i
$879$		0			0
$880$	−5.81703	−	5.73272i	−0.196092	−	0.193250i
$881$		−	16.5800i		−	0.558594i	−0.960205	−	0.279297i	$-0.909899\pi$
$881$		−	16.5800i		−	0.558594i	0.960205	−	0.279297i	$-0.0901014\pi$
$882$		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	0.451448	+	0.892297i	$0.350908\pi$
$887$	−16.2919	+	28.2184i	−0.547028	+	0.947480i	−0.998476	+	0.0551831i	$0.982426\pi$
$888$		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	0.974290	+	0.225296i	$0.0723350\pi$
$907$	20.5472	+	35.5887i	0.682257	+	1.18170i	−0.292033	+	0.956408i	$0.594332\pi$
$908$	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
$913$	−8.91626	−	32.3300i	−0.295085	−	1.06997i
$914$	−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	$-0.110151\pi$
$919$	33.8721	+	19.5561i	1.11734	+	0.645095i	0.176618	+	0.984280i	$0.443484\pi$
$920$	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	0.106930	−	0.994267i	$-0.465898\pi$
$929$	−21.3559	−	12.3298i	−0.700665	−	0.404529i	−0.807595	+	0.589737i	$0.799231\pi$
$930$		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
$935$	−35.2309	+	9.71627i	−1.15217	+	0.317756i
$936$		0			0
$937$	10.7483			0.351133			0.175566	−	0.984468i	$-0.443824\pi$
$937$	10.7483			0.351133			0.175566	+	0.984468i	$0.443824\pi$
$938$	−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	−0.998121	−	0.0612732i	$-0.980484\pi$
$941$	−16.9368	−	29.3354i	−0.552125	−	0.956308i	0.445996	−	0.895035i	$-0.352849\pi$
$942$		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	−0.646464	−	0.762944i	$-0.723753\pi$
$947$	10.3859	−	17.9889i	0.337497	−	0.584562i	0.983961	+	0.178382i	$0.0570863\pi$
$948$		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	$-0.252041\pi$
$968$	5.63849	+	9.44497i	0.181228	+	0.303573i
$969$		0			0
$970$	−2.93885	+	1.69674i	−0.0943607	+	0.0544792i
$971$	34.5497	+	19.9473i	1.10875	+	0.640138i	0.938506	−	0.345263i	$-0.112210\pi$
$971$	34.5497	+	19.9473i	1.10875	+	0.640138i	0.170246	+	0.985402i	$0.445544\pi$
$972$		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	0.852887	−	0.522095i	$-0.174849\pi$
$977$	−0.803424	−	1.39157i	−0.0257038	−	0.0445203i	−0.878591	+	0.477575i	$0.841516\pi$
$978$		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	−0.515575	−	0.856845i	$-0.672422\pi$
$983$	−0.981757	+	0.566818i	−0.0313132	+	0.0180787i	0.484262	+	0.874923i	$0.339088\pi$
$984$		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	0.904951	−	0.425515i	$-0.139907\pi$
$991$	2.64334	+	4.57840i	0.0839684	+	0.145438i	−0.820983	+	0.570953i	$0.806574\pi$
$992$	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	$-0.172163\pi$
$997$	−0.545190	−	0.944297i	−0.0172663	−	0.0299062i	−0.874529	+	0.484972i	$0.838830\pi$
$998$	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.a.901.4		16
3.2	odd	2		462.2.p.a.439.5	yes	16
7.3	odd	6		1386.2.bk.b.703.8		16
11.10	odd	2		1386.2.bk.b.901.8		16
21.2	odd	6		3234.2.e.a.2155.7		16
21.5	even	6		3234.2.e.b.2155.2		16
21.17	even	6		462.2.p.b.241.1	yes	16
33.32	even	2		462.2.p.b.439.1	yes	16
77.10	even	6	inner	1386.2.bk.a.703.4		16
231.65	even	6		3234.2.e.b.2155.15		16
231.131	odd	6		3234.2.e.a.2155.10		16
231.164	odd	6		462.2.p.a.241.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.5	✓	16	231.164	odd	6
462.2.p.a.439.5	yes	16	3.2	odd	2
462.2.p.b.241.1	yes	16	21.17	even	6
462.2.p.b.439.1	yes	16	33.32	even	2
1386.2.bk.a.703.4		16	77.10	even	6	inner
1386.2.bk.a.901.4		16	1.1	even	1	trivial
1386.2.bk.b.703.8		16	7.3	odd	6
1386.2.bk.b.901.8		16	11.10	odd	2
3234.2.e.a.2155.7		16	21.2	odd	6
3234.2.e.a.2155.10		16	231.131	odd	6
3234.2.e.b.2155.2		16	21.5	even	6
3234.2.e.b.2155.15		16	231.65	even	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.13257 + 1.23124i) q^{5} +(-0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.13257 + 1.23124i) q^{5} +(-0.941950 - 2.47239i) q^{7} -1.00000i q^{8} +(-1.23124 - 2.13257i) q^{10} +(0.881768 + 3.19726i) q^{11} -1.32035 q^{13} +(-0.420444 + 2.61213i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.23739 + 3.87528i) q^{17} +(-2.21589 + 3.83803i) q^{19} +2.46248i q^{20} +(0.834997 - 3.20979i) q^{22} +(-4.14497 + 7.17931i) q^{23} +(0.531907 + 0.921289i) q^{25} +(1.14346 + 0.660177i) q^{26} +(1.67018 - 2.05195i) q^{28} -1.44409i q^{29} +(2.34801 - 1.35562i) q^{31} +(0.866025 - 0.500000i) q^{32} -4.47479i q^{34} +(1.03534 - 6.43232i) q^{35} +(2.46563 - 4.27060i) q^{37} +(3.83803 - 2.21589i) q^{38} +(1.23124 - 2.13257i) q^{40} +8.18233 q^{41} +9.63797i q^{43} +(-2.32803 + 2.36226i) q^{44} +(7.17931 - 4.14497i) q^{46} +(0.664664 + 0.383744i) q^{47} +(-5.22546 + 4.65774i) q^{49} -1.06381i q^{50} +(-0.660177 - 1.14346i) q^{52} +(-0.945971 - 1.63847i) q^{53} +(-2.05616 + 7.90406i) q^{55} +(-2.47239 + 0.941950i) q^{56} +(-0.722047 + 1.25062i) q^{58} +(-6.74444 + 3.89390i) q^{59} +(-2.23943 + 3.87880i) q^{61} -2.71125 q^{62} -1.00000 q^{64} +(-2.81575 - 1.62567i) q^{65} +(0.861844 + 1.49276i) q^{67} +(-2.23739 + 3.87528i) q^{68} +(-4.11279 + 5.05289i) q^{70} +10.3771 q^{71} +(-5.58622 - 9.67562i) q^{73} +(-4.27060 + 2.46563i) q^{74} -4.43177 q^{76} +(7.07431 - 5.19174i) q^{77} +(2.53630 + 1.46433i) q^{79} +(-2.13257 + 1.23124i) q^{80} +(-7.08611 - 4.09116i) q^{82} -10.1118 q^{83} +11.0191i q^{85} +(4.81898 - 8.34672i) q^{86} +(3.19726 - 0.881768i) q^{88} +(10.9590 + 6.32720i) q^{89} +(1.24371 + 3.26444i) q^{91} -8.28995 q^{92} +(-0.383744 - 0.664664i) q^{94} +(-9.45107 + 5.45658i) q^{95} -1.37808i q^{97} +(6.85425 - 1.42099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7} + 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} - 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} + 8 q^{35} + 14 q^{37} + 12 q^{38} - 2 q^{40} - 32 q^{41} - 4 q^{44} + 18 q^{46} + 24 q^{47} - 6 q^{49} - 14 q^{55} - 4 q^{56} + 28 q^{61} + 8 q^{62} - 16 q^{64} - 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} - 44 q^{73} - 24 q^{74} - 20 q^{76} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} + 14 q^{94} - 72 q^{95} + 40 q^{98}+O(q^{100}) \) 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 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 + 14 * q^94 - 72 * q^95 + 40 * q^98

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