LMFDB - Embedded newform 2646.2.f.n.1765.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1765.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2646.1765
Dual form			2646.2.f.n.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} -1.00000 q^{8} -1.76088 q^{10} +(3.06238 + 5.30420i) q^{11} +(0.380438 - 0.658939i) q^{13} +(-0.500000 - 0.866025i) q^{16} +6.84213 q^{17} +1.94282 q^{19} +(-0.880438 - 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} +(-0.210533 + 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +0.760877 q^{26} +(-0.732287 - 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.42107 + 5.92546i) q^{34} -2.88564 q^{37} +(0.971410 + 1.68253i) q^{38} +(0.880438 - 1.52496i) q^{40} +(-3.47141 + 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} -6.12476 q^{44} -0.421067 q^{46} +(-0.830095 - 1.43777i) q^{47} +(-0.949657 + 1.64485i) q^{50} +(0.380438 + 0.658939i) q^{52} -0.225450 q^{53} -10.7850 q^{55} +(0.732287 - 1.26836i) q^{58} +(-0.993163 + 1.72021i) q^{59} +(-5.17511 - 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(0.669905 + 1.16031i) q^{65} +(-3.39248 + 5.87594i) q^{67} +(-3.42107 + 5.92546i) q^{68} -10.7850 q^{71} +0.306707 q^{73} +(-1.44282 - 2.49904i) q^{74} +(-0.971410 + 1.68253i) q^{76} +(6.72257 + 11.6438i) q^{79} +1.76088 q^{80} -6.94282 q^{82} +(-1.56238 - 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +(-4.33009 + 7.49994i) q^{86} +(-3.06238 - 5.30420i) q^{88} -2.60301 q^{89} +(-0.210533 - 0.364654i) q^{92} +(0.830095 - 1.43777i) q^{94} +(-1.71053 + 2.96273i) q^{95} +(1.81806 + 3.14897i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8} - 10 q^{10} + q^{11} + 2 q^{13} - 3 q^{16} + 8 q^{17} - 6 q^{19} - 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} + 4 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34}+ \cdots + 28 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 5 * q^5 - 6 * q^8 - 10 * q^10 + q^11 + 2 * q^13 - 3 * q^16 + 8 * q^17 - 6 * q^19 - 5 * q^20 - q^22 + 7 * q^23 - 2 * q^25 + 4 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 + 18 * q^37 - 3 * q^38 + 5 * q^40 - 12 * q^41 + 18 * q^43 - 2 * q^44 + 14 * q^46 + 3 * q^47 + 2 * q^50 + 2 * q^52 + 18 * q^53 - 14 * q^55 - 5 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 - 4 * q^68 - 14 * q^71 - 50 * q^73 + 9 * q^74 + 3 * q^76 + 7 * q^79 + 10 * q^80 - 24 * q^82 + 8 * q^83 + 14 * q^85 - 18 * q^86 - q^88 + 18 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	−0.992940	−	0.118618i	$-0.962154\pi$
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	0.599196	+	0.800602i	$0.295487\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.76088			−0.556838
$11$	3.06238	+	5.30420i	0.923343	+	1.59928i	0.794205	+	0.607650i	$0.207888\pi$
$11$	3.06238	+	5.30420i	0.923343	+	1.59928i	0.129138	+	0.991627i	$0.458779\pi$
$12$		0			0
$13$	0.380438	−	0.658939i	0.105515	−	0.182757i	−0.808434	−	0.588587i	$-0.799684\pi$
$13$	0.380438	−	0.658939i	0.105515	−	0.182757i	0.913948	+	0.405831i	$0.133018\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.84213			1.65946			0.829731	−	0.558164i	$-0.188494\pi$
$17$	6.84213			1.65946			0.829731	+	0.558164i	$0.188494\pi$
$18$		0			0
$19$	1.94282			0.445713			0.222857	−	0.974851i	$-0.428462\pi$
$19$	1.94282			0.445713			0.222857	+	0.974851i	$0.428462\pi$
$20$	−0.880438	−	1.52496i	−0.196872	−	0.340992i
$21$		0			0
$22$	−3.06238	+	5.30420i	−0.652902	+	1.13086i
$23$	−0.210533	+	0.364654i	−0.0438992	+	0.0760357i	−0.887140	−	0.461500i	$-0.847311\pi$
$23$	−0.210533	+	0.364654i	−0.0438992	+	0.0760357i	0.843241	+	0.537536i	$0.180645\pi$
$24$		0			0
$25$	0.949657	+	1.64485i	0.189931	+	0.328971i
$26$	0.760877			0.149220
$27$		0			0
$28$		0			0
$29$	−0.732287	−	1.26836i	−0.135982	−	0.235528i	0.789990	−	0.613120i	$-0.210086\pi$
$29$	−0.732287	−	1.26836i	−0.135982	−	0.235528i	−0.925972	+	0.377592i	$0.876752\pi$
$30$		0			0
$31$	3.85185	−	6.67160i	0.691812	−	1.19825i	−0.279431	−	0.960166i	$-0.590146\pi$
$31$	3.85185	−	6.67160i	0.691812	−	1.19825i	0.971243	−	0.238088i	$-0.0765208\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.42107	+	5.92546i	0.586708	+	1.01621i
$35$		0			0
$36$		0			0
$37$	−2.88564			−0.474396			−0.237198	−	0.971461i	$-0.576229\pi$
$37$	−2.88564			−0.474396			−0.237198	+	0.971461i	$0.576229\pi$
$38$	0.971410	+	1.68253i	0.157584	+	0.272943i
$39$		0			0
$40$	0.880438	−	1.52496i	0.139210	−	0.241118i
$41$	−3.47141	+	6.01266i	−0.542143	+	0.939020i	0.456638	+	0.889653i	$0.349054\pi$
$41$	−3.47141	+	6.01266i	−0.542143	+	0.939020i	−0.998781	+	0.0493667i	$0.984280\pi$
$42$		0			0
$43$	4.33009	+	7.49994i	0.660333	+	1.14373i	0.980528	+	0.196379i	$0.0629183\pi$
$43$	4.33009	+	7.49994i	0.660333	+	1.14373i	−0.320195	+	0.947352i	$0.603748\pi$
$44$	−6.12476			−0.923343
$45$		0			0
$46$	−0.421067			−0.0620829
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	0.799113	−	0.601181i	$-0.205303\pi$
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	−0.920195	+	0.391461i	$0.871970\pi$
$48$		0			0
$49$		0			0
$50$	−0.949657	+	1.64485i	−0.134302	+	0.232617i
$51$		0			0
$52$	0.380438	+	0.658939i	0.0527573	+	0.0913783i
$53$	−0.225450			−0.0309680			−0.0154840	−	0.999880i	$-0.504929\pi$
$53$	−0.225450			−0.0309680			−0.0154840	+	0.999880i	$0.504929\pi$
$54$		0			0
$55$	−10.7850			−1.45424
$56$		0			0
$57$		0			0
$58$	0.732287	−	1.26836i	0.0961540	−	0.166544i
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	−0.923405	−	0.383827i	$-0.874606\pi$
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	0.794106	+	0.607779i	$0.207939\pi$
$60$		0			0
$61$	−5.17511	−	8.96355i	−0.662605	−	1.14766i	−0.979929	−	0.199348i	$-0.936118\pi$
$61$	−5.17511	−	8.96355i	−0.662605	−	1.14766i	0.317324	−	0.948317i	$-0.397216\pi$
$62$	7.70370			0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	0.669905	+	1.16031i	0.0830915	+	0.143919i
$66$		0			0
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	−0.995371	−	0.0961042i	$-0.969362\pi$
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	0.580914	+	0.813965i	$0.302695\pi$
$68$	−3.42107	+	5.92546i	−0.414865	+	0.718568i
$69$		0			0
$70$		0			0
$71$	−10.7850			−1.27994			−0.639969	−	0.768401i	$-0.721053\pi$
$71$	−10.7850			−1.27994			−0.639969	+	0.768401i	$0.721053\pi$
$72$		0			0
$73$	0.306707			0.0358973			0.0179487	−	0.999839i	$-0.494286\pi$
$73$	0.306707			0.0358973			0.0179487	+	0.999839i	$0.494286\pi$
$74$	−1.44282	−	2.49904i	−0.167724	−	0.290507i
$75$		0			0
$76$	−0.971410	+	1.68253i	−0.111428	+	0.193000i
$77$		0			0
$78$		0			0
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	0.944701	+	0.327932i	$0.106352\pi$
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	−0.188353	+	0.982101i	$0.560315\pi$
$80$	1.76088			0.196872
$81$		0			0
$82$	−6.94282			−0.766706
$83$	−1.56238	−	2.70612i	−0.171494	−	0.297036i	0.767449	−	0.641110i	$-0.221526\pi$
$83$	−1.56238	−	2.70612i	−0.171494	−	0.297036i	−0.938942	+	0.344075i	$0.888193\pi$
$84$		0			0
$85$	−6.02408	+	10.4340i	−0.653403	+	1.13173i
$86$	−4.33009	+	7.49994i	−0.466926	+	0.808740i
$87$		0			0
$88$	−3.06238	−	5.30420i	−0.326451	−	0.565430i
$89$	−2.60301			−0.275919			−0.137959	−	0.990438i	$-0.544054\pi$
$89$	−2.60301			−0.275919			−0.137959	+	0.990438i	$0.544054\pi$
$90$		0			0
$91$		0			0
$92$	−0.210533	−	0.364654i	−0.0219496	−	0.0380178i
$93$		0			0
$94$	0.830095	−	1.43777i	0.0856178	−	0.148294i
$95$	−1.71053	+	2.96273i	−0.175497	+	0.303970i
$96$		0			0
$97$	1.81806	+	3.14897i	0.184596	+	0.319729i	0.943440	−	0.331543i	$-0.107569\pi$
$97$	1.81806	+	3.14897i	0.184596	+	0.319729i	−0.758845	+	0.651272i	$0.774236\pi$
$98$		0			0
$99$		0			0
$100$	−1.89931			−0.189931
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	0.993545	−	0.113438i	$-0.0361863\pi$
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	−0.595013	+	0.803716i	$0.702853\pi$
$102$		0			0
$103$	−3.41423	+	5.91362i	−0.336414	+	0.582686i	−0.983755	−	0.179514i	$-0.942548\pi$
$103$	−3.41423	+	5.91362i	−0.336414	+	0.582686i	0.647341	+	0.762200i	$0.275881\pi$
$104$	−0.380438	+	0.658939i	−0.0373051	+	0.0646142i
$105$		0			0
$106$	−0.112725	−	0.195246i	−0.0109488	−	0.0189639i
$107$	3.54583			0.342788			0.171394	−	0.985203i	$-0.445173\pi$
$107$	3.54583			0.342788			0.171394	+	0.985203i	$0.445173\pi$
$108$		0			0
$109$	−0.703697			−0.0674019			−0.0337010	−	0.999432i	$-0.510729\pi$
$109$	−0.703697			−0.0674019			−0.0337010	+	0.999432i	$0.510729\pi$
$110$	−5.39248	−	9.34004i	−0.514152	−	0.890538i
$111$		0			0
$112$		0			0
$113$	−4.25116	+	7.36323i	−0.399916	+	0.692674i	−0.993715	−	0.111939i	$-0.964294\pi$
$113$	−4.25116	+	7.36323i	−0.399916	+	0.692674i	0.593799	+	0.804613i	$0.297627\pi$
$114$		0			0
$115$	−0.370723	−	0.642111i	−0.0345701	−	0.0598772i
$116$	1.46457			0.135982
$117$		0			0
$118$	−1.98633			−0.182856
$119$		0			0
$120$		0			0
$121$	−13.2564	+	22.9607i	−1.20512	+	2.08734i
$122$	5.17511	−	8.96355i	0.468532	−	0.811521i
$123$		0			0
$124$	3.85185	+	6.67160i	0.345906	+	0.599127i
$125$	−12.1488			−1.08663
$126$		0			0
$127$	−18.9532			−1.68183			−0.840913	−	0.541170i	$-0.817982\pi$
$127$	−18.9532			−1.68183			−0.840913	+	0.541170i	$0.817982\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.669905	+	1.16031i	−0.0587546	+	0.101766i
$131$	3.64652	−	6.31595i	0.318598	−	0.551827i	−0.661598	−	0.749859i	$-0.730121\pi$
$131$	3.64652	−	6.31595i	0.318598	−	0.551827i	0.980196	+	0.198031i	$0.0634548\pi$
$132$		0			0
$133$		0			0
$134$	−6.78495			−0.586131
$135$		0			0
$136$	−6.84213			−0.586708
$137$	−4.09097	−	7.08577i	−0.349515	−	0.605378i	0.636648	−	0.771154i	$-0.280320\pi$
$137$	−4.09097	−	7.08577i	−0.349515	−	0.605378i	−0.986163	+	0.165776i	$0.946987\pi$
$138$		0			0
$139$	6.23229	−	10.7946i	0.528616	−	0.915589i	−0.470828	−	0.882225i	$-0.656045\pi$
$139$	6.23229	−	10.7946i	0.528616	−	0.915589i	0.999443	−	0.0333640i	$-0.0106220\pi$
$140$		0			0
$141$		0			0
$142$	−5.39248	−	9.34004i	−0.452527	−	0.783799i
$143$	4.66019			0.389705
$144$		0			0
$145$	2.57893			0.214169
$146$	0.153353	+	0.265616i	0.0126916	+	0.0219825i
$147$		0			0
$148$	1.44282	−	2.49904i	0.118599	−	0.205420i
$149$	4.41423	−	7.64567i	0.361628	−	0.626358i	−0.626601	−	0.779340i	$-0.715554\pi$
$149$	4.41423	−	7.64567i	0.361628	−	0.626358i	0.988229	+	0.152982i	$0.0488878\pi$
$150$		0			0
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	0.991276	+	0.131806i	$0.0420775\pi$
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	−0.381491	+	0.924373i	$0.624589\pi$
$152$	−1.94282			−0.157584
$153$		0			0
$154$		0			0
$155$	6.78263	+	11.7479i	0.544794	+	0.943611i
$156$		0			0
$157$	9.49028	−	16.4377i	0.757407	−	1.31187i	−0.186761	−	0.982405i	$-0.559799\pi$
$157$	9.49028	−	16.4377i	0.757407	−	1.31187i	0.944169	−	0.329462i	$-0.106868\pi$
$158$	−6.72257	+	11.6438i	−0.534819	+	0.926334i
$159$		0			0
$160$	0.880438	+	1.52496i	0.0696048	+	0.120559i
$161$		0			0
$162$		0			0
$163$	15.0377			1.17785			0.588924	−	0.808189i	$-0.299552\pi$
$163$	15.0377			1.17785			0.588924	+	0.808189i	$0.299552\pi$
$164$	−3.47141	−	6.01266i	−0.271072	−	0.469510i
$165$		0			0
$166$	1.56238	−	2.70612i	0.121264	−	0.210036i
$167$	0.572097	−	0.990901i	0.0442702	−	0.0766782i	−0.843041	−	0.537849i	$-0.819237\pi$
$167$	0.572097	−	0.990901i	0.0442702	−	0.0766782i	0.887311	+	0.461171i	$0.152570\pi$
$168$		0			0
$169$	6.21053	+	10.7570i	0.477733	+	0.827458i
$170$	−12.0482			−0.924051
$171$		0			0
$172$	−8.66019			−0.660333
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	0.856411	−	0.516295i	$-0.172689\pi$
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	−0.875330	+	0.483526i	$0.839356\pi$
$174$		0			0
$175$		0			0
$176$	3.06238	−	5.30420i	0.230836	−	0.399819i
$177$		0			0
$178$	−1.30150	−	2.25427i	−0.0975519	−	0.168965i
$179$	8.82846			0.659870			0.329935	−	0.944004i	$-0.392973\pi$
$179$	8.82846			0.659870			0.329935	+	0.944004i	$0.392973\pi$
$180$		0			0
$181$	−1.32941			−0.0988140			−0.0494070	−	0.998779i	$-0.515733\pi$
$181$	−1.32941			−0.0988140			−0.0494070	+	0.998779i	$0.515733\pi$
$182$		0			0
$183$		0			0
$184$	0.210533	−	0.364654i	0.0155207	−	0.0268827i
$185$	2.54063	−	4.40050i	0.186791	−	0.323531i
$186$		0			0
$187$	20.9532	+	36.2920i	1.53225	+	2.65394i
$188$	1.66019			0.121082
$189$		0			0
$190$	−3.42107			−0.248190
$191$	−8.08414	−	14.0021i	−0.584947	−	1.01316i	−0.994882	−	0.101044i	$-0.967782\pi$
$191$	−8.08414	−	14.0021i	−0.584947	−	1.01316i	0.409934	−	0.912115i	$-0.365552\pi$
$192$		0			0
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	−0.490007	−	0.871719i	$-0.663006\pi$
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	0.999934	−	0.0115011i	$-0.00366101\pi$
$194$	−1.81806	+	3.14897i	−0.130529	+	0.226083i
$195$		0			0
$196$		0			0
$197$	−15.8421			−1.12871			−0.564353	−	0.825534i	$-0.690874\pi$
$197$	−15.8421			−1.12871			−0.564353	+	0.825534i	$0.690874\pi$
$198$		0			0
$199$	−8.94282			−0.633940			−0.316970	−	0.948436i	$-0.602665\pi$
$199$	−8.94282			−0.633940			−0.316970	+	0.948436i	$0.602665\pi$
$200$	−0.949657	−	1.64485i	−0.0671509	−	0.116309i
$201$		0			0
$202$	−4.00520	+	6.93721i	−0.281805	+	0.488101i
$203$		0			0
$204$		0			0
$205$	−6.11273	−	10.5876i	−0.426931	−	0.739467i
$206$	−6.82846			−0.475761
$207$		0			0
$208$	−0.760877			−0.0527573
$209$	5.94966	+	10.3051i	0.411546	+	0.712819i
$210$		0			0
$211$	11.3856	−	19.7205i	0.783820	−	1.35762i	−0.145882	−	0.989302i	$-0.546602\pi$
$211$	11.3856	−	19.7205i	0.783820	−	1.35762i	0.929702	−	0.368314i	$-0.120065\pi$
$212$	0.112725	−	0.195246i	0.00774199	−	0.0134095i
$213$		0			0
$214$	1.77292	+	3.07078i	0.121194	+	0.209914i
$215$	−15.2495			−1.04001
$216$		0			0
$217$		0			0
$218$	−0.351848	−	0.609419i	−0.0238302	−	0.0412751i
$219$		0			0
$220$	5.39248	−	9.34004i	0.363561	−	0.629706i
$221$	2.60301	−	4.50855i	0.175097	−	0.303278i
$222$		0			0
$223$	6.44282	+	11.1593i	0.431443	+	0.747281i	0.996998	−	0.0774293i	$-0.0246712\pi$
$223$	6.44282	+	11.1593i	0.431443	+	0.747281i	−0.565555	+	0.824711i	$0.691338\pi$
$224$		0			0
$225$		0			0
$226$	−8.50232			−0.565566
$227$	−10.9984	−	19.0497i	−0.729987	−	1.26437i	−0.956888	−	0.290457i	$-0.906193\pi$
$227$	−10.9984	−	19.0497i	−0.729987	−	1.26437i	0.226901	−	0.973918i	$-0.427141\pi$
$228$		0			0
$229$	−1.89931	+	3.28971i	−0.125510	+	0.217390i	−0.921932	−	0.387351i	$-0.873390\pi$
$229$	−1.89931	+	3.28971i	−0.125510	+	0.217390i	0.796422	+	0.604741i	$0.206723\pi$
$230$	0.370723	−	0.642111i	0.0244448	−	0.0423396i
$231$		0			0
$232$	0.732287	+	1.26836i	0.0480770	+	0.0832718i
$233$	−6.67059			−0.437005			−0.218503	−	0.975836i	$-0.570117\pi$
$233$	−6.67059			−0.437005			−0.218503	+	0.975836i	$0.570117\pi$
$234$		0			0
$235$	2.92339			0.190701
$236$	−0.993163	−	1.72021i	−0.0646494	−	0.111976i
$237$		0			0
$238$		0			0
$239$	7.82038	−	13.5453i	0.505858	−	0.876172i	−0.494119	−	0.869394i	$-0.664509\pi$
$239$	7.82038	−	13.5453i	0.505858	−	0.876172i	0.999977	−	0.00677786i	$-0.00215748\pi$
$240$		0			0
$241$	10.7060	+	18.5434i	0.689635	+	1.19448i	0.971956	+	0.235163i	$0.0755625\pi$
$241$	10.7060	+	18.5434i	0.689635	+	1.19448i	−0.282320	+	0.959320i	$0.591104\pi$
$242$	−26.5127			−1.70430
$243$		0			0
$244$	10.3502			0.662605
$245$		0			0
$246$		0			0
$247$	0.739123	−	1.28020i	0.0470293	−	0.0814571i
$248$	−3.85185	+	6.67160i	−0.244593	+	0.423647i
$249$		0			0
$250$	−6.07442	−	10.5212i	−0.384180	−	0.665419i
$251$	−23.6030			−1.48981			−0.744904	−	0.667171i	$-0.767505\pi$
$251$	−23.6030			−1.48981			−0.744904	+	0.667171i	$0.767505\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$	−9.47661	−	16.4140i	−0.594616	−	1.02990i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	0.355275	+	0.934762i	$0.384387\pi$
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	−0.987165	+	0.159704i	$0.948946\pi$
$258$		0			0
$259$		0			0
$260$	−1.33981			−0.0830915
$261$		0			0
$262$	7.29303			0.450565
$263$	−11.2443	−	19.4757i	−0.693355	−	1.20093i	−0.970732	−	0.240165i	$-0.922799\pi$
$263$	−11.2443	−	19.4757i	−0.693355	−	1.20093i	0.277377	−	0.960761i	$-0.410535\pi$
$264$		0			0
$265$	0.198495	−	0.343803i	0.0121935	−	0.0211197i
$266$		0			0
$267$		0			0
$268$	−3.39248	−	5.87594i	−0.207228	−	0.358930i
$269$	25.3412			1.54508			0.772540	−	0.634966i	$-0.218986\pi$
$269$	25.3412			1.54508			0.772540	+	0.634966i	$0.218986\pi$
$270$		0			0
$271$	−13.7576			−0.835715			−0.417858	−	0.908513i	$-0.637219\pi$
$271$	−13.7576			−0.835715			−0.417858	+	0.908513i	$0.637219\pi$
$272$	−3.42107	−	5.92546i	−0.207433	−	0.359284i
$273$		0			0
$274$	4.09097	−	7.08577i	0.247145	−	0.428067i
$275$	−5.81642	+	10.0743i	−0.350743	+	0.607505i
$276$		0			0
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	0.911112	−	0.412158i	$-0.135225\pi$
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	−0.812495	+	0.582968i	$0.801891\pi$
$278$	12.4646			0.747575
$279$		0			0
$280$		0			0
$281$	−0.634479	−	1.09895i	−0.0378498	−	0.0655578i	0.846480	−	0.532421i	$-0.178718\pi$
$281$	−0.634479	−	1.09895i	−0.0378498	−	0.0655578i	−0.884330	+	0.466863i	$0.845384\pi$
$282$		0			0
$283$	−4.09617	+	7.09478i	−0.243492	+	0.421741i	−0.961707	−	0.274081i	$-0.911626\pi$
$283$	−4.09617	+	7.09478i	−0.243492	+	0.421741i	0.718214	+	0.695822i	$0.244960\pi$
$284$	5.39248	−	9.34004i	0.319985	−	0.554230i
$285$		0			0
$286$	2.33009	+	4.03584i	0.137781	+	0.238644i
$287$		0			0
$288$		0			0
$289$	29.8148			1.75381
$290$	1.28947	+	2.23342i	0.0757201	+	0.131151i
$291$		0			0
$292$	−0.153353	+	0.265616i	−0.00897433	+	0.0155440i
$293$	7.72545	−	13.3809i	0.451326	−	0.781719i	−0.547143	−	0.837039i	$-0.684285\pi$
$293$	7.72545	−	13.3809i	0.451326	−	0.781719i	0.998469	+	0.0553202i	$0.0176180\pi$
$294$		0			0
$295$	−1.74884	−	3.02908i	−0.101821	−	0.176360i
$296$	2.88564			0.167724
$297$		0			0
$298$	8.82846			0.511419
$299$	0.160190	+	0.277457i	0.00926402	+	0.0160458i
$300$		0			0
$301$		0			0
$302$	−7.49316	+	12.9785i	−0.431183	+	0.746831i
$303$		0			0
$304$	−0.971410	−	1.68253i	−0.0557142	−	0.0964998i
$305$	18.2255			1.04359
$306$		0			0
$307$	−4.89931			−0.279619			−0.139809	−	0.990178i	$-0.544649\pi$
$307$	−4.89931			−0.279619			−0.139809	+	0.990178i	$0.544649\pi$
$308$		0			0
$309$		0			0
$310$	−6.78263	+	11.7479i	−0.385228	+	0.667234i
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	−0.736175	−	0.676791i	$-0.763370\pi$
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	0.954206	+	0.299151i	$0.0967034\pi$
$312$		0			0
$313$	−0.861564	−	1.49227i	−0.0486985	−	0.0843482i	0.840649	−	0.541581i	$-0.182174\pi$
$313$	−0.861564	−	1.49227i	−0.0486985	−	0.0843482i	−0.889347	+	0.457233i	$0.848841\pi$
$314$	18.9806			1.07114
$315$		0			0
$316$	−13.4451			−0.756348
$317$	16.6014	+	28.7544i	0.932426	+	1.61501i	0.779161	+	0.626824i	$0.215646\pi$
$317$	16.6014	+	28.7544i	0.932426	+	1.61501i	0.153266	+	0.988185i	$0.451021\pi$
$318$		0			0
$319$	4.48508	−	7.76839i	0.251116	−	0.434946i
$320$	−0.880438	+	1.52496i	−0.0492180	+	0.0852481i
$321$		0			0
$322$		0			0
$323$	13.2930			0.739644
$324$		0			0
$325$	1.44514			0.0801621
$326$	7.51887	+	13.0231i	0.416432	+	0.721281i
$327$		0			0
$328$	3.47141	−	6.01266i	0.191677	−	0.331994i
$329$		0			0
$330$		0			0
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	0.823594	−	0.567179i	$-0.191965\pi$
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	−0.902989	+	0.429664i	$0.858632\pi$
$332$	3.12476			0.171494
$333$		0			0
$334$	1.14419			0.0626075
$335$	−5.97373	−	10.3468i	−0.326380	−	0.565307i
$336$		0			0
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	−0.960022	−	0.279924i	$-0.909691\pi$
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	0.722433	+	0.691441i	$0.243024\pi$
$338$	−6.21053	+	10.7570i	−0.337808	+	0.585101i
$339$		0			0
$340$	−6.02408	−	10.4340i	−0.326701	−	0.565863i
$341$	47.1833			2.55512
$342$		0			0
$343$		0			0
$344$	−4.33009	−	7.49994i	−0.233463	−	0.404370i
$345$		0			0
$346$	0.248838	−	0.431001i	0.0133776	−	0.0231707i
$347$	4.84733	−	8.39583i	0.260219	−	0.450712i	−0.706081	−	0.708131i	$-0.749539\pi$
$347$	4.84733	−	8.39583i	0.260219	−	0.450712i	0.966300	+	0.257419i	$0.0828720\pi$
$348$		0			0
$349$	−14.1992	−	24.5937i	−0.760065	−	1.31647i	−0.942817	−	0.333312i	$-0.891834\pi$
$349$	−14.1992	−	24.5937i	−0.760065	−	1.31647i	0.182752	−	0.983159i	$-0.441500\pi$
$350$		0			0
$351$		0			0
$352$	6.12476			0.326451
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	0.918548	−	0.395308i	$-0.129362\pi$
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	−0.801621	+	0.597832i	$0.796029\pi$
$354$		0			0
$355$	9.49549	−	16.4467i	0.503968	−	0.872898i
$356$	1.30150	−	2.25427i	0.0689796	−	0.119476i
$357$		0			0
$358$	4.41423	+	7.64567i	0.233299	+	0.404086i
$359$	32.1592			1.69730			0.848650	−	0.528955i	$-0.177416\pi$
$359$	32.1592			1.69730			0.848650	+	0.528955i	$0.177416\pi$
$360$		0			0
$361$	−15.2255			−0.801339
$362$	−0.664703	−	1.15130i	−0.0349360	−	0.0605110i
$363$		0			0
$364$		0			0
$365$	−0.270036	+	0.467717i	−0.0141343	+	0.0244814i
$366$		0			0
$367$	17.3015	+	29.9671i	0.903131	+	1.56427i	0.823406	+	0.567452i	$0.192071\pi$
$367$	17.3015	+	29.9671i	0.903131	+	1.56427i	0.0797249	+	0.996817i	$0.474596\pi$
$368$	0.421067			0.0219496
$369$		0			0
$370$	5.08126			0.264162
$371$		0			0
$372$		0			0
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$374$	−20.9532	+	36.2920i	−1.08347	+	1.87662i
$375$		0			0
$376$	0.830095	+	1.43777i	0.0428089	+	0.0741472i
$377$	−1.11436			−0.0573925
$378$		0			0
$379$	33.9877			1.74583			0.872916	−	0.487871i	$-0.162226\pi$
$379$	33.9877			1.74583			0.872916	+	0.487871i	$0.162226\pi$
$380$	−1.71053	−	2.96273i	−0.0877485	−	0.151985i
$381$		0			0
$382$	8.08414	−	14.0021i	0.413620	−	0.716411i
$383$	10.5120	−	18.2074i	0.537140	−	0.930354i	−0.461916	−	0.886923i	$-0.652838\pi$
$383$	10.5120	−	18.2074i	0.537140	−	0.930354i	0.999056	−	0.0434304i	$-0.0138287\pi$
$384$		0			0
$385$		0			0
$386$	14.1683			0.721146
$387$		0			0
$388$	−3.63611			−0.184596
$389$	6.86909	+	11.8976i	0.348277	+	0.603233i	0.985943	−	0.167080i	$-0.0534337\pi$
$389$	6.86909	+	11.8976i	0.348277	+	0.603233i	−0.637667	+	0.770312i	$0.720100\pi$
$390$		0			0
$391$	−1.44050	+	2.49501i	−0.0728491	+	0.126178i
$392$		0			0
$393$		0			0
$394$	−7.92107	−	13.7197i	−0.399058	−	0.691188i
$395$	−23.6752			−1.19123
$396$		0			0
$397$	−7.15787			−0.359243			−0.179622	−	0.983736i	$-0.557487\pi$
$397$	−7.15787			−0.359243			−0.179622	+	0.983736i	$0.557487\pi$
$398$	−4.47141	−	7.74471i	−0.224132	−	0.388207i
$399$		0			0
$400$	0.949657	−	1.64485i	0.0474828	−	0.0822427i
$401$	−4.63968	+	8.03616i	−0.231695	+	0.401307i	−0.958307	−	0.285741i	$-0.907760\pi$
$401$	−4.63968	+	8.03616i	−0.231695	+	0.401307i	0.726612	+	0.687048i	$0.241094\pi$
$402$		0			0
$403$	−2.93078	−	5.07626i	−0.145993	−	0.252867i
$404$	−8.01040			−0.398532
$405$		0			0
$406$		0			0
$407$	−8.83693	−	15.3060i	−0.438030	−	0.758691i
$408$		0			0
$409$	7.58414	−	13.1361i	0.375011	−	0.649539i	−0.615317	−	0.788279i	$-0.710972\pi$
$409$	7.58414	−	13.1361i	0.375011	−	0.649539i	0.990329	+	0.138741i	$0.0443055\pi$
$410$	6.11273	−	10.5876i	0.301886	−	0.522882i
$411$		0			0
$412$	−3.41423	−	5.91362i	−0.168207	−	0.291343i
$413$		0			0
$414$		0			0
$415$	5.50232			0.270098
$416$	−0.380438	−	0.658939i	−0.0186525	−	0.0323071i
$417$		0			0
$418$	−5.94966	+	10.3051i	−0.291007	+	0.504039i
$419$	−4.16827	+	7.21966i	−0.203633	+	0.352703i	−0.949696	−	0.313172i	$-0.898608\pi$
$419$	−4.16827	+	7.21966i	−0.203633	+	0.352703i	0.746063	+	0.665875i	$0.231942\pi$
$420$		0			0
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	0.767969	−	0.640486i	$-0.221267\pi$
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	−0.938662	+	0.344838i	$0.887934\pi$
$422$	22.7713			1.10849
$423$		0			0
$424$	0.225450			0.0109488
$425$	6.49768	+	11.2543i	0.315184	+	0.545914i
$426$		0			0
$427$		0			0
$428$	−1.77292	+	3.07078i	−0.0856971	+	0.148432i
$429$		0			0
$430$	−7.62476	−	13.2065i	−0.367699	−	0.636873i
$431$	−3.45090			−0.166224			−0.0831120	−	0.996540i	$-0.526486\pi$
$431$	−3.45090			−0.166224			−0.0831120	+	0.996540i	$0.526486\pi$
$432$		0			0
$433$	−28.2599			−1.35809			−0.679043	−	0.734099i	$-0.737605\pi$
$433$	−28.2599			−1.35809			−0.679043	+	0.734099i	$0.737605\pi$
$434$		0			0
$435$		0			0
$436$	0.351848	−	0.609419i	0.0168505	−	0.0291859i
$437$	−0.409028	+	0.708458i	−0.0195665	+	0.0338901i
$438$		0			0
$439$	−14.4480	−	25.0247i	−0.689566	−	1.19436i	−0.971978	−	0.235071i	$-0.924468\pi$
$439$	−14.4480	−	25.0247i	−0.689566	−	1.19436i	0.282412	−	0.959293i	$-0.408866\pi$
$440$	10.7850			0.514152
$441$		0			0
$442$	5.20602			0.247625
$443$	−6.88044	−	11.9173i	−0.326899	−	0.566207i	0.654995	−	0.755633i	$-0.272671\pi$
$443$	−6.88044	−	11.9173i	−0.326899	−	0.566207i	−0.981895	+	0.189426i	$0.939337\pi$
$444$		0			0
$445$	2.29179	−	3.96950i	0.108641	−	0.188172i
$446$	−6.44282	+	11.1593i	−0.305076	+	0.528408i
$447$		0			0
$448$		0			0
$449$	20.2003			0.953309			0.476655	−	0.879091i	$-0.341849\pi$
$449$	20.2003			0.953309			0.476655	+	0.879091i	$0.341849\pi$
$450$		0			0
$451$	−42.5231			−2.00234
$452$	−4.25116	−	7.36323i	−0.199958	−	0.346337i
$453$		0			0
$454$	10.9984	−	19.0497i	0.516179	−	0.894048i
$455$		0			0
$456$		0			0
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	0.530873	−	0.847451i	$-0.321864\pi$
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	−0.999351	+	0.0360237i	$0.988531\pi$
$458$	−3.79863			−0.177498
$459$		0			0
$460$	0.741446			0.0345701
$461$	5.97661	+	10.3518i	0.278359	+	0.482131i	0.970977	−	0.239173i	$-0.0768763\pi$
$461$	5.97661	+	10.3518i	0.278359	+	0.482131i	−0.692618	+	0.721304i	$0.743543\pi$
$462$		0			0
$463$	6.64527	−	11.5100i	0.308832	−	0.534913i	−0.669275	−	0.743015i	$-0.733395\pi$
$463$	6.64527	−	11.5100i	0.308832	−	0.534913i	0.978107	+	0.208102i	$0.0667286\pi$
$464$	−0.732287	+	1.26836i	−0.0339956	+	0.0588820i
$465$		0			0
$466$	−3.33530	−	5.77690i	−0.154505	−	0.267610i
$467$	11.2301			0.519667			0.259833	−	0.965653i	$-0.416332\pi$
$467$	11.2301			0.519667			0.259833	+	0.965653i	$0.416332\pi$
$468$		0			0
$469$		0			0
$470$	1.46169	+	2.53173i	0.0674230	+	0.116780i
$471$		0			0
$472$	0.993163	−	1.72021i	0.0457141	−	0.0791791i
$473$	−26.5208	+	45.9354i	−1.21943	+	2.11211i
$474$		0			0
$475$	1.84501	+	3.19565i	0.0846550	+	0.146627i
$476$		0			0
$477$		0			0
$478$	15.6408			0.715392
$479$	16.3135	+	28.2559i	0.745385	+	1.29104i	0.950015	+	0.312205i	$0.101068\pi$
$479$	16.3135	+	28.2559i	0.745385	+	1.29104i	−0.204630	+	0.978839i	$0.565599\pi$
$480$		0			0
$481$	−1.09781	+	1.90146i	−0.0500557	+	0.0866991i
$482$	−10.7060	+	18.5434i	−0.487646	+	0.844627i
$483$		0			0
$484$	−13.2564	−	22.9607i	−0.602562	−	1.04367i
$485$	−6.40275			−0.290734
$486$		0			0
$487$	−3.69794			−0.167570			−0.0837848	−	0.996484i	$-0.526701\pi$
$487$	−3.69794			−0.167570			−0.0837848	+	0.996484i	$0.526701\pi$
$488$	5.17511	+	8.96355i	0.234266	+	0.405761i
$489$		0			0
$490$		0			0
$491$	18.7804	−	32.5287i	0.847549	−	1.46800i	−0.0358393	−	0.999358i	$-0.511410\pi$
$491$	18.7804	−	32.5287i	0.847549	−	1.46800i	0.883389	−	0.468641i	$-0.155256\pi$
$492$		0			0
$493$	−5.01040	−	8.67827i	−0.225657	−	0.390850i
$494$	1.47825			0.0665095
$495$		0			0
$496$	−7.70370			−0.345906
$497$		0			0
$498$		0			0
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	−0.252549	−	0.967584i	$-0.581269\pi$
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	0.964227	−	0.265078i	$-0.0853977\pi$
$500$	6.07442	−	10.5212i	0.271656	−	0.470523i
$501$		0			0
$502$	−11.8015	−	20.4408i	−0.526727	−	0.912318i
$503$	30.8252			1.37443			0.687214	−	0.726455i	$-0.258834\pi$
$503$	30.8252			1.37443			0.687214	+	0.726455i	$0.258834\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$	−1.28947	−	2.23342i	−0.0573238	−	0.0992877i
$507$		0			0
$508$	9.47661	−	16.4140i	0.420457	−	0.728252i
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	−0.941077	−	0.338193i	$-0.890184\pi$
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	0.763422	+	0.645900i	$0.223518\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−20.2599			−0.893627
$515$	−6.01204	−	10.4132i	−0.264922	−	0.458858i
$516$		0			0
$517$	5.08414	−	8.80598i	0.223600	−	0.387287i
$518$		0			0
$519$		0			0
$520$	−0.669905	−	1.16031i	−0.0293773	−	0.0508829i
$521$	−29.7292			−1.30246			−0.651229	−	0.758881i	$-0.725746\pi$
$521$	−29.7292			−1.30246			−0.651229	+	0.758881i	$0.725746\pi$
$522$		0			0
$523$	26.9396			1.17798			0.588992	−	0.808139i	$-0.299525\pi$
$523$	26.9396			1.17798			0.588992	+	0.808139i	$0.299525\pi$
$524$	3.64652	+	6.31595i	0.159299	+	0.275914i
$525$		0			0
$526$	11.2443	−	19.4757i	0.490276	−	0.849183i
$527$	26.3549	−	45.6480i	1.14804	−	1.98846i
$528$		0			0
$529$	11.4114	+	19.7650i	0.496146	+	0.859350i
$530$	0.396990			0.0172441
$531$		0			0
$532$		0			0
$533$	2.64132	+	4.57489i	0.114408	+	0.198161i
$534$		0			0
$535$	−3.12188	+	5.40726i	−0.134971	+	0.233776i
$536$	3.39248	−	5.87594i	0.146533	−	0.253802i
$537$		0			0
$538$	12.6706	+	21.9461i	0.546268	+	0.946164i
$539$		0			0
$540$		0			0
$541$	−14.3114			−0.615293			−0.307647	−	0.951501i	$-0.599541\pi$
$541$	−14.3114			−0.615293			−0.307647	+	0.951501i	$0.599541\pi$
$542$	−6.87880	−	11.9144i	−0.295470	−	0.511769i
$543$		0			0
$544$	3.42107	−	5.92546i	0.146677	−	0.254052i
$545$	0.619562	−	1.07311i	0.0265391	−	0.0459671i
$546$		0			0
$547$	1.02463	+	1.77471i	0.0438101	+	0.0758813i	0.887099	−	0.461579i	$-0.152717\pi$
$547$	1.02463	+	1.77471i	0.0438101	+	0.0758813i	−0.843289	+	0.537461i	$0.819384\pi$
$548$	8.18194			0.349515
$549$		0			0
$550$	−11.6328			−0.496026
$551$	−1.42270	−	2.46419i	−0.0606091	−	0.104978i
$552$		0			0
$553$		0			0
$554$	−1.64132	+	2.84284i	−0.0697328	+	0.120781i
$555$		0			0
$556$	6.23229	+	10.7946i	0.264308	+	0.457795i
$557$	17.6868			0.749412			0.374706	−	0.927144i	$-0.377744\pi$
$557$	17.6868			0.749412			0.374706	+	0.927144i	$0.377744\pi$
$558$		0			0
$559$	6.58934			0.278699
$560$		0			0
$561$		0			0
$562$	0.634479	−	1.09895i	0.0267639	−	0.0463564i
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	−0.875730	−	0.482802i	$-0.839619\pi$
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	0.855983	+	0.517003i	$0.172952\pi$
$564$		0			0
$565$	−7.48577	−	12.9657i	−0.314929	−	0.545473i
$566$	−8.19235			−0.344350
$567$		0			0
$568$	10.7850			0.452527
$569$	11.7632	+	20.3745i	0.493139	+	0.854142i	0.999969	−	0.00790437i	$-0.00251607\pi$
$569$	11.7632	+	20.3745i	0.493139	+	0.854142i	−0.506830	+	0.862046i	$0.669183\pi$
$570$		0			0
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	−0.860917	−	0.508745i	$-0.830110\pi$
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	0.871045	+	0.491204i	$0.163443\pi$
$572$	−2.33009	+	4.03584i	−0.0974262	+	0.168747i
$573$		0			0
$574$		0			0
$575$	−0.799737			−0.0333514
$576$		0			0
$577$	−4.46130			−0.185727			−0.0928633	−	0.995679i	$-0.529602\pi$
$577$	−4.46130			−0.185727			−0.0928633	+	0.995679i	$0.529602\pi$
$578$	14.9074	+	25.8204i	0.620066	+	1.07399i
$579$		0			0
$580$	−1.28947	+	2.23342i	−0.0535422	+	0.0927378i
$581$		0			0
$582$		0			0
$583$	−0.690415	−	1.19583i	−0.0285941	−	0.0495264i
$584$	−0.306707			−0.0126916
$585$		0			0
$586$	15.4509			0.638271
$587$	8.31518	+	14.4023i	0.343204	+	0.594447i	0.985026	−	0.172407i	$-0.0551544\pi$
$587$	8.31518	+	14.4023i	0.343204	+	0.594447i	−0.641822	+	0.766854i	$0.721821\pi$
$588$		0			0
$589$	7.48345	−	12.9617i	0.308350	−	0.534078i
$590$	1.74884	−	3.02908i	0.0719985	−	0.124705i
$591$		0			0
$592$	1.44282	+	2.49904i	0.0592995	+	0.102710i
$593$	−41.5264			−1.70528			−0.852642	−	0.522495i	$-0.825001\pi$
$593$	−41.5264			−1.70528			−0.852642	+	0.522495i	$0.825001\pi$
$594$		0			0
$595$		0			0
$596$	4.41423	+	7.64567i	0.180814	+	0.313179i
$597$		0			0
$598$	−0.160190	+	0.277457i	−0.00655065	+	0.0113461i
$599$	7.53831	−	13.0567i	0.308007	−	0.533483i	−0.669919	−	0.742434i	$-0.733671\pi$
$599$	7.53831	−	13.0567i	0.308007	−	0.533483i	0.977926	+	0.208950i	$0.0670047\pi$
$600$		0			0
$601$	8.05555	+	13.9526i	0.328593	+	0.569139i	0.982233	−	0.187666i	$-0.0600924\pi$
$601$	8.05555	+	13.9526i	0.328593	+	0.569139i	−0.653640	+	0.756805i	$0.726759\pi$
$602$		0			0
$603$		0			0
$604$	−14.9863			−0.609785
$605$	−23.3428	−	40.4310i	−0.949021	−	1.64375i
$606$		0			0
$607$	9.78659	−	16.9509i	0.397225	−	0.688014i	−0.596157	−	0.802868i	$-0.703306\pi$
$607$	9.78659	−	16.9509i	0.397225	−	0.688014i	0.993382	+	0.114853i	$0.0366398\pi$
$608$	0.971410	−	1.68253i	0.0393959	−	0.0682357i
$609$		0			0
$610$	9.11273	+	15.7837i	0.368963	+	0.639063i
$611$	−1.26320			−0.0511036
$612$		0			0
$613$	5.55159			0.224226			0.112113	−	0.993695i	$-0.464238\pi$
$613$	5.55159			0.224226			0.112113	+	0.993695i	$0.464238\pi$
$614$	−2.44966	−	4.24293i	−0.0988601	−	0.171231i
$615$		0			0
$616$		0			0
$617$	−0.634479	+	1.09895i	−0.0255431	+	0.0442420i	−0.878514	−	0.477716i	$-0.841465\pi$
$617$	−0.634479	+	1.09895i	−0.0255431	+	0.0442420i	0.852971	+	0.521958i	$0.174798\pi$
$618$		0			0
$619$	2.25116	+	3.89913i	0.0904818	+	0.156719i	0.907714	−	0.419589i	$-0.137826\pi$
$619$	2.25116	+	3.89913i	0.0904818	+	0.156719i	−0.817232	+	0.576309i	$0.804493\pi$
$620$	−13.5653			−0.544794
$621$		0			0
$622$	7.69002			0.308342
$623$		0			0
$624$		0			0
$625$	5.94802	−	10.3023i	0.237921	−	0.412091i
$626$	0.861564	−	1.49227i	0.0344350	−	0.0596432i
$627$		0			0
$628$	9.49028	+	16.4377i	0.378704	+	0.655934i
$629$	−19.7439			−0.787242
$630$		0			0
$631$	−1.69905			−0.0676381			−0.0338191	−	0.999428i	$-0.510767\pi$
$631$	−1.69905			−0.0676381			−0.0338191	+	0.999428i	$0.510767\pi$
$632$	−6.72257	−	11.6438i	−0.267410	−	0.463167i
$633$		0			0
$634$	−16.6014	+	28.7544i	−0.659325	+	1.14198i
$635$	16.6871	−	28.9030i	0.662209	−	1.14698i
$636$		0			0
$637$		0			0
$638$	8.97017			0.355132
$639$		0			0
$640$	−1.76088			−0.0696048
$641$	−0.474289	−	0.821492i	−0.0187333	−	0.0324470i	0.856507	−	0.516136i	$-0.172630\pi$
$641$	−0.474289	−	0.821492i	−0.0187333	−	0.0324470i	−0.875240	+	0.483689i	$0.839297\pi$
$642$		0			0
$643$	9.84897	−	17.0589i	0.388405	−	0.672738i	−0.603830	−	0.797113i	$-0.706359\pi$
$643$	9.84897	−	17.0589i	0.388405	−	0.672738i	0.992235	+	0.124375i	$0.0396927\pi$
$644$		0			0
$645$		0			0
$646$	6.64652	+	11.5121i	0.261504	+	0.452938i
$647$	−23.4542			−0.922079			−0.461039	−	0.887380i	$-0.652523\pi$
$647$	−23.4542			−0.922079			−0.461039	+	0.887380i	$0.652523\pi$
$648$		0			0
$649$	−12.1658			−0.477549
$650$	0.722572	+	1.25153i	0.0283416	+	0.0490891i
$651$		0			0
$652$	−7.51887	+	13.0231i	−0.294462	+	0.510023i
$653$	11.3954	−	19.7373i	0.445935	−	0.772382i	−0.552182	−	0.833724i	$-0.686205\pi$
$653$	11.3954	−	19.7373i	0.445935	−	0.772382i	0.998117	+	0.0613420i	$0.0195380\pi$
$654$		0			0
$655$	6.42107	+	11.1216i	0.250892	+	0.434557i
$656$	6.94282			0.271072
$657$		0			0
$658$		0			0
$659$	13.2398	+	22.9320i	0.515750	+	0.893305i	0.999833	+	0.0182828i	$0.00581993\pi$
$659$	13.2398	+	22.9320i	0.515750	+	0.893305i	−0.484083	+	0.875022i	$0.660847\pi$
$660$		0			0
$661$	−13.3691	+	23.1559i	−0.519997	+	0.900662i	0.479732	+	0.877415i	$0.340734\pi$
$661$	−13.3691	+	23.1559i	−0.519997	+	0.900662i	−0.999730	+	0.0232469i	$0.992600\pi$
$662$	1.44445	−	2.50187i	0.0561403	−	0.0972379i
$663$		0			0
$664$	1.56238	+	2.70612i	0.0606322	+	0.105018i
$665$		0			0
$666$		0			0
$667$	0.616683			0.0238781
$668$	0.572097	+	0.990901i	0.0221351	+	0.0383391i
$669$		0			0
$670$	5.97373	−	10.3468i	0.230785	−	0.399732i
$671$	31.6963	−	54.8996i	1.22362	−	2.11938i
$672$		0			0
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	0.593429	−	0.804886i	$-0.297774\pi$
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	−0.993766	+	0.111482i	$0.964440\pi$
$674$	−8.72313			−0.336002
$675$		0			0
$676$	−12.4211			−0.477733
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	0.993447	−	0.114293i	$-0.0364602\pi$
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	−0.595704	+	0.803204i	$0.703127\pi$
$678$		0			0
$679$		0			0
$680$	6.02408	−	10.4340i	0.231013	−	0.400126i
$681$		0			0
$682$	23.5917	+	40.8620i	0.903371	+	1.56469i
$683$	28.5836			1.09372			0.546860	−	0.837224i	$-0.315823\pi$
$683$	28.5836			1.09372			0.546860	+	0.837224i	$0.315823\pi$
$684$		0			0
$685$	14.4074			0.550478
$686$		0			0
$687$		0			0
$688$	4.33009	−	7.49994i	0.165083	−	0.285933i
$689$	−0.0857699	+	0.148558i	−0.00326757	+	0.00565960i
$690$		0			0
$691$	−3.34897	−	5.80059i	−0.127401	−	0.220665i	0.795268	−	0.606258i	$-0.207330\pi$
$691$	−3.34897	−	5.80059i	−0.127401	−	0.220665i	−0.922669	+	0.385593i	$0.873997\pi$
$692$	0.497677			0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	10.9743	+	19.0080i	0.416278	+	0.721016i
$696$		0			0
$697$	−23.7518	+	41.1394i	−0.899665	+	1.55827i
$698$	14.1992	−	24.5937i	0.537447	−	0.930886i
$699$		0			0
$700$		0			0
$701$	25.1442			0.949683			0.474842	−	0.880071i	$-0.342505\pi$
$701$	25.1442			0.949683			0.474842	+	0.880071i	$0.342505\pi$
$702$		0			0
$703$	−5.60628			−0.211445
$704$	3.06238	+	5.30420i	0.115418	+	0.199910i
$705$		0			0
$706$	−2.19686	+	3.80507i	−0.0826799	+	0.143206i
$707$		0			0
$708$		0			0
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	0.770694	−	0.637205i	$-0.219910\pi$
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	−0.937183	+	0.348838i	$0.886576\pi$
$710$	18.9910			0.712719
$711$		0			0
$712$	2.60301			0.0975519
$713$	1.62188	+	2.80919i	0.0607401	+	0.105205i
$714$		0			0
$715$	−4.10301	+	7.10662i	−0.153444	+	0.265773i
$716$	−4.41423	+	7.64567i	−0.164968	+	0.285732i
$717$		0			0
$718$	16.0796	+	27.8507i	0.600086	+	1.03938i
$719$	−23.6030			−0.880244			−0.440122	−	0.897938i	$-0.645065\pi$
$719$	−23.6030			−0.880244			−0.440122	+	0.897938i	$0.645065\pi$
$720$		0			0
$721$		0			0
$722$	−7.61273	−	13.1856i	−0.283316	−	0.490718i
$723$		0			0
$724$	0.664703	−	1.15130i	0.0247035	−	0.0427877i
$725$	1.39084	−	2.40901i	0.0516546	−	0.0894683i
$726$		0			0
$727$	−3.25692	−	5.64115i	−0.120792	−	0.209219i	0.799288	−	0.600948i	$-0.205210\pi$
$727$	−3.25692	−	5.64115i	−0.120792	−	0.209219i	−0.920080	+	0.391730i	$0.871877\pi$
$728$		0			0
$729$		0			0
$730$	−0.540073			−0.0199890
$731$	29.6271	+	51.3156i	1.09580	+	1.89798i
$732$		0			0
$733$	−11.5991	+	20.0901i	−0.428421	+	0.742047i	−0.996733	−	0.0807664i	$-0.974263\pi$
$733$	−11.5991	+	20.0901i	−0.428421	+	0.742047i	0.568312	+	0.822813i	$0.307597\pi$
$734$	−17.3015	+	29.9671i	−0.638610	+	1.10611i
$735$		0			0
$736$	0.210533	+	0.364654i	0.00776036	+	0.0134413i
$737$	−41.5562			−1.53074
$738$		0			0
$739$	15.1568			0.557550			0.278775	−	0.960356i	$-0.410072\pi$
$739$	15.1568			0.557550			0.278775	+	0.960356i	$0.410072\pi$
$740$	2.54063	+	4.40050i	0.0933954	+	0.161765i
$741$		0			0
$742$		0			0
$743$	5.21737	−	9.03675i	0.191407	−	0.331526i	−0.754310	−	0.656518i	$-0.772028\pi$
$743$	5.21737	−	9.03675i	0.191407	−	0.331526i	0.945717	+	0.324992i	$0.105362\pi$
$744$		0			0
$745$	7.77292	+	13.4631i	0.284778	+	0.493249i
$746$	−10.9759			−0.401857
$747$		0			0
$748$	−41.9064			−1.53225
$749$		0			0
$750$		0			0
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	0.221628	+	0.975131i	$0.428863\pi$
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	−0.955303	+	0.295630i	$0.904470\pi$
$752$	−0.830095	+	1.43777i	−0.0302704	+	0.0524300i
$753$		0			0
$754$	−0.557180	−	0.965064i	−0.0202913	−	0.0351456i
$755$	−26.3891			−0.960397
$756$		0			0
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$	16.9939	+	29.4342i	0.617244	+	1.06910i
$759$		0			0
$760$	1.71053	−	2.96273i	0.0620476	−	0.107470i
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	−0.567889	−	0.823105i	$-0.692240\pi$
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	0.996774	+	0.0802535i	$0.0255730\pi$
$762$		0			0
$763$		0			0
$764$	16.1683			0.584947
$765$		0			0
$766$	21.0241			0.759631
$767$	0.755675	+	1.30887i	0.0272858	+	0.0472605i
$768$		0			0
$769$	5.62764	−	9.74736i	0.202938	−	0.351499i	−0.746536	−	0.665345i	$-0.768284\pi$
$769$	5.62764	−	9.74736i	0.202938	−	0.351499i	0.949474	+	0.313846i	$0.101618\pi$
$770$		0			0
$771$		0			0
$772$	7.08414	+	12.2701i	0.254964	+	0.441610i
$773$	−0.277984			−0.00999839			−0.00499919	−	0.999988i	$-0.501591\pi$
$773$	−0.277984			−0.00999839			−0.00499919	+	0.999988i	$0.501591\pi$
$774$		0			0
$775$	14.6317			0.525587
$776$	−1.81806	−	3.14897i	−0.0652644	−	0.113041i
$777$		0			0
$778$	−6.86909	+	11.8976i	−0.246269	+	0.426550i
$779$	−6.74433	+	11.6815i	−0.241641	+	0.418534i
$780$		0			0
$781$	−33.0276	−	57.2056i	−1.18182	−	2.04698i
$782$	−2.88099			−0.103024
$783$		0			0
$784$		0			0
$785$	16.7112	+	28.9447i	0.596449	+	1.03308i
$786$		0			0
$787$	−14.6940	+	25.4507i	−0.523784	+	0.907220i	0.475833	+	0.879536i	$0.342147\pi$
$787$	−14.6940	+	25.4507i	−0.523784	+	0.907220i	−0.999617	+	0.0276845i	$0.991187\pi$
$788$	7.92107	−	13.7197i	0.282176	−	0.488744i
$789$		0			0
$790$	−11.8376	−	20.5034i	−0.421164	−	0.729477i
$791$		0			0
$792$		0			0
$793$	−7.87524			−0.279658
$794$	−3.57893	−	6.19889i	−0.127012	−	0.219991i
$795$		0			0
$796$	4.47141	−	7.74471i	0.158485	−	0.274504i
$797$	0.433105	−	0.750160i	0.0153414	−	0.0265720i	−0.858253	−	0.513227i	$-0.828450\pi$
$797$	0.433105	−	0.750160i	0.0153414	−	0.0265720i	0.873594	+	0.486655i	$0.161783\pi$
$798$		0			0
$799$	−5.67962	−	9.83739i	−0.200931	−	0.348022i
$800$	1.89931			0.0671509
$801$		0			0
$802$	−9.27936			−0.327666
$803$	0.939253	+	1.62683i	0.0331455	+	0.0574097i
$804$		0			0
$805$		0			0
$806$	2.93078	−	5.07626i	0.103232	−	0.178804i
$807$		0			0
$808$	−4.00520	−	6.93721i	−0.140903	−	0.244050i
$809$	19.3341			0.679749			0.339875	−	0.940471i	$-0.389615\pi$
$809$	19.3341			0.679749			0.339875	+	0.940471i	$0.389615\pi$
$810$		0			0
$811$	47.0391			1.65177			0.825884	−	0.563841i	$-0.190677\pi$
$811$	47.0391			1.65177			0.825884	+	0.563841i	$0.190677\pi$
$812$		0			0
$813$		0			0
$814$	8.83693	−	15.3060i	0.309734	−	0.536476i
$815$	−13.2398	+	22.9320i	−0.463770	+	0.803274i
$816$		0			0
$817$	8.41260	+	14.5710i	0.294319	+	0.509776i
$818$	15.1683			0.530346
$819$		0			0
$820$	12.2255			0.426931
$821$	0.705332	+	1.22167i	0.0246162	+	0.0426366i	0.878071	−	0.478530i	$-0.158830\pi$
$821$	0.705332	+	1.22167i	0.0246162	+	0.0426366i	−0.853455	+	0.521167i	$0.825497\pi$
$822$		0			0
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	−0.380430	−	0.924810i	$-0.624224\pi$
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	0.991124	−	0.132943i	$-0.0424426\pi$
$824$	3.41423	−	5.91362i	0.118940	−	0.206011i
$825$		0			0
$826$		0			0
$827$	18.5997			0.646776			0.323388	−	0.946266i	$-0.395178\pi$
$827$	18.5997			0.646776			0.323388	+	0.946266i	$0.395178\pi$
$828$		0			0
$829$	38.1696			1.32569			0.662843	−	0.748758i	$-0.269350\pi$
$829$	38.1696			1.32569			0.662843	+	0.748758i	$0.269350\pi$
$830$	2.75116	+	4.76515i	0.0954942	+	0.165401i
$831$		0			0
$832$	0.380438	−	0.658939i	0.0131893	−	0.0228446i
$833$		0			0
$834$		0			0
$835$	1.00739	+	1.74485i	0.0348622	+	0.0603832i
$836$	−11.8993			−0.411546
$837$		0			0
$838$	−8.33654			−0.287981
$839$	17.3691	+	30.0841i	0.599648	+	1.03862i	0.992873	+	0.119178i	$0.0380259\pi$
$839$	17.3691	+	30.0841i	0.599648	+	1.03862i	−0.393225	+	0.919442i	$0.628641\pi$
$840$		0			0
$841$	13.4275	−	23.2571i	0.463018	−	0.801970i
$842$	3.50232	−	6.06620i	0.120698	−	0.209055i
$843$		0			0
$844$	11.3856	+	19.7205i	0.391910	+	0.678808i
$845$	−21.8720			−0.752419
$846$		0			0
$847$		0			0
$848$	0.112725	+	0.195246i	0.00387100	+	0.00670476i
$849$		0			0
$850$	−6.49768	+	11.2543i	−0.222868	+	0.386020i
$851$	0.607523	−	1.05226i	0.0208256	−	0.0360711i
$852$		0			0
$853$	21.1586	+	36.6477i	0.724455	+	1.25479i	0.959198	+	0.282736i	$0.0912419\pi$
$853$	21.1586	+	36.6477i	0.724455	+	1.25479i	−0.234743	+	0.972058i	$0.575425\pi$
$854$		0			0
$855$		0			0
$856$	−3.54583			−0.121194
$857$	−7.46169	−	12.9240i	−0.254887	−	0.441477i	0.709978	−	0.704224i	$-0.248705\pi$
$857$	−7.46169	−	12.9240i	−0.254887	−	0.441477i	−0.964865	+	0.262747i	$0.915371\pi$
$858$		0			0
$859$	9.70658	−	16.8123i	0.331184	−	0.573628i	−0.651560	−	0.758597i	$-0.725885\pi$
$859$	9.70658	−	16.8123i	0.331184	−	0.573628i	0.982744	+	0.184969i	$0.0592186\pi$
$860$	7.62476	−	13.2065i	0.260002	−	0.450337i
$861$		0			0
$862$	−1.72545	−	2.98857i	−0.0587691	−	0.101791i
$863$	−1.08453			−0.0369177			−0.0184588	−	0.999830i	$-0.505876\pi$
$863$	−1.08453			−0.0369177			−0.0184588	+	0.999830i	$0.505876\pi$
$864$		0			0
$865$	0.876348			0.0297967
$866$	−14.1300	−	24.4738i	−0.480156	−	0.831654i
$867$		0			0
$868$		0			0
$869$	−41.1742	+	71.3157i	−1.39674	+	2.41922i
$870$		0			0
$871$	2.58126	+	4.47087i	0.0874625	+	0.151490i
$872$	0.703697			0.0238302
$873$		0			0
$874$	−0.818057			−0.0276712
$875$		0			0
$876$		0			0
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	−0.517427	−	0.855728i	$-0.673110\pi$
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	0.999795	+	0.0202407i	$0.00644326\pi$
$878$	14.4480	−	25.0247i	0.487597	−	0.844543i
$879$		0			0
$880$	5.39248	+	9.34004i	0.181780	+	0.314853i
$881$	45.9967			1.54967			0.774835	−	0.632164i	$-0.217833\pi$
$881$	45.9967			1.54967			0.774835	+	0.632164i	$0.217833\pi$
$882$		0			0
$883$	32.9384			1.10847			0.554233	−	0.832361i	$-0.313012\pi$
$883$	32.9384			1.10847			0.554233	+	0.832361i	$0.313012\pi$
$884$	2.60301	+	4.50855i	0.0875487	+	0.151639i
$885$		0			0
$886$	6.88044	−	11.9173i	0.231153	−	0.400368i
$887$	14.1699	−	24.5430i	0.475779	−	0.824073i	−0.523836	−	0.851819i	$-0.675500\pi$
$887$	14.1699	−	24.5430i	0.475779	−	0.824073i	0.999615	+	0.0277459i	$0.00883293\pi$
$888$		0			0
$889$		0			0
$890$	4.58358			0.153642
$891$		0			0
$892$	−12.8856			−0.431443
$893$	−1.61273	−	2.79332i	−0.0539678	−	0.0934750i
$894$		0			0
$895$	−7.77292	+	13.4631i	−0.259820	+	0.450021i
$896$		0			0
$897$		0			0
$898$	10.1001	+	17.4939i	0.337046	+	0.583780i
$899$	−11.2826			−0.376297
$900$		0			0
$901$	−1.54256			−0.0513901
$902$	−21.2616	−	36.8261i	−0.707933	−	1.22618i
$903$		0			0
$904$	4.25116	−	7.36323i	0.141392	−	0.244897i
$905$	1.17046	−	2.02730i	0.0389074	−	0.0673896i
$906$		0			0
$907$	−3.97373	−	6.88271i	−0.131946	−	0.228537i	0.792481	−	0.609897i	$-0.208789\pi$
$907$	−3.97373	−	6.88271i	−0.131946	−	0.228537i	−0.924427	+	0.381360i	$0.875456\pi$
$908$	21.9967			0.729987
$909$		0			0
$910$		0			0
$911$	4.00808	+	6.94220i	0.132794	+	0.230005i	0.924752	−	0.380569i	$-0.124272\pi$
$911$	4.00808	+	6.94220i	0.132794	+	0.230005i	−0.791959	+	0.610575i	$0.790939\pi$
$912$		0			0
$913$	9.56922	−	16.5744i	0.316695	−	0.548532i
$914$	10.0149	−	17.3463i	0.331264	−	0.573766i
$915$		0			0
$916$	−1.89931	−	3.28971i	−0.0627551	−	0.108695i
$917$		0			0
$918$		0			0
$919$	24.0449			0.793168			0.396584	−	0.917999i	$-0.370196\pi$
$919$	24.0449			0.793168			0.396584	+	0.917999i	$0.370196\pi$
$920$	0.370723	+	0.642111i	0.0122224	+	0.0211698i
$921$		0			0
$922$	−5.97661	+	10.3518i	−0.196829	+	0.340918i
$923$	−4.10301	+	7.10662i	−0.135052	+	0.233917i
$924$		0			0
$925$	−2.74037	−	4.74646i	−0.0901027	−	0.156062i
$926$	13.2905			0.436754
$927$		0			0
$928$	−1.46457			−0.0480770
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	0.541678	−	0.840586i	$-0.317789\pi$
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	−0.998808	+	0.0488134i	$0.984456\pi$
$930$		0			0
$931$		0			0
$932$	3.33530	−	5.77690i	0.109251	−	0.189229i
$933$		0			0
$934$	5.61505	+	9.72555i	0.183730	+	0.318230i
$935$	−73.7921			−2.41326
$936$		0			0
$937$	−53.2211			−1.73866			−0.869328	−	0.494235i	$-0.835448\pi$
$937$	−53.2211			−1.73866			−0.869328	+	0.494235i	$0.835448\pi$
$938$		0			0
$939$		0			0
$940$	−1.46169	+	2.53173i	−0.0476752	+	0.0825759i
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	−0.510160	−	0.860080i	$-0.670414\pi$
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	0.999931	+	0.0117715i	$0.00374709\pi$
$942$		0			0
$943$	−1.46169	−	2.53173i	−0.0475993	−	0.0824445i
$944$	1.98633			0.0646494
$945$		0			0
$946$	−53.0416			−1.72453
$947$	−19.8445	−	34.3716i	−0.644858	−	1.11693i	−0.984334	−	0.176312i	$-0.943583\pi$
$947$	−19.8445	−	34.3716i	−0.644858	−	1.11693i	0.339476	−	0.940615i	$-0.389750\pi$
$948$		0			0
$949$	0.116683	−	0.202101i	0.00378769	−	0.00656047i
$950$	−1.84501	+	3.19565i	−0.0598601	+	0.103681i
$951$		0			0
$952$		0			0
$953$	−23.0643			−0.747126			−0.373563	−	0.927605i	$-0.621864\pi$
$953$	−23.0643			−0.747126			−0.373563	+	0.927605i	$0.621864\pi$
$954$		0			0
$955$	28.4703			0.921278
$956$	7.82038	+	13.5453i	0.252929	+	0.438086i
$957$		0			0
$958$	−16.3135	+	28.2559i	−0.527067	+	0.912906i
$959$		0			0
$960$		0			0
$961$	−14.1735	−	24.5492i	−0.457209	−	0.791909i
$962$	−2.19562			−0.0707895
$963$		0			0
$964$	−21.4120			−0.689635
$965$	12.4743	+	21.6061i	0.401562	+	0.695525i
$966$		0			0
$967$	15.2902	−	26.4833i	0.491698	−	0.851646i	−0.508256	−	0.861206i	$-0.669710\pi$
$967$	15.2902	−	26.4833i	0.491698	−	0.851646i	0.999954	+	0.00955967i	$0.00304298\pi$
$968$	13.2564	−	22.9607i	0.426076	−	0.737985i
$969$		0			0
$970$	−3.20137	−	5.54494i	−0.102790	−	0.178037i
$971$	−26.2060			−0.840991			−0.420496	−	0.907295i	$-0.638144\pi$
$971$	−26.2060			−0.840991			−0.420496	+	0.907295i	$0.638144\pi$
$972$		0			0
$973$		0			0
$974$	−1.84897	−	3.20251i	−0.0592448	−	0.102615i
$975$		0			0
$976$	−5.17511	+	8.96355i	−0.165651	+	0.286916i
$977$	10.5270	−	18.2332i	0.336787	−	0.583332i	−0.647039	−	0.762457i	$-0.723993\pi$
$977$	10.5270	−	18.2332i	0.336787	−	0.583332i	0.983826	+	0.179124i	$0.0573264\pi$
$978$		0			0
$979$	−7.97141	−	13.8069i	−0.254767	−	0.441270i
$980$		0			0
$981$		0			0
$982$	37.5609			1.19862
$983$	9.76483	+	16.9132i	0.311450	+	0.539447i	0.978676	−	0.205408i	$-0.0658521\pi$
$983$	9.76483	+	16.9132i	0.311450	+	0.539447i	−0.667227	+	0.744855i	$0.732519\pi$
$984$		0			0
$985$	13.9480	−	24.1587i	0.444421	−	0.769760i
$986$	5.01040	−	8.67827i	0.159564	−	0.276373i
$987$		0			0
$988$	0.739123	+	1.28020i	0.0235146	+	0.0407286i
$989$	−3.64652			−0.115952
$990$		0			0
$991$	14.9967			0.476387			0.238193	−	0.971218i	$-0.423445\pi$
$991$	14.9967			0.476387			0.238193	+	0.971218i	$0.423445\pi$
$992$	−3.85185	−	6.67160i	−0.122296	−	0.211823i
$993$		0			0
$994$		0			0
$995$	7.87360	−	13.6375i	0.249610	−	0.432337i
$996$		0			0
$997$	−29.2821	−	50.7180i	−0.927373	−	1.60626i	−0.787700	−	0.616059i	$-0.788728\pi$
$997$	−29.2821	−	50.7180i	−0.927373	−	1.60626i	−0.139672	−	0.990198i	$-0.544605\pi$
$998$	31.7954			1.00646
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.n.1765.2		6
3.2	odd	2		882.2.f.m.589.3		6
7.2	even	3		2646.2.h.p.361.2		6
7.3	odd	6		378.2.e.c.37.2		6
7.4	even	3		2646.2.e.o.1549.2		6
7.5	odd	6		378.2.h.d.361.2		6
7.6	odd	2		2646.2.f.o.1765.2		6
9.2	odd	6		882.2.f.m.295.3		6
9.4	even	3		7938.2.a.bx.1.2		3
9.5	odd	6		7938.2.a.by.1.2		3
9.7	even	3	inner	2646.2.f.n.883.2		6
21.2	odd	6		882.2.h.o.67.2		6
21.5	even	6		126.2.h.c.67.2	yes	6
21.11	odd	6		882.2.e.p.373.1		6
21.17	even	6		126.2.e.d.121.3	yes	6
21.20	even	2		882.2.f.l.589.1		6
28.3	even	6		3024.2.q.h.2305.2		6
28.19	even	6		3024.2.t.g.1873.2		6
63.2	odd	6		882.2.e.p.655.1		6
63.5	even	6		1134.2.g.k.487.2		6
63.11	odd	6		882.2.h.o.79.2		6
63.13	odd	6		7938.2.a.bu.1.2		3
63.16	even	3		2646.2.e.o.2125.2		6
63.20	even	6		882.2.f.l.295.1		6
63.25	even	3		2646.2.h.p.667.2		6
63.31	odd	6		1134.2.g.n.163.2		6
63.34	odd	6		2646.2.f.o.883.2		6
63.38	even	6		126.2.h.c.79.2	yes	6
63.40	odd	6		1134.2.g.n.487.2		6
63.41	even	6		7938.2.a.cb.1.2		3
63.47	even	6		126.2.e.d.25.3	✓	6
63.52	odd	6		378.2.h.d.289.2		6
63.59	even	6		1134.2.g.k.163.2		6
63.61	odd	6		378.2.e.c.235.2		6
84.47	odd	6		1008.2.t.g.193.2		6
84.59	odd	6		1008.2.q.h.625.1		6
252.47	odd	6		1008.2.q.h.529.1		6
252.115	even	6		3024.2.t.g.289.2		6
252.187	even	6		3024.2.q.h.2881.2		6
252.227	odd	6		1008.2.t.g.961.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	63.47	even	6
126.2.e.d.121.3	yes	6	21.17	even	6
126.2.h.c.67.2	yes	6	21.5	even	6
126.2.h.c.79.2	yes	6	63.38	even	6
378.2.e.c.37.2		6	7.3	odd	6
378.2.e.c.235.2		6	63.61	odd	6
378.2.h.d.289.2		6	63.52	odd	6
378.2.h.d.361.2		6	7.5	odd	6
882.2.e.p.373.1		6	21.11	odd	6
882.2.e.p.655.1		6	63.2	odd	6
882.2.f.l.295.1		6	63.20	even	6
882.2.f.l.589.1		6	21.20	even	2
882.2.f.m.295.3		6	9.2	odd	6
882.2.f.m.589.3		6	3.2	odd	2
882.2.h.o.67.2		6	21.2	odd	6
882.2.h.o.79.2		6	63.11	odd	6
1008.2.q.h.529.1		6	252.47	odd	6
1008.2.q.h.625.1		6	84.59	odd	6
1008.2.t.g.193.2		6	84.47	odd	6
1008.2.t.g.961.2		6	252.227	odd	6
1134.2.g.k.163.2		6	63.59	even	6
1134.2.g.k.487.2		6	63.5	even	6
1134.2.g.n.163.2		6	63.31	odd	6
1134.2.g.n.487.2		6	63.40	odd	6
2646.2.e.o.1549.2		6	7.4	even	3
2646.2.e.o.2125.2		6	63.16	even	3
2646.2.f.n.883.2		6	9.7	even	3	inner
2646.2.f.n.1765.2		6	1.1	even	1	trivial
2646.2.f.o.883.2		6	63.34	odd	6
2646.2.f.o.1765.2		6	7.6	odd	2
2646.2.h.p.361.2		6	7.2	even	3
2646.2.h.p.667.2		6	63.25	even	3
3024.2.q.h.2305.2		6	28.3	even	6
3024.2.q.h.2881.2		6	252.187	even	6
3024.2.t.g.289.2		6	252.115	even	6
3024.2.t.g.1873.2		6	28.19	even	6
7938.2.a.bu.1.2		3	63.13	odd	6
7938.2.a.bx.1.2		3	9.4	even	3
7938.2.a.by.1.2		3	9.5	odd	6
7938.2.a.cb.1.2		3	63.41	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} -1.00000 q^{8} -1.76088 q^{10} +(3.06238 + 5.30420i) q^{11} +(0.380438 - 0.658939i) q^{13} +(-0.500000 - 0.866025i) q^{16} +6.84213 q^{17} +1.94282 q^{19} +(-0.880438 - 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} +(-0.210533 + 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +0.760877 q^{26} +(-0.732287 - 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.42107 + 5.92546i) q^{34} -2.88564 q^{37} +(0.971410 + 1.68253i) q^{38} +(0.880438 - 1.52496i) q^{40} +(-3.47141 + 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} -6.12476 q^{44} -0.421067 q^{46} +(-0.830095 - 1.43777i) q^{47} +(-0.949657 + 1.64485i) q^{50} +(0.380438 + 0.658939i) q^{52} -0.225450 q^{53} -10.7850 q^{55} +(0.732287 - 1.26836i) q^{58} +(-0.993163 + 1.72021i) q^{59} +(-5.17511 - 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(0.669905 + 1.16031i) q^{65} +(-3.39248 + 5.87594i) q^{67} +(-3.42107 + 5.92546i) q^{68} -10.7850 q^{71} +0.306707 q^{73} +(-1.44282 - 2.49904i) q^{74} +(-0.971410 + 1.68253i) q^{76} +(6.72257 + 11.6438i) q^{79} +1.76088 q^{80} -6.94282 q^{82} +(-1.56238 - 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +(-4.33009 + 7.49994i) q^{86} +(-3.06238 - 5.30420i) q^{88} -2.60301 q^{89} +(-0.210533 - 0.364654i) q^{92} +(0.830095 - 1.43777i) q^{94} +(-1.71053 + 2.96273i) q^{95} +(1.81806 + 3.14897i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8} - 10 q^{10} + q^{11} + 2 q^{13} - 3 q^{16} + 8 q^{17} - 6 q^{19} - 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} + 4 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34}+ \cdots + 28 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 5 * q^5 - 6 * q^8 - 10 * q^10 + q^11 + 2 * q^13 - 3 * q^16 + 8 * q^17 - 6 * q^19 - 5 * q^20 - q^22 + 7 * q^23 - 2 * q^25 + 4 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 + 18 * q^37 - 3 * q^38 + 5 * q^40 - 12 * q^41 + 18 * q^43 - 2 * q^44 + 14 * q^46 + 3 * q^47 + 2 * q^50 + 2 * q^52 + 18 * q^53 - 14 * q^55 - 5 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 - 4 * q^68 - 14 * q^71 - 50 * q^73 + 9 * q^74 + 3 * q^76 + 7 * q^79 + 10 * q^80 - 24 * q^82 + 8 * q^83 + 14 * q^85 - 18 * q^86 - q^88 + 18 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more