LMFDB - Embedded newform 2646.2.h.q.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.q.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.517638 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.517638 q^{5} +1.00000 q^{8} +(0.258819 + 0.448288i) q^{10} +1.46410 q^{11} +(1.22474 + 2.12132i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.74238 - 3.01790i) q^{17} +(-0.258819 + 0.448288i) q^{19} +(0.258819 - 0.448288i) q^{20} +(-0.732051 - 1.26795i) q^{22} -7.92820 q^{23} -4.73205 q^{25} +(1.22474 - 2.12132i) q^{26} +(1.36603 - 2.36603i) q^{29} +(-3.67423 + 6.36396i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.74238 + 3.01790i) q^{34} +(4.00000 - 6.92820i) q^{37} +0.517638 q^{38} -0.517638 q^{40} +(2.82843 + 4.89898i) q^{41} +(6.09808 - 10.5622i) q^{43} +(-0.732051 + 1.26795i) q^{44} +(3.96410 + 6.86603i) q^{46} +(-2.31079 - 4.00240i) q^{47} +(2.36603 + 4.09808i) q^{50} -2.44949 q^{52} +(3.36603 + 5.83013i) q^{53} -0.757875 q^{55} -2.73205 q^{58} +(7.39924 - 12.8159i) q^{59} +(-2.19067 - 3.79435i) q^{61} +7.34847 q^{62} +1.00000 q^{64} +(-0.633975 - 1.09808i) q^{65} +(1.90192 - 3.29423i) q^{67} +3.48477 q^{68} +0.803848 q^{71} +(-2.31079 - 4.00240i) q^{73} -8.00000 q^{74} +(-0.258819 - 0.448288i) q^{76} +(-7.06218 - 12.2321i) q^{79} +(0.258819 + 0.448288i) q^{80} +(2.82843 - 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(0.901924 + 1.56218i) q^{85} -12.1962 q^{86} +1.46410 q^{88} +(-8.05558 + 13.9527i) q^{89} +(3.96410 - 6.86603i) q^{92} +(-2.31079 + 4.00240i) q^{94} +(0.133975 - 0.232051i) q^{95} +(0.517638 - 0.896575i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 24 q^{25} + 4 q^{29} - 4 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} - 8 q^{58} + 8 q^{64} - 12 q^{65} + 36 q^{67} + 48 q^{71} - 64 q^{74} - 8 q^{79} + 28 q^{85} - 56 q^{86} - 16 q^{88} + 4 q^{92} + 8 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 24 * q^25 + 4 * q^29 - 4 * q^32 + 32 * q^37 + 28 * q^43 + 8 * q^44 + 4 * q^46 + 12 * q^50 + 20 * q^53 - 8 * q^58 + 8 * q^64 - 12 * q^65 + 36 * q^67 + 48 * q^71 - 64 * q^74 - 8 * q^79 + 28 * q^85 - 56 * q^86 - 16 * q^88 + 4 * q^92 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.517638			−0.231495			−0.115747	−	0.993279i	$-0.536926\pi$
$5$	−0.517638			−0.231495			−0.115747	+	0.993279i	$0.536926\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	0.258819	+	0.448288i	0.0818458	+	0.141761i
$11$	1.46410			0.441443			0.220722	−	0.975337i	$-0.429159\pi$
$11$	1.46410			0.441443			0.220722	+	0.975337i	$0.429159\pi$
$12$		0			0
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	0.984373	−	0.176096i	$-0.0563468\pi$
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	−0.644690	+	0.764444i	$0.723014\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.74238	−	3.01790i	−0.422590	−	0.731947i	0.573602	−	0.819134i	$-0.305546\pi$
$17$	−1.74238	−	3.01790i	−0.422590	−	0.731947i	−0.996192	+	0.0871869i	$0.972212\pi$
$18$		0			0
$19$	−0.258819	+	0.448288i	−0.0593772	+	0.102844i	−0.894186	−	0.447696i	$-0.852245\pi$
$19$	−0.258819	+	0.448288i	−0.0593772	+	0.102844i	0.834809	+	0.550540i	$0.185578\pi$
$20$	0.258819	−	0.448288i	0.0578737	−	0.100240i
$21$		0			0
$22$	−0.732051	−	1.26795i	−0.156074	−	0.270328i
$23$	−7.92820			−1.65314			−0.826572	−	0.562831i	$-0.809712\pi$
$23$	−7.92820			−1.65314			−0.826572	+	0.562831i	$0.809712\pi$
$24$		0			0
$25$	−4.73205			−0.946410
$26$	1.22474	−	2.12132i	0.240192	−	0.416025i
$27$		0			0
$28$		0			0
$29$	1.36603	−	2.36603i	0.253665	−	0.439360i	−0.710867	−	0.703326i	$-0.751697\pi$
$29$	1.36603	−	2.36603i	0.253665	−	0.439360i	0.964532	+	0.263966i	$0.0850307\pi$
$30$		0			0
$31$	−3.67423	+	6.36396i	−0.659912	+	1.14300i	0.320726	+	0.947172i	$0.396073\pi$
$31$	−3.67423	+	6.36396i	−0.659912	+	1.14300i	−0.980638	+	0.195829i	$0.937260\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.74238	+	3.01790i	−0.298816	+	0.517565i
$35$		0			0
$36$		0			0
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$	0.517638			0.0839720
$39$		0			0
$40$	−0.517638			−0.0818458
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	0.997818	−	0.0660290i	$-0.0210330\pi$
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	−0.556092	+	0.831121i	$0.687700\pi$
$42$		0			0
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.146544	−	0.989204i	$-0.453185\pi$
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.783404	−	0.621513i	$-0.213482\pi$
$44$	−0.732051	+	1.26795i	−0.110361	+	0.191151i
$45$		0			0
$46$	3.96410	+	6.86603i	0.584475	+	1.01234i
$47$	−2.31079	−	4.00240i	−0.337063	−	0.583811i	0.646816	−	0.762646i	$-0.276100\pi$
$47$	−2.31079	−	4.00240i	−0.337063	−	0.583811i	−0.983879	+	0.178836i	$0.942767\pi$
$48$		0			0
$49$		0			0
$50$	2.36603	+	4.09808i	0.334607	+	0.579555i
$51$		0			0
$52$	−2.44949			−0.339683
$53$	3.36603	+	5.83013i	0.462359	+	0.800830i	0.999078	−	0.0429316i	$-0.0136698\pi$
$53$	3.36603	+	5.83013i	0.462359	+	0.800830i	−0.536719	+	0.843761i	$0.680336\pi$
$54$		0			0
$55$	−0.757875			−0.102192
$56$		0			0
$57$		0			0
$58$	−2.73205			−0.358736
$59$	7.39924	−	12.8159i	0.963299	−	1.66848i	0.249180	−	0.968457i	$-0.419839\pi$
$59$	7.39924	−	12.8159i	0.963299	−	1.66848i	0.714118	−	0.700025i	$-0.246828\pi$
$60$		0			0
$61$	−2.19067	−	3.79435i	−0.280487	−	0.485817i	0.691018	−	0.722838i	$-0.257163\pi$
$61$	−2.19067	−	3.79435i	−0.280487	−	0.485817i	−0.971505	+	0.237020i	$0.923829\pi$
$62$	7.34847			0.933257
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.633975	−	1.09808i	−0.0786349	−	0.136200i
$66$		0			0
$67$	1.90192	−	3.29423i	0.232357	−	0.402454i	−0.726144	−	0.687542i	$-0.758690\pi$
$67$	1.90192	−	3.29423i	0.232357	−	0.402454i	0.958501	+	0.285088i	$0.0920229\pi$
$68$	3.48477			0.422590
$69$		0			0
$70$		0			0
$71$	0.803848			0.0953992			0.0476996	−	0.998862i	$-0.484811\pi$
$71$	0.803848			0.0953992			0.0476996	+	0.998862i	$0.484811\pi$
$72$		0			0
$73$	−2.31079	−	4.00240i	−0.270457	−	0.468446i	0.698522	−	0.715589i	$-0.253842\pi$
$73$	−2.31079	−	4.00240i	−0.270457	−	0.468446i	−0.968979	+	0.247143i	$0.920508\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$	−0.258819	−	0.448288i	−0.0296886	−	0.0514221i
$77$		0			0
$78$		0			0
$79$	−7.06218	−	12.2321i	−0.794557	−	1.37621i	−0.923120	−	0.384512i	$-0.874370\pi$
$79$	−7.06218	−	12.2321i	−0.794557	−	1.37621i	0.128563	−	0.991701i	$-0.458964\pi$
$80$	0.258819	+	0.448288i	0.0289368	+	0.0501201i
$81$		0			0
$82$	2.82843	−	4.89898i	0.312348	−	0.541002i
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	0.455406	+	0.890284i	$0.349494\pi$
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	−0.998711	+	0.0507487i	$0.983839\pi$
$84$		0			0
$85$	0.901924	+	1.56218i	0.0978274	+	0.169442i
$86$	−12.1962			−1.31514
$87$		0			0
$88$	1.46410			0.156074
$89$	−8.05558	+	13.9527i	−0.853889	+	1.47898i	0.0237822	+	0.999717i	$0.492429\pi$
$89$	−8.05558	+	13.9527i	−0.853889	+	1.47898i	−0.877672	+	0.479263i	$0.840904\pi$
$90$		0			0
$91$		0			0
$92$	3.96410	−	6.86603i	0.413286	−	0.715833i
$93$		0			0
$94$	−2.31079	+	4.00240i	−0.238340	+	0.412816i
$95$	0.133975	−	0.232051i	0.0137455	−	0.0238079i
$96$		0			0
$97$	0.517638	−	0.896575i	0.0525582	−	0.0910334i	−0.838549	−	0.544826i	$-0.816596\pi$
$97$	0.517638	−	0.896575i	0.0525582	−	0.0910334i	0.891108	+	0.453792i	$0.149929\pi$
$98$		0			0
$99$		0			0
$100$	2.36603	−	4.09808i	0.236603	−	0.409808i
$101$	−5.79555			−0.576679			−0.288340	−	0.957528i	$-0.593103\pi$
$101$	−5.79555			−0.576679			−0.288340	+	0.957528i	$0.593103\pi$
$102$		0			0
$103$	−11.2122			−1.10477			−0.552384	−	0.833590i	$-0.686282\pi$
$103$	−11.2122			−1.10477			−0.552384	+	0.833590i	$0.686282\pi$
$104$	1.22474	+	2.12132i	0.120096	+	0.208013i
$105$		0			0
$106$	3.36603	−	5.83013i	0.326937	−	0.566272i
$107$	1.53590	−	2.66025i	0.148481	−	0.257176i	−0.782185	−	0.623046i	$-0.785895\pi$
$107$	1.53590	−	2.66025i	0.148481	−	0.257176i	0.930666	+	0.365869i	$0.119228\pi$
$108$		0			0
$109$	−5.29423	−	9.16987i	−0.507095	−	0.878315i	−0.999966	−	0.00821222i	$-0.997386\pi$
$109$	−5.29423	−	9.16987i	−0.507095	−	0.878315i	0.492871	−	0.870102i	$-0.335947\pi$
$110$	0.378937	+	0.656339i	0.0361303	+	0.0625794i
$111$		0			0
$112$		0			0
$113$	−7.33013	−	12.6962i	−0.689560	−	1.19435i	−0.971980	−	0.235063i	$-0.924470\pi$
$113$	−7.33013	−	12.6962i	−0.689560	−	1.19435i	0.282420	−	0.959291i	$-0.408863\pi$
$114$		0			0
$115$	4.10394			0.382694
$116$	1.36603	+	2.36603i	0.126832	+	0.219680i
$117$		0			0
$118$	−14.7985			−1.36231
$119$		0			0
$120$		0			0
$121$	−8.85641			−0.805128
$122$	−2.19067	+	3.79435i	−0.198334	+	0.343525i
$123$		0			0
$124$	−3.67423	−	6.36396i	−0.329956	−	0.571501i
$125$	5.03768			0.450584
$126$		0			0
$127$	−5.92820			−0.526043			−0.263021	−	0.964790i	$-0.584719\pi$
$127$	−5.92820			−0.526043			−0.263021	+	0.964790i	$0.584719\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.633975	+	1.09808i	−0.0556033	+	0.0963077i
$131$	−12.4877			−1.09105			−0.545527	−	0.838093i	$-0.683670\pi$
$131$	−12.4877			−1.09105			−0.545527	+	0.838093i	$0.683670\pi$
$132$		0			0
$133$		0			0
$134$	−3.80385			−0.328602
$135$		0			0
$136$	−1.74238	−	3.01790i	−0.149408	−	0.258782i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$	10.1075	+	17.5068i	0.857311	+	1.48491i	0.874485	+	0.485053i	$0.161200\pi$
$139$	10.1075	+	17.5068i	0.857311	+	1.48491i	−0.0171736	+	0.999853i	$0.505467\pi$
$140$		0			0
$141$		0			0
$142$	−0.401924	−	0.696152i	−0.0337287	−	0.0584198i
$143$	1.79315	+	3.10583i	0.149951	+	0.259722i
$144$		0			0
$145$	−0.707107	+	1.22474i	−0.0587220	+	0.101710i
$146$	−2.31079	+	4.00240i	−0.191242	+	0.331241i
$147$		0			0
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	2.39230			0.195985			0.0979926	−	0.995187i	$-0.468758\pi$
$149$	2.39230			0.195985			0.0979926	+	0.995187i	$0.468758\pi$
$150$		0			0
$151$	−17.3923			−1.41537			−0.707683	−	0.706530i	$-0.750259\pi$
$151$	−17.3923			−1.41537			−0.707683	+	0.706530i	$0.750259\pi$
$152$	−0.258819	+	0.448288i	−0.0209930	+	0.0363609i
$153$		0			0
$154$		0			0
$155$	1.90192	−	3.29423i	0.152766	−	0.264599i
$156$		0			0
$157$	8.64256	−	14.9694i	0.689752	−	1.19469i	−0.282166	−	0.959366i	$-0.591053\pi$
$157$	8.64256	−	14.9694i	0.689752	−	1.19469i	0.971918	−	0.235320i	$-0.0756137\pi$
$158$	−7.06218	+	12.2321i	−0.561837	+	0.973130i
$159$		0			0
$160$	0.258819	−	0.448288i	0.0204614	−	0.0354403i
$161$		0			0
$162$		0			0
$163$	3.53590	−	6.12436i	0.276953	−	0.479697i	−0.693673	−	0.720290i	$-0.744009\pi$
$163$	3.53590	−	6.12436i	0.276953	−	0.479697i	0.970626	+	0.240593i	$0.0773421\pi$
$164$	−5.65685			−0.441726
$165$		0			0
$166$	9.89949			0.768350
$167$	6.64136	+	11.5032i	0.513924	+	0.890143i	0.999870	+	0.0161534i	$0.00514202\pi$
$167$	6.64136	+	11.5032i	0.513924	+	0.890143i	−0.485945	+	0.873989i	$0.661525\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$	0.901924	−	1.56218i	0.0691744	−	0.119814i
$171$		0			0
$172$	6.09808	+	10.5622i	0.464974	+	0.805359i
$173$	−9.71003	−	16.8183i	−0.738240	−	1.27867i	−0.953287	−	0.302065i	$-0.902324\pi$
$173$	−9.71003	−	16.8183i	−0.738240	−	1.27867i	0.215048	−	0.976604i	$-0.431009\pi$
$174$		0			0
$175$		0			0
$176$	−0.732051	−	1.26795i	−0.0551804	−	0.0955753i
$177$		0			0
$178$	16.1112			1.20758
$179$	−4.09808	−	7.09808i	−0.306305	−	0.530535i	0.671246	−	0.741234i	$-0.265759\pi$
$179$	−4.09808	−	7.09808i	−0.306305	−	0.530535i	−0.977551	+	0.210699i	$0.932426\pi$
$180$		0			0
$181$	−20.9730			−1.55891			−0.779454	−	0.626459i	$-0.784503\pi$
$181$	−20.9730			−1.55891			−0.779454	+	0.626459i	$0.784503\pi$
$182$		0			0
$183$		0			0
$184$	−7.92820			−0.584475
$185$	−2.07055	+	3.58630i	−0.152230	+	0.263670i
$186$		0			0
$187$	−2.55103	−	4.41851i	−0.186549	−	0.323113i
$188$	4.62158			0.337063
$189$		0			0
$190$	−0.267949			−0.0194391
$191$	−3.59808	−	6.23205i	−0.260348	−	0.450935i	0.705987	−	0.708225i	$-0.250504\pi$
$191$	−3.59808	−	6.23205i	−0.260348	−	0.450935i	−0.966334	+	0.257290i	$0.917171\pi$
$192$		0			0
$193$	11.8660	−	20.5526i	0.854135	−	1.47941i	−0.0233098	−	0.999728i	$-0.507420\pi$
$193$	11.8660	−	20.5526i	0.854135	−	1.47941i	0.877445	−	0.479677i	$-0.159246\pi$
$194$	−1.03528			−0.0743285
$195$		0			0
$196$		0			0
$197$	−9.66025			−0.688265			−0.344132	−	0.938921i	$-0.611827\pi$
$197$	−9.66025			−0.688265			−0.344132	+	0.938921i	$0.611827\pi$
$198$		0			0
$199$	−5.79555	−	10.0382i	−0.410836	−	0.711589i	0.584145	−	0.811649i	$-0.301430\pi$
$199$	−5.79555	−	10.0382i	−0.410836	−	0.711589i	−0.994981	+	0.100060i	$0.968096\pi$
$200$	−4.73205			−0.334607
$201$		0			0
$202$	2.89778	+	5.01910i	0.203887	+	0.353142i
$203$		0			0
$204$		0			0
$205$	−1.46410	−	2.53590i	−0.102257	−	0.177115i
$206$	5.60609	+	9.71003i	0.390595	+	0.676530i
$207$		0			0
$208$	1.22474	−	2.12132i	0.0849208	−	0.147087i
$209$	−0.378937	+	0.656339i	−0.0262116	+	0.0453999i
$210$		0			0
$211$	−0.633975	−	1.09808i	−0.0436446	−	0.0755947i	0.843378	−	0.537321i	$-0.180564\pi$
$211$	−0.633975	−	1.09808i	−0.0436446	−	0.0755947i	−0.887022	+	0.461726i	$0.847230\pi$
$212$	−6.73205			−0.462359
$213$		0			0
$214$	−3.07180			−0.209984
$215$	−3.15660	+	5.46739i	−0.215278	+	0.372873i
$216$		0			0
$217$		0			0
$218$	−5.29423	+	9.16987i	−0.358570	+	0.621062i
$219$		0			0
$220$	0.378937	−	0.656339i	0.0255480	−	0.0442504i
$221$	4.26795	−	7.39230i	0.287093	−	0.497260i
$222$		0			0
$223$	−1.88108	+	3.25813i	−0.125967	+	0.218181i	−0.922110	−	0.386927i	$-0.873537\pi$
$223$	−1.88108	+	3.25813i	−0.125967	+	0.218181i	0.796144	+	0.605108i	$0.206870\pi$
$224$		0			0
$225$		0			0
$226$	−7.33013	+	12.6962i	−0.487593	+	0.844535i
$227$	−3.34607			−0.222086			−0.111043	−	0.993816i	$-0.535419\pi$
$227$	−3.34607			−0.222086			−0.111043	+	0.993816i	$0.535419\pi$
$228$		0			0
$229$	13.8004			0.911954			0.455977	−	0.889992i	$-0.349290\pi$
$229$	13.8004			0.911954			0.455977	+	0.889992i	$0.349290\pi$
$230$	−2.05197	−	3.55412i	−0.135303	−	0.234351i
$231$		0			0
$232$	1.36603	−	2.36603i	0.0896840	−	0.155337i
$233$	0.696152	−	1.20577i	0.0456065	−	0.0789927i	−0.842321	−	0.538976i	$-0.818811\pi$
$233$	0.696152	−	1.20577i	0.0456065	−	0.0789927i	0.887928	+	0.459983i	$0.152145\pi$
$234$		0			0
$235$	1.19615	+	2.07180i	0.0780284	+	0.135149i
$236$	7.39924	+	12.8159i	0.481649	+	0.834241i
$237$		0			0
$238$		0			0
$239$	−6.23205	−	10.7942i	−0.403118	−	0.698221i	0.590983	−	0.806684i	$-0.298740\pi$
$239$	−6.23205	−	10.7942i	−0.403118	−	0.698221i	−0.994100	+	0.108464i	$0.965407\pi$
$240$		0			0
$241$	12.7279			0.819878			0.409939	−	0.912113i	$-0.365550\pi$
$241$	12.7279			0.819878			0.409939	+	0.912113i	$0.365550\pi$
$242$	4.42820	+	7.66987i	0.284656	+	0.493038i
$243$		0			0
$244$	4.38134			0.280487
$245$		0			0
$246$		0			0
$247$	−1.26795			−0.0806777
$248$	−3.67423	+	6.36396i	−0.233314	+	0.404112i
$249$		0			0
$250$	−2.51884	−	4.36276i	−0.159305	−	0.275925i
$251$	0.517638			0.0326730			0.0163365	−	0.999867i	$-0.494800\pi$
$251$	0.517638			0.0326730			0.0163365	+	0.999867i	$0.494800\pi$
$252$		0			0
$253$	−11.6077			−0.729770
$254$	2.96410	+	5.13397i	0.185984	+	0.322134i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.76217			−0.234678			−0.117339	−	0.993092i	$-0.537436\pi$
$257$	−3.76217			−0.234678			−0.117339	+	0.993092i	$0.537436\pi$
$258$		0			0
$259$		0			0
$260$	1.26795			0.0786349
$261$		0			0
$262$	6.24384	+	10.8147i	0.385746	+	0.668131i
$263$	−2.66025			−0.164038			−0.0820191	−	0.996631i	$-0.526137\pi$
$263$	−2.66025			−0.164038			−0.0820191	+	0.996631i	$0.526137\pi$
$264$		0			0
$265$	−1.74238	−	3.01790i	−0.107034	−	0.185388i
$266$		0			0
$267$		0			0
$268$	1.90192	+	3.29423i	0.116178	+	0.201227i
$269$	13.4536	+	23.3023i	0.820281	+	1.42077i	0.905473	+	0.424404i	$0.139516\pi$
$269$	13.4536	+	23.3023i	0.820281	+	1.42077i	−0.0851918	+	0.996365i	$0.527150\pi$
$270$		0			0
$271$	−7.39924	+	12.8159i	−0.449472	+	0.778508i	−0.998352	−	0.0573934i	$-0.981721\pi$
$271$	−7.39924	+	12.8159i	−0.449472	+	0.778508i	0.548880	+	0.835901i	$0.315054\pi$
$272$	−1.74238	+	3.01790i	−0.105647	+	0.182987i
$273$		0			0
$274$		0			0
$275$	−6.92820			−0.417786
$276$		0			0
$277$	−16.1962			−0.973132			−0.486566	−	0.873644i	$-0.661751\pi$
$277$	−16.1962			−0.973132			−0.486566	+	0.873644i	$0.661751\pi$
$278$	10.1075	−	17.5068i	0.606210	−	1.04999i
$279$		0			0
$280$		0			0
$281$	−8.69615	+	15.0622i	−0.518769	+	0.898534i	0.480993	+	0.876724i	$0.340276\pi$
$281$	−8.69615	+	15.0622i	−0.518769	+	0.898534i	−0.999762	+	0.0218099i	$0.993057\pi$
$282$		0			0
$283$	−4.88040	+	8.45310i	−0.290109	+	0.502484i	−0.973835	−	0.227255i	$-0.927025\pi$
$283$	−4.88040	+	8.45310i	−0.290109	+	0.502484i	0.683726	+	0.729739i	$0.260358\pi$
$284$	−0.401924	+	0.696152i	−0.0238498	+	0.0413090i
$285$		0			0
$286$	1.79315	−	3.10583i	0.106031	−	0.183651i
$287$		0			0
$288$		0			0
$289$	2.42820	−	4.20577i	0.142835	−	0.247398i
$290$	1.41421			0.0830455
$291$		0			0
$292$	4.62158			0.270457
$293$	−1.48356	−	2.56961i	−0.0866707	−	0.150118i	0.819431	−	0.573178i	$-0.194289\pi$
$293$	−1.48356	−	2.56961i	−0.0866707	−	0.150118i	−0.906102	+	0.423059i	$0.860956\pi$
$294$		0			0
$295$	−3.83013	+	6.63397i	−0.222999	+	0.386245i
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$	−1.19615	−	2.07180i	−0.0692912	−	0.120016i
$299$	−9.71003	−	16.8183i	−0.561545	−	0.972625i
$300$		0			0
$301$		0			0
$302$	8.69615	+	15.0622i	0.500407	+	0.866731i
$303$		0			0
$304$	0.517638			0.0296886
$305$	1.13397	+	1.96410i	0.0649312	+	0.112464i
$306$		0			0
$307$	−11.9329			−0.681046			−0.340523	−	0.940236i	$-0.610604\pi$
$307$	−11.9329			−0.681046			−0.340523	+	0.940236i	$0.610604\pi$
$308$		0			0
$309$		0			0
$310$	−3.80385			−0.216044
$311$	9.09085	−	15.7458i	0.515495	−	0.892863i	−0.484343	−	0.874878i	$-0.660941\pi$
$311$	9.09085	−	15.7458i	0.515495	−	0.892863i	0.999838	−	0.0179854i	$-0.00572524\pi$
$312$		0			0
$313$	3.34607	+	5.79555i	0.189131	+	0.327584i	0.944961	−	0.327184i	$-0.106100\pi$
$313$	3.34607	+	5.79555i	0.189131	+	0.327584i	−0.755830	+	0.654768i	$0.772766\pi$
$314$	−17.2851			−0.975456
$315$		0			0
$316$	14.1244			0.794557
$317$	16.2942	+	28.2224i	0.915175	+	1.58513i	0.806645	+	0.591037i	$0.201281\pi$
$317$	16.2942	+	28.2224i	0.915175	+	1.58513i	0.108530	+	0.994093i	$0.465386\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	−0.517638			−0.0289368
$321$		0			0
$322$		0			0
$323$	1.80385			0.100369
$324$		0			0
$325$	−5.79555	−	10.0382i	−0.321480	−	0.556819i
$326$	−7.07180			−0.391671
$327$		0			0
$328$	2.82843	+	4.89898i	0.156174	+	0.270501i
$329$		0			0
$330$		0			0
$331$	6.02628	+	10.4378i	0.331234	+	0.573715i	0.982754	−	0.184917i	$-0.0592016\pi$
$331$	6.02628	+	10.4378i	0.331234	+	0.573715i	−0.651520	+	0.758632i	$0.725868\pi$
$332$	−4.94975	−	8.57321i	−0.271653	−	0.470516i
$333$		0			0
$334$	6.64136	−	11.5032i	0.363399	−	0.629426i
$335$	−0.984508	+	1.70522i	−0.0537894	+	0.0931660i
$336$		0			0
$337$	10.6603	+	18.4641i	0.580701	+	1.00580i	0.995396	+	0.0958434i	$0.0305548\pi$
$337$	10.6603	+	18.4641i	0.580701	+	1.00580i	−0.414695	+	0.909960i	$0.636112\pi$
$338$	−7.00000			−0.380750
$339$		0			0
$340$	−1.80385			−0.0978274
$341$	−5.37945	+	9.31749i	−0.291314	+	0.504570i
$342$		0			0
$343$		0			0
$344$	6.09808	−	10.5622i	0.328786	−	0.569474i
$345$		0			0
$346$	−9.71003	+	16.8183i	−0.522014	+	0.904155i
$347$	10.8564	−	18.8038i	0.582802	−	1.00944i	−0.412343	−	0.911029i	$-0.635289\pi$
$347$	10.8564	−	18.8038i	0.582802	−	1.00944i	0.995145	−	0.0984148i	$-0.0313772\pi$
$348$		0			0
$349$	17.2987	−	29.9623i	0.925980	−	1.60384i	0.136002	−	0.990709i	$-0.456575\pi$
$349$	17.2987	−	29.9623i	0.925980	−	1.60384i	0.789978	−	0.613136i	$-0.210092\pi$
$350$		0			0
$351$		0			0
$352$	−0.732051	+	1.26795i	−0.0390184	+	0.0675819i
$353$	−0.101536			−0.00540421			−0.00270211	−	0.999996i	$-0.500860\pi$
$353$	−0.101536			−0.00540421			−0.00270211	+	0.999996i	$0.500860\pi$
$354$		0			0
$355$	−0.416102			−0.0220844
$356$	−8.05558	−	13.9527i	−0.426945	−	0.739490i
$357$		0			0
$358$	−4.09808	+	7.09808i	−0.216590	+	0.375145i
$359$	−6.96410	+	12.0622i	−0.367551	+	0.636617i	−0.989182	−	0.146693i	$-0.953137\pi$
$359$	−6.96410	+	12.0622i	−0.367551	+	0.636617i	0.621631	+	0.783310i	$0.286470\pi$
$360$		0			0
$361$	9.36603	+	16.2224i	0.492949	+	0.853812i
$362$	10.4865	+	18.1631i	0.551157	+	0.954632i
$363$		0			0
$364$		0			0
$365$	1.19615	+	2.07180i	0.0626095	+	0.108443i
$366$		0			0
$367$	−0.277401			−0.0144802			−0.00724012	−	0.999974i	$-0.502305\pi$
$367$	−0.277401			−0.0144802			−0.00724012	+	0.999974i	$0.502305\pi$
$368$	3.96410	+	6.86603i	0.206643	+	0.357916i
$369$		0			0
$370$	4.14110			0.215286
$371$		0			0
$372$		0			0
$373$	19.1244			0.990222			0.495111	−	0.868830i	$-0.335127\pi$
$373$	19.1244			0.990222			0.495111	+	0.868830i	$0.335127\pi$
$374$	−2.55103	+	4.41851i	−0.131910	+	0.228476i
$375$		0			0
$376$	−2.31079	−	4.00240i	−0.119170	−	0.206408i
$377$	6.69213			0.344662
$378$		0			0
$379$	−27.5167			−1.41344			−0.706718	−	0.707495i	$-0.749825\pi$
$379$	−27.5167			−1.41344			−0.706718	+	0.707495i	$0.749825\pi$
$380$	0.133975	+	0.232051i	0.00687275	+	0.0119040i
$381$		0			0
$382$	−3.59808	+	6.23205i	−0.184094	+	0.318859i
$383$	34.2185			1.74849			0.874243	−	0.485489i	$-0.161359\pi$
$383$	34.2185			1.74849			0.874243	+	0.485489i	$0.161359\pi$
$384$		0			0
$385$		0			0
$386$	−23.7321			−1.20793
$387$		0			0
$388$	0.517638	+	0.896575i	0.0262791	+	0.0455167i
$389$	4.87564			0.247205			0.123602	−	0.992332i	$-0.460555\pi$
$389$	4.87564			0.247205			0.123602	+	0.992332i	$0.460555\pi$
$390$		0			0
$391$	13.8140	+	23.9265i	0.698602	+	1.21001i
$392$		0			0
$393$		0			0
$394$	4.83013	+	8.36603i	0.243338	+	0.421474i
$395$	3.65565	+	6.33178i	0.183936	+	0.318586i
$396$		0			0
$397$	−13.1948	+	22.8541i	−0.662228	+	1.14701i	0.317801	+	0.948157i	$0.397055\pi$
$397$	−13.1948	+	22.8541i	−0.662228	+	1.14701i	−0.980029	+	0.198855i	$0.936278\pi$
$398$	−5.79555	+	10.0382i	−0.290505	+	0.503169i
$399$		0			0
$400$	2.36603	+	4.09808i	0.118301	+	0.204904i
$401$	25.0526			1.25107			0.625533	−	0.780198i	$-0.284882\pi$
$401$	25.0526			1.25107			0.625533	+	0.780198i	$0.284882\pi$
$402$		0			0
$403$	−18.0000			−0.896644
$404$	2.89778	−	5.01910i	0.144170	−	0.249709i
$405$		0			0
$406$		0			0
$407$	5.85641	−	10.1436i	0.290291	−	0.502799i
$408$		0			0
$409$	−8.90138	+	15.4176i	−0.440145	+	0.762354i	−0.997700	−	0.0677865i	$-0.978406\pi$
$409$	−8.90138	+	15.4176i	−0.440145	+	0.762354i	0.557555	+	0.830140i	$0.311740\pi$
$410$	−1.46410	+	2.53590i	−0.0723068	+	0.125239i
$411$		0			0
$412$	5.60609	−	9.71003i	0.276192	−	0.478379i
$413$		0			0
$414$		0			0
$415$	2.56218	−	4.43782i	0.125772	−	0.217844i
$416$	−2.44949			−0.120096
$417$		0			0
$418$	0.757875			0.0370689
$419$	−11.3323	−	19.6281i	−0.553619	−	0.958896i	−0.998010	−	0.0630626i	$-0.979913\pi$
$419$	−11.3323	−	19.6281i	−0.553619	−	0.958896i	0.444391	−	0.895833i	$-0.353420\pi$
$420$		0			0
$421$	−14.0263	+	24.2942i	−0.683599	+	1.18403i	0.290276	+	0.956943i	$0.406253\pi$
$421$	−14.0263	+	24.2942i	−0.683599	+	1.18403i	−0.973875	+	0.227085i	$0.927080\pi$
$422$	−0.633975	+	1.09808i	−0.0308614	+	0.0534535i
$423$		0			0
$424$	3.36603	+	5.83013i	0.163469	+	0.283136i
$425$	8.24504	+	14.2808i	0.399943	+	0.692722i
$426$		0			0
$427$		0			0
$428$	1.53590	+	2.66025i	0.0742405	+	0.128588i
$429$		0			0
$430$	6.31319			0.304449
$431$	−13.3923	−	23.1962i	−0.645085	−	1.11732i	−0.984282	−	0.176604i	$-0.943489\pi$
$431$	−13.3923	−	23.1962i	−0.645085	−	1.11732i	0.339197	−	0.940715i	$-0.389845\pi$
$432$		0			0
$433$	−20.2523			−0.973261			−0.486631	−	0.873608i	$-0.661774\pi$
$433$	−20.2523			−0.973261			−0.486631	+	0.873608i	$0.661774\pi$
$434$		0			0
$435$		0			0
$436$	10.5885			0.507095
$437$	2.05197	−	3.55412i	0.0981590	−	0.170016i
$438$		0			0
$439$	−9.14162	−	15.8338i	−0.436306	−	0.755704i	0.561095	−	0.827751i	$-0.310380\pi$
$439$	−9.14162	−	15.8338i	−0.436306	−	0.755704i	−0.997401	+	0.0720474i	$0.977047\pi$
$440$	−0.757875			−0.0361303
$441$		0			0
$442$	−8.53590			−0.406011
$443$	−18.4904	−	32.0263i	−0.878505	−	1.52161i	−0.852982	−	0.521940i	$-0.825208\pi$
$443$	−18.4904	−	32.0263i	−0.878505	−	1.52161i	−0.0255224	−	0.999674i	$-0.508125\pi$
$444$		0			0
$445$	4.16987	−	7.22243i	0.197671	−	0.342376i
$446$	3.76217			0.178144
$447$		0			0
$448$		0			0
$449$	23.7846			1.12247			0.561233	−	0.827658i	$-0.310327\pi$
$449$	23.7846			1.12247			0.561233	+	0.827658i	$0.310327\pi$
$450$		0			0
$451$	4.14110	+	7.17260i	0.194997	+	0.337745i
$452$	14.6603			0.689560
$453$		0			0
$454$	1.67303	+	2.89778i	0.0785193	+	0.135999i
$455$		0			0
$456$		0			0
$457$	11.1340	+	19.2846i	0.520825	+	0.902096i	0.999707	+	0.0242164i	$0.00770906\pi$
$457$	11.1340	+	19.2846i	0.520825	+	0.902096i	−0.478881	+	0.877880i	$0.658958\pi$
$458$	−6.90018	−	11.9515i	−0.322424	−	0.558455i
$459$		0			0
$460$	−2.05197	+	3.55412i	−0.0956736	+	0.165712i
$461$	19.4894	−	33.7566i	0.907712	−	1.57220i	0.0904771	−	0.995899i	$-0.471161\pi$
$461$	19.4894	−	33.7566i	0.907712	−	1.57220i	0.817235	−	0.576305i	$-0.195506\pi$
$462$		0			0
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	0.778209	−	0.628005i	$-0.216128\pi$
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	−0.932973	+	0.359946i	$0.882795\pi$
$464$	−2.73205			−0.126832
$465$		0			0
$466$	−1.39230			−0.0644973
$467$	12.2982	−	21.3011i	0.569094	−	0.985699i	−0.427562	−	0.903986i	$-0.640628\pi$
$467$	12.2982	−	21.3011i	0.569094	−	0.985699i	0.996656	−	0.0817131i	$-0.0260391\pi$
$468$		0			0
$469$		0			0
$470$	1.19615	−	2.07180i	0.0551744	−	0.0955649i
$471$		0			0
$472$	7.39924	−	12.8159i	0.340577	−	0.589898i
$473$	8.92820	−	15.4641i	0.410519	−	0.711040i
$474$		0			0
$475$	1.22474	−	2.12132i	0.0561951	−	0.0973329i
$476$		0			0
$477$		0			0
$478$	−6.23205	+	10.7942i	−0.285047	+	0.493717i
$479$	13.2827			0.606903			0.303452	−	0.952847i	$-0.401861\pi$
$479$	13.2827			0.606903			0.303452	+	0.952847i	$0.401861\pi$
$480$		0			0
$481$	19.5959			0.893497
$482$	−6.36396	−	11.0227i	−0.289870	−	0.502070i
$483$		0			0
$484$	4.42820	−	7.66987i	0.201282	−	0.348631i
$485$	−0.267949	+	0.464102i	−0.0121669	+	0.0210738i
$486$		0			0
$487$	16.1603	+	27.9904i	0.732291	+	1.26837i	0.955902	+	0.293687i	$0.0948822\pi$
$487$	16.1603	+	27.9904i	0.732291	+	1.26837i	−0.223611	+	0.974679i	$0.571784\pi$
$488$	−2.19067	−	3.79435i	−0.0991670	−	0.171762i
$489$		0			0
$490$		0			0
$491$	−2.53590	−	4.39230i	−0.114443	−	0.198222i	0.803114	−	0.595826i	$-0.203175\pi$
$491$	−2.53590	−	4.39230i	−0.114443	−	0.198222i	−0.917557	+	0.397604i	$0.869842\pi$
$492$		0			0
$493$	−9.52056			−0.428784
$494$	0.633975	+	1.09808i	0.0285239	+	0.0494048i
$495$		0			0
$496$	7.34847			0.329956
$497$		0			0
$498$		0			0
$499$	7.32051			0.327711			0.163855	−	0.986484i	$-0.447607\pi$
$499$	7.32051			0.327711			0.163855	+	0.986484i	$0.447607\pi$
$500$	−2.51884	+	4.36276i	−0.112646	+	0.195109i
$501$		0			0
$502$	−0.258819	−	0.448288i	−0.0115517	−	0.0200081i
$503$	−28.9406			−1.29040			−0.645199	−	0.764015i	$-0.723226\pi$
$503$	−28.9406			−1.29040			−0.645199	+	0.764015i	$0.723226\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	5.80385	+	10.0526i	0.258012	+	0.446891i
$507$		0			0
$508$	2.96410	−	5.13397i	0.131511	−	0.227783i
$509$	7.62587			0.338011			0.169005	−	0.985615i	$-0.445944\pi$
$509$	7.62587			0.338011			0.169005	+	0.985615i	$0.445944\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.88108	+	3.25813i	0.0829710	+	0.143710i
$515$	5.80385			0.255748
$516$		0			0
$517$	−3.38323	−	5.85993i	−0.148794	−	0.257719i
$518$		0			0
$519$		0			0
$520$	−0.633975	−	1.09808i	−0.0278016	−	0.0481538i
$521$	−16.2635	−	28.1691i	−0.712515	−	1.23411i	−0.963910	−	0.266228i	$-0.914223\pi$
$521$	−16.2635	−	28.1691i	−0.712515	−	1.23411i	0.251395	−	0.967885i	$-0.419111\pi$
$522$		0			0
$523$	−19.6281	+	33.9969i	−0.858277	+	1.48658i	0.0152941	+	0.999883i	$0.495132\pi$
$523$	−19.6281	+	33.9969i	−0.858277	+	1.48658i	−0.873571	+	0.486696i	$0.838202\pi$
$524$	6.24384	−	10.8147i	0.272764	−	0.472440i
$525$		0			0
$526$	1.33013	+	2.30385i	0.0579963	+	0.100453i
$527$	25.6077			1.11549
$528$		0			0
$529$	39.8564			1.73289
$530$	−1.74238	+	3.01790i	−0.0756843	+	0.131089i
$531$		0			0
$532$		0			0
$533$	−6.92820	+	12.0000i	−0.300094	+	0.519778i
$534$		0			0
$535$	−0.795040	+	1.37705i	−0.0343726	+	0.0595350i
$536$	1.90192	−	3.29423i	0.0821506	−	0.142289i
$537$		0			0
$538$	13.4536	−	23.3023i	0.580026	−	1.00464i
$539$		0			0
$540$		0			0
$541$	−10.3660	+	17.9545i	−0.445670	+	0.771924i	−0.998099	−	0.0616369i	$-0.980368\pi$
$541$	−10.3660	+	17.9545i	−0.445670	+	0.771924i	0.552428	+	0.833560i	$0.313701\pi$
$542$	14.7985			0.635649
$543$		0			0
$544$	3.48477			0.149408
$545$	2.74049	+	4.74668i	0.117390	+	0.203325i
$546$		0			0
$547$	5.73205	−	9.92820i	0.245085	−	0.424499i	−0.717071	−	0.697000i	$-0.754518\pi$
$547$	5.73205	−	9.92820i	0.245085	−	0.424499i	0.962155	+	0.272501i	$0.0878509\pi$
$548$		0			0
$549$		0			0
$550$	3.46410	+	6.00000i	0.147710	+	0.255841i
$551$	0.707107	+	1.22474i	0.0301238	+	0.0521759i
$552$		0			0
$553$		0			0
$554$	8.09808	+	14.0263i	0.344054	+	0.595920i
$555$		0			0
$556$	−20.2151			−0.857311
$557$	1.43782	+	2.49038i	0.0609225	+	0.105521i	0.894878	−	0.446311i	$-0.147262\pi$
$557$	1.43782	+	2.49038i	0.0609225	+	0.105521i	−0.833956	+	0.551832i	$0.813929\pi$
$558$		0			0
$559$	29.8744			1.26355
$560$		0			0
$561$		0			0
$562$	17.3923			0.733650
$563$	−0.637756	+	1.10463i	−0.0268782	+	0.0465545i	−0.879152	−	0.476542i	$-0.841890\pi$
$563$	−0.637756	+	1.10463i	−0.0268782	+	0.0465545i	0.852273	+	0.523097i	$0.175223\pi$
$564$		0			0
$565$	3.79435	+	6.57201i	0.159630	+	0.276487i
$566$	9.76079			0.410277
$567$		0			0
$568$	0.803848			0.0337287
$569$	13.4641	+	23.3205i	0.564445	+	0.977647i	0.997101	+	0.0760878i	$0.0242429\pi$
$569$	13.4641	+	23.3205i	0.564445	+	0.977647i	−0.432657	+	0.901559i	$0.642424\pi$
$570$		0			0
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	−3.58630			−0.149951
$573$		0			0
$574$		0			0
$575$	37.5167			1.56455
$576$		0			0
$577$	−13.1440	−	22.7661i	−0.547193	−	0.947766i	−0.998465	−	0.0553797i	$-0.982363\pi$
$577$	−13.1440	−	22.7661i	−0.547193	−	0.947766i	0.451272	−	0.892386i	$-0.350970\pi$
$578$	−4.85641			−0.202000
$579$		0			0
$580$	−0.707107	−	1.22474i	−0.0293610	−	0.0508548i
$581$		0			0
$582$		0			0
$583$	4.92820	+	8.53590i	0.204105	+	0.353521i
$584$	−2.31079	−	4.00240i	−0.0956211	−	0.165621i
$585$		0			0
$586$	−1.48356	+	2.56961i	−0.0612855	+	0.106150i
$587$	1.76097	−	3.05008i	0.0726828	−	0.125890i	−0.827393	−	0.561623i	$-0.810177\pi$
$587$	1.76097	−	3.05008i	0.0726828	−	0.125890i	0.900076	+	0.435732i	$0.143511\pi$
$588$		0			0
$589$	−1.90192	−	3.29423i	−0.0783674	−	0.135736i
$590$	7.66025			0.315368
$591$		0			0
$592$	−8.00000			−0.328798
$593$	−3.39683	+	5.88349i	−0.139491	+	0.241606i	−0.927304	−	0.374309i	$-0.877880\pi$
$593$	−3.39683	+	5.88349i	−0.139491	+	0.241606i	0.787813	+	0.615915i	$0.211213\pi$
$594$		0			0
$595$		0			0
$596$	−1.19615	+	2.07180i	−0.0489963	+	0.0848641i
$597$		0			0
$598$	−9.71003	+	16.8183i	−0.397073	+	0.687750i
$599$	−6.19615	+	10.7321i	−0.253168	+	0.438500i	−0.964396	−	0.264461i	$-0.914806\pi$
$599$	−6.19615	+	10.7321i	−0.253168	+	0.438500i	0.711228	+	0.702961i	$0.248139\pi$
$600$		0			0
$601$	20.9730	−	36.3262i	0.855505	−	1.48178i	−0.0206704	−	0.999786i	$-0.506580\pi$
$601$	20.9730	−	36.3262i	0.855505	−	1.48178i	0.876176	−	0.481992i	$-0.160087\pi$
$602$		0			0
$603$		0			0
$604$	8.69615	−	15.0622i	0.353841	−	0.612871i
$605$	4.58441			0.186383
$606$		0			0
$607$	−21.3891			−0.868156			−0.434078	−	0.900875i	$-0.642926\pi$
$607$	−21.3891			−0.868156			−0.434078	+	0.900875i	$0.642926\pi$
$608$	−0.258819	−	0.448288i	−0.0104965	−	0.0181805i
$609$		0			0
$610$	1.13397	−	1.96410i	0.0459133	−	0.0795241i
$611$	5.66025	−	9.80385i	0.228989	−	0.396621i
$612$		0			0
$613$	−10.2224	−	17.7058i	−0.412880	−	0.715129i	0.582323	−	0.812957i	$-0.302144\pi$
$613$	−10.2224	−	17.7058i	−0.412880	−	0.715129i	−0.995203	+	0.0978280i	$0.968810\pi$
$614$	5.96644	+	10.3342i	0.240786	+	0.417054i
$615$		0			0
$616$		0			0
$617$	21.1962	+	36.7128i	0.853325	+	1.47800i	0.878190	+	0.478311i	$0.158751\pi$
$617$	21.1962	+	36.7128i	0.853325	+	1.47800i	−0.0248653	+	0.999691i	$0.507916\pi$
$618$		0			0
$619$	−7.48717			−0.300935			−0.150467	−	0.988615i	$-0.548078\pi$
$619$	−7.48717			−0.300935			−0.150467	+	0.988615i	$0.548078\pi$
$620$	1.90192	+	3.29423i	0.0763831	+	0.132299i
$621$		0			0
$622$	−18.1817			−0.729020
$623$		0			0
$624$		0			0
$625$	21.0526			0.842102
$626$	3.34607	−	5.79555i	0.133736	−	0.231637i
$627$		0			0
$628$	8.64256	+	14.9694i	0.344876	+	0.597343i
$629$	−27.8781			−1.11157
$630$		0			0
$631$	−3.87564			−0.154287			−0.0771435	−	0.997020i	$-0.524580\pi$
$631$	−3.87564			−0.154287			−0.0771435	+	0.997020i	$0.524580\pi$
$632$	−7.06218	−	12.2321i	−0.280918	−	0.486565i
$633$		0			0
$634$	16.2942	−	28.2224i	0.647126	−	1.12086i
$635$	3.06866			0.121776
$636$		0			0
$637$		0			0
$638$	−4.00000			−0.158362
$639$		0			0
$640$	0.258819	+	0.448288i	0.0102307	+	0.0177201i
$641$	3.05256			0.120569			0.0602844	−	0.998181i	$-0.480799\pi$
$641$	3.05256			0.120569			0.0602844	+	0.998181i	$0.480799\pi$
$642$		0			0
$643$	0.845807	+	1.46498i	0.0333554	+	0.0577732i	0.882221	−	0.470835i	$-0.156047\pi$
$643$	0.845807	+	1.46498i	0.0333554	+	0.0577732i	−0.848866	+	0.528608i	$0.822714\pi$
$644$		0			0
$645$		0			0
$646$	−0.901924	−	1.56218i	−0.0354857	−	0.0614631i
$647$	−7.91688	−	13.7124i	−0.311244	−	0.539091i	0.667388	−	0.744711i	$-0.267412\pi$
$647$	−7.91688	−	13.7124i	−0.311244	−	0.539091i	−0.978632	+	0.205619i	$0.934079\pi$
$648$		0			0
$649$	10.8332	−	18.7637i	0.425242	−	0.736540i
$650$	−5.79555	+	10.0382i	−0.227320	+	0.393730i
$651$		0			0
$652$	3.53590	+	6.12436i	0.138476	+	0.239848i
$653$	41.3205			1.61700			0.808498	−	0.588499i	$-0.200281\pi$
$653$	41.3205			1.61700			0.808498	+	0.588499i	$0.200281\pi$
$654$		0			0
$655$	6.46410			0.252573
$656$	2.82843	−	4.89898i	0.110432	−	0.191273i
$657$		0			0
$658$		0			0
$659$	−19.5622	+	33.8827i	−0.762034	+	1.31988i	0.179766	+	0.983709i	$0.442466\pi$
$659$	−19.5622	+	33.8827i	−0.762034	+	1.31988i	−0.941800	+	0.336173i	$0.890867\pi$
$660$		0			0
$661$	−10.7267	+	18.5792i	−0.417221	+	0.722648i	−0.995659	−	0.0930785i	$-0.970329\pi$
$661$	−10.7267	+	18.5792i	−0.417221	+	0.722648i	0.578438	+	0.815727i	$0.303663\pi$
$662$	6.02628	−	10.4378i	0.234218	−	0.405677i
$663$		0			0
$664$	−4.94975	+	8.57321i	−0.192087	+	0.332705i
$665$		0			0
$666$		0			0
$667$	−10.8301	+	18.7583i	−0.419344	+	0.726325i
$668$	−13.2827			−0.513924
$669$		0			0
$670$	1.96902			0.0760697
$671$	−3.20736	−	5.55532i	−0.123819	−	0.214461i
$672$		0			0
$673$	20.0885	−	34.7942i	0.774353	−	1.34122i	−0.160804	−	0.986986i	$-0.551409\pi$
$673$	20.0885	−	34.7942i	0.774353	−	1.34122i	0.935157	−	0.354233i	$-0.115258\pi$
$674$	10.6603	−	18.4641i	0.410618	−	0.711211i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	0.568406	+	0.984508i	0.0218456	+	0.0378377i	0.876742	−	0.480962i	$-0.159712\pi$
$677$	0.568406	+	0.984508i	0.0218456	+	0.0378377i	−0.854896	+	0.518800i	$0.826379\pi$
$678$		0			0
$679$		0			0
$680$	0.901924	+	1.56218i	0.0345872	+	0.0599068i
$681$		0			0
$682$	10.7589			0.411980
$683$	−6.80385	−	11.7846i	−0.260342	−	0.450926i	0.705991	−	0.708221i	$-0.250502\pi$
$683$	−6.80385	−	11.7846i	−0.260342	−	0.450926i	−0.966333	+	0.257295i	$0.917169\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−12.1962			−0.464974
$689$	−8.24504	+	14.2808i	−0.314111	+	0.544057i
$690$		0			0
$691$	18.4913	+	32.0279i	0.703442	+	1.21840i	0.967251	+	0.253822i	$0.0816878\pi$
$691$	18.4913	+	32.0279i	0.703442	+	1.21840i	−0.263809	+	0.964575i	$0.584979\pi$
$692$	19.4201			0.738240
$693$		0			0
$694$	−21.7128			−0.824207
$695$	−5.23205	−	9.06218i	−0.198463	−	0.343748i
$696$		0			0
$697$	9.85641	−	17.0718i	0.373338	−	0.646640i
$698$	−34.5975			−1.30953
$699$		0			0
$700$		0			0
$701$	−20.5359			−0.775630			−0.387815	−	0.921737i	$-0.626770\pi$
$701$	−20.5359			−0.775630			−0.387815	+	0.921737i	$0.626770\pi$
$702$		0			0
$703$	2.07055	+	3.58630i	0.0780924	+	0.135260i
$704$	1.46410			0.0551804
$705$		0			0
$706$	0.0507680	+	0.0879327i	0.00191068	+	0.00330939i
$707$		0			0
$708$		0			0
$709$	11.2679	+	19.5167i	0.423177	+	0.732964i	0.996248	−	0.0865418i	$-0.0275816\pi$
$709$	11.2679	+	19.5167i	0.423177	+	0.732964i	−0.573072	+	0.819505i	$0.694248\pi$
$710$	0.208051	+	0.360355i	0.00780802	+	0.0135239i
$711$		0			0
$712$	−8.05558	+	13.9527i	−0.301895	+	0.522898i
$713$	29.1301	−	50.4548i	1.09093	−	1.88955i
$714$		0			0
$715$	−0.928203	−	1.60770i	−0.0347128	−	0.0601244i
$716$	8.19615			0.306305
$717$		0			0
$718$	13.9282			0.519796
$719$	−17.0077	+	29.4582i	−0.634281	+	1.09861i	0.352386	+	0.935855i	$0.385371\pi$
$719$	−17.0077	+	29.4582i	−0.634281	+	1.09861i	−0.986667	+	0.162752i	$0.947963\pi$
$720$		0			0
$721$		0			0
$722$	9.36603	−	16.2224i	0.348567	−	0.603736i
$723$		0			0
$724$	10.4865	−	18.1631i	0.389727	−	0.675027i
$725$	−6.46410	+	11.1962i	−0.240071	+	0.415815i
$726$		0			0
$727$	14.8864	−	25.7840i	0.552106	−	0.956276i	−0.446016	−	0.895025i	$-0.647158\pi$
$727$	14.8864	−	25.7840i	0.552106	−	0.956276i	0.998122	−	0.0612512i	$-0.0195091\pi$
$728$		0			0
$729$		0			0
$730$	1.19615	−	2.07180i	0.0442716	−	0.0766806i
$731$	−42.5007			−1.57195
$732$		0			0
$733$	30.1146			1.11231			0.556154	−	0.831079i	$-0.312277\pi$
$733$	30.1146			1.11231			0.556154	+	0.831079i	$0.312277\pi$
$734$	0.138701	+	0.240237i	0.00511954	+	0.00886730i
$735$		0			0
$736$	3.96410	−	6.86603i	0.146119	−	0.253085i
$737$	2.78461	−	4.82309i	0.102572	−	0.177661i
$738$		0			0
$739$	8.07180	+	13.9808i	0.296926	+	0.514291i	0.975431	−	0.220305i	$-0.0707052\pi$
$739$	8.07180	+	13.9808i	0.296926	+	0.514291i	−0.678505	+	0.734596i	$0.737372\pi$
$740$	−2.07055	−	3.58630i	−0.0761150	−	0.131835i
$741$		0			0
$742$		0			0
$743$	−14.1244	−	24.4641i	−0.518172	−	0.897501i	−0.999777	−	0.0211123i	$-0.993279\pi$
$743$	−14.1244	−	24.4641i	−0.518172	−	0.897501i	0.481605	−	0.876389i	$-0.340054\pi$
$744$		0			0
$745$	−1.23835			−0.0453696
$746$	−9.56218	−	16.5622i	−0.350096	−	0.606384i
$747$		0			0
$748$	5.10205			0.186549
$749$		0			0
$750$		0			0
$751$	−50.1769			−1.83098			−0.915491	−	0.402339i	$-0.868197\pi$
$751$	−50.1769			−1.83098			−0.915491	+	0.402339i	$0.868197\pi$
$752$	−2.31079	+	4.00240i	−0.0842658	+	0.145953i
$753$		0			0
$754$	−3.34607	−	5.79555i	−0.121857	−	0.211062i
$755$	9.00292			0.327650
$756$		0			0
$757$	20.2487			0.735952			0.367976	−	0.929835i	$-0.380051\pi$
$757$	20.2487			0.735952			0.367976	+	0.929835i	$0.380051\pi$
$758$	13.7583	+	23.8301i	0.499725	+	0.865549i
$759$		0			0
$760$	0.133975	−	0.232051i	0.00485977	−	0.00841737i
$761$	39.7738			1.44180			0.720900	−	0.693039i	$-0.243729\pi$
$761$	39.7738			1.44180			0.720900	+	0.693039i	$0.243729\pi$
$762$		0			0
$763$		0			0
$764$	7.19615			0.260348
$765$		0			0
$766$	−17.1093	−	29.6341i	−0.618183	−	1.07072i
$767$	36.2487			1.30887
$768$		0			0
$769$	−14.9372	−	25.8719i	−0.538648	−	0.932966i	−0.998977	−	0.0452178i	$-0.985602\pi$
$769$	−14.9372	−	25.8719i	−0.538648	−	0.932966i	0.460329	−	0.887748i	$-0.347732\pi$
$770$		0			0
$771$		0			0
$772$	11.8660	+	20.5526i	0.427068	+	0.739703i
$773$	6.76148	+	11.7112i	0.243194	+	0.421224i	0.961622	−	0.274377i	$-0.0884716\pi$
$773$	6.76148	+	11.7112i	0.243194	+	0.421224i	−0.718429	+	0.695601i	$0.755138\pi$
$774$		0			0
$775$	17.3867	−	30.1146i	0.624547	−	1.08175i
$776$	0.517638	−	0.896575i	0.0185821	−	0.0321852i
$777$		0			0
$778$	−2.43782	−	4.22243i	−0.0874002	−	0.151382i
$779$	−2.92820			−0.104914
$780$		0			0
$781$	1.17691			0.0421133
$782$	13.8140	−	23.9265i	0.493986	−	0.855610i
$783$		0			0
$784$		0			0
$785$	−4.47372	+	7.74871i	−0.159674	+	0.276563i
$786$		0			0
$787$	18.0938	−	31.3393i	0.644973	−	1.11713i	−0.339334	−	0.940666i	$-0.610202\pi$
$787$	18.0938	−	31.3393i	0.644973	−	1.11713i	0.984308	−	0.176461i	$-0.0564649\pi$
$788$	4.83013	−	8.36603i	0.172066	−	0.298027i
$789$		0			0
$790$	3.65565	−	6.33178i	0.130062	−	0.225274i
$791$		0			0
$792$		0			0
$793$	5.36603	−	9.29423i	0.190553	−	0.330048i
$794$	26.3896			0.936531
$795$		0			0
$796$	11.5911			0.410836
$797$	12.2796	+	21.2690i	0.434967	+	0.753385i	0.997293	−	0.0735308i	$-0.0234267\pi$
$797$	12.2796	+	21.2690i	0.434967	+	0.753385i	−0.562326	+	0.826916i	$0.690093\pi$
$798$		0			0
$799$	−8.05256	+	13.9474i	−0.284879	+	0.493425i
$800$	2.36603	−	4.09808i	0.0836516	−	0.144889i
$801$		0			0
$802$	−12.5263	−	21.6962i	−0.442318	−	0.766118i
$803$	−3.38323	−	5.85993i	−0.119392	−	0.206792i
$804$		0			0
$805$		0			0
$806$	9.00000	+	15.5885i	0.317011	+	0.549080i
$807$		0			0
$808$	−5.79555			−0.203887
$809$	16.6603	+	28.8564i	0.585743	+	1.01454i	0.994782	+	0.102020i	$0.0325307\pi$
$809$	16.6603	+	28.8564i	0.585743	+	1.01454i	−0.409039	+	0.912517i	$0.634136\pi$
$810$		0			0
$811$	7.82894			0.274911			0.137456	−	0.990508i	$-0.456108\pi$
$811$	7.82894			0.274911			0.137456	+	0.990508i	$0.456108\pi$
$812$		0			0
$813$		0			0
$814$	−11.7128			−0.410534
$815$	−1.83032	+	3.17020i	−0.0641132	+	0.111047i
$816$		0			0
$817$	3.15660	+	5.46739i	0.110435	+	0.191280i
$818$	17.8028			0.622459
$819$		0			0
$820$	2.92820			0.102257
$821$	−3.33975	−	5.78461i	−0.116558	−	0.201884i	0.801844	−	0.597534i	$-0.203853\pi$
$821$	−3.33975	−	5.78461i	−0.116558	−	0.201884i	−0.918401	+	0.395650i	$0.870519\pi$
$822$		0			0
$823$	3.66025	−	6.33975i	0.127588	−	0.220990i	−0.795153	−	0.606408i	$-0.792610\pi$
$823$	3.66025	−	6.33975i	0.127588	−	0.220990i	0.922742	+	0.385419i	$0.125943\pi$
$824$	−11.2122			−0.390595
$825$		0			0
$826$		0			0
$827$	52.7321			1.83367			0.916837	−	0.399263i	$-0.130734\pi$
$827$	52.7321			1.83367			0.916837	+	0.399263i	$0.130734\pi$
$828$		0			0
$829$	0.947343	+	1.64085i	0.0329026	+	0.0569890i	0.882008	−	0.471235i	$-0.156192\pi$
$829$	0.947343	+	1.64085i	0.0329026	+	0.0569890i	−0.849105	+	0.528224i	$0.822858\pi$
$830$	−5.12436			−0.177869
$831$		0			0
$832$	1.22474	+	2.12132i	0.0424604	+	0.0735436i
$833$		0			0
$834$		0			0
$835$	−3.43782	−	5.95448i	−0.118971	−	0.206063i
$836$	−0.378937	−	0.656339i	−0.0131058	−	0.0227000i
$837$		0			0
$838$	−11.3323	+	19.6281i	−0.391467	+	0.678042i
$839$	−22.4751	+	38.9280i	−0.775927	+	1.34395i	0.158345	+	0.987384i	$0.449384\pi$
$839$	−22.4751	+	38.9280i	−0.775927	+	1.34395i	−0.934272	+	0.356561i	$0.883949\pi$
$840$		0			0
$841$	10.7679	+	18.6506i	0.371309	+	0.643125i
$842$	28.0526			0.966755
$843$		0			0
$844$	1.26795			0.0436446
$845$	−1.81173	+	3.13801i	−0.0623255	+	0.107951i
$846$		0			0
$847$		0			0
$848$	3.36603	−	5.83013i	0.115590	−	0.200207i
$849$		0			0
$850$	8.24504	−	14.2808i	0.282803	−	0.489829i
$851$	−31.7128	+	54.9282i	−1.08710	+	1.88291i
$852$		0			0
$853$	−11.7992	+	20.4367i	−0.403996	+	0.699741i	−0.994204	−	0.107510i	$-0.965712\pi$
$853$	−11.7992	+	20.4367i	−0.403996	+	0.699741i	0.590208	+	0.807251i	$0.299046\pi$
$854$		0			0
$855$		0			0
$856$	1.53590	−	2.66025i	0.0524959	−	0.0909256i
$857$	−5.45378			−0.186298			−0.0931488	−	0.995652i	$-0.529693\pi$
$857$	−5.45378			−0.186298			−0.0931488	+	0.995652i	$0.529693\pi$
$858$		0			0
$859$	9.69642			0.330838			0.165419	−	0.986223i	$-0.447102\pi$
$859$	9.69642			0.330838			0.165419	+	0.986223i	$0.447102\pi$
$860$	−3.15660	−	5.46739i	−0.107639	−	0.186436i
$861$		0			0
$862$	−13.3923	+	23.1962i	−0.456144	+	0.790064i
$863$	10.5981	−	18.3564i	0.360763	−	0.624859i	−0.627324	−	0.778758i	$-0.715850\pi$
$863$	10.5981	−	18.3564i	0.360763	−	0.624859i	0.988087	+	0.153899i	$0.0491831\pi$
$864$		0			0
$865$	5.02628	+	8.70577i	0.170899	+	0.296005i
$866$	10.1261	+	17.5390i	0.344100	+	0.595998i
$867$		0			0
$868$		0			0
$869$	−10.3397	−	17.9090i	−0.350752	−	0.607520i
$870$		0			0
$871$	9.31749			0.315711
$872$	−5.29423	−	9.16987i	−0.179285	−	0.310531i
$873$		0			0
$874$	−4.10394			−0.138818
$875$		0			0
$876$		0			0
$877$	24.0526			0.812197			0.406099	−	0.913829i	$-0.366889\pi$
$877$	24.0526			0.812197			0.406099	+	0.913829i	$0.366889\pi$
$878$	−9.14162	+	15.8338i	−0.308515	+	0.534363i
$879$		0			0
$880$	0.378937	+	0.656339i	0.0127740	+	0.0221252i
$881$	−0.480473			−0.0161876			−0.00809378	−	0.999967i	$-0.502576\pi$
$881$	−0.480473			−0.0161876			−0.00809378	+	0.999967i	$0.502576\pi$
$882$		0			0
$883$	38.2487			1.28717			0.643586	−	0.765374i	$-0.277446\pi$
$883$	38.2487			1.28717			0.643586	+	0.765374i	$0.277446\pi$
$884$	4.26795	+	7.39230i	0.143547	+	0.248630i
$885$		0			0
$886$	−18.4904	+	32.0263i	−0.621197	+	1.07594i
$887$	−26.9716			−0.905617			−0.452809	−	0.891608i	$-0.649578\pi$
$887$	−26.9716			−0.905617			−0.452809	+	0.891608i	$0.649578\pi$
$888$		0			0
$889$		0			0
$890$	−8.33975			−0.279549
$891$		0			0
$892$	−1.88108	−	3.25813i	−0.0629833	−	0.109090i
$893$	2.39230			0.0800554
$894$		0			0
$895$	2.12132	+	3.67423i	0.0709079	+	0.122816i
$896$		0			0
$897$		0			0
$898$	−11.8923	−	20.5981i	−0.396851	−	0.687367i
$899$	10.0382	+	17.3867i	0.334793	+	0.579878i
$900$		0			0
$901$	11.7298	−	20.3166i	0.390777	−	0.676845i
$902$	4.14110	−	7.17260i	0.137884	−	0.238822i
$903$		0			0
$904$	−7.33013	−	12.6962i	−0.243796	−	0.422268i
$905$	10.8564			0.360879
$906$		0			0
$907$	−5.12436			−0.170151			−0.0850757	−	0.996374i	$-0.527113\pi$
$907$	−5.12436			−0.170151			−0.0850757	+	0.996374i	$0.527113\pi$
$908$	1.67303	−	2.89778i	0.0555215	−	0.0961661i
$909$		0			0
$910$		0			0
$911$	13.8923	−	24.0622i	0.460273	−	0.797216i	−0.538702	−	0.842497i	$-0.681085\pi$
$911$	13.8923	−	24.0622i	0.460273	−	0.797216i	0.998974	+	0.0452811i	$0.0144183\pi$
$912$		0			0
$913$	−7.24693	+	12.5521i	−0.239838	+	0.415412i
$914$	11.1340	−	19.2846i	0.368279	−	0.637878i
$915$		0			0
$916$	−6.90018	+	11.9515i	−0.227988	+	0.394888i
$917$		0			0
$918$		0			0
$919$	−8.18653	+	14.1795i	−0.270049	+	0.467738i	−0.968874	−	0.247554i	$-0.920373\pi$
$919$	−8.18653	+	14.1795i	−0.270049	+	0.467738i	0.698825	+	0.715292i	$0.253707\pi$
$920$	4.10394			0.135303
$921$		0			0
$922$	−38.9788			−1.28370
$923$	0.984508	+	1.70522i	0.0324055	+	0.0561279i
$924$		0			0
$925$	−18.9282	+	32.7846i	−0.622355	+	1.07795i
$926$	−3.33013	+	5.76795i	−0.109435	+	0.189547i
$927$		0			0
$928$	1.36603	+	2.36603i	0.0448420	+	0.0776686i
$929$	2.01978	+	3.49837i	0.0662670	+	0.114778i	0.897255	−	0.441512i	$-0.145558\pi$
$929$	2.01978	+	3.49837i	0.0662670	+	0.114778i	−0.830988	+	0.556290i	$0.812224\pi$
$930$		0			0
$931$		0			0
$932$	0.696152	+	1.20577i	0.0228032	+	0.0394964i
$933$		0			0
$934$	−24.5964			−0.804820
$935$	1.32051	+	2.28719i	0.0431852	+	0.0747990i
$936$		0			0
$937$	31.7690			1.03785			0.518925	−	0.854820i	$-0.326333\pi$
$937$	31.7690			1.03785			0.518925	+	0.854820i	$0.326333\pi$
$938$		0			0
$939$		0			0
$940$	−2.39230			−0.0780284
$941$	−29.1994	+	50.5749i	−0.951874	+	1.64869i	−0.210510	+	0.977592i	$0.567512\pi$
$941$	−29.1994	+	50.5749i	−0.951874	+	1.64869i	−0.741364	+	0.671103i	$0.765821\pi$
$942$		0			0
$943$	−22.4243	−	38.8401i	−0.730237	−	1.26481i
$944$	−14.7985			−0.481649
$945$		0			0
$946$	−17.8564			−0.580562
$947$	−17.8301	−	30.8827i	−0.579401	−	1.00355i	−0.995548	−	0.0942550i	$-0.969953\pi$
$947$	−17.8301	−	30.8827i	−0.579401	−	1.00355i	0.416147	−	0.909297i	$-0.363380\pi$
$948$		0			0
$949$	5.66025	−	9.80385i	0.183740	−	0.318246i
$950$	−2.44949			−0.0794719
$951$		0			0
$952$		0			0
$953$	−23.7128			−0.768133			−0.384067	−	0.923305i	$-0.625477\pi$
$953$	−23.7128			−0.768133			−0.384067	+	0.923305i	$0.625477\pi$
$954$		0			0
$955$	1.86250	+	3.22595i	0.0602691	+	0.104389i
$956$	12.4641			0.403118
$957$		0			0
$958$	−6.64136	−	11.5032i	−0.214573	−	0.371651i
$959$		0			0
$960$		0			0
$961$	−11.5000	−	19.9186i	−0.370968	−	0.642535i
$962$	−9.79796	−	16.9706i	−0.315899	−	0.547153i
$963$		0			0
$964$	−6.36396	+	11.0227i	−0.204969	+	0.355017i
$965$	−6.14231	+	10.6388i	−0.197728	+	0.342475i
$966$		0			0
$967$	0.232051	+	0.401924i	0.00746225	+	0.0129250i	0.869732	−	0.493524i	$-0.164291\pi$
$967$	0.232051	+	0.401924i	0.00746225	+	0.0129250i	−0.862270	+	0.506449i	$0.830958\pi$
$968$	−8.85641			−0.284656
$969$		0			0
$970$	0.535898			0.0172067
$971$	14.2994	−	24.7673i	0.458890	−	0.794821i	−0.540012	−	0.841657i	$-0.681580\pi$
$971$	14.2994	−	24.7673i	0.458890	−	0.794821i	0.998903	+	0.0468359i	$0.0149138\pi$
$972$		0			0
$973$		0			0
$974$	16.1603	−	27.9904i	0.517808	−	0.896870i
$975$		0			0
$976$	−2.19067	+	3.79435i	−0.0701217	+	0.121454i
$977$	−8.07180	+	13.9808i	−0.258240	+	0.447284i	−0.965770	−	0.259398i	$-0.916476\pi$
$977$	−8.07180	+	13.9808i	−0.258240	+	0.447284i	0.707531	+	0.706683i	$0.249809\pi$
$978$		0			0
$979$	−11.7942	+	20.4281i	−0.376944	+	0.652886i
$980$		0			0
$981$		0			0
$982$	−2.53590	+	4.39230i	−0.0809238	+	0.140164i
$983$	23.6355			0.753855			0.376927	−	0.926243i	$-0.376981\pi$
$983$	23.6355			0.753855			0.376927	+	0.926243i	$0.376981\pi$
$984$		0			0
$985$	5.00052			0.159330
$986$	4.76028	+	8.24504i	0.151598	+	0.262576i
$987$		0			0
$988$	0.633975	−	1.09808i	0.0201694	−	0.0349345i
$989$	−48.3468	+	83.7391i	−1.53734	+	2.66275i
$990$		0			0
$991$	−7.33975	−	12.7128i	−0.233155	−	0.403836i	0.725580	−	0.688138i	$-0.241572\pi$
$991$	−7.33975	−	12.7128i	−0.233155	−	0.403836i	−0.958735	+	0.284302i	$0.908238\pi$
$992$	−3.67423	−	6.36396i	−0.116657	−	0.202056i
$993$		0			0
$994$		0			0
$995$	3.00000	+	5.19615i	0.0951064	+	0.164729i
$996$		0			0
$997$	43.8778			1.38962			0.694812	−	0.719192i	$-0.255488\pi$
$997$	43.8778			1.38962			0.694812	+	0.719192i	$0.255488\pi$
$998$	−3.66025	−	6.33975i	−0.115863	−	0.200681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.q.667.2		8
3.2	odd	2		882.2.h.t.79.4		8
7.2	even	3		2646.2.f.q.883.3		8
7.3	odd	6		2646.2.e.t.2125.2		8
7.4	even	3		2646.2.e.t.2125.3		8
7.5	odd	6		2646.2.f.q.883.2		8
7.6	odd	2	inner	2646.2.h.q.667.3		8
9.4	even	3		2646.2.e.t.1549.3		8
9.5	odd	6		882.2.e.q.373.2		8
21.2	odd	6		882.2.f.s.295.2	✓	8
21.5	even	6		882.2.f.s.295.3	yes	8
21.11	odd	6		882.2.e.q.655.2		8
21.17	even	6		882.2.e.q.655.3		8
21.20	even	2		882.2.h.t.79.1		8
63.2	odd	6		7938.2.a.cj.1.3		4
63.4	even	3	inner	2646.2.h.q.361.2		8
63.5	even	6		882.2.f.s.589.4	yes	8
63.13	odd	6		2646.2.e.t.1549.2		8
63.16	even	3		7938.2.a.co.1.2		4
63.23	odd	6		882.2.f.s.589.1	yes	8
63.31	odd	6	inner	2646.2.h.q.361.3		8
63.32	odd	6		882.2.h.t.67.4		8
63.40	odd	6		2646.2.f.q.1765.2		8
63.41	even	6		882.2.e.q.373.3		8
63.47	even	6		7938.2.a.cj.1.2		4
63.58	even	3		2646.2.f.q.1765.3		8
63.59	even	6		882.2.h.t.67.1		8
63.61	odd	6		7938.2.a.co.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.q.373.2		8	9.5	odd	6
882.2.e.q.373.3		8	63.41	even	6
882.2.e.q.655.2		8	21.11	odd	6
882.2.e.q.655.3		8	21.17	even	6
882.2.f.s.295.2	✓	8	21.2	odd	6
882.2.f.s.295.3	yes	8	21.5	even	6
882.2.f.s.589.1	yes	8	63.23	odd	6
882.2.f.s.589.4	yes	8	63.5	even	6
882.2.h.t.67.1		8	63.59	even	6
882.2.h.t.67.4		8	63.32	odd	6
882.2.h.t.79.1		8	21.20	even	2
882.2.h.t.79.4		8	3.2	odd	2
2646.2.e.t.1549.2		8	63.13	odd	6
2646.2.e.t.1549.3		8	9.4	even	3
2646.2.e.t.2125.2		8	7.3	odd	6
2646.2.e.t.2125.3		8	7.4	even	3
2646.2.f.q.883.2		8	7.5	odd	6
2646.2.f.q.883.3		8	7.2	even	3
2646.2.f.q.1765.2		8	63.40	odd	6
2646.2.f.q.1765.3		8	63.58	even	3
2646.2.h.q.361.2		8	63.4	even	3	inner
2646.2.h.q.361.3		8	63.31	odd	6	inner
2646.2.h.q.667.2		8	1.1	even	1	trivial
2646.2.h.q.667.3		8	7.6	odd	2	inner
7938.2.a.cj.1.2		4	63.47	even	6
7938.2.a.cj.1.3		4	63.2	odd	6
7938.2.a.co.1.2		4	63.16	even	3
7938.2.a.co.1.3		4	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.517638 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.517638 q^{5} +1.00000 q^{8} +(0.258819 + 0.448288i) q^{10} +1.46410 q^{11} +(1.22474 + 2.12132i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.74238 - 3.01790i) q^{17} +(-0.258819 + 0.448288i) q^{19} +(0.258819 - 0.448288i) q^{20} +(-0.732051 - 1.26795i) q^{22} -7.92820 q^{23} -4.73205 q^{25} +(1.22474 - 2.12132i) q^{26} +(1.36603 - 2.36603i) q^{29} +(-3.67423 + 6.36396i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.74238 + 3.01790i) q^{34} +(4.00000 - 6.92820i) q^{37} +0.517638 q^{38} -0.517638 q^{40} +(2.82843 + 4.89898i) q^{41} +(6.09808 - 10.5622i) q^{43} +(-0.732051 + 1.26795i) q^{44} +(3.96410 + 6.86603i) q^{46} +(-2.31079 - 4.00240i) q^{47} +(2.36603 + 4.09808i) q^{50} -2.44949 q^{52} +(3.36603 + 5.83013i) q^{53} -0.757875 q^{55} -2.73205 q^{58} +(7.39924 - 12.8159i) q^{59} +(-2.19067 - 3.79435i) q^{61} +7.34847 q^{62} +1.00000 q^{64} +(-0.633975 - 1.09808i) q^{65} +(1.90192 - 3.29423i) q^{67} +3.48477 q^{68} +0.803848 q^{71} +(-2.31079 - 4.00240i) q^{73} -8.00000 q^{74} +(-0.258819 - 0.448288i) q^{76} +(-7.06218 - 12.2321i) q^{79} +(0.258819 + 0.448288i) q^{80} +(2.82843 - 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(0.901924 + 1.56218i) q^{85} -12.1962 q^{86} +1.46410 q^{88} +(-8.05558 + 13.9527i) q^{89} +(3.96410 - 6.86603i) q^{92} +(-2.31079 + 4.00240i) q^{94} +(0.133975 - 0.232051i) q^{95} +(0.517638 - 0.896575i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 24 q^{25} + 4 q^{29} - 4 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} - 8 q^{58} + 8 q^{64} - 12 q^{65} + 36 q^{67} + 48 q^{71} - 64 q^{74} - 8 q^{79} + 28 q^{85} - 56 q^{86} - 16 q^{88} + 4 q^{92} + 8 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 24 * q^25 + 4 * q^29 - 4 * q^32 + 32 * q^37 + 28 * q^43 + 8 * q^44 + 4 * q^46 + 12 * q^50 + 20 * q^53 - 8 * q^58 + 8 * q^64 - 12 * q^65 + 36 * q^67 + 48 * q^71 - 64 * q^74 - 8 * q^79 + 28 * q^85 - 56 * q^86 - 16 * q^88 + 4 * q^92 + 8 * q^95

Introduction

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