LMFDB - Embedded newform 1323.2.i.b.1097.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (of order $6$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.4
Root			$-1.04536 - 1.81062i$ of defining polynomial
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.b.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.51009i q^{2} -0.280386 q^{4} +(-0.387938 - 0.671929i) q^{5} +2.59678i q^{8} +O(q^{10})$	\(q+1.51009i q^{2} -0.280386 q^{4} +(-0.387938 - 0.671929i) q^{5} +2.59678i q^{8} +(1.01468 - 0.585823i) q^{10} +(3.32830 + 1.92159i) q^{11} +(-2.54198 - 1.46761i) q^{13} -4.48216 q^{16} +(2.69901 + 4.67482i) q^{17} +(0.376551 + 0.217402i) q^{19} +(0.108773 + 0.188400i) q^{20} +(-2.90179 + 5.02605i) q^{22} +(0.0482537 - 0.0278593i) q^{23} +(2.19901 - 3.80879i) q^{25} +(2.21624 - 3.83863i) q^{26} +(0.187994 - 0.108538i) q^{29} +6.55646i q^{31} -1.57492i q^{32} +(-7.05942 + 4.07576i) q^{34} +(3.14698 - 5.45073i) q^{37} +(-0.328298 + 0.568628i) q^{38} +(1.74485 - 1.00739i) q^{40} +(-3.78757 + 6.56026i) q^{41} +(6.42703 + 11.1319i) q^{43} +(-0.933209 - 0.538789i) q^{44} +(0.0420702 + 0.0728677i) q^{46} +0.965544 q^{47} +(5.75164 + 3.32071i) q^{50} +(0.712737 + 0.411499i) q^{52} +(-6.46438 + 3.73221i) q^{53} -2.98184i q^{55} +(0.163903 + 0.283889i) q^{58} -3.12439 q^{59} +3.48424i q^{61} -9.90087 q^{62} -6.58603 q^{64} +2.27737i q^{65} -4.20177 q^{67} +(-0.756765 - 1.31076i) q^{68} +3.50812i q^{71} +(7.05942 - 4.07576i) q^{73} +(8.23112 + 4.75224i) q^{74} +(-0.105580 - 0.0609566i) q^{76} -4.96220 q^{79} +(1.73880 + 3.01169i) q^{80} +(-9.90662 - 5.71959i) q^{82} +(4.31033 + 7.46571i) q^{83} +(2.09410 - 3.62708i) q^{85} +(-16.8103 + 9.70542i) q^{86} +(-4.98996 + 8.64286i) q^{88} +(-7.82041 + 13.5453i) q^{89} +(-0.0135297 + 0.00781136i) q^{92} +1.45806i q^{94} -0.337354i q^{95} +(1.24162 - 0.716849i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{4}+O(q^{10}) $ 10 * q - 8 * q^4	$ 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} + 30 q^{47} - 3 q^{50} + 12 q^{52} - 9 q^{53} + 8 q^{58} - 36 q^{59} - 12 q^{62} + 6 q^{64} + 20 q^{67} - 27 q^{68} - 3 q^{73} + 30 q^{74} + 9 q^{76} - 40 q^{79} + 30 q^{80} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} - 24 q^{89} - 39 q^{92} + 6 q^{97}+O(q^{100}) $ 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.51009i			1.06780i	0.845548	+	0.533899i	$0.179274\pi$
$2$			1.51009i			1.06780i	−0.845548	+	0.533899i	$0.820726\pi$
$3$		0			0
$3$		0			0
$4$	−0.280386			−0.140193
$5$	−0.387938	−	0.671929i	−0.173491	−	0.300496i	0.766147	−	0.642666i	$-0.222171\pi$
$5$	−0.387938	−	0.671929i	−0.173491	−	0.300496i	−0.939638	+	0.342170i	$0.888838\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.59678i			0.918100i
$9$		0			0
$10$	1.01468	−	0.585823i	0.320869	−	0.185254i
$11$	3.32830	+	1.92159i	1.00352	+	0.579382i	0.909288	−	0.416168i	$-0.136627\pi$
$11$	3.32830	+	1.92159i	1.00352	+	0.579382i	0.0942318	+	0.995550i	$0.469961\pi$
$12$		0			0
$13$	−2.54198	−	1.46761i	−0.705019	−	0.407043i	0.104195	−	0.994557i	$-0.466773\pi$
$13$	−2.54198	−	1.46761i	−0.705019	−	0.407043i	−0.809214	+	0.587514i	$0.800107\pi$
$14$		0			0
$15$		0			0
$16$	−4.48216			−1.12054
$17$	2.69901	+	4.67482i	0.654606	+	1.13381i	0.981993	+	0.188920i	$0.0604986\pi$
$17$	2.69901	+	4.67482i	0.654606	+	1.13381i	−0.327387	+	0.944890i	$0.606168\pi$
$18$		0			0
$19$	0.376551	+	0.217402i	0.0863868	+	0.0498755i	0.542571	−	0.840010i	$-0.317451\pi$
$19$	0.376551	+	0.217402i	0.0863868	+	0.0498755i	−0.456184	+	0.889885i	$0.650784\pi$
$20$	0.108773	+	0.188400i	0.0243223	+	0.0421274i
$21$		0			0
$22$	−2.90179	+	5.02605i	−0.618663	+	1.07156i
$23$	0.0482537	−	0.0278593i	0.0100616	−	0.00580906i	−0.494961	−	0.868915i	$-0.664818\pi$
$23$	0.0482537	−	0.0278593i	0.0100616	−	0.00580906i	0.505022	+	0.863106i	$0.331484\pi$
$24$		0			0
$25$	2.19901	−	3.80879i	0.439802	−	0.761759i
$26$	2.21624	−	3.83863i	0.434640	−	0.752818i
$27$		0			0
$28$		0			0
$29$	0.187994	−	0.108538i	0.0349096	−	0.0201551i	−0.482444	−	0.875927i	$-0.660251\pi$
$29$	0.187994	−	0.108538i	0.0349096	−	0.0201551i	0.517353	+	0.855772i	$0.326917\pi$
$30$		0			0
$31$			6.55646i			1.17757i	0.808288	+	0.588787i	$0.200394\pi$
$31$			6.55646i			1.17757i	−0.808288	+	0.588787i	$0.799606\pi$
$32$		−	1.57492i		−	0.278409i
$33$		0			0
$34$	−7.05942	+	4.07576i	−1.21068	+	0.698987i
$35$		0			0
$36$		0			0
$37$	3.14698	−	5.45073i	0.517361	−	0.896095i	−0.482436	−	0.875931i	$-0.660248\pi$
$37$	3.14698	−	5.45073i	0.517361	−	0.896095i	0.999797	−	0.0201636i	$-0.00641872\pi$
$38$	−0.328298	+	0.568628i	−0.0532569	+	0.0922437i
$39$		0			0
$40$	1.74485	−	1.00739i	0.275885	−	0.159282i
$41$	−3.78757	+	6.56026i	−0.591519	+	1.02454i	0.402509	+	0.915416i	$0.368138\pi$
$41$	−3.78757	+	6.56026i	−0.591519	+	1.02454i	−0.994028	+	0.109125i	$0.965195\pi$
$42$		0			0
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.661914	+	0.749580i	$0.269745\pi$
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.318198	+	0.948024i	$0.396922\pi$
$44$	−0.933209	−	0.538789i	−0.140687	−	0.0812254i
$45$		0			0
$46$	0.0420702	+	0.0728677i	0.00620291	+	0.0107437i
$47$	0.965544			0.140839			0.0704195	−	0.997517i	$-0.477566\pi$
$47$	0.965544			0.140839			0.0704195	+	0.997517i	$0.477566\pi$
$48$		0			0
$49$		0			0
$50$	5.75164	+	3.32071i	0.813405	+	0.469619i
$51$		0			0
$52$	0.712737	+	0.411499i	0.0988388	+	0.0570646i
$53$	−6.46438	+	3.73221i	−0.887950	+	0.512658i	−0.873272	−	0.487234i	$-0.838006\pi$
$53$	−6.46438	+	3.73221i	−0.887950	+	0.512658i	−0.0146788	+	0.999892i	$0.504673\pi$
$54$		0			0
$55$		−	2.98184i		−	0.402071i
$56$		0			0
$57$		0			0
$58$	0.163903	+	0.283889i	0.0215215	+	0.0372764i
$59$	−3.12439			−0.406760			−0.203380	−	0.979100i	$-0.565193\pi$
$59$	−3.12439			−0.406760			−0.203380	+	0.979100i	$0.565193\pi$
$60$		0			0
$61$			3.48424i			0.446111i	0.974806	+	0.223055i	$0.0716031\pi$
$61$			3.48424i			0.446111i	−0.974806	+	0.223055i	$0.928397\pi$
$62$	−9.90087			−1.25741
$63$		0			0
$64$	−6.58603			−0.823254
$65$			2.27737i			0.282473i
$66$		0			0
$67$	−4.20177			−0.513328			−0.256664	−	0.966501i	$-0.582623\pi$
$67$	−4.20177			−0.513328			−0.256664	+	0.966501i	$0.582623\pi$
$68$	−0.756765	−	1.31076i	−0.0917712	−	0.158952i
$69$		0			0
$70$		0			0
$71$			3.50812i			0.416337i	0.978093	+	0.208169i	$0.0667503\pi$
$71$			3.50812i			0.416337i	−0.978093	+	0.208169i	$0.933250\pi$
$72$		0			0
$73$	7.05942	−	4.07576i	0.826243	−	0.477031i	−0.0263219	−	0.999654i	$-0.508379\pi$
$73$	7.05942	−	4.07576i	0.826243	−	0.477031i	0.852564	+	0.522622i	$0.175046\pi$
$74$	8.23112	+	4.75224i	0.956848	+	0.552437i
$75$		0			0
$76$	−0.105580	−	0.0609566i	−0.0121108	−	0.00699220i
$77$		0			0
$78$		0			0
$79$	−4.96220			−0.558291			−0.279145	−	0.960249i	$-0.590051\pi$
$79$	−4.96220			−0.558291			−0.279145	+	0.960249i	$0.590051\pi$
$80$	1.73880	+	3.01169i	0.194404	+	0.336717i
$81$		0			0
$82$	−9.90662	−	5.71959i	−1.09400	−	0.631623i
$83$	4.31033	+	7.46571i	0.473120	+	0.819469i	0.999527	−	0.0307645i	$-0.00979420\pi$
$83$	4.31033	+	7.46571i	0.473120	+	0.819469i	−0.526406	+	0.850233i	$0.676461\pi$
$84$		0			0
$85$	2.09410	−	3.62708i	0.227137	−	0.393412i
$86$	−16.8103	+	9.70542i	−1.81270	+	1.04656i
$87$		0			0
$88$	−4.98996	+	8.64286i	−0.531931	+	0.921332i
$89$	−7.82041	+	13.5453i	−0.828962	+	1.43580i	0.0698916	+	0.997555i	$0.477735\pi$
$89$	−7.82041	+	13.5453i	−0.828962	+	1.43580i	−0.898853	+	0.438249i	$0.855599\pi$
$90$		0			0
$91$		0			0
$92$	−0.0135297	+	0.00781136i	−0.00141057	+	0.000814391i
$93$		0			0
$94$			1.45806i			0.150388i
$95$		−	0.337354i		−	0.0346118i
$96$		0			0
$97$	1.24162	−	0.716849i	0.126067	−	0.0727850i	−0.435640	−	0.900121i	$-0.643478\pi$
$97$	1.24162	−	0.716849i	0.126067	−	0.0727850i	0.561708	+	0.827336i	$0.310145\pi$
$98$		0			0
$99$		0			0
$100$	−0.616572	+	1.06793i	−0.0616572	+	0.106793i
$101$	8.01096	−	13.8754i	0.797120	−	1.38065i	−0.124364	−	0.992237i	$-0.539689\pi$
$101$	8.01096	−	13.8754i	0.797120	−	1.38065i	0.921484	−	0.388416i	$-0.126977\pi$
$102$		0			0
$103$	14.6064	−	8.43299i	1.43921	−	0.830928i	0.441414	−	0.897303i	$-0.354477\pi$
$103$	14.6064	−	8.43299i	1.43921	−	0.830928i	0.997795	+	0.0663758i	$0.0211436\pi$
$104$	3.81107	−	6.60097i	0.373706	−	0.647278i
$105$		0			0
$106$	−5.63599	−	9.76182i	−0.547416	−	0.948152i
$107$	−3.36444	−	1.94246i	−0.325253	−	0.187785i	0.328479	−	0.944511i	$-0.393464\pi$
$107$	−3.36444	−	1.94246i	−0.325253	−	0.187785i	−0.653731	+	0.756727i	$0.726797\pi$
$108$		0			0
$109$	1.28254	+	2.22143i	0.122845	+	0.212774i	0.920889	−	0.389826i	$-0.127465\pi$
$109$	1.28254	+	2.22143i	0.122845	+	0.212774i	−0.798043	+	0.602600i	$0.794131\pi$
$110$	4.50286			0.429331
$111$		0			0
$112$		0			0
$113$	9.79043	+	5.65251i	0.921006	+	0.531743i	0.883956	−	0.467570i	$-0.154871\pi$
$113$	9.79043	+	5.65251i	0.921006	+	0.531743i	0.0370501	+	0.999313i	$0.488204\pi$
$114$		0			0
$115$	−0.0374389	−	0.0216154i	−0.00349120	−	0.00201564i
$116$	−0.0527109	+	0.0304327i	−0.00489408	+	0.00282560i
$117$		0			0
$118$		−	4.71812i		−	0.434338i
$119$		0			0
$120$		0			0
$121$	1.88504	+	3.26499i	0.171368	+	0.296817i
$122$	−5.26153			−0.476356
$123$		0			0
$124$		−	1.83834i		−	0.165088i
$125$	−7.29170			−0.652189
$126$		0			0
$127$	2.65660			0.235735			0.117867	−	0.993029i	$-0.462394\pi$
$127$	2.65660			0.235735			0.117867	+	0.993029i	$0.462394\pi$
$128$		−	13.0954i		−	1.15748i
$129$		0			0
$130$	−3.43905			−0.301625
$131$	−4.11811	−	7.13278i	−0.359801	−	0.623194i	0.628126	−	0.778111i	$-0.283822\pi$
$131$	−4.11811	−	7.13278i	−0.359801	−	0.623194i	−0.987927	+	0.154918i	$0.950489\pi$
$132$		0			0
$133$		0			0
$134$		−	6.34507i		−	0.548131i
$135$		0			0
$136$	−12.1395	+	7.00873i	−1.04095	+	0.600994i
$137$	−15.0058	−	8.66359i	−1.28203	−	0.740180i	−0.304811	−	0.952413i	$-0.598593\pi$
$137$	−15.0058	−	8.66359i	−1.28203	−	0.740180i	−0.977219	+	0.212233i	$0.931927\pi$
$138$		0			0
$139$	−5.47677	−	3.16201i	−0.464533	−	0.268198i	0.249415	−	0.968397i	$-0.419762\pi$
$139$	−5.47677	−	3.16201i	−0.464533	−	0.268198i	−0.713949	+	0.700198i	$0.753095\pi$
$140$		0			0
$141$		0			0
$142$	−5.29759			−0.444564
$143$	−5.64031	−	9.76931i	−0.471667	−	0.816951i
$144$		0			0
$145$	−0.145860	−	0.0842123i	−0.0121130	−	0.00699345i
$146$	6.15478	+	10.6604i	0.509373	+	0.882260i
$147$		0			0
$148$	−0.882370	+	1.52831i	−0.0725304	+	0.125626i
$149$	11.1061	−	6.41211i	0.909847	−	0.525300i	0.0294650	−	0.999566i	$-0.490620\pi$
$149$	11.1061	−	6.41211i	0.909847	−	0.525300i	0.880382	+	0.474265i	$0.157286\pi$
$150$		0			0
$151$	−2.62759	+	4.55111i	−0.213830	+	0.370364i	−0.952910	−	0.303253i	$-0.901927\pi$
$151$	−2.62759	+	4.55111i	−0.213830	+	0.370364i	0.739080	+	0.673618i	$0.235260\pi$
$152$	−0.564545	+	0.977821i	−0.0457907	+	0.0793118i
$153$		0			0
$154$		0			0
$155$	4.40547	−	2.54350i	0.353856	−	0.204299i
$156$		0			0
$157$		−	7.98815i		−	0.637523i	−0.947835	−	0.318762i	$-0.896733\pi$
$157$		−	7.98815i		−	0.637523i	0.947835	−	0.318762i	$-0.103267\pi$
$158$		−	7.49339i		−	0.596142i
$159$		0			0
$160$	−1.05823	+	0.610972i	−0.0836608	+	0.0483016i
$161$		0			0
$162$		0			0
$163$	5.75231	−	9.96329i	0.450556	−	0.780385i	−0.547865	−	0.836567i	$-0.684559\pi$
$163$	5.75231	−	9.96329i	0.450556	−	0.780385i	0.998421	+	0.0561817i	$0.0178926\pi$
$164$	1.06198	−	1.83941i	0.0829269	−	0.143634i
$165$		0			0
$166$	−11.2739	+	6.50901i	−0.875027	+	0.505197i
$167$	8.38240	−	14.5187i	0.648650	−	1.12349i	−0.334796	−	0.942291i	$-0.608667\pi$
$167$	8.38240	−	14.5187i	0.648650	−	1.12349i	0.983446	−	0.181204i	$-0.0579994\pi$
$168$		0			0
$169$	−2.19222	−	3.79704i	−0.168632	−	0.292080i
$170$	5.47724	+	3.16228i	0.420085	+	0.242536i
$171$		0			0
$172$	−1.80205	−	3.12124i	−0.137405	−	0.237992i
$173$	1.71279			0.130221			0.0651106	−	0.997878i	$-0.479260\pi$
$173$	1.71279			0.130221			0.0651106	+	0.997878i	$0.479260\pi$
$174$		0			0
$175$		0			0
$176$	−14.9180	−	8.61288i	−1.12448	−	0.649220i
$177$		0			0
$178$	−20.4548	−	11.8096i	−1.53315	−	0.885164i
$179$	−12.4141	+	7.16731i	−0.927877	+	0.535710i	−0.886139	−	0.463419i	$-0.846623\pi$
$179$	−12.4141	+	7.16731i	−0.927877	+	0.535710i	−0.0417372	+	0.999129i	$0.513289\pi$
$180$		0			0
$181$			4.83147i			0.359121i	0.983747	+	0.179560i	$0.0574675\pi$
$181$			4.83147i			0.359121i	−0.983747	+	0.179560i	$0.942532\pi$
$182$		0			0
$183$		0			0
$184$	0.0723444	+	0.125304i	0.00533330	+	0.00923755i
$185$	−4.88334			−0.359030
$186$		0			0
$187$			20.7456i			1.51707i
$188$	−0.270725			−0.0197447
$189$		0			0
$190$	0.509437			0.0369584
$191$		−	3.14210i		−	0.227355i	−0.993518	−	0.113677i	$-0.963737\pi$
$191$		−	3.14210i		−	0.227355i	0.993518	−	0.113677i	$-0.0362630\pi$
$192$		0			0
$193$	6.01017			0.432621			0.216311	−	0.976325i	$-0.430598\pi$
$193$	6.01017			0.432621			0.216311	+	0.976325i	$0.430598\pi$
$194$	1.08251	+	1.87496i	0.0777197	+	0.134615i
$195$		0			0
$196$		0			0
$197$		−	14.0902i		−	1.00388i	−0.864901	−	0.501942i	$-0.832619\pi$
$197$		−	14.0902i		−	1.00388i	0.864901	−	0.501942i	$-0.167381\pi$
$198$		0			0
$199$	6.84234	−	3.95043i	0.485041	−	0.280038i	−0.237474	−	0.971394i	$-0.576319\pi$
$199$	6.84234	−	3.95043i	0.485041	−	0.280038i	0.722515	+	0.691355i	$0.242986\pi$
$200$	9.89060	+	5.71034i	0.699371	+	0.403782i
$201$		0			0
$202$	20.9531	+	12.0973i	1.47426	+	0.851163i
$203$		0			0
$204$		0			0
$205$	5.87737			0.410493
$206$	12.7346	+	22.0570i	0.887263	+	1.53678i
$207$		0			0
$208$	11.3936	+	6.57807i	0.790001	+	0.456107i
$209$	0.835517	+	1.44716i	0.0577939	+	0.100102i
$210$		0			0
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	−0.763529	−	0.645773i	$-0.776535\pi$
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	0.941021	+	0.338349i	$0.109868\pi$
$212$	1.81252	−	1.04646i	0.124485	−	0.0718712i
$213$		0			0
$214$	2.93330	−	5.08062i	0.200516	−	0.347304i
$215$	4.98658	−	8.63701i	0.340082	−	0.589039i
$216$		0			0
$217$		0			0
$218$	−3.35457	+	1.93676i	−0.227200	+	0.131174i
$219$		0			0
$220$			0.836067i			0.0563676i
$221$		−	15.8444i		−	1.06581i
$222$		0			0
$223$	3.79823	−	2.19291i	0.254348	−	0.146848i	−0.367405	−	0.930061i	$-0.619754\pi$
$223$	3.79823	−	2.19291i	0.254348	−	0.146848i	0.621754	+	0.783213i	$0.286420\pi$
$224$		0			0
$225$		0			0
$226$	−8.53582	+	14.7845i	−0.567794	+	0.983449i
$227$	4.83697	−	8.37788i	0.321041	−	0.556059i	−0.659662	−	0.751562i	$-0.729301\pi$
$227$	4.83697	−	8.37788i	0.321041	−	0.556059i	0.980703	+	0.195503i	$0.0626340\pi$
$228$		0			0
$229$	−7.66705	+	4.42657i	−0.506653	+	0.292516i	−0.731457	−	0.681888i	$-0.761159\pi$
$229$	−7.66705	+	4.42657i	−0.506653	+	0.292516i	0.224804	+	0.974404i	$0.427826\pi$
$230$	0.0326412	−	0.0565363i	0.00215230	−	0.00372789i
$231$		0			0
$232$	0.281850	+	0.488179i	0.0185044	+	0.0320505i
$233$	11.1612	+	6.44391i	0.731194	+	0.422155i	0.818859	−	0.573995i	$-0.194607\pi$
$233$	11.1612	+	6.44391i	0.731194	+	0.422155i	−0.0876651	+	0.996150i	$0.527941\pi$
$234$		0			0
$235$	−0.374571	−	0.648777i	−0.0244343	−	0.0423215i
$236$	0.876035			0.0570250
$237$		0			0
$238$		0			0
$239$	−4.18421	−	2.41575i	−0.270654	−	0.156262i	0.358531	−	0.933518i	$-0.383278\pi$
$239$	−4.18421	−	2.41575i	−0.270654	−	0.156262i	−0.629185	+	0.777256i	$0.716611\pi$
$240$		0			0
$241$	8.68938	+	5.01681i	0.559732	+	0.323161i	0.753038	−	0.657977i	$-0.228588\pi$
$241$	8.68938	+	5.01681i	0.559732	+	0.323161i	−0.193306	+	0.981139i	$0.561921\pi$
$242$	−4.93045	+	2.84659i	−0.316941	+	0.182986i
$243$		0			0
$244$		−	0.976932i		−	0.0625417i
$245$		0			0
$246$		0			0
$247$	−0.638125	−	1.10526i	−0.0406029	−	0.0703263i
$248$	−17.0257			−1.08113
$249$		0			0
$250$		−	11.0112i		−	0.696407i
$251$	7.98203			0.503821			0.251911	−	0.967751i	$-0.418941\pi$
$251$	7.98203			0.503821			0.251911	+	0.967751i	$0.418941\pi$
$252$		0			0
$253$	0.214137			0.0134627
$254$			4.01171i			0.251717i
$255$		0			0
$256$	6.60319			0.412700
$257$	−1.34115	−	2.32294i	−0.0836585	−	0.144901i	0.821160	−	0.570698i	$-0.193327\pi$
$257$	−1.34115	−	2.32294i	−0.0836585	−	0.144901i	−0.904819	+	0.425797i	$0.859994\pi$
$258$		0			0
$259$		0			0
$260$		−	0.638544i		−	0.0396008i
$261$		0			0
$262$	10.7712	−	6.21874i	0.665445	−	0.384195i
$263$	20.2961	+	11.7179i	1.25151	+	0.722560i	0.971409	−	0.237411i	$-0.0762989\pi$
$263$	20.2961	+	11.7179i	1.25151	+	0.722560i	0.280101	+	0.959971i	$0.409632\pi$
$264$		0			0
$265$	5.01556	+	2.89573i	0.308103	+	0.177883i
$266$		0			0
$267$		0			0
$268$	1.17812			0.0719651
$269$	1.98955	+	3.44600i	0.121305	+	0.210106i	0.920283	−	0.391254i	$-0.127959\pi$
$269$	1.98955	+	3.44600i	0.121305	+	0.210106i	−0.798978	+	0.601361i	$0.794625\pi$
$270$		0			0
$271$	−10.8303	−	6.25288i	−0.657895	−	0.379836i	0.133580	−	0.991038i	$-0.457353\pi$
$271$	−10.8303	−	6.25288i	−0.657895	−	0.379836i	−0.791474	+	0.611202i	$0.790686\pi$
$272$	−12.0974	−	20.9533i	−0.733511	−	1.27048i
$273$		0			0
$274$	13.0828	−	22.6601i	0.790363	−	1.36895i
$275$	14.6379	−	8.45120i	0.882699	−	0.509626i
$276$		0			0
$277$	9.84547	−	17.0529i	0.591557	−	1.02461i	−0.402466	−	0.915435i	$-0.631847\pi$
$277$	9.84547	−	17.0529i	0.591557	−	1.02461i	0.994023	−	0.109172i	$-0.0348199\pi$
$278$	4.77494	−	8.27044i	0.286382	−	0.496028i
$279$		0			0
$280$		0			0
$281$	−7.03456	+	4.06141i	−0.419647	+	0.242283i	−0.694926	−	0.719081i	$-0.744563\pi$
$281$	−7.03456	+	4.06141i	−0.419647	+	0.242283i	0.275279	+	0.961364i	$0.411230\pi$
$282$		0			0
$283$			1.34396i			0.0798899i	0.999202	+	0.0399450i	$0.0127183\pi$
$283$			1.34396i			0.0798899i	−0.999202	+	0.0399450i	$0.987282\pi$
$284$		−	0.983629i		−	0.0583676i
$285$		0			0
$286$	14.7526	−	8.51741i	0.872339	−	0.503645i
$287$		0			0
$288$		0			0
$289$	−6.06929	+	10.5123i	−0.357017	+	0.618371i
$290$	0.127169	−	0.220262i	0.00746760	−	0.0129343i
$291$		0			0
$292$	−1.97936	+	1.14279i	−0.115834	+	0.0668765i
$293$	10.6300	−	18.4117i	0.621012	−	1.07562i	−0.368285	−	0.929713i	$-0.620055\pi$
$293$	10.6300	−	18.4117i	0.621012	−	1.07562i	0.989298	−	0.145912i	$-0.0466116\pi$
$294$		0			0
$295$	1.21207	+	2.09936i	0.0705693	+	0.122230i
$296$	14.1543	+	8.17202i	0.822705	+	0.474989i
$297$		0			0
$298$	9.68289	+	16.7713i	0.560915	+	0.971533i
$299$	−0.163547			−0.00945815
$300$		0			0
$301$		0			0
$302$	−6.87261	−	3.96790i	−0.395474	−	0.228327i
$303$		0			0
$304$	−1.68776	−	0.974430i	−0.0967998	−	0.0558874i
$305$	2.34116	−	1.35167i	0.134054	−	0.0773963i
$306$		0			0
$307$			13.2098i			0.753925i	0.926229	+	0.376962i	$0.123031\pi$
$307$			13.2098i			0.753925i	−0.926229	+	0.376962i	$0.876969\pi$
$308$		0			0
$309$		0			0
$310$	3.84093	+	6.65268i	0.218150	+	0.377847i
$311$	20.5373			1.16457			0.582283	−	0.812986i	$-0.302160\pi$
$311$	20.5373			1.16457			0.582283	+	0.812986i	$0.302160\pi$
$312$		0			0
$313$		−	16.5094i		−	0.933168i	−0.884477	−	0.466584i	$-0.845485\pi$
$313$		−	16.5094i		−	0.933168i	0.884477	−	0.466584i	$-0.154515\pi$
$314$	12.0629			0.680746
$315$		0			0
$316$	1.39133			0.0782685
$317$			9.36591i			0.526042i	0.964790	+	0.263021i	$0.0847188\pi$
$317$			9.36591i			0.526042i	−0.964790	+	0.263021i	$0.915281\pi$
$318$		0			0
$319$	0.834266			0.0467099
$320$	2.55497	+	4.42534i	0.142827	+	0.247384i
$321$		0			0
$322$		0			0
$323$			2.34708i			0.130595i
$324$		0			0
$325$	−11.1797	+	6.45459i	−0.620137	+	0.358036i
$326$	15.0455	+	8.68653i	0.833294	+	0.481102i
$327$		0			0
$328$	−17.0356	−	9.83548i	−0.940631	−	0.543074i
$329$		0			0
$330$		0			0
$331$	28.8439			1.58540			0.792702	−	0.609609i	$-0.208674\pi$
$331$	28.8439			1.58540			0.792702	+	0.609609i	$0.208674\pi$
$332$	−1.20856	−	2.09328i	−0.0663282	−	0.114884i
$333$		0			0
$334$	21.9247	+	12.6582i	1.19967	+	0.692627i
$335$	1.63003	+	2.82329i	0.0890579	+	0.154253i
$336$		0			0
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	−0.984640	−	0.174596i	$-0.944138\pi$
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	0.643525	+	0.765425i	$0.277471\pi$
$338$	5.73388	−	3.31046i	0.311882	−	0.180065i
$339$		0			0
$340$	−0.587156	+	1.01698i	−0.0318430	+	0.0551537i
$341$	−12.5988	+	21.8218i	−0.682266	+	1.18172i
$342$		0			0
$343$		0			0
$344$	−28.9072	+	16.6896i	−1.55857	+	0.899841i
$345$		0			0
$346$			2.58648i			0.139050i
$347$		−	28.7220i		−	1.54188i	−0.636908	−	0.770939i	$-0.719787\pi$
$347$		−	28.7220i		−	1.54188i	0.636908	−	0.770939i	$-0.280213\pi$
$348$		0			0
$349$	11.0854	−	6.40017i	0.593389	−	0.342593i	−0.173048	−	0.984913i	$-0.555361\pi$
$349$	11.0854	−	6.40017i	0.593389	−	0.342593i	0.766436	+	0.642320i	$0.222028\pi$
$350$		0			0
$351$		0			0
$352$	3.02636	−	5.24181i	0.161305	−	0.279389i
$353$	−13.4991	+	23.3811i	−0.718485	+	1.24445i	0.243115	+	0.969998i	$0.421831\pi$
$353$	−13.4991	+	23.3811i	−0.718485	+	1.24445i	−0.961600	+	0.274455i	$0.911502\pi$
$354$		0			0
$355$	2.35721	−	1.36093i	0.125108	−	0.0722309i
$356$	2.19274	−	3.79793i	0.116215	−	0.201290i
$357$		0			0
$358$	−10.8233	−	18.7465i	−0.572030	−	0.990785i
$359$	−24.2669	−	14.0105i	−1.28076	−	0.739445i	−0.303770	−	0.952745i	$-0.598245\pi$
$359$	−24.2669	−	14.0105i	−1.28076	−	0.739445i	−0.976987	+	0.213300i	$0.931579\pi$
$360$		0			0
$361$	−9.40547	−	16.2908i	−0.495025	−	0.857408i
$362$	−7.29598			−0.383468
$363$		0			0
$364$		0			0
$365$	−5.47724	−	3.16228i	−0.286692	−	0.165522i
$366$		0			0
$367$	28.9584	+	16.7191i	1.51161	+	0.872731i	0.999908	+	0.0135705i	$0.00431975\pi$
$367$	28.9584	+	16.7191i	1.51161	+	0.872731i	0.511706	+	0.859160i	$0.329014\pi$
$368$	−0.216281	+	0.124870i	−0.0112744	+	0.00650928i
$369$		0			0
$370$		−	7.37430i		−	0.383372i
$371$		0			0
$372$		0			0
$373$	3.98403	+	6.90053i	0.206285	+	0.357296i	0.950541	−	0.310598i	$-0.100529\pi$
$373$	3.98403	+	6.90053i	0.206285	+	0.357296i	−0.744256	+	0.667894i	$0.767196\pi$
$374$	−31.3278			−1.61992
$375$		0			0
$376$			2.50730i			0.129304i
$377$	−0.637169			−0.0328159
$378$		0			0
$379$	3.88714			0.199669			0.0998345	−	0.995004i	$-0.468169\pi$
$379$	3.88714			0.199669			0.0998345	+	0.995004i	$0.468169\pi$
$380$			0.0945895i			0.00485234i
$381$		0			0
$382$	4.74487			0.242769
$383$	6.34150	+	10.9838i	0.324036	+	0.561246i	0.981317	−	0.192399i	$-0.0616269\pi$
$383$	6.34150	+	10.9838i	0.324036	+	0.561246i	−0.657281	+	0.753646i	$0.728294\pi$
$384$		0			0
$385$		0			0
$386$			9.07592i			0.461952i
$387$		0			0
$388$	−0.348133	+	0.200995i	−0.0176738	+	0.0102040i
$389$	−17.8067	−	10.2807i	−0.902835	−	0.521252i	−0.0247163	−	0.999695i	$-0.507868\pi$
$389$	−17.8067	−	10.2807i	−0.902835	−	0.521252i	−0.878119	+	0.478442i	$0.841202\pi$
$390$		0			0
$391$	0.260474	+	0.150385i	0.0131727	+	0.00760529i
$392$		0			0
$393$		0			0
$394$	21.2775			1.07195
$395$	1.92503	+	3.33424i	0.0968586	+	0.167764i
$396$		0			0
$397$	−12.9646	−	7.48513i	−0.650676	−	0.375668i	0.138039	−	0.990427i	$-0.455920\pi$
$397$	−12.9646	−	7.48513i	−0.650676	−	0.375668i	−0.788715	+	0.614759i	$0.789253\pi$
$398$	5.96552	+	10.3326i	0.299025	+	0.517926i
$399$		0			0
$400$	−9.85630	+	17.0716i	−0.492815	+	0.853580i
$401$	−8.93429	+	5.15821i	−0.446157	+	0.257589i	−0.706206	−	0.708007i	$-0.749595\pi$
$401$	−8.93429	+	5.15821i	−0.446157	+	0.257589i	0.260049	+	0.965595i	$0.416261\pi$
$402$		0			0
$403$	9.62235	−	16.6664i	0.479323	−	0.830212i
$404$	−2.24616	+	3.89047i	−0.111751	+	0.193558i
$405$		0			0
$406$		0			0
$407$	20.9482	−	12.0944i	1.03836	−	0.599499i
$408$		0			0
$409$		−	18.5199i		−	0.915750i	−0.889017	−	0.457875i	$-0.848611\pi$
$409$		−	18.5199i		−	0.915750i	0.889017	−	0.457875i	$-0.151389\pi$
$410$			8.87539i			0.438324i
$411$		0			0
$412$	−4.09543	+	2.36450i	−0.201767	+	0.116490i
$413$		0			0
$414$		0			0
$415$	3.34429	−	5.79247i	0.164165	−	0.284341i
$416$	−2.31138	+	4.00342i	−0.113325	+	0.196284i
$417$		0			0
$418$	−2.18535	+	1.26171i	−0.106889	+	0.0617122i
$419$	−6.37677	+	11.0449i	−0.311526	+	0.539578i	−0.978693	−	0.205330i	$-0.934173\pi$
$419$	−6.37677	+	11.0449i	−0.311526	+	0.539578i	0.667167	+	0.744908i	$0.267507\pi$
$420$		0			0
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	0.982674	−	0.185345i	$-0.0593402\pi$
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	−0.651850	+	0.758348i	$0.726007\pi$
$422$	6.74347	+	3.89334i	0.328267	+	0.189525i
$423$		0			0
$424$	−9.69173	−	16.7866i	−0.470672	−	0.815227i
$425$	23.7406			1.15159
$426$		0			0
$427$		0			0
$428$	0.943342	+	0.544639i	0.0455982	+	0.0263261i
$429$		0			0
$430$	13.0427	+	7.53020i	0.628975	+	0.363139i
$431$	31.3069	−	18.0750i	1.50800	−	0.870643i	0.508041	−	0.861333i	$-0.330370\pi$
$431$	31.3069	−	18.0750i	1.50800	−	0.870643i	0.999957	−	0.00931038i	$-0.00296363\pi$
$432$		0			0
$433$			33.0085i			1.58629i	0.609034	+	0.793144i	$0.291557\pi$
$433$			33.0085i			1.58629i	−0.609034	+	0.793144i	$0.708443\pi$
$434$		0			0
$435$		0			0
$436$	−0.359608	−	0.622859i	−0.0172221	−	0.0298295i
$437$	0.0242267			0.00115892
$438$		0			0
$439$		−	30.5618i		−	1.45863i	−0.684176	−	0.729317i	$-0.739838\pi$
$439$		−	30.5618i		−	1.45863i	0.684176	−	0.729317i	$-0.260162\pi$
$440$	7.74318			0.369141
$441$		0			0
$442$	23.9266			1.13807
$443$		−	20.7026i		−	0.983612i	−0.870705	−	0.491806i	$-0.836337\pi$
$443$		−	20.7026i		−	0.983612i	0.870705	−	0.491806i	$-0.163663\pi$
$444$		0			0
$445$	12.1353			0.575270
$446$	3.31150	+	5.73569i	0.156804	+	0.271593i
$447$		0			0
$448$		0			0
$449$			6.40243i			0.302150i	0.988522	+	0.151075i	$0.0482734\pi$
$449$			6.40243i			0.302150i	−0.988522	+	0.151075i	$0.951727\pi$
$450$		0			0
$451$	−25.2123	+	14.5563i	−1.18720	+	0.685431i
$452$	−2.74510	−	1.58489i	−0.129119	−	0.0745467i
$453$		0			0
$454$	12.6514	+	7.30428i	0.593759	+	0.342807i
$455$		0			0
$456$		0			0
$457$	−3.14680			−0.147201			−0.0736007	−	0.997288i	$-0.523449\pi$
$457$	−3.14680			−0.147201			−0.0736007	+	0.997288i	$0.523449\pi$
$458$	−6.68454	−	11.5780i	−0.312348	−	0.541003i
$459$		0			0
$460$	0.0104974	+	0.00606065i	0.000489442	+	0.000282579i
$461$	−7.44225	−	12.8904i	−0.346620	−	0.600364i	0.639026	−	0.769185i	$-0.279337\pi$
$461$	−7.44225	−	12.8904i	−0.346620	−	0.600364i	−0.985647	+	0.168821i	$0.946004\pi$
$462$		0			0
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	−0.368342	−	0.929690i	$-0.620075\pi$
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	0.989307	−	0.145851i	$-0.0465921\pi$
$464$	−0.842618	+	0.486486i	−0.0391175	+	0.0225845i
$465$		0			0
$466$	−9.73092	+	16.8544i	−0.450776	+	0.780767i
$467$	12.3967	−	21.4717i	0.573650	−	0.993591i	−0.422537	−	0.906346i	$-0.638860\pi$
$467$	12.3967	−	21.4717i	0.573650	−	0.993591i	0.996187	−	0.0872454i	$-0.0278064\pi$
$468$		0			0
$469$		0			0
$470$	0.979714	−	0.565638i	0.0451908	−	0.0260909i
$471$		0			0
$472$		−	8.11334i		−	0.373447i
$473$			49.4005i			2.27144i
$474$		0			0
$475$	1.65608	−	0.956138i	0.0759861	−	0.0438706i
$476$		0			0
$477$		0			0
$478$	3.64801	−	6.31855i	0.166856	−	0.289004i
$479$	6.26354	−	10.8488i	0.286189	−	0.495693i	−0.686708	−	0.726933i	$-0.740945\pi$
$479$	6.26354	−	10.8488i	0.286189	−	0.495693i	0.972897	+	0.231240i	$0.0742783\pi$
$480$		0			0
$481$	−15.9991	+	9.23711i	−0.729498	+	0.421176i
$482$	−7.57587	+	13.1218i	−0.345071	+	0.597681i
$483$		0			0
$484$	−0.528540	−	0.915459i	−0.0240246	−	0.0416118i
$485$	−0.963343	−	0.556187i	−0.0437432	−	0.0252551i
$486$		0			0
$487$	1.69748	+	2.94012i	0.0769202	+	0.133230i	0.901920	−	0.431904i	$-0.142158\pi$
$487$	1.69748	+	2.94012i	0.0769202	+	0.133230i	−0.824999	+	0.565133i	$0.808825\pi$
$488$	−9.04780			−0.409575
$489$		0			0
$490$		0			0
$491$	−0.780171	−	0.450432i	−0.0352086	−	0.0203277i	0.482292	−	0.876010i	$-0.339804\pi$
$491$	−0.780171	−	0.450432i	−0.0352086	−	0.0203277i	−0.517501	+	0.855683i	$0.673138\pi$
$492$		0			0
$493$	1.01479	+	0.585891i	0.0457040	+	0.0263872i
$494$	1.66905	−	0.963629i	0.0750943	−	0.0433557i
$495$		0			0
$496$		−	29.3871i		−	1.31952i
$497$		0			0
$498$		0			0
$499$	−10.9344	−	18.9390i	−0.489492	−	0.847825i	0.510435	−	0.859916i	$-0.329484\pi$
$499$	−10.9344	−	18.9390i	−0.489492	−	0.847825i	−0.999927	+	0.0120916i	$0.996151\pi$
$500$	2.04449			0.0914325
$501$		0			0
$502$			12.0536i			0.537979i
$503$	−42.9876			−1.91672			−0.958362	−	0.285557i	$-0.907821\pi$
$503$	−42.9876			−1.91672			−0.958362	+	0.285557i	$0.907821\pi$
$504$		0			0
$505$	−12.4310			−0.553173
$506$			0.323367i			0.0143754i
$507$		0			0
$508$	−0.744873			−0.0330484
$509$	−15.0416	−	26.0528i	−0.666708	−	1.15477i	−0.978819	−	0.204727i	$-0.934369\pi$
$509$	−15.0416	−	26.0528i	−0.666708	−	1.15477i	0.312111	−	0.950046i	$-0.398964\pi$
$510$		0			0
$511$		0			0
$512$		−	16.2193i		−	0.716799i
$513$		0			0
$514$	3.50785	−	2.02526i	0.154725	−	0.0893304i
$515$	−11.3327	−	6.54296i	−0.499380	−	0.288317i
$516$		0			0
$517$	3.21362	+	1.85538i	0.141335	+	0.0815997i
$518$		0			0
$519$		0			0
$520$	−5.91384			−0.259339
$521$	−6.00837	−	10.4068i	−0.263231	−	0.455930i	0.703867	−	0.710331i	$-0.251455\pi$
$521$	−6.00837	−	10.4068i	−0.263231	−	0.455930i	−0.967099	+	0.254401i	$0.918122\pi$
$522$		0			0
$523$	16.1185	+	9.30602i	0.704813	+	0.406924i	0.809137	−	0.587620i	$-0.199935\pi$
$523$	16.1185	+	9.30602i	0.704813	+	0.406924i	−0.104325	+	0.994543i	$0.533268\pi$
$524$	1.15466	+	1.99993i	0.0504417	+	0.0873675i
$525$		0			0
$526$	−17.6952	+	30.6490i	−0.771548	+	1.33636i
$527$	−30.6503	+	17.6959i	−1.33515	+	0.770847i
$528$		0			0
$529$	−11.4984	+	19.9159i	−0.499933	+	0.865909i
$530$	−4.37283	+	7.57397i	−0.189944	+	0.328992i
$531$		0			0
$532$		0			0
$533$	19.2559	−	11.1174i	0.834064	−	0.481547i
$534$		0			0
$535$			3.01422i			0.130316i
$536$		−	10.9111i		−	0.471286i
$537$		0			0
$538$	−5.20379	+	3.00441i	−0.224351	+	0.129529i
$539$		0			0
$540$		0			0
$541$	−21.1242	+	36.5882i	−0.908201	+	1.57305i	−0.0916391	+	0.995792i	$0.529211\pi$
$541$	−21.1242	+	36.5882i	−0.908201	+	1.57305i	−0.816562	+	0.577258i	$0.804123\pi$
$542$	9.44245	−	16.3548i	0.405588	−	0.702499i
$543$		0			0
$544$	7.36247	−	4.25072i	0.315663	−	0.182248i
$545$	0.995095	−	1.72356i	0.0426252	−	0.0738290i
$546$		0			0
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	0.679196	−	0.733957i	$-0.262329\pi$
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	−0.975223	+	0.221223i	$0.928995\pi$
$548$	4.20741	+	2.42915i	0.179732	+	0.103768i
$549$		0			0
$550$	12.7621	+	22.1046i	0.544178	+	0.942544i
$551$	0.0943858			0.00402097
$552$		0			0
$553$		0			0
$554$	25.7514	+	14.8676i	1.09407	+	0.631664i
$555$		0			0
$556$	1.53561	+	0.886585i	0.0651244	+	0.0375996i
$557$	−27.2305	+	15.7215i	−1.15379	+	0.666143i	−0.949809	−	0.312831i	$-0.898723\pi$
$557$	−27.2305	+	15.7215i	−1.15379	+	0.666143i	−0.203985	+	0.978974i	$0.565389\pi$
$558$		0			0
$559$		−	37.7296i		−	1.59579i
$560$		0			0
$561$		0			0
$562$	−6.13311	−	10.6229i	−0.258710	−	0.448098i
$563$	34.1657			1.43991			0.719956	−	0.694019i	$-0.244162\pi$
$563$	34.1657			1.43991			0.719956	+	0.694019i	$0.244162\pi$
$564$		0			0
$565$		−	8.77129i		−	0.369011i
$566$	−2.02950			−0.0853063
$567$		0			0
$568$	−9.10981			−0.382239
$569$			22.7074i			0.951944i	0.879461	+	0.475972i	$0.157904\pi$
$569$			22.7074i			0.951944i	−0.879461	+	0.475972i	$0.842096\pi$
$570$		0			0
$571$	−10.5986			−0.443538			−0.221769	−	0.975099i	$-0.571183\pi$
$571$	−10.5986			−0.443538			−0.221769	+	0.975099i	$0.571183\pi$
$572$	1.58147	+	2.73918i	0.0661245	+	0.114531i
$573$		0			0
$574$		0			0
$575$		−	0.245051i		−	0.0102193i
$576$		0			0
$577$	12.6222	−	7.28745i	0.525471	−	0.303381i	−0.213699	−	0.976899i	$-0.568551\pi$
$577$	12.6222	−	7.28745i	0.525471	−	0.303381i	0.739170	+	0.673519i	$0.235218\pi$
$578$	−15.8746	−	9.16520i	−0.660296	−	0.381222i
$579$		0			0
$580$	0.0408971	+	0.0236120i	0.00169816	+	0.000980434i
$581$		0			0
$582$		0			0
$583$	−28.6872			−1.18810
$584$	10.5838	+	18.3318i	0.437963	+	0.758574i
$585$		0			0
$586$	27.8035	+	16.0523i	1.14855	+	0.663116i
$587$	15.0927	+	26.1414i	0.622944	+	1.07897i	0.988935	+	0.148352i	$0.0473969\pi$
$587$	15.0927	+	26.1414i	0.622944	+	1.07897i	−0.365991	+	0.930619i	$0.619270\pi$
$588$		0			0
$589$	−1.42539	+	2.46884i	−0.0587321	+	0.101727i
$590$	−3.17024	+	1.83034i	−0.130517	+	0.0753538i
$591$		0			0
$592$	−14.1053	+	24.4310i	−0.579723	+	1.00411i
$593$	−15.2911	+	26.4850i	−0.627930	+	1.08761i	0.360036	+	0.932938i	$0.382764\pi$
$593$	−15.2911	+	26.4850i	−0.627930	+	1.08761i	−0.987966	+	0.154669i	$0.950569\pi$
$594$		0			0
$595$		0			0
$596$	−3.11400	+	1.79787i	−0.127554	+	0.0736435i
$597$		0			0
$598$		−	0.246971i		−	0.0100994i
$599$		−	2.70052i		−	0.110340i	−0.998477	−	0.0551701i	$-0.982430\pi$
$599$		−	2.70052i		−	0.110340i	0.998477	−	0.0551701i	$-0.0175701\pi$
$600$		0			0
$601$	−21.0197	+	12.1357i	−0.857411	+	0.495026i	−0.863144	−	0.504957i	$-0.831508\pi$
$601$	−21.0197	+	12.1357i	−0.857411	+	0.495026i	0.00573343	+	0.999984i	$0.498175\pi$
$602$		0			0
$603$		0			0
$604$	0.736739	−	1.27607i	0.0299775	−	0.0519225i
$605$	1.46256	−	2.53323i	0.0594616	−	0.102990i
$606$		0			0
$607$	−18.5486	+	10.7090i	−0.752865	+	0.434667i	−0.826728	−	0.562601i	$-0.809801\pi$
$607$	−18.5486	+	10.7090i	−0.752865	+	0.434667i	0.0738631	+	0.997268i	$0.476467\pi$
$608$	0.342391	−	0.593039i	0.0138858	−	0.0240509i
$609$		0			0
$610$	2.04115	+	3.53537i	0.0826437	+	0.143143i
$611$	−2.45439	−	1.41705i	−0.0992942	−	0.0573275i
$612$		0			0
$613$	−2.95306	−	5.11485i	−0.119273	−	0.206587i	0.800207	−	0.599724i	$-0.204723\pi$
$613$	−2.95306	−	5.11485i	−0.119273	−	0.206587i	−0.919480	+	0.393137i	$0.871390\pi$
$614$	−19.9481			−0.805039
$615$		0			0
$616$		0			0
$617$	1.19246	+	0.688465i	0.0480065	+	0.0277166i	0.523811	−	0.851834i	$-0.324510\pi$
$617$	1.19246	+	0.688465i	0.0480065	+	0.0277166i	−0.475805	+	0.879551i	$0.657843\pi$
$618$		0			0
$619$	−29.2918	−	16.9116i	−1.17734	−	0.679736i	−0.221941	−	0.975060i	$-0.571239\pi$
$619$	−29.2918	−	16.9116i	−1.17734	−	0.679736i	−0.955397	+	0.295324i	$0.904572\pi$
$620$	−1.23523	+	0.713163i	−0.0496082	+	0.0286413i
$621$		0			0
$622$			31.0133i			1.24352i
$623$		0			0
$624$		0			0
$625$	−8.16631	−	14.1445i	−0.326652	−	0.565779i
$626$	24.9308			0.996435
$627$		0			0
$628$			2.23977i			0.0893764i
$629$	33.9749			1.35467
$630$		0			0
$631$	−25.0205			−0.996049			−0.498024	−	0.867163i	$-0.665941\pi$
$631$	−25.0205			−0.996049			−0.498024	+	0.867163i	$0.665941\pi$
$632$		−	12.8857i		−	0.512567i
$633$		0			0
$634$	−14.1434			−0.561707
$635$	−1.03059	−	1.78504i	−0.0408979	−	0.0708373i
$636$		0			0
$637$		0			0
$638$			1.25982i			0.0498768i
$639$		0			0
$640$	−8.79916	+	5.08020i	−0.347817	+	0.200812i
$641$	−9.25173	−	5.34149i	−0.365421	−	0.210976i	0.306035	−	0.952020i	$-0.400998\pi$
$641$	−9.25173	−	5.34149i	−0.365421	−	0.210976i	−0.671456	+	0.741044i	$0.734331\pi$
$642$		0			0
$643$	−38.1128	−	22.0044i	−1.50302	−	0.867771i	−0.999994	−	0.00350106i	$-0.998886\pi$
$643$	−38.1128	−	22.0044i	−1.50302	−	0.867771i	−0.503029	−	0.864270i	$-0.667781\pi$
$644$		0			0
$645$		0			0
$646$	−3.54431			−0.139449
$647$	−23.5043	−	40.7107i	−0.924050	−	1.60050i	−0.793082	−	0.609115i	$-0.791525\pi$
$647$	−23.5043	−	40.7107i	−0.924050	−	1.60050i	−0.130968	−	0.991387i	$-0.541808\pi$
$648$		0			0
$649$	−10.3989	−	6.00380i	−0.408192	−	0.235670i
$650$	−9.74704	−	16.8824i	−0.382310	−	0.662181i
$651$		0			0
$652$	−1.61287	+	2.79357i	−0.0631648	+	0.109405i
$653$	29.3918	−	16.9694i	1.15019	−	0.664063i	0.201257	−	0.979538i	$-0.435497\pi$
$653$	29.3918	−	16.9694i	1.15019	−	0.664063i	0.948934	+	0.315475i	$0.102164\pi$
$654$		0			0
$655$	−3.19515	+	5.53416i	−0.124845	+	0.216237i
$656$	16.9765	−	29.4041i	0.662820	−	1.14804i
$657$		0			0
$658$		0			0
$659$	1.36652	−	0.788962i	0.0532322	−	0.0307336i	−0.473148	−	0.880983i	$-0.656882\pi$
$659$	1.36652	−	0.788962i	0.0532322	−	0.0307336i	0.526380	+	0.850249i	$0.323549\pi$
$660$		0			0
$661$			2.40720i			0.0936293i	0.998904	+	0.0468147i	$0.0149070\pi$
$661$			2.40720i			0.0936293i	−0.998904	+	0.0468147i	$0.985093\pi$
$662$			43.5570i			1.69289i
$663$		0			0
$664$	−19.3868	+	11.1930i	−0.752354	+	0.434372i
$665$		0			0
$666$		0			0
$667$	0.00604760	−	0.0104747i	0.000234164	−	0.000405584i
$668$	−2.35031	+	4.07086i	−0.0909363	+	0.157506i
$669$		0			0
$670$	−4.26344	+	2.46150i	−0.164711	+	0.0950959i
$671$	−6.69529	+	11.5966i	−0.258469	+	0.447681i
$672$		0			0
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	0.999387	−	0.0350069i	$-0.0111453\pi$
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	−0.530010	+	0.847991i	$0.677812\pi$
$674$	−16.3788	−	9.45629i	−0.630887	−	0.364243i
$675$		0			0
$676$	0.614668	+	1.06464i	0.0236411	+	0.0409476i
$677$	−9.67694			−0.371915			−0.185958	−	0.982558i	$-0.559539\pi$
$677$	−9.67694			−0.371915			−0.185958	+	0.982558i	$0.559539\pi$
$678$		0			0
$679$		0			0
$680$	9.41873	+	5.43791i	0.361192	+	0.208534i
$681$		0			0
$682$	−32.9531	−	19.0255i	−1.26184	−	0.728522i
$683$	18.6341	−	10.7584i	0.713012	−	0.411658i	−0.0991632	−	0.995071i	$-0.531617\pi$
$683$	18.6341	−	10.7584i	0.713012	−	0.411658i	0.812175	+	0.583413i	$0.198283\pi$
$684$		0			0
$685$			13.4437i			0.513659i
$686$		0			0
$687$		0			0
$688$	−28.8069	−	49.8951i	−1.09825	−	1.90223i
$689$	21.9098			0.834696
$690$		0			0
$691$			29.4425i			1.12005i	0.828477	+	0.560023i	$0.189208\pi$
$691$			29.4425i			1.12005i	−0.828477	+	0.560023i	$0.810792\pi$
$692$	−0.480244			−0.0182561
$693$		0			0
$694$	43.3730			1.64642
$695$			4.90666i			0.186120i
$696$		0			0
$697$	−40.8907			−1.54885
$698$	9.66486	+	16.7400i	0.365820	+	0.633619i
$699$		0			0
$700$		0			0
$701$			40.4325i			1.52712i	0.645740	+	0.763558i	$0.276549\pi$
$701$			40.4325i			1.52712i	−0.645740	+	0.763558i	$0.723451\pi$
$702$		0			0
$703$	2.37000	−	1.36832i	0.0893863	−	0.0516072i
$704$	−21.9203	−	12.6557i	−0.826151	−	0.476979i
$705$		0			0
$706$	−35.3077	−	20.3849i	−1.32882	−	0.767197i
$707$		0			0
$708$		0			0
$709$	−15.9023			−0.597223			−0.298611	−	0.954375i	$-0.596523\pi$
$709$	−15.9023			−0.597223			−0.298611	+	0.954375i	$0.596523\pi$
$710$	2.05514	+	3.55960i	0.0771280	+	0.133590i
$711$		0			0
$712$	−35.1743	−	20.3079i	−1.31821	−	0.761070i
$713$	0.182658	+	0.316373i	0.00684061	+	0.0118483i
$714$		0			0
$715$	−4.37619	+	7.57978i	−0.163660	+	0.283468i
$716$	3.48076	−	2.00962i	0.130082	−	0.0751028i
$717$		0			0
$718$	21.1572	−	36.6453i	0.789578	−	1.36759i
$719$	13.0488	−	22.6012i	0.486638	−	0.842883i	−0.513244	−	0.858243i	$-0.671556\pi$
$719$	13.0488	−	22.6012i	0.486638	−	0.842883i	0.999882	+	0.0153605i	$0.00488959\pi$
$720$		0			0
$721$		0			0
$722$	24.6006	−	14.2032i	0.915539	−	0.528587i
$723$		0			0
$724$		−	1.35468i		−	0.0503463i
$725$		−	0.954706i		−	0.0354569i
$726$		0			0
$727$	3.74533	−	2.16237i	0.138907	−	0.0801977i	−0.428936	−	0.903335i	$-0.641111\pi$
$727$	3.74533	−	2.16237i	0.138907	−	0.0801977i	0.567843	+	0.823137i	$0.307778\pi$
$728$		0			0
$729$		0			0
$730$	4.77535	−	8.27115i	0.176744	−	0.306129i
$731$	−34.6932	+	60.0904i	−1.28317	+	2.22252i
$732$		0			0
$733$	36.6480	−	21.1587i	1.35362	−	0.781515i	0.364869	−	0.931059i	$-0.381114\pi$
$733$	36.6480	−	21.1587i	1.35362	−	0.781515i	0.988755	+	0.149544i	$0.0477805\pi$
$734$	−25.2475	+	43.7299i	−0.931901	+	1.61410i
$735$		0			0
$736$	−0.0438762	−	0.0759958i	−0.00161730	−	0.00280124i
$737$	−13.9847	−	8.07409i	−0.515135	−	0.297413i
$738$		0			0
$739$	1.62120	+	2.80801i	0.0596369	+	0.103294i	0.894302	−	0.447463i	$-0.147672\pi$
$739$	1.62120	+	2.80801i	0.0596369	+	0.103294i	−0.834666	+	0.550757i	$0.814339\pi$
$740$	1.36922			0.0503336
$741$		0			0
$742$		0			0
$743$	−5.41770	−	3.12791i	−0.198756	−	0.114752i	0.397319	−	0.917681i	$-0.369941\pi$
$743$	−5.41770	−	3.12791i	−0.198756	−	0.114752i	−0.596075	+	0.802929i	$0.703274\pi$
$744$		0			0
$745$	−8.61696	−	4.97500i	−0.315701	−	0.182270i
$746$	−10.4205	+	6.01626i	−0.381520	+	0.220271i
$747$		0			0
$748$		−	5.81678i		−	0.212682i
$749$		0			0
$750$		0			0
$751$	9.45315	+	16.3733i	0.344950	+	0.597471i	0.985345	−	0.170575i	$-0.0545625\pi$
$751$	9.45315	+	16.3733i	0.344950	+	0.597471i	−0.640395	+	0.768046i	$0.721229\pi$
$752$	−4.32772			−0.157816
$753$		0			0
$754$		−	0.962186i		−	0.0350407i
$755$	4.07736			0.148390
$756$		0			0
$757$	−40.7873			−1.48244			−0.741220	−	0.671262i	$-0.765752\pi$
$757$	−40.7873			−1.48244			−0.741220	+	0.671262i	$0.765752\pi$
$758$			5.86995i			0.213206i
$759$		0			0
$760$	0.876035			0.0317771
$761$	−21.3106	−	36.9110i	−0.772508	−	1.33802i	−0.936184	−	0.351509i	$-0.885669\pi$
$761$	−21.3106	−	36.9110i	−0.772508	−	1.33802i	0.163676	−	0.986514i	$-0.447665\pi$
$762$		0			0
$763$		0			0
$764$			0.881003i			0.0318736i
$765$		0			0
$766$	−16.5866	+	9.57627i	−0.599298	+	0.346005i
$767$	7.94213	+	4.58539i	0.286774	+	0.165569i
$768$		0			0
$769$	−0.932209	−	0.538211i	−0.0336163	−	0.0194084i	0.483098	−	0.875566i	$-0.339512\pi$
$769$	−0.932209	−	0.538211i	−0.0336163	−	0.0194084i	−0.516714	+	0.856158i	$0.672845\pi$
$770$		0			0
$771$		0			0
$772$	−1.68517			−0.0606506
$773$	−2.96855	−	5.14169i	−0.106771	−	0.184934i	0.807689	−	0.589609i	$-0.200718\pi$
$773$	−2.96855	−	5.14169i	−0.106771	−	0.184934i	−0.914461	+	0.404675i	$0.867385\pi$
$774$		0			0
$775$	24.9722	+	14.4177i	0.897028	+	0.517899i
$776$	1.86150	+	3.22421i	0.0668240	+	0.115742i
$777$		0			0
$778$	15.5248	−	26.8898i	0.556592	−	0.964046i
$779$	−2.85243	+	1.64685i	−0.102199	+	0.0590046i
$780$		0			0
$781$	−6.74118	+	11.6761i	−0.241218	+	0.417802i
$782$	−0.227095	+	0.393341i	−0.00812091	+	0.0140658i
$783$		0			0
$784$		0			0
$785$	−5.36746	+	3.09891i	−0.191573	+	0.110605i
$786$		0			0
$787$		−	8.83847i		−	0.315057i	−0.987514	−	0.157529i	$-0.949647\pi$
$787$		−	8.83847i		−	0.315057i	0.987514	−	0.157529i	$-0.0503527\pi$
$788$			3.95069i			0.140738i
$789$		0			0
$790$	−5.03502	+	2.90697i	−0.179138	+	0.103425i
$791$		0			0
$792$		0			0
$793$	5.11351	−	8.85687i	0.181586	−	0.314517i
$794$	11.3033	−	19.5778i	0.401138	−	0.694791i
$795$		0			0
$796$	−1.91850	+	1.10765i	−0.0679994	+	0.0392595i
$797$	−19.0123	+	32.9303i	−0.673450	+	1.16645i	0.303469	+	0.952841i	$0.401855\pi$
$797$	−19.0123	+	32.9303i	−0.673450	+	1.16645i	−0.976919	+	0.213609i	$0.931478\pi$
$798$		0			0
$799$	2.60601	+	4.51374i	0.0921940	+	0.159685i
$800$	−5.99855	−	3.46326i	−0.212081	−	0.122445i
$801$		0			0
$802$	−7.78939	−	13.4916i	−0.275053	−	0.476406i
$803$	31.3278			1.10553
$804$		0			0
$805$		0			0
$806$	25.1678	+	14.5307i	0.886499	+	0.511821i
$807$		0			0
$808$	36.0313	+	20.8027i	1.26758	+	0.731836i
$809$	14.6570	−	8.46222i	0.515312	−	0.297516i	−0.219702	−	0.975567i	$-0.570509\pi$
$809$	14.6570	−	8.46222i	0.515312	−	0.297516i	0.735015	+	0.678051i	$0.237175\pi$
$810$		0			0
$811$			26.9840i			0.947536i	0.880650	+	0.473768i	$0.157106\pi$
$811$			26.9840i			0.947536i	−0.880650	+	0.473768i	$0.842894\pi$
$812$		0			0
$813$		0			0
$814$	18.2637	+	31.6337i	0.640144	+	1.10876i
$815$	−8.92616			−0.312670
$816$		0			0
$817$			5.58899i			0.195534i
$818$	27.9668			0.977836
$819$		0			0
$820$	−1.64793			−0.0575484
$821$			32.0512i			1.11859i	0.828967	+	0.559297i	$0.188929\pi$
$821$			32.0512i			1.11859i	−0.828967	+	0.559297i	$0.811071\pi$
$822$		0			0
$823$	20.7948			0.724863			0.362431	−	0.932011i	$-0.381947\pi$
$823$	20.7948			0.724863			0.362431	+	0.932011i	$0.381947\pi$
$824$	21.8986	+	37.9295i	0.762875	+	1.32134i
$825$		0			0
$826$		0			0
$827$		−	34.0792i		−	1.18505i	−0.805552	−	0.592525i	$-0.798131\pi$
$827$		−	34.0792i		−	1.18505i	0.805552	−	0.592525i	$-0.201869\pi$
$828$		0			0
$829$	29.3229	−	16.9296i	1.01843	−	0.587988i	0.104778	−	0.994496i	$-0.466587\pi$
$829$	29.3229	−	16.9296i	1.01843	−	0.587988i	0.913648	+	0.406507i	$0.133253\pi$
$830$	8.74718	+	5.05019i	0.303619	+	0.175295i
$831$		0			0
$832$	16.7416	+	9.66575i	0.580410	+	0.335100i
$833$		0			0
$834$		0			0
$835$	−13.0074			−0.450140
$836$	−0.234267	−	0.405763i	−0.00810231	−	0.0140336i
$837$		0			0
$838$	−16.6788	−	9.62953i	−0.576161	−	0.332647i
$839$	−11.7633	−	20.3747i	−0.406115	−	0.703412i	0.588335	−	0.808617i	$-0.299784\pi$
$839$	−11.7633	−	20.3747i	−0.406115	−	0.703412i	−0.994451	+	0.105205i	$0.966450\pi$
$840$		0			0
$841$	−14.4764	+	25.0739i	−0.499188	+	0.864618i
$842$	−17.7542	+	10.2504i	−0.611852	+	0.353253i
$843$		0			0
$844$	−0.722895	+	1.25209i	−0.0248831	+	0.0430987i
$845$	−1.70089	+	2.94603i	−0.0585124	+	0.101347i
$846$		0			0
$847$		0			0
$848$	28.9743	−	16.7283i	0.994983	−	0.574454i
$849$		0			0
$850$			35.8505i			1.22966i
$851$		−	0.350691i		−	0.0120215i
$852$		0			0
$853$	39.7270	−	22.9364i	1.36023	−	0.785328i	0.370574	−	0.928803i	$-0.379161\pi$
$853$	39.7270	−	22.9364i	1.36023	−	0.785328i	0.989654	+	0.143475i	$0.0458277\pi$
$854$		0			0
$855$		0			0
$856$	5.04414	−	8.73670i	0.172405	−	0.298614i
$857$	9.12274	−	15.8010i	0.311627	−	0.539753i	−0.667088	−	0.744979i	$-0.732460\pi$
$857$	9.12274	−	15.8010i	0.311627	−	0.539753i	0.978715	+	0.205226i	$0.0657928\pi$
$858$		0			0
$859$	5.03737	−	2.90833i	0.171873	−	0.0992309i	−0.411596	−	0.911367i	$-0.635028\pi$
$859$	5.03737	−	2.90833i	0.171873	−	0.0992309i	0.583469	+	0.812136i	$0.301695\pi$
$860$	−1.39817	+	2.42170i	−0.0476771	+	0.0825792i
$861$		0			0
$862$	27.2950	+	47.2763i	0.929671	+	1.61024i
$863$	−27.7060	−	15.9961i	−0.943123	−	0.544513i	−0.0521854	−	0.998637i	$-0.516619\pi$
$863$	−27.7060	−	15.9961i	−0.943123	−	0.544513i	−0.890938	+	0.454125i	$0.849952\pi$
$864$		0			0
$865$	−0.664458	−	1.15087i	−0.0225922	−	0.0391309i
$866$	−49.8460			−1.69384
$867$		0			0
$868$		0			0
$869$	−16.5157	−	9.53533i	−0.560256	−	0.323464i
$870$		0			0
$871$	10.6808	+	6.16658i	0.361906	+	0.208946i
$872$	−5.76857	+	3.33048i	−0.195348	+	0.112784i
$873$		0			0
$874$			0.0365846i			0.00123749i
$875$		0			0
$876$		0			0
$877$	24.1949	+	41.9068i	0.817004	+	1.41509i	0.907880	+	0.419231i	$0.137700\pi$
$877$	24.1949	+	41.9068i	0.817004	+	1.41509i	−0.0908756	+	0.995862i	$0.528967\pi$
$878$	46.1512			1.55753
$879$		0			0
$880$			13.3651i			0.450536i
$881$	−26.6822			−0.898946			−0.449473	−	0.893294i	$-0.648388\pi$
$881$	−26.6822			−0.898946			−0.449473	+	0.893294i	$0.648388\pi$
$882$		0			0
$883$	35.0484			1.17947			0.589737	−	0.807595i	$-0.299231\pi$
$883$	35.0484			1.17947			0.589737	+	0.807595i	$0.299231\pi$
$884$			4.44255i			0.149419i
$885$		0			0
$886$	31.2629			1.05030
$887$	6.48380	+	11.2303i	0.217705	+	0.377076i	0.954106	−	0.299469i	$-0.0968096\pi$
$887$	6.48380	+	11.2303i	0.217705	+	0.377076i	−0.736401	+	0.676545i	$0.763476\pi$
$888$		0			0
$889$		0			0
$890$			18.3255i			0.614273i
$891$		0			0
$892$	−1.06497	+	0.614862i	−0.0356579	+	0.0205871i
$893$	0.363577	+	0.209911i	0.0121666	+	0.00702441i
$894$		0			0
$895$	9.63184	+	5.56095i	0.321957	+	0.185882i
$896$		0			0
$897$		0			0
$898$	−9.66828			−0.322635
$899$	0.711627	+	1.23257i	0.0237341	+	0.0411086i
$900$		0			0
$901$	−34.8948	−	20.1465i	−1.16251	−	0.671178i
$902$	−21.9815	−	38.0730i	−0.731902	−	1.26769i
$903$		0			0
$904$	−14.6783	+	25.4236i	−0.488193	+	0.845576i
$905$	3.24641	−	1.87431i	0.107914	−	0.0623043i
$906$		0			0
$907$	4.56307	−	7.90346i	0.151514	−	0.262430i	−0.780270	−	0.625443i	$-0.784918\pi$
$907$	4.56307	−	7.90346i	0.151514	−	0.262430i	0.931784	+	0.363012i	$0.118252\pi$
$908$	−1.35622	+	2.34904i	−0.0450077	+	0.0779557i
$909$		0			0
$910$		0			0
$911$	−41.5720	+	24.0016i	−1.37734	+	0.795209i	−0.991839	−	0.127498i	$-0.959305\pi$
$911$	−41.5720	+	24.0016i	−1.37734	+	0.795209i	−0.385503	+	0.922707i	$0.625972\pi$
$912$		0			0
$913$			33.1308i			1.09647i
$914$		−	4.75197i		−	0.157181i
$915$		0			0
$916$	2.14973	−	1.24115i	0.0710292	−	0.0410087i
$917$		0			0
$918$		0			0
$919$	19.8096	−	34.3113i	0.653459	−	1.13182i	−0.328818	−	0.944393i	$-0.606650\pi$
$919$	19.8096	−	34.3113i	0.653459	−	1.13182i	0.982278	−	0.187432i	$-0.0600163\pi$
$920$	0.0561303	−	0.0972206i	0.00185056	−	0.00320527i
$921$		0			0
$922$	19.4657	−	11.2385i	0.641068	−	0.370121i
$923$	5.14856	−	8.91757i	0.169467	−	0.293526i
$924$		0			0
$925$	−13.8405	−	23.9724i	−0.455072	−	0.788208i
$926$	34.9480	+	20.1772i	1.14846	+	0.663065i
$927$		0			0
$928$	−0.170939	−	0.296076i	−0.00561136	−	0.00971915i
$929$	−23.5795			−0.773618			−0.386809	−	0.922160i	$-0.626423\pi$
$929$	−23.5795			−0.773618			−0.386809	+	0.922160i	$0.626423\pi$
$930$		0			0
$931$		0			0
$932$	−3.12944	−	1.80679i	−0.102508	−	0.0591832i
$933$		0			0
$934$	32.4243	+	18.7202i	1.06096	+	0.612543i
$935$	13.9396	−	8.04801i	0.455872	−	0.263198i
$936$		0			0
$937$		−	52.5144i		−	1.71557i	−0.514007	−	0.857786i	$-0.671840\pi$
$937$		−	52.5144i		−	1.71557i	0.514007	−	0.857786i	$-0.328160\pi$
$938$		0			0
$939$		0			0
$940$	0.105025	+	0.181908i	0.00342553	+	0.00593319i
$941$	−49.1425			−1.60200			−0.801000	−	0.598664i	$-0.795698\pi$
$941$	−49.1425			−1.60200			−0.801000	+	0.598664i	$0.795698\pi$
$942$		0			0
$943$			0.422076i			0.0137447i
$944$	14.0040			0.455791
$945$		0			0
$946$	−74.5995			−2.42544
$947$			9.29426i			0.302023i	0.988532	+	0.151012i	$0.0482531\pi$
$947$			9.29426i			0.302023i	−0.988532	+	0.151012i	$0.951747\pi$
$948$		0			0
$949$	−23.9266			−0.776689
$950$	1.44386	+	2.50084i	0.0468450	+	0.0811379i
$951$		0			0
$952$		0			0
$953$			40.3761i			1.30791i	0.756534	+	0.653955i	$0.226891\pi$
$953$			40.3761i			1.30791i	−0.756534	+	0.653955i	$0.773109\pi$
$954$		0			0
$955$	−2.11127	+	1.21894i	−0.0683191	+	0.0394440i
$956$	1.17319	+	0.677344i	0.0379438	+	0.0219069i
$957$		0			0
$958$	16.3827	+	9.45854i	0.529300	+	0.305592i
$959$		0			0
$960$		0			0
$961$	−11.9872			−0.386682
$962$	−13.9489	−	24.1602i	−0.449731	−	0.778957i
$963$		0			0
$964$	−2.43638	−	1.40665i	−0.0784706	−	0.0453050i
$965$	−2.33157	−	4.03840i	−0.0750560	−	0.130001i
$966$		0			0
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	−0.689466	−	0.724318i	$-0.742155\pi$
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	0.972011	+	0.234936i	$0.0754879\pi$
$968$	−8.47846	+	4.89504i	−0.272508	+	0.157333i
$969$		0			0
$970$	0.839894	−	1.45474i	0.0269674	−	0.0467089i
$971$	20.1321	−	34.8697i	0.646068	−	1.11902i	−0.337985	−	0.941151i	$-0.609745\pi$
$971$	20.1321	−	34.8697i	0.646068	−	1.11902i	0.984054	−	0.177872i	$-0.0569212\pi$
$972$		0			0
$973$		0			0
$974$	−4.43986	+	2.56336i	−0.142262	+	0.0821353i
$975$		0			0
$976$		−	15.6169i		−	0.499885i
$977$			26.5109i			0.848159i	0.905625	+	0.424080i	$0.139402\pi$
$977$			26.5109i			0.848159i	−0.905625	+	0.424080i	$0.860598\pi$
$978$		0			0
$979$	−52.0573	+	30.0553i	−1.66376	+	0.960572i
$980$		0			0
$981$		0			0
$982$	0.680195	−	1.17813i	0.0217059	−	0.0375957i
$983$	−19.1357	+	33.1440i	−0.610334	+	1.05713i	0.380850	+	0.924637i	$0.375632\pi$
$983$	−19.1357	+	33.1440i	−0.610334	+	1.05713i	−0.991184	+	0.132493i	$0.957702\pi$
$984$		0			0
$985$	−9.46759	+	5.46612i	−0.301663	+	0.174165i
$986$	−0.884752	+	1.53243i	−0.0281762	+	0.0488027i
$987$		0			0
$988$	0.178921	+	0.309901i	0.00569225	+	0.00985926i
$989$	0.620255	+	0.358105i	0.0197230	+	0.0113871i
$990$		0			0
$991$	30.4509	+	52.7425i	0.967305	+	1.67542i	0.703289	+	0.710904i	$0.251714\pi$
$991$	30.4509	+	52.7425i	0.967305	+	1.67542i	0.264016	+	0.964518i	$0.414953\pi$
$992$	10.3259			0.327848
$993$		0			0
$994$		0			0
$995$	−5.30881	−	3.06504i	−0.168301	−	0.0971684i
$996$		0			0
$997$	−12.4807	−	7.20573i	−0.395267	−	0.228208i	0.289173	−	0.957277i	$-0.406620\pi$
$997$	−12.4807	−	7.20573i	−0.395267	−	0.228208i	−0.684440	+	0.729069i	$0.739953\pi$
$998$	28.5996	−	16.5120i	0.905306	−	0.522679i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.b.1097.4		10
3.2	odd	2		441.2.i.b.68.2		10
7.2	even	3		1323.2.o.d.881.4		10
7.3	odd	6		1323.2.s.b.962.2		10
7.4	even	3		189.2.s.b.17.2		10
7.5	odd	6		1323.2.o.c.881.4		10
7.6	odd	2		189.2.i.b.152.4		10
9.2	odd	6		1323.2.s.b.656.2		10
9.7	even	3		441.2.s.b.362.4		10
21.2	odd	6		441.2.o.c.293.2		10
21.5	even	6		441.2.o.d.293.2		10
21.11	odd	6		63.2.s.b.59.4	yes	10
21.17	even	6		441.2.s.b.374.4		10
21.20	even	2		63.2.i.b.5.2	✓	10
28.11	odd	6		3024.2.df.b.17.3		10
28.27	even	2		3024.2.ca.b.2609.3		10
63.2	odd	6		1323.2.o.c.440.4		10
63.4	even	3		567.2.p.d.80.4		10
63.11	odd	6		189.2.i.b.143.2		10
63.13	odd	6		567.2.p.c.404.2		10
63.16	even	3		441.2.o.d.146.2		10
63.20	even	6		189.2.s.b.89.2		10
63.25	even	3		63.2.i.b.38.4	yes	10
63.32	odd	6		567.2.p.c.80.2		10
63.34	odd	6		63.2.s.b.47.4	yes	10
63.38	even	6	inner	1323.2.i.b.521.2		10
63.41	even	6		567.2.p.d.404.4		10
63.47	even	6		1323.2.o.d.440.4		10
63.52	odd	6		441.2.i.b.227.4		10
63.61	odd	6		441.2.o.c.146.2		10
84.11	even	6		1008.2.df.b.689.4		10
84.83	odd	2		1008.2.ca.b.257.2		10
252.11	even	6		3024.2.ca.b.2033.3		10
252.83	odd	6		3024.2.df.b.1601.3		10
252.151	odd	6		1008.2.ca.b.353.2		10
252.223	even	6		1008.2.df.b.929.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.2	✓	10	21.20	even	2
63.2.i.b.38.4	yes	10	63.25	even	3
63.2.s.b.47.4	yes	10	63.34	odd	6
63.2.s.b.59.4	yes	10	21.11	odd	6
189.2.i.b.143.2		10	63.11	odd	6
189.2.i.b.152.4		10	7.6	odd	2
189.2.s.b.17.2		10	7.4	even	3
189.2.s.b.89.2		10	63.20	even	6
441.2.i.b.68.2		10	3.2	odd	2
441.2.i.b.227.4		10	63.52	odd	6
441.2.o.c.146.2		10	63.61	odd	6
441.2.o.c.293.2		10	21.2	odd	6
441.2.o.d.146.2		10	63.16	even	3
441.2.o.d.293.2		10	21.5	even	6
441.2.s.b.362.4		10	9.7	even	3
441.2.s.b.374.4		10	21.17	even	6
567.2.p.c.80.2		10	63.32	odd	6
567.2.p.c.404.2		10	63.13	odd	6
567.2.p.d.80.4		10	63.4	even	3
567.2.p.d.404.4		10	63.41	even	6
1008.2.ca.b.257.2		10	84.83	odd	2
1008.2.ca.b.353.2		10	252.151	odd	6
1008.2.df.b.689.4		10	84.11	even	6
1008.2.df.b.929.4		10	252.223	even	6
1323.2.i.b.521.2		10	63.38	even	6	inner
1323.2.i.b.1097.4		10	1.1	even	1	trivial
1323.2.o.c.440.4		10	63.2	odd	6
1323.2.o.c.881.4		10	7.5	odd	6
1323.2.o.d.440.4		10	63.47	even	6
1323.2.o.d.881.4		10	7.2	even	3
1323.2.s.b.656.2		10	9.2	odd	6
1323.2.s.b.962.2		10	7.3	odd	6
3024.2.ca.b.2033.3		10	252.11	even	6
3024.2.ca.b.2609.3		10	28.27	even	2
3024.2.df.b.17.3		10	28.11	odd	6
3024.2.df.b.1601.3		10	252.83	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.51009i q^{2} -0.280386 q^{4} +(-0.387938 - 0.671929i) q^{5} +2.59678i q^{8} +O(q^{10})\)	\(q+1.51009i q^{2} -0.280386 q^{4} +(-0.387938 - 0.671929i) q^{5} +2.59678i q^{8} +(1.01468 - 0.585823i) q^{10} +(3.32830 + 1.92159i) q^{11} +(-2.54198 - 1.46761i) q^{13} -4.48216 q^{16} +(2.69901 + 4.67482i) q^{17} +(0.376551 + 0.217402i) q^{19} +(0.108773 + 0.188400i) q^{20} +(-2.90179 + 5.02605i) q^{22} +(0.0482537 - 0.0278593i) q^{23} +(2.19901 - 3.80879i) q^{25} +(2.21624 - 3.83863i) q^{26} +(0.187994 - 0.108538i) q^{29} +6.55646i q^{31} -1.57492i q^{32} +(-7.05942 + 4.07576i) q^{34} +(3.14698 - 5.45073i) q^{37} +(-0.328298 + 0.568628i) q^{38} +(1.74485 - 1.00739i) q^{40} +(-3.78757 + 6.56026i) q^{41} +(6.42703 + 11.1319i) q^{43} +(-0.933209 - 0.538789i) q^{44} +(0.0420702 + 0.0728677i) q^{46} +0.965544 q^{47} +(5.75164 + 3.32071i) q^{50} +(0.712737 + 0.411499i) q^{52} +(-6.46438 + 3.73221i) q^{53} -2.98184i q^{55} +(0.163903 + 0.283889i) q^{58} -3.12439 q^{59} +3.48424i q^{61} -9.90087 q^{62} -6.58603 q^{64} +2.27737i q^{65} -4.20177 q^{67} +(-0.756765 - 1.31076i) q^{68} +3.50812i q^{71} +(7.05942 - 4.07576i) q^{73} +(8.23112 + 4.75224i) q^{74} +(-0.105580 - 0.0609566i) q^{76} -4.96220 q^{79} +(1.73880 + 3.01169i) q^{80} +(-9.90662 - 5.71959i) q^{82} +(4.31033 + 7.46571i) q^{83} +(2.09410 - 3.62708i) q^{85} +(-16.8103 + 9.70542i) q^{86} +(-4.98996 + 8.64286i) q^{88} +(-7.82041 + 13.5453i) q^{89} +(-0.0135297 + 0.00781136i) q^{92} +1.45806i q^{94} -0.337354i q^{95} +(1.24162 - 0.716849i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{4}+O(q^{10}) \) 10 * q - 8 * q^4	\( 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} + 30 q^{47} - 3 q^{50} + 12 q^{52} - 9 q^{53} + 8 q^{58} - 36 q^{59} - 12 q^{62} + 6 q^{64} + 20 q^{67} - 27 q^{68} - 3 q^{73} + 30 q^{74} + 9 q^{76} - 40 q^{79} + 30 q^{80} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} - 24 q^{89} - 39 q^{92} + 6 q^{97}+O(q^{100}) \) 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Introduction

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