LMFDB - Embedded newform 756.2.be.e.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	756.107
Dual form			756.2.be.e.431.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32269 + 0.500480i) q^{2} +(1.49904 - 1.32396i) q^{4} +(2.34508 + 1.35394i) q^{5} +(1.75134 + 1.98313i) q^{7} +(-1.32015 + 2.50144i) q^{8} +O(q^{10})$	\(q+(-1.32269 + 0.500480i) q^{2} +(1.49904 - 1.32396i) q^{4} +(2.34508 + 1.35394i) q^{5} +(1.75134 + 1.98313i) q^{7} +(-1.32015 + 2.50144i) q^{8} +(-3.77945 - 0.617175i) q^{10} +(2.60820 + 4.51754i) q^{11} +3.52108 q^{13} +(-3.30901 - 1.74656i) q^{14} +(0.494241 - 3.96935i) q^{16} +(-3.14229 + 1.81420i) q^{17} +(-4.01162 - 2.31611i) q^{19} +(5.30794 - 1.07520i) q^{20} +(-5.71079 - 4.66997i) q^{22} +(-2.93134 + 5.07724i) q^{23} +(1.16628 + 2.02006i) q^{25} +(-4.65732 + 1.76223i) q^{26} +(5.25092 + 0.654072i) q^{28} -7.09346i q^{29} +(-4.15625 + 2.39961i) q^{31} +(1.33285 + 5.49759i) q^{32} +(3.24832 - 3.97229i) q^{34} +(1.42202 + 7.02181i) q^{35} +(6.04365 - 10.4679i) q^{37} +(6.46531 + 1.05577i) q^{38} +(-6.48266 + 4.07868i) q^{40} -4.04595i q^{41} +4.45239i q^{43} +(9.89085 + 3.31880i) q^{44} +(1.33622 - 8.18271i) q^{46} +(4.78883 - 8.29450i) q^{47} +(-0.865590 + 6.94628i) q^{49} +(-2.55363 - 2.08822i) q^{50} +(5.27824 - 4.66179i) q^{52} +(-6.75522 + 3.90013i) q^{53} +14.1253i q^{55} +(-7.27271 + 1.76284i) q^{56} +(3.55013 + 9.38247i) q^{58} +(-0.574990 - 0.995912i) q^{59} +(-1.68554 + 2.91944i) q^{61} +(4.29649 - 5.25407i) q^{62} +(-4.51438 - 6.60457i) q^{64} +(8.25724 + 4.76732i) q^{65} +(-2.21965 + 1.28151i) q^{67} +(-2.30848 + 6.87984i) q^{68} +(-5.39518 - 8.57601i) q^{70} -1.99539 q^{71} +(4.87793 + 8.44882i) q^{73} +(-2.75492 + 16.8706i) q^{74} +(-9.08002 + 1.83930i) q^{76} +(-4.39099 + 13.0842i) q^{77} +(6.35219 + 3.66744i) q^{79} +(6.53328 - 8.63929i) q^{80} +(2.02491 + 5.35155i) q^{82} +2.10467 q^{83} -9.82526 q^{85} +(-2.22833 - 5.88915i) q^{86} +(-14.7436 + 0.560407i) q^{88} +(-3.63992 - 2.10151i) q^{89} +(6.16663 + 6.98276i) q^{91} +(2.32787 + 11.4920i) q^{92} +(-2.18293 + 13.3678i) q^{94} +(-6.27173 - 10.8629i) q^{95} +16.0081 q^{97} +(-2.33156 - 9.62101i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) $ 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.32269	+	0.500480i	−0.935286	+	0.353893i
$2$	−1.32269	+	0.500480i	−0.935286	+	0.353893i
$3$		0			0
$3$		0			0
$4$	1.49904	−	1.32396i	0.749520	−	0.661982i
$5$	2.34508	+	1.35394i	1.04875	+	0.605498i	0.922300	−	0.386474i	$-0.126307\pi$
$5$	2.34508	+	1.35394i	1.04875	+	0.605498i	0.126454	+	0.991973i	$0.459641\pi$
$6$		0			0
$7$	1.75134	+	1.98313i	0.661946	+	0.749552i
$7$	1.75134	+	1.98313i	0.661946	+	0.749552i
$8$	−1.32015	+	2.50144i	−0.466745	+	0.884392i
$9$		0			0
$10$	−3.77945	−	0.617175i	−1.19517	−	0.195168i
$11$	2.60820	+	4.51754i	0.786402	+	1.36209i	0.928158	+	0.372187i	$0.121392\pi$
$11$	2.60820	+	4.51754i	0.786402	+	1.36209i	−0.141756	+	0.989902i	$0.545275\pi$
$12$		0			0
$13$	3.52108			0.976573			0.488286	−	0.872683i	$-0.337622\pi$
$13$	3.52108			0.976573			0.488286	+	0.872683i	$0.337622\pi$
$14$	−3.30901	−	1.74656i	−0.884369	−	0.466788i
$15$		0			0
$16$	0.494241	−	3.96935i	0.123560	−	0.992337i
$17$	−3.14229	+	1.81420i	−0.762118	+	0.440009i	−0.830056	−	0.557681i	$-0.811691\pi$
$17$	−3.14229	+	1.81420i	−0.762118	+	0.440009i	0.0679377	+	0.997690i	$0.478358\pi$
$18$		0			0
$19$	−4.01162	−	2.31611i	−0.920329	−	0.531352i	−0.0365889	−	0.999330i	$-0.511649\pi$
$19$	−4.01162	−	2.31611i	−0.920329	−	0.531352i	−0.883740	+	0.467978i	$0.844983\pi$
$20$	5.30794	−	1.07520i	1.18689	−	0.240423i
$21$		0			0
$22$	−5.71079	−	4.66997i	−1.21754	−	0.995640i
$23$	−2.93134	+	5.07724i	−0.611227	+	1.05868i	0.379806	+	0.925066i	$0.375991\pi$
$23$	−2.93134	+	5.07724i	−0.611227	+	1.05868i	−0.991034	+	0.133611i	$0.957343\pi$
$24$		0			0
$25$	1.16628	+	2.02006i	0.233256	+	0.404012i
$26$	−4.65732	+	1.76223i	−0.913375	+	0.345602i
$27$		0			0
$28$	5.25092	+	0.654072i	0.992331	+	0.123608i
$29$		−	7.09346i		−	1.31722i	−0.752484	−	0.658611i	$-0.771144\pi$
$29$		−	7.09346i		−	1.31722i	0.752484	−	0.658611i	$-0.228856\pi$
$30$		0			0
$31$	−4.15625	+	2.39961i	−0.746485	+	0.430983i	−0.824422	−	0.565975i	$-0.808500\pi$
$31$	−4.15625	+	2.39961i	−0.746485	+	0.430983i	0.0779377	+	0.996958i	$0.475166\pi$
$32$	1.33285	+	5.49759i	0.235617	+	0.971846i
$33$		0			0
$34$	3.24832	−	3.97229i	0.557082	−	0.681242i
$35$	1.42202	+	7.02181i	0.240366	+	1.18690i
$36$		0			0
$37$	6.04365	−	10.4679i	0.993569	−	1.72091i	0.398728	−	0.917069i	$-0.369452\pi$
$37$	6.04365	−	10.4679i	0.993569	−	1.72091i	0.594841	−	0.803843i	$-0.297215\pi$
$38$	6.46531	+	1.05577i	1.04881	+	0.171269i
$39$		0			0
$40$	−6.48266	+	4.07868i	−1.02500	+	0.644896i
$41$		−	4.04595i		−	0.631871i	−0.948781	−	0.315935i	$-0.897682\pi$
$41$		−	4.04595i		−	0.631871i	0.948781	−	0.315935i	$-0.102318\pi$
$42$		0			0
$43$			4.45239i			0.678983i	0.940609	+	0.339492i	$0.110255\pi$
$43$			4.45239i			0.678983i	−0.940609	+	0.339492i	$0.889745\pi$
$44$	9.89085	+	3.31880i	1.49110	+	0.500329i
$45$		0			0
$46$	1.33622	−	8.18271i	0.197014	−	1.20647i
$47$	4.78883	−	8.29450i	0.698523	−	1.20988i	−0.270455	−	0.962733i	$-0.587174\pi$
$47$	4.78883	−	8.29450i	0.698523	−	1.20988i	0.968978	−	0.247145i	$-0.0794924\pi$
$48$		0			0
$49$	−0.865590	+	6.94628i	−0.123656	+	0.992325i
$50$	−2.55363	−	2.08822i	−0.361138	−	0.295319i
$51$		0			0
$52$	5.27824	−	4.66179i	0.731961	−	0.646473i
$53$	−6.75522	+	3.90013i	−0.927901	+	0.535724i	−0.886147	−	0.463404i	$-0.846628\pi$
$53$	−6.75522	+	3.90013i	−0.927901	+	0.535724i	−0.0417537	+	0.999128i	$0.513294\pi$
$54$		0			0
$55$			14.1253i			1.90466i
$56$	−7.27271	+	1.76284i	−0.971857	+	0.235570i
$57$		0			0
$58$	3.55013	+	9.38247i	0.466155	+	1.23198i
$59$	−0.574990	−	0.995912i	−0.0748574	−	0.129657i	0.826167	−	0.563425i	$-0.190517\pi$
$59$	−0.574990	−	0.995912i	−0.0748574	−	0.129657i	−0.901024	+	0.433769i	$0.857183\pi$
$60$		0			0
$61$	−1.68554	+	2.91944i	−0.215811	+	0.373795i	−0.953523	−	0.301320i	$-0.902573\pi$
$61$	−1.68554	+	2.91944i	−0.215811	+	0.373795i	0.737712	+	0.675115i	$0.235906\pi$
$62$	4.29649	−	5.25407i	0.545655	−	0.667268i
$63$		0			0
$64$	−4.51438	−	6.60457i	−0.564298	−	0.825571i
$65$	8.25724	+	4.76732i	1.02418	+	0.591313i
$66$		0			0
$67$	−2.21965	+	1.28151i	−0.271173	+	0.156562i	−0.629421	−	0.777065i	$-0.716708\pi$
$67$	−2.21965	+	1.28151i	−0.271173	+	0.156562i	0.358248	+	0.933627i	$0.383374\pi$
$68$	−2.30848	+	6.87984i	−0.279945	+	0.834304i
$69$		0			0
$70$	−5.39518	−	8.57601i	−0.644847	−	1.02503i
$71$	−1.99539			−0.236809			−0.118404	−	0.992965i	$-0.537778\pi$
$71$	−1.99539			−0.236809			−0.118404	+	0.992965i	$0.537778\pi$
$72$		0			0
$73$	4.87793	+	8.44882i	0.570918	+	0.988860i	0.996472	+	0.0839264i	$0.0267461\pi$
$73$	4.87793	+	8.44882i	0.570918	+	0.988860i	−0.425554	+	0.904933i	$0.639921\pi$
$74$	−2.75492	+	16.8706i	−0.320253	+	1.96116i
$75$		0			0
$76$	−9.08002	+	1.83930i	−1.04155	+	0.210982i
$77$	−4.39099	+	13.0842i	−0.500400	+	1.49108i
$78$		0			0
$79$	6.35219	+	3.66744i	0.714677	+	0.412619i	0.812790	−	0.582556i	$-0.197947\pi$
$79$	6.35219	+	3.66744i	0.714677	+	0.412619i	−0.0981134	+	0.995175i	$0.531281\pi$
$80$	6.53328	−	8.63929i	0.730443	−	0.965902i
$81$		0			0
$82$	2.02491	+	5.35155i	0.223614	+	0.590980i
$83$	2.10467			0.231017			0.115509	−	0.993306i	$-0.463150\pi$
$83$	2.10467			0.231017			0.115509	+	0.993306i	$0.463150\pi$
$84$		0			0
$85$	−9.82526			−1.06570
$86$	−2.22833	−	5.88915i	−0.240287	−	0.635044i
$87$		0			0
$88$	−14.7436	+	0.560407i	−1.57167	+	0.0597396i
$89$	−3.63992	−	2.10151i	−0.385830	−	0.222759i	0.294521	−	0.955645i	$-0.404840\pi$
$89$	−3.63992	−	2.10151i	−0.385830	−	0.222759i	−0.680352	+	0.732886i	$0.738173\pi$
$90$		0			0
$91$	6.16663	+	6.98276i	0.646438	+	0.731992i
$92$	2.32787	+	11.4920i	0.242698	+	1.19812i
$93$		0			0
$94$	−2.18293	+	13.3678i	−0.225152	+	1.37878i
$95$	−6.27173	−	10.8629i	−0.643466	−	1.11452i
$96$		0			0
$97$	16.0081			1.62538			0.812689	−	0.582697i	$-0.198003\pi$
$97$	16.0081			1.62538			0.812689	+	0.582697i	$0.198003\pi$
$98$	−2.33156	−	9.62101i	−0.235523	−	0.971869i
$99$		0			0
$100$	4.42279	+	1.48403i	0.442279	+	0.148403i
$101$	−0.266525	+	0.153878i	−0.0265203	+	0.0153115i	−0.513202	−	0.858268i	$-0.671541\pi$
$101$	−0.266525	+	0.153878i	−0.0265203	+	0.0153115i	0.486681	+	0.873580i	$0.338207\pi$
$102$		0			0
$103$	3.31116	+	1.91170i	0.326258	+	0.188365i	0.654178	−	0.756340i	$-0.273015\pi$
$103$	3.31116	+	1.91170i	0.326258	+	0.188365i	−0.327921	+	0.944705i	$0.606348\pi$
$104$	−4.64837	+	8.80777i	−0.455810	+	0.863673i
$105$		0			0
$106$	6.98315	−	8.53953i	0.678264	−	0.829432i
$107$	−0.748999	+	1.29730i	−0.0724085	+	0.125415i	−0.899956	−	0.435980i	$-0.856402\pi$
$107$	−0.748999	+	1.29730i	−0.0724085	+	0.125415i	0.827548	+	0.561395i	$0.189735\pi$
$108$		0			0
$109$	4.58655	+	7.94413i	0.439311	+	0.760910i	0.997636	−	0.0687126i	$-0.0218892\pi$
$109$	4.58655	+	7.94413i	0.439311	+	0.760910i	−0.558325	+	0.829622i	$0.688556\pi$
$110$	−7.06945	−	18.6835i	−0.674045	−	1.78140i
$111$		0			0
$112$	8.73731	−	5.97155i	0.825598	−	0.564258i
$113$		−	11.4442i		−	1.07658i	−0.842760	−	0.538290i	$-0.819071\pi$
$113$		−	11.4442i		−	1.07658i	0.842760	−	0.538290i	$-0.180929\pi$
$114$		0			0
$115$	−13.7485	+	7.93770i	−1.28205	+	0.740194i
$116$	−9.39148	−	10.6334i	−0.871977	−	0.987284i
$117$		0			0
$118$	1.25897	+	1.02952i	0.115898	+	0.0947747i
$119$	−9.10103	−	3.05427i	−0.834290	−	0.279985i
$120$		0			0
$121$	−8.10542	+	14.0390i	−0.736856	+	1.27627i
$122$	0.768331	−	4.70510i	0.0695614	−	0.425979i
$123$		0			0
$124$	−3.05339	+	9.09984i	−0.274202	+	0.817190i
$125$		−	7.22307i		−	0.646051i
$126$		0			0
$127$		−	16.1373i		−	1.43196i	−0.698123	−	0.715978i	$-0.745981\pi$
$127$		−	16.1373i		−	1.43196i	0.698123	−	0.715978i	$-0.254019\pi$
$128$	9.27660	+	6.47647i	0.819944	+	0.572444i
$129$		0			0
$130$	−13.3077	−	2.17312i	−1.16717	−	0.190596i
$131$	5.24244	−	9.08017i	0.458034	−	0.793338i	−0.540823	−	0.841136i	$-0.681887\pi$
$131$	5.24244	−	9.08017i	0.458034	−	0.793338i	0.998857	+	0.0477983i	$0.0152205\pi$
$132$		0			0
$133$	−2.43258	−	12.0119i	−0.210932	−	1.04156i
$134$	2.29454	−	2.80594i	0.198218	−	0.242396i
$135$		0			0
$136$	−0.389806	−	10.2553i	−0.0334256	−	0.879383i
$137$	5.66120	−	3.26849i	0.483669	−	0.279246i	−0.238275	−	0.971198i	$-0.576582\pi$
$137$	5.66120	−	3.26849i	0.483669	−	0.279246i	0.721944	+	0.691951i	$0.243249\pi$
$138$		0			0
$139$		−	11.5623i		−	0.980703i	−0.871525	−	0.490351i	$-0.836868\pi$
$139$		−	11.5623i		−	0.980703i	0.871525	−	0.490351i	$-0.163132\pi$
$140$	11.4283	+	8.64326i	0.965867	+	0.730489i
$141$		0			0
$142$	2.63929	−	0.998651i	0.221484	−	0.0838049i
$143$	9.18369	+	15.9066i	0.767979	+	1.33018i
$144$		0			0
$145$	9.60408	−	16.6348i	0.797576	−	1.38144i
$146$	−10.6805	−	8.73390i	−0.883922	−	0.722823i
$147$		0			0
$148$	−4.79945	−	23.6934i	−0.394513	−	1.94758i
$149$	6.70019	+	3.86836i	0.548901	+	0.316908i	0.748679	−	0.662933i	$-0.230689\pi$
$149$	6.70019	+	3.86836i	0.548901	+	0.316908i	−0.199778	+	0.979841i	$0.564022\pi$
$150$		0			0
$151$	2.01607	−	1.16398i	0.164065	−	0.0947231i	−0.415719	−	0.909493i	$-0.636470\pi$
$151$	2.01607	−	1.16398i	0.164065	−	0.0947231i	0.579784	+	0.814770i	$0.303137\pi$
$152$	11.0896	−	6.97720i	0.899482	−	0.565925i
$153$		0			0
$154$	−0.740412	−	19.5039i	−0.0596641	−	1.57167i
$155$	−12.9957			−1.04384
$156$		0			0
$157$	−2.19648	−	3.80441i	−0.175298	−	0.303625i	0.764966	−	0.644070i	$-0.222756\pi$
$157$	−2.19648	−	3.80441i	−0.175298	−	0.303625i	−0.940264	+	0.340445i	$0.889422\pi$
$158$	−10.2375	−	1.67176i	−0.814450	−	0.132998i
$159$		0			0
$160$	−4.31774	+	14.6969i	−0.341347	+	1.16189i
$161$	−15.2026	+	3.07876i	−1.19813	+	0.242640i
$162$		0			0
$163$	7.32905	+	4.23143i	0.574055	+	0.331431i	0.758767	−	0.651362i	$-0.225802\pi$
$163$	7.32905	+	4.23143i	0.574055	+	0.331431i	−0.184712	+	0.982793i	$0.559135\pi$
$164$	−5.35669	−	6.06504i	−0.418287	−	0.473600i
$165$		0			0
$166$	−2.78383	+	1.05334i	−0.216067	+	0.0817553i
$167$	1.93288			0.149571			0.0747853	−	0.997200i	$-0.476173\pi$
$167$	1.93288			0.149571			0.0747853	+	0.997200i	$0.476173\pi$
$168$		0			0
$169$	−0.601975			−0.0463057
$170$	12.9958	−	4.91734i	0.996733	−	0.377143i
$171$		0			0
$172$	5.89480	+	6.67431i	0.449475	+	0.508912i
$173$	17.8599	+	10.3114i	1.35787	+	0.783964i	0.989336	−	0.145652i	$-0.0465279\pi$
$173$	17.8599	+	10.3114i	1.35787	+	0.783964i	0.368530	+	0.929616i	$0.379861\pi$
$174$		0			0
$175$	−1.96347	+	5.85070i	−0.148425	+	0.442272i
$176$	19.2208	−	8.12010i	1.44882	−	0.612076i
$177$		0			0
$178$	5.86626	+	0.957946i	0.439695	+	0.0718011i
$179$	−0.944455	−	1.63584i	−0.0705919	−	0.122269i	0.828569	−	0.559887i	$-0.189155\pi$
$179$	−0.944455	−	1.63584i	−0.0705919	−	0.122269i	−0.899161	+	0.437618i	$0.855822\pi$
$180$		0			0
$181$	0.887214			0.0659461			0.0329731	−	0.999456i	$-0.489502\pi$
$181$	0.887214			0.0659461			0.0329731	+	0.999456i	$0.489502\pi$
$182$	−11.6513	−	6.14978i	−0.863651	−	0.455852i
$183$		0			0
$184$	−8.83057	−	14.0353i	−0.650998	−	1.03470i
$185$	28.3457	−	16.3654i	2.08402	−	1.20321i
$186$		0			0
$187$	−16.3915	−	9.46361i	−1.19866	−	0.692048i
$188$	−3.80297	−	18.7740i	−0.277360	−	1.36924i
$189$		0			0
$190$	13.7323	+	11.2295i	0.996243	+	0.814673i
$191$	9.23347	−	15.9928i	0.668111	−	1.15720i	−0.310321	−	0.950632i	$-0.600437\pi$
$191$	9.23347	−	15.9928i	0.668111	−	1.15720i	0.978432	−	0.206570i	$-0.0662301\pi$
$192$		0			0
$193$	7.38495	+	12.7911i	0.531581	+	0.920725i	0.999320	+	0.0368584i	$0.0117351\pi$
$193$	7.38495	+	12.7911i	0.531581	+	0.920725i	−0.467740	+	0.883866i	$0.654932\pi$
$194$	−21.1738	+	8.01174i	−1.52019	+	0.575209i
$195$		0			0
$196$	7.89906	+	11.5588i	0.564219	+	0.825625i
$197$			12.2606i			0.873535i	0.899574	+	0.436768i	$0.143877\pi$
$197$			12.2606i			0.873535i	−0.899574	+	0.436768i	$0.856123\pi$
$198$		0			0
$199$	−9.82741	+	5.67386i	−0.696647	+	0.402209i	−0.806097	−	0.591783i	$-0.798424\pi$
$199$	−9.82741	+	5.67386i	−0.696647	+	0.402209i	0.109450	+	0.993992i	$0.465091\pi$
$200$	−6.59272	+	0.250592i	−0.466176	+	0.0177195i
$201$		0			0
$202$	0.275518	−	0.336925i	0.0193854	−	0.0237059i
$203$	14.0672	−	12.4231i	0.987326	−	0.871929i
$204$		0			0
$205$	5.47795	−	9.48809i	0.382597	−	0.662677i
$206$	−5.33641	−	0.871423i	−0.371805	−	0.0607150i
$207$		0			0
$208$	1.74026	−	13.9764i	0.120666	−	0.969089i
$209$		−	24.1635i		−	1.67143i
$210$		0			0
$211$			21.5334i			1.48242i	0.671274	+	0.741209i	$0.265747\pi$
$211$			21.5334i			1.48242i	−0.671274	+	0.741209i	$0.734253\pi$
$212$	−4.96272	+	14.7901i	−0.340841	+	1.01579i
$213$		0			0
$214$	0.341422	−	2.09080i	0.0233391	−	0.142924i
$215$	−6.02825	+	10.4412i	−0.411123	+	0.712086i
$216$		0			0
$217$	−12.0378	−	4.03983i	−0.817176	−	0.274241i
$218$	−10.0425	−	8.21218i	−0.680162	−	0.556199i
$219$		0			0
$220$	18.7014	+	21.1744i	1.26085	+	1.42758i
$221$	−11.0643	+	6.38796i	−0.744264	+	0.429701i
$222$		0			0
$223$		−	20.8337i		−	1.39513i	−0.716524	−	0.697563i	$-0.754268\pi$
$223$		−	20.8337i		−	1.39513i	0.716524	−	0.697563i	$-0.245732\pi$
$224$	−8.56815	+	12.2714i	−0.572484	+	0.819916i
$225$		0			0
$226$	5.72759	+	15.1372i	0.380994	+	1.00691i
$227$	−10.2594	−	17.7698i	−0.680939	−	1.17942i	−0.974695	−	0.223540i	$-0.928239\pi$
$227$	−10.2594	−	17.7698i	−0.680939	−	1.17942i	0.293756	−	0.955881i	$-0.405095\pi$
$228$		0			0
$229$	9.04155	−	15.6604i	0.597483	−	1.03487i	−0.395709	−	0.918376i	$-0.629501\pi$
$229$	9.04155	−	15.6604i	0.597483	−	1.03487i	0.993191	−	0.116494i	$-0.0371656\pi$
$230$	14.2124	−	17.3800i	0.937138	−	1.14600i
$231$		0			0
$232$	17.7438	+	9.36446i	1.16494	+	0.614807i
$233$	5.81169	+	3.35538i	0.380737	+	0.219818i	0.678139	−	0.734934i	$-0.262787\pi$
$233$	5.81169	+	3.35538i	0.380737	+	0.219818i	−0.297402	+	0.954752i	$0.596120\pi$
$234$		0			0
$235$	22.4604	−	12.9675i	1.46516	−	0.845909i
$236$	−2.18048	−	0.731646i	−0.141937	−	0.0476261i
$237$		0			0
$238$	13.5665	−	0.515013i	0.879385	−	0.0333834i
$239$	−6.71775			−0.434535			−0.217268	−	0.976112i	$-0.569714\pi$
$239$	−6.71775			−0.434535			−0.217268	+	0.976112i	$0.569714\pi$
$240$		0			0
$241$	−12.6618	−	21.9308i	−0.815616	−	1.41269i	−0.908885	−	0.417048i	$-0.863065\pi$
$241$	−12.6618	−	21.9308i	−0.815616	−	1.41269i	0.0932685	−	0.995641i	$-0.470268\pi$
$242$	3.69476	−	22.6259i	0.237508	−	1.45445i
$243$		0			0
$244$	1.33854	+	6.60794i	0.0856912	+	0.423030i
$245$	−11.4347	+	15.1177i	−0.730536	+	0.965831i
$246$		0			0
$247$	−14.1252	−	8.15522i	−0.898768	−	0.518904i
$248$	−0.515589	−	13.5645i	−0.0327400	−	0.861344i
$249$		0			0
$250$	3.61500	+	9.55392i	0.228633	+	0.604243i
$251$	1.84731			0.116601			0.0583007	−	0.998299i	$-0.481432\pi$
$251$	1.84731			0.116601			0.0583007	+	0.998299i	$0.481432\pi$
$252$		0			0
$253$	−30.5821			−1.92268
$254$	8.07640	+	21.3447i	0.506759	+	1.33929i
$255$		0			0
$256$	−15.5115	−	3.92363i	−0.969466	−	0.245227i
$257$	−21.3448	−	12.3235i	−1.33145	−	0.768716i	−0.345932	−	0.938260i	$-0.612437\pi$
$257$	−21.3448	−	12.3235i	−1.33145	−	0.768716i	−0.985523	+	0.169544i	$0.945771\pi$
$258$		0			0
$259$	31.3437	−	6.34757i	1.94760	−	0.394419i
$260$	18.6897	−	3.78588i	1.15909	−	0.234790i
$261$		0			0
$262$	−2.38970	+	14.6340i	−0.147636	+	0.904093i
$263$	−4.79770	−	8.30986i	−0.295839	−	0.512408i	0.679341	−	0.733823i	$-0.262266\pi$
$263$	−4.79770	−	8.30986i	−0.295839	−	0.512408i	−0.975180	+	0.221415i	$0.928933\pi$
$264$		0			0
$265$	−21.1221			−1.29752
$266$	9.22926	+	14.6706i	0.565882	+	0.899510i
$267$		0			0
$268$	−1.63066	+	4.85977i	−0.0996085	+	0.296858i
$269$	−24.6346	+	14.2228i	−1.50200	+	0.867180i	−0.502002	+	0.864866i	$0.667403\pi$
$269$	−24.6346	+	14.2228i	−1.50200	+	0.867180i	−0.999997	+	0.00231318i	$0.999264\pi$
$270$		0			0
$271$	−22.7905	−	13.1581i	−1.38443	−	0.799298i	−0.391745	−	0.920074i	$-0.628129\pi$
$271$	−22.7905	−	13.1581i	−1.38443	−	0.799298i	−0.992680	+	0.120776i	$0.961462\pi$
$272$	5.64816	+	13.3695i	0.342470	+	0.810646i
$273$		0			0
$274$	−5.85222	+	7.15653i	−0.353545	+	0.432342i
$275$	−6.08379	+	10.5374i	−0.366867	+	0.635431i
$276$		0			0
$277$	15.1856	+	26.3022i	0.912414	+	1.58035i	0.810644	+	0.585539i	$0.199117\pi$
$277$	15.1856	+	26.3022i	0.912414	+	1.58035i	0.101770	+	0.994808i	$0.467549\pi$
$278$	5.78670	+	15.2934i	0.347063	+	0.917237i
$279$		0			0
$280$	−19.4419	−	5.71277i	−1.16188	−	0.341403i
$281$		−	0.205690i		−	0.0122704i	−0.999981	−	0.00613521i	$-0.998047\pi$
$281$		−	0.205690i		−	0.0122704i	0.999981	−	0.00613521i	$-0.00195291\pi$
$282$		0			0
$283$	16.2180	−	9.36346i	0.964059	−	0.556600i	0.0666391	−	0.997777i	$-0.478772\pi$
$283$	16.2180	−	9.36346i	0.964059	−	0.556600i	0.897420	+	0.441177i	$0.145439\pi$
$284$	−2.99116	+	2.64182i	−0.177493	+	0.156763i
$285$		0			0
$286$	−20.1082	−	16.4433i	−1.18902	−	0.972315i
$287$	8.02363	−	7.08584i	0.473620	−	0.418264i
$288$		0			0
$289$	−1.91733	+	3.32091i	−0.112784	+	0.195348i
$290$	−4.37790	+	26.8093i	−0.257079	+	1.57430i
$291$		0			0
$292$	18.4981	+	6.20692i	1.08252	+	0.363232i
$293$			3.33599i			0.194891i	0.995241	+	0.0974453i	$0.0310671\pi$
$293$			3.33599i			0.194891i	−0.995241	+	0.0974453i	$0.968933\pi$
$294$		0			0
$295$		−	3.11400i		−	0.181304i
$296$	18.2063	+	28.9371i	1.05822	+	1.68193i
$297$		0			0
$298$	−10.7983	−	1.76334i	−0.625531	−	0.102148i
$299$	−10.3215	+	17.8774i	−0.596908	+	1.03388i
$300$		0			0
$301$	−8.82966	+	7.79767i	−0.508933	+	0.449450i
$302$	−2.08409	+	2.54859i	−0.119926	+	0.146655i
$303$		0			0
$304$	−11.1762	+	14.7788i	−0.640996	+	0.847622i
$305$	−7.90545	+	4.56422i	−0.452665	+	0.261346i
$306$		0			0
$307$			1.16179i			0.0663067i	0.999450	+	0.0331534i	$0.0105550\pi$
$307$			1.16179i			0.0663067i	−0.999450	+	0.0331534i	$0.989445\pi$
$308$	10.7407	+	25.4272i	0.612006	+	1.44885i
$309$		0			0
$310$	17.1893	−	6.50407i	0.976287	−	0.369407i
$311$	4.20003	+	7.27467i	0.238162	+	0.412509i	0.960187	−	0.279358i	$-0.0901217\pi$
$311$	4.20003	+	7.27467i	0.238162	+	0.412509i	−0.722025	+	0.691867i	$0.756788\pi$
$312$		0			0
$313$	−1.91923	+	3.32421i	−0.108482	+	0.187895i	−0.915155	−	0.403101i	$-0.867932\pi$
$313$	−1.91923	+	3.32421i	−0.108482	+	0.187895i	0.806674	+	0.590997i	$0.201265\pi$
$314$	4.80930	+	3.93278i	0.271405	+	0.221940i
$315$		0			0
$316$	14.3777	−	2.91243i	0.808811	−	0.163837i
$317$	13.5185	+	7.80493i	0.759277	+	0.438369i	0.829036	−	0.559195i	$-0.188890\pi$
$317$	13.5185	+	7.80493i	0.759277	+	0.438369i	−0.0697593	+	0.997564i	$0.522223\pi$
$318$		0			0
$319$	32.0449	−	18.5012i	1.79417	−	1.03587i
$320$	−1.64446	−	21.6005i	−0.0919279	−	1.20750i
$321$		0			0
$322$	18.5675	−	11.6808i	1.03473	−	0.650948i
$323$	16.8076			0.935199
$324$		0			0
$325$	4.10657	+	7.11280i	0.227792	+	0.394547i
$326$	−11.8118	−	1.92884i	−0.654197	−	0.106829i
$327$		0			0
$328$	10.1207	+	5.34127i	0.558821	+	0.294923i
$329$	24.8360	−	5.02966i	1.36925	−	0.277294i
$330$		0			0
$331$	−8.78658	−	5.07293i	−0.482954	−	0.278834i	0.238693	−	0.971095i	$-0.423281\pi$
$331$	−8.78658	−	5.07293i	−0.482954	−	0.278834i	−0.721647	+	0.692261i	$0.756614\pi$
$332$	3.15498	−	2.78650i	0.173152	−	0.152929i
$333$		0			0
$334$	−2.55661	+	0.967366i	−0.139891	+	0.0529319i
$335$	−6.94035			−0.379192
$336$		0			0
$337$	10.8597			0.591563			0.295782	−	0.955256i	$-0.404420\pi$
$337$	10.8597			0.591563			0.295782	+	0.955256i	$0.404420\pi$
$338$	0.796228	−	0.301276i	0.0433091	−	0.0163873i
$339$		0			0
$340$	−14.7285	+	13.0083i	−0.798762	+	0.705473i
$341$	−21.6807	−	12.5173i	−1.17407	−	0.677852i
$342$		0			0
$343$	−15.2913	+	10.4487i	−0.825652	+	0.564179i
$344$	−11.1374	−	5.87784i	−0.600487	−	0.316912i
$345$		0			0
$346$	−28.7839	−	4.70034i	−1.54743	−	0.252692i
$347$	2.45703	+	4.25570i	0.131900	+	0.228458i	0.924409	−	0.381403i	$-0.124559\pi$
$347$	2.45703	+	4.25570i	0.131900	+	0.228458i	−0.792509	+	0.609860i	$0.791226\pi$
$348$		0			0
$349$	−12.2318			−0.654753			−0.327377	−	0.944894i	$-0.606165\pi$
$349$	−12.2318			−0.654753			−0.327377	+	0.944894i	$0.606165\pi$
$350$	−0.331082	−	8.72137i	−0.0176971	−	0.466177i
$351$		0			0
$352$	−21.3592	+	20.3600i	−1.13845	+	1.08519i
$353$	10.0718	−	5.81493i	0.536065	−	0.309498i	−0.207417	−	0.978253i	$-0.566506\pi$
$353$	10.0718	−	5.81493i	0.536065	−	0.309498i	0.743483	+	0.668755i	$0.233172\pi$
$354$		0			0
$355$	−4.67935	−	2.70162i	−0.248354	−	0.143387i
$356$	−8.23870	+	1.66887i	−0.436650	+	0.0884502i
$357$		0			0
$358$	2.06793	+	1.69104i	0.109294	+	0.0893743i
$359$	−10.1939	+	17.6563i	−0.538012	+	0.931865i	0.460999	+	0.887401i	$0.347491\pi$
$359$	−10.1939	+	17.6563i	−0.538012	+	0.931865i	−0.999011	+	0.0444637i	$0.985842\pi$
$360$		0			0
$361$	1.22873	+	2.12823i	0.0646701	+	0.112012i
$362$	−1.17351	+	0.444033i	−0.0616785	+	0.0233379i
$363$		0			0
$364$	18.4889	+	2.30304i	0.969083	+	0.120712i
$365$			26.4176i			1.38276i
$366$		0			0
$367$	6.46373	−	3.73184i	0.337404	−	0.194800i	−0.321719	−	0.946835i	$-0.604261\pi$
$367$	6.46373	−	3.73184i	0.337404	−	0.194800i	0.659123	+	0.752035i	$0.270927\pi$
$368$	18.7045	+	14.1449i	0.975041	+	0.737354i
$369$		0			0
$370$	−29.3022	+	35.8329i	−1.52335	+	1.86286i
$371$	−19.5652	−	6.56600i	−1.01577	−	0.340890i
$372$		0			0
$373$	7.57945	−	13.1280i	0.392449	−	0.679742i	−0.600323	−	0.799758i	$-0.704961\pi$
$373$	7.57945	−	13.1280i	0.392449	−	0.679742i	0.992772	+	0.120016i	$0.0382946\pi$
$374$	26.4172	+	4.31387i	1.36600	+	0.223065i
$375$		0			0
$376$	14.4262	+	22.9290i	0.743974	+	1.18247i
$377$		−	24.9766i		−	1.28636i
$378$		0			0
$379$		−	4.21116i		−	0.216313i	−0.994134	−	0.108156i	$-0.965505\pi$
$379$		−	4.21116i		−	0.216313i	0.994134	−	0.108156i	$-0.0344947\pi$
$380$	−23.7837	−	7.98046i	−1.22008	−	0.409389i
$381$		0			0
$382$	−4.20897	+	25.7748i	−0.215349	+	1.31875i
$383$	−8.24304	+	14.2774i	−0.421200	+	0.729539i	−0.996057	−	0.0887143i	$-0.971724\pi$
$383$	−8.24304	+	14.2774i	−0.421200	+	0.729539i	0.574857	+	0.818254i	$0.305058\pi$
$384$		0			0
$385$	−28.0123	+	24.7383i	−1.42764	+	1.26078i
$386$	−16.1697	−	13.2227i	−0.823018	−	0.673018i
$387$		0			0
$388$	23.9968	−	21.1942i	1.21825	−	1.07597i
$389$	−3.73607	+	2.15702i	−0.189426	+	0.109365i	−0.591714	−	0.806148i	$-0.701549\pi$
$389$	−3.73607	+	2.15702i	−0.189426	+	0.109365i	0.402288	+	0.915513i	$0.368215\pi$
$390$		0			0
$391$		−	21.2722i		−	1.07578i
$392$	−16.2330	−	11.3354i	−0.819889	−	0.572523i
$393$		0			0
$394$	−6.13621	−	16.2171i	−0.309138	−	0.817005i
$395$	9.93095	+	17.2009i	0.499680	+	0.865471i
$396$		0			0
$397$	−5.78541	+	10.0206i	−0.290361	+	0.502921i	−0.973895	−	0.226998i	$-0.927109\pi$
$397$	−5.78541	+	10.0206i	−0.290361	+	0.502921i	0.683534	+	0.729919i	$0.260442\pi$
$398$	10.1590	−	12.4232i	0.509225	−	0.622719i
$399$		0			0
$400$	8.59474	−	3.63098i	0.429737	−	0.181549i
$401$	3.27603	+	1.89142i	0.163597	+	0.0944528i	0.579563	−	0.814927i	$-0.303223\pi$
$401$	3.27603	+	1.89142i	0.163597	+	0.0944528i	−0.415966	+	0.909380i	$0.636557\pi$
$402$		0			0
$403$	−14.6345	+	8.44923i	−0.728996	+	0.420886i
$404$	−0.195803	+	0.583540i	−0.00974155	+	0.0290322i
$405$		0			0
$406$	−12.3891	+	23.4723i	−0.614863	+	1.16491i
$407$	63.0522			3.12538
$408$		0			0
$409$	−15.4801	−	26.8124i	−0.765444	−	1.32579i	−0.940011	−	0.341143i	$-0.889186\pi$
$409$	−15.4801	−	26.8124i	−0.765444	−	1.32579i	0.174567	−	0.984645i	$-0.444147\pi$
$410$	−2.49706	+	15.2914i	−0.123321	+	0.755190i
$411$		0			0
$412$	7.49457	−	1.51814i	0.369231	−	0.0747934i
$413$	0.968016	−	2.88446i	0.0476329	−	0.141935i
$414$		0			0
$415$	4.93562	+	2.84958i	0.242280	+	0.139881i
$416$	4.69307	+	19.3575i	0.230097	+	0.949078i
$417$		0			0
$418$	12.0934	+	31.9609i	0.591505	+	1.56326i
$419$	12.6957			0.620226			0.310113	−	0.950700i	$-0.399633\pi$
$419$	12.6957			0.620226			0.310113	+	0.950700i	$0.399633\pi$
$420$		0			0
$421$	−37.2936			−1.81758			−0.908789	−	0.417256i	$-0.862992\pi$
$421$	−37.2936			−1.81758			−0.908789	+	0.417256i	$0.862992\pi$
$422$	−10.7770	−	28.4821i	−0.524617	−	1.38649i
$423$		0			0
$424$	−0.837995	−	22.0465i	−0.0406967	−	1.07067i
$425$	−7.32960	−	4.23174i	−0.355538	−	0.205270i
$426$		0			0
$427$	−8.74157	+	1.77030i	−0.423034	+	0.0856708i
$428$	0.594804	+	2.93636i	0.0287509	+	0.141934i
$429$		0			0
$430$	2.74790	−	16.8276i	0.132516	−	0.811498i
$431$	8.54169	+	14.7946i	0.411439	+	0.712633i	0.995047	−	0.0994025i	$-0.0316931\pi$
$431$	8.54169	+	14.7946i	0.411439	+	0.712633i	−0.583609	+	0.812035i	$0.698360\pi$
$432$		0			0
$433$	3.73945			0.179706			0.0898532	−	0.995955i	$-0.471360\pi$
$433$	3.73945			0.179706			0.0898532	+	0.995955i	$0.471360\pi$
$434$	17.9441	−	0.681198i	0.861346	−	0.0326986i
$435$		0			0
$436$	17.3932	+	5.83615i	0.832981	+	0.279501i
$437$	23.5189	−	13.5786i	1.12506	−	0.649554i
$438$		0			0
$439$	30.4990	+	17.6086i	1.45564	+	0.840413i	0.998792	−	0.0491324i	$-0.0156456\pi$
$439$	30.4990	+	17.6086i	1.45564	+	0.840413i	0.456846	+	0.889546i	$0.348979\pi$
$440$	−35.3337	−	18.6476i	−1.68447	−	0.888991i
$441$		0			0
$442$	11.4376	−	13.9868i	0.544031	−	0.665283i
$443$	−9.87357	+	17.1015i	−0.469107	+	0.812518i	−0.999376	−	0.0353117i	$-0.988758\pi$
$443$	−9.87357	+	17.1015i	−0.469107	+	0.812518i	0.530269	+	0.847829i	$0.322091\pi$
$444$		0			0
$445$	−5.69061	−	9.85643i	−0.269761	−	0.467239i
$446$	10.4268	+	27.5566i	0.493725	+	1.30484i
$447$		0			0
$448$	5.19146	−	20.5195i	0.245274	−	0.969454i
$449$		−	11.3969i		−	0.537855i	−0.963160	−	0.268927i	$-0.913331\pi$
$449$		−	11.3969i		−	0.537855i	0.963160	−	0.268927i	$-0.0866692\pi$
$450$		0			0
$451$	18.2777	−	10.5526i	0.860664	−	0.496904i
$452$	−15.1517	−	17.1553i	−0.712676	−	0.806918i
$453$		0			0
$454$	22.4634	+	18.3694i	1.05426	+	0.862117i
$455$	5.00706	+	24.7244i	0.234735	+	1.15910i
$456$		0			0
$457$	2.32433	−	4.02586i	0.108728	−	0.188322i	−0.806527	−	0.591197i	$-0.798656\pi$
$457$	2.32433	−	4.02586i	0.108728	−	0.188322i	0.915255	+	0.402875i	$0.131989\pi$
$458$	−4.12148	+	25.2391i	−0.192584	+	1.17934i
$459$		0			0
$460$	−10.1003	+	30.1014i	−0.470930	+	1.40349i
$461$			7.66696i			0.357086i	0.983932	+	0.178543i	$0.0571384\pi$
$461$			7.66696i			0.357086i	−0.983932	+	0.178543i	$0.942862\pi$
$462$		0			0
$463$			17.5007i			0.813329i	0.913578	+	0.406664i	$0.133308\pi$
$463$			17.5007i			0.813329i	−0.913578	+	0.406664i	$0.866692\pi$
$464$	−28.1564	−	3.50588i	−1.30713	−	0.162756i
$465$		0			0
$466$	−9.36639	−	1.52951i	−0.433890	−	0.0708532i
$467$	10.5852	−	18.3342i	0.489827	−	0.848405i	−0.510105	−	0.860112i	$-0.670393\pi$
$467$	10.5852	−	18.3342i	0.489827	−	0.848405i	0.999931	+	0.0117074i	$0.00372667\pi$
$468$		0			0
$469$	−6.42877	−	2.15747i	−0.296853	−	0.0996228i
$470$	−23.2183	+	28.3931i	−1.07098	+	1.30968i
$471$		0			0
$472$	3.25029	−	0.123544i	0.149607	−	0.00568660i
$473$	−20.1138	+	11.6127i	−0.924835	+	0.533954i
$474$		0			0
$475$		−	10.8049i		−	0.495765i
$476$	−17.6866	+	7.47096i	−0.810662	+	0.342431i
$477$		0			0
$478$	8.88553	−	3.36210i	0.406415	−	0.153779i
$479$	0.545751	+	0.945269i	0.0249360	+	0.0431904i	0.878224	−	0.478249i	$-0.158728\pi$
$479$	0.545751	+	0.945269i	0.0249360	+	0.0431904i	−0.853288	+	0.521440i	$0.825395\pi$
$480$		0			0
$481$	21.2802	−	36.8584i	0.970293	−	1.68060i
$482$	27.7236	+	22.6708i	1.26277	+	1.03263i
$483$		0			0
$484$	6.43677	+	31.7763i	0.292581	+	1.44438i
$485$	37.5404	+	21.6740i	1.70462	+	0.984164i
$486$		0			0
$487$	29.4856	−	17.0235i	1.33612	−	0.771409i	0.349891	−	0.936791i	$-0.386219\pi$
$487$	29.4856	−	17.0235i	1.33612	−	0.771409i	0.986230	+	0.165381i	$0.0528854\pi$
$488$	−5.07762	−	8.07037i	−0.229853	−	0.365329i
$489$		0			0
$490$	7.55852	−	25.7189i	0.341459	−	1.16186i
$491$	−22.4308			−1.01229			−0.506143	−	0.862449i	$-0.668929\pi$
$491$	−22.4308			−1.01229			−0.506143	+	0.862449i	$0.668929\pi$
$492$		0			0
$493$	12.8690	+	22.2897i	0.579589	+	1.00388i
$494$	22.7649	+	3.71745i	1.02424	+	0.167256i
$495$		0			0
$496$	7.47071	+	17.6836i	0.335445	+	0.794017i
$497$	−3.49461	−	3.95711i	−0.156755	−	0.177500i
$498$		0			0
$499$	−23.6847	−	13.6743i	−1.06027	−	0.612148i	−0.134764	−	0.990878i	$-0.543028\pi$
$499$	−23.6847	−	13.6743i	−1.06027	−	0.612148i	−0.925507	+	0.378730i	$0.876361\pi$
$500$	−9.56309	−	10.8277i	−0.427674	−	0.484228i
$501$		0			0
$502$	−2.44343	+	0.924544i	−0.109056	+	0.0412644i
$503$	−18.0714			−0.805766			−0.402883	−	0.915252i	$-0.631992\pi$
$503$	−18.0714			−0.805766			−0.402883	+	0.915252i	$0.631992\pi$
$504$		0			0
$505$	−0.833366			−0.0370843
$506$	40.4508	−	15.3057i	1.79826	−	0.680423i
$507$		0			0
$508$	−21.3652	−	24.1905i	−0.947929	−	1.07328i
$509$	−21.1118	−	12.1889i	−0.935763	−	0.540263i	−0.0471333	−	0.998889i	$-0.515009\pi$
$509$	−21.1118	−	12.1889i	−0.935763	−	0.540263i	−0.888630	+	0.458626i	$0.848342\pi$
$510$		0			0
$511$	−8.21216	+	24.4703i	−0.363284	+	1.08250i
$512$	22.4806	−	2.57340i	0.993512	−	0.113729i
$513$		0			0
$514$	34.4003	+	5.61749i	1.51733	+	0.247777i
$515$	5.17663	+	8.96618i	0.228109	+	0.395097i
$516$		0			0
$517$	49.9610			2.19728
$518$	−38.2813	+	24.0828i	−1.68198	+	1.05814i
$519$		0			0
$520$	−22.8260	+	14.3614i	−1.00099	+	0.629788i
$521$	20.9445	−	12.0923i	0.917594	−	0.529773i	0.0347271	−	0.999397i	$-0.488944\pi$
$521$	20.9445	−	12.0923i	0.917594	−	0.529773i	0.882867	+	0.469624i	$0.155610\pi$
$522$		0			0
$523$	−32.2824	−	18.6382i	−1.41161	−	0.814993i	−0.416069	−	0.909333i	$-0.636592\pi$
$523$	−32.2824	−	18.6382i	−1.41161	−	0.814993i	−0.995540	+	0.0943405i	$0.969926\pi$
$524$	−4.16319	−	20.5523i	−0.181870	−	0.897833i
$525$		0			0
$526$	10.5048	+	8.59026i	0.458032	+	0.374553i
$527$	8.70677	−	15.0806i	0.379273	−	0.656920i
$528$		0			0
$529$	−5.68555	−	9.84767i	−0.247198	−	0.428160i
$530$	27.9381	−	10.5712i	1.21355	−	0.459183i
$531$		0			0
$532$	−19.5498	−	14.7856i	−0.847592	−	0.641037i
$533$		−	14.2461i		−	0.617068i
$534$		0			0
$535$	−3.51293	+	2.02819i	−0.151877	+	0.0876864i
$536$	−0.275351	−	7.24410i	−0.0118933	−	0.312898i
$537$		0			0
$538$	25.4658	−	31.1416i	1.09791	−	1.34261i
$539$	−33.6377	+	14.2069i	−1.44888	+	0.611937i
$540$		0			0
$541$	−13.3439	+	23.1123i	−0.573698	+	0.993675i	0.422483	+	0.906371i	$0.361158\pi$
$541$	−13.3439	+	23.1123i	−0.573698	+	0.993675i	−0.996182	+	0.0873039i	$0.972175\pi$
$542$	36.7302	+	5.99796i	1.57770	+	0.257635i
$543$		0			0
$544$	−14.1620	−	14.8570i	−0.607189	−	0.636988i
$545$			24.8395i			1.06401i
$546$		0			0
$547$			22.3708i			0.956508i	0.878222	+	0.478254i	$0.158730\pi$
$547$			22.3708i			0.956508i	−0.878222	+	0.478254i	$0.841270\pi$
$548$	4.15899	−	12.3948i	0.177663	−	0.529481i
$549$		0			0
$550$	2.77322	−	16.9826i	0.118251	−	0.724142i
$551$	−16.4292	+	28.4563i	−0.699909	+	1.21228i
$552$		0			0
$553$	3.85187	+	19.0201i	0.163798	+	0.808819i
$554$	−33.2496	−	27.1897i	−1.41264	−	1.15518i
$555$		0			0
$556$	−15.3081	−	17.3324i	−0.649207	−	0.735056i
$557$	−18.0665	+	10.4307i	−0.765501	+	0.441962i	−0.831267	−	0.555873i	$-0.812384\pi$
$557$	−18.0665	+	10.4307i	−0.765501	+	0.441962i	0.0657663	+	0.997835i	$0.479051\pi$
$558$		0			0
$559$			15.6772i			0.663077i
$560$	28.5748	−	2.17404i	1.20751	−	0.0918699i
$561$		0			0
$562$	0.102943	+	0.272064i	0.00434241	+	0.0114763i
$563$	−19.4534	−	33.6943i	−0.819863	−	1.42005i	−0.905782	−	0.423743i	$-0.860716\pi$
$563$	−19.4534	−	33.6943i	−0.819863	−	1.42005i	0.0859189	−	0.996302i	$-0.472617\pi$
$564$		0			0
$565$	15.4947	−	26.8376i	0.651867	−	1.12907i
$566$	−16.7652	+	20.5018i	−0.704694	+	0.861753i
$567$		0			0
$568$	2.63422	−	4.99134i	0.110529	−	0.209432i
$569$	−7.87778	−	4.54824i	−0.330254	−	0.190672i	0.325700	−	0.945473i	$-0.394400\pi$
$569$	−7.87778	−	4.54824i	−0.330254	−	0.190672i	−0.655954	+	0.754801i	$0.727733\pi$
$570$		0			0
$571$	−19.0441	+	10.9951i	−0.796971	+	0.460131i	−0.842411	−	0.538836i	$-0.818864\pi$
$571$	−19.0441	+	10.9951i	−0.796971	+	0.460131i	0.0454400	+	0.998967i	$0.485531\pi$
$572$	34.8265	+	11.6858i	1.45617	+	0.488607i
$573$		0			0
$574$	−7.06648	+	13.3881i	−0.294949	+	0.558807i
$575$	−13.6751			−0.570291
$576$		0			0
$577$	−20.7080	−	35.8673i	−0.862086	−	1.49318i	−0.869912	−	0.493208i	$-0.835824\pi$
$577$	−20.7080	−	35.8673i	−0.862086	−	1.49318i	0.00782547	−	0.999969i	$-0.497509\pi$
$578$	0.873992	−	5.35214i	0.0363533	−	0.222620i
$579$		0			0
$580$	−7.62691	−	37.6516i	−0.316690	−	1.56340i
$581$	3.68600	+	4.17382i	0.152921	+	0.173159i
$582$		0			0
$583$	−35.2379	−	20.3446i	−1.45941	−	0.842588i
$584$	−27.5738	+	1.04809i	−1.14101	+	0.0433702i
$585$		0			0
$586$	−1.66960	−	4.41250i	−0.0689704	−	0.182279i
$587$	33.7332			1.39232			0.696158	−	0.717888i	$-0.254891\pi$
$587$	33.7332			1.39232			0.696158	+	0.717888i	$0.254891\pi$
$588$		0			0
$589$	22.2311			0.916015
$590$	1.55849	+	4.11887i	0.0641622	+	0.169571i
$591$		0			0
$592$	−38.5637	−	29.1630i	−1.58496	−	1.19859i
$593$	6.56363	+	3.78951i	0.269536	+	0.155617i	0.628677	−	0.777667i	$-0.283597\pi$
$593$	6.56363	+	3.78951i	0.269536	+	0.155617i	−0.359141	+	0.933283i	$0.616930\pi$
$594$		0			0
$595$	−17.2074	−	19.4847i	−0.705435	−	0.798796i
$596$	15.1654	−	3.07199i	0.621200	−	0.125834i
$597$		0			0
$598$	4.70493	−	28.8120i	0.192399	−	1.17821i
$599$	−3.46912	−	6.00870i	−0.141745	−	0.245509i	0.786409	−	0.617706i	$-0.211938\pi$
$599$	−3.46912	−	6.00870i	−0.141745	−	0.245509i	−0.928154	+	0.372197i	$0.878604\pi$
$600$		0			0
$601$	14.2305			0.580475			0.290238	−	0.956955i	$-0.406266\pi$
$601$	14.2305			0.580475			0.290238	+	0.956955i	$0.406266\pi$
$602$	7.77636	−	14.7330i	0.316941	−	0.600472i
$603$		0			0
$604$	1.48110	−	4.41405i	0.0602652	−	0.179605i
$605$	−38.0158	+	21.9484i	−1.54556	+	0.892330i
$606$		0			0
$607$	11.4240	+	6.59565i	0.463686	+	0.267709i	0.713593	−	0.700561i	$-0.247067\pi$
$607$	11.4240	+	6.59565i	0.463686	+	0.267709i	−0.249907	+	0.968270i	$0.580400\pi$
$608$	7.38614	−	25.1413i	0.299548	−	1.01961i
$609$		0			0
$610$	8.17220	−	9.99358i	0.330883	−	0.404628i
$611$	16.8619	−	29.2056i	0.682159	−	1.18153i
$612$		0			0
$613$	20.9433	+	36.2749i	0.845892	+	1.46513i	0.884844	+	0.465888i	$0.154265\pi$
$613$	20.9433	+	36.2749i	0.845892	+	1.46513i	−0.0389516	+	0.999241i	$0.512402\pi$
$614$	−0.581451	−	1.53669i	−0.0234655	−	0.0620158i
$615$		0			0
$616$	−26.9324	−	28.2569i	−1.08514	−	1.13850i
$617$		−	26.7991i		−	1.07889i	−0.842021	−	0.539445i	$-0.818634\pi$
$617$		−	26.7991i		−	1.07889i	0.842021	−	0.539445i	$-0.181366\pi$
$618$		0			0
$619$	6.70031	−	3.86843i	0.269308	−	0.155485i	−0.359265	−	0.933236i	$-0.616973\pi$
$619$	6.70031	−	3.86843i	0.269308	−	0.155485i	0.628573	+	0.777750i	$0.283639\pi$
$620$	−19.4810	+	17.2058i	−0.782377	+	0.691002i
$621$		0			0
$622$	−9.19619	−	7.52013i	−0.368734	−	0.301530i
$623$	−2.20719	−	10.8989i	−0.0884292	−	0.436655i
$624$		0			0
$625$	15.6110	−	27.0390i	0.624439	−	1.08156i
$626$	0.874859	−	5.35745i	0.0349664	−	0.214127i
$627$		0			0
$628$	−8.32952	−	2.79491i	−0.332384	−	0.111529i
$629$			43.8576i			1.74872i
$630$		0			0
$631$			18.0815i			0.719814i	0.932988	+	0.359907i	$0.117192\pi$
$631$			18.0815i			0.719814i	−0.932988	+	0.359907i	$0.882808\pi$
$632$	−17.5597	+	11.0480i	−0.698489	+	0.439467i
$633$		0			0
$634$	−21.7871	−	3.55778i	−0.865276	−	0.141298i
$635$	21.8489	−	37.8434i	0.867047	−	1.50177i
$636$		0			0
$637$	−3.04781	+	24.4584i	−0.120759	+	0.969078i
$638$	−33.1262	+	40.5092i	−1.31148	+	1.60378i
$639$		0			0
$640$	12.9857	+	27.7478i	0.513305	+	1.09683i
$641$	29.2136	−	16.8665i	1.15387	−	0.666185i	0.204040	−	0.978963i	$-0.434593\pi$
$641$	29.2136	−	16.8665i	1.15387	−	0.666185i	0.949826	+	0.312778i	$0.101260\pi$
$642$		0			0
$643$		−	12.8978i		−	0.508639i	−0.967120	−	0.254319i	$-0.918149\pi$
$643$		−	12.8978i		−	0.508639i	0.967120	−	0.254319i	$-0.0818515\pi$
$644$	−18.7131	+	24.7429i	−0.737401	+	0.975006i
$645$		0			0
$646$	−22.2313	+	8.41185i	−0.874678	+	0.330960i
$647$	−21.4352	−	37.1268i	−0.842704	−	1.45961i	−0.887600	−	0.460614i	$-0.847629\pi$
$647$	−21.4352	−	37.1268i	−0.842704	−	1.45961i	0.0448964	−	0.998992i	$-0.485704\pi$
$648$		0			0
$649$	2.99938	−	5.19508i	0.117736	−	0.203925i
$650$	−8.99155	−	7.35280i	−0.352678	−	0.288400i
$651$		0			0
$652$	16.5888	−	3.36031i	0.649667	−	0.131600i
$653$	−32.6041	−	18.8240i	−1.27590	−	0.736639i	−0.299806	−	0.954000i	$-0.596922\pi$
$653$	−32.6041	−	18.8240i	−1.27590	−	0.736639i	−0.976091	+	0.217361i	$0.930255\pi$
$654$		0			0
$655$	24.5879	−	14.1958i	0.960730	−	0.554678i
$656$	−16.0598	−	1.99967i	−0.627029	−	0.0780741i
$657$		0			0
$658$	−30.3331	+	19.0826i	−1.18251	+	0.743917i
$659$	12.7823			0.497927			0.248964	−	0.968513i	$-0.419910\pi$
$659$	12.7823			0.497927			0.248964	+	0.968513i	$0.419910\pi$
$660$		0			0
$661$	3.25771	+	5.64252i	0.126710	+	0.219469i	0.922400	−	0.386236i	$-0.126225\pi$
$661$	3.25771	+	5.64252i	0.126710	+	0.219469i	−0.795690	+	0.605704i	$0.792891\pi$
$662$	14.1609	+	2.31243i	0.550377	+	0.0898753i
$663$		0			0
$664$	−2.77849	+	5.26470i	−0.107826	+	0.204310i
$665$	10.5587	−	31.4624i	0.409447	−	1.22006i
$666$		0			0
$667$	36.0152	+	20.7934i	1.39451	+	0.805122i
$668$	2.89746	−	2.55906i	0.112106	−	0.0990130i
$669$		0			0
$670$	9.17995	−	3.47350i	0.354653	−	0.134193i
$671$	−17.5849			−0.678856
$672$		0			0
$673$	4.32889			0.166866			0.0834331	−	0.996513i	$-0.473411\pi$
$673$	4.32889			0.166866			0.0834331	+	0.996513i	$0.473411\pi$
$674$	−14.3640	+	5.43504i	−0.553281	+	0.209350i
$675$		0			0
$676$	−0.902384	+	0.796992i	−0.0347071	+	0.0306536i
$677$	21.9749	+	12.6872i	0.844565	+	0.487610i	0.858813	−	0.512289i	$-0.171202\pi$
$677$	21.9749	+	12.6872i	0.844565	+	0.487610i	−0.0142486	+	0.999898i	$0.504536\pi$
$678$		0			0
$679$	28.0357	+	31.7461i	1.07591	+	1.21831i
$680$	12.9709	−	24.5773i	0.497410	−	0.942495i
$681$		0			0
$682$	34.9416	+	5.70588i	1.33798	+	0.218489i
$683$	−8.29736	−	14.3714i	−0.317490	−	0.549908i	0.662474	−	0.749085i	$-0.269507\pi$
$683$	−8.29736	−	14.3714i	−0.317490	−	0.549908i	−0.979964	+	0.199177i	$0.936173\pi$
$684$		0			0
$685$	17.7013			0.676333
$686$	14.9963	−	21.4735i	0.572562	−	0.819861i
$687$		0			0
$688$	17.6731	+	2.20056i	0.673780	+	0.0838954i
$689$	−23.7857	+	13.7327i	−0.906162	+	0.523173i
$690$		0			0
$691$	−14.8016	−	8.54571i	−0.563079	−	0.325094i	0.191301	−	0.981531i	$-0.438729\pi$
$691$	−14.8016	−	8.54571i	−0.563079	−	0.325094i	−0.754381	+	0.656437i	$0.772063\pi$
$692$	40.4247	−	8.18864i	1.53672	−	0.311286i
$693$		0			0
$694$	−5.37979	−	4.39929i	−0.204214	−	0.166995i
$695$	15.6546	−	27.1146i	0.593814	−	1.02852i
$696$		0			0
$697$	7.34017	+	12.7135i	0.278029	+	0.481560i
$698$	16.1789	−	6.12177i	0.612382	−	0.231712i
$699$		0			0
$700$	4.80279	+	11.3700i	0.181528	+	0.429746i
$701$			39.1536i			1.47881i	0.673260	+	0.739406i	$0.264894\pi$
$701$			39.1536i			1.47881i	−0.673260	+	0.739406i	$0.735106\pi$
$702$		0			0
$703$	−48.4896	+	27.9955i	−1.82882	+	1.05587i
$704$	18.0620	−	37.6199i	0.680736	−	1.41785i
$705$		0			0
$706$	−10.4116	+	12.7321i	−0.391846	+	0.479178i
$707$	−0.771938	−	0.259060i	−0.0290317	−	0.00974294i
$708$		0			0
$709$	−2.35273	+	4.07505i	−0.0883588	+	0.153042i	−0.906818	−	0.421523i	$-0.861496\pi$
$709$	−2.35273	+	4.07505i	−0.0883588	+	0.153042i	0.818459	+	0.574565i	$0.194829\pi$
$710$	7.54146	+	1.23150i	0.283026	+	0.0462175i
$711$		0			0
$712$	10.0620	−	6.33071i	0.377091	−	0.237254i
$713$		−	28.1364i		−	1.05371i
$714$		0			0
$715$			49.7365i			1.86004i
$716$	−3.58157	−	1.20177i	−0.133850	−	0.0449123i
$717$		0			0
$718$	4.64675	−	28.4557i	0.173415	−	1.06196i
$719$	16.1702	−	28.0077i	0.603048	−	1.04451i	−0.389309	−	0.921107i	$-0.627286\pi$
$719$	16.1702	−	28.0077i	0.603048	−	1.04451i	0.992357	−	0.123402i	$-0.0393806\pi$
$720$		0			0
$721$	2.00783	+	9.91448i	0.0747756	+	0.369235i
$722$	−2.69037	−	2.20004i	−0.100125	−	0.0818769i
$723$		0			0
$724$	1.32997	−	1.17464i	0.0494279	−	0.0436551i
$725$	14.3292	−	8.27297i	0.532173	−	0.307250i
$726$		0			0
$727$		−	20.8055i		−	0.771632i	−0.922576	−	0.385816i	$-0.873920\pi$
$727$		−	20.8055i		−	0.771632i	0.922576	−	0.385816i	$-0.126080\pi$
$728$	−25.6078	+	6.20712i	−0.949089	+	0.230051i
$729$		0			0
$730$	−13.2215	−	34.9424i	−0.489349	−	1.29328i
$731$	−8.07754	−	13.9907i	−0.298759	−	0.517465i
$732$		0			0
$733$	−15.7829	+	27.3369i	−0.582956	+	1.00971i	0.412170	+	0.911107i	$0.364771\pi$
$733$	−15.7829	+	27.3369i	−0.582956	+	1.00971i	−0.995127	+	0.0986034i	$0.968562\pi$
$734$	−6.68183	+	8.17104i	−0.246631	+	0.301599i
$735$		0			0
$736$	−31.8196	−	9.34814i	−1.17289	−	0.344577i
$737$	−11.5786	−	6.68489i	−0.426502	−	0.246241i
$738$		0			0
$739$	43.3475	−	25.0267i	1.59456	−	0.920622i	0.602055	−	0.798454i	$-0.294349\pi$
$739$	43.3475	−	25.0267i	1.59456	−	0.920622i	0.992509	−	0.122168i	$-0.0389846\pi$
$740$	20.8242	−	62.0611i	0.765511	−	2.28141i
$741$		0			0
$742$	29.1649	−	1.10716i	1.07068	−	0.0406452i
$743$	−17.7020			−0.649423			−0.324711	−	0.945813i	$-0.605267\pi$
$743$	−17.7020			−0.649423			−0.324711	+	0.945813i	$0.605267\pi$
$744$		0			0
$745$	10.4750	+	18.1433i	0.383775	+	0.664717i
$746$	−3.45500	+	21.1577i	−0.126497	+	0.774638i
$747$		0			0
$748$	−37.1009	+	7.51536i	−1.35654	+	0.274789i
$749$	−3.88447	+	0.786665i	−0.141936	+	0.0287441i
$750$		0			0
$751$	18.7788	+	10.8420i	0.685249	+	0.395629i	0.801830	−	0.597552i	$-0.203860\pi$
$751$	18.7788	+	10.8420i	0.685249	+	0.395629i	−0.116581	+	0.993181i	$0.537193\pi$
$752$	−30.5569	−	23.1080i	−1.11430	−	0.842663i
$753$		0			0
$754$	12.5003	+	33.0365i	0.455234	+	1.20312i
$755$	6.30380			0.229419
$756$		0			0
$757$	8.03995			0.292217			0.146108	−	0.989269i	$-0.453325\pi$
$757$	8.03995			0.292217			0.146108	+	0.989269i	$0.453325\pi$
$758$	2.10760	+	5.57008i	0.0765515	+	0.202314i
$759$		0			0
$760$	35.4526	−	1.34757i	1.28600	−	0.0488813i
$761$	17.8621	+	10.3127i	0.647502	+	0.373836i	0.787499	−	0.616316i	$-0.211376\pi$
$761$	17.8621	+	10.3127i	0.647502	+	0.373836i	−0.139996	+	0.990152i	$0.544709\pi$
$762$		0			0
$763$	−7.72160	+	23.0086i	−0.279541	+	0.832967i
$764$	−7.33260	−	36.1987i	−0.265284	−	1.30962i
$765$		0			0
$766$	3.75749	−	23.0101i	0.135764	−	0.831387i
$767$	−2.02459	−	3.50669i	−0.0731037	−	0.126619i
$768$		0			0
$769$	10.3179			0.372074			0.186037	−	0.982543i	$-0.440436\pi$
$769$	10.3179			0.372074			0.186037	+	0.982543i	$0.440436\pi$
$770$	24.6707	−	46.7409i	0.889072	−	1.68442i
$771$		0			0
$772$	28.0053	+	9.39698i	1.00793	+	0.338205i
$773$	32.6161	−	18.8309i	1.17312	−	0.677302i	0.218708	−	0.975790i	$-0.429816\pi$
$773$	32.6161	−	18.8309i	1.17312	−	0.677302i	0.954413	+	0.298489i	$0.0964826\pi$
$774$		0			0
$775$	−9.69472	−	5.59725i	−0.348244	−	0.201059i
$776$	−21.1332	+	40.0433i	−0.758637	+	1.43747i
$777$		0			0
$778$	3.86213	−	4.72291i	0.138464	−	0.169324i
$779$	−9.37086	+	16.2308i	−0.335746	+	0.581529i
$780$		0			0
$781$	−5.20437	−	9.01423i	−0.186227	−	0.322555i
$782$	10.6463	+	28.1366i	0.380711	+	1.00616i
$783$		0			0
$784$	27.1444	+	6.86896i	0.969442	+	0.245320i
$785$		−	11.8956i		−	0.424571i
$786$		0			0
$787$	−4.15052	+	2.39631i	−0.147950	+	0.0854191i	−0.572148	−	0.820151i	$-0.693890\pi$
$787$	−4.15052	+	2.39631i	−0.147950	+	0.0854191i	0.424197	+	0.905570i	$0.360556\pi$
$788$	16.2327	+	18.3792i	0.578264	+	0.654732i
$789$		0			0
$790$	−21.7443	−	17.7813i	−0.773628	−	0.632630i
$791$	22.6953	−	20.0427i	0.806952	−	0.712637i
$792$		0			0
$793$	−5.93491	+	10.2796i	−0.210755	+	0.365038i
$794$	2.63721	−	16.1497i	0.0935910	−	0.573132i
$795$		0			0
$796$	−7.21970	+	21.5165i	−0.255896	+	0.762631i
$797$			20.5153i			0.726689i	0.931655	+	0.363345i	$0.118365\pi$
$797$			20.5153i			0.726689i	−0.931655	+	0.363345i	$0.881635\pi$
$798$		0			0
$799$			34.7517i			1.22943i
$800$	−9.55098	+	9.10417i	−0.337678	+	0.321881i
$801$		0			0
$802$	−5.27980	−	0.862179i	−0.186436	−	0.0304446i
$803$	−25.4452	+	44.0724i	−0.897943	+	1.55528i
$804$		0			0
$805$	−39.8198	−	13.3634i	−1.40346	−	0.470998i
$806$	15.1283	−	18.5000i	0.532872	−	0.651636i
$807$		0			0
$808$	−0.0330629	−	0.869840i	−0.00116315	−	0.0306009i
$809$	44.0885	−	25.4545i	1.55007	−	0.894933i	0.551934	−	0.833888i	$-0.313890\pi$
$809$	44.0885	−	25.4545i	1.55007	−	0.894933i	0.998135	−	0.0610447i	$-0.0194432\pi$
$810$		0			0
$811$			53.2904i			1.87128i	0.352959	+	0.935639i	$0.385176\pi$
$811$			53.2904i			1.87128i	−0.352959	+	0.935639i	$0.614824\pi$
$812$	4.63963	−	37.2472i	0.162819	−	1.30712i
$813$		0			0
$814$	−83.3987	+	31.5563i	−2.92312	+	1.10605i
$815$	11.4582	+	19.8461i	0.401362	+	0.695179i
$816$		0			0
$817$	10.3122	−	17.8613i	0.360779	−	0.624888i
$818$	33.8946	+	27.7171i	1.18510	+	0.969106i
$819$		0			0
$820$	−4.35022	−	21.4756i	−0.151916	−	0.749961i
$821$	−18.7916	−	10.8493i	−0.655832	−	0.378645i	0.134855	−	0.990865i	$-0.456943\pi$
$821$	−18.7916	−	10.8493i	−0.655832	−	0.378645i	−0.790687	+	0.612221i	$0.790276\pi$
$822$		0			0
$823$	−17.7199	+	10.2306i	−0.617676	+	0.356616i	−0.775964	−	0.630777i	$-0.782736\pi$
$823$	−17.7199	+	10.2306i	−0.617676	+	0.356616i	0.158287	+	0.987393i	$0.449403\pi$
$824$	−9.15323	+	5.75892i	−0.318868	+	0.200621i
$825$		0			0
$826$	0.163227	+	4.29974i	0.00567941	+	0.149607i
$827$	−44.9844			−1.56426			−0.782131	−	0.623114i	$-0.785867\pi$
$827$	−44.9844			−1.56426			−0.782131	+	0.623114i	$0.785867\pi$
$828$		0			0
$829$	−17.2166	−	29.8200i	−0.597957	−	1.03569i	−0.993122	−	0.117082i	$-0.962646\pi$
$829$	−17.2166	−	29.8200i	−0.597957	−	1.03569i	0.395165	−	0.918610i	$-0.370687\pi$
$830$	−7.95448	−	1.29895i	−0.276104	−	0.0450871i
$831$		0			0
$832$	−15.8955	−	23.2552i	−0.551078	−	0.806230i
$833$	−9.88202	−	23.3976i	−0.342392	−	0.810678i
$834$		0			0
$835$	4.53276	+	2.61699i	0.156863	+	0.0905647i
$836$	−31.9916	−	36.2221i	−1.10645	−	1.25277i
$837$		0			0
$838$	−16.7925	+	6.35394i	−0.580089	+	0.219493i
$839$	−18.4672			−0.637558			−0.318779	−	0.947829i	$-0.603273\pi$
$839$	−18.4672			−0.637558			−0.318779	+	0.947829i	$0.603273\pi$
$840$		0			0
$841$	−21.3171			−0.735073
$842$	49.3280	−	18.6647i	1.69995	−	0.643227i
$843$		0			0
$844$	28.5094	+	32.2794i	0.981334	+	1.11110i
$845$	−1.41168	−	0.815035i	−0.0485633	−	0.0280380i
$846$		0			0
$847$	−42.0365	+	8.51303i	−1.44439	+	0.292511i
$848$	12.1423	+	28.7414i	0.416967	+	0.986984i
$849$		0			0
$850$	11.8127	+	1.92899i	0.405173	+	0.0661638i
$851$	35.4320	+	61.3700i	1.21459	+	2.10374i
$852$		0			0
$853$	19.8472			0.679554			0.339777	−	0.940506i	$-0.389648\pi$
$853$	19.8472			0.679554			0.339777	+	0.940506i	$0.389648\pi$
$854$	10.6764	−	6.71654i	0.365340	−	0.229835i
$855$		0			0
$856$	−2.25633	−	3.58622i	−0.0771198	−	0.122574i
$857$	−22.4524	+	12.9629i	−0.766959	+	0.442804i	−0.831789	−	0.555092i	$-0.812683\pi$
$857$	−22.4524	+	12.9629i	−0.766959	+	0.442804i	0.0648294	+	0.997896i	$0.479350\pi$
$858$		0			0
$859$	−8.68624	−	5.01500i	−0.296371	−	0.171110i	0.344441	−	0.938808i	$-0.388069\pi$
$859$	−8.68624	−	5.01500i	−0.296371	−	0.171110i	−0.640811	+	0.767698i	$0.721402\pi$
$860$	4.78723	+	23.6330i	0.163243	+	0.805879i
$861$		0			0
$862$	−18.7025	−	15.2938i	−0.637008	−	0.520910i
$863$	−11.5277	+	19.9665i	−0.392407	+	0.679668i	−0.992766	−	0.120062i	$-0.961691\pi$
$863$	−11.5277	+	19.9665i	−0.392407	+	0.679668i	0.600360	+	0.799730i	$0.295024\pi$
$864$		0			0
$865$	27.9220	+	48.3624i	0.949378	+	1.64437i
$866$	−4.94615	+	1.87152i	−0.168077	+	0.0635968i
$867$		0			0
$868$	−23.3937	+	9.88169i	−0.794033	+	0.335406i
$869$			38.2616i			1.29794i
$870$		0			0
$871$	−7.81556	+	4.51232i	−0.264820	+	0.152894i
$872$	−25.9267	+	0.985482i	−0.877989	+	0.0333726i
$873$		0			0
$874$	−24.3125	+	29.7311i	−0.822381	+	1.00567i
$875$	14.3243	−	12.6501i	0.484249	−	0.427651i
$876$		0			0
$877$	−18.6586	+	32.3176i	−0.630055	+	1.09129i	0.357485	+	0.933919i	$0.383634\pi$
$877$	−18.6586	+	32.3176i	−0.630055	+	1.09129i	−0.987540	+	0.157368i	$0.949699\pi$
$878$	−49.1536	−	8.02667i	−1.65885	−	0.270887i
$879$		0			0
$880$	56.0684	+	6.98133i	1.89007	+	0.235340i
$881$		−	39.5671i		−	1.33305i	−0.745483	−	0.666524i	$-0.767781\pi$
$881$		−	39.5671i		−	1.33305i	0.745483	−	0.666524i	$-0.232219\pi$
$882$		0			0
$883$			43.8816i			1.47673i	0.674400	+	0.738366i	$0.264402\pi$
$883$			43.8816i			1.47673i	−0.674400	+	0.738366i	$0.735598\pi$
$884$	−8.12836	+	24.2245i	−0.273386	+	0.814758i
$885$		0			0
$886$	4.50074	−	27.5616i	0.151205	−	0.925950i
$887$	17.1379	−	29.6837i	0.575435	−	0.996683i	−0.420559	−	0.907265i	$-0.638166\pi$
$887$	17.1379	−	29.6837i	0.575435	−	0.996683i	0.995994	−	0.0894175i	$-0.0285006\pi$
$888$		0			0
$889$	32.0024	−	28.2620i	1.07332	−	0.947877i
$890$	12.4599	+	10.1890i	0.417656	+	0.341536i
$891$		0			0
$892$	−27.5830	−	31.2305i	−0.923548	−	1.04567i
$893$	−38.4220	+	22.1829i	−1.28574	+	0.742324i
$894$		0			0
$895$		−	5.11492i		−	0.170973i
$896$	3.40286	+	29.7392i	0.113682	+	0.993517i
$897$		0			0
$898$	5.70394	+	15.0747i	0.190343	+	0.503048i
$899$	17.0215	+	29.4822i	0.567700	+	0.983286i
$900$		0			0
$901$	14.1513	−	24.5107i	0.471447	−	0.816569i
$902$	−18.8944	+	23.1055i	−0.629116	+	0.769330i
$903$		0			0
$904$	28.6270	+	15.1081i	0.952118	+	0.502488i
$905$	2.08059	+	1.20123i	0.0691613	+	0.0399303i
$906$		0			0
$907$	−40.3297	+	23.2844i	−1.33913	+	0.773145i	−0.986678	−	0.162686i	$-0.947984\pi$
$907$	−40.3297	+	23.2844i	−1.33913	+	0.773145i	−0.352449	+	0.935831i	$0.614651\pi$
$908$	−38.9057	−	13.0545i	−1.29113	−	0.433230i
$909$		0			0
$910$	−18.9969	−	30.1968i	−0.629740	−	1.00102i
$911$	−14.5617			−0.482450			−0.241225	−	0.970469i	$-0.577549\pi$
$911$	−14.5617			−0.482450			−0.241225	+	0.970469i	$0.577549\pi$
$912$		0			0
$913$	5.48940	+	9.50791i	0.181672	+	0.314666i
$914$	−1.05952	+	6.48826i	−0.0350457	+	0.214613i
$915$		0			0
$916$	−7.18019	−	35.4463i	−0.237240	−	1.17118i
$917$	27.1884	−	5.50607i	0.897842	−	0.181827i
$918$		0			0
$919$	−24.1621	−	13.9500i	−0.797033	−	0.460167i	0.0453999	−	0.998969i	$-0.485544\pi$
$919$	−24.1621	−	13.9500i	−0.797033	−	0.460167i	−0.842433	+	0.538802i	$0.818877\pi$
$920$	−1.70552	−	44.8700i	−0.0562294	−	1.47932i
$921$		0			0
$922$	−3.83716	−	10.1410i	−0.126370	−	0.333978i
$923$	−7.02592			−0.231261
$924$		0			0
$925$	28.1944			0.927025
$926$	−8.75877	−	23.1481i	−0.287831	−	0.760695i
$927$		0			0
$928$	38.9969	−	9.45450i	1.28014	−	0.310359i
$929$	21.2485	+	12.2678i	0.697141	+	0.402494i	0.806282	−	0.591532i	$-0.201477\pi$
$929$	21.2485	+	12.2678i	0.697141	+	0.402494i	−0.109141	+	0.994026i	$0.534810\pi$
$930$		0			0
$931$	19.5608	−	25.8610i	0.641078	−	0.847561i
$932$	13.1544	−	2.66462i	0.430886	−	0.0872824i
$933$		0			0
$934$	−4.82515	+	29.5482i	−0.157884	+	0.966847i
$935$	−25.6262	−	44.3860i	−0.838068	−	1.45158i
$936$		0			0
$937$	−21.2877			−0.695439			−0.347719	−	0.937599i	$-0.613044\pi$
$937$	−21.2877			−0.695439			−0.347719	+	0.937599i	$0.613044\pi$
$938$	9.58307	−	0.363794i	0.312898	−	0.0118783i
$939$		0			0
$940$	16.5005	−	49.1757i	0.538188	−	1.60393i
$941$	12.0167	−	6.93786i	0.391734	−	0.226168i	−0.291177	−	0.956669i	$-0.594047\pi$
$941$	12.0167	−	6.93786i	0.391734	−	0.226168i	0.682911	+	0.730501i	$0.260714\pi$
$942$		0			0
$943$	20.5422	+	11.8601i	0.668947	+	0.386217i
$944$	−4.23731	+	1.79012i	−0.137913	+	0.0582633i
$945$		0			0
$946$	20.7925	−	25.4267i	0.676023	−	0.826692i
$947$	7.71469	−	13.3622i	0.250694	−	0.434214i	−0.713023	−	0.701140i	$-0.752675\pi$
$947$	7.71469	−	13.3622i	0.250694	−	0.434214i	0.963717	+	0.266926i	$0.0860080\pi$
$948$		0			0
$949$	17.1756	+	29.7490i	0.557543	+	0.965693i
$950$	5.40766	+	14.2916i	0.175448	+	0.463682i
$951$		0			0
$952$	19.6548	−	18.7336i	0.637017	−	0.607158i
$953$			5.54532i			0.179630i	0.995958	+	0.0898152i	$0.0286276\pi$
$953$			5.54532i			0.179630i	−0.995958	+	0.0898152i	$0.971372\pi$
$954$		0			0
$955$	43.3066	−	25.0031i	1.40137	−	0.809080i
$956$	−10.0702	+	8.89406i	−0.325693	+	0.287654i
$957$		0			0
$958$	−1.19495	−	0.977164i	−0.0386071	−	0.0315707i
$959$	16.3965	+	5.50262i	0.529472	+	0.177689i
$960$		0			0
$961$	−3.98372	+	6.90001i	−0.128507	+	0.222581i
$962$	−9.70031	+	59.4026i	−0.312750	+	1.91522i
$963$		0			0
$964$	−48.0161	−	16.1115i	−1.54649	−	0.518915i
$965$			39.9950i			1.28748i
$966$		0			0
$967$		−	55.2834i		−	1.77779i	−0.458107	−	0.888897i	$-0.651472\pi$
$967$		−	55.2834i		−	1.77779i	0.458107	−	0.888897i	$-0.348528\pi$
$968$	−24.4173	−	38.8089i	−0.784801	−	1.24736i
$969$		0			0
$970$	−60.5018	−	9.87981i	−1.94260	−	0.317222i
$971$	16.1692	−	28.0059i	0.518894	−	0.898750i	−0.480865	−	0.876795i	$-0.659677\pi$
$971$	16.1692	−	28.0059i	0.518894	−	0.898750i	0.999759	−	0.0219559i	$-0.00698934\pi$
$972$		0			0
$973$	22.9295	−	20.2496i	0.735087	−	0.649172i
$974$	−30.4805	+	37.2739i	−0.976659	+	1.19433i
$975$		0			0
$976$	10.7552	+	8.13339i	0.344265	+	0.260343i
$977$	2.05622	−	1.18716i	0.0657842	−	0.0379805i	−0.466747	−	0.884391i	$-0.654574\pi$
$977$	2.05622	−	1.18716i	0.0657842	−	0.0379805i	0.532531	+	0.846410i	$0.321241\pi$
$978$		0			0
$979$		−	21.9246i		−	0.700714i
$980$	2.87417	+	37.8011i	0.0918118	+	1.20751i
$981$		0			0
$982$	29.6691	−	11.2262i	0.946778	−	0.358241i
$983$	16.8532	+	29.1907i	0.537535	+	0.931038i	0.999036	+	0.0438983i	$0.0139777\pi$
$983$	16.8532	+	29.1907i	0.537535	+	0.931038i	−0.461501	+	0.887140i	$0.652689\pi$
$984$		0			0
$985$	−16.6001	+	28.7523i	−0.528924	+	0.916123i
$986$	−28.1773	−	23.0418i	−0.897347	−	0.733801i
$987$		0			0
$988$	−31.9715	+	6.47632i	−1.01715	+	0.206039i
$989$	−22.6058	−	13.0515i	−0.718824	−	0.415013i
$990$		0			0
$991$	−26.2104	+	15.1326i	−0.832602	+	0.480703i	−0.854743	−	0.519052i	$-0.826285\pi$
$991$	−26.2104	+	15.1326i	−0.832602	+	0.480703i	0.0221406	+	0.999755i	$0.492952\pi$
$992$	−18.7317	−	19.6510i	−0.594733	−	0.623921i
$993$		0			0
$994$	6.60275	+	3.48506i	0.209427	+	0.110539i
$995$	−30.7282			−0.974148
$996$		0			0
$997$	−8.89414	−	15.4051i	−0.281680	−	0.487885i	0.690118	−	0.723697i	$-0.257558\pi$
$997$	−8.89414	−	15.4051i	−0.281680	−	0.487885i	−0.971799	+	0.235812i	$0.924225\pi$
$998$	38.1713	+	6.23328i	1.20829	+	0.197311i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.e.107.4	✓	64
3.2	odd	2	inner	756.2.be.e.107.29	yes	64
4.3	odd	2	inner	756.2.be.e.107.15	yes	64
7.4	even	3	inner	756.2.be.e.431.18	yes	64
12.11	even	2	inner	756.2.be.e.107.18	yes	64
21.11	odd	6	inner	756.2.be.e.431.15	yes	64
28.11	odd	6	inner	756.2.be.e.431.29	yes	64
84.11	even	6	inner	756.2.be.e.431.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.e.107.4	✓	64	1.1	even	1	trivial
756.2.be.e.107.15	yes	64	4.3	odd	2	inner
756.2.be.e.107.18	yes	64	12.11	even	2	inner
756.2.be.e.107.29	yes	64	3.2	odd	2	inner
756.2.be.e.431.4	yes	64	84.11	even	6	inner
756.2.be.e.431.15	yes	64	21.11	odd	6	inner
756.2.be.e.431.18	yes	64	7.4	even	3	inner
756.2.be.e.431.29	yes	64	28.11	odd	6	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32269 + 0.500480i) q^{2} +(1.49904 - 1.32396i) q^{4} +(2.34508 + 1.35394i) q^{5} +(1.75134 + 1.98313i) q^{7} +(-1.32015 + 2.50144i) q^{8} +O(q^{10})\)	\(q+(-1.32269 + 0.500480i) q^{2} +(1.49904 - 1.32396i) q^{4} +(2.34508 + 1.35394i) q^{5} +(1.75134 + 1.98313i) q^{7} +(-1.32015 + 2.50144i) q^{8} +(-3.77945 - 0.617175i) q^{10} +(2.60820 + 4.51754i) q^{11} +3.52108 q^{13} +(-3.30901 - 1.74656i) q^{14} +(0.494241 - 3.96935i) q^{16} +(-3.14229 + 1.81420i) q^{17} +(-4.01162 - 2.31611i) q^{19} +(5.30794 - 1.07520i) q^{20} +(-5.71079 - 4.66997i) q^{22} +(-2.93134 + 5.07724i) q^{23} +(1.16628 + 2.02006i) q^{25} +(-4.65732 + 1.76223i) q^{26} +(5.25092 + 0.654072i) q^{28} -7.09346i q^{29} +(-4.15625 + 2.39961i) q^{31} +(1.33285 + 5.49759i) q^{32} +(3.24832 - 3.97229i) q^{34} +(1.42202 + 7.02181i) q^{35} +(6.04365 - 10.4679i) q^{37} +(6.46531 + 1.05577i) q^{38} +(-6.48266 + 4.07868i) q^{40} -4.04595i q^{41} +4.45239i q^{43} +(9.89085 + 3.31880i) q^{44} +(1.33622 - 8.18271i) q^{46} +(4.78883 - 8.29450i) q^{47} +(-0.865590 + 6.94628i) q^{49} +(-2.55363 - 2.08822i) q^{50} +(5.27824 - 4.66179i) q^{52} +(-6.75522 + 3.90013i) q^{53} +14.1253i q^{55} +(-7.27271 + 1.76284i) q^{56} +(3.55013 + 9.38247i) q^{58} +(-0.574990 - 0.995912i) q^{59} +(-1.68554 + 2.91944i) q^{61} +(4.29649 - 5.25407i) q^{62} +(-4.51438 - 6.60457i) q^{64} +(8.25724 + 4.76732i) q^{65} +(-2.21965 + 1.28151i) q^{67} +(-2.30848 + 6.87984i) q^{68} +(-5.39518 - 8.57601i) q^{70} -1.99539 q^{71} +(4.87793 + 8.44882i) q^{73} +(-2.75492 + 16.8706i) q^{74} +(-9.08002 + 1.83930i) q^{76} +(-4.39099 + 13.0842i) q^{77} +(6.35219 + 3.66744i) q^{79} +(6.53328 - 8.63929i) q^{80} +(2.02491 + 5.35155i) q^{82} +2.10467 q^{83} -9.82526 q^{85} +(-2.22833 - 5.88915i) q^{86} +(-14.7436 + 0.560407i) q^{88} +(-3.63992 - 2.10151i) q^{89} +(6.16663 + 6.98276i) q^{91} +(2.32787 + 11.4920i) q^{92} +(-2.18293 + 13.3678i) q^{94} +(-6.27173 - 10.8629i) q^{95} +16.0081 q^{97} +(-2.33156 - 9.62101i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) \) 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

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