LMFDB - Embedded newform 756.2.be.e.431.15

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			431.15
Character	$\chi$	$=$	756.431
Dual form			756.2.be.e.107.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.227919 + 1.39573i) q^{2} +(-1.89611 - 0.636225i) q^{4} +(2.34508 - 1.35394i) q^{5} +(-1.75134 + 1.98313i) q^{7} +(1.32015 - 2.50144i) q^{8} +O(q^{10})$	\(q+(-0.227919 + 1.39573i) q^{2} +(-1.89611 - 0.636225i) q^{4} +(2.34508 - 1.35394i) q^{5} +(-1.75134 + 1.98313i) q^{7} +(1.32015 - 2.50144i) q^{8} +(1.35523 + 3.58168i) q^{10} +(-2.60820 + 4.51754i) q^{11} +3.52108 q^{13} +(-2.36874 - 2.89639i) q^{14} +(3.19044 + 2.41270i) q^{16} +(-3.14229 - 1.81420i) q^{17} +(4.01162 - 2.31611i) q^{19} +(-5.30794 + 1.07520i) q^{20} +(-5.71079 - 4.66997i) q^{22} +(2.93134 + 5.07724i) q^{23} +(1.16628 - 2.02006i) q^{25} +(-0.802521 + 4.91447i) q^{26} +(4.58245 - 2.64597i) q^{28} +7.09346i q^{29} +(4.15625 + 2.39961i) q^{31} +(-4.09463 + 3.90308i) q^{32} +(3.24832 - 3.97229i) q^{34} +(-1.42202 + 7.02181i) q^{35} +(6.04365 + 10.4679i) q^{37} +(2.31833 + 6.12701i) q^{38} +(-0.290911 - 7.65349i) q^{40} +4.04595i q^{41} +4.45239i q^{43} +(7.81959 - 6.90632i) q^{44} +(-7.75454 + 2.93416i) q^{46} +(-4.78883 - 8.29450i) q^{47} +(-0.865590 - 6.94628i) q^{49} +(2.55363 + 2.08822i) q^{50} +(-6.67635 - 2.24020i) q^{52} +(-6.75522 - 3.90013i) q^{53} +14.1253i q^{55} +(2.64863 + 6.99891i) q^{56} +(-9.90053 - 1.61673i) q^{58} +(0.574990 - 0.995912i) q^{59} +(-1.68554 - 2.91944i) q^{61} +(-4.29649 + 5.25407i) q^{62} +(-4.51438 - 6.60457i) q^{64} +(8.25724 - 4.76732i) q^{65} +(2.21965 + 1.28151i) q^{67} +(4.80388 + 5.43913i) q^{68} +(-9.47642 - 3.58516i) q^{70} +1.99539 q^{71} +(4.87793 - 8.44882i) q^{73} +(-15.9878 + 6.04945i) q^{74} +(-9.08002 + 1.83930i) q^{76} +(-4.39099 - 13.0842i) q^{77} +(-6.35219 + 3.66744i) q^{79} +(10.7485 + 1.33834i) q^{80} +(-5.64704 - 0.922147i) q^{82} -2.10467 q^{83} -9.82526 q^{85} +(-6.21432 - 1.01478i) q^{86} +(7.85711 + 12.4881i) q^{88} +(-3.63992 + 2.10151i) q^{89} +(-6.16663 + 6.98276i) q^{91} +(-2.32787 - 11.4920i) q^{92} +(12.6683 - 4.79343i) q^{94} +(6.27173 - 10.8629i) q^{95} +16.0081 q^{97} +(9.89239 + 0.375061i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.227919	+	1.39573i	−0.161163	+	0.986928i
$2$	−0.227919	+	1.39573i	−0.161163	+	0.986928i
$3$		0			0
$3$		0			0
$4$	−1.89611	−	0.636225i	−0.948053	−	0.318112i
$5$	2.34508	−	1.35394i	1.04875	−	0.605498i	0.126454	−	0.991973i	$-0.459641\pi$
$5$	2.34508	−	1.35394i	1.04875	−	0.605498i	0.922300	+	0.386474i	$0.126307\pi$
$6$		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
$10$	1.35523	+	3.58168i	0.428563	+	1.13263i
$11$	−2.60820	+	4.51754i	−0.786402	+	1.36209i	0.141756	+	0.989902i	$0.454725\pi$
$11$	−2.60820	+	4.51754i	−0.786402	+	1.36209i	−0.928158	+	0.372187i	$0.878608\pi$
$12$		0			0
$13$	3.52108			0.976573			0.488286	−	0.872683i	$-0.337622\pi$
$13$	3.52108			0.976573			0.488286	+	0.872683i	$0.337622\pi$
$14$	−2.36874	−	2.89639i	−0.633072	−	0.774093i
$15$		0			0
$16$	3.19044	+	2.41270i	0.797609	+	0.603175i
$17$	−3.14229	−	1.81420i	−0.762118	−	0.440009i	0.0679377	−	0.997690i	$-0.478358\pi$
$17$	−3.14229	−	1.81420i	−0.762118	−	0.440009i	−0.830056	+	0.557681i	$0.811691\pi$
$18$		0			0
$19$	4.01162	−	2.31611i	0.920329	−	0.531352i	0.0365889	−	0.999330i	$-0.488351\pi$
$19$	4.01162	−	2.31611i	0.920329	−	0.531352i	0.883740	+	0.467978i	$0.155017\pi$
$20$	−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	0.991034	+	0.133611i	$0.0426573\pi$
$23$	2.93134	+	5.07724i	0.611227	+	1.05868i	−0.379806	+	0.925066i	$0.624009\pi$
$24$		0			0
$25$	1.16628	−	2.02006i	0.233256	−	0.404012i
$26$	−0.802521	+	4.91447i	−0.157387	+	0.963807i
$27$		0			0
$28$	4.58245	−	2.64597i	0.866001	−	0.500042i
$29$			7.09346i			1.31722i	0.752484	+	0.658611i	$0.228856\pi$
$29$			7.09346i			1.31722i	−0.752484	+	0.658611i	$0.771144\pi$
$30$		0			0
$31$	4.15625	+	2.39961i	0.746485	+	0.430983i	0.824422	−	0.565975i	$-0.191500\pi$
$31$	4.15625	+	2.39961i	0.746485	+	0.430983i	−0.0779377	+	0.996958i	$0.524834\pi$
$32$	−4.09463	+	3.90308i	−0.723835	+	0.689973i
$33$		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	0.594841	+	0.803843i	$0.297215\pi$
$37$	6.04365	+	10.4679i	0.993569	+	1.72091i	0.398728	+	0.917069i	$0.369452\pi$
$38$	2.31833	+	6.12701i	0.376083	+	0.993932i
$39$		0			0
$40$	−0.290911	−	7.65349i	−0.0459971	−	1.21012i
$41$			4.04595i			0.631871i	0.948781	+	0.315935i	$0.102318\pi$
$41$			4.04595i			0.631871i	−0.948781	+	0.315935i	$0.897682\pi$
$42$		0			0
$43$			4.45239i			0.678983i	0.940609	+	0.339492i	$0.110255\pi$
$43$			4.45239i			0.678983i	−0.940609	+	0.339492i	$0.889745\pi$
$44$	7.81959	−	6.90632i	1.17885	−	1.04117i
$45$		0			0
$46$	−7.75454	+	2.93416i	−1.14335	+	0.432618i
$47$	−4.78883	−	8.29450i	−0.698523	−	1.20988i	−0.968978	−	0.247145i	$-0.920508\pi$
$47$	−4.78883	−	8.29450i	−0.698523	−	1.20988i	0.270455	−	0.962733i	$-0.412826\pi$
$48$		0			0
$49$	−0.865590	−	6.94628i	−0.123656	−	0.992325i
$50$	2.55363	+	2.08822i	0.361138	+	0.295319i
$51$		0			0
$52$	−6.67635	−	2.24020i	−0.925843	−	0.310660i
$53$	−6.75522	−	3.90013i	−0.927901	−	0.535724i	−0.0417537	−	0.999128i	$-0.513294\pi$
$53$	−6.75522	−	3.90013i	−0.927901	−	0.535724i	−0.886147	+	0.463404i	$0.846628\pi$
$54$		0			0
$55$			14.1253i			1.90466i
$56$	2.64863	+	6.99891i	0.353938	+	0.935269i
$57$		0			0
$58$	−9.90053	−	1.61673i	−1.30000	−	0.212287i
$59$	0.574990	−	0.995912i	0.0748574	−	0.129657i	−0.826167	−	0.563425i	$-0.809483\pi$
$59$	0.574990	−	0.995912i	0.0748574	−	0.129657i	0.901024	+	0.433769i	$0.142817\pi$
$60$		0			0
$61$	−1.68554	−	2.91944i	−0.215811	−	0.373795i	0.737712	−	0.675115i	$-0.235906\pi$
$61$	−1.68554	−	2.91944i	−0.215811	−	0.373795i	−0.953523	+	0.301320i	$0.902573\pi$
$62$	−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	$-0.283292\pi$
$67$	2.21965	+	1.28151i	0.271173	+	0.156562i	−0.358248	+	0.933627i	$0.616626\pi$
$68$	4.80388	+	5.43913i	0.582556	+	0.659591i
$69$		0			0
$70$	−9.47642	−	3.58516i	−1.13265	−	0.428508i
$71$	1.99539			0.236809			0.118404	−	0.992965i	$-0.462222\pi$
$71$	1.99539			0.236809			0.118404	+	0.992965i	$0.462222\pi$
$72$		0			0
$73$	4.87793	−	8.44882i	0.570918	−	0.988860i	−0.425554	−	0.904933i	$-0.639921\pi$
$73$	4.87793	−	8.44882i	0.570918	−	0.988860i	0.996472	−	0.0839264i	$-0.0267461\pi$
$74$	−15.9878	+	6.04945i	−1.85854	+	0.703234i
$75$		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	$-0.802053\pi$
$79$	−6.35219	+	3.66744i	−0.714677	+	0.412619i	0.0981134	+	0.995175i	$0.468719\pi$
$80$	10.7485	+	1.33834i	1.20172	+	0.149631i
$81$		0			0
$82$	−5.64704	−	0.922147i	−0.623611	−	0.101834i
$83$	−2.10467			−0.231017			−0.115509	−	0.993306i	$-0.536850\pi$
$83$	−2.10467			−0.231017			−0.115509	+	0.993306i	$0.536850\pi$
$84$		0			0
$85$	−9.82526			−1.06570
$86$	−6.21432	−	1.01478i	−0.670107	−	0.109427i
$87$		0			0
$88$	7.85711	+	12.4881i	0.837571	+	1.33124i
$89$	−3.63992	+	2.10151i	−0.385830	+	0.222759i	−0.680352	−	0.732886i	$-0.738173\pi$
$89$	−3.63992	+	2.10151i	−0.385830	+	0.222759i	0.294521	+	0.955645i	$0.404840\pi$
$90$		0			0
$91$	−6.16663	+	6.98276i	−0.646438	+	0.731992i
$92$	−2.32787	−	11.4920i	−0.242698	−	1.19812i
$93$		0			0
$94$	12.6683	−	4.79343i	1.30664	−	0.494404i
$95$	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	$0.198003\pi$
$98$	9.89239	+	0.375061i	0.999282	+	0.0378868i
$99$		0			0
$100$	−3.49661	+	3.08823i	−0.349661	+	0.308823i
$101$	−0.266525	−	0.153878i	−0.0265203	−	0.0153115i	0.486681	−	0.873580i	$-0.338207\pi$
$101$	−0.266525	−	0.153878i	−0.0265203	−	0.0153115i	−0.513202	+	0.858268i	$0.671541\pi$
$102$		0			0
$103$	−3.31116	+	1.91170i	−0.326258	+	0.188365i	−0.654178	−	0.756340i	$-0.726985\pi$
$103$	−3.31116	+	1.91170i	−0.326258	+	0.188365i	0.327921	+	0.944705i	$0.393652\pi$
$104$	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	$-0.143598\pi$
$107$	0.748999	+	1.29730i	0.0724085	+	0.125415i	−0.827548	+	0.561395i	$0.810265\pi$
$108$		0			0
$109$	4.58655	−	7.94413i	0.439311	−	0.760910i	−0.558325	−	0.829622i	$-0.688556\pi$
$109$	4.58655	−	7.94413i	0.439311	−	0.760910i	0.997636	+	0.0687126i	$0.0218892\pi$
$110$	−19.7151	−	3.21943i	−1.87976	−	0.306961i
$111$		0			0
$112$	−10.3722	+	2.10157i	−0.980085	+	0.198580i
$113$			11.4442i			1.07658i	0.842760	+	0.538290i	$0.180929\pi$
$113$			11.4442i			1.07658i	−0.842760	+	0.538290i	$0.819071\pi$
$114$		0			0
$115$	13.7485	+	7.93770i	1.28205	+	0.740194i
$116$	4.51303	−	13.4499i	0.419025	−	1.24880i
$117$		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
$122$	4.45890	−	1.68715i	0.403690	−	0.152748i
$123$		0			0
$124$	−6.35400	−	7.19423i	−0.570606	−	0.646061i
$125$			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	$-0.254019\pi$
$128$	10.2471	−	4.79554i	0.905723	−	0.423870i
$129$		0			0
$130$	4.77189	+	12.6114i	0.418523	+	1.10609i
$131$	−5.24244	−	9.08017i	−0.458034	−	0.793338i	0.540823	−	0.841136i	$-0.318113\pi$
$131$	−5.24244	−	9.08017i	−0.458034	−	0.793338i	−0.998857	+	0.0477983i	$0.984780\pi$
$132$		0			0
$133$	−2.43258	+	12.0119i	−0.210932	+	1.04156i
$134$	−2.29454	+	2.80594i	−0.198218	+	0.242396i
$135$		0			0
$136$	−8.68643	+	5.46522i	−0.744855	+	0.468639i
$137$	5.66120	+	3.26849i	0.483669	+	0.279246i	0.721944	−	0.691951i	$-0.243249\pi$
$137$	5.66120	+	3.26849i	0.483669	+	0.279246i	−0.238275	+	0.971198i	$0.576582\pi$
$138$		0			0
$139$		−	11.5623i		−	0.980703i	−0.871525	−	0.490351i	$-0.836868\pi$
$139$		−	11.5623i		−	0.980703i	0.871525	−	0.490351i	$-0.163132\pi$
$140$	7.16376	−	12.4094i	0.605448	−	1.04878i
$141$		0			0
$142$	−0.454786	+	2.78501i	−0.0381648	+	0.233713i
$143$	−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	−0.199778	−	0.979841i	$-0.564022\pi$
$149$	6.70019	−	3.86836i	0.548901	−	0.316908i	0.748679	+	0.662933i	$0.230689\pi$
$150$		0			0
$151$	−2.01607	−	1.16398i	−0.164065	−	0.0947231i	0.415719	−	0.909493i	$-0.363530\pi$
$151$	−2.01607	−	1.16398i	−0.164065	−	0.0947231i	−0.579784	+	0.814770i	$0.696863\pi$
$152$	−0.497648	−	13.0924i	−0.0403646	−	1.06194i
$153$		0			0
$154$	19.2627	−	3.14650i	1.55223	−	0.253552i
$155$	12.9957			1.04384
$156$		0			0
$157$	−2.19648	+	3.80441i	−0.175298	+	0.303625i	−0.940264	−	0.340445i	$-0.889422\pi$
$157$	−2.19648	+	3.80441i	−0.175298	+	0.303625i	0.764966	+	0.644070i	$0.222756\pi$
$158$	−3.67096	−	9.70180i	−0.292046	−	0.771833i
$159$		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	$-0.774198\pi$
$163$	−7.32905	+	4.23143i	−0.574055	+	0.331431i	0.184712	+	0.982793i	$0.440865\pi$
$164$	2.57413	−	7.67154i	0.201006	−	0.599047i
$165$		0			0
$166$	0.479693	−	2.93754i	0.0372314	−	0.227997i
$167$	−1.93288			−0.149571			−0.0747853	−	0.997200i	$-0.523827\pi$
$167$	−1.93288			−0.149571			−0.0747853	+	0.997200i	$0.523827\pi$
$168$		0			0
$169$	−0.601975			−0.0463057
$170$	2.23936	−	13.7134i	0.171751	−	1.05177i
$171$		0			0
$172$	2.83272	−	8.44221i	0.215993	−	0.643712i
$173$	17.8599	−	10.3114i	1.35787	−	0.783964i	0.368530	−	0.929616i	$-0.379861\pi$
$173$	17.8599	−	10.3114i	1.35787	−	0.783964i	0.989336	+	0.145652i	$0.0465279\pi$
$174$		0			0
$175$	1.96347	+	5.85070i	0.148425	+	0.442272i
$176$	−19.2208	+	8.12010i	−1.44882	+	0.612076i
$177$		0			0
$178$	−2.10352	−	5.55930i	−0.157666	−	0.416687i
$179$	0.944455	−	1.63584i	0.0705919	−	0.122269i	−0.828569	−	0.559887i	$-0.810845\pi$
$179$	0.944455	−	1.63584i	0.0705919	−	0.122269i	0.899161	+	0.437618i	$0.144178\pi$
$180$		0			0
$181$	0.887214			0.0659461			0.0329731	−	0.999456i	$-0.489502\pi$
$181$	0.887214			0.0659461			0.0329731	+	0.999456i	$0.489502\pi$
$182$	−8.34053	−	10.1984i	−0.618241	−	0.755958i
$183$		0			0
$184$	16.5702	−	0.629839i	1.22157	−	0.0464324i
$185$	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	−0.978432	−	0.206570i	$-0.933770\pi$
$191$	−9.23347	−	15.9928i	−0.668111	−	1.15720i	0.310321	−	0.950632i	$-0.399563\pi$
$192$		0			0
$193$	7.38495	−	12.7911i	0.531581	−	0.920725i	−0.467740	−	0.883866i	$-0.654932\pi$
$193$	7.38495	−	12.7911i	0.531581	−	0.920725i	0.999320	−	0.0368584i	$-0.0117351\pi$
$194$	−3.64855	+	22.3430i	−0.261951	+	1.60413i
$195$		0			0
$196$	−2.77814	+	13.7216i	−0.198439	+	0.980113i
$197$		−	12.2606i		−	0.873535i	−0.899574	−	0.436768i	$-0.856123\pi$
$197$		−	12.2606i		−	0.873535i	0.899574	−	0.436768i	$-0.143877\pi$
$198$		0			0
$199$	9.82741	+	5.67386i	0.696647	+	0.402209i	0.806097	−	0.591783i	$-0.201576\pi$
$199$	9.82741	+	5.67386i	0.696647	+	0.402209i	−0.109450	+	0.993992i	$0.534909\pi$
$200$	−3.51338	−	5.58417i	−0.248434	−	0.394861i
$201$		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
$206$	−1.91353	−	5.05718i	−0.133322	−	0.352350i
$207$		0			0
$208$	11.2338	+	8.49532i	0.778923	+	0.589044i
$209$			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	$0.734253\pi$
$212$	10.3273	+	11.6929i	0.709279	+	0.803071i
$213$		0			0
$214$	−1.98139	+	0.749718i	−0.135445	+	0.0512496i
$215$	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
$220$	8.98689	−	26.7831i	0.605896	−	1.80572i
$221$	−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	$-0.245732\pi$
$224$	−0.569194	−	14.9558i	−0.0380309	−	0.999277i
$225$		0			0
$226$	−15.9730	−	2.60835i	−1.06251	−	0.173505i
$227$	10.2594	−	17.7698i	0.680939	−	1.17942i	−0.293756	−	0.955881i	$-0.594905\pi$
$227$	10.2594	−	17.7698i	0.680939	−	1.17942i	0.974695	−	0.223540i	$-0.0717614\pi$
$228$		0			0
$229$	9.04155	+	15.6604i	0.597483	+	1.03487i	0.993191	+	0.116494i	$0.0371656\pi$
$229$	9.04155	+	15.6604i	0.597483	+	1.03487i	−0.395709	+	0.918376i	$0.629501\pi$
$230$	−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	−0.297402	−	0.954752i	$-0.596120\pi$
$233$	5.81169	−	3.35538i	0.380737	−	0.219818i	0.678139	+	0.734934i	$0.262787\pi$
$234$		0			0
$235$	−22.4604	−	12.9675i	−1.46516	−	0.845909i
$236$	−1.72387	+	1.52253i	−0.112214	+	0.0991084i
$237$		0			0
$238$	2.18863	+	13.3987i	0.141868	+	0.868507i
$239$	6.71775			0.434535			0.217268	−	0.976112i	$-0.430286\pi$
$239$	6.71775			0.434535			0.217268	+	0.976112i	$0.430286\pi$
$240$		0			0
$241$	−12.6618	+	21.9308i	−0.815616	+	1.41269i	0.0932685	+	0.995641i	$0.470268\pi$
$241$	−12.6618	+	21.9308i	−0.815616	+	1.41269i	−0.908885	+	0.417048i	$0.863065\pi$
$242$	21.4420	−	8.11320i	1.37834	−	0.521536i
$243$		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
$248$	11.4894	−	7.22874i	0.729576	−	0.459026i
$249$		0			0
$250$	−10.0814	−	1.64627i	−0.637606	−	0.104120i
$251$	−1.84731			−0.116601			−0.0583007	−	0.998299i	$-0.518568\pi$
$251$	−1.84731			−0.116601			−0.0583007	+	0.998299i	$0.518568\pi$
$252$		0			0
$253$	−30.5821			−1.92268
$254$	22.5233	+	3.67800i	1.41324	+	0.230778i
$255$		0			0
$256$	4.35776	+	15.3951i	0.272360	+	0.962195i
$257$	−21.3448	+	12.3235i	−1.33145	+	0.768716i	−0.985523	−	0.169544i	$-0.945771\pi$
$257$	−21.3448	+	12.3235i	−1.33145	+	0.768716i	−0.345932	+	0.938260i	$0.612437\pi$
$258$		0			0
$259$	−31.3437	−	6.34757i	−1.94760	−	0.394419i
$260$	−18.6897	+	3.78588i	−1.15909	+	0.234790i
$261$		0			0
$262$	13.8683	−	5.24747i	0.856786	−	0.324190i
$263$	4.79770	−	8.30986i	0.295839	−	0.512408i	−0.679341	−	0.733823i	$-0.737734\pi$
$263$	4.79770	−	8.30986i	0.295839	−	0.512408i	0.975180	+	0.221415i	$0.0710675\pi$
$264$		0			0
$265$	−21.1221			−1.29752
$266$	−16.2108	−	6.13295i	−0.993950	−	0.376035i
$267$		0			0
$268$	−3.39335	−	3.84208i	−0.207282	−	0.234692i
$269$	−24.6346	−	14.2228i	−1.50200	−	0.867180i	−0.999997	−	0.00231318i	$-0.999264\pi$
$269$	−24.6346	−	14.2228i	−1.50200	−	0.867180i	−0.502002	−	0.864866i	$-0.667403\pi$
$270$		0			0
$271$	22.7905	−	13.1581i	1.38443	−	0.799298i	0.391745	−	0.920074i	$-0.371871\pi$
$271$	22.7905	−	13.1581i	1.38443	−	0.799298i	0.992680	+	0.120776i	$0.0385382\pi$
$272$	−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	0.101770	−	0.994808i	$-0.467549\pi$
$277$	15.1856	−	26.3022i	0.912414	−	1.58035i	0.810644	−	0.585539i	$-0.199117\pi$
$278$	16.1378	+	2.63527i	0.967883	+	0.158053i
$279$		0			0
$280$	15.6873	+	12.8270i	0.937497	+	0.766558i
$281$			0.205690i			0.0122704i	0.999981	+	0.00613521i	$0.00195291\pi$
$281$			0.205690i			0.0122704i	−0.999981	+	0.00613521i	$0.998047\pi$
$282$		0			0
$283$	−16.2180	−	9.36346i	−0.964059	−	0.556600i	−0.0666391	−	0.997777i	$-0.521228\pi$
$283$	−16.2180	−	9.36346i	−0.964059	−	0.556600i	−0.897420	+	0.441177i	$0.854561\pi$
$284$	−3.78346	−	1.26951i	−0.224507	−	0.0753318i
$285$		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
$290$	−25.4065	+	9.61330i	−1.49192	+	0.564512i
$291$		0			0
$292$	−14.6244	+	12.9164i	−0.855829	+	0.755875i
$293$		−	3.33599i		−	0.194891i	−0.995241	−	0.0974453i	$-0.968933\pi$
$293$		−	3.33599i		−	0.194891i	0.995241	−	0.0974453i	$-0.0310671\pi$
$294$		0			0
$295$		−	3.11400i		−	0.181304i
$296$	34.1634	−	1.29856i	1.98570	−	0.0754772i
$297$		0			0
$298$	3.87207	+	10.2333i	0.224303	+	0.592800i
$299$	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
$304$	18.3869	+	2.28943i	1.05456	+	0.131308i
$305$	−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	$0.989445\pi$
$308$	0.00132643	+	27.6026i	7.55803e−5	+	1.57280i
$309$		0			0
$310$	−2.96196	+	18.1384i	−0.168228	+	1.03019i
$311$	−4.20003	+	7.27467i	−0.238162	+	0.412509i	−0.960187	−	0.279358i	$-0.909878\pi$
$311$	−4.20003	+	7.27467i	−0.238162	+	0.412509i	0.722025	+	0.691867i	$0.243212\pi$
$312$		0			0
$313$	−1.91923	−	3.32421i	−0.108482	−	0.187895i	0.806674	−	0.590997i	$-0.201265\pi$
$313$	−1.91923	−	3.32421i	−0.108482	−	0.187895i	−0.915155	+	0.403101i	$0.867932\pi$
$314$	−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	−0.0697593	−	0.997564i	$-0.522223\pi$
$317$	13.5185	−	7.80493i	0.759277	−	0.438369i	0.829036	+	0.559195i	$0.188890\pi$
$318$		0			0
$319$	−32.0449	−	18.5012i	−1.79417	−	1.03587i
$320$	−19.5288	−	9.37609i	−1.09169	−	0.524139i
$321$		0			0
$322$	7.76206	−	20.5170i	0.432563	−	1.14337i
$323$	−16.8076			−0.935199
$324$		0			0
$325$	4.10657	−	7.11280i	0.227792	−	0.394547i
$326$	−4.23549	−	11.1938i	−0.234582	−	0.619966i
$327$		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	$-0.576719\pi$
$331$	8.78658	−	5.07293i	0.482954	−	0.278834i	0.721647	+	0.692261i	$0.243386\pi$
$332$	3.99067	+	1.33904i	0.219017	+	0.0734895i
$333$		0			0
$334$	0.440539	−	2.69777i	0.0241052	−	0.147615i
$335$	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	$0.404420\pi$
$338$	0.137201	−	0.840192i	0.00746277	−	0.0457004i
$339$		0			0
$340$	18.6297	+	6.25107i	1.01034	+	0.339012i
$341$	−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
$346$	10.3213	+	27.2778i	0.554878	+	1.46646i
$347$	−2.45703	+	4.25570i	−0.131900	+	0.228458i	−0.924409	−	0.381403i	$-0.875441\pi$
$347$	−2.45703	+	4.25570i	−0.131900	+	0.228458i	0.792509	+	0.609860i	$0.208774\pi$
$348$		0			0
$349$	−12.2318			−0.654753			−0.327377	−	0.944894i	$-0.606165\pi$
$349$	−12.2318			−0.654753			−0.327377	+	0.944894i	$0.606165\pi$
$350$	−8.61350	+	1.40699i	−0.460411	+	0.0752067i
$351$		0			0
$352$	−6.95267	−	28.6776i	−0.370579	−	1.52852i
$353$	10.0718	+	5.81493i	0.536065	+	0.309498i	0.743483	−	0.668755i	$-0.233172\pi$
$353$	10.0718	+	5.81493i	0.536065	+	0.309498i	−0.207417	+	0.978253i	$0.566506\pi$
$354$		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	0.999011	+	0.0444637i	$0.0141579\pi$
$359$	10.1939	+	17.6563i	0.538012	+	0.931865i	−0.460999	+	0.887401i	$0.652509\pi$
$360$		0			0
$361$	1.22873	−	2.12823i	0.0646701	−	0.112012i
$362$	−0.202213	+	1.23831i	−0.0106281	+	0.0650841i
$363$		0			0
$364$	16.1352	−	9.31669i	0.845713	−	0.488327i
$365$		−	26.4176i		−	1.38276i
$366$		0			0
$367$	−6.46373	−	3.73184i	−0.337404	−	0.194800i	0.321719	−	0.946835i	$-0.395739\pi$
$367$	−6.46373	−	3.73184i	−0.337404	−	0.194800i	−0.659123	+	0.752035i	$0.729073\pi$
$368$	−2.89758	+	23.2710i	−0.151047	+	1.21309i
$369$		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	0.992772	−	0.120016i	$-0.0382946\pi$
$373$	7.57945	+	13.1280i	0.392449	+	0.679742i	−0.600323	+	0.799758i	$0.704961\pi$
$374$	9.47270	+	25.0349i	0.489821	+	1.29453i
$375$		0			0
$376$	−27.0702	+	1.02895i	−1.39604	+	0.0530638i
$377$			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	$-0.0344947\pi$
$380$	−18.8031	+	16.6071i	−0.964581	+	0.851925i
$381$		0			0
$382$	24.4261	−	9.24233i	1.24975	−	0.472879i
$383$	8.24304	+	14.2774i	0.421200	+	0.729539i	0.996057	−	0.0887143i	$-0.0282758\pi$
$383$	8.24304	+	14.2774i	0.421200	+	0.729539i	−0.574857	+	0.818254i	$0.694942\pi$
$384$		0			0
$385$	−28.0123	−	24.7383i	−1.42764	−	1.26078i
$386$	16.1697	+	13.2227i	0.823018	+	0.673018i
$387$		0			0
$388$	−30.3531	−	10.1848i	−1.54094	−	0.517053i
$389$	−3.73607	−	2.15702i	−0.189426	−	0.109365i	0.402288	−	0.915513i	$-0.368215\pi$
$389$	−3.73607	−	2.15702i	−0.189426	−	0.109365i	−0.591714	+	0.806148i	$0.701549\pi$
$390$		0			0
$391$		−	21.2722i		−	1.07578i
$392$	−18.5184	−	7.00494i	−0.935320	−	0.353803i
$393$		0			0
$394$	17.1125	+	2.79443i	0.862116	+	0.140782i
$395$	−9.93095	+	17.2009i	−0.499680	+	0.865471i
$396$		0			0
$397$	−5.78541	−	10.0206i	−0.290361	−	0.502921i	0.683534	−	0.729919i	$-0.260442\pi$
$397$	−5.78541	−	10.0206i	−0.290361	−	0.502921i	−0.973895	+	0.226998i	$0.927109\pi$
$398$	−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	−0.415966	−	0.909380i	$-0.636557\pi$
$401$	3.27603	−	1.89142i	0.163597	−	0.0944528i	0.579563	+	0.814927i	$0.303223\pi$
$402$		0			0
$403$	14.6345	+	8.44923i	0.728996	+	0.420886i
$404$	0.407459	+	0.461340i	0.0202718	+	0.0229525i
$405$		0			0
$406$	20.5454	−	16.8026i	1.01965	−	0.833897i
$407$	−63.0522			−3.12538
$408$		0			0
$409$	−15.4801	+	26.8124i	−0.765444	+	1.32579i	0.174567	+	0.984645i	$0.444147\pi$
$409$	−15.4801	+	26.8124i	−0.765444	+	1.32579i	−0.940011	+	0.341143i	$0.889186\pi$
$410$	−14.4913	+	5.48321i	−0.715675	+	0.270796i
$411$		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
$416$	−14.4175	+	13.7431i	−0.706878	+	0.673809i
$417$		0			0
$418$	−33.7257	−	5.50732i	−1.64958	−	0.269372i
$419$	−12.6957			−0.620226			−0.310113	−	0.950700i	$-0.600367\pi$
$419$	−12.6957			−0.620226			−0.310113	+	0.950700i	$0.600367\pi$
$420$		0			0
$421$	−37.2936			−1.81758			−0.908789	−	0.417256i	$-0.862992\pi$
$421$	−37.2936			−1.81758			−0.908789	+	0.417256i	$0.862992\pi$
$422$	−30.0547	−	4.90786i	−1.46304	−	0.238911i
$423$		0			0
$424$	−18.6739	+	11.7490i	−0.906883	+	0.570581i
$425$	−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
$430$	−15.9471	+	6.03403i	−0.769036	+	0.290987i
$431$	−8.54169	+	14.7946i	−0.411439	+	0.712633i	−0.995047	−	0.0994025i	$-0.968307\pi$
$431$	−8.54169	+	14.7946i	−0.411439	+	0.712633i	0.583609	+	0.812035i	$0.301640\pi$
$432$		0			0
$433$	3.73945			0.179706			0.0898532	−	0.995955i	$-0.471360\pi$
$433$	3.73945			0.179706			0.0898532	+	0.995955i	$0.471360\pi$
$434$	−2.89486	−	17.7222i	−0.138958	−	0.850692i
$435$		0			0
$436$	−13.7508	+	12.1448i	−0.658545	+	0.581632i
$437$	23.5189	+	13.5786i	1.12506	+	0.649554i
$438$		0			0
$439$	−30.4990	+	17.6086i	−1.45564	+	0.840413i	−0.998792	−	0.0491324i	$-0.984354\pi$
$439$	−30.4990	+	17.6086i	−1.45564	+	0.840413i	−0.456846	+	0.889546i	$0.651021\pi$
$440$	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	$-0.0112424\pi$
$443$	9.87357	+	17.1015i	0.469107	+	0.812518i	−0.530269	+	0.847829i	$0.677909\pi$
$444$		0			0
$445$	−5.69061	+	9.85643i	−0.269761	+	0.467239i
$446$	29.0781	+	4.74839i	1.37689	+	0.224843i
$447$		0			0
$448$	21.0039	+	2.61427i	0.992343	+	0.123513i
$449$			11.3969i			0.537855i	0.963160	+	0.268927i	$0.0866692\pi$
$449$			11.3969i			0.537855i	−0.963160	+	0.268927i	$0.913331\pi$
$450$		0			0
$451$	−18.2777	−	10.5526i	−0.860664	−	0.496904i
$452$	7.28108	−	21.6994i	0.342473	−	1.02065i
$453$		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	0.915255	−	0.402875i	$-0.131989\pi$
$457$	2.32433	+	4.02586i	0.108728	+	0.188322i	−0.806527	+	0.591197i	$0.798656\pi$
$458$	−23.9184	+	9.05023i	−1.11763	+	0.422889i
$459$		0			0
$460$	−21.0185	−	23.7979i	−0.979990	−	1.10958i
$461$		−	7.66696i		−	0.357086i	−0.983932	−	0.178543i	$-0.942862\pi$
$461$		−	7.66696i		−	0.357086i	0.983932	−	0.178543i	$-0.0571384\pi$
$462$		0			0
$463$			17.5007i			0.813329i	0.913578	+	0.406664i	$0.133308\pi$
$463$			17.5007i			0.813329i	−0.913578	+	0.406664i	$0.866692\pi$
$464$	−17.1144	+	22.6312i	−0.794515	+	1.05063i
$465$		0			0
$466$	3.35860	+	8.87629i	0.155584	+	0.411186i
$467$	−10.5852	−	18.3342i	−0.489827	−	0.848405i	0.510105	−	0.860112i	$-0.329607\pi$
$467$	−10.5852	−	18.3342i	−0.489827	−	0.848405i	−0.999931	+	0.0117074i	$0.996273\pi$
$468$		0			0
$469$	−6.42877	+	2.15747i	−0.296853	+	0.0996228i
$470$	23.2183	−	28.3931i	1.07098	−	1.30968i
$471$		0			0
$472$	−1.73214	−	2.75306i	−0.0797281	−	0.126720i
$473$	−20.1138	−	11.6127i	−0.924835	−	0.533954i
$474$		0			0
$475$		−	10.8049i		−	0.495765i
$476$	−19.1997		0.000922633i	−0.880018		4.22888e-5i
$477$		0			0
$478$	−1.53110	+	9.37615i	−0.0700310	+	0.428855i
$479$	−0.545751	+	0.945269i	−0.0249360	+	0.0431904i	−0.878224	−	0.478249i	$-0.841272\pi$
$479$	−0.545751	+	0.945269i	−0.0249360	+	0.0431904i	0.853288	+	0.521440i	$0.174605\pi$
$480$		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	$-0.613781\pi$
$487$	−29.4856	−	17.0235i	−1.33612	−	0.771409i	−0.986230	+	0.165381i	$0.947115\pi$
$488$	−9.52795	+	0.362160i	−0.431310	+	0.0163942i
$489$		0			0
$490$	23.7063	−	12.5141i	1.07094	−	0.565330i
$491$	22.4308			1.01229			0.506143	−	0.862449i	$-0.331071\pi$
$491$	22.4308			1.01229			0.506143	+	0.862449i	$0.331071\pi$
$492$		0			0
$493$	12.8690	−	22.2897i	0.579589	−	1.00388i
$494$	8.16304	+	21.5737i	0.367273	+	0.970647i
$495$		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	$-0.456972\pi$
$499$	23.6847	−	13.6743i	1.06027	−	0.612148i	0.925507	+	0.378730i	$0.123639\pi$
$500$	4.59550	−	13.6957i	0.205517	−	0.612491i
$501$		0			0
$502$	0.421038	−	2.57835i	0.0187918	−	0.115077i
$503$	18.0714			0.805766			0.402883	−	0.915252i	$-0.368008\pi$
$503$	18.0714			0.805766			0.402883	+	0.915252i	$0.368008\pi$
$504$		0			0
$505$	−0.833366			−0.0370843
$506$	6.97024	−	42.6843i	0.309865	−	1.89755i
$507$		0			0
$508$	−10.2670	+	30.5981i	−0.455523	+	1.35757i
$509$	−21.1118	+	12.1889i	−0.935763	+	0.540263i	−0.888630	−	0.458626i	$-0.848342\pi$
$509$	−21.1118	+	12.1889i	−0.935763	+	0.540263i	−0.0471333	+	0.998889i	$0.515009\pi$
$510$		0			0
$511$	8.21216	+	24.4703i	0.363284	+	1.08250i
$512$	−22.4806	+	2.57340i	−0.993512	+	0.113729i
$513$		0			0
$514$	−12.3353	−	32.6003i	−0.544086	−	1.43794i
$515$	−5.17663	+	8.96618i	−0.228109	+	0.395097i
$516$		0			0
$517$	49.9610			2.19728
$518$	16.0033	−	42.3005i	0.703144	−	1.85858i
$519$		0			0
$520$	−1.02432	−	26.9486i	−0.0449195	−	1.18177i
$521$	20.9445	+	12.0923i	0.917594	+	0.529773i	0.882867	−	0.469624i	$-0.155610\pi$
$521$	20.9445	+	12.0923i	0.917594	+	0.529773i	0.0347271	+	0.999397i	$0.488944\pi$
$522$		0			0
$523$	32.2824	−	18.6382i	1.41161	−	0.814993i	0.416069	−	0.909333i	$-0.363408\pi$
$523$	32.2824	−	18.6382i	1.41161	−	0.814993i	0.995540	+	0.0943405i	$0.0300742\pi$
$524$	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
$530$	4.81412	−	29.4807i	0.209112	−	1.28056i
$531$		0			0
$532$	12.2547	−	21.2281i	0.531308	−	0.920354i
$533$			14.2461i			0.617068i
$534$		0			0
$535$	3.51293	+	2.02819i	0.151877	+	0.0876864i
$536$	6.13590	−	3.86051i	0.265031	−	0.166749i
$537$		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	−0.996182	−	0.0873039i	$-0.972175\pi$
$541$	−13.3439	−	23.1123i	−0.573698	−	0.993675i	0.422483	−	0.906371i	$-0.361158\pi$
$542$	13.1707	+	34.8083i	0.565732	+	1.49514i
$543$		0			0
$544$	19.9475	−	4.83612i	0.855242	−	0.207347i
$545$		−	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	$0.841270\pi$
$548$	−8.65473	−	9.79921i	−0.369712	−	0.418601i
$549$		0			0
$550$	−16.0940	+	6.08963i	−0.686250	+	0.259663i
$551$	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
$556$	−7.35623	+	21.9234i	−0.311974	+	0.929758i
$557$	−18.0665	−	10.4307i	−0.765501	−	0.441962i	0.0657663	−	0.997835i	$-0.479051\pi$
$557$	−18.0665	−	10.4307i	−0.765501	−	0.441962i	−0.831267	+	0.555873i	$0.812384\pi$
$558$		0			0
$559$			15.6772i			0.663077i
$560$	−21.4784	+	18.9717i	−0.907628	+	0.801701i
$561$		0			0
$562$	−0.287086	−	0.0468805i	−0.0121100	−	0.00197754i
$563$	19.4534	−	33.6943i	0.819863	−	1.42005i	−0.0859189	−	0.996302i	$-0.527383\pi$
$563$	19.4534	−	33.6943i	0.819863	−	1.42005i	0.905782	−	0.423743i	$-0.139284\pi$
$564$		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	−0.655954	−	0.754801i	$-0.727733\pi$
$569$	−7.87778	+	4.54824i	−0.330254	+	0.190672i	0.325700	+	0.945473i	$0.394400\pi$
$570$		0			0
$571$	19.0441	+	10.9951i	0.796971	+	0.460131i	0.842411	−	0.538836i	$-0.181136\pi$
$571$	19.0441	+	10.9951i	0.796971	+	0.460131i	−0.0454400	+	0.998967i	$0.514469\pi$
$572$	27.5334	−	24.3177i	1.15123	−	1.01678i
$573$		0			0
$574$	11.7186	−	9.58379i	0.489126	−	0.400020i
$575$	13.6751			0.570291
$576$		0			0
$577$	−20.7080	+	35.8673i	−0.862086	+	1.49318i	0.00782547	+	0.999969i	$0.497509\pi$
$577$	−20.7080	+	35.8673i	−0.862086	+	1.49318i	−0.869912	+	0.493208i	$0.835824\pi$
$578$	5.07208	−	1.91917i	0.210971	−	0.0798270i
$579$		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
$584$	−14.6946	−	23.3556i	−0.608066	−	0.966461i
$585$		0			0
$586$	4.65613	+	0.760335i	0.192343	+	0.0314092i
$587$	−33.7332			−1.39232			−0.696158	−	0.717888i	$-0.745109\pi$
$587$	−33.7332			−1.39232			−0.696158	+	0.717888i	$0.745109\pi$
$588$		0			0
$589$	22.2311			0.916015
$590$	4.34629	+	0.709739i	0.178934	+	0.0292195i
$591$		0			0
$592$	−5.97404	+	47.9787i	−0.245531	+	1.97191i
$593$	6.56363	−	3.78951i	0.269536	−	0.155617i	−0.359141	−	0.933283i	$-0.616930\pi$
$593$	6.56363	−	3.78951i	0.269536	−	0.155617i	0.628677	+	0.777667i	$0.283597\pi$
$594$		0			0
$595$	17.2074	−	19.4847i	0.705435	−	0.798796i
$596$	−15.1654	+	3.07199i	−0.621200	+	0.125834i
$597$		0			0
$598$	−27.3044	+	10.3314i	−1.11656	+	0.422483i
$599$	3.46912	−	6.00870i	0.141745	−	0.245509i	−0.786409	−	0.617706i	$-0.788062\pi$
$599$	3.46912	−	6.00870i	0.141745	−	0.245509i	0.928154	+	0.372197i	$0.121396\pi$
$600$		0			0
$601$	14.2305			0.580475			0.290238	−	0.956955i	$-0.406266\pi$
$601$	14.2305			0.580475			0.290238	+	0.956955i	$0.406266\pi$
$602$	12.8959	−	10.5466i	0.525596	−	0.429846i
$603$		0			0
$604$	3.08213	+	3.48970i	0.125410	+	0.141994i
$605$	−38.0158	−	21.9484i	−1.54556	−	0.892330i
$606$		0			0
$607$	−11.4240	+	6.59565i	−0.463686	+	0.267709i	−0.713593	−	0.700561i	$-0.752933\pi$
$607$	−11.4240	+	6.59565i	−0.463686	+	0.267709i	0.249907	+	0.968270i	$0.419600\pi$
$608$	−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	−0.0389516	−	0.999241i	$-0.512402\pi$
$613$	20.9433	−	36.2749i	0.845892	−	1.46513i	0.884844	−	0.465888i	$-0.154265\pi$
$614$	−1.62154	−	0.264793i	−0.0654400	−	0.0106862i
$615$		0			0
$616$	−38.5260	−	6.28930i	−1.55226	−	0.253403i
$617$			26.7991i			1.07889i	0.842021	+	0.539445i	$0.181366\pi$
$617$			26.7991i			1.07889i	−0.842021	+	0.539445i	$0.818634\pi$
$618$		0			0
$619$	−6.70031	−	3.86843i	−0.269308	−	0.155485i	0.359265	−	0.933236i	$-0.383027\pi$
$619$	−6.70031	−	3.86843i	−0.269308	−	0.155485i	−0.628573	+	0.777750i	$0.716361\pi$
$620$	−24.6412	−	8.26817i	−0.989614	−	0.332058i
$621$		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
$626$	5.07712	−	1.92108i	0.202922	−	0.0767816i
$627$		0			0
$628$	6.58522	−	5.81612i	0.262779	−	0.232088i
$629$		−	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	$0.882808\pi$
$632$	0.787999	+	20.7312i	0.0313449	+	0.824642i
$633$		0			0
$634$	7.81242	+	20.6471i	0.310271	+	0.820000i
$635$	−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
$640$	17.5374	−	25.1198i	0.693228	−	0.992949i
$641$	29.2136	+	16.8665i	1.15387	+	0.666185i	0.949826	−	0.312778i	$-0.101260\pi$
$641$	29.2136	+	16.8665i	1.15387	+	0.666185i	0.204040	+	0.978963i	$0.434593\pi$
$642$		0			0
$643$		−	12.8978i		−	0.508639i	−0.967120	−	0.254319i	$-0.918149\pi$
$643$		−	12.8978i		−	0.508639i	0.967120	−	0.254319i	$-0.0818515\pi$
$644$	26.8670	+	15.5099i	1.05871	+	0.611177i
$645$		0			0
$646$	3.83076	−	23.4588i	0.150719	−	0.922974i
$647$	21.4352	−	37.1268i	0.842704	−	1.45961i	−0.0448964	−	0.998992i	$-0.514296\pi$
$647$	21.4352	−	37.1268i	0.842704	−	1.45961i	0.887600	−	0.460614i	$-0.152371\pi$
$648$		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	−0.976091	−	0.217361i	$-0.930255\pi$
$653$	−32.6041	+	18.8240i	−1.27590	+	0.736639i	−0.299806	+	0.954000i	$0.596922\pi$
$654$		0			0
$655$	−24.5879	−	14.1958i	−0.960730	−	0.554678i
$656$	−9.76165	+	12.9083i	−0.381129	+	0.503986i
$657$		0			0
$658$	−12.6806	+	33.5178i	−0.494342	+	1.30666i
$659$	−12.7823			−0.497927			−0.248964	−	0.968513i	$-0.580090\pi$
$659$	−12.7823			−0.497927			−0.248964	+	0.968513i	$0.580090\pi$
$660$		0			0
$661$	3.25771	−	5.64252i	0.126710	−	0.219469i	−0.795690	−	0.605704i	$-0.792891\pi$
$661$	3.25771	−	5.64252i	0.126710	−	0.219469i	0.922400	+	0.386236i	$0.126225\pi$
$662$	5.07780	+	13.4199i	0.197354	+	0.521578i
$663$		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
$668$	3.66494	+	1.22974i	0.141801	+	0.0475803i
$669$		0			0
$670$	−1.58184	+	9.68683i	−0.0611116	+	0.374235i
$671$	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	$0.473411\pi$
$674$	−2.47512	+	15.1571i	−0.0953381	+	0.583830i
$675$		0			0
$676$	1.14141	+	0.382991i	0.0439003	+	0.0147304i
$677$	21.9749	−	12.6872i	0.844565	−	0.487610i	−0.0142486	−	0.999898i	$-0.504536\pi$
$677$	21.9749	−	12.6872i	0.844565	−	0.487610i	0.858813	+	0.512289i	$0.171202\pi$
$678$		0			0
$679$	−28.0357	+	31.7461i	−1.07591	+	1.21831i
$680$	−12.9709	+	24.5773i	−0.497410	+	0.942495i
$681$		0			0
$682$	−12.5294	−	33.1132i	−0.479774	−	1.26797i
$683$	8.29736	−	14.3714i	0.317490	−	0.549908i	−0.662474	−	0.749085i	$-0.730493\pi$
$683$	8.29736	−	14.3714i	0.317490	−	0.549908i	0.979964	+	0.199177i	$0.0638268\pi$
$684$		0			0
$685$	17.7013			0.676333
$686$	−18.0688	+	18.9610i	−0.689869	+	0.723935i
$687$		0			0
$688$	−10.7423	+	14.2051i	−0.409546	+	0.541563i
$689$	−23.7857	−	13.7327i	−0.906162	−	0.523173i
$690$		0			0
$691$	14.8016	−	8.54571i	0.563079	−	0.325094i	−0.191301	−	0.981531i	$-0.561271\pi$
$691$	14.8016	−	8.54571i	0.563079	−	0.325094i	0.754381	+	0.656437i	$0.227937\pi$
$692$	−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
$698$	2.78786	−	17.0723i	0.105522	−	0.646194i
$699$		0			0
$700$	−0.000593125	−	12.3428i	−2.24180e−5	−	0.466513i
$701$		−	39.1536i		−	1.47881i	−0.673260	−	0.739406i	$-0.735106\pi$
$701$		−	39.1536i		−	1.47881i	0.673260	−	0.739406i	$-0.264894\pi$
$702$		0			0
$703$	48.4896	+	27.9955i	1.82882	+	1.05587i
$704$	41.6108	−	3.16786i	1.56827	−	0.119393i
$705$		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	0.818459	−	0.574565i	$-0.194829\pi$
$709$	−2.35273	−	4.07505i	−0.0883588	−	0.153042i	−0.906818	+	0.421523i	$0.861496\pi$
$710$	2.70422	+	7.14685i	0.101487	+	0.268216i
$711$		0			0
$712$	0.451537	+	11.8793i	0.0169221	+	0.445197i
$713$			28.1364i			1.05371i
$714$		0			0
$715$			49.7365i			1.86004i
$716$	−2.83155	+	2.50085i	−0.105820	+	0.0934610i
$717$		0			0
$718$	−26.9668	+	10.2037i	−1.00639	+	0.380797i
$719$	−16.1702	−	28.0077i	−0.603048	−	1.04451i	−0.992357	−	0.123402i	$-0.960619\pi$
$719$	−16.1702	−	28.0077i	−0.603048	−	1.04451i	0.389309	−	0.921107i	$-0.372714\pi$
$720$		0			0
$721$	2.00783	−	9.91448i	0.0747756	−	0.369235i
$722$	2.69037	+	2.20004i	0.100125	+	0.0818769i
$723$		0			0
$724$	−1.68225	−	0.564468i	−0.0625204	−	0.0209783i
$725$	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	$-0.126080\pi$
$728$	9.32603	+	24.6438i	0.345646	+	0.913358i
$729$		0			0
$730$	36.8717	+	6.02107i	1.36468	+	0.222850i
$731$	8.07754	−	13.9907i	0.298759	−	0.517465i
$732$		0			0
$733$	−15.7829	−	27.3369i	−0.582956	−	1.00971i	−0.995127	−	0.0986034i	$-0.968562\pi$
$733$	−15.7829	−	27.3369i	−0.582956	−	1.00971i	0.412170	−	0.911107i	$-0.364771\pi$
$734$	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	−0.992509	−	0.122168i	$-0.961015\pi$
$739$	−43.3475	−	25.0267i	−1.59456	−	0.920622i	−0.602055	−	0.798454i	$-0.705651\pi$
$740$	−43.3344	−	49.0648i	−1.59300	−	1.80366i
$741$		0			0
$742$	4.70507	+	28.8041i	0.172728	+	1.05743i
$743$	17.7020			0.649423			0.324711	−	0.945813i	$-0.394733\pi$
$743$	17.7020			0.649423			0.324711	+	0.945813i	$0.394733\pi$
$744$		0			0
$745$	10.4750	−	18.1433i	0.383775	−	0.664717i
$746$	−20.0506	+	7.58672i	−0.734104	+	0.277770i
$747$		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	$-0.796140\pi$
$751$	−18.7788	+	10.8420i	−0.685249	+	0.395629i	0.116581	+	0.993181i	$0.462807\pi$
$752$	4.73368	−	38.0171i	0.172619	−	1.38634i
$753$		0			0
$754$	−34.8606	−	5.69265i	−1.26955	−	0.207314i
$755$	−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	$0.453325\pi$
$758$	5.87763	+	0.959803i	0.213485	+	0.0348616i
$759$		0			0
$760$	−18.8933	−	30.0291i	−0.685334	−	1.08927i
$761$	17.8621	−	10.3127i	0.647502	−	0.373836i	−0.139996	−	0.990152i	$-0.544709\pi$
$761$	17.8621	−	10.3127i	0.647502	−	0.373836i	0.787499	+	0.616316i	$0.211376\pi$
$762$		0			0
$763$	7.72160	+	23.0086i	0.279541	+	0.832967i
$764$	7.33260	+	36.1987i	0.265284	+	1.30962i
$765$		0			0
$766$	−21.8060	+	8.25095i	−0.787884	+	0.298119i
$767$	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	$0.440436\pi$
$770$	40.9125	−	33.4593i	1.47438	−	1.20579i
$771$		0			0
$772$	−22.1407	+	19.5548i	−0.796861	+	0.703793i
$773$	32.6161	+	18.8309i	1.17312	+	0.677302i	0.954413	−	0.298489i	$-0.0964826\pi$
$773$	32.6161	+	18.8309i	1.17312	+	0.677302i	0.218708	+	0.975790i	$0.429816\pi$
$774$		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
$782$	29.6902	+	4.84834i	1.06172	+	0.173376i
$783$		0			0
$784$	13.9977	−	24.2501i	0.499917	−	0.866073i
$785$			11.8956i			0.424571i
$786$		0			0
$787$	4.15052	+	2.39631i	0.147950	+	0.0854191i	0.572148	−	0.820151i	$-0.306110\pi$
$787$	4.15052	+	2.39631i	0.147950	+	0.0854191i	−0.424197	+	0.905570i	$0.639444\pi$
$788$	−7.80053	+	23.2475i	−0.277882	+	0.828158i
$789$		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
$794$	15.3047	−	5.79096i	0.543142	−	0.205514i
$795$		0			0
$796$	−15.0240	−	17.0107i	−0.532510	−	0.602928i
$797$		−	20.5153i		−	0.726689i	−0.931655	−	0.363345i	$-0.881635\pi$
$797$		−	20.5153i		−	0.726689i	0.931655	−	0.363345i	$-0.118365\pi$
$798$		0			0
$799$			34.7517i			1.22943i
$800$	3.10895	+	12.8235i	0.109918	+	0.453379i
$801$		0			0
$802$	1.89323	+	5.00353i	0.0668523	+	0.176681i
$803$	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
$808$	−0.736772	+	0.463553i	−0.0259196	+	0.0163077i
$809$	44.0885	+	25.4545i	1.55007	+	0.894933i	0.998135	+	0.0610447i	$0.0194432\pi$
$809$	44.0885	+	25.4545i	1.55007	+	0.894933i	0.551934	+	0.833888i	$0.313890\pi$
$810$		0			0
$811$			53.2904i			1.87128i	0.352959	+	0.935639i	$0.385176\pi$
$811$			53.2904i			1.87128i	−0.352959	+	0.935639i	$0.614824\pi$
$812$	18.7691	+	32.5054i	0.658666	+	1.14072i
$813$		0			0
$814$	14.3708	−	88.0036i	0.503695	−	3.08452i
$815$	−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	−0.790687	−	0.612221i	$-0.790276\pi$
$821$	−18.7916	+	10.8493i	−0.655832	+	0.378645i	0.134855	+	0.990865i	$0.456943\pi$
$822$		0			0
$823$	17.7199	+	10.2306i	0.617676	+	0.356616i	0.775964	−	0.630777i	$-0.217264\pi$
$823$	17.7199	+	10.2306i	0.617676	+	0.356616i	−0.158287	+	0.987393i	$0.550597\pi$
$824$	0.410754	+	10.8064i	0.0143093	+	0.376458i
$825$		0			0
$826$	−4.24655	+	0.693661i	−0.147756	+	0.0241356i
$827$	44.9844			1.56426			0.782131	−	0.623114i	$-0.214133\pi$
$827$	44.9844			1.56426			0.782131	+	0.623114i	$0.214133\pi$
$828$		0			0
$829$	−17.2166	+	29.8200i	−0.597957	+	1.03569i	0.395165	+	0.918610i	$0.370687\pi$
$829$	−17.2166	+	29.8200i	−0.597957	+	1.03569i	−0.993122	+	0.117082i	$0.962646\pi$
$830$	−2.85232	−	7.53826i	−0.0990054	−	0.261657i
$831$		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
$836$	15.3734	−	45.8166i	0.531701	−	1.58460i
$837$		0			0
$838$	2.89359	−	17.7197i	0.0999574	−	0.612118i
$839$	18.4672			0.637558			0.318779	−	0.947829i	$-0.396727\pi$
$839$	18.4672			0.637558			0.318779	+	0.947829i	$0.396727\pi$
$840$		0			0
$841$	−21.3171			−0.735073
$842$	8.49991	−	52.0516i	0.292926	−	1.79382i
$843$		0			0
$844$	13.7001	−	40.8295i	0.471576	−	1.40541i
$845$	−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
$850$	−4.23581	−	11.1946i	−0.145287	−	0.383972i
$851$	−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	$0.389648\pi$
$854$	−4.46322	+	11.7974i	−0.152728	+	0.403697i
$855$		0			0
$856$	4.23392	−	0.160933i	0.144712	−	0.00550056i
$857$	−22.4524	−	12.9629i	−0.766959	−	0.442804i	0.0648294	−	0.997896i	$-0.479350\pi$
$857$	−22.4524	−	12.9629i	−0.766959	−	0.442804i	−0.831789	+	0.555092i	$0.812683\pi$
$858$		0			0
$859$	8.68624	−	5.01500i	0.296371	−	0.171110i	−0.344441	−	0.938808i	$-0.611931\pi$
$859$	8.68624	−	5.01500i	0.296371	−	0.171110i	0.640811	+	0.767698i	$0.278598\pi$
$860$	−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	$-0.0383092\pi$
$863$	11.5277	+	19.9665i	0.392407	+	0.679668i	−0.600360	+	0.799730i	$0.704976\pi$
$864$		0			0
$865$	27.9220	−	48.3624i	0.949378	−	1.64437i
$866$	−0.852291	+	5.21925i	−0.0289620	+	0.177357i
$867$		0			0
$868$	25.3951	−	0.00122035i	0.861966	−	4.14213e-5i
$869$		−	38.2616i		−	1.29794i
$870$		0			0
$871$	7.81556	+	4.51232i	0.264820	+	0.152894i
$872$	−13.8168	−	21.9604i	−0.467896	−	0.743674i
$873$		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	−0.987540	−	0.157368i	$-0.949699\pi$
$877$	−18.6586	−	32.3176i	−0.630055	−	1.09129i	0.357485	−	0.933919i	$-0.383634\pi$
$878$	−17.6255	−	46.5816i	−0.594832	−	1.57205i
$879$		0			0
$880$	−34.0802	+	45.0660i	−1.14884	+	1.51917i
$881$			39.5671i			1.33305i	0.745483	+	0.666524i	$0.232219\pi$
$881$			39.5671i			1.33305i	−0.745483	+	0.666524i	$0.767781\pi$
$882$		0			0
$883$			43.8816i			1.47673i	0.674400	+	0.738366i	$0.264402\pi$
$883$			43.8816i			1.47673i	−0.674400	+	0.738366i	$0.735598\pi$
$884$	16.9149	+	19.1516i	0.568908	+	0.644139i
$885$		0			0
$886$	−26.1194	+	9.88304i	−0.877499	+	0.332027i
$887$	−17.1379	−	29.6837i	−0.575435	−	0.996683i	−0.995994	−	0.0894175i	$-0.971499\pi$
$887$	−17.1379	−	29.6837i	−0.575435	−	0.996683i	0.420559	−	0.907265i	$-0.361834\pi$
$888$		0			0
$889$	32.0024	+	28.2620i	1.07332	+	0.947877i
$890$	−12.4599	−	10.1890i	−0.417656	−	0.341536i
$891$		0			0
$892$	−13.2549	+	39.5028i	−0.443807	+	1.32265i
$893$	−38.4220	−	22.1829i	−1.28574	−	0.742324i
$894$		0			0
$895$		−	5.11492i		−	0.170973i
$896$	−8.43600	+	28.7199i	−0.281827	+	0.959465i
$897$		0			0
$898$	−15.9070	−	2.59758i	−0.530824	−	0.0866823i
$899$	−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	$-0.0520157\pi$
$907$	40.3297	+	23.2844i	1.33913	+	0.773145i	0.352449	+	0.935831i	$0.385349\pi$
$908$	−30.7584	+	27.1661i	−1.02075	+	0.901538i
$909$		0			0
$910$	−33.3673	−	12.6236i	−1.10611	−	0.418470i
$911$	14.5617			0.482450			0.241225	−	0.970469i	$-0.422451\pi$
$911$	14.5617			0.482450			0.241225	+	0.970469i	$0.422451\pi$
$912$		0			0
$913$	5.48940	−	9.50791i	0.181672	−	0.314666i
$914$	−6.14876	+	2.32656i	−0.203383	+	0.0769558i
$915$		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	$-0.514456\pi$
$919$	24.1621	−	13.9500i	0.797033	−	0.460167i	0.842433	+	0.538802i	$0.181123\pi$
$920$	38.0058	−	23.9120i	1.25301	−	0.788356i
$921$		0			0
$922$	10.7010	+	1.74745i	0.352418	+	0.0575490i
$923$	7.02592			0.231261
$924$		0			0
$925$	28.1944			0.927025
$926$	−24.4263	−	3.98875i	−0.802697	−	0.131078i
$927$		0			0
$928$	−27.6863	−	29.0451i	−0.908847	−	0.953451i
$929$	21.2485	−	12.2678i	0.697141	−	0.402494i	−0.109141	−	0.994026i	$-0.534810\pi$
$929$	21.2485	−	12.2678i	0.697141	−	0.402494i	0.806282	+	0.591532i	$0.201477\pi$
$930$		0			0
$931$	−19.5608	−	25.8610i	−0.641078	−	0.847561i
$932$	−13.1544	+	2.66462i	−0.430886	+	0.0872824i
$933$		0			0
$934$	28.0021	−	10.5954i	0.916256	−	0.346692i
$935$	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	$0.613044\pi$
$938$	−1.54600	−	9.46453i	−0.0504788	−	0.309028i
$939$		0			0
$940$	34.3371	+	38.8777i	1.11995	+	1.26805i
$941$	12.0167	+	6.93786i	0.391734	+	0.226168i	0.682911	−	0.730501i	$-0.260714\pi$
$941$	12.0167	+	6.93786i	0.391734	+	0.226168i	−0.291177	+	0.956669i	$0.594047\pi$
$942$		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	$-0.247325\pi$
$947$	−7.71469	−	13.3622i	−0.250694	−	0.434214i	−0.963717	+	0.266926i	$0.913992\pi$
$948$		0			0
$949$	17.1756	−	29.7490i	0.557543	−	0.965693i
$950$	15.0808	+	2.46265i	0.489284	+	0.0798990i
$951$		0			0
$952$	4.37469	−	26.7978i	0.141785	−	0.868521i
$953$		−	5.54532i		−	0.179630i	−0.995958	−	0.0898152i	$-0.971372\pi$
$953$		−	5.54532i		−	0.179630i	0.995958	−	0.0898152i	$-0.0286276\pi$
$954$		0			0
$955$	−43.3066	−	25.0031i	−1.40137	−	0.809080i
$956$	−12.7376	−	4.27400i	−0.411962	−	0.138231i
$957$		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
$962$	−56.2943	+	21.3006i	−1.81500	+	0.686759i
$963$		0			0
$964$	37.9610	−	33.5274i	1.22264	−	1.07985i
$965$		−	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	$-0.348528\pi$
$968$	−45.8181	+	1.74156i	−1.47265	+	0.0559759i
$969$		0			0
$970$	21.6948	+	57.3360i	0.696577	+	1.84095i
$971$	−16.1692	−	28.0059i	−0.518894	−	0.898750i	−0.999759	−	0.0219559i	$-0.993011\pi$
$971$	−16.1692	−	28.0059i	−0.518894	−	0.898750i	0.480865	−	0.876795i	$-0.340323\pi$
$972$		0			0
$973$	22.9295	+	20.2496i	0.735087	+	0.649172i
$974$	30.4805	−	37.2739i	0.976659	−	1.19433i
$975$		0			0
$976$	1.66612	−	13.3810i	0.0533313	−	0.428314i
$977$	2.05622	+	1.18716i	0.0657842	+	0.0379805i	0.532531	−	0.846410i	$-0.321241\pi$
$977$	2.05622	+	1.18716i	0.0657842	+	0.0379805i	−0.466747	+	0.884391i	$0.654574\pi$
$978$		0			0
$979$		−	21.9246i		−	0.700714i
$980$	12.0632	+	35.9397i	0.385343	+	1.14805i
$981$		0			0
$982$	−5.11240	+	31.3072i	−0.163143	+	0.999054i
$983$	−16.8532	+	29.1907i	−0.537535	+	0.931038i	0.461501	+	0.887140i	$0.347311\pi$
$983$	−16.8532	+	29.1907i	−0.537535	+	0.931038i	−0.999036	+	0.0438983i	$0.986022\pi$
$984$		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	$-0.173715\pi$
$991$	26.2104	+	15.1326i	0.832602	+	0.480703i	−0.0221406	+	0.999755i	$0.507048\pi$
$992$	−26.3842	+	6.39664i	−0.837698	+	0.203093i
$993$		0			0
$994$	−4.72655	−	5.77942i	−0.149917	−	0.183312i
$995$	30.7282			0.974148
$996$		0			0
$997$	−8.89414	+	15.4051i	−0.281680	+	0.487885i	−0.971799	−	0.235812i	$-0.924225\pi$
$997$	−8.89414	+	15.4051i	−0.281680	+	0.487885i	0.690118	+	0.723697i	$0.257558\pi$
$998$	13.6875	+	36.1739i	0.433269	+	1.14507i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.e.107.4	✓	64	21.2	odd	6	inner
756.2.be.e.107.15	yes	64	84.23	even	6	inner
756.2.be.e.107.18	yes	64	28.23	odd	6	inner
756.2.be.e.107.29	yes	64	7.2	even	3	inner
756.2.be.e.431.4	yes	64	4.3	odd	2	inner
756.2.be.e.431.15	yes	64	1.1	even	1	trivial
756.2.be.e.431.18	yes	64	3.2	odd	2	inner
756.2.be.e.431.29	yes	64	12.11	even	2	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)

\(f(q)\)	\(=\)	\(q+(-0.227919 + 1.39573i) q^{2} +(-1.89611 - 0.636225i) q^{4} +(2.34508 - 1.35394i) q^{5} +(-1.75134 + 1.98313i) q^{7} +(1.32015 - 2.50144i) q^{8} +O(q^{10})\)	\(q+(-0.227919 + 1.39573i) q^{2} +(-1.89611 - 0.636225i) q^{4} +(2.34508 - 1.35394i) q^{5} +(-1.75134 + 1.98313i) q^{7} +(1.32015 - 2.50144i) q^{8} +(1.35523 + 3.58168i) q^{10} +(-2.60820 + 4.51754i) q^{11} +3.52108 q^{13} +(-2.36874 - 2.89639i) q^{14} +(3.19044 + 2.41270i) q^{16} +(-3.14229 - 1.81420i) q^{17} +(4.01162 - 2.31611i) q^{19} +(-5.30794 + 1.07520i) q^{20} +(-5.71079 - 4.66997i) q^{22} +(2.93134 + 5.07724i) q^{23} +(1.16628 - 2.02006i) q^{25} +(-0.802521 + 4.91447i) q^{26} +(4.58245 - 2.64597i) q^{28} +7.09346i q^{29} +(4.15625 + 2.39961i) q^{31} +(-4.09463 + 3.90308i) q^{32} +(3.24832 - 3.97229i) q^{34} +(-1.42202 + 7.02181i) q^{35} +(6.04365 + 10.4679i) q^{37} +(2.31833 + 6.12701i) q^{38} +(-0.290911 - 7.65349i) q^{40} +4.04595i q^{41} +4.45239i q^{43} +(7.81959 - 6.90632i) q^{44} +(-7.75454 + 2.93416i) q^{46} +(-4.78883 - 8.29450i) q^{47} +(-0.865590 - 6.94628i) q^{49} +(2.55363 + 2.08822i) q^{50} +(-6.67635 - 2.24020i) q^{52} +(-6.75522 - 3.90013i) q^{53} +14.1253i q^{55} +(2.64863 + 6.99891i) q^{56} +(-9.90053 - 1.61673i) q^{58} +(0.574990 - 0.995912i) q^{59} +(-1.68554 - 2.91944i) q^{61} +(-4.29649 + 5.25407i) q^{62} +(-4.51438 - 6.60457i) q^{64} +(8.25724 - 4.76732i) q^{65} +(2.21965 + 1.28151i) q^{67} +(4.80388 + 5.43913i) q^{68} +(-9.47642 - 3.58516i) q^{70} +1.99539 q^{71} +(4.87793 - 8.44882i) q^{73} +(-15.9878 + 6.04945i) q^{74} +(-9.08002 + 1.83930i) q^{76} +(-4.39099 - 13.0842i) q^{77} +(-6.35219 + 3.66744i) q^{79} +(10.7485 + 1.33834i) q^{80} +(-5.64704 - 0.922147i) q^{82} -2.10467 q^{83} -9.82526 q^{85} +(-6.21432 - 1.01478i) q^{86} +(7.85711 + 12.4881i) q^{88} +(-3.63992 + 2.10151i) q^{89} +(-6.16663 + 6.98276i) q^{91} +(-2.32787 - 11.4920i) q^{92} +(12.6683 - 4.79343i) q^{94} +(6.27173 - 10.8629i) q^{95} +16.0081 q^{97} +(9.89239 + 0.375061i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more