LMFDB - Embedded newform 944.2.m.c.593.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [944,2,Mod(17,944)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(944, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 0, 40]))

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

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

chi := DirichletCharacter("944.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 944 = 2^{4} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	944.m (of order $29$, degree $28$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.53787795081$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$4$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 59)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			593.1
Character	$\chi$	$=$	944.593
Dual form			944.2.m.c.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.89290 - 0.974731i) q^{3} +(-2.81882 - 1.69603i) q^{5} +(-0.0467597 + 0.862432i) q^{7} +(5.03048 + 3.82407i) q^{9} +O(q^{10})$	\(q+(-2.89290 - 0.974731i) q^{3} +(-2.81882 - 1.69603i) q^{5} +(-0.0467597 + 0.862432i) q^{7} +(5.03048 + 3.82407i) q^{9} +(-0.631059 + 3.84929i) q^{11} +(-1.31325 + 0.998305i) q^{13} +(6.50140 + 7.65404i) q^{15} +(0.182290 + 3.36214i) q^{17} +(3.16614 - 2.99913i) q^{19} +(0.975910 - 2.44935i) q^{21} +(2.04440 - 0.450007i) q^{23} +(2.72721 + 5.14406i) q^{25} +(-5.68582 - 8.38596i) q^{27} +(-3.93910 - 1.82242i) q^{29} +(-5.88624 - 5.57574i) q^{31} +(5.57761 - 10.5205i) q^{33} +(1.59452 - 2.35174i) q^{35} +(-0.331878 - 1.19532i) q^{37} +(4.77217 - 1.60793i) q^{39} +(-3.25469 - 0.716412i) q^{41} +(0.471222 + 2.87433i) q^{43} +(-7.69430 - 19.3112i) q^{45} +(-5.86181 + 3.52693i) q^{47} +(6.21736 + 0.676179i) q^{49} +(2.74983 - 9.90400i) q^{51} +(2.19994 - 0.239258i) q^{53} +(8.30736 - 9.78018i) q^{55} +(-12.0827 + 5.59003i) q^{57} +(3.82919 - 6.65863i) q^{59} +(10.6495 - 4.92699i) q^{61} +(-3.53322 + 4.15963i) q^{63} +(5.39497 - 0.586739i) q^{65} +(-1.13948 + 4.10403i) q^{67} +(-6.35288 - 0.690918i) q^{69} +(9.08556 - 5.46660i) q^{71} +(-4.53863 - 11.3911i) q^{73} +(-2.87546 - 17.5395i) q^{75} +(-3.29024 - 0.724237i) q^{77} +(9.88675 - 3.33123i) q^{79} +(3.20295 + 11.5360i) q^{81} +(-3.22744 + 4.76012i) q^{83} +(5.18844 - 9.78644i) q^{85} +(9.61904 + 9.11164i) q^{87} +(2.24597 + 1.03910i) q^{89} +(-0.799563 - 1.17927i) q^{91} +(11.5934 + 21.8676i) q^{93} +(-14.0114 + 3.08414i) q^{95} +(3.53517 - 8.87260i) q^{97} +(-17.8945 + 16.9506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9}+O(q^{10}) $ 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9	$ 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9} + 15 q^{11} - 23 q^{13} - 4 q^{15} - 10 q^{17} + 15 q^{19} - 12 q^{21} - 3 q^{23} - 5 q^{25} - 22 q^{27} - 13 q^{29} - 3 q^{31} + 33 q^{33} - 28 q^{35} - 9 q^{37} - 45 q^{39} + 23 q^{41} - 19 q^{43} + 19 q^{45} - 10 q^{47} - 31 q^{49} + 61 q^{51} - 23 q^{53} + 24 q^{55} - 91 q^{57} + 33 q^{59} - 47 q^{61} + 58 q^{63} - 16 q^{65} + 19 q^{67} - 45 q^{69} + 18 q^{71} + 24 q^{73} - 58 q^{75} + 65 q^{77} - 41 q^{79} + 95 q^{81} - 49 q^{83} + 39 q^{85} - 80 q^{87} + 51 q^{89} - 77 q^{91} + 93 q^{93} - 65 q^{95} + 91 q^{97} - 44 q^{99}+O(q^{100}) $ 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9 + 15 * q^11 - 23 * q^13 - 4 * q^15 - 10 * q^17 + 15 * q^19 - 12 * q^21 - 3 * q^23 - 5 * q^25 - 22 * q^27 - 13 * q^29 - 3 * q^31 + 33 * q^33 - 28 * q^35 - 9 * q^37 - 45 * q^39 + 23 * q^41 - 19 * q^43 + 19 * q^45 - 10 * q^47 - 31 * q^49 + 61 * q^51 - 23 * q^53 + 24 * q^55 - 91 * q^57 + 33 * q^59 - 47 * q^61 + 58 * q^63 - 16 * q^65 + 19 * q^67 - 45 * q^69 + 18 * q^71 + 24 * q^73 - 58 * q^75 + 65 * q^77 - 41 * q^79 + 95 * q^81 - 49 * q^83 + 39 * q^85 - 80 * q^87 + 51 * q^89 - 77 * q^91 + 93 * q^93 - 65 * q^95 + 91 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/944\mathbb{Z}\right)^\times$.

$n$	$591$	$709$	$769$
$\chi(n)$	$1$	$1$	$e\left(\frac{25}{29}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.89290	−	0.974731i	−1.67022	−	0.562761i	−0.684182	−	0.729311i	$-0.739841\pi$
$3$	−2.89290	−	0.974731i	−1.67022	−	0.562761i	−0.986033	+	0.166550i	$0.946737\pi$
$4$		0			0
$5$	−2.81882	−	1.69603i	−1.26062	−	0.758488i	−0.281066	−	0.959688i	$-0.590688\pi$
$5$	−2.81882	−	1.69603i	−1.26062	−	0.758488i	−0.979550	+	0.201201i	$0.935516\pi$
$6$		0			0
$7$	−0.0467597	+	0.862432i	−0.0176735	+	0.325969i	0.976305	+	0.216397i	$0.0694306\pi$
$7$	−0.0467597	+	0.862432i	−0.0176735	+	0.325969i	−0.993979	+	0.109571i	$0.965052\pi$
$8$		0			0
$9$	5.03048	+	3.82407i	1.67683	+	1.27469i
$10$		0			0
$11$	−0.631059	+	3.84929i	−0.190272	+	1.16061i	0.703034	+	0.711156i	$0.251828\pi$
$11$	−0.631059	+	3.84929i	−0.190272	+	1.16061i	−0.893306	+	0.449449i	$0.851620\pi$
$12$		0			0
$13$	−1.31325	+	0.998305i	−0.364230	+	0.276880i	−0.771241	−	0.636543i	$-0.780364\pi$
$13$	−1.31325	+	0.998305i	−0.364230	+	0.276880i	0.407012	+	0.913423i	$0.366571\pi$
$14$		0			0
$15$	6.50140	+	7.65404i	1.67865	+	1.97626i
$16$		0			0
$17$	0.182290	+	3.36214i	0.0442117	+	0.815438i	0.933607	+	0.358299i	$0.116643\pi$
$17$	0.182290	+	3.36214i	0.0442117	+	0.815438i	−0.889395	+	0.457139i	$0.848874\pi$
$18$		0			0
$19$	3.16614	−	2.99913i	0.726362	−	0.688047i	−0.232284	−	0.972648i	$-0.574620\pi$
$19$	3.16614	−	2.99913i	0.726362	−	0.688047i	0.958646	+	0.284601i	$0.0918612\pi$
$20$		0			0
$21$	0.975910	−	2.44935i	0.212961	−	0.534492i
$22$		0			0
$23$	2.04440	−	0.450007i	0.426287	−	0.0938330i	0.00335541	−	0.999994i	$-0.498932\pi$
$23$	2.04440	−	0.450007i	0.426287	−	0.0938330i	0.422932	+	0.906161i	$0.361001\pi$
$24$		0			0
$25$	2.72721	+	5.14406i	0.545442	+	1.02881i
$26$		0			0
$27$	−5.68582	−	8.38596i	−1.09424	−	1.61388i
$28$		0			0
$29$	−3.93910	−	1.82242i	−0.731472	−	0.338415i	0.0185498	−	0.999828i	$-0.494095\pi$
$29$	−3.93910	−	1.82242i	−0.731472	−	0.338415i	−0.750022	+	0.661413i	$0.769957\pi$
$30$		0			0
$31$	−5.88624	−	5.57574i	−1.05720	−	1.00143i	−0.999995	−	0.00307034i	$-0.999023\pi$
$31$	−5.88624	−	5.57574i	−1.05720	−	1.00143i	−0.0572045	−	0.998362i	$-0.518219\pi$
$32$		0			0
$33$	5.57761	−	10.5205i	0.970938	−	1.83138i
$34$		0			0
$35$	1.59452	−	2.35174i	0.269523	−	0.397516i
$36$		0			0
$37$	−0.331878	−	1.19532i	−0.0545604	−	0.196509i	0.931247	−	0.364388i	$-0.118722\pi$
$37$	−0.331878	−	1.19532i	−0.0545604	−	0.196509i	−0.985808	+	0.167879i	$0.946308\pi$
$38$		0			0
$39$	4.77217	−	1.60793i	0.764159	−	0.257475i
$40$		0			0
$41$	−3.25469	−	0.716412i	−0.508297	−	0.111885i	−0.0465849	−	0.998914i	$-0.514834\pi$
$41$	−3.25469	−	0.716412i	−0.508297	−	0.111885i	−0.461713	+	0.887030i	$0.652765\pi$
$42$		0			0
$43$	0.471222	+	2.87433i	0.0718607	+	0.438331i	0.998112	+	0.0614239i	$0.0195642\pi$
$43$	0.471222	+	2.87433i	0.0718607	+	0.438331i	−0.926251	+	0.376907i	$0.876988\pi$
$44$		0			0
$45$	−7.69430	−	19.3112i	−1.14700	−	2.87875i
$46$		0			0
$47$	−5.86181	+	3.52693i	−0.855032	+	0.514456i	−0.874315	−	0.485358i	$-0.838689\pi$
$47$	−5.86181	+	3.52693i	−0.855032	+	0.514456i	0.0192832	+	0.999814i	$0.493862\pi$
$48$		0			0
$49$	6.21736	+	0.676179i	0.888195	+	0.0965970i
$50$		0			0
$51$	2.74983	−	9.90400i	0.385053	−	1.38684i
$52$		0			0
$53$	2.19994	−	0.239258i	0.302185	−	0.0328645i	0.0442293	−	0.999021i	$-0.485917\pi$
$53$	2.19994	−	0.239258i	0.302185	−	0.0328645i	0.257955	+	0.966157i	$0.416951\pi$
$54$		0			0
$55$	8.30736	−	9.78018i	1.12016	−	1.31876i
$56$		0			0
$57$	−12.0827	+	5.59003i	−1.60039	+	0.740418i
$58$		0			0
$59$	3.82919	−	6.65863i	0.498518	−	0.866879i
$59$	3.82919	−	6.65863i	0.498518	−	0.866879i
$60$		0			0
$61$	10.6495	−	4.92699i	1.36353	−	0.630837i	0.404605	−	0.914491i	$-0.367409\pi$
$61$	10.6495	−	4.92699i	1.36353	−	0.630837i	0.958927	+	0.283655i	$0.0915469\pi$
$62$		0			0
$63$	−3.53322	+	4.15963i	−0.445144	+	0.524064i
$64$		0			0
$65$	5.39497	−	0.586739i	0.669164	−	0.0727760i
$66$		0			0
$67$	−1.13948	+	4.10403i	−0.139209	+	0.501387i	−0.999971	−	0.00762130i	$-0.997574\pi$
$67$	−1.13948	+	4.10403i	−0.139209	+	0.501387i	0.860761	+	0.509009i	$0.169988\pi$
$68$		0			0
$69$	−6.35288	−	0.690918i	−0.764797	−	0.0831767i
$70$		0			0
$71$	9.08556	−	5.46660i	1.07826	−	0.648766i	0.138415	−	0.990374i	$-0.455799\pi$
$71$	9.08556	−	5.46660i	1.07826	−	0.648766i	0.939842	+	0.341608i	$0.110972\pi$
$72$		0			0
$73$	−4.53863	−	11.3911i	−0.531207	−	1.33323i	−0.912614	−	0.408822i	$-0.865940\pi$
$73$	−4.53863	−	11.3911i	−0.531207	−	1.33323i	0.381408	−	0.924407i	$-0.375439\pi$
$74$		0			0
$75$	−2.87546	−	17.5395i	−0.332030	−	2.02529i
$76$		0			0
$77$	−3.29024	−	0.724237i	−0.374958	−	0.0825345i
$78$		0			0
$79$	9.88675	−	3.33123i	1.11235	−	0.374793i	0.297647	−	0.954676i	$-0.403798\pi$
$79$	9.88675	−	3.33123i	1.11235	−	0.374793i	0.814700	+	0.579883i	$0.196902\pi$
$80$		0			0
$81$	3.20295	+	11.5360i	0.355883	+	1.28177i
$82$		0			0
$83$	−3.22744	+	4.76012i	−0.354258	+	0.522491i	−0.962508	−	0.271254i	$-0.912562\pi$
$83$	−3.22744	+	4.76012i	−0.354258	+	0.522491i	0.608250	+	0.793746i	$0.291872\pi$
$84$		0			0
$85$	5.18844	−	9.78644i	0.562765	−	1.06149i
$86$		0			0
$87$	9.61904	+	9.11164i	1.03127	+	0.976870i
$88$		0			0
$89$	2.24597	+	1.03910i	0.238073	+	0.110144i	0.535298	−	0.844663i	$-0.320199\pi$
$89$	2.24597	+	1.03910i	0.238073	+	0.110144i	−0.297225	+	0.954807i	$0.596061\pi$
$90$		0			0
$91$	−0.799563	−	1.17927i	−0.0838170	−	0.123621i
$92$		0			0
$93$	11.5934	+	21.8676i	1.20218	+	2.26756i
$94$		0			0
$95$	−14.0114	+	3.08414i	−1.43754	+	0.316426i
$96$		0			0
$97$	3.53517	−	8.87260i	0.358942	−	0.900876i	−0.632997	−	0.774155i	$-0.718175\pi$
$97$	3.53517	−	8.87260i	0.358942	−	0.900876i	0.991938	−	0.126721i	$-0.0404454\pi$
$98$		0			0
$99$	−17.8945	+	16.9506i	−1.79846	+	1.70360i
$100$		0			0
$101$	0.496317	+	9.15403i	0.0493854	+	0.910860i	0.913317	+	0.407250i	$0.133512\pi$
$101$	0.496317	+	9.15403i	0.0493854	+	0.910860i	−0.863931	+	0.503610i	$0.832005\pi$
$102$		0			0
$103$	−0.373198	−	0.439363i	−0.0367723	−	0.0432917i	0.743468	−	0.668771i	$-0.233179\pi$
$103$	−0.373198	−	0.439363i	−0.0367723	−	0.0432917i	−0.780241	+	0.625479i	$0.784903\pi$
$104$		0			0
$105$	−6.90509	+	5.24911i	−0.673868	+	0.512261i
$106$		0			0
$107$	−0.758075	+	4.62405i	−0.0732859	+	0.447024i	0.924538	+	0.381090i	$0.124451\pi$
$107$	−0.758075	+	4.62405i	−0.0732859	+	0.447024i	−0.997824	+	0.0659343i	$0.978997\pi$
$108$		0			0
$109$	−3.62962	−	2.75917i	−0.347655	−	0.264280i	0.416744	−	0.909024i	$-0.363171\pi$
$109$	−3.62962	−	2.75917i	−0.347655	−	0.264280i	−0.764399	+	0.644743i	$0.776964\pi$
$110$		0			0
$111$	−0.205023	+	3.78142i	−0.0194599	+	0.358917i
$112$		0			0
$113$	6.98819	+	4.20465i	0.657393	+	0.395540i	0.804809	−	0.593534i	$-0.202268\pi$
$113$	6.98819	+	4.20465i	0.657393	+	0.395540i	−0.147415	+	0.989075i	$0.547095\pi$
$114$		0			0
$115$	−6.52604	−	2.19888i	−0.608556	−	0.205046i
$116$		0			0
$117$	−10.4239			−0.963686
$118$		0			0
$119$	−2.90814			−0.266588
$120$		0			0
$121$	−3.99463	−	1.34595i	−0.363148	−	0.122359i
$122$		0			0
$123$	8.71718	+	5.24495i	0.786002	+	0.472922i
$124$		0			0
$125$	0.146451	−	2.70113i	0.0130990	−	0.241597i
$126$		0			0
$127$	6.40397	+	4.86817i	0.568260	+	0.431980i	0.849448	−	0.527673i	$-0.176935\pi$
$127$	6.40397	+	4.86817i	0.568260	+	0.431980i	−0.281188	+	0.959653i	$0.590728\pi$
$128$		0			0
$129$	1.43850	−	8.77446i	0.126653	−	0.772548i
$130$		0			0
$131$	6.48615	−	4.93064i	0.566697	−	0.430792i	−0.282196	−	0.959357i	$-0.591063\pi$
$131$	6.48615	−	4.93064i	0.566697	−	0.430792i	0.848893	+	0.528565i	$0.177270\pi$
$132$		0			0
$133$	2.43849	+	2.87082i	0.211444	+	0.248931i
$134$		0			0
$135$	1.80449	+	33.2819i	0.155306	+	2.86445i
$136$		0			0
$137$	−5.89436	+	5.58343i	−0.503589	+	0.477025i	−0.896808	−	0.442420i	$-0.854120\pi$
$137$	−5.89436	+	5.58343i	−0.503589	+	0.477025i	0.393219	+	0.919445i	$0.371361\pi$
$138$		0			0
$139$	−1.57818	+	3.96094i	−0.133860	+	0.335963i	−0.980593	−	0.196055i	$-0.937187\pi$
$139$	−1.57818	+	3.96094i	−0.133860	+	0.335963i	0.846733	+	0.532018i	$0.178566\pi$
$140$		0			0
$141$	20.3954	−	4.48937i	1.71760	−	0.378073i
$142$		0			0
$143$	−3.01403	−	5.68507i	−0.252046	−	0.475409i
$144$		0			0
$145$	8.01275	+	11.8179i	0.665422	+	0.981424i
$146$		0			0
$147$	−17.3271	−	8.01637i	−1.42912	−	0.661179i
$148$		0			0
$149$	−6.70502	−	6.35133i	−0.549296	−	0.520321i	0.361942	−	0.932201i	$-0.382114\pi$
$149$	−6.70502	−	6.35133i	−0.549296	−	0.520321i	−0.911238	+	0.411880i	$0.864872\pi$
$150$		0			0
$151$	10.4138	−	19.6425i	0.847464	−	1.59849i	0.0471626	−	0.998887i	$-0.484982\pi$
$151$	10.4138	−	19.6425i	0.847464	−	1.59849i	0.800301	−	0.599599i	$-0.204673\pi$
$152$		0			0
$153$	−11.9400	+	17.6102i	−0.965295	+	1.42370i
$154$		0			0
$155$	7.13565	+	25.7003i	0.573149	+	2.06430i
$156$		0			0
$157$	7.71264	−	2.59869i	0.615536	−	0.207398i	0.00577445	−	0.999983i	$-0.498162\pi$
$157$	7.71264	−	2.59869i	0.615536	−	0.207398i	0.609761	+	0.792585i	$0.291265\pi$
$158$		0			0
$159$	−6.59740	−	1.45220i	−0.523208	−	0.115167i
$160$		0			0
$161$	0.292505	+	1.78420i	0.0230526	+	0.140615i
$162$		0			0
$163$	−5.39519	−	13.5409i	−0.422584	−	1.06061i	−0.974035	−	0.226398i	$-0.927305\pi$
$163$	−5.39519	−	13.5409i	−0.422584	−	1.06061i	0.551451	−	0.834207i	$-0.314074\pi$
$164$		0			0
$165$	−33.5654	+	20.1956i	−2.61306	+	1.57223i
$166$		0			0
$167$	−16.8909	−	1.83700i	−1.30706	−	0.142151i	−0.572056	−	0.820215i	$-0.693854\pi$
$167$	−16.8909	−	1.83700i	−1.30706	−	0.142151i	−0.735004	+	0.678063i	$0.762820\pi$
$168$		0			0
$169$	−2.74986	+	9.90410i	−0.211528	+	0.761854i
$170$		0			0
$171$	27.3961	−	2.97950i	2.09503	−	0.227848i
$172$		0			0
$173$	12.2858	−	14.4639i	0.934071	−	1.09967i	−0.0607624	−	0.998152i	$-0.519353\pi$
$173$	12.2858	−	14.4639i	0.934071	−	1.09967i	0.994833	−	0.101521i	$-0.0323709\pi$
$174$		0			0
$175$	−4.56392	+	2.11150i	−0.345000	+	0.159614i
$176$		0			0
$177$	−17.5678	+	15.5303i	−1.32048	+	1.16733i
$178$		0			0
$179$	16.2981	−	7.54030i	1.21818	−	0.563588i	0.297802	−	0.954628i	$-0.403746\pi$
$179$	16.2981	−	7.54030i	1.21818	−	0.563588i	0.920374	+	0.391039i	$0.127884\pi$
$180$		0			0
$181$	15.3849	−	18.1125i	1.14355	−	1.34629i	0.214327	−	0.976762i	$-0.431244\pi$
$181$	15.3849	−	18.1125i	1.14355	−	1.34629i	0.929220	−	0.369526i	$-0.120480\pi$
$182$		0			0
$183$	−35.6105	+	3.87287i	−2.63240	+	0.286291i
$184$		0			0
$185$	−1.09179	+	3.93226i	−0.0802698	+	0.289106i
$186$		0			0
$187$	−13.0569	−	1.42002i	−0.954813	−	0.103842i
$188$		0			0
$189$	7.49818	−	4.51151i	0.545413	−	0.328164i
$190$		0			0
$191$	1.82504	+	4.58050i	0.132055	+	0.331433i	0.980104	−	0.198485i	$-0.0636020\pi$
$191$	1.82504	+	4.58050i	0.132055	+	0.331433i	−0.848049	+	0.529918i	$0.822223\pi$
$192$		0			0
$193$	−3.09323	−	18.8679i	−0.222656	−	1.35814i	−0.827352	−	0.561684i	$-0.810154\pi$
$193$	−3.09323	−	18.8679i	−0.222656	−	1.35814i	0.604696	−	0.796456i	$-0.293294\pi$
$194$		0			0
$195$	−16.1790	−	3.56127i	−1.15860	−	0.255028i
$196$		0			0
$197$	−8.62732	+	2.90688i	−0.614671	+	0.207107i	−0.609379	−	0.792879i	$-0.708581\pi$
$197$	−8.62732	+	2.90688i	−0.614671	+	0.207107i	−0.00529224	+	0.999986i	$0.501685\pi$
$198$		0			0
$199$	−2.53614	−	9.13434i	−0.179782	−	0.647517i	−0.997420	−	0.0717840i	$-0.977131\pi$
$199$	−2.53614	−	9.13434i	−0.179782	−	0.647517i	0.817638	−	0.575733i	$-0.195283\pi$
$200$		0			0
$201$	7.29672	−	10.7619i	0.514671	−	0.759083i
$202$		0			0
$203$	1.75590	−	3.31199i	0.123240	−	0.232456i
$204$		0			0
$205$	7.95935	+	7.53949i	0.555905	+	0.526581i
$206$		0			0
$207$	12.0052	+	5.55419i	0.834418	+	0.386043i
$208$		0			0
$209$	9.54649	+	14.0800i	0.660345	+	0.973935i
$210$		0			0
$211$	13.0562	+	24.6267i	0.898828	+	1.69537i	0.698461	+	0.715648i	$0.253868\pi$
$211$	13.0562	+	24.6267i	0.898828	+	1.69537i	0.200367	+	0.979721i	$0.435787\pi$
$212$		0			0
$213$	−31.6121	+	6.95834i	−2.16602	+	0.476778i
$214$		0			0
$215$	3.54666	−	8.90144i	0.241880	−	0.607073i
$216$		0			0
$217$	5.08394	−	4.81576i	0.345120	−	0.326915i
$218$		0			0
$219$	2.02654	+	37.3773i	0.136941	+	2.52572i
$220$		0			0
$221$	−3.59583	−	4.23334i	−0.241882	−	0.284765i
$222$		0			0
$223$	2.30497	−	1.75219i	0.154352	−	0.117336i	−0.525148	−	0.851011i	$-0.675990\pi$
$223$	2.30497	−	1.75219i	0.154352	−	0.117336i	0.679500	+	0.733676i	$0.262197\pi$
$224$		0			0
$225$	−5.95209	+	36.3061i	−0.396806	+	2.42041i
$226$		0			0
$227$	13.3785	+	10.1700i	0.887960	+	0.675010i	0.946301	−	0.323287i	$-0.104788\pi$
$227$	13.3785	+	10.1700i	0.887960	+	0.675010i	−0.0583409	+	0.998297i	$0.518581\pi$
$228$		0			0
$229$	−0.880892	+	16.2471i	−0.0582110	+	1.07364i	0.812853	+	0.582469i	$0.197913\pi$
$229$	−0.880892	+	16.2471i	−0.0582110	+	1.07364i	−0.871064	+	0.491169i	$0.836570\pi$
$230$		0			0
$231$	8.81240	+	5.30225i	0.579814	+	0.348862i
$232$		0			0
$233$	5.77225	+	1.94490i	0.378153	+	0.127414i	0.501958	−	0.864892i	$-0.332613\pi$
$233$	5.77225	+	1.94490i	0.378153	+	0.127414i	−0.123805	+	0.992307i	$0.539510\pi$
$234$		0			0
$235$	22.5052			1.46808
$236$		0			0
$237$	−31.8484			−2.06878
$238$		0			0
$239$	−4.28355	−	1.44330i	−0.277080	−	0.0933592i	0.177331	−	0.984151i	$-0.443254\pi$
$239$	−4.28355	−	1.44330i	−0.277080	−	0.0933592i	−0.454411	+	0.890792i	$0.650150\pi$
$240$		0			0
$241$	24.1172	+	14.5108i	1.55352	+	0.934724i	0.994405	+	0.105637i	$0.0336881\pi$
$241$	24.1172	+	14.5108i	1.55352	+	0.934724i	0.559119	+	0.829087i	$0.311139\pi$
$242$		0			0
$243$	0.333099	−	6.14364i	0.0213683	−	0.394115i
$244$		0			0
$245$	−16.3788	−	12.4509i	−1.04641	−	0.795457i
$246$		0			0
$247$	−1.16388	+	7.09937i	−0.0740561	+	0.451722i
$248$		0			0
$249$	13.9765	−	10.6247i	0.885724	−	0.673310i
$250$		0			0
$251$	3.53436	+	4.16097i	0.223087	+	0.262638i	0.862307	−	0.506385i	$-0.169019\pi$
$251$	3.53436	+	4.16097i	0.223087	+	0.262638i	−0.639220	+	0.769024i	$0.720743\pi$
$252$		0			0
$253$	0.442069	+	8.15349i	0.0277926	+	0.512605i
$254$		0			0
$255$	−24.5488	+	23.2538i	−1.53730	+	1.45621i
$256$		0			0
$257$	−2.21814	+	5.56710i	−0.138364	+	0.347266i	−0.981788	−	0.189982i	$-0.939157\pi$
$257$	−2.21814	+	5.56710i	−0.138364	+	0.347266i	0.843424	+	0.537249i	$0.180536\pi$
$258$		0			0
$259$	1.04640	−	0.230330i	0.0650200	−	0.0143120i
$260$		0			0
$261$	−12.8465	−	24.2310i	−0.795178	−	1.49986i
$262$		0			0
$263$	−4.32309	−	6.37609i	−0.266573	−	0.393166i	0.670718	−	0.741712i	$-0.265986\pi$
$263$	−4.32309	−	6.37609i	−0.266573	−	0.393166i	−0.937292	+	0.348546i	$0.886676\pi$
$264$		0			0
$265$	−6.60702	−	3.05673i	−0.405866	−	0.187774i
$266$		0			0
$267$	−5.48453	−	5.19522i	−0.335648	−	0.317943i
$268$		0			0
$269$	−2.56485	+	4.83783i	−0.156382	+	0.294968i	−0.949306	−	0.314352i	$-0.898213\pi$
$269$	−2.56485	+	4.83783i	−0.156382	+	0.294968i	0.792924	+	0.609320i	$0.208557\pi$
$270$		0			0
$271$	5.05394	−	7.45400i	0.307005	−	0.452798i	−0.642621	−	0.766184i	$-0.722153\pi$
$271$	5.05394	−	7.45400i	0.307005	−	0.452798i	0.949626	+	0.313386i	$0.101463\pi$
$272$		0			0
$273$	1.16359	+	4.19086i	0.0704235	+	0.253642i
$274$		0			0
$275$	−21.5220	+	7.25161i	−1.29783	+	0.437289i
$276$		0			0
$277$	9.76763	+	2.15002i	0.586880	+	0.129182i	0.498477	−	0.866903i	$-0.333893\pi$
$277$	9.76763	+	2.15002i	0.586880	+	0.129182i	0.0884027	+	0.996085i	$0.471824\pi$
$278$		0			0
$279$	−8.28857	−	50.5580i	−0.496224	−	3.02683i
$280$		0			0
$281$	−4.69259	−	11.7775i	−0.279937	−	0.702588i	−0.999963	−	0.00864103i	$-0.997249\pi$
$281$	−4.69259	−	11.7775i	−0.279937	−	0.702588i	0.720026	−	0.693947i	$-0.244130\pi$
$282$		0			0
$283$	26.5719	−	15.9878i	1.57953	−	0.950374i	0.589785	−	0.807561i	$-0.299213\pi$
$283$	26.5719	−	15.9878i	1.57953	−	0.950374i	0.989750	−	0.142814i	$-0.0456150\pi$
$284$		0			0
$285$	43.5397	+	4.73523i	2.57907	+	0.280491i
$286$		0			0
$287$	0.770045	−	2.77345i	0.0454543	−	0.163712i
$288$		0			0
$289$	5.62962	−	0.612258i	0.331154	−	0.0360152i
$290$		0			0
$291$	−18.8753	+	22.2217i	−1.10649	+	1.30266i
$292$		0			0
$293$	−4.59598	+	2.12633i	−0.268500	+	0.124221i	−0.549520	−	0.835481i	$-0.685189\pi$
$293$	−4.59598	+	2.12633i	−0.268500	+	0.124221i	0.281020	+	0.959702i	$0.409327\pi$
$294$		0			0
$295$	−22.0870	+	12.2751i	−1.28596	+	0.714683i
$296$		0			0
$297$	35.8681	−	16.5943i	2.08128	−	0.962902i
$298$		0			0
$299$	−2.23556	+	2.63191i	−0.129286	+	0.152207i
$300$		0			0
$301$	−2.50095	+	0.271994i	−0.144152	+	0.0156775i
$302$		0			0
$303$	7.48692	−	26.9655i	0.430112	−	1.54913i
$304$		0			0
$305$	−38.3755	−	4.17358i	−2.19737	−	0.238979i
$306$		0			0
$307$	4.14617	−	2.49467i	0.236635	−	0.142378i	−0.392298	−	0.919838i	$-0.628320\pi$
$307$	4.14617	−	2.49467i	0.236635	−	0.142378i	0.628932	+	0.777460i	$0.283492\pi$
$308$		0			0
$309$	0.651363	+	1.63480i	0.0370548	+	0.0930005i
$310$		0			0
$311$	−3.92141	−	23.9195i	−0.222362	−	1.35635i	−0.828053	−	0.560650i	$-0.810551\pi$
$311$	−3.92141	−	23.9195i	−0.222362	−	1.35635i	0.605690	−	0.795701i	$-0.292897\pi$
$312$		0			0
$313$	−33.1029	−	7.28650i	−1.87109	−	0.411857i	−0.873853	−	0.486191i	$-0.838386\pi$
$313$	−33.1029	−	7.28650i	−1.87109	−	0.411857i	−0.997233	+	0.0743338i	$0.976317\pi$
$314$		0			0
$315$	17.0144	−	5.73282i	0.958653	−	0.323008i
$316$		0			0
$317$	−5.88706	−	21.2033i	−0.330650	−	1.19090i	−0.922868	−	0.385117i	$-0.874161\pi$
$317$	−5.88706	−	21.2033i	−0.330650	−	1.19090i	0.592217	−	0.805778i	$-0.298253\pi$
$318$		0			0
$319$	9.50084	−	14.0127i	0.531945	−	0.784560i
$320$		0			0
$321$	6.70024	−	12.6380i	0.373971	−	0.705384i
$322$		0			0
$323$	10.6606	+	10.0983i	0.593173	+	0.561883i
$324$		0			0
$325$	−8.71685	−	4.03284i	−0.483524	−	0.223702i
$326$		0			0
$327$	7.81068	+	11.5199i	0.431932	+	0.637052i
$328$		0			0
$329$	−2.76764	−	5.22033i	−0.152585	−	0.287806i
$330$		0			0
$331$	1.85821	−	0.409024i	0.102137	−	0.0224820i	−0.163608	−	0.986525i	$-0.552313\pi$
$331$	1.85821	−	0.409024i	0.102137	−	0.0224820i	0.265745	+	0.964043i	$0.414382\pi$
$332$		0			0
$333$	2.90147	−	7.28214i	0.159000	−	0.399059i
$334$		0			0
$335$	10.1726	−	9.63595i	0.555786	−	0.526468i
$336$		0			0
$337$	1.17193	+	21.6150i	0.0638392	+	1.17744i	0.838440	+	0.544994i	$0.183468\pi$
$337$	1.17193	+	21.6150i	0.0638392	+	1.17744i	−0.774601	+	0.632450i	$0.782049\pi$
$338$		0			0
$339$	−16.1177	−	18.9752i	−0.875394	−	1.03059i
$340$		0			0
$341$	25.1772	−	19.1392i	1.36342	−	1.03645i
$342$		0			0
$343$	−1.85200	+	11.2967i	−0.0999984	+	0.609963i
$344$		0			0
$345$	16.7358	+	12.7223i	0.901028	+	0.684943i
$346$		0			0
$347$	0.0961070	−	1.77259i	0.00515929	−	0.0951576i	−0.994820	−	0.101656i	$-0.967586\pi$
$347$	0.0961070	−	1.77259i	0.00515929	−	0.0951576i	0.999979	+	0.00649863i	$0.00206859\pi$
$348$		0			0
$349$	−0.965567	−	0.580962i	−0.0516856	−	0.0310982i	0.489477	−	0.872016i	$-0.337188\pi$
$349$	−0.965567	−	0.580962i	−0.0516856	−	0.0310982i	−0.541162	+	0.840918i	$0.682015\pi$
$350$		0			0
$351$	15.8386	+	5.33666i	0.845404	+	0.284850i
$352$		0			0
$353$	33.0859			1.76098			0.880491	−	0.474062i	$-0.157213\pi$
$353$	33.0859			1.76098			0.880491	+	0.474062i	$0.157213\pi$
$354$		0			0
$355$	−34.8821			−1.85135
$356$		0			0
$357$	8.41294	+	2.83465i	0.445260	+	0.150026i
$358$		0			0
$359$	−9.44626	−	5.68363i	−0.498555	−	0.299970i	0.243977	−	0.969781i	$-0.421548\pi$
$359$	−9.44626	−	5.68363i	−0.498555	−	0.299970i	−0.742532	+	0.669811i	$0.766375\pi$
$360$		0			0
$361$	0.00103907	−	0.0191644i	5.46877e−5	−	0.00100865i
$362$		0			0
$363$	10.2441	+	7.78738i	0.537677	+	0.408731i
$364$		0			0
$365$	−6.52606	+	39.8072i	−0.341589	+	2.08360i
$366$		0			0
$367$	1.82954	−	1.39078i	0.0955014	−	0.0725983i	−0.556334	−	0.830959i	$-0.687792\pi$
$367$	1.82954	−	1.39078i	0.0955014	−	0.0725983i	0.651835	+	0.758361i	$0.273999\pi$
$368$		0			0
$369$	−13.6330	−	16.0501i	−0.709708	−	0.835533i
$370$		0			0
$371$	0.103475	+	1.90848i	0.00537215	+	0.0990835i
$372$		0			0
$373$	0.723584	−	0.685415i	0.0374658	−	0.0354895i	−0.668738	−	0.743498i	$-0.733165\pi$
$373$	0.723584	−	0.685415i	0.0374658	−	0.0354895i	0.706203	+	0.708009i	$0.250406\pi$
$374$		0			0
$375$	−3.05654	+	7.67135i	−0.157839	+	0.396147i
$376$		0			0
$377$	6.99235	−	1.53913i	0.360124	−	0.0792693i
$378$		0			0
$379$	9.54753	+	18.0086i	0.490424	+	0.925037i	0.997987	+	0.0634226i	$0.0202016\pi$
$379$	9.54753	+	18.0086i	0.490424	+	0.925037i	−0.507563	+	0.861615i	$0.669454\pi$
$380$		0			0
$381$	−13.7809	−	20.3253i	−0.706015	−	1.04129i
$382$		0			0
$383$	23.5937	+	10.9156i	1.20558	+	0.557760i	0.916689	−	0.399602i	$-0.130852\pi$
$383$	23.5937	+	10.9156i	1.20558	+	0.557760i	0.288890	+	0.957362i	$0.406714\pi$
$384$		0			0
$385$	8.04629	+	7.62185i	0.410077	+	0.388445i
$386$		0			0
$387$	−8.62116	+	16.2612i	−0.438238	+	0.826605i
$388$		0			0
$389$	13.6598	−	20.1467i	0.692580	−	1.02148i	−0.305028	−	0.952343i	$-0.598666\pi$
$389$	13.6598	−	20.1467i	0.692580	−	1.02148i	0.997607	−	0.0691350i	$-0.0220239\pi$
$390$		0			0
$391$	1.88566	+	6.79153i	0.0953618	+	0.343462i
$392$		0			0
$393$	−23.5698	+	7.94159i	−1.18894	+	0.400600i
$394$		0			0
$395$	−33.5189	−	7.37806i	−1.68652	−	0.371231i
$396$		0			0
$397$	−2.12527	−	12.9636i	−0.106664	−	0.650623i	−0.984997	−	0.172573i	$-0.944792\pi$
$397$	−2.12527	−	12.9636i	−0.106664	−	0.650623i	0.878333	−	0.478050i	$-0.158656\pi$
$398$		0			0
$399$	−4.25604	−	10.6819i	−0.213068	−	0.534762i
$400$		0			0
$401$	17.8154	−	10.7192i	0.889660	−	0.535291i	0.00419205	−	0.999991i	$-0.498666\pi$
$401$	17.8154	−	10.7192i	0.889660	−	0.535291i	0.885468	+	0.464701i	$0.153838\pi$
$402$		0			0
$403$	13.2964	+	1.44607i	0.662340	+	0.0720338i
$404$		0			0
$405$	10.5368	−	37.9502i	0.523578	−	1.88576i
$406$		0			0
$407$	4.81056	−	0.523180i	0.238451	−	0.0259331i
$408$		0			0
$409$	−23.1163	+	27.2147i	−1.14303	+	1.34568i	−0.213495	+	0.976944i	$0.568485\pi$
$409$	−23.1163	+	27.2147i	−1.14303	+	1.34568i	−0.929535	+	0.368734i	$0.879791\pi$
$410$		0			0
$411$	22.4941	−	10.4069i	1.10955	−	0.513334i
$412$		0			0
$413$	5.56356	+	3.61377i	0.273765	+	0.177822i
$414$		0			0
$415$	17.1709	−	7.94410i	0.842886	−	0.389961i
$416$		0			0
$417$	8.42638	−	9.92030i	0.412641	−	0.485799i
$418$		0			0
$419$	−27.2597	+	2.96467i	−1.33172	+	0.144834i	−0.746146	−	0.665782i	$-0.768098\pi$
$419$	−27.2597	+	2.96467i	−1.33172	+	0.144834i	−0.585578	+	0.810616i	$0.699132\pi$
$420$		0			0
$421$	−1.28680	+	4.63464i	−0.0627148	+	0.225878i	−0.988266	−	0.152745i	$-0.951189\pi$
$421$	−1.28680	+	4.63464i	−0.0627148	+	0.225878i	0.925551	+	0.378623i	$0.123602\pi$
$422$		0			0
$423$	−42.9749	−	4.67380i	−2.08951	−	0.227248i
$424$		0			0
$425$	−16.7979	+	10.1070i	−0.814817	+	0.490259i
$426$		0			0
$427$	3.75123	+	9.41487i	0.181535	+	0.455618i
$428$		0			0
$429$	3.17788	+	19.3842i	0.153429	+	0.935877i
$430$		0			0
$431$	−1.70525	−	0.375355i	−0.0821392	−	0.0180802i	0.173711	−	0.984797i	$-0.444424\pi$
$431$	−1.70525	−	0.375355i	−0.0821392	−	0.0180802i	−0.255850	+	0.966717i	$0.582355\pi$
$432$		0			0
$433$	21.0612	−	7.09634i	1.01214	−	0.341028i	0.236108	−	0.971727i	$-0.424128\pi$
$433$	21.0612	−	7.09634i	1.01214	−	0.341028i	0.776028	+	0.630699i	$0.217232\pi$
$434$		0			0
$435$	−11.6608	−	41.9983i	−0.559091	−	2.01366i
$436$		0			0
$437$	5.12324	−	7.55621i	0.245078	−	0.361462i
$438$		0			0
$439$	−6.10646	+	11.5180i	−0.291446	+	0.549725i	−0.985392	−	0.170302i	$-0.945526\pi$
$439$	−6.10646	+	11.5180i	−0.291446	+	0.549725i	0.693946	+	0.720027i	$0.255870\pi$
$440$		0			0
$441$	28.6906	+	27.1771i	1.36622	+	1.29415i
$442$		0			0
$443$	−37.6159	−	17.4030i	−1.78719	−	0.826840i	−0.967015	−	0.254721i	$-0.918016\pi$
$443$	−37.6159	−	17.4030i	−1.78719	−	0.826840i	−0.820171	−	0.572119i	$-0.806122\pi$
$444$		0			0
$445$	−4.56866	−	6.73827i	−0.216575	−	0.319425i
$446$		0			0
$447$	13.2061	+	24.9093i	0.624627	+	1.17817i
$448$		0			0
$449$	6.58499	−	1.44947i	0.310765	−	0.0684046i	−0.0568497	−	0.998383i	$-0.518106\pi$
$449$	6.58499	−	1.44947i	0.310765	−	0.0684046i	0.367615	+	0.929978i	$0.380175\pi$
$450$		0			0
$451$	4.81158	−	12.0762i	0.226569	−	0.568644i
$452$		0			0
$453$	−49.2722	+	46.6732i	−2.31501	+	2.19290i
$454$		0			0
$455$	0.253755	+	4.68023i	0.0118962	+	0.219413i
$456$		0			0
$457$	−19.9001	−	23.4282i	−0.930889	−	1.09593i	−0.995187	−	0.0979960i	$-0.968757\pi$
$457$	−19.9001	−	23.4282i	−0.930889	−	1.09593i	0.0642983	−	0.997931i	$-0.479519\pi$
$458$		0			0
$459$	27.1583	−	20.6452i	1.26764	−	0.963634i
$460$		0			0
$461$	−5.30727	+	32.3729i	−0.247184	+	1.50776i	0.513193	+	0.858273i	$0.328463\pi$
$461$	−5.30727	+	32.3729i	−0.247184	+	1.50776i	−0.760377	+	0.649482i	$0.774986\pi$
$462$		0			0
$463$	−0.0515587	−	0.0391939i	−0.00239614	−	0.00182150i	0.603975	−	0.797003i	$-0.293582\pi$
$463$	−0.0515587	−	0.0391939i	−0.00239614	−	0.00182150i	−0.606372	+	0.795181i	$0.707376\pi$
$464$		0			0
$465$	4.40815	−	81.3036i	0.204423	−	3.77036i
$466$		0			0
$467$	22.3545	+	13.4503i	1.03444	+	0.622404i	0.928256	−	0.371942i	$-0.121308\pi$
$467$	22.3545	+	13.4503i	1.03444	+	0.622404i	0.106188	+	0.994346i	$0.466136\pi$
$468$		0			0
$469$	−3.48616	−	1.17463i	−0.160976	−	0.0542392i
$470$		0			0
$471$	−24.8449			−1.14479
$472$		0			0
$473$	−11.3615			−0.522403
$474$		0			0
$475$	24.0624	+	8.10757i	1.10406	+	0.372001i
$476$		0			0
$477$	11.9817	+	7.20913i	0.548603	+	0.330084i
$478$		0			0
$479$	0.163608	−	3.01758i	0.00747545	−	0.137877i	−0.992413	−	0.122948i	$-0.960765\pi$
$479$	0.163608	−	3.01758i	0.00747545	−	0.137877i	0.999889	−	0.0149285i	$-0.00475208\pi$
$480$		0			0
$481$	1.62913	+	1.23843i	0.0742820	+	0.0564677i
$482$		0			0
$483$	0.892928	−	5.44662i	0.0406296	−	0.247830i
$484$		0			0
$485$	−25.0132	+	19.0145i	−1.13579	+	0.863406i
$486$		0			0
$487$	11.2027	+	13.1889i	0.507645	+	0.597646i	0.954961	−	0.296730i	$-0.0958962\pi$
$487$	11.2027	+	13.1889i	0.507645	+	0.597646i	−0.447317	+	0.894376i	$0.647620\pi$
$488$		0			0
$489$	2.40900	+	44.4313i	0.108939	+	2.00925i
$490$		0			0
$491$	11.7240	−	11.1056i	0.529098	−	0.501188i	−0.375867	−	0.926673i	$-0.622655\pi$
$491$	11.7240	−	11.1056i	0.529098	−	0.501188i	0.904965	+	0.425485i	$0.139897\pi$
$492$		0			0
$493$	5.40917	−	13.5760i	0.243617	−	0.611432i
$494$		0			0
$495$	79.1901	−	17.4311i	3.55933	−	0.783468i
$496$		0			0
$497$	4.28973	+	8.09129i	0.192421	+	0.362944i
$498$		0			0
$499$	−2.09302	−	3.08697i	−0.0936963	−	0.138192i	0.777952	−	0.628324i	$-0.216259\pi$
$499$	−2.09302	−	3.08697i	−0.0936963	−	0.138192i	−0.871648	+	0.490132i	$0.836948\pi$
$500$		0			0
$501$	47.0732	+	21.7784i	2.10307	+	0.972986i
$502$		0			0
$503$	12.9800	+	12.2953i	0.578750	+	0.548222i	0.920084	−	0.391721i	$-0.128120\pi$
$503$	12.9800	+	12.2953i	0.578750	+	0.548222i	−0.341334	+	0.939942i	$0.610879\pi$
$504$		0			0
$505$	14.1265	−	26.6454i	0.628620	−	1.18570i
$506$		0			0
$507$	17.6089	−	25.9712i	0.782039	−	1.15342i
$508$		0			0
$509$	−8.85505	−	31.8930i	−0.392493	−	1.41363i	−0.851105	−	0.524996i	$-0.824067\pi$
$509$	−8.85505	−	31.8930i	−0.392493	−	1.41363i	0.458612	−	0.888637i	$-0.348347\pi$
$510$		0			0
$511$	10.0363	−	3.38162i	0.443979	−	0.149594i
$512$		0			0
$513$	−43.1526	−	9.49861i	−1.90524	−	0.419374i
$514$		0			0
$515$	0.306807	+	1.87144i	0.0135195	+	0.0824655i
$516$		0			0
$517$	−9.87704	−	24.7895i	−0.434392	−	1.09024i
$518$		0			0
$519$	−49.6400	+	29.8674i	−2.17895	+	1.31103i
$520$		0			0
$521$	−17.5054	−	1.90383i	−0.766926	−	0.0834082i	−0.283711	−	0.958910i	$-0.591566\pi$
$521$	−17.5054	−	1.90383i	−0.766926	−	0.0834082i	−0.483215	+	0.875502i	$0.660531\pi$
$522$		0			0
$523$	2.68104	−	9.65623i	0.117234	−	0.422237i	−0.881520	−	0.472146i	$-0.843479\pi$
$523$	2.68104	−	9.65623i	0.117234	−	0.422237i	0.998754	+	0.0499091i	$0.0158932\pi$
$524$		0			0
$525$	15.2611	−	1.65975i	0.666049	−	0.0724372i
$526$		0			0
$527$	17.6734	−	20.8067i	0.769865	−	0.906355i
$528$		0			0
$529$	−16.8972	+	7.81746i	−0.734659	+	0.339889i
$530$		0			0
$531$	44.7257	−	18.8530i	1.94093	−	0.818151i
$532$		0			0
$533$	4.98942	−	2.30835i	0.216116	−	0.0999857i
$534$		0			0
$535$	9.97941	−	11.7487i	0.431448	−	0.507939i
$536$		0			0
$537$	−54.4985	+	5.92707i	−2.35178	+	0.255772i
$538$		0			0
$539$	−6.52634	+	23.5057i	−0.281109	+	1.01246i
$540$		0			0
$541$	−1.04324	−	0.113459i	−0.0448523	−	0.00487799i	0.0856653	−	0.996324i	$-0.472698\pi$
$541$	−1.04324	−	0.113459i	−0.0448523	−	0.00487799i	−0.130518	+	0.991446i	$0.541664\pi$
$542$		0			0
$543$	−62.1616	+	37.4014i	−2.66761	+	1.60505i
$544$		0			0
$545$	5.55164	+	13.9336i	0.237806	+	0.596848i
$546$		0			0
$547$	5.26270	+	32.1010i	0.225017	+	1.37254i	0.821634	+	0.570015i	$0.193063\pi$
$547$	5.26270	+	32.1010i	0.225017	+	1.37254i	−0.596618	+	0.802526i	$0.703489\pi$
$548$		0			0
$549$	72.4134	+	15.9394i	3.09053	+	0.680277i
$550$		0			0
$551$	−17.9374	+	6.04382i	−0.764159	+	0.257475i
$552$		0			0
$553$	2.41066	+	8.68242i	0.102512	+	0.369214i
$554$		0			0
$555$	6.99133	−	10.3114i	0.296765	−	0.437696i
$556$		0			0
$557$	−9.43266	+	17.7919i	−0.399675	+	0.753866i	−0.998909	−	0.0467076i	$-0.985127\pi$
$557$	−9.43266	+	17.7919i	−0.399675	+	0.753866i	0.599234	+	0.800574i	$0.295472\pi$
$558$		0			0
$559$	−3.48829	−	3.30428i	−0.147539	−	0.139756i
$560$		0			0
$561$	36.3881	+	16.8349i	1.53631	+	0.710771i
$562$		0			0
$563$	−12.6330	−	18.6324i	−0.532420	−	0.785260i	0.462426	−	0.886658i	$-0.346979\pi$
$563$	−12.6330	−	18.6324i	−0.532420	−	0.785260i	−0.994846	+	0.101398i	$0.967669\pi$
$564$		0			0
$565$	−12.5673	−	23.7044i	−0.528708	−	0.997250i
$566$		0			0
$567$	−10.0988	+	2.22290i	−0.424108	+	0.0933532i
$568$		0			0
$569$	9.68713	−	24.3129i	0.406105	−	1.01925i	−0.573659	−	0.819094i	$-0.694477\pi$
$569$	9.68713	−	24.3129i	0.406105	−	1.01925i	0.979765	−	0.200154i	$-0.0641441\pi$
$570$		0			0
$571$	−2.96218	+	2.80592i	−0.123963	+	0.117424i	−0.747170	−	0.664633i	$-0.768588\pi$
$571$	−2.96218	+	2.80592i	−0.123963	+	0.117424i	0.623207	+	0.782057i	$0.285829\pi$
$572$		0			0
$573$	−0.814894	−	15.0298i	−0.0340427	−	0.627880i
$574$		0			0
$575$	7.89038	+	9.28927i	0.329051	+	0.387389i
$576$		0			0
$577$	29.8122	−	22.6627i	1.24110	−	0.943460i	0.241463	−	0.970410i	$-0.422373\pi$
$577$	29.8122	−	22.6627i	1.24110	−	0.943460i	0.999637	+	0.0269505i	$0.00857965\pi$
$578$		0			0
$579$	−9.44270	+	57.5979i	−0.392425	+	2.39369i
$580$		0			0
$581$	−3.95436	−	3.00603i	−0.164055	−	0.124711i
$582$		0			0
$583$	−0.467319	+	8.61919i	−0.0193544	+	0.356970i
$584$		0			0
$585$	29.3830	+	17.6792i	1.21484	+	0.730944i
$586$		0			0
$587$	0.957172	+	0.322509i	0.0395067	+	0.0133114i	0.338986	−	0.940792i	$-0.389916\pi$
$587$	0.957172	+	0.322509i	0.0395067	+	0.0133114i	−0.299479	+	0.954103i	$0.596813\pi$
$588$		0			0
$589$	−35.3590			−1.45694
$590$		0			0
$591$	27.7914			1.14318
$592$		0			0
$593$	0.117791	+	0.0396884i	0.00483710	+	0.00162981i	0.321719	−	0.946835i	$-0.395739\pi$
$593$	0.117791	+	0.0396884i	0.00483710	+	0.00162981i	−0.316882	+	0.948465i	$0.602636\pi$
$594$		0			0
$595$	8.19752	+	4.93229i	0.336066	+	0.202204i
$596$		0			0
$597$	−1.56674	+	28.8968i	−0.0641223	+	1.18267i
$598$		0			0
$599$	−28.1892	−	21.4289i	−1.15178	−	0.875561i	−0.158057	−	0.987430i	$-0.550523\pi$
$599$	−28.1892	−	21.4289i	−1.15178	−	0.875561i	−0.993723	+	0.111869i	$0.964316\pi$
$600$		0			0
$601$	−1.82016	+	11.1025i	−0.0742460	+	0.452880i	0.923372	+	0.383905i	$0.125421\pi$
$601$	−1.82016	+	11.1025i	−0.0742460	+	0.452880i	−0.997618	+	0.0689749i	$0.978027\pi$
$602$		0			0
$603$	−21.4262	+	16.2878i	−0.872543	+	0.663290i
$604$		0			0
$605$	8.97739	+	10.5690i	0.364983	+	0.429691i
$606$		0			0
$607$	−1.95540	−	36.0652i	−0.0793672	−	1.46384i	−0.718919	−	0.695094i	$-0.755363\pi$
$607$	−1.95540	−	36.0652i	−0.0793672	−	1.46384i	0.639552	−	0.768748i	$-0.279120\pi$
$608$		0			0
$609$	−8.30795	+	7.86971i	−0.336655	+	0.318897i
$610$		0			0
$611$	4.17705	−	10.4836i	0.168985	−	0.424121i
$612$		0			0
$613$	20.8802	−	4.59608i	0.843343	−	0.185634i	0.227771	−	0.973715i	$-0.426856\pi$
$613$	20.8802	−	4.59608i	0.843343	−	0.185634i	0.615572	+	0.788081i	$0.288925\pi$
$614$		0			0
$615$	−15.6766	−	29.5692i	−0.632142	−	1.19235i
$616$		0			0
$617$	22.4267	+	33.0769i	0.902863	+	1.33162i	0.943126	+	0.332435i	$0.107870\pi$
$617$	22.4267	+	33.0769i	0.902863	+	1.33162i	−0.0402627	+	0.999189i	$0.512819\pi$
$618$		0			0
$619$	−5.22870	−	2.41905i	−0.210159	−	0.0972300i	0.311986	−	0.950087i	$-0.399006\pi$
$619$	−5.22870	−	2.41905i	−0.210159	−	0.0972300i	−0.522145	+	0.852857i	$0.674868\pi$
$620$		0			0
$621$	−15.3978	−	14.5856i	−0.617894	−	0.585301i
$622$		0			0
$623$	−1.00117	+	1.88841i	−0.0401111	+	0.0756576i
$624$		0			0
$625$	11.3429	−	16.7296i	0.453718	−	0.669183i
$626$		0			0
$627$	−13.8928	−	50.0373i	−0.554825	−	1.99830i
$628$		0			0
$629$	3.95832	−	1.33371i	0.157829	−	0.0531786i
$630$		0			0
$631$	17.7841	+	3.91458i	0.707975	+	0.155837i	0.554340	−	0.832291i	$-0.312971\pi$
$631$	17.7841	+	3.91458i	0.707975	+	0.155837i	0.153635	+	0.988128i	$0.450902\pi$
$632$		0			0
$633$	−13.7660	−	83.9687i	−0.547148	−	3.33746i
$634$		0			0
$635$	−9.79510	−	24.5838i	−0.388707	−	0.975580i
$636$		0			0
$637$	−8.83998	+	5.31884i	−0.350253	+	0.210740i
$638$		0			0
$639$	66.6094	+	7.24420i	2.63503	+	0.286576i
$640$		0			0
$641$	−7.33079	+	26.4031i	−0.289549	+	1.04286i	0.665496	+	0.746401i	$0.268220\pi$
$641$	−7.33079	+	26.4031i	−0.289549	+	1.04286i	−0.955045	+	0.296460i	$0.904194\pi$
$642$		0			0
$643$	−32.4751	+	3.53188i	−1.28069	+	0.139284i	−0.723049	−	0.690797i	$-0.757260\pi$
$643$	−32.4751	+	3.53188i	−1.28069	+	0.139284i	−0.557643	+	0.830081i	$0.688294\pi$
$644$		0			0
$645$	−18.9366	+	22.2939i	−0.745629	+	0.877822i
$646$		0			0
$647$	−11.9292	+	5.51901i	−0.468983	+	0.216975i	−0.640124	−	0.768272i	$-0.721117\pi$
$647$	−11.9292	+	5.51901i	−0.468983	+	0.216975i	0.171140	+	0.985247i	$0.445255\pi$
$648$		0			0
$649$	23.2146	+	18.9417i	0.911251	+	0.743525i
$650$		0			0
$651$	−19.4014	+	8.97603i	−0.760400	+	0.351798i
$652$		0			0
$653$	−18.4221	+	21.6882i	−0.720912	+	0.848723i	−0.993550	−	0.113394i	$-0.963828\pi$
$653$	−18.4221	+	21.6882i	−0.720912	+	0.848723i	0.272638	+	0.962117i	$0.412104\pi$
$654$		0			0
$655$	−26.6458	+	2.89791i	−1.04114	+	0.113231i
$656$		0			0
$657$	20.7289	−	74.6588i	0.808712	−	2.91272i
$658$		0			0
$659$	2.36068	+	0.256739i	0.0919590	+	0.0100011i	0.153983	−	0.988074i	$-0.450790\pi$
$659$	2.36068	+	0.256739i	0.0919590	+	0.0100011i	−0.0620238	+	0.998075i	$0.519755\pi$
$660$		0			0
$661$	−2.79652	+	1.68261i	−0.108772	+	0.0654461i	−0.568900	−	0.822406i	$-0.692631\pi$
$661$	−2.79652	+	1.68261i	−0.108772	+	0.0654461i	0.460128	+	0.887852i	$0.347803\pi$
$662$		0			0
$663$	6.27600	+	15.7516i	0.243740	+	0.611741i
$664$		0			0
$665$	−2.00469	−	12.2281i	−0.0777387	−	0.474185i
$666$		0			0
$667$	−8.87321	−	1.95314i	−0.343572	−	0.0756259i
$668$		0			0
$669$	−8.37596	+	2.82219i	−0.323833	+	0.109112i
$670$		0			0
$671$	12.2450	+	44.1024i	0.472711	+	1.70255i
$672$		0			0
$673$	−1.19515	+	1.76272i	−0.0460698	+	0.0679479i	−0.850026	−	0.526740i	$-0.823414\pi$
$673$	−1.19515	+	1.76272i	−0.0460698	+	0.0679479i	0.803957	+	0.594688i	$0.202724\pi$
$674$		0			0
$675$	27.6315	−	52.1185i	1.06354	−	2.00604i
$676$		0			0
$677$	22.8644	+	21.6583i	0.878750	+	0.832396i	0.986832	−	0.161746i	$-0.0517124\pi$
$677$	22.8644	+	21.6583i	0.878750	+	0.832396i	−0.108082	+	0.994142i	$0.534471\pi$
$678$		0			0
$679$	7.48671	+	3.46372i	0.287313	+	0.132925i
$680$		0			0
$681$	−28.7895	−	42.4613i	−1.10322	−	1.62712i
$682$		0			0
$683$	5.55731	+	10.4822i	0.212644	+	0.401090i	0.966773	−	0.255637i	$-0.0822852\pi$
$683$	5.55731	+	10.4822i	0.212644	+	0.401090i	−0.754128	+	0.656727i	$0.771940\pi$
$684$		0			0
$685$	26.0848	−	5.74171i	0.996650	−	0.219379i
$686$		0			0
$687$	18.3849	−	46.1425i	0.701427	−	1.76045i
$688$		0			0
$689$	−2.65021	+	2.51041i	−0.100965	+	0.0956391i
$690$		0			0
$691$	−1.54514	−	28.4984i	−0.0587799	−	1.08413i	−0.867980	−	0.496599i	$-0.834582\pi$
$691$	−1.54514	−	28.4984i	−0.0587799	−	1.08413i	0.809200	−	0.587533i	$-0.199901\pi$
$692$		0			0
$693$	−13.7820	−	16.2254i	−0.523534	−	0.616351i
$694$		0			0
$695$	11.1665	−	8.48855i	0.423569	−	0.321989i
$696$		0			0
$697$	1.81538	−	11.0733i	0.0687623	−	0.419431i
$698$		0			0
$699$	−14.8028	−	11.2528i	−0.559892	−	0.425619i
$700$		0			0
$701$	−0.137246	+	2.53135i	−0.00518371	+	0.0956079i	−0.999980	−	0.00627291i	$-0.998003\pi$
$701$	−0.137246	+	2.53135i	−0.00518371	+	0.0956079i	0.994797	+	0.101881i	$0.0324860\pi$
$702$		0			0
$703$	−4.63568	−	2.78920i	−0.174838	−	0.105197i
$704$		0			0
$705$	−65.1052	−	21.9365i	−2.45200	−	0.826176i
$706$		0			0
$707$	−7.91794			−0.297785
$708$		0			0
$709$	−8.23468			−0.309260			−0.154630	−	0.987972i	$-0.549419\pi$
$709$	−8.23468			−0.309260			−0.154630	+	0.987972i	$0.549419\pi$
$710$		0			0
$711$	62.4740	+	21.0499i	2.34296	+	0.789434i
$712$		0			0
$713$	−14.5430	−	8.75021i	−0.544638	−	0.327698i
$714$		0			0
$715$	−1.14602	+	21.1371i	−0.0428587	+	0.790482i
$716$		0			0
$717$	10.9851	+	8.35063i	0.410245	+	0.311860i
$718$		0			0
$719$	−1.97588	+	12.0523i	−0.0736878	+	0.449475i	0.924051	+	0.382269i	$0.124857\pi$
$719$	−1.97588	+	12.0523i	−0.0736878	+	0.449475i	−0.997739	+	0.0672070i	$0.978591\pi$
$720$		0			0
$721$	0.396371	−	0.301313i	0.0147616	−	0.0112215i
$722$		0			0
$723$	−55.6244	−	65.4861i	−2.06869	−	2.43545i
$724$		0			0
$725$	−1.36810	−	25.2331i	−0.0508099	−	0.937133i
$726$		0			0
$727$	1.46664	−	1.38927i	0.0543946	−	0.0515253i	−0.660019	−	0.751249i	$-0.729452\pi$
$727$	1.46664	−	1.38927i	0.0543946	−	0.0515253i	0.714414	+	0.699723i	$0.246693\pi$
$728$		0			0
$729$	6.34227	−	15.9179i	0.234899	−	0.589551i
$730$		0			0
$731$	−9.57799	+	2.10827i	−0.354255	+	0.0779773i
$732$		0			0
$733$	21.4119	+	40.3871i	0.790866	+	1.49173i	0.869013	+	0.494789i	$0.164755\pi$
$733$	21.4119	+	40.3871i	0.790866	+	1.49173i	−0.0781477	+	0.996942i	$0.524901\pi$
$734$		0			0
$735$	35.2461	+	51.9840i	1.30007	+	1.91746i
$736$		0			0
$737$	−15.0785	−	6.97607i	−0.555425	−	0.256967i
$738$		0			0
$739$	−15.8300	−	14.9950i	−0.582316	−	0.551599i	0.338814	−	0.940853i	$-0.389974\pi$
$739$	−15.8300	−	14.9950i	−0.582316	−	0.551599i	−0.921130	+	0.389254i	$0.872733\pi$
$740$		0			0
$741$	10.2870	−	19.4033i	0.377901	−	0.712797i
$742$		0			0
$743$	10.2596	−	15.1318i	0.376389	−	0.555132i	−0.591566	−	0.806257i	$-0.701490\pi$
$743$	10.2596	−	15.1318i	0.376389	−	0.555132i	0.967955	+	0.251124i	$0.0808003\pi$
$744$		0			0
$745$	8.12821	+	29.2752i	0.297795	+	1.07256i
$746$		0			0
$747$	−34.4386	+	11.6037i	−1.26004	+	0.424558i
$748$		0			0
$749$	−3.95248	−	0.870007i	−0.144421	−	0.0317894i
$750$		0			0
$751$	3.12564	+	19.0655i	0.114056	+	0.695711i	0.980512	+	0.196458i	$0.0629440\pi$
$751$	3.12564	+	19.0655i	0.114056	+	0.695711i	−0.866456	+	0.499253i	$0.833608\pi$
$752$		0			0
$753$	−6.16872	−	15.4823i	−0.224801	−	0.564207i
$754$		0			0
$755$	−62.6690	+	37.7067i	−2.28076	+	1.37229i
$756$		0			0
$757$	25.2047	+	2.74118i	0.916080	+	0.0996297i	0.554000	−	0.832517i	$-0.313101\pi$
$757$	25.2047	+	2.74118i	0.916080	+	0.0996297i	0.362081	+	0.932147i	$0.382066\pi$
$758$		0			0
$759$	6.66859	−	24.0181i	0.242055	−	0.871802i
$760$		0			0
$761$	28.8725	−	3.14007i	1.04663	−	0.113827i	0.431386	−	0.902167i	$-0.358025\pi$
$761$	28.8725	−	3.14007i	1.04663	−	0.113827i	0.615240	+	0.788340i	$0.289059\pi$
$762$		0			0
$763$	2.54931	−	3.00128i	0.0922914	−	0.108654i
$764$		0			0
$765$	63.5244	−	29.3895i	2.29673	−	1.06258i
$766$		0			0
$767$	1.61867	+	12.5671i	0.0584468	+	0.453773i
$768$		0			0
$769$	−23.7797	+	11.0016i	−0.857517	+	0.396730i	−0.798837	−	0.601547i	$-0.794551\pi$
$769$	−23.7797	+	11.0016i	−0.857517	+	0.396730i	−0.0586798	+	0.998277i	$0.518689\pi$
$770$		0			0
$771$	11.8433	−	13.9430i	0.426525	−	0.502144i
$772$		0			0
$773$	−11.1976	+	1.21781i	−0.402748	+	0.0438015i	−0.307252	−	0.951628i	$-0.599409\pi$
$773$	−11.1976	+	1.21781i	−0.402748	+	0.0438015i	−0.0954964	+	0.995430i	$0.530444\pi$
$774$		0			0
$775$	12.6290	−	45.4854i	0.453645	−	1.63388i
$776$		0			0
$777$	−3.25163	−	0.353636i	−0.116652	−	0.0126866i
$778$		0			0
$779$	−12.4534	+	7.49297i	−0.446190	+	0.268464i
$780$		0			0
$781$	15.3090	+	38.4227i	0.547799	+	1.37487i
$782$		0			0
$783$	7.11426	+	43.3951i	0.254243	+	1.55081i
$784$		0			0
$785$	−26.1480	−	5.75562i	−0.933263	−	0.205427i
$786$		0			0
$787$	−2.53734	+	0.854929i	−0.0904463	+	0.0304749i	−0.364161	−	0.931336i	$-0.618644\pi$
$787$	−2.53734	+	0.854929i	−0.0904463	+	0.0304749i	0.273715	+	0.961811i	$0.411748\pi$
$788$		0			0
$789$	6.29130	+	22.6592i	0.223976	+	0.806690i
$790$		0			0
$791$	−3.95299	+	5.83023i	−0.140552	+	0.207299i
$792$		0			0
$793$	−9.06682	+	17.1018i	−0.321972	+	0.607304i
$794$		0			0
$795$	16.1339	+	15.2829i	0.572212	+	0.542028i
$796$		0			0
$797$	−44.8844	−	20.7658i	−1.58989	−	0.735561i	−0.592350	−	0.805681i	$-0.701800\pi$
$797$	−44.8844	−	20.7658i	−1.58989	−	0.735561i	−0.997539	+	0.0701197i	$0.977662\pi$
$798$		0			0
$799$	−12.9266	−	19.0653i	−0.457309	−	0.674480i
$800$		0			0
$801$	7.32474	+	13.8159i	0.258807	+	0.488162i
$802$		0			0
$803$	46.7119	−	10.2821i	1.64843	−	0.362846i
$804$		0			0
$805$	2.20154	−	5.52544i	0.0775940	−	0.194746i
$806$		0			0
$807$	12.1354	−	11.4953i	0.427188	−	0.404654i
$808$		0			0
$809$	−2.76044	−	50.9133i	−0.0970518	−	1.79001i	−0.491279	−	0.871002i	$-0.663471\pi$
$809$	−2.76044	−	50.9133i	−0.0970518	−	1.79001i	0.394228	−	0.919013i	$-0.371012\pi$
$810$		0			0
$811$	−19.6189	−	23.0971i	−0.688911	−	0.811049i	0.300867	−	0.953666i	$-0.402724\pi$
$811$	−19.6189	−	23.0971i	−0.688911	−	0.811049i	−0.989778	+	0.142617i	$0.954448\pi$
$812$		0			0
$813$	−21.8862	+	16.6374i	−0.767581	+	0.583500i
$814$		0			0
$815$	−7.75769	+	47.3198i	−0.271740	+	1.65754i
$816$		0			0
$817$	10.1124	+	7.68727i	0.353789	+	0.268944i
$818$		0			0
$819$	0.487416	−	8.98987i	0.0170317	−	0.314131i
$820$		0			0
$821$	28.1561	+	16.9410i	0.982656	+	0.591244i	0.913706	−	0.406376i	$-0.133208\pi$
$821$	28.1561	+	16.9410i	0.982656	+	0.591244i	0.0689495	+	0.997620i	$0.478035\pi$
$822$		0			0
$823$	0.0856482	+	0.0288582i	0.00298551	+	0.00100593i	0.320794	−	0.947149i	$-0.396050\pi$
$823$	0.0856482	+	0.0288582i	0.00298551	+	0.00100593i	−0.317808	+	0.948155i	$0.602947\pi$
$824$		0			0
$825$	69.3294			2.41374
$826$		0			0
$827$	−22.6616			−0.788021			−0.394011	−	0.919106i	$-0.628913\pi$
$827$	−22.6616			−0.788021			−0.394011	+	0.919106i	$0.628913\pi$
$828$		0			0
$829$	2.20038	+	0.741395i	0.0764225	+	0.0257497i	0.357253	−	0.934008i	$-0.383713\pi$
$829$	2.20038	+	0.741395i	0.0764225	+	0.0257497i	−0.280831	+	0.959757i	$0.590610\pi$
$830$		0			0
$831$	−26.1611	−	15.7406i	−0.907517	−	0.546035i
$832$		0			0
$833$	−1.14004	+	21.0269i	−0.0395002	+	0.728538i
$834$		0			0
$835$	44.4970	+	33.8257i	1.53988	+	1.17059i
$836$		0			0
$837$	−13.2898	+	81.0644i	−0.459364	+	2.80200i
$838$		0			0
$839$	3.25521	−	2.47454i	0.112382	−	0.0854308i	−0.547474	−	0.836823i	$-0.684410\pi$
$839$	3.25521	−	2.47454i	0.112382	−	0.0854308i	0.659856	+	0.751392i	$0.270617\pi$
$840$		0			0
$841$	−6.57892	−	7.74531i	−0.226859	−	0.267080i
$842$		0			0
$843$	2.09528	+	38.6452i	0.0721653	+	1.33101i
$844$		0			0
$845$	24.5490	−	23.2541i	0.844512	−	0.799965i
$846$		0			0
$847$	1.34758	−	3.38216i	0.0463032	−	0.116212i
$848$		0			0
$849$	−92.4535	+	20.3506i	−3.17300	+	0.698429i
$850$		0			0
$851$	−1.21639	−	2.29436i	−0.0416974	−	0.0786497i
$852$		0			0
$853$	−14.4324	−	21.2861i	−0.494155	−	0.728824i	0.496073	−	0.868281i	$-0.334775\pi$
$853$	−14.4324	−	21.2861i	−0.494155	−	0.728824i	−0.990228	+	0.139457i	$0.955464\pi$
$854$		0			0
$855$	−82.2780	−	38.0659i	−2.81385	−	1.30183i
$856$		0			0
$857$	−9.45774	−	8.95885i	−0.323070	−	0.306028i	0.508925	−	0.860811i	$-0.330043\pi$
$857$	−9.45774	−	8.95885i	−0.323070	−	0.306028i	−0.831996	+	0.554782i	$0.812802\pi$
$858$		0			0
$859$	−15.8610	+	29.9171i	−0.541171	+	1.02076i	0.450599	+	0.892726i	$0.351210\pi$
$859$	−15.8610	+	29.9171i	−0.541171	+	1.02076i	−0.991770	+	0.128031i	$0.959134\pi$
$860$		0			0
$861$	−4.93103	+	7.27272i	−0.168049	+	0.247854i
$862$		0			0
$863$	9.41164	+	33.8977i	0.320376	+	1.15389i	0.931915	+	0.362676i	$0.118137\pi$
$863$	9.41164	+	33.8977i	0.320376	+	1.15389i	−0.611540	+	0.791214i	$0.709449\pi$
$864$		0			0
$865$	−59.1628	+	19.9343i	−2.01159	+	0.677785i
$866$		0			0
$867$	−16.8827	−	3.71616i	−0.573367	−	0.126208i
$868$		0			0
$869$	6.58377	+	40.1592i	0.223339	+	1.36231i
$870$		0			0
$871$	−2.60066	−	6.52716i	−0.0881199	−	0.221164i
$872$		0			0
$873$	51.7130	−	31.1147i	1.75022	−	1.05307i
$874$		0			0
$875$	2.32269	+	0.252608i	0.0785214	+	0.00853972i
$876$		0			0
$877$	9.63720	−	34.7101i	0.325425	−	1.17208i	−0.602133	−	0.798396i	$-0.705682\pi$
$877$	9.63720	−	34.7101i	0.325425	−	1.17208i	0.927558	−	0.373679i	$-0.121904\pi$
$878$		0			0
$879$	15.3683	−	1.67140i	0.518360	−	0.0563751i
$880$		0			0
$881$	−13.4962	+	15.8889i	−0.454698	+	0.535312i	−0.940967	−	0.338497i	$-0.890081\pi$
$881$	−13.4962	+	15.8889i	−0.454698	+	0.535312i	0.486270	+	0.873809i	$0.338357\pi$
$882$		0			0
$883$	1.53759	−	0.711363i	0.0517439	−	0.0239393i	−0.393847	−	0.919176i	$-0.628856\pi$
$883$	1.53759	−	0.711363i	0.0517439	−	0.0239393i	0.445590	+	0.895237i	$0.352994\pi$
$884$		0			0
$885$	75.8605	−	13.9816i	2.55002	−	0.469988i
$886$		0			0
$887$	−33.4483	+	15.4748i	−1.12308	+	0.519594i	−0.891409	−	0.453199i	$-0.850283\pi$
$887$	−33.4483	+	15.4748i	−1.12308	+	0.519594i	−0.231675	+	0.972793i	$0.574421\pi$
$888$		0			0
$889$	−4.49791	+	5.29535i	−0.150855	+	0.177600i
$890$		0			0
$891$	−46.4266	+	5.04919i	−1.55535	+	0.169154i
$892$		0			0
$893$	−7.98158	+	28.7470i	−0.267093	+	0.961983i
$894$		0			0
$895$	−58.7300	−	6.38727i	−1.96313	−	0.213503i
$896$		0			0
$897$	9.03266	−	5.43477i	0.301592	−	0.181462i
$898$		0			0
$899$	13.0251	+	32.6906i	0.434412	+	1.09029i
$900$		0			0
$901$	1.20544	+	7.35287i	0.0401591	+	0.244960i
$902$		0			0
$903$	7.50011	+	1.65090i	0.249588	+	0.0549385i
$904$		0			0
$905$	−74.0865	+	24.9626i	−2.46272	+	0.829786i
$906$		0			0
$907$	−3.16656	−	11.4049i	−0.105144	−	0.378694i	0.892191	−	0.451659i	$-0.149168\pi$
$907$	−3.16656	−	11.4049i	−0.105144	−	0.378694i	−0.997334	+	0.0729651i	$0.976754\pi$
$908$		0			0
$909$	−32.5090	+	47.9471i	−1.07825	+	1.59031i
$910$		0			0
$911$	21.2453	−	40.0729i	0.703888	−	1.32767i	−0.231078	−	0.972935i	$-0.574225\pi$
$911$	21.2453	−	40.0729i	0.703888	−	1.32767i	0.934966	−	0.354738i	$-0.115430\pi$
$912$		0			0
$913$	−16.2864	−	15.4273i	−0.539001	−	0.510569i
$914$		0			0
$915$	106.948	+	49.4795i	3.53560	+	1.63574i
$916$		0			0
$917$	3.94905	+	5.82441i	0.130409	+	0.192339i
$918$		0			0
$919$	27.1248	+	51.1628i	0.894764	+	1.68770i	0.709121	+	0.705086i	$0.249092\pi$
$919$	27.1248	+	51.1628i	0.894764	+	1.68770i	0.185643	+	0.982617i	$0.440563\pi$
$920$		0			0
$921$	−14.4261	+	3.17542i	−0.475356	+	0.104634i
$922$		0			0
$923$	−6.47426	+	16.2492i	−0.213103	+	0.534848i
$924$		0			0
$925$	5.24368	−	4.96708i	0.172411	−	0.163317i
$926$		0			0
$927$	−0.197211	−	3.63734i	−0.00647725	−	0.119466i
$928$		0			0
$929$	3.14956	+	3.70795i	0.103334	+	0.121654i	0.811398	−	0.584494i	$-0.198707\pi$
$929$	3.14956	+	3.70795i	0.103334	+	0.121654i	−0.708064	+	0.706148i	$0.750431\pi$
$930$		0			0
$931$	21.7130	−	16.5058i	0.711614	−	0.540955i
$932$		0			0
$933$	−11.9709	+	73.0190i	−0.391908	+	2.39054i
$934$		0			0
$935$	34.3966	+	26.1476i	1.12489	+	0.855119i
$936$		0			0
$937$	−1.98456	+	36.6030i	−0.0648326	+	1.19577i	0.767336	+	0.641245i	$0.221582\pi$
$937$	−1.98456	+	36.6030i	−0.0648326	+	1.19577i	−0.832169	+	0.554522i	$0.812901\pi$
$938$		0			0
$939$	88.6609	+	53.3455i	2.89334	+	1.74086i
$940$		0			0
$941$	35.8735	+	12.0872i	1.16944	+	0.394031i	0.835995	−	0.548737i	$-0.184891\pi$
$941$	35.8735	+	12.0872i	1.16944	+	0.394031i	0.333448	+	0.942769i	$0.391788\pi$
$942$		0			0
$943$	−6.97629			−0.227179
$944$		0			0
$945$	−28.7877			−0.936464
$946$		0			0
$947$	29.5903	+	9.97014i	0.961556	+	0.323986i	0.755936	−	0.654646i	$-0.227182\pi$
$947$	29.5903	+	9.97014i	0.961556	+	0.323986i	0.205620	+	0.978632i	$0.434079\pi$
$948$		0			0
$949$	17.3322	+	10.4284i	0.562626	+	0.338521i
$950$		0			0
$951$	−3.63682	+	67.0773i	−0.117932	+	2.17513i
$952$		0			0
$953$	15.7000	+	11.9349i	0.508574	+	0.386608i	0.827758	−	0.561085i	$-0.189616\pi$
$953$	15.7000	+	11.9349i	0.508574	+	0.386608i	−0.319184	+	0.947693i	$0.603409\pi$
$954$		0			0
$955$	2.62420	−	16.0069i	0.0849172	−	0.517972i
$956$		0			0
$957$	−41.1435	+	31.2765i	−1.32998	+	1.01103i
$958$		0			0
$959$	−4.53971	−	5.34456i	−0.146595	−	0.172585i
$960$		0			0
$961$	1.88061	+	34.6858i	0.0606648	+	1.11890i
$962$		0			0
$963$	−21.4962	+	20.3623i	−0.692705	+	0.656165i
$964$		0			0
$965$	−23.2812	+	58.4314i	−0.749449	+	1.88097i
$966$		0			0
$967$	−21.6134	+	4.75746i	−0.695039	+	0.152990i	−0.548420	−	0.836203i	$-0.684770\pi$
$967$	−21.6134	+	4.75746i	−0.695039	+	0.152990i	−0.146620	+	0.989193i	$0.546839\pi$
$968$		0			0
$969$	−20.9970	−	39.6045i	−0.674520	−	1.27228i
$970$		0			0
$971$	2.95958	+	4.36506i	0.0949775	+	0.140081i	0.872209	−	0.489133i	$-0.162687\pi$
$971$	2.95958	+	4.36506i	0.0949775	+	0.140081i	−0.777231	+	0.629215i	$0.783377\pi$
$972$		0			0
$973$	−3.34225	−	1.54629i	−0.107148	−	0.0495717i
$974$		0			0
$975$	21.2860	+	20.1632i	0.681698	+	0.645739i
$976$		0			0
$977$	2.72270	−	5.13555i	0.0871068	−	0.164301i	−0.836131	−	0.548530i	$-0.815188\pi$
$977$	2.72270	−	5.13555i	0.0871068	−	0.164301i	0.923238	+	0.384229i	$0.125533\pi$
$978$		0			0
$979$	−5.41714	+	7.98968i	−0.173132	+	0.255351i
$980$		0			0
$981$	−7.70749	−	27.7599i	−0.246081	−	0.886305i
$982$		0			0
$983$	−46.3529	+	15.6181i	−1.47843	+	0.498140i	−0.939007	−	0.343898i	$-0.888253\pi$
$983$	−46.3529	+	15.6181i	−1.47843	+	0.498140i	−0.539419	+	0.842037i	$0.681356\pi$
$984$		0			0
$985$	29.2491	+	6.43820i	0.931952	+	0.205138i
$986$		0			0
$987$	2.91809	+	17.7996i	0.0928839	+	0.566567i
$988$		0			0
$989$	2.25684	+	5.66423i	0.0717632	+	0.180112i
$990$		0			0
$991$	−8.32741	+	5.01044i	−0.264529	+	0.159162i	−0.641639	−	0.767007i	$-0.721745\pi$
$991$	−8.32741	+	5.01044i	−0.264529	+	0.159162i	0.377110	+	0.926168i	$0.376918\pi$
$992$		0			0
$993$	−5.77431	−	0.627994i	−0.183242	−	0.0199288i
$994$		0			0
$995$	−8.34320	+	30.0495i	−0.264497	+	0.952633i
$996$		0			0
$997$	−2.19246	+	0.238444i	−0.0694359	+	0.00755161i	−0.142771	−	0.989756i	$-0.545601\pi$
$997$	−2.19246	+	0.238444i	−0.0694359	+	0.00755161i	0.0733351	+	0.997307i	$0.476636\pi$
$998$		0			0
$999$	−8.13688	+	9.57948i	−0.257440	+	0.303081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	944.2.m.c.593.1		112
4.3	odd	2		59.2.c.a.3.3	✓	112
12.11	even	2		531.2.i.a.298.2		112
59.20	even	29	inner	944.2.m.c.433.1		112
236.43	even	58		3481.2.a.q.1.30		56
236.75	odd	58		3481.2.a.p.1.27		56
236.79	odd	58		59.2.c.a.20.3	yes	112
708.551	even	58		531.2.i.a.433.2		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.c.a.3.3	✓	112	4.3	odd	2
59.2.c.a.20.3	yes	112	236.79	odd	58
531.2.i.a.298.2		112	12.11	even	2
531.2.i.a.433.2		112	708.551	even	58
944.2.m.c.433.1		112	59.20	even	29	inner
944.2.m.c.593.1		112	1.1	even	1	trivial
3481.2.a.p.1.27		56	236.75	odd	58
3481.2.a.q.1.30		56	236.43	even	58

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:	\( N \)	\(=\)	\( 944 = 2^{4} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	944.m (of order \(29\), degree \(28\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.89290 - 0.974731i) q^{3} +(-2.81882 - 1.69603i) q^{5} +(-0.0467597 + 0.862432i) q^{7} +(5.03048 + 3.82407i) q^{9} +O(q^{10})\)	\(q+(-2.89290 - 0.974731i) q^{3} +(-2.81882 - 1.69603i) q^{5} +(-0.0467597 + 0.862432i) q^{7} +(5.03048 + 3.82407i) q^{9} +(-0.631059 + 3.84929i) q^{11} +(-1.31325 + 0.998305i) q^{13} +(6.50140 + 7.65404i) q^{15} +(0.182290 + 3.36214i) q^{17} +(3.16614 - 2.99913i) q^{19} +(0.975910 - 2.44935i) q^{21} +(2.04440 - 0.450007i) q^{23} +(2.72721 + 5.14406i) q^{25} +(-5.68582 - 8.38596i) q^{27} +(-3.93910 - 1.82242i) q^{29} +(-5.88624 - 5.57574i) q^{31} +(5.57761 - 10.5205i) q^{33} +(1.59452 - 2.35174i) q^{35} +(-0.331878 - 1.19532i) q^{37} +(4.77217 - 1.60793i) q^{39} +(-3.25469 - 0.716412i) q^{41} +(0.471222 + 2.87433i) q^{43} +(-7.69430 - 19.3112i) q^{45} +(-5.86181 + 3.52693i) q^{47} +(6.21736 + 0.676179i) q^{49} +(2.74983 - 9.90400i) q^{51} +(2.19994 - 0.239258i) q^{53} +(8.30736 - 9.78018i) q^{55} +(-12.0827 + 5.59003i) q^{57} +(3.82919 - 6.65863i) q^{59} +(10.6495 - 4.92699i) q^{61} +(-3.53322 + 4.15963i) q^{63} +(5.39497 - 0.586739i) q^{65} +(-1.13948 + 4.10403i) q^{67} +(-6.35288 - 0.690918i) q^{69} +(9.08556 - 5.46660i) q^{71} +(-4.53863 - 11.3911i) q^{73} +(-2.87546 - 17.5395i) q^{75} +(-3.29024 - 0.724237i) q^{77} +(9.88675 - 3.33123i) q^{79} +(3.20295 + 11.5360i) q^{81} +(-3.22744 + 4.76012i) q^{83} +(5.18844 - 9.78644i) q^{85} +(9.61904 + 9.11164i) q^{87} +(2.24597 + 1.03910i) q^{89} +(-0.799563 - 1.17927i) q^{91} +(11.5934 + 21.8676i) q^{93} +(-14.0114 + 3.08414i) q^{95} +(3.53517 - 8.87260i) q^{97} +(-17.8945 + 16.9506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9}+O(q^{10}) \) 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9	\( 112 q + 23 q^{3} - 25 q^{5} + 23 q^{7} - 21 q^{9} + 15 q^{11} - 23 q^{13} - 4 q^{15} - 10 q^{17} + 15 q^{19} - 12 q^{21} - 3 q^{23} - 5 q^{25} - 22 q^{27} - 13 q^{29} - 3 q^{31} + 33 q^{33} - 28 q^{35} - 9 q^{37} - 45 q^{39} + 23 q^{41} - 19 q^{43} + 19 q^{45} - 10 q^{47} - 31 q^{49} + 61 q^{51} - 23 q^{53} + 24 q^{55} - 91 q^{57} + 33 q^{59} - 47 q^{61} + 58 q^{63} - 16 q^{65} + 19 q^{67} - 45 q^{69} + 18 q^{71} + 24 q^{73} - 58 q^{75} + 65 q^{77} - 41 q^{79} + 95 q^{81} - 49 q^{83} + 39 q^{85} - 80 q^{87} + 51 q^{89} - 77 q^{91} + 93 q^{93} - 65 q^{95} + 91 q^{97} - 44 q^{99}+O(q^{100}) \) 112 * q + 23 * q^3 - 25 * q^5 + 23 * q^7 - 21 * q^9 + 15 * q^11 - 23 * q^13 - 4 * q^15 - 10 * q^17 + 15 * q^19 - 12 * q^21 - 3 * q^23 - 5 * q^25 - 22 * q^27 - 13 * q^29 - 3 * q^31 + 33 * q^33 - 28 * q^35 - 9 * q^37 - 45 * q^39 + 23 * q^41 - 19 * q^43 + 19 * q^45 - 10 * q^47 - 31 * q^49 + 61 * q^51 - 23 * q^53 + 24 * q^55 - 91 * q^57 + 33 * q^59 - 47 * q^61 + 58 * q^63 - 16 * q^65 + 19 * q^67 - 45 * q^69 + 18 * q^71 + 24 * q^73 - 58 * q^75 + 65 * q^77 - 41 * q^79 + 95 * q^81 - 49 * q^83 + 39 * q^85 - 80 * q^87 + 51 * q^89 - 77 * q^91 + 93 * q^93 - 65 * q^95 + 91 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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