LMFDB - Embedded newform 396.2.r.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(19,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("396.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$396 = 2^{2} \cdot 3^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	396.r (of order $10$ , degree $4$ , 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256$ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.4
Root			$1.40958 + 0.114404i$ of defining polynomial
Character	$\chi$	$=$	396.19
Dual form			396.2.r.a.271.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40958 - 0.114404i) q^{2} +(1.97382 - 0.322523i) q^{4} +(-1.09089 - 0.792578i) q^{5} +(0.503194 - 1.54867i) q^{7} +(2.74536 - 0.680436i) q^{8} +(-1.62837 - 0.992398i) q^{10} +(3.29726 - 0.357912i) q^{11} +(-2.09089 - 2.87786i) q^{13} +(0.532117 - 2.24054i) q^{14} +(3.79196 - 1.27321i) q^{16} +(0.0411247 - 0.0566033i) q^{17} +(2.45716 + 7.56236i) q^{19} +(-2.40885 - 1.21257i) q^{20} +(4.60680 - 0.881725i) q^{22} +5.30988i q^{23} +(-0.983224 - 3.02605i) q^{25} +(-3.27651 - 3.81737i) q^{26} +(0.493733 - 3.21909i) q^{28} +(-3.74364 - 1.21638i) q^{29} +(-2.17121 - 2.98842i) q^{31} +(5.19940 - 2.22850i) q^{32} +(0.0514928 - 0.0844916i) q^{34} +(-1.77637 + 1.29061i) q^{35} +(-2.12561 + 6.54194i) q^{37} +(4.32873 + 10.3786i) q^{38} +(-3.53418 - 1.43363i) q^{40} +(-5.50305 + 1.78805i) q^{41} +1.89516 q^{43} +(6.39277 - 1.76990i) q^{44} +(0.607472 + 7.48469i) q^{46} +(-9.32545 + 3.03002i) q^{47} +(3.51794 + 2.55593i) q^{49} +(-1.73212 - 4.15297i) q^{50} +(-5.05523 - 5.00603i) q^{52} +(-3.14518 + 2.28511i) q^{53} +(-3.88062 - 2.22289i) q^{55} +(0.327678 - 4.59405i) q^{56} +(-5.41611 - 1.28630i) q^{58} +(4.62366 + 1.50232i) q^{59} +(0.791173 - 1.08896i) q^{61} +(-3.40238 - 3.96401i) q^{62} +(7.07402 - 3.73608i) q^{64} +4.79662i q^{65} +4.91303i q^{67} +(0.0629170 - 0.124989i) q^{68} +(-2.35628 + 2.02244i) q^{70} +(4.10014 - 5.64335i) q^{71} +(-9.62677 - 3.12793i) q^{73} +(-2.24778 + 9.46456i) q^{74} +(7.28904 + 14.1343i) q^{76} +(1.10487 - 5.28646i) q^{77} +(4.85779 - 3.52939i) q^{79} +(-5.14572 - 1.61649i) q^{80} +(-7.55242 + 3.14997i) q^{82} +(-2.92211 - 2.12304i) q^{83} +(-0.0897250 + 0.0291534i) q^{85} +(2.67138 - 0.216814i) q^{86} +(8.80862 - 3.22617i) q^{88} +5.39711 q^{89} +(-5.50899 + 1.78998i) q^{91} +(1.71256 + 10.4808i) q^{92} +(-12.7983 + 5.33792i) q^{94} +(3.31327 - 10.1972i) q^{95} +(-5.92705 + 4.30625i) q^{97} +(5.25122 + 3.20032i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 5 q^{2} - q^{4} + 6 q^{5} + 5 q^{8} - 10 q^{13} - 8 q^{14} + 23 q^{16} + 10 q^{17} - 16 q^{20} + 17 q^{22} + 6 q^{25} + 4 q^{26} + 20 q^{28} + 10 q^{29} - 6 q^{34} + 18 q^{37} + 38 q^{38} - 40 q^{40}+ \cdots - 68 q^{97}+O(q^{100})$ 16 * q + 5 * q^2 - q^4 + 6 * q^5 + 5 * q^8 - 10 * q^13 - 8 * q^14 + 23 * q^16 + 10 * q^17 - 16 * q^20 + 17 * q^22 + 6 * q^25 + 4 * q^26 + 20 * q^28 + 10 * q^29 - 6 * q^34 + 18 * q^37 + 38 * q^38 - 40 * q^40 - 10 * q^41 + 28 * q^44 - 30 * q^46 + 6 * q^49 + 15 * q^50 - 10 * q^52 - 38 * q^53 + 12 * q^56 + 30 * q^58 - 10 * q^61 - 70 * q^62 + 23 * q^64 - 60 * q^68 + 12 * q^70 - 30 * q^73 - 40 * q^74 - 2 * q^77 + 28 * q^80 - 59 * q^82 - 50 * q^85 + 39 * q^86 - 53 * q^88 + 36 * q^89 - 36 * q^92 - 30 * q^94 - 68 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$ .

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.40958	−	0.114404i	0.996723	−	0.0808960i
$2$	1.40958	−	0.114404i	0.996723	−	0.0808960i
$3$		0			0
$3$		0			0
$4$	1.97382	−	0.322523i	0.986912	−	0.161262i
$5$	−1.09089	−	0.792578i	−0.487861	−	0.354452i	0.316500	−	0.948592i	$-0.397492\pi$
$5$	−1.09089	−	0.792578i	−0.487861	−	0.354452i	−0.804361	+	0.594141i	$0.797492\pi$
$6$		0			0
$7$	0.503194	−	1.54867i	0.190189	−	0.585343i	−0.809810	−	0.586693i	$-0.800430\pi$
$7$	0.503194	−	1.54867i	0.190189	−	0.585343i	0.999999	+	0.00134995i	$0.000429701\pi$
$8$	2.74536	−	0.680436i	0.970632	−	0.240570i
$9$		0			0
$10$	−1.62837	−	0.992398i	−0.514936	−	0.313824i
$11$	3.29726	−	0.357912i	0.994160	−	0.107915i
$11$	3.29726	−	0.357912i	0.994160	−	0.107915i
$12$		0			0
$13$	−2.09089	−	2.87786i	−0.579909	−	0.798176i	0.413777	−	0.910378i	$-0.364209\pi$
$13$	−2.09089	−	2.87786i	−0.579909	−	0.798176i	−0.993685	+	0.112203i	$0.964209\pi$
$14$	0.532117	−	2.24054i	0.142214	−	0.598810i
$15$		0			0
$16$	3.79196	−	1.27321i	0.947989	−	0.318302i
$17$	0.0411247	−	0.0566033i	0.00997420	−	0.0137283i	−0.804001	−	0.594628i	$-0.797299\pi$
$17$	0.0411247	−	0.0566033i	0.00997420	−	0.0137283i	0.813975	+	0.580900i	$0.197299\pi$
$18$		0			0
$19$	2.45716	+	7.56236i	0.563711	+	1.73493i	0.671749	+	0.740778i	$0.265543\pi$
$19$	2.45716	+	7.56236i	0.563711	+	1.73493i	−0.108038	+	0.994147i	$0.534457\pi$
$20$	−2.40885	−	1.21257i	−0.538635	−	0.271139i
$21$		0			0
$22$	4.60680	−	0.881725i	0.982172	−	0.187984i
$23$			5.30988i			1.10719i	0.832787	+	0.553593i	$0.186744\pi$
$23$			5.30988i			1.10719i	−0.832787	+	0.553593i	$0.813256\pi$
$24$		0			0
$25$	−0.983224	−	3.02605i	−0.196645	−	0.605210i
$26$	−3.27651	−	3.81737i	−0.642577	−	0.748647i
$27$		0			0
$28$	0.493733	−	3.21909i	0.0933068	−	0.608352i
$29$	−3.74364	−	1.21638i	−0.695177	−	0.225877i	−0.0599489	−	0.998201i	$-0.519094\pi$
$29$	−3.74364	−	1.21638i	−0.695177	−	0.225877i	−0.635228	+	0.772325i	$0.719094\pi$
$30$		0			0
$31$	−2.17121	−	2.98842i	−0.389961	−	0.536735i	0.568228	−	0.822871i	$-0.307629\pi$
$31$	−2.17121	−	2.98842i	−0.389961	−	0.536735i	−0.958189	+	0.286136i	$0.907629\pi$
$32$	5.19940	−	2.22850i	0.919133	−	0.393947i
$33$		0			0
$34$	0.0514928	−	0.0844916i	0.00883095	−	0.0144902i
$35$	−1.77637	+	1.29061i	−0.300262	+	0.218153i
$36$		0			0
$37$	−2.12561	+	6.54194i	−0.349448	+	1.07549i	0.609712	+	0.792623i	$0.291285\pi$
$37$	−2.12561	+	6.54194i	−0.349448	+	1.07549i	−0.959159	+	0.282866i	$0.908715\pi$
$38$	4.32873	+	10.3786i	0.702212	+	1.68364i
$39$		0			0
$40$	−3.53418	−	1.43363i	−0.558804	−	0.226677i
$41$	−5.50305	+	1.78805i	−0.859432	+	0.279246i	−0.705391	−	0.708818i	$-0.749229\pi$
$41$	−5.50305	+	1.78805i	−0.859432	+	0.279246i	−0.154041	+	0.988065i	$0.549229\pi$
$42$		0			0
$43$	1.89516			0.289009			0.144505	−	0.989504i	$-0.453841\pi$
$43$	1.89516			0.289009			0.144505	+	0.989504i	$0.453841\pi$
$44$	6.39277	−	1.76990i	0.963746	−	0.266822i
$45$		0			0
$46$	0.607472	+	7.48469i	0.0895669	+	1.10356i
$47$	−9.32545	+	3.03002i	−1.36026	+	0.441974i	−0.896129	−	0.443794i	$-0.853632\pi$
$47$	−9.32545	+	3.03002i	−1.36026	+	0.441974i	−0.464128	+	0.885768i	$0.653632\pi$
$48$		0			0
$49$	3.51794	+	2.55593i	0.502563	+	0.365133i
$50$	−1.73212	−	4.15297i	−0.244959	−	0.587319i
$51$		0			0
$52$	−5.05523	−	5.00603i	−0.701034	−	0.694212i
$53$	−3.14518	+	2.28511i	−0.432023	+	0.313883i	−0.782457	−	0.622704i	$-0.786034\pi$
$53$	−3.14518	+	2.28511i	−0.432023	+	0.313883i	0.350434	+	0.936587i	$0.386034\pi$
$54$		0			0
$55$	−3.88062	−	2.22289i	−0.523262	−	0.299734i
$56$	0.327678	−	4.59405i	0.0437878	−	0.613906i
$57$		0			0
$58$	−5.41611	−	1.28630i	−0.711171	−	0.168899i
$59$	4.62366	+	1.50232i	0.601950	+	0.195585i	0.594110	−	0.804384i	$-0.297504\pi$
$59$	4.62366	+	1.50232i	0.601950	+	0.195585i	0.00783982	+	0.999969i	$0.497504\pi$
$60$		0			0
$61$	0.791173	−	1.08896i	0.101299	−	0.139427i	−0.755358	−	0.655312i	$-0.772537\pi$
$61$	0.791173	−	1.08896i	0.101299	−	0.139427i	0.856657	+	0.515886i	$0.172537\pi$
$62$	−3.40238	−	3.96401i	−0.432103	−	0.503430i
$63$		0			0
$64$	7.07402	−	3.73608i	0.884252	−	0.467010i
$65$			4.79662i			0.594948i
$66$		0			0
$67$			4.91303i			0.600223i	0.953904	+	0.300111i	$0.0970238\pi$
$67$			4.91303i			0.600223i	−0.953904	+	0.300111i	$0.902976\pi$
$68$	0.0629170	−	0.124989i	0.00762981	−	0.0151571i
$69$		0			0
$70$	−2.35628	+	2.02244i	−0.281630	+	0.241728i
$71$	4.10014	−	5.64335i	0.486597	−	0.669743i	−0.493159	−	0.869939i	$-0.664158\pi$
$71$	4.10014	−	5.64335i	0.486597	−	0.669743i	0.979756	+	0.200196i	$0.0641580\pi$
$72$		0			0
$73$	−9.62677	−	3.12793i	−1.12673	−	0.366096i	−0.314397	−	0.949292i	$-0.601802\pi$
$73$	−9.62677	−	3.12793i	−1.12673	−	0.366096i	−0.812332	+	0.583195i	$0.801802\pi$
$74$	−2.24778	+	9.46456i	−0.261300	+	1.10023i
$75$		0			0
$76$	7.28904	+	14.1343i	0.836110	+	1.62131i
$77$	1.10487	−	5.28646i	0.125912	−	0.602449i
$78$		0			0
$79$	4.85779	−	3.52939i	0.546544	−	0.397088i	−0.279966	−	0.960010i	$-0.590323\pi$
$79$	4.85779	−	3.52939i	0.546544	−	0.397088i	0.826510	+	0.562923i	$0.190323\pi$
$80$	−5.14572	−	1.61649i	−0.575309	−	0.180729i
$81$		0			0
$82$	−7.55242	+	3.14997i	−0.834025	+	0.347856i
$83$	−2.92211	−	2.12304i	−0.320744	−	0.233034i	0.415749	−	0.909479i	$-0.363519\pi$
$83$	−2.92211	−	2.12304i	−0.320744	−	0.233034i	−0.736493	+	0.676446i	$0.763519\pi$
$84$		0			0
$85$	−0.0897250	+	0.0291534i	−0.00973205	+	0.00316213i
$86$	2.67138	−	0.216814i	0.288062	−	0.0233797i
$87$		0			0
$88$	8.80862	−	3.22617i	0.939002	−	0.343911i
$89$	5.39711			0.572093			0.286046	−	0.958216i	$-0.407659\pi$
$89$	5.39711			0.572093			0.286046	+	0.958216i	$0.407659\pi$
$90$		0			0
$91$	−5.50899	+	1.78998i	−0.577499	+	0.187641i
$92$	1.71256	+	10.4808i	0.178547	+	1.09269i
$93$		0			0
$94$	−12.7983	+	5.33792i	−1.32004	+	0.550565i
$95$	3.31327	−	10.1972i	0.339934	−	1.04621i
$96$		0			0
$97$	−5.92705	+	4.30625i	−0.601801	+	0.437234i	−0.846518	−	0.532361i	$-0.821305\pi$
$97$	−5.92705	+	4.30625i	−0.601801	+	0.437234i	0.244717	+	0.969595i	$0.421305\pi$
$98$	5.25122	+	3.20032i	0.530454	+	0.323281i
$99$		0			0
$100$	−2.91668	−	5.65578i	−0.291668	−	0.565578i
$101$	5.62667	+	7.74445i	0.559875	+	0.770602i	0.991311	−	0.131542i	$-0.0419928\pi$
$101$	5.62667	+	7.74445i	0.559875	+	0.770602i	−0.431436	+	0.902144i	$0.641993\pi$
$102$		0			0
$103$	−9.81631	−	3.18951i	−0.967230	−	0.314272i	−0.217533	−	0.976053i	$-0.569801\pi$
$103$	−9.81631	−	3.18951i	−0.967230	−	0.314272i	−0.749697	+	0.661781i	$0.769801\pi$
$104$	−7.69845	−	6.47806i	−0.754895	−	0.635226i
$105$		0			0
$106$	−4.17195	+	3.58086i	−0.405216	+	0.347804i
$107$	3.42303	+	10.5350i	0.330917	+	1.01846i	0.968699	+	0.248240i	$0.0798522\pi$
$107$	3.42303	+	10.5350i	0.330917	+	1.01846i	−0.637782	+	0.770217i	$0.720148\pi$
$108$		0			0
$109$			8.95933i			0.858149i	0.903269	+	0.429074i	$0.141160\pi$
$109$			8.95933i			0.858149i	−0.903269	+	0.429074i	$0.858840\pi$
$110$	−5.72434	−	2.68938i	−0.545795	−	0.256422i
$111$		0			0
$112$	−0.0636912	−	6.51317i	−0.00601825	−	0.615436i
$113$	−3.40631	−	10.4836i	−0.320439	−	0.986210i	−0.973457	−	0.228868i	$-0.926498\pi$
$113$	−3.40631	−	10.4836i	−0.320439	−	0.986210i	0.653018	−	0.757342i	$-0.273502\pi$
$114$		0			0
$115$	4.20849	−	5.79249i	0.392444	−	0.540153i
$116$	−7.78160	−	1.19351i	−0.722503	−	0.110815i
$117$		0			0
$118$	6.68929	+	1.58867i	0.615799	+	0.146249i
$119$	−0.0669662	−	0.0921710i	−0.00613878	−	0.00844931i
$120$		0			0
$121$	10.7438	−	2.36026i	0.976709	−	0.214569i
$122$	0.990640	−	1.62548i	0.0896883	−	0.147164i
$123$		0			0
$124$	−5.24942	−	5.19834i	−0.471412	−	0.466825i
$125$	−3.40921	+	10.4925i	−0.304929	+	0.938474i
$126$		0			0
$127$	8.32668	+	6.04969i	0.738874	+	0.536823i	0.892358	−	0.451328i	$-0.149050\pi$
$127$	8.32668	+	6.04969i	0.738874	+	0.536823i	−0.153485	+	0.988151i	$0.549050\pi$
$128$	9.54396	−	6.07560i	0.843575	−	0.537012i
$129$		0			0
$130$	0.548754	+	6.76122i	0.0481289	+	0.592998i
$131$	−1.86768			−0.163180			−0.0815901	−	0.996666i	$-0.526000\pi$
$131$	−1.86768			−0.163180			−0.0815901	+	0.996666i	$0.526000\pi$
$132$		0			0
$133$	12.9480			1.12274
$134$	0.562072	+	6.92531i	0.0485556	+	0.598255i
$135$		0			0
$136$	0.0743873	−	0.183379i	0.00637865	−	0.0157246i
$137$	−1.01489	−	0.737362i	−0.0867080	−	0.0629971i	0.543587	−	0.839353i	$-0.317066\pi$
$137$	−1.01489	−	0.737362i	−0.0867080	−	0.0629971i	−0.630295	+	0.776356i	$0.717066\pi$
$138$		0			0
$139$	1.94407	−	5.98323i	0.164894	−	0.507491i	−0.834135	−	0.551561i	$-0.814032\pi$
$139$	1.94407	−	5.98323i	0.164894	−	0.507491i	0.999028	+	0.0440698i	$0.0140324\pi$
$140$	−3.08999	+	3.12036i	−0.261152	+	0.263718i
$141$		0			0
$142$	5.13384	−	8.42382i	0.430822	−	0.706912i
$143$	−7.92422	−	8.74070i	−0.662657	−	0.730934i
$144$		0			0
$145$	3.11982	+	4.29407i	0.259087	+	0.356603i
$146$	−13.9275	−	3.30772i	−1.15265	−	0.273749i
$147$		0			0
$148$	−2.08564	+	13.5982i	−0.171439	+	1.11777i
$149$	10.0839	−	13.8792i	0.826102	−	1.13703i	−0.162534	−	0.986703i	$-0.551967\pi$
$149$	10.0839	−	13.8792i	0.826102	−	1.13703i	0.988636	−	0.150329i	$-0.0480332\pi$
$150$		0			0
$151$	−3.75712	−	11.5632i	−0.305750	−	0.941002i	−0.979396	−	0.201948i	$-0.935273\pi$
$151$	−3.75712	−	11.5632i	−0.305750	−	0.941002i	0.673646	−	0.739054i	$-0.264727\pi$
$152$	11.8915	+	19.0895i	0.964528	+	1.54836i
$153$		0			0
$154$	0.952608	−	7.57809i	0.0767633	−	0.610660i
$155$			4.98089i			0.400074i
$156$		0			0
$157$	−1.63833	−	5.04225i	−0.130753	−	0.402415i	0.864153	−	0.503230i	$-0.167855\pi$
$157$	−1.63833	−	5.04225i	−0.130753	−	0.402415i	−0.994905	+	0.100815i	$0.967855\pi$
$158$	6.44366	−	5.53071i	0.512630	−	0.439999i
$159$		0			0
$160$	−7.43824	−	1.68988i	−0.588044	−	0.133597i
$161$	8.22325	+	2.67190i	0.648083	+	0.210575i
$162$		0			0
$163$	5.91168	+	8.13673i	0.463039	+	0.637318i	0.975135	−	0.221610i	$-0.0711311\pi$
$163$	5.91168	+	8.13673i	0.463039	+	0.637318i	−0.512097	+	0.858928i	$0.671131\pi$
$164$	−10.2854	+	5.30415i	−0.803152	+	0.414185i
$165$		0			0
$166$	−4.36183	−	2.65829i	−0.338544	−	0.206323i
$167$	17.7237	−	12.8770i	1.37150	−	0.996451i	0.373879	−	0.927478i	$-0.378028\pi$
$167$	17.7237	−	12.8770i	1.37150	−	0.996451i	0.997618	−	0.0689735i	$-0.0219724\pi$
$168$		0			0
$169$	0.106946	−	0.329146i	0.00822661	−	0.0253189i
$170$	−0.123139	+	0.0513590i	−0.00944435	+	0.00393905i
$171$		0			0
$172$	3.74071	−	0.611233i	0.285226	−	0.0466061i
$173$	11.2531	−	3.65635i	0.855557	−	0.277987i	0.151785	−	0.988413i	$-0.451498\pi$
$173$	11.2531	−	3.65635i	0.855557	−	0.277987i	0.703772	+	0.710426i	$0.251498\pi$
$174$		0			0
$175$	−5.18111			−0.391655
$176$	12.0474	−	5.55528i	0.908104	−	0.418745i
$177$		0			0
$178$	7.60765	−	0.617452i	0.570218	−	0.0462800i
$179$	−0.887979	+	0.288522i	−0.0663707	+	0.0215651i	−0.342014	−	0.939695i	$-0.611109\pi$
$179$	−0.887979	+	0.288522i	−0.0663707	+	0.0215651i	0.275643	+	0.961260i	$0.411109\pi$
$180$		0			0
$181$	−15.2414	−	11.0736i	−1.13289	−	0.823091i	−0.146775	−	0.989170i	$-0.546889\pi$
$181$	−15.2414	−	11.0736i	−1.13289	−	0.823091i	−0.986113	+	0.166079i	$0.946889\pi$
$182$	−7.56057	+	3.15337i	−0.560427	+	0.233743i
$183$		0			0
$184$	3.61303	+	14.5775i	0.266356	+	1.07467i
$185$	7.50380	−	5.45183i	0.551691	−	0.400827i
$186$		0			0
$187$	0.115340	−	0.201355i	0.00843447	−	0.0147245i
$188$	−17.4295	+	8.98840i	−1.27118	+	0.655547i
$189$		0			0
$190$	3.50371	−	14.7528i	0.254186	−	1.07028i
$191$	−19.4435	−	6.31757i	−1.40688	−	0.457124i	−0.495472	−	0.868624i	$-0.665005\pi$
$191$	−19.4435	−	6.31757i	−1.40688	−	0.457124i	−0.911410	+	0.411500i	$0.865005\pi$
$192$		0			0
$193$	10.1927	−	14.0291i	0.733690	−	1.00984i	−0.265267	−	0.964175i	$-0.585460\pi$
$193$	10.1927	−	14.0291i	0.733690	−	1.00984i	0.998957	−	0.0456628i	$-0.0145400\pi$
$194$	−7.86199	+	6.74808i	−0.564458	+	0.484484i
$195$		0			0
$196$	7.76814	+	3.91034i	0.554867	+	0.279310i
$197$		−	3.49133i		−	0.248747i	−0.992235	−	0.124374i	$-0.960308\pi$
$197$		−	3.49133i		−	0.248747i	0.992235	−	0.124374i	$-0.0396921\pi$
$198$		0			0
$199$			11.2660i			0.798625i	0.916815	+	0.399313i	$0.130751\pi$
$199$			11.2660i			0.798625i	−0.916815	+	0.399313i	$0.869249\pi$
$200$	−4.75834	−	7.63859i	−0.336465	−	0.540130i
$201$		0			0
$202$	8.81724	+	10.2727i	0.620379	+	0.722785i
$203$	−3.76755	+	5.18559i	−0.264430	+	0.363957i
$204$		0			0
$205$	7.42039	+	2.41103i	0.518262	+	0.168394i
$206$	−14.2018	−	3.37284i	−0.989483	−	0.234997i
$207$		0			0
$208$	−11.5927	−	8.25060i	−0.803808	−	0.572076i
$209$	10.8086	+	24.0556i	0.747643	+	1.66396i
$210$		0			0
$211$	−2.21909	+	1.61227i	−0.152769	+	0.110993i	−0.661544	−	0.749906i	$-0.730098\pi$
$211$	−2.21909	+	1.61227i	−0.152769	+	0.110993i	0.508775	+	0.860899i	$0.330098\pi$
$212$	−5.47103	+	5.52479i	−0.375752	+	0.379444i
$213$		0			0
$214$	6.03028	+	14.4583i	0.412221	+	0.988349i
$215$	−2.06741	−	1.50206i	−0.140996	−	0.102440i
$216$		0			0
$217$	−5.72061	+	1.85874i	−0.388341	+	0.126180i
$218$	1.02499	+	12.6289i	0.0694207	+	0.855336i
$219$		0			0
$220$	−8.37659	−	3.13600i	−0.564749	−	0.211429i
$221$	−0.248884			−0.0167417
$222$		0			0
$223$	−22.5646	+	7.33167i	−1.51103	+	0.490965i	−0.943213	−	0.332187i	$-0.892213\pi$
$223$	−22.5646	+	7.33167i	−1.51103	+	0.490965i	−0.567821	+	0.823152i	$0.692213\pi$
$224$	−0.834911	−	9.17353i	−0.0557848	−	0.612932i
$225$		0			0
$226$	−6.00083	−	14.3877i	−0.399169	−	0.957056i
$227$	−0.247473	+	0.761643i	−0.0164254	+	0.0505520i	−0.958933	−	0.283632i	$-0.908461\pi$
$227$	−0.247473	+	0.761643i	−0.0164254	+	0.0505520i	0.942508	+	0.334184i	$0.108461\pi$
$228$		0			0
$229$	19.0839	−	13.8652i	1.26110	−	0.916241i	0.262286	−	0.964990i	$-0.415524\pi$
$229$	19.0839	−	13.8652i	1.26110	−	0.916241i	0.998811	+	0.0487497i	$0.0155237\pi$
$230$	5.26951	−	8.64644i	0.347461	−	0.570129i
$231$		0			0
$232$	−11.1053	−	0.792103i	−0.729100	−	0.0520041i
$233$	−10.2812	−	14.1509i	−0.673547	−	0.927058i	0.326287	−	0.945271i	$-0.394202\pi$
$233$	−10.2812	−	14.1509i	−0.673547	−	0.927058i	−0.999834	+	0.0182127i	$0.994202\pi$
$234$		0			0
$235$	12.5746	+	4.08572i	0.820274	+	0.266523i
$236$	9.61083	+	1.47407i	0.625611	+	0.0959540i
$237$		0			0
$238$	−0.104939	−	0.122261i	−0.00680217	−	0.00792501i
$239$	2.06577	+	6.35778i	0.133623	+	0.411251i	0.995373	−	0.0960826i	$-0.0306313\pi$
$239$	2.06577	+	6.35778i	0.133623	+	0.411251i	−0.861750	+	0.507333i	$0.830631\pi$
$240$		0			0
$241$		−	4.28655i		−	0.276121i	−0.990424	−	0.138061i	$-0.955913\pi$
$241$		−	4.28655i		−	0.276121i	0.990424	−	0.138061i	$-0.0440868\pi$
$242$	14.8742	−	4.55610i	0.956150	−	0.292877i
$243$		0			0
$244$	1.21042	−	2.40458i	0.0774894	−	0.153937i
$245$	−1.81191	−	5.57648i	−0.115759	−	0.356268i
$246$		0			0
$247$	16.6258	−	22.8834i	1.05787	−	1.45604i
$248$	−7.99418	−	6.72691i	−0.507631	−	0.427159i
$249$		0			0
$250$	−3.60516	+	15.1800i	−0.228011	+	0.960066i
$251$	2.87878	+	3.96230i	0.181707	+	0.250098i	0.890148	−	0.455672i	$-0.150601\pi$
$251$	2.87878	+	3.96230i	0.181707	+	0.250098i	−0.708441	+	0.705770i	$0.750601\pi$
$252$		0			0
$253$	1.90047	+	17.5080i	0.119482	+	1.10072i
$254$	12.4292	+	7.57491i	0.779879	+	0.475292i
$255$		0			0
$256$	12.7579	−	9.65590i	0.797368	−	0.603494i
$257$	3.82696	−	11.7782i	0.238719	−	0.734702i	−0.757887	−	0.652386i	$-0.773768\pi$
$257$	3.82696	−	11.7782i	0.238719	−	0.734702i	0.996606	−	0.0823161i	$-0.0262317\pi$
$258$		0			0
$259$	9.06173	+	6.58373i	0.563068	+	0.409093i
$260$	1.54702	+	9.46769i	0.0959423	+	0.587161i
$261$		0			0
$262$	−2.63265	+	0.213671i	−0.162645	+	0.0132006i
$263$	16.9489			1.04511			0.522556	−	0.852605i	$-0.324979\pi$
$263$	16.9489			1.04511			0.522556	+	0.852605i	$0.324979\pi$
$264$		0			0
$265$	5.24217			0.322024
$266$	18.2513	−	1.48131i	1.11906	−	0.0908249i
$267$		0			0
$268$	1.58457	+	9.69746i	0.0967929	+	0.592367i
$269$	3.19947	+	2.32455i	0.195075	+	0.141730i	0.681035	−	0.732251i	$-0.261530\pi$
$269$	3.19947	+	2.32455i	0.195075	+	0.141730i	−0.485960	+	0.873981i	$0.661530\pi$
$270$		0			0
$271$	7.33528	−	22.5757i	0.445587	−	1.37137i	−0.436252	−	0.899824i	$-0.643695\pi$
$271$	7.33528	−	22.5757i	0.445587	−	1.37137i	0.881839	−	0.471550i	$-0.156305\pi$
$272$	0.0838753	−	0.266998i	0.00508569	−	0.0161891i
$273$		0			0
$274$	−1.51493	−	0.923261i	−0.0915200	−	0.0557763i
$275$	−4.32500	−	9.62576i	−0.260807	−	0.580455i
$276$		0			0
$277$	−8.82329	−	12.1442i	−0.530140	−	0.729675i	0.457012	−	0.889461i	$-0.348920\pi$
$277$	−8.82329	−	12.1442i	−0.530140	−	0.729675i	−0.987152	+	0.159786i	$0.948920\pi$
$278$	2.05581	−	8.65625i	0.123299	−	0.519167i
$279$		0			0
$280$	−3.99860	+	4.75189i	−0.238962	+	0.283980i
$281$	−3.37468	+	4.64485i	−0.201317	+	0.277089i	−0.897724	−	0.440558i	$-0.854781\pi$
$281$	−3.37468	+	4.64485i	−0.201317	+	0.277089i	0.696408	+	0.717647i	$0.254781\pi$
$282$		0			0
$283$	3.45938	+	10.6469i	0.205639	+	0.632890i	0.999687	+	0.0250353i	$0.00796982\pi$
$283$	3.45938	+	10.6469i	0.205639	+	0.632890i	−0.794048	+	0.607855i	$0.792030\pi$
$284$	6.27283	−	12.4614i	0.372224	−	0.739447i
$285$		0			0
$286$	−12.1698	−	11.4141i	−0.719614	−	0.674932i
$287$			9.42215i			0.556172i
$288$		0			0
$289$	5.25178	+	16.1633i	0.308928	+	0.950783i
$290$	4.88889	+	5.69590i	0.287086	+	0.334475i
$291$		0			0
$292$	−20.0104	−	3.06912i	−1.17102	−	0.179607i
$293$	−5.04336	−	1.63869i	−0.294636	−	0.0957331i	0.157969	−	0.987444i	$-0.449505\pi$
$293$	−5.04336	−	1.63869i	−0.294636	−	0.0957331i	−0.452605	+	0.891711i	$0.649505\pi$
$294$		0			0
$295$	−3.85320	−	5.30348i	−0.224342	−	0.308780i
$296$	−1.38419	+	19.4063i	−0.0804542	+	1.12797i
$297$		0			0
$298$	12.6261	−	20.7175i	0.731413	−	1.20013i
$299$	15.2811	−	11.1024i	0.883729	−	0.642066i
$300$		0			0
$301$	0.953632	−	2.93498i	0.0549664	−	0.169169i
$302$	−6.61883	−	15.8694i	−0.380871	−	0.913184i
$303$		0			0
$304$	18.9459	+	25.5477i	1.08662	+	1.46526i
$305$	−1.72617	+	0.560865i	−0.0988400	+	0.0321150i
$306$		0			0
$307$	−2.27014			−0.129564			−0.0647820	−	0.997899i	$-0.520635\pi$
$307$	−2.27014			−0.129564			−0.0647820	+	0.997899i	$0.520635\pi$
$308$	0.475811	−	10.7909i	0.0271119	−	0.614868i
$309$		0			0
$310$	0.569834	+	7.02095i	0.0323644	+	0.398763i
$311$	−19.1795	+	6.23180i	−1.08757	+	0.353373i	−0.797307	−	0.603574i	$-0.793743\pi$
$311$	−19.1795	+	6.23180i	−1.08757	+	0.353373i	−0.290263	+	0.956947i	$0.593743\pi$
$312$		0			0
$313$	−1.24741	−	0.906296i	−0.0705078	−	0.0512269i	0.551973	−	0.833862i	$-0.313875\pi$
$313$	−1.24741	−	0.906296i	−0.0705078	−	0.0512269i	−0.622481	+	0.782635i	$0.713875\pi$
$314$	−2.88620	−	6.92001i	−0.162878	−	0.390519i
$315$		0			0
$316$	8.45011	−	8.53314i	0.475356	−	0.480027i
$317$	−13.6418	+	9.91136i	−0.766201	+	0.556678i	−0.900806	−	0.434222i	$-0.857023\pi$
$317$	−13.6418	+	9.91136i	−0.766201	+	0.556678i	0.134605	+	0.990899i	$0.457023\pi$
$318$		0			0
$319$	−12.7791	−	2.67083i	−0.715492	−	0.149538i
$320$	−10.6781	−	1.53105i	−0.596924	−	0.0855885i
$321$		0			0
$322$	11.8970	+	2.82547i	0.662994	+	0.157458i
$323$	0.529105	+	0.171917i	0.0294402	+	0.00956569i
$324$		0			0
$325$	−6.65275	+	9.15673i	−0.369028	+	0.507924i
$326$	9.26386	+	10.7930i	0.513077	+	0.597771i
$327$		0			0
$328$	−13.8912	+	8.65331i	−0.767014	+	0.477799i
$329$			15.9667i			0.880275i
$330$		0			0
$331$			33.9735i			1.86735i	0.358115	+	0.933677i	$0.383419\pi$
$331$			33.9735i			1.86735i	−0.358115	+	0.933677i	$0.616581\pi$
$332$	−6.45246	−	3.24805i	−0.354125	−	0.178260i
$333$		0			0
$334$	23.5097	−	20.1788i	1.28639	−	1.10413i
$335$	3.89396	−	5.35958i	0.212750	−	0.292825i
$336$		0			0
$337$	−16.2590	−	5.28286i	−0.885683	−	0.287776i	−0.169368	−	0.985553i	$-0.554173\pi$
$337$	−16.2590	−	5.28286i	−0.885683	−	0.287776i	−0.716315	+	0.697777i	$0.754173\pi$
$338$	0.113093	−	0.476192i	0.00615145	−	0.0259014i
$339$		0			0
$340$	−0.167699	+	0.0864821i	−0.00909474	+	0.00469015i
$341$	−8.22863	−	9.07647i	−0.445605	−	0.491518i
$342$		0			0
$343$	14.9502	−	10.8619i	0.807232	−	0.586489i
$344$	5.20290	−	1.28953i	0.280521	−	0.0695270i
$345$		0			0
$346$	15.4438	−	6.44132i	0.830265	−	0.346287i
$347$	2.02180	+	1.46893i	0.108536	+	0.0788561i	0.640729	−	0.767767i	$-0.278632\pi$
$347$	2.02180	+	1.46893i	0.108536	+	0.0788561i	−0.532193	+	0.846623i	$0.678632\pi$
$348$		0			0
$349$	−6.66811	+	2.16660i	−0.356936	+	0.115975i	−0.481995	−	0.876174i	$-0.660088\pi$
$349$	−6.66811	+	2.16660i	−0.356936	+	0.115975i	0.125060	+	0.992149i	$0.460088\pi$
$350$	−7.30318	+	0.592741i	−0.390372	+	0.0316833i
$351$		0			0
$352$	16.3462	−	9.20887i	0.871253	−	0.490835i
$353$	−17.9431			−0.955017			−0.477509	−	0.878627i	$-0.658460\pi$
$353$	−17.9431			−0.955017			−0.477509	+	0.878627i	$0.658460\pi$
$354$		0			0
$355$	−8.94560	+	2.90660i	−0.474783	+	0.154266i
$356$	10.6529	−	1.74069i	0.564605	−	0.0922566i
$357$		0			0
$358$	−1.21867	+	0.508283i	−0.0644086	+	0.0268636i
$359$	2.99112	−	9.20572i	0.157865	−	0.485859i	−0.840575	−	0.541696i	$-0.817783\pi$
$359$	2.99112	−	9.20572i	0.157865	−	0.485859i	0.998440	+	0.0558363i	$0.0177825\pi$
$360$		0			0
$361$	−35.7804	+	25.9960i	−1.88318	+	1.36821i
$362$	−22.7509	−	13.8654i	−1.19576	−	0.728748i
$363$		0			0
$364$	−10.2965	+	5.30988i	−0.539681	+	0.278313i
$365$	8.02262	+	11.0422i	0.419923	+	0.577975i
$366$		0			0
$367$	−29.4325	−	9.56319i	−1.53636	−	0.499194i	−0.585992	−	0.810317i	$-0.699295\pi$
$367$	−29.4325	−	9.56319i	−1.53636	−	0.499194i	−0.950370	+	0.311122i	$0.899295\pi$
$368$	6.76058	+	20.1348i	0.352419	+	1.04960i
$369$		0			0
$370$	9.95349	−	8.54325i	0.517457	−	0.444143i
$371$	1.95624	+	6.02070i	0.101563	+	0.312579i
$372$		0			0
$373$		−	4.92658i		−	0.255088i	−0.991833	−	0.127544i	$-0.959291\pi$
$373$		−	4.92658i		−	0.255088i	0.991833	−	0.127544i	$-0.0407095\pi$
$374$	0.139544	−	0.297020i	0.00721567	−	0.0153586i
$375$		0			0
$376$	−23.5400	+	14.6639i	−1.21398	+	0.756231i
$377$	4.32696	+	13.3170i	0.222850	+	0.685861i
$378$		0			0
$379$	−2.36592	+	3.25642i	−0.121529	+	0.167271i	−0.865447	−	0.501000i	$-0.832965\pi$
$379$	−2.36592	+	3.25642i	−0.121529	+	0.167271i	0.743918	+	0.668271i	$0.232965\pi$
$380$	3.25098	−	21.1961i	0.166772	−	1.08734i
$381$		0			0
$382$	−28.1299	−	6.68070i	−1.43925	−	0.341814i
$383$	7.04690	+	9.69922i	0.360080	+	0.495607i	0.950171	−	0.311729i	$-0.100908\pi$
$383$	7.04690	+	9.69922i	0.360080	+	0.495607i	−0.590091	+	0.807337i	$0.700908\pi$
$384$		0			0
$385$	−5.39523	+	4.89125i	−0.274966	+	0.249281i
$386$	12.7625	−	20.9412i	0.649594	−	1.06588i
$387$		0			0
$388$	−10.3101	+	10.4114i	−0.523415	+	0.528559i
$389$	−4.24498	+	13.0647i	−0.215229	+	0.662407i	0.783908	+	0.620877i	$0.213223\pi$
$389$	−4.24498	+	13.0647i	−0.215229	+	0.662407i	−0.999137	+	0.0415304i	$0.986777\pi$
$390$		0			0
$391$	0.300556	+	0.218367i	0.0151998	+	0.0110433i
$392$	11.3972	+	4.62323i	0.575644	+	0.233508i
$393$		0			0
$394$	−0.399423	−	4.92131i	−0.0201226	−	0.247932i
$395$	−8.09663			−0.407386
$396$		0			0
$397$	−12.1547			−0.610027			−0.305014	−	0.952348i	$-0.598661\pi$
$397$	−12.1547			−0.610027			−0.305014	+	0.952348i	$0.598661\pi$
$398$	1.28888	+	15.8803i	0.0646056	+	0.796008i
$399$		0			0
$400$	−7.58114	−	10.2228i	−0.379057	−	0.511141i
$401$	−23.2839	−	16.9167i	−1.16274	−	0.844782i	−0.172620	−	0.984989i	$-0.555223\pi$
$401$	−23.2839	−	16.9167i	−1.16274	−	0.844782i	−0.990122	+	0.140207i	$0.955223\pi$
$402$		0			0
$403$	−4.06049	+	12.4969i	−0.202267	+	0.622515i
$404$	13.6038	+	13.4714i	0.676816	+	0.670230i
$405$		0			0
$406$	−4.71741	+	7.74052i	−0.234121	+	0.384156i
$407$	−4.66723	+	22.3312i	−0.231346	+	1.10692i
$408$		0			0
$409$	11.1416	+	15.3351i	0.550917	+	0.758272i	0.990136	−	0.140108i	$-0.0447449\pi$
$409$	11.1416	+	15.3351i	0.550917	+	0.758272i	−0.439219	+	0.898380i	$0.644745\pi$
$410$	10.7355	+	2.54961i	0.530186	+	0.125916i
$411$		0			0
$412$	−20.4044	−	3.12955i	−1.00525	−	0.154182i
$413$	4.65320	−	6.40457i	0.228969	−	0.315149i
$414$		0			0
$415$	1.50503	+	4.63200i	0.0738790	+	0.227376i
$416$	−17.2847	−	10.3036i	−0.847452	−	0.505176i
$417$		0			0
$418$	17.9876	+	32.6717i	0.879800	+	1.59803i
$419$			15.3705i			0.750898i	0.926843	+	0.375449i	$0.122512\pi$
$419$			15.3705i			0.750898i	−0.926843	+	0.375449i	$0.877488\pi$
$420$		0			0
$421$	5.97047	+	18.3752i	0.290983	+	0.895553i	0.984541	+	0.175153i	$0.0560419\pi$
$421$	5.97047	+	18.3752i	0.290983	+	0.895553i	−0.693558	+	0.720400i	$0.743958\pi$
$422$	−2.94354	+	2.52649i	−0.143289	+	0.122988i
$423$		0			0
$424$	−7.07978	+	8.41353i	−0.343825	+	0.408597i
$425$	−0.211719	−	0.0687918i	−0.0102699	−	0.00333689i
$426$		0			0
$427$	−1.28832	−	1.77322i	−0.0623463	−	0.0858123i
$428$	10.1542	+	19.6902i	0.490824	+	0.951763i
$429$		0			0
$430$	−3.08602	−	1.88075i	−0.148821	−	0.0906980i
$431$	−21.9276	+	15.9313i	−1.05621	+	0.767385i	−0.973384	−	0.229179i	$-0.926396\pi$
$431$	−21.9276	+	15.9313i	−1.05621	+	0.767385i	−0.0828305	+	0.996564i	$0.526396\pi$
$432$		0			0
$433$	1.34612	−	4.14294i	0.0646905	−	0.199097i	−0.913487	−	0.406868i	$-0.866621\pi$
$433$	1.34612	−	4.14294i	0.0646905	−	0.199097i	0.978177	+	0.207771i	$0.0666209\pi$
$434$	−7.85101	+	3.27450i	−0.376860	+	0.157181i
$435$		0			0
$436$	2.88959	+	17.6841i	0.138386	+	0.846917i
$437$	−40.1552	+	13.0472i	−1.92088	+	0.624133i
$438$		0			0
$439$	24.0996			1.15021			0.575105	−	0.818080i	$-0.304961\pi$
$439$	24.0996			1.15021			0.575105	+	0.818080i	$0.304961\pi$
$440$	−12.1662	−	3.46213i	−0.580002	−	0.165050i
$441$		0			0
$442$	−0.350821	+	0.0284733i	−0.0166869	+	0.00135434i
$443$	−21.9169	+	7.12124i	−1.04130	+	0.338340i	−0.779250	−	0.626713i	$-0.784400\pi$
$443$	−21.9169	+	7.12124i	−1.04130	+	0.338340i	−0.262054	+	0.965053i	$0.584400\pi$
$444$		0			0
$445$	−5.88765	−	4.27763i	−0.279102	−	0.202779i
$446$	−30.9677	+	12.9160i	−1.46637	+	0.611592i
$447$		0			0
$448$	−2.22636	−	12.8353i	−0.105186	−	0.606411i
$449$	−3.05281	+	2.21800i	−0.144071	+	0.104674i	−0.657486	−	0.753467i	$-0.728380\pi$
$449$	−3.05281	+	2.21800i	−0.144071	+	0.104674i	0.513415	+	0.858140i	$0.328380\pi$
$450$		0			0
$451$	−17.5050	+	7.86527i	−0.824278	+	0.370361i
$452$	−10.1047	−	19.5941i	−0.475283	−	0.921628i
$453$		0			0
$454$	−0.261697	+	1.10191i	−0.0122821	+	0.0517151i
$455$	7.42839	+	2.41363i	0.348248	+	0.113153i
$456$		0			0
$457$	20.7236	−	28.5236i	0.969409	−	1.33428i	0.0270646	−	0.999634i	$-0.491384\pi$
$457$	20.7236	−	28.5236i	0.969409	−	1.33428i	0.942345	−	0.334644i	$-0.108616\pi$
$458$	25.3140	−	21.7274i	1.18284	−	1.01526i
$459$		0			0
$460$	6.43860	−	12.7907i	0.300201	−	0.596369i
$461$		−	38.5074i		−	1.79347i	−0.442571	−	0.896734i	$-0.645933\pi$
$461$		−	38.5074i		−	1.79347i	0.442571	−	0.896734i	$-0.354067\pi$
$462$		0			0
$463$		−	10.7672i		−	0.500394i	−0.968195	−	0.250197i	$-0.919505\pi$
$463$		−	10.7672i		−	0.500394i	0.968195	−	0.250197i	$-0.0804954\pi$
$464$	−15.7444	+	0.153962i	−0.730917	+	0.00714752i
$465$		0			0
$466$	−16.1112	−	18.7706i	−0.746335	−	0.869532i
$467$	12.1553	−	16.7304i	0.562481	−	0.774189i	−0.429158	−	0.903229i	$-0.641190\pi$
$467$	12.1553	−	16.7304i	0.562481	−	0.774189i	0.991639	+	0.129040i	$0.0411897\pi$
$468$		0			0
$469$	7.60867	+	2.47221i	0.351336	+	0.114156i
$470$	18.1923	+	4.32057i	0.839147	+	0.199293i
$471$		0			0
$472$	13.7159	+	0.978304i	0.631323	+	0.0450301i
$473$	6.24883	−	0.678301i	0.287321	−	0.0311883i
$474$		0			0
$475$	20.4682	−	14.8710i	0.939144	−	0.682328i
$476$	−0.161907	−	0.160331i	−0.00742098	−	0.00734877i
$477$		0			0
$478$	3.63922	+	8.72546i	0.166454	+	0.399093i
$479$	9.23398	+	6.70888i	0.421911	+	0.306536i	0.778406	−	0.627761i	$-0.216028\pi$
$479$	9.23398	+	6.70888i	0.421911	+	0.306536i	−0.356495	+	0.934297i	$0.616028\pi$
$480$		0			0
$481$	23.2712	−	7.56128i	1.06108	−	0.344765i
$482$	−0.490399	−	6.04223i	−0.0223371	−	0.275216i
$483$		0			0
$484$	20.4451	−	8.12385i	0.929324	−	0.369266i
$485$	9.87880			0.448573
$486$		0			0
$487$	3.80894	−	1.23760i	0.172600	−	0.0560810i	−0.221442	−	0.975173i	$-0.571076\pi$
$487$	3.80894	−	1.23760i	0.172600	−	0.0560810i	0.394042	+	0.919092i	$0.371076\pi$
$488$	1.43109	−	3.52792i	0.0647825	−	0.159701i
$489$		0			0
$490$	−3.19200	−	7.65320i	−0.144200	−	0.345736i
$491$	3.45914	−	10.6461i	0.156109	−	0.480454i	−0.842163	−	0.539223i	$-0.818718\pi$
$491$	3.45914	−	10.6461i	0.156109	−	0.480454i	0.998272	+	0.0587698i	$0.0187178\pi$
$492$		0			0
$493$	−0.222807	+	0.161879i	−0.0100347	+	0.00729066i
$494$	20.8174	−	34.1581i	0.936619	−	1.53684i
$495$		0			0
$496$	−12.0380	−	8.56754i	−0.540523	−	0.384694i
$497$	−6.67654	−	9.18946i	−0.299484	−	0.412204i
$498$		0			0
$499$	−37.4389	−	12.1646i	−1.67599	−	0.544564i	−0.691867	−	0.722025i	$-0.743211\pi$
$499$	−37.4389	−	12.1646i	−1.67599	−	0.544564i	−0.984128	+	0.177462i	$0.943211\pi$
$500$	−3.34511	+	21.8098i	−0.149598	+	0.975365i
$501$		0			0
$502$	4.51117	+	5.25583i	0.201343	+	0.234579i
$503$	−5.97544	−	18.3905i	−0.266432	−	0.819993i	−0.991360	−	0.131168i	$-0.958127\pi$
$503$	−5.97544	−	18.3905i	−0.266432	−	0.819993i	0.724928	−	0.688824i	$-0.241873\pi$
$504$		0			0
$505$		−	12.9079i		−	0.574395i
$506$	4.68185	+	24.4615i	0.208134	+	1.08745i
$507$		0			0
$508$	18.3866	+	9.25547i	0.815772	+	0.410645i
$509$	13.2867	+	40.8921i	0.588920	+	1.81251i	0.582921	+	0.812529i	$0.301910\pi$
$509$	13.2867	+	40.8921i	0.588920	+	1.81251i	0.00599915	+	0.999982i	$0.498090\pi$
$510$		0			0
$511$	−9.68826	+	13.3347i	−0.428583	+	0.589895i
$512$	16.8786	−	15.0703i	0.745934	−	0.666020i
$513$		0			0
$514$	4.04693	−	17.0401i	0.178502	−	0.751605i
$515$	8.18058	+	11.2596i	0.360479	+	0.496157i
$516$		0			0
$517$	−29.6639	+	13.3285i	−1.30462	+	0.586185i
$518$	13.5264	+	8.24359i	0.594317	+	0.362202i
$519$		0			0
$520$	3.26379	+	13.1685i	0.143127	+	0.577475i
$521$	4.55221	−	14.0103i	0.199436	−	0.613801i	−0.800460	−	0.599386i	$-0.795411\pi$
$521$	4.55221	−	14.0103i	0.199436	−	0.613801i	0.999896	−	0.0144150i	$-0.00458858\pi$
$522$		0			0
$523$	32.7270	+	23.7776i	1.43105	+	1.03972i	0.989819	+	0.142329i	$0.0454591\pi$
$523$	32.7270	+	23.7776i	1.43105	+	1.03972i	0.441234	+	0.897392i	$0.354541\pi$
$524$	−3.68648	+	0.602371i	−0.161045	+	0.0263147i
$525$		0			0
$526$	23.8907	−	1.93902i	1.04169	−	0.0845453i
$527$	−0.258445			−0.0112580
$528$		0			0
$529$	−5.19479			−0.225860
$530$	7.38925	−	0.599726i	0.320968	−	0.0260504i
$531$		0			0
$532$	25.5571	−	4.17604i	1.10804	−	0.181055i
$533$	16.6520	+	12.0984i	0.721280	+	0.524040i
$534$		0			0
$535$	4.61566	−	14.2055i	0.199552	−	0.614159i
$536$	3.34300	+	13.4881i	0.144396	+	0.582595i
$537$		0			0
$538$	4.77584	+	2.91060i	0.205901	+	0.125485i
$539$	12.5144	+	7.16845i	0.539031	+	0.308767i
$540$		0			0
$541$	−9.83661	−	13.5389i	−0.422909	−	0.582084i	0.543399	−	0.839475i	$-0.317137\pi$
$541$	−9.83661	−	13.5389i	−0.422909	−	0.582084i	−0.966307	+	0.257391i	$0.917137\pi$
$542$	7.75691	−	32.6614i	0.333188	−	1.40293i
$543$		0			0
$544$	0.0876832	−	0.385950i	0.00375939	−	0.0165475i
$545$	7.10097	−	9.77365i	0.304172	−	0.418657i
$546$		0			0
$547$	2.87078	+	8.83536i	0.122746	+	0.377773i	0.993484	−	0.113975i	$-0.0363583\pi$
$547$	2.87078	+	8.83536i	0.122746	+	0.377773i	−0.870738	+	0.491747i	$0.836358\pi$
$548$	−2.24103	−	1.12810i	−0.0957322	−	0.0481899i
$549$		0			0
$550$	−7.19766	−	13.0735i	−0.306909	−	0.557455i
$551$		−	31.2996i		−	1.33341i
$552$		0			0
$553$	−3.02146	−	9.29909i	−0.128485	−	0.395437i
$554$	−13.8265	−	16.1088i	−0.587430	−	0.684397i
$555$		0			0
$556$	1.90752	−	12.4369i	0.0808968	−	0.527440i
$557$	−12.6129	−	4.09818i	−0.534425	−	0.173645i	0.0293567	−	0.999569i	$-0.490654\pi$
$557$	−12.6129	−	4.09818i	−0.534425	−	0.173645i	−0.563782	+	0.825924i	$0.690654\pi$
$558$		0			0
$559$	−3.96257	−	5.45401i	−0.167599	−	0.230680i
$560$	−5.09271	+	7.15563i	−0.215206	+	0.302380i
$561$		0			0
$562$	−4.22549	+	6.93336i	−0.178241	+	0.292466i
$563$	−19.0155	+	13.8156i	−0.801408	+	0.582257i	−0.911327	−	0.411684i	$-0.864941\pi$
$563$	−19.0155	+	13.8156i	−0.801408	+	0.582257i	0.109919	+	0.993941i	$0.464941\pi$
$564$		0			0
$565$	−4.59312	+	14.1362i	−0.193234	+	0.594713i
$566$	6.09431	+	14.6118i	0.256163	+	0.614181i
$567$		0			0
$568$	7.41642	−	18.2829i	0.311186	−	0.767134i
$569$	12.2494	−	3.98008i	0.513523	−	0.166854i	−0.0407811	−	0.999168i	$-0.512985\pi$
$569$	12.2494	−	3.98008i	0.513523	−	0.166854i	0.554304	+	0.832315i	$0.312985\pi$
$570$		0			0
$571$	20.4261			0.854806			0.427403	−	0.904061i	$-0.359429\pi$
$571$	20.4261			0.854806			0.427403	+	0.904061i	$0.359429\pi$
$572$	−18.4601	−	14.6968i	−0.771855	−	0.614506i
$573$		0			0
$574$	1.07793	+	13.2813i	0.0449921	+	0.554349i
$575$	16.0680	−	5.22080i	0.670080	−	0.217722i
$576$		0			0
$577$	−5.53777	−	4.02342i	−0.230540	−	0.167497i	0.466518	−	0.884512i	$-0.345508\pi$
$577$	−5.53777	−	4.02342i	−0.230540	−	0.167497i	−0.697058	+	0.717014i	$0.745508\pi$
$578$	9.25194	+	22.1826i	0.384830	+	0.922675i
$579$		0			0
$580$	7.54291	+	7.46951i	0.313202	+	0.310155i
$581$	−4.75828	+	3.45709i	−0.197407	+	0.143424i
$582$		0			0
$583$	−9.55259	+	8.66028i	−0.395628	+	0.358672i
$584$	−28.5573	−	2.03689i	−1.18171	−	0.0842873i
$585$		0			0
$586$	−7.29648	−	1.73288i	−0.301415	−	0.0715844i
$587$	0.607533	+	0.197399i	0.0250756	+	0.00814754i	0.321528	−	0.946900i	$-0.395804\pi$
$587$	0.607533	+	0.197399i	0.0250756	+	0.00814754i	−0.296452	+	0.955048i	$0.595804\pi$
$588$		0			0
$589$	17.2645	−	23.7625i	0.711370	−	0.979117i
$590$	−6.03813	−	7.03484i	−0.248586	−	0.289620i
$591$		0			0
$592$	0.269046	+	27.5131i	0.0110577	+	1.13078i
$593$			17.0480i			0.700077i	0.936735	+	0.350039i	$0.113832\pi$
$593$			17.0480i			0.700077i	−0.936735	+	0.350039i	$0.886168\pi$
$594$		0			0
$595$			0.153624i			0.00629799i
$596$	15.4274	−	30.6475i	0.631930	−	1.25537i
$597$		0			0
$598$	20.2698	−	17.3979i	0.828892	−	0.711452i
$599$	1.16656	−	1.60564i	0.0476645	−	0.0656045i	−0.784519	−	0.620104i	$-0.787090\pi$
$599$	1.16656	−	1.60564i	0.0476645	−	0.0656045i	0.832184	+	0.554500i	$0.187090\pi$
$600$		0			0
$601$	15.6571	+	5.08729i	0.638665	+	0.207515i	0.610410	−	0.792086i	$-0.291005\pi$
$601$	15.6571	+	5.08729i	0.638665	+	0.207515i	0.0282553	+	0.999601i	$0.491005\pi$
$602$	1.00845	−	4.24618i	0.0411012	−	0.173061i
$603$		0			0
$604$	−11.1453	−	21.6120i	−0.453496	−	0.879380i
$605$	−13.5910	−	5.94052i	−0.552552	−	0.241516i
$606$		0			0
$607$	−23.2353	+	16.8814i	−0.943091	+	0.685196i	−0.949163	−	0.314786i	$-0.898067\pi$
$607$	−23.2353	+	16.8814i	−0.943091	+	0.685196i	0.00607141	+	0.999982i	$0.498067\pi$
$608$	29.6285	+	33.8440i	1.20159	+	1.37255i
$609$		0			0
$610$	−2.36900	+	0.988064i	−0.0959180	+	0.0400055i
$611$	28.2185	+	20.5019i	1.14160	+	0.829419i
$612$		0			0
$613$	6.32812	−	2.05613i	0.255590	−	0.0830464i	−0.178419	−	0.983955i	$-0.557098\pi$
$613$	6.32812	−	2.05613i	0.255590	−	0.0830464i	0.434010	+	0.900908i	$0.357098\pi$
$614$	−3.19995	+	0.259714i	−0.129139	+	0.0104812i
$615$		0			0
$616$	−0.563830	−	15.2650i	−0.0227174	−	0.615046i
$617$	17.8948			0.720416			0.360208	−	0.932872i	$-0.382706\pi$
$617$	17.8948			0.720416			0.360208	+	0.932872i	$0.382706\pi$
$618$		0			0
$619$	22.1005	−	7.18088i	0.888293	−	0.288624i	0.170897	−	0.985289i	$-0.445334\pi$
$619$	22.1005	−	7.18088i	0.888293	−	0.288624i	0.717397	+	0.696665i	$0.245334\pi$
$620$	1.60645	+	9.83139i	0.0645167	+	0.394838i
$621$		0			0
$622$	−26.3221	+	10.9784i	−1.05542	+	0.440195i
$623$	2.71579	−	8.35835i	0.108806	−	0.334870i
$624$		0			0
$625$	−0.835407	+	0.606959i	−0.0334163	+	0.0242784i
$626$	−1.86201	−	1.13479i	−0.0744208	−	0.0453552i
$627$		0			0
$628$	−4.86001	−	9.42411i	−0.193935	−	0.376063i
$629$	0.282881	+	0.389352i	0.0112792	+	0.0155245i
$630$		0			0
$631$	44.0545	+	14.3142i	1.75378	+	0.569838i	0.996526	−	0.0832806i	$-0.0265398\pi$
$631$	44.0545	+	14.3142i	1.75378	+	0.569838i	0.757255	+	0.653119i	$0.226540\pi$
$632$	10.9349	−	12.9949i	0.434966	−	0.516908i
$633$		0			0
$634$	−18.0953	+	15.5315i	−0.718657	+	0.616836i
$635$	−4.28864	−	13.1991i	−0.170190	−	0.523790i
$636$		0			0
$637$		−	15.4683i		−	0.612877i
$638$	−18.3187	−	2.30276i	−0.725244	−	0.0911673i
$639$		0			0
$640$	−15.2268	−	0.936520i	−0.601892	−	0.0370192i
$641$	−8.39773	−	25.8456i	−0.331691	−	1.02084i	−0.968329	−	0.249676i	$-0.919676\pi$
$641$	−8.39773	−	25.8456i	−0.331691	−	1.02084i	0.636639	−	0.771162i	$-0.280324\pi$
$642$		0			0
$643$	18.2352	−	25.0987i	0.719128	−	0.989794i	−0.280425	−	0.959876i	$-0.590475\pi$
$643$	18.2352	−	25.0987i	0.719128	−	0.989794i	0.999552	−	0.0299182i	$-0.00952467\pi$
$644$	17.0930	+	2.62166i	0.673558	+	0.103308i
$645$		0			0
$646$	0.765482	+	0.181798i	0.0301175	+	0.00715275i
$647$	−24.7877	−	34.1173i	−0.974505	−	1.34129i	−0.939738	−	0.341895i	$-0.888931\pi$
$647$	−24.7877	−	34.1173i	−0.974505	−	1.34129i	−0.0347664	−	0.999395i	$-0.511069\pi$
$648$		0			0
$649$	15.7831	+	3.29867i	0.619541	+	0.129484i
$650$	−8.33001	+	13.6682i	−0.326730	+	0.536112i
$651$		0			0
$652$	14.2929	+	14.1538i	0.559753	+	0.554306i
$653$	1.25077	−	3.84947i	0.0489464	−	0.150641i	−0.923596	−	0.383367i	$-0.874764\pi$
$653$	1.25077	−	3.84947i	0.0489464	−	0.150641i	0.972542	+	0.232726i	$0.0747644\pi$
$654$		0			0
$655$	2.03744	+	1.48028i	0.0796093	+	0.0578395i
$656$	−18.5908	+	13.7867i	−0.725848	+	0.538281i
$657$		0			0
$658$	1.82666	+	22.5064i	0.0712107	+	0.877390i
$659$	6.46292			0.251760			0.125880	−	0.992045i	$-0.459825\pi$
$659$	6.46292			0.251760			0.125880	+	0.992045i	$0.459825\pi$
$660$		0			0
$661$	26.6232			1.03552			0.517761	−	0.855525i	$-0.326766\pi$
$661$	26.6232			1.03552			0.517761	+	0.855525i	$0.326766\pi$
$662$	3.88671	+	47.8884i	0.151061	+	1.86123i
$663$		0			0
$664$	−9.46685	−	3.84020i	−0.367385	−	0.149029i
$665$	−14.1249	−	10.2623i	−0.547740	−	0.397956i
$666$		0			0
$667$	6.45884	−	19.8783i	0.250087	−	0.769690i
$668$	30.8302	−	31.1332i	1.19286	−	1.20458i
$669$		0			0
$670$	4.87569	−	8.00023i	0.188364	−	0.309076i
$671$	2.21895	−	3.87374i	0.0856616	−	0.149544i
$672$		0			0
$673$	−4.89033	−	6.73096i	−0.188508	−	0.259460i	0.704294	−	0.709909i	$-0.251264\pi$
$673$	−4.89033	−	6.73096i	−0.188508	−	0.259460i	−0.892802	+	0.450449i	$0.851264\pi$
$674$	−23.5227	−	5.58651i	−0.906060	−	0.215184i
$675$		0			0
$676$	0.104935	−	0.684168i	0.00403597	−	0.0263142i
$677$	8.97132	−	12.3480i	0.344796	−	0.474571i	−0.601039	−	0.799220i	$-0.705246\pi$
$677$	8.97132	−	12.3480i	0.344796	−	0.474571i	0.945834	+	0.324649i	$0.105246\pi$
$678$		0			0
$679$	3.68652	+	11.3459i	0.141476	+	0.435417i
$680$	−0.226491	+	0.141089i	−0.00868552	+	0.00541051i
$681$		0			0
$682$	−12.6373	−	11.8526i	−0.483907	−	0.453860i
$683$			32.9156i			1.25948i	0.776806	+	0.629740i	$0.216839\pi$
$683$			32.9156i			1.25948i	−0.776806	+	0.629740i	$0.783161\pi$
$684$		0			0
$685$	0.522718	+	1.60876i	0.0199720	+	0.0614676i
$686$	19.8308	−	17.0211i	0.757142	−	0.649868i
$687$		0			0
$688$	7.18636	−	2.41293i	0.273978	−	0.0919922i
$689$	13.1524	+	4.27349i	0.501068	+	0.162807i
$690$		0			0
$691$	−26.7545	−	36.8244i	−1.01779	−	1.40087i	−0.913742	−	0.406294i	$-0.866821\pi$
$691$	−26.7545	−	36.8244i	−1.01779	−	1.40087i	−0.104047	−	0.994572i	$-0.533179\pi$
$692$	21.0324	−	10.8464i	0.799531	−	0.412318i
$693$		0			0
$694$	3.01794	+	1.83926i	0.114559	+	0.0698175i
$695$	−6.86294	+	4.98622i	−0.260326	+	0.189138i
$696$		0			0
$697$	−0.125102	+	0.385024i	−0.00473857	+	0.0145838i
$698$	−9.15135	+	3.81685i	−0.346384	+	0.144470i
$699$		0			0
$700$	−10.2266	+	1.67103i	−0.386529	+	0.0631590i
$701$	47.6330	−	15.4769i	1.79907	−	0.584555i	0.799210	−	0.601052i	$-0.205252\pi$
$701$	47.6330	−	15.4769i	1.79907	−	0.584555i	0.999864	+	0.0164975i	$0.00525154\pi$
$702$		0			0
$703$	−54.6955			−2.06288
$704$	21.9877	−	14.8507i	0.828691	−	0.559707i
$705$		0			0
$706$	−25.2923	+	2.05277i	−0.951887	+	0.0772570i
$707$	14.8249	−	4.81691i	0.557548	−	0.181158i
$708$		0			0
$709$	6.87556	+	4.99539i	0.258217	+	0.187606i	0.709361	−	0.704846i	$-0.248984\pi$
$709$	6.87556	+	4.99539i	0.258217	+	0.187606i	−0.451144	+	0.892451i	$0.648984\pi$
$710$	−12.2770	+	5.12049i	−0.460747	+	0.192169i
$711$		0			0
$712$	14.8170	−	3.67239i	0.555291	−	0.137628i
$713$	15.8681	−	11.5289i	0.594266	−	0.431759i
$714$		0			0
$715$	1.71677	+	15.8157i	0.0642036	+	0.591474i
$716$	−1.65966	+	0.855885i	−0.0620243	+	0.0319859i
$717$		0			0
$718$	3.16305	−	13.3184i	0.118044	−	0.497038i
$719$	−6.94019	−	2.25500i	−0.258825	−	0.0840974i	0.176730	−	0.984259i	$-0.443448\pi$
$719$	−6.94019	−	2.25500i	−0.258825	−	0.0840974i	−0.435555	+	0.900162i	$0.643448\pi$
$720$		0			0
$721$	−9.87901	+	13.5973i	−0.367914	+	0.506390i
$722$	−47.4612	+	40.7368i	−1.76632	+	1.51607i
$723$		0			0
$724$	−33.6554	−	16.9415i	−1.25079	−	0.629627i
$725$			12.5244i			0.465146i
$726$		0			0
$727$		−	1.85004i		−	0.0686140i	−0.999411	−	0.0343070i	$-0.989078\pi$
$727$		−	1.85004i		−	0.0686140i	0.999411	−	0.0343070i	$-0.0109224\pi$
$728$	−13.9062	+	8.66265i	−0.515398	+	0.321059i
$729$		0			0
$730$	12.5718	+	14.6470i	0.465303	+	0.542110i
$731$	0.0779378	−	0.107272i	0.00288264	−	0.00396761i
$732$		0			0
$733$	17.9690	+	5.83849i	0.663701	+	0.215650i	0.621446	−	0.783457i	$-0.286546\pi$
$733$	17.9690	+	5.83849i	0.663701	+	0.215650i	0.0422555	+	0.999107i	$0.486546\pi$
$734$	−42.5814	−	10.1129i	−1.57171	−	0.373273i
$735$		0			0
$736$	11.8331	+	27.6082i	0.436173	+	1.01765i
$737$	1.75843	+	16.1995i	0.0647728	+	0.596717i
$738$		0			0
$739$	−12.7166	+	9.23916i	−0.467788	+	0.339868i	−0.796579	−	0.604535i	$-0.793359\pi$
$739$	−12.7166	+	9.23916i	−0.467788	+	0.339868i	0.328791	+	0.944403i	$0.393359\pi$
$740$	13.0528	−	13.1811i	0.479832	−	0.484547i
$741$		0			0
$742$	3.44627	+	8.26284i	0.126517	+	0.303339i
$743$	4.69746	+	3.41290i	0.172333	+	0.125207i	0.670608	−	0.741812i	$-0.266033\pi$
$743$	4.69746	+	3.41290i	0.172333	+	0.125207i	−0.498275	+	0.867019i	$0.666033\pi$
$744$		0			0
$745$	−22.0008	+	7.14848i	−0.806045	+	0.261900i
$746$	−0.563621	−	6.94440i	−0.0206356	−	0.254252i
$747$		0			0
$748$	0.162719	−	0.434638i	0.00594958	−	0.0158919i
$749$	18.0377			0.659083
$750$		0			0
$751$	−2.85643	+	0.928110i	−0.104233	+	0.0338672i	−0.360669	−	0.932694i	$-0.617452\pi$
$751$	−2.85643	+	0.928110i	−0.104233	+	0.0338672i	0.256436	+	0.966561i	$0.417452\pi$
$752$	−31.5039	+	23.3630i	−1.14883	+	0.851959i
$753$		0			0
$754$	7.62271	+	18.2763i	0.277603	+	0.665585i
$755$	−5.06615	+	15.5920i	−0.184376	+	0.567451i
$756$		0			0
$757$	21.1049	−	15.3336i	0.767071	−	0.557310i	−0.134000	−	0.990981i	$-0.542782\pi$
$757$	21.1049	−	15.3336i	0.767071	−	0.557310i	0.901071	+	0.433672i	$0.142782\pi$
$758$	−2.96241	+	4.86085i	−0.107600	+	0.176554i
$759$		0			0
$760$	2.15759	−	30.2495i	0.0782639	−	1.09726i
$761$	18.7813	+	25.8502i	0.680820	+	0.937068i	0.999943	−	0.0106450i	$-0.00338846\pi$
$761$	18.7813	+	25.8502i	0.680820	+	0.937068i	−0.319123	+	0.947713i	$0.603388\pi$
$762$		0			0
$763$	13.8751	+	4.50828i	0.502311	+	0.163211i
$764$	−40.4156	−	6.19879i	−1.46218	−	0.224265i
$765$		0			0
$766$	11.0428	+	12.8656i	0.398992	+	0.464854i
$767$	−5.34410	−	16.4474i	−0.192964	−	0.593883i
$768$		0			0
$769$			22.3560i			0.806176i	0.915161	+	0.403088i	$0.132063\pi$
$769$			22.3560i			0.806176i	−0.915161	+	0.403088i	$0.867937\pi$
$770$	−7.04542	+	7.51184i	−0.253899	+	0.270708i
$771$		0			0
$772$	15.5940	−	30.9784i	0.561239	−	1.11494i
$773$	−1.56889	−	4.82855i	−0.0564291	−	0.173671i	0.918869	−	0.394562i	$-0.129104\pi$
$773$	−1.56889	−	4.82855i	−0.0564291	−	0.173671i	−0.975299	+	0.220891i	$0.929104\pi$
$774$		0			0
$775$	−6.90832	+	9.50848i	−0.248154	+	0.341555i
$776$	−13.3418	+	15.8552i	−0.478942	+	0.569169i
$777$		0			0
$778$	−4.48898	+	18.9014i	−0.160938	+	0.677648i
$779$	−27.0438	−	37.2225i	−0.968943	−	1.33364i
$780$		0			0
$781$	11.4994	−	20.0751i	0.411480	−	0.718343i
$782$	0.448640	+	0.273421i	0.0160433	+	0.00977750i
$783$		0			0
$784$	16.5941	+	5.21292i	0.592647	+	0.186176i
$785$	−2.20914	+	6.79904i	−0.0788476	+	0.242668i
$786$		0			0
$787$	−2.38155	−	1.73029i	−0.0848930	−	0.0616783i	0.544529	−	0.838742i	$-0.316708\pi$
$787$	−2.38155	−	1.73029i	−0.0848930	−	0.0616783i	−0.629422	+	0.777064i	$0.716708\pi$
$788$	−1.12604	−	6.89127i	−0.0401134	−	0.245491i
$789$		0			0
$790$	−11.4128	+	0.926288i	−0.406051	+	0.0329559i
$791$	−17.9496			−0.638215
$792$		0			0
$793$	−4.78812			−0.170031
$794$	−17.1330	+	1.39055i	−0.608028	+	0.0493487i
$795$		0			0
$796$	3.63355	+	22.2371i	0.128788	+	0.788173i
$797$	6.06111	+	4.40365i	0.214695	+	0.155985i	0.689936	−	0.723871i	$-0.257639\pi$
$797$	6.06111	+	4.40365i	0.214695	+	0.155985i	−0.475240	+	0.879856i	$0.657639\pi$
$798$		0			0
$799$	−0.211997	+	0.652460i	−0.00749992	+	0.0230824i
$800$	−11.8557	−	13.5425i	−0.419164	−	0.478801i
$801$		0			0
$802$	−34.7558	−	21.1817i	−1.22727	−	0.747952i
$803$	−32.8615	−	6.86804i	−1.15966	−	0.242368i
$804$		0			0
$805$	−6.85298	−	9.43231i	−0.241536	−	0.332445i
$806$	−4.29388	+	18.0799i	−0.151245	+	0.636837i
$807$		0			0
$808$	20.7169	+	17.4327i	0.728816	+	0.613281i
$809$	−23.4091	+	32.2199i	−0.823022	+	1.13279i	0.166160	+	0.986099i	$0.446863\pi$
$809$	−23.4091	+	32.2199i	−0.823022	+	1.13279i	−0.989182	+	0.146694i	$0.953137\pi$
$810$		0			0
$811$	−13.1790	−	40.5607i	−0.462777	−	1.42428i	−0.861757	−	0.507321i	$-0.830636\pi$
$811$	−13.1790	−	40.5607i	−0.462777	−	1.42428i	0.398981	−	0.916959i	$-0.369364\pi$
$812$	−5.76401	+	11.4506i	−0.202277	+	0.401836i
$813$		0			0
$814$	−4.02404	+	32.0116i	−0.141042	+	1.12201i
$815$		−	13.5617i		−	0.475047i
$816$		0			0
$817$	4.65671	+	14.3319i	0.162918	+	0.501409i
$818$	17.4594	+	20.3414i	0.610452	+	0.711220i
$819$		0			0
$820$	15.4242	+	2.36570i	0.538635	+	0.0826138i
$821$	18.3658	+	5.96742i	0.640972	+	0.208264i	0.611429	−	0.791299i	$-0.290595\pi$
$821$	18.3658	+	5.96742i	0.640972	+	0.208264i	0.0295426	+	0.999564i	$0.490595\pi$
$822$		0			0
$823$	5.83041	+	8.02487i	0.203235	+	0.279729i	0.898453	−	0.439070i	$-0.144692\pi$
$823$	5.83041	+	8.02487i	0.203235	+	0.279729i	−0.695218	+	0.718799i	$0.744692\pi$
$824$	−29.1196	−	2.07700i	−1.01443	−	0.0723557i
$825$		0			0
$826$	5.82633	−	9.56010i	0.202724	−	0.332638i
$827$	35.2981	−	25.6455i	1.22743	−	0.891783i	0.230738	−	0.973016i	$-0.425886\pi$
$827$	35.2981	−	25.6455i	1.22743	−	0.891783i	0.996695	+	0.0812332i	$0.0258859\pi$
$828$		0			0
$829$	−8.69871	+	26.7719i	−0.302119	+	0.929826i	0.678618	+	0.734491i	$0.262579\pi$
$829$	−8.69871	+	26.7719i	−0.302119	+	0.929826i	−0.980737	+	0.195335i	$0.937421\pi$
$830$	2.65138	+	6.35699i	0.0920306	+	0.220654i
$831$		0			0
$832$	−25.5429	−	12.5463i	−0.885541	−	0.434965i
$833$	0.289348	−	0.0940150i	0.0100253	−	0.00325743i
$834$		0			0
$835$	−29.5406			−1.02229
$836$	29.0927	+	43.9955i	1.00619	+	1.52162i
$837$		0			0
$838$	1.75845	+	21.6659i	0.0607446	+	0.748437i
$839$	33.2421	−	10.8010i	1.14764	−	0.372892i	0.327388	−	0.944890i	$-0.393831\pi$
$839$	33.2421	−	10.8010i	1.14764	−	0.372892i	0.820255	+	0.571998i	$0.193831\pi$
$840$		0			0
$841$	−10.9262	−	7.93837i	−0.376767	−	0.273737i
$842$	10.5180	+	25.2183i	0.362476	+	0.869079i
$843$		0			0
$844$	−3.86011	+	3.89804i	−0.132870	+	0.134176i
$845$	−0.377540	+	0.274299i	−0.0129878	+	0.00943617i
$846$		0			0
$847$	1.75095	−	17.8263i	0.0601634	−	0.612518i
$848$	−9.01697	+	12.6695i	−0.309644	+	0.435072i
$849$		0			0
$850$	−0.306305	−	0.0727458i	−0.0105062	−	0.00249516i
$851$	−34.7369	−	11.2867i	−1.19077	−	0.386903i
$852$		0			0
$853$	−15.9973	+	22.0183i	−0.547736	+	0.753894i	−0.989703	−	0.143138i	$-0.954281\pi$
$853$	−15.9973	+	22.0183i	−0.547736	+	0.753894i	0.441967	+	0.897031i	$0.354281\pi$
$854$	−2.01886	−	2.35211i	−0.0690838	−	0.0804875i
$855$		0			0
$856$	16.5658	+	26.5932i	0.566209	+	0.908938i
$857$		−	37.5541i		−	1.28282i	−0.767197	−	0.641412i	$-0.778349\pi$
$857$		−	37.5541i		−	1.28282i	0.767197	−	0.641412i	$-0.221651\pi$
$858$		0			0
$859$			4.50293i			0.153638i	0.997045	+	0.0768190i	$0.0244764\pi$
$859$			4.50293i			0.153638i	−0.997045	+	0.0768190i	$0.975524\pi$
$860$	−4.56515	−	2.29802i	−0.155670	−	0.0783617i
$861$		0			0
$862$	−29.0860	+	24.9651i	−0.990675	+	0.850313i
$863$	−10.6014	+	14.5915i	−0.360875	+	0.496702i	−0.950392	−	0.311054i	$-0.899318\pi$
$863$	−10.6014	+	14.5915i	−0.360875	+	0.496702i	0.589517	+	0.807756i	$0.299318\pi$
$864$		0			0
$865$	−15.1738	−	4.93028i	−0.515926	−	0.167634i
$866$	1.42349	−	5.99380i	0.0483723	−	0.203677i
$867$		0			0
$868$	−10.6920	+	5.51386i	−0.362910	+	0.187152i
$869$	14.7542	−	13.3760i	0.500501	−	0.453749i
$870$		0			0
$871$	14.1390	−	10.2726i	0.479083	−	0.348074i
$872$	6.09625	+	24.5966i	0.206445	+	0.832946i
$873$		0			0
$874$	−55.1093	+	22.9850i	−1.86410	+	0.777479i
$875$	14.5339	+	10.5595i	0.491335	+	0.356976i
$876$		0			0
$877$	−12.9541	+	4.20903i	−0.437428	+	0.142129i	−0.519449	−	0.854502i	$-0.673863\pi$
$877$	−12.9541	+	4.20903i	−0.437428	+	0.142129i	0.0820206	+	0.996631i	$0.473863\pi$
$878$	33.9702	−	2.75709i	1.14644	−	0.0930473i
$879$		0			0
$880$	−17.5453	−	3.48827i	−0.591453	−	0.117590i
$881$	−5.44549			−0.183463			−0.0917317	−	0.995784i	$-0.529240\pi$
$881$	−5.44549			−0.183463			−0.0917317	+	0.995784i	$0.529240\pi$
$882$		0			0
$883$	−26.8480	+	8.72345i	−0.903508	+	0.293568i	−0.723684	−	0.690131i	$-0.757553\pi$
$883$	−26.8480	+	8.72345i	−0.903508	+	0.293568i	−0.179824	+	0.983699i	$0.557553\pi$
$884$	−0.491252	+	0.0802708i	−0.0165226	+	0.00269980i
$885$		0			0
$886$	−30.0789	+	12.5453i	−1.01052	+	0.421469i
$887$	−13.1145	+	40.3623i	−0.440342	+	1.35523i	0.447171	+	0.894449i	$0.352432\pi$
$887$	−13.1145	+	40.3623i	−0.440342	+	1.35523i	−0.887512	+	0.460784i	$0.847568\pi$
$888$		0			0
$889$	13.5589	−	9.85113i	0.454751	−	0.330396i
$890$	−8.78849	−	5.35608i	−0.294591	−	0.179536i
$891$		0			0
$892$	−42.1738	+	21.7490i	−1.41208	+	0.728211i
$893$	−45.8283	−	63.0772i	−1.53358	−	2.11080i
$894$		0			0
$895$	1.19736	+	0.389047i	0.0400234	+	0.0130044i
$896$	−4.60664	−	17.8377i	−0.153897	−	0.595914i
$897$		0			0
$898$	−4.04943	+	3.47570i	−0.135131	+	0.115986i
$899$	4.49318	+	13.8286i	0.149856	+	0.461209i
$900$		0			0
$901$			0.272002i			0.00906169i
$902$	−23.7749	+	13.0894i	−0.791616	+	0.435828i
$903$		0			0
$904$	−16.4849	−	26.4634i	−0.548281	−	0.880159i
$905$	7.85008	+	24.1601i	0.260946	+	0.803108i
$906$		0			0
$907$	20.3902	−	28.0647i	0.677046	−	0.931873i	−0.322848	−	0.946451i	$-0.604640\pi$
$907$	20.3902	−	28.0647i	0.677046	−	0.931873i	0.999894	+	0.0145776i	$0.00464034\pi$
$908$	−0.242820	+	1.58317i	−0.00805827	+	0.0525392i
$909$		0			0
$910$	10.7470	+	2.55236i	0.356261	+	0.0846100i
$911$	17.4380	+	24.0014i	0.577748	+	0.795202i	0.993446	−	0.114300i	$-0.0364627\pi$
$911$	17.4380	+	24.0014i	0.577748	+	0.795202i	−0.415698	+	0.909503i	$0.636463\pi$
$912$		0			0
$913$	−10.3948	−	5.95434i	−0.344018	−	0.197060i
$914$	25.9483	−	42.5771i	0.858294	−	1.40833i
$915$		0			0
$916$	33.1963	−	33.5225i	1.09684	−	1.10762i
$917$	−0.939807	+	2.89243i	−0.0310352	+	0.0955164i
$918$		0			0
$919$	17.4823	+	12.7016i	0.576687	+	0.418988i	0.837528	−	0.546394i	$-0.184000\pi$
$919$	17.4823	+	12.7016i	0.576687	+	0.418988i	−0.260841	+	0.965382i	$0.584000\pi$
$920$	7.61241	−	18.7661i	0.250974	−	0.618699i
$921$		0			0
$922$	−4.40540	−	54.2792i	−0.145084	−	1.78759i
$923$	−24.8137			−0.816754
$924$		0			0
$925$	21.8862			0.719614
$926$	−1.23181	−	15.1772i	−0.0404798	−	0.498754i
$927$		0			0
$928$	−22.1754	+	2.01825i	−0.727943	+	0.0662523i
$929$	38.2024	+	27.7557i	1.25338	+	0.910635i	0.998413	−	0.0563145i	$-0.0179350\pi$
$929$	38.2024	+	27.7557i	1.25338	+	0.910635i	0.254968	+	0.966949i	$0.417935\pi$
$930$		0			0
$931$	−10.6848	+	32.8843i	−0.350179	+	1.07774i
$932$	−24.8574	−	24.6155i	−0.814230	−	0.806307i
$933$		0			0
$934$	15.2199	−	24.9734i	0.498009	−	0.817154i
$935$	−0.285412	+	0.128240i	−0.00933397	+	0.00419390i
$936$		0			0
$937$	27.2659	+	37.5283i	0.890738	+	1.22600i	0.973329	+	0.229412i	$0.0736804\pi$
$937$	27.2659	+	37.5283i	0.890738	+	1.22600i	−0.0825914	+	0.996583i	$0.526320\pi$
$938$	11.0079	+	2.61431i	0.359419	+	0.0853602i
$939$		0			0
$940$	26.1377	+	4.00891i	0.852518	+	0.130756i
$941$	−23.1708	+	31.8919i	−0.755347	+	1.03965i	0.242240	+	0.970216i	$0.422118\pi$
$941$	−23.1708	+	31.8919i	−0.755347	+	1.03965i	−0.997587	+	0.0694293i	$0.977882\pi$
$942$		0			0
$943$	−9.49432	−	29.2205i	−0.309178	−	0.951551i
$944$	19.4455	−	0.190154i	0.632897	−	0.00618900i
$945$		0			0
$946$	8.73061	−	1.67101i	0.283857	−	0.0543292i
$947$		−	24.9488i		−	0.810725i	−0.914156	−	0.405363i	$-0.867145\pi$
$947$		−	24.9488i		−	0.810725i	0.914156	−	0.405363i	$-0.132855\pi$
$948$		0			0
$949$	11.1268	+	34.2447i	0.361190	+	1.11163i
$950$	27.1502	−	23.3035i	0.880868	−	0.756065i
$951$		0			0
$952$	−0.246563	−	0.207477i	−0.00799115	−	0.00672436i
$953$	−38.9090	−	12.6423i	−1.26039	−	0.409524i	−0.398754	−	0.917058i	$-0.630557\pi$
$953$	−38.9090	−	12.6423i	−1.26039	−	0.409524i	−0.861632	+	0.507534i	$0.830557\pi$
$954$		0			0
$955$	16.2035	+	22.3023i	0.524334	+	0.721684i
$956$	6.12800	+	11.8829i	0.198194	+	0.384320i
$957$		0			0
$958$	13.7835	+	8.40029i	0.445326	+	0.271401i
$959$	−1.65262	+	1.20070i	−0.0533658	+	0.0387725i
$960$		0			0
$961$	5.36305	−	16.5058i	0.173002	−	0.532445i
$962$	31.9376	−	13.3205i	1.02971	−	0.429472i
$963$		0			0
$964$	−1.38251	−	8.46089i	−0.0445277	−	0.272507i
$965$	−22.2383	+	7.22567i	−0.715877	+	0.232603i
$966$		0			0
$967$	23.6696			0.761164			0.380582	−	0.924747i	$-0.375724\pi$
$967$	23.6696			0.761164			0.380582	+	0.924747i	$0.375724\pi$
$968$	27.8896	−	13.7902i	0.896406	−	0.443234i
$969$		0			0
$970$	13.9249	−	1.13018i	0.447103	−	0.0362878i
$971$	51.2925	−	16.6659i	1.64606	−	0.534836i	0.668176	−	0.744004i	$-0.267076\pi$
$971$	51.2925	−	16.6659i	1.64606	−	0.534836i	0.977880	+	0.209168i	$0.0670755\pi$
$972$		0			0
$973$	−8.28781	−	6.02145i	−0.265695	−	0.193039i
$974$	5.22741	−	2.18025i	0.167497	−	0.0698598i
$975$		0			0
$976$	1.61363	−	5.13660i	0.0516509	−	0.164419i
$977$	−7.76321	+	5.64030i	−0.248367	+	0.180449i	−0.705003	−	0.709204i	$-0.749054\pi$
$977$	−7.76321	+	5.64030i	−0.248367	+	0.180449i	0.456636	+	0.889654i	$0.349054\pi$
$978$		0			0
$979$	17.7957	−	1.93169i	0.568752	−	0.0617371i
$980$	−5.37494	−	10.4226i	−0.171696	−	0.332938i
$981$		0			0
$982$	3.65797	−	15.4023i	0.116730	−	0.491508i
$983$	33.5747	+	10.9091i	1.07087	+	0.347945i	0.790824	−	0.612043i	$-0.209652\pi$
$983$	33.5747	+	10.9091i	1.07087	+	0.347945i	0.280041	+	0.959988i	$0.409652\pi$
$984$		0			0
$985$	−2.76715	+	3.80866i	−0.0881688	+	0.121354i
$986$	−0.295545	+	0.253671i	−0.00941206	+	0.00807854i
$987$		0			0
$988$	25.4359	−	50.5301i	0.809225	−	1.60758i
$989$			10.0631i			0.319987i
$990$		0			0
$991$			17.8021i			0.565502i	0.959193	+	0.282751i	$0.0912471\pi$
$991$			17.8021i			0.565502i	−0.959193	+	0.282751i	$0.908753\pi$
$992$	−17.9487	−	10.6994i	−0.569872	−	0.339707i
$993$		0			0
$994$	−10.4624	−	12.1894i	−0.331848	−	0.386626i
$995$	8.92918	−	12.2900i	0.283074	−	0.389618i
$996$		0			0
$997$	−59.8586	−	19.4492i	−1.89574	−	0.615963i	−0.973144	−	0.230197i	$-0.926063\pi$
$997$	−59.8586	−	19.4492i	−1.89574	−	0.615963i	−0.922596	−	0.385766i	$-0.873937\pi$
$998$	−54.1647	−	12.8638i	−1.71455	−	0.407198i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.r.a.19.4		16
3.2	odd	2		44.2.g.a.19.1	yes	16
4.3	odd	2	inner	396.2.r.a.19.2		16
11.7	odd	10	inner	396.2.r.a.271.2		16
12.11	even	2		44.2.g.a.19.3	yes	16
24.5	odd	2		704.2.u.c.63.2		16
24.11	even	2		704.2.u.c.63.3		16
33.2	even	10		484.2.c.d.483.3		16
33.5	odd	10		484.2.g.f.475.4		16
33.8	even	10		484.2.g.f.215.3		16
33.14	odd	10		484.2.g.j.215.2		16
33.17	even	10		484.2.g.j.475.1		16
33.20	odd	10		484.2.c.d.483.14		16
33.26	odd	10		484.2.g.i.403.2		16
33.29	even	10		44.2.g.a.7.3	yes	16
33.32	even	2		484.2.g.i.239.4		16
44.7	even	10	inner	396.2.r.a.271.4		16
132.35	odd	10		484.2.c.d.483.13		16
132.47	even	10		484.2.g.j.215.1		16
132.59	even	10		484.2.g.i.403.4		16
132.71	even	10		484.2.g.f.475.3		16
132.83	odd	10		484.2.g.j.475.2		16
132.95	odd	10		44.2.g.a.7.1	✓	16
132.107	odd	10		484.2.g.f.215.4		16
132.119	even	10		484.2.c.d.483.4		16
132.131	odd	2		484.2.g.i.239.2		16
264.29	even	10		704.2.u.c.447.3		16
264.227	odd	10		704.2.u.c.447.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.7.1	✓	16	132.95	odd	10
44.2.g.a.7.3	yes	16	33.29	even	10
44.2.g.a.19.1	yes	16	3.2	odd	2
44.2.g.a.19.3	yes	16	12.11	even	2
396.2.r.a.19.2		16	4.3	odd	2	inner
396.2.r.a.19.4		16	1.1	even	1	trivial
396.2.r.a.271.2		16	11.7	odd	10	inner
396.2.r.a.271.4		16	44.7	even	10	inner
484.2.c.d.483.3		16	33.2	even	10
484.2.c.d.483.4		16	132.119	even	10
484.2.c.d.483.13		16	132.35	odd	10
484.2.c.d.483.14		16	33.20	odd	10
484.2.g.f.215.3		16	33.8	even	10
484.2.g.f.215.4		16	132.107	odd	10
484.2.g.f.475.3		16	132.71	even	10
484.2.g.f.475.4		16	33.5	odd	10
484.2.g.i.239.2		16	132.131	odd	2
484.2.g.i.239.4		16	33.32	even	2
484.2.g.i.403.2		16	33.26	odd	10
484.2.g.i.403.4		16	132.59	even	10
484.2.g.j.215.1		16	132.47	even	10
484.2.g.j.215.2		16	33.14	odd	10
484.2.g.j.475.1		16	33.17	even	10
484.2.g.j.475.2		16	132.83	odd	10
704.2.u.c.63.2		16	24.5	odd	2
704.2.u.c.63.3		16	24.11	even	2
704.2.u.c.447.2		16	264.227	odd	10
704.2.u.c.447.3		16	264.29	even	10

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	396.2.r.a.19.4

Level	$396$
Weight	$2$
Character	396.19
Analytic conductor	$3.162$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$