LMFDB - Embedded newform 392.2.e.e.195.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(195,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("392.195");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.e (of order $2$, degree $1$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.4
Root			$2.00233 - 0.854000i$ of defining polynomial
Character	$\chi$	$=$	392.195
Dual form			392.2.e.e.195.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30084 + 0.554812i) q^{2} +0.480901i q^{3} +(1.38437 - 1.44344i) q^{4} +3.19427 q^{5} +(-0.266810 - 0.625575i) q^{6} +(-1.00000 + 2.64575i) q^{8} +2.76873 q^{9} +(-4.15523 + 1.77222i) q^{10} -1.60168 q^{11} +(0.694153 + 0.665743i) q^{12} +1.38831 q^{13} +1.53613i q^{15} +(-0.167055 - 3.99651i) q^{16} -4.02534i q^{17} +(-3.60168 + 1.53613i) q^{18} -5.27649i q^{19} +(4.42204 - 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +4.42301i q^{23} +(-1.27234 - 0.480901i) q^{24} +5.20336 q^{25} +(-1.80596 + 0.770249i) q^{26} +2.77419i q^{27} +5.10613i q^{29} +(-0.852262 - 1.99826i) q^{30} -0.115962 q^{31} +(2.43462 + 5.10613i) q^{32} -0.770249i q^{33} +(2.23331 + 5.23632i) q^{34} +(3.83294 - 3.99651i) q^{36} +5.34727i q^{37} +(2.92746 + 6.86387i) q^{38} +0.667638i q^{39} +(-3.19427 + 8.45124i) q^{40} -4.21689i q^{41} +(-2.21731 + 2.31193i) q^{44} +8.84408 q^{45} +(-2.45394 - 5.75363i) q^{46} +10.1164 q^{47} +(1.92193 - 0.0803370i) q^{48} +(-6.76873 + 2.88689i) q^{50} +1.93579 q^{51} +(1.92193 - 2.00394i) q^{52} +7.08425i q^{53} +(-1.53915 - 3.60878i) q^{54} -5.11619 q^{55} +2.53747 q^{57} +(-2.83294 - 6.64226i) q^{58} +5.06748i q^{59} +(2.21731 + 2.12656i) q^{60} -8.42643 q^{61} +(0.150848 - 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +4.43462 q^{65} +(0.427343 + 1.00197i) q^{66} -10.0363 q^{67} +(-5.81035 - 5.57255i) q^{68} -2.12703 q^{69} -5.29150i q^{71} +(-2.76873 + 7.32538i) q^{72} -10.7445i q^{73} +(-2.96673 - 6.95594i) q^{74} +2.50230i q^{75} +(-7.61631 - 7.30460i) q^{76} +(-0.370413 - 0.868490i) q^{78} -11.9338i q^{79} +(-0.533619 - 12.7659i) q^{80} +6.97209 q^{81} +(2.33958 + 5.48550i) q^{82} +14.9789i q^{83} -12.8580i q^{85} -2.45554 q^{87} +(1.60168 - 4.23764i) q^{88} +1.73205i q^{89} +(-11.5047 + 4.90680i) q^{90} +(6.38437 + 6.12307i) q^{92} -0.0557662i q^{93} +(-13.1598 + 5.61272i) q^{94} -16.8545i q^{95} +(-2.45554 + 1.17081i) q^{96} -2.87198i q^{97} -4.43462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8} + 12 q^{11} - 12 q^{18} + 24 q^{22} + 24 q^{30} + 48 q^{36} - 12 q^{44} + 36 q^{46} - 48 q^{50} - 12 q^{51} - 36 q^{57} - 36 q^{58} + 12 q^{60} - 72 q^{64} + 24 q^{65} - 60 q^{67} - 24 q^{74}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q - 12 * q^8 + 12 * q^11 - 12 * q^18 + 24 * q^22 + 24 * q^30 + 48 * q^36 - 12 * q^44 + 36 * q^46 - 48 * q^50 - 12 * q^51 - 36 * q^57 - 36 * q^58 + 12 * q^60 - 72 * q^64 + 24 * q^65 - 60 * q^67 - 24 * q^74 + 60 * q^78 - 12 * q^81 - 12 * q^88 + 60 * q^92 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.30084	+	0.554812i	−0.919832	+	0.392311i
$2$	−1.30084	+	0.554812i	−0.919832	+	0.392311i
$3$			0.480901i			0.277648i	0.990317	+	0.138824i	$0.0443323\pi$
$3$			0.480901i			0.277648i	−0.990317	+	0.138824i	$0.955668\pi$
$4$	1.38437	−	1.44344i	0.692184	−	0.721721i
$5$	3.19427			1.42852			0.714260	−	0.699880i	$-0.246763\pi$
$5$	3.19427			1.42852			0.714260	+	0.699880i	$0.246763\pi$
$6$	−0.266810	−	0.625575i	−0.108925	−	0.255390i
$7$		0			0
$7$		0			0
$8$	−1.00000	+	2.64575i	−0.353553	+	0.935414i
$9$	2.76873			0.922911
$10$	−4.15523	+	1.77222i	−1.31400	+	0.560425i
$11$	−1.60168			−0.482924			−0.241462	−	0.970410i	$-0.577627\pi$
$11$	−1.60168			−0.482924			−0.241462	+	0.970410i	$0.577627\pi$
$12$	0.694153	+	0.665743i	0.200385	+	0.192184i
$13$	1.38831			0.385047			0.192523	−	0.981292i	$-0.438333\pi$
$13$	1.38831			0.385047			0.192523	+	0.981292i	$0.438333\pi$
$14$		0			0
$15$			1.53613i			0.396626i
$16$	−0.167055	−	3.99651i	−0.0417638	−	0.999128i
$17$		−	4.02534i		−	0.976288i	−0.872763	−	0.488144i	$-0.837674\pi$
$17$		−	4.02534i		−	0.976288i	0.872763	−	0.488144i	$-0.162326\pi$
$18$	−3.60168	+	1.53613i	−0.848924	+	0.362069i
$19$		−	5.27649i		−	1.21051i	−0.796032	−	0.605255i	$-0.793071\pi$
$19$		−	5.27649i		−	1.21051i	0.796032	−	0.605255i	$-0.206929\pi$
$20$	4.42204	−	4.61075i	0.988799	−	1.03099i
$21$		0			0
$22$	2.08353	−	0.888631i	0.444210	−	0.189457i
$23$			4.42301i			0.922262i	0.887332	+	0.461131i	$0.152556\pi$
$23$			4.42301i			0.922262i	−0.887332	+	0.461131i	$0.847444\pi$
$24$	−1.27234	−	0.480901i	−0.259716	−	0.0981635i
$25$	5.20336			1.04067
$26$	−1.80596	+	0.770249i	−0.354179	+	0.151058i
$27$			2.77419i			0.533893i
$28$		0			0
$29$			5.10613i			0.948185i	0.880475	+	0.474093i	$0.157224\pi$
$29$			5.10613i			0.948185i	−0.880475	+	0.474093i	$0.842776\pi$
$30$	−0.852262	−	1.99826i	−0.155601	−	0.364830i
$31$	−0.115962			−0.0208274			−0.0104137	−	0.999946i	$-0.503315\pi$
$31$	−0.115962			−0.0208274			−0.0104137	+	0.999946i	$0.503315\pi$
$32$	2.43462	+	5.10613i	0.430385	+	0.902646i
$33$		−	0.770249i		−	0.134083i
$34$	2.23331	+	5.23632i	0.383009	+	0.898022i
$35$		0			0
$36$	3.83294	−	3.99651i	0.638824	−	0.666085i
$37$			5.34727i			0.879086i	0.898222	+	0.439543i	$0.144860\pi$
$37$			5.34727i			0.879086i	−0.898222	+	0.439543i	$0.855140\pi$
$38$	2.92746	+	6.86387i	0.474897	+	1.11347i
$39$			0.667638i			0.106908i
$40$	−3.19427	+	8.45124i	−0.505058	+	1.33626i
$41$		−	4.21689i		−	0.658568i	−0.944231	−	0.329284i	$-0.893193\pi$
$41$		−	4.21689i		−	0.658568i	0.944231	−	0.329284i	$-0.106807\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−2.21731	+	2.31193i	−0.334272	+	0.348537i
$45$	8.84408			1.31840
$46$	−2.45394	−	5.75363i	−0.361814	−	0.848327i
$47$	10.1164			1.47563			0.737816	−	0.675002i	$-0.235857\pi$
$47$	10.1164			1.47563			0.737816	+	0.675002i	$0.235857\pi$
$48$	1.92193	−	0.0803370i	0.277406	−	0.0115956i
$49$		0			0
$50$	−6.76873	+	2.88689i	−0.957244	+	0.408267i
$51$	1.93579			0.271065
$52$	1.92193	−	2.00394i	0.266523	−	0.277897i
$53$			7.08425i			0.973096i	0.873654	+	0.486548i	$0.161744\pi$
$53$			7.08425i			0.973096i	−0.873654	+	0.486548i	$0.838256\pi$
$54$	−1.53915	−	3.60878i	−0.209452	−	0.491092i
$55$	−5.11619			−0.689868
$56$		0			0
$57$	2.53747			0.336096
$58$	−2.83294	−	6.64226i	−0.371984	−	0.872172i
$59$			5.06748i			0.659729i	0.944028	+	0.329865i	$0.107003\pi$
$59$			5.06748i			0.659729i	−0.944028	+	0.329865i	$0.892997\pi$
$60$	2.21731	+	2.12656i	0.286254	+	0.274538i
$61$	−8.42643			−1.07889			−0.539447	−	0.842020i	$-0.681367\pi$
$61$	−8.42643			−1.07889			−0.539447	+	0.842020i	$0.681367\pi$
$62$	0.150848	−	0.0643370i	0.0191577	−	0.00817081i
$63$		0			0
$64$	−6.00000	−	5.29150i	−0.750000	−	0.661438i
$65$	4.43462			0.550047
$66$	0.427343	+	1.00197i	0.0526023	+	0.123334i
$67$	−10.0363			−1.22613			−0.613065	−	0.790033i	$-0.710064\pi$
$67$	−10.0363			−1.22613			−0.613065	+	0.790033i	$0.710064\pi$
$68$	−5.81035	−	5.57255i	−0.704608	−	0.675771i
$69$	−2.12703			−0.256064
$70$		0			0
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$	−2.76873	+	7.32538i	−0.326298	+	0.863305i
$73$		−	10.7445i		−	1.25755i	−0.777586	−	0.628776i	$-0.783556\pi$
$73$		−	10.7445i		−	1.25755i	0.777586	−	0.628776i	$-0.216444\pi$
$74$	−2.96673	−	6.95594i	−0.344875	−	0.808611i
$75$			2.50230i			0.288941i
$76$	−7.61631	−	7.30460i	−0.873651	−	0.837895i
$77$		0			0
$78$	−0.370413	−	0.868490i	−0.0419411	−	0.0983371i
$79$		−	11.9338i		−	1.34265i	−0.741162	−	0.671327i	$-0.765725\pi$
$79$		−	11.9338i		−	1.34265i	0.741162	−	0.671327i	$-0.234275\pi$
$80$	−0.533619	−	12.7659i	−0.0596604	−	1.42727i
$81$	6.97209			0.774677
$82$	2.33958	+	5.48550i	0.258364	+	0.605772i
$83$			14.9789i			1.64415i	0.569382	+	0.822073i	$0.307182\pi$
$83$			14.9789i			1.64415i	−0.569382	+	0.822073i	$0.692818\pi$
$84$		0			0
$85$		−	12.8580i		−	1.39465i
$86$		0			0
$87$	−2.45554			−0.263262
$88$	1.60168	−	4.23764i	0.170740	−	0.451734i
$89$			1.73205i			0.183597i	0.995778	+	0.0917985i	$0.0292616\pi$
$89$			1.73205i			0.183597i	−0.995778	+	0.0917985i	$0.970738\pi$
$90$	−11.5047	+	4.90680i	−1.21271	+	0.517223i
$91$		0			0
$92$	6.38437	+	6.12307i	0.665616	+	0.638375i
$93$		−	0.0557662i		−	0.00578268i
$94$	−13.1598	+	5.61272i	−1.35733	+	0.578907i
$95$		−	16.8545i		−	1.72924i
$96$	−2.45554	+	1.17081i	−0.250618	+	0.119496i
$97$		−	2.87198i		−	0.291606i	−0.989314	−	0.145803i	$-0.953423\pi$
$97$		−	2.87198i		−	0.291606i	0.989314	−	0.145803i	$-0.0465765\pi$
$98$		0			0
$99$	−4.43462			−0.445696
$100$	7.20336	−	7.51075i	0.720336	−	0.751075i
$101$	−6.80620			−0.677242			−0.338621	−	0.940923i	$-0.609960\pi$
$101$	−6.80620			−0.677242			−0.338621	+	0.940923i	$0.609960\pi$
$102$	−2.51815	+	1.07400i	−0.249334	+	0.106342i
$103$	−14.0494			−1.38433			−0.692165	−	0.721739i	$-0.743343\pi$
$103$	−14.0494			−1.38433			−0.692165	+	0.721739i	$0.743343\pi$
$104$	−1.38831	+	3.67311i	−0.136135	+	0.360178i
$105$		0			0
$106$	−3.93043	−	9.21547i	−0.381757	−	0.895086i
$107$	−5.13915			−0.496820			−0.248410	−	0.968655i	$-0.579908\pi$
$107$	−5.13915			−0.496820			−0.248410	+	0.968655i	$0.579908\pi$
$108$	4.00438	+	3.84050i	0.385322	+	0.369552i
$109$		−	2.83112i		−	0.271172i	−0.990766	−	0.135586i	$-0.956708\pi$
$109$		−	2.83112i		−	0.271172i	0.990766	−	0.135586i	$-0.0432917\pi$
$110$	6.65535	−	2.83853i	0.634563	−	0.270643i
$111$	−2.57151			−0.244077
$112$		0			0
$113$	−1.43695			−0.135177			−0.0675887	−	0.997713i	$-0.521531\pi$
$113$	−1.43695			−0.135177			−0.0675887	+	0.997713i	$0.521531\pi$
$114$	−3.30084	+	1.40782i	−0.309152	+	0.131854i
$115$			14.1283i			1.31747i
$116$	7.37041	+	7.06876i	0.684326	+	0.656318i
$117$	3.84385			0.355364
$118$	−2.81150	−	6.59198i	−0.258819	−	0.606841i
$119$		0			0
$120$	−4.06421	−	1.53613i	−0.371010	−	0.140229i
$121$	−8.43462			−0.766784
$122$	10.9614	−	4.67508i	0.992401	−	0.423262i
$123$	2.02791			0.182850
$124$	−0.160534	+	0.167384i	−0.0144164	+	0.0150316i
$125$	0.649581			0.0581003
$126$		0			0
$127$			4.92077i			0.436647i	0.975876	+	0.218324i	$0.0700589\pi$
$127$			4.92077i			0.436647i	−0.975876	+	0.218324i	$0.929941\pi$
$128$	10.7408	+	3.55452i	0.949364	+	0.314178i
$129$		0			0
$130$	−5.76873	+	2.46038i	−0.505951	+	0.215790i
$131$		−	3.94500i		−	0.344676i	−0.985038	−	0.172338i	$-0.944868\pi$
$131$		−	3.94500i		−	0.344676i	0.985038	−	0.172338i	$-0.0551322\pi$
$132$	−1.11181	−	1.06631i	−0.0967707	−	0.0928101i
$133$		0			0
$134$	13.0556	−	5.56826i	1.12783	−	0.481025i
$135$			8.86151i			0.762677i
$136$	10.6500	+	4.02534i	0.913234	+	0.345170i
$137$	−0.102845			−0.00878661			−0.00439331	−	0.999990i	$-0.501398\pi$
$137$	−0.102845			−0.00878661			−0.00439331	+	0.999990i	$0.501398\pi$
$138$	2.76693	−	1.18010i	0.235536	−	0.100457i
$139$		−	14.9789i		−	1.27049i	−0.772310	−	0.635246i	$-0.780899\pi$
$139$		−	14.9789i		−	1.27049i	0.772310	−	0.635246i	$-0.219101\pi$
$140$		0			0
$141$			4.86500i			0.409707i
$142$	2.93579	+	6.88340i	0.246366	+	0.577642i
$143$	−2.22362			−0.185949
$144$	−0.462531	−	11.0653i	−0.0385443	−	0.922106i
$145$			16.3104i			1.35450i
$146$	5.96120	+	13.9769i	0.493352	+	1.15674i
$147$		0			0
$148$	7.71848	+	7.40258i	0.634455	+	0.608489i
$149$		−	11.3064i		−	0.926257i	−0.886291	−	0.463129i	$-0.846727\pi$
$149$		−	11.3064i		−	0.926257i	0.886291	−	0.463129i	$-0.153273\pi$
$150$	−1.38831	−	3.25509i	−0.113355	−	0.265777i
$151$			14.8206i			1.20609i	0.797708	+	0.603044i	$0.206046\pi$
$151$			14.8206i			1.20609i	−0.797708	+	0.603044i	$0.793954\pi$
$152$	13.9603	+	5.27649i	1.13233	+	0.427980i
$153$		−	11.1451i		−	0.901028i
$154$		0			0
$155$	−0.370413			−0.0297523
$156$	0.963697	+	0.924256i	0.0771575	+	0.0739997i
$157$	−0.738725			−0.0589567			−0.0294783	−	0.999565i	$-0.509385\pi$
$157$	−0.738725			−0.0589567			−0.0294783	+	0.999565i	$0.509385\pi$
$158$	6.62100	+	15.5239i	0.526738	+	1.23502i
$159$	−3.40682			−0.270179
$160$	7.77685	+	16.3104i	0.614814	+	1.28945i
$161$		0			0
$162$	−9.06957	+	3.86820i	−0.712573	+	0.303915i
$163$	−8.70452			−0.681791			−0.340895	−	0.940101i	$-0.610730\pi$
$163$	−8.70452			−0.681791			−0.340895	+	0.940101i	$0.610730\pi$
$164$	−6.08684	−	5.83773i	−0.475303	−	0.455850i
$165$		−	2.46038i		−	0.191541i
$166$	−8.31046	−	19.4851i	−0.645017	−	1.51234i
$167$	1.38831			0.107430			0.0537152	−	0.998556i	$-0.482894\pi$
$167$	1.38831			0.107430			0.0537152	+	0.998556i	$0.482894\pi$
$168$		0			0
$169$	−11.0726			−0.851739
$170$	7.13378	+	16.7262i	0.547136	+	1.28284i
$171$		−	14.6092i		−	1.11719i
$172$		0			0
$173$	0.970649			0.0737971			0.0368985	−	0.999319i	$-0.488252\pi$
$173$	0.970649			0.0737971			0.0368985	+	0.999319i	$0.488252\pi$
$174$	3.19427	−	1.36237i	0.242157	−	0.103281i
$175$		0			0
$176$	0.267569	+	6.40113i	0.0201688	+	0.482503i
$177$	−2.43695			−0.183173
$178$	−0.960963	−	2.25312i	−0.0720272	−	0.168879i
$179$	−14.2699			−1.06658			−0.533291	−	0.845932i	$-0.679045\pi$
$179$	−14.2699			−1.06658			−0.533291	+	0.845932i	$0.679045\pi$
$180$	12.2435	−	12.7659i	0.912574	−	0.951516i
$181$	15.3218			1.13886			0.569429	−	0.822041i	$-0.307164\pi$
$181$	15.3218			1.13886			0.569429	+	0.822041i	$0.307164\pi$
$182$		0			0
$183$		−	4.05228i		−	0.299553i
$184$	−11.7022	−	4.42301i	−0.862697	−	0.326069i
$185$			17.0806i			1.25579i
$186$	0.0309397	+	0.0725428i	0.00226861	+	0.00531910i
$187$			6.44730i			0.471473i
$188$	14.0049	−	14.6025i	1.02141	−	1.06500i
$189$		0			0
$190$	9.35110	+	21.9250i	0.678400	+	1.59061i
$191$		−	2.50067i		−	0.180942i	−0.995899	−	0.0904709i	$-0.971163\pi$
$191$		−	2.50067i		−	0.180942i	0.995899	−	0.0904709i	$-0.0288372\pi$
$192$	2.54469	−	2.88541i	0.183647	−	0.208236i
$193$	−3.10051			−0.223180			−0.111590	−	0.993754i	$-0.535594\pi$
$193$	−3.10051			−0.223180			−0.111590	+	0.993754i	$0.535594\pi$
$194$	1.59341	+	3.73599i	0.114400	+	0.268229i
$195$			2.13261i			0.152720i
$196$		0			0
$197$			15.6891i			1.11780i	0.829233	+	0.558902i	$0.188777\pi$
$197$			15.6891i			1.11780i	−0.829233	+	0.558902i	$0.811223\pi$
$198$	5.76873	−	2.46038i	0.409966	−	0.174852i
$199$	−11.8258			−0.838309			−0.419154	−	0.907915i	$-0.637673\pi$
$199$	−11.8258			−0.838309			−0.419154	+	0.907915i	$0.637673\pi$
$200$	−5.20336	+	13.7668i	−0.367933	+	0.973459i
$201$		−	4.82647i		−	0.340433i
$202$	8.85377	−	3.77616i	0.622949	−	0.265690i
$203$		0			0
$204$	2.67984	−	2.79420i	0.187627	−	0.195633i
$205$		−	13.4699i		−	0.940778i
$206$	18.2760	−	7.79479i	1.27335	−	0.543089i
$207$			12.2461i			0.851166i
$208$	−0.231924	−	5.54838i	−0.0160810	−	0.384711i
$209$			8.45124i			0.584585i
$210$		0			0
$211$	10.0726			0.693427			0.346713	−	0.937971i	$-0.387298\pi$
$211$	10.0726			0.693427			0.346713	+	0.937971i	$0.387298\pi$
$212$	10.2257	+	9.80720i	0.702304	+	0.673561i
$213$	2.54469			0.174359
$214$	6.68521	−	2.85126i	0.456991	−	0.194908i
$215$		0			0
$216$	−7.33982	−	2.77419i	−0.499411	−	0.188760i
$217$		0			0
$218$	1.57074	+	3.68283i	0.106384	+	0.249433i
$219$	5.16706			0.349157
$220$	−7.08269	+	7.38494i	−0.477515	+	0.497892i
$221$		−	5.58840i		−	0.375917i
$222$	3.34512	−	1.42670i	0.224510	−	0.0957540i
$223$	24.3086			1.62783			0.813913	−	0.580987i	$-0.197333\pi$
$223$	24.3086			1.62783			0.813913	+	0.580987i	$0.197333\pi$
$224$		0			0
$225$	14.4067			0.960448
$226$	1.86925	−	0.797240i	0.124341	−	0.0530316i
$227$			14.3239i			0.950710i	0.879794	+	0.475355i	$0.157680\pi$
$227$			14.3239i			0.950710i	−0.879794	+	0.475355i	$0.842320\pi$
$228$	3.51279	−	3.66269i	0.232640	−	0.242568i
$229$	−10.6500			−0.703775			−0.351887	−	0.936042i	$-0.614460\pi$
$229$	−10.6500			−0.703775			−0.351887	+	0.936042i	$0.614460\pi$
$230$	−7.83855	−	18.3786i	−0.516859	−	1.21185i
$231$		0			0
$232$	−13.5096	−	5.10613i	−0.886946	−	0.335234i
$233$	−0.637982			−0.0417956			−0.0208978	−	0.999782i	$-0.506652\pi$
$233$	−0.637982			−0.0417956			−0.0208978	+	0.999782i	$0.506652\pi$
$234$	−5.00023	+	2.13261i	−0.326875	+	0.139413i
$235$	32.3146			2.10797
$236$	7.31462	+	7.01525i	0.476141	+	0.456654i
$237$	5.73896			0.372785
$238$		0			0
$239$		−	4.73540i		−	0.306307i	−0.988202	−	0.153154i	$-0.951057\pi$
$239$		−	4.73540i		−	0.306307i	0.988202	−	0.153154i	$-0.0489430\pi$
$240$	6.13915	−	0.256618i	0.396280	−	0.0165646i
$241$			11.7063i			0.754071i	0.926199	+	0.377036i	$0.123057\pi$
$241$			11.7063i			0.754071i	−0.926199	+	0.377036i	$0.876943\pi$
$242$	10.9721	−	4.67963i	0.705313	−	0.300818i
$243$			11.6755i			0.748981i
$244$	−11.6653	+	12.1631i	−0.746792	+	0.778661i
$245$		0			0
$246$	−2.63798	+	1.12511i	−0.168192	+	0.0717342i
$247$		−	7.32538i		−	0.466103i
$248$	0.115962	−	0.306806i	0.00736359	−	0.0194822i
$249$	−7.20336			−0.456494
$250$	−0.845001	+	0.360395i	−0.0534425	+	0.0227934i
$251$		−	11.5631i		−	0.729858i	−0.931035	−	0.364929i	$-0.881093\pi$
$251$		−	11.5631i		−	0.729858i	0.931035	−	0.364929i	$-0.118907\pi$
$252$		0			0
$253$		−	7.08425i		−	0.445383i
$254$	−2.73010	−	6.40113i	−0.171302	−	0.401642i
$255$	6.18343			0.387222
$256$	−15.9442	+	1.33528i	−0.996512	+	0.0834547i
$257$		−	23.5908i		−	1.47155i	−0.677224	−	0.735777i	$-0.736817\pi$
$257$		−	23.5908i		−	1.47155i	0.677224	−	0.735777i	$-0.263183\pi$
$258$		0			0
$259$		0			0
$260$	6.13915	−	6.40113i	0.380734	−	0.396981i
$261$			14.1375i			0.875091i
$262$	2.18873	+	5.13182i	0.135220	+	0.317045i
$263$		−	10.6791i		−	0.658499i	−0.944243	−	0.329249i	$-0.893204\pi$
$263$		−	10.6791i		−	0.658499i	0.944243	−	0.329249i	$-0.106796\pi$
$264$	2.03789	+	0.770249i	0.125423	+	0.0474055i
$265$			22.6290i			1.39009i
$266$		0			0
$267$	−0.832945			−0.0509754
$268$	−13.8939	+	14.4868i	−0.848707	+	0.884924i
$269$	−23.3380			−1.42294			−0.711471	−	0.702716i	$-0.751971\pi$
$269$	−23.3380			−1.42294			−0.711471	+	0.702716i	$0.751971\pi$
$270$	−4.91647	−	11.5274i	−0.299207	−	0.701535i
$271$	13.6392			0.828523			0.414262	−	0.910158i	$-0.364040\pi$
$271$	13.6392			0.828523			0.414262	+	0.910158i	$0.364040\pi$
$272$	−16.0873	+	0.672454i	−0.975436	+	0.0407735i
$273$		0			0
$274$	0.133784	−	0.0570595i	0.00808221	−	0.00344709i
$275$	−8.33411			−0.502566
$276$	−2.94459	+	3.07025i	−0.177244	+	0.184807i
$277$		−	0.457470i		−	0.0274867i	−0.999906	−	0.0137433i	$-0.995625\pi$
$277$		−	0.457470i		−	0.0274867i	0.999906	−	0.0137433i	$-0.00437478\pi$
$278$	8.31046	+	19.4851i	0.498429	+	1.16864i
$279$	−0.321068			−0.0192218
$280$		0			0
$281$	1.43695			0.0857215			0.0428608	−	0.999081i	$-0.486353\pi$
$281$	1.43695			0.0857215			0.0428608	+	0.999081i	$0.486353\pi$
$282$	−2.69916	−	6.32858i	−0.160733	−	0.376862i
$283$		−	31.2264i		−	1.85622i	−0.372312	−	0.928108i	$-0.621435\pi$
$283$		−	31.2264i		−	1.85622i	0.372312	−	0.928108i	$-0.378565\pi$
$284$	−7.63798	−	7.32538i	−0.453231	−	0.434681i
$285$	8.10536			0.480120
$286$	2.89257	−	1.23369i	0.171041	−	0.0729497i
$287$		0			0
$288$	6.74083	+	14.1375i	0.397207	+	0.833062i
$289$	0.796642			0.0468613
$290$	−9.04919	−	21.2172i	−0.531387	−	1.24592i
$291$	1.38114			0.0809639
$292$	−15.5091	−	14.8744i	−0.907603	−	0.870457i
$293$	−31.3006			−1.82860			−0.914299	−	0.405040i	$-0.867258\pi$
$293$	−31.3006			−1.82860			−0.914299	+	0.405040i	$0.867258\pi$
$294$		0			0
$295$			16.1869i			0.942437i
$296$	−14.1475	−	5.34727i	−0.822309	−	0.310804i
$297$		−	4.44336i		−	0.257830i
$298$	6.27293	+	14.7078i	0.363381	+	0.852001i
$299$			6.14050i			0.355114i
$300$	3.61193	+	3.46410i	0.208535	+	0.200000i
$301$		0			0
$302$	−8.22268	−	19.2793i	−0.473162	−	1.10940i
$303$		−	3.27311i		−	0.188035i
$304$	−21.0875	+	0.881465i	−1.20945	+	0.0505555i
$305$	−26.9163			−1.54122
$306$	6.18343	+	14.4980i	0.353483	+	0.828794i
$307$		−	14.7215i		−	0.840202i	−0.907477	−	0.420101i	$-0.861995\pi$
$307$		−	14.7215i		−	0.840202i	0.907477	−	0.420101i	$-0.138005\pi$
$308$		0			0
$309$		−	6.75638i		−	0.384357i
$310$	0.481848	−	0.205510i	0.0273672	−	0.0116722i
$311$	15.5805			0.883490			0.441745	−	0.897141i	$-0.354360\pi$
$311$	15.5805			0.883490			0.441745	+	0.897141i	$0.354360\pi$
$312$	−1.76640	−	0.667638i	−0.100003	−	0.0377975i
$313$			13.0862i			0.739673i	0.929097	+	0.369837i	$0.120586\pi$
$313$			13.0862i			0.739673i	−0.929097	+	0.369837i	$0.879414\pi$
$314$	0.960963	−	0.409854i	0.0542303	−	0.0231294i
$315$		0			0
$316$	−17.2257	−	16.5207i	−0.969022	−	0.929363i
$317$			23.5526i			1.32284i	0.750014	+	0.661422i	$0.230047\pi$
$317$			23.5526i			1.32284i	−0.750014	+	0.661422i	$0.769953\pi$
$318$	4.43173	−	1.89015i	0.248519	−	0.105994i
$319$		−	8.17839i		−	0.457902i
$320$	−19.1656	−	16.9025i	−1.07139	−	0.944878i
$321$		−	2.47142i		−	0.137941i
$322$		0			0
$323$	−21.2397			−1.18181
$324$	9.65194	−	10.0638i	0.536219	−	0.559101i
$325$	7.22385			0.400707
$326$	11.3232	−	4.82937i	0.627133	−	0.267474i
$327$	1.36149			0.0752905
$328$	11.1568	+	4.21689i	0.616034	+	0.232839i
$329$		0			0
$330$	1.36505	+	3.20056i	0.0751435	+	0.176185i
$331$	33.0554			1.81689			0.908445	−	0.418004i	$-0.137270\pi$
$331$	33.0554			1.81689			0.908445	+	0.418004i	$0.137270\pi$
$332$	21.6212	+	20.7363i	1.18662	+	1.13805i
$333$			14.8052i			0.811318i
$334$	−1.80596	+	0.770249i	−0.0988179	+	0.0421461i
$335$	−32.0587			−1.75155
$336$		0			0
$337$	−15.5096			−0.844860			−0.422430	−	0.906396i	$-0.638823\pi$
$337$	−15.5096			−0.844860			−0.422430	+	0.906396i	$0.638823\pi$
$338$	14.4037	−	6.14322i	0.783457	−	0.334147i
$339$		−	0.691033i		−	0.0375318i
$340$	−18.5598	−	17.8002i	−1.00655	−	0.965352i
$341$	0.185734			0.0100580
$342$	8.10536	+	19.0042i	0.438288	+	1.02763i
$343$		0			0
$344$		0			0
$345$	−6.79431			−0.365793
$346$	−1.26266	+	0.538528i	−0.0678809	+	0.0289514i
$347$	22.4988			1.20780			0.603900	−	0.797060i	$-0.293612\pi$
$347$	22.4988			1.20780			0.603900	+	0.797060i	$0.293612\pi$
$348$	−3.39938	+	3.54444i	−0.182226	+	0.190002i
$349$	−28.4735			−1.52415			−0.762077	−	0.647486i	$-0.775820\pi$
$349$	−28.4735			−1.52415			−0.762077	+	0.647486i	$0.775820\pi$
$350$		0			0
$351$			3.85142i			0.205574i
$352$	−3.89949	−	8.17839i	−0.207843	−	0.435910i
$353$			9.57372i			0.509558i	0.966999	+	0.254779i	$0.0820027\pi$
$353$			9.57372i			0.509558i	−0.966999	+	0.254779i	$0.917997\pi$
$354$	3.17009	−	1.35205i	0.168488	−	0.0718608i
$355$		−	16.9025i		−	0.897091i
$356$	2.50012	+	2.39779i	0.132506	+	0.127083i
$357$		0			0
$358$	18.5629	−	7.91711i	0.981077	−	0.418432i
$359$		−	3.75538i		−	0.198201i	−0.995077	−	0.0991006i	$-0.968403\pi$
$359$		−	3.75538i		−	0.198201i	0.995077	−	0.0991006i	$-0.0315966\pi$
$360$	−8.84408	+	23.3992i	−0.466124	+	1.23325i
$361$	−8.84134			−0.465334
$362$	−19.9312	+	8.50070i	−1.04756	+	0.446787i
$363$		−	4.05622i		−	0.212896i
$364$		0			0
$365$		−	34.3209i		−	1.79644i
$366$	2.24825	+	5.27136i	0.117518	+	0.275538i
$367$	16.8260			0.878312			0.439156	−	0.898411i	$-0.355278\pi$
$367$	16.8260			0.878312			0.439156	+	0.898411i	$0.355278\pi$
$368$	17.6766	−	0.738887i	0.921457	−	0.0385172i
$369$		−	11.6755i		−	0.607800i
$370$	−9.47653	−	22.2191i	−0.492661	−	1.15512i
$371$		0			0
$372$	−0.0804953	−	0.0772008i	−0.00417349	−	0.00400268i
$373$		−	12.8580i		−	0.665763i	−0.942969	−	0.332882i	$-0.891979\pi$
$373$		−	12.8580i		−	0.665763i	0.942969	−	0.332882i	$-0.108021\pi$
$374$	−3.57704	−	8.38691i	−0.184964	−	0.433677i
$375$			0.312384i			0.0161314i
$376$	−10.1164	+	26.7656i	−0.521715	+	1.38033i
$377$			7.08888i			0.365096i
$378$		0			0
$379$	25.5822			1.31407			0.657034	−	0.753861i	$-0.271811\pi$
$379$	25.5822			1.31407			0.657034	+	0.753861i	$0.271811\pi$
$380$	−24.3286	−	23.3329i	−1.24803	−	1.19695i
$381$	−2.36640			−0.121234
$382$	1.38740	+	3.25296i	0.0709855	+	0.166436i
$383$	−26.9693			−1.37807			−0.689033	−	0.724730i	$-0.741964\pi$
$383$	−26.9693			−1.37807			−0.689033	+	0.724730i	$0.741964\pi$
$384$	−1.70937	+	5.16527i	−0.0872311	+	0.263589i
$385$		0			0
$386$	4.03327	−	1.72020i	0.205288	−	0.0875560i
$387$		0			0
$388$	−4.14555	−	3.97588i	−0.210458	−	0.201845i
$389$		−	31.9902i		−	1.62197i	−0.585070	−	0.810983i	$-0.698933\pi$
$389$		−	31.9902i		−	1.62197i	0.585070	−	0.810983i	$-0.301067\pi$
$390$	−1.18320	−	2.77419i	−0.0599137	−	0.140477i
$391$	17.8041			0.900394
$392$		0			0
$393$	1.89716			0.0956988
$394$	−8.70452	−	20.4091i	−0.438528	−	1.02819i
$395$		−	38.1197i		−	1.91801i
$396$	−6.13915	+	6.40113i	−0.308504	+	0.321669i
$397$	17.0386			0.855142			0.427571	−	0.903982i	$-0.359369\pi$
$397$	17.0386			0.855142			0.427571	+	0.903982i	$0.359369\pi$
$398$	15.3835	−	6.56110i	0.771104	−	0.328878i
$399$		0			0
$400$	−0.869248	−	20.7953i	−0.0434624	−	1.03976i
$401$	−5.89716			−0.294490			−0.147245	−	0.989100i	$-0.547041\pi$
$401$	−5.89716			−0.294490			−0.147245	+	0.989100i	$0.547041\pi$
$402$	2.67778	+	6.27846i	0.133556	+	0.313141i
$403$	−0.160991			−0.00801951
$404$	−9.42228	+	9.82436i	−0.468776	+	0.488780i
$405$	22.2707			1.10664
$406$		0			0
$407$		−	8.56461i		−	0.424532i
$408$	−1.93579	+	5.12162i	−0.0958359	+	0.253558i
$409$			0.239890i			0.0118618i	0.999982	+	0.00593090i	$0.00188787\pi$
$409$			0.239890i			0.0118618i	−0.999982	+	0.00593090i	$0.998112\pi$
$410$	7.47326	+	17.5222i	0.369078	+	0.865358i
$411$		−	0.0494581i		−	0.00243959i
$412$	−19.4496	+	20.2795i	−0.958211	+	0.999101i
$413$		0			0
$414$	−6.79431	−	15.9303i	−0.333922	−	0.782930i
$415$			47.8466i			2.34870i
$416$	3.38000	+	7.08888i	0.165718	+	0.347561i
$417$	7.20336			0.352750
$418$	−4.68885	−	10.9937i	−0.229339	−	0.537720i
$419$			29.4140i			1.43697i	0.695544	+	0.718484i	$0.255163\pi$
$419$			29.4140i			1.43697i	−0.695544	+	0.718484i	$0.744837\pi$
$420$		0			0
$421$			32.1265i			1.56575i	0.622180	+	0.782874i	$0.286247\pi$
$421$			32.1265i			1.56575i	−0.622180	+	0.782874i	$0.713753\pi$
$422$	−13.1028	+	5.58840i	−0.637836	+	0.272039i
$423$	28.0097			1.36188
$424$	−18.7432	−	7.08425i	−0.910248	−	0.344041i
$425$		−	20.9453i		−	1.01600i
$426$	−3.31023	+	1.41182i	−0.160381	+	0.0684031i
$427$		0			0
$428$	−7.11447	+	7.41807i	−0.343891	+	0.358566i
$429$		−	1.06934i		−	0.0516283i
$430$		0			0
$431$			37.8352i			1.82246i	0.411902	+	0.911228i	$0.364865\pi$
$431$			37.8352i			1.82246i	−0.411902	+	0.911228i	$0.635135\pi$
$432$	11.0871	−	0.463443i	0.533427	−	0.0222974i
$433$			25.4835i			1.22466i	0.790602	+	0.612330i	$0.209768\pi$
$433$			25.4835i			1.22466i	−0.790602	+	0.612330i	$0.790232\pi$
$434$		0			0
$435$	−7.84367			−0.376075
$436$	−4.08656	−	3.91931i	−0.195711	−	0.187701i
$437$	23.3380			1.11641
$438$	−6.72151	+	2.86674i	−0.321166	+	0.136978i
$439$	23.9607			1.14358			0.571792	−	0.820399i	$-0.306248\pi$
$439$	23.9607			1.14358			0.571792	+	0.820399i	$0.306248\pi$
$440$	5.11619	−	13.5362i	0.243905	−	0.645312i
$441$		0			0
$442$	3.10051	+	7.26962i	0.147476	+	0.345780i
$443$	10.2699			0.487938			0.243969	−	0.969783i	$-0.421551\pi$
$443$	10.2699			0.487938			0.243969	+	0.969783i	$0.421551\pi$
$444$	−3.55991	+	3.71182i	−0.168946	+	0.176155i
$445$			5.53264i			0.262272i
$446$	−31.6216	+	13.4867i	−1.49733	+	0.638615i
$447$	5.43726			0.257174
$448$		0			0
$449$	11.5096			0.543170			0.271585	−	0.962414i	$-0.412452\pi$
$449$	11.5096			0.543170			0.271585	+	0.962414i	$0.412452\pi$
$450$	−18.7408	+	7.99302i	−0.883451	+	0.376795i
$451$			6.75411i			0.318039i
$452$	−1.98927	+	2.07416i	−0.0935675	+	0.0975604i
$453$	−7.12726			−0.334868
$454$	−7.94707	−	18.6331i	−0.372974	−	0.874494i
$455$		0			0
$456$	−2.53747	+	6.71351i	−0.118828	+	0.314389i
$457$	30.6101			1.43188			0.715939	−	0.698162i	$-0.245999\pi$
$457$	30.6101			1.43188			0.715939	+	0.698162i	$0.245999\pi$
$458$	13.8540	−	5.90877i	0.647355	−	0.276099i
$459$	11.1671			0.521233
$460$	20.3934	+	19.5587i	0.950847	+	0.911931i
$461$	17.3671			0.808866			0.404433	−	0.914568i	$-0.367469\pi$
$461$	17.3671			0.808866			0.404433	+	0.914568i	$0.367469\pi$
$462$		0			0
$463$		−	21.7288i		−	1.00983i	−0.863171	−	0.504913i	$-0.831525\pi$
$463$		−	21.7288i		−	1.00983i	0.863171	−	0.504913i	$-0.168475\pi$
$464$	20.4067	−	0.853006i	0.947358	−	0.0395998i
$465$		−	0.178132i		−	0.00826068i
$466$	0.829913	−	0.353960i	0.0384450	−	0.0163969i
$467$		−	0.676491i		−	0.0313043i	−0.999877	−	0.0156521i	$-0.995018\pi$
$467$		−	0.676491i		−	0.0313043i	0.999877	−	0.0156521i	$-0.00498243\pi$
$468$	5.32130	−	5.54838i	0.245977	−	0.256474i
$469$		0			0
$470$	−42.0361	+	17.9285i	−1.93898	+	0.826981i
$471$		−	0.355254i		−	0.0163692i
$472$	−13.4073	−	5.06748i	−0.617120	−	0.233250i
$473$		0			0
$474$	−7.46546	+	3.18404i	−0.342900	+	0.146248i
$475$		−	27.4555i		−	1.25974i
$476$		0			0
$477$			19.6144i			0.898082i
$478$	2.62726	+	6.15999i	0.120168	+	0.281751i
$479$	−28.7678			−1.31443			−0.657217	−	0.753701i	$-0.728267\pi$
$479$	−28.7678			−1.31443			−0.657217	+	0.753701i	$0.728267\pi$
$480$	−7.84367	+	3.73989i	−0.358013	+	0.170702i
$481$			7.42365i			0.338489i
$482$	−6.49482	−	15.2281i	−0.295831	−	0.693619i
$483$		0			0
$484$	−11.6766	+	12.1749i	−0.530755	+	0.553404i
$485$		−	9.17389i		−	0.416565i
$486$	−6.47768	−	15.1879i	−0.293834	−	0.688937i
$487$			1.83303i			0.0830624i	0.999137	+	0.0415312i	$0.0132236\pi$
$487$			1.83303i			0.0830624i	−0.999137	+	0.0415312i	$0.986776\pi$
$488$	8.42643	−	22.2942i	0.381446	−	1.00921i
$489$		−	4.18601i		−	0.189298i
$490$		0			0
$491$	13.4370			0.606401			0.303201	−	0.952927i	$-0.401945\pi$
$491$	13.4370			0.606401			0.303201	+	0.952927i	$0.401945\pi$
$492$	2.80737	−	2.92717i	0.126566	−	0.131967i
$493$	20.5539			0.925702
$494$	4.06421	+	9.52915i	0.182857	+	0.428737i
$495$	−14.1654			−0.636687
$496$	0.0193720	+	0.463443i	0.000869830	+	0.0208092i
$497$		0			0
$498$	9.37041	−	3.99651i	0.419898	−	0.179088i
$499$	−11.3681			−0.508905			−0.254453	−	0.967085i	$-0.581895\pi$
$499$	−11.3681			−0.508905			−0.254453	+	0.967085i	$0.581895\pi$
$500$	0.899259	−	0.937633i	0.0402161	−	0.0419322i
$501$			0.667638i			0.0298279i
$502$	6.41536	+	15.0418i	0.286331	+	0.671347i
$503$	−13.2022			−0.588656			−0.294328	−	0.955704i	$-0.595096\pi$
$503$	−13.2022			−0.588656			−0.294328	+	0.955704i	$0.595096\pi$
$504$		0			0
$505$	−21.7408			−0.967454
$506$	3.93043	+	9.21547i	0.174729	+	0.409678i
$507$		−	5.32483i		−	0.236484i
$508$	7.10284	+	6.81215i	0.315138	+	0.302240i
$509$	26.4357			1.17174			0.585870	−	0.810405i	$-0.300753\pi$
$509$	26.4357			1.17174			0.585870	+	0.810405i	$0.300753\pi$
$510$	−8.04365	+	3.43064i	−0.356179	+	0.151911i
$511$		0			0
$512$	20.0000	−	10.5830i	0.883883	−	0.467707i
$513$	14.6380			0.646283
$514$	13.0885	+	30.6878i	0.577307	+	1.35358i
$515$	−44.8776			−1.97755
$516$		0			0
$517$	−16.2033			−0.712619
$518$		0			0
$519$			0.466786i			0.0204896i
$520$	−4.43462	+	11.7329i	−0.194471	+	0.514522i
$521$			12.0277i			0.526942i	0.964667	+	0.263471i	$0.0848674\pi$
$521$			12.0277i			0.526942i	−0.964667	+	0.263471i	$0.915133\pi$
$522$	−7.84367	−	18.3907i	−0.343308	−	0.804937i
$523$			2.80911i			0.122834i	0.998112	+	0.0614168i	$0.0195619\pi$
$523$			2.80911i			0.122834i	−0.998112	+	0.0614168i	$0.980438\pi$
$524$	−5.69439	−	5.46133i	−0.248760	−	0.238579i
$525$		0			0
$526$	5.92487	+	13.8917i	0.258337	+	0.605708i
$527$			0.466786i			0.0203335i
$528$	−3.07831	+	0.128674i	−0.133966	+	0.00559982i
$529$	3.43695			0.149433
$530$	−12.5548	−	29.4367i	−0.545347	−	1.27865i
$531$			14.0305i			0.608872i
$532$		0			0
$533$		−	5.85434i		−	0.253580i
$534$	1.08353	−	0.462128i	0.0468888	−	0.0199982i
$535$	−16.4158			−0.709718
$536$	10.0363	−	26.5536i	0.433502	−	1.14694i
$537$		−	6.86241i		−	0.296135i
$538$	30.3590	−	12.9482i	1.30887	−	0.558236i
$539$		0			0
$540$	12.7911	+	12.2676i	0.550441	+	0.527913i
$541$			1.94715i			0.0837144i	0.999124	+	0.0418572i	$0.0133275\pi$
$541$			1.94715i			0.0837144i	−0.999124	+	0.0418572i	$0.986673\pi$
$542$	−17.7424	+	7.56720i	−0.762102	+	0.325039i
$543$			7.36825i			0.316202i
$544$	20.5539	−	9.80019i	0.881242	−	0.420180i
$545$		−	9.04336i		−	0.387375i
$546$		0			0
$547$	28.4561			1.21669			0.608347	−	0.793671i	$-0.291833\pi$
$547$	28.4561			1.21669			0.608347	+	0.793671i	$0.291833\pi$
$548$	−0.142375	+	0.148450i	−0.00608195	+	0.00634149i
$549$	−23.3305			−0.995723
$550$	10.8413	−	4.62386i	0.462276	−	0.197162i
$551$	26.9425			1.14779
$552$	2.12703	−	5.62760i	0.0905325	−	0.239526i
$553$		0			0
$554$	0.253810	+	0.595095i	0.0107833	+	0.0252832i
$555$	−8.21408			−0.348668
$556$	−21.6212	−	20.7363i	−0.916942	−	0.879414i
$557$		−	9.19869i		−	0.389761i	−0.980827	−	0.194881i	$-0.937568\pi$
$557$		−	9.19869i		−	0.389761i	0.980827	−	0.194881i	$-0.0624319\pi$
$558$	0.417657	−	0.178132i	0.0176808	−	0.00754094i
$559$		0			0
$560$		0			0
$561$	−3.10051			−0.130904
$562$	−1.86925	+	0.797240i	−0.0788495	+	0.0336295i
$563$			27.1970i			1.14622i	0.819480	+	0.573108i	$0.194263\pi$
$563$			27.1970i			1.14622i	−0.819480	+	0.573108i	$0.805737\pi$
$564$	7.02235	+	6.73495i	0.295694	+	0.283592i
$565$	−4.59002			−0.193104
$566$	17.3248	+	40.6205i	0.728214	+	1.70741i
$567$		0			0
$568$	14.0000	+	5.29150i	0.587427	+	0.222027i
$569$	−23.5398			−0.986840			−0.493420	−	0.869791i	$-0.664253\pi$
$569$	−23.5398			−0.986840			−0.493420	+	0.869791i	$0.664253\pi$
$570$	−10.5438	+	4.49695i	−0.441630	+	0.188357i
$571$	30.3425			1.26979			0.634897	−	0.772597i	$-0.281042\pi$
$571$	30.3425			1.26979			0.634897	+	0.772597i	$0.281042\pi$
$572$	−3.07831	+	3.20967i	−0.128711	+	0.134203i
$573$	1.20257			0.0502382
$574$		0			0
$575$			23.0145i			0.959772i
$576$	−16.6124	−	14.6508i	−0.692184	−	0.610449i
$577$		−	28.6088i		−	1.19100i	−0.803355	−	0.595500i	$-0.796954\pi$
$577$		−	28.6088i		−	1.19100i	0.803355	−	0.595500i	$-0.203046\pi$
$578$	−1.03630	+	0.441986i	−0.0431045	+	0.0183842i
$579$		−	1.49104i		−	0.0619655i
$580$	23.5431	+	22.5795i	0.977574	+	0.937564i
$581$		0			0
$582$	−1.79664	+	0.766273i	−0.0744732	+	0.0317630i
$583$		−	11.3467i		−	0.469932i
$584$	28.4274	+	10.7445i	1.17633	+	0.444612i
$585$	12.2783			0.507645
$586$	40.7170	−	17.3659i	1.68200	−	0.717380i
$587$		−	15.2362i		−	0.628867i	−0.949280	−	0.314433i	$-0.898186\pi$
$587$		−	15.2362i		−	0.628867i	0.949280	−	0.314433i	$-0.101814\pi$
$588$		0			0
$589$			0.611872i			0.0252117i
$590$	−8.98068	−	21.0565i	−0.369729	−	0.866884i
$591$	−7.54492			−0.310357
$592$	21.3704	−	0.893289i	0.878319	−	0.0367139i
$593$			21.1234i			0.867435i	0.901049	+	0.433717i	$0.142798\pi$
$593$			21.1234i			0.867435i	−0.901049	+	0.433717i	$0.857202\pi$
$594$	2.46523	+	5.78010i	0.101150	+	0.237160i
$595$		0			0
$596$	−16.3202	−	15.6522i	−0.668500	−	0.641140i
$597$		−	5.68704i		−	0.232755i
$598$	−3.40682	−	7.98780i	−0.139315	−	0.326645i
$599$		−	33.6936i		−	1.37668i	−0.725387	−	0.688341i	$-0.758339\pi$
$599$		−	33.6936i		−	1.37668i	0.725387	−	0.688341i	$-0.241661\pi$
$600$	−6.62046	−	2.50230i	−0.270279	−	0.102156i
$601$		−	24.3960i		−	0.995132i	−0.867426	−	0.497566i	$-0.834227\pi$
$601$		−	24.3960i		−	0.995132i	0.867426	−	0.497566i	$-0.165773\pi$
$602$		0			0
$603$	−27.7879			−1.13161
$604$	21.3928	+	20.5172i	0.870459	+	0.834834i
$605$	−26.9425			−1.09537
$606$	1.81596	+	4.25779i	0.0737683	+	0.172961i
$607$	−8.17513			−0.331818			−0.165909	−	0.986141i	$-0.553056\pi$
$607$	−8.17513			−0.331818			−0.165909	+	0.986141i	$0.553056\pi$
$608$	26.9425	−	12.8463i	1.09266	−	0.520985i
$609$		0			0
$610$	35.0138	−	14.9335i	1.41767	−	0.604639i
$611$	14.0447			0.568188
$612$	−16.0873	−	15.4289i	−0.650291	−	0.623676i
$613$			16.9996i			0.686608i	0.939224	+	0.343304i	$0.111546\pi$
$613$			16.9996i			0.686608i	−0.939224	+	0.343304i	$0.888454\pi$
$614$	8.16768	+	19.1504i	0.329621	+	0.772845i
$615$	6.47768			0.261205
$616$		0			0
$617$	39.6548			1.59644			0.798221	−	0.602365i	$-0.205775\pi$
$617$	39.6548			1.59644			0.798221	+	0.602365i	$0.205775\pi$
$618$	3.74852	+	8.78897i	0.150788	+	0.353544i
$619$			14.4013i			0.578837i	0.957203	+	0.289419i	$0.0934620\pi$
$619$			14.4013i			0.578837i	−0.957203	+	0.289419i	$0.906538\pi$
$620$	−0.512788	+	0.534671i	−0.0205941	+	0.0214729i
$621$	−12.2703			−0.492389
$622$	−20.2677	+	8.64425i	−0.812662	+	0.346603i
$623$		0			0
$624$	2.66822	−	0.111532i	0.106814	−	0.00446487i
$625$	−23.9419			−0.957674
$626$	−7.26036	−	17.0230i	−0.290182	−	0.680376i
$627$	−4.06421			−0.162309
$628$	−1.02267	+	1.06631i	−0.0408088	+	0.0425503i
$629$	21.5246			0.858241
$630$		0			0
$631$			36.6698i			1.45980i	0.683553	+	0.729900i	$0.260434\pi$
$631$			36.6698i			1.45980i	−0.683553	+	0.729900i	$0.739566\pi$
$632$	31.5738	+	11.9338i	1.25594	+	0.474700i
$633$			4.84393i			0.192529i
$634$	−13.0672	−	30.6381i	−0.518967	−	1.21679i
$635$			15.7183i			0.623760i
$636$	−4.71629	+	4.91755i	−0.187013	+	0.194994i
$637$		0			0
$638$	4.53747	+	10.6388i	0.179640	+	0.421193i
$639$		−	14.6508i		−	0.579575i
$640$	34.3091	+	11.3541i	1.35619	+	0.448810i
$641$	18.2760			0.721857			0.360929	−	0.932593i	$-0.382460\pi$
$641$	18.2760			0.721857			0.360929	+	0.932593i	$0.382460\pi$
$642$	1.37117	+	3.21492i	0.0541159	+	0.126883i
$643$			13.6340i			0.537671i	0.963186	+	0.268836i	$0.0866389\pi$
$643$			13.6340i			0.537671i	−0.963186	+	0.268836i	$0.913361\pi$
$644$		0			0
$645$		0			0
$646$	27.6294	−	11.7840i	1.08706	−	0.463636i
$647$	−17.4831			−0.687330			−0.343665	−	0.939092i	$-0.611668\pi$
$647$	−17.4831			−0.687330			−0.343665	+	0.939092i	$0.611668\pi$
$648$	−6.97209	+	18.4464i	−0.273890	+	0.724644i
$649$		−	8.11647i		−	0.318599i
$650$	−9.39708	+	4.00788i	−0.368584	+	0.157202i
$651$		0			0
$652$	−12.0503	+	12.5645i	−0.471924	+	0.492063i
$653$			9.70520i			0.379794i	0.981804	+	0.189897i	$0.0608154\pi$
$653$			9.70520i			0.379794i	−0.981804	+	0.189897i	$0.939185\pi$
$654$	−1.77108	+	0.755370i	−0.0692546	+	0.0295373i
$655$		−	12.6014i		−	0.492378i
$656$	−16.8529	+	0.704454i	−0.657993	+	0.0275043i
$657$		−	29.7488i		−	1.16061i
$658$		0			0
$659$	−28.9465			−1.12760			−0.563798	−	0.825913i	$-0.690660\pi$
$659$	−28.9465			−1.12760			−0.563798	+	0.825913i	$0.690660\pi$
$660$	−3.55142	−	3.40607i	−0.138239	−	0.132581i
$661$	−12.8737			−0.500728			−0.250364	−	0.968152i	$-0.580550\pi$
$661$	−12.8737			−0.500728			−0.250364	+	0.968152i	$0.580550\pi$
$662$	−42.9998	+	18.3395i	−1.67123	+	0.712787i
$663$	2.68747			0.104373
$664$	−39.6304	−	14.9789i	−1.53796	−	0.581293i
$665$		0			0
$666$	−8.21408	−	19.2591i	−0.318289	−	0.746277i
$667$	−22.5845			−0.874475
$668$	1.92193	−	2.00394i	0.0743615	−	0.0775348i
$669$			11.6900i			0.451963i
$670$	41.7032	−	17.7865i	1.61113	−	0.687154i
$671$	13.4964			0.521024
$672$		0			0
$673$	−23.6548			−0.911825			−0.455912	−	0.890025i	$-0.650687\pi$
$673$	−23.6548			−0.911825			−0.455912	+	0.890025i	$0.650687\pi$
$674$	20.1755	−	8.60489i	0.777129	−	0.331448i
$675$			14.4351i			0.555607i
$676$	−15.3286	+	15.9827i	−0.589560	+	0.614718i
$677$	−3.60448			−0.138531			−0.0692657	−	0.997598i	$-0.522066\pi$
$677$	−3.60448			−0.138531			−0.0692657	+	0.997598i	$0.522066\pi$
$678$	0.383393	+	0.898923i	0.0147241	+	0.0345229i
$679$		0			0
$680$	34.0191	+	12.8580i	1.30457	+	0.493083i
$681$	−6.88837			−0.263963
$682$	−0.241610	+	0.103047i	−0.00925171	+	0.00394588i
$683$	−7.61847			−0.291513			−0.145756	−	0.989321i	$-0.546562\pi$
$683$	−7.61847			−0.291513			−0.145756	+	0.989321i	$0.546562\pi$
$684$	−21.0875	−	20.2245i	−0.806302	−	0.773303i
$685$	−0.328514			−0.0125519
$686$		0			0
$687$		−	5.12162i		−	0.195402i
$688$		0			0
$689$			9.83510i			0.374688i
$690$	8.83831	−	3.76957i	0.336469	−	0.143505i
$691$		−	51.9277i		−	1.97542i	−0.156285	−	0.987712i	$-0.549952\pi$
$691$		−	51.9277i		−	1.97542i	0.156285	−	0.987712i	$-0.450048\pi$
$692$	1.34373	−	1.40108i	0.0510811	−	0.0532609i
$693$		0			0
$694$	−29.2674	+	12.4826i	−1.11097	+	0.473834i
$695$		−	47.8466i		−	1.81492i
$696$	2.45554	−	6.49676i	0.0930772	−	0.246259i
$697$	−16.9744			−0.642952
$698$	37.0395	−	15.7975i	1.40197	−	0.597943i
$699$		−	0.306806i		−	0.0116045i
$700$		0			0
$701$		−	0.741474i		−	0.0280051i	−0.999902	−	0.0140025i	$-0.995543\pi$
$701$		−	0.741474i		−	0.0280051i	0.999902	−	0.0140025i	$-0.00445729\pi$
$702$	−2.13682	−	5.01009i	−0.0806489	−	0.189093i
$703$	28.2148			1.06414
$704$	9.61007	+	8.47529i	0.362193	+	0.319424i
$705$			15.5401i			0.585275i
$706$	−5.31161	−	12.4539i	−0.199905	−	0.468708i
$707$		0			0
$708$	−3.37364	+	3.51761i	−0.126789	+	0.132200i
$709$			41.1640i			1.54595i	0.634438	+	0.772974i	$0.281232\pi$
$709$			41.1640i			1.54595i	−0.634438	+	0.772974i	$0.718768\pi$
$710$	9.37770	+	21.9874i	0.351939	+	0.825173i
$711$		−	33.0414i		−	1.23915i
$712$	−4.58258	−	1.73205i	−0.171739	−	0.0649113i
$713$		−	0.512901i		−	0.0192083i
$714$		0			0
$715$	−7.10284			−0.265631
$716$	−19.7548	+	20.5978i	−0.738271	+	0.769775i
$717$	2.27726			0.0850457
$718$	2.08353	+	4.88514i	0.0777566	+	0.182312i
$719$	−14.0494			−0.523955			−0.261978	−	0.965074i	$-0.584375\pi$
$719$	−14.0494			−0.523955			−0.261978	+	0.965074i	$0.584375\pi$
$720$	−1.47745	−	35.3455i	−0.0550613	−	1.31725i
$721$		0			0
$722$	11.5012	−	4.90528i	0.428029	−	0.182556i
$723$	−5.62959			−0.209367
$724$	21.2110	−	22.1161i	0.788299	−	0.821938i
$725$			26.5690i			0.986750i
$726$	2.25044	+	5.27649i	0.0835216	+	0.195829i
$727$	13.2022			0.489642			0.244821	−	0.969568i	$-0.421271\pi$
$727$	13.2022			0.489642			0.244821	+	0.969568i	$0.421271\pi$
$728$		0			0
$729$	15.3015			0.566724
$730$	19.0417	+	44.6460i	0.704764	+	1.65242i
$731$		0			0
$732$	−5.84923	−	5.60984i	−0.216194	−	0.207346i
$733$	−49.9594			−1.84529			−0.922646	−	0.385648i	$-0.873978\pi$
$733$	−49.9594			−1.84529			−0.922646	+	0.385648i	$0.873978\pi$
$734$	−21.8880	+	9.33529i	−0.807900	+	0.344572i
$735$		0			0
$736$	−22.5845	+	10.7684i	−0.832476	+	0.396928i
$737$	16.0749			0.592128
$738$	6.47768	+	15.1879i	0.238447	+	0.559074i
$739$	−36.5435			−1.34428			−0.672138	−	0.740426i	$-0.734624\pi$
$739$	−36.5435			−1.34428			−0.672138	+	0.740426i	$0.734624\pi$
$740$	24.6549	+	23.6458i	0.906332	+	0.869239i
$741$	3.52278			0.129413
$742$		0			0
$743$		−	15.1330i		−	0.555177i	−0.960700	−	0.277589i	$-0.910465\pi$
$743$		−	15.1330i		−	0.555177i	0.960700	−	0.277589i	$-0.0895352\pi$
$744$	0.147543	+	0.0557662i	0.00540920	+	0.00204449i
$745$		−	36.1157i		−	1.32318i
$746$	7.13378	+	16.7262i	0.261186	+	0.612390i
$747$			41.4725i			1.51740i
$748$	9.30631	+	8.92543i	0.340273	+	0.326346i
$749$		0			0
$750$	−0.173314	−	0.406362i	−0.00632855	−	0.0148382i
$751$			13.8561i			0.505617i	0.967516	+	0.252808i	$0.0813542\pi$
$751$			13.8561i			0.505617i	−0.967516	+	0.252808i	$0.918646\pi$
$752$	−1.69000	−	40.4304i	−0.0616280	−	1.47435i
$753$	5.56071			0.202644
$754$	−3.93299	−	9.22149i	−0.143231	−	0.335827i
$755$			47.3412i			1.72292i
$756$		0			0
$757$		−	46.6967i		−	1.69722i	−0.529019	−	0.848610i	$-0.677440\pi$
$757$		−	46.6967i		−	1.69722i	0.529019	−	0.848610i	$-0.322560\pi$
$758$	−33.2783	+	14.1933i	−1.20872	+	0.515524i
$759$	3.40682			0.123660
$760$	44.5929	+	16.8545i	1.61755	+	0.611378i
$761$			47.1001i			1.70738i	0.520783	+	0.853689i	$0.325640\pi$
$761$			47.1001i			1.70738i	−0.520783	+	0.853689i	$0.674360\pi$
$762$	3.07831	−	1.31291i	0.111515	−	0.0475616i
$763$		0			0
$764$	−3.60957	−	3.46184i	−0.130590	−	0.125245i
$765$		−	35.6004i		−	1.28714i
$766$	35.0827	−	14.9629i	1.26759	−	0.540631i
$767$			7.03521i			0.254027i
$768$	−0.642135	−	7.66757i	−0.0231711	−	0.276680i
$769$			17.3071i			0.624110i	0.950064	+	0.312055i	$0.101017\pi$
$769$			17.3071i			0.624110i	−0.950064	+	0.312055i	$0.898983\pi$
$770$		0			0
$771$	11.3448			0.408574
$772$	−4.29225	+	4.47541i	−0.154481	+	0.161074i
$773$	27.0778			0.973921			0.486960	−	0.873424i	$-0.338106\pi$
$773$	27.0778			0.973921			0.486960	+	0.873424i	$0.338106\pi$
$774$		0			0
$775$	−0.603391			−0.0216744
$776$	7.59856	+	2.87198i	0.272772	+	0.103098i
$777$		0			0
$778$	17.7485	+	41.6141i	0.636315	+	1.49194i
$779$	−22.2504			−0.797203
$780$	3.07831	+	2.95232i	0.110221	+	0.105710i
$781$			8.47529i			0.303270i
$782$	−23.1603	+	9.87795i	−0.828211	+	0.353235i
$783$	−14.1654			−0.506230
$784$		0			0
$785$	−2.35969			−0.0842208
$786$	−2.46789	+	1.05256i	−0.0880269	+	0.0375437i
$787$			54.2344i			1.93325i	0.256197	+	0.966624i	$0.417530\pi$
$787$			54.2344i			1.93325i	−0.256197	+	0.966624i	$0.582470\pi$
$788$	22.6464	+	21.7195i	0.806744	+	0.773726i
$789$	5.13557			0.182831
$790$	21.1492	+	49.5876i	0.752456	+	1.76425i
$791$		0			0
$792$	4.43462	−	11.7329i	0.157578	−	0.416911i
$793$	−11.6985			−0.415424
$794$	−22.1645	+	9.45321i	−0.786588	+	0.335482i
$795$	−10.8823			−0.385956
$796$	−16.3713	+	17.0699i	−0.580264	+	0.605026i
$797$	20.1437			0.713527			0.356763	−	0.934195i	$-0.383880\pi$
$797$	20.1437			0.713527			0.356763	+	0.934195i	$0.383880\pi$
$798$		0			0
$799$		−	40.7221i		−	1.44064i
$800$	12.6682	+	26.5690i	0.447889	+	0.939358i
$801$			4.79559i			0.169444i
$802$	7.67125	−	3.27181i	0.270881	−	0.115532i
$803$			17.2093i			0.607303i
$804$	−6.96673	−	6.68160i	−0.245698	−	0.235642i
$805$		0			0
$806$	0.209423	−	0.0893195i	0.00737661	−	0.00314615i
$807$		−	11.2233i		−	0.395077i
$808$	6.80620	−	18.0075i	0.239441	−	0.633502i
$809$	34.5543			1.21486			0.607432	−	0.794372i	$-0.292200\pi$
$809$	34.5543			1.21486			0.607432	+	0.794372i	$0.292200\pi$
$810$	−28.9707	+	12.3561i	−1.01793	+	0.434148i
$811$		−	13.6340i		−	0.478754i	−0.970927	−	0.239377i	$-0.923057\pi$
$811$		−	13.6340i		−	0.478754i	0.970927	−	0.239377i	$-0.0769431\pi$
$812$		0			0
$813$			6.55911i			0.230038i
$814$	4.75175	+	11.1412i	0.166549	+	0.390498i
$815$	−27.8046			−0.973953
$816$	−0.323384	−	7.73640i	−0.0113207	−	0.270828i
$817$		0			0
$818$	−0.133094	−	0.312058i	−0.00465352	−	0.0109109i
$819$		0			0
$820$	−19.4430	−	18.6473i	−0.678980	−	0.651191i
$821$		−	32.0211i		−	1.11754i	−0.829321	−	0.558772i	$-0.811273\pi$
$821$		−	32.0211i		−	1.11754i	0.829321	−	0.558772i	$-0.188727\pi$
$822$	0.0274399	+	0.0643370i	0.000957078	+	0.00224401i
$823$			30.9921i			1.08032i	0.841564	+	0.540158i	$0.181635\pi$
$823$			30.9921i			1.08032i	−0.841564	+	0.540158i	$0.818365\pi$
$824$	14.0494	−	37.1713i	0.489435	−	1.29492i
$825$		−	4.00788i		−	0.139537i
$826$		0			0
$827$	−11.0191			−0.383172			−0.191586	−	0.981476i	$-0.561363\pi$
$827$	−11.0191			−0.383172			−0.191586	+	0.981476i	$0.561363\pi$
$828$	17.6766	+	16.9532i	0.614305	+	0.589163i
$829$	37.9672			1.31866			0.659328	−	0.751856i	$-0.270841\pi$
$829$	37.9672			1.31866			0.659328	+	0.751856i	$0.270841\pi$
$830$	−26.5459	−	62.2407i	−0.921420	−	2.16041i
$831$	0.219998			0.00763163
$832$	−8.32984	−	7.34623i	−0.288785	−	0.254685i
$833$		0			0
$834$	−9.37041	+	3.99651i	−0.324471	+	0.138388i
$835$	4.43462			0.153466
$836$	12.1989	+	11.6996i	0.421907	+	0.404640i
$837$		−	0.321700i		−	0.0111196i
$838$	−16.3192	−	38.2629i	−0.563739	−	1.32177i
$839$	−8.32984			−0.287578			−0.143789	−	0.989608i	$-0.545929\pi$
$839$	−8.32984			−0.287578			−0.143789	+	0.989608i	$0.545929\pi$
$840$		0			0
$841$	2.92739			0.100945
$842$	−17.8242	−	41.7914i	−0.614261	−	1.44023i
$843$			0.691033i			0.0238004i
$844$	13.9442	−	14.5392i	0.479979	−	0.500461i
$845$	−35.3689			−1.21673
$846$	−36.4361	+	15.5401i	−1.25270	+	0.534280i
$847$		0			0
$848$	28.3123	−	1.18346i	0.972247	−	0.0406402i
$849$	15.0168			0.515375
$850$	11.6207	+	27.2465i	0.398587	+	0.934546i
$851$	−23.6510			−0.810747
$852$	3.52278	−	3.67311i	0.120689	−	0.125839i
$853$	−6.94153			−0.237673			−0.118837	−	0.992914i	$-0.537917\pi$
$853$	−6.94153			−0.237673			−0.118837	+	0.992914i	$0.537917\pi$
$854$		0			0
$855$		−	46.6657i		−	1.59593i
$856$	5.13915	−	13.5969i	0.175652	−	0.464733i
$857$		−	2.21407i		−	0.0756313i	−0.999285	−	0.0378156i	$-0.987960\pi$
$857$		−	2.21407i		−	0.0756313i	0.999285	−	0.0378156i	$-0.0120400\pi$
$858$	0.593283	+	1.39104i	0.0202544	+	0.0474894i
$859$			6.07762i			0.207366i	0.994610	+	0.103683i	$0.0330627\pi$
$859$			6.07762i			0.207366i	−0.994610	+	0.103683i	$0.966937\pi$
$860$		0			0
$861$		0			0
$862$	−20.9914	−	49.2175i	−0.714970	−	1.67635i
$863$		−	8.83054i		−	0.300595i	−0.988641	−	0.150298i	$-0.951977\pi$
$863$		−	8.83054i		−	0.300595i	0.988641	−	0.150298i	$-0.0480232\pi$
$864$	−14.1654	+	6.75411i	−0.481916	+	0.229779i
$865$	3.10051			0.105421
$866$	−14.1386	−	33.1500i	−0.480448	−	1.12648i
$867$			0.383106i			0.0130110i
$868$		0			0
$869$			19.1141i			0.648400i
$870$	10.2034	−	4.35176i	0.345926	−	0.147539i
$871$	−13.9335			−0.472117
$872$	7.49044	+	2.83112i	0.253658	+	0.0958738i
$873$		−	7.95176i		−	0.269126i
$874$	−30.3590	+	12.9482i	−1.02691	+	0.437979i
$875$		0			0
$876$	7.15310	−	7.45835i	0.241681	−	0.251994i
$877$		−	11.9002i		−	0.401842i	−0.979607	−	0.200921i	$-0.935607\pi$
$877$		−	11.9002i		−	0.401842i	0.979607	−	0.200921i	$-0.0643934\pi$
$878$	−31.1691	+	13.2937i	−1.05191	+	0.448641i
$879$		−	15.0525i		−	0.507707i
$880$	0.854687	+	20.4469i	0.0288115	+	0.689266i
$881$		−	53.9142i		−	1.81642i	−0.418519	−	0.908208i	$-0.637451\pi$
$881$		−	53.9142i		−	1.81642i	0.418519	−	0.908208i	$-0.362549\pi$
$882$		0			0
$883$	11.1987			0.376866			0.188433	−	0.982086i	$-0.439659\pi$
$883$	11.1987			0.376866			0.188433	+	0.982086i	$0.439659\pi$
$884$	−8.06654	−	7.73640i	−0.271307	−	0.260203i
$885$	−7.78429			−0.261666
$886$	−13.3595	+	5.69786i	−0.448821	+	0.191423i
$887$	−36.3664			−1.22106			−0.610531	−	0.791992i	$-0.709044\pi$
$887$	−36.3664			−1.22106			−0.610531	+	0.791992i	$0.709044\pi$
$888$	2.57151	−	6.80357i	0.0862941	−	0.228313i
$889$		0			0
$890$	−3.06957	−	7.19707i	−0.102892	−	0.241246i
$891$	−11.1671			−0.374110
$892$	33.6521	−	35.0881i	1.12675	−	1.17484i
$893$		−	53.3792i		−	1.78627i
$894$	−7.07301	+	3.01666i	−0.236557	+	0.100892i
$895$	−45.5819			−1.52364
$896$		0			0
$897$	−2.95297			−0.0985968
$898$	−14.9721	+	6.38564i	−0.499625	+	0.213092i
$899$		−	0.592117i		−	0.0197482i
$900$	19.9442	−	20.7953i	0.664806	−	0.693176i
$901$	28.5165			0.950022
$902$	−3.74726	−	8.78601i	−0.124770	−	0.292542i
$903$		0			0
$904$	1.43695	−	3.80183i	0.0477924	−	0.126447i
$905$	48.9419			1.62688
$906$	9.27143	−	3.95429i	0.308023	−	0.131373i
$907$	−17.8474			−0.592613			−0.296307	−	0.955093i	$-0.595755\pi$
$907$	−17.8474			−0.592613			−0.296307	+	0.955093i	$0.595755\pi$
$908$	20.6757	+	19.8295i	0.686148	+	0.658066i
$909$	−18.8446			−0.625034
$910$		0			0
$911$			11.1458i			0.369278i	0.982806	+	0.184639i	$0.0591116\pi$
$911$			11.1458i			0.369278i	−0.982806	+	0.184639i	$0.940888\pi$
$912$	−0.423897	−	10.1410i	−0.0140366	−	0.335803i
$913$		−	23.9914i		−	0.793998i
$914$	−39.8188	+	16.9828i	−1.31709	+	0.561742i
$915$		−	12.9441i		−	0.427918i
$916$	−14.7436	+	15.3727i	−0.487141	+	0.507929i
$917$		0			0
$918$	−14.5265	+	6.19562i	−0.479448	+	0.204486i
$919$			32.6552i			1.07720i	0.842563	+	0.538598i	$0.181046\pi$
$919$			32.6552i			1.07720i	−0.842563	+	0.538598i	$0.818954\pi$
$920$	−37.3800	−	14.1283i	−1.23238	−	0.465796i
$921$	7.07960			0.233281
$922$	−22.5918	+	9.63548i	−0.744022	+	0.317328i
$923$		−	7.34623i		−	0.241804i
$924$		0			0
$925$			27.8238i			0.914839i
$926$	12.0554	+	28.2657i	0.396166	+	0.928870i
$927$	−38.8991			−1.27761
$928$	−26.0726	+	12.4315i	−0.855875	+	0.408085i
$929$		−	26.9076i		−	0.882811i	−0.897308	−	0.441406i	$-0.854480\pi$
$929$		−	26.9076i		−	0.882811i	0.897308	−	0.441406i	$-0.145520\pi$
$930$	0.0988299	+	0.231721i	0.00324076	+	0.00759844i
$931$		0			0
$932$	−0.883202	+	0.920891i	−0.0289302	+	0.0301648i
$933$			7.49268i			0.245299i
$934$	0.375326	+	0.880007i	0.0122810	+	0.0287947i
$935$			20.5944i			0.673510i
$936$	−3.84385	+	10.1699i	−0.125640	+	0.332413i
$937$			32.6476i			1.06655i	0.845942	+	0.533275i	$0.179039\pi$
$937$			32.6476i			1.06655i	−0.845942	+	0.533275i	$0.820961\pi$
$938$		0			0
$939$	−6.29315			−0.205369
$940$	44.7353	−	46.6443i	1.45910	−	1.52137i
$941$	12.6417			0.412109			0.206055	−	0.978541i	$-0.433938\pi$
$941$	12.6417			0.412109			0.206055	+	0.978541i	$0.433938\pi$
$942$	0.197099	+	0.462128i	0.00642183	+	0.0150569i
$943$	18.6514			0.607372
$944$	20.2522	−	0.846548i	0.659154	−	0.0275528i
$945$		0			0
$946$		0			0
$947$	−42.2541			−1.37307			−0.686537	−	0.727095i	$-0.740870\pi$
$947$	−42.2541			−1.37307			−0.686537	+	0.727095i	$0.740870\pi$
$948$	7.94483	−	8.28386i	0.258036	−	0.269047i
$949$		−	14.9167i		−	0.484217i
$950$	15.2326	+	35.7152i	0.494212	+	1.15875i
$951$	−11.3264			−0.367285
$952$		0			0
$953$	−44.4561			−1.44007			−0.720037	−	0.693936i	$-0.755875\pi$
$953$	−44.4561			−1.44007			−0.720037	+	0.693936i	$0.755875\pi$
$954$	−10.8823	−	25.5152i	−0.352328	−	0.826085i
$955$		−	7.98780i		−	0.258479i
$956$	−6.83528	−	6.55553i	−0.221069	−	0.212021i
$957$	3.93299			0.127136
$958$	37.4223	−	15.9607i	1.20906	−	0.515668i
$959$		0			0
$960$	8.12842	−	9.21676i	0.262344	−	0.297470i
$961$	−30.9866			−0.999566
$962$	−4.11873	−	9.65697i	−0.132793	−	0.311353i
$963$	−14.2289			−0.458521
$964$	16.8974	+	16.2059i	0.544229	+	0.521956i
$965$	−9.90388			−0.318817
$966$		0			0
$967$			25.7160i			0.826972i	0.910510	+	0.413486i	$0.135689\pi$
$967$			25.7160i			0.826972i	−0.910510	+	0.413486i	$0.864311\pi$
$968$	8.43462	−	22.3159i	0.271099	−	0.717261i
$969$		−	10.2142i		−	0.328127i
$970$	5.08979	+	11.9338i	0.163423	+	0.383170i
$971$		−	46.5051i		−	1.49242i	−0.665711	−	0.746210i	$-0.731871\pi$
$971$		−	46.5051i		−	1.49242i	0.665711	−	0.746210i	$-0.268129\pi$
$972$	16.8529	+	16.1631i	0.540556	+	0.518432i
$973$		0			0
$974$	−1.01699	−	2.38448i	−0.0325863	−	0.0764035i
$975$			3.47396i			0.111256i
$976$	1.40768	+	33.6763i	0.0450587	+	1.07795i
$977$	34.2695			1.09638			0.548189	−	0.836354i	$-0.315317\pi$
$977$	34.2695			1.09638			0.548189	+	0.836354i	$0.315317\pi$
$978$	2.32245	+	5.44533i	0.0742638	+	0.174123i
$979$		−	2.77419i		−	0.0886635i
$980$		0			0
$981$		−	7.83862i		−	0.250268i
$982$	−17.4793	+	7.45498i	−0.557788	+	0.237898i
$983$	1.55467			0.0495862			0.0247931	−	0.999693i	$-0.492107\pi$
$983$	1.55467			0.0495862			0.0247931	+	0.999693i	$0.492107\pi$
$984$	−2.02791	+	5.36534i	−0.0646473	+	0.171041i
$985$			50.1153i			1.59681i
$986$	−26.7374	+	11.4036i	−0.851491	+	0.363163i
$987$		0			0
$988$	−10.5738	−	10.1410i	−0.336396	−	0.322629i
$989$		0			0
$990$	18.4269	−	7.85913i	0.585645	−	0.249779i
$991$		−	26.1519i		−	0.830741i	−0.909652	−	0.415371i	$-0.863652\pi$
$991$		−	26.1519i		−	0.830741i	0.909652	−	0.415371i	$-0.136348\pi$
$992$	−0.282324	−	0.592117i	−0.00896378	−	0.0187997i
$993$			15.8964i			0.504457i
$994$		0			0
$995$	−37.7748			−1.19754
$996$	−9.97209	+	10.3976i	−0.315978	+	0.329462i
$997$	−36.2933			−1.14942			−0.574711	−	0.818356i	$-0.694886\pi$
$997$	−36.2933			−1.14942			−0.574711	+	0.818356i	$0.694886\pi$
$998$	14.7881	−	6.30715i	0.468108	−	0.199649i
$999$	−14.8343			−0.469338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.e.e.195.4		12
4.3	odd	2		1568.2.e.e.783.6		12
7.2	even	3		56.2.m.a.3.6	yes	12
7.3	odd	6		56.2.m.a.19.3	yes	12
7.4	even	3		392.2.m.g.19.3		12
7.5	odd	6		392.2.m.g.227.6		12
7.6	odd	2	inner	392.2.e.e.195.3		12
8.3	odd	2	inner	392.2.e.e.195.2		12
8.5	even	2		1568.2.e.e.783.5		12
21.2	odd	6		504.2.bk.a.451.1		12
21.17	even	6		504.2.bk.a.19.4		12
28.3	even	6		224.2.q.a.47.4		12
28.11	odd	6		1568.2.q.g.1391.3		12
28.19	even	6		1568.2.q.g.815.4		12
28.23	odd	6		224.2.q.a.143.3		12
28.27	even	2		1568.2.e.e.783.7		12
56.3	even	6		56.2.m.a.19.5	yes	12
56.5	odd	6		1568.2.q.g.815.3		12
56.11	odd	6		392.2.m.g.19.5		12
56.13	odd	2		1568.2.e.e.783.8		12
56.19	even	6		392.2.m.g.227.4		12
56.27	even	2	inner	392.2.e.e.195.1		12
56.37	even	6		224.2.q.a.143.4		12
56.45	odd	6		224.2.q.a.47.3		12
56.51	odd	6		56.2.m.a.3.4	✓	12
56.53	even	6		1568.2.q.g.1391.4		12
84.23	even	6		2016.2.bs.a.1711.6		12
84.59	odd	6		2016.2.bs.a.271.1		12
168.59	odd	6		504.2.bk.a.19.2		12
168.101	even	6		2016.2.bs.a.271.6		12
168.107	even	6		504.2.bk.a.451.3		12
168.149	odd	6		2016.2.bs.a.1711.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.4	✓	12	56.51	odd	6
56.2.m.a.3.6	yes	12	7.2	even	3
56.2.m.a.19.3	yes	12	7.3	odd	6
56.2.m.a.19.5	yes	12	56.3	even	6
224.2.q.a.47.3		12	56.45	odd	6
224.2.q.a.47.4		12	28.3	even	6
224.2.q.a.143.3		12	28.23	odd	6
224.2.q.a.143.4		12	56.37	even	6
392.2.e.e.195.1		12	56.27	even	2	inner
392.2.e.e.195.2		12	8.3	odd	2	inner
392.2.e.e.195.3		12	7.6	odd	2	inner
392.2.e.e.195.4		12	1.1	even	1	trivial
392.2.m.g.19.3		12	7.4	even	3
392.2.m.g.19.5		12	56.11	odd	6
392.2.m.g.227.4		12	56.19	even	6
392.2.m.g.227.6		12	7.5	odd	6
504.2.bk.a.19.2		12	168.59	odd	6
504.2.bk.a.19.4		12	21.17	even	6
504.2.bk.a.451.1		12	21.2	odd	6
504.2.bk.a.451.3		12	168.107	even	6
1568.2.e.e.783.5		12	8.5	even	2
1568.2.e.e.783.6		12	4.3	odd	2
1568.2.e.e.783.7		12	28.27	even	2
1568.2.e.e.783.8		12	56.13	odd	2
1568.2.q.g.815.3		12	56.5	odd	6
1568.2.q.g.815.4		12	28.19	even	6
1568.2.q.g.1391.3		12	28.11	odd	6
1568.2.q.g.1391.4		12	56.53	even	6
2016.2.bs.a.271.1		12	84.59	odd	6
2016.2.bs.a.271.6		12	168.101	even	6
2016.2.bs.a.1711.1		12	168.149	odd	6
2016.2.bs.a.1711.6		12	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30084 + 0.554812i) q^{2} +0.480901i q^{3} +(1.38437 - 1.44344i) q^{4} +3.19427 q^{5} +(-0.266810 - 0.625575i) q^{6} +(-1.00000 + 2.64575i) q^{8} +2.76873 q^{9} +(-4.15523 + 1.77222i) q^{10} -1.60168 q^{11} +(0.694153 + 0.665743i) q^{12} +1.38831 q^{13} +1.53613i q^{15} +(-0.167055 - 3.99651i) q^{16} -4.02534i q^{17} +(-3.60168 + 1.53613i) q^{18} -5.27649i q^{19} +(4.42204 - 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +4.42301i q^{23} +(-1.27234 - 0.480901i) q^{24} +5.20336 q^{25} +(-1.80596 + 0.770249i) q^{26} +2.77419i q^{27} +5.10613i q^{29} +(-0.852262 - 1.99826i) q^{30} -0.115962 q^{31} +(2.43462 + 5.10613i) q^{32} -0.770249i q^{33} +(2.23331 + 5.23632i) q^{34} +(3.83294 - 3.99651i) q^{36} +5.34727i q^{37} +(2.92746 + 6.86387i) q^{38} +0.667638i q^{39} +(-3.19427 + 8.45124i) q^{40} -4.21689i q^{41} +(-2.21731 + 2.31193i) q^{44} +8.84408 q^{45} +(-2.45394 - 5.75363i) q^{46} +10.1164 q^{47} +(1.92193 - 0.0803370i) q^{48} +(-6.76873 + 2.88689i) q^{50} +1.93579 q^{51} +(1.92193 - 2.00394i) q^{52} +7.08425i q^{53} +(-1.53915 - 3.60878i) q^{54} -5.11619 q^{55} +2.53747 q^{57} +(-2.83294 - 6.64226i) q^{58} +5.06748i q^{59} +(2.21731 + 2.12656i) q^{60} -8.42643 q^{61} +(0.150848 - 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +4.43462 q^{65} +(0.427343 + 1.00197i) q^{66} -10.0363 q^{67} +(-5.81035 - 5.57255i) q^{68} -2.12703 q^{69} -5.29150i q^{71} +(-2.76873 + 7.32538i) q^{72} -10.7445i q^{73} +(-2.96673 - 6.95594i) q^{74} +2.50230i q^{75} +(-7.61631 - 7.30460i) q^{76} +(-0.370413 - 0.868490i) q^{78} -11.9338i q^{79} +(-0.533619 - 12.7659i) q^{80} +6.97209 q^{81} +(2.33958 + 5.48550i) q^{82} +14.9789i q^{83} -12.8580i q^{85} -2.45554 q^{87} +(1.60168 - 4.23764i) q^{88} +1.73205i q^{89} +(-11.5047 + 4.90680i) q^{90} +(6.38437 + 6.12307i) q^{92} -0.0557662i q^{93} +(-13.1598 + 5.61272i) q^{94} -16.8545i q^{95} +(-2.45554 + 1.17081i) q^{96} -2.87198i q^{97} -4.43462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8} + 12 q^{11} - 12 q^{18} + 24 q^{22} + 24 q^{30} + 48 q^{36} - 12 q^{44} + 36 q^{46} - 48 q^{50} - 12 q^{51} - 36 q^{57} - 36 q^{58} + 12 q^{60} - 72 q^{64} + 24 q^{65} - 60 q^{67} - 24 q^{74}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q - 12 * q^8 + 12 * q^11 - 12 * q^18 + 24 * q^22 + 24 * q^30 + 48 * q^36 - 12 * q^44 + 36 * q^46 - 48 * q^50 - 12 * q^51 - 36 * q^57 - 36 * q^58 + 12 * q^60 - 72 * q^64 + 24 * q^65 - 60 * q^67 - 24 * q^74 + 60 * q^78 - 12 * q^81 - 12 * q^88 + 60 * q^92 - 24 * q^99

Introduction

L-functions

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Database

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