LMFDB - Embedded newform 288.2.v.b.253.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(37,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$288 = 2^{5} \cdot 3^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	288.v (of order $8$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,4,0,0,-8,4,0,0,-4,0,-8,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2$ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			253.1
Root			$0.500000 + 1.44392i$ of defining polynomial
Character	$\chi$	$=$	288.253
Dual form			288.2.v.b.181.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11137 - 0.874559i) q^{2} +(0.470294 + 1.94392i) q^{4} +(0.707107 + 1.70711i) q^{5} +(-0.665096 + 0.665096i) q^{7} +(1.17740 - 2.57172i) q^{8} +(0.707107 - 2.51564i) q^{10} +(-3.69304 + 1.52971i) q^{11} +(-1.76652 + 4.26475i) q^{13} +(1.32083 - 0.157503i) q^{14} +(-3.55765 + 1.82843i) q^{16} +3.61706i q^{17} +(0.194802 - 0.470294i) q^{19} +(-2.98593 + 2.17740i) q^{20} +(5.44215 + 1.52971i) q^{22} +(1.33490 + 1.33490i) q^{23} +(1.12132 - 1.12132i) q^{25} +(5.69304 - 3.19480i) q^{26} +(-1.60568 - 0.980103i) q^{28} +(5.73838 + 2.37691i) q^{29} +1.17157 q^{31} +(5.55294 + 1.07931i) q^{32} +(3.16333 - 4.01990i) q^{34} +(-1.60568 - 0.665096i) q^{35} +(0.510925 + 1.23348i) q^{37} +(-0.627797 + 0.352305i) q^{38} +(5.22274 + 0.191470i) q^{40} +(-1.66981 - 1.66981i) q^{41} +(-2.54960 + 1.05608i) q^{43} +(-4.71044 - 6.45956i) q^{44} +(-0.316122 - 2.65103i) q^{46} -1.49824i q^{47} +6.11529i q^{49} +(-2.22686 + 0.265543i) q^{50} +(-9.12112 - 1.42828i) q^{52} +(-4.59495 + 1.90329i) q^{53} +(-5.22274 - 5.22274i) q^{55} +(0.927354 + 2.49352i) q^{56} +(-4.29872 - 7.66019i) q^{58} +(-2.04784 - 4.94392i) q^{59} +(13.7102 + 5.67897i) q^{61} +(-1.30205 - 1.02461i) q^{62} +(-5.22746 - 6.05588i) q^{64} -8.52951 q^{65} +(-3.40617 - 1.41088i) q^{67} +(-7.03127 + 1.70108i) q^{68} +(1.20285 + 2.14343i) q^{70} +(9.66157 - 9.66157i) q^{71} +(-7.55765 - 7.55765i) q^{73} +(0.510925 - 1.81769i) q^{74} +(1.00583 + 0.157503i) q^{76} +(1.43882 - 3.47363i) q^{77} -17.2176i q^{79} +(-5.63696 - 4.78039i) q^{80} +(0.395432 + 3.31612i) q^{82} +(-4.82981 + 11.6602i) q^{83} +(-6.17471 + 2.55765i) q^{85} +(3.75716 + 1.05608i) q^{86} +(-0.414214 + 11.2985i) q^{88} +(5.43882 - 5.43882i) q^{89} +(-1.66157 - 4.01138i) q^{91} +(-1.96715 + 3.22274i) q^{92} +(-1.31029 + 1.66510i) q^{94} +0.940588 q^{95} +6.15862 q^{97} +(5.34818 - 6.79637i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} - 4 q^{11} - 8 q^{13} - 12 q^{14} + 4 q^{19} - 4 q^{20} + 4 q^{22} + 8 q^{23} - 8 q^{25} + 20 q^{26} - 16 q^{28} + 32 q^{31} + 24 q^{32} - 16 q^{35} - 8 q^{37}+ \cdots + 24 q^{98}+O(q^{100})$ 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 - 4 * q^11 - 8 * q^13 - 12 * q^14 + 4 * q^19 - 4 * q^20 + 4 * q^22 + 8 * q^23 - 8 * q^25 + 20 * q^26 - 16 * q^28 + 32 * q^31 + 24 * q^32 - 16 * q^35 - 8 * q^37 - 8 * q^38 + 16 * q^40 - 8 * q^41 - 12 * q^43 - 20 * q^44 + 12 * q^46 - 16 * q^50 + 12 * q^52 - 8 * q^53 - 16 * q^55 - 8 * q^56 - 12 * q^58 + 20 * q^59 + 24 * q^61 + 24 * q^62 - 8 * q^64 - 36 * q^67 - 16 * q^68 - 8 * q^70 + 24 * q^71 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 8 * q^80 - 20 * q^82 - 20 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 + 16 * q^89 + 40 * q^91 + 16 * q^92 - 24 * q^94 + 8 * q^95 + 32 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$ .

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

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

)

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

$2$	−1.11137	−	0.874559i	−0.785858	−	0.618406i
$2$	−1.11137	−	0.874559i	−0.785858	−	0.618406i
$3$		0			0
$3$		0			0
$4$	0.470294	+	1.94392i	0.235147	+	0.971960i
$5$	0.707107	+	1.70711i	0.316228	+	0.763441i	0.999448	+	0.0332288i	$0.0105790\pi$
$5$	0.707107	+	1.70711i	0.316228	+	0.763441i	−0.683220	+	0.730213i	$0.739421\pi$
$6$		0			0
$7$	−0.665096	+	0.665096i	−0.251383	+	0.251383i	−0.821537	−	0.570155i	$-0.806883\pi$
$7$	−0.665096	+	0.665096i	−0.251383	+	0.251383i	0.570155	+	0.821537i	$0.306883\pi$
$8$	1.17740	−	2.57172i	0.416274	−	0.909239i
$9$		0			0
$10$	0.707107	−	2.51564i	0.223607	−	0.795514i
$11$	−3.69304	+	1.52971i	−1.11349	+	0.461224i	−0.862139	−	0.506672i	$-0.830876\pi$
$11$	−3.69304	+	1.52971i	−1.11349	+	0.461224i	−0.251353	+	0.967895i	$0.580876\pi$
$12$		0			0
$13$	−1.76652	+	4.26475i	−0.489944	+	1.18283i	0.464804	+	0.885414i	$0.346125\pi$
$13$	−1.76652	+	4.26475i	−0.489944	+	1.18283i	−0.954748	+	0.297416i	$0.903875\pi$
$14$	1.32083	−	0.157503i	0.353008	−	0.0420945i
$15$		0			0
$16$	−3.55765	+	1.82843i	−0.889412	+	0.457107i
$17$			3.61706i			0.877266i	0.898666	+	0.438633i	$0.144537\pi$
$17$			3.61706i			0.877266i	−0.898666	+	0.438633i	$0.855463\pi$
$18$		0			0
$19$	0.194802	−	0.470294i	0.0446907	−	0.107893i	−0.899958	−	0.435977i	$-0.856403\pi$
$19$	0.194802	−	0.470294i	0.0446907	−	0.107893i	0.944649	+	0.328084i	$0.106403\pi$
$20$	−2.98593	+	2.17740i	−0.667674	+	0.486882i
$21$		0			0
$22$	5.44215	+	1.52971i	1.16027	+	0.326134i
$23$	1.33490	+	1.33490i	0.278347	+	0.278347i	0.832449	−	0.554102i	$-0.186938\pi$
$23$	1.33490	+	1.33490i	0.278347	+	0.278347i	−0.554102	+	0.832449i	$0.686938\pi$
$24$		0			0
$25$	1.12132	−	1.12132i	0.224264	−	0.224264i
$26$	5.69304	−	3.19480i	1.11650	−	0.626552i
$27$		0			0
$28$	−1.60568	−	0.980103i	−0.303446	−	0.185222i
$29$	5.73838	+	2.37691i	1.06559	+	0.441382i	0.845433	−	0.534082i	$-0.179343\pi$
$29$	5.73838	+	2.37691i	1.06559	+	0.441382i	0.220158	+	0.975464i	$0.429343\pi$
$30$		0			0
$31$	1.17157			0.210421			0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157			0.210421			0.105210	+	0.994450i	$0.466448\pi$
$32$	5.55294	+	1.07931i	0.981630	+	0.190797i
$33$		0			0
$34$	3.16333	−	4.01990i	0.542507	−	0.689407i
$35$	−1.60568	−	0.665096i	−0.271410	−	0.112422i
$36$		0			0
$37$	0.510925	+	1.23348i	0.0839955	+	0.202783i	0.960297	−	0.278980i	$-0.0899965\pi$
$37$	0.510925	+	1.23348i	0.0839955	+	0.202783i	−0.876301	+	0.481763i	$0.839996\pi$
$38$	−0.627797	+	0.352305i	−0.101842	+	0.0571515i
$39$		0			0
$40$	5.22274	+	0.191470i	0.825788	+	0.0302741i
$41$	−1.66981	−	1.66981i	−0.260780	−	0.260780i	0.564591	−	0.825371i	$-0.309034\pi$
$41$	−1.66981	−	1.66981i	−0.260780	−	0.260780i	−0.825371	+	0.564591i	$0.809034\pi$
$42$		0			0
$43$	−2.54960	+	1.05608i	−0.388811	+	0.161051i	−0.568521	−	0.822669i	$-0.692484\pi$
$43$	−2.54960	+	1.05608i	−0.388811	+	0.161051i	0.179710	+	0.983720i	$0.442484\pi$
$44$	−4.71044	−	6.45956i	−0.710125	−	0.973815i
$45$		0			0
$46$	−0.316122	−	2.65103i	−0.0466097	−	0.390873i
$47$		−	1.49824i		−	0.218540i	−0.994012	−	0.109270i	$-0.965149\pi$
$47$		−	1.49824i		−	0.218540i	0.994012	−	0.109270i	$-0.0348513\pi$
$48$		0			0
$49$			6.11529i			0.873614i
$50$	−2.22686	+	0.265543i	−0.314926	+	0.0375535i
$51$		0			0
$52$	−9.12112	−	1.42828i	−1.26487	−	0.198067i
$53$	−4.59495	+	1.90329i	−0.631164	+	0.261437i	−0.675248	−	0.737591i	$-0.735963\pi$
$53$	−4.59495	+	1.90329i	−0.631164	+	0.261437i	0.0440833	+	0.999028i	$0.485963\pi$
$54$		0			0
$55$	−5.22274	−	5.22274i	−0.704235	−	0.704235i
$56$	0.927354	+	2.49352i	0.123923	+	0.333211i
$57$		0			0
$58$	−4.29872	−	7.66019i	−0.564450	−	1.00583i
$59$	−2.04784	−	4.94392i	−0.266606	−	0.643644i	0.732713	−	0.680537i	$-0.238254\pi$
$59$	−2.04784	−	4.94392i	−0.266606	−	0.643644i	−0.999319	+	0.0368939i	$0.988254\pi$
$60$		0			0
$61$	13.7102	+	5.67897i	1.75542	+	0.727117i	0.997173	+	0.0751463i	$0.0239424\pi$
$61$	13.7102	+	5.67897i	1.75542	+	0.727117i	0.758244	+	0.651971i	$0.226058\pi$
$62$	−1.30205	−	1.02461i	−0.165361	−	0.130126i
$63$		0			0
$64$	−5.22746	−	6.05588i	−0.653432	−	0.756985i
$65$	−8.52951			−1.05796
$66$		0			0
$67$	−3.40617	−	1.41088i	−0.416130	−	0.172367i	0.164788	−	0.986329i	$-0.447306\pi$
$67$	−3.40617	−	1.41088i	−0.416130	−	0.172367i	−0.580918	+	0.813962i	$0.697306\pi$
$68$	−7.03127	+	1.70108i	−0.852667	+	0.206286i
$69$		0			0
$70$	1.20285	+	2.14343i	0.143768	+	0.256189i
$71$	9.66157	−	9.66157i	1.14662	−	1.14662i	0.159403	−	0.987214i	$-0.449043\pi$
$71$	9.66157	−	9.66157i	1.14662	−	1.14662i	0.987214	−	0.159403i	$-0.0509571\pi$
$72$		0			0
$73$	−7.55765	−	7.55765i	−0.884556	−	0.884556i	0.109438	−	0.993994i	$-0.465095\pi$
$73$	−7.55765	−	7.55765i	−0.884556	−	0.884556i	−0.993994	+	0.109438i	$0.965095\pi$
$74$	0.510925	−	1.81769i	0.0593938	−	0.211302i
$75$		0			0
$76$	1.00583	+	0.157503i	0.115376	+	0.0180669i
$77$	1.43882	−	3.47363i	0.163969	−	0.395856i
$78$		0			0
$79$		−	17.2176i		−	1.93714i	−0.248750	−	0.968568i	$-0.580020\pi$
$79$		−	17.2176i		−	1.93714i	0.248750	−	0.968568i	$-0.419980\pi$
$80$	−5.63696	−	4.78039i	−0.630231	−	0.534464i
$81$		0			0
$82$	0.395432	+	3.31612i	0.0436682	+	0.366204i
$83$	−4.82981	+	11.6602i	−0.530140	+	1.27987i	0.401290	+	0.915951i	$0.368562\pi$
$83$	−4.82981	+	11.6602i	−0.530140	+	1.27987i	−0.931430	+	0.363921i	$0.881438\pi$
$84$		0			0
$85$	−6.17471	+	2.55765i	−0.669741	+	0.277416i
$86$	3.75716	+	1.05608i	0.405145	+	0.113880i
$87$		0			0
$88$	−0.414214	+	11.2985i	−0.0441553	+	1.20443i
$89$	5.43882	−	5.43882i	0.576514	−	0.576514i	−0.357427	−	0.933941i	$-0.616346\pi$
$89$	5.43882	−	5.43882i	0.576514	−	0.576514i	0.933941	+	0.357427i	$0.116346\pi$
$90$		0			0
$91$	−1.66157	−	4.01138i	−0.174179	−	0.420506i
$92$	−1.96715	+	3.22274i	−0.205089	+	0.335994i
$93$		0			0
$94$	−1.31029	+	1.66510i	−0.135147	+	0.171742i
$95$	0.940588			0.0965023
$96$		0			0
$97$	6.15862			0.625313			0.312657	−	0.949866i	$-0.398781\pi$
$97$	6.15862			0.625313			0.312657	+	0.949866i	$0.398781\pi$
$98$	5.34818	−	6.79637i	0.540248	−	0.686537i
$99$		0			0
$100$	2.70711	+	1.65241i	0.270711	+	0.165241i
$101$	3.09671	+	7.47612i	0.308134	+	0.743902i	0.999766	+	0.0216512i	$0.00689233\pi$
$101$	3.09671	+	7.47612i	0.308134	+	0.743902i	−0.691631	+	0.722251i	$0.743108\pi$
$102$		0			0
$103$	−4.72764	+	4.72764i	−0.465828	+	0.465828i	−0.900560	−	0.434732i	$-0.856843\pi$
$103$	−4.72764	+	4.72764i	−0.465828	+	0.465828i	0.434732	+	0.900560i	$0.356843\pi$
$104$	8.88784	+	9.56431i	0.871524	+	0.937858i
$105$		0			0
$106$	6.77123	+	1.90329i	0.657680	+	0.184864i
$107$	−2.57774	+	1.06774i	−0.249200	+	0.103222i	−0.503787	−	0.863828i	$-0.668060\pi$
$107$	−2.57774	+	1.06774i	−0.249200	+	0.103222i	0.254587	+	0.967050i	$0.418060\pi$
$108$		0			0
$109$	3.46094	−	8.35544i	0.331498	−	0.800306i	−0.666976	−	0.745079i	$-0.732412\pi$
$109$	3.46094	−	8.35544i	0.331498	−	0.800306i	0.998474	−	0.0552270i	$-0.0175882\pi$
$110$	1.23681	+	10.3720i	0.117925	+	0.988932i
$111$		0			0
$112$	1.15010	−	3.58226i	0.108674	−	0.338491i
$113$		−	11.7757i		−	1.10776i	−0.832596	−	0.553881i	$-0.813146\pi$
$113$		−	11.7757i		−	1.10776i	0.832596	−	0.553881i	$-0.186854\pi$
$114$		0			0
$115$	−1.33490	+	3.22274i	−0.124480	+	0.300522i
$116$	−1.92181	+	12.2728i	−0.178435	+	1.13950i
$117$		0			0
$118$	−2.04784	+	7.28549i	−0.188519	+	0.670683i
$119$	−2.40569	−	2.40569i	−0.220529	−	0.220529i
$120$		0			0
$121$	3.52035	−	3.52035i	0.320032	−	0.320032i
$122$	−10.2706	−	18.3019i	−0.929855	−	1.65697i
$123$		0			0
$124$	0.550984	+	2.27744i	0.0494798	+	0.204520i
$125$	11.2426	+	4.65685i	1.00557	+	0.416522i
$126$		0			0
$127$	13.0590			1.15880			0.579400	−	0.815043i	$-0.303287\pi$
$127$	13.0590			1.15880			0.579400	+	0.815043i	$0.303287\pi$
$128$	0.513421	+	11.3021i	0.0453804	+	0.998970i
$129$		0			0
$130$	9.47945	+	7.45956i	0.831403	+	0.654246i
$131$	6.52146	+	2.70128i	0.569783	+	0.236012i	0.648926	−	0.760851i	$-0.275218\pi$
$131$	6.52146	+	2.70128i	0.569783	+	0.236012i	−0.0791431	+	0.996863i	$0.525218\pi$
$132$		0			0
$133$	0.183228	+	0.442353i	0.0158879	+	0.0383568i
$134$	2.55162	+	4.54691i	0.220427	+	0.392793i
$135$		0			0
$136$	9.30205	+	4.25873i	0.797644	+	0.365183i
$137$	−4.88118	−	4.88118i	−0.417027	−	0.417027i	0.467151	−	0.884178i	$-0.345281\pi$
$137$	−4.88118	−	4.88118i	−0.417027	−	0.417027i	−0.884178	+	0.467151i	$0.845281\pi$
$138$		0			0
$139$	−11.7837	+	4.88098i	−0.999482	+	0.413999i	−0.821607	−	0.570054i	$-0.806922\pi$
$139$	−11.7837	+	4.88098i	−0.999482	+	0.413999i	−0.177875	+	0.984053i	$0.556922\pi$
$140$	0.537750	−	3.43411i	0.0454482	−	0.290235i
$141$		0			0
$142$	−19.1872	+	2.28798i	−1.61015	+	0.192003i
$143$		−	18.4522i		−	1.54305i
$144$		0			0
$145$			11.4768i			0.953093i
$146$	1.78975	+	15.0090i	0.148121	+	1.24215i
$147$		0			0
$148$	−2.15750	+	1.57329i	−0.177346	+	0.129324i
$149$	5.73838	−	2.37691i	0.470106	−	0.194724i	−0.135038	−	0.990840i	$-0.543116\pi$
$149$	5.73838	−	2.37691i	0.470106	−	0.194724i	0.605144	+	0.796116i	$0.293116\pi$
$150$		0			0
$151$	11.1504	+	11.1504i	0.907405	+	0.907405i	0.996062	−	0.0886573i	$-0.0282576\pi$
$151$	11.1504	+	11.1504i	0.907405	+	0.907405i	−0.0886573	+	0.996062i	$0.528258\pi$
$152$	−0.980103	−	1.05470i	−0.0794968	−	0.0855475i
$153$		0			0
$154$	−4.63696	+	2.60215i	−0.373657	+	0.209688i
$155$	0.828427	+	2.00000i	0.0665409	+	0.160644i
$156$		0			0
$157$	1.22496	+	0.507395i	0.0977624	+	0.0404945i	0.431029	−	0.902338i	$-0.358151\pi$
$157$	1.22496	+	0.507395i	0.0977624	+	0.0404945i	−0.333266	+	0.942833i	$0.608151\pi$
$158$	−15.0578	+	19.1352i	−1.19794	+	1.52231i
$159$		0			0
$160$	2.08402	+	10.2426i	0.164756	+	0.809752i
$161$	−1.77568			−0.139943
$162$		0			0
$163$	21.3218	+	8.83176i	1.67005	+	0.691757i	0.998776	−	0.0494542i	$-0.0157482\pi$
$163$	21.3218	+	8.83176i	1.67005	+	0.691757i	0.671272	+	0.741211i	$0.265748\pi$
$164$	2.46067	−	4.03127i	0.192146	−	0.314790i
$165$		0			0
$166$	15.5652	−	8.73485i	1.20810	−	0.677956i
$167$	−10.8863	+	10.8863i	−0.842404	+	0.842404i	−0.989171	−	0.146767i	$-0.953113\pi$
$167$	−10.8863	+	10.8863i	−0.842404	+	0.842404i	0.146767	+	0.989171i	$0.453113\pi$
$168$		0			0
$169$	−5.87515	−	5.87515i	−0.451935	−	0.451935i
$170$	9.09921	+	2.55765i	0.697877	+	0.196163i
$171$		0			0
$172$	−3.25200	−	4.45956i	−0.247963	−	0.340038i
$173$	−0.735246	+	1.77504i	−0.0558997	+	0.134954i	−0.949362	−	0.314184i	$-0.898269\pi$
$173$	−0.735246	+	1.77504i	−0.0558997	+	0.134954i	0.893462	+	0.449138i	$0.148269\pi$
$174$		0			0
$175$			1.49157i			0.112752i
$176$	10.3416	−	12.1946i	0.779525	−	0.919203i
$177$		0			0
$178$	−10.8011	+	1.28798i	−0.809578	+	0.0965384i
$179$	1.87980	−	4.53823i	0.140503	−	0.339203i	−0.837928	−	0.545782i	$-0.816233\pi$
$179$	1.87980	−	4.53823i	0.140503	−	0.339203i	0.978430	+	0.206578i	$0.0662329\pi$
$180$		0			0
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	−0.311768	−	0.950158i	$-0.600921\pi$
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	0.451410	+	0.892317i	$0.350921\pi$
$182$	−1.66157	+	5.91127i	−0.123163	+	0.438172i
$183$		0			0
$184$	5.00471	−	1.86128i	0.368952	−	0.137215i
$185$	−1.74441	+	1.74441i	−0.128251	+	0.128251i
$186$		0			0
$187$	−5.53304	−	13.3579i	−0.404616	−	0.976829i
$188$	2.91245	−	0.704611i	0.212412	−	0.0513890i
$189$		0			0
$190$	−1.04534	−	0.822599i	−0.0758371	−	0.0596776i
$191$	19.4022			1.40389			0.701946	−	0.712231i	$-0.252315\pi$
$191$	19.4022			1.40389			0.701946	+	0.712231i	$0.252315\pi$
$192$		0			0
$193$	−18.0461			−1.29898			−0.649492	−	0.760368i	$-0.725018\pi$
$193$	−18.0461			−1.29898			−0.649492	+	0.760368i	$0.725018\pi$
$194$	−6.84451	−	5.38607i	−0.491408	−	0.386698i
$195$		0			0
$196$	−11.8876	+	2.87599i	−0.849117	+	0.205428i
$197$	0.0865175	+	0.208872i	0.00616412	+	0.0148815i	0.926932	−	0.375230i	$-0.122436\pi$
$197$	0.0865175	+	0.208872i	0.00616412	+	0.0148815i	−0.920768	+	0.390112i	$0.872436\pi$
$198$		0			0
$199$	−11.8992	+	11.8992i	−0.843513	+	0.843513i	−0.989314	−	0.145801i	$-0.953424\pi$
$199$	−11.8992	+	11.8992i	−0.843513	+	0.843513i	0.145801	+	0.989314i	$0.453424\pi$
$200$	−1.56348	−	4.20396i	−0.110554	−	0.297265i
$201$		0			0
$202$	3.09671	−	11.0170i	0.217884	−	0.775154i
$203$	−5.39745	+	2.23570i	−0.378827	+	0.156915i
$204$		0			0
$205$	1.66981	−	4.03127i	0.116624	−	0.281556i
$206$	9.38877	−	1.11957i	0.654146	−	0.0780039i
$207$		0			0
$208$	−1.51314	−	18.4024i	−0.104917	−	1.27598i
$209$			2.03480i			0.140750i
$210$		0			0
$211$	−3.73060	+	9.00647i	−0.256825	+	0.620031i	−0.998725	−	0.0504799i	$-0.983925\pi$
$211$	−3.73060	+	9.00647i	−0.256825	+	0.620031i	0.741900	+	0.670511i	$0.233925\pi$
$212$	−5.86082	−	8.03710i	−0.402522	−	0.551990i
$213$		0			0
$214$	3.79863	+	1.06774i	0.259669	+	0.0729889i
$215$	−3.60568	−	3.60568i	−0.245906	−	0.245906i
$216$		0			0
$217$	−0.779208	+	0.779208i	−0.0528961	+	0.0528961i
$218$	−11.1537	+	6.25921i	−0.755425	+	0.423927i
$219$		0			0
$220$	7.69637	−	12.6088i	0.518889	−	0.850086i
$221$	−15.4259	−	6.38960i	−1.03766	−	0.429811i
$222$		0			0
$223$	22.6174			1.51458			0.757288	−	0.653081i	$-0.226524\pi$
$223$	22.6174			1.51458			0.757288	+	0.653081i	$0.226524\pi$
$224$	−4.41108	+	2.97539i	−0.294728	+	0.198802i
$225$		0			0
$226$	−10.2985	+	13.0872i	−0.685048	+	0.870545i
$227$	9.51294	+	3.94039i	0.631396	+	0.261533i	0.675346	−	0.737501i	$-0.263994\pi$
$227$	9.51294	+	3.94039i	0.631396	+	0.261533i	−0.0439500	+	0.999034i	$0.513994\pi$
$228$		0			0
$229$	−6.53200	−	15.7697i	−0.431647	−	1.04209i	−0.978756	−	0.205027i	$-0.934272\pi$
$229$	−6.53200	−	15.7697i	−0.431647	−	1.04209i	0.547109	−	0.837061i	$-0.315728\pi$
$230$	4.30205	−	2.41421i	0.283669	−	0.159189i
$231$		0			0
$232$	12.8691	−	11.9589i	0.844899	−	0.785141i
$233$	−10.4486	−	10.4486i	−0.684512	−	0.684512i	0.276502	−	0.961013i	$-0.410825\pi$
$233$	−10.4486	−	10.4486i	−0.684512	−	0.684512i	−0.961013	+	0.276502i	$0.910825\pi$
$234$		0			0
$235$	2.55765	−	1.05941i	0.166843	−	0.0691084i
$236$	8.64750	−	6.30593i	0.562904	−	0.410481i
$237$		0			0
$238$	0.569699	+	4.77754i	0.0369281	+	0.309682i
$239$			11.6733i			0.755085i	0.925992	+	0.377543i	$0.123231\pi$
$239$			11.6733i			0.755085i	−0.925992	+	0.377543i	$0.876769\pi$
$240$		0			0
$241$		−	13.8288i		−	0.890791i	−0.895334	−	0.445396i	$-0.853063\pi$
$241$		−	13.8288i		−	0.890791i	0.895334	−	0.445396i	$-0.146937\pi$
$242$	−6.99117	+	0.833664i	−0.449409	+	0.0535899i
$243$		0			0
$244$	−4.59161	+	29.3224i	−0.293948	+	1.87717i
$245$	−10.4395	+	4.32417i	−0.666953	+	0.276261i
$246$		0			0
$247$	1.66157	+	1.66157i	0.105723	+	0.105723i
$248$	1.37941	−	3.01295i	0.0875927	−	0.191323i
$249$		0			0
$250$	−8.42206	−	15.0078i	−0.532658	−	0.949180i
$251$	−5.38745	−	13.0065i	−0.340053	−	0.820961i	−0.997710	−	0.0676429i	$-0.978452\pi$
$251$	−5.38745	−	13.0065i	−0.340053	−	0.820961i	0.657656	−	0.753318i	$-0.271548\pi$
$252$		0			0
$253$	−6.97186	−	2.88784i	−0.438317	−	0.181557i
$254$	−14.5134	−	11.4209i	−0.910653	−	0.716610i
$255$		0			0
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	18.9043			1.17922			0.589609	−	0.807689i	$-0.299282\pi$
$257$	18.9043			1.17922			0.589609	+	0.807689i	$0.299282\pi$
$258$		0			0
$259$	−1.16020	−	0.480569i	−0.0720911	−	0.0298611i
$260$	−4.01138	−	16.5807i	−0.248775	−	1.02829i
$261$		0			0
$262$	−4.88534	−	8.70553i	−0.301818	−	0.537829i
$263$	−13.9086	+	13.9086i	−0.857643	+	0.857643i	−0.991060	−	0.133417i	$-0.957405\pi$
$263$	−13.9086	+	13.9086i	−0.857643	+	0.857643i	0.133417	+	0.991060i	$0.457405\pi$
$264$		0			0
$265$	−6.49824	−	6.49824i	−0.399183	−	0.399183i
$266$	0.183228	−	0.651862i	0.0112345	−	0.0399682i
$267$		0			0
$268$	1.14074	−	7.28485i	0.0696818	−	0.444993i
$269$	−5.05209	+	12.1968i	−0.308031	+	0.743653i	0.691737	+	0.722149i	$0.256846\pi$
$269$	−5.05209	+	12.1968i	−0.308031	+	0.743653i	−0.999769	+	0.0215042i	$0.993154\pi$
$270$		0			0
$271$			4.41512i			0.268199i	0.990968	+	0.134100i	$0.0428142\pi$
$271$			4.41512i			0.268199i	−0.990968	+	0.134100i	$0.957186\pi$
$272$	−6.61353	−	12.8682i	−0.401004	−	0.780251i
$273$		0			0
$274$	1.15593	+	9.69368i	0.0698320	+	0.585616i
$275$	−2.42579	+	5.85637i	−0.146280	+	0.353152i
$276$		0			0
$277$	−23.0454	+	9.54573i	−1.38467	+	0.573547i	−0.945725	−	0.324969i	$-0.894646\pi$
$277$	−23.0454	+	9.54573i	−1.38467	+	0.573547i	−0.438941	+	0.898516i	$0.644646\pi$
$278$	17.3648	+	4.88098i	1.04147	+	0.292742i
$279$		0			0
$280$	−3.60097	+	3.34628i	−0.215199	+	0.199978i
$281$	5.83509	−	5.83509i	0.348092	−	0.348092i	−0.511306	−	0.859399i	$-0.670838\pi$
$281$	5.83509	−	5.83509i	0.348092	−	0.348092i	0.859399	+	0.511306i	$0.170838\pi$
$282$		0			0
$283$	1.31992	+	3.18656i	0.0784609	+	0.189421i	0.958243	−	0.285957i	$-0.0923113\pi$
$283$	1.31992	+	3.18656i	0.0784609	+	0.189421i	−0.879782	+	0.475378i	$0.842311\pi$
$284$	23.3251	+	14.2375i	1.38409	+	0.844842i
$285$		0			0
$286$	−16.1375	+	20.5072i	−0.954230	+	1.21262i
$287$	2.22117			0.131111
$288$		0			0
$289$	3.91688			0.230405
$290$	10.0371	−	12.7549i	0.589399	−	0.748996i
$291$		0			0
$292$	11.1371	−	18.2458i	0.651752	−	1.06775i
$293$	−2.89663	−	6.99307i	−0.169223	−	0.408540i	0.816403	−	0.577482i	$-0.195965\pi$
$293$	−2.89663	−	6.99307i	−0.169223	−	0.408540i	−0.985626	+	0.168943i	$0.945965\pi$
$294$		0			0
$295$	6.99176	−	6.99176i	0.407076	−	0.407076i
$296$	3.77373	+	0.138348i	0.219343	+	0.00804132i
$297$		0			0
$298$	−8.45622	−	2.37691i	−0.489856	−	0.137691i
$299$	−8.05117	+	3.33490i	−0.465611	+	0.192862i
$300$		0			0
$301$	0.993336	−	2.39813i	0.0572550	−	0.138226i
$302$	−2.64055	−	22.1439i	−0.151947	−	1.27424i
$303$		0			0
$304$	0.166861	+	2.02932i	0.00957013	+	0.116390i
$305$			27.4205i			1.57009i
$306$		0			0
$307$	−3.14481	+	7.59225i	−0.179484	+	0.433313i	−0.987859	−	0.155356i	$-0.950348\pi$
$307$	−3.14481	+	7.59225i	−0.179484	+	0.433313i	0.808375	+	0.588668i	$0.200348\pi$
$308$	7.42912	+	1.16333i	0.423313	+	0.0662869i
$309$		0			0
$310$	0.828427	−	2.94725i	0.0470515	−	0.167393i
$311$	15.0543	+	15.0543i	0.853651	+	0.853651i	0.990581	−	0.136930i	$-0.0437234\pi$
$311$	15.0543	+	15.0543i	0.853651	+	0.853651i	−0.136930	+	0.990581i	$0.543723\pi$
$312$		0			0
$313$	18.3365	−	18.3365i	1.03644	−	1.03644i	0.0371274	−	0.999311i	$-0.488179\pi$
$313$	18.3365	−	18.3365i	1.03644	−	1.03644i	0.999311	−	0.0371274i	$-0.0118208\pi$
$314$	−0.917639	−	1.63520i	−0.0517853	−	0.0922798i
$315$		0			0
$316$	33.4697	−	8.09735i	1.88282	−	0.455511i
$317$	9.52348	+	3.94476i	0.534892	+	0.221560i	0.633744	−	0.773543i	$-0.281517\pi$
$317$	9.52348	+	3.94476i	0.534892	+	0.221560i	−0.0988523	+	0.995102i	$0.531517\pi$
$318$		0			0
$319$	−24.8280			−1.39010
$320$	6.64167	−	13.2060i	0.371281	−	0.738237i
$321$		0			0
$322$	1.97344	+	1.55294i	0.109975	+	0.0865417i
$323$	1.70108	+	0.704611i	0.0946507	+	0.0392056i
$324$		0			0
$325$	2.80132	+	6.76299i	0.155389	+	0.375143i
$326$	−15.9725	−	28.4625i	−0.884635	−	1.57639i
$327$		0			0
$328$	−6.26031	+	2.32824i	−0.345668	+	0.128556i
$329$	0.996470	+	0.996470i	0.0549372	+	0.0549372i
$330$		0			0
$331$	7.57421	−	3.13734i	0.416316	−	0.172444i	−0.164685	−	0.986346i	$-0.552661\pi$
$331$	7.57421	−	3.13734i	0.416316	−	0.172444i	0.581002	+	0.813902i	$0.302661\pi$
$332$	−24.9379	−	3.90504i	−1.36864	−	0.214317i
$333$		0			0
$334$	21.6194	−	2.57801i	1.18296	−	0.141062i
$335$		−	6.81234i		−	0.372198i
$336$		0			0
$337$			16.8910i			0.920110i	0.887890	+	0.460055i	$0.152170\pi$
$337$			16.8910i			0.920110i	−0.887890	+	0.460055i	$0.847830\pi$
$338$	1.39131	+	11.6676i	0.0756773	+	0.634636i
$339$		0			0
$340$	−7.87579	−	10.8003i	−0.427125	−	0.585728i
$341$	−4.32666	+	1.79216i	−0.234302	+	0.0970510i
$342$		0			0
$343$	−8.72293	−	8.72293i	−0.470994	−	0.470994i
$344$	−0.285965	+	7.80029i	−0.0154182	+	0.420563i
$345$		0			0
$346$	2.36951	−	1.32971i	0.127386	−	0.0714859i
$347$	11.6582	+	28.1455i	0.625847	+	1.51093i	0.844739	+	0.535179i	$0.179756\pi$
$347$	11.6582	+	28.1455i	0.625847	+	1.51093i	−0.218892	+	0.975749i	$0.570244\pi$
$348$		0			0
$349$	9.99044	+	4.13818i	0.534776	+	0.221512i	0.633694	−	0.773584i	$-0.281538\pi$
$349$	9.99044	+	4.13818i	0.534776	+	0.221512i	−0.0989174	+	0.995096i	$0.531538\pi$
$350$	1.30447	−	1.65769i	0.0697267	−	0.0886073i
$351$		0			0
$352$	−22.1582	+	4.50843i	−1.18104	+	0.240300i
$353$	−0.673711			−0.0358580			−0.0179290	−	0.999839i	$-0.505707\pi$
$353$	−0.673711			−0.0358580			−0.0179290	+	0.999839i	$0.505707\pi$
$354$		0			0
$355$	23.3251	+	9.66157i	1.23797	+	0.512783i
$356$	13.1305	+	8.01479i	0.695914	+	0.424783i
$357$		0			0
$358$	−6.05810	+	3.39967i	−0.320180	+	0.179678i
$359$	−3.92568	+	3.92568i	−0.207190	+	0.207190i	−0.803072	−	0.595882i	$-0.796802\pi$
$359$	−3.92568	+	3.92568i	−0.207190	+	0.207190i	0.595882	+	0.803072i	$0.296802\pi$
$360$		0			0
$361$	13.2518	+	13.2518i	0.697463	+	0.697463i
$362$	−2.76847	−	0.778175i	−0.145508	−	0.0408999i
$363$		0			0
$364$	7.01637	−	5.11648i	0.367758	−	0.268176i
$365$	7.55765	−	18.2458i	0.395585	−	0.955027i
$366$		0			0
$367$			16.4759i			0.860033i	0.902821	+	0.430016i	$0.141492\pi$
$367$			16.4759i			0.860033i	−0.902821	+	0.430016i	$0.858508\pi$
$368$	−7.18989	−	2.30834i	−0.374799	−	0.120331i
$369$		0			0
$370$	3.46427	−	0.413098i	0.180099	−	0.0214759i
$371$	1.79021	−	4.32195i	0.0929431	−	0.224384i
$372$		0			0
$373$	−12.6790	+	5.25180i	−0.656492	+	0.271928i	−0.685962	−	0.727638i	$-0.740618\pi$
$373$	−12.6790	+	5.25180i	−0.656492	+	0.271928i	0.0294695	+	0.999566i	$0.490618\pi$
$374$	−5.53304	+	19.6846i	−0.286107	+	1.01787i
$375$		0			0
$376$	−3.85304	−	1.76402i	−0.198705	−	0.0909725i
$377$	−20.2739	+	20.2739i	−1.04416	+	1.04416i
$378$		0			0
$379$	−5.06746	−	12.2339i	−0.260298	−	0.628414i	0.738659	−	0.674079i	$-0.235459\pi$
$379$	−5.06746	−	12.2339i	−0.260298	−	0.628414i	−0.998957	+	0.0456649i	$0.985459\pi$
$380$	0.442353	+	1.82843i	0.0226922	+	0.0937963i
$381$		0			0
$382$	−21.5630	−	16.9683i	−1.10326	−	0.868175i
$383$	−14.5667			−0.744322			−0.372161	−	0.928168i	$-0.621383\pi$
$383$	−14.5667			−0.744322			−0.372161	+	0.928168i	$0.621383\pi$
$384$		0			0
$385$	6.94725			0.354065
$386$	20.0559	+	15.7823i	1.02082	+	0.803300i
$387$		0			0
$388$	2.89636	+	11.9719i	0.147040	+	0.607779i
$389$	−14.2795	−	34.4739i	−0.724002	−	1.74789i	−0.661617	−	0.749842i	$-0.730129\pi$
$389$	−14.2795	−	34.4739i	−0.724002	−	1.74789i	−0.0623850	−	0.998052i	$-0.519871\pi$
$390$		0			0
$391$	−4.82843	+	4.82843i	−0.244184	+	0.244184i
$392$	15.7268	+	7.20015i	0.794324	+	0.363663i
$393$		0			0
$394$	0.0865175	−	0.307799i	0.00435869	−	0.0155067i
$395$	29.3923	−	12.1747i	1.47889	−	0.612576i
$396$		0			0
$397$	8.88405	−	21.4480i	0.445877	−	1.07644i	−0.527975	−	0.849260i	$-0.677048\pi$
$397$	8.88405	−	21.4480i	0.445877	−	1.07644i	0.973852	−	0.227183i	$-0.0729516\pi$
$398$	23.6310	−	2.81789i	1.18452	−	0.141248i
$399$		0			0
$400$	−1.93901	+	6.03951i	−0.0969505	+	0.301976i
$401$		−	2.51509i		−	0.125598i	−0.998026	−	0.0627989i	$-0.979997\pi$
$401$		−	2.51509i		−	0.125598i	0.998026	−	0.0627989i	$-0.0200027\pi$
$402$		0			0
$403$	−2.06961	+	4.99647i	−0.103094	+	0.248892i
$404$	−13.0766	+	9.53573i	−0.650586	+	0.474420i
$405$		0			0
$406$	7.95382	+	2.23570i	0.394742	+	0.110956i
$407$	−3.77373	−	3.77373i	−0.187057	−	0.187057i
$408$		0			0
$409$	−5.32666	+	5.32666i	−0.263386	+	0.263386i	−0.826428	−	0.563042i	$-0.809631\pi$
$409$	−5.32666	+	5.32666i	−0.263386	+	0.263386i	0.563042	+	0.826428i	$0.309631\pi$
$410$	−5.38136	+	3.01990i	−0.265767	+	0.149142i
$411$		0			0
$412$	−11.4135	−	6.96678i	−0.562305	−	0.343228i
$413$	4.65019	+	1.92617i	0.228821	+	0.0947807i
$414$		0			0
$415$	−23.3204			−1.14475
$416$	−14.4124	+	21.7753i	−0.706624	+	1.06762i
$417$		0			0
$418$	1.77955	−	2.26142i	0.0870409	−	0.110610i
$419$	−10.5509	−	4.37032i	−0.515444	−	0.213504i	0.109770	−	0.993957i	$-0.464988\pi$
$419$	−10.5509	−	4.37032i	−0.515444	−	0.213504i	−0.625214	+	0.780453i	$0.714988\pi$
$420$		0			0
$421$	1.72505	+	4.16464i	0.0840739	+	0.202972i	0.960326	−	0.278881i	$-0.0899636\pi$
$421$	1.72505	+	4.16464i	0.0840739	+	0.202972i	−0.876252	+	0.481854i	$0.839964\pi$
$422$	12.0228	−	6.74690i	0.585259	−	0.328434i
$423$		0			0
$424$	−0.515372	+	14.0578i	−0.0250287	+	0.682709i
$425$	4.05588	+	4.05588i	0.196739	+	0.196739i
$426$		0			0
$427$	−12.8957	+	5.34157i	−0.624066	+	0.258497i
$428$	−3.28789	−	4.50877i	−0.158926	−	0.217940i
$429$		0			0
$430$	0.853872	+	7.16064i	0.0411774	+	0.345317i
$431$			16.9800i			0.817897i	0.912557	+	0.408949i	$0.134104\pi$
$431$			16.9800i			0.817897i	−0.912557	+	0.408949i	$0.865896\pi$
$432$		0			0
$433$			16.9567i			0.814886i	0.913231	+	0.407443i	$0.133579\pi$
$433$			16.9567i			0.814886i	−0.913231	+	0.407443i	$0.866421\pi$
$434$	1.54745	−	0.184527i	0.0742802	−	0.00885756i
$435$		0			0
$436$	17.8700	+	2.79827i	0.855816	+	0.134013i
$437$	0.887839	−	0.367755i	0.0424711	−	0.0175921i
$438$		0			0
$439$	10.5596	+	10.5596i	0.503982	+	0.503982i	0.912673	−	0.408691i	$-0.134015\pi$
$439$	10.5596	+	10.5596i	0.503982	+	0.503982i	−0.408691	+	0.912673i	$0.634015\pi$
$440$	−19.5807	+	7.28216i	−0.933472	+	0.347163i
$441$		0			0
$442$	11.5558	+	20.5921i	0.549653	+	0.979464i
$443$	−6.31087	−	15.2358i	−0.299838	−	0.723874i	−0.999952	−	0.00984190i	$-0.996867\pi$
$443$	−6.31087	−	15.2358i	−0.299838	−	0.723874i	0.700113	−	0.714032i	$-0.253133\pi$
$444$		0			0
$445$	13.1305	+	5.43882i	0.622444	+	0.257825i
$446$	−25.1364	−	19.7803i	−1.19024	−	0.936623i
$447$		0			0
$448$	7.50450	+	0.550984i	0.354554	+	0.0260315i
$449$	−8.07197			−0.380940			−0.190470	−	0.981693i	$-0.561001\pi$
$449$	−8.07197			−0.380940			−0.190470	+	0.981693i	$0.561001\pi$
$450$		0			0
$451$	8.72098	+	3.61235i	0.410655	+	0.170099i
$452$	22.8910	−	5.53803i	1.07670	−	0.260487i
$453$		0			0
$454$	−7.12631	−	12.6989i	−0.334454	−	0.595987i
$455$	5.67294	−	5.67294i	0.265952	−	0.265952i
$456$		0			0
$457$	−7.68314	−	7.68314i	−0.359402	−	0.359402i	0.504191	−	0.863592i	$-0.331791\pi$
$457$	−7.68314	−	7.68314i	−0.359402	−	0.359402i	−0.863592	+	0.504191i	$0.831791\pi$
$458$	−6.53200	+	23.2386i	−0.305221	+	1.08587i
$459$		0			0
$460$	−6.89255	−	1.07931i	−0.321367	−	0.0503231i
$461$	5.90199	−	14.2487i	0.274883	−	0.663627i	−0.724796	−	0.688964i	$-0.758066\pi$
$461$	5.90199	−	14.2487i	0.274883	−	0.663627i	0.999679	+	0.0253371i	$0.00806593\pi$
$462$		0			0
$463$		−	27.3231i		−	1.26981i	−0.772589	−	0.634907i	$-0.781038\pi$
$463$		−	27.3231i		−	1.26981i	0.772589	−	0.634907i	$-0.218962\pi$
$464$	−24.7611	+	2.03599i	−1.14951	+	0.0945182i
$465$		0			0
$466$	2.47437	+	20.7502i	0.114623	+	0.961236i
$467$	9.40577	−	22.7075i	0.435247	−	1.05078i	−0.542323	−	0.840170i	$-0.682455\pi$
$467$	9.40577	−	22.7075i	0.435247	−	1.05078i	0.977570	−	0.210610i	$-0.0675449\pi$
$468$		0			0
$469$	3.20380	−	1.32706i	0.147938	−	0.0612779i
$470$	−3.76901	−	1.05941i	−0.173852	−	0.0488670i
$471$		0			0
$472$	−15.1255	−	0.554513i	−0.696207	−	0.0255235i
$473$	7.80029	−	7.80029i	0.358658	−	0.358658i
$474$		0			0
$475$	−0.308915	−	0.745786i	−0.0141740	−	0.0342190i
$476$	3.54509	−	5.80785i	0.162489	−	0.266203i
$477$		0			0
$478$	10.2090	−	12.9734i	0.466950	−	0.593390i
$479$	−3.91155			−0.178723			−0.0893616	−	0.995999i	$-0.528483\pi$
$479$	−3.91155			−0.178723			−0.0893616	+	0.995999i	$0.528483\pi$
$480$		0			0
$481$	−6.16305			−0.281011
$482$	−12.0941	+	15.3689i	−0.550871	+	0.700036i
$483$		0			0
$484$	8.49887	+	5.18768i	0.386312	+	0.235803i
$485$	4.35480	+	10.5134i	0.197741	+	0.477390i
$486$		0			0
$487$	−8.14685	+	8.14685i	−0.369169	+	0.369169i	−0.867174	−	0.498005i	$-0.834066\pi$
$487$	−8.14685	+	8.14685i	−0.369169	+	0.369169i	0.498005	+	0.867174i	$0.334066\pi$
$488$	30.7471	−	28.5724i	1.39186	−	1.29341i
$489$		0			0
$490$	15.3839	+	4.32417i	0.694972	+	0.195346i
$491$	−11.2886	+	4.67590i	−0.509448	+	0.211020i	−0.622575	−	0.782560i	$-0.713913\pi$
$491$	−11.2886	+	4.67590i	−0.509448	+	0.211020i	0.113127	+	0.993581i	$0.463913\pi$
$492$		0			0
$493$	−8.59744	+	20.7561i	−0.387209	+	0.934806i
$494$	−0.393480	−	3.29975i	−0.0177035	−	0.148463i
$495$		0			0
$496$	−4.16804	+	2.14214i	−0.187151	+	0.0961847i
$497$			12.8517i			0.576479i
$498$		0			0
$499$	12.4071	−	29.9533i	0.555417	−	1.34089i	−0.357944	−	0.933743i	$-0.616522\pi$
$499$	12.4071	−	29.9533i	0.555417	−	1.34089i	0.913361	−	0.407152i	$-0.133478\pi$
$500$	−3.76521	+	24.0449i	−0.168385	+	1.07532i
$501$		0			0
$502$	−5.38745	+	19.1667i	−0.240454	+	0.855450i
$503$	−8.77059	−	8.77059i	−0.391061	−	0.391061i	0.484004	−	0.875066i	$-0.339182\pi$
$503$	−8.77059	−	8.77059i	−0.391061	−	0.391061i	−0.875066	+	0.484004i	$0.839182\pi$
$504$		0			0
$505$	−10.5728	+	10.5728i	−0.470485	+	0.470485i
$506$	5.22274	+	9.30676i	0.232179	+	0.413736i
$507$		0			0
$508$	6.14158	+	25.3857i	0.272488	+	1.12631i
$509$	−20.0994	−	8.32546i	−0.890892	−	0.369020i	−0.110181	−	0.993912i	$-0.535143\pi$
$509$	−20.0994	−	8.32546i	−0.890892	−	0.369020i	−0.780711	+	0.624892i	$0.785143\pi$
$510$		0			0
$511$	10.0531			0.444724
$512$	−21.7288	+	6.31333i	−0.960287	+	0.279013i
$513$		0			0
$514$	−21.0097	−	16.5329i	−0.926698	−	0.729236i
$515$	−11.4135	−	4.72764i	−0.502941	−	0.208325i
$516$		0			0
$517$	2.29186	+	5.53304i	0.100796	+	0.243343i
$518$	0.869124	+	1.54875i	0.0381871	+	0.0680483i
$519$		0			0
$520$	−10.0426	+	21.9355i	−0.440399	+	0.961934i
$521$	29.8910	+	29.8910i	1.30955	+	1.30955i	0.921741	+	0.387807i	$0.126767\pi$
$521$	29.8910	+	29.8910i	1.30955	+	1.30955i	0.387807	+	0.921741i	$0.373233\pi$
$522$		0			0
$523$	32.7654	−	13.5719i	1.43273	−	0.593456i	0.474706	−	0.880144i	$-0.342554\pi$
$523$	32.7654	−	13.5719i	1.43273	−	0.593456i	0.958024	+	0.286688i	$0.0925544\pi$
$524$	−2.18406	+	13.9476i	−0.0954113	+	0.609304i
$525$		0			0
$526$	27.6216	−	3.29374i	1.20436	−	0.143614i
$527$			4.23765i			0.184595i
$528$		0			0
$529$		−	19.4361i		−	0.845046i
$530$	1.53887	+	12.9050i	0.0668441	+	0.560559i
$531$		0			0
$532$	−0.773727	+	0.564217i	−0.0335453	+	0.0244619i
$533$	10.0711	−	4.17157i	0.436226	−	0.180691i
$534$		0			0
$535$	−3.64548	−	3.64548i	−0.157608	−	0.157608i
$536$	−7.63881	+	7.09853i	−0.329947	+	0.306610i
$537$		0			0
$538$	16.2816	−	9.13685i	0.701949	−	0.393918i
$539$	−9.35460	−	22.5840i	−0.402931	−	0.972762i
$540$		0			0
$541$	−11.2925	−	4.67751i	−0.485502	−	0.201102i	0.126486	−	0.991968i	$-0.459630\pi$
$541$	−11.2925	−	4.67751i	−0.485502	−	0.201102i	−0.611988	+	0.790867i	$0.709630\pi$
$542$	3.86128	−	4.90683i	0.165856	−	0.210767i
$543$		0			0
$544$	−3.90393	+	20.0853i	−0.167379	+	0.861150i
$545$	16.7109			0.715815
$546$		0			0
$547$	−19.1256	−	7.92207i	−0.817750	−	0.338723i	−0.0657087	−	0.997839i	$-0.520931\pi$
$547$	−19.1256	−	7.92207i	−0.817750	−	0.338723i	−0.752042	+	0.659116i	$0.770931\pi$
$548$	7.19303	−	11.7842i	0.307271	−	0.503396i
$549$		0			0
$550$	7.81769	−	4.38711i	0.333347	−	0.187067i
$551$	2.23570	−	2.23570i	0.0952439	−	0.0952439i
$552$		0			0
$553$	11.4514	+	11.4514i	0.486962	+	0.486962i
$554$	33.9603	+	9.54573i	1.44284	+	0.405559i
$555$		0			0
$556$	−15.0300	−	20.6111i	−0.637416	−	0.874106i
$557$	−12.3617	+	29.8439i	−0.523783	+	1.26452i	0.411753	+	0.911295i	$0.364916\pi$
$557$	−12.3617	+	29.8439i	−0.523783	+	1.26452i	−0.935537	+	0.353229i	$0.885084\pi$
$558$		0			0
$559$		−	12.7390i		−	0.538803i
$560$	6.92854	−	0.569699i	0.292784	−	0.0240742i
$561$		0			0
$562$	−11.5881	+	1.38182i	−0.488814	+	0.0582888i
$563$	10.5540	−	25.4797i	0.444800	−	1.07384i	−0.529444	−	0.848345i	$-0.677600\pi$
$563$	10.5540	−	25.4797i	0.444800	−	1.07384i	0.974244	−	0.225497i	$-0.0724004\pi$
$564$		0			0
$565$	20.1023	−	8.32666i	0.845712	−	0.350305i
$566$	1.31992	−	4.69580i	0.0554802	−	0.197379i
$567$		0			0
$568$	−13.4713	−	36.2223i	−0.565242	−	1.51986i
$569$	23.7855	−	23.7855i	0.997139	−	0.997139i	−0.00285688	−	0.999996i	$-0.500909\pi$
$569$	23.7855	−	23.7855i	0.997139	−	0.997139i	0.999996	+	0.00285688i	$0.000909375\pi$
$570$		0			0
$571$	−0.904405	−	2.18343i	−0.0378482	−	0.0913736i	0.903825	−	0.427902i	$-0.140747\pi$
$571$	−0.904405	−	2.18343i	−0.0378482	−	0.0913736i	−0.941673	+	0.336528i	$0.890747\pi$
$572$	35.8695	−	8.67793i	1.49978	−	0.362843i
$573$		0			0
$574$	−2.46854	−	1.94254i	−0.103035	−	0.0810800i
$575$	2.99371			0.124846
$576$		0			0
$577$	24.8839			1.03593			0.517965	−	0.855402i	$-0.326690\pi$
$577$	24.8839			1.03593			0.517965	+	0.855402i	$0.326690\pi$
$578$	−4.35311	−	3.42554i	−0.181066	−	0.142484i
$579$		0			0
$580$	−22.3099	+	5.39745i	−0.926368	+	0.224117i
$581$	−4.54286	−	10.9674i	−0.188469	−	0.455006i
$582$		0			0
$583$	14.0578	−	14.0578i	0.582216	−	0.582216i
$584$	−28.3345	+	10.5377i	−1.17249	+	0.436055i
$585$		0			0
$586$	−2.89663	+	10.3052i	−0.119658	+	0.425703i
$587$	40.1685	−	16.6383i	1.65793	−	0.686738i	0.660015	−	0.751253i	$-0.270550\pi$
$587$	40.1685	−	16.6383i	1.65793	−	0.686738i	0.997917	+	0.0645151i	$0.0205501\pi$
$588$		0			0
$589$	0.228225	−	0.550984i	0.00940384	−	0.0227029i
$590$	−13.8851	+	1.65574i	−0.571642	+	0.0681657i
$591$		0			0
$592$	−4.07302	−	3.45410i	−0.167400	−	0.141963i
$593$			9.10197i			0.373773i	0.982382	+	0.186886i	$0.0598397\pi$
$593$			9.10197i			0.373773i	−0.982382	+	0.186886i	$0.940160\pi$
$594$		0			0
$595$	2.40569	−	5.80785i	0.0986238	−	0.238099i
$596$	7.31926	+	10.0371i	0.299808	+	0.411136i
$597$		0			0
$598$	11.8644	+	3.33490i	0.485172	+	0.136374i
$599$	−3.04488	−	3.04488i	−0.124410	−	0.124410i	0.642160	−	0.766571i	$-0.278038\pi$
$599$	−3.04488	−	3.04488i	−0.124410	−	0.124410i	−0.766571	+	0.642160i	$0.778038\pi$
$600$		0			0
$601$	9.53880	−	9.53880i	0.389096	−	0.389096i	−0.485269	−	0.874365i	$-0.661278\pi$
$601$	9.53880	−	9.53880i	0.389096	−	0.389096i	0.874365	+	0.485269i	$0.161278\pi$
$602$	−3.20127	+	1.79648i	−0.130474	+	0.0732190i
$603$		0			0
$604$	−16.4315	+	26.9194i	−0.668588	+	1.09533i
$605$	8.49887	+	3.52035i	0.345528	+	0.143123i
$606$		0			0
$607$	−3.66391			−0.148714			−0.0743568	−	0.997232i	$-0.523690\pi$
$607$	−3.66391			−0.148714			−0.0743568	+	0.997232i	$0.523690\pi$
$608$	1.58932	−	2.40126i	0.0644553	−	0.0973839i
$609$		0			0
$610$	23.9808	−	30.4743i	0.970955	−	1.23387i
$611$	6.38960	+	2.64666i	0.258496	+	0.107072i
$612$		0			0
$613$	−11.6012	−	28.0079i	−0.468570	−	1.13123i	−0.964788	−	0.263029i	$-0.915278\pi$
$613$	−11.6012	−	28.0079i	−0.468570	−	1.13123i	0.496218	−	0.868198i	$-0.334722\pi$
$614$	10.1349	−	5.68749i	0.409012	−	0.229528i
$615$		0			0
$616$	−7.23911	−	7.79009i	−0.291672	−	0.313872i
$617$	−5.86100	−	5.86100i	−0.235955	−	0.235955i	0.579218	−	0.815173i	$-0.303358\pi$
$617$	−5.86100	−	5.86100i	−0.235955	−	0.235955i	−0.815173	+	0.579218i	$0.803358\pi$
$618$		0			0
$619$	−36.9173	+	15.2917i	−1.48383	+	0.614624i	−0.969965	−	0.243245i	$-0.921788\pi$
$619$	−36.9173	+	15.2917i	−1.48383	+	0.614624i	−0.513868	+	0.857869i	$0.671788\pi$
$620$	−3.49824	+	2.55098i	−0.140493	+	0.102450i
$621$		0			0
$622$	−3.56505	−	29.8968i	−0.142946	−	1.19875i
$623$			7.23468i			0.289851i
$624$		0			0
$625$			14.5563i			0.582254i
$626$	−36.4149	+	4.34231i	−1.45543	+	0.173554i
$627$		0			0
$628$	−0.410244	+	2.61985i	−0.0163705	+	0.104543i
$629$	−4.46157	+	1.84804i	−0.177895	+	0.0736864i
$630$		0			0
$631$	−21.0543	−	21.0543i	−0.838159	−	0.838159i	0.150458	−	0.988616i	$-0.451925\pi$
$631$	−21.0543	−	21.0543i	−0.838159	−	0.838159i	−0.988616	+	0.150458i	$0.951925\pi$
$632$	−44.2789	−	20.2721i	−1.76132	−	0.806379i
$633$		0			0
$634$	−7.13421	−	12.7129i	−0.283336	−	0.504895i
$635$	9.23412	+	22.2931i	0.366445	+	0.884676i
$636$		0			0
$637$	−26.0802	−	10.8028i	−1.03334	−	0.428022i
$638$	27.5932	+	21.7136i	1.09242	+	0.859649i
$639$		0			0
$640$	−18.9308	+	8.86822i	−0.748304	+	0.350547i
$641$	6.57429			0.259669			0.129835	−	0.991536i	$-0.458555\pi$
$641$	6.57429			0.259669			0.129835	+	0.991536i	$0.458555\pi$
$642$		0			0
$643$	−24.1050	−	9.98462i	−0.950608	−	0.393755i	−0.147149	−	0.989114i	$-0.547010\pi$
$643$	−24.1050	−	9.98462i	−0.950608	−	0.393755i	−0.803459	+	0.595360i	$0.797010\pi$
$644$	−0.835091	−	3.45178i	−0.0329072	−	0.136019i
$645$		0			0
$646$	−1.27431	−	2.27078i	−0.0501370	−	0.0893426i
$647$	−19.1598	+	19.1598i	−0.753250	+	0.753250i	−0.975084	−	0.221835i	$-0.928795\pi$
$647$	−19.1598	+	19.1598i	−0.753250	+	0.753250i	0.221835	+	0.975084i	$0.428795\pi$
$648$		0			0
$649$	15.1255	+	15.1255i	0.593727	+	0.593727i
$650$	2.80132	−	9.96612i	0.109877	−	0.390903i
$651$		0			0
$652$	−7.14074	+	45.6013i	−0.279653	+	1.78588i
$653$	5.73339	−	13.8416i	0.224365	−	0.541665i	−0.771109	−	0.636703i	$-0.780298\pi$
$653$	5.73339	−	13.8416i	0.224365	−	0.541665i	0.995474	+	0.0950389i	$0.0302975\pi$
$654$		0			0
$655$			13.0429i			0.509629i
$656$	8.99371	+	2.88747i	0.351145	+	0.112737i
$657$		0			0
$658$	−0.235977	−	1.97892i	−0.00919934	−	0.0771464i
$659$	0.202554	−	0.489009i	0.00789039	−	0.0190491i	−0.919885	−	0.392188i	$-0.871718\pi$
$659$	0.202554	−	0.489009i	0.00789039	−	0.0190491i	0.927776	+	0.373139i	$0.121718\pi$
$660$		0			0
$661$	6.45241	−	2.67268i	0.250970	−	0.103955i	−0.253652	−	0.967295i	$-0.581632\pi$
$661$	6.45241	−	2.67268i	0.250970	−	0.103955i	0.504622	+	0.863340i	$0.331632\pi$
$662$	−11.1616	−	3.13734i	−0.433806	−	0.121936i
$663$		0			0
$664$	24.3001	+	26.1496i	0.943026	+	1.01480i
$665$	−0.625581	+	0.625581i	−0.0242590	+	0.0242590i
$666$		0			0
$667$	4.48723	+	10.8331i	0.173746	+	0.419461i
$668$	−26.2818	−	16.0423i	−1.01687	−	0.620694i
$669$		0			0
$670$	−5.95779	+	7.57104i	−0.230170	+	0.292495i
$671$	−59.3196			−2.29001
$672$		0			0
$673$	−24.3285			−0.937793			−0.468897	−	0.883253i	$-0.655348\pi$
$673$	−24.3285			−0.937793			−0.468897	+	0.883253i	$0.655348\pi$
$674$	14.7721	−	18.7721i	0.569002	−	0.723076i
$675$		0			0
$676$	8.65777	−	14.1839i	0.332991	−	0.545533i
$677$	−1.60737	−	3.88054i	−0.0617763	−	0.149141i	0.889977	−	0.456005i	$-0.150720\pi$
$677$	−1.60737	−	3.88054i	−0.0617763	−	0.149141i	−0.951753	+	0.306864i	$0.900720\pi$
$678$		0			0
$679$	−4.09607	+	4.09607i	−0.157193	+	0.157193i
$680$	−0.692559	+	18.8910i	−0.0265584	+	0.724436i
$681$		0			0
$682$	6.37588	+	1.79216i	0.244145	+	0.0686254i
$683$	−24.8133	+	10.2780i	−0.949455	+	0.393277i	−0.803026	−	0.595944i	$-0.796778\pi$
$683$	−24.8133	+	10.2780i	−0.949455	+	0.393277i	−0.146429	+	0.989221i	$0.546778\pi$
$684$		0			0
$685$	4.88118	−	11.7842i	0.186500	−	0.450251i
$686$	2.06570	+	17.3231i	0.0788689	+	0.661400i
$687$		0			0
$688$	7.13962	−	8.41893i	0.272196	−	0.320969i
$689$		−	22.9585i		−	0.874650i
$690$		0			0
$691$	8.56885	−	20.6870i	0.325974	−	0.786972i	−0.672909	−	0.739725i	$-0.734955\pi$
$691$	8.56885	−	20.6870i	0.325974	−	0.786972i	0.998883	−	0.0472463i	$-0.0150446\pi$
$692$	−3.79632	−	0.594468i	−0.144314	−	0.0225983i
$693$		0			0
$694$	11.6582	−	41.4759i	0.442541	−	1.57440i
$695$	−16.6647	−	16.6647i	−0.632128	−	0.632128i
$696$		0			0
$697$	6.03979	−	6.03979i	0.228774	−	0.228774i
$698$	−7.48402	−	13.3363i	−0.283274	−	0.504786i
$699$		0			0
$700$	−2.89949	+	0.701477i	−0.109591	+	0.0265133i
$701$	−28.1557	−	11.6625i	−1.06343	−	0.440486i	−0.218760	−	0.975779i	$-0.570201\pi$
$701$	−28.1557	−	11.6625i	−1.06343	−	0.440486i	−0.844667	+	0.535293i	$0.820201\pi$
$702$		0			0
$703$	0.679628			0.0256326
$704$	28.5689	+	14.3681i	1.07673	+	0.541519i
$705$		0			0
$706$	0.748744	+	0.589200i	0.0281793	+	0.0221748i
$707$	−7.03195	−	2.91273i	−0.264464	−	0.109544i
$708$		0			0
$709$	12.4408	+	30.0346i	0.467223	+	1.12797i	0.965370	+	0.260883i	$0.0840136\pi$
$709$	12.4408	+	30.0346i	0.467223	+	1.12797i	−0.498148	+	0.867092i	$0.665986\pi$
$710$	−17.4732	−	31.1367i	−0.655759	−	1.16854i
$711$		0			0
$712$	−7.58344	−	20.3908i	−0.284201	−	0.764177i
$713$	1.56394	+	1.56394i	0.0585699	+	0.0585699i
$714$		0			0
$715$	31.4998	−	13.0476i	1.17803	−	0.487954i
$716$	9.70601	+	1.51987i	0.362730	+	0.0568002i
$717$		0			0
$718$	7.79613	−	0.929652i	0.290949	−	0.0346943i
$719$		−	33.6333i		−	1.25431i	−0.778894	−	0.627155i	$-0.784219\pi$
$719$		−	33.6333i		−	1.25431i	0.778894	−	0.627155i	$-0.215781\pi$
$720$		0			0
$721$		−	6.28867i		−	0.234202i
$722$	−3.13820	−	26.3172i	−0.116792	−	0.979423i
$723$		0			0
$724$	2.39624	+	3.28603i	0.0890556	+	0.122124i
$725$	9.09984	−	3.76928i	0.337960	−	0.139988i
$726$		0			0
$727$	−7.43334	−	7.43334i	−0.275687	−	0.275687i	0.555697	−	0.831385i	$-0.312451\pi$
$727$	−7.43334	−	7.43334i	−0.275687	−	0.275687i	−0.831385	+	0.555697i	$0.812451\pi$
$728$	−12.2725	−	0.449919i	−0.454847	−	0.0166751i
$729$		0			0
$730$	−24.3564	+	13.6682i	−0.901469	+	0.505884i
$731$	−3.81991	−	9.22207i	−0.141284	−	0.341090i
$732$		0			0
$733$	−0.328598	−	0.136110i	−0.0121371	−	0.00502733i	0.376607	−	0.926373i	$-0.377091\pi$
$733$	−0.328598	−	0.136110i	−0.0121371	−	0.00502733i	−0.388744	+	0.921346i	$0.627091\pi$
$734$	14.4091	−	18.3108i	0.531850	−	0.675864i
$735$		0			0
$736$	5.97186	+	8.85341i	0.220126	+	0.326341i
$737$	14.7373			0.542857
$738$		0			0
$739$	−43.8857	−	18.1780i	−1.61436	−	0.668690i	−0.621008	−	0.783804i	$-0.713277\pi$
$739$	−43.8857	−	18.1780i	−1.61436	−	0.668690i	−0.993352	+	0.115114i	$0.963277\pi$
$740$	−4.21137	−	2.57060i	−0.154813	−	0.0944972i
$741$		0			0
$742$	−5.76939	+	3.23765i	−0.211801	+	0.118858i
$743$	30.3220	−	30.3220i	1.11240	−	1.11240i	0.119580	−	0.992825i	$-0.461845\pi$
$743$	30.3220	−	30.3220i	1.11240	−	1.11240i	0.992825	−	0.119580i	$-0.0381548\pi$
$744$		0			0
$745$	8.11529	+	8.11529i	0.297321	+	0.297321i
$746$	18.6841	+	5.25180i	0.684072	+	0.192282i
$747$		0			0
$748$	23.3646	−	17.0379i	0.854294	−	0.622969i
$749$	1.00430	−	2.42459i	0.0366963	−	0.0885927i
$750$		0			0
$751$			51.3686i			1.87447i	0.348701	+	0.937234i	$0.386623\pi$
$751$			51.3686i			1.87447i	−0.348701	+	0.937234i	$0.613377\pi$
$752$	2.73941	+	5.33019i	0.0998961	+	0.194372i
$753$		0			0
$754$	40.2626	−	4.80112i	1.46628	−	0.174847i
$755$	−11.1504	+	26.9194i	−0.405804	+	0.979697i
$756$		0			0
$757$	15.2644	−	6.32270i	0.554793	−	0.229803i	−0.0876302	−	0.996153i	$-0.527929\pi$
$757$	15.2644	−	6.32270i	0.554793	−	0.229803i	0.642423	+	0.766350i	$0.277929\pi$
$758$	−5.06746	+	18.0282i	−0.184058	+	0.654814i
$759$		0			0
$760$	1.10745	−	2.41893i	0.0401714	−	0.0877437i
$761$	−26.6859	+	26.6859i	−0.967362	+	0.967362i	−0.999484	−	0.0321218i	$-0.989774\pi$
$761$	−26.6859	+	26.6859i	−0.967362	+	0.967362i	0.0321218	+	0.999484i	$0.489774\pi$
$762$		0			0
$763$	3.25531	+	7.85902i	0.117850	+	0.284516i
$764$	9.12472	+	37.7162i	0.330121	+	1.36453i
$765$		0			0
$766$	16.1890	+	12.7394i	0.584932	+	0.460294i
$767$	24.7021			0.891943
$768$		0			0
$769$	44.0390			1.58809			0.794044	−	0.607861i	$-0.207972\pi$
$769$	44.0390			1.58809			0.794044	+	0.607861i	$0.207972\pi$
$770$	−7.72098	−	6.07578i	−0.278245	−	0.218956i
$771$		0			0
$772$	−8.48695	−	35.0801i	−0.305452	−	1.26256i
$773$	15.4001	+	37.1790i	0.553902	+	1.33724i	0.914526	+	0.404526i	$0.132564\pi$
$773$	15.4001	+	37.1790i	0.553902	+	1.33724i	−0.360625	+	0.932711i	$0.617436\pi$
$774$		0			0
$775$	1.31371	−	1.31371i	0.0471898	−	0.0471898i
$776$	7.25116	−	15.8382i	0.260302	−	0.568559i
$777$		0			0
$778$	−14.2795	+	50.8016i	−0.511946	+	1.82132i
$779$	−1.11058	+	0.460018i	−0.0397908	+	0.0164819i
$780$		0			0
$781$	−20.9012	+	50.4599i	−0.747903	+	1.80560i
$782$	9.58892	−	1.14343i	0.342899	−	0.0408891i
$783$		0			0
$784$	−11.1814	−	21.7561i	−0.399335	−	0.777002i
$785$			2.44992i			0.0874413i
$786$		0			0
$787$	0.948632	−	2.29020i	0.0338151	−	0.0816368i	−0.906070	−	0.423128i	$-0.860932\pi$
$787$	0.948632	−	2.29020i	0.0338151	−	0.0816368i	0.939885	+	0.341491i	$0.110932\pi$
$788$	−0.365341	+	0.266414i	−0.0130147	+	0.00949061i
$789$		0			0
$790$	−43.3133	−	12.1747i	−1.54102	−	0.433157i
$791$	7.83196	+	7.83196i	0.278472	+	0.278472i
$792$		0			0
$793$	−48.4388	+	48.4388i	−1.72011	+	1.72011i
$794$	−28.6310	+	16.0671i	−1.01608	+	0.570199i
$795$		0			0
$796$	−28.7272	−	17.5350i	−1.01821	−	0.621511i
$797$	2.76562	+	1.14556i	0.0979632	+	0.0405777i	0.431127	−	0.902291i	$-0.358116\pi$
$797$	2.76562	+	1.14556i	0.0979632	+	0.0405777i	−0.333164	+	0.942869i	$0.608116\pi$
$798$		0			0
$799$	5.41921			0.191718
$800$	7.43687	−	5.01637i	0.262933	−	0.177355i
$801$		0			0
$802$	−2.19960	+	2.79520i	−0.0776704	+	0.0987020i
$803$	39.4717	+	16.3497i	1.39292	+	0.576968i
$804$		0			0
$805$	−1.25559	−	3.03127i	−0.0442539	−	0.106838i
$806$	6.66981	−	3.74294i	0.234934	−	0.131840i
$807$		0			0
$808$	22.8725	+	0.838527i	0.804653	+	0.0294993i
$809$	7.12825	+	7.12825i	0.250616	+	0.250616i	0.821223	−	0.570607i	$-0.193292\pi$
$809$	7.12825	+	7.12825i	0.250616	+	0.250616i	−0.570607	+	0.821223i	$0.693292\pi$
$810$		0			0
$811$	27.4750	−	11.3805i	0.964777	−	0.399624i	0.156012	−	0.987755i	$-0.450136\pi$
$811$	27.4750	−	11.3805i	0.964777	−	0.399624i	0.808765	+	0.588131i	$0.200136\pi$
$812$	−6.88440	−	9.44077i	−0.241595	−	0.331306i
$813$		0			0
$814$	0.893667	+	7.49436i	0.0313230	+	0.262677i
$815$			42.6435i			1.49374i
$816$		0			0
$817$			1.40479i			0.0491474i
$818$	10.5784	−	1.26142i	0.369864	−	0.0441046i
$819$		0			0
$820$	8.62177	+	1.35009i	0.301085	+	0.0471472i
$821$	−34.1861	+	14.1603i	−1.19310	+	0.494199i	−0.888764	−	0.458364i	$-0.848435\pi$
$821$	−34.1861	+	14.1603i	−1.19310	+	0.494199i	−0.304339	+	0.952564i	$0.598435\pi$
$822$		0			0
$823$	27.3810	+	27.3810i	0.954440	+	0.954440i	0.999006	−	0.0445659i	$-0.0141905\pi$
$823$	27.3810	+	27.3810i	0.954440	+	0.954440i	−0.0445659	+	0.999006i	$0.514190\pi$
$824$	6.59183	+	17.7245i	0.229637	+	0.617462i
$825$		0			0
$826$	−3.48354	−	6.20756i	−0.121208	−	0.215989i
$827$	−7.98030	−	19.2661i	−0.277502	−	0.669950i	0.722263	−	0.691619i	$-0.243102\pi$
$827$	−7.98030	−	19.2661i	−0.277502	−	0.669950i	−0.999765	+	0.0216689i	$0.993102\pi$
$828$		0			0
$829$	−3.59585	−	1.48945i	−0.124889	−	0.0517307i	0.319364	−	0.947632i	$-0.396531\pi$
$829$	−3.59585	−	1.48945i	−0.124889	−	0.0517307i	−0.444253	+	0.895901i	$0.646531\pi$
$830$	25.9176	+	20.3950i	0.899613	+	0.707922i
$831$		0			0
$832$	35.0612	−	11.5960i	1.21553	−	0.402018i
$833$	−22.1194			−0.766391
$834$		0			0
$835$	−26.2818	−	10.8863i	−0.909518	−	0.376735i
$836$	−3.95549	+	0.956955i	−0.136804	+	0.0330970i
$837$		0			0
$838$	7.90385	+	14.0844i	0.273034	+	0.486538i
$839$	−13.8461	+	13.8461i	−0.478020	+	0.478020i	−0.904498	−	0.426478i	$-0.859754\pi$
$839$	−13.8461	+	13.8461i	−0.478020	+	0.478020i	0.426478	+	0.904498i	$0.359754\pi$
$840$		0			0
$841$	6.77318	+	6.77318i	0.233558	+	0.233558i
$842$	1.72505	−	6.13713i	0.0594492	−	0.211499i
$843$		0			0
$844$	−19.2623	−	3.01630i	−0.663037	−	0.103825i
$845$	5.87515	−	14.1839i	0.202111	−	0.487940i
$846$		0			0
$847$			4.68274i			0.160901i
$848$	12.8672	−	15.1728i	0.441861	−	0.521035i
$849$		0			0
$850$	−0.960485	−	8.05470i	−0.0329444	−	0.276274i
$851$	−0.964543	+	2.32861i	−0.0330641	+	0.0798239i
$852$		0			0
$853$	18.0597	−	7.48055i	0.618351	−	0.256129i	−0.0514436	−	0.998676i	$-0.516382\pi$
$853$	18.0597	−	7.48055i	0.618351	−	0.256129i	0.669794	+	0.742547i	$0.266382\pi$
$854$	19.0034	+	5.34157i	0.650283	+	0.182785i
$855$		0			0
$856$	−0.289121	+	7.88638i	−0.00988196	+	0.269551i
$857$	6.35294	−	6.35294i	0.217012	−	0.217012i	−0.590226	−	0.807238i	$-0.700961\pi$
$857$	6.35294	−	6.35294i	0.217012	−	0.217012i	0.807238	+	0.590226i	$0.200961\pi$
$858$		0			0
$859$	9.72800	+	23.4855i	0.331915	+	0.801314i	0.998440	+	0.0558315i	$0.0177810\pi$
$859$	9.72800	+	23.4855i	0.331915	+	0.801314i	−0.666525	+	0.745483i	$0.732219\pi$
$860$	5.31343	−	8.70489i	0.181186	−	0.296834i
$861$		0			0
$862$	14.8500	−	18.8711i	0.505793	−	0.642751i
$863$	0.0884535			0.00301099			0.00150550	−	0.999999i	$-0.499521\pi$
$863$	0.0884535			0.00301099			0.00150550	+	0.999999i	$0.499521\pi$
$864$		0			0
$865$	−3.55008			−0.120706
$866$	14.8296	−	18.8452i	0.503931	−	0.640385i
$867$		0			0
$868$	−1.88118	−	1.14826i	−0.0638513	−	0.0389745i
$869$	26.3379	+	63.5854i	0.893453	+	2.15699i
$870$		0			0
$871$	12.0341	−	12.0341i	0.407761	−	0.407761i
$872$	−17.4129	−	18.7382i	−0.589676	−	0.634557i
$873$		0			0
$874$	−1.30834	−	0.367755i	−0.0442554	−	0.0124395i
$875$	−10.5747	+	4.38018i	−0.357490	+	0.148077i
$876$		0			0
$877$	−4.24514	+	10.2487i	−0.143348	+	0.346073i	−0.979205	−	0.202875i	$-0.934971\pi$
$877$	−4.24514	+	10.2487i	−0.143348	+	0.346073i	0.835857	+	0.548948i	$0.184971\pi$
$878$	−2.50065	−	20.9706i	−0.0843928	−	0.707724i
$879$		0			0
$880$	28.1301	+	9.03127i	0.948265	+	0.304444i
$881$		−	23.9859i		−	0.808105i	−0.914736	−	0.404052i	$-0.867601\pi$
$881$		−	23.9859i		−	0.808105i	0.914736	−	0.404052i	$-0.132399\pi$
$882$		0			0
$883$	−7.74892	+	18.7075i	−0.260772	+	0.629559i	−0.998987	−	0.0450067i	$-0.985669\pi$
$883$	−7.74892	+	18.7075i	−0.260772	+	0.629559i	0.738215	+	0.674566i	$0.235669\pi$
$884$	5.16619	−	32.9916i	0.173758	−	1.10963i
$885$		0			0
$886$	−6.31087	+	22.4518i	−0.212018	+	0.754284i
$887$	36.4494	+	36.4494i	1.22385	+	1.22385i	0.966252	+	0.257600i	$0.0829315\pi$
$887$	36.4494	+	36.4494i	1.22385	+	1.22385i	0.257600	+	0.966252i	$0.417068\pi$
$888$		0			0
$889$	−8.68550	+	8.68550i	−0.291302	+	0.291302i
$890$	−9.83627	−	17.5279i	−0.329713	−	0.587538i
$891$		0			0
$892$	10.6368	+	43.9665i	0.356148	+	1.47211i
$893$	−0.704611	−	0.291859i	−0.0235789	−	0.00976670i
$894$		0			0
$895$	9.07646			0.303392
$896$	−7.85842	−	7.17548i	−0.262532	−	0.239716i
$897$		0			0
$898$	8.97096	+	7.05941i	0.299365	+	0.235576i
$899$	6.72293	+	2.78473i	0.224222	+	0.0928759i
$900$		0			0
$901$	−6.88431	−	16.6202i	−0.229350	−	0.553699i
$902$	−6.53304	−	11.6417i	−0.217526	−	0.387625i
$903$		0			0
$904$	−30.2837	−	13.8647i	−1.00722	−	0.461133i
$905$	2.65685	+	2.65685i	0.0883168	+	0.0883168i
$906$		0			0
$907$	−38.2753	+	15.8541i	−1.27091	+	0.526428i	−0.913241	−	0.407421i	$-0.866428\pi$
$907$	−38.2753	+	15.8541i	−1.27091	+	0.526428i	−0.357669	+	0.933848i	$0.616428\pi$
$908$	−3.18592	+	20.3455i	−0.105729	+	0.675190i
$909$		0			0
$910$	−11.2661	+	1.34343i	−0.373467	+	0.0445341i
$911$			12.5214i			0.414851i	0.978251	+	0.207426i	$0.0665085\pi$
$911$			12.5214i			0.414851i	−0.978251	+	0.207426i	$0.933492\pi$
$912$		0			0
$913$		−	50.4497i		−	1.66964i
$914$	1.81947	+	15.2582i	0.0601826	+	0.504695i
$915$		0			0
$916$	27.5830	−	20.1141i	0.911367	−	0.664587i
$917$	−6.13401	+	2.54079i	−0.202563	+	0.0839043i
$918$		0			0
$919$	1.19513	+	1.19513i	0.0394238	+	0.0394238i	0.726544	−	0.687120i	$-0.241125\pi$
$919$	1.19513	+	1.19513i	0.0394238	+	0.0394238i	−0.687120	+	0.726544i	$0.741125\pi$
$920$	6.71627	+	7.22746i	0.221429	+	0.238282i
$921$		0			0
$922$	−19.0206	+	10.6739i	−0.626410	+	0.351527i
$923$	24.1369	+	58.2715i	0.794475	+	1.91803i
$924$		0			0
$925$	1.95604	+	0.810217i	0.0643141	+	0.0266398i
$926$	−23.8957	+	30.3662i	−0.785261	+	0.997894i
$927$		0			0
$928$	29.2994	+	19.3923i	0.961801	+	0.636585i
$929$	−45.1410			−1.48103			−0.740514	−	0.672041i	$-0.765418\pi$
$929$	−45.1410			−1.48103			−0.740514	+	0.672041i	$0.765418\pi$
$930$		0			0
$931$	2.87599	+	1.19127i	0.0942566	+	0.0390424i
$932$	15.3974	−	25.2252i	0.504357	−	0.826279i
$933$		0			0
$934$	−30.3124	+	17.0106i	−0.991852	+	0.556605i
$935$	18.8910	−	18.8910i	0.617801	−	0.617801i
$936$		0			0
$937$	2.58002	+	2.58002i	0.0842857	+	0.0842857i	0.747993	−	0.663707i	$-0.231018\pi$
$937$	2.58002	+	2.58002i	0.0842857	+	0.0842857i	−0.663707	+	0.747993i	$0.731018\pi$
$938$	−4.72120	−	1.32706i	−0.154153	−	0.0433300i
$939$		0			0
$940$	3.26226	+	4.47363i	0.106403	+	0.145914i
$941$	−2.24720	+	5.42523i	−0.0732568	+	0.176857i	−0.956266	−	0.292498i	$-0.905514\pi$
$941$	−2.24720	+	5.42523i	−0.0732568	+	0.176857i	0.883009	+	0.469355i	$0.155514\pi$
$942$		0			0
$943$		−	4.45807i		−	0.145175i
$944$	16.3251	+	13.8444i	0.531336	+	0.450597i
$945$		0			0
$946$	−15.4908	+	1.84721i	−0.503650	+	0.0600579i
$947$	−17.5640	+	42.4032i	−0.570753	+	1.37792i	0.330162	+	0.943924i	$0.392897\pi$
$947$	−17.5640	+	42.4032i	−0.570753	+	1.37792i	−0.900915	+	0.433996i	$0.857103\pi$
$948$		0			0
$949$	45.5822	−	18.8808i	1.47966	−	0.612896i
$950$	−0.308915	+	1.09901i	−0.0100225	+	0.0356566i
$951$		0			0
$952$	−9.01922	+	3.35430i	−0.292315	+	0.108713i
$953$	−14.8079	+	14.8079i	−0.479673	+	0.479673i	−0.905027	−	0.425354i	$-0.860150\pi$
$953$	−14.8079	+	14.8079i	−0.479673	+	0.479673i	0.425354	+	0.905027i	$0.360150\pi$
$954$		0			0
$955$	13.7194	+	33.1216i	0.443949	+	1.07179i
$956$	−22.6920	+	5.48990i	−0.733913	+	0.177556i
$957$		0			0
$958$	4.34718	+	3.42088i	0.140451	+	0.110524i
$959$	6.49290			0.209667
$960$		0			0
$961$	−29.6274			−0.955723
$962$	6.84944	+	5.38995i	0.220835	+	0.173779i
$963$		0			0
$964$	26.8821	−	6.50360i	0.865813	−	0.209467i
$965$	−12.7605	−	30.8066i	−0.410775	−	0.991698i
$966$		0			0
$967$	24.8604	−	24.8604i	0.799455	−	0.799455i	−0.183554	−	0.983010i	$-0.558760\pi$
$967$	24.8604	−	24.8604i	0.799455	−	0.799455i	0.983010	+	0.183554i	$0.0587604\pi$
$968$	−4.90848	−	13.1982i	−0.157764	−	0.424206i
$969$		0			0
$970$	4.35480	−	15.4928i	0.139824	−	0.497445i
$971$	23.3388	−	9.66725i	0.748978	−	0.310237i	0.0246533	−	0.999696i	$-0.492152\pi$
$971$	23.3388	−	9.66725i	0.748978	−	0.310237i	0.724324	+	0.689459i	$0.242152\pi$
$972$		0			0
$973$	4.59099	−	11.0836i	0.147180	−	0.355325i
$974$	16.1791	−	1.92928i	0.518411	−	0.0618181i
$975$		0			0
$976$	−59.1598	+	4.86441i	−1.89366	+	0.155706i
$977$		−	54.7057i		−	1.75019i	−0.483952	−	0.875094i	$-0.660799\pi$
$977$		−	54.7057i		−	1.75019i	0.483952	−	0.875094i	$-0.339201\pi$
$978$		0			0
$979$	−11.7660	+	28.4056i	−0.376042	+	0.907846i
$980$	−13.3154	−	18.2598i	−0.425346	−	0.583289i
$981$		0			0
$982$	16.6352	+	4.67590i	0.530851	+	0.149214i
$983$	7.85315	+	7.85315i	0.250477	+	0.250477i	0.821166	−	0.570689i	$-0.193324\pi$
$983$	7.85315	+	7.85315i	0.250477	+	0.250477i	−0.570689	+	0.821166i	$0.693324\pi$
$984$		0			0
$985$	−0.295389	+	0.295389i	−0.00941188	+	0.00941188i
$986$	27.7073	−	15.5487i	0.882382	−	0.495172i
$987$		0			0
$988$	−2.44853	+	4.01138i	−0.0778980	+	0.127619i
$989$	−4.81324	−	1.99371i	−0.153052	−	0.0633963i
$990$		0			0
$991$	−52.4878			−1.66733			−0.833665	−	0.552270i	$-0.813762\pi$
$991$	−52.4878			−1.66733			−0.833665	+	0.552270i	$0.813762\pi$
$992$	6.50567	+	1.26449i	0.206555	+	0.0401476i
$993$		0			0
$994$	11.2396	−	14.2831i	0.356498	−	0.453031i
$995$	−28.7272	−	11.8992i	−0.910715	−	0.377230i
$996$		0			0
$997$	12.8431	+	31.0060i	0.406745	+	0.981970i	0.985988	+	0.166815i	$0.0533483\pi$
$997$	12.8431	+	31.0060i	0.406745	+	0.981970i	−0.579243	+	0.815155i	$0.696652\pi$
$998$	−39.9848	+	22.4386i	−1.26570	+	0.710280i
$999$		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	288.2.v.b.253.1		8
3.2	odd	2		32.2.g.b.29.2	yes	8
4.3	odd	2		1152.2.v.b.721.1		8
12.11	even	2		128.2.g.b.81.2		8
15.2	even	4		800.2.ba.d.349.1		8
15.8	even	4		800.2.ba.c.349.2		8
15.14	odd	2		800.2.y.b.701.1		8
24.5	odd	2		256.2.g.d.161.2		8
24.11	even	2		256.2.g.c.161.1		8
32.11	odd	8		1152.2.v.b.433.1		8
32.21	even	8	inner	288.2.v.b.181.1		8
48.5	odd	4		512.2.g.h.65.1		8
48.11	even	4		512.2.g.f.65.2		8
48.29	odd	4		512.2.g.e.65.2		8
48.35	even	4		512.2.g.g.65.1		8
96.5	odd	8		256.2.g.d.97.2		8
96.11	even	8		128.2.g.b.49.2		8
96.29	odd	8		512.2.g.h.449.1		8
96.35	even	8		512.2.g.f.449.2		8
96.53	odd	8		32.2.g.b.21.2	✓	8
96.59	even	8		256.2.g.c.97.1		8
96.77	odd	8		512.2.g.e.449.2		8
96.83	even	8		512.2.g.g.449.1		8
192.11	even	16		4096.2.a.q.1.7		8
192.53	odd	16		4096.2.a.k.1.2		8
192.107	even	16		4096.2.a.q.1.2		8
192.149	odd	16		4096.2.a.k.1.7		8
480.53	even	8		800.2.ba.d.149.1		8
480.149	odd	8		800.2.y.b.501.1		8
480.437	even	8		800.2.ba.c.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.2	✓	8	96.53	odd	8
32.2.g.b.29.2	yes	8	3.2	odd	2
128.2.g.b.49.2		8	96.11	even	8
128.2.g.b.81.2		8	12.11	even	2
256.2.g.c.97.1		8	96.59	even	8
256.2.g.c.161.1		8	24.11	even	2
256.2.g.d.97.2		8	96.5	odd	8
256.2.g.d.161.2		8	24.5	odd	2
288.2.v.b.181.1		8	32.21	even	8	inner
288.2.v.b.253.1		8	1.1	even	1	trivial
512.2.g.e.65.2		8	48.29	odd	4
512.2.g.e.449.2		8	96.77	odd	8
512.2.g.f.65.2		8	48.11	even	4
512.2.g.f.449.2		8	96.35	even	8
512.2.g.g.65.1		8	48.35	even	4
512.2.g.g.449.1		8	96.83	even	8
512.2.g.h.65.1		8	48.5	odd	4
512.2.g.h.449.1		8	96.29	odd	8
800.2.y.b.501.1		8	480.149	odd	8
800.2.y.b.701.1		8	15.14	odd	2
800.2.ba.c.149.2		8	480.437	even	8
800.2.ba.c.349.2		8	15.8	even	4
800.2.ba.d.149.1		8	480.53	even	8
800.2.ba.d.349.1		8	15.2	even	4
1152.2.v.b.433.1		8	32.11	odd	8
1152.2.v.b.721.1		8	4.3	odd	2
4096.2.a.k.1.2		8	192.53	odd	16
4096.2.a.k.1.7		8	192.149	odd	16
4096.2.a.q.1.2		8	192.107	even	16
4096.2.a.q.1.7		8	192.11	even	16

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	288.2.v.b.253.1

Level	$288$
Weight	$2$
Character	288.253
Analytic conductor	$2.300$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$