LMFDB - Embedded newform 588.2.n.h.275.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$588 = 2^{2} \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	588.n (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.7
Character	$\chi$	$=$	588.275
Dual form			588.2.n.h.263.7

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.164567 - 1.40461i) q^{2} +(-1.36816 - 1.06214i) q^{3} +(-1.94584 - 0.462303i) q^{4} +(-3.44057 - 1.98641i) q^{5} +(-1.71704 + 1.74694i) q^{6} +(-0.969574 + 2.65705i) q^{8} +(0.743736 + 2.90635i) q^{9} +(-3.35633 + 4.50574i) q^{10} +(-1.65172 - 2.86086i) q^{11} +(2.17119 + 2.69925i) q^{12} +0.850601 q^{13} +(2.59742 + 6.37208i) q^{15} +(3.57255 + 1.79913i) q^{16} +(-0.499236 + 0.288234i) q^{17} +(4.20467 - 0.566368i) q^{18} +(-3.11023 - 1.79569i) q^{19} +(5.77645 + 5.45582i) q^{20} +(-4.29021 + 1.84921i) q^{22} +(1.98085 - 3.43094i) q^{23} +(4.14868 - 2.60546i) q^{24} +(5.39167 + 9.33865i) q^{25} +(0.139981 - 1.19476i) q^{26} +(2.06938 - 4.76630i) q^{27} +3.37929i q^{29} +(9.37772 - 2.59971i) q^{30} +(4.24264 - 2.44949i) q^{31} +(3.11500 - 4.72195i) q^{32} +(-0.778803 + 5.66848i) q^{33} +(0.322697 + 0.748663i) q^{34} +(-0.103574 - 5.99911i) q^{36} +(-2.14510 + 3.71543i) q^{37} +(-3.03408 + 4.07314i) q^{38} +(-1.16376 - 0.903453i) q^{39} +(8.61389 - 7.21579i) q^{40} +5.35550i q^{41} -7.66518i q^{43} +(1.89139 + 6.33037i) q^{44} +(3.21433 - 11.4769i) q^{45} +(-4.49314 - 3.34694i) q^{46} +(-4.54525 + 7.87260i) q^{47} +(-2.97691 - 6.25604i) q^{48} +(14.0044 - 6.03634i) q^{50} +(0.989179 + 0.135905i) q^{51} +(-1.65513 - 0.393236i) q^{52} +(-0.527096 + 0.304319i) q^{53} +(-6.35423 - 3.69104i) q^{54} +13.1240i q^{55} +(2.34803 + 5.76029i) q^{57} +(4.74657 + 0.556119i) q^{58} +(3.93980 + 6.82394i) q^{59} +(-2.10831 - 13.5998i) q^{60} +(-4.87315 + 8.44054i) q^{61} +(-2.74237 - 6.36234i) q^{62} +(-6.11985 - 5.15242i) q^{64} +(-2.92655 - 1.68964i) q^{65} +(7.83381 + 2.02676i) q^{66} +(-7.83384 + 4.52287i) q^{67} +(1.10468 - 0.330057i) q^{68} +(-6.35425 + 2.59015i) q^{69} -9.15654 q^{71} +(-8.44342 - 0.841773i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(4.86570 + 3.62446i) q^{74} +(2.54223 - 18.5035i) q^{75} +(5.22185 + 4.93200i) q^{76} +(-1.46051 + 1.48595i) q^{78} +(-6.00000 - 3.46410i) q^{79} +(-8.71779 - 13.2866i) q^{80} +(-7.89371 + 4.32311i) q^{81} +(7.52237 + 0.881339i) q^{82} -4.13877 q^{83} +2.29021 q^{85} +(-10.7666 - 1.26143i) q^{86} +(3.58926 - 4.62341i) q^{87} +(9.20293 - 1.61489i) q^{88} +(-4.98550 - 2.87838i) q^{89} +(-15.5915 - 6.40358i) q^{90} +(-5.44055 + 5.76029i) q^{92} +(-8.40631 - 1.15496i) q^{93} +(10.3099 + 7.67985i) q^{94} +(7.13398 + 12.3564i) q^{95} +(-9.27717 + 3.15185i) q^{96} +13.5487 q^{97} +(7.08622 - 6.92820i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100})$ 24 * q + 12 * q^4 + 60 * q^16 + 24 * q^18 + 12 * q^25 + 36 * q^30 + 12 * q^36 - 96 * q^39 + 24 * q^46 + 12 * q^51 - 24 * q^57 + 48 * q^58 + 12 * q^60 - 48 * q^64 - 48 * q^67 - 36 * q^72 - 24 * q^78 - 144 * q^79 + 12 * q^81 - 48 * q^85 + 192 * q^88 - 24 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$ .

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.164567	−	1.40461i	0.116366	−	0.993206i
$2$	0.164567	−	1.40461i	0.116366	−	0.993206i
$3$	−1.36816	−	1.06214i	−0.789909	−	0.613224i
$3$	−1.36816	−	1.06214i	−0.789909	−	0.613224i
$4$	−1.94584	−	0.462303i	−0.972918	−	0.231152i
$5$	−3.44057	−	1.98641i	−1.53867	−	0.888351i	−0.998917	−	0.0465264i	$-0.985185\pi$
$5$	−3.44057	−	1.98641i	−1.53867	−	0.888351i	−0.539752	−	0.841824i	$-0.681482\pi$
$6$	−1.71704	+	1.74694i	−0.700977	+	0.713184i
$7$		0			0
$7$		0			0
$8$	−0.969574	+	2.65705i	−0.342796	+	0.939410i
$9$	0.743736	+	2.90635i	0.247912	+	0.968783i
$10$	−3.35633	+	4.50574i	−1.06136	+	1.42484i
$11$	−1.65172	−	2.86086i	−0.498013	−	0.862583i	0.501985	−	0.864876i	$-0.332603\pi$
$11$	−1.65172	−	2.86086i	−0.498013	−	0.862583i	−0.999997	+	0.00229340i	$0.999270\pi$
$12$	2.17119	+	2.69925i	0.626769	+	0.779205i
$13$	0.850601			0.235914			0.117957	−	0.993019i	$-0.462365\pi$
$13$	0.850601			0.235914			0.117957	+	0.993019i	$0.462365\pi$
$14$		0			0
$15$	2.59742	+	6.37208i	0.670650	+	1.64527i
$16$	3.57255	+	1.79913i	0.893138	+	0.449783i
$17$	−0.499236	+	0.288234i	−0.121082	+	0.0699070i	−0.559318	−	0.828953i	$-0.688937\pi$
$17$	−0.499236	+	0.288234i	−0.121082	+	0.0699070i	0.438236	+	0.898860i	$0.355604\pi$
$18$	4.20467	−	0.566368i	0.991050	−	0.133494i
$19$	−3.11023	−	1.79569i	−0.713537	−	0.411960i	0.0988326	−	0.995104i	$-0.468489\pi$
$19$	−3.11023	−	1.79569i	−0.713537	−	0.411960i	−0.812369	+	0.583144i	$0.801822\pi$
$20$	5.77645	+	5.45582i	1.29165	+	1.21996i
$21$		0			0
$22$	−4.29021	+	1.84921i	−0.914675	+	0.394254i
$23$	1.98085	−	3.43094i	0.413037	−	0.715401i	−0.582183	−	0.813057i	$-0.697801\pi$
$23$	1.98085	−	3.43094i	0.413037	−	0.715401i	0.995220	+	0.0976569i	$0.0311348\pi$
$24$	4.14868	−	2.60546i	0.846847	−	0.531837i
$25$	5.39167	+	9.33865i	1.07833	+	1.86773i
$26$	0.139981	−	1.19476i	0.0274525	−	0.234311i
$27$	2.06938	−	4.76630i	0.398253	−	0.917276i
$28$		0			0
$29$			3.37929i			0.627518i	0.949503	+	0.313759i	$0.101588\pi$
$29$			3.37929i			0.627518i	−0.949503	+	0.313759i	$0.898412\pi$
$30$	9.37772	−	2.59971i	1.71213	−	0.474640i
$31$	4.24264	−	2.44949i	0.762001	−	0.439941i	−0.0680129	−	0.997684i	$-0.521666\pi$
$31$	4.24264	−	2.44949i	0.762001	−	0.439941i	0.830014	+	0.557743i	$0.188333\pi$
$32$	3.11500	−	4.72195i	0.550659	−	0.834731i
$33$	−0.778803	+	5.66848i	−0.135572	+	0.986755i
$34$	0.322697	+	0.748663i	0.0553421	+	0.128395i
$35$		0			0
$36$	−0.103574	−	5.99911i	−0.0172624	−	0.999851i
$37$	−2.14510	+	3.71543i	−0.352653	+	0.610812i	−0.986713	−	0.162471i	$-0.948054\pi$
$37$	−2.14510	+	3.71543i	−0.352653	+	0.610812i	0.634061	+	0.773283i	$0.281387\pi$
$38$	−3.03408	+	4.07314i	−0.492193	+	0.660751i
$39$	−1.16376	−	0.903453i	−0.186351	−	0.144668i
$40$	8.61389	−	7.21579i	1.36198	−	1.14092i
$41$			5.35550i			0.836389i	0.908357	+	0.418195i	$0.137337\pi$
$41$			5.35550i			0.836389i	−0.908357	+	0.418195i	$0.862663\pi$
$42$		0			0
$43$		−	7.66518i		−	1.16893i	−0.811419	−	0.584464i	$-0.801305\pi$
$43$		−	7.66518i		−	1.16893i	0.811419	−	0.584464i	$-0.198695\pi$
$44$	1.89139	+	6.33037i	0.285138	+	0.954339i
$45$	3.21433	−	11.4769i	0.479164	−	1.71087i
$46$	−4.49314	−	3.34694i	−0.662477	−	0.493479i
$47$	−4.54525	+	7.87260i	−0.662993	+	1.14834i	0.316833	+	0.948481i	$0.397381\pi$
$47$	−4.54525	+	7.87260i	−0.662993	+	1.14834i	−0.979825	+	0.199856i	$0.935953\pi$
$48$	−2.97691	−	6.25604i	−0.429680	−	0.902981i
$49$		0			0
$50$	14.0044	−	6.03634i	1.98052	−	0.853667i
$51$	0.989179	+	0.135905i	0.138513	+	0.0190305i
$52$	−1.65513	−	0.393236i	−0.229525	−	0.0545320i
$53$	−0.527096	+	0.304319i	−0.0724023	+	0.0418015i	−0.535764	−	0.844368i	$-0.679976\pi$
$53$	−0.527096	+	0.304319i	−0.0724023	+	0.0418015i	0.463362	+	0.886169i	$0.346643\pi$
$54$	−6.35423	−	3.69104i	−0.864701	−	0.502287i
$55$			13.1240i			1.76964i
$56$		0			0
$57$	2.34803	+	5.76029i	0.311005	+	0.762969i
$58$	4.74657	+	0.556119i	0.623255	+	0.0730220i
$59$	3.93980	+	6.82394i	0.512919	+	0.888401i	0.999888	+	0.0149820i	$0.00476911\pi$
$59$	3.93980	+	6.82394i	0.512919	+	0.888401i	−0.486969	+	0.873419i	$0.661898\pi$
$60$	−2.10831	−	13.5998i	−0.272181	−	1.75573i
$61$	−4.87315	+	8.44054i	−0.623943	+	1.08070i	0.364802	+	0.931085i	$0.381137\pi$
$61$	−4.87315	+	8.44054i	−0.623943	+	1.08070i	−0.988744	+	0.149615i	$0.952197\pi$
$62$	−2.74237	−	6.36234i	−0.348281	−	0.808018i
$63$		0			0
$64$	−6.11985	−	5.15242i	−0.764982	−	0.644052i
$65$	−2.92655	−	1.68964i	−0.362994	−	0.209575i
$66$	7.83381	+	2.02676i	0.964276	+	0.249476i
$67$	−7.83384	+	4.52287i	−0.957056	+	0.552557i	−0.895266	−	0.445532i	$-0.853014\pi$
$67$	−7.83384	+	4.52287i	−0.957056	+	0.552557i	−0.0617904	+	0.998089i	$0.519681\pi$
$68$	1.10468	−	0.330057i	0.133962	−	0.0400253i
$69$	−6.35425	+	2.59015i	−0.764962	+	0.311817i
$70$		0			0
$71$	−9.15654			−1.08668			−0.543341	−	0.839512i	$-0.682841\pi$
$71$	−9.15654			−1.08668			−0.543341	+	0.839512i	$0.682841\pi$
$72$	−8.44342	−	0.841773i	−0.995067	−	0.0992039i
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	0.821674	−	0.569958i	$-0.193040\pi$
$73$	−0.707107	−	1.22474i	−0.0827606	−	0.143346i	−0.904435	+	0.426612i	$0.859707\pi$
$74$	4.86570	+	3.62446i	0.565626	+	0.421335i
$75$	2.54223	−	18.5035i	0.293551	−	2.13660i
$76$	5.22185	+	4.93200i	0.598987	+	0.565739i
$77$		0			0
$78$	−1.46051	+	1.48595i	−0.165370	+	0.168250i
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	0.122936	−	0.992415i	$-0.460769\pi$
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	−0.797988	+	0.602673i	$0.794102\pi$
$80$	−8.71779	−	13.2866i	−0.974678	−	1.48549i
$81$	−7.89371	+	4.32311i	−0.877079	+	0.480346i
$82$	7.52237	+	0.881339i	0.830707	+	0.0973276i
$83$	−4.13877			−0.454289			−0.227144	−	0.973861i	$-0.572939\pi$
$83$	−4.13877			−0.454289			−0.227144	+	0.973861i	$0.572939\pi$
$84$		0			0
$85$	2.29021			0.248408
$86$	−10.7666	−	1.26143i	−1.16099	−	0.136024i
$87$	3.58926	−	4.62341i	0.384809	−	0.495682i
$88$	9.20293	−	1.61489i	0.981036	−	0.172148i
$89$	−4.98550	−	2.87838i	−0.528462	−	0.305108i	0.211928	−	0.977285i	$-0.432026\pi$
$89$	−4.98550	−	2.87838i	−0.528462	−	0.305108i	−0.740390	+	0.672177i	$0.765359\pi$
$90$	−15.5915	−	6.40358i	−1.64349	−	0.674996i
$91$		0			0
$92$	−5.44055	+	5.76029i	−0.567217	+	0.600552i
$93$	−8.40631	−	1.15496i	−0.871694	−	0.119764i
$94$	10.3099	+	7.67985i	1.06339	+	0.792116i
$95$	7.13398	+	12.3564i	0.731931	+	1.26774i
$96$	−9.27717	+	3.15185i	−0.946847	+	0.321684i
$97$	13.5487			1.37567			0.687833	−	0.725869i	$-0.258562\pi$
$97$	13.5487			1.37567			0.687833	+	0.725869i	$0.258562\pi$
$98$		0			0
$99$	7.08622	−	6.92820i	0.712192	−	0.696311i
$100$	−6.17402	−	20.6641i	−0.617402	−	2.06641i
$101$	−6.18294	+	3.56972i	−0.615225	+	0.355200i	−0.775008	−	0.631952i	$-0.782254\pi$
$101$	−6.18294	+	3.56972i	−0.615225	+	0.355200i	0.159782	+	0.987152i	$0.448921\pi$
$102$	0.353679	−	1.36704i	0.0350195	−	0.135357i
$103$	9.10090	+	5.25441i	0.896738	+	0.517732i	0.876141	−	0.482056i	$-0.160110\pi$
$103$	9.10090	+	5.25441i	0.896738	+	0.517732i	0.0205978	+	0.999788i	$0.493443\pi$
$104$	−0.824720	+	2.26009i	−0.0808705	+	0.221620i
$105$		0			0
$106$	0.340706	+	0.790444i	0.0330923	+	0.0767747i
$107$	0.616561	−	1.06792i	0.0596052	−	0.103239i	−0.834683	−	0.550731i	$-0.814349\pi$
$107$	0.616561	−	1.06792i	0.0596052	−	0.103239i	0.894288	+	0.447491i	$0.147682\pi$
$108$	−6.23016	+	8.31776i	−0.599497	+	0.800377i
$109$	1.60147	+	2.77382i	0.153393	+	0.265684i	0.932473	−	0.361241i	$-0.117647\pi$
$109$	1.60147	+	2.77382i	0.153393	+	0.265684i	−0.779080	+	0.626925i	$0.784313\pi$
$110$	18.4340	+	2.15978i	1.75762	+	0.205927i
$111$	6.88114	−	2.80492i	0.653128	−	0.266231i
$112$		0			0
$113$		−	19.9097i		−	1.87294i	−0.350744	−	0.936471i	$-0.614071\pi$
$113$		−	19.9097i		−	1.87294i	0.350744	−	0.936471i	$-0.385929\pi$
$114$	8.47735	−	2.35011i	0.793976	−	0.220108i
$115$	−13.6305	+	7.86959i	−1.27105	+	0.733843i
$116$	1.56226	−	6.57554i	0.145052	−	0.610523i
$117$	0.632623	+	2.47214i	0.0584860	+	0.228550i
$118$	10.2333	−	4.41088i	0.942052	−	0.406054i
$119$		0			0
$120$	−19.4493	+	0.723262i	−1.77547	+	0.0660244i
$121$	0.0436371	−	0.0755817i	0.00396701	−	0.00687107i
$122$	11.0537	+	8.23388i	1.00075	+	0.745461i
$123$	5.68827	−	7.32720i	0.512894	−	0.660671i
$124$	−9.38789	+	2.80492i	−0.843057	+	0.251889i
$125$		−	22.9762i		−	2.05505i
$126$		0			0
$127$			16.4426i			1.45904i	0.683957	+	0.729522i	$0.260258\pi$
$127$			16.4426i			1.45904i	−0.683957	+	0.729522i	$0.739742\pi$
$128$	−8.24424	+	7.74806i	−0.728695	+	0.684839i
$129$	−8.14146	+	10.4872i	−0.716815	+	0.923347i
$130$	−2.85490	+	3.83259i	−0.250391	+	0.336140i
$131$	1.13845	−	1.97186i	0.0994670	−	0.172282i	−0.811997	−	0.583661i	$-0.801620\pi$
$131$	1.13845	−	1.97186i	0.0994670	−	0.172282i	0.911464	+	0.411379i	$0.134953\pi$
$132$	4.13598	−	10.6699i	0.359991	−	0.928694i
$133$		0			0
$134$	5.06366	+	11.7478i	0.437434	+	1.01485i
$135$	−16.5877	+	12.2881i	−1.42764	+	1.05759i
$136$	−0.281806	−	1.60596i	−0.0241647	−	0.137710i
$137$	−7.97118	+	4.60216i	−0.681024	+	0.393189i	−0.800241	−	0.599679i	$-0.795295\pi$
$137$	−7.97118	+	4.60216i	−0.681024	+	0.393189i	0.119217	+	0.992868i	$0.461962\pi$
$138$	2.59244	+	9.35148i	0.220683	+	0.796051i
$139$		−	11.1056i		−	0.941960i	−0.882144	−	0.470980i	$-0.843900\pi$
$139$		−	11.1056i		−	0.941960i	0.882144	−	0.470980i	$-0.156100\pi$
$140$		0			0
$141$	14.5804	−	5.94333i	1.22789	−	0.500519i
$142$	−1.50686	+	12.8613i	−0.126453	+	1.07930i
$143$	−1.40495	−	2.43345i	−0.117488	−	0.203496i
$144$	−2.57187	+	11.7212i	−0.214322	+	0.976763i
$145$	6.71266	−	11.6267i	0.557456	−	0.965542i
$146$	−1.83665	+	0.791654i	−0.152002	+	0.0655177i
$147$		0			0
$148$	5.89167	−	6.23792i	0.484292	−	0.512754i
$149$	5.81744	+	3.35870i	0.476584	+	0.275156i	0.718992	−	0.695019i	$-0.244604\pi$
$149$	5.81744	+	3.35870i	0.476584	+	0.275156i	−0.242408	+	0.970174i	$0.577937\pi$
$150$	−25.5717	−	6.61589i	−2.08792	−	0.540185i
$151$	−11.4426	+	6.60641i	−0.931188	+	0.537622i	−0.887187	−	0.461410i	$-0.847344\pi$
$151$	−11.4426	+	6.60641i	−0.931188	+	0.537622i	−0.0440012	+	0.999031i	$0.514011\pi$
$152$	7.78685	−	6.52299i	0.631597	−	0.529085i
$153$	−1.20901	−	1.23658i	−0.0977425	−	0.0999718i
$154$		0			0
$155$	−19.4628			−1.56329
$156$	1.84682	+	2.29598i	0.147864	+	0.183826i
$157$	−1.19412	−	2.06828i	−0.0953011	−	0.165066i	0.814433	−	0.580257i	$-0.197048\pi$
$157$	−1.19412	−	2.06828i	−0.0953011	−	0.165066i	−0.909734	+	0.415191i	$0.863715\pi$
$158$	−5.85310	+	7.85756i	−0.465648	+	0.625114i
$159$	1.04438	+	0.143490i	0.0828249	+	0.0113795i
$160$	−20.0971	+	10.0585i	−1.58881	+	0.795196i
$161$		0			0
$162$	4.77323	+	11.7990i	0.375020	+	0.927017i
$163$	15.8412	+	9.14590i	1.24078	+	0.716362i	0.969252	−	0.246069i	$-0.0791390\pi$
$163$	15.8412	+	9.14590i	1.24078	+	0.716362i	0.271524	+	0.962432i	$0.412472\pi$
$164$	2.47587	−	10.4209i	0.193333	−	0.813738i
$165$	13.9395	−	17.9558i	1.08519	−	1.39785i
$166$	−0.681104	+	5.81334i	−0.0528639	+	0.451202i
$167$	−19.3650			−1.49851			−0.749253	−	0.662284i	$-0.769587\pi$
$167$	−19.3650			−1.49851			−0.749253	+	0.662284i	$0.769587\pi$
$168$		0			0
$169$	−12.2765			−0.944344
$170$	0.376892	−	3.21684i	0.0289063	−	0.246720i
$171$	2.90572	−	10.3749i	0.222206	−	0.793392i
$172$	−3.54364	+	14.9152i	−0.270200	+	1.13727i
$173$	4.83696	+	2.79262i	0.367748	+	0.212319i	0.672474	−	0.740121i	$-0.265232\pi$
$173$	4.83696	+	2.79262i	0.367748	+	0.212319i	−0.304726	+	0.952440i	$0.598565\pi$
$174$	−5.90340	−	5.80236i	−0.447536	−	0.439876i
$175$		0			0
$176$	−0.753784	−	13.1922i	−0.0568186	−	0.994403i
$177$	1.85766	−	13.5209i	0.139630	−	1.01629i
$178$	−4.86344	+	6.52898i	−0.364530	+	0.489368i
$179$	−9.68969	−	16.7830i	−0.724241	−	1.25442i	−0.959286	−	0.282438i	$-0.908857\pi$
$179$	−9.68969	−	16.7830i	−0.724241	−	1.25442i	0.235044	−	0.971985i	$-0.424477\pi$
$180$	−11.5603	+	20.8461i	−0.861657	+	1.55377i
$181$	−10.8735			−0.808222			−0.404111	−	0.914710i	$-0.632419\pi$
$181$	−10.8735			−0.808222			−0.404111	+	0.914710i	$0.632419\pi$
$182$		0			0
$183$	15.6323	−	6.37208i	1.15557	−	0.471038i
$184$	7.19560	+	8.58978i	0.530467	+	0.633247i
$185$	14.7607	−	8.52212i	1.08523	−	0.626559i
$186$	−3.00566	+	11.6175i	−0.220386	+	0.851835i
$187$	1.64920	+	0.952164i	0.120601	+	0.0696291i
$188$	12.4838	−	13.2175i	0.910477	−	0.963986i
$189$		0			0
$190$	18.5299	−	7.98697i	1.34430	−	0.579436i
$191$	0.616561	−	1.06792i	0.0446128	−	0.0772716i	−0.842857	−	0.538138i	$-0.819128\pi$
$191$	0.616561	−	1.06792i	0.0446128	−	0.0772716i	0.887470	+	0.460866i	$0.152461\pi$
$192$	2.90039	+	13.5495i	0.209317	+	0.977848i
$193$	−7.89167	−	13.6688i	−0.568055	−	0.983900i	−0.996758	−	0.0804546i	$-0.974363\pi$
$193$	−7.89167	−	13.6688i	−0.568055	−	0.983900i	0.428703	−	0.903445i	$-0.358971\pi$
$194$	2.22968	−	19.0306i	0.160081	−	1.36632i
$195$	2.20936	+	5.42010i	0.158216	+	0.388141i
$196$		0			0
$197$			17.3868i			1.23876i	0.785092	+	0.619379i	$0.212615\pi$
$197$			17.3868i			1.23876i	−0.785092	+	0.619379i	$0.787385\pi$
$198$	−8.56524	−	11.0935i	−0.608705	−	0.788381i
$199$	−3.95565	+	2.28380i	−0.280409	+	0.161894i	−0.633608	−	0.773654i	$-0.718427\pi$
$199$	−3.95565	+	2.28380i	−0.280409	+	0.161894i	0.353200	+	0.935548i	$0.385094\pi$
$200$	−30.0409	+	5.27144i	−2.12421	+	0.372747i
$201$	15.5219	+	2.13258i	1.09483	+	0.150421i
$202$	3.99654	+	9.27205i	0.281196	+	0.652379i
$203$		0			0
$204$	−1.86195	−	0.721750i	−0.130363	−	0.0505326i
$205$	10.6382	−	18.4260i	0.743007	−	1.28693i
$206$	8.87808	−	11.9185i	0.618565	−	0.830400i
$207$	11.4447	+	3.20534i	0.795464	+	0.222786i
$208$	3.03881	+	1.53034i	0.210704	+	0.106110i
$209$			11.8639i			0.820646i
$210$		0			0
$211$		−	1.11224i		−	0.0765696i	−0.999267	−	0.0382848i	$-0.987811\pi$
$211$		−	1.11224i		−	0.0765696i	0.999267	−	0.0382848i	$-0.0121894\pi$
$212$	1.16633	−	0.348477i	0.0801039	−	0.0239335i
$213$	12.5276	+	9.72549i	0.858379	+	0.666379i
$214$	−1.39853	−	1.04177i	−0.0956018	−	0.0712139i
$215$	−15.2262	+	26.3726i	−1.03842	+	1.79859i
$216$	10.6579	+	10.1197i	0.725178	+	0.688561i
$217$		0			0
$218$	4.15967	−	1.79295i	0.281729	−	0.121434i
$219$	−0.333408	+	2.42669i	−0.0225296	+	0.163981i
$220$	6.06727	−	25.5371i	0.409055	−	1.72171i
$221$	−0.424650	+	0.245172i	−0.0285651	+	0.0164920i
$222$	−2.80740	−	10.1269i	−0.188420	−	0.679672i
$223$		−	23.6328i		−	1.58257i	−0.611447	−	0.791285i	$-0.709412\pi$
$223$		−	23.6328i		−	1.58257i	0.611447	−	0.791285i	$-0.290588\pi$
$224$		0			0
$225$	−23.1314	+	22.6156i	−1.54209	+	1.50770i
$226$	−27.9652	−	3.27647i	−1.86022	−	0.217948i
$227$	6.14917	+	10.6507i	0.408135	+	0.706910i	0.994681	−	0.103006i	$-0.0328461\pi$
$227$	6.14917	+	10.6507i	0.408135	+	0.706910i	−0.586546	+	0.809916i	$0.699513\pi$
$228$	−1.90589	−	12.2941i	−0.126220	−	0.814195i
$229$	4.51474	−	7.81976i	0.298342	−	0.516744i	−0.677414	−	0.735602i	$-0.736900\pi$
$229$	4.51474	−	7.81976i	0.298342	−	0.516744i	0.975757	+	0.218857i	$0.0702329\pi$
$230$	8.81054	+	20.4406i	0.580950	+	1.34781i
$231$		0			0
$232$	−8.97895	−	3.27647i	−0.589497	−	0.215111i
$233$	6.55912	+	3.78691i	0.429703	+	0.248089i	0.699220	−	0.714907i	$-0.253531\pi$
$233$	6.55912	+	3.78691i	0.429703	+	0.248089i	−0.269517	+	0.962996i	$0.586864\pi$
$234$	3.57649	−	0.481753i	0.233803	−	0.0314932i
$235$	31.2765	−	18.0575i	2.04025	−	1.17794i
$236$	−4.51148	−	15.0996i	−0.293672	−	0.982903i
$237$	4.52963	+	11.1123i	0.294231	+	0.721819i
$238$		0			0
$239$	9.25206			0.598466			0.299233	−	0.954180i	$-0.403269\pi$
$239$	9.25206			0.598466			0.299233	+	0.954180i	$0.403269\pi$
$240$	−2.18482	+	27.4377i	−0.141030	+	1.77110i
$241$	7.83018	+	13.5623i	0.504386	+	0.873623i	0.999987	+	0.00507224i	$0.00161455\pi$
$241$	7.83018	+	13.5623i	0.504386	+	0.873623i	−0.495601	+	0.868550i	$0.665052\pi$
$242$	−0.0989813	−	0.0737312i	−0.00636276	−	0.00473962i
$243$	15.3916	+	2.46947i	0.987372	+	0.158417i
$244$	13.3844	−	14.1710i	0.856850	−	0.907207i
$245$		0			0
$246$	−9.35572	−	9.19559i	−0.596499	−	0.586290i
$247$	−2.64557	−	1.52742i	−0.168333	−	0.0971873i
$248$	2.39487	+	13.6479i	0.152074	+	0.866641i
$249$	5.66250	+	4.39593i	0.358847	+	0.278581i
$250$	−32.2725	−	3.78112i	−2.04109	−	0.239139i
$251$	−3.08987			−0.195031			−0.0975155	−	0.995234i	$-0.531090\pi$
$251$	−3.08987			−0.195031			−0.0975155	+	0.995234i	$0.531090\pi$
$252$		0			0
$253$	−13.0873			−0.822790
$254$	23.0954	+	2.70591i	1.44913	+	0.169784i
$255$	−3.13337	−	2.43251i	−0.196219	−	0.152330i
$256$	9.52625	+	12.8550i	0.595390	+	0.803437i
$257$	6.38190	+	3.68459i	0.398092	+	0.229839i	0.685660	−	0.727922i	$-0.259514\pi$
$257$	6.38190	+	3.68459i	0.398092	+	0.229839i	−0.287568	+	0.957760i	$0.592847\pi$
$258$	13.3906	+	13.1614i	0.833661	+	0.819392i
$259$		0			0
$260$	4.91346	+	4.64072i	0.304720	+	0.287805i
$261$	−9.82139	+	2.51330i	−0.607929	+	0.155569i
$262$	−2.58233	−	1.92358i	−0.159537	−	0.118839i
$263$	11.1017	+	19.2288i	0.684563	+	1.18570i	0.973574	+	0.228372i	$0.0733401\pi$
$263$	11.1017	+	19.2288i	0.684563	+	1.18570i	−0.289011	+	0.957326i	$0.593327\pi$
$264$	−14.3063	−	7.56533i	−0.880494	−	0.465614i
$265$	2.41801			0.148537
$266$		0			0
$267$	3.76375	+	9.23337i	0.230338	+	0.565073i
$268$	17.3343	−	5.17915i	1.05886	−	0.316367i
$269$	−8.67226	+	5.00693i	−0.528757	+	0.305278i	−0.740510	−	0.672045i	$-0.765416\pi$
$269$	−8.67226	+	5.00693i	−0.528757	+	0.305278i	0.211753	+	0.977323i	$0.432083\pi$
$270$	14.5302	+	25.3214i	0.884281	+	1.54101i
$271$	−20.4250	−	11.7924i	−1.24073	−	0.716335i	−0.271486	−	0.962442i	$-0.587515\pi$
$271$	−20.4250	−	11.7924i	−1.24073	−	0.716335i	−0.969243	+	0.246107i	$0.920848\pi$
$272$	−2.30212	+	0.131539i	−0.139586	+	0.00797574i
$273$		0			0
$274$	5.15243	+	11.9537i	0.311270	+	0.722151i
$275$	17.8111	−	30.8497i	1.07405	−	1.86031i
$276$	13.5618	−	2.10241i	0.816322	−	0.126550i
$277$	−14.5299	−	25.1665i	−0.873018	−	1.51211i	−0.858860	−	0.512211i	$-0.828826\pi$
$277$	−14.5299	−	25.1665i	−0.873018	−	1.51211i	−0.0141582	−	0.999900i	$-0.504507\pi$
$278$	−15.5989	−	1.82761i	−0.935561	−	0.109613i
$279$	10.2745	+	10.5088i	0.615117	+	0.629146i
$280$		0			0
$281$		−	23.2889i		−	1.38930i	−0.719347	−	0.694651i	$-0.755559\pi$
$281$		−	23.2889i		−	1.38930i	0.719347	−	0.694651i	$-0.244441\pi$
$282$	−5.94858	−	21.4578i	−0.354233	−	1.27779i
$283$	15.0916	−	8.71312i	0.897101	−	0.517941i	0.0208421	−	0.999783i	$-0.493365\pi$
$283$	15.0916	−	8.71312i	0.897101	−	0.517941i	0.876258	+	0.481842i	$0.160032\pi$
$284$	17.8171	+	4.23310i	1.05725	+	0.251188i
$285$	3.36375	−	24.4828i	0.199251	−	1.45024i
$286$	−3.64925	+	1.57294i	−0.215785	+	0.0930100i
$287$		0			0
$288$	16.0404	+	5.54137i	0.945187	+	0.326529i
$289$	−8.33384	+	14.4346i	−0.490226	+	0.849096i
$290$	−15.2262	−	11.3420i	−0.894114	−	0.666026i
$291$	−18.5369	−	14.3906i	−1.08665	−	0.843592i
$292$	0.809710	+	2.71005i	0.0473847	+	0.158594i
$293$		−	1.20747i		−	0.0705412i	−0.999378	−	0.0352706i	$-0.988771\pi$
$293$		−	1.20747i		−	0.0705412i	0.999378	−	0.0352706i	$-0.0112293\pi$
$294$		0			0
$295$		−	31.3043i		−	1.82261i
$296$	−7.79225	−	9.30203i	−0.452915	−	0.540670i
$297$	−17.0538	+	1.95238i	−0.989561	+	0.113289i
$298$	5.67501	−	7.61849i	0.328745	−	0.441327i
$299$	1.68492	−	2.91836i	0.0974412	−	0.168773i
$300$	−13.5010	+	34.8294i	−0.779479	+	2.01088i
$301$		0			0
$302$	7.39632	+	17.1596i	0.425610	+	0.987423i
$303$	12.2508	+	1.68316i	0.703789	+	0.0966950i
$304$	−7.88078	−	12.0109i	−0.451994	−	0.688874i
$305$	33.5328	−	19.3602i	1.92008	−	1.10856i
$306$	−1.93587	+	1.49468i	−0.110667	+	0.0854451i
$307$			34.0275i			1.94205i	0.238973	+	0.971026i	$0.423189\pi$
$307$			34.0275i			1.94205i	−0.238973	+	0.971026i	$0.576811\pi$
$308$		0			0
$309$	−6.87062	−	16.8553i	−0.390856	−	0.958863i
$310$	−3.20293	+	27.3376i	−0.181914	+	1.55267i
$311$	−13.3558	−	23.1329i	−0.757337	−	1.31175i	−0.944204	−	0.329361i	$-0.893167\pi$
$311$	−13.3558	−	23.1329i	−0.757337	−	1.31175i	0.186867	−	0.982385i	$-0.440167\pi$
$312$	3.52887	−	2.21621i	0.199783	−	0.125468i
$313$	4.66276	−	8.07614i	0.263555	−	0.456490i	−0.703629	−	0.710567i	$-0.748438\pi$
$313$	4.66276	−	8.07614i	0.263555	−	0.456490i	0.967184	+	0.254077i	$0.0817717\pi$
$314$	−3.10162	+	1.33690i	−0.175035	+	0.0754455i
$315$		0			0
$316$	10.0735	+	9.51439i	0.566681	+	0.535226i
$317$	23.3767	+	13.4966i	1.31297	+	0.758043i	0.982587	−	0.185805i	$-0.0594891\pi$
$317$	23.3767	+	13.4966i	1.31297	+	0.758043i	0.330382	+	0.943847i	$0.392822\pi$
$318$	0.373417	−	1.44333i	0.0209402	−	0.0809380i
$319$	9.66769	−	5.58164i	0.541286	−	0.312512i
$320$	10.8209	+	29.8838i	0.604909	+	1.67055i
$321$	−1.97783	+	0.806210i	−0.110392	+	0.0449982i
$322$		0			0
$323$	2.07032			0.115196
$324$	17.3585	−	4.76278i	0.964359	−	0.264599i
$325$	4.58616	+	7.94346i	0.254394	+	0.440624i
$326$	15.4533	−	20.7455i	0.855880	−	1.14899i
$327$	0.755108	−	5.49601i	0.0417575	−	0.303930i
$328$	−14.2299	−	5.19256i	−0.785712	−	0.286711i
$329$		0			0
$330$	−22.9268	−	22.5344i	−1.26208	−	1.24048i
$331$	−12.6382	−	7.29669i	−0.694660	−	0.401062i	0.110695	−	0.993854i	$-0.464692\pi$
$331$	−12.6382	−	7.29669i	−0.694660	−	0.401062i	−0.805356	+	0.592792i	$0.798026\pi$
$332$	8.05336	+	1.91337i	0.441985	+	0.105010i
$333$	−12.3937	−	3.47112i	−0.679171	−	0.190216i
$334$	−3.18683	+	27.2002i	−0.174376	+	1.48833i
$335$	35.9372			1.96346
$336$		0			0
$337$	31.6823			1.72585			0.862924	−	0.505335i	$-0.168631\pi$
$337$	31.6823			1.72585			0.862924	+	0.505335i	$0.168631\pi$
$338$	−2.02030	+	17.2436i	−0.109890	+	0.937929i
$339$	−21.1468	+	27.2396i	−1.14853	+	1.47945i
$340$	−4.45636	−	1.05877i	−0.241680	−	0.0574198i
$341$	−14.0153	−	8.09175i	−0.758972	−	0.438193i
$342$	−14.0945	−	5.78876i	−0.762144	−	0.313020i
$343$		0			0
$344$	20.3668	+	7.43196i	1.09810	+	0.400704i
$345$	27.0073	+	3.71059i	1.45403	+	0.199772i
$346$	4.71854	−	6.33446i	0.253670	−	0.340542i
$347$	1.07687	+	1.86519i	0.0578092	+	0.100128i	0.893482	−	0.449100i	$-0.148255\pi$
$347$	1.07687	+	1.86519i	0.0578092	+	0.100128i	−0.835673	+	0.549228i	$0.814922\pi$
$348$	−9.12153	+	7.33708i	−0.488966	+	0.393309i
$349$	−33.0517			−1.76922			−0.884608	−	0.466335i	$-0.845574\pi$
$349$	−33.0517			−1.76922			−0.884608	+	0.466335i	$0.845574\pi$
$350$		0			0
$351$	1.76022	−	4.05422i	0.0939535	−	0.216398i
$352$	−18.6540	−	1.11224i	−0.994259	−	0.0592825i
$353$	−13.5161	+	7.80351i	−0.719388	+	0.415339i	−0.814528	−	0.580125i	$-0.803004\pi$
$353$	−13.5161	+	7.80351i	−0.719388	+	0.415339i	0.0951392	+	0.995464i	$0.469670\pi$
$354$	−18.6858	−	4.83436i	−0.993138	−	0.256944i
$355$	31.5037	+	18.1887i	1.67204	+	0.965354i
$356$	8.37028	+	7.90567i	0.443624	+	0.419000i
$357$		0			0
$358$	−25.1681	+	10.8483i	−1.33018	+	0.573348i
$359$	−16.8237	+	29.1394i	−0.887919	+	1.53792i	−0.0455885	+	0.998960i	$0.514516\pi$
$359$	−16.8237	+	29.1394i	−0.887919	+	1.53792i	−0.842331	+	0.538961i	$0.818817\pi$
$360$	27.3781	+	19.6683i	1.44295	+	1.03661i
$361$	−3.05096	−	5.28443i	−0.160577	−	0.278128i
$362$	−1.78942	+	15.2730i	−0.0940499	+	0.802732i
$363$	−0.139981	+	0.0570595i	−0.00734708	+	0.00299485i
$364$		0			0
$365$			5.61842i			0.294082i
$366$	−6.37772	−	23.0058i	−0.333369	−	1.20253i
$367$	6.79444	−	3.92277i	0.354667	−	0.204767i	−0.312072	−	0.950059i	$-0.601023\pi$
$367$	6.79444	−	3.92277i	0.354667	−	0.204767i	0.666739	+	0.745291i	$0.267690\pi$
$368$	13.2494	−	8.69339i	0.690674	−	0.453174i
$369$	−15.5650	+	3.98308i	−0.810279	+	0.207351i
$370$	−9.54109	−	22.1355i	−0.496018	−	1.15077i
$371$		0			0
$372$	15.8234	+	6.13363i	0.820403	+	0.318014i
$373$	−0.493136	+	0.854137i	−0.0255336	+	0.0442256i	−0.878510	−	0.477724i	$-0.841462\pi$
$373$	−0.493136	+	0.854137i	−0.0255336	+	0.0442256i	0.852976	+	0.521950i	$0.174795\pi$
$374$	1.60882	−	2.15978i	0.0831900	−	0.111679i
$375$	−24.4038	+	31.4352i	−1.26021	+	1.62331i
$376$	−16.5110	−	19.7100i	−0.851488	−	1.01647i
$377$			2.87443i			0.148040i
$378$		0			0
$379$			18.8285i			0.967153i	0.875302	+	0.483576i	$0.160663\pi$
$379$			18.8285i			0.967153i	−0.875302	+	0.483576i	$0.839337\pi$
$380$	−8.16914	−	27.3416i	−0.419068	−	1.40260i
$381$	17.4643	−	22.4961i	0.894721	−	1.15251i
$382$	−1.39853	−	1.04177i	−0.0715552	−	0.0533015i
$383$	−1.81144	+	3.13750i	−0.0925602	+	0.160319i	−0.908588	−	0.417694i	$-0.862838\pi$
$383$	−1.81144	+	3.13750i	−0.0925602	+	0.160319i	0.816028	+	0.578013i	$0.196172\pi$
$384$	19.5090	−	1.84411i	0.995562	−	0.0941067i
$385$		0			0
$386$	−20.4979	+	8.83526i	−1.04332	+	0.449703i
$387$	22.2777	−	5.70087i	1.13244	−	0.289792i
$388$	−26.3636	−	6.26363i	−1.33841	−	0.317988i
$389$	−12.6579	+	7.30807i	−0.641783	+	0.370534i	−0.785301	−	0.619114i	$-0.787492\pi$
$389$	−12.6579	+	7.30807i	−0.641783	+	0.370534i	0.143518	+	0.989648i	$0.454159\pi$
$390$	7.97669	−	2.21132i	0.403916	−	0.111974i
$391$			2.28380i			0.115497i
$392$		0			0
$393$	−3.65197	+	1.48863i	−0.184217	+	0.0750914i
$394$	24.4216	+	2.86129i	1.23034	+	0.144150i
$395$	13.7623	+	23.8370i	0.692455	+	1.19937i
$396$	−16.9916	+	10.2052i	−0.853858	+	0.512829i
$397$	−3.04852	+	5.28019i	−0.153001	+	0.265005i	−0.932329	−	0.361610i	$-0.882227\pi$
$397$	−3.04852	+	5.28019i	−0.153001	+	0.265005i	0.779328	+	0.626616i	$0.215560\pi$
$398$	2.55687	+	5.93197i	0.128164	+	0.297343i
$399$		0			0
$400$	2.46056	+	43.0631i	0.123028	+	2.15316i
$401$	−6.31340	−	3.64505i	−0.315276	−	0.182025i	0.334009	−	0.942570i	$-0.391598\pi$
$401$	−6.31340	−	3.64505i	−0.315276	−	0.182025i	−0.649285	+	0.760545i	$0.724932\pi$
$402$	5.54982	−	21.4512i	0.276800	−	1.06989i
$403$	3.60879	−	2.08354i	0.179767	−	0.103788i
$404$	13.6813	−	4.08770i	0.680669	−	0.203371i
$405$	35.7463	+	0.806210i	1.77625	+	0.0400609i
$406$		0			0
$407$	14.1724			0.702502
$408$	−1.32019	+	2.49653i	−0.0653591	+	0.123597i
$409$	−10.0950	−	17.4850i	−0.499165	−	0.864580i	0.500834	−	0.865543i	$-0.333027\pi$
$409$	−10.0950	−	17.4850i	−0.499165	−	0.864580i	−1.00000		0.000963491i	$0.999693\pi$
$410$	−24.1305	−	17.9748i	−1.19172	−	0.887714i
$411$	15.7940	+	2.16997i	0.779060	+	0.107037i
$412$	−15.2797	−	14.4316i	−0.752778	−	0.710993i
$413$		0			0
$414$	6.38566	−	15.5479i	0.313838	−	0.764135i
$415$	14.2397	+	8.22130i	0.699000	+	0.403568i
$416$	2.64962	−	4.01649i	0.129908	−	0.196925i
$417$	−11.7956	+	15.1942i	−0.577633	+	0.744063i
$418$	16.6642	+	1.95241i	0.815071	+	0.0954956i
$419$	−1.32886			−0.0649189			−0.0324594	−	0.999473i	$-0.510334\pi$
$419$	−1.32886			−0.0649189			−0.0324594	+	0.999473i	$0.510334\pi$
$420$		0			0
$421$	−7.31859			−0.356686			−0.178343	−	0.983968i	$-0.557074\pi$
$421$	−7.31859			−0.356686			−0.178343	+	0.983968i	$0.557074\pi$
$422$	−1.56226	−	0.183038i	−0.0760494	−	0.00891013i
$423$	−26.2610	−	7.35493i	−1.27685	−	0.357609i
$424$	−0.297533	−	1.69558i	−0.0144495	−	0.0823448i
$425$	−5.38343	−	3.10812i	−0.261135	−	0.150766i
$426$	15.7221	−	15.9959i	0.761739	−	0.775004i
$427$		0			0
$428$	−1.69343	+	1.79295i	−0.0818549	+	0.0866655i
$429$	−0.662451	+	4.82161i	−0.0319834	+	0.232790i
$430$	34.5373	+	25.7269i	1.66554	+	1.24066i
$431$	−0.0894647	−	0.154957i	−0.00430936	−	0.00746403i	0.863863	−	0.503727i	$-0.168038\pi$
$431$	−0.0894647	−	0.154957i	−0.00430936	−	0.00746403i	−0.868172	+	0.496263i	$0.834705\pi$
$432$	15.9682	−	13.3048i	0.768270	−	0.640126i
$433$	−15.2499			−0.732866			−0.366433	−	0.930444i	$-0.619421\pi$
$433$	−15.2499			−0.732866			−0.366433	+	0.930444i	$0.619421\pi$
$434$		0			0
$435$	−21.5331	+	8.77742i	−1.03243	+	0.420845i
$436$	−1.83384	−	6.13776i	−0.0878251	−	0.293945i
$437$	−12.3218	+	7.11402i	−0.589434	+	0.340310i
$438$	3.35368	+	0.867660i	0.160245	+	0.0414584i
$439$	−25.8988	−	14.9527i	−1.23608	−	0.713654i	−0.267793	−	0.963476i	$-0.586294\pi$
$439$	−25.8988	−	14.9527i	−1.23608	−	0.713654i	−0.968292	+	0.249823i	$0.919628\pi$
$440$	−34.8711	−	12.7247i	−1.66242	−	0.606626i
$441$		0			0
$442$	0.274487	+	0.636813i	0.0130560	+	0.0302901i
$443$	−2.50795	+	4.34390i	−0.119156	+	0.206385i	−0.919434	−	0.393245i	$-0.871352\pi$
$443$	−2.50795	+	4.34390i	−0.119156	+	0.206385i	0.800277	+	0.599630i	$0.204686\pi$
$444$	−14.6863	+	2.27674i	−0.696980	+	0.108049i
$445$	11.4353	+	19.8065i	0.542086	+	0.938920i
$446$	−33.1948	−	3.88918i	−1.57182	−	0.184158i
$447$	−4.39181	−	10.7742i	−0.207725	−	0.509601i
$448$		0			0
$449$			14.4978i			0.684195i	0.939664	+	0.342098i	$0.111137\pi$
$449$			14.4978i			0.684195i	−0.939664	+	0.342098i	$0.888863\pi$
$450$	27.9593	+	36.2122i	1.31801	+	1.70706i
$451$	15.3214	−	8.84580i	0.721455	−	0.416532i
$452$	−9.20430	+	38.7409i	−0.432934	+	1.82222i
$453$	22.6723	+	3.11499i	1.06524	+	0.146355i
$454$	15.9719	−	6.88441i	0.749600	−	0.323101i
$455$		0			0
$456$	−17.5820	+	0.653820i	−0.823352	+	0.0306179i
$457$	9.92844	−	17.1966i	0.464433	−	0.804422i	−0.534743	−	0.845015i	$-0.679591\pi$
$457$	9.92844	−	17.1966i	0.464433	−	0.804422i	0.999176	+	0.0405933i	$0.0129248\pi$
$458$	−10.2407	−	7.62831i	−0.478517	−	0.356447i
$459$	0.340700	+	2.97598i	0.0159025	+	0.138907i
$460$	30.1609	−	9.01149i	1.40626	−	0.420163i
$461$			17.3910i			0.809978i	0.914322	+	0.404989i	$0.132725\pi$
$461$			17.3910i			0.809978i	−0.914322	+	0.404989i	$0.867275\pi$
$462$		0			0
$463$			15.3304i			0.712462i	0.934398	+	0.356231i	$0.115938\pi$
$463$			15.3304i			0.712462i	−0.934398	+	0.356231i	$0.884062\pi$
$464$	−6.07979	+	12.0727i	−0.282247	+	0.560460i
$465$	26.6283	+	20.6721i	1.23486	+	0.958647i
$466$	6.39853	−	8.58978i	0.296406	−	0.397914i
$467$	10.5410	−	18.2575i	0.487778	−	0.844857i	−0.512123	−	0.858912i	$-0.671141\pi$
$467$	10.5410	−	18.2575i	0.487778	−	0.844857i	0.999901	+	0.0140554i	$0.00447412\pi$
$468$	−0.0881005	−	5.10284i	−0.00407245	−	0.235879i
$469$		0			0
$470$	−20.2166	−	46.9028i	−0.932521	−	2.16346i
$471$	−0.563040	+	4.09805i	−0.0259435	+	0.188828i
$472$	−21.9515	+	3.85195i	−1.01040	+	0.177300i
$473$	−21.9290	+	12.6607i	−1.00830	+	0.582141i
$474$	16.3538	−	4.53363i	0.751154	−	0.208237i
$475$		−	38.7272i		−	1.77692i
$476$		0			0
$477$	−1.27648	−	1.30559i	−0.0584459	−	0.0597790i
$478$	1.52258	−	12.9955i	0.0696413	−	0.594400i
$479$	3.79982	+	6.58149i	0.173618	+	0.300716i	0.939682	−	0.342049i	$-0.111121\pi$
$479$	3.79982	+	6.58149i	0.173618	+	0.300716i	−0.766064	+	0.642764i	$0.777787\pi$
$480$	38.1796	+	7.58415i	1.74265	+	0.346167i
$481$	−1.82463	+	3.16034i	−0.0831958	+	0.144099i
$482$	20.3382	−	8.76642i	0.926381	−	0.399299i
$483$		0			0
$484$	−0.119852	+	0.126896i	−0.00544784	+	0.00576800i
$485$	−46.6154	−	26.9134i	−2.11670	−	1.22207i
$486$	6.00159	−	21.2128i	0.272237	−	0.962230i
$487$	−13.3691	+	7.71865i	−0.605811	+	0.349765i	−0.771324	−	0.636442i	$-0.780405\pi$
$487$	−13.3691	+	7.71865i	−0.605811	+	0.349765i	0.165513	+	0.986208i	$0.447072\pi$
$488$	−17.7021	−	21.1319i	−0.801335	−	0.956598i
$489$	−11.9591	−	29.3386i	−0.540809	−	1.32674i
$490$		0			0
$491$	−40.5166			−1.82849			−0.914243	−	0.405165i	$-0.867214\pi$
$491$	−40.5166			−1.82849			−0.914243	+	0.405165i	$0.867214\pi$
$492$	−14.4558	+	11.6278i	−0.651719	+	0.524222i
$493$	−0.974025	−	1.68706i	−0.0438679	−	0.0759814i
$494$	−2.58079	+	3.46462i	−0.116115	+	0.155880i
$495$	−38.1429	+	9.76079i	−1.71440	+	0.438715i
$496$	19.5640	−	1.11786i	0.878450	−	0.0501932i
$497$		0			0
$498$	7.10641	−	7.23016i	0.318446	−	0.323991i
$499$	−26.2986	−	15.1835i	−1.17729	−	0.679707i	−0.221902	−	0.975069i	$-0.571226\pi$
$499$	−26.2986	−	15.1835i	−1.17729	−	0.679707i	−0.955385	+	0.295362i	$0.904560\pi$
$500$	−10.6220	+	44.7079i	−0.475029	+	1.99940i
$501$	26.4944	+	20.5682i	1.18368	+	0.918921i
$502$	−0.508491	+	4.34005i	−0.0226950	+	0.193706i
$503$	−13.8974			−0.619652			−0.309826	−	0.950793i	$-0.600271\pi$
$503$	−13.8974			−0.619652			−0.309826	+	0.950793i	$0.600271\pi$
$504$		0			0
$505$	28.3638			1.26217
$506$	−2.15373	+	18.3825i	−0.0957451	+	0.817200i
$507$	16.7962	+	13.0393i	0.745946	+	0.579095i
$508$	7.60147	−	31.9946i	0.337260	−	1.41953i
$509$	25.6830	+	14.8281i	1.13838	+	0.657243i	0.946029	−	0.324083i	$-0.105056\pi$
$509$	25.6830	+	14.8281i	1.13838	+	0.657243i	0.192350	+	0.981326i	$0.438389\pi$
$510$	−3.93237	+	4.00084i	−0.174128	+	0.177160i
$511$		0			0
$512$	19.6239	−	11.2651i	0.867262	−	0.497853i
$513$	−14.9951	+	11.1083i	−0.662049	+	0.490445i
$514$	6.22565	−	8.35769i	0.274602	−	0.368642i
$515$	−20.8748	−	36.1563i	−0.919855	−	1.59324i
$516$	20.6902	−	16.6426i	0.910836	−	0.732648i
$517$	30.0299			1.32071
$518$		0			0
$519$	−3.65161	−	8.95827i	−0.160288	−	0.393225i
$520$	7.32698	−	6.13776i	0.321309	−	0.269159i
$521$	29.0727	−	16.7851i	1.27370	−	0.735369i	0.298015	−	0.954561i	$-0.403675\pi$
$521$	29.0727	−	16.7851i	1.27370	−	0.735369i	0.975682	+	0.219192i	$0.0703421\pi$
$522$	1.91392	+	14.2088i	0.0837700	+	0.621902i
$523$	8.82946	+	5.09769i	0.386085	+	0.222906i	0.680463	−	0.732783i	$-0.261779\pi$
$523$	8.82946	+	5.09769i	0.386085	+	0.222906i	−0.294377	+	0.955689i	$0.595112\pi$
$524$	−3.12684	+	3.31060i	−0.136596	+	0.144624i
$525$		0			0
$526$	28.8358	−	12.4291i	1.25730	−	0.541937i
$527$	−1.41205	+	2.44575i	−0.0615099	+	0.106538i
$528$	−12.9807	+	18.8498i	−0.564911	+	0.820330i
$529$	3.65243	+	6.32620i	0.158801	+	0.275052i
$530$	0.397925	−	3.39636i	0.0172848	−	0.147528i
$531$	−16.9026	+	16.5256i	−0.733509	+	0.717152i
$532$		0			0
$533$			4.55539i			0.197316i
$534$	13.5886	−	3.76707i	0.588038	−	0.163017i
$535$	−4.24264	+	2.44949i	−0.183425	+	0.105901i
$536$	−4.42201	−	25.2002i	−0.191002	−	1.08848i
$537$	−4.56879	+	33.2537i	−0.197158	+	1.43500i
$538$	5.60560	+	13.0051i	0.241675	+	0.560689i
$539$		0			0
$540$	37.9578	−	16.2422i	1.63344	−	0.698951i
$541$	−5.15243	+	8.92427i	−0.221520	+	0.383684i	−0.955270	−	0.295736i	$-0.904435\pi$
$541$	−5.15243	+	8.92427i	−0.221520	+	0.383684i	0.733750	+	0.679420i	$0.237769\pi$
$542$	−19.9249	+	26.7484i	−0.855848	+	1.14894i
$543$	14.8767	+	11.5492i	0.638422	+	0.495622i
$544$	−0.194091	+	3.25521i	−0.00832160	+	0.139566i
$545$		−	12.7247i		−	0.545066i
$546$		0			0
$547$		−	5.44070i		−	0.232628i	−0.993213	−	0.116314i	$-0.962892\pi$
$547$		−	5.44070i		−	0.232628i	0.993213	−	0.116314i	$-0.0371078\pi$
$548$	17.6382	−	5.26995i	0.753466	−	0.225121i
$549$	−28.1555	−	7.88552i	−1.20165	−	0.336546i
$550$	−40.4005	−	30.0944i	−1.72268	−	1.28323i
$551$	6.06817	−	10.5104i	0.258513	−	0.447757i
$552$	−0.721238	−	19.3949i	−0.0306979	−	0.825503i
$553$		0			0
$554$	−37.7402	+	16.2672i	−1.60343	+	0.691128i
$555$	−29.2467	−	4.01827i	−1.24145	−	0.170566i
$556$	−5.13413	+	21.6096i	−0.217736	+	0.916450i
$557$	3.84264	−	2.21855i	0.162818	−	0.0940030i	−0.416377	−	0.909192i	$-0.636700\pi$
$557$	3.84264	−	2.21855i	0.162818	−	0.0940030i	0.579195	+	0.815189i	$0.303367\pi$
$558$	16.4516	−	12.7022i	0.696451	−	0.537726i
$559$		−	6.52001i		−	0.275767i
$560$		0			0
$561$	−1.24504	−	3.05438i	−0.0525657	−	0.128956i
$562$	−32.7118	−	3.83259i	−1.37986	−	0.161668i
$563$	−19.5639	−	33.8857i	−0.824522	−	1.42811i	−0.902284	−	0.431141i	$-0.858111\pi$
$563$	−19.5639	−	33.8857i	−0.824522	−	1.42811i	0.0777627	−	0.996972i	$-0.475222\pi$
$564$	−31.1187	+	4.82417i	−1.31033	+	0.203134i
$565$	−39.5488	+	68.5005i	−1.66383	+	2.88184i
$566$	−9.75493	−	22.6316i	−0.410030	−	0.951277i
$567$		0			0
$568$	8.87794	−	24.3294i	0.372510	−	1.02084i
$569$	−38.4653	−	22.2079i	−1.61255	−	0.931005i	−0.988777	−	0.149398i	$-0.952266\pi$
$569$	−38.4653	−	22.2079i	−1.61255	−	0.931005i	−0.623771	−	0.781607i	$-0.714400\pi$
$570$	−33.8352	−	8.75380i	−1.41720	−	0.366656i
$571$	−2.15883	+	1.24640i	−0.0903442	+	0.0521603i	−0.544491	−	0.838766i	$-0.683277\pi$
$571$	−2.15883	+	1.24640i	−0.0903442	+	0.0521603i	0.454147	+	0.890927i	$0.349944\pi$
$572$	1.60882	+	5.38461i	0.0672680	+	0.225142i
$573$	−1.97783	+	0.806210i	−0.0826249	+	0.0336799i
$574$		0			0
$575$	42.7205			1.78157
$576$	10.4232	−	21.6185i	0.434298	−	0.900769i
$577$	−18.2933	−	31.6849i	−0.761560	−	1.31906i	−0.942046	−	0.335482i	$-0.891101\pi$
$577$	−18.2933	−	31.6849i	−0.761560	−	1.31906i	0.180487	−	0.983577i	$-0.442233\pi$
$578$	18.9035	+	14.0812i	0.786282	+	0.585702i
$579$	−3.72100	+	27.0831i	−0.154640	+	1.12554i
$580$	−18.4368	+	19.5203i	−0.765546	+	0.810536i
$581$		0			0
$582$	−23.2637	+	23.6688i	−0.964311	+	0.981103i
$583$	1.74123	+	1.00530i	0.0721145	+	0.0416353i
$584$	3.93980	−	0.691339i	0.163030	−	0.0286078i
$585$	2.73411	−	9.76222i	0.113042	−	0.403618i
$586$	−1.69602	−	0.198710i	−0.0700619	−	0.00820862i
$587$	−36.8412			−1.52060			−0.760299	−	0.649573i	$-0.774948\pi$
$587$	−36.8412			−1.52060			−0.760299	+	0.649573i	$0.774948\pi$
$588$		0			0
$589$	−17.5941			−0.724954
$590$	−43.9702	−	5.15165i	−1.81022	−	0.212090i
$591$	18.4671	−	23.7879i	0.759636	−	0.978505i
$592$	−14.3480	+	9.41423i	−0.589701	+	0.386922i
$593$	−14.9125	−	8.60972i	−0.612382	−	0.353559i	0.161515	−	0.986870i	$-0.448362\pi$
$593$	−14.9125	−	8.60972i	−0.612382	−	0.353559i	−0.773897	+	0.633311i	$0.781695\pi$
$594$	−0.0641660	+	24.2752i	−0.00263276	+	0.996022i
$595$		0			0
$596$	−9.76705	−	9.22491i	−0.400074	−	0.377867i
$597$	7.83768	+	1.07683i	0.320775	+	0.0440719i
$598$	−3.82187	−	2.84691i	−0.156288	−	0.116419i
$599$	9.51076	+	16.4731i	0.388599	+	0.673073i	0.992261	−	0.124167i	$-0.0396258\pi$
$599$	9.51076	+	16.4731i	0.388599	+	0.673073i	−0.603662	+	0.797240i	$0.706292\pi$
$600$	46.6998	+	24.6953i	1.90651	+	1.00818i
$601$	7.95144			0.324346			0.162173	−	0.986762i	$-0.448150\pi$
$601$	7.95144			0.324346			0.162173	+	0.986762i	$0.448150\pi$
$602$		0			0
$603$	−18.9713	−	19.4040i	−0.772573	−	0.790194i
$604$	25.3197	−	7.56502i	1.03024	−	0.307816i
$605$	−0.300273	+	0.173363i	−0.0122078	+	0.00704820i
$606$	4.38025	−	16.9305i	0.177936	−	0.687756i
$607$	−20.5976	−	11.8920i	−0.836030	−	0.482682i	0.0198827	−	0.999802i	$-0.493671\pi$
$607$	−20.5976	−	11.8920i	−0.836030	−	0.482682i	−0.855913	+	0.517120i	$0.827004\pi$
$608$	−18.1675	+	9.09279i	−0.736791	+	0.368761i
$609$		0			0
$610$	−21.6750	−	50.2864i	−0.877596	−	2.03604i
$611$	−3.86619	+	6.69644i	−0.156409	+	0.270909i
$612$	1.78085	+	2.96511i	0.0719867	+	0.119858i
$613$	14.8779	+	25.7694i	0.600914	+	1.04081i	0.992683	+	0.120751i	$0.0385301\pi$
$613$	14.8779	+	25.7694i	0.600914	+	1.04081i	−0.391768	+	0.920064i	$0.628137\pi$
$614$	47.7952	+	5.59980i	1.92886	+	0.225990i
$615$	−34.1257	+	13.9105i	−1.37608	+	0.560924i
$616$		0			0
$617$			28.7008i			1.15545i	0.816232	+	0.577724i	$0.196059\pi$
$617$			28.7008i			1.15545i	−0.816232	+	0.577724i	$0.803941\pi$
$618$	−24.8057	+	6.87669i	−0.997831	+	0.276621i
$619$	−19.9082	+	11.4940i	−0.800177	+	0.461983i	−0.843533	−	0.537077i	$-0.819528\pi$
$619$	−19.9082	+	11.4940i	−0.800177	+	0.461983i	0.0433558	+	0.999060i	$0.486195\pi$
$620$	37.8714	+	8.99771i	1.52095	+	0.361357i
$621$	−12.2538	−	16.5413i	−0.491726	−	0.663779i
$622$	−34.6905	+	14.9527i	−1.39096	+	0.599549i
$623$		0			0
$624$	−2.53216	−	5.32139i	−0.101368	−	0.213026i
$625$	−18.6819	+	32.3580i	−0.747275	+	1.29432i
$626$	−10.5765	−	7.87840i	−0.422720	−	0.314884i
$627$	12.6011	−	16.2318i	0.503240	−	0.648236i
$628$	1.36739	+	4.57657i	0.0545648	+	0.182625i
$629$		−	2.47316i		−	0.0986115i
$630$		0			0
$631$			15.3304i			0.610292i	0.952306	+	0.305146i	$0.0987052\pi$
$631$			15.3304i			0.610292i	−0.952306	+	0.305146i	$0.901295\pi$
$632$	15.0217	−	12.5836i	0.597533	−	0.500549i
$633$	−1.18135	+	1.52172i	−0.0469543	+	0.0604830i
$634$	22.8044	−	30.6140i	0.905678	−	1.21584i
$635$	32.6618	−	56.5719i	1.29614	−	2.24499i
$636$	−1.96586	−	0.762028i	−0.0779514	−	0.0302164i
$637$		0			0
$638$	−6.24902	−	14.4978i	−0.247401	−	0.573975i
$639$	−6.81005	−	26.6121i	−0.269401	−	1.05276i
$640$	43.7557	−	10.2813i	1.72960	−	0.406403i
$641$	11.6038	−	6.69943i	0.458321	−	0.264612i	−0.253017	−	0.967462i	$-0.581423\pi$
$641$	11.6038	−	6.69943i	0.458321	−	0.264612i	0.711338	+	0.702850i	$0.248090\pi$
$642$	0.806922	+	2.91074i	0.0318467	+	0.114878i
$643$			2.68122i			0.105737i	0.998601	+	0.0528684i	$0.0168364\pi$
$643$			2.68122i			0.105737i	−0.998601	+	0.0528684i	$0.983164\pi$
$644$		0			0
$645$	48.8432	−	19.9097i	1.92320	−	0.783942i
$646$	0.340706	−	2.90798i	0.0134049	−	0.114413i
$647$	9.86799	+	17.0919i	0.387951	+	0.671950i	0.992174	−	0.124865i	$-0.0398497\pi$
$647$	9.86799	+	17.0919i	0.387951	+	0.671950i	−0.604223	+	0.796815i	$0.706516\pi$
$648$	−3.83320	−	25.1656i	−0.150582	−	0.988597i
$649$	13.0149	−	22.5425i	0.510880	−	0.884870i
$650$	11.9122	−	5.13452i	0.467233	−	0.201392i
$651$		0			0
$652$	−26.5961	−	25.1198i	−1.04158	−	0.983769i
$653$	30.5038	+	17.6114i	1.19371	+	0.689186i	0.959145	−	0.282915i	$-0.0913015\pi$
$653$	30.5038	+	17.6114i	1.19371	+	0.689186i	0.234561	+	0.972101i	$0.424635\pi$
$654$	−7.59546	−	1.96509i	−0.297006	−	0.0768411i
$655$	−7.83384	+	4.52287i	−0.306094	+	0.176723i
$656$	−9.63526	+	19.1328i	−0.376194	+	0.747011i
$657$	3.03363	−	2.96599i	0.118353	−	0.115714i
$658$		0			0
$659$	39.7628			1.54894			0.774469	−	0.632612i	$-0.218017\pi$
$659$	39.7628			1.54894			0.774469	+	0.632612i	$0.218017\pi$
$660$	−35.4249	+	28.4947i	−1.37891	+	1.10915i
$661$	7.46659	+	12.9325i	0.290417	+	0.503017i	0.973908	−	0.226942i	$-0.0728727\pi$
$661$	7.46659	+	12.9325i	0.290417	+	0.503017i	−0.683492	+	0.729958i	$0.739539\pi$
$662$	−12.3288	+	16.5510i	−0.479173	+	0.643271i
$663$	0.841396	+	0.115601i	0.0326771	+	0.00448957i
$664$	4.01284	−	10.9969i	0.155728	−	0.426763i
$665$		0			0
$666$	−6.91515	+	16.8371i	−0.267956	+	0.652422i
$667$	11.5941	+	6.69388i	0.448927	+	0.259188i
$668$	37.6811	+	8.95249i	1.45792	+	0.346382i
$669$	−25.1012	+	32.3335i	−0.970470	+	1.25009i
$670$	5.91407	−	50.4775i	0.228480	−	1.95012i
$671$	32.1963			1.24292
$672$		0			0
$673$	1.52059			0.0586145			0.0293072	−	0.999570i	$-0.490670\pi$
$673$	1.52059			0.0586145			0.0293072	+	0.999570i	$0.490670\pi$
$674$	5.21386	−	44.5012i	0.200831	−	1.71412i
$675$	55.6683	−	6.37310i	2.14267	−	0.245301i
$676$	23.8880	+	5.67546i	0.918770	+	0.218287i
$677$	−14.2074	−	8.20266i	−0.546036	−	0.315254i	0.201486	−	0.979491i	$-0.435423\pi$
$677$	−14.2074	−	8.20266i	−0.546036	−	0.315254i	−0.747522	+	0.664238i	$0.768756\pi$
$678$	34.7809	+	34.1856i	1.33575	+	1.31289i
$679$		0			0
$680$	−2.22052	+	6.08520i	−0.0851532	+	0.233357i
$681$	2.89940	−	21.1031i	0.111105	−	0.808672i
$682$	−13.6722	+	18.3544i	−0.523534	+	0.702825i
$683$	−4.57827	−	7.92980i	−0.175183	−	0.303425i	0.765042	−	0.643981i	$-0.222718\pi$
$683$	−4.57827	−	7.92980i	−0.175183	−	0.303425i	−0.940224	+	0.340555i	$0.889385\pi$
$684$	−10.4504	+	18.8446i	−0.399582	+	0.720542i
$685$	36.5672			1.39716
$686$		0			0
$687$	−14.4825	+	5.90343i	−0.552543	+	0.225230i
$688$	13.7907	−	27.3842i	0.525764	−	1.04401i
$689$	−0.448349	+	0.258854i	−0.0170807	+	0.00986156i
$690$	9.65644	−	37.3240i	0.367614	−	1.42090i
$691$	−28.7221	−	16.5827i	−1.09264	−	0.630836i	−0.158362	−	0.987381i	$-0.550621\pi$
$691$	−28.7221	−	16.5827i	−1.09264	−	0.630836i	−0.934278	+	0.356545i	$0.883955\pi$
$692$	−8.12090	−	7.67013i	−0.308710	−	0.291575i
$693$		0			0
$694$	2.79707	−	1.20562i	0.106175	−	0.0457649i
$695$	−22.0602	+	38.2094i	−0.836791	+	1.44937i
$696$	8.80460	+	14.0196i	0.333737	+	0.531412i
$697$	−1.54364	−	2.67366i	−0.0584694	−	0.101272i
$698$	−5.43922	+	46.4246i	−0.205877	+	1.75720i
$699$	−4.95173	−	12.1478i	−0.187292	−	0.459472i
$700$		0			0
$701$		−	38.1529i		−	1.44101i	−0.693448	−	0.720507i	$-0.743909\pi$
$701$		−	38.1529i		−	1.44101i	0.693448	−	0.720507i	$-0.256091\pi$
$702$	−5.40491	−	3.13960i	−0.203995	−	0.118497i
$703$	13.3435	−	7.70390i	0.503261	−	0.290558i
$704$	−4.63208	+	26.0184i	−0.174578	+	0.980606i
$705$	−61.9708	−	8.51429i	−2.33396	−	0.320667i
$706$	8.73656	+	20.2690i	0.328805	+	0.762833i
$707$		0			0
$708$	−9.86544	+	25.4506i	−0.370766	+	0.956491i
$709$	−6.97895	+	12.0879i	−0.262100	+	0.453970i	−0.966800	−	0.255535i	$-0.917748\pi$
$709$	−6.97895	+	12.0879i	−0.262100	+	0.453970i	0.704700	+	0.709505i	$0.251082\pi$
$710$	30.7324	−	41.2570i	1.15337	−	1.54835i
$711$	5.60547	−	20.0145i	0.210221	−	0.750601i
$712$	12.4818	−	10.4559i	0.467776	−	0.391853i
$713$		−	19.4083i		−	0.726848i
$714$		0			0
$715$			11.1633i			0.417483i
$716$	11.0957	+	37.1366i	0.414665	+	1.38786i
$717$	−12.6583	−	9.82694i	−0.472733	−	0.366994i
$718$	38.1608	+	28.4260i	1.42415	+	1.06085i
$719$	−10.0890	+	17.4746i	−0.376255	+	0.651693i	−0.990514	−	0.137412i	$-0.956122\pi$
$719$	−10.0890	+	17.4746i	−0.376255	+	0.651693i	0.614259	+	0.789105i	$0.289455\pi$
$720$	32.1317	−	35.2186i	1.19748	−	1.31252i
$721$		0			0
$722$	−7.92462	+	3.41576i	−0.294924	+	0.127121i
$723$	3.69201	−	26.8721i	0.137307	−	0.999384i
$724$	21.1581	+	5.02686i	0.786334	+	0.186822i
$725$	−31.5580	+	18.2200i	−1.17203	+	0.676674i
$726$	0.0571100	+	0.206008i	0.00211955	+	0.00764567i
$727$			1.62103i			0.0601206i	0.999548	+	0.0300603i	$0.00956993\pi$
$727$			1.62103i			0.0601206i	−0.999548	+	0.0300603i	$0.990430\pi$
$728$		0			0
$729$	−18.4353	−	19.7266i	−0.682789	−	0.730615i
$730$	7.89167	+	0.924607i	0.292084	+	0.0342212i
$731$	2.20936	+	3.82673i	0.0817163	+	0.141537i
$732$	−33.3636	+	5.17219i	−1.23316	+	0.191169i
$733$	13.9026	−	24.0801i	0.513505	−	0.889417i	−0.486372	−	0.873752i	$-0.661680\pi$
$733$	13.9026	−	24.0801i	0.513505	−	0.889417i	0.999877	−	0.0156654i	$-0.00498666\pi$
$734$	−4.39181	−	10.1891i	−0.162105	−	0.376086i
$735$		0			0
$736$	−10.0304	−	20.0409i	−0.369725	−	0.738716i
$737$	25.8786	+	14.9410i	0.953252	+	0.550360i
$738$	3.03318	+	22.5181i	0.111653	+	0.828903i
$739$	−25.1030	+	14.4932i	−0.923429	+	0.533142i	−0.884727	−	0.466109i	$-0.845655\pi$
$739$	−25.1030	+	14.4932i	−0.923429	+	0.533142i	−0.0387013	+	0.999251i	$0.512322\pi$
$740$	−32.6618	+	9.75870i	−1.20067	+	0.358737i
$741$	1.99724	+	4.89971i	0.0733704	+	0.179995i
$742$		0			0
$743$	−10.4018			−0.381604			−0.190802	−	0.981629i	$-0.561109\pi$
$743$	−10.4018			−0.381604			−0.190802	+	0.981629i	$0.561109\pi$
$744$	11.2193	−	21.2162i	0.411321	−	0.777823i
$745$	−13.3435	−	23.1117i	−0.488870	−	0.846747i
$746$	1.11857	+	0.833225i	0.0409539	+	0.0305065i
$747$	−3.07815	−	12.0287i	−0.112624	−	0.440107i
$748$	−2.76888	−	2.61518i	−0.101240	−	0.0956205i
$749$		0			0
$750$	40.1380	+	39.4510i	1.46563	+	1.44055i
$751$	−14.7045	−	8.48962i	−0.536573	−	0.309791i	0.207116	−	0.978316i	$-0.433592\pi$
$751$	−14.7045	−	8.48962i	−0.536573	−	0.309791i	−0.743689	+	0.668526i	$0.766926\pi$
$752$	−30.4020	+	19.9478i	−1.10865	+	0.727420i
$753$	4.22745	+	3.28186i	0.154057	+	0.119598i
$754$	4.03743	+	0.473035i	0.147035	+	0.0172269i
$755$	52.4922			1.91039
$756$		0			0
$757$	−10.9716			−0.398770			−0.199385	−	0.979921i	$-0.563894\pi$
$757$	−10.9716			−0.398770			−0.199385	+	0.979921i	$0.563894\pi$
$758$	26.4466	+	3.09854i	0.960583	+	0.112544i
$759$	17.9055	+	13.9005i	0.649929	+	0.504555i
$760$	−39.7486	+	6.97490i	−1.44183	+	0.253006i
$761$	10.0723	+	5.81526i	0.365121	+	0.210803i	0.671325	−	0.741163i	$-0.265726\pi$
$761$	10.0723	+	5.81526i	0.365121	+	0.210803i	−0.306204	+	0.951966i	$0.599059\pi$
$762$	−28.7242	−	28.2325i	−1.04057	−	1.02276i
$763$		0			0
$764$	−1.69343	+	1.79295i	−0.0612660	+	0.0648666i
$765$	1.70331	+	6.65613i	0.0615833	+	0.240653i
$766$	4.10885	+	3.06069i	0.148459	+	0.110587i
$767$	3.35120	+	5.80445i	0.121005	+	0.209586i
$768$	0.620285	−	27.7059i	0.0223826	−	0.999749i
$769$	−0.123424			−0.00445080			−0.00222540	−	0.999998i	$-0.500708\pi$
$769$	−0.123424			−0.00445080			−0.00222540	+	0.999998i	$0.500708\pi$
$770$		0			0
$771$	−4.81794	−	11.8196i	−0.173514	−	0.425671i
$772$	9.03677	+	30.2455i	0.325241	+	1.08856i
$773$	13.4620	−	7.77229i	0.484194	−	0.279550i	−0.237968	−	0.971273i	$-0.576481\pi$
$773$	13.4620	−	7.77229i	0.484194	−	0.279550i	0.722163	+	0.691723i	$0.243148\pi$
$774$	−4.34131	−	32.2295i	−0.156045	−	1.15847i
$775$	45.7498	+	26.4137i	1.64338	+	0.948808i
$776$	−13.1365	+	35.9997i	−0.471573	+	1.29231i
$777$		0			0
$778$	8.18188	+	18.9821i	0.293334	+	0.680541i
$779$	9.61685	−	16.6569i	0.344559	−	0.596794i
$780$	−1.79333	−	11.5680i	−0.0642115	−	0.414201i
$781$	15.1240	+	26.1956i	0.541181	+	0.937353i
$782$	3.20783	+	0.375837i	0.114712	+	0.0134399i
$783$	16.1067	+	6.99304i	0.575607	+	0.249911i
$784$		0			0
$785$			9.48806i			0.338643i
$786$	1.48995	+	5.37455i	0.0531446	+	0.191704i
$787$	−36.3048	+	20.9606i	−1.29413	+	0.747164i	−0.979383	−	0.202014i	$-0.935252\pi$
$787$	−36.3048	+	20.9606i	−1.29413	+	0.747164i	−0.314743	+	0.949177i	$0.601918\pi$
$788$	8.03797	−	33.8318i	0.286341	−	1.20521i
$789$	5.23459	−	38.0996i	0.186356	−	1.35638i
$790$	35.7463	−	15.4078i	1.27180	−	0.548185i
$791$		0			0
$792$	11.5380	+	25.5459i	0.409984	+	0.907733i
$793$	−4.14510	+	7.17953i	−0.147197	+	0.254953i
$794$	6.91491	+	5.15092i	0.245401	+	0.182799i
$795$	−3.30824	−	2.56826i	−0.117331	−	0.0910868i
$796$	8.75286	−	2.61518i	0.310237	−	0.0926927i
$797$			20.7831i			0.736175i	0.929791	+	0.368088i	$0.119987\pi$
$797$			20.7831i			0.736175i	−0.929791	+	0.368088i	$0.880013\pi$
$798$		0			0
$799$		−	5.24038i		−	0.185391i
$800$	60.8917	+	3.63065i	2.15284	+	0.128363i
$801$	4.65768	−	16.6304i	0.164571	−	0.587605i
$802$	−6.15883	+	8.26799i	−0.217476	+	0.291953i
$803$	−2.33589	+	4.04587i	−0.0824316	+	0.142776i
$804$	−29.2171	−	11.3255i	−1.03041	−	0.399418i
$805$		0			0
$806$	−2.33266	−	5.41181i	−0.0821645	−	0.190623i
$807$	17.1831	+	2.36082i	0.604874	+	0.0831048i
$808$	−3.49012	−	19.8895i	−0.122782	−	0.699710i
$809$	1.65777	−	0.957115i	0.0582842	−	0.0336504i	−0.470575	−	0.882360i	$-0.655953\pi$
$809$	1.65777	−	0.957115i	0.0582842	−	0.0336504i	0.528859	+	0.848710i	$0.322620\pi$
$810$	7.01507	−	50.0768i	0.246484	−	1.75952i
$811$			4.68171i			0.164397i	0.996616	+	0.0821986i	$0.0261942\pi$
$811$			4.68171i			0.164397i	−0.996616	+	0.0821986i	$0.973806\pi$
$812$		0			0
$813$	15.4196	+	37.8280i	0.540789	+	1.32668i
$814$	2.33231	−	19.9067i	0.0817476	−	0.697729i
$815$	−36.3351	−	62.9342i	−1.27276	−	2.20449i
$816$	3.28938	+	2.26519i	0.115151	+	0.0792976i
$817$	−13.7643	+	23.8405i	−0.481552	+	0.834073i
$818$	−26.2209	+	11.3020i	−0.916792	+	0.395166i
$819$		0			0
$820$	−29.2186	+	30.9358i	−1.02036	+	1.08033i
$821$	1.44771	+	0.835834i	0.0505253	+	0.0291708i	0.525050	−	0.851071i	$-0.324047\pi$
$821$	1.44771	+	0.835834i	0.0505253	+	0.0291708i	−0.474525	+	0.880242i	$0.657380\pi$
$822$	5.64711	−	21.8272i	0.196966	−	0.761312i
$823$	−23.7559	+	13.7155i	−0.828078	+	0.478091i	−0.853194	−	0.521593i	$-0.825338\pi$
$823$	−23.7559	+	13.7155i	−0.828078	+	0.478091i	0.0251160	+	0.999685i	$0.492004\pi$
$824$	−22.7852	+	19.0870i	−0.793761	+	0.664928i
$825$	−57.1350	+	23.2896i	−1.98918	+	0.810840i
$826$		0			0
$827$	25.9621			0.902789			0.451395	−	0.892324i	$-0.350927\pi$
$827$	25.9621			0.902789			0.451395	+	0.892324i	$0.350927\pi$
$828$	−20.7877	−	11.5280i	−0.722424	−	0.400626i
$829$	14.5674	+	25.2315i	0.505948	+	0.876328i	0.999976	+	0.00688179i	$0.00219056\pi$
$829$	14.5674	+	25.2315i	0.505948	+	0.876328i	−0.494028	+	0.869446i	$0.664476\pi$
$830$	13.8911	−	18.6482i	0.482166	−	0.647289i
$831$	−6.85100	+	49.8646i	−0.237659	+	1.72979i
$832$	−5.20555	−	4.38265i	−0.180470	−	0.151941i
$833$		0			0
$834$	19.4007	+	19.0686i	0.671791	+	0.660293i
$835$	66.6265	+	38.4668i	2.30571	+	1.33120i
$836$	5.48474	−	23.0853i	0.189694	−	0.798421i
$837$	−2.89536	−	25.2906i	−0.100078	−	0.874173i
$838$	−0.218686	+	1.86652i	−0.00755437	+	0.0644778i
$839$	14.3863			0.496671			0.248336	−	0.968674i	$-0.420116\pi$
$839$	14.3863			0.496671			0.248336	+	0.968674i	$0.420116\pi$
$840$		0			0
$841$	17.5804			0.606221
$842$	−1.20440	+	10.2797i	−0.0415063	+	0.354263i
$843$	−24.7360	+	31.8631i	−0.851954	+	1.09742i
$844$	−0.514191	+	2.16423i	−0.0176992	+	0.0744959i
$845$	42.2381	+	24.3862i	1.45303	+	0.838909i
$846$	−14.6525	+	35.6760i	−0.503762	+	1.22656i
$847$		0			0
$848$	−2.43059	+	0.138880i	−0.0834668	+	0.00476916i
$849$	−29.9022	−	4.10833i	−1.02624	−	0.140997i
$850$	−5.25162	+	7.05010i	−0.180129	+	0.241816i
$851$	8.49827	+	14.7194i	0.291317	+	0.504576i
$852$	−19.8806	−	24.7158i	−0.681098	−	0.846748i
$853$	−49.4483			−1.69308			−0.846539	−	0.532327i	$-0.821318\pi$
$853$	−49.4483			−1.69308			−0.846539	+	0.532327i	$0.821318\pi$
$854$		0			0
$855$	−30.6062	+	29.9237i	−1.04671	+	1.02337i
$856$	2.23970	+	2.67366i	0.0765515	+	0.0913837i
$857$	10.0283	−	5.78983i	0.342560	−	0.197777i	−0.318844	−	0.947807i	$-0.603295\pi$
$857$	10.0283	−	5.78983i	0.342560	−	0.197777i	0.661403	+	0.750030i	$0.269961\pi$
$858$	6.66345	+	1.72396i	0.227486	+	0.0588550i
$859$	6.27765	+	3.62441i	0.214191	+	0.123663i	0.603258	−	0.797546i	$-0.293869\pi$
$859$	6.27765	+	3.62441i	0.214191	+	0.123663i	−0.389067	+	0.921210i	$0.627202\pi$
$860$	41.8198	−	44.2775i	1.42604	−	1.50985i
$861$		0			0
$862$	−0.232377	+	0.100162i	−0.00791479	+	0.00341152i
$863$	10.4435	−	18.0886i	0.355500	−	0.615744i	−0.631703	−	0.775210i	$-0.717644\pi$
$863$	10.4435	−	18.0886i	0.355500	−	0.615744i	0.987203	+	0.159466i	$0.0509773\pi$
$864$	−16.0601	−	24.6185i	−0.546377	−	0.837540i
$865$	−11.0946	−	19.2164i	−0.377228	−	0.653378i
$866$	−2.50964	+	21.4202i	−0.0852809	+	0.727887i
$867$	26.7336	−	10.8973i	0.907920	−	0.370090i
$868$		0			0
$869$			22.8869i			0.776385i
$870$	8.78517	+	31.6900i	0.297845	+	1.07439i
$871$	−6.66347	+	3.84716i	−0.225783	+	0.130356i
$872$	−8.92292	+	1.56575i	−0.302168	+	0.0530231i
$873$	10.0767	+	39.3774i	0.341044	+	1.33272i
$874$	7.96462	+	18.4781i	0.269407	+	0.625030i
$875$		0			0
$876$	1.77063	−	4.56781i	0.0598239	−	0.154332i
$877$	28.5877	−	49.5154i	0.965339	−	1.67202i	0.256639	−	0.966507i	$-0.417385\pi$
$877$	28.5877	−	49.5154i	0.965339	−	1.67202i	0.708701	−	0.705509i	$-0.249282\pi$
$878$	−25.2648	+	33.9170i	−0.852644	+	1.14464i
$879$	−1.28250	+	1.65202i	−0.0432576	+	0.0557211i
$880$	−23.6118	+	46.8862i	−0.795954	+	1.58053i
$881$			26.8284i			0.903870i	0.892051	+	0.451935i	$0.149266\pi$
$881$			26.8284i			0.903870i	−0.892051	+	0.451935i	$0.850734\pi$
$882$		0			0
$883$		−	27.6059i		−	0.929012i	−0.885570	−	0.464506i	$-0.846232\pi$
$883$		−	27.6059i		−	0.929012i	0.885570	−	0.464506i	$-0.153768\pi$
$884$	0.939643	−	0.280747i	0.0316036	−	0.00944254i
$885$	−33.2494	+	42.8294i	−1.11767	+	1.43969i
$886$	5.68874	+	4.23754i	0.191117	+	0.142363i
$887$	13.1703	−	22.8116i	0.442215	−	0.765939i	−0.555639	−	0.831424i	$-0.687526\pi$
$887$	13.1703	−	22.8116i	0.442215	−	0.765939i	0.997854	+	0.0654853i	$0.0208595\pi$
$888$	0.781041	+	21.0031i	0.0262100	+	0.704818i
$889$		0			0
$890$	29.7022	−	12.8026i	0.995622	−	0.429144i
$891$	25.4060	+	15.4423i	0.851135	+	0.517335i
$892$	−10.9255	+	45.9856i	−0.365814	+	1.53971i
$893$	28.2736	−	16.3238i	0.946139	−	0.546254i
$894$	−15.8562	+	4.39569i	−0.530311	+	0.147014i
$895$			76.9909i			2.57352i
$896$		0			0
$897$	−5.40493	+	2.20318i	−0.180465	+	0.0735621i
$898$	20.3638	+	2.38586i	0.679547	+	0.0796173i
$899$	8.27753	+	14.3371i	0.276071	+	0.478169i
$900$	55.4651	−	33.3125i	1.84884	−	1.11042i
$901$	0.175430	−	0.303854i	0.00584443	−	0.0101228i
$902$	−9.90347	−	22.9762i	−0.329749	−	0.765024i
$903$		0			0
$904$	52.9010	+	19.3039i	1.75946	+	0.642038i
$905$	37.4111	+	21.5993i	1.24359	+	0.717985i
$906$	8.10644	−	31.3330i	0.269318	−	1.04097i
$907$	−9.51618	+	5.49417i	−0.315980	+	0.182431i	−0.649599	−	0.760277i	$-0.725063\pi$
$907$	−9.51618	+	5.49417i	−0.315980	+	0.182431i	0.333619	+	0.942708i	$0.391730\pi$
$908$	−7.04143	−	23.5672i	−0.233678	−	0.782106i
$909$	−14.9733	−	15.3148i	−0.496634	−	0.507961i
$910$		0			0
$911$	−6.42795			−0.212968			−0.106484	−	0.994314i	$-0.533959\pi$
$911$	−6.42795			−0.212968			−0.106484	+	0.994314i	$0.533959\pi$
$912$	−1.97505	+	24.8034i	−0.0654006	+	0.821321i
$913$	6.83609	+	11.8404i	0.226241	+	0.391862i
$914$	−22.5205	−	16.7755i	−0.744912	−	0.554885i
$915$	−66.4414	−	9.12852i	−2.19649	−	0.301779i
$916$	−12.4000	+	13.1288i	−0.409709	+	0.433787i
$917$		0			0
$918$	4.23614	+	0.0111973i	0.139813	+	0.000369566i
$919$	−47.7559	−	27.5719i	−1.57532	−	0.909512i	−0.995499	−	0.0947691i	$-0.969789\pi$
$919$	−47.7559	−	27.5719i	−1.57532	−	0.909512i	−0.579822	−	0.814743i	$-0.696878\pi$
$920$	−7.69410	−	43.8472i	−0.253667	−	1.44560i
$921$	36.1418	−	46.5552i	1.19091	−	1.53404i
$922$	24.4274	+	2.86198i	0.804475	+	0.0942542i
$923$	−7.78856			−0.256364
$924$		0			0
$925$	−46.2628			−1.52111
$926$	21.5331	+	2.52287i	0.707622	+	0.0829066i
$927$	−8.50246	+	30.3583i	−0.279258	+	0.997096i
$928$	15.9568	+	10.5265i	0.523809	+	0.345548i
$929$	41.5330	+	23.9791i	1.36265	+	0.786728i	0.989976	−	0.141233i	$-0.0451065\pi$
$929$	41.5330	+	23.9791i	1.36265	+	0.786728i	0.372677	+	0.927961i	$0.378440\pi$
$930$	33.4183	−	34.0003i	1.09583	−	1.11491i
$931$		0			0
$932$	−11.0123	−	10.4010i	−0.360719	−	0.340697i
$933$	−6.29739	+	45.8352i	−0.206167	+	1.50058i
$934$	−23.9099	−	17.8105i	−0.782356	−	0.582777i
$935$	−3.78278	−	6.55197i	−0.123710	−	0.214272i
$936$	−7.18198	−	0.716013i	−0.234750	−	0.0234036i
$937$	36.7501			1.20057			0.600287	−	0.799784i	$-0.295053\pi$
$937$	36.7501			1.20057			0.600287	+	0.799784i	$0.295053\pi$
$938$		0			0
$939$	−14.9574	+	6.09698i	−0.488115	+	0.198968i
$940$	−69.2069	+	20.6777i	−2.25728	+	0.674431i
$941$	34.3080	−	19.8077i	1.11841	−	0.645714i	0.177415	−	0.984136i	$-0.443226\pi$
$941$	34.3080	−	19.8077i	1.11841	−	0.645714i	0.940994	+	0.338422i	$0.109893\pi$
$942$	5.66349	+	1.46525i	0.184527	+	0.0477405i
$943$	18.3744	+	10.6085i	0.598353	+	0.345459i
$944$	1.79798	+	31.4671i	0.0585193	+	1.02417i
$945$		0			0
$946$	14.1745	+	32.8852i	0.460854	+	1.06919i
$947$	5.92594	−	10.2640i	0.192567	−	0.333536i	−0.753533	−	0.657410i	$-0.771652\pi$
$947$	5.92594	−	10.2640i	0.192567	−	0.333536i	0.946100	+	0.323874i	$0.104985\pi$
$948$	−3.67667	−	23.7167i	−0.119413	−	0.770283i
$949$	−0.601466	−	1.04177i	−0.0195244	−	0.0338172i
$950$	−54.3964	−	6.37321i	−1.76485	−	0.206774i
$951$	−17.6480	−	43.2948i	−0.572275	−	1.40393i
$952$		0			0
$953$			39.8193i			1.28987i	0.764236	+	0.644937i	$0.223116\pi$
$953$			39.8193i			1.28987i	−0.764236	+	0.644937i	$0.776884\pi$
$954$	−2.04391	+	1.57809i	−0.0661740	+	0.0510926i
$955$	−4.24264	+	2.44949i	−0.137289	+	0.0792636i
$956$	−18.0030	−	4.27726i	−0.582258	−	0.138336i
$957$	−19.1554	−	2.63180i	−0.619207	−	0.0850741i
$958$	9.86972	−	4.25416i	0.318876	−	0.137446i
$959$		0			0
$960$	16.9358	−	52.3792i	0.546602	−	1.69053i
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$	4.13877	+	3.08297i	0.133439	+	0.0993989i
$963$	3.56229	+	0.997694i	0.114793	+	0.0321502i
$964$	−8.96636	−	30.0099i	−0.288787	−	0.966553i
$965$			62.7045i			2.01853i
$966$		0			0
$967$			23.4388i			0.753741i	0.926266	+	0.376871i	$0.123000\pi$
$967$			23.4388i			0.753741i	−0.926266	+	0.376871i	$0.877000\pi$
$968$	0.158515	+	0.189228i	0.00509487	+	0.00608203i
$969$	−2.83253	−	2.19896i	−0.0909941	−	0.0706408i
$970$	−45.4741	+	61.0472i	−1.46008	+	1.96011i
$971$	5.55718	−	9.62532i	0.178338	−	0.308891i	−0.762973	−	0.646430i	$-0.776261\pi$
$971$	5.55718	−	9.62532i	0.178338	−	0.308891i	0.941312	+	0.337539i	$0.109595\pi$
$972$	−28.8079	−	11.9208i	−0.924014	−	0.382359i
$973$		0			0
$974$	8.64155	+	20.0485i	0.276893	+	0.642396i
$975$	2.16242	−	15.7391i	0.0692529	−	0.504054i
$976$	−32.5952	+	21.3868i	−1.04335	+	0.684575i
$977$	9.58812	−	5.53570i	0.306751	−	0.177103i	−0.338721	−	0.940887i	$-0.609994\pi$
$977$	9.58812	−	5.53570i	0.306751	−	0.177103i	0.645472	+	0.763784i	$0.276661\pi$
$978$	−43.1772	+	11.9697i	−1.38065	+	0.382748i
$979$			19.0171i			0.607790i
$980$		0			0
$981$	−6.87062	+	6.71741i	−0.219362	+	0.214470i
$982$	−6.66769	+	56.9098i	−0.212774	+	1.81606i
$983$	15.9716	+	27.6637i	0.509416	+	0.882334i	0.999941	+	0.0109070i	$0.00347189\pi$
$983$	15.9716	+	27.6637i	0.509416	+	0.882334i	−0.490524	+	0.871427i	$0.663195\pi$
$984$	13.9535	+	22.2183i	0.444823	+	0.708293i
$985$	34.5373	−	59.8204i	1.10045	−	1.90604i
$986$	−2.52995	+	1.09049i	−0.0805700	+	0.0347282i
$987$		0			0
$988$	4.44171	+	4.19516i	0.141310	+	0.133466i
$989$	−26.2988	−	15.1836i	−0.836252	−	0.482811i
$990$	7.43301	+	55.1820i	0.236237	+	1.75380i
$991$	18.0000	−	10.3923i	0.571789	−	0.330122i	−0.186075	−	0.982536i	$-0.559577\pi$
$991$	18.0000	−	10.3923i	0.571789	−	0.330122i	0.757863	+	0.652413i	$0.226243\pi$
$992$	1.64944	−	27.6637i	0.0523698	−	0.878323i
$993$	9.54109	+	23.4066i	0.302777	+	0.742785i
$994$		0			0
$995$	18.1463			0.575275
$996$	−8.98605	−	11.1716i	−0.284734	−	0.353984i
$997$	20.7685	+	35.9721i	0.657745	+	1.13925i	0.981198	+	0.193003i	$0.0618228\pi$
$997$	20.7685	+	35.9721i	0.657745	+	1.13925i	−0.323453	+	0.946244i	$0.604844\pi$
$998$	−25.6547	+	34.4405i	−0.812086	+	1.09019i
$999$	13.2698	+	17.9129i	0.419838	+	0.566738i

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	588.2.n.h.275.7		24
3.2	odd	2	inner	588.2.n.h.275.6		24
4.3	odd	2		588.2.n.d.275.2		24
7.2	even	3		588.2.e.f.491.4	yes	24
7.3	odd	6		588.2.n.d.263.12		24
7.4	even	3		588.2.n.d.263.11		24
7.5	odd	6		588.2.e.f.491.3	yes	24
7.6	odd	2	inner	588.2.n.h.275.8		24
12.11	even	2		588.2.n.d.275.11		24
21.2	odd	6		588.2.e.f.491.21	yes	24
21.5	even	6		588.2.e.f.491.22	yes	24
21.11	odd	6		588.2.n.d.263.2		24
21.17	even	6		588.2.n.d.263.1		24
21.20	even	2	inner	588.2.n.h.275.5		24
28.3	even	6	inner	588.2.n.h.263.5		24
28.11	odd	6	inner	588.2.n.h.263.6		24
28.19	even	6		588.2.e.f.491.24	yes	24
28.23	odd	6		588.2.e.f.491.23	yes	24
28.27	even	2		588.2.n.d.275.1		24
84.11	even	6	inner	588.2.n.h.263.7		24
84.23	even	6		588.2.e.f.491.2	yes	24
84.47	odd	6		588.2.e.f.491.1	✓	24
84.59	odd	6	inner	588.2.n.h.263.8		24
84.83	odd	2		588.2.n.d.275.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.1	✓	24	84.47	odd	6
588.2.e.f.491.2	yes	24	84.23	even	6
588.2.e.f.491.3	yes	24	7.5	odd	6
588.2.e.f.491.4	yes	24	7.2	even	3
588.2.e.f.491.21	yes	24	21.2	odd	6
588.2.e.f.491.22	yes	24	21.5	even	6
588.2.e.f.491.23	yes	24	28.23	odd	6
588.2.e.f.491.24	yes	24	28.19	even	6
588.2.n.d.263.1		24	21.17	even	6
588.2.n.d.263.2		24	21.11	odd	6
588.2.n.d.263.11		24	7.4	even	3
588.2.n.d.263.12		24	7.3	odd	6
588.2.n.d.275.1		24	28.27	even	2
588.2.n.d.275.2		24	4.3	odd	2
588.2.n.d.275.11		24	12.11	even	2
588.2.n.d.275.12		24	84.83	odd	2
588.2.n.h.263.5		24	28.3	even	6	inner
588.2.n.h.263.6		24	28.11	odd	6	inner
588.2.n.h.263.7		24	84.11	even	6	inner
588.2.n.h.263.8		24	84.59	odd	6	inner
588.2.n.h.275.5		24	21.20	even	2	inner
588.2.n.h.275.6		24	3.2	odd	2	inner
588.2.n.h.275.7		24	1.1	even	1	trivial
588.2.n.h.275.8		24	7.6	odd	2	inner

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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

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Varieties

Fields

Representations

Groups

Database

Properties

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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	588.2.n.h.275.7

Level	$588$
Weight	$2$
Character	588.275
Analytic conductor	$4.695$
Analytic rank	$0$
Dimension	$24$
Inner twists	$8$