LMFDB - Embedded newform 588.2.n.h.275.8

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			275.8
Character	$\chi$	$=$	588.275
Dual form			588.2.n.h.263.8

$q$ -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	$0.0148152\pi$
$5$	3.44057	+	1.98641i	1.53867	+	0.888351i	0.539752	+	0.841824i	$0.318518\pi$
$6$	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	$-0.537635\pi$
$13$	−0.850601			−0.235914			−0.117957	+	0.993019i	$0.537635\pi$
$14$		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	−0.438236	−	0.898860i	$-0.644396\pi$
$17$	0.499236	−	0.288234i	0.121082	−	0.0699070i	0.559318	+	0.828953i	$0.311063\pi$
$18$	4.20467	−	0.566368i	0.991050	−	0.133494i
$19$	3.11023	+	1.79569i	0.713537	+	0.411960i	0.812369	−	0.583144i	$-0.198178\pi$
$19$	3.11023	+	1.79569i	0.713537	+	0.411960i	−0.0988326	+	0.995104i	$0.531511\pi$
$20$	−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	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	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	$-0.862663\pi$
$41$		−	5.35550i		−	0.836389i	0.908357	−	0.418195i	$-0.137337\pi$
$42$		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	$-0.602619\pi$
$47$	4.54525	−	7.87260i	0.662993	−	1.14834i	0.979825	−	0.199856i	$-0.0640473\pi$
$48$	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	$-0.995231\pi$
$59$	−3.93980	−	6.82394i	−0.512919	−	0.888401i	0.486969	−	0.873419i	$-0.338102\pi$
$60$	−2.10831	−	13.5998i	−0.272181	−	1.75573i
$61$	4.87315	−	8.44054i	0.623943	−	1.08070i	−0.364802	−	0.931085i	$-0.618863\pi$
$61$	4.87315	−	8.44054i	0.623943	−	1.08070i	0.988744	−	0.149615i	$-0.0478034\pi$
$62$	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	0.904435	−	0.426612i	$-0.140293\pi$
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	−0.821674	+	0.569958i	$0.806960\pi$
$74$	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	$-0.427061\pi$
$83$	4.13877			0.454289			0.227144	+	0.973861i	$0.427061\pi$
$84$		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	0.740390	−	0.672177i	$-0.234641\pi$
$89$	4.98550	+	2.87838i	0.528462	+	0.305108i	−0.211928	+	0.977285i	$0.567974\pi$
$90$	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	$-0.741438\pi$
$97$	−13.5487			−1.37567			−0.687833	+	0.725869i	$0.741438\pi$
$98$		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	−0.159782	−	0.987152i	$-0.551079\pi$
$101$	6.18294	−	3.56972i	0.615225	−	0.355200i	0.775008	+	0.631952i	$0.217746\pi$
$102$	0.353679	−	1.36704i	0.0350195	−	0.135357i
$103$	−9.10090	−	5.25441i	−0.896738	−	0.517732i	−0.0205978	−	0.999788i	$-0.506557\pi$
$103$	−9.10090	−	5.25441i	−0.896738	−	0.517732i	−0.876141	+	0.482056i	$0.839890\pi$
$104$	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	−0.911464	−	0.411379i	$-0.865047\pi$
$131$	−1.13845	+	1.97186i	−0.0994670	+	0.172282i	0.811997	+	0.583661i	$0.198380\pi$
$132$	−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	$0.156100\pi$
$139$			11.1056i			0.941960i	−0.882144	+	0.470980i	$0.843900\pi$
$140$		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	0.909734	−	0.415191i	$-0.136285\pi$
$157$	1.19412	+	2.06828i	0.0953011	+	0.165066i	−0.814433	+	0.580257i	$0.802952\pi$
$158$	−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	$-0.230413\pi$
$167$	19.3650			1.49851			0.749253	+	0.662284i	$0.230413\pi$
$168$		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	0.304726	−	0.952440i	$-0.401435\pi$
$173$	−4.83696	−	2.79262i	−0.367748	−	0.212319i	−0.672474	+	0.740121i	$0.734768\pi$
$174$	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	$-0.367581\pi$
$181$	10.8735			0.808222			0.404111	+	0.914710i	$0.367581\pi$
$182$		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	−0.353200	−	0.935548i	$-0.614906\pi$
$199$	3.95565	−	2.28380i	0.280409	−	0.161894i	0.633608	+	0.773654i	$0.281573\pi$
$200$	−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	$0.290588\pi$
$223$			23.6328i			1.58257i	−0.611447	+	0.791285i	$0.709412\pi$
$224$		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	0.586546	−	0.809916i	$-0.300487\pi$
$227$	−6.14917	−	10.6507i	−0.408135	−	0.706910i	−0.994681	+	0.103006i	$0.967154\pi$
$228$	−1.90589	−	12.2941i	−0.126220	−	0.814195i
$229$	−4.51474	+	7.81976i	−0.298342	+	0.516744i	−0.975757	−	0.218857i	$-0.929767\pi$
$229$	−4.51474	+	7.81976i	−0.298342	+	0.516744i	0.677414	+	0.735602i	$0.263100\pi$
$230$	−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	$-0.998385\pi$
$241$	−7.83018	−	13.5623i	−0.504386	−	0.873623i	0.495601	−	0.868550i	$-0.334948\pi$
$242$	−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	$-0.468910\pi$
$251$	3.08987			0.195031			0.0975155	+	0.995234i	$0.468910\pi$
$252$		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	0.287568	−	0.957760i	$-0.407153\pi$
$257$	−6.38190	−	3.68459i	−0.398092	−	0.229839i	−0.685660	+	0.727922i	$0.740486\pi$
$258$	−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	−0.211753	−	0.977323i	$-0.567917\pi$
$269$	8.67226	−	5.00693i	0.528757	−	0.305278i	0.740510	+	0.672045i	$0.234584\pi$
$270$	14.5302	+	25.3214i	0.884281	+	1.54101i
$271$	20.4250	+	11.7924i	1.24073	+	0.716335i	0.969243	−	0.246107i	$-0.0791516\pi$
$271$	20.4250	+	11.7924i	1.24073	+	0.716335i	0.271486	+	0.962442i	$0.412485\pi$
$272$	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	−0.876258	−	0.481842i	$-0.839968\pi$
$283$	−15.0916	+	8.71312i	−0.897101	+	0.517941i	−0.0208421	+	0.999783i	$0.506635\pi$
$284$	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	$0.0112293\pi$
$293$			1.20747i			0.0705412i	−0.999378	+	0.0352706i	$0.988771\pi$
$294$		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	$-0.576811\pi$
$307$		−	34.0275i		−	1.94205i	0.238973	−	0.971026i	$-0.423189\pi$
$308$		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	$0.106833\pi$
$311$	13.3558	+	23.1329i	0.757337	+	1.31175i	−0.186867	+	0.982385i	$0.559833\pi$
$312$	3.52887	−	2.21621i	0.199783	−	0.125468i
$313$	−4.66276	+	8.07614i	−0.263555	+	0.456490i	−0.967184	−	0.254077i	$-0.918228\pi$
$313$	−4.66276	+	8.07614i	−0.263555	+	0.456490i	0.703629	+	0.710567i	$0.251562\pi$
$314$	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	$-0.154426\pi$
$349$	33.0517			1.76922			0.884608	+	0.466335i	$0.154426\pi$
$350$		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	−0.0951392	−	0.995464i	$-0.530330\pi$
$353$	13.5161	−	7.80351i	0.719388	−	0.415339i	0.814528	+	0.580125i	$0.196996\pi$
$354$	−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	−0.666739	−	0.745291i	$-0.732310\pi$
$367$	−6.79444	+	3.92277i	−0.354667	+	0.204767i	0.312072	+	0.950059i	$0.398977\pi$
$368$	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	−0.816028	−	0.578013i	$-0.803828\pi$
$383$	1.81144	−	3.13750i	0.0925602	−	0.160319i	0.908588	+	0.417694i	$0.137162\pi$
$384$	−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	−0.779328	−	0.626616i	$-0.784440\pi$
$397$	3.04852	−	5.28019i	0.153001	−	0.265005i	0.932329	+	0.361610i	$0.117773\pi$
$398$	−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	1.00000		0.000963491i	$-0.000306689\pi$
$409$	10.0950	+	17.4850i	0.499165	+	0.864580i	−0.500834	+	0.865543i	$0.666973\pi$
$410$	−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	$-0.489666\pi$
$419$	1.32886			0.0649189			0.0324594	+	0.999473i	$0.489666\pi$
$420$		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	$-0.380579\pi$
$433$	15.2499			0.732866			0.366433	+	0.930444i	$0.380579\pi$
$434$		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	0.968292	−	0.249823i	$-0.0803723\pi$
$439$	25.8988	+	14.9527i	1.23608	+	0.713654i	0.267793	+	0.963476i	$0.413706\pi$
$440$	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	$-0.867275\pi$
$461$		−	17.3910i		−	0.809978i	0.914322	−	0.404989i	$-0.132725\pi$
$462$		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	−0.999901	−	0.0140554i	$-0.995526\pi$
$467$	−10.5410	+	18.2575i	−0.487778	+	0.844857i	0.512123	+	0.858912i	$0.328859\pi$
$468$	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	0.766064	−	0.642764i	$-0.222213\pi$
$479$	−3.79982	−	6.58149i	−0.173618	−	0.300716i	−0.939682	+	0.342049i	$0.888879\pi$
$480$	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	$-0.399729\pi$
$503$	13.8974			0.619652			0.309826	+	0.950793i	$0.399729\pi$
$504$		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	−0.192350	−	0.981326i	$-0.561611\pi$
$509$	−25.6830	−	14.8281i	−1.13838	−	0.657243i	−0.946029	+	0.324083i	$0.894944\pi$
$510$	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	−0.975682	−	0.219192i	$-0.929658\pi$
$521$	−29.0727	+	16.7851i	−1.27370	+	0.735369i	−0.298015	+	0.954561i	$0.596325\pi$
$522$	1.91392	+	14.2088i	0.0837700	+	0.621902i
$523$	−8.82946	−	5.09769i	−0.386085	−	0.222906i	0.294377	−	0.955689i	$-0.404888\pi$
$523$	−8.82946	−	5.09769i	−0.386085	−	0.222906i	−0.680463	+	0.732783i	$0.738221\pi$
$524$	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	$0.141889\pi$
$563$	19.5639	+	33.8857i	0.824522	+	1.42811i	−0.0777627	+	0.996972i	$0.524778\pi$
$564$	−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	$0.108899\pi$
$577$	18.2933	+	31.6849i	0.761560	+	1.31906i	−0.180487	+	0.983577i	$0.557767\pi$
$578$	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	$-0.225052\pi$
$587$	36.8412			1.52060			0.760299	+	0.649573i	$0.225052\pi$
$588$		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	0.773897	−	0.633311i	$-0.218305\pi$
$593$	14.9125	+	8.60972i	0.612382	+	0.353559i	−0.161515	+	0.986870i	$0.551638\pi$
$594$	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	$-0.551850\pi$
$601$	−7.95144			−0.324346			−0.162173	+	0.986762i	$0.551850\pi$
$602$		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	0.855913	−	0.517120i	$-0.172996\pi$
$607$	20.5976	+	11.8920i	0.836030	+	0.482682i	−0.0198827	+	0.999802i	$0.506329\pi$
$608$	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	−0.0433558	−	0.999060i	$-0.513805\pi$
$619$	19.9082	−	11.4940i	0.800177	−	0.461983i	0.843533	+	0.537077i	$0.180472\pi$
$620$	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	$-0.983164\pi$
$643$		−	2.68122i		−	0.105737i	0.998601	−	0.0528684i	$-0.0168364\pi$
$644$		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	0.604223	−	0.796815i	$-0.293484\pi$
$647$	−9.86799	−	17.0919i	−0.387951	−	0.671950i	−0.992174	+	0.124865i	$0.960150\pi$
$648$	−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	0.683492	−	0.729958i	$-0.260461\pi$
$661$	−7.46659	−	12.9325i	−0.290417	−	0.503017i	−0.973908	+	0.226942i	$0.927127\pi$
$662$	−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	0.747522	−	0.664238i	$-0.231244\pi$
$677$	14.2074	+	8.20266i	0.546036	+	0.315254i	−0.201486	+	0.979491i	$0.564577\pi$
$678$	−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	0.934278	−	0.356545i	$-0.116045\pi$
$691$	28.7221	+	16.5827i	1.09264	+	0.630836i	0.158362	+	0.987381i	$0.449379\pi$
$692$	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	−0.614259	−	0.789105i	$-0.710545\pi$
$719$	10.0890	−	17.4746i	0.376255	−	0.651693i	0.990514	+	0.137412i	$0.0438783\pi$
$720$	−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	$-0.990430\pi$
$727$		−	1.62103i		−	0.0601206i	0.999548	−	0.0300603i	$-0.00956993\pi$
$728$		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	$0.338320\pi$
$733$	−13.9026	+	24.0801i	−0.513505	+	0.889417i	−0.999877	+	0.0156654i	$0.995013\pi$
$734$	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	0.306204	−	0.951966i	$-0.400941\pi$
$761$	−10.0723	−	5.81526i	−0.365121	−	0.210803i	−0.671325	+	0.741163i	$0.734274\pi$
$762$	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	$-0.499292\pi$
$769$	0.123424			0.00445080			0.00222540	+	0.999998i	$0.499292\pi$
$770$		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	−0.722163	−	0.691723i	$-0.756852\pi$
$773$	−13.4620	+	7.77229i	−0.484194	+	0.279550i	0.237968	+	0.971273i	$0.423519\pi$
$774$	−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	0.314743	−	0.949177i	$-0.398082\pi$
$787$	36.3048	−	20.9606i	1.29413	−	0.747164i	0.979383	+	0.202014i	$0.0647485\pi$
$788$	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	$-0.880013\pi$
$797$		−	20.7831i		−	0.736175i	0.929791	−	0.368088i	$-0.119987\pi$
$798$		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	$-0.973806\pi$
$811$		−	4.68171i		−	0.164397i	0.996616	−	0.0821986i	$-0.0261942\pi$
$812$		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	$-0.997809\pi$
$829$	−14.5674	−	25.2315i	−0.505948	−	0.876328i	0.494028	−	0.869446i	$-0.335524\pi$
$830$	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	$-0.579884\pi$
$839$	−14.3863			−0.496671			−0.248336	+	0.968674i	$0.579884\pi$
$840$		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	$-0.178682\pi$
$853$	49.4483			1.69308			0.846539	+	0.532327i	$0.178682\pi$
$854$		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	−0.661403	−	0.750030i	$-0.730039\pi$
$857$	−10.0283	+	5.78983i	−0.342560	+	0.197777i	0.318844	+	0.947807i	$0.396705\pi$
$858$	6.66345	+	1.72396i	0.227486	+	0.0588550i
$859$	−6.27765	−	3.62441i	−0.214191	−	0.123663i	0.389067	−	0.921210i	$-0.372798\pi$
$859$	−6.27765	−	3.62441i	−0.214191	−	0.123663i	−0.603258	+	0.797546i	$0.706131\pi$
$860$	−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	$-0.850734\pi$
$881$		−	26.8284i		−	0.903870i	0.892051	−	0.451935i	$-0.149266\pi$
$882$		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	−0.997854	−	0.0654853i	$-0.979140\pi$
$887$	−13.1703	+	22.8116i	−0.442215	+	0.765939i	0.555639	+	0.831424i	$0.312474\pi$
$888$	−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	−0.372677	−	0.927961i	$-0.621560\pi$
$929$	−41.5330	−	23.9791i	−1.36265	−	0.786728i	−0.989976	+	0.141233i	$0.954893\pi$
$930$	−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	$-0.704947\pi$
$937$	−36.7501			−1.20057			−0.600287	+	0.799784i	$0.704947\pi$
$938$		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	−0.940994	−	0.338422i	$-0.890107\pi$
$941$	−34.3080	+	19.8077i	−1.11841	+	0.645714i	−0.177415	+	0.984136i	$0.556774\pi$
$942$	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	−0.941312	−	0.337539i	$-0.890405\pi$
$971$	−5.55718	+	9.62532i	−0.178338	+	0.308891i	0.762973	+	0.646430i	$0.223739\pi$
$972$	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	$-0.996528\pi$
$983$	−15.9716	−	27.6637i	−0.509416	−	0.882334i	0.490524	−	0.871427i	$-0.336805\pi$
$984$	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	$-0.938177\pi$
$997$	−20.7685	−	35.9721i	−0.657745	−	1.13925i	0.323453	−	0.946244i	$-0.395156\pi$
$998$	−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

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a_p

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a_p

)

Twists

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

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

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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

Modular forms

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.275.8

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