LMFDB - Embedded newform 588.2.n.d.275.11

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			275.11
Character	$\chi$	$=$	588.275
Dual form			588.2.n.d.263.11

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13414 - 0.844822i) q^{2} +(-0.235755 - 1.71593i) q^{3} +(0.572551 - 1.91629i) q^{4} +(3.44057 + 1.98641i) q^{5} +(-1.71704 - 1.74694i) q^{6} +(-0.969574 - 2.65705i) q^{8} +(-2.88884 + 0.809079i) q^{9} +(5.58025 - 0.653796i) q^{10} +(-1.65172 - 2.86086i) q^{11} +(-3.42321 - 0.530682i) q^{12} +0.850601 q^{13} +(2.59742 - 6.37208i) q^{15} +(-3.34437 - 2.19435i) q^{16} +(0.499236 - 0.288234i) q^{17} +(-2.59282 + 3.35816i) 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} +(-4.33074 + 2.29014i) q^{24} +(5.39167 + 9.33865i) q^{25} +(0.964701 - 0.718606i) q^{26} +(2.06938 + 4.76630i) q^{27} -3.37929i q^{29} +(-2.43744 - 9.42120i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(-5.64683 + 0.336691i) q^{32} +(-4.51964 + 3.50870i) q^{33} +(0.322697 - 0.748663i) q^{34} +(-0.103574 + 5.99911i) q^{36} +(-2.14510 + 3.71543i) q^{37} +(5.04449 - 0.591024i) q^{38} +(-0.200534 - 1.45957i) q^{39} +(1.94212 - 11.0677i) q^{40} -5.35550i q^{41} +7.66518i q^{43} +(-6.42795 + 1.52719i) q^{44} +(-11.5464 - 2.95473i) q^{45} +(-0.651966 - 5.56464i) q^{46} +(-4.54525 + 7.87260i) q^{47} +(-2.97691 + 6.25604i) q^{48} +(14.0044 + 6.03634i) q^{50} +(-0.612287 - 0.788701i) q^{51} +(0.487013 - 1.63000i) q^{52} +(0.527096 - 0.304319i) q^{53} +(6.37365 + 3.65740i) q^{54} -13.1240i q^{55} +(2.34803 - 5.76029i) q^{57} +(-2.85490 - 3.83259i) q^{58} +(3.93980 + 6.82394i) q^{59} +(-10.7236 - 8.62576i) 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} +(-2.16168 + 7.79766i) q^{66} +(7.83384 - 4.52287i) q^{67} +(-0.266503 - 1.12171i) q^{68} +(-6.35425 - 2.59015i) q^{69} -9.15654 q^{71} +(4.95071 + 6.89133i) q^{72} +(-0.707107 - 1.22474i) q^{73} +(0.706026 + 6.02605i) q^{74} +(14.7534 - 11.4534i) q^{75} +(5.22185 - 4.93200i) q^{76} +(-1.46051 - 1.48595i) q^{78} +(6.00000 + 3.46410i) q^{79} +(-7.14764 - 14.1931i) q^{80} +(7.69078 - 4.67460i) q^{81} +(-4.52445 - 6.07390i) q^{82} -4.13877 q^{83} +2.29021 q^{85} +(6.47571 + 8.69339i) q^{86} +(-5.79863 + 0.796685i) q^{87} +(-6.00000 + 7.16253i) q^{88} +(4.98550 + 2.87838i) q^{89} +(-15.5915 + 6.40358i) q^{90} +(-5.44055 - 5.76029i) q^{92} +(5.20338 + 6.70260i) q^{93} +(1.49600 + 12.7686i) q^{94} +(7.13398 + 12.3564i) q^{95} +(1.90901 + 9.61019i) q^{96} +13.5487 q^{97} +(7.08622 + 6.92820i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100})$ 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * 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

)

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

$2$	1.13414	−	0.844822i	0.801959	−	0.597379i
$2$	1.13414	−	0.844822i	0.801959	−	0.597379i
$3$	−0.235755	−	1.71593i	−0.136113	−	0.990693i
$3$	−0.235755	−	1.71593i	−0.136113	−	0.990693i
$4$	0.572551	−	1.91629i	0.286276	−	0.958147i
$5$	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
$9$	−2.88884	+	0.809079i	−0.962946	+	0.269693i
$10$	5.58025	−	0.653796i	1.76463	−	0.206748i
$11$	−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	$0.999270\pi$
$12$	−3.42321	−	0.530682i	−0.988196	−	0.153195i
$13$	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
$16$	−3.34437	−	2.19435i	−0.836092	−	0.548589i
$17$	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	$0.311063\pi$
$18$	−2.59282	+	3.35816i	−0.611134	+	0.791527i
$19$	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	$0.0311348\pi$
$24$	−4.33074	+	2.29014i	−0.884008	+	0.467472i
$25$	5.39167	+	9.33865i	1.07833	+	1.86773i
$26$	0.964701	−	0.718606i	0.189193	−	0.140930i
$27$	2.06938	+	4.76630i	0.398253	+	0.917276i
$28$		0			0
$29$		−	3.37929i		−	0.627518i	−0.949503	−	0.313759i	$-0.898412\pi$
$29$		−	3.37929i		−	0.627518i	0.949503	−	0.313759i	$-0.101588\pi$
$30$	−2.43744	−	9.42120i	−0.445014	−	1.72007i
$31$	−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	$0.478334\pi$
$32$	−5.64683	+	0.336691i	−0.998227	+	0.0595191i
$33$	−4.51964	+	3.50870i	−0.786769	+	0.610787i
$34$	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	$0.281387\pi$
$38$	5.04449	−	0.591024i	0.818324	−	0.0958767i
$39$	−0.200534	−	1.45957i	−0.0321111	−	0.233719i
$40$	1.94212	−	11.0677i	0.307076	−	1.74996i
$41$		−	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	$0.198695\pi$
$43$			7.66518i			1.16893i	−0.811419	+	0.584464i	$0.801305\pi$
$44$	−6.42795	+	1.52719i	−0.969050	+	0.230233i
$45$	−11.5464	−	2.95473i	−1.72124	−	0.440466i
$46$	−0.651966	−	5.56464i	−0.0961272	−	0.820461i
$47$	−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
$51$	−0.612287	−	0.788701i	−0.0857373	−	0.110440i
$52$	0.487013	−	1.63000i	0.0675365	−	0.226041i
$53$	0.527096	−	0.304319i	0.0724023	−	0.0418015i	−0.463362	−	0.886169i	$-0.653357\pi$
$53$	0.527096	−	0.304319i	0.0724023	−	0.0418015i	0.535764	+	0.844368i	$0.320024\pi$
$54$	6.37365	+	3.65740i	0.867344	+	0.497709i
$55$		−	13.1240i		−	1.76964i
$56$		0			0
$57$	2.34803	−	5.76029i	0.311005	−	0.762969i
$58$	−2.85490	−	3.83259i	−0.374866	−	0.503244i
$59$	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	$0.661898\pi$
$60$	−10.7236	−	8.62576i	−1.38442	−	1.11358i
$61$	−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
$66$	−2.16168	+	7.79766i	−0.266085	+	0.959825i
$67$	7.83384	−	4.52287i	0.957056	−	0.552557i	0.0617904	−	0.998089i	$-0.480319\pi$
$67$	7.83384	−	4.52287i	0.957056	−	0.552557i	0.895266	+	0.445532i	$0.146986\pi$
$68$	−0.266503	−	1.12171i	−0.0323182	−	0.136027i
$69$	−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	$0.682841\pi$
$72$	4.95071	+	6.89133i	0.583447	+	0.812151i
$73$	−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	$0.859707\pi$
$74$	0.706026	+	6.02605i	0.0820738	+	0.700514i
$75$	14.7534	−	11.4534i	1.70357	−	1.32252i
$76$	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	0.797988	−	0.602673i	$-0.205898\pi$
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	−0.122936	+	0.992415i	$0.539231\pi$
$80$	−7.14764	−	14.1931i	−0.799130	−	1.58684i
$81$	7.69078	−	4.67460i	0.854531	−	0.519400i
$82$	−4.52445	−	6.07390i	−0.499642	−	0.670750i
$83$	−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
$86$	6.47571	+	8.69339i	0.698294	+	0.937433i
$87$	−5.79863	+	0.796685i	−0.621678	+	0.0854136i
$88$	−6.00000	+	7.16253i	−0.639602	+	0.763528i
$89$	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
$93$	5.20338	+	6.70260i	0.539565	+	0.695027i
$94$	1.49600	+	12.7686i	0.154300	+	1.31698i
$95$	7.13398	+	12.3564i	0.731931	+	1.26774i
$96$	1.90901	+	9.61019i	0.194837	+	0.980836i
$97$	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
$100$	20.9826	−	4.98517i	2.09826	−	0.498517i
$101$	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	$0.217746\pi$
$102$	−1.36073	−	0.377225i	−0.134733	−	0.0373509i
$103$	−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	$0.147682\pi$
$108$	10.3185	−	1.23659i	0.992895	−	0.118991i
$109$	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	$0.784313\pi$
$110$	−11.0874	−	14.8845i	−1.05715	−	1.41918i
$111$	6.88114	+	2.80492i	0.653128	+	0.266231i
$112$		0			0
$113$			19.9097i			1.87294i	0.350744	+	0.936471i	$0.385929\pi$
$113$			19.9097i			1.87294i	−0.350744	+	0.936471i	$0.614071\pi$
$114$	−2.20342	−	8.51665i	−0.206369	−	0.797658i
$115$	13.6305	−	7.86959i	1.27105	−	0.733843i
$116$	−6.47571	−	1.93482i	−0.601255	−	0.179643i
$117$	−2.45725	+	0.688203i	−0.227173	+	0.0636244i
$118$	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
$122$	1.60392	+	13.6897i	0.145212	+	1.23941i
$123$	−9.18967	+	1.26259i	−0.828605	+	0.113844i
$124$	2.26481	+	9.53261i	0.203386	+	0.856053i
$125$			22.9762i			2.05505i
$126$		0			0
$127$		−	16.4426i		−	1.45904i	−0.683957	−	0.729522i	$-0.739742\pi$
$127$		−	16.4426i		−	1.45904i	0.683957	−	0.729522i	$-0.260258\pi$
$128$	−2.58790	+	11.0138i	−0.228740	+	0.973488i
$129$	13.1529	−	1.80711i	1.15805	−	0.159107i
$130$	4.74657	−	0.556119i	0.416302	−	0.0487749i
$131$	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
$135$	−2.34799	+	20.5094i	−0.202083	+	1.76517i
$136$	−1.24990	−	1.04703i	−0.107178	−	0.0897822i
$137$	7.97118	−	4.60216i	0.681024	−	0.393189i	−0.119217	−	0.992868i	$-0.538038\pi$
$137$	7.97118	−	4.60216i	0.681024	−	0.393189i	0.800241	+	0.599679i	$0.204705\pi$
$138$	−9.39483	+	2.43062i	−0.799741	+	0.206908i
$139$			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
$142$	−10.3848	+	7.73565i	−0.871474	+	0.649161i
$143$	−1.40495	−	2.43345i	−0.117488	−	0.203496i
$144$	11.4368	+	3.63328i	0.953063	+	0.302773i
$145$	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	0.242408	−	0.970174i	$-0.422063\pi$
$149$	−5.81744	−	3.35870i	−0.476584	−	0.275156i	−0.718992	+	0.695019i	$0.755396\pi$
$150$	7.05633	−	25.4537i	0.576147	−	2.07829i
$151$	11.4426	−	6.60641i	0.931188	−	0.537622i	0.0440012	−	0.999031i	$-0.485989\pi$
$151$	11.4426	−	6.60641i	0.931188	−	0.537622i	0.887187	+	0.461410i	$0.152656\pi$
$152$	1.75565	−	10.0051i	0.142402	−	0.811522i
$153$	−1.20901	+	1.23658i	−0.0977425	+	0.0999718i
$154$		0			0
$155$	−19.4628			−1.56329
$156$	−2.91179	−	0.451399i	−0.233129	−	0.0361408i
$157$	−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	$0.863715\pi$
$158$	9.73140	−	1.14015i	0.774188	−	0.0907057i
$159$	−0.646457	−	0.832716i	−0.0512673	−	0.0660387i
$160$	−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	−0.271524	−	0.962432i	$-0.587528\pi$
$163$	−15.8412	−	9.14590i	−1.24078	−	0.716362i	−0.969252	+	0.246069i	$0.920861\pi$
$164$	−10.2627	−	3.06630i	−0.801384	−	0.239438i
$165$	−22.5199	+	3.09405i	−1.75317	+	0.240871i
$166$	−4.69394	+	3.49652i	−0.364321	+	0.271383i
$167$	−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
$170$	2.59742	−	1.93482i	0.199213	−	0.148394i
$171$	−10.4378	−	2.67105i	−0.798200	−	0.204260i
$172$	14.6887	+	4.38871i	1.12001	+	0.334636i
$173$	−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
$177$	10.7806	−	8.36921i	0.810318	−	0.629068i
$178$	8.08598	−	0.947373i	0.606070	−	0.0710086i
$179$	−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	$-0.424477\pi$
$180$	−12.2731	+	20.4346i	−0.914780	+	1.52310i
$181$	−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
$184$	−11.0368	−	1.93668i	−0.813642	−	0.142774i
$185$	−14.7607	+	8.52212i	−1.08523	+	0.626559i
$186$	11.5639	+	3.20576i	0.847904	+	0.235058i
$187$	−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	$0.152461\pi$
$192$	10.2840	+	9.28654i	0.742182	+	0.670198i
$193$	−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	$-0.358971\pi$
$194$	15.3662	−	11.4463i	1.10323	−	0.821795i
$195$	2.20936	−	5.42010i	0.158216	−	0.388141i
$196$		0			0
$197$		−	17.3868i		−	1.23876i	−0.785092	−	0.619379i	$-0.787385\pi$
$197$		−	17.3868i		−	1.23876i	0.785092	−	0.619379i	$-0.212615\pi$
$198$	13.8899	+	1.87096i	0.987110	+	0.132964i
$199$	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	$0.281573\pi$
$200$	19.5857	−	23.3805i	1.38491	−	1.65325i
$201$	−9.60780	−	12.3760i	−0.677682	−	0.872939i
$202$	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
$206$	−14.7607	+	1.72940i	−1.02843	+	0.120493i
$207$	−2.94647	+	11.5141i	−0.204794	+	0.800286i
$208$	−2.84472	−	1.86652i	−0.197246	−	0.129420i
$209$		−	11.8639i		−	0.820646i
$210$		0			0
$211$			1.11224i			0.0765696i	0.999267	+	0.0382848i	$0.0121894\pi$
$211$			1.11224i			0.0765696i	−0.999267	+	0.0382848i	$0.987811\pi$
$212$	−0.281376	−	1.18431i	−0.0193250	−	0.0813388i
$213$	2.15870	+	15.7120i	0.147912	+	1.07657i
$214$	−0.202931	−	1.73205i	−0.0138721	−	0.118401i
$215$	−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
$219$	−1.93487	+	1.50209i	−0.130747	+	0.101502i
$220$	−25.1494	−	7.51416i	−1.69558	−	0.506605i
$221$	0.424650	−	0.245172i	0.0285651	−	0.0164920i
$222$	10.1738	−	2.63216i	0.682823	−	0.176659i
$223$			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
$226$	16.8201	+	22.5804i	1.11886	+	1.50202i
$227$	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	$0.699513\pi$
$228$	−9.69404	−	7.79759i	−0.642004	−	0.516408i
$229$	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	0.269517	−	0.962996i	$-0.413136\pi$
$233$	−6.55912	−	3.78691i	−0.429703	−	0.248089i	−0.699220	+	0.714907i	$0.746469\pi$
$234$	−2.20546	+	2.85646i	−0.144175	+	0.186732i
$235$	−31.2765	+	18.0575i	−2.04025	+	1.17794i
$236$	15.3324	−	3.64277i	0.998055	−	0.237124i
$237$	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	$0.403269\pi$
$240$	−22.6693	+	15.6110i	−1.46330	+	1.00768i
$241$	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	$0.665052\pi$
$242$	−0.0143625	−	0.122586i	−0.000923254	−	0.00788012i
$243$	−9.83443	−	12.0948i	−0.630879	−	0.775881i
$244$	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
$248$	10.6220	+	8.89796i	0.674496	+	0.565021i
$249$	0.975735	+	7.10184i	0.0618347	+	0.450061i
$250$	19.4108	+	26.0583i	1.22765	+	1.64807i
$251$	−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
$254$	−13.8911	−	18.6482i	−0.871603	−	1.17009i
$255$	−0.539928	−	3.92983i	−0.0338116	−	0.246096i
$256$	6.36962	+	14.6775i	0.398101	+	0.917341i
$257$	−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
$261$	2.73411	+	9.76222i	0.169237	+	0.604266i
$262$	−0.374703	−	3.19815i	−0.0231492	−	0.197583i
$263$	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	$0.593327\pi$
$264$	13.7049	+	8.60698i	0.843480	+	0.529723i
$265$	2.41801			0.148537
$266$		0			0
$267$	3.76375	−	9.23337i	0.230338	−	0.565073i
$268$	−4.18188	−	17.6015i	−0.255449	−	1.07518i
$269$	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	$0.234584\pi$
$270$	14.6639	+	25.2442i	0.892415	+	1.53632i
$271$	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
$276$	−8.60162	+	10.6936i	−0.517757	+	0.643681i
$277$	−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	$-0.504507\pi$
$278$	9.38221	+	12.5953i	0.562708	+	0.755413i
$279$	10.2745	−	10.5088i	0.615117	−	0.629146i
$280$		0			0
$281$			23.2889i			1.38930i	0.719347	+	0.694651i	$0.244441\pi$
$281$			23.2889i			1.38930i	−0.719347	+	0.694651i	$0.755559\pi$
$282$	21.5573	−	5.57728i	1.28372	−	0.332122i
$283$	−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	$0.506635\pi$
$284$	−5.24259	+	17.5466i	−0.311090	+	1.04120i
$285$	19.5209	−	15.1545i	1.15632	−	0.897675i
$286$	−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
$290$	−2.20936	−	18.8573i	−0.129738	−	1.10734i
$291$	−3.19419	−	23.2487i	−0.187247	−	1.36286i
$292$	−2.75183	+	0.653796i	−0.161038	+	0.0382605i
$293$			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
$296$	11.9519	+	2.09727i	0.694691	+	0.121901i
$297$	10.2177	−	13.7928i	0.592891	−	0.800341i
$298$	−9.43531	+	1.10546i	−0.546573	+	0.0640377i
$299$	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
$303$	−7.58305	−	9.76791i	−0.435635	−	0.561152i
$304$	−6.46138	−	12.8304i	−0.370586	−	0.735875i
$305$	−33.5328	+	19.3602i	−1.92008	+	1.10856i
$306$	−0.326493	+	2.42385i	−0.0186643	+	0.138563i
$307$		−	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
$310$	−22.0735	+	16.4426i	−1.25369	+	0.933877i
$311$	−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	$-0.440167\pi$
$312$	−3.68373	+	1.94799i	−0.208550	+	0.110283i
$313$	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	−0.330382	−	0.943847i	$-0.607178\pi$
$317$	−23.3767	−	13.4966i	−1.31297	−	0.758043i	−0.982587	+	0.185805i	$0.940511\pi$
$318$	−1.43667	−	0.398277i	−0.0805645	−	0.0223343i
$319$	−9.66769	+	5.58164i	−0.541286	+	0.312512i
$320$	−31.2906	+	5.57069i	−1.74920	+	0.311411i
$321$	−1.97783	−	0.806210i	−0.110392	−	0.0449982i
$322$		0			0
$323$	2.07032			0.115196
$324$	−4.55454	−	17.4143i	−0.253030	−	0.967458i
$325$	4.58616	+	7.94346i	0.254394	+	0.440624i
$326$	−25.6928	+	3.01023i	−1.42299	+	0.166721i
$327$	4.38213	−	3.40195i	0.242332	−	0.188128i
$328$	−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	0.805356	−	0.592792i	$-0.201974\pi$
$331$	12.6382	+	7.29669i	0.694660	+	0.401062i	−0.110695	+	0.993854i	$0.535308\pi$
$332$	−2.36966	+	7.93109i	−0.130052	+	0.435275i
$333$	3.19078	−	12.4688i	0.174854	−	0.683288i
$334$	−21.9626	+	16.3600i	−1.20174	+	0.895177i
$335$	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	$0.168631\pi$
$338$	−13.9233	+	10.3714i	−0.757325	+	0.564132i
$339$	34.1636	−	4.69380i	1.85551	−	0.254932i
$340$	1.31126	−	4.38871i	0.0711131	−	0.238011i
$341$	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
$345$	−16.7171	−	21.5338i	−0.900021	−	1.15934i
$346$	−7.84507	+	0.919147i	−0.421753	+	0.0494136i
$347$	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	$0.814922\pi$
$348$	−1.79333	+	11.5680i	−0.0961325	+	0.620111i
$349$	−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
$352$	10.2902	+	15.5987i	0.548470	+	0.831413i
$353$	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	$0.196996\pi$
$354$	5.15620	−	18.5995i	0.274049	−	0.988554i
$355$	−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	$0.818817\pi$
$360$	3.34422	+	33.5443i	0.176256	+	1.76794i
$361$	−3.05096	−	5.28443i	−0.160577	−	0.278128i
$362$	−12.3321	+	9.18619i	−0.648161	+	0.482815i
$363$	−0.139981	−	0.0570595i	−0.00734708	−	0.00299485i
$364$		0			0
$365$		−	5.61842i		−	0.294082i
$366$	23.1125	−	5.97963i	1.20811	−	0.312560i
$367$	−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	$0.398977\pi$
$368$	−14.1534	+	7.12764i	−0.737797	+	0.371554i
$369$	4.33303	+	15.4712i	0.225568	+	0.805398i
$370$	−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	$0.174795\pi$
$374$	−2.67483	+	0.313389i	−0.138312	+	0.0162050i
$375$	39.4256	−	5.41676i	2.03593	−	0.279720i
$376$	25.3249	+	4.44389i	1.30603	+	0.229176i
$377$		−	2.87443i		−	0.148040i
$378$		0			0
$379$		−	18.8285i		−	0.967153i	−0.875302	−	0.483576i	$-0.839337\pi$
$379$		−	18.8285i		−	0.967153i	0.875302	−	0.483576i	$-0.160663\pi$
$380$	27.7631	−	6.59612i	1.42422	−	0.338374i
$381$	−28.2144	+	3.87643i	−1.44547	+	0.198595i
$382$	−0.202931	−	1.73205i	−0.0103829	−	0.0886194i
$383$	−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
$387$	−6.20174	−	22.1435i	−0.315252	−	1.12562i
$388$	7.75735	−	25.9634i	0.393820	−	1.31809i
$389$	12.6579	−	7.30807i	0.641783	−	0.370534i	−0.143518	−	0.989648i	$-0.545841\pi$
$389$	12.6579	−	7.30807i	0.641783	−	0.370534i	0.785301	+	0.619114i	$0.212508\pi$
$390$	−2.07329	−	8.01368i	−0.104985	−	0.405788i
$391$		−	2.28380i		−	0.115497i
$392$		0			0
$393$	−3.65197	−	1.48863i	−0.184217	−	0.0750914i
$394$	−14.6887	−	19.7191i	−0.740008	−	0.993432i
$395$	13.7623	+	23.8370i	0.692455	+	1.19937i
$396$	17.3337	−	9.61254i	0.871051	−	0.483048i
$397$	−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	0.649285	−	0.760545i	$-0.275068\pi$
$401$	6.31340	+	3.64505i	0.315276	+	0.182025i	−0.334009	+	0.942570i	$0.608402\pi$
$402$	−21.3522	−	5.91929i	−1.06495	−	0.295227i
$403$	−3.60879	+	2.08354i	−0.179767	+	0.103788i
$404$	−3.30059	−	13.8922i	−0.164210	−	0.691162i
$405$	35.7463	−	0.806210i	1.77625	−	0.0400609i
$406$		0			0
$407$	14.1724			0.702502
$408$	−1.50196	+	2.39158i	−0.0743583	+	0.118401i
$409$	−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	$0.999693\pi$
$410$	−3.50140	−	29.8851i	−0.172922	−	1.47592i
$411$	−9.77624	−	12.5930i	−0.482226	−	0.621167i
$412$	−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
$416$	−4.80319	+	0.286389i	−0.235496	+	0.0140414i
$417$	19.0564	−	2.61819i	0.933194	−	0.128213i
$418$	−10.0229	−	13.4554i	−0.490237	−	0.658124i
$419$	−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	$0.557074\pi$
$422$	0.939643	+	1.26143i	0.0457411	+	0.0614057i
$423$	6.76093	−	26.4202i	0.328728	−	1.28459i
$424$	−1.31965	−	1.10546i	−0.0640879	−	0.0536860i
$425$	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
$429$	−3.84441	+	2.98450i	−0.185610	+	0.144093i
$430$	5.01146	+	42.7736i	0.241674	+	2.06273i
$431$	−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	$0.834705\pi$
$432$	3.53818	−	20.4812i	0.170231	−	0.985404i
$433$	−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
$436$	6.23238	−	1.48073i	0.298477	−	0.0709139i
$437$	12.3218	−	7.11402i	0.589434	−	0.340310i
$438$	−0.925424	+	3.33820i	−0.0442185	+	0.159505i
$439$	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	$0.204686\pi$
$444$	9.31485	−	11.5803i	0.442063	−	0.549578i
$445$	11.4353	+	19.8065i	0.542086	+	0.938920i
$446$	19.9655	+	26.8029i	0.945395	+	1.26916i
$447$	−4.39181	+	10.7742i	−0.207725	+	0.509601i
$448$		0			0
$449$		−	14.4978i		−	0.684195i	−0.939664	−	0.342098i	$-0.888863\pi$
$449$		−	14.4978i		−	0.684195i	0.939664	−	0.342098i	$-0.111137\pi$
$450$	−45.3404	−	6.10734i	−2.13737	−	0.287903i
$451$	−15.3214	+	8.84580i	−0.721455	+	0.416532i
$452$	38.1528	+	11.3993i	1.79456	+	0.536178i
$453$	−14.0338	−	18.0773i	−0.659366	−	0.849345i
$454$	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	$0.0129248\pi$
$458$	−1.48595	−	12.6829i	−0.0694341	−	0.592631i
$459$	2.40692	+	1.78304i	0.112345	+	0.0832253i
$460$	−7.27627	−	30.6259i	−0.339258	−	1.42794i
$461$		−	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	$-0.884062\pi$
$463$		−	15.3304i		−	0.712462i	0.934398	−	0.356231i	$-0.115938\pi$
$464$	−7.41536	+	11.3016i	−0.344249	+	0.524663i
$465$	4.58845	+	33.3968i	0.212784	+	1.54874i
$466$	−10.6382	+	1.24640i	−0.492807	+	0.0577384i
$467$	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
$471$	−3.26750	+	2.53663i	−0.150558	+	0.116882i
$472$	14.3116	−	17.0846i	0.658746	−	0.786381i
$473$	21.9290	−	12.6607i	1.00830	−	0.582141i
$474$	−4.25065	−	16.4296i	−0.195239	−	0.754637i
$475$			38.7272i			1.77692i
$476$		0			0
$477$	−1.27648	+	1.30559i	−0.0584459	+	0.0597790i
$478$	10.4931	−	7.81634i	0.479945	−	0.357511i
$479$	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	$0.777787\pi$
$480$	−12.5217	+	36.8566i	−0.571536	+	1.68226i
$481$	−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
$486$	−21.3716	−	5.40885i	−0.969434	−	0.245350i
$487$	13.3691	−	7.71865i	0.605811	−	0.349765i	−0.165513	−	0.986208i	$-0.552928\pi$
$487$	13.3691	−	7.71865i	0.605811	−	0.349765i	0.771324	+	0.636442i	$0.219595\pi$
$488$	27.1518	+	4.76448i	1.22911	+	0.215678i
$489$	−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	$0.867214\pi$
$492$	−2.84207	+	18.3330i	−0.128130	+	0.826516i
$493$	−0.974025	−	1.68706i	−0.0438679	−	0.0759814i
$494$	4.29084	−	0.502725i	0.193054	−	0.0226187i
$495$	10.6184	+	37.9131i	0.477259	+	1.70407i
$496$	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	0.955385	−	0.295362i	$-0.0954403\pi$
$499$	26.2986	+	15.1835i	1.17729	+	0.679707i	0.221902	+	0.975069i	$0.428774\pi$
$500$	44.0292	+	13.1551i	1.96904	+	0.588312i
$501$	4.56539	+	33.2290i	0.203967	+	1.48456i
$502$	−3.50435	+	2.61039i	−0.156407	+	0.116507i
$503$	−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
$506$	−14.8428	+	11.0564i	−0.659844	+	0.491518i
$507$	2.89424	+	21.0656i	0.128538	+	0.935556i
$508$	−31.5089	−	9.41423i	−1.39798	−	0.417689i
$509$	−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
$513$	−2.12256	+	18.5403i	−0.0937133	+	0.818574i
$514$	−10.3508	+	1.21272i	−0.456554	+	0.0534909i
$515$	−20.8748	−	36.1563i	−0.919855	−	1.59324i
$516$	4.06777	−	26.2395i	0.179074	−	1.15513i
$517$	30.0299			1.32071
$518$		0			0
$519$	−3.65161	+	8.95827i	−0.160288	+	0.393225i
$520$	1.65197	−	9.41423i	0.0724435	−	0.412841i
$521$	−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	$0.596325\pi$
$522$	11.3482	+	8.76189i	0.496698	+	0.383498i
$523$	−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
$528$	22.8147	−	1.81670i	0.992882	−	0.0790617i
$529$	3.65243	+	6.32620i	0.158801	+	0.275052i
$530$	2.74237	−	2.04279i	0.119121	−	0.0887332i
$531$	−16.9026	−	16.5256i	−0.733509	−	0.717152i
$532$		0			0
$533$		−	4.55539i		−	0.197316i
$534$	−3.53194	−	13.6516i	−0.152842	−	0.590764i
$535$	4.24264	−	2.44949i	0.183425	−	0.105901i
$536$	−19.6130	−	16.4297i	−0.847152	−	0.709654i
$537$	−26.5141	+	20.5835i	−1.14417	+	0.888245i
$538$	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	$0.237769\pi$
$542$	33.1272	−	3.88127i	1.42294	−	0.166715i
$543$	2.56349	+	18.6582i	0.110010	+	0.800700i
$544$	−2.72205	+	1.79569i	−0.116707	+	0.0769898i
$545$			12.7247i			0.545066i
$546$		0			0
$547$			5.44070i			0.232628i	0.993213	+	0.116314i	$0.0371078\pi$
$547$			5.44070i			0.232628i	−0.993213	+	0.116314i	$0.962892\pi$
$548$	−4.25519	−	17.9101i	−0.181773	−	0.765081i
$549$	7.24867	−	28.3261i	0.309366	−	1.20893i
$550$	−5.86223	−	50.0351i	−0.249966	−	2.13350i
$551$	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
$555$	18.1033	+	23.3193i	0.768442	+	0.989848i
$556$	21.2815	+	6.35850i	0.902537	+	0.269660i
$557$	−3.84264	+	2.21855i	−0.162818	+	0.0940030i	−0.579195	−	0.815189i	$-0.696633\pi$
$557$	−3.84264	+	2.21855i	−0.162818	+	0.0940030i	0.416377	+	0.909192i	$0.363300\pi$
$558$	2.77462	−	20.5986i	0.117459	−	0.872007i
$559$			6.52001i			0.275767i
$560$		0			0
$561$	−1.24504	+	3.05438i	−0.0525657	+	0.128956i
$562$	19.6750	+	26.4129i	0.829940	+	1.11416i
$563$	−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	$-0.475222\pi$
$564$	19.7372	−	24.5375i	0.831086	−	1.03322i
$565$	−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	$0.0477336\pi$
$569$	38.4653	+	22.2079i	1.61255	+	0.931005i	0.623771	+	0.781607i	$0.285600\pi$
$570$	9.33657	−	33.6790i	0.391066	−	1.41066i
$571$	2.15883	−	1.24640i	0.0903442	−	0.0521603i	−0.454147	−	0.890927i	$-0.650056\pi$
$571$	2.15883	−	1.24640i	0.0903442	−	0.0521603i	0.544491	+	0.838766i	$0.316723\pi$
$572$	−5.46762	+	1.29903i	−0.228613	+	0.0543152i
$573$	−1.97783	−	0.806210i	−0.0826249	−	0.0336799i
$574$		0			0
$575$	42.7205			1.78157
$576$	13.5106	−	19.8360i	0.562940	−	0.826498i
$577$	−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	$-0.442233\pi$
$578$	2.74295	+	23.4115i	0.114092	+	0.973791i
$579$	−21.5942	+	16.7640i	−0.897423	+	0.696690i
$580$	−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
$584$	−2.56862	+	3.06630i	−0.106290	+	0.126884i
$585$	−9.82139	−	2.51330i	−0.406064	−	0.103912i
$586$	1.02010	+	1.36944i	0.0421398	+	0.0565711i
$587$	−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
$590$	26.4466	+	35.5035i	1.08879	+	1.46166i
$591$	−29.8345	+	4.09902i	−1.22723	+	0.168611i
$592$	15.3270	−	7.71865i	0.629935	−	0.317234i
$593$	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
$597$	−4.85140	−	6.24921i	−0.198555	−	0.255763i
$598$	−0.554563	−	4.73329i	−0.0226778	−	0.193558i
$599$	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	$0.706292\pi$
$600$	−44.7367	−	28.0956i	−1.82637	−	1.14700i
$601$	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
$604$	−6.10833	−	25.7100i	−0.248544	−	1.04612i
$605$	0.300273	−	0.173363i	0.0122078	−	0.00704820i
$606$	−16.8524	−	4.67186i	−0.684582	−	0.189781i
$607$	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
$612$	1.67744	+	3.02482i	0.0678064	+	0.122271i
$613$	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	$0.628137\pi$
$614$	−28.7472	−	38.5920i	−1.16014	−	1.55745i
$615$	−34.1257	−	13.9105i	−1.37608	−	0.560924i
$616$		0			0
$617$		−	28.7008i		−	1.15545i	−0.816232	−	0.577724i	$-0.803941\pi$
$617$		−	28.7008i		−	1.15545i	0.816232	−	0.577724i	$-0.196059\pi$
$618$	6.44746	+	24.9207i	0.259355	+	1.00246i
$619$	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	$0.180472\pi$
$620$	−11.1434	+	37.2964i	−0.447532	+	1.49786i
$621$	20.4521	+	2.34142i	0.820713	+	0.0939581i
$622$	−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
$626$	−1.53467	−	13.0987i	−0.0613378	−	0.523529i
$627$	−20.3577	+	2.79699i	−0.813008	+	0.111701i
$628$	−4.64712	+	1.10409i	−0.185440	+	0.0440580i
$629$			2.47316i			0.0986115i
$630$		0			0
$631$		−	15.3304i		−	0.610292i	−0.952306	−	0.305146i	$-0.901295\pi$
$631$		−	15.3304i		−	0.610292i	0.952306	−	0.305146i	$-0.0987052\pi$
$632$	3.38685	−	19.3010i	0.134722	−	0.767753i
$633$	1.90852	−	0.262216i	0.0758570	−	0.0104221i
$634$	−37.9147	+	4.44218i	−1.50579	+	0.176421i
$635$	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
$639$	26.4518	−	7.40837i	1.04642	−	0.293070i
$640$	−30.7817	+	32.7529i	−1.21675	+	1.29467i
$641$	−11.6038	+	6.69943i	−0.458321	+	0.264612i	−0.711338	−	0.702850i	$-0.751910\pi$
$641$	−11.6038	+	6.69943i	−0.458321	+	0.264612i	0.253017	+	0.967462i	$0.418577\pi$
$642$	−2.92424	+	0.756556i	−0.115410	+	0.0298589i
$643$		−	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
$646$	2.34803	−	1.74905i	0.0923822	−	0.0688155i
$647$	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	$0.706516\pi$
$648$	−19.8774	−	15.9024i	−0.780859	−	0.624707i
$649$	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	−0.234561	−	0.972101i	$-0.575365\pi$
$653$	−30.5038	−	17.6114i	−1.19371	−	0.689186i	−0.959145	+	0.282915i	$0.908698\pi$
$654$	2.09591	−	7.56041i	0.0819567	−	0.295635i
$655$	7.83384	−	4.52287i	0.306094	−	0.176723i
$656$	−11.7519	+	17.9108i	−0.458833	+	0.699299i
$657$	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	$0.218017\pi$
$660$	−6.96467	+	44.9262i	−0.271100	+	1.74875i
$661$	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	$0.739539\pi$
$662$	20.4979	−	2.40159i	0.796675	−	0.0933404i
$663$	−0.520812	−	0.670870i	−0.0202266	−	0.0260544i
$664$	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
$668$	−11.0874	+	37.1090i	−0.428986	+	1.43579i
$669$	40.5523	−	5.57156i	1.56784	−	0.215409i
$670$	40.7578	−	30.3605i	1.57461	−	1.17293i
$671$	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	$0.490670\pi$
$674$	35.9322	−	26.7659i	1.38406	−	1.03099i
$675$	−33.3534	+	45.0236i	−1.28377	+	1.73296i
$676$	−7.02891	+	23.5253i	−0.270343	+	0.904821i
$677$	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
$681$	16.8261	−	13.0625i	0.644778	−	0.500556i
$682$	22.7314	−	2.66327i	0.870431	−	0.101982i
$683$	−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	$0.889385\pi$
$684$	−11.0947	+	18.4726i	−0.424216	+	0.706319i
$685$	36.5672			1.39716
$686$		0			0
$687$	−14.4825	−	5.90343i	−0.552543	−	0.225230i
$688$	16.8201	−	25.6352i	0.641261	−	0.977333i
$689$	0.448349	−	0.258854i	0.0170807	−	0.00986156i
$690$	−37.1518	−	10.2993i	−1.41434	−	0.392088i
$691$	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
$696$	7.73903	+	14.6348i	0.293347	+	0.554731i
$697$	−1.54364	−	2.67366i	−0.0584694	−	0.101272i
$698$	−37.4853	+	27.9228i	−1.41884	+	1.05689i
$699$	−4.95173	+	12.1478i	−0.187292	+	0.459472i
$700$		0			0
$701$			38.1529i			1.44101i	0.693448	+	0.720507i	$0.256091\pi$
$701$			38.1529i			1.44101i	−0.693448	+	0.720507i	$0.743909\pi$
$702$	5.42143	+	3.11099i	0.204619	+	0.117417i
$703$	−13.3435	+	7.70390i	−0.503261	+	0.290558i
$704$	24.8487	+	8.99771i	0.936519	+	0.339114i
$705$	38.3590	+	49.4111i	1.44468	+	1.86093i
$706$	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	$0.251082\pi$
$710$	−51.0958	+	5.98651i	−1.91759	+	0.224670i
$711$	−20.1358	−	5.15276i	−0.755150	−	0.193243i
$712$	2.81420	−	16.0375i	0.105466	−	0.601032i
$713$			19.4083i			0.726848i
$714$		0			0
$715$		−	11.1633i		−	0.417483i
$716$	−37.7091	+	8.95915i	−1.40925	+	0.334819i
$717$	−2.18122	−	15.8759i	−0.0814592	−	0.592896i
$718$	5.53724	+	47.2612i	0.206648	+	1.76377i
$719$	−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
$723$	21.4259	−	16.6334i	0.796838	−	0.618604i
$724$	−6.22565	+	20.8369i	−0.231374	+	0.774396i
$725$	31.5580	−	18.2200i	1.17203	−	0.676674i
$726$	−0.206963	+	0.0535453i	−0.00768112	+	0.00198725i
$727$		−	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
$730$	−4.74657	−	6.37208i	−0.175678	−	0.235841i
$731$	2.20936	+	3.82673i	0.0817163	+	0.141537i
$732$	21.1611	−	26.3077i	0.782135	−	0.972359i
$733$	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
$738$	17.9847	+	13.8859i	0.662025	+	0.511146i
$739$	25.1030	−	14.4932i	0.923429	−	0.533142i	0.0387013	−	0.999251i	$-0.487678\pi$
$739$	25.1030	−	14.4932i	0.923429	−	0.533142i	0.884727	+	0.466109i	$0.154345\pi$
$740$	7.87961	+	33.1653i	0.289660	+	1.21918i
$741$	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	$0.561109\pi$
$744$	12.7641	−	20.3243i	0.467954	−	0.745126i
$745$	−13.3435	−	23.1117i	−0.488870	−	0.846747i
$746$	0.162308	+	1.38532i	0.00594251	+	0.0507203i
$747$	11.9562	−	3.34859i	0.437456	−	0.122518i
$748$	−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	0.743689	−	0.668526i	$-0.233074\pi$
$751$	14.7045	+	8.48962i	0.536573	+	0.309791i	−0.207116	+	0.978316i	$0.566408\pi$
$752$	32.4763	−	16.3550i	1.18429	−	0.596406i
$753$	0.728453	+	5.30201i	0.0265463	+	0.193216i
$754$	−2.42838	−	3.26000i	−0.0884363	−	0.118722i
$755$	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	$0.563894\pi$
$758$	−15.9067	−	21.3541i	−0.577757	−	0.775617i
$759$	3.08539	+	22.4569i	0.111993	+	0.815132i
$760$	25.9147	−	30.9358i	0.940026	−	1.12216i
$761$	−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
$765$	−6.61603	+	1.85296i	−0.239203	+	0.0669938i
$766$	0.596206	+	5.08871i	0.0215418	+	0.183863i
$767$	3.35120	+	5.80445i	0.121005	+	0.209586i
$768$	23.6838	−	14.3901i	0.854617	−	0.519259i
$769$	−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
$772$	−30.7118	+	7.29669i	−1.10534	+	0.262614i
$773$	−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	$0.423519\pi$
$774$	−25.7409	−	19.8744i	−0.925239	−	0.714372i
$775$	−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
$780$	−9.12153	−	7.33708i	−0.326603	−	0.262710i
$781$	15.1240	+	26.1956i	0.541181	+	0.937353i
$782$	−1.92940	−	2.59015i	−0.0689953	−	0.0926235i
$783$	16.1067	−	6.99304i	0.575607	−	0.249911i
$784$		0			0
$785$		−	9.48806i		−	0.338643i
$786$	−5.39947	+	1.39695i	−0.192593	+	0.0498274i
$787$	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	$0.0647485\pi$
$788$	−33.3182	−	9.95483i	−1.18691	−	0.354626i
$789$	30.3780	−	23.5831i	1.08148	−	0.839581i
$790$	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
$794$	1.00337	+	8.56394i	0.0356083	+	0.303923i
$795$	−0.570059	−	4.14915i	−0.0202179	−	0.147155i
$796$	−2.11161	−	8.88779i	−0.0748442	−	0.315019i
$797$		−	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
$800$	−33.5901	−	50.9184i	−1.18759	−	1.80024i
$801$	−16.7312	−	4.28151i	−0.591166	−	0.151280i
$802$	10.2397	−	1.19971i	0.361577	−	0.0423632i
$803$	−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
$807$	−10.6361	−	13.7006i	−0.374408	−	0.482284i
$808$	−15.4797	−	12.9673i	−0.544576	−	0.456187i
$809$	−1.65777	+	0.957115i	−0.0582842	+	0.0336504i	−0.528859	−	0.848710i	$-0.677380\pi$
$809$	−1.65777	+	0.957115i	−0.0582842	+	0.0336504i	0.470575	+	0.882360i	$0.344047\pi$
$810$	39.8603	−	31.1137i	1.40055	−	1.09322i
$811$		−	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
$814$	16.0735	−	11.9732i	0.563378	−	0.419660i
$815$	−36.3351	−	62.9342i	−1.27276	−	2.20449i
$816$	0.317023	+	3.98128i	0.0110980	+	0.139373i
$817$	−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	0.474525	−	0.880242i	$-0.342620\pi$
$821$	−1.44771	−	0.835834i	−0.0505253	−	0.0291708i	−0.525050	+	0.851071i	$0.675953\pi$
$822$	−21.7265	−	6.02306i	−0.757798	−	0.210078i
$823$	23.7559	−	13.7155i	0.828078	−	0.478091i	−0.0251160	−	0.999685i	$-0.507996\pi$
$823$	23.7559	−	13.7155i	0.828078	−	0.478091i	0.853194	+	0.521593i	$0.174662\pi$
$824$	−5.13724	+	29.2761i	−0.178964	+	1.01988i
$825$	−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	$0.350927\pi$
$828$	20.3774	+	12.2387i	0.708164	+	0.425325i
$829$	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	$0.664476\pi$
$830$	−23.0954	+	2.70591i	−0.801652	+	0.0939234i
$831$	−39.7586	+	30.8655i	−1.37921	+	1.07071i
$832$	−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
$836$	−22.7348	−	6.79272i	−0.786300	−	0.234931i
$837$	−20.4547	−	15.1528i	−0.707017	−	0.523757i
$838$	−1.50711	+	1.12265i	−0.0520623	+	0.0387812i
$839$	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
$842$	−8.30031	+	6.18290i	−0.286048	+	0.213077i
$843$	39.9622	−	5.49049i	1.37637	−	0.189102i
$844$	2.13138	+	0.636813i	0.0733650	+	0.0219200i
$845$	−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
$849$	18.5090	+	23.8419i	0.635228	+	0.818253i
$850$	8.73138	−	1.02299i	0.299484	−	0.0350882i
$851$	8.49827	+	14.7194i	0.291317	+	0.504576i
$852$	31.3448	+	4.85921i	1.07385	+	0.166474i
$853$	−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
$856$	−3.43531	−	0.602812i	−0.117416	−	0.0206037i
$857$	−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	$0.396705\pi$
$858$	−1.83873	+	6.63269i	−0.0627732	+	0.226436i
$859$	−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	$0.0509773\pi$
$864$	−13.2902	−	26.2177i	−0.452142	−	0.891946i
$865$	−11.0946	−	19.2164i	−0.377228	−	0.653378i
$866$	−17.2956	+	12.8835i	−0.587728	+	0.437799i
$867$	26.7336	+	10.8973i	0.907920	+	0.370090i
$868$		0			0
$869$		−	22.8869i		−	0.776385i
$870$	−31.8369	+	8.23682i	−1.07937	+	0.279254i
$871$	6.66347	−	3.84716i	0.225783	−	0.130356i
$872$	5.81744	−	6.94460i	0.197004	−	0.235174i
$873$	−39.1401	+	10.9620i	−1.32469	+	0.371008i
$874$	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	$-0.249282\pi$
$878$	42.0053	−	4.92144i	1.41761	−	0.166091i
$879$	2.07194	−	0.284667i	0.0698847	−	0.00960159i
$880$	−28.7987	+	43.8915i	−0.970804	+	1.47958i
$881$		−	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	$0.153768\pi$
$883$			27.6059i			0.929012i	−0.885570	+	0.464506i	$0.846232\pi$
$884$	−0.226688	−	0.954128i	−0.00762433	−	0.0320908i
$885$	53.7160	−	7.38015i	1.80564	−	0.248081i
$886$	0.825451	+	7.04537i	0.0277316	+	0.236694i
$887$	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
$891$	−26.0764	−	14.2811i	−0.873593	−	0.478436i
$892$	45.2874	+	13.5310i	1.51634	+	0.453051i
$893$	−28.2736	+	16.3238i	−0.946139	+	0.546254i
$894$	4.12132	+	15.9297i	0.137838	+	0.532770i
$895$		−	76.9909i		−	2.57352i
$896$		0			0
$897$	−5.40493	−	2.20318i	−0.180465	−	0.0735621i
$898$	−12.2481	−	16.4426i	−0.408724	−	0.548696i
$899$	8.27753	+	14.3371i	0.276071	+	0.478169i
$900$	−56.5820	+	31.3780i	−1.88607	+	1.04593i
$901$	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
$906$	−31.1884	−	8.64612i	−1.03617	−	0.287248i
$907$	9.51618	−	5.49417i	0.315980	−	0.182431i	−0.333619	−	0.942708i	$-0.608270\pi$
$907$	9.51618	−	5.49417i	0.315980	−	0.182431i	0.649599	+	0.760277i	$0.274937\pi$
$908$	23.9305	−	5.68556i	0.794163	−	0.188682i
$909$	−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	$0.533959\pi$
$912$	−20.4928	+	14.1121i	−0.678585	+	0.467299i
$913$	6.83609	+	11.8404i	0.226241	+	0.391862i
$914$	−3.26779	−	27.8911i	−0.108089	−	0.922556i
$915$	41.1262	+	52.9757i	1.35959	+	1.75132i
$916$	−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	$0.0302113\pi$
$919$	47.7559	+	27.5719i	1.57532	+	0.909512i	0.579822	+	0.814743i	$0.303122\pi$
$920$	−34.1257	−	28.5869i	−1.12509	−	0.942481i
$921$	−58.3889	+	8.02216i	−1.92398	+	0.264339i
$922$	−14.6923	−	19.7238i	−0.483864	−	0.649569i
$923$	−7.78856			−0.256364
$924$		0			0
$925$	−46.2628			−1.52111
$926$	−12.9514	−	17.3868i	−0.425610	−	0.571365i
$927$	30.5423	+	7.81579i	1.00314	+	0.256704i
$928$	1.13777	+	19.0823i	0.0373493	+	0.626406i
$929$	−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
$933$	−36.5458	+	28.3713i	−1.19645	+	0.928835i
$934$	−3.46939	−	29.6118i	−0.113522	−	0.968929i
$935$	−3.78278	−	6.55197i	−0.123710	−	0.214272i
$936$	4.21108	+	5.86177i	0.137643	+	0.191598i
$937$	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
$940$	16.6961	+	70.2738i	0.544566	+	2.29208i
$941$	−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	$0.556774\pi$
$942$	−1.56280	+	5.63735i	−0.0509188	+	0.183675i
$943$	−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	$0.104985\pi$
$948$	−18.7009	−	15.0424i	−0.607378	−	0.488556i
$949$	−0.601466	−	1.04177i	−0.0195244	−	0.0338172i
$950$	32.7176	+	43.9221i	1.06150	+	1.42502i
$951$	−17.6480	+	43.2948i	−0.572275	+	1.40393i
$952$		0			0
$953$		−	39.8193i		−	1.28987i	−0.764236	−	0.644937i	$-0.776884\pi$
$953$		−	39.8193i		−	1.28987i	0.764236	−	0.644937i	$-0.223116\pi$
$954$	−0.344713	+	2.55912i	−0.0111605	+	0.0828547i
$955$	4.24264	−	2.44949i	0.137289	−	0.0792636i
$956$	5.29728	−	17.7297i	0.171326	−	0.573418i
$957$	11.8569	+	15.2732i	0.383280	+	0.493712i
$958$	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
$962$	0.600546	+	5.12576i	0.0193624	+	0.165261i
$963$	−0.917118	+	3.58388i	−0.0295537	+	0.115489i
$964$	30.4725	−	7.23984i	0.981453	−	0.233179i
$965$		−	62.7045i		−	2.01853i
$966$		0			0
$967$		−	23.4388i		−	0.753741i	−0.926266	−	0.376871i	$-0.877000\pi$
$967$		−	23.4388i		−	0.753741i	0.926266	−	0.376871i	$-0.123000\pi$
$968$	−0.243134	−	0.0426641i	−0.00781462	−	0.00137127i
$969$	−0.488088	−	3.55253i	−0.0156797	−	0.114124i
$970$	75.6054	−	8.85811i	2.42754	−	0.284417i
$971$	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
$975$	12.5492	−	9.74225i	0.401897	−	0.312002i
$976$	34.8191	−	17.5349i	1.11453	−	0.561278i
$977$	−9.58812	+	5.53570i	−0.306751	+	0.177103i	−0.645472	−	0.763784i	$-0.723339\pi$
$977$	−9.58812	+	5.53570i	−0.306751	+	0.177103i	0.338721	+	0.940887i	$0.390006\pi$
$978$	11.2225	+	43.3774i	0.358857	+	1.38706i
$979$		−	19.0171i		−	0.607790i
$980$		0			0
$981$	−6.87062	−	6.71741i	−0.219362	−	0.214470i
$982$	−45.9515	+	34.2293i	−1.46637	+	1.09230i
$983$	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	$0.663195\pi$
$984$	12.2648	+	23.1933i	0.390989	+	0.739374i
$985$	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
$990$	44.0725	+	34.0282i	1.40072	+	1.08149i
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	−0.757863	−	0.652413i	$-0.773757\pi$
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	0.186075	+	0.982536i	$0.440423\pi$
$992$	23.1327	−	15.2603i	0.734465	−	0.484515i
$993$	9.54109	−	23.4066i	0.302777	−	0.742785i
$994$		0			0
$995$	18.1463			0.575275
$996$	14.1679	+	2.19637i	0.448926	+	0.0695946i
$997$	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	$0.604844\pi$
$998$	42.6537	−	4.99740i	1.35018	−	0.158190i
$999$	−22.1479	−	2.53557i	−0.700728	−	0.0802219i

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

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a_p

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)

Twists

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

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

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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.d.275.11

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