LMFDB - Embedded newform 702.2.t.a.415.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(181,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.181"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$702 = 2 \cdot 3^{3} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	702.t (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.7
Character	$\chi$	$=$	702.415
Dual form			702.2.t.a.181.7

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.73536 + 1.57926i) q^{5} +(-1.36392 + 0.787458i) q^{7} +1.00000i q^{8} -3.15852 q^{10} +(-3.26194 + 1.88328i) q^{11} +(0.899453 + 3.49156i) q^{13} +(0.787458 - 1.36392i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.06565 q^{17} +3.76656i q^{19} +(2.73536 - 1.57926i) q^{20} +(1.88328 - 3.26194i) q^{22} +(1.84873 - 3.20209i) q^{23} +(2.48812 + 4.30955i) q^{25} +(-2.52473 - 2.57405i) q^{26} +1.57492i q^{28} +(-0.109128 - 0.189015i) q^{29} +(2.65792 + 1.53455i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.11904 - 3.53283i) q^{34} -4.97440 q^{35} +0.292126i q^{37} +(-1.88328 - 3.26194i) q^{38} +(-1.57926 + 2.73536i) q^{40} +(6.39272 + 3.69084i) q^{41} +(-3.05835 - 5.29722i) q^{43} +3.76656i q^{44} +3.69746i q^{46} +(-6.17888 + 3.56738i) q^{47} +(-2.25982 + 3.91412i) q^{49} +(-4.30955 - 2.48812i) q^{50} +(3.47351 + 0.966830i) q^{52} +14.4175 q^{53} -11.8968 q^{55} +(-0.787458 - 1.36392i) q^{56} +(0.189015 + 0.109128i) q^{58} +(-9.04745 - 5.22355i) q^{59} +(3.00007 + 5.19627i) q^{61} -3.06910 q^{62} -1.00000 q^{64} +(-3.05375 + 10.9711i) q^{65} +(-6.33583 - 3.65799i) q^{67} +(-3.53283 + 6.11904i) q^{68} +(4.30796 - 2.48720i) q^{70} -0.772410i q^{71} +13.5342i q^{73} +(-0.146063 - 0.252988i) q^{74} +(3.26194 + 1.88328i) q^{76} +(2.96601 - 5.13728i) q^{77} +(6.34033 + 10.9818i) q^{79} -3.15852i q^{80} -7.38168 q^{82} +(0.314795 - 0.181747i) q^{83} +(-19.3271 - 11.1585i) q^{85} +(5.29722 + 3.05835i) q^{86} +(-1.88328 - 3.26194i) q^{88} +7.06555i q^{89} +(-3.97624 - 4.05392i) q^{91} +(-1.84873 - 3.20209i) q^{92} +(3.56738 - 6.17888i) q^{94} +(-5.94838 + 10.3029i) q^{95} +(-0.535716 + 0.309296i) q^{97} -4.51964i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100})$ 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$ .

$n$	$379$	$677$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.73536	+	1.57926i	1.22329	+	0.706266i	0.965618	−	0.259967i	$-0.0837115\pi$
$5$	2.73536	+	1.57926i	1.22329	+	0.706266i	0.257671	+	0.966233i	$0.417045\pi$
$6$		0			0
$7$	−1.36392	+	0.787458i	−0.515512	+	0.297631i	−0.735097	−	0.677962i	$-0.762863\pi$
$7$	−1.36392	+	0.787458i	−0.515512	+	0.297631i	0.219584	+	0.975594i	$0.429530\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.15852			−0.998811
$11$	−3.26194	+	1.88328i	−0.983511	+	0.567830i	−0.903328	−	0.428950i	$-0.858884\pi$
$11$	−3.26194	+	1.88328i	−0.983511	+	0.567830i	−0.0801828	+	0.996780i	$0.525550\pi$
$12$		0			0
$13$	0.899453	+	3.49156i	0.249463	+	0.968384i
$13$	0.899453	+	3.49156i	0.249463	+	0.968384i
$14$	0.787458	−	1.36392i	0.210457	−	0.364522i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−7.06565			−1.71367			−0.856836	−	0.515588i	$-0.827573\pi$
$17$	−7.06565			−1.71367			−0.856836	+	0.515588i	$0.827573\pi$
$18$		0			0
$19$			3.76656i			0.864108i	0.901848	+	0.432054i	$0.142211\pi$
$19$			3.76656i			0.864108i	−0.901848	+	0.432054i	$0.857789\pi$
$20$	2.73536	−	1.57926i	0.611644	−	0.353133i
$21$		0			0
$22$	1.88328	−	3.26194i	0.401517	−	0.695447i
$23$	1.84873	−	3.20209i	0.385487	−	0.667683i	−0.606350	−	0.795198i	$-0.707367\pi$
$23$	1.84873	−	3.20209i	0.385487	−	0.667683i	0.991837	+	0.127515i	$0.0407002\pi$
$24$		0			0
$25$	2.48812	+	4.30955i	0.497624	+	0.861910i
$26$	−2.52473	−	2.57405i	−0.495140	−	0.504813i
$27$		0			0
$28$			1.57492i			0.297631i
$29$	−0.109128	−	0.189015i	−0.0202645	−	0.0350992i	0.855715	−	0.517447i	$-0.173118\pi$
$29$	−0.109128	−	0.189015i	−0.0202645	−	0.0350992i	−0.875980	+	0.482348i	$0.839784\pi$
$30$		0			0
$31$	2.65792	+	1.53455i	0.477376	+	0.275613i	0.719322	−	0.694676i	$-0.244452\pi$
$31$	2.65792	+	1.53455i	0.477376	+	0.275613i	−0.241946	+	0.970290i	$0.577786\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	6.11904	−	3.53283i	1.04941	−	0.605875i
$35$	−4.97440			−0.840827
$36$		0			0
$37$			0.292126i			0.0480251i	0.999712	+	0.0240126i	$0.00764417\pi$
$37$			0.292126i			0.0480251i	−0.999712	+	0.0240126i	$0.992356\pi$
$38$	−1.88328	−	3.26194i	−0.305508	−	0.529156i
$39$		0			0
$40$	−1.57926	+	2.73536i	−0.249703	+	0.432498i
$41$	6.39272	+	3.69084i	0.998375	+	0.576412i	0.907767	−	0.419474i	$-0.137786\pi$
$41$	6.39272	+	3.69084i	0.998375	+	0.576412i	0.0906081	+	0.995887i	$0.471119\pi$
$42$		0			0
$43$	−3.05835	−	5.29722i	−0.466395	−	0.807819i	0.532869	−	0.846198i	$-0.321114\pi$
$43$	−3.05835	−	5.29722i	−0.466395	−	0.807819i	−0.999263	+	0.0383789i	$0.987781\pi$
$44$			3.76656i			0.567830i
$45$		0			0
$46$			3.69746i			0.545161i
$47$	−6.17888	+	3.56738i	−0.901282	+	0.520356i	−0.877616	−	0.479364i	$-0.840867\pi$
$47$	−6.17888	+	3.56738i	−0.901282	+	0.520356i	−0.0236662	+	0.999720i	$0.507534\pi$
$48$		0			0
$49$	−2.25982	+	3.91412i	−0.322831	+	0.559160i
$50$	−4.30955	−	2.48812i	−0.609462	−	0.351873i
$51$		0			0
$52$	3.47351	+	0.966830i	0.481689	+	0.134075i
$53$	14.4175			1.98040			0.990201	−	0.139649i	$-0.0445973\pi$
$53$	14.4175			1.98040			0.990201	+	0.139649i	$0.0445973\pi$
$54$		0			0
$55$	−11.8968			−1.60416
$56$	−0.787458	−	1.36392i	−0.105229	−	0.182261i
$57$		0			0
$58$	0.189015	+	0.109128i	0.0248188	+	0.0143292i
$59$	−9.04745	−	5.22355i	−1.17788	−	0.680048i	−0.222355	−	0.974966i	$-0.571374\pi$
$59$	−9.04745	−	5.22355i	−1.17788	−	0.680048i	−0.955523	+	0.294918i	$0.904708\pi$
$60$		0			0
$61$	3.00007	+	5.19627i	0.384119	+	0.665314i	0.991647	−	0.128985i	$-0.0411718\pi$
$61$	3.00007	+	5.19627i	0.384119	+	0.665314i	−0.607527	+	0.794299i	$0.707838\pi$
$62$	−3.06910			−0.389776
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.05375	+	10.9711i	−0.378771	+	1.36080i
$66$		0			0
$67$	−6.33583	−	3.65799i	−0.774045	−	0.446895i	0.0602708	−	0.998182i	$-0.480804\pi$
$67$	−6.33583	−	3.65799i	−0.774045	−	0.446895i	−0.834316	+	0.551287i	$0.814137\pi$
$68$	−3.53283	+	6.11904i	−0.428418	+	0.742042i
$69$		0			0
$70$	4.30796	−	2.48720i	0.514900	−	0.297277i
$71$		−	0.772410i		−	0.0916682i	−0.998949	−	0.0458341i	$-0.985405\pi$
$71$		−	0.772410i		−	0.0916682i	0.998949	−	0.0458341i	$-0.0145946\pi$
$72$		0			0
$73$			13.5342i			1.58406i	0.610480	+	0.792032i	$0.290976\pi$
$73$			13.5342i			1.58406i	−0.610480	+	0.792032i	$0.709024\pi$
$74$	−0.146063	−	0.252988i	−0.0169795	−	0.0294093i
$75$		0			0
$76$	3.26194	+	1.88328i	0.374170	+	0.216027i
$77$	2.96601	−	5.13728i	0.338008	−	0.585447i
$78$		0			0
$79$	6.34033	+	10.9818i	0.713343	+	1.23555i	0.963595	+	0.267366i	$0.0861532\pi$
$79$	6.34033	+	10.9818i	0.713343	+	1.23555i	−0.250252	+	0.968181i	$0.580513\pi$
$80$		−	3.15852i		−	0.353133i
$81$		0			0
$82$	−7.38168			−0.815170
$83$	0.314795	−	0.181747i	0.0345533	−	0.0199494i	−0.482624	−	0.875828i	$-0.660316\pi$
$83$	0.314795	−	0.181747i	0.0345533	−	0.0199494i	0.517177	+	0.855878i	$0.326983\pi$
$84$		0			0
$85$	−19.3271	−	11.1585i	−2.09632	−	1.21031i
$86$	5.29722	+	3.05835i	0.571214	+	0.329791i
$87$		0			0
$88$	−1.88328	−	3.26194i	−0.200758	−	0.347724i
$89$			7.06555i			0.748947i	0.927238	+	0.374473i	$0.122176\pi$
$89$			7.06555i			0.748947i	−0.927238	+	0.374473i	$0.877824\pi$
$90$		0			0
$91$	−3.97624	−	4.05392i	−0.416823	−	0.424966i
$92$	−1.84873	−	3.20209i	−0.192743	−	0.333841i
$93$		0			0
$94$	3.56738	−	6.17888i	0.367947	−	0.637303i
$95$	−5.94838	+	10.3029i	−0.610290	+	1.05705i
$96$		0			0
$97$	−0.535716	+	0.309296i	−0.0543937	+	0.0314042i	−0.526950	−	0.849896i	$-0.676665\pi$
$97$	−0.535716	+	0.309296i	−0.0543937	+	0.0314042i	0.472557	+	0.881300i	$0.343331\pi$
$98$		−	4.51964i		−	0.456552i
$99$		0			0
$100$	4.97624			0.497624
$101$	4.16781	+	7.21887i	0.414713	+	0.718304i	0.995398	−	0.0958241i	$-0.0305486\pi$
$101$	4.16781	+	7.21887i	0.414713	+	0.718304i	−0.580685	+	0.814128i	$0.697215\pi$
$102$		0			0
$103$	4.94838	−	8.57084i	0.487578	−	0.844510i	−0.512320	−	0.858795i	$-0.671214\pi$
$103$	4.94838	−	8.57084i	0.487578	−	0.844510i	0.999898	+	0.0142849i	$0.00454717\pi$
$104$	−3.49156	+	0.899453i	−0.342376	+	0.0881987i
$105$		0			0
$106$	−12.4860	+	7.20877i	−1.21274	+	0.700178i
$107$	−0.115559			−0.0111715			−0.00558574	−	0.999984i	$-0.501778\pi$
$107$	−0.115559			−0.0111715			−0.00558574	+	0.999984i	$0.501778\pi$
$108$		0			0
$109$		−	14.1301i		−	1.35342i	−0.736251	−	0.676708i	$-0.763406\pi$
$109$		−	14.1301i		−	1.35342i	0.736251	−	0.676708i	$-0.236594\pi$
$110$	10.3029	−	5.94838i	0.982342	−	0.567155i
$111$		0			0
$112$	1.36392	+	0.787458i	0.128878	+	0.0744078i
$113$	9.70968	−	16.8177i	0.913410	−	1.58207i	0.104197	−	0.994557i	$-0.466773\pi$
$113$	9.70968	−	16.8177i	0.913410	−	1.58207i	0.809213	−	0.587516i	$-0.199894\pi$
$114$		0			0
$115$	10.1139	−	5.83925i	0.943124	−	0.544513i
$116$	−0.218255			−0.0202645
$117$		0			0
$118$	10.4471			0.961733
$119$	9.63697	−	5.56391i	0.883420	−	0.510043i
$120$		0			0
$121$	1.59349	−	2.76001i	0.144863	−	0.250910i
$122$	−5.19627	−	3.00007i	−0.470448	−	0.271613i
$123$		0			0
$124$	2.65792	−	1.53455i	0.238688	−	0.137807i
$125$		−	0.0750557i		−	0.00671318i
$126$		0			0
$127$	5.42904			0.481750			0.240875	−	0.970556i	$-0.422566\pi$
$127$	5.42904			0.481750			0.240875	+	0.970556i	$0.422566\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.84094	−	11.0282i	−0.249167	−	0.967233i
$131$	−6.34342	+	10.9871i	−0.554227	+	0.959950i	0.443736	+	0.896158i	$0.353653\pi$
$131$	−6.34342	+	10.9871i	−0.554227	+	0.959950i	−0.997963	+	0.0637922i	$0.979681\pi$
$132$		0			0
$133$	−2.96601	−	5.13728i	−0.257186	−	0.445459i
$134$	7.31599			0.632005
$135$		0			0
$136$		−	7.06565i		−	0.605875i
$137$	6.36997	−	3.67770i	0.544223	−	0.314207i	−0.202566	−	0.979269i	$-0.564928\pi$
$137$	6.36997	−	3.67770i	0.544223	−	0.314207i	0.746789	+	0.665061i	$0.231595\pi$
$138$		0			0
$139$	3.65559	−	6.33167i	0.310063	−	0.537046i	−0.668312	−	0.743881i	$-0.732983\pi$
$139$	3.65559	−	6.33167i	0.310063	−	0.537046i	0.978376	+	0.206835i	$0.0663164\pi$
$140$	−2.48720	+	4.30796i	−0.210207	+	0.364089i
$141$		0			0
$142$	0.386205	+	0.668927i	0.0324096	+	0.0561351i
$143$	−9.50955	−	9.69532i	−0.795228	−	0.810764i
$144$		0			0
$145$		−	0.689364i		−	0.0572485i
$146$	−6.76712	−	11.7210i	−0.560051	−	0.970037i
$147$		0			0
$148$	0.252988	+	0.146063i	0.0207955	+	0.0120063i
$149$	20.5800	+	11.8819i	1.68598	+	0.973401i	0.957544	+	0.288289i	$0.0930862\pi$
$149$	20.5800	+	11.8819i	1.68598	+	0.973401i	0.728437	+	0.685113i	$0.240247\pi$
$150$		0			0
$151$	8.99711	−	5.19448i	0.732174	−	0.422721i	−0.0870428	−	0.996205i	$-0.527742\pi$
$151$	8.99711	−	5.19448i	0.732174	−	0.422721i	0.819217	+	0.573484i	$0.194408\pi$
$152$	−3.76656			−0.305508
$153$		0			0
$154$			5.93202i			0.478016i
$155$	4.84690	+	8.39509i	0.389313	+	0.674310i
$156$		0			0
$157$	4.57412	−	7.92261i	0.365054	−	0.632293i	−0.623730	−	0.781640i	$-0.714384\pi$
$157$	4.57412	−	7.92261i	0.365054	−	0.632293i	0.988785	+	0.149347i	$0.0477170\pi$
$158$	−10.9818	−	6.34033i	−0.873663	−	0.504410i
$159$		0			0
$160$	1.57926	+	2.73536i	0.124851	+	0.216249i
$161$			5.82319i			0.458932i
$162$		0			0
$163$			13.5935i			1.06473i	0.846516	+	0.532363i	$0.178696\pi$
$163$			13.5935i			1.06473i	−0.846516	+	0.532363i	$0.821304\pi$
$164$	6.39272	−	3.69084i	0.499188	−	0.288206i
$165$		0			0
$166$	−0.181747	+	0.314795i	−0.0141063	+	0.0244329i
$167$	−6.20607	−	3.58308i	−0.480240	−	0.277267i	0.240276	−	0.970705i	$-0.422762\pi$
$167$	−6.20607	−	3.58308i	−0.480240	−	0.277267i	−0.720517	+	0.693438i	$0.756095\pi$
$168$		0			0
$169$	−11.3820	+	6.28099i	−0.875536	+	0.483153i
$170$	22.3170			1.71164
$171$		0			0
$172$	−6.11671			−0.466395
$173$	1.50582	+	2.60815i	0.114485	+	0.198294i	0.917574	−	0.397566i	$-0.130145\pi$
$173$	1.50582	+	2.60815i	0.114485	+	0.198294i	−0.803089	+	0.595859i	$0.796812\pi$
$174$		0			0
$175$	−6.78718	−	3.91858i	−0.513062	−	0.296217i
$176$	3.26194	+	1.88328i	0.245878	+	0.141958i
$177$		0			0
$178$	−3.53277	−	6.11894i	−0.264793	−	0.458634i
$179$	19.2107			1.43587			0.717936	−	0.696109i	$-0.245087\pi$
$179$	19.2107			1.43587			0.717936	+	0.696109i	$0.245087\pi$
$180$		0			0
$181$	9.14810			0.679973			0.339987	−	0.940430i	$-0.389577\pi$
$181$	9.14810			0.679973			0.339987	+	0.940430i	$0.389577\pi$
$182$	5.47048	+	1.52268i	0.405499	+	0.112868i
$183$		0			0
$184$	3.20209	+	1.84873i	0.236062	+	0.136290i
$185$	−0.461342	+	0.799068i	−0.0339185	+	0.0587486i
$186$		0			0
$187$	23.0477	−	13.3066i	1.68542	−	0.973076i
$188$			7.13476i			0.520356i
$189$		0			0
$190$		−	11.8968i		−	0.863081i
$191$	0.131627	+	0.227985i	0.00952420	+	0.0164964i	0.870748	−	0.491729i	$-0.163635\pi$
$191$	0.131627	+	0.227985i	0.00952420	+	0.0164964i	−0.861224	+	0.508226i	$0.830302\pi$
$192$		0			0
$193$	10.1470	+	5.85837i	0.730397	+	0.421695i	0.818567	−	0.574410i	$-0.194769\pi$
$193$	10.1470	+	5.85837i	0.730397	+	0.421695i	−0.0881704	+	0.996105i	$0.528102\pi$
$194$	0.309296	−	0.535716i	0.0222061	−	0.0384622i
$195$		0			0
$196$	2.25982	+	3.91412i	0.161416	+	0.279580i
$197$		−	20.5283i		−	1.46258i	−0.682066	−	0.731291i	$-0.738918\pi$
$197$		−	20.5283i		−	1.46258i	0.682066	−	0.731291i	$-0.261082\pi$
$198$		0			0
$199$	5.95247			0.421960			0.210980	−	0.977490i	$-0.432335\pi$
$199$	5.95247			0.421960			0.210980	+	0.977490i	$0.432335\pi$
$200$	−4.30955	+	2.48812i	−0.304731	+	0.175937i
$201$		0			0
$202$	−7.21887	−	4.16781i	−0.507918	−	0.293246i
$203$	0.297682	+	0.171867i	0.0208932	+	0.0120627i
$204$		0			0
$205$	11.6576	+	20.1915i	0.814201	+	1.41024i
$206$			9.89675i			0.689539i
$207$		0			0
$208$	2.57405	−	2.52473i	0.178478	−	0.175058i
$209$	−7.09349	−	12.2863i	−0.490667	−	0.849860i
$210$		0			0
$211$	8.69625	−	15.0623i	0.598674	−	1.03693i	−0.394343	−	0.918963i	$-0.629028\pi$
$211$	8.69625	−	15.0623i	0.598674	−	1.03693i	0.993017	−	0.117971i	$-0.0376389\pi$
$212$	7.20877	−	12.4860i	0.495101	−	0.857539i
$213$		0			0
$214$	0.100077	−	0.0577794i	0.00684111	−	0.00394972i
$215$		−	19.3197i		−	1.31759i
$216$		0			0
$217$	−4.83358			−0.328125
$218$	7.06504	+	12.2370i	0.478505	+	0.828795i
$219$		0			0
$220$	−5.94838	+	10.3029i	−0.401039	+	0.694621i
$221$	−6.35523	−	24.6701i	−0.427499	−	1.65949i
$222$		0			0
$223$	−20.5643	+	11.8728i	−1.37709	+	0.795062i	−0.991808	−	0.127737i	$-0.959229\pi$
$223$	−20.5643	+	11.8728i	−1.37709	+	0.795062i	−0.385280	+	0.922800i	$0.625895\pi$
$224$	−1.57492			−0.105229
$225$		0			0
$226$			19.4194i			1.29176i
$227$	3.93292	−	2.27067i	0.261037	−	0.150710i	−0.363770	−	0.931489i	$-0.618511\pi$
$227$	3.93292	−	2.27067i	0.261037	−	0.150710i	0.624808	+	0.780779i	$0.285177\pi$
$228$		0			0
$229$	−10.3673	−	5.98556i	−0.685091	−	0.395537i	0.116680	−	0.993170i	$-0.462775\pi$
$229$	−10.3673	−	5.98556i	−0.685091	−	0.395537i	−0.801770	+	0.597632i	$0.796108\pi$
$230$	−5.83925	+	10.1139i	−0.385029	+	0.666889i
$231$		0			0
$232$	0.189015	−	0.109128i	0.0124094	−	0.00716458i
$233$	−10.6895			−0.700290			−0.350145	−	0.936696i	$-0.613868\pi$
$233$	−10.6895			−0.700290			−0.350145	+	0.936696i	$0.613868\pi$
$234$		0			0
$235$	−22.5353			−1.47004
$236$	−9.04745	+	5.22355i	−0.588939	+	0.340024i
$237$		0			0
$238$	−5.56391	+	9.63697i	−0.360655	+	0.624672i
$239$	20.8684	+	12.0484i	1.34987	+	0.779346i	0.988230	−	0.152974i	$-0.0488849\pi$
$239$	20.8684	+	12.0484i	1.34987	+	0.779346i	0.361636	+	0.932319i	$0.382218\pi$
$240$		0			0
$241$	−9.63879	+	5.56496i	−0.620889	+	0.358470i	−0.777215	−	0.629235i	$-0.783368\pi$
$241$	−9.63879	+	5.56496i	−0.620889	+	0.358470i	0.156326	+	0.987705i	$0.450035\pi$
$242$			3.18698i			0.204867i
$243$		0			0
$244$	6.00013			0.384119
$245$	−12.3628	+	7.13768i	−0.789832	+	0.456010i
$246$		0			0
$247$	−13.1512	+	3.38785i	−0.836789	+	0.215563i
$248$	−1.53455	+	2.65792i	−0.0974440	+	0.168778i
$249$		0			0
$250$	0.0375278	+	0.0650001i	0.00237347	+	0.00411097i
$251$	−11.3356			−0.715499			−0.357749	−	0.933818i	$-0.616456\pi$
$251$	−11.3356			−0.715499			−0.357749	+	0.933818i	$0.616456\pi$
$252$		0			0
$253$			13.9267i			0.875565i
$254$	−4.70169	+	2.71452i	−0.295010	+	0.170324i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.16026	−	7.20579i	0.259510	−	0.449485i	−0.706601	−	0.707613i	$-0.749772\pi$
$257$	4.16026	−	7.20579i	0.259510	−	0.449485i	0.966111	+	0.258128i	$0.0831056\pi$
$258$		0			0
$259$	−0.230037	−	0.398435i	−0.0142938	−	0.0247576i
$260$	7.97440	+	8.13019i	0.494551	+	0.504213i
$261$		0			0
$262$		−	12.6868i		−	0.783796i
$263$	−7.19133	−	12.4557i	−0.443436	−	0.768054i	0.554506	−	0.832180i	$-0.312907\pi$
$263$	−7.19133	−	12.4557i	−0.443436	−	0.768054i	−0.997942	+	0.0641260i	$0.979574\pi$
$264$		0			0
$265$	39.4371	+	22.7690i	2.42260	+	1.39869i
$266$	5.13728	+	2.96601i	0.314987	+	0.181858i
$267$		0			0
$268$	−6.33583	+	3.65799i	−0.387022	+	0.223447i
$269$	−9.01366			−0.549572			−0.274786	−	0.961505i	$-0.588607\pi$
$269$	−9.01366			−0.549572			−0.274786	+	0.961505i	$0.588607\pi$
$270$		0			0
$271$		−	19.9094i		−	1.20941i	−0.796449	−	0.604705i	$-0.793291\pi$
$271$		−	19.9094i		−	1.20941i	0.796449	−	0.604705i	$-0.206709\pi$
$272$	3.53283	+	6.11904i	0.214209	+	0.371021i
$273$		0			0
$274$	−3.67770	+	6.36997i	−0.222178	+	0.384824i
$275$	−16.2322	−	9.37165i	−0.978837	−	0.565132i
$276$		0			0
$277$	−6.69157	−	11.5901i	−0.402058	−	0.696384i	0.591916	−	0.805999i	$-0.298372\pi$
$277$	−6.69157	−	11.5901i	−0.402058	−	0.696384i	−0.993974	+	0.109615i	$0.965038\pi$
$278$			7.31119i			0.438496i
$279$		0			0
$280$		−	4.97440i		−	0.297277i
$281$	0.606470	−	0.350146i	0.0361790	−	0.0208879i	−0.481801	−	0.876280i	$-0.660017\pi$
$281$	0.606470	−	0.350146i	0.0361790	−	0.0208879i	0.517980	+	0.855392i	$0.326684\pi$
$282$		0			0
$283$	−9.71783	+	16.8318i	−0.577665	+	1.00055i	0.418081	+	0.908410i	$0.362703\pi$
$283$	−9.71783	+	16.8318i	−0.577665	+	1.00055i	−0.995746	+	0.0921358i	$0.970631\pi$
$284$	−0.668927	−	0.386205i	−0.0396935	−	0.0229170i
$285$		0			0
$286$	13.0832	+	3.64162i	0.773624	+	0.215334i
$287$	−11.6255			−0.686233
$288$		0			0
$289$	32.9235			1.93668
$290$	0.344682	+	0.597006i	0.0202404	+	0.0350574i
$291$		0			0
$292$	11.7210	+	6.76712i	0.685919	+	0.396016i
$293$	−3.68719	−	2.12880i	−0.215408	−	0.124366i	0.388414	−	0.921485i	$-0.373023\pi$
$293$	−3.68719	−	2.12880i	−0.215408	−	0.124366i	−0.603822	+	0.797119i	$0.706356\pi$
$294$		0			0
$295$	−16.4987	−	28.5765i	−0.960589	−	1.66379i
$296$	−0.292126			−0.0169795
$297$		0			0
$298$	−23.7638			−1.37660
$299$	12.8431	+	3.57482i	0.742738	+	0.206737i
$300$		0			0
$301$	8.34268	+	4.81665i	0.480864	+	0.277627i
$302$	−5.19448	+	8.99711i	−0.298909	+	0.517725i
$303$		0			0
$304$	3.26194	−	1.88328i	0.187085	−	0.108014i
$305$			18.9515i			1.08516i
$306$		0			0
$307$			7.35088i			0.419537i	0.977751	+	0.209768i	$0.0672710\pi$
$307$			7.35088i			0.419537i	−0.977751	+	0.209768i	$0.932729\pi$
$308$	−2.96601	−	5.13728i	−0.169004	−	0.292724i
$309$		0			0
$310$	−8.39509	−	4.84690i	−0.476809	−	0.275286i
$311$	−1.40756	+	2.43796i	−0.0798152	+	0.138244i	−0.903170	−	0.429283i	$-0.858766\pi$
$311$	−1.40756	+	2.43796i	−0.0798152	+	0.138244i	0.823355	+	0.567527i	$0.192100\pi$
$312$		0			0
$313$	−13.5459	−	23.4621i	−0.765657	−	1.32616i	−0.939898	−	0.341454i	$-0.889081\pi$
$313$	−13.5459	−	23.4621i	−0.765657	−	1.32616i	0.174241	−	0.984703i	$-0.444253\pi$
$314$			9.14824i			0.516265i
$315$		0			0
$316$	12.6807			0.713343
$317$	0.655352	−	0.378368i	0.0368083	−	0.0212513i	−0.481483	−	0.876455i	$-0.659902\pi$
$317$	0.655352	−	0.378368i	0.0368083	−	0.0212513i	0.518291	+	0.855204i	$0.326568\pi$
$318$		0			0
$319$	0.711935	+	0.411036i	0.0398607	+	0.0230136i
$320$	−2.73536	−	1.57926i	−0.152911	−	0.0882833i
$321$		0			0
$322$	−2.91160	−	5.04303i	−0.162257	−	0.281037i
$323$		−	26.6132i		−	1.48080i
$324$		0			0
$325$	−12.8091	+	12.5636i	−0.710521	+	0.696906i
$326$	−6.79676	−	11.7723i	−0.376438	−	0.652009i
$327$		0			0
$328$	−3.69084	+	6.39272i	−0.203792	+	0.352979i
$329$	5.61832	−	9.73122i	0.309748	−	0.536499i
$330$		0			0
$331$	28.5504	−	16.4836i	1.56927	−	0.906021i	0.573020	−	0.819541i	$-0.305772\pi$
$331$	28.5504	−	16.4836i	1.56927	−	0.906021i	0.996254	−	0.0864792i	$-0.0275616\pi$
$332$		−	0.363495i		−	0.0199494i
$333$		0			0
$334$	7.16615			0.392114
$335$	−11.5538	−	20.0118i	−0.631254	−	1.09336i
$336$		0			0
$337$	−2.25348	+	3.90313i	−0.122755	+	0.212617i	−0.920853	−	0.389910i	$-0.872506\pi$
$337$	−2.25348	+	3.90313i	−0.122755	+	0.212617i	0.798098	+	0.602527i	$0.205839\pi$
$338$	6.71658	−	11.1305i	0.365334	−	0.605418i
$339$		0			0
$340$	−19.3271	+	11.1585i	−1.04816	+	0.605155i
$341$	−11.5600			−0.626007
$342$		0			0
$343$		−	18.1425i		−	0.979601i
$344$	5.29722	−	3.05835i	0.285607	−	0.164895i
$345$		0			0
$346$	−2.60815	−	1.50582i	−0.140215	−	0.0809532i
$347$	−14.9859	+	25.9563i	−0.804484	+	1.39341i	0.112155	+	0.993691i	$0.464225\pi$
$347$	−14.9859	+	25.9563i	−0.804484	+	1.39341i	−0.916639	+	0.399716i	$0.869109\pi$
$348$		0			0
$349$	−15.0992	+	8.71753i	−0.808242	+	0.466639i	−0.846345	−	0.532635i	$-0.821202\pi$
$349$	−15.0992	+	8.71753i	−0.808242	+	0.466639i	0.0381029	+	0.999274i	$0.487869\pi$
$350$	7.83716			0.418914
$351$		0			0
$352$	−3.76656			−0.200758
$353$	3.91310	−	2.25923i	0.208273	−	0.120247i	−0.392235	−	0.919865i	$-0.628298\pi$
$353$	3.91310	−	2.25923i	0.208273	−	0.120247i	0.600509	+	0.799618i	$0.294965\pi$
$354$		0			0
$355$	1.21984	−	2.11282i	0.0647421	−	0.112137i
$356$	6.11894	+	3.53277i	0.324303	+	0.187237i
$357$		0			0
$358$	−16.6369	+	9.60533i	−0.879288	+	0.507657i
$359$			30.5681i			1.61332i	0.591013	+	0.806662i	$0.298728\pi$
$359$			30.5681i			1.61332i	−0.591013	+	0.806662i	$0.701272\pi$
$360$		0			0
$361$	4.81302			0.253317
$362$	−7.92249	+	4.57405i	−0.416397	+	0.240407i
$363$		0			0
$364$	−5.49891	+	1.41656i	−0.288221	+	0.0742481i
$365$	−21.3741	+	37.0210i	−1.11877	+	1.93777i
$366$		0			0
$367$	5.33420	+	9.23911i	0.278443	+	0.482278i	0.970998	−	0.239087i	$-0.0768483\pi$
$367$	5.33420	+	9.23911i	0.278443	+	0.482278i	−0.692555	+	0.721365i	$0.743515\pi$
$368$	−3.69746			−0.192743
$369$		0			0
$370$		−	0.922684i		−	0.0479681i
$371$	−19.6643	+	11.3532i	−1.02092	+	0.589430i
$372$		0			0
$373$	−4.18223	+	7.24383i	−0.216548	+	0.375072i	−0.953750	−	0.300600i	$-0.902813\pi$
$373$	−4.18223	+	7.24383i	−0.216548	+	0.375072i	0.737203	+	0.675672i	$0.236146\pi$
$374$	−13.3066	+	23.0477i	−0.688068	+	1.19177i
$375$		0			0
$376$	−3.56738	−	6.17888i	−0.183973	−	0.318651i
$377$	0.561801	−	0.551036i	0.0289342	−	0.0283798i
$378$		0			0
$379$		−	26.5494i		−	1.36375i	−0.731467	−	0.681877i	$-0.761164\pi$
$379$		−	26.5494i		−	1.36375i	0.731467	−	0.681877i	$-0.238836\pi$
$380$	5.94838	+	10.3029i	0.305145	+	0.528527i
$381$		0			0
$382$	−0.227985	−	0.131627i	−0.0116647	−	0.00673463i
$383$	−2.83624	−	1.63751i	−0.144925	−	0.0836727i	0.425784	−	0.904825i	$-0.359998\pi$
$383$	−2.83624	−	1.63751i	−0.144925	−	0.0836727i	−0.570709	+	0.821152i	$0.693332\pi$
$384$		0			0
$385$	16.2262	−	9.36819i	0.826963	−	0.477447i
$386$	−11.7167			−0.596367
$387$		0			0
$388$			0.618592i			0.0314042i
$389$	12.7599	+	22.1008i	0.646951	+	1.12055i	0.983847	+	0.179011i	$0.0572897\pi$
$389$	12.7599	+	22.1008i	0.646951	+	1.12055i	−0.336896	+	0.941542i	$0.609377\pi$
$390$		0			0
$391$	−13.0625	+	22.6249i	−0.660598	+	1.14419i
$392$	−3.91412	−	2.25982i	−0.197693	−	0.114138i
$393$		0			0
$394$	10.2642	+	17.7780i	0.517101	+	0.895645i
$395$			40.0521i			2.01524i
$396$		0			0
$397$		−	4.70957i		−	0.236367i	−0.992992	−	0.118183i	$-0.962293\pi$
$397$		−	4.70957i		−	0.236367i	0.992992	−	0.118183i	$-0.0377071\pi$
$398$	−5.15499	+	2.97624i	−0.258396	+	0.149185i
$399$		0			0
$400$	2.48812	−	4.30955i	0.124406	−	0.215477i
$401$	12.5429	+	7.24166i	0.626364	+	0.361631i	0.779343	−	0.626598i	$-0.215553\pi$
$401$	12.5429	+	7.24166i	0.626364	+	0.361631i	−0.152979	+	0.988229i	$0.548887\pi$
$402$		0			0
$403$	−2.96730	+	10.6605i	−0.147812	+	0.531039i
$404$	8.33563			0.414713
$405$		0			0
$406$	−0.343734			−0.0170592
$407$	−0.550154	−	0.952895i	−0.0272701	−	0.0472333i
$408$		0			0
$409$	14.2191	+	8.20943i	0.703091	+	0.405930i	0.808498	−	0.588499i	$-0.200281\pi$
$409$	14.2191	+	8.20943i	0.703091	+	0.405930i	−0.105406	+	0.994429i	$0.533614\pi$
$410$	−20.1915	−	11.6576i	−0.997188	−	0.575727i
$411$		0			0
$412$	−4.94838	−	8.57084i	−0.243789	−	0.422255i
$413$	16.4533			0.809614
$414$		0			0
$415$	1.14810			0.0563582
$416$	−0.966830	+	3.47351i	−0.0474027	+	0.170303i
$417$		0			0
$418$	12.2863	+	7.09349i	0.600942	+	0.346954i
$419$	7.15411	−	12.3913i	0.349501	−	0.605354i	−0.636660	−	0.771145i	$-0.719684\pi$
$419$	7.15411	−	12.3913i	0.349501	−	0.605354i	0.986161	+	0.165791i	$0.0530178\pi$
$420$		0			0
$421$	−20.8668	+	12.0475i	−1.01699	+	0.587158i	−0.913230	−	0.407445i	$-0.866420\pi$
$421$	−20.8668	+	12.0475i	−1.01699	+	0.587158i	−0.103757	+	0.994603i	$0.533087\pi$
$422$			17.3925i			0.846653i
$423$		0			0
$424$			14.4175i			0.700178i
$425$	−17.5802	−	30.4498i	−0.852764	−	1.47703i
$426$		0			0
$427$	−8.18369	−	4.72486i	−0.396036	−	0.228652i
$428$	−0.0577794	+	0.100077i	−0.00279287	+	0.00483740i
$429$		0			0
$430$	9.65986	+	16.7314i	0.465840	+	0.806859i
$431$			9.12376i			0.439476i	0.975559	+	0.219738i	$0.0705202\pi$
$431$			9.12376i			0.439476i	−0.975559	+	0.219738i	$0.929480\pi$
$432$		0			0
$433$	0.372606			0.0179063			0.00895315	−	0.999960i	$-0.497150\pi$
$433$	0.372606			0.0179063			0.00895315	+	0.999960i	$0.497150\pi$
$434$	4.18600	−	2.41679i	0.200934	−	0.116010i
$435$		0			0
$436$	−12.2370	−	7.06504i	−0.586047	−	0.338354i
$437$	12.0609	+	6.96335i	0.576950	+	0.333102i
$438$		0			0
$439$	1.91160	+	3.31098i	0.0912355	+	0.158024i	0.908031	−	0.418902i	$-0.137585\pi$
$439$	1.91160	+	3.31098i	0.0912355	+	0.158024i	−0.816796	+	0.576927i	$0.804252\pi$
$440$		−	11.8968i		−	0.567155i
$441$		0			0
$442$	17.8389	+	18.1874i	0.848508	+	0.865085i
$443$	−3.98203	−	6.89708i	−0.189192	−	0.327690i	0.755789	−	0.654815i	$-0.227254\pi$
$443$	−3.98203	−	6.89708i	−0.189192	−	0.327690i	−0.944981	+	0.327125i	$0.893920\pi$
$444$		0			0
$445$	−11.1583	+	19.3268i	−0.528956	+	0.916178i
$446$	11.8728	−	20.5643i	0.562194	−	0.973749i
$447$		0			0
$448$	1.36392	−	0.787458i	0.0644391	−	0.0372039i
$449$		−	26.4088i		−	1.24631i	−0.782098	−	0.623155i	$-0.785851\pi$
$449$		−	26.4088i		−	1.24631i	0.782098	−	0.623155i	$-0.214149\pi$
$450$		0			0
$451$	−27.8035			−1.30922
$452$	−9.70968	−	16.8177i	−0.456705	−	0.791036i
$453$		0			0
$454$	−2.27067	+	3.93292i	−0.106568	+	0.184581i
$455$	−4.47424	−	17.3684i	−0.209756	−	0.814244i
$456$		0			0
$457$	−7.46066	+	4.30742i	−0.348995	+	0.201492i	−0.664243	−	0.747517i	$-0.731246\pi$
$457$	−7.46066	+	4.30742i	−0.348995	+	0.201492i	0.315248	+	0.949009i	$0.397912\pi$
$458$	11.9711			0.559374
$459$		0			0
$460$		−	11.6785i		−	0.544513i
$461$	−24.0754	+	13.8999i	−1.12130	+	0.647384i	−0.941733	−	0.336362i	$-0.890803\pi$
$461$	−24.0754	+	13.8999i	−1.12130	+	0.647384i	−0.179569	+	0.983745i	$0.557470\pi$
$462$		0			0
$463$	31.4451	+	18.1548i	1.46138	+	0.843727i	0.999075	−	0.0429960i	$-0.0136903\pi$
$463$	31.4451	+	18.1548i	1.46138	+	0.843727i	0.462302	+	0.886723i	$0.347024\pi$
$464$	−0.109128	+	0.189015i	−0.00506613	+	0.00877479i
$465$		0			0
$466$	9.25734	−	5.34473i	0.428838	−	0.247590i
$467$	−13.8295			−0.639954			−0.319977	−	0.947425i	$-0.603675\pi$
$467$	−13.8295			−0.639954			−0.319977	+	0.947425i	$0.603675\pi$
$468$		0			0
$469$	11.5221			0.532040
$470$	19.5161	−	11.2676i	0.900211	−	0.519737i
$471$		0			0
$472$	5.22355	−	9.04745i	0.240433	−	0.416442i
$473$	19.9523	+	11.5195i	0.917408	+	0.529666i
$474$		0			0
$475$	−16.2322	+	9.37165i	−0.744783	+	0.430001i
$476$		−	11.1278i		−	0.510043i
$477$		0			0
$478$	−24.0968			−1.10216
$479$	24.4509	−	14.1167i	1.11719	−	0.645010i	0.176508	−	0.984299i	$-0.443520\pi$
$479$	24.4509	−	14.1167i	1.11719	−	0.645010i	0.940682	+	0.339289i	$0.110187\pi$
$480$		0			0
$481$	−1.01997	+	0.262753i	−0.0465068	+	0.0119805i
$482$	5.56496	−	9.63879i	0.253477	−	0.439035i
$483$		0			0
$484$	−1.59349	−	2.76001i	−0.0724314	−	0.125455i
$485$	−1.95383			−0.0887190
$486$		0			0
$487$			15.5579i			0.704995i	0.935813	+	0.352498i	$0.114668\pi$
$487$			15.5579i			0.704995i	−0.935813	+	0.352498i	$0.885332\pi$
$488$	−5.19627	+	3.00007i	−0.235224	+	0.135807i
$489$		0			0
$490$	7.13768	−	12.3628i	0.322448	−	0.558495i
$491$	7.48935	−	12.9719i	0.337990	−	0.585416i	−0.646065	−	0.763283i	$-0.723586\pi$
$491$	7.48935	−	12.9719i	0.337990	−	0.585416i	0.984055	+	0.177867i	$0.0569197\pi$
$492$		0			0
$493$	0.771059	+	1.33551i	0.0347267	+	0.0601485i
$494$	9.69532	−	9.50955i	0.436213	−	0.427855i
$495$		0			0
$496$		−	3.06910i		−	0.137807i
$497$	0.608241	+	1.05350i	0.0272833	+	0.0472561i
$498$		0			0
$499$	29.5341	+	17.0515i	1.32213	+	0.763330i	0.984068	−	0.177795i	$-0.0568963\pi$
$499$	29.5341	+	17.0515i	1.32213	+	0.763330i	0.338059	+	0.941125i	$0.390230\pi$
$500$	−0.0650001	−	0.0375278i	−0.00290689	−	0.00167830i
$501$		0			0
$502$	9.81694	−	5.66781i	0.438152	−	0.252967i
$503$	22.7259			1.01330			0.506648	−	0.862153i	$-0.330884\pi$
$503$	22.7259			1.01330			0.506648	+	0.862153i	$0.330884\pi$
$504$		0			0
$505$			26.3282i			1.17159i
$506$	−6.96335	−	12.0609i	−0.309559	−	0.536172i
$507$		0			0
$508$	2.71452	−	4.70169i	0.120437	−	0.208604i
$509$	−5.48563	−	3.16713i	−0.243146	−	0.140380i	0.373476	−	0.927640i	$-0.378166\pi$
$509$	−5.48563	−	3.16713i	−0.243146	−	0.140380i	−0.616622	+	0.787259i	$0.711499\pi$
$510$		0			0
$511$	−10.6576	−	18.4596i	−0.471467	−	0.816604i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			8.32053i			0.367003i
$515$	27.0711	−	15.6295i	1.19290	−	0.688720i
$516$		0			0
$517$	13.4367	−	23.2731i	0.590947	−	1.02355i
$518$	0.398435	+	0.230037i	0.0175062	+	0.0101072i
$519$		0			0
$520$	−10.9711	−	3.05375i	−0.481116	−	0.133916i
$521$	−19.5169			−0.855052			−0.427526	−	0.904003i	$-0.640615\pi$
$521$	−19.5169			−0.855052			−0.427526	+	0.904003i	$0.640615\pi$
$522$		0			0
$523$	4.76549			0.208380			0.104190	−	0.994557i	$-0.466775\pi$
$523$	4.76549			0.208380			0.104190	+	0.994557i	$0.466775\pi$
$524$	6.34342	+	10.9871i	0.277114	+	0.479975i
$525$		0			0
$526$	12.4557	+	7.19133i	0.543096	+	0.313557i
$527$	−18.7799	−	10.8426i	−0.818067	−	0.472311i
$528$		0			0
$529$	4.66439	+	8.07897i	0.202800	+	0.351259i
$530$	−45.5381			−1.97805
$531$		0			0
$532$	−5.93202			−0.257186
$533$	−7.13683	+	25.6403i	−0.309130	+	1.11060i
$534$		0			0
$535$	−0.316094	−	0.182497i	−0.0136660	−	0.00789004i
$536$	3.65799	−	6.33583i	0.158001	−	0.273666i
$537$		0			0
$538$	7.80606	−	4.50683i	0.336543	−	0.194303i
$539$		−	17.0235i		−	0.733254i
$540$		0			0
$541$		−	25.2325i		−	1.08483i	−0.840111	−	0.542414i	$-0.817510\pi$
$541$		−	25.2325i		−	1.08483i	0.840111	−	0.542414i	$-0.182490\pi$
$542$	9.95470	+	17.2420i	0.427591	+	0.740609i
$543$		0			0
$544$	−6.11904	−	3.53283i	−0.262352	−	0.151469i
$545$	22.3151	−	38.6508i	0.955872	−	1.65562i
$546$		0			0
$547$	−14.3916	−	24.9271i	−0.615343	−	1.06580i	−0.990324	−	0.138772i	$-0.955684\pi$
$547$	−14.3916	−	24.9271i	−0.615343	−	1.06580i	0.374982	−	0.927032i	$-0.377649\pi$
$548$		−	7.35541i		−	0.314207i
$549$		0			0
$550$	18.7433			0.799217
$551$	0.711935	−	0.411036i	0.0303295	−	0.0175107i
$552$		0			0
$553$	−17.2954	−	9.98549i	−0.735475	−	0.424626i
$554$	11.5901	+	6.69157i	0.492418	+	0.284298i
$555$		0			0
$556$	−3.65559	−	6.33167i	−0.155032	−	0.268523i
$557$		−	11.4847i		−	0.486624i	−0.969948	−	0.243312i	$-0.921766\pi$
$557$		−	11.4847i		−	0.486624i	0.969948	−	0.243312i	$-0.0782339\pi$
$558$		0			0
$559$	15.7447	−	15.4430i	0.665931	−	0.653170i
$560$	2.48720	+	4.30796i	0.105103	+	0.182044i
$561$		0			0
$562$	−0.350146	+	0.606470i	−0.0147700	+	0.0255824i
$563$	7.42388	−	12.8585i	0.312879	−	0.541923i	−0.666105	−	0.745858i	$-0.732040\pi$
$563$	7.42388	−	12.8585i	0.312879	−	0.541923i	0.978984	+	0.203935i	$0.0653731\pi$
$564$		0			0
$565$	53.1189	−	30.6682i	2.23473	−	1.29022i
$566$		−	19.4357i		−	0.816942i
$567$		0			0
$568$	0.772410			0.0324096
$569$	13.8881	+	24.0549i	0.582220	+	1.00843i	0.995216	+	0.0977019i	$0.0311492\pi$
$569$	13.8881	+	24.0549i	0.582220	+	1.00843i	−0.412996	+	0.910733i	$0.635517\pi$
$570$		0			0
$571$	9.56039	−	16.5591i	0.400090	−	0.692976i	−0.593646	−	0.804726i	$-0.702312\pi$
$571$	9.56039	−	16.5591i	0.400090	−	0.692976i	0.993736	+	0.111750i	$0.0356455\pi$
$572$	−13.1512	+	3.38785i	−0.549878	+	0.141653i
$573$		0			0
$574$	10.0680	−	5.81276i	0.420230	−	0.242620i
$575$	18.3994			0.767310
$576$		0			0
$577$		−	26.8961i		−	1.11970i	−0.828595	−	0.559849i	$-0.810859\pi$
$577$		−	26.8961i		−	1.11970i	0.828595	−	0.559849i	$-0.189141\pi$
$578$	−28.5126	+	16.4617i	−1.18597	+	0.684718i
$579$		0			0
$580$	−0.597006	−	0.344682i	−0.0247893	−	0.0143121i
$581$	−0.286237	+	0.495777i	−0.0118751	+	0.0205683i
$582$		0			0
$583$	−47.0291	+	27.1523i	−1.94775	+	1.12453i
$584$	−13.5342			−0.560051
$585$		0			0
$586$	4.25760			0.175880
$587$	−33.7791	+	19.5024i	−1.39421	+	0.804949i	−0.993778	−	0.111376i	$-0.964474\pi$
$587$	−33.7791	+	19.5024i	−1.39421	+	0.804949i	−0.400434	+	0.916325i	$0.631141\pi$
$588$		0			0
$589$	−5.77998	+	10.0112i	−0.238160	+	0.412505i
$590$	28.5765	+	16.4987i	1.17648	+	0.679239i
$591$		0			0
$592$	0.252988	−	0.146063i	0.0103977	−	0.00600314i
$593$		−	24.2756i		−	0.996881i	−0.866924	−	0.498441i	$-0.833906\pi$
$593$		−	24.2756i		−	0.996881i	0.866924	−	0.498441i	$-0.166094\pi$
$594$		0			0
$595$	35.1474			1.44090
$596$	20.5800	−	11.8819i	0.842990	−	0.486701i
$597$		0			0
$598$	−12.9099	+	3.32569i	−0.527925	+	0.135998i
$599$	−9.53752	+	16.5195i	−0.389692	+	0.674967i	−0.992408	−	0.122989i	$-0.960752\pi$
$599$	−9.53752	+	16.5195i	−0.389692	+	0.674967i	0.602716	+	0.797956i	$0.294085\pi$
$600$		0			0
$601$	7.43342	+	12.8751i	0.303216	+	0.525185i	0.976862	−	0.213869i	$-0.0686064\pi$
$601$	7.43342	+	12.8751i	0.303216	+	0.525185i	−0.673647	+	0.739053i	$0.735273\pi$
$602$	−9.63330			−0.392624
$603$		0			0
$604$		−	10.3890i		−	0.422721i
$605$	8.71753	−	5.03307i	0.354418	−	0.204623i
$606$		0			0
$607$	−18.3898	+	31.8521i	−0.746419	+	1.29284i	0.203110	+	0.979156i	$0.434895\pi$
$607$	−18.3898	+	31.8521i	−0.746419	+	1.29284i	−0.949529	+	0.313680i	$0.898438\pi$
$608$	−1.88328	+	3.26194i	−0.0763771	+	0.132289i
$609$		0			0
$610$	−9.47577	−	16.4125i	−0.383663	−	0.664523i
$611$	−18.0133	−	18.3652i	−0.728741	−	0.742978i
$612$		0			0
$613$		−	9.13501i		−	0.368959i	−0.982836	−	0.184480i	$-0.940940\pi$
$613$		−	9.13501i		−	0.368959i	0.982836	−	0.184480i	$-0.0590600\pi$
$614$	−3.67544	−	6.36605i	−0.148329	−	0.256913i
$615$		0			0
$616$	5.13728	+	2.96601i	0.206987	+	0.119504i
$617$	12.3504	+	7.13051i	0.497209	+	0.287063i	0.727560	−	0.686044i	$-0.240654\pi$
$617$	12.3504	+	7.13051i	0.497209	+	0.287063i	−0.230352	+	0.973107i	$0.573988\pi$
$618$		0			0
$619$	5.16609	−	2.98264i	0.207643	−	0.119883i	−0.392573	−	0.919721i	$-0.628415\pi$
$619$	5.16609	−	2.98264i	0.207643	−	0.119883i	0.600215	+	0.799838i	$0.295082\pi$
$620$	9.69381			0.389313
$621$		0			0
$622$		−	2.81511i		−	0.112876i
$623$	−5.56382	−	9.63683i	−0.222910	−	0.386091i
$624$		0			0
$625$	12.5591	−	21.7530i	0.502365	−	0.870122i
$626$	23.4621	+	13.5459i	0.937735	+	0.541401i
$627$		0			0
$628$	−4.57412	−	7.92261i	−0.182527	−	0.316146i
$629$		−	2.06406i		−	0.0822994i
$630$		0			0
$631$			3.19802i			0.127311i	0.997972	+	0.0636557i	$0.0202759\pi$
$631$			3.19802i			0.127311i	−0.997972	+	0.0636557i	$0.979724\pi$
$632$	−10.9818	+	6.34033i	−0.436832	+	0.252205i
$633$		0			0
$634$	−0.378368	+	0.655352i	−0.0150269	+	0.0260274i
$635$	14.8504	+	8.57387i	0.589319	+	0.340243i
$636$		0			0
$637$	−15.6990	−	4.36972i	−0.622017	−	0.173135i
$638$	−0.822072			−0.0325462
$639$		0			0
$640$	3.15852			0.124851
$641$	15.4801	+	26.8123i	0.611426	+	1.05902i	0.991000	+	0.133860i	$0.0427373\pi$
$641$	15.4801	+	26.8123i	0.611426	+	1.05902i	−0.379574	+	0.925161i	$0.623929\pi$
$642$		0			0
$643$	−25.5058	−	14.7258i	−1.00585	−	0.580729i	−0.0958776	−	0.995393i	$-0.530566\pi$
$643$	−25.5058	−	14.7258i	−1.00585	−	0.580729i	−0.909975	+	0.414664i	$0.863899\pi$
$644$	5.04303	+	2.91160i	0.198723	+	0.114733i
$645$		0			0
$646$	13.3066	+	23.0477i	0.523542	+	0.906801i
$647$	27.8656			1.09551			0.547756	−	0.836638i	$-0.315482\pi$
$647$	27.8656			1.09551			0.547756	+	0.836638i	$0.315482\pi$
$648$		0			0
$649$	39.3496			1.54461
$650$	4.81118	−	17.2850i	0.188710	−	0.677973i
$651$		0			0
$652$	11.7723	+	6.79676i	0.461040	+	0.266182i
$653$	9.48617	−	16.4305i	0.371223	−	0.642976i	−0.618531	−	0.785760i	$-0.712272\pi$
$653$	9.48617	−	16.4305i	0.371223	−	0.642976i	0.989754	+	0.142784i	$0.0456053\pi$
$654$		0			0
$655$	−34.7030	+	20.0358i	−1.35596	+	0.782864i
$656$		−	7.38168i		−	0.288206i
$657$		0			0
$658$			11.2366i			0.438050i
$659$	9.05886	+	15.6904i	0.352883	+	0.611211i	0.986753	−	0.162228i	$-0.0518681\pi$
$659$	9.05886	+	15.6904i	0.352883	+	0.611211i	−0.633870	+	0.773439i	$0.718535\pi$
$660$		0			0
$661$	−20.5705	−	11.8764i	−0.800101	−	0.461939i	0.0434052	−	0.999058i	$-0.486179\pi$
$661$	−20.5705	−	11.8764i	−0.800101	−	0.461939i	−0.843507	+	0.537119i	$0.819513\pi$
$662$	−16.4836	+	28.5504i	−0.640653	+	1.10964i
$663$		0			0
$664$	0.181747	+	0.314795i	0.00705316	+	0.0122164i
$665$		−	18.7364i		−	0.726566i
$666$		0			0
$667$	−0.806991			−0.0312468
$668$	−6.20607	+	3.58308i	−0.240120	+	0.138633i
$669$		0			0
$670$	20.0118	+	11.5538i	0.773125	+	0.446364i
$671$	−19.5721	−	11.2999i	−0.755571	−	0.436229i
$672$		0			0
$673$	−12.1157	−	20.9850i	−0.467026	−	0.808913i	0.532264	−	0.846578i	$-0.321341\pi$
$673$	−12.1157	−	20.9850i	−0.467026	−	0.808913i	−0.999290	+	0.0376653i	$0.988008\pi$
$674$		−	4.50695i		−	0.173601i
$675$		0			0
$676$	−0.251488	+	12.9976i	−0.00967261	+	0.499906i
$677$	9.77002	+	16.9222i	0.375492	+	0.650372i	0.990401	−	0.138227i	$-0.0441403\pi$
$677$	9.77002	+	16.9222i	0.375492	+	0.650372i	−0.614908	+	0.788599i	$0.710807\pi$
$678$		0			0
$679$	0.487115	−	0.843708i	0.0186938	−	0.0323785i
$680$	11.1585	−	19.3271i	0.427909	−	0.741160i
$681$		0			0
$682$	10.0112	−	5.77998i	0.383349	−	0.221327i
$683$			40.5718i			1.55244i	0.630465	+	0.776218i	$0.282864\pi$
$683$			40.5718i			1.55244i	−0.630465	+	0.776218i	$0.717136\pi$
$684$		0			0
$685$	23.2322			0.887656
$686$	9.07123	+	15.7118i	0.346341	+	0.599881i
$687$		0			0
$688$	−3.05835	+	5.29722i	−0.116599	+	0.201955i
$689$	12.9679	+	50.3397i	0.494038	+	1.91779i
$690$		0			0
$691$	−25.6366	+	14.8013i	−0.975264	+	0.563069i	−0.900837	−	0.434158i	$-0.857046\pi$
$691$	−25.6366	+	14.8013i	−0.975264	+	0.563069i	−0.0744270	+	0.997226i	$0.523713\pi$
$692$	3.01163			0.114485
$693$		0			0
$694$		−	29.9717i		−	1.13771i
$695$	19.9987	−	11.5463i	0.758594	−	0.437975i
$696$		0			0
$697$	−45.1688	−	26.0782i	−1.71089	−	0.987782i
$698$	8.71753	−	15.0992i	0.329964	−	0.571514i
$699$		0			0
$700$	−6.78718	+	3.91858i	−0.256531	+	0.148108i
$701$	14.6213			0.552238			0.276119	−	0.961123i	$-0.410952\pi$
$701$	14.6213			0.552238			0.276119	+	0.961123i	$0.410952\pi$
$702$		0			0
$703$	−1.10031			−0.0414989
$704$	3.26194	−	1.88328i	0.122939	−	0.0709788i
$705$		0			0
$706$	−2.25923	+	3.91310i	−0.0850272	+	0.147271i
$707$	−11.3691	−	6.56396i	−0.427579	−	0.246863i
$708$		0			0
$709$	5.54229	−	3.19984i	0.208145	−	0.120173i	−0.392304	−	0.919836i	$-0.628322\pi$
$709$	5.54229	−	3.19984i	0.208145	−	0.120173i	0.600449	+	0.799663i	$0.294989\pi$
$710$			2.43967i			0.0915592i
$711$		0			0
$712$	−7.06555			−0.264793
$713$	9.82755	−	5.67394i	0.368045	−	0.212491i
$714$		0			0
$715$	−10.7006	−	41.5382i	−0.400179	−	1.55344i
$716$	9.60533	−	16.6369i	0.358968	−	0.621751i
$717$		0			0
$718$	−15.2841	−	26.4728i	−0.570396	−	0.987955i
$719$	−13.5954			−0.507022			−0.253511	−	0.967332i	$-0.581585\pi$
$719$	−13.5954			−0.507022			−0.253511	+	0.967332i	$0.581585\pi$
$720$		0			0
$721$			15.5866i			0.580474i
$722$	−4.16820	+	2.40651i	−0.155124	+	0.0895610i
$723$		0			0
$724$	4.57405	−	7.92249i	0.169993	−	0.294437i
$725$	0.543045	−	0.940582i	0.0201682	−	0.0349323i
$726$		0			0
$727$	11.1176	+	19.2562i	0.412329	+	0.714174i	0.995144	−	0.0984307i	$-0.0313823\pi$
$727$	11.1176	+	19.2562i	0.412329	+	0.714174i	−0.582815	+	0.812605i	$0.698049\pi$
$728$	4.05392	−	3.97624i	0.150248	−	0.147369i
$729$		0			0
$730$		−	42.7481i		−	1.58218i
$731$	21.6093	+	37.4284i	0.799248	+	1.38434i
$732$		0			0
$733$	14.7765	+	8.53119i	0.545781	+	0.315107i	0.747419	−	0.664354i	$-0.231293\pi$
$733$	14.7765	+	8.53119i	0.545781	+	0.315107i	−0.201638	+	0.979460i	$0.564626\pi$
$734$	−9.23911	−	5.33420i	−0.341022	−	0.196889i
$735$		0			0
$736$	3.20209	−	1.84873i	0.118031	−	0.0681451i
$737$	27.5561			1.01504
$738$		0			0
$739$		−	47.4169i		−	1.74426i	−0.489274	−	0.872130i	$-0.662738\pi$
$739$		−	47.4169i		−	1.74426i	0.489274	−	0.872130i	$-0.337262\pi$
$740$	0.461342	+	0.799068i	0.0169593	+	0.0293743i
$741$		0			0
$742$	11.3532	−	19.6643i	0.416790	−	0.721901i
$743$	−22.7717	−	13.1472i	−0.835411	−	0.482325i	0.0202905	−	0.999794i	$-0.493541\pi$
$743$	−22.7717	−	13.1472i	−0.835411	−	0.482325i	−0.855702	+	0.517469i	$0.826874\pi$
$744$		0			0
$745$	37.5291	+	65.0024i	1.37496	+	2.38150i
$746$		−	8.36446i		−	0.306245i
$747$		0			0
$748$		−	26.6132i		−	0.973076i
$749$	0.157613	−	0.0909977i	0.00575904	−	0.00332498i
$750$		0			0
$751$	−16.9255	+	29.3158i	−0.617620	+	1.06975i	0.372299	+	0.928113i	$0.378570\pi$
$751$	−16.9255	+	29.3158i	−0.617620	+	1.06975i	−0.989919	+	0.141636i	$0.954764\pi$
$752$	6.17888	+	3.56738i	0.225321	+	0.130089i
$753$		0			0
$754$	−0.211016	+	0.758111i	−0.00768474	+	0.0276088i
$755$	32.8137			1.19421
$756$		0			0
$757$	−35.4490			−1.28841			−0.644207	−	0.764851i	$-0.722813\pi$
$757$	−35.4490			−1.28841			−0.644207	+	0.764851i	$0.722813\pi$
$758$	13.2747	+	22.9925i	0.482160	+	0.835125i
$759$		0			0
$760$	−10.3029	−	5.94838i	−0.373725	−	0.215770i
$761$	−23.7086	−	13.6882i	−0.859436	−	0.496196i	0.00438738	−	0.999990i	$-0.498603\pi$
$761$	−23.7086	−	13.6882i	−0.859436	−	0.496196i	−0.863823	+	0.503795i	$0.831937\pi$
$762$		0			0
$763$	11.1269	+	19.2723i	0.402819	+	0.697703i
$764$	0.263254			0.00952420
$765$		0			0
$766$	3.27501			0.118331
$767$	10.1006	−	36.2880i	0.364710	−	1.31028i
$768$		0			0
$769$	−12.8943	−	7.44450i	−0.464979	−	0.268456i	0.249157	−	0.968463i	$-0.419847\pi$
$769$	−12.8943	−	7.44450i	−0.464979	−	0.268456i	−0.714135	+	0.700008i	$0.753180\pi$
$770$	−9.36819	+	16.2262i	−0.337606	+	0.584751i
$771$		0			0
$772$	10.1470	−	5.85837i	0.365199	−	0.210847i
$773$			47.2807i			1.70057i	0.526324	+	0.850284i	$0.323570\pi$
$773$			47.2807i			1.70057i	−0.526324	+	0.850284i	$0.676430\pi$
$774$		0			0
$775$			15.2726i			0.548607i
$776$	−0.309296	−	0.535716i	−0.0111031	−	0.0192311i
$777$		0			0
$778$	−22.1008	−	12.7599i	−0.792350	−	0.457464i
$779$	−13.9018	+	24.0786i	−0.498083	+	0.862704i
$780$		0			0
$781$	1.45466	+	2.51955i	0.0520520	+	0.0901567i
$782$		−	26.1250i		−	0.934227i
$783$		0			0
$784$	4.51964			0.161416
$785$	25.0237	−	14.4474i	0.893134	−	0.515651i
$786$		0			0
$787$	1.23135	+	0.710921i	0.0438929	+	0.0253416i	0.521786	−	0.853076i	$-0.325266\pi$
$787$	1.23135	+	0.710921i	0.0438929	+	0.0253416i	−0.477893	+	0.878418i	$0.658599\pi$
$788$	−17.7780	−	10.2642i	−0.633317	−	0.365645i
$789$		0			0
$790$	−20.0261	−	34.6861i	−0.712495	−	1.23408i
$791$			30.5839i			1.08744i
$792$		0			0
$793$	−15.4447	+	15.1487i	−0.548456	+	0.537947i
$794$	2.35479	+	4.07861i	0.0835683	+	0.144744i
$795$		0			0
$796$	2.97624	−	5.15499i	0.105490	−	0.182714i
$797$	−21.8473	+	37.8407i	−0.773872	+	1.34039i	0.161554	+	0.986864i	$0.448349\pi$
$797$	−21.8473	+	37.8407i	−0.773872	+	1.34039i	−0.935426	+	0.353522i	$0.884984\pi$
$798$		0			0
$799$	43.6578	−	25.2059i	1.54450	−	0.891719i
$800$			4.97624i			0.175937i
$801$		0			0
$802$	−14.4833			−0.511424
$803$	−25.4888	−	44.1478i	−0.899479	−	1.55794i
$804$		0			0
$805$	−9.19633	+	15.9285i	−0.324128	+	0.561406i
$806$	−2.76051	−	10.7159i	−0.0972349	−	0.377453i
$807$		0			0
$808$	−7.21887	+	4.16781i	−0.253959	+	0.146623i
$809$	−5.70765			−0.200670			−0.100335	−	0.994954i	$-0.531992\pi$
$809$	−5.70765			−0.200670			−0.100335	+	0.994954i	$0.531992\pi$
$810$		0			0
$811$			50.0141i			1.75623i	0.478446	+	0.878117i	$0.341200\pi$
$811$			50.0141i			1.75623i	−0.478446	+	0.878117i	$0.658800\pi$
$812$	0.297682	−	0.171867i	0.0104466	−	0.00603135i
$813$		0			0
$814$	0.952895	+	0.550154i	0.0333990	+	0.0192829i
$815$	−21.4677	+	37.1831i	−0.751980	+	1.30247i
$816$		0			0
$817$	19.9523	−	11.5195i	0.698043	−	0.403015i
$818$	−16.4189			−0.574072
$819$		0			0
$820$	23.3152			0.814201
$821$	−45.2025	+	26.0977i	−1.57758	+	0.910815i	−0.582381	+	0.812916i	$0.697879\pi$
$821$	−45.2025	+	26.0977i	−1.57758	+	0.910815i	−0.995196	+	0.0978991i	$0.968788\pi$
$822$		0			0
$823$	18.5278	−	32.0910i	0.645837	−	1.11862i	−0.338271	−	0.941049i	$-0.609842\pi$
$823$	18.5278	−	32.0910i	0.645837	−	1.11862i	0.984108	−	0.177573i	$-0.0568247\pi$
$824$	8.57084	+	4.94838i	0.298579	+	0.172385i
$825$		0			0
$826$	−14.2490	+	8.22665i	−0.495785	+	0.286242i
$827$			14.2975i			0.497174i	0.968610	+	0.248587i	$0.0799662\pi$
$827$			14.2975i			0.497174i	−0.968610	+	0.248587i	$0.920034\pi$
$828$		0			0
$829$	−29.4062			−1.02132			−0.510659	−	0.859783i	$-0.670599\pi$
$829$	−29.4062			−1.02132			−0.510659	+	0.859783i	$0.670599\pi$
$830$	−0.994287	+	0.574052i	−0.0345122	+	0.0199256i
$831$		0			0
$832$	−0.899453	−	3.49156i	−0.0311829	−	0.121048i
$833$	15.9671	−	27.6558i	0.553227	−	0.958218i
$834$		0			0
$835$	−11.3172	−	19.6020i	−0.391648	−	0.678355i
$836$	−14.1870			−0.490667
$837$		0			0
$838$			14.3082i			0.494269i
$839$	10.4838	−	6.05284i	0.361942	−	0.208967i	−0.307990	−	0.951389i	$-0.599656\pi$
$839$	10.4838	−	6.05284i	0.361942	−	0.208967i	0.669932	+	0.742422i	$0.266323\pi$
$840$		0			0
$841$	14.4762	−	25.0735i	0.499179	−	0.864603i
$842$	12.0475	−	20.8668i	0.415183	−	0.719119i
$843$		0			0
$844$	−8.69625	−	15.0623i	−0.299337	−	0.518467i
$845$	−41.0531	−	0.794329i	−1.41227	−	0.0273257i
$846$		0			0
$847$			5.01923i			0.172463i
$848$	−7.20877	−	12.4860i	−0.247550	−	0.428770i
$849$		0			0
$850$	30.4498	+	17.5802i	1.04442	+	0.602995i
$851$	0.935414	+	0.540061i	0.0320656	+	0.0185131i
$852$		0			0
$853$	0.647074	−	0.373588i	0.0221554	−	0.0127914i	−0.488881	−	0.872350i	$-0.662595\pi$
$853$	0.647074	−	0.373588i	0.0221554	−	0.0127914i	0.511037	+	0.859559i	$0.329262\pi$
$854$	9.44971			0.323362
$855$		0			0
$856$		−	0.115559i		−	0.00394972i
$857$	−25.0361	−	43.3638i	−0.855217	−	1.48128i	−0.876443	−	0.481505i	$-0.840090\pi$
$857$	−25.0361	−	43.3638i	−0.855217	−	1.48128i	0.0212258	−	0.999775i	$-0.493243\pi$
$858$		0			0
$859$	−14.3680	+	24.8861i	−0.490230	+	0.849103i	−0.999937	−	0.0112448i	$-0.996421\pi$
$859$	−14.3680	+	24.8861i	−0.490230	+	0.849103i	0.509707	+	0.860348i	$0.329754\pi$
$860$	−16.7314	−	9.65986i	−0.570535	−	0.329399i
$861$		0			0
$862$	−4.56188	−	7.90141i	−0.155378	−	0.269123i
$863$		−	6.03591i		−	0.205465i	−0.994709	−	0.102732i	$-0.967241\pi$
$863$		−	6.03591i		−	0.205465i	0.994709	−	0.102732i	$-0.0327585\pi$
$864$		0			0
$865$			9.51229i			0.323428i
$866$	−0.322686	+	0.186303i	−0.0109653	+	0.00633083i
$867$		0			0
$868$	−2.41679	+	4.18600i	−0.0820311	+	0.142082i
$869$	−41.3635	−	23.8812i	−1.40316	−	0.810116i
$870$		0			0
$871$	7.07331	−	25.4121i	0.239670	−	0.861057i
$872$	14.1301			0.478505
$873$		0			0
$874$	−13.9267			−0.471078
$875$	0.0591032	+	0.102370i	0.00199805	+	0.00346073i
$876$		0			0
$877$	13.8233	+	7.98087i	0.466779	+	0.269495i	0.714890	−	0.699237i	$-0.246477\pi$
$877$	13.8233	+	7.98087i	0.466779	+	0.269495i	−0.248111	+	0.968731i	$0.579810\pi$
$878$	−3.31098	−	1.91160i	−0.111740	−	0.0645132i
$879$		0			0
$880$	5.94838	+	10.3029i	0.200520	+	0.347310i
$881$	18.2622			0.615269			0.307635	−	0.951505i	$-0.400463\pi$
$881$	18.2622			0.615269			0.307635	+	0.951505i	$0.400463\pi$
$882$		0			0
$883$	6.17305			0.207740			0.103870	−	0.994591i	$-0.466877\pi$
$883$	6.17305			0.207740			0.103870	+	0.994591i	$0.466877\pi$
$884$	−24.5426	−	6.83129i	−0.825457	−	0.229761i
$885$		0			0
$886$	6.89708	+	3.98203i	0.231712	+	0.133779i
$887$	5.00963	−	8.67693i	0.168207	−	0.291343i	−0.769583	−	0.638547i	$-0.779536\pi$
$887$	5.00963	−	8.67693i	0.168207	−	0.291343i	0.937789	+	0.347204i	$0.112869\pi$
$888$		0			0
$889$	−7.40477	+	4.27514i	−0.248348	+	0.143384i
$890$		−	22.3167i		−	0.748056i
$891$		0			0
$892$			23.7456i			0.795062i
$893$	−13.4367	−	23.2731i	−0.449644	−	0.778805i
$894$		0			0
$895$	52.5480	+	30.3386i	1.75649	+	1.01411i
$896$	−0.787458	+	1.36392i	−0.0263071	+	0.0455653i
$897$		0			0
$898$	13.2044	+	22.8707i	0.440637	+	0.763206i
$899$		−	0.669848i		−	0.0223407i
$900$		0			0
$901$	−101.869			−3.39376
$902$	24.0786	−	13.9018i	0.801729	−	0.462878i
$903$		0			0
$904$	16.8177	+	9.70968i	0.559347	+	0.322939i
$905$	25.0233	+	14.4472i	0.831804	+	0.480242i
$906$		0			0
$907$	28.7735	+	49.8371i	0.955408	+	1.65481i	0.733433	+	0.679762i	$0.237917\pi$
$907$	28.7735	+	49.8371i	0.955408	+	1.65481i	0.221975	+	0.975052i	$0.428750\pi$
$908$		−	4.54135i		−	0.150710i
$909$		0			0
$910$	12.5590	+	12.8044i	0.416327	+	0.424461i
$911$	−7.88991	−	13.6657i	−0.261404	−	0.452765i	0.705211	−	0.708997i	$-0.250852\pi$
$911$	−7.88991	−	13.6657i	−0.261404	−	0.452765i	−0.966615	+	0.256232i	$0.917519\pi$
$912$		0			0
$913$	−0.684562	+	1.18570i	−0.0226557	+	0.0392408i
$914$	4.30742	−	7.46066i	0.142477	−	0.246777i
$915$		0			0
$916$	−10.3673	+	5.98556i	−0.342545	+	0.197769i
$917$		−	19.9807i		−	0.659821i
$918$		0			0
$919$	42.9349			1.41629			0.708146	−	0.706066i	$-0.249532\pi$
$919$	42.9349			1.41629			0.708146	+	0.706066i	$0.249532\pi$
$920$	5.83925	+	10.1139i	0.192514	+	0.333445i
$921$		0			0
$922$	13.8999	−	24.0754i	0.457769	−	0.792880i
$923$	2.69691	−	0.694747i	0.0887700	−	0.0228679i
$924$		0			0
$925$	−1.25893	+	0.726843i	−0.0413933	+	0.0238985i
$926$	−36.3097			−1.19321
$927$		0			0
$928$		−	0.218255i		−	0.00716458i
$929$	−8.98486	+	5.18741i	−0.294784	+	0.170193i	−0.640097	−	0.768294i	$-0.721106\pi$
$929$	−8.98486	+	5.18741i	−0.294784	+	0.170193i	0.345314	+	0.938487i	$0.387773\pi$
$930$		0			0
$931$	−14.7428	−	8.51175i	−0.483175	−	0.278961i
$932$	−5.34473	+	9.25734i	−0.175072	+	0.303234i
$933$		0			0
$934$	11.9767	−	6.91477i	0.391890	−	0.226258i
$935$	84.0583			2.74900
$936$		0			0
$937$	−26.4110			−0.862809			−0.431404	−	0.902159i	$-0.641982\pi$
$937$	−26.4110			−0.862809			−0.431404	+	0.902159i	$0.641982\pi$
$938$	−9.97840	+	5.76103i	−0.325806	+	0.188104i
$939$		0			0
$940$	−11.2676	+	19.5161i	−0.367509	+	0.636545i
$941$	−11.0738	−	6.39347i	−0.360996	−	0.208421i	0.308522	−	0.951217i	$-0.400166\pi$
$941$	−11.0738	−	6.39347i	−0.360996	−	0.208421i	−0.669518	+	0.742796i	$0.733499\pi$
$942$		0			0
$943$	23.6368	−	13.6467i	0.769721	−	0.444399i
$944$			10.4471i			0.340024i
$945$		0			0
$946$	−23.0389			−0.749061
$947$	−0.400885	+	0.231451i	−0.0130270	+	0.00752114i	−0.506499	−	0.862240i	$-0.669061\pi$
$947$	−0.400885	+	0.231451i	−0.0130270	+	0.00752114i	0.493472	+	0.869761i	$0.335727\pi$
$948$		0			0
$949$	−47.2556	+	12.1734i	−1.53398	+	0.395166i
$950$	9.37165	−	16.2322i	0.304056	−	0.526641i
$951$		0			0
$952$	5.56391	+	9.63697i	0.180327	+	0.312336i
$953$	−12.0901			−0.391636			−0.195818	−	0.980640i	$-0.562736\pi$
$953$	−12.0901			−0.391636			−0.195818	+	0.980640i	$0.562736\pi$
$954$		0			0
$955$			0.831493i			0.0269065i
$956$	20.8684	−	12.0484i	0.674933	−	0.389673i
$957$		0			0
$958$	−14.1167	+	24.4509i	−0.456091	+	0.789973i
$959$	−5.79207	+	10.0322i	−0.187036	+	0.323956i
$960$		0			0
$961$	−10.7903	−	18.6894i	−0.348075	−	0.602883i
$962$	0.751946	−	0.737538i	0.0242437	−	0.0237792i
$963$		0			0
$964$			11.1299i			0.358470i
$965$	18.5038	+	32.0495i	0.595658	+	1.03171i
$966$		0			0
$967$	−25.8211	−	14.9078i	−0.830352	−	0.479404i	0.0236211	−	0.999721i	$-0.492480\pi$
$967$	−25.8211	−	14.9078i	−0.830352	−	0.479404i	−0.853973	+	0.520317i	$0.825814\pi$
$968$	2.76001	+	1.59349i	0.0887100	+	0.0512167i
$969$		0			0
$970$	1.69207	−	0.976916i	0.0543291	−	0.0313669i
$971$	61.4263			1.97126			0.985632	−	0.168908i	$-0.0540242\pi$
$971$	61.4263			1.97126			0.985632	+	0.168908i	$0.0540242\pi$
$972$		0			0
$973$			11.5145i			0.369138i
$974$	−7.77895	−	13.4735i	−0.249254	−	0.431720i
$975$		0			0
$976$	3.00007	−	5.19627i	0.0960298	−	0.166329i
$977$	−19.8036	−	11.4336i	−0.633575	−	0.365794i	0.148561	−	0.988903i	$-0.452536\pi$
$977$	−19.8036	−	11.4336i	−0.633575	−	0.365794i	−0.782135	+	0.623109i	$0.785869\pi$
$978$		0			0
$979$	−13.3064	−	23.0474i	−0.425275	−	0.736597i
$980$			14.2754i			0.456010i
$981$		0			0
$982$			14.9787i			0.477990i
$983$	−25.0365	+	14.4549i	−0.798541	+	0.461038i	−0.842961	−	0.537975i	$-0.819190\pi$
$983$	−25.0365	+	14.4549i	−0.798541	+	0.461038i	0.0444194	+	0.999013i	$0.485856\pi$
$984$		0			0
$985$	32.4195	−	56.1523i	1.03297	−	1.78916i
$986$	−1.33551	−	0.771059i	−0.0425314	−	0.0245555i
$987$		0			0
$988$	−3.64162	+	13.0832i	−0.115855	+	0.416231i
$989$	−22.6163			−0.719156
$990$		0			0
$991$	21.3095			0.676917			0.338459	−	0.940981i	$-0.390095\pi$
$991$	21.3095			0.676917			0.338459	+	0.940981i	$0.390095\pi$
$992$	1.53455	+	2.65792i	0.0487220	+	0.0843890i
$993$		0			0
$994$	−1.05350	−	0.608241i	−0.0334151	−	0.0192922i
$995$	16.2821	+	9.40050i	0.516179	+	0.298016i
$996$		0			0
$997$	26.9037	+	46.5986i	0.852049	+	1.47579i	0.879356	+	0.476166i	$0.157974\pi$
$997$	26.9037	+	46.5986i	0.852049	+	1.47579i	−0.0273064	+	0.999627i	$0.508693\pi$
$998$	−34.1030			−1.07951
$999$		0			0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.t.a.415.7		28
3.2	odd	2		234.2.t.a.103.13	yes	28
9.2	odd	6		234.2.t.a.25.6	✓	28
9.4	even	3		2106.2.b.d.649.1		14
9.5	odd	6		2106.2.b.c.649.14		14
9.7	even	3	inner	702.2.t.a.181.8		28
13.12	even	2	inner	702.2.t.a.415.8		28
39.38	odd	2		234.2.t.a.103.6	yes	28
117.25	even	6	inner	702.2.t.a.181.7		28
117.38	odd	6		234.2.t.a.25.13	yes	28
117.77	odd	6		2106.2.b.c.649.1		14
117.103	even	6		2106.2.b.d.649.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.6	✓	28	9.2	odd	6
234.2.t.a.25.13	yes	28	117.38	odd	6
234.2.t.a.103.6	yes	28	39.38	odd	2
234.2.t.a.103.13	yes	28	3.2	odd	2
702.2.t.a.181.7		28	117.25	even	6	inner
702.2.t.a.181.8		28	9.7	even	3	inner
702.2.t.a.415.7		28	1.1	even	1	trivial
702.2.t.a.415.8		28	13.12	even	2	inner
2106.2.b.c.649.1		14	117.77	odd	6
2106.2.b.c.649.14		14	9.5	odd	6
2106.2.b.d.649.1		14	9.4	even	3
2106.2.b.d.649.14		14	117.103	even	6

Overview	Random
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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

Related objects

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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	702.2.t.a.415.7

Level	$702$
Weight	$2$
Character	702.415
Analytic conductor	$5.605$
Analytic rank	$0$
Dimension	$28$
Inner twists	$4$