LMFDB - Embedded newform 896.2.bi.a.271.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(47,896)] 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("896.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 20])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$896 = 2^{7} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	896.bi (of order $24$ , degree $8$ , 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			271.18
Character	$\chi$	$=$	896.271
Dual form			896.2.bi.a.367.18

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.360299 - 0.469551i) q^{3} +(2.24363 + 2.92396i) q^{5} +(-2.53705 + 0.750581i) q^{7} +(0.685795 + 2.55942i) q^{9} +(-0.0254955 - 0.193658i) q^{11} +(-1.79545 - 4.33461i) q^{13} +2.18132 q^{15} +(1.63000 + 2.82324i) q^{17} +(-0.981731 + 7.45699i) q^{19} +(-0.561661 + 1.46171i) q^{21} +(0.849490 - 0.227620i) q^{23} +(-2.22155 + 8.29094i) q^{25} +(3.08928 + 1.27962i) q^{27} +(-0.793041 - 1.91457i) q^{29} +(-1.85113 - 3.20626i) q^{31} +(-0.100118 - 0.0578032i) q^{33} +(-7.88688 - 5.73420i) q^{35} +(-8.19504 + 6.28828i) q^{37} +(-2.68222 - 0.718698i) q^{39} +(-3.81582 - 3.81582i) q^{41} +(2.28159 + 0.945065i) q^{43} +(-5.94497 + 7.74763i) q^{45} +(1.58163 + 0.913157i) q^{47} +(5.87326 - 3.80853i) q^{49} +(1.91294 + 0.251843i) q^{51} +(8.93961 - 1.17692i) q^{53} +(0.509044 - 0.509044i) q^{55} +(3.14772 + 3.14772i) q^{57} +(1.11273 + 8.45206i) q^{59} +(-0.828697 + 6.29458i) q^{61} +(-3.66095 - 5.97864i) q^{63} +(8.64588 - 14.9751i) q^{65} +(9.50532 + 7.29369i) q^{67} +(0.199191 - 0.480890i) q^{69} +(4.95899 - 4.95899i) q^{71} +(2.03722 - 7.60300i) q^{73} +(3.09259 + 4.03035i) q^{75} +(0.210039 + 0.472183i) q^{77} +(-2.39290 + 4.14462i) q^{79} +(-5.17023 + 2.98503i) q^{81} +(5.02518 - 2.08150i) q^{83} +(-4.59792 + 11.1004i) q^{85} +(-1.18472 - 0.317445i) q^{87} +(0.0259571 + 0.0968732i) q^{89} +(7.80863 + 9.64949i) q^{91} +(-2.17246 - 0.286010i) q^{93} +(-24.0066 + 13.8602i) q^{95} -9.39885i q^{97} +(0.478166 - 0.198063i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$240 q + 12 q^{3} - 12 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} + 32 q^{15} + 12 q^{19} - 8 q^{21} - 4 q^{23} - 4 q^{25} - 16 q^{29} - 24 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} + 32 q^{43} - 48 q^{45} + 24 q^{47}+ \cdots + 40 q^{99}+O(q^{100})$ 240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 + 32 * q^15 + 12 * q^19 - 8 * q^21 - 4 * q^23 - 4 * q^25 - 16 * q^29 - 24 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 + 32 * q^43 - 48 * q^45 + 24 * q^47 - 20 * q^51 - 20 * q^53 - 16 * q^57 - 84 * q^59 - 12 * q^61 - 8 * q^65 - 36 * q^67 + 80 * q^71 - 12 * q^73 + 72 * q^75 - 8 * q^77 + 8 * q^79 + 24 * q^85 + 12 * q^87 - 12 * q^89 - 40 * q^91 + 20 * q^93 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$ .

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$

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			0
$2$		0			0
$3$	0.360299	−	0.469551i	0.208019	−	0.271095i	−0.677679	−	0.735358i	$-0.737014\pi$
$3$	0.360299	−	0.469551i	0.208019	−	0.271095i	0.885697	+	0.464263i	$0.153681\pi$
$4$		0			0
$5$	2.24363	+	2.92396i	1.00338	+	1.30763i	0.951061	+	0.309003i	$0.0999954\pi$
$5$	2.24363	+	2.92396i	1.00338	+	1.30763i	0.0523216	+	0.998630i	$0.483338\pi$
$6$		0			0
$7$	−2.53705	+	0.750581i	−0.958915	+	0.283693i
$7$	−2.53705	+	0.750581i	−0.958915	+	0.283693i
$8$		0			0
$9$	0.685795	+	2.55942i	0.228598	+	0.853140i
$10$		0			0
$11$	−0.0254955	−	0.193658i	−0.00768718	−	0.0583899i	0.987171	−	0.159665i	$-0.0510413\pi$
$11$	−0.0254955	−	0.193658i	−0.00768718	−	0.0583899i	−0.994859	+	0.101275i	$0.967708\pi$
$12$		0			0
$13$	−1.79545	−	4.33461i	−0.497969	−	1.20220i	−0.950575	−	0.310494i	$-0.899506\pi$
$13$	−1.79545	−	4.33461i	−0.497969	−	1.20220i	0.452606	−	0.891711i	$-0.350494\pi$
$14$		0			0
$15$	2.18132			0.563215
$16$		0			0
$17$	1.63000	+	2.82324i	0.395333	+	0.684736i	0.993144	−	0.116901i	$-0.0372960\pi$
$17$	1.63000	+	2.82324i	0.395333	+	0.684736i	−0.597811	+	0.801637i	$0.703963\pi$
$18$		0			0
$19$	−0.981731	+	7.45699i	−0.225225	+	1.71075i	0.388682	+	0.921372i	$0.372930\pi$
$19$	−0.981731	+	7.45699i	−0.225225	+	1.71075i	−0.613907	+	0.789378i	$0.710403\pi$
$20$		0			0
$21$	−0.561661	+	1.46171i	−0.122564	+	0.318971i
$22$		0			0
$23$	0.849490	−	0.227620i	0.177131	−	0.0474621i	−0.169163	−	0.985588i	$-0.554107\pi$
$23$	0.849490	−	0.227620i	0.177131	−	0.0474621i	0.346294	+	0.938126i	$0.387440\pi$
$24$		0			0
$25$	−2.22155	+	8.29094i	−0.444310	+	1.65819i
$26$		0			0
$27$	3.08928	+	1.27962i	0.594532	+	0.246263i
$28$		0			0
$29$	−0.793041	−	1.91457i	−0.147264	−	0.355527i	0.832985	−	0.553296i	$-0.186630\pi$
$29$	−0.793041	−	1.91457i	−0.147264	−	0.355527i	−0.980249	+	0.197769i	$0.936630\pi$
$30$		0			0
$31$	−1.85113	−	3.20626i	−0.332473	−	0.575861i	0.650523	−	0.759487i	$-0.274550\pi$
$31$	−1.85113	−	3.20626i	−0.332473	−	0.575861i	−0.982996	+	0.183626i	$0.941216\pi$
$32$		0			0
$33$	−0.100118	−	0.0578032i	−0.0174283	−	0.0100622i
$34$		0			0
$35$	−7.88688	−	5.73420i	−1.33313	−	0.969257i
$36$		0			0
$37$	−8.19504	+	6.28828i	−1.34726	+	1.03379i	−0.352051	+	0.935981i	$0.614516\pi$
$37$	−8.19504	+	6.28828i	−1.34726	+	1.03379i	−0.995206	+	0.0978057i	$0.968818\pi$
$38$		0			0
$39$	−2.68222	−	0.718698i	−0.429499	−	0.115084i
$40$		0			0
$41$	−3.81582	−	3.81582i	−0.595930	−	0.595930i	0.343297	−	0.939227i	$-0.388456\pi$
$41$	−3.81582	−	3.81582i	−0.595930	−	0.595930i	−0.939227	+	0.343297i	$0.888456\pi$
$42$		0			0
$43$	2.28159	+	0.945065i	0.347939	+	0.144121i	0.549807	−	0.835292i	$-0.314701\pi$
$43$	2.28159	+	0.945065i	0.347939	+	0.144121i	−0.201868	+	0.979413i	$0.564701\pi$
$44$		0			0
$45$	−5.94497	+	7.74763i	−0.886223	+	1.15495i
$46$		0			0
$47$	1.58163	+	0.913157i	0.230705	+	0.133198i	0.610897	−	0.791710i	$-0.290809\pi$
$47$	1.58163	+	0.913157i	0.230705	+	0.133198i	−0.380192	+	0.924907i	$0.624142\pi$
$48$		0			0
$49$	5.87326	−	3.80853i	0.839037	−	0.544075i
$50$		0			0
$51$	1.91294	+	0.251843i	0.267865	+	0.0352651i
$52$		0			0
$53$	8.93961	−	1.17692i	1.22795	−	0.161663i	0.511489	−	0.859290i	$-0.329094\pi$
$53$	8.93961	−	1.17692i	1.22795	−	0.161663i	0.716461	+	0.697627i	$0.245761\pi$
$54$		0			0
$55$	0.509044	−	0.509044i	0.0686395	−	0.0686395i
$56$		0			0
$57$	3.14772	+	3.14772i	0.416925	+	0.416925i
$58$		0			0
$59$	1.11273	+	8.45206i	0.144866	+	1.10036i	0.897213	+	0.441598i	$0.145588\pi$
$59$	1.11273	+	8.45206i	0.144866	+	1.10036i	−0.752347	+	0.658767i	$0.771079\pi$
$60$		0			0
$61$	−0.828697	+	6.29458i	−0.106104	+	0.805938i	0.852806	+	0.522228i	$0.174899\pi$
$61$	−0.828697	+	6.29458i	−0.106104	+	0.805938i	−0.958910	+	0.283711i	$0.908434\pi$
$62$		0			0
$63$	−3.66095	−	5.97864i	−0.461236	−	0.753237i
$64$		0			0
$65$	8.64588	−	14.9751i	1.07239	−	1.85743i
$66$		0			0
$67$	9.50532	+	7.29369i	1.16126	+	0.891066i	0.995468	−	0.0950951i	$-0.0303155\pi$
$67$	9.50532	+	7.29369i	1.16126	+	0.891066i	0.165791	+	0.986161i	$0.446982\pi$
$68$		0			0
$69$	0.199191	−	0.480890i	0.0239798	−	0.0578923i
$70$		0			0
$71$	4.95899	−	4.95899i	0.588524	−	0.588524i	−0.348708	−	0.937231i	$-0.613379\pi$
$71$	4.95899	−	4.95899i	0.588524	−	0.588524i	0.937231	+	0.348708i	$0.113379\pi$
$72$		0			0
$73$	2.03722	−	7.60300i	0.238438	−	0.889864i	−0.738130	−	0.674658i	$-0.764291\pi$
$73$	2.03722	−	7.60300i	0.238438	−	0.889864i	0.976569	−	0.215206i	$-0.0690422\pi$
$74$		0			0
$75$	3.09259	+	4.03035i	0.357102	+	0.465384i
$76$		0			0
$77$	0.210039	+	0.472183i	0.0239362	+	0.0538102i
$78$		0			0
$79$	−2.39290	+	4.14462i	−0.269222	+	0.466306i	−0.968661	−	0.248386i	$-0.920100\pi$
$79$	−2.39290	+	4.14462i	−0.269222	+	0.466306i	0.699439	+	0.714692i	$0.253433\pi$
$80$		0			0
$81$	−5.17023	+	2.98503i	−0.574470	+	0.331670i
$82$		0			0
$83$	5.02518	−	2.08150i	0.551585	−	0.228474i	−0.0894425	−	0.995992i	$-0.528509\pi$
$83$	5.02518	−	2.08150i	0.551585	−	0.228474i	0.641027	+	0.767518i	$0.278509\pi$
$84$		0			0
$85$	−4.59792	+	11.1004i	−0.498714	+	1.20400i
$86$		0			0
$87$	−1.18472	−	0.317445i	−0.127015	−	0.0340336i
$88$		0			0
$89$	0.0259571	+	0.0968732i	0.00275145	+	0.0102685i	0.967288	−	0.253681i	$-0.0816414\pi$
$89$	0.0259571	+	0.0968732i	0.00275145	+	0.0102685i	−0.964536	+	0.263950i	$0.914975\pi$
$90$		0			0
$91$	7.80863	+	9.64949i	0.818567	+	1.01154i
$92$		0			0
$93$	−2.17246	−	0.286010i	−0.225274	−	0.0296578i
$94$		0			0
$95$	−24.0066	+	13.8602i	−2.46302	+	1.42203i
$96$		0			0
$97$		−	9.39885i		−	0.954309i	−0.878819	−	0.477155i	$-0.841668\pi$
$97$		−	9.39885i		−	0.954309i	0.878819	−	0.477155i	$-0.158332\pi$
$98$		0			0
$99$	0.478166	−	0.198063i	0.0480575	−	0.0199061i
$100$		0			0
$101$	1.36609	−	0.179849i	0.135931	−	0.0178956i	−0.0622538	−	0.998060i	$-0.519829\pi$
$101$	1.36609	−	0.179849i	0.135931	−	0.0178956i	0.198184	+	0.980165i	$0.436495\pi$
$102$		0			0
$103$	11.1523	−	2.98824i	1.09887	−	0.294440i	0.336563	−	0.941661i	$-0.390735\pi$
$103$	11.1523	−	2.98824i	1.09887	−	0.294440i	0.762303	+	0.647221i	$0.224069\pi$
$104$		0			0
$105$	−5.53413	+	1.63726i	−0.540076	+	0.159780i
$106$		0			0
$107$	5.10252	−	3.91530i	0.493279	−	0.378507i	−0.331957	−	0.943295i	$-0.607709\pi$
$107$	5.10252	−	3.91530i	0.493279	−	0.378507i	0.825236	+	0.564788i	$0.191042\pi$
$108$		0			0
$109$	−5.56613	−	4.27104i	−0.533139	−	0.409092i	0.306799	−	0.951774i	$-0.400742\pi$
$109$	−5.56613	−	4.27104i	−0.533139	−	0.409092i	−0.839938	+	0.542683i	$0.817409\pi$
$110$		0			0
$111$			6.11365i			0.580282i
$112$		0			0
$113$		−	1.27034i		−	0.119504i	−0.998213	−	0.0597519i	$-0.980969\pi$
$113$		−	1.27034i		−	0.119504i	0.998213	−	0.0597519i	$-0.0190310\pi$
$114$		0			0
$115$	2.57149	+	1.97318i	0.239793	+	0.184000i
$116$		0			0
$117$	9.86277	−	7.56797i	0.911814	−	0.699659i
$118$		0			0
$119$	−6.25446	−	5.93926i	−0.573345	−	0.544451i
$120$		0			0
$121$	10.5883	−	2.83713i	0.962576	−	0.257921i
$122$		0			0
$123$	−3.16655	+	0.416885i	−0.285518	+	0.0375892i
$124$		0			0
$125$	−12.2016	+	5.05406i	−1.09134	+	0.452049i
$126$		0			0
$127$		−	6.29532i		−	0.558619i	−0.960201	−	0.279310i	$-0.909894\pi$
$127$		−	6.29532i		−	0.558619i	0.960201	−	0.279310i	$-0.0901056\pi$
$128$		0			0
$129$	1.26581	−	0.730815i	0.111448	−	0.0643447i
$130$		0			0
$131$	−20.1751	−	2.65611i	−1.76271	−	0.232065i	−0.821575	−	0.570100i	$-0.806905\pi$
$131$	−20.1751	−	2.65611i	−1.76271	−	0.232065i	−0.941134	+	0.338035i	$0.890238\pi$
$132$		0			0
$133$	−3.10637	−	19.6556i	−0.269357	−	1.70436i
$134$		0			0
$135$	3.18964	+	11.9039i	0.274521	+	1.02453i
$136$		0			0
$137$	21.1540	+	5.66819i	1.80731	+	0.484266i	0.995080	−	0.0990762i	$-0.0315888\pi$
$137$	21.1540	+	5.66819i	1.80731	+	0.484266i	0.812226	+	0.583342i	$0.198255\pi$
$138$		0			0
$139$	−7.25213	+	17.5082i	−0.615118	+	1.48503i	0.242194	+	0.970228i	$0.422133\pi$
$139$	−7.25213	+	17.5082i	−0.615118	+	1.48503i	−0.857311	+	0.514798i	$0.827867\pi$
$140$		0			0
$141$	0.998634	−	0.413648i	0.0841002	−	0.0348354i
$142$		0			0
$143$	−0.793654	+	0.458216i	−0.0663687	+	0.0383180i
$144$		0			0
$145$	3.81883	−	6.61441i	0.317137	−	0.549297i
$146$		0			0
$147$	0.327832	−	4.13000i	0.0270391	−	0.340636i
$148$		0			0
$149$	4.47610	+	5.83337i	0.366696	+	0.477888i	0.939863	−	0.341551i	$-0.110952\pi$
$149$	4.47610	+	5.83337i	0.366696	+	0.477888i	−0.573167	+	0.819439i	$0.694285\pi$
$150$		0			0
$151$	5.48853	−	20.4835i	0.446650	−	1.66692i	−0.264892	−	0.964278i	$-0.585336\pi$
$151$	5.48853	−	20.4835i	0.446650	−	1.66692i	0.711542	−	0.702643i	$-0.247997\pi$
$152$		0			0
$153$	−6.10801	+	6.10801i	−0.493804	+	0.493804i
$154$		0			0
$155$	5.22170	−	12.6063i	0.419417	−	1.01256i
$156$		0			0
$157$	−2.93506	−	2.25215i	−0.234244	−	0.179741i	0.484969	−	0.874531i	$-0.338831\pi$
$157$	−2.93506	−	2.25215i	−0.234244	−	0.179741i	−0.719213	+	0.694790i	$0.755497\pi$
$158$		0			0
$159$	2.66831	−	4.62164i	0.211610	−	0.366520i
$160$		0			0
$161$	−1.98435	+	1.21509i	−0.156389	+	0.0957629i
$162$		0			0
$163$	1.88541	−	14.3211i	0.147676	−	1.12171i	−0.743721	−	0.668491i	$-0.766941\pi$
$163$	1.88541	−	14.3211i	0.147676	−	1.12171i	0.891397	−	0.453223i	$-0.149726\pi$
$164$		0			0
$165$	−0.0556139	−	0.422430i	−0.00432954	−	0.0328861i
$166$		0			0
$167$	8.50231	+	8.50231i	0.657929	+	0.657929i	0.954890	−	0.296961i	$-0.0959732\pi$
$167$	8.50231	+	8.50231i	0.657929	+	0.657929i	−0.296961	+	0.954890i	$0.595973\pi$
$168$		0			0
$169$	−6.37280	+	6.37280i	−0.490215	+	0.490215i
$170$		0			0
$171$	−19.7588	+	2.60130i	−1.51100	+	0.198926i
$172$		0			0
$173$	7.20683	+	0.948797i	0.547925	+	0.0721357i	0.399407	−	0.916774i	$-0.369216\pi$
$173$	7.20683	+	0.948797i	0.547925	+	0.0721357i	0.148519	+	0.988910i	$0.452550\pi$
$174$		0			0
$175$	−0.586835	−	22.7020i	−0.0443606	−	1.71611i
$176$		0			0
$177$	4.36959	+	2.52278i	0.328438	+	0.189624i
$178$		0			0
$179$	10.2369	−	13.3410i	0.765143	−	0.997154i	−0.234543	−	0.972106i	$-0.575359\pi$
$179$	10.2369	−	13.3410i	0.765143	−	0.997154i	0.999686	−	0.0250486i	$-0.00797405\pi$
$180$		0			0
$181$	−1.48033	−	0.613171i	−0.110032	−	0.0455767i	0.326988	−	0.945028i	$-0.393966\pi$
$181$	−1.48033	−	0.613171i	−0.110032	−	0.0455767i	−0.437020	+	0.899452i	$0.643966\pi$
$182$		0			0
$183$	2.65704	+	2.65704i	0.196414	+	0.196414i
$184$		0			0
$185$	−36.7733	−	9.85338i	−2.70363	−	0.724435i
$186$		0			0
$187$	0.505184	−	0.387641i	0.0369427	−	0.0283471i
$188$		0			0
$189$	−8.79812	−	0.927710i	−0.639969	−	0.0674810i
$190$		0			0
$191$	−7.04481	−	4.06732i	−0.509745	−	0.294301i	0.222984	−	0.974822i	$-0.428420\pi$
$191$	−7.04481	−	4.06732i	−0.509745	−	0.294301i	−0.732729	+	0.680521i	$0.761754\pi$
$192$		0			0
$193$	1.59700	+	2.76608i	0.114954	+	0.199107i	0.917761	−	0.397132i	$-0.129995\pi$
$193$	1.59700	+	2.76608i	0.114954	+	0.199107i	−0.802807	+	0.596239i	$0.796661\pi$
$194$		0			0
$195$	−3.91647	−	9.45519i	−0.280464	−	0.677100i
$196$		0			0
$197$	−22.7704	−	9.43182i	−1.62233	−	0.671989i	−0.627985	−	0.778226i	$-0.716120\pi$
$197$	−22.7704	−	9.43182i	−1.62233	−	0.671989i	−0.994341	+	0.106237i	$0.966120\pi$
$198$		0			0
$199$	3.74470	−	13.9754i	0.265455	−	0.990690i	−0.696517	−	0.717540i	$-0.745268\pi$
$199$	3.74470	−	13.9754i	0.265455	−	0.990690i	0.961972	−	0.273150i	$-0.0880654\pi$
$200$		0			0
$201$	6.84951	−	1.83532i	0.483127	−	0.129454i
$202$		0			0
$203$	3.44903	+	4.26212i	0.242074	+	0.299142i
$204$		0			0
$205$	2.59600	−	19.7186i	0.181312	−	1.37720i
$206$		0			0
$207$	1.16515	+	2.01810i	0.0809836	+	0.140268i
$208$		0			0
$209$	1.46913			0.101622
$210$		0			0
$211$	−6.84963	−	16.5365i	−0.471548	−	1.13842i	−0.963479	−	0.267784i	$-0.913709\pi$
$211$	−6.84963	−	16.5365i	−0.471548	−	1.13842i	0.491931	−	0.870634i	$-0.336291\pi$
$212$		0			0
$213$	−0.541778	−	4.11521i	−0.0371220	−	0.281970i
$214$		0			0
$215$	2.35571	+	8.79164i	0.160658	+	0.599585i
$216$		0			0
$217$	7.10297	+	6.74501i	0.482181	+	0.457881i
$218$		0			0
$219$	−2.83599	−	3.69593i	−0.191638	−	0.249748i
$220$		0			0
$221$	9.31105	−	12.1344i	0.626329	−	0.816248i
$222$		0			0
$223$	2.20295			0.147520			0.0737601	−	0.997276i	$-0.476500\pi$
$223$	2.20295			0.147520			0.0737601	+	0.997276i	$0.476500\pi$
$224$		0			0
$225$	−22.7435			−1.51623
$226$		0			0
$227$	−3.47455	+	4.52812i	−0.230614	+	0.300542i	−0.894299	−	0.447470i	$-0.852325\pi$
$227$	−3.47455	+	4.52812i	−0.230614	+	0.300542i	0.663685	+	0.748012i	$0.268992\pi$
$228$		0			0
$229$	14.7391	+	19.2084i	0.973988	+	1.26933i	0.963032	+	0.269386i	$0.0868207\pi$
$229$	14.7391	+	19.2084i	0.973988	+	1.26933i	0.0109556	+	0.999940i	$0.496513\pi$
$230$		0			0
$231$	0.297390	+	0.0715029i	0.0195669	+	0.00470454i
$232$		0			0
$233$	−4.59370	−	17.1439i	−0.300944	−	1.12314i	−0.936381	−	0.350984i	$-0.885847\pi$
$233$	−4.59370	−	17.1439i	−0.300944	−	1.12314i	0.635438	−	0.772152i	$-0.280820\pi$
$234$		0			0
$235$	0.878572	+	6.67342i	0.0573117	+	0.435326i
$236$		0			0
$237$	1.08395	+	2.61689i	0.0704102	+	0.169985i
$238$		0			0
$239$	−12.6706			−0.819591			−0.409796	−	0.912177i	$-0.634400\pi$
$239$	−12.6706			−0.819591			−0.409796	+	0.912177i	$0.634400\pi$
$240$		0			0
$241$	4.33725	+	7.51235i	0.279387	+	0.483913i	0.971233	−	0.238133i	$-0.0765354\pi$
$241$	4.33725	+	7.51235i	0.279387	+	0.483913i	−0.691845	+	0.722046i	$0.743202\pi$
$242$		0			0
$243$	−1.77057	+	13.4488i	−0.113582	+	0.862741i
$244$		0			0
$245$	24.3134	+	8.62822i	1.55333	+	0.551237i
$246$		0			0
$247$	34.0858	−	9.13326i	2.16883	−	0.581135i
$248$		0			0
$249$	0.833197	−	3.10953i	0.0528017	−	0.197059i
$250$		0			0
$251$	−4.22400	−	1.74964i	−0.266617	−	0.110436i	0.245370	−	0.969429i	$-0.421090\pi$
$251$	−4.22400	−	1.74964i	−0.266617	−	0.110436i	−0.511987	+	0.858993i	$0.671090\pi$
$252$		0			0
$253$	−0.0657385	−	0.158707i	−0.00413294	−	0.00997781i
$254$		0			0
$255$	3.55555	+	6.15840i	0.222657	+	0.385654i
$256$		0			0
$257$	−0.0444799	−	0.0256805i	−0.00277458	−	0.00160190i	0.498612	−	0.866825i	$-0.333843\pi$
$257$	−0.0444799	−	0.0256805i	−0.00277458	−	0.00160190i	−0.501387	+	0.865223i	$0.667177\pi$
$258$		0			0
$259$	16.0714	−	22.1047i	0.998627	−	1.37352i
$260$		0			0
$261$	4.35633	−	3.34273i	0.269650	−	0.206910i
$262$		0			0
$263$	−1.65899	−	0.444526i	−0.102298	−	0.0274106i	0.207307	−	0.978276i	$-0.433530\pi$
$263$	−1.65899	−	0.444526i	−0.102298	−	0.0274106i	−0.309605	+	0.950865i	$0.600197\pi$
$264$		0			0
$265$	23.4985	+	23.4985i	1.44350	+	1.44350i
$266$		0			0
$267$	0.0548392	+	0.0227151i	0.00335610	+	0.00139014i
$268$		0			0
$269$	−1.33922	+	1.74531i	−0.0816539	+	0.106413i	−0.832394	−	0.554184i	$-0.813030\pi$
$269$	−1.33922	+	1.74531i	−0.0816539	+	0.106413i	0.750740	+	0.660598i	$0.229697\pi$
$270$		0			0
$271$	3.98800	+	2.30247i	0.242254	+	0.139865i	0.616212	−	0.787580i	$-0.288666\pi$
$271$	3.98800	+	2.30247i	0.242254	+	0.139865i	−0.373959	+	0.927445i	$0.622000\pi$
$272$		0			0
$273$	7.34437	−	0.189848i	0.444501	−	0.0114901i
$274$		0			0
$275$	1.66224	+	0.218838i	0.100237	+	0.0131964i
$276$		0			0
$277$	5.24024	−	0.689891i	0.314855	−	0.0414515i	0.0285575	−	0.999592i	$-0.490909\pi$
$277$	5.24024	−	0.689891i	0.314855	−	0.0414515i	0.286298	+	0.958141i	$0.407575\pi$
$278$		0			0
$279$	6.93666	−	6.93666i	0.415287	−	0.415287i
$280$		0			0
$281$	6.51561	+	6.51561i	0.388689	+	0.388689i	0.874220	−	0.485531i	$-0.161374\pi$
$281$	6.51561	+	6.51561i	0.388689	+	0.388689i	−0.485531	+	0.874220i	$0.661374\pi$
$282$		0			0
$283$	1.59733	+	12.1329i	0.0949514	+	0.721227i	0.971013	+	0.239028i	$0.0768287\pi$
$283$	1.59733	+	12.1329i	0.0949514	+	0.721227i	−0.876061	+	0.482200i	$0.839838\pi$
$284$		0			0
$285$	−2.14147	+	16.2661i	−0.126850	+	0.963521i
$286$		0			0
$287$	12.5450	+	6.81684i	0.740508	+	0.402385i
$288$		0			0
$289$	3.18621	−	5.51868i	0.187424	−	0.324628i
$290$		0			0
$291$	−4.41324	−	3.38640i	−0.258709	−	0.198514i
$292$		0			0
$293$	−9.68853	+	23.3902i	−0.566010	+	1.36647i	0.338883	+	0.940829i	$0.389951\pi$
$293$	−9.68853	+	23.3902i	−0.566010	+	1.36647i	−0.904892	+	0.425640i	$0.860049\pi$
$294$		0			0
$295$	−22.2169	+	22.2169i	−1.29352	+	1.29352i
$296$		0			0
$297$	0.169046	−	0.630887i	0.00980902	−	0.0366078i
$298$		0			0
$299$	−2.51186	−	3.27352i	−0.145265	−	0.189313i
$300$		0			0
$301$	−6.49785	−	0.685161i	−0.374530	−	0.0394920i
$302$		0			0
$303$	0.407751	−	0.706246i	0.0234247	−	0.0405728i
$304$		0			0
$305$	−20.2644	+	11.6996i	−1.16033	+	0.669919i
$306$		0			0
$307$	1.39053	−	0.575975i	0.0793616	−	0.0328727i	−0.342649	−	0.939463i	$-0.611324\pi$
$307$	1.39053	−	0.575975i	0.0793616	−	0.0328727i	0.422011	+	0.906591i	$0.361324\pi$
$308$		0			0
$309$	2.61502	−	6.31322i	0.148763	−	0.359146i
$310$		0			0
$311$	−29.2400	−	7.83483i	−1.65805	−	0.444273i	−0.696198	−	0.717850i	$-0.745126\pi$
$311$	−29.2400	−	7.83483i	−1.65805	−	0.444273i	−0.961850	+	0.273577i	$0.911793\pi$
$312$		0			0
$313$	0.740609	+	2.76399i	0.0418617	+	0.156230i	0.983693	−	0.179856i	$-0.0575633\pi$
$313$	0.740609	+	2.76399i	0.0418617	+	0.156230i	−0.941831	+	0.336086i	$0.890897\pi$
$314$		0			0
$315$	9.26746	−	24.1183i	0.522162	−	1.35891i
$316$		0			0
$317$	5.28998	+	0.696439i	0.297115	+	0.0391159i	0.277610	−	0.960694i	$-0.410458\pi$
$317$	5.28998	+	0.696439i	0.297115	+	0.0391159i	0.0195048	+	0.999810i	$0.493791\pi$
$318$		0			0
$319$	−0.350552	+	0.202391i	−0.0196271	+	0.0113317i
$320$		0			0
$321$		−	3.80657i		−	0.212462i
$322$		0			0
$323$	−22.6531	+	9.38321i	−1.26045	+	0.522096i
$324$		0			0
$325$	39.9267	−	5.25645i	2.21473	−	0.291575i
$326$		0			0
$327$	−4.01094	+	1.07473i	−0.221805	+	0.0594326i
$328$		0			0
$329$	−4.69808	−	1.12958i	−0.259014	−	0.0622758i
$330$		0			0
$331$	12.7330	−	9.77040i	0.699871	−	0.537030i	−0.196407	−	0.980522i	$-0.562927\pi$
$331$	12.7330	−	9.77040i	0.699871	−	0.537030i	0.896278	+	0.443493i	$0.146261\pi$
$332$		0			0
$333$	−21.7145	−	16.6621i	−1.18995	−	0.913077i
$334$		0			0
$335$			44.1575i			2.41258i
$336$		0			0
$337$		−	25.9961i		−	1.41610i	−0.706163	−	0.708049i	$-0.749575\pi$
$337$		−	25.9961i		−	1.41610i	0.706163	−	0.708049i	$-0.250425\pi$
$338$		0			0
$339$	−0.596490	−	0.457703i	−0.0323969	−	0.0248590i
$340$		0			0
$341$	−0.573720	+	0.440231i	−0.0310687	+	0.0238398i
$342$		0			0
$343$	−12.0421	+	14.0708i	−0.650215	+	0.759751i
$344$		0			0
$345$	1.85301	−	0.496513i	0.0997628	−	0.0267314i
$346$		0			0
$347$	25.7655	−	3.39209i	1.38317	−	0.182097i	0.598056	−	0.801454i	$-0.295940\pi$
$347$	25.7655	−	3.39209i	1.38317	−	0.182097i	0.785109	+	0.619357i	$0.212607\pi$
$348$		0			0
$349$	9.97430	−	4.13149i	0.533912	−	0.221154i	−0.0994037	−	0.995047i	$-0.531694\pi$
$349$	9.97430	−	4.13149i	0.533912	−	0.221154i	0.633316	+	0.773894i	$0.281694\pi$
$350$		0			0
$351$		−	15.6883i		−	0.837380i
$352$		0			0
$353$	−8.89552	+	5.13583i	−0.473461	+	0.273353i	−0.717687	−	0.696365i	$-0.754799\pi$
$353$	−8.89552	+	5.13583i	−0.473461	+	0.273353i	0.244226	+	0.969718i	$0.421466\pi$
$354$		0			0
$355$	25.6260	+	3.37373i	1.36009	+	0.179059i
$356$		0			0
$357$	−5.04226	+	0.796877i	−0.266865	+	0.0421752i
$358$		0			0
$359$	−8.49961	−	31.7210i	−0.448592	−	1.67417i	−0.706274	−	0.707939i	$-0.749625\pi$
$359$	−8.49961	−	31.7210i	−0.448592	−	1.67417i	0.257682	−	0.966230i	$-0.417041\pi$
$360$		0			0
$361$	−36.2903	−	9.72395i	−1.91001	−	0.511787i
$362$		0			0
$363$	2.48279	−	5.99397i	0.130312	−	0.314602i
$364$		0			0
$365$	26.8016	−	11.1016i	1.40286	−	0.581084i
$366$		0			0
$367$	4.93261	−	2.84784i	0.257480	−	0.148656i	−0.365704	−	0.930731i	$-0.619172\pi$
$367$	4.93261	−	2.84784i	0.257480	−	0.148656i	0.623185	+	0.782075i	$0.285839\pi$
$368$		0			0
$369$	7.14941	−	12.3831i	0.372183	−	0.644641i
$370$		0			0
$371$	−21.7969	+	9.69581i	−1.13164	+	0.503381i
$372$		0			0
$373$	−1.55936	−	2.03219i	−0.0807404	−	0.105223i	0.751237	−	0.660033i	$-0.229458\pi$
$373$	−1.55936	−	2.03219i	−0.0807404	−	0.105223i	−0.831977	+	0.554810i	$0.812791\pi$
$374$		0			0
$375$	−2.02308	+	7.55024i	−0.104471	+	0.389893i
$376$		0			0
$377$	−6.87505	+	6.87505i	−0.354083	+	0.354083i
$378$		0			0
$379$	−7.46656	+	18.0259i	−0.383531	+	0.925926i	0.607746	+	0.794132i	$0.292074\pi$
$379$	−7.46656	+	18.0259i	−0.383531	+	0.925926i	−0.991277	+	0.131795i	$0.957926\pi$
$380$		0			0
$381$	−2.95597	−	2.26820i	−0.151439	−	0.116203i
$382$		0			0
$383$	−9.29771	+	16.1041i	−0.475091	+	0.822882i	−0.999593	−	0.0285276i	$-0.990918\pi$
$383$	−9.29771	+	16.1041i	−0.475091	+	0.822882i	0.524502	+	0.851409i	$0.324251\pi$
$384$		0			0
$385$	−0.909392	+	1.67355i	−0.0463469	+	0.0852920i
$386$		0			0
$387$	−0.854117	+	6.48766i	−0.0434172	+	0.329786i
$388$		0			0
$389$	0.470226	+	3.57172i	0.0238414	+	0.181093i	0.999222	−	0.0394341i	$-0.0125555\pi$
$389$	0.470226	+	3.57172i	0.0238414	+	0.181093i	−0.975381	+	0.220527i	$0.929222\pi$
$390$		0			0
$391$	2.02729	+	2.02729i	0.102525	+	0.102525i
$392$		0			0
$393$	−8.51625	+	8.51625i	−0.429588	+	0.429588i
$394$		0			0
$395$	−17.4875	+	2.30227i	−0.879891	+	0.115840i
$396$		0			0
$397$	−13.9742	−	1.83974i	−0.701344	−	0.0923337i	−0.228583	−	0.973524i	$-0.573409\pi$
$397$	−13.9742	−	1.83974i	−0.701344	−	0.0923337i	−0.472761	+	0.881191i	$0.656743\pi$
$398$		0			0
$399$	−10.3485	−	5.62330i	−0.518075	−	0.281517i
$400$		0			0
$401$	9.96747	+	5.75472i	0.497752	+	0.287377i	0.727785	−	0.685806i	$-0.240550\pi$
$401$	9.96747	+	5.75472i	0.497752	+	0.287377i	−0.230033	+	0.973183i	$0.573883\pi$
$402$		0			0
$403$	−10.5742	+	13.7806i	−0.526741	+	0.686462i
$404$		0			0
$405$	−20.3282	−	8.42022i	−1.01012	−	0.418404i
$406$		0			0
$407$	1.42671	+	1.42671i	0.0707193	+	0.0707193i
$408$		0			0
$409$	−10.4818	−	2.80860i	−0.518294	−	0.138876i	−0.00981657	−	0.999952i	$-0.503125\pi$
$409$	−10.4818	−	2.80860i	−0.518294	−	0.138876i	−0.508477	+	0.861075i	$0.669791\pi$
$410$		0			0
$411$	10.2833	−	7.89062i	0.507236	−	0.389216i
$412$		0			0
$413$	−9.16702	−	20.6081i	−0.451080	−	1.01406i
$414$		0			0
$415$	17.3608	+	10.0233i	0.852211	+	0.492024i
$416$		0			0
$417$	5.60805	+	9.71343i	0.274627	+	0.475669i
$418$		0			0
$419$	1.14858	+	2.77292i	0.0561119	+	0.135466i	0.949449	−	0.313920i	$-0.101643\pi$
$419$	1.14858	+	2.77292i	0.0561119	+	0.135466i	−0.893337	+	0.449387i	$0.851643\pi$
$420$		0			0
$421$	18.6016	+	7.70504i	0.906587	+	0.375521i	0.786749	−	0.617273i	$-0.211762\pi$
$421$	18.6016	+	7.70504i	0.906587	+	0.375521i	0.119838	+	0.992793i	$0.461762\pi$
$422$		0			0
$423$	−1.25248	+	4.67430i	−0.0608975	+	0.227272i
$424$		0			0
$425$	−27.0284	+	7.24225i	−1.31107	+	0.351301i
$426$		0			0
$427$	−2.62215	−	16.5917i	−0.126894	−	0.802927i
$428$		0			0
$429$	−0.0707968	+	0.537755i	−0.00341810	+	0.0259631i
$430$		0			0
$431$	0.410242	+	0.710561i	0.0197607	+	0.0342265i	0.875737	−	0.482789i	$-0.160376\pi$
$431$	0.410242	+	0.710561i	0.0197607	+	0.0342265i	−0.855976	+	0.517016i	$0.827043\pi$
$432$		0			0
$433$	19.1887			0.922148			0.461074	−	0.887362i	$-0.347464\pi$
$433$	19.1887			0.922148			0.461074	+	0.887362i	$0.347464\pi$
$434$		0			0
$435$	−1.72988	−	4.17630i	−0.0829414	−	0.200238i
$436$		0			0
$437$	0.863390	+	6.55809i	0.0413015	+	0.313716i
$438$		0			0
$439$	8.03114	+	29.9726i	0.383305	+	1.43051i	0.840821	+	0.541313i	$0.182073\pi$
$439$	8.03114	+	29.9726i	0.383305	+	1.43051i	−0.457516	+	0.889201i	$0.651261\pi$
$440$		0			0
$441$	13.7755	+	12.4203i	0.655974	+	0.591441i
$442$		0			0
$443$	−4.04691	−	5.27404i	−0.192275	−	0.250577i	0.687261	−	0.726411i	$-0.258813\pi$
$443$	−4.04691	−	5.27404i	−0.192275	−	0.250577i	−0.879535	+	0.475834i	$0.842146\pi$
$444$		0			0
$445$	−0.225015	+	0.293245i	−0.0106667	+	0.0139012i
$446$		0			0
$447$	4.35179			0.205833
$448$		0			0
$449$	−21.8843			−1.03278			−0.516392	−	0.856352i	$-0.672725\pi$
$449$	−21.8843			−1.03278			−0.516392	+	0.856352i	$0.672725\pi$
$450$		0			0
$451$	−0.641675	+	0.836248i	−0.0302153	+	0.0393774i
$452$		0			0
$453$	−7.64051	−	9.95731i	−0.358983	−	0.467835i
$454$		0			0
$455$	−10.6950	+	44.4820i	−0.501390	+	2.08535i
$456$		0			0
$457$	5.04748	+	18.8375i	0.236111	+	0.881179i	0.977645	+	0.210263i	$0.0674321\pi$
$457$	5.04748	+	18.8375i	0.236111	+	0.881179i	−0.741534	+	0.670916i	$0.765901\pi$
$458$		0			0
$459$	1.42284	+	10.8076i	0.0664125	+	0.504453i
$460$		0			0
$461$	5.00740	+	12.0889i	0.233218	+	0.563038i	0.996552	−	0.0829658i	$-0.0264392\pi$
$461$	5.00740	+	12.0889i	0.233218	+	0.563038i	−0.763335	+	0.646003i	$0.776439\pi$
$462$		0			0
$463$	37.5037			1.74294			0.871472	−	0.490445i	$-0.163166\pi$
$463$	37.5037			1.74294			0.871472	+	0.490445i	$0.163166\pi$
$464$		0			0
$465$	−4.03792	−	6.99388i	−0.187254	−	0.324334i
$466$		0			0
$467$	−2.46339	+	18.7113i	−0.113992	+	0.865856i	0.834932	+	0.550353i	$0.185507\pi$
$467$	−2.46339	+	18.7113i	−0.113992	+	0.865856i	−0.948924	+	0.315504i	$0.897827\pi$
$468$		0			0
$469$	−29.5900	−	11.3699i	−1.36634	−	0.525015i
$470$		0			0
$471$	−2.11500	+	0.566713i	−0.0974541	+	0.0261127i
$472$		0			0
$473$	0.124849	−	0.465942i	0.00574055	−	0.0214240i
$474$		0			0
$475$	−59.6445	−	24.7055i	−2.73668	−	1.13357i
$476$		0			0
$477$	9.14297	+	22.0731i	0.418628	+	1.01066i
$478$		0			0
$479$	9.26849	+	16.0535i	0.423488	+	0.733503i	0.996278	−	0.0861993i	$-0.0274722\pi$
$479$	9.26849	+	16.0535i	0.423488	+	0.733503i	−0.572790	+	0.819702i	$0.694139\pi$
$480$		0			0
$481$	41.9710	+	24.2320i	1.91372	+	1.10488i
$482$		0			0
$483$	−0.144411	+	1.36955i	−0.00657093	+	0.0623167i
$484$		0			0
$485$	27.4819	−	21.0876i	1.24789	−	0.957537i
$486$		0			0
$487$	5.44957	+	1.46021i	0.246944	+	0.0661684i	0.380168	−	0.924918i	$-0.375866\pi$
$487$	5.44957	+	1.46021i	0.246944	+	0.0661684i	−0.133224	+	0.991086i	$0.542533\pi$
$488$		0			0
$489$	−6.04516	−	6.04516i	−0.273372	−	0.273372i
$490$		0			0
$491$	27.2761	+	11.2981i	1.23095	+	0.509878i	0.900877	−	0.434075i	$-0.142925\pi$
$491$	27.2761	+	11.2981i	1.23095	+	0.509878i	0.330078	+	0.943954i	$0.392925\pi$
$492$		0			0
$493$	4.11264	−	5.35969i	0.185224	−	0.241388i
$494$		0			0
$495$	1.65196	+	0.953758i	0.0742499	+	0.0428682i
$496$		0			0
$497$	−8.85908	+	16.3033i	−0.397384	+	0.731304i
$498$		0			0
$499$	11.2114	+	1.47600i	0.501890	+	0.0660750i	0.377221	−	0.926123i	$-0.376880\pi$
$499$	11.2114	+	1.47600i	0.501890	+	0.0660750i	0.124669	+	0.992198i	$0.460213\pi$
$500$		0			0
$501$	7.05564	−	0.928892i	0.315223	−	0.0414998i
$502$		0			0
$503$	20.3957	−	20.3957i	0.909400	−	0.909400i	−0.0868238	−	0.996224i	$-0.527672\pi$
$503$	20.3957	−	20.3957i	0.909400	−	0.909400i	0.996224	+	0.0868238i	$0.0276717\pi$
$504$		0			0
$505$	3.59086	+	3.59086i	0.159791	+	0.159791i
$506$		0			0
$507$	0.696239	+	5.28846i	0.0309211	+	0.234869i
$508$		0			0
$509$	−3.36741	+	25.5780i	−0.149258	+	1.13372i	0.738778	+	0.673949i	$0.235403\pi$
$509$	−3.36741	+	25.5780i	−0.149258	+	1.13372i	−0.888035	+	0.459775i	$0.847930\pi$
$510$		0			0
$511$	0.538143	+	20.8183i	0.0238060	+	0.920947i
$512$		0			0
$513$	−12.5750	+	21.7805i	−0.555198	+	0.961631i
$514$		0			0
$515$	33.7591	+	25.9043i	1.48760	+	1.14148i
$516$		0			0
$517$	0.136515	−	0.329577i	0.00600393	−	0.0144948i
$518$		0			0
$519$	3.04212	−	3.04212i	0.133534	−	0.133534i
$520$		0			0
$521$	−0.409945	+	1.52994i	−0.0179600	+	0.0670277i	−0.974324	−	0.225149i	$-0.927713\pi$
$521$	−0.409945	+	1.52994i	−0.0179600	+	0.0670277i	0.956364	+	0.292177i	$0.0943797\pi$
$522$		0			0
$523$	−12.4581	−	16.2357i	−0.544756	−	0.709939i	0.437133	−	0.899397i	$-0.355994\pi$
$523$	−12.4581	−	16.2357i	−0.544756	−	0.709939i	−0.981889	+	0.189457i	$0.939327\pi$
$524$		0			0
$525$	−10.8712	−	7.90395i	−0.474457	−	0.344957i
$526$		0			0
$527$	6.03469	−	10.4524i	0.262875	−	0.455313i
$528$		0			0
$529$	−19.2488	+	11.1133i	−0.836903	+	0.483186i
$530$		0			0
$531$	−20.8693	+	8.64433i	−0.905649	+	0.375132i
$532$		0			0
$533$	−9.68895	+	23.3912i	−0.419675	+	1.01319i
$534$		0			0
$535$	22.8964	+	6.13506i	0.989896	+	0.265242i
$536$		0			0
$537$	−2.57593	−	9.61351i	−0.111160	−	0.414853i
$538$		0			0
$539$	−0.887291	−	1.04030i	−0.0382183	−	0.0448089i
$540$		0			0
$541$	33.4196	+	4.39978i	1.43682	+	0.189161i	0.808365	−	0.588682i	$-0.200353\pi$
$541$	33.4196	+	4.39978i	1.43682	+	0.189161i	0.628458	+	0.777844i	$0.283686\pi$
$542$		0			0
$543$	−0.821275	+	0.474163i	−0.0352443	+	0.0203483i
$544$		0			0
$545$		−	25.8578i		−	1.10763i
$546$		0			0
$547$	1.87204	−	0.775425i	0.0800427	−	0.0331548i	−0.342303	−	0.939590i	$-0.611207\pi$
$547$	1.87204	−	0.775425i	0.0800427	−	0.0331548i	0.422346	+	0.906435i	$0.361207\pi$
$548$		0			0
$549$	−16.6788	+	2.19580i	−0.711833	+	0.0937146i
$550$		0			0
$551$	15.0555	−	4.03410i	0.641385	−	0.171859i
$552$		0			0
$553$	2.96003	−	12.3112i	0.125873	−	0.523525i
$554$		0			0
$555$	−17.8760	+	13.7168i	−0.758796	+	0.582244i
$556$		0			0
$557$	20.3854	+	15.6423i	0.863758	+	0.662785i	0.942535	−	0.334108i	$-0.108435\pi$
$557$	20.3854	+	15.6423i	0.863758	+	0.662785i	−0.0787771	+	0.996892i	$0.525102\pi$
$558$		0			0
$559$		−	11.5866i		−	0.490062i
$560$		0			0
$561$		−	0.376876i		−	0.0159117i
$562$		0			0
$563$	−10.1022	−	7.75169i	−0.425757	−	0.326695i	0.373558	−	0.927607i	$-0.378138\pi$
$563$	−10.1022	−	7.75169i	−0.425757	−	0.326695i	−0.799315	+	0.600912i	$0.794804\pi$
$564$		0			0
$565$	3.71443	−	2.85018i	0.156267	−	0.119908i
$566$		0			0
$567$	10.8766	−	11.4539i	0.456775	−	0.481017i
$568$		0			0
$569$	−29.9072	+	8.01362i	−1.25378	+	0.335948i	−0.823794	−	0.566889i	$-0.808147\pi$
$569$	−29.9072	+	8.01362i	−1.25378	+	0.335948i	−0.429982	+	0.902837i	$0.641480\pi$
$570$		0			0
$571$	−16.4367	+	2.16393i	−0.687853	+	0.0905576i	−0.466348	−	0.884602i	$-0.654430\pi$
$571$	−16.4367	+	2.16393i	−0.687853	+	0.0905576i	−0.221505	+	0.975159i	$0.571097\pi$
$572$		0			0
$573$	−4.44805	+	1.84244i	−0.185820	+	0.0769692i
$574$		0			0
$575$			7.54873i			0.314804i
$576$		0			0
$577$	−30.5815	+	17.6562i	−1.27312	+	0.735038i	−0.975575	−	0.219668i	$-0.929502\pi$
$577$	−30.5815	+	17.6562i	−1.27312	+	0.735038i	−0.297549	+	0.954707i	$0.596169\pi$
$578$		0			0
$579$	1.87421	+	0.246744i	0.0778894	+	0.0102543i
$580$		0			0
$581$	−11.1868	+	9.05266i	−0.464107	+	0.375568i
$582$		0			0
$583$	−0.455840	−	1.70122i	−0.0188789	−	0.0704572i
$584$		0			0
$585$	44.2569	+	11.8586i	1.82980	+	0.490292i
$586$		0			0
$587$	5.67657	−	13.7044i	0.234297	−	0.565643i	−0.762377	−	0.647133i	$-0.775968\pi$
$587$	5.67657	−	13.7044i	0.234297	−	0.565643i	0.996674	+	0.0814899i	$0.0259678\pi$
$588$		0			0
$589$	25.7263	−	10.6562i	1.06003	−	0.439081i
$590$		0			0
$591$	−12.6329	+	7.29359i	−0.519647	+	0.300018i
$592$		0			0
$593$	−19.0770	+	33.0424i	−0.783400	+	1.35689i	0.146550	+	0.989203i	$0.453183\pi$
$593$	−19.0770	+	33.0424i	−0.783400	+	1.35689i	−0.929950	+	0.367685i	$0.880150\pi$
$594$		0			0
$595$	3.33344	−	31.6133i	0.136658	−	1.29602i
$596$		0			0
$597$	−5.21295	−	6.79365i	−0.213352	−	0.278045i
$598$		0			0
$599$	−5.33450	+	19.9086i	−0.217962	+	0.813444i	0.767141	+	0.641478i	$0.221679\pi$
$599$	−5.33450	+	19.9086i	−0.217962	+	0.813444i	−0.985103	+	0.171966i	$0.944988\pi$
$600$		0			0
$601$	11.0600	−	11.0600i	0.451146	−	0.451146i	−0.444589	−	0.895735i	$-0.646650\pi$
$601$	11.0600	−	11.0600i	0.451146	−	0.451146i	0.895735	+	0.444589i	$0.146650\pi$
$602$		0			0
$603$	−12.1489	+	29.3301i	−0.494742	+	1.19441i
$604$		0			0
$605$	32.0520	+	24.5943i	1.30310	+	0.999902i
$606$		0			0
$607$	5.10135	−	8.83580i	0.207057	−	0.358634i	−0.743729	−	0.668481i	$-0.766945\pi$
$607$	5.10135	−	8.83580i	0.207057	−	0.358634i	0.950786	+	0.309847i	$0.100278\pi$
$608$		0			0
$609$	3.24396	−	0.0838548i	0.131452	−	0.00339797i
$610$		0			0
$611$	1.11843	−	8.49530i	0.0452467	−	0.343683i
$612$		0			0
$613$	−2.74075	−	20.8180i	−0.110698	−	0.840832i	−0.953243	−	0.302206i	$-0.902277\pi$
$613$	−2.74075	−	20.8180i	−0.110698	−	0.840832i	0.842545	−	0.538626i	$-0.181056\pi$
$614$		0			0
$615$	−8.32353	−	8.32353i	−0.335637	−	0.335637i
$616$		0			0
$617$	24.2795	−	24.2795i	0.977456	−	0.977456i	−0.0222958	−	0.999751i	$-0.507098\pi$
$617$	24.2795	−	24.2795i	0.977456	−	0.977456i	0.999751	+	0.0222958i	$0.00709757\pi$
$618$		0			0
$619$	5.89248	−	0.775760i	0.236839	−	0.0311804i	−0.0111723	−	0.999938i	$-0.503556\pi$
$619$	5.89248	−	0.775760i	0.236839	−	0.0311804i	0.248011	+	0.968757i	$0.420223\pi$
$620$		0			0
$621$	2.91558	+	0.383843i	0.116998	+	0.0154031i
$622$		0			0
$623$	−0.138566	−	0.226289i	−0.00555152	−	0.00906609i
$624$		0			0
$625$	−4.98648	−	2.87894i	−0.199459	−	0.115158i
$626$		0			0
$627$	0.529326	−	0.689832i	0.0211393	−	0.0275492i
$628$		0			0
$629$	−31.1112	−	12.8867i	−1.24049	−	0.513826i
$630$		0			0
$631$	2.39818	+	2.39818i	0.0954700	+	0.0954700i	0.753229	−	0.657759i	$-0.228495\pi$
$631$	2.39818	+	2.39818i	0.0954700	+	0.0954700i	−0.657759	+	0.753229i	$0.728495\pi$
$632$		0			0
$633$	−10.2326	−	2.74182i	−0.406711	−	0.108978i
$634$		0			0
$635$	18.4072	−	14.1244i	0.730469	−	0.560509i
$636$		0			0
$637$	−27.0536	−	18.6202i	−1.07190	−	0.737761i
$638$		0			0
$639$	16.0930	+	9.29129i	0.636629	+	0.367558i
$640$		0			0
$641$	5.60572	+	9.70939i	0.221413	+	0.383498i	0.955237	−	0.295841i	$-0.0955999\pi$
$641$	5.60572	+	9.70939i	0.221413	+	0.383498i	−0.733825	+	0.679339i	$0.762267\pi$
$642$		0			0
$643$	−1.05264	−	2.54130i	−0.0415121	−	0.100219i	0.901764	−	0.432230i	$-0.142273\pi$
$643$	−1.05264	−	2.54130i	−0.0415121	−	0.100219i	−0.943276	+	0.332011i	$0.892273\pi$
$644$		0			0
$645$	4.97688	+	2.06149i	0.195965	+	0.0811712i
$646$		0			0
$647$	7.76092	−	28.9642i	0.305113	−	1.13870i	−0.627734	−	0.778428i	$-0.716018\pi$
$647$	7.76092	−	28.9642i	0.305113	−	1.13870i	0.932848	−	0.360271i	$-0.117316\pi$
$648$		0			0
$649$	1.60844	−	0.430979i	0.0631366	−	0.0169174i
$650$		0			0
$651$	5.72632	−	0.904986i	0.224432	−	0.0354692i
$652$		0			0
$653$	−1.26276	+	9.59163i	−0.0494157	+	0.375349i	0.948812	+	0.315841i	$0.102287\pi$
$653$	−1.26276	+	9.59163i	−0.0494157	+	0.375349i	−0.998228	+	0.0595084i	$0.981047\pi$
$654$		0			0
$655$	−37.4992	−	64.9505i	−1.46522	−	2.53783i
$656$		0			0
$657$	20.8564			0.813685
$658$		0			0
$659$	−8.00070	−	19.3154i	−0.311663	−	0.752421i	−0.999644	−	0.0266921i	$-0.991503\pi$
$659$	−8.00070	−	19.3154i	−0.311663	−	0.752421i	0.687981	−	0.725729i	$-0.258497\pi$
$660$		0			0
$661$	−1.79532	−	13.6368i	−0.0698298	−	0.530410i	−0.990231	−	0.139435i	$-0.955471\pi$
$661$	−1.79532	−	13.6368i	−0.0698298	−	0.530410i	0.920401	−	0.390975i	$-0.127862\pi$
$662$		0			0
$663$	−2.34295	−	8.74402i	−0.0909928	−	0.339590i
$664$		0			0
$665$	50.5027	−	53.1829i	1.95841	−	2.06234i
$666$		0			0
$667$	−1.10947	−	1.44590i	−0.0429590	−	0.0559853i
$668$		0			0
$669$	0.793720	−	1.03440i	0.0306870	−	0.0399920i
$670$		0			0
$671$	1.24012			0.0478743
$672$		0			0
$673$	28.1723			1.08596			0.542982	−	0.839744i	$-0.317295\pi$
$673$	28.1723			1.08596			0.542982	+	0.839744i	$0.317295\pi$
$674$		0			0
$675$	−17.4722	+	22.7703i	−0.672507	+	0.876428i
$676$		0			0
$677$	−5.06366	−	6.59909i	−0.194612	−	0.253624i	0.685847	−	0.727746i	$-0.259432\pi$
$677$	−5.06366	−	6.59909i	−0.194612	−	0.253624i	−0.880459	+	0.474122i	$0.842765\pi$
$678$		0			0
$679$	7.05460	+	23.8454i	0.270731	+	0.915101i
$680$		0			0
$681$	0.874306	+	3.26295i	0.0335035	+	0.125037i
$682$		0			0
$683$	−2.02274	−	15.3642i	−0.0773980	−	0.587896i	−0.985566	−	0.169291i	$-0.945852\pi$
$683$	−2.02274	−	15.3642i	−0.0773980	−	0.587896i	0.908168	−	0.418606i	$-0.137481\pi$
$684$		0			0
$685$	30.8882	+	74.5707i	1.18018	+	2.84920i
$686$		0			0
$687$	14.3298			0.546716
$688$		0			0
$689$	−21.1522	−	36.6366i	−0.805833	−	1.39574i
$690$		0			0
$691$	1.59354	−	12.1041i	0.0606211	−	0.460463i	−0.934032	−	0.357189i	$-0.883735\pi$
$691$	1.59354	−	12.1041i	0.0606211	−	0.460463i	0.994653	−	0.103273i	$-0.0329316\pi$
$692$		0			0
$693$	−1.06447	+	0.861399i	−0.0404359	+	0.0327218i
$694$		0			0
$695$	−67.4643	+	18.0770i	−2.55907	+	0.685700i
$696$		0			0
$697$	4.55319	−	16.9927i	0.172464	−	0.643646i
$698$		0			0
$699$	−9.70505	−	4.01996i	−0.367079	−	0.152049i
$700$		0			0
$701$	−10.0224	−	24.1963i	−0.378542	−	0.913881i	−0.992240	−	0.124340i	$-0.960319\pi$
$701$	−10.0224	−	24.1963i	−0.378542	−	0.913881i	0.613698	−	0.789541i	$-0.289681\pi$
$702$		0			0
$703$	−38.8463	−	67.2837i	−1.46512	−	2.53765i
$704$		0			0
$705$	3.45006	+	1.99189i	0.129937	+	0.0750189i
$706$		0			0
$707$	−3.33084	+	1.48164i	−0.125269	+	0.0557229i
$708$		0			0
$709$	−26.5977	+	20.4091i	−0.998898	+	0.766482i	−0.972436	−	0.233168i	$-0.925091\pi$
$709$	−26.5977	+	20.4091i	−0.998898	+	0.766482i	−0.0264620	+	0.999650i	$0.508424\pi$
$710$		0			0
$711$	−12.2489	−	3.28207i	−0.459368	−	0.123087i
$712$		0			0
$713$	−2.30233	−	2.30233i	−0.0862228	−	0.0862228i
$714$		0			0
$715$	−3.12047	−	1.29254i	−0.116699	−	0.0483383i
$716$		0			0
$717$	−4.56519	+	5.94948i	−0.170490	+	0.222187i
$718$		0			0
$719$	−22.7929	−	13.1595i	−0.850031	−	0.490766i	0.0106300	−	0.999943i	$-0.496616\pi$
$719$	−22.7929	−	13.1595i	−0.850031	−	0.490766i	−0.860661	+	0.509178i	$0.829950\pi$
$720$		0			0
$721$	−26.0510	+	15.9520i	−0.970189	+	0.594084i
$722$		0			0
$723$	5.09013	+	0.670129i	0.189304	+	0.0249224i
$724$		0			0
$725$	17.6354	−	2.32174i	0.654961	−	0.0862273i
$726$		0			0
$727$	−32.3640	+	32.3640i	−1.20031	+	1.20031i	−0.226244	+	0.974071i	$0.572645\pi$
$727$	−32.3640	+	32.3640i	−1.20031	+	1.20031i	−0.974071	+	0.226244i	$0.927355\pi$
$728$		0			0
$729$	−6.98747	−	6.98747i	−0.258795	−	0.258795i
$730$		0			0
$731$	1.05084	+	7.98192i	0.0388667	+	0.295222i
$732$		0			0
$733$	5.72060	−	43.4522i	0.211295	−	1.60495i	−0.476590	−	0.879126i	$-0.658127\pi$
$733$	5.72060	−	43.4522i	0.211295	−	1.60495i	0.687885	−	0.725820i	$-0.258539\pi$
$734$		0			0
$735$	12.8115	−	8.30763i	0.472558	−	0.306431i
$736$		0			0
$737$	1.17013	−	2.02673i	0.0431025	−	0.0746557i
$738$		0			0
$739$	−15.5293	−	11.9160i	−0.571253	−	0.438338i	0.282313	−	0.959322i	$-0.408898\pi$
$739$	−15.5293	−	11.9160i	−0.571253	−	0.438338i	−0.853566	+	0.520984i	$0.825565\pi$
$740$		0			0
$741$	7.99254	−	19.2957i	0.293613	−	0.708845i
$742$		0			0
$743$	−6.32677	+	6.32677i	−0.232107	+	0.232107i	−0.813572	−	0.581465i	$-0.802480\pi$
$743$	−6.32677	+	6.32677i	−0.232107	+	0.232107i	0.581465	+	0.813572i	$0.302480\pi$
$744$		0			0
$745$	−7.01380	+	26.1759i	−0.256966	+	0.959009i
$746$		0			0
$747$	8.77366	+	11.4341i	0.321012	+	0.418350i
$748$		0			0
$749$	−10.0066	+	13.7632i	−0.365633	+	0.502896i
$750$		0			0
$751$	−20.1360	+	34.8765i	−0.734772	+	1.27266i	0.220051	+	0.975488i	$0.429377\pi$
$751$	−20.1360	+	34.8765i	−0.734772	+	1.27266i	−0.954823	+	0.297174i	$0.903956\pi$
$752$		0			0
$753$	−2.34345	+	1.35299i	−0.0853999	+	0.0493057i
$754$		0			0
$755$	72.2070	−	29.9091i	2.62788	−	1.08850i
$756$		0			0
$757$	−12.9976	+	31.3791i	−0.472408	+	1.14049i	0.490688	+	0.871335i	$0.336745\pi$
$757$	−12.9976	+	31.3791i	−0.472408	+	1.14049i	−0.963096	+	0.269158i	$0.913255\pi$
$758$		0			0
$759$	−0.0982064	−	0.0263143i	−0.00356466	−	0.000955149i
$760$		0			0
$761$	−1.20598	−	4.50078i	−0.0437167	−	0.163153i	0.940617	−	0.339471i	$-0.110248\pi$
$761$	−1.20598	−	4.50078i	−0.0437167	−	0.163153i	−0.984333	+	0.176318i	$0.943581\pi$
$762$		0			0
$763$	17.3273	+	6.65802i	0.627291	+	0.241036i
$764$		0			0
$765$	−31.5637	−	4.15544i	−1.14119	−	0.150240i
$766$		0			0
$767$	34.6385	−	19.9986i	1.25072	−	0.722106i
$768$		0			0
$769$		−	17.4876i		−	0.630619i	−0.948989	−	0.315310i	$-0.897892\pi$
$769$		−	17.4876i		−	0.630619i	0.948989	−	0.315310i	$-0.102108\pi$
$770$		0			0
$771$	−0.0280843	+	0.0116329i	−0.00101143	+	0.000418949i
$772$		0			0
$773$	−28.5620	+	3.76026i	−1.02730	+	0.135247i	−0.625294	−	0.780389i	$-0.715021\pi$
$773$	−28.5620	+	3.76026i	−1.02730	+	0.135247i	−0.402008	+	0.915636i	$0.631688\pi$
$774$		0			0
$775$	30.6953	−	8.22477i	1.10261	−	0.295442i
$776$		0			0
$777$	−4.58879	−	15.5106i	−0.164622	−	0.556441i
$778$		0			0
$779$	32.2006	−	24.7084i	1.15371	−	0.885270i
$780$		0			0
$781$	−1.08678	−	0.833914i	−0.0388880	−	0.0298398i
$782$		0			0
$783$		−	6.92943i		−	0.247638i
$784$		0			0
$785$		−	13.6350i		−	0.486654i
$786$		0			0
$787$	32.1084	+	24.6377i	1.14454	+	0.878237i	0.993893	−	0.110350i	$-0.0351971\pi$
$787$	32.1084	+	24.6377i	1.14454	+	0.878237i	0.150649	+	0.988587i	$0.451864\pi$
$788$		0			0
$789$	−0.806460	+	0.618819i	−0.0287107	+	0.0220305i
$790$		0			0
$791$	0.953496	+	3.22293i	0.0339024	+	0.114594i
$792$		0			0
$793$	28.7724	−	7.70955i	1.02174	−	0.273774i
$794$		0			0
$795$	19.5002	−	2.56725i	0.691600	−	0.0910509i
$796$		0			0
$797$	30.2358	−	12.5241i	1.07101	−	0.443625i	0.223660	−	0.974667i	$-0.428199\pi$
$797$	30.2358	−	12.5241i	1.07101	−	0.443625i	0.847345	+	0.531042i	$0.178199\pi$
$798$		0			0
$799$			5.95378i			0.210629i
$800$		0			0
$801$	−0.230138	+	0.132870i	−0.00813153	+	0.00469474i
$802$		0			0
$803$	−1.52432	−	0.200680i	−0.0537920	−	0.00708185i
$804$		0			0
$805$	−8.00504	−	3.07593i	−0.282140	−	0.108412i
$806$		0			0
$807$	0.336991	+	1.25767i	0.0118626	+	0.0442720i
$808$		0			0
$809$	−21.7114	−	5.81756i	−0.763333	−	0.204535i	−0.143909	−	0.989591i	$-0.545967\pi$
$809$	−21.7114	−	5.81756i	−0.763333	−	0.204535i	−0.619424	+	0.785056i	$0.712634\pi$
$810$		0			0
$811$	−0.866622	+	2.09221i	−0.0304312	+	0.0734675i	−0.938365	−	0.345647i	$-0.887659\pi$
$811$	−0.866622	+	2.09221i	−0.0304312	+	0.0734675i	0.907933	+	0.419115i	$0.137659\pi$
$812$		0			0
$813$	2.51800	−	1.04299i	0.0883100	−	0.0365792i
$814$		0			0
$815$	46.1044	−	26.6184i	1.61497	−	0.932402i
$816$		0			0
$817$	−9.28724	+	16.0860i	−0.324919	+	0.562777i
$818$		0			0
$819$	−19.3420	+	26.6031i	−0.675864	+	0.929589i
$820$		0			0
$821$	−26.6553	−	34.7378i	−0.930276	−	1.21236i	−0.976954	−	0.213449i	$-0.931530\pi$
$821$	−26.6553	−	34.7378i	−0.930276	−	1.21236i	0.0466784	−	0.998910i	$-0.485136\pi$
$822$		0			0
$823$	−9.34890	+	34.8906i	−0.325882	+	1.21621i	0.587540	+	0.809195i	$0.300097\pi$
$823$	−9.34890	+	34.8906i	−0.325882	+	1.21621i	−0.913422	+	0.407014i	$0.866570\pi$
$824$		0			0
$825$	0.701660	−	0.701660i	0.0244287	−	0.0244287i
$826$		0			0
$827$	−8.76859	+	21.1692i	−0.304914	+	0.736127i	0.694941	+	0.719067i	$0.255431\pi$
$827$	−8.76859	+	21.1692i	−0.304914	+	0.736127i	−0.999854	+	0.0170597i	$0.994569\pi$
$828$		0			0
$829$	34.7510	+	26.6654i	1.20695	+	0.926126i	0.998650	−	0.0519385i	$-0.0165400\pi$
$829$	34.7510	+	26.6654i	1.20695	+	0.926126i	0.208301	+	0.978065i	$0.433207\pi$
$830$		0			0
$831$	1.56411	−	2.70912i	0.0542585	−	0.0939785i
$832$		0			0
$833$	20.3258	+	10.3737i	0.704246	+	0.359428i
$834$		0			0
$835$	−5.78434	+	43.9364i	−0.200175	+	1.52048i
$836$		0			0
$837$	−1.61587	−	12.2738i	−0.0558527	−	0.424243i
$838$		0			0
$839$	−37.8886	−	37.8886i	−1.30806	−	1.30806i	−0.922813	−	0.385248i	$-0.874116\pi$
$839$	−37.8886	−	37.8886i	−1.30806	−	1.30806i	−0.385248	−	0.922813i	$-0.625884\pi$
$840$		0			0
$841$	17.4694	−	17.4694i	0.602394	−	0.602394i
$842$		0			0
$843$	5.40698	−	0.711842i	0.186226	−	0.0245172i
$844$		0			0
$845$	−32.9320	−	4.33558i	−1.13289	−	0.149148i
$846$		0			0
$847$	−24.7336	+	15.1454i	−0.849858	+	0.520401i
$848$		0			0
$849$	6.27254	+	3.62145i	0.215273	+	0.124288i
$850$		0			0
$851$	−5.53027	+	7.20718i	−0.189575	+	0.247059i
$852$		0			0
$853$	−18.0841	−	7.49066i	−0.619186	−	0.256475i	0.0509644	−	0.998700i	$-0.483770\pi$
$853$	−18.0841	−	7.49066i	−0.619186	−	0.256475i	−0.670151	+	0.742225i	$0.733770\pi$
$854$		0			0
$855$	−51.9376	−	51.9376i	−1.77623	−	1.77623i
$856$		0			0
$857$	22.2379	+	5.95862i	0.759631	+	0.203543i	0.617786	−	0.786346i	$-0.288030\pi$
$857$	22.2379	+	5.95862i	0.759631	+	0.203543i	0.141845	+	0.989889i	$0.454696\pi$
$858$		0			0
$859$	−0.714878	+	0.548545i	−0.0243913	+	0.0187161i	−0.620885	−	0.783902i	$-0.713227\pi$
$859$	−0.714878	+	0.548545i	−0.0243913	+	0.0187161i	0.596494	+	0.802618i	$0.296560\pi$
$860$		0			0
$861$	7.72080	−	3.43441i	0.263124	−	0.117044i
$862$		0			0
$863$	−26.9099	−	15.5365i	−0.916024	−	0.528867i	−0.0336599	−	0.999433i	$-0.510716\pi$
$863$	−26.9099	−	15.5365i	−0.916024	−	0.528867i	−0.882365	+	0.470566i	$0.844050\pi$
$864$		0			0
$865$	13.3952	+	23.2012i	0.455451	+	0.788865i
$866$		0			0
$867$	−1.44331	−	3.48446i	−0.0490174	−	0.118339i
$868$		0			0
$869$	0.863646	+	0.357734i	0.0292972	+	0.0121353i
$870$		0			0
$871$	14.5489	−	54.2973i	0.492972	−	1.83979i
$872$		0			0
$873$	24.0556	−	6.44568i	0.814159	−	0.218153i
$874$		0			0
$875$	27.1626	−	21.9807i	0.918262	−	0.743083i
$876$		0			0
$877$	−4.47664	+	34.0035i	−0.151165	+	1.14822i	0.732726	+	0.680524i	$0.238248\pi$
$877$	−4.47664	+	34.0035i	−0.151165	+	1.14822i	−0.883892	+	0.467692i	$0.845086\pi$
$878$		0			0
$879$	7.49211	+	12.9767i	0.252702	+	0.437694i
$880$		0			0
$881$	−8.67844			−0.292384			−0.146192	−	0.989256i	$-0.546702\pi$
$881$	−8.67844			−0.292384			−0.146192	+	0.989256i	$0.546702\pi$
$882$		0			0
$883$	3.72606	+	8.99549i	0.125392	+	0.302722i	0.974092	−	0.226151i	$-0.0726144\pi$
$883$	3.72606	+	8.99549i	0.125392	+	0.302722i	−0.848700	+	0.528874i	$0.822614\pi$
$884$		0			0
$885$	2.42723	+	18.4367i	0.0815906	+	0.619742i
$886$		0			0
$887$	−5.31881	−	19.8501i	−0.178588	−	0.666501i	−0.995913	−	0.0903226i	$-0.971210\pi$
$887$	−5.31881	−	19.8501i	−0.178588	−	0.666501i	0.817324	−	0.576178i	$-0.195456\pi$
$888$		0			0
$889$	4.72515	+	15.9715i	0.158476	+	0.535668i
$890$		0			0
$891$	0.709892	+	0.925149i	0.0237823	+	0.0309937i
$892$		0			0
$893$	−8.36214	+	10.8977i	−0.279828	+	0.364679i
$894$		0			0
$895$	61.9765			2.07164
$896$		0			0
$897$	−2.44211			−0.0815396
$898$		0			0
$899$	−4.67058	+	6.08682i	−0.155773	+	0.203007i
$900$		0			0
$901$	17.8943	+	23.3203i	0.596145	+	0.776911i
$902$		0			0
$903$	−2.66289	+	2.80421i	−0.0886153	+	0.0933182i
$904$		0			0
$905$	−1.52842	−	5.70414i	−0.0508064	−	0.189612i
$906$		0			0
$907$	−1.82736	−	13.8802i	−0.0606765	−	0.460884i	−0.994630	−	0.103491i	$-0.966999\pi$
$907$	−1.82736	−	13.8802i	−0.0606765	−	0.460884i	0.933954	−	0.357393i	$-0.116334\pi$
$908$		0			0
$909$	1.39716	+	3.37305i	0.0463410	+	0.111877i
$910$		0			0
$911$	29.8181			0.987917			0.493958	−	0.869486i	$-0.335550\pi$
$911$	29.8181			0.987917			0.493958	+	0.869486i	$0.335550\pi$
$912$		0			0
$913$	−0.531217	−	0.920094i	−0.0175807	−	0.0304507i
$914$		0			0
$915$	−1.80766	+	13.7305i	−0.0597593	+	0.453917i
$916$		0			0
$917$	53.1790	−	8.40439i	1.75612	−	0.277538i
$918$		0			0
$919$	17.5490	−	4.70223i	0.578887	−	0.155112i	0.0425176	−	0.999096i	$-0.486462\pi$
$919$	17.5490	−	4.70223i	0.578887	−	0.155112i	0.536369	+	0.843983i	$0.319795\pi$
$920$		0			0
$921$	0.230556	−	0.860446i	0.00759708	−	0.0283527i
$922$		0			0
$923$	−30.3989	−	12.5916i	−1.00059	−	0.414459i
$924$		0			0
$925$	−33.9300	−	81.9143i	−1.11561	−	2.69333i
$926$		0			0
$927$	15.2963	+	26.4940i	0.502398	+	0.870178i
$928$		0			0
$929$	−44.1260	−	25.4762i	−1.44773	−	0.835846i	−0.449382	−	0.893340i	$-0.648356\pi$
$929$	−44.1260	−	25.4762i	−1.44773	−	0.835846i	−0.998346	+	0.0574938i	$0.981689\pi$
$930$		0			0
$931$	22.6342	+	47.5357i	0.741805	+	1.55792i
$932$		0			0
$933$	−14.2140	+	10.9068i	−0.465345	+	0.357072i
$934$		0			0
$935$	2.26689	+	0.607412i	0.0741354	+	0.0198645i
$936$		0			0
$937$	−21.8870	−	21.8870i	−0.715016	−	0.715016i	0.252564	−	0.967580i	$-0.418726\pi$
$937$	−21.8870	−	21.8870i	−0.715016	−	0.715016i	−0.967580	+	0.252564i	$0.918726\pi$
$938$		0			0
$939$	1.56467	+	0.648109i	0.0510612	+	0.0211503i
$940$		0			0
$941$	−15.5346	+	20.2450i	−0.506412	+	0.659969i	−0.974677	−	0.223619i	$-0.928213\pi$
$941$	−15.5346	+	20.2450i	−0.506412	+	0.659969i	0.468265	+	0.883588i	$0.344879\pi$
$942$		0			0
$943$	−4.11005	−	2.37294i	−0.133842	−	0.0772735i
$944$		0			0
$945$	−17.0271	−	27.8068i	−0.553893	−	0.904554i
$946$		0			0
$947$	−15.5424	−	2.04619i	−0.505060	−	0.0664924i	−0.126309	−	0.991991i	$-0.540313\pi$
$947$	−15.5424	−	2.04619i	−0.505060	−	0.0664924i	−0.378751	+	0.925499i	$0.623646\pi$
$948$		0			0
$949$	−36.6138	+	4.82029i	−1.18853	+	0.156473i
$950$		0			0
$951$	2.23299	−	2.23299i	0.0724095	−	0.0724095i
$952$		0			0
$953$	35.1047	+	35.1047i	1.13715	+	1.13715i	0.988958	+	0.148196i	$0.0473467\pi$
$953$	35.1047	+	35.1047i	1.13715	+	1.13715i	0.148196	+	0.988958i	$0.452653\pi$
$954$		0			0
$955$	−3.91328	−	29.7243i	−0.126631	−	0.961856i
$956$		0			0
$957$	−0.0312705	+	0.237523i	−0.00101083	+	0.00767804i
$958$		0			0
$959$	−57.9232	+	1.49729i	−1.87044	+	0.0483499i
$960$		0			0
$961$	8.64661	−	14.9764i	0.278923	−	0.483109i
$962$		0			0
$963$	13.5202	+	10.3744i	0.435682	+	0.334311i
$964$		0			0
$965$	−4.50482	+	10.8756i	−0.145015	+	0.350098i
$966$		0			0
$967$	−4.13197	+	4.13197i	−0.132875	+	0.132875i	−0.770416	−	0.637541i	$-0.779952\pi$
$967$	−4.13197	+	4.13197i	−0.132875	+	0.132875i	0.637541	+	0.770416i	$0.279952\pi$
$968$		0			0
$969$	−3.75599	+	14.0175i	−0.120660	+	0.450308i
$970$		0			0
$971$	−23.8366	−	31.0644i	−0.764952	−	0.996905i	−0.999691	−	0.0248466i	$-0.992090\pi$
$971$	−23.8366	−	31.0644i	−0.764952	−	0.996905i	0.234739	−	0.972058i	$-0.424576\pi$
$972$		0			0
$973$	5.25771	−	49.8625i	0.168554	−	1.59852i
$974$		0			0
$975$	11.9174	−	20.6415i	0.381661	−	0.661057i
$976$		0			0
$977$	26.3775	−	15.2291i	0.843892	−	0.487221i	−0.0146935	−	0.999892i	$-0.504677\pi$
$977$	26.3775	−	15.2291i	0.843892	−	0.487221i	0.858585	+	0.512671i	$0.171344\pi$
$978$		0			0
$979$	0.0180984	−	0.00749662i	0.000578429	−	0.000239593i
$980$		0			0
$981$	7.11417	−	17.1751i	0.227138	−	0.548359i
$982$		0			0
$983$	32.2311	+	8.63630i	1.02801	+	0.275455i	0.733138	−	0.680080i	$-0.238055\pi$
$983$	32.2311	+	8.63630i	1.02801	+	0.275455i	0.294875	+	0.955536i	$0.404722\pi$
$984$		0			0
$985$	−23.5102	−	87.7413i	−0.749097	−	2.79567i
$986$		0			0
$987$	−2.22311	+	1.79900i	−0.0707624	+	0.0572628i
$988$		0			0
$989$	2.15330	+	0.283487i	0.0684710	+	0.00901438i
$990$		0			0
$991$	14.8667	−	8.58331i	0.472257	−	0.272658i	−0.244927	−	0.969542i	$-0.578764\pi$
$991$	14.8667	−	8.58331i	0.472257	−	0.272658i	0.717184	+	0.696884i	$0.245431\pi$
$992$		0			0
$993$		−	9.49907i		−	0.301444i
$994$		0			0
$995$	49.2652	−	20.4063i	1.56181	−	0.646924i
$996$		0			0
$997$	11.9613	−	1.57473i	0.378817	−	0.0498723i	0.0612866	−	0.998120i	$-0.480480\pi$
$997$	11.9613	−	1.57473i	0.378817	−	0.0498723i	0.317531	+	0.948248i	$0.397146\pi$
$998$		0			0
$999$	−33.3634	+	8.93969i	−1.05557	+	0.282839i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bi.a.271.18		240
4.3	odd	2		224.2.be.a.187.17	yes	240
7.3	odd	6	inner	896.2.bi.a.143.18		240
28.3	even	6		224.2.be.a.59.24	yes	240
32.13	even	8		224.2.be.a.19.24	✓	240
32.19	odd	8	inner	896.2.bi.a.495.18		240
224.45	odd	24		224.2.be.a.115.17	yes	240
224.115	even	24	inner	896.2.bi.a.367.18		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.24	✓	240	32.13	even	8
224.2.be.a.59.24	yes	240	28.3	even	6
224.2.be.a.115.17	yes	240	224.45	odd	24
224.2.be.a.187.17	yes	240	4.3	odd	2
896.2.bi.a.143.18		240	7.3	odd	6	inner
896.2.bi.a.271.18		240	1.1	even	1	trivial
896.2.bi.a.367.18		240	224.115	even	24	inner
896.2.bi.a.495.18		240	32.19	odd	8	inner

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

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	896.2.bi.a.271.18

Level	$896$
Weight	$2$
Character	896.271
Analytic conductor	$7.155$
Analytic rank	$0$
Dimension	$240$
Inner twists	$4$