LMFDB - Embedded newform 820.2.bi.a.189.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(189,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bi (of order $10$, degree $4$, 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:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.15
Character	$\chi$	$=$	820.189
Dual form			820.2.bi.a.269.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.56760 q^{3} +(1.56013 + 1.60188i) q^{5} +(0.633766 + 1.95053i) q^{7} -0.542630 q^{9} +(1.38893 + 1.91169i) q^{11} +(1.71055 - 5.26453i) q^{13} +(2.44565 + 2.51110i) q^{15} +(-2.66273 + 1.93459i) q^{17} +(4.64430 - 1.50902i) q^{19} +(0.993492 + 3.05766i) q^{21} +(3.85536 + 1.25268i) q^{23} +(-0.132010 + 4.99826i) q^{25} -5.55343 q^{27} +(-4.79455 + 6.59914i) q^{29} +(-1.10550 + 0.803189i) q^{31} +(2.17728 + 2.99677i) q^{33} +(-2.13575 + 4.05829i) q^{35} +(2.20655 - 3.03706i) q^{37} +(2.68146 - 8.25267i) q^{39} +(5.74848 + 2.82045i) q^{41} +(-7.75606 - 2.52010i) q^{43} +(-0.846571 - 0.869226i) q^{45} +(2.11720 - 6.51607i) q^{47} +(2.26020 - 1.64213i) q^{49} +(-4.17410 + 3.03266i) q^{51} +(-5.04491 - 3.66534i) q^{53} +(-0.895393 + 5.20737i) q^{55} +(7.28041 - 2.36555i) q^{57} +(-0.236097 + 0.726632i) q^{59} +(4.10788 + 12.6428i) q^{61} +(-0.343901 - 1.05842i) q^{63} +(11.1018 - 5.47324i) q^{65} +(1.01458 + 0.737135i) q^{67} +(6.04366 + 1.96370i) q^{69} +(-4.40729 - 6.06611i) q^{71} -11.5112i q^{73} +(-0.206940 + 7.83527i) q^{75} +(-2.84856 + 3.92071i) q^{77} -7.50717i q^{79} -7.07766 q^{81} -10.8365i q^{83} +(-7.25317 - 1.24716i) q^{85} +(-7.51594 + 10.3448i) q^{87} +(5.11512 - 1.66200i) q^{89} +11.3527 q^{91} +(-1.73297 + 1.25908i) q^{93} +(9.66297 + 5.08532i) q^{95} +(7.36715 + 5.35255i) q^{97} +(-0.753673 - 1.03734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) $ 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

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
$3$	1.56760			0.905054			0.452527	−	0.891751i	$-0.350523\pi$
$3$	1.56760			0.905054			0.452527	+	0.891751i	$0.350523\pi$
$4$		0			0
$5$	1.56013	+	1.60188i	0.697710	+	0.716381i
$5$	1.56013	+	1.60188i	0.697710	+	0.716381i
$6$		0			0
$7$	0.633766	+	1.95053i	0.239541	+	0.737232i	0.996486	+	0.0837537i	$0.0266909\pi$
$7$	0.633766	+	1.95053i	0.239541	+	0.737232i	−0.756945	+	0.653478i	$0.773309\pi$
$8$		0			0
$9$	−0.542630			−0.180877
$10$		0			0
$11$	1.38893	+	1.91169i	0.418777	+	0.576397i	0.965332	−	0.261026i	$-0.0840610\pi$
$11$	1.38893	+	1.91169i	0.418777	+	0.576397i	−0.546555	+	0.837423i	$0.684061\pi$
$12$		0			0
$13$	1.71055	−	5.26453i	0.474421	−	1.46012i	−0.372317	−	0.928106i	$-0.621436\pi$
$13$	1.71055	−	5.26453i	0.474421	−	1.46012i	0.846737	−	0.532011i	$-0.178564\pi$
$14$		0			0
$15$	2.44565	+	2.51110i	0.631465	+	0.648363i
$16$		0			0
$17$	−2.66273	+	1.93459i	−0.645808	+	0.469207i	−0.861841	−	0.507179i	$-0.830688\pi$
$17$	−2.66273	+	1.93459i	−0.645808	+	0.469207i	0.216033	+	0.976386i	$0.430688\pi$
$18$		0			0
$19$	4.64430	−	1.50902i	1.06548	−	0.346194i	0.276752	−	0.960941i	$-0.410742\pi$
$19$	4.64430	−	1.50902i	1.06548	−	0.346194i	0.788724	+	0.614747i	$0.210742\pi$
$20$		0			0
$21$	0.993492	+	3.05766i	0.216798	+	0.667235i
$22$		0			0
$23$	3.85536	+	1.25268i	0.803897	+	0.261202i	0.682011	−	0.731342i	$-0.261106\pi$
$23$	3.85536	+	1.25268i	0.803897	+	0.261202i	0.121886	+	0.992544i	$0.461106\pi$
$24$		0			0
$25$	−0.132010	+	4.99826i	−0.0264021	+	0.999651i
$26$		0			0
$27$	−5.55343			−1.06876
$28$		0			0
$29$	−4.79455	+	6.59914i	−0.890326	+	1.22543i	0.0831260	+	0.996539i	$0.473510\pi$
$29$	−4.79455	+	6.59914i	−0.890326	+	1.22543i	−0.973452	+	0.228890i	$0.926490\pi$
$30$		0			0
$31$	−1.10550	+	0.803189i	−0.198553	+	0.144257i	−0.682619	−	0.730774i	$-0.739159\pi$
$31$	−1.10550	+	0.803189i	−0.198553	+	0.144257i	0.484067	+	0.875031i	$0.339159\pi$
$32$		0			0
$33$	2.17728	+	2.99677i	0.379016	+	0.521671i
$34$		0			0
$35$	−2.13575	+	4.05829i	−0.361008	+	0.685977i
$36$		0			0
$37$	2.20655	−	3.03706i	0.362755	−	0.499289i	−0.588159	−	0.808745i	$-0.700147\pi$
$37$	2.20655	−	3.03706i	0.362755	−	0.499289i	0.950914	+	0.309456i	$0.100147\pi$
$38$		0			0
$39$	2.68146	−	8.25267i	0.429377	−	1.32149i
$40$		0			0
$41$	5.74848	+	2.82045i	0.897762	+	0.440481i
$41$	5.74848	+	2.82045i	0.897762	+	0.440481i
$42$		0			0
$43$	−7.75606	−	2.52010i	−1.18279	−	0.384311i	−0.349386	−	0.936979i	$-0.613610\pi$
$43$	−7.75606	−	2.52010i	−1.18279	−	0.384311i	−0.833402	+	0.552668i	$0.813610\pi$
$44$		0			0
$45$	−0.846571	−	0.869226i	−0.126199	−	0.129576i
$46$		0			0
$47$	2.11720	−	6.51607i	0.308825	−	0.950467i	−0.669397	−	0.742905i	$-0.733447\pi$
$47$	2.11720	−	6.51607i	0.308825	−	0.950467i	0.978222	−	0.207562i	$-0.0665527\pi$
$48$		0			0
$49$	2.26020	−	1.64213i	0.322886	−	0.234590i
$50$		0			0
$51$	−4.17410	+	3.03266i	−0.584491	+	0.424658i
$52$		0			0
$53$	−5.04491	−	3.66534i	−0.692972	−	0.503474i	0.184664	−	0.982802i	$-0.440880\pi$
$53$	−5.04491	−	3.66534i	−0.692972	−	0.503474i	−0.877636	+	0.479328i	$0.840880\pi$
$54$		0			0
$55$	−0.895393	+	5.20737i	−0.120735	+	0.702161i
$56$		0			0
$57$	7.28041	−	2.36555i	0.964313	−	0.313324i
$58$		0			0
$59$	−0.236097	+	0.726632i	−0.0307372	+	0.0945994i	−0.965248	−	0.261335i	$-0.915837\pi$
$59$	−0.236097	+	0.726632i	−0.0307372	+	0.0945994i	0.934511	+	0.355934i	$0.115837\pi$
$60$		0			0
$61$	4.10788	+	12.6428i	0.525960	+	1.61874i	0.762409	+	0.647096i	$0.224017\pi$
$61$	4.10788	+	12.6428i	0.525960	+	1.61874i	−0.236448	+	0.971644i	$0.575983\pi$
$62$		0			0
$63$	−0.343901	−	1.05842i	−0.0433274	−	0.133348i
$64$		0			0
$65$	11.1018	−	5.47324i	1.37701	−	0.678872i
$66$		0			0
$67$	1.01458	+	0.737135i	0.123951	+	0.0900554i	0.648033	−	0.761612i	$-0.275592\pi$
$67$	1.01458	+	0.737135i	0.123951	+	0.0900554i	−0.524083	+	0.851667i	$0.675592\pi$
$68$		0			0
$69$	6.04366	+	1.96370i	0.727571	+	0.236402i
$70$		0			0
$71$	−4.40729	−	6.06611i	−0.523049	−	0.719915i	0.463002	−	0.886357i	$-0.346772\pi$
$71$	−4.40729	−	6.06611i	−0.523049	−	0.719915i	−0.986051	+	0.166442i	$0.946772\pi$
$72$		0			0
$73$		−	11.5112i		−	1.34728i	−0.739058	−	0.673641i	$-0.764729\pi$
$73$		−	11.5112i		−	1.34728i	0.739058	−	0.673641i	$-0.235271\pi$
$74$		0			0
$75$	−0.206940	+	7.83527i	−0.0238953	+	0.904739i
$76$		0			0
$77$	−2.84856	+	3.92071i	−0.324624	+	0.446807i
$78$		0			0
$79$		−	7.50717i		−	0.844623i	−0.906451	−	0.422312i	$-0.861219\pi$
$79$		−	7.50717i		−	0.844623i	0.906451	−	0.422312i	$-0.138781\pi$
$80$		0			0
$81$	−7.07766			−0.786407
$82$		0			0
$83$		−	10.8365i		−	1.18946i	−0.803924	−	0.594732i	$-0.797258\pi$
$83$		−	10.8365i		−	1.18946i	0.803924	−	0.594732i	$-0.202742\pi$
$84$		0			0
$85$	−7.25317	−	1.24716i	−0.786717	−	0.135274i
$86$		0			0
$87$	−7.51594	+	10.3448i	−0.805794	+	1.10908i
$88$		0			0
$89$	5.11512	−	1.66200i	0.542202	−	0.176172i	−0.0250956	−	0.999685i	$-0.507989\pi$
$89$	5.11512	−	1.66200i	0.542202	−	0.176172i	0.567297	+	0.823513i	$0.307989\pi$
$90$		0			0
$91$	11.3527			1.19009
$92$		0			0
$93$	−1.73297	+	1.25908i	−0.179701	+	0.130560i
$94$		0			0
$95$	9.66297	+	5.08532i	0.991400	+	0.521743i
$96$		0			0
$97$	7.36715	+	5.35255i	0.748021	+	0.543469i	0.895213	−	0.445639i	$-0.147024\pi$
$97$	7.36715	+	5.35255i	0.748021	+	0.543469i	−0.147192	+	0.989108i	$0.547024\pi$
$98$		0			0
$99$	−0.753673	−	1.03734i	−0.0757470	−	0.104257i
$100$		0			0
$101$	−6.32712	+	2.05581i	−0.629572	+	0.204560i	−0.606386	−	0.795171i	$-0.707381\pi$
$101$	−6.32712	+	2.05581i	−0.629572	+	0.204560i	−0.0231867	+	0.999731i	$0.507381\pi$
$102$		0			0
$103$	−14.6879	+	4.77238i	−1.44724	+	0.470236i	−0.924146	−	0.382039i	$-0.875222\pi$
$103$	−14.6879	+	4.77238i	−1.44724	+	0.470236i	−0.523093	+	0.852276i	$0.675222\pi$
$104$		0			0
$105$	−3.34801	+	6.36178i	−0.326732	+	0.620846i
$106$		0			0
$107$	4.48072	−	1.45587i	0.433167	−	0.140745i	−0.0843137	−	0.996439i	$-0.526870\pi$
$107$	4.48072	−	1.45587i	0.433167	−	0.140745i	0.517481	+	0.855695i	$0.326870\pi$
$108$		0			0
$109$		−	7.45117i		−	0.713693i	−0.934163	−	0.356847i	$-0.883852\pi$
$109$		−	7.45117i		−	0.713693i	0.934163	−	0.356847i	$-0.116148\pi$
$110$		0			0
$111$	3.45899	−	4.76089i	0.328313	−	0.451884i
$112$		0			0
$113$	2.80089	+	3.85509i	0.263485	+	0.362657i	0.920177	−	0.391503i	$-0.128045\pi$
$113$	2.80089	+	3.85509i	0.263485	+	0.362657i	−0.656691	+	0.754159i	$0.728045\pi$
$114$		0			0
$115$	4.00820	+	8.13014i	0.373767	+	0.758140i
$116$		0			0
$117$	−0.928195	+	2.85669i	−0.0858116	+	0.264101i
$118$		0			0
$119$	−5.46103	−	3.96767i	−0.500612	−	0.363716i
$120$		0			0
$121$	1.67373	−	5.15122i	0.152158	−	0.468293i
$122$		0			0
$123$	9.01132	+	4.42134i	0.812523	+	0.398659i
$124$		0			0
$125$	−8.21254	+	7.58645i	−0.734552	+	0.678553i
$126$		0			0
$127$	5.06071	−	6.96546i	0.449065	−	0.618085i	−0.523131	−	0.852252i	$-0.675236\pi$
$127$	5.06071	−	6.96546i	0.449065	−	0.618085i	0.972196	+	0.234167i	$0.0752363\pi$
$128$		0			0
$129$	−12.1584	−	3.95050i	−1.07049	−	0.347822i
$130$		0			0
$131$	1.11999	−	0.813721i	0.0978541	−	0.0710951i	−0.537782	−	0.843084i	$-0.680738\pi$
$131$	1.11999	−	0.813721i	0.0978541	−	0.0710951i	0.635636	+	0.771989i	$0.280738\pi$
$132$		0			0
$133$	5.88680	+	8.10249i	0.510451	+	0.702575i
$134$		0			0
$135$	−8.66405	−	8.89590i	−0.745683	−	0.765637i
$136$		0			0
$137$	−13.9457			−1.19146			−0.595729	−	0.803185i	$-0.703137\pi$
$137$	−13.9457			−1.19146			−0.595729	+	0.803185i	$0.703137\pi$
$138$		0			0
$139$	−5.94577	−	18.2992i	−0.504314	−	1.55212i	−0.801921	−	0.597430i	$-0.796189\pi$
$139$	−5.94577	−	18.2992i	−0.504314	−	1.55212i	0.297608	−	0.954688i	$-0.403811\pi$
$140$		0			0
$141$	3.31892	−	10.2146i	0.279504	−	0.860224i
$142$		0			0
$143$	12.4400	−	4.04199i	1.04028	−	0.338009i
$144$		0			0
$145$	−18.0511	+	2.61521i	−1.49906	+	0.217181i
$146$		0			0
$147$	3.54309	−	2.57421i	0.292229	−	0.212317i
$148$		0			0
$149$	5.06076	−	6.96554i	0.414594	−	0.570639i	−0.549738	−	0.835337i	$-0.685272\pi$
$149$	5.06076	−	6.96554i	0.414594	−	0.570639i	0.964331	+	0.264698i	$0.0852723\pi$
$150$		0			0
$151$	−13.4972	−	4.38551i	−1.09839	−	0.356888i	−0.296906	−	0.954907i	$-0.595955\pi$
$151$	−13.4972	−	4.38551i	−1.09839	−	0.356888i	−0.801482	+	0.598019i	$0.795955\pi$
$152$		0			0
$153$	1.44488	−	1.04977i	0.116812	−	0.0848685i
$154$		0			0
$155$	−3.01132	−	0.517789i	−0.241875	−	0.0415898i
$156$		0			0
$157$	6.49607	+	19.9928i	0.518443	+	1.59560i	0.776929	+	0.629588i	$0.216776\pi$
$157$	6.49607	+	19.9928i	0.518443	+	1.59560i	−0.258486	+	0.966015i	$0.583224\pi$
$158$		0			0
$159$	−7.90841	−	5.74579i	−0.627178	−	0.455671i
$160$		0			0
$161$			8.31391i			0.655228i
$162$		0			0
$163$		−	13.9512i		−	1.09274i	−0.837544	−	0.546370i	$-0.816009\pi$
$163$		−	13.9512i		−	1.09274i	0.837544	−	0.546370i	$-0.183991\pi$
$164$		0			0
$165$	−1.40362	+	8.16307i	−0.109272	+	0.635494i
$166$		0			0
$167$	12.8433			0.993842			0.496921	−	0.867796i	$-0.334464\pi$
$167$	12.8433			0.993842			0.496921	+	0.867796i	$0.334464\pi$
$168$		0			0
$169$	−14.2720	−	10.3692i	−1.09785	−	0.797634i
$170$		0			0
$171$	−2.52014	+	0.818842i	−0.192720	+	0.0626184i
$172$		0			0
$173$			16.0980i			1.22391i	0.790894	+	0.611953i	$0.209616\pi$
$173$			16.0980i			1.22391i	−0.790894	+	0.611953i	$0.790384\pi$
$174$		0			0
$175$	−9.83293	+	2.91024i	−0.743299	+	0.219993i
$176$		0			0
$177$	−0.370106	+	1.13907i	−0.0278188	+	0.0856176i
$178$		0			0
$179$	11.9848	−	16.4957i	0.895786	−	1.23294i	−0.0760070	−	0.997107i	$-0.524217\pi$
$179$	11.9848	−	16.4957i	0.895786	−	1.23294i	0.971793	−	0.235836i	$-0.0757829\pi$
$180$		0			0
$181$	−9.84209	−	13.5465i	−0.731557	−	1.00690i	−0.999060	−	0.0433450i	$-0.986199\pi$
$181$	−9.84209	−	13.5465i	−0.731557	−	1.00690i	0.267503	−	0.963557i	$-0.413801\pi$
$182$		0			0
$183$	6.43952	+	19.8188i	0.476023	+	1.46505i
$184$		0			0
$185$	8.30748	−	1.20357i	0.610778	−	0.0884884i
$186$		0			0
$187$	−7.39668	−	2.40333i	−0.540899	−	0.175749i
$188$		0			0
$189$	−3.51958	−	10.8321i	−0.256011	−	0.787922i
$190$		0			0
$191$			23.8932i			1.72885i	0.502762	+	0.864425i	$0.332317\pi$
$191$			23.8932i			1.72885i	−0.502762	+	0.864425i	$0.667683\pi$
$192$		0			0
$193$	9.93160	+	7.21573i	0.714892	+	0.519400i	0.884748	−	0.466069i	$-0.154330\pi$
$193$	9.93160	+	7.21573i	0.714892	+	0.519400i	−0.169856	+	0.985469i	$0.554330\pi$
$194$		0			0
$195$	17.4032	−	8.57985i	1.24627	−	0.614416i
$196$		0			0
$197$	−9.78396	−	13.4665i	−0.697078	−	0.959446i	−0.999979	−	0.00642374i	$-0.997955\pi$
$197$	−9.78396	−	13.4665i	−0.697078	−	0.959446i	0.302901	−	0.953022i	$-0.402045\pi$
$198$		0			0
$199$	−5.67082	−	1.84256i	−0.401994	−	0.130616i	0.101040	−	0.994882i	$-0.467783\pi$
$199$	−5.67082	−	1.84256i	−0.401994	−	0.130616i	−0.503034	+	0.864267i	$0.667783\pi$
$200$		0			0
$201$	1.59045	+	1.15553i	0.112182	+	0.0815050i
$202$		0			0
$203$	−15.9105	−	5.16962i	−1.11670	−	0.362836i
$204$		0			0
$205$	4.45035	+	13.6086i	0.310826	+	0.950467i
$206$		0			0
$207$	−2.09203	−	0.679742i	−0.145406	−	0.0472454i
$208$		0			0
$209$	9.33538	+	6.78255i	0.645742	+	0.469159i
$210$		0			0
$211$	−16.4928	−	5.35884i	−1.13541	−	0.368918i	−0.319781	−	0.947491i	$-0.603609\pi$
$211$	−16.4928	−	5.35884i	−1.13541	−	0.368918i	−0.815630	+	0.578574i	$0.803609\pi$
$212$		0			0
$213$	−6.90887	−	9.50924i	−0.473388	−	0.651562i
$214$		0			0
$215$	−8.06355	−	16.3559i	−0.549930	−	1.11546i
$216$		0			0
$217$	−2.26727	−	1.64727i	−0.153912	−	0.111824i
$218$		0			0
$219$		−	18.0449i		−	1.21936i
$220$		0			0
$221$	5.62996	+	17.3272i	0.378712	+	1.16556i
$222$		0			0
$223$	−19.0198	−	6.17992i	−1.27366	−	0.413838i	−0.407319	−	0.913286i	$-0.633536\pi$
$223$	−19.0198	−	6.17992i	−1.27366	−	0.413838i	−0.866344	+	0.499448i	$0.833536\pi$
$224$		0			0
$225$	0.0716328	−	2.71220i	0.00477552	−	0.180814i
$226$		0			0
$227$	3.34675	+	10.3003i	0.222132	+	0.683652i	0.998570	+	0.0534583i	$0.0170244\pi$
$227$	3.34675	+	10.3003i	0.222132	+	0.683652i	−0.776438	+	0.630193i	$0.782976\pi$
$228$		0			0
$229$	−0.814843	−	1.12154i	−0.0538463	−	0.0741131i	0.781245	−	0.624225i	$-0.214585\pi$
$229$	−0.814843	−	1.12154i	−0.0538463	−	0.0741131i	−0.835091	+	0.550112i	$0.814585\pi$
$230$		0			0
$231$	−4.46541	+	6.14611i	−0.293802	+	0.404384i
$232$		0			0
$233$	3.18247	−	9.79464i	0.208491	−	0.641668i	−0.791061	−	0.611737i	$-0.790471\pi$
$233$	3.18247	−	9.79464i	0.208491	−	0.641668i	0.999552	−	0.0299312i	$-0.00952882\pi$
$234$		0			0
$235$	13.7410	−	6.77441i	0.896366	−	0.441914i
$236$		0			0
$237$		−	11.7682i		−	0.764430i
$238$		0			0
$239$	−2.35975	+	0.766731i	−0.152640	+	0.0495957i	−0.384340	−	0.923191i	$-0.625571\pi$
$239$	−2.35975	+	0.766731i	−0.152640	+	0.0495957i	0.231701	+	0.972787i	$0.425571\pi$
$240$		0			0
$241$	10.5356	+	7.65454i	0.678656	+	0.493072i	0.872912	−	0.487878i	$-0.162229\pi$
$241$	10.5356	+	7.65454i	0.678656	+	0.493072i	−0.194256	+	0.980951i	$0.562229\pi$
$242$		0			0
$243$	5.56534			0.357016
$244$		0			0
$245$	6.15669	+	1.05863i	0.393337	+	0.0676332i
$246$		0			0
$247$		−	27.0313i		−	1.71996i
$248$		0			0
$249$		−	16.9874i		−	1.07653i
$250$		0			0
$251$	−2.20252	−	1.60022i	−0.139022	−	0.101005i	0.516101	−	0.856528i	$-0.327383\pi$
$251$	−2.20252	−	1.60022i	−0.139022	−	0.101005i	−0.655122	+	0.755523i	$0.727383\pi$
$252$		0			0
$253$	2.96006	+	9.11014i	0.186098	+	0.572749i
$254$		0			0
$255$	−11.3701	−	1.95505i	−0.712022	−	0.122430i
$256$		0			0
$257$	−14.1017	+	10.2455i	−0.879642	+	0.639098i	−0.933157	−	0.359470i	$-0.882958\pi$
$257$	−14.1017	+	10.2455i	−0.879642	+	0.639098i	0.0535145	+	0.998567i	$0.482958\pi$
$258$		0			0
$259$	7.32231	+	2.37916i	0.454986	+	0.147834i
$260$		0			0
$261$	2.60167	−	3.58089i	0.161039	−	0.221651i
$262$		0			0
$263$	−4.60908	+	3.34869i	−0.284208	+	0.206489i	−0.720751	−	0.693194i	$-0.756203\pi$
$263$	−4.60908	+	3.34869i	−0.284208	+	0.206489i	0.436543	+	0.899684i	$0.356203\pi$
$264$		0			0
$265$	−1.99928	−	13.7997i	−0.122815	−	0.847710i
$266$		0			0
$267$	8.01846	−	2.60536i	0.490722	−	0.159445i
$268$		0			0
$269$	−2.16973	+	6.67774i	−0.132291	+	0.407149i	−0.995159	−	0.0982801i	$-0.968666\pi$
$269$	−2.16973	+	6.67774i	−0.132291	+	0.407149i	0.862868	+	0.505429i	$0.168666\pi$
$270$		0			0
$271$	−7.43132	−	22.8713i	−0.451421	−	1.38933i	−0.875287	−	0.483605i	$-0.839327\pi$
$271$	−7.43132	−	22.8713i	−0.451421	−	1.38933i	0.423866	−	0.905725i	$-0.360673\pi$
$272$		0			0
$273$	17.7965			1.07709
$274$		0			0
$275$	−9.73848	+	6.68985i	−0.587253	+	0.403413i
$276$		0			0
$277$	−6.37942	−	8.78052i	−0.383302	−	0.527571i	0.573153	−	0.819448i	$-0.305720\pi$
$277$	−6.37942	−	8.78052i	−0.383302	−	0.527571i	−0.956456	+	0.291878i	$0.905720\pi$
$278$		0			0
$279$	0.599875	−	0.435834i	0.0359136	−	0.0260927i
$280$		0			0
$281$	7.76850	+	2.52414i	0.463430	+	0.150577i	0.531420	−	0.847108i	$-0.321659\pi$
$281$	7.76850	+	2.52414i	0.463430	+	0.150577i	−0.0679901	+	0.997686i	$0.521659\pi$
$282$		0			0
$283$	−13.6604	+	18.8019i	−0.812026	+	1.11766i	0.178982	+	0.983852i	$0.442720\pi$
$283$	−13.6604	+	18.8019i	−0.812026	+	1.11766i	−0.991008	+	0.133805i	$0.957280\pi$
$284$		0			0
$285$	15.1477	+	7.97175i	0.897270	+	0.472206i
$286$		0			0
$287$	−1.85819	+	13.0001i	−0.109685	+	0.767372i
$288$		0			0
$289$	−1.90577	+	5.86537i	−0.112104	+	0.345022i
$290$		0			0
$291$	11.5487	+	8.39065i	0.676999	+	0.491869i
$292$		0			0
$293$	−7.25696	+	22.3346i	−0.423956	+	1.30480i	0.480034	+	0.877250i	$0.340624\pi$
$293$	−7.25696	+	22.3346i	−0.423956	+	1.30480i	−0.903990	+	0.427553i	$0.859376\pi$
$294$		0			0
$295$	−1.53231	+	0.755439i	−0.0892148	+	0.0439834i
$296$		0			0
$297$	−7.71330	−	10.6164i	−0.447571	−	0.616029i
$298$		0			0
$299$	13.1895	−	18.1539i	0.762771	−	1.04986i
$300$		0			0
$301$		−	16.7256i		−	0.964047i
$302$		0			0
$303$	−9.91840	+	3.22268i	−0.569797	+	0.185138i
$304$		0			0
$305$	−13.8433	+	26.3046i	−0.792666	+	1.50620i
$306$		0			0
$307$	18.8763	−	6.13329i	1.07733	−	0.350045i	0.283991	−	0.958827i	$-0.408341\pi$
$307$	18.8763	−	6.13329i	1.07733	−	0.350045i	0.793338	+	0.608781i	$0.208341\pi$
$308$		0			0
$309$	−23.0247	+	7.48118i	−1.30983	+	0.425590i
$310$		0			0
$311$	12.4283	+	17.1061i	0.704746	+	0.969999i	0.999894	+	0.0145477i	$0.00463083\pi$
$311$	12.4283	+	17.1061i	0.704746	+	0.969999i	−0.295149	+	0.955451i	$0.595369\pi$
$312$		0			0
$313$	−20.8454	−	15.1451i	−1.17825	−	0.856051i	−0.186280	−	0.982497i	$-0.559643\pi$
$313$	−20.8454	−	15.1451i	−1.17825	−	0.856051i	−0.991974	+	0.126445i	$0.959643\pi$
$314$		0			0
$315$	1.15892	−	2.20215i	0.0652980	−	0.124077i
$316$		0			0
$317$	−14.0101	+	10.1789i	−0.786886	+	0.571706i	−0.907038	−	0.421049i	$-0.861662\pi$
$317$	−14.0101	+	10.1789i	−0.786886	+	0.571706i	0.120152	+	0.992756i	$0.461662\pi$
$318$		0			0
$319$	−19.2748			−1.07918
$320$		0			0
$321$	7.02398	−	2.28223i	0.392040	−	0.127382i
$322$		0			0
$323$	−9.44719	+	13.0029i	−0.525656	+	0.723503i
$324$		0			0
$325$	26.0876	+	9.24473i	1.44708	+	0.512805i
$326$		0			0
$327$		−	11.6805i		−	0.645931i
$328$		0			0
$329$	14.0516			0.774691
$330$		0			0
$331$		−	3.84564i		−	0.211375i	−0.994399	−	0.105688i	$-0.966296\pi$
$331$		−	3.84564i		−	0.211375i	0.994399	−	0.105688i	$-0.0337044\pi$
$332$		0			0
$333$	−1.19734	+	1.64800i	−0.0656138	+	0.0903097i
$334$		0			0
$335$	0.402073	+	2.77525i	0.0219676	+	0.151628i
$336$		0			0
$337$			7.87239i			0.428836i	0.976742	+	0.214418i	$0.0687855\pi$
$337$			7.87239i			0.428836i	−0.976742	+	0.214418i	$0.931214\pi$
$338$		0			0
$339$	4.39067	+	6.04324i	0.238469	+	0.328224i
$340$		0			0
$341$	−3.07090	−	0.997796i	−0.166299	−	0.0540337i
$342$		0			0
$343$	16.2500	+	11.8063i	0.877419	+	0.637482i
$344$		0			0
$345$	6.28326	+	12.7448i	0.338279	+	0.686158i
$346$		0			0
$347$	−9.71323	−	29.8943i	−0.521434	−	1.60481i	−0.771262	−	0.636518i	$-0.780374\pi$
$347$	−9.71323	−	29.8943i	−0.521434	−	1.60481i	0.249829	−	0.968290i	$-0.419626\pi$
$348$		0			0
$349$	3.29132	+	10.1296i	0.176180	+	0.542227i	0.999685	−	0.0250818i	$-0.00798462\pi$
$349$	3.29132	+	10.1296i	0.176180	+	0.542227i	−0.823505	+	0.567309i	$0.807985\pi$
$350$		0			0
$351$	−9.49941	+	29.2362i	−0.507041	+	1.56051i
$352$		0			0
$353$	29.9422	−	9.72882i	1.59366	−	0.517813i	0.628134	−	0.778105i	$-0.283819\pi$
$353$	29.9422	−	9.72882i	1.59366	−	0.517813i	0.965530	+	0.260292i	$0.0838189\pi$
$354$		0			0
$355$	2.84123	−	16.5238i	0.150797	−	0.876994i
$356$		0			0
$357$	−8.56071	−	6.21972i	−0.453081	−	0.329183i
$358$		0			0
$359$	9.45150	−	6.86692i	0.498831	−	0.362422i	−0.309739	−	0.950822i	$-0.600242\pi$
$359$	9.45150	−	6.86692i	0.498831	−	0.362422i	0.808570	+	0.588399i	$0.200242\pi$
$360$		0			0
$361$	3.92105	−	2.84881i	0.206371	−	0.149937i
$362$		0			0
$363$	2.62375	−	8.07506i	0.137711	−	0.423831i
$364$		0			0
$365$	18.4395	−	17.9589i	0.965167	−	0.940012i
$366$		0			0
$367$	8.54981	+	2.77800i	0.446297	+	0.145011i	0.523539	−	0.852002i	$-0.324611\pi$
$367$	8.54981	+	2.77800i	0.446297	+	0.145011i	−0.0772422	+	0.997012i	$0.524611\pi$
$368$		0			0
$369$	−3.11930	−	1.53046i	−0.162384	−	0.0796727i
$370$		0			0
$371$	3.95208	−	12.1632i	0.205182	−	0.631484i
$372$		0			0
$373$	−10.6417	+	14.6471i	−0.551007	+	0.758396i	−0.990148	−	0.140022i	$-0.955283\pi$
$373$	−10.6417	+	14.6471i	−0.551007	+	0.758396i	0.439142	+	0.898418i	$0.355283\pi$
$374$		0			0
$375$	−12.8740	+	11.8925i	−0.664809	+	0.614127i
$376$		0			0
$377$	26.5400	+	36.5292i	1.36688	+	1.88135i
$378$		0			0
$379$	−1.32002	+	0.959053i	−0.0678050	+	0.0492632i	−0.621171	−	0.783675i	$-0.713343\pi$
$379$	−1.32002	+	0.959053i	−0.0678050	+	0.0492632i	0.553366	+	0.832938i	$0.313343\pi$
$380$		0			0
$381$	7.93316	−	10.9191i	0.406428	−	0.559401i
$382$		0			0
$383$	27.0643			1.38292			0.691459	−	0.722415i	$-0.256968\pi$
$383$	27.0643			1.38292			0.691459	+	0.722415i	$0.256968\pi$
$384$		0			0
$385$	−10.7246	+	1.55376i	−0.546577	+	0.0791870i
$386$		0			0
$387$	4.20867	+	1.36748i	0.213939	+	0.0695129i
$388$		0			0
$389$	10.0004	+	30.7781i	0.507042	+	1.56051i	0.797311	+	0.603569i	$0.206255\pi$
$389$	10.0004	+	30.7781i	0.507042	+	1.56051i	−0.290269	+	0.956945i	$0.593745\pi$
$390$		0			0
$391$	−12.6892	+	4.12297i	−0.641721	+	0.208508i
$392$		0			0
$393$	1.75570	−	1.27559i	0.0885632	−	0.0643450i
$394$		0			0
$395$	12.0256	−	11.7121i	0.605072	−	0.589302i
$396$		0			0
$397$	−4.75458	+	14.6331i	−0.238625	+	0.734413i	0.757995	+	0.652261i	$0.226179\pi$
$397$	−4.75458	+	14.6331i	−0.238625	+	0.734413i	−0.996620	+	0.0821522i	$0.973821\pi$
$398$		0			0
$399$	9.22816	+	12.7015i	0.461986	+	0.635869i
$400$		0			0
$401$	2.45711			0.122702			0.0613511	−	0.998116i	$-0.480459\pi$
$401$	2.45711			0.122702			0.0613511	+	0.998116i	$0.480459\pi$
$402$		0			0
$403$	2.33741	+	7.19380i	0.116435	+	0.358349i
$404$		0			0
$405$	−11.0420	−	11.3375i	−0.548684	−	0.563367i
$406$		0			0
$407$	8.87065			0.439702
$408$		0			0
$409$	23.1016			1.14230			0.571150	−	0.820845i	$-0.306497\pi$
$409$	23.1016			1.14230			0.571150	+	0.820845i	$0.306497\pi$
$410$		0			0
$411$	−21.8612			−1.07834
$412$		0			0
$413$	−1.56695			−0.0771045
$414$		0			0
$415$	17.3588	−	16.9064i	0.852109	−	0.829901i
$416$		0			0
$417$	−9.32059	−	28.6858i	−0.456431	−	1.40475i
$418$		0			0
$419$	15.5028			0.757360			0.378680	−	0.925528i	$-0.376378\pi$
$419$	15.5028			0.757360			0.378680	+	0.925528i	$0.376378\pi$
$420$		0			0
$421$	−0.991178	−	1.36424i	−0.0483071	−	0.0664890i	0.784180	−	0.620533i	$-0.213084\pi$
$421$	−0.991178	−	1.36424i	−0.0483071	−	0.0664890i	−0.832487	+	0.554044i	$0.813084\pi$
$422$		0			0
$423$	−1.14886	+	3.53582i	−0.0558593	+	0.171917i
$424$		0			0
$425$	−9.31807	−	13.5644i	−0.451993	−	0.657971i
$426$		0			0
$427$	−22.0567	+	16.0251i	−1.06740	+	0.775510i
$428$		0			0
$429$	19.5009	−	6.33623i	0.941513	−	0.305916i
$430$		0			0
$431$	12.3304	+	37.9492i	0.593936	+	1.82795i	0.559951	+	0.828526i	$0.310820\pi$
$431$	12.3304	+	37.9492i	0.593936	+	1.82795i	0.0339852	+	0.999422i	$0.489180\pi$
$432$		0			0
$433$	19.9769	+	6.49088i	0.960027	+	0.311932i	0.746783	−	0.665067i	$-0.231597\pi$
$433$	19.9769	+	6.49088i	0.960027	+	0.311932i	0.213244	+	0.976999i	$0.431597\pi$
$434$		0			0
$435$	−28.2969	+	4.09960i	−1.35673	+	0.196561i
$436$		0			0
$437$	19.7958			0.946960
$438$		0			0
$439$	−4.26443	+	5.86949i	−0.203530	+	0.280135i	−0.898565	−	0.438841i	$-0.855389\pi$
$439$	−4.26443	+	5.86949i	−0.203530	+	0.280135i	0.695034	+	0.718976i	$0.255389\pi$
$440$		0			0
$441$	−1.22645	+	0.891070i	−0.0584025	+	0.0424319i
$442$		0			0
$443$	−1.24132	−	1.70852i	−0.0589767	−	0.0811744i	0.778510	−	0.627632i	$-0.215976\pi$
$443$	−1.24132	−	1.70852i	−0.0589767	−	0.0811744i	−0.837487	+	0.546458i	$0.815976\pi$
$444$		0			0
$445$	10.6426	+	5.60085i	0.504506	+	0.265506i
$446$		0			0
$447$	7.93325	−	10.9192i	0.375230	−	0.516459i
$448$		0			0
$449$	−10.8156	+	33.2871i	−0.510422	+	1.57092i	0.281039	+	0.959696i	$0.409321\pi$
$449$	−10.8156	+	33.2871i	−0.510422	+	1.57092i	−0.791461	+	0.611220i	$0.790679\pi$
$450$		0			0
$451$	2.59238	+	14.9067i	0.122070	+	0.701930i
$452$		0			0
$453$	−21.1582	−	6.87473i	−0.994101	−	0.323003i
$454$		0			0
$455$	17.7117	+	18.1856i	0.830336	+	0.852556i
$456$		0			0
$457$	−12.7339	+	39.1909i	−0.595667	+	1.83328i	−0.0442908	+	0.999019i	$0.514103\pi$
$457$	−12.7339	+	39.1909i	−0.595667	+	1.83328i	−0.551376	+	0.834257i	$0.685897\pi$
$458$		0			0
$459$	14.7873	−	10.7436i	0.690212	−	0.501468i
$460$		0			0
$461$	−10.5894	+	7.69366i	−0.493198	+	0.358330i	−0.806413	−	0.591353i	$-0.798594\pi$
$461$	−10.5894	+	7.69366i	−0.493198	+	0.358330i	0.313215	+	0.949682i	$0.398594\pi$
$462$		0			0
$463$	24.7206	+	17.9606i	1.14887	+	0.834699i	0.988330	−	0.152331i	$-0.0486778\pi$
$463$	24.7206	+	17.9606i	1.14887	+	0.834699i	0.160536	+	0.987030i	$0.448678\pi$
$464$		0			0
$465$	−4.72055	−	0.811686i	−0.218910	−	0.0376410i
$466$		0			0
$467$	8.00856	−	2.60214i	0.370592	−	0.120413i	−0.117799	−	0.993037i	$-0.537584\pi$
$467$	8.00856	−	2.60214i	0.370592	−	0.120413i	0.488391	+	0.872625i	$0.337584\pi$
$468$		0			0
$469$	−0.794799	+	2.44614i	−0.0367004	+	0.112952i
$470$		0			0
$471$	10.1832	+	31.3408i	0.469219	+	1.44411i
$472$		0			0
$473$	−5.95494	−	18.3274i	−0.273808	−	0.842696i
$474$		0			0
$475$	6.92940	+	23.4126i	0.317943	+	1.07424i
$476$		0			0
$477$	2.73752	+	1.98893i	0.125342	+	0.0910667i
$478$		0			0
$479$	−10.7336	−	3.48756i	−0.490431	−	0.159351i	0.0533531	−	0.998576i	$-0.483009\pi$
$479$	−10.7336	−	3.48756i	−0.490431	−	0.159351i	−0.543785	+	0.839225i	$0.683009\pi$
$480$		0			0
$481$	−12.2143	−	16.8115i	−0.556922	−	0.766537i
$482$		0			0
$483$			13.0329i			0.593017i
$484$		0			0
$485$	2.91957	+	20.1519i	0.132571	+	0.915051i
$486$		0			0
$487$	−20.4628	+	28.1646i	−0.927256	+	1.27626i	0.0336641	+	0.999433i	$0.489282\pi$
$487$	−20.4628	+	28.1646i	−0.927256	+	1.27626i	−0.960920	+	0.276825i	$0.910718\pi$
$488$		0			0
$489$		−	21.8698i		−	0.988988i
$490$		0			0
$491$	16.1040			0.726763			0.363381	−	0.931640i	$-0.381622\pi$
$491$	16.1040			0.726763			0.363381	+	0.931640i	$0.381622\pi$
$492$		0			0
$493$		−	26.8472i		−	1.20914i
$494$		0			0
$495$	0.485867	−	2.82567i	0.0218381	−	0.127005i
$496$		0			0
$497$	9.03896	−	12.4411i	0.405453	−	0.558058i
$498$		0			0
$499$	−6.63307	+	2.15521i	−0.296937	+	0.0964806i	−0.453697	−	0.891156i	$-0.649895\pi$
$499$	−6.63307	+	2.15521i	−0.296937	+	0.0964806i	0.156760	+	0.987637i	$0.449895\pi$
$500$		0			0
$501$	20.1331			0.899481
$502$		0			0
$503$	15.7940	−	11.4750i	0.704218	−	0.511644i	−0.177085	−	0.984196i	$-0.556667\pi$
$503$	15.7940	−	11.4750i	0.704218	−	0.511644i	0.881303	+	0.472551i	$0.156667\pi$
$504$		0			0
$505$	−13.1643	−	6.92795i	−0.585802	−	0.308290i
$506$		0			0
$507$	−22.3729	−	16.2548i	−0.993613	−	0.721902i
$508$		0			0
$509$	−7.46330	−	10.2724i	−0.330805	−	0.455314i	0.610923	−	0.791690i	$-0.290799\pi$
$509$	−7.46330	−	10.2724i	−0.330805	−	0.455314i	−0.941728	+	0.336376i	$0.890799\pi$
$510$		0			0
$511$	22.4529	−	7.29540i	0.993260	−	0.322730i
$512$		0			0
$513$	−25.7918	+	8.38026i	−1.13874	+	0.369998i
$514$		0			0
$515$	−30.5597	−	16.0826i	−1.34662	−	0.708685i
$516$		0			0
$517$	15.3974	−	5.00291i	0.677175	−	0.220028i
$518$		0			0
$519$			25.2352i			1.10770i
$520$		0			0
$521$	13.3134	−	18.3243i	0.583270	−	0.802802i	−0.410780	−	0.911735i	$-0.634743\pi$
$521$	13.3134	−	18.3243i	0.583270	−	0.802802i	0.994049	+	0.108933i	$0.0347434\pi$
$522$		0			0
$523$	−9.05757	−	12.4667i	−0.396060	−	0.545130i	0.563690	−	0.825987i	$-0.309381\pi$
$523$	−9.05757	−	12.4667i	−0.396060	−	0.545130i	−0.959750	+	0.280857i	$0.909381\pi$
$524$		0			0
$525$	−15.4141	+	4.56209i	−0.672726	+	0.199106i
$526$		0			0
$527$	1.38980	−	4.27736i	0.0605405	−	0.186325i
$528$		0			0
$529$	−5.31283	−	3.86000i	−0.230993	−	0.167826i
$530$		0			0
$531$	0.128113	−	0.394292i	0.00555964	−	0.0171108i
$532$		0			0
$533$	24.6814	−	25.4385i	1.06907	−	1.10186i
$534$		0			0
$535$	9.32262	+	4.90621i	0.403052	+	0.212114i
$536$		0			0
$537$	18.7874	−	25.8586i	0.810735	−	1.11588i
$538$		0			0
$539$	6.27851	+	2.04001i	0.270434	+	0.0878695i
$540$		0			0
$541$	31.5903	−	22.9517i	1.35817	−	0.986771i	0.359614	−	0.933101i	$-0.382908\pi$
$541$	31.5903	−	22.9517i	1.35817	−	0.986771i	0.998559	−	0.0536696i	$-0.0170918\pi$
$542$		0			0
$543$	−15.4285	−	21.2355i	−0.662099	−	0.911301i
$544$		0			0
$545$	11.9359	−	11.6248i	0.511276	−	0.497951i
$546$		0			0
$547$	21.5147			0.919903			0.459951	−	0.887944i	$-0.347867\pi$
$547$	21.5147			0.919903			0.459951	+	0.887944i	$0.347867\pi$
$548$		0			0
$549$	−2.22906	−	6.86034i	−0.0951340	−	0.292792i
$550$		0			0
$551$	−12.3091	+	37.8835i	−0.524385	+	1.61389i
$552$		0			0
$553$	14.6430	−	4.75780i	0.622683	−	0.202322i
$554$		0			0
$555$	13.0228	−	1.88672i	0.552788	−	0.0800868i
$556$		0			0
$557$	26.1445	−	18.9951i	1.10778	−	0.804849i	0.125467	−	0.992098i	$-0.459957\pi$
$557$	26.1445	−	18.9951i	1.10778	−	0.804849i	0.982313	+	0.187249i	$0.0599571\pi$
$558$		0			0
$559$	−26.5342	+	36.5212i	−1.12228	+	1.54468i
$560$		0			0
$561$	−11.5950	−	3.76746i	−0.489543	−	0.159062i
$562$		0			0
$563$	2.61774	−	1.90190i	0.110325	−	0.0801555i	−0.531255	−	0.847212i	$-0.678279\pi$
$563$	2.61774	−	1.90190i	0.110325	−	0.0801555i	0.641580	+	0.767056i	$0.278279\pi$
$564$		0			0
$565$	−1.80564	+	10.5011i	−0.0759638	+	0.441785i
$566$		0			0
$567$	−4.48559	−	13.8052i	−0.188377	−	0.579764i
$568$		0			0
$569$	−8.42351	−	6.12004i	−0.353132	−	0.256565i	0.397050	−	0.917797i	$-0.370034\pi$
$569$	−8.42351	−	6.12004i	−0.353132	−	0.256565i	−0.750182	+	0.661232i	$0.770034\pi$
$570$		0			0
$571$			12.6810i			0.530684i	0.964154	+	0.265342i	$0.0854849\pi$
$571$			12.6810i			0.530684i	−0.964154	+	0.265342i	$0.914515\pi$
$572$		0			0
$573$			37.4549i			1.56470i
$574$		0			0
$575$	−6.77017	+	19.1047i	−0.282336	+	0.796721i
$576$		0			0
$577$	−4.16182			−0.173259			−0.0866295	−	0.996241i	$-0.527610\pi$
$577$	−4.16182			−0.173259			−0.0866295	+	0.996241i	$0.527610\pi$
$578$		0			0
$579$	15.5688	+	11.3114i	0.647016	+	0.470085i
$580$		0			0
$581$	21.1370	−	6.86783i	0.876911	−	0.284926i
$582$		0			0
$583$		−	14.7352i		−	0.610270i
$584$		0			0
$585$	−6.02416	+	2.96994i	−0.249068	+	0.122792i
$586$		0			0
$587$	−6.59927	+	20.3105i	−0.272381	+	0.838302i	0.717520	+	0.696538i	$0.245277\pi$
$587$	−6.59927	+	20.3105i	−0.272381	+	0.838302i	−0.989901	+	0.141764i	$0.954723\pi$
$588$		0			0
$589$	−3.92222	+	5.39847i	−0.161612	+	0.222440i
$590$		0			0
$591$	−15.3373	−	21.1100i	−0.630894	−	0.868350i
$592$		0			0
$593$	−9.09313	−	27.9858i	−0.373410	−	1.14924i	−0.944545	−	0.328382i	$-0.893497\pi$
$593$	−9.09313	−	27.9858i	−0.373410	−	1.14924i	0.571135	−	0.820856i	$-0.306503\pi$
$594$		0			0
$595$	−2.16418	−	14.9380i	−0.0887229	−	0.612397i
$596$		0			0
$597$	−8.88957	−	2.88840i	−0.363826	−	0.118214i
$598$		0			0
$599$	6.56661	+	20.2099i	0.268304	+	0.825756i	0.990914	+	0.134499i	$0.0429425\pi$
$599$	6.56661	+	20.2099i	0.268304	+	0.825756i	−0.722609	+	0.691257i	$0.757057\pi$
$600$		0			0
$601$		−	22.9007i		−	0.934139i	−0.884221	−	0.467070i	$-0.845310\pi$
$601$		−	22.9007i		−	0.934139i	0.884221	−	0.467070i	$-0.154690\pi$
$602$		0			0
$603$	−0.550541	−	0.399991i	−0.0224198	−	0.0162889i
$604$		0			0
$605$	10.8629	−	5.35545i	0.441638	−	0.217730i
$606$		0			0
$607$	−1.59160	−	2.19064i	−0.0646009	−	0.0889155i	0.775494	−	0.631355i	$-0.217501\pi$
$607$	−1.59160	−	2.19064i	−0.0646009	−	0.0889155i	−0.840095	+	0.542439i	$0.817501\pi$
$608$		0			0
$609$	−24.9412	−	8.10390i	−1.01067	−	0.328387i
$610$		0			0
$611$	−30.6825	−	22.2921i	−1.24128	−	0.901842i
$612$		0			0
$613$	−40.5399	−	13.1722i	−1.63739	−	0.532021i	−0.661439	−	0.749999i	$-0.730054\pi$
$613$	−40.5399	−	13.1722i	−1.63739	−	0.532021i	−0.975954	+	0.217978i	$0.930054\pi$
$614$		0			0
$615$	6.97636	+	21.3329i	0.281314	+	0.860224i
$616$		0			0
$617$	7.73429	+	2.51302i	0.311371	+	0.101171i	0.460534	−	0.887642i	$-0.347658\pi$
$617$	7.73429	+	2.51302i	0.311371	+	0.101171i	−0.149163	+	0.988813i	$0.547658\pi$
$618$		0			0
$619$	7.36503	+	5.35101i	0.296025	+	0.215075i	0.725877	−	0.687824i	$-0.241434\pi$
$619$	7.36503	+	5.35101i	0.296025	+	0.215075i	−0.429852	+	0.902900i	$0.641434\pi$
$620$		0			0
$621$	−21.4104	−	6.95667i	−0.859171	−	0.279162i
$622$		0			0
$623$	6.48358	+	8.92389i	0.259759	+	0.357528i
$624$		0			0
$625$	−24.9651	−	1.31964i	−0.998606	−	0.0527858i
$626$		0			0
$627$	14.6341	+	10.6323i	0.584431	+	0.424614i
$628$		0			0
$629$			12.3556i			0.492652i
$630$		0			0
$631$	−6.99561	−	21.5303i	−0.278491	−	0.857107i	−0.988275	−	0.152687i	$-0.951207\pi$
$631$	−6.99561	−	21.5303i	−0.278491	−	0.857107i	0.709784	−	0.704420i	$-0.248793\pi$
$632$		0			0
$633$	−25.8541	−	8.40051i	−1.02761	−	0.333890i
$634$		0			0
$635$	19.0531	−	2.76038i	0.756101	−	0.109543i
$636$		0			0
$637$	−4.77887	−	14.7078i	−0.189346	−	0.582746i
$638$		0			0
$639$	2.39153	+	3.29165i	0.0946073	+	0.130216i
$640$		0			0
$641$	3.46390	−	4.76765i	0.136816	−	0.188311i	−0.735111	−	0.677946i	$-0.762870\pi$
$641$	3.46390	−	4.76765i	0.136816	−	0.188311i	0.871927	+	0.489636i	$0.162870\pi$
$642$		0			0
$643$	7.98958	−	24.5894i	0.315078	−	0.969711i	−0.660644	−	0.750699i	$-0.729717\pi$
$643$	7.98958	−	24.5894i	0.315078	−	0.969711i	0.975722	−	0.219012i	$-0.0702832\pi$
$644$		0			0
$645$	−12.6404	−	25.6395i	−0.497716	−	1.00956i
$646$		0			0
$647$			40.6644i			1.59868i	0.600877	+	0.799341i	$0.294818\pi$
$647$			40.6644i			1.59868i	−0.600877	+	0.799341i	$0.705182\pi$
$648$		0			0
$649$	−1.71702	+	0.557893i	−0.0673988	+	0.0218992i
$650$		0			0
$651$	−3.55418	−	2.58226i	−0.139299	−	0.101207i
$652$		0			0
$653$	−22.8502			−0.894196			−0.447098	−	0.894485i	$-0.647542\pi$
$653$	−22.8502			−0.894196			−0.447098	+	0.894485i	$0.647542\pi$
$654$		0			0
$655$	3.05081	+	0.524578i	0.119205	+	0.0204970i
$656$		0			0
$657$			6.24631i			0.243692i
$658$		0			0
$659$		−	33.2386i		−	1.29479i	−0.762153	−	0.647397i	$-0.775858\pi$
$659$		−	33.2386i		−	1.29479i	0.762153	−	0.647397i	$-0.224142\pi$
$660$		0			0
$661$	−25.4766	−	18.5098i	−0.990923	−	0.719948i	−0.0308001	−	0.999526i	$-0.509806\pi$
$661$	−25.4766	−	18.5098i	−0.990923	−	0.719948i	−0.960123	+	0.279578i	$0.909806\pi$
$662$		0			0
$663$	8.82553	+	27.1622i	0.342755	+	1.05489i
$664$		0			0
$665$	−3.79502	+	22.0708i	−0.147165	+	0.855870i
$666$		0			0
$667$	−26.7513	+	19.4360i	−1.03582	+	0.752564i
$668$		0			0
$669$	−29.8155	−	9.68764i	−1.15273	−	0.374546i
$670$		0			0
$671$	−18.4635	+	25.4129i	−0.712777	+	0.981053i
$672$		0			0
$673$	−21.2431	+	15.4340i	−0.818862	+	0.594938i	−0.916386	−	0.400295i	$-0.868908\pi$
$673$	−21.2431	+	15.4340i	−0.818862	+	0.594938i	0.0975244	+	0.995233i	$0.468908\pi$
$674$		0			0
$675$	0.733110	−	27.7575i	0.0282174	−	1.06838i
$676$		0			0
$677$	3.57989	−	1.16318i	0.137586	−	0.0447045i	−0.239414	−	0.970917i	$-0.576955\pi$
$677$	3.57989	−	1.16318i	0.137586	−	0.0447045i	0.377001	+	0.926213i	$0.376955\pi$
$678$		0			0
$679$	−5.77127	+	17.7621i	−0.221481	+	0.681648i
$680$		0			0
$681$	5.24637	+	16.1467i	0.201041	+	0.618742i
$682$		0			0
$683$	−16.4783			−0.630525			−0.315263	−	0.949004i	$-0.602093\pi$
$683$	−16.4783			−0.630525			−0.315263	+	0.949004i	$0.602093\pi$
$684$		0			0
$685$	−21.7570	−	22.3392i	−0.831293	−	0.853538i
$686$		0			0
$687$	−1.27735	−	1.75812i	−0.0487339	−	0.0670764i
$688$		0			0
$689$	−27.9259	+	20.2893i	−1.06389	+	0.772962i
$690$		0			0
$691$	−19.2415	−	6.25194i	−0.731981	−	0.237835i	−0.0807709	−	0.996733i	$-0.525738\pi$
$691$	−19.2415	−	6.25194i	−0.731981	−	0.237835i	−0.651210	+	0.758898i	$0.725738\pi$
$692$		0			0
$693$	1.54572	−	2.12750i	0.0587169	−	0.0808169i
$694$		0			0
$695$	20.0369	−	38.0734i	0.760042	−	1.44421i
$696$		0			0
$697$	−20.7631	+	3.61084i	−0.786458	+	0.136770i
$698$		0			0
$699$	4.98884	−	15.3541i	0.188695	−	0.580744i
$700$		0			0
$701$	11.6086	+	8.43414i	0.438451	+	0.318553i	0.785019	−	0.619472i	$-0.212653\pi$
$701$	11.6086	+	8.43414i	0.438451	+	0.318553i	−0.346568	+	0.938025i	$0.612653\pi$
$702$		0			0
$703$	5.66489	−	17.4347i	0.213655	−	0.657564i
$704$		0			0
$705$	21.5405	−	10.6196i	0.811260	−	0.399956i
$706$		0			0
$707$	−8.01984	−	11.0384i	−0.301617	−	0.415140i
$708$		0			0
$709$	3.41476	−	4.70002i	0.128244	−	0.176513i	−0.740067	−	0.672534i	$-0.765206\pi$
$709$	3.41476	−	4.70002i	0.128244	−	0.176513i	0.868311	+	0.496021i	$0.165206\pi$
$710$		0			0
$711$			4.07362i			0.152773i
$712$		0			0
$713$	−5.26822	+	1.71175i	−0.197296	+	0.0641055i
$714$		0			0
$715$	25.8827	+	13.6213i	0.967959	+	0.509407i
$716$		0			0
$717$	−3.69915	+	1.20193i	−0.138147	+	0.0448868i
$718$		0			0
$719$	−46.4003	+	15.0764i	−1.73044	+	0.562254i	−0.993513	−	0.113718i	$-0.963724\pi$
$719$	−46.4003	+	15.0764i	−1.73044	+	0.562254i	−0.736927	+	0.675972i	$0.763724\pi$
$720$		0			0
$721$	−18.6174	−	25.6246i	−0.693347	−	0.954310i
$722$		0			0
$723$	16.5156	+	11.9993i	0.614221	+	0.446257i
$724$		0			0
$725$	−32.3513	−	24.8356i	−1.20150	−	0.922370i
$726$		0			0
$727$	4.36609	−	3.17215i	0.161929	−	0.117649i	−0.503870	−	0.863780i	$-0.668091\pi$
$727$	4.36609	−	3.17215i	0.161929	−	0.117649i	0.665799	+	0.746131i	$0.268091\pi$
$728$		0			0
$729$	29.9572			1.10953
$730$		0			0
$731$	25.5277	−	8.29444i	0.944175	−	0.306781i
$732$		0			0
$733$	7.24203	−	9.96780i	0.267491	−	0.368169i	−0.654050	−	0.756451i	$-0.726931\pi$
$733$	7.24203	−	9.96780i	0.267491	−	0.368169i	0.921541	+	0.388282i	$0.126931\pi$
$734$		0			0
$735$	9.65123	+	1.65950i	0.355991	+	0.0612117i
$736$		0			0
$737$			2.96339i			0.109158i
$738$		0			0
$739$	39.1685			1.44084			0.720419	−	0.693539i	$-0.243950\pi$
$739$	39.1685			1.44084			0.720419	+	0.693539i	$0.243950\pi$
$740$		0			0
$741$		−	42.3743i		−	1.55666i
$742$		0			0
$743$	−21.4529	+	29.5274i	−0.787031	+	1.08326i	0.207440	+	0.978248i	$0.433487\pi$
$743$	−21.4529	+	29.5274i	−0.787031	+	1.08326i	−0.994471	+	0.105008i	$0.966513\pi$
$744$		0			0
$745$	19.0534	−	2.76041i	0.698061	−	0.101134i
$746$		0			0
$747$			5.88023i			0.215146i
$748$		0			0
$749$	5.67946	+	7.81710i	0.207523	+	0.285631i
$750$		0			0
$751$	17.1294	+	5.56568i	0.625061	+	0.203095i	0.604386	−	0.796692i	$-0.293418\pi$
$751$	17.1294	+	5.56568i	0.625061	+	0.203095i	0.0206750	+	0.999786i	$0.493418\pi$
$752$		0			0
$753$	−3.45266	−	2.50851i	−0.125822	−	0.0914151i
$754$		0			0
$755$	−14.0323	−	28.4628i	−0.510689	−	1.03587i
$756$		0			0
$757$	4.06859	+	12.5218i	0.147875	+	0.455113i	0.997370	−	0.0724845i	$-0.0230928\pi$
$757$	4.06859	+	12.5218i	0.147875	+	0.455113i	−0.849494	+	0.527598i	$0.823093\pi$
$758$		0			0
$759$	4.64019	+	14.2811i	0.168428	+	0.518369i
$760$		0			0
$761$	0.493120	−	1.51767i	0.0178756	−	0.0550154i	−0.941721	−	0.336395i	$-0.890792\pi$
$761$	0.493120	−	1.51767i	0.0178756	−	0.0550154i	0.959596	+	0.281380i	$0.0907921\pi$
$762$		0			0
$763$	14.5338	−	4.72230i	0.526157	−	0.170959i
$764$		0			0
$765$	3.93579	+	0.676748i	0.142299	+	0.0244679i
$766$		0			0
$767$	3.42152	+	2.48588i	0.123544	+	0.0897598i
$768$		0			0
$769$	20.4743	−	14.8754i	0.738321	−	0.536421i	−0.153864	−	0.988092i	$-0.549172\pi$
$769$	20.4743	−	14.8754i	0.738321	−	0.536421i	0.892185	+	0.451671i	$0.149172\pi$
$770$		0			0
$771$	−22.1059	+	16.0609i	−0.796124	+	0.578418i
$772$		0			0
$773$	−8.04747	+	24.7676i	−0.289448	+	0.890828i	0.695583	+	0.718446i	$0.255146\pi$
$773$	−8.04747	+	24.7676i	−0.289448	+	0.890828i	−0.985030	+	0.172382i	$0.944854\pi$
$774$		0			0
$775$	−3.86861	−	5.63158i	−0.138965	−	0.202292i
$776$		0			0
$777$	11.4785	+	3.72958i	0.411787	+	0.133798i
$778$		0			0
$779$	30.9538	+	4.42443i	1.10904	+	0.158522i
$780$		0			0
$781$	5.47514	−	16.8508i	0.195916	−	0.602968i
$782$		0			0
$783$	26.6262	−	36.6478i	0.951543	−	1.30969i
$784$		0			0
$785$	−21.8914	+	41.5973i	−0.781336	+	1.48467i
$786$		0			0
$787$	6.11011	+	8.40984i	0.217802	+	0.299778i	0.903911	−	0.427720i	$-0.140683\pi$
$787$	6.11011	+	8.40984i	0.217802	+	0.299778i	−0.686110	+	0.727498i	$0.740683\pi$
$788$		0			0
$789$	−7.22520	+	5.24941i	−0.257224	+	0.186884i
$790$		0			0
$791$	−5.74437	+	7.90645i	−0.204246	+	0.281121i
$792$		0			0
$793$	73.5849			2.61308
$794$		0			0
$795$	−3.13407	−	21.6325i	−0.111154	−	0.767224i
$796$		0			0
$797$	15.6376	+	5.08096i	0.553912	+	0.179977i	0.572580	−	0.819849i	$-0.305943\pi$
$797$	15.6376	+	5.08096i	0.553912	+	0.179977i	−0.0186681	+	0.999826i	$0.505943\pi$
$798$		0			0
$799$	6.96838	+	21.4465i	0.246524	+	0.758722i
$800$		0			0
$801$	−2.77562	+	0.901853i	−0.0980716	+	0.0318654i
$802$		0			0
$803$	22.0058	−	15.9882i	0.776570	−	0.564211i
$804$		0			0
$805$	−13.3178	+	12.9707i	−0.469392	+	0.457159i
$806$		0			0
$807$	−3.40127	+	10.4680i	−0.119730	+	0.368492i
$808$		0			0
$809$	−8.65975	−	11.9191i	−0.304461	−	0.419054i	0.629183	−	0.777257i	$-0.283390\pi$
$809$	−8.65975	−	11.9191i	−0.304461	−	0.419054i	−0.933644	+	0.358203i	$0.883390\pi$
$810$		0			0
$811$	−11.4745			−0.402924			−0.201462	−	0.979496i	$-0.564569\pi$
$811$	−11.4745			−0.402924			−0.201462	+	0.979496i	$0.564569\pi$
$812$		0			0
$813$	−11.6493	−	35.8530i	−0.408560	−	1.25742i
$814$		0			0
$815$	22.3480	−	21.7656i	0.782817	−	0.762415i
$816$		0			0
$817$	−39.8243			−1.39328
$818$		0			0
$819$	−6.16032			−0.215259
$820$		0			0
$821$	39.9447			1.39408			0.697040	−	0.717032i	$-0.254500\pi$
$821$	39.9447			1.39408			0.697040	+	0.717032i	$0.254500\pi$
$822$		0			0
$823$	−46.9212			−1.63557			−0.817786	−	0.575523i	$-0.804799\pi$
$823$	−46.9212			−1.63557			−0.817786	+	0.575523i	$0.804799\pi$
$824$		0			0
$825$	−15.2660	+	10.4870i	−0.531496	+	0.365111i
$826$		0			0
$827$	−2.44323	−	7.51947i	−0.0849593	−	0.261478i	0.899548	−	0.436822i	$-0.143896\pi$
$827$	−2.44323	−	7.51947i	−0.0849593	−	0.261478i	−0.984507	+	0.175344i	$0.943896\pi$
$828$		0			0
$829$	30.3041			1.05251			0.526253	−	0.850328i	$-0.323596\pi$
$829$	30.3041			1.05251			0.526253	+	0.850328i	$0.323596\pi$
$830$		0			0
$831$	−10.0004	−	13.7643i	−0.346910	−	0.477480i
$832$		0			0
$833$	−2.84146	+	8.74512i	−0.0984509	+	0.303001i
$834$		0			0
$835$	20.0371	+	20.5733i	0.693413	+	0.711969i
$836$		0			0
$837$	6.13929	−	4.46045i	0.212205	−	0.154176i
$838$		0			0
$839$	−28.4434	+	9.24184i	−0.981977	+	0.319064i	−0.755641	−	0.654986i	$-0.772675\pi$
$839$	−28.4434	+	9.24184i	−0.981977	+	0.319064i	−0.226336	+	0.974049i	$0.572675\pi$
$840$		0			0
$841$	−11.5994	−	35.6992i	−0.399978	−	1.23101i
$842$		0			0
$843$	12.1779	+	3.95684i	0.419429	+	0.136281i
$844$		0			0
$845$	−5.65595	−	39.0394i	−0.194571	−	1.34300i
$846$		0			0
$847$	11.1084			0.381689
$848$		0			0
$849$	−21.4140	+	29.4739i	−0.734927	+	1.01154i
$850$		0			0
$851$	12.3115	−	8.94483i	0.422033	−	0.306625i
$852$		0			0
$853$	15.2900	+	21.0449i	0.523519	+	0.720562i	0.986126	−	0.166001i	$-0.0530856\pi$
$853$	15.2900	+	21.0449i	0.523519	+	0.720562i	−0.462606	+	0.886564i	$0.653086\pi$
$854$		0			0
$855$	−5.24341	−	2.75945i	−0.179321	−	0.0943711i
$856$		0			0
$857$	−31.5997	+	43.4933i	−1.07943	+	1.48570i	−0.219275	+	0.975663i	$0.570369\pi$
$857$	−31.5997	+	43.4933i	−1.07943	+	1.48570i	−0.860151	+	0.510040i	$0.829631\pi$
$858$		0			0
$859$	−6.53175	+	20.1027i	−0.222861	+	0.685894i	0.775641	+	0.631174i	$0.217427\pi$
$859$	−6.53175	+	20.1027i	−0.222861	+	0.685894i	−0.998502	+	0.0547201i	$0.982573\pi$
$860$		0			0
$861$	−2.91290	+	20.3790i	−0.0992713	+	0.694514i
$862$		0			0
$863$	−24.5772	−	7.98561i	−0.836617	−	0.271833i	−0.140787	−	0.990040i	$-0.544963\pi$
$863$	−24.5772	−	7.98561i	−0.836617	−	0.271833i	−0.695830	+	0.718207i	$0.744963\pi$
$864$		0			0
$865$	−25.7869	+	25.1149i	−0.876782	+	0.853931i
$866$		0			0
$867$	−2.98749	+	9.19455i	−0.101461	+	0.312263i
$868$		0			0
$869$	14.3514	−	10.4269i	0.486838	−	0.353709i
$870$		0			0
$871$	5.61615	−	4.08037i	0.190296	−	0.138258i
$872$		0			0
$873$	−3.99764	−	2.90445i	−0.135299	−	0.0983008i
$874$		0			0
$875$	−20.0024	−	11.2108i	−0.676206	−	0.378994i
$876$		0			0
$877$	22.3877	−	7.27422i	0.755980	−	0.245633i	0.0944276	−	0.995532i	$-0.469898\pi$
$877$	22.3877	−	7.27422i	0.755980	−	0.245633i	0.661552	+	0.749899i	$0.269898\pi$
$878$		0			0
$879$	−11.3760	+	35.0118i	−0.383703	+	1.18092i
$880$		0			0
$881$	−12.5134	−	38.5124i	−0.421588	−	1.29752i	−0.906224	−	0.422799i	$-0.861048\pi$
$881$	−12.5134	−	38.5124i	−0.421588	−	1.29752i	0.484635	−	0.874716i	$-0.338952\pi$
$882$		0			0
$883$	3.92305	+	12.0739i	0.132021	+	0.406319i	0.995115	−	0.0987246i	$-0.0314763\pi$
$883$	3.92305	+	12.0739i	0.132021	+	0.406319i	−0.863094	+	0.505044i	$0.831476\pi$
$884$		0			0
$885$	−2.40206	+	1.18423i	−0.0807442	+	0.0398074i
$886$		0			0
$887$	−36.4347	−	26.4713i	−1.22336	−	0.888820i	−0.226982	−	0.973899i	$-0.572886\pi$
$887$	−36.4347	−	26.4713i	−1.22336	−	0.888820i	−0.996374	+	0.0850787i	$0.972886\pi$
$888$		0			0
$889$	16.7937	+	5.45659i	0.563242	+	0.183008i
$890$		0			0
$891$	−9.83035	−	13.5303i	−0.329329	−	0.453283i
$892$		0			0
$893$		−	33.4575i		−	1.11961i
$894$		0			0
$895$	45.1218	−	6.53716i	1.50826	−	0.218513i
$896$		0			0
$897$	20.6759	−	28.4580i	0.690349	−	0.950184i
$898$		0			0
$899$		−	11.1462i		−	0.371748i
$900$		0			0
$901$	20.5242			0.683760
$902$		0			0
$903$		−	26.2190i		−	0.872515i
$904$		0			0
$905$	6.34486	−	36.9000i	0.210910	−	1.22660i
$906$		0			0
$907$	19.5539	−	26.9137i	0.649278	−	0.893655i	−0.349789	−	0.936828i	$-0.613747\pi$
$907$	19.5539	−	26.9137i	0.649278	−	0.893655i	0.999068	+	0.0431737i	$0.0137469\pi$
$908$		0			0
$909$	3.43329	−	1.11554i	0.113875	−	0.0370002i
$910$		0			0
$911$	−39.2530			−1.30051			−0.650255	−	0.759716i	$-0.725338\pi$
$911$	−39.2530			−1.30051			−0.650255	+	0.759716i	$0.725338\pi$
$912$		0			0
$913$	20.7161	−	15.0511i	0.685604	−	0.498120i
$914$		0			0
$915$	−21.7008	+	41.2351i	−0.717406	+	1.36319i
$916$		0			0
$917$	2.29700	+	1.66887i	0.0758537	+	0.0551109i
$918$		0			0
$919$	21.0216	+	28.9337i	0.693438	+	0.954436i	0.999997	+	0.00258414i	$0.000822557\pi$
$919$	21.0216	+	28.9337i	0.693438	+	0.954436i	−0.306558	+	0.951852i	$0.599177\pi$
$920$		0			0
$921$	29.5905	−	9.61455i	0.975041	−	0.316810i
$922$		0			0
$923$	−39.4741	+	12.8259i	−1.29931	+	0.422170i
$924$		0			0
$925$	14.8887	+	11.4298i	0.489537	+	0.375810i
$926$		0			0
$927$	7.97008	−	2.58964i	0.261772	−	0.0850548i
$928$		0			0
$929$			29.4494i			0.966204i	0.875564	+	0.483102i	$0.160490\pi$
$929$			29.4494i			0.966204i	−0.875564	+	0.483102i	$0.839510\pi$
$930$		0			0
$931$	8.01904	−	11.0373i	0.262813	−	0.361732i
$932$		0			0
$933$	19.4826	+	26.8156i	0.637833	+	0.877902i
$934$		0			0
$935$	−7.68993	−	15.5981i	−0.251487	−	0.510111i
$936$		0			0
$937$	−6.72068	+	20.6841i	−0.219555	+	0.675721i	0.779244	+	0.626721i	$0.215603\pi$
$937$	−6.72068	+	20.6841i	−0.219555	+	0.675721i	−0.998799	+	0.0490002i	$0.984397\pi$
$938$		0			0
$939$	−32.6773	−	23.7415i	−1.06638	−	0.774773i
$940$		0			0
$941$	−4.84531	+	14.9123i	−0.157952	+	0.486128i	−0.998448	−	0.0556907i	$-0.982264\pi$
$941$	−4.84531	+	14.9123i	−0.157952	+	0.486128i	0.840496	+	0.541818i	$0.182264\pi$
$942$		0			0
$943$	18.6293	+	18.0749i	0.606654	+	0.588599i
$944$		0			0
$945$	11.8608	−	22.5374i	0.385830	−	0.733143i
$946$		0			0
$947$	6.68770	−	9.20484i	0.217321	−	0.299117i	−0.686412	−	0.727213i	$-0.740815\pi$
$947$	6.68770	−	9.20484i	0.217321	−	0.299117i	0.903733	+	0.428096i	$0.140815\pi$
$948$		0			0
$949$	−60.6009	−	19.6904i	−1.96719	−	0.639179i
$950$		0			0
$951$	−21.9622	+	15.9565i	−0.712175	+	0.517425i
$952$		0			0
$953$	24.8527	+	34.2069i	0.805059	+	1.10807i	0.992067	+	0.125711i	$0.0401211\pi$
$953$	24.8527	+	34.2069i	0.805059	+	1.10807i	−0.187008	+	0.982358i	$0.559879\pi$
$954$		0			0
$955$	−38.2739	+	37.2764i	−1.23851	+	1.20624i
$956$		0			0
$957$	−30.2152			−0.976718
$958$		0			0
$959$	−8.83830	−	27.2015i	−0.285403	−	0.878382i
$960$		0			0
$961$	−9.00252	+	27.7069i	−0.290404	+	0.893771i
$962$		0			0
$963$	−2.43137	+	0.790001i	−0.0783499	+	0.0254574i
$964$		0			0
$965$	3.93585	+	27.1666i	0.126700	+	0.874525i
$966$		0			0
$967$	−12.0751	+	8.77306i	−0.388308	+	0.282123i	−0.764762	−	0.644313i	$-0.777143\pi$
$967$	−12.0751	+	8.77306i	−0.388308	+	0.282123i	0.376454	+	0.926435i	$0.377143\pi$
$968$		0			0
$969$	−14.8094	+	20.3834i	−0.475747	+	0.654810i
$970$		0			0
$971$	−18.5600	−	6.03050i	−0.595618	−	0.193528i	−0.00433274	−	0.999991i	$-0.501379\pi$
$971$	−18.5600	−	6.03050i	−0.595618	−	0.193528i	−0.591285	+	0.806463i	$0.701379\pi$
$972$		0			0
$973$	31.9250	−	23.1948i	1.02347	−	0.743592i
$974$		0			0
$975$	40.8950	+	14.4920i	1.30969	+	0.464117i
$976$		0			0
$977$	6.22227	+	19.1502i	0.199068	+	0.612669i	0.999905	+	0.0137862i	$0.00438844\pi$
$977$	6.22227	+	19.1502i	0.199068	+	0.612669i	−0.800837	+	0.598883i	$0.795612\pi$
$978$		0			0
$979$	10.2818	+	7.47014i	0.328607	+	0.238747i
$980$		0			0
$981$			4.04323i			0.129090i
$982$		0			0
$983$		−	13.3444i		−	0.425619i	−0.977094	−	0.212809i	$-0.931739\pi$
$983$		−	13.3444i		−	0.425619i	0.977094	−	0.212809i	$-0.0682613\pi$
$984$		0			0
$985$	6.30738	−	36.6821i	0.200970	−	1.16879i
$986$		0			0
$987$	22.0273			0.701137
$988$		0			0
$989$	−26.7455	−	19.4317i	−0.850457	−	0.617893i
$990$		0			0
$991$	13.0779	−	4.24928i	0.415434	−	0.134983i	−0.0938397	−	0.995587i	$-0.529914\pi$
$991$	13.0779	−	4.24928i	0.415434	−	0.134983i	0.509274	+	0.860605i	$0.329914\pi$
$992$		0			0
$993$		−	6.02842i		−	0.191306i
$994$		0			0
$995$	−5.89564	−	11.9586i	−0.186904	−	0.379112i
$996$		0			0
$997$	14.6047	−	44.9486i	0.462535	−	1.42354i	−0.399521	−	0.916724i	$-0.630824\pi$
$997$	14.6047	−	44.9486i	0.462535	−	1.42354i	0.862056	−	0.506812i	$-0.169176\pi$
$998$		0			0
$999$	−12.2539	+	16.8661i	−0.387697	+	0.533619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bi.a.189.15	yes	80
5.4	even	2	inner	820.2.bi.a.189.6	✓	80
41.23	even	10	inner	820.2.bi.a.269.6	yes	80
205.64	even	10	inner	820.2.bi.a.269.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bi.a.189.6	✓	80	5.4	even	2	inner
820.2.bi.a.189.15	yes	80	1.1	even	1	trivial
820.2.bi.a.269.6	yes	80	41.23	even	10	inner
820.2.bi.a.269.15	yes	80	205.64	even	10	inner

Overview	Random
Universe	Knowledge

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.56760 q^{3} +(1.56013 + 1.60188i) q^{5} +(0.633766 + 1.95053i) q^{7} -0.542630 q^{9} +(1.38893 + 1.91169i) q^{11} +(1.71055 - 5.26453i) q^{13} +(2.44565 + 2.51110i) q^{15} +(-2.66273 + 1.93459i) q^{17} +(4.64430 - 1.50902i) q^{19} +(0.993492 + 3.05766i) q^{21} +(3.85536 + 1.25268i) q^{23} +(-0.132010 + 4.99826i) q^{25} -5.55343 q^{27} +(-4.79455 + 6.59914i) q^{29} +(-1.10550 + 0.803189i) q^{31} +(2.17728 + 2.99677i) q^{33} +(-2.13575 + 4.05829i) q^{35} +(2.20655 - 3.03706i) q^{37} +(2.68146 - 8.25267i) q^{39} +(5.74848 + 2.82045i) q^{41} +(-7.75606 - 2.52010i) q^{43} +(-0.846571 - 0.869226i) q^{45} +(2.11720 - 6.51607i) q^{47} +(2.26020 - 1.64213i) q^{49} +(-4.17410 + 3.03266i) q^{51} +(-5.04491 - 3.66534i) q^{53} +(-0.895393 + 5.20737i) q^{55} +(7.28041 - 2.36555i) q^{57} +(-0.236097 + 0.726632i) q^{59} +(4.10788 + 12.6428i) q^{61} +(-0.343901 - 1.05842i) q^{63} +(11.1018 - 5.47324i) q^{65} +(1.01458 + 0.737135i) q^{67} +(6.04366 + 1.96370i) q^{69} +(-4.40729 - 6.06611i) q^{71} -11.5112i q^{73} +(-0.206940 + 7.83527i) q^{75} +(-2.84856 + 3.92071i) q^{77} -7.50717i q^{79} -7.07766 q^{81} -10.8365i q^{83} +(-7.25317 - 1.24716i) q^{85} +(-7.51594 + 10.3448i) q^{87} +(5.11512 - 1.66200i) q^{89} +11.3527 q^{91} +(-1.73297 + 1.25908i) q^{93} +(9.66297 + 5.08532i) q^{95} +(7.36715 + 5.35255i) q^{97} +(-0.753673 - 1.03734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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