LMFDB - Embedded newform 820.2.bi.a.189.6

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			189.6
Character	$\chi$	$=$	820.189
Dual form			820.2.bi.a.269.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.56760 q^{3} +(2.00558 + 0.988762i) q^{5} +(-0.633766 - 1.95053i) q^{7} -0.542630 q^{9} +(1.38893 + 1.91169i) q^{11} +(-1.71055 + 5.26453i) q^{13} +(-3.14395 - 1.54998i) q^{15} +(2.66273 - 1.93459i) q^{17} +(4.64430 - 1.50902i) q^{19} +(0.993492 + 3.05766i) q^{21} +(-3.85536 - 1.25268i) q^{23} +(3.04470 + 3.96608i) q^{25} +5.55343 q^{27} +(-4.79455 + 6.59914i) q^{29} +(-1.10550 + 0.803189i) q^{31} +(-2.17728 - 2.99677i) q^{33} +(0.657543 - 4.53859i) q^{35} +(-2.20655 + 3.03706i) q^{37} +(2.68146 - 8.25267i) q^{39} +(5.74848 + 2.82045i) q^{41} +(7.75606 + 2.52010i) q^{43} +(-1.08829 - 0.536532i) q^{45} +(-2.11720 + 6.51607i) q^{47} +(2.26020 - 1.64213i) q^{49} +(-4.17410 + 3.03266i) q^{51} +(5.04491 + 3.66534i) q^{53} +(0.895393 + 5.20737i) q^{55} +(-7.28041 + 2.36555i) q^{57} +(-0.236097 + 0.726632i) q^{59} +(4.10788 + 12.6428i) q^{61} +(0.343901 + 1.05842i) q^{63} +(-8.63600 + 8.86710i) q^{65} +(-1.01458 - 0.737135i) q^{67} +(6.04366 + 1.96370i) q^{69} +(-4.40729 - 6.06611i) q^{71} +11.5112i q^{73} +(-4.77287 - 6.21723i) q^{75} +(2.84856 - 3.92071i) q^{77} -7.50717i q^{79} -7.07766 q^{81} +10.8365i q^{83} +(7.25317 - 1.24716i) q^{85} +(7.51594 - 10.3448i) q^{87} +(5.11512 - 1.66200i) q^{89} +11.3527 q^{91} +(1.73297 - 1.25908i) q^{93} +(10.8066 + 1.56564i) q^{95} +(-7.36715 - 5.35255i) q^{97} +(-0.753673 - 1.03734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.649477\pi$
$3$	−1.56760			−0.905054			−0.452527	+	0.891751i	$0.649477\pi$
$4$		0			0
$5$	2.00558	+	0.988762i	0.896923	+	0.442188i
$5$	2.00558	+	0.988762i	0.896923	+	0.442188i
$6$		0			0
$7$	−0.633766	−	1.95053i	−0.239541	−	0.737232i	−0.996486	−	0.0837537i	$-0.973309\pi$
$7$	−0.633766	−	1.95053i	−0.239541	−	0.737232i	0.756945	−	0.653478i	$-0.226691\pi$
$8$		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	$0.378564\pi$
$13$	−1.71055	+	5.26453i	−0.474421	+	1.46012i	−0.846737	+	0.532011i	$0.821436\pi$
$14$		0			0
$15$	−3.14395	−	1.54998i	−0.811764	−	0.400204i
$16$		0			0
$17$	2.66273	−	1.93459i	0.645808	−	0.469207i	−0.216033	−	0.976386i	$-0.569312\pi$
$17$	2.66273	−	1.93459i	0.645808	−	0.469207i	0.861841	+	0.507179i	$0.169312\pi$
$18$		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	−0.121886	−	0.992544i	$-0.538894\pi$
$23$	−3.85536	−	1.25268i	−0.803897	−	0.261202i	−0.682011	+	0.731342i	$0.738894\pi$
$24$		0			0
$25$	3.04470	+	3.96608i	0.608940	+	0.793216i
$26$		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
$35$	0.657543	−	4.53859i	0.111145	−	0.767162i
$36$		0			0
$37$	−2.20655	+	3.03706i	−0.362755	+	0.499289i	−0.950914	−	0.309456i	$-0.899853\pi$
$37$	−2.20655	+	3.03706i	−0.362755	+	0.499289i	0.588159	+	0.808745i	$0.299853\pi$
$38$		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	0.833402	−	0.552668i	$-0.186390\pi$
$43$	7.75606	+	2.52010i	1.18279	+	0.384311i	0.349386	+	0.936979i	$0.386390\pi$
$44$		0			0
$45$	−1.08829	−	0.536532i	−0.162232	−	0.0799814i
$46$		0			0
$47$	−2.11720	+	6.51607i	−0.308825	+	0.950467i	0.669397	+	0.742905i	$0.266553\pi$
$47$	−2.11720	+	6.51607i	−0.308825	+	0.950467i	−0.978222	+	0.207562i	$0.933447\pi$
$48$		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	0.877636	−	0.479328i	$-0.159120\pi$
$53$	5.04491	+	3.66534i	0.692972	+	0.503474i	−0.184664	+	0.982802i	$0.559120\pi$
$54$		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
$65$	−8.63600	+	8.86710i	−1.07116	+	1.09983i
$66$		0			0
$67$	−1.01458	−	0.737135i	−0.123951	−	0.0900554i	0.524083	−	0.851667i	$-0.324408\pi$
$67$	−1.01458	−	0.737135i	−0.123951	−	0.0900554i	−0.648033	+	0.761612i	$0.724408\pi$
$68$		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	$0.235271\pi$
$73$			11.5112i			1.34728i	−0.739058	+	0.673641i	$0.764729\pi$
$74$		0			0
$75$	−4.77287	−	6.21723i	−0.551124	−	0.717904i
$76$		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	$0.202742\pi$
$83$			10.8365i			1.18946i	−0.803924	+	0.594732i	$0.797258\pi$
$84$		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
$95$	10.8066	+	1.56564i	1.10873	+	0.160631i
$96$		0			0
$97$	−7.36715	−	5.35255i	−0.748021	−	0.543469i	0.147192	−	0.989108i	$-0.452976\pi$
$97$	−7.36715	−	5.35255i	−0.748021	−	0.543469i	−0.895213	+	0.445639i	$0.852976\pi$
$98$		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	0.523093	−	0.852276i	$-0.324778\pi$
$103$	14.6879	−	4.77238i	1.44724	−	0.470236i	0.924146	+	0.382039i	$0.124778\pi$
$104$		0			0
$105$	−1.03076	+	7.11470i	−0.100592	+	0.694323i
$106$		0			0
$107$	−4.48072	+	1.45587i	−0.433167	+	0.140745i	−0.517481	−	0.855695i	$-0.673130\pi$
$107$	−4.48072	+	1.45587i	−0.433167	+	0.140745i	0.0843137	+	0.996439i	$0.473130\pi$
$108$		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	0.656691	−	0.754159i	$-0.271955\pi$
$113$	−2.80089	−	3.85509i	−0.263485	−	0.362657i	−0.920177	+	0.391503i	$0.871955\pi$
$114$		0			0
$115$	−6.49362	−	6.32438i	−0.605533	−	0.589752i
$116$		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
$125$	2.18488	+	10.9648i	0.195422	+	0.980719i
$126$		0			0
$127$	−5.06071	+	6.96546i	−0.449065	+	0.618085i	−0.972196	−	0.234167i	$-0.924764\pi$
$127$	−5.06071	+	6.96546i	−0.449065	+	0.618085i	0.523131	+	0.852252i	$0.324764\pi$
$128$		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
$135$	11.1378	+	5.49102i	0.958593	+	0.472591i
$136$		0			0
$137$	13.9457			1.19146			0.595729	−	0.803185i	$-0.296863\pi$
$137$	13.9457			1.19146			0.595729	+	0.803185i	$0.296863\pi$
$138$		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
$145$	−16.1408	+	8.49442i	−1.34042	+	0.705424i
$146$		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	$-0.783224\pi$
$157$	−6.49607	−	19.9928i	−0.518443	−	1.59560i	0.258486	−	0.966015i	$-0.416776\pi$
$158$		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	$0.183991\pi$
$163$			13.9512i			1.09274i	−0.837544	+	0.546370i	$0.816009\pi$
$164$		0			0
$165$	−1.40362	−	8.16307i	−0.109272	−	0.635494i
$166$		0			0
$167$	−12.8433			−0.993842			−0.496921	−	0.867796i	$-0.665536\pi$
$167$	−12.8433			−0.993842			−0.496921	+	0.867796i	$0.665536\pi$
$168$		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	$-0.790384\pi$
$173$		−	16.0980i		−	1.22391i	0.790894	−	0.611953i	$-0.209616\pi$
$174$		0			0
$175$	5.80634	−	8.45236i	0.438918	−	0.638938i
$176$		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
$185$	−7.42834	+	3.90931i	−0.546142	+	0.287418i
$186$		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	0.169856	−	0.985469i	$-0.445670\pi$
$193$	−9.93160	−	7.21573i	−0.714892	−	0.519400i	−0.884748	+	0.466069i	$0.845670\pi$
$194$		0			0
$195$	13.5378	−	13.9001i	0.969462	−	0.995405i
$196$		0			0
$197$	9.78396	+	13.4665i	0.697078	+	0.959446i	0.999979	+	0.00642374i	$0.00204475\pi$
$197$	9.78396	+	13.4665i	0.697078	+	0.959446i	−0.302901	+	0.953022i	$0.597955\pi$
$198$		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
$205$	8.74028	+	11.3405i	0.610448	+	0.792056i
$206$		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
$215$	13.0636	+	12.7231i	0.890931	+	0.867711i
$216$		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	0.866344	−	0.499448i	$-0.166464\pi$
$223$	19.0198	+	6.17992i	1.27366	+	0.413838i	0.407319	+	0.913286i	$0.366464\pi$
$224$		0			0
$225$	−1.65215	−	2.15211i	−0.110143	−	0.143474i
$226$		0			0
$227$	−3.34675	−	10.3003i	−0.222132	−	0.683652i	−0.998570	−	0.0534583i	$-0.982976\pi$
$227$	−3.34675	−	10.3003i	−0.222132	−	0.683652i	0.776438	−	0.630193i	$-0.217024\pi$
$228$		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	$0.209529\pi$
$233$	−3.18247	+	9.79464i	−0.208491	+	0.641668i	−0.999552	+	0.0299312i	$0.990471\pi$
$234$		0			0
$235$	−10.6891	+	10.9751i	−0.697277	+	0.715936i
$236$		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	−0.0535145	−	0.998567i	$-0.517042\pi$
$257$	14.1017	−	10.2455i	0.879642	−	0.639098i	0.933157	+	0.359470i	$0.117042\pi$
$258$		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	−0.436543	−	0.899684i	$-0.643797\pi$
$263$	4.60908	−	3.34869i	0.284208	−	0.206489i	0.720751	+	0.693194i	$0.243797\pi$
$264$		0			0
$265$	6.49383	+	12.3394i	0.398913	+	0.758001i
$266$		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
$275$	−3.35306	+	11.3291i	−0.202197	+	0.683172i
$276$		0			0
$277$	6.37942	+	8.78052i	0.383302	+	0.527571i	0.956456	−	0.291878i	$-0.0942800\pi$
$277$	6.37942	+	8.78052i	0.383302	+	0.527571i	−0.573153	+	0.819448i	$0.694280\pi$
$278$		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	$-0.557280\pi$
$283$	13.6604	−	18.8019i	0.812026	−	1.11766i	0.991008	−	0.133805i	$-0.0427197\pi$
$284$		0			0
$285$	−16.9404	−	2.45429i	−1.00346	−	0.145380i
$286$		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	$-0.659376\pi$
$293$	7.25696	−	22.3346i	0.423956	−	1.30480i	0.903990	−	0.427553i	$-0.140624\pi$
$294$		0			0
$295$	−1.19198	+	1.22387i	−0.0693996	+	0.0712567i
$296$		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
$305$	−4.26199	+	29.4178i	−0.244041	+	1.68446i
$306$		0			0
$307$	−18.8763	+	6.13329i	−1.07733	+	0.350045i	−0.793338	−	0.608781i	$-0.791659\pi$
$307$	−18.8763	+	6.13329i	−1.07733	+	0.350045i	−0.283991	+	0.958827i	$0.591659\pi$
$308$		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	0.991974	−	0.126445i	$-0.0403568\pi$
$313$	20.8454	+	15.1451i	1.17825	+	0.856051i	0.186280	+	0.982497i	$0.440357\pi$
$314$		0			0
$315$	−0.356802	+	2.46278i	−0.0201035	+	0.138762i
$316$		0			0
$317$	14.0101	−	10.1789i	0.786886	−	0.571706i	−0.120152	−	0.992756i	$-0.538338\pi$
$317$	14.0101	−	10.1789i	0.786886	−	0.571706i	0.907038	+	0.421049i	$0.138338\pi$
$318$		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
$335$	−1.30597	−	2.48156i	−0.0713527	−	0.135582i
$336$		0			0
$337$		−	7.87239i		−	0.428836i	−0.976742	−	0.214418i	$-0.931214\pi$
$337$		−	7.87239i		−	0.428836i	0.976742	−	0.214418i	$-0.0687855\pi$
$338$		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
$345$	10.1794	+	9.91410i	0.548041	+	0.533757i
$346$		0			0
$347$	9.71323	+	29.8943i	0.521434	+	1.60481i	0.771262	+	0.636518i	$0.219626\pi$
$347$	9.71323	+	29.8943i	0.521434	+	1.60481i	−0.249829	+	0.968290i	$0.580374\pi$
$348$		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	−0.965530	−	0.260292i	$-0.916181\pi$
$353$	−29.9422	+	9.72882i	−1.59366	+	0.517813i	−0.628134	+	0.778105i	$0.716181\pi$
$354$		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
$365$	−11.3818	+	23.0866i	−0.595752	+	1.20841i
$366$		0			0
$367$	−8.54981	−	2.77800i	−0.446297	−	0.145011i	0.0772422	−	0.997012i	$-0.475389\pi$
$367$	−8.54981	−	2.77800i	−0.446297	−	0.145011i	−0.523539	+	0.852002i	$0.675389\pi$
$368$		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	−0.439142	−	0.898418i	$-0.644717\pi$
$373$	10.6417	−	14.6471i	0.551007	−	0.758396i	0.990148	+	0.140022i	$0.0447173\pi$
$374$		0			0
$375$	−3.42502	−	17.1884i	−0.176867	−	0.887604i
$376$		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	$-0.743032\pi$
$383$	−27.0643			−1.38292			−0.691459	+	0.722415i	$0.743032\pi$
$384$		0			0
$385$	9.58967	−	5.04675i	0.488735	−	0.257206i
$386$		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
$395$	7.42281	−	15.0562i	0.373482	−	0.757562i
$396$		0			0
$397$	4.75458	−	14.6331i	0.238625	−	0.734413i	−0.757995	−	0.652261i	$-0.773821\pi$
$397$	4.75458	−	14.6331i	0.238625	−	0.734413i	0.996620	−	0.0821522i	$-0.0261794\pi$
$398$		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
$405$	−14.1948	−	6.99812i	−0.705346	−	0.347740i
$406$		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
$415$	−10.7148	+	21.7335i	−0.525967	+	1.06686i
$416$		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
$425$	15.7800	+	4.67037i	0.765441	+	0.226546i
$426$		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	−0.213244	−	0.976999i	$-0.568403\pi$
$433$	−19.9769	−	6.49088i	−0.960027	−	0.311932i	−0.746783	+	0.665067i	$0.768403\pi$
$434$		0			0
$435$	25.3024	−	13.3159i	1.21316	−	0.638447i
$436$		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	0.837487	−	0.546458i	$-0.184024\pi$
$443$	1.24132	+	1.70852i	0.0589767	+	0.0811744i	−0.778510	+	0.627632i	$0.784024\pi$
$444$		0			0
$445$	11.9021	+	1.72436i	0.564214	+	0.0817423i
$446$		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
$455$	22.7688	+	11.2251i	1.06742	+	0.526242i
$456$		0			0
$457$	12.7339	−	39.1909i	0.595667	−	1.83328i	0.0442908	−	0.999019i	$-0.485897\pi$
$457$	12.7339	−	39.1909i	0.595667	−	1.83328i	0.551376	−	0.834257i	$-0.314103\pi$
$458$		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	−0.160536	−	0.987030i	$-0.551322\pi$
$463$	−24.7206	−	17.9606i	−1.14887	−	0.834699i	−0.988330	+	0.152331i	$0.951322\pi$
$464$		0			0
$465$	4.72055	−	0.811686i	0.218910	−	0.0376410i
$466$		0			0
$467$	−8.00856	+	2.60214i	−0.370592	+	0.120413i	−0.488391	−	0.872625i	$-0.662416\pi$
$467$	−8.00856	+	2.60214i	−0.370592	+	0.120413i	0.117799	+	0.993037i	$0.462416\pi$
$468$		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
$475$	20.1254	+	13.8251i	0.923418	+	0.634341i
$476$		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
$485$	−9.48301	−	18.0193i	−0.430601	−	0.818215i
$486$		0			0
$487$	20.4628	−	28.1646i	0.927256	−	1.27626i	−0.0336641	−	0.999433i	$-0.510718\pi$
$487$	20.4628	−	28.1646i	0.927256	−	1.27626i	0.960920	−	0.276825i	$-0.0892824\pi$
$488$		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	−0.881303	−	0.472551i	$-0.843333\pi$
$503$	−15.7940	+	11.4750i	−0.704218	+	0.511644i	0.177085	+	0.984196i	$0.443333\pi$
$504$		0			0
$505$	−14.7223	−	2.13293i	−0.655132	−	0.0949143i
$506$		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
$515$	34.1764	+	4.95142i	1.50599	+	0.218186i
$516$		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	0.959750	−	0.280857i	$-0.0906186\pi$
$523$	9.05757	+	12.4667i	0.396060	+	0.545130i	−0.563690	+	0.825987i	$0.690619\pi$
$524$		0			0
$525$	−9.10202	+	13.2499i	−0.397245	+	0.578274i
$526$		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
$535$	−10.4260	−	1.51049i	−0.450753	−	0.0653043i
$536$		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
$545$	7.36744	−	14.9439i	0.315586	−	0.640127i
$546$		0			0
$547$	−21.5147			−0.919903			−0.459951	−	0.887944i	$-0.652133\pi$
$547$	−21.5147			−0.919903			−0.459951	+	0.887944i	$0.652133\pi$
$548$		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
$555$	11.6447	−	6.12823i	0.494288	−	0.260129i
$556$		0			0
$557$	−26.1445	+	18.9951i	−1.10778	+	0.804849i	−0.982313	−	0.187249i	$-0.940043\pi$
$557$	−26.1445	+	18.9951i	−1.10778	+	0.804849i	−0.125467	+	0.992098i	$0.540043\pi$
$558$		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	−0.641580	−	0.767056i	$-0.721721\pi$
$563$	−2.61774	+	1.90190i	−0.110325	+	0.0801555i	0.531255	+	0.847212i	$0.321721\pi$
$564$		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	$-0.472390\pi$
$577$	4.16182			0.173259			0.0866295	+	0.996241i	$0.472390\pi$
$578$		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
$585$	4.68615	−	4.81156i	0.193749	−	0.198933i
$586$		0			0
$587$	6.59927	−	20.3105i	0.272381	−	0.838302i	−0.717520	−	0.696538i	$-0.754723\pi$
$587$	6.59927	−	20.3105i	0.272381	−	0.838302i	0.989901	−	0.141764i	$-0.0452773\pi$
$588$		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	$0.106503\pi$
$593$	9.09313	+	27.9858i	0.373410	+	1.14924i	−0.571135	+	0.820856i	$0.693497\pi$
$594$		0			0
$595$	−7.02945	−	13.3571i	−0.288179	−	0.547589i
$596$		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
$605$	8.45014	−	8.67627i	0.343547	−	0.352740i
$606$		0			0
$607$	1.59160	+	2.19064i	0.0646009	+	0.0889155i	0.840095	−	0.542439i	$-0.182499\pi$
$607$	1.59160	+	2.19064i	0.0646009	+	0.0889155i	−0.775494	+	0.631355i	$0.782499\pi$
$608$		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	0.975954	−	0.217978i	$-0.0699462\pi$
$613$	40.5399	+	13.1722i	1.63739	+	0.532021i	0.661439	+	0.749999i	$0.269946\pi$
$614$		0			0
$615$	−13.7013	−	17.7774i	−0.552489	−	0.716854i
$616$		0			0
$617$	−7.73429	−	2.51302i	−0.311371	−	0.101171i	0.149163	−	0.988813i	$-0.452342\pi$
$617$	−7.73429	−	2.51302i	−0.311371	−	0.101171i	−0.460534	+	0.887642i	$0.652342\pi$
$618$		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
$625$	−6.45960	+	24.1511i	−0.258384	+	0.966042i
$626$		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
$635$	−17.0368	+	8.96596i	−0.676086	+	0.355803i
$636$		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	$0.270283\pi$
$643$	−7.98958	+	24.5894i	−0.315078	+	0.969711i	−0.975722	+	0.219012i	$0.929717\pi$
$644$		0			0
$645$	−20.4785	−	19.9448i	−0.806341	−	0.785326i
$646$		0			0
$647$		−	40.6644i		−	1.59868i	−0.600877	−	0.799341i	$-0.705182\pi$
$647$		−	40.6644i		−	1.59868i	0.600877	−	0.799341i	$-0.294818\pi$
$648$		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	$-0.352458\pi$
$653$	22.8502			0.894196			0.447098	+	0.894485i	$0.352458\pi$
$654$		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	−0.0975244	−	0.995233i	$-0.531092\pi$
$673$	21.2431	−	15.4340i	0.818862	−	0.594938i	0.916386	+	0.400295i	$0.131092\pi$
$674$		0			0
$675$	16.9085	+	22.0253i	0.650809	+	0.847756i
$676$		0			0
$677$	−3.57989	+	1.16318i	−0.137586	+	0.0447045i	−0.377001	−	0.926213i	$-0.623045\pi$
$677$	−3.57989	+	1.16318i	−0.137586	+	0.0447045i	0.239414	+	0.970917i	$0.423045\pi$
$678$		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	$-0.397907\pi$
$683$	16.4783			0.630525			0.315263	+	0.949004i	$0.397907\pi$
$684$		0			0
$685$	27.9692	+	13.7889i	1.06865	+	0.526848i
$686$		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
$695$	6.16883	−	42.5795i	0.233997	−	1.61513i
$696$		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
$705$	16.7562	−	17.2046i	0.631074	−	0.647961i
$706$		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
$715$	−28.9459	−	4.19363i	−1.08252	−	0.156833i
$716$		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
$725$	−40.7707	+	1.07681i	−1.51419	+	0.0399916i
$726$		0			0
$727$	−4.36609	+	3.17215i	−0.161929	+	0.117649i	−0.665799	−	0.746131i	$-0.731909\pi$
$727$	−4.36609	+	3.17215i	−0.161929	+	0.117649i	0.503870	+	0.863780i	$0.331909\pi$
$728$		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	−0.921541	−	0.388282i	$-0.873069\pi$
$733$	−7.24203	+	9.96780i	−0.267491	+	0.368169i	0.654050	+	0.756451i	$0.273069\pi$
$734$		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	$-0.566513\pi$
$743$	21.4529	−	29.5274i	0.787031	−	1.08326i	0.994471	−	0.105008i	$-0.0334868\pi$
$744$		0			0
$745$	17.0370	−	8.96606i	0.624188	−	0.328491i
$746$		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
$755$	−22.7335	−	22.1410i	−0.827358	−	0.805795i
$756$		0			0
$757$	−4.06859	−	12.5218i	−0.147875	−	0.455113i	0.849494	−	0.527598i	$-0.176907\pi$
$757$	−4.06859	−	12.5218i	−0.147875	−	0.455113i	−0.997370	+	0.0724845i	$0.976907\pi$
$758$		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	$-0.744854\pi$
$773$	8.04747	−	24.7676i	0.289448	−	0.890828i	0.985030	−	0.172382i	$-0.0551463\pi$
$774$		0			0
$775$	−6.55141	−	1.93901i	−0.235334	−	0.0696514i
$776$		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
$785$	6.73978	−	46.5203i	0.240553	−	1.66038i
$786$		0			0
$787$	−6.11011	−	8.40984i	−0.217802	−	0.299778i	0.686110	−	0.727498i	$-0.259317\pi$
$787$	−6.11011	−	8.40984i	−0.217802	−	0.299778i	−0.903911	+	0.427720i	$0.859317\pi$
$788$		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
$795$	−10.1797	−	19.3432i	−0.361038	−	0.686032i
$796$		0			0
$797$	−15.6376	−	5.08096i	−0.553912	−	0.179977i	0.0186681	−	0.999826i	$-0.494057\pi$
$797$	−15.6376	−	5.08096i	−0.553912	−	0.179977i	−0.572580	+	0.819849i	$0.694057\pi$
$798$		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
$805$	−8.22047	+	16.6742i	−0.289734	+	0.587688i
$806$		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
$815$	−13.7944	+	27.9802i	−0.483196	+	0.980102i
$816$		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	$-0.195201\pi$
$823$	46.9212			1.63557			0.817786	+	0.575523i	$0.195201\pi$
$824$		0			0
$825$	5.25626	−	17.7595i	0.183000	−	0.618308i
$826$		0			0
$827$	2.44323	+	7.51947i	0.0849593	+	0.261478i	0.984507	−	0.175344i	$-0.0561039\pi$
$827$	2.44323	+	7.51947i	0.0849593	+	0.261478i	−0.899548	+	0.436822i	$0.856104\pi$
$828$		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
$835$	−25.7582	−	12.6989i	−0.891399	−	0.439465i
$836$		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
$845$	−18.3710	−	34.9080i	−0.631982	−	1.20087i
$846$		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	0.462606	−	0.886564i	$-0.346914\pi$
$853$	−15.2900	−	21.0449i	−0.523519	−	0.720562i	−0.986126	+	0.166001i	$0.946914\pi$
$854$		0			0
$855$	−5.86397	−	0.849562i	−0.200544	−	0.0290544i
$856$		0			0
$857$	31.5997	−	43.4933i	1.07943	−	1.48570i	0.219275	−	0.975663i	$-0.429631\pi$
$857$	31.5997	−	43.4933i	1.07943	−	1.48570i	0.860151	−	0.510040i	$-0.170369\pi$
$858$		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	0.695830	−	0.718207i	$-0.255037\pi$
$863$	24.5772	+	7.98561i	0.836617	+	0.271833i	0.140787	+	0.990040i	$0.455037\pi$
$864$		0			0
$865$	15.9171	−	32.2858i	0.541196	−	1.09775i
$866$		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	−0.661552	−	0.749899i	$-0.730102\pi$
$877$	−22.3877	+	7.27422i	−0.755980	+	0.245633i	−0.0944276	+	0.995532i	$0.530102\pi$
$878$		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	0.863094	−	0.505044i	$-0.168524\pi$
$883$	−3.92305	−	12.0739i	−0.132021	−	0.406319i	−0.995115	+	0.0987246i	$0.968524\pi$
$884$		0			0
$885$	1.86854	−	1.91855i	0.0628104	−	0.0644912i
$886$		0			0
$887$	36.4347	+	26.4713i	1.22336	+	0.888820i	0.996374	−	0.0850787i	$-0.0271142\pi$
$887$	36.4347	+	26.4713i	1.22336	+	0.888820i	0.226982	+	0.973899i	$0.427114\pi$
$888$		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
$895$	40.3467	−	21.2333i	1.34864	−	0.709749i
$896$		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	−0.999068	−	0.0431737i	$-0.986253\pi$
$907$	−19.5539	+	26.9137i	−0.649278	+	0.893655i	0.349789	+	0.936828i	$0.386253\pi$
$908$		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
$915$	6.68110	−	46.1153i	0.220870	−	1.52453i
$916$		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
$925$	−18.7635	+	0.495568i	−0.616940	+	0.0162942i
$926$		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
$935$	12.4583	+	12.1336i	0.407430	+	0.396812i
$936$		0			0
$937$	6.72068	−	20.6841i	0.219555	−	0.675721i	−0.779244	−	0.626721i	$-0.784397\pi$
$937$	6.72068	−	20.6841i	0.219555	−	0.675721i	0.998799	−	0.0490002i	$-0.0156035\pi$
$938$		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
$945$	3.65162	−	25.2047i	0.118787	−	0.819910i
$946$		0			0
$947$	−6.68770	+	9.20484i	−0.217321	+	0.299117i	−0.903733	−	0.428096i	$-0.859185\pi$
$947$	−6.68770	+	9.20484i	−0.217321	+	0.299117i	0.686412	+	0.727213i	$0.259185\pi$
$948$		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	$-0.959879\pi$
$953$	−24.8527	−	34.2069i	−0.805059	−	1.10807i	0.187008	−	0.982358i	$-0.440121\pi$
$954$		0			0
$955$	−23.6247	+	47.9197i	−0.764476	+	1.55064i
$956$		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
$965$	−12.7840	−	24.2917i	−0.411531	−	0.781978i
$966$		0			0
$967$	12.0751	−	8.77306i	0.388308	−	0.282123i	−0.376454	−	0.926435i	$-0.622857\pi$
$967$	12.0751	−	8.77306i	0.388308	−	0.282123i	0.764762	+	0.644313i	$0.222857\pi$
$968$		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	$-0.995612\pi$
$977$	−6.22227	−	19.1502i	−0.199068	−	0.612669i	0.800837	−	0.598883i	$-0.204388\pi$
$978$		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	$0.0682613\pi$
$983$			13.3444i			0.425619i	−0.977094	+	0.212809i	$0.931739\pi$
$984$		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
$995$	−9.55142	−	9.30249i	−0.302800	−	0.294909i
$996$		0			0
$997$	−14.6047	+	44.9486i	−0.462535	+	1.42354i	0.399521	+	0.916724i	$0.369176\pi$
$997$	−14.6047	+	44.9486i	−0.462535	+	1.42354i	−0.862056	+	0.506812i	$0.830824\pi$
$998$		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.189.6	✓	80
5.4	even	2	inner	820.2.bi.a.189.15	yes	80
41.23	even	10	inner	820.2.bi.a.269.15	yes	80
205.64	even	10	inner	820.2.bi.a.269.6	yes	80

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

\(f(q)\)	\(=\)	\(q-1.56760 q^{3} +(2.00558 + 0.988762i) q^{5} +(-0.633766 - 1.95053i) q^{7} -0.542630 q^{9} +(1.38893 + 1.91169i) q^{11} +(-1.71055 + 5.26453i) q^{13} +(-3.14395 - 1.54998i) q^{15} +(2.66273 - 1.93459i) q^{17} +(4.64430 - 1.50902i) q^{19} +(0.993492 + 3.05766i) q^{21} +(-3.85536 - 1.25268i) q^{23} +(3.04470 + 3.96608i) q^{25} +5.55343 q^{27} +(-4.79455 + 6.59914i) q^{29} +(-1.10550 + 0.803189i) q^{31} +(-2.17728 - 2.99677i) q^{33} +(0.657543 - 4.53859i) q^{35} +(-2.20655 + 3.03706i) q^{37} +(2.68146 - 8.25267i) q^{39} +(5.74848 + 2.82045i) q^{41} +(7.75606 + 2.52010i) q^{43} +(-1.08829 - 0.536532i) q^{45} +(-2.11720 + 6.51607i) q^{47} +(2.26020 - 1.64213i) q^{49} +(-4.17410 + 3.03266i) q^{51} +(5.04491 + 3.66534i) q^{53} +(0.895393 + 5.20737i) q^{55} +(-7.28041 + 2.36555i) q^{57} +(-0.236097 + 0.726632i) q^{59} +(4.10788 + 12.6428i) q^{61} +(0.343901 + 1.05842i) q^{63} +(-8.63600 + 8.86710i) q^{65} +(-1.01458 - 0.737135i) q^{67} +(6.04366 + 1.96370i) q^{69} +(-4.40729 - 6.06611i) q^{71} +11.5112i q^{73} +(-4.77287 - 6.21723i) q^{75} +(2.84856 - 3.92071i) q^{77} -7.50717i q^{79} -7.07766 q^{81} +10.8365i q^{83} +(7.25317 - 1.24716i) q^{85} +(7.51594 - 10.3448i) q^{87} +(5.11512 - 1.66200i) q^{89} +11.3527 q^{91} +(1.73297 - 1.25908i) q^{93} +(10.8066 + 1.56564i) q^{95} +(-7.36715 - 5.35255i) q^{97} +(-0.753673 - 1.03734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 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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