LMFDB - Embedded newform 1040.2.df.c.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(49,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$-1.17644i$ of defining polynomial
Character	$\chi$	$=$	1040.49
Dual form			1040.2.df.c.849.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01883 - 0.588222i) q^{3} +(0.235468 + 2.22364i) q^{5} +(1.04346 - 1.80732i) q^{7} +(-0.807991 + 1.39948i) q^{9} +(-2.59135 + 1.49612i) q^{11} +(1.51883 + 3.27004i) q^{13} +(1.54789 + 2.12700i) q^{15} +(1.09135 + 0.630092i) q^{17} +(3.37028 + 1.94583i) q^{19} -2.45514i q^{21} +(-0.778928 + 0.449714i) q^{23} +(-4.88911 + 1.04719i) q^{25} +5.43044i q^{27} +(-0.235468 - 0.407843i) q^{29} +0.277015i q^{31} +(-1.76010 + 3.04858i) q^{33} +(4.26453 + 1.89470i) q^{35} +(3.51883 + 6.09479i) q^{37} +(3.47094 + 2.43820i) q^{39} +(9.66804 - 5.58184i) q^{41} +(6.74056 + 3.89166i) q^{43} +(-3.30219 - 1.46714i) q^{45} -11.3189 q^{47} +(1.32239 + 2.29044i) q^{49} +1.48254 q^{51} -12.0148i q^{53} +(-3.93700 - 5.40993i) q^{55} +4.57832 q^{57} +(-10.7029 - 6.17932i) q^{59} +(-3.82102 + 6.61820i) q^{61} +(1.68621 + 2.92060i) q^{63} +(-6.91374 + 4.14731i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-0.529063 + 0.916364i) q^{69} +(-4.07532 - 2.35289i) q^{71} +15.2984 q^{73} +(-4.36519 + 3.94279i) q^{75} +6.24455i q^{77} +1.63645 q^{79} +(0.770331 + 1.33425i) q^{81} +11.1943 q^{83} +(-1.14412 + 2.57514i) q^{85} +(-0.479805 - 0.277015i) q^{87} +(-5.98533 + 3.45563i) q^{89} +(7.49486 + 0.667134i) q^{91} +(0.162946 + 0.282231i) q^{93} +(-3.53323 + 7.95245i) q^{95} +(-1.28916 + 2.23289i) q^{97} -4.83540i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} - 5 q^{7} + 8 q^{9} + 3 q^{11} + 4 q^{13} + 2 q^{15} - 15 q^{17} - 9 q^{19} + 6 q^{23} + 5 q^{25} - 3 q^{29} - 10 q^{33} + 33 q^{35} + 20 q^{37} + 30 q^{39} + 21 q^{41} - 18 q^{43} - 9 q^{45}+ \cdots - 4 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 - 5 * q^7 + 8 * q^9 + 3 * q^11 + 4 * q^13 + 2 * q^15 - 15 * q^17 - 9 * q^19 + 6 * q^23 + 5 * q^25 - 3 * q^29 - 10 * q^33 + 33 * q^35 + 20 * q^37 + 30 * q^39 + 21 * q^41 - 18 * q^43 - 9 * q^45 - 6 * q^47 - 15 * q^49 + 20 * q^51 + 23 * q^55 + 24 * q^57 - 30 * q^59 - 5 * q^61 + 25 * q^63 - 6 * q^65 + 16 * q^67 - 2 * q^69 + 26 * q^73 - 72 * q^75 - 4 * q^79 + 8 * q^81 + 48 * q^83 - 34 * q^85 - 12 * q^87 - 39 * q^89 - 19 * q^91 + 18 * q^93 - 9 * q^95 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.01883	−	0.588222i	0.588222	−	0.339610i	−0.176172	−	0.984359i	$-0.556372\pi$
$3$	1.01883	−	0.588222i	0.588222	−	0.339610i	0.764394	+	0.644749i	$0.223038\pi$
$4$		0			0
$5$	0.235468	+	2.22364i	0.105305	+	0.994440i
$5$	0.235468	+	2.22364i	0.105305	+	0.994440i
$6$		0			0
$7$	1.04346	−	1.80732i	0.394390	−	0.683104i	−0.598633	−	0.801024i	$-0.704289\pi$
$7$	1.04346	−	1.80732i	0.394390	−	0.683104i	0.993023	+	0.117919i	$0.0376224\pi$
$8$		0			0
$9$	−0.807991	+	1.39948i	−0.269330	+	0.466494i
$10$		0			0
$11$	−2.59135	+	1.49612i	−0.781322	+	0.451096i	−0.836899	−	0.547358i	$-0.815634\pi$
$11$	−2.59135	+	1.49612i	−0.781322	+	0.451096i	0.0555766	+	0.998454i	$0.482300\pi$
$12$		0			0
$13$	1.51883	+	3.27004i	0.421248	+	0.906946i
$13$	1.51883	+	3.27004i	0.421248	+	0.906946i
$14$		0			0
$15$	1.54789	+	2.12700i	0.399664	+	0.549189i
$16$		0			0
$17$	1.09135	+	0.630092i	0.264692	+	0.152820i	0.626473	−	0.779443i	$-0.284498\pi$
$17$	1.09135	+	0.630092i	0.264692	+	0.152820i	−0.361781	+	0.932263i	$0.617831\pi$
$18$		0			0
$19$	3.37028	+	1.94583i	0.773195	+	0.446404i	0.834013	−	0.551744i	$-0.186038\pi$
$19$	3.37028	+	1.94583i	0.773195	+	0.446404i	−0.0608181	+	0.998149i	$0.519371\pi$
$20$		0			0
$21$		−	2.45514i		−	0.535756i
$22$		0			0
$23$	−0.778928	+	0.449714i	−0.162418	+	0.0937719i	−0.579006	−	0.815324i	$-0.696559\pi$
$23$	−0.778928	+	0.449714i	−0.162418	+	0.0937719i	0.416588	+	0.909095i	$0.363226\pi$
$24$		0			0
$25$	−4.88911	+	1.04719i	−0.977822	+	0.209438i
$26$		0			0
$27$			5.43044i			1.04509i
$28$		0			0
$29$	−0.235468	−	0.407843i	−0.0437254	−	0.0757346i	0.843334	−	0.537389i	$-0.180589\pi$
$29$	−0.235468	−	0.407843i	−0.0437254	−	0.0757346i	−0.887060	+	0.461654i	$0.847256\pi$
$30$		0			0
$31$			0.277015i			0.0497534i	0.999691	+	0.0248767i	$0.00791932\pi$
$31$			0.277015i			0.0497534i	−0.999691	+	0.0248767i	$0.992081\pi$
$32$		0			0
$33$	−1.76010	+	3.04858i	−0.306394	+	0.530689i
$34$		0			0
$35$	4.26453	+	1.89470i	0.720837	+	0.320264i
$36$		0			0
$37$	3.51883	+	6.09479i	0.578492	+	1.00198i	0.995653	+	0.0931448i	$0.0296920\pi$
$37$	3.51883	+	6.09479i	0.578492	+	1.00198i	−0.417161	+	0.908833i	$0.636975\pi$
$38$		0			0
$39$	3.47094	+	2.43820i	0.555795	+	0.390425i
$40$		0			0
$41$	9.66804	−	5.58184i	1.50989	−	0.871738i	0.509960	−	0.860198i	$-0.329660\pi$
$41$	9.66804	−	5.58184i	1.50989	−	0.871738i	0.999933	−	0.0115395i	$-0.00367323\pi$
$42$		0			0
$43$	6.74056	+	3.89166i	1.02793	+	0.593473i	0.916390	−	0.400287i	$-0.131090\pi$
$43$	6.74056	+	3.89166i	1.02793	+	0.593473i	0.111536	+	0.993760i	$0.464423\pi$
$44$		0			0
$45$	−3.30219	−	1.46714i	−0.492262	−	0.218709i
$46$		0			0
$47$	−11.3189			−1.65103			−0.825514	−	0.564381i	$-0.809115\pi$
$47$	−11.3189			−1.65103			−0.825514	+	0.564381i	$0.809115\pi$
$48$		0			0
$49$	1.32239	+	2.29044i	0.188912	+	0.327206i
$50$		0			0
$51$	1.48254			0.207597
$52$		0			0
$53$		−	12.0148i		−	1.65036i	−0.564868	−	0.825181i	$-0.691073\pi$
$53$		−	12.0148i		−	1.65036i	0.564868	−	0.825181i	$-0.308927\pi$
$54$		0			0
$55$	−3.93700	−	5.40993i	−0.530865	−	0.729475i
$56$		0			0
$57$	4.57832			0.606413
$58$		0			0
$59$	−10.7029	−	6.17932i	−1.39340	−	0.804479i	−0.399709	−	0.916642i	$-0.630889\pi$
$59$	−10.7029	−	6.17932i	−1.39340	−	0.804479i	−0.993690	+	0.112163i	$0.964222\pi$
$60$		0			0
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	−0.999923	−	0.0123900i	$-0.996056\pi$
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	0.510692	+	0.859764i	$0.329389\pi$
$62$		0			0
$63$	1.68621	+	2.92060i	0.212442	+	0.367961i
$64$		0			0
$65$	−6.91374	+	4.14731i	−0.857544	+	0.514411i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$	−0.529063	+	0.916364i	−0.0636917	+	0.110317i
$70$		0			0
$71$	−4.07532	−	2.35289i	−0.483651	−	0.279236i	0.238286	−	0.971195i	$-0.423415\pi$
$71$	−4.07532	−	2.35289i	−0.483651	−	0.279236i	−0.721937	+	0.691959i	$0.756748\pi$
$72$		0			0
$73$	15.2984			1.79054			0.895272	−	0.445520i	$-0.146981\pi$
$73$	15.2984			1.79054			0.895272	+	0.445520i	$0.146981\pi$
$74$		0			0
$75$	−4.36519	+	3.94279i	−0.504049	+	0.455274i
$76$		0			0
$77$			6.24455i			0.711633i
$78$		0			0
$79$	1.63645			0.184115			0.0920574	−	0.995754i	$-0.470656\pi$
$79$	1.63645			0.184115			0.0920574	+	0.995754i	$0.470656\pi$
$80$		0			0
$81$	0.770331	+	1.33425i	0.0855923	+	0.148250i
$82$		0			0
$83$	11.1943			1.22873			0.614367	−	0.789020i	$-0.289411\pi$
$83$	11.1943			1.22873			0.614367	+	0.789020i	$0.289411\pi$
$84$		0			0
$85$	−1.14412	+	2.57514i	−0.124097	+	0.279313i
$86$		0			0
$87$	−0.479805	−	0.277015i	−0.0514405	−	0.0296992i
$88$		0			0
$89$	−5.98533	+	3.45563i	−0.634444	+	0.366296i	−0.782471	−	0.622687i	$-0.786041\pi$
$89$	−5.98533	+	3.45563i	−0.634444	+	0.366296i	0.148027	+	0.988983i	$0.452708\pi$
$90$		0			0
$91$	7.49486	+	0.667134i	0.785674	+	0.0699347i
$92$		0			0
$93$	0.162946	+	0.282231i	0.0168968	+	0.0292660i
$94$		0			0
$95$	−3.53323	+	7.95245i	−0.362501	+	0.815905i
$96$		0			0
$97$	−1.28916	+	2.23289i	−0.130894	+	0.226716i	−0.924022	−	0.382340i	$-0.875118\pi$
$97$	−1.28916	+	2.23289i	−0.130894	+	0.226716i	0.793127	+	0.609056i	$0.208452\pi$
$98$		0			0
$99$		−	4.83540i		−	0.485976i
$100$		0			0
$101$	−0.783361	−	1.35682i	−0.0779474	−	0.135009i	0.824417	−	0.565983i	$-0.191503\pi$
$101$	−0.783361	−	1.35682i	−0.0779474	−	0.135009i	−0.902364	+	0.430974i	$0.858170\pi$
$102$		0			0
$103$		−	0.916364i		−	0.0902920i	−0.998980	−	0.0451460i	$-0.985625\pi$
$103$		−	0.916364i		−	0.0902920i	0.998980	−	0.0451460i	$-0.0143753\pi$
$104$		0			0
$105$	5.45934	−	0.578108i	0.532777	−	0.0564176i
$106$		0			0
$107$	10.1345	−	5.85118i	0.979743	−	0.565655i	0.0775504	−	0.996988i	$-0.475290\pi$
$107$	10.1345	−	5.85118i	0.979743	−	0.565655i	0.902193	+	0.431334i	$0.141957\pi$
$108$		0			0
$109$		−	15.9902i		−	1.53159i	−0.643087	−	0.765793i	$-0.722347\pi$
$109$		−	15.9902i		−	1.53159i	0.643087	−	0.765793i	$-0.277653\pi$
$110$		0			0
$111$	7.17018	+	4.13970i	0.680563	+	0.392923i
$112$		0			0
$113$	−2.40930	−	1.39101i	−0.226648	−	0.130855i	0.382377	−	0.924007i	$-0.375106\pi$
$113$	−2.40930	−	1.39101i	−0.226648	−	0.130855i	−0.609025	+	0.793151i	$0.708439\pi$
$114$		0			0
$115$	−1.18341	−	1.62616i	−0.110354	−	0.151640i
$116$		0			0
$117$	−5.80356	−	0.516588i	−0.536539	−	0.0477586i
$118$		0			0
$119$	2.27756	−	1.31495i	0.208784	−	0.120541i
$120$		0			0
$121$	−1.02326	+	1.77234i	−0.0930240	+	0.161122i
$122$		0			0
$123$	6.56672	−	11.3739i	0.592101	−	1.02555i
$124$		0			0
$125$	−3.47980	−	10.6250i	−0.311243	−	0.950330i
$126$		0			0
$127$	−7.53415	+	4.34985i	−0.668548	+	0.385986i	−0.795526	−	0.605919i	$-0.792805\pi$
$127$	−7.53415	+	4.34985i	−0.668548	+	0.385986i	0.126978	+	0.991906i	$0.459472\pi$
$128$		0			0
$129$	9.15664			0.806197
$130$		0			0
$131$	15.8740			1.38692			0.693459	−	0.720496i	$-0.256086\pi$
$131$	15.8740			1.38692			0.693459	+	0.720496i	$0.256086\pi$
$132$		0			0
$133$	7.03350	−	4.06079i	0.609882	−	0.352115i
$134$		0			0
$135$	−12.0753	+	1.27870i	−1.03928	+	0.110053i
$136$		0			0
$137$	3.61155	−	6.25538i	0.308555	−	0.534433i	−0.669491	−	0.742820i	$-0.733488\pi$
$137$	3.61155	−	6.25538i	0.308555	−	0.534433i	0.978047	+	0.208386i	$0.0668212\pi$
$138$		0			0
$139$	−9.93700	+	17.2114i	−0.842846	+	1.45985i	0.0446337	+	0.999003i	$0.485788\pi$
$139$	−9.93700	+	17.2114i	−0.842846	+	1.45985i	−0.887479	+	0.460848i	$0.847545\pi$
$140$		0			0
$141$	−11.5320	+	6.65801i	−0.971171	+	0.560706i
$142$		0			0
$143$	−8.82819	−	6.20147i	−0.738250	−	0.518593i
$144$		0			0
$145$	0.851450	−	0.619630i	0.0707090	−	0.0514575i
$146$		0			0
$147$	2.69457	+	1.55571i	0.222245	+	0.128313i
$148$		0			0
$149$	−0.851450	−	0.491585i	−0.0697535	−	0.0402722i	0.464718	−	0.885459i	$-0.346156\pi$
$149$	−0.851450	−	0.491585i	−0.0697535	−	0.0402722i	−0.534471	+	0.845187i	$0.679489\pi$
$150$		0			0
$151$		−	8.06034i		−	0.655941i	−0.944688	−	0.327971i	$-0.893635\pi$
$151$		−	8.06034i		−	0.655941i	0.944688	−	0.327971i	$-0.106365\pi$
$152$		0			0
$153$	−1.76360	+	1.01822i	−0.142579	+	0.0823180i
$154$		0			0
$155$	−0.615981	+	0.0652284i	−0.0494768	+	0.00523927i
$156$		0			0
$157$			2.73373i			0.218176i	0.994032	+	0.109088i	$0.0347930\pi$
$157$			2.73373i			0.218176i	−0.994032	+	0.109088i	$0.965207\pi$
$158$		0			0
$159$	−7.06738	−	12.2411i	−0.560480	−	0.970779i
$160$		0			0
$161$			1.87703i			0.147931i
$162$		0			0
$163$	12.2885	−	21.2842i	0.962506	−	1.66711i	0.246334	−	0.969185i	$-0.420774\pi$
$163$	12.2885	−	21.2842i	0.962506	−	1.66711i	0.716172	−	0.697924i	$-0.245893\pi$
$164$		0			0
$165$	−7.19338	−	3.19597i	−0.560003	−	0.248806i
$166$		0			0
$167$	−6.91817	−	11.9826i	−0.535344	−	0.927243i	−0.999147	−	0.0413047i	$-0.986849\pi$
$167$	−6.91817	−	11.9826i	−0.535344	−	0.927243i	0.463802	−	0.885939i	$-0.346485\pi$
$168$		0			0
$169$	−8.38631	+	9.93327i	−0.645101	+	0.764097i
$170$		0			0
$171$	−5.44631	+	3.14443i	−0.416490	+	0.240460i
$172$		0			0
$173$	11.4079	+	6.58638i	0.867330	+	0.500753i	0.866460	−	0.499247i	$-0.166390\pi$
$173$	11.4079	+	6.58638i	0.867330	+	0.500753i	0.000869643		1.00000i	$0.499723\pi$
$174$		0			0
$175$	−3.20897	+	9.92891i	−0.242575	+	0.750555i
$176$		0			0
$177$	−14.5392			−1.09284
$178$		0			0
$179$	1.55786	+	2.69828i	0.116440	+	0.201679i	0.918354	−	0.395759i	$-0.129519\pi$
$179$	1.55786	+	2.69828i	0.116440	+	0.201679i	−0.801915	+	0.597438i	$0.796185\pi$
$180$		0			0
$181$	7.91439			0.588272			0.294136	−	0.955764i	$-0.404968\pi$
$181$	7.91439			0.588272			0.294136	+	0.955764i	$0.404968\pi$
$182$		0			0
$183$			8.99043i			0.664592i
$184$		0			0
$185$	−12.7240	+	9.25973i	−0.935489	+	0.680789i
$186$		0			0
$187$	−3.77077			−0.275746
$188$		0			0
$189$	9.81457	+	5.66644i	0.713905	+	0.412173i
$190$		0			0
$191$	6.98046	−	12.0905i	0.505088	−	0.874839i	−0.494894	−	0.868953i	$-0.664793\pi$
$191$	6.98046	−	12.0905i	0.505088	−	0.874839i	0.999983	−	0.00588562i	$-0.00187346\pi$
$192$		0			0
$193$	−6.81379	−	11.8018i	−0.490467	−	0.849514i	0.509472	−	0.860487i	$-0.329841\pi$
$193$	−6.81379	−	11.8018i	−0.490467	−	0.849514i	−0.999940	+	0.0109726i	$0.996507\pi$
$194$		0			0
$195$	−4.60438	+	8.29222i	−0.329727	+	0.593818i
$196$		0			0
$197$	−8.86097	−	15.3477i	−0.631318	−	1.09348i	−0.987282	−	0.158976i	$-0.949181\pi$
$197$	−8.86097	−	15.3477i	−0.631318	−	1.09348i	0.355964	−	0.934500i	$-0.384152\pi$
$198$		0			0
$199$	−7.18270	+	12.4408i	−0.509168	+	0.881905i	0.490775	+	0.871286i	$0.336714\pi$
$199$	−7.18270	+	12.4408i	−0.509168	+	0.881905i	−0.999944	+	0.0106193i	$0.996620\pi$
$200$		0			0
$201$	4.07532	+	2.35289i	0.287451	+	0.165960i
$202$		0			0
$203$	−0.982807			−0.0689795
$204$		0			0
$205$	14.6885	+	20.1838i	1.02589	+	1.40970i
$206$		0			0
$207$		−	1.45346i		−	0.101022i
$208$		0			0
$209$	−11.6448			−0.805486
$210$		0			0
$211$	−10.1115	−	17.5137i	−0.696108	−	1.20569i	−0.969806	−	0.243878i	$-0.921580\pi$
$211$	−10.1115	−	17.5137i	−0.696108	−	1.20569i	0.273698	−	0.961816i	$-0.411753\pi$
$212$		0			0
$213$	−5.53608			−0.379326
$214$		0			0
$215$	−7.06645	+	15.9049i	−0.481928	+	1.08471i
$216$		0			0
$217$	0.500656	+	0.289054i	0.0339868	+	0.0196223i
$218$		0			0
$219$	15.5865	−	8.99886i	1.05324	−	0.608086i
$220$		0			0
$221$	−0.402849	+	4.52577i	−0.0270985	+	0.304436i
$222$		0			0
$223$	−5.57252	−	9.65189i	−0.373164	−	0.646338i	0.616887	−	0.787052i	$-0.288394\pi$
$223$	−5.57252	−	9.65189i	−0.373164	−	0.646338i	−0.990050	+	0.140714i	$0.955060\pi$
$224$		0			0
$225$	2.48483	−	7.68834i	0.165655	−	0.512556i
$226$		0			0
$227$	−8.65364	+	14.9885i	−0.574362	+	0.994825i	0.421748	+	0.906713i	$0.361417\pi$
$227$	−8.65364	+	14.9885i	−0.574362	+	0.994825i	−0.996111	+	0.0881117i	$0.971917\pi$
$228$		0			0
$229$		−	9.90350i		−	0.654442i	−0.944948	−	0.327221i	$-0.893888\pi$
$229$		−	9.90350i		−	0.654442i	0.944948	−	0.327221i	$-0.106112\pi$
$230$		0			0
$231$	3.67318	+	6.36213i	0.241677	+	0.418598i
$232$		0			0
$233$		−	19.1742i		−	1.25614i	−0.778156	−	0.628070i	$-0.783845\pi$
$233$		−	19.1742i		−	1.25614i	0.778156	−	0.628070i	$-0.216155\pi$
$234$		0			0
$235$	−2.66524	−	25.1691i	−0.173861	−	1.64185i
$236$		0			0
$237$	1.66726	−	0.962594i	0.108300	−	0.0625272i
$238$		0			0
$239$			2.16448i			0.140009i	0.997547	+	0.0700043i	$0.0223013\pi$
$239$			2.16448i			0.140009i	−0.997547	+	0.0700043i	$0.977699\pi$
$240$		0			0
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.0215996	−	0.999767i	$-0.506876\pi$
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.876623	+	0.481178i	$0.840209\pi$
$242$		0			0
$243$	−12.5390	−	7.23941i	−0.804379	−	0.464408i
$244$		0			0
$245$	−4.78172	+	3.47983i	−0.305493	+	0.222318i
$246$		0			0
$247$	−1.24407	+	13.9763i	−0.0791580	+	0.889293i
$248$		0			0
$249$	11.4051	−	6.58473i	0.722768	−	0.417290i
$250$		0			0
$251$	−9.04439	+	15.6653i	−0.570877	+	0.988787i	0.425600	+	0.904912i	$0.360063\pi$
$251$	−9.04439	+	15.6653i	−0.570877	+	0.988787i	−0.996476	+	0.0838757i	$0.973270\pi$
$252$		0			0
$253$	1.34565	−	2.33073i	0.0846003	−	0.146532i
$254$		0			0
$255$	0.349090	+	3.29662i	0.0218609	+	0.206442i
$256$		0			0
$257$	−8.69939	+	5.02260i	−0.542653	+	0.313301i	−0.746154	−	0.665774i	$-0.768102\pi$
$257$	−8.69939	+	5.02260i	−0.542653	+	0.313301i	0.203500	+	0.979075i	$0.434768\pi$
$258$		0			0
$259$	14.6870			0.912607
$260$		0			0
$261$	0.761025			0.0471063
$262$		0			0
$263$	−13.6855	+	7.90133i	−0.843884	+	0.487217i	−0.858583	−	0.512675i	$-0.828654\pi$
$263$	−13.6855	+	7.90133i	−0.843884	+	0.487217i	0.0146985	+	0.999892i	$0.495321\pi$
$264$		0			0
$265$	26.7166	−	2.82911i	1.64119	−	0.173791i
$266$		0			0
$267$	−4.06536	+	7.04141i	−0.248796	+	0.430927i
$268$		0			0
$269$	−3.69294	+	6.39635i	−0.225162	+	0.389993i	−0.956368	−	0.292164i	$-0.905625\pi$
$269$	−3.69294	+	6.39635i	−0.225162	+	0.389993i	0.731206	+	0.682157i	$0.238958\pi$
$270$		0			0
$271$	−26.8493	+	15.5014i	−1.63098	+	0.941645i	−0.647184	+	0.762334i	$0.724053\pi$
$271$	−26.8493	+	15.5014i	−1.63098	+	0.941645i	−0.983793	+	0.179310i	$0.942613\pi$
$272$		0			0
$273$	8.02841	−	3.72894i	0.485901	−	0.225686i
$274$		0			0
$275$	11.1027	−	10.0283i	0.669517	−	0.604731i
$276$		0			0
$277$	−4.07668	−	2.35368i	−0.244944	−	0.141419i	0.372503	−	0.928031i	$-0.378500\pi$
$277$	−4.07668	−	2.35368i	−0.244944	−	0.141419i	−0.617447	+	0.786612i	$0.711833\pi$
$278$		0			0
$279$	−0.387678	−	0.223826i	−0.0232097	−	0.0134001i
$280$		0			0
$281$		−	10.7771i		−	0.642910i	−0.946925	−	0.321455i	$-0.895828\pi$
$281$		−	10.7771i		−	0.642910i	0.946925	−	0.321455i	$-0.104172\pi$
$282$		0			0
$283$	25.2204	−	14.5610i	1.49919	−	0.865561i	0.499195	−	0.866489i	$-0.333629\pi$
$283$	25.2204	−	14.5610i	1.49919	−	0.865561i	1.00000		0.000928800i	$0.000295646\pi$
$284$		0			0
$285$	1.07805	+	10.1805i	0.0638582	+	0.603042i
$286$		0			0
$287$		−	23.2977i		−	1.37522i
$288$		0			0
$289$	−7.70597	−	13.3471i	−0.453292	−	0.785125i
$290$		0			0
$291$			3.03325i			0.177812i
$292$		0			0
$293$	12.7124	−	22.0186i	0.742668	−	1.28634i	−0.208609	−	0.977999i	$-0.566894\pi$
$293$	12.7124	−	22.0186i	0.742668	−	1.28634i	0.951277	−	0.308339i	$-0.0997731\pi$
$294$		0			0
$295$	11.2204	−	25.2544i	0.653275	−	1.47037i
$296$		0			0
$297$	−8.12458	−	14.0722i	−0.471436	−	0.816551i
$298$		0			0
$299$	−2.65364	−	1.86408i	−0.153464	−	0.107803i
$300$		0			0
$301$	14.0670	−	8.12158i	0.810808	−	0.468120i
$302$		0			0
$303$	−1.59622	−	0.921580i	−0.0917007	−	0.0529434i
$304$		0			0
$305$	−15.6162	−	6.93818i	−0.894181	−	0.397279i
$306$		0			0
$307$	25.3305			1.44569			0.722843	−	0.691012i	$-0.242835\pi$
$307$	25.3305			1.44569			0.722843	+	0.691012i	$0.242835\pi$
$308$		0			0
$309$	−0.539025	−	0.933619i	−0.0306641	−	0.0531117i
$310$		0			0
$311$	24.3495			1.38074			0.690368	−	0.723459i	$-0.257449\pi$
$311$	24.3495			1.38074			0.690368	+	0.723459i	$0.257449\pi$
$312$		0			0
$313$		−	15.6891i		−	0.886802i	−0.896323	−	0.443401i	$-0.853772\pi$
$313$		−	15.6891i		−	0.886802i	0.896323	−	0.443401i	$-0.146228\pi$
$314$		0			0
$315$	−6.09730	+	4.43723i	−0.343544	+	0.250009i
$316$		0			0
$317$	−19.4607			−1.09302			−0.546510	−	0.837453i	$-0.684044\pi$
$317$	−19.4607			−1.09302			−0.546510	+	0.837453i	$0.684044\pi$
$318$		0			0
$319$	1.22036	+	0.704577i	0.0683272	+	0.0394487i
$320$		0			0
$321$	6.88358	−	11.9227i	0.384204	−	0.665461i
$322$		0			0
$323$	2.45211	+	4.24717i	0.136439	+	0.236319i
$324$		0			0
$325$	−10.8501	−	14.3971i	−0.601854	−	0.798606i
$326$		0			0
$327$	−9.40580	−	16.2913i	−0.520142	−	0.900912i
$328$		0			0
$329$	−11.8108	+	20.4569i	−0.651150	+	1.12782i
$330$		0			0
$331$	−5.73925	−	3.31356i	−0.315457	−	0.182129i	0.333909	−	0.942605i	$-0.391632\pi$
$331$	−5.73925	−	3.31356i	−0.315457	−	0.182129i	−0.649366	+	0.760476i	$0.724966\pi$
$332$		0			0
$333$	−11.3727			−0.623221
$334$		0			0
$335$	−7.23196	+	5.26296i	−0.395124	+	0.287546i
$336$		0			0
$337$			11.0614i			0.602555i	0.953537	+	0.301277i	$0.0974130\pi$
$337$			11.0614i			0.602555i	−0.953537	+	0.301277i	$0.902587\pi$
$338$		0			0
$339$	−3.27290			−0.177759
$340$		0			0
$341$	−0.414448	−	0.717844i	−0.0224436	−	0.0388734i
$342$		0			0
$343$	20.1279			1.08680
$344$		0			0
$345$	−2.16224	−	0.960668i	−0.116411	−	0.0517207i
$346$		0			0
$347$	15.3466	+	8.86035i	0.823847	+	0.475649i	0.851741	−	0.523962i	$-0.175547\pi$
$347$	15.3466	+	8.86035i	0.823847	+	0.475649i	−0.0278940	+	0.999611i	$0.508880\pi$
$348$		0			0
$349$	15.3172	−	8.84341i	0.819913	−	0.473377i	−0.0304733	−	0.999536i	$-0.509701\pi$
$349$	15.3172	−	8.84341i	0.819913	−	0.473377i	0.850387	+	0.526158i	$0.176368\pi$
$350$		0			0
$351$	−17.7578	+	8.24791i	−0.947839	+	0.440241i
$352$		0			0
$353$	16.8114	+	29.1183i	0.894783	+	1.54981i	0.834073	+	0.551654i	$0.186003\pi$
$353$	16.8114	+	29.1183i	0.894783	+	1.54981i	0.0607098	+	0.998155i	$0.480664\pi$
$354$		0			0
$355$	4.27235	−	9.61605i	0.226753	−	0.510367i
$356$		0			0
$357$	1.54697	−	2.67942i	0.0818741	−	0.141810i
$358$		0			0
$359$		−	17.4880i		−	0.922981i	−0.887145	−	0.461490i	$-0.847315\pi$
$359$		−	17.4880i		−	0.922981i	0.887145	−	0.461490i	$-0.152685\pi$
$360$		0			0
$361$	−1.92748	−	3.33849i	−0.101446	−	0.175710i
$362$		0			0
$363$			2.40762i			0.126367i
$364$		0			0
$365$	3.60229	+	34.0181i	0.188553	+	1.78059i
$366$		0			0
$367$	6.37373	−	3.67988i	0.332706	−	0.192088i	−0.324336	−	0.945942i	$-0.605141\pi$
$367$	6.37373	−	3.67988i	0.332706	−	0.192088i	0.657042	+	0.753854i	$0.271807\pi$
$368$		0			0
$369$			18.0403i			0.939141i
$370$		0			0
$371$	−21.7147	−	12.5370i	−1.12737	−	0.650887i
$372$		0			0
$373$	25.2893	+	14.6008i	1.30943	+	0.756000i	0.982001	−	0.188875i	$-0.0604841\pi$
$373$	25.2893	+	14.6008i	1.30943	+	0.756000i	0.327430	+	0.944875i	$0.393817\pi$
$374$		0			0
$375$	−9.79519	−	8.77819i	−0.505822	−	0.453304i
$376$		0			0
$377$	0.976027	−	1.38944i	0.0502680	−	0.0715596i
$378$		0			0
$379$	13.2943	−	7.67544i	0.682880	−	0.394261i	−0.118059	−	0.993007i	$-0.537667\pi$
$379$	13.2943	−	7.67544i	0.682880	−	0.394261i	0.800939	+	0.598746i	$0.204334\pi$
$380$		0			0
$381$	−5.11735	+	8.86350i	−0.262170	+	0.454091i
$382$		0			0
$383$	1.59622	−	2.76474i	0.0815632	−	0.141272i	−0.822358	−	0.568970i	$-0.807342\pi$
$383$	1.59622	−	2.76474i	0.0815632	−	0.141272i	0.903922	+	0.427698i	$0.140675\pi$
$384$		0			0
$385$	−13.8856	+	1.47039i	−0.707676	+	0.0749383i
$386$		0			0
$387$	−10.8926	+	6.28885i	−0.553703	+	0.319680i
$388$		0			0
$389$	28.9316			1.46689			0.733445	−	0.679749i	$-0.237911\pi$
$389$	28.9316			1.46689			0.733445	+	0.679749i	$0.237911\pi$
$390$		0			0
$391$	−1.13345			−0.0573208
$392$		0			0
$393$	16.1729	−	9.33743i	0.815815	−	0.471011i
$394$		0			0
$395$	0.385332	+	3.63886i	0.0193881	+	0.183091i
$396$		0			0
$397$	2.49557	−	4.32245i	0.125249	−	0.216937i	−0.796581	−	0.604531i	$-0.793360\pi$
$397$	2.49557	−	4.32245i	0.125249	−	0.216937i	0.921830	+	0.387594i	$0.126694\pi$
$398$		0			0
$399$	4.77729	−	8.27451i	0.239164	−	0.414244i
$400$		0			0
$401$	3.46032	−	1.99782i	0.172800	−	0.0997662i	−0.411105	−	0.911588i	$-0.634857\pi$
$401$	3.46032	−	1.99782i	0.172800	−	0.0997662i	0.583905	+	0.811822i	$0.301524\pi$
$402$		0			0
$403$	−0.905851	+	0.420739i	−0.0451236	+	0.0209585i
$404$		0			0
$405$	−2.78550	+	2.02711i	−0.138413	+	0.100728i
$406$		0			0
$407$	−18.2371	−	10.5292i	−0.903977	−	0.521911i
$408$		0			0
$409$	2.53695	+	1.46471i	0.125444	+	0.0724252i	0.561409	−	0.827538i	$-0.310259\pi$
$409$	2.53695	+	1.46471i	0.125444	+	0.0724252i	−0.435965	+	0.899964i	$0.643593\pi$
$410$		0			0
$411$		−	8.49756i		−	0.419154i
$412$		0			0
$413$	−22.3361	+	12.8957i	−1.09909	+	0.634558i
$414$		0			0
$415$	2.63591	+	24.8920i	0.129392	+	1.22190i
$416$		0			0
$417$			23.3806i			1.14495i
$418$		0			0
$419$	4.85425	+	8.40780i	0.237145	+	0.410748i	0.959894	−	0.280363i	$-0.0904549\pi$
$419$	4.85425	+	8.40780i	0.237145	+	0.410748i	−0.722749	+	0.691111i	$0.757122\pi$
$420$		0			0
$421$			22.8217i			1.11226i	0.831094	+	0.556132i	$0.187715\pi$
$421$			22.8217i			1.11226i	−0.831094	+	0.556132i	$0.812285\pi$
$422$		0			0
$423$	9.14555	−	15.8406i	0.444672	−	0.770194i
$424$		0			0
$425$	−5.99557	−	1.93773i	−0.290828	−	0.0939940i
$426$		0			0
$427$	7.97416	+	13.8116i	0.385897	+	0.668392i
$428$		0			0
$429$	−12.6423	−	1.12532i	−0.610374	−	0.0543308i
$430$		0			0
$431$	−10.0125	+	5.78073i	−0.482286	+	0.278448i	−0.721369	−	0.692551i	$-0.756487\pi$
$431$	−10.0125	+	5.78073i	−0.482286	+	0.278448i	0.239082	+	0.970999i	$0.423153\pi$
$432$		0			0
$433$	10.8821	+	6.28278i	0.522960	+	0.301931i	0.738145	−	0.674642i	$-0.235702\pi$
$433$	10.8821	+	6.28278i	0.522960	+	0.301931i	−0.215185	+	0.976573i	$0.569035\pi$
$434$		0			0
$435$	0.503002	−	1.13214i	0.0241171	−	0.0542819i
$436$		0			0
$437$	−3.50027			−0.167441
$438$		0			0
$439$	0.905142	+	1.56775i	0.0432001	+	0.0748247i	0.886817	−	0.462121i	$-0.152911\pi$
$439$	0.905142	+	1.56775i	0.0432001	+	0.0748247i	−0.843617	+	0.536946i	$0.819578\pi$
$440$		0			0
$441$	−4.27390			−0.203519
$442$		0			0
$443$			16.7633i			0.796450i	0.917288	+	0.398225i	$0.130374\pi$
$443$			16.7633i			0.796450i	−0.917288	+	0.398225i	$0.869626\pi$
$444$		0			0
$445$	−9.09343	−	12.4955i	−0.431070	−	0.592344i
$446$		0			0
$447$	−1.15664			−0.0547073
$448$		0			0
$449$	6.13311	+	3.54095i	0.289439	+	0.167108i	0.637689	−	0.770294i	$-0.279891\pi$
$449$	6.13311	+	3.54095i	0.289439	+	0.167108i	−0.348250	+	0.937402i	$0.613224\pi$
$450$		0			0
$451$	−16.7022	+	28.9290i	−0.786475	+	1.36222i
$452$		0			0
$453$	−4.74127	−	8.21212i	−0.222764	−	0.385839i
$454$		0			0
$455$	0.281339	+	16.8229i	0.0131894	+	0.788671i
$456$		0			0
$457$	0.545096	+	0.944133i	0.0254985	+	0.0441647i	0.878493	−	0.477755i	$-0.158549\pi$
$457$	0.545096	+	0.944133i	0.0254985	+	0.0441647i	−0.852995	+	0.521920i	$0.825216\pi$
$458$		0			0
$459$	−3.42168	+	5.92652i	−0.159710	+	0.276626i
$460$		0			0
$461$	−13.5007	−	7.79465i	−0.628791	−	0.363033i	0.151493	−	0.988458i	$-0.451592\pi$
$461$	−13.5007	−	7.79465i	−0.628791	−	0.363033i	−0.780284	+	0.625426i	$0.784925\pi$
$462$		0			0
$463$	19.1896			0.891817			0.445908	−	0.895079i	$-0.352881\pi$
$463$	19.1896			0.891817			0.445908	+	0.895079i	$0.352881\pi$
$464$		0			0
$465$	−0.589211	+	0.428790i	−0.0273240	+	0.0198847i
$466$		0			0
$467$			23.1857i			1.07290i	0.843931	+	0.536452i	$0.180236\pi$
$467$			23.1857i			1.07290i	−0.843931	+	0.536452i	$0.819764\pi$
$468$		0			0
$469$	8.34767			0.385460
$470$		0			0
$471$	1.60804	+	2.78521i	0.0740946	+	0.128336i
$472$		0			0
$473$	−23.2895			−1.07085
$474$		0			0
$475$	−18.5153	−	5.98405i	−0.849541	−	0.274567i
$476$		0			0
$477$	16.8145	+	9.70786i	0.769884	+	0.444493i
$478$		0			0
$479$	−3.01812	+	1.74251i	−0.137901	+	0.0796174i	−0.567363	−	0.823467i	$-0.692037\pi$
$479$	−3.01812	+	1.74251i	−0.137901	+	0.0796174i	0.429462	+	0.903085i	$0.358703\pi$
$480$		0			0
$481$	−14.5857	+	20.7637i	−0.665051	+	0.946742i
$482$		0			0
$483$	1.10411	+	1.91238i	0.0502388	+	0.0870162i
$484$		0			0
$485$	−5.26869	−	2.34085i	−0.239239	−	0.106292i
$486$		0			0
$487$	1.07023	−	1.85369i	0.0484967	−	0.0839988i	−0.840758	−	0.541411i	$-0.817890\pi$
$487$	1.07023	−	1.85369i	0.0484967	−	0.0839988i	0.889255	+	0.457412i	$0.151224\pi$
$488$		0			0
$489$		−	28.9133i		−	1.30751i
$490$		0			0
$491$	13.6201	+	23.5908i	0.614668	+	1.06464i	0.990443	+	0.137926i	$0.0440435\pi$
$491$	13.6201	+	23.5908i	0.614668	+	1.06464i	−0.375774	+	0.926711i	$0.622623\pi$
$492$		0			0
$493$		−	0.593468i		−	0.0267284i
$494$		0			0
$495$	10.7522	−	1.13858i	0.483274	−	0.0511755i
$496$		0			0
$497$	−8.50486	+	4.91028i	−0.381495	+	0.220256i
$498$		0			0
$499$			22.7855i			1.02002i	0.860169	+	0.510010i	$0.170358\pi$
$499$			22.7855i			1.02002i	−0.860169	+	0.510010i	$0.829642\pi$
$500$		0			0
$501$	−14.0969	−	8.13884i	−0.629802	−	0.363616i
$502$		0			0
$503$	−8.31665	−	4.80162i	−0.370821	−	0.214094i	0.302996	−	0.952992i	$-0.402013\pi$
$503$	−8.31665	−	4.80162i	−0.370821	−	0.214094i	−0.673817	+	0.738898i	$0.735346\pi$
$504$		0			0
$505$	2.83262	−	2.06140i	0.126050	−	0.0917310i
$506$		0			0
$507$	−2.70126	+	15.0533i	−0.119967	+	0.668541i
$508$		0			0
$509$	−13.5627	+	7.83041i	−0.601155	+	0.347077i	−0.769496	−	0.638652i	$-0.779492\pi$
$509$	−13.5627	+	7.83041i	−0.601155	+	0.347077i	0.168341	+	0.985729i	$0.446159\pi$
$510$		0			0
$511$	15.9633	−	27.6492i	0.706173	−	1.22313i
$512$		0			0
$513$	−10.5667	+	18.3021i	−0.466532	+	0.808057i
$514$		0			0
$515$	2.03766	−	0.215775i	0.0897900	−	0.00950818i
$516$		0			0
$517$	29.3312	−	16.9344i	1.28998	−	0.744773i
$518$		0			0
$519$	15.4970			0.680243
$520$		0			0
$521$	3.26689			0.143125			0.0715625	−	0.997436i	$-0.477201\pi$
$521$	3.26689			0.143125			0.0715625	+	0.997436i	$0.477201\pi$
$522$		0			0
$523$	−13.8479	+	7.99511i	−0.605528	+	0.349602i	−0.771213	−	0.636577i	$-0.780350\pi$
$523$	−13.8479	+	7.99511i	−0.605528	+	0.349602i	0.165685	+	0.986179i	$0.447016\pi$
$524$		0			0
$525$	2.57100	+	12.0035i	0.112208	+	0.523874i
$526$		0			0
$527$	−0.174545	+	0.302321i	−0.00760331	+	0.0131693i
$528$		0			0
$529$	−11.0955	+	19.2180i	−0.482414	+	0.835565i
$530$		0			0
$531$	17.2957	−	9.98567i	0.750569	−	0.433341i
$532$		0			0
$533$	32.9369	+	23.1370i	1.42666	+	1.00217i
$534$		0			0
$535$	15.3973	+	21.1578i	0.665681	+	0.914729i
$536$		0			0
$537$	3.17438	+	1.83273i	0.136985	+	0.0790881i
$538$		0			0
$539$	−6.85354	−	3.95689i	−0.295203	−	0.170435i
$540$		0			0
$541$		−	7.38554i		−	0.317529i	−0.987316	−	0.158765i	$-0.949249\pi$
$541$		−	7.38554i		−	0.317529i	0.987316	−	0.158765i	$-0.0507511\pi$
$542$		0			0
$543$	8.06342	−	4.65542i	0.346035	−	0.199783i
$544$		0			0
$545$	35.5564	−	3.76519i	1.52307	−	0.161283i
$546$		0			0
$547$			11.4488i			0.489515i	0.969584	+	0.244757i	$0.0787083\pi$
$547$			11.4488i			0.489515i	−0.969584	+	0.244757i	$0.921292\pi$
$548$		0			0
$549$	−6.17470	−	10.6949i	−0.263530	−	0.456447i
$550$		0			0
$551$		−	1.83273i		−	0.0780768i
$552$		0			0
$553$	1.70757	−	2.95759i	0.0726131	−	0.125770i
$554$		0			0
$555$	−7.51684	+	16.9186i	−0.319072	+	0.718156i
$556$		0			0
$557$	9.70356	+	16.8071i	0.411153	+	0.712138i	0.995016	−	0.0997144i	$-0.0317929\pi$
$557$	9.70356	+	16.8071i	0.411153	+	0.712138i	−0.583863	+	0.811852i	$0.698460\pi$
$558$		0			0
$559$	−2.48813	+	27.9527i	−0.105237	+	1.18227i
$560$		0			0
$561$	−3.84177	+	2.21805i	−0.162200	+	0.0936461i
$562$		0			0
$563$	−7.70563	−	4.44885i	−0.324754	−	0.187497i	0.328756	−	0.944415i	$-0.393371\pi$
$563$	−7.70563	−	4.44885i	−0.324754	−	0.187497i	−0.653509	+	0.756918i	$0.726704\pi$
$564$		0			0
$565$	2.52579	−	5.68495i	0.106261	−	0.239168i
$566$		0			0
$567$	3.21524			0.135027
$568$		0			0
$569$	3.44997	+	5.97552i	0.144630	+	0.250507i	0.929235	−	0.369490i	$-0.120467\pi$
$569$	3.44997	+	5.97552i	0.144630	+	0.250507i	−0.784605	+	0.619996i	$0.787134\pi$
$570$		0			0
$571$	32.4491			1.35795			0.678975	−	0.734161i	$-0.262424\pi$
$571$	32.4491			1.35795			0.678975	+	0.734161i	$0.262424\pi$
$572$		0			0
$573$		−	16.4242i		−	0.686132i
$574$		0			0
$575$	3.33732	−	3.01439i	0.139176	−	0.125709i
$576$		0			0
$577$	25.3915			1.05706			0.528530	−	0.848914i	$-0.322743\pi$
$577$	25.3915			1.05706			0.528530	+	0.848914i	$0.322743\pi$
$578$		0			0
$579$	−13.8842	−	8.01604i	−0.577007	−	0.333135i
$580$		0			0
$581$	11.6808	−	20.2317i	0.484601	−	0.839354i
$582$		0			0
$583$	17.9756	+	31.1346i	0.744473	+	1.28946i
$584$		0			0
$585$	−0.217852	−	13.0266i	−0.00900707	−	0.538585i
$586$		0			0
$587$	−1.23196	−	2.13382i	−0.0508485	−	0.0880722i	0.839481	−	0.543389i	$-0.182859\pi$
$587$	−1.23196	−	2.13382i	−0.0508485	−	0.0880722i	−0.890329	+	0.455317i	$0.849526\pi$
$588$		0			0
$589$	−0.539025	+	0.933619i	−0.0222101	+	0.0384691i
$590$		0			0
$591$	−18.0556	−	10.4244i	−0.742710	−	0.428804i
$592$		0			0
$593$	40.6651			1.66992			0.834958	−	0.550313i	$-0.185492\pi$
$593$	40.6651			1.66992			0.834958	+	0.550313i	$0.185492\pi$
$594$		0			0
$595$	3.46027	+	4.75484i	0.141857	+	0.194929i
$596$		0			0
$597$			16.9001i			0.691675i
$598$		0			0
$599$	−26.1916			−1.07016			−0.535079	−	0.844802i	$-0.679718\pi$
$599$	−26.1916			−1.07016			−0.535079	+	0.844802i	$0.679718\pi$
$600$		0			0
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	0.970212	−	0.242259i	$-0.0778882\pi$
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	−0.694908	+	0.719099i	$0.744555\pi$
$602$		0			0
$603$	−6.46392			−0.263231
$604$		0			0
$605$	−4.18199	−	1.85803i	−0.170022	−	0.0755398i
$606$		0			0
$607$	8.51183	+	4.91431i	0.345485	+	0.199466i	0.662695	−	0.748890i	$-0.269413\pi$
$607$	8.51183	+	4.91431i	0.345485	+	0.199466i	−0.317210	+	0.948355i	$0.602746\pi$
$608$		0			0
$609$	−1.00131	+	0.578108i	−0.0405752	+	0.0234261i
$610$		0			0
$611$	−17.1915	−	37.0132i	−0.695492	−	1.49739i
$612$		0			0
$613$	−10.3086	−	17.8551i	−0.416362	−	0.721161i	0.579208	−	0.815180i	$-0.303362\pi$
$613$	−10.3086	−	17.8551i	−0.416362	−	0.721161i	−0.995570	+	0.0940190i	$0.970029\pi$
$614$		0			0
$615$	26.8377	+	11.9238i	1.08220	+	0.480814i
$616$		0			0
$617$	8.90958	−	15.4318i	0.358686	−	0.621262i	−0.629056	−	0.777360i	$-0.716558\pi$
$617$	8.90958	−	15.4318i	0.358686	−	0.621262i	0.987742	+	0.156098i	$0.0498915\pi$
$618$		0			0
$619$		−	29.3377i		−	1.17918i	−0.807701	−	0.589592i	$-0.799289\pi$
$619$		−	29.3377i		−	1.17918i	0.807701	−	0.589592i	$-0.200711\pi$
$620$		0			0
$621$	−2.44214	−	4.22992i	−0.0979999	−	0.169741i
$622$		0			0
$623$			14.4232i			0.577855i
$624$		0			0
$625$	22.8068	−	10.2397i	0.912271	−	0.409587i
$626$		0			0
$627$	−11.8640	+	6.84971i	−0.473804	+	0.273551i
$628$		0			0
$629$			8.86875i			0.353620i
$630$		0			0
$631$	15.5662	+	8.98714i	0.619680	+	0.357772i	0.776744	−	0.629816i	$-0.216870\pi$
$631$	15.5662	+	8.98714i	0.619680	+	0.357772i	−0.157064	+	0.987588i	$0.550203\pi$
$632$		0			0
$633$	−20.6039	−	11.8957i	−0.818931	−	0.472810i
$634$		0			0
$635$	−11.4465	−	15.7290i	−0.454242	−	0.624185i
$636$		0			0
$637$	−5.48135	+	7.80305i	−0.217179	+	0.309168i
$638$		0			0
$639$	6.58564	−	3.80222i	0.260524	−	0.150414i
$640$		0			0
$641$	−12.7805	+	22.1365i	−0.504800	+	0.874339i	0.495185	+	0.868788i	$0.335100\pi$
$641$	−12.7805	+	22.1365i	−0.504800	+	0.874339i	−0.999985	+	0.00555129i	$0.998233\pi$
$642$		0			0
$643$	10.9914	−	19.0376i	0.433457	−	0.750769i	−0.563712	−	0.825972i	$-0.690627\pi$
$643$	10.9914	−	19.0376i	0.433457	−	0.750769i	0.997168	+	0.0752028i	$0.0239604\pi$
$644$		0			0
$645$	2.15610	+	20.3610i	0.0848964	+	0.801715i
$646$		0			0
$647$	26.9769	−	15.5751i	1.06057	−	0.612321i	0.134981	−	0.990848i	$-0.456903\pi$
$647$	26.9769	−	15.5751i	1.06057	−	0.612321i	0.925590	+	0.378527i	$0.123569\pi$
$648$		0			0
$649$	36.9800			1.45159
$650$		0			0
$651$	0.680112			0.0266557
$652$		0			0
$653$	−15.4449	+	8.91711i	−0.604405	+	0.348954i	−0.770773	−	0.637110i	$-0.780130\pi$
$653$	−15.4449	+	8.91711i	−0.604405	+	0.348954i	0.166367	+	0.986064i	$0.446796\pi$
$654$		0			0
$655$	3.73783	+	35.2980i	0.146049	+	1.37921i
$656$		0			0
$657$	−12.3610	+	21.4098i	−0.482248	+	0.835277i
$658$		0			0
$659$	−9.89464	+	17.1380i	−0.385440	+	0.667602i	−0.991830	−	0.127565i	$-0.959284\pi$
$659$	−9.89464	+	17.1380i	−0.385440	+	0.667602i	0.606390	+	0.795168i	$0.292617\pi$
$660$		0			0
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	−0.774584	−	0.632471i	$-0.782041\pi$
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	0.160444	+	0.987045i	$0.448707\pi$
$662$		0			0
$663$	2.25172	+	4.84795i	0.0874495	+	0.188279i
$664$		0			0
$665$	10.6859	+	14.6837i	0.414381	+	0.569411i
$666$		0			0
$667$	0.366826	+	0.211787i	0.0142035	+	0.00820042i
$668$		0			0
$669$	−11.3549	−	6.55576i	−0.439006	−	0.253460i
$670$		0			0
$671$		−	22.8668i		−	0.882763i
$672$		0			0
$673$	−17.1875	+	9.92322i	−0.662530	+	0.382512i	−0.793240	−	0.608909i	$-0.791608\pi$
$673$	−17.1875	+	9.92322i	−0.662530	+	0.382512i	0.130710	+	0.991421i	$0.458274\pi$
$674$		0			0
$675$	−5.68671	−	26.5500i	−0.218882	−	1.02191i
$676$		0			0
$677$			4.02129i			0.154551i	0.997010	+	0.0772753i	$0.0246220\pi$
$677$			4.02129i			0.154551i	−0.997010	+	0.0772753i	$0.975378\pi$
$678$		0			0
$679$	2.69037	+	4.65986i	0.103247	+	0.178829i
$680$		0			0
$681$			20.3610i			0.780237i
$682$		0			0
$683$	−5.19430	+	8.99680i	−0.198754	+	0.344253i	−0.948125	−	0.317898i	$-0.897023\pi$
$683$	−5.19430	+	8.99680i	−0.198754	+	0.344253i	0.749370	+	0.662151i	$0.230356\pi$
$684$		0			0
$685$	14.7601	+	6.55782i	0.563954	+	0.250561i
$686$		0			0
$687$	−5.82545	−	10.0900i	−0.222255	−	0.384957i
$688$		0			0
$689$	39.2889	−	18.2485i	1.49679	−	0.695211i
$690$		0			0
$691$	24.5864	−	14.1949i	0.935309	−	0.540001i	0.0468225	−	0.998903i	$-0.485090\pi$
$691$	24.5864	−	14.1949i	0.935309	−	0.540001i	0.888487	+	0.458902i	$0.151757\pi$
$692$		0			0
$693$	−8.73913	−	5.04554i	−0.331972	−	0.191664i
$694$		0			0
$695$	−40.6117	−	18.0435i	−1.54049	−	0.684430i
$696$		0			0
$697$	14.0683			0.532875
$698$		0			0
$699$	−11.2787	−	19.5352i	−0.426598	−	0.738889i
$700$		0			0
$701$	16.7917			0.634213			0.317106	−	0.948390i	$-0.397289\pi$
$701$	16.7917			0.634213			0.317106	+	0.948390i	$0.397289\pi$
$702$		0			0
$703$			27.3882i			1.03297i
$704$		0			0
$705$	−17.5204	−	24.0752i	−0.659857	−	0.906726i
$706$		0			0
$707$	−3.26962			−0.122967
$708$		0			0
$709$	−41.9846	−	24.2398i	−1.57676	−	0.910345i	−0.995307	−	0.0967675i	$-0.969150\pi$
$709$	−41.9846	−	24.2398i	−1.57676	−	0.910345i	−0.581457	−	0.813577i	$-0.697517\pi$
$710$		0			0
$711$	−1.32223	+	2.29018i	−0.0495877	+	0.0858883i
$712$		0			0
$713$	−0.124578	−	0.215775i	−0.00466547	−	0.00808083i
$714$		0			0
$715$	11.7111	−	21.0909i	0.437969	−	0.788756i
$716$		0			0
$717$	1.27319	+	2.20524i	0.0475483	+	0.0823561i
$718$		0			0
$719$	−6.14778	+	10.6483i	−0.229273	+	0.397113i	−0.957593	−	0.288125i	$-0.906968\pi$
$719$	−6.14778	+	10.6483i	−0.229273	+	0.397113i	0.728320	+	0.685238i	$0.240302\pi$
$720$		0			0
$721$	−1.65617	−	0.956188i	−0.0616789	−	0.0356103i
$722$		0			0
$723$	−18.9423			−0.704472
$724$		0			0
$725$	1.57832	+	1.74741i	0.0586174	+	0.0648972i
$726$		0			0
$727$		−	36.1491i		−	1.34070i	−0.742046	−	0.670349i	$-0.766145\pi$
$727$		−	36.1491i		−	1.34070i	0.742046	−	0.670349i	$-0.233855\pi$
$728$		0			0
$729$	−21.6555			−0.802055
$730$		0			0
$731$	4.90421	+	8.49435i	0.181389	+	0.314175i
$732$		0			0
$733$	−22.4789			−0.830278			−0.415139	−	0.909758i	$-0.636267\pi$
$733$	−22.4789			−0.830278			−0.415139	+	0.909758i	$0.636267\pi$
$734$		0			0
$735$	−2.82485	+	6.35807i	−0.104196	+	0.234521i
$736$		0			0
$737$	−10.3654	−	5.98447i	−0.381815	−	0.220441i
$738$		0			0
$739$	−10.6967	+	6.17575i	−0.393485	+	0.227179i	−0.683669	−	0.729792i	$-0.739617\pi$
$739$	−10.6967	+	6.17575i	−0.393485	+	0.227179i	0.290184	+	0.956971i	$0.406283\pi$
$740$		0			0
$741$	6.95369	+	14.9713i	0.255450	+	0.549984i
$742$		0			0
$743$	11.4818	+	19.8871i	0.421227	+	0.729587i	0.996060	−	0.0886839i	$-0.0282661\pi$
$743$	11.4818	+	19.8871i	0.421227	+	0.729587i	−0.574832	+	0.818271i	$0.694933\pi$
$744$		0			0
$745$	0.892615	−	2.00907i	0.0327029	−	0.0736065i
$746$		0			0
$747$	−9.04489	+	15.6662i	−0.330935	+	0.573197i
$748$		0			0
$749$		−	24.4219i		−	0.892355i
$750$		0			0
$751$	16.4263	+	28.4511i	0.599403	+	1.03820i	0.992909	+	0.118874i	$0.0379286\pi$
$751$	16.4263	+	28.4511i	0.599403	+	1.03820i	−0.393506	+	0.919322i	$0.628738\pi$
$752$		0			0
$753$			21.2804i			0.775501i
$754$		0			0
$755$	17.9233	−	1.89796i	0.652294	−	0.0690737i
$756$		0			0
$757$	28.6323	−	16.5309i	1.04066	−	0.600826i	0.120640	−	0.992696i	$-0.461505\pi$
$757$	28.6323	−	16.5309i	1.04066	−	0.600826i	0.920020	+	0.391871i	$0.128172\pi$
$758$		0			0
$759$		−	3.16616i		−	0.114924i
$760$		0			0
$761$	−27.3347	−	15.7817i	−0.990882	−	0.572086i	−0.0853441	−	0.996352i	$-0.527199\pi$
$761$	−27.3347	−	15.7817i	−0.990882	−	0.572086i	−0.905538	+	0.424266i	$0.860532\pi$
$762$		0			0
$763$	−28.8995	−	16.6851i	−1.04623	−	0.604043i
$764$		0			0
$765$	−2.67942	−	3.68185i	−0.0968745	−	0.133118i
$766$		0			0
$767$	3.95074	−	44.3842i	0.142653	−	1.60262i
$768$		0			0
$769$	−36.8445	+	21.2722i	−1.32865	+	0.767095i	−0.985090	−	0.172037i	$-0.944965\pi$
$769$	−36.8445	+	21.2722i	−1.32865	+	0.767095i	−0.343556	+	0.939132i	$0.611632\pi$
$770$		0			0
$771$	−5.90880	+	10.2343i	−0.212800	+	0.368581i
$772$		0			0
$773$	0.533226	−	0.923574i	0.0191788	−	0.0332187i	−0.856277	−	0.516517i	$-0.827228\pi$
$773$	0.533226	−	0.923574i	0.0191788	−	0.0332187i	0.875456	+	0.483299i	$0.160561\pi$
$774$		0			0
$775$	−0.290088	−	1.35436i	−0.0104203	−	0.0486500i
$776$		0			0
$777$	14.9636	−	8.63922i	0.536815	−	0.309930i
$778$		0			0
$779$	43.4453			1.55659
$780$		0			0
$781$	14.0808			0.503850
$782$		0			0
$783$	2.21477	−	1.27870i	0.0791494	−	0.0456969i
$784$		0			0
$785$	−6.07883	+	0.643708i	−0.216963	+	0.0229749i
$786$		0			0
$787$	0.0215610	−	0.0373447i	0.000768565	−	0.00133119i	−0.865641	−	0.500665i	$-0.833089\pi$
$787$	0.0215610	−	0.0373447i	0.000768565	−	0.00133119i	0.866409	+	0.499334i	$0.166422\pi$
$788$		0			0
$789$	−9.29546	+	16.1002i	−0.330927	+	0.573183i
$790$		0			0
$791$	−5.02802	+	2.90293i	−0.178776	+	0.103216i
$792$		0			0
$793$	−27.4453	−	2.44296i	−0.974610	−	0.0867522i
$794$		0			0
$795$	25.5555	−	18.5977i	0.906361	−	0.659591i
$796$		0			0
$797$	−29.9559	−	17.2951i	−1.06109	−	0.612623i	−0.135359	−	0.990797i	$-0.543219\pi$
$797$	−29.9559	−	17.2951i	−1.06109	−	0.612623i	−0.925735	+	0.378174i	$0.876552\pi$
$798$		0			0
$799$	−12.3529	−	7.13194i	−0.437014	−	0.252310i
$800$		0			0
$801$		−	11.1685i		−	0.394619i
$802$		0			0
$803$	−39.6436	+	22.8882i	−1.39899	+	0.807708i
$804$		0			0
$805$	−4.17384	+	0.441982i	−0.147108	+	0.0155778i
$806$		0			0
$807$			8.68906i			0.305869i
$808$		0			0
$809$	−3.04046	−	5.26623i	−0.106897	−	0.185151i	0.807615	−	0.589710i	$-0.200758\pi$
$809$	−3.04046	−	5.26623i	−0.106897	−	0.185151i	−0.914512	+	0.404560i	$0.867425\pi$
$810$		0			0
$811$		−	5.47145i		−	0.192129i	−0.995375	−	0.0960644i	$-0.969375\pi$
$811$		−	5.47145i		−	0.192129i	0.995375	−	0.0960644i	$-0.0306255\pi$
$812$		0			0
$813$	−18.2365	+	31.5866i	−0.639584	+	1.10779i
$814$		0			0
$815$	50.2219	+	22.3133i	1.75920	+	0.781600i
$816$		0			0
$817$	15.1450	+	26.2320i	0.529858	+	0.917741i
$818$		0			0
$819$	−6.98942	+	9.94987i	−0.244230	+	0.347677i
$820$		0			0
$821$	38.1625	−	22.0331i	1.33188	−	0.768961i	0.346291	−	0.938127i	$-0.387441\pi$
$821$	38.1625	−	22.0331i	1.33188	−	0.768961i	0.985588	+	0.169166i	$0.0541075\pi$
$822$		0			0
$823$	10.8396	+	6.25823i	0.377844	+	0.218148i	0.676880	−	0.736094i	$-0.263332\pi$
$823$	10.8396	+	6.25823i	0.377844	+	0.218148i	−0.299036	+	0.954242i	$0.596665\pi$
$824$		0			0
$825$	5.41286	−	16.7480i	0.188452	−	0.583090i
$826$		0			0
$827$	−51.7679			−1.80015			−0.900074	−	0.435738i	$-0.856488\pi$
$827$	−51.7679			−1.80015			−0.900074	+	0.435738i	$0.856488\pi$
$828$		0			0
$829$	6.95883	+	12.0531i	0.241690	+	0.418620i	0.961196	−	0.275867i	$-0.0889649\pi$
$829$	6.95883	+	12.0531i	0.241690	+	0.418620i	−0.719506	+	0.694487i	$0.755632\pi$
$830$		0			0
$831$	−5.53793			−0.192109
$832$		0			0
$833$			3.33290i			0.115478i
$834$		0			0
$835$	25.0160	−	18.2050i	0.865714	−	0.630011i
$836$		0			0
$837$	−1.50432			−0.0519967
$838$		0			0
$839$	43.3416	+	25.0233i	1.49632	+	0.863899i	0.999991	−	0.00423634i	$-0.00134847\pi$
$839$	43.3416	+	25.0233i	1.49632	+	0.863899i	0.496327	+	0.868136i	$0.334682\pi$
$840$		0			0
$841$	14.3891	−	24.9227i	0.496176	−	0.859402i
$842$		0			0
$843$	−6.33935	−	10.9801i	−0.218339	−	0.378174i
$844$		0			0
$845$	−24.0627	−	16.3091i	−0.827781	−	0.561051i
$846$		0			0
$847$	2.13547	+	3.69874i	0.0733755	+	0.127090i
$848$		0			0
$849$	17.1302	−	29.6703i	0.587906	−	1.01828i
$850$		0			0
$851$	−5.48183	−	3.16493i	−0.187915	−	0.108493i
$852$		0			0
$853$	12.7392			0.436183			0.218092	−	0.975928i	$-0.430017\pi$
$853$	12.7392			0.436183			0.218092	+	0.975928i	$0.430017\pi$
$854$		0			0
$855$	−8.27449	−	11.3702i	−0.282982	−	0.388852i
$856$		0			0
$857$		−	30.3306i		−	1.03607i	−0.855359	−	0.518036i	$-0.826663\pi$
$857$		−	30.3306i		−	1.03607i	0.855359	−	0.518036i	$-0.173337\pi$
$858$		0			0
$859$	−48.7446			−1.66314			−0.831572	−	0.555417i	$-0.812559\pi$
$859$	−48.7446			−1.66314			−0.831572	+	0.555417i	$0.812559\pi$
$860$		0			0
$861$	−13.7042	−	23.7364i	−0.467038	−	0.808934i
$862$		0			0
$863$	−17.6100			−0.599451			−0.299725	−	0.954026i	$-0.596895\pi$
$863$	−17.6100			−0.599451			−0.299725	+	0.954026i	$0.596895\pi$
$864$		0			0
$865$	−11.9595	+	26.9180i	−0.406635	+	0.915239i
$866$		0			0
$867$	−15.7021	−	9.06563i	−0.533273	−	0.307885i
$868$		0			0
$869$	−4.24061	+	2.44832i	−0.143853	+	0.0830535i
$870$		0			0
$871$	−8.29009	+	11.8015i	−0.280899	+	0.399877i
$872$		0			0
$873$	−2.08326	−	3.60831i	−0.0705076	−	0.122123i
$874$		0			0
$875$	−22.8339	−	4.79763i	−0.771926	−	0.162190i
$876$		0			0
$877$	−20.9644	+	36.3115i	−0.707918	+	1.22615i	0.257709	+	0.966222i	$0.417032\pi$
$877$	−20.9644	+	36.3115i	−0.707918	+	1.22615i	−0.965628	+	0.259928i	$0.916301\pi$
$878$		0			0
$879$		−	29.9109i		−	1.00887i
$880$		0			0
$881$	14.9695	+	25.9280i	0.504336	+	0.873535i	0.999987	+	0.00501392i	$0.00159599\pi$
$881$	14.9695	+	25.9280i	0.504336	+	0.873535i	−0.495652	+	0.868521i	$0.665071\pi$
$882$		0			0
$883$		−	35.3391i		−	1.18926i	−0.804001	−	0.594629i	$-0.797299\pi$
$883$		−	35.3391i		−	1.18926i	0.804001	−	0.594629i	$-0.202701\pi$
$884$		0			0
$885$	−3.42353	−	32.3300i	−0.115081	−	1.08676i
$886$		0			0
$887$	36.8682	−	21.2859i	1.23791	−	0.714709i	0.269246	−	0.963071i	$-0.413226\pi$
$887$	36.8682	−	21.2859i	1.23791	−	0.714709i	0.968667	+	0.248362i	$0.0798922\pi$
$888$		0			0
$889$			18.1555i			0.608917i
$890$		0			0
$891$	−3.99240	−	2.30501i	−0.133750	−	0.0772208i
$892$		0			0
$893$	−38.1478	−	22.0246i	−1.27657	−	0.737026i
$894$		0			0
$895$	−5.63317	+	4.09946i	−0.188296	+	0.137030i
$896$		0			0
$897$	−3.80010	−	0.338256i	−0.126882	−	0.0112940i
$898$		0			0
$899$	0.112979	−	0.0652284i	0.00376806	−	0.00217549i
$900$		0			0
$901$	7.57045	−	13.1124i	0.252208	−	0.436837i
$902$		0			0
$903$	9.55458	−	16.5490i	0.317957	−	0.550717i
$904$		0			0
$905$	1.86359	+	17.5987i	0.0619478	+	0.585002i
$906$		0			0
$907$	−12.5097	+	7.22247i	−0.415377	+	0.239818i	−0.693098	−	0.720844i	$-0.743755\pi$
$907$	−12.5097	+	7.22247i	−0.415377	+	0.239818i	0.277720	+	0.960662i	$0.410421\pi$
$908$		0			0
$909$	2.53179			0.0839743
$910$		0			0
$911$	42.9419			1.42273			0.711364	−	0.702824i	$-0.248078\pi$
$911$	42.9419			1.42273			0.711364	+	0.702824i	$0.248078\pi$
$912$		0			0
$913$	−29.0084	+	16.7480i	−0.960037	+	0.554278i
$914$		0			0
$915$	−19.9914	+	2.11696i	−0.660897	+	0.0699846i
$916$		0			0
$917$	16.5639	−	28.6895i	0.546987	−	0.947410i
$918$		0			0
$919$	20.3770	−	35.2940i	0.672175	−	1.16424i	−0.305111	−	0.952317i	$-0.598693\pi$
$919$	20.3770	−	35.2940i	0.672175	−	1.16424i	0.977286	−	0.211925i	$-0.0679733\pi$
$920$		0			0
$921$	25.8074	−	14.8999i	0.850384	−	0.490970i
$922$		0			0
$923$	1.50432	−	16.9001i	0.0495151	−	0.556273i
$924$		0			0
$925$	−23.5864	−	26.1132i	−0.775515	−	0.858597i
$926$		0			0
$927$	1.28243	+	0.740414i	0.0421207	+	0.0243184i
$928$		0			0
$929$	−11.3326	−	6.54286i	−0.371809	−	0.214664i	0.302439	−	0.953169i	$-0.402199\pi$
$929$	−11.3326	−	6.54286i	−0.371809	−	0.214664i	−0.674249	+	0.738504i	$0.735532\pi$
$930$		0			0
$931$			10.2926i			0.337325i
$932$		0			0
$933$	24.8080	−	14.3229i	0.812178	−	0.468911i
$934$		0			0
$935$	−0.887897	−	8.38482i	−0.0290373	−	0.274213i
$936$		0			0
$937$		−	41.0546i		−	1.34120i	−0.741821	−	0.670598i	$-0.766038\pi$
$937$		−	41.0546i		−	1.34120i	0.741821	−	0.670598i	$-0.233962\pi$
$938$		0			0
$939$	−9.22869	−	15.9846i	−0.301167	−	0.521636i
$940$		0			0
$941$			24.4162i			0.795945i	0.917397	+	0.397973i	$0.130286\pi$
$941$			24.4162i			0.795945i	−0.917397	+	0.397973i	$0.869714\pi$
$942$		0			0
$943$	−5.02047	+	8.69570i	−0.163489	+	0.283171i
$944$		0			0
$945$	−10.2891	+	23.1583i	−0.334704	+	0.753339i
$946$		0			0
$947$	2.30433	+	3.99122i	0.0748807	+	0.129697i	0.901034	−	0.433748i	$-0.142809\pi$
$947$	2.30433	+	3.99122i	0.0748807	+	0.129697i	−0.826154	+	0.563445i	$0.809476\pi$
$948$		0			0
$949$	23.2357	+	50.0264i	0.754262	+	1.62393i
$950$		0			0
$951$	−19.8271	+	11.4472i	−0.642937	+	0.371200i
$952$		0			0
$953$	−4.09617	−	2.36493i	−0.132688	−	0.0766075i	0.432187	−	0.901784i	$-0.357742\pi$
$953$	−4.09617	−	2.36493i	−0.132688	−	0.0766075i	−0.564875	+	0.825177i	$0.691075\pi$
$954$		0			0
$955$	28.5286	+	12.6751i	0.923163	+	0.410156i
$956$		0			0
$957$	1.65779			0.0535887
$958$		0			0
$959$	−7.53700	−	13.0545i	−0.243383	−	0.421551i
$960$		0			0
$961$	30.9233			0.997525
$962$		0			0
$963$			18.9108i			0.609392i
$964$		0			0
$965$	24.6385	−	17.9303i	0.793143	−	0.577198i
$966$		0			0
$967$	−23.8186			−0.765955			−0.382977	−	0.923758i	$-0.625101\pi$
$967$	−23.8186			−0.765955			−0.382977	+	0.923758i	$0.625101\pi$
$968$		0			0
$969$	4.99656	+	2.88477i	0.160513	+	0.0926720i
$970$		0			0
$971$	−15.8349	+	27.4269i	−0.508167	+	0.880170i	0.491789	+	0.870715i	$0.336343\pi$
$971$	−15.8349	+	27.4269i	−0.508167	+	0.880170i	−0.999955	+	0.00945572i	$0.996990\pi$
$972$		0			0
$973$	20.7377	+	35.9188i	0.664820	+	1.15150i
$974$		0			0
$975$	−19.5231	−	8.28591i	−0.625238	−	0.265362i
$976$		0			0
$977$	−13.4354	−	23.2707i	−0.429835	−	0.744497i	0.567023	−	0.823702i	$-0.308095\pi$
$977$	−13.4354	−	23.2707i	−0.429835	−	0.744497i	−0.996858	+	0.0792052i	$0.974762\pi$
$978$		0			0
$979$	10.3401	−	17.9095i	0.330470	−	0.572391i
$980$		0			0
$981$	22.3780	+	12.9200i	0.714475	+	0.412502i
$982$		0			0
$983$	−8.22637			−0.262380			−0.131190	−	0.991357i	$-0.541880\pi$
$983$	−8.22637			−0.262380			−0.131190	+	0.991357i	$0.541880\pi$
$984$		0			0
$985$	32.0411	−	23.3175i	1.02091	−	0.742956i
$986$		0			0
$987$			27.7894i			0.884548i
$988$		0			0
$989$	−7.00054			−0.222604
$990$		0			0
$991$	−11.1157	−	19.2530i	−0.353102	−	0.611591i	0.633689	−	0.773588i	$-0.281540\pi$
$991$	−11.1157	−	19.2530i	−0.353102	−	0.611591i	−0.986791	+	0.161997i	$0.948207\pi$
$992$		0			0
$993$	−7.79642			−0.247412
$994$		0			0
$995$	−29.3551	−	13.0423i	−0.930620	−	0.413469i
$996$		0			0
$997$	−20.4122	−	11.7850i	−0.646459	−	0.373234i	0.140639	−	0.990061i	$-0.455084\pi$
$997$	−20.4122	−	11.7850i	−0.646459	−	0.373234i	−0.787098	+	0.616827i	$0.788418\pi$
$998$		0			0
$999$	−33.0974	+	19.1088i	−1.04716	+	0.604576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.df.c.49.3		8
4.3	odd	2		130.2.m.a.49.2	✓	8
5.4	even	2		1040.2.df.a.49.2		8
12.11	even	2		1170.2.bj.b.829.3		8
13.4	even	6		1040.2.df.a.849.2		8
20.3	even	4		650.2.m.e.101.2		16
20.7	even	4		650.2.m.e.101.7		16
20.19	odd	2		130.2.m.b.49.3	yes	8
52.3	odd	6		1690.2.c.f.1689.4		8
52.11	even	12		1690.2.b.e.339.12		16
52.15	even	12		1690.2.b.e.339.4		16
52.23	odd	6		1690.2.c.e.1689.4		8
52.43	odd	6		130.2.m.b.69.3	yes	8
60.59	even	2		1170.2.bj.a.829.2		8
65.4	even	6	inner	1040.2.df.c.849.3		8
156.95	even	6		1170.2.bj.a.199.2		8
260.43	even	12		650.2.m.e.251.2		16
260.63	odd	12		8450.2.a.cs.1.5		8
260.67	odd	12		8450.2.a.cs.1.4		8
260.119	even	12		1690.2.b.e.339.13		16
260.147	even	12		650.2.m.e.251.7		16
260.159	odd	6		1690.2.c.e.1689.5		8
260.167	odd	12		8450.2.a.cr.1.4		8
260.179	odd	6		1690.2.c.f.1689.5		8
260.199	odd	6		130.2.m.a.69.2	yes	8
260.219	even	12		1690.2.b.e.339.5		16
260.223	odd	12		8450.2.a.cr.1.5		8
780.719	even	6		1170.2.bj.b.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.2	✓	8	4.3	odd	2
130.2.m.a.69.2	yes	8	260.199	odd	6
130.2.m.b.49.3	yes	8	20.19	odd	2
130.2.m.b.69.3	yes	8	52.43	odd	6
650.2.m.e.101.2		16	20.3	even	4
650.2.m.e.101.7		16	20.7	even	4
650.2.m.e.251.2		16	260.43	even	12
650.2.m.e.251.7		16	260.147	even	12
1040.2.df.a.49.2		8	5.4	even	2
1040.2.df.a.849.2		8	13.4	even	6
1040.2.df.c.49.3		8	1.1	even	1	trivial
1040.2.df.c.849.3		8	65.4	even	6	inner
1170.2.bj.a.199.2		8	156.95	even	6
1170.2.bj.a.829.2		8	60.59	even	2
1170.2.bj.b.199.3		8	780.719	even	6
1170.2.bj.b.829.3		8	12.11	even	2
1690.2.b.e.339.4		16	52.15	even	12
1690.2.b.e.339.5		16	260.219	even	12
1690.2.b.e.339.12		16	52.11	even	12
1690.2.b.e.339.13		16	260.119	even	12
1690.2.c.e.1689.4		8	52.23	odd	6
1690.2.c.e.1689.5		8	260.159	odd	6
1690.2.c.f.1689.4		8	52.3	odd	6
1690.2.c.f.1689.5		8	260.179	odd	6
8450.2.a.cr.1.4		8	260.167	odd	12
8450.2.a.cr.1.5		8	260.223	odd	12
8450.2.a.cs.1.4		8	260.67	odd	12
8450.2.a.cs.1.5		8	260.63	odd	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.01883 - 0.588222i) q^{3} +(0.235468 + 2.22364i) q^{5} +(1.04346 - 1.80732i) q^{7} +(-0.807991 + 1.39948i) q^{9} +(-2.59135 + 1.49612i) q^{11} +(1.51883 + 3.27004i) q^{13} +(1.54789 + 2.12700i) q^{15} +(1.09135 + 0.630092i) q^{17} +(3.37028 + 1.94583i) q^{19} -2.45514i q^{21} +(-0.778928 + 0.449714i) q^{23} +(-4.88911 + 1.04719i) q^{25} +5.43044i q^{27} +(-0.235468 - 0.407843i) q^{29} +0.277015i q^{31} +(-1.76010 + 3.04858i) q^{33} +(4.26453 + 1.89470i) q^{35} +(3.51883 + 6.09479i) q^{37} +(3.47094 + 2.43820i) q^{39} +(9.66804 - 5.58184i) q^{41} +(6.74056 + 3.89166i) q^{43} +(-3.30219 - 1.46714i) q^{45} -11.3189 q^{47} +(1.32239 + 2.29044i) q^{49} +1.48254 q^{51} -12.0148i q^{53} +(-3.93700 - 5.40993i) q^{55} +4.57832 q^{57} +(-10.7029 - 6.17932i) q^{59} +(-3.82102 + 6.61820i) q^{61} +(1.68621 + 2.92060i) q^{63} +(-6.91374 + 4.14731i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-0.529063 + 0.916364i) q^{69} +(-4.07532 - 2.35289i) q^{71} +15.2984 q^{73} +(-4.36519 + 3.94279i) q^{75} +6.24455i q^{77} +1.63645 q^{79} +(0.770331 + 1.33425i) q^{81} +11.1943 q^{83} +(-1.14412 + 2.57514i) q^{85} +(-0.479805 - 0.277015i) q^{87} +(-5.98533 + 3.45563i) q^{89} +(7.49486 + 0.667134i) q^{91} +(0.162946 + 0.282231i) q^{93} +(-3.53323 + 7.95245i) q^{95} +(-1.28916 + 2.23289i) q^{97} -4.83540i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} - 5 q^{7} + 8 q^{9} + 3 q^{11} + 4 q^{13} + 2 q^{15} - 15 q^{17} - 9 q^{19} + 6 q^{23} + 5 q^{25} - 3 q^{29} - 10 q^{33} + 33 q^{35} + 20 q^{37} + 30 q^{39} + 21 q^{41} - 18 q^{43} - 9 q^{45}+ \cdots - 4 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 - 5 * q^7 + 8 * q^9 + 3 * q^11 + 4 * q^13 + 2 * q^15 - 15 * q^17 - 9 * q^19 + 6 * q^23 + 5 * q^25 - 3 * q^29 - 10 * q^33 + 33 * q^35 + 20 * q^37 + 30 * q^39 + 21 * q^41 - 18 * q^43 - 9 * q^45 - 6 * q^47 - 15 * q^49 + 20 * q^51 + 23 * q^55 + 24 * q^57 - 30 * q^59 - 5 * q^61 + 25 * q^63 - 6 * q^65 + 16 * q^67 - 2 * q^69 + 26 * q^73 - 72 * q^75 - 4 * q^79 + 8 * q^81 + 48 * q^83 - 34 * q^85 - 12 * q^87 - 39 * q^89 - 19 * q^91 + 18 * q^93 - 9 * q^95 - 4 * q^97

Introduction

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