LMFDB - Embedded newform 736.2.r.a.687.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [736,2,Mod(15,736)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(736, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("736.15"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 736 = 2^{5} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	736.r (of order $22$, degree $10$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.87698958877$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			687.17
Character	$\chi$	$=$	736.687
Dual form			736.2.r.a.15.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.871631 - 1.90861i) q^{3} +(-1.73345 + 2.00050i) q^{5} +(-0.195105 + 0.125386i) q^{7} +(-0.918456 - 1.05995i) q^{9} +(5.40936 + 0.777748i) q^{11} +(0.562994 - 0.876035i) q^{13} +(2.30725 + 5.05217i) q^{15} +(1.07685 - 3.66741i) q^{17} +(0.315114 + 1.07318i) q^{19} +(0.0692537 + 0.481670i) q^{21} +(1.59750 - 4.52195i) q^{23} +(-0.285605 - 1.98643i) q^{25} +(3.21609 - 0.944328i) q^{27} +(-0.188299 + 0.641289i) q^{29} +(7.20592 - 3.29083i) q^{31} +(6.19938 - 9.64643i) q^{33} +(0.0873683 - 0.607660i) q^{35} +(6.74958 + 7.78943i) q^{37} +(-1.18128 - 1.83811i) q^{39} +(-2.98130 + 3.44060i) q^{41} +(-6.46217 - 2.95117i) q^{43} +3.71254 q^{45} -3.52533i q^{47} +(-2.88556 + 6.31850i) q^{49} +(-6.06102 - 5.25190i) q^{51} +(4.45868 - 2.86542i) q^{53} +(-10.9327 + 9.47326i) q^{55} +(2.32294 + 0.333988i) q^{57} +(-6.52016 - 4.19025i) q^{59} +(-3.83630 - 8.40033i) q^{61} +(0.312099 + 0.0916406i) q^{63} +(0.776593 + 2.64483i) q^{65} +(14.5473 - 2.09159i) q^{67} +(-7.23819 - 6.99047i) q^{69} +(-6.17276 + 0.887509i) q^{71} +(-7.57709 + 2.22483i) q^{73} +(-4.04025 - 1.18633i) q^{75} +(-1.15291 + 0.526518i) q^{77} +(2.74726 + 1.76556i) q^{79} +(1.59969 - 11.1261i) q^{81} +(-4.93001 + 4.27188i) q^{83} +(5.47000 + 8.51149i) q^{85} +(1.05984 + 0.918357i) q^{87} +(-1.81651 - 0.829570i) q^{89} +0.241511i q^{91} -16.6217i q^{93} +(-2.69313 - 1.22991i) q^{95} +(11.8432 + 10.2622i) q^{97} +(-4.14388 - 6.44800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 18 q^{3} - 36 q^{9} + 22 q^{11} - 22 q^{17} + 22 q^{19} - 32 q^{25} + 18 q^{27} - 22 q^{33} - 2 q^{35} - 18 q^{41} + 22 q^{43} - 28 q^{49} + 22 q^{51} - 22 q^{57} + 6 q^{59} - 22 q^{65} + 22 q^{67}+ \cdots + 22 q^{99}+O(q^{100}) $ 220 * q + 18 * q^3 - 36 * q^9 + 22 * q^11 - 22 * q^17 + 22 * q^19 - 32 * q^25 + 18 * q^27 - 22 * q^33 - 2 * q^35 - 18 * q^41 + 22 * q^43 - 28 * q^49 + 22 * q^51 - 22 * q^57 + 6 * q^59 - 22 * q^65 + 22 * q^67 - 18 * q^73 - 14 * q^75 + 4 * q^81 + 22 * q^83 - 22 * q^89 - 22 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/736\mathbb{Z}\right)^\times$.

$n$	$97$	$415$	$645$
$\chi(n)$	$e\left(\frac{5}{22}\right)$	$-1$	$-1$

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
$3$	0.871631	−	1.90861i	0.503237	−	1.10193i	−0.472167	−	0.881509i	$-0.656528\pi$
$3$	0.871631	−	1.90861i	0.503237	−	1.10193i	0.975404	−	0.220425i	$-0.0707446\pi$
$4$		0			0
$5$	−1.73345	+	2.00050i	−0.775221	+	0.894653i	−0.996755	−	0.0805000i	$-0.974348\pi$
$5$	−1.73345	+	2.00050i	−0.775221	+	0.894653i	0.221534	+	0.975153i	$0.428894\pi$
$6$		0			0
$7$	−0.195105	+	0.125386i	−0.0737428	+	0.0473916i	−0.576993	−	0.816749i	$-0.695774\pi$
$7$	−0.195105	+	0.125386i	−0.0737428	+	0.0473916i	0.503250	+	0.864141i	$0.332138\pi$
$8$		0			0
$9$	−0.918456	−	1.05995i	−0.306152	−	0.353318i
$10$		0			0
$11$	5.40936	+	0.777748i	1.63098	+	0.234500i	0.896151	−	0.443749i	$-0.146352\pi$
$11$	5.40936	+	0.777748i	1.63098	+	0.234500i	0.734832	+	0.678249i	$0.237261\pi$
$12$		0			0
$13$	0.562994	−	0.876035i	0.156146	−	0.242969i	−0.754362	−	0.656458i	$-0.772054\pi$
$13$	0.562994	−	0.876035i	0.156146	−	0.242969i	0.910509	+	0.413490i	$0.135690\pi$
$14$		0			0
$15$	2.30725	+	5.05217i	0.595729	+	1.30446i
$16$		0			0
$17$	1.07685	−	3.66741i	0.261174	−	0.889477i	−0.719610	−	0.694379i	$-0.755679\pi$
$17$	1.07685	−	3.66741i	0.261174	−	0.889477i	0.980784	−	0.195098i	$-0.0625025\pi$
$18$		0			0
$19$	0.315114	+	1.07318i	0.0722921	+	0.246204i	0.987709	−	0.156302i	$-0.0499573\pi$
$19$	0.315114	+	1.07318i	0.0722921	+	0.246204i	−0.915417	+	0.402506i	$0.868139\pi$
$20$		0			0
$21$	0.0692537	+	0.481670i	0.0151124	+	0.105109i
$22$		0			0
$23$	1.59750	−	4.52195i	0.333102	−	0.942891i
$23$	1.59750	−	4.52195i	0.333102	−	0.942891i
$24$		0			0
$25$	−0.285605	−	1.98643i	−0.0571211	−	0.397286i
$26$		0			0
$27$	3.21609	−	0.944328i	0.618936	−	0.181736i
$28$		0			0
$29$	−0.188299	+	0.641289i	−0.0349663	+	0.119084i	−0.975127	−	0.221647i	$-0.928857\pi$
$29$	−0.188299	+	0.641289i	−0.0349663	+	0.119084i	0.940161	+	0.340732i	$0.110675\pi$
$30$		0			0
$31$	7.20592	−	3.29083i	1.29422	−	0.591051i	0.355161	−	0.934805i	$-0.384426\pi$
$31$	7.20592	−	3.29083i	1.29422	−	0.591051i	0.939060	+	0.343754i	$0.111699\pi$
$32$		0			0
$33$	6.19938	−	9.64643i	1.07917	−	1.67923i
$34$		0			0
$35$	0.0873683	−	0.607660i	0.0147679	−	0.102713i
$36$		0			0
$37$	6.74958	+	7.78943i	1.10962	+	1.28057i	0.956297	+	0.292398i	$0.0944532\pi$
$37$	6.74958	+	7.78943i	1.10962	+	1.28057i	0.153327	+	0.988176i	$0.451001\pi$
$38$		0			0
$39$	−1.18128	−	1.83811i	−0.189157	−	0.294334i
$40$		0			0
$41$	−2.98130	+	3.44060i	−0.465601	+	0.537332i	−0.939183	−	0.343418i	$-0.888415\pi$
$41$	−2.98130	+	3.44060i	−0.465601	+	0.537332i	0.473582	+	0.880750i	$0.342961\pi$
$42$		0			0
$43$	−6.46217	−	2.95117i	−0.985471	−	0.450050i	−0.143546	−	0.989644i	$-0.545850\pi$
$43$	−6.46217	−	2.95117i	−0.985471	−	0.450050i	−0.841925	+	0.539594i	$0.818578\pi$
$44$		0			0
$45$	3.71254			0.553432
$46$		0			0
$47$		−	3.52533i		−	0.514223i	−0.966382	−	0.257111i	$-0.917229\pi$
$47$		−	3.52533i		−	0.514223i	0.966382	−	0.257111i	$-0.0827707\pi$
$48$		0			0
$49$	−2.88556	+	6.31850i	−0.412223	+	0.902642i
$50$		0			0
$51$	−6.06102	−	5.25190i	−0.848713	−	0.735414i
$52$		0			0
$53$	4.45868	−	2.86542i	0.612447	−	0.393596i	−0.197327	−	0.980338i	$-0.563226\pi$
$53$	4.45868	−	2.86542i	0.612447	−	0.393596i	0.809774	+	0.586742i	$0.199590\pi$
$54$		0			0
$55$	−10.9327	+	9.47326i	−1.47417	+	1.27737i
$56$		0			0
$57$	2.32294	+	0.333988i	0.307681	+	0.0442378i
$58$		0			0
$59$	−6.52016	−	4.19025i	−0.848853	−	0.545525i	0.0423639	−	0.999102i	$-0.486511\pi$
$59$	−6.52016	−	4.19025i	−0.848853	−	0.545525i	−0.891217	+	0.453578i	$0.850147\pi$
$60$		0			0
$61$	−3.83630	−	8.40033i	−0.491188	−	1.07555i	−0.979234	−	0.202734i	$-0.935017\pi$
$61$	−3.83630	−	8.40033i	−0.491188	−	1.07555i	0.488046	−	0.872818i	$-0.337710\pi$
$62$		0			0
$63$	0.312099	+	0.0916406i	0.0393208	+	0.0115456i
$64$		0			0
$65$	0.776593	+	2.64483i	0.0963245	+	0.328051i
$66$		0			0
$67$	14.5473	−	2.09159i	1.77724	−	0.255529i	0.825932	−	0.563769i	$-0.190649\pi$
$67$	14.5473	−	2.09159i	1.77724	−	0.255529i	0.951308	+	0.308240i	$0.0997401\pi$
$68$		0			0
$69$	−7.23819	−	6.99047i	−0.871375	−	0.841553i
$70$		0			0
$71$	−6.17276	+	0.887509i	−0.732572	+	0.105328i	−0.498498	−	0.866891i	$-0.666115\pi$
$71$	−6.17276	+	0.887509i	−0.732572	+	0.105328i	−0.234074	+	0.972219i	$0.575206\pi$
$72$		0			0
$73$	−7.57709	+	2.22483i	−0.886832	+	0.260397i	−0.693259	−	0.720689i	$-0.743826\pi$
$73$	−7.57709	+	2.22483i	−0.886832	+	0.260397i	−0.193573	+	0.981086i	$0.562008\pi$
$74$		0			0
$75$	−4.04025	−	1.18633i	−0.466528	−	0.136985i
$76$		0			0
$77$	−1.15291	+	0.526518i	−0.131387	+	0.0600023i
$78$		0			0
$79$	2.74726	+	1.76556i	0.309091	+	0.198641i	0.685985	−	0.727616i	$-0.259372\pi$
$79$	2.74726	+	1.76556i	0.309091	+	0.198641i	−0.376894	+	0.926256i	$0.623008\pi$
$80$		0			0
$81$	1.59969	−	11.1261i	0.177743	−	1.23623i
$82$		0			0
$83$	−4.93001	+	4.27188i	−0.541139	+	0.468900i	−0.882023	−	0.471206i	$-0.843819\pi$
$83$	−4.93001	+	4.27188i	−0.541139	+	0.468900i	0.340884	+	0.940105i	$0.389274\pi$
$84$		0			0
$85$	5.47000	+	8.51149i	0.593305	+	0.923201i
$86$		0			0
$87$	1.05984	+	0.918357i	0.113627	+	0.0984583i
$88$		0			0
$89$	−1.81651	−	0.829570i	−0.192549	−	0.0879343i	0.316807	−	0.948490i	$-0.397389\pi$
$89$	−1.81651	−	0.829570i	−0.192549	−	0.0879343i	−0.509356	+	0.860556i	$0.670116\pi$
$90$		0			0
$91$			0.241511i			0.0253172i
$92$		0			0
$93$		−	16.6217i		−	1.72358i
$94$		0			0
$95$	−2.69313	−	1.22991i	−0.276310	−	0.126186i
$96$		0			0
$97$	11.8432	+	10.2622i	1.20249	+	1.04197i	0.998007	+	0.0630964i	$0.0200976\pi$
$97$	11.8432	+	10.2622i	1.20249	+	1.04197i	0.204485	+	0.978870i	$0.434448\pi$
$98$		0			0
$99$	−4.14388	−	6.44800i	−0.416475	−	0.648048i
$100$		0			0
$101$	−14.2148	+	12.3172i	−1.41442	+	1.22561i	−0.476312	+	0.879276i	$0.658027\pi$
$101$	−14.2148	+	12.3172i	−1.41442	+	1.22561i	−0.938113	+	0.346330i	$0.887428\pi$
$102$		0			0
$103$	−1.72699	+	12.0115i	−0.170165	+	1.18353i	0.708367	+	0.705844i	$0.249432\pi$
$103$	−1.72699	+	12.0115i	−0.170165	+	1.18353i	−0.878533	+	0.477682i	$0.841477\pi$
$104$		0			0
$105$	−1.08363	−	0.696407i	−0.105751	−	0.0679623i
$106$		0			0
$107$	1.19686	−	0.546588i	0.115705	−	0.0528407i	−0.356722	−	0.934211i	$-0.616106\pi$
$107$	1.19686	−	0.546588i	0.115705	−	0.0528407i	0.472426	+	0.881370i	$0.343378\pi$
$108$		0			0
$109$	12.1967	+	3.58129i	1.16824	+	0.343025i	0.807628	−	0.589692i	$-0.200751\pi$
$109$	12.1967	+	3.58129i	1.16824	+	0.343025i	0.360608	+	0.932717i	$0.382569\pi$
$110$		0			0
$111$	20.7501	−	6.09278i	1.96951	−	0.578301i
$112$		0			0
$113$	−0.899099	+	0.129271i	−0.0845801	+	0.0121608i	−0.184475	−	0.982837i	$-0.559058\pi$
$113$	−0.899099	+	0.129271i	−0.0845801	+	0.0121608i	0.0998948	+	0.994998i	$0.468149\pi$
$114$		0			0
$115$	6.27699	+	11.0344i	0.585333	+	1.02896i
$116$		0			0
$117$	−1.44564	+	0.207852i	−0.133650	+	0.0192159i
$118$		0			0
$119$	0.249745	+	0.850552i	0.0228940	+	0.0779700i
$120$		0			0
$121$	18.1018	+	5.31518i	1.64562	+	0.483198i
$122$		0			0
$123$	3.96816	+	8.68907i	0.357797	+	0.783467i
$124$		0			0
$125$	−6.66524	−	4.28349i	−0.596158	−	0.383127i
$126$		0			0
$127$	−13.5729	−	1.95148i	−1.20440	−	0.173166i	−0.489252	−	0.872142i	$-0.662730\pi$
$127$	−13.5729	−	1.95148i	−1.20440	−	0.173166i	−0.715145	+	0.698976i	$0.753639\pi$
$128$		0			0
$129$	−11.2653	+	9.76140i	−0.991850	+	0.859443i
$130$		0			0
$131$	−11.6133	+	7.46340i	−1.01466	+	0.652080i	−0.938594	−	0.345023i	$-0.887871\pi$
$131$	−11.6133	+	7.46340i	−1.01466	+	0.652080i	−0.0760626	+	0.997103i	$0.524235\pi$
$132$		0			0
$133$	−0.196042	−	0.169872i	−0.0169990	−	0.0147298i
$134$		0			0
$135$	−3.68578	+	8.07074i	−0.317222	+	0.694619i
$136$		0			0
$137$			4.91402i			0.419833i	0.977719	+	0.209916i	$0.0673192\pi$
$137$			4.91402i			0.419833i	−0.977719	+	0.209916i	$0.932681\pi$
$138$		0			0
$139$	6.93551			0.588262			0.294131	−	0.955765i	$-0.404970\pi$
$139$	6.93551			0.588262			0.294131	+	0.955765i	$0.404970\pi$
$140$		0			0
$141$	−6.72848	−	3.07279i	−0.566640	−	0.258776i
$142$		0			0
$143$	3.72677	−	4.30092i	0.311648	−	0.359661i
$144$		0			0
$145$	−0.956495	−	1.48833i	−0.0794326	−	0.123599i
$146$		0			0
$147$	9.54438	+	11.0148i	0.787207	+	0.908485i
$148$		0			0
$149$	2.12037	−	14.7475i	0.173707	−	1.20816i	−0.697259	−	0.716819i	$-0.745597\pi$
$149$	2.12037	−	14.7475i	0.173707	−	1.20816i	0.870966	−	0.491343i	$-0.163494\pi$
$150$		0			0
$151$	−1.26372	+	1.96638i	−0.102840	+	0.160022i	−0.888860	−	0.458179i	$-0.848502\pi$
$151$	−1.26372	+	1.96638i	−0.102840	+	0.160022i	0.786020	+	0.618201i	$0.212138\pi$
$152$		0			0
$153$	−4.87632	+	2.22694i	−0.394227	+	0.180037i
$154$		0			0
$155$	−5.90775	+	20.1199i	−0.474522	+	1.61607i
$156$		0			0
$157$	−4.29660	+	1.26160i	−0.342906	+	0.100686i	−0.448651	−	0.893707i	$-0.648095\pi$
$157$	−4.29660	+	1.26160i	−0.342906	+	0.100686i	0.105745	+	0.994393i	$0.466277\pi$
$158$		0			0
$159$	−1.58263	−	11.0075i	−0.125511	−	0.872948i
$160$		0			0
$161$	0.255311	+	1.08256i	0.0201213	+	0.0853177i
$162$		0			0
$163$	−2.26816	−	15.7754i	−0.177656	−	1.23562i	−0.862168	−	0.506622i	$-0.830894\pi$
$163$	−2.26816	−	15.7754i	−0.177656	−	1.23562i	0.684513	−	0.729001i	$-0.260015\pi$
$164$		0			0
$165$	8.55142	+	29.1235i	0.665727	+	2.26726i
$166$		0			0
$167$	5.12618	−	17.4582i	0.396676	−	1.35095i	−0.483100	−	0.875565i	$-0.660489\pi$
$167$	5.12618	−	17.4582i	0.396676	−	1.35095i	0.879776	−	0.475389i	$-0.157693\pi$
$168$		0			0
$169$	4.94992	+	10.8388i	0.380763	+	0.833755i
$170$		0			0
$171$	0.848103	−	1.31967i	0.0648560	−	0.100918i
$172$		0			0
$173$	11.6415	+	1.67379i	0.885086	+	0.127256i	0.569842	−	0.821754i	$-0.307005\pi$
$173$	11.6415	+	1.67379i	0.885086	+	0.127256i	0.315244	+	0.949011i	$0.397914\pi$
$174$		0			0
$175$	0.304794	+	0.351752i	0.0230403	+	0.0265899i
$176$		0			0
$177$	−13.6807	+	8.79207i	−1.02831	+	0.660852i
$178$		0			0
$179$	−9.49210	+	10.9545i	−0.709473	+	0.818775i	−0.990000	−	0.141071i	$-0.954945\pi$
$179$	−9.49210	+	10.9545i	−0.709473	+	0.818775i	0.280527	+	0.959846i	$0.409491\pi$
$180$		0			0
$181$	2.26043	−	4.94966i	0.168017	−	0.367905i	−0.806829	−	0.590785i	$-0.798818\pi$
$181$	2.26043	−	4.94966i	0.168017	−	0.367905i	0.974846	+	0.222879i	$0.0715456\pi$
$182$		0			0
$183$	−19.3768			−1.43237
$184$		0			0
$185$	−27.2828			−2.00587
$186$		0			0
$187$	8.67737	−	19.0008i	0.634552	−	1.38948i
$188$		0			0
$189$	−0.509069	+	0.587497i	−0.0370293	+	0.0427341i
$190$		0			0
$191$	3.09897	−	1.99159i	0.224234	−	0.144106i	−0.423701	−	0.905802i	$-0.639269\pi$
$191$	3.09897	−	1.99159i	0.224234	−	0.144106i	0.647935	+	0.761696i	$0.275633\pi$
$192$		0			0
$193$	−8.97482	−	10.3575i	−0.646022	−	0.745549i	0.334406	−	0.942429i	$-0.391464\pi$
$193$	−8.97482	−	10.3575i	−0.646022	−	0.745549i	−0.980427	+	0.196881i	$0.936919\pi$
$194$		0			0
$195$	5.72485	+	0.823109i	0.409965	+	0.0589440i
$196$		0			0
$197$	−11.0568	+	17.2047i	−0.787763	+	1.22578i	0.182375	+	0.983229i	$0.441621\pi$
$197$	−11.0568	+	17.2047i	−0.787763	+	1.22578i	−0.970138	+	0.242554i	$0.922015\pi$
$198$		0			0
$199$	−3.92613	−	8.59702i	−0.278316	−	0.609426i	0.717919	−	0.696127i	$-0.245095\pi$
$199$	−3.92613	−	8.59702i	−0.278316	−	0.609426i	−0.996234	+	0.0867006i	$0.972368\pi$
$200$		0			0
$201$	8.68790	−	29.5883i	0.612797	−	2.08699i
$202$		0			0
$203$	−0.0436708	−	0.148729i	−0.00306509	−	0.0104387i
$204$		0			0
$205$	−1.71502	−	11.9282i	−0.119782	−	0.833102i
$206$		0			0
$207$	−6.26029	+	2.45993i	−0.435120	+	0.170977i
$208$		0			0
$209$	0.869900	+	6.05029i	0.0601723	+	0.418507i
$210$		0			0
$211$	−16.4899	+	4.84187i	−1.13521	+	0.333328i	−0.794754	−	0.606932i	$-0.792400\pi$
$211$	−16.4899	+	4.84187i	−1.13521	+	0.333328i	−0.340458	+	0.940260i	$0.610582\pi$
$212$		0			0
$213$	−3.68646	+	12.5549i	−0.252592	+	0.860251i
$214$		0			0
$215$	17.1057	−	7.81189i	1.16660	−	0.532767i
$216$		0			0
$217$	−0.993286	+	1.54558i	−0.0674286	+	0.104921i
$218$		0			0
$219$	−2.35810	+	16.4009i	−0.159345	+	1.10827i
$220$		0			0
$221$	−2.60652	−	3.00808i	−0.175333	−	0.202346i
$222$		0			0
$223$	−4.27051	−	6.64504i	−0.285974	−	0.444985i	0.668311	−	0.743882i	$-0.267018\pi$
$223$	−4.27051	−	6.64504i	−0.285974	−	0.444985i	−0.954285	+	0.298897i	$0.903381\pi$
$224$		0			0
$225$	−1.84321	+	2.12718i	−0.122881	+	0.141812i
$226$		0			0
$227$	3.21856	+	1.46987i	0.213623	+	0.0975584i	0.519353	−	0.854560i	$-0.326173\pi$
$227$	3.21856	+	1.46987i	0.213623	+	0.0975584i	−0.305730	+	0.952118i	$0.598900\pi$
$228$		0			0
$229$	−24.4621			−1.61650			−0.808251	−	0.588838i	$-0.799586\pi$
$229$	−24.4621			−1.61650			−0.808251	+	0.588838i	$0.799586\pi$
$230$		0			0
$231$			2.65939i			0.174975i
$232$		0			0
$233$	5.84924	−	12.8081i	0.383197	−	0.839083i	−0.615505	−	0.788133i	$-0.711048\pi$
$233$	5.84924	−	12.8081i	0.383197	−	0.839083i	0.998701	−	0.0509502i	$-0.0162250\pi$
$234$		0			0
$235$	7.05245	+	6.11098i	0.460051	+	0.398636i
$236$		0			0
$237$	5.76435	−	3.70452i	0.374435	−	0.240635i
$238$		0			0
$239$	−20.4667	+	17.7345i	−1.32388	+	1.14715i	−0.345945	+	0.938255i	$0.612442\pi$
$239$	−20.4667	+	17.7345i	−1.32388	+	1.14715i	−0.977938	+	0.208896i	$0.933013\pi$
$240$		0			0
$241$	−3.17391	−	0.456339i	−0.204449	−	0.0293954i	0.0393292	−	0.999226i	$-0.487478\pi$
$241$	−3.17391	−	0.456339i	−0.204449	−	0.0293954i	−0.243779	+	0.969831i	$0.578387\pi$
$242$		0			0
$243$	−11.3817	−	7.31457i	−0.730135	−	0.469230i
$244$		0			0
$245$	−7.63821	−	16.7254i	−0.487988	−	1.06854i
$246$		0			0
$247$	1.11755	+	0.328142i	0.0711080	+	0.0208792i
$248$		0			0
$249$	3.85618	+	13.1330i	0.244376	+	0.832267i
$250$		0			0
$251$	−13.0955	+	1.88286i	−0.826584	+	0.118845i	−0.542607	−	0.839986i	$-0.682563\pi$
$251$	−13.0955	+	1.88286i	−0.826584	+	0.118845i	−0.283976	+	0.958831i	$0.591654\pi$
$252$		0			0
$253$	12.1584	−	23.2184i	0.764391	−	1.45973i
$254$		0			0
$255$	21.0129	−	3.02120i	1.31588	−	0.189195i
$256$		0			0
$257$	−19.3658	+	5.68632i	−1.20801	+	0.354703i	−0.822909	−	0.568173i	$-0.807650\pi$
$257$	−19.3658	+	5.68632i	−1.20801	+	0.354703i	−0.385097	+	0.922876i	$0.625832\pi$
$258$		0			0
$259$	−2.29357	−	0.673452i	−0.142515	−	0.0418463i
$260$		0			0
$261$	0.852682	−	0.389407i	0.0527797	−	0.0241037i
$262$		0			0
$263$	5.34016	+	3.43191i	0.329288	+	0.211621i	0.694830	−	0.719174i	$-0.255480\pi$
$263$	5.34016	+	3.43191i	0.329288	+	0.211621i	−0.365541	+	0.930795i	$0.619116\pi$
$264$		0			0
$265$	−1.99660	+	13.8867i	−0.122650	+	0.853051i
$266$		0			0
$267$	−3.16665	+	2.74391i	−0.193796	+	0.167925i
$268$		0			0
$269$	−15.4290	−	24.0080i	−0.940723	−	1.46379i	−0.885132	−	0.465340i	$-0.845932\pi$
$269$	−15.4290	−	24.0080i	−0.940723	−	1.46379i	−0.0555912	−	0.998454i	$-0.517704\pi$
$270$		0			0
$271$	2.54079	+	2.20161i	0.154342	+	0.133738i	0.728609	−	0.684930i	$-0.240167\pi$
$271$	2.54079	+	2.20161i	0.154342	+	0.133738i	−0.574267	+	0.818668i	$0.694713\pi$
$272$		0			0
$273$	0.460949	+	0.210508i	0.0278979	+	0.0127406i
$274$		0			0
$275$		−	10.9674i		−	0.661361i
$276$		0			0
$277$			26.1434i			1.57080i	0.618986	+	0.785402i	$0.287544\pi$
$277$			26.1434i			1.57080i	−0.618986	+	0.785402i	$0.712456\pi$
$278$		0			0
$279$	−10.1064	−	4.61546i	−0.605057	−	0.276320i
$280$		0			0
$281$	−14.8385	−	12.8576i	−0.885189	−	0.767021i	0.0882184	−	0.996101i	$-0.471883\pi$
$281$	−14.8385	−	12.8576i	−0.885189	−	0.767021i	−0.973407	+	0.229080i	$0.926428\pi$
$282$		0			0
$283$	−5.82943	−	9.07077i	−0.346524	−	0.539201i	0.623621	−	0.781726i	$-0.285661\pi$
$283$	−5.82943	−	9.07077i	−0.346524	−	0.539201i	−0.970145	+	0.242525i	$0.922024\pi$
$284$		0			0
$285$	−4.69484	+	4.06810i	−0.278098	+	0.240973i
$286$		0			0
$287$	0.150262	−	1.04509i	0.00886968	−	0.0616900i
$288$		0			0
$289$	2.01104	+	1.29242i	0.118297	+	0.0760247i
$290$		0			0
$291$	29.9093	−	13.6591i	1.75332	−	0.800713i
$292$		0			0
$293$	10.4435	+	3.06650i	0.610118	+	0.179147i	0.572173	−	0.820133i	$-0.306101\pi$
$293$	10.4435	+	3.06650i	0.610118	+	0.179147i	0.0379450	+	0.999280i	$0.487919\pi$
$294$		0			0
$295$	19.6850	−	5.78003i	1.14610	−	0.336526i
$296$		0			0
$297$	18.1314	−	2.60690i	1.05209	−	0.151268i
$298$		0			0
$299$	−3.06200	−	3.94529i	−0.177080	−	0.228162i
$300$		0			0
$301$	1.63084	−	0.234479i	0.0940000	−	0.0135152i
$302$		0			0
$303$	11.1186	+	37.8665i	0.638747	+	2.17537i
$304$		0			0
$305$	23.4549	+	6.88699i	1.34303	+	0.394348i
$306$		0			0
$307$	2.54247	+	5.56723i	0.145106	+	0.317739i	0.968204	−	0.250161i	$-0.0804835\pi$
$307$	2.54247	+	5.56723i	0.145106	+	0.317739i	−0.823098	+	0.567900i	$0.807756\pi$
$308$		0			0
$309$	21.4199	+	13.7657i	1.21853	+	0.783105i
$310$		0			0
$311$	16.3351	+	2.34863i	0.926279	+	0.133179i	0.588914	−	0.808195i	$-0.299555\pi$
$311$	16.3351	+	2.34863i	0.926279	+	0.133179i	0.337364	+	0.941374i	$0.390465\pi$
$312$		0			0
$313$	17.6131	−	15.2618i	0.995552	−	0.862650i	0.00502732	−	0.999987i	$-0.498400\pi$
$313$	17.6131	−	15.2618i	0.995552	−	0.862650i	0.990524	+	0.137337i	$0.0438543\pi$
$314$		0			0
$315$	−0.724335	+	0.465502i	−0.0408117	+	0.0262281i
$316$		0			0
$317$	1.99082	+	1.72506i	0.111816	+	0.0968888i	0.708974	−	0.705234i	$-0.249158\pi$
$317$	1.99082	+	1.72506i	0.111816	+	0.0968888i	−0.597159	+	0.802123i	$0.703704\pi$
$318$		0			0
$319$	−1.51734	+	3.32251i	−0.0849548	+	0.186025i
$320$		0			0
$321$		−	2.76076i		−	0.154091i
$322$		0			0
$323$	4.27511			0.237874
$324$		0			0
$325$	−1.90098	−	0.868147i	−0.105447	−	0.0481561i
$326$		0			0
$327$	17.4663	−	20.1572i	0.965890	−	1.11470i
$328$		0			0
$329$	0.442029	+	0.687811i	0.0243699	+	0.0379202i
$330$		0			0
$331$	−0.211824	−	0.244458i	−0.0116429	−	0.0134366i	0.749898	−	0.661553i	$-0.230102\pi$
$331$	−0.211824	−	0.244458i	−0.0116429	−	0.0134366i	−0.761541	+	0.648117i	$0.775557\pi$
$332$		0			0
$333$	2.05725	−	14.3085i	0.112737	−	0.784100i
$334$		0			0
$335$	−21.0328	+	32.7277i	−1.14915	+	1.78810i
$336$		0			0
$337$	4.53017	−	2.06886i	0.246774	−	0.112698i	−0.288188	−	0.957574i	$-0.593053\pi$
$337$	4.53017	−	2.06886i	0.246774	−	0.112698i	0.534963	+	0.844876i	$0.320326\pi$
$338$		0			0
$339$	−0.536955	+	1.82870i	−0.0291634	+	0.0993215i
$340$		0			0
$341$	41.5388	−	12.1969i	2.24945	−	0.660499i
$342$		0			0
$343$	−0.460308	−	3.20151i	−0.0248543	−	0.172865i
$344$		0			0
$345$	26.5315	−	2.36242i	1.42841	−	0.127188i
$346$		0			0
$347$	−2.97848	−	20.7158i	−0.159893	−	1.11208i	−0.898827	−	0.438303i	$-0.855580\pi$
$347$	−2.97848	−	20.7158i	−0.159893	−	1.11208i	0.738934	−	0.673778i	$-0.235329\pi$
$348$		0			0
$349$	5.81078	+	19.7897i	0.311044	+	1.05932i	0.955577	+	0.294742i	$0.0952337\pi$
$349$	5.81078	+	19.7897i	0.311044	+	1.05932i	−0.644533	+	0.764577i	$0.722948\pi$
$350$		0			0
$351$	0.983372	−	3.34906i	0.0524885	−	0.178759i
$352$		0			0
$353$	−3.45440	−	7.56407i	−0.183859	−	0.402595i	0.795150	−	0.606413i	$-0.207392\pi$
$353$	−3.45440	−	7.56407i	−0.183859	−	0.402595i	−0.979009	+	0.203818i	$0.934665\pi$
$354$		0			0
$355$	8.92468	−	13.8871i	0.473673	−	0.737050i
$356$		0			0
$357$	1.84105	+	0.264704i	0.0974389	+	0.0140096i
$358$		0			0
$359$	−7.34108	−	8.47206i	−0.387448	−	0.447138i	0.528200	−	0.849120i	$-0.322867\pi$
$359$	−7.34108	−	8.47206i	−0.387448	−	0.447138i	−0.915648	+	0.401982i	$0.868322\pi$
$360$		0			0
$361$	14.9314	−	9.59583i	0.785863	−	0.505044i
$362$		0			0
$363$	25.9227	−	29.9164i	1.36059	−	1.57020i
$364$		0			0
$365$	8.68369	−	19.0146i	0.454525	−	0.995272i
$366$		0			0
$367$	−26.8593			−1.40204			−0.701022	−	0.713140i	$-0.747273\pi$
$367$	−26.8593			−1.40204			−0.701022	+	0.713140i	$0.747273\pi$
$368$		0			0
$369$	6.38507			0.332394
$370$		0			0
$371$	−0.510627	+	1.11812i	−0.0265104	+	0.0580497i
$372$		0			0
$373$	−4.17335	+	4.81631i	−0.216088	+	0.249379i	−0.853436	−	0.521197i	$-0.825486\pi$
$373$	−4.17335	+	4.81631i	−0.216088	+	0.249379i	0.637348	+	0.770576i	$0.280031\pi$
$374$		0			0
$375$	−13.9851	+	8.98770i	−0.722189	+	0.464123i
$376$		0			0
$377$	0.455781	+	0.525999i	0.0234739	+	0.0270903i
$378$		0			0
$379$	1.69018	+	0.243012i	0.0868189	+	0.0124827i	0.185587	−	0.982628i	$-0.440581\pi$
$379$	1.69018	+	0.243012i	0.0868189	+	0.0124827i	−0.0987685	+	0.995110i	$0.531490\pi$
$380$		0			0
$381$	−15.5552	+	24.2043i	−0.796914	+	1.24002i
$382$		0			0
$383$	−7.38537	−	16.1717i	−0.377375	−	0.826335i	−0.999072	−	0.0430776i	$-0.986284\pi$
$383$	−7.38537	−	16.1717i	−0.377375	−	0.826335i	0.621697	−	0.783258i	$-0.286444\pi$
$384$		0			0
$385$	0.945212	−	3.21910i	0.0481725	−	0.164060i
$386$		0			0
$387$	2.80710	+	9.56012i	0.142693	+	0.485968i
$388$		0			0
$389$	1.22741	+	8.53683i	0.0622322	+	0.432834i	0.996989	+	0.0775456i	$0.0247083\pi$
$389$	1.22741	+	8.53683i	0.0622322	+	0.432834i	−0.934757	+	0.355289i	$0.884383\pi$
$390$		0			0
$391$	−14.8635	−	10.7281i	−0.751682	−	0.542545i
$392$		0			0
$393$	4.12220	+	28.6705i	0.207937	+	1.44624i
$394$		0			0
$395$	−8.29423	+	2.43541i	−0.417328	+	0.122539i
$396$		0			0
$397$	4.18304	−	14.2461i	0.209941	−	0.714993i	−0.785436	−	0.618943i	$-0.787561\pi$
$397$	4.18304	−	14.2461i	0.209941	−	0.714993i	0.995377	−	0.0960494i	$-0.0306207\pi$
$398$		0			0
$399$	−0.495095	+	0.226102i	−0.0247858	+	0.0113193i
$400$		0			0
$401$	−3.31858	+	5.16381i	−0.165722	+	0.257868i	−0.914175	−	0.405319i	$-0.867160\pi$
$401$	−3.31858	+	5.16381i	−0.165722	+	0.257868i	0.748453	+	0.663187i	$0.230797\pi$
$402$		0			0
$403$	1.17400	−	8.16536i	0.0584811	−	0.406745i
$404$		0			0
$405$	19.4848	+	22.4867i	0.968208	+	1.11737i
$406$		0			0
$407$	30.4527	+	47.3853i	1.50948	+	2.34880i
$408$		0			0
$409$	0.709016	−	0.818249i	0.0350586	−	0.0404598i	−0.737949	−	0.674856i	$-0.764206\pi$
$409$	0.709016	−	0.818249i	0.0350586	−	0.0404598i	0.773008	+	0.634396i	$0.218751\pi$
$410$		0			0
$411$	9.37893	+	4.28321i	0.462628	+	0.211275i
$412$		0			0
$413$	1.79752			0.0884501
$414$		0			0
$415$		−	17.2676i		−	0.847633i
$416$		0			0
$417$	6.04521	−	13.2372i	0.296035	−	0.648226i
$418$		0			0
$419$	4.92875	+	4.27079i	0.240785	+	0.208642i	0.766891	−	0.641778i	$-0.221803\pi$
$419$	4.92875	+	4.27079i	0.240785	+	0.208642i	−0.526105	+	0.850419i	$0.676348\pi$
$420$		0			0
$421$	−25.0910	+	16.1250i	−1.22286	+	0.785884i	−0.982764	−	0.184865i	$-0.940815\pi$
$421$	−25.0910	+	16.1250i	−1.22286	+	0.785884i	−0.240096	+	0.970749i	$0.577179\pi$
$422$		0			0
$423$	−3.73669	+	3.23786i	−0.181684	+	0.157430i
$424$		0			0
$425$	−7.59260	−	1.09165i	−0.368295	−	0.0529528i
$426$		0			0
$427$	1.80177	+	1.15793i	0.0871938	+	0.0560360i
$428$		0			0
$429$	−4.96040	−	10.8618i	−0.239490	−	0.524411i
$430$		0			0
$431$	−10.5655	−	3.10231i	−0.508923	−	0.149433i	0.0171830	−	0.999852i	$-0.494530\pi$
$431$	−10.5655	−	3.10231i	−0.508923	−	0.149433i	−0.526106	+	0.850419i	$0.676348\pi$
$432$		0			0
$433$	−4.77674	−	16.2681i	−0.229555	−	0.781793i	−0.991035	−	0.133604i	$-0.957345\pi$
$433$	−4.77674	−	16.2681i	−0.229555	−	0.781793i	0.761480	−	0.648189i	$-0.224473\pi$
$434$		0			0
$435$	−3.67436	+	0.528293i	−0.176172	+	0.0253297i
$436$		0			0
$437$	5.35625	+	0.289475i	0.256224	+	0.0138475i
$438$		0			0
$439$	25.6145	−	3.68281i	1.22251	−	0.175771i	0.499321	−	0.866417i	$-0.333583\pi$
$439$	25.6145	−	3.68281i	1.22251	−	0.175771i	0.723193	+	0.690646i	$0.242674\pi$
$440$		0			0
$441$	9.34758	−	2.74470i	0.445123	−	0.130700i
$442$		0			0
$443$	−5.09227	−	1.49523i	−0.241941	−	0.0710404i	0.158514	−	0.987357i	$-0.449330\pi$
$443$	−5.09227	−	1.49523i	−0.241941	−	0.0710404i	−0.400455	+	0.916316i	$0.631148\pi$
$444$		0			0
$445$	4.80837	−	2.19591i	0.227939	−	0.104096i
$446$		0			0
$447$	−26.2990	−	16.9013i	−1.24390	−	0.799406i
$448$		0			0
$449$	2.91460	−	20.2715i	0.137549	−	0.956671i	−0.797794	−	0.602930i	$-0.794000\pi$
$449$	2.91460	−	20.2715i	0.137549	−	0.956671i	0.935343	−	0.353742i	$-0.115091\pi$
$450$		0			0
$451$	−18.8028	+	16.2928i	−0.885392	+	0.767196i
$452$		0			0
$453$	2.65155	+	4.12590i	0.124581	+	0.193852i
$454$		0			0
$455$	−0.483144	−	0.418646i	−0.0226501	−	0.0196264i
$456$		0			0
$457$	−1.68945	−	0.771547i	−0.0790292	−	0.0360914i	0.375508	−	0.926819i	$-0.377468\pi$
$457$	−1.68945	−	0.771547i	−0.0790292	−	0.0360914i	−0.454537	+	0.890728i	$0.650195\pi$
$458$		0			0
$459$		−	12.8116i		−	0.597994i
$460$		0			0
$461$		−	4.59846i		−	0.214172i	−0.994250	−	0.107086i	$-0.965848\pi$
$461$		−	4.59846i		−	0.214172i	0.994250	−	0.107086i	$-0.0341520\pi$
$462$		0			0
$463$	12.2671	+	5.60219i	0.570100	+	0.260356i	0.679541	−	0.733637i	$-0.262179\pi$
$463$	12.2671	+	5.60219i	0.570100	+	0.260356i	−0.109441	+	0.993993i	$0.534906\pi$
$464$		0			0
$465$	33.2517	+	28.8128i	1.54201	+	1.33616i
$466$		0			0
$467$	−3.87387	−	6.02785i	−0.179261	−	0.278936i	0.739981	−	0.672627i	$-0.234834\pi$
$467$	−3.87387	−	6.02785i	−0.179261	−	0.278936i	−0.919243	+	0.393691i	$0.871198\pi$
$468$		0			0
$469$	−2.57600	+	2.23212i	−0.118949	+	0.103070i
$470$		0			0
$471$	−1.33716	+	9.30017i	−0.0616132	+	0.428529i
$472$		0			0
$473$	−32.6609	−	20.9899i	−1.50175	−	0.965116i
$474$		0			0
$475$	2.04180	−	0.932457i	0.0936840	−	0.0427841i
$476$		0			0
$477$	−7.13231	−	2.09424i	−0.326566	−	0.0958885i
$478$		0			0
$479$	3.57227	−	1.04891i	0.163221	−	0.0479260i	−0.199101	−	0.979979i	$-0.563802\pi$
$479$	3.57227	−	1.04891i	0.163221	−	0.0479260i	0.362322	+	0.932053i	$0.381984\pi$
$480$		0			0
$481$	10.6238	−	1.52747i	0.484403	−	0.0696466i
$482$		0			0
$483$	2.28872	+	0.456306i	0.104140	+	0.0207626i
$484$		0			0
$485$	−41.0591	+	5.90340i	−1.86440	+	0.268060i
$486$		0			0
$487$	10.0603	+	34.2621i	0.455874	+	1.55256i	0.791863	+	0.610699i	$0.209111\pi$
$487$	10.0603	+	34.2621i	0.455874	+	1.55256i	−0.335989	+	0.941866i	$0.609070\pi$
$488$		0			0
$489$	−32.0860	−	9.42129i	−1.45098	−	0.426046i
$490$		0			0
$491$	−8.30345	−	18.1820i	−0.374729	−	0.820543i	−0.999219	−	0.0395097i	$-0.987420\pi$
$491$	−8.30345	−	18.1820i	−0.374729	−	0.820543i	0.624490	−	0.781033i	$-0.285307\pi$
$492$		0			0
$493$	2.14910	+	1.38114i	0.0967905	+	0.0622035i
$494$		0			0
$495$	20.0824	+	2.88742i	0.902639	+	0.129780i
$496$		0			0
$497$	1.09306	−	0.947138i	0.0490302	−	0.0424849i
$498$		0			0
$499$	19.4119	−	12.4753i	0.868998	−	0.558471i	−0.0284483	−	0.999595i	$-0.509057\pi$
$499$	19.4119	−	12.4753i	0.868998	−	0.558471i	0.897446	+	0.441124i	$0.145420\pi$
$500$		0			0
$501$	−28.8526	−	25.0010i	−1.28904	−	1.11696i
$502$		0			0
$503$	13.6583	−	29.9074i	0.608991	−	1.33351i	−0.314270	−	0.949334i	$-0.601760\pi$
$503$	13.6583	−	29.9074i	0.608991	−	1.33351i	0.923262	−	0.384172i	$-0.125513\pi$
$504$		0			0
$505$		−	49.7879i		−	2.21553i
$506$		0			0
$507$	25.0015			1.11036
$508$		0			0
$509$	12.5151	+	5.71544i	0.554720	+	0.253332i	0.672993	−	0.739649i	$-0.265008\pi$
$509$	12.5151	+	5.71544i	0.554720	+	0.253332i	−0.118273	+	0.992981i	$0.537736\pi$
$510$		0			0
$511$	1.19937	−	1.38414i	0.0530568	−	0.0612308i
$512$		0			0
$513$	2.02687	+	3.15387i	0.0894884	+	0.139247i
$514$		0			0
$515$	−21.0354	−	24.2761i	−0.926929	−	1.06973i
$516$		0			0
$517$	2.74182	−	19.0698i	0.120585	−	0.838689i
$518$		0			0
$519$	13.3417	−	20.7601i	0.585636	−	0.911267i
$520$		0			0
$521$	−24.9989	+	11.4166i	−1.09522	+	0.500171i	−0.879314	−	0.476243i	$-0.841998\pi$
$521$	−24.9989	+	11.4166i	−1.09522	+	0.500171i	−0.215908	+	0.976414i	$0.569271\pi$
$522$		0			0
$523$	−3.07855	+	10.4846i	−0.134616	+	0.458459i	−0.999016	−	0.0443449i	$-0.985880\pi$
$523$	−3.07855	+	10.4846i	−0.134616	+	0.458459i	0.864401	+	0.502804i	$0.167698\pi$
$524$		0			0
$525$	0.937024	−	0.275135i	0.0408951	−	0.0120079i
$526$		0			0
$527$	−4.30914	−	29.9707i	−0.187709	−	1.30555i
$528$		0			0
$529$	−17.8960	−	14.4476i	−0.778087	−	0.628157i
$530$		0			0
$531$	1.54700	+	10.7596i	0.0671342	+	0.466928i
$532$		0			0
$533$	1.33564	+	4.54876i	0.0578529	+	0.197029i
$534$		0			0
$535$	−0.981243	+	3.34181i	−0.0424228	+	0.144479i
$536$		0			0
$537$	12.6342	+	27.6649i	0.545204	+	1.19383i
$538$		0			0
$539$	−20.5232	+	31.9348i	−0.883998	+	1.37553i
$540$		0			0
$541$	22.9179	+	3.29509i	0.985316	+	0.141667i	0.616093	−	0.787674i	$-0.288715\pi$
$541$	22.9179	+	3.29509i	0.985316	+	0.141667i	0.369223	+	0.929341i	$0.379624\pi$
$542$		0			0
$543$	−7.47668	−	8.62855i	−0.320855	−	0.370287i
$544$		0			0
$545$	−28.3068	+	18.1917i	−1.21253	+	0.779245i
$546$		0			0
$547$	5.88980	−	6.79719i	0.251830	−	0.290627i	−0.615733	−	0.787955i	$-0.711140\pi$
$547$	5.88980	−	6.79719i	0.251830	−	0.290627i	0.867563	+	0.497328i	$0.165685\pi$
$548$		0			0
$549$	−5.38049	+	11.7816i	−0.229634	+	0.502828i
$550$		0			0
$551$	−0.747554			−0.0318469
$552$		0			0
$553$	−0.757382			−0.0322071
$554$		0			0
$555$	−23.7806	+	52.0722i	−1.00943	+	2.21034i
$556$		0			0
$557$	21.3758	−	24.6690i	0.905722	−	1.04526i	−0.0930477	−	0.995662i	$-0.529661\pi$
$557$	21.3758	−	24.6690i	0.905722	−	1.04526i	0.998769	−	0.0495969i	$-0.0157936\pi$
$558$		0			0
$559$	−6.22349	+	3.99959i	−0.263226	+	0.169165i
$560$		0			0
$561$	−28.7016	−	33.1234i	−1.21178	−	1.39847i
$562$		0			0
$563$	33.0414	+	4.75063i	1.39253	+	0.200215i	0.797417	−	0.603428i	$-0.206199\pi$
$563$	33.0414	+	4.75063i	1.39253	+	0.200215i	0.595111	+	0.803644i	$0.297108\pi$
$564$		0			0
$565$	1.29993	−	2.02273i	0.0546886	−	0.0850971i
$566$		0			0
$567$	1.08295	+	2.37134i	0.0454798	+	0.0995868i
$568$		0			0
$569$	−7.11158	+	24.2198i	−0.298133	+	1.01535i	0.665117	+	0.746739i	$0.268382\pi$
$569$	−7.11158	+	24.2198i	−0.298133	+	1.01535i	−0.963250	+	0.268608i	$0.913436\pi$
$570$		0			0
$571$	7.66226	+	26.0953i	0.320656	+	1.09205i	0.949303	+	0.314362i	$0.101791\pi$
$571$	7.66226	+	26.0953i	0.320656	+	1.09205i	−0.628647	+	0.777690i	$0.716391\pi$
$572$		0			0
$573$	−1.10000	−	7.65065i	−0.0459531	−	0.319611i
$574$		0			0
$575$	−9.43878	−	1.88183i	−0.393624	−	0.0784776i
$576$		0			0
$577$	0.684268	+	4.75919i	0.0284864	+	0.198127i	0.999095	−	0.0425366i	$-0.0135439\pi$
$577$	0.684268	+	4.75919i	0.0284864	+	0.198127i	−0.970608	+	0.240664i	$0.922635\pi$
$578$		0			0
$579$	−27.5911	+	8.10148i	−1.14665	+	0.336686i
$580$		0			0
$581$	0.426235	−	1.45162i	0.0176832	−	0.0602235i
$582$		0			0
$583$	26.3472	−	12.0323i	1.09119	−	0.498329i
$584$		0			0
$585$	2.09014	−	3.25231i	0.0864165	−	0.134467i
$586$		0			0
$587$	−0.477970	+	3.32436i	−0.0197279	+	0.137211i	−0.997305	−	0.0733671i	$-0.976626\pi$
$587$	−0.477970	+	3.32436i	−0.0197279	+	0.137211i	0.977577	+	0.210578i	$0.0675346\pi$
$588$		0			0
$589$	5.80234	+	6.69625i	0.239081	+	0.275914i
$590$		0			0
$591$	23.1995	+	36.0992i	0.954301	+	1.48492i
$592$		0			0
$593$	−8.82091	+	10.1799i	−0.362231	+	0.418037i	−0.907386	−	0.420298i	$-0.861925\pi$
$593$	−8.82091	+	10.1799i	−0.362231	+	0.418037i	0.545155	+	0.838335i	$0.316471\pi$
$594$		0			0
$595$	−2.13445	−	0.974772i	−0.0875040	−	0.0399617i
$596$		0			0
$597$	−19.8305			−0.811607
$598$		0			0
$599$		−	0.00414983i		−	0.000169558i	−1.00000		8.47788e-5i	$-0.999973\pi$
$599$		−	0.00414983i		−	0.000169558i	1.00000		8.47788e-5i	$-2.69859e-5\pi$
$600$		0			0
$601$	−18.8359	+	41.2449i	−0.768333	+	1.68241i	−0.0380440	+	0.999276i	$0.512113\pi$
$601$	−18.8359	+	41.2449i	−0.768333	+	1.68241i	−0.730289	+	0.683138i	$0.760615\pi$
$602$		0			0
$603$	−15.5781	−	13.4985i	−0.634388	−	0.549701i
$604$		0			0
$605$	−42.0116	+	26.9992i	−1.70802	+	1.09767i
$606$		0			0
$607$	−2.93700	+	2.54492i	−0.119209	+	0.103295i	−0.712425	−	0.701748i	$-0.752403\pi$
$607$	−2.93700	+	2.54492i	−0.119209	+	0.103295i	0.593216	+	0.805043i	$0.297858\pi$
$608$		0			0
$609$	−0.321930	−	0.0462866i	−0.0130453	−	0.00187563i
$610$		0			0
$611$	−3.08832	−	1.98474i	−0.124940	−	0.0802940i
$612$		0			0
$613$	13.6865	+	29.9692i	0.552791	+	1.21044i	0.955466	+	0.295101i	$0.0953534\pi$
$613$	13.6865	+	29.9692i	0.552791	+	1.21044i	−0.402675	+	0.915343i	$0.631919\pi$
$614$		0			0
$615$	−24.2611	−	7.12371i	−0.978303	−	0.287256i
$616$		0			0
$617$	10.9689	+	37.3567i	0.441592	+	1.50392i	0.816766	+	0.576969i	$0.195765\pi$
$617$	10.9689	+	37.3567i	0.441592	+	1.50392i	−0.375175	+	0.926954i	$0.622417\pi$
$618$		0			0
$619$	13.8546	−	1.99199i	0.556863	−	0.0800648i	0.141863	−	0.989886i	$-0.454691\pi$
$619$	13.8546	−	1.99199i	0.556863	−	0.0800648i	0.415000	+	0.909822i	$0.363782\pi$
$620$		0			0
$621$	0.867495	−	16.0515i	0.0348114	−	0.644126i
$622$		0			0
$623$	0.458426	−	0.0659118i	0.0183665	−	0.00264070i
$624$		0			0
$625$	29.7508	−	8.73563i	1.19003	−	0.349425i
$626$		0			0
$627$	12.3059	+	3.61333i	0.491449	+	0.144302i
$628$		0			0
$629$	35.8353	−	16.3654i	1.42885	−	0.652532i
$630$		0			0
$631$	9.28355	+	5.96617i	0.369572	+	0.237510i	0.712223	−	0.701953i	$-0.247688\pi$
$631$	9.28355	+	5.96617i	0.369572	+	0.237510i	−0.342651	+	0.939463i	$0.611325\pi$
$632$		0			0
$633$	−5.13189	+	35.6931i	−0.203974	+	1.41867i
$634$		0			0
$635$	27.4318	−	23.7698i	1.08860	−	0.943275i
$636$		0			0
$637$	3.91067	+	6.08513i	0.154947	+	0.241102i
$638$		0			0
$639$	6.61012	+	5.72770i	0.261492	+	0.226584i
$640$		0			0
$641$	21.7105	+	9.91484i	0.857512	+	0.391612i	0.795129	−	0.606440i	$-0.207403\pi$
$641$	21.7105	+	9.91484i	0.857512	+	0.391612i	0.0623823	+	0.998052i	$0.480130\pi$
$642$		0			0
$643$			28.5391i			1.12547i	0.826636	+	0.562737i	$0.190252\pi$
$643$			28.5391i			1.12547i	−0.826636	+	0.562737i	$0.809748\pi$
$644$		0			0
$645$		−	39.4571i		−	1.55362i
$646$		0			0
$647$	−39.7855	−	18.1694i	−1.56413	−	0.714315i	−0.569914	−	0.821704i	$-0.693023\pi$
$647$	−39.7855	−	18.1694i	−1.56413	−	0.714315i	−0.994217	+	0.107390i	$0.965751\pi$
$648$		0			0
$649$	−32.0109	−	27.7376i	−1.25654	−	1.08880i
$650$		0			0
$651$	2.08413	+	3.24297i	0.0816835	+	0.127102i
$652$		0			0
$653$	−25.7258	+	22.2916i	−1.00673	+	0.872337i	−0.991832	−	0.127552i	$-0.959288\pi$
$653$	−25.7258	+	22.2916i	−1.00673	+	0.872337i	−0.0148983	+	0.999889i	$0.504742\pi$
$654$		0			0
$655$	5.20044	−	36.1698i	0.203198	−	1.41327i
$656$		0			0
$657$	9.31745	+	5.98796i	0.363508	+	0.233613i
$658$		0			0
$659$	−29.4596	+	13.4538i	−1.14758	+	0.524084i	−0.896133	−	0.443786i	$-0.853635\pi$
$659$	−29.4596	+	13.4538i	−1.14758	+	0.524084i	−0.251451	+	0.967870i	$0.580908\pi$
$660$		0			0
$661$	−0.756713	−	0.222191i	−0.0294327	−	0.00864223i	0.266983	−	0.963701i	$-0.413973\pi$
$661$	−0.756713	−	0.222191i	−0.0294327	−	0.00864223i	−0.296416	+	0.955059i	$0.595791\pi$
$662$		0			0
$663$	−8.01317	+	2.35288i	−0.311206	+	0.0913783i
$664$		0			0
$665$	0.679658	−	0.0977201i	0.0263560	−	0.00378942i
$666$		0			0
$667$	2.59907	+	1.87594i	0.100636	+	0.0726367i
$668$		0			0
$669$	−16.4051	+	2.35869i	−0.634257	+	0.0911923i
$670$		0			0
$671$	−14.2186	−	48.4241i	−0.548903	−	1.86939i
$672$		0			0
$673$	−25.9405	−	7.61680i	−0.999931	−	0.293606i	−0.259503	−	0.965742i	$-0.583559\pi$
$673$	−25.9405	−	7.61680i	−0.999931	−	0.293606i	−0.740428	+	0.672136i	$0.765377\pi$
$674$		0			0
$675$	−2.79437	−	6.11882i	−0.107555	−	0.235514i
$676$		0			0
$677$	3.03667	+	1.95155i	0.116709	+	0.0750041i	0.597693	−	0.801725i	$-0.296084\pi$
$677$	3.03667	+	1.95155i	0.116709	+	0.0750041i	−0.480984	+	0.876729i	$0.659721\pi$
$678$		0			0
$679$	−3.59740	−	0.517229i	−0.138056	−	0.0198494i
$680$		0			0
$681$	5.61079	−	4.86178i	0.215006	−	0.186304i
$682$		0			0
$683$	24.1407	−	15.5143i	0.923720	−	0.593639i	0.00998539	−	0.999950i	$-0.496821\pi$
$683$	24.1407	−	15.5143i	0.923720	−	0.593639i	0.913735	+	0.406311i	$0.133185\pi$
$684$		0			0
$685$	−9.83052	−	8.51819i	−0.375605	−	0.325463i
$686$		0			0
$687$	−21.3220	+	46.6886i	−0.813483	+	1.78128i
$688$		0			0
$689$		−	5.51917i		−	0.210264i
$690$		0			0
$691$	−21.0241			−0.799793			−0.399897	−	0.916560i	$-0.630954\pi$
$691$	−21.0241			−0.799793			−0.399897	+	0.916560i	$0.630954\pi$
$692$		0			0
$693$	1.61698	+	0.738452i	0.0614241	+	0.0280515i
$694$		0			0
$695$	−12.0223	+	13.8745i	−0.456033	+	0.526290i
$696$		0			0
$697$	9.40769	+	14.6386i	0.356342	+	0.554478i
$698$		0			0
$699$	−19.3472	−	22.3278i	−0.731777	−	0.844515i
$700$		0			0
$701$	2.56176	−	17.8174i	0.0967562	−	0.672954i	−0.882498	−	0.470317i	$-0.844140\pi$
$701$	2.56176	−	17.8174i	0.0967562	−	0.672954i	0.979254	−	0.202637i	$-0.0649512\pi$
$702$		0			0
$703$	−6.23256	+	9.69806i	−0.235066	+	0.365769i
$704$		0			0
$705$	17.8106	−	8.13382i	0.670786	−	0.306338i
$706$		0			0
$707$	1.22897	−	4.18549i	0.0462202	−	0.157412i
$708$		0			0
$709$	−9.10838	+	2.67446i	−0.342072	+	0.100441i	−0.448256	−	0.893905i	$-0.647955\pi$
$709$	−9.10838	+	2.67446i	−0.342072	+	0.100441i	0.106184	+	0.994346i	$0.466137\pi$
$710$		0			0
$711$	−0.651827	−	4.53356i	−0.0244454	−	0.170022i
$712$		0			0
$713$	−3.36952	−	37.8419i	−0.126189	−	1.41719i
$714$		0			0
$715$	2.14386	+	14.9108i	0.0801756	+	0.557634i
$716$		0			0
$717$	16.0088	+	54.5209i	0.597859	+	2.03612i
$718$		0			0
$719$	3.55001	−	12.0902i	0.132393	−	0.450889i	−0.866435	−	0.499290i	$-0.833594\pi$
$719$	3.55001	−	12.0902i	0.132393	−	0.450889i	0.998828	+	0.0484006i	$0.0154124\pi$
$720$		0			0
$721$	−1.16913	−	2.56004i	−0.0435408	−	0.0953410i
$722$		0			0
$723$	−3.63745	+	5.65998i	−0.135278	+	0.210497i
$724$		0			0
$725$	1.32765	+	0.190888i	0.0493079	+	0.00708940i
$726$		0			0
$727$	32.9604	+	38.0384i	1.22243	+	1.41076i	0.882498	+	0.470317i	$0.155860\pi$
$727$	32.9604	+	38.0384i	1.22243	+	1.41076i	0.339937	+	0.940448i	$0.389594\pi$
$728$		0			0
$729$	4.48706	−	2.88366i	0.166188	−	0.106802i
$730$		0			0
$731$	−17.7819	+	20.5214i	−0.657688	+	0.759012i
$732$		0			0
$733$	−2.21203	+	4.84367i	−0.0817033	+	0.178905i	−0.946075	−	0.323949i	$-0.894989\pi$
$733$	−2.21203	+	4.84367i	−0.0817033	+	0.178905i	0.864371	+	0.502854i	$0.167717\pi$
$734$		0			0
$735$	−38.5798			−1.42304
$736$		0			0
$737$	80.3185			2.95857
$738$		0			0
$739$	8.12862	−	17.7992i	0.299016	−	0.654754i	−0.699170	−	0.714955i	$-0.746447\pi$
$739$	8.12862	−	17.7992i	0.299016	−	0.654754i	0.998186	+	0.0602012i	$0.0191742\pi$
$740$		0			0
$741$	1.60039	−	1.84694i	0.0587917	−	0.0678492i
$742$		0			0
$743$	5.75417	−	3.69798i	0.211100	−	0.135666i	−0.430819	−	0.902439i	$-0.641775\pi$
$743$	5.75417	−	3.69798i	0.211100	−	0.135666i	0.641919	+	0.766773i	$0.278139\pi$
$744$		0			0
$745$	25.8269	+	29.8058i	0.946224	+	1.09200i
$746$		0			0
$747$	9.05599	+	1.30206i	0.331341	+	0.0476397i
$748$		0			0
$749$	−0.164979	+	0.256712i	−0.00602820	+	0.00938006i
$750$		0			0
$751$	22.5353	+	49.3454i	0.822325	+	1.80064i	0.540984	+	0.841033i	$0.318052\pi$
$751$	22.5353	+	49.3454i	0.822325	+	1.80064i	0.281341	+	0.959608i	$0.409221\pi$
$752$		0			0
$753$	−7.82086	+	26.6354i	−0.285008	+	0.970648i
$754$		0			0
$755$	−1.74317	−	5.93669i	−0.0634404	−	0.216058i
$756$		0			0
$757$	−1.90048	−	13.2181i	−0.0690741	−	0.480421i	−0.994769	−	0.102150i	$-0.967428\pi$
$757$	−1.90048	−	13.2181i	−0.0690741	−	0.480421i	0.925695	−	0.378271i	$-0.123481\pi$
$758$		0			0
$759$	−33.7171	−	43.4434i	−1.22385	−	1.57690i
$760$		0			0
$761$	−2.42660	−	16.8774i	−0.0879643	−	0.611805i	−0.985348	−	0.170554i	$-0.945444\pi$
$761$	−2.42660	−	16.8774i	−0.0879643	−	0.611805i	0.897384	−	0.441251i	$-0.145465\pi$
$762$		0			0
$763$	−2.82869	+	0.830579i	−0.102406	+	0.0300690i
$764$		0			0
$765$	3.99784	−	13.6154i	0.144542	−	0.492265i
$766$		0			0
$767$	−7.34162	+	3.35281i	−0.265091	+	0.121063i
$768$		0			0
$769$	−21.8575	+	34.0110i	−0.788203	+	1.22647i	0.181791	+	0.983337i	$0.441811\pi$
$769$	−21.8575	+	34.0110i	−0.788203	+	1.22647i	−0.969994	+	0.243130i	$0.921826\pi$
$770$		0			0
$771$	−6.02691	+	41.9181i	−0.217054	+	1.50964i
$772$		0			0
$773$	−14.2175	−	16.4079i	−0.511368	−	0.590150i	0.440081	−	0.897958i	$-0.354950\pi$
$773$	−14.2175	−	16.4079i	−0.511368	−	0.590150i	−0.951448	+	0.307809i	$0.900404\pi$
$774$		0			0
$775$	−8.59505	−	13.3742i	−0.308743	−	0.480414i
$776$		0			0
$777$	−3.28450	+	3.79051i	−0.117831	+	0.135984i
$778$		0			0
$779$	−4.63183	−	2.11529i	−0.165953	−	0.0757880i
$780$		0			0
$781$	−34.0809			−1.21951
$782$		0			0
$783$			2.24026i			0.0800603i
$784$		0			0
$785$	4.92411	−	10.7823i	0.175749	−	0.384836i
$786$		0			0
$787$	14.8925	+	12.9045i	0.530861	+	0.459994i	0.878573	−	0.477607i	$-0.158496\pi$
$787$	14.8925	+	12.9045i	0.530861	+	0.459994i	−0.347712	+	0.937601i	$0.613041\pi$
$788$		0			0
$789$	11.2048	−	7.20090i	0.398902	−	0.256359i
$790$		0			0
$791$	0.159210	−	0.137956i	0.00566086	−	0.00490516i
$792$		0			0
$793$	−9.51880	−	1.36860i	−0.338023	−	0.0486003i
$794$		0			0
$795$	24.7639	+	15.9148i	0.878284	+	0.564439i
$796$		0			0
$797$	19.5341	+	42.7737i	0.691932	+	1.51512i	0.849486	+	0.527610i	$0.176912\pi$
$797$	19.5341	+	42.7737i	0.691932	+	1.51512i	−0.157554	+	0.987510i	$0.550361\pi$
$798$		0			0
$799$	−12.9288	−	3.79625i	−0.457389	−	0.134302i
$800$		0			0
$801$	0.789073	+	2.68734i	0.0278805	+	0.0949523i
$802$		0			0
$803$	−42.7176	+	6.14186i	−1.50747	+	0.216742i
$804$		0			0
$805$	−2.60823	−	1.36581i	−0.0919281	−	0.0481385i
$806$		0			0
$807$	−59.2702	+	8.52177i	−2.08641	+	0.299981i
$808$		0			0
$809$	−28.0523	+	8.23691i	−0.986268	+	0.289594i	−0.734809	−	0.678274i	$-0.762728\pi$
$809$	−28.0523	+	8.23691i	−0.986268	+	0.289594i	−0.251458	+	0.967868i	$0.580910\pi$
$810$		0			0
$811$	−36.6315	−	10.7560i	−1.28631	−	0.377694i	−0.434084	−	0.900872i	$-0.642928\pi$
$811$	−36.6315	−	10.7560i	−1.28631	−	0.377694i	−0.852223	+	0.523179i	$0.824746\pi$
$812$		0			0
$813$	6.41664	−	2.93038i	0.225041	−	0.102773i
$814$		0			0
$815$	35.4904	+	22.8083i	1.24318	+	0.798940i
$816$		0			0
$817$	1.13082	−	7.86502i	0.0395623	−	0.275162i
$818$		0			0
$819$	0.255990	−	0.221817i	0.00894503	−	0.00775091i
$820$		0			0
$821$	9.06040	+	14.0983i	0.316210	+	0.492033i	0.962582	−	0.270990i	$-0.0873510\pi$
$821$	9.06040	+	14.0983i	0.316210	+	0.492033i	−0.646372	+	0.763022i	$0.723715\pi$
$822$		0			0
$823$	−7.75200	−	6.71715i	−0.270218	−	0.234145i	0.509202	−	0.860647i	$-0.329941\pi$
$823$	−7.75200	−	6.71715i	−0.270218	−	0.234145i	−0.779420	+	0.626502i	$0.784486\pi$
$824$		0			0
$825$	−20.9325	−	9.55956i	−0.728777	−	0.332821i
$826$		0			0
$827$		−	8.50642i		−	0.295797i	−0.989003	−	0.147899i	$-0.952749\pi$
$827$		−	8.50642i		−	0.295797i	0.989003	−	0.147899i	$-0.0472509\pi$
$828$		0			0
$829$		−	37.9306i		−	1.31738i	−0.752413	−	0.658692i	$-0.771110\pi$
$829$		−	37.9306i		−	1.31738i	0.752413	−	0.658692i	$-0.228890\pi$
$830$		0			0
$831$	49.8974	+	22.7874i	1.73092	+	0.790486i
$832$		0			0
$833$	20.0652	+	17.3866i	0.695217	+	0.602409i
$834$		0			0
$835$	26.0392	+	40.5178i	0.901123	+	1.40218i
$836$		0			0
$837$	20.0672	−	17.3884i	0.693625	−	0.601029i
$838$		0			0
$839$	2.51864	−	17.5176i	0.0869532	−	0.604773i	−0.899025	−	0.437898i	$-0.855723\pi$
$839$	2.51864	−	17.5176i	0.0869532	−	0.604773i	0.985978	−	0.166875i	$-0.0533677\pi$
$840$		0			0
$841$	24.0206	+	15.4371i	0.828295	+	0.532313i
$842$		0			0
$843$	−37.4738	+	17.1137i	−1.29067	+	0.589427i
$844$		0			0
$845$	−30.2635	−	8.88617i	−1.04110	−	0.305693i
$846$		0			0
$847$	−4.19822	+	1.23271i	−0.144252	+	0.0423563i
$848$		0			0
$849$	−22.3936	+	3.21972i	−0.768548	+	0.110501i
$850$		0			0
$851$	46.0058	−	18.0776i	1.57706	−	0.619693i
$852$		0			0
$853$	−26.9922	+	3.88090i	−0.924196	+	0.132879i	−0.587952	−	0.808896i	$-0.700066\pi$
$853$	−26.9922	+	3.88090i	−0.924196	+	0.132879i	−0.336244	+	0.941775i	$0.609157\pi$
$854$		0			0
$855$	1.16987	+	3.98422i	0.0400088	+	0.136257i
$856$		0			0
$857$	37.4158	+	10.9863i	1.27810	+	0.375284i	0.849201	−	0.528069i	$-0.177084\pi$
$857$	37.4158	+	10.9863i	1.27810	+	0.375284i	0.428898	+	0.903353i	$0.358902\pi$
$858$		0			0
$859$	−2.14536	−	4.69768i	−0.0731987	−	0.160283i	0.869495	−	0.493941i	$-0.164444\pi$
$859$	−2.14536	−	4.69768i	−0.0731987	−	0.160283i	−0.942694	+	0.333658i	$0.891717\pi$
$860$		0			0
$861$	−1.86370	−	1.19773i	−0.0635148	−	0.0408185i
$862$		0			0
$863$	12.3957	+	1.78224i	0.421955	+	0.0606680i	0.350022	−	0.936741i	$-0.386174\pi$
$863$	12.3957	+	1.78224i	0.421955	+	0.0606680i	0.0719333	+	0.997409i	$0.477083\pi$
$864$		0			0
$865$	−23.5283	+	20.3874i	−0.799987	+	0.693193i
$866$		0			0
$867$	4.21961	−	2.71178i	0.143305	−	0.0920968i
$868$		0			0
$869$	13.4878	+	11.6872i	0.457541	+	0.396461i
$870$		0			0
$871$	6.35776	−	13.9215i	0.215424	−	0.471713i
$872$		0			0
$873$		−	21.9786i		−	0.743862i
$874$		0			0
$875$	1.83752			0.0621194
$876$		0			0
$877$	23.4424	+	10.7058i	0.791595	+	0.361509i	0.769826	−	0.638254i	$-0.220343\pi$
$877$	23.4424	+	10.7058i	0.791595	+	0.361509i	0.0217690	+	0.999763i	$0.493070\pi$
$878$		0			0
$879$	14.9557	−	17.2597i	0.504442	−	0.582157i
$880$		0			0
$881$	−9.02958	−	14.0503i	−0.304214	−	0.473367i	0.655165	−	0.755486i	$-0.272599\pi$
$881$	−9.02958	−	14.0503i	−0.304214	−	0.473367i	−0.959379	+	0.282119i	$0.908963\pi$
$882$		0			0
$883$	−37.8512	−	43.6826i	−1.27379	−	1.47004i	−0.812695	−	0.582689i	$-0.802001\pi$
$883$	−37.8512	−	43.6826i	−1.27379	−	1.47004i	−0.461099	−	0.887349i	$-0.652545\pi$
$884$		0			0
$885$	6.12624	−	42.6089i	0.205931	−	1.43228i
$886$		0			0
$887$	−15.7811	+	24.5558i	−0.529876	+	0.824503i	−0.998257	−	0.0590237i	$-0.981201\pi$
$887$	−15.7811	+	24.5558i	−0.529876	+	0.824503i	0.468381	+	0.883527i	$0.344838\pi$
$888$		0			0
$889$	2.89283	−	1.32111i	0.0970223	−	0.0443086i
$890$		0			0
$891$	17.3066	−	58.9408i	0.579793	−	1.97459i
$892$		0			0
$893$	3.78331	−	1.11088i	0.126604	−	0.0371742i
$894$		0			0
$895$	−5.46041	−	37.9780i	−0.182521	−	1.26946i
$896$		0			0
$897$	−10.1990	+	2.40532i	−0.340533	+	0.0803112i
$898$		0			0
$899$	0.753504	+	5.24074i	0.0251308	+	0.174788i
$900$		0			0
$901$	−5.70734	−	19.4374i	−0.190139	−	0.647554i
$902$		0			0
$903$	0.973962	−	3.31701i	0.0324114	−	0.110383i
$904$		0			0
$905$	5.98347	+	13.1020i	0.198897	+	0.435524i
$906$		0			0
$907$	−13.1980	+	20.5364i	−0.438231	+	0.681901i	−0.988180	−	0.153297i	$-0.951011\pi$
$907$	−13.1980	+	20.5364i	−0.438231	+	0.681901i	0.549949	+	0.835198i	$0.314647\pi$
$908$		0			0
$909$	26.1113	+	3.75424i	0.866058	+	0.124520i
$910$		0			0
$911$	9.95697	+	11.4910i	0.329889	+	0.380712i	0.896328	−	0.443391i	$-0.146225\pi$
$911$	9.95697	+	11.4910i	0.329889	+	0.380712i	−0.566439	+	0.824104i	$0.691679\pi$
$912$		0			0
$913$	−29.9907	+	19.2738i	−0.992546	+	0.637870i
$914$		0			0
$915$	33.5886	−	38.7633i	1.11041	−	1.28148i
$916$		0			0
$917$	1.33000	−	2.91230i	0.0439205	−	0.0961725i
$918$		0			0
$919$	4.82897			0.159293			0.0796464	−	0.996823i	$-0.474621\pi$
$919$	4.82897			0.159293			0.0796464	+	0.996823i	$0.474621\pi$
$920$		0			0
$921$	12.8418			0.423150
$922$		0			0
$923$	−2.69774	+	5.90722i	−0.0887970	+	0.194438i
$924$		0			0
$925$	13.5454	−	15.6323i	0.445371	−	0.513985i
$926$		0			0
$927$	14.3178	−	9.20148i	0.470258	−	0.302216i
$928$		0			0
$929$	−19.1496	−	22.0998i	−0.628277	−	0.725070i	0.348980	−	0.937130i	$-0.386528\pi$
$929$	−19.1496	−	22.0998i	−0.628277	−	0.725070i	−0.977257	+	0.212060i	$0.931983\pi$
$930$		0			0
$931$	−7.69016	−	1.10568i	−0.252035	−	0.0362371i
$932$		0			0
$933$	18.7208	−	29.1301i	0.612892	−	0.953678i
$934$		0			0
$935$	22.9694	+	50.2960i	0.751180	+	1.64486i
$936$		0			0
$937$	−1.35165	+	4.60330i	−0.0441565	+	0.150383i	−0.978620	−	0.205675i	$-0.934061\pi$
$937$	−1.35165	+	4.60330i	−0.0441565	+	0.150383i	0.934464	+	0.356058i	$0.115879\pi$
$938$		0			0
$939$	−13.7767	−	46.9192i	−0.449586	−	1.53115i
$940$		0			0
$941$	−0.189521	−	1.31815i	−0.00617821	−	0.0429704i	0.986499	−	0.163766i	$-0.0523644\pi$
$941$	−0.189521	−	1.31815i	−0.00617821	−	0.0429704i	−0.992677	+	0.120796i	$0.961455\pi$
$942$		0			0
$943$	10.7956	+	18.9776i	0.351553	+	0.617997i
$944$		0			0
$945$	−0.292846	−	2.03679i	−0.00952629	−	0.0662568i
$946$		0			0
$947$	5.77719	−	1.69634i	0.187733	−	0.0551235i	−0.186514	−	0.982452i	$-0.559719\pi$
$947$	5.77719	−	1.69634i	0.187733	−	0.0551235i	0.374248	+	0.927329i	$0.377901\pi$
$948$		0			0
$949$	−2.31682	+	7.89037i	−0.0752072	+	0.256132i
$950$		0			0
$951$	5.02772	−	2.29608i	0.163035	−	0.0744555i
$952$		0			0
$953$	−14.6914	+	22.8603i	−0.475901	+	0.740517i	−0.993342	−	0.115202i	$-0.963248\pi$
$953$	−14.6914	+	22.8603i	−0.475901	+	0.740517i	0.517441	+	0.855719i	$0.326885\pi$
$954$		0			0
$955$	−1.38772	+	9.65182i	−0.0449057	+	0.312326i
$956$		0			0
$957$	5.01881	+	5.79201i	0.162235	+	0.187229i
$958$		0			0
$959$	−0.616152	−	0.958750i	−0.0198966	−	0.0309597i
$960$		0			0
$961$	20.7950	−	23.9987i	0.670806	−	0.774151i
$962$		0			0
$963$	−1.67862	−	0.766601i	−0.0540928	−	0.0247034i
$964$		0			0
$965$	36.2776			1.16782
$966$		0			0
$967$		−	5.45269i		−	0.175347i	−0.996149	−	0.0876734i	$-0.972057\pi$
$967$		−	5.45269i		−	0.175347i	0.996149	−	0.0876734i	$-0.0279432\pi$
$968$		0			0
$969$	3.72632	−	8.15951i	0.119707	−	0.262121i
$970$		0			0
$971$	13.4254	+	11.6331i	0.430840	+	0.373325i	0.843114	−	0.537735i	$-0.180720\pi$
$971$	13.4254	+	11.6331i	0.430840	+	0.373325i	−0.412274	+	0.911060i	$0.635265\pi$
$972$		0			0
$973$	−1.35315	+	0.869619i	−0.0433801	+	0.0278787i
$974$		0			0
$975$	−3.31390	+	2.87151i	−0.106130	+	0.0919620i
$976$		0			0
$977$	5.45952	+	0.784960i	0.174665	+	0.0251131i	0.229093	−	0.973405i	$-0.426424\pi$
$977$	5.45952	+	0.784960i	0.174665	+	0.0251131i	−0.0544271	+	0.998518i	$0.517333\pi$
$978$		0			0
$979$	−9.18093	−	5.90023i	−0.293424	−	0.188572i
$980$		0			0
$981$	−7.40617	−	16.2172i	−0.236461	−	0.517777i
$982$		0			0
$983$	−32.7632	−	9.62014i	−1.04498	−	0.306835i	−0.286195	−	0.958171i	$-0.592390\pi$
$983$	−32.7632	−	9.62014i	−1.04498	−	0.306835i	−0.758789	+	0.651337i	$0.774209\pi$
$984$		0			0
$985$	−15.2517	−	51.9425i	−0.485960	−	1.65503i
$986$		0			0
$987$	1.69805	−	0.244142i	0.0540494	−	0.00777114i
$988$		0			0
$989$	−23.6683	+	24.5071i	−0.752610	+	0.779279i
$990$		0			0
$991$	11.1650	−	1.60529i	0.354669	−	0.0509937i	0.0373222	−	0.999303i	$-0.488117\pi$
$991$	11.1650	−	1.60529i	0.354669	−	0.0509937i	0.317347	+	0.948310i	$0.397208\pi$
$992$		0			0
$993$	−0.651206	+	0.191211i	−0.0206654	+	0.00606791i
$994$		0			0
$995$	24.0041	+	7.04824i	0.760981	+	0.223444i
$996$		0			0
$997$	−48.2883	+	22.0525i	−1.52930	+	0.698410i	−0.989653	−	0.143479i	$-0.954171\pi$
$997$	−48.2883	+	22.0525i	−1.52930	+	0.698410i	−0.539651	+	0.841889i	$0.681444\pi$
$998$		0			0
$999$	29.0630	+	18.6777i	0.919513	+	0.590935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	736.2.r.a.687.17		220
4.3	odd	2		184.2.j.a.43.4	✓	220
8.3	odd	2	inner	736.2.r.a.687.18		220
8.5	even	2		184.2.j.a.43.20	yes	220
23.15	odd	22	inner	736.2.r.a.15.18		220
92.15	even	22		184.2.j.a.107.20	yes	220
184.61	odd	22		184.2.j.a.107.4	yes	220
184.107	even	22	inner	736.2.r.a.15.17		220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.j.a.43.4	✓	220	4.3	odd	2
184.2.j.a.43.20	yes	220	8.5	even	2
184.2.j.a.107.4	yes	220	184.61	odd	22
184.2.j.a.107.20	yes	220	92.15	even	22
736.2.r.a.15.17		220	184.107	even	22	inner
736.2.r.a.15.18		220	23.15	odd	22	inner
736.2.r.a.687.17		220	1.1	even	1	trivial
736.2.r.a.687.18		220	8.3	odd	2	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:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	736.r (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.871631 - 1.90861i) q^{3} +(-1.73345 + 2.00050i) q^{5} +(-0.195105 + 0.125386i) q^{7} +(-0.918456 - 1.05995i) q^{9} +(5.40936 + 0.777748i) q^{11} +(0.562994 - 0.876035i) q^{13} +(2.30725 + 5.05217i) q^{15} +(1.07685 - 3.66741i) q^{17} +(0.315114 + 1.07318i) q^{19} +(0.0692537 + 0.481670i) q^{21} +(1.59750 - 4.52195i) q^{23} +(-0.285605 - 1.98643i) q^{25} +(3.21609 - 0.944328i) q^{27} +(-0.188299 + 0.641289i) q^{29} +(7.20592 - 3.29083i) q^{31} +(6.19938 - 9.64643i) q^{33} +(0.0873683 - 0.607660i) q^{35} +(6.74958 + 7.78943i) q^{37} +(-1.18128 - 1.83811i) q^{39} +(-2.98130 + 3.44060i) q^{41} +(-6.46217 - 2.95117i) q^{43} +3.71254 q^{45} -3.52533i q^{47} +(-2.88556 + 6.31850i) q^{49} +(-6.06102 - 5.25190i) q^{51} +(4.45868 - 2.86542i) q^{53} +(-10.9327 + 9.47326i) q^{55} +(2.32294 + 0.333988i) q^{57} +(-6.52016 - 4.19025i) q^{59} +(-3.83630 - 8.40033i) q^{61} +(0.312099 + 0.0916406i) q^{63} +(0.776593 + 2.64483i) q^{65} +(14.5473 - 2.09159i) q^{67} +(-7.23819 - 6.99047i) q^{69} +(-6.17276 + 0.887509i) q^{71} +(-7.57709 + 2.22483i) q^{73} +(-4.04025 - 1.18633i) q^{75} +(-1.15291 + 0.526518i) q^{77} +(2.74726 + 1.76556i) q^{79} +(1.59969 - 11.1261i) q^{81} +(-4.93001 + 4.27188i) q^{83} +(5.47000 + 8.51149i) q^{85} +(1.05984 + 0.918357i) q^{87} +(-1.81651 - 0.829570i) q^{89} +0.241511i q^{91} -16.6217i q^{93} +(-2.69313 - 1.22991i) q^{95} +(11.8432 + 10.2622i) q^{97} +(-4.14388 - 6.44800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 18 q^{3} - 36 q^{9} + 22 q^{11} - 22 q^{17} + 22 q^{19} - 32 q^{25} + 18 q^{27} - 22 q^{33} - 2 q^{35} - 18 q^{41} + 22 q^{43} - 28 q^{49} + 22 q^{51} - 22 q^{57} + 6 q^{59} - 22 q^{65} + 22 q^{67}+ \cdots + 22 q^{99}+O(q^{100}) \) 220 * q + 18 * q^3 - 36 * q^9 + 22 * q^11 - 22 * q^17 + 22 * q^19 - 32 * q^25 + 18 * q^27 - 22 * q^33 - 2 * q^35 - 18 * q^41 + 22 * q^43 - 28 * q^49 + 22 * q^51 - 22 * q^57 + 6 * q^59 - 22 * q^65 + 22 * q^67 - 18 * q^73 - 14 * q^75 + 4 * q^81 + 22 * q^83 - 22 * q^89 - 22 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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