LMFDB - Embedded newform 544.2.cc.c.175.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(79,544)] 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("544.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.cc (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			175.3
Character	$\chi$	$=$	544.175
Dual form			544.2.cc.c.143.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.921778 - 1.37954i) q^{3} +(-3.91277 - 0.778297i) q^{5} +(-1.72342 + 0.342810i) q^{7} +(0.0945986 - 0.228381i) q^{9} +(2.25700 + 1.50808i) q^{11} +(1.43844 - 1.43844i) q^{13} +(2.53301 + 6.11523i) q^{15} +(-3.43525 + 2.28014i) q^{17} +(2.12471 + 5.12951i) q^{19} +(2.06153 + 2.06153i) q^{21} +(-1.05741 - 0.706536i) q^{23} +(10.0846 + 4.17717i) q^{25} +(-5.28409 + 1.05107i) q^{27} +(-1.64434 + 8.26664i) q^{29} +(3.07326 + 4.59945i) q^{31} -4.50373i q^{33} +7.01015 q^{35} +(-3.15531 + 2.10831i) q^{37} +(-3.31031 - 0.658462i) q^{39} +(-0.810929 - 4.07682i) q^{41} +(2.93119 - 7.07653i) q^{43} +(-0.547891 + 0.819977i) q^{45} +(2.10492 - 2.10492i) q^{47} +(-3.61450 + 1.49717i) q^{49} +(6.31208 + 2.63728i) q^{51} +(5.83351 - 2.41632i) q^{53} +(-7.65738 - 7.65738i) q^{55} +(5.11785 - 7.65940i) q^{57} +(-3.89198 - 1.61211i) q^{59} +(0.411419 + 2.06835i) q^{61} +(-0.0847419 + 0.426026i) q^{63} +(-6.74782 + 4.50875i) q^{65} +0.474710i q^{67} +2.11000i q^{69} +(-9.48983 + 6.34090i) q^{71} +(-1.48381 + 7.45963i) q^{73} +(-3.53318 - 17.7625i) q^{75} +(-4.40675 - 1.82533i) q^{77} +(0.405234 - 0.606476i) q^{79} +(5.79637 + 5.79637i) q^{81} +(-14.3632 + 5.94945i) q^{83} +(15.2160 - 6.24801i) q^{85} +(12.9199 - 5.35158i) q^{87} +(-5.56406 + 5.56406i) q^{89} +(-1.98593 + 2.97215i) q^{91} +(3.51226 - 8.47935i) q^{93} +(-4.32122 - 21.7242i) q^{95} +(-2.52059 - 0.501377i) q^{97} +(0.557926 - 0.372794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 16 q^{3} - 16 q^{9} + 16 q^{11} - 16 q^{17} + 16 q^{19} - 16 q^{25} - 32 q^{27} + 32 q^{35} - 16 q^{41} + 96 q^{43} - 16 q^{49} + 16 q^{51} + 32 q^{57} + 16 q^{59} + 64 q^{65} - 96 q^{73} + 16 q^{75}+ \cdots - 48 q^{99}+O(q^{100}) $ 112 * q + 16 * q^3 - 16 * q^9 + 16 * q^11 - 16 * q^17 + 16 * q^19 - 16 * q^25 - 32 * q^27 + 32 * q^35 - 16 * q^41 + 96 * q^43 - 16 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^59 + 64 * q^65 - 96 * q^73 + 16 * q^75 - 96 * q^81 - 128 * q^83 - 16 * q^89 + 16 * q^91 - 16 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.921778	−	1.37954i	−0.532189	−	0.796477i	0.463801	−	0.885939i	$-0.346485\pi$
$3$	−0.921778	−	1.37954i	−0.532189	−	0.796477i	−0.995990	+	0.0894623i	$0.971485\pi$
$4$		0			0
$5$	−3.91277	−	0.778297i	−1.74984	−	0.348065i	−0.786757	−	0.617263i	$-0.788241\pi$
$5$	−3.91277	−	0.778297i	−1.74984	−	0.348065i	−0.963085	+	0.269198i	$0.913241\pi$
$6$		0			0
$7$	−1.72342	+	0.342810i	−0.651392	+	0.129570i	−0.509715	−	0.860343i	$-0.670249\pi$
$7$	−1.72342	+	0.342810i	−0.651392	+	0.129570i	−0.141677	+	0.989913i	$0.545249\pi$
$8$		0			0
$9$	0.0945986	−	0.228381i	0.0315329	−	0.0761271i
$10$		0			0
$11$	2.25700	+	1.50808i	0.680511	+	0.454703i	0.847177	−	0.531310i	$-0.178300\pi$
$11$	2.25700	+	1.50808i	0.680511	+	0.454703i	−0.166666	+	0.986013i	$0.553300\pi$
$12$		0			0
$13$	1.43844	−	1.43844i	0.398952	−	0.398952i	−0.478911	−	0.877863i	$-0.658968\pi$
$13$	1.43844	−	1.43844i	0.398952	−	0.398952i	0.877863	+	0.478911i	$0.158968\pi$
$14$		0			0
$15$	2.53301	+	6.11523i	0.654021	+	1.57895i
$16$		0			0
$17$	−3.43525	+	2.28014i	−0.833171	+	0.553015i
$17$	−3.43525	+	2.28014i	−0.833171	+	0.553015i
$18$		0			0
$19$	2.12471	+	5.12951i	0.487443	+	1.17679i	0.956002	+	0.293359i	$0.0947732\pi$
$19$	2.12471	+	5.12951i	0.487443	+	1.17679i	−0.468559	+	0.883432i	$0.655227\pi$
$20$		0			0
$21$	2.06153	+	2.06153i	0.449863	+	0.449863i
$22$		0			0
$23$	−1.05741	−	0.706536i	−0.220484	−	0.147323i	0.440423	−	0.897790i	$-0.354828\pi$
$23$	−1.05741	−	0.706536i	−0.220484	−	0.147323i	−0.660907	+	0.750467i	$0.729828\pi$
$24$		0			0
$25$	10.0846	+	4.17717i	2.01692	+	0.835435i
$26$		0			0
$27$	−5.28409	+	1.05107i	−1.01692	+	0.202279i
$28$		0			0
$29$	−1.64434	+	8.26664i	−0.305346	+	1.53508i	0.457921	+	0.888993i	$0.348594\pi$
$29$	−1.64434	+	8.26664i	−0.305346	+	1.53508i	−0.763267	+	0.646083i	$0.776406\pi$
$30$		0			0
$31$	3.07326	+	4.59945i	0.551973	+	0.826086i	0.997608	−	0.0691289i	$-0.0220220\pi$
$31$	3.07326	+	4.59945i	0.551973	+	0.826086i	−0.445635	+	0.895215i	$0.647022\pi$
$32$		0			0
$33$		−	4.50373i		−	0.783999i
$34$		0			0
$35$	7.01015			1.18493
$36$		0			0
$37$	−3.15531	+	2.10831i	−0.518731	+	0.346605i	−0.787214	−	0.616680i	$-0.788477\pi$
$37$	−3.15531	+	2.10831i	−0.518731	+	0.346605i	0.268484	+	0.963284i	$0.413477\pi$
$38$		0			0
$39$	−3.31031	−	0.658462i	−0.530074	−	0.105438i
$40$		0			0
$41$	−0.810929	−	4.07682i	−0.126646	−	0.636692i	−0.991006	−	0.133818i	$-0.957276\pi$
$41$	−0.810929	−	4.07682i	−0.126646	−	0.636692i	0.864360	−	0.502874i	$-0.167724\pi$
$42$		0			0
$43$	2.93119	−	7.07653i	0.447003	−	1.07916i	−0.526436	−	0.850215i	$-0.676472\pi$
$43$	2.93119	−	7.07653i	0.447003	−	1.07916i	0.973439	−	0.228946i	$-0.0735279\pi$
$44$		0			0
$45$	−0.547891	+	0.819977i	−0.0816747	+	0.122235i
$46$		0			0
$47$	2.10492	−	2.10492i	0.307034	−	0.307034i	−0.536724	−	0.843758i	$-0.680338\pi$
$47$	2.10492	−	2.10492i	0.307034	−	0.307034i	0.843758	+	0.536724i	$0.180338\pi$
$48$		0			0
$49$	−3.61450	+	1.49717i	−0.516357	+	0.213882i
$50$		0			0
$51$	6.31208	+	2.63728i	0.883868	+	0.369293i
$52$		0			0
$53$	5.83351	−	2.41632i	0.801295	−	0.331907i	0.0558197	−	0.998441i	$-0.482223\pi$
$53$	5.83351	−	2.41632i	0.801295	−	0.331907i	0.745475	+	0.666534i	$0.232223\pi$
$54$		0			0
$55$	−7.65738	−	7.65738i	−1.03252	−	1.03252i
$56$		0			0
$57$	5.11785	−	7.65940i	0.677875	−	1.01451i
$58$		0			0
$59$	−3.89198	−	1.61211i	−0.506693	−	0.209879i	0.114668	−	0.993404i	$-0.463420\pi$
$59$	−3.89198	−	1.61211i	−0.506693	−	0.209879i	−0.621360	+	0.783525i	$0.713420\pi$
$60$		0			0
$61$	0.411419	+	2.06835i	0.0526769	+	0.264824i	0.998144	−	0.0608920i	$-0.0193945\pi$
$61$	0.411419	+	2.06835i	0.0526769	+	0.264824i	−0.945468	+	0.325716i	$0.894395\pi$
$62$		0			0
$63$	−0.0847419	+	0.426026i	−0.0106765	+	0.0536743i
$64$		0			0
$65$	−6.74782	+	4.50875i	−0.836964	+	0.559242i
$66$		0			0
$67$			0.474710i			0.0579951i	0.999579	+	0.0289975i	$0.00923149\pi$
$67$			0.474710i			0.0579951i	−0.999579	+	0.0289975i	$0.990769\pi$
$68$		0			0
$69$			2.11000i			0.254014i
$70$		0			0
$71$	−9.48983	+	6.34090i	−1.12624	+	0.752526i	−0.971877	−	0.235489i	$-0.924331\pi$
$71$	−9.48983	+	6.34090i	−1.12624	+	0.752526i	−0.154358	+	0.988015i	$0.549331\pi$
$72$		0			0
$73$	−1.48381	+	7.45963i	−0.173667	+	0.873084i	0.791444	+	0.611242i	$0.209330\pi$
$73$	−1.48381	+	7.45963i	−0.173667	+	0.873084i	−0.965111	+	0.261842i	$0.915670\pi$
$74$		0			0
$75$	−3.53318	−	17.7625i	−0.407977	−	2.05104i
$76$		0			0
$77$	−4.40675	−	1.82533i	−0.502195	−	0.208016i
$78$		0			0
$79$	0.405234	−	0.606476i	0.0455924	−	0.0682339i	−0.807973	−	0.589219i	$-0.799435\pi$
$79$	0.405234	−	0.606476i	0.0455924	−	0.0682339i	0.853566	+	0.520985i	$0.174435\pi$
$80$		0			0
$81$	5.79637	+	5.79637i	0.644041	+	0.644041i
$82$		0			0
$83$	−14.3632	+	5.94945i	−1.57657	+	0.653037i	−0.987866	−	0.155311i	$-0.950362\pi$
$83$	−14.3632	+	5.94945i	−1.57657	+	0.653037i	−0.588705	+	0.808348i	$0.700362\pi$
$84$		0			0
$85$	15.2160	−	6.24801i	1.65040	−	0.677692i
$86$		0			0
$87$	12.9199	−	5.35158i	1.38515	−	0.573750i
$88$		0			0
$89$	−5.56406	+	5.56406i	−0.589789	+	0.589789i	−0.937574	−	0.347785i	$-0.886934\pi$
$89$	−5.56406	+	5.56406i	−0.589789	+	0.589789i	0.347785	+	0.937574i	$0.386934\pi$
$90$		0			0
$91$	−1.98593	+	2.97215i	−0.208182	+	0.311566i
$92$		0			0
$93$	3.51226	−	8.47935i	0.364205	−	0.879268i
$94$		0			0
$95$	−4.32122	−	21.7242i	−0.443348	−	2.22886i
$96$		0			0
$97$	−2.52059	−	0.501377i	−0.255927	−	0.0509071i	0.0654591	−	0.997855i	$-0.479149\pi$
$97$	−2.52059	−	0.501377i	−0.255927	−	0.0509071i	−0.321386	+	0.946948i	$0.604149\pi$
$98$		0			0
$99$	0.557926	−	0.372794i	0.0560737	−	0.0374672i
$100$		0			0
$101$	−12.5095			−1.24474			−0.622370	−	0.782724i	$-0.713830\pi$
$101$	−12.5095			−1.24474			−0.622370	+	0.782724i	$0.713830\pi$
$102$		0			0
$103$			0.883647i			0.0870683i	0.999052	+	0.0435341i	$0.0138617\pi$
$103$			0.883647i			0.0870683i	−0.999052	+	0.0435341i	$0.986138\pi$
$104$		0			0
$105$	−6.46180	−	9.67077i	−0.630607	−	0.943771i
$106$		0			0
$107$	−3.40001	+	17.0930i	−0.328691	+	1.65244i	0.364142	+	0.931343i	$0.381362\pi$
$107$	−3.40001	+	17.0930i	−0.328691	+	1.65244i	−0.692833	+	0.721098i	$0.743638\pi$
$108$		0			0
$109$	16.2497	−	3.23227i	1.55644	−	0.309596i	0.659486	−	0.751716i	$-0.270774\pi$
$109$	16.2497	−	3.23227i	1.55644	−	0.309596i	0.896955	+	0.442121i	$0.145774\pi$
$110$		0			0
$111$	5.81700	+	2.40948i	0.552125	+	0.228698i
$112$		0			0
$113$	−3.17941	−	2.12441i	−0.299093	−	0.199848i	0.396964	−	0.917834i	$-0.370064\pi$
$113$	−3.17941	−	2.12441i	−0.299093	−	0.199848i	−0.696057	+	0.717986i	$0.745064\pi$
$114$		0			0
$115$	3.58748	+	3.58748i	0.334535	+	0.334535i
$116$		0			0
$117$	−0.192439	−	0.464588i	−0.0177910	−	0.0429512i
$118$		0			0
$119$	5.13873	−	5.10728i	0.471067	−	0.468184i
$120$		0			0
$121$	−1.38977	−	3.35521i	−0.126343	−	0.305019i
$122$		0			0
$123$	−4.87663	+	4.87663i	−0.439711	+	0.439711i
$124$		0			0
$125$	−19.6221	−	13.1111i	−1.75506	−	1.17269i
$126$		0			0
$127$	−4.56457	+	11.0198i	−0.405040	+	0.977852i	0.581384	+	0.813630i	$0.302512\pi$
$127$	−4.56457	+	11.0198i	−0.405040	+	0.977852i	−0.986423	+	0.164223i	$0.947488\pi$
$128$		0			0
$129$	−12.4643	+	2.47929i	−1.09742	+	0.218290i
$130$		0			0
$131$	8.64991	+	1.72057i	0.755746	+	0.150327i	0.557903	−	0.829906i	$-0.311606\pi$
$131$	8.64991	+	1.72057i	0.755746	+	0.150327i	0.197843	+	0.980234i	$0.436606\pi$
$132$		0			0
$133$	−5.42022	−	8.11194i	−0.469993	−	0.703394i
$134$		0			0
$135$	21.4934			1.84986
$136$		0			0
$137$	2.20919			0.188744			0.0943718	−	0.995537i	$-0.469916\pi$
$137$	2.20919			0.188744			0.0943718	+	0.995537i	$0.469916\pi$
$138$		0			0
$139$	−10.7069	−	16.0240i	−0.908147	−	1.35914i	−0.933164	−	0.359452i	$-0.882964\pi$
$139$	−10.7069	−	16.0240i	−0.908147	−	1.35914i	0.0250163	−	0.999687i	$-0.492036\pi$
$140$		0			0
$141$	−4.84408	−	0.963548i	−0.407946	−	0.0811454i
$142$		0			0
$143$	5.41585	−	1.07728i	0.452896	−	0.0900866i
$144$		0			0
$145$	12.8678	−	31.0656i	1.06861	−	2.57986i
$146$		0			0
$147$	5.39717	+	3.60627i	0.445151	+	0.297441i
$148$		0			0
$149$	−0.306372	+	0.306372i	−0.0250990	+	0.0250990i	−0.719545	−	0.694446i	$-0.755650\pi$
$149$	−0.306372	+	0.306372i	−0.0250990	+	0.0250990i	0.694446	+	0.719545i	$0.255650\pi$
$150$		0			0
$151$	7.80521	+	18.8434i	0.635179	+	1.53346i	0.833032	+	0.553225i	$0.186603\pi$
$151$	7.80521	+	18.8434i	0.635179	+	1.53346i	−0.197853	+	0.980232i	$0.563397\pi$
$152$		0			0
$153$	0.195771	+	1.00025i	0.0158272	+	0.0808651i
$154$		0			0
$155$	−8.44519	−	20.3885i	−0.678334	−	1.63764i
$156$		0			0
$157$	1.99680	+	1.99680i	0.159362	+	0.159362i	0.782284	−	0.622922i	$-0.214055\pi$
$157$	1.99680	+	1.99680i	0.159362	+	0.159362i	−0.622922	+	0.782284i	$0.714055\pi$
$158$		0			0
$159$	−8.71061	−	5.82024i	−0.690796	−	0.461575i
$160$		0			0
$161$	2.06456	+	0.855170i	0.162710	+	0.0673968i
$162$		0			0
$163$	11.6113	−	2.30962i	0.909464	−	0.180904i	0.281878	−	0.959450i	$-0.409043\pi$
$163$	11.6113	−	2.30962i	0.909464	−	0.180904i	0.627587	+	0.778547i	$0.284043\pi$
$164$		0			0
$165$	−3.50524	+	17.6221i	−0.272883	+	1.37187i
$166$		0			0
$167$	−4.20835	−	6.29824i	−0.325652	−	0.487373i	0.632132	−	0.774860i	$-0.282180\pi$
$167$	−4.20835	−	6.29824i	−0.325652	−	0.487373i	−0.957784	+	0.287488i	$0.907180\pi$
$168$		0			0
$169$			8.86177i			0.681675i
$170$		0			0
$171$	1.37248			0.104956
$172$		0			0
$173$	9.61075	−	6.42170i	0.730692	−	0.488233i	−0.133719	−	0.991019i	$-0.542692\pi$
$173$	9.61075	−	6.42170i	0.730692	−	0.488233i	0.864410	+	0.502787i	$0.167692\pi$
$174$		0			0
$175$	−18.8120	−	3.74193i	−1.42205	−	0.282864i
$176$		0			0
$177$	1.36357	+	6.85514i	0.102492	+	0.515264i
$178$		0			0
$179$	−3.08040	+	7.43674i	−0.230240	+	0.555848i	−0.996205	−	0.0870337i	$-0.972261\pi$
$179$	−3.08040	+	7.43674i	−0.230240	+	0.555848i	0.765966	+	0.642881i	$0.222261\pi$
$180$		0			0
$181$	0.209700	−	0.313838i	0.0155869	−	0.0233274i	−0.823594	−	0.567179i	$-0.808035\pi$
$181$	0.209700	−	0.313838i	0.0155869	−	0.0233274i	0.839181	+	0.543852i	$0.183035\pi$
$182$		0			0
$183$	2.47412	−	2.47412i	0.182893	−	0.182893i
$184$		0			0
$185$	13.9869	−	5.79356i	1.02834	−	0.425951i
$186$		0			0
$187$	−11.1920	−	0.0343542i	−0.818440	−	0.00251223i
$188$		0			0
$189$	8.74639	−	3.62287i	0.636207	−	0.263525i
$190$		0			0
$191$	9.71409	+	9.71409i	0.702887	+	0.702887i	0.965029	−	0.262142i	$-0.0844290\pi$
$191$	9.71409	+	9.71409i	0.702887	+	0.702887i	−0.262142	+	0.965029i	$0.584429\pi$
$192$		0			0
$193$	−5.42709	+	8.12221i	−0.390650	+	0.584650i	−0.973713	−	0.227777i	$-0.926854\pi$
$193$	−5.42709	+	8.12221i	−0.390650	+	0.584650i	0.583063	+	0.812427i	$0.301854\pi$
$194$		0			0
$195$	12.4400	+	5.15281i	0.890846	+	0.369001i
$196$		0			0
$197$	−3.67141	−	18.4574i	−0.261577	−	1.31504i	−0.858532	−	0.512761i	$-0.828623\pi$
$197$	−3.67141	−	18.4574i	−0.261577	−	1.31504i	0.596955	−	0.802275i	$-0.296377\pi$
$198$		0			0
$199$	1.48032	−	7.44206i	0.104937	−	0.527553i	−0.892180	−	0.451679i	$-0.850825\pi$
$199$	1.48032	−	7.44206i	0.104937	−	0.527553i	0.997117	−	0.0758743i	$-0.0241748\pi$
$200$		0			0
$201$	0.654881	−	0.437577i	0.0461917	−	0.0308643i
$202$		0			0
$203$		−	14.8106i		−	1.03950i
$204$		0			0
$205$			16.5828i			1.15819i
$206$		0			0
$207$	−0.261389	+	0.174654i	−0.0181678	+	0.0121393i
$208$		0			0
$209$	−2.94023	+	14.7816i	−0.203380	+	1.02246i
$210$		0			0
$211$	0.296827	+	1.49225i	0.0204344	+	0.102731i	0.989657	−	0.143457i	$-0.0458220\pi$
$211$	0.296827	+	1.49225i	0.0204344	+	0.102731i	−0.969222	+	0.246188i	$0.920822\pi$
$212$		0			0
$213$	17.4950	+	7.24668i	1.19874	+	0.496534i
$214$		0			0
$215$	−16.9767	+	25.4075i	−1.15780	+	1.73277i
$216$		0			0
$217$	−6.87325	−	6.87325i	−0.466587	−	0.466587i
$218$		0			0
$219$	11.6586	−	4.82915i	0.787815	−	0.326324i
$220$		0			0
$221$	−1.66156	+	8.22126i	−0.111769	+	0.553022i
$222$		0			0
$223$	−5.90153	+	2.44449i	−0.395195	+	0.163695i	−0.571426	−	0.820654i	$-0.693610\pi$
$223$	−5.90153	+	2.44449i	−0.395195	+	0.163695i	0.176231	+	0.984349i	$0.443610\pi$
$224$		0			0
$225$	1.90798	−	1.90798i	0.127198	−	0.127198i
$226$		0			0
$227$	−7.11025	+	10.6412i	−0.471924	+	0.706284i	−0.988712	−	0.149829i	$-0.952128\pi$
$227$	−7.11025	+	10.6412i	−0.471924	+	0.706284i	0.516788	+	0.856113i	$0.327128\pi$
$228$		0			0
$229$	−9.46723	+	22.8559i	−0.625612	+	1.51036i	0.219412	+	0.975632i	$0.429586\pi$
$229$	−9.46723	+	22.8559i	−0.625612	+	1.51036i	−0.845024	+	0.534729i	$0.820414\pi$
$230$		0			0
$231$	1.54392	+	7.76183i	0.101583	+	0.510691i
$232$		0			0
$233$	−1.74882	−	0.347862i	−0.114569	−	0.0227892i	0.137473	−	0.990506i	$-0.456102\pi$
$233$	−1.74882	−	0.347862i	−0.114569	−	0.0227892i	−0.252042	+	0.967716i	$0.581102\pi$
$234$		0			0
$235$	−9.87431	+	6.59780i	−0.644129	+	0.430393i
$236$		0			0
$237$	−1.21019			−0.0786105
$238$		0			0
$239$		−	25.4829i		−	1.64835i	−0.566335	−	0.824175i	$-0.691639\pi$
$239$		−	25.4829i		−	1.64835i	0.566335	−	0.824175i	$-0.308361\pi$
$240$		0			0
$241$	10.4034	+	15.5698i	0.670141	+	1.00294i	0.998298	+	0.0583139i	$0.0185724\pi$
$241$	10.4034	+	15.5698i	0.670141	+	1.00294i	−0.328157	+	0.944623i	$0.606428\pi$
$242$		0			0
$243$	−0.499866	+	2.51300i	−0.0320664	+	0.161209i
$244$		0			0
$245$	15.3079	−	3.04493i	0.977987	−	0.194534i
$246$		0			0
$247$	10.4348	+	4.32223i	0.663950	+	0.275017i
$248$		0			0
$249$	21.4472	+	14.3306i	1.35916	+	0.908163i
$250$		0			0
$251$	4.97402	+	4.97402i	0.313957	+	0.313957i	0.846440	−	0.532483i	$-0.178741\pi$
$251$	4.97402	+	4.97402i	0.313957	+	0.313957i	−0.532483	+	0.846440i	$0.678741\pi$
$252$		0			0
$253$	−1.32105	−	3.18930i	−0.0830539	−	0.200510i
$254$		0			0
$255$	−22.6451	−	15.2317i	−1.41809	−	0.953848i
$256$		0			0
$257$	−2.37545	−	5.73484i	−0.148176	−	0.357729i	0.832312	−	0.554308i	$-0.187017\pi$
$257$	−2.37545	−	5.73484i	−0.148176	−	0.357729i	−0.980488	+	0.196578i	$0.937017\pi$
$258$		0			0
$259$	4.71518	−	4.71518i	0.292987	−	0.292987i
$260$		0			0
$261$	1.73239	+	1.15755i	0.107232	+	0.0716505i
$262$		0			0
$263$	2.91136	−	7.02865i	0.179522	−	0.433405i	−0.808344	−	0.588710i	$-0.799636\pi$
$263$	2.91136	−	7.02865i	0.179522	−	0.433405i	0.987867	+	0.155305i	$0.0496360\pi$
$264$		0			0
$265$	−24.7058	+	4.91429i	−1.51766	+	0.301882i
$266$		0			0
$267$	12.8047	+	2.54701i	0.783633	+	0.155874i
$268$		0			0
$269$	0.468100	+	0.700560i	0.0285405	+	0.0427139i	0.845466	−	0.534030i	$-0.179323\pi$
$269$	0.468100	+	0.700560i	0.0285405	+	0.0427139i	−0.816925	+	0.576744i	$0.804323\pi$
$270$		0			0
$271$	−0.495347			−0.0300902			−0.0150451	−	0.999887i	$-0.504789\pi$
$271$	−0.495347			−0.0300902			−0.0150451	+	0.999887i	$0.504789\pi$
$272$		0			0
$273$	5.93079			0.358947
$274$		0			0
$275$	16.4614	+	24.6362i	0.992660	+	1.48562i
$276$		0			0
$277$	−7.81295	−	1.55409i	−0.469434	−	0.0933763i	−0.0452959	−	0.998974i	$-0.514423\pi$
$277$	−7.81295	−	1.55409i	−0.469434	−	0.0933763i	−0.424139	+	0.905597i	$0.639423\pi$
$278$		0			0
$279$	1.34115	−	0.266772i	0.0802928	−	0.0159712i
$280$		0			0
$281$	−7.93869	+	19.1657i	−0.473583	+	1.14333i	0.488986	+	0.872292i	$0.337367\pi$
$281$	−7.93869	+	19.1657i	−0.473583	+	1.14333i	−0.962569	+	0.271038i	$0.912633\pi$
$282$		0			0
$283$	−3.88907	−	2.59860i	−0.231181	−	0.154470i	0.434585	−	0.900631i	$-0.356895\pi$
$283$	−3.88907	−	2.59860i	−0.231181	−	0.154470i	−0.665766	+	0.746160i	$0.731895\pi$
$284$		0			0
$285$	−25.9862	+	25.9862i	−1.53929	+	1.53929i
$286$		0			0
$287$	2.79514	+	6.74808i	0.164992	+	0.398326i
$288$		0			0
$289$	6.60191	−	15.6657i	0.388348	−	0.921513i
$290$		0			0
$291$	1.63176	+	3.93941i	0.0956553	+	0.230932i
$292$		0			0
$293$	−14.3466	−	14.3466i	−0.838135	−	0.838135i	0.150478	−	0.988613i	$-0.451919\pi$
$293$	−14.3466	−	14.3466i	−0.838135	−	0.838135i	−0.988613	+	0.150478i	$0.951919\pi$
$294$		0			0
$295$	13.9737	+	9.33693i	0.813580	+	0.543617i
$296$		0			0
$297$	−13.5113	−	5.59656i	−0.784005	−	0.324745i
$298$		0			0
$299$	−2.53733	+	0.504706i	−0.146737	+	0.0291879i
$300$		0			0
$301$	−2.62578	+	13.2007i	−0.151347	+	0.760875i
$302$		0			0
$303$	11.5310	+	17.2573i	0.662436	+	0.991406i
$304$		0			0
$305$		−	8.41316i		−	0.481736i
$306$		0			0
$307$	10.3982			0.593455			0.296727	−	0.954962i	$-0.404105\pi$
$307$	10.3982			0.593455			0.296727	+	0.954962i	$0.404105\pi$
$308$		0			0
$309$	1.21902	−	0.814526i	0.0693479	−	0.0463368i
$310$		0			0
$311$	−32.5176	−	6.46816i	−1.84391	−	0.366776i	−0.855401	−	0.517967i	$-0.826689\pi$
$311$	−32.5176	−	6.46816i	−1.84391	−	0.366776i	−0.988505	+	0.151191i	$0.951689\pi$
$312$		0			0
$313$	−4.09832	−	20.6037i	−0.231651	−	1.16459i	−0.905049	−	0.425307i	$-0.860166\pi$
$313$	−4.09832	−	20.6037i	−0.231651	−	1.16459i	0.673398	−	0.739280i	$-0.264834\pi$
$314$		0			0
$315$	0.663151	−	1.60099i	0.0373643	−	0.0902054i
$316$		0			0
$317$	−4.02641	+	6.02595i	−0.226146	+	0.338451i	−0.927139	−	0.374716i	$-0.877740\pi$
$317$	−4.02641	+	6.02595i	−0.226146	+	0.338451i	0.700994	+	0.713167i	$0.252740\pi$
$318$		0			0
$319$	−16.1780	+	16.1780i	−0.905795	+	0.905795i
$320$		0			0
$321$	26.7145	−	11.0655i	1.49106	−	0.617616i
$322$		0			0
$323$	−18.9949	−	12.7765i	−1.05691	−	0.710905i
$324$		0			0
$325$	20.5147	−	8.49747i	1.13795	−	0.471355i
$326$		0			0
$327$	−19.4377	−	19.4377i	−1.07491	−	1.07491i
$328$		0			0
$329$	−2.90607	+	4.34925i	−0.160217	+	0.239782i
$330$		0			0
$331$	−13.2900	−	5.50492i	−0.730487	−	0.302578i	−0.0137350	−	0.999906i	$-0.504372\pi$
$331$	−13.2900	−	5.50492i	−0.730487	−	0.302578i	−0.716752	+	0.697328i	$0.754372\pi$
$332$		0			0
$333$	0.183011	+	0.920059i	0.0100289	+	0.0504189i
$334$		0			0
$335$	0.369466	−	1.85743i	0.0201861	−	0.101482i
$336$		0			0
$337$	4.56567	−	3.05068i	0.248708	−	0.166181i	−0.424968	−	0.905208i	$-0.639715\pi$
$337$	4.56567	−	3.05068i	0.248708	−	0.166181i	0.673675	+	0.739027i	$0.264715\pi$
$338$		0			0
$339$			6.34435i			0.344578i
$340$		0			0
$341$			15.0157i			0.813145i
$342$		0			0
$343$	15.9434	−	10.6530i	0.860861	−	0.575209i
$344$		0			0
$345$	1.64221	−	8.25594i	0.0884135	−	0.444485i
$346$		0			0
$347$	−0.457262	−	2.29881i	−0.0245471	−	0.123407i	0.966569	−	0.256407i	$-0.0825388\pi$
$347$	−0.457262	−	2.29881i	−0.0245471	−	0.123407i	−0.991116	+	0.133000i	$0.957539\pi$
$348$		0			0
$349$	−2.99685	−	1.24134i	−0.160418	−	0.0664472i	0.301030	−	0.953615i	$-0.402670\pi$
$349$	−2.99685	−	1.24134i	−0.160418	−	0.0664472i	−0.461447	+	0.887168i	$0.652670\pi$
$350$		0			0
$351$	−6.08895	+	9.11276i	−0.325004	+	0.486403i
$352$		0			0
$353$	9.74006	+	9.74006i	0.518411	+	0.518411i	0.917090	−	0.398679i	$-0.130531\pi$
$353$	9.74006	+	9.74006i	0.518411	+	0.518411i	−0.398679	+	0.917090i	$0.630531\pi$
$354$		0			0
$355$	42.0666	−	17.4245i	2.23266	−	0.924799i
$356$		0			0
$357$	−11.7825	−	2.38130i	−0.623594	−	0.126032i
$358$		0			0
$359$	0.00216710		0.000897642i	0.000114375		4.73758e-5i	−0.382626	−	0.923903i	$-0.624980\pi$
$359$	0.00216710		0.000897642i	0.000114375		4.73758e-5i	0.382741	+	0.923856i	$0.374980\pi$
$360$		0			0
$361$	−8.36248	+	8.36248i	−0.440130	+	0.440130i
$362$		0			0
$363$	−3.34757	+	5.01000i	−0.175702	+	0.262957i
$364$		0			0
$365$	11.6116	−	28.0329i	0.607780	−	1.46731i
$366$		0			0
$367$	−0.489357	−	2.46017i	−0.0255442	−	0.128420i	0.965909	−	0.258882i	$-0.0833539\pi$
$367$	−0.489357	−	2.46017i	−0.0255442	−	0.128420i	−0.991453	+	0.130462i	$0.958354\pi$
$368$		0			0
$369$	−1.00778	−	0.200460i	−0.0524630	−	0.0104355i
$370$		0			0
$371$	−9.22526	+	6.16412i	−0.478952	+	0.320025i
$372$		0			0
$373$	−14.0865			−0.729370			−0.364685	−	0.931131i	$-0.618823\pi$
$373$	−14.0865			−0.729370			−0.364685	+	0.931131i	$0.618823\pi$
$374$		0			0
$375$			39.1550i			2.02196i
$376$		0			0
$377$	9.52580	+	14.2564i	0.490603	+	0.734240i
$378$		0			0
$379$	2.62326	−	13.1880i	0.134748	−	0.677424i	−0.853068	−	0.521799i	$-0.825261\pi$
$379$	2.62326	−	13.1880i	0.134748	−	0.677424i	0.987816	−	0.155625i	$-0.0497390\pi$
$380$		0			0
$381$	19.4098	−	3.86085i	0.994394	−	0.197797i
$382$		0			0
$383$	32.2120	+	13.3426i	1.64595	+	0.681777i	0.996879	−	0.0789472i	$-0.0251559\pi$
$383$	32.2120	+	13.3426i	1.64595	+	0.681777i	0.649076	+	0.760724i	$0.275156\pi$
$384$		0			0
$385$	15.8219	+	10.5719i	0.806359	+	0.538792i
$386$		0			0
$387$	−1.33886	−	1.33886i	−0.0680581	−	0.0680581i
$388$		0			0
$389$	7.40045	+	17.8663i	0.375218	+	0.905856i	0.992848	+	0.119387i	$0.0380929\pi$
$389$	7.40045	+	17.8663i	0.375218	+	0.905856i	−0.617630	+	0.786469i	$0.711907\pi$
$390$		0			0
$391$	5.24346	+	0.0160949i	0.265173	+	0.000813956i
$392$		0			0
$393$	−5.59970	−	13.5189i	−0.282467	−	0.681937i
$394$		0			0
$395$	−2.05760	+	2.05760i	−0.103529	+	0.103529i
$396$		0			0
$397$	11.2307	+	7.50410i	0.563652	+	0.376620i	0.804509	−	0.593940i	$-0.202429\pi$
$397$	11.2307	+	7.50410i	0.563652	+	0.376620i	−0.240857	+	0.970561i	$0.577429\pi$
$398$		0			0
$399$	−6.19449	+	14.9548i	−0.310112	+	0.748677i
$400$		0			0
$401$	38.5529	−	7.66865i	1.92524	−	0.382954i	0.925247	−	0.379366i	$-0.123858\pi$
$401$	38.5529	−	7.66865i	1.92524	−	0.382954i	0.999994	−	0.00358817i	$-0.00114215\pi$
$402$		0			0
$403$	11.0367	+	2.19535i	0.549779	+	0.109358i
$404$		0			0
$405$	−18.1685	−	27.1911i	−0.902801	−	1.35114i
$406$		0			0
$407$	−10.3010			−0.510604
$408$		0			0
$409$	11.9403			0.590408			0.295204	−	0.955434i	$-0.404612\pi$
$409$	11.9403			0.590408			0.295204	+	0.955434i	$0.404612\pi$
$410$		0			0
$411$	−2.03638	−	3.04766i	−0.100447	−	0.150330i
$412$		0			0
$413$	7.26017	+	1.44414i	0.357249	+	0.0710613i
$414$		0			0
$415$	60.8304	−	12.0999i	2.98605	−	0.593962i
$416$		0			0
$417$	−12.2364	+	29.5412i	−0.599217	+	1.44664i
$418$		0			0
$419$	8.58305	+	5.73501i	0.419309	+	0.280174i	0.747273	−	0.664517i	$-0.231363\pi$
$419$	8.58305	+	5.73501i	0.419309	+	0.280174i	−0.327964	+	0.944690i	$0.606363\pi$
$420$		0			0
$421$	−19.1617	+	19.1617i	−0.933883	+	0.933883i	−0.997946	−	0.0640632i	$-0.979594\pi$
$421$	−19.1617	+	19.1617i	−0.933883	+	0.933883i	0.0640632	+	0.997946i	$0.479594\pi$
$422$		0			0
$423$	−0.281602	−	0.679847i	−0.0136919	−	0.0330553i
$424$		0			0
$425$	−44.1676	+	8.64464i	−2.14245	+	0.419327i
$426$		0			0
$427$	−1.41810	−	3.42359i	−0.0686266	−	0.165679i
$428$		0			0
$429$	−6.47836	−	6.47836i	−0.312778	−	0.312778i
$430$		0			0
$431$	1.10864	+	0.740767i	0.0534011	+	0.0356815i	0.581984	−	0.813200i	$-0.302277\pi$
$431$	1.10864	+	0.740767i	0.0534011	+	0.0356815i	−0.528583	+	0.848882i	$0.677277\pi$
$432$		0			0
$433$	−27.7088	−	11.4773i	−1.33160	−	0.551566i	−0.400488	−	0.916302i	$-0.631159\pi$
$433$	−27.7088	−	11.4773i	−1.33160	−	0.551566i	−0.931111	+	0.364736i	$0.881159\pi$
$434$		0			0
$435$	−54.7175	+	10.8840i	−2.62350	+	0.521847i
$436$		0			0
$437$	1.37750	−	6.92516i	0.0658948	−	0.331276i
$438$		0			0
$439$	−18.7585	−	28.0741i	−0.895296	−	1.33990i	−0.940096	−	0.340909i	$-0.889265\pi$
$439$	−18.7585	−	28.0741i	−0.895296	−	1.33990i	0.0448004	−	0.998996i	$-0.485735\pi$
$440$		0			0
$441$			0.967114i			0.0460530i
$442$		0			0
$443$	−26.4412			−1.25626			−0.628130	−	0.778108i	$-0.716179\pi$
$443$	−26.4412			−1.25626			−0.628130	+	0.778108i	$0.716179\pi$
$444$		0			0
$445$	26.1014	−	17.4404i	1.23732	−	0.826753i
$446$		0			0
$447$	0.705060	+	0.140245i	0.0333482	+	0.00663337i
$448$		0			0
$449$	−4.71747	−	23.7163i	−0.222631	−	1.11924i	−0.916774	−	0.399406i	$-0.869216\pi$
$449$	−4.71747	−	23.7163i	−0.222631	−	1.11924i	0.694143	−	0.719837i	$-0.255784\pi$
$450$		0			0
$451$	4.31790	−	10.4243i	0.203322	−	0.490862i
$452$		0			0
$453$	18.8006	−	28.1370i	0.883328	−	1.32199i
$454$		0			0
$455$	10.0837	−	10.0837i	0.472731	−	0.472731i
$456$		0			0
$457$	−3.16113	+	1.30938i	−0.147871	+	0.0612504i	−0.455392	−	0.890291i	$-0.650501\pi$
$457$	−3.16113	+	1.30938i	−0.147871	+	0.0612504i	0.307520	+	0.951542i	$0.400501\pi$
$458$		0			0
$459$	15.7556	−	15.6592i	0.735408	−	0.730907i
$460$		0			0
$461$	−20.0966	+	8.32428i	−0.935992	+	0.387700i	−0.797948	−	0.602726i	$-0.794081\pi$
$461$	−20.0966	+	8.32428i	−0.935992	+	0.387700i	−0.138043	+	0.990426i	$0.544081\pi$
$462$		0			0
$463$	18.4645	+	18.4645i	0.858120	+	0.858120i	0.991117	−	0.132996i	$-0.0424599\pi$
$463$	18.4645	+	18.4645i	0.858120	+	0.858120i	−0.132996	+	0.991117i	$0.542460\pi$
$464$		0			0
$465$	−20.3421	+	30.4441i	−0.943343	+	1.41181i
$466$		0			0
$467$	−10.3991	−	4.30747i	−0.481215	−	0.199326i	0.128870	−	0.991661i	$-0.458865\pi$
$467$	−10.3991	−	4.30747i	−0.481215	−	0.199326i	−0.610085	+	0.792336i	$0.708865\pi$
$468$		0			0
$469$	−0.162735	−	0.818125i	−0.00751441	−	0.0377775i
$470$		0			0
$471$	0.914054	−	4.59526i	0.0421174	−	0.211739i
$472$		0			0
$473$	17.2877	−	11.5513i	0.794888	−	0.531127i
$474$		0			0
$475$			60.6043i			2.78072i
$476$		0			0
$477$		−	1.56085i		−	0.0714662i
$478$		0			0
$479$	13.6004	−	9.08748i	0.621417	−	0.415217i	−0.204614	−	0.978843i	$-0.565594\pi$
$479$	13.6004	−	9.08748i	0.621417	−	0.415217i	0.826030	+	0.563625i	$0.190594\pi$
$480$		0			0
$481$	−1.50605	+	7.57142i	−0.0686700	+	0.345227i
$482$		0			0
$483$	−0.723329	−	3.63642i	−0.0329126	−	0.165463i
$484$		0			0
$485$	9.47226	+	3.92354i	0.430113	+	0.178159i
$486$		0			0
$487$	−11.2391	+	16.8204i	−0.509290	+	0.762207i	−0.993632	−	0.112672i	$-0.964059\pi$
$487$	−11.2391	+	16.8204i	−0.509290	+	0.762207i	0.484342	+	0.874879i	$0.339059\pi$
$488$		0			0
$489$	−13.8892	−	13.8892i	−0.628092	−	0.628092i
$490$		0			0
$491$	19.3271	−	8.00557i	0.872222	−	0.361286i	0.0987466	−	0.995113i	$-0.468517\pi$
$491$	19.3271	−	8.00557i	0.872222	−	0.361286i	0.773475	+	0.633826i	$0.218517\pi$
$492$		0			0
$493$	−13.2004	−	32.1473i	−0.594516	−	1.44784i
$494$		0			0
$495$	−2.47318	+	1.02442i	−0.111161	+	0.0460445i
$496$		0			0
$497$	14.1812	−	14.1812i	0.636116	−	0.636116i
$498$		0			0
$499$	−5.07487	+	7.59508i	−0.227182	+	0.340002i	−0.927496	−	0.373833i	$-0.878043\pi$
$499$	−5.07487	+	7.59508i	−0.227182	+	0.340002i	0.700314	+	0.713835i	$0.253043\pi$
$500$		0			0
$501$	−4.80950	+	11.6112i	−0.214873	+	0.518749i
$502$		0			0
$503$	−4.29208	−	21.5777i	−0.191374	−	0.962103i	−0.950397	−	0.311039i	$-0.899323\pi$
$503$	−4.29208	−	21.5777i	−0.191374	−	0.962103i	0.759023	−	0.651064i	$-0.225677\pi$
$504$		0			0
$505$	48.9466	+	9.73609i	2.17810	+	0.433250i
$506$		0			0
$507$	12.2252	−	8.16859i	0.542938	−	0.362780i
$508$		0			0
$509$	−7.32849			−0.324830			−0.162415	−	0.986723i	$-0.551928\pi$
$509$	−7.32849			−0.324830			−0.162415	+	0.986723i	$0.551928\pi$
$510$		0			0
$511$		−	13.3648i		−	0.591222i
$512$		0			0
$513$	−16.6187	−	24.8716i	−0.733732	−	1.09811i
$514$		0			0
$515$	0.687740	−	3.45750i	0.0303054	−	0.152356i
$516$		0			0
$517$	7.92519	−	1.57642i	0.348549	−	0.0693308i
$518$		0			0
$519$	−17.7180	−	7.33902i	−0.777732	−	0.322147i
$520$		0			0
$521$	−21.4087	−	14.3048i	−0.937932	−	0.626706i	−0.0101977	−	0.999948i	$-0.503246\pi$
$521$	−21.4087	−	14.3048i	−0.937932	−	0.626706i	−0.927734	+	0.373242i	$0.878246\pi$
$522$		0			0
$523$	−3.54456	−	3.54456i	−0.154993	−	0.154993i	0.625351	−	0.780344i	$-0.284956\pi$
$523$	−3.54456	−	3.54456i	−0.154993	−	0.154993i	−0.780344	+	0.625351i	$0.784956\pi$
$524$		0			0
$525$	12.1783	+	29.4011i	0.531505	+	1.28317i
$526$		0			0
$527$	−21.0448	−	8.79282i	−0.916726	−	0.383021i
$528$		0			0
$529$	−8.18281	−	19.7550i	−0.355774	−	0.858915i
$530$		0			0
$531$	−0.736352	+	0.736352i	−0.0319550	+	0.0319550i
$532$		0			0
$533$	−7.03074	−	4.69779i	−0.304535	−	0.203484i
$534$		0			0
$535$	26.6069	−	64.2346i	1.15031	−	2.77711i
$536$		0			0
$537$	13.0987	−	2.60549i	0.565251	−	0.112435i
$538$		0			0
$539$	−10.4158	−	2.07183i	−0.448639	−	0.0892399i
$540$		0			0
$541$	−18.1292	−	27.1323i	−0.779436	−	1.16651i	−0.982302	−	0.187303i	$-0.940026\pi$
$541$	−18.1292	−	27.1323i	−0.779436	−	1.16651i	0.202866	−	0.979207i	$-0.434974\pi$
$542$		0			0
$543$	−0.626248			−0.0268749
$544$		0			0
$545$	−66.0971			−2.83129
$546$		0			0
$547$	−12.9644	−	19.4026i	−0.554318	−	0.829596i	0.443455	−	0.896297i	$-0.353753\pi$
$547$	−12.9644	−	19.4026i	−0.554318	−	0.829596i	−0.997773	+	0.0667009i	$0.978753\pi$
$548$		0			0
$549$	0.511291	+	0.101702i	0.0218214	+	0.00434054i
$550$		0			0
$551$	−45.8976	+	9.12960i	−1.95530	+	0.388934i
$552$		0			0
$553$	−0.490483	+	1.18413i	−0.0208575	+	0.0503544i
$554$		0			0
$555$	−20.8853	−	13.9551i	−0.886530	−	0.592361i
$556$		0			0
$557$	13.8015	−	13.8015i	0.584786	−	0.584786i	−0.351428	−	0.936215i	$-0.614304\pi$
$557$	13.8015	−	13.8015i	0.584786	−	0.584786i	0.936215	+	0.351428i	$0.114304\pi$
$558$		0			0
$559$	−5.96282	−	14.3955i	−0.252201	−	0.608866i
$560$		0			0
$561$	10.2691	+	15.4715i	0.433564	+	0.653206i
$562$		0			0
$563$	−11.3315	−	27.3567i	−0.477567	−	1.15295i	−0.960747	−	0.277428i	$-0.910518\pi$
$563$	−11.3315	−	27.3567i	−0.477567	−	1.15295i	0.483180	−	0.875521i	$-0.339482\pi$
$564$		0			0
$565$	10.7869	+	10.7869i	0.453806	+	0.453806i
$566$		0			0
$567$	−11.9766	−	8.00253i	−0.502971	−	0.336075i
$568$		0			0
$569$	−8.65964	−	3.58694i	−0.363031	−	0.150372i	0.193709	−	0.981059i	$-0.437948\pi$
$569$	−8.65964	−	3.58694i	−0.363031	−	0.150372i	−0.556740	+	0.830687i	$0.687948\pi$
$570$		0			0
$571$	12.2859	−	2.44381i	0.514147	−	0.102270i	0.0688038	−	0.997630i	$-0.478082\pi$
$571$	12.2859	−	2.44381i	0.514147	−	0.102270i	0.445343	+	0.895360i	$0.353082\pi$
$572$		0			0
$573$	4.44673	−	22.3552i	0.185765	−	0.933902i
$574$		0			0
$575$	−7.71218	−	11.5421i	−0.321620	−	0.481338i
$576$		0			0
$577$		−	5.73217i		−	0.238633i	−0.992856	−	0.119317i	$-0.961930\pi$
$577$		−	5.73217i		−	0.238633i	0.992856	−	0.119317i	$-0.0380704\pi$
$578$		0			0
$579$	16.2075			0.673560
$580$		0			0
$581$	22.7144	−	15.1773i	0.942351	−	0.629659i
$582$		0			0
$583$	16.8102	+	3.34376i	0.696209	+	0.138485i
$584$		0			0
$585$	0.391380	+	1.96760i	0.0161816	+	0.0813502i
$586$		0			0
$587$	−1.26920	+	3.06413i	−0.0523856	+	0.126470i	−0.947906	−	0.318551i	$-0.896804\pi$
$587$	−1.26920	+	3.06413i	−0.0523856	+	0.126470i	0.895520	+	0.445021i	$0.146804\pi$
$588$		0			0
$589$	−17.0632	+	25.5368i	−0.703075	+	1.05223i
$590$		0			0
$591$	−22.0785	+	22.0785i	−0.908187	+	0.908187i
$592$		0			0
$593$	12.2414	−	5.07054i	0.502693	−	0.208222i	−0.116903	−	0.993143i	$-0.537297\pi$
$593$	12.2414	−	5.07054i	0.502693	−	0.208222i	0.619596	+	0.784921i	$0.287297\pi$
$594$		0			0
$595$	−24.0816	+	15.9841i	−0.987251	+	0.655285i
$596$		0			0
$597$	−11.6311	+	4.81777i	−0.476030	+	0.197178i
$598$		0			0
$599$	−4.43417	−	4.43417i	−0.181175	−	0.181175i	0.610693	−	0.791868i	$-0.290891\pi$
$599$	−4.43417	−	4.43417i	−0.181175	−	0.181175i	−0.791868	+	0.610693i	$0.790891\pi$
$600$		0			0
$601$	4.36634	−	6.53469i	0.178107	−	0.266556i	−0.731665	−	0.681664i	$-0.761256\pi$
$601$	4.36634	−	6.53469i	0.178107	−	0.266556i	0.909772	+	0.415109i	$0.136256\pi$
$602$		0			0
$603$	0.108415	+	0.0449069i	0.00441500	+	0.00182875i
$604$		0			0
$605$	2.82650	+	14.2098i	0.114914	+	0.577710i
$606$		0			0
$607$	−2.60650	+	13.1038i	−0.105795	+	0.531866i	0.891147	+	0.453715i	$0.149902\pi$
$607$	−2.60650	+	13.1038i	−0.105795	+	0.531866i	−0.996942	+	0.0781510i	$0.975098\pi$
$608$		0			0
$609$	−20.4318	+	13.6521i	−0.827938	+	0.553210i
$610$		0			0
$611$		−	6.05561i		−	0.244984i
$612$		0			0
$613$			2.78252i			0.112385i	0.998420	+	0.0561924i	$0.0178960\pi$
$613$			2.78252i			0.112385i	−0.998420	+	0.0561924i	$0.982104\pi$
$614$		0			0
$615$	22.8766	−	15.2856i	0.922472	−	0.616376i
$616$		0			0
$617$	−3.33870	+	16.7848i	−0.134411	+	0.675730i	0.853548	+	0.521014i	$0.174446\pi$
$617$	−3.33870	+	16.7848i	−0.134411	+	0.675730i	−0.987959	+	0.154716i	$0.950554\pi$
$618$		0			0
$619$	6.44112	+	32.3817i	0.258891	+	1.30153i	0.863233	+	0.504806i	$0.168436\pi$
$619$	6.44112	+	32.3817i	0.258891	+	1.30153i	−0.604342	+	0.796725i	$0.706564\pi$
$620$		0			0
$621$	6.33005	+	2.62199i	0.254016	+	0.105217i
$622$		0			0
$623$	7.68181	−	11.4966i	0.307765	−	0.460603i
$624$		0			0
$625$	27.9804	+	27.9804i	1.11922	+	1.11922i
$626$		0			0
$627$	23.1020	−	9.56915i	0.922604	−	0.382155i
$628$		0			0
$629$	6.03205	−	14.4372i	0.240514	−	0.575647i
$630$		0			0
$631$	19.1037	−	7.91302i	0.760507	−	0.315012i	0.0314865	−	0.999504i	$-0.489976\pi$
$631$	19.1037	−	7.91302i	0.760507	−	0.315012i	0.729021	+	0.684492i	$0.239976\pi$
$632$		0			0
$633$	1.78501	−	1.78501i	0.0709476	−	0.0709476i
$634$		0			0
$635$	26.4368	−	39.5654i	1.04911	−	1.57011i
$636$		0			0
$637$	−3.04565	+	7.35284i	−0.120673	+	0.291330i
$638$		0			0
$639$	0.550418	+	2.76714i	0.0217742	+	0.109466i
$640$		0			0
$641$	−8.54254	−	1.69922i	−0.337410	−	0.0671150i	0.0234775	−	0.999724i	$-0.492526\pi$
$641$	−8.54254	−	1.69922i	−0.337410	−	0.0671150i	−0.360888	+	0.932609i	$0.617526\pi$
$642$		0			0
$643$	−19.0459	+	12.7260i	−0.751095	+	0.501866i	−0.871220	−	0.490893i	$-0.836671\pi$
$643$	−19.0459	+	12.7260i	−0.751095	+	0.501866i	0.120125	+	0.992759i	$0.461671\pi$
$644$		0			0
$645$	50.6993			1.99628
$646$		0			0
$647$			44.2598i			1.74003i	0.493024	+	0.870016i	$0.335891\pi$
$647$			44.2598i			1.74003i	−0.493024	+	0.870016i	$0.664109\pi$
$648$		0			0
$649$	−6.35301	−	9.50795i	−0.249377	−	0.373220i
$650$		0			0
$651$	−3.14630	+	15.8175i	−0.123313	+	0.619938i
$652$		0			0
$653$	−11.9296	+	2.37294i	−0.466841	+	0.0928604i	−0.422905	−	0.906174i	$-0.638990\pi$
$653$	−11.9296	+	2.37294i	−0.466841	+	0.0928604i	−0.0439355	+	0.999034i	$0.513990\pi$
$654$		0			0
$655$	−32.5059	−	13.4644i	−1.27011	−	0.526098i
$656$		0			0
$657$	1.56327	+	1.04455i	0.0609891	+	0.0407516i
$658$		0			0
$659$	26.0905	+	26.0905i	1.01634	+	1.01634i	0.999864	+	0.0164765i	$0.00524487\pi$
$659$	26.0905	+	26.0905i	1.01634	+	1.01634i	0.0164765	+	0.999864i	$0.494755\pi$
$660$		0			0
$661$	−4.70510	−	11.3591i	−0.183007	−	0.441818i	0.805577	−	0.592492i	$-0.201856\pi$
$661$	−4.70510	−	11.3591i	−0.183007	−	0.441818i	−0.988584	+	0.150674i	$0.951856\pi$
$662$		0			0
$663$	12.8731	−	5.28599i	0.499951	−	0.205291i
$664$		0			0
$665$	14.8946	+	35.9587i	0.577586	+	1.39442i
$666$		0			0
$667$	7.57941	−	7.57941i	0.293476	−	0.293476i
$668$		0			0
$669$	8.81217	+	5.88810i	0.340698	+	0.227647i
$670$		0			0
$671$	−2.19065	+	5.28871i	−0.0845693	+	0.204168i
$672$		0			0
$673$	−31.4502	+	6.25584i	−1.21232	+	0.241145i	−0.759529	−	0.650473i	$-0.774571\pi$
$673$	−31.4502	+	6.25584i	−1.21232	+	0.241145i	−0.452788	+	0.891618i	$0.649571\pi$
$674$		0			0
$675$	−57.6784	−	11.4729i	−2.22004	−	0.441594i
$676$		0			0
$677$	25.6042	+	38.3193i	0.984047	+	1.47273i	0.878168	+	0.478352i	$0.158766\pi$
$677$	25.6042	+	38.3193i	0.984047	+	1.47273i	0.105879	+	0.994379i	$0.466234\pi$
$678$		0			0
$679$	4.51592			0.173305
$680$		0			0
$681$	21.2341			0.813692
$682$		0			0
$683$	17.8349	+	26.6918i	0.682433	+	1.02133i	0.997388	+	0.0722266i	$0.0230105\pi$
$683$	17.8349	+	26.6918i	0.682433	+	1.02133i	−0.314955	+	0.949107i	$0.601990\pi$
$684$		0			0
$685$	−8.64404	−	1.71941i	−0.330272	−	0.0656951i
$686$		0			0
$687$	40.2573	−	8.00767i	1.53591	−	0.305512i
$688$		0			0
$689$	4.91543	−	11.8669i	0.187263	−	0.452093i
$690$		0			0
$691$	21.0814	+	14.0862i	0.801975	+	0.535863i	0.887682	−	0.460458i	$-0.152315\pi$
$691$	21.0814	+	14.0862i	0.801975	+	0.535863i	−0.0857066	+	0.996320i	$0.527315\pi$
$692$		0			0
$693$	−0.833744	+	0.833744i	−0.0316713	+	0.0316713i
$694$		0			0
$695$	29.4221	+	71.0313i	1.11605	+	2.69437i
$696$		0			0
$697$	12.0815	+	12.1559i	0.457618	+	0.460436i
$698$		0			0
$699$	1.13214	+	2.73322i	0.0428213	+	0.103380i
$700$		0			0
$701$	13.1199	+	13.1199i	0.495533	+	0.495533i	0.910044	−	0.414511i	$-0.136048\pi$
$701$	13.1199	+	13.1199i	0.495533	+	0.495533i	−0.414511	+	0.910044i	$0.636048\pi$
$702$		0			0
$703$	−17.5188	−	11.7057i	−0.660733	−	0.441488i
$704$		0			0
$705$	18.2038	+	7.54028i	0.685596	+	0.283983i
$706$		0			0
$707$	21.5591	−	4.28837i	0.810813	−	0.161281i
$708$		0			0
$709$	0.00545205	−	0.0274093i	0.000204756	−	0.00102938i	−0.980683	−	0.195605i	$-0.937333\pi$
$709$	0.00545205	−	0.0274093i	0.000204756	−	0.00102938i	0.980888	+	0.194576i	$0.0623330\pi$
$710$		0			0
$711$	−0.100173	−	0.149920i	−0.00375679	−	0.00562243i
$712$		0			0
$713$		−	7.03485i		−	0.263457i
$714$		0			0
$715$	−22.0294			−0.823852
$716$		0			0
$717$	−35.1546	+	23.4896i	−1.31287	+	0.877234i
$718$		0			0
$719$	50.0003	+	9.94567i	1.86469	+	0.370911i	0.992899	−	0.118959i	$-0.0379556\pi$
$719$	50.0003	+	9.94567i	1.86469	+	0.370911i	0.871796	+	0.489870i	$0.162956\pi$
$720$		0			0
$721$	−0.302923	−	1.52290i	−0.0112814	−	0.0567156i
$722$		0			0
$723$	11.8895	−	28.7037i	0.442175	−	1.06750i
$724$		0			0
$725$	−51.1136	+	76.4970i	−1.89831	+	2.84103i
$726$		0			0
$727$	−26.1689	+	26.1689i	−0.970549	+	0.970549i	−0.999579	−	0.0290292i	$-0.990758\pi$
$727$	−26.1689	+	26.1689i	−0.970549	+	0.970549i	0.0290292	+	0.999579i	$0.490758\pi$
$728$		0			0
$729$	26.6475	−	11.0378i	0.986944	−	0.408806i
$730$		0			0
$731$	6.06609	+	30.9932i	0.224363	+	1.14632i
$732$		0			0
$733$	27.7420	−	11.4911i	1.02467	−	0.424434i	0.193887	−	0.981024i	$-0.437891\pi$
$733$	27.7420	−	11.4911i	1.02467	−	0.424434i	0.830787	+	0.556590i	$0.187891\pi$
$734$		0			0
$735$	−18.3111	−	18.3111i	−0.675416	−	0.675416i
$736$		0			0
$737$	−0.715900	+	1.07142i	−0.0263705	+	0.0394663i
$738$		0			0
$739$	−5.46559	−	2.26392i	−0.201055	−	0.0832797i	0.279884	−	0.960034i	$-0.409704\pi$
$739$	−5.46559	−	2.26392i	−0.201055	−	0.0832797i	−0.480939	+	0.876754i	$0.659704\pi$
$740$		0			0
$741$	−3.65588	−	18.3793i	−0.134302	−	0.675182i
$742$		0			0
$743$	1.93989	−	9.75248i	0.0711677	−	0.357784i	−0.928749	−	0.370710i	$-0.879114\pi$
$743$	1.93989	−	9.75248i	0.0711677	−	0.357784i	0.999916	+	0.0129257i	$0.00411449\pi$
$744$		0			0
$745$	1.43721	−	0.960315i	0.0526554	−	0.0351832i
$746$		0			0
$747$			3.84311i			0.140612i
$748$		0			0
$749$		−	30.6240i		−	1.11898i
$750$		0			0
$751$	−35.8721	+	23.9690i	−1.30899	+	0.874641i	−0.997146	−	0.0754921i	$-0.975947\pi$
$751$	−35.8721	+	23.9690i	−1.30899	+	0.874641i	−0.311846	+	0.950133i	$0.600947\pi$
$752$		0			0
$753$	2.27691	−	11.4468i	0.0829751	−	0.417144i
$754$		0			0
$755$	−15.8741	−	79.8047i	−0.577719	−	2.90439i
$756$		0			0
$757$	−11.6970	−	4.84507i	−0.425136	−	0.176097i	0.159848	−	0.987142i	$-0.448899\pi$
$757$	−11.6970	−	4.84507i	−0.425136	−	0.176097i	−0.584985	+	0.811044i	$0.698899\pi$
$758$		0			0
$759$	−3.18205	+	4.76227i	−0.115501	+	0.172860i
$760$		0			0
$761$	14.9604	+	14.9604i	0.542315	+	0.542315i	0.924207	−	0.381892i	$-0.124727\pi$
$761$	14.9604	+	14.9604i	0.542315	+	0.542315i	−0.381892	+	0.924207i	$0.624727\pi$
$762$		0			0
$763$	−26.8971	+	11.1411i	−0.973739	+	0.403336i
$764$		0			0
$765$	0.0124810	−	4.06609i	0.000451251	−	0.147010i
$766$		0			0
$767$	−7.91731	+	3.27946i	−0.285878	+	0.118414i
$768$		0			0
$769$	5.62268	−	5.62268i	0.202759	−	0.202759i	−0.598422	−	0.801181i	$-0.704205\pi$
$769$	5.62268	−	5.62268i	0.202759	−	0.202759i	0.801181	+	0.598422i	$0.204205\pi$
$770$		0			0
$771$	−5.72179	+	8.56327i	−0.206065	+	0.308399i
$772$		0			0
$773$	16.6372	−	40.1658i	0.598399	−	1.44466i	−0.276813	−	0.960924i	$-0.589278\pi$
$773$	16.6372	−	40.1658i	0.598399	−	1.44466i	0.875212	−	0.483740i	$-0.160722\pi$
$774$		0			0
$775$	11.7798	+	59.2211i	0.423143	+	2.12728i
$776$		0			0
$777$	−10.8511	−	2.15842i	−0.389282	−	0.0774331i
$778$		0			0
$779$	19.1891	−	12.8217i	0.687521	−	0.459387i
$780$		0			0
$781$	−30.9811			−1.10859
$782$		0			0
$783$		−	45.4100i		−	1.62282i
$784$		0			0
$785$	−6.25890	−	9.36710i	−0.223390	−	0.334326i
$786$		0			0
$787$	5.54976	−	27.9005i	0.197827	−	0.994546i	−0.746462	−	0.665429i	$-0.768249\pi$
$787$	5.54976	−	27.9005i	0.197827	−	0.994546i	0.944289	−	0.329117i	$-0.106751\pi$
$788$		0			0
$789$	−12.3799	+	2.46252i	−0.440737	+	0.0876680i
$790$		0			0
$791$	6.20773	+	2.57132i	0.220721	+	0.0914258i
$792$		0			0
$793$	3.56700	+	2.38339i	0.126668	+	0.0846367i
$794$		0			0
$795$	29.5527	+	29.5527i	1.04813	+	1.04813i
$796$		0			0
$797$	16.1567	+	39.0057i	0.572299	+	1.38165i	0.899593	+	0.436729i	$0.143863\pi$
$797$	16.1567	+	39.0057i	0.572299	+	1.38165i	−0.327295	+	0.944922i	$0.606137\pi$
$798$		0			0
$799$	−2.43142	+	12.0304i	−0.0860173	+	0.425606i
$800$		0			0
$801$	0.744375	+	1.79708i	0.0263012	+	0.0634967i
$802$		0			0
$803$	−14.5987	+	14.5987i	−0.515176	+	0.515176i
$804$		0			0
$805$	−7.41257	−	4.95292i	−0.261259	−	0.174568i
$806$		0			0
$807$	0.534966	−	1.29152i	0.0188317	−	0.0454638i
$808$		0			0
$809$	20.4694	−	4.07161i	0.719664	−	0.143150i	0.178346	−	0.983968i	$-0.442925\pi$
$809$	20.4694	−	4.07161i	0.719664	−	0.143150i	0.541318	+	0.840818i	$0.317925\pi$
$810$		0			0
$811$	19.7791	+	3.93431i	0.694538	+	0.138152i	0.529721	−	0.848172i	$-0.322297\pi$
$811$	19.7791	+	3.93431i	0.694538	+	0.138152i	0.164817	+	0.986324i	$0.447297\pi$
$812$		0			0
$813$	0.456601	+	0.683351i	0.0160137	+	0.0239662i
$814$		0			0
$815$	−47.2297			−1.65438
$816$		0			0
$817$	42.5271			1.48784
$818$		0			0
$819$	0.490918	+	0.734711i	0.0171541	+	0.0256729i
$820$		0			0
$821$	−39.9253	−	7.94163i	−1.39340	−	0.277165i	−0.559387	−	0.828907i	$-0.688963\pi$
$821$	−39.9253	−	7.94163i	−1.39340	−	0.277165i	−0.834015	+	0.551742i	$0.813963\pi$
$822$		0			0
$823$	1.01321	−	0.201541i	0.0353184	−	0.00702527i	−0.177399	−	0.984139i	$-0.556768\pi$
$823$	1.01321	−	0.201541i	0.0353184	−	0.00702527i	0.212718	+	0.977114i	$0.431768\pi$
$824$		0			0
$825$	18.8129	−	45.4183i	0.654980	−	1.58126i
$826$		0			0
$827$	32.4708	+	21.6963i	1.12912	+	0.754454i	0.972430	−	0.233194i	$-0.0749176\pi$
$827$	32.4708	+	21.6963i	1.12912	+	0.754454i	0.156690	+	0.987648i	$0.449918\pi$
$828$		0			0
$829$	−10.1880	+	10.1880i	−0.353845	+	0.353845i	−0.861538	−	0.507693i	$-0.830498\pi$
$829$	−10.1880	+	10.1880i	−0.353845	+	0.353845i	0.507693	+	0.861538i	$0.330498\pi$
$830$		0			0
$831$	5.05787	+	12.2108i	0.175456	+	0.423588i
$832$		0			0
$833$	9.00294	−	13.3847i	0.311933	−	0.463753i
$834$		0			0
$835$	11.5644	+	27.9189i	0.400202	+	0.966173i
$836$		0			0
$837$	−21.0737	−	21.0737i	−0.728414	−	0.728414i
$838$		0			0
$839$	5.81558	+	3.88585i	0.200776	+	0.134154i	0.651894	−	0.758310i	$-0.273975\pi$
$839$	5.81558	+	3.88585i	0.200776	+	0.134154i	−0.451118	+	0.892464i	$0.648975\pi$
$840$		0			0
$841$	−38.8410	−	16.0885i	−1.33934	−	0.554774i
$842$		0			0
$843$	33.7575	−	6.71479i	1.16267	−	0.231270i
$844$		0			0
$845$	6.89709	−	34.6740i	0.237267	−	1.19282i
$846$		0			0
$847$	3.54536	+	5.30600i	0.121820	+	0.182316i
$848$		0			0
$849$			7.76046i			0.266338i
$850$		0			0
$851$	4.82605			0.165435
$852$		0			0
$853$	−24.7676	+	16.5492i	−0.848026	+	0.566633i	−0.901915	−	0.431914i	$-0.857838\pi$
$853$	−24.7676	+	16.5492i	−0.848026	+	0.566633i	0.0538885	+	0.998547i	$0.482838\pi$
$854$		0			0
$855$	−5.37019	−	1.06820i	−0.183657	−	0.0365316i
$856$		0			0
$857$	−1.68953	−	8.49385i	−0.0577133	−	0.290145i	0.941140	−	0.338017i	$-0.109756\pi$
$857$	−1.68953	−	8.49385i	−0.0577133	−	0.290145i	−0.998853	+	0.0478721i	$0.984756\pi$
$858$		0			0
$859$	−5.35005	+	12.9162i	−0.182541	+	0.440694i	−0.988489	−	0.151293i	$-0.951656\pi$
$859$	−5.35005	+	12.9162i	−0.182541	+	0.440694i	0.805948	+	0.591987i	$0.201656\pi$
$860$		0			0
$861$	6.73273	−	10.0762i	0.229451	−	0.343397i
$862$		0			0
$863$	−21.9763	+	21.9763i	−0.748081	+	0.748081i	−0.974119	−	0.226038i	$-0.927423\pi$
$863$	−21.9763	+	21.9763i	−0.748081	+	0.748081i	0.226038	+	0.974119i	$0.427423\pi$
$864$		0			0
$865$	−42.6026	+	17.6466i	−1.44853	+	0.600001i
$866$		0			0
$867$	−27.6970	+	5.33272i	−0.940638	+	0.181109i
$868$		0			0
$869$	1.82923	−	0.757691i	0.0620523	−	0.0257029i
$870$		0			0
$871$	0.682843	+	0.682843i	0.0231372	+	0.0231372i
$872$		0			0
$873$	−0.352950	+	0.528226i	−0.0119455	+	0.0178778i
$874$		0			0
$875$	38.3118	+	15.8693i	1.29518	+	0.536479i
$876$		0			0
$877$	0.471143	+	2.36860i	0.0159094	+	0.0799818i	0.987924	−	0.154937i	$-0.0495175\pi$
$877$	0.471143	+	2.36860i	0.0159094	+	0.0799818i	−0.972015	+	0.234919i	$0.924518\pi$
$878$		0			0
$879$	−6.56729	+	33.0160i	−0.221509	+	1.11360i
$880$		0			0
$881$	−30.2718	+	20.2270i	−1.01988	+	0.681464i	−0.948758	−	0.316003i	$-0.897659\pi$
$881$	−30.2718	+	20.2270i	−1.01988	+	0.681464i	−0.0711250	+	0.997467i	$0.522659\pi$
$882$		0			0
$883$		−	45.6924i		−	1.53767i	−0.639446	−	0.768836i	$-0.720836\pi$
$883$		−	45.6924i		−	1.53767i	0.639446	−	0.768836i	$-0.279164\pi$
$884$		0			0
$885$		−	27.8838i		−	0.937305i
$886$		0			0
$887$	11.7069	−	7.82227i	0.393078	−	0.262646i	−0.343288	−	0.939230i	$-0.611541\pi$
$887$	11.7069	−	7.82227i	0.393078	−	0.262646i	0.736365	+	0.676584i	$0.236541\pi$
$888$		0			0
$889$	4.08896	−	20.5566i	0.137139	−	0.689446i
$890$		0			0
$891$	4.34102	+	21.8238i	0.145430	+	0.731124i
$892$		0			0
$893$	15.2696	+	6.32486i	0.510976	+	0.211653i
$894$		0			0
$895$	17.8409	−	26.7007i	0.596354	−	0.892507i
$896$		0			0
$897$	3.03511	+	3.03511i	0.101340	+	0.101340i
$898$		0			0
$899$	−43.0755	+	17.8424i	−1.43665	+	0.595079i
$900$		0			0
$901$	−14.5300	+	21.6019i	−0.484066	+	0.719664i
$902$		0			0
$903$	20.6312	−	8.54574i	0.686564	−	0.284384i
$904$		0			0
$905$	−1.06477	+	1.06477i	−0.0353940	+	0.0353940i
$906$		0			0
$907$	−0.670220	+	1.00305i	−0.0222543	+	0.0333059i	−0.842430	−	0.538806i	$-0.818876\pi$
$907$	−0.670220	+	1.00305i	−0.0222543	+	0.0333059i	0.820176	+	0.572112i	$0.193876\pi$
$908$		0			0
$909$	−1.18338	+	2.85693i	−0.0392502	+	0.0947584i
$910$		0			0
$911$	−4.49473	−	22.5965i	−0.148917	−	0.748656i	−0.981000	−	0.194006i	$-0.937852\pi$
$911$	−4.49473	−	22.5965i	−0.148917	−	0.748656i	0.832084	−	0.554650i	$-0.187148\pi$
$912$		0			0
$913$	−41.3901	−	8.23300i	−1.36981	−	0.272473i
$914$		0			0
$915$	−11.6063	+	7.75506i	−0.383692	+	0.256374i
$916$		0			0
$917$	−15.4973			−0.511765
$918$		0			0
$919$			21.8485i			0.720717i	0.932814	+	0.360358i	$0.117346\pi$
$919$			21.8485i			0.720717i	−0.932814	+	0.360358i	$0.882654\pi$
$920$		0			0
$921$	−9.58480	−	14.3447i	−0.315830	−	0.472673i
$922$		0			0
$923$	−4.52955	+	22.7716i	−0.149092	+	0.749536i
$924$		0			0
$925$	−40.6268	+	8.08118i	−1.33580	+	0.265708i
$926$		0			0
$927$	0.201808	+	0.0835918i	0.00662826	+	0.00274551i
$928$		0			0
$929$	44.3386	+	29.6261i	1.45470	+	0.972000i	0.996539	+	0.0831312i	$0.0264921\pi$
$929$	44.3386	+	29.6261i	1.45470	+	0.972000i	0.458162	+	0.888869i	$0.348508\pi$
$930$		0			0
$931$	−15.3595	−	15.3595i	−0.503389	−	0.503389i
$932$		0			0
$933$	21.0510	+	50.8215i	0.689178	+	1.66382i
$934$		0			0
$935$	43.7649	+	8.84512i	1.43127	+	0.289266i
$936$		0			0
$937$	12.1271	+	29.2774i	0.396175	+	0.956451i	0.988564	+	0.150799i	$0.0481847\pi$
$937$	12.1271	+	29.2774i	0.396175	+	0.956451i	−0.592389	+	0.805652i	$0.701815\pi$
$938$		0			0
$939$	−24.6458	+	24.6458i	−0.804285	+	0.804285i
$940$		0			0
$941$	12.7817	+	8.54045i	0.416671	+	0.278411i	0.746183	−	0.665741i	$-0.231884\pi$
$941$	12.7817	+	8.54045i	0.416671	+	0.278411i	−0.329512	+	0.944151i	$0.606884\pi$
$942$		0			0
$943$	−2.02294	+	4.88380i	−0.0658759	+	0.159038i
$944$		0			0
$945$	−37.0423	+	7.36816i	−1.20498	+	0.239686i
$946$		0			0
$947$	5.57771	+	1.10948i	0.181251	+	0.0360531i	0.284881	−	0.958563i	$-0.408046\pi$
$947$	5.57771	+	1.10948i	0.181251	+	0.0360531i	−0.103630	+	0.994616i	$0.533046\pi$
$948$		0			0
$949$	8.59587	+	12.8646i	0.279034	+	0.417604i
$950$		0			0
$951$	12.0245			0.389921
$952$		0			0
$953$	50.4072			1.63285			0.816425	−	0.577451i	$-0.195952\pi$
$953$	50.4072			1.63285			0.816425	+	0.577451i	$0.195952\pi$
$954$		0			0
$955$	−30.4485	−	45.5694i	−0.985290	−	1.47459i
$956$		0			0
$957$	37.2307	+	7.40565i	1.20350	+	0.239391i
$958$		0			0
$959$	−3.80736	+	0.757331i	−0.122946	+	0.0244555i
$960$		0			0
$961$	0.153126	−	0.369678i	0.00493954	−	0.0119251i
$962$		0			0
$963$	3.58208	+	2.39347i	0.115431	+	0.0771285i
$964$		0			0
$965$	27.5564	−	27.5564i	0.887072	−	0.887072i
$966$		0			0
$967$	−20.5670	−	49.6531i	−0.661389	−	1.59674i	−0.795628	−	0.605786i	$-0.792859\pi$
$967$	−20.5670	−	49.6531i	−0.661389	−	1.59674i	0.134238	−	0.990949i	$-0.457141\pi$
$968$		0			0
$969$	−0.116585	+	37.9814i	−0.00374525	+	1.22014i
$970$		0			0
$971$	6.40801	+	15.4703i	0.205643	+	0.496466i	0.992728	−	0.120378i	$-0.0384108\pi$
$971$	6.40801	+	15.4703i	0.205643	+	0.496466i	−0.787085	+	0.616844i	$0.788411\pi$
$972$		0			0
$973$	23.9457	+	23.9457i	0.767663	+	0.767663i
$974$		0			0
$975$	−30.6326	−	20.4681i	−0.981029	−	0.655502i
$976$		0			0
$977$	51.9957	+	21.5373i	1.66349	+	0.689040i	0.998336	−	0.0576654i	$-0.0183657\pi$
$977$	51.9957	+	21.5373i	1.66349	+	0.689040i	0.665155	+	0.746706i	$0.268366\pi$
$978$		0			0
$979$	−20.9491	+	4.16704i	−0.669537	+	0.133179i
$980$		0			0
$981$	0.799012	−	4.01690i	0.0255105	−	0.128250i
$982$		0			0
$983$	−20.2455	−	30.2995i	−0.645731	−	0.966404i	−0.999517	−	0.0310779i	$-0.990106\pi$
$983$	−20.2455	−	30.2995i	−0.645731	−	0.966404i	0.353786	−	0.935326i	$-0.384894\pi$
$984$		0			0
$985$			75.0769i			2.39215i
$986$		0			0
$987$	8.67871			0.276246
$988$		0			0
$989$	−8.09928	+	5.41177i	−0.257542	+	0.172084i
$990$		0			0
$991$	−8.06621	−	1.60447i	−0.256232	−	0.0509677i	0.0653029	−	0.997865i	$-0.479199\pi$
$991$	−8.06621	−	1.60447i	−0.256232	−	0.0509677i	−0.321535	+	0.946898i	$0.604199\pi$
$992$		0			0
$993$	4.65623	+	23.4085i	0.147761	+	0.742845i
$994$		0			0
$995$	−11.5843	+	27.9669i	−0.367246	+	0.886610i
$996$		0			0
$997$	15.0804	−	22.5694i	0.477601	−	0.714780i	−0.511942	−	0.859020i	$-0.671074\pi$
$997$	15.0804	−	22.5694i	0.477601	−	0.714780i	0.989543	+	0.144240i	$0.0460737\pi$
$998$		0			0
$999$	14.4570	−	14.4570i	0.457399	−	0.457399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.cc.c.175.3		112
4.3	odd	2		136.2.s.c.107.13	yes	112
8.3	odd	2	inner	544.2.cc.c.175.4		112
8.5	even	2		136.2.s.c.107.6	yes	112
17.7	odd	16	inner	544.2.cc.c.143.4		112
68.7	even	16		136.2.s.c.75.6	✓	112
136.75	even	16	inner	544.2.cc.c.143.3		112
136.109	odd	16		136.2.s.c.75.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.6	✓	112	68.7	even	16
136.2.s.c.75.13	yes	112	136.109	odd	16
136.2.s.c.107.6	yes	112	8.5	even	2
136.2.s.c.107.13	yes	112	4.3	odd	2
544.2.cc.c.143.3		112	136.75	even	16	inner
544.2.cc.c.143.4		112	17.7	odd	16	inner
544.2.cc.c.175.3		112	1.1	even	1	trivial
544.2.cc.c.175.4		112	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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.cc (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.921778 - 1.37954i) q^{3} +(-3.91277 - 0.778297i) q^{5} +(-1.72342 + 0.342810i) q^{7} +(0.0945986 - 0.228381i) q^{9} +(2.25700 + 1.50808i) q^{11} +(1.43844 - 1.43844i) q^{13} +(2.53301 + 6.11523i) q^{15} +(-3.43525 + 2.28014i) q^{17} +(2.12471 + 5.12951i) q^{19} +(2.06153 + 2.06153i) q^{21} +(-1.05741 - 0.706536i) q^{23} +(10.0846 + 4.17717i) q^{25} +(-5.28409 + 1.05107i) q^{27} +(-1.64434 + 8.26664i) q^{29} +(3.07326 + 4.59945i) q^{31} -4.50373i q^{33} +7.01015 q^{35} +(-3.15531 + 2.10831i) q^{37} +(-3.31031 - 0.658462i) q^{39} +(-0.810929 - 4.07682i) q^{41} +(2.93119 - 7.07653i) q^{43} +(-0.547891 + 0.819977i) q^{45} +(2.10492 - 2.10492i) q^{47} +(-3.61450 + 1.49717i) q^{49} +(6.31208 + 2.63728i) q^{51} +(5.83351 - 2.41632i) q^{53} +(-7.65738 - 7.65738i) q^{55} +(5.11785 - 7.65940i) q^{57} +(-3.89198 - 1.61211i) q^{59} +(0.411419 + 2.06835i) q^{61} +(-0.0847419 + 0.426026i) q^{63} +(-6.74782 + 4.50875i) q^{65} +0.474710i q^{67} +2.11000i q^{69} +(-9.48983 + 6.34090i) q^{71} +(-1.48381 + 7.45963i) q^{73} +(-3.53318 - 17.7625i) q^{75} +(-4.40675 - 1.82533i) q^{77} +(0.405234 - 0.606476i) q^{79} +(5.79637 + 5.79637i) q^{81} +(-14.3632 + 5.94945i) q^{83} +(15.2160 - 6.24801i) q^{85} +(12.9199 - 5.35158i) q^{87} +(-5.56406 + 5.56406i) q^{89} +(-1.98593 + 2.97215i) q^{91} +(3.51226 - 8.47935i) q^{93} +(-4.32122 - 21.7242i) q^{95} +(-2.52059 - 0.501377i) q^{97} +(0.557926 - 0.372794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 16 q^{3} - 16 q^{9} + 16 q^{11} - 16 q^{17} + 16 q^{19} - 16 q^{25} - 32 q^{27} + 32 q^{35} - 16 q^{41} + 96 q^{43} - 16 q^{49} + 16 q^{51} + 32 q^{57} + 16 q^{59} + 64 q^{65} - 96 q^{73} + 16 q^{75}+ \cdots - 48 q^{99}+O(q^{100}) \) 112 * q + 16 * q^3 - 16 * q^9 + 16 * q^11 - 16 * q^17 + 16 * q^19 - 16 * q^25 - 32 * q^27 + 32 * q^35 - 16 * q^41 + 96 * q^43 - 16 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^59 + 64 * q^65 - 96 * q^73 + 16 * q^75 - 96 * q^81 - 128 * q^83 - 16 * q^89 + 16 * q^91 - 16 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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