LMFDB - Embedded newform 504.2.cc.a.293.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{12} + 19x^{8} + 810x^{4} + 6561 $ x^16 + 10x^12 + 19x^8 + 810*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			293.3
Root			$-1.24461 - 1.20455i$ of defining polynomial
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.a.461.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(0.420861 + 1.68014i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.87242 + 2.23574i) q^{5} +(-1.70349 - 1.76015i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +(-2.64575 + 1.41421i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(0.420861 + 1.68014i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.87242 + 2.23574i) q^{5} +(-1.70349 - 1.76015i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +(-2.64575 + 1.41421i) q^{9} -6.32364 q^{10} +(3.33095 + 0.951188i) q^{12} +(-2.79694 + 4.84444i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.12661 + 7.44716i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.24037 - 3.60288i) q^{18} +3.48300 q^{19} +(7.74485 - 4.47149i) q^{20} +(3.29294 - 3.18693i) q^{21} +(1.25963 + 0.727248i) q^{23} +(-4.75216 + 1.19038i) q^{24} +(7.49711 + 12.9854i) q^{25} -7.91094i q^{26} +(-3.48957 - 3.85005i) q^{27} -5.29150 q^{28} +(-2.66138 - 10.6246i) q^{30} +(4.89898 + 2.82843i) q^{32} -11.8304i q^{35} +(-0.196262 + 5.99679i) q^{36} +(-4.26578 + 2.46285i) q^{38} +(-9.31647 - 2.66042i) q^{39} +(-6.32364 + 10.9529i) q^{40} +(-1.77951 + 6.23164i) q^{42} +(-13.4073 - 0.438791i) q^{45} -2.05697 q^{46} +(4.97846 - 4.81819i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-18.3641 - 10.6025i) q^{50} +(5.59388 + 9.68889i) q^{52} +(6.99623 + 2.24783i) q^{54} +(6.48074 - 3.74166i) q^{56} +(1.46586 + 5.85193i) q^{57} +(12.4887 + 7.21033i) q^{59} +(10.7722 + 11.1306i) q^{60} +(-6.62389 - 11.4729i) q^{61} +(6.74037 + 4.19135i) q^{63} -8.00000 q^{64} +(-21.6619 + 12.5065i) q^{65} +(-0.691749 + 2.42243i) q^{69} +(8.36539 + 14.4893i) q^{70} -16.5762i q^{71} +(-4.00000 - 7.48331i) q^{72} +(-18.6620 + 18.0613i) q^{75} +(3.48300 - 6.03273i) q^{76} +(13.2915 - 3.32941i) q^{78} +(-6.02559 - 10.4366i) q^{79} -17.8860i q^{80} +(5.00000 - 7.48331i) q^{81} +(-1.21349 + 0.700610i) q^{83} +(-2.22699 - 8.89047i) q^{84} +(16.7308 - 8.94298i) q^{90} +14.8000 q^{91} +(2.51926 - 1.45450i) q^{92} +(13.4876 + 7.78709i) q^{95} +(-2.69037 + 9.42135i) q^{96} -9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4}+O(q^{10}) $ 16 * q + 16 * q^4	$ 16 q + 16 q^{4} - 16 q^{15} - 32 q^{16} - 16 q^{18} + 72 q^{23} + 40 q^{25} + 32 q^{30} - 40 q^{39} - 56 q^{49} - 144 q^{50} + 8 q^{57} - 16 q^{60} + 56 q^{63} - 128 q^{64} - 72 q^{65} - 64 q^{72} + 128 q^{78} + 80 q^{81} + 144 q^{92}+O(q^{100}) $ 16 * q + 16 * q^4 - 16 * q^15 - 32 * q^16 - 16 * q^18 + 72 * q^23 + 40 * q^25 + 32 * q^30 - 40 * q^39 - 56 * q^49 - 144 * q^50 + 8 * q^57 - 16 * q^60 + 56 * q^63 - 128 * q^64 - 72 * q^65 - 64 * q^72 + 128 * q^78 + 80 * q^81 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$3$	0.420861	+	1.68014i	0.242984	+	0.970030i
$3$	0.420861	+	1.68014i	0.242984	+	0.970030i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	3.87242	+	2.23574i	1.73180	+	0.999856i	0.874400	+	0.485206i	$0.161255\pi$
$5$	3.87242	+	2.23574i	1.73180	+	0.999856i	0.857401	+	0.514649i	$0.172078\pi$
$6$	−1.70349	−	1.76015i	−0.695446	−	0.718579i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$			2.82843i			1.00000i
$9$	−2.64575	+	1.41421i	−0.881917	+	0.471405i
$10$	−6.32364			−1.99971
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	3.33095	+	0.951188i	0.961563	+	0.274584i
$13$	−2.79694	+	4.84444i	−0.775732	+	1.34361i	0.158651	+	0.987335i	$0.449286\pi$
$13$	−2.79694	+	4.84444i	−0.775732	+	1.34361i	−0.934382	+	0.356272i	$0.884048\pi$
$14$	3.24037	+	1.87083i	0.866025	+	0.500000i
$15$	−2.12661	+	7.44716i	−0.549089	+	1.92285i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	2.24037	−	3.60288i	0.528060	−	0.849207i
$19$	3.48300			0.799054			0.399527	−	0.916721i	$-0.369174\pi$
$19$	3.48300			0.799054			0.399527	+	0.916721i	$0.369174\pi$
$20$	7.74485	−	4.47149i	1.73180	−	0.999856i
$21$	3.29294	−	3.18693i	0.718579	−	0.695446i
$22$		0			0
$23$	1.25963	+	0.727248i	0.262651	+	0.151642i	0.625543	−	0.780189i	$-0.284877\pi$
$23$	1.25963	+	0.727248i	0.262651	+	0.151642i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	−4.75216	+	1.19038i	−0.970030	+	0.242984i
$25$	7.49711	+	12.9854i	1.49942	+	2.59708i
$26$		−	7.91094i		−	1.55146i
$27$	−3.48957	−	3.85005i	−0.671569	−	0.740942i
$28$	−5.29150			−1.00000
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	−2.66138	−	10.6246i	−0.485899	−	1.93978i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	4.89898	+	2.82843i	0.866025	+	0.500000i
$33$		0			0
$34$		0			0
$35$		−	11.8304i		−	1.99971i
$36$	−0.196262	+	5.99679i	−0.0327103	+	0.999465i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−4.26578	+	2.46285i	−0.692001	+	0.399527i
$39$	−9.31647	−	2.66042i	−1.49183	−	0.426008i
$40$	−6.32364	+	10.9529i	−0.999856	+	1.73180i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$	−1.77951	+	6.23164i	−0.274584	+	0.961563i
$43$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$43$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$44$		0			0
$45$	−13.4073	−	0.438791i	−1.99864	−	0.0654111i
$46$	−2.05697			−0.303283
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	4.97846	−	4.81819i	0.718579	−	0.695446i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	−18.3641	−	10.6025i	−2.59708	−	1.49942i
$51$		0			0
$52$	5.59388	+	9.68889i	0.775732	+	1.34361i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	6.99623	+	2.24783i	0.952067	+	0.305890i
$55$		0			0
$56$	6.48074	−	3.74166i	0.866025	−	0.500000i
$57$	1.46586	+	5.85193i	0.194158	+	0.775107i
$58$		0			0
$59$	12.4887	+	7.21033i	1.62589	+	0.938705i	0.985303	+	0.170816i	$0.0546403\pi$
$59$	12.4887	+	7.21033i	1.62589	+	0.938705i	0.640582	+	0.767890i	$0.278693\pi$
$60$	10.7722	+	11.1306i	1.39069	+	1.43695i
$61$	−6.62389	−	11.4729i	−0.848103	−	1.46896i	−0.882899	−	0.469562i	$-0.844412\pi$
$61$	−6.62389	−	11.4729i	−0.848103	−	1.46896i	0.0347968	−	0.999394i	$-0.488922\pi$
$62$		0			0
$63$	6.74037	+	4.19135i	0.849207	+	0.528060i
$64$	−8.00000			−1.00000
$65$	−21.6619	+	12.5065i	−2.68683	+	1.55124i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	−0.691749	+	2.42243i	−0.0832768	+	0.291626i
$70$	8.36539	+	14.4893i	0.999856	+	1.73180i
$71$		−	16.5762i		−	1.96723i	−0.180288	−	0.983614i	$-0.557703\pi$
$71$		−	16.5762i		−	1.96723i	0.180288	−	0.983614i	$-0.442297\pi$
$72$	−4.00000	−	7.48331i	−0.471405	−	0.881917i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−18.6620	+	18.0613i	−2.15491	+	2.08553i
$76$	3.48300	−	6.03273i	0.399527	−	0.692001i
$77$		0			0
$78$	13.2915	−	3.32941i	1.50497	−	0.376981i
$79$	−6.02559	−	10.4366i	−0.677932	−	1.17421i	−0.975603	−	0.219544i	$-0.929543\pi$
$79$	−6.02559	−	10.4366i	−0.677932	−	1.17421i	0.297670	−	0.954669i	$-0.403790\pi$
$80$		−	17.8860i		−	1.99971i
$81$	5.00000	−	7.48331i	0.555556	−	0.831479i
$82$		0			0
$83$	−1.21349	+	0.700610i	−0.133198	+	0.0769020i	−0.565118	−	0.825010i	$-0.691170\pi$
$83$	−1.21349	+	0.700610i	−0.133198	+	0.0769020i	0.431920	+	0.901912i	$0.357836\pi$
$84$	−2.22699	−	8.89047i	−0.242984	−	0.970030i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	16.7308	−	8.94298i	1.76358	−	0.942673i
$91$	14.8000			1.55146
$92$	2.51926	−	1.45450i	0.262651	−	0.151642i
$93$		0			0
$94$		0			0
$95$	13.4876	+	7.78709i	1.38380	+	0.798939i
$96$	−2.69037	+	9.42135i	−0.274584	+	0.961563i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$		−	9.89949i		−	1.00000i
$99$		0			0
$100$	29.9884			2.99884
$101$	14.5113	−	8.37808i	1.44392	−	0.833650i	0.445815	−	0.895125i	$-0.352914\pi$
$101$	14.5113	−	8.37808i	1.44392	−	0.833650i	0.998109	+	0.0614754i	$0.0195806\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	−13.7022	−	7.91094i	−1.34361	−	0.775732i
$105$	19.8768	−	4.97898i	1.93978	−	0.485899i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−10.1581	+	2.19407i	−0.977459	+	0.211124i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	−5.29150	+	9.16515i	−0.500000	+	0.866025i
$113$	18.0296	+	10.4094i	1.69608	+	0.979234i	0.949409	+	0.314044i	$0.101684\pi$
$113$	18.0296	+	10.4094i	1.69608	+	0.979234i	0.746674	+	0.665190i	$0.231650\pi$
$114$	−5.93324	−	6.13060i	−0.555699	−	0.574183i
$115$	3.25188	+	5.63242i	0.303239	+	0.525226i
$116$		0			0
$117$	0.548932	−	16.7727i	0.0507488	−	1.55063i
$118$	−20.3939			−1.87741
$119$		0			0
$120$	−21.0637	−	6.01497i	−1.92285	−	0.549089i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	16.2252	+	9.36760i	1.46896	+	0.848103i
$123$		0			0
$124$		0			0
$125$			44.6891i			3.99711i
$126$	−11.2190	−	0.367172i	−0.999465	−	0.0327103i
$127$	−20.4422			−1.81395			−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−20.4422			−1.81395			−0.906977	+	0.421180i	$0.861616\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$		0			0
$130$	17.6868	−	30.6345i	1.55124	−	2.68683i
$131$	−1.71390	−	0.989523i	−0.149744	−	0.0864550i	0.423256	−	0.906010i	$-0.360887\pi$
$131$	−1.71390	−	0.989523i	−0.149744	−	0.0864550i	−0.573000	+	0.819555i	$0.694221\pi$
$132$		0			0
$133$	−4.60757	−	7.98055i	−0.399527	−	0.692001i
$134$		0			0
$135$	−4.90538	−	22.7108i	−0.422188	−	1.95464i
$136$		0			0
$137$	12.9615	−	7.48331i	1.10737	−	0.639343i	0.169226	−	0.985577i	$-0.445873\pi$
$137$	12.9615	−	7.48331i	1.10737	−	0.639343i	0.938148	+	0.346235i	$0.112540\pi$
$138$	−0.865698	−	3.45600i	−0.0736931	−	0.294194i
$139$	4.87789	−	8.44875i	0.413737	−	0.716614i	−0.581558	−	0.813505i	$-0.697557\pi$
$139$	4.87789	−	8.44875i	0.413737	−	0.716614i	0.995295	+	0.0968913i	$0.0308899\pi$
$140$	−20.4909	−	11.8304i	−1.73180	−	0.999856i
$141$		0			0
$142$	11.7211	+	20.3016i	0.983614	+	1.70367i
$143$		0			0
$144$	10.1905	+	6.33672i	0.849207	+	0.528060i
$145$		0			0
$146$		0			0
$147$	−11.6583	−	3.32916i	−0.961563	−	0.274584i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	10.0850	−	35.3165i	0.823436	−	2.88358i
$151$	7.22111	+	12.5073i	0.587646	+	1.01783i	0.994540	+	0.104357i	$0.0332784\pi$
$151$	7.22111	+	12.5073i	0.587646	+	1.01783i	−0.406894	+	0.913475i	$0.633388\pi$
$152$			9.85140i			0.799054i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−13.9245	+	13.4762i	−1.11485	+	1.07896i
$157$	3.14090	−	5.44019i	0.250671	−	0.434174i	−0.713040	−	0.701123i	$-0.752682\pi$
$157$	3.14090	−	5.44019i	0.250671	−	0.434174i	0.963711	+	0.266949i	$0.0860155\pi$
$158$	14.7596	+	8.52148i	1.17421	+	0.677932i
$159$		0			0
$160$	12.6473	+	21.9057i	0.999856	+	1.73180i
$161$		−	3.84823i		−	0.303283i
$162$	−0.832222	+	12.7007i	−0.0653855	+	0.997860i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$	0.990812	−	1.71614i	0.0769020	−	0.133198i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$	9.01401	+	9.31384i	0.695446	+	0.718579i
$169$	−9.14575	−	15.8409i	−0.703519	−	1.21853i
$170$		0			0
$171$	−9.21515	+	4.92570i	−0.704700	+	0.376678i
$172$		0			0
$173$	8.06457	−	4.65608i	0.613138	−	0.353995i	−0.161055	−	0.986945i	$-0.551490\pi$
$173$	8.06457	−	4.65608i	0.613138	−	0.353995i	0.774193	+	0.632950i	$0.218156\pi$
$174$		0			0
$175$	19.8355	−	34.3561i	1.49942	−	2.59708i
$176$		0			0
$177$	−6.85838	+	24.0173i	−0.515508	+	1.80525i
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−14.1673	+	22.7833i	−1.05597	+	1.69817i
$181$	16.0794			1.19517			0.597587	−	0.801804i	$-0.296126\pi$
$181$	16.0794			1.19517			0.597587	+	0.801804i	$0.296126\pi$
$182$	−18.1262	+	10.4652i	−1.34361	+	0.775732i
$183$	16.4884	−	15.9576i	1.21886	−	1.17962i
$184$	−2.05697	+	3.56277i	−0.151642	+	0.262651i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−4.20530	+	13.0888i	−0.305890	+	0.952067i
$190$	−22.0252			−1.59788
$191$	−21.7038	+	12.5307i	−1.57043	+	0.906691i	−0.574320	+	0.818631i	$0.694733\pi$
$191$	−21.7038	+	12.5307i	−1.57043	+	0.906691i	−0.996115	+	0.0880597i	$0.971933\pi$
$192$	−3.36689	−	13.4411i	−0.242984	−	0.970030i
$193$	−2.94014	+	5.09248i	−0.211636	+	0.366565i	−0.952227	−	0.305392i	$-0.901213\pi$
$193$	−2.94014	+	5.09248i	−0.211636	+	0.366565i	0.740591	+	0.671957i	$0.234546\pi$
$194$		0			0
$195$	−30.1293	−	31.1315i	−2.15761	−	2.22937i
$196$	7.00000	+	12.1244i	0.500000	+	0.866025i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−36.7282	+	21.2050i	−2.59708	+	1.49942i
$201$		0			0
$202$	−11.8484	+	20.5220i	−0.833650	+	1.44392i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.36115	−	0.142731i	−0.303121	−	0.00992047i
$208$	22.3755			1.55146
$209$		0			0
$210$	−20.8234	+	20.1530i	−1.43695	+	1.39069i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	27.8503	−	6.97626i	1.90827	−	0.478006i
$214$		0			0
$215$		0			0
$216$	10.8896	−	9.87000i	0.740942	−	0.671569i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$		−	14.9666i		−	1.00000i
$225$	−38.1996	−	23.7536i	−2.54664	−	1.58357i
$226$	−29.4422			−1.95847
$227$	0.331069	−	0.191143i	0.0219738	−	0.0126866i	−0.488973	−	0.872299i	$-0.662628\pi$
$227$	0.331069	−	0.191143i	0.0219738	−	0.0126866i	0.510947	+	0.859612i	$0.329295\pi$
$228$	11.6017	+	3.31299i	0.768341	+	0.219408i
$229$	10.9312	−	18.9334i	0.722355	−	1.25116i	−0.237699	−	0.971339i	$-0.576393\pi$
$229$	10.9312	−	18.9334i	0.722355	−	1.25116i	0.960053	−	0.279817i	$-0.0902736\pi$
$230$	−7.96545	−	4.59885i	−0.525226	−	0.303239i
$231$		0			0
$232$		0			0
$233$			9.77048i			0.640085i	0.947403	+	0.320043i	$0.103697\pi$
$233$			9.77048i			0.640085i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	11.1878	+	20.9304i	0.731367	+	1.36826i
$235$		0			0
$236$	24.9773	−	14.4207i	1.62589	−	0.938705i
$237$	14.9991	−	14.5162i	0.974295	−	0.942930i
$238$		0			0
$239$	−25.7404	−	14.8612i	−1.66501	−	0.961292i	−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−25.7404	−	14.8612i	−1.66501	−	0.961292i	−0.694737	−	0.719264i	$-0.744479\pi$
$240$	30.0509	−	7.52751i	1.93978	−	0.485899i
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$			15.5563i			1.00000i
$243$	14.6773	+	5.25127i	0.941551	+	0.336869i
$244$	−26.4956			−1.69621
$245$	−27.1070	+	15.6502i	−1.73180	+	0.999856i
$246$		0			0
$247$	−9.74174	+	16.8732i	−0.619852	+	1.07361i
$248$		0			0
$249$	−1.68784	−	1.74398i	−0.106962	−	0.110520i
$250$	−31.5999	−	54.7327i	−1.99856	−	3.46160i
$251$		−	9.32527i		−	0.588606i	−0.955712	−	0.294303i	$-0.904913\pi$
$251$		−	9.32527i		−	0.588606i	0.955712	−	0.294303i	$-0.0950874\pi$
$252$	14.0000	−	7.48331i	0.881917	−	0.471405i
$253$		0			0
$254$	25.0365	−	14.4548i	1.57093	−	0.906977i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$		0			0
$260$			50.0260i			3.10248i
$261$		0			0
$262$	2.79879			0.172910
$263$	0.341568	−	0.197204i	0.0210620	−	0.0121601i	−0.489432	−	0.872041i	$-0.662796\pi$
$263$	0.341568	−	0.197204i	0.0210620	−	0.0121601i	0.510494	+	0.859881i	$0.329463\pi$
$264$		0			0
$265$		0			0
$266$	11.2862	+	6.51609i	0.692001	+	0.399527i
$267$		0			0
$268$		0			0
$269$			30.5656i			1.86362i	0.362946	+	0.931810i	$0.381771\pi$
$269$			30.5656i			1.86362i	−0.362946	+	0.931810i	$0.618229\pi$
$270$	22.0668	+	24.3463i	1.34294	+	1.48167i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	6.22876	+	24.8661i	0.376981	+	1.50497i
$274$	−10.5830	+	18.3303i	−0.639343	+	1.10737i
$275$		0			0
$276$	3.50402	+	3.62057i	0.210917	+	0.217933i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$			13.7968i			0.827474i
$279$		0			0
$280$	33.4616			1.99971
$281$	16.0193	−	9.24872i	0.955629	−	0.551733i	0.0608039	−	0.998150i	$-0.480634\pi$
$281$	16.0193	−	9.24872i	0.955629	−	0.551733i	0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−11.5063	+	19.9295i	−0.683978	+	1.18468i	0.289779	+	0.957094i	$0.406418\pi$
$283$	−11.5063	+	19.9295i	−0.683978	+	1.18468i	−0.973757	+	0.227591i	$0.926915\pi$
$284$	−28.7107	−	16.5762i	−1.70367	−	0.983614i
$285$	−7.40699	+	25.9384i	−0.438752	+	1.53646i
$286$		0			0
$287$		0			0
$288$	−16.9615	−	0.555112i	−0.999465	−	0.0327103i
$289$	−17.0000			−1.00000
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.55188	−	1.47333i	−0.149082	−	0.0860728i	0.423603	−	0.905848i	$-0.360765\pi$
$293$	−2.55188	−	1.47333i	−0.149082	−	0.0860728i	−0.572686	+	0.819775i	$0.694098\pi$
$294$	16.6326	−	4.16632i	0.970030	−	0.242984i
$295$	32.2409	+	55.8429i	1.87714	+	3.25130i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.04622	+	4.06814i	−0.407493	+	0.235266i
$300$	12.6210	+	50.3848i	0.728673	+	2.90897i
$301$		0			0
$302$	−17.6880	−	10.2122i	−1.01783	−	0.587646i
$303$	20.1836	+	20.8550i	1.15952	+	1.19809i
$304$	−6.96600	−	12.0655i	−0.399527	−	0.692001i
$305$		−	59.2373i		−	3.39192i
$306$		0			0
$307$	28.1861			1.60866			0.804332	−	0.594180i	$-0.202523\pi$
$307$	28.1861			1.60866			0.804332	+	0.594180i	$0.202523\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	7.52479	−	26.3510i	0.426008	−	1.49183i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$			8.88379i			0.501341i
$315$	16.7308	+	31.3004i	0.942673	+	1.76358i
$316$	−24.1024			−1.35586
$317$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$317$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$318$		0			0
$319$		0			0
$320$	−30.9794	−	17.8860i	−1.73180	−	0.999856i
$321$		0			0
$322$	2.72111	+	4.71310i	0.151642	+	0.262651i
$323$		0			0
$324$	−7.96148	−	16.1436i	−0.442305	−	0.896865i
$325$	−83.8759			−4.65260
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$			2.80244i			0.153804i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−17.6257	−	5.03321i	−0.961563	−	0.274584i
$337$	13.2288	−	22.9129i	0.720616	−	1.24814i	−0.240137	−	0.970739i	$-0.577192\pi$
$337$	13.2288	−	22.9129i	0.720616	−	1.24814i	0.960753	−	0.277405i	$-0.0894744\pi$
$338$	22.4024	+	12.9340i	1.21853	+	0.703519i
$339$	−9.90130	+	34.6732i	−0.537765	+	1.88319i
$340$		0			0
$341$		0			0
$342$	7.80320	−	12.5488i	0.421949	−	0.678562i
$343$	18.5203			1.00000
$344$		0			0
$345$	−8.09467	+	7.83409i	−0.435803	+	0.421773i
$346$	−6.58469	+	11.4050i	−0.353995	+	0.613138i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	−12.0031	−	20.7899i	−0.642510	−	1.11286i	−0.984871	−	0.173291i	$-0.944560\pi$
$349$	−12.0031	−	20.7899i	−0.642510	−	1.11286i	0.342361	−	0.939569i	$-0.388774\pi$
$350$			56.1032i			2.99884i
$351$	28.4115	−	6.13668i	1.51649	−	0.327552i
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$	−8.58301	−	34.2646i	−0.456182	−	1.82114i
$355$	37.0601	−	64.1899i	1.96694	−	3.40685i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	23.9044i		−	1.26163i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$		−	23.9044i		−	1.26163i	0.775934	−	0.630814i	$-0.217279\pi$
$360$	1.24109	−	37.9215i	0.0654111	−	1.99864i
$361$	−6.86873			−0.361512
$362$	−19.6932	+	11.3699i	−1.03505	+	0.597587i
$363$	18.3202	+	5.23153i	0.961563	+	0.274584i
$364$	14.8000	−	25.6344i	0.775732	−	1.34361i
$365$		0			0
$366$	−8.91035	+	31.2030i	−0.465751	+	1.63101i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$		−	5.81798i		−	0.303283i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−75.0839	+	18.8079i	−3.87732	+	0.971236i
$376$		0			0
$377$		0			0
$378$	−4.10473	−	19.0040i	−0.211124	−	0.977459i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	26.9753	−	15.5742i	1.38380	−	0.798939i
$381$	−8.60334	−	34.3458i	−0.440763	−	1.75959i
$382$	17.7211	−	30.6939i	0.906691	−	1.57043i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	13.6279	+	14.0812i	0.695446	+	0.718579i
$385$		0			0
$386$		−	8.31598i		−	0.423272i
$387$		0			0
$388$		0			0
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$	58.9140	+	16.8235i	2.98323	+	0.851892i
$391$		0			0
$392$	−17.1464	−	9.89949i	−0.866025	−	0.500000i
$393$	0.941222	−	3.29605i	0.0474784	−	0.166264i
$394$		0			0
$395$		−	53.8868i		−	2.71134i
$396$		0			0
$397$	−12.8184			−0.643337			−0.321668	−	0.946852i	$-0.604244\pi$
$397$	−12.8184			−0.643337			−0.321668	+	0.946852i	$0.604244\pi$
$398$		0			0
$399$	11.4693	−	11.1001i	0.574183	−	0.555699i
$400$	29.9884	−	51.9415i	1.49942	−	2.59708i
$401$	−4.01580	−	2.31852i	−0.200540	−	0.115782i	0.396368	−	0.918092i	$-0.370271\pi$
$401$	−4.01580	−	2.31852i	−0.200540	−	0.115782i	−0.596907	+	0.802310i	$0.703604\pi$
$402$		0			0
$403$		0			0
$404$		−	33.5123i		−	1.66730i
$405$	36.0929	−	17.7998i	1.79347	−	0.884481i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$	18.0280	+	18.6277i	0.889256	+	0.918836i
$412$		0			0
$413$		−	38.1535i		−	1.87741i
$414$	5.44222	−	2.90899i	0.267471	−	0.142969i
$415$	−6.26554			−0.307563
$416$	−27.4043	+	15.8219i	−1.34361	+	0.775732i
$417$	16.2480	+	4.63979i	0.795669	+	0.227212i
$418$		0			0
$419$	−23.5656	−	13.6056i	−1.15126	−	0.664678i	−0.202063	−	0.979373i	$-0.564764\pi$
$419$	−23.5656	−	13.6056i	−1.15126	−	0.664678i	−0.949193	+	0.314695i	$0.898098\pi$
$420$	11.2530	−	39.4067i	0.549089	−	1.92285i
$421$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$421$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−29.1765	+	28.2373i	−1.41361	+	1.36810i
$427$	−17.5252	+	30.3545i	−0.848103	+	1.46896i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			37.4166i			1.80229i	0.433515	+	0.901146i	$0.357273\pi$
$431$			37.4166i			1.80229i	−0.433515	+	0.901146i	$0.642727\pi$
$432$	−6.35781	+	19.7883i	−0.305890	+	0.952067i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.38729	+	2.53300i	0.209872	+	0.121170i
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	0.686915	−	20.9888i	0.0327103	−	0.999465i
$442$		0			0
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	10.5830	+	18.3303i	0.500000	+	0.866025i
$449$			40.9474i			1.93243i	0.257743	+	0.966213i	$0.417021\pi$
$449$			40.9474i			1.93243i	−0.257743	+	0.966213i	$0.582979\pi$
$450$	63.5810	+	2.08087i	2.99724	+	0.0980930i
$451$		0			0
$452$	36.0592	−	20.8188i	1.69608	−	0.979234i
$453$	−17.9750	+	17.3963i	−0.844539	+	0.817351i
$454$	−0.270317	+	0.468203i	−0.0126866	+	0.0219738i
$455$	57.3119	+	33.0891i	2.68683	+	1.55124i
$456$	−16.5518	+	4.14608i	−0.775107	+	0.194158i
$457$	−17.0483	−	29.5285i	−0.797486	−	1.38129i	−0.921249	−	0.388974i	$-0.872830\pi$
$457$	−17.0483	−	29.5285i	−0.797486	−	1.38129i	0.123763	−	0.992312i	$-0.460504\pi$
$458$			30.9181i			1.44471i
$459$		0			0
$460$	13.0075			0.606479
$461$	−23.0428	+	13.3038i	−1.07321	+	0.619619i	−0.929057	−	0.369937i	$-0.879379\pi$
$461$	−23.0428	+	13.3038i	−1.07321	+	0.619619i	−0.144154	+	0.989555i	$0.546046\pi$
$462$		0			0
$463$	8.08256	−	13.9994i	0.375628	−	0.650608i	−0.614792	−	0.788689i	$-0.710760\pi$
$463$	8.08256	−	13.9994i	0.375628	−	0.650608i	0.990421	+	0.138081i	$0.0440936\pi$
$464$		0			0
$465$		0			0
$466$	−6.90877	−	11.9663i	−0.320043	−	0.554330i
$467$			11.6182i			0.537627i	0.963192	+	0.268814i	$0.0866316\pi$
$467$			11.6182i			0.537627i	−0.963192	+	0.268814i	$0.913368\pi$
$468$	−28.5022	−	17.7234i	−1.31751	−	0.819266i
$469$		0			0
$470$		0			0
$471$	10.4622	+	2.98758i	0.482071	+	0.137661i
$472$	−20.3939	+	35.3233i	−0.938705	+	1.62589i
$473$		0			0
$474$	−8.10553	+	28.3846i	−0.372299	+	1.30375i
$475$	26.1124	+	45.2280i	1.19812	+	2.07520i
$476$		0			0
$477$		0			0
$478$	42.0338			1.92258
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	−31.4820	+	30.4685i	−1.43695	+	1.39069i
$481$		0			0
$482$		0			0
$483$	6.46557	−	1.61957i	0.294194	−	0.0736931i
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	−21.6892	+	3.94698i	−0.983842	+	0.179039i
$487$	−38.4422			−1.74198			−0.870992	−	0.491298i	$-0.836523\pi$
$487$	−38.4422			−1.74198			−0.870992	+	0.491298i	$0.836523\pi$
$488$	32.4503	−	18.7352i	1.46896	−	0.848103i
$489$		0			0
$490$	22.1327	−	38.3350i	0.999856	−	1.73180i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$		0			0
$494$		−	27.5538i		−	1.23970i
$495$		0			0
$496$		0			0
$497$	−37.9807	+	21.9282i	−1.70367	+	0.983614i
$498$	3.30035	+	0.942449i	0.147892	+	0.0422322i
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	77.4037	+	44.6891i	3.46160	+	1.99856i
$501$		0			0
$502$	6.59396	+	11.4211i	0.294303	+	0.509747i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−11.8549	+	19.0646i	−0.528060	+	0.849207i
$505$	74.9250			3.33412
$506$		0			0
$507$	22.7659	−	22.0330i	1.01107	−	0.978519i
$508$	−20.4422	+	35.4070i	−0.906977	+	1.57093i
$509$	21.7667	+	12.5670i	0.964793	+	0.557024i	0.897645	−	0.440719i	$-0.145277\pi$
$509$	21.7667	+	12.5670i	0.964793	+	0.557024i	0.0671482	+	0.997743i	$0.478610\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	1.00000i
$513$	−12.1542	−	13.4097i	−0.536620	−	0.592053i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	11.2169	+	11.5901i	0.492369	+	0.508747i
$520$	−35.3737	−	61.2690i	−1.55124	−	2.68683i
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	−40.8334			−1.78552			−0.892759	−	0.450535i	$-0.851233\pi$
$523$	−40.8334			−1.78552			−0.892759	+	0.450535i	$0.851233\pi$
$524$	−3.42781	+	1.97905i	−0.149744	+	0.0864550i
$525$	66.0711	+	18.8673i	2.88358	+	0.823436i
$526$	−0.278889	+	0.483050i	−0.0121601	+	0.0210620i
$527$		0			0
$528$		0			0
$529$	−10.4422	−	18.0865i	−0.454010	−	0.786368i
$530$		0			0
$531$	−43.2388	−	1.41511i	−1.87641	−	0.0614106i
$532$	−18.4303			−0.799054
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−21.6132	−	37.4351i	−0.931810	−	1.61394i
$539$		0			0
$540$	−44.2417	−	14.2144i	−1.90386	−	0.611692i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	6.76721	+	27.0157i	0.290409	+	1.15935i
$544$		0			0
$545$		0			0
$546$	−25.2116	−	26.0503i	−1.07896	−	1.11485i
$547$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$547$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$548$		−	29.9333i		−	1.27869i
$549$	33.7503	+	20.9869i	1.44043	+	0.895699i
$550$		0			0
$551$		0			0
$552$	−6.85166	−	1.95656i	−0.291626	−	0.0832768i
$553$	−15.9422	+	27.6127i	−0.677932	+	1.17421i
$554$		0			0
$555$		0			0
$556$	−9.75578	−	16.8975i	−0.413737	−	0.716614i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	−40.9819	+	23.6609i	−1.73180	+	0.999856i
$561$		0			0
$562$	−13.0797	+	22.6547i	−0.551733	+	0.955629i
$563$	31.3105	+	18.0771i	1.31958	+	0.761859i	0.983661	−	0.180032i	$-0.0576202\pi$
$563$	31.3105	+	18.0771i	1.31958	+	0.761859i	0.335918	+	0.941891i	$0.390954\pi$
$564$		0			0
$565$	46.5455	+	80.6192i	1.95818	+	3.39168i
$566$		−	32.5447i		−	1.36796i
$567$	−23.7608	−	1.55694i	−0.997860	−	0.0653855i
$568$	46.8844			1.96723
$569$	−2.44949	+	1.41421i	−0.102688	+	0.0592869i	−0.550464	−	0.834859i	$-0.685549\pi$
$569$	−2.44949	+	1.41421i	−0.102688	+	0.0592869i	0.447777	+	0.894146i	$0.352216\pi$
$570$	−9.26957	−	37.0055i	−0.388260	−	1.54999i
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	−30.1877	−	31.1918i	−1.26111	−	1.30306i
$574$		0			0
$575$			21.8090i			0.909499i
$576$	21.1660	−	11.3137i	0.881917	−	0.471405i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	20.8207	−	12.0208i	0.866025	−	0.500000i
$579$	−9.79348	−	2.79663i	−0.407003	−	0.116224i
$580$		0			0
$581$	3.21060	+	1.85364i	0.133198	+	0.0769020i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	39.6251	−	63.7236i	1.63830	−	2.63465i
$586$	4.16720			0.172146
$587$	13.6733	−	7.89427i	0.564357	−	0.325831i	−0.190536	−	0.981680i	$-0.561022\pi$
$587$	13.6733	−	7.89427i	0.564357	−	0.325831i	0.754892	+	0.655849i	$0.227689\pi$
$588$	−17.4246	+	16.8637i	−0.718579	+	0.695446i
$589$		0			0
$590$	−78.9738	−	45.5956i	−3.25130	−	1.87714i
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	5.75321	−	9.96486i	0.235266	−	0.407493i
$599$	9.79796	+	5.65685i	0.400334	+	0.231133i	0.686628	−	0.727009i	$-0.259090\pi$
$599$	9.79796	+	5.65685i	0.400334	+	0.231133i	−0.286294	+	0.958142i	$0.592423\pi$
$600$	−51.0849	−	52.7842i	−2.08553	−	2.15491i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	28.8844			1.17529
$605$	42.5967	−	24.5932i	1.73180	−	0.999856i
$606$	−39.4664	−	11.2700i	−1.60321	−	0.457814i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	17.0631	+	9.85140i	0.692001	+	0.399527i
$609$		0			0
$610$	41.8871	+	72.5506i	1.69596	+	2.93749i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−34.5207	+	19.9306i	−1.39314	+	0.804332i
$615$		0			0
$616$		0			0
$617$	−12.2474	−	7.07107i	−0.493064	−	0.284670i	0.232781	−	0.972529i	$-0.425218\pi$
$617$	−12.2474	−	7.07107i	−0.493064	−	0.284670i	−0.725845	+	0.687859i	$0.758551\pi$
$618$		0			0
$619$	−21.9553	−	38.0277i	−0.882457	−	1.52846i	−0.848601	−	0.529034i	$-0.822554\pi$
$619$	−21.9553	−	38.0277i	−0.882457	−	1.52846i	−0.0338565	−	0.999427i	$-0.510779\pi$
$620$		0			0
$621$	−1.59563	−	7.38742i	−0.0640305	−	0.296447i
$622$		0			0
$623$		0			0
$624$	9.41699	+	37.5940i	0.376981	+	1.50497i
$625$	−62.4278	+	108.128i	−2.49711	+	4.32512i
$626$		0			0
$627$		0			0
$628$	−6.28179	−	10.8804i	−0.250671	−	0.434174i
$629$		0			0
$630$	−42.6237	−	26.5046i	−1.69817	−	1.05597i
$631$	−47.9141			−1.90743			−0.953716	−	0.300709i	$-0.902777\pi$
$631$	−47.9141			−1.90743			−0.953716	+	0.300709i	$0.902777\pi$
$632$	29.5193	−	17.0430i	1.17421	−	0.677932i
$633$		0			0
$634$		0			0
$635$	−79.1609	−	45.7036i	−3.14141	−	1.81369i
$636$		0			0
$637$	−19.5786	−	33.9111i	−0.775732	−	1.34361i
$638$		0			0
$639$	23.4422	+	43.8564i	0.927360	+	1.73493i
$640$	50.5891			1.99971
$641$	−32.7265	+	18.8947i	−1.29262	+	0.746295i	−0.979118	−	0.203292i	$-0.934836\pi$
$641$	−32.7265	+	18.8947i	−1.29262	+	0.746295i	−0.313503	+	0.949587i	$0.601502\pi$
$642$		0			0
$643$	−24.1817	+	41.8838i	−0.953631	+	1.65174i	−0.216161	+	0.976358i	$0.569354\pi$
$643$	−24.1817	+	41.8838i	−0.953631	+	1.65174i	−0.737470	+	0.675380i	$0.763980\pi$
$644$	−6.66533	−	3.84823i	−0.262651	−	0.151642i
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	21.1660	+	14.1421i	0.831479	+	0.555556i
$649$		0			0
$650$	102.727	−	59.3092i	4.02927	−	2.32630i
$651$		0			0
$652$		0			0
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$		0			0
$655$	−4.42464	−	7.66370i	−0.172885	−	0.299446i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	−23.5785	+	40.8392i	−0.917097	+	1.58846i	−0.113296	+	0.993561i	$0.536141\pi$
$661$	−23.5785	+	40.8392i	−0.917097	+	1.58846i	−0.803801	+	0.594898i	$0.797193\pi$
$662$		0			0
$663$		0			0
$664$	−1.98162	−	3.43228i	−0.0769020	−	0.133198i
$665$		−	41.2054i		−	1.59788i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	25.1461	−	6.29888i	0.970030	−	0.242984i
$673$	−12.9422	−	22.4166i	−0.498886	−	0.864096i	0.501113	−	0.865382i	$-0.332924\pi$
$673$	−12.9422	−	22.4166i	−0.498886	−	0.864096i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$			37.4166i			1.44123i
$675$	23.8326	−	74.1777i	0.917318	−	2.85510i
$676$	−36.5830			−1.40704
$677$	−44.3171	+	25.5865i	−1.70324	+	0.983368i	−0.760809	+	0.648976i	$0.775198\pi$
$677$	−44.3171	+	25.5865i	−1.70324	+	0.983368i	−0.942434	+	0.334392i	$0.891469\pi$
$678$	−12.3911	−	49.4671i	−0.475877	−	1.89977i
$679$		0			0
$680$		0			0
$681$	0.460482	+	0.475799i	0.0176457	+	0.0182326i
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$	−0.683579	+	20.8868i	−0.0261373	+	0.798627i
$685$	66.9231			2.55700
$686$	−22.6826	+	13.0958i	−0.866025	+	0.500000i
$687$	36.4113	+	10.3976i	1.38918	+	0.396695i
$688$		0			0
$689$		0			0
$690$	4.37437	−	15.3186i	0.166530	−	0.583167i
$691$	23.8488	+	41.3074i	0.907252	+	1.57141i	0.817866	+	0.575409i	$0.195157\pi$
$691$	23.8488	+	41.3074i	0.907252	+	1.57141i	0.0893857	+	0.995997i	$0.471510\pi$
$692$		−	18.6243i		−	0.707991i
$693$		0			0
$694$		0			0
$695$	37.7785	−	21.8114i	1.43302	−	0.827355i
$696$		0			0
$697$		0			0
$698$	29.4014	+	16.9749i	1.11286	+	0.642510i
$699$	−16.4158	+	4.11202i	−0.620902	+	0.155531i
$700$	−39.6710	−	68.7122i	−1.49942	−	2.59708i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−30.4575	+	27.6058i	−1.14954	+	1.04191i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−38.3932	−	22.1663i	−1.44392	−	0.833650i
$708$	34.7407	+	35.8963i	1.30564	+	1.34907i
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$			104.822i			3.93389i
$711$	30.7019	+	19.0913i	1.15141	+	0.715978i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	14.1358	−	49.5020i	0.527911	−	1.84869i
$718$	16.9030	+	29.2768i	0.630814	+	1.09260i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	25.2946	+	47.3218i	0.942673	+	1.76358i
$721$		0			0
$722$	8.41244	−	4.85692i	0.313079	−	0.180756i
$723$		0			0
$724$	16.0794	−	27.8504i	0.597587	−	1.03505i
$725$		0			0
$726$	−26.1369	+	6.54707i	−0.970030	+	0.242984i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$			41.8608i			1.55146i
$729$	−2.64575	+	26.8701i	−0.0979908	+	0.995187i
$730$		0			0
$731$		0			0
$732$	−11.1510	−	44.5163i	−0.412151	−	1.64537i
$733$	−26.8377	+	46.4842i	−0.991272	+	1.71693i	−0.381466	+	0.924383i	$0.624581\pi$
$733$	−26.8377	+	46.4842i	−0.991272	+	1.71693i	−0.609806	+	0.792551i	$0.708753\pi$
$734$		0			0
$735$	−37.7029	−	38.9570i	−1.39069	−	1.43695i
$736$	4.11393	+	7.12554i	0.151642	+	0.262651i
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$	−32.4493	−	9.26622i	−1.19205	−	0.340403i
$742$		0			0
$743$	6.48074	+	3.74166i	0.237755	+	0.137268i	0.614145	−	0.789193i	$-0.289501\pi$
$743$	6.48074	+	3.74166i	0.237755	+	0.137268i	−0.376389	+	0.926462i	$0.622834\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.21979	−	3.56978i	0.0812178	−	0.130611i
$748$		0			0
$749$		0			0
$750$	78.6595	−	76.1272i	2.87224	−	2.77977i
$751$	22.2211	−	38.4881i	0.810860	−	1.40445i	−0.101403	−	0.994845i	$-0.532333\pi$
$751$	22.2211	−	38.4881i	0.810860	−	1.40445i	0.912263	−	0.409605i	$-0.134333\pi$
$752$		0			0
$753$	15.6678	−	3.92464i	0.570965	−	0.143022i
$754$		0			0
$755$			64.5782i			2.35024i
$756$	18.4651	+	20.3725i	0.671569	+	0.740942i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	−22.0252	+	38.1488i	−0.798939	+	1.38380i
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$	34.8231	+	35.9814i	1.26151	+	1.30347i
$763$		0			0
$764$			50.1229i			1.81338i
$765$		0			0
$766$		0			0
$767$	−69.8601	+	40.3337i	−2.52250	+	1.45637i
$768$	−26.6476	−	7.60951i	−0.961563	−	0.274584i
$769$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$769$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$		0			0
$772$	5.88029	+	10.1850i	0.211636	+	0.366565i
$773$		−	54.2265i		−	1.95039i	−0.221340	−	0.975197i	$-0.571043\pi$
$773$		−	54.2265i		−	1.95039i	0.221340	−	0.975197i	$-0.428957\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−84.0507	+	21.0540i	−3.00950	+	0.753854i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	28.0000			1.00000
$785$	24.3258	−	14.0445i	0.868223	−	0.501269i
$786$	1.17790	+	4.70237i	0.0420144	+	0.167728i
$787$	−16.6061	+	28.7627i	−0.591945	+	1.02528i	0.402025	+	0.915629i	$0.368306\pi$
$787$	−16.6061	+	28.7627i	−0.591945	+	1.02528i	−0.993970	+	0.109650i	$0.965027\pi$
$788$		0			0
$789$	0.475084	+	0.490887i	0.0169134	+	0.0174760i
$790$	38.1037	+	65.9975i	1.35567	+	2.34809i
$791$		−	55.0814i		−	1.95847i
$792$		0			0
$793$	74.1065			2.63160
$794$	15.6993	−	9.06397i	0.557146	−	0.321668i
$795$		0			0
$796$		0			0
$797$	−38.4300	−	22.1876i	−1.36126	−	0.785924i	−0.371469	−	0.928445i	$-0.621146\pi$
$797$	−38.4300	−	22.1876i	−1.36126	−	0.785924i	−0.989792	+	0.142521i	$0.954479\pi$
$798$	−6.19803	+	21.7048i	−0.219408	+	0.768341i
$799$		0			0
$800$			84.8201i			2.99884i
$801$		0			0
$802$	6.55778			0.231563
$803$		0			0
$804$		0			0
$805$	8.60367	−	14.9020i	0.303239	−	0.525226i
$806$		0			0
$807$	−51.3546	+	12.8639i	−1.80777	+	0.452831i
$808$	23.6968	+	41.0440i	0.833650	+	1.44392i
$809$			31.1127i			1.09386i	0.837177	+	0.546932i	$0.184204\pi$
$809$			31.1127i			1.09386i	−0.837177	+	0.546932i	$0.815796\pi$
$810$	−31.6182	+	47.3218i	−1.11095	+	1.66272i
$811$	29.9510			1.05172			0.525861	−	0.850570i	$-0.323743\pi$
$811$	29.9510			1.05172			0.525861	+	0.850570i	$0.323743\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−39.1572	+	20.9304i	−1.36826	+	0.731367i
$820$		0			0
$821$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$821$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$822$	−35.2515	−	10.0664i	−1.22954	−	0.351107i
$823$	13.2288	−	22.9129i	0.461125	−	0.798693i	−0.537892	−	0.843014i	$-0.680779\pi$
$823$	13.2288	−	22.9129i	0.461125	−	0.798693i	0.999017	+	0.0443211i	$0.0141125\pi$
$824$		0			0
$825$		0			0
$826$	26.9786	+	46.7283i	0.938705	+	1.62589i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	−4.60837	+	7.41100i	−0.160152	+	0.257550i
$829$	57.5694			1.99947			0.999735	−	0.0230361i	$-0.00733328\pi$
$829$	57.5694			1.99947			0.999735	+	0.0230361i	$0.00733328\pi$
$830$	7.67369	−	4.43041i	0.266358	−	0.153782i
$831$		0			0
$832$	22.3755	−	38.7555i	0.775732	−	1.34361i
$833$		0			0
$834$	−23.1805	+	5.80652i	−0.802675	+	0.201063i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	38.4825			1.32936
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	14.0827	+	56.2202i	0.485899	+	1.93978i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$		0			0
$843$	22.2811	+	23.0222i	0.767400	+	0.792926i
$844$		0			0
$845$		−	81.7903i		−	2.81367i
$846$		0			0
$847$	−29.1033			−1.00000
$848$		0			0
$849$	−38.3269	−	10.9446i	−1.31538	−	0.375619i
$850$		0			0
$851$		0			0
$852$	15.7670	−	55.2144i	0.540170	−	1.89161i
$853$	−27.0106	−	46.7838i	−0.924827	−	1.60185i	−0.791840	−	0.610729i	$-0.790877\pi$
$853$	−27.0106	−	46.7838i	−0.924827	−	1.60185i	−0.132987	−	0.991118i	$-0.542457\pi$
$854$		−	49.5687i		−	1.69621i
$855$	−46.6976	−	1.52831i	−1.59702	−	0.0522670i
$856$		0			0
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	11.0123	−	19.0738i	0.375734	−	0.650790i	−0.614703	−	0.788759i	$-0.710724\pi$
$859$	11.0123	−	19.0738i	0.375734	−	0.650790i	0.990437	+	0.137969i	$0.0440574\pi$
$860$		0			0
$861$		0			0
$862$	−26.4575	−	45.8258i	−0.901146	−	1.56083i
$863$		−	42.0320i		−	1.43079i	−0.698722	−	0.715393i	$-0.746248\pi$
$863$		−	42.0320i		−	1.43079i	0.698722	−	0.715393i	$-0.253752\pi$
$864$	−6.20577	−	28.7313i	−0.211124	−	0.977459i
$865$	41.6392			1.41578
$866$		0			0
$867$	−7.15464	−	28.5624i	−0.242984	−	0.970030i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−7.16441			−0.242340
$875$	102.395	−	59.1181i	3.46160	−	1.99856i
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$	1.40141	−	4.90759i	0.0472685	−	0.165529i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	14.0000	+	26.1916i	0.471405	+	0.881917i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	−80.2550	+	77.6714i	−2.69774	+	2.61090i
$886$		0			0
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$	27.0425	+	46.8390i	0.906977	+	1.57093i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−25.9230	−	14.9666i	−0.866025	−	0.500000i
$897$	−9.80053	−	10.1265i	−0.327230	−	0.338115i
$898$	−28.9542	−	50.1501i	−0.966213	−	1.67353i
$899$		0			0
$900$	−79.3420	+	42.4101i	−2.64473	+	1.41367i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−29.4422	+	50.9954i	−0.979234	+	1.69608i
$905$	62.2663	+	35.9495i	2.06980	+	1.19500i
$906$	9.71372	−	34.0163i	0.322717	−	1.13012i
$907$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$907$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$908$		−	0.764572i		−	0.0253732i
$909$	−26.5448	+	42.6883i	−0.880435	+	1.41588i
$910$	−93.5900			−3.10248
$911$	45.1826	−	26.0862i	1.49697	−	0.864274i	0.496972	−	0.867766i	$-0.334445\pi$
$911$	45.1826	−	26.0862i	1.49697	−	0.864274i	0.999994	+	0.00349271i	$0.00111177\pi$
$912$	17.3400	−	16.7817i	0.574183	−	0.555699i
$913$		0			0
$914$	41.7596	+	24.1099i	1.38129	+	0.797486i
$915$	99.5271	−	24.9307i	3.29026	−	0.824184i
$916$	−21.8624	−	37.8668i	−0.722355	−	1.25116i
$917$			5.23606i			0.172910i
$918$		0			0
$919$	43.8002			1.44484			0.722418	−	0.691457i	$-0.243031\pi$
$919$	43.8002			1.44484			0.722418	+	0.691457i	$0.243031\pi$
$920$	−15.9309	+	9.19771i	−0.525226	+	0.303239i
$921$	11.8624	+	47.3566i	0.390880	+	1.56045i
$922$	18.8144	−	32.5875i	0.619619	−	1.07321i
$923$	80.3022	+	46.3625i	2.64318	+	1.52604i
$924$		0			0
$925$		0			0
$926$			22.8609i			0.751257i
$927$		0			0
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$		0			0
$931$	−12.1905	+	21.1146i	−0.399527	+	0.692001i
$932$	16.9230	+	9.77048i	0.554330	+	0.320043i
$933$		0			0
$934$	−8.21532	−	14.2294i	−0.268814	−	0.465599i
$935$		0			0
$936$	47.4403	+	1.55261i	1.55063	+	0.0507488i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.9551	−	6.32495i	−0.357127	−	0.206187i	0.310693	−	0.950510i	$-0.399439\pi$
$941$	−10.9551	−	6.32495i	−0.357127	−	0.206187i	−0.667820	+	0.744323i	$0.732772\pi$
$942$	−14.9260	+	3.73885i	−0.486316	+	0.121818i
$943$		0			0
$944$		−	57.6827i		−	1.87741i
$945$	−45.5478	+	41.2832i	−1.48167	+	1.34294i
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	−10.1438	−	40.4954i	−0.329454	−	1.31523i
$949$		0			0
$950$	−63.9621	−	36.9285i	−2.07520	−	1.19812i
$951$		0			0
$952$		0			0
$953$		−	29.9333i		−	0.969633i	−0.874616	−	0.484817i	$-0.838886\pi$
$953$		−	29.9333i		−	0.969633i	0.874616	−	0.484817i	$-0.161114\pi$
$954$		0			0
$955$	−112.062			−3.62624
$956$	−51.4807	+	29.7224i	−1.66501	+	0.961292i
$957$		0			0
$958$		0			0
$959$	−34.2929	−	19.7990i	−1.10737	−	0.639343i
$960$	17.0129	−	59.5773i	0.549089	−	1.92285i
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−22.7710	+	13.1468i	−0.733023	+	0.423211i
$966$	−6.77347	+	6.55541i	−0.217933	+	0.210917i
$967$	−4.77889	+	8.27728i	−0.153679	+	0.266179i	−0.932577	−	0.360971i	$-0.882445\pi$
$967$	−4.77889	+	8.27728i	−0.153679	+	0.266179i	0.778898	+	0.627150i	$0.215779\pi$
$968$	26.9444	+	15.5563i	0.866025	+	0.500000i
$969$		0			0
$970$		0			0
$971$			54.0402i			1.73423i	0.498107	+	0.867116i	$0.334029\pi$
$971$			54.0402i			1.73423i	−0.498107	+	0.867116i	$0.665971\pi$
$972$	23.7728	−	20.1706i	0.762513	−	0.646973i
$973$	−25.8114			−0.827474
$974$	47.0819	−	27.1828i	1.50860	−	0.870992i
$975$	−35.3001	−	140.923i	−1.13051	−	4.51316i
$976$	−26.4956	+	45.8917i	−0.848103	+	1.46896i
$977$	−51.8459	−	29.9333i	−1.65870	−	0.957650i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−51.8459	−	29.9333i	−1.65870	−	0.957650i	−0.685381	−	0.728184i	$-0.740364\pi$
$978$		0			0
$979$		0			0
$980$			62.6009i			1.99971i
$981$		0			0
$982$		0			0
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	19.4835	+	33.7464i	0.619852	+	1.07361i
$989$		0			0
$990$		0			0
$991$	37.0405			1.17663			0.588315	−	0.808632i	$-0.299791\pi$
$991$	37.0405			1.17663			0.588315	+	0.808632i	$0.299791\pi$
$992$		0			0
$993$		0			0
$994$	31.0111	−	53.7129i	0.983614	−	1.70367i
$995$		0			0
$996$	−4.70850	+	1.17944i	−0.149194	+	0.0373720i
$997$	29.9021	+	51.7920i	0.947010	+	1.64027i	0.751675	+	0.659533i	$0.229246\pi$
$997$	29.9021	+	51.7920i	0.947010	+	1.64027i	0.195335	+	0.980737i	$0.437421\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.a.293.3	yes	16
7.6	odd	2	inner	504.2.cc.a.293.2	✓	16
8.5	even	2	inner	504.2.cc.a.293.2	✓	16
9.2	odd	6	inner	504.2.cc.a.461.3	yes	16
56.13	odd	2	CM	504.2.cc.a.293.3	yes	16
63.20	even	6	inner	504.2.cc.a.461.2	yes	16
72.29	odd	6	inner	504.2.cc.a.461.2	yes	16
504.461	even	6	inner	504.2.cc.a.461.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.a.293.2	✓	16	7.6	odd	2	inner
504.2.cc.a.293.2	✓	16	8.5	even	2	inner
504.2.cc.a.293.3	yes	16	1.1	even	1	trivial
504.2.cc.a.293.3	yes	16	56.13	odd	2	CM
504.2.cc.a.461.2	yes	16	63.20	even	6	inner
504.2.cc.a.461.2	yes	16	72.29	odd	6	inner
504.2.cc.a.461.3	yes	16	9.2	odd	6	inner
504.2.cc.a.461.3	yes	16	504.461	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.420861 + 1.68014i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.87242 + 2.23574i) q^{5} +(-1.70349 - 1.76015i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +(-2.64575 + 1.41421i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.420861 + 1.68014i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.87242 + 2.23574i) q^{5} +(-1.70349 - 1.76015i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +(-2.64575 + 1.41421i) q^{9} -6.32364 q^{10} +(3.33095 + 0.951188i) q^{12} +(-2.79694 + 4.84444i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.12661 + 7.44716i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.24037 - 3.60288i) q^{18} +3.48300 q^{19} +(7.74485 - 4.47149i) q^{20} +(3.29294 - 3.18693i) q^{21} +(1.25963 + 0.727248i) q^{23} +(-4.75216 + 1.19038i) q^{24} +(7.49711 + 12.9854i) q^{25} -7.91094i q^{26} +(-3.48957 - 3.85005i) q^{27} -5.29150 q^{28} +(-2.66138 - 10.6246i) q^{30} +(4.89898 + 2.82843i) q^{32} -11.8304i q^{35} +(-0.196262 + 5.99679i) q^{36} +(-4.26578 + 2.46285i) q^{38} +(-9.31647 - 2.66042i) q^{39} +(-6.32364 + 10.9529i) q^{40} +(-1.77951 + 6.23164i) q^{42} +(-13.4073 - 0.438791i) q^{45} -2.05697 q^{46} +(4.97846 - 4.81819i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-18.3641 - 10.6025i) q^{50} +(5.59388 + 9.68889i) q^{52} +(6.99623 + 2.24783i) q^{54} +(6.48074 - 3.74166i) q^{56} +(1.46586 + 5.85193i) q^{57} +(12.4887 + 7.21033i) q^{59} +(10.7722 + 11.1306i) q^{60} +(-6.62389 - 11.4729i) q^{61} +(6.74037 + 4.19135i) q^{63} -8.00000 q^{64} +(-21.6619 + 12.5065i) q^{65} +(-0.691749 + 2.42243i) q^{69} +(8.36539 + 14.4893i) q^{70} -16.5762i q^{71} +(-4.00000 - 7.48331i) q^{72} +(-18.6620 + 18.0613i) q^{75} +(3.48300 - 6.03273i) q^{76} +(13.2915 - 3.32941i) q^{78} +(-6.02559 - 10.4366i) q^{79} -17.8860i q^{80} +(5.00000 - 7.48331i) q^{81} +(-1.21349 + 0.700610i) q^{83} +(-2.22699 - 8.89047i) q^{84} +(16.7308 - 8.94298i) q^{90} +14.8000 q^{91} +(2.51926 - 1.45450i) q^{92} +(13.4876 + 7.78709i) q^{95} +(-2.69037 + 9.42135i) q^{96} -9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4}+O(q^{10}) \) 16 * q + 16 * q^4	\( 16 q + 16 q^{4} - 16 q^{15} - 32 q^{16} - 16 q^{18} + 72 q^{23} + 40 q^{25} + 32 q^{30} - 40 q^{39} - 56 q^{49} - 144 q^{50} + 8 q^{57} - 16 q^{60} + 56 q^{63} - 128 q^{64} - 72 q^{65} - 64 q^{72} + 128 q^{78} + 80 q^{81} + 144 q^{92}+O(q^{100}) \) 16 * q + 16 * q^4 - 16 * q^15 - 32 * q^16 - 16 * q^18 + 72 * q^23 + 40 * q^25 + 32 * q^30 - 40 * q^39 - 56 * q^49 - 144 * q^50 + 8 * q^57 - 16 * q^60 + 56 * q^63 - 128 * q^64 - 72 * q^65 - 64 * q^72 + 128 * q^78 + 80 * q^81 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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