LMFDB - Embedded newform 351.2.t.c.64.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(64,351)] 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("351.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			64.6
Root			$-0.219737 - 1.71806i$ of defining polynomial
Character	$\chi$	$=$	351.64
Dual form			351.2.t.c.181.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.784270 - 0.452798i) q^{2} +(-0.589947 + 1.02182i) q^{4} +(-1.94254 - 1.12153i) q^{5} +(-2.97576 + 1.71806i) q^{7} +2.87970i q^{8} -2.03130 q^{10} +(-3.20133 + 1.84829i) q^{11} +(0.351567 + 3.58837i) q^{13} +(-1.55587 + 2.69484i) q^{14} +(0.124029 + 0.214825i) q^{16} +4.21120 q^{17} -4.25298i q^{19} +(2.29200 - 1.32329i) q^{20} +(-1.67380 + 2.89911i) q^{22} +(-1.89162 + 3.27639i) q^{23} +(0.0156524 + 0.0271108i) q^{25} +(1.90053 + 2.65506i) q^{26} -4.05425i q^{28} +(1.18945 + 2.06020i) q^{29} +(-6.37163 - 3.67866i) q^{31} +(-4.79325 - 2.76738i) q^{32} +(3.30272 - 1.90682i) q^{34} +7.70739 q^{35} +5.49928i q^{37} +(-1.92574 - 3.33549i) q^{38} +(3.22967 - 5.59395i) q^{40} +(6.86085 + 3.96111i) q^{41} +(-0.450266 - 0.779883i) q^{43} -4.36157i q^{44} +3.42609i q^{46} +(4.80060 - 2.77163i) q^{47} +(2.40343 - 4.16287i) q^{49} +(0.0245514 + 0.0141748i) q^{50} +(-3.87407 - 1.75771i) q^{52} -7.59566 q^{53} +8.29163 q^{55} +(-4.94749 - 8.56930i) q^{56} +(1.86571 + 1.07717i) q^{58} +(-4.44379 - 2.56562i) q^{59} +(6.50907 + 11.2740i) q^{61} -6.66277 q^{62} -5.50838 q^{64} +(3.34152 - 7.36486i) q^{65} +(11.7002 + 6.75511i) q^{67} +(-2.48439 + 4.30308i) q^{68} +(6.04468 - 3.48989i) q^{70} +2.65506i q^{71} +5.45741i q^{73} +(2.49006 + 4.31292i) q^{74} +(4.34578 + 2.50904i) q^{76} +(6.35092 - 11.0001i) q^{77} +(-5.46886 - 9.47234i) q^{79} -0.556410i q^{80} +7.17434 q^{82} +(-0.465547 + 0.268784i) q^{83} +(-8.18044 - 4.72298i) q^{85} +(-0.706259 - 0.407759i) q^{86} +(-5.32252 - 9.21887i) q^{88} +5.75227i q^{89} +(-7.21120 - 10.0741i) q^{91} +(-2.23192 - 3.86579i) q^{92} +(2.50998 - 4.34740i) q^{94} +(-4.76984 + 8.26161i) q^{95} +(-5.87585 + 3.39243i) q^{97} -4.35308i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) $ 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.784270	−	0.452798i	0.554562	−	0.320177i	−0.196398	−	0.980524i	$-0.562924\pi$
$2$	0.784270	−	0.452798i	0.554562	−	0.320177i	0.750960	+	0.660348i	$0.229591\pi$
$3$		0			0
$3$		0			0
$4$	−0.589947	+	1.02182i	−0.294974	+	0.510909i
$5$	−1.94254	−	1.12153i	−0.868732	−	0.501563i	−0.00180550	−	0.999998i	$-0.500575\pi$
$5$	−1.94254	−	1.12153i	−0.868732	−	0.501563i	−0.866927	+	0.498436i	$0.833908\pi$
$6$		0			0
$7$	−2.97576	+	1.71806i	−1.12473	+	0.649364i	−0.942605	−	0.333911i	$-0.891632\pi$
$7$	−2.97576	+	1.71806i	−1.12473	+	0.649364i	−0.182127	+	0.983275i	$0.558298\pi$
$8$			2.87970i			1.01813i
$9$		0			0
$10$	−2.03130			−0.642355
$11$	−3.20133	+	1.84829i	−0.965236	+	0.557279i	−0.897781	−	0.440443i	$-0.854821\pi$
$11$	−3.20133	+	1.84829i	−0.965236	+	0.557279i	−0.0674557	+	0.997722i	$0.521488\pi$
$12$		0			0
$13$	0.351567	+	3.58837i	0.0975072	+	0.995235i
$13$	0.351567	+	3.58837i	0.0975072	+	0.995235i
$14$	−1.55587	+	2.69484i	−0.415823	+	0.720226i
$15$		0			0
$16$	0.124029	+	0.214825i	0.0310073	+	0.0537063i
$17$	4.21120			1.02137			0.510683	−	0.859769i	$-0.329393\pi$
$17$	4.21120			1.02137			0.510683	+	0.859769i	$0.329393\pi$
$18$		0			0
$19$		−	4.25298i		−	0.975701i	−0.872927	−	0.487851i	$-0.837781\pi$
$19$		−	4.25298i		−	0.975701i	0.872927	−	0.487851i	$-0.162219\pi$
$20$	2.29200	−	1.32329i	0.512506	−	0.295896i
$21$		0			0
$22$	−1.67380	+	2.89911i	−0.356856	+	0.618092i
$23$	−1.89162	+	3.27639i	−0.394431	+	0.683174i	−0.993028	−	0.117876i	$-0.962392\pi$
$23$	−1.89162	+	3.27639i	−0.394431	+	0.683174i	0.598598	+	0.801050i	$0.295725\pi$
$24$		0			0
$25$	0.0156524	+	0.0271108i	0.00313048	+	0.00542215i
$26$	1.90053	+	2.65506i	0.372725	+	0.520700i
$27$		0			0
$28$		−	4.05425i		−	0.766181i
$29$	1.18945	+	2.06020i	0.220876	+	0.382569i	0.955074	−	0.296367i	$-0.0957750\pi$
$29$	1.18945	+	2.06020i	0.220876	+	0.382569i	−0.734198	+	0.678935i	$0.762442\pi$
$30$		0			0
$31$	−6.37163	−	3.67866i	−1.14438	−	0.660707i	−0.196868	−	0.980430i	$-0.563077\pi$
$31$	−6.37163	−	3.67866i	−1.14438	−	0.660707i	−0.947511	+	0.319723i	$0.896410\pi$
$32$	−4.79325	−	2.76738i	−0.847334	−	0.489209i
$33$		0			0
$34$	3.30272	−	1.90682i	0.566411	−	0.327018i
$35$	7.70739			1.30279
$36$		0			0
$37$			5.49928i			0.904076i	0.891999	+	0.452038i	$0.149303\pi$
$37$			5.49928i			0.904076i	−0.891999	+	0.452038i	$0.850697\pi$
$38$	−1.92574	−	3.33549i	−0.312397	−	0.541087i
$39$		0			0
$40$	3.22967	−	5.59395i	0.510655	−	0.884481i
$41$	6.86085	+	3.96111i	1.07148	+	0.618622i	0.928587	−	0.371116i	$-0.121025\pi$
$41$	6.86085	+	3.96111i	1.07148	+	0.618622i	0.142898	+	0.989737i	$0.454358\pi$
$42$		0			0
$43$	−0.450266	−	0.779883i	−0.0686649	−	0.118931i	0.829649	−	0.558285i	$-0.188541\pi$
$43$	−0.450266	−	0.779883i	−0.0686649	−	0.118931i	−0.898314	+	0.439354i	$0.855207\pi$
$44$		−	4.36157i		−	0.657531i
$45$		0			0
$46$			3.42609i			0.505150i
$47$	4.80060	−	2.77163i	0.700239	−	0.404283i	−0.107197	−	0.994238i	$-0.534188\pi$
$47$	4.80060	−	2.77163i	0.700239	−	0.404283i	0.807436	+	0.589955i	$0.200854\pi$
$48$		0			0
$49$	2.40343	−	4.16287i	0.343347	−	0.594695i
$50$	0.0245514	+	0.0141748i	0.00347209	+	0.00200461i
$51$		0			0
$52$	−3.87407	−	1.75771i	−0.537237	−	0.243751i
$53$	−7.59566			−1.04334			−0.521672	−	0.853146i	$-0.674692\pi$
$53$	−7.59566			−1.04334			−0.521672	+	0.853146i	$0.674692\pi$
$54$		0			0
$55$	8.29163			1.11804
$56$	−4.94749	−	8.56930i	−0.661136	−	1.14512i
$57$		0			0
$58$	1.86571	+	1.07717i	0.244979	+	0.141439i
$59$	−4.44379	−	2.56562i	−0.578532	−	0.334016i	0.182018	−	0.983295i	$-0.441737\pi$
$59$	−4.44379	−	2.56562i	−0.578532	−	0.334016i	−0.760550	+	0.649279i	$0.775071\pi$
$60$		0			0
$61$	6.50907	+	11.2740i	0.833401	+	1.44349i	0.895326	+	0.445412i	$0.146943\pi$
$61$	6.50907	+	11.2740i	0.833401	+	1.44349i	−0.0619247	+	0.998081i	$0.519724\pi$
$62$	−6.66277			−0.846173
$63$		0			0
$64$	−5.50838			−0.688547
$65$	3.34152	−	7.36486i	0.414465	−	0.913499i
$66$		0			0
$67$	11.7002	+	6.75511i	1.42941	+	0.825269i	0.997074	−	0.0764454i	$-0.0243571\pi$
$67$	11.7002	+	6.75511i	1.42941	+	0.825269i	0.432333	+	0.901714i	$0.357690\pi$
$68$	−2.48439	+	4.30308i	−0.301276	+	0.521825i
$69$		0			0
$70$	6.04468	−	3.48989i	0.722477	−	0.417122i
$71$			2.65506i			0.315098i	0.987511	+	0.157549i	$0.0503592\pi$
$71$			2.65506i			0.315098i	−0.987511	+	0.157549i	$0.949641\pi$
$72$		0			0
$73$			5.45741i			0.638741i	0.947630	+	0.319371i	$0.103472\pi$
$73$			5.45741i			0.638741i	−0.947630	+	0.319371i	$0.896528\pi$
$74$	2.49006	+	4.31292i	0.289464	+	0.501366i
$75$		0			0
$76$	4.34578	+	2.50904i	0.498495	+	0.287806i
$77$	6.35092	−	11.0001i	0.723755	−	1.25358i
$78$		0			0
$79$	−5.46886	−	9.47234i	−0.615294	−	1.06572i	−0.990333	−	0.138712i	$-0.955704\pi$
$79$	−5.46886	−	9.47234i	−0.615294	−	1.06572i	0.375038	−	0.927009i	$-0.377630\pi$
$80$		−	0.556410i		−	0.0622085i
$81$		0			0
$82$	7.17434			0.792273
$83$	−0.465547	+	0.268784i	−0.0511004	+	0.0295029i	−0.525333	−	0.850897i	$-0.676059\pi$
$83$	−0.465547	+	0.268784i	−0.0511004	+	0.0295029i	0.474232	+	0.880400i	$0.342726\pi$
$84$		0			0
$85$	−8.18044	−	4.72298i	−0.887294	−	0.512279i
$86$	−0.706259	−	0.407759i	−0.0761579	−	0.0439698i
$87$		0			0
$88$	−5.32252	−	9.21887i	−0.567382	−	0.982735i
$89$			5.75227i			0.609739i	0.952394	+	0.304870i	$0.0986129\pi$
$89$			5.75227i			0.609739i	−0.952394	+	0.304870i	$0.901387\pi$
$90$		0			0
$91$	−7.21120	−	10.0741i	−0.755939	−	1.05605i
$92$	−2.23192	−	3.86579i	−0.232693	−	0.403037i
$93$		0			0
$94$	2.50998	−	4.34740i	0.258884	−	0.448401i
$95$	−4.76984	+	8.26161i	−0.489375	+	0.847623i
$96$		0			0
$97$	−5.87585	+	3.39243i	−0.596603	+	0.344449i	−0.767704	−	0.640805i	$-0.778601\pi$
$97$	−5.87585	+	3.39243i	−0.596603	+	0.344449i	0.171101	+	0.985253i	$0.445267\pi$
$98$		−	4.35308i		−	0.439727i
$99$		0			0
$100$	−0.0369364			−0.00369364
$101$	−2.48116	−	4.29749i	−0.246884	−	0.427616i	0.715776	−	0.698330i	$-0.246073\pi$
$101$	−2.48116	−	4.29749i	−0.246884	−	0.427616i	−0.962660	+	0.270715i	$0.912740\pi$
$102$		0			0
$103$	−1.05587	+	1.82881i	−0.104038	+	0.180198i	−0.913345	−	0.407188i	$-0.866510\pi$
$103$	−1.05587	+	1.82881i	−0.104038	+	0.180198i	0.809307	+	0.587386i	$0.199843\pi$
$104$	−10.3334	+	1.01241i	−1.01328	+	0.0992748i
$105$		0			0
$106$	−5.95705	+	3.43930i	−0.578600	+	0.334055i
$107$	8.07404			0.780547			0.390274	−	0.920699i	$-0.372380\pi$
$107$	8.07404			0.780547			0.390274	+	0.920699i	$0.372380\pi$
$108$		0			0
$109$			10.0020i			0.958021i	0.877809	+	0.479011i	$0.159004\pi$
$109$			10.0020i			0.958021i	−0.877809	+	0.479011i	$0.840996\pi$
$110$	6.50287	−	3.75443i	0.620024	−	0.357971i
$111$		0			0
$112$	−0.738163	−	0.426179i	−0.0697498	−	0.0402701i
$113$	9.71733	−	16.8309i	0.914130	−	1.58332i	0.105959	−	0.994371i	$-0.466209\pi$
$113$	9.71733	−	16.8309i	0.914130	−	1.58332i	0.808171	−	0.588948i	$-0.200458\pi$
$114$		0			0
$115$	7.34912	−	4.24302i	0.685309	−	0.395664i
$116$	−2.80686			−0.260611
$117$		0			0
$118$	−4.64684			−0.427776
$119$	−12.5315	+	7.23508i	−1.14876	+	0.663238i
$120$		0			0
$121$	1.33233	−	2.30766i	0.121121	−	0.209787i
$122$	10.2097	+	5.89459i	0.924346	+	0.533671i
$123$		0			0
$124$	7.51786	−	4.34044i	0.675123	−	0.389783i
$125$			11.1451i			0.996845i
$126$		0			0
$127$	−1.76413			−0.156541			−0.0782704	−	0.996932i	$-0.524940\pi$
$127$	−1.76413			−0.156541			−0.0782704	+	0.996932i	$0.524940\pi$
$128$	5.26644	−	3.04058i	0.465492	−	0.268752i
$129$		0			0
$130$	−0.714140	−	7.28907i	−0.0626342	−	0.639294i
$131$	−3.56490	+	6.17458i	−0.311466	+	0.539476i	−0.978680	−	0.205391i	$-0.934153\pi$
$131$	−3.56490	+	6.17458i	−0.311466	+	0.539476i	0.667214	+	0.744866i	$0.267487\pi$
$132$		0			0
$133$	7.30686	+	12.6559i	0.633585	+	1.09740i
$134$	12.2348			1.05693
$135$		0			0
$136$			12.1270i			1.03988i
$137$	−3.91494	+	2.26029i	−0.334476	+	0.193110i	−0.657826	−	0.753170i	$-0.728524\pi$
$137$	−3.91494	+	2.26029i	−0.334476	+	0.193110i	0.323351	+	0.946279i	$0.395191\pi$
$138$		0			0
$139$	−7.05496	+	12.2195i	−0.598394	+	1.03645i	0.394664	+	0.918825i	$0.370861\pi$
$139$	−7.05496	+	12.2195i	−0.598394	+	1.03645i	−0.993058	+	0.117623i	$0.962472\pi$
$140$	−4.54696	+	7.87556i	−0.384288	+	0.665606i
$141$		0			0
$142$	1.20221	+	2.08228i	0.100887	+	0.174741i
$143$	−7.75782	−	10.8377i	−0.648741	−	0.906298i
$144$		0			0
$145$		−	5.33603i		−	0.443133i
$146$	2.47111	+	4.28008i	0.204510	+	0.354222i
$147$		0			0
$148$	−5.61927	−	3.24428i	−0.461901	−	0.266679i
$149$	5.02499	+	2.90118i	0.411663	+	0.237674i	0.691504	−	0.722372i	$-0.256948\pi$
$149$	5.02499	+	2.90118i	0.411663	+	0.237674i	−0.279841	+	0.960046i	$0.590282\pi$
$150$		0			0
$151$	8.44018	−	4.87294i	0.686852	−	0.396554i	−0.115580	−	0.993298i	$-0.536873\pi$
$151$	8.44018	−	4.87294i	0.686852	−	0.396554i	0.802432	+	0.596744i	$0.203539\pi$
$152$	12.2473			0.993389
$153$		0			0
$154$		−	11.5027i		−	0.926917i
$155$	8.25145	+	14.2919i	0.662773	+	1.14796i
$156$		0			0
$157$	0.539798	−	0.934957i	0.0430806	−	0.0746177i	−0.843681	−	0.536845i	$-0.819616\pi$
$157$	0.539798	−	0.934957i	0.0430806	−	0.0746177i	0.886762	+	0.462227i	$0.152949\pi$
$158$	−8.57812	−	4.95258i	−0.682438	−	0.394006i
$159$		0			0
$160$	6.20739	+	10.7515i	0.490738	+	0.849982i
$161$		−	12.9997i		−	1.02452i
$162$		0			0
$163$		−	5.54857i		−	0.434598i	−0.976105	−	0.217299i	$-0.930275\pi$
$163$		−	5.54857i		−	0.434598i	0.976105	−	0.217299i	$-0.0697247\pi$
$164$	−8.09508	+	4.67370i	−0.632120	+	0.364954i
$165$		0			0
$166$	−0.243410	+	0.421598i	−0.0188923	+	0.0327223i
$167$	11.5515	+	6.66925i	0.893880	+	0.516082i	0.875210	−	0.483744i	$-0.160723\pi$
$167$	11.5515	+	6.66925i	0.893880	+	0.516082i	0.0186702	+	0.999826i	$0.494057\pi$
$168$		0			0
$169$	−12.7528	+	2.52311i	−0.980985	+	0.194085i
$170$	−8.55423			−0.656079
$171$		0			0
$172$	1.06253			0.0810173
$173$	3.72080	+	6.44461i	0.282887	+	0.489975i	0.972095	−	0.234589i	$-0.0753745\pi$
$173$	3.72080	+	6.44461i	0.282887	+	0.489975i	−0.689208	+	0.724564i	$0.742041\pi$
$174$		0			0
$175$	−0.0931556	−	0.0537834i	−0.00704190	−	0.00406564i
$176$	−0.794117	−	0.458484i	−0.0598588	−	0.0345595i
$177$		0			0
$178$	2.60462	+	4.51133i	0.195224	+	0.338138i
$179$	−23.2047			−1.73440			−0.867202	−	0.497957i	$-0.834084\pi$
$179$	−23.2047			−1.73440			−0.867202	+	0.497957i	$0.834084\pi$
$180$		0			0
$181$	5.18439			0.385353			0.192676	−	0.981262i	$-0.438283\pi$
$181$	5.18439			0.385353			0.192676	+	0.981262i	$0.438283\pi$
$182$	−10.2171	−	4.63560i	−0.757339	−	0.343614i
$183$		0			0
$184$	−9.43502	−	5.44731i	−0.695559	−	0.401581i
$185$	6.16760	−	10.6826i	0.453451	−	0.785400i
$186$		0			0
$187$	−13.4814	+	7.78351i	−0.985860	+	0.569186i
$188$			6.54045i			0.477012i
$189$		0			0
$190$			8.63911i			0.626747i
$191$	8.07057	+	13.9786i	0.583966	+	1.01146i	0.995003	+	0.0998406i	$0.0318333\pi$
$191$	8.07057	+	13.9786i	0.583966	+	1.01146i	−0.411037	+	0.911619i	$0.634833\pi$
$192$		0			0
$193$	−2.83991	−	1.63962i	−0.204421	−	0.118023i	0.394295	−	0.918984i	$-0.370989\pi$
$193$	−2.83991	−	1.63962i	−0.204421	−	0.118023i	−0.598716	+	0.800961i	$0.704322\pi$
$194$	−3.07217	+	5.32115i	−0.220569	+	0.382037i
$195$		0			0
$196$	2.83580	+	4.91174i	0.202557	+	0.350839i
$197$		−	7.11249i		−	0.506744i	−0.967369	−	0.253372i	$-0.918460\pi$
$197$		−	7.11249i		−	0.506744i	0.967369	−	0.253372i	$-0.0815396\pi$
$198$		0			0
$199$	−13.8449			−0.981437			−0.490719	−	0.871318i	$-0.663266\pi$
$199$	−13.8449			−0.981437			−0.490719	+	0.871318i	$0.663266\pi$
$200$	−0.0780709	+	0.0450743i	−0.00552045	+	0.00318723i
$201$		0			0
$202$	−3.89179	−	2.24693i	−0.273825	−	0.158093i
$203$	−7.07906	−	4.08710i	−0.496853	−	0.286858i
$204$		0			0
$205$	−8.88500	−	15.3893i	−0.620555	−	1.07483i
$206$			1.91238i			0.133242i
$207$		0			0
$208$	−0.727267	+	0.520589i	−0.0504269	+	0.0360963i
$209$	7.86073	+	13.6152i	0.543738	+	0.941782i
$210$		0			0
$211$	−7.21695	+	12.5001i	−0.496836	+	0.860545i	−0.999993	−	0.00365007i	$-0.998838\pi$
$211$	−7.21695	+	12.5001i	−0.496836	+	0.860545i	0.503158	+	0.864195i	$0.332171\pi$
$212$	4.48104	−	7.76139i	0.307759	−	0.533055i
$213$		0			0
$214$	6.33223	−	3.65591i	0.432862	−	0.249913i
$215$			2.01994i			0.137759i
$216$		0			0
$217$	25.2806			1.71616
$218$	4.52890	+	7.84429i	0.306736	+	0.531283i
$219$		0			0
$220$	−4.89162	+	8.47254i	−0.329793	+	0.571219i
$221$	1.48052	+	15.1113i	0.0995905	+	1.01650i
$222$		0			0
$223$	−9.52959	+	5.50191i	−0.638149	+	0.368435i	−0.783901	−	0.620886i	$-0.786773\pi$
$223$	−9.52959	+	5.50191i	−0.638149	+	0.368435i	0.145752	+	0.989321i	$0.453440\pi$
$224$	19.0181			1.27070
$225$		0			0
$226$		−	17.6000i		−	1.17073i
$227$	−7.03055	+	4.05909i	−0.466634	+	0.269411i	−0.714830	−	0.699299i	$-0.753496\pi$
$227$	−7.03055	+	4.05909i	−0.466634	+	0.269411i	0.248196	+	0.968710i	$0.420162\pi$
$228$		0			0
$229$	4.65740	+	2.68895i	0.307769	+	0.177691i	0.645928	−	0.763398i	$-0.276471\pi$
$229$	4.65740	+	2.68895i	0.307769	+	0.177691i	−0.338158	+	0.941089i	$0.609804\pi$
$230$	3.84246	−	6.65534i	0.253365	−	0.438840i
$231$		0			0
$232$	−5.93275	+	3.42528i	−0.389504	+	0.224880i
$233$	−20.0992			−1.31675			−0.658373	−	0.752692i	$-0.728755\pi$
$233$	−20.0992			−1.31675			−0.658373	+	0.752692i	$0.728755\pi$
$234$		0			0
$235$	−12.4338			−0.811094
$236$	5.24321	−	3.02717i	0.341304	−	0.197052i
$237$		0			0
$238$	−6.55206	+	11.3485i	−0.424707	+	0.735614i
$239$	−12.2635	−	7.08034i	−0.793261	−	0.457989i	0.0478485	−	0.998855i	$-0.484764\pi$
$239$	−12.2635	−	7.08034i	−0.793261	−	0.457989i	−0.841109	+	0.540865i	$0.818097\pi$
$240$		0			0
$241$	26.2041	−	15.1289i	1.68795	−	0.974539i	0.731867	−	0.681447i	$-0.238649\pi$
$241$	26.2041	−	15.1289i	1.68795	−	0.974539i	0.956084	−	0.293092i	$-0.0946842\pi$
$242$		−	2.41310i		−	0.155120i
$243$		0			0
$244$	−15.3600			−0.983326
$245$	−9.33754	+	5.39103i	−0.596554	+	0.344421i
$246$		0			0
$247$	15.2613	−	1.49521i	0.971052	−	0.0951379i
$248$	10.5935	−	18.3484i	0.672685	−	1.16512i
$249$		0			0
$250$	5.04647	+	8.74074i	0.319167	+	0.552813i
$251$	17.5085			1.10512			0.552562	−	0.833472i	$-0.313650\pi$
$251$	17.5085			1.10512			0.552562	+	0.833472i	$0.313650\pi$
$252$		0			0
$253$		−	13.9850i		−	0.879232i
$254$	−1.38355	+	0.798793i	−0.0868117	+	0.0501208i
$255$		0			0
$256$	8.26192	−	14.3101i	0.516370	−	0.894379i
$257$	9.15211	−	15.8519i	0.570893	−	0.988815i	−0.425582	−	0.904920i	$-0.639931\pi$
$257$	9.15211	−	15.8519i	0.570893	−	0.988815i	0.996475	−	0.0838952i	$-0.0267361\pi$
$258$		0			0
$259$	−9.44807	−	16.3645i	−0.587074	−	1.01684i
$260$	5.55423	+	7.75931i	0.344459	+	0.481212i
$261$		0			0
$262$			6.45672i			0.398897i
$263$	−4.19661	−	7.26875i	−0.258774	−	0.448210i	0.707140	−	0.707074i	$-0.249985\pi$
$263$	−4.19661	−	7.26875i	−0.258774	−	0.448210i	−0.965914	+	0.258864i	$0.916652\pi$
$264$		0			0
$265$	14.7549	+	8.51875i	0.906387	+	0.523303i
$266$	11.4611	+	6.61707i	0.702725	+	0.405719i
$267$		0			0
$268$	−13.8050	+	7.97032i	−0.843275	+	0.486865i
$269$	−21.3238			−1.30014			−0.650069	−	0.759875i	$-0.725260\pi$
$269$	−21.3238			−1.30014			−0.650069	+	0.759875i	$0.725260\pi$
$270$		0			0
$271$			18.4587i			1.12129i	0.828057	+	0.560643i	$0.189446\pi$
$271$			18.4587i			1.12129i	−0.828057	+	0.560643i	$0.810554\pi$
$272$	0.522312	+	0.904671i	0.0316698	+	0.0548538i
$273$		0			0
$274$	−2.04691	+	3.54535i	−0.123658	+	0.214183i
$275$	−0.100217	−	0.0578603i	−0.00604331	−	0.00348911i
$276$		0			0
$277$	4.31390	+	7.47189i	0.259197	+	0.448943i	0.966027	−	0.258441i	$-0.0832087\pi$
$277$	4.31390	+	7.47189i	0.259197	+	0.448943i	−0.706830	+	0.707383i	$0.749875\pi$
$278$			12.7779i			0.766367i
$279$		0			0
$280$			22.1950i			1.32640i
$281$	3.00928	−	1.73741i	0.179518	−	0.103645i	−0.407548	−	0.913184i	$-0.633616\pi$
$281$	3.00928	−	1.73741i	0.179518	−	0.103645i	0.587066	+	0.809539i	$0.300283\pi$
$282$		0			0
$283$	6.89178	−	11.9369i	0.409674	−	0.709576i	−0.585179	−	0.810904i	$-0.698976\pi$
$283$	6.89178	−	11.9369i	0.409674	−	0.709576i	0.994853	+	0.101328i	$0.0323091\pi$
$284$	−2.71299	−	1.56635i	−0.160986	−	0.0929456i
$285$		0			0
$286$	−10.9915	−	4.98699i	−0.649943	−	0.294887i
$287$	−27.2217			−1.60684
$288$		0			0
$289$	0.734202			0.0431884
$290$	−2.41615	−	4.18489i	−0.141881	−	0.245745i
$291$		0			0
$292$	−5.57648	−	3.21958i	−0.326339	−	0.188412i
$293$	24.6911	+	14.2554i	1.44247	+	0.832810i	0.998014	−	0.0629917i	$-0.0200642\pi$
$293$	24.6911	+	14.2554i	1.44247	+	0.832810i	0.444455	+	0.895801i	$0.353397\pi$
$294$		0			0
$295$	5.75484	+	9.96768i	0.335060	+	0.580341i
$296$	−15.8363			−0.920465
$297$		0			0
$298$	5.25460			0.304391
$299$	−12.4219	−	5.63597i	−0.718378	−	0.325937i
$300$		0			0
$301$	2.67977	+	1.54716i	0.154459	+	0.0891770i
$302$	4.41292	−	7.64340i	0.253935	−	0.439828i
$303$		0			0
$304$	0.913648	−	0.527495i	0.0524013	−	0.0302539i
$305$		−	29.2004i		−	1.67201i
$306$		0			0
$307$		−	21.8137i		−	1.24497i	−0.782631	−	0.622486i	$-0.786123\pi$
$307$		−	21.8137i		−	1.24497i	0.782631	−	0.622486i	$-0.213877\pi$
$308$	7.49342	+	12.9790i	0.426977	+	0.739546i
$309$		0			0
$310$	12.9427	+	7.47249i	0.735097	+	0.424409i
$311$	−3.48161	+	6.03032i	−0.197424	+	0.341948i	−0.947692	−	0.319185i	$-0.896591\pi$
$311$	−3.48161	+	6.03032i	−0.197424	+	0.341948i	0.750268	+	0.661133i	$0.229924\pi$
$312$		0			0
$313$	−11.2253	−	19.4428i	−0.634491	−	1.09897i	−0.986623	−	0.163020i	$-0.947876\pi$
$313$	−11.2253	−	19.4428i	−0.634491	−	1.09897i	0.352131	−	0.935951i	$-0.385457\pi$
$314$		−	0.977678i		−	0.0551736i
$315$		0			0
$316$	12.9054			0.725983
$317$	−8.84739	+	5.10804i	−0.496919	+	0.286896i	−0.727440	−	0.686171i	$-0.759290\pi$
$317$	−8.84739	+	5.10804i	−0.496919	+	0.286896i	0.230522	+	0.973067i	$0.425957\pi$
$318$		0			0
$319$	−7.61567	−	4.39691i	−0.426395	−	0.246180i
$320$	10.7003	+	6.17780i	0.598163	+	0.345350i
$321$		0			0
$322$	−5.88622	−	10.1952i	−0.328026	−	0.568158i
$323$		−	17.9102i		−	0.996548i
$324$		0			0
$325$	−0.0917806	+	0.0656979i	−0.00509107	+	0.00364426i
$326$	−2.51239	−	4.35158i	−0.139148	−	0.241012i
$327$		0			0
$328$	−11.4068	+	19.7572i	−0.629836	+	1.09091i
$329$	−9.52362	+	16.4954i	−0.525054	+	0.909420i
$330$		0			0
$331$	4.67794	−	2.70081i	0.257123	−	0.148450i	−0.365898	−	0.930655i	$-0.619238\pi$
$331$	4.67794	−	2.70081i	0.257123	−	0.148450i	0.623021	+	0.782205i	$0.285905\pi$
$332$		−	0.634273i		−	0.0348103i
$333$		0			0
$334$	12.0793			0.660949
$335$	−15.1521	−	26.2442i	−0.827848	−	1.43387i
$336$		0			0
$337$	16.4621	−	28.5132i	0.896749	−	1.55321i	0.0651239	−	0.997877i	$-0.479256\pi$
$337$	16.4621	−	28.5132i	0.896749	−	1.55321i	0.831625	−	0.555338i	$-0.187411\pi$
$338$	−8.85918	+	7.75324i	−0.481876	+	0.421721i
$339$		0			0
$340$	9.65206	−	5.57262i	0.523457	−	0.302218i
$341$	27.1969			1.47279
$342$		0			0
$343$		−	7.53586i		−	0.406898i
$344$	2.24583	−	1.29663i	0.121087	−	0.0699097i
$345$		0			0
$346$	5.83622	+	3.36954i	0.313757	+	0.181148i
$347$	6.81390	−	11.8020i	0.365789	−	0.633566i	−0.623113	−	0.782132i	$-0.714132\pi$
$347$	6.81390	−	11.8020i	0.365789	−	0.633566i	0.988902	+	0.148566i	$0.0474658\pi$
$348$		0			0
$349$	9.76413	−	5.63732i	0.522662	−	0.301759i	−0.215361	−	0.976534i	$-0.569093\pi$
$349$	9.76413	−	5.63732i	0.522662	−	0.301759i	0.738023	+	0.674776i	$0.235760\pi$
$350$	−0.0974121			−0.00520690
$351$		0			0
$352$	20.4597			1.09050
$353$	23.0629	−	13.3154i	1.22751	−	0.708706i	0.261005	−	0.965337i	$-0.415946\pi$
$353$	23.0629	−	13.3154i	1.22751	−	0.708706i	0.966509	+	0.256631i	$0.0826126\pi$
$354$		0			0
$355$	2.97773	−	5.15757i	0.158041	−	0.273736i
$356$	−5.87778	−	3.39354i	−0.311522	−	0.179857i
$357$		0			0
$358$	−18.1988	+	10.5071i	−0.961835	+	0.555316i
$359$		−	34.9036i		−	1.84214i	−0.389396	−	0.921071i	$-0.627316\pi$
$359$		−	34.9036i		−	1.84214i	0.389396	−	0.921071i	$-0.372684\pi$
$360$		0			0
$361$	0.912132			0.0480069
$362$	4.06596	−	2.34748i	0.213702	−	0.123381i
$363$		0			0
$364$	14.5482	−	1.42534i	0.762530	−	0.0747082i
$365$	6.12064	−	10.6013i	0.320369	−	0.554895i
$366$		0			0
$367$	1.35716	+	2.35068i	0.0708434	+	0.122704i	0.899271	−	0.437392i	$-0.144098\pi$
$367$	1.35716	+	2.35068i	0.0708434	+	0.122704i	−0.828428	+	0.560096i	$0.810764\pi$
$368$	−0.938467			−0.0489210
$369$		0			0
$370$		−	11.1707i		−	0.580737i
$371$	22.6029	−	13.0498i	1.17348	−	0.677510i
$372$		0			0
$373$	0.875481	−	1.51638i	0.0453307	−	0.0785150i	−0.842470	−	0.538744i	$-0.818899\pi$
$373$	0.875481	−	1.51638i	0.0453307	−	0.0785150i	0.887800	+	0.460229i	$0.152233\pi$
$374$	−7.04872	+	12.2087i	−0.364480	+	0.631299i
$375$		0			0
$376$	7.98146	+	13.8243i	0.411612	+	0.712933i
$377$	−6.97457	+	4.99250i	−0.359209	+	0.257127i
$378$		0			0
$379$		−	2.90941i		−	0.149446i	−0.997204	−	0.0747231i	$-0.976193\pi$
$379$		−	2.90941i		−	0.149446i	0.997204	−	0.0747231i	$-0.0238073\pi$
$380$	−5.62791	−	9.74783i	−0.288706	−	0.500053i
$381$		0			0
$382$	12.6590	+	7.30868i	0.647691	+	0.373945i
$383$	−17.7065	−	10.2229i	−0.904760	−	0.522363i	−0.0260185	−	0.999661i	$-0.508283\pi$
$383$	−17.7065	−	10.2229i	−0.904760	−	0.522363i	−0.878741	+	0.477298i	$0.841616\pi$
$384$		0			0
$385$	−24.6739	+	14.2455i	−1.25750	+	0.726017i
$386$	−2.96968			−0.151152
$387$		0			0
$388$		−	8.00541i		−	0.406413i
$389$	6.48161	+	11.2265i	0.328631	+	0.569205i	0.982240	−	0.187627i	$-0.0600795\pi$
$389$	6.48161	+	11.2265i	0.328631	+	0.569205i	−0.653610	+	0.756832i	$0.726746\pi$
$390$		0			0
$391$	−7.96600	+	13.7975i	−0.402858	+	0.697771i
$392$	11.9878	+	6.92117i	0.605476	+	0.349572i
$393$		0			0
$394$	−3.22052	−	5.57811i	−0.162248	−	0.281021i
$395$			24.5339i			1.23444i
$396$		0			0
$397$			29.1809i			1.46455i	0.681010	+	0.732274i	$0.261541\pi$
$397$			29.1809i			1.46455i	−0.681010	+	0.732274i	$0.738459\pi$
$398$	−10.8581	+	6.26894i	−0.544268	+	0.314233i
$399$		0			0
$400$	−0.00388271	+	0.00672506i	−0.000194136	+	0.000336253i
$401$	−19.2018	−	11.0862i	−0.958894	−	0.553617i	−0.0630612	−	0.998010i	$-0.520086\pi$
$401$	−19.2018	−	11.0862i	−0.958894	−	0.553617i	−0.895832	+	0.444392i	$0.853420\pi$
$402$		0			0
$403$	10.9603	−	24.1571i	0.545974	−	1.20335i
$404$	5.85500			0.291297
$405$		0			0
$406$	−7.40253			−0.367381
$407$	−10.1642	−	17.6050i	−0.503823	−	0.872647i
$408$		0			0
$409$	−1.81749	−	1.04933i	−0.0898689	−	0.0518858i	0.454392	−	0.890802i	$-0.349857\pi$
$409$	−1.81749	−	1.04933i	−0.0898689	−	0.0518858i	−0.544261	+	0.838916i	$0.683190\pi$
$410$	−13.9365	−	8.04623i	−0.688273	−	0.397375i
$411$		0			0
$412$	−1.24581	−	2.15781i	−0.0613767	−	0.106307i
$413$	17.6315			0.867591
$414$		0			0
$415$	1.20579			0.0591901
$416$	8.24524	−	18.1729i	0.404256	−	0.890998i
$417$		0			0
$418$	12.3299	+	7.11865i	0.603074	+	0.348185i
$419$	0.195699	−	0.338961i	0.00956053	−	0.0165593i	−0.861206	−	0.508257i	$-0.830290\pi$
$419$	0.195699	−	0.338961i	0.00956053	−	0.0165593i	0.870766	+	0.491697i	$0.163623\pi$
$420$		0			0
$421$	9.59987	−	5.54249i	0.467869	−	0.270124i	−0.247478	−	0.968893i	$-0.579602\pi$
$421$	9.59987	−	5.54249i	0.467869	−	0.270124i	0.715347	+	0.698769i	$0.246269\pi$
$422$			13.0713i			0.636301i
$423$		0			0
$424$		−	21.8732i		−	1.06226i
$425$	0.0659154	+	0.114169i	0.00319737	+	0.00553800i
$426$		0			0
$427$	−38.7389	−	22.3659i	−1.87470	−	1.08236i
$428$	−4.76326	+	8.25021i	−0.230241	+	0.398789i
$429$		0			0
$430$	0.914627	+	1.58418i	0.0441072	+	0.0763960i
$431$			36.4573i			1.75609i	0.478580	+	0.878044i	$0.341152\pi$
$431$			36.4573i			1.75609i	−0.478580	+	0.878044i	$0.658848\pi$
$432$		0			0
$433$	8.82757			0.424226			0.212113	−	0.977245i	$-0.431966\pi$
$433$	8.82757			0.424226			0.212113	+	0.977245i	$0.431966\pi$
$434$	19.8268	−	11.4470i	0.951717	−	0.549474i
$435$		0			0
$436$	−10.2203	−	5.90067i	−0.489462	−	0.282591i
$437$	13.9344	+	8.04504i	0.666574	+	0.384847i
$438$		0			0
$439$	17.5672	+	30.4273i	0.838438	+	1.45222i	0.891200	+	0.453610i	$0.149864\pi$
$439$	17.5672	+	30.4273i	0.838438	+	1.45222i	−0.0527626	+	0.998607i	$0.516803\pi$
$440$			23.8774i			1.13831i
$441$		0			0
$442$	8.00352	+	11.1810i	0.380688	+	0.531826i
$443$	11.9526	+	20.7025i	0.567885	+	0.983606i	0.996775	+	0.0802490i	$0.0255715\pi$
$443$	11.9526	+	20.7025i	0.567885	+	0.983606i	−0.428890	+	0.903357i	$0.641095\pi$
$444$		0			0
$445$	6.45133	−	11.1740i	0.305822	−	0.529700i
$446$	−4.98251	+	8.62997i	−0.235929	+	0.408641i
$447$		0			0
$448$	16.3916	−	9.46370i	0.774431	−	0.447118i
$449$			13.9683i			0.659206i	0.944120	+	0.329603i	$0.106915\pi$
$449$			13.9683i			0.659206i	−0.944120	+	0.329603i	$0.893085\pi$
$450$		0			0
$451$	−29.2851			−1.37898
$452$	11.4654	+	19.8587i	0.539288	+	0.934075i
$453$		0			0
$454$	−3.67590	+	6.36684i	−0.172518	+	0.298811i
$455$	2.70967	+	27.6570i	0.127031	+	1.29658i
$456$		0			0
$457$	15.0872	−	8.71058i	0.705748	−	0.407464i	−0.103737	−	0.994605i	$-0.533080\pi$
$457$	15.0872	−	8.71058i	0.705748	−	0.407464i	0.809485	+	0.587141i	$0.199747\pi$
$458$	4.87021			0.227570
$459$		0			0
$460$			10.0126i			0.466841i
$461$	−20.6691	+	11.9333i	−0.962658	+	0.555791i	−0.896990	−	0.442051i	$-0.854251\pi$
$461$	−20.6691	+	11.9333i	−0.962658	+	0.555791i	−0.0656678	+	0.997842i	$0.520918\pi$
$462$		0			0
$463$	−9.12555	−	5.26864i	−0.424100	−	0.244854i	0.272730	−	0.962091i	$-0.412074\pi$
$463$	−9.12555	−	5.26864i	−0.424100	−	0.244854i	−0.696830	+	0.717236i	$0.745407\pi$
$464$	−0.295055	+	0.511049i	−0.0136976	+	0.0237249i
$465$		0			0
$466$	−15.7632	+	9.10090i	−0.730217	+	0.421591i
$467$	8.40923			0.389133			0.194566	−	0.980889i	$-0.437670\pi$
$467$	8.40923			0.389133			0.194566	+	0.980889i	$0.437670\pi$
$468$		0			0
$469$	−46.4227			−2.14360
$470$	−9.75148	+	5.63002i	−0.449802	+	0.259693i
$471$		0			0
$472$	7.38823	−	12.7968i	0.340071	−	0.589020i
$473$	2.88290	+	1.66444i	0.132556	+	0.0765310i
$474$		0			0
$475$	0.115302	−	0.0665694i	0.00529040	−	0.00305441i
$476$		−	17.0733i		−	0.782551i
$477$		0			0
$478$	−12.8239			−0.586550
$479$	13.6025	−	7.85338i	0.621512	−	0.358830i	−0.155945	−	0.987766i	$-0.549842\pi$
$479$	13.6025	−	7.85338i	0.621512	−	0.358830i	0.777457	+	0.628935i	$0.216509\pi$
$480$		0			0
$481$	−19.7334	+	1.93337i	−0.899768	+	0.0881539i
$482$	13.7007	−	23.7303i	0.624050	−	1.08089i
$483$		0			0
$484$	1.57201	+	2.72280i	0.0714549	+	0.123764i
$485$	15.2188			0.691051
$486$		0			0
$487$			37.8948i			1.71718i	0.512666	+	0.858588i	$0.328658\pi$
$487$			37.8948i			1.71718i	−0.512666	+	0.858588i	$0.671342\pi$
$488$	−32.4659	+	18.7442i	−1.46966	+	0.848509i
$489$		0			0
$490$	−4.88210	+	8.45605i	−0.220551	+	0.382005i
$491$	−1.88027	+	3.25672i	−0.0848553	+	0.146974i	−0.905330	−	0.424710i	$-0.860376\pi$
$491$	−1.88027	+	3.25672i	−0.0848553	+	0.146974i	0.820474	+	0.571684i	$0.193709\pi$
$492$		0			0
$493$	5.00903	+	8.67590i	0.225595	+	0.390743i
$494$	11.2919	−	8.08293i	0.508048	−	0.363668i
$495$		0			0
$496$		−	1.82505i		−	0.0819471i
$497$	−4.56154	−	7.90082i	−0.204613	−	0.354400i
$498$		0			0
$499$	−7.15464	−	4.13073i	−0.320286	−	0.184917i	0.331234	−	0.943549i	$-0.392535\pi$
$499$	−7.15464	−	4.13073i	−0.320286	−	0.184917i	−0.651520	+	0.758632i	$0.725868\pi$
$500$	−11.3882	−	6.57500i	−0.509298	−	0.294043i
$501$		0			0
$502$	13.7314	−	7.92780i	0.612860	−	0.353835i
$503$	12.9954			0.579434			0.289717	−	0.957112i	$-0.406439\pi$
$503$	12.9954			0.579434			0.289717	+	0.957112i	$0.406439\pi$
$504$		0			0
$505$			11.1307i			0.495312i
$506$	−6.33241	−	10.9680i	−0.281510	−	0.487589i
$507$		0			0
$508$	1.04074	−	1.80262i	0.0461754	−	0.0799782i
$509$	−23.2712	−	13.4356i	−1.03148	−	0.595524i	−0.114070	−	0.993473i	$-0.536389\pi$
$509$	−23.2712	−	13.4356i	−1.03148	−	0.595524i	−0.917408	+	0.397949i	$0.869722\pi$
$510$		0			0
$511$	−9.37613	−	16.2399i	−0.414776	−	0.718413i
$512$		−	2.80162i		−	0.123815i
$513$		0			0
$514$		−	16.5762i		−	0.731146i
$515$	4.10213	−	2.36837i	0.180761	−	0.104363i
$516$		0			0
$517$	−10.2455	+	17.7458i	−0.450597	+	0.780458i
$518$	−14.8197	−	8.55614i	−0.651139	−	0.375935i
$519$		0			0
$520$	21.2086	+	9.62260i	0.930059	+	0.421979i
$521$	−14.2080			−0.622464			−0.311232	−	0.950334i	$-0.600742\pi$
$521$	−14.2080			−0.622464			−0.311232	+	0.950334i	$0.600742\pi$
$522$		0			0
$523$	7.07846			0.309519			0.154760	−	0.987952i	$-0.450540\pi$
$523$	7.07846			0.309519			0.154760	+	0.987952i	$0.450540\pi$
$524$	−4.20620	−	7.28536i	−0.183749	−	0.318262i
$525$		0			0
$526$	−6.58255	−	3.80044i	−0.287013	−	0.165707i
$527$	−26.8322	−	15.4916i	−1.16883	−	0.674824i
$528$		0			0
$529$	4.34352	+	7.52320i	0.188849	+	0.327096i
$530$	15.4291			0.670198
$531$		0			0
$532$	−17.2427			−0.747564
$533$	−11.8019	+	26.0119i	−0.511197	+	1.12670i
$534$		0			0
$535$	−15.6842	−	9.05527i	−0.678086	−	0.391493i
$536$	−19.4527	+	33.6931i	−0.840229	+	1.45532i
$537$		0			0
$538$	−16.7236	+	9.65540i	−0.721007	+	0.416274i
$539$			17.7689i			0.765362i
$540$		0			0
$541$		−	7.18897i		−	0.309078i	−0.987987	−	0.154539i	$-0.950611\pi$
$541$		−	7.18897i		−	0.309078i	0.987987	−	0.154539i	$-0.0493892\pi$
$542$	8.35807	+	14.4766i	0.359010	+	0.621823i
$543$		0			0
$544$	−20.1853	−	11.6540i	−0.865438	−	0.499661i
$545$	11.2176	−	19.4294i	0.480508	−	0.832264i
$546$		0			0
$547$	15.8887	+	27.5201i	0.679353	+	1.17667i	0.975176	+	0.221431i	$0.0710729\pi$
$547$	15.8887	+	27.5201i	0.679353	+	1.17667i	−0.295823	+	0.955243i	$0.595594\pi$
$548$		−	5.33381i		−	0.227849i
$549$		0			0
$550$	−0.104796			−0.00446852
$551$	8.76198	−	5.05873i	0.373273	−	0.215509i
$552$		0			0
$553$	32.5480	+	18.7916i	1.38408	+	0.799100i
$554$	6.76652	+	3.90665i	0.287482	+	0.165978i
$555$		0			0
$556$	−8.32411	−	14.4178i	−0.353021	−	0.611450i
$557$		−	32.2223i		−	1.36530i	−0.730745	−	0.682650i	$-0.760827\pi$
$557$		−	32.2223i		−	1.36530i	0.730745	−	0.682650i	$-0.239173\pi$
$558$		0			0
$559$	2.64021	−	1.88990i	0.111669	−	0.0799343i
$560$	0.955943	+	1.65574i	0.0403960	+	0.0699679i
$561$		0			0
$562$	1.57339	−	2.72519i	0.0663694	−	0.114955i
$563$	−16.8257	+	29.1430i	−0.709119	+	1.22823i	0.256065	+	0.966659i	$0.417574\pi$
$563$	−16.8257	+	29.1430i	−0.709119	+	1.22823i	−0.965184	+	0.261571i	$0.915760\pi$
$564$		0			0
$565$	−37.7527	+	21.7965i	−1.58827	+	0.916987i
$566$		−	12.4824i		−	0.524672i
$567$		0			0
$568$	−7.64578			−0.320810
$569$	−5.66793	−	9.81715i	−0.237612	−	0.411556i	0.722416	−	0.691458i	$-0.243031\pi$
$569$	−5.66793	−	9.81715i	−0.237612	−	0.411556i	−0.960029	+	0.279902i	$0.909698\pi$
$570$		0			0
$571$	0.127260	−	0.220421i	0.00532568	−	0.00922435i	−0.863350	−	0.504605i	$-0.831638\pi$
$571$	0.127260	−	0.220421i	0.00532568	−	0.00922435i	0.868676	+	0.495381i	$0.164971\pi$
$572$	15.6509	−	1.53338i	0.654398	−	0.0641140i
$573$		0			0
$574$	−21.3491	+	12.3259i	−0.891095	+	0.514474i
$575$	−0.118434			−0.00493903
$576$		0			0
$577$			1.91400i			0.0796807i	0.999206	+	0.0398403i	$0.0126849\pi$
$577$			1.91400i			0.0796807i	−0.999206	+	0.0398403i	$0.987315\pi$
$578$	0.575812	−	0.332445i	0.0239506	−	0.0138279i
$579$		0			0
$580$	5.45246	+	3.14798i	0.226401	+	0.130713i
$581$	0.923571	−	1.59967i	0.0383162	−	0.0663656i
$582$		0			0
$583$	24.3162	−	14.0390i	1.00707	−	0.581435i
$584$	−15.7157			−0.650321
$585$		0			0
$586$	25.8193			1.06659
$587$	7.69412	−	4.44220i	0.317570	−	0.183349i	−0.332739	−	0.943019i	$-0.607973\pi$
$587$	7.69412	−	4.44220i	0.317570	−	0.183349i	0.650309	+	0.759670i	$0.274639\pi$
$588$		0			0
$589$	−15.6453	+	27.0984i	−0.644653	+	1.11657i
$590$	9.02670	+	5.21156i	0.371623	+	0.214557i
$591$		0			0
$592$	−1.18138	+	0.682072i	−0.0485545	+	0.0280330i
$593$			43.1136i			1.77046i	0.465152	+	0.885231i	$0.346000\pi$
$593$			43.1136i			1.77046i	−0.465152	+	0.885231i	$0.654000\pi$
$594$		0			0
$595$	32.4574			1.33062
$596$	−5.92896	+	3.42309i	−0.242860	+	0.140215i
$597$		0			0
$598$	−12.2941	+	1.20450i	−0.502743	+	0.0492558i
$599$	−5.59868	+	9.69720i	−0.228756	+	0.396217i	−0.957440	−	0.288634i	$-0.906799\pi$
$599$	−5.59868	+	9.69720i	−0.228756	+	0.396217i	0.728684	+	0.684850i	$0.240132\pi$
$600$		0			0
$601$	−2.96273	−	5.13159i	−0.120852	−	0.209322i	0.799252	−	0.600996i	$-0.205229\pi$
$601$	−2.96273	−	5.13159i	−0.120852	−	0.209322i	−0.920104	+	0.391674i	$0.871896\pi$
$602$	2.80221			0.114210
$603$		0			0
$604$			11.4991i			0.467892i
$605$	−5.17622	+	2.98849i	−0.210443	+	0.121499i
$606$		0			0
$607$	−2.53470	+	4.39022i	−0.102880	+	0.178194i	−0.912870	−	0.408250i	$-0.866139\pi$
$607$	−2.53470	+	4.39022i	−0.102880	+	0.178194i	0.809990	+	0.586444i	$0.199472\pi$
$608$	−11.7696	+	20.3856i	−0.477321	+	0.826745i
$609$		0			0
$610$	−13.2219	−	22.9010i	−0.535339	−	0.927235i
$611$	11.6334	+	16.2519i	0.470635	+	0.657482i
$612$		0			0
$613$		−	24.6393i		−	0.995173i	−0.867414	−	0.497587i	$-0.834220\pi$
$613$		−	24.6393i		−	0.995173i	0.867414	−	0.497587i	$-0.165780\pi$
$614$	−9.87719	−	17.1078i	−0.398611	−	0.690414i
$615$		0			0
$616$	31.6771	+	18.2888i	1.27630	+	0.736875i
$617$	38.0933	+	21.9932i	1.53358	+	0.885413i	0.999193	+	0.0401727i	$0.0127908\pi$
$617$	38.0933	+	21.9932i	1.53358	+	0.885413i	0.534387	+	0.845240i	$0.320543\pi$
$618$		0			0
$619$	−17.7979	+	10.2756i	−0.715358	+	0.413012i	−0.813042	−	0.582206i	$-0.802190\pi$
$619$	−17.7979	+	10.2756i	−0.715358	+	0.413012i	0.0976839	+	0.995217i	$0.468857\pi$
$620$	−19.4717			−0.782002
$621$		0			0
$622$			6.30587i			0.252842i
$623$	−9.88272	−	17.1174i	−0.395943	−	0.685793i
$624$		0			0
$625$	12.5778	−	21.7853i	0.503111	−	0.871414i
$626$	−17.6073	−	10.1656i	−0.703730	−	0.406299i
$627$		0			0
$628$	0.636905	+	1.10315i	0.0254153	+	0.0440205i
$629$			23.1586i			0.923392i
$630$		0			0
$631$		−	25.1460i		−	1.00105i	−0.865723	−	0.500523i	$-0.833141\pi$
$631$		−	25.1460i		−	1.00105i	0.865723	−	0.500523i	$-0.166859\pi$
$632$	27.2775	−	15.7487i	1.08504	−	0.626449i
$633$		0			0
$634$	−4.62582	+	8.01216i	−0.183715	+	0.318204i
$635$	3.42689	+	1.97852i	0.135992	+	0.0785151i
$636$		0			0
$637$	15.7829	+	7.16088i	0.625340	+	0.283724i
$638$	−7.96365			−0.315284
$639$		0			0
$640$	−13.6404			−0.539183
$641$	−16.6711	−	28.8751i	−0.658467	−	1.14050i	−0.981012	−	0.193945i	$-0.937872\pi$
$641$	−16.6711	−	28.8751i	−0.658467	−	1.14050i	0.322545	−	0.946554i	$-0.395462\pi$
$642$		0			0
$643$	27.1759	+	15.6900i	1.07171	+	0.618754i	0.928649	−	0.370959i	$-0.120971\pi$
$643$	27.1759	+	15.6900i	1.07171	+	0.618754i	0.143065	+	0.989713i	$0.454304\pi$
$644$	13.2833	+	7.66911i	0.523435	+	0.302205i
$645$		0			0
$646$	−8.10969	−	14.0464i	−0.319072	−	0.552648i
$647$	47.5495			1.86936			0.934681	−	0.355486i	$-0.115685\pi$
$647$	47.5495			1.86936			0.934681	+	0.355486i	$0.115685\pi$
$648$		0			0
$649$	18.9680			0.744561
$650$	−0.0422328	+	0.0930829i	−0.00165651	+	0.00365101i
$651$		0			0
$652$	5.66964	+	3.27337i	0.222040	+	0.128195i
$653$	−13.8728	+	24.0284i	−0.542884	+	0.940302i	0.455853	+	0.890055i	$0.349334\pi$
$653$	−13.8728	+	24.0284i	−0.542884	+	0.940302i	−0.998737	+	0.0502473i	$0.983999\pi$
$654$		0			0
$655$	13.8499	−	7.99627i	0.541162	−	0.312440i
$656$			1.96518i			0.0767273i
$657$		0			0
$658$			17.2491i			0.672440i
$659$	7.80940	+	13.5263i	0.304211	+	0.526909i	0.977085	−	0.212848i	$-0.0682738\pi$
$659$	7.80940	+	13.5263i	0.304211	+	0.526909i	−0.672874	+	0.739757i	$0.734940\pi$
$660$		0			0
$661$	−15.5161	−	8.95822i	−0.603506	−	0.348434i	0.166914	−	0.985972i	$-0.446620\pi$
$661$	−15.5161	−	8.95822i	−0.603506	−	0.348434i	−0.770420	+	0.637537i	$0.779953\pi$
$662$	2.44585	−	4.23633i	0.0950605	−	0.164650i
$663$		0			0
$664$	−0.774017	−	1.34064i	−0.0300377	−	0.0520268i
$665$		−	32.7794i		−	1.27113i
$666$		0			0
$667$	−9.00000			−0.348481
$668$	−13.6295	+	7.86901i	−0.527342	+	0.304461i
$669$		0			0
$670$	−23.7667	−	13.7217i	−0.918187	−	0.530115i
$671$	−41.6753	−	24.0613i	−1.60886	−	0.928875i
$672$		0			0
$673$	2.94960	+	5.10885i	0.113699	+	0.196932i	0.917259	−	0.398292i	$-0.130397\pi$
$673$	2.94960	+	5.10885i	0.113699	+	0.196932i	−0.803560	+	0.595224i	$0.797064\pi$
$674$		−	29.8161i		−	1.14847i
$675$		0			0
$676$	4.94532	−	14.5196i	0.190205	−	0.558444i
$677$	13.7045	+	23.7369i	0.526707	+	0.912283i	0.999516	+	0.0311180i	$0.00990678\pi$
$677$	13.7045	+	23.7369i	0.526707	+	0.912283i	−0.472809	+	0.881165i	$0.656760\pi$
$678$		0			0
$679$	11.6568	−	20.1901i	0.447345	−	0.774825i
$680$	13.6008	−	23.5572i	0.521566	−	0.903379i
$681$		0			0
$682$	21.3297	−	12.3147i	0.816757	−	0.471555i
$683$			16.0989i			0.616006i	0.951385	+	0.308003i	$0.0996607\pi$
$683$			16.0989i			0.616006i	−0.951385	+	0.308003i	$0.900339\pi$
$684$		0			0
$685$	10.1399			0.387427
$686$	−3.41223	−	5.91015i	−0.130279	−	0.225651i
$687$		0			0
$688$	0.111692	−	0.193457i	0.00425823	−	0.00737547i
$689$	−2.67039	−	27.2561i	−0.101734	−	1.03837i
$690$		0			0
$691$	−23.9736	+	13.8412i	−0.912000	+	0.526543i	−0.881074	−	0.472979i	$-0.843179\pi$
$691$	−23.9736	+	13.8412i	−0.912000	+	0.526543i	−0.0309256	+	0.999522i	$0.509845\pi$
$692$	−8.78030			−0.333777
$693$		0			0
$694$		−	12.3413i		−	0.468469i
$695$	27.4091	−	15.8247i	1.03969	−	0.600264i
$696$		0			0
$697$	28.8924	+	16.6810i	1.09438	+	0.631839i
$698$	5.10514	−	8.84236i	0.193232	−	0.334688i
$699$		0			0
$700$	0.109914	−	0.0634588i	0.00415435	−	0.00239852i
$701$	10.0776			0.380624			0.190312	−	0.981724i	$-0.439050\pi$
$701$	10.0776			0.380624			0.190312	+	0.981724i	$0.439050\pi$
$702$		0			0
$703$	23.3883			0.882108
$704$	17.6341	−	10.1811i	0.664611	−	0.383713i
$705$		0			0
$706$	12.0584	−	20.8857i	0.453822	−	0.786043i
$707$	14.7666	+	8.52553i	0.555357	+	0.320635i
$708$		0			0
$709$	−2.79484	+	1.61360i	−0.104962	+	0.0606000i	−0.551562	−	0.834134i	$-0.685968\pi$
$709$	−2.79484	+	1.61360i	−0.104962	+	0.0606000i	0.446600	+	0.894734i	$0.352635\pi$
$710$		−	5.39324i		−	0.202405i
$711$		0			0
$712$	−16.5648			−0.620793
$713$	24.1055	−	13.9173i	0.902756	−	0.521207i
$714$		0			0
$715$	2.91506	+	29.7534i	0.109017	+	1.11271i
$716$	13.6896	−	23.7110i	0.511604	−	0.886123i
$717$		0			0
$718$	−15.8043	−	27.3738i	−0.589811	−	1.02158i
$719$	30.0712			1.12147			0.560733	−	0.827996i	$-0.310519\pi$
$719$	30.0712			1.12147			0.560733	+	0.827996i	$0.310519\pi$
$720$		0			0
$721$		−	7.25614i		−	0.270233i
$722$	0.715357	−	0.413012i	0.0266228	−	0.0153707i
$723$		0			0
$724$	−3.05852	+	5.29751i	−0.113669	+	0.196880i
$725$	−0.0372356	+	0.0644940i	−0.00138290	+	0.00239525i
$726$		0			0
$727$	9.68860	+	16.7811i	0.359330	+	0.622378i	0.987849	−	0.155416i	$-0.0496719\pi$
$727$	9.68860	+	16.7811i	0.359330	+	0.622378i	−0.628519	+	0.777794i	$0.716339\pi$
$728$	29.0105	−	20.7661i	1.07520	−	0.769643i
$729$		0			0
$730$		−	11.0857i		−	0.410299i
$731$	−1.89616	−	3.28424i	−0.0701320	−	0.121472i
$732$		0			0
$733$	−21.1938	−	12.2362i	−0.782810	−	0.451955i	0.0546155	−	0.998507i	$-0.482607\pi$
$733$	−21.1938	−	12.2362i	−0.782810	−	0.451955i	−0.837425	+	0.546552i	$0.815940\pi$
$734$	2.12877	+	1.22904i	0.0785742	+	0.0453648i
$735$		0			0
$736$	18.1340	−	10.4697i	0.668429	−	0.385918i
$737$	−49.9416			−1.83962
$738$		0			0
$739$			3.30687i			0.121645i	0.998149	+	0.0608226i	$0.0193724\pi$
$739$			3.30687i			0.121645i	−0.998149	+	0.0608226i	$0.980628\pi$
$740$	7.27712	+	12.6043i	0.267512	+	0.463344i
$741$		0			0
$742$	11.8178	−	20.4691i	0.433846	−	0.751444i
$743$	15.1394	+	8.74076i	0.555412	+	0.320667i	0.751302	−	0.659959i	$-0.229426\pi$
$743$	15.1394	+	8.74076i	0.555412	+	0.320667i	−0.195890	+	0.980626i	$0.562760\pi$
$744$		0			0
$745$	−6.50751	−	11.2713i	−0.238417	−	0.412950i
$746$		−	1.58566i		−	0.0580553i
$747$		0			0
$748$		−	18.3674i		−	0.671580i
$749$	−24.0264	+	13.8717i	−0.877906	+	0.506859i
$750$		0			0
$751$	14.2922	−	24.7548i	0.521528	−	0.903314i	−0.478158	−	0.878274i	$-0.658695\pi$
$751$	14.2922	−	24.7548i	0.521528	−	0.903314i	0.999686	−	0.0250400i	$-0.00797130\pi$
$752$	1.19083	+	0.687526i	0.0434251	+	0.0250715i
$753$		0			0
$754$	−3.20935	+	7.07354i	−0.116878	+	0.257603i
$755$	−21.8606			−0.795587
$756$		0			0
$757$	11.9611			0.434733			0.217367	−	0.976090i	$-0.430253\pi$
$757$	11.9611			0.434733			0.217367	+	0.976090i	$0.430253\pi$
$758$	−1.31737	−	2.28176i	−0.0478492	−	0.0828772i
$759$		0			0
$760$	−23.7910	−	13.7357i	−0.862989	−	0.498247i
$761$	1.84327	+	1.06421i	0.0668185	+	0.0385777i	0.533037	−	0.846092i	$-0.321051\pi$
$761$	1.84327	+	1.06421i	0.0668185	+	0.0385777i	−0.466219	+	0.884670i	$0.654384\pi$
$762$		0			0
$763$	−17.1841	−	29.7637i	−0.622105	−	1.07752i
$764$	−19.0449			−0.689019
$765$		0			0
$766$	−18.5156			−0.668994
$767$	7.64412	−	16.8480i	0.276013	−	0.608345i
$768$		0			0
$769$	6.62584	+	3.82543i	0.238934	+	0.137949i	0.614687	−	0.788771i	$-0.289282\pi$
$769$	6.62584	+	3.82543i	0.238934	+	0.137949i	−0.375753	+	0.926720i	$0.622616\pi$
$770$	−12.9007	+	22.3446i	−0.464907	+	0.805243i
$771$		0			0
$772$	3.35080	−	1.93458i	0.120598	−	0.0696272i
$773$		−	24.6440i		−	0.886383i	−0.896427	−	0.443191i	$-0.853846\pi$
$773$		−	24.6440i		−	0.886383i	0.896427	−	0.443191i	$-0.146154\pi$
$774$		0			0
$775$		−	0.230320i		−	0.00827333i
$776$	−9.76918	−	16.9207i	−0.350693	−	0.607418i
$777$		0			0
$778$	10.1667	+	5.86972i	0.364492	+	0.210440i
$779$	16.8465	−	29.1791i	0.603590	−	1.04545i
$780$		0			0
$781$	−4.90731	−	8.49972i	−0.175598	−	0.304144i
$782$			14.4280i			0.515943i
$783$		0			0
$784$	1.19238			0.0425851
$785$	−2.09716	+	1.21080i	−0.0748509	+	0.0432152i
$786$		0			0
$787$	36.2586	+	20.9339i	1.29248	+	0.746214i	0.979093	−	0.203411i	$-0.0652027\pi$
$787$	36.2586	+	20.9339i	1.29248	+	0.746214i	0.313388	+	0.949625i	$0.398536\pi$
$788$	7.26768	+	4.19599i	0.258900	+	0.149476i
$789$		0			0
$790$	11.1089	+	19.2412i	0.395237	+	0.684571i
$791$			66.7797i			2.37441i
$792$		0			0
$793$	−38.1671	+	27.3205i	−1.35535	+	0.970181i
$794$	13.2131	+	22.8857i	0.468914	+	0.812183i
$795$		0			0
$796$	8.16775	−	14.1470i	0.289498	−	0.501426i
$797$	−20.8781	+	36.1620i	−0.739541	+	1.28092i	0.213161	+	0.977017i	$0.431624\pi$
$797$	−20.8781	+	36.1620i	−0.739541	+	1.28092i	−0.952702	+	0.303906i	$0.901709\pi$
$798$		0			0
$799$	20.2163	−	11.6719i	0.715200	−	0.412921i
$800$		−	0.173265i		−	0.00612583i
$801$		0			0
$802$	−20.0792			−0.709022
$803$	−10.0869	−	17.4709i	−0.355957	−	0.616536i
$804$		0			0
$805$	−14.5795	+	25.2524i	−0.513859	+	0.890030i
$806$	−2.34241	−	23.9085i	−0.0825079	−	0.842140i
$807$		0			0
$808$	12.3755	−	7.14499i	0.435368	−	0.251360i
$809$	−45.2476			−1.59082			−0.795410	−	0.606072i	$-0.792744\pi$
$809$	−45.2476			−1.59082			−0.795410	+	0.606072i	$0.792744\pi$
$810$		0			0
$811$			52.8820i			1.85694i	0.371410	+	0.928469i	$0.378874\pi$
$811$			52.8820i			1.85694i	−0.371410	+	0.928469i	$0.621126\pi$
$812$	8.35255	−	4.82235i	0.293117	−	0.169231i
$813$		0			0
$814$	−15.9430	−	9.20470i	−0.558802	−	0.322625i
$815$	−6.22288	+	10.7784i	−0.217978	+	0.377549i
$816$		0			0
$817$	−3.31683	+	1.91497i	−0.116041	+	0.0669964i
$818$	−1.90053			−0.0664505
$819$		0			0
$820$	20.9667			0.732190
$821$	−29.8105	+	17.2111i	−1.04039	+	0.600671i	−0.919945	−	0.392048i	$-0.871767\pi$
$821$	−29.8105	+	17.2111i	−1.04039	+	0.600671i	−0.120449	+	0.992720i	$0.538433\pi$
$822$		0			0
$823$	5.99853	−	10.3898i	0.209096	−	0.362164i	−0.742334	−	0.670030i	$-0.766281\pi$
$823$	5.99853	−	10.3898i	0.209096	−	0.362164i	0.951430	+	0.307866i	$0.0996147\pi$
$824$	−5.26644	−	3.04058i	−0.183465	−	0.105924i
$825$		0			0
$826$	13.8279	−	7.98353i	0.481134	−	0.277783i
$827$		−	4.35092i		−	0.151296i	−0.997135	−	0.0756482i	$-0.975897\pi$
$827$		−	4.35092i		−	0.151296i	0.997135	−	0.0756482i	$-0.0241026\pi$
$828$		0			0
$829$	45.6204			1.58446			0.792230	−	0.610222i	$-0.208920\pi$
$829$	45.6204			1.58446			0.792230	+	0.610222i	$0.208920\pi$
$830$	0.945668	−	0.545982i	0.0328246	−	0.0189513i
$831$		0			0
$832$	−1.93657	−	19.7661i	−0.0671383	−	0.685266i
$833$	10.1213	−	17.5307i	0.350683	−	0.607401i
$834$		0			0
$835$	−14.9595	−	25.9106i	−0.517695	−	0.896674i
$836$	−18.5497			−0.641554
$837$		0			0
$838$		−	0.354449i		−	0.0122442i
$839$	21.3626	−	12.3337i	0.737520	−	0.425808i	−0.0836466	−	0.996495i	$-0.526657\pi$
$839$	21.3626	−	12.3337i	0.737520	−	0.425808i	0.821167	+	0.570688i	$0.193323\pi$
$840$		0			0
$841$	11.6704	−	20.2137i	0.402427	−	0.697025i
$842$	5.01926	−	8.69361i	0.172975	−	0.299602i
$843$		0			0
$844$	−8.51525	−	14.7488i	−0.293107	−	0.507676i
$845$	27.6026	+	9.40138i	0.949559	+	0.323417i
$846$		0			0
$847$			9.15606i			0.314606i
$848$	−0.942085	−	1.63174i	−0.0323513	−	0.0560341i
$849$		0			0
$850$	0.103391	+	0.0596928i	0.00354628	+	0.00204744i
$851$	−18.0178	−	10.4026i	−0.617641	−	0.356595i
$852$		0			0
$853$	−22.9668	+	13.2599i	−0.786369	+	0.454010i	−0.838683	−	0.544620i	$-0.816674\pi$
$853$	−22.9668	+	13.2599i	−0.786369	+	0.454010i	0.0523138	+	0.998631i	$0.483340\pi$
$854$	−40.5089			−1.38619
$855$		0			0
$856$			23.2508i			0.794697i
$857$	−3.20474	−	5.55077i	−0.109472	−	0.189611i	0.806085	−	0.591800i	$-0.201583\pi$
$857$	−3.20474	−	5.55077i	−0.109472	−	0.189611i	−0.915556	+	0.402190i	$0.868249\pi$
$858$		0			0
$859$	−12.7998	+	22.1699i	−0.436723	+	0.756427i	−0.997435	−	0.0715846i	$-0.977194\pi$
$859$	−12.7998	+	22.1699i	−0.436723	+	0.756427i	0.560711	+	0.828011i	$0.310528\pi$
$860$	−2.06402	−	1.19166i	−0.0703824	−	0.0406353i
$861$		0			0
$862$	16.5078	+	28.5924i	0.562258	+	0.973860i
$863$		−	48.4823i		−	1.65036i	−0.564873	−	0.825178i	$-0.691075\pi$
$863$		−	48.4823i		−	1.65036i	0.564873	−	0.825178i	$-0.308925\pi$
$864$		0			0
$865$		−	16.6919i		−	0.567542i
$866$	6.92319	−	3.99711i	0.235260	−	0.135827i
$867$		0			0
$868$	−14.9142	+	25.8322i	−0.506222	+	0.876802i
$869$	35.0152	+	20.2160i	1.18781	+	0.685782i
$870$		0			0
$871$	−20.1264	+	44.3595i	−0.681959	+	1.50307i
$872$	−28.8029			−0.975389
$873$		0			0
$874$	14.5711			0.492876
$875$	−19.1478	−	33.1650i	−0.647315	−	1.12118i
$876$		0			0
$877$	−27.0023	−	15.5898i	−0.911801	−	0.526429i	−0.0307911	−	0.999526i	$-0.509803\pi$
$877$	−27.0023	−	15.5898i	−0.911801	−	0.526429i	−0.881010	+	0.473097i	$0.843136\pi$
$878$	27.5549	+	15.9088i	0.929932	+	0.536897i
$879$		0			0
$880$	1.02840	+	1.78125i	0.0346675	+	0.0600459i
$881$	49.6614			1.67314			0.836568	−	0.547863i	$-0.184558\pi$
$881$	49.6614			1.67314			0.836568	+	0.547863i	$0.184558\pi$
$882$		0			0
$883$	30.3523			1.02144			0.510718	−	0.859748i	$-0.329380\pi$
$883$	30.3523			1.02144			0.510718	+	0.859748i	$0.329380\pi$
$884$	−16.3145	−	7.40207i	−0.548715	−	0.248959i
$885$		0			0
$886$	18.7481	+	10.8242i	0.629855	+	0.363647i
$887$	6.42161	−	11.1226i	0.215616	−	0.373459i	−0.737847	−	0.674968i	$-0.764157\pi$
$887$	6.42161	−	11.1226i	0.215616	−	0.373459i	0.953463	+	0.301510i	$0.0974906\pi$
$888$		0			0
$889$	5.24962	−	3.03087i	0.176066	−	0.101652i
$890$		−	11.6846i		−	0.391669i
$891$		0			0
$892$		−	12.9834i		−	0.434715i
$893$	−11.7877	−	20.4169i	−0.394460	−	0.683224i
$894$		0			0
$895$	45.0762	+	26.0248i	1.50673	+	0.869912i
$896$	−10.4478	+	18.0961i	−0.349035	+	0.604547i
$897$		0			0
$898$	6.32484	+	10.9549i	0.211063	+	0.365571i
$899$		−	17.5024i		−	0.583738i
$900$		0			0
$901$	−31.9869			−1.06564
$902$	−22.9674	+	13.2602i	−0.764731	+	0.441518i
$903$		0			0
$904$	48.4680	+	27.9830i	1.61202	+	0.930701i
$905$	−10.0709	−	5.81444i	−0.334768	−	0.193279i
$906$		0			0
$907$	10.2993	+	17.8389i	0.341983	+	0.592331i	0.984801	−	0.173688i	$-0.0555683\pi$
$907$	10.2993	+	17.8389i	0.341983	+	0.592331i	−0.642818	+	0.766019i	$0.722235\pi$
$908$		−	9.57860i		−	0.317877i
$909$		0			0
$910$	14.6481	+	20.4636i	0.485581	+	0.678362i
$911$	21.1949	+	36.7107i	0.702219	+	1.21628i	0.967686	+	0.252159i	$0.0811407\pi$
$911$	21.1949	+	36.7107i	0.702219	+	1.21628i	−0.265466	+	0.964120i	$0.585526\pi$
$912$		0			0
$913$	0.993579	−	1.72093i	0.0328827	−	0.0569545i
$914$	7.88827	−	13.6629i	0.260921	−	0.451928i
$915$		0			0
$916$	−5.49524	+	3.17268i	−0.181568	+	0.104828i
$917$		−	24.4988i		−	0.809021i
$918$		0			0
$919$	−42.7987			−1.41180			−0.705899	−	0.708313i	$-0.749457\pi$
$919$	−42.7987			−1.41180			−0.705899	+	0.708313i	$0.749457\pi$
$920$	12.2186	+	21.1633i	0.402836	+	0.697733i
$921$		0			0
$922$	−10.8068	+	18.7179i	−0.355903	+	0.616441i
$923$	−9.52734	+	0.933432i	−0.313596	+	0.0307243i
$924$		0			0
$925$	−0.149090	+	0.0860769i	−0.00490203	+	0.00283019i
$926$	−9.54253			−0.313587
$927$		0			0
$928$		−	13.1667i		−	0.432218i
$929$	−10.2242	+	5.90296i	−0.335446	+	0.193670i	−0.658257	−	0.752794i	$-0.728706\pi$
$929$	−10.2242	+	5.90296i	−0.335446	+	0.193670i	0.322810	+	0.946464i	$0.395372\pi$
$930$		0			0
$931$	−17.7046	−	10.2218i	−0.580245	−	0.335004i
$932$	11.8575	−	20.5378i	0.388405	−	0.672738i
$933$		0			0
$934$	6.59511	−	3.80769i	0.215799	−	0.124591i
$935$	34.9177			1.14193
$936$		0			0
$937$	24.7925			0.809935			0.404967	−	0.914331i	$-0.367283\pi$
$937$	24.7925			0.809935			0.404967	+	0.914331i	$0.367283\pi$
$938$	−36.4079	+	21.0201i	−1.18876	+	0.686331i
$939$		0			0
$940$	7.33531	−	12.7051i	0.239251	−	0.414395i
$941$	−20.6367	−	11.9146i	−0.672737	−	0.388405i	0.124376	−	0.992235i	$-0.460307\pi$
$941$	−20.6367	−	11.9146i	−0.672737	−	0.388405i	−0.797113	+	0.603830i	$0.793640\pi$
$942$		0			0
$943$	−25.9563	+	14.9859i	−0.845253	+	0.488007i
$944$		−	1.27285i		−	0.0414278i
$945$		0			0
$946$	3.01462			0.0980138
$947$	−42.4532	+	24.5104i	−1.37954	+	0.796480i	−0.992104	−	0.125415i	$-0.959974\pi$
$947$	−42.4532	+	24.5104i	−1.37954	+	0.796480i	−0.387440	+	0.921895i	$0.626641\pi$
$948$		0			0
$949$	−19.5832	+	1.91865i	−0.635698	+	0.0622819i
$950$	0.0602850	−	0.104417i	0.00195590	−	0.00338773i
$951$		0			0
$952$	−20.8349	−	36.0870i	−0.675262	−	1.16959i
$953$	−7.78372			−0.252140			−0.126070	−	0.992021i	$-0.540236\pi$
$953$	−7.78372			−0.252140			−0.126070	+	0.992021i	$0.540236\pi$
$954$		0			0
$955$		−	36.2055i		−	1.17158i
$956$	14.4697	−	8.35406i	0.467982	−	0.270190i
$957$		0			0
$958$	7.11200	−	12.3183i	0.229778	−	0.397987i
$959$	7.76661	−	13.4522i	0.250797	−	0.434393i
$960$		0			0
$961$	11.5651	+	20.0314i	0.373069	+	0.646174i
$962$	−14.6009	+	10.4515i	−0.470752	+	0.336971i
$963$		0			0
$964$			35.7011i			1.14985i
$965$	3.67777	+	6.37008i	0.118392	+	0.205060i
$966$		0			0
$967$	−32.5591	−	18.7980i	−1.04703	−	0.604502i	−0.125213	−	0.992130i	$-0.539961\pi$
$967$	−32.5591	−	18.7980i	−1.04703	−	0.604502i	−0.921816	+	0.387627i	$0.873295\pi$
$968$	6.64538	+	3.83671i	0.213590	+	0.123317i
$969$		0			0
$970$	11.9357	−	6.89105i	0.383231	−	0.221258i
$971$	9.16512			0.294123			0.147061	−	0.989127i	$-0.453019\pi$
$971$	9.16512			0.294123			0.147061	+	0.989127i	$0.453019\pi$
$972$		0			0
$973$		−	48.4833i		−	1.55430i
$974$	17.1587	+	29.7197i	0.549800	+	0.952281i
$975$		0			0
$976$	−1.61463	+	2.79662i	−0.0516831	+	0.0895177i
$977$	41.0043	+	23.6739i	1.31184	+	0.757394i	0.982401	−	0.186782i	$-0.0598058\pi$
$977$	41.0043	+	23.6739i	1.31184	+	0.757394i	0.329443	+	0.944176i	$0.393139\pi$
$978$		0			0
$979$	−10.6318	−	18.4149i	−0.339795	−	0.588542i
$980$		−	12.7217i		−	0.406380i
$981$		0			0
$982$			3.40553i			0.108675i
$983$	−14.0634	+	8.11949i	−0.448552	+	0.258972i	−0.707219	−	0.706995i	$-0.750050\pi$
$983$	−14.0634	+	8.11949i	−0.448552	+	0.258972i	0.258666	+	0.965967i	$0.416717\pi$
$984$		0			0
$985$	−7.97686	+	13.8163i	−0.254164	+	0.440225i
$986$	7.85686	+	4.53616i	0.250213	+	0.144461i
$987$		0			0
$988$	−7.47552	+	16.4764i	−0.237828	+	0.524183i
$989$	3.40693			0.108334
$990$		0			0
$991$	−37.7634			−1.19959			−0.599797	−	0.800152i	$-0.704752\pi$
$991$	−37.7634			−1.19959			−0.599797	+	0.800152i	$0.704752\pi$
$992$	20.3605	+	35.2655i	0.646447	+	1.11968i
$993$		0			0
$994$	−7.15496	−	4.13092i	−0.226942	−	0.131025i
$995$	26.8943	+	15.5274i	0.852606	+	0.492252i
$996$		0			0
$997$	−23.8283	−	41.2718i	−0.754649	−	1.30709i	−0.945549	−	0.325481i	$-0.894474\pi$
$997$	−23.8283	−	41.2718i	−0.754649	−	1.30709i	0.190899	−	0.981610i	$-0.438860\pi$
$998$	−7.48156			−0.236824
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.t.c.64.6		20
3.2	odd	2		117.2.t.c.103.5	yes	20
9.2	odd	6		117.2.t.c.25.6	yes	20
9.4	even	3		1053.2.b.i.649.6		10
9.5	odd	6		1053.2.b.j.649.5		10
9.7	even	3	inner	351.2.t.c.181.5		20
13.12	even	2	inner	351.2.t.c.64.5		20
39.38	odd	2		117.2.t.c.103.6	yes	20
117.25	even	6	inner	351.2.t.c.181.6		20
117.38	odd	6		117.2.t.c.25.5	✓	20
117.77	odd	6		1053.2.b.j.649.6		10
117.103	even	6		1053.2.b.i.649.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.5	✓	20	117.38	odd	6
117.2.t.c.25.6	yes	20	9.2	odd	6
117.2.t.c.103.5	yes	20	3.2	odd	2
117.2.t.c.103.6	yes	20	39.38	odd	2
351.2.t.c.64.5		20	13.12	even	2	inner
351.2.t.c.64.6		20	1.1	even	1	trivial
351.2.t.c.181.5		20	9.7	even	3	inner
351.2.t.c.181.6		20	117.25	even	6	inner
1053.2.b.i.649.5		10	117.103	even	6
1053.2.b.i.649.6		10	9.4	even	3
1053.2.b.j.649.5		10	9.5	odd	6
1053.2.b.j.649.6		10	117.77	odd	6

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.784270 - 0.452798i) q^{2} +(-0.589947 + 1.02182i) q^{4} +(-1.94254 - 1.12153i) q^{5} +(-2.97576 + 1.71806i) q^{7} +2.87970i q^{8} -2.03130 q^{10} +(-3.20133 + 1.84829i) q^{11} +(0.351567 + 3.58837i) q^{13} +(-1.55587 + 2.69484i) q^{14} +(0.124029 + 0.214825i) q^{16} +4.21120 q^{17} -4.25298i q^{19} +(2.29200 - 1.32329i) q^{20} +(-1.67380 + 2.89911i) q^{22} +(-1.89162 + 3.27639i) q^{23} +(0.0156524 + 0.0271108i) q^{25} +(1.90053 + 2.65506i) q^{26} -4.05425i q^{28} +(1.18945 + 2.06020i) q^{29} +(-6.37163 - 3.67866i) q^{31} +(-4.79325 - 2.76738i) q^{32} +(3.30272 - 1.90682i) q^{34} +7.70739 q^{35} +5.49928i q^{37} +(-1.92574 - 3.33549i) q^{38} +(3.22967 - 5.59395i) q^{40} +(6.86085 + 3.96111i) q^{41} +(-0.450266 - 0.779883i) q^{43} -4.36157i q^{44} +3.42609i q^{46} +(4.80060 - 2.77163i) q^{47} +(2.40343 - 4.16287i) q^{49} +(0.0245514 + 0.0141748i) q^{50} +(-3.87407 - 1.75771i) q^{52} -7.59566 q^{53} +8.29163 q^{55} +(-4.94749 - 8.56930i) q^{56} +(1.86571 + 1.07717i) q^{58} +(-4.44379 - 2.56562i) q^{59} +(6.50907 + 11.2740i) q^{61} -6.66277 q^{62} -5.50838 q^{64} +(3.34152 - 7.36486i) q^{65} +(11.7002 + 6.75511i) q^{67} +(-2.48439 + 4.30308i) q^{68} +(6.04468 - 3.48989i) q^{70} +2.65506i q^{71} +5.45741i q^{73} +(2.49006 + 4.31292i) q^{74} +(4.34578 + 2.50904i) q^{76} +(6.35092 - 11.0001i) q^{77} +(-5.46886 - 9.47234i) q^{79} -0.556410i q^{80} +7.17434 q^{82} +(-0.465547 + 0.268784i) q^{83} +(-8.18044 - 4.72298i) q^{85} +(-0.706259 - 0.407759i) q^{86} +(-5.32252 - 9.21887i) q^{88} +5.75227i q^{89} +(-7.21120 - 10.0741i) q^{91} +(-2.23192 - 3.86579i) q^{92} +(2.50998 - 4.34740i) q^{94} +(-4.76984 + 8.26161i) q^{95} +(-5.87585 + 3.39243i) q^{97} -4.35308i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

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