LMFDB - Embedded newform 243.2.g.a.10.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			10.8
Character	$\chi$	$=$	243.10
Dual form			243.2.g.a.73.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38576 + 1.19817i) q^{2} +(3.06192 + 4.11287i) q^{4} +(-0.727126 - 2.42877i) q^{5} +(0.202369 + 0.469143i) q^{7} +(1.44988 + 8.22270i) q^{8} +O(q^{10})$	\(q+(2.38576 + 1.19817i) q^{2} +(3.06192 + 4.11287i) q^{4} +(-0.727126 - 2.42877i) q^{5} +(0.202369 + 0.469143i) q^{7} +(1.44988 + 8.22270i) q^{8} +(1.17534 - 6.66569i) q^{10} +(-1.49541 + 0.354419i) q^{11} +(-4.71325 - 3.09996i) q^{13} +(-0.0793122 + 1.36174i) q^{14} +(-3.45199 + 11.5305i) q^{16} +(1.33086 - 0.484393i) q^{17} +(0.986977 + 0.359230i) q^{19} +(7.76282 - 10.4273i) q^{20} +(-3.99235 - 0.946204i) q^{22} +(-0.103125 + 0.239071i) q^{23} +(-1.19278 + 0.784502i) q^{25} +(-7.53041 - 13.0431i) q^{26} +(-1.30989 + 2.26880i) q^{28} +(0.103412 + 1.77552i) q^{29} +(-5.13181 + 0.599822i) q^{31} +(-10.5915 + 11.2264i) q^{32} +(3.75550 + 0.438955i) q^{34} +(0.992294 - 0.832634i) q^{35} +(-5.04999 - 4.23745i) q^{37} +(1.92427 + 2.03961i) q^{38} +(18.9168 - 9.50037i) q^{40} +(6.03866 - 3.03273i) q^{41} +(4.19282 + 4.44412i) q^{43} +(-6.03650 - 5.06523i) q^{44} +(-0.532481 + 0.446804i) q^{46} +(7.26206 + 0.848813i) q^{47} +(4.62455 - 4.90174i) q^{49} +(-3.78565 + 0.442479i) q^{50} +(-1.68188 - 28.8768i) q^{52} +(-4.74440 + 8.21755i) q^{53} +(1.94815 + 3.37430i) q^{55} +(-3.56421 + 2.34422i) q^{56} +(-1.88066 + 4.35987i) q^{58} +(4.82144 + 1.14270i) q^{59} +(-7.70381 + 10.3480i) q^{61} +(-12.9620 - 4.71777i) q^{62} +(-16.0995 + 5.85975i) q^{64} +(-4.10195 + 13.7015i) q^{65} +(-0.373231 + 6.40814i) q^{67} +(6.06723 + 3.99048i) q^{68} +(3.36502 - 0.797524i) q^{70} +(0.896716 - 5.08553i) q^{71} +(-1.03528 - 5.87137i) q^{73} +(-6.97088 - 16.1603i) q^{74} +(1.54458 + 5.15924i) q^{76} +(-0.468897 - 0.629838i) q^{77} +(8.88455 + 4.46199i) q^{79} +30.5149 q^{80} +18.0405 q^{82} +(-11.5744 - 5.81289i) q^{83} +(-2.14418 - 2.88014i) q^{85} +(4.67822 + 15.6263i) q^{86} +(-5.08245 - 11.7824i) q^{88} +(1.71260 + 9.71264i) q^{89} +(0.500509 - 2.83853i) q^{91} +(-1.29903 + 0.307875i) q^{92} +(16.3085 + 10.7263i) q^{94} +(0.154831 - 2.65835i) q^{95} +(1.03163 - 3.44589i) q^{97} +(16.9062 - 6.15336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	2.38576	+	1.19817i	1.68699	+	0.847237i	0.991710	+	0.128497i	$0.0410152\pi$
$2$	2.38576	+	1.19817i	1.68699	+	0.847237i	0.695278	+	0.718741i	$0.255281\pi$
$3$		0			0
$3$		0			0
$4$	3.06192	+	4.11287i	1.53096	+	2.05644i
$5$	−0.727126	−	2.42877i	−0.325181	−	1.08618i	−0.951766	−	0.306826i	$-0.900733\pi$
$5$	−0.727126	−	2.42877i	−0.325181	−	1.08618i	0.626585	−	0.779353i	$-0.284452\pi$
$6$		0			0
$7$	0.202369	+	0.469143i	0.0764882	+	0.177320i	0.952170	−	0.305569i	$-0.0988468\pi$
$7$	0.202369	+	0.469143i	0.0764882	+	0.177320i	−0.875682	+	0.482889i	$0.839588\pi$
$8$	1.44988	+	8.22270i	0.512611	+	2.90716i
$9$		0			0
$10$	1.17534	−	6.66569i	0.371676	−	2.10788i
$11$	−1.49541	+	0.354419i	−0.450883	+	0.106861i	−0.449782	−	0.893138i	$-0.648498\pi$
$11$	−1.49541	+	0.354419i	−0.450883	+	0.106861i	−0.00110057	+	0.999999i	$0.500350\pi$
$12$		0			0
$13$	−4.71325	−	3.09996i	−1.30722	−	0.859773i	−0.311327	−	0.950303i	$-0.600774\pi$
$13$	−4.71325	−	3.09996i	−1.30722	−	0.859773i	−0.995894	+	0.0905298i	$0.971144\pi$
$14$	−0.0793122	+	1.36174i	−0.0211971	+	0.363940i
$15$		0			0
$16$	−3.45199	+	11.5305i	−0.862998	+	2.88261i
$17$	1.33086	−	0.484393i	0.322781	−	0.117483i	−0.175548	−	0.984471i	$-0.556170\pi$
$17$	1.33086	−	0.484393i	0.322781	−	0.117483i	0.498328	+	0.866988i	$0.333947\pi$
$18$		0			0
$19$	0.986977	+	0.359230i	0.226428	+	0.0824131i	0.452743	−	0.891641i	$-0.350446\pi$
$19$	0.986977	+	0.359230i	0.226428	+	0.0824131i	−0.226315	+	0.974054i	$0.572668\pi$
$20$	7.76282	−	10.4273i	1.73582	−	2.33161i
$21$		0			0
$22$	−3.99235	−	0.946204i	−0.851171	−	0.201731i
$23$	−0.103125	+	0.239071i	−0.0215031	+	0.0498497i	−0.928629	−	0.371009i	$-0.879012\pi$
$23$	−0.103125	+	0.239071i	−0.0215031	+	0.0498497i	0.907126	+	0.420859i	$0.138271\pi$
$24$		0			0
$25$	−1.19278	+	0.784502i	−0.238555	+	0.156900i
$26$	−7.53041	−	13.0431i	−1.47684	−	2.55795i
$27$		0			0
$28$	−1.30989	+	2.26880i	−0.247546	+	0.428762i
$29$	0.103412	+	1.77552i	0.0192031	+	0.329705i	0.994204	+	0.107506i	$0.0342865\pi$
$29$	0.103412	+	1.77552i	0.0192031	+	0.329705i	−0.975001	+	0.222199i	$0.928676\pi$
$30$		0			0
$31$	−5.13181	+	0.599822i	−0.921700	+	0.107731i	−0.563690	−	0.825986i	$-0.690619\pi$
$31$	−5.13181	+	0.599822i	−0.921700	+	0.107731i	−0.358010	+	0.933718i	$0.616545\pi$
$32$	−10.5915	+	11.2264i	−1.87233	+	1.98456i
$33$		0			0
$34$	3.75550	+	0.438955i	0.644063	+	0.0752802i
$35$	0.992294	−	0.832634i	0.167728	−	0.140741i
$36$		0			0
$37$	−5.04999	−	4.23745i	−0.830214	−	0.696632i	0.125126	−	0.992141i	$-0.460066\pi$
$37$	−5.04999	−	4.23745i	−0.830214	−	0.696632i	−0.955340	+	0.295509i	$0.904511\pi$
$38$	1.92427	+	2.03961i	0.312158	+	0.330868i
$39$		0			0
$40$	18.9168	−	9.50037i	2.99101	−	1.50214i
$41$	6.03866	−	3.03273i	0.943080	−	0.473633i	0.0903071	−	0.995914i	$-0.471215\pi$
$41$	6.03866	−	3.03273i	0.943080	−	0.473633i	0.852773	+	0.522281i	$0.174919\pi$
$42$		0			0
$43$	4.19282	+	4.44412i	0.639398	+	0.677723i	0.963318	−	0.268362i	$-0.0864823\pi$
$43$	4.19282	+	4.44412i	0.639398	+	0.677723i	−0.323920	+	0.946085i	$0.605001\pi$
$44$	−6.03650	−	5.06523i	−0.910037	−	0.763612i
$45$		0			0
$46$	−0.532481	+	0.446804i	−0.0785100	+	0.0658777i
$47$	7.26206	+	0.848813i	1.05928	+	0.123812i	0.627850	−	0.778334i	$-0.283935\pi$
$47$	7.26206	+	0.848813i	1.05928	+	0.123812i	0.431430	+	0.902146i	$0.358009\pi$
$48$		0			0
$49$	4.62455	−	4.90174i	0.660650	−	0.700248i
$50$	−3.78565	+	0.442479i	−0.535372	+	0.0625760i
$51$		0			0
$52$	−1.68188	−	28.8768i	−0.233235	−	4.00449i
$53$	−4.74440	+	8.21755i	−0.651694	+	1.12877i	0.331018	+	0.943624i	$0.392608\pi$
$53$	−4.74440	+	8.21755i	−0.651694	+	1.12877i	−0.982712	+	0.185142i	$0.940725\pi$
$54$		0			0
$55$	1.94815	+	3.37430i	0.262689	+	0.454991i
$56$	−3.56421	+	2.34422i	−0.476288	+	0.313259i
$57$		0			0
$58$	−1.88066	+	4.35987i	−0.246943	+	0.572479i
$59$	4.82144	+	1.14270i	0.627698	+	0.148767i	0.532140	−	0.846657i	$-0.321388\pi$
$59$	4.82144	+	1.14270i	0.627698	+	0.148767i	0.0955586	+	0.995424i	$0.469536\pi$
$60$		0			0
$61$	−7.70381	+	10.3480i	−0.986372	+	1.32493i	−0.0409219	+	0.999162i	$0.513029\pi$
$61$	−7.70381	+	10.3480i	−0.986372	+	1.32493i	−0.945451	+	0.325766i	$0.894378\pi$
$62$	−12.9620	−	4.71777i	−1.64617	−	0.599157i
$63$		0			0
$64$	−16.0995	+	5.85975i	−2.01244	+	0.732468i
$65$	−4.10195	+	13.7015i	−0.508784	+	1.69946i
$66$		0			0
$67$	−0.373231	+	6.40814i	−0.0455975	+	0.782878i	0.895566	+	0.444928i	$0.146771\pi$
$67$	−0.373231	+	6.40814i	−0.0455975	+	0.782878i	−0.941164	+	0.337951i	$0.890266\pi$
$68$	6.06723	+	3.99048i	0.735760	+	0.483917i
$69$		0			0
$70$	3.36502	−	0.797524i	0.402197	−	0.0953223i
$71$	0.896716	−	5.08553i	0.106421	−	0.603541i	−0.884223	−	0.467065i	$-0.845311\pi$
$71$	0.896716	−	5.08553i	0.106421	−	0.603541i	0.990643	−	0.136476i	$-0.0435776\pi$
$72$		0			0
$73$	−1.03528	−	5.87137i	−0.121171	−	0.687192i	−0.983509	−	0.180860i	$-0.942112\pi$
$73$	−1.03528	−	5.87137i	−0.121171	−	0.687192i	0.862338	−	0.506332i	$-0.168999\pi$
$74$	−6.97088	−	16.1603i	−0.810348	−	1.87860i
$75$		0			0
$76$	1.54458	+	5.15924i	0.177175	+	0.591806i
$77$	−0.468897	−	0.629838i	−0.0534358	−	0.0717767i
$78$		0			0
$79$	8.88455	+	4.46199i	0.999590	+	0.502013i	0.871838	−	0.489793i	$-0.162928\pi$
$79$	8.88455	+	4.46199i	0.999590	+	0.502013i	0.127751	+	0.991806i	$0.459224\pi$
$80$	30.5149			3.41167
$81$		0			0
$82$	18.0405			1.99224
$83$	−11.5744	−	5.81289i	−1.27046	−	0.638048i	−0.319564	−	0.947565i	$-0.603536\pi$
$83$	−11.5744	−	5.81289i	−1.27046	−	0.638048i	−0.950894	+	0.309517i	$0.899833\pi$
$84$		0			0
$85$	−2.14418	−	2.88014i	−0.232569	−	0.312395i
$86$	4.67822	+	15.6263i	0.504466	+	1.68503i
$87$		0			0
$88$	−5.08245	−	11.7824i	−0.541790	−	1.25601i
$89$	1.71260	+	9.71264i	0.181535	+	1.02954i	0.930327	+	0.366732i	$0.119523\pi$
$89$	1.71260	+	9.71264i	0.181535	+	1.02954i	−0.748791	+	0.662806i	$0.769366\pi$
$90$		0			0
$91$	0.500509	−	2.83853i	0.0524676	−	0.297558i
$92$	−1.29903	+	0.307875i	−0.135433	+	0.0320982i
$93$		0			0
$94$	16.3085	+	10.7263i	1.68209	+	1.10633i
$95$	0.154831	−	2.65835i	0.0158853	−	0.272741i
$96$		0			0
$97$	1.03163	−	3.44589i	0.104746	−	0.349877i	−0.889508	−	0.456919i	$-0.848953\pi$
$97$	1.03163	−	3.44589i	0.104746	−	0.349877i	0.994254	+	0.107042i	$0.0341380\pi$
$98$	16.9062	−	6.15336i	1.70778	−	0.621583i
$99$		0			0
$100$	−6.87874	−	2.50366i	−0.687874	−	0.250366i
$101$	−10.6434	+	14.2965i	−1.05906	+	1.42256i	−0.158741	+	0.987320i	$0.550744\pi$
$101$	−10.6434	+	14.2965i	−1.05906	+	1.42256i	−0.900315	+	0.435239i	$0.856664\pi$
$102$		0			0
$103$	4.20113	+	0.995685i	0.413949	+	0.0981078i	0.432313	−	0.901724i	$-0.357698\pi$
$103$	4.20113	+	0.995685i	0.413949	+	0.0981078i	−0.0183637	+	0.999831i	$0.505846\pi$
$104$	18.6563	−	43.2502i	1.82940	−	4.24103i
$105$		0			0
$106$	−21.1651	+	13.9205i	−2.05573	+	1.35208i
$107$	−3.98940	−	6.90985i	−0.385670	−	0.668000i	0.606192	−	0.795319i	$-0.292696\pi$
$107$	−3.98940	−	6.90985i	−0.385670	−	0.668000i	−0.991862	+	0.127318i	$0.959363\pi$
$108$		0			0
$109$	0.106432	−	0.184345i	0.0101943	−	0.0176571i	−0.860883	−	0.508803i	$-0.830088\pi$
$109$	0.106432	−	0.184345i	0.0101943	−	0.0176571i	0.871078	+	0.491145i	$0.163422\pi$
$110$	0.604829	+	10.3845i	0.0576681	+	0.990124i
$111$		0			0
$112$	−6.10801	+	0.713924i	−0.577153	+	0.0674595i
$113$	3.80609	−	4.03422i	0.358047	−	0.379508i	−0.523163	−	0.852233i	$-0.675248\pi$
$113$	3.80609	−	4.03422i	0.358047	−	0.379508i	0.881210	+	0.472725i	$0.156730\pi$
$114$		0			0
$115$	0.655633	+	0.0766326i	0.0611381	+	0.00714602i
$116$	−6.98584	+	5.86181i	−0.648619	+	0.544256i
$117$		0			0
$118$	10.1337	+	8.50315i	0.932878	+	0.782778i
$119$	0.496574	+	0.526338i	0.0455209	+	0.0482493i
$120$		0			0
$121$	−7.71932	+	3.87679i	−0.701756	+	0.352435i
$122$	−30.7782	+	15.4574i	−2.78653	+	1.39945i
$123$		0			0
$124$	−18.1802	−	19.2699i	−1.63263	−	1.73048i
$125$	−6.93801	−	5.82168i	−0.620554	−	0.520707i
$126$		0			0
$127$	−13.9870	+	11.7365i	−1.24115	+	1.04145i	−0.243713	+	0.969847i	$0.578365\pi$
$127$	−13.9870	+	11.7365i	−1.24115	+	1.04145i	−0.997434	+	0.0715979i	$0.977190\pi$
$128$	−14.7711	−	1.72650i	−1.30560	−	0.152602i
$129$		0			0
$130$	−26.2030	+	27.7736i	−2.29816	+	2.43591i
$131$	7.98597	−	0.933426i	0.697738	−	0.0815538i	0.240173	−	0.970730i	$-0.422796\pi$
$131$	7.98597	−	0.933426i	0.697738	−	0.0815538i	0.457565	+	0.889176i	$0.348722\pi$
$132$		0			0
$133$	0.0312028	+	0.535731i	0.00270562	+	0.0464537i
$134$	−8.56851	+	14.8411i	−0.740206	+	1.28207i
$135$		0			0
$136$	5.91261	+	10.2409i	0.507002	+	0.878153i
$137$	7.12884	−	4.68871i	0.609058	−	0.400583i	−0.207177	−	0.978303i	$-0.566428\pi$
$137$	7.12884	−	4.68871i	0.609058	−	0.400583i	0.816235	+	0.577720i	$0.196057\pi$
$138$		0			0
$139$	5.16860	−	11.9822i	0.438395	−	1.01631i	−0.545588	−	0.838053i	$-0.683694\pi$
$139$	5.16860	−	11.9822i	0.438395	−	1.01631i	0.983983	−	0.178260i	$-0.0570469\pi$
$140$	6.46284	+	1.53172i	0.546210	+	0.129454i
$141$		0			0
$142$	8.23270	−	11.0584i	0.690873	−	0.928003i
$143$	8.14693	+	2.96524i	0.681280	+	0.247966i
$144$		0			0
$145$	4.23713	−	1.54219i	0.351875	−	0.128072i
$146$	4.56500	−	15.2481i	0.377802	−	1.26195i
$147$		0			0
$148$	1.96540	−	33.7447i	0.161555	−	2.77380i
$149$	−13.6307	−	8.96505i	−1.11667	−	0.734446i	−0.149547	−	0.988755i	$-0.547782\pi$
$149$	−13.6307	−	8.96505i	−1.11667	−	0.734446i	−0.967123	+	0.254309i	$0.918152\pi$
$150$		0			0
$151$	21.0726	−	4.99431i	1.71487	−	0.406431i	0.748405	−	0.663242i	$-0.230820\pi$
$151$	21.0726	−	4.99431i	1.71487	−	0.406431i	0.966462	+	0.256811i	$0.0826718\pi$
$152$	−1.52284	+	8.63645i	−0.123519	+	0.700509i
$153$		0			0
$154$	−0.364021	−	2.06446i	−0.0293336	−	0.166359i
$155$	5.18830	+	12.0278i	0.416735	+	0.966100i
$156$		0			0
$157$	0.723891	+	2.41796i	0.0577728	+	0.192974i	0.982004	−	0.188858i	$-0.0604785\pi$
$157$	0.723891	+	2.41796i	0.0577728	+	0.192974i	−0.924232	+	0.381832i	$0.875293\pi$
$158$	15.8502	+	21.2905i	1.26097	+	1.69378i
$159$		0			0
$160$	34.9676	+	17.5614i	2.76443	+	1.38835i
$161$	−0.133028			−0.0104841
$162$		0			0
$163$	7.30888			0.572476			0.286238	−	0.958159i	$-0.407595\pi$
$163$	7.30888			0.572476			0.286238	+	0.958159i	$0.407595\pi$
$164$	30.9631	+	15.5503i	2.41781	+	1.21427i
$165$		0			0
$166$	−20.6490	−	27.7364i	−1.60267	−	2.15276i
$167$	−1.83892	−	6.14244i	−0.142300	−	0.475316i	0.856892	−	0.515496i	$-0.172392\pi$
$167$	−1.83892	−	6.14244i	−0.142300	−	0.475316i	−0.999192	+	0.0401796i	$0.987207\pi$
$168$		0			0
$169$	7.45599	+	17.2849i	0.573538	+	1.32961i
$170$	−1.66460	−	9.44043i	−0.127669	−	0.724048i
$171$		0			0
$172$	−5.44005	+	30.8521i	−0.414800	+	2.35245i
$173$	4.75678	−	1.12738i	0.361651	−	0.0857129i	−0.0457733	−	0.998952i	$-0.514575\pi$
$173$	4.75678	−	1.12738i	0.361651	−	0.0857129i	0.407424	+	0.913239i	$0.366427\pi$
$174$		0			0
$175$	−0.609425	−	0.400825i	−0.0460682	−	0.0302995i
$176$	1.07553	−	18.4662i	0.0810714	−	1.39194i
$177$		0			0
$178$	−7.55158	+	25.2240i	−0.566015	+	1.89062i
$179$	−0.481678	+	0.175316i	−0.0360023	+	0.0131038i	−0.359959	−	0.932968i	$-0.617209\pi$
$179$	−0.481678	+	0.175316i	−0.0360023	+	0.0131038i	0.323956	+	0.946072i	$0.394987\pi$
$180$		0			0
$181$	3.55046	+	1.29226i	0.263904	+	0.0960531i	0.470583	−	0.882356i	$-0.344044\pi$
$181$	3.55046	+	1.29226i	0.263904	+	0.0960531i	−0.206680	+	0.978409i	$0.566266\pi$
$182$	4.59514	−	6.17235i	0.340615	−	0.457525i
$183$		0			0
$184$	−2.11533	−	0.501342i	−0.155944	−	0.0369594i
$185$	−6.61981	+	15.3464i	−0.486698	+	1.12829i
$186$		0			0
$187$	−1.81850	+	1.19605i	−0.132982	+	0.0874636i
$188$	18.7448	+	32.4669i	1.36710	+	2.36789i
$189$		0			0
$190$	3.55455	−	6.15667i	0.257874	−	0.446652i
$191$	−1.31763	−	22.6229i	−0.0953406	−	1.63693i	−0.619274	−	0.785175i	$-0.712573\pi$
$191$	−1.31763	−	22.6229i	−0.0953406	−	1.63693i	0.523933	−	0.851759i	$-0.324464\pi$
$192$		0			0
$193$	5.68482	−	0.664460i	0.409202	−	0.0478289i	0.0909979	−	0.995851i	$-0.470994\pi$
$193$	5.68482	−	0.664460i	0.409202	−	0.0478289i	0.318204	+	0.948022i	$0.396920\pi$
$194$	6.59000	−	6.98499i	0.473134	−	0.501493i
$195$		0			0
$196$	34.3202	+	4.01146i	2.45144	+	0.286533i
$197$	1.85381	−	1.55553i	0.132078	−	0.110827i	−0.574356	−	0.818606i	$-0.694747\pi$
$197$	1.85381	−	1.55553i	0.132078	−	0.110827i	0.706434	+	0.707779i	$0.250303\pi$
$198$		0			0
$199$	−7.49610	−	6.28997i	−0.531384	−	0.445884i	0.337195	−	0.941435i	$-0.390522\pi$
$199$	−7.49610	−	6.28997i	−0.531384	−	0.445884i	−0.868579	+	0.495550i	$0.834966\pi$
$200$	−8.18011	−	8.67041i	−0.578421	−	0.613091i
$201$		0			0
$202$	−42.5223	+	21.3555i	−2.99186	+	1.50257i
$203$	−0.812045	+	0.407824i	−0.0569944	+	0.0286236i
$204$		0			0
$205$	−11.7567	−	12.4613i	−0.821122	−	0.870338i
$206$	8.82988	+	7.40915i	0.615207	+	0.516220i
$207$		0			0
$208$	52.0140	−	43.6449i	3.60652	−	3.02623i
$209$	−1.60325	−	0.187393i	−0.110899	−	0.0129623i
$210$		0			0
$211$	13.4585	−	14.2651i	0.926518	−	0.982052i	−0.0733655	−	0.997305i	$-0.523374\pi$
$211$	13.4585	−	14.2651i	0.926518	−	0.982052i	0.999884	+	0.0152532i	$0.00485543\pi$
$212$	−48.3247	+	5.64835i	−3.31895	+	0.387930i
$213$		0			0
$214$	−1.23856	−	21.2653i	−0.0846662	−	1.45366i
$215$	7.74505	−	13.4148i	0.528208	−	0.914884i
$216$		0			0
$217$	−1.31992	−	2.28617i	−0.0896020	−	0.155195i
$218$	0.474799	−	0.312280i	0.0321574	−	0.0211503i
$219$		0			0
$220$	−7.91298	+	18.3443i	−0.533493	+	1.23678i
$221$	−7.77427	−	1.84254i	−0.522954	−	0.123942i
$222$		0			0
$223$	1.56459	−	2.10161i	0.104773	−	0.140734i	−0.746644	−	0.665223i	$-0.768336\pi$
$223$	1.56459	−	2.10161i	0.104773	−	0.140734i	0.851417	+	0.524489i	$0.175744\pi$
$224$	−7.41017	−	2.69708i	−0.495113	−	0.180206i
$225$		0			0
$226$	13.9141	−	5.06433i	0.925555	−	0.336874i
$227$	0.354239	−	1.18324i	0.0235117	−	0.0785344i	−0.945429	−	0.325829i	$-0.894356\pi$
$227$	0.354239	−	1.18324i	0.0235117	−	0.0785344i	0.968940	+	0.247295i	$0.0795417\pi$
$228$		0			0
$229$	−0.284859	+	4.89085i	−0.0188240	+	0.323196i	0.975730	+	0.218976i	$0.0702717\pi$
$229$	−0.284859	+	4.89085i	−0.0188240	+	0.323196i	−0.994554	+	0.104220i	$0.966765\pi$
$230$	1.47237	+	0.968390i	0.0970849	+	0.0638538i
$231$		0			0
$232$	−14.4496	+	3.42462i	−0.948663	+	0.224837i
$233$	0.664049	−	3.76601i	0.0435033	−	0.246719i	−0.955299	−	0.295640i	$-0.904467\pi$
$233$	0.664049	−	3.76601i	0.0435033	−	0.246719i	0.998803	+	0.0489208i	$0.0155782\pi$
$234$		0			0
$235$	−3.21886	−	18.2551i	−0.209975	−	1.19083i
$236$	10.0631	+	23.3288i	0.655051	+	1.51858i
$237$		0			0
$238$	0.554063	+	1.85070i	0.0359146	+	0.119963i
$239$	5.40255	+	7.25689i	0.349462	+	0.469409i	0.941748	−	0.336319i	$-0.109182\pi$
$239$	5.40255	+	7.25689i	0.349462	+	0.469409i	−0.592286	+	0.805728i	$0.701774\pi$
$240$		0			0
$241$	−20.9343	−	10.5136i	−1.34849	−	0.677239i	−0.379701	−	0.925109i	$-0.623973\pi$
$241$	−20.9343	−	10.5136i	−1.34849	−	0.677239i	−0.968793	+	0.247870i	$0.920269\pi$
$242$	−23.0615			−1.48245
$243$		0			0
$244$	−66.1485			−4.23473
$245$	−15.2678	−	7.66779i	−0.975426	−	0.489877i
$246$		0			0
$247$	−3.53827	−	4.75273i	−0.225135	−	0.302409i
$248$	−12.3727	−	41.3276i	−0.785666	−	2.62431i
$249$		0			0
$250$	−9.57704	−	22.2021i	−0.605705	−	1.40418i
$251$	2.14133	+	12.1441i	0.135160	+	0.766530i	0.974748	+	0.223307i	$0.0716851\pi$
$251$	2.14133	+	12.1441i	0.135160	+	0.766530i	−0.839588	+	0.543223i	$0.817204\pi$
$252$		0			0
$253$	0.0694831	−	0.394058i	0.00436837	−	0.0247742i
$254$	−47.4320	+	11.2416i	−2.97615	+	0.705361i
$255$		0			0
$256$	−4.54335	−	2.98821i	−0.283959	−	0.186763i
$257$	1.71411	−	29.4301i	0.106923	−	1.83580i	−0.339066	−	0.940763i	$-0.610111\pi$
$257$	1.71411	−	29.4301i	0.106923	−	1.83580i	0.445989	−	0.895039i	$-0.352852\pi$
$258$		0			0
$259$	0.966010	−	3.22670i	0.0600249	−	0.200497i
$260$	−68.9122	+	25.0820i	−4.27376	+	1.55552i
$261$		0			0
$262$	20.1710	+	7.34166i	1.24617	+	0.453569i
$263$	12.2951	−	16.5151i	0.758145	−	1.01837i	−0.240713	−	0.970596i	$-0.577381\pi$
$263$	12.2951	−	16.5151i	0.758145	−	1.01837i	0.998858	−	0.0477695i	$-0.0152113\pi$
$264$		0			0
$265$	23.4083	+	5.54787i	1.43796	+	0.340803i
$266$	−0.567456	+	1.31551i	−0.0347930	+	0.0806592i
$267$		0			0
$268$	−27.4986	+	18.0861i	−1.67975	+	1.10479i
$269$	6.08593	+	10.5411i	0.371066	+	0.642705i	0.989730	−	0.142951i	$-0.0456591\pi$
$269$	6.08593	+	10.5411i	0.371066	+	0.642705i	−0.618664	+	0.785656i	$0.712326\pi$
$270$		0			0
$271$	−11.5577	+	20.0185i	−0.702078	+	1.21603i	0.265658	+	0.964067i	$0.414411\pi$
$271$	−11.5577	+	20.0185i	−0.702078	+	1.21603i	−0.967736	+	0.251967i	$0.918922\pi$
$272$	0.991159	+	17.0175i	0.0600978	+	1.03184i
$273$		0			0
$274$	22.6256	−	2.64455i	1.36686	−	0.159763i
$275$	1.50565	−	1.59589i	0.0907940	−	0.0962361i
$276$		0			0
$277$	−1.35949	−	0.158902i	−0.0816840	−	0.00954749i	0.0751527	−	0.997172i	$-0.476056\pi$
$277$	−1.35949	−	0.158902i	−0.0816840	−	0.00954749i	−0.156837	+	0.987625i	$0.550130\pi$
$278$	26.6878	−	22.3937i	1.60063	−	1.34308i
$279$		0			0
$280$	8.28520	+	6.95211i	0.495136	+	0.415468i
$281$	−12.2869	−	13.0233i	−0.732972	−	0.776905i	0.248475	−	0.968638i	$-0.420071\pi$
$281$	−12.2869	−	13.0233i	−0.732972	−	0.776905i	−0.981447	+	0.191733i	$0.938589\pi$
$282$		0			0
$283$	8.71883	−	4.37876i	0.518280	−	0.260290i	−0.170375	−	0.985379i	$-0.554498\pi$
$283$	8.71883	−	4.37876i	0.518280	−	0.260290i	0.688655	+	0.725089i	$0.258201\pi$
$284$	23.6618	−	11.8834i	1.40407	−	0.705150i
$285$		0			0
$286$	15.8838	+	16.8358i	0.939226	+	0.995521i
$287$	2.64482	+	2.21927i	0.156119	+	0.130999i
$288$		0			0
$289$	−11.4862	+	9.63807i	−0.675659	+	0.566945i
$290$	11.9566	+	1.39753i	0.702116	+	0.0820656i
$291$		0			0
$292$	20.9783	−	22.2357i	1.22766	−	1.30124i
$293$	3.05115	−	0.356629i	0.178250	−	0.0208345i	−0.0264995	−	0.999649i	$-0.508436\pi$
$293$	3.05115	−	0.356629i	0.178250	−	0.0208345i	0.204750	+	0.978814i	$0.434362\pi$
$294$		0			0
$295$	−0.730434	−	12.5411i	−0.0425275	−	0.730169i
$296$	27.5213	−	47.6684i	1.59965	−	2.77067i
$297$		0			0
$298$	−21.7779	−	37.7204i	−1.26156	−	2.18509i
$299$	1.22716	−	0.807118i	0.0709687	−	0.0466769i
$300$		0			0
$301$	−1.23644	+	2.86638i	−0.0712670	+	0.165216i
$302$	56.2583	+	13.3335i	3.23730	+	0.767255i
$303$		0			0
$304$	−7.54913	+	10.1402i	−0.432972	+	0.581582i
$305$	30.7346	+	11.1865i	1.75986	+	0.640536i
$306$		0			0
$307$	5.34825	−	1.94660i	0.305241	−	0.111099i	−0.184859	−	0.982765i	$-0.559183\pi$
$307$	5.34825	−	1.94660i	0.305241	−	0.111099i	0.490099	+	0.871667i	$0.336960\pi$
$308$	1.15472	−	3.85703i	0.0657962	−	0.219775i
$309$		0			0
$310$	−2.03340	+	34.9121i	−0.115489	+	1.98287i
$311$	−2.71659	−	1.78673i	−0.154044	−	0.101316i	0.470147	−	0.882588i	$-0.344201\pi$
$311$	−2.71659	−	1.78673i	−0.154044	−	0.101316i	−0.624191	+	0.781272i	$0.714571\pi$
$312$		0			0
$313$	−9.20441	+	2.18148i	−0.520264	+	0.123305i	−0.482354	−	0.875976i	$-0.660218\pi$
$313$	−9.20441	+	2.18148i	−0.520264	+	0.123305i	−0.0379098	+	0.999281i	$0.512070\pi$
$314$	−1.17011	+	6.63603i	−0.0660332	+	0.374493i
$315$		0			0
$316$	8.85219	+	50.2032i	0.497974	+	2.82415i
$317$	−8.12346	−	18.8323i	−0.456259	−	1.05773i	−0.978745	−	0.205080i	$-0.934255\pi$
$317$	−8.12346	−	18.8323i	−0.456259	−	1.05773i	0.522486	−	0.852648i	$-0.325005\pi$
$318$		0			0
$319$	−0.783920	−	2.61847i	−0.0438911	−	0.146606i
$320$	25.9384	+	34.8413i	1.45000	+	1.94769i
$321$		0			0
$322$	−0.317373	−	0.159391i	−0.0176865	−	0.00888249i
$323$	1.48754			0.0827687
$324$		0			0
$325$	8.05378			0.446744
$326$	17.4372	+	8.75731i	0.965760	+	0.485023i
$327$		0			0
$328$	33.6926	+	45.2570i	1.86036	+	2.49890i
$329$	1.07140	+	3.57872i	0.0590681	+	0.197301i
$330$		0			0
$331$	−2.73358	−	6.33714i	−0.150251	−	0.348321i	0.826423	−	0.563050i	$-0.190372\pi$
$331$	−2.73358	−	6.33714i	−0.150251	−	0.348321i	−0.976674	+	0.214730i	$0.931113\pi$
$332$	−11.5323	−	65.4027i	−0.632915	−	3.58944i
$333$		0			0
$334$	2.97247	−	16.8577i	0.162647	−	0.922415i
$335$	15.8353	−	3.75303i	0.865174	−	0.205050i
$336$		0			0
$337$	−22.6583	−	14.9026i	−1.23428	−	0.811796i	−0.246724	−	0.969086i	$-0.579354\pi$
$337$	−22.6583	−	14.9026i	−1.23428	−	0.811796i	−0.987553	+	0.157290i	$0.949724\pi$
$338$	−2.92215	+	50.1713i	−0.158944	+	2.72896i
$339$		0			0
$340$	5.28032	−	17.6375i	0.286366	−	0.956527i
$341$	7.46157	−	2.71579i	0.404067	−	0.147068i
$342$		0			0
$343$	6.59630	+	2.40086i	0.356166	+	0.129634i
$344$	−30.4636	+	40.9197i	−1.64249	+	2.20624i
$345$		0			0
$346$	12.6993	+	3.00980i	0.682720	+	0.161808i
$347$	−9.19427	+	21.3147i	−0.493574	+	1.14423i	0.471407	+	0.881916i	$0.343746\pi$
$347$	−9.19427	+	21.3147i	−0.493574	+	1.14423i	−0.964981	+	0.262318i	$0.915513\pi$
$348$		0			0
$349$	−2.56480	+	1.68689i	−0.137290	+	0.0902974i	−0.616296	−	0.787514i	$-0.711368\pi$
$349$	−2.56480	+	1.68689i	−0.137290	+	0.0902974i	0.479006	+	0.877812i	$0.340997\pi$
$350$	−0.973684	−	1.68647i	−0.0520456	−	0.0901456i
$351$		0			0
$352$	11.8598	−	20.5418i	0.632131	−	1.09488i
$353$	0.610598	+	10.4836i	0.0324988	+	0.557983i	0.974781	+	0.223164i	$0.0716384\pi$
$353$	0.610598	+	10.4836i	0.0324988	+	0.557983i	−0.942282	+	0.334820i	$0.891325\pi$
$354$		0			0
$355$	−13.0036	+	1.51990i	−0.690160	+	0.0806681i
$356$	−34.7030	+	36.7830i	−1.83925	+	1.94950i
$357$		0			0
$358$	−1.35923	−	0.158871i	−0.0718375	−	0.00839660i
$359$	−23.6540	+	19.8481i	−1.24841	+	1.04754i	−0.251594	+	0.967833i	$0.580955\pi$
$359$	−23.6540	+	19.8481i	−1.24841	+	1.04754i	−0.996818	+	0.0797090i	$0.974601\pi$
$360$		0			0
$361$	−13.7098	−	11.5039i	−0.721567	−	0.605466i
$362$	6.92220	+	7.33710i	0.363823	+	0.385630i
$363$		0			0
$364$	13.2070	−	6.63281i	0.692235	−	0.347654i
$365$	−13.5074	+	6.78369i	−0.707012	+	0.355075i
$366$		0			0
$367$	−10.4473	−	11.0735i	−0.545343	−	0.578030i	0.394819	−	0.918759i	$-0.370807\pi$
$367$	−10.4473	−	11.0735i	−0.545343	−	0.578030i	−0.940161	+	0.340730i	$0.889326\pi$
$368$	−2.40061	−	2.01435i	−0.125140	−	0.105005i
$369$		0			0
$370$	−34.1810	+	28.6813i	−1.77699	+	1.49107i
$371$	−4.81533	−	0.562831i	−0.249999	−	0.0292207i
$372$		0			0
$373$	0.640492	−	0.678882i	0.0331634	−	0.0351512i	−0.710580	−	0.703617i	$-0.751567\pi$
$373$	0.640492	−	0.678882i	0.0331634	−	0.0351512i	0.743743	+	0.668466i	$0.233049\pi$
$374$	−5.77158	+	0.674601i	−0.298442	+	0.0348828i
$375$		0			0
$376$	3.54960	+	60.9444i	0.183057	+	3.14297i
$377$	5.01662	−	8.68904i	0.258369	−	0.447508i
$378$		0			0
$379$	19.2328	+	33.3122i	0.987924	+	1.71113i	0.628143	+	0.778098i	$0.283815\pi$
$379$	19.2328	+	33.3122i	0.987924	+	1.71113i	0.359781	+	0.933037i	$0.382851\pi$
$380$	11.4075	−	7.50284i	0.585193	−	0.384888i
$381$		0			0
$382$	23.9626	−	55.5516i	1.22603	−	2.84226i
$383$	−14.3550	−	3.40219i	−0.733505	−	0.173844i	−0.153145	−	0.988204i	$-0.548940\pi$
$383$	−14.3550	−	3.40219i	−0.733505	−	0.173844i	−0.580360	+	0.814360i	$0.697088\pi$
$384$		0			0
$385$	−1.18879	+	1.59682i	−0.0605861	+	0.0813813i
$386$	14.3588	+	5.22616i	0.730841	+	0.266005i
$387$		0			0
$388$	17.3313	−	6.30806i	0.879862	−	0.320243i
$389$	−4.90111	+	16.3708i	−0.248496	+	0.830035i	0.739178	+	0.673510i	$0.235214\pi$
$389$	−4.90111	+	16.3708i	−0.248496	+	0.830035i	−0.987674	+	0.156525i	$0.949971\pi$
$390$		0			0
$391$	−0.0214407	+	0.368123i	−0.00108430	+	0.0186168i
$392$	47.0105	+	30.9193i	2.37439	+	1.56166i
$393$		0			0
$394$	6.28653	−	1.48994i	0.316711	−	0.0750619i
$395$	4.37696	−	24.8230i	0.220229	−	1.24898i
$396$		0			0
$397$	−4.37414	−	24.8070i	−0.219532	−	1.24503i	−0.872867	−	0.487958i	$-0.837742\pi$
$397$	−4.37414	−	24.8070i	−0.219532	−	1.24503i	0.653335	−	0.757069i	$-0.273369\pi$
$398$	−10.3474	−	23.9880i	−0.518669	−	1.20241i
$399$		0			0
$400$	−4.92821	−	16.4614i	−0.246410	−	0.823068i
$401$	12.3196	+	16.5481i	0.615212	+	0.826373i	0.995122	−	0.0986500i	$-0.0314524\pi$
$401$	12.3196	+	16.5481i	0.615212	+	0.826373i	−0.379910	+	0.925023i	$0.624045\pi$
$402$		0			0
$403$	26.0469	+	13.0813i	1.29749	+	0.651624i
$404$	−91.3890			−4.54677
$405$		0			0
$406$	−2.42599			−0.120400
$407$	9.05364	+	4.54691i	0.448772	+	0.225382i
$408$		0			0
$409$	21.0083	+	28.2191i	1.03879	+	1.39534i	0.915195	+	0.403012i	$0.132037\pi$
$409$	21.0083	+	28.2191i	1.03879	+	1.39534i	0.123600	+	0.992332i	$0.460556\pi$
$410$	−13.1178	−	43.8164i	−0.647840	−	2.16394i
$411$		0			0
$412$	8.76839	+	20.3274i	0.431987	+	1.00146i
$413$	0.439618	+	2.49319i	0.0216322	+	0.122682i
$414$		0			0
$415$	−5.70212	+	32.3383i	−0.279906	+	1.58743i
$416$	84.7217	−	20.0794i	4.15383	−	0.984475i
$417$		0			0
$418$	−3.60045	−	2.36805i	−0.176104	−	0.115825i
$419$	−1.57605	+	27.0598i	−0.0769953	+	1.32196i	0.709651	+	0.704554i	$0.248853\pi$
$419$	−1.57605	+	27.0598i	−0.0769953	+	1.32196i	−0.786646	+	0.617404i	$0.788184\pi$
$420$		0			0
$421$	8.72981	−	29.1596i	0.425465	−	1.42115i	−0.429783	−	0.902932i	$-0.641410\pi$
$421$	8.72981	−	29.1596i	0.425465	−	1.42115i	0.855248	−	0.518219i	$-0.173405\pi$
$422$	49.2008	−	17.9076i	2.39506	−	0.871729i
$423$		0			0
$424$	−74.4492	−	27.0973i	−3.61557	−	1.31596i
$425$	−1.20741	+	1.62183i	−0.0585680	+	0.0786705i
$426$		0			0
$427$	−6.41372	−	1.52008i	−0.310381	−	0.0735618i
$428$	16.2041	−	37.5653i	0.783254	−	1.81579i
$429$		0			0
$430$	34.5512	−	22.7247i	1.66620	−	1.09588i
$431$	4.50933	+	7.81039i	0.217207	+	0.376213i	0.953953	−	0.299956i	$-0.0969720\pi$
$431$	4.50933	+	7.81039i	0.217207	+	0.376213i	−0.736746	+	0.676170i	$0.763639\pi$
$432$		0			0
$433$	−11.8523	+	20.5287i	−0.569584	+	0.986548i	0.427023	+	0.904241i	$0.359562\pi$
$433$	−11.8523	+	20.5287i	−0.569584	+	0.986548i	−0.996607	+	0.0823075i	$0.973771\pi$
$434$	−0.409786	−	7.03575i	−0.0196703	−	0.337727i
$435$		0			0
$436$	1.08407	−	0.126710i	0.0519178	−	0.00606832i
$437$	−0.187664	+	0.198912i	−0.00897717	+	0.00951524i
$438$		0			0
$439$	−3.99751	−	0.467242i	−0.190791	−	0.0223002i	0.0201608	−	0.999797i	$-0.493582\pi$
$439$	−3.99751	−	0.467242i	−0.190791	−	0.0223002i	−0.210952	+	0.977497i	$0.567656\pi$
$440$	−24.9213	+	20.9114i	−1.18807	+	0.996913i
$441$		0			0
$442$	−16.3399	−	13.7108i	−0.777209	−	0.652156i
$443$	5.46086	+	5.78817i	0.259453	+	0.275004i	0.843985	−	0.536366i	$-0.180203\pi$
$443$	5.46086	+	5.78817i	0.259453	+	0.275004i	−0.584532	+	0.811371i	$0.698722\pi$
$444$		0			0
$445$	22.3445	−	11.2218i	1.05923	−	0.531966i
$446$	6.25083	−	3.13929i	0.295986	−	0.148650i
$447$		0			0
$448$	−6.00710	−	6.36715i	−0.283809	−	0.300820i
$449$	11.2889	+	9.47253i	0.532757	+	0.447037i	0.869052	−	0.494720i	$-0.164729\pi$
$449$	11.2889	+	9.47253i	0.532757	+	0.447037i	−0.336295	+	0.941757i	$0.609174\pi$
$450$		0			0
$451$	−7.95542	+	6.67539i	−0.374606	+	0.314332i
$452$	28.2462	+	3.30151i	1.32859	+	0.155290i
$453$		0			0
$454$	2.26286	−	2.39849i	0.106201	−	0.112567i
$455$	−7.25806	+	0.848346i	−0.340263	+	0.0397711i
$456$		0			0
$457$	0.457057	+	7.84736i	0.0213802	+	0.367084i	0.991981	+	0.126388i	$0.0403385\pi$
$457$	0.457057	+	7.84736i	0.0213802	+	0.367084i	−0.970601	+	0.240696i	$0.922624\pi$
$458$	−6.53970	+	11.3271i	−0.305580	+	0.529280i
$459$		0			0
$460$	1.69232	+	2.93118i	0.0789047	+	0.136667i
$461$	2.76030	−	1.81548i	0.128560	−	0.0845552i	−0.483600	−	0.875289i	$-0.660671\pi$
$461$	2.76030	−	1.81548i	0.128560	−	0.0845552i	0.612160	+	0.790734i	$0.290301\pi$
$462$		0			0
$463$	−7.01120	+	16.2538i	−0.325838	+	0.755377i	0.674023	+	0.738710i	$0.264565\pi$
$463$	−7.01120	+	16.2538i	−0.325838	+	0.755377i	−0.999861	+	0.0166670i	$0.994694\pi$
$464$	−20.8295	−	4.93668i	−0.966986	−	0.229180i
$465$		0			0
$466$	6.09660	−	8.18915i	0.282419	−	0.379355i
$467$	−37.4545	−	13.6323i	−1.73319	−	0.630829i	−0.734338	−	0.678784i	$-0.762507\pi$
$467$	−37.4545	−	13.6323i	−1.73319	−	0.630829i	−0.998849	+	0.0479555i	$0.984729\pi$
$468$		0			0
$469$	−3.08187	+	1.12171i	−0.142307	+	0.0517956i
$470$	14.1933	−	47.4090i	0.654689	−	2.18681i
$471$		0			0
$472$	−2.40557	+	41.3020i	−0.110725	+	1.90108i
$473$	−7.84506	−	5.15978i	−0.360716	−	0.237247i
$474$		0			0
$475$	−1.45906	+	0.345804i	−0.0669463	+	0.0158666i
$476$	−0.644290	+	3.65395i	−0.0295310	+	0.167478i
$477$		0			0
$478$	4.19419	+	23.7864i	0.191838	+	1.08797i
$479$	15.5227	+	35.9856i	0.709250	+	1.64423i	0.763588	+	0.645704i	$0.223436\pi$
$479$	15.5227	+	35.9856i	0.709250	+	1.64423i	−0.0543383	+	0.998523i	$0.517305\pi$
$480$		0			0
$481$	10.6660	+	35.6269i	0.486328	+	1.62445i
$482$	−37.3470	−	50.1658i	−1.70111	−	2.28499i
$483$		0			0
$484$	−39.5807	−	19.8782i	−1.79912	−	0.903553i
$485$	−9.11940			−0.414091
$486$		0			0
$487$	35.0579			1.58863			0.794313	−	0.607509i	$-0.207831\pi$
$487$	35.0579			1.58863			0.794313	+	0.607509i	$0.207831\pi$
$488$	−96.2582	−	48.3427i	−4.35741	−	2.18837i
$489$		0			0
$490$	−27.2380	−	36.5870i	−1.23049	−	1.65283i
$491$	5.90302	+	19.7175i	0.266400	+	0.889836i	0.981605	+	0.190922i	$0.0611479\pi$
$491$	5.90302	+	19.7175i	0.266400	+	0.889836i	−0.715206	+	0.698914i	$0.753667\pi$
$492$		0			0
$493$	0.997675	+	2.31287i	0.0449330	+	0.104166i
$494$	−2.74688	−	15.5783i	−0.123588	−	0.700903i
$495$		0			0
$496$	10.7987	−	61.2427i	0.484878	−	2.74988i
$497$	2.56731	−	0.608464i	0.115160	−	0.0272933i
$498$		0			0
$499$	−6.88882	−	4.53085i	−0.308386	−	0.202829i	0.385877	−	0.922550i	$-0.373899\pi$
$499$	−6.88882	−	4.53085i	−0.308386	−	0.202829i	−0.694263	+	0.719722i	$0.744269\pi$
$500$	2.70020	−	46.3606i	0.120757	−	2.07331i
$501$		0			0
$502$	−9.44205	+	31.5387i	−0.421419	+	1.40764i
$503$	−15.9904	+	5.82003i	−0.712977	+	0.259503i	−0.672941	−	0.739696i	$-0.734969\pi$
$503$	−15.9904	+	5.82003i	−0.712977	+	0.259503i	−0.0400358	+	0.999198i	$0.512747\pi$
$504$		0			0
$505$	42.4621	+	15.4549i	1.88954	+	0.687736i
$506$	0.637921	−	0.856876i	0.0283590	−	0.0380928i
$507$		0			0
$508$	−91.0978	−	21.5906i	−4.04181	−	0.957927i
$509$	6.49778	−	15.0635i	0.288009	−	0.667680i	−0.711374	−	0.702814i	$-0.751927\pi$
$509$	6.49778	−	15.0635i	0.288009	−	0.667680i	0.999383	+	0.0351342i	$0.0111859\pi$
$510$		0			0
$511$	2.54501	−	1.67388i	0.112585	−	0.0740480i
$512$	7.61274	+	13.1856i	0.336439	+	0.582729i
$513$		0			0
$514$	39.3519	−	68.1595i	1.73574	−	3.00639i
$515$	−0.636458	−	10.9276i	−0.0280457	−	0.481526i
$516$		0			0
$517$	−11.1606	+	1.30449i	−0.490842	+	0.0573712i
$518$	6.17082	−	6.54068i	0.271130	−	0.287381i
$519$		0			0
$520$	−118.610	−	13.8636i	−5.20141	−	0.607958i
$521$	9.25237	−	7.76366i	0.405354	−	0.340132i	−0.417205	−	0.908812i	$-0.636990\pi$
$521$	9.25237	−	7.76366i	0.405354	−	0.340132i	0.822559	+	0.568680i	$0.192546\pi$
$522$		0			0
$523$	−5.53110	−	4.64114i	−0.241858	−	0.202943i	0.513799	−	0.857911i	$-0.328238\pi$
$523$	−5.53110	−	4.64114i	−0.241858	−	0.202943i	−0.755657	+	0.654968i	$0.772682\pi$
$524$	28.2915	+	29.9872i	1.23592	+	1.31000i
$525$		0			0
$526$	49.1211	−	24.6695i	2.14178	−	1.07564i
$527$	−6.53916	+	3.28409i	−0.284850	+	0.143057i
$528$		0			0
$529$	15.7370	+	16.6803i	0.684219	+	0.725230i
$530$	49.1993	+	41.2832i	2.13708	+	1.79323i
$531$		0			0
$532$	−2.10785	+	1.76870i	−0.0913869	+	0.0766827i
$533$	−37.8631	−	4.42556i	−1.64003	−	0.191692i
$534$		0			0
$535$	−13.8816	+	14.7137i	−0.600156	+	0.636128i
$536$	−53.2333	+	6.22208i	−2.29933	+	0.268753i
$537$		0			0
$538$	1.88945	+	32.4407i	0.0814601	+	1.39862i
$539$	−5.17833	+	8.96913i	−0.223046	+	0.386328i
$540$		0			0
$541$	−19.0806	−	33.0486i	−0.820339	−	1.42087i	−0.905430	−	0.424496i	$-0.860451\pi$
$541$	−19.0806	−	33.0486i	−0.820339	−	1.42087i	0.0850910	−	0.996373i	$-0.472882\pi$
$542$	−51.5594	+	33.9112i	−2.21467	+	1.45661i
$543$		0			0
$544$	−8.65785	+	20.0712i	−0.371202	+	0.860544i
$545$	−0.525122	−	0.124456i	−0.0224938	−	0.00533112i
$546$		0			0
$547$	−22.2042	+	29.8254i	−0.949384	+	1.27524i	0.0119703	+	0.999928i	$0.496190\pi$
$547$	−22.2042	+	29.8254i	−0.949384	+	1.27524i	−0.961354	+	0.275315i	$0.911218\pi$
$548$	41.1120	+	14.9635i	1.75622	+	0.639211i
$549$		0			0
$550$	5.50428	−	2.00339i	0.234703	−	0.0854250i
$551$	−0.535754	+	1.78954i	−0.0228239	+	0.0762371i
$552$		0			0
$553$	−0.295358	+	5.07109i	−0.0125599	+	0.215645i
$554$	−3.05303	−	2.00801i	−0.129711	−	0.0853122i
$555$		0			0
$556$	65.1069	−	15.4306i	2.76115	−	0.654404i
$557$	−4.26215	+	24.1719i	−0.180593	+	1.02420i	0.750894	+	0.660422i	$0.229623\pi$
$557$	−4.26215	+	24.1719i	−0.180593	+	1.02420i	−0.931488	+	0.363773i	$0.881488\pi$
$558$		0			0
$559$	−5.98521	−	33.9438i	−0.253147	−	1.43567i
$560$	6.17526	+	14.3159i	0.260952	+	0.604955i
$561$		0			0
$562$	−13.7093	−	45.7923i	−0.578293	−	1.93163i
$563$	−4.21597	−	5.66303i	−0.177682	−	0.238668i	0.704356	−	0.709847i	$-0.251236\pi$
$563$	−4.21597	−	5.66303i	−0.177682	−	0.238668i	−0.882038	+	0.471179i	$0.843829\pi$
$564$		0			0
$565$	−12.5657	−	6.31074i	−0.528644	−	0.265495i
$566$	26.0476			1.09486
$567$		0			0
$568$	43.1169			1.80914
$569$	7.56120	+	3.79738i	0.316982	+	0.159194i	0.600175	−	0.799868i	$-0.295097\pi$
$569$	7.56120	+	3.79738i	0.316982	+	0.159194i	−0.283193	+	0.959063i	$0.591394\pi$
$570$		0			0
$571$	−0.263870	−	0.354439i	−0.0110426	−	0.0148328i	0.796568	−	0.604549i	$-0.206647\pi$
$571$	−0.263870	−	0.354439i	−0.0110426	−	0.0148328i	−0.807610	+	0.589717i	$0.799239\pi$
$572$	12.7496	+	42.5866i	0.533087	+	1.78063i
$573$		0			0
$574$	3.65084	+	8.46360i	0.152383	+	0.353264i
$575$	−0.0645463	−	0.366060i	−0.00269177	−	0.0152658i
$576$		0			0
$577$	1.80812	−	10.2544i	0.0752730	−	0.426894i	−0.923762	−	0.382968i	$-0.874902\pi$
$577$	1.80812	−	10.2544i	0.0752730	−	0.426894i	0.999035	−	0.0439266i	$-0.0139868\pi$
$578$	−38.9514	+	9.23166i	−1.62017	+	0.383987i
$579$		0			0
$580$	19.3166	+	12.7047i	0.802077	+	0.527535i
$581$	0.384780	−	6.60641i	0.0159633	−	0.274080i
$582$		0			0
$583$	4.18237	−	13.9701i	0.173216	−	0.578582i
$584$	46.7775	−	17.0256i	1.93567	−	0.704525i
$585$		0			0
$586$	7.70663	+	2.80498i	0.318358	+	0.115873i
$587$	22.0521	−	29.6212i	0.910189	−	1.22260i	−0.0642474	−	0.997934i	$-0.520465\pi$
$587$	22.0521	−	29.6212i	0.910189	−	1.22260i	0.974437	−	0.224662i	$-0.0721279\pi$
$588$		0			0
$589$	−5.28045	−	1.25149i	−0.217577	−	0.0515667i
$590$	13.2837	−	30.7952i	0.546883	−	1.26782i
$591$		0			0
$592$	66.2922	−	43.6011i	2.72459	−	1.79199i
$593$	−1.15692	−	2.00385i	−0.0475091	−	0.0822881i	0.841293	−	0.540579i	$-0.181795\pi$
$593$	−1.15692	−	2.00385i	−0.0475091	−	0.0822881i	−0.888802	+	0.458291i	$0.848462\pi$
$594$		0			0
$595$	0.917282	−	1.58878i	0.0376049	−	0.0651336i
$596$	−4.86400	−	83.5116i	−0.199237	−	3.42077i
$597$		0			0
$598$	3.89479	−	0.455236i	0.159270	−	0.0186160i
$599$	5.53806	−	5.87000i	0.226279	−	0.239842i	−0.604280	−	0.796772i	$-0.706539\pi$
$599$	5.53806	−	5.87000i	0.226279	−	0.239842i	0.830559	+	0.556930i	$0.188021\pi$
$600$		0			0
$601$	−15.1344	−	1.76896i	−0.617347	−	0.0721575i	−0.198329	−	0.980136i	$-0.563551\pi$
$601$	−15.1344	−	1.76896i	−0.617347	−	0.0721575i	−0.419018	+	0.907978i	$0.637625\pi$
$602$	−6.38427	+	5.35704i	−0.260203	+	0.218337i
$603$		0			0
$604$	85.0636	+	71.3769i	3.46119	+	2.90428i
$605$	15.0288	+	15.9295i	0.611006	+	0.647628i
$606$		0			0
$607$	−26.1727	+	13.1444i	−1.06232	+	0.533516i	−0.892076	−	0.451886i	$-0.850751\pi$
$607$	−26.1727	+	13.1444i	−1.06232	+	0.533516i	−0.170243	+	0.985402i	$0.554455\pi$
$608$	−14.4864	+	7.27536i	−0.587503	+	0.295055i
$609$		0			0
$610$	59.9221	+	63.5137i	2.42618	+	2.57160i
$611$	−31.5966	−	26.5127i	−1.27826	−	1.07259i
$612$		0			0
$613$	5.16392	−	4.33305i	0.208569	−	0.175010i	−0.532519	−	0.846418i	$-0.678755\pi$
$613$	5.16392	−	4.33305i	0.208569	−	0.175010i	0.741088	+	0.671408i	$0.234310\pi$
$614$	15.0920	+	1.76400i	0.609064	+	0.0711894i
$615$		0			0
$616$	4.49912	−	4.76879i	0.181275	−	0.192140i
$617$	11.9625	−	1.39821i	0.481591	−	0.0562899i	0.128166	−	0.991753i	$-0.459091\pi$
$617$	11.9625	−	1.39821i	0.481591	−	0.0562899i	0.353425	+	0.935463i	$0.385017\pi$
$618$		0			0
$619$	0.781192	+	13.4126i	0.0313988	+	0.539096i	0.976929	+	0.213563i	$0.0685068\pi$
$619$	0.781192	+	13.4126i	0.0313988	+	0.539096i	−0.945531	+	0.325533i	$0.894456\pi$
$620$	−33.5828	+	58.1671i	−1.34872	+	2.33605i
$621$		0			0
$622$	−4.34032	−	7.51765i	−0.174031	−	0.301430i
$623$	−4.21004	+	2.76899i	−0.168672	+	0.110937i
$624$		0			0
$625$	−11.9220	+	27.6383i	−0.476881	+	1.10553i
$626$	−24.5733	−	5.82398i	−0.982147	−	0.232773i
$627$		0			0
$628$	−7.72828	+	10.3809i	−0.308392	+	0.414242i
$629$	−8.77342	−	3.19326i	−0.349819	−	0.127324i
$630$		0			0
$631$	−0.571023	+	0.207835i	−0.0227321	+	0.00827379i	−0.353361	−	0.935487i	$-0.614961\pi$
$631$	−0.571023	+	0.207835i	−0.0227321	+	0.00827379i	0.330629	+	0.943761i	$0.392739\pi$
$632$	−23.8080	+	79.5243i	−0.947032	+	3.16331i
$633$		0			0
$634$	3.18374	−	54.6627i	0.126443	−	2.17093i
$635$	38.6756	+	25.4373i	1.53479	+	1.00945i
$636$		0			0
$637$	−36.9918	+	8.76722i	−1.46567	+	0.347370i
$638$	1.26714	−	7.18633i	0.0501667	−	0.284510i
$639$		0			0
$640$	6.54721	+	37.1311i	0.258801	+	1.46774i
$641$	8.97249	+	20.8006i	0.354392	+	0.821574i	0.998400	+	0.0565542i	$0.0180114\pi$
$641$	8.97249	+	20.8006i	0.354392	+	0.821574i	−0.644007	+	0.765019i	$0.722729\pi$
$642$		0			0
$643$	−13.9782	−	46.6903i	−0.551245	−	1.84129i	−0.540501	−	0.841343i	$-0.681765\pi$
$643$	−13.9782	−	46.6903i	−0.551245	−	1.84129i	−0.0107436	−	0.999942i	$-0.503420\pi$
$644$	−0.407320	−	0.547126i	−0.0160507	−	0.0215598i
$645$		0			0
$646$	3.54891	+	1.78233i	0.139630	+	0.0701247i
$647$	20.1953			0.793960			0.396980	−	0.917827i	$-0.370058\pi$
$647$	20.1953			0.793960			0.396980	+	0.917827i	$0.370058\pi$
$648$		0			0
$649$	−7.61503			−0.298916
$650$	19.2144	+	9.64984i	0.753651	+	0.378498i
$651$		0			0
$652$	22.3792	+	30.0605i	0.876437	+	1.17726i
$653$	5.49056	+	18.3397i	0.214862	+	0.717690i	0.995673	+	0.0929227i	$0.0296209\pi$
$653$	5.49056	+	18.3397i	0.214862	+	0.717690i	−0.780811	+	0.624767i	$0.785194\pi$
$654$		0			0
$655$	−8.07389	−	18.7174i	−0.315473	−	0.731349i
$656$	14.1233	+	80.0975i	0.551424	+	3.12728i
$657$		0			0
$658$	−1.73183	+	9.82169i	−0.0675137	+	0.382889i
$659$	40.0459	−	9.49106i	1.55997	−	0.369719i	0.642105	−	0.766617i	$-0.278061\pi$
$659$	40.0459	−	9.49106i	1.55997	−	0.369719i	0.917863	+	0.396897i	$0.129913\pi$
$660$		0			0
$661$	23.7935	+	15.6493i	0.925462	+	0.608686i	0.920263	−	0.391301i	$-0.127975\pi$
$661$	23.7935	+	15.6493i	0.925462	+	0.608686i	0.00519884	+	0.999986i	$0.498345\pi$
$662$	1.07134	−	18.3942i	0.0416388	−	0.714911i
$663$		0			0
$664$	31.0161	−	103.601i	1.20366	−	4.02050i
$665$	1.27848	−	0.465328i	0.0495773	−	0.0180447i
$666$		0			0
$667$	−0.435139	−	0.158378i	−0.0168486	−	0.00613241i
$668$	19.6324	−	26.3709i	0.759601	−	1.02032i
$669$		0			0
$670$	42.2760	+	10.0196i	1.63326	+	0.387091i
$671$	7.85283	−	18.2049i	0.303155	−	0.702792i
$672$		0			0
$673$	30.5056	−	20.0639i	1.17591	−	0.773406i	0.197542	−	0.980294i	$-0.436704\pi$
$673$	30.5056	−	20.0639i	1.17591	−	0.773406i	0.978364	+	0.206889i	$0.0663338\pi$
$674$	−36.2014	−	62.7027i	−1.39443	−	2.41522i
$675$		0			0
$676$	−48.2611	+	83.5906i	−1.85620	+	3.21502i
$677$	0.102919	+	1.76706i	0.00395551	+	0.0679136i	0.999708	−	0.0241544i	$-0.00768933\pi$
$677$	0.102919	+	1.76706i	0.00395551	+	0.0679136i	−0.995753	+	0.0920680i	$0.970652\pi$
$678$		0			0
$679$	1.82539	−	0.213357i	0.0700519	−	0.00818789i
$680$	20.5737	−	21.8068i	0.788964	−	0.836253i
$681$		0			0
$682$	21.0555	+	2.46104i	0.806257	+	0.0942380i
$683$	−17.5030	+	14.6868i	−0.669734	+	0.561973i	−0.912987	−	0.407989i	$-0.866230\pi$
$683$	−17.5030	+	14.6868i	−0.669734	+	0.561973i	0.243253	+	0.969963i	$0.421786\pi$
$684$		0			0
$685$	−16.5714	−	13.9050i	−0.633159	−	0.531284i
$686$	12.8605	+	13.6314i	0.491018	+	0.520449i
$687$		0			0
$688$	−65.7164	+	33.0040i	−2.50541	+	1.25827i
$689$	47.8356	−	24.0239i	1.82239	−	0.915239i
$690$		0			0
$691$	−3.88197	−	4.11465i	−0.147677	−	0.156529i	0.649312	−	0.760522i	$-0.275057\pi$
$691$	−3.88197	−	4.11465i	−0.147677	−	0.156529i	−0.796989	+	0.603993i	$0.793575\pi$
$692$	19.2016	+	16.1121i	0.729936	+	0.612489i
$693$		0			0
$694$	−47.4741	+	39.8355i	−1.80209	+	1.51213i
$695$	−32.8601	−	3.84080i	−1.24646	−	0.145690i
$696$		0			0
$697$	6.56757	−	6.96122i	0.248765	−	0.263675i
$698$	−8.14019	+	0.951452i	−0.308111	+	0.0360130i
$699$		0			0
$700$	−0.217468	−	3.73378i	−0.00821951	−	0.141124i
$701$	12.8656	−	22.2838i	0.485926	−	0.841648i	−0.513944	−	0.857824i	$-0.671816\pi$
$701$	12.8656	−	22.2838i	0.485926	−	0.841648i	0.999869	+	0.0161763i	$0.00514928\pi$
$702$		0			0
$703$	−3.46201	−	5.99637i	−0.130572	−	0.226157i
$704$	21.9986	−	14.4687i	0.829103	−	0.545309i
$705$		0			0
$706$	−11.1044	+	25.7429i	−0.417919	+	0.968846i
$707$	−8.86102	−	2.10010i	−0.333253	−	0.0789824i
$708$		0			0
$709$	20.0095	−	26.8775i	0.751473	−	1.00940i	−0.247703	−	0.968836i	$-0.579676\pi$
$709$	20.0095	−	26.8775i	0.751473	−	1.00940i	0.999177	−	0.0405681i	$-0.0129168\pi$
$710$	−32.8446	−	11.9545i	−1.23264	−	0.448643i
$711$		0			0
$712$	−77.3810	+	28.1644i	−2.89997	+	1.05550i
$713$	0.385818	−	1.28872i	0.0144490	−	0.0482630i
$714$		0			0
$715$	1.27804	−	21.9431i	0.0477960	−	0.820626i
$716$	−2.19591	−	1.44427i	−0.0820651	−	0.0539751i
$717$		0			0
$718$	−80.2144	+	19.0112i	−2.99357	+	0.709490i
$719$	0.373099	−	2.11595i	0.0139143	−	0.0789116i	−0.977060	−	0.212965i	$-0.931688\pi$
$719$	0.373099	−	2.11595i	0.0139143	−	0.0789116i	0.990974	+	0.134053i	$0.0427992\pi$
$720$		0			0
$721$	0.383057	+	2.17243i	0.0142658	+	0.0809054i
$722$	−18.9246	−	43.8722i	−0.704301	−	1.63275i
$723$		0			0
$724$	5.55632	+	18.5594i	0.206499	+	0.689755i
$725$	−1.51624	−	2.03667i	−0.0563119	−	0.0756400i
$726$		0			0
$727$	9.88649	+	4.96518i	0.366669	+	0.184148i	0.622588	−	0.782550i	$-0.286081\pi$
$727$	9.88649	+	4.96518i	0.366669	+	0.184148i	−0.255918	+	0.966698i	$0.582378\pi$
$728$	24.0660			0.891946
$729$		0			0
$730$	−40.3536			−1.49355
$731$	7.73275	+	3.88353i	0.286006	+	0.143638i
$732$		0			0
$733$	−10.1536	−	13.6386i	−0.375030	−	0.503753i	0.574036	−	0.818830i	$-0.305377\pi$
$733$	−10.1536	−	13.6386i	−0.375030	−	0.503753i	−0.949066	+	0.315077i	$0.897970\pi$
$734$	−11.6568	−	38.9363i	−0.430259	−	1.43716i
$735$		0			0
$736$	−1.59164	−	3.68984i	−0.0586688	−	0.136009i
$737$	−1.71303	−	9.71507i	−0.0631002	−	0.357859i
$738$		0			0
$739$	−4.23694	+	24.0289i	−0.155858	+	0.883917i	0.802138	+	0.597138i	$0.203696\pi$
$739$	−4.23694	+	24.0289i	−0.155858	+	0.883917i	−0.957997	+	0.286779i	$0.907416\pi$
$740$	−83.3872	+	19.7631i	−3.06538	+	0.726507i
$741$		0			0
$742$	−10.8138	−	7.11238i	−0.396989	−	0.261104i
$743$	−0.343262	+	5.89357i	−0.0125930	+	0.216214i	0.986141	+	0.165910i	$0.0530561\pi$
$743$	−0.343262	+	5.89357i	−0.0125930	+	0.216214i	−0.998734	+	0.0503042i	$0.983981\pi$
$744$		0			0
$745$	−11.8628	+	39.6246i	−0.434620	+	1.45173i
$746$	2.34148	−	0.852230i	0.0857277	−	0.0312023i
$747$		0			0
$748$	−10.4873	−	3.81706i	−0.383453	−	0.139566i
$749$	2.43438	−	3.26994i	0.0889503	−	0.119481i
$750$		0			0
$751$	−33.6209	−	7.96830i	−1.22684	−	0.290767i	−0.434405	−	0.900718i	$-0.643041\pi$
$751$	−33.6209	−	7.96830i	−1.22684	−	0.290767i	−0.792440	+	0.609950i	$0.791189\pi$
$752$	−34.8558	+	80.8047i	−1.27106	+	2.94665i
$753$		0			0
$754$	22.3794	−	14.7192i	0.815011	−	0.536041i
$755$	−27.4525	−	47.5491i	−0.999099	−	1.73049i
$756$		0			0
$757$	19.4091	−	33.6176i	0.705437	−	1.22185i	−0.261097	−	0.965313i	$-0.584084\pi$
$757$	19.4091	−	33.6176i	0.705437	−	1.22185i	0.966534	−	0.256540i	$-0.0825824\pi$
$758$	5.97107	+	102.519i	0.216879	+	3.72367i
$759$		0			0
$760$	22.0833	−	2.58116i	0.801044	−	0.0936286i
$761$	−28.0481	+	29.7293i	−1.01674	+	1.07769i	−0.0197809	+	0.999804i	$0.506297\pi$
$761$	−28.0481	+	29.7293i	−1.01674	+	1.07769i	−0.996963	+	0.0778808i	$0.975185\pi$
$762$		0			0
$763$	0.108023	+	0.0126261i	0.00391069	+	0.000457094i
$764$	89.0105	−	74.6887i	3.22029	−	2.70214i
$765$		0			0
$766$	−30.1711	−	25.3166i	−1.09013	−	0.914725i
$767$	−19.1823	−	20.3321i	−0.692634	−	0.734150i
$768$		0			0
$769$	−27.6178	+	13.8702i	−0.995922	+	0.500171i	−0.870624	−	0.491948i	$-0.836285\pi$
$769$	−27.6178	+	13.8702i	−0.995922	+	0.500171i	−0.125298	+	0.992119i	$0.539989\pi$
$770$	−4.74942	+	2.38525i	−0.171157	+	0.0859584i
$771$		0			0
$772$	20.1393	+	21.3464i	0.724829	+	0.768274i
$773$	−22.5762	−	18.9437i	−0.812009	−	0.681356i	0.139077	−	0.990282i	$-0.455586\pi$
$773$	−22.5762	−	18.9437i	−0.812009	−	0.681356i	−0.951086	+	0.308925i	$0.900031\pi$
$774$		0			0
$775$	5.65054	−	4.74137i	0.202974	−	0.170315i
$776$	29.8302	+	3.48665i	1.07084	+	0.125164i
$777$		0			0
$778$	−31.3080	+	33.1846i	−1.12245	+	1.18972i
$779$	7.04947	−	0.823965i	0.252573	−	0.0295216i
$780$		0			0
$781$	0.461448	+	7.92276i	0.0165119	+	0.283499i
$782$	−0.492228	+	0.852563i	−0.0176020	+	0.0304876i
$783$		0			0
$784$	40.5553	+	70.2439i	1.44841	+	2.50871i
$785$	5.34632	−	3.51633i	0.190818	−	0.125503i
$786$		0			0
$787$	6.50825	−	15.0878i	0.231994	−	0.537823i	−0.761959	−	0.647625i	$-0.775762\pi$
$787$	6.50825	−	15.0878i	0.231994	−	0.537823i	0.993953	+	0.109802i	$0.0350217\pi$
$788$	12.0739	+	2.86156i	0.430114	+	0.101939i
$789$		0			0
$790$	40.1846	−	53.9773i	1.42970	−	1.92043i
$791$	2.66286	+	0.969203i	0.0946805	+	0.0344609i
$792$		0			0
$793$	68.3884	−	24.8914i	2.42854	−	0.883918i
$794$	19.2874	−	64.4246i	0.684486	−	2.28634i
$795$		0			0
$796$	2.91740	−	50.0899i	0.103405	−	1.77539i
$797$	−7.02608	−	4.62112i	−0.248876	−	0.163689i	0.418942	−	0.908013i	$-0.362401\pi$
$797$	−7.02608	−	4.62112i	−0.248876	−	0.163689i	−0.667818	+	0.744325i	$0.732772\pi$
$798$		0			0
$799$	10.0759	−	2.38804i	0.356461	−	0.0844828i
$800$	3.82623	−	21.6996i	0.135278	−	0.767198i
$801$		0			0
$802$	9.56414	+	54.2409i	0.337721	+	1.91531i
$803$	3.62909	+	8.41319i	0.128068	+	0.296895i
$804$		0			0
$805$	0.0967280	+	0.323094i	0.00340922	+	0.0113876i
$806$	46.4681	+	62.4176i	1.63677	+	2.19856i
$807$		0			0
$808$	−132.988	−	66.7890i	−4.67849	−	2.34963i
$809$	1.83823			0.0646289			0.0323144	−	0.999478i	$-0.489712\pi$
$809$	1.83823			0.0646289			0.0323144	+	0.999478i	$0.489712\pi$
$810$		0			0
$811$	−8.25761			−0.289964			−0.144982	−	0.989434i	$-0.546312\pi$
$811$	−8.25761			−0.289964			−0.144982	+	0.989434i	$0.546312\pi$
$812$	−4.16374	−	2.09111i	−0.146119	−	0.0733836i
$813$		0			0
$814$	16.1518	+	21.6957i	0.566121	+	0.760433i
$815$	−5.31448	−	17.7516i	−0.186158	−	0.621811i
$816$		0			0
$817$	2.54175	+	5.89243i	0.0889245	+	0.206150i
$818$	16.3095	+	92.4956i	0.570248	+	3.23403i
$819$		0			0
$820$	15.2539	−	86.5093i	0.532690	−	3.02104i
$821$	24.8430	−	5.88790i	0.867026	−	0.205489i	0.227050	−	0.973883i	$-0.427092\pi$
$821$	24.8430	−	5.88790i	0.867026	−	0.205489i	0.639977	+	0.768394i	$0.278944\pi$
$822$		0			0
$823$	2.93406	+	1.92976i	0.102275	+	0.0672672i	0.599616	−	0.800288i	$-0.295320\pi$
$823$	2.93406	+	1.92976i	0.102275	+	0.0672672i	−0.497341	+	0.867555i	$0.665690\pi$
$824$	−2.09607	+	35.9882i	−0.0730202	+	1.25371i
$825$		0			0
$826$	−1.93846	+	6.47491i	−0.0674476	+	0.225291i
$827$	−29.3726	+	10.6908i	−1.02139	+	0.371754i	−0.797795	−	0.602929i	$-0.794000\pi$
$827$	−29.3726	+	10.6908i	−1.02139	+	0.371754i	−0.223591	+	0.974683i	$0.571778\pi$
$828$		0			0
$829$	44.5589	+	16.2181i	1.54759	+	0.563278i	0.967852	−	0.251521i	$-0.0809308\pi$
$829$	44.5589	+	16.2181i	1.54759	+	0.563278i	0.579743	+	0.814800i	$0.303153\pi$
$830$	−52.3509	+	70.3194i	−1.81712	+	2.44082i
$831$		0			0
$832$	94.0461	+	22.2893i	3.26046	+	0.772743i
$833$	3.78026	−	8.76362i	0.130978	−	0.303641i
$834$		0			0
$835$	−13.5814	+	8.93265i	−0.470005	+	0.309127i
$836$	−4.13831	−	7.16776i	−0.143126	−	0.247902i
$837$		0			0
$838$	−36.1825	+	62.6699i	−1.24990	+	2.16489i
$839$	1.72814	+	29.6710i	0.0596620	+	1.02436i	0.886740	+	0.462269i	$0.152965\pi$
$839$	1.72814	+	29.6710i	0.0596620	+	1.02436i	−0.827078	+	0.562087i	$0.809998\pi$
$840$		0			0
$841$	25.6621	−	2.99947i	0.884902	−	0.103430i
$842$	55.7655	−	59.1080i	1.92181	−	2.03700i
$843$		0			0
$844$	99.8793	+	11.6742i	3.43799	+	0.401843i
$845$	36.5597	−	30.6772i	1.25769	−	1.05533i
$846$		0			0
$847$	−3.38092	−	2.83693i	−0.116170	−	0.0974780i
$848$	−78.3744	−	83.0720i	−2.69139	−	2.85271i
$849$		0			0
$850$	−4.82384	+	2.42262i	−0.165456	+	0.0830952i
$851$	1.53383	−	0.770319i	0.0525791	−	0.0264062i
$852$		0			0
$853$	−7.23571	−	7.66940i	−0.247746	−	0.262595i	0.591552	−	0.806267i	$-0.298515\pi$
$853$	−7.23571	−	7.66940i	−0.247746	−	0.262595i	−0.839298	+	0.543671i	$0.817034\pi$
$854$	−13.4803	−	11.3113i	−0.461286	−	0.387065i
$855$		0			0
$856$	51.0334	−	42.8221i	1.74429	−	1.46363i
$857$	14.7298	+	1.72167i	0.503162	+	0.0588112i	0.363888	−	0.931443i	$-0.381449\pi$
$857$	14.7298	+	1.72167i	0.503162	+	0.0588112i	0.139274	+	0.990254i	$0.455523\pi$
$858$		0			0
$859$	−21.6923	+	22.9925i	−0.740131	+	0.784493i	−0.982614	−	0.185663i	$-0.940557\pi$
$859$	−21.6923	+	22.9925i	−0.740131	+	0.784493i	0.242483	+	0.970156i	$0.422038\pi$
$860$	78.8882	−	9.22071i	2.69007	−	0.314424i
$861$		0			0
$862$	1.39998	+	24.0367i	0.0476835	+	0.818693i
$863$	−1.64562	+	2.85030i	−0.0560177	+	0.0970255i	−0.892674	−	0.450702i	$-0.851174\pi$
$863$	−1.64562	+	2.85030i	−0.0560177	+	0.0970255i	0.836657	+	0.547728i	$0.184507\pi$
$864$		0			0
$865$	−6.19692	−	10.7334i	−0.210701	−	0.364946i
$866$	−52.8737	+	34.7756i	−1.79672	+	1.18172i
$867$		0			0
$868$	5.36123	−	12.4287i	0.181972	−	0.421858i
$869$	−14.8674	−	3.52365i	−0.504344	−	0.119532i
$870$		0			0
$871$	21.6241	−	29.0462i	0.732704	−	0.984192i
$872$	1.67013	+	0.607878i	0.0565577	+	0.0205853i
$873$		0			0
$874$	−0.686052	+	0.249702i	−0.0232060	+	0.00844631i
$875$	1.32717	−	4.43305i	0.0448664	−	0.149864i
$876$		0			0
$877$	2.14761	−	36.8731i	0.0725197	−	1.24511i	−0.744151	−	0.668011i	$-0.767146\pi$
$877$	2.14761	−	36.8731i	0.0725197	−	1.24511i	0.816671	−	0.577104i	$-0.195817\pi$
$878$	−8.97727	−	5.90444i	−0.302968	−	0.199265i
$879$		0			0
$880$	−45.6322	+	10.8150i	−1.53826	+	0.364575i
$881$	−5.05857	+	28.6886i	−0.170427	+	0.966542i	0.772863	+	0.634573i	$0.218824\pi$
$881$	−5.05857	+	28.6886i	−0.170427	+	0.966542i	−0.943290	+	0.331969i	$0.892287\pi$
$882$		0			0
$883$	−3.27904	−	18.5963i	−0.110348	−	0.625817i	−0.988949	−	0.148259i	$-0.952633\pi$
$883$	−3.27904	−	18.5963i	−0.110348	−	0.625817i	0.878600	−	0.477558i	$-0.158478\pi$
$884$	−16.2261	−	37.6163i	−0.545742	−	1.26517i
$885$		0			0
$886$	6.09307	+	20.3523i	0.204701	+	0.683748i
$887$	−14.5048	−	19.4834i	−0.487024	−	0.654187i	0.488889	−	0.872346i	$-0.337402\pi$
$887$	−14.5048	−	19.4834i	−0.487024	−	0.654187i	−0.975913	+	0.218159i	$0.929995\pi$
$888$		0			0
$889$	−8.33663	−	4.18681i	−0.279602	−	0.140421i
$890$	66.7543			2.23761
$891$		0			0
$892$	13.4343			0.449814
$893$	6.86256	+	3.44651i	0.229647	+	0.115333i
$894$		0			0
$895$	0.776044	+	1.04241i	0.0259403	+	0.0348439i
$896$	−2.17924	−	7.27917i	−0.0728033	−	0.243180i
$897$		0			0
$898$	15.5829	+	36.1253i	0.520009	+	1.20552i
$899$	−1.59569	−	9.04959i	−0.0532191	−	0.301821i
$900$		0			0
$901$	−2.33361	+	13.2346i	−0.0777438	+	0.440907i
$902$	−26.9780	+	6.39391i	−0.898269	+	0.212894i
$903$		0			0
$904$	38.6906	+	25.4472i	1.28683	+	0.846361i
$905$	0.556975	−	9.56290i	0.0185145	−	0.317881i
$906$		0			0
$907$	−11.3074	+	37.7694i	−0.375456	+	1.25411i	0.536526	+	0.843884i	$0.319736\pi$
$907$	−11.3074	+	37.7694i	−0.375456	+	1.25411i	−0.911983	+	0.410228i	$0.865449\pi$
$908$	5.95117	−	2.16605i	0.197496	−	0.0718828i
$909$		0			0
$910$	−18.3325	−	6.67247i	−0.607715	−	0.221190i
$911$	−24.7111	+	33.1927i	−0.818715	+	1.09972i	0.174640	+	0.984632i	$0.444124\pi$
$911$	−24.7111	+	33.1927i	−0.818715	+	1.09972i	−0.993355	+	0.115092i	$0.963284\pi$
$912$		0			0
$913$	19.3687	+	4.59047i	0.641010	+	0.151922i
$914$	−8.31208	+	19.2696i	−0.274939	+	0.637381i
$915$		0			0
$916$	−20.9876	+	13.8038i	−0.693451	+	0.456090i
$917$	2.05402	+	3.55767i	0.0678298	+	0.117485i
$918$		0			0
$919$	0.677038	−	1.17266i	0.0223334	−	0.0386826i	−0.854643	−	0.519217i	$-0.826224\pi$
$919$	0.677038	−	1.17266i	0.0223334	−	0.0386826i	0.876976	+	0.480534i	$0.159557\pi$
$920$	0.320466	+	5.50218i	0.0105654	+	0.181402i
$921$		0			0
$922$	8.76068	−	1.02398i	0.288517	−	0.0337229i
$923$	−19.9914	+	21.1896i	−0.658024	+	0.697464i
$924$		0			0
$925$	9.34780	+	1.09260i	0.307354	+	0.0359245i
$926$	−36.2019	+	30.3770i	−1.18967	+	0.998250i
$927$		0			0
$928$	−21.0279	−	17.6445i	−0.690274	−	0.579209i
$929$	−18.3365	−	19.4355i	−0.601601	−	0.637659i	0.352973	−	0.935633i	$-0.385171\pi$
$929$	−18.3365	−	19.4355i	−0.601601	−	0.637659i	−0.954574	+	0.297974i	$0.903689\pi$
$930$		0			0
$931$	6.32517	−	3.17662i	0.207299	−	0.104110i
$932$	17.5224	−	8.80006i	0.573964	−	0.288256i
$933$		0			0
$934$	−73.0236	−	77.4005i	−2.38941	−	2.53262i
$935$	4.22721	+	3.54705i	0.138244	+	0.116001i
$936$		0			0
$937$	−2.08507	+	1.74958i	−0.0681162	+	0.0571563i	−0.676210	−	0.736709i	$-0.736379\pi$
$937$	−2.08507	+	1.74958i	−0.0681162	+	0.0571563i	0.608094	+	0.793865i	$0.291934\pi$
$938$	−8.69660	−	1.01649i	−0.283954	−	0.0331895i
$939$		0			0
$940$	65.2249	−	69.1343i	2.12740	−	2.25491i
$941$	22.6491	−	2.64730i	0.738341	−	0.0862996i	0.261394	−	0.965232i	$-0.415818\pi$
$941$	22.6491	−	2.64730i	0.738341	−	0.0862996i	0.476946	+	0.878932i	$0.341744\pi$
$942$		0			0
$943$	0.102300	+	1.75642i	0.00333134	+	0.0571969i
$944$	−29.8195	+	51.6488i	−0.970541	+	1.68103i
$945$		0			0
$946$	−12.5341	−	21.7097i	−0.407520	−	0.705845i
$947$	13.6906	−	9.00447i	0.444886	−	0.292606i	−0.307232	−	0.951635i	$-0.599403\pi$
$947$	13.6906	−	9.00447i	0.444886	−	0.292606i	0.752118	+	0.659029i	$0.229032\pi$
$948$		0			0
$949$	−13.3215	+	30.8826i	−0.432433	+	1.00249i
$950$	−3.89530	−	0.923204i	−0.126380	−	0.0299527i
$951$		0			0
$952$	−3.60794	+	4.84630i	−0.116934	+	0.157070i
$953$	−33.5144	−	12.1982i	−1.08564	−	0.395140i	−0.263634	−	0.964623i	$-0.584921\pi$
$953$	−33.5144	−	12.1982i	−1.08564	−	0.395140i	−0.822003	+	0.569483i	$0.807143\pi$
$954$		0			0
$955$	−53.9877	+	19.6499i	−1.74700	+	0.635857i
$956$	−13.3045	+	44.4400i	−0.430297	+	1.43729i
$957$		0			0
$958$	−6.08364	+	104.452i	−0.196553	+	3.37469i
$959$	3.64233	+	2.39560i	0.117617	+	0.0773579i
$960$		0			0
$961$	−4.18872	+	0.992744i	−0.135120	+	0.0320240i
$962$	−17.2407	+	97.7770i	−0.555863	+	3.15246i
$963$		0			0
$964$	−20.8580	−	118.292i	−0.671791	−	3.80992i
$965$	−5.74740	−	13.3240i	−0.185015	−	0.428914i
$966$		0			0
$967$	2.30791	+	7.70895i	0.0742174	+	0.247903i	0.987045	−	0.160441i	$-0.0512916\pi$
$967$	2.30791	+	7.70895i	0.0742174	+	0.247903i	−0.912828	+	0.408344i	$0.866106\pi$
$968$	−43.0698	−	57.8527i	−1.38431	−	1.85946i
$969$		0			0
$970$	−21.7567	−	10.9266i	−0.698566	−	0.350833i
$971$	44.9410			1.44223			0.721113	−	0.692818i	$-0.243631\pi$
$971$	44.9410			1.44223			0.721113	+	0.692818i	$0.243631\pi$
$972$		0			0
$973$	6.66731			0.213744
$974$	83.6398	+	42.0055i	2.67999	+	1.34594i
$975$		0			0
$976$	−92.7239	−	124.550i	−2.96802	−	3.98674i
$977$	−7.96425	−	26.6024i	−0.254799	−	0.851088i	−0.985686	−	0.168590i	$-0.946079\pi$
$977$	−7.96425	−	26.6024i	−0.254799	−	0.851088i	0.730887	−	0.682498i	$-0.239106\pi$
$978$		0			0
$979$	−6.00338	−	13.9174i	−0.191869	−	0.444802i
$980$	−15.2122	−	86.2728i	−0.485936	−	2.75588i
$981$		0			0
$982$	−9.54176	+	54.1140i	−0.304490	+	1.72685i
$983$	6.81336	−	1.61479i	0.217312	−	0.0515040i	−0.120517	−	0.992711i	$-0.538455\pi$
$983$	6.81336	−	1.61479i	0.217312	−	0.0515040i	0.337830	+	0.941207i	$0.390307\pi$
$984$		0			0
$985$	−5.12597	−	3.37140i	−0.163327	−	0.107422i
$986$	−0.391008	+	6.71335i	−0.0124522	+	0.213797i
$987$		0			0
$988$	8.71345	−	29.1049i	0.277212	−	0.925951i
$989$	−1.49485	+	0.544079i	−0.0475333	+	0.0173007i
$990$		0			0
$991$	55.0238	+	20.0270i	1.74789	+	0.636179i	0.999629	−	0.0272280i	$-0.00866800\pi$
$991$	55.0238	+	20.0270i	1.74789	+	0.636179i	0.748259	+	0.663407i	$0.230890\pi$
$992$	47.6199	−	63.9646i	1.51193	−	2.03088i
$993$		0			0
$994$	6.85403	+	1.62444i	0.217397	+	0.0515240i
$995$	−9.82630	+	22.7799i	−0.311515	+	0.722172i
$996$		0			0
$997$	32.1641	−	21.1546i	1.01865	−	0.669974i	0.0737275	−	0.997278i	$-0.476511\pi$
$997$	32.1641	−	21.1546i	1.01865	−	0.669974i	0.944919	+	0.327304i	$0.106140\pi$
$998$	−11.0063	−	19.0635i	−0.348400	−	0.603446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.10.8		144
3.2	odd	2		81.2.g.a.13.1	✓	144
9.2	odd	6		729.2.g.d.514.8		144
9.4	even	3		729.2.g.b.28.1		144
9.5	odd	6		729.2.g.c.28.8		144
9.7	even	3		729.2.g.a.514.1		144
81.2	odd	54		729.2.g.c.703.8		144
81.5	odd	54		6561.2.a.c.1.2		72
81.25	even	27	inner	243.2.g.a.73.8		144
81.29	odd	54		729.2.g.d.217.8		144
81.52	even	27		729.2.g.a.217.1		144
81.56	odd	54		81.2.g.a.25.1	yes	144
81.76	even	27		6561.2.a.d.1.71		72
81.79	even	27		729.2.g.b.703.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.1	✓	144	3.2	odd	2
81.2.g.a.25.1	yes	144	81.56	odd	54
243.2.g.a.10.8		144	1.1	even	1	trivial
243.2.g.a.73.8		144	81.25	even	27	inner
729.2.g.a.217.1		144	81.52	even	27
729.2.g.a.514.1		144	9.7	even	3
729.2.g.b.28.1		144	9.4	even	3
729.2.g.b.703.1		144	81.79	even	27
729.2.g.c.28.8		144	9.5	odd	6
729.2.g.c.703.8		144	81.2	odd	54
729.2.g.d.217.8		144	81.29	odd	54
729.2.g.d.514.8		144	9.2	odd	6
6561.2.a.c.1.2		72	81.5	odd	54
6561.2.a.d.1.71		72	81.76	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.38576 + 1.19817i) q^{2} +(3.06192 + 4.11287i) q^{4} +(-0.727126 - 2.42877i) q^{5} +(0.202369 + 0.469143i) q^{7} +(1.44988 + 8.22270i) q^{8} +O(q^{10})\)	\(q+(2.38576 + 1.19817i) q^{2} +(3.06192 + 4.11287i) q^{4} +(-0.727126 - 2.42877i) q^{5} +(0.202369 + 0.469143i) q^{7} +(1.44988 + 8.22270i) q^{8} +(1.17534 - 6.66569i) q^{10} +(-1.49541 + 0.354419i) q^{11} +(-4.71325 - 3.09996i) q^{13} +(-0.0793122 + 1.36174i) q^{14} +(-3.45199 + 11.5305i) q^{16} +(1.33086 - 0.484393i) q^{17} +(0.986977 + 0.359230i) q^{19} +(7.76282 - 10.4273i) q^{20} +(-3.99235 - 0.946204i) q^{22} +(-0.103125 + 0.239071i) q^{23} +(-1.19278 + 0.784502i) q^{25} +(-7.53041 - 13.0431i) q^{26} +(-1.30989 + 2.26880i) q^{28} +(0.103412 + 1.77552i) q^{29} +(-5.13181 + 0.599822i) q^{31} +(-10.5915 + 11.2264i) q^{32} +(3.75550 + 0.438955i) q^{34} +(0.992294 - 0.832634i) q^{35} +(-5.04999 - 4.23745i) q^{37} +(1.92427 + 2.03961i) q^{38} +(18.9168 - 9.50037i) q^{40} +(6.03866 - 3.03273i) q^{41} +(4.19282 + 4.44412i) q^{43} +(-6.03650 - 5.06523i) q^{44} +(-0.532481 + 0.446804i) q^{46} +(7.26206 + 0.848813i) q^{47} +(4.62455 - 4.90174i) q^{49} +(-3.78565 + 0.442479i) q^{50} +(-1.68188 - 28.8768i) q^{52} +(-4.74440 + 8.21755i) q^{53} +(1.94815 + 3.37430i) q^{55} +(-3.56421 + 2.34422i) q^{56} +(-1.88066 + 4.35987i) q^{58} +(4.82144 + 1.14270i) q^{59} +(-7.70381 + 10.3480i) q^{61} +(-12.9620 - 4.71777i) q^{62} +(-16.0995 + 5.85975i) q^{64} +(-4.10195 + 13.7015i) q^{65} +(-0.373231 + 6.40814i) q^{67} +(6.06723 + 3.99048i) q^{68} +(3.36502 - 0.797524i) q^{70} +(0.896716 - 5.08553i) q^{71} +(-1.03528 - 5.87137i) q^{73} +(-6.97088 - 16.1603i) q^{74} +(1.54458 + 5.15924i) q^{76} +(-0.468897 - 0.629838i) q^{77} +(8.88455 + 4.46199i) q^{79} +30.5149 q^{80} +18.0405 q^{82} +(-11.5744 - 5.81289i) q^{83} +(-2.14418 - 2.88014i) q^{85} +(4.67822 + 15.6263i) q^{86} +(-5.08245 - 11.7824i) q^{88} +(1.71260 + 9.71264i) q^{89} +(0.500509 - 2.83853i) q^{91} +(-1.29903 + 0.307875i) q^{92} +(16.3085 + 10.7263i) q^{94} +(0.154831 - 2.65835i) q^{95} +(1.03163 - 3.44589i) q^{97} +(16.9062 - 6.15336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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