LMFDB - Embedded newform 243.2.g.a.19.4

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			19.4
Character	$\chi$	$=$	243.19
Dual form			243.2.g.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.186105 - 0.0217526i) q^{2} +(-1.91193 + 0.453135i) q^{4} +(-1.41557 - 0.710926i) q^{5} +(1.16062 + 3.87673i) q^{7} +(-0.698107 + 0.254090i) q^{8} +O(q^{10})$	\(q+(0.186105 - 0.0217526i) q^{2} +(-1.91193 + 0.453135i) q^{4} +(-1.41557 - 0.710926i) q^{5} +(1.16062 + 3.87673i) q^{7} +(-0.698107 + 0.254090i) q^{8} +(-0.278909 - 0.101515i) q^{10} +(-0.223537 + 3.83798i) q^{11} +(-0.955113 + 1.28294i) q^{13} +(0.300325 + 0.696232i) q^{14} +(3.38739 - 1.70121i) q^{16} +(-5.79317 + 4.86105i) q^{17} +(1.26984 + 1.06552i) q^{19} +(3.02861 + 0.717794i) q^{20} +(0.0418845 + 0.719129i) q^{22} +(1.83889 - 6.14233i) q^{23} +(-1.48737 - 1.99789i) q^{25} +(-0.149844 + 0.259538i) q^{26} +(-3.97569 - 6.88610i) q^{28} +(0.108478 - 0.251480i) q^{29} +(1.27012 + 1.34625i) q^{31} +(1.83479 - 1.20676i) q^{32} +(-0.972398 + 1.03068i) q^{34} +(1.11313 - 6.31289i) q^{35} +(-0.295248 - 1.67443i) q^{37} +(0.259501 + 0.170677i) q^{38} +(1.16886 + 0.136620i) q^{40} +(2.97293 + 0.347486i) q^{41} +(4.06748 + 2.67523i) q^{43} +(-1.31174 - 7.43922i) q^{44} +(0.208616 - 1.18312i) q^{46} +(0.0915512 - 0.0970386i) q^{47} +(-7.83356 + 5.15221i) q^{49} +(-0.320267 - 0.339463i) q^{50} +(1.24476 - 2.88568i) q^{52} +(4.93888 + 8.55438i) q^{53} +(3.04495 - 5.27400i) q^{55} +(-1.79527 - 2.41147i) q^{56} +(0.0147179 - 0.0491613i) q^{58} +(0.450368 + 7.73252i) q^{59} +(4.02160 + 0.953136i) q^{61} +(0.265660 + 0.222915i) q^{62} +(-5.49230 + 4.60858i) q^{64} +(2.26410 - 1.13707i) q^{65} +(-5.32612 - 12.3473i) q^{67} +(8.87341 - 11.9191i) q^{68} +(0.0698381 - 1.19907i) q^{70} +(-2.39924 - 0.873251i) q^{71} +(5.29149 - 1.92595i) q^{73} +(-0.0913704 - 0.305198i) q^{74} +(-2.91066 - 1.46179i) q^{76} +(-15.1382 + 3.58782i) q^{77} +(-8.04919 + 0.940816i) q^{79} -6.00452 q^{80} +0.560836 q^{82} +(5.44690 - 0.636652i) q^{83} +(11.6565 - 2.76264i) q^{85} +(0.815172 + 0.409395i) q^{86} +(-0.819139 - 2.73612i) q^{88} +(6.33932 - 2.30732i) q^{89} +(-6.08212 - 2.21371i) q^{91} +(-0.732524 + 12.5770i) q^{92} +(0.0149273 - 0.0200509i) q^{94} +(-1.04004 - 2.41108i) q^{95} +(1.67247 - 0.839945i) q^{97} +(-1.34579 + 1.12925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{26}{27}\right)$

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 $

$2$	0.186105	−	0.0217526i	0.131596	−	0.0153814i	−0.0500398	−	0.998747i	$-0.515935\pi$
$2$	0.186105	−	0.0217526i	0.131596	−	0.0153814i	0.181636	+	0.983366i	$0.441861\pi$
$3$		0			0
$3$		0			0
$4$	−1.91193	+	0.453135i	−0.955964	+	0.226568i
$5$	−1.41557	−	0.710926i	−0.633062	−	0.317936i	0.103171	−	0.994664i	$-0.467101\pi$
$5$	−1.41557	−	0.710926i	−0.633062	−	0.317936i	−0.736233	+	0.676728i	$0.763397\pi$
$6$		0			0
$7$	1.16062	+	3.87673i	0.438671	+	1.46526i	0.836583	+	0.547841i	$0.184550\pi$
$7$	1.16062	+	3.87673i	0.438671	+	1.46526i	−0.397911	+	0.917424i	$0.630265\pi$
$8$	−0.698107	+	0.254090i	−0.246818	+	0.0898344i
$9$		0			0
$10$	−0.278909	−	0.101515i	−0.0881988	−	0.0321017i
$11$	−0.223537	+	3.83798i	−0.0673988	+	1.15719i	0.779839	+	0.625980i	$0.215301\pi$
$11$	−0.223537	+	3.83798i	−0.0673988	+	1.15719i	−0.847238	+	0.531213i	$0.821736\pi$
$12$		0			0
$13$	−0.955113	+	1.28294i	−0.264901	+	0.355823i	−0.914594	−	0.404373i	$-0.867490\pi$
$13$	−0.955113	+	1.28294i	−0.264901	+	0.355823i	0.649694	+	0.760196i	$0.274897\pi$
$14$	0.300325	+	0.696232i	0.0802653	+	0.186076i
$15$		0			0
$16$	3.38739	−	1.70121i	0.846847	−	0.425303i
$17$	−5.79317	+	4.86105i	−1.40505	+	1.17898i	−0.446246	+	0.894910i	$0.647239\pi$
$17$	−5.79317	+	4.86105i	−1.40505	+	1.17898i	−0.958804	+	0.284067i	$0.908316\pi$
$18$		0			0
$19$	1.26984	+	1.06552i	0.291321	+	0.244447i	0.776721	−	0.629845i	$-0.216882\pi$
$19$	1.26984	+	1.06552i	0.291321	+	0.244447i	−0.485400	+	0.874292i	$0.661326\pi$
$20$	3.02861	+	0.717794i	0.677218	+	0.160504i
$21$		0			0
$22$	0.0418845	+	0.719129i	0.00892981	+	0.153319i
$23$	1.83889	−	6.14233i	0.383435	−	1.28076i	−0.520781	−	0.853690i	$-0.674359\pi$
$23$	1.83889	−	6.14233i	0.383435	−	1.28076i	0.904217	−	0.427074i	$-0.140455\pi$
$24$		0			0
$25$	−1.48737	−	1.99789i	−0.297474	−	0.399577i
$26$	−0.149844	+	0.259538i	−0.0293868	+	0.0508995i
$27$		0			0
$28$	−3.97569	−	6.88610i	−0.751336	−	1.30135i
$29$	0.108478	−	0.251480i	0.0201438	−	0.0466986i	−0.907847	−	0.419301i	$-0.862275\pi$
$29$	0.108478	−	0.251480i	0.0201438	−	0.0466986i	0.927991	+	0.372602i	$0.121534\pi$
$30$		0			0
$31$	1.27012	+	1.34625i	0.228120	+	0.241794i	0.831316	−	0.555800i	$-0.187588\pi$
$31$	1.27012	+	1.34625i	0.228120	+	0.241794i	−0.603196	+	0.797593i	$0.706106\pi$
$32$	1.83479	−	1.20676i	0.324348	−	0.213327i
$33$		0			0
$34$	−0.972398	+	1.03068i	−0.166765	+	0.176761i
$35$	1.11313	−	6.31289i	0.188154	−	1.06707i
$36$		0			0
$37$	−0.295248	−	1.67443i	−0.0485385	−	0.275275i	0.950873	−	0.309582i	$-0.100189\pi$
$37$	−0.295248	−	1.67443i	−0.0485385	−	0.275275i	−0.999411	+	0.0343062i	$0.989078\pi$
$38$	0.259501	+	0.170677i	0.0420966	+	0.0276874i
$39$		0			0
$40$	1.16886	+	0.136620i	0.184813	+	0.0216015i
$41$	2.97293	+	0.347486i	0.464294	+	0.0542682i	0.345024	−	0.938594i	$-0.387871\pi$
$41$	2.97293	+	0.347486i	0.464294	+	0.0542682i	0.119269	+	0.992862i	$0.461945\pi$
$42$		0			0
$43$	4.06748	+	2.67523i	0.620286	+	0.407968i	0.820388	−	0.571807i	$-0.193757\pi$
$43$	4.06748	+	2.67523i	0.620286	+	0.407968i	−0.200103	+	0.979775i	$0.564128\pi$
$44$	−1.31174	−	7.43922i	−0.197752	−	1.12151i
$45$		0			0
$46$	0.208616	−	1.18312i	0.0307587	−	0.174441i
$47$	0.0915512	−	0.0970386i	0.0133541	−	0.0141545i	−0.720662	−	0.693286i	$-0.756162\pi$
$47$	0.0915512	−	0.0970386i	0.0133541	−	0.0141545i	0.734016	+	0.679132i	$0.237644\pi$
$48$		0			0
$49$	−7.83356	+	5.15221i	−1.11908	+	0.736030i
$50$	−0.320267	−	0.339463i	−0.0452925	−	0.0480073i
$51$		0			0
$52$	1.24476	−	2.88568i	0.172617	−	0.400172i
$53$	4.93888	+	8.55438i	0.678407	+	1.17504i	0.975461	+	0.220174i	$0.0706626\pi$
$53$	4.93888	+	8.55438i	0.678407	+	1.17504i	−0.297054	+	0.954861i	$0.596004\pi$
$54$		0			0
$55$	3.04495	−	5.27400i	0.410580	−	0.711146i
$56$	−1.79527	−	2.41147i	−0.239903	−	0.322246i
$57$		0			0
$58$	0.0147179	−	0.0491613i	0.00193256	−	0.00645520i
$59$	0.450368	+	7.73252i	0.0586329	+	1.00669i	0.891444	+	0.453131i	$0.149693\pi$
$59$	0.450368	+	7.73252i	0.0586329	+	1.00669i	−0.832811	+	0.553558i	$0.813270\pi$
$60$		0			0
$61$	4.02160	+	0.953136i	0.514913	+	0.122037i	0.479853	−	0.877349i	$-0.340690\pi$
$61$	4.02160	+	0.953136i	0.514913	+	0.122037i	0.0350594	+	0.999385i	$0.488838\pi$
$62$	0.265660	+	0.222915i	0.0337389	+	0.0283103i
$63$		0			0
$64$	−5.49230	+	4.60858i	−0.686537	+	0.576073i
$65$	2.26410	−	1.13707i	0.280827	−	0.141037i
$66$		0			0
$67$	−5.32612	−	12.3473i	−0.650689	−	1.50847i	−0.849036	−	0.528335i	$-0.822817\pi$
$67$	−5.32612	−	12.3473i	−0.650689	−	1.50847i	0.198347	−	0.980132i	$-0.436443\pi$
$68$	8.87341	−	11.9191i	1.07606	−	1.44540i
$69$		0			0
$70$	0.0698381	−	1.19907i	0.00834725	−	0.143317i
$71$	−2.39924	−	0.873251i	−0.284737	−	0.103636i	0.195703	−	0.980663i	$-0.437301\pi$
$71$	−2.39924	−	0.873251i	−0.284737	−	0.103636i	−0.480441	+	0.877027i	$0.659523\pi$
$72$		0			0
$73$	5.29149	−	1.92595i	0.619322	−	0.225415i	−0.0132549	−	0.999912i	$-0.504219\pi$
$73$	5.29149	−	1.92595i	0.619322	−	0.225415i	0.632577	+	0.774497i	$0.281997\pi$
$74$	−0.0913704	−	0.305198i	−0.0106216	−	0.0354786i
$75$		0			0
$76$	−2.91066	−	1.46179i	−0.333876	−	0.167679i
$77$	−15.1382	+	3.58782i	−1.72516	+	0.408870i
$78$		0			0
$79$	−8.04919	+	0.940816i	−0.905605	+	0.105850i	−0.556130	−	0.831096i	$-0.687714\pi$
$79$	−8.04919	+	0.940816i	−0.905605	+	0.105850i	−0.349475	+	0.936946i	$0.613640\pi$
$80$	−6.00452			−0.671325
$81$		0			0
$82$	0.560836			0.0619340
$83$	5.44690	−	0.636652i	0.597875	−	0.0698816i	0.188228	−	0.982125i	$-0.439726\pi$
$83$	5.44690	−	0.636652i	0.597875	−	0.0698816i	0.409648	+	0.912244i	$0.365652\pi$
$84$		0			0
$85$	11.6565	−	2.76264i	1.26432	−	0.299650i
$86$	0.815172	+	0.409395i	0.0879023	+	0.0441462i
$87$		0			0
$88$	−0.819139	−	2.73612i	−0.0873205	−	0.291671i
$89$	6.33932	−	2.30732i	0.671966	−	0.244576i	0.0165720	−	0.999863i	$-0.494725\pi$
$89$	6.33932	−	2.30732i	0.671966	−	0.244576i	0.655394	+	0.755287i	$0.272503\pi$
$90$		0			0
$91$	−6.08212	−	2.21371i	−0.637580	−	0.232060i
$92$	−0.732524	+	12.5770i	−0.0763709	+	1.31124i
$93$		0			0
$94$	0.0149273	−	0.0200509i	0.00153963	−	0.00206809i
$95$	−1.04004	−	2.41108i	−0.106706	−	0.247371i
$96$		0			0
$97$	1.67247	−	0.839945i	0.169813	−	0.0852835i	−0.361862	−	0.932232i	$-0.617859\pi$
$97$	1.67247	−	0.839945i	0.169813	−	0.0852835i	0.531675	+	0.846948i	$0.321563\pi$
$98$	−1.34579	+	1.12925i	−0.135945	+	0.114072i
$99$		0			0
$100$	3.74906	+	3.14584i	0.374906	+	0.314584i
$101$	16.2329	+	3.84728i	1.61524	+	0.382818i	0.936251	−	0.351332i	$-0.114271\pi$
$101$	16.2329	+	3.84728i	1.61524	+	0.382818i	0.678987	+	0.734151i	$0.262419\pi$
$102$		0			0
$103$	0.334674	+	5.74614i	0.0329765	+	0.566184i	0.973817	+	0.227334i	$0.0730009\pi$
$103$	0.334674	+	5.74614i	0.0329765	+	0.566184i	−0.940840	+	0.338850i	$0.889962\pi$
$104$	0.340789	−	1.13831i	0.0334171	−	0.111621i
$105$		0			0
$106$	1.10523	+	1.48458i	0.107349	+	0.144195i
$107$	−0.810593	+	1.40399i	−0.0783630	+	0.135729i	−0.902544	−	0.430598i	$-0.858303\pi$
$107$	−0.810593	+	1.40399i	−0.0783630	+	0.135729i	0.824181	+	0.566327i	$0.191636\pi$
$108$		0			0
$109$	5.75519	+	9.96829i	0.551248	+	0.954789i	0.998185	+	0.0602237i	$0.0191814\pi$
$109$	5.75519	+	9.96829i	0.551248	+	0.954789i	−0.446937	+	0.894565i	$0.647485\pi$
$110$	0.451957	−	1.04775i	0.0430924	−	0.0998994i
$111$		0			0
$112$	10.5266	+	11.1575i	0.994669	+	1.05429i
$113$	−7.29428	+	4.79752i	−0.686188	+	0.451313i	−0.844132	−	0.536135i	$-0.819884\pi$
$113$	−7.29428	+	4.79752i	−0.686188	+	0.451313i	0.157944	+	0.987448i	$0.449513\pi$
$114$		0			0
$115$	−6.96982	+	7.38757i	−0.649939	+	0.688895i
$116$	−0.0934474	+	0.529966i	−0.00867637	+	0.0492061i
$117$		0			0
$118$	0.252018	+	1.42926i	0.0232001	+	0.131575i
$119$	−25.5686	−	16.8167i	−2.34387	−	1.54159i
$120$		0			0
$121$	−3.75446	−	0.438834i	−0.341315	−	0.0398940i
$122$	0.769173	+	0.0899034i	0.0696376	+	0.00813947i
$123$		0			0
$124$	−3.03841	−	1.99840i	−0.272857	−	0.179461i
$125$	2.06048	+	11.6855i	0.184295	+	1.04519i
$126$		0			0
$127$	−3.29466	+	18.6850i	−0.292354	+	1.65802i	0.385411	+	0.922745i	$0.374060\pi$
$127$	−3.29466	+	18.6850i	−0.292354	+	1.65802i	−0.677766	+	0.735278i	$0.737052\pi$
$128$	−3.93596	+	4.17188i	−0.347893	+	0.368745i
$129$		0			0
$130$	0.396627	−	0.260865i	0.0347865	−	0.0228794i
$131$	4.15364	+	4.40261i	0.362906	+	0.384657i	0.882938	−	0.469489i	$-0.155562\pi$
$131$	4.15364	+	4.40261i	0.362906	+	0.384657i	−0.520033	+	0.854146i	$0.674080\pi$
$132$		0			0
$133$	−2.65694	+	6.15947i	−0.230386	+	0.534094i
$134$	−1.25980	−	2.18204i	−0.108830	−	0.188500i
$135$		0			0
$136$	2.80911	−	4.86552i	0.240879	−	0.417215i
$137$	−13.2796	−	17.8376i	−1.13455	−	1.52397i	−0.817840	−	0.575446i	$-0.804829\pi$
$137$	−13.2796	−	17.8376i	−1.13455	−	1.52397i	−0.316712	−	0.948522i	$-0.602579\pi$
$138$		0			0
$139$	3.64872	−	12.1876i	0.309481	−	1.03374i	−0.651852	−	0.758347i	$-0.726007\pi$
$139$	3.64872	−	12.1876i	0.309481	−	1.03374i	0.961332	−	0.275391i	$-0.0888073\pi$
$140$	0.732363	+	12.5742i	0.0618959	+	1.06271i
$141$		0			0
$142$	−0.465506	−	0.110327i	−0.0390644	−	0.00925843i
$143$	−4.71039	−	3.95248i	−0.393902	−	0.330523i
$144$		0			0
$145$	−0.332341	+	0.278867i	−0.0275994	+	0.0231587i
$146$	0.942879	−	0.473532i	0.0780332	−	0.0391898i
$147$		0			0
$148$	1.32324	+	3.06761i	0.108770	+	0.252156i
$149$	−5.85078	+	7.85896i	−0.479314	+	0.643831i	−0.974349	−	0.225042i	$-0.927748\pi$
$149$	−5.85078	+	7.85896i	−0.479314	+	0.643831i	0.495035	+	0.868873i	$0.335155\pi$
$150$		0			0
$151$	0.553679	−	9.50631i	0.0450578	−	0.773612i	−0.897797	−	0.440409i	$-0.854833\pi$
$151$	0.553679	−	9.50631i	0.0450578	−	0.773612i	0.942855	−	0.333203i	$-0.108130\pi$
$152$	−1.15722	−	0.421194i	−0.0938630	−	0.0341633i
$153$		0			0
$154$	−2.73925	+	0.997007i	−0.220735	+	0.0803411i
$155$	−0.840861	−	2.80867i	−0.0675396	−	0.225598i
$156$		0			0
$157$	6.63837	+	3.33391i	0.529799	+	0.266075i	0.693527	−	0.720430i	$-0.256056\pi$
$157$	6.63837	+	3.33391i	0.529799	+	0.266075i	−0.163728	+	0.986506i	$0.552352\pi$
$158$	−1.47753	+	0.350181i	−0.117546	+	0.0278589i
$159$		0			0
$160$	−3.45519	+	0.403853i	−0.273157	+	0.0319274i
$161$	25.9464			2.04486
$162$		0			0
$163$	4.98806			0.390695			0.195347	−	0.980734i	$-0.437417\pi$
$163$	4.98806			0.390695			0.195347	+	0.980734i	$0.437417\pi$
$164$	−5.84149	+	0.682772i	−0.456143	+	0.0533155i
$165$		0			0
$166$	0.999848	−	0.236968i	0.0776032	−	0.0183923i
$167$	3.89691	+	1.95710i	0.301552	+	0.151445i	0.593141	−	0.805099i	$-0.297888\pi$
$167$	3.89691	+	1.95710i	0.301552	+	0.151445i	−0.291589	+	0.956544i	$0.594184\pi$
$168$		0			0
$169$	2.99475	+	10.0032i	0.230365	+	0.769474i
$170$	2.10924	−	0.767699i	0.161771	−	0.0588798i
$171$		0			0
$172$	−8.98898	−	3.27172i	−0.685403	−	0.249466i
$173$	−0.932829	+	16.0160i	−0.0709216	+	1.21768i	0.755699	+	0.654919i	$0.227297\pi$
$173$	−0.932829	+	16.0160i	−0.0709216	+	1.21768i	−0.826621	+	0.562759i	$0.809740\pi$
$174$		0			0
$175$	6.01899	−	8.08491i	0.454993	−	0.611162i
$176$	5.77200	+	13.3810i	0.435081	+	1.00863i
$177$		0			0
$178$	1.12959	−	0.567301i	0.0846663	−	0.0425210i
$179$	14.7729	−	12.3960i	1.10418	−	0.926518i	0.106483	−	0.994315i	$-0.466041\pi$
$179$	14.7729	−	12.3960i	1.10418	−	0.926518i	0.997699	+	0.0677961i	$0.0215967\pi$
$180$		0			0
$181$	0.116035	+	0.0973645i	0.00862478	+	0.00723705i	0.647090	−	0.762414i	$-0.275986\pi$
$181$	0.116035	+	0.0973645i	0.00862478	+	0.00723705i	−0.638465	+	0.769651i	$0.720430\pi$
$182$	−1.18007	−	0.279681i	−0.0874724	−	0.0207313i
$183$		0			0
$184$	0.276961	+	4.75524i	0.0204179	+	0.350561i
$185$	−0.772455	+	2.58018i	−0.0567920	+	0.189698i
$186$		0			0
$187$	−17.3616	−	23.3207i	−1.26961	−	1.70538i
$188$	−0.131068	+	0.227016i	−0.00955910	+	0.0165568i
$189$		0			0
$190$	−0.246003	−	0.426090i	−0.0178470	−	0.0309119i
$191$	4.24093	−	9.83158i	0.306863	−	0.711388i	−0.693092	−	0.720849i	$-0.743752\pi$
$191$	4.24093	−	9.83158i	0.306863	−	0.711388i	0.999955	+	0.00946057i	$0.00301144\pi$
$192$		0			0
$193$	−10.8912	−	11.5440i	−0.783964	−	0.830954i	0.205053	−	0.978751i	$-0.434263\pi$
$193$	−10.8912	−	11.5440i	−0.783964	−	0.830954i	−0.989018	+	0.147797i	$0.952782\pi$
$194$	0.292984	−	0.192698i	0.0210350	−	0.0138349i
$195$		0			0
$196$	12.6426	−	13.4003i	0.903039	−	0.957166i
$197$	0.213838	−	1.21273i	0.0152353	−	0.0864037i	−0.976242	−	0.216683i	$-0.930476\pi$
$197$	0.213838	−	1.21273i	0.0152353	−	0.0864037i	0.991477	+	0.130279i	$0.0415874\pi$
$198$		0			0
$199$	0.406772	+	2.30692i	0.0288353	+	0.163533i	0.995825	−	0.0912821i	$-0.0290965\pi$
$199$	0.406772	+	2.30692i	0.0288353	+	0.163533i	−0.966990	+	0.254815i	$0.917985\pi$
$200$	1.54599	+	1.01681i	0.109318	+	0.0718995i
$201$		0			0
$202$	3.10472	+	0.362890i	0.218447	+	0.0255328i
$203$	1.10082	+	0.128667i	0.0772624	+	0.00903068i
$204$		0			0
$205$	−3.96135	−	2.60542i	−0.276673	−	0.181971i
$206$	0.187278	+	1.06211i	0.0130483	+	0.0740004i
$207$		0			0
$208$	−1.05279	+	5.97066i	−0.0729978	+	0.413991i
$209$	−4.37330	+	4.63542i	−0.302507	+	0.320639i
$210$		0			0
$211$	9.51574	−	6.25860i	0.655090	−	0.430860i	−0.177975	−	0.984035i	$-0.556954\pi$
$211$	9.51574	−	6.25860i	0.655090	−	0.430860i	0.833065	+	0.553175i	$0.186584\pi$
$212$	−13.3191	−	14.1174i	−0.914757	−	0.969586i
$213$		0			0
$214$	−0.120315	+	0.278922i	−0.00822458	+	0.0190667i
$215$	−3.85592	−	6.67865i	−0.262971	−	0.455480i
$216$		0			0
$217$	−3.74492	+	6.48639i	−0.254222	+	0.440325i
$218$	1.28791	+	1.72996i	0.0872281	+	0.117168i
$219$		0			0
$220$	−3.43188	+	11.4633i	−0.231377	+	0.772854i
$221$	−0.703296	−	12.0751i	−0.0473088	−	0.812261i
$222$		0			0
$223$	−14.7184	−	3.48832i	−0.985614	−	0.233595i	−0.293955	−	0.955819i	$-0.594972\pi$
$223$	−14.7184	−	3.48832i	−0.985614	−	0.233595i	−0.691659	+	0.722224i	$0.743120\pi$
$224$	6.80776	+	5.71239i	0.454863	+	0.381675i
$225$		0			0
$226$	−1.25314	+	1.05151i	−0.0833579	+	0.0699456i
$227$	19.0155	−	9.54996i	1.26211	−	0.633853i	0.313282	−	0.949660i	$-0.398571\pi$
$227$	19.0155	−	9.54996i	1.26211	−	0.633853i	0.948824	+	0.315807i	$0.102275\pi$
$228$		0			0
$229$	1.54545	+	3.58276i	0.102126	+	0.236755i	0.961617	−	0.274397i	$-0.0884781\pi$
$229$	1.54545	+	3.58276i	0.102126	+	0.236755i	−0.859490	+	0.511152i	$0.829219\pi$
$230$	−1.13642	+	1.52648i	−0.0749333	+	0.100653i
$231$		0			0
$232$	−0.0118306	+	0.203123i	−0.000776714	+	0.0133357i
$233$	−18.1958	−	6.62273i	−1.19205	−	0.433869i	−0.331604	−	0.943419i	$-0.607590\pi$
$233$	−18.1958	−	6.62273i	−1.19205	−	0.433869i	−0.860441	+	0.509549i	$0.829812\pi$
$234$		0			0
$235$	−0.198584	+	0.0722788i	−0.0129542	+	0.00471495i
$236$	−4.36495	−	14.5799i	−0.284134	−	0.949074i
$237$		0			0
$238$	−5.12425	−	2.57350i	−0.332156	−	0.166815i
$239$	13.8167	−	3.27461i	0.893726	−	0.211817i	0.242004	−	0.970275i	$-0.422195\pi$
$239$	13.8167	−	3.27461i	0.893726	−	0.211817i	0.651722	+	0.758458i	$0.274047\pi$
$240$		0			0
$241$	11.0922	−	1.29650i	0.714513	−	0.0835146i	0.248934	−	0.968521i	$-0.419920\pi$
$241$	11.0922	−	1.29650i	0.714513	−	0.0835146i	0.465580	+	0.885006i	$0.345846\pi$
$242$	−0.708270			−0.0455293
$243$		0			0
$244$	−8.12090			−0.519888
$245$	14.7518	−	1.72424i	0.942457	−	0.110157i
$246$		0			0
$247$	−2.57984	+	0.611432i	−0.164151	+	0.0389045i
$248$	−1.22875	−	0.617101i	−0.0780256	−	0.0391859i
$249$		0			0
$250$	0.637655	+	2.12992i	0.0403289	+	0.134708i
$251$	8.61554	−	3.13580i	0.543808	−	0.197930i	−0.0554853	−	0.998460i	$-0.517671\pi$
$251$	8.61554	−	3.13580i	0.543808	−	0.197930i	0.599293	+	0.800530i	$0.295448\pi$
$252$		0			0
$253$	23.1630	+	8.43066i	1.45625	+	0.530031i
$254$	−0.206708	+	3.54903i	−0.0129700	+	0.222686i
$255$		0			0
$256$	7.92112	−	10.6399i	0.495070	−	0.664995i
$257$	−6.84056	−	15.8582i	−0.426703	−	0.989208i	−0.986971	−	0.160897i	$-0.948561\pi$
$257$	−6.84056	−	15.8582i	−0.426703	−	0.989208i	0.560269	−	0.828311i	$-0.310698\pi$
$258$		0			0
$259$	6.14865	−	3.08797i	0.382059	−	0.191877i
$260$	−3.81355	+	3.19995i	−0.236506	+	0.198452i
$261$		0			0
$262$	0.868782	+	0.728995i	0.0536735	+	0.0450375i
$263$	4.56819	+	1.08268i	0.281687	+	0.0667610i	0.369031	−	0.929417i	$-0.379690\pi$
$263$	4.56819	+	1.08268i	0.281687	+	0.0667610i	−0.0873438	+	0.996178i	$0.527838\pi$
$264$		0			0
$265$	−0.909790	−	15.6205i	−0.0558880	−	0.959560i
$266$	−0.360485	+	1.20410i	−0.0221028	+	0.0738284i
$267$		0			0
$268$	15.7782	+	21.1938i	0.963805	+	1.29461i
$269$	−6.52546	+	11.3024i	−0.397864	+	0.689121i	−0.993462	−	0.114162i	$-0.963582\pi$
$269$	−6.52546	+	11.3024i	−0.397864	+	0.689121i	0.595598	+	0.803283i	$0.296915\pi$
$270$		0			0
$271$	−11.8170	−	20.4676i	−0.717832	−	1.24332i	−0.961857	−	0.273552i	$-0.911801\pi$
$271$	−11.8170	−	20.4676i	−0.717832	−	1.24332i	0.244026	−	0.969769i	$-0.421532\pi$
$272$	−11.3541	+	26.3217i	−0.688441	+	1.59599i
$273$		0			0
$274$	−2.85941	−	3.03080i	−0.172743	−	0.183097i
$275$	8.00032	−	5.26189i	0.482438	−	0.317304i
$276$		0			0
$277$	−16.3299	+	17.3087i	−0.981170	+	1.03998i	0.0180238	+	0.999838i	$0.494263\pi$
$277$	−16.3299	+	17.3087i	−0.981170	+	1.03998i	−0.999194	+	0.0401420i	$0.987219\pi$
$278$	0.413935	−	2.34754i	0.0248262	−	0.140796i
$279$		0			0
$280$	0.826957	+	4.68990i	0.0494201	+	0.280275i
$281$	−11.5348	−	7.58657i	−0.688109	−	0.452577i	0.156699	−	0.987646i	$-0.449915\pi$
$281$	−11.5348	−	7.58657i	−0.688109	−	0.452577i	−0.844808	+	0.535070i	$0.820285\pi$
$282$		0			0
$283$	−14.5793	−	1.70408i	−0.866649	−	0.101297i	−0.328863	−	0.944378i	$-0.606665\pi$
$283$	−14.5793	−	1.70408i	−0.866649	−	0.101297i	−0.537787	+	0.843081i	$0.680739\pi$
$284$	4.98287	+	0.582414i	0.295679	+	0.0345599i
$285$		0			0
$286$	−0.962603	−	0.633114i	−0.0569199	−	0.0374368i
$287$	2.10332	+	11.9285i	0.124155	+	0.704119i
$288$		0			0
$289$	6.97903	−	39.5800i	0.410531	−	2.32824i
$290$	−0.0557843	+	0.0591279i	−0.00327577	+	0.00347211i
$291$		0			0
$292$	−9.24424	+	6.08003i	−0.540978	+	0.355807i
$293$	2.67199	+	2.83215i	0.156099	+	0.165456i	0.800704	−	0.599061i	$-0.204459\pi$
$293$	2.67199	+	2.83215i	0.156099	+	0.165456i	−0.644604	+	0.764517i	$0.722978\pi$
$294$		0			0
$295$	4.85972	−	11.2661i	0.282944	−	0.655938i
$296$	0.631572	+	1.09391i	0.0367094	+	0.0635825i
$297$		0			0
$298$	−0.917907	+	1.58986i	−0.0531729	+	0.0920982i
$299$	6.12388	+	8.22580i	0.354153	+	0.475710i
$300$		0			0
$301$	−5.65033	+	18.8734i	−0.325680	+	1.08785i
$302$	−0.103744	−	1.78122i	−0.00596980	−	0.102497i
$303$		0			0
$304$	6.11411	+	1.44907i	0.350668	+	0.0831099i
$305$	−5.01524	−	4.20829i	−0.287172	−	0.240966i
$306$		0			0
$307$	−0.636621	+	0.534188i	−0.0363339	+	0.0304877i	−0.660774	−	0.750585i	$-0.729772\pi$
$307$	−0.636621	+	0.534188i	−0.0363339	+	0.0304877i	0.624440	+	0.781073i	$0.285327\pi$
$308$	27.3174	−	13.7193i	1.55655	−	0.781731i
$309$		0			0
$310$	−0.217584	−	0.504417i	−0.0123580	−	0.0286490i
$311$	−6.56100	+	8.81295i	−0.372040	+	0.499737i	−0.948232	−	0.317578i	$-0.897131\pi$
$311$	−6.56100	+	8.81295i	−0.372040	+	0.499737i	0.576192	+	0.817314i	$0.304538\pi$
$312$		0			0
$313$	−1.00539	+	17.2620i	−0.0568282	+	0.975703i	0.842574	+	0.538581i	$0.181039\pi$
$313$	−1.00539	+	17.2620i	−0.0568282	+	0.975703i	−0.899402	+	0.437122i	$0.855998\pi$
$314$	1.30795	+	0.476057i	0.0738121	+	0.0268654i
$315$		0			0
$316$	14.9632	−	5.44614i	0.841743	−	0.306370i
$317$	−5.22233	−	17.4438i	−0.293315	−	0.979741i	−0.969926	−	0.243400i	$-0.921737\pi$
$317$	−5.22233	−	17.4438i	−0.293315	−	0.979741i	0.676611	−	0.736341i	$-0.263448\pi$
$318$		0			0
$319$	0.940925	+	0.472550i	0.0526817	+	0.0264577i
$320$	11.0511	−	2.61916i	0.617775	−	0.146415i
$321$		0			0
$322$	4.82875	−	0.564400i	0.269096	−	0.0314528i
$323$	−12.5359			−0.697518
$324$		0			0
$325$	3.98377			0.220980
$326$	0.928303	−	0.108503i	0.0514139	−	0.00600943i
$327$		0			0
$328$	−2.16372	+	0.512810i	−0.119471	+	0.0283152i
$329$	0.482448	+	0.242294i	0.0265982	+	0.0133581i
$330$		0			0
$331$	−5.18510	−	17.3194i	−0.284999	−	0.951962i	−0.973875	−	0.227083i	$-0.927081\pi$
$331$	−5.18510	−	17.3194i	−0.284999	−	0.951962i	0.688877	−	0.724879i	$-0.258104\pi$
$332$	−10.1256	+	3.68542i	−0.555714	+	0.202263i
$333$		0			0
$334$	0.767807	+	0.279459i	0.0420125	+	0.0152913i
$335$	−1.23854	+	21.2650i	−0.0676689	+	1.16183i
$336$		0			0
$337$	−12.5360	+	16.8388i	−0.682880	+	0.917267i	−0.999511	−	0.0312823i	$-0.990041\pi$
$337$	−12.5360	+	16.8388i	−0.682880	+	0.917267i	0.316631	+	0.948549i	$0.397448\pi$
$338$	0.774933	+	1.79650i	0.0421508	+	0.0977165i
$339$		0			0
$340$	−21.0345	+	10.5639i	−1.14076	+	0.572909i
$341$	−5.45079	+	4.57376i	−0.295177	+	0.247683i
$342$		0			0
$343$	−7.36564	−	6.18050i	−0.397707	−	0.333716i
$344$	−3.51929	−	0.834086i	−0.189747	−	0.0449709i
$345$		0			0
$346$	0.174786	+	3.00096i	0.00939655	+	0.161333i
$347$	−5.84820	+	19.5344i	−0.313948	+	1.04866i	0.644788	+	0.764361i	$0.276946\pi$
$347$	−5.84820	+	19.5344i	−0.313948	+	1.04866i	−0.958736	+	0.284298i	$0.908240\pi$
$348$		0			0
$349$	10.5755	+	14.2053i	0.566093	+	0.760395i	0.989341	−	0.145619i	$-0.0465175\pi$
$349$	10.5755	+	14.2053i	0.566093	+	0.760395i	−0.423248	+	0.906014i	$0.639110\pi$
$350$	0.944298	−	1.63557i	0.0504748	−	0.0874250i
$351$		0			0
$352$	4.22137	+	7.31163i	0.225000	+	0.389711i
$353$	−8.23144	+	19.0826i	−0.438115	+	1.01567i	0.545943	+	0.837822i	$0.316171\pi$
$353$	−8.23144	+	19.0826i	−0.438115	+	1.01567i	−0.984059	+	0.177844i	$0.943088\pi$
$354$		0			0
$355$	2.77547	+	2.94183i	0.147307	+	0.156136i
$356$	−11.0748	+	7.28400i	−0.586963	+	0.386051i
$357$		0			0
$358$	2.47968	−	2.62830i	0.131055	−	0.138910i
$359$	−3.40920	+	19.3346i	−0.179931	+	1.02044i	0.752366	+	0.658745i	$0.228912\pi$
$359$	−3.40920	+	19.3346i	−0.179931	+	1.02044i	−0.932297	+	0.361693i	$0.882199\pi$
$360$		0			0
$361$	−2.82216	−	16.0053i	−0.148535	−	0.842383i
$362$	0.0237125	+	0.0155960i	0.00124630	+	0.000819707i
$363$		0			0
$364$	12.6317	+	1.47643i	0.662080	+	0.0773861i
$365$	−8.85968	−	1.03555i	−0.463737	−	0.0542031i
$366$		0			0
$367$	27.2424	+	17.9176i	1.42204	+	0.935292i	0.999582	+	0.0289098i	$0.00920357\pi$
$367$	27.2424	+	17.9176i	1.42204	+	0.935292i	0.422460	+	0.906382i	$0.361167\pi$
$368$	−4.22035	−	23.9348i	−0.220001	−	1.24769i
$369$		0			0
$370$	−0.0876322	+	0.496987i	−0.00455578	+	0.0258371i
$371$	−27.4309	+	29.0750i	−1.42414	+	1.50950i
$372$		0			0
$373$	14.8326	−	9.75554i	0.768002	−	0.505123i	−0.104029	−	0.994574i	$-0.533173\pi$
$373$	14.8326	−	9.75554i	0.768002	−	0.505123i	0.872031	+	0.489451i	$0.162803\pi$
$374$	−3.73837	−	3.96244i	−0.193306	−	0.204893i
$375$		0			0
$376$	−0.0392560	+	0.0910056i	−0.00202447	+	0.00469326i
$377$	0.219025	+	0.379362i	0.0112803	+	0.0195381i
$378$		0			0
$379$	−13.5735	+	23.5099i	−0.697222	+	1.20762i	0.272204	+	0.962240i	$0.412247\pi$
$379$	−13.5735	+	23.5099i	−0.697222	+	1.20762i	−0.969426	+	0.245384i	$0.921086\pi$
$380$	3.08102	+	4.13853i	0.158053	+	0.212302i
$381$		0			0
$382$	0.575397	−	1.92196i	0.0294398	−	0.0983359i
$383$	−2.06766	−	35.5003i	−0.105652	−	1.81398i	−0.469945	−	0.882696i	$-0.655726\pi$
$383$	−2.06766	−	35.5003i	−0.105652	−	1.81398i	0.364292	−	0.931285i	$-0.381311\pi$
$384$		0			0
$385$	23.9799	+	5.68333i	1.22213	+	0.289650i
$386$	−2.27802	−	1.91148i	−0.115948	−	0.0972919i
$387$		0			0
$388$	−2.81703	+	2.36377i	−0.143013	+	0.120002i
$389$	18.1831	−	9.13191i	0.921921	−	0.463006i	0.0764780	−	0.997071i	$-0.475633\pi$
$389$	18.1831	−	9.13191i	0.921921	−	0.463006i	0.845443	+	0.534065i	$0.179336\pi$
$390$		0			0
$391$	19.2051	+	44.5225i	0.971245	+	2.25160i
$392$	4.15954	−	5.58723i	0.210088	−	0.282197i
$393$		0			0
$394$	0.0134162	−	0.230347i	0.000675899	−	0.0116047i
$395$	12.0630	+	4.39059i	0.606957	+	0.220914i
$396$		0			0
$397$	−24.9491	+	9.08072i	−1.25216	+	0.455748i	−0.881130	−	0.472874i	$-0.843217\pi$
$397$	−24.9491	+	9.08072i	−1.25216	+	0.455748i	−0.371028	+	0.928622i	$0.620995\pi$
$398$	0.125884	+	0.420481i	0.00630998	+	0.0210768i
$399$		0			0
$400$	−8.43713	−	4.23729i	−0.421857	−	0.211864i
$401$	25.0296	−	5.93213i	1.24992	−	0.296236i	0.448198	−	0.893934i	$-0.352066\pi$
$401$	25.0296	−	5.93213i	1.24992	−	0.296236i	0.801722	+	0.597698i	$0.203918\pi$
$402$		0			0
$403$	−2.94026	+	0.343668i	−0.146465	+	0.0171193i
$404$	−32.7795			−1.63084
$405$		0			0
$406$	0.207667			0.0103063
$407$	6.49244	−	0.758857i	0.321818	−	0.0376152i
$408$		0			0
$409$	−27.1005	+	6.42293i	−1.34003	+	0.317593i	−0.837250	−	0.546820i	$-0.815838\pi$
$409$	−27.1005	+	6.42293i	−1.34003	+	0.317593i	−0.502782	+	0.864413i	$0.667690\pi$
$410$	−0.793902	−	0.398713i	−0.0392080	−	0.0196910i
$411$		0			0
$412$	−3.24365	−	10.8345i	−0.159803	−	0.533780i
$413$	−29.4542	+	10.7204i	−1.44934	+	0.527518i
$414$		0			0
$415$	−8.16308	−	2.97112i	−0.400710	−	0.145846i
$416$	−0.204231	+	3.50651i	−0.0100133	+	0.171921i
$417$		0			0
$418$	−0.713060	+	0.957806i	−0.0348769	+	0.0468478i
$419$	−0.426987	−	0.989868i	−0.0208597	−	0.0483582i	0.907468	−	0.420122i	$-0.138013\pi$
$419$	−0.426987	−	0.989868i	−0.0208597	−	0.0483582i	−0.928328	+	0.371763i	$0.878753\pi$
$420$		0			0
$421$	7.02193	−	3.52655i	0.342228	−	0.171873i	−0.269381	−	0.963034i	$-0.586819\pi$
$421$	7.02193	−	3.52655i	0.342228	−	0.171873i	0.611609	+	0.791160i	$0.290523\pi$
$422$	1.63479	−	1.37175i	0.0795801	−	0.0667757i
$423$		0			0
$424$	−5.62145	−	4.71695i	−0.273002	−	0.229076i
$425$	18.3284	+	4.34392i	0.889059	+	0.210711i
$426$		0			0
$427$	0.972481	+	16.6969i	0.0470617	+	0.808018i
$428$	0.913599	−	3.05163i	0.0441605	−	0.147506i
$429$		0			0
$430$	−0.862884	−	1.15905i	−0.0416119	−	0.0558945i
$431$	13.8447	−	23.9798i	0.666877	−	1.15507i	−0.311895	−	0.950116i	$-0.600964\pi$
$431$	13.8447	−	23.9798i	0.666877	−	1.15507i	0.978773	−	0.204949i	$-0.0657028\pi$
$432$		0			0
$433$	9.89513	+	17.1389i	0.475530	+	0.823642i	0.999607	−	0.0280289i	$-0.00892305\pi$
$433$	9.89513	+	17.1389i	0.475530	+	0.823642i	−0.524077	+	0.851671i	$0.675590\pi$
$434$	−0.555853	+	1.28861i	−0.0266818	+	0.0618553i
$435$		0			0
$436$	−15.5205	−	16.4508i	−0.743297	−	0.787849i
$437$	8.87987	−	5.84038i	0.424782	−	0.279383i
$438$		0			0
$439$	23.0859	−	24.4696i	1.10183	−	1.16787i	0.117220	−	0.993106i	$-0.462602\pi$
$439$	23.0859	−	24.4696i	1.10183	−	1.16787i	0.984610	−	0.174766i	$-0.0559169\pi$
$440$	−0.785626	+	4.45551i	−0.0374533	+	0.212408i
$441$		0			0
$442$	−0.393552	−	2.23195i	−0.0187194	−	0.106163i
$443$	−13.2562	−	8.71877i	−0.629823	−	0.414241i	0.194069	−	0.980988i	$-0.437831\pi$
$443$	−13.2562	−	8.71877i	−0.629823	−	0.414241i	−0.823892	+	0.566747i	$0.808202\pi$
$444$		0			0
$445$	−10.6141	−	1.24061i	−0.503155	−	0.0588104i
$446$	−2.81504	−	0.329031i	−0.133296	−	0.0155801i
$447$		0			0
$448$	−24.2407	−	15.9433i	−1.14526	−	0.753252i
$449$	−0.153072	−	0.868114i	−0.00722391	−	0.0409688i	0.980983	−	0.194095i	$-0.0621770\pi$
$449$	−0.153072	−	0.868114i	−0.00722391	−	0.0409688i	−0.988207	+	0.153126i	$0.951066\pi$
$450$		0			0
$451$	−1.99820	+	11.3324i	−0.0940916	+	0.533620i
$452$	11.7722	−	12.4778i	0.553718	−	0.586907i
$453$		0			0
$454$	3.33115	−	2.19093i	0.156339	−	0.102826i
$455$	7.03588	+	7.45760i	0.329847	+	0.349618i
$456$		0			0
$457$	−7.35564	+	17.0523i	−0.344082	+	0.797672i	0.655032	+	0.755601i	$0.272655\pi$
$457$	−7.35564	+	17.0523i	−0.344082	+	0.797672i	−0.999115	+	0.0420714i	$0.986604\pi$
$458$	0.365551	+	0.633152i	0.0170811	+	0.0295853i
$459$		0			0
$460$	9.97822	−	17.2828i	0.465237	−	0.805814i
$461$	1.83333	+	2.46259i	0.0853868	+	0.114694i	0.842764	−	0.538283i	$-0.180927\pi$
$461$	1.83333	+	2.46259i	0.0853868	+	0.114694i	−0.757377	+	0.652978i	$0.773520\pi$
$462$		0			0
$463$	8.21916	−	27.4539i	0.381977	−	1.27589i	−0.523693	−	0.851907i	$-0.675446\pi$
$463$	8.21916	−	27.4539i	0.381977	−	1.27589i	0.905670	−	0.423984i	$-0.139369\pi$
$464$	−0.0603636	−	1.03640i	−0.00280231	−	0.0481138i
$465$		0			0
$466$	−3.53039	−	0.836718i	−0.163542	−	0.0387602i
$467$	−10.6188	−	8.91027i	−0.491382	−	0.412318i	0.363139	−	0.931735i	$-0.381705\pi$
$467$	−10.6188	−	8.91027i	−0.491382	−	0.412318i	−0.854521	+	0.519417i	$0.826149\pi$
$468$		0			0
$469$	41.6856	−	34.9784i	1.92486	−	1.61515i
$470$	−0.0353853	+	0.0177712i	−0.00163220	+	0.000819723i
$471$		0			0
$472$	−2.27916	−	5.28369i	−0.104907	−	0.243202i
$473$	−11.1767	+	15.0129i	−0.513904	+	0.690293i
$474$		0			0
$475$	0.240069	−	4.12182i	0.0110151	−	0.189122i
$476$	56.5056	+	20.5663i	2.58993	+	0.942657i
$477$		0			0
$478$	2.50012	−	0.909969i	0.114353	−	0.0416210i
$479$	7.29590	+	24.3700i	0.333358	+	1.11349i	0.946280	+	0.323350i	$0.104809\pi$
$479$	7.29590	+	24.3700i	0.333358	+	1.11349i	−0.612922	+	0.790144i	$0.710006\pi$
$480$		0			0
$481$	2.43019	+	1.22049i	0.110807	+	0.0556495i
$482$	2.03612	−	0.482569i	0.0927426	−	0.0219804i
$483$		0			0
$484$	7.37711	−	0.862261i	0.335323	−	0.0391937i
$485$	−2.96463			−0.134617
$486$		0			0
$487$	−1.98229			−0.0898263			−0.0449132	−	0.998991i	$-0.514301\pi$
$487$	−1.98229			−0.0898263			−0.0449132	+	0.998991i	$0.514301\pi$
$488$	−3.04969	+	0.356457i	−0.138053	+	0.0161361i
$489$		0			0
$490$	2.70788	−	0.641778i	0.122329	−	0.0289926i
$491$	0.418541	+	0.210199i	0.0188885	+	0.00948615i	0.458218	−	0.888840i	$-0.348488\pi$
$491$	0.418541	+	0.210199i	0.0188885	+	0.00948615i	−0.439330	+	0.898326i	$0.644784\pi$
$492$		0			0
$493$	0.594025	+	1.98418i	0.0267535	+	0.0893630i
$494$	−0.466820	+	0.169909i	−0.0210032	+	0.00764456i
$495$		0			0
$496$	6.59265	+	2.39953i	0.296019	+	0.107742i
$497$	0.600763	−	10.3147i	0.0269479	−	0.462678i
$498$		0			0
$499$	−14.1463	+	19.0018i	−0.633276	+	0.850638i	−0.996716	−	0.0809800i	$-0.974195\pi$
$499$	−14.1463	+	19.0018i	−0.633276	+	0.850638i	0.363439	+	0.931618i	$0.381602\pi$
$500$	−9.23461	−	21.4082i	−0.412984	−	0.957405i
$501$		0			0
$502$	1.53518	−	0.770998i	0.0685186	−	0.0344113i
$503$	0.513245	−	0.430663i	0.0228844	−	0.0192023i	−0.631274	−	0.775560i	$-0.717468\pi$
$503$	0.513245	−	0.430663i	0.0228844	−	0.0192023i	0.654158	+	0.756358i	$0.273023\pi$
$504$		0			0
$505$	−20.2437	−	16.9865i	−0.900834	−	0.755889i
$506$	4.49415	+	1.06513i	0.199789	+	0.0473509i
$507$		0			0
$508$	−2.16766	−	37.2172i	−0.0961742	−	1.65125i
$509$	−2.09930	+	7.01215i	−0.0930499	+	0.310808i	−0.991826	−	0.127600i	$-0.959273\pi$
$509$	−2.09930	+	7.01215i	−0.0930499	+	0.310808i	0.898776	+	0.438409i	$0.144458\pi$
$510$		0			0
$511$	13.6078	+	18.2784i	0.601971	+	0.808588i
$512$	6.97825	−	12.0867i	0.308398	−	0.534161i
$513$		0			0
$514$	−1.61802	−	2.80249i	−0.0713678	−	0.123613i
$515$	3.61132	−	8.37199i	0.159134	−	0.368914i
$516$		0			0
$517$	0.351967	+	0.373063i	0.0154795	+	0.0164073i
$518$	1.07712	−	0.708436i	0.0473261	−	0.0311269i
$519$		0			0
$520$	−1.29167	+	1.36909i	−0.0566433	+	0.0600384i
$521$	−0.747254	+	4.23789i	−0.0327378	+	0.185665i	−0.996791	−	0.0800423i	$-0.974494\pi$
$521$	−0.747254	+	4.23789i	−0.0327378	+	0.185665i	0.964054	+	0.265708i	$0.0856056\pi$
$522$		0			0
$523$	−1.42678	−	8.09165i	−0.0623885	−	0.353823i	−0.999981	−	0.00608816i	$-0.998062\pi$
$523$	−1.42678	−	8.09165i	−0.0623885	−	0.353823i	0.937593	−	0.347735i	$-0.113049\pi$
$524$	−9.93644	−	6.53530i	−0.434076	−	0.285496i
$525$		0			0
$526$	0.873715	+	0.102123i	0.0380958	+	0.00445276i
$527$	−13.9022	−	1.62494i	−0.605590	−	0.0707833i
$528$		0			0
$529$	−15.1304	−	9.95144i	−0.657845	−	0.432671i
$530$	−0.509102	−	2.88726i	−0.0221140	−	0.125415i
$531$		0			0
$532$	2.28880	−	12.9804i	0.0992320	−	0.562773i
$533$	−3.28529	+	3.48220i	−0.142302	+	0.150831i
$534$		0			0
$535$	2.14558	−	1.41117i	0.0927616	−	0.0610103i
$536$	6.85553	+	7.26644i	0.296114	+	0.313862i
$537$		0			0
$538$	−0.968564	+	2.24538i	−0.0417578	+	0.0968054i
$539$	−18.0230	−	31.2167i	−0.776305	−	1.34460i
$540$		0			0
$541$	−1.90293	+	3.29597i	−0.0818132	+	0.141705i	−0.904029	−	0.427472i	$-0.859404\pi$
$541$	−1.90293	+	3.29597i	−0.0818132	+	0.141705i	0.822216	+	0.569176i	$0.192738\pi$
$542$	−2.64443	−	3.55208i	−0.113588	−	0.152575i
$543$		0			0
$544$	−4.76313	+	15.9100i	−0.204217	+	0.682134i
$545$	−1.06016	−	18.2023i	−0.0454125	−	0.779702i
$546$		0			0
$547$	−28.0332	−	6.64400i	−1.19861	−	0.284077i	−0.417624	−	0.908620i	$-0.637137\pi$
$547$	−28.0332	−	6.64400i	−1.19861	−	0.284077i	−0.780990	+	0.624543i	$0.785285\pi$
$548$	33.4725	+	28.0867i	1.42987	+	1.19981i
$549$		0			0
$550$	1.37444	−	1.15329i	0.0586064	−	0.0491766i
$551$	0.405706	−	0.203753i	0.0172837	−	0.00868018i
$552$		0			0
$553$	−12.9893	−	30.1126i	−0.552361	−	1.28052i
$554$	−2.66257	+	3.57646i	−0.113122	+	0.151949i
$555$		0			0
$556$	−1.45347	+	24.9552i	−0.0616410	+	1.05833i
$557$	0.617137	+	0.224620i	0.0261489	+	0.00951744i	0.355062	−	0.934843i	$-0.384460\pi$
$557$	0.617137	+	0.224620i	0.0261489	+	0.00951744i	−0.328913	+	0.944360i	$0.606682\pi$
$558$		0			0
$559$	−7.31706	+	2.66319i	−0.309479	+	0.112641i
$560$	−6.96894	−	23.2779i	−0.294491	−	0.983669i
$561$		0			0
$562$	−2.31171	−	1.16099i	−0.0975138	−	0.0489733i
$563$	9.32459	−	2.20997i	0.392985	−	0.0931391i	−0.0293726	−	0.999569i	$-0.509351\pi$
$563$	9.32459	−	2.20997i	0.392985	−	0.0931391i	0.422357	+	0.906429i	$0.361203\pi$
$564$		0			0
$565$	13.7362	−	1.60554i	0.577888	−	0.0675454i
$566$	−2.75035			−0.115606
$567$		0			0
$568$	1.89681			0.0795884
$569$	25.1871	−	2.94395i	1.05590	−	0.123417i	0.429614	−	0.903013i	$-0.358650\pi$
$569$	25.1871	−	2.94395i	1.05590	−	0.123417i	0.626283	+	0.779596i	$0.284576\pi$
$570$		0			0
$571$	7.87959	−	1.86750i	0.329750	−	0.0781523i	−0.0624060	−	0.998051i	$-0.519877\pi$
$571$	7.87959	−	1.86750i	0.329750	−	0.0781523i	0.392156	+	0.919899i	$0.371729\pi$
$572$	10.7969	+	5.42242i	0.451442	+	0.226723i
$573$		0			0
$574$	0.650915	+	2.17421i	0.0271687	+	0.0907497i
$575$	−15.0068	+	5.46202i	−0.625826	+	0.227782i
$576$		0			0
$577$	2.58521	+	0.940940i	0.107624	+	0.0391718i	0.395271	−	0.918565i	$-0.370651\pi$
$577$	2.58521	+	0.940940i	0.107624	+	0.0391718i	−0.287647	+	0.957736i	$0.592873\pi$
$578$	0.437865	−	7.51786i	0.0182128	−	0.312702i
$579$		0			0
$580$	0.509048	−	0.683770i	0.0211371	−	0.0283920i
$581$	8.78988	+	20.3772i	0.364666	+	0.845390i
$582$		0			0
$583$	−33.9355	+	17.0431i	−1.40547	+	0.705852i
$584$	−3.20466	+	2.68903i	−0.132610	+	0.111273i
$585$		0			0
$586$	0.558878	+	0.468954i	0.0230870	+	0.0193723i
$587$	−40.9529	−	9.70602i	−1.69031	−	0.400610i	−0.730867	−	0.682520i	$-0.760884\pi$
$587$	−40.9529	−	9.70602i	−1.69031	−	0.400610i	−0.959441	+	0.281910i	$0.909032\pi$
$588$		0			0
$589$	0.178391	+	3.06286i	0.00735048	+	0.126203i
$590$	0.659352	−	2.20239i	0.0271451	−	0.0906709i
$591$		0			0
$592$	−3.84869	−	5.16968i	−0.158180	−	0.212473i
$593$	−3.28564	+	5.69090i	−0.134925	+	0.233697i	−0.925569	−	0.378579i	$-0.876413\pi$
$593$	−3.28564	+	5.69090i	−0.134925	+	0.233697i	0.790644	+	0.612277i	$0.209746\pi$
$594$		0			0
$595$	24.2387	+	41.9826i	0.993689	+	1.72112i
$596$	7.62510	−	17.6770i	0.312336	−	0.724076i
$597$		0			0
$598$	1.31862	+	1.39765i	0.0539223	+	0.0571543i
$599$	12.4533	−	8.19068i	0.508829	−	0.334662i	−0.268998	−	0.963141i	$-0.586692\pi$
$599$	12.4533	−	8.19068i	0.508829	−	0.334662i	0.777827	+	0.628479i	$0.216322\pi$
$600$		0			0
$601$	17.5194	−	18.5695i	0.714633	−	0.757467i	−0.263677	−	0.964611i	$-0.584935\pi$
$601$	17.5194	−	18.5695i	0.714633	−	0.757467i	0.978310	+	0.207144i	$0.0664169\pi$
$602$	−0.641010	+	3.63535i	−0.0261256	+	0.148166i
$603$		0			0
$604$	3.24905	+	18.4263i	0.132202	+	0.749754i
$605$	5.00272	+	3.29034i	0.203390	+	0.133771i
$606$		0			0
$607$	29.8398	+	3.48777i	1.21116	+	0.141564i	0.697599	−	0.716489i	$-0.254252\pi$
$607$	29.8398	+	3.48777i	1.21116	+	0.141564i	0.513561	+	0.858053i	$0.328326\pi$
$608$	3.61571	+	0.422616i	0.146636	+	0.0171393i
$609$		0			0
$610$	−1.02490	−	0.674089i	−0.0414971	−	0.0272931i
$611$	0.0370529	+	0.210137i	0.00149900	+	0.00850125i
$612$		0			0
$613$	−2.50656	+	14.2154i	−0.101239	+	0.574154i	0.891417	+	0.453183i	$0.149712\pi$
$613$	−2.50656	+	14.2154i	−0.101239	+	0.574154i	−0.992656	+	0.120970i	$0.961399\pi$
$614$	−0.106858	+	0.113263i	−0.00431245	+	0.00457093i
$615$		0			0
$616$	9.65646	−	6.35116i	0.389070	−	0.255895i
$617$	9.33958	+	9.89938i	0.375997	+	0.398534i	0.887545	−	0.460721i	$-0.152409\pi$
$617$	9.33958	+	9.89938i	0.375997	+	0.398534i	−0.511548	+	0.859255i	$0.670928\pi$
$618$		0			0
$619$	8.65504	−	20.0646i	0.347875	−	0.806466i	−0.651001	−	0.759077i	$-0.725651\pi$
$619$	8.65504	−	20.0646i	0.347875	−	0.806466i	0.998877	−	0.0473890i	$-0.0150901\pi$
$620$	2.88037	+	4.98895i	0.115679	+	0.200361i
$621$		0			0
$622$	−1.02933	+	1.78285i	−0.0412724	+	0.0714859i
$623$	16.3024	+	21.8979i	0.653140	+	0.877320i
$624$		0			0
$625$	1.81903	−	6.07598i	0.0727612	−	0.243039i
$626$	0.188383	+	3.23441i	0.00752929	+	0.129273i
$627$		0			0
$628$	−14.2028	−	3.36612i	−0.566753	−	0.134323i
$629$	9.84993	+	8.26507i	0.392742	+	0.329550i
$630$		0			0
$631$	−18.5327	+	15.5508i	−0.737775	+	0.619066i	−0.932239	−	0.361843i	$-0.882148\pi$
$631$	−18.5327	+	15.5508i	−0.737775	+	0.619066i	0.194464	+	0.980910i	$0.437703\pi$
$632$	5.38014	−	2.70201i	0.214011	−	0.107480i
$633$		0			0
$634$	−1.35135	−	3.13278i	−0.0536689	−	0.124419i
$635$	17.9474	−	24.1076i	0.712223	−	0.956681i
$636$		0			0
$637$	0.871957	−	14.9709i	0.0345482	−	0.593170i
$638$	0.185390	+	0.0674764i	0.00733966	+	0.00267142i
$639$		0			0
$640$	8.53752	−	3.10740i	0.337475	−	0.122831i
$641$	−10.2534	−	34.2489i	−0.404987	−	1.35275i	−0.880919	−	0.473267i	$-0.843074\pi$
$641$	−10.2534	−	34.2489i	−0.404987	−	1.35275i	0.475932	−	0.879482i	$-0.342111\pi$
$642$		0			0
$643$	40.5491	+	20.3645i	1.59910	+	0.803099i	0.999997	+	0.00242755i	$0.000772715\pi$
$643$	40.5491	+	20.3645i	1.59910	+	0.803099i	0.599104	+	0.800671i	$0.295524\pi$
$644$	−49.6076	+	11.7572i	−1.95481	+	0.463299i
$645$		0			0
$646$	−2.33300	+	0.272689i	−0.0917907	+	0.0107288i
$647$	18.8974			0.742935			0.371468	−	0.928446i	$-0.378855\pi$
$647$	18.8974			0.742935			0.371468	+	0.928446i	$0.378855\pi$
$648$		0			0
$649$	−29.7779			−1.16888
$650$	0.741401	−	0.0866573i	0.0290801	−	0.00339898i
$651$		0			0
$652$	−9.53680	+	2.26026i	−0.373490	+	0.0885188i
$653$	−19.4303	−	9.75824i	−0.760365	−	0.381870i	0.0259759	−	0.999663i	$-0.491731\pi$
$653$	−19.4303	−	9.75824i	−0.760365	−	0.381870i	−0.786341	+	0.617793i	$0.788027\pi$
$654$		0			0
$655$	−2.74985	−	9.18513i	−0.107445	−	0.358893i
$656$	10.6616	−	3.88051i	0.416266	−	0.151509i
$657$		0			0
$658$	0.0950565	+	0.0345978i	0.00370569	+	0.00134876i
$659$	−0.951940	+	16.3442i	−0.0370823	+	0.636678i	0.927651	+	0.373449i	$0.121825\pi$
$659$	−0.951940	+	16.3442i	−0.0370823	+	0.636678i	−0.964733	+	0.263230i	$0.915212\pi$
$660$		0			0
$661$	12.3565	−	16.5977i	0.480613	−	0.645576i	−0.494002	−	0.869461i	$-0.664467\pi$
$661$	12.3565	−	16.5977i	0.480613	−	0.645576i	0.974616	+	0.223885i	$0.0718740\pi$
$662$	−1.34172	−	3.11045i	−0.0521472	−	0.120891i
$663$		0			0
$664$	−3.64075	+	1.82846i	−0.141289	+	0.0709578i
$665$	8.14001	−	6.83028i	0.315656	−	0.264867i
$666$		0			0
$667$	−1.34519	−	1.12875i	−0.0520860	−	0.0437054i
$668$	−8.33744	−	1.97601i	−0.322585	−	0.0764541i
$669$		0			0
$670$	0.232068	+	3.98446i	0.00896559	+	0.153933i
$671$	−4.55709	+	15.2217i	−0.175924	+	0.587628i
$672$		0			0
$673$	−14.3433	−	19.2664i	−0.552894	−	0.742666i	0.434548	−	0.900649i	$-0.356908\pi$
$673$	−14.3433	−	19.2664i	−0.552894	−	0.742666i	−0.987442	+	0.157983i	$0.949501\pi$
$674$	−1.96673	+	3.40647i	−0.0757555	+	0.131212i
$675$		0			0
$676$	−10.2585	−	17.7683i	−0.394559	−	0.683396i
$677$	−17.9649	+	41.6474i	−0.690449	+	1.60064i	0.104896	+	0.994483i	$0.466549\pi$
$677$	−17.9649	+	41.6474i	−0.690449	+	1.60064i	−0.795345	+	0.606157i	$0.792710\pi$
$678$		0			0
$679$	5.19733	+	5.50884i	0.199455	+	0.211410i
$680$	−7.43551	+	4.89041i	−0.285139	+	0.187539i
$681$		0			0
$682$	−0.914929	+	0.969768i	−0.0350344	+	0.0371343i
$683$	3.38555	−	19.2004i	0.129544	−	0.734683i	−0.848960	−	0.528457i	$-0.822771\pi$
$683$	3.38555	−	19.2004i	0.129544	−	0.734683i	0.978504	−	0.206226i	$-0.0661181\pi$
$684$		0			0
$685$	6.11698	+	34.6911i	0.233718	+	1.32548i
$686$	−1.50522	−	0.990002i	−0.0574697	−	0.0377984i
$687$		0			0
$688$	18.3293	+	2.14238i	0.698797	+	0.0816777i
$689$	−15.6919	−	1.83412i	−0.597815	−	0.0698746i
$690$		0			0
$691$	−17.1519	−	11.2810i	−0.652490	−	0.429149i	0.179638	−	0.983733i	$-0.442507\pi$
$691$	−17.1519	−	11.2810i	−0.652490	−	0.429149i	−0.832128	+	0.554584i	$0.812878\pi$
$692$	−5.47393	−	31.0442i	−0.208088	−	1.18012i
$693$		0			0
$694$	−0.663458	+	3.76266i	−0.0251845	+	0.142828i
$695$	−13.8295	+	14.6584i	−0.524583	+	0.556025i
$696$		0			0
$697$	−18.9118	+	12.4385i	−0.716337	+	0.471142i
$698$	2.27715	+	2.41364i	0.0861916	+	0.0913577i
$699$		0			0
$700$	−7.84432	+	18.1852i	−0.296488	+	0.687335i
$701$	3.27119	+	5.66587i	0.123551	+	0.213997i	0.921166	−	0.389171i	$-0.127238\pi$
$701$	3.27119	+	5.66587i	0.123551	+	0.213997i	−0.797615	+	0.603168i	$0.793905\pi$
$702$		0			0
$703$	1.40923	−	2.44085i	0.0531500	−	0.0920585i
$704$	−16.4599	−	22.1095i	−0.620356	−	0.833283i
$705$		0			0
$706$	−1.11682	+	3.73043i	−0.0420320	+	0.140397i
$707$	3.92536	+	67.3958i	0.147628	+	2.53468i
$708$		0			0
$709$	9.33823	+	2.21320i	0.350705	+	0.0831185i	0.402193	−	0.915555i	$-0.368248\pi$
$709$	9.33823	+	2.21320i	0.350705	+	0.0831185i	−0.0514879	+	0.998674i	$0.516396\pi$
$710$	0.580522	+	0.487116i	0.0217866	+	0.0182811i
$711$		0			0
$712$	−3.83925	+	3.22152i	−0.143882	+	0.120731i
$713$	10.6047	−	5.32589i	0.397150	−	0.199456i
$714$		0			0
$715$	3.85796	+	8.94375i	0.144279	+	0.334477i
$716$	−22.6278	+	30.3943i	−0.845639	+	1.13589i
$717$		0			0
$718$	−0.213894	+	3.67242i	−0.00798245	+	0.137053i
$719$	−24.3548	−	8.86441i	−0.908280	−	0.330587i	−0.154714	−	0.987959i	$-0.549446\pi$
$719$	−24.3548	−	8.86441i	−0.908280	−	0.330587i	−0.753566	+	0.657372i	$0.771668\pi$
$720$		0			0
$721$	−21.8878	+	7.96650i	−0.815143	+	0.296688i
$722$	−0.873374	−	2.91727i	−0.0325036	−	0.108570i
$723$		0			0
$724$	−0.265969	−	0.133575i	−0.00988466	−	0.00496426i
$725$	−0.663775	+	0.157318i	−0.0246520	+	0.00584263i
$726$		0			0
$727$	20.6920	−	2.41855i	0.767424	−	0.0896990i	0.276632	−	0.960976i	$-0.410782\pi$
$727$	20.6920	−	2.41855i	0.767424	−	0.0896990i	0.490792	+	0.871277i	$0.336708\pi$
$728$	4.80845			0.178213
$729$		0			0
$730$	−1.67136			−0.0618597
$731$	−36.5680	+	4.27419i	−1.35252	+	0.158087i
$732$		0			0
$733$	8.29536	−	1.96604i	0.306396	−	0.0726172i	−0.0745416	−	0.997218i	$-0.523749\pi$
$733$	8.29536	−	1.96604i	0.306396	−	0.0726172i	0.380938	+	0.924601i	$0.375601\pi$
$734$	5.45970	+	2.74197i	0.201521	+	0.101208i
$735$		0			0
$736$	−4.03833	−	13.4890i	−0.148855	−	0.497210i
$737$	48.5793	−	17.6814i	1.78944	−	0.651304i
$738$		0			0
$739$	34.6163	+	12.5993i	1.27338	+	0.463473i	0.888238	−	0.459384i	$-0.151930\pi$
$739$	34.6163	+	12.5993i	1.27338	+	0.463473i	0.385143	+	0.922857i	$0.374152\pi$
$740$	0.307708	−	5.28314i	0.0113116	−	0.194212i
$741$		0			0
$742$	−4.47257	+	6.00770i	−0.164193	+	0.220550i
$743$	11.8642	+	27.5043i	0.435256	+	1.00904i	0.984819	+	0.173584i	$0.0555349\pi$
$743$	11.8642	+	27.5043i	0.435256	+	1.00904i	−0.549563	+	0.835452i	$0.685206\pi$
$744$		0			0
$745$	13.8693	−	6.96543i	0.508133	−	0.255194i
$746$	2.54821	−	2.13820i	0.0932966	−	0.0782852i
$747$		0			0
$748$	43.7615	+	36.7203i	1.60008	+	1.34263i
$749$	−6.38367	−	1.51296i	−0.233254	−	0.0552822i
$750$		0			0
$751$	−0.407517	−	6.99680i	−0.0148705	−	0.255317i	−0.997548	−	0.0699909i	$-0.977703\pi$
$751$	−0.407517	−	6.99680i	−0.0148705	−	0.255317i	0.982677	−	0.185326i	$-0.0593341\pi$
$752$	0.145036	−	0.484455i	0.00528894	−	0.0176663i
$753$		0			0
$754$	0.0490137	+	0.0658368i	0.00178497	+	0.00239764i
$755$	−7.54205	+	13.0632i	−0.274483	+	0.475419i
$756$		0			0
$757$	−11.1739	−	19.3538i	−0.406123	−	0.703426i	0.588328	−	0.808622i	$-0.299786\pi$
$757$	−11.1739	−	19.3538i	−0.406123	−	0.703426i	−0.994452	+	0.105196i	$0.966453\pi$
$758$	−2.01469	+	4.67057i	−0.0731768	+	0.169643i
$759$		0			0
$760$	1.33869	+	1.41893i	0.0485593	+	0.0514699i
$761$	2.68760	−	1.76766i	0.0974254	−	0.0640777i	−0.499861	−	0.866105i	$-0.666616\pi$
$761$	2.68760	−	1.76766i	0.0974254	−	0.0640777i	0.597287	+	0.802028i	$0.296245\pi$
$762$		0			0
$763$	−31.9648	+	33.8807i	−1.15720	+	1.22656i
$764$	−3.65332	+	20.7190i	−0.132172	+	0.749587i
$765$		0			0
$766$	−1.15702	−	6.56181i	−0.0418050	−	0.237088i
$767$	−10.3505	−	6.80764i	−0.373735	−	0.245809i
$768$		0			0
$769$	5.58041	+	0.652257i	0.201235	+	0.0235210i	0.216113	−	0.976368i	$-0.430662\pi$
$769$	5.58041	+	0.652257i	0.201235	+	0.0235210i	−0.0148783	+	0.999889i	$0.504736\pi$
$770$	4.58640	+	0.536074i	0.165282	+	0.0193188i
$771$		0			0
$772$	26.0541	+	17.1361i	0.937709	+	0.616741i
$773$	9.17966	+	52.0604i	0.330169	+	1.87248i	0.470531	+	0.882383i	$0.344062\pi$
$773$	9.17966	+	52.0604i	0.330169	+	1.87248i	−0.140362	+	0.990100i	$0.544827\pi$
$774$		0			0
$775$	0.800512	−	4.53993i	0.0287552	−	0.163079i
$776$	−0.954139	+	1.01133i	−0.0342516	+	0.0363046i
$777$		0			0
$778$	3.18533	−	2.09503i	0.114200	−	0.0751103i
$779$	3.40489	+	3.60897i	0.121993	+	0.129305i
$780$		0			0
$781$	3.88784	−	9.01301i	0.139118	−	0.322511i
$782$	4.54265	+	7.86810i	0.162445	+	0.281363i
$783$		0			0
$784$	−17.7703	+	30.7791i	−0.634654	+	1.09925i
$785$	−7.02690	−	9.43877i	−0.250801	−	0.336884i
$786$		0			0
$787$	4.41524	−	14.7479i	0.157386	−	0.525707i	−0.842530	−	0.538650i	$-0.818935\pi$
$787$	4.41524	−	14.7479i	0.157386	−	0.525707i	0.999916	+	0.0129424i	$0.00411980\pi$
$788$	0.140690	+	2.41556i	0.00501188	+	0.0860507i
$789$		0			0
$790$	2.34050	+	0.554709i	0.0832712	+	0.0197356i
$791$	−27.0645	−	22.7098i	−0.962304	−	0.807469i
$792$		0			0
$793$	−5.06389	+	4.24911i	−0.179824	+	0.150890i
$794$	−4.44562	+	2.23267i	−0.157769	+	0.0792346i
$795$		0			0
$796$	−1.82306	−	4.22634i	−0.0646168	−	0.149799i
$797$	−12.8662	+	17.2824i	−0.455746	+	0.612173i	−0.969299	−	0.245885i	$-0.920921\pi$
$797$	−12.8662	+	17.2824i	−0.455746	+	0.612173i	0.513553	+	0.858058i	$0.328329\pi$
$798$		0			0
$799$	−0.0586625	+	1.00720i	−0.00207533	+	0.0356320i
$800$	−5.13998	−	1.87080i	−0.181726	−	0.0661428i
$801$		0			0
$802$	4.52910	−	1.64846i	0.159928	−	0.0582091i
$803$	6.20889	+	20.7391i	0.219107	+	0.731868i
$804$		0			0
$805$	−36.7289	−	18.4459i	−1.29452	−	0.650134i
$806$	−0.539722	+	0.127917i	−0.0190109	+	0.00450567i
$807$		0			0
$808$	−12.3099	+	1.43882i	−0.433060	+	0.0506174i
$809$	19.2040			0.675177			0.337588	−	0.941294i	$-0.390389\pi$
$809$	19.2040			0.675177			0.337588	+	0.941294i	$0.390389\pi$
$810$		0			0
$811$	−4.66474			−0.163801			−0.0819006	−	0.996641i	$-0.526099\pi$
$811$	−4.66474			−0.163801			−0.0819006	+	0.996641i	$0.526099\pi$
$812$	−2.16299	+	0.252817i	−0.0759061	+	0.00887215i
$813$		0			0
$814$	1.19177	−	0.282454i	0.0417715	−	0.00990002i
$815$	−7.06094	−	3.54614i	−0.247334	−	0.124216i
$816$		0			0
$817$	2.31454	+	7.73109i	0.0809754	+	0.270477i
$818$	−4.90382	+	1.78484i	−0.171458	+	0.0624056i
$819$		0			0
$820$	8.75443	+	3.18635i	0.305718	+	0.111272i
$821$	2.45152	−	42.0910i	0.0855587	−	1.46899i	−0.633341	−	0.773873i	$-0.718317\pi$
$821$	2.45152	−	42.0910i	0.0855587	−	1.46899i	0.718900	−	0.695114i	$-0.244646\pi$
$822$		0			0
$823$	−5.08089	+	6.82482i	−0.177109	+	0.237898i	−0.881809	−	0.471607i	$-0.843674\pi$
$823$	−5.08089	+	6.82482i	−0.177109	+	0.237898i	0.704700	+	0.709505i	$0.251082\pi$
$824$	−1.69368	−	3.92638i	−0.0590020	−	0.136782i
$825$		0			0
$826$	−5.24837	+	2.63583i	−0.182614	+	0.0917123i
$827$	28.1921	−	23.6560i	0.980336	−	0.822600i	−0.00380365	−	0.999993i	$-0.501211\pi$
$827$	28.1921	−	23.6560i	0.980336	−	0.822600i	0.984140	+	0.177393i	$0.0567663\pi$
$828$		0			0
$829$	−16.2832	−	13.6632i	−0.565537	−	0.474542i	0.314624	−	0.949216i	$-0.398121\pi$
$829$	−16.2832	−	13.6632i	−0.565537	−	0.474542i	−0.880162	+	0.474674i	$0.842566\pi$
$830$	−1.58382	−	0.375372i	−0.0549752	−	0.0130294i
$831$		0			0
$832$	−0.666770	−	11.4480i	−0.0231161	−	0.396888i
$833$	20.3360	−	67.9270i	0.704601	−	2.35353i
$834$		0			0
$835$	−4.12499	−	5.54083i	−0.142751	−	0.191748i
$836$	6.26095	−	10.8443i	0.216540	−	0.375058i
$837$		0			0
$838$	−0.100997	−	0.174931i	−0.00348887	−	0.00604290i
$839$	16.4368	−	38.1048i	0.567461	−	1.31552i	−0.356950	−	0.934124i	$-0.616183\pi$
$839$	16.4368	−	38.1048i	0.567461	−	1.31552i	0.924411	−	0.381399i	$-0.124558\pi$
$840$		0			0
$841$	19.8495	+	21.0393i	0.684467	+	0.725492i
$842$	1.23011	−	0.809053i	0.0423922	−	0.0278818i
$843$		0			0
$844$	−15.3574	+	16.2779i	−0.528624	+	0.560309i
$845$	2.87223	−	16.2892i	0.0988076	−	0.560366i
$846$		0			0
$847$	−2.65625	−	15.0643i	−0.0912698	−	0.517617i
$848$	31.2827	+	20.5750i	1.07425	+	0.706547i
$849$		0			0
$850$	3.50550	+	0.409735i	0.120238	+	0.0140538i
$851$	−10.8279	−	1.26559i	−0.371174	−	0.0433840i
$852$		0			0
$853$	19.0962	+	12.5598i	0.653842	+	0.430039i	0.832615	−	0.553851i	$-0.186842\pi$
$853$	19.0962	+	12.5598i	0.653842	+	0.430039i	−0.178773	+	0.983890i	$0.557213\pi$
$854$	0.544183	+	3.08622i	0.0186216	+	0.105608i
$855$		0			0
$856$	0.209141	−	1.18610i	0.00714829	−	0.0405400i
$857$	35.3809	−	37.5016i	1.20859	−	1.28103i	0.259601	−	0.965716i	$-0.416409\pi$
$857$	35.3809	−	37.5016i	1.20859	−	1.28103i	0.948988	−	0.315313i	$-0.102110\pi$
$858$		0			0
$859$	22.1750	−	14.5847i	0.756602	−	0.497625i	−0.111651	−	0.993748i	$-0.535614\pi$
$859$	22.1750	−	14.5847i	0.756602	−	0.497625i	0.868252	+	0.496123i	$0.165243\pi$
$860$	10.3986	+	11.0218i	0.354588	+	0.375842i
$861$		0			0
$862$	2.05495	−	4.76392i	0.0699920	−	0.162260i
$863$	−1.22953	−	2.12962i	−0.0418538	−	0.0724930i	0.844340	−	0.535808i	$-0.179993\pi$
$863$	−1.22953	−	2.12962i	−0.0418538	−	0.0724930i	−0.886193	+	0.463315i	$0.846660\pi$
$864$		0			0
$865$	12.7067	−	22.0087i	0.432041	−	0.748317i
$866$	2.21435	+	2.97439i	0.0752467	+	0.101074i
$867$		0			0
$868$	4.22080	−	14.0985i	0.143263	−	0.478533i
$869$	−1.81154	−	31.1029i	−0.0614522	−	1.05509i
$870$		0			0
$871$	20.9279	+	4.96001i	0.709115	+	0.168063i
$872$	−6.55058	−	5.49659i	−0.221831	−	0.186138i
$873$		0			0
$874$	1.52555	−	1.28008i	0.0516023	−	0.0432995i
$875$	−42.9102	+	21.5503i	−1.45063	+	0.728534i
$876$		0			0
$877$	1.00178	+	2.32239i	0.0338277	+	0.0784215i	0.934292	−	0.356508i	$-0.116033\pi$
$877$	1.00178	+	2.32239i	0.0338277	+	0.0784215i	−0.900465	+	0.434929i	$0.856773\pi$
$878$	3.76413	−	5.05610i	0.127033	−	0.170635i
$879$		0			0
$880$	1.34223	−	23.0452i	0.0452465	−	0.776853i
$881$	−46.6808	−	16.9904i	−1.57272	−	0.572421i	−0.599111	−	0.800666i	$-0.704479\pi$
$881$	−46.6808	−	16.9904i	−1.57272	−	0.572421i	−0.973604	+	0.228244i	$0.926702\pi$
$882$		0			0
$883$	29.8038	−	10.8477i	1.00298	−	0.365054i	0.212245	−	0.977216i	$-0.431922\pi$
$883$	29.8038	−	10.8477i	1.00298	−	0.365054i	0.790732	+	0.612162i	$0.209700\pi$
$884$	6.81632	+	22.7681i	0.229258	+	0.765774i
$885$		0			0
$886$	−2.65671	−	1.33425i	−0.0892539	−	0.0448250i
$887$	−2.81045	+	0.666089i	−0.0943658	+	0.0223651i	−0.277527	−	0.960718i	$-0.589515\pi$
$887$	−2.81045	+	0.666089i	−0.0943658	+	0.0223651i	0.183162	+	0.983083i	$0.441367\pi$
$888$		0			0
$889$	−76.2603	+	8.91355i	−2.55769	+	0.298951i
$890$	−2.00232			−0.0671179
$891$		0			0
$892$	29.7211			0.995137
$893$	0.219652	−	0.0256736i	0.00735037	−	0.000859135i
$894$		0			0
$895$	−29.7247	+	7.04489i	−0.993589	+	0.235485i
$896$	−20.7414	−	10.4167i	−0.692920	−	0.347998i
$897$		0			0
$898$	−0.0473712	−	0.158231i	−0.00158080	−	0.00528023i
$899$	0.476334	−	0.173372i	0.0158866	−	0.00578227i
$900$		0			0
$901$	−70.1950	−	25.5489i	−2.33854	−	0.851157i
$902$	−0.125367	+	2.15248i	−0.00417428	+	0.0716696i
$903$		0			0
$904$	3.87318	−	5.20259i	0.128820	−	0.173036i
$905$	−0.0950360	−	0.220318i	−0.00315910	−	0.00732362i
$906$		0			0
$907$	27.6164	−	13.8695i	0.916986	−	0.460528i	0.0732670	−	0.997312i	$-0.476657\pi$
$907$	27.6164	−	13.8695i	0.916986	−	0.460528i	0.843719	+	0.536784i	$0.180361\pi$
$908$	−32.0289	+	26.8755i	−1.06292	+	0.891893i
$909$		0			0
$910$	1.47163	+	1.23485i	0.0487842	+	0.0409348i
$911$	41.5683	+	9.85188i	1.37722	+	0.326407i	0.851547	−	0.524279i	$-0.175665\pi$
$911$	41.5683	+	9.85188i	1.37722	+	0.326407i	0.525674	+	0.850686i	$0.323813\pi$
$912$		0			0
$913$	1.22587	+	21.0474i	0.0405704	+	0.696567i
$914$	−0.997990	+	3.33352i	−0.0330106	+	0.110263i
$915$		0			0
$916$	−4.57827	−	6.14968i	−0.151270	−	0.203191i
$917$	−12.2469	+	21.2123i	−0.404429	+	0.700491i
$918$		0			0
$919$	−10.3318	−	17.8951i	−0.340813	−	0.590306i	0.643771	−	0.765218i	$-0.277369\pi$
$919$	−10.3318	−	17.8951i	−0.340813	−	0.590306i	−0.984584	+	0.174913i	$0.944036\pi$
$920$	2.98857	−	6.92828i	0.0985301	−	0.228419i
$921$		0			0
$922$	0.394760	+	0.418421i	0.0130007	+	0.0137800i
$923$	3.41187	−	2.24402i	0.112303	−	0.0738629i
$924$		0			0
$925$	−2.90619	+	3.08038i	−0.0955549	+	0.101282i
$926$	0.932434	−	5.28810i	0.0306417	−	0.173778i
$927$		0			0
$928$	−0.104442	−	0.592319i	−0.00342847	−	0.0194438i
$929$	35.1854	+	23.1418i	1.15439	+	0.759257i	0.974491	−	0.224427i	$-0.0720510\pi$
$929$	35.1854	+	23.1418i	1.15439	+	0.759257i	0.179904	+	0.983684i	$0.442421\pi$
$930$		0			0
$931$	−15.4371	−	1.80434i	−0.505932	−	0.0591350i
$932$	37.7900	+	4.41702i	1.23785	+	0.144684i
$933$		0			0
$934$	−2.17004	−	1.42726i	−0.0710060	−	0.0467014i
$935$	7.99728	+	45.3548i	0.261539	+	1.48326i
$936$		0			0
$937$	5.62432	−	31.8971i	0.183738	−	1.04203i	−0.743827	−	0.668372i	$-0.766991\pi$
$937$	5.62432	−	31.8971i	0.183738	−	1.04203i	0.927566	−	0.373660i	$-0.121897\pi$
$938$	6.99704	−	7.41643i	0.228461	−	0.242155i
$939$		0			0
$940$	0.346927	−	0.228177i	0.0113155	−	0.00744233i
$941$	3.42432	+	3.62957i	0.111630	+	0.118321i	0.780779	−	0.624808i	$-0.214823\pi$
$941$	3.42432	+	3.62957i	0.111630	+	0.118321i	−0.669149	+	0.743128i	$0.733341\pi$
$942$		0			0
$943$	7.60127	−	17.6217i	0.247531	−	0.573842i
$944$	14.6802	+	25.4269i	0.477800	+	0.827575i
$945$		0			0
$946$	−1.75347	+	3.03710i	−0.0570102	+	0.0987445i
$947$	−0.820571	−	1.10222i	−0.0266650	−	0.0358173i	0.788591	−	0.614918i	$-0.210811\pi$
$947$	−0.820571	−	1.10222i	−0.0266650	−	0.0358173i	−0.815256	+	0.579101i	$0.803404\pi$
$948$		0			0
$949$	−2.58310	+	8.62816i	−0.0838510	+	0.280082i
$950$	−0.0449821	−	0.772313i	−0.00145941	−	0.0250572i
$951$		0			0
$952$	22.1226	+	5.24315i	0.716997	+	0.169931i
$953$	−23.8952	−	20.0504i	−0.774041	−	0.649497i	0.167699	−	0.985838i	$-0.446366\pi$
$953$	−23.8952	−	20.0504i	−0.774041	−	0.649497i	−0.941740	+	0.336341i	$0.890811\pi$
$954$		0			0
$955$	−12.9929	+	10.9023i	−0.420439	+	0.352790i
$956$	−24.9326	+	12.5216i	−0.806379	+	0.404979i
$957$		0			0
$958$	1.88791	+	4.37667i	0.0609957	+	0.141404i
$959$	53.7389	−	72.1839i	1.73532	−	2.33094i
$960$		0			0
$961$	1.60331	−	27.5278i	0.0517196	−	0.887992i
$962$	0.478820	+	0.174276i	0.0154378	+	0.00561889i
$963$		0			0
$964$	−20.6201	+	7.50509i	−0.664127	+	0.241723i
$965$	7.21031	+	24.0841i	0.232108	+	0.775295i
$966$		0			0
$967$	20.0396	+	10.0643i	0.644430	+	0.323645i	0.740825	−	0.671698i	$-0.234435\pi$
$967$	20.0396	+	10.0643i	0.644430	+	0.323645i	−0.0963950	+	0.995343i	$0.530731\pi$
$968$	2.73252	−	0.647619i	0.0878265	−	0.0208153i
$969$		0			0
$970$	−0.551733	+	0.0644883i	−0.0177151	+	0.00207060i
$971$	25.8564			0.829773			0.414886	−	0.909873i	$-0.363821\pi$
$971$	25.8564			0.829773			0.414886	+	0.909873i	$0.363821\pi$
$972$		0			0
$973$	51.4827			1.65046
$974$	−0.368915	+	0.0431200i	−0.0118208	+	0.00138165i
$975$		0			0
$976$	15.2442	−	3.61294i	0.487955	−	0.115647i
$977$	−23.7980	−	11.9518i	−0.761366	−	0.382372i	0.0253574	−	0.999678i	$-0.491928\pi$
$977$	−23.7980	−	11.9518i	−0.761366	−	0.382372i	−0.786723	+	0.617306i	$0.788224\pi$
$978$		0			0
$979$	7.43838	+	24.8459i	0.237732	+	0.794079i
$980$	−27.4230	+	9.98117i	−0.875997	+	0.318837i
$981$		0			0
$982$	0.0824649	+	0.0300148i	0.00263156	+	0.000957810i
$983$	−0.415058	+	7.12627i	−0.0132383	+	0.227293i	0.985199	+	0.171413i	$0.0548333\pi$
$983$	−0.415058	+	7.12627i	−0.0132383	+	0.227293i	−0.998438	+	0.0558796i	$0.982204\pi$
$984$		0			0
$985$	−1.16487	+	1.56469i	−0.0371157	+	0.0498550i
$986$	0.153712	+	0.356345i	0.00489519	+	0.0113483i
$987$		0			0
$988$	4.65540	−	2.33803i	0.148108	−	0.0743826i
$989$	23.9118	−	20.0644i	0.760350	−	0.638010i
$990$		0			0
$991$	33.2529	+	27.9025i	1.05631	+	0.886353i	0.993743	−	0.111688i	$-0.0356256\pi$
$991$	33.2529	+	27.9025i	1.05631	+	0.886353i	0.0625710	+	0.998041i	$0.480070\pi$
$992$	3.95500	+	0.937353i	0.125571	+	0.0297610i
$993$		0			0
$994$	−0.112566	−	1.93269i	−0.00357038	−	0.0613011i
$995$	1.06423	−	3.55479i	0.0337385	−	0.112694i
$996$		0			0
$997$	−1.68819	−	2.26763i	−0.0534654	−	0.0718164i	0.774586	−	0.632468i	$-0.217958\pi$
$997$	−1.68819	−	2.26763i	−0.0534654	−	0.0718164i	−0.828052	+	0.560652i	$0.810551\pi$
$998$	−2.21936	+	3.84405i	−0.0702528	+	0.121681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.19.4		144
3.2	odd	2		81.2.g.a.61.5	yes	144
9.2	odd	6		729.2.g.c.541.4		144
9.4	even	3		729.2.g.a.55.5		144
9.5	odd	6		729.2.g.d.55.4		144
9.7	even	3		729.2.g.b.541.5		144
81.2	odd	54		6561.2.a.c.1.40		72
81.4	even	27	inner	243.2.g.a.64.4		144
81.23	odd	54		729.2.g.d.676.4		144
81.31	even	27		729.2.g.b.190.5		144
81.50	odd	54		729.2.g.c.190.4		144
81.58	even	27		729.2.g.a.676.5		144
81.77	odd	54		81.2.g.a.4.5	✓	144
81.79	even	27		6561.2.a.d.1.33		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.5	✓	144	81.77	odd	54
81.2.g.a.61.5	yes	144	3.2	odd	2
243.2.g.a.19.4		144	1.1	even	1	trivial
243.2.g.a.64.4		144	81.4	even	27	inner
729.2.g.a.55.5		144	9.4	even	3
729.2.g.a.676.5		144	81.58	even	27
729.2.g.b.190.5		144	81.31	even	27
729.2.g.b.541.5		144	9.7	even	3
729.2.g.c.190.4		144	81.50	odd	54
729.2.g.c.541.4		144	9.2	odd	6
729.2.g.d.55.4		144	9.5	odd	6
729.2.g.d.676.4		144	81.23	odd	54
6561.2.a.c.1.40		72	81.2	odd	54
6561.2.a.d.1.33		72	81.79	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)

\(f(q)\)	\(=\)	\(q+(0.186105 - 0.0217526i) q^{2} +(-1.91193 + 0.453135i) q^{4} +(-1.41557 - 0.710926i) q^{5} +(1.16062 + 3.87673i) q^{7} +(-0.698107 + 0.254090i) q^{8} +O(q^{10})\)	\(q+(0.186105 - 0.0217526i) q^{2} +(-1.91193 + 0.453135i) q^{4} +(-1.41557 - 0.710926i) q^{5} +(1.16062 + 3.87673i) q^{7} +(-0.698107 + 0.254090i) q^{8} +(-0.278909 - 0.101515i) q^{10} +(-0.223537 + 3.83798i) q^{11} +(-0.955113 + 1.28294i) q^{13} +(0.300325 + 0.696232i) q^{14} +(3.38739 - 1.70121i) q^{16} +(-5.79317 + 4.86105i) q^{17} +(1.26984 + 1.06552i) q^{19} +(3.02861 + 0.717794i) q^{20} +(0.0418845 + 0.719129i) q^{22} +(1.83889 - 6.14233i) q^{23} +(-1.48737 - 1.99789i) q^{25} +(-0.149844 + 0.259538i) q^{26} +(-3.97569 - 6.88610i) q^{28} +(0.108478 - 0.251480i) q^{29} +(1.27012 + 1.34625i) q^{31} +(1.83479 - 1.20676i) q^{32} +(-0.972398 + 1.03068i) q^{34} +(1.11313 - 6.31289i) q^{35} +(-0.295248 - 1.67443i) q^{37} +(0.259501 + 0.170677i) q^{38} +(1.16886 + 0.136620i) q^{40} +(2.97293 + 0.347486i) q^{41} +(4.06748 + 2.67523i) q^{43} +(-1.31174 - 7.43922i) q^{44} +(0.208616 - 1.18312i) q^{46} +(0.0915512 - 0.0970386i) q^{47} +(-7.83356 + 5.15221i) q^{49} +(-0.320267 - 0.339463i) q^{50} +(1.24476 - 2.88568i) q^{52} +(4.93888 + 8.55438i) q^{53} +(3.04495 - 5.27400i) q^{55} +(-1.79527 - 2.41147i) q^{56} +(0.0147179 - 0.0491613i) q^{58} +(0.450368 + 7.73252i) q^{59} +(4.02160 + 0.953136i) q^{61} +(0.265660 + 0.222915i) q^{62} +(-5.49230 + 4.60858i) q^{64} +(2.26410 - 1.13707i) q^{65} +(-5.32612 - 12.3473i) q^{67} +(8.87341 - 11.9191i) q^{68} +(0.0698381 - 1.19907i) q^{70} +(-2.39924 - 0.873251i) q^{71} +(5.29149 - 1.92595i) q^{73} +(-0.0913704 - 0.305198i) q^{74} +(-2.91066 - 1.46179i) q^{76} +(-15.1382 + 3.58782i) q^{77} +(-8.04919 + 0.940816i) q^{79} -6.00452 q^{80} +0.560836 q^{82} +(5.44690 - 0.636652i) q^{83} +(11.6565 - 2.76264i) q^{85} +(0.815172 + 0.409395i) q^{86} +(-0.819139 - 2.73612i) q^{88} +(6.33932 - 2.30732i) q^{89} +(-6.08212 - 2.21371i) q^{91} +(-0.732524 + 12.5770i) q^{92} +(0.0149273 - 0.0200509i) q^{94} +(-1.04004 - 2.41108i) q^{95} +(1.67247 - 0.839945i) q^{97} +(-1.34579 + 1.12925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) 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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