LMFDB - Embedded newform 729.2.g.c.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.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:	$5.82109430735$
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			109.1
Character	$\chi$	$=$	729.109
Dual form			729.2.g.c.622.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74340 - 1.84790i) q^{2} +(-0.258987 + 4.44663i) q^{4} +(3.16528 - 0.369969i) q^{5} +(-1.48402 - 0.745301i) q^{7} +(4.77615 - 4.00766i) q^{8} +O(q^{10})$	\(q+(-1.74340 - 1.84790i) q^{2} +(-0.258987 + 4.44663i) q^{4} +(3.16528 - 0.369969i) q^{5} +(-1.48402 - 0.745301i) q^{7} +(4.77615 - 4.00766i) q^{8} +(-6.20202 - 5.20411i) q^{10} +(0.777030 + 1.80136i) q^{11} +(-3.77585 - 0.894892i) q^{13} +(1.21000 + 4.04167i) q^{14} +(-6.88438 - 0.804669i) q^{16} +(0.757018 - 4.29326i) q^{17} +(0.245992 + 1.39509i) q^{19} +(0.825347 + 14.1707i) q^{20} +(1.97405 - 4.57636i) q^{22} +(2.02703 - 1.01801i) q^{23} +(5.01692 - 1.18903i) q^{25} +(4.92914 + 8.53753i) q^{26} +(3.69842 - 6.40585i) q^{28} +(2.70787 - 9.04493i) q^{29} +(3.49112 + 2.29614i) q^{31} +(3.06894 + 4.12230i) q^{32} +(-9.25329 + 6.08598i) q^{34} +(-4.97307 - 1.81005i) q^{35} +(6.43466 - 2.34203i) q^{37} +(2.14912 - 2.88676i) q^{38} +(13.6351 - 14.4524i) q^{40} +(2.44835 - 2.59510i) q^{41} +(4.45230 - 5.98048i) q^{43} +(-8.21121 + 2.98864i) q^{44} +(-5.41510 - 1.97094i) q^{46} +(5.79465 - 3.81120i) q^{47} +(-2.53328 - 3.40278i) q^{49} +(-10.9437 - 7.19779i) q^{50} +(4.95715 - 16.5580i) q^{52} +(1.35317 - 2.34375i) q^{53} +(3.12597 + 5.41433i) q^{55} +(-10.0748 + 2.38777i) q^{56} +(-21.4350 + 10.7651i) q^{58} +(-1.40028 + 3.24620i) q^{59} +(0.162221 + 2.78523i) q^{61} +(-1.84338 - 10.4543i) q^{62} +(-0.140001 + 0.793987i) q^{64} +(-12.2827 - 1.43564i) q^{65} +(0.528909 + 1.76668i) q^{67} +(18.8945 + 4.47807i) q^{68} +(5.32527 + 12.3454i) q^{70} +(1.75933 + 1.47625i) q^{71} +(-8.76373 + 7.35364i) q^{73} +(-15.5460 - 7.80750i) q^{74} +(-6.26714 + 0.732524i) q^{76} +(0.189429 - 3.25237i) q^{77} +(-4.78302 - 5.06970i) q^{79} -22.0887 q^{80} -9.06394 q^{82} +(0.0736322 + 0.0780456i) q^{83} +(0.807804 - 13.8695i) q^{85} +(-18.8134 + 2.19898i) q^{86} +(10.9304 + 5.48947i) q^{88} +(4.04918 - 3.39767i) q^{89} +(4.93645 + 4.14218i) q^{91} +(4.00175 + 9.27709i) q^{92} +(-17.1451 - 4.06347i) q^{94} +(1.29477 + 4.32484i) q^{95} +(4.32681 + 0.505732i) q^{97} +(-1.87147 + 10.6136i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−1.74340	−	1.84790i	−1.23277	−	1.30666i	−0.936123	−	0.351673i	$-0.885613\pi$
$2$	−1.74340	−	1.84790i	−1.23277	−	1.30666i	−0.296647	−	0.954987i	$-0.595868\pi$
$3$		0			0
$3$		0			0
$4$	−0.258987	+	4.44663i	−0.129493	+	2.22331i
$5$	3.16528	−	0.369969i	1.41556	−	0.165455i	0.626331	−	0.779557i	$-0.284556\pi$
$5$	3.16528	−	0.369969i	1.41556	−	0.165455i	0.789227	+	0.614102i	$0.210482\pi$
$6$		0			0
$7$	−1.48402	−	0.745301i	−0.560906	−	0.281697i	0.145672	−	0.989333i	$-0.453466\pi$
$7$	−1.48402	−	0.745301i	−0.560906	−	0.281697i	−0.706578	+	0.707636i	$0.749762\pi$
$8$	4.77615	−	4.00766i	1.68862	−	1.41692i
$9$		0			0
$10$	−6.20202	−	5.20411i	−1.96125	−	1.64568i
$11$	0.777030	+	1.80136i	0.234283	+	0.543130i	0.994281	−	0.106796i	$-0.0340592\pi$
$11$	0.777030	+	1.80136i	0.234283	+	0.543130i	−0.759998	+	0.649926i	$0.774800\pi$
$12$		0			0
$13$	−3.77585	−	0.894892i	−1.04723	−	0.248198i	−0.329237	−	0.944247i	$-0.606791\pi$
$13$	−3.77585	−	0.894892i	−1.04723	−	0.248198i	−0.717994	+	0.696049i	$0.754940\pi$
$14$	1.21000	+	4.04167i	0.323385	+	1.08018i
$15$		0			0
$16$	−6.88438	−	0.804669i	−1.72110	−	0.201167i
$17$	0.757018	−	4.29326i	0.183604	−	1.04127i	−0.744132	−	0.668032i	$-0.767137\pi$
$17$	0.757018	−	4.29326i	0.183604	−	1.04127i	0.927736	−	0.373237i	$-0.121752\pi$
$18$		0			0
$19$	0.245992	+	1.39509i	0.0564343	+	0.320055i	0.999936	−	0.0113127i	$-0.00360103\pi$
$19$	0.245992	+	1.39509i	0.0564343	+	0.320055i	−0.943502	+	0.331368i	$0.892490\pi$
$20$	0.825347	+	14.1707i	0.184553	+	3.16866i
$21$		0			0
$22$	1.97405	−	4.57636i	0.420868	−	0.975683i
$23$	2.02703	−	1.01801i	0.422665	−	0.212270i	−0.224737	−	0.974420i	$-0.572152\pi$
$23$	2.02703	−	1.01801i	0.422665	−	0.212270i	0.647401	+	0.762149i	$0.275856\pi$
$24$		0			0
$25$	5.01692	−	1.18903i	1.00338	−	0.237806i
$26$	4.92914	+	8.53753i	0.966684	+	1.67435i
$27$		0			0
$28$	3.69842	−	6.40585i	0.698935	−	1.21059i
$29$	2.70787	−	9.04493i	0.502840	−	1.67960i	−0.209535	−	0.977801i	$-0.567195\pi$
$29$	2.70787	−	9.04493i	0.502840	−	1.67960i	0.712374	−	0.701800i	$-0.247620\pi$
$30$		0			0
$31$	3.49112	+	2.29614i	0.627023	+	0.412399i	0.822866	−	0.568236i	$-0.192374\pi$
$31$	3.49112	+	2.29614i	0.627023	+	0.412399i	−0.195843	+	0.980635i	$0.562744\pi$
$32$	3.06894	+	4.12230i	0.542517	+	0.728727i
$33$		0			0
$34$	−9.25329	+	6.08598i	−1.58693	+	1.04374i
$35$	−4.97307	−	1.81005i	−0.840603	−	0.305954i
$36$		0			0
$37$	6.43466	−	2.34203i	1.05785	−	0.385027i	0.246231	−	0.969211i	$-0.420808\pi$
$37$	6.43466	−	2.34203i	1.05785	−	0.385027i	0.811621	+	0.584185i	$0.198586\pi$
$38$	2.14912	−	2.88676i	0.348633	−	0.468295i
$39$		0			0
$40$	13.6351	−	14.4524i	2.15591	−	2.28513i
$41$	2.44835	−	2.59510i	0.382368	−	0.405287i	−0.507392	−	0.861716i	$-0.669390\pi$
$41$	2.44835	−	2.59510i	0.382368	−	0.405287i	0.889760	+	0.456429i	$0.150872\pi$
$42$		0			0
$43$	4.45230	−	5.98048i	0.678970	−	0.912014i	−0.320408	−	0.947279i	$-0.603820\pi$
$43$	4.45230	−	5.98048i	0.678970	−	0.912014i	0.999378	+	0.0352651i	$0.0112276\pi$
$44$	−8.21121	+	2.98864i	−1.23789	+	0.450554i
$45$		0			0
$46$	−5.41510	−	1.97094i	−0.798413	−	0.290599i
$47$	5.79465	−	3.81120i	0.845237	−	0.555921i	−0.0514047	−	0.998678i	$-0.516370\pi$
$47$	5.79465	−	3.81120i	0.845237	−	0.555921i	0.896642	+	0.442757i	$0.145999\pi$
$48$		0			0
$49$	−2.53328	−	3.40278i	−0.361897	−	0.486112i
$50$	−10.9437	−	7.19779i	−1.54767	−	1.01792i
$51$		0			0
$52$	4.95715	−	16.5580i	0.687432	−	2.29618i
$53$	1.35317	−	2.34375i	0.185872	−	0.321939i	−0.757998	−	0.652257i	$-0.773822\pi$
$53$	1.35317	−	2.34375i	0.185872	−	0.321939i	0.943870	+	0.330317i	$0.107156\pi$
$54$		0			0
$55$	3.12597	+	5.41433i	0.421505	+	0.730068i
$56$	−10.0748	+	2.38777i	−1.34630	+	0.319079i
$57$		0			0
$58$	−21.4350	+	10.7651i	−2.81455	+	1.41352i
$59$	−1.40028	+	3.24620i	−0.182300	+	0.422620i	−0.984721	−	0.174139i	$-0.944286\pi$
$59$	−1.40028	+	3.24620i	−0.182300	+	0.422620i	0.802421	+	0.596759i	$0.203545\pi$
$60$		0			0
$61$	0.162221	+	2.78523i	0.0207703	+	0.356613i	0.992641	+	0.121097i	$0.0386411\pi$
$61$	0.162221	+	2.78523i	0.0207703	+	0.356613i	−0.971870	+	0.235516i	$0.924322\pi$
$62$	−1.84338	−	10.4543i	−0.234109	−	1.32770i
$63$		0			0
$64$	−0.140001	+	0.793987i	−0.0175002	+	0.0992484i
$65$	−12.2827	−	1.43564i	−1.52348	−	0.178070i
$66$		0			0
$67$	0.528909	+	1.76668i	0.0646165	+	0.215834i	0.984200	−	0.177061i	$-0.0566588\pi$
$67$	0.528909	+	1.76668i	0.0646165	+	0.215834i	−0.919583	+	0.392895i	$0.871474\pi$
$68$	18.8945	+	4.47807i	2.29129	+	0.543046i
$69$		0			0
$70$	5.32527	+	12.3454i	0.636491	+	1.47555i
$71$	1.75933	+	1.47625i	0.208794	+	0.175199i	0.741187	−	0.671298i	$-0.234263\pi$
$71$	1.75933	+	1.47625i	0.208794	+	0.175199i	−0.532394	+	0.846497i	$0.678707\pi$
$72$		0			0
$73$	−8.76373	+	7.35364i	−1.02572	+	0.860679i	−0.990335	−	0.138695i	$-0.955709\pi$
$73$	−8.76373	+	7.35364i	−1.02572	+	0.860679i	−0.0353822	+	0.999374i	$0.511265\pi$
$74$	−15.5460	−	7.80750i	−1.80719	−	0.907603i
$75$		0			0
$76$	−6.26714	+	0.732524i	−0.718891	+	0.0840263i
$77$	0.189429	−	3.25237i	0.0215874	−	0.370641i
$78$		0			0
$79$	−4.78302	−	5.06970i	−0.538132	−	0.570386i	0.400066	−	0.916486i	$-0.368987\pi$
$79$	−4.78302	−	5.06970i	−0.538132	−	0.570386i	−0.938198	+	0.346100i	$0.887506\pi$
$80$	−22.0887			−2.46959
$81$		0			0
$82$	−9.06394			−1.00094
$83$	0.0736322	+	0.0780456i	0.00808219	+	0.00856662i	0.731402	−	0.681946i	$-0.238866\pi$
$83$	0.0736322	+	0.0780456i	0.00808219	+	0.00856662i	−0.723320	+	0.690513i	$0.757385\pi$
$84$		0			0
$85$	0.807804	−	13.8695i	0.0876187	−	1.50435i
$86$	−18.8134	+	2.19898i	−2.02871	+	0.237122i
$87$		0			0
$88$	10.9304	+	5.48947i	1.16519	+	0.585180i
$89$	4.04918	−	3.39767i	0.429212	−	0.360152i	−0.402442	−	0.915445i	$-0.631838\pi$
$89$	4.04918	−	3.39767i	0.429212	−	0.360152i	0.831654	+	0.555293i	$0.187394\pi$
$90$		0			0
$91$	4.93645	+	4.14218i	0.517481	+	0.434218i
$92$	4.00175	+	9.27709i	0.417211	+	0.967204i
$93$		0			0
$94$	−17.1451	−	4.06347i	−1.76838	−	0.419114i
$95$	1.29477	+	4.32484i	0.132841	+	0.443719i
$96$		0			0
$97$	4.32681	+	0.505732i	0.439321	+	0.0513493i	0.332879	−	0.942970i	$-0.391980\pi$
$97$	4.32681	+	0.505732i	0.439321	+	0.0513493i	0.106442	+	0.994319i	$0.466054\pi$
$98$	−1.87147	+	10.6136i	−0.189047	+	1.07214i
$99$		0			0
$100$	3.98787	+	22.6163i	0.398787	+	2.26163i
$101$	0.651395	+	11.1840i	0.0648163	+	1.11285i	0.861268	+	0.508150i	$0.169671\pi$
$101$	0.651395	+	11.1840i	0.0648163	+	1.11285i	−0.796452	+	0.604702i	$0.793292\pi$
$102$		0			0
$103$	−1.59549	+	3.69875i	−0.157208	+	0.364449i	−0.978557	−	0.205977i	$-0.933963\pi$
$103$	−1.59549	+	3.69875i	−0.157208	+	0.364449i	0.821349	+	0.570426i	$0.193222\pi$
$104$	−21.6204	+	10.8582i	−2.12006	+	1.06473i
$105$		0			0
$106$	−6.69012	+	1.58559i	−0.649802	+	0.154006i
$107$	−8.10012	−	14.0298i	−0.783068	−	1.35631i	−0.930147	−	0.367188i	$-0.880320\pi$
$107$	−8.10012	−	14.0298i	−0.783068	−	1.35631i	0.147079	−	0.989125i	$-0.453013\pi$
$108$		0			0
$109$	−6.44548	+	11.1639i	−0.617365	+	1.06931i	0.372600	+	0.927992i	$0.378466\pi$
$109$	−6.44548	+	11.1639i	−0.617365	+	1.06931i	−0.989965	+	0.141315i	$0.954867\pi$
$110$	4.55531	−	15.2158i	0.434332	−	1.45077i
$111$		0			0
$112$	9.61682	+	6.32508i	0.908704	+	0.597664i
$113$	−9.63364	−	12.9402i	−0.906256	−	1.21731i	−0.975563	−	0.219718i	$-0.929486\pi$
$113$	−9.63364	−	12.9402i	−0.906256	−	1.21731i	0.0693069	−	0.997595i	$-0.477921\pi$
$114$		0			0
$115$	6.03949	−	3.97223i	0.563185	−	0.370413i
$116$	39.5181	+	14.3834i	3.66917	+	1.33547i
$117$		0			0
$118$	8.43989	−	3.07187i	0.776955	−	0.282788i
$119$	−4.32320	+	5.80707i	−0.396307	+	0.532333i
$120$		0			0
$121$	4.90754	−	5.20169i	0.446140	−	0.472881i
$122$	4.86401	−	5.15555i	0.440367	−	0.466761i
$123$		0			0
$124$	−11.1142	+	14.9290i	−0.998089	+	1.34067i
$125$	0.466861	−	0.169924i	0.0417573	−	0.0151984i
$126$		0			0
$127$	3.75129	+	1.36536i	0.332873	+	0.121156i	0.503049	−	0.864258i	$-0.332211\pi$
$127$	3.75129	+	1.36536i	0.332873	+	0.121156i	−0.170176	+	0.985414i	$0.554434\pi$
$128$	10.2988	−	6.77365i	0.910296	−	0.598711i
$129$		0			0
$130$	18.7608	+	25.2001i	1.64543	+	2.21019i
$131$	8.15796	+	5.36557i	0.712764	+	0.468792i	0.853392	−	0.521270i	$-0.174542\pi$
$131$	8.15796	+	5.36557i	0.712764	+	0.468792i	−0.140628	+	0.990063i	$0.544912\pi$
$132$		0			0
$133$	0.674705	−	2.25367i	0.0585043	−	0.195418i
$134$	2.34254	−	4.05740i	0.202365	−	0.350506i
$135$		0			0
$136$	−13.5903	−	23.5391i	−1.16536	−	2.01846i
$137$	−7.22924	+	1.71336i	−0.617636	+	0.146382i	−0.527511	−	0.849548i	$-0.676875\pi$
$137$	−7.22924	+	1.71336i	−0.617636	+	0.146382i	−0.0901247	+	0.995930i	$0.528727\pi$
$138$		0			0
$139$	15.8653	−	7.96784i	1.34567	−	0.675823i	0.377479	−	0.926018i	$-0.376791\pi$
$139$	15.8653	−	7.96784i	1.34567	−	0.675823i	0.968195	+	0.250195i	$0.0804947\pi$
$140$	9.33658	−	21.6446i	0.789085	−	1.82930i
$141$		0			0
$142$	−0.339253	−	5.82475i	−0.0284695	−	0.488802i
$143$	−1.32192	−	7.49701i	−0.110545	−	0.626931i
$144$		0			0
$145$	5.22485	−	29.6316i	0.433900	−	2.46077i
$146$	28.8675	+	3.37412i	2.38909	+	0.279244i
$147$		0			0
$148$	8.74762	+	29.2191i	0.719050	+	2.40180i
$149$	−13.6664	−	3.23898i	−1.11959	−	0.265348i	−0.371166	−	0.928567i	$-0.621042\pi$
$149$	−13.6664	−	3.23898i	−1.11959	−	0.265348i	−0.748426	+	0.663219i	$0.769190\pi$
$150$		0			0
$151$	1.09547	+	2.53958i	0.0891481	+	0.206668i	0.956957	−	0.290229i	$-0.0937316\pi$
$151$	1.09547	+	2.53958i	0.0891481	+	0.206668i	−0.867809	+	0.496898i	$0.834472\pi$
$152$	6.76593	+	5.67729i	0.548789	+	0.460489i
$153$		0			0
$154$	−6.34028	+	5.32013i	−0.510915	+	0.428708i
$155$	11.8999	+	5.97634i	0.955821	+	0.480031i
$156$		0			0
$157$	−4.96356	+	0.580157i	−0.396135	+	0.0463016i	−0.311829	−	0.950138i	$-0.600942\pi$
$157$	−4.96356	+	0.580157i	−0.396135	+	0.0463016i	−0.0843064	+	0.996440i	$0.526867\pi$
$158$	−1.02957	+	17.6770i	−0.0819082	+	1.40631i
$159$		0			0
$160$	11.2392	+	11.9128i	0.888536	+	0.941793i
$161$	−3.76687			−0.296871
$162$		0			0
$163$	12.7147			0.995894			0.497947	−	0.867208i	$-0.334087\pi$
$163$	12.7147			0.995894			0.497947	+	0.867208i	$0.334087\pi$
$164$	10.9054	+	11.5590i	0.851566	+	0.902607i
$165$		0			0
$166$	0.0158497	−	0.272129i	0.00123018	−	0.0211213i
$167$	20.1090	−	2.35041i	1.55608	−	0.181880i	0.705879	−	0.708333i	$-0.250552\pi$
$167$	20.1090	−	2.35041i	1.55608	−	0.181880i	0.850205	+	0.526452i	$0.176478\pi$
$168$		0			0
$169$	1.83896	+	0.923560i	0.141458	+	0.0710430i
$170$	−27.0377	+	22.6873i	−2.07369	+	1.74004i
$171$		0			0
$172$	25.4399	+	21.3466i	1.93977	+	1.62766i
$173$	−2.69120	−	6.23889i	−0.204608	−	0.474334i	0.784754	−	0.619807i	$-0.212789\pi$
$173$	−2.69120	−	6.23889i	−0.204608	−	0.474334i	−0.989362	+	0.145472i	$0.953530\pi$
$174$		0			0
$175$	−8.33138	−	1.97457i	−0.629793	−	0.149264i
$176$	−3.89987	−	13.0265i	−0.293964	−	0.981908i
$177$		0			0
$178$	−13.3379	−	1.55897i	−0.999716	−	0.116850i
$179$	−3.89030	+	22.0630i	−0.290775	+	1.64907i	0.393122	+	0.919486i	$0.371395\pi$
$179$	−3.89030	+	22.0630i	−0.290775	+	1.64907i	−0.683897	+	0.729579i	$0.739716\pi$
$180$		0			0
$181$	−3.94361	−	22.3653i	−0.293126	−	1.66240i	−0.674721	−	0.738073i	$-0.735736\pi$
$181$	−3.94361	−	22.3653i	−0.293126	−	1.66240i	0.381595	−	0.924330i	$-0.375375\pi$
$182$	−0.951902	−	16.3435i	−0.0705597	−	1.21146i
$183$		0			0
$184$	5.60153	−	12.9858i	0.412950	−	0.957327i
$185$	19.5011	−	9.79380i	1.43375	−	0.720054i
$186$		0			0
$187$	8.32192	−	1.97233i	0.608559	−	0.144231i
$188$	15.4463	+	26.7537i	1.12653	+	1.95122i
$189$		0			0
$190$	5.73455	−	9.93253i	0.416028	−	0.720581i
$191$	−5.24469	+	17.5185i	−0.379493	+	1.26759i	0.528616	+	0.848861i	$0.322711\pi$
$191$	−5.24469	+	17.5185i	−0.379493	+	1.26759i	−0.908109	+	0.418733i	$0.862474\pi$
$192$		0			0
$193$	−7.34429	−	4.83042i	−0.528654	−	0.347701i	0.256956	−	0.966423i	$-0.417280\pi$
$193$	−7.34429	−	4.83042i	−0.528654	−	0.347701i	−0.785610	+	0.618722i	$0.787651\pi$
$194$	−6.60883	−	8.87719i	−0.474486	−	0.637345i
$195$		0			0
$196$	15.7870	−	10.3833i	1.12764	−	0.741662i
$197$	−1.74796	−	0.636207i	−0.124537	−	0.0453279i	0.279000	−	0.960291i	$-0.409997\pi$
$197$	−1.74796	−	0.636207i	−0.124537	−	0.0453279i	−0.403537	+	0.914963i	$0.632219\pi$
$198$		0			0
$199$	−12.5821	+	4.57950i	−0.891919	+	0.324632i	−0.747010	−	0.664813i	$-0.768511\pi$
$199$	−12.5821	+	4.57950i	−0.891919	+	0.324632i	−0.144909	+	0.989445i	$0.546289\pi$
$200$	19.1963	−	25.7851i	1.35738	−	1.82328i
$201$		0			0
$202$	19.5313	−	20.7019i	1.37422	−	1.45658i
$203$	−10.7597	+	11.4046i	−0.755185	+	0.800449i
$204$		0			0
$205$	6.78962	−	9.12005i	0.474208	−	0.636972i
$206$	9.61648	−	3.50011i	0.670012	−	0.243865i
$207$		0			0
$208$	25.2743	+	9.19908i	1.75246	+	0.637842i
$209$	−2.32191	+	1.52714i	−0.160610	+	0.105635i
$210$		0			0
$211$	14.5524	+	19.5473i	1.00183	+	1.34569i	0.937585	+	0.347757i	$0.113057\pi$
$211$	14.5524	+	19.5473i	1.00183	+	1.34569i	0.0642457	+	0.997934i	$0.479536\pi$
$212$	10.0713	+	6.62403i	0.691703	+	0.454940i
$213$		0			0
$214$	−11.8039	+	39.4277i	−0.806897	+	2.69523i
$215$	11.8802	−	20.5771i	0.810223	−	1.40335i
$216$		0			0
$217$	−3.46956	−	6.00945i	−0.235529	−	0.407948i
$218$	31.8668	−	7.55256i	2.15829	−	0.511524i
$219$		0			0
$220$	−24.8851	+	12.4978i	−1.67775	+	0.842599i
$221$	−6.70039	+	15.5332i	−0.450717	+	1.04488i
$222$		0			0
$223$	1.68329	+	28.9009i	0.112721	+	1.93535i	0.301766	+	0.953382i	$0.402424\pi$
$223$	1.68329	+	28.9009i	0.112721	+	1.93535i	−0.189044	+	0.981969i	$0.560539\pi$
$224$	−1.48200	−	8.40485i	−0.0990204	−	0.561573i
$225$		0			0
$226$	−7.11690	+	40.3619i	−0.473409	+	2.68484i
$227$	−5.72571	−	0.669240i	−0.380029	−	0.0444190i	−0.0760658	−	0.997103i	$-0.524236\pi$
$227$	−5.72571	−	0.669240i	−0.380029	−	0.0444190i	−0.303963	+	0.952684i	$0.598310\pi$
$228$		0			0
$229$	6.56007	+	21.9122i	0.433502	+	1.44800i	0.844103	+	0.536182i	$0.180134\pi$
$229$	6.56007	+	21.9122i	0.433502	+	1.44800i	−0.410601	+	0.911815i	$0.634681\pi$
$230$	−17.8695	−	4.23515i	−1.17828	−	0.279258i
$231$		0			0
$232$	−23.3158	−	54.0521i	−1.53076	−	3.54870i
$233$	15.6563	+	13.1372i	1.02568	+	0.860647i	0.990330	−	0.138728i	$-0.0443015\pi$
$233$	15.6563	+	13.1372i	1.02568	+	0.860647i	0.0353483	+	0.999375i	$0.488746\pi$
$234$		0			0
$235$	16.9317	−	14.2074i	1.10450	−	0.926787i
$236$	−14.0720	−	7.06723i	−0.916010	−	0.460037i
$237$		0			0
$238$	18.2679	−	2.13521i	1.18413	−	0.138405i
$239$	0.675153	−	11.5919i	0.0436720	−	0.749820i	−0.903400	−	0.428799i	$-0.858937\pi$
$239$	0.675153	−	11.5919i	0.0436720	−	0.749820i	0.947072	−	0.321021i	$-0.104026\pi$
$240$		0			0
$241$	−9.10551	−	9.65127i	−0.586537	−	0.621693i	0.364338	−	0.931267i	$-0.381295\pi$
$241$	−9.10551	−	9.65127i	−0.586537	−	0.621693i	−0.950876	+	0.309573i	$0.899814\pi$
$242$	−18.1680			−1.16788
$243$		0			0
$244$	−12.4269			−0.795552
$245$	−9.27747	−	9.83354i	−0.592716	−	0.628242i
$246$		0			0
$247$	0.319626	−	5.48777i	0.0203373	−	0.349179i
$248$	25.8762	−	3.02450i	1.64314	−	0.192056i
$249$		0			0
$250$	−1.12793	−	0.566466i	−0.0713364	−	0.0358265i
$251$	−5.58921	+	4.68990i	−0.352788	+	0.296024i	−0.801908	−	0.597447i	$-0.796182\pi$
$251$	−5.58921	+	4.68990i	−0.352788	+	0.296024i	0.449121	+	0.893471i	$0.351737\pi$
$252$		0			0
$253$	3.40886	+	2.86038i	0.214313	+	0.179830i
$254$	−4.01696	−	9.31235i	−0.252046	−	0.584309i
$255$		0			0
$256$	−28.9030	−	6.85013i	−1.80644	−	0.428133i
$257$	3.92569	+	13.1127i	0.244878	+	0.817948i	0.988744	+	0.149619i	$0.0478049\pi$
$257$	3.92569	+	13.1127i	0.244878	+	0.817948i	−0.743866	+	0.668329i	$0.767010\pi$
$258$		0			0
$259$	−11.2947	−	1.32016i	−0.701816	−	0.0820305i
$260$	9.56483	−	54.2448i	0.593185	−	3.36412i
$261$		0			0
$262$	−4.30756	−	24.4294i	−0.266122	−	1.50925i
$263$	0.0102305	+	0.175651i	0.000630840	+	0.0108311i	0.998609	−	0.0527284i	$-0.0167918\pi$
$263$	0.0102305	+	0.175651i	0.000630840	+	0.0108311i	−0.997978	+	0.0635595i	$0.979755\pi$
$264$		0			0
$265$	3.41604	−	7.91927i	0.209846	−	0.486477i
$266$	−5.34083	+	2.68227i	−0.327467	+	0.164460i
$267$		0			0
$268$	−7.99275	+	1.89432i	−0.488235	+	0.115714i
$269$	4.02592	+	6.97309i	0.245464	+	0.425157i	0.962262	−	0.272124i	$-0.0877262\pi$
$269$	4.02592	+	6.97309i	0.245464	+	0.425157i	−0.716798	+	0.697281i	$0.754393\pi$
$270$		0			0
$271$	−9.57442	+	16.5834i	−0.581605	+	1.00737i	0.413685	+	0.910420i	$0.364242\pi$
$271$	−9.57442	+	16.5834i	−0.581605	+	1.00737i	−0.995289	+	0.0969488i	$0.969092\pi$
$272$	−8.66625	+	28.9473i	−0.525469	+	1.75519i
$273$		0			0
$274$	15.7696	+	10.3718i	0.952675	+	0.626584i
$275$	6.04017	+	8.11335i	0.364236	+	0.489254i
$276$		0			0
$277$	−17.7854	+	11.6976i	−1.06862	+	0.702841i	−0.956759	−	0.290883i	$-0.906051\pi$
$277$	−17.7854	+	11.6976i	−1.06862	+	0.702841i	−0.111860	+	0.993724i	$0.535681\pi$
$278$	−42.3832	−	15.4262i	−2.54198	−	0.925204i
$279$		0			0
$280$	−31.0062	+	11.2853i	−1.85297	+	0.674427i
$281$	5.97587	−	8.02698i	0.356490	−	0.478849i	−0.587312	−	0.809361i	$-0.699814\pi$
$281$	5.97587	−	8.02698i	0.356490	−	0.478849i	0.943802	+	0.330511i	$0.107221\pi$
$282$		0			0
$283$	−18.9383	+	20.0734i	−1.12577	+	1.19324i	−0.146812	+	0.989164i	$0.546901\pi$
$283$	−18.9383	+	20.0734i	−1.12577	+	1.19324i	−0.978955	+	0.204078i	$0.934580\pi$
$284$	−7.01998	+	7.44074i	−0.416559	+	0.441527i
$285$		0			0
$286$	−11.5490	+	15.5131i	−0.682909	+	0.917307i
$287$	−5.56753	+	2.02641i	−0.328641	+	0.119615i
$288$		0			0
$289$	−1.88425	−	0.685809i	−0.110838	−	0.0403417i
$290$	−63.8651	+	42.0047i	−3.75029	+	2.46660i
$291$		0			0
$292$	−30.4292	−	40.8736i	−1.78074	−	2.39194i
$293$	6.12519	+	4.02860i	0.357837	+	0.235353i	0.715680	−	0.698429i	$-0.246117\pi$
$293$	6.12519	+	4.02860i	0.357837	+	0.235353i	−0.357842	+	0.933782i	$0.616487\pi$
$294$		0			0
$295$	−3.23128	+	10.7932i	−0.188132	+	0.628405i
$296$	21.3468	−	36.9738i	1.24076	−	2.14906i
$297$		0			0
$298$	17.8406	+	30.9008i	1.03348	+	1.79004i
$299$	−8.56476	+	2.02988i	−0.495313	+	0.117391i
$300$		0			0
$301$	−11.0645	+	5.55682i	−0.637750	+	0.320290i
$302$	2.78305	−	6.45183i	0.160146	−	0.371261i
$303$		0			0
$304$	−0.570916	−	9.80226i	−0.0327443	−	0.562198i
$305$	1.54393	+	8.75604i	0.0884050	+	0.501369i
$306$		0			0
$307$	1.01208	−	5.73982i	0.0577627	−	0.327589i	−0.942210	−	0.335024i	$-0.891256\pi$
$307$	1.01208	−	5.73982i	0.0577627	−	0.327589i	0.999972	+	0.00743517i	$0.00236671\pi$
$308$	14.4130	+	1.68464i	0.821257	+	0.0959912i
$309$		0			0
$310$	−9.70258	−	32.4089i	−0.551070	−	1.84070i
$311$	8.87535	+	2.10350i	0.503275	+	0.119278i	0.474408	−	0.880305i	$-0.342662\pi$
$311$	8.87535	+	2.10350i	0.503275	+	0.119278i	0.0288667	+	0.999583i	$0.490810\pi$
$312$		0			0
$313$	2.53218	+	5.87025i	0.143127	+	0.331806i	0.974668	−	0.223658i	$-0.0717999\pi$
$313$	2.53218	+	5.87025i	0.143127	+	0.331806i	−0.831541	+	0.555464i	$0.812541\pi$
$314$	9.72554	+	8.16070i	0.548844	+	0.460535i
$315$		0			0
$316$	23.7818	−	19.9553i	1.33783	−	1.12257i
$317$	22.0800	+	11.0890i	1.24014	+	0.622820i	0.943247	−	0.332092i	$-0.107755\pi$
$317$	22.0800	+	11.0890i	1.24014	+	0.622820i	0.296889	+	0.954912i	$0.404051\pi$
$318$		0			0
$319$	18.3972	−	2.15033i	1.03005	−	0.120395i
$320$	−0.149394	+	2.56499i	−0.00835136	+	0.143387i
$321$		0			0
$322$	6.56716	+	6.96078i	0.365973	+	0.387909i
$323$	6.17570			0.343625
$324$		0			0
$325$	−20.0072			−1.10980
$326$	−22.1668	−	23.4955i	−1.22771	−	1.30129i
$327$		0			0
$328$	1.29340	−	22.2068i	0.0714159	−	1.22616i
$329$	−11.4399	+	1.33713i	−0.630700	+	0.0737182i
$330$		0			0
$331$	−6.31682	−	3.17243i	−0.347204	−	0.174372i	0.266647	−	0.963794i	$-0.414084\pi$
$331$	−6.31682	−	3.17243i	−0.347204	−	0.174372i	−0.613851	+	0.789422i	$0.710380\pi$
$332$	−0.366110	+	0.307202i	−0.0200929	+	0.0168599i
$333$		0			0
$334$	−39.4014	−	33.0617i	−2.15595	−	1.80906i
$335$	2.32776	+	5.39636i	0.127179	+	0.294835i
$336$		0			0
$337$	0.476716	+	0.112984i	0.0259684	+	0.00615461i	0.243580	−	0.969881i	$-0.421678\pi$
$337$	0.476716	+	0.112984i	0.0259684	+	0.00615461i	−0.217611	+	0.976036i	$0.569826\pi$
$338$	−1.49940	−	5.00834i	−0.0815565	−	0.272418i
$339$		0			0
$340$	61.4631	+	7.18401i	3.33331	+	0.389608i
$341$	−1.42347	+	8.07292i	−0.0770854	+	0.437173i
$342$		0			0
$343$	3.24192	+	18.3858i	0.175047	+	0.992742i
$344$	−2.70290	−	46.4070i	−0.145730	−	2.50210i
$345$		0			0
$346$	−6.83700	+	15.8499i	−0.367559	+	0.852098i
$347$	−16.8482	+	8.46148i	−0.904458	+	0.454236i	−0.839318	−	0.543640i	$-0.817046\pi$
$347$	−16.8482	+	8.46148i	−0.904458	+	0.454236i	−0.0651396	+	0.997876i	$0.520749\pi$
$348$		0			0
$349$	34.5051	−	8.17787i	1.84702	−	0.437751i	0.850865	−	0.525384i	$-0.176078\pi$
$349$	34.5051	−	8.17787i	1.84702	−	0.437751i	0.996153	+	0.0876323i	$0.0279301\pi$
$350$	10.8761	+	18.8380i	0.581353	+	1.00693i
$351$		0			0
$352$	−5.04108	+	8.73141i	−0.268691	+	0.465386i
$353$	−0.566782	+	1.89318i	−0.0301668	+	0.100764i	−0.971747	−	0.236024i	$-0.924155\pi$
$353$	−0.566782	+	1.89318i	−0.0301668	+	0.100764i	0.941580	+	0.336788i	$0.109341\pi$
$354$		0			0
$355$	6.11494	+	4.02186i	0.324547	+	0.213458i
$356$	14.0595	+	18.8852i	0.745151	+	1.00091i
$357$		0			0
$358$	47.5525	−	31.2757i	2.51323	−	1.65297i
$359$	−7.57144	−	2.75578i	−0.399605	−	0.145444i	0.134397	−	0.990928i	$-0.457090\pi$
$359$	−7.57144	−	2.75578i	−0.399605	−	0.145444i	−0.534002	+	0.845483i	$0.679313\pi$
$360$		0			0
$361$	15.9684	−	5.81202i	0.840442	−	0.305896i
$362$	−34.4535	+	46.2791i	−1.81084	+	2.43238i
$363$		0			0
$364$	−19.6972	+	20.8778i	−1.03241	+	1.09429i
$365$	−25.0191	+	26.5187i	−1.30956	+	1.38805i
$366$		0			0
$367$	10.6360	−	14.2867i	0.555196	−	0.745758i	−0.432587	−	0.901592i	$-0.642399\pi$
$367$	10.6360	−	14.2867i	0.555196	−	0.745758i	0.987783	+	0.155834i	$0.0498065\pi$
$368$	−14.7740	+	5.37729i	−0.770148	+	0.280311i
$369$		0			0
$370$	−52.0961	−	18.9614i	−2.70835	−	0.985757i
$371$	−3.75492	+	2.46965i	−0.194946	+	0.128218i
$372$		0			0
$373$	1.40417	+	1.88613i	0.0727052	+	0.0976601i	0.836988	−	0.547221i	$-0.184314\pi$
$373$	1.40417	+	1.88613i	0.0727052	+	0.0976601i	−0.764283	+	0.644881i	$0.776907\pi$
$374$	−18.1531	−	11.9395i	−0.938675	−	0.617376i
$375$		0			0
$376$	12.4021	−	41.4259i	0.639589	−	2.13638i
$377$	−18.3187	+	31.7290i	−0.943463	+	1.63413i
$378$		0			0
$379$	−5.81489	−	10.0717i	−0.298691	−	0.517348i	0.677146	−	0.735849i	$-0.263217\pi$
$379$	−5.81489	−	10.0717i	−0.298691	−	0.517348i	−0.975837	+	0.218501i	$0.929883\pi$
$380$	−19.5663	+	4.63729i	−1.00373	+	0.237888i
$381$		0			0
$382$	41.5160	−	20.8501i	2.12414	−	1.06678i
$383$	11.8590	−	27.4924i	0.605969	−	1.40479i	−0.288420	−	0.957504i	$-0.593130\pi$
$383$	11.8590	−	27.4924i	0.605969	−	1.40479i	0.894389	−	0.447290i	$-0.147611\pi$
$384$		0			0
$385$	−0.603678	−	10.3647i	−0.0307663	−	0.528236i
$386$	3.87793	+	21.9928i	0.197381	+	1.11941i
$387$		0			0
$388$	−3.36939	+	19.1088i	−0.171055	+	0.970100i
$389$	3.38863	+	0.396074i	0.171810	+	0.0200817i	0.201563	−	0.979476i	$-0.435398\pi$
$389$	3.38863	+	0.396074i	0.171810	+	0.0200817i	−0.0297527	+	0.999557i	$0.509472\pi$
$390$		0			0
$391$	−2.83609	−	9.47321i	−0.143427	−	0.479081i
$392$	−25.7365	−	6.09967i	−1.29989	−	0.308080i
$393$		0			0
$394$	1.87176	+	4.33922i	0.0942978	+	0.218607i
$395$	−17.0152	−	14.2775i	−0.856130	−	0.718378i
$396$		0			0
$397$	−2.18658	+	1.83476i	−0.109741	+	0.0920838i	−0.696007	−	0.718035i	$-0.745042\pi$
$397$	−2.18658	+	1.83476i	−0.109741	+	0.0920838i	0.586266	+	0.810119i	$0.300597\pi$
$398$	30.3980	+	15.2665i	1.52371	+	0.765238i
$399$		0			0
$400$	−35.4952	+	4.14879i	−1.77476	+	0.207440i
$401$	1.44343	−	24.7827i	0.0720813	−	1.23759i	−0.747358	−	0.664422i	$-0.768678\pi$
$401$	1.44343	−	24.7827i	0.0720813	−	1.23759i	0.819439	−	0.573166i	$-0.194285\pi$
$402$		0			0
$403$	−11.1271	−	11.7941i	−0.554281	−	0.587504i
$404$	−49.8999			−2.48261
$405$		0			0
$406$	39.8331			1.97688
$407$	9.21875	+	9.77130i	0.456956	+	0.484345i
$408$		0			0
$409$	0.835488	−	14.3448i	0.0413122	−	0.709303i	−0.912533	−	0.409004i	$-0.865876\pi$
$409$	0.835488	−	14.3448i	0.0413122	−	0.709303i	0.953845	−	0.300300i	$-0.0970867\pi$
$410$	−28.6899	+	3.35337i	−1.41689	+	0.165611i
$411$		0			0
$412$	−16.0338	−	8.05246i	−0.789927	−	0.396716i
$413$	4.49743	−	3.77379i	0.221304	−	0.185696i
$414$		0			0
$415$	0.261941	+	0.219795i	0.0128582	+	0.0107893i
$416$	−7.89883	−	18.3116i	−0.387272	−	0.897798i
$417$		0			0
$418$	6.87002	+	1.62822i	0.336024	+	0.0796390i
$419$	−5.29195	−	17.6763i	−0.258529	−	0.863546i	−0.984435	−	0.175752i	$-0.943764\pi$
$419$	−5.29195	−	17.6763i	−0.258529	−	0.863546i	0.725906	−	0.687794i	$-0.241421\pi$
$420$		0			0
$421$	−17.6729	−	2.06567i	−0.861325	−	0.100674i	−0.326050	−	0.945353i	$-0.605718\pi$
$421$	−17.6729	−	2.06567i	−0.861325	−	0.100674i	−0.535275	+	0.844678i	$0.679792\pi$
$422$	10.7507	−	60.9701i	0.523335	−	2.96798i
$423$		0			0
$424$	−2.93005	−	16.6171i	−0.142296	−	0.807000i
$425$	−1.30693	−	22.4391i	−0.0633953	−	1.08845i
$426$		0			0
$427$	1.83510	−	4.25424i	0.0888067	−	0.205877i
$428$	64.4832	−	32.3847i	3.11691	−	1.56537i
$429$		0			0
$430$	−58.7363	+	13.9208i	−2.83252	+	0.671319i
$431$	−5.41651	−	9.38166i	−0.260904	−	0.451899i	0.705578	−	0.708632i	$-0.250687\pi$
$431$	−5.41651	−	9.38166i	−0.260904	−	0.451899i	−0.966482	+	0.256733i	$0.917354\pi$
$432$		0			0
$433$	15.0647	−	26.0928i	0.723962	−	1.25394i	−0.235438	−	0.971889i	$-0.575653\pi$
$433$	15.0647	−	26.0928i	0.723962	−	1.25394i	0.959400	−	0.282049i	$-0.0910141\pi$
$434$	−5.05601	+	16.8882i	−0.242696	+	0.810662i
$435$		0			0
$436$	−47.9724	−	31.5519i	−2.29746	−	1.51106i
$437$	1.91885	+	2.57746i	0.0917909	+	0.123297i
$438$		0			0
$439$	−23.4552	+	15.4267i	−1.11945	+	0.736276i	−0.967691	−	0.252140i	$-0.918866\pi$
$439$	−23.4552	+	15.4267i	−1.11945	+	0.736276i	−0.151763	+	0.988417i	$0.548495\pi$
$440$	36.6289	+	13.3318i	1.74621	+	0.635570i
$441$		0			0
$442$	40.3853	−	14.6990i	1.92093	−	0.699162i
$443$	−8.66672	+	11.6414i	−0.411768	+	0.553101i	−0.958826	−	0.283994i	$-0.908340\pi$
$443$	−8.66672	+	11.6414i	−0.411768	+	0.553101i	0.547058	+	0.837095i	$0.315748\pi$
$444$		0			0
$445$	11.5598	−	12.2527i	0.547986	−	0.580831i
$446$	50.4713	−	53.4965i	2.38989	−	2.53313i
$447$		0			0
$448$	0.799524	−	1.07395i	0.0377740	−	0.0507392i
$449$	7.39003	−	2.68975i	0.348757	−	0.126937i	−0.161701	−	0.986840i	$-0.551698\pi$
$449$	7.39003	−	2.68975i	0.348757	−	0.126937i	0.510458	+	0.859903i	$0.329476\pi$
$450$		0			0
$451$	6.57715	+	2.39389i	0.309706	+	0.112724i
$452$	60.0353	−	39.4859i	2.82382	−	1.85726i
$453$		0			0
$454$	8.74553	+	11.7473i	0.410448	+	0.551327i
$455$	17.1578	+	11.2848i	0.804368	+	0.529041i
$456$		0			0
$457$	−7.29734	+	24.3748i	−0.341355	+	1.14021i	0.599210	+	0.800592i	$0.295481\pi$
$457$	−7.29734	+	24.3748i	−0.341355	+	1.14021i	−0.940565	+	0.339613i	$0.889704\pi$
$458$	29.0546	−	50.3240i	1.35763	−	2.35149i
$459$		0			0
$460$	16.0989	+	27.8841i	0.750615	+	1.30010i
$461$	19.8804	−	4.71173i	0.925920	−	0.219447i	0.260119	−	0.965576i	$-0.416238\pi$
$461$	19.8804	−	4.71173i	0.925920	−	0.219447i	0.665801	+	0.746129i	$0.268090\pi$
$462$		0			0
$463$	24.6987	−	12.4042i	1.14785	−	0.576470i	0.229916	−	0.973211i	$-0.426155\pi$
$463$	24.6987	−	12.4042i	1.14785	−	0.576470i	0.917931	+	0.396741i	$0.129859\pi$
$464$	−25.9202	+	60.0898i	−1.20332	+	2.78960i
$465$		0			0
$466$	−3.01902	−	51.8346i	−0.139854	−	2.40119i
$467$	−1.59148	−	9.02572i	−0.0736448	−	0.417661i	−0.999234	−	0.0391312i	$-0.987541\pi$
$467$	−1.59148	−	9.02572i	−0.0736448	−	0.417661i	0.925589	−	0.378529i	$-0.123570\pi$
$468$		0			0
$469$	0.531798	−	3.01598i	0.0245562	−	0.139265i
$470$	−55.7725	−	6.51887i	−2.57259	−	0.300693i
$471$		0			0
$472$	6.32177	+	21.1162i	0.290983	+	0.971951i
$473$	14.2326	+	3.37318i	0.654413	+	0.155099i
$474$		0			0
$475$	2.89292	+	6.70655i	0.132736	+	0.307718i
$476$	−24.7022	−	20.7276i	−1.13222	−	0.950049i
$477$		0			0
$478$	−22.5977	+	18.9618i	−1.03360	+	0.867291i
$479$	−6.03701	−	3.03190i	−0.275838	−	0.138531i	0.305503	−	0.952191i	$-0.401175\pi$
$479$	−6.03701	−	3.03190i	−0.275838	−	0.138531i	−0.581341	+	0.813660i	$0.697472\pi$
$480$		0			0
$481$	−26.3922	+	3.08480i	−1.20338	+	0.140655i
$482$	−1.96001	+	33.6521i	−0.0892760	+	1.53281i
$483$		0			0
$484$	21.8590	+	23.1692i	0.993591	+	1.05315i
$485$	13.8827			0.630381
$486$		0			0
$487$	−19.6769			−0.891646			−0.445823	−	0.895121i	$-0.647089\pi$
$487$	−19.6769			−0.891646			−0.445823	+	0.895121i	$0.647089\pi$
$488$	11.9371	+	12.6526i	0.540366	+	0.572754i
$489$		0			0
$490$	−1.99703	+	34.2876i	−0.0902164	+	1.54896i
$491$	−32.9888	+	3.85583i	−1.48876	+	0.174011i	−0.821242	−	0.570580i	$-0.806718\pi$
$491$	−32.9888	+	3.85583i	−1.48876	+	0.174011i	−0.667521	+	0.744591i	$0.732644\pi$
$492$		0			0
$493$	−36.7823	−	18.4728i	−1.65659	−	0.831972i
$494$	−10.6981	+	8.97675i	−0.481329	+	0.403883i
$495$		0			0
$496$	−22.1865	−	18.6167i	−0.996205	−	0.835915i
$497$	−1.51062	−	3.50201i	−0.0677605	−	0.157087i
$498$		0			0
$499$	31.2916	+	7.41625i	1.40081	+	0.331997i	0.860491	−	0.509466i	$-0.170157\pi$
$499$	31.2916	+	7.41625i	1.40081	+	0.331997i	0.540315	+	0.841463i	$0.318305\pi$
$500$	0.634676	+	2.11997i	0.0283836	+	0.0948078i
$501$		0			0
$502$	18.4107	+	2.15190i	0.821709	+	0.0960440i
$503$	−2.99418	+	16.9809i	−0.133504	+	0.757139i	0.842386	+	0.538875i	$0.181150\pi$
$503$	−2.99418	+	16.9809i	−0.133504	+	0.757139i	−0.975890	+	0.218264i	$0.929961\pi$
$504$		0			0
$505$	6.19959	+	35.1596i	0.275878	+	1.56458i
$506$	−0.657335	−	11.2860i	−0.0292221	−	0.501724i
$507$		0			0
$508$	−7.04277	+	16.3270i	−0.312472	+	0.724392i
$509$	−28.7481	+	14.4379i	−1.27424	+	0.639947i	−0.951822	−	0.306651i	$-0.900791\pi$
$509$	−28.7481	+	14.4379i	−1.27424	+	0.639947i	−0.322416	+	0.946598i	$0.604495\pi$
$510$		0			0
$511$	18.4862	−	4.38131i	0.817782	−	0.193818i
$512$	25.4044	+	44.0017i	1.12273	+	1.94462i
$513$		0			0
$514$	17.3869	−	30.1150i	0.766902	−	1.32831i
$515$	−3.68175	+	12.2979i	−0.162237	+	0.541910i
$516$		0			0
$517$	11.3680	+	7.47682i	0.499962	+	0.328830i
$518$	17.2516	+	23.1729i	0.757992	+	1.01816i
$519$		0			0
$520$	−64.4176	+	42.3681i	−2.82490	+	1.85796i
$521$	23.1431	+	8.42341i	1.01392	+	0.369036i	0.794936	−	0.606693i	$-0.207504\pi$
$521$	23.1431	+	8.42341i	1.01392	+	0.369036i	0.218982	+	0.975729i	$0.429726\pi$
$522$		0			0
$523$	−5.49055	+	1.99840i	−0.240085	+	0.0873838i	−0.459260	−	0.888302i	$-0.651886\pi$
$523$	−5.49055	+	1.99840i	−0.240085	+	0.0873838i	0.219175	+	0.975685i	$0.429663\pi$
$524$	−25.9715	+	34.8858i	−1.13457	+	1.52399i
$525$		0			0
$526$	0.306749	−	0.325135i	0.0133749	−	0.0141765i
$527$	12.5008	−	13.2501i	0.544542	−	0.577181i
$528$		0			0
$529$	−10.6622	+	14.3218i	−0.463572	+	0.622685i
$530$	−20.5895	+	7.49397i	−0.894352	+	0.325517i
$531$		0			0
$532$	9.84650	+	3.58383i	0.426900	+	0.155379i
$533$	−11.5669	+	7.60770i	−0.501020	+	0.329526i
$534$		0			0
$535$	−30.8298	−	41.4115i	−1.33289	−	1.79038i
$536$	9.60640	+	6.31823i	0.414933	+	0.272906i
$537$		0			0
$538$	5.86677	−	19.5964i	0.252934	−	0.844859i
$539$	4.16120	−	7.20740i	0.179235	−	0.310445i
$540$		0			0
$541$	4.25140	+	7.36363i	0.182782	+	0.316587i	0.942827	−	0.333283i	$-0.108156\pi$
$541$	4.25140	+	7.36363i	0.182782	+	0.316587i	−0.760045	+	0.649870i	$0.774823\pi$
$542$	47.3364	−	11.2189i	2.03327	−	0.481895i
$543$		0			0
$544$	20.0214	−	10.0551i	0.858409	−	0.431109i
$545$	−16.2715	+	37.7215i	−0.696993	+	1.61581i
$546$		0			0
$547$	2.61420	+	44.8841i	0.111775	+	1.91911i	0.331346	+	0.943509i	$0.392497\pi$
$547$	2.61420	+	44.8841i	0.111775	+	1.91911i	−0.219571	+	0.975597i	$0.570466\pi$
$548$	−5.74641	−	32.5895i	−0.245474	−	1.39215i
$549$		0			0
$550$	4.46221	−	25.3064i	0.190269	−	1.07907i
$551$	13.2846	+	1.55274i	0.565942	+	0.0661491i
$552$		0			0
$553$	3.31962	+	11.0883i	0.141165	+	0.471523i
$554$	52.6230	+	12.4719i	2.23574	+	0.529879i
$555$		0			0
$556$	31.3211	+	72.6105i	1.32831	+	3.07937i
$557$	18.7402	+	15.7249i	0.794047	+	0.666285i	0.946744	−	0.321988i	$-0.104351\pi$
$557$	18.7402	+	15.7249i	0.794047	+	0.666285i	−0.152696	+	0.988273i	$0.548796\pi$
$558$		0			0
$559$	−22.1631	+	18.5970i	−0.937399	+	0.786571i
$560$	32.7800	+	16.4628i	1.38521	+	0.695678i
$561$		0			0
$562$	−25.2513	+	2.95146i	−1.06516	+	0.124500i
$563$	0.352934	−	6.05965i	0.0148744	−	0.255384i	−0.982671	−	0.185359i	$-0.940655\pi$
$563$	0.352934	−	6.05965i	0.0148744	−	0.255384i	0.997545	−	0.0700247i	$-0.0223078\pi$
$564$		0			0
$565$	−35.2807	−	37.3953i	−1.48427	−	1.57323i
$566$	70.1107			2.94697
$567$		0			0
$568$	14.3191			0.600817
$569$	7.29454	+	7.73176i	0.305803	+	0.324132i	0.861990	−	0.506925i	$-0.169218\pi$
$569$	7.29454	+	7.73176i	0.305803	+	0.324132i	−0.556187	+	0.831057i	$0.687736\pi$
$570$		0			0
$571$	−1.59819	+	27.4399i	−0.0668822	+	1.14832i	0.783234	+	0.621727i	$0.213569\pi$
$571$	−1.59819	+	27.4399i	−0.0668822	+	1.14832i	−0.850116	+	0.526595i	$0.823468\pi$
$572$	33.6788	−	3.93648i	1.40818	−	0.164593i
$573$		0			0
$574$	13.4510	+	6.75536i	0.561435	+	0.281963i
$575$	8.95899	−	7.51748i	0.373616	−	0.313501i
$576$		0			0
$577$	−4.54811	−	3.81632i	−0.189340	−	0.158875i	0.543190	−	0.839610i	$-0.317216\pi$
$577$	−4.54811	−	3.81632i	−0.189340	−	0.158875i	−0.732530	+	0.680734i	$0.761661\pi$
$578$	2.01769	+	4.67753i	0.0839248	+	0.194560i
$579$		0			0
$580$	130.408	+	30.9071i	5.41488	+	1.28335i
$581$	−0.0511040	−	0.170699i	−0.00212015	−	0.00708180i
$582$		0			0
$583$	5.27339	+	0.616371i	0.218401	+	0.0255275i
$584$	−12.3859	+	70.2442i	−0.512534	+	2.90672i
$585$		0			0
$586$	−3.23422	−	18.3422i	−0.133604	−	0.757708i
$587$	−0.645821	−	11.0883i	−0.0266559	−	0.457664i	−0.985056	−	0.172235i	$-0.944901\pi$
$587$	−0.645821	−	11.0883i	−0.0266559	−	0.457664i	0.958400	−	0.285429i	$-0.0921360\pi$
$588$		0			0
$589$	−2.34453	+	5.43524i	−0.0966049	+	0.223955i
$590$	25.5781	−	12.8458i	1.05304	−	0.528854i
$591$		0			0
$592$	−46.1832	+	10.9456i	−1.89812	+	0.449862i
$593$	1.02536	+	1.77597i	0.0421064	+	0.0729304i	0.886311	−	0.463091i	$-0.153260\pi$
$593$	1.02536	+	1.77597i	0.0421064	+	0.0729304i	−0.844204	+	0.536022i	$0.819926\pi$
$594$		0			0
$595$	−11.5357	+	19.9805i	−0.472919	+	0.819119i
$596$	17.9420	−	59.9303i	0.734931	−	2.45484i
$597$		0			0
$598$	18.6828	+	12.2879i	0.763997	+	0.502489i
$599$	−1.67467	−	2.24947i	−0.0684250	−	0.0919107i	0.766593	−	0.642133i	$-0.221950\pi$
$599$	−1.67467	−	2.24947i	−0.0684250	−	0.0919107i	−0.835018	+	0.550222i	$0.814543\pi$
$600$		0			0
$601$	30.1111	−	19.8044i	1.22826	−	0.807839i	0.241558	−	0.970386i	$-0.422341\pi$
$601$	30.1111	−	19.8044i	1.22826	−	0.807839i	0.986701	+	0.162548i	$0.0519711\pi$
$602$	29.5584	+	10.7584i	1.20471	+	0.438478i
$603$		0			0
$604$	−11.5763	+	4.21343i	−0.471033	+	0.171442i
$605$	13.6093	−	18.2805i	0.553297	−	0.743207i
$606$		0			0
$607$	−26.4300	+	28.0142i	−1.07276	+	1.13706i	−0.0826783	+	0.996576i	$0.526347\pi$
$607$	−26.4300	+	28.0142i	−1.07276	+	1.13706i	−0.990083	+	0.140484i	$0.955134\pi$
$608$	−4.99604	+	5.29549i	−0.202616	+	0.214761i
$609$		0			0
$610$	13.4886	−	18.1183i	0.546136	−	0.733588i
$611$	−25.2903	+	9.20493i	−1.02314	+	0.372392i
$612$		0			0
$613$	−1.37170	−	0.499257i	−0.0554024	−	0.0201648i	0.314170	−	0.949367i	$-0.398274\pi$
$613$	−1.37170	−	0.499257i	−0.0554024	−	0.0201648i	−0.369573	+	0.929202i	$0.620496\pi$
$614$	−12.3711	+	8.13657i	−0.499255	+	0.328365i
$615$		0			0
$616$	−12.1296	−	16.2929i	−0.488717	−	0.656461i
$617$	−10.0466	−	6.60776i	−0.404461	−	0.266018i	0.330938	−	0.943653i	$-0.392635\pi$
$617$	−10.0466	−	6.60776i	−0.404461	−	0.266018i	−0.735399	+	0.677634i	$0.763005\pi$
$618$		0			0
$619$	−8.99692	+	30.0518i	−0.361617	+	1.20788i	0.562830	+	0.826573i	$0.309713\pi$
$619$	−8.99692	+	30.0518i	−0.361617	+	1.20788i	−0.924447	+	0.381312i	$0.875472\pi$
$620$	−29.6565	+	51.3665i	−1.19103	+	2.06293i
$621$		0			0
$622$	−11.5862	−	20.0680i	−0.464566	−	0.804652i
$623$	−8.54134	+	2.02433i	−0.342202	+	0.0811033i
$624$		0			0
$625$	−21.6225	+	10.8592i	−0.864901	+	0.434369i
$626$	6.43301	−	14.9134i	0.257115	−	0.596059i
$627$		0			0
$628$	−1.29425	−	22.2214i	−0.0516461	−	0.886729i
$629$	−5.18377	−	29.3986i	−0.206691	−	1.17220i
$630$		0			0
$631$	−3.02986	+	17.1832i	−0.120617	+	0.684053i	0.863198	+	0.504865i	$0.168458\pi$
$631$	−3.02986	+	17.1832i	−0.120617	+	0.684053i	−0.983815	+	0.179187i	$0.942653\pi$
$632$	−43.1620	−	5.04492i	−1.71689	−	0.200676i
$633$		0			0
$634$	−18.0030	−	60.1341i	−0.714989	−	2.38823i
$635$	12.3790	+	2.93388i	0.491247	+	0.116428i
$636$		0			0
$637$	6.52015	+	15.1154i	0.258338	+	0.598894i
$638$	−36.0473	−	30.2473i	−1.42713	−	1.19750i
$639$		0			0
$640$	30.0927	−	25.2508i	1.18952	−	0.998124i
$641$	−8.24662	−	4.14161i	−0.325722	−	0.163584i	0.278422	−	0.960459i	$-0.410189\pi$
$641$	−8.24662	−	4.14161i	−0.325722	−	0.163584i	−0.604144	+	0.796875i	$0.706485\pi$
$642$		0			0
$643$	−7.25189	+	0.847625i	−0.285987	+	0.0334271i	−0.257877	−	0.966178i	$-0.583023\pi$
$643$	−7.25189	+	0.847625i	−0.285987	+	0.0334271i	−0.0281099	+	0.999605i	$0.508949\pi$
$644$	0.975568	−	16.7499i	0.0384428	−	0.660037i
$645$		0			0
$646$	−10.7667	−	11.4120i	−0.423610	−	0.449001i
$647$	−34.3969			−1.35228			−0.676142	−	0.736772i	$-0.736349\pi$
$647$	−34.3969			−1.35228			−0.676142	+	0.736772i	$0.736349\pi$
$648$		0			0
$649$	−6.93563			−0.272247
$650$	34.8805	+	36.9712i	1.36813	+	1.45013i
$651$		0			0
$652$	−3.29294	+	56.5376i	−0.128962	+	2.21418i
$653$	14.1528	−	1.65422i	0.553842	−	0.0647348i	0.165431	−	0.986221i	$-0.447098\pi$
$653$	14.1528	−	1.65422i	0.553842	−	0.0647348i	0.388410	+	0.921486i	$0.373024\pi$
$654$		0			0
$655$	27.8073	+	13.9654i	1.08652	+	0.545672i
$656$	−18.9436	+	15.8956i	−0.739623	+	0.620617i
$657$		0			0
$658$	22.4151	+	18.8085i	0.873832	+	0.733232i
$659$	−17.4643	−	40.4868i	−0.680312	−	1.57714i	−0.810558	−	0.585659i	$-0.800836\pi$
$659$	−17.4643	−	40.4868i	−0.680312	−	1.57714i	0.130246	−	0.991482i	$-0.458423\pi$
$660$		0			0
$661$	−2.56181	−	0.607159i	−0.0996427	−	0.0236158i	0.180492	−	0.983576i	$-0.442231\pi$
$661$	−2.56181	−	0.607159i	−0.0996427	−	0.0236158i	−0.280135	+	0.959961i	$0.590379\pi$
$662$	5.15043	+	17.2036i	0.200177	+	0.668638i
$663$		0			0
$664$	0.664459	+	0.0776641i	0.0257860	+	0.00301395i
$665$	1.30184	−	7.38313i	0.0504834	−	0.286305i
$666$		0			0
$667$	−3.71891	−	21.0910i	−0.143997	−	0.816645i
$668$	5.24342	+	90.0261i	0.202874	+	3.48321i
$669$		0			0
$670$	5.91369	−	13.7095i	0.228466	−	0.529644i
$671$	−4.89115	+	2.45643i	−0.188821	+	0.0948294i
$672$		0			0
$673$	−3.32499	+	0.788037i	−0.128169	+	0.0303766i	−0.294200	−	0.955744i	$-0.595053\pi$
$673$	−3.32499	+	0.788037i	−0.128169	+	0.0303766i	0.166031	+	0.986121i	$0.446905\pi$
$674$	−0.622324	−	1.07790i	−0.0239710	−	0.0415190i
$675$		0			0
$676$	−4.58299	+	7.93797i	−0.176269	+	0.305307i
$677$	11.1529	−	37.2531i	0.428639	−	1.43175i	−0.422283	−	0.906464i	$-0.638771\pi$
$677$	11.1529	−	37.2531i	0.428639	−	1.43175i	0.850923	−	0.525291i	$-0.176044\pi$
$678$		0			0
$679$	−6.04414	−	3.97529i	−0.231953	−	0.152558i
$680$	−51.7259	−	69.4800i	−1.98360	−	2.66444i
$681$		0			0
$682$	17.3996	−	11.4439i	0.666265	−	0.438209i
$683$	21.7804	+	7.92743i	0.833405	+	0.303335i	0.723256	−	0.690581i	$-0.242645\pi$
$683$	21.7804	+	7.92743i	0.833405	+	0.303335i	0.110149	+	0.993915i	$0.464867\pi$
$684$		0			0
$685$	−22.2487	+	8.09787i	−0.850080	+	0.309404i
$686$	28.3231	−	38.0446i	1.08138	−	1.45255i
$687$		0			0
$688$	−35.4636	+	37.5893i	−1.35204	+	1.43308i
$689$	−7.20675	+	7.63871i	−0.274555	+	0.291012i
$690$		0			0
$691$	10.3864	−	13.9514i	0.395119	−	0.530737i	−0.559396	−	0.828901i	$-0.688967\pi$
$691$	10.3864	−	13.9514i	0.395119	−	0.530737i	0.954515	+	0.298164i	$0.0963741\pi$
$692$	28.4390	−	10.3510i	1.08109	−	0.393484i
$693$		0			0
$694$	45.0091	+	16.3820i	1.70852	+	0.621851i
$695$	47.2702	−	31.0901i	1.79306	−	1.17932i
$696$		0			0
$697$	−9.28801	−	12.4760i	−0.351808	−	0.472561i
$698$	−75.2681	−	49.5046i	−2.84894	−	1.87378i
$699$		0			0
$700$	10.9379	−	36.5352i	0.413414	−	1.38090i
$701$	−9.46247	+	16.3895i	−0.357393	+	0.619022i	−0.987524	−	0.157466i	$-0.949668\pi$
$701$	−9.46247	+	16.3895i	−0.357393	+	0.619022i	0.630132	+	0.776488i	$0.283001\pi$
$702$		0			0
$703$	4.85020	+	8.40080i	0.182929	+	0.316842i
$704$	−1.53904	+	0.364759i	−0.0580048	+	0.0137474i
$705$		0			0
$706$	4.48654	−	2.25322i	0.168853	−	0.0848012i
$707$	7.36879	−	17.0828i	0.277132	−	0.642464i
$708$		0			0
$709$	−2.48630	−	42.6881i	−0.0933749	−	1.60319i	−0.641724	−	0.766936i	$-0.721780\pi$
$709$	−2.48630	−	42.6881i	−0.0933749	−	1.60319i	0.548349	−	0.836250i	$-0.315257\pi$
$710$	−3.22881	−	18.3115i	−0.121175	−	0.687217i
$711$		0			0
$712$	5.72278	−	32.4555i	0.214470	−	1.21632i
$713$	9.41409	+	1.10035i	0.352560	+	0.0412084i
$714$		0			0
$715$	−6.95792	−	23.2411i	−0.260212	−	0.869167i
$716$	−97.0984	−	23.0127i	−3.62874	−	0.860026i
$717$		0			0
$718$	8.10766	+	18.7957i	0.302575	+	0.701448i
$719$	−9.96902	−	8.36500i	−0.371782	−	0.311962i	0.437684	−	0.899129i	$-0.355799\pi$
$719$	−9.96902	−	8.36500i	−0.371782	−	0.311962i	−0.809466	+	0.587167i	$0.800243\pi$
$720$		0			0
$721$	5.12441	−	4.29989i	0.190843	−	0.160136i
$722$	−38.5793	−	19.3753i	−1.43577	−	0.721073i
$723$		0			0
$724$	100.472	−	11.7435i	3.73400	−	0.436442i
$725$	2.83048	−	48.5974i	0.105121	−	1.80486i
$726$		0			0
$727$	34.6254	+	36.7007i	1.28418	+	1.36116i	0.898776	+	0.438409i	$0.144458\pi$
$727$	34.6254	+	36.7007i	1.28418	+	1.36116i	0.385408	+	0.922746i	$0.374061\pi$
$728$	40.1777			1.48908
$729$		0			0
$730$	92.6220			3.42810
$731$	−22.3053	−	23.6422i	−0.824991	−	0.874439i
$732$		0			0
$733$	0.929614	−	15.9609i	0.0343361	−	0.589528i	−0.936631	−	0.350316i	$-0.886074\pi$
$733$	0.929614	−	15.9609i	0.0343361	−	0.589528i	0.970968	−	0.239211i	$-0.0768889\pi$
$734$	−44.9431	+	5.25310i	−1.65888	+	0.193895i
$735$		0			0
$736$	10.4174	+	5.23181i	0.383990	+	0.192847i
$737$	−2.77144	+	2.32552i	−0.102087	+	0.0856615i
$738$		0			0
$739$	−5.46648	−	4.58692i	−0.201088	−	0.168733i	0.536683	−	0.843784i	$-0.319677\pi$
$739$	−5.46648	−	4.58692i	−0.201088	−	0.168733i	−0.737771	+	0.675051i	$0.764122\pi$
$740$	38.4989	+	89.2504i	1.41525	+	3.28091i
$741$		0			0
$742$	11.1100	+	2.63312i	0.407861	+	0.0966648i
$743$	−9.72576	−	32.4863i	−0.356804	−	1.19181i	−0.928497	−	0.371340i	$-0.878898\pi$
$743$	−9.72576	−	32.4863i	−0.356804	−	1.19181i	0.571693	−	0.820467i	$-0.306287\pi$
$744$		0			0
$745$	−44.4562	−	5.19619i	−1.62875	−	0.190374i
$746$	1.03734	−	5.88304i	0.0379797	−	0.215393i
$747$		0			0
$748$	6.61496	+	37.5153i	0.241867	+	1.37170i
$749$	1.56427	+	26.8575i	0.0571572	+	0.981352i
$750$		0			0
$751$	−16.6089	+	38.5039i	−0.606069	+	1.40503i	0.288232	+	0.957561i	$0.406933\pi$
$751$	−16.6089	+	38.5039i	−0.606069	+	1.40503i	−0.894301	+	0.447466i	$0.852327\pi$
$752$	−42.9594	+	21.5750i	−1.56657	+	0.786759i
$753$		0			0
$754$	90.5688	−	21.4652i	3.29832	−	0.781717i
$755$	4.40704	+	7.63321i	0.160389	+	0.277801i
$756$		0			0
$757$	−13.0903	+	22.6730i	−0.475774	+	0.824065i	−0.999615	−	0.0277513i	$-0.991165\pi$
$757$	−13.0903	+	22.6730i	−0.475774	+	0.824065i	0.523841	+	0.851816i	$0.324499\pi$
$758$	−8.47375	+	28.3043i	−0.307780	+	1.02806i
$759$		0			0
$760$	23.5165	+	15.4671i	0.853033	+	0.561049i
$761$	27.9919	+	37.5996i	1.01470	+	1.36298i	0.930401	+	0.366544i	$0.119459\pi$
$761$	27.9919	+	37.5996i	1.01470	+	1.36298i	0.0843029	+	0.996440i	$0.473134\pi$
$762$		0			0
$763$	17.8857	−	11.7636i	0.647504	−	0.425870i
$764$	−76.5400	−	27.8583i	−2.76912	−	1.00788i
$765$		0			0
$766$	−71.4781	+	26.0159i	−2.58261	+	0.939992i
$767$	8.19223	−	11.0041i	0.295804	−	0.397334i
$768$		0			0
$769$	9.40859	−	9.97253i	0.339283	−	0.359619i	−0.535157	−	0.844752i	$-0.679748\pi$
$769$	9.40859	−	9.97253i	0.339283	−	0.359619i	0.874440	+	0.485134i	$0.161229\pi$
$770$	−18.1005	+	19.1854i	−0.652297	+	0.691395i
$771$		0			0
$772$	23.3811	−	31.4063i	0.841505	−	1.13034i
$773$	14.3319	−	5.21640i	0.515484	−	0.187621i	−0.0711615	−	0.997465i	$-0.522671\pi$
$773$	14.3319	−	5.21640i	0.515484	−	0.187621i	0.586645	+	0.809844i	$0.300448\pi$
$774$		0			0
$775$	20.2448	+	7.36852i	0.727216	+	0.264685i
$776$	22.6923	−	14.9250i	0.814606	−	0.535775i
$777$		0			0
$778$	−5.17583	−	6.95235i	−0.185563	−	0.249254i
$779$	4.22267	+	2.77729i	0.151293	+	0.0995068i
$780$		0			0
$781$	−1.29221	+	4.31627i	−0.0462388	+	0.154448i
$782$	−12.5611	+	21.7564i	−0.449183	+	0.778008i
$783$		0			0
$784$	14.7019	+	25.4645i	0.525069	+	0.909447i
$785$	−15.4964	+	3.67272i	−0.553091	+	0.131085i
$786$		0			0
$787$	−18.7666	+	9.42492i	−0.668955	+	0.335962i	−0.750654	−	0.660695i	$-0.770262\pi$
$787$	−18.7666	+	9.42492i	−0.668955	+	0.335962i	0.0816990	+	0.996657i	$0.473965\pi$
$788$	3.28168	−	7.60778i	0.116905	−	0.271016i
$789$		0			0
$790$	3.28107	+	56.3338i	0.116735	+	2.00427i
$791$	4.65212	+	26.3835i	0.165410	+	0.938088i
$792$		0			0
$793$	1.87996	−	10.6618i	0.0667594	−	0.378611i
$794$	7.20252	+	0.841854i	0.255608	+	0.0298763i
$795$		0			0
$796$	−17.1047	−	57.1338i	−0.606261	−	2.02505i
$797$	−44.9133	−	10.6446i	−1.59091	−	0.377053i	−0.662634	−	0.748943i	$-0.730562\pi$
$797$	−44.9133	−	10.6446i	−1.59091	−	0.377053i	−0.928277	+	0.371890i	$0.878710\pi$
$798$		0			0
$799$	−11.9758	−	27.7631i	−0.423675	−	0.982188i
$800$	20.2982	+	17.0322i	0.717649	+	0.602179i
$801$		0			0
$802$	−48.3123	+	40.5388i	−1.70597	+	1.43148i
$803$	−20.0562	−	10.0726i	−0.707769	−	0.355455i
$804$		0			0
$805$	−11.9232	+	1.39362i	−0.420238	+	0.0491188i
$806$	−2.39517	+	41.1235i	−0.0843663	+	1.44851i
$807$		0			0
$808$	47.9330	+	50.8060i	1.68628	+	1.78735i
$809$	−15.0049			−0.527545			−0.263772	−	0.964585i	$-0.584967\pi$
$809$	−15.0049			−0.527545			−0.263772	+	0.964585i	$0.584967\pi$
$810$		0			0
$811$	47.0448			1.65197			0.825983	−	0.563695i	$-0.190621\pi$
$811$	47.0448			1.65197			0.825983	+	0.563695i	$0.190621\pi$
$812$	−47.9256	−	50.7981i	−1.68186	−	1.78267i
$813$		0			0
$814$	1.98439	−	34.0706i	0.0695527	−	1.19417i
$815$	40.2457	−	4.70405i	1.40975	−	0.164776i
$816$		0			0
$817$	9.43852	+	4.74020i	0.330212	+	0.165839i
$818$	−27.9642	+	23.4648i	−0.977747	+	0.820427i
$819$		0			0
$820$	38.7950	+	32.5529i	1.35478	+	1.13680i
$821$	−0.605806	−	1.40442i	−0.0211428	−	0.0490145i	0.907318	−	0.420446i	$-0.138126\pi$
$821$	−0.605806	−	1.40442i	−0.0211428	−	0.0490145i	−0.928460	+	0.371431i	$0.878867\pi$
$822$		0			0
$823$	2.10591	+	0.499110i	0.0734075	+	0.0173979i	0.267155	−	0.963653i	$-0.413916\pi$
$823$	2.10591	+	0.499110i	0.0734075	+	0.0173979i	−0.193748	+	0.981051i	$0.562064\pi$
$824$	7.20308	+	24.0600i	0.250931	+	0.838168i
$825$		0			0
$826$	−14.8144	−	1.73156i	−0.515459	−	0.0602485i
$827$	7.09126	−	40.2166i	0.246587	−	1.39847i	−0.570190	−	0.821513i	$-0.693130\pi$
$827$	7.09126	−	40.2166i	0.246587	−	1.39847i	0.816777	−	0.576954i	$-0.195759\pi$
$828$		0			0
$829$	2.97142	+	16.8518i	0.103202	+	0.585287i	0.991923	+	0.126839i	$0.0404832\pi$
$829$	2.97142	+	16.8518i	0.103202	+	0.585287i	−0.888721	+	0.458448i	$0.848406\pi$
$830$	−0.0505105	−	0.867231i	−0.00175324	−	0.0301020i
$831$		0			0
$832$	1.23916	−	2.87269i	0.0429600	−	0.0995925i
$833$	−16.5268	+	8.30006i	−0.572619	+	0.287580i
$834$		0			0
$835$	62.7812	−	14.8794i	2.17263	−	0.514924i
$836$	−6.18930	−	10.7202i	−0.214061	−	0.370765i
$837$		0			0
$838$	−23.4381	+	40.5959i	−0.809654	+	1.40236i
$839$	−5.26637	+	17.5909i	−0.181815	+	0.607305i	0.817684	+	0.575667i	$0.195258\pi$
$839$	−5.26637	+	17.5909i	−0.181815	+	0.607305i	−0.999499	+	0.0316382i	$0.989928\pi$
$840$		0			0
$841$	−50.2490	−	33.0493i	−1.73272	−	1.13963i
$842$	26.9938	+	36.2590i	0.930268	+	1.24957i
$843$		0			0
$844$	−90.6885	+	59.6467i	−3.12163	+	2.05313i
$845$	6.16251	+	2.24297i	0.211997	+	0.0771606i
$846$		0			0
$847$	−11.1597	+	4.06180i	−0.383452	+	0.139565i
$848$	−11.2017	+	15.0464i	−0.384667	+	0.516697i
$849$		0			0
$850$	−39.1866	+	41.5353i	−1.34409	+	1.42465i
$851$	10.6590	−	11.2979i	0.365387	−	0.387287i
$852$		0			0
$853$	9.26111	−	12.4398i	0.317094	−	0.425932i	−0.614788	−	0.788693i	$-0.710758\pi$
$853$	9.26111	−	12.4398i	0.317094	−	0.425932i	0.931882	+	0.362761i	$0.118166\pi$
$854$	−11.0607	+	4.02577i	−0.378489	+	0.137759i
$855$		0			0
$856$	−94.9141	−	34.5459i	−3.24410	−	1.18075i
$857$	15.9554	−	10.4940i	0.545026	−	0.358469i	−0.246944	−	0.969030i	$-0.579426\pi$
$857$	15.9554	−	10.4940i	0.545026	−	0.358469i	0.791969	+	0.610561i	$0.209056\pi$
$858$		0			0
$859$	1.69074	+	2.27106i	0.0576874	+	0.0774876i	0.830031	−	0.557718i	$-0.188323\pi$
$859$	1.69074	+	2.27106i	0.0576874	+	0.0774876i	−0.772343	+	0.635205i	$0.780915\pi$
$860$	88.4220	+	58.1561i	3.01517	+	1.98311i
$861$		0			0
$862$	−7.89320	+	26.3651i	−0.268844	+	0.898000i
$863$	1.50608	−	2.60861i	0.0512675	−	0.0887980i	−0.839253	−	0.543741i	$-0.817007\pi$
$863$	1.50608	−	2.60861i	0.0512675	−	0.0887980i	0.890520	+	0.454943i	$0.150341\pi$
$864$		0			0
$865$	−10.8266	−	18.7522i	−0.368115	−	0.637594i
$866$	−74.4805	+	17.6522i	−2.53095	+	0.599846i
$867$		0			0
$868$	27.6203	−	13.8715i	0.937495	−	0.470828i
$869$	5.41580	−	12.5552i	0.183718	−	0.425907i
$870$		0			0
$871$	−0.416092	−	7.14403i	−0.0140987	−	0.242066i
$872$	13.9566	+	79.1517i	0.472629	+	2.68041i
$873$		0			0
$874$	1.41756	−	8.03937i	0.0479496	−	0.271936i
$875$	−0.819474	−	0.0957828i	−0.0277033	−	0.00323805i
$876$		0			0
$877$	−4.16361	−	13.9074i	−0.140595	−	0.469620i	0.858469	−	0.512865i	$-0.171416\pi$
$877$	−4.16361	−	13.9074i	−0.140595	−	0.469620i	−0.999065	+	0.0432444i	$0.986231\pi$
$878$	69.3987	+	16.4478i	2.34209	+	0.555086i
$879$		0			0
$880$	−17.1636	−	39.7897i	−0.578585	−	1.34131i
$881$	−4.96691	−	4.16773i	−0.167340	−	0.140415i	0.555272	−	0.831669i	$-0.312614\pi$
$881$	−4.96691	−	4.16773i	−0.167340	−	0.140415i	−0.722612	+	0.691254i	$0.757059\pi$
$882$		0			0
$883$	19.4524	−	16.3225i	0.654626	−	0.549297i	−0.253844	−	0.967245i	$-0.581695\pi$
$883$	19.4524	−	16.3225i	0.654626	−	0.549297i	0.908471	+	0.417948i	$0.137251\pi$
$884$	−67.3353	−	33.8170i	−2.26473	−	1.13739i
$885$		0			0
$886$	36.6217	−	4.28046i	1.23033	−	0.143805i
$887$	0.00622271	−	0.106840i	0.000208938	−	0.00358733i	−0.998202	−	0.0599384i	$-0.980910\pi$
$887$	0.00622271	−	0.106840i	0.000208938	−	0.00358733i	0.998411	+	0.0563511i	$0.0179466\pi$
$888$		0			0
$889$	−4.54937	−	4.82205i	−0.152581	−	0.161726i
$890$	−42.7950			−1.43449
$891$		0			0
$892$	−128.948			−4.31749
$893$	6.74240	+	7.14653i	0.225626	+	0.239149i
$894$		0			0
$895$	−4.15129	+	71.2749i	−0.138762	+	2.38246i
$896$	−20.3320	+	2.37647i	−0.679246	+	0.0793924i
$897$		0			0
$898$	−17.8542	−	8.96670i	−0.595801	−	0.299223i
$899$	30.2219	−	25.3592i	1.00796	−	0.845777i
$900$		0			0
$901$	−9.03797	−	7.58376i	−0.301099	−	0.252652i
$902$	−7.04295	−	16.3274i	−0.234505	−	0.543643i
$903$		0			0
$904$	−97.8717	−	23.1960i	−3.25516	−	0.771488i
$905$	−20.7571	−	69.3336i	−0.689990	−	2.30473i
$906$		0			0
$907$	−43.3024	−	5.06132i	−1.43783	−	0.168058i	−0.638812	−	0.769363i	$-0.720574\pi$
$907$	−43.3024	−	5.06132i	−1.43783	−	0.168058i	−0.799020	+	0.601305i	$0.794648\pi$
$908$	4.45875	−	25.2868i	0.147969	−	0.839172i
$909$		0			0
$910$	−9.05963	−	51.3797i	−0.300324	−	1.70322i
$911$	3.22195	+	55.3187i	0.106748	+	1.83279i	0.449405	+	0.893328i	$0.351636\pi$
$911$	3.22195	+	55.3187i	0.106748	+	1.83279i	−0.342657	+	0.939461i	$0.611327\pi$
$912$		0			0
$913$	−0.0833736	+	0.193282i	−0.00275926	+	0.00639669i
$914$	57.7643	−	29.0103i	1.91067	−	0.959576i
$915$		0			0
$916$	−99.1342	+	23.4952i	−3.27549	+	0.776305i
$917$	−8.10758	−	14.0427i	−0.267736	−	0.463732i
$918$		0			0
$919$	20.4721	−	35.4586i	0.675311	−	1.16967i	−0.301067	−	0.953603i	$-0.597343\pi$
$919$	20.4721	−	35.4586i	0.675311	−	1.16967i	0.976378	−	0.216069i	$-0.0693238\pi$
$920$	12.9261	−	43.1762i	0.426161	−	1.42348i
$921$		0			0
$922$	−43.3662	−	28.5224i	−1.42819	−	0.939335i
$923$	−5.32186	−	7.14850i	−0.175171	−	0.235296i
$924$		0			0
$925$	29.4974	−	19.4008i	0.969870	−	0.637894i
$926$	−65.9813	−	24.0152i	−2.16828	−	0.789190i
$927$		0			0
$928$	45.5962	−	16.5957i	1.49677	−	0.544780i
$929$	19.2912	−	25.9126i	0.632925	−	0.850166i	−0.363763	−	0.931492i	$-0.618508\pi$
$929$	19.2912	−	25.9126i	0.632925	−	0.850166i	0.996688	+	0.0813261i	$0.0259155\pi$
$930$		0			0
$931$	4.12402	−	4.37120i	0.135159	−	0.143260i
$932$	−62.4710	+	66.2154i	−2.04631	+	2.16896i
$933$		0			0
$934$	−13.9040	+	18.6763i	−0.454953	+	0.611108i
$935$	25.6116	−	9.32184i	0.837587	−	0.304857i
$936$		0			0
$937$	8.51549	+	3.09939i	0.278189	+	0.101253i	0.477347	−	0.878715i	$-0.341598\pi$
$937$	8.51549	+	3.09939i	0.278189	+	0.101253i	−0.199158	+	0.979967i	$0.563821\pi$
$938$	−6.50035	+	4.27535i	−0.212244	+	0.139595i
$939$		0			0
$940$	58.7899	+	78.9685i	1.91751	+	2.57567i
$941$	19.9719	+	13.1357i	0.651064	+	0.428212i	0.831614	−	0.555354i	$-0.187417\pi$
$941$	19.9719	+	13.1357i	0.651064	+	0.428212i	−0.180550	+	0.983566i	$0.557788\pi$
$942$		0			0
$943$	2.32103	−	7.75280i	0.0755833	−	0.252466i
$944$	12.2522	−	21.2213i	0.398774	−	0.690696i
$945$		0			0
$946$	−18.5797	−	32.1811i	−0.604080	−	1.04630i
$947$	−8.00977	+	1.89835i	−0.260282	+	0.0616881i	−0.358685	−	0.933459i	$-0.616775\pi$
$947$	−8.00977	+	1.89835i	−0.260282	+	0.0616881i	0.0984027	+	0.995147i	$0.468627\pi$
$948$		0			0
$949$	39.6712	−	19.9236i	1.28778	−	0.646749i
$950$	7.34949	−	17.0380i	0.238449	−	0.552787i
$951$		0			0
$952$	2.62452	+	45.0613i	0.0850613	+	1.46045i
$953$	2.96512	+	16.8161i	0.0960498	+	0.544725i	0.994421	+	0.105488i	$0.0336403\pi$
$953$	2.96512	+	16.8161i	0.0960498	+	0.544725i	−0.898371	+	0.439238i	$0.855249\pi$
$954$		0			0
$955$	−10.1197	+	57.3914i	−0.327464	+	1.85714i
$956$	51.3701	+	6.00431i	1.66143	+	0.194193i
$957$		0			0
$958$	4.92229	+	16.4416i	0.159032	+	0.531204i
$959$	12.0053	+	2.84531i	0.387671	+	0.0918797i
$960$		0			0
$961$	−5.36286	−	12.4325i	−0.172995	−	0.401048i
$962$	51.7125	+	43.3919i	1.66728	+	1.39901i
$963$		0			0
$964$	45.2738	−	37.9893i	1.45817	−	1.22355i
$965$	−25.0339	−	12.5725i	−0.805869	−	0.404722i
$966$		0			0
$967$	−15.2485	+	1.78230i	−0.490360	+	0.0573149i	−0.357680	−	0.933844i	$-0.616432\pi$
$967$	−15.2485	+	1.78230i	−0.490360	+	0.0573149i	−0.132680	+	0.991159i	$0.542358\pi$
$968$	2.59252	−	44.5118i	0.0833267	−	1.43066i
$969$		0			0
$970$	−24.2031	−	25.6538i	−0.777115	−	0.823693i
$971$	10.5213			0.337645			0.168822	−	0.985646i	$-0.446004\pi$
$971$	10.5213			0.337645			0.168822	+	0.985646i	$0.446004\pi$
$972$		0			0
$973$	−29.4828			−0.945174
$974$	34.3047	+	36.3609i	1.09919	+	1.16508i
$975$		0			0
$976$	1.12440	−	19.3052i	0.0359911	−	0.617943i
$977$	22.9381	−	2.68108i	0.733854	−	0.0857752i	0.259046	−	0.965865i	$-0.416592\pi$
$977$	22.9381	−	2.68108i	0.733854	−	0.0857752i	0.474807	+	0.880090i	$0.342518\pi$
$978$		0			0
$979$	9.26675	+	4.65394i	0.296167	+	0.148740i
$980$	46.1288	−	38.7067i	1.47353	−	1.23644i
$981$		0			0
$982$	64.6378	+	54.2376i	2.06268	+	1.73079i
$983$	−0.474181	−	1.09927i	−0.0151240	−	0.0350614i	0.910487	−	0.413538i	$-0.135707\pi$
$983$	−0.474181	−	1.09927i	−0.0151240	−	0.0350614i	−0.925611	+	0.378477i	$0.876448\pi$
$984$		0			0
$985$	−5.76818	−	1.36708i	−0.183790	−	0.0435589i
$986$	29.9905	+	100.175i	0.955093	+	3.19023i
$987$		0			0
$988$	24.3193	+	2.84252i	0.773700	+	0.0904326i
$989$	2.93674	−	16.6551i	0.0933830	−	0.529601i
$990$		0			0
$991$	−3.76949	−	21.3778i	−0.119742	−	0.679089i	−0.984293	−	0.176544i	$-0.943508\pi$
$991$	−3.76949	−	21.3778i	−0.119742	−	0.679089i	0.864551	−	0.502545i	$-0.167603\pi$
$992$	1.24863	+	21.4382i	0.0396441	+	0.680662i
$993$		0			0
$994$	−3.83774	+	8.89687i	−0.121726	+	0.282192i
$995$	−38.1315	+	19.1504i	−1.20885	+	0.607108i
$996$		0			0
$997$	−33.5761	+	7.95769i	−1.06337	+	0.252023i	−0.724828	−	0.688930i	$-0.758081\pi$
$997$	−33.5761	+	7.95769i	−1.06337	+	0.252023i	−0.338539	+	0.940952i	$0.609933\pi$
$998$	−40.8494	−	70.7532i	−1.29306	−	2.23965i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.109.1		144
3.2	odd	2		729.2.g.b.109.8		144
9.2	odd	6		243.2.g.a.37.8		144
9.4	even	3		729.2.g.d.595.8		144
9.5	odd	6		729.2.g.a.595.1		144
9.7	even	3		81.2.g.a.49.1	yes	144
81.11	odd	54		729.2.g.b.622.8		144
81.16	even	27		81.2.g.a.43.1	✓	144
81.31	even	27		6561.2.a.c.1.70		72
81.38	odd	54		729.2.g.a.136.1		144
81.43	even	27		729.2.g.d.136.8		144
81.50	odd	54		6561.2.a.d.1.3		72
81.65	odd	54		243.2.g.a.46.8		144
81.70	even	27	inner	729.2.g.c.622.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.43.1	✓	144	81.16	even	27
81.2.g.a.49.1	yes	144	9.7	even	3
243.2.g.a.37.8		144	9.2	odd	6
243.2.g.a.46.8		144	81.65	odd	54
729.2.g.a.136.1		144	81.38	odd	54
729.2.g.a.595.1		144	9.5	odd	6
729.2.g.b.109.8		144	3.2	odd	2
729.2.g.b.622.8		144	81.11	odd	54
729.2.g.c.109.1		144	1.1	even	1	trivial
729.2.g.c.622.1		144	81.70	even	27	inner
729.2.g.d.136.8		144	81.43	even	27
729.2.g.d.595.8		144	9.4	even	3
6561.2.a.c.1.70		72	81.31	even	27
6561.2.a.d.1.3		72	81.50	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.74340 - 1.84790i) q^{2} +(-0.258987 + 4.44663i) q^{4} +(3.16528 - 0.369969i) q^{5} +(-1.48402 - 0.745301i) q^{7} +(4.77615 - 4.00766i) q^{8} +O(q^{10})\)	\(q+(-1.74340 - 1.84790i) q^{2} +(-0.258987 + 4.44663i) q^{4} +(3.16528 - 0.369969i) q^{5} +(-1.48402 - 0.745301i) q^{7} +(4.77615 - 4.00766i) q^{8} +(-6.20202 - 5.20411i) q^{10} +(0.777030 + 1.80136i) q^{11} +(-3.77585 - 0.894892i) q^{13} +(1.21000 + 4.04167i) q^{14} +(-6.88438 - 0.804669i) q^{16} +(0.757018 - 4.29326i) q^{17} +(0.245992 + 1.39509i) q^{19} +(0.825347 + 14.1707i) q^{20} +(1.97405 - 4.57636i) q^{22} +(2.02703 - 1.01801i) q^{23} +(5.01692 - 1.18903i) q^{25} +(4.92914 + 8.53753i) q^{26} +(3.69842 - 6.40585i) q^{28} +(2.70787 - 9.04493i) q^{29} +(3.49112 + 2.29614i) q^{31} +(3.06894 + 4.12230i) q^{32} +(-9.25329 + 6.08598i) q^{34} +(-4.97307 - 1.81005i) q^{35} +(6.43466 - 2.34203i) q^{37} +(2.14912 - 2.88676i) q^{38} +(13.6351 - 14.4524i) q^{40} +(2.44835 - 2.59510i) q^{41} +(4.45230 - 5.98048i) q^{43} +(-8.21121 + 2.98864i) q^{44} +(-5.41510 - 1.97094i) q^{46} +(5.79465 - 3.81120i) q^{47} +(-2.53328 - 3.40278i) q^{49} +(-10.9437 - 7.19779i) q^{50} +(4.95715 - 16.5580i) q^{52} +(1.35317 - 2.34375i) q^{53} +(3.12597 + 5.41433i) q^{55} +(-10.0748 + 2.38777i) q^{56} +(-21.4350 + 10.7651i) q^{58} +(-1.40028 + 3.24620i) q^{59} +(0.162221 + 2.78523i) q^{61} +(-1.84338 - 10.4543i) q^{62} +(-0.140001 + 0.793987i) q^{64} +(-12.2827 - 1.43564i) q^{65} +(0.528909 + 1.76668i) q^{67} +(18.8945 + 4.47807i) q^{68} +(5.32527 + 12.3454i) q^{70} +(1.75933 + 1.47625i) q^{71} +(-8.76373 + 7.35364i) q^{73} +(-15.5460 - 7.80750i) q^{74} +(-6.26714 + 0.732524i) q^{76} +(0.189429 - 3.25237i) q^{77} +(-4.78302 - 5.06970i) q^{79} -22.0887 q^{80} -9.06394 q^{82} +(0.0736322 + 0.0780456i) q^{83} +(0.807804 - 13.8695i) q^{85} +(-18.8134 + 2.19898i) q^{86} +(10.9304 + 5.48947i) q^{88} +(4.04918 - 3.39767i) q^{89} +(4.93645 + 4.14218i) q^{91} +(4.00175 + 9.27709i) q^{92} +(-17.1451 - 4.06347i) q^{94} +(1.29477 + 4.32484i) q^{95} +(4.32681 + 0.505732i) q^{97} +(-1.87147 + 10.6136i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more