LMFDB - Embedded newform 729.2.g.b.676.2

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			676.2
Character	$\chi$	$=$	729.676
Dual form			729.2.g.b.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.614147 - 1.42375i) q^{2} +(-0.277410 + 0.294037i) q^{4} +(0.184768 - 3.17234i) q^{5} +(0.284960 - 0.0675368i) q^{7} +(-2.32510 - 0.846267i) q^{8} +O(q^{10})$	\(q+(-0.614147 - 1.42375i) q^{2} +(-0.277410 + 0.294037i) q^{4} +(0.184768 - 3.17234i) q^{5} +(0.284960 - 0.0675368i) q^{7} +(-2.32510 - 0.846267i) q^{8} +(-4.63010 + 1.68522i) q^{10} +(-4.85926 + 3.19599i) q^{11} +(-0.249784 + 0.0291955i) q^{13} +(-0.271163 - 0.364235i) q^{14} +(0.270087 + 4.63722i) q^{16} +(-3.14189 - 2.63636i) q^{17} +(-3.55906 + 2.98641i) q^{19} +(0.881528 + 0.934365i) q^{20} +(7.53459 + 4.95558i) q^{22} +(4.46184 + 1.05748i) q^{23} +(-5.06339 - 0.591826i) q^{25} +(0.194971 + 0.337700i) q^{26} +(-0.0591924 + 0.102524i) q^{28} +(3.05471 - 4.10319i) q^{29} +(-1.69894 - 5.67485i) q^{31} +(2.01411 - 1.01152i) q^{32} +(-1.82394 + 6.09239i) q^{34} +(-0.161598 - 0.916469i) q^{35} +(0.850864 - 4.82549i) q^{37} +(6.43769 + 3.23313i) q^{38} +(-3.11425 + 7.21964i) q^{40} +(0.721490 - 1.67260i) q^{41} +(1.95203 + 0.980348i) q^{43} +(0.408268 - 2.31540i) q^{44} +(-1.23464 - 7.00200i) q^{46} +(-2.19683 + 7.33791i) q^{47} +(-6.17879 + 3.10310i) q^{49} +(2.26705 + 7.57248i) q^{50} +(0.0607078 - 0.0815448i) q^{52} +(3.52502 - 6.10552i) q^{53} +(9.24092 + 16.0057i) q^{55} +(-0.719715 - 0.0841226i) q^{56} +(-7.71797 - 1.82919i) q^{58} +(-7.68465 - 5.05427i) q^{59} +(2.13742 + 2.26554i) q^{61} +(-7.03618 + 5.90406i) q^{62} +(4.43955 + 3.72523i) q^{64} +(0.0464661 + 0.797793i) q^{65} +(-4.08333 - 5.48486i) q^{67} +(1.64678 - 0.192481i) q^{68} +(-1.20558 + 0.792922i) q^{70} +(-4.71278 + 1.71531i) q^{71} +(-1.71510 - 0.624247i) q^{73} +(-7.39286 + 1.75214i) q^{74} +(0.109204 - 1.87495i) q^{76} +(-1.16885 + 1.23891i) q^{77} +(-4.28100 - 9.92448i) q^{79} +14.7607 q^{80} -2.82447 q^{82} +(3.99948 + 9.27184i) q^{83} +(-8.94395 + 9.48003i) q^{85} +(0.196938 - 3.38129i) q^{86} +(14.0029 - 3.31875i) q^{88} +(-9.79723 - 3.56590i) q^{89} +(-0.0692067 + 0.0251892i) q^{91} +(-1.54869 + 1.01859i) q^{92} +(11.7965 - 1.37882i) q^{94} +(8.81629 + 11.8423i) q^{95} +(-0.379561 - 6.51682i) q^{97} +(8.21273 + 6.89130i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	−0.614147	−	1.42375i	−0.434267	−	1.00674i	−0.985077	−	0.172114i	$-0.944940\pi$
$2$	−0.614147	−	1.42375i	−0.434267	−	1.00674i	0.550810	−	0.834631i	$-0.314319\pi$
$3$		0			0
$3$		0			0
$4$	−0.277410	+	0.294037i	−0.138705	+	0.147018i
$5$	0.184768	−	3.17234i	0.0826306	−	1.41871i	−0.661133	−	0.750269i	$-0.729924\pi$
$5$	0.184768	−	3.17234i	0.0826306	−	1.41871i	0.743763	−	0.668443i	$-0.233039\pi$
$6$		0			0
$7$	0.284960	−	0.0675368i	0.107705	−	0.0255265i	−0.176410	−	0.984317i	$-0.556448\pi$
$7$	0.284960	−	0.0675368i	0.107705	−	0.0255265i	0.284115	+	0.958790i	$0.408300\pi$
$8$	−2.32510	−	0.846267i	−0.822047	−	0.299200i
$9$		0			0
$10$	−4.63010	+	1.68522i	−1.46416	+	0.532912i
$11$	−4.85926	+	3.19599i	−1.46512	+	0.963626i	−0.468334	+	0.883552i	$0.655146\pi$
$11$	−4.85926	+	3.19599i	−1.46512	+	0.963626i	−0.996789	+	0.0800749i	$0.974484\pi$
$12$		0			0
$13$	−0.249784	+	0.0291955i	−0.0692776	+	0.00809739i	−0.150661	−	0.988585i	$-0.548140\pi$
$13$	−0.249784	+	0.0291955i	−0.0692776	+	0.00809739i	0.0813835	+	0.996683i	$0.474066\pi$
$14$	−0.271163	−	0.364235i	−0.0724714	−	0.0973460i
$15$		0			0
$16$	0.270087	+	4.63722i	0.0675218	+	1.15930i
$17$	−3.14189	−	2.63636i	−0.762021	−	0.639411i	0.176631	−	0.984277i	$-0.443480\pi$
$17$	−3.14189	−	2.63636i	−0.762021	−	0.639411i	−0.938652	+	0.344866i	$0.887924\pi$
$18$		0			0
$19$	−3.55906	+	2.98641i	−0.816505	+	0.685129i	−0.952151	−	0.305629i	$-0.901133\pi$
$19$	−3.55906	+	2.98641i	−0.816505	+	0.685129i	0.135646	+	0.990757i	$0.456689\pi$
$20$	0.881528	+	0.934365i	0.197116	+	0.208930i
$21$		0			0
$22$	7.53459	+	4.95558i	1.60638	+	1.05653i
$23$	4.46184	+	1.05748i	0.930358	+	0.220499i	0.667735	−	0.744399i	$-0.267264\pi$
$23$	4.46184	+	1.05748i	0.930358	+	0.220499i	0.262624	+	0.964898i	$0.415412\pi$
$24$		0			0
$25$	−5.06339	−	0.591826i	−1.01268	−	0.118365i
$26$	0.194971	+	0.337700i	0.0382370	+	0.0662284i
$27$		0			0
$28$	−0.0591924	+	0.102524i	−0.0111863	+	0.0193753i
$29$	3.05471	−	4.10319i	0.567246	−	0.761944i	−0.422254	−	0.906478i	$-0.638761\pi$
$29$	3.05471	−	4.10319i	0.567246	−	0.761944i	0.989500	+	0.144534i	$0.0461683\pi$
$30$		0			0
$31$	−1.69894	−	5.67485i	−0.305139	−	1.01923i	−0.963763	−	0.266762i	$-0.914046\pi$
$31$	−1.69894	−	5.67485i	−0.305139	−	1.01923i	0.658624	−	0.752472i	$-0.271139\pi$
$32$	2.01411	−	1.01152i	0.356047	−	0.178814i
$33$		0			0
$34$	−1.82394	+	6.09239i	−0.312803	+	1.04484i
$35$	−0.161598	−	0.916469i	−0.0273151	−	0.154912i
$36$		0			0
$37$	0.850864	−	4.82549i	0.139881	−	0.793306i	−0.831454	−	0.555593i	$-0.812491\pi$
$37$	0.850864	−	4.82549i	0.139881	−	0.793306i	0.971336	−	0.237713i	$-0.0763977\pi$
$38$	6.43769	+	3.23313i	1.04433	+	0.524483i
$39$		0			0
$40$	−3.11425	+	7.21964i	−0.492406	+	1.14152i
$41$	0.721490	−	1.67260i	0.112678	−	0.261217i	−0.852541	−	0.522661i	$-0.824939\pi$
$41$	0.721490	−	1.67260i	0.112678	−	0.261217i	0.965219	+	0.261444i	$0.0841987\pi$
$42$		0			0
$43$	1.95203	+	0.980348i	0.297682	+	0.149502i	0.591371	−	0.806399i	$-0.298587\pi$
$43$	1.95203	+	0.980348i	0.297682	+	0.149502i	−0.293689	+	0.955901i	$0.594883\pi$
$44$	0.408268	−	2.31540i	0.0615486	−	0.349060i
$45$		0			0
$46$	−1.23464	−	7.00200i	−0.182038	−	1.03239i
$47$	−2.19683	+	7.33791i	−0.320440	+	1.07034i	0.634346	+	0.773050i	$0.281270\pi$
$47$	−2.19683	+	7.33791i	−0.320440	+	1.07034i	−0.954786	+	0.297295i	$0.903916\pi$
$48$		0			0
$49$	−6.17879	+	3.10310i	−0.882684	+	0.443301i
$50$	2.26705	+	7.57248i	0.320610	+	1.07091i
$51$		0			0
$52$	0.0607078	−	0.0815448i	0.00841866	−	0.0113082i
$53$	3.52502	−	6.10552i	0.484199	−	0.838657i	−0.515636	−	0.856808i	$-0.672444\pi$
$53$	3.52502	−	6.10552i	0.484199	−	0.838657i	0.999835	+	0.0181502i	$0.00577771\pi$
$54$		0			0
$55$	9.24092	+	16.0057i	1.24604	+	2.15821i
$56$	−0.719715	−	0.0841226i	−0.0961760	−	0.0112414i
$57$		0			0
$58$	−7.71797	−	1.82919i	−1.01342	−	0.240185i
$59$	−7.68465	−	5.05427i	−1.00046	−	0.658010i	−0.0600966	−	0.998193i	$-0.519141\pi$
$59$	−7.68465	−	5.05427i	−1.00046	−	0.658010i	−0.940360	+	0.340182i	$0.889511\pi$
$60$		0			0
$61$	2.13742	+	2.26554i	0.273669	+	0.290072i	0.849602	−	0.527425i	$-0.176842\pi$
$61$	2.13742	+	2.26554i	0.273669	+	0.290072i	−0.575933	+	0.817497i	$0.695361\pi$
$62$	−7.03618	+	5.90406i	−0.893596	+	0.749816i
$63$		0			0
$64$	4.43955	+	3.72523i	0.554944	+	0.465653i
$65$	0.0464661	+	0.797793i	0.00576342	+	0.0989540i
$66$		0			0
$67$	−4.08333	−	5.48486i	−0.498858	−	0.670083i	0.479371	−	0.877613i	$-0.340865\pi$
$67$	−4.08333	−	5.48486i	−0.498858	−	0.670083i	−0.978229	+	0.207530i	$0.933458\pi$
$68$	1.64678	−	0.192481i	0.199701	−	0.0233417i
$69$		0			0
$70$	−1.20558	+	0.792922i	−0.144094	+	0.0947723i
$71$	−4.71278	+	1.71531i	−0.559304	+	0.203570i	−0.606175	−	0.795331i	$-0.707297\pi$
$71$	−4.71278	+	1.71531i	−0.559304	+	0.203570i	0.0468717	+	0.998901i	$0.485075\pi$
$72$		0			0
$73$	−1.71510	−	0.624247i	−0.200738	−	0.0730626i	0.239695	−	0.970848i	$-0.422953\pi$
$73$	−1.71510	−	0.624247i	−0.200738	−	0.0730626i	−0.440432	+	0.897786i	$0.645175\pi$
$74$	−7.39286	+	1.75214i	−0.859402	+	0.203682i
$75$		0			0
$76$	0.109204	−	1.87495i	0.0125265	−	0.215072i
$77$	−1.16885	+	1.23891i	−0.133203	+	0.141187i
$78$		0			0
$79$	−4.28100	−	9.92448i	−0.481650	−	1.11659i	−0.969816	−	0.243840i	$-0.921593\pi$
$79$	−4.28100	−	9.92448i	−0.481650	−	1.11659i	0.488165	−	0.872751i	$-0.337666\pi$
$80$	14.7607			1.65030
$81$		0			0
$82$	−2.82447			−0.311911
$83$	3.99948	+	9.27184i	0.439000	+	1.01772i	0.983819	+	0.179163i	$0.0573389\pi$
$83$	3.99948	+	9.27184i	0.439000	+	1.01772i	−0.544819	+	0.838553i	$0.683402\pi$
$84$		0			0
$85$	−8.94395	+	9.48003i	−0.970107	+	1.02825i
$86$	0.196938	−	3.38129i	0.0212363	−	0.364614i
$87$		0			0
$88$	14.0029	−	3.31875i	1.49272	−	0.353780i
$89$	−9.79723	−	3.56590i	−1.03850	−	0.377985i	−0.234192	−	0.972190i	$-0.575244\pi$
$89$	−9.79723	−	3.56590i	−1.03850	−	0.377985i	−0.804313	+	0.594206i	$0.797467\pi$
$90$		0			0
$91$	−0.0692067	+	0.0251892i	−0.00725483	+	0.00264054i
$92$	−1.54869	+	1.01859i	−0.161463	+	0.106196i
$93$		0			0
$94$	11.7965	−	1.37882i	1.21672	−	0.142214i
$95$	8.81629	+	11.8423i	0.904532	+	1.21500i
$96$		0			0
$97$	−0.379561	−	6.51682i	−0.0385386	−	0.661683i	−0.961163	−	0.275982i	$-0.910997\pi$
$97$	−0.379561	−	6.51682i	−0.0385386	−	0.661683i	0.922624	−	0.385700i	$-0.126040\pi$
$98$	8.21273	+	6.89130i	0.829611	+	0.696126i
$99$		0			0
$100$	1.57865	−	1.32465i	0.157865	−	0.132465i
$101$	0.212738	+	0.225489i	0.0211683	+	0.0224370i	0.737871	−	0.674941i	$-0.235831\pi$
$101$	0.212738	+	0.225489i	0.0211683	+	0.0224370i	−0.716703	+	0.697379i	$0.754350\pi$
$102$		0			0
$103$	8.06674	+	5.30558i	0.794840	+	0.522774i	0.880780	−	0.473526i	$-0.157019\pi$
$103$	8.06674	+	5.30558i	0.794840	+	0.522774i	−0.0859399	+	0.996300i	$0.527389\pi$
$104$	0.605479	+	0.143501i	0.0593721	+	0.0140715i
$105$		0			0
$106$	−10.8576	−	1.26907i	−1.05459	−	0.123263i
$107$	5.31399	+	9.20410i	0.513723	+	0.889794i	0.999873	+	0.0159189i	$0.00506736\pi$
$107$	5.31399	+	9.20410i	0.513723	+	0.889794i	−0.486150	+	0.873875i	$0.661599\pi$
$108$		0			0
$109$	8.57766	−	14.8569i	0.821590	−	1.42304i	−0.0829070	−	0.996557i	$-0.526420\pi$
$109$	8.57766	−	14.8569i	0.821590	−	1.42304i	0.904497	−	0.426479i	$-0.140246\pi$
$110$	17.1129	−	22.9866i	1.63165	−	2.19169i
$111$		0			0
$112$	0.390147	+	1.30318i	0.0368654	+	0.123139i
$113$	−9.46527	+	4.75364i	−0.890418	+	0.447185i	−0.834345	−	0.551242i	$-0.814154\pi$
$113$	−9.46527	+	4.75364i	−0.890418	+	0.447185i	−0.0560723	+	0.998427i	$0.517858\pi$
$114$		0			0
$115$	4.17907	−	13.9591i	0.389701	−	1.30169i
$116$	0.359083	+	2.03646i	0.0333401	+	0.189081i
$117$		0			0
$118$	−2.47653	+	14.0451i	−0.227983	+	1.29296i
$119$	−1.07337	−	0.539065i	−0.0983953	−	0.0494160i
$120$		0			0
$121$	9.04122	−	20.9599i	0.821929	−	1.90545i
$122$	1.91287	−	4.43453i	0.173183	−	0.401484i
$123$		0			0
$124$	2.13992	+	1.07471i	0.192170	+	0.0965116i
$125$	−0.0540020	+	0.306261i	−0.00483008	+	0.0273928i
$126$		0			0
$127$	−2.51136	−	14.2427i	−0.222848	−	1.26383i	−0.866757	−	0.498730i	$-0.833800\pi$
$127$	−2.51136	−	14.2427i	−0.222848	−	1.26383i	0.643910	−	0.765101i	$-0.277311\pi$
$128$	3.87008	−	12.9270i	0.342070	−	1.14259i
$129$		0			0
$130$	1.10732	−	0.556118i	0.0971186	−	0.0487748i
$131$	−1.09756	−	3.66609i	−0.0958939	−	0.320308i	0.896561	−	0.442921i	$-0.146058\pi$
$131$	−1.09756	−	3.66609i	−0.0958939	−	0.320308i	−0.992455	+	0.122613i	$0.960873\pi$
$132$		0			0
$133$	−0.812499	+	1.09138i	−0.0704526	+	0.0946342i
$134$	−5.30132	+	9.18216i	−0.457964	+	0.793217i
$135$		0			0
$136$	5.07415	+	8.78868i	0.435104	+	0.753623i
$137$	−14.1689	−	1.65610i	−1.21053	−	0.141490i	−0.513217	−	0.858259i	$-0.671546\pi$
$137$	−14.1689	−	1.65610i	−1.21053	−	0.141490i	−0.697311	+	0.716768i	$0.745620\pi$
$138$		0			0
$139$	5.73451	+	1.35910i	0.486395	+	0.115278i	0.466494	−	0.884524i	$-0.345517\pi$
$139$	5.73451	+	1.35910i	0.486395	+	0.115278i	0.0199006	+	0.999802i	$0.493665\pi$
$140$	0.314305	+	0.206721i	0.0265636	+	0.0174711i
$141$		0			0
$142$	5.33651	+	5.65637i	0.447830	+	0.474672i
$143$	1.12046	−	0.940175i	0.0936973	−	0.0786213i
$144$		0			0
$145$	−12.4523	−	10.4487i	−1.03411	−	0.867719i
$146$	0.164553	+	2.82526i	0.0136185	+	0.233820i
$147$		0			0
$148$	1.18283	+	1.58882i	0.0972284	+	0.130600i
$149$	13.9939	−	1.63565i	1.14642	−	0.133998i	0.478402	−	0.878141i	$-0.341216\pi$
$149$	13.9939	−	1.63565i	1.14642	−	0.133998i	0.668020	+	0.744143i	$0.267142\pi$
$150$		0			0
$151$	−1.32326	+	0.870321i	−0.107685	+	0.0708257i	−0.602209	−	0.798338i	$-0.705713\pi$
$151$	−1.32326	+	0.870321i	−0.107685	+	0.0708257i	0.494524	+	0.869164i	$0.335342\pi$
$152$	10.8025	−	3.93178i	0.876196	−	0.318909i
$153$		0			0
$154$	2.48174	+	0.903281i	0.199985	+	0.0727884i
$155$	−18.3165	+	4.34108i	−1.47121	+	0.348684i
$156$		0			0
$157$	−0.297956	+	5.11570i	−0.0237794	+	0.408277i	0.965324	+	0.261055i	$0.0840703\pi$
$157$	−0.297956	+	5.11570i	−0.0237794	+	0.408277i	−0.989103	+	0.147222i	$0.952967\pi$
$158$	−11.5008	+	12.1902i	−0.914957	+	0.969797i
$159$		0			0
$160$	−2.83675	−	6.57633i	−0.224265	−	0.519904i
$161$	1.34287			0.105833
$162$		0			0
$163$	−17.6764			−1.38452			−0.692262	−	0.721646i	$-0.743386\pi$
$163$	−17.6764			−1.38452			−0.692262	+	0.721646i	$0.743386\pi$
$164$	0.291659	+	0.676141i	0.0227747	+	0.0527977i
$165$		0			0
$166$	10.7445	−	11.3885i	0.833937	−	0.883922i
$167$	0.0801450	−	1.37604i	0.00620181	−	0.106481i	−0.993787	−	0.111303i	$-0.964498\pi$
$167$	0.0801450	−	1.37604i	0.00620181	−	0.106481i	0.999988	+	0.00482161i	$0.00153477\pi$
$168$		0			0
$169$	−12.5880	+	2.98342i	−0.968311	+	0.229494i
$170$	18.9901	+	6.91183i	1.45647	+	0.530113i
$171$		0			0
$172$	−0.829771	+	0.302012i	−0.0632695	+	0.0230282i
$173$	10.8612	−	7.14352i	0.825762	−	0.543112i	−0.0648402	−	0.997896i	$-0.520654\pi$
$173$	10.8612	−	7.14352i	0.825762	−	0.543112i	0.890602	+	0.454784i	$0.150283\pi$
$174$		0			0
$175$	−1.48284	+	0.173319i	−0.112092	+	0.0131017i
$176$	−16.1329	−	21.6703i	−1.21606	−	1.63346i
$177$		0			0
$178$	0.939979	+	16.1388i	0.0704544	+	1.20966i
$179$	−19.1637	−	16.0803i	−1.43237	−	1.20190i	−0.944298	−	0.329091i	$-0.893258\pi$
$179$	−19.1637	−	16.0803i	−1.43237	−	1.20190i	−0.488067	−	0.872806i	$-0.662298\pi$
$180$		0			0
$181$	3.52910	−	2.96126i	0.262316	−	0.220109i	−0.502138	−	0.864787i	$-0.667453\pi$
$181$	3.52910	−	2.96126i	0.262316	−	0.220109i	0.764454	+	0.644678i	$0.223009\pi$
$182$	0.0783662	+	0.0830633i	0.00580889	+	0.00615706i
$183$		0			0
$184$	−9.47932	−	6.23464i	−0.698824	−	0.459624i
$185$	−15.1509	−	3.59082i	−1.11391	−	0.264003i
$186$		0			0
$187$	23.6931	+	2.76932i	1.73261	+	0.202513i
$188$	−1.54820	−	2.68156i	−0.112914	−	0.195573i
$189$		0			0
$190$	11.4460	−	19.8251i	0.830384	−	1.43827i
$191$	−1.60520	+	2.15616i	−0.116148	+	0.156014i	−0.856395	−	0.516321i	$-0.827301\pi$
$191$	−1.60520	+	2.15616i	−0.116148	+	0.156014i	0.740247	+	0.672335i	$0.234709\pi$
$192$		0			0
$193$	−1.89464	−	6.32854i	−0.136379	−	0.455538i	0.862329	−	0.506348i	$-0.169005\pi$
$193$	−1.89464	−	6.32854i	−0.136379	−	0.455538i	−0.998708	+	0.0508098i	$0.983820\pi$
$194$	−9.04522	+	4.54268i	−0.649409	+	0.326146i
$195$		0			0
$196$	0.801628	−	2.67762i	0.0572591	−	0.191259i
$197$	2.65657	+	15.0662i	0.189273	+	1.07342i	0.920341	+	0.391116i	$0.127911\pi$
$197$	2.65657	+	15.0662i	0.189273	+	1.07342i	−0.731068	+	0.682304i	$0.760978\pi$
$198$		0			0
$199$	2.44426	−	13.8621i	0.173269	−	0.982657i	−0.766854	−	0.641821i	$-0.778179\pi$
$199$	2.44426	−	13.8621i	0.173269	−	0.982657i	0.940123	−	0.340835i	$-0.110710\pi$
$200$	11.2721	+	5.66104i	0.797054	+	0.400296i
$201$		0			0
$202$	0.190388	−	0.441370i	0.0133957	−	0.0310547i
$203$	0.593356	−	1.37555i	0.0416454	−	0.0965449i
$204$		0			0
$205$	−5.17275	−	2.59785i	−0.361281	−	0.181442i
$206$	2.59967	−	14.7434i	0.181127	−	1.02722i
$207$		0			0
$208$	−0.202849	−	1.15042i	−0.0140651	−	0.0797670i
$209$	7.74989	−	25.8864i	0.536071	−	1.79060i
$210$		0			0
$211$	13.8113	−	6.93632i	0.950812	−	0.477516i	0.0953860	−	0.995440i	$-0.469591\pi$
$211$	13.8113	−	6.93632i	0.950812	−	0.477516i	0.855426	+	0.517924i	$0.173295\pi$
$212$	0.817373	+	2.73022i	0.0561374	+	0.187512i
$213$		0			0
$214$	9.84079	−	13.2185i	0.672702	−	0.903596i
$215$	3.47067	−	6.01137i	0.236698	−	0.409972i
$216$		0			0
$217$	−0.867392	−	1.50237i	−0.0588824	−	0.101987i
$218$	−26.4205	−	3.08812i	−1.78942	−	0.209154i
$219$		0			0
$220$	−7.26980	−	1.72297i	−0.490130	−	0.116163i
$221$	0.861764	+	0.566791i	0.0579685	+	0.0381265i
$222$		0			0
$223$	−3.33129	−	3.53096i	−0.223080	−	0.236451i	0.606161	−	0.795342i	$-0.292709\pi$
$223$	−3.33129	−	3.53096i	−0.223080	−	0.236451i	−0.829241	+	0.558891i	$0.811227\pi$
$224$	0.505626	−	0.424270i	0.0337836	−	0.0283478i
$225$		0			0
$226$	12.5811	+	10.5568i	0.836880	+	0.702225i
$227$	−1.12523	−	19.3195i	−0.0746844	−	1.28228i	−0.802559	−	0.596572i	$-0.796529\pi$
$227$	−1.12523	−	19.3195i	−0.0746844	−	1.28228i	0.727875	−	0.685710i	$-0.240508\pi$
$228$		0			0
$229$	−2.19967	−	2.95467i	−0.145358	−	0.195250i	0.723481	−	0.690344i	$-0.242541\pi$
$229$	−2.19967	−	2.95467i	−0.145358	−	0.195250i	−0.868839	+	0.495094i	$0.835133\pi$
$230$	−22.4408	+	2.62296i	−1.47970	+	0.172953i
$231$		0			0
$232$	−10.5749	+	6.95523i	−0.694277	+	0.456633i
$233$	1.43618	−	0.522727i	0.0940872	−	0.0342450i	−0.294548	−	0.955637i	$-0.595169\pi$
$233$	1.43618	−	0.522727i	0.0940872	−	0.0342450i	0.388635	+	0.921392i	$0.372947\pi$
$234$		0			0
$235$	22.8724	+	8.32488i	1.49203	+	0.543056i
$236$	3.61794	−	0.857467i	0.235508	−	0.0558164i
$237$		0			0
$238$	−0.108290	+	1.85927i	−0.00701941	+	0.120519i
$239$	3.26580	−	3.46154i	0.211247	−	0.223909i	−0.613083	−	0.790019i	$-0.710071\pi$
$239$	3.26580	−	3.46154i	0.211247	−	0.223909i	0.824330	+	0.566110i	$0.191552\pi$
$240$		0			0
$241$	10.0224	+	23.2345i	0.645598	+	1.49666i	0.854889	+	0.518811i	$0.173625\pi$
$241$	10.0224	+	23.2345i	0.645598	+	1.49666i	−0.209291	+	0.977853i	$0.567116\pi$
$242$	−35.3943			−2.27523
$243$		0			0
$244$	−1.25909			−0.0806052
$245$	8.70245	+	20.1746i	0.555979	+	1.28890i
$246$		0			0
$247$	0.801806	−	0.849865i	0.0510177	−	0.0540756i
$248$	−0.852237	+	14.6324i	−0.0541171	+	0.929155i
$249$		0			0
$250$	0.469204	−	0.111203i	0.0296751	−	0.00703312i
$251$	2.06755	+	0.752528i	0.130503	+	0.0474991i	0.406446	−	0.913675i	$-0.366768\pi$
$251$	2.06755	+	0.752528i	0.130503	+	0.0474991i	−0.275943	+	0.961174i	$0.588990\pi$
$252$		0			0
$253$	−25.0609	+	9.12143i	−1.57557	+	0.573460i
$254$	−18.7357	+	12.3226i	−1.17558	+	0.773191i
$255$		0			0
$256$	−9.26912	+	1.08340i	−0.579320	+	0.0677128i
$257$	6.13071	+	8.23498i	0.382423	+	0.513684i	0.951102	−	0.308876i	$-0.0999527\pi$
$257$	6.13071	+	8.23498i	0.382423	+	0.513684i	−0.568679	+	0.822560i	$0.692545\pi$
$258$		0			0
$259$	−0.0834358	−	1.43254i	−0.00518445	−	0.0890136i
$260$	−0.247471	−	0.207653i	−0.0153475	−	0.0128781i
$261$		0			0
$262$	−4.54554	+	3.81416i	−0.280825	+	0.235640i
$263$	1.08901	+	1.15428i	0.0671512	+	0.0711761i	0.760078	−	0.649832i	$-0.225161\pi$
$263$	1.08901	+	1.15428i	0.0671512	+	0.0711761i	−0.692927	+	0.721008i	$0.743679\pi$
$264$		0			0
$265$	−18.7175	−	12.3107i	−1.14980	−	0.756238i
$266$	2.05284	+	0.486532i	0.125868	+	0.0298312i
$267$		0			0
$268$	2.74551	+	0.320904i	0.167709	+	0.0196023i
$269$	−2.49753	−	4.32585i	−0.152277	−	0.263752i	0.779787	−	0.626045i	$-0.215327\pi$
$269$	−2.49753	−	4.32585i	−0.152277	−	0.263752i	−0.932064	+	0.362293i	$0.881994\pi$
$270$		0			0
$271$	−4.63580	+	8.02944i	−0.281605	+	0.487754i	−0.971780	−	0.235888i	$-0.924200\pi$
$271$	−4.63580	+	8.02944i	−0.281605	+	0.487754i	0.690175	+	0.723642i	$0.257533\pi$
$272$	11.3768	−	15.2817i	0.689819	−	0.926588i
$273$		0			0
$274$	6.34388	+	21.1900i	0.383248	+	1.28014i
$275$	26.4958	−	13.3067i	1.59776	−	0.802425i
$276$		0			0
$277$	7.41215	−	24.7583i	0.445353	−	1.48758i	−0.381077	−	0.924543i	$-0.624447\pi$
$277$	7.41215	−	24.7583i	0.445353	−	1.48758i	0.826430	−	0.563039i	$-0.190368\pi$
$278$	−1.58680	−	8.99921i	−0.0951701	−	0.539737i
$279$		0			0
$280$	−0.399845	+	2.26764i	−0.0238953	+	0.135517i
$281$	25.8792	+	12.9970i	1.54382	+	0.775336i	0.998039	−	0.0625905i	$-0.0199362\pi$
$281$	25.8792	+	12.9970i	1.54382	+	0.775336i	0.545782	+	0.837927i	$0.316233\pi$
$282$		0			0
$283$	0.408756	−	0.947602i	0.0242980	−	0.0563291i	−0.905635	−	0.424058i	$-0.860605\pi$
$283$	0.408756	−	0.947602i	0.0242980	−	0.0563291i	0.929933	+	0.367729i	$0.119865\pi$
$284$	0.803005	−	1.86157i	0.0476496	−	0.110464i
$285$		0			0
$286$	−2.02670	−	1.01785i	−0.119841	−	0.0601865i
$287$	0.0926338	−	0.525353i	0.00546800	−	0.0310106i
$288$		0			0
$289$	−0.0309285	−	0.175404i	−0.00181932	−	0.0103179i
$290$	−7.22885	+	24.1460i	−0.424492	+	1.41790i
$291$		0			0
$292$	0.659338	−	0.331132i	0.0385848	−	0.0193780i
$293$	1.99047	+	6.64865i	0.116285	+	0.388418i	0.996240	−	0.0866389i	$-0.0276126\pi$
$293$	1.99047	+	6.64865i	0.116285	+	0.388418i	−0.879955	+	0.475057i	$0.842427\pi$
$294$		0			0
$295$	−17.4537	+	23.4444i	−1.01620	+	1.36499i
$296$	−6.06200	+	10.4997i	−0.352346	+	0.610282i
$297$		0			0
$298$	−10.9230	−	18.9193i	−0.632755	−	1.09596i
$299$	−1.14537	−	0.133874i	−0.0662384	−	0.00774216i
$300$		0			0
$301$	0.622462	+	0.147526i	0.0358781	+	0.00850326i
$302$	2.05180	+	1.34949i	0.118068	+	0.0776543i
$303$		0			0
$304$	−14.8099	−	15.6975i	−0.849404	−	0.900316i
$305$	7.58197	−	6.36203i	0.434143	−	0.364289i
$306$		0			0
$307$	14.0395	+	11.7805i	0.801275	+	0.672350i	0.948508	−	0.316752i	$-0.102592\pi$
$307$	14.0395	+	11.7805i	0.801275	+	0.672350i	−0.147233	+	0.989102i	$0.547037\pi$
$308$	−0.0400348	−	0.687370i	−0.00228119	−	0.0391666i
$309$		0			0
$310$	17.4296	+	23.4120i	0.989935	+	1.32971i
$311$	14.5964	−	1.70608i	0.827686	−	0.0967427i	0.308307	−	0.951287i	$-0.400237\pi$
$311$	14.5964	−	1.70608i	0.827686	−	0.0967427i	0.519379	+	0.854544i	$0.326163\pi$
$312$		0			0
$313$	−4.72821	+	3.10979i	−0.267254	+	0.175776i	−0.676062	−	0.736845i	$-0.736315\pi$
$313$	−4.72821	+	3.10979i	−0.267254	+	0.175776i	0.408808	+	0.912620i	$0.365945\pi$
$314$	7.46647	−	2.71757i	0.421358	−	0.153362i
$315$		0			0
$316$	4.10575	+	1.49437i	0.230967	+	0.0840650i
$317$	22.2986	−	5.28486i	1.25241	−	0.296827i	0.449693	−	0.893183i	$-0.351533\pi$
$317$	22.2986	−	5.28486i	1.25241	−	0.296827i	0.802720	+	0.596356i	$0.203385\pi$
$318$		0			0
$319$	−1.72990	+	29.7013i	−0.0968561	+	1.66295i
$320$	12.6380	−	13.3955i	0.706484	−	0.748829i
$321$		0			0
$322$	−0.824717	−	1.91191i	−0.0459597	−	0.106546i
$323$	19.0554			1.06027
$324$		0			0
$325$	1.28203			0.0711144
$326$	10.8559	+	25.1668i	0.601253	+	1.39386i
$327$		0			0
$328$	−3.09300	+	3.27839i	−0.170783	+	0.181019i
$329$	−0.130429	+	2.23938i	−0.00719079	+	0.123461i
$330$		0			0
$331$	2.99454	−	0.709719i	0.164595	−	0.0390097i	−0.147492	−	0.989063i	$-0.547120\pi$
$331$	2.99454	−	0.709719i	0.164595	−	0.0390097i	0.312087	+	0.950054i	$0.398972\pi$
$332$	−3.83576	−	1.39610i	−0.210515	−	0.0766210i
$333$		0			0
$334$	−2.00836	+	0.730982i	−0.109892	+	0.0399975i
$335$	−18.1543	+	11.9403i	−0.991876	+	0.652367i
$336$		0			0
$337$	4.08195	−	0.477112i	0.222358	−	0.0259899i	−0.00418429	−	0.999991i	$-0.501332\pi$
$337$	4.08195	−	0.477112i	0.222358	−	0.0259899i	0.226542	+	0.974001i	$0.427258\pi$
$338$	11.9786	+	16.0900i	0.651547	+	0.875180i
$339$		0			0
$340$	−0.306343	−	5.25970i	−0.0166138	−	0.285247i
$341$	26.3924	+	22.1458i	1.42923	+	1.19926i
$342$		0			0
$343$	−3.12151	+	2.61926i	−0.168546	+	0.141427i
$344$	−3.70903	−	3.93135i	−0.199978	−	0.211964i
$345$		0			0
$346$	−16.8410	−	11.0765i	−0.905376	−	0.595475i
$347$	8.70882	+	2.06403i	0.467514	+	0.110803i	0.457619	−	0.889148i	$-0.348702\pi$
$347$	8.70882	+	2.06403i	0.467514	+	0.110803i	0.00989464	+	0.999951i	$0.496850\pi$
$348$		0			0
$349$	−4.92593	−	0.575758i	−0.263679	−	0.0308196i	−0.0167738	−	0.999859i	$-0.505340\pi$
$349$	−4.92593	−	0.575758i	−0.263679	−	0.0308196i	−0.246905	+	0.969040i	$0.579414\pi$
$350$	1.15744	+	2.00475i	0.0618679	+	0.107158i
$351$		0			0
$352$	−6.55427	+	11.3523i	−0.349344	+	0.605081i
$353$	−12.1208	+	16.2811i	−0.645125	+	0.866554i	−0.997598	−	0.0692685i	$-0.977933\pi$
$353$	−12.1208	+	16.2811i	−0.645125	+	0.866554i	0.352473	+	0.935822i	$0.385341\pi$
$354$		0			0
$355$	4.57077	+	15.2675i	0.242592	+	0.810312i
$356$	3.76635	−	1.89153i	0.199616	−	0.100251i
$357$		0			0
$358$	−11.1250	+	37.1601i	−0.587974	+	1.96397i
$359$	1.35166	+	7.66566i	0.0713380	+	0.404578i	0.999477	+	0.0323438i	$0.0102971\pi$
$359$	1.35166	+	7.66566i	0.0713380	+	0.404578i	−0.928139	+	0.372234i	$0.878592\pi$
$360$		0			0
$361$	0.448974	−	2.54626i	0.0236302	−	0.134014i
$362$	−6.38349	−	3.20591i	−0.335509	−	0.168499i
$363$		0			0
$364$	0.0117920	−	0.0273370i	0.000618071	−	0.00143285i
$365$	−2.29722	+	5.32555i	−0.120242	+	0.278752i
$366$		0			0
$367$	−0.173614	−	0.0871922i	−0.00906258	−	0.00455140i	0.444262	−	0.895897i	$-0.353466\pi$
$367$	−0.173614	−	0.0871922i	−0.00906258	−	0.00455140i	−0.453325	+	0.891345i	$0.649762\pi$
$368$	−3.69866	+	20.9761i	−0.192806	+	1.09346i
$369$		0			0
$370$	4.19242	+	23.7764i	0.217953	+	1.23607i
$371$	0.592144	−	1.97790i	0.0307426	−	0.102687i
$372$		0			0
$373$	2.04320	−	1.02613i	0.105793	−	0.0531312i	−0.395116	−	0.918631i	$-0.629296\pi$
$373$	2.04320	−	1.02613i	0.105793	−	0.0531312i	0.500909	+	0.865500i	$0.332999\pi$
$374$	−10.6082	−	35.4338i	−0.548536	−	1.83224i
$375$		0			0
$376$	11.3177	−	15.2023i	0.583664	−	0.783997i
$377$	−0.643223	+	1.11409i	−0.0331277	+	0.0573788i
$378$		0			0
$379$	3.62704	+	6.28222i	0.186309	+	0.322696i	0.944017	−	0.329898i	$-0.107014\pi$
$379$	3.62704	+	6.28222i	0.186309	+	0.322696i	−0.757708	+	0.652594i	$0.773681\pi$
$380$	−5.92781	−	0.692861i	−0.304090	−	0.0355430i
$381$		0			0
$382$	4.05567	+	0.961210i	0.207506	+	0.0491798i
$383$	22.6113	+	14.8717i	1.15538	+	0.759907i	0.974674	−	0.223630i	$-0.0717908\pi$
$383$	22.6113	+	14.8717i	1.15538	+	0.759907i	0.180708	+	0.983537i	$0.442161\pi$
$384$		0			0
$385$	3.71427	+	3.93690i	0.189297	+	0.200643i
$386$	−7.84669	+	6.58415i	−0.399386	+	0.335124i
$387$		0			0
$388$	2.02148	+	1.69622i	0.102625	+	0.0861126i
$389$	−1.33071	−	22.8473i	−0.0674694	−	1.15841i	−0.846842	−	0.531845i	$-0.821499\pi$
$389$	−1.33071	−	22.8473i	−0.0674694	−	1.15841i	0.779372	−	0.626561i	$-0.215538\pi$
$390$		0			0
$391$	−11.2307	−	15.0855i	−0.567963	−	0.762906i
$392$	16.9923	−	1.98612i	0.858243	−	0.100314i
$393$		0			0
$394$	19.8190	−	13.0351i	0.998465	−	0.656701i
$395$	−32.2748	+	11.7471i	−1.62392	+	0.591059i
$396$		0			0
$397$	−16.8844	−	6.14542i	−0.847403	−	0.308430i	−0.118422	−	0.992963i	$-0.537784\pi$
$397$	−16.8844	−	6.14542i	−0.847403	−	0.308430i	−0.728981	+	0.684534i	$0.760006\pi$
$398$	−21.2373	+	5.03333i	−1.06453	+	0.252298i
$399$		0			0
$400$	1.37687	−	23.6399i	0.0688434	−	1.18200i
$401$	−0.985267	+	1.04432i	−0.0492019	+	0.0521509i	−0.751507	−	0.659725i	$-0.770673\pi$
$401$	−0.985267	+	1.04432i	−0.0492019	+	0.0521509i	0.702305	+	0.711876i	$0.252154\pi$
$402$		0			0
$403$	0.590048	+	1.36789i	0.0293924	+	0.0681392i
$404$	−0.125318			−0.00623480
$405$		0			0
$406$	−2.32285			−0.115281
$407$	11.2876	+	26.1677i	0.559507	+	1.29708i
$408$		0			0
$409$	−8.94258	+	9.47858i	−0.442182	+	0.468686i	−0.909681	−	0.415308i	$-0.863674\pi$
$409$	−8.94258	+	9.47858i	−0.442182	+	0.468686i	0.467499	+	0.883994i	$0.345155\pi$
$410$	−0.521871	+	8.96018i	−0.0257734	+	0.442512i
$411$		0			0
$412$	−3.79783	+	0.900102i	−0.187106	+	0.0443448i
$413$	−2.53117	−	0.921270i	−0.124551	−	0.0453328i
$414$		0			0
$415$	30.1524	−	10.9746i	1.48012	−	0.538720i
$416$	−0.473560	+	0.311465i	−0.0232182	+	0.0152708i
$417$		0			0
$418$	−41.6154	+	4.86415i	−2.03548	+	0.237913i
$419$	−17.8833	−	24.0214i	−0.873655	−	1.17352i	−0.983740	−	0.179600i	$-0.942520\pi$
$419$	−17.8833	−	24.0214i	−0.873655	−	1.17352i	0.110084	−	0.993922i	$-0.464888\pi$
$420$		0			0
$421$	−1.87836	−	32.2502i	−0.0915458	−	1.57178i	−0.661399	−	0.750034i	$-0.730037\pi$
$421$	−1.87836	−	32.2502i	−0.0915458	−	1.57178i	0.569853	−	0.821746i	$-0.307000\pi$
$422$	−18.3578	−	15.4040i	−0.893643	−	0.749856i
$423$		0			0
$424$	−13.3629	+	11.2128i	−0.648961	+	0.544543i
$425$	14.3484	+	15.2084i	0.695998	+	0.737715i
$426$		0			0
$427$	0.762088	+	0.501233i	0.0368800	+	0.0242564i
$428$	−4.18050	−	0.990796i	−0.202072	−	0.0478919i
$429$		0			0
$430$	−10.6902	−	1.24951i	−0.515527	−	0.0602565i
$431$	−15.3414	−	26.5721i	−0.738970	−	1.27993i	−0.952960	−	0.303098i	$-0.901979\pi$
$431$	−15.3414	−	26.5721i	−0.738970	−	1.27993i	0.213989	−	0.976836i	$-0.431354\pi$
$432$		0			0
$433$	−19.2517	+	33.3449i	−0.925176	+	1.60245i	−0.133899	+	0.990995i	$0.542750\pi$
$433$	−19.2517	+	33.3449i	−0.925176	+	1.60245i	−0.791277	+	0.611457i	$0.790584\pi$
$434$	−1.60629	+	2.15762i	−0.0771045	+	0.103569i
$435$		0			0
$436$	1.98896	+	6.64360i	0.0952541	+	0.318171i
$437$	−19.0380	+	9.56125i	−0.910712	+	0.457377i
$438$		0			0
$439$	−11.3520	+	37.9182i	−0.541800	+	1.80974i	0.0436707	+	0.999046i	$0.486095\pi$
$439$	−11.3520	+	37.9182i	−0.541800	+	1.80974i	−0.585471	+	0.810693i	$0.699090\pi$
$440$	−7.94092	−	45.0352i	−0.378569	−	2.14697i
$441$		0			0
$442$	0.277720	−	1.57503i	0.0132098	−	0.0749166i
$443$	−5.39874	−	2.71135i	−0.256502	−	0.128820i	0.315902	−	0.948792i	$-0.397693\pi$
$443$	−5.39874	−	2.71135i	−0.256502	−	0.128820i	−0.572404	+	0.819972i	$0.693989\pi$
$444$		0			0
$445$	−13.1225	+	30.4213i	−0.622064	+	1.44211i
$446$	−2.98131	+	6.91146i	−0.141169	+	0.327267i
$447$		0			0
$448$	1.51669	+	0.761709i	0.0716567	+	0.0359873i
$449$	0.417057	−	2.36525i	0.0196821	−	0.111623i	−0.973384	−	0.229181i	$-0.926395\pi$
$449$	0.417057	−	2.36525i	0.0196821	−	0.111623i	0.993066	+	0.117558i	$0.0375065\pi$
$450$		0			0
$451$	1.83971	+	10.4335i	0.0866284	+	0.491294i
$452$	1.22801	−	4.10184i	0.0577608	−	0.192934i
$453$		0			0
$454$	−26.8152	+	13.4671i	−1.25850	+	0.632041i
$455$	0.0671214	+	0.224201i	0.00314670	+	0.0105107i
$456$		0			0
$457$	−7.70284	+	10.3467i	−0.360323	+	0.483998i	−0.944909	−	0.327334i	$-0.893850\pi$
$457$	−7.70284	+	10.3467i	−0.360323	+	0.483998i	0.584585	+	0.811332i	$0.301257\pi$
$458$	−2.85579	+	4.94638i	−0.133442	+	0.231129i
$459$		0			0
$460$	2.94517	+	5.10118i	0.137319	+	0.237844i
$461$	−29.3843	−	3.43453i	−1.36856	−	0.159962i	−0.600135	−	0.799899i	$-0.704887\pi$
$461$	−29.3843	−	3.43453i	−1.36856	−	0.159962i	−0.768428	+	0.639937i	$0.778961\pi$
$462$		0			0
$463$	33.6433	+	7.97361i	1.56354	+	0.370565i	0.919079	−	0.394074i	$-0.128935\pi$
$463$	33.6433	+	7.97361i	1.56354	+	0.370565i	0.644458	+	0.764639i	$0.277083\pi$
$464$	19.8524	+	13.0572i	0.921626	+	0.606163i
$465$		0			0
$466$	−1.62626	−	1.72373i	−0.0753349	−	0.0798503i
$467$	24.0070	−	20.1443i	1.11091	−	0.932165i	0.112801	−	0.993618i	$-0.464018\pi$
$467$	24.0070	−	20.1443i	1.11091	−	0.932165i	0.998110	+	0.0614529i	$0.0195734\pi$
$468$		0			0
$469$	−1.53402	−	1.28719i	−0.0708343	−	0.0594371i
$470$	−2.19446	−	37.6774i	−0.101223	−	1.73793i
$471$		0			0
$472$	13.5903	+	18.2549i	0.625545	+	0.840252i
$473$	−12.6186	+	1.47491i	−0.580205	+	0.0678162i
$474$		0			0
$475$	19.7884	−	13.0150i	0.907952	−	0.597170i
$476$	0.456267	−	0.166068i	0.0209130	−	0.00761170i
$477$		0			0
$478$	−6.93405	−	2.52379i	−0.317156	−	0.115435i
$479$	9.22501	−	2.18637i	0.421502	−	0.0998977i	−0.0143909	−	0.999896i	$-0.504581\pi$
$479$	9.22501	−	2.18637i	0.421502	−	0.0998977i	0.435893	+	0.899999i	$0.356433\pi$
$480$		0			0
$481$	−0.0716493	+	1.23017i	−0.00326693	+	0.0560910i
$482$	26.9249	−	28.5388i	1.22640	−	1.29990i
$483$		0			0
$484$	3.65487	+	8.47293i	0.166130	+	0.385133i
$485$	−20.7437			−0.941922
$486$		0			0
$487$	−16.8494			−0.763520			−0.381760	−	0.924261i	$-0.624682\pi$
$487$	−16.8494			−0.763520			−0.381760	+	0.924261i	$0.624682\pi$
$488$	−3.05247	−	7.07643i	−0.138179	−	0.320335i
$489$		0			0
$490$	23.3790	−	24.7803i	1.05615	−	1.11946i
$491$	0.904688	−	15.5329i	0.0408280	−	0.700989i	−0.914344	−	0.404938i	$-0.867293\pi$
$491$	0.904688	−	15.5329i	0.0408280	−	0.700989i	0.955172	−	0.296051i	$-0.0956699\pi$
$492$		0			0
$493$	−20.4151	+	4.83846i	−0.919449	+	0.217913i
$494$	−1.70242	−	0.619631i	−0.0765956	−	0.0278785i
$495$		0			0
$496$	25.8567	−	9.41106i	1.16100	−	0.422569i
$497$	−1.22711	+	0.807081i	−0.0550433	+	0.0362025i
$498$		0			0
$499$	18.1512	−	2.12157i	0.812559	−	0.0949745i	0.300343	−	0.953831i	$-0.402899\pi$
$499$	18.1512	−	2.12157i	0.812559	−	0.0949745i	0.512216	+	0.858857i	$0.328825\pi$
$500$	−0.0750712	−	0.100838i	−0.00335729	−	0.00450962i
$501$		0			0
$502$	−0.198368	−	3.40584i	−0.00885359	−	0.152010i
$503$	22.0539	+	18.5054i	0.983333	+	0.825114i	0.984589	−	0.174885i	$-0.0559554\pi$
$503$	22.0539	+	18.5054i	0.983333	+	0.825114i	−0.00125604	+	0.999999i	$0.500400\pi$
$504$		0			0
$505$	0.754636	−	0.633215i	0.0335808	−	0.0281777i
$506$	28.3777	+	30.0787i	1.26154	+	1.33716i
$507$		0			0
$508$	4.88454	+	3.21262i	0.216717	+	0.142537i
$509$	−9.00835	−	2.13502i	−0.399288	−	0.0946330i	0.0260655	−	0.999660i	$-0.491702\pi$
$509$	−9.00835	−	2.13502i	−0.399288	−	0.0946330i	−0.425354	+	0.905027i	$0.639850\pi$
$510$		0			0
$511$	−0.530896	−	0.0620529i	−0.0234855	−	0.00274506i
$512$	−6.25876	−	10.8405i	−0.276601	−	0.479086i
$513$		0			0
$514$	7.95941	−	13.7861i	0.351074	−	0.608079i
$515$	18.3216	−	24.6101i	0.807345	−	1.08445i
$516$		0			0
$517$	−12.7769	−	42.6779i	−0.561928	−	1.87697i
$518$	−1.98834	+	0.998580i	−0.0873625	+	0.0438751i
$519$		0			0
$520$	0.567107	−	1.89427i	0.0248693	−	0.0830692i
$521$	0.982915	+	5.57439i	0.0430623	+	0.244218i	0.998739	−	0.0501990i	$-0.0159855\pi$
$521$	0.982915	+	5.57439i	0.0430623	+	0.244218i	−0.955677	+	0.294417i	$0.904874\pi$
$522$		0			0
$523$	2.68166	−	15.2084i	0.117261	−	0.665018i	−0.868345	−	0.495960i	$-0.834816\pi$
$523$	2.68166	−	15.2084i	0.117261	−	0.665018i	0.985606	−	0.169058i	$-0.0540726\pi$
$524$	1.38244	+	0.694287i	0.0603921	+	0.0303301i
$525$		0			0
$526$	0.974600	−	2.25938i	0.0424946	−	0.0985135i
$527$	−9.62308	+	22.3088i	−0.419188	+	0.971787i
$528$		0			0
$529$	−1.76378	−	0.885804i	−0.0766861	−	0.0385132i
$530$	−6.03207	+	34.2096i	−0.262016	+	1.48597i
$531$		0			0
$532$	−0.0955097	−	0.541662i	−0.00414087	−	0.0234840i
$533$	−0.131384	+	0.438853i	−0.00569088	+	0.0190088i
$534$		0			0
$535$	30.1804	−	15.1572i	1.30481	−	0.655301i
$536$	4.85249	+	16.2084i	0.209596	+	0.700098i
$537$		0			0
$538$	−4.62508	+	6.21257i	−0.199402	+	0.267843i
$539$	20.1069	−	34.8261i	0.866064	−	1.50007i
$540$		0			0
$541$	−19.5695	−	33.8953i	−0.841357	−	1.45727i	−0.888747	−	0.458397i	$-0.848424\pi$
$541$	−19.5695	−	33.8953i	−0.841357	−	1.45727i	0.0473898	−	0.998876i	$-0.484910\pi$
$542$	14.2790	+	1.66898i	0.613335	+	0.0716886i
$543$		0			0
$544$	−8.99485	−	2.13182i	−0.385651	−	0.0914010i
$545$	−45.5463	−	29.9563i	−1.95099	−	1.28319i
$546$		0			0
$547$	14.5580	+	15.4305i	0.622453	+	0.659762i	0.959494	−	0.281728i	$-0.0909076\pi$
$547$	14.5580	+	15.4305i	0.622453	+	0.659762i	−0.337041	+	0.941490i	$0.609426\pi$
$548$	4.41754	−	3.70675i	0.188708	−	0.158345i
$549$		0			0
$550$	−35.2178	−	29.5512i	−1.50169	−	1.26007i
$551$	1.38189	+	23.7261i	0.0588705	+	1.01077i
$552$		0			0
$553$	−1.89018	−	2.53896i	−0.0803788	−	0.107967i
$554$	−39.8018	+	4.65217i	−1.69102	+	0.197652i
$555$		0			0
$556$	−1.99043	+	1.30913i	−0.0844132	+	0.0555195i
$557$	−2.55364	+	0.929451i	−0.108201	+	0.0393821i	−0.395554	−	0.918443i	$-0.629447\pi$
$557$	−2.55364	+	0.929451i	−0.108201	+	0.0393821i	0.287352	+	0.957825i	$0.407225\pi$
$558$		0			0
$559$	−0.516208	−	0.187884i	−0.0218333	−	0.00794666i
$560$	4.20622	−	0.996892i	0.177745	−	0.0421264i
$561$		0			0
$562$	2.61091	−	44.8276i	0.110135	−	1.89094i
$563$	−12.5763	+	13.3301i	−0.530028	+	0.561797i	−0.935960	−	0.352106i	$-0.885465\pi$
$563$	−12.5763	+	13.3301i	−0.530028	+	0.561797i	0.405932	+	0.913903i	$0.366947\pi$
$564$		0			0
$565$	13.3313	+	30.9053i	0.560851	+	1.30020i
$566$	−1.60019			−0.0672608
$567$		0			0
$568$	12.4093			0.520682
$569$	−4.43905	−	10.2909i	−0.186095	−	0.431416i	0.799472	−	0.600703i	$-0.205113\pi$
$569$	−4.43905	−	10.2909i	−0.186095	−	0.431416i	−0.985567	+	0.169288i	$0.945853\pi$
$570$		0			0
$571$	−0.299771	+	0.317738i	−0.0125450	+	0.0132969i	−0.733616	−	0.679565i	$-0.762169\pi$
$571$	−0.299771	+	0.317738i	−0.0125450	+	0.0132969i	0.721071	+	0.692861i	$0.243650\pi$
$572$	−0.0343793	+	0.590269i	−0.00143747	+	0.0246804i
$573$		0			0
$574$	−0.804862	+	0.190756i	−0.0335943	+	0.00796200i
$575$	−21.9662	−	7.99505i	−0.916055	−	0.333417i
$576$		0			0
$577$	34.0165	−	12.3810i	1.41612	−	0.515427i	0.483203	−	0.875508i	$-0.339473\pi$
$577$	34.0165	−	12.3810i	1.41612	−	0.515427i	0.932921	+	0.360081i	$0.117251\pi$
$578$	−0.230737	+	0.151758i	−0.00959741	+	0.00631232i
$579$		0			0
$580$	6.52670	−	0.762861i	0.271006	−	0.0316761i
$581$	1.76588	+	2.37199i	0.0732612	+	0.0984069i
$582$		0			0
$583$	2.38415	+	40.9342i	0.0987413	+	1.69532i
$584$	3.45951	+	2.90287i	0.143155	+	0.120122i
$585$		0			0
$586$	8.24358	−	6.91718i	0.340539	−	0.285746i
$587$	−0.551710	−	0.584778i	−0.0227715	−	0.0241364i	0.715888	−	0.698215i	$-0.246022\pi$
$587$	−0.551710	−	0.584778i	−0.0227715	−	0.0241364i	−0.738659	+	0.674079i	$0.764541\pi$
$588$		0			0
$589$	22.9941	+	15.1234i	0.947453	+	0.623150i
$590$	44.0982	+	10.4515i	1.81549	+	0.430280i
$591$		0			0
$592$	22.6067	+	2.64234i	0.929128	+	0.108599i
$593$	18.8891	+	32.7169i	0.775683	+	1.34352i	0.934410	+	0.356200i	$0.115928\pi$
$593$	18.8891	+	32.7169i	0.775683	+	1.34352i	−0.158726	+	0.987323i	$0.550739\pi$
$594$		0			0
$595$	−1.90842	+	3.30548i	−0.0782375	+	0.135511i
$596$	−3.40109	+	4.56846i	−0.139314	+	0.187131i
$597$		0			0
$598$	0.512820	+	1.71294i	0.0209708	+	0.0700473i
$599$	26.1795	−	13.1479i	1.06967	−	0.537207i	0.175288	−	0.984517i	$-0.443914\pi$
$599$	26.1795	−	13.1479i	1.06967	−	0.537207i	0.894379	+	0.447310i	$0.147618\pi$
$600$		0			0
$601$	−1.14204	+	3.81467i	−0.0465846	+	0.155603i	−0.978117	−	0.208054i	$-0.933287\pi$
$601$	−1.14204	+	3.81467i	−0.0465846	+	0.155603i	0.931533	+	0.363658i	$0.118472\pi$
$602$	−0.172242	−	0.976833i	−0.00702006	−	0.0398128i
$603$		0			0
$604$	0.111178	−	0.630523i	0.00452377	−	0.0256556i
$605$	−64.8214	−	32.5545i	−2.63536	−	1.32353i
$606$		0			0
$607$	−13.3712	+	30.9980i	−0.542721	+	1.25817i	0.397500	+	0.917602i	$0.369878\pi$
$607$	−13.3712	+	30.9980i	−0.542721	+	1.25817i	−0.940221	+	0.340566i	$0.889381\pi$
$608$	−4.14751	+	9.61502i	−0.168204	+	0.389941i
$609$		0			0
$610$	−13.7144	−	6.88763i	−0.555280	−	0.278872i
$611$	0.334497	−	1.89703i	0.0135323	−	0.0767456i
$612$		0			0
$613$	7.41615	+	42.0591i	0.299536	+	1.69875i	0.648173	+	0.761493i	$0.275533\pi$
$613$	7.41615	+	42.0591i	0.299536	+	1.69875i	−0.348637	+	0.937258i	$0.613355\pi$
$614$	8.15024	−	27.2237i	0.328917	−	1.09866i
$615$		0			0
$616$	3.76614	−	1.89143i	0.151742	−	0.0762077i
$617$	−2.15522	−	7.19894i	−0.0867660	−	0.289819i	0.903583	−	0.428412i	$-0.140927\pi$
$617$	−2.15522	−	7.19894i	−0.0867660	−	0.289819i	−0.990349	+	0.138594i	$0.955742\pi$
$618$		0			0
$619$	12.5342	−	16.8364i	0.503793	−	0.676712i	−0.475370	−	0.879786i	$-0.657686\pi$
$619$	12.5342	−	16.8364i	0.503793	−	0.676712i	0.979163	+	0.203074i	$0.0650932\pi$
$620$	3.80472	−	6.58997i	0.152801	−	0.264660i
$621$		0			0
$622$	−11.3934	−	19.7339i	−0.456832	−	0.791256i
$623$	−3.03265	−	0.354466i	−0.121501	−	0.0142014i
$624$		0			0
$625$	−23.8407	−	5.65034i	−0.953627	−	0.226014i
$626$	7.33138	+	4.82193i	0.293021	+	0.192723i
$627$		0			0
$628$	−1.42155	−	1.50675i	−0.0567260	−	0.0601260i
$629$	−15.3951	+	12.9180i	−0.613841	+	0.515074i
$630$		0			0
$631$	−23.1956	−	19.4634i	−0.923403	−	0.774827i	0.0512179	−	0.998688i	$-0.483690\pi$
$631$	−23.1956	−	19.4634i	−0.923403	−	0.774827i	−0.974621	+	0.223860i	$0.928134\pi$
$632$	1.55500	+	26.6983i	0.0618544	+	1.06200i
$633$		0			0
$634$	−21.2189	−	28.5020i	−0.842712	−	1.13196i
$635$	−45.6465	+	5.33532i	−1.81143	+	0.211726i
$636$		0			0
$637$	1.45276	−	0.955498i	0.0575606	−	0.0378582i
$638$	43.3497	−	15.7780i	1.71623	−	0.624657i
$639$		0			0
$640$	−40.2937	−	14.6657i	−1.59275	−	0.579712i
$641$	16.0562	−	3.80539i	0.634182	−	0.150304i	0.0990640	−	0.995081i	$-0.468415\pi$
$641$	16.0562	−	3.80539i	0.634182	−	0.150304i	0.535118	+	0.844777i	$0.320267\pi$
$642$		0			0
$643$	1.05055	−	18.0372i	0.0414296	−	0.711318i	−0.912091	−	0.409989i	$-0.865533\pi$
$643$	1.05055	−	18.0372i	0.0414296	−	0.711318i	0.953520	−	0.301329i	$-0.0974304\pi$
$644$	−0.372524	+	0.394852i	−0.0146795	+	0.0155594i
$645$		0			0
$646$	−11.7028	−	27.1302i	−0.460442	−	1.06742i
$647$	4.14445			0.162935			0.0814676	−	0.996676i	$-0.474039\pi$
$647$	4.14445			0.162935			0.0814676	+	0.996676i	$0.474039\pi$
$648$		0			0
$649$	53.4951			2.09987
$650$	−0.787356	−	1.82530i	−0.0308826	−	0.0715940i
$651$		0			0
$652$	4.90361	−	5.19752i	0.192040	−	0.203551i
$653$	1.17463	−	20.1677i	0.0459669	−	0.789222i	−0.894023	−	0.448020i	$-0.852129\pi$
$653$	1.17463	−	20.1677i	0.0459669	−	0.789222i	0.939990	−	0.341201i	$-0.110834\pi$
$654$		0			0
$655$	−11.8329	+	2.80444i	−0.462348	+	0.109579i
$656$	7.95109	+	2.89396i	0.310438	+	0.112990i
$657$		0			0
$658$	3.26842	−	1.18961i	0.127416	−	0.0463758i
$659$	6.41002	−	4.21594i	0.249699	−	0.164230i	−0.418490	−	0.908222i	$-0.637440\pi$
$659$	6.41002	−	4.21594i	0.249699	−	0.164230i	0.668188	+	0.743992i	$0.267070\pi$
$660$		0			0
$661$	5.21185	−	0.609178i	0.202718	−	0.0236943i	−0.0141280	−	0.999900i	$-0.504497\pi$
$661$	5.21185	−	0.609178i	0.202718	−	0.0236943i	0.216846	+	0.976206i	$0.430423\pi$
$662$	−2.84955	−	3.82761i	−0.110751	−	0.148764i
$663$		0			0
$664$	−1.45274	−	24.9426i	−0.0563772	−	0.967959i
$665$	3.31209	+	2.77917i	0.128437	+	0.107772i
$666$		0			0
$667$	17.9687	−	15.0775i	0.695750	−	0.583803i
$668$	0.382373	+	0.405291i	0.0147944	+	0.0156812i
$669$		0			0
$670$	28.1494	+	18.5141i	1.08751	+	0.715264i
$671$	−17.6269	−	4.17766i	−0.680480	−	0.161277i
$672$		0			0
$673$	−3.30793	−	0.386642i	−0.127512	−	0.0149040i	0.0520977	−	0.998642i	$-0.483409\pi$
$673$	−3.30793	−	0.386642i	−0.127512	−	0.0149040i	−0.179609	+	0.983738i	$0.557483\pi$
$674$	−3.18620	−	5.51867i	−0.122728	−	0.212571i
$675$		0			0
$676$	2.61481	−	4.52898i	0.100570	−	0.174192i
$677$	14.2005	−	19.0746i	0.545771	−	0.733098i	−0.440587	−	0.897710i	$-0.645230\pi$
$677$	14.2005	−	19.0746i	0.545771	−	0.733098i	0.986358	+	0.164612i	$0.0526371\pi$
$678$		0			0
$679$	−0.548285	−	1.83140i	−0.0210413	−	0.0702827i
$680$	28.8182	−	14.4730i	1.10513	−	0.555016i
$681$		0			0
$682$	15.3214	−	51.1769i	0.586686	−	1.95967i
$683$	3.07677	+	17.4492i	0.117729	+	0.667676i	0.985363	+	0.170472i	$0.0545291\pi$
$683$	3.07677	+	17.4492i	0.117729	+	0.667676i	−0.867633	+	0.497205i	$0.834360\pi$
$684$		0			0
$685$	−7.87167	+	44.6424i	−0.300761	+	1.70570i
$686$	5.64624	+	2.83565i	0.215574	+	0.108266i
$687$		0			0
$688$	−4.01887	+	9.31678i	−0.153218	+	0.355199i
$689$	−0.702240	+	1.62797i	−0.0267532	+	0.0620209i
$690$		0			0
$691$	25.3721	+	12.7423i	0.965199	+	0.484741i	0.860326	−	0.509744i	$-0.170260\pi$
$691$	25.3721	+	12.7423i	0.965199	+	0.484741i	0.104873	+	0.994486i	$0.466556\pi$
$692$	−0.912541	+	5.17528i	−0.0346896	+	0.196734i
$693$		0			0
$694$	−2.40983	−	13.6668i	−0.0914758	−	0.518785i
$695$	5.37109	−	17.9407i	0.203737	−	0.680529i
$696$		0			0
$697$	−6.67643	+	3.35303i	−0.252888	+	0.127005i
$698$	2.20550	+	7.36690i	0.0834796	+	0.278841i
$699$		0			0
$700$	0.360391	−	0.484089i	0.0136215	−	0.0182968i
$701$	−19.6318	+	34.0032i	−0.741482	+	1.28428i	0.210338	+	0.977629i	$0.432544\pi$
$701$	−19.6318	+	34.0032i	−0.741482	+	1.28428i	−0.951820	+	0.306656i	$0.900790\pi$
$702$		0			0
$703$	11.3826	+	19.7152i	0.429303	+	0.743574i
$704$	−33.4787	−	3.91310i	−1.26178	−	0.147481i
$705$		0			0
$706$	30.6241	+	7.25805i	1.15255	+	0.273160i
$707$	0.0758508	+	0.0498879i	0.00285266	+	0.00187623i
$708$		0			0
$709$	−34.3548	−	36.4139i	−1.29022	−	1.36755i	−0.893146	−	0.449767i	$-0.851507\pi$
$709$	−34.3548	−	36.4139i	−1.29022	−	1.36755i	−0.397074	−	0.917786i	$-0.629975\pi$
$710$	18.9299	−	15.8841i	0.710428	−	0.596120i
$711$		0			0
$712$	19.7618	+	16.5821i	0.740606	+	0.621442i
$713$	−1.57938	−	27.1169i	−0.0591482	−	1.01554i
$714$		0			0
$715$	−2.77553	−	3.72818i	−0.103799	−	0.139426i
$716$	10.0444	−	1.17402i	0.375377	−	0.0438753i
$717$		0			0
$718$	10.0839	−	6.63227i	0.376327	−	0.247514i
$719$	−17.5102	+	6.37320i	−0.653021	+	0.237680i	−0.647220	−	0.762303i	$-0.724069\pi$
$719$	−17.5102	+	6.37320i	−0.653021	+	0.237680i	−0.00580045	+	0.999983i	$0.501846\pi$
$720$		0			0
$721$	2.65702	+	0.967078i	0.0989528	+	0.0360159i
$722$	−3.90097	+	0.924548i	−0.145179	+	0.0344081i
$723$		0			0
$724$	−0.108284	+	1.85917i	−0.00402435	+	0.0690954i
$725$	−17.8956	+	18.9682i	−0.664626	+	0.704462i
$726$		0			0
$727$	−16.6006	−	38.4844i	−0.615680	−	1.42731i	−0.885611	−	0.464428i	$-0.846260\pi$
$727$	−16.6006	−	38.4844i	−0.615680	−	1.42731i	0.269930	−	0.962880i	$-0.412999\pi$
$728$	0.182229			0.00675386
$729$		0			0
$730$	8.99309			0.332849
$731$	−3.54853	−	8.22641i	−0.131247	−	0.304265i
$732$		0			0
$733$	−9.79629	+	10.3835i	−0.361834	+	0.383522i	−0.882558	−	0.470203i	$-0.844181\pi$
$733$	−9.79629	+	10.3835i	−0.361834	+	0.383522i	0.520724	+	0.853725i	$0.325662\pi$
$734$	−0.0175156	+	0.300732i	−0.000646514	+	0.0111002i
$735$		0			0
$736$	10.0563	−	2.38339i	0.370680	−	0.0878527i
$737$	37.3715	+	13.6021i	1.37660	+	0.501041i
$738$		0			0
$739$	−17.4197	+	6.34025i	−0.640794	+	0.233230i	−0.641923	−	0.766769i	$-0.721863\pi$
$739$	−17.4197	+	6.34025i	−0.640794	+	0.233230i	0.00112859	+	0.999999i	$0.499641\pi$
$740$	5.25883	−	3.45879i	0.193318	−	0.127148i
$741$		0			0
$742$	−3.17970	+	0.371654i	−0.116730	+	0.0136438i
$743$	17.6072	+	23.6506i	0.645945	+	0.867655i	0.997654	−	0.0684547i	$-0.0218069\pi$
$743$	17.6072	+	23.6506i	0.645945	+	0.867655i	−0.351709	+	0.936109i	$0.614399\pi$
$744$		0			0
$745$	−2.60322	−	44.6955i	−0.0953745	−	1.63752i
$746$	−2.71579	−	2.27882i	−0.0994320	−	0.0834334i
$747$		0			0
$748$	−7.38696	+	6.19840i	−0.270094	+	0.226636i
$749$	2.13589	+	2.26391i	0.0780438	+	0.0827216i
$750$		0			0
$751$	13.9418	+	9.16968i	0.508744	+	0.334606i	0.777793	−	0.628520i	$-0.216339\pi$
$751$	13.9418	+	9.16968i	0.508744	+	0.334606i	−0.269049	+	0.963126i	$0.586709\pi$
$752$	−34.6208	−	8.20529i	−1.26249	−	0.299216i
$753$		0			0
$754$	1.98123	+	0.231572i	0.0721521	+	0.00843337i
$755$	2.51646	+	4.35863i	0.0915833	+	0.158627i
$756$		0			0
$757$	−16.3993	+	28.4044i	−0.596042	+	1.03237i	0.397357	+	0.917664i	$0.369927\pi$
$757$	−16.3993	+	28.4044i	−0.596042	+	1.03237i	−0.993399	+	0.114710i	$0.963406\pi$
$758$	6.71679	−	9.02221i	0.243965	−	0.327702i
$759$		0			0
$760$	−10.4770	−	34.9955i	−0.380040	−	1.26942i
$761$	−30.2651	+	15.1997i	−1.09711	+	0.550988i	−0.902847	−	0.429962i	$-0.858527\pi$
$761$	−30.2651	+	15.1997i	−1.09711	+	0.550988i	−0.194261	+	0.980950i	$0.562231\pi$
$762$		0			0
$763$	1.44090	−	4.81294i	0.0521641	−	0.174240i
$764$	−0.188692	−	1.07013i	−0.00682665	−	0.0387159i
$765$		0			0
$766$	7.28693	−	41.3262i	0.263287	−	1.49318i
$767$	2.06706	+	1.03812i	0.0746373	+	0.0374843i
$768$		0			0
$769$	−0.585556	+	1.35747i	−0.0211157	+	0.0489517i	−0.928448	−	0.371463i	$-0.878856\pi$
$769$	−0.585556	+	1.35747i	−0.0211157	+	0.0489517i	0.907332	+	0.420415i	$0.138115\pi$
$770$	3.32406	−	7.70603i	0.119791	−	0.277706i
$771$		0			0
$772$	2.38642	+	1.19850i	0.0858890	+	0.0431351i
$773$	−0.387181	+	2.19581i	−0.0139259	+	0.0789779i	−0.990979	−	0.134020i	$-0.957211\pi$
$773$	−0.387181	+	2.19581i	−0.0139259	+	0.0789779i	0.977053	+	0.212997i	$0.0683226\pi$
$774$		0			0
$775$	5.24388	+	29.7395i	0.188366	+	1.06827i
$776$	−4.63245	+	15.4735i	−0.166295	+	0.555465i
$777$		0			0
$778$	−31.7117	+	15.9262i	−1.13692	+	0.570982i
$779$	2.42724	+	8.10756i	0.0869650	+	0.290483i
$780$		0			0
$781$	17.4185	−	23.3971i	0.623283	−	0.837215i
$782$	−14.5807	+	25.2545i	−0.521404	+	0.903099i
$783$		0			0
$784$	−16.0586	−	27.8143i	−0.573521	−	0.993367i
$785$	16.1737	+	1.89043i	0.577263	+	0.0674724i
$786$		0			0
$787$	3.02636	+	0.717261i	0.107878	+	0.0255676i	0.284200	−	0.958765i	$-0.408272\pi$
$787$	3.02636	+	0.717261i	0.107878	+	0.0255676i	−0.176322	+	0.984333i	$0.556420\pi$
$788$	−5.16697	−	3.39837i	−0.184066	−	0.121062i
$789$		0			0
$790$	36.5463	+	38.7368i	1.30026	+	1.37820i
$791$	−2.37618	+	1.99385i	−0.0844872	+	0.0708932i
$792$		0			0
$793$	−0.600037	−	0.503491i	−0.0213080	−	0.0178795i
$794$	1.61994	+	27.8134i	0.0574897	+	0.987059i
$795$		0			0
$796$	3.39790	+	4.56418i	0.120435	+	0.161773i
$797$	19.6200	−	2.29325i	0.694977	−	0.0812312i	0.238732	−	0.971085i	$-0.423268\pi$
$797$	19.6200	−	2.29325i	0.694977	−	0.0812312i	0.456245	+	0.889854i	$0.349194\pi$
$798$		0			0
$799$	26.2476	−	17.2633i	0.928573	−	0.610732i
$800$	−10.7969	+	3.92974i	−0.381727	+	0.138937i
$801$		0			0
$802$	2.09195	+	0.761409i	0.0738694	+	0.0268863i
$803$	10.3292	−	2.44807i	0.364511	−	0.0863906i
$804$		0			0
$805$	0.248118	−	4.26002i	0.00874502	−	0.150146i
$806$	1.58515	−	1.68016i	0.0558346	−	0.0591812i
$807$		0			0
$808$	−0.303813	−	0.704319i	−0.0106881	−	0.0247778i
$809$	19.4534			0.683945			0.341973	−	0.939710i	$-0.388905\pi$
$809$	19.4534			0.683945			0.341973	+	0.939710i	$0.388905\pi$
$810$		0			0
$811$	27.6759			0.971832			0.485916	−	0.874005i	$-0.338486\pi$
$811$	27.6759			0.971832			0.485916	+	0.874005i	$0.338486\pi$
$812$	0.239861	+	0.556060i	0.00841747	+	0.0195139i
$813$		0			0
$814$	30.3240	−	32.1416i	1.06286	−	1.12656i
$815$	−3.26603	+	56.0756i	−0.114404	+	1.96424i
$816$		0			0
$817$	−9.87512	+	2.34045i	−0.345487	+	0.0818819i
$818$	18.9872	+	6.91078i	0.663872	+	0.241630i
$819$		0			0
$820$	2.19884	−	0.800311i	0.0767867	−	0.0279481i
$821$	8.72148	−	5.73621i	0.304382	−	0.200195i	−0.388124	−	0.921607i	$-0.626877\pi$
$821$	8.72148	−	5.73621i	0.304382	−	0.200195i	0.692506	+	0.721412i	$0.256507\pi$
$822$		0			0
$823$	−11.3913	+	1.33145i	−0.397074	+	0.0464113i	−0.312287	−	0.949988i	$-0.601095\pi$
$823$	−11.3913	+	1.33145i	−0.397074	+	0.0464113i	−0.0847872	+	0.996399i	$0.527021\pi$
$824$	−14.2660	−	19.1626i	−0.496981	−	0.667562i
$825$		0			0
$826$	0.242849	+	4.16955i	0.00844979	+	0.145077i
$827$	−8.85255	−	7.42817i	−0.307833	−	0.258303i	0.475763	−	0.879574i	$-0.342172\pi$
$827$	−8.85255	−	7.42817i	−0.307833	−	0.258303i	−0.783596	+	0.621271i	$0.786617\pi$
$828$		0			0
$829$	22.8861	−	19.2037i	0.794866	−	0.666972i	−0.152078	−	0.988368i	$-0.548597\pi$
$829$	22.8861	−	19.2037i	0.794866	−	0.666972i	0.946945	+	0.321396i	$0.104152\pi$
$830$	−34.1430	−	36.1895i	−1.18512	−	1.25616i
$831$		0			0
$832$	−1.21769	−	0.800886i	−0.0422158	−	0.0277657i
$833$	27.5940	+	6.53990i	0.956075	+	0.226594i
$834$		0			0
$835$	−4.35045	−	0.508494i	−0.150553	−	0.0175972i
$836$	5.46168	+	9.45990i	0.188896	+	0.327178i
$837$		0			0
$838$	−23.2176	+	40.2140i	−0.802038	+	1.38917i
$839$	−23.2903	+	31.2843i	−0.804071	+	1.08005i	0.191068	+	0.981577i	$0.438805\pi$
$839$	−23.2903	+	31.2843i	−0.804071	+	1.08005i	−0.995139	+	0.0984779i	$0.968603\pi$
$840$		0			0
$841$	0.812380	+	2.71354i	0.0280131	+	0.0935703i
$842$	−44.7627	+	22.4807i	−1.54263	+	0.774736i
$843$		0			0
$844$	−1.79187	+	5.98525i	−0.0616786	+	0.206021i
$845$	7.13856	+	40.4848i	0.245574	+	1.39272i
$846$		0			0
$847$	1.16082	−	6.58336i	0.0398864	−	0.226207i
$848$	29.2647	+	14.6973i	1.00495	+	0.504706i
$849$		0			0
$850$	12.8410	−	29.7687i	0.440441	−	1.02106i
$851$	8.89926	−	20.6308i	0.305063	−	0.707215i
$852$		0			0
$853$	22.4768	+	11.2883i	0.769591	+	0.386503i	0.789857	−	0.613292i	$-0.210155\pi$
$853$	22.4768	+	11.2883i	0.769591	+	0.386503i	−0.0202658	+	0.999795i	$0.506451\pi$
$854$	0.245598	−	1.39286i	0.00840419	−	0.0476625i
$855$		0			0
$856$	−4.56643	−	25.8975i	−0.156077	−	0.885158i
$857$	−15.8547	+	52.9585i	−0.541587	+	1.80903i	0.0448000	+	0.998996i	$0.485735\pi$
$857$	−15.8547	+	52.9585i	−0.541587	+	1.80903i	−0.586387	+	0.810031i	$0.699450\pi$
$858$		0			0
$859$	−23.2701	+	11.6867i	−0.793967	+	0.398745i	−0.799067	−	0.601242i	$-0.794673\pi$
$859$	−23.2701	+	11.6867i	−0.793967	+	0.398745i	0.00510038	+	0.999987i	$0.498376\pi$
$860$	0.804769	+	2.68812i	0.0274424	+	0.0916640i
$861$		0			0
$862$	−28.4102	+	38.1615i	−0.967656	+	1.29979i
$863$	10.0819	−	17.4623i	0.343191	−	0.594425i	−0.641832	−	0.766845i	$-0.721825\pi$
$863$	10.0819	−	17.4623i	0.343191	−	0.594425i	0.985023	+	0.172420i	$0.0551587\pi$
$864$		0			0
$865$	−20.6549	−	35.7753i	−0.702287	−	1.21640i
$866$	59.2982	+	6.93096i	2.01503	+	0.235524i
$867$		0			0
$868$	0.682374	+	0.161726i	0.0231613	+	0.00548933i
$869$	52.5210	+	34.5436i	1.78165	+	1.17181i
$870$		0			0
$871$	1.18008	+	1.25081i	0.0399856	+	0.0423822i
$872$	−32.5168	+	27.2849i	−1.10116	+	0.923982i
$873$		0			0
$874$	25.3050	+	21.2334i	0.855954	+	0.718230i
$875$	0.00529544	+	0.0909192i	0.000179019	+	0.00307363i
$876$		0			0
$877$	6.64211	+	8.92190i	0.224288	+	0.301271i	0.899996	−	0.435898i	$-0.143569\pi$
$877$	6.64211	+	8.92190i	0.224288	+	0.301271i	−0.675708	+	0.737170i	$0.736162\pi$
$878$	60.9579	−	7.12496i	2.05723	−	0.240456i
$879$		0			0
$880$	−71.7262	+	47.1751i	−2.41789	+	1.59027i
$881$	−7.85029	+	2.85727i	−0.264483	+	0.0962639i	−0.470858	−	0.882209i	$-0.656056\pi$
$881$	−7.85029	+	2.85727i	−0.264483	+	0.0962639i	0.206375	+	0.978473i	$0.433833\pi$
$882$		0			0
$883$	51.2586	+	18.6566i	1.72499	+	0.627845i	0.998254	−	0.0590722i	$-0.0188142\pi$
$883$	51.2586	+	18.6566i	1.72499	+	0.627845i	0.726736	+	0.686917i	$0.241036\pi$
$884$	−0.405719	+	0.0961572i	−0.0136458	+	0.00323412i
$885$		0			0
$886$	−0.544670	+	9.35163i	−0.0182986	+	0.314174i
$887$	26.3063	−	27.8831i	0.883280	−	0.936222i	−0.115087	−	0.993355i	$-0.536715\pi$
$887$	26.3063	−	27.8831i	0.883280	−	0.936222i	0.998367	+	0.0571336i	$0.0181961\pi$
$888$		0			0
$889$	−1.67754	−	3.88898i	−0.0562630	−	0.130432i
$890$	51.3714			1.72197
$891$		0			0
$892$	1.96237			0.0657049
$893$	−14.0953	−	32.6767i	−0.471683	−	1.09348i
$894$		0			0
$895$	−54.5529	+	57.8227i	−1.82350	+	1.93280i
$896$	0.229773	−	3.94505i	0.00767617	−	0.131795i
$897$		0			0
$898$	−3.62366	+	0.858823i	−0.120923	+	0.0286593i
$899$	−28.4748	−	10.3640i	−0.949687	−	0.345658i
$900$		0			0
$901$	−27.1716	+	9.88965i	−0.905217	+	0.329472i
$902$	13.7248	−	9.02697i	0.456987	−	0.300565i
$903$		0			0
$904$	26.0305	−	3.04253i	0.865763	−	0.101193i
$905$	−8.74207	−	11.7426i	−0.290596	−	0.390338i
$906$		0			0
$907$	1.66379	+	28.5663i	0.0552454	+	0.948527i	0.906084	+	0.423099i	$0.139058\pi$
$907$	1.66379	+	28.5663i	0.0552454	+	0.948527i	−0.850838	+	0.525428i	$0.823905\pi$
$908$	5.99281	+	5.02856i	0.198878	+	0.166879i
$909$		0			0
$910$	0.277984	−	0.233257i	0.00921509	−	0.00773238i
$911$	−4.46293	−	4.73043i	−0.147864	−	0.156726i	0.649208	−	0.760611i	$-0.275100\pi$
$911$	−4.46293	−	4.73043i	−0.147864	−	0.156726i	−0.797072	+	0.603884i	$0.793619\pi$
$912$		0			0
$913$	−49.0672	−	32.2720i	−1.62389	−	1.06805i
$914$	19.4618	+	4.61253i	0.643739	+	0.152569i
$915$		0			0
$916$	1.47899	+	0.172869i	0.0488672	+	0.00571176i
$917$	−0.560356	−	0.970565i	−0.0185046	−	0.0320509i
$918$		0			0
$919$	9.92642	−	17.1931i	0.327442	−	0.567147i	−0.654561	−	0.756009i	$-0.727147\pi$
$919$	9.92642	−	17.1931i	0.327442	−	0.567147i	0.982004	+	0.188862i	$0.0604800\pi$
$920$	−21.5299	+	28.9196i	−0.709819	+	0.953452i
$921$		0			0
$922$	13.1563	+	43.9452i	0.433281	+	1.44726i
$923$	1.12710	−	0.566049i	0.0370988	−	0.0186317i
$924$		0			0
$925$	−7.16411	+	23.9298i	−0.235555	+	0.786807i
$926$	−9.30948	−	52.7967i	−0.305928	−	1.73501i
$927$		0			0
$928$	2.00205	−	11.3542i	0.0657205	−	0.372720i
$929$	43.1814	+	21.6865i	1.41674	+	0.711512i	0.981971	−	0.189032i	$-0.0605351\pi$
$929$	43.1814	+	21.6865i	1.41674	+	0.711512i	0.434765	+	0.900544i	$0.356831\pi$
$930$		0			0
$931$	12.7236	−	29.4965i	0.416998	−	0.966709i
$932$	−0.244709	+	0.567299i	−0.00801571	+	0.0185825i
$933$		0			0
$934$	−43.4242	−	21.8085i	−1.42088	−	0.713595i
$935$	13.1629	−	74.6507i	0.430474	−	2.44134i
$936$		0			0
$937$	−9.55499	−	54.1890i	−0.312148	−	1.77028i	−0.587785	−	0.809017i	$-0.700000\pi$
$937$	−9.55499	−	54.1890i	−0.312148	−	1.77028i	0.275637	−	0.961262i	$-0.411111\pi$
$938$	−0.890532	+	2.97458i	−0.0290769	+	0.0971236i
$939$		0			0
$940$	−8.79285	+	4.41594i	−0.286791	+	0.144032i
$941$	−9.64098	−	32.2031i	−0.314287	−	1.04979i	−0.958535	−	0.284975i	$-0.908015\pi$
$941$	−9.64098	−	32.2031i	−0.314287	−	1.04979i	0.644248	−	0.764817i	$-0.277170\pi$
$942$		0			0
$943$	4.98791	−	6.69993i	0.162429	−	0.218180i
$944$	21.3622	−	37.0005i	0.695282	−	1.20426i
$945$		0			0
$946$	9.84958	+	17.0600i	0.320238	+	0.554668i
$947$	28.5919	+	3.34191i	0.929112	+	0.108598i	0.567168	−	0.823602i	$-0.308039\pi$
$947$	28.5919	+	3.34191i	0.929112	+	0.108598i	0.361944	+	0.932200i	$0.382113\pi$
$948$		0			0
$949$	0.446630	+	0.105853i	0.0144982	+	0.00343615i
$950$	−30.6831	−	20.1806i	−0.995491	−	0.654745i
$951$		0			0
$952$	2.03949	+	2.16173i	0.0661003	+	0.0700622i
$953$	31.9098	−	26.7755i	1.03366	−	0.867343i	0.0423778	−	0.999102i	$-0.486507\pi$
$953$	31.9098	−	26.7755i	1.03366	−	0.867343i	0.991282	+	0.131758i	$0.0420622\pi$
$954$		0			0
$955$	6.54348	+	5.49063i	0.211742	+	0.177673i
$956$	0.111858	+	1.92053i	0.00361775	+	0.0621144i
$957$		0			0
$958$	−8.77836	−	11.7914i	−0.283616	−	0.380962i
$959$	−4.14941	+	0.484997i	−0.133992	+	0.0156614i
$960$		0			0
$961$	−3.41745	+	2.24769i	−0.110240	+	0.0725061i
$962$	1.79546	−	0.653494i	0.0578880	−	0.0210695i
$963$		0			0
$964$	−9.61210	−	3.49852i	−0.309585	−	0.112680i
$965$	−20.4263	+	4.84113i	−0.657547	+	0.155842i
$966$		0			0
$967$	−0.466927	+	8.01684i	−0.0150154	+	0.257804i	0.982444	+	0.186560i	$0.0597339\pi$
$967$	−0.466927	+	8.01684i	−0.0150154	+	0.257804i	−0.997459	+	0.0712439i	$0.977303\pi$
$968$	−38.7594	+	41.0826i	−1.24577	+	1.32044i
$969$		0			0
$970$	12.7397	+	29.5338i	0.409046	+	0.948274i
$971$	−47.3974			−1.52105			−0.760527	−	0.649306i	$-0.775059\pi$
$971$	−47.3974			−1.52105			−0.760527	+	0.649306i	$0.775059\pi$
$972$		0			0
$973$	1.72590			0.0553297
$974$	10.3480	+	23.9894i	0.331572	+	0.768669i
$975$		0			0
$976$	−9.92850	+	10.5236i	−0.317803	+	0.336852i
$977$	3.43744	−	59.0186i	0.109973	−	1.88817i	−0.269546	−	0.962987i	$-0.586874\pi$
$977$	3.43744	−	59.0186i	0.109973	−	1.88817i	0.379520	−	0.925184i	$-0.376089\pi$
$978$		0			0
$979$	59.0039	−	13.9842i	1.88577	−	0.446936i
$980$	−8.34621	−	3.03777i	−0.266610	−	0.0970380i
$981$		0			0
$982$	−22.6706	+	8.25142i	−0.723447	+	0.263313i
$983$	−15.8213	+	10.4058i	−0.504621	+	0.331894i	−0.776163	−	0.630532i	$-0.782837\pi$
$983$	−15.8213	+	10.4058i	−0.504621	+	0.331894i	0.271542	+	0.962426i	$0.412466\pi$
$984$		0			0
$985$	48.2858	−	5.64381i	1.53851	−	0.179827i
$986$	19.4266	+	26.0945i	0.618670	+	0.831017i
$987$		0			0
$988$	0.0274630	+	0.471521i	0.000873714	+	0.0150011i
$989$	7.67297	+	6.43839i	0.243986	+	0.204729i
$990$		0			0
$991$	7.60140	−	6.37833i	0.241466	−	0.202614i	−0.514021	−	0.857778i	$-0.671845\pi$
$991$	7.60140	−	6.37833i	0.241466	−	0.202614i	0.755487	+	0.655163i	$0.227400\pi$
$992$	−9.16210	−	9.71125i	−0.290897	−	0.308333i
$993$		0			0
$994$	1.90271	+	1.25143i	0.0603502	+	0.0396930i
$995$	−43.5236	−	10.3153i	−1.37979	−	0.327016i
$996$		0			0
$997$	20.6151	+	2.40956i	0.652887	+	0.0763116i	0.436087	−	0.899904i	$-0.356364\pi$
$997$	20.6151	+	2.40956i	0.652887	+	0.0763116i	0.216800	+	0.976216i	$0.430438\pi$
$998$	−14.1681	−	24.5398i	−0.448483	−	0.776795i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.676.2		144
3.2	odd	2		729.2.g.c.676.7		144
9.2	odd	6		81.2.g.a.58.7	yes	144
9.4	even	3		729.2.g.a.433.7		144
9.5	odd	6		729.2.g.d.433.2		144
9.7	even	3		243.2.g.a.226.2		144
81.7	even	27		729.2.g.a.298.7		144
81.14	odd	54		6561.2.a.c.1.57		72
81.20	odd	54		81.2.g.a.7.7	✓	144
81.34	even	27	inner	729.2.g.b.55.2		144
81.47	odd	54		729.2.g.c.55.7		144
81.61	even	27		243.2.g.a.100.2		144
81.67	even	27		6561.2.a.d.1.16		72
81.74	odd	54		729.2.g.d.298.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.7	✓	144	81.20	odd	54
81.2.g.a.58.7	yes	144	9.2	odd	6
243.2.g.a.100.2		144	81.61	even	27
243.2.g.a.226.2		144	9.7	even	3
729.2.g.a.298.7		144	81.7	even	27
729.2.g.a.433.7		144	9.4	even	3
729.2.g.b.55.2		144	81.34	even	27	inner
729.2.g.b.676.2		144	1.1	even	1	trivial
729.2.g.c.55.7		144	81.47	odd	54
729.2.g.c.676.7		144	3.2	odd	2
729.2.g.d.298.2		144	81.74	odd	54
729.2.g.d.433.2		144	9.5	odd	6
6561.2.a.c.1.57		72	81.14	odd	54
6561.2.a.d.1.16		72	81.67	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.614147 - 1.42375i) q^{2} +(-0.277410 + 0.294037i) q^{4} +(0.184768 - 3.17234i) q^{5} +(0.284960 - 0.0675368i) q^{7} +(-2.32510 - 0.846267i) q^{8} +O(q^{10})\)	\(q+(-0.614147 - 1.42375i) q^{2} +(-0.277410 + 0.294037i) q^{4} +(0.184768 - 3.17234i) q^{5} +(0.284960 - 0.0675368i) q^{7} +(-2.32510 - 0.846267i) q^{8} +(-4.63010 + 1.68522i) q^{10} +(-4.85926 + 3.19599i) q^{11} +(-0.249784 + 0.0291955i) q^{13} +(-0.271163 - 0.364235i) q^{14} +(0.270087 + 4.63722i) q^{16} +(-3.14189 - 2.63636i) q^{17} +(-3.55906 + 2.98641i) q^{19} +(0.881528 + 0.934365i) q^{20} +(7.53459 + 4.95558i) q^{22} +(4.46184 + 1.05748i) q^{23} +(-5.06339 - 0.591826i) q^{25} +(0.194971 + 0.337700i) q^{26} +(-0.0591924 + 0.102524i) q^{28} +(3.05471 - 4.10319i) q^{29} +(-1.69894 - 5.67485i) q^{31} +(2.01411 - 1.01152i) q^{32} +(-1.82394 + 6.09239i) q^{34} +(-0.161598 - 0.916469i) q^{35} +(0.850864 - 4.82549i) q^{37} +(6.43769 + 3.23313i) q^{38} +(-3.11425 + 7.21964i) q^{40} +(0.721490 - 1.67260i) q^{41} +(1.95203 + 0.980348i) q^{43} +(0.408268 - 2.31540i) q^{44} +(-1.23464 - 7.00200i) q^{46} +(-2.19683 + 7.33791i) q^{47} +(-6.17879 + 3.10310i) q^{49} +(2.26705 + 7.57248i) q^{50} +(0.0607078 - 0.0815448i) q^{52} +(3.52502 - 6.10552i) q^{53} +(9.24092 + 16.0057i) q^{55} +(-0.719715 - 0.0841226i) q^{56} +(-7.71797 - 1.82919i) q^{58} +(-7.68465 - 5.05427i) q^{59} +(2.13742 + 2.26554i) q^{61} +(-7.03618 + 5.90406i) q^{62} +(4.43955 + 3.72523i) q^{64} +(0.0464661 + 0.797793i) q^{65} +(-4.08333 - 5.48486i) q^{67} +(1.64678 - 0.192481i) q^{68} +(-1.20558 + 0.792922i) q^{70} +(-4.71278 + 1.71531i) q^{71} +(-1.71510 - 0.624247i) q^{73} +(-7.39286 + 1.75214i) q^{74} +(0.109204 - 1.87495i) q^{76} +(-1.16885 + 1.23891i) q^{77} +(-4.28100 - 9.92448i) q^{79} +14.7607 q^{80} -2.82447 q^{82} +(3.99948 + 9.27184i) q^{83} +(-8.94395 + 9.48003i) q^{85} +(0.196938 - 3.38129i) q^{86} +(14.0029 - 3.31875i) q^{88} +(-9.79723 - 3.56590i) q^{89} +(-0.0692067 + 0.0251892i) q^{91} +(-1.54869 + 1.01859i) q^{92} +(11.7965 - 1.37882i) q^{94} +(8.81629 + 11.8423i) q^{95} +(-0.379561 - 6.51682i) q^{97} +(8.21273 + 6.89130i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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

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Database

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