LMFDB - Embedded newform 729.2.g.c.55.7

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			55.7
Character	$\chi$	$=$	729.55
Dual form			729.2.g.c.676.7

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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	−0.550810	−	0.834631i	$-0.685681\pi$
$2$	0.614147	−	1.42375i	0.434267	−	1.00674i	0.985077	−	0.172114i	$-0.0550597\pi$
$3$		0			0
$3$		0			0
$4$	−0.277410	−	0.294037i	−0.138705	−	0.147018i
$5$	−0.184768	−	3.17234i	−0.0826306	−	1.41871i	−0.743763	−	0.668443i	$-0.766961\pi$
$5$	−0.184768	−	3.17234i	−0.0826306	−	1.41871i	0.661133	−	0.750269i	$-0.270076\pi$
$6$		0			0
$7$	0.284960	+	0.0675368i	0.107705	+	0.0255265i	0.284115	−	0.958790i	$-0.408300\pi$
$7$	0.284960	+	0.0675368i	0.107705	+	0.0255265i	−0.176410	+	0.984317i	$0.556448\pi$
$8$	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	0.996789	+	0.0800749i	$0.0255159\pi$
$11$	4.85926	+	3.19599i	1.46512	+	0.963626i	0.468334	+	0.883552i	$0.344854\pi$
$12$		0			0
$13$	−0.249784	−	0.0291955i	−0.0692776	−	0.00809739i	0.0813835	−	0.996683i	$-0.474066\pi$
$13$	−0.249784	−	0.0291955i	−0.0692776	−	0.00809739i	−0.150661	+	0.988585i	$0.548140\pi$
$14$	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	$-0.556520\pi$
$17$	3.14189	−	2.63636i	0.762021	−	0.639411i	0.938652	+	0.344866i	$0.112076\pi$
$18$		0			0
$19$	−3.55906	−	2.98641i	−0.816505	−	0.685129i	0.135646	−	0.990757i	$-0.456689\pi$
$19$	−3.55906	−	2.98641i	−0.816505	−	0.685129i	−0.952151	+	0.305629i	$0.901133\pi$
$20$	−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	$-0.732736\pi$
$23$	−4.46184	+	1.05748i	−0.930358	+	0.220499i	−0.262624	+	0.964898i	$0.584588\pi$
$24$		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	$-0.361239\pi$
$29$	−3.05471	−	4.10319i	−0.567246	−	0.761944i	−0.989500	+	0.144534i	$0.953832\pi$
$30$		0			0
$31$	−1.69894	+	5.67485i	−0.305139	+	1.01923i	0.658624	+	0.752472i	$0.271139\pi$
$31$	−1.69894	+	5.67485i	−0.305139	+	1.01923i	−0.963763	+	0.266762i	$0.914046\pi$
$32$	−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	0.971336	+	0.237713i	$0.0763977\pi$
$37$	0.850864	+	4.82549i	0.139881	+	0.793306i	−0.831454	+	0.555593i	$0.812491\pi$
$38$	−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	$-0.175061\pi$
$41$	−0.721490	−	1.67260i	−0.112678	−	0.261217i	−0.965219	+	0.261444i	$0.915801\pi$
$42$		0			0
$43$	1.95203	−	0.980348i	0.297682	−	0.149502i	−0.293689	−	0.955901i	$-0.594883\pi$
$43$	1.95203	−	0.980348i	0.297682	−	0.149502i	0.591371	+	0.806399i	$0.298587\pi$
$44$	−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	0.954786	+	0.297295i	$0.0960844\pi$
$47$	2.19683	+	7.33791i	0.320440	+	1.07034i	−0.634346	+	0.773050i	$0.718730\pi$
$48$		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	$-0.327556\pi$
$53$	−3.52502	−	6.10552i	−0.484199	−	0.838657i	−0.999835	+	0.0181502i	$0.994222\pi$
$54$		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	$-0.480859\pi$
$59$	7.68465	−	5.05427i	1.00046	−	0.658010i	0.940360	+	0.340182i	$0.110489\pi$
$60$		0			0
$61$	2.13742	−	2.26554i	0.273669	−	0.290072i	−0.575933	−	0.817497i	$-0.695361\pi$
$61$	2.13742	−	2.26554i	0.273669	−	0.290072i	0.849602	+	0.527425i	$0.176842\pi$
$62$	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	−0.978229	−	0.207530i	$-0.933458\pi$
$67$	−4.08333	+	5.48486i	−0.498858	+	0.670083i	0.479371	+	0.877613i	$0.340865\pi$
$68$	−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	$-0.292703\pi$
$71$	4.71278	+	1.71531i	0.559304	+	0.203570i	−0.0468717	+	0.998901i	$0.514925\pi$
$72$		0			0
$73$	−1.71510	+	0.624247i	−0.200738	+	0.0730626i	−0.440432	−	0.897786i	$-0.645175\pi$
$73$	−1.71510	+	0.624247i	−0.200738	+	0.0730626i	0.239695	+	0.970848i	$0.422953\pi$
$74$	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	0.488165	+	0.872751i	$0.337666\pi$
$79$	−4.28100	+	9.92448i	−0.481650	+	1.11659i	−0.969816	+	0.243840i	$0.921593\pi$
$80$	−14.7607			−1.65030
$81$		0			0
$82$	−2.82447			−0.311911
$83$	−3.99948	+	9.27184i	−0.439000	+	1.01772i	0.544819	+	0.838553i	$0.316598\pi$
$83$	−3.99948	+	9.27184i	−0.439000	+	1.01772i	−0.983819	+	0.179163i	$0.942661\pi$
$84$		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	$-0.424756\pi$
$89$	9.79723	−	3.56590i	1.03850	−	0.377985i	0.804313	+	0.594206i	$0.202533\pi$
$90$		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	0.922624	+	0.385700i	$0.126040\pi$
$97$	−0.379561	+	6.51682i	−0.0385386	+	0.661683i	−0.961163	+	0.275982i	$0.910997\pi$
$98$	−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	$-0.764169\pi$
$101$	−0.212738	+	0.225489i	−0.0211683	+	0.0224370i	0.716703	+	0.697379i	$0.245650\pi$
$102$		0			0
$103$	8.06674	−	5.30558i	0.794840	−	0.522774i	−0.0859399	−	0.996300i	$-0.527389\pi$
$103$	8.06674	−	5.30558i	0.794840	−	0.522774i	0.880780	+	0.473526i	$0.157019\pi$
$104$	−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	0.486150	+	0.873875i	$0.338401\pi$
$107$	−5.31399	+	9.20410i	−0.513723	+	0.889794i	−0.999873	+	0.0159189i	$0.994933\pi$
$108$		0			0
$109$	8.57766	+	14.8569i	0.821590	+	1.42304i	0.904497	+	0.426479i	$0.140246\pi$
$109$	8.57766	+	14.8569i	0.821590	+	1.42304i	−0.0829070	+	0.996557i	$0.526420\pi$
$110$	−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	$-0.185846\pi$
$113$	9.46527	+	4.75364i	0.890418	+	0.447185i	0.0560723	+	0.998427i	$0.482142\pi$
$114$		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	0.643910	+	0.765101i	$0.277311\pi$
$127$	−2.51136	+	14.2427i	−0.222848	+	1.26383i	−0.866757	+	0.498730i	$0.833800\pi$
$128$	−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	$-0.853942\pi$
$131$	1.09756	−	3.66609i	0.0958939	−	0.320308i	0.992455	+	0.122613i	$0.0391274\pi$
$132$		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	$-0.328454\pi$
$137$	14.1689	−	1.65610i	1.21053	−	0.141490i	0.697311	+	0.716768i	$0.254380\pi$
$138$		0			0
$139$	5.73451	−	1.35910i	0.486395	−	0.115278i	0.0199006	−	0.999802i	$-0.493665\pi$
$139$	5.73451	−	1.35910i	0.486395	−	0.115278i	0.466494	+	0.884524i	$0.345517\pi$
$140$	−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	$-0.658784\pi$
$149$	−13.9939	−	1.63565i	−1.14642	−	0.133998i	−0.668020	+	0.744143i	$0.732858\pi$
$150$		0			0
$151$	−1.32326	−	0.870321i	−0.107685	−	0.0708257i	0.494524	−	0.869164i	$-0.335342\pi$
$151$	−1.32326	−	0.870321i	−0.107685	−	0.0708257i	−0.602209	+	0.798338i	$0.705713\pi$
$152$	−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	−0.989103	−	0.147222i	$-0.952967\pi$
$157$	−0.297956	−	5.11570i	−0.0237794	−	0.408277i	0.965324	−	0.261055i	$-0.0840703\pi$
$158$	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	$-0.0355023\pi$
$167$	−0.0801450	−	1.37604i	−0.00620181	−	0.106481i	−0.999988	+	0.00482161i	$0.998465\pi$
$168$		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	$-0.479346\pi$
$173$	−10.8612	−	7.14352i	−0.825762	−	0.543112i	−0.890602	+	0.454784i	$0.849717\pi$
$174$		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	0.488067	−	0.872806i	$-0.337702\pi$
$179$	19.1637	−	16.0803i	1.43237	−	1.20190i	0.944298	−	0.329091i	$-0.106742\pi$
$180$		0			0
$181$	3.52910	+	2.96126i	0.262316	+	0.220109i	0.764454	−	0.644678i	$-0.223009\pi$
$181$	3.52910	+	2.96126i	0.262316	+	0.220109i	−0.502138	+	0.864787i	$0.667453\pi$
$182$	−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	$-0.172699\pi$
$191$	1.60520	+	2.15616i	0.116148	+	0.156014i	−0.740247	+	0.672335i	$0.765291\pi$
$192$		0			0
$193$	−1.89464	+	6.32854i	−0.136379	+	0.455538i	−0.998708	−	0.0508098i	$-0.983820\pi$
$193$	−1.89464	+	6.32854i	−0.136379	+	0.455538i	0.862329	+	0.506348i	$0.169005\pi$
$194$	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	0.731068	+	0.682304i	$0.239022\pi$
$197$	−2.65657	+	15.0662i	−0.189273	+	1.07342i	−0.920341	+	0.391116i	$0.872089\pi$
$198$		0			0
$199$	2.44426	+	13.8621i	0.173269	+	0.982657i	0.940123	+	0.340835i	$0.110710\pi$
$199$	2.44426	+	13.8621i	0.173269	+	0.982657i	−0.766854	+	0.641821i	$0.778179\pi$
$200$	−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	0.855426	−	0.517924i	$-0.173295\pi$
$211$	13.8113	+	6.93632i	0.950812	+	0.477516i	0.0953860	+	0.995440i	$0.469591\pi$
$212$	−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	−0.829241	−	0.558891i	$-0.811227\pi$
$223$	−3.33129	+	3.53096i	−0.223080	+	0.236451i	0.606161	+	0.795342i	$0.292709\pi$
$224$	−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	−0.727875	−	0.685710i	$-0.759492\pi$
$227$	1.12523	−	19.3195i	0.0746844	−	1.28228i	0.802559	−	0.596572i	$-0.203471\pi$
$228$		0			0
$229$	−2.19967	+	2.95467i	−0.145358	+	0.195250i	−0.868839	−	0.495094i	$-0.835133\pi$
$229$	−2.19967	+	2.95467i	−0.145358	+	0.195250i	0.723481	+	0.690344i	$0.242541\pi$
$230$	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	$-0.404831\pi$
$233$	−1.43618	−	0.522727i	−0.0940872	−	0.0342450i	−0.388635	+	0.921392i	$0.627053\pi$
$234$		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	$-0.289929\pi$
$239$	−3.26580	−	3.46154i	−0.211247	−	0.223909i	−0.824330	+	0.566110i	$0.808448\pi$
$240$		0			0
$241$	10.0224	−	23.2345i	0.645598	−	1.49666i	−0.209291	−	0.977853i	$-0.567116\pi$
$241$	10.0224	−	23.2345i	0.645598	−	1.49666i	0.854889	−	0.518811i	$-0.173625\pi$
$242$	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	$-0.633232\pi$
$251$	−2.06755	+	0.752528i	−0.130503	+	0.0474991i	0.275943	+	0.961174i	$0.411010\pi$
$252$		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	$-0.900047\pi$
$257$	−6.13071	+	8.23498i	−0.382423	+	0.513684i	0.568679	+	0.822560i	$0.307455\pi$
$258$		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	$-0.774839\pi$
$263$	−1.08901	+	1.15428i	−0.0671512	+	0.0711761i	0.692927	+	0.721008i	$0.256321\pi$
$264$		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	$-0.784673\pi$
$269$	2.49753	−	4.32585i	0.152277	−	0.263752i	0.932064	+	0.362293i	$0.118006\pi$
$270$		0			0
$271$	−4.63580	−	8.02944i	−0.281605	−	0.487754i	0.690175	−	0.723642i	$-0.257533\pi$
$271$	−4.63580	−	8.02944i	−0.281605	−	0.487754i	−0.971780	+	0.235888i	$0.924200\pi$
$272$	−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	0.826430	+	0.563039i	$0.190368\pi$
$277$	7.41215	+	24.7583i	0.445353	+	1.48758i	−0.381077	+	0.924543i	$0.624447\pi$
$278$	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	$-0.980064\pi$
$281$	−25.8792	+	12.9970i	−1.54382	+	0.775336i	−0.545782	+	0.837927i	$0.683767\pi$
$282$		0			0
$283$	0.408756	+	0.947602i	0.0242980	+	0.0563291i	0.929933	−	0.367729i	$-0.119865\pi$
$283$	0.408756	+	0.947602i	0.0242980	+	0.0563291i	−0.905635	+	0.424058i	$0.860605\pi$
$284$	−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	$-0.972387\pi$
$293$	−1.99047	+	6.64865i	−0.116285	+	0.388418i	0.879955	+	0.475057i	$0.157573\pi$
$294$		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	−0.147233	−	0.989102i	$-0.547037\pi$
$307$	14.0395	−	11.7805i	0.801275	−	0.672350i	0.948508	+	0.316752i	$0.102592\pi$
$308$	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	$-0.599763\pi$
$311$	−14.5964	−	1.70608i	−0.827686	−	0.0967427i	−0.519379	+	0.854544i	$0.673837\pi$
$312$		0			0
$313$	−4.72821	−	3.10979i	−0.267254	−	0.175776i	0.408808	−	0.912620i	$-0.365945\pi$
$313$	−4.72821	−	3.10979i	−0.267254	−	0.175776i	−0.676062	+	0.736845i	$0.736315\pi$
$314$	−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	$-0.648467\pi$
$317$	−22.2986	−	5.28486i	−1.25241	−	0.296827i	−0.802720	+	0.596356i	$0.796615\pi$
$318$		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	0.312087	−	0.950054i	$-0.398972\pi$
$331$	2.99454	+	0.709719i	0.164595	+	0.0390097i	−0.147492	+	0.989063i	$0.547120\pi$
$332$	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	0.226542	−	0.974001i	$-0.427258\pi$
$337$	4.08195	+	0.477112i	0.222358	+	0.0259899i	−0.00418429	+	0.999991i	$0.501332\pi$
$338$	−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	$-0.651298\pi$
$347$	−8.70882	+	2.06403i	−0.467514	+	0.110803i	−0.00989464	+	0.999951i	$0.503150\pi$
$348$		0			0
$349$	−4.92593	+	0.575758i	−0.263679	+	0.0308196i	−0.246905	−	0.969040i	$-0.579414\pi$
$349$	−4.92593	+	0.575758i	−0.263679	+	0.0308196i	−0.0167738	+	0.999859i	$0.505340\pi$
$350$	−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	$-0.0220665\pi$
$353$	12.1208	+	16.2811i	0.645125	+	0.866554i	−0.352473	+	0.935822i	$0.614659\pi$
$354$		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	0.928139	+	0.372234i	$0.121408\pi$
$359$	−1.35166	+	7.66566i	−0.0713380	+	0.404578i	−0.999477	+	0.0323438i	$0.989703\pi$
$360$		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	−0.453325	−	0.891345i	$-0.649762\pi$
$367$	−0.173614	+	0.0871922i	−0.00906258	+	0.00455140i	0.444262	+	0.895897i	$0.353466\pi$
$368$	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	0.500909	−	0.865500i	$-0.332999\pi$
$373$	2.04320	+	1.02613i	0.105793	+	0.0531312i	−0.395116	+	0.918631i	$0.629296\pi$
$374$	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	−0.757708	−	0.652594i	$-0.773681\pi$
$379$	3.62704	−	6.28222i	0.186309	−	0.322696i	0.944017	+	0.329898i	$0.107014\pi$
$380$	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	$-0.928209\pi$
$383$	−22.6113	+	14.8717i	−1.15538	+	0.759907i	−0.180708	+	0.983537i	$0.557839\pi$
$384$		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	−0.779372	−	0.626561i	$-0.784462\pi$
$389$	1.33071	−	22.8473i	0.0674694	−	1.15841i	0.846842	−	0.531845i	$-0.178501\pi$
$390$		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	−0.728981	−	0.684534i	$-0.760006\pi$
$397$	−16.8844	+	6.14542i	−0.847403	+	0.308430i	−0.118422	+	0.992963i	$0.537784\pi$
$398$	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	$-0.229327\pi$
$401$	0.985267	+	1.04432i	0.0492019	+	0.0521509i	−0.702305	+	0.711876i	$0.747846\pi$
$402$		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	0.467499	−	0.883994i	$-0.345155\pi$
$409$	−8.94258	−	9.47858i	−0.442182	−	0.468686i	−0.909681	+	0.415308i	$0.863674\pi$
$410$	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	−0.110084	−	0.993922i	$-0.535112\pi$
$419$	17.8833	−	24.0214i	0.873655	−	1.17352i	0.983740	−	0.179600i	$-0.0574805\pi$
$420$		0			0
$421$	−1.87836	+	32.2502i	−0.0915458	+	1.57178i	0.569853	+	0.821746i	$0.307000\pi$
$421$	−1.87836	+	32.2502i	−0.0915458	+	1.57178i	−0.661399	+	0.750034i	$0.730037\pi$
$422$	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	−0.213989	−	0.976836i	$-0.568646\pi$
$431$	15.3414	−	26.5721i	0.738970	−	1.27993i	0.952960	−	0.303098i	$-0.0980208\pi$
$432$		0			0
$433$	−19.2517	−	33.3449i	−0.925176	−	1.60245i	−0.791277	−	0.611457i	$-0.790584\pi$
$433$	−19.2517	−	33.3449i	−0.925176	−	1.60245i	−0.133899	−	0.990995i	$-0.542750\pi$
$434$	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	−0.585471	−	0.810693i	$-0.699090\pi$
$439$	−11.3520	−	37.9182i	−0.541800	−	1.80974i	0.0436707	−	0.999046i	$-0.486095\pi$
$440$	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	$-0.602307\pi$
$443$	5.39874	−	2.71135i	0.256502	−	0.128820i	0.572404	+	0.819972i	$0.306011\pi$
$444$		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	$-0.0736046\pi$
$449$	−0.417057	−	2.36525i	−0.0196821	−	0.111623i	−0.993066	+	0.117558i	$0.962494\pi$
$450$		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	0.584585	−	0.811332i	$-0.301257\pi$
$457$	−7.70284	−	10.3467i	−0.360323	−	0.483998i	−0.944909	+	0.327334i	$0.893850\pi$
$458$	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	$-0.295113\pi$
$461$	29.3843	−	3.43453i	1.36856	−	0.159962i	0.768428	+	0.639937i	$0.221039\pi$
$462$		0			0
$463$	33.6433	−	7.97361i	1.56354	−	0.370565i	0.644458	−	0.764639i	$-0.277083\pi$
$463$	33.6433	−	7.97361i	1.56354	−	0.370565i	0.919079	+	0.394074i	$0.128935\pi$
$464$	−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	$-0.535982\pi$
$467$	−24.0070	−	20.1443i	−1.11091	−	0.932165i	−0.998110	+	0.0614529i	$0.980427\pi$
$468$		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	$-0.495419\pi$
$479$	−9.22501	−	2.18637i	−0.421502	−	0.0998977i	−0.435893	+	0.899999i	$0.643567\pi$
$480$		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	−0.955172	−	0.296051i	$-0.904330\pi$
$491$	−0.904688	−	15.5329i	−0.0408280	−	0.700989i	0.914344	−	0.404938i	$-0.132707\pi$
$492$		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	0.512216	−	0.858857i	$-0.328825\pi$
$499$	18.1512	+	2.12157i	0.812559	+	0.0949745i	0.300343	+	0.953831i	$0.402899\pi$
$500$	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	$-0.944045\pi$
$503$	−22.0539	+	18.5054i	−0.983333	+	0.825114i	0.00125604	+	0.999999i	$0.499600\pi$
$504$		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	$-0.508298\pi$
$509$	9.00835	−	2.13502i	0.399288	−	0.0946330i	0.425354	+	0.905027i	$0.360150\pi$
$510$		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	$-0.984014\pi$
$521$	−0.982915	+	5.57439i	−0.0430623	+	0.244218i	0.955677	+	0.294417i	$0.0951256\pi$
$522$		0			0
$523$	2.68166	+	15.2084i	0.117261	+	0.665018i	0.985606	+	0.169058i	$0.0540726\pi$
$523$	2.68166	+	15.2084i	0.117261	+	0.665018i	−0.868345	+	0.495960i	$0.834816\pi$
$524$	−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	0.0473898	+	0.998876i	$0.484910\pi$
$541$	−19.5695	+	33.8953i	−0.841357	+	1.45727i	−0.888747	+	0.458397i	$0.848424\pi$
$542$	−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	−0.337041	−	0.941490i	$-0.609426\pi$
$547$	14.5580	−	15.4305i	0.622453	−	0.659762i	0.959494	+	0.281728i	$0.0909076\pi$
$548$	−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	$-0.370553\pi$
$557$	2.55364	+	0.929451i	0.108201	+	0.0393821i	−0.287352	+	0.957825i	$0.592775\pi$
$558$		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	$-0.114535\pi$
$563$	12.5763	+	13.3301i	0.530028	+	0.561797i	−0.405932	+	0.913903i	$0.633053\pi$
$564$		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	$-0.794887\pi$
$569$	4.43905	−	10.2909i	0.186095	−	0.431416i	0.985567	+	0.169288i	$0.0541466\pi$
$570$		0			0
$571$	−0.299771	−	0.317738i	−0.0125450	−	0.0132969i	0.721071	−	0.692861i	$-0.243650\pi$
$571$	−0.299771	−	0.317738i	−0.0125450	−	0.0132969i	−0.733616	+	0.679565i	$0.762169\pi$
$572$	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	0.932921	−	0.360081i	$-0.117251\pi$
$577$	34.0165	+	12.3810i	1.41612	+	0.515427i	0.483203	+	0.875508i	$0.339473\pi$
$578$	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	$-0.753978\pi$
$587$	0.551710	−	0.584778i	0.0227715	−	0.0241364i	0.738659	+	0.674079i	$0.235459\pi$
$588$		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	0.158726	+	0.987323i	$0.449261\pi$
$593$	−18.8891	+	32.7169i	−0.775683	+	1.34352i	−0.934410	+	0.356200i	$0.884072\pi$
$594$		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	$-0.556086\pi$
$599$	−26.1795	−	13.1479i	−1.06967	−	0.537207i	−0.894379	+	0.447310i	$0.852382\pi$
$600$		0			0
$601$	−1.14204	−	3.81467i	−0.0465846	−	0.155603i	0.931533	−	0.363658i	$-0.118472\pi$
$601$	−1.14204	−	3.81467i	−0.0465846	−	0.155603i	−0.978117	+	0.208054i	$0.933287\pi$
$602$	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	−0.940221	−	0.340566i	$-0.889381\pi$
$607$	−13.3712	−	30.9980i	−0.542721	−	1.25817i	0.397500	−	0.917602i	$-0.369878\pi$
$608$	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	−0.348637	−	0.937258i	$-0.613355\pi$
$613$	7.41615	−	42.0591i	0.299536	−	1.69875i	0.648173	−	0.761493i	$-0.275533\pi$
$614$	−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	$-0.859073\pi$
$617$	2.15522	−	7.19894i	0.0867660	−	0.289819i	0.990349	+	0.138594i	$0.0442582\pi$
$618$		0			0
$619$	12.5342	+	16.8364i	0.503793	+	0.676712i	0.979163	−	0.203074i	$-0.0650932\pi$
$619$	12.5342	+	16.8364i	0.503793	+	0.676712i	−0.475370	+	0.879786i	$0.657686\pi$
$620$	−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	−0.974621	−	0.223860i	$-0.928134\pi$
$631$	−23.1956	+	19.4634i	−0.923403	+	0.774827i	0.0512179	+	0.998688i	$0.483690\pi$
$632$	−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	$-0.531585\pi$
$641$	−16.0562	−	3.80539i	−0.634182	−	0.150304i	−0.535118	+	0.844777i	$0.679733\pi$
$642$		0			0
$643$	1.05055	+	18.0372i	0.0414296	+	0.711318i	0.953520	+	0.301329i	$0.0974304\pi$
$643$	1.05055	+	18.0372i	0.0414296	+	0.711318i	−0.912091	+	0.409989i	$0.865533\pi$
$644$	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	$-0.525961\pi$
$647$	−4.14445			−0.162935			−0.0814676	+	0.996676i	$0.525961\pi$
$648$		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	−0.939990	−	0.341201i	$-0.889166\pi$
$653$	−1.17463	−	20.1677i	−0.0459669	−	0.789222i	0.894023	−	0.448020i	$-0.147871\pi$
$654$		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	$-0.362560\pi$
$659$	−6.41002	−	4.21594i	−0.249699	−	0.164230i	−0.668188	+	0.743992i	$0.732930\pi$
$660$		0			0
$661$	5.21185	+	0.609178i	0.202718	+	0.0236943i	0.216846	−	0.976206i	$-0.430423\pi$
$661$	5.21185	+	0.609178i	0.202718	+	0.0236943i	−0.0141280	+	0.999900i	$0.504497\pi$
$662$	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	−0.179609	−	0.983738i	$-0.557483\pi$
$673$	−3.30793	+	0.386642i	−0.127512	+	0.0149040i	0.0520977	+	0.998642i	$0.483409\pi$
$674$	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	$-0.354770\pi$
$677$	−14.2005	−	19.0746i	−0.545771	−	0.733098i	−0.986358	+	0.164612i	$0.947363\pi$
$678$		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	0.867633	+	0.497205i	$0.165640\pi$
$683$	−3.07677	+	17.4492i	−0.117729	+	0.667676i	−0.985363	+	0.170472i	$0.945471\pi$
$684$		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	0.104873	−	0.994486i	$-0.466556\pi$
$691$	25.3721	−	12.7423i	0.965199	−	0.484741i	0.860326	+	0.509744i	$0.170260\pi$
$692$	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	0.951820	+	0.306656i	$0.0992102\pi$
$701$	19.6318	+	34.0032i	0.741482	+	1.28428i	−0.210338	+	0.977629i	$0.567456\pi$
$702$		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	−0.397074	+	0.917786i	$0.629975\pi$
$709$	−34.3548	+	36.4139i	−1.29022	+	1.36755i	−0.893146	+	0.449767i	$0.851507\pi$
$710$	−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	$-0.275931\pi$
$719$	17.5102	+	6.37320i	0.653021	+	0.237680i	0.00580045	+	0.999983i	$0.498154\pi$
$720$		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	0.269930	+	0.962880i	$0.412999\pi$
$727$	−16.6006	+	38.4844i	−0.615680	+	1.42731i	−0.885611	+	0.464428i	$0.846260\pi$
$728$	−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	0.520724	−	0.853725i	$-0.325662\pi$
$733$	−9.79629	−	10.3835i	−0.361834	−	0.383522i	−0.882558	+	0.470203i	$0.844181\pi$
$734$	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	0.00112859	−	0.999999i	$-0.499641\pi$
$739$	−17.4197	−	6.34025i	−0.640794	−	0.233230i	−0.641923	+	0.766769i	$0.721863\pi$
$740$	−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	$-0.978193\pi$
$743$	−17.6072	+	23.6506i	−0.645945	+	0.867655i	0.351709	+	0.936109i	$0.385601\pi$
$744$		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	−0.269049	−	0.963126i	$-0.586709\pi$
$751$	13.9418	−	9.16968i	0.508744	−	0.334606i	0.777793	+	0.628520i	$0.216339\pi$
$752$	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	−0.993399	−	0.114710i	$-0.963406\pi$
$757$	−16.3993	−	28.4044i	−0.596042	−	1.03237i	0.397357	−	0.917664i	$-0.369927\pi$
$758$	−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	$-0.141473\pi$
$761$	30.2651	+	15.1997i	1.09711	+	0.550988i	0.194261	+	0.980950i	$0.437769\pi$
$762$		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	0.907332	−	0.420415i	$-0.138115\pi$
$769$	−0.585556	−	1.35747i	−0.0211157	−	0.0489517i	−0.928448	+	0.371463i	$0.878856\pi$
$770$	−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	$-0.0427885\pi$
$773$	0.387181	+	2.19581i	0.0139259	+	0.0789779i	−0.977053	+	0.212997i	$0.931677\pi$
$774$		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	−0.176322	−	0.984333i	$-0.556420\pi$
$787$	3.02636	−	0.717261i	0.107878	−	0.0255676i	0.284200	+	0.958765i	$0.408272\pi$
$788$	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	$-0.576732\pi$
$797$	−19.6200	−	2.29325i	−0.694977	−	0.0812312i	−0.456245	+	0.889854i	$0.650806\pi$
$798$		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	$-0.611095\pi$
$809$	−19.4534			−0.683945			−0.341973	+	0.939710i	$0.611095\pi$
$810$		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	$-0.373123\pi$
$821$	−8.72148	−	5.73621i	−0.304382	−	0.200195i	−0.692506	+	0.721412i	$0.743493\pi$
$822$		0			0
$823$	−11.3913	−	1.33145i	−0.397074	−	0.0464113i	−0.0847872	−	0.996399i	$-0.527021\pi$
$823$	−11.3913	−	1.33145i	−0.397074	−	0.0464113i	−0.312287	+	0.949988i	$0.601095\pi$
$824$	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	$-0.657828\pi$
$827$	8.85255	−	7.42817i	0.307833	−	0.258303i	0.783596	+	0.621271i	$0.213383\pi$
$828$		0			0
$829$	22.8861	+	19.2037i	0.794866	+	0.666972i	0.946945	−	0.321396i	$-0.104152\pi$
$829$	22.8861	+	19.2037i	0.794866	+	0.666972i	−0.152078	+	0.988368i	$0.548597\pi$
$830$	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	0.995139	+	0.0984779i	$0.0313974\pi$
$839$	23.2903	+	31.2843i	0.804071	+	1.08005i	−0.191068	+	0.981577i	$0.561195\pi$
$840$		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	−0.0202658	−	0.999795i	$-0.506451\pi$
$853$	22.4768	−	11.2883i	0.769591	−	0.386503i	0.789857	+	0.613292i	$0.210155\pi$
$854$	−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	0.586387	+	0.810031i	$0.300550\pi$
$857$	15.8547	+	52.9585i	0.541587	+	1.80903i	−0.0448000	+	0.998996i	$0.514265\pi$
$858$		0			0
$859$	−23.2701	−	11.6867i	−0.793967	−	0.398745i	0.00510038	−	0.999987i	$-0.498376\pi$
$859$	−23.2701	−	11.6867i	−0.793967	−	0.398745i	−0.799067	+	0.601242i	$0.794673\pi$
$860$	−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	$-0.278175\pi$
$863$	−10.0819	−	17.4623i	−0.343191	−	0.594425i	−0.985023	+	0.172420i	$0.944841\pi$
$864$		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	−0.675708	−	0.737170i	$-0.736162\pi$
$877$	6.64211	−	8.92190i	0.224288	−	0.301271i	0.899996	+	0.435898i	$0.143569\pi$
$878$	−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	$-0.343944\pi$
$881$	7.85029	+	2.85727i	0.264483	+	0.0962639i	−0.206375	+	0.978473i	$0.566167\pi$
$882$		0			0
$883$	51.2586	−	18.6566i	1.72499	−	0.627845i	0.726736	−	0.686917i	$-0.241036\pi$
$883$	51.2586	−	18.6566i	1.72499	−	0.627845i	0.998254	+	0.0590722i	$0.0188142\pi$
$884$	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	$-0.463285\pi$
$887$	−26.3063	−	27.8831i	−0.883280	−	0.936222i	−0.998367	+	0.0571336i	$0.981804\pi$
$888$		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	−0.850838	−	0.525428i	$-0.823905\pi$
$907$	1.66379	−	28.5663i	0.0552454	−	0.948527i	0.906084	−	0.423099i	$-0.139058\pi$
$908$	−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	$-0.724900\pi$
$911$	4.46293	−	4.73043i	0.147864	−	0.156726i	0.797072	+	0.603884i	$0.206381\pi$
$912$		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	0.982004	−	0.188862i	$-0.0604800\pi$
$919$	9.92642	+	17.1931i	0.327442	+	0.567147i	−0.654561	+	0.756009i	$0.727147\pi$
$920$	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	$-0.939465\pi$
$929$	−43.1814	+	21.6865i	−1.41674	+	0.711512i	−0.434765	+	0.900544i	$0.643169\pi$
$930$		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	0.275637	+	0.961262i	$0.411111\pi$
$937$	−9.55499	+	54.1890i	−0.312148	+	1.77028i	−0.587785	+	0.809017i	$0.700000\pi$
$938$	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	−0.644248	−	0.764817i	$-0.722830\pi$
$941$	9.64098	−	32.2031i	0.314287	−	1.04979i	0.958535	−	0.284975i	$-0.0919852\pi$
$942$		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	$-0.691961\pi$
$947$	−28.5919	+	3.34191i	−0.929112	+	0.108598i	−0.361944	+	0.932200i	$0.617887\pi$
$948$		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	$-0.513493\pi$
$953$	−31.9098	−	26.7755i	−1.03366	−	0.867343i	−0.991282	+	0.131758i	$0.957938\pi$
$954$		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	−0.997459	−	0.0712439i	$-0.977303\pi$
$967$	−0.466927	−	8.01684i	−0.0150154	−	0.257804i	0.982444	−	0.186560i	$-0.0597339\pi$
$968$	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	$-0.224941\pi$
$971$	47.3974			1.52105			0.760527	+	0.649306i	$0.224941\pi$
$972$		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	−0.379520	−	0.925184i	$-0.623911\pi$
$977$	−3.43744	−	59.0186i	−0.109973	−	1.88817i	0.269546	−	0.962987i	$-0.413126\pi$
$978$		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	$-0.217163\pi$
$983$	15.8213	+	10.4058i	0.504621	+	0.331894i	−0.271542	+	0.962426i	$0.587534\pi$
$984$		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	0.755487	−	0.655163i	$-0.227400\pi$
$991$	7.60140	+	6.37833i	0.241466	+	0.202614i	−0.514021	+	0.857778i	$0.671845\pi$
$992$	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	0.216800	−	0.976216i	$-0.430438\pi$
$997$	20.6151	−	2.40956i	0.652887	−	0.0763116i	0.436087	+	0.899904i	$0.356364\pi$
$998$	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.c.55.7		144
3.2	odd	2		729.2.g.b.55.2		144
9.2	odd	6		729.2.g.a.298.7		144
9.4	even	3		81.2.g.a.7.7	✓	144
9.5	odd	6		243.2.g.a.100.2		144
9.7	even	3		729.2.g.d.298.2		144
81.4	even	27		81.2.g.a.58.7	yes	144
81.23	odd	54		729.2.g.a.433.7		144
81.29	odd	54		6561.2.a.d.1.16		72
81.31	even	27	inner	729.2.g.c.676.7		144
81.50	odd	54		729.2.g.b.676.2		144
81.52	even	27		6561.2.a.c.1.57		72
81.58	even	27		729.2.g.d.433.2		144
81.77	odd	54		243.2.g.a.226.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.7	✓	144	9.4	even	3
81.2.g.a.58.7	yes	144	81.4	even	27
243.2.g.a.100.2		144	9.5	odd	6
243.2.g.a.226.2		144	81.77	odd	54
729.2.g.a.298.7		144	9.2	odd	6
729.2.g.a.433.7		144	81.23	odd	54
729.2.g.b.55.2		144	3.2	odd	2
729.2.g.b.676.2		144	81.50	odd	54
729.2.g.c.55.7		144	1.1	even	1	trivial
729.2.g.c.676.7		144	81.31	even	27	inner
729.2.g.d.298.2		144	9.7	even	3
729.2.g.d.433.2		144	81.58	even	27
6561.2.a.c.1.57		72	81.52	even	27
6561.2.a.d.1.16		72	81.29	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)

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

Modular forms

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Database

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