LMFDB - Embedded newform 243.2.g.a.199.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(10,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			199.5
Character	$\chi$	$=$	243.199
Dual form			243.2.g.a.127.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.165895 + 0.175839i) q^{2} +(0.112892 - 1.93827i) q^{4} +(-4.21919 + 0.493153i) q^{5} +(-1.02960 - 0.517085i) q^{7} +(0.729927 - 0.612481i) q^{8} +(-0.786660 - 0.660086i) q^{10} +(-0.782094 - 1.81310i) q^{11} +(-3.89722 - 0.923659i) q^{13} +(-0.0798824 - 0.266826i) q^{14} +(-3.62807 - 0.424061i) q^{16} +(0.731666 - 4.14948i) q^{17} +(0.525049 + 2.97770i) q^{19} +(0.479554 + 8.23363i) q^{20} +(0.189067 - 0.438307i) q^{22} +(1.09019 - 0.547514i) q^{23} +(12.6932 - 3.00834i) q^{25} +(-0.484116 - 0.838513i) q^{26} +(-1.11849 + 1.93728i) q^{28} +(-0.171179 + 0.571777i) q^{29} +(1.62541 + 1.06905i) q^{31} +(-1.66532 - 2.23691i) q^{32} +(0.851020 - 0.559725i) q^{34} +(4.59909 + 1.67393i) q^{35} +(-4.95333 + 1.80287i) q^{37} +(-0.436492 + 0.586310i) q^{38} +(-2.77766 + 2.94414i) q^{40} +(3.93113 - 4.16676i) q^{41} +(4.35863 - 5.85466i) q^{43} +(-3.60257 + 1.31123i) q^{44} +(0.277132 + 0.100868i) q^{46} +(-0.364825 + 0.239949i) q^{47} +(-3.38741 - 4.55008i) q^{49} +(2.63472 + 1.73288i) q^{50} +(-2.23027 + 7.44961i) q^{52} +(2.23695 - 3.87450i) q^{53} +(4.19394 + 7.26412i) q^{55} +(-1.06824 + 0.253177i) q^{56} +(-0.128938 + 0.0647553i) q^{58} +(-3.30053 + 7.65148i) q^{59} +(0.613247 + 10.5290i) q^{61} +(0.0816677 + 0.463161i) q^{62} +(-1.15153 + 6.53063i) q^{64} +(16.8986 + 1.97517i) q^{65} +(-2.10105 - 7.01801i) q^{67} +(-7.96024 - 1.88661i) q^{68} +(0.468625 + 1.08640i) q^{70} +(3.66891 + 3.07858i) q^{71} +(5.52198 - 4.63349i) q^{73} +(-1.13875 - 0.571901i) q^{74} +(5.83087 - 0.681531i) q^{76} +(-0.132281 + 2.27118i) q^{77} +(-8.64862 - 9.16700i) q^{79} +15.5167 q^{80} +1.38483 q^{82} +(-7.94414 - 8.42030i) q^{83} +(-1.04071 + 17.8683i) q^{85} +(1.75255 - 0.204844i) q^{86} +(-1.68136 - 0.844410i) q^{88} +(-8.43420 + 7.07713i) q^{89} +(3.53497 + 2.96620i) q^{91} +(-0.938159 - 2.17490i) q^{92} +(-0.102715 - 0.0243439i) q^{94} +(-3.68374 - 12.3046i) q^{95} +(-6.24523 - 0.729963i) q^{97} +(0.238125 - 1.35047i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.165895	+	0.175839i	0.117306	+	0.124337i	0.783365	−	0.621562i	$-0.213502\pi$
$2$	0.165895	+	0.175839i	0.117306	+	0.124337i	−0.666059	+	0.745899i	$0.732020\pi$
$3$		0			0
$3$		0			0
$4$	0.112892	−	1.93827i	0.0564458	−	0.969137i
$5$	−4.21919	+	0.493153i	−1.88688	+	0.220545i	−0.979739	−	0.200280i	$-0.935815\pi$
$5$	−4.21919	+	0.493153i	−1.88688	+	0.220545i	−0.907142	+	0.420824i	$0.861741\pi$
$6$		0			0
$7$	−1.02960	−	0.517085i	−0.389153	−	0.195440i	0.243455	−	0.969912i	$-0.421719\pi$
$7$	−1.02960	−	0.517085i	−0.389153	−	0.195440i	−0.632608	+	0.774472i	$0.718015\pi$
$8$	0.729927	−	0.612481i	0.258068	−	0.216545i
$9$		0			0
$10$	−0.786660	−	0.660086i	−0.248764	−	0.208738i
$11$	−0.782094	−	1.81310i	−0.235810	−	0.546669i	0.758684	−	0.651458i	$-0.225843\pi$
$11$	−0.782094	−	1.81310i	−0.235810	−	0.546669i	−0.994494	+	0.104789i	$0.966583\pi$
$12$		0			0
$13$	−3.89722	−	0.923659i	−1.08089	−	0.256177i	−0.348674	−	0.937244i	$-0.613368\pi$
$13$	−3.89722	−	0.923659i	−1.08089	−	0.256177i	−0.732221	+	0.681067i	$0.761516\pi$
$14$	−0.0798824	−	0.266826i	−0.0213495	−	0.0713122i
$15$		0			0
$16$	−3.62807	−	0.424061i	−0.907018	−	0.106015i
$17$	0.731666	−	4.14948i	0.177455	−	1.00640i	−0.757817	−	0.652467i	$-0.773734\pi$
$17$	0.731666	−	4.14948i	0.177455	−	1.00640i	0.935272	−	0.353930i	$-0.115155\pi$
$18$		0			0
$19$	0.525049	+	2.97770i	0.120454	+	0.683131i	0.983904	+	0.178696i	$0.0571880\pi$
$19$	0.525049	+	2.97770i	0.120454	+	0.683131i	−0.863450	+	0.504435i	$0.831701\pi$
$20$	0.479554	+	8.23363i	0.107232	+	1.84110i
$21$		0			0
$22$	0.189067	−	0.438307i	0.0403092	−	0.0934473i
$23$	1.09019	−	0.547514i	0.227320	−	0.114165i	−0.331494	−	0.943457i	$-0.607553\pi$
$23$	1.09019	−	0.547514i	0.227320	−	0.114165i	0.558814	+	0.829293i	$0.311256\pi$
$24$		0			0
$25$	12.6932	−	3.00834i	2.53863	−	0.601667i
$26$	−0.484116	−	0.838513i	−0.0949430	−	0.164446i
$27$		0			0
$28$	−1.11849	+	1.93728i	−0.211374	+	0.366111i
$29$	−0.171179	+	0.571777i	−0.0317871	+	0.106176i	−0.972411	−	0.233274i	$-0.925056\pi$
$29$	−0.171179	+	0.571777i	−0.0317871	+	0.106176i	0.940624	+	0.339451i	$0.110241\pi$
$30$		0			0
$31$	1.62541	+	1.06905i	0.291932	+	0.192007i	0.687024	−	0.726635i	$-0.258917\pi$
$31$	1.62541	+	1.06905i	0.291932	+	0.192007i	−0.395091	+	0.918642i	$0.629287\pi$
$32$	−1.66532	−	2.23691i	−0.294390	−	0.395434i
$33$		0			0
$34$	0.851020	−	0.559725i	0.145949	−	0.0959920i
$35$	4.59909	+	1.67393i	0.777388	+	0.282946i
$36$		0			0
$37$	−4.95333	+	1.80287i	−0.814323	+	0.296389i	−0.715408	−	0.698706i	$-0.753759\pi$
$37$	−4.95333	+	1.80287i	−0.814323	+	0.296389i	−0.0989148	+	0.995096i	$0.531537\pi$
$38$	−0.436492	+	0.586310i	−0.0708083	+	0.0951121i
$39$		0			0
$40$	−2.77766	+	2.94414i	−0.439186	+	0.465510i
$41$	3.93113	−	4.16676i	0.613940	−	0.650738i	−0.343574	−	0.939126i	$-0.611638\pi$
$41$	3.93113	−	4.16676i	0.613940	−	0.650738i	0.957514	+	0.288387i	$0.0931190\pi$
$42$		0			0
$43$	4.35863	−	5.85466i	0.664685	−	0.892827i	−0.334078	−	0.942545i	$-0.608425\pi$
$43$	4.35863	−	5.85466i	0.664685	−	0.892827i	0.998763	+	0.0497186i	$0.0158324\pi$
$44$	−3.60257	+	1.31123i	−0.543108	+	0.197675i
$45$		0			0
$46$	0.277132	+	0.100868i	0.0408608	+	0.0148721i
$47$	−0.364825	+	0.239949i	−0.0532152	+	0.0350002i	−0.575838	−	0.817564i	$-0.695324\pi$
$47$	−0.364825	+	0.239949i	−0.0532152	+	0.0350002i	0.522623	+	0.852564i	$0.324954\pi$
$48$		0			0
$49$	−3.38741	−	4.55008i	−0.483915	−	0.650011i
$50$	2.63472	+	1.73288i	0.372606	+	0.245067i
$51$		0			0
$52$	−2.23027	+	7.44961i	−0.309282	+	1.03308i
$53$	2.23695	−	3.87450i	0.307268	−	0.532204i	−0.670496	−	0.741913i	$-0.733919\pi$
$53$	2.23695	−	3.87450i	0.307268	−	0.532204i	0.977764	+	0.209710i	$0.0672518\pi$
$54$		0			0
$55$	4.19394	+	7.26412i	0.565511	+	0.979493i
$56$	−1.06824	+	0.253177i	−0.142749	+	0.0338322i
$57$		0			0
$58$	−0.128938	+	0.0647553i	−0.0169304	+	0.00850279i
$59$	−3.30053	+	7.65148i	−0.429692	+	0.996138i	0.556548	+	0.830816i	$0.312126\pi$
$59$	−3.30053	+	7.65148i	−0.429692	+	0.996138i	−0.986240	+	0.165322i	$0.947134\pi$
$60$		0			0
$61$	0.613247	+	10.5290i	0.0785182	+	1.34811i	0.775650	+	0.631163i	$0.217422\pi$
$61$	0.613247	+	10.5290i	0.0785182	+	1.34811i	−0.697132	+	0.716943i	$0.745541\pi$
$62$	0.0816677	+	0.463161i	0.0103718	+	0.0588215i
$63$		0			0
$64$	−1.15153	+	6.53063i	−0.143941	+	0.816329i
$65$	16.8986	+	1.97517i	2.09602	+	0.244989i
$66$		0			0
$67$	−2.10105	−	7.01801i	−0.256685	−	0.857387i	−0.985060	−	0.172209i	$-0.944910\pi$
$67$	−2.10105	−	7.01801i	−0.256685	−	0.857387i	0.728376	−	0.685178i	$-0.240276\pi$
$68$	−7.96024	−	1.88661i	−0.965321	−	0.228785i
$69$		0			0
$70$	0.468625	+	1.08640i	0.0560115	+	0.129849i
$71$	3.66891	+	3.07858i	0.435420	+	0.365361i	0.833992	−	0.551776i	$-0.186050\pi$
$71$	3.66891	+	3.07858i	0.435420	+	0.365361i	−0.398572	+	0.917137i	$0.630494\pi$
$72$		0			0
$73$	5.52198	−	4.63349i	0.646298	−	0.542309i	−0.259647	−	0.965704i	$-0.583606\pi$
$73$	5.52198	−	4.63349i	0.646298	−	0.542309i	0.905945	+	0.423395i	$0.139162\pi$
$74$	−1.13875	−	0.571901i	−0.132377	−	0.0664822i
$75$		0			0
$76$	5.83087	−	0.681531i	0.668847	−	0.0781770i
$77$	−0.132281	+	2.27118i	−0.0150748	+	0.258825i
$78$		0			0
$79$	−8.64862	−	9.16700i	−0.973046	−	1.03137i	−0.999497	−	0.0317183i	$-0.989902\pi$
$79$	−8.64862	−	9.16700i	−0.973046	−	1.03137i	0.0264509	−	0.999650i	$-0.491579\pi$
$80$	15.5167			1.73482
$81$		0			0
$82$	1.38483			0.152929
$83$	−7.94414	−	8.42030i	−0.871983	−	0.924248i	0.125715	−	0.992066i	$-0.459878\pi$
$83$	−7.94414	−	8.42030i	−0.871983	−	0.924248i	−0.997698	+	0.0678183i	$0.978396\pi$
$84$		0			0
$85$	−1.04071	+	17.8683i	−0.112881	+	1.93809i
$86$	1.75255	−	0.204844i	0.188983	−	0.0220889i
$87$		0			0
$88$	−1.68136	−	0.844410i	−0.179233	−	0.0900144i
$89$	−8.43420	+	7.07713i	−0.894023	+	0.750174i	−0.969013	−	0.247010i	$-0.920552\pi$
$89$	−8.43420	+	7.07713i	−0.894023	+	0.750174i	0.0749899	+	0.997184i	$0.476108\pi$
$90$		0			0
$91$	3.53497	+	2.96620i	0.370566	+	0.310942i
$92$	−0.938159	−	2.17490i	−0.0978098	−	0.226749i
$93$		0			0
$94$	−0.102715	−	0.0243439i	−0.0105943	−	0.00251088i
$95$	−3.68374	−	12.3046i	−0.377944	−	1.26242i
$96$		0			0
$97$	−6.24523	−	0.729963i	−0.634107	−	0.0741165i	−0.207034	−	0.978334i	$-0.566381\pi$
$97$	−6.24523	−	0.729963i	−0.634107	−	0.0741165i	−0.427073	+	0.904217i	$0.640455\pi$
$98$	0.238125	−	1.35047i	0.0240543	−	0.136419i
$99$		0			0
$100$	−4.39803	−	24.9425i	−0.439803	−	2.49425i
$101$	−0.235359	−	4.04096i	−0.0234191	−	0.402090i	−0.989564	−	0.144092i	$-0.953974\pi$
$101$	−0.235359	−	4.04096i	−0.0234191	−	0.402090i	0.966145	−	0.257999i	$-0.0830630\pi$
$102$		0			0
$103$	3.28144	−	7.60723i	0.323330	−	0.749563i	−0.676583	−	0.736366i	$-0.736540\pi$
$103$	3.28144	−	7.60723i	0.323330	−	0.749563i	0.999913	−	0.0131964i	$-0.00420066\pi$
$104$	−3.41041	+	1.71277i	−0.334418	+	0.167951i
$105$		0			0
$106$	1.05239	−	0.249420i	0.102217	−	0.0242258i
$107$	−7.95369	−	13.7762i	−0.768912	−	1.33179i	−0.938153	−	0.346220i	$-0.887465\pi$
$107$	−7.95369	−	13.7762i	−0.768912	−	1.33179i	0.169241	−	0.985575i	$-0.445868\pi$
$108$		0			0
$109$	1.81056	−	3.13598i	0.173420	−	0.300372i	−0.766193	−	0.642610i	$-0.777852\pi$
$109$	1.81056	−	3.13598i	0.173420	−	0.300372i	0.939613	+	0.342238i	$0.111185\pi$
$110$	−0.581558	+	1.94254i	−0.0554494	+	0.185214i
$111$		0			0
$112$	3.51619	+	2.31264i	0.332249	+	0.218524i
$113$	5.67010	+	7.61626i	0.533398	+	0.716477i	0.984380	−	0.176055i	$-0.0563338\pi$
$113$	5.67010	+	7.61626i	0.533398	+	0.716477i	−0.450983	+	0.892533i	$0.648926\pi$
$114$		0			0
$115$	−4.32971	+	2.84770i	−0.403748	+	0.265549i
$116$	1.08894	+	0.396341i	0.101105	+	0.0367993i
$117$		0			0
$118$	−1.89297	+	0.688984i	−0.174262	+	0.0634261i
$119$	−2.89896	+	3.89398i	−0.265747	+	0.356961i
$120$		0			0
$121$	4.87301	−	5.16509i	0.443001	−	0.469553i
$122$	−1.74968	+	1.85455i	−0.158409	+	0.167903i
$123$		0			0
$124$	2.25561	−	3.02981i	0.202560	−	0.272085i
$125$	−32.1127	+	11.6881i	−2.87225	+	1.04541i
$126$		0			0
$127$	−10.4753	−	3.81269i	−0.929532	−	0.338322i	−0.167508	−	0.985871i	$-0.553572\pi$
$127$	−10.4753	−	3.81269i	−0.929532	−	0.338322i	−0.762024	+	0.647549i	$0.775794\pi$
$128$	−5.99929	+	3.94580i	−0.530267	+	0.348762i
$129$		0			0
$130$	2.45609	+	3.29911i	0.215414	+	0.289351i
$131$	10.1355	+	6.66624i	0.885545	+	0.582432i	0.908770	−	0.417298i	$-0.137023\pi$
$131$	10.1355	+	6.66624i	0.885545	+	0.582432i	−0.0232244	+	0.999730i	$0.507393\pi$
$132$		0			0
$133$	0.999133	−	3.33734i	0.0866359	−	0.289384i
$134$	0.885484	−	1.53370i	0.0764941	−	0.132492i
$135$		0			0
$136$	−2.00742	−	3.47695i	−0.172135	−	0.298146i
$137$	0.291152	−	0.0690043i	0.0248748	−	0.00589543i	−0.218160	−	0.975913i	$-0.570005\pi$
$137$	0.291152	−	0.0690043i	0.0248748	−	0.00589543i	0.243034	+	0.970018i	$0.421857\pi$
$138$		0			0
$139$	−5.01291	+	2.51758i	−0.425189	+	0.213538i	−0.648509	−	0.761207i	$-0.724607\pi$
$139$	−5.01291	+	2.51758i	−0.425189	+	0.213538i	0.223319	+	0.974745i	$0.428311\pi$
$140$	3.76374	−	8.72533i	0.318094	−	0.737425i
$141$		0			0
$142$	0.0673212	+	1.15586i	0.00564947	+	0.0969976i
$143$	1.37331	+	7.78843i	0.114842	+	0.651301i
$144$		0			0
$145$	0.440263	−	2.49686i	0.0365619	−	0.207353i
$146$	1.73082	+	0.202304i	0.143243	+	0.0167428i
$147$		0			0
$148$	2.93526	+	9.80445i	0.241277	+	0.805921i
$149$	13.2590	+	3.14244i	1.08622	+	0.257438i	0.734460	−	0.678652i	$-0.237436\pi$
$149$	13.2590	+	3.14244i	1.08622	+	0.257438i	0.351759	+	0.936091i	$0.385584\pi$
$150$		0			0
$151$	−3.74426	−	8.68017i	−0.304703	−	0.706382i	0.695219	−	0.718798i	$-0.255307\pi$
$151$	−3.74426	−	8.68017i	−0.304703	−	0.706382i	−0.999923	+	0.0124155i	$0.996048\pi$
$152$	2.20703	+	1.85192i	0.179014	+	0.150211i
$153$		0			0
$154$	−0.421306	+	0.353517i	−0.0339498	+	0.0284872i
$155$	−7.38513	−	3.70895i	−0.593188	−	0.297910i
$156$		0			0
$157$	9.06059	−	1.05903i	0.723114	−	0.0845199i	0.253429	−	0.967354i	$-0.418442\pi$
$157$	9.06059	−	1.05903i	0.723114	−	0.0845199i	0.469685	+	0.882834i	$0.344368\pi$
$158$	0.177149	−	3.04153i	0.0140932	−	0.241971i
$159$		0			0
$160$	8.12945	+	8.61672i	0.642690	+	0.681211i
$161$	−1.40557			−0.110775
$162$		0			0
$163$	7.94158			0.622033			0.311016	−	0.950405i	$-0.399331\pi$
$163$	7.94158			0.622033			0.311016	+	0.950405i	$0.399331\pi$
$164$	−7.63253	−	8.09001i	−0.596001	−	0.631724i
$165$		0			0
$166$	0.162719	−	2.79378i	0.0126294	−	0.216839i
$167$	−4.41487	+	0.516025i	−0.341633	+	0.0399312i	−0.285180	−	0.958474i	$-0.592053\pi$
$167$	−4.41487	+	0.516025i	−0.341633	+	0.0399312i	−0.0564535	+	0.998405i	$0.517979\pi$
$168$		0			0
$169$	2.71797	+	1.36502i	0.209074	+	0.105001i
$170$	−3.31459	+	2.78127i	−0.254217	+	0.213314i
$171$		0			0
$172$	−10.8559	−	9.10916i	−0.827753	−	0.694567i
$173$	−1.23517	−	2.86344i	−0.0939080	−	0.217703i	0.864787	−	0.502138i	$-0.167453\pi$
$173$	−1.23517	−	2.86344i	−0.0939080	−	0.217703i	−0.958695	+	0.284435i	$0.908194\pi$
$174$		0			0
$175$	−14.6245	−	3.46606i	−1.10551	−	0.262010i
$176$	2.06863	+	6.90970i	0.155929	+	0.520839i
$177$		0			0
$178$	−2.64363	−	0.308996i	−0.198148	−	0.0231602i
$179$	2.47200	−	14.0194i	0.184766	−	1.04786i	−0.741489	−	0.670965i	$-0.765880\pi$
$179$	2.47200	−	14.0194i	0.184766	−	1.04786i	0.926255	−	0.376897i	$-0.123009\pi$
$180$		0			0
$181$	2.75966	+	15.6508i	0.205124	+	1.16332i	0.897244	+	0.441535i	$0.145566\pi$
$181$	2.75966	+	15.6508i	0.205124	+	1.16332i	−0.692120	+	0.721783i	$0.743323\pi$
$182$	0.0648635	+	1.11366i	0.00480800	+	0.0825502i
$183$		0			0
$184$	0.460417	−	1.06737i	0.0339424	−	0.0786872i
$185$	20.0100	−	10.0494i	1.47116	−	0.738846i
$186$		0			0
$187$	−8.09565	+	1.91870i	−0.592012	+	0.140310i
$188$	0.423901	+	0.734219i	0.0309162	+	0.0535484i
$189$		0			0
$190$	1.55250	−	2.68901i	0.112630	−	0.195082i
$191$	5.82426	−	19.4544i	0.421429	−	1.40767i	−0.439178	−	0.898400i	$-0.644730\pi$
$191$	5.82426	−	19.4544i	0.421429	−	1.40767i	0.860607	−	0.509270i	$-0.170085\pi$
$192$		0			0
$193$	2.23280	+	1.46854i	0.160720	+	0.105707i	0.627321	−	0.778760i	$-0.284151\pi$
$193$	2.23280	+	1.46854i	0.160720	+	0.105707i	−0.466601	+	0.884468i	$0.654522\pi$
$194$	−0.907699	−	1.21925i	−0.0651690	−	0.0875372i
$195$		0			0
$196$	−9.20171	+	6.05206i	−0.657265	+	0.432290i
$197$	15.7132	+	5.71915i	1.11952	+	0.407473i	0.834478	−	0.551042i	$-0.185770\pi$
$197$	15.7132	+	5.71915i	1.11952	+	0.407473i	0.285044	+	0.958514i	$0.407992\pi$
$198$		0			0
$199$	−1.83812	+	0.669021i	−0.130301	+	0.0474257i	−0.406348	−	0.913719i	$-0.633198\pi$
$199$	−1.83812	+	0.669021i	−0.130301	+	0.0474257i	0.276047	+	0.961144i	$0.410976\pi$
$200$	7.42253	−	9.97019i	0.524852	−	0.704999i
$201$		0			0
$202$	0.671512	−	0.711761i	0.0472474	−	0.0500794i
$203$	0.471904	−	0.500189i	0.0331211	−	0.0351064i
$204$		0			0
$205$	−14.5314	+	19.5190i	−1.01491	+	1.36327i
$206$	1.88202	−	0.685000i	0.131127	−	0.0477262i
$207$		0			0
$208$	13.7477	+	5.00376i	0.953233	+	0.346948i
$209$	4.98822	−	3.28080i	0.345042	−	0.226938i
$210$		0			0
$211$	6.18914	+	8.31346i	0.426078	+	0.572322i	0.962381	−	0.271704i	$-0.0875870\pi$
$211$	6.18914	+	8.31346i	0.426078	+	0.572322i	−0.536303	+	0.844025i	$0.680180\pi$
$212$	−7.25732	−	4.77321i	−0.498435	−	0.327826i
$213$		0			0
$214$	1.10291	−	3.68397i	0.0753933	−	0.251831i
$215$	−15.5027	+	26.8514i	−1.05727	+	1.83125i
$216$		0			0
$217$	−1.12074	−	1.94117i	−0.0760805	−	0.131775i
$218$	0.851789	−	0.201878i	0.0576904	−	0.0136729i
$219$		0			0
$220$	14.5533	−	7.30895i	0.981184	−	0.492769i
$221$	−6.68417	+	15.4956i	−0.449626	+	1.04235i
$222$		0			0
$223$	−0.426091	−	7.31569i	−0.0285331	−	0.489895i	−0.982058	−	0.188580i	$-0.939611\pi$
$223$	−0.426091	−	7.31569i	−0.0285331	−	0.489895i	0.953525	−	0.301315i	$-0.0974256\pi$
$224$	0.557941	+	3.16424i	0.0372790	+	0.211420i
$225$		0			0
$226$	−0.398592	+	2.26052i	−0.0265139	+	0.150368i
$227$	−23.1203	−	2.70238i	−1.53455	−	0.179363i	−0.693554	−	0.720404i	$-0.743956\pi$
$227$	−23.1203	−	2.70238i	−1.53455	−	0.179363i	−0.840996	+	0.541041i	$0.818030\pi$
$228$		0			0
$229$	0.0143156	+	0.0478175i	0.000946003	+	0.00315987i	0.958461	−	0.285223i	$-0.0920676\pi$
$229$	0.0143156	+	0.0478175i	0.000946003	+	0.00315987i	−0.957515	+	0.288383i	$0.906882\pi$
$230$	−1.21901	−	0.288912i	−0.0803795	−	0.0190503i
$231$		0			0
$232$	0.225255	+	0.522199i	0.0147887	+	0.0342841i
$233$	17.1664	+	14.4043i	1.12461	+	0.943660i	0.998828	−	0.0483977i	$-0.0154115\pi$
$233$	17.1664	+	14.4043i	1.12461	+	0.943660i	0.125782	+	0.992058i	$0.459856\pi$
$234$		0			0
$235$	1.42093	−	1.19231i	0.0926916	−	0.0777775i
$236$	14.4581	+	7.26111i	0.941140	+	0.472658i
$237$		0			0
$238$	−1.16564	+	0.136243i	−0.0755570	+	0.00883135i
$239$	−1.19389	+	20.4983i	−0.0772265	+	1.32593i	0.707777	+	0.706436i	$0.249698\pi$
$239$	−1.19389	+	20.4983i	−0.0772265	+	1.32593i	−0.785003	+	0.619491i	$0.787339\pi$
$240$		0			0
$241$	19.7548	+	20.9389i	1.27252	+	1.34879i	0.908772	+	0.417292i	$0.137021\pi$
$241$	19.7548	+	20.9389i	1.27252	+	1.34879i	0.363746	+	0.931498i	$0.381498\pi$
$242$	1.71663			0.110349
$243$		0			0
$244$	20.4774			1.31093
$245$	16.5360	+	17.5272i	1.05645	+	1.11977i
$246$		0			0
$247$	0.704146	−	12.0897i	0.0448037	−	0.769251i
$248$	1.84120	−	0.215206i	0.116917	−	0.0136656i
$249$		0			0
$250$	−7.38256	−	3.70766i	−0.466914	−	0.234493i
$251$	7.80826	−	6.55190i	0.492853	−	0.413553i	−0.362195	−	0.932102i	$-0.617972\pi$
$251$	7.80826	−	6.55190i	0.492853	−	0.413553i	0.855047	+	0.518550i	$0.173528\pi$
$252$		0			0
$253$	−1.84533	−	1.54841i	−0.116015	−	0.0973479i
$254$	−1.06738	−	2.47447i	−0.0669735	−	0.155262i
$255$		0			0
$256$	11.2162	+	2.65828i	0.701011	+	0.166143i
$257$	1.73817	+	5.80588i	0.108424	+	0.362161i	0.994932	−	0.100553i	$-0.0320610\pi$
$257$	1.73817	+	5.80588i	0.108424	+	0.362161i	−0.886508	+	0.462714i	$0.846876\pi$
$258$		0			0
$259$	6.03220	+	0.705063i	0.374822	+	0.0438105i
$260$	5.73613	−	32.5312i	0.355740	−	2.01750i
$261$		0			0
$262$	0.509253	+	2.88812i	0.0314618	+	0.178429i
$263$	0.780181	+	13.3952i	0.0481080	+	0.825983i	0.932931	+	0.360055i	$0.117242\pi$
$263$	0.780181	+	13.3952i	0.0481080	+	0.825983i	−0.884823	+	0.465927i	$0.845721\pi$
$264$		0			0
$265$	−7.52738	+	17.4504i	−0.462403	+	1.07197i
$266$	0.752585	−	0.377962i	0.0461440	−	0.0231744i
$267$		0			0
$268$	−13.8400	+	3.28015i	−0.845414	+	0.200367i
$269$	−1.44120	−	2.49623i	−0.0878715	−	0.152198i	0.818740	−	0.574165i	$-0.194673\pi$
$269$	−1.44120	−	2.49623i	−0.0878715	−	0.152198i	−0.906611	+	0.421967i	$0.861340\pi$
$270$		0			0
$271$	−1.60573	+	2.78120i	−0.0975410	+	0.168946i	−0.910666	−	0.413143i	$-0.864431\pi$
$271$	−1.60573	+	2.78120i	−0.0975410	+	0.168946i	0.813125	+	0.582089i	$0.197764\pi$
$272$	−4.41417	+	14.7444i	−0.267648	+	0.894008i
$273$		0			0
$274$	0.0604344	+	0.0397483i	0.00365098	+	0.00240128i
$275$	−15.3817	−	20.6612i	−0.927549	−	1.24591i
$276$		0			0
$277$	2.84591	−	1.87178i	0.170994	−	0.112465i	−0.461127	−	0.887334i	$-0.652555\pi$
$277$	2.84591	−	1.87178i	0.170994	−	0.112465i	0.632121	+	0.774869i	$0.282184\pi$
$278$	−1.27431	−	0.463810i	−0.0764278	−	0.0278174i
$279$		0			0
$280$	4.38225	−	1.59501i	0.261889	−	0.0953200i
$281$	6.85829	−	9.21228i	0.409131	−	0.549558i	−0.549025	−	0.835806i	$-0.685001\pi$
$281$	6.85829	−	9.21228i	0.409131	−	0.549558i	0.958156	+	0.286248i	$0.0924081\pi$
$282$		0			0
$283$	−17.3905	+	18.4328i	−1.03376	+	1.09572i	−0.0384196	+	0.999262i	$0.512232\pi$
$283$	−17.3905	+	18.4328i	−1.03376	+	1.09572i	−0.995337	+	0.0964565i	$0.969249\pi$
$284$	6.38133	−	6.76381i	0.378662	−	0.401358i
$285$		0			0
$286$	−1.14168	+	1.53355i	−0.0675091	+	0.0906804i
$287$	−6.20207	+	2.25737i	−0.366097	+	0.133248i
$288$		0			0
$289$	−0.708104	−	0.257729i	−0.0416532	−	0.0151605i
$290$	0.512082	−	0.336802i	0.0300705	−	0.0197777i
$291$		0			0
$292$	−8.35759	−	11.2262i	−0.489091	−	0.656963i
$293$	−3.35543	−	2.20690i	−0.196027	−	0.128929i	0.447701	−	0.894183i	$-0.352243\pi$
$293$	−3.35543	−	2.20690i	−0.196027	−	0.128929i	−0.643728	+	0.765254i	$0.722613\pi$
$294$		0			0
$295$	10.1522	−	33.9107i	0.591084	−	1.97436i
$296$	−2.51135	+	4.34978i	−0.145969	+	0.252826i
$297$		0			0
$298$	1.64704	+	2.85276i	0.0954106	+	0.165256i
$299$	−4.75443	+	1.12682i	−0.274956	+	0.0651657i
$300$		0			0
$301$	−7.51501	+	3.77418i	−0.433158	+	0.217540i
$302$	0.905155	−	2.09839i	0.0520858	−	0.120749i
$303$		0			0
$304$	−0.642189	−	11.0260i	−0.0368321	−	0.632382i
$305$	−7.77984	−	44.1216i	−0.445472	−	2.52640i
$306$		0			0
$307$	3.45206	−	19.5776i	0.197020	−	1.11735i	−0.712493	−	0.701679i	$-0.752434\pi$
$307$	3.45206	−	19.5776i	0.197020	−	1.11735i	0.909513	−	0.415675i	$-0.136455\pi$
$308$	4.38723	+	0.512794i	0.249986	+	0.0292191i
$309$		0			0
$310$	−0.572981	−	1.91389i	−0.0325431	−	0.108702i
$311$	−1.50256	−	0.356114i	−0.0852026	−	0.0201934i	0.187793	−	0.982209i	$-0.439866\pi$
$311$	−1.50256	−	0.356114i	−0.0852026	−	0.0201934i	−0.272996	+	0.962015i	$0.588015\pi$
$312$		0			0
$313$	−6.93106	−	16.0680i	−0.391767	−	0.908218i	−0.993947	−	0.109858i	$-0.964961\pi$
$313$	−6.93106	−	16.0680i	−0.391767	−	0.908218i	0.602181	−	0.798360i	$-0.294299\pi$
$314$	1.68933	+	1.41751i	0.0953343	+	0.0799950i
$315$		0			0
$316$	−18.7445	+	15.7285i	−1.05446	+	0.884799i
$317$	−1.75554	−	0.881664i	−0.0986008	−	0.0495192i	0.398815	−	0.917031i	$-0.369421\pi$
$317$	−1.75554	−	0.881664i	−0.0986008	−	0.0495192i	−0.497416	+	0.867512i	$0.665718\pi$
$318$		0			0
$319$	1.17057	−	0.136819i	0.0655391	−	0.00766042i
$320$	1.63791	−	28.1219i	0.0915622	−	1.57206i
$321$		0			0
$322$	−0.233178	−	0.247154i	−0.0129945	−	0.0137734i
$323$	12.7401			0.708877
$324$		0			0
$325$	−52.2468			−2.89813
$326$	1.31747	+	1.39644i	0.0729680	+	0.0773416i
$327$		0			0
$328$	0.317378	−	5.44917i	0.0175243	−	0.300880i
$329$	0.499698	−	0.0584063i	0.0275492	−	0.00322005i
$330$		0			0
$331$	30.8145	+	15.4756i	1.69372	+	0.850616i	0.990154	+	0.139982i	$0.0447045\pi$
$331$	30.8145	+	15.4756i	1.69372	+	0.850616i	0.703562	+	0.710634i	$0.251592\pi$
$332$	−17.2177	+	14.4474i	−0.944943	+	0.792901i
$333$		0			0
$334$	−0.823144	−	0.690700i	−0.0450405	−	0.0377934i
$335$	12.3257	+	28.5742i	0.673426	+	1.56118i
$336$		0			0
$337$	15.7401	+	3.73046i	0.857415	+	0.203211i	0.635734	−	0.771908i	$-0.280697\pi$
$337$	15.7401	+	3.73046i	0.857415	+	0.203211i	0.221681	+	0.975119i	$0.428846\pi$
$338$	0.210876	+	0.704374i	0.0114701	+	0.0383129i
$339$		0			0
$340$	34.5162	+	4.03436i	1.87190	+	0.218794i
$341$	0.667067	−	3.78313i	0.0361237	−	0.204868i
$342$		0			0
$343$	2.53539	+	14.3789i	0.136898	+	0.776387i
$344$	−0.404387	−	6.94305i	−0.0218031	−	0.374344i
$345$		0			0
$346$	0.298595	−	0.692221i	0.0160526	−	0.0372141i
$347$	−28.4307	+	14.2785i	−1.52624	+	0.766508i	−0.996653	−	0.0817463i	$-0.973950\pi$
$347$	−28.4307	+	14.2785i	−1.52624	+	0.766508i	−0.529589	+	0.848254i	$0.677654\pi$
$348$		0			0
$349$	−16.8680	+	3.99780i	−0.902925	+	0.213997i	−0.655754	−	0.754975i	$-0.727649\pi$
$349$	−16.8680	+	3.99780i	−0.902925	+	0.213997i	−0.247171	+	0.968972i	$0.579501\pi$
$350$	−1.81666	−	3.14655i	−0.0971048	−	0.168190i
$351$		0			0
$352$	−2.75331	+	4.76887i	−0.146752	+	0.254181i
$353$	−0.975076	+	3.25698i	−0.0518981	+	0.173352i	−0.980009	−	0.198951i	$-0.936247\pi$
$353$	−0.975076	+	3.25698i	−0.0518981	+	0.173352i	0.928111	+	0.372303i	$0.121432\pi$
$354$		0			0
$355$	−16.9981	−	11.1798i	−0.902164	−	0.593362i
$356$	12.7653	+	17.1467i	0.676558	+	0.908775i
$357$		0			0
$358$	2.87525	−	1.89108i	0.151962	−	0.0999469i
$359$	−9.53489	−	3.47042i	−0.503232	−	0.183162i	0.0779150	−	0.996960i	$-0.475174\pi$
$359$	−9.53489	−	3.47042i	−0.503232	−	0.183162i	−0.581147	+	0.813798i	$0.697396\pi$
$360$		0			0
$361$	9.26314	−	3.37151i	0.487534	−	0.177448i
$362$	−2.29421	+	3.08166i	−0.120581	+	0.161968i
$363$		0			0
$364$	6.14837	−	6.51689i	0.322262	−	0.341578i
$365$	−21.0133	+	22.2728i	−1.09988	+	1.16581i
$366$		0			0
$367$	8.87614	−	11.9227i	0.463331	−	0.622362i	−0.507637	−	0.861571i	$-0.669481\pi$
$367$	8.87614	−	11.9227i	0.463331	−	0.622362i	0.970968	+	0.239210i	$0.0768883\pi$
$368$	−4.18747	+	1.52411i	−0.218287	+	0.0794499i
$369$		0			0
$370$	5.08664	+	1.85138i	0.264442	+	0.0962489i
$371$	−4.30661	+	2.83250i	−0.223588	+	0.147056i
$372$		0			0
$373$	−12.5886	−	16.9094i	−0.651814	−	0.875538i	0.346224	−	0.938152i	$-0.387464\pi$
$373$	−12.5886	−	16.9094i	−0.651814	−	0.875538i	−0.998038	+	0.0626138i	$0.980056\pi$
$374$	−1.68041	−	1.10523i	−0.0868921	−	0.0571498i
$375$		0			0
$376$	−0.119331	+	0.398593i	−0.00615403	+	0.0205559i
$377$	1.19525	−	2.07023i	0.0615585	−	0.106622i
$378$		0			0
$379$	−3.47462	−	6.01822i	−0.178479	−	0.309135i	0.762880	−	0.646540i	$-0.223784\pi$
$379$	−3.47462	−	6.01822i	−0.178479	−	0.309135i	−0.941360	+	0.337404i	$0.890451\pi$
$380$	−24.2655	+	5.75103i	−1.24479	+	0.295021i
$381$		0			0
$382$	4.38706	−	2.20326i	0.224461	−	0.112729i
$383$	13.9944	−	32.4427i	0.715081	−	1.65774i	−0.0375433	−	0.999295i	$-0.511953\pi$
$383$	13.9944	−	32.4427i	0.715081	−	1.65774i	0.752625	−	0.658450i	$-0.228788\pi$
$384$		0			0
$385$	−0.561918	−	9.64777i	−0.0286380	−	0.491696i
$386$	0.112186	+	0.636236i	0.00571010	+	0.0323836i
$387$		0			0
$388$	−2.11990	+	12.0226i	−0.107622	+	0.610354i
$389$	−25.5497	−	2.98633i	−1.29542	−	0.151413i	−0.559698	−	0.828697i	$-0.689083\pi$
$389$	−25.5497	−	2.98633i	−1.29542	−	0.151413i	−0.735722	+	0.677284i	$0.763157\pi$
$390$		0			0
$391$	−1.47424	−	4.92432i	−0.0745558	−	0.249034i
$392$	−5.25940	−	1.24650i	−0.265640	−	0.0629578i
$393$		0			0
$394$	1.60110	+	3.71178i	0.0806625	+	0.186997i
$395$	41.0109	+	34.4123i	2.06348	+	1.73147i
$396$		0			0
$397$	14.2470	−	11.9547i	0.715038	−	0.599988i	−0.210970	−	0.977493i	$-0.567662\pi$
$397$	14.2470	−	11.9547i	0.715038	−	0.599988i	0.926008	+	0.377504i	$0.123218\pi$
$398$	−0.422576	−	0.212225i	−0.0211818	−	0.0106379i
$399$		0			0
$400$	−47.3275	+	5.53179i	−2.36637	+	0.276589i
$401$	−0.268845	+	4.61589i	−0.0134255	+	0.230506i	0.984920	+	0.173009i	$0.0553490\pi$
$401$	−0.268845	+	4.61589i	−0.0134255	+	0.230506i	−0.998346	+	0.0574971i	$0.981688\pi$
$402$		0			0
$403$	−5.34715	−	5.66765i	−0.266361	−	0.282326i
$404$	−7.85906			−0.391003
$405$		0			0
$406$	0.166239			0.00825031
$407$	7.14274	+	7.57087i	0.354053	+	0.375274i
$408$		0			0
$409$	0.636048	−	10.9205i	0.0314505	−	0.539985i	−0.945380	−	0.325971i	$-0.894309\pi$
$409$	0.636048	−	10.9205i	0.0314505	−	0.539985i	0.976830	−	0.214015i	$-0.0686540\pi$
$410$	−5.84289	+	0.682936i	−0.288560	+	0.0337278i
$411$		0			0
$412$	−14.3745	−	7.21912i	−0.708178	−	0.355661i
$413$	7.35469	−	6.17132i	0.361901	−	0.303671i
$414$		0			0
$415$	37.6704	+	31.6092i	1.84917	+	1.55163i
$416$	4.42398	+	10.2559i	0.216903	+	0.502839i
$417$		0			0
$418$	1.40442	+	0.332853i	0.0686922	+	0.0162804i
$419$	−9.61972	−	32.1321i	−0.469954	−	1.56976i	−0.784259	−	0.620434i	$-0.786956\pi$
$419$	−9.61972	−	32.1321i	−0.469954	−	1.56976i	0.314304	−	0.949322i	$-0.398229\pi$
$420$		0			0
$421$	−1.64743	−	0.192557i	−0.0802908	−	0.00938465i	0.0758527	−	0.997119i	$-0.475832\pi$
$421$	−1.64743	−	0.192557i	−0.0802908	−	0.00938465i	−0.156143	+	0.987734i	$0.549906\pi$
$422$	−0.435079	+	2.46745i	−0.0211793	+	0.120114i
$423$		0			0
$424$	−0.740254	−	4.19819i	−0.0359499	−	0.203882i
$425$	−3.19588	−	54.8712i	−0.155023	−	2.66164i
$426$		0			0
$427$	4.81301	−	11.1578i	0.232918	−	0.539965i
$428$	−27.5999	+	13.8612i	−1.33409	+	0.670007i
$429$		0			0
$430$	−7.29334	+	1.72855i	−0.351716	+	0.0833582i
$431$	−7.55425	−	13.0843i	−0.363876	−	0.630251i	0.624720	−	0.780849i	$-0.285213\pi$
$431$	−7.55425	−	13.0843i	−0.363876	−	0.630251i	−0.988595	+	0.150598i	$0.951880\pi$
$432$		0			0
$433$	−2.46655	+	4.27218i	−0.118535	+	0.205308i	−0.919187	−	0.393821i	$-0.871153\pi$
$433$	−2.46655	+	4.27218i	−0.118535	+	0.205308i	0.800653	+	0.599129i	$0.204486\pi$
$434$	0.155408	−	0.519100i	0.00745984	−	0.0249176i
$435$		0			0
$436$	−5.87399	−	3.86338i	−0.281313	−	0.185022i
$437$	2.20273	+	2.95879i	0.105371	+	0.141538i
$438$		0			0
$439$	16.8607	−	11.0894i	0.804716	−	0.529270i	−0.0792316	−	0.996856i	$-0.525247\pi$
$439$	16.8607	−	11.0894i	0.804716	−	0.529270i	0.883947	+	0.467586i	$0.154876\pi$
$440$	7.51040	+	2.73356i	0.358044	+	0.130318i
$441$		0			0
$442$	−3.83361	+	1.39532i	−0.182346	+	0.0663686i
$443$	−16.8317	+	22.6089i	−0.799699	+	1.07418i	0.195915	+	0.980621i	$0.437232\pi$
$443$	−16.8317	+	22.6089i	−0.799699	+	1.07418i	−0.995614	+	0.0935608i	$0.970175\pi$
$444$		0			0
$445$	32.0954	−	34.0191i	1.52147	−	1.61266i
$446$	1.21570	−	1.28856i	0.0575649	−	0.0610152i
$447$		0			0
$448$	4.56251	−	6.12851i	0.215558	−	0.289545i
$449$	0.407937	−	0.148477i	0.0192517	−	0.00700706i	−0.332376	−	0.943147i	$-0.607850\pi$
$449$	0.407937	−	0.148477i	0.0192517	−	0.00700706i	0.351628	+	0.936140i	$0.385628\pi$
$450$		0			0
$451$	−10.6293	−	3.86873i	−0.500512	−	0.182171i
$452$	15.4025	−	10.1304i	0.724473	−	0.476493i
$453$		0			0
$454$	−3.36037	−	4.51376i	−0.157710	−	0.211841i
$455$	−16.3775	−	10.7717i	−0.767790	−	0.504984i
$456$		0			0
$457$	−7.77292	+	25.9634i	−0.363602	+	1.21452i	0.559132	+	0.829079i	$0.311134\pi$
$457$	−7.77292	+	25.9634i	−0.363602	+	1.21452i	−0.922734	+	0.385437i	$0.874051\pi$
$458$	−0.00603328	+	0.0104499i	−0.000281917	+	0.000488294i
$459$		0			0
$460$	5.03083	+	8.71365i	0.234564	+	0.406276i
$461$	41.5746	−	9.85335i	1.93632	−	0.458916i	0.945081	−	0.326837i	$-0.105983\pi$
$461$	41.5746	−	9.85335i	1.93632	−	0.458916i	0.991239	−	0.132079i	$-0.0421653\pi$
$462$		0			0
$463$	−27.1142	+	13.6173i	−1.26011	+	0.632849i	−0.948324	−	0.317305i	$-0.897222\pi$
$463$	−27.1142	+	13.6173i	−1.26011	+	0.632849i	−0.311782	+	0.950154i	$0.600926\pi$
$464$	0.863518	−	2.00186i	0.0400878	−	0.0929340i
$465$		0			0
$466$	0.314988	+	5.40814i	0.0145915	+	0.250527i
$467$	−2.33662	−	13.2516i	−0.108126	−	0.613212i	−0.989926	−	0.141588i	$-0.954779\pi$
$467$	−2.33662	−	13.2516i	−0.108126	−	0.613212i	0.881800	−	0.471624i	$-0.156332\pi$
$468$		0			0
$469$	−1.46566	+	8.31218i	−0.0676779	+	0.383821i
$470$	0.445380	+	0.0520575i	0.0205439	+	0.00240123i
$471$		0			0
$472$	2.27725	+	7.60653i	0.104819	+	0.350119i
$473$	−14.0239	−	3.32373i	−0.644820	−	0.152825i
$474$		0			0
$475$	15.6225	+	36.2169i	0.716808	+	1.66175i
$476$	7.22033	+	6.05858i	0.330943	+	0.277695i
$477$		0			0
$478$	−3.80246	+	3.19065i	−0.173921	+	0.145937i
$479$	23.2134	+	11.6582i	1.06065	+	0.532677i	0.891550	−	0.452922i	$-0.149618\pi$
$479$	23.2134	+	11.6582i	1.06065	+	0.532677i	0.169098	+	0.985599i	$0.445915\pi$
$480$		0			0
$481$	20.9695	−	2.45098i	0.956126	−	0.111755i
$482$	−0.404635	+	6.94732i	−0.0184306	+	0.316442i
$483$		0			0
$484$	−9.46123	−	10.0283i	−0.430056	−	0.455833i
$485$	26.7098			1.21283
$486$		0			0
$487$	2.70578			0.122611			0.0613053	−	0.998119i	$-0.480474\pi$
$487$	2.70578			0.122611			0.0613053	+	0.998119i	$0.480474\pi$
$488$	6.89647	+	7.30983i	0.312188	+	0.330900i
$489$		0			0
$490$	−0.338705	+	5.81535i	−0.0153012	+	0.262711i
$491$	39.5384	−	4.62138i	1.78435	−	0.208560i	0.841151	−	0.540801i	$-0.181879\pi$
$491$	39.5384	−	4.62138i	1.78435	−	0.208560i	0.943195	+	0.332241i	$0.107805\pi$
$492$		0			0
$493$	2.24733	+	1.12865i	0.101215	+	0.0508320i
$494$	2.24266	−	1.88181i	0.100902	−	0.0846667i
$495$		0			0
$496$	−5.44377	−	4.56786i	−0.244432	−	0.205103i
$497$	−2.18563	−	5.06685i	−0.0980388	−	0.227279i
$498$		0			0
$499$	2.41838	+	0.573166i	0.108261	+	0.0256584i	0.284389	−	0.958709i	$-0.408209\pi$
$499$	2.41838	+	0.573166i	0.108261	+	0.0256584i	−0.176128	+	0.984367i	$0.556357\pi$
$500$	19.0294	+	63.5627i	0.851022	+	2.84261i
$501$		0			0
$502$	2.44743	+	0.286064i	0.109234	+	0.0127677i
$503$	2.56729	−	14.5598i	0.114470	−	0.649191i	−0.872541	−	0.488540i	$-0.837530\pi$
$503$	2.56729	−	14.5598i	0.114470	−	0.649191i	0.987011	−	0.160651i	$-0.0513594\pi$
$504$		0			0
$505$	2.98584	+	16.9335i	0.132868	+	0.753532i
$506$	−0.0338600	−	0.581354i	−0.00150526	−	0.0258444i
$507$		0			0
$508$	−8.57262	+	19.8736i	−0.380349	+	0.881747i
$509$	21.4552	−	10.7752i	0.950983	−	0.477602i	0.0954985	−	0.995430i	$-0.469556\pi$
$509$	21.4552	−	10.7752i	0.950983	−	0.477602i	0.855485	+	0.517828i	$0.173259\pi$
$510$		0			0
$511$	−8.08134	+	1.91531i	−0.357498	+	0.0847285i
$512$	8.57387	+	14.8504i	0.378915	+	0.656300i
$513$		0			0
$514$	−0.732546	+	1.26881i	−0.0323112	+	0.0559646i
$515$	−10.0935	+	33.7146i	−0.444773	+	1.48564i
$516$		0			0
$517$	0.720378	+	0.473800i	0.0316822	+	0.0208377i
$518$	0.876736	+	1.17766i	0.0385216	+	0.0517434i
$519$		0			0
$520$	13.5445	−	8.90837i	0.593966	−	0.390658i
$521$	−18.5919	−	6.76690i	−0.814526	−	0.296463i	−0.0990342	−	0.995084i	$-0.531575\pi$
$521$	−18.5919	−	6.76690i	−0.814526	−	0.296463i	−0.715492	+	0.698621i	$0.753798\pi$
$522$		0			0
$523$	32.2975	−	11.7553i	1.41227	−	0.514025i	0.480477	−	0.877007i	$-0.340464\pi$
$523$	32.2975	−	11.7553i	1.41227	−	0.514025i	0.931796	+	0.362982i	$0.118241\pi$
$524$	14.0652	−	18.8929i	0.614442	−	0.825339i
$525$		0			0
$526$	−2.22597	+	2.35939i	−0.0970567	+	0.102874i
$527$	5.62526	−	5.96243i	0.245040	−	0.259728i
$528$		0			0
$529$	−12.8459	+	17.2550i	−0.558518	+	0.750219i
$530$	−4.31722	+	1.57134i	−0.187528	+	0.0682547i
$531$		0			0
$532$	−6.35588	−	2.31335i	−0.275563	−	0.100297i
$533$	−19.1692	+	12.6078i	−0.830309	+	0.546103i
$534$		0			0
$535$	40.3519	+	54.2020i	1.74457	+	2.34336i
$536$	−5.83202	−	3.83578i	−0.251905	−	0.165680i
$537$		0			0
$538$	0.199846	−	0.667532i	0.00861597	−	0.0287794i
$539$	−5.60046	+	9.70029i	−0.241229	+	0.417821i
$540$		0			0
$541$	−18.0270	−	31.2237i	−0.775042	−	1.34241i	−0.934771	−	0.355252i	$-0.884395\pi$
$541$	−18.0270	−	31.2237i	−0.775042	−	1.34241i	0.159728	−	0.987161i	$-0.448938\pi$
$542$	−0.755426	+	0.179039i	−0.0324483	+	0.00769040i
$543$		0			0
$544$	−10.5005	+	5.27355i	−0.450205	+	0.226102i
$545$	−6.09257	+	14.1242i	−0.260977	+	0.605013i
$546$		0			0
$547$	−0.502380	−	8.62553i	−0.0214802	−	0.368801i	−0.991870	−	0.127256i	$-0.959383\pi$
$547$	−0.502380	−	8.62553i	−0.0214802	−	0.368801i	0.970390	−	0.241545i	$-0.0776541\pi$
$548$	−0.100881	−	0.572123i	−0.00430941	−	0.0244399i
$549$		0			0
$550$	1.08129	−	6.13228i	0.0461062	−	0.261481i
$551$	−1.79246	−	0.209508i	−0.0763613	−	0.00892535i
$552$		0			0
$553$	4.16451	+	13.9104i	0.177093	+	0.591532i
$554$	0.801255	+	0.189901i	0.0340421	+	0.00806812i
$555$		0			0
$556$	4.31384	+	10.0006i	0.182948	+	0.424120i
$557$	−16.3664	−	13.7330i	−0.693466	−	0.581887i	0.226441	−	0.974025i	$-0.427291\pi$
$557$	−16.3664	−	13.7330i	−0.693466	−	0.581887i	−0.919906	+	0.392138i	$0.871736\pi$
$558$		0			0
$559$	−22.3943	+	18.7910i	−0.947176	+	0.794775i
$560$	−15.9760	−	8.02344i	−0.675109	−	0.339052i
$561$		0			0
$562$	2.75763	−	0.322321i	0.116324	−	0.0135963i
$563$	1.60839	−	27.6150i	0.0677856	−	1.16383i	−0.777274	−	0.629162i	$-0.783398\pi$
$563$	1.60839	−	27.6150i	0.0677856	−	1.16383i	0.845060	−	0.534672i	$-0.179565\pi$
$564$		0			0
$565$	−27.6792	−	29.3383i	−1.16447	−	1.23427i
$566$	−6.12621			−0.257504
$567$		0			0
$568$	4.56361			0.191485
$569$	15.1704	+	16.0796i	0.635975	+	0.674094i	0.962558	−	0.271075i	$-0.0873790\pi$
$569$	15.1704	+	16.0796i	0.635975	+	0.674094i	−0.326584	+	0.945168i	$0.605898\pi$
$570$		0			0
$571$	−0.123744	+	2.12459i	−0.00517851	+	0.0889115i	−0.999907	−	0.0136314i	$-0.995661\pi$
$571$	−0.123744	+	2.12459i	−0.00517851	+	0.0889115i	0.994729	+	0.102543i	$0.0326979\pi$
$572$	15.2511	−	1.78260i	0.637683	−	0.0745344i
$573$		0			0
$574$	−1.42583	−	0.716078i	−0.0595129	−	0.0298885i
$575$	12.1909	−	10.2293i	0.508394	−	0.426593i
$576$		0			0
$577$	−15.8954	−	13.3378i	−0.661733	−	0.555260i	0.248872	−	0.968536i	$-0.419940\pi$
$577$	−15.8954	−	13.3378i	−0.661733	−	0.555260i	−0.910606	+	0.413276i	$0.864384\pi$
$578$	−0.0721525	−	0.167268i	−0.00300115	−	0.00695744i
$579$		0			0
$580$	−4.78989	−	1.13523i	−0.198889	−	0.0471377i
$581$	3.82529	+	12.7774i	0.158700	+	0.530094i
$582$		0			0
$583$	−8.77435	−	1.02557i	−0.363396	−	0.0424750i
$584$	1.19271	−	6.76421i	0.0493548	−	0.279905i
$585$		0			0
$586$	−0.168592	−	0.956131i	−0.00696446	−	0.0394974i
$587$	0.682898	+	11.7249i	0.0281862	+	0.483939i	0.982633	+	0.185558i	$0.0594094\pi$
$587$	0.682898	+	11.7249i	0.0281862	+	0.483939i	−0.954447	+	0.298380i	$0.903554\pi$
$588$		0			0
$589$	−2.32989	+	5.40129i	−0.0960014	+	0.222556i
$590$	7.64703	−	3.84048i	0.314823	−	0.158110i
$591$		0			0
$592$	18.7356	−	4.44042i	0.770028	−	0.182500i
$593$	−10.8840	−	18.8516i	−0.446952	−	0.774144i	0.551234	−	0.834351i	$-0.314157\pi$
$593$	−10.8840	−	18.8516i	−0.446952	−	0.774144i	−0.998186	+	0.0602070i	$0.980824\pi$
$594$		0			0
$595$	10.3109	−	17.8591i	0.422708	−	0.732151i
$596$	7.58774	−	25.3448i	0.310806	−	1.03816i
$597$		0			0
$598$	−0.986876	−	0.649078i	−0.0403564	−	0.0265428i
$599$	−6.11729	−	8.21695i	−0.249946	−	0.335736i	0.659388	−	0.751803i	$-0.270815\pi$
$599$	−6.11729	−	8.21695i	−0.249946	−	0.335736i	−0.909334	+	0.416067i	$0.863408\pi$
$600$		0			0
$601$	−2.35821	+	1.55102i	−0.0961935	+	0.0632674i	−0.596694	−	0.802469i	$-0.703520\pi$
$601$	−2.35821	+	1.55102i	−0.0961935	+	0.0632674i	0.500501	+	0.865736i	$0.333149\pi$
$602$	−1.91035	−	0.695311i	−0.0778601	−	0.0283388i
$603$		0			0
$604$	−17.2472	+	6.27748i	−0.701780	+	0.255427i
$605$	−18.0130	+	24.1956i	−0.732332	+	0.983693i
$606$		0			0
$607$	−9.33562	+	9.89518i	−0.378921	+	0.401633i	−0.888564	−	0.458753i	$-0.848296\pi$
$607$	−9.33562	+	9.89518i	−0.378921	+	0.401633i	0.509643	+	0.860386i	$0.329778\pi$
$608$	5.78648	−	6.13331i	0.234673	−	0.248739i
$609$		0			0
$610$	6.46766	−	8.68757i	0.261868	−	0.351750i
$611$	1.64343	−	0.598161i	0.0664862	−	0.0241990i
$612$		0			0
$613$	15.3111	+	5.57278i	0.618410	+	0.225083i	0.632179	−	0.774823i	$-0.282161\pi$
$613$	15.3111	+	5.57278i	0.618410	+	0.225083i	−0.0137693	+	0.999905i	$0.504383\pi$
$614$	4.01519	−	2.64083i	0.162040	−	0.106575i
$615$		0			0
$616$	1.29450	+	1.73881i	0.0521568	+	0.0700587i
$617$	−6.48426	−	4.26476i	−0.261046	−	0.171693i	0.412239	−	0.911076i	$-0.364747\pi$
$617$	−6.48426	−	4.26476i	−0.261046	−	0.171693i	−0.673285	+	0.739383i	$0.735117\pi$
$618$		0			0
$619$	−12.5687	+	41.9823i	−0.505178	+	1.68741i	0.201178	+	0.979555i	$0.435523\pi$
$619$	−12.5687	+	41.9823i	−0.505178	+	1.68741i	−0.706356	+	0.707857i	$0.749662\pi$
$620$	−8.02269	+	13.8957i	−0.322199	+	0.558065i
$621$		0			0
$622$	−0.186650	−	0.323287i	−0.00748397	−	0.0129626i
$623$	12.3433	−	2.92543i	0.494525	−	0.117205i
$624$		0			0
$625$	71.4394	−	35.8782i	2.85758	−	1.43513i
$626$	1.67555	−	3.88436i	0.0669684	−	0.155250i
$627$		0			0
$628$	−1.02983	−	17.6815i	−0.0410946	−	0.705567i
$629$	3.85678	+	21.8729i	0.153780	+	0.872129i
$630$		0			0
$631$	3.55734	−	20.1747i	0.141615	−	0.803141i	−0.828407	−	0.560126i	$-0.810753\pi$
$631$	3.55734	−	20.1747i	0.141615	−	0.803141i	0.970023	−	0.243015i	$-0.0781363\pi$
$632$	−11.9275	−	1.39412i	−0.474450	−	0.0554552i
$633$		0			0
$634$	−0.136205	−	0.454956i	−0.00540938	−	0.0180686i
$635$	46.0775	+	10.9206i	1.82853	+	0.433370i
$636$		0			0
$637$	8.99876	+	20.8615i	0.356544	+	0.826562i
$638$	0.218250	+	0.183133i	0.00864058	+	0.00725031i
$639$		0			0
$640$	23.3663	−	19.6066i	0.923634	−	0.775021i
$641$	−30.8827	−	15.5099i	−1.21979	−	0.612603i	−0.281872	−	0.959452i	$-0.590955\pi$
$641$	−30.8827	−	15.5099i	−1.21979	−	0.612603i	−0.937921	+	0.346849i	$0.887252\pi$
$642$		0			0
$643$	−29.5404	+	3.45278i	−1.16496	+	0.136164i	−0.676514	−	0.736430i	$-0.736510\pi$
$643$	−29.5404	+	3.45278i	−1.16496	+	0.136164i	−0.488446	+	0.872594i	$0.662436\pi$
$644$	−0.158677	+	2.72438i	−0.00625276	+	0.107356i
$645$		0			0
$646$	2.11352	+	2.24020i	0.0831553	+	0.0881395i
$647$	−43.1443			−1.69618			−0.848089	−	0.529853i	$-0.822247\pi$
$647$	−43.1443			−1.69618			−0.848089	+	0.529853i	$0.822247\pi$
$648$		0			0
$649$	16.4542			0.645884
$650$	−8.66750	−	9.18701i	−0.339967	−	0.360344i
$651$		0			0
$652$	0.896538	−	15.3930i	0.0351111	−	0.602835i
$653$	−30.9788	+	3.62090i	−1.21229	+	0.141697i	−0.698114	−	0.715987i	$-0.745977\pi$
$653$	−30.9788	+	3.62090i	−1.21229	+	0.141697i	−0.514178	+	0.857683i	$0.671903\pi$
$654$		0			0
$655$	−46.0512	−	23.1278i	−1.79937	−	0.903678i
$656$	−16.0294	+	13.4503i	−0.625843	+	0.525145i
$657$		0			0
$658$	0.0931677	+	0.0781770i	0.00363205	+	0.00304766i
$659$	−16.1073	−	37.3409i	−0.627452	−	1.45460i	−0.874224	−	0.485523i	$-0.838629\pi$
$659$	−16.1073	−	37.3409i	−0.627452	−	1.45460i	0.246772	−	0.969073i	$-0.420630\pi$
$660$		0			0
$661$	16.8947	+	4.00411i	0.657126	+	0.155742i	0.545634	−	0.838024i	$-0.316289\pi$
$661$	16.8947	+	4.00411i	0.657126	+	0.155742i	0.111492	+	0.993765i	$0.464437\pi$
$662$	2.39076	+	7.98571i	0.0929197	+	0.310373i
$663$		0			0
$664$	−10.9559	−	1.28056i	−0.425172	−	0.0496955i
$665$	−2.56972	+	14.5736i	−0.0996494	+	0.565140i
$666$		0			0
$667$	0.126439	+	0.717068i	0.00489572	+	0.0277650i
$668$	0.501795	+	8.61550i	0.0194150	+	0.333344i
$669$		0			0
$670$	−2.97968	+	6.90767i	−0.115115	+	0.266866i
$671$	18.6106	−	9.34658i	0.718453	−	0.360821i
$672$		0			0
$673$	42.9001	−	10.1675i	1.65368	−	0.391928i	0.705258	−	0.708951i	$-0.250831\pi$
$673$	42.9001	−	10.1675i	1.65368	−	0.391928i	0.948418	+	0.317023i	$0.102683\pi$
$674$	1.95524	+	3.38658i	0.0753131	+	0.130446i
$675$		0			0
$676$	2.95261	−	5.11407i	0.113562	−	0.196695i
$677$	9.95022	−	33.2361i	0.382418	−	1.27737i	−0.522814	−	0.852447i	$-0.675118\pi$
$677$	9.95022	−	33.2361i	0.382418	−	1.27737i	0.905232	−	0.424918i	$-0.139697\pi$
$678$		0			0
$679$	6.05265	+	3.98089i	0.232279	+	0.152772i
$680$	10.1844	+	13.6800i	0.390552	+	0.524603i
$681$		0			0
$682$	0.775884	−	0.510307i	0.0297101	−	0.0195407i
$683$	40.1564	+	14.6157i	1.53654	+	0.559256i	0.965213	−	0.261465i	$-0.0842057\pi$
$683$	40.1564	+	14.6157i	1.53654	+	0.559256i	0.571329	+	0.820721i	$0.306428\pi$
$684$		0			0
$685$	−1.19440	+	0.434725i	−0.0456356	+	0.0166100i
$686$	−2.10776	+	2.83121i	−0.0804746	+	0.108096i
$687$		0			0
$688$	−18.2962	+	19.3928i	−0.697535	+	0.739343i
$689$	−12.2966	+	13.0336i	−0.468463	+	0.496542i
$690$		0			0
$691$	−9.57368	+	12.8597i	−0.364200	+	0.489205i	−0.946018	−	0.324113i	$-0.894934\pi$
$691$	−9.57368	+	12.8597i	−0.364200	+	0.489205i	0.581818	+	0.813319i	$0.302341\pi$
$692$	−5.68957	+	2.07083i	−0.216285	+	0.0787213i
$693$		0			0
$694$	−7.22724	−	2.63050i	−0.274342	−	0.0998524i
$695$	19.9089	−	13.0943i	0.755187	−	0.496694i
$696$		0			0
$697$	−14.4136	−	19.3609i	−0.545955	−	0.733345i
$698$	−3.50129	−	2.30284i	−0.132526	−	0.0871637i
$699$		0			0
$700$	−8.36916	+	27.9550i	−0.316325	+	1.05660i
$701$	−20.8919	+	36.1858i	−0.789075	+	1.36672i	0.137459	+	0.990507i	$0.456106\pi$
$701$	−20.8919	+	36.1858i	−0.789075	+	1.36672i	−0.926534	+	0.376211i	$0.877227\pi$
$702$		0			0
$703$	−7.96914	−	13.8029i	−0.300562	−	0.520588i
$704$	12.7413	−	3.01974i	0.480205	−	0.113811i
$705$		0			0
$706$	−0.734464	+	0.368862i	−0.0276419	+	0.0138823i
$707$	−1.84719	+	4.28228i	−0.0694709	+	0.161052i
$708$		0			0
$709$	0.982391	+	16.8670i	0.0368945	+	0.633453i	0.965180	+	0.261586i	$0.0842454\pi$
$709$	0.982391	+	16.8670i	0.0368945	+	0.633453i	−0.928286	+	0.371868i	$0.878718\pi$
$710$	−0.854057	−	4.84360i	−0.0320522	−	0.181777i
$711$		0			0
$712$	−1.82174	+	10.3316i	−0.0682724	+	0.387192i
$713$	2.35733	+	0.275532i	0.0882825	+	0.0103187i
$714$		0			0
$715$	−9.63515	−	32.1836i	−0.360334	−	1.20360i
$716$	−26.8944	−	6.37410i	−1.00509	−	0.238211i
$717$		0			0
$718$	−0.971560	−	2.25233i	−0.0362583	−	0.0840562i
$719$	12.7933	+	10.7349i	0.477111	+	0.400344i	0.849381	−	0.527781i	$-0.176976\pi$
$719$	12.7933	+	10.7349i	0.477111	+	0.400344i	−0.372269	+	0.928125i	$0.621420\pi$
$720$		0			0
$721$	−7.31216	+	6.13563i	−0.272319	+	0.228503i
$722$	2.12955	+	1.06950i	0.0792538	+	0.0398028i
$723$		0			0
$724$	30.6472	−	3.58214i	1.13899	−	0.133129i
$725$	−0.452704	+	7.77263i	−0.0168130	+	0.288668i
$726$		0			0
$727$	−15.1791	−	16.0889i	−0.562963	−	0.596706i	0.381887	−	0.924209i	$-0.375274\pi$
$727$	−15.1791	−	16.0889i	−0.562963	−	0.596706i	−0.944850	+	0.327503i	$0.893793\pi$
$728$	4.39701			0.162964
$729$		0			0
$730$	−7.40242			−0.273976
$731$	−21.1047	−	22.3697i	−0.780587	−	0.827374i
$732$		0			0
$733$	0.763834	−	13.1145i	0.0282128	−	0.484396i	−0.954377	−	0.298606i	$-0.903479\pi$
$733$	0.763834	−	13.1145i	0.0282128	−	0.484396i	0.982589	−	0.185790i	$-0.0594845\pi$
$734$	3.56899	−	0.417155i	0.131734	−	0.0153975i
$735$		0			0
$736$	−3.04026	−	1.52687i	−0.112065	−	0.0562813i
$737$	−11.0811	+	9.29816i	−0.408178	+	0.342502i
$738$		0			0
$739$	−34.4177	−	28.8799i	−1.26608	−	1.06236i	−0.995007	−	0.0998052i	$-0.968178\pi$
$739$	−34.4177	−	28.8799i	−1.26608	−	1.06236i	−0.271070	−	0.962560i	$-0.587378\pi$
$740$	−17.2195	−	39.9193i	−0.633002	−	1.46746i
$741$		0			0
$742$	−1.21251	−	0.287370i	−0.0445127	−	0.0105497i
$743$	−6.41571	−	21.4300i	−0.235370	−	0.786189i	−0.991310	−	0.131548i	$-0.958005\pi$
$743$	−6.41571	−	21.4300i	−0.235370	−	0.786189i	0.755940	−	0.654641i	$-0.227180\pi$
$744$		0			0
$745$	−57.4919	−	6.71984i	−2.10634	−	0.246196i
$746$	0.884944	−	5.01877i	0.0324001	−	0.183750i
$747$		0			0
$748$	2.80504	+	15.9082i	0.102563	+	0.581661i
$749$	1.06566	+	18.2967i	0.0389385	+	0.668547i
$750$		0			0
$751$	4.70782	−	10.9140i	0.171791	−	0.398256i	−0.810469	−	0.585782i	$-0.800788\pi$
$751$	4.70782	−	10.9140i	0.171791	−	0.398256i	0.982260	+	0.187526i	$0.0600469\pi$
$752$	1.42536	−	0.715845i	0.0519777	−	0.0261042i
$753$		0			0
$754$	0.562313	−	0.133271i	0.0204782	−	0.00485343i
$755$	20.0784	+	34.7768i	0.730728	+	1.26566i
$756$		0			0
$757$	−2.60890	+	4.51875i	−0.0948221	+	0.164237i	−0.909534	−	0.415629i	$-0.863562\pi$
$757$	−2.60890	+	4.51875i	−0.0948221	+	0.164237i	0.814712	+	0.579865i	$0.196895\pi$
$758$	0.481813	−	1.60937i	0.0175003	−	0.0584549i
$759$		0			0
$760$	−10.2252	−	6.72520i	−0.370906	−	0.243949i
$761$	0.417060	+	0.560209i	0.0151184	+	0.0203075i	0.809618	−	0.586957i	$-0.199674\pi$
$761$	0.417060	+	0.560209i	0.0151184	+	0.0203075i	−0.794500	+	0.607265i	$0.792267\pi$
$762$		0			0
$763$	−3.48572	+	2.29259i	−0.126191	+	0.0829974i
$764$	−37.0505	−	13.4853i	−1.34044	−	0.487880i
$765$		0			0
$766$	8.02630	−	2.92133i	0.290002	−	0.105552i
$767$	19.9302	−	26.7710i	0.719639	−	0.966643i
$768$		0			0
$769$	−7.63552	+	8.09318i	−0.275344	+	0.291848i	−0.850258	−	0.526366i	$-0.823554\pi$
$769$	−7.63552	+	8.09318i	−0.275344	+	0.291848i	0.574914	+	0.818214i	$0.305036\pi$
$770$	1.60323	−	1.69933i	0.0577765	−	0.0612395i
$771$		0			0
$772$	3.09849	−	4.16199i	0.111517	−	0.149793i
$773$	14.5554	−	5.29774i	0.523522	−	0.190546i	−0.0667217	−	0.997772i	$-0.521254\pi$
$773$	14.5554	−	5.29774i	0.523522	−	0.190546i	0.590243	+	0.807225i	$0.299032\pi$
$774$		0			0
$775$	23.8477	+	8.67985i	0.856634	+	0.311789i
$776$	−5.00565	+	3.29227i	−0.179692	+	0.118186i
$777$		0			0
$778$	−3.71346	−	4.98804i	−0.133134	−	0.178830i
$779$	14.4714	+	9.51799i	0.518491	+	0.341017i
$780$		0			0
$781$	2.71234	−	9.05983i	0.0970550	−	0.324186i
$782$	0.621316	−	1.07615i	0.0222182	−	0.0384831i
$783$		0			0
$784$	10.3603	+	17.9445i	0.370009	+	0.640875i
$785$	−37.7061	+	8.93651i	−1.34579	+	0.318958i
$786$		0			0
$787$	−31.4879	+	15.8138i	−1.12242	+	0.563702i	−0.910469	−	0.413578i	$-0.864279\pi$
$787$	−31.4879	+	15.8138i	−1.12242	+	0.563702i	−0.211954	+	0.977280i	$0.567983\pi$
$788$	12.8592	−	29.8109i	0.458089	−	1.06197i
$789$		0			0
$790$	0.752513	+	12.9202i	0.0267732	+	0.459678i
$791$	−1.89968	−	10.7736i	−0.0675449	−	0.383066i
$792$		0			0
$793$	7.33528	−	41.6004i	0.260483	−	1.47728i
$794$	4.46561	+	0.521955i	0.158479	+	0.0185235i
$795$		0			0
$796$	1.08924	+	3.63831i	0.0386070	+	0.128956i
$797$	25.7981	+	6.11427i	0.913816	+	0.216578i	0.660518	−	0.750810i	$-0.270337\pi$
$797$	25.7981	+	6.11427i	0.913816	+	0.216578i	0.253298	+	0.967388i	$0.418485\pi$
$798$		0			0
$799$	0.728735	+	1.68940i	0.0257808	+	0.0597666i
$800$	−27.8676	−	23.3837i	−0.985268	−	0.826738i
$801$		0			0
$802$	−0.856252	+	0.718481i	−0.0302353	+	0.0253704i
$803$	−12.7197	−	6.38806i	−0.448867	−	0.225430i
$804$		0			0
$805$	5.93038	−	0.693162i	0.209018	−	0.0244308i
$806$	0.109525	−	1.88047i	0.00385786	−	0.0662368i
$807$		0			0
$808$	−2.64681	−	2.80545i	−0.0931143	−	0.0986954i
$809$	4.72350			0.166070			0.0830348	−	0.996547i	$-0.473539\pi$
$809$	4.72350			0.166070			0.0830348	+	0.996547i	$0.473539\pi$
$810$		0			0
$811$	−14.2884			−0.501733			−0.250866	−	0.968022i	$-0.580716\pi$
$811$	−14.2884			−0.501733			−0.250866	+	0.968022i	$0.580716\pi$
$812$	−0.916229	−	0.971146i	−0.0321533	−	0.0340805i
$813$		0			0
$814$	−0.146304	+	2.51194i	−0.00512795	+	0.0880436i
$815$	−33.5071	+	3.91642i	−1.17370	+	0.137186i
$816$		0			0
$817$	19.7219	+	9.90471i	0.689982	+	0.346522i
$818$	2.02577	−	1.69982i	0.0708294	−	0.0594329i
$819$		0			0
$820$	36.1927	+	30.3693i	1.26391	+	1.06054i
$821$	8.66239	+	20.0817i	0.302319	+	0.700855i	0.999877	−	0.0156735i	$-0.00498924\pi$
$821$	8.66239	+	20.0817i	0.302319	+	0.700855i	−0.697558	+	0.716528i	$0.745730\pi$
$822$		0			0
$823$	22.8742	+	5.42129i	0.797346	+	0.188974i	0.609044	−	0.793137i	$-0.291553\pi$
$823$	22.8742	+	5.42129i	0.797346	+	0.188974i	0.188302	+	0.982111i	$0.439702\pi$
$824$	−2.26408	−	7.56254i	−0.0788728	−	0.263454i
$825$		0			0
$826$	2.30527	+	0.269447i	0.0802105	+	0.00937526i
$827$	−3.09330	+	17.5430i	−0.107565	+	0.610030i	0.882600	+	0.470124i	$0.155791\pi$
$827$	−3.09330	+	17.5430i	−0.107565	+	0.610030i	−0.990165	+	0.139905i	$0.955320\pi$
$828$		0			0
$829$	−9.35023	−	53.0278i	−0.324747	−	1.84173i	−0.511447	−	0.859315i	$-0.670890\pi$
$829$	−9.35023	−	53.0278i	−0.324747	−	1.84173i	0.186700	−	0.982417i	$-0.440221\pi$
$830$	0.691217	+	11.8677i	0.0239925	+	0.411935i
$831$		0			0
$832$	10.5198	−	24.3877i	0.364710	−	0.845492i
$833$	−21.3589	+	10.7269i	−0.740043	+	0.371664i
$834$		0			0
$835$	18.3727	−	4.35442i	0.635815	−	0.150691i
$836$	−5.79597	−	10.0389i	−0.200458	−	0.347203i
$837$		0			0
$838$	4.05420	−	7.02209i	0.140050	−	0.242574i
$839$	−14.9376	+	49.8951i	−0.515703	+	1.72257i	0.161591	+	0.986858i	$0.448337\pi$
$839$	−14.9376	+	49.8951i	−0.515703	+	1.72257i	−0.677295	+	0.735712i	$0.736848\pi$
$840$		0			0
$841$	23.9315	+	15.7400i	0.825225	+	0.542759i
$842$	−0.239442	−	0.321626i	−0.00825171	−	0.0110840i
$843$		0			0
$844$	16.8125	−	11.0577i	0.578709	−	0.380623i
$845$	−12.1408	−	4.41889i	−0.417656	−	0.152014i
$846$		0			0
$847$	−7.68804	+	2.79822i	−0.264164	+	0.0961480i
$848$	−9.75883	+	13.1084i	−0.335119	+	0.450144i
$849$		0			0
$850$	9.11831	−	9.66484i	0.312755	−	0.331501i
$851$	−4.41298	+	4.67749i	−0.151275	+	0.160342i
$852$		0			0
$853$	28.9997	−	38.9533i	0.992930	−	1.33374i	0.0507205	−	0.998713i	$-0.483848\pi$
$853$	28.9997	−	38.9533i	0.992930	−	1.33374i	0.942210	−	0.335024i	$-0.108744\pi$
$854$	2.76043	−	1.00472i	0.0944601	−	0.0343807i
$855$		0			0
$856$	−14.2433	−	5.18412i	−0.486825	−	0.177190i
$857$	36.4270	−	23.9584i	1.24432	−	0.818403i	0.255399	−	0.966836i	$-0.417793\pi$
$857$	36.4270	−	23.9584i	1.24432	−	0.818403i	0.988922	+	0.148433i	$0.0474229\pi$
$858$		0			0
$859$	9.73608	+	13.0778i	0.332191	+	0.446209i	0.936567	−	0.350490i	$-0.113985\pi$
$859$	9.73608	+	13.0778i	0.332191	+	0.446209i	−0.604376	+	0.796699i	$0.706577\pi$
$860$	50.2953	+	33.0797i	1.71505	+	1.12801i
$861$		0			0
$862$	1.04752	−	3.49896i	0.0356787	−	0.119175i
$863$	25.0920	−	43.4607i	0.854142	−	1.47942i	−0.0232963	−	0.999729i	$-0.507416\pi$
$863$	25.0920	−	43.4607i	0.854142	−	1.47942i	0.877439	−	0.479689i	$-0.159251\pi$
$864$		0			0
$865$	6.62352	+	11.4723i	0.225207	+	0.390069i
$866$	−1.16040	+	0.275021i	−0.0394322	+	0.00934559i
$867$		0			0
$868$	−3.88904	+	1.95315i	−0.132003	+	0.0662943i
$869$	−9.85663	+	22.8502i	−0.334363	+	0.775142i
$870$		0			0
$871$	1.70603	+	29.2914i	0.0578066	+	0.992501i
$872$	−0.599153	−	3.39796i	−0.0202899	−	0.115070i
$873$		0			0
$874$	−0.154846	+	0.878175i	−0.00523774	+	0.0297047i
$875$	39.1070	+	4.57095i	1.32206	+	0.154526i
$876$		0			0
$877$	12.8676	+	42.9809i	0.434509	+	1.45136i	0.842660	+	0.538446i	$0.180988\pi$
$877$	12.8676	+	42.9809i	0.434509	+	1.45136i	−0.408151	+	0.912914i	$0.633826\pi$
$878$	4.74706	+	1.12507i	0.160206	+	0.0379694i
$879$		0			0
$880$	−12.1355	−	28.1332i	−0.409087	−	0.948371i
$881$	−13.9661	−	11.7190i	−0.470531	−	0.394822i	0.376457	−	0.926434i	$-0.377142\pi$
$881$	−13.9661	−	11.7190i	−0.470531	−	0.394822i	−0.846988	+	0.531612i	$0.821587\pi$
$882$		0			0
$883$	−13.4700	+	11.3026i	−0.453300	+	0.380364i	−0.840659	−	0.541565i	$-0.817832\pi$
$883$	−13.4700	+	11.3026i	−0.453300	+	0.380364i	0.387359	+	0.921929i	$0.373388\pi$
$884$	29.2802	+	14.7051i	0.984801	+	0.494586i
$885$		0			0
$886$	−6.76783	+	0.791045i	−0.227370	+	0.0265757i
$887$	−1.91686	+	32.9112i	−0.0643618	+	1.10505i	0.799285	+	0.600952i	$0.205212\pi$
$887$	−1.91686	+	32.9112i	−0.0643618	+	1.10505i	−0.863647	+	0.504097i	$0.831825\pi$
$888$		0			0
$889$	8.81389	+	9.34217i	0.295608	+	0.313326i
$890$	11.3064			0.378990
$891$		0			0
$892$	−14.2279			−0.476386
$893$	−0.906047	−	0.960353i	−0.0303197	−	0.0321370i
$894$		0			0
$895$	−3.51614	+	60.3698i	−0.117532	+	2.01794i
$896$	8.21719	−	0.960452i	0.274517	−	0.0320864i
$897$		0			0
$898$	0.0937829	+	0.0470995i	0.00312957	+	0.00157173i
$899$	−0.889494	+	0.746374i	−0.0296663	+	0.0248930i
$900$		0			0
$901$	−14.4405	−	12.1170i	−0.481082	−	0.403676i
$902$	−1.08307	−	2.51084i	−0.0360623	−	0.0836018i
$903$		0			0
$904$	8.80357	+	2.08648i	0.292802	+	0.0693954i
$905$	−19.3618	−	64.6730i	−0.643609	−	2.14980i
$906$		0			0
$907$	38.9906	+	4.55734i	1.29466	+	0.151324i	0.735380	−	0.677655i	$-0.237004\pi$
$907$	38.9906	+	4.55734i	1.29466	+	0.151324i	0.559280	+	0.828979i	$0.311078\pi$
$908$	−7.84805	+	44.5085i	−0.260447	+	1.47707i
$909$		0			0
$910$	−0.822878	−	4.66678i	−0.0272782	−	0.154702i
$911$	0.885525	+	15.2039i	0.0293388	+	0.503727i	0.980684	+	0.195600i	$0.0626653\pi$
$911$	0.885525	+	15.2039i	0.0293388	+	0.503727i	−0.951345	+	0.308127i	$0.900298\pi$
$912$		0			0
$913$	−9.05376	+	20.9890i	−0.299636	+	0.694634i
$914$	−5.85486	+	2.94042i	−0.193662	+	0.0972605i
$915$		0			0
$916$	0.0942996	−	0.0223494i	0.00311575	−	0.000738445i
$917$	−6.98854	−	12.1045i	−0.230782	−	0.399726i
$918$		0			0
$919$	−7.39953	+	12.8164i	−0.244088	+	0.422773i	−0.961875	−	0.273490i	$-0.911822\pi$
$919$	−7.39953	+	12.8164i	−0.244088	+	0.422773i	0.717787	+	0.696263i	$0.245155\pi$
$920$	−1.41621	+	4.73048i	−0.0466911	+	0.155959i
$921$		0			0
$922$	8.62963	+	5.67579i	0.284202	+	0.186922i
$923$	−11.4550	−	15.3867i	−0.377046	−	0.506461i
$924$		0			0
$925$	−57.4499	+	37.7854i	−1.88894	+	1.24238i
$926$	−6.89258	−	2.50869i	−0.226504	−	0.0824407i
$927$		0			0
$928$	1.56408	−	0.569280i	0.0513436	−	0.0186875i
$929$	−18.2773	+	24.5506i	−0.599658	+	0.805480i	−0.993516	−	0.113691i	$-0.963733\pi$
$929$	−18.2773	+	24.5506i	−0.599658	+	0.805480i	0.393858	+	0.919171i	$0.371140\pi$
$930$		0			0
$931$	11.7702	−	12.4757i	0.385753	−	0.408874i
$932$	29.8575	−	31.6471i	0.978016	−	1.03664i
$933$		0			0
$934$	1.94252	−	2.60925i	0.0635610	−	0.0853773i
$935$	33.2109	−	12.0878i	1.08611	−	0.395313i
$936$		0			0
$937$	3.22880	+	1.17519i	0.105480	+	0.0383917i	0.394221	−	0.919016i	$-0.371014\pi$
$937$	3.22880	+	1.17519i	0.105480	+	0.0383917i	−0.288741	+	0.957407i	$0.593237\pi$
$938$	−1.70475	+	1.12123i	−0.0556621	+	0.0366095i
$939$		0			0
$940$	−2.15060	−	2.88876i	−0.0701450	−	0.0942211i
$941$	−16.1846	−	10.6448i	−0.527603	−	0.347010i	0.257596	−	0.966253i	$-0.417069\pi$
$941$	−16.1846	−	10.6448i	−0.527603	−	0.347010i	−0.785200	+	0.619242i	$0.787440\pi$
$942$		0			0
$943$	2.00432	−	6.69491i	0.0652698	−	0.218016i
$944$	15.2192	−	26.3605i	0.495344	−	0.857961i
$945$		0			0
$946$	−1.74206	−	3.01734i	−0.0566393	−	0.0981022i
$947$	−13.4174	+	3.17998i	−0.436006	+	0.103335i	−0.442757	−	0.896642i	$-0.645999\pi$
$947$	−13.4174	+	3.17998i	−0.436006	+	0.103335i	0.00675038	+	0.999977i	$0.497851\pi$
$948$		0			0
$949$	−25.8001	+	12.9573i	−0.837508	+	0.420612i
$950$	−3.77665	+	8.75525i	−0.122531	+	0.284058i
$951$		0			0
$952$	0.268961	+	4.61788i	0.00871707	+	0.149666i
$953$	6.51937	+	36.9732i	0.211183	+	1.19768i	0.887408	+	0.460984i	$0.152503\pi$
$953$	6.51937	+	36.9732i	0.211183	+	1.19768i	−0.676225	+	0.736695i	$0.736385\pi$
$954$		0			0
$955$	−14.9797	+	84.9541i	−0.484732	+	2.74905i
$956$	39.5966	+	4.62818i	1.28065	+	0.149686i
$957$		0			0
$958$	1.80103	+	6.01586i	0.0581887	+	0.194364i
$959$	−0.335452	−	0.0795035i	−0.0108323	−	0.00256730i
$960$		0			0
$961$	−10.7794	−	24.9894i	−0.347722	−	0.806110i
$962$	3.90972	+	3.28064i	0.126054	+	0.105772i
$963$		0			0
$964$	42.8154	−	35.9264i	1.37899	−	1.15711i
$965$	−10.1448	−	5.09492i	−0.326574	−	0.164011i
$966$		0			0
$967$	−24.4158	+	2.85380i	−0.785160	+	0.0917720i	−0.499220	−	0.866475i	$-0.666380\pi$
$967$	−24.4158	+	2.85380i	−0.785160	+	0.0917720i	−0.285940	+	0.958248i	$0.592306\pi$
$968$	0.393420	−	6.75476i	0.0126450	−	0.217106i
$969$		0			0
$970$	4.43104	+	4.69663i	0.142272	+	0.150800i
$971$	−13.0415			−0.418522			−0.209261	−	0.977860i	$-0.567106\pi$
$971$	−13.0415			−0.418522			−0.209261	+	0.977860i	$0.567106\pi$
$972$		0			0
$973$	6.46310			0.207197
$974$	0.448877	+	0.475782i	0.0143829	+	0.0152450i
$975$		0			0
$976$	2.24005	−	38.4602i	0.0717023	−	1.23108i
$977$	48.1120	−	5.62348i	1.53924	−	0.179911i	0.696233	−	0.717816i	$-0.254858\pi$
$977$	48.1120	−	5.62348i	1.53924	−	0.179911i	0.843006	+	0.537905i	$0.180784\pi$
$978$		0			0
$979$	19.4279	+	9.75704i	0.620917	+	0.311836i
$980$	35.8392	−	30.0727i	1.14484	−	0.960636i
$981$		0			0
$982$	7.37186	+	6.18573i	0.235246	+	0.197394i
$983$	13.1111	+	30.3950i	0.418179	+	0.969449i	0.988938	+	0.148331i	$0.0473900\pi$
$983$	13.1111	+	30.3950i	0.418179	+	0.969449i	−0.570759	+	0.821118i	$0.693351\pi$
$984$		0			0
$985$	−69.1176	−	16.3812i	−2.20227	−	0.521948i
$986$	0.174361	+	0.582407i	0.00555279	+	0.0185476i
$987$		0			0
$988$	−23.3537	−	2.72966i	−0.742980	−	0.0868420i
$989$	1.54623	−	8.76910i	0.0491672	−	0.278841i
$990$		0			0
$991$	−3.02007	−	17.1276i	−0.0959355	−	0.544078i	−0.994457	−	0.105147i	$-0.966469\pi$
$991$	−3.02007	−	17.1276i	−0.0959355	−	0.544078i	0.898521	−	0.438930i	$-0.144642\pi$
$992$	−0.315459	−	5.41622i	−0.0100158	−	0.171965i
$993$		0			0
$994$	0.528364	−	1.22489i	0.0167587	−	0.0388510i
$995$	7.42546	−	3.72921i	0.235403	−	0.118224i
$996$		0			0
$997$	−16.8175	+	3.98582i	−0.532615	+	0.126232i	−0.488119	−	0.872777i	$-0.662317\pi$
$997$	−16.8175	+	3.98582i	−0.532615	+	0.126232i	−0.0444969	+	0.999010i	$0.514168\pi$
$998$	0.300413	+	0.520330i	0.00950940	+	0.0164708i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.199.5		144
3.2	odd	2		81.2.g.a.22.4	✓	144
9.2	odd	6		729.2.g.d.352.4		144
9.4	even	3		729.2.g.b.595.4		144
9.5	odd	6		729.2.g.c.595.5		144
9.7	even	3		729.2.g.a.352.5		144
81.11	odd	54		81.2.g.a.70.4	yes	144
81.16	even	27		729.2.g.a.379.5		144
81.31	even	27		6561.2.a.d.1.32		72
81.38	odd	54		729.2.g.c.136.5		144
81.43	even	27		729.2.g.b.136.4		144
81.50	odd	54		6561.2.a.c.1.41		72
81.65	odd	54		729.2.g.d.379.4		144
81.70	even	27	inner	243.2.g.a.127.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.4	✓	144	3.2	odd	2
81.2.g.a.70.4	yes	144	81.11	odd	54
243.2.g.a.127.5		144	81.70	even	27	inner
243.2.g.a.199.5		144	1.1	even	1	trivial
729.2.g.a.352.5		144	9.7	even	3
729.2.g.a.379.5		144	81.16	even	27
729.2.g.b.136.4		144	81.43	even	27
729.2.g.b.595.4		144	9.4	even	3
729.2.g.c.136.5		144	81.38	odd	54
729.2.g.c.595.5		144	9.5	odd	6
729.2.g.d.352.4		144	9.2	odd	6
729.2.g.d.379.4		144	81.65	odd	54
6561.2.a.c.1.41		72	81.50	odd	54
6561.2.a.d.1.32		72	81.31	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.165895 + 0.175839i) q^{2} +(0.112892 - 1.93827i) q^{4} +(-4.21919 + 0.493153i) q^{5} +(-1.02960 - 0.517085i) q^{7} +(0.729927 - 0.612481i) q^{8} +(-0.786660 - 0.660086i) q^{10} +(-0.782094 - 1.81310i) q^{11} +(-3.89722 - 0.923659i) q^{13} +(-0.0798824 - 0.266826i) q^{14} +(-3.62807 - 0.424061i) q^{16} +(0.731666 - 4.14948i) q^{17} +(0.525049 + 2.97770i) q^{19} +(0.479554 + 8.23363i) q^{20} +(0.189067 - 0.438307i) q^{22} +(1.09019 - 0.547514i) q^{23} +(12.6932 - 3.00834i) q^{25} +(-0.484116 - 0.838513i) q^{26} +(-1.11849 + 1.93728i) q^{28} +(-0.171179 + 0.571777i) q^{29} +(1.62541 + 1.06905i) q^{31} +(-1.66532 - 2.23691i) q^{32} +(0.851020 - 0.559725i) q^{34} +(4.59909 + 1.67393i) q^{35} +(-4.95333 + 1.80287i) q^{37} +(-0.436492 + 0.586310i) q^{38} +(-2.77766 + 2.94414i) q^{40} +(3.93113 - 4.16676i) q^{41} +(4.35863 - 5.85466i) q^{43} +(-3.60257 + 1.31123i) q^{44} +(0.277132 + 0.100868i) q^{46} +(-0.364825 + 0.239949i) q^{47} +(-3.38741 - 4.55008i) q^{49} +(2.63472 + 1.73288i) q^{50} +(-2.23027 + 7.44961i) q^{52} +(2.23695 - 3.87450i) q^{53} +(4.19394 + 7.26412i) q^{55} +(-1.06824 + 0.253177i) q^{56} +(-0.128938 + 0.0647553i) q^{58} +(-3.30053 + 7.65148i) q^{59} +(0.613247 + 10.5290i) q^{61} +(0.0816677 + 0.463161i) q^{62} +(-1.15153 + 6.53063i) q^{64} +(16.8986 + 1.97517i) q^{65} +(-2.10105 - 7.01801i) q^{67} +(-7.96024 - 1.88661i) q^{68} +(0.468625 + 1.08640i) q^{70} +(3.66891 + 3.07858i) q^{71} +(5.52198 - 4.63349i) q^{73} +(-1.13875 - 0.571901i) q^{74} +(5.83087 - 0.681531i) q^{76} +(-0.132281 + 2.27118i) q^{77} +(-8.64862 - 9.16700i) q^{79} +15.5167 q^{80} +1.38483 q^{82} +(-7.94414 - 8.42030i) q^{83} +(-1.04071 + 17.8683i) q^{85} +(1.75255 - 0.204844i) q^{86} +(-1.68136 - 0.844410i) q^{88} +(-8.43420 + 7.07713i) q^{89} +(3.53497 + 2.96620i) q^{91} +(-0.938159 - 2.17490i) q^{92} +(-0.102715 - 0.0243439i) q^{94} +(-3.68374 - 12.3046i) q^{95} +(-6.24523 - 0.729963i) q^{97} +(0.238125 - 1.35047i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

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