LMFDB - Embedded newform 243.2.g.a.208.7

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			208.7
Character	$\chi$	$=$	243.208
Dual form			243.2.g.a.118.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.96496 + 0.465704i) q^{2} +(1.85693 + 0.932584i) q^{4} +(1.65302 - 2.22039i) q^{5} +(0.510715 + 0.335902i) q^{7} +(0.120591 + 0.101188i) q^{8} +(4.28217 - 3.59317i) q^{10} +(-3.71952 + 0.434749i) q^{11} +(-0.980843 + 3.27624i) q^{13} +(0.847104 + 0.897877i) q^{14} +(-2.29190 - 3.07856i) q^{16} +(1.31516 + 7.45862i) q^{17} +(0.132568 - 0.751830i) q^{19} +(5.14024 - 2.58153i) q^{20} +(-7.51117 - 0.877930i) q^{22} +(1.81630 - 1.19460i) q^{23} +(-0.763650 - 2.55077i) q^{25} +(-3.45308 + 5.98091i) q^{26} +(0.635103 + 1.10003i) q^{28} +(-3.11741 + 3.30426i) q^{29} +(-0.475949 - 8.17173i) q^{31} +(-3.19450 - 7.40569i) q^{32} +(-0.889281 + 15.2684i) q^{34} +(1.59006 - 0.578734i) q^{35} +(3.96908 + 1.44463i) q^{37} +(0.610621 - 1.41558i) q^{38} +(0.424016 - 0.100494i) q^{40} +(-8.79832 + 2.08524i) q^{41} +(0.695014 - 1.61122i) q^{43} +(-7.31231 - 2.66146i) q^{44} +(4.12528 - 1.50148i) q^{46} +(0.684001 - 11.7438i) q^{47} +(-2.62456 - 6.08441i) q^{49} +(-0.312638 - 5.36779i) q^{50} +(-4.87673 + 5.16903i) q^{52} +(2.80062 + 4.85082i) q^{53} +(-5.18313 + 8.97744i) q^{55} +(0.0275984 + 0.0921849i) q^{56} +(-7.66439 + 5.04095i) q^{58} +(1.50297 + 0.175672i) q^{59} +(2.70194 - 1.35697i) q^{61} +(2.87039 - 16.2788i) q^{62} +(-1.49529 - 8.48019i) q^{64} +(5.65319 + 7.59356i) q^{65} +(5.25122 + 5.56597i) q^{67} +(-4.51364 + 15.0766i) q^{68} +(3.39392 - 0.396693i) q^{70} +(5.19850 - 4.36206i) q^{71} +(0.438511 + 0.367955i) q^{73} +(7.12633 + 4.68706i) q^{74} +(0.947314 - 1.27246i) q^{76} +(-2.04565 - 1.02736i) q^{77} +(8.96673 + 2.12515i) q^{79} -10.6242 q^{80} -18.2595 q^{82} +(6.02162 + 1.42715i) q^{83} +(18.7350 + 9.40909i) q^{85} +(2.11603 - 2.84232i) q^{86} +(-0.492531 - 0.323943i) q^{88} +(3.52742 + 2.95986i) q^{89} +(-1.60143 + 1.34376i) q^{91} +(4.48680 - 0.524431i) q^{92} +(6.81319 - 22.7577i) q^{94} +(-1.45022 - 1.53714i) q^{95} +(-6.28024 - 8.43582i) q^{97} +(-2.32362 - 13.1779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.96496	+	0.465704i	1.38944	+	0.329303i	0.856192	−	0.516658i	$-0.172824\pi$
$2$	1.96496	+	0.465704i	1.38944	+	0.329303i	0.533246	+	0.845961i	$0.320972\pi$
$3$		0			0
$3$		0			0
$4$	1.85693	+	0.932584i	0.928464	+	0.466292i
$5$	1.65302	−	2.22039i	0.739254	−	0.992990i	−0.260369	−	0.965509i	$-0.583844\pi$
$5$	1.65302	−	2.22039i	0.739254	−	0.992990i	0.999622	−	0.0274807i	$-0.00874849\pi$
$6$		0			0
$7$	0.510715	+	0.335902i	0.193032	+	0.126959i	0.642346	−	0.766415i	$-0.277961\pi$
$7$	0.510715	+	0.335902i	0.193032	+	0.126959i	−0.449314	+	0.893374i	$0.648332\pi$
$8$	0.120591	+	0.101188i	0.0426353	+	0.0357753i
$9$		0			0
$10$	4.28217	−	3.59317i	1.35414	−	1.13626i
$11$	−3.71952	+	0.434749i	−1.12148	+	0.131082i	−0.656561	−	0.754273i	$-0.727989\pi$
$11$	−3.71952	+	0.434749i	−1.12148	+	0.131082i	−0.464916	+	0.885355i	$0.653915\pi$
$12$		0			0
$13$	−0.980843	+	3.27624i	−0.272037	+	0.908666i	0.707383	+	0.706831i	$0.249876\pi$
$13$	−0.980843	+	3.27624i	−0.272037	+	0.908666i	−0.979419	+	0.201835i	$0.935309\pi$
$14$	0.847104	+	0.897877i	0.226398	+	0.239968i
$15$		0			0
$16$	−2.29190	−	3.07856i	−0.572976	−	0.769640i
$17$	1.31516	+	7.45862i	0.318972	+	1.80898i	0.549030	+	0.835803i	$0.314997\pi$
$17$	1.31516	+	7.45862i	0.318972	+	1.80898i	−0.230058	+	0.973177i	$0.573891\pi$
$18$		0			0
$19$	0.132568	−	0.751830i	0.0304132	−	0.172482i	−0.965818	−	0.259222i	$-0.916534\pi$
$19$	0.132568	−	0.751830i	0.0304132	−	0.172482i	0.996231	+	0.0867403i	$0.0276450\pi$
$20$	5.14024	−	2.58153i	1.14939	−	0.577247i
$21$		0			0
$22$	−7.51117	−	0.877930i	−1.60139	−	0.187175i
$23$	1.81630	−	1.19460i	0.378724	−	0.249091i	−0.345847	−	0.938291i	$-0.612408\pi$
$23$	1.81630	−	1.19460i	0.378724	−	0.249091i	0.724571	+	0.689200i	$0.242038\pi$
$24$		0			0
$25$	−0.763650	−	2.55077i	−0.152730	−	0.510153i
$26$	−3.45308	+	5.98091i	−0.677205	+	1.17295i
$27$		0			0
$28$	0.635103	+	1.10003i	0.120023	+	0.207886i
$29$	−3.11741	+	3.30426i	−0.578888	+	0.613585i	−0.948952	−	0.315421i	$-0.897854\pi$
$29$	−3.11741	+	3.30426i	−0.578888	+	0.613585i	0.370064	+	0.929006i	$0.379336\pi$
$30$		0			0
$31$	−0.475949	−	8.17173i	−0.0854830	−	1.46769i	−0.719568	−	0.694422i	$-0.755660\pi$
$31$	−0.475949	−	8.17173i	−0.0854830	−	1.46769i	0.634085	−	0.773264i	$-0.281377\pi$
$32$	−3.19450	−	7.40569i	−0.564714	−	1.30915i
$33$		0			0
$34$	−0.889281	+	15.2684i	−0.152510	+	2.61850i
$35$	1.59006	−	0.578734i	0.268769	−	0.0978239i
$36$		0			0
$37$	3.96908	+	1.44463i	0.652513	+	0.237495i	0.647001	−	0.762489i	$-0.276023\pi$
$37$	3.96908	+	1.44463i	0.652513	+	0.237495i	0.00551256	+	0.999985i	$0.498245\pi$
$38$	0.610621	−	1.41558i	0.0990559	−	0.229637i
$39$		0			0
$40$	0.424016	−	0.100494i	0.0670428	−	0.0158894i
$41$	−8.79832	+	2.08524i	−1.37407	+	0.325660i	−0.850343	−	0.526229i	$-0.823606\pi$
$41$	−8.79832	+	2.08524i	−1.37407	+	0.325660i	−0.523723	+	0.851888i	$0.675457\pi$
$42$		0			0
$43$	0.695014	−	1.61122i	0.105989	−	0.245709i	−0.856966	−	0.515373i	$-0.827653\pi$
$43$	0.695014	−	1.61122i	0.105989	−	0.245709i	0.962955	+	0.269664i	$0.0869126\pi$
$44$	−7.31231	−	2.66146i	−1.10237	−	0.401231i
$45$		0			0
$46$	4.12528	−	1.50148i	0.608240	−	0.221381i
$47$	0.684001	−	11.7438i	0.0997718	−	1.71302i	−0.462963	−	0.886378i	$-0.653214\pi$
$47$	0.684001	−	11.7438i	0.0997718	−	1.71302i	0.562734	−	0.826638i	$-0.309749\pi$
$48$		0			0
$49$	−2.62456	−	6.08441i	−0.374937	−	0.869202i
$50$	−0.312638	−	5.36779i	−0.0442137	−	0.759121i
$51$		0			0
$52$	−4.87673	+	5.16903i	−0.676280	+	0.716815i
$53$	2.80062	+	4.85082i	0.384695	+	0.666312i	0.991727	−	0.128366i	$-0.0409732\pi$
$53$	2.80062	+	4.85082i	0.384695	+	0.666312i	−0.607032	+	0.794678i	$0.707640\pi$
$54$		0			0
$55$	−5.18313	+	8.97744i	−0.698893	+	1.21052i
$56$	0.0275984	+	0.0921849i	0.00368799	+	0.0123187i
$57$		0			0
$58$	−7.66439	+	5.04095i	−1.00638	+	0.661909i
$59$	1.50297	+	0.175672i	0.195670	+	0.0228705i	0.213363	−	0.976973i	$-0.431558\pi$
$59$	1.50297	+	0.175672i	0.195670	+	0.0228705i	−0.0176936	+	0.999843i	$0.505632\pi$
$60$		0			0
$61$	2.70194	−	1.35697i	0.345949	−	0.173742i	−0.267337	−	0.963603i	$-0.586144\pi$
$61$	2.70194	−	1.35697i	0.345949	−	0.173742i	0.613286	+	0.789861i	$0.289847\pi$
$62$	2.87039	−	16.2788i	0.364540	−	2.06741i
$63$		0			0
$64$	−1.49529	−	8.48019i	−0.186911	−	1.06002i
$65$	5.65319	+	7.59356i	0.701192	+	0.941865i
$66$		0			0
$67$	5.25122	+	5.56597i	0.641539	+	0.679992i	0.963790	−	0.266662i	$-0.0859209\pi$
$67$	5.25122	+	5.56597i	0.641539	+	0.679992i	−0.322251	+	0.946654i	$0.604439\pi$
$68$	−4.51364	+	15.0766i	−0.547359	+	1.82831i
$69$		0			0
$70$	3.39392	−	0.396693i	0.405651	−	0.0474138i
$71$	5.19850	−	4.36206i	0.616948	−	0.517681i	−0.279895	−	0.960031i	$-0.590299\pi$
$71$	5.19850	−	4.36206i	0.616948	−	0.517681i	0.896843	+	0.442350i	$0.145855\pi$
$72$		0			0
$73$	0.438511	+	0.367955i	0.0513238	+	0.0430658i	0.668089	−	0.744082i	$-0.267113\pi$
$73$	0.438511	+	0.367955i	0.0513238	+	0.0430658i	−0.616765	+	0.787147i	$0.711557\pi$
$74$	7.12633	+	4.68706i	0.828419	+	0.544859i
$75$		0			0
$76$	0.947314	−	1.27246i	0.108664	−	0.145962i
$77$	−2.04565	−	1.02736i	−0.233123	−	0.117079i
$78$		0			0
$79$	8.96673	+	2.12515i	1.00884	+	0.239098i	0.701628	−	0.712544i	$-0.252457\pi$
$79$	8.96673	+	2.12515i	1.00884	+	0.239098i	0.307208	+	0.951642i	$0.400605\pi$
$80$	−10.6242			−1.18782
$81$		0			0
$82$	−18.2595			−2.01642
$83$	6.02162	+	1.42715i	0.660959	+	0.156650i	0.547387	−	0.836880i	$-0.315623\pi$
$83$	6.02162	+	1.42715i	0.660959	+	0.156650i	0.113572	+	0.993530i	$0.463771\pi$
$84$		0			0
$85$	18.7350	+	9.40909i	2.03210	+	1.02056i
$86$	2.11603	−	2.84232i	0.228177	−	0.306495i
$87$		0			0
$88$	−0.492531	−	0.323943i	−0.0525040	−	0.0345324i
$89$	3.52742	+	2.95986i	0.373906	+	0.313744i	0.810304	−	0.586009i	$-0.199302\pi$
$89$	3.52742	+	2.95986i	0.373906	+	0.313744i	−0.436399	+	0.899753i	$0.643746\pi$
$90$		0			0
$91$	−1.60143	+	1.34376i	−0.167875	+	0.140864i
$92$	4.48680	−	0.524431i	0.467781	−	0.0546757i
$93$		0			0
$94$	6.81319	−	22.7577i	0.702727	−	2.34727i
$95$	−1.45022	−	1.53714i	−0.148789	−	0.157708i
$96$		0			0
$97$	−6.28024	−	8.43582i	−0.637661	−	0.856528i	0.359396	−	0.933185i	$-0.382983\pi$
$97$	−6.28024	−	8.43582i	−0.637661	−	0.856528i	−0.997058	+	0.0766573i	$0.975575\pi$
$98$	−2.32362	−	13.1779i	−0.234721	−	1.33117i
$99$		0			0
$100$	0.960763	−	5.44876i	0.0960763	−	0.544876i
$101$	−2.18810	+	1.09890i	−0.217724	+	0.109345i	−0.554318	−	0.832305i	$-0.687021\pi$
$101$	−2.18810	+	1.09890i	−0.217724	+	0.109345i	0.336595	+	0.941650i	$0.390725\pi$
$102$		0			0
$103$	−16.9425	−	1.98030i	−1.66940	−	0.195125i	−0.771777	−	0.635893i	$-0.780632\pi$
$103$	−16.9425	−	1.98030i	−1.66940	−	0.195125i	−0.897621	+	0.440768i	$0.854706\pi$
$104$	−0.449797	+	0.295836i	−0.0441062	+	0.0290091i
$105$		0			0
$106$	3.24407	+	10.8359i	0.315092	+	1.05248i
$107$	−0.402056	+	0.696381i	−0.0388682	+	0.0673217i	−0.884805	−	0.465961i	$-0.845709\pi$
$107$	−0.402056	+	0.696381i	−0.0388682	+	0.0673217i	0.845937	+	0.533283i	$0.179042\pi$
$108$		0			0
$109$	2.11135	+	3.65696i	0.202230	+	0.350273i	0.949247	−	0.314532i	$-0.101848\pi$
$109$	2.11135	+	3.65696i	0.202230	+	0.350273i	−0.747016	+	0.664806i	$0.768514\pi$
$110$	−14.3655	+	15.2265i	−1.36969	+	1.45179i
$111$		0			0
$112$	−0.136413	−	2.34212i	−0.0128898	−	0.221310i
$113$	4.88889	+	11.3337i	0.459908	+	1.06619i	0.977572	+	0.210602i	$0.0675425\pi$
$113$	4.88889	+	11.3337i	0.459908	+	1.06619i	−0.517664	+	0.855584i	$0.673198\pi$
$114$		0			0
$115$	0.349902	−	6.00759i	0.0326286	−	0.560211i
$116$	−8.87030	+	3.22852i	−0.823586	+	0.299761i
$117$		0			0
$118$	2.87146	+	1.04513i	0.264339	+	0.0962116i
$119$	−1.83370	+	4.25099i	−0.168095	+	0.389688i
$120$		0			0
$121$	2.94230	−	0.697338i	0.267482	−	0.0633944i
$122$	5.94116	−	1.40808i	0.537888	−	0.127482i
$123$		0			0
$124$	6.73702	−	15.6182i	0.605002	−	1.40255i
$125$	6.07999	+	2.21294i	0.543811	+	0.197931i
$126$		0			0
$127$	−9.37360	+	3.41171i	−0.831772	+	0.302740i	−0.722586	−	0.691281i	$-0.757047\pi$
$127$	−9.37360	+	3.41171i	−0.831772	+	0.302740i	−0.109186	+	0.994021i	$0.534824\pi$
$128$	0.0731698	−	1.25628i	0.00646736	−	0.111040i
$129$		0			0
$130$	7.57195	+	17.5538i	0.664104	+	1.53957i
$131$	0.319398	+	5.48385i	0.0279059	+	0.479127i	0.983091	+	0.183117i	$0.0586189\pi$
$131$	0.319398	+	5.48385i	0.0279059	+	0.479127i	−0.955185	+	0.296009i	$0.904344\pi$
$132$		0			0
$133$	0.320246	−	0.339441i	0.0277688	−	0.0294333i
$134$	7.72636	+	13.3824i	0.667456	+	1.15607i
$135$		0			0
$136$	−0.596125	+	1.03252i	−0.0511173	+	0.0885378i
$137$	−4.36818	−	14.5907i	−0.373199	−	1.24657i	−0.914102	−	0.405485i	$-0.867103\pi$
$137$	−4.36818	−	14.5907i	−0.373199	−	1.24657i	0.540903	−	0.841085i	$-0.318083\pi$
$138$		0			0
$139$	−13.3814	+	8.80109i	−1.13500	+	0.746498i	−0.970791	−	0.239928i	$-0.922876\pi$
$139$	−13.3814	+	8.80109i	−1.13500	+	0.746498i	−0.164205	+	0.986426i	$0.552506\pi$
$140$	3.49234	+	0.408196i	0.295157	+	0.0344989i
$141$		0			0
$142$	12.2463	−	6.15031i	1.02768	−	0.516123i
$143$	2.22392	−	12.6125i	0.185973	−	1.05471i
$144$		0			0
$145$	2.18361	+	12.3839i	0.181339	+	1.02842i
$146$	0.690299	+	0.927233i	0.0571296	+	0.0767384i
$147$		0			0
$148$	6.02306	+	6.38407i	0.495093	+	0.524768i
$149$	2.53544	−	8.46898i	0.207712	−	0.693806i	−0.789118	−	0.614242i	$-0.789462\pi$
$149$	2.53544	−	8.46898i	0.207712	−	0.693806i	0.996830	−	0.0795639i	$-0.0253528\pi$
$150$		0			0
$151$	−0.981167	+	0.114682i	−0.0798462	+	0.00933268i	−0.155922	−	0.987769i	$-0.549835\pi$
$151$	−0.981167	+	0.114682i	−0.0798462	+	0.00933268i	0.0760760	+	0.997102i	$0.475761\pi$
$152$	0.0920625	−	0.0772496i	0.00746726	−	0.00626577i
$153$		0			0
$154$	−3.54117	−	2.97139i	−0.285355	−	0.239442i
$155$	−18.9312	−	12.4512i	−1.52059	−	1.00011i
$156$		0			0
$157$	10.8674	−	14.5975i	0.867314	−	1.16500i	−0.117789	−	0.993039i	$-0.537581\pi$
$157$	10.8674	−	14.5975i	0.867314	−	1.16500i	0.985103	−	0.171966i	$-0.0550119\pi$
$158$	16.6296	+	8.35169i	1.32298	+	0.664425i
$159$		0			0
$160$	−21.7241	−	5.14872i	−1.71744	−	0.407042i
$161$	1.32888			0.104730
$162$		0			0
$163$	17.1469			1.34305			0.671524	−	0.740983i	$-0.265640\pi$
$163$	17.1469			1.34305			0.671524	+	0.740983i	$0.265640\pi$
$164$	−18.2825	−	4.33303i	−1.42762	−	0.338353i
$165$		0			0
$166$	11.1676	+	5.60859i	0.866776	+	0.435311i
$167$	−3.52393	+	4.73346i	−0.272690	+	0.366286i	−0.917280	−	0.398242i	$-0.869620\pi$
$167$	−3.52393	+	4.73346i	−0.272690	+	0.366286i	0.644591	+	0.764528i	$0.277028\pi$
$168$		0			0
$169$	1.08962	+	0.716658i	0.0838173	+	0.0551275i
$170$	32.4318	+	27.2135i	2.48740	+	2.08718i
$171$		0			0
$172$	2.79319	−	2.34377i	0.212979	−	0.178711i
$173$	8.93192	−	1.04399i	0.679081	−	0.0793732i	0.230442	−	0.973086i	$-0.425983\pi$
$173$	8.93192	−	1.04399i	0.679081	−	0.0793732i	0.448639	+	0.893713i	$0.351909\pi$
$174$		0			0
$175$	0.466802	−	1.55923i	0.0352869	−	0.117866i
$176$	9.86317	+	10.4544i	0.743465	+	0.788027i
$177$		0			0
$178$	5.55283	+	7.45874i	0.416202	+	0.559056i
$179$	−0.223820	−	1.26935i	−0.0167291	−	0.0948754i	0.975300	−	0.220884i	$-0.0708943\pi$
$179$	−0.223820	−	1.26935i	−0.0167291	−	0.0948754i	−0.992029	+	0.126009i	$0.959783\pi$
$180$		0			0
$181$	0.645386	−	3.66017i	0.0479712	−	0.272058i	−0.951382	−	0.308013i	$-0.900336\pi$
$181$	0.645386	−	3.66017i	0.0479712	−	0.272058i	0.999353	+	0.0359546i	$0.0114472\pi$
$182$	−3.77254	+	1.89464i	−0.279639	+	0.140440i
$183$		0			0
$184$	0.339908	+	0.0397295i	0.0250583	+	0.00292890i
$185$	9.76862	−	6.42492i	0.718203	−	0.472370i
$186$		0			0
$187$	−8.13437	−	27.1707i	−0.594844	−	1.98692i
$188$	12.2223	−	21.1696i	0.891400	−	1.54395i
$189$		0			0
$190$	−2.13377	−	3.69580i	−0.154800	−	0.268122i
$191$	5.00273	−	5.30258i	0.361985	−	0.383681i	−0.520627	−	0.853784i	$-0.674302\pi$
$191$	5.00273	−	5.30258i	0.361985	−	0.383681i	0.882612	+	0.470103i	$0.155783\pi$
$192$		0			0
$193$	0.559769	+	9.61086i	0.0402931	+	0.691805i	0.956614	+	0.291360i	$0.0941076\pi$
$193$	0.559769	+	9.61086i	0.0402931	+	0.691805i	−0.916321	+	0.400446i	$0.868855\pi$
$194$	−8.41182	−	19.5008i	−0.603934	−	1.40008i
$195$		0			0
$196$	0.800610	−	13.7459i	0.0571864	−	0.981853i
$197$	−4.63898	+	1.68845i	−0.330513	+	0.120297i	−0.501946	−	0.864899i	$-0.667383\pi$
$197$	−4.63898	+	1.68845i	−0.330513	+	0.120297i	0.171433	+	0.985196i	$0.445160\pi$
$198$		0			0
$199$	−2.36550	−	0.860973i	−0.167686	−	0.0610327i	0.256813	−	0.966461i	$-0.417328\pi$
$199$	−2.36550	−	0.860973i	−0.167686	−	0.0610327i	−0.424499	+	0.905428i	$0.639550\pi$
$200$	0.166017	−	0.384872i	0.0117392	−	0.0272145i
$201$		0			0
$202$	−4.81129	+	1.14030i	−0.338521	+	0.0802309i
$203$	−2.70201	+	0.640389i	−0.189644	+	0.0449465i
$204$		0			0
$205$	−9.91376	+	22.9827i	−0.692407	+	1.60518i
$206$	−32.3692	−	11.7814i	−2.25527	−	0.820851i
$207$		0			0
$208$	12.3341	−	4.48925i	0.855217	−	0.311273i
$209$	−0.166231	+	2.85408i	−0.0114984	+	0.197421i
$210$		0			0
$211$	2.76773	+	6.41632i	0.190538	+	0.441718i	0.986528	−	0.163593i	$-0.0523083\pi$
$211$	2.76773	+	6.41632i	0.190538	+	0.441718i	−0.795990	+	0.605310i	$0.793049\pi$
$212$	0.676756	+	11.6194i	0.0464798	+	0.798027i
$213$		0			0
$214$	−1.11433	+	1.18112i	−0.0761741	+	0.0807399i
$215$	−2.42868	−	4.20659i	−0.165634	−	0.286887i
$216$		0			0
$217$	2.50183	−	4.33330i	0.169835	−	0.294163i
$218$	2.44565	+	8.16905i	0.165641	+	0.553278i
$219$		0			0
$220$	−17.9969	+	11.8368i	−1.21335	+	0.798034i
$221$	−25.7262	−	3.00696i	−1.73053	−	0.202270i
$222$		0			0
$223$	−16.0838	+	8.07758i	−1.07705	+	0.540915i	−0.896678	−	0.442684i	$-0.854026\pi$
$223$	−16.0838	+	8.07758i	−1.07705	+	0.540915i	−0.180372	+	0.983598i	$0.557730\pi$
$224$	0.856110	−	4.85524i	0.0572012	−	0.324404i
$225$		0			0
$226$	4.32831	+	24.5471i	0.287915	+	1.63285i
$227$	0.366363	+	0.492111i	0.0243164	+	0.0326626i	0.814115	−	0.580704i	$-0.197222\pi$
$227$	0.366363	+	0.492111i	0.0243164	+	0.0326626i	−0.789799	+	0.613366i	$0.789815\pi$
$228$		0			0
$229$	3.42793	+	3.63340i	0.226524	+	0.240102i	0.830660	−	0.556779i	$-0.187963\pi$
$229$	3.42793	+	3.63340i	0.226524	+	0.240102i	−0.604136	+	0.796881i	$0.706482\pi$
$230$	3.48531	−	11.6417i	0.229814	−	0.767633i
$231$		0			0
$232$	−0.710282	+	0.0830200i	−0.0466323	+	0.00545053i
$233$	−10.0792	+	8.45747i	−0.660311	+	0.554067i	−0.910180	−	0.414213i	$-0.864057\pi$
$233$	−10.0792	+	8.45747i	−0.660311	+	0.554067i	0.249869	+	0.968280i	$0.419613\pi$
$234$		0			0
$235$	−24.9453	−	20.9316i	−1.62725	−	1.36543i
$236$	2.62707	+	1.72785i	0.171008	+	0.112474i
$237$		0			0
$238$	−5.58285	+	7.49907i	−0.361882	+	0.486092i
$239$	8.13043	+	4.08325i	0.525914	+	0.264124i	0.691886	−	0.722007i	$-0.256780\pi$
$239$	8.13043	+	4.08325i	0.525914	+	0.264124i	−0.165972	+	0.986130i	$0.553076\pi$
$240$		0			0
$241$	−13.8660	−	3.28630i	−0.893188	−	0.211689i	−0.241702	−	0.970350i	$-0.577706\pi$
$241$	−13.8660	−	3.28630i	−0.893188	−	0.211689i	−0.651486	+	0.758661i	$0.725854\pi$
$242$	6.10626			0.392526
$243$		0			0
$244$	6.28280			0.402215
$245$	−17.8482	−	4.23011i	−1.14028	−	0.270252i
$246$		0			0
$247$	2.33315	+	1.17175i	0.148455	+	0.0745568i
$248$	0.769484	−	1.03360i	0.0488623	−	0.0656335i
$249$		0			0
$250$	10.9164	+	7.17981i	0.690412	+	0.454091i
$251$	−6.58379	−	5.52445i	−0.415565	−	0.348700i	0.410908	−	0.911677i	$-0.365212\pi$
$251$	−6.58379	−	5.52445i	−0.415565	−	0.348700i	−0.826473	+	0.562976i	$0.809656\pi$
$252$		0			0
$253$	−6.23640	+	5.23296i	−0.392079	+	0.328993i
$254$	−20.0076	+	2.33855i	−1.25539	+	0.146734i
$255$		0			0
$256$	−4.21050	+	14.0640i	−0.263156	+	0.879003i
$257$	−15.2323	−	16.1453i	−0.950164	−	1.00711i	−0.999965	−	0.00835579i	$-0.997340\pi$
$257$	−15.2323	−	16.1453i	−0.950164	−	1.00711i	0.0498011	−	0.998759i	$-0.484141\pi$
$258$		0			0
$259$	1.54182	+	2.07102i	0.0958038	+	0.128687i
$260$	3.41594	+	19.3728i	0.211848	+	1.20145i
$261$		0			0
$262$	−1.92625	+	10.9243i	−0.119004	+	0.674906i
$263$	−4.70276	+	2.36182i	−0.289985	+	0.145636i	−0.587845	−	0.808974i	$-0.700023\pi$
$263$	−4.70276	+	2.36182i	−0.289985	+	0.145636i	0.297860	+	0.954610i	$0.403727\pi$
$264$		0			0
$265$	15.4002	+	1.80003i	0.946029	+	0.110575i
$266$	0.787350	−	0.517848i	0.0482755	−	0.0317513i
$267$		0			0
$268$	4.56041	+	15.2328i	0.278571	+	0.930493i
$269$	3.11423	−	5.39401i	0.189878	−	0.328878i	−0.755331	−	0.655343i	$-0.772524\pi$
$269$	3.11423	−	5.39401i	0.189878	−	0.328878i	0.945209	+	0.326465i	$0.105857\pi$
$270$		0			0
$271$	−3.65935	−	6.33818i	−0.222290	−	0.385017i	0.733213	−	0.679999i	$-0.238020\pi$
$271$	−3.65935	−	6.33818i	−0.222290	−	0.385017i	−0.955503	+	0.294982i	$0.904686\pi$
$272$	19.9476	−	21.1432i	1.20950	−	1.28200i
$273$		0			0
$274$	−1.78833	−	30.7045i	−0.108037	−	1.85493i
$275$	3.94935	+	9.15562i	0.238155	+	0.552105i
$276$		0			0
$277$	1.08332	−	18.5999i	0.0650903	−	1.11756i	−0.794731	−	0.606962i	$-0.792388\pi$
$277$	1.08332	−	18.5999i	0.0650903	−	1.11756i	0.859821	−	0.510595i	$-0.170575\pi$
$278$	−30.3926	+	11.0620i	−1.82283	+	0.663456i
$279$		0			0
$280$	0.250307	+	0.0911045i	0.0149587	+	0.00544453i
$281$	0.404770	−	0.938363i	0.0241466	−	0.0559780i	−0.905716	−	0.423885i	$-0.860666\pi$
$281$	0.404770	−	0.938363i	0.0241466	−	0.0559780i	0.929863	+	0.367907i	$0.119925\pi$
$282$		0			0
$283$	−10.6678	+	2.52831i	−0.634134	+	0.150293i	−0.535096	−	0.844791i	$-0.679725\pi$
$283$	−10.6678	+	2.52831i	−0.634134	+	0.150293i	−0.0990378	+	0.995084i	$0.531576\pi$
$284$	13.7212	−	3.25199i	0.814204	−	0.192970i
$285$		0			0
$286$	10.2436	−	23.7473i	0.605716	−	1.40421i
$287$	−5.19387	−	1.89041i	−0.306584	−	0.111588i
$288$		0			0
$289$	−37.9265	+	13.8041i	−2.23097	+	0.812008i
$290$	−1.47651	+	25.3508i	−0.0867039	+	1.48865i
$291$		0			0
$292$	0.471135	+	1.09221i	0.0275711	+	0.0639170i
$293$	1.41173	+	24.2385i	0.0824741	+	1.41603i	0.745039	+	0.667021i	$0.232431\pi$
$293$	1.41173	+	24.2385i	0.0824741	+	1.41603i	−0.662565	+	0.749005i	$0.730532\pi$
$294$		0			0
$295$	2.87450	−	3.04679i	0.167360	−	0.177391i
$296$	0.332457	+	0.575832i	0.0193237	+	0.0334696i
$297$		0			0
$298$	8.92609	−	15.4604i	0.517075	−	0.895599i
$299$	2.13229	+	7.12235i	0.123314	+	0.411896i
$300$		0			0
$301$	0.896168	−	0.589419i	0.0516543	−	0.0339735i
$302$	−1.98136	−	0.231588i	−0.114015	−	0.0133264i
$303$		0			0
$304$	−2.61839	+	1.31500i	−0.150175	+	0.0754206i
$305$	1.45337	−	8.24247i	0.0832198	−	0.471963i
$306$		0			0
$307$	−4.31169	−	24.4528i	−0.246081	−	1.39560i	−0.817968	−	0.575264i	$-0.804899\pi$
$307$	−4.31169	−	24.4528i	−0.246081	−	1.39560i	0.571887	−	0.820333i	$-0.306212\pi$
$308$	−2.84051	−	3.81547i	−0.161853	−	0.217407i
$309$		0			0
$310$	−31.4005	−	33.2826i	−1.78343	−	1.89032i
$311$	0.530789	−	1.77296i	0.0300983	−	0.100535i	−0.941621	−	0.336676i	$-0.890697\pi$
$311$	0.530789	−	1.77296i	0.0300983	−	0.100535i	0.971719	+	0.236140i	$0.0758826\pi$
$312$		0			0
$313$	6.90453	−	0.807024i	0.390267	−	0.0456157i	0.0813032	−	0.996689i	$-0.474092\pi$
$313$	6.90453	−	0.807024i	0.390267	−	0.0456157i	0.308964	+	0.951074i	$0.400018\pi$
$314$	28.1521	−	23.6225i	1.58872	−	1.33309i
$315$		0			0
$316$	14.6687	+	12.3085i	0.825178	+	0.692406i
$317$	21.7538	+	14.3077i	1.22182	+	0.803602i	0.985763	−	0.168138i	$-0.0537754\pi$
$317$	21.7538	+	14.3077i	1.22182	+	0.803602i	0.236054	+	0.971740i	$0.424146\pi$
$318$		0			0
$319$	10.1587	−	13.6455i	0.568779	−	0.764003i
$320$	−21.3011	−	10.6978i	−1.19077	−	0.598026i
$321$		0			0
$322$	2.61120	+	0.618865i	0.145516	+	0.0344880i
$323$	5.78196			0.321717
$324$		0			0
$325$	9.10595			0.505107
$326$	33.6930	+	7.98538i	1.86608	+	0.442269i
$327$		0			0
$328$	−1.27200	−	0.638822i	−0.0702344	−	0.0352730i
$329$	4.29411	−	5.76800i	0.236742	−	0.318000i
$330$		0			0
$331$	21.7523	+	14.3067i	1.19562	+	0.786369i	0.981691	−	0.190481i	$-0.0610049\pi$
$331$	21.7523	+	14.3067i	1.19562	+	0.786369i	0.213925	+	0.976850i	$0.431375\pi$
$332$	9.85078	+	8.26579i	0.540632	+	0.453644i
$333$		0			0
$334$	−9.12878	+	7.65996i	−0.499505	+	0.419134i
$335$	21.0390	−	2.45911i	1.14949	−	0.134356i
$336$		0			0
$337$	4.31097	−	14.3996i	0.234834	−	0.784399i	−0.756610	−	0.653866i	$-0.773146\pi$
$337$	4.31097	−	14.3996i	0.234834	−	0.784399i	0.991444	−	0.130533i	$-0.0416688\pi$
$338$	1.80732	+	1.91565i	0.0983053	+	0.104197i
$339$		0			0
$340$	26.0148	+	34.9440i	1.41085	+	1.89510i
$341$	5.32295	+	30.1880i	0.288254	+	1.63477i
$342$		0			0
$343$	1.44640	−	8.20293i	0.0780981	−	0.442917i
$344$	0.246849	−	0.123972i	0.0133092	−	0.00668413i
$345$		0			0
$346$	18.0371	+	2.10823i	0.969679	+	0.113339i
$347$	−21.2399	+	13.9697i	−1.14022	+	0.749931i	−0.971805	−	0.235786i	$-0.924234\pi$
$347$	−21.2399	+	13.9697i	−1.14022	+	0.749931i	−0.168410	+	0.985717i	$0.553863\pi$
$348$		0			0
$349$	8.39345	+	28.0361i	0.449291	+	1.50074i	0.820205	+	0.572070i	$0.193859\pi$
$349$	8.39345	+	28.0361i	0.449291	+	1.50074i	−0.370913	+	0.928667i	$0.620955\pi$
$350$	1.64339	−	2.84643i	0.0878427	−	0.152148i
$351$		0			0
$352$	15.1016	+	26.1568i	0.804920	+	1.39416i
$353$	19.6894	−	20.8696i	1.04796	−	1.11077i	0.0542820	−	0.998526i	$-0.482713\pi$
$353$	19.6894	−	20.8696i	1.04796	−	1.11077i	0.993680	−	0.112249i	$-0.0358055\pi$
$354$		0			0
$355$	−1.09225	−	18.7533i	−0.0579708	−	0.995321i
$356$	3.78985	+	8.78586i	0.200862	+	0.465650i
$357$		0			0
$358$	0.151342	−	2.59845i	0.00799870	−	0.137332i
$359$	−19.5984	+	7.13322i	−1.03436	+	0.376477i	−0.802740	−	0.596329i	$-0.796625\pi$
$359$	−19.5984	+	7.13322i	−1.03436	+	0.376477i	−0.231622	+	0.972806i	$0.574403\pi$
$360$		0			0
$361$	17.3065	+	6.29905i	0.910868	+	0.331529i
$362$	2.97272	−	6.89153i	0.156242	−	0.362211i
$363$		0			0
$364$	−4.22691	+	1.00180i	−0.221550	+	0.0525083i
$365$	1.54187	−	0.365430i	0.0807053	−	0.0191275i
$366$		0			0
$367$	−13.6912	+	31.7398i	−0.714675	+	1.65680i	0.0387337	+	0.999250i	$0.487668\pi$
$367$	−13.6912	+	31.7398i	−0.714675	+	1.65680i	−0.753408	+	0.657553i	$0.771592\pi$
$368$	−7.84042	−	2.85368i	−0.408710	−	0.148758i
$369$		0			0
$370$	22.1871	−	8.07544i	1.15345	−	0.419822i
$371$	−0.199083	+	3.41812i	−0.0103359	+	0.177460i
$372$		0			0
$373$	−3.71104	−	8.60317i	−0.192151	−	0.445455i	0.794718	−	0.606978i	$-0.207619\pi$
$373$	−3.71104	−	8.60317i	−0.192151	−	0.445455i	−0.986869	+	0.161523i	$0.948359\pi$
$374$	−3.33021	−	57.1775i	−0.172201	−	2.95658i
$375$		0			0
$376$	1.27082	−	1.34699i	0.0655374	−	0.0694656i
$377$	−7.76787	−	13.4543i	−0.400065	−	0.692934i
$378$		0			0
$379$	0.963771	−	1.66930i	0.0495056	−	0.0857462i	−0.840211	−	0.542260i	$-0.817569\pi$
$379$	0.963771	−	1.66930i	0.0495056	−	0.0857462i	0.889716	+	0.456514i	$0.150902\pi$
$380$	−1.25944	−	4.20682i	−0.0646078	−	0.215805i
$381$		0			0
$382$	12.2996	−	8.08957i	0.629302	−	0.413899i
$383$	19.3602	+	2.26289i	0.989263	+	0.115628i	0.595304	−	0.803500i	$-0.297031\pi$
$383$	19.3602	+	2.26289i	0.989263	+	0.115628i	0.393958	+	0.919128i	$0.371106\pi$
$384$		0			0
$385$	−5.66264	+	2.84389i	−0.288595	+	0.144938i
$386$	−3.37590	+	19.1457i	−0.171829	+	0.974489i
$387$		0			0
$388$	−3.79483	−	21.5216i	−0.192653	−	1.09259i
$389$	5.45798	+	7.33134i	0.276730	+	0.371714i	0.918659	−	0.395051i	$-0.129273\pi$
$389$	5.45798	+	7.33134i	0.276730	+	0.371714i	−0.641929	+	0.766764i	$0.721866\pi$
$390$		0			0
$391$	11.2988	+	11.9760i	0.571403	+	0.605652i
$392$	0.299170	−	0.999299i	0.0151104	−	0.0504722i
$393$		0			0
$394$	−9.90173	+	1.15735i	−0.498842	+	0.0583062i
$395$	19.5409	−	16.3967i	0.983208	−	0.825009i
$396$		0			0
$397$	25.5466	+	21.4361i	1.28215	+	1.07585i	0.992944	+	0.118581i	$0.0378344\pi$
$397$	25.5466	+	21.4361i	1.28215	+	1.07585i	0.289202	+	0.957268i	$0.406610\pi$
$398$	−4.24716	−	2.79340i	−0.212891	−	0.140021i
$399$		0			0
$400$	−6.10248	+	8.19705i	−0.305124	+	0.409853i
$401$	3.17125	+	1.59266i	0.158365	+	0.0795337i	0.526216	−	0.850351i	$-0.323610\pi$
$401$	3.17125	+	1.59266i	0.158365	+	0.0795337i	−0.367852	+	0.929885i	$0.619907\pi$
$402$		0			0
$403$	27.2394	+	6.45586i	1.35689	+	0.321589i
$404$	−5.08795			−0.253135
$405$		0			0
$406$	−5.60758			−0.278300
$407$	−15.3911	−	3.64776i	−0.762910	−	0.180813i
$408$		0			0
$409$	−28.6274	−	14.3772i	−1.41553	−	0.710908i	−0.433772	−	0.901023i	$-0.642818\pi$
$409$	−28.6274	−	14.3772i	−1.41553	−	0.710908i	−0.981762	+	0.190115i	$0.939114\pi$
$410$	−30.1833	+	40.5432i	−1.49065	+	2.00228i
$411$		0			0
$412$	−29.6143	−	19.4776i	−1.45899	−	0.959593i
$413$	0.708579	+	0.594568i	0.0348669	+	0.0292568i
$414$		0			0
$415$	13.1227	−	11.0113i	0.644168	−	0.540522i
$416$	27.3962	−	3.20215i	1.34321	−	0.156998i
$417$		0			0
$418$	−1.65579	+	5.53074i	−0.0809875	+	0.270517i
$419$	−10.1803	−	10.7904i	−0.497338	−	0.527147i	0.429270	−	0.903176i	$-0.358771\pi$
$419$	−10.1803	−	10.7904i	−0.497338	−	0.527147i	−0.926608	+	0.376029i	$0.877289\pi$
$420$		0			0
$421$	−9.30357	−	12.4969i	−0.453428	−	0.609060i	0.515353	−	0.856978i	$-0.327661\pi$
$421$	−9.30357	−	12.4969i	−0.453428	−	0.609060i	−0.968781	+	0.247918i	$0.920254\pi$
$422$	2.45037	+	13.8968i	0.119282	+	0.676484i
$423$		0			0
$424$	−0.153114	+	0.868355i	−0.00743589	+	0.0421710i
$425$	18.0209	−	9.05042i	0.874141	−	0.439010i
$426$		0			0
$427$	1.83573	+	0.214566i	0.0888373	+	0.0103836i
$428$	−1.39602	+	0.918178i	−0.0674793	+	0.0443818i
$429$		0			0
$430$	−2.81323	−	9.39684i	−0.135666	−	0.453156i
$431$	0.648713	−	1.12360i	0.0312474	−	0.0541221i	−0.849979	−	0.526817i	$-0.823385\pi$
$431$	0.648713	−	1.12360i	0.0312474	−	0.0541221i	0.881226	+	0.472695i	$0.156719\pi$
$432$		0			0
$433$	−8.76506	−	15.1815i	−0.421222	−	0.729577i	0.574838	−	0.818268i	$-0.305065\pi$
$433$	−8.76506	−	15.1815i	−0.421222	−	0.729577i	−0.996059	+	0.0886901i	$0.971732\pi$
$434$	6.93403	−	7.34965i	0.332844	−	0.352794i
$435$		0			0
$436$	0.510196	+	8.75972i	0.0244339	+	0.419515i
$437$	−0.657352	−	1.52391i	−0.0314454	−	0.0728986i
$438$		0			0
$439$	−1.26280	+	21.6815i	−0.0602702	+	1.03480i	0.823631	+	0.567126i	$0.191945\pi$
$439$	−1.26280	+	21.6815i	−0.0602702	+	1.03480i	−0.883901	+	0.467674i	$0.845092\pi$
$440$	−1.53345	+	0.558129i	−0.0731042	+	0.0266077i
$441$		0			0
$442$	−49.1506	−	17.8894i	−2.33786	−	0.850910i
$443$	−3.62162	+	8.39585i	−0.172068	+	0.398899i	−0.982327	−	0.187174i	$-0.940067\pi$
$443$	−3.62162	+	8.39585i	−0.172068	+	0.398899i	0.810259	+	0.586072i	$0.199327\pi$
$444$		0			0
$445$	12.4030	−	2.93955i	0.587956	−	0.139348i
$446$	−35.3658	+	8.38185i	−1.67462	+	0.396892i
$447$		0			0
$448$	2.08485	−	4.83323i	0.0984999	−	0.228348i
$449$	11.6732	+	4.24870i	0.550893	+	0.200509i	0.602443	−	0.798162i	$-0.294194\pi$
$449$	11.6732	+	4.24870i	0.550893	+	0.200509i	−0.0515501	+	0.998670i	$0.516416\pi$
$450$		0			0
$451$	31.8189	−	11.5811i	1.49829	−	0.545335i
$452$	−1.49133	+	25.6052i	−0.0701464	+	1.20437i
$453$		0			0
$454$	0.490711	+	1.13760i	0.0230302	+	0.0533901i
$455$	0.336476	+	5.77706i	0.0157742	+	0.270833i
$456$		0			0
$457$	12.8292	−	13.5982i	0.600125	−	0.636096i	−0.354092	−	0.935211i	$-0.615210\pi$
$457$	12.8292	−	13.5982i	0.600125	−	0.636096i	0.954217	+	0.299115i	$0.0966914\pi$
$458$	5.04367	+	8.73589i	0.235675	+	0.408201i
$459$		0			0
$460$	6.25233	−	10.8293i	0.291516	−	0.504921i
$461$	11.7824	+	39.3560i	0.548762	+	1.83299i	0.553268	+	0.833003i	$0.313381\pi$
$461$	11.7824	+	39.3560i	0.548762	+	1.83299i	−0.00450593	+	0.999990i	$0.501434\pi$
$462$		0			0
$463$	3.45041	−	2.26937i	0.160354	−	0.105466i	−0.466796	−	0.884365i	$-0.654592\pi$
$463$	3.45041	−	2.26937i	0.160354	−	0.105466i	0.627150	+	0.778899i	$0.284221\pi$
$464$	17.3172	+	2.02408i	0.803929	+	0.0939658i
$465$		0			0
$466$	−23.7440	+	11.9247i	−1.09992	+	0.552399i
$467$	4.38922	−	24.8925i	0.203109	−	1.15189i	−0.697279	−	0.716799i	$-0.745606\pi$
$467$	4.38922	−	24.8925i	0.203109	−	1.15189i	0.900388	−	0.435087i	$-0.143283\pi$
$468$		0			0
$469$	0.812254	+	4.60652i	0.0375064	+	0.212710i
$470$	−39.2686	−	52.7469i	−1.81132	−	2.43303i
$471$		0			0
$472$	0.163468	+	0.173266i	0.00752424	+	0.00797523i
$473$	−1.88464	+	6.29513i	−0.0866558	+	0.289450i
$474$		0			0
$475$	−2.01898	+	0.235985i	−0.0926371	+	0.0108277i
$476$	−7.36945	+	6.18370i	−0.337778	+	0.283430i
$477$		0			0
$478$	14.0744	+	11.8098i	0.643748	+	0.540168i
$479$	−17.3799	−	11.4309i	−0.794107	−	0.522293i	0.0864365	−	0.996257i	$-0.472452\pi$
$479$	−17.3799	−	11.4309i	−0.794107	−	0.522293i	−0.880544	+	0.473965i	$0.842822\pi$
$480$		0			0
$481$	−8.62600	+	11.5867i	−0.393312	+	0.528309i
$482$	−25.7157	−	12.9149i	−1.17132	−	0.588258i
$483$		0			0
$484$	6.11397	+	1.44904i	0.277908	+	0.0658653i
$485$	−29.1122			−1.32192
$486$		0			0
$487$	−6.60060			−0.299102			−0.149551	−	0.988754i	$-0.547783\pi$
$487$	−6.60060			−0.299102			−0.149551	+	0.988754i	$0.547783\pi$
$488$	0.463139	+	0.109766i	0.0209653	+	0.00496887i
$489$		0			0
$490$	−33.1011	−	16.6240i	−1.49536	−	0.750996i
$491$	21.8233	−	29.3138i	0.984873	−	1.32291i	0.0387011	−	0.999251i	$-0.487678\pi$
$491$	21.8233	−	29.3138i	0.984873	−	1.32291i	0.946172	−	0.323664i	$-0.104915\pi$
$492$		0			0
$493$	−28.7451	−	18.9059i	−1.29461	−	0.851480i
$494$	4.03886	+	3.38900i	0.181717	+	0.152479i
$495$		0			0
$496$	−24.0663	+	20.1941i	−1.08061	+	0.906740i
$497$	4.12017	−	0.481579i	0.184815	−	0.0216018i
$498$		0			0
$499$	−10.4379	+	34.8650i	−0.467264	+	1.56077i	0.322014	+	0.946735i	$0.395640\pi$
$499$	−10.4379	+	34.8650i	−0.467264	+	1.56077i	−0.789278	+	0.614036i	$0.789545\pi$
$500$	9.22635	+	9.77936i	0.412615	+	0.437346i
$501$		0			0
$502$	−10.3641	−	13.9214i	−0.462574	−	0.621344i
$503$	−1.38230	−	7.83939i	−0.0616335	−	0.349541i	−0.999992	−	0.00387871i	$-0.998765\pi$
$503$	−1.38230	−	7.83939i	−0.0616335	−	0.349541i	0.938359	−	0.345662i	$-0.112346\pi$
$504$		0			0
$505$	−1.17697	+	6.67494i	−0.0523746	+	0.297031i
$506$	−14.6913	+	7.37825i	−0.653108	+	0.328003i
$507$		0			0
$508$	−20.5878	−	2.40637i	−0.913436	−	0.106765i
$509$	−1.39427	+	0.917026i	−0.0617999	+	0.0406464i	−0.580033	−	0.814593i	$-0.696960\pi$
$509$	−1.39427	+	0.917026i	−0.0617999	+	0.0406464i	0.518233	+	0.855239i	$0.326590\pi$
$510$		0			0
$511$	0.100357	+	0.335217i	0.00443955	+	0.0148291i
$512$	−16.0816	+	27.8541i	−0.710711	+	1.23099i
$513$		0			0
$514$	−22.4119	−	38.8186i	−0.988548	−	1.71221i
$515$	−32.4034	+	34.3456i	−1.42787	+	1.51345i
$516$		0			0
$517$	2.56147	+	43.9788i	0.112653	+	1.93418i
$518$	2.06513	+	4.78750i	0.0907364	+	0.210351i
$519$		0			0
$520$	−0.0866515	+	1.48775i	−0.00379992	+	0.0652421i
$521$	−32.9725	+	12.0010i	−1.44455	+	0.525773i	−0.941063	−	0.338230i	$-0.890172\pi$
$521$	−32.9725	+	12.0010i	−1.44455	+	0.525773i	−0.503486	+	0.864003i	$0.667950\pi$
$522$		0			0
$523$	11.3086	+	4.11600i	0.494491	+	0.179980i	0.577214	−	0.816593i	$-0.304140\pi$
$523$	11.3086	+	4.11600i	0.494491	+	0.179980i	−0.0827236	+	0.996573i	$0.526362\pi$
$524$	−4.52106	+	10.4810i	−0.197503	+	0.457864i
$525$		0			0
$526$	−10.3407	+	2.45078i	−0.450874	+	0.106859i
$527$	60.3238	−	14.2970i	2.62775	−	0.622788i
$528$		0			0
$529$	−7.23796	+	16.7795i	−0.314694	+	0.729543i
$530$	29.4226	+	10.7089i	1.27803	+	0.465167i
$531$		0			0
$532$	0.911231	−	0.331661i	0.0395069	−	0.0143793i
$533$	1.79801	−	30.8707i	0.0778807	−	1.33716i
$534$		0			0
$535$	0.881633	+	2.04385i	0.0381163	+	0.0883635i
$536$	0.0700415	+	1.20257i	0.00302533	+	0.0519429i
$537$		0			0
$538$	8.63136	−	9.14870i	0.372124	−	0.394429i
$539$	12.4073	+	21.4900i	0.534420	+	0.925642i
$540$		0			0
$541$	−9.81306	+	16.9967i	−0.421896	+	0.730746i	−0.996125	−	0.0879490i	$-0.971969\pi$
$541$	−9.81306	+	16.9967i	−0.421896	+	0.730746i	0.574229	+	0.818695i	$0.305302\pi$
$542$	−4.23876	−	14.1585i	−0.182071	−	0.608158i
$543$		0			0
$544$	51.0350	−	33.5662i	2.18811	−	1.43914i
$545$	11.6100	+	1.35701i	0.497318	+	0.0581281i
$546$		0			0
$547$	7.79596	−	3.91528i	0.333331	−	0.167405i	−0.274259	−	0.961656i	$-0.588433\pi$
$547$	7.79596	−	3.91528i	0.333331	−	0.167405i	0.607590	+	0.794251i	$0.292136\pi$
$548$	5.49569	−	31.1676i	0.234764	−	1.33141i
$549$		0			0
$550$	3.49651	+	19.8297i	0.149092	+	0.845540i
$551$	2.07097	+	2.78180i	0.0882264	+	0.118509i
$552$		0			0
$553$	3.86560	+	4.09729i	0.164382	+	0.174235i
$554$	10.7907	−	36.0435i	0.458453	−	1.53134i
$555$		0			0
$556$	−33.0560	+	3.86370i	−1.40189	+	0.163857i
$557$	−15.1698	+	12.7290i	−0.642765	+	0.539344i	−0.904866	−	0.425696i	$-0.860029\pi$
$557$	−15.1698	+	12.7290i	−0.642765	+	0.539344i	0.262101	+	0.965041i	$0.415585\pi$
$558$		0			0
$559$	4.59706	+	3.85739i	0.194435	+	0.163150i
$560$	−5.42593	−	3.56869i	−0.229287	−	0.150805i
$561$		0			0
$562$	1.23236	−	1.65534i	0.0519839	−	0.0698264i
$563$	−30.3446	−	15.2396i	−1.27887	−	0.642274i	−0.325922	−	0.945397i	$-0.605675\pi$
$563$	−30.3446	−	15.2396i	−1.27887	−	0.642274i	−0.952952	+	0.303122i	$0.901971\pi$
$564$		0			0
$565$	33.2467	+	7.87962i	1.39870	+	0.331498i
$566$	−22.1392			−0.930581
$567$		0			0
$568$	1.06828			0.0448240
$569$	18.7206	+	4.43686i	0.784807	+	0.186003i	0.603435	−	0.797412i	$-0.293798\pi$
$569$	18.7206	+	4.43686i	0.784807	+	0.186003i	0.181372	+	0.983415i	$0.441946\pi$
$570$		0			0
$571$	−2.22239	−	1.11613i	−0.0930042	−	0.0467085i	0.401689	−	0.915776i	$-0.368423\pi$
$571$	−2.22239	−	1.11613i	−0.0930042	−	0.0467085i	−0.494693	+	0.869068i	$0.664720\pi$
$572$	15.8918	−	21.3464i	0.664471	−	0.892539i
$573$		0			0
$574$	−9.32538	−	6.13340i	−0.389234	−	0.256003i
$575$	−4.43416	−	3.72070i	−0.184917	−	0.155164i
$576$		0			0
$577$	19.5278	−	16.3857i	0.812951	−	0.682147i	−0.138359	−	0.990382i	$-0.544183\pi$
$577$	19.5278	−	16.3857i	0.812951	−	0.682147i	0.951310	+	0.308235i	$0.0997383\pi$
$578$	−80.9528	+	9.46203i	−3.36719	+	0.393568i
$579$		0			0
$580$	−7.49420	+	25.0324i	−0.311180	+	1.03941i
$581$	2.59595	+	2.75155i	0.107698	+	0.114153i
$582$		0			0
$583$	−12.5259	−	16.8252i	−0.518768	−	0.696827i
$584$	0.0156480	+	0.0887440i	0.000647517	+	0.00367225i
$585$		0			0
$586$	−8.51396	+	48.2851i	−0.351709	+	1.99464i
$587$	−0.800141	+	0.401846i	−0.0330254	+	0.0165860i	−0.465235	−	0.885187i	$-0.654030\pi$
$587$	−0.800141	+	0.401846i	−0.0330254	+	0.0165860i	0.432210	+	0.901773i	$0.357734\pi$
$588$		0			0
$589$	−6.20685	−	0.725476i	−0.255749	−	0.0298927i
$590$	7.06717	−	4.64815i	0.290951	−	0.191361i
$591$		0			0
$592$	−4.64938	−	15.5300i	−0.191088	−	0.638280i
$593$	16.2145	−	28.0843i	0.665848	−	1.15328i	−0.313207	−	0.949685i	$-0.601403\pi$
$593$	16.2145	−	28.0843i	0.665848	−	1.15328i	0.979055	−	0.203597i	$-0.0652634\pi$
$594$		0			0
$595$	6.40773	+	11.0985i	0.262691	+	0.454994i
$596$	12.6062	−	13.3618i	0.516369	−	0.547319i
$597$		0			0
$598$	0.872961	+	14.9882i	0.0356980	+	0.612911i
$599$	16.6725	+	38.6512i	0.681221	+	1.57925i	0.809242	+	0.587476i	$0.199878\pi$
$599$	16.6725	+	38.6512i	0.681221	+	1.57925i	−0.128021	+	0.991771i	$0.540863\pi$
$600$		0			0
$601$	1.79898	−	30.8872i	0.0733818	−	1.25992i	−0.737758	−	0.675065i	$-0.764116\pi$
$601$	1.79898	−	30.8872i	0.0733818	−	1.25992i	0.811140	−	0.584852i	$-0.198847\pi$
$602$	2.03543	−	0.740836i	0.0829580	−	0.0301942i
$603$		0			0
$604$	−1.92891	−	0.702064i	−0.0784861	−	0.0285666i
$605$	3.31532	−	7.68578i	0.134787	−	0.312472i
$606$		0			0
$607$	−14.5707	+	3.45331i	−0.591406	+	0.140166i	−0.515412	−	0.856943i	$-0.672361\pi$
$607$	−14.5707	+	3.45331i	−0.591406	+	0.140166i	−0.0759938	+	0.997108i	$0.524213\pi$
$608$	−5.99131	+	1.41997i	−0.242980	+	0.0575873i
$609$		0			0
$610$	6.69437	−	15.5193i	0.271047	−	0.628358i
$611$	37.8048	+	13.7598i	1.52942	+	0.556663i
$612$		0			0
$613$	17.2467	−	6.27730i	0.696589	−	0.253538i	0.0306353	−	0.999531i	$-0.490247\pi$
$613$	17.2467	−	6.27730i	0.696589	−	0.253538i	0.665954	+	0.745993i	$0.268025\pi$
$614$	2.91548	−	50.0568i	0.117659	−	2.02013i
$615$		0			0
$616$	−0.142730	−	0.330885i	−0.00575075	−	0.0133317i
$617$	−1.90572	−	32.7199i	−0.0767212	−	1.31725i	−0.788581	−	0.614931i	$-0.789184\pi$
$617$	−1.90572	−	32.7199i	−0.0767212	−	1.31725i	0.711860	−	0.702322i	$-0.247853\pi$
$618$		0			0
$619$	4.11905	−	4.36594i	0.165559	−	0.175482i	−0.639283	−	0.768972i	$-0.720769\pi$
$619$	4.11905	−	4.36594i	0.165559	−	0.175482i	0.804842	+	0.593490i	$0.202250\pi$
$620$	−23.5420	−	40.7760i	−0.945471	−	1.63760i
$621$		0			0
$622$	1.86865	−	3.23661i	0.0749262	−	0.129776i
$623$	0.807283	+	2.69651i	0.0323431	+	0.108033i
$624$		0			0
$625$	26.0869	−	17.1576i	1.04348	−	0.686305i
$626$	13.9430	+	1.62970i	0.557273	+	0.0651359i
$627$		0			0
$628$	33.7934	−	16.9717i	1.34850	−	0.677243i
$629$	−5.55497	+	31.5038i	−0.221491	+	1.25614i
$630$		0			0
$631$	−4.24361	−	24.0667i	−0.168935	−	0.958080i	−0.944914	−	0.327320i	$-0.893854\pi$
$631$	−4.24361	−	24.0667i	−0.168935	−	0.958080i	0.775978	−	0.630760i	$-0.217257\pi$
$632$	0.866267	+	1.16360i	0.0344582	+	0.0462854i
$633$		0			0
$634$	36.0823	+	38.2450i	1.43301	+	1.51890i
$635$	−7.91942	+	26.4527i	−0.314273	+	1.04974i
$636$		0			0
$637$	22.5083	−	2.63084i	0.891811	−	0.104238i
$638$	26.3163	−	22.0820i	1.04187	−	0.874234i
$639$		0			0
$640$	−2.66848	−	2.23912i	−0.105481	−	0.0885089i
$641$	8.61817	+	5.66826i	0.340397	+	0.223883i	0.708185	−	0.706027i	$-0.249514\pi$
$641$	8.61817	+	5.66826i	0.340397	+	0.223883i	−0.367788	+	0.929910i	$0.619885\pi$
$642$		0			0
$643$	−25.8610	+	34.7374i	−1.01986	+	1.36991i	−0.0925089	+	0.995712i	$0.529489\pi$
$643$	−25.8610	+	34.7374i	−1.01986	+	1.36991i	−0.927350	+	0.374196i	$0.877919\pi$
$644$	2.46763	+	1.23929i	0.0972383	+	0.0488349i
$645$		0			0
$646$	11.3613	+	2.69268i	0.447005	+	0.105942i
$647$	−6.50021			−0.255550			−0.127775	−	0.991803i	$-0.540783\pi$
$647$	−6.50021			−0.255550			−0.127775	+	0.991803i	$0.540783\pi$
$648$		0			0
$649$	−5.66668			−0.222437
$650$	17.8928	+	4.24068i	0.701815	+	0.166333i
$651$		0			0
$652$	31.8405	+	15.9909i	1.24697	+	0.626252i
$653$	−1.77780	+	2.38800i	−0.0695706	+	0.0934496i	−0.835546	−	0.549420i	$-0.814849\pi$
$653$	−1.77780	+	2.38800i	−0.0695706	+	0.0934496i	0.765976	+	0.642869i	$0.222256\pi$
$654$		0			0
$655$	12.7043	+	8.35574i	0.496397	+	0.326486i
$656$	26.5844	+	22.3070i	1.03795	+	0.870941i
$657$		0			0
$658$	11.1240	−	9.33410i	0.433657	−	0.363881i
$659$	−27.9198	+	3.26336i	−1.08760	+	0.127123i	−0.640948	−	0.767584i	$-0.721459\pi$
$659$	−27.9198	+	3.26336i	−1.08760	+	0.127123i	−0.446654	+	0.894707i	$0.647385\pi$
$660$		0			0
$661$	0.932296	−	3.11408i	0.0362621	−	0.121124i	−0.937942	−	0.346791i	$-0.887271\pi$
$661$	0.932296	−	3.11408i	0.0362621	−	0.121124i	0.974204	+	0.225668i	$0.0724563\pi$
$662$	36.0798	+	38.2423i	1.40228	+	1.48633i
$663$		0			0
$664$	0.581743	+	0.781417i	0.0225760	+	0.0303248i
$665$	−0.224319	−	1.27217i	−0.00869871	−	0.0493328i
$666$		0			0
$667$	−1.71488	+	9.72556i	−0.0664004	+	0.376575i
$668$	−10.9580	+	5.50333i	−0.423979	+	0.212930i
$669$		0			0
$670$	42.4861	+	4.96591i	1.64138	+	0.191850i
$671$	−9.45999	+	6.22193i	−0.365199	+	0.240195i
$672$		0			0
$673$	−3.98495	−	13.3107i	−0.153609	−	0.513088i	0.846196	−	0.532872i	$-0.178887\pi$
$673$	−3.98495	−	13.3107i	−0.153609	−	0.513088i	−0.999804	+	0.0197840i	$0.993702\pi$
$674$	15.1769	−	26.2871i	0.584591	−	1.01254i
$675$		0			0
$676$	1.35501	+	2.34695i	0.0521158	+	0.0902672i
$677$	−7.45030	+	7.89686i	−0.286338	+	0.303501i	−0.854537	−	0.519390i	$-0.826159\pi$
$677$	−7.45030	+	7.89686i	−0.286338	+	0.303501i	0.568199	+	0.822891i	$0.307641\pi$
$678$		0			0
$679$	−0.373797	−	6.41784i	−0.0143450	−	0.246294i
$680$	1.30719	+	3.03041i	0.0501285	+	0.116211i
$681$		0			0
$682$	−3.59927	+	61.7971i	−0.137823	+	2.36633i
$683$	31.5858	−	11.4963i	1.20860	−	0.439893i	0.342380	−	0.939562i	$-0.388767\pi$
$683$	31.5858	−	11.4963i	1.20860	−	0.439893i	0.866217	+	0.499668i	$0.166545\pi$
$684$		0			0
$685$	−39.6178	−	14.4197i	−1.51372	−	0.550949i
$686$	6.66226	−	15.4448i	0.254366	−	0.589687i
$687$		0			0
$688$	−6.55316	+	1.55313i	−0.249837	+	0.0592124i
$689$	−18.6395	+	4.41763i	−0.710107	+	0.168298i
$690$		0			0
$691$	−0.177311	+	0.411052i	−0.00674522	+	0.0156372i	−0.921555	−	0.388247i	$-0.873081\pi$
$691$	−0.177311	+	0.411052i	−0.00674522	+	0.0156372i	0.914810	+	0.403884i	$0.132340\pi$
$692$	17.5595	+	6.39115i	0.667513	+	0.242955i
$693$		0			0
$694$	−48.2412	+	17.5584i	−1.83121	+	0.666507i
$695$	−2.57787	+	44.2604i	−0.0977843	+	1.67889i
$696$		0			0
$697$	−27.1242	−	62.8808i	−1.02740	−	2.38178i
$698$	3.43628	+	58.9987i	0.130065	+	2.23313i
$699$		0			0
$700$	2.32093	−	2.46004i	0.0877228	−	0.0929807i
$701$	−1.94332	−	3.36593i	−0.0733982	−	0.127129i	0.826990	−	0.562216i	$-0.190051\pi$
$701$	−1.94332	−	3.36593i	−0.0733982	−	0.127129i	−0.900389	+	0.435087i	$0.856718\pi$
$702$		0			0
$703$	1.61229	−	2.79256i	0.0608086	−	0.105324i
$704$	9.24849	+	30.8921i	0.348566	+	1.16429i
$705$		0			0
$706$	48.4080	−	31.8384i	1.82186	−	1.19826i
$707$	−1.48662	−	0.173761i	−0.0559100	−	0.00653494i
$708$		0			0
$709$	−13.1721	+	6.61529i	−0.494690	+	0.248442i	−0.678610	−	0.734499i	$-0.737417\pi$
$709$	−13.1721	+	6.61529i	−0.494690	+	0.248442i	0.183921	+	0.982941i	$0.441121\pi$
$710$	6.58725	−	37.3581i	0.247215	−	1.40203i
$711$		0			0
$712$	0.125874	+	0.713864i	0.00471731	+	0.0267532i
$713$	−10.6264	−	14.2737i	−0.397962	−	0.534555i
$714$		0			0
$715$	−24.3284	−	25.7866i	−0.909832	−	0.964366i
$716$	0.768154	−	2.56581i	0.0287073	−	0.0958890i
$717$		0			0
$718$	−41.8320	+	4.88946i	−1.56116	+	0.182473i
$719$	−24.7821	+	20.7947i	−0.924218	+	0.775511i	−0.974770	−	0.223210i	$-0.928346\pi$
$719$	−24.7821	+	20.7947i	−0.924218	+	0.775511i	0.0505523	+	0.998721i	$0.483902\pi$
$720$		0			0
$721$	−7.98762	−	6.70241i	−0.297474	−	0.249611i
$722$	31.0731	+	20.4371i	1.15642	+	0.760590i
$723$		0			0
$724$	4.61185	−	6.19479i	0.171398	−	0.230228i
$725$	10.8090	+	5.42848i	0.401436	+	0.201609i
$726$		0			0
$727$	−8.98140	−	2.12863i	−0.333102	−	0.0789465i	0.0606617	−	0.998158i	$-0.480679\pi$
$727$	−8.98140	−	2.12863i	−0.333102	−	0.0789465i	−0.393763	+	0.919212i	$0.628827\pi$
$728$	−0.329090			−0.0121969
$729$		0			0
$730$	3.19990			0.118434
$731$	12.9315	+	3.06483i	0.478291	+	0.113357i
$732$		0			0
$733$	−47.3569	−	23.7835i	−1.74917	−	0.878464i	−0.966756	−	0.255699i	$-0.917694\pi$
$733$	−47.3569	−	23.7835i	−1.74917	−	0.878464i	−0.782409	−	0.622765i	$-0.786009\pi$
$734$	−41.6840	+	55.9914i	−1.53859	+	2.06668i
$735$		0			0
$736$	−14.6490	−	9.63480i	−0.539969	−	0.355143i
$737$	−21.9518	−	18.4198i	−0.808606	−	0.678501i
$738$		0			0
$739$	2.18316	−	1.83188i	0.0803087	−	0.0673870i	−0.601750	−	0.798685i	$-0.705529\pi$
$739$	2.18316	−	1.83188i	0.0803087	−	0.0673870i	0.682058	+	0.731298i	$0.261085\pi$
$740$	24.1314	−	2.82056i	0.887088	−	0.103686i
$741$		0			0
$742$	−1.98303	+	6.62377i	−0.0727992	+	0.243166i
$743$	−20.1842	−	21.3940i	−0.740485	−	0.784868i	0.242185	−	0.970230i	$-0.422136\pi$
$743$	−20.1842	−	21.3940i	−0.740485	−	0.784868i	−0.982670	+	0.185362i	$0.940654\pi$
$744$		0			0
$745$	−14.6133	−	19.6291i	−0.535390	−	0.719154i
$746$	−3.28553	−	18.6331i	−0.120292	−	0.682208i
$747$		0			0
$748$	10.2340	−	58.0400i	0.374193	−	2.12215i
$749$	−0.439252	+	0.220601i	−0.0160499	+	0.00806057i
$750$		0			0
$751$	27.2443	+	3.18440i	0.994159	+	0.116200i	0.597588	−	0.801804i	$-0.296126\pi$
$751$	27.2443	+	3.18440i	0.994159	+	0.116200i	0.396571	+	0.918004i	$0.370200\pi$
$752$	−37.7218	+	24.8100i	−1.37557	+	0.904728i
$753$		0			0
$754$	−8.99781	−	30.0548i	−0.327681	−	1.09453i
$755$	−1.36725	+	2.36815i	−0.0497593	+	0.0861857i
$756$		0			0
$757$	14.2323	+	24.6511i	0.517282	+	0.895959i	0.999799	+	0.0200719i	$0.00638952\pi$
$757$	14.2323	+	24.6511i	0.517282	+	0.895959i	−0.482516	+	0.875887i	$0.660277\pi$
$758$	2.67117	−	2.83128i	0.0970213	−	0.102837i
$759$		0			0
$760$	−0.0193432	−	0.332110i	−0.000701652	−	0.0120469i
$761$	−11.0792	−	25.6846i	−0.401622	−	0.931064i	−0.992266	−	0.124132i	$-0.960385\pi$
$761$	−11.0792	−	25.6846i	−0.401622	−	0.931064i	0.590644	−	0.806932i	$-0.298874\pi$
$762$		0			0
$763$	−0.150086	+	2.57687i	−0.00543347	+	0.0932890i
$764$	14.2348	−	5.18104i	0.514997	−	0.187444i
$765$		0			0
$766$	36.9883	+	13.4626i	1.33644	+	0.486425i
$767$	−2.04972	+	4.75178i	−0.0740110	+	0.171577i
$768$		0			0
$769$	45.6978	−	10.8306i	1.64790	−	0.390561i	0.701277	−	0.712889i	$-0.252614\pi$
$769$	45.6978	−	10.8306i	1.64790	−	0.390561i	0.946628	+	0.322328i	$0.104466\pi$
$770$	−12.4513	+	2.95101i	−0.448713	+	0.106347i
$771$		0			0
$772$	−7.92349	+	18.3687i	−0.285173	+	0.661104i
$773$	−41.5507	−	15.1232i	−1.49447	−	0.543944i	−0.539851	−	0.841761i	$-0.681519\pi$
$773$	−41.5507	−	15.1232i	−1.49447	−	0.543944i	−0.954623	+	0.297816i	$0.903742\pi$
$774$		0			0
$775$	−20.4807	+	7.45437i	−0.735689	+	0.267769i
$776$	0.0962627	−	1.65277i	0.00345563	−	0.0593309i
$777$		0			0
$778$	7.31048	+	16.9476i	0.262093	+	0.607601i
$779$	0.401371	+	6.89127i	0.0143806	+	0.246906i
$780$		0			0
$781$	−17.4395	+	18.4848i	−0.624034	+	0.661438i
$782$	16.6244	+	28.7942i	0.594486	+	1.02968i
$783$		0			0
$784$	−12.7160	+	22.0247i	−0.454143	+	0.786598i
$785$	−14.4481	−	48.2599i	−0.515673	−	1.72247i
$786$		0			0
$787$	−30.4809	+	20.0476i	−1.08653	+	0.714619i	−0.960743	−	0.277439i	$-0.910514\pi$
$787$	−30.4809	+	20.0476i	−1.08653	+	0.714619i	−0.125782	+	0.992058i	$0.540144\pi$
$788$	−10.1889	−	1.19091i	−0.362963	−	0.0424243i
$789$		0			0
$790$	46.0331	−	23.1187i	1.63778	−	0.822526i
$791$	−1.31019	+	7.43049i	−0.0465852	+	0.264198i
$792$		0			0
$793$	1.79557	+	10.1832i	0.0637627	+	0.361616i
$794$	40.2152	+	54.0183i	1.42718	+	1.91704i
$795$		0			0
$796$	−3.58964	−	3.80479i	−0.127231	−	0.134857i
$797$	−4.33567	+	14.4822i	−0.153577	+	0.512984i	−0.999803	−	0.0198402i	$-0.993684\pi$
$797$	−4.33567	+	14.4822i	−0.153577	+	0.512984i	0.846226	+	0.532825i	$0.178869\pi$
$798$		0			0
$799$	88.4924	−	10.3433i	3.13063	−	0.365919i
$800$	−16.4507	+	13.8038i	−0.581621	+	0.488038i
$801$		0			0
$802$	5.48967	+	4.60638i	0.193847	+	0.162657i
$803$	−1.79102	−	1.17797i	−0.0632036	−	0.0415697i
$804$		0			0
$805$	2.19666	−	2.95063i	0.0774223	−	0.103996i
$806$	50.5179	+	25.3710i	1.77942	+	0.893656i
$807$		0			0
$808$	−0.375060	−	0.0888909i	−0.0131946	−	0.00312717i
$809$	49.6978			1.74728			0.873641	−	0.486571i	$-0.161753\pi$
$809$	49.6978			1.74728			0.873641	+	0.486571i	$0.161753\pi$
$810$		0			0
$811$	−8.76133			−0.307652			−0.153826	−	0.988098i	$-0.549159\pi$
$811$	−8.76133			−0.307652			−0.153826	+	0.988098i	$0.549159\pi$
$812$	−5.61466	−	1.33070i	−0.197036	−	0.0466984i
$813$		0			0
$814$	−28.5442	−	14.3354i	−1.00047	−	0.502456i
$815$	28.3442	−	38.0728i	0.992853	−	1.33363i
$816$		0			0
$817$	−1.11923	−	0.736129i	−0.0391569	−	0.0257539i
$818$	−49.5562	−	41.5826i	−1.73269	−	1.45390i
$819$		0			0
$820$	−39.8424	+	33.4317i	−1.39136	+	1.16749i
$821$	−35.2243	+	4.11713i	−1.22934	+	0.143689i	−0.705860	−	0.708351i	$-0.749439\pi$
$821$	−35.2243	+	4.11713i	−1.22934	+	0.143689i	−0.523476	+	0.852040i	$0.675365\pi$
$822$		0			0
$823$	0.538945	−	1.80020i	0.0187864	−	0.0627511i	−0.948082	−	0.318025i	$-0.896980\pi$
$823$	0.538945	−	1.80020i	0.0187864	−	0.0627511i	0.966869	+	0.255274i	$0.0821656\pi$
$824$	−1.84273	−	1.95318i	−0.0641947	−	0.0680424i
$825$		0			0
$826$	1.11544	+	1.49829i	0.0388110	+	0.0521322i
$827$	−1.66995	−	9.47075i	−0.0580698	−	0.329330i	0.941909	−	0.335869i	$-0.109030\pi$
$827$	−1.66995	−	9.47075i	−0.0580698	−	0.329330i	−0.999979	+	0.00653851i	$0.997919\pi$
$828$		0			0
$829$	−1.31856	+	7.47791i	−0.0457954	+	0.259719i	−0.999106	−	0.0422726i	$-0.986540\pi$
$829$	−1.31856	+	7.47791i	−0.0457954	+	0.259719i	0.953311	+	0.301991i	$0.0976513\pi$
$830$	30.9136	−	15.5254i	1.07303	−	0.538894i
$831$		0			0
$832$	29.2498	+	3.41881i	1.01405	+	0.118526i
$833$	41.9296	−	27.5775i	1.45277	−	0.955505i
$834$		0			0
$835$	4.68501	+	15.6490i	0.162131	+	0.541557i
$836$	−2.97035	+	5.14479i	−0.102732	+	0.177936i
$837$		0			0
$838$	−14.9786	−	25.9438i	−0.517429	−	0.896213i
$839$	−27.1907	+	28.8204i	−0.938727	+	0.994992i	−0.999995	−	0.00312917i	$-0.999004\pi$
$839$	−27.1907	+	28.8204i	−0.938727	+	0.994992i	0.0612684	+	0.998121i	$0.480485\pi$
$840$		0			0
$841$	0.486303	+	8.34951i	0.0167691	+	0.287914i
$842$	−12.4613	−	28.8886i	−0.429445	−	0.995566i
$843$		0			0
$844$	−0.844283	+	14.4958i	−0.0290614	+	0.498965i
$845$	3.39243	−	1.23475i	0.116703	−	0.0424765i
$846$		0			0
$847$	1.73692	+	0.632185i	0.0596811	+	0.0217221i
$848$	8.51479	−	19.7395i	0.292399	−	0.677858i
$849$		0			0
$850$	39.6251	−	9.39133i	1.35913	−	0.322120i
$851$	8.93479	−	2.11758i	0.306281	−	0.0725898i
$852$		0			0
$853$	1.36398	−	3.16206i	0.0467018	−	0.108267i	−0.893268	−	0.449524i	$-0.851594\pi$
$853$	1.36398	−	3.16206i	0.0467018	−	0.108267i	0.939970	+	0.341257i	$0.110853\pi$
$854$	3.50722	+	1.27652i	0.120015	+	0.0436817i
$855$		0			0
$856$	−0.118950	+	0.0432941i	−0.00406561	+	0.00147976i
$857$	−1.28770	+	22.1090i	−0.0439870	+	0.755228i	0.902142	+	0.431439i	$0.141994\pi$
$857$	−1.28770	+	22.1090i	−0.0439870	+	0.755228i	−0.946129	+	0.323789i	$0.895043\pi$
$858$		0			0
$859$	14.1094	+	32.7093i	0.481407	+	1.11603i	0.969910	+	0.243464i	$0.0782838\pi$
$859$	14.1094	+	32.7093i	0.481407	+	1.11603i	−0.488503	+	0.872562i	$0.662457\pi$
$860$	−0.586877	−	10.0763i	−0.0200123	−	0.343598i
$861$		0			0
$862$	1.79796	−	1.90573i	0.0612389	−	0.0649094i
$863$	−10.4873	−	18.1645i	−0.356992	−	0.618328i	0.630465	−	0.776218i	$-0.282864\pi$
$863$	−10.4873	−	18.1645i	−0.356992	−	0.618328i	−0.987457	+	0.157890i	$0.949531\pi$
$864$		0			0
$865$	12.4466	−	21.5581i	0.423196	−	0.732998i
$866$	−10.1529	−	33.9130i	−0.345009	−	1.15241i
$867$		0			0
$868$	8.68688	−	5.71345i	0.294852	−	0.193927i
$869$	−34.2758	−	4.00627i	−1.16273	−	0.135903i
$870$		0			0
$871$	−23.3861	+	11.7449i	−0.792408	+	0.397962i
$872$	−0.115431	+	0.654639i	−0.00390897	+	0.0221689i
$873$		0			0
$874$	−0.581978	−	3.30056i	−0.0196857	−	0.111643i
$875$	2.36181	+	3.17246i	0.0798438	+	0.107249i
$876$		0			0
$877$	−28.9686	−	30.7050i	−0.978202	−	1.03683i	−0.999313	−	0.0370560i	$-0.988202\pi$
$877$	−28.9686	−	30.7050i	−0.978202	−	1.03683i	0.0211115	−	0.999777i	$-0.493279\pi$
$878$	−12.5785	+	42.0152i	−0.424504	+	1.41794i
$879$		0			0
$880$	39.5168	−	4.61885i	1.33211	−	0.155702i
$881$	29.2913	−	24.5783i	0.986848	−	0.828064i	0.00173943	−	0.999998i	$-0.499446\pi$
$881$	29.2913	−	24.5783i	0.986848	−	0.828064i	0.985108	+	0.171935i	$0.0550019\pi$
$882$		0			0
$883$	−22.0694	−	18.5184i	−0.742693	−	0.623194i	0.190866	−	0.981616i	$-0.438870\pi$
$883$	−22.0694	−	18.5184i	−0.742693	−	0.623194i	−0.933560	+	0.358422i	$0.883315\pi$
$884$	−44.9674	−	29.5756i	−1.51242	−	0.994733i
$885$		0			0
$886$	−11.0263	+	14.8109i	−0.370437	+	0.497583i
$887$	12.2591	+	6.15675i	0.411620	+	0.206724i	0.642545	−	0.766248i	$-0.277879\pi$
$887$	12.2591	+	6.15675i	0.411620	+	0.206724i	−0.230924	+	0.972972i	$0.574175\pi$
$888$		0			0
$889$	−5.93324	−	1.40620i	−0.198994	−	0.0471625i
$890$	25.7403			0.862816
$891$		0			0
$892$	−37.3995			−1.25223
$893$	−8.73870	−	2.07111i	−0.292429	−	0.0693070i
$894$		0			0
$895$	−3.18843	−	1.60129i	−0.106577	−	0.0535251i
$896$	0.459355	−	0.617021i	0.0153460	−	0.0206132i
$897$		0			0
$898$	20.9588	+	13.7848i	0.699404	+	0.460005i
$899$	28.4852	+	23.9019i	0.950035	+	0.797174i
$900$		0			0
$901$	−32.4972	+	27.2684i	−1.08264	+	0.908441i
$902$	67.9164	−	7.93828i	2.26137	−	0.264316i
$903$		0			0
$904$	−0.557278	+	1.86144i	−0.0185348	+	0.0619106i
$905$	−7.06018	−	7.48335i	−0.234688	−	0.248755i
$906$		0			0
$907$	33.8810	+	45.5101i	1.12500	+	1.51114i	0.831789	+	0.555092i	$0.187317\pi$
$907$	33.8810	+	45.5101i	1.12500	+	1.51114i	0.293212	+	0.956047i	$0.405276\pi$
$908$	0.221375	+	1.25548i	0.00734659	+	0.0416646i
$909$		0			0
$910$	−2.02924	+	11.5084i	−0.0672687	+	0.381500i
$911$	0.637799	−	0.320315i	0.0211312	−	0.0106125i	−0.438202	−	0.898876i	$-0.644385\pi$
$911$	0.637799	−	0.320315i	0.0211312	−	0.0106125i	0.459333	+	0.888264i	$0.348088\pi$
$912$		0			0
$913$	−23.0180	−	2.69042i	−0.761784	−	0.0890398i
$914$	31.5416	−	20.7453i	1.04330	−	0.686192i
$915$		0			0
$916$	2.97698	+	9.94380i	0.0983621	+	0.328552i
$917$	−1.67892	+	2.90797i	−0.0554428	+	0.0960297i
$918$		0			0
$919$	28.6606	+	49.6416i	0.945425	+	1.63752i	0.754898	+	0.655842i	$0.227686\pi$
$919$	28.6606	+	49.6416i	0.945425	+	1.63752i	0.190527	+	0.981682i	$0.438980\pi$
$920$	0.650090	−	0.689055i	0.0214328	−	0.0227175i
$921$		0			0
$922$	4.82373	+	82.8202i	0.158861	+	2.72754i
$923$	9.19225	+	21.3100i	0.302567	+	0.701428i
$924$		0			0
$925$	0.653921	−	11.2274i	0.0215008	−	0.369155i
$926$	7.83677	−	2.85235i	0.257532	−	0.0937341i
$927$		0			0
$928$	34.4289	+	12.5311i	1.13018	+	0.411353i
$929$	−5.92659	+	13.7394i	−0.194445	+	0.450775i	−0.987347	−	0.158575i	$-0.949310\pi$
$929$	−5.92659	+	13.7394i	−0.194445	+	0.450775i	0.792902	+	0.609349i	$0.208569\pi$
$930$		0			0
$931$	−4.92238	+	1.16662i	−0.161324	+	0.0382346i
$932$	−26.6037	+	6.30519i	−0.871432	+	0.206533i
$933$		0			0
$934$	20.2172	−	46.8687i	0.661526	−	1.53359i
$935$	−73.7759	−	26.8522i	−2.41273	−	0.878162i
$936$		0			0
$937$	23.1819	−	8.43751i	0.757319	−	0.275641i	0.0656366	−	0.997844i	$-0.479092\pi$
$937$	23.1819	−	8.43751i	0.757319	−	0.275641i	0.691682	+	0.722202i	$0.256870\pi$
$938$	−0.549230	+	9.42991i	−0.0179330	+	0.307898i
$939$		0			0
$940$	−26.8011	−	62.1320i	−0.874156	−	2.02652i
$941$	−1.35247	−	23.2210i	−0.0440893	−	0.756984i	−0.945821	−	0.324688i	$-0.894741\pi$
$941$	−1.35247	−	23.2210i	−0.0440893	−	0.756984i	0.901732	−	0.432296i	$-0.142296\pi$
$942$		0			0
$943$	−13.4893	+	14.2979i	−0.439273	+	0.465603i
$944$	−2.90384	−	5.02959i	−0.0945119	−	0.163699i
$945$		0			0
$946$	−6.63491	+	11.4920i	−0.215720	+	0.373637i
$947$	−5.50014	−	18.3718i	−0.178731	−	0.597002i	−0.999663	−	0.0259757i	$-0.991731\pi$
$947$	−5.50014	−	18.3718i	−0.178731	−	0.597002i	0.820932	−	0.571026i	$-0.193454\pi$
$948$		0			0
$949$	−1.63562	+	1.07576i	−0.0530944	+	0.0349208i
$950$	−4.07711	−	0.476546i	−0.132279	−	0.0154612i
$951$		0			0
$952$	−0.651276	+	0.327083i	−0.0211080	+	0.0106008i
$953$	−5.37991	+	30.5110i	−0.174272	+	0.988348i	0.764708	+	0.644377i	$0.222883\pi$
$953$	−5.37991	+	30.5110i	−0.174272	+	0.988348i	−0.938980	+	0.343971i	$0.888228\pi$
$954$		0			0
$955$	−3.50420	−	19.8733i	−0.113393	−	0.643085i
$956$	11.2896	+	15.1646i	0.365133	+	0.490459i
$957$		0			0
$958$	−28.8274	−	30.5552i	−0.931370	−	0.987195i
$959$	2.67017	−	8.91898i	0.0862242	−	0.288009i
$960$		0			0
$961$	−35.7602	+	4.17977i	−1.15356	+	0.134831i
$962$	−22.3457	+	18.7503i	−0.720456	+	0.604534i
$963$		0			0
$964$	−22.6834	−	19.0336i	−0.730583	−	0.613032i
$965$	22.2652	+	14.6441i	0.716742	+	0.471409i
$966$		0			0
$967$	11.8582	−	15.9284i	0.381335	−	0.512221i	−0.569470	−	0.822012i	$-0.692852\pi$
$967$	11.8582	−	15.9284i	0.381335	−	0.512221i	0.950805	+	0.309791i	$0.100259\pi$
$968$	0.425377	+	0.213632i	0.0136721	+	0.00686641i
$969$		0			0
$970$	−57.2044	−	13.5577i	−1.83672	−	0.435311i
$971$	3.39436			0.108930			0.0544651	−	0.998516i	$-0.482655\pi$
$971$	3.39436			0.108930			0.0544651	+	0.998516i	$0.482655\pi$
$972$		0			0
$973$	−9.79039			−0.313865
$974$	−12.9699	−	3.07393i	−0.415583	−	0.0984950i
$975$		0			0
$976$	−10.3701	−	5.20806i	−0.331939	−	0.166706i
$977$	31.9883	−	42.9678i	1.02340	−	1.37466i	0.0982031	−	0.995166i	$-0.468691\pi$
$977$	31.9883	−	42.9678i	1.02340	−	1.37466i	0.925194	−	0.379495i	$-0.123902\pi$
$978$		0			0
$979$	−14.4071	−	9.47570i	−0.460453	−	0.302845i
$980$	−29.1980	−	24.5000i	−0.932694	−	0.782624i
$981$		0			0
$982$	56.5336	−	47.4373i	1.80406	−	1.51379i
$983$	27.6347	−	3.23004i	0.881411	−	0.103022i	0.336666	−	0.941624i	$-0.390701\pi$
$983$	27.6347	−	3.23004i	0.881411	−	0.103022i	0.544745	+	0.838602i	$0.316626\pi$
$984$		0			0
$985$	−3.91931	+	13.0914i	−0.124879	+	0.417126i
$986$	−47.6784	−	50.5361i	−1.51839	−	1.60940i
$987$		0			0
$988$	3.23973	+	4.35172i	0.103070	+	0.138447i
$989$	−0.662412	−	3.75672i	−0.0210635	−	0.119457i
$990$		0			0
$991$	2.53438	−	14.3732i	0.0805071	−	0.456579i	−0.917729	−	0.397207i	$-0.869979\pi$
$991$	2.53438	−	14.3732i	0.0805071	−	0.456579i	0.998236	−	0.0593711i	$-0.0189095\pi$
$992$	−58.9969	+	29.6294i	−1.87315	+	0.940733i
$993$		0			0
$994$	8.32026	+	0.972499i	0.263903	+	0.0308458i
$995$	−5.82193	+	3.82914i	−0.184567	+	0.121392i
$996$		0			0
$997$	0.698934	+	2.33460i	0.0221355	+	0.0739376i	0.968344	−	0.249621i	$-0.0803060\pi$
$997$	0.698934	+	2.33460i	0.0221355	+	0.0739376i	−0.946208	+	0.323558i	$0.895121\pi$
$998$	−36.7468	+	63.6474i	−1.16320	+	2.01472i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.208.7		144
3.2	odd	2		81.2.g.a.16.2	✓	144
9.2	odd	6		729.2.g.c.379.7		144
9.4	even	3		729.2.g.a.622.2		144
9.5	odd	6		729.2.g.d.622.7		144
9.7	even	3		729.2.g.b.379.2		144
81.5	odd	54		81.2.g.a.76.2	yes	144
81.20	odd	54		6561.2.a.c.1.14		72
81.22	even	27		729.2.g.b.352.2		144
81.32	odd	54		729.2.g.d.109.7		144
81.49	even	27		729.2.g.a.109.2		144
81.59	odd	54		729.2.g.c.352.7		144
81.61	even	27		6561.2.a.d.1.59		72
81.76	even	27	inner	243.2.g.a.118.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.2	✓	144	3.2	odd	2
81.2.g.a.76.2	yes	144	81.5	odd	54
243.2.g.a.118.7		144	81.76	even	27	inner
243.2.g.a.208.7		144	1.1	even	1	trivial
729.2.g.a.109.2		144	81.49	even	27
729.2.g.a.622.2		144	9.4	even	3
729.2.g.b.352.2		144	81.22	even	27
729.2.g.b.379.2		144	9.7	even	3
729.2.g.c.352.7		144	81.59	odd	54
729.2.g.c.379.7		144	9.2	odd	6
729.2.g.d.109.7		144	81.32	odd	54
729.2.g.d.622.7		144	9.5	odd	6
6561.2.a.c.1.14		72	81.20	odd	54
6561.2.a.d.1.59		72	81.61	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)

\(f(q)\)	\(=\)	\(q+(1.96496 + 0.465704i) q^{2} +(1.85693 + 0.932584i) q^{4} +(1.65302 - 2.22039i) q^{5} +(0.510715 + 0.335902i) q^{7} +(0.120591 + 0.101188i) q^{8} +(4.28217 - 3.59317i) q^{10} +(-3.71952 + 0.434749i) q^{11} +(-0.980843 + 3.27624i) q^{13} +(0.847104 + 0.897877i) q^{14} +(-2.29190 - 3.07856i) q^{16} +(1.31516 + 7.45862i) q^{17} +(0.132568 - 0.751830i) q^{19} +(5.14024 - 2.58153i) q^{20} +(-7.51117 - 0.877930i) q^{22} +(1.81630 - 1.19460i) q^{23} +(-0.763650 - 2.55077i) q^{25} +(-3.45308 + 5.98091i) q^{26} +(0.635103 + 1.10003i) q^{28} +(-3.11741 + 3.30426i) q^{29} +(-0.475949 - 8.17173i) q^{31} +(-3.19450 - 7.40569i) q^{32} +(-0.889281 + 15.2684i) q^{34} +(1.59006 - 0.578734i) q^{35} +(3.96908 + 1.44463i) q^{37} +(0.610621 - 1.41558i) q^{38} +(0.424016 - 0.100494i) q^{40} +(-8.79832 + 2.08524i) q^{41} +(0.695014 - 1.61122i) q^{43} +(-7.31231 - 2.66146i) q^{44} +(4.12528 - 1.50148i) q^{46} +(0.684001 - 11.7438i) q^{47} +(-2.62456 - 6.08441i) q^{49} +(-0.312638 - 5.36779i) q^{50} +(-4.87673 + 5.16903i) q^{52} +(2.80062 + 4.85082i) q^{53} +(-5.18313 + 8.97744i) q^{55} +(0.0275984 + 0.0921849i) q^{56} +(-7.66439 + 5.04095i) q^{58} +(1.50297 + 0.175672i) q^{59} +(2.70194 - 1.35697i) q^{61} +(2.87039 - 16.2788i) q^{62} +(-1.49529 - 8.48019i) q^{64} +(5.65319 + 7.59356i) q^{65} +(5.25122 + 5.56597i) q^{67} +(-4.51364 + 15.0766i) q^{68} +(3.39392 - 0.396693i) q^{70} +(5.19850 - 4.36206i) q^{71} +(0.438511 + 0.367955i) q^{73} +(7.12633 + 4.68706i) q^{74} +(0.947314 - 1.27246i) q^{76} +(-2.04565 - 1.02736i) q^{77} +(8.96673 + 2.12515i) q^{79} -10.6242 q^{80} -18.2595 q^{82} +(6.02162 + 1.42715i) q^{83} +(18.7350 + 9.40909i) q^{85} +(2.11603 - 2.84232i) q^{86} +(-0.492531 - 0.323943i) q^{88} +(3.52742 + 2.95986i) q^{89} +(-1.60143 + 1.34376i) q^{91} +(4.48680 - 0.524431i) q^{92} +(6.81319 - 22.7577i) q^{94} +(-1.45022 - 1.53714i) q^{95} +(-6.28024 - 8.43582i) q^{97} +(-2.32362 - 13.1779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 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

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