LMFDB - Embedded newform 729.2.g.a.298.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] 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("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			298.6
Character	$\chi$	$=$	729.298
Dual form			729.2.g.a.433.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.782176 - 0.0914233i) q^{2} +(-1.34265 + 0.318213i) q^{4} +(2.48948 + 1.25026i) q^{5} +(-1.42895 - 4.77302i) q^{7} +(-2.50111 + 0.910331i) q^{8} +(2.06152 + 0.750330i) q^{10} +(0.101002 - 1.73414i) q^{11} +(1.29643 - 1.74141i) q^{13} +(-1.55406 - 3.60270i) q^{14} +(0.593056 - 0.297844i) q^{16} +(3.39468 - 2.84848i) q^{17} +(-1.63306 - 1.37030i) q^{19} +(-3.74035 - 0.886478i) q^{20} +(-0.0795392 - 1.36564i) q^{22} +(-0.194482 + 0.649615i) q^{23} +(1.64856 + 2.21440i) q^{25} +(0.854835 - 1.48062i) q^{26} +(3.43741 + 5.95378i) q^{28} +(2.27909 - 5.28353i) q^{29} +(4.03553 + 4.27741i) q^{31} +(4.88416 - 3.21236i) q^{32} +(2.39482 - 2.53836i) q^{34} +(2.41020 - 13.6689i) q^{35} +(0.131814 + 0.747552i) q^{37} +(-1.40262 - 0.922517i) q^{38} +(-7.36463 - 0.860801i) q^{40} +(0.122631 + 0.0143335i) q^{41} +(-2.12747 - 1.39926i) q^{43} +(0.416216 + 2.36048i) q^{44} +(-0.0927292 + 0.525894i) q^{46} +(1.16557 - 1.23544i) q^{47} +(-14.8914 + 9.79424i) q^{49} +(1.49191 + 1.58133i) q^{50} +(-1.18651 + 2.75065i) q^{52} +(5.02192 + 8.69822i) q^{53} +(2.41957 - 4.19082i) q^{55} +(7.91899 + 10.6371i) q^{56} +(1.29962 - 4.34102i) q^{58} +(-0.676232 - 11.6105i) q^{59} +(7.70658 + 1.82649i) q^{61} +(3.54755 + 2.97675i) q^{62} +(2.50983 - 2.10599i) q^{64} +(5.40467 - 2.71433i) q^{65} +(-0.184347 - 0.427364i) q^{67} +(-3.65144 + 4.90473i) q^{68} +(0.635542 - 10.9118i) q^{70} +(-11.4588 - 4.17067i) q^{71} +(-2.01159 + 0.732160i) q^{73} +(0.171445 + 0.572667i) q^{74} +(2.62867 + 1.32017i) q^{76} +(-8.42140 + 1.99591i) q^{77} +(-6.96575 + 0.814179i) q^{79} +1.84879 q^{80} +0.0972297 q^{82} +(-3.28752 + 0.384257i) q^{83} +(12.0123 - 2.84698i) q^{85} +(-1.79198 - 0.899965i) q^{86} +(1.32602 + 4.42922i) q^{88} +(4.72182 - 1.71860i) q^{89} +(-10.1643 - 3.69952i) q^{91} +(0.0544046 - 0.934091i) q^{92} +(0.798737 - 1.07289i) q^{94} +(-2.35223 - 5.45309i) q^{95} +(-6.70871 + 3.36924i) q^{97} +(-10.7523 + 9.02224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{26}{27}\right)$

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 $

$2$	0.782176	−	0.0914233i	0.553082	−	0.0646460i	0.165039	−	0.986287i	$-0.447225\pi$
$2$	0.782176	−	0.0914233i	0.553082	−	0.0646460i	0.388044	+	0.921641i	$0.373151\pi$
$3$		0			0
$3$		0			0
$4$	−1.34265	+	0.318213i	−0.671324	+	0.159107i
$5$	2.48948	+	1.25026i	1.11333	+	0.559135i	0.907753	−	0.419506i	$-0.137797\pi$
$5$	2.48948	+	1.25026i	1.11333	+	0.559135i	0.205577	+	0.978641i	$0.434093\pi$
$6$		0			0
$7$	−1.42895	−	4.77302i	−0.540092	−	1.80403i	−0.592708	−	0.805417i	$-0.701941\pi$
$7$	−1.42895	−	4.77302i	−0.540092	−	1.80403i	0.0526165	−	0.998615i	$-0.483244\pi$
$8$	−2.50111	+	0.910331i	−0.884277	+	0.321851i
$9$		0			0
$10$	2.06152	+	0.750330i	0.651909	+	0.237275i
$11$	0.101002	−	1.73414i	0.0304532	−	0.522862i	−0.948243	−	0.317547i	$-0.897141\pi$
$11$	0.101002	−	1.73414i	0.0304532	−	0.522862i	0.978696	−	0.205315i	$-0.0658220\pi$
$12$		0			0
$13$	1.29643	−	1.74141i	0.359566	−	0.482981i	−0.585125	−	0.810943i	$-0.698954\pi$
$13$	1.29643	−	1.74141i	0.359566	−	0.482981i	0.944691	+	0.327962i	$0.106362\pi$
$14$	−1.55406	−	3.60270i	−0.415339	−	0.962863i
$15$		0			0
$16$	0.593056	−	0.297844i	0.148264	−	0.0744610i
$17$	3.39468	−	2.84848i	0.823331	−	0.690857i	−0.130419	−	0.991459i	$-0.541632\pi$
$17$	3.39468	−	2.84848i	0.823331	−	0.690857i	0.953750	+	0.300602i	$0.0971877\pi$
$18$		0			0
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	0.435948	−	0.899972i	$-0.356413\pi$
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	−0.810598	+	0.585603i	$0.800858\pi$
$20$	−3.74035	−	0.886478i	−0.836367	−	0.198223i
$21$		0			0
$22$	−0.0795392	−	1.36564i	−0.0169578	−	0.291154i
$23$	−0.194482	+	0.649615i	−0.0405523	+	0.135454i	−0.975869	−	0.218359i	$-0.929930\pi$
$23$	−0.194482	+	0.649615i	−0.0405523	+	0.135454i	0.935316	+	0.353813i	$0.115115\pi$
$24$		0			0
$25$	1.64856	+	2.21440i	0.329712	+	0.442880i
$26$	0.854835	−	1.48062i	0.167647	−	0.290373i
$27$		0			0
$28$	3.43741	+	5.95378i	0.649610	+	1.12516i
$29$	2.27909	−	5.28353i	0.423217	−	0.981127i	−0.564580	−	0.825379i	$-0.690962\pi$
$29$	2.27909	−	5.28353i	0.423217	−	0.981127i	0.987797	−	0.155749i	$-0.0497790\pi$
$30$		0			0
$31$	4.03553	+	4.27741i	0.724803	+	0.768246i	0.980076	−	0.198623i	$-0.0636468\pi$
$31$	4.03553	+	4.27741i	0.724803	+	0.768246i	−0.255273	+	0.966869i	$0.582165\pi$
$32$	4.88416	−	3.21236i	0.863406	−	0.567871i
$33$		0			0
$34$	2.39482	−	2.53836i	0.410709	−	0.435326i
$35$	2.41020	−	13.6689i	0.407397	−	2.31047i
$36$		0			0
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	0.993724	−	0.111861i	$-0.0356813\pi$
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	−0.972054	+	0.234758i	$0.924570\pi$
$38$	−1.40262	−	0.922517i	−0.227535	−	0.149652i
$39$		0			0
$40$	−7.36463	−	0.860801i	−1.16445	−	0.136105i
$41$	0.122631	+	0.0143335i	0.0191518	+	0.00223852i	0.125663	−	0.992073i	$-0.459894\pi$
$41$	0.122631	+	0.0143335i	0.0191518	+	0.00223852i	−0.106512	+	0.994311i	$0.533968\pi$
$42$		0			0
$43$	−2.12747	−	1.39926i	−0.324435	−	0.213385i	0.376834	−	0.926281i	$-0.377013\pi$
$43$	−2.12747	−	1.39926i	−0.324435	−	0.213385i	−0.701270	+	0.712896i	$0.747383\pi$
$44$	0.416216	+	2.36048i	0.0627469	+	0.355855i
$45$		0			0
$46$	−0.0927292	+	0.525894i	−0.0136722	+	0.0775388i
$47$	1.16557	−	1.23544i	0.170017	−	0.180207i	−0.636763	−	0.771060i	$-0.719727\pi$
$47$	1.16557	−	1.23544i	0.170017	−	0.180207i	0.806780	+	0.590853i	$0.201209\pi$
$48$		0			0
$49$	−14.8914	+	9.79424i	−2.12734	+	1.39918i
$50$	1.49191	+	1.58133i	0.210988	+	0.223634i
$51$		0			0
$52$	−1.18651	+	2.75065i	−0.164540	+	0.381446i
$53$	5.02192	+	8.69822i	0.689814	+	1.19479i	0.971898	+	0.235403i	$0.0756410\pi$
$53$	5.02192	+	8.69822i	0.689814	+	1.19479i	−0.282084	+	0.959390i	$0.591026\pi$
$54$		0			0
$55$	2.41957	−	4.19082i	0.326255	−	0.565090i
$56$	7.91899	+	10.6371i	1.05822	+	1.42144i
$57$		0			0
$58$	1.29962	−	4.34102i	0.170648	−	0.570004i
$59$	−0.676232	−	11.6105i	−0.0880379	−	1.51155i	−0.696262	−	0.717788i	$-0.745155\pi$
$59$	−0.676232	−	11.6105i	−0.0880379	−	1.51155i	0.608224	−	0.793765i	$-0.291882\pi$
$60$		0			0
$61$	7.70658	+	1.82649i	0.986727	+	0.233859i	0.692138	−	0.721766i	$-0.256669\pi$
$61$	7.70658	+	1.82649i	0.986727	+	0.233859i	0.294589	+	0.955624i	$0.404817\pi$
$62$	3.54755	+	2.97675i	0.450540	+	0.378048i
$63$		0			0
$64$	2.50983	−	2.10599i	0.313728	−	0.263249i
$65$	5.40467	−	2.71433i	0.670367	−	0.336671i
$66$		0			0
$67$	−0.184347	−	0.427364i	−0.0225216	−	0.0522108i	0.906584	−	0.422025i	$-0.138681\pi$
$67$	−0.184347	−	0.427364i	−0.0225216	−	0.0522108i	−0.929106	+	0.369814i	$0.879421\pi$
$68$	−3.65144	+	4.90473i	−0.442802	+	0.594786i
$69$		0			0
$70$	0.635542	−	10.9118i	0.0759618	−	1.30421i
$71$	−11.4588	−	4.17067i	−1.35991	−	0.494968i	−0.443885	−	0.896084i	$-0.646400\pi$
$71$	−11.4588	−	4.17067i	−1.35991	−	0.494968i	−0.916027	+	0.401116i	$0.868622\pi$
$72$		0			0
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	−0.457045	−	0.889443i	$-0.651092\pi$
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	0.221606	+	0.975136i	$0.428870\pi$
$74$	0.171445	+	0.572667i	0.0199301	+	0.0665712i
$75$		0			0
$76$	2.62867	+	1.32017i	0.301530	+	0.151434i
$77$	−8.42140	+	1.99591i	−0.959707	+	0.227455i
$78$		0			0
$79$	−6.96575	+	0.814179i	−0.783708	+	0.0916023i	−0.498530	−	0.866872i	$-0.666127\pi$
$79$	−6.96575	+	0.814179i	−0.783708	+	0.0916023i	−0.285178	+	0.958475i	$0.592053\pi$
$80$	1.84879			0.206701
$81$		0			0
$82$	0.0972297			0.0107372
$83$	−3.28752	+	0.384257i	−0.360853	+	0.0421776i	−0.294588	−	0.955624i	$-0.595182\pi$
$83$	−3.28752	+	0.384257i	−0.360853	+	0.0421776i	−0.0662650	+	0.997802i	$0.521108\pi$
$84$		0			0
$85$	12.0123	−	2.84698i	1.30292	−	0.308798i
$86$	−1.79198	−	0.899965i	−0.193234	−	0.0970457i
$87$		0			0
$88$	1.32602	+	4.42922i	0.141354	+	0.472156i
$89$	4.72182	−	1.71860i	0.500512	−	0.182171i	−0.0794124	−	0.996842i	$-0.525304\pi$
$89$	4.72182	−	1.71860i	0.500512	−	0.182171i	0.579924	+	0.814670i	$0.303082\pi$
$90$		0			0
$91$	−10.1643	−	3.69952i	−1.06551	−	0.387815i
$92$	0.0544046	−	0.934091i	0.00567207	−	0.0973857i
$93$		0			0
$94$	0.798737	−	1.07289i	0.0823835	−	0.110660i
$95$	−2.35223	−	5.45309i	−0.241334	−	0.559476i
$96$		0			0
$97$	−6.70871	+	3.36924i	−0.681166	+	0.342095i	−0.755509	−	0.655138i	$-0.772610\pi$
$97$	−6.70871	+	3.36924i	−0.681166	+	0.342095i	0.0743428	+	0.997233i	$0.476314\pi$
$98$	−10.7523	+	9.02224i	−1.08615	+	0.911384i
$99$		0			0
$100$	−2.91808	−	2.44856i	−0.291808	−	0.244856i
$101$	−2.19888	−	0.521143i	−0.218796	−	0.0518557i	0.119755	−	0.992803i	$-0.461789\pi$
$101$	−2.19888	−	0.521143i	−0.218796	−	0.0518557i	−0.338552	+	0.940948i	$0.609937\pi$
$102$		0			0
$103$	0.0155730	+	0.267378i	0.00153445	+	0.0263456i	0.998988	−	0.0449670i	$-0.0143183\pi$
$103$	0.0155730	+	0.267378i	0.00153445	+	0.0263456i	−0.997454	+	0.0713126i	$0.977281\pi$
$104$	−1.65727	+	5.53566i	−0.162508	+	0.542816i
$105$		0			0
$106$	4.72325	+	6.34442i	0.458762	+	0.616225i
$107$	−4.97987	+	8.62539i	−0.481423	+	0.833848i	−0.999773	−	0.0213201i	$-0.993213\pi$
$107$	−4.97987	+	8.62539i	−0.481423	+	0.833848i	0.518350	+	0.855169i	$0.326546\pi$
$108$		0			0
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	0.984887	+	0.173198i	$0.0554102\pi$
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	−0.342449	+	0.939536i	$0.611256\pi$
$110$	1.50939	−	3.49917i	0.143915	−	0.333632i
$111$		0			0
$112$	−2.26906	−	2.40507i	−0.214406	−	0.227257i
$113$	0.335122	−	0.220413i	0.0315257	−	0.0207348i	−0.533648	−	0.845706i	$-0.679179\pi$
$113$	0.335122	−	0.220413i	0.0315257	−	0.0207348i	0.565174	+	0.824972i	$0.308809\pi$
$114$		0			0
$115$	−1.29635	+	1.37405i	−0.120885	+	0.128131i
$116$	−1.37873	+	7.81916i	−0.128012	+	0.725991i
$117$		0			0
$118$	−1.59040	−	9.01960i	−0.146408	−	0.830322i
$119$	−18.4467	−	12.1326i	−1.69100	−	1.11219i
$120$		0			0
$121$	7.92859	+	0.926719i	0.720781	+	0.0842472i
$122$	6.19489	+	0.724079i	0.560859	+	0.0655550i
$123$		0			0
$124$	−6.77943	−	4.45890i	−0.608811	−	0.400421i
$125$	−1.08327	−	6.14355i	−0.0968909	−	0.549495i
$126$		0			0
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	0.792037	+	0.610474i	$0.209021\pi$
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	−0.953065	+	0.302765i	$0.902090\pi$
$128$	−6.25278	+	6.62756i	−0.552673	+	0.585799i
$129$		0			0
$130$	3.97926	−	2.61720i	0.349004	−	0.229543i
$131$	9.23051	+	9.78377i	0.806473	+	0.854812i	0.991791	−	0.127867i	$-0.0408130\pi$
$131$	9.23051	+	9.78377i	0.806473	+	0.854812i	−0.185318	+	0.982679i	$0.559332\pi$
$132$		0			0
$133$	−4.20691	+	9.75272i	−0.364786	+	0.845668i
$134$	−0.183263	−	0.317421i	−0.0158315	−	0.0274210i
$135$		0			0
$136$	−5.89743	+	10.2146i	−0.505700	+	0.875898i
$137$	8.53855	+	11.4693i	0.729498	+	0.979886i	0.999853	+	0.0171251i	$0.00545137\pi$
$137$	8.53855	+	11.4693i	0.729498	+	0.979886i	−0.270355	+	0.962761i	$0.587141\pi$
$138$		0			0
$139$	0.0928721	−	0.310214i	0.00787731	−	0.0263120i	−0.953961	−	0.299932i	$-0.903036\pi$
$139$	0.0928721	−	0.310214i	0.00787731	−	0.0263120i	0.961838	+	0.273620i	$0.0882211\pi$
$140$	1.11358	+	19.1195i	0.0941149	+	1.61589i
$141$		0			0
$142$	−9.34412	−	2.21460i	−0.784141	−	0.185845i
$143$	−2.88891	−	2.42408i	−0.241583	−	0.202712i
$144$		0			0
$145$	12.2796	−	10.3038i	1.01976	−	0.855682i
$146$	−1.50648	+	0.756585i	−0.124677	+	0.0626154i
$147$		0			0
$148$	−0.414860	−	0.961755i	−0.0341013	−	0.0790557i
$149$	1.83804	−	2.46891i	0.150578	−	0.202261i	−0.720434	−	0.693524i	$-0.756057\pi$
$149$	1.83804	−	2.46891i	0.150578	−	0.202261i	0.871011	+	0.491263i	$0.163465\pi$
$150$		0			0
$151$	−0.728324	+	12.5048i	−0.0592702	+	1.01763i	0.829275	+	0.558841i	$0.188754\pi$
$151$	−0.728324	+	12.5048i	−0.0592702	+	1.01763i	−0.888545	+	0.458789i	$0.848283\pi$
$152$	5.33190	+	1.94065i	0.432474	+	0.157408i
$153$		0			0
$154$	−6.40455	+	2.33106i	−0.516093	+	0.187843i
$155$	4.69848	+	15.6940i	0.377391	+	1.26057i
$156$		0			0
$157$	5.20202	+	2.61255i	0.415166	+	0.208504i	0.644106	−	0.764936i	$-0.277230\pi$
$157$	5.20202	+	2.61255i	0.415166	+	0.208504i	−0.228940	+	0.973441i	$0.573526\pi$
$158$	−5.37401	+	1.27366i	−0.427533	+	0.101327i
$159$		0			0
$160$	16.1753	−	1.89062i	1.27877	−	0.149467i
$161$	3.37853			0.266265
$162$		0			0
$163$	−6.75084			−0.528767			−0.264383	−	0.964418i	$-0.585168\pi$
$163$	−6.75084			−0.528767			−0.264383	+	0.964418i	$0.585168\pi$
$164$	−0.169212	+	0.0197780i	−0.0132132	+	0.00154440i
$165$		0			0
$166$	−2.53629	+	0.601113i	−0.196855	+	0.0466554i
$167$	15.5387	+	7.80382i	1.20242	+	0.603877i	0.933254	−	0.359217i	$-0.116956\pi$
$167$	15.5387	+	7.80382i	1.20242	+	0.603877i	0.269165	+	0.963094i	$0.413252\pi$
$168$		0			0
$169$	2.37666	+	7.93861i	0.182820	+	0.610662i
$170$	9.13549	−	3.32504i	0.700660	−	0.255019i
$171$		0			0
$172$	3.30170	+	1.20172i	0.251752	+	0.0916303i
$173$	−0.799204	+	13.7218i	−0.0607624	+	1.04325i	0.820810	+	0.571201i	$0.193522\pi$
$173$	−0.799204	+	13.7218i	−0.0607624	+	1.04325i	−0.881573	+	0.472049i	$0.843515\pi$
$174$		0			0
$175$	8.21366	−	11.0329i	0.620894	−	0.834006i
$176$	−0.456603	−	1.05852i	−0.0344177	−	0.0797892i
$177$		0			0
$178$	3.53618	−	1.77593i	0.265048	−	0.133112i
$179$	−1.66053	+	1.39335i	−0.124114	+	0.104144i	−0.702732	−	0.711455i	$-0.748037\pi$
$179$	−1.66053	+	1.39335i	−0.124114	+	0.104144i	0.578618	+	0.815599i	$0.303592\pi$
$180$		0			0
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.986950	−	0.161028i	$-0.948519\pi$
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.329963	−	0.943994i	$-0.607036\pi$
$182$	−8.28853	−	1.96442i	−0.614387	−	0.145612i
$183$		0			0
$184$	−0.104943	−	1.80180i	−0.00773651	−	0.132831i
$185$	−0.606490	+	2.02582i	−0.0445900	+	0.148941i
$186$		0			0
$187$	−4.59678	−	6.17454i	−0.336150	−	0.451527i
$188$	−1.17182	+	2.02966i	−0.0854640	+	0.148028i
$189$		0			0
$190$	−2.33840	−	4.05023i	−0.169646	−	0.293835i
$191$	8.66905	−	20.0971i	0.627271	−	1.45418i	−0.247135	−	0.968981i	$-0.579489\pi$
$191$	8.66905	−	20.0971i	0.627271	−	1.45418i	0.874406	−	0.485196i	$-0.161252\pi$
$192$		0			0
$193$	4.95097	+	5.24773i	0.356379	+	0.377740i	0.880614	−	0.473834i	$-0.157130\pi$
$193$	4.95097	+	5.24773i	0.356379	+	0.377740i	−0.524235	+	0.851573i	$0.675649\pi$
$194$	−4.93937	+	3.24867i	−0.354626	+	0.233241i
$195$		0			0
$196$	16.8773	−	17.8889i	1.20552	−	1.27778i
$197$	−2.84835	+	16.1538i	−0.202936	+	1.15091i	0.697718	+	0.716373i	$0.254199\pi$
$197$	−2.84835	+	16.1538i	−0.202936	+	1.15091i	−0.900654	+	0.434537i	$0.856912\pi$
$198$		0			0
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	−0.993338	−	0.115238i	$-0.963237\pi$
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	0.894019	−	0.448030i	$-0.147874\pi$
$200$	−6.13907	−	4.03773i	−0.434098	−	0.285510i
$201$		0			0
$202$	−1.76755	−	0.206598i	−0.124365	−	0.0145362i
$203$	−28.4751	−	3.32826i	−1.99856	−	0.233598i
$204$		0			0
$205$	0.287367	+	0.189004i	0.0200706	+	0.0132006i
$206$	0.0366255	+	0.207713i	0.00255182	+	0.0144721i
$207$		0			0
$208$	0.250189	−	1.41889i	0.0173475	−	0.0983824i
$209$	−2.54123	+	2.69355i	−0.175781	+	0.186317i
$210$		0			0
$211$	19.9870	−	13.1457i	1.37596	−	0.904984i	0.376194	−	0.926541i	$-0.377233\pi$
$211$	19.9870	−	13.1457i	1.37596	−	0.904984i	0.999768	+	0.0215570i	$0.00686233\pi$
$212$	−9.51056	−	10.0806i	−0.653188	−	0.692339i
$213$		0			0
$214$	−3.10658	+	7.20186i	−0.212361	+	0.492309i
$215$	−3.54684	−	6.14331i	−0.241893	−	0.418970i
$216$		0			0
$217$	14.6496	−	25.3739i	0.994481	−	1.72249i
$218$	6.30834	+	8.47357i	0.427255	+	0.573903i
$219$		0			0
$220$	−1.91506	+	6.39674i	−0.129113	+	0.431268i
$221$	−0.559393	−	9.60440i	−0.0376288	−	0.646062i
$222$		0			0
$223$	11.6432	+	2.75949i	0.779688	+	0.184789i	0.601142	−	0.799142i	$-0.294713\pi$
$223$	11.6432	+	2.75949i	0.779688	+	0.184789i	0.178546	+	0.983932i	$0.442861\pi$
$224$	−22.3119	−	18.7219i	−1.49078	−	1.25091i
$225$		0			0
$226$	0.241974	−	0.203040i	0.0160959	−	0.0135060i
$227$	22.4417	−	11.2706i	1.48951	−	0.748058i	0.496715	−	0.867914i	$-0.334539\pi$
$227$	22.4417	−	11.2706i	1.48951	−	0.748058i	0.992791	+	0.119856i	$0.0382432\pi$
$228$		0			0
$229$	−10.2084	−	23.6658i	−0.674592	−	1.56388i	−0.818638	−	0.574310i	$-0.805270\pi$
$229$	−10.2084	−	23.6658i	−0.674592	−	1.56388i	0.144045	−	0.989571i	$-0.453989\pi$
$230$	−0.888353	+	1.19327i	−0.0585763	+	0.0786816i
$231$		0			0
$232$	−0.890509	+	15.2894i	−0.0584648	+	1.00380i
$233$	8.58260	+	3.12381i	0.562265	+	0.204648i	0.607488	−	0.794329i	$-0.292177\pi$
$233$	8.58260	+	3.12381i	0.562265	+	0.204648i	−0.0452226	+	0.998977i	$0.514400\pi$
$234$		0			0
$235$	4.44630	−	1.61832i	0.290044	−	0.105568i
$236$	4.60254	+	15.3736i	0.299600	+	1.00073i
$237$		0			0
$238$	−15.5377	−	7.80334i	−1.00716	−	0.505816i
$239$	21.1730	−	5.01810i	1.36957	−	0.324594i	0.520944	−	0.853591i	$-0.325580\pi$
$239$	21.1730	−	5.01810i	1.36957	−	0.324594i	0.848624	+	0.528997i	$0.177432\pi$
$240$		0			0
$241$	−13.7710	+	1.60960i	−0.887067	+	0.103683i	−0.547408	−	0.836866i	$-0.684386\pi$
$241$	−13.7710	+	1.60960i	−0.887067	+	0.103683i	−0.339659	+	0.940549i	$0.610311\pi$
$242$	6.28628			0.404097
$243$		0			0
$244$	−10.9284			−0.699622
$245$	−49.3173	+	5.76436i	−3.15076	+	0.368271i
$246$		0			0
$247$	−4.50342	+	1.06733i	−0.286546	+	0.0679125i
$248$	−13.9872	−	7.02463i	−0.888187	−	0.446064i
$249$		0			0
$250$	−1.40897	−	4.70630i	−0.0891113	−	0.297653i
$251$	10.0143	−	3.64492i	0.632099	−	0.230065i	−0.00604584	−	0.999982i	$-0.501924\pi$
$251$	10.0143	−	3.64492i	0.632099	−	0.230065i	0.638144	+	0.769917i	$0.279702\pi$
$252$		0			0
$253$	1.10688	+	0.402871i	0.0695888	+	0.0253283i
$254$	−0.478517	+	8.21582i	−0.0300248	+	0.515506i
$255$		0			0
$256$	−8.19786	+	11.0116i	−0.512366	+	0.688228i
$257$	0.465607	+	1.07940i	0.0290438	+	0.0673310i	0.932121	−	0.362148i	$-0.117956\pi$
$257$	0.465607	+	1.07940i	0.0290438	+	0.0673310i	−0.903077	+	0.429479i	$0.858697\pi$
$258$		0			0
$259$	3.37973	−	1.69736i	0.210006	−	0.105469i
$260$	−6.39284	+	5.36423i	−0.396467	+	0.332675i
$261$		0			0
$262$	8.11435	+	6.80875i	0.501306	+	0.420646i
$263$	−9.08124	−	2.15229i	−0.559973	−	0.132716i	−0.0591241	−	0.998251i	$-0.518831\pi$
$263$	−9.08124	−	2.15229i	−0.559973	−	0.132716i	−0.500849	+	0.865535i	$0.666979\pi$
$264$		0			0
$265$	1.62690	+	27.9328i	0.0999396	+	1.71590i
$266$	−2.39892	+	8.01296i	−0.147087	+	0.491306i
$267$		0			0
$268$	0.383506	+	0.515138i	0.0234264	+	0.0314671i
$269$	1.25116	−	2.16707i	0.0762845	−	0.132129i	−0.825360	−	0.564607i	$-0.809028\pi$
$269$	1.25116	−	2.16707i	0.0762845	−	0.132129i	0.901644	+	0.432479i	$0.142361\pi$
$270$		0			0
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	0.769842	−	0.638234i	$-0.220335\pi$
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	−0.937648	+	0.347586i	$0.887002\pi$
$272$	1.16484	−	2.70039i	0.0706285	−	0.163735i
$273$		0			0
$274$	7.72721	+	8.19037i	0.466818	+	0.494798i
$275$	4.00658	−	2.63517i	0.241606	−	0.158907i
$276$		0			0
$277$	−18.3318	+	19.4306i	−1.10145	+	1.16747i	−0.116759	+	0.993160i	$0.537251\pi$
$277$	−18.3318	+	19.4306i	−1.10145	+	1.16747i	−0.984691	+	0.174309i	$0.944231\pi$
$278$	0.0442815	−	0.251133i	0.00265583	−	0.0150620i
$279$		0			0
$280$	6.41505	+	36.3816i	0.383373	+	2.17421i
$281$	26.3020	+	17.2991i	1.56905	+	1.03198i	0.973508	+	0.228653i	$0.0734322\pi$
$281$	26.3020	+	17.2991i	1.56905	+	1.03198i	0.595540	+	0.803326i	$0.296938\pi$
$282$		0			0
$283$	−6.64605	−	0.776812i	−0.395067	−	0.0461767i	−0.0837594	−	0.996486i	$-0.526693\pi$
$283$	−6.64605	−	0.776812i	−0.395067	−	0.0461767i	−0.311307	+	0.950309i	$0.600767\pi$
$284$	16.7123	+	1.95339i	0.991694	+	0.115912i
$285$		0			0
$286$	−2.48125	−	1.63195i	−0.146720	−	0.0964990i
$287$	−0.106819	−	0.605803i	−0.00630535	−	0.0357594i
$288$		0			0
$289$	0.458026	−	2.59759i	0.0269427	−	0.152800i
$290$	8.66278	−	9.18201i	0.508696	−	0.539186i
$291$		0			0
$292$	2.46788	−	1.62315i	0.144422	−	0.0949876i
$293$	2.57603	+	2.73044i	0.150493	+	0.159514i	0.798234	−	0.602347i	$-0.205768\pi$
$293$	2.57603	+	2.73044i	0.150493	+	0.159514i	−0.647741	+	0.761861i	$0.724286\pi$
$294$		0			0
$295$	12.8327	−	29.7495i	0.747147	−	1.73208i
$296$	−1.01020	−	1.74972i	−0.0587167	−	0.101700i
$297$		0			0
$298$	1.21195	−	2.09916i	0.0702066	−	0.121601i
$299$	0.879115	+	1.18086i	0.0508405	+	0.0682907i
$300$		0			0
$301$	−3.63864	+	12.1539i	−0.209728	+	0.700539i
$302$	0.573556	+	9.84758i	0.0330044	+	0.566664i
$303$		0			0
$304$	−1.37663	−	0.326268i	−0.0789553	−	0.0187128i
$305$	16.9018	+	14.1823i	0.967793	+	0.812075i
$306$		0			0
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.321406	+	0.946942i	$0.604155\pi$
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.988367	+	0.152088i	$0.951400\pi$
$308$	10.6718	−	5.35960i	0.608085	−	0.305392i
$309$		0			0
$310$	5.10984	+	11.8459i	0.290219	+	0.672804i
$311$	−2.65632	+	3.56805i	−0.150626	+	0.202326i	−0.871031	−	0.491228i	$-0.836548\pi$
$311$	−2.65632	+	3.56805i	−0.150626	+	0.202326i	0.720405	+	0.693553i	$0.243956\pi$
$312$		0			0
$313$	1.81546	−	31.1702i	0.102616	−	1.76184i	−0.418369	−	0.908277i	$-0.637398\pi$
$313$	1.81546	−	31.1702i	0.102616	−	1.76184i	0.520985	−	0.853566i	$-0.325565\pi$
$314$	4.30775	+	1.56789i	0.243100	+	0.0884812i
$315$		0			0
$316$	9.09346	−	3.30975i	0.511547	−	0.186188i
$317$	−7.98146	−	26.6599i	−0.448284	−	1.49737i	−0.821815	−	0.569754i	$-0.807038\pi$
$317$	−7.98146	−	26.6599i	−0.448284	−	1.49737i	0.373531	−	0.927618i	$-0.378147\pi$
$318$		0			0
$319$	−8.93218	−	4.48591i	−0.500106	−	0.251163i
$320$	8.88121	−	2.10489i	0.496475	−	0.117667i
$321$		0			0
$322$	2.64261	−	0.308876i	0.147267	−	0.0172130i
$323$	−9.44699			−0.525644
$324$		0			0
$325$	5.99343			0.332456
$326$	−5.28035	+	0.617185i	−0.292452	+	0.0341827i
$327$		0			0
$328$	−0.319763	+	0.0757852i	−0.0176560	+	0.00418454i
$329$	−7.56231	−	3.79794i	−0.416924	−	0.209387i
$330$		0			0
$331$	−0.0565245	−	0.188805i	−0.00310687	−	0.0103777i	0.956422	−	0.291988i	$-0.0943167\pi$
$331$	−0.0565245	−	0.188805i	−0.00310687	−	0.0103777i	−0.959529	+	0.281610i	$0.909132\pi$
$332$	4.29171	−	1.56206i	0.235538	−	0.0857289i
$333$		0			0
$334$	12.8674	+	4.68336i	0.704075	+	0.256262i
$335$	0.0753900	−	1.29440i	0.00411900	−	0.0707204i
$336$		0			0
$337$	−10.6919	+	14.3617i	−0.582424	+	0.782331i	−0.991491	−	0.130173i	$-0.958447\pi$
$337$	−10.6919	+	14.3617i	−0.582424	+	0.782331i	0.409068	+	0.912504i	$0.365854\pi$
$338$	2.58474	+	5.99211i	0.140592	+	0.325928i
$339$		0			0
$340$	−15.2224	+	7.64497i	−0.825550	+	0.414607i
$341$	7.82522	−	6.56614i	0.423759	−	0.355576i
$342$		0			0
$343$	41.3103	+	34.6635i	2.23055	+	1.87165i
$344$	6.59482	+	1.56300i	0.355569	+	0.0842714i
$345$		0			0
$346$	0.629374	+	10.8059i	0.0338354	+	0.580931i
$347$	6.46215	−	21.5851i	0.346906	−	1.15875i	−0.589482	−	0.807782i	$-0.700668\pi$
$347$	6.46215	−	21.5851i	0.346906	−	1.15875i	0.936388	−	0.350966i	$-0.114147\pi$
$348$		0			0
$349$	−7.07995	−	9.51003i	−0.378981	−	0.509060i	0.571178	−	0.820826i	$-0.306487\pi$
$349$	−7.07995	−	9.51003i	−0.378981	−	0.509060i	−0.950159	+	0.311766i	$0.899079\pi$
$350$	5.41587	−	9.38056i	0.289490	−	0.501412i
$351$		0			0
$352$	−5.07737	−	8.79426i	−0.270625	−	0.468736i
$353$	7.44792	−	17.2662i	0.396413	−	0.918989i	−0.596769	−	0.802413i	$-0.703549\pi$
$353$	7.44792	−	17.2662i	0.396413	−	0.918989i	0.993182	−	0.116575i	$-0.0371917\pi$
$354$		0			0
$355$	−23.3121	−	24.7094i	−1.23728	−	1.31144i
$356$	−5.79286	+	3.81002i	−0.307021	+	0.201931i
$357$		0			0
$358$	−1.17144	+	1.24166i	−0.0619126	+	0.0656236i
$359$	1.61227	−	9.14366i	0.0850926	−	0.482584i	−0.912244	−	0.409647i	$-0.865652\pi$
$359$	1.61227	−	9.14366i	0.0850926	−	0.482584i	0.997337	−	0.0729368i	$-0.0232371\pi$
$360$		0			0
$361$	−2.51015	−	14.2358i	−0.132113	−	0.749251i
$362$	−15.2172	−	10.0085i	−0.799797	−	0.526034i
$363$		0			0
$364$	14.8244	+	1.73272i	0.777008	+	0.0908192i
$365$	−5.92321	−	0.692324i	−0.310035	−	0.0362379i
$366$		0			0
$367$	24.4128	+	16.0566i	1.27434	+	0.838145i	0.992610	−	0.121349i	$-0.0387221\pi$
$367$	24.4128	+	16.0566i	1.27434	+	0.838145i	0.281728	+	0.959494i	$0.409092\pi$
$368$	0.0781452	+	0.443183i	0.00407360	+	0.0231025i
$369$		0			0
$370$	−0.289175	+	1.63999i	−0.0150335	+	0.0852593i
$371$	34.3407	−	36.3990i	1.78288	−	1.88974i
$372$		0			0
$373$	−4.64920	+	3.05782i	−0.240726	+	0.158328i	−0.664140	−	0.747608i	$-0.731202\pi$
$373$	−4.64920	+	3.05782i	−0.240726	+	0.158328i	0.423414	+	0.905936i	$0.360832\pi$
$374$	−4.15999	−	4.40933i	−0.215108	−	0.228001i
$375$		0			0
$376$	−1.79058	+	4.15103i	−0.0923420	+	0.214073i
$377$	−6.24612	−	10.8186i	−0.321692	−	0.557186i
$378$		0			0
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	0.183140	+	0.983087i	$0.441374\pi$
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	−0.942948	+	0.332940i	$0.891959\pi$
$380$	4.89347	+	6.57307i	0.251030	+	0.337191i
$381$		0			0
$382$	4.94338	−	16.5120i	0.252925	−	0.844830i
$383$	−0.720228	−	12.3658i	−0.0368019	−	0.631865i	−0.965399	−	0.260776i	$-0.916022\pi$
$383$	−0.720228	−	12.3658i	−0.0368019	−	0.631865i	0.928597	−	0.371089i	$-0.121015\pi$
$384$		0			0
$385$	−23.4603	−	5.56020i	−1.19565	−	0.283374i
$386$	4.35230	+	3.65201i	0.221526	+	0.185883i
$387$		0			0
$388$	7.93530	−	6.65850i	0.402854	−	0.338034i
$389$	−16.6026	+	8.33812i	−0.841784	+	0.422760i	−0.816795	−	0.576928i	$-0.804251\pi$
$389$	−16.6026	+	8.33812i	−0.841784	+	0.422760i	−0.0249887	+	0.999688i	$0.507955\pi$
$390$		0			0
$391$	1.19021	+	2.75921i	0.0601914	+	0.139539i
$392$	28.3291	−	38.0526i	1.43084	−	1.92195i
$393$		0			0
$394$	−0.751078	+	12.8955i	−0.0378388	+	0.649667i
$395$	−18.3590	−	6.68214i	−0.923743	−	0.336215i
$396$		0			0
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	−0.0897688	−	0.995963i	$-0.528613\pi$
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	0.571426	+	0.820654i	$0.306391\pi$
$398$	−1.82232	−	6.08698i	−0.0913448	−	0.305113i
$399$		0			0
$400$	1.63723	+	0.822249i	0.0818617	+	0.0411125i
$401$	−1.96445	+	0.465583i	−0.0980998	+	0.0232501i	−0.279373	−	0.960183i	$-0.590126\pi$
$401$	−1.96445	+	0.465583i	−0.0980998	+	0.0232501i	0.181273	+	0.983433i	$0.441978\pi$
$402$		0			0
$403$	12.6806	−	1.48214i	0.631663	−	0.0738308i
$404$	3.11815			0.155134
$405$		0			0
$406$	−22.5768			−1.12047
$407$	1.30967	−	0.153079i	0.0649180	−	0.00758783i
$408$		0			0
$409$	−0.846252	+	0.200565i	−0.0418445	+	0.00991732i	−0.251485	−	0.967861i	$-0.580919\pi$
$409$	−0.846252	+	0.200565i	−0.0418445	+	0.00991732i	0.209640	+	0.977779i	$0.432771\pi$
$410$	0.242051	+	0.121563i	0.0119541	+	0.00600356i
$411$		0			0
$412$	−0.105992	−	0.354039i	−0.00522187	−	0.0174423i
$413$	−54.4506	+	19.8184i	−2.67934	+	0.975200i
$414$		0			0
$415$	−8.66465	−	3.15367i	−0.425331	−	0.154808i
$416$	0.737942	−	12.6700i	0.0361806	−	0.621196i
$417$		0			0
$418$	−1.74144	+	2.33916i	−0.0851766	+	0.114412i
$419$	9.99881	+	23.1799i	0.488474	+	1.13241i	0.967101	+	0.254392i	$0.0818753\pi$
$419$	9.99881	+	23.1799i	0.488474	+	1.13241i	−0.478627	+	0.878018i	$0.658865\pi$
$420$		0			0
$421$	14.9708	−	7.51861i	0.729631	−	0.366435i	−0.0448820	−	0.998992i	$-0.514291\pi$
$421$	14.9708	−	7.51861i	0.729631	−	0.366435i	0.774513	+	0.632558i	$0.217995\pi$
$422$	14.4315	−	12.1095i	0.702516	−	0.589481i
$423$		0			0
$424$	−20.4787	−	17.1836i	−0.994532	−	0.834511i
$425$	11.9040	+	2.82130i	0.577428	+	0.136853i
$426$		0			0
$427$	−2.29442	−	39.3936i	−0.111035	−	1.90639i
$428$	3.94150	−	13.1655i	0.190520	−	0.636380i
$429$		0			0
$430$	−3.33590	−	4.48089i	−0.160871	−	0.216088i
$431$	13.1811	−	22.8303i	0.634911	−	1.09970i	−0.351623	−	0.936142i	$-0.614370\pi$
$431$	13.1811	−	22.8303i	0.634911	−	1.09970i	0.986534	−	0.163556i	$-0.0522966\pi$
$432$		0			0
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	0.976689	−	0.214660i	$-0.0688642\pi$
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	−0.674245	+	0.738508i	$0.735531\pi$
$434$	9.13882	−	21.1862i	0.438678	−	1.01697i
$435$		0			0
$436$	−12.7022	−	13.4636i	−0.608327	−	0.644789i
$437$	1.20777	−	0.794362i	0.0577754	−	0.0379995i
$438$		0			0
$439$	−6.03805	+	6.39996i	−0.288181	+	0.305454i	−0.855249	−	0.518217i	$-0.826596\pi$
$439$	−6.03805	+	6.39996i	−0.288181	+	0.305454i	0.567069	+	0.823671i	$0.308077\pi$
$440$	−2.23659	+	12.6843i	−0.106625	+	0.604702i
$441$		0			0
$442$	−1.31561	−	7.46120i	−0.0625772	−	0.354893i
$443$	−12.7182	−	8.36487i	−0.604258	−	0.397427i	0.210192	−	0.977660i	$-0.432591\pi$
$443$	−12.7182	−	8.36487i	−0.604258	−	0.397427i	−0.814450	+	0.580233i	$0.802961\pi$
$444$		0			0
$445$	13.9036	+	1.62510i	0.659093	+	0.0770369i
$446$	9.35933	+	1.09395i	0.443177	+	0.0518000i
$447$		0			0
$448$	−13.6384	−	8.97010i	−0.644352	−	0.423797i
$449$	0.214786	+	1.21811i	0.0101364	+	0.0574862i	0.989456	−	0.144831i	$-0.0462639\pi$
$449$	0.214786	+	1.21811i	0.0101364	+	0.0574862i	−0.979320	+	0.202317i	$0.935153\pi$
$450$		0			0
$451$	0.0372423	−	0.211212i	0.00175367	−	0.00994557i
$452$	−0.379813	+	0.402578i	−0.0178649	+	0.0189357i
$453$		0			0
$454$	16.5230	−	10.8673i	0.775460	−	0.510028i
$455$	−20.6785	−	21.9180i	−0.969425	−	1.02753i
$456$		0			0
$457$	12.2727	−	28.4513i	0.574092	−	1.33089i	−0.345648	−	0.938364i	$-0.612341\pi$
$457$	12.2727	−	28.4513i	0.574092	−	1.33089i	0.919739	−	0.392530i	$-0.128400\pi$
$458$	−10.1484	−	17.5776i	−0.474204	−	0.821345i
$459$		0			0
$460$	1.30330	−	2.25738i	0.0607666	−	0.105251i
$461$	10.1168	+	13.5892i	0.471185	+	0.632912i	0.972653	−	0.232265i	$-0.0746136\pi$
$461$	10.1168	+	13.5892i	0.471185	+	0.632912i	−0.501467	+	0.865177i	$0.667206\pi$
$462$		0			0
$463$	−10.2352	+	34.1880i	−0.475671	+	1.58885i	0.297543	+	0.954708i	$0.403833\pi$
$463$	−10.2352	+	34.1880i	−0.475671	+	1.58885i	−0.773215	+	0.634144i	$0.781353\pi$
$464$	−0.222038	−	3.81225i	−0.0103079	−	0.176979i
$465$		0			0
$466$	6.99870	+	1.65872i	0.324208	+	0.0768388i
$467$	32.1894	+	27.0101i	1.48955	+	1.24988i	0.895195	+	0.445675i	$0.147036\pi$
$467$	32.1894	+	27.0101i	1.48955	+	1.24988i	0.594353	+	0.804204i	$0.297408\pi$
$468$		0			0
$469$	−1.77640	+	1.49057i	−0.0820263	+	0.0688282i
$470$	3.32984	−	1.67231i	0.153594	−	0.0771378i
$471$		0			0
$472$	12.2607	+	28.4235i	0.564344	+	1.30830i
$473$	−2.64138	+	3.54799i	−0.121451	+	0.163137i
$474$		0			0
$475$	0.342195	−	5.87527i	0.0157010	−	0.269576i
$476$	28.6281	+	10.4198i	1.31217	+	0.477590i
$477$		0			0
$478$	16.1023	−	5.86074i	0.736500	−	0.268064i
$479$	10.3510	+	34.5748i	0.472950	+	1.57976i	0.778537	+	0.627598i	$0.215962\pi$
$479$	10.3510	+	34.5748i	0.472950	+	1.57976i	−0.305588	+	0.952164i	$0.598853\pi$
$480$		0			0
$481$	1.47269	+	0.739610i	0.0671487	+	0.0337233i
$482$	−10.6242	+	2.51798i	−0.483918	+	0.114691i
$483$		0			0
$484$	−10.9402	+	1.27873i	−0.497282	+	0.0581239i
$485$	−20.9136			−0.949639
$486$		0			0
$487$	27.8890			1.26377			0.631885	−	0.775062i	$-0.282282\pi$
$487$	27.8890			1.26377			0.631885	+	0.775062i	$0.282282\pi$
$488$	−20.9378	+	2.44727i	−0.947807	+	0.110783i
$489$		0			0
$490$	−38.0478	+	9.01749i	−1.71882	+	0.407369i
$491$	−19.4382	−	9.76222i	−0.877233	−	0.440563i	−0.0475961	−	0.998867i	$-0.515156\pi$
$491$	−19.4382	−	9.76222i	−0.877233	−	0.440563i	−0.829637	+	0.558304i	$0.811452\pi$
$492$		0			0
$493$	−7.31322	−	24.4278i	−0.329371	−	1.10017i
$494$	−3.42489	+	1.24656i	−0.154093	+	0.0560853i
$495$		0			0
$496$	3.66730	+	1.33479i	0.164667	+	0.0599338i
$497$	−3.53263	+	60.6529i	−0.158460	+	2.72065i
$498$		0			0
$499$	−1.78214	+	2.39383i	−0.0797794	+	0.107162i	−0.840221	−	0.542244i	$-0.817575\pi$
$499$	−1.78214	+	2.39383i	−0.0797794	+	0.107162i	0.760442	+	0.649406i	$0.224982\pi$
$500$	3.40941	+	7.90391i	0.152474	+	0.353473i
$501$		0			0
$502$	7.49974	−	3.76651i	0.334730	−	0.168108i
$503$	30.5223	−	25.6113i	1.36092	−	1.14195i	0.385227	−	0.922822i	$-0.374123\pi$
$503$	30.5223	−	25.6113i	1.36092	−	1.14195i	0.975696	−	0.219128i	$-0.0703214\pi$
$504$		0			0
$505$	−4.82249	−	4.04655i	−0.214598	−	0.180069i
$506$	0.902606	+	0.213922i	0.0401257	+	0.00950997i
$507$		0			0
$508$	−0.838446	−	14.3956i	−0.0372000	−	0.638700i
$509$	−5.71537	+	19.0907i	−0.253329	+	0.846178i	0.732835	+	0.680406i	$0.238197\pi$
$509$	−5.71537	+	19.0907i	−0.253329	+	0.846178i	−0.986164	+	0.165772i	$0.946988\pi$
$510$		0			0
$511$	6.36908	+	8.55515i	0.281751	+	0.378458i
$512$	3.70618	−	6.41930i	0.163792	−	0.283695i
$513$		0			0
$514$	0.462869	+	0.801713i	0.0204163	+	0.0353620i
$515$	−0.295525	+	0.685103i	−0.0130224	+	0.0301893i
$516$		0			0
$517$	−2.02469	−	2.14605i	−0.0890459	−	0.0943831i
$518$	2.48836	−	1.63662i	0.109332	−	0.0719091i
$519$		0			0
$520$	−11.0468	+	11.7089i	−0.484433	+	0.513469i
$521$	6.17183	−	35.0022i	0.270393	−	1.53347i	−0.482833	−	0.875713i	$-0.660392\pi$
$521$	6.17183	−	35.0022i	0.270393	−	1.53347i	0.753226	−	0.657762i	$-0.228497\pi$
$522$		0			0
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	0.928845	+	0.370469i	$0.120803\pi$
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	−0.746121	+	0.665810i	$0.768086\pi$
$524$	−15.5067	−	10.1989i	−0.677411	−	0.445540i
$525$		0			0
$526$	−7.29990	−	0.853236i	−0.318291	−	0.0372029i
$527$	25.8835	+	3.02534i	1.12750	+	0.131786i
$528$		0			0
$529$	18.8320	+	12.3860i	0.818784	+	0.538523i
$530$	3.82623	+	21.6996i	0.166201	+	0.942571i
$531$		0			0
$532$	2.54496	−	14.4332i	0.110338	−	0.625757i
$533$	0.183944	−	0.194969i	0.00796750	−	0.00844505i
$534$		0			0
$535$	−23.1813	+	15.2466i	−1.00222	+	0.659168i
$536$	0.850115	+	0.901069i	0.0367194	+	0.0389203i
$537$		0			0
$538$	0.780507	−	1.80942i	0.0336500	−	0.0780095i
$539$	15.4805	+	26.8130i	0.666792	+	1.15492i
$540$		0			0
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	−0.728511	−	0.685034i	$-0.759787\pi$
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	0.957512	+	0.288392i	$0.0931206\pi$
$542$	−2.59814	−	3.48991i	−0.111600	−	0.149904i
$543$		0			0
$544$	7.42983	−	24.8174i	0.318551	−	1.06404i
$545$	2.17288	+	37.3068i	0.0930758	+	1.59805i
$546$		0			0
$547$	13.2337	+	3.13643i	0.565830	+	0.134104i	0.503568	−	0.863956i	$-0.332020\pi$
$547$	13.2337	+	3.13643i	0.565830	+	0.134104i	0.0622623	+	0.998060i	$0.480168\pi$
$548$	−15.1139	−	12.6821i	−0.645636	−	0.541753i
$549$		0			0
$550$	2.89293	−	2.42746i	0.123355	−	0.103507i
$551$	−10.9619	+	5.50529i	−0.466994	+	0.234533i
$552$		0			0
$553$	13.8398	+	32.0842i	0.588527	+	1.36436i
$554$	−12.5623	+	16.8741i	−0.533720	+	0.716911i
$555$		0			0
$556$	−0.0259801	+	0.446062i	−0.00110180	+	0.0189172i
$557$	−4.31357	−	1.57001i	−0.182772	−	0.0665235i	0.249013	−	0.968500i	$-0.419894\pi$
$557$	−4.31357	−	1.57001i	−0.182772	−	0.0665235i	−0.431785	+	0.901977i	$0.642116\pi$
$558$		0			0
$559$	−5.19480	+	1.89075i	−0.219717	+	0.0799704i
$560$	−2.64182	−	8.82429i	−0.111637	−	0.372894i
$561$		0			0
$562$	22.1544	+	11.1263i	0.934526	+	0.469337i
$563$	−0.964385	+	0.228563i	−0.0406440	+	0.00963280i	−0.250888	−	0.968016i	$-0.580722\pi$
$563$	−0.964385	+	0.228563i	−0.0406440	+	0.00963280i	0.210244	+	0.977649i	$0.432574\pi$
$564$		0			0
$565$	1.10986	−	0.129723i	0.0466920	−	0.00545751i
$566$	−5.26940			−0.221489
$567$		0			0
$568$	32.4565			1.36185
$569$	−7.71668	+	0.901950i	−0.323500	+	0.0378117i	−0.276293	−	0.961073i	$-0.589106\pi$
$569$	−7.71668	+	0.901950i	−0.323500	+	0.0378117i	−0.0472068	+	0.998885i	$0.515032\pi$
$570$		0			0
$571$	20.8205	−	4.93455i	0.871312	−	0.206505i	0.229446	−	0.973321i	$-0.426309\pi$
$571$	20.8205	−	4.93455i	0.871312	−	0.206505i	0.641866	+	0.766817i	$0.278161\pi$
$572$	4.65016	+	2.33540i	0.194433	+	0.0976479i
$573$		0			0
$574$	−0.138936	−	0.464079i	−0.00579909	−	0.0193703i
$575$	−1.75912	+	0.640267i	−0.0733604	+	0.0267010i
$576$		0			0
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	0.166995	−	0.985958i	$-0.446594\pi$
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	−0.505836	+	0.862630i	$0.668816\pi$
$578$	0.120776	−	2.07365i	0.00502364	−	0.0862525i
$579$		0			0
$580$	−13.2083	+	17.7419i	−0.548446	+	0.736691i
$581$	6.53177	+	15.1423i	0.270983	+	0.628210i
$582$		0			0
$583$	15.5911	−	7.83016i	0.645719	−	0.324292i
$584$	4.36471	−	3.66243i	0.180613	−	0.151552i
$585$		0			0
$586$	2.26454	+	1.90017i	0.0935472	+	0.0784954i
$587$	−10.2303	−	2.42462i	−0.422249	−	0.100075i	0.0139973	−	0.999902i	$-0.495544\pi$
$587$	−10.2303	−	2.42462i	−0.422249	−	0.100075i	−0.436247	+	0.899827i	$0.643693\pi$
$588$		0			0
$589$	−0.728926	−	12.5152i	−0.0300349	−	0.515679i
$590$	7.31762	−	24.4425i	0.301261	−	1.00628i
$591$		0			0
$592$	0.300827	+	0.404081i	0.0123639	+	0.0166076i
$593$	−14.0175	+	24.2790i	−0.575630	+	0.997020i	0.420343	+	0.907365i	$0.361910\pi$
$593$	−14.0175	+	24.2790i	−0.575630	+	0.997020i	−0.995973	+	0.0896551i	$0.971424\pi$
$594$		0			0
$595$	−30.7537	−	53.2669i	−1.26078	−	2.18373i
$596$	−1.68220	+	3.89977i	−0.0689054	+	0.159741i
$597$		0			0
$598$	0.795581	+	0.843266i	0.0325337	+	0.0344837i
$599$	−19.4428	+	12.7878i	−0.794413	+	0.522494i	−0.880642	−	0.473782i	$-0.842889\pi$
$599$	−19.4428	+	12.7878i	−0.794413	+	0.522494i	0.0862293	+	0.996275i	$0.472518\pi$
$600$		0			0
$601$	−14.7481	+	15.6320i	−0.601586	+	0.637644i	−0.954570	−	0.297985i	$-0.903685\pi$
$601$	−14.7481	+	15.6320i	−0.601586	+	0.637644i	0.352984	+	0.935629i	$0.385167\pi$
$602$	−1.73491	+	9.83915i	−0.0707096	+	0.401014i
$603$		0			0
$604$	−3.00133	−	17.0214i	−0.122122	−	0.692589i
$605$	18.5794	+	12.2199i	0.755361	+	0.496809i
$606$		0			0
$607$	−4.81123	−	0.562352i	−0.195282	−	0.0228252i	0.0178897	−	0.999840i	$-0.494305\pi$
$607$	−4.81123	−	0.562352i	−0.195282	−	0.0228252i	−0.213171	+	0.977015i	$0.568379\pi$
$608$	−12.3780	−	1.44679i	−0.501996	−	0.0586749i
$609$		0			0
$610$	14.5168	+	9.54783i	0.587767	+	0.386580i
$611$	−0.640316	−	3.63141i	−0.0259044	−	0.146911i
$612$		0			0
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	−0.895924	−	0.444207i	$-0.853485\pi$
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	0.993821	−	0.110994i	$-0.0354034\pi$
$614$	−16.1897	+	17.1601i	−0.653364	+	0.692525i
$615$		0			0
$616$	19.2459	−	12.6583i	0.775441	−	0.510016i
$617$	13.8691	+	14.7004i	0.558351	+	0.591817i	0.943638	−	0.330980i	$-0.107379\pi$
$617$	13.8691	+	14.7004i	0.558351	+	0.591817i	−0.385287	+	0.922797i	$0.625898\pi$
$618$		0			0
$619$	−11.4319	+	26.5020i	−0.459485	+	1.06521i	0.518224	+	0.855245i	$0.326593\pi$
$619$	−11.4319	+	26.5020i	−0.459485	+	1.06521i	−0.977710	+	0.209962i	$0.932666\pi$
$620$	−11.3025	−	19.5764i	−0.453917	−	0.786208i
$621$		0			0
$622$	−1.75151	+	3.03370i	−0.0702290	+	0.121640i
$623$	−14.9502	−	20.0815i	−0.598965	−	0.804550i
$624$		0			0
$625$	8.94311	−	29.8721i	0.357725	−	1.19488i
$626$	−1.42967	−	24.5466i	−0.0571413	−	0.981078i
$627$		0			0
$628$	−7.81583	−	1.85239i	−0.311886	−	0.0739182i
$629$	2.57685	+	2.16223i	0.102746	+	0.0862139i
$630$		0			0
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.451558	+	0.892242i	$0.649132\pi$
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.957099	+	0.289762i	$0.906424\pi$
$632$	16.6809	−	8.37749i	0.663533	−	0.333239i
$633$		0			0
$634$	−8.68025	−	20.1231i	−0.344737	−	0.799190i
$635$	−17.3850	+	23.3521i	−0.689902	+	0.926699i
$636$		0			0
$637$	−2.24992	+	38.6297i	−0.0891452	+	1.53056i
$638$	−7.39666	−	2.69216i	−0.292836	−	0.106584i
$639$		0			0
$640$	−23.8524	+	8.68156i	−0.942848	+	0.343169i
$641$	−7.13913	−	23.8464i	−0.281979	−	0.941874i	−0.975233	−	0.221181i	$-0.929009\pi$
$641$	−7.13913	−	23.8464i	−0.281979	−	0.941874i	0.693254	−	0.720693i	$-0.256176\pi$
$642$		0			0
$643$	1.97867	+	0.993725i	0.0780311	+	0.0391887i	0.487387	−	0.873186i	$-0.337950\pi$
$643$	1.97867	+	0.993725i	0.0780311	+	0.0391887i	−0.409356	+	0.912375i	$0.634246\pi$
$644$	−4.53618	+	1.07509i	−0.178750	+	0.0423646i
$645$		0			0
$646$	−7.38921	+	0.863675i	−0.290725	+	0.0339808i
$647$	−26.5378			−1.04331			−0.521654	−	0.853157i	$-0.674685\pi$
$647$	−26.5378			−1.04331			−0.521654	+	0.853157i	$0.674685\pi$
$648$		0			0
$649$	−20.2024			−0.793015
$650$	4.68792	−	0.547939i	0.183875	−	0.0214919i
$651$		0			0
$652$	9.06401	−	2.14821i	0.354974	−	0.0841304i
$653$	−0.189664	−	0.0952529i	−0.00742213	−	0.00372753i	0.445084	−	0.895489i	$-0.353174\pi$
$653$	−0.189664	−	0.0952529i	−0.00742213	−	0.00372753i	−0.452506	+	0.891761i	$0.649470\pi$
$654$		0			0
$655$	10.7469	+	35.8971i	0.419915	+	1.40261i
$656$	0.0769964	−	0.0280244i	0.00300620	−	0.00109417i
$657$		0			0
$658$	−6.26228	−	2.27928i	−0.244129	−	0.0888558i
$659$	−1.57427	+	27.0291i	−0.0613247	+	1.05290i	0.817552	+	0.575855i	$0.195331\pi$
$659$	−1.57427	+	27.0291i	−0.0613247	+	1.05290i	−0.878876	+	0.477050i	$0.841706\pi$
$660$		0			0
$661$	21.3649	−	28.6980i	0.830998	−	1.11622i	−0.160620	−	0.987016i	$-0.551349\pi$
$661$	21.3649	−	28.6980i	0.830998	−	1.11622i	0.991618	−	0.129207i	$-0.0412432\pi$
$662$	−0.0614733	−	0.142511i	−0.00238923	−	0.00553885i
$663$		0			0
$664$	7.87267	−	3.95381i	0.305519	−	0.153437i
$665$	−22.6665	+	19.0195i	−0.878969	+	0.737543i
$666$		0			0
$667$	2.98902	+	2.50808i	0.115735	+	0.0971134i
$668$	−23.3463	−	5.53316i	−0.903294	−	0.214085i
$669$		0			0
$670$	−0.0593697	−	1.01934i	−0.00229365	−	0.0393805i
$671$	3.94577	−	13.1798i	0.152325	−	0.508800i
$672$		0			0
$673$	−17.0503	−	22.9025i	−0.657240	−	0.882827i	0.341123	−	0.940019i	$-0.389193\pi$
$673$	−17.0503	−	22.9025i	−0.657240	−	0.882827i	−0.998363	+	0.0571917i	$0.981785\pi$
$674$	−7.04994	+	12.2109i	−0.271554	+	0.470345i
$675$		0			0
$676$	−5.71719	−	9.90247i	−0.219892	−	0.380864i
$677$	−5.83223	+	13.5206i	−0.224151	+	0.519640i	−0.992765	−	0.120073i	$-0.961687\pi$
$677$	−5.83223	+	13.5206i	−0.224151	+	0.519640i	0.768614	+	0.639712i	$0.220947\pi$
$678$		0			0
$679$	25.6679	+	27.2063i	0.985042	+	1.04408i
$680$	−27.4525	+	18.0558i	−1.05276	+	0.692409i
$681$		0			0
$682$	5.52041	−	5.85129i	0.211387	−	0.224057i
$683$	−0.764140	+	4.33365i	−0.0292390	+	0.165823i	−0.995931	−	0.0901204i	$-0.971275\pi$
$683$	−0.764140	+	4.33365i	−0.0292390	+	0.165823i	0.966692	+	0.255943i	$0.0823859\pi$
$684$		0			0
$685$	6.91695	+	39.2280i	0.264283	+	1.49882i
$686$	35.4810	+	23.3362i	1.35467	+	0.890982i
$687$		0			0
$688$	−1.67847	−	0.196185i	−0.0639910	−	0.00747947i
$689$	21.6578	+	2.53143i	0.825096	+	0.0964399i
$690$		0			0
$691$	−2.53025	−	1.66417i	−0.0962553	−	0.0633081i	0.500469	−	0.865755i	$-0.333161\pi$
$691$	−2.53025	−	1.66417i	−0.0962553	−	0.0633081i	−0.596724	+	0.802446i	$0.703531\pi$
$692$	−3.29341	−	18.6779i	−0.125197	−	0.710026i
$693$		0			0
$694$	3.08116	−	17.4741i	0.116959	−	0.663309i
$695$	0.619053	−	0.656158i	0.0234820	−	0.0248895i
$696$		0			0
$697$	0.457123	−	0.300654i	0.0173148	−	0.0113881i
$698$	−6.40721	−	6.79125i	−0.242516	−	0.257052i
$699$		0			0
$700$	−7.51725	+	17.4269i	−0.284125	+	0.658677i
$701$	21.6147	+	37.4378i	0.816377	+	1.41401i	0.908335	+	0.418243i	$0.137354\pi$
$701$	21.6147	+	37.4378i	0.816377	+	1.41401i	−0.0919585	+	0.995763i	$0.529313\pi$
$702$		0			0
$703$	0.809112	−	1.40142i	0.0305162	−	0.0528557i
$704$	−3.39859	−	4.56509i	−0.128089	−	0.172053i
$705$		0			0
$706$	4.24706	−	14.1862i	0.159840	−	0.533903i
$707$	0.654654	+	11.2400i	0.0246208	+	0.422723i
$708$		0			0
$709$	−31.3091	−	7.42039i	−1.17584	−	0.278679i	−0.404157	−	0.914690i	$-0.632435\pi$
$709$	−31.3091	−	7.42039i	−1.17584	−	0.278679i	−0.771680	+	0.636011i	$0.780583\pi$
$710$	−20.4932	−	17.1958i	−0.769095	−	0.645347i
$711$		0			0
$712$	−10.2453	+	8.59684i	−0.383959	+	0.322180i
$713$	−3.56351	+	1.78966i	−0.133454	+	0.0670234i
$714$		0			0
$715$	−4.16114	−	9.64660i	−0.155618	−	0.360762i
$716$	1.78612	−	2.39918i	0.0667506	−	0.0896616i
$717$		0			0
$718$	0.425139	−	7.29936i	0.0158661	−	0.272410i
$719$	9.54600	+	3.47446i	0.356006	+	0.129576i	0.513831	−	0.857892i	$-0.328226\pi$
$719$	9.54600	+	3.47446i	0.356006	+	0.129576i	−0.157825	+	0.987467i	$0.550448\pi$
$720$		0			0
$721$	1.25395	−	0.456400i	0.0466995	−	0.0169972i
$722$	−3.26486	−	10.9054i	−0.121506	−	0.405857i
$723$		0			0
$724$	28.5188	+	14.3227i	1.05989	+	0.532298i
$725$	15.4571	−	3.66339i	0.574061	−	0.136055i
$726$		0			0
$727$	−13.9993	+	1.63629i	−0.519206	+	0.0606865i	−0.371660	−	0.928369i	$-0.621211\pi$
$727$	−13.9993	+	1.63629i	−0.519206	+	0.0606865i	−0.147546	+	0.989055i	$0.547137\pi$
$728$	28.7900			1.06703
$729$		0			0
$730$	−4.69629			−0.173818
$731$	−11.2078	+	1.31001i	−0.414536	+	0.0484523i
$732$		0			0
$733$	−15.2752	+	3.62028i	−0.564201	+	0.133718i	−0.502812	−	0.864396i	$-0.667701\pi$
$733$	−15.2752	+	3.62028i	−0.564201	+	0.133718i	−0.0613890	+	0.998114i	$0.519553\pi$
$734$	20.5631	+	10.3272i	0.758996	+	0.381182i
$735$		0			0
$736$	1.13692	+	3.79757i	0.0419074	+	0.139980i
$737$	−0.759727	+	0.276518i	−0.0279849	+	0.0101857i
$738$		0			0
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	0.278345	−	0.960481i	$-0.410214\pi$
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	−0.404161	+	0.914688i	$0.632436\pi$
$740$	0.169660	−	2.91295i	0.00623683	−	0.107082i
$741$		0			0
$742$	23.5328	−	31.6100i	0.863916	−	1.16044i
$743$	−9.22126	−	21.3773i	−0.338295	−	0.784257i	−0.999422	−	0.0339829i	$-0.989181\pi$
$743$	−9.22126	−	21.3773i	−0.338295	−	0.784257i	0.661127	−	0.750274i	$-0.270078\pi$
$744$		0			0
$745$	7.66255	−	3.84828i	0.280734	−	0.140990i
$746$	−3.35694	+	2.81680i	−0.122906	+	0.103130i
$747$		0			0
$748$	8.13668	+	6.82748i	0.297506	+	0.249637i
$749$	48.2852	+	11.4438i	1.76430	+	0.418147i
$750$		0			0
$751$	−0.459295	−	7.88578i	−0.0167599	−	0.287756i	−0.996266	−	0.0863404i	$-0.972483\pi$
$751$	−0.459295	−	7.88578i	−0.0167599	−	0.287756i	0.979506	−	0.201416i	$-0.0645543\pi$
$752$	0.323284	−	1.07984i	0.0117890	−	0.0393778i
$753$		0			0
$754$	−5.87464	−	7.89101i	−0.213942	−	0.287374i
$755$	−17.4475	+	30.2200i	−0.634980	+	1.09982i
$756$		0			0
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	0.824909	−	0.565265i	$-0.191226\pi$
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	−0.901989	+	0.431760i	$0.857893\pi$
$758$	−9.22757	+	21.3919i	−0.335161	+	0.776990i
$759$		0			0
$760$	10.8473	+	11.4975i	0.393474	+	0.417058i
$761$	34.1615	−	22.4684i	1.23835	−	0.814477i	0.250236	−	0.968185i	$-0.419492\pi$
$761$	34.1615	−	22.4684i	1.23835	−	0.814477i	0.988116	+	0.153707i	$0.0491213\pi$
$762$		0			0
$763$	45.8653	−	48.6143i	1.66043	−	1.75996i
$764$	−5.24431	+	29.7420i	−0.189733	+	1.07603i
$765$		0			0
$766$	−1.69387	−	9.60642i	−0.0612020	−	0.347094i
$767$	−21.0953	−	13.8746i	−0.761707	−	0.500983i
$768$		0			0
$769$	−32.4744	−	3.79571i	−1.17106	−	0.136877i	−0.491753	−	0.870735i	$-0.663644\pi$
$769$	−32.4744	−	3.79571i	−1.17106	−	0.136877i	−0.679303	+	0.733858i	$0.737718\pi$
$770$	−18.8584	−	2.20424i	−0.679611	−	0.0794351i
$771$		0			0
$772$	−8.31731	−	5.47038i	−0.299347	−	0.196883i
$773$	6.74796	+	38.2696i	0.242707	+	1.37646i	0.825757	+	0.564025i	$0.190748\pi$
$773$	6.74796	+	38.2696i	0.242707	+	1.37646i	−0.583050	+	0.812436i	$0.698141\pi$
$774$		0			0
$775$	−2.81909	+	15.9878i	−0.101265	+	0.574300i
$776$	13.7121	−	14.5340i	0.492236	−	0.521740i
$777$		0			0
$778$	−12.2238	+	8.03975i	−0.438246	+	0.288239i
$779$	−0.180623	−	0.191449i	−0.00647149	−	0.00685938i
$780$		0			0
$781$	−8.38988	+	19.4499i	−0.300214	+	0.695973i
$782$	1.18321	+	2.04938i	0.0423115	+	0.0732856i
$783$		0			0
$784$	−5.91429	+	10.2439i	−0.211225	+	0.365852i
$785$	9.68394	+	13.0078i	0.345635	+	0.464268i
$786$		0			0
$787$	−0.654240	+	2.18531i	−0.0233211	+	0.0778980i	−0.968858	−	0.247617i	$-0.920353\pi$
$787$	−0.654240	+	2.18531i	−0.0233211	+	0.0778980i	0.945537	+	0.325515i	$0.105538\pi$
$788$	−1.31602	−	22.5952i	−0.0468813	−	0.804922i
$789$		0			0
$790$	−14.9709	−	3.54817i	−0.532641	−	0.126238i
$791$	−1.53091	−	1.28459i	−0.0544329	−	0.0456746i
$792$		0			0
$793$	13.1718	−	11.0524i	0.467743	−	0.392483i
$794$	7.18716	−	3.60953i	0.255063	−	0.128097i
$795$		0			0
$796$	4.40963	+	10.2227i	0.156295	+	0.362333i
$797$	−20.4260	+	27.4369i	−0.723526	+	0.971864i	0.276416	+	0.961038i	$0.410853\pi$
$797$	−20.4260	+	27.4369i	−0.723526	+	0.971864i	−0.999941	+	0.0108254i	$0.996554\pi$
$798$		0			0
$799$	0.437642	−	7.51403i	0.0154827	−	0.265827i
$800$	15.1653	+	5.51971i	0.536174	+	0.195151i
$801$		0			0
$802$	−1.49398	+	0.543764i	−0.0527543	+	0.0192010i
$803$	1.06649	+	3.56233i	0.0376356	+	0.125712i
$804$		0			0
$805$	8.41078	+	4.22405i	0.296441	+	0.148878i
$806$	9.78293	−	2.31860i	0.344589	−	0.0816691i
$807$		0			0
$808$	5.97406	−	0.698267i	0.210167	−	0.0245649i
$809$	22.5844			0.794027			0.397013	−	0.917813i	$-0.370047\pi$
$809$	22.5844			0.794027			0.397013	+	0.917813i	$0.370047\pi$
$810$		0			0
$811$	15.6809			0.550631			0.275315	−	0.961354i	$-0.411218\pi$
$811$	15.6809			0.550631			0.275315	+	0.961354i	$0.411218\pi$
$812$	39.2912	−	4.59248i	1.37885	−	0.161164i
$813$		0			0
$814$	1.01040	−	0.239469i	0.0354145	−	0.00839339i
$815$	−16.8061	−	8.44034i	−0.588692	−	0.295652i
$816$		0			0
$817$	1.55688	+	5.20034i	0.0544683	+	0.181937i
$818$	−0.643582	+	0.234245i	−0.0225023	+	0.00819017i
$819$		0			0
$820$	−0.445977	−	0.162322i	−0.0155742	−	0.00566854i
$821$	2.97242	−	51.0345i	0.103738	−	1.78112i	−0.399269	−	0.916834i	$-0.630736\pi$
$821$	2.97242	−	51.0345i	0.103738	−	1.78112i	0.503007	−	0.864282i	$-0.332227\pi$
$822$		0			0
$823$	1.96916	−	2.64504i	0.0686407	−	0.0922004i	−0.766477	−	0.642272i	$-0.777992\pi$
$823$	1.96916	−	2.64504i	0.0686407	−	0.0922004i	0.835118	+	0.550071i	$0.185399\pi$
$824$	−0.282353	−	0.654567i	−0.00983622	−	0.0228029i
$825$		0			0
$826$	−40.7781	+	20.4796i	−1.41885	+	0.712575i
$827$	−15.7734	+	13.2354i	−0.548494	+	0.460241i	−0.874431	−	0.485151i	$-0.838765\pi$
$827$	−15.7734	+	13.2354i	−0.548494	+	0.460241i	0.325937	+	0.945392i	$0.394320\pi$
$828$		0			0
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	0.801552	−	0.597925i	$-0.204008\pi$
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	−0.449654	+	0.893203i	$0.648453\pi$
$830$	−7.06560	−	1.67458i	−0.245251	−	0.0581255i
$831$		0			0
$832$	−0.413582	−	7.10093i	−0.0143384	−	0.246180i
$833$	−22.6530	+	75.6661i	−0.784878	+	2.62168i
$834$		0			0
$835$	28.9264	+	38.8549i	1.00104	+	1.34463i
$836$	2.55486	−	4.42514i	0.0883616	−	0.153047i
$837$		0			0
$838$	9.94002	+	17.2166i	0.343372	+	0.594738i
$839$	−2.49892	+	5.79314i	−0.0862721	+	0.200001i	−0.955891	−	0.293723i	$-0.905106\pi$
$839$	−2.49892	+	5.79314i	−0.0862721	+	0.200001i	0.869618	+	0.493724i	$0.164365\pi$
$840$		0			0
$841$	−2.82044	−	2.98950i	−0.0972567	−	0.103086i
$842$	11.0224	−	7.24956i	0.379858	−	0.249836i
$843$		0			0
$844$	−22.6524	+	24.0101i	−0.779727	+	0.826462i
$845$	−4.00870	+	22.7345i	−0.137903	+	0.782089i
$846$		0			0
$847$	−6.90630	−	39.1676i	−0.237303	−	1.34581i
$848$	5.56900	+	3.66279i	0.191240	+	0.125781i
$849$		0			0
$850$	9.56895	+	1.11845i	0.328212	+	0.0383625i
$851$	−0.511256	−	0.0597573i	−0.0175256	−	0.00204845i
$852$		0			0
$853$	−15.1422	−	9.95918i	−0.518459	−	0.340996i	0.263160	−	0.964752i	$-0.415235\pi$
$853$	−15.1422	−	9.95918i	−0.518459	−	0.340996i	−0.781619	+	0.623756i	$0.785606\pi$
$854$	−5.39614	−	30.6030i	−0.184652	−	1.04721i
$855$		0			0
$856$	4.60327	−	26.1064i	0.157336	−	0.892299i
$857$	−23.3373	+	24.7360i	−0.797185	+	0.844967i	−0.990691	−	0.136132i	$-0.956533\pi$
$857$	−23.3373	+	24.7360i	−0.797185	+	0.844967i	0.193505	+	0.981099i	$0.438014\pi$
$858$		0			0
$859$	−39.7658	+	26.1544i	−1.35679	+	0.892376i	−0.999139	−	0.0414781i	$-0.986793\pi$
$859$	−39.7658	+	26.1544i	−1.35679	+	0.892376i	−0.357653	+	0.933855i	$0.616423\pi$
$860$	6.71705	+	7.11965i	0.229049	+	0.242778i
$861$		0			0
$862$	8.22272	−	19.0624i	0.280067	−	0.649268i
$863$	−26.7851	−	46.3932i	−0.911777	−	1.57924i	−0.811553	−	0.584279i	$-0.801377\pi$
$863$	−26.7851	−	46.3932i	−0.911777	−	1.57924i	−0.100224	−	0.994965i	$-0.531956\pi$
$864$		0			0
$865$	−19.1455	+	33.1610i	−0.650966	+	1.12751i
$866$	5.91915	+	7.95080i	0.201141	+	0.270179i
$867$		0			0
$868$	−11.5950	+	38.7299i	−0.393559	+	1.31458i
$869$	0.708344	+	12.1618i	0.0240289	+	0.412561i
$870$		0			0
$871$	−0.983211	−	0.233025i	−0.0333148	−	0.00789576i
$872$	−27.3512	−	22.9504i	−0.926227	−	0.777197i
$873$		0			0
$874$	0.872065	−	0.731749i	0.0294980	−	0.0247518i
$875$	−27.7753	+	13.9493i	−0.938977	+	0.471572i
$876$		0			0
$877$	−5.69036	−	13.1917i	−0.192150	−	0.445453i	0.794719	−	0.606977i	$-0.207618\pi$
$877$	−5.69036	−	13.1917i	−0.192150	−	0.445453i	−0.986869	+	0.161524i	$0.948359\pi$
$878$	−4.13772	+	5.55792i	−0.139641	+	0.187571i
$879$		0			0
$880$	0.186731	−	3.20605i	0.00629470	−	0.108076i
$881$	−0.647962	−	0.235839i	−0.0218304	−	0.00794561i	0.331082	−	0.943602i	$-0.392586\pi$
$881$	−0.647962	−	0.235839i	−0.0218304	−	0.00794561i	−0.352912	+	0.935656i	$0.614809\pi$
$882$		0			0
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.710407	−	0.703791i	$-0.751489\pi$
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.0918148	+	0.995776i	$0.529267\pi$
$884$	3.80732	+	12.7173i	0.128054	+	0.427730i
$885$		0			0
$886$	−10.7126	−	5.38007i	−0.359897	−	0.180747i
$887$	−40.5894	+	9.61987i	−1.36286	+	0.323004i	−0.846053	−	0.533099i	$-0.821027\pi$
$887$	−40.5894	+	9.61987i	−1.36286	+	0.323004i	−0.516806	+	0.856102i	$0.672879\pi$
$888$		0			0
$889$	51.7155	−	6.04468i	1.73448	−	0.202732i
$890$	11.0236			0.369513
$891$		0			0
$892$	−16.5109			−0.552824
$893$	−3.59638	+	0.420356i	−0.120348	+	0.0140667i
$894$		0			0
$895$	−5.87591	+	1.39262i	−0.196410	+	0.0465500i
$896$	40.5684	+	20.3742i	1.35530	+	0.680655i
$897$		0			0
$898$	0.279364	+	0.933141i	0.00932250	+	0.0311393i
$899$	31.7972	−	11.5732i	1.06050	−	0.385989i
$900$		0			0
$901$	41.8245	+	15.2229i	1.39338	+	0.507147i
$902$	0.00982039	−	0.168610i	0.000326983	−	0.00561409i
$903$		0			0
$904$	−0.637530	+	0.856351i	−0.0212039	+	0.0284818i
$905$	−25.5197	−	59.1612i	−0.848302	−	1.96658i
$906$		0			0
$907$	−35.4778	+	17.8176i	−1.17802	+	0.591624i	−0.926525	−	0.376234i	$-0.877219\pi$
$907$	−35.4778	+	17.8176i	−1.17802	+	0.591624i	−0.251496	+	0.967858i	$0.580923\pi$
$908$	−26.5448	+	22.2737i	−0.880920	+	0.739180i
$909$		0			0
$910$	−18.1781	−	15.2532i	−0.602598	−	0.505640i
$911$	−38.3314	−	9.08471i	−1.26998	−	0.300990i	−0.460246	−	0.887792i	$-0.652239\pi$
$911$	−38.3314	−	9.08471i	−1.26998	−	0.300990i	−0.809731	+	0.586802i	$0.800387\pi$
$912$		0			0
$913$	0.334307	+	5.73983i	0.0110639	+	0.189961i
$914$	6.99829	−	23.3759i	0.231483	−	0.773207i
$915$		0			0
$916$	21.2371	+	28.5264i	0.701694	+	0.942539i
$917$	33.5082	−	58.0379i	1.10654	−	1.91658i
$918$		0			0
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	0.967069	−	0.254513i	$-0.0819150\pi$
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	−0.703949	+	0.710250i	$0.748582\pi$
$920$	1.99148	−	4.61676i	0.0656570	−	0.152210i
$921$		0			0
$922$	9.15548	+	9.70424i	0.301520	+	0.319592i
$923$	−22.1185	+	14.5476i	−0.728039	+	0.478838i
$924$		0			0
$925$	−1.43808	+	1.52427i	−0.0472836	+	0.0501177i
$926$	−4.88017	+	27.6768i	−0.160372	+	0.909516i
$927$		0			0
$928$	−5.84117	−	33.1269i	−0.191746	−	1.08744i
$929$	−20.9718	−	13.7934i	−0.688064	−	0.452547i	0.156728	−	0.987642i	$-0.449905\pi$
$929$	−20.9718	−	13.7934i	−0.688064	−	0.452547i	−0.844792	+	0.535095i	$0.820276\pi$
$930$		0			0
$931$	37.7396	+	4.41113i	1.23687	+	0.144569i
$932$	−12.5175	−	1.46308i	−0.410023	−	0.0479248i
$933$		0			0
$934$	27.6471	+	18.1838i	0.904642	+	0.594993i
$935$	−3.72378	−	21.1186i	−0.121781	−	0.690652i
$936$		0			0
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	0.649140	+	0.760669i	$0.275129\pi$
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	−0.870156	+	0.492776i	$0.835982\pi$
$938$	−1.25318	+	1.32829i	−0.0409178	+	0.0433704i
$939$		0			0
$940$	−5.45484	+	3.58771i	−0.177917	+	0.117018i
$941$	22.6965	+	24.0569i	0.739884	+	0.784231i	0.982574	−	0.185873i	$-0.0595112\pi$
$941$	22.6965	+	24.0569i	0.739884	+	0.784231i	−0.242690	+	0.970104i	$0.578030\pi$
$942$		0			0
$943$	−0.0331608	+	0.0768755i	−0.00107987	+	0.00250341i
$944$	−3.85915	−	6.68424i	−0.125605	−	0.217554i
$945$		0			0
$946$	−1.74166	+	3.01664i	−0.0566261	+	0.0980793i
$947$	−8.66134	−	11.6342i	−0.281456	−	0.378060i	0.638804	−	0.769370i	$-0.279430\pi$
$947$	−8.66134	−	11.6342i	−0.281456	−	0.378060i	−0.920259	+	0.391309i	$0.872022\pi$
$948$		0			0
$949$	−1.33290	+	4.45221i	−0.0432679	+	0.144525i
$950$	−0.269479	−	4.62678i	−0.00874306	−	0.150113i
$951$		0			0
$952$	57.1818	+	13.5523i	1.85327	+	0.439234i
$953$	4.46031	+	3.74265i	0.144484	+	0.121236i	0.712165	−	0.702012i	$-0.247715\pi$
$953$	4.46031	+	3.74265i	0.144484	+	0.121236i	−0.567681	+	0.823249i	$0.692159\pi$
$954$		0			0
$955$	46.7081	−	39.1928i	1.51144	−	1.26825i
$956$	−26.8311	+	13.4751i	−0.867779	+	0.435815i
$957$		0			0
$958$	11.2573	+	26.0973i	0.363706	+	0.843164i
$959$	42.5419	−	57.1437i	1.37375	−	1.84527i
$960$		0			0
$961$	−0.208263	+	3.57574i	−0.00671816	+	0.115346i
$962$	1.21952	+	0.443868i	0.0393188	+	0.0143109i
$963$		0			0
$964$	17.9774	−	6.54323i	0.579013	−	0.210743i
$965$	5.76431	+	19.2541i	0.185560	+	0.619813i
$966$		0			0
$967$	−40.8302	−	20.5057i	−1.31301	−	0.659418i	−0.352018	−	0.935993i	$-0.614504\pi$
$967$	−40.8302	−	20.5057i	−1.31301	−	0.659418i	−0.960992	+	0.276575i	$0.910801\pi$
$968$	−20.6739	+	4.89981i	−0.664485	+	0.157486i
$969$		0			0
$970$	−16.3582	+	1.91199i	−0.525229	+	0.0613904i
$971$	−1.52462			−0.0489275			−0.0244638	−	0.999701i	$-0.507788\pi$
$971$	−1.52462			−0.0489275			−0.0244638	+	0.999701i	$0.507788\pi$
$972$		0			0
$973$	−1.61337			−0.0517222
$974$	21.8141	−	2.54970i	0.698969	−	0.0816977i
$975$		0			0
$976$	5.11445	−	1.21215i	0.163709	−	0.0387999i
$977$	−18.2252	−	9.15302i	−0.583075	−	0.292831i	0.132707	−	0.991155i	$-0.457633\pi$
$977$	−18.2252	−	9.15302i	−0.583075	−	0.292831i	−0.715782	+	0.698324i	$0.753929\pi$
$978$		0			0
$979$	−2.50338	−	8.36186i	−0.0800083	−	0.267246i
$980$	64.3814	−	23.4329i	2.05659	−	0.748537i
$981$		0			0
$982$	−16.0966	−	5.85868i	−0.513662	−	0.186958i
$983$	2.45164	−	42.0930i	0.0781952	−	1.34256i	−0.699822	−	0.714317i	$-0.746738\pi$
$983$	2.45164	−	42.0930i	0.0781952	−	1.34256i	0.778018	−	0.628242i	$-0.216225\pi$
$984$		0			0
$985$	−27.2874	+	36.6533i	−0.869449	+	1.16787i
$986$	−7.95350	−	18.4383i	−0.253291	−	0.587195i
$987$		0			0
$988$	5.70686	−	2.86609i	0.181560	−	0.0911826i
$989$	1.32273	−	1.10990i	0.0420604	−	0.0352929i
$990$		0			0
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	0.623632	−	0.781718i	$-0.285656\pi$
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	−0.661550	+	0.749901i	$0.730101\pi$
$992$	33.4508	+	7.92799i	1.06206	+	0.251714i
$993$		0			0
$994$	2.78195	+	47.7642i	0.0882381	+	1.51499i
$995$	6.44650	−	21.5328i	0.204368	−	0.682636i
$996$		0			0
$997$	−31.2532	−	41.9803i	−0.989799	−	1.32953i	−0.943774	−	0.330590i	$-0.892752\pi$
$997$	−31.2532	−	41.9803i	−0.989799	−	1.32953i	−0.0460247	−	0.998940i	$-0.514655\pi$
$998$	−1.17509	+	2.03532i	−0.0371970	+	0.0644270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.298.6		144
3.2	odd	2		729.2.g.d.298.3		144
9.2	odd	6		81.2.g.a.7.6	✓	144
9.4	even	3		729.2.g.b.55.3		144
9.5	odd	6		729.2.g.c.55.6		144
9.7	even	3		243.2.g.a.100.3		144
81.2	odd	54		6561.2.a.c.1.48		72
81.4	even	27	inner	729.2.g.a.433.6		144
81.23	odd	54		729.2.g.c.676.6		144
81.31	even	27		243.2.g.a.226.3		144
81.50	odd	54		81.2.g.a.58.6	yes	144
81.58	even	27		729.2.g.b.676.3		144
81.77	odd	54		729.2.g.d.433.3		144
81.79	even	27		6561.2.a.d.1.25		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.6	✓	144	9.2	odd	6
81.2.g.a.58.6	yes	144	81.50	odd	54
243.2.g.a.100.3		144	9.7	even	3
243.2.g.a.226.3		144	81.31	even	27
729.2.g.a.298.6		144	1.1	even	1	trivial
729.2.g.a.433.6		144	81.4	even	27	inner
729.2.g.b.55.3		144	9.4	even	3
729.2.g.b.676.3		144	81.58	even	27
729.2.g.c.55.6		144	9.5	odd	6
729.2.g.c.676.6		144	81.23	odd	54
729.2.g.d.298.3		144	3.2	odd	2
729.2.g.d.433.3		144	81.77	odd	54
6561.2.a.c.1.48		72	81.2	odd	54
6561.2.a.d.1.25		72	81.79	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.782176 - 0.0914233i) q^{2} +(-1.34265 + 0.318213i) q^{4} +(2.48948 + 1.25026i) q^{5} +(-1.42895 - 4.77302i) q^{7} +(-2.50111 + 0.910331i) q^{8} +(2.06152 + 0.750330i) q^{10} +(0.101002 - 1.73414i) q^{11} +(1.29643 - 1.74141i) q^{13} +(-1.55406 - 3.60270i) q^{14} +(0.593056 - 0.297844i) q^{16} +(3.39468 - 2.84848i) q^{17} +(-1.63306 - 1.37030i) q^{19} +(-3.74035 - 0.886478i) q^{20} +(-0.0795392 - 1.36564i) q^{22} +(-0.194482 + 0.649615i) q^{23} +(1.64856 + 2.21440i) q^{25} +(0.854835 - 1.48062i) q^{26} +(3.43741 + 5.95378i) q^{28} +(2.27909 - 5.28353i) q^{29} +(4.03553 + 4.27741i) q^{31} +(4.88416 - 3.21236i) q^{32} +(2.39482 - 2.53836i) q^{34} +(2.41020 - 13.6689i) q^{35} +(0.131814 + 0.747552i) q^{37} +(-1.40262 - 0.922517i) q^{38} +(-7.36463 - 0.860801i) q^{40} +(0.122631 + 0.0143335i) q^{41} +(-2.12747 - 1.39926i) q^{43} +(0.416216 + 2.36048i) q^{44} +(-0.0927292 + 0.525894i) q^{46} +(1.16557 - 1.23544i) q^{47} +(-14.8914 + 9.79424i) q^{49} +(1.49191 + 1.58133i) q^{50} +(-1.18651 + 2.75065i) q^{52} +(5.02192 + 8.69822i) q^{53} +(2.41957 - 4.19082i) q^{55} +(7.91899 + 10.6371i) q^{56} +(1.29962 - 4.34102i) q^{58} +(-0.676232 - 11.6105i) q^{59} +(7.70658 + 1.82649i) q^{61} +(3.54755 + 2.97675i) q^{62} +(2.50983 - 2.10599i) q^{64} +(5.40467 - 2.71433i) q^{65} +(-0.184347 - 0.427364i) q^{67} +(-3.65144 + 4.90473i) q^{68} +(0.635542 - 10.9118i) q^{70} +(-11.4588 - 4.17067i) q^{71} +(-2.01159 + 0.732160i) q^{73} +(0.171445 + 0.572667i) q^{74} +(2.62867 + 1.32017i) q^{76} +(-8.42140 + 1.99591i) q^{77} +(-6.96575 + 0.814179i) q^{79} +1.84879 q^{80} +0.0972297 q^{82} +(-3.28752 + 0.384257i) q^{83} +(12.0123 - 2.84698i) q^{85} +(-1.79198 - 0.899965i) q^{86} +(1.32602 + 4.42922i) q^{88} +(4.72182 - 1.71860i) q^{89} +(-10.1643 - 3.69952i) q^{91} +(0.0544046 - 0.934091i) q^{92} +(0.798737 - 1.07289i) q^{94} +(-2.35223 - 5.45309i) q^{95} +(-6.70871 + 3.36924i) q^{97} +(-10.7523 + 9.02224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more