LMFDB - Embedded newform 243.2.g.a.226.3

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			226.3
Character	$\chi$	$=$	243.226
Dual form			243.2.g.a.100.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.470263 + 0.631673i) q^{2} +(0.395743 + 1.32187i) q^{4} +(-2.32750 - 1.53082i) q^{5} +(-3.41908 - 3.62402i) q^{7} +(-2.50111 - 0.910331i) q^{8} +(2.06152 - 0.750330i) q^{10} +(-1.55231 - 0.779598i) q^{11} +(0.859891 - 1.99345i) q^{13} +(3.89706 - 0.455501i) q^{14} +(-0.554469 + 0.364680i) q^{16} +(3.39468 + 2.84848i) q^{17} +(-1.63306 + 1.37030i) q^{19} +(1.10246 - 3.68247i) q^{20} +(1.22244 - 0.613935i) q^{22} +(-0.465342 + 0.493234i) q^{23} +(1.09345 + 2.53489i) q^{25} +(0.854835 + 1.48062i) q^{26} +(3.43741 - 5.95378i) q^{28} +(-5.71522 - 0.668013i) q^{29} +(-5.72212 - 1.35617i) q^{31} +(0.339908 - 5.83599i) q^{32} +(-3.39570 + 0.804795i) q^{34} +(2.41020 + 13.6689i) q^{35} +(0.131814 - 0.747552i) q^{37} +(-0.0976137 - 1.67596i) q^{38} +(4.42779 + 5.94755i) q^{40} +(-0.0737288 - 0.0990350i) q^{41} +(-0.148059 - 2.54207i) q^{43} +(0.416216 - 2.36048i) q^{44} +(-0.0927292 - 0.525894i) q^{46} +(-1.65271 + 0.391699i) q^{47} +(-1.03635 + 17.7935i) q^{49} +(-2.11543 - 0.501366i) q^{50} +(2.97539 + 0.347773i) q^{52} +(5.02192 - 8.69822i) q^{53} +(2.41957 + 4.19082i) q^{55} +(5.25246 + 12.1766i) q^{56} +(3.10962 - 3.29601i) q^{58} +(10.3931 - 5.21959i) q^{59} +(-2.27150 + 7.58734i) q^{61} +(3.54755 - 2.97675i) q^{62} +(2.50983 + 2.10599i) q^{64} +(-5.05301 + 3.32342i) q^{65} +(0.462282 - 0.0540330i) q^{67} +(-2.42190 + 5.61460i) q^{68} +(-9.76770 - 4.90552i) q^{70} +(-11.4588 + 4.17067i) q^{71} +(-2.01159 - 0.732160i) q^{73} +(0.410222 + 0.434809i) q^{74} +(-2.45764 - 1.61641i) q^{76} +(2.48219 + 8.29110i) q^{77} +(4.18797 - 5.62542i) q^{79} +1.84879 q^{80} +0.0972297 q^{82} +(1.97654 - 2.65495i) q^{83} +(-3.54061 - 11.8265i) q^{85} +(1.67538 + 1.10192i) q^{86} +(3.17281 + 3.36298i) q^{88} +(4.72182 + 1.71860i) q^{89} +(-10.1643 + 3.69952i) q^{91} +(-0.836149 - 0.419930i) q^{92} +(0.529782 - 1.22817i) q^{94} +(5.89863 - 0.689452i) q^{95} +(6.27220 - 4.12529i) q^{97} +(-10.7523 - 9.02224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{27}\right)$

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 $

$2$	−0.470263	+	0.631673i	−0.332526	+	0.446660i	−0.936669	−	0.350216i	$-0.886108\pi$
$2$	−0.470263	+	0.631673i	−0.332526	+	0.446660i	0.604143	+	0.796876i	$0.293516\pi$
$3$		0			0
$3$		0			0
$4$	0.395743	+	1.32187i	0.197872	+	0.660937i
$5$	−2.32750	−	1.53082i	−1.04089	−	0.684604i	−0.0905734	−	0.995890i	$-0.528870\pi$
$5$	−2.32750	−	1.53082i	−1.04089	−	0.684604i	−0.950316	+	0.311286i	$0.899240\pi$
$6$		0			0
$7$	−3.41908	−	3.62402i	−1.29229	−	1.36975i	−0.891134	−	0.453740i	$-0.850089\pi$
$7$	−3.41908	−	3.62402i	−1.29229	−	1.36975i	−0.401158	−	0.916009i	$-0.631392\pi$
$8$	−2.50111	−	0.910331i	−0.884277	−	0.321851i
$9$		0			0
$10$	2.06152	−	0.750330i	0.651909	−	0.237275i
$11$	−1.55231	−	0.779598i	−0.468038	−	0.235058i	0.199118	−	0.979976i	$-0.436192\pi$
$11$	−1.55231	−	0.779598i	−0.468038	−	0.235058i	−0.667156	+	0.744918i	$0.732489\pi$
$12$		0			0
$13$	0.859891	−	1.99345i	0.238491	−	0.552884i	−0.756369	−	0.654145i	$-0.773029\pi$
$13$	0.859891	−	1.99345i	0.238491	−	0.552884i	0.994860	+	0.101261i	$0.0322878\pi$
$14$	3.89706	−	0.455501i	1.04153	−	0.121738i
$15$		0			0
$16$	−0.554469	+	0.364680i	−0.138617	+	0.0911700i
$17$	3.39468	+	2.84848i	0.823331	+	0.690857i	0.953750	−	0.300602i	$-0.0971877\pi$
$17$	3.39468	+	2.84848i	0.823331	+	0.690857i	−0.130419	+	0.991459i	$0.541632\pi$
$18$		0			0
$19$	−1.63306	+	1.37030i	−0.374650	+	0.314369i	−0.810598	−	0.585603i	$-0.800858\pi$
$19$	−1.63306	+	1.37030i	−0.374650	+	0.314369i	0.435948	+	0.899972i	$0.356413\pi$
$20$	1.10246	−	3.68247i	0.246518	−	0.823426i
$21$		0			0
$22$	1.22244	−	0.613935i	0.260626	−	0.130891i
$23$	−0.465342	+	0.493234i	−0.0970305	+	0.102846i	−0.774069	−	0.633101i	$-0.781782\pi$
$23$	−0.465342	+	0.493234i	−0.0970305	+	0.102846i	0.677038	+	0.735948i	$0.263263\pi$
$24$		0			0
$25$	1.09345	+	2.53489i	0.218689	+	0.506978i
$26$	0.854835	+	1.48062i	0.167647	+	0.290373i
$27$		0			0
$28$	3.43741	−	5.95378i	0.649610	−	1.12516i
$29$	−5.71522	−	0.668013i	−1.06129	−	0.124047i	−0.432509	−	0.901630i	$-0.642372\pi$
$29$	−5.71522	−	0.668013i	−1.06129	−	0.124047i	−0.628781	+	0.777583i	$0.716446\pi$
$30$		0			0
$31$	−5.72212	−	1.35617i	−1.02772	−	0.243575i	−0.318026	−	0.948082i	$-0.603020\pi$
$31$	−5.72212	−	1.35617i	−1.02772	−	0.243575i	−0.709697	+	0.704507i	$0.751168\pi$
$32$	0.339908	−	5.83599i	0.0600878	−	1.03167i
$33$		0			0
$34$	−3.39570	+	0.804795i	−0.582357	+	0.138021i
$35$	2.41020	+	13.6689i	0.407397	+	2.31047i
$36$		0			0
$37$	0.131814	−	0.747552i	0.0216700	−	0.122897i	−0.972054	−	0.234758i	$-0.924570\pi$
$37$	0.131814	−	0.747552i	0.0216700	−	0.122897i	0.993724	+	0.111861i	$0.0356813\pi$
$38$	−0.0976137	−	1.67596i	−0.0158350	−	0.271877i
$39$		0			0
$40$	4.42779	+	5.94755i	0.700095	+	0.940391i
$41$	−0.0737288	−	0.0990350i	−0.0115145	−	0.0154667i	0.796329	−	0.604864i	$-0.206773\pi$
$41$	−0.0737288	−	0.0990350i	−0.0115145	−	0.0154667i	−0.807843	+	0.589398i	$0.799365\pi$
$42$		0			0
$43$	−0.148059	−	2.54207i	−0.0225787	−	0.387662i	−0.990600	−	0.136792i	$-0.956321\pi$
$43$	−0.148059	−	2.54207i	−0.0225787	−	0.387662i	0.968021	−	0.250869i	$-0.0807164\pi$
$44$	0.416216	−	2.36048i	0.0627469	−	0.355855i
$45$		0			0
$46$	−0.0927292	−	0.525894i	−0.0136722	−	0.0775388i
$47$	−1.65271	+	0.391699i	−0.241072	+	0.0571351i	−0.349376	−	0.936983i	$-0.613606\pi$
$47$	−1.65271	+	0.391699i	−0.241072	+	0.0571351i	0.108304	+	0.994118i	$0.465458\pi$
$48$		0			0
$49$	−1.03635	+	17.7935i	−0.148050	+	2.54192i
$50$	−2.11543	−	0.501366i	−0.299167	−	0.0709039i
$51$		0			0
$52$	2.97539	+	0.347773i	0.412612	+	0.0482274i
$53$	5.02192	−	8.69822i	0.689814	−	1.19479i	−0.282084	−	0.959390i	$-0.591026\pi$
$53$	5.02192	−	8.69822i	0.689814	−	1.19479i	0.971898	−	0.235403i	$-0.0756410\pi$
$54$		0			0
$55$	2.41957	+	4.19082i	0.326255	+	0.565090i
$56$	5.25246	+	12.1766i	0.701890	+	1.62716i
$57$		0			0
$58$	3.10962	−	3.29601i	0.408314	−	0.432787i
$59$	10.3931	−	5.21959i	1.35306	−	0.679533i	0.383309	−	0.923620i	$-0.374785\pi$
$59$	10.3931	−	5.21959i	1.35306	−	0.679533i	0.969753	+	0.244087i	$0.0784883\pi$
$60$		0			0
$61$	−2.27150	+	7.58734i	−0.290836	+	0.971460i	0.680300	+	0.732934i	$0.261849\pi$
$61$	−2.27150	+	7.58734i	−0.290836	+	0.971460i	−0.971136	+	0.238526i	$0.923336\pi$
$62$	3.54755	−	2.97675i	0.450540	−	0.378048i
$63$		0			0
$64$	2.50983	+	2.10599i	0.313728	+	0.263249i
$65$	−5.05301	+	3.32342i	−0.626749	+	0.412220i
$66$		0			0
$67$	0.462282	−	0.0540330i	0.0564767	−	0.00660118i	−0.0878076	−	0.996137i	$-0.527986\pi$
$67$	0.462282	−	0.0540330i	0.0564767	−	0.00660118i	0.144284	+	0.989536i	$0.453912\pi$
$68$	−2.42190	+	5.61460i	−0.293699	+	0.680871i
$69$		0			0
$70$	−9.76770	−	4.90552i	−1.16746	−	0.586322i
$71$	−11.4588	+	4.17067i	−1.35991	+	0.494968i	−0.916027	−	0.401116i	$-0.868622\pi$
$71$	−11.4588	+	4.17067i	−1.35991	+	0.494968i	−0.443885	+	0.896084i	$0.646400\pi$
$72$		0			0
$73$	−2.01159	−	0.732160i	−0.235439	−	0.0856928i	0.221606	−	0.975136i	$-0.428870\pi$
$73$	−2.01159	−	0.732160i	−0.235439	−	0.0856928i	−0.457045	+	0.889443i	$0.651092\pi$
$74$	0.410222	+	0.434809i	0.0476873	+	0.0505456i
$75$		0			0
$76$	−2.45764	−	1.61641i	−0.281910	−	0.185415i
$77$	2.48219	+	8.29110i	0.282872	+	0.944858i
$78$		0			0
$79$	4.18797	−	5.62542i	0.471184	−	0.632910i	−0.501469	−	0.865176i	$-0.667207\pi$
$79$	4.18797	−	5.62542i	0.471184	−	0.632910i	0.972652	+	0.232266i	$0.0746141\pi$
$80$	1.84879			0.206701
$81$		0			0
$82$	0.0972297			0.0107372
$83$	1.97654	−	2.65495i	0.216953	−	0.291419i	−0.680301	−	0.732933i	$-0.738151\pi$
$83$	1.97654	−	2.65495i	0.216953	−	0.291419i	0.897254	+	0.441514i	$0.145558\pi$
$84$		0			0
$85$	−3.54061	−	11.8265i	−0.384034	−	1.28276i
$86$	1.67538	+	1.10192i	0.180661	+	0.118823i
$87$		0			0
$88$	3.17281	+	3.36298i	0.338222	+	0.358495i
$89$	4.72182	+	1.71860i	0.500512	+	0.182171i	0.579924	−	0.814670i	$-0.303082\pi$
$89$	4.72182	+	1.71860i	0.500512	+	0.182171i	−0.0794124	+	0.996842i	$0.525304\pi$
$90$		0			0
$91$	−10.1643	+	3.69952i	−1.06551	+	0.387815i
$92$	−0.836149	−	0.419930i	−0.0871745	−	0.0437807i
$93$		0			0
$94$	0.529782	−	1.22817i	0.0546428	−	0.126676i
$95$	5.89863	−	0.689452i	0.605187	−	0.0707362i
$96$		0			0
$97$	6.27220	−	4.12529i	0.636846	−	0.418860i	−0.189612	−	0.981859i	$-0.560723\pi$
$97$	6.27220	−	4.12529i	0.636846	−	0.418860i	0.826457	+	0.562999i	$0.190353\pi$
$98$	−10.7523	−	9.02224i	−1.08615	−	0.911384i
$99$		0			0
$100$	−2.91808	+	2.44856i	−0.291808	+	0.244856i
$101$	0.648115	−	2.16486i	0.0644899	−	0.215411i	−0.919671	−	0.392690i	$-0.871544\pi$
$101$	0.648115	−	2.16486i	0.0644899	−	0.215411i	0.984161	+	0.177279i	$0.0567296\pi$
$102$		0			0
$103$	−0.239343	+	0.120203i	−0.0235832	+	0.0118439i	−0.460552	−	0.887633i	$-0.652348\pi$
$103$	−0.239343	+	0.120203i	−0.0235832	+	0.0118439i	0.436969	+	0.899477i	$0.356052\pi$
$104$	−3.96539	+	4.20306i	−0.388838	+	0.412144i
$105$		0			0
$106$	3.13281	+	7.26267i	0.304285	+	0.705412i
$107$	−4.97987	−	8.62539i	−0.481423	−	0.833848i	0.518350	−	0.855169i	$-0.326546\pi$
$107$	−4.97987	−	8.62539i	−0.481423	−	0.833848i	−0.999773	+	0.0213201i	$0.993213\pi$
$108$		0			0
$109$	6.70725	−	11.6173i	0.642438	−	1.11273i	−0.342449	−	0.939536i	$-0.611256\pi$
$109$	6.70725	−	11.6173i	0.642438	−	1.11273i	0.984887	−	0.173198i	$-0.0554102\pi$
$110$	−3.78506	−	0.442411i	−0.360892	−	0.0421822i
$111$		0			0
$112$	3.21738	+	0.762533i	0.304014	+	0.0720526i
$113$	0.0233225	−	0.400431i	0.00219399	−	0.0376694i	−0.997033	−	0.0769692i	$-0.975476\pi$
$113$	0.0233225	−	0.400431i	0.00219399	−	0.0376694i	0.999227	+	0.0392998i	$0.0125127\pi$
$114$		0			0
$115$	1.83814	−	0.435646i	0.171407	−	0.0406242i
$116$	−1.37873	−	7.81916i	−0.128012	−	0.725991i
$117$		0			0
$118$	−1.59040	+	9.01960i	−0.146408	+	0.830322i
$119$	−1.28377	−	22.0415i	−0.117683	−	2.02055i
$120$		0			0
$121$	−4.76686	−	6.40300i	−0.433351	−	0.582091i
$122$	−3.72452	−	5.00289i	−0.337202	−	0.452941i
$123$		0			0
$124$	−0.471807	−	8.10061i	−0.0423695	−	0.727456i
$125$	−1.08327	+	6.14355i	−0.0968909	+	0.549495i
$126$		0			0
$127$	−1.81470	−	10.2917i	−0.161029	−	0.913239i	−0.953065	−	0.302765i	$-0.902090\pi$
$127$	−1.81470	−	10.2917i	−0.161029	−	0.913239i	0.792037	−	0.610474i	$-0.209021\pi$
$128$	8.86603	−	2.10129i	0.783654	−	0.185729i
$129$		0			0
$130$	0.276932	−	4.75474i	0.0242885	−	0.417018i
$131$	−13.0882	−	3.10197i	−1.14353	−	0.271021i	−0.385160	−	0.922850i	$-0.625854\pi$
$131$	−13.0882	−	3.10197i	−1.14353	−	0.271021i	−0.758366	+	0.651829i	$0.774002\pi$
$132$		0			0
$133$	10.5496	+	1.23307i	0.914763	+	0.106920i
$134$	−0.183263	+	0.317421i	−0.0158315	+	0.0274210i
$135$		0			0
$136$	−5.89743	−	10.2146i	−0.505700	−	0.875898i
$137$	5.66340	+	13.1292i	0.483857	+	1.12171i	0.968953	+	0.247246i	$0.0795254\pi$
$137$	5.66340	+	13.1292i	0.483857	+	1.12171i	−0.485096	+	0.874461i	$0.661215\pi$
$138$		0			0
$139$	0.222217	−	0.235537i	0.0188482	−	0.0199780i	−0.717881	−	0.696166i	$-0.754888\pi$
$139$	0.222217	−	0.235537i	0.0188482	−	0.0199780i	0.736729	+	0.676188i	$0.236369\pi$
$140$	−17.1147	+	8.59535i	−1.44646	+	0.726439i
$141$		0			0
$142$	2.75416	−	9.19954i	0.231124	−	0.772009i
$143$	−2.88891	+	2.42408i	−0.241583	+	0.202712i
$144$		0			0
$145$	12.2796	+	10.3038i	1.01976	+	0.855682i
$146$	1.40846	−	0.926361i	0.116565	−	0.0766662i
$147$		0			0
$148$	1.04033	−	0.121598i	0.0855149	−	0.00999526i
$149$	1.21912	−	2.82624i	0.0998744	−	0.231535i	−0.860952	−	0.508687i	$-0.830131\pi$
$149$	1.21912	−	2.82624i	0.0998744	−	0.231535i	0.960826	+	0.277152i	$0.0893905\pi$
$150$		0			0
$151$	11.1937	+	5.62167i	0.910928	+	0.457485i	0.841596	−	0.540108i	$-0.181617\pi$
$151$	11.1937	+	5.62167i	0.910928	+	0.457485i	0.0693326	+	0.997594i	$0.477913\pi$
$152$	5.33190	−	1.94065i	0.432474	−	0.157408i
$153$		0			0
$154$	−6.40455	−	2.33106i	−0.516093	−	0.187843i
$155$	11.2422	+	11.9160i	0.902993	+	0.957117i
$156$		0			0
$157$	−4.86355	−	3.19881i	−0.388153	−	0.255292i	0.340401	−	0.940280i	$-0.389437\pi$
$157$	−4.86355	−	3.19881i	−0.388153	−	0.255292i	−0.728554	+	0.684988i	$0.759807\pi$
$158$	1.58398	+	5.29086i	0.126015	+	0.420918i
$159$		0			0
$160$	−9.72499	+	13.0629i	−0.768828	+	1.03272i
$161$	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	$0.585168\pi$
$164$	0.101734	−	0.136653i	0.00794410	−	0.0106708i
$165$		0			0
$166$	0.747568	+	2.49705i	0.0580226	+	0.193809i
$167$	−14.5276	−	9.55498i	−1.12418	−	0.739387i	−0.155536	−	0.987830i	$-0.549711\pi$
$167$	−14.5276	−	9.55498i	−1.12418	−	0.739387i	−0.968646	+	0.248444i	$0.920081\pi$
$168$		0			0
$169$	5.68670	+	6.02755i	0.437439	+	0.463658i
$170$	9.13549	+	3.32504i	0.700660	+	0.255019i
$171$		0			0
$172$	3.30170	−	1.20172i	0.251752	−	0.0916303i
$173$	12.2830	+	6.16877i	0.933862	+	0.469003i	0.849592	−	0.527440i	$-0.176848\pi$
$173$	12.2830	+	6.16877i	0.933862	+	0.469003i	0.0842696	+	0.996443i	$0.473144\pi$
$174$		0			0
$175$	5.44791	−	12.6297i	0.411823	−	0.954713i
$176$	1.14501	−	0.133832i	0.0863084	−	0.0100880i
$177$		0			0
$178$	−3.30609	+	2.17445i	−0.247802	+	0.162982i
$179$	−1.66053	−	1.39335i	−0.124114	−	0.104144i	0.578618	−	0.815599i	$-0.303592\pi$
$179$	−1.66053	−	1.39335i	−0.124114	−	0.104144i	−0.702732	+	0.711455i	$0.748037\pi$
$180$		0			0
$181$	−17.7173	+	14.8665i	−1.31691	+	1.10502i	−0.329963	+	0.943994i	$0.607036\pi$
$181$	−17.7173	+	14.8665i	−1.31691	+	1.10502i	−0.986950	+	0.161028i	$0.948519\pi$
$182$	2.44303	−	8.16029i	0.181089	−	0.604881i
$183$		0			0
$184$	1.61288	−	0.810018i	0.118903	−	0.0597153i
$185$	−1.45116	+	1.53814i	−0.106692	+	0.113087i
$186$		0			0
$187$	−3.04892	−	7.06820i	−0.222959	−	0.516878i
$188$	−1.17182	−	2.02966i	−0.0854640	−	0.148028i
$189$		0			0
$190$	−2.33840	+	4.05023i	−0.169646	+	0.293835i
$191$	−21.7391	−	2.54094i	−1.57299	−	0.183856i	−0.715595	−	0.698516i	$-0.753844\pi$
$191$	−21.7391	−	2.54094i	−1.57299	−	0.183856i	−0.857395	+	0.514660i	$0.827918\pi$
$192$		0			0
$193$	−7.02015	−	1.66381i	−0.505322	−	0.119763i	−0.0299550	−	0.999551i	$-0.509536\pi$
$193$	−7.02015	−	1.66381i	−0.505322	−	0.119763i	−0.475367	+	0.879788i	$0.657685\pi$
$194$	−0.343750	+	5.90195i	−0.0246798	+	0.423736i
$195$		0			0
$196$	−23.9308	+	5.67171i	−1.70935	+	0.405122i
$197$	−2.84835	−	16.1538i	−0.202936	−	1.15091i	−0.900654	−	0.434537i	$-0.856912\pi$
$197$	−2.84835	−	16.1538i	−0.202936	−	1.15091i	0.697718	−	0.716373i	$-0.254199\pi$
$198$		0			0
$199$	−1.40107	+	7.94587i	−0.0993193	+	0.563268i	0.894019	+	0.448030i	$0.147874\pi$
$199$	−1.40107	+	7.94587i	−0.0993193	+	0.563268i	−0.993338	+	0.115238i	$0.963237\pi$
$200$	−0.427241	−	7.33545i	−0.0302105	−	0.518695i
$201$		0			0
$202$	1.06270	+	1.42745i	0.0747710	+	0.100435i
$203$	17.1199	+	22.9960i	1.20158	+	1.61401i
$204$		0			0
$205$	0.0199990	+	0.343370i	0.00139679	+	0.0239820i
$206$	0.0366255	−	0.207713i	0.00255182	−	0.0144721i
$207$		0			0
$208$	0.250189	+	1.41889i	0.0173475	+	0.0983824i
$209$	3.60330	−	0.853997i	0.249245	−	0.0590722i
$210$		0			0
$211$	1.39097	−	23.8821i	0.0957585	−	1.64411i	−0.518553	−	0.855046i	$-0.673529\pi$
$211$	1.39097	−	23.8821i	0.0957585	−	1.64411i	0.614311	−	0.789064i	$-0.289434\pi$
$212$	13.4853	+	3.19609i	0.926177	+	0.219508i
$213$		0			0
$214$	7.79028	+	0.910553i	0.532533	+	0.0622441i
$215$	−3.54684	+	6.14331i	−0.241893	+	0.418970i
$216$		0			0
$217$	14.6496	+	25.3739i	0.994481	+	1.72249i
$218$	4.18416	+	9.69997i	0.283387	+	0.656965i
$219$		0			0
$220$	−4.58221	+	4.85686i	−0.308932	+	0.327449i
$221$	8.59735	−	4.31775i	0.578321	−	0.290444i
$222$		0			0
$223$	−3.43182	+	11.4631i	−0.229812	+	0.767624i	0.762837	+	0.646591i	$0.223806\pi$
$223$	−3.43182	+	11.4631i	−0.229812	+	0.767624i	−0.992648	+	0.121033i	$0.961379\pi$
$224$	−22.3119	+	18.7219i	−1.49078	+	1.25091i
$225$		0			0
$226$	0.241974	+	0.203040i	0.0160959	+	0.0135060i
$227$	−20.9815	+	13.7997i	−1.39259	+	0.915921i	−0.999993	−	0.00378925i	$-0.998794\pi$
$227$	−20.9815	+	13.7997i	−1.39259	+	0.915921i	−0.392598	+	0.919710i	$0.628423\pi$
$228$		0			0
$229$	25.5994	−	2.99214i	1.69166	−	0.197726i	0.784971	−	0.619533i	$-0.212678\pi$
$229$	25.5994	−	2.99214i	1.69166	−	0.197726i	0.906686	+	0.421806i	$0.138604\pi$
$230$	−0.589222	+	1.36597i	−0.0388521	+	0.0900694i
$231$		0			0
$232$	13.6863	+	6.87352i	0.898550	+	0.451269i
$233$	8.58260	−	3.12381i	0.562265	−	0.204648i	−0.0452226	−	0.998977i	$-0.514400\pi$
$233$	8.58260	−	3.12381i	0.562265	−	0.204648i	0.607488	+	0.794329i	$0.292177\pi$
$234$		0			0
$235$	4.44630	+	1.61832i	0.290044	+	0.105568i
$236$	11.0126	+	11.6727i	0.716861	+	0.759828i
$237$		0			0
$238$	14.5268	+	9.55440i	0.941630	+	0.619320i
$239$	−6.24071	−	20.8454i	−0.403678	−	1.34838i	−0.882437	−	0.470431i	$-0.844098\pi$
$239$	−6.24071	−	20.8454i	−0.403678	−	1.34838i	0.478759	−	0.877946i	$-0.341087\pi$
$240$		0			0
$241$	8.27944	−	11.1212i	0.533326	−	0.716381i	−0.451043	−	0.892502i	$-0.648948\pi$
$241$	8.27944	−	11.1212i	0.533326	−	0.716381i	0.984368	+	0.176122i	$0.0563552\pi$
$242$	6.28628			0.404097
$243$		0			0
$244$	−10.9284			−0.699622
$245$	29.6507	−	39.8278i	1.89431	−	2.54451i
$246$		0			0
$247$	1.32737	+	4.43374i	0.0844588	+	0.282112i
$248$	13.0771	+	8.60095i	0.830397	+	0.546161i
$249$		0			0
$250$	−3.37129	−	3.57336i	−0.213219	−	0.225999i
$251$	10.0143	+	3.64492i	0.632099	+	0.230065i	0.638144	−	0.769917i	$-0.279702\pi$
$251$	10.0143	+	3.64492i	0.632099	+	0.230065i	−0.00604584	+	0.999982i	$0.501924\pi$
$252$		0			0
$253$	1.10688	−	0.402871i	0.0695888	−	0.0253283i
$254$	7.35436	+	3.69350i	0.461454	+	0.231751i
$255$		0			0
$256$	−5.43743	+	12.6054i	−0.339839	+	0.787836i
$257$	−1.16759	+	0.136472i	−0.0728323	+	0.00851287i	−0.152431	−	0.988314i	$-0.548710\pi$
$257$	−1.16759	+	0.136472i	−0.0728323	+	0.00851287i	0.0795987	+	0.996827i	$0.474636\pi$
$258$		0			0
$259$	−3.15982	+	2.07825i	−0.196342	+	0.129136i
$260$	−6.39284	−	5.36423i	−0.396467	−	0.332675i
$261$		0			0
$262$	8.11435	−	6.80875i	0.501306	−	0.420646i
$263$	2.67668	−	8.94073i	0.165051	−	0.551309i	−0.834948	−	0.550328i	$-0.814503\pi$
$263$	2.67668	−	8.94073i	0.165051	−	0.551309i	1.00000		0.000980948i	$-0.000312246\pi$
$264$		0			0
$265$	−25.0039	+	12.5575i	−1.53598	+	0.771398i
$266$	−5.73996	+	6.08401i	−0.351940	+	0.373034i
$267$		0			0
$268$	0.254369	+	0.589695i	0.0155381	+	0.0360213i
$269$	1.25116	+	2.16707i	0.0762845	+	0.132129i	0.901644	−	0.432479i	$-0.142361\pi$
$269$	1.25116	+	2.16707i	0.0762845	+	0.132129i	−0.825360	+	0.564607i	$0.809028\pi$
$270$		0			0
$271$	−2.76243	+	4.78467i	−0.167806	+	0.290648i	−0.937648	−	0.347586i	$-0.887002\pi$
$271$	−2.76243	+	4.78467i	−0.167806	+	0.290648i	0.769842	+	0.638234i	$0.220335\pi$
$272$	−2.92103	−	0.341419i	−0.177113	−	0.0207016i
$273$		0			0
$274$	−10.9567	−	2.59678i	−0.661917	−	0.156877i
$275$	0.278833	−	4.78738i	0.0168143	−	0.288690i
$276$		0			0
$277$	25.9932	−	6.16051i	1.56178	−	0.370149i	0.643301	−	0.765613i	$-0.277564\pi$
$277$	25.9932	−	6.16051i	1.56178	−	0.370149i	0.918482	+	0.395464i	$0.129416\pi$
$278$	0.0442815	+	0.251133i	0.00265583	+	0.0150620i
$279$		0			0
$280$	6.41505	−	36.3816i	0.383373	−	2.17421i
$281$	1.83046	+	31.4278i	0.109196	+	1.87482i	0.397930	+	0.917416i	$0.369729\pi$
$281$	1.83046	+	31.4278i	0.109196	+	1.87482i	−0.288734	+	0.957409i	$0.593234\pi$
$282$		0			0
$283$	3.99576	+	5.36724i	0.237523	+	0.319049i	0.904862	−	0.425705i	$-0.139974\pi$
$283$	3.99576	+	5.36724i	0.237523	+	0.319049i	−0.667338	+	0.744755i	$0.732567\pi$
$284$	−10.0479	−	13.4966i	−0.596230	−	0.800876i
$285$		0			0
$286$	−0.172680	−	2.96480i	−0.0102108	−	0.175312i
$287$	−0.106819	+	0.605803i	−0.00630535	+	0.0357594i
$288$		0			0
$289$	0.458026	+	2.59759i	0.0269427	+	0.152800i
$290$	−12.2832	+	2.91118i	−0.721297	+	0.170951i
$291$		0			0
$292$	0.171749	−	2.94882i	0.0100509	−	0.172567i
$293$	−3.65264	−	0.865692i	−0.213390	−	0.0505743i	0.122530	−	0.992465i	$-0.460899\pi$
$293$	−3.65264	−	0.865692i	−0.213390	−	0.0505743i	−0.335920	+	0.941890i	$0.609047\pi$
$294$		0			0
$295$	−32.1801	−	3.76132i	−1.87360	−	0.218992i
$296$	−1.01020	+	1.74972i	−0.0587167	+	0.101700i
$297$		0			0
$298$	1.21195	+	2.09916i	0.0702066	+	0.121601i
$299$	0.583094	+	1.35176i	0.0337212	+	0.0781745i
$300$		0			0
$301$	−8.70627	+	9.22810i	−0.501821	+	0.531899i
$302$	−8.81503	+	4.42708i	−0.507248	+	0.254750i
$303$		0			0
$304$	0.405760	−	1.35533i	0.0232719	−	0.0777337i
$305$	16.9018	−	14.1823i	0.967793	−	0.812075i
$306$		0			0
$307$	−22.9491	−	19.2566i	−1.30977	−	1.09903i	−0.988367	−	0.152088i	$-0.951400\pi$
$307$	−22.9491	−	19.2566i	−1.30977	−	1.09903i	−0.321406	−	0.946942i	$-0.604155\pi$
$308$	−9.97748	+	6.56229i	−0.568520	+	0.373921i
$309$		0			0
$310$	−12.8138	+	1.49772i	−0.727775	+	0.0850647i
$311$	−1.76187	+	4.08446i	−0.0999062	+	0.231609i	−0.960837	−	0.277113i	$-0.910622\pi$
$311$	−1.76187	+	4.08446i	−0.0999062	+	0.231609i	0.860931	+	0.508721i	$0.169882\pi$
$312$		0			0
$313$	−27.9019	−	14.0129i	−1.57711	−	0.792054i	−0.577406	−	0.816457i	$-0.695935\pi$
$313$	−27.9019	−	14.0129i	−1.57711	−	0.792054i	−0.999702	+	0.0244032i	$0.992231\pi$
$314$	4.30775	−	1.56789i	0.243100	−	0.0884812i
$315$		0			0
$316$	9.09346	+	3.30975i	0.511547	+	0.186188i
$317$	−19.0975	−	20.2421i	−1.07262	−	1.13691i	−0.990106	−	0.140321i	$-0.955187\pi$
$317$	−19.0975	−	20.2421i	−1.07262	−	1.13691i	−0.0825140	−	0.996590i	$-0.526295\pi$
$318$		0			0
$319$	8.35100	+	5.49254i	0.467566	+	0.307523i
$320$	−2.61772	−	8.74380i	−0.146335	−	0.488793i
$321$		0			0
$322$	−1.58880	+	2.13413i	−0.0885402	+	0.118930i
$323$	−9.44699			−0.525644
$324$		0			0
$325$	5.99343			0.332456
$326$	3.17467	−	4.26433i	0.175829	−	0.236179i
$327$		0			0
$328$	0.0942496	+	0.314815i	0.00520406	+	0.0173828i
$329$	7.07027	+	4.65019i	0.389796	+	0.256373i
$330$		0			0
$331$	−0.135248	−	0.143354i	−0.00743388	−	0.00787946i	0.723646	−	0.690171i	$-0.242465\pi$
$331$	−0.135248	−	0.143354i	−0.00743388	−	0.00787946i	−0.731080	+	0.682292i	$0.760983\pi$
$332$	4.29171	+	1.56206i	0.235538	+	0.0857289i
$333$		0			0
$334$	12.8674	−	4.68336i	0.704075	−	0.256262i
$335$	−1.15868	−	0.581909i	−0.0633052	−	0.0317931i
$336$		0			0
$337$	−7.09164	+	16.4403i	−0.386306	+	0.895559i	0.608479	+	0.793570i	$0.291780\pi$
$337$	−7.09164	+	16.4403i	−0.386306	+	0.895559i	−0.994786	+	0.101989i	$0.967479\pi$
$338$	−6.48169	+	0.757601i	−0.352557	+	0.0412081i
$339$		0			0
$340$	14.2319	−	9.36049i	0.771835	−	0.507644i
$341$	7.82522	+	6.56614i	0.423759	+	0.355576i
$342$		0			0
$343$	41.3103	−	34.6635i	2.23055	−	1.87165i
$344$	−1.94381	+	6.49278i	−0.104803	+	0.350067i
$345$		0			0
$346$	−9.67291	+	4.85792i	−0.520019	+	0.261163i
$347$	15.4622	−	16.3889i	0.830052	−	0.879804i	−0.164248	−	0.986419i	$-0.552520\pi$
$347$	15.4622	−	16.3889i	0.830052	−	0.879804i	0.994300	+	0.106615i	$0.0340013\pi$
$348$		0			0
$349$	−4.69595	−	10.8864i	−0.251368	−	0.582737i	0.745077	−	0.666978i	$-0.232413\pi$
$349$	−4.69595	−	10.8864i	−0.251368	−	0.582737i	−0.996445	+	0.0842411i	$0.973153\pi$
$350$	5.41587	+	9.38056i	0.289490	+	0.501412i
$351$		0			0
$352$	−5.07737	+	8.79426i	−0.270625	+	0.468736i
$353$	−18.6770	−	2.18302i	−0.994074	−	0.116191i	−0.396526	−	0.918024i	$-0.629784\pi$
$353$	−18.6770	−	2.18302i	−0.994074	−	0.116191i	−0.597548	+	0.801833i	$0.703858\pi$
$354$		0			0
$355$	33.0550	+	7.83417i	1.75438	+	0.415795i
$356$	−0.403147	+	6.92177i	−0.0213668	+	0.366853i
$357$		0			0
$358$	1.66103	−	0.393671i	0.0877880	−	0.0208061i
$359$	1.61227	+	9.14366i	0.0850926	+	0.482584i	0.997337	+	0.0729368i	$0.0232371\pi$
$359$	1.61227	+	9.14366i	0.0850926	+	0.482584i	−0.912244	+	0.409647i	$0.865652\pi$
$360$		0			0
$361$	−2.51015	+	14.2358i	−0.132113	+	0.749251i
$362$	−1.05902	−	18.1827i	−0.0556609	−	0.955661i
$363$		0			0
$364$	−8.91276	−	11.9719i	−0.467156	−	0.627499i
$365$	3.56118	+	4.78349i	0.186401	+	0.250379i
$366$		0			0
$367$	1.69898	+	29.1704i	0.0886861	+	1.52268i	0.690083	+	0.723731i	$0.257574\pi$
$367$	1.69898	+	29.1704i	0.0886861	+	1.52268i	−0.601396	+	0.798951i	$0.705389\pi$
$368$	0.0781452	−	0.443183i	0.00407360	−	0.0231025i
$369$		0			0
$370$	−0.289175	−	1.63999i	−0.0150335	−	0.0852593i
$371$	−48.6929	+	11.5404i	−2.52801	+	0.599149i
$372$		0			0
$373$	−0.323556	+	5.55523i	−0.0167531	+	0.287639i	0.979518	+	0.201358i	$0.0645354\pi$
$373$	−0.323556	+	5.55523i	−0.0167531	+	0.287639i	−0.996271	+	0.0862813i	$0.972502\pi$
$374$	5.89859	+	1.39799i	0.305009	+	0.0722884i
$375$		0			0
$376$	4.49018	+	0.524827i	0.231564	+	0.0270659i
$377$	−6.24612	+	10.8186i	−0.321692	+	0.557186i
$378$		0			0
$379$	−14.7919	−	25.6203i	−0.759808	−	1.31603i	−0.942948	−	0.332940i	$-0.891959\pi$
$379$	−14.7919	−	25.6203i	−0.759808	−	1.31603i	0.183140	−	0.983087i	$-0.441374\pi$
$380$	3.24571	+	7.52441i	0.166501	+	0.385994i
$381$		0			0
$382$	11.8282	−	12.5371i	0.605181	−	0.641455i
$383$	11.0692	−	5.55918i	0.565612	−	0.284061i	−0.142926	−	0.989733i	$-0.545651\pi$
$383$	11.0692	−	5.55918i	0.565612	−	0.284061i	0.708538	+	0.705672i	$0.249355\pi$
$384$		0			0
$385$	6.91489	−	23.0973i	0.352415	−	1.17715i
$386$	4.35230	−	3.65201i	0.221526	−	0.185883i
$387$		0			0
$388$	7.93530	+	6.65850i	0.402854	+	0.338034i
$389$	15.5223	−	10.2092i	0.787012	−	0.517626i	−0.0912370	−	0.995829i	$-0.529082\pi$
$389$	15.5223	−	10.2092i	0.787012	−	0.517626i	0.878249	+	0.478203i	$0.158712\pi$
$390$		0			0
$391$	−2.98465	+	0.348856i	−0.150940	+	0.0176424i
$392$	18.7900	−	43.5600i	0.949037	−	2.20011i
$393$		0			0
$394$	11.5434	+	5.79730i	0.581547	+	0.292064i
$395$	−18.3590	+	6.68214i	−0.923743	+	0.336215i
$396$		0			0
$397$	9.59694	+	3.49300i	0.481657	+	0.175309i	0.571426	−	0.820654i	$-0.306391\pi$
$397$	9.59694	+	3.49300i	0.481657	+	0.175309i	−0.0897688	+	0.995963i	$0.528613\pi$
$398$	−4.36032	−	4.62167i	−0.218563	−	0.231663i
$399$		0			0
$400$	−1.53071	−	1.00676i	−0.0765353	−	0.0503380i
$401$	0.579017	+	1.93405i	0.0289148	+	0.0965820i	0.971229	−	0.238148i	$-0.0765402\pi$
$401$	0.579017	+	1.93405i	0.0289148	+	0.0965820i	−0.942314	+	0.334730i	$0.891355\pi$
$402$		0			0
$403$	−7.62385	+	10.2406i	−0.379771	+	0.510121i
$404$	3.11815			0.155134
$405$		0			0
$406$	−22.5768			−1.12047
$407$	−0.787406	+	1.05767i	−0.0390303	+	0.0524267i
$408$		0			0
$409$	0.249431	+	0.833158i	0.0123336	+	0.0411970i	0.963935	−	0.266138i	$-0.0857478\pi$
$409$	0.249431	+	0.833158i	0.0123336	+	0.0411970i	−0.951601	+	0.307335i	$0.900563\pi$
$410$	−0.226302	−	0.148841i	−0.0111763	−	0.00735075i
$411$		0			0
$412$	−0.253611	−	0.268812i	−0.0124945	−	0.0132434i
$413$	−54.4506	−	19.8184i	−2.67934	−	0.975200i
$414$		0			0
$415$	−8.66465	+	3.15367i	−0.425331	+	0.154808i
$416$	−11.3415	−	5.69591i	−0.556062	−	0.279265i
$417$		0			0
$418$	−1.15505	+	2.67771i	−0.0564954	+	0.130971i
$419$	−25.0738	+	2.93070i	−1.22493	+	0.143174i	−0.703860	−	0.710338i	$-0.748542\pi$
$419$	−25.0738	+	2.93070i	−1.22493	+	0.143174i	−0.521072	+	0.853512i	$0.674468\pi$
$420$		0			0
$421$	−13.9967	+	9.20577i	−0.682157	+	0.448662i	−0.842712	−	0.538365i	$-0.819042\pi$
$421$	−13.9967	+	9.20577i	−0.682157	+	0.448662i	0.160554	+	0.987027i	$0.448672\pi$
$422$	14.4315	+	12.1095i	0.702516	+	0.589481i
$423$		0			0
$424$	−20.4787	+	17.1836i	−0.994532	+	0.834511i
$425$	−3.50868	+	11.7198i	−0.170196	+	0.568494i
$426$		0			0
$427$	35.2631	−	17.7098i	1.70650	−	0.857037i
$428$	9.43093	−	9.99621i	0.455861	−	0.483185i
$429$		0			0
$430$	−2.21262	−	5.12942i	−0.106702	−	0.247363i
$431$	13.1811	+	22.8303i	0.634911	+	1.09970i	0.986534	+	0.163556i	$0.0522966\pi$
$431$	13.1811	+	22.8303i	0.634911	+	1.09970i	−0.351623	+	0.936142i	$0.614370\pi$
$432$		0			0
$433$	6.29345	−	10.9006i	0.302444	−	0.523848i	−0.674245	−	0.738508i	$-0.735531\pi$
$433$	6.29345	−	10.9006i	0.302444	−	0.523848i	0.976689	+	0.214660i	$0.0688642\pi$
$434$	−22.9172	−	2.67863i	−1.10006	−	0.128579i
$435$		0			0
$436$	18.0109	+	4.26867i	0.862568	+	0.204432i
$437$	0.0840533	−	1.44314i	0.00402081	−	0.0690347i
$438$		0			0
$439$	8.56156	−	2.02913i	0.408621	−	0.0968449i	−0.0211645	−	0.999776i	$-0.506737\pi$
$439$	8.56156	−	2.02913i	0.408621	−	0.0968449i	0.429785	+	0.902931i	$0.358589\pi$
$440$	−2.23659	−	12.6843i	−0.106625	−	0.604702i
$441$		0			0
$442$	−1.31561	+	7.46120i	−0.0625772	+	0.354893i
$443$	−0.885106	−	15.1967i	−0.0420527	−	0.722017i	−0.951775	−	0.306798i	$-0.900742\pi$
$443$	−0.885106	−	15.1967i	−0.0420527	−	0.722017i	0.909722	−	0.415218i	$-0.136295\pi$
$444$		0			0
$445$	−8.35916	−	11.2283i	−0.396262	−	0.532273i
$446$	−5.62705	−	7.55845i	−0.266449	−	0.357903i
$447$		0			0
$448$	−0.949147	−	16.2962i	−0.0448430	−	0.769924i
$449$	0.214786	−	1.21811i	0.0101364	−	0.0574862i	−0.979320	−	0.202317i	$-0.935153\pi$
$449$	0.214786	−	1.21811i	0.0101364	−	0.0574862i	0.989456	+	0.144831i	$0.0462639\pi$
$450$		0			0
$451$	0.0372423	+	0.211212i	0.00175367	+	0.00994557i
$452$	0.538549	−	0.127639i	0.0253312	−	0.00600361i
$453$		0			0
$454$	1.14990	−	19.7430i	0.0539673	−	0.926583i
$455$	29.3208	+	6.94916i	1.37458	+	0.325782i
$456$		0			0
$457$	−30.7759	−	3.59718i	−1.43963	−	0.168269i	−0.639824	−	0.768522i	$-0.720993\pi$
$457$	−30.7759	−	3.59718i	−1.43963	−	0.168269i	−0.799810	+	0.600253i	$0.795067\pi$
$458$	−10.1484	+	17.5776i	−0.474204	+	0.821345i
$459$		0			0
$460$	1.30330	+	2.25738i	0.0607666	+	0.105251i
$461$	6.71020	+	15.5560i	0.312525	+	0.724514i	0.999999	−	0.00169503i	$-0.000539544\pi$
$461$	6.71020	+	15.5560i	0.312525	+	0.724514i	−0.687474	+	0.726209i	$0.741280\pi$
$462$		0			0
$463$	−24.4901	+	25.9580i	−1.13815	+	1.20637i	−0.162578	+	0.986696i	$0.551981\pi$
$463$	−24.4901	+	25.9580i	−1.13815	+	1.20637i	−0.975573	+	0.219674i	$0.929501\pi$
$464$	3.41252	−	1.71383i	0.158422	−	0.0795627i
$465$		0			0
$466$	−2.06285	+	6.89041i	−0.0955599	+	0.319192i
$467$	32.1894	−	27.0101i	1.48955	−	1.24988i	0.594353	−	0.804204i	$-0.297408\pi$
$467$	32.1894	−	27.0101i	1.48955	−	1.24988i	0.895195	−	0.445675i	$-0.147036\pi$
$468$		0			0
$469$	−1.77640	−	1.49057i	−0.0820263	−	0.0688282i
$470$	−3.11318	+	2.04757i	−0.143600	+	0.0944474i
$471$		0			0
$472$	−30.7458	+	3.59367i	−1.41519	+	0.165412i
$473$	−1.75196	+	4.06150i	−0.0805552	+	0.186748i
$474$		0			0
$475$	−5.25923	−	2.64128i	−0.241310	−	0.121190i
$476$	28.6281	−	10.4198i	1.31217	−	0.477590i
$477$		0			0
$478$	16.1023	+	5.86074i	0.736500	+	0.268064i
$479$	24.7671	+	26.2516i	1.13164	+	1.19947i	0.977392	+	0.211435i	$0.0678138\pi$
$479$	24.7671	+	26.2516i	1.13164	+	1.19947i	0.154247	+	0.988032i	$0.450705\pi$
$480$		0			0
$481$	−1.37686	−	0.905578i	−0.0627796	−	0.0412908i
$482$	3.13146	+	10.4598i	0.142634	+	0.476431i
$483$		0			0
$484$	6.57751	−	8.83513i	0.298978	−	0.401597i
$485$	−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	$0.282282\pi$
$488$	12.5883	−	16.9090i	0.569844	−	0.765434i
$489$		0			0
$490$	11.2145	+	37.4591i	0.506620	+	1.69223i
$491$	18.1734	+	11.9528i	0.820155	+	0.539424i	0.888842	−	0.458214i	$-0.151511\pi$
$491$	18.1734	+	11.9528i	0.820155	+	0.539424i	−0.0686871	+	0.997638i	$0.521881\pi$
$492$		0			0
$493$	−17.4985	−	18.5474i	−0.788094	−	0.835331i
$494$	−3.42489	−	1.24656i	−0.154093	−	0.0560853i
$495$		0			0
$496$	3.66730	−	1.33479i	0.164667	−	0.0599338i
$497$	54.2932	+	27.2671i	2.43538	+	1.22310i
$498$		0			0
$499$	−1.18204	+	2.74029i	−0.0529156	+	0.122672i	−0.942623	−	0.333859i	$-0.891649\pi$
$499$	−1.18204	+	2.74029i	−0.0529156	+	0.122672i	0.889707	+	0.456531i	$0.150908\pi$
$500$	−8.54969	+	0.999316i	−0.382354	+	0.0446908i
$501$		0			0
$502$	−7.01176	+	4.61171i	−0.312950	+	0.205831i
$503$	30.5223	+	25.6113i	1.36092	+	1.14195i	0.975696	+	0.219128i	$0.0703214\pi$
$503$	30.5223	+	25.6113i	1.36092	+	1.14195i	0.385227	+	0.922822i	$0.374123\pi$
$504$		0			0
$505$	−4.82249	+	4.04655i	−0.214598	+	0.180069i
$506$	−0.266041	+	0.888640i	−0.0118270	+	0.0395049i
$507$		0			0
$508$	12.8861	−	6.47167i	0.571730	−	0.287134i
$509$	−13.6753	+	14.4950i	−0.606147	+	0.642479i	−0.955667	−	0.294451i	$-0.904863\pi$
$509$	−13.6753	+	14.4950i	−0.606147	+	0.642479i	0.349519	+	0.936929i	$0.386345\pi$
$510$		0			0
$511$	4.22444	+	9.79336i	0.186878	+	0.433233i
$512$	3.70618	+	6.41930i	0.163792	+	0.283695i
$513$		0			0
$514$	0.462869	−	0.801713i	0.0204163	−	0.0353620i
$515$	0.741079	+	0.0866197i	0.0326559	+	0.00381692i
$516$		0			0
$517$	2.87088	+	0.680411i	0.126261	+	0.0299244i
$518$	0.173175	−	2.97330i	0.00760887	−	0.130639i
$519$		0			0
$520$	15.6636	−	3.71234i	0.686893	−	0.162797i
$521$	6.17183	+	35.0022i	0.270393	+	1.53347i	0.753226	+	0.657762i	$0.228497\pi$
$521$	6.17183	+	35.0022i	0.270393	+	1.53347i	−0.482833	+	0.875713i	$0.660392\pi$
$522$		0			0
$523$	4.17875	−	23.6989i	0.182724	−	1.03628i	−0.746121	−	0.665810i	$-0.768086\pi$
$523$	4.17875	−	23.6989i	0.182724	−	1.03628i	0.928845	−	0.370469i	$-0.120803\pi$
$524$	−1.07917	−	18.5286i	−0.0471437	−	0.809425i
$525$		0			0
$526$	4.38888	+	5.89528i	0.191364	+	0.257047i
$527$	−15.5617	−	20.9031i	−0.677880	−	0.910551i
$528$		0			0
$529$	1.31059	+	22.5020i	0.0569824	+	0.978350i
$530$	3.82623	−	21.6996i	0.166201	−	0.942571i
$531$		0			0
$532$	2.54496	+	14.4332i	0.110338	+	0.625757i
$533$	−0.260820	+	0.0618155i	−0.0112974	+	0.00267753i
$534$		0			0
$535$	−1.61328	+	27.6989i	−0.0697481	+	1.19753i
$536$	−1.20541	−	0.285687i	−0.0520656	−	0.0123398i
$537$		0			0
$538$	−1.95726	−	0.228770i	−0.0843833	−	0.00986299i
$539$	15.4805	−	26.8130i	0.666792	−	1.15492i
$540$		0			0
$541$	5.32644	+	9.22567i	0.229002	+	0.396642i	0.957512	−	0.288392i	$-0.0931206\pi$
$541$	5.32644	+	9.22567i	0.229002	+	0.396642i	−0.728511	+	0.685034i	$0.759787\pi$
$542$	−1.72328	−	3.99501i	−0.0740212	−	0.171600i
$543$		0			0
$544$	17.7776	−	18.8431i	0.762206	−	0.807892i
$545$	−33.3951	+	16.7717i	−1.43049	+	0.718419i
$546$		0			0
$547$	−3.90060	+	13.0289i	−0.166777	+	0.557076i	0.833214	+	0.552951i	$0.186498\pi$
$547$	−3.90060	+	13.0289i	−0.166777	+	0.557076i	−0.999991	+	0.00412495i	$0.998687\pi$
$548$	−15.1139	+	12.6821i	−0.645636	+	0.541753i
$549$		0			0
$550$	2.89293	+	2.42746i	0.123355	+	0.103507i
$551$	10.2487	−	6.74066i	0.436609	−	0.287162i
$552$		0			0
$553$	−34.7056	+	4.05651i	−1.47583	+	0.172500i
$554$	−8.33224	+	19.3163i	−0.354003	+	0.820671i
$555$		0			0
$556$	0.399291	+	0.200531i	0.0169337	+	0.00850443i
$557$	−4.31357	+	1.57001i	−0.182772	+	0.0665235i	−0.431785	−	0.901977i	$-0.642116\pi$
$557$	−4.31357	+	1.57001i	−0.182772	+	0.0665235i	0.249013	+	0.968500i	$0.419894\pi$
$558$		0			0
$559$	−5.19480	−	1.89075i	−0.219717	−	0.0799704i
$560$	−6.32115	−	6.70003i	−0.267117	−	0.283128i
$561$		0			0
$562$	−20.7129	−	13.6231i	−0.873720	−	0.574655i
$563$	0.284251	+	0.949463i	0.0119797	+	0.0400151i	0.963770	−	0.266733i	$-0.0859442\pi$
$563$	0.284251	+	0.949463i	0.0119797	+	0.0400151i	−0.951791	+	0.306748i	$0.900759\pi$
$564$		0			0
$565$	−0.667271	+	0.896301i	−0.0280723	+	0.0377077i
$566$	−5.26940			−0.221489
$567$		0			0
$568$	32.4565			1.36185
$569$	4.63945	−	6.23186i	0.194496	−	0.261253i	−0.694167	−	0.719814i	$-0.744227\pi$
$569$	4.63945	−	6.23186i	0.194496	−	0.261253i	0.888663	+	0.458560i	$0.151635\pi$
$570$		0			0
$571$	−6.13681	−	20.4984i	−0.256818	−	0.857830i	−0.985016	−	0.172464i	$-0.944827\pi$
$571$	−6.13681	−	20.4984i	−0.256818	−	0.857830i	0.728198	−	0.685367i	$-0.240358\pi$
$572$	−4.34760	−	2.85946i	−0.181782	−	0.119560i
$573$		0			0
$574$	−0.332436	−	0.352362i	−0.0138756	−	0.0147073i
$575$	−1.75912	−	0.640267i	−0.0733604	−	0.0267010i
$576$		0			0
$577$	−8.13925	+	2.96244i	−0.338841	+	0.123328i	−0.505836	−	0.862630i	$-0.668816\pi$
$577$	−8.13925	+	2.96244i	−0.338841	+	0.123328i	0.166995	+	0.985958i	$0.446594\pi$
$578$	−1.85622	−	0.932230i	−0.0772087	−	0.0387757i
$579$		0			0
$580$	−8.76075	+	20.3097i	−0.363770	+	0.843314i
$581$	−16.3795	+	1.91449i	−0.679538	+	0.0794266i
$582$		0			0
$583$	−14.5767	+	9.58724i	−0.603705	+	0.397063i
$584$	4.36471	+	3.66243i	0.180613	+	0.151552i
$585$		0			0
$586$	2.26454	−	1.90017i	0.0935472	−	0.0784954i
$587$	3.01536	−	10.0720i	0.124457	−	0.415716i	−0.872939	−	0.487829i	$-0.837789\pi$
$587$	3.01536	−	10.0720i	0.124457	−	0.415716i	0.997396	+	0.0721128i	$0.0229741\pi$
$588$		0			0
$589$	11.2029	−	5.62632i	0.461608	−	0.231828i
$590$	17.5091	−	18.5585i	0.720836	−	0.764042i
$591$		0			0
$592$	0.199531	+	0.462564i	0.00820066	+	0.0190113i
$593$	−14.0175	−	24.2790i	−0.575630	−	0.997020i	−0.995973	−	0.0896551i	$-0.971424\pi$
$593$	−14.0175	−	24.2790i	−0.575630	−	0.997020i	0.420343	−	0.907365i	$-0.361910\pi$
$594$		0			0
$595$	−30.7537	+	53.2669i	−1.26078	+	2.18373i
$596$	4.21840	+	0.493060i	0.172792	+	0.0201965i
$597$		0			0
$598$	−1.12808	−	0.267360i	−0.0461306	−	0.0109332i
$599$	−1.35310	+	23.2319i	−0.0552863	+	0.949229i	0.850628	+	0.525768i	$0.176222\pi$
$599$	−1.35310	+	23.2319i	−0.0552863	+	0.949229i	−0.905914	+	0.423461i	$0.860815\pi$
$600$		0			0
$601$	20.9118	−	4.95618i	0.853009	−	0.202167i	0.219222	−	0.975675i	$-0.429648\pi$
$601$	20.9118	−	4.95618i	0.853009	−	0.202167i	0.633786	+	0.773508i	$0.281500\pi$
$602$	−1.73491	−	9.83915i	−0.0707096	−	0.401014i
$603$		0			0
$604$	−3.00133	+	17.0214i	−0.122122	+	0.692589i
$605$	1.29301	+	22.2002i	0.0525685	+	0.902566i
$606$		0			0
$607$	2.89262	+	3.88547i	0.117408	+	0.157706i	0.856942	−	0.515413i	$-0.172361\pi$
$607$	2.89262	+	3.88547i	0.117408	+	0.157706i	−0.739534	+	0.673119i	$0.764954\pi$
$608$	7.44197	+	9.99631i	0.301812	+	0.405404i
$609$		0			0
$610$	1.01028	+	17.3458i	0.0409050	+	0.702311i
$611$	−0.640316	+	3.63141i	−0.0259044	+	0.146911i
$612$		0			0
$613$	2.42381	+	13.7461i	0.0978969	+	0.555201i	0.993821	+	0.110994i	$0.0354034\pi$
$613$	2.42381	+	13.7461i	0.0978969	+	0.555201i	−0.895924	+	0.444207i	$0.853485\pi$
$614$	22.9559	−	5.44066i	0.926427	−	0.219567i
$615$		0			0
$616$	1.33940	−	22.9966i	0.0539659	−	0.926559i
$617$	−19.6655	−	4.66081i	−0.791704	−	0.187637i	−0.185182	−	0.982704i	$-0.559288\pi$
$617$	−19.6655	−	4.66081i	−0.791704	−	0.187637i	−0.606522	+	0.795067i	$0.707436\pi$
$618$		0			0
$619$	28.6674	+	3.35073i	1.15224	+	0.134677i	0.670687	−	0.741740i	$-0.265999\pi$
$619$	28.6674	+	3.35073i	1.15224	+	0.134677i	0.481552	+	0.876418i	$0.340073\pi$
$620$	−11.3025	+	19.5764i	−0.453917	+	0.786208i
$621$		0			0
$622$	−1.75151	−	3.03370i	−0.0702290	−	0.121640i
$623$	−9.91605	−	22.9880i	−0.397278	−	0.920994i
$624$		0			0
$625$	21.3984	−	22.6810i	0.855937	−	0.907240i
$626$	21.9728	−	11.0351i	0.878209	−	0.441053i
$627$		0			0
$628$	2.30370	−	7.69490i	0.0919277	−	0.307060i
$629$	2.57685	−	2.16223i	0.102746	−	0.0862139i
$630$		0			0
$631$	−35.3851	−	29.6916i	−1.40866	−	1.18200i	−0.957099	−	0.289762i	$-0.906424\pi$
$631$	−35.3851	−	29.6916i	−1.40866	−	1.18200i	−0.451558	−	0.892242i	$-0.649132\pi$
$632$	−15.5956	+	10.2574i	−0.620359	+	0.408017i
$633$		0			0
$634$	21.7672	−	2.54422i	0.864487	−	0.101044i
$635$	−11.5310	+	26.7319i	−0.457594	+	1.06082i
$636$		0			0
$637$	34.5793	+	17.3664i	1.37008	+	0.688080i
$638$	−7.39666	+	2.69216i	−0.292836	+	0.106584i
$639$		0			0
$640$	−23.8524	−	8.68156i	−0.942848	−	0.343169i
$641$	−17.0820	−	18.1058i	−0.674698	−	0.715138i	0.296068	−	0.955167i	$-0.404325\pi$
$641$	−17.0820	−	18.1058i	−0.674698	−	0.715138i	−0.970766	+	0.240029i	$0.922843\pi$
$642$		0			0
$643$	−1.84993	−	1.21672i	−0.0729540	−	0.0479826i	0.512508	−	0.858682i	$-0.328716\pi$
$643$	−1.84993	−	1.21672i	−0.0729540	−	0.0479826i	−0.585462	+	0.810700i	$0.699087\pi$
$644$	1.33703	+	4.46599i	0.0526863	+	0.175985i
$645$		0			0
$646$	4.44257	−	5.96741i	0.174791	−	0.234784i
$647$	−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
$650$	−2.81849	+	3.78589i	−0.110550	+	0.148495i
$651$		0			0
$652$	−2.67160	−	8.92377i	−0.104628	−	0.349482i
$653$	0.177323	+	0.116627i	0.00693920	+	0.00456398i	0.552974	−	0.833199i	$-0.313493\pi$
$653$	0.177323	+	0.116627i	0.00693920	+	0.00456398i	−0.546035	+	0.837763i	$0.683863\pi$
$654$		0			0
$655$	25.7143	+	27.2556i	1.00474	+	1.06496i
$656$	0.0769964	+	0.0280244i	0.00300620	+	0.00109417i
$657$		0			0
$658$	−6.26228	+	2.27928i	−0.244129	+	0.0888558i
$659$	24.1950	+	12.1512i	0.942505	+	0.473344i	0.852575	−	0.522604i	$-0.175040\pi$
$659$	24.1950	+	12.1512i	0.942505	+	0.473344i	0.0899295	+	0.995948i	$0.471336\pi$
$660$		0			0
$661$	14.1708	−	32.8515i	0.551179	−	1.27778i	−0.383912	−	0.923370i	$-0.625423\pi$
$661$	14.1708	−	32.8515i	0.551179	−	1.27778i	0.935091	−	0.354407i	$-0.115317\pi$
$662$	0.154155	−	0.0180181i	0.00599140	−	0.000700294i
$663$		0			0
$664$	−7.36043	+	4.84103i	−0.285640	+	0.187868i
$665$	−22.6665	−	19.0195i	−0.878969	−	0.737543i
$666$		0			0
$667$	2.98902	−	2.50808i	0.115735	−	0.0971134i
$668$	6.88127	−	22.9850i	0.266244	−	0.889317i
$669$		0			0
$670$	0.912458	−	0.458254i	0.0352513	−	0.0177039i
$671$	9.44115	−	10.0070i	0.364471	−	0.386317i
$672$		0			0
$673$	−11.3090	−	26.2172i	−0.435930	−	1.01060i	−0.984642	−	0.174588i	$-0.944141\pi$
$673$	−11.3090	−	26.2172i	−0.435930	−	1.01060i	0.548711	−	0.836012i	$-0.315119\pi$
$674$	−7.04994	−	12.2109i	−0.271554	−	0.470345i
$675$		0			0
$676$	−5.71719	+	9.90247i	−0.219892	+	0.380864i
$677$	14.6253	+	1.70945i	0.562097	+	0.0656997i	0.392397	−	0.919796i	$-0.371646\pi$
$677$	14.6253	+	1.70945i	0.562097	+	0.0656997i	0.169700	+	0.985496i	$0.445720\pi$
$678$		0			0
$679$	−36.3953	−	8.62584i	−1.39672	−	0.331030i
$680$	−1.91053	+	32.8025i	−0.0732654	+	1.25792i
$681$		0			0
$682$	−7.82757	+	1.85517i	−0.299733	+	0.0710380i
$683$	−0.764140	−	4.33365i	−0.0292390	−	0.165823i	0.966692	−	0.255943i	$-0.0823859\pi$
$683$	−0.764140	−	4.33365i	−0.0292390	−	0.165823i	−0.995931	+	0.0901204i	$0.971275\pi$
$684$		0			0
$685$	6.91695	−	39.2280i	0.264283	−	1.49882i
$686$	2.46926	+	42.3956i	0.0942769	+	1.61867i
$687$		0			0
$688$	1.00913	+	1.35550i	0.0384729	+	0.0516781i
$689$	−13.0212	−	17.4905i	−0.496068	−	0.666334i
$690$		0			0
$691$	−0.176090	−	3.02335i	−0.00669878	−	0.115014i	0.993301	−	0.115555i	$-0.0368647\pi$
$691$	−0.176090	−	3.02335i	−0.00669878	−	0.115014i	−1.00000		0.000541509i	$0.999828\pi$
$692$	−3.29341	+	18.6779i	−0.125197	+	0.710026i
$693$		0			0
$694$	3.08116	+	17.4741i	0.116959	+	0.663309i
$695$	−0.877776	+	0.208037i	−0.0332959	+	0.00789128i
$696$		0			0
$697$	0.0318129	−	0.546207i	0.00120500	−	0.0206891i
$698$	9.08500	+	2.15318i	0.343872	+	0.0814992i
$699$		0			0
$700$	18.8508	+	2.20334i	0.712493	+	0.0832785i
$701$	21.6147	−	37.4378i	0.816377	−	1.41401i	−0.0919585	−	0.995763i	$-0.529313\pi$
$701$	21.6147	−	37.4378i	0.816377	−	1.41401i	0.908335	−	0.418243i	$-0.137354\pi$
$702$		0			0
$703$	0.809112	+	1.40142i	0.0305162	+	0.0528557i
$704$	−2.25419	−	5.22581i	−0.0849581	−	0.196955i
$705$		0			0
$706$	10.1620	−	10.7711i	0.382453	−	0.405377i
$707$	−10.0614	+	5.05304i	−0.378399	+	0.190039i
$708$		0			0
$709$	9.22829	−	30.8246i	0.346576	−	1.15764i	−0.590066	−	0.807355i	$-0.700898\pi$
$709$	9.22829	−	30.8246i	0.346576	−	1.15764i	0.936642	−	0.350289i	$-0.113917\pi$
$710$	−20.4932	+	17.1958i	−0.769095	+	0.645347i
$711$		0			0
$712$	−10.2453	−	8.59684i	−0.383959	−	0.322180i
$713$	3.33165	−	2.19126i	0.124771	−	0.0820633i
$714$		0			0
$715$	10.4348	−	1.21965i	0.390238	−	0.0456123i
$716$	1.18469	−	2.74642i	0.0442739	−	0.102638i
$717$		0			0
$718$	−6.53400	−	3.28150i	−0.243847	−	0.122464i
$719$	9.54600	−	3.47446i	0.356006	−	0.129576i	−0.157825	−	0.987467i	$-0.550448\pi$
$719$	9.54600	−	3.47446i	0.356006	−	0.129576i	0.513831	+	0.857892i	$0.328226\pi$
$720$		0			0
$721$	1.25395	+	0.456400i	0.0466995	+	0.0169972i
$722$	−7.81193	−	8.28016i	−0.290730	−	0.308156i
$723$		0			0
$724$	−26.6632	−	17.5366i	−0.990929	−	0.651744i
$725$	−4.55594	−	15.2179i	−0.169203	−	0.565179i
$726$		0			0
$727$	8.41672	−	11.3056i	0.312159	−	0.419302i	−0.618161	−	0.786052i	$-0.712122\pi$
$727$	8.41672	−	11.3056i	0.312159	−	0.419302i	0.930320	+	0.366749i	$0.119529\pi$
$728$	28.7900			1.06703
$729$		0			0
$730$	−4.69629			−0.173818
$731$	6.73840	−	9.05125i	0.249229	−	0.334772i
$732$		0			0
$733$	4.50233	+	15.0388i	0.166297	+	0.555471i	0.999995	+	0.00324994i	$0.00103449\pi$
$733$	4.50233	+	15.0388i	0.166297	+	0.555471i	−0.833698	+	0.552221i	$0.813780\pi$
$734$	−19.2251	−	12.6446i	−0.709612	−	0.466719i
$735$		0			0
$736$	2.72033	+	2.88339i	0.100273	+	0.106283i
$737$	−0.759727	−	0.276518i	−0.0279849	−	0.0101857i
$738$		0			0
$739$	−3.42025	+	1.24487i	−0.125816	+	0.0457933i	−0.404161	−	0.914688i	$-0.632436\pi$
$739$	−3.42025	+	1.24487i	−0.125816	+	0.0457933i	0.278345	+	0.960481i	$0.410214\pi$
$740$	−2.60752	−	1.30955i	−0.0958544	−	0.0481399i
$741$		0			0
$742$	15.6087	−	36.1850i	0.573013	−	1.32839i
$743$	23.1239	−	2.70280i	0.848334	−	0.0991560i	0.319193	−	0.947690i	$-0.396588\pi$
$743$	23.1239	−	2.70280i	0.848334	−	0.0991560i	0.529141	+	0.848534i	$0.322514\pi$
$744$		0			0
$745$	−7.16398	+	4.71182i	−0.262468	+	0.172628i
$746$	−3.35694	−	2.81680i	−0.122906	−	0.103130i
$747$		0			0
$748$	8.13668	−	6.82748i	0.297506	−	0.249637i
$749$	−14.2320	+	47.5381i	−0.520025	+	1.73700i
$750$		0			0
$751$	7.05894	−	3.54513i	0.257584	−	0.129364i	−0.315322	−	0.948985i	$-0.602112\pi$
$751$	7.05894	−	3.54513i	0.257584	−	0.129364i	0.572906	+	0.819621i	$0.305816\pi$
$752$	0.773530	−	0.819894i	0.0282077	−	0.0298985i
$753$		0			0
$754$	−3.89650	−	9.03309i	−0.141902	−	0.328966i
$755$	−17.4475	−	30.2200i	−0.634980	−	1.09982i
$756$		0			0
$757$	−2.12074	+	3.67323i	−0.0770795	+	0.133506i	−0.901989	−	0.431760i	$-0.857893\pi$
$757$	−2.12074	+	3.67323i	−0.0770795	+	0.133506i	0.824909	+	0.565265i	$0.191226\pi$
$758$	23.1397	+	2.70465i	0.840473	+	0.0982372i
$759$		0			0
$760$	−15.3808	−	3.64531i	−0.557920	−	0.132229i
$761$	2.37743	−	40.8189i	0.0861818	−	1.47968i	−0.627173	−	0.778880i	$-0.715788\pi$
$761$	2.37743	−	40.8189i	0.0861818	−	1.47968i	0.713354	−	0.700803i	$-0.247175\pi$
$762$		0			0
$763$	−65.0339	+	15.4133i	−2.35438	+	0.557999i
$764$	−5.24431	−	29.7420i	−0.189733	−	1.07603i
$765$		0			0
$766$	−1.69387	+	9.60642i	−0.0612020	+	0.347094i
$767$	−1.46810	−	25.2064i	−0.0530101	−	0.910149i
$768$		0			0
$769$	19.5244	+	26.2258i	0.704066	+	0.945725i	0.999955	−	0.00949722i	$-0.00302310\pi$
$769$	19.5244	+	26.2258i	0.704066	+	0.945725i	−0.295889	+	0.955222i	$0.595616\pi$
$770$	11.3381	+	15.2298i	0.408598	+	0.548843i
$771$		0			0
$772$	−0.578834	−	9.93820i	−0.0208327	−	0.357684i
$773$	6.74796	−	38.2696i	0.242707	−	1.37646i	−0.583050	−	0.812436i	$-0.698141\pi$
$773$	6.74796	−	38.2696i	0.242707	−	1.37646i	0.825757	−	0.564025i	$-0.190748\pi$
$774$		0			0
$775$	−2.81909	−	15.9878i	−0.101265	−	0.574300i
$776$	−19.4429	+	4.60805i	−0.697958	+	0.165419i
$777$		0			0
$778$	−0.850704	+	14.6060i	−0.0304992	+	0.523651i
$779$	0.256111	+	0.0606995i	0.00917614	+	0.00217479i
$780$		0			0
$781$	21.0391	+	2.45911i	0.752837	+	0.0879940i
$782$	1.18321	−	2.04938i	0.0423115	−	0.0732856i
$783$		0			0
$784$	−5.91429	−	10.2439i	−0.211225	−	0.365852i
$785$	6.42311	+	14.8904i	0.229251	+	0.531463i
$786$		0			0
$787$	−1.56542	+	1.65925i	−0.0558011	+	0.0591457i	−0.754673	−	0.656101i	$-0.772204\pi$
$787$	−1.56542	+	1.65925i	−0.0558011	+	0.0591457i	0.698872	+	0.715247i	$0.253686\pi$
$788$	20.2260	−	10.1579i	0.720523	−	0.361860i
$789$		0			0
$790$	4.41265	−	14.7393i	0.156995	−	0.524399i
$791$	−1.53091	+	1.28459i	−0.0544329	+	0.0456746i
$792$		0			0
$793$	13.1718	+	11.0524i	0.467743	+	0.392483i
$794$	−6.71952	+	4.41950i	−0.238467	+	0.156842i
$795$		0			0
$796$	−11.0579	+	1.29248i	−0.391937	+	0.0458109i
$797$	−13.5480	+	31.4079i	−0.479896	+	1.11252i	0.490596	+	0.871387i	$0.336779\pi$
$797$	−13.5480	+	31.4079i	−0.479896	+	1.11252i	−0.970491	+	0.241136i	$0.922480\pi$
$798$		0			0
$799$	−6.72616	−	3.37800i	−0.237954	−	0.119505i
$800$	15.1653	−	5.51971i	0.536174	−	0.195151i
$801$		0			0
$802$	−1.49398	−	0.543764i	−0.0527543	−	0.0192010i
$803$	2.55182	+	2.70477i	0.0900518	+	0.0954493i
$804$		0			0
$805$	−7.86353	−	5.17192i	−0.277153	−	0.182286i
$806$	−2.88350	−	9.63156i	−0.101567	−	0.339257i
$807$		0			0
$808$	−3.59174	+	4.82455i	−0.126357	+	0.169727i
$809$	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	$0.411218\pi$
$812$	−23.6228	+	31.7309i	−0.828997	+	1.11354i
$813$		0			0
$814$	−0.297813	−	0.994766i	−0.0104384	−	0.0348665i
$815$	15.7126	+	10.3343i	0.550388	+	0.361996i
$816$		0			0
$817$	3.72519	+	3.94847i	0.130328	+	0.138139i
$818$	−0.643582	−	0.234245i	−0.0225023	−	0.00819017i
$819$		0			0
$820$	−0.445977	+	0.162322i	−0.0155742	+	0.00566854i
$821$	−45.6834	−	22.9431i	−1.59436	−	0.800718i	−0.594367	−	0.804194i	$-0.702597\pi$
$821$	−45.6834	−	22.9431i	−1.59436	−	0.800718i	−0.999994	+	0.00347568i	$0.998894\pi$
$822$		0			0
$823$	1.30609	−	3.02787i	0.0455276	−	0.105545i	−0.893935	−	0.448197i	$-0.852066\pi$
$823$	1.30609	−	3.02787i	0.0455276	−	0.105545i	0.939462	+	0.342653i	$0.111325\pi$
$824$	0.708048	−	0.0827589i	0.0246660	−	0.00288304i
$825$		0			0
$826$	38.1249	−	25.0751i	1.32653	−	0.872475i
$827$	−15.7734	−	13.2354i	−0.548494	−	0.460241i	0.325937	−	0.945392i	$-0.394320\pi$
$827$	−15.7734	−	13.2354i	−0.548494	−	0.460241i	−0.874431	+	0.485151i	$0.838765\pi$
$828$		0			0
$829$	10.1320	−	8.50174i	0.351898	−	0.295278i	−0.449654	−	0.893203i	$-0.648453\pi$
$829$	10.1320	−	8.50174i	0.351898	−	0.295278i	0.801552	+	0.597925i	$0.204008\pi$
$830$	2.08257	−	6.95628i	0.0722872	−	0.241456i
$831$		0			0
$832$	6.35638	−	3.19229i	0.220368	−	0.110673i
$833$	−54.2023	+	57.4511i	−1.87800	+	1.99056i
$834$		0			0
$835$	19.1861	+	44.4784i	0.663963	+	1.53924i
$836$	2.55486	+	4.42514i	0.0883616	+	0.153047i
$837$		0			0
$838$	9.94002	−	17.2166i	0.343372	−	0.594738i
$839$	6.26646	+	0.732444i	0.216342	+	0.0252868i	0.223574	−	0.974687i	$-0.428228\pi$
$839$	6.26646	+	0.732444i	0.216342	+	0.0252868i	−0.00723124	+	0.999974i	$0.502302\pi$
$840$		0			0
$841$	3.99920	+	0.947828i	0.137904	+	0.0326837i
$842$	0.767093	−	13.1705i	0.0264358	−	0.453884i
$843$		0			0
$844$	32.1196	−	7.61247i	1.10560	−	0.262032i
$845$	−4.00870	−	22.7345i	−0.137903	−	0.782089i
$846$		0			0
$847$	−6.90630	+	39.1676i	−0.237303	+	1.34581i
$848$	0.387568	+	6.65429i	0.0133091	+	0.228509i
$849$		0			0
$850$	−5.75308	−	7.72773i	−0.197329	−	0.265059i
$851$	0.307380	+	0.412882i	0.0105368	+	0.0141534i
$852$		0			0
$853$	−1.05380	−	18.0931i	−0.0360816	−	0.619496i	−0.967080	−	0.254473i	$-0.918098\pi$
$853$	−1.05380	−	18.0931i	−0.0360816	−	0.619496i	0.930998	−	0.365023i	$-0.118939\pi$
$854$	−5.39614	+	30.6030i	−0.184652	+	1.04721i
$855$		0			0
$856$	4.60327	+	26.1064i	0.157336	+	0.892299i
$857$	33.0907	−	7.84263i	1.13036	−	0.267899i	0.377452	−	0.926029i	$-0.376800\pi$
$857$	33.0907	−	7.84263i	1.13036	−	0.267899i	0.752904	+	0.658130i	$0.228652\pi$
$858$		0			0
$859$	−2.76746	+	47.5154i	−0.0944244	+	1.62120i	0.535491	+	0.844541i	$0.320127\pi$
$859$	−2.76746	+	47.5154i	−0.0944244	+	1.62120i	−0.629915	+	0.776664i	$0.716910\pi$
$860$	−9.52432	−	2.25731i	−0.324777	−	0.0769735i
$861$		0			0
$862$	−20.6199	−	2.41012i	−0.702316	−	0.0820890i
$863$	−26.7851	+	46.3932i	−0.911777	+	1.57924i	−0.100224	+	0.994965i	$0.531956\pi$
$863$	−26.7851	+	46.3932i	−0.911777	+	1.57924i	−0.811553	+	0.584279i	$0.801377\pi$
$864$		0			0
$865$	−19.1455	−	33.1610i	−0.650966	−	1.12751i
$866$	3.92602	+	9.10154i	0.133412	+	0.309283i
$867$		0			0
$868$	−27.7436	+	29.4065i	−0.941679	+	0.998121i
$869$	−10.8866	+	5.46745i	−0.369302	+	0.185471i
$870$		0			0
$871$	0.289800	−	0.967998i	0.00981949	−	0.0327994i
$872$	−27.3512	+	22.9504i	−0.926227	+	0.777197i
$873$		0			0
$874$	0.872065	+	0.731749i	0.0294980	+	0.0247518i
$875$	25.9681	−	17.0795i	0.877882	−	0.577392i
$876$		0			0
$877$	14.2696	−	1.66787i	0.481848	−	0.0563200i	0.128298	−	0.991736i	$-0.459048\pi$
$877$	14.2696	−	1.66787i	0.481848	−	0.0563200i	0.353550	+	0.935416i	$0.384974\pi$
$878$	−2.74444	+	6.36233i	−0.0926204	+	0.214718i
$879$		0			0
$880$	−2.86988	−	1.44131i	−0.0967438	−	0.0485866i
$881$	−0.647962	+	0.235839i	−0.0218304	+	0.00794561i	−0.352912	−	0.935656i	$-0.614809\pi$
$881$	−0.647962	+	0.235839i	−0.0218304	+	0.00794561i	0.331082	+	0.943602i	$0.392586\pi$
$882$		0			0
$883$	−23.8383	−	8.67642i	−0.802222	−	0.291985i	−0.0918148	−	0.995776i	$-0.529267\pi$
$883$	−23.8383	−	8.67642i	−0.802222	−	0.291985i	−0.710407	+	0.703791i	$0.751489\pi$
$884$	9.10987	+	9.65590i	0.306398	+	0.324763i
$885$		0			0
$886$	10.0156	+	6.58735i	0.336480	+	0.221306i
$887$	11.9637	+	39.9614i	0.401700	+	1.34177i	0.884704	+	0.466154i	$0.154361\pi$
$887$	11.9637	+	39.9614i	0.401700	+	1.34177i	−0.483003	+	0.875619i	$0.660454\pi$
$888$		0			0
$889$	−31.0926	+	41.7646i	−1.04281	+	1.40074i
$890$	11.0236			0.369513
$891$		0			0
$892$	−16.5109			−0.552824
$893$	2.16223	−	2.90437i	0.0723562	−	0.0971912i
$894$		0			0
$895$	1.73191	+	5.78499i	0.0578915	+	0.193371i
$896$	−37.9288	−	24.9462i	−1.26711	−	0.833393i
$897$		0			0
$898$	0.668442	+	0.708507i	0.0223062	+	0.0236432i
$899$	31.7972	+	11.5732i	1.06050	+	0.385989i
$900$		0			0
$901$	41.8245	−	15.2229i	1.39338	−	0.507147i
$902$	−0.150930	−	0.0758001i	−0.00502543	−	0.00252387i
$903$		0			0
$904$	−0.422857	+	0.980293i	−0.0140640	+	0.0326041i
$905$	63.9949	−	7.47993i	2.12726	−	0.248641i
$906$		0			0
$907$	33.1694	−	21.8159i	1.10137	−	0.724384i	0.137434	−	0.990511i	$-0.456115\pi$
$907$	33.1694	−	21.8159i	1.10137	−	0.724384i	0.963938	+	0.266127i	$0.0857442\pi$
$908$	−26.5448	−	22.2737i	−0.880920	−	0.739180i
$909$		0			0
$910$	−18.1781	+	15.2532i	−0.602598	+	0.505640i
$911$	11.2981	−	37.7383i	0.374323	−	1.25033i	−0.538727	−	0.842480i	$-0.681095\pi$
$911$	11.2981	−	37.7383i	0.374323	−	1.25033i	0.913051	−	0.407846i	$-0.133720\pi$
$912$		0			0
$913$	−5.13799	+	2.58040i	−0.170043	+	0.0853987i
$914$	16.7450	−	17.7487i	0.553875	−	0.587073i
$915$		0			0
$916$	14.0860	+	32.6551i	0.465415	+	1.07895i
$917$	33.5082	+	58.0379i	1.10654	+	1.91658i
$918$		0			0
$919$	7.97650	−	13.8157i	0.263120	−	0.455738i	−0.703949	−	0.710250i	$-0.748582\pi$
$919$	7.97650	−	13.8157i	0.263120	−	0.455738i	0.967069	+	0.254513i	$0.0819150\pi$
$920$	−4.99397	−	0.583711i	−0.164646	−	0.0192444i
$921$		0			0
$922$	−12.9819	−	3.07676i	−0.427535	−	0.101328i
$923$	−1.53931	+	26.4289i	−0.0506670	+	0.869919i
$924$		0			0
$925$	2.03910	−	0.483274i	0.0670450	−	0.0158900i
$926$	−4.88017	−	27.6768i	−0.160372	−	0.909516i
$927$		0			0
$928$	−5.84117	+	33.1269i	−0.191746	+	1.08744i
$929$	−1.45951	−	25.0588i	−0.0478850	−	0.822154i	−0.933687	−	0.358090i	$-0.883428\pi$
$929$	−1.45951	−	25.0588i	−0.0478850	−	0.822154i	0.885802	−	0.464064i	$-0.153609\pi$
$930$		0			0
$931$	−22.6900	−	30.4779i	−0.743634	−	0.998873i
$932$	7.52579	+	10.1089i	0.246515	+	0.331128i
$933$		0			0
$934$	1.92407	+	33.0350i	0.0629576	+	1.08094i
$935$	−3.72378	+	21.1186i	−0.121781	+	0.690652i
$936$		0			0
$937$	−6.76540	−	38.3685i	−0.221016	−	1.25344i	−0.870156	−	0.492776i	$-0.835982\pi$
$937$	−6.76540	−	38.3685i	−0.221016	−	1.25344i	0.649140	−	0.760669i	$-0.275129\pi$
$938$	1.77693	−	0.421140i	0.0580187	−	0.0137507i
$939$		0			0
$940$	−0.379624	+	6.51788i	−0.0123820	+	0.212590i
$941$	−32.1821	−	7.62730i	−1.04911	−	0.248643i	−0.330317	−	0.943870i	$-0.607156\pi$
$941$	−32.1821	−	7.62730i	−1.04911	−	0.248643i	−0.718790	+	0.695227i	$0.755304\pi$
$942$		0			0
$943$	0.0831565	+	0.00971960i	0.00270795	+	0.000316514i
$944$	−3.85915	+	6.68424i	−0.125605	+	0.217554i
$945$		0			0
$946$	−1.74166	−	3.01664i	−0.0566261	−	0.0980793i
$947$	−5.74484	−	13.3180i	−0.186682	−	0.432778i	0.799013	−	0.601313i	$-0.205356\pi$
$947$	−5.74484	−	13.3180i	−0.186682	−	0.432778i	−0.985696	+	0.168535i	$0.946096\pi$
$948$		0			0
$949$	−3.18928	+	3.38044i	−0.103528	+	0.109734i
$950$	4.14165	−	2.08001i	0.134373	−	0.0674846i
$951$		0			0
$952$	−16.8542	+	56.2971i	−0.546249	+	1.82460i
$953$	4.46031	−	3.74265i	0.144484	−	0.121236i	−0.567681	−	0.823249i	$-0.692159\pi$
$953$	4.46031	−	3.74265i	0.144484	−	0.121236i	0.712165	+	0.702012i	$0.247715\pi$
$954$		0			0
$955$	46.7081	+	39.1928i	1.51144	+	1.26825i
$956$	25.0853	−	16.4989i	0.811316	−	0.533611i
$957$		0			0
$958$	−28.2295	+	3.29956i	−0.912054	+	0.106604i
$959$	28.2169	−	65.4142i	0.911172	−	2.11233i
$960$		0			0
$961$	3.20081	+	1.60751i	0.103252	+	0.0518551i
$962$	1.21952	−	0.443868i	0.0393188	−	0.0143109i
$963$		0			0
$964$	17.9774	+	6.54323i	0.579013	+	0.210743i
$965$	13.7924	+	14.6191i	0.443994	+	0.470606i
$966$		0			0
$967$	38.1735	+	25.1071i	1.22758	+	0.807391i	0.986603	−	0.163140i	$-0.0521623\pi$
$967$	38.1735	+	25.1071i	1.22758	+	0.807391i	0.240975	+	0.970531i	$0.422533\pi$
$968$	6.09360	+	20.3541i	0.195856	+	0.654204i
$969$		0			0
$970$	9.83491	−	13.2106i	0.315780	−	0.424166i
$971$	−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
$974$	−13.1152	+	17.6167i	−0.420237	+	0.564476i
$975$		0			0
$976$	−1.50747	−	5.03531i	−0.0482531	−	0.161176i
$977$	17.0393	+	11.2069i	0.545137	+	0.358542i	0.792012	−	0.610505i	$-0.209034\pi$
$977$	17.0393	+	11.2069i	0.545137	+	0.358542i	−0.246876	+	0.969047i	$0.579404\pi$
$978$		0			0
$979$	−5.98990	−	6.34892i	−0.191438	−	0.202912i
$980$	64.3814	+	23.4329i	2.05659	+	0.748537i
$981$		0			0
$982$	−16.0966	+	5.85868i	−0.513662	+	0.186958i
$983$	−37.6795	−	18.9233i	−1.20179	−	0.603561i	−0.268705	−	0.963222i	$-0.586596\pi$
$983$	−37.6795	−	18.9233i	−1.20179	−	0.603561i	−0.933083	+	0.359662i	$0.882892\pi$
$984$		0			0
$985$	−18.0990	+	41.9582i	−0.576683	+	1.33690i
$986$	19.9448	−	2.33121i	0.635171	−	0.0742409i
$987$		0			0
$988$	−5.33554	+	3.50924i	−0.169746	+	0.111644i
$989$	1.32273	+	1.10990i	0.0420604	+	0.0352929i
$990$		0			0
$991$	−1.19365	+	1.00159i	−0.0379176	+	0.0318167i	−0.661550	−	0.749901i	$-0.730101\pi$
$991$	−1.19365	+	1.00159i	−0.0379176	+	0.0318167i	0.623632	+	0.781718i	$0.285656\pi$
$992$	−9.85957	+	32.9332i	−0.313042	+	1.04563i
$993$		0			0
$994$	−42.7560	+	21.4729i	−1.35614	+	0.681078i
$995$	15.4247	−	16.3492i	0.488996	−	0.518305i
$996$		0			0
$997$	−20.7294	−	48.0562i	−0.656508	−	1.52196i	−0.842095	−	0.539329i	$-0.818678\pi$
$997$	−20.7294	−	48.0562i	−0.656508	−	1.52196i	0.185587	−	0.982628i	$-0.440581\pi$
$998$	−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	243.2.g.a.226.3		144
3.2	odd	2		81.2.g.a.58.6	yes	144
9.2	odd	6		729.2.g.d.433.3		144
9.4	even	3		729.2.g.b.676.3		144
9.5	odd	6		729.2.g.c.676.6		144
9.7	even	3		729.2.g.a.433.6		144
81.7	even	27	inner	243.2.g.a.100.3		144
81.13	even	27		6561.2.a.d.1.25		72
81.20	odd	54		729.2.g.c.55.6		144
81.34	even	27		729.2.g.a.298.6		144
81.47	odd	54		729.2.g.d.298.3		144
81.61	even	27		729.2.g.b.55.3		144
81.68	odd	54		6561.2.a.c.1.48		72
81.74	odd	54		81.2.g.a.7.6	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.6	✓	144	81.74	odd	54
81.2.g.a.58.6	yes	144	3.2	odd	2
243.2.g.a.100.3		144	81.7	even	27	inner
243.2.g.a.226.3		144	1.1	even	1	trivial
729.2.g.a.298.6		144	81.34	even	27
729.2.g.a.433.6		144	9.7	even	3
729.2.g.b.55.3		144	81.61	even	27
729.2.g.b.676.3		144	9.4	even	3
729.2.g.c.55.6		144	81.20	odd	54
729.2.g.c.676.6		144	9.5	odd	6
729.2.g.d.298.3		144	81.47	odd	54
729.2.g.d.433.3		144	9.2	odd	6
6561.2.a.c.1.48		72	81.68	odd	54
6561.2.a.d.1.25		72	81.13	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.470263 + 0.631673i) q^{2} +(0.395743 + 1.32187i) q^{4} +(-2.32750 - 1.53082i) q^{5} +(-3.41908 - 3.62402i) q^{7} +(-2.50111 - 0.910331i) q^{8} +(2.06152 - 0.750330i) q^{10} +(-1.55231 - 0.779598i) q^{11} +(0.859891 - 1.99345i) q^{13} +(3.89706 - 0.455501i) q^{14} +(-0.554469 + 0.364680i) q^{16} +(3.39468 + 2.84848i) q^{17} +(-1.63306 + 1.37030i) q^{19} +(1.10246 - 3.68247i) q^{20} +(1.22244 - 0.613935i) q^{22} +(-0.465342 + 0.493234i) q^{23} +(1.09345 + 2.53489i) q^{25} +(0.854835 + 1.48062i) q^{26} +(3.43741 - 5.95378i) q^{28} +(-5.71522 - 0.668013i) q^{29} +(-5.72212 - 1.35617i) q^{31} +(0.339908 - 5.83599i) q^{32} +(-3.39570 + 0.804795i) q^{34} +(2.41020 + 13.6689i) q^{35} +(0.131814 - 0.747552i) q^{37} +(-0.0976137 - 1.67596i) q^{38} +(4.42779 + 5.94755i) q^{40} +(-0.0737288 - 0.0990350i) q^{41} +(-0.148059 - 2.54207i) q^{43} +(0.416216 - 2.36048i) q^{44} +(-0.0927292 - 0.525894i) q^{46} +(-1.65271 + 0.391699i) q^{47} +(-1.03635 + 17.7935i) q^{49} +(-2.11543 - 0.501366i) q^{50} +(2.97539 + 0.347773i) q^{52} +(5.02192 - 8.69822i) q^{53} +(2.41957 + 4.19082i) q^{55} +(5.25246 + 12.1766i) q^{56} +(3.10962 - 3.29601i) q^{58} +(10.3931 - 5.21959i) q^{59} +(-2.27150 + 7.58734i) q^{61} +(3.54755 - 2.97675i) q^{62} +(2.50983 + 2.10599i) q^{64} +(-5.05301 + 3.32342i) q^{65} +(0.462282 - 0.0540330i) q^{67} +(-2.42190 + 5.61460i) q^{68} +(-9.76770 - 4.90552i) q^{70} +(-11.4588 + 4.17067i) q^{71} +(-2.01159 - 0.732160i) q^{73} +(0.410222 + 0.434809i) q^{74} +(-2.45764 - 1.61641i) q^{76} +(2.48219 + 8.29110i) q^{77} +(4.18797 - 5.62542i) q^{79} +1.84879 q^{80} +0.0972297 q^{82} +(1.97654 - 2.65495i) q^{83} +(-3.54061 - 11.8265i) q^{85} +(1.67538 + 1.10192i) q^{86} +(3.17281 + 3.36298i) q^{88} +(4.72182 + 1.71860i) q^{89} +(-10.1643 + 3.69952i) q^{91} +(-0.836149 - 0.419930i) q^{92} +(0.529782 - 1.22817i) q^{94} +(5.89863 - 0.689452i) q^{95} +(6.27220 - 4.12529i) q^{97} +(-10.7523 - 9.02224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 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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