LMFDB - Embedded newform 243.2.g.a.100.3

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			100.3
Character	$\chi$	$=$	243.100
Dual form			243.2.g.a.226.3

$q$-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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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	0.604143	−	0.796876i	$-0.293516\pi$
$2$	−0.470263	−	0.631673i	−0.332526	−	0.446660i	−0.936669	+	0.350216i	$0.886108\pi$
$3$		0			0
$3$		0			0
$4$	0.395743	−	1.32187i	0.197872	−	0.660937i
$5$	−2.32750	+	1.53082i	−1.04089	+	0.684604i	−0.950316	−	0.311286i	$-0.899240\pi$
$5$	−2.32750	+	1.53082i	−1.04089	+	0.684604i	−0.0905734	+	0.995890i	$0.528870\pi$
$6$		0			0
$7$	−3.41908	+	3.62402i	−1.29229	+	1.36975i	−0.401158	+	0.916009i	$0.631392\pi$
$7$	−3.41908	+	3.62402i	−1.29229	+	1.36975i	−0.891134	+	0.453740i	$0.850089\pi$
$8$	−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	−0.667156	−	0.744918i	$-0.732489\pi$
$11$	−1.55231	+	0.779598i	−0.468038	+	0.235058i	0.199118	+	0.979976i	$0.436192\pi$
$12$		0			0
$13$	0.859891	+	1.99345i	0.238491	+	0.552884i	0.994860	−	0.101261i	$-0.0322878\pi$
$13$	0.859891	+	1.99345i	0.238491	+	0.552884i	−0.756369	+	0.654145i	$0.773029\pi$
$14$	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	−0.130419	−	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	$0.800858\pi$
$20$	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	0.677038	−	0.735948i	$-0.263263\pi$
$23$	−0.465342	−	0.493234i	−0.0970305	−	0.102846i	−0.774069	+	0.633101i	$0.781782\pi$
$24$		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	−0.628781	−	0.777583i	$-0.716446\pi$
$29$	−5.71522	+	0.668013i	−1.06129	+	0.124047i	−0.432509	+	0.901630i	$0.642372\pi$
$30$		0			0
$31$	−5.72212	+	1.35617i	−1.02772	+	0.243575i	−0.709697	−	0.704507i	$-0.751168\pi$
$31$	−5.72212	+	1.35617i	−1.02772	+	0.243575i	−0.318026	+	0.948082i	$0.603020\pi$
$32$	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	0.993724	−	0.111861i	$-0.0356813\pi$
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	−0.972054	+	0.234758i	$0.924570\pi$
$38$	−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	−0.807843	−	0.589398i	$-0.799365\pi$
$41$	−0.0737288	+	0.0990350i	−0.0115145	+	0.0154667i	0.796329	+	0.604864i	$0.206773\pi$
$42$		0			0
$43$	−0.148059	+	2.54207i	−0.0225787	+	0.387662i	0.968021	+	0.250869i	$0.0807164\pi$
$43$	−0.148059	+	2.54207i	−0.0225787	+	0.387662i	−0.990600	+	0.136792i	$0.956321\pi$
$44$	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	0.108304	−	0.994118i	$-0.465458\pi$
$47$	−1.65271	−	0.391699i	−0.241072	−	0.0571351i	−0.349376	+	0.936983i	$0.613606\pi$
$48$		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	0.971898	+	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
$56$	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	0.969753	−	0.244087i	$-0.0784883\pi$
$59$	10.3931	+	5.21959i	1.35306	+	0.679533i	0.383309	+	0.923620i	$0.374785\pi$
$60$		0			0
$61$	−2.27150	−	7.58734i	−0.290836	−	0.971460i	−0.971136	−	0.238526i	$-0.923336\pi$
$61$	−2.27150	−	7.58734i	−0.290836	−	0.971460i	0.680300	−	0.732934i	$-0.261849\pi$
$62$	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	0.144284	−	0.989536i	$-0.453912\pi$
$67$	0.462282	+	0.0540330i	0.0564767	+	0.00660118i	−0.0878076	+	0.996137i	$0.527986\pi$
$68$	−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	−0.443885	−	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	$0.428870\pi$
$74$	0.410222	−	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	0.972652	−	0.232266i	$-0.0746141\pi$
$79$	4.18797	+	5.62542i	0.471184	+	0.632910i	−0.501469	+	0.865176i	$0.667207\pi$
$80$	1.84879			0.206701
$81$		0			0
$82$	0.0972297			0.0107372
$83$	1.97654	+	2.65495i	0.216953	+	0.291419i	0.897254	−	0.441514i	$-0.145558\pi$
$83$	1.97654	+	2.65495i	0.216953	+	0.291419i	−0.680301	+	0.732933i	$0.738151\pi$
$84$		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	−0.0794124	−	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
$92$	−0.836149	+	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	0.826457	−	0.562999i	$-0.190353\pi$
$97$	6.27220	+	4.12529i	0.636846	+	0.418860i	−0.189612	+	0.981859i	$0.560723\pi$
$98$	−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	0.984161	−	0.177279i	$-0.0567296\pi$
$101$	0.648115	+	2.16486i	0.0644899	+	0.215411i	−0.919671	+	0.392690i	$0.871544\pi$
$102$		0			0
$103$	−0.239343	−	0.120203i	−0.0235832	−	0.0118439i	0.436969	−	0.899477i	$-0.356052\pi$
$103$	−0.239343	−	0.120203i	−0.0235832	−	0.0118439i	−0.460552	+	0.887633i	$0.652348\pi$
$104$	−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	−0.999773	−	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	$0.611256\pi$
$110$	−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	0.999227	−	0.0392998i	$-0.0125127\pi$
$113$	0.0233225	+	0.400431i	0.00219399	+	0.0376694i	−0.997033	+	0.0769692i	$0.975476\pi$
$114$		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	0.792037	+	0.610474i	$0.209021\pi$
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	−0.953065	+	0.302765i	$0.902090\pi$
$128$	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	−0.758366	−	0.651829i	$-0.774002\pi$
$131$	−13.0882	+	3.10197i	−1.14353	+	0.271021i	−0.385160	+	0.922850i	$0.625854\pi$
$132$		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	−0.485096	−	0.874461i	$-0.661215\pi$
$137$	5.66340	−	13.1292i	0.483857	−	1.12171i	0.968953	−	0.247246i	$-0.0795254\pi$
$138$		0			0
$139$	0.222217	+	0.235537i	0.0188482	+	0.0199780i	0.736729	−	0.676188i	$-0.236369\pi$
$139$	0.222217	+	0.235537i	0.0188482	+	0.0199780i	−0.717881	+	0.696166i	$0.754888\pi$
$140$	−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	0.960826	−	0.277152i	$-0.0893905\pi$
$149$	1.21912	+	2.82624i	0.0998744	+	0.231535i	−0.860952	+	0.508687i	$0.830131\pi$
$150$		0			0
$151$	11.1937	−	5.62167i	0.910928	−	0.457485i	0.0693326	−	0.997594i	$-0.477913\pi$
$151$	11.1937	−	5.62167i	0.910928	−	0.457485i	0.841596	+	0.540108i	$0.181617\pi$
$152$	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	−0.728554	−	0.684988i	$-0.759807\pi$
$157$	−4.86355	+	3.19881i	−0.388153	+	0.255292i	0.340401	+	0.940280i	$0.389437\pi$
$158$	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	−0.968646	−	0.248444i	$-0.920081\pi$
$167$	−14.5276	+	9.55498i	−1.12418	+	0.739387i	−0.155536	+	0.987830i	$0.549711\pi$
$168$		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	0.0842696	−	0.996443i	$-0.473144\pi$
$173$	12.2830	−	6.16877i	0.933862	−	0.469003i	0.849592	+	0.527440i	$0.176848\pi$
$174$		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	−0.702732	−	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	$-0.607036\pi$
$182$	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	−0.857395	−	0.514660i	$-0.827918\pi$
$191$	−21.7391	+	2.54094i	−1.57299	+	0.183856i	−0.715595	+	0.698516i	$0.753844\pi$
$192$		0			0
$193$	−7.02015	+	1.66381i	−0.505322	+	0.119763i	−0.475367	−	0.879788i	$-0.657685\pi$
$193$	−7.02015	+	1.66381i	−0.505322	+	0.119763i	−0.0299550	+	0.999551i	$0.509536\pi$
$194$	−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	0.697718	+	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	$-0.147874\pi$
$200$	−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	0.614311	+	0.789064i	$0.289434\pi$
$211$	1.39097	+	23.8821i	0.0957585	+	1.64411i	−0.518553	+	0.855046i	$0.673529\pi$
$212$	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	−0.992648	−	0.121033i	$-0.961379\pi$
$223$	−3.43182	−	11.4631i	−0.229812	−	0.767624i	0.762837	−	0.646591i	$-0.223806\pi$
$224$	−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	−0.392598	−	0.919710i	$-0.628423\pi$
$227$	−20.9815	−	13.7997i	−1.39259	−	0.915921i	−0.999993	+	0.00378925i	$0.998794\pi$
$228$		0			0
$229$	25.5994	+	2.99214i	1.69166	+	0.197726i	0.906686	−	0.421806i	$-0.138604\pi$
$229$	25.5994	+	2.99214i	1.69166	+	0.197726i	0.784971	+	0.619533i	$0.212678\pi$
$230$	−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	0.607488	−	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
$236$	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	0.478759	+	0.877946i	$0.341087\pi$
$239$	−6.24071	+	20.8454i	−0.403678	+	1.34838i	−0.882437	+	0.470431i	$0.844098\pi$
$240$		0			0
$241$	8.27944	+	11.1212i	0.533326	+	0.716381i	0.984368	−	0.176122i	$-0.0563552\pi$
$241$	8.27944	+	11.1212i	0.533326	+	0.716381i	−0.451043	+	0.892502i	$0.648948\pi$
$242$	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	−0.00604584	−	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
$254$	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	0.0795987	−	0.996827i	$-0.474636\pi$
$257$	−1.16759	−	0.136472i	−0.0728323	−	0.00851287i	−0.152431	+	0.988314i	$0.548710\pi$
$258$		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	1.00000		0.000980948i	$0.000312246\pi$
$263$	2.67668	+	8.94073i	0.165051	+	0.551309i	−0.834948	+	0.550328i	$0.814503\pi$
$264$		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	−0.825360	−	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	$0.887002\pi$
$272$	−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	0.918482	−	0.395464i	$-0.129416\pi$
$277$	25.9932	+	6.16051i	1.56178	+	0.370149i	0.643301	+	0.765613i	$0.277564\pi$
$278$	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	−0.288734	−	0.957409i	$-0.593234\pi$
$281$	1.83046	−	31.4278i	0.109196	−	1.87482i	0.397930	−	0.917416i	$-0.369729\pi$
$282$		0			0
$283$	3.99576	−	5.36724i	0.237523	−	0.319049i	−0.667338	−	0.744755i	$-0.732567\pi$
$283$	3.99576	−	5.36724i	0.237523	−	0.319049i	0.904862	+	0.425705i	$0.139974\pi$
$284$	−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	−0.335920	−	0.941890i	$-0.609047\pi$
$293$	−3.65264	+	0.865692i	−0.213390	+	0.0505743i	0.122530	+	0.992465i	$0.460899\pi$
$294$		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	−0.321406	+	0.946942i	$0.604155\pi$
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.988367	+	0.152088i	$0.951400\pi$
$308$	−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	0.860931	−	0.508721i	$-0.169882\pi$
$311$	−1.76187	−	4.08446i	−0.0999062	−	0.231609i	−0.960837	+	0.277113i	$0.910622\pi$
$312$		0			0
$313$	−27.9019	+	14.0129i	−1.57711	+	0.792054i	−0.999702	−	0.0244032i	$-0.992231\pi$
$313$	−27.9019	+	14.0129i	−1.57711	+	0.792054i	−0.577406	+	0.816457i	$0.695935\pi$
$314$	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	−0.0825140	+	0.996590i	$0.526295\pi$
$317$	−19.0975	+	20.2421i	−1.07262	+	1.13691i	−0.990106	+	0.140321i	$0.955187\pi$
$318$		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	−0.731080	−	0.682292i	$-0.760983\pi$
$331$	−0.135248	+	0.143354i	−0.00743388	+	0.00787946i	0.723646	+	0.690171i	$0.242465\pi$
$332$	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	−0.994786	−	0.101989i	$-0.967479\pi$
$337$	−7.09164	−	16.4403i	−0.386306	−	0.895559i	0.608479	−	0.793570i	$-0.291780\pi$
$338$	−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	0.994300	−	0.106615i	$-0.0340013\pi$
$347$	15.4622	+	16.3889i	0.830052	+	0.879804i	−0.164248	+	0.986419i	$0.552520\pi$
$348$		0			0
$349$	−4.69595	+	10.8864i	−0.251368	+	0.582737i	−0.996445	−	0.0842411i	$-0.973153\pi$
$349$	−4.69595	+	10.8864i	−0.251368	+	0.582737i	0.745077	+	0.666978i	$0.232413\pi$
$350$	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	−0.597548	−	0.801833i	$-0.703858\pi$
$353$	−18.6770	+	2.18302i	−0.994074	+	0.116191i	−0.396526	+	0.918024i	$0.629784\pi$
$354$		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	−0.912244	−	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
$362$	−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	−0.601396	−	0.798951i	$-0.705389\pi$
$367$	1.69898	−	29.1704i	0.0886861	−	1.52268i	0.690083	−	0.723731i	$-0.257574\pi$
$368$	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	−0.996271	−	0.0862813i	$-0.972502\pi$
$373$	−0.323556	−	5.55523i	−0.0167531	−	0.287639i	0.979518	−	0.201358i	$-0.0645354\pi$
$374$	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	0.183140	+	0.983087i	$0.441374\pi$
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	−0.942948	+	0.332940i	$0.891959\pi$
$380$	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	0.708538	−	0.705672i	$-0.249355\pi$
$383$	11.0692	+	5.55918i	0.565612	+	0.284061i	−0.142926	+	0.989733i	$0.545651\pi$
$384$		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	0.878249	−	0.478203i	$-0.158712\pi$
$389$	15.5223	+	10.2092i	0.787012	+	0.517626i	−0.0912370	+	0.995829i	$0.529082\pi$
$390$		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	−0.0897688	−	0.995963i	$-0.528613\pi$
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	0.571426	+	0.820654i	$0.306391\pi$
$398$	−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	−0.942314	−	0.334730i	$-0.891355\pi$
$401$	0.579017	−	1.93405i	0.0289148	−	0.0965820i	0.971229	+	0.238148i	$0.0765402\pi$
$402$		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	−0.951601	−	0.307335i	$-0.900563\pi$
$409$	0.249431	−	0.833158i	0.0123336	−	0.0411970i	0.963935	+	0.266138i	$0.0857478\pi$
$410$	−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	−0.521072	−	0.853512i	$-0.674468\pi$
$419$	−25.0738	−	2.93070i	−1.22493	−	0.143174i	−0.703860	+	0.710338i	$0.748542\pi$
$420$		0			0
$421$	−13.9967	−	9.20577i	−0.682157	−	0.448662i	0.160554	−	0.987027i	$-0.448672\pi$
$421$	−13.9967	−	9.20577i	−0.682157	−	0.448662i	−0.842712	+	0.538365i	$0.819042\pi$
$422$	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	−0.351623	−	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	$0.735531\pi$
$434$	−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	0.429785	−	0.902931i	$-0.358589\pi$
$439$	8.56156	+	2.02913i	0.408621	+	0.0968449i	−0.0211645	+	0.999776i	$0.506737\pi$
$440$	−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	0.909722	+	0.415218i	$0.136295\pi$
$443$	−0.885106	+	15.1967i	−0.0420527	+	0.722017i	−0.951775	+	0.306798i	$0.900742\pi$
$444$		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	0.989456	−	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
$452$	0.538549	+	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	−0.799810	−	0.600253i	$-0.795067\pi$
$457$	−30.7759	+	3.59718i	−1.43963	+	0.168269i	−0.639824	+	0.768522i	$0.720993\pi$
$458$	−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	−0.687474	−	0.726209i	$-0.741280\pi$
$461$	6.71020	−	15.5560i	0.312525	−	0.724514i	0.999999	+	0.00169503i	$0.000539544\pi$
$462$		0			0
$463$	−24.4901	−	25.9580i	−1.13815	−	1.20637i	−0.975573	−	0.219674i	$-0.929501\pi$
$463$	−24.4901	−	25.9580i	−1.13815	−	1.20637i	−0.162578	−	0.986696i	$-0.551981\pi$
$464$	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	0.895195	+	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
$470$	−3.11318	−	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	0.154247	−	0.988032i	$-0.450705\pi$
$479$	24.7671	−	26.2516i	1.13164	−	1.19947i	0.977392	−	0.211435i	$-0.0678138\pi$
$480$		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	−0.0686871	−	0.997638i	$-0.521881\pi$
$491$	18.1734	−	11.9528i	0.820155	−	0.539424i	0.888842	+	0.458214i	$0.151511\pi$
$492$		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	0.889707	−	0.456531i	$-0.150908\pi$
$499$	−1.18204	−	2.74029i	−0.0529156	−	0.122672i	−0.942623	+	0.333859i	$0.891649\pi$
$500$	−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	0.385227	−	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
$506$	−0.266041	−	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	0.349519	−	0.936929i	$-0.386345\pi$
$509$	−13.6753	−	14.4950i	−0.606147	−	0.642479i	−0.955667	+	0.294451i	$0.904863\pi$
$510$		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	−0.482833	−	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	$0.768086\pi$
$524$	−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	−0.728511	−	0.685034i	$-0.759787\pi$
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	0.957512	+	0.288392i	$0.0931206\pi$
$542$	−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	−0.999991	−	0.00412495i	$-0.998687\pi$
$547$	−3.90060	−	13.0289i	−0.166777	−	0.557076i	0.833214	−	0.552951i	$-0.186498\pi$
$548$	−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	0.249013	−	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
$560$	−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	−0.951791	−	0.306748i	$-0.900759\pi$
$563$	0.284251	−	0.949463i	0.0119797	−	0.0400151i	0.963770	+	0.266733i	$0.0859442\pi$
$564$		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	0.888663	−	0.458560i	$-0.151635\pi$
$569$	4.63945	+	6.23186i	0.194496	+	0.261253i	−0.694167	+	0.719814i	$0.744227\pi$
$570$		0			0
$571$	−6.13681	+	20.4984i	−0.256818	+	0.857830i	0.728198	+	0.685367i	$0.240358\pi$
$571$	−6.13681	+	20.4984i	−0.256818	+	0.857830i	−0.985016	+	0.172464i	$0.944827\pi$
$572$	−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	0.166995	−	0.985958i	$-0.446594\pi$
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	−0.505836	+	0.862630i	$0.668816\pi$
$578$	−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	0.997396	−	0.0721128i	$-0.0229741\pi$
$587$	3.01536	+	10.0720i	0.124457	+	0.415716i	−0.872939	+	0.487829i	$0.837789\pi$
$588$		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	0.420343	+	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
$596$	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	−0.905914	−	0.423461i	$-0.860815\pi$
$599$	−1.35310	−	23.2319i	−0.0552863	−	0.949229i	0.850628	−	0.525768i	$-0.176222\pi$
$600$		0			0
$601$	20.9118	+	4.95618i	0.853009	+	0.202167i	0.633786	−	0.773508i	$-0.281500\pi$
$601$	20.9118	+	4.95618i	0.853009	+	0.202167i	0.219222	+	0.975675i	$0.429648\pi$
$602$	−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	−0.739534	−	0.673119i	$-0.764954\pi$
$607$	2.89262	−	3.88547i	0.117408	−	0.157706i	0.856942	+	0.515413i	$0.172361\pi$
$608$	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	−0.895924	−	0.444207i	$-0.853485\pi$
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	0.993821	−	0.110994i	$-0.0354034\pi$
$614$	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	−0.606522	−	0.795067i	$-0.707436\pi$
$617$	−19.6655	+	4.66081i	−0.791704	+	0.187637i	−0.185182	+	0.982704i	$0.559288\pi$
$618$		0			0
$619$	28.6674	−	3.35073i	1.15224	−	0.134677i	0.481552	−	0.876418i	$-0.340073\pi$
$619$	28.6674	−	3.35073i	1.15224	−	0.134677i	0.670687	+	0.741740i	$0.265999\pi$
$620$	−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	−0.451558	+	0.892242i	$0.649132\pi$
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.957099	+	0.289762i	$0.906424\pi$
$632$	−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	−0.970766	−	0.240029i	$-0.922843\pi$
$641$	−17.0820	+	18.1058i	−0.674698	+	0.715138i	0.296068	+	0.955167i	$0.404325\pi$
$642$		0			0
$643$	−1.84993	+	1.21672i	−0.0729540	+	0.0479826i	−0.585462	−	0.810700i	$-0.699087\pi$
$643$	−1.84993	+	1.21672i	−0.0729540	+	0.0479826i	0.512508	+	0.858682i	$0.328716\pi$
$644$	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	−0.546035	−	0.837763i	$-0.683863\pi$
$653$	0.177323	−	0.116627i	0.00693920	−	0.00456398i	0.552974	+	0.833199i	$0.313493\pi$
$654$		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	0.0899295	−	0.995948i	$-0.471336\pi$
$659$	24.1950	−	12.1512i	0.942505	−	0.473344i	0.852575	+	0.522604i	$0.175040\pi$
$660$		0			0
$661$	14.1708	+	32.8515i	0.551179	+	1.27778i	0.935091	+	0.354407i	$0.115317\pi$
$661$	14.1708	+	32.8515i	0.551179	+	1.27778i	−0.383912	+	0.923370i	$0.625423\pi$
$662$	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	0.548711	+	0.836012i	$0.315119\pi$
$673$	−11.3090	+	26.2172i	−0.435930	+	1.01060i	−0.984642	+	0.174588i	$0.944141\pi$
$674$	−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	0.169700	−	0.985496i	$-0.445720\pi$
$677$	14.6253	−	1.70945i	0.562097	−	0.0656997i	0.392397	+	0.919796i	$0.371646\pi$
$678$		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	−0.995931	−	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
$686$	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	−1.00000		0.000541509i	$-0.999828\pi$
$691$	−0.176090	+	3.02335i	−0.00669878	+	0.115014i	0.993301	+	0.115555i	$0.0368647\pi$
$692$	−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	0.908335	+	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
$704$	−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	0.936642	+	0.350289i	$0.113917\pi$
$709$	9.22829	+	30.8246i	0.346576	+	1.15764i	−0.590066	+	0.807355i	$0.700898\pi$
$710$	−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	0.513831	−	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
$722$	−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	0.930320	−	0.366749i	$-0.119529\pi$
$727$	8.41672	+	11.3056i	0.312159	+	0.419302i	−0.618161	+	0.786052i	$0.712122\pi$
$728$	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	−0.833698	−	0.552221i	$-0.813780\pi$
$733$	4.50233	−	15.0388i	0.166297	−	0.555471i	0.999995	−	0.00324994i	$-0.00103449\pi$
$734$	−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	0.278345	−	0.960481i	$-0.410214\pi$
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	−0.404161	+	0.914688i	$0.632436\pi$
$740$	−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	0.529141	−	0.848534i	$-0.322514\pi$
$743$	23.1239	+	2.70280i	0.848334	+	0.0991560i	0.319193	+	0.947690i	$0.396588\pi$
$744$		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	0.572906	−	0.819621i	$-0.305816\pi$
$751$	7.05894	+	3.54513i	0.257584	+	0.129364i	−0.315322	+	0.948985i	$0.602112\pi$
$752$	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	0.824909	−	0.565265i	$-0.191226\pi$
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	−0.901989	+	0.431760i	$0.857893\pi$
$758$	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	0.713354	+	0.700803i	$0.247175\pi$
$761$	2.37743	+	40.8189i	0.0861818	+	1.47968i	−0.627173	+	0.778880i	$0.715788\pi$
$762$		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	−0.295889	−	0.955222i	$-0.595616\pi$
$769$	19.5244	−	26.2258i	0.704066	−	0.945725i	0.999955	+	0.00949722i	$0.00302310\pi$
$770$	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	0.825757	+	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
$776$	−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	0.698872	−	0.715247i	$-0.253686\pi$
$787$	−1.56542	−	1.65925i	−0.0558011	−	0.0591457i	−0.754673	+	0.656101i	$0.772204\pi$
$788$	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	−0.970491	−	0.241136i	$-0.922480\pi$
$797$	−13.5480	−	31.4079i	−0.479896	−	1.11252i	0.490596	−	0.871387i	$-0.336779\pi$
$798$		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	−0.999994	−	0.00347568i	$-0.998894\pi$
$821$	−45.6834	+	22.9431i	−1.59436	+	0.800718i	−0.594367	+	0.804194i	$0.702597\pi$
$822$		0			0
$823$	1.30609	+	3.02787i	0.0455276	+	0.105545i	0.939462	−	0.342653i	$-0.111325\pi$
$823$	1.30609	+	3.02787i	0.0455276	+	0.105545i	−0.893935	+	0.448197i	$0.852066\pi$
$824$	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	−0.874431	−	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	$0.648453\pi$
$830$	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	−0.00723124	−	0.999974i	$-0.502302\pi$
$839$	6.26646	−	0.732444i	0.216342	−	0.0252868i	0.223574	+	0.974687i	$0.428228\pi$
$840$		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	0.930998	+	0.365023i	$0.118939\pi$
$853$	−1.05380	+	18.0931i	−0.0360816	+	0.619496i	−0.967080	+	0.254473i	$0.918098\pi$
$854$	−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	0.752904	−	0.658130i	$-0.228652\pi$
$857$	33.0907	+	7.84263i	1.13036	+	0.267899i	0.377452	+	0.926029i	$0.376800\pi$
$858$		0			0
$859$	−2.76746	−	47.5154i	−0.0944244	−	1.62120i	−0.629915	−	0.776664i	$-0.716910\pi$
$859$	−2.76746	−	47.5154i	−0.0944244	−	1.62120i	0.535491	−	0.844541i	$-0.320127\pi$
$860$	−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	−0.811553	−	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
$866$	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	0.353550	−	0.935416i	$-0.384974\pi$
$877$	14.2696	+	1.66787i	0.481848	+	0.0563200i	0.128298	+	0.991736i	$0.459048\pi$
$878$	−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	0.331082	−	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	$0.529267\pi$
$884$	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	−0.483003	−	0.875619i	$-0.660454\pi$
$887$	11.9637	−	39.9614i	0.401700	−	1.34177i	0.884704	−	0.466154i	$-0.154361\pi$
$888$		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	0.963938	−	0.266127i	$-0.0857442\pi$
$907$	33.1694	+	21.8159i	1.10137	+	0.724384i	0.137434	+	0.990511i	$0.456115\pi$
$908$	−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	0.913051	+	0.407846i	$0.133720\pi$
$911$	11.2981	+	37.7383i	0.374323	+	1.25033i	−0.538727	+	0.842480i	$0.681095\pi$
$912$		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	0.967069	−	0.254513i	$-0.0819150\pi$
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	−0.703949	+	0.710250i	$0.748582\pi$
$920$	−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	0.885802	+	0.464064i	$0.153609\pi$
$929$	−1.45951	+	25.0588i	−0.0478850	+	0.822154i	−0.933687	+	0.358090i	$0.883428\pi$
$930$		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	0.649140	+	0.760669i	$0.275129\pi$
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	−0.870156	+	0.492776i	$0.835982\pi$
$938$	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	−0.718790	−	0.695227i	$-0.755304\pi$
$941$	−32.1821	+	7.62730i	−1.04911	+	0.248643i	−0.330317	+	0.943870i	$0.607156\pi$
$942$		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	−0.985696	−	0.168535i	$-0.946096\pi$
$947$	−5.74484	+	13.3180i	−0.186682	+	0.432778i	0.799013	+	0.601313i	$0.205356\pi$
$948$		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	0.712165	−	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
$956$	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	0.240975	−	0.970531i	$-0.422533\pi$
$967$	38.1735	−	25.1071i	1.22758	−	0.807391i	0.986603	+	0.163140i	$0.0521623\pi$
$968$	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	−0.246876	−	0.969047i	$-0.579404\pi$
$977$	17.0393	−	11.2069i	0.545137	−	0.358542i	0.792012	+	0.610505i	$0.209034\pi$
$978$		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	−0.933083	−	0.359662i	$-0.882892\pi$
$983$	−37.6795	+	18.9233i	−1.20179	+	0.603561i	−0.268705	+	0.963222i	$0.586596\pi$
$984$		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	0.623632	−	0.781718i	$-0.285656\pi$
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	−0.661550	+	0.749901i	$0.730101\pi$
$992$	−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	0.185587	+	0.982628i	$0.440581\pi$
$997$	−20.7294	+	48.0562i	−0.656508	+	1.52196i	−0.842095	+	0.539329i	$0.818678\pi$
$998$	−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.100.3		144
3.2	odd	2		81.2.g.a.7.6	✓	144
9.2	odd	6		729.2.g.c.55.6		144
9.4	even	3		729.2.g.a.298.6		144
9.5	odd	6		729.2.g.d.298.3		144
9.7	even	3		729.2.g.b.55.3		144
81.4	even	27		729.2.g.b.676.3		144
81.23	odd	54		81.2.g.a.58.6	yes	144
81.25	even	27		6561.2.a.d.1.25		72
81.31	even	27		729.2.g.a.433.6		144
81.50	odd	54		729.2.g.d.433.3		144
81.56	odd	54		6561.2.a.c.1.48		72
81.58	even	27	inner	243.2.g.a.226.3		144
81.77	odd	54		729.2.g.c.676.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.6	✓	144	3.2	odd	2
81.2.g.a.58.6	yes	144	81.23	odd	54
243.2.g.a.100.3		144	1.1	even	1	trivial
243.2.g.a.226.3		144	81.58	even	27	inner
729.2.g.a.298.6		144	9.4	even	3
729.2.g.a.433.6		144	81.31	even	27
729.2.g.b.55.3		144	9.7	even	3
729.2.g.b.676.3		144	81.4	even	27
729.2.g.c.55.6		144	9.2	odd	6
729.2.g.c.676.6		144	81.77	odd	54
729.2.g.d.298.3		144	9.5	odd	6
729.2.g.d.433.3		144	81.50	odd	54
6561.2.a.c.1.48		72	81.56	odd	54
6561.2.a.d.1.25		72	81.25	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

Modular forms

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