LMFDB - Embedded newform 243.2.g.a.73.1

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			73.1
Character	$\chi$	$=$	243.73
Dual form			243.2.g.a.10.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.94437 + 0.976500i) q^{2} +(1.63271 - 2.19311i) q^{4} +(0.185416 - 0.619334i) q^{5} +(-0.724564 + 1.67973i) q^{7} +(-0.277373 + 1.57306i) q^{8} +(0.244261 + 1.38527i) q^{10} +(1.17723 + 0.279008i) q^{11} +(4.45604 - 2.93078i) q^{13} +(-0.231433 - 3.97355i) q^{14} +(0.571538 + 1.90907i) q^{16} +(6.43434 + 2.34191i) q^{17} +(-5.97823 + 2.17590i) q^{19} +(-1.05554 - 1.41783i) q^{20} +(-2.56142 + 0.607068i) q^{22} +(1.23445 + 2.86177i) q^{23} +(3.82824 + 2.51788i) q^{25} +(-5.80229 + 10.0499i) q^{26} +(2.50083 + 4.33156i) q^{28} +(-0.342261 + 5.87639i) q^{29} +(2.75457 + 0.321963i) q^{31} +(-5.16779 - 5.47754i) q^{32} +(-14.7976 + 1.72959i) q^{34} +(0.905967 + 0.760197i) q^{35} +(-1.09453 + 0.918418i) q^{37} +(9.49913 - 10.0685i) q^{38} +(0.922821 + 0.463458i) q^{40} +(-0.996758 - 0.500591i) q^{41} +(6.61155 - 7.00783i) q^{43} +(2.53397 - 2.12625i) q^{44} +(-5.19473 - 4.35890i) q^{46} +(6.06108 - 0.708439i) q^{47} +(2.50720 + 2.65747i) q^{49} +(-9.90223 - 1.15740i) q^{50} +(0.847890 - 14.5577i) q^{52} +(-4.26135 - 7.38088i) q^{53} +(0.391077 - 0.677365i) q^{55} +(-2.44134 - 1.60569i) q^{56} +(-5.07281 - 11.7601i) q^{58} +(-2.03183 + 0.481552i) q^{59} +(-2.14382 - 2.87965i) q^{61} +(-5.67029 + 2.06382i) q^{62} +(11.6517 + 4.24088i) q^{64} +(-0.988911 - 3.30319i) q^{65} +(-0.0709235 - 1.21771i) q^{67} +(15.6415 - 10.2876i) q^{68} +(-2.50387 - 0.593428i) q^{70} +(-1.41528 - 8.02646i) q^{71} +(1.11524 - 6.32482i) q^{73} +(1.23133 - 2.85455i) q^{74} +(-4.98873 + 16.6635i) q^{76} +(-1.32164 + 1.77527i) q^{77} +(-12.7417 + 6.39915i) q^{79} +1.28832 q^{80} +2.42689 q^{82} +(-6.00472 + 3.01569i) q^{83} +(2.64346 - 3.55078i) q^{85} +(-6.01216 + 20.0820i) q^{86} +(-0.765429 + 1.77446i) q^{88} +(2.70557 - 15.3441i) q^{89} +(1.69423 + 9.60848i) q^{91} +(8.29166 + 1.96516i) q^{92} +(-11.0932 + 7.29611i) q^{94} +(0.239145 + 4.10597i) q^{95} +(1.06957 + 3.57262i) q^{97} +(-7.46994 - 2.71884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

Coefficient data

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

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

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

$2$	−1.94437	+	0.976500i	−1.37488	+	0.690490i	−0.974191	−	0.225725i	$-0.927525\pi$
$2$	−1.94437	+	0.976500i	−1.37488	+	0.690490i	−0.400687	+	0.916215i	$0.631229\pi$
$3$		0			0
$3$		0			0
$4$	1.63271	−	2.19311i	0.816355	−	1.09656i
$5$	0.185416	−	0.619334i	0.0829208	−	0.276975i	−0.906466	−	0.422278i	$-0.861231\pi$
$5$	0.185416	−	0.619334i	0.0829208	−	0.276975i	0.989387	+	0.145303i	$0.0464158\pi$
$6$		0			0
$7$	−0.724564	+	1.67973i	−0.273860	+	0.634878i	−0.998529	−	0.0542188i	$-0.982733\pi$
$7$	−0.724564	+	1.67973i	−0.273860	+	0.634878i	0.724670	+	0.689097i	$0.241992\pi$
$8$	−0.277373	+	1.57306i	−0.0980662	+	0.556161i
$9$		0			0
$10$	0.244261	+	1.38527i	0.0772422	+	0.438062i
$11$	1.17723	+	0.279008i	0.354948	+	0.0841242i	0.404222	−	0.914661i	$-0.367542\pi$
$11$	1.17723	+	0.279008i	0.354948	+	0.0841242i	−0.0492736	+	0.998785i	$0.515691\pi$
$12$		0			0
$13$	4.45604	−	2.93078i	1.23588	−	0.812853i	0.248107	−	0.968733i	$-0.420191\pi$
$13$	4.45604	−	2.93078i	1.23588	−	0.812853i	0.987776	+	0.155879i	$0.0498211\pi$
$14$	−0.231433	−	3.97355i	−0.0618531	−	1.06198i
$15$		0			0
$16$	0.571538	+	1.90907i	0.142885	+	0.477268i
$17$	6.43434	+	2.34191i	1.56056	+	0.567996i	0.970864	−	0.239631i	$-0.0770266\pi$
$17$	6.43434	+	2.34191i	1.56056	+	0.567996i	0.589693	+	0.807628i	$0.299249\pi$
$18$		0			0
$19$	−5.97823	+	2.17590i	−1.37150	+	0.499185i	−0.919590	−	0.392879i	$-0.871479\pi$
$19$	−5.97823	+	2.17590i	−1.37150	+	0.499185i	−0.451909	+	0.892064i	$0.649257\pi$
$20$	−1.05554	−	1.41783i	−0.236025	−	0.317037i
$21$		0			0
$22$	−2.56142	+	0.607068i	−0.546097	+	0.129427i
$23$	1.23445	+	2.86177i	0.257400	+	0.596719i	0.997090	−	0.0762275i	$-0.0242875\pi$
$23$	1.23445	+	2.86177i	0.257400	+	0.596719i	−0.739691	+	0.672947i	$0.765028\pi$
$24$		0			0
$25$	3.82824	+	2.51788i	0.765649	+	0.503575i
$26$	−5.80229	+	10.0499i	−1.13792	+	1.97094i
$27$		0			0
$28$	2.50083	+	4.33156i	0.472612	+	0.818588i
$29$	−0.342261	+	5.87639i	−0.0635562	+	1.09122i	0.804242	+	0.594301i	$0.202571\pi$
$29$	−0.342261	+	5.87639i	−0.0635562	+	1.09122i	−0.867799	+	0.496916i	$0.834466\pi$
$30$		0			0
$31$	2.75457	+	0.321963i	0.494735	+	0.0578262i	0.359802	−	0.933029i	$-0.382844\pi$
$31$	2.75457	+	0.321963i	0.494735	+	0.0578262i	0.134932	+	0.990855i	$0.456918\pi$
$32$	−5.16779	−	5.47754i	−0.913546	−	0.968302i
$33$		0			0
$34$	−14.7976	+	1.72959i	−2.53777	+	0.296623i
$35$	0.905967	+	0.760197i	0.153136	+	0.128497i
$36$		0			0
$37$	−1.09453	+	0.918418i	−0.179939	+	0.150987i	−0.728309	−	0.685249i	$-0.759693\pi$
$37$	−1.09453	+	0.918418i	−0.179939	+	0.150987i	0.548369	+	0.836236i	$0.315249\pi$
$38$	9.49913	−	10.0685i	1.54096	−	1.63332i
$39$		0			0
$40$	0.922821	+	0.463458i	0.145911	+	0.0732791i
$41$	−0.996758	−	0.500591i	−0.155667	−	0.0781791i	0.369260	−	0.929326i	$-0.379611\pi$
$41$	−0.996758	−	0.500591i	−0.155667	−	0.0781791i	−0.524927	+	0.851147i	$0.675908\pi$
$42$		0			0
$43$	6.61155	−	7.00783i	1.00825	−	1.06868i	0.0106171	−	0.999944i	$-0.496620\pi$
$43$	6.61155	−	7.00783i	1.00825	−	1.06868i	0.997635	−	0.0687407i	$-0.0218981\pi$
$44$	2.53397	−	2.12625i	0.382010	−	0.320545i
$45$		0			0
$46$	−5.19473	−	4.35890i	−0.765922	−	0.642685i
$47$	6.06108	−	0.708439i	0.884099	−	0.103336i	0.338088	−	0.941114i	$-0.390220\pi$
$47$	6.06108	−	0.708439i	0.884099	−	0.103336i	0.546011	+	0.837778i	$0.316146\pi$
$48$		0			0
$49$	2.50720	+	2.65747i	0.358171	+	0.379639i
$50$	−9.90223	−	1.15740i	−1.40039	−	0.163682i
$51$		0			0
$52$	0.847890	−	14.5577i	0.117581	−	2.01879i
$53$	−4.26135	−	7.38088i	−0.585342	−	1.01384i	−0.994833	−	0.101528i	$-0.967627\pi$
$53$	−4.26135	−	7.38088i	−0.585342	−	1.01384i	0.409491	−	0.912314i	$-0.365706\pi$
$54$		0			0
$55$	0.391077	−	0.677365i	0.0527328	−	0.0913359i
$56$	−2.44134	−	1.60569i	−0.326238	−	0.214570i
$57$		0			0
$58$	−5.07281	−	11.7601i	−0.666093	−	1.54418i
$59$	−2.03183	+	0.481552i	−0.264521	+	0.0626927i	−0.360736	−	0.932668i	$-0.617475\pi$
$59$	−2.03183	+	0.481552i	−0.264521	+	0.0626927i	0.0962148	+	0.995361i	$0.469326\pi$
$60$		0			0
$61$	−2.14382	−	2.87965i	−0.274488	−	0.368702i	0.643407	−	0.765524i	$-0.277520\pi$
$61$	−2.14382	−	2.87965i	−0.274488	−	0.368702i	−0.917895	+	0.396822i	$0.870113\pi$
$62$	−5.67029	+	2.06382i	−0.720128	+	0.262105i
$63$		0			0
$64$	11.6517	+	4.24088i	1.45646	+	0.530110i
$65$	−0.988911	−	3.30319i	−0.122659	−	0.409711i
$66$		0			0
$67$	−0.0709235	−	1.21771i	−0.00866469	−	0.148767i	−0.999866	−	0.0164003i	$-0.994779\pi$
$67$	−0.0709235	−	1.21771i	−0.00866469	−	0.148767i	0.991201	−	0.132367i	$-0.0422576\pi$
$68$	15.6415	−	10.2876i	1.89681	−	1.24755i
$69$		0			0
$70$	−2.50387	−	0.593428i	−0.299270	−	0.0709282i
$71$	−1.41528	−	8.02646i	−0.167963	−	0.952565i	−0.945957	−	0.324293i	$-0.894874\pi$
$71$	−1.41528	−	8.02646i	−0.167963	−	0.952565i	0.777994	−	0.628272i	$-0.216237\pi$
$72$		0			0
$73$	1.11524	−	6.32482i	0.130529	−	0.740264i	−0.847341	−	0.531049i	$-0.821798\pi$
$73$	1.11524	−	6.32482i	0.130529	−	0.740264i	0.977870	−	0.209215i	$-0.0670909\pi$
$74$	1.23133	−	2.85455i	0.143140	−	0.331835i
$75$		0			0
$76$	−4.98873	+	16.6635i	−0.572247	+	1.91144i
$77$	−1.32164	+	1.77527i	−0.150614	+	0.202310i
$78$		0			0
$79$	−12.7417	+	6.39915i	−1.43356	+	0.719960i	−0.984800	−	0.173693i	$-0.944430\pi$
$79$	−12.7417	+	6.39915i	−1.43356	+	0.719960i	−0.448759	+	0.893653i	$0.648134\pi$
$80$	1.28832			0.144039
$81$		0			0
$82$	2.42689			0.268006
$83$	−6.00472	+	3.01569i	−0.659104	+	0.331015i	−0.746719	−	0.665140i	$-0.768372\pi$
$83$	−6.00472	+	3.01569i	−0.659104	+	0.331015i	0.0876146	+	0.996154i	$0.472076\pi$
$84$		0			0
$85$	2.64346	−	3.55078i	0.286723	−	0.385136i
$86$	−6.01216	+	20.0820i	−0.648308	+	2.16550i
$87$		0			0
$88$	−0.765429	+	1.77446i	−0.0815950	+	0.189158i
$89$	2.70557	−	15.3441i	0.286790	−	1.62647i	−0.412030	−	0.911170i	$-0.635180\pi$
$89$	2.70557	−	15.3441i	0.286790	−	1.62647i	0.698820	−	0.715297i	$-0.253709\pi$
$90$		0			0
$91$	1.69423	+	9.60848i	0.177604	+	1.00724i
$92$	8.29166	+	1.96516i	0.864465	+	0.204882i
$93$		0			0
$94$	−11.0932	+	7.29611i	−1.14418	+	0.752536i
$95$	0.239145	+	4.10597i	0.0245358	+	0.421263i
$96$		0			0
$97$	1.06957	+	3.57262i	0.108599	+	0.362745i	0.994963	−	0.100244i	$-0.0319622\pi$
$97$	1.06957	+	3.57262i	0.108599	+	0.362745i	−0.886364	+	0.462989i	$0.846777\pi$
$98$	−7.46994	−	2.71884i	−0.754578	−	0.274644i
$99$		0			0
$100$	11.7724	−	4.28480i	1.17724	−	0.428480i
$101$	2.77713	+	3.73034i	0.276335	+	0.371182i	0.918525	−	0.395363i	$-0.129381\pi$
$101$	2.77713	+	3.73034i	0.276335	+	0.371182i	−0.642190	+	0.766546i	$0.721974\pi$
$102$		0			0
$103$	5.02919	−	1.19194i	0.495541	−	0.117445i	0.0247562	−	0.999694i	$-0.492119\pi$
$103$	5.02919	−	1.19194i	0.495541	−	0.117445i	0.470785	+	0.882248i	$0.343971\pi$
$104$	3.37432	+	7.82254i	0.330879	+	0.767063i
$105$		0			0
$106$	15.4931	+	10.1900i	1.50482	+	0.989737i
$107$	−6.49528	+	11.2502i	−0.627922	+	1.08759i	0.360046	+	0.932935i	$0.382761\pi$
$107$	−6.49528	+	11.2502i	−0.627922	+	1.08759i	−0.987968	+	0.154659i	$0.950572\pi$
$108$		0			0
$109$	−0.888686	−	1.53925i	−0.0851207	−	0.147433i	0.820322	−	0.571902i	$-0.193794\pi$
$109$	−0.888686	−	1.53925i	−0.0851207	−	0.147433i	−0.905443	+	0.424469i	$0.860461\pi$
$110$	−0.0989518	+	1.69894i	−0.00943468	+	0.161987i
$111$		0			0
$112$	−3.62084	−	0.423215i	−0.342137	−	0.0399901i
$113$	9.53060	+	10.1018i	0.896563	+	0.950302i	0.999012	−	0.0444366i	$-0.0141493\pi$
$113$	9.53060	+	10.1018i	0.896563	+	0.950302i	−0.102449	+	0.994738i	$0.532668\pi$
$114$		0			0
$115$	2.00128	−	0.233916i	0.186620	−	0.0218127i
$116$	12.3288	+	10.3451i	1.14470	+	0.960514i
$117$		0			0
$118$	3.48039	−	2.92040i	0.320396	−	0.268844i
$119$	−8.59586	+	9.11108i	−0.787982	+	0.835212i
$120$		0			0
$121$	−8.52194	−	4.27988i	−0.774722	−	0.389080i
$122$	6.98037	+	3.50567i	0.631973	+	0.317389i
$123$		0			0
$124$	5.20351	−	5.51539i	0.467289	−	0.495297i
$125$	4.74544	−	3.98190i	0.424445	−	0.356152i
$126$		0			0
$127$	−8.72949	−	7.32491i	−0.774617	−	0.649981i	0.167270	−	0.985911i	$-0.446505\pi$
$127$	−8.72949	−	7.32491i	−0.774617	−	0.649981i	−0.941887	+	0.335930i	$0.890949\pi$
$128$	−11.8372	+	1.38357i	−1.04627	+	0.122291i
$129$		0			0
$130$	5.14838	+	5.45696i	0.451543	+	0.478607i
$131$	−14.4822	−	1.69272i	−1.26531	−	0.147894i	−0.543160	−	0.839629i	$-0.682772\pi$
$131$	−14.4822	−	1.69272i	−1.26531	−	0.147894i	−0.722151	+	0.691735i	$0.756847\pi$
$132$		0			0
$133$	0.676693	−	11.6184i	0.0586768	−	1.00744i
$134$	1.32700	+	2.29842i	0.114635	+	0.198554i
$135$		0			0
$136$	−5.46868	+	9.47202i	−0.468935	+	0.812219i
$137$	−0.309806	−	0.203762i	−0.0264685	−	0.0174086i	0.536206	−	0.844087i	$-0.319857\pi$
$137$	−0.309806	−	0.203762i	−0.0264685	−	0.0174086i	−0.562674	+	0.826679i	$0.690227\pi$
$138$		0			0
$139$	5.93229	+	13.7526i	0.503170	+	1.16648i	0.960776	+	0.277325i	$0.0894479\pi$
$139$	5.93229	+	13.7526i	0.503170	+	1.16648i	−0.457606	+	0.889155i	$0.651293\pi$
$140$	3.14638	−	0.745705i	0.265917	−	0.0630236i
$141$		0			0
$142$	10.5897	+	14.2244i	0.888665	+	1.19368i
$143$	6.06349	−	2.20693i	0.507055	−	0.184553i
$144$		0			0
$145$	3.57599	+	1.30155i	0.296970	+	0.108088i
$146$	4.00775	+	13.3868i	0.331684	+	1.10790i
$147$		0			0
$148$	0.227145	+	3.89993i	0.0186712	+	0.320572i
$149$	−0.835701	+	0.549649i	−0.0684633	+	0.0450290i	−0.583279	−	0.812272i	$-0.698231\pi$
$149$	−0.835701	+	0.549649i	−0.0684633	+	0.0450290i	0.514816	+	0.857301i	$0.327860\pi$
$150$		0			0
$151$	0.0191032	+	0.00452754i	0.00155460	+	0.000368446i	0.231393	−	0.972860i	$-0.425672\pi$
$151$	0.0191032	+	0.00452754i	0.00155460	+	0.000368446i	−0.229838	+	0.973229i	$0.573820\pi$
$152$	−1.76462	−	10.0076i	−0.143129	−	0.811727i
$153$		0			0
$154$	0.836205	−	4.74235i	0.0673833	−	0.382150i
$155$	0.710144	−	1.64630i	0.0570402	−	0.132234i
$156$		0			0
$157$	2.23838	−	7.47669i	0.178642	−	0.596705i	−0.821025	−	0.570892i	$-0.806597\pi$
$157$	2.23838	−	7.47669i	0.178642	−	0.596705i	0.999667	−	0.0258129i	$-0.00821741\pi$
$158$	18.5259	−	24.8846i	1.47384	−	1.97972i
$159$		0			0
$160$	−4.35062	+	2.18497i	−0.343947	+	0.172737i
$161$	−5.70142			−0.449335
$162$		0			0
$163$	−15.3947			−1.20581			−0.602905	−	0.797813i	$-0.705990\pi$
$163$	−15.3947			−1.20581			−0.602905	+	0.797813i	$0.705990\pi$
$164$	−2.72527	+	1.36868i	−0.212808	+	0.106876i
$165$		0			0
$166$	8.73060	−	11.7272i	0.677626	−	0.910209i
$167$	1.04821	−	3.50128i	0.0811132	−	0.270937i	−0.907806	−	0.419390i	$-0.862244\pi$
$167$	1.04821	−	3.50128i	0.0811132	−	0.270937i	0.988919	+	0.148453i	$0.0474293\pi$
$168$		0			0
$169$	6.11777	−	14.1826i	0.470597	−	1.09097i
$170$	−1.67253	+	9.48537i	−0.128277	+	0.727494i
$171$		0			0
$172$	−4.57421	−	25.9416i	−0.348780	−	1.97803i
$173$	−12.9245	−	3.06317i	−0.982635	−	0.232889i	−0.292259	−	0.956339i	$-0.594407\pi$
$173$	−12.9245	−	3.06317i	−0.982635	−	0.232889i	−0.690376	+	0.723450i	$0.742555\pi$
$174$		0			0
$175$	−7.00316	+	4.60605i	−0.529389	+	0.348185i
$176$	0.140185	+	2.40688i	0.0105668	+	0.181425i
$177$		0			0
$178$	9.72284	+	32.4765i	0.728758	+	2.43422i
$179$	0.392738	+	0.142945i	0.0293546	+	0.0106842i	0.356656	−	0.934236i	$-0.383917\pi$
$179$	0.392738	+	0.142945i	0.0293546	+	0.0106842i	−0.327301	+	0.944920i	$0.606139\pi$
$180$		0			0
$181$	−19.5881	+	7.12947i	−1.45597	+	0.529929i	−0.944252	−	0.329225i	$-0.893213\pi$
$181$	−19.5881	+	7.12947i	−1.45597	+	0.529929i	−0.511717	+	0.859154i	$0.670990\pi$
$182$	−12.6769	−	17.0280i	−0.939675	−	1.26220i
$183$		0			0
$184$	−4.84413	+	1.14808i	−0.357114	+	0.0846376i
$185$	0.365864	+	0.848169i	0.0268989	+	0.0623586i
$186$		0			0
$187$	6.92128	+	4.55220i	0.506134	+	0.332890i
$188$	8.34230	−	14.4493i	0.608425	−	1.05382i
$189$		0			0
$190$	−4.47446	−	7.75000i	−0.324612	−	0.562244i
$191$	0.400574	−	6.87758i	0.0289845	−	0.497645i	−0.952310	−	0.305132i	$-0.901299\pi$
$191$	0.400574	−	6.87758i	0.0289845	−	0.497645i	0.981295	−	0.192512i	$-0.0616636\pi$
$192$		0			0
$193$	8.68725	+	1.01539i	0.625322	+	0.0730897i	0.422852	−	0.906199i	$-0.361029\pi$
$193$	8.68725	+	1.01539i	0.625322	+	0.0730897i	0.202470	+	0.979288i	$0.435103\pi$
$194$	−5.56831	−	5.90207i	−0.399782	−	0.423744i
$195$		0			0
$196$	9.92166	−	1.15968i	0.708690	−	0.0828339i
$197$	6.47094	+	5.42976i	0.461035	+	0.386855i	0.843512	−	0.537111i	$-0.180484\pi$
$197$	6.47094	+	5.42976i	0.461035	+	0.386855i	−0.382476	+	0.923965i	$0.624929\pi$
$198$		0			0
$199$	9.66790	−	8.11233i	0.685339	−	0.575068i	−0.232222	−	0.972663i	$-0.574599\pi$
$199$	9.66790	−	8.11233i	0.685339	−	0.575068i	0.917561	+	0.397595i	$0.130155\pi$
$200$	−5.02262	+	5.32367i	−0.355153	+	0.376440i
$201$		0			0
$202$	−9.04245	−	4.54129i	−0.636225	−	0.319524i
$203$	−9.62275	−	4.83272i	−0.675384	−	0.339191i
$204$		0			0
$205$	−0.494848	+	0.524508i	−0.0345617	+	0.0366333i
$206$	−8.61468	+	7.22858i	−0.600213	+	0.503639i
$207$		0			0
$208$	8.14187	+	6.83184i	0.564537	+	0.473703i
$209$	−7.64484	+	0.893553i	−0.528804	+	0.0618084i
$210$		0			0
$211$	3.89505	+	4.12851i	0.268146	+	0.284218i	0.847429	−	0.530908i	$-0.178149\pi$
$211$	3.89505	+	4.12851i	0.268146	+	0.284218i	−0.579283	+	0.815126i	$0.696668\pi$
$212$	−23.1446	−	2.70522i	−1.58958	−	0.185795i
$213$		0			0
$214$	1.64346	−	28.2171i	0.112345	−	1.92888i
$215$	−3.11430	−	5.39413i	−0.212393	−	0.367876i
$216$		0			0
$217$	−2.53667	+	4.39364i	−0.172200	+	0.298260i
$218$	3.23101	+	2.12507i	0.218832	+	0.143928i
$219$		0			0
$220$	−0.847021	−	1.96362i	−0.0571062	−	0.132387i
$221$	35.5353	−	8.42202i	2.39036	−	0.566527i
$222$		0			0
$223$	4.49831	+	6.04228i	0.301229	+	0.404621i	0.926805	−	0.375542i	$-0.122543\pi$
$223$	4.49831	+	6.04228i	0.301229	+	0.404621i	−0.625576	+	0.780163i	$0.715136\pi$
$224$	12.9452	−	4.71166i	0.864936	−	0.314811i
$225$		0			0
$226$	−28.3955	−	10.3351i	−1.88884	−	0.687481i
$227$	−3.91290	−	13.0700i	−0.259708	−	0.867485i	−0.984027	−	0.178020i	$-0.943031\pi$
$227$	−3.91290	−	13.0700i	−0.259708	−	0.867485i	0.724319	−	0.689465i	$-0.242154\pi$
$228$		0			0
$229$	−0.929998	−	15.9675i	−0.0614560	−	1.05516i	−0.878241	−	0.478218i	$-0.841283\pi$
$229$	−0.929998	−	15.9675i	−0.0614560	−	1.05516i	0.816785	−	0.576942i	$-0.195754\pi$
$230$	−3.66280	+	2.40906i	−0.241518	+	0.158849i
$231$		0			0
$232$	−9.14898	−	2.16835i	−0.600660	−	0.142359i
$233$	0.930605	+	5.27772i	0.0609660	+	0.345755i	0.999998	+	0.00192589i	$0.000613031\pi$
$233$	0.930605	+	5.27772i	0.0609660	+	0.345755i	−0.939032	+	0.343829i	$0.888276\pi$
$234$		0			0
$235$	0.685064	−	3.88519i	0.0446886	−	0.253442i
$236$	−2.26129	+	5.24226i	−0.147197	+	0.341242i
$237$		0			0
$238$	7.81658	−	26.1092i	0.506673	−	1.69241i
$239$	9.64028	−	12.9491i	0.623578	−	0.837611i	−0.372319	−	0.928105i	$-0.621437\pi$
$239$	9.64028	−	12.9491i	0.623578	−	0.837611i	0.995897	+	0.0904942i	$0.0288447\pi$
$240$		0			0
$241$	−20.9003	+	10.4965i	−1.34630	+	0.676139i	−0.968329	−	0.249677i	$-0.919676\pi$
$241$	−20.9003	+	10.4965i	−1.34630	+	0.676139i	−0.377975	+	0.925816i	$0.623379\pi$
$242$	20.7491			1.33380
$243$		0			0
$244$	−9.81564			−0.628382
$245$	2.11074	−	1.06005i	0.134850	−	0.0677243i
$246$		0			0
$247$	−20.2621	+	27.2168i	−1.28925	+	1.73176i
$248$	−1.27051	+	4.24380i	−0.0806774	+	0.269481i
$249$		0			0
$250$	−5.33858	+	12.3762i	−0.337641	+	0.782740i
$251$	−4.21745	+	23.9183i	−0.266203	+	1.50971i	0.499385	+	0.866380i	$0.333559\pi$
$251$	−4.21745	+	23.9183i	−0.266203	+	1.50971i	−0.765588	+	0.643331i	$0.777552\pi$
$252$		0			0
$253$	0.654768	+	3.71337i	0.0411649	+	0.233458i
$254$	24.1261	+	5.71800i	1.51381	+	0.358779i
$255$		0			0
$256$	0.945527	−	0.621883i	0.0590954	−	0.0388677i
$257$	0.560163	+	9.61763i	0.0349420	+	0.599931i	0.969647	+	0.244508i	$0.0786263\pi$
$257$	0.560163	+	9.61763i	0.0349420	+	0.599931i	−0.934705	+	0.355423i	$0.884337\pi$
$258$		0			0
$259$	−0.749638	−	2.50396i	−0.0465802	−	0.155589i
$260$	−8.85887	−	3.22437i	−0.549404	−	0.199967i
$261$		0			0
$262$	29.8116	−	10.8505i	1.84177	−	0.670349i
$263$	−3.96621	−	5.32754i	−0.244567	−	0.328510i	0.662842	−	0.748759i	$-0.269350\pi$
$263$	−3.96621	−	5.32754i	−0.244567	−	0.328510i	−0.907409	+	0.420249i	$0.861943\pi$
$264$		0			0
$265$	−5.36136	+	1.27067i	−0.329346	+	0.0780564i
$266$	10.0296	+	23.2512i	0.614954	+	1.42562i
$267$		0			0
$268$	−2.78637	−	1.83262i	−0.170205	−	0.111945i
$269$	14.6832	−	25.4321i	0.895251	−	1.55062i	0.0617568	−	0.998091i	$-0.480330\pi$
$269$	14.6832	−	25.4321i	0.895251	−	1.55062i	0.833494	−	0.552529i	$-0.186337\pi$
$270$		0			0
$271$	9.43957	+	16.3498i	0.573413	+	0.993180i	0.996212	+	0.0869568i	$0.0277142\pi$
$271$	9.43957	+	16.3498i	0.573413	+	0.993180i	−0.422799	+	0.906223i	$0.638952\pi$
$272$	−0.793397	+	13.6221i	−0.0481067	+	0.825961i
$273$		0			0
$274$	0.801351	+	0.0936645i	0.0484114	+	0.00565848i
$275$	3.80421	+	4.03223i	0.229403	+	0.243152i
$276$		0			0
$277$	−13.9438	+	1.62979i	−0.837801	+	0.0979249i	−0.524163	−	0.851618i	$-0.675622\pi$
$277$	−13.9438	+	1.62979i	−0.837801	+	0.0979249i	−0.313638	+	0.949543i	$0.601548\pi$
$278$	−24.9640	−	20.9473i	−1.49724	−	1.25633i
$279$		0			0
$280$	−1.44713	+	1.21428i	−0.0864824	+	0.0725673i
$281$	−15.1525	+	16.0607i	−0.903924	+	0.958103i	−0.999303	−	0.0373380i	$-0.988112\pi$
$281$	−15.1525	+	16.0607i	−0.903924	+	0.958103i	0.0953791	+	0.995441i	$0.469594\pi$
$282$		0			0
$283$	3.53563	+	1.77566i	0.210172	+	0.105552i	0.550771	−	0.834656i	$-0.314334\pi$
$283$	3.53563	+	1.77566i	0.210172	+	0.105552i	−0.340599	+	0.940208i	$0.610630\pi$
$284$	−19.9136	−	10.0010i	−1.18166	−	0.593451i
$285$		0			0
$286$	−9.63461	+	10.2121i	−0.569707	+	0.603854i
$287$	1.56307	−	1.31157i	0.0922652	−	0.0774197i
$288$		0			0
$289$	22.8934	+	19.2099i	1.34667	+	1.12999i
$290$	−8.22401	+	0.961249i	−0.482931	+	0.0564465i
$291$		0			0
$292$	−12.0502	−	12.7724i	−0.705183	−	0.747450i
$293$	7.92333	+	0.926104i	0.462886	+	0.0541036i	0.344340	−	0.938845i	$-0.388103\pi$
$293$	7.92333	+	0.926104i	0.462886	+	0.0541036i	0.118546	+	0.992949i	$0.462177\pi$
$294$		0			0
$295$	−0.0784927	+	1.34767i	−0.00457002	+	0.0784643i
$296$	−1.14114	−	1.97650i	−0.0663271	−	0.114882i
$297$		0			0
$298$	1.08818	−	1.88478i	0.0630366	−	0.109183i
$299$	13.8880	+	9.13425i	0.803161	+	0.528247i
$300$		0			0
$301$	6.98076	+	16.1832i	0.402365	+	0.932786i
$302$	−0.0415649	+	0.00985106i	−0.00239179	+	0.000566865i
$303$		0			0
$304$	−7.57072	−	10.1692i	−0.434211	−	0.583246i
$305$	−2.18097	+	0.793808i	−0.124882	+	0.0454533i
$306$		0			0
$307$	1.95823	+	0.712736i	0.111762	+	0.0406780i	0.397296	−	0.917691i	$-0.369949\pi$
$307$	1.95823	+	0.712736i	0.111762	+	0.0406780i	−0.285534	+	0.958369i	$0.592171\pi$
$308$	1.73550	+	5.79699i	0.0988895	+	0.330314i
$309$		0			0
$310$	0.226827	+	3.89447i	0.0128829	+	0.221191i
$311$	−12.5444	+	8.25056i	−0.711326	+	0.467846i	−0.852895	−	0.522082i	$-0.825155\pi$
$311$	−12.5444	+	8.25056i	−0.711326	+	0.467846i	0.141570	+	0.989928i	$0.454785\pi$
$312$		0			0
$313$	4.95368	+	1.17404i	0.279998	+	0.0663608i	0.368216	−	0.929740i	$-0.379969\pi$
$313$	4.95368	+	1.17404i	0.279998	+	0.0663608i	−0.0882173	+	0.996101i	$0.528117\pi$
$314$	2.94876	+	16.7232i	0.166408	+	0.943747i
$315$		0			0
$316$	−6.76955	+	38.3920i	−0.380817	+	2.15972i
$317$	10.9746	−	25.4420i	0.616396	−	1.42897i	−0.268547	−	0.963267i	$-0.586543\pi$
$317$	10.9746	−	25.4420i	0.616396	−	1.42897i	0.884943	−	0.465700i	$-0.154197\pi$
$318$		0			0
$319$	−2.04248	+	6.82236i	−0.114357	+	0.381979i
$320$	4.78694	−	6.42998i	0.267598	−	0.359447i
$321$		0			0
$322$	11.0857	−	5.56744i	0.617781	−	0.310261i
$323$	−43.5617			−2.42384
$324$		0			0
$325$	24.4382			1.35559
$326$	29.9331	−	15.0330i	1.65784	−	0.832599i
$327$		0			0
$328$	1.06393	−	1.42911i	0.0587459	−	0.0789094i
$329$	−3.20166	+	10.6943i	−0.176513	+	0.589595i
$330$		0			0
$331$	10.8007	−	25.0389i	0.593663	−	1.37626i	−0.311112	−	0.950373i	$-0.600701\pi$
$331$	10.8007	−	25.0389i	0.593663	−	1.37626i	0.904774	−	0.425891i	$-0.140039\pi$
$332$	−3.19024	+	18.0928i	−0.175087	+	0.992969i
$333$		0			0
$334$	1.38088	+	7.83136i	0.0755584	+	0.428513i
$335$	−0.767320	−	0.181858i	−0.0419232	−	0.00993597i
$336$		0			0
$337$	10.6262	−	6.98897i	0.578846	−	0.380713i	−0.226062	−	0.974113i	$-0.572585\pi$
$337$	10.6262	−	6.98897i	0.578846	−	0.380713i	0.804908	+	0.593400i	$0.202215\pi$
$338$	1.95408	+	33.5502i	0.106288	+	1.82489i
$339$		0			0
$340$	−3.47125	−	11.5948i	−0.188255	−	0.628815i
$341$	3.15292	+	1.14757i	0.170740	+	0.0621444i
$342$		0			0
$343$	−18.3136	+	6.66560i	−0.988840	+	0.359908i
$344$	9.18988	+	12.3441i	0.495485	+	0.665552i
$345$		0			0
$346$	28.1213	−	6.66487i	1.51181	−	0.358306i
$347$	−3.33227	−	7.72507i	−0.178886	−	0.414703i	0.805055	−	0.593200i	$-0.202136\pi$
$347$	−3.33227	−	7.72507i	−0.178886	−	0.414703i	−0.983940	+	0.178497i	$0.942877\pi$
$348$		0			0
$349$	−25.1843	−	16.5640i	−1.34808	−	0.886649i	−0.349352	−	0.936992i	$-0.613598\pi$
$349$	−25.1843	−	16.5640i	−1.34808	−	0.886649i	−0.998732	+	0.0503430i	$0.983969\pi$
$350$	9.11893	−	15.7944i	0.487427	−	0.844249i
$351$		0			0
$352$	−4.55540	−	7.89018i	−0.242803	−	0.420548i
$353$	1.35078	−	23.1921i	0.0718950	−	1.23439i	−0.748711	−	0.662896i	$-0.769327\pi$
$353$	1.35078	−	23.1921i	0.0718950	−	1.23439i	0.820606	−	0.571494i	$-0.193636\pi$
$354$		0			0
$355$	−5.23347	−	0.611705i	−0.277764	−	0.0324660i
$356$	−29.2338	−	30.9860i	−1.54939	−	1.64226i
$357$		0			0
$358$	−0.903214	+	0.105571i	−0.0477364	+	0.00557958i
$359$	−3.19290	−	2.67916i	−0.168515	−	0.141401i	0.554630	−	0.832097i	$-0.312860\pi$
$359$	−3.19290	−	2.67916i	−0.168515	−	0.141401i	−0.723145	+	0.690696i	$0.757304\pi$
$360$		0			0
$361$	16.4498	−	13.8030i	0.865780	−	0.726476i
$362$	31.1245	−	32.9901i	1.63587	−	1.73392i
$363$		0			0
$364$	23.8387	+	11.9722i	1.24948	+	0.627515i
$365$	−3.71039	−	1.86343i	−0.194211	−	0.0975364i
$366$		0			0
$367$	8.04346	−	8.52557i	0.419865	−	0.445031i	−0.482569	−	0.875858i	$-0.660296\pi$
$367$	8.04346	−	8.52557i	0.419865	−	0.445031i	0.902435	+	0.430826i	$0.141778\pi$
$368$	−4.75778	+	3.99225i	−0.248016	+	0.208110i
$369$		0			0
$370$	−1.53961	−	1.29189i	−0.0800407	−	0.0671621i
$371$	15.4855	−	1.81000i	0.803967	−	0.0939703i
$372$		0			0
$373$	−24.9598	−	26.4559i	−1.29237	−	1.36983i	−0.891057	−	0.453891i	$-0.850036\pi$
$373$	−24.9598	−	26.4559i	−1.29237	−	1.36983i	−0.401313	−	0.915941i	$-0.631446\pi$
$374$	−17.9028	−	2.09253i	−0.925729	−	0.108202i
$375$		0			0
$376$	−0.566763	+	9.73095i	−0.0292286	+	0.501835i
$377$	15.6973	+	27.1885i	0.808452	+	1.40028i
$378$		0			0
$379$	5.02516	−	8.70383i	0.258125	−	0.447086i	−0.707615	−	0.706599i	$-0.750229\pi$
$379$	5.02516	−	8.70383i	0.258125	−	0.447086i	0.965740	+	0.259513i	$0.0835620\pi$
$380$	9.39529	+	6.17938i	0.481968	+	0.316996i
$381$		0			0
$382$	5.93710	+	13.7637i	0.303768	+	0.704214i
$383$	0.294453	−	0.0697866i	0.0150458	−	0.00356593i	−0.223086	−	0.974799i	$-0.571613\pi$
$383$	0.294453	−	0.0697866i	0.0150458	−	0.00356593i	0.238132	+	0.971233i	$0.423465\pi$
$384$		0			0
$385$	0.854430	+	1.14770i	0.0435458	+	0.0584921i
$386$	−17.8828	+	6.50880i	−0.910209	+	0.331289i
$387$		0			0
$388$	9.58146	+	3.48737i	0.486425	+	0.177044i
$389$	2.15663	+	7.20364i	0.109345	+	0.365239i	0.995095	−	0.0989244i	$-0.0315402\pi$
$389$	2.15663	+	7.20364i	0.109345	+	0.365239i	−0.885750	+	0.464164i	$0.846355\pi$
$390$		0			0
$391$	1.24085	+	21.3045i	0.0627524	+	1.07742i
$392$	−4.87579	+	3.20686i	−0.246265	+	0.161971i
$393$		0			0
$394$	−17.8841	−	4.23860i	−0.900987	−	0.213538i
$395$	1.60068	+	9.07791i	0.0805390	+	0.456759i
$396$		0			0
$397$	2.95983	−	16.7860i	0.148549	−	0.842466i	−0.815899	−	0.578195i	$-0.803757\pi$
$397$	2.95983	−	16.7860i	0.148549	−	0.842466i	0.964448	−	0.264271i	$-0.0851314\pi$
$398$	−10.8763	+	25.2141i	−0.545180	+	1.26387i
$399$		0			0
$400$	−2.61881	+	8.74745i	−0.130941	+	0.437372i
$401$	−8.10789	+	10.8908i	−0.404889	+	0.543860i	−0.957067	−	0.289866i	$-0.906389\pi$
$401$	−8.10789	+	10.8908i	−0.404889	+	0.543860i	0.552179	+	0.833726i	$0.313797\pi$
$402$		0			0
$403$	13.2181	−	6.63836i	0.658438	−	0.330680i
$404$	12.7153			0.632609
$405$		0			0
$406$	23.4293			1.16278
$407$	−1.54476	+	0.775806i	−0.0765708	+	0.0384553i
$408$		0			0
$409$	−0.401500	+	0.539308i	−0.0198529	+	0.0266671i	−0.811939	−	0.583743i	$-0.801588\pi$
$409$	−0.401500	+	0.539308i	−0.0198529	+	0.0266671i	0.792086	+	0.610410i	$0.208995\pi$
$410$	0.449986	−	1.50306i	0.0222232	−	0.0742308i
$411$		0			0
$412$	5.59715	−	12.9757i	0.275752	−	0.639265i
$413$	0.663313	−	3.76184i	0.0326395	−	0.185108i
$414$		0			0
$415$	0.754343	+	4.27809i	0.0370292	+	0.210003i
$416$	−39.0814	−	9.26246i	−1.91612	−	0.454130i
$417$		0			0
$418$	13.9918	−	9.20258i	0.684363	−	0.450113i
$419$	−1.15627	−	19.8524i	−0.0564876	−	0.969855i	−0.900863	−	0.434103i	$-0.857065\pi$
$419$	−1.15627	−	19.8524i	−0.0564876	−	0.969855i	0.844376	−	0.535752i	$-0.179972\pi$
$420$		0			0
$421$	−3.60098	−	12.0281i	−0.175501	−	0.586214i	−0.999799	−	0.0200574i	$-0.993615\pi$
$421$	−3.60098	−	12.0281i	−0.175501	−	0.586214i	0.824298	−	0.566156i	$-0.191570\pi$
$422$	−11.6049	−	4.22384i	−0.564918	−	0.205613i
$423$		0			0
$424$	12.7926	−	4.65611i	0.621262	−	0.226121i
$425$	18.7356	+	25.1663i	0.908809	+	1.22074i
$426$		0			0
$427$	6.39038	−	1.51455i	0.309252	−	0.0732941i
$428$	14.0679	+	32.6131i	0.679999	+	1.57641i
$429$		0			0
$430$	11.3227	+	7.44707i	0.546030	+	0.359130i
$431$	−10.8013	+	18.7084i	−0.520281	+	0.901153i	0.479441	+	0.877574i	$0.340839\pi$
$431$	−10.8013	+	18.7084i	−0.520281	+	0.901153i	−0.999722	+	0.0235787i	$0.992494\pi$
$432$		0			0
$433$	−1.99970	−	3.46358i	−0.0960993	−	0.166449i	0.813968	−	0.580910i	$-0.197303\pi$
$433$	−1.99970	−	3.46358i	−0.0960993	−	0.166449i	−0.910067	+	0.414461i	$0.863970\pi$
$434$	0.641838	−	11.0199i	0.0308092	−	0.528973i
$435$		0			0
$436$	−4.82671	−	0.564162i	−0.231158	−	0.0270184i
$437$	−13.6067	−	14.4223i	−0.650897	−	0.689910i
$438$		0			0
$439$	31.0001	−	3.62339i	1.47955	−	0.172935i	0.662312	−	0.749228i	$-0.269575\pi$
$439$	31.0001	−	3.62339i	1.47955	−	0.172935i	0.817243	+	0.576293i	$0.195501\pi$
$440$	0.957063	+	0.803071i	0.0456262	+	0.0382849i
$441$		0			0
$442$	−60.8697	+	51.0758i	−2.89528	+	2.42943i
$443$	1.09948	−	1.16538i	0.0522379	−	0.0553689i	−0.700728	−	0.713429i	$-0.747141\pi$
$443$	1.09948	−	1.16538i	0.0522379	−	0.0553689i	0.752966	+	0.658060i	$0.228623\pi$
$444$		0			0
$445$	−9.00144	−	4.52070i	−0.426709	−	0.214302i
$446$	−14.6467	−	7.35584i	−0.693540	−	0.348309i
$447$		0			0
$448$	−15.5659	+	16.4989i	−0.735421	+	0.779501i
$449$	−8.04720	+	6.75241i	−0.379771	+	0.318666i	−0.812613	−	0.582804i	$-0.801955\pi$
$449$	−8.04720	+	6.75241i	−0.379771	+	0.318666i	0.432841	+	0.901470i	$0.357511\pi$
$450$		0			0
$451$	−1.03374	−	0.867414i	−0.0486771	−	0.0408449i
$452$	37.7152	−	4.40827i	1.77397	−	0.207348i
$453$		0			0
$454$	20.3710	+	21.5920i	0.956057	+	1.01336i
$455$	6.26500	+	0.732273i	0.293708	+	0.0343295i
$456$		0			0
$457$	−2.39213	+	41.0713i	−0.111899	+	1.92123i	0.215777	+	0.976443i	$0.430772\pi$
$457$	−2.39213	+	41.0713i	−0.111899	+	1.92123i	−0.327676	+	0.944790i	$0.606265\pi$
$458$	17.4005	+	30.1385i	0.813071	+	1.40828i
$459$		0			0
$460$	2.75450	−	4.77093i	0.128429	−	0.222446i
$461$	−28.6563	−	18.8476i	−1.33466	−	0.877819i	−0.336696	−	0.941613i	$-0.609309\pi$
$461$	−28.6563	−	18.8476i	−1.33466	−	0.877819i	−0.997963	+	0.0637944i	$0.979680\pi$
$462$		0			0
$463$	−13.2025	−	30.6068i	−0.613572	−	1.42242i	−0.887562	−	0.460688i	$-0.847603\pi$
$463$	−13.2025	−	30.6068i	−0.613572	−	1.42242i	0.273990	−	0.961732i	$-0.411656\pi$
$464$	−11.4140	+	2.70518i	−0.529884	+	0.125585i
$465$		0			0
$466$	−6.96314	−	9.35312i	−0.322561	−	0.433275i
$467$	9.76380	−	3.55373i	0.451815	−	0.164447i	−0.106082	−	0.994357i	$-0.533831\pi$
$467$	9.76380	−	3.55373i	0.451815	−	0.164447i	0.557897	+	0.829910i	$0.311608\pi$
$468$		0			0
$469$	2.09681	+	0.763177i	0.0968218	+	0.0352402i
$470$	2.46187	+	8.22322i	0.113558	+	0.379309i
$471$		0			0
$472$	−0.193936	−	3.32976i	−0.00892664	−	0.153265i
$473$	9.73855	−	6.40515i	0.447779	−	0.294509i
$474$		0			0
$475$	−28.3647	−	6.72257i	−1.30146	−	0.308453i
$476$	5.94706	+	33.7274i	0.272583	+	1.54589i
$477$		0			0
$478$	−6.09945	+	34.5917i	−0.278982	+	1.58219i
$479$	−8.03903	+	18.6366i	−0.367313	+	0.851526i	0.629883	+	0.776690i	$0.283103\pi$
$479$	−8.03903	+	18.6366i	−0.367313	+	0.851526i	−0.997196	+	0.0748364i	$0.976157\pi$
$480$		0			0
$481$	−2.18558	+	7.30034i	−0.0996538	+	0.332867i
$482$	30.3880	−	40.8182i	1.38414	−	1.85922i
$483$		0			0
$484$	−23.3001	+	11.7017i	−1.05910	+	0.531898i
$485$	2.41096			0.109476
$486$		0			0
$487$	−27.5716			−1.24939			−0.624694	−	0.780870i	$-0.714776\pi$
$487$	−27.5716			−1.24939			−0.624694	+	0.780870i	$0.714776\pi$
$488$	5.12451	−	2.57363i	0.231976	−	0.116503i
$489$		0			0
$490$	−3.06892	+	4.12227i	−0.138640	+	0.186225i
$491$	2.93035	−	9.78804i	0.132245	−	0.441728i	−0.866059	−	0.499941i	$-0.833355\pi$
$491$	2.93035	−	9.78804i	0.132245	−	0.441728i	0.998304	+	0.0582128i	$0.0185402\pi$
$492$		0			0
$493$	−15.9642	+	37.0091i	−0.718991	+	1.66681i
$494$	12.8199	−	72.7055i	0.576796	−	3.27117i
$495$		0			0
$496$	0.959690	+	5.44267i	0.0430914	+	0.244383i
$497$	14.5077	+	3.43840i	0.650761	+	0.154233i
$498$		0			0
$499$	7.30520	−	4.80470i	0.327026	−	0.215088i	−0.375370	−	0.926875i	$-0.622484\pi$
$499$	7.30520	−	4.80470i	0.327026	−	0.215088i	0.702395	+	0.711787i	$0.252114\pi$
$500$	−0.984811	−	16.9086i	−0.0440421	−	0.756174i
$501$		0			0
$502$	−15.1560	−	50.6244i	−0.676444	−	2.25948i
$503$	12.2947	+	4.47489i	0.548192	+	0.199526i	0.601243	−	0.799066i	$-0.294672\pi$
$503$	12.2947	+	4.47489i	0.548192	+	0.199526i	−0.0530509	+	0.998592i	$0.516895\pi$
$504$		0			0
$505$	2.82525	−	1.02831i	0.125722	−	0.0457591i
$506$	−4.89922	−	6.58080i	−0.217797	−	0.292552i
$507$		0			0
$508$	−30.3171	+	7.18528i	−1.34510	+	0.318795i
$509$	12.0492	+	27.9331i	0.534070	+	1.23811i	0.945187	+	0.326530i	$0.105880\pi$
$509$	12.0492	+	27.9331i	0.534070	+	1.23811i	−0.411117	+	0.911583i	$0.634861\pi$
$510$		0			0
$511$	9.81592	+	6.45603i	0.434231	+	0.285598i
$512$	10.6866	−	18.5097i	0.472284	−	0.818019i
$513$		0			0
$514$	−10.4808	−	18.1532i	−0.462287	−	0.800705i
$515$	0.194286	−	3.33575i	0.00856124	−	0.146991i
$516$		0			0
$517$	7.33294	+	0.857098i	0.322502	+	0.0376951i
$518$	3.90269	+	4.13661i	0.171475	+	0.181752i
$519$		0			0
$520$	5.47042	−	0.639401i	0.239894	−	0.0280396i
$521$	−8.25925	−	6.93034i	−0.361845	−	0.303624i	0.443681	−	0.896185i	$-0.353672\pi$
$521$	−8.25925	−	6.93034i	−0.361845	−	0.303624i	−0.805525	+	0.592561i	$0.798117\pi$
$522$		0			0
$523$	9.44644	−	7.92650i	0.413064	−	0.346602i	−0.412453	−	0.910979i	$-0.635328\pi$
$523$	9.44644	−	7.92650i	0.413064	−	0.346602i	0.825517	+	0.564377i	$0.190884\pi$
$524$	−27.3575	+	28.9972i	−1.19512	+	1.26675i
$525$		0			0
$526$	12.9141	+	6.48572i	0.563083	+	0.282791i
$527$	16.9698	+	8.52256i	0.739216	+	0.371248i
$528$		0			0
$529$	9.11771	−	9.66421i	0.396422	−	0.420183i
$530$	9.18367	−	7.70601i	0.398913	−	0.334728i
$531$		0			0
$532$	−24.3755	−	20.4535i	−1.05681	−	0.886772i
$533$	−5.90872	+	0.690630i	−0.255935	+	0.0299145i
$534$		0			0
$535$	5.76327	+	6.10871i	0.249168	+	0.264103i
$536$	1.93520	+	0.226193i	0.0835881	+	0.00977005i
$537$		0			0
$538$	−3.71520	+	63.7875i	−0.160174	+	2.75007i
$539$	2.21009	+	3.82798i	0.0951952	+	0.164883i
$540$		0			0
$541$	7.99279	−	13.8439i	0.343637	−	0.595196i	−0.641468	−	0.767149i	$-0.721674\pi$
$541$	7.99279	−	13.8439i	0.343637	−	0.595196i	0.985105	+	0.171953i	$0.0550078\pi$
$542$	−34.3196	−	22.5724i	−1.47415	−	0.969566i
$543$		0			0
$544$	−20.4234	−	47.3469i	−0.875648	−	2.02998i
$545$	−1.11809	+	0.264991i	−0.0478936	+	0.0113510i
$546$		0			0
$547$	0.738452	+	0.991913i	0.0315739	+	0.0424111i	0.817630	−	0.575744i	$-0.195288\pi$
$547$	0.738452	+	0.991913i	0.0315739	+	0.0424111i	−0.786056	+	0.618155i	$0.787880\pi$
$548$	−0.952696	+	0.346753i	−0.0406972	+	0.0148126i
$549$		0			0
$550$	−11.3343	−	4.12534i	−0.483295	−	0.175905i
$551$	−10.7403	−	35.8751i	−0.457552	−	1.52833i
$552$		0			0
$553$	−1.51662	−	26.0393i	−0.0644930	−	1.10730i
$554$	25.5204	−	16.7850i	1.08426	−	0.713128i
$555$		0			0
$556$	39.8467	+	9.44384i	1.68988	+	0.400508i
$557$	−2.28246	−	12.9445i	−0.0967109	−	0.548475i	−0.994210	−	0.107458i	$-0.965729\pi$
$557$	−2.28246	−	12.9445i	−0.0967109	−	0.548475i	0.897499	−	0.441017i	$-0.145382\pi$
$558$		0			0
$559$	8.92289	−	50.6042i	0.377398	−	2.14033i
$560$	−0.933474	+	2.16404i	−0.0394465	+	0.0914472i
$561$		0			0
$562$	13.7788	−	46.0245i	0.581224	−	1.94142i
$563$	−3.63605	+	4.88406i	−0.153241	+	0.205838i	−0.872114	−	0.489303i	$-0.837251\pi$
$563$	−3.63605	+	4.88406i	−0.153241	+	0.205838i	0.718873	+	0.695142i	$0.244658\pi$
$564$		0			0
$565$	8.02355	−	4.02958i	0.337553	−	0.169526i
$566$	−8.60852			−0.361843
$567$		0			0
$568$	13.0187			0.546251
$569$	−14.8144	+	7.44006i	−0.621051	+	0.311904i	−0.731358	−	0.681994i	$-0.761113\pi$
$569$	−14.8144	+	7.44006i	−0.621051	+	0.311904i	0.110307	+	0.993898i	$0.464817\pi$
$570$		0			0
$571$	20.8094	−	27.9518i	0.870844	−	1.16975i	−0.113508	−	0.993537i	$-0.536209\pi$
$571$	20.8094	−	27.9518i	0.870844	−	1.16975i	0.984353	−	0.176210i	$-0.0563838\pi$
$572$	5.05988	−	16.9012i	0.211564	−	0.706674i
$573$		0			0
$574$	−1.75844	+	4.07652i	−0.0733959	+	0.170151i
$575$	−2.47981	+	14.0637i	−0.103415	+	0.586497i
$576$		0			0
$577$	5.38675	+	30.5498i	0.224254	+	1.27180i	0.864107	+	0.503308i	$0.167884\pi$
$577$	5.38675	+	30.5498i	0.224254	+	1.27180i	−0.639854	+	0.768497i	$0.721005\pi$
$578$	−63.2718	−	14.9957i	−2.63176	−	0.623739i
$579$		0			0
$580$	8.69300	−	5.71747i	0.360957	−	0.237405i
$581$	−0.714726	−	12.2714i	−0.0296518	−	0.509102i
$582$		0			0
$583$	−2.95726	−	9.87794i	−0.122477	−	0.409103i
$584$	9.63999	+	3.50867i	0.398906	+	0.145190i
$585$		0			0
$586$	−16.3102	+	5.93644i	−0.673769	+	0.245232i
$587$	26.6000	+	35.7300i	1.09790	+	1.47474i	0.864687	+	0.502311i	$0.167517\pi$
$587$	26.6000	+	35.7300i	1.09790	+	1.47474i	0.233214	+	0.972425i	$0.425076\pi$
$588$		0			0
$589$	−17.1680	+	4.06889i	−0.707394	+	0.167655i
$590$	−1.16338	−	2.69702i	−0.0478956	−	0.111034i
$591$		0			0
$592$	−2.37889	−	1.56462i	−0.0977718	−	0.0643055i
$593$	−9.90549	+	17.1568i	−0.406770	+	0.704546i	−0.994526	−	0.104493i	$-0.966678\pi$
$593$	−9.90549	+	17.1568i	−0.406770	+	0.704546i	0.587756	+	0.809038i	$0.300011\pi$
$594$		0			0
$595$	4.04899	+	7.01306i	0.165992	+	0.287507i
$596$	−0.159016	+	2.73020i	−0.00651356	+	0.111833i
$597$		0			0
$598$	−35.9229	−	4.19879i	−1.46900	−	0.171701i
$599$	−19.1656	−	20.3143i	−0.783084	−	0.830020i	0.205818	−	0.978590i	$-0.434014\pi$
$599$	−19.1656	−	20.3143i	−0.783084	−	0.830020i	−0.988902	+	0.148570i	$0.952533\pi$
$600$		0			0
$601$	10.0762	−	1.17774i	0.411015	−	0.0480408i	0.0919270	−	0.995766i	$-0.470697\pi$
$601$	10.0762	−	1.17774i	0.411015	−	0.0480408i	0.319088	+	0.947725i	$0.396623\pi$
$602$	−29.3761	−	24.6495i	−1.19728	−	1.00464i
$603$		0			0
$604$	0.0411194	−	0.0345033i	0.00167313	−	0.00140392i
$605$	−4.23078	+	4.48437i	−0.172006	+	0.182315i
$606$		0			0
$607$	9.66590	+	4.85440i	0.392327	+	0.197034i	0.634016	−	0.773320i	$-0.281405\pi$
$607$	9.66590	+	4.85440i	0.392327	+	0.197034i	−0.241690	+	0.970354i	$0.577702\pi$
$608$	42.8128	+	21.5014i	1.73629	+	0.871997i
$609$		0			0
$610$	3.46546	−	3.67317i	0.140312	−	0.148722i
$611$	24.9321	−	20.9205i	1.00865	−	0.846355i
$612$		0			0
$613$	4.13859	+	3.47269i	0.167156	+	0.140261i	0.722528	−	0.691341i	$-0.242980\pi$
$613$	4.13859	+	3.47269i	0.167156	+	0.140261i	−0.555372	+	0.831602i	$0.687424\pi$
$614$	−4.50351	+	0.526385i	−0.181747	+	0.0212432i
$615$		0			0
$616$	−2.42601	−	2.57143i	−0.0977469	−	0.103606i
$617$	−24.8710	−	2.90700i	−1.00127	−	0.117031i	−0.400367	−	0.916355i	$-0.631117\pi$
$617$	−24.8710	−	2.90700i	−1.00127	−	0.117031i	−0.600901	+	0.799324i	$0.705191\pi$
$618$		0			0
$619$	−1.48183	+	25.4420i	−0.0595596	+	1.02260i	0.827654	+	0.561239i	$0.189675\pi$
$619$	−1.48183	+	25.4420i	−0.0595596	+	1.02260i	−0.887213	+	0.461360i	$0.847362\pi$
$620$	−2.45106	−	4.24535i	−0.0984368	−	0.170498i
$621$		0			0
$622$	16.3342	−	28.2917i	0.654943	−	1.13439i
$623$	23.8135	+	15.6624i	0.954068	+	0.627500i
$624$		0			0
$625$	7.48804	+	17.3592i	0.299521	+	0.694369i
$626$	−10.7782	+	2.55449i	−0.430785	+	0.102098i
$627$		0			0
$628$	−12.7426	−	17.1163i	−0.508485	−	0.683014i
$629$	−9.19342	+	3.34613i	−0.366566	+	0.133419i
$630$		0			0
$631$	−18.7709	−	6.83203i	−0.747256	−	0.271979i	−0.0598054	−	0.998210i	$-0.519048\pi$
$631$	−18.7709	−	6.83203i	−0.747256	−	0.271979i	−0.687451	+	0.726231i	$0.741270\pi$
$632$	−6.53203	−	21.8185i	−0.259830	−	0.867893i
$633$		0			0
$634$	3.50540	+	60.1854i	0.139217	+	2.39027i
$635$	−6.15516	+	4.04831i	−0.244260	+	0.160652i
$636$		0			0
$637$	18.9606	+	4.49376i	0.751248	+	0.178049i
$638$	−2.69069	−	15.2597i	−0.106526	−	0.604137i
$639$		0			0
$640$	−1.33792	+	7.58769i	−0.0528857	+	0.299930i
$641$	3.53682	−	8.19927i	0.139696	−	0.323852i	−0.833978	−	0.551798i	$-0.813942\pi$
$641$	3.53682	−	8.19927i	0.139696	−	0.323852i	0.973674	+	0.227947i	$0.0732011\pi$
$642$		0			0
$643$	−3.84314	+	12.8370i	−0.151559	+	0.506241i	−0.999724	−	0.0234904i	$-0.992522\pi$
$643$	−3.84314	+	12.8370i	−0.151559	+	0.506241i	0.848165	+	0.529731i	$0.177707\pi$
$644$	−9.30877	+	12.5039i	−0.366817	+	0.492721i
$645$		0			0
$646$	84.7001	−	42.5380i	3.33248	−	1.67363i
$647$	48.7223			1.91547			0.957736	−	0.287649i	$-0.0928736\pi$
$647$	48.7223			1.91547			0.957736	+	0.287649i	$0.0928736\pi$
$648$		0			0
$649$	−2.52628			−0.0991653
$650$	−47.5169	+	23.8639i	−1.86376	+	0.936018i
$651$		0			0
$652$	−25.1351	+	33.7624i	−0.984368	+	1.32224i
$653$	1.37807	−	4.60307i	0.0539280	−	0.180132i	−0.926782	−	0.375599i	$-0.877437\pi$
$653$	1.37807	−	4.60307i	0.0539280	−	0.180132i	0.980710	+	0.195467i	$0.0626222\pi$
$654$		0			0
$655$	−3.73359	+	8.65544i	−0.145883	+	0.338196i
$656$	0.385978	−	2.18899i	0.0150699	−	0.0854656i
$657$		0			0
$658$	−4.21775	−	23.9201i	−0.164425	−	0.932501i
$659$	24.6111	+	5.83293i	0.958712	+	0.227219i	0.680046	−	0.733169i	$-0.261960\pi$
$659$	24.6111	+	5.83293i	0.958712	+	0.227219i	0.278666	+	0.960388i	$0.410108\pi$
$660$		0			0
$661$	11.8107	−	7.76805i	0.459385	−	0.302142i	−0.298642	−	0.954365i	$-0.596534\pi$
$661$	11.8107	−	7.76805i	0.459385	−	0.302142i	0.758027	+	0.652223i	$0.226163\pi$
$662$	3.44987	+	59.2319i	0.134083	+	2.30211i
$663$		0			0
$664$	−3.07831	−	10.2823i	−0.119462	−	0.399029i
$665$	−7.07019	−	2.57334i	−0.274170	−	0.0997898i
$666$		0			0
$667$	−17.2393	+	6.27461i	−0.667510	+	0.242954i
$668$	−5.96725	−	8.01541i	−0.230880	−	0.310126i
$669$		0			0
$670$	1.66954	−	0.395688i	0.0644999	−	0.0152868i
$671$	−1.72032	−	3.98816i	−0.0664123	−	0.153961i
$672$		0			0
$673$	−2.22854	−	1.46573i	−0.0859039	−	0.0564999i	0.505830	−	0.862633i	$-0.331186\pi$
$673$	−2.22854	−	1.46573i	−0.0859039	−	0.0564999i	−0.591734	+	0.806133i	$0.701557\pi$
$674$	−13.8366	+	23.9656i	−0.532965	+	0.923122i
$675$		0			0
$676$	−21.1154	−	36.5730i	−0.812131	−	1.40665i
$677$	−0.858366	+	14.7376i	−0.0329897	+	0.566411i	0.940800	+	0.338962i	$0.110076\pi$
$677$	−0.858366	+	14.7376i	−0.0329897	+	0.566411i	−0.973790	+	0.227449i	$0.926961\pi$
$678$		0			0
$679$	−6.77601	−	0.792002i	−0.260040	−	0.0303943i
$680$	4.85237	+	5.14321i	0.186080	+	0.197233i
$681$		0			0
$682$	−7.25106	+	0.847527i	−0.277657	+	0.0324535i
$683$	16.0712	+	13.4854i	0.614948	+	0.516003i	0.896211	−	0.443628i	$-0.146309\pi$
$683$	16.0712	+	13.4854i	0.614948	+	0.516003i	−0.281263	+	0.959631i	$0.590753\pi$
$684$		0			0
$685$	−0.183640	+	0.154092i	−0.00701653	+	0.00588756i
$686$	29.0994	−	30.8436i	1.11102	−	1.17761i
$687$		0			0
$688$	17.1572	+	8.61667i	0.654112	+	0.328507i
$689$	−40.6205	−	20.4004i	−1.54752	−	0.777194i
$690$		0			0
$691$	−23.9044	+	25.3372i	−0.909366	+	0.963872i	−0.999486	−	0.0320589i	$-0.989794\pi$
$691$	−23.9044	+	25.3372i	−0.909366	+	0.963872i	0.0901196	+	0.995931i	$0.471275\pi$
$692$	−27.8199	+	23.3437i	−1.05755	+	0.887394i
$693$		0			0
$694$	14.0227	+	11.7664i	0.532294	+	0.446648i
$695$	9.61740	−	1.12411i	0.364809	−	0.0426400i
$696$		0			0
$697$	−5.24114	−	5.55529i	−0.198522	−	0.210421i
$698$	65.1423	+	7.61404i	2.46567	+	0.288196i
$699$		0			0
$700$	−1.33255	+	22.8790i	−0.0503657	+	0.864746i
$701$	−21.8053	−	37.7679i	−0.823576	−	1.42647i	−0.903003	−	0.429634i	$-0.858643\pi$
$701$	−21.8053	−	37.7679i	−0.823576	−	1.42647i	0.0794276	−	0.996841i	$-0.474691\pi$
$702$		0			0
$703$	4.54496	−	7.87209i	0.171416	−	0.296902i
$704$	12.5335	+	8.24341i	0.472374	+	0.310685i
$705$		0			0
$706$	20.0206	+	46.4130i	0.753487	+	1.74678i
$707$	−8.27816	+	1.96196i	−0.311332	+	0.0737871i
$708$		0			0
$709$	10.9085	+	14.6527i	0.409677	+	0.550292i	0.958295	−	0.285781i	$-0.0922530\pi$
$709$	10.9085	+	14.6527i	0.409677	+	0.550292i	−0.548617	+	0.836074i	$0.684846\pi$
$710$	10.7731	−	3.92111i	0.404309	−	0.147156i
$711$		0			0
$712$	23.3867	+	8.51206i	0.876453	+	0.319003i
$713$	2.47898	+	8.28037i	0.0928385	+	0.310102i
$714$		0			0
$715$	−0.242556	−	4.16453i	−0.00907109	−	0.155745i
$716$	0.954722	−	0.627930i	0.0356796	−	0.0234669i
$717$		0			0
$718$	8.82440	+	2.09142i	0.329324	+	0.0780511i
$719$	3.15002	+	17.8647i	0.117476	+	0.666240i	0.985494	+	0.169708i	$0.0542824\pi$
$719$	3.15002	+	17.8647i	0.117476	+	0.666240i	−0.868018	+	0.496532i	$0.834607\pi$
$720$		0			0
$721$	−1.64184	+	9.31131i	−0.0611451	+	0.346771i
$722$	−18.5059	+	42.9015i	−0.688718	+	1.59663i
$723$		0			0
$724$	−16.3459	+	54.5991i	−0.607491	+	2.02916i
$725$	−16.1063	+	21.6345i	−0.598172	+	0.803484i
$726$		0			0
$727$	18.0996	−	9.08994i	0.671276	−	0.337127i	−0.0803032	−	0.996770i	$-0.525589\pi$
$727$	18.0996	−	9.08994i	0.671276	−	0.337127i	0.751579	+	0.659643i	$0.229293\pi$
$728$	−15.5847			−0.577606
$729$		0			0
$730$	9.03402			0.334364
$731$	58.9526	−	29.6071i	2.18044	−	1.09506i
$732$		0			0
$733$	−1.05577	+	1.41814i	−0.0389957	+	0.0523803i	−0.821193	−	0.570650i	$-0.806691\pi$
$733$	−1.05577	+	1.41814i	−0.0389957	+	0.0523803i	0.782198	+	0.623030i	$0.214099\pi$
$734$	−7.31426	+	24.4313i	−0.269974	+	0.901776i
$735$		0			0
$736$	9.29608	−	21.5507i	0.342658	−	0.794371i
$737$	0.256258	−	1.45331i	0.00943939	−	0.0535334i
$738$		0			0
$739$	−1.58340	−	8.97988i	−0.0582461	−	0.330330i	0.941736	−	0.336354i	$-0.109194\pi$
$739$	−1.58340	−	8.97988i	−0.0582461	−	0.330330i	−0.999982	+	0.00602346i	$0.998083\pi$
$740$	2.45748	+	0.582433i	0.0903387	+	0.0214107i
$741$		0			0
$742$	−28.3421	+	18.6409i	−1.04047	+	0.684329i
$743$	−1.15833	−	19.8878i	−0.0424951	−	0.729613i	−0.950514	−	0.310683i	$-0.899442\pi$
$743$	−1.15833	−	19.8878i	−0.0424951	−	0.729613i	0.908018	−	0.418930i	$-0.137595\pi$
$744$		0			0
$745$	0.185464	+	0.619492i	0.00679487	+	0.0226964i
$746$	74.3653	+	27.0667i	2.72271	+	0.990984i
$747$		0			0
$748$	21.2839	−	7.74671i	0.778217	−	0.283248i
$749$	−14.1910	−	19.0618i	−0.518526	−	0.696502i
$750$		0			0
$751$	−37.5165	+	8.89157i	−1.36900	+	0.324458i	−0.848405	−	0.529348i	$-0.822437\pi$
$751$	−37.5165	+	8.89157i	−1.36900	+	0.324458i	−0.520591	+	0.853806i	$0.674289\pi$
$752$	4.81660	+	11.1661i	0.175643	+	0.407187i
$753$		0			0
$754$	−57.0709	−	37.5362i	−2.07840	−	1.36699i
$755$	0.00634611	−	0.0109918i	0.000230959	−	0.000400032i
$756$		0			0
$757$	25.4729	+	44.1204i	0.925829	+	1.60358i	0.790223	+	0.612820i	$0.209965\pi$
$757$	25.4729	+	44.1204i	0.925829	+	1.60358i	0.135606	+	0.990763i	$0.456702\pi$
$758$	−1.27148	+	21.8305i	−0.0461824	+	0.792921i
$759$		0			0
$760$	−6.52527	−	0.762694i	−0.236696	−	0.0276658i
$761$	26.7225	+	28.3242i	0.968690	+	1.02675i	0.999629	+	0.0272302i	$0.00866872\pi$
$761$	26.7225	+	28.3242i	0.968690	+	1.02675i	−0.0309391	+	0.999521i	$0.509850\pi$
$762$		0			0
$763$	3.22943	−	0.377466i	0.116913	−	0.0136652i
$764$	−14.4293	−	12.1076i	−0.522033	−	0.438038i
$765$		0			0
$766$	−0.504379	+	0.423224i	−0.0182239	+	0.0152917i
$767$	−7.64258	+	8.10067i	−0.275958	+	0.292498i
$768$		0			0
$769$	30.5189	+	15.3272i	1.10054	+	0.552711i	0.903891	−	0.427763i	$-0.140698\pi$
$769$	30.5189	+	15.3272i	1.10054	+	0.552711i	0.196648	+	0.980474i	$0.436995\pi$
$770$	−2.78206	−	1.39720i	−0.100258	−	0.0503516i
$771$		0			0
$772$	16.4106	−	17.3943i	0.590632	−	0.626033i
$773$	2.31945	−	1.94625i	0.0834247	−	0.0700016i	−0.600122	−	0.799909i	$-0.704881\pi$
$773$	2.31945	−	1.94625i	0.0834247	−	0.0700016i	0.683546	+	0.729907i	$0.260437\pi$
$774$		0			0
$775$	9.73449	+	8.16820i	0.349673	+	0.293411i
$776$	−5.91662	+	0.691554i	−0.212394	+	0.0248254i
$777$		0			0
$778$	−11.2276	−	11.9006i	−0.402530	−	0.426657i
$779$	7.04808	+	0.823802i	0.252524	+	0.0295158i
$780$		0			0
$781$	0.573339	−	9.84385i	0.0205157	−	0.352241i
$782$	−23.2165	−	40.2122i	−0.830222	−	1.43799i
$783$		0			0
$784$	−3.64034	+	6.30526i	−0.130012	+	0.225188i
$785$	−4.21554	−	2.77260i	−0.150459	−	0.0989585i
$786$		0			0
$787$	0.899575	+	2.08545i	0.0320664	+	0.0743382i	0.933497	−	0.358586i	$-0.116741\pi$
$787$	0.899575	+	2.08545i	0.0320664	+	0.0743382i	−0.901430	+	0.432924i	$0.857482\pi$
$788$	22.4732	−	5.32626i	0.800576	−	0.189740i
$789$		0			0
$790$	−11.9769	−	16.0878i	−0.426119	−	0.572377i
$791$	−23.8739	+	8.68939i	−0.848858	+	0.308959i
$792$		0			0
$793$	−17.9926	−	6.54878i	−0.638936	−	0.232554i
$794$	10.6365	+	35.5285i	0.377477	+	1.26086i
$795$		0			0
$796$	−2.00636	−	34.4479i	−0.0711135	−	1.22097i
$797$	10.5130	−	6.91452i	0.372390	−	0.244925i	−0.349494	−	0.936939i	$-0.613647\pi$
$797$	10.5130	−	6.91452i	0.372390	−	0.244925i	0.721884	+	0.692014i	$0.243276\pi$
$798$		0			0
$799$	40.6581	+	9.63616i	1.43838	+	0.340903i
$800$	−5.99181	−	33.9812i	−0.211842	−	1.20142i
$801$		0			0
$802$	5.12989	−	29.0931i	0.181143	−	1.02731i
$803$	3.07757	−	7.13460i	0.108605	−	0.251775i
$804$		0			0
$805$	−1.05714	+	3.53109i	−0.0372592	+	0.124454i
$806$	−19.2185	+	25.8149i	−0.676941	+	0.909290i
$807$		0			0
$808$	−6.63835	+	3.33390i	−0.233536	+	0.117286i
$809$	13.7132			0.482129			0.241065	−	0.970509i	$-0.422503\pi$
$809$	13.7132			0.482129			0.241065	+	0.970509i	$0.422503\pi$
$810$		0			0
$811$	1.72288			0.0604985			0.0302493	−	0.999542i	$-0.490370\pi$
$811$	1.72288			0.0604985			0.0302493	+	0.999542i	$0.490370\pi$
$812$	−26.3099	+	13.2133i	−0.923295	+	0.463696i
$813$		0			0
$814$	2.24601	−	3.01691i	0.0787225	−	0.105743i
$815$	−2.85444	+	9.53449i	−0.0999866	+	0.333979i
$816$		0			0
$817$	−24.2770	+	56.2805i	−0.849345	+	1.96900i
$818$	0.254031	−	1.44068i	0.00888198	−	0.0503722i
$819$		0			0
$820$	0.342361	+	1.94163i	0.0119558	+	0.0678046i
$821$	50.3105	+	11.9238i	1.75585	+	0.416144i	0.977372	−	0.211530i	$-0.0678445\pi$
$821$	50.3105	+	11.9238i	1.75585	+	0.416144i	0.778477	+	0.627673i	$0.215993\pi$
$822$		0			0
$823$	−17.0312	+	11.2016i	−0.593669	+	0.390463i	−0.810493	−	0.585748i	$-0.800801\pi$
$823$	−17.0312	+	11.2016i	−0.593669	+	0.390463i	0.216824	+	0.976211i	$0.430430\pi$
$824$	0.480032	+	8.24183i	0.0167227	+	0.287118i
$825$		0			0
$826$	2.38371	+	7.96213i	0.0829397	+	0.277038i
$827$	−40.3124	−	14.6725i	−1.40180	−	0.510213i	−0.473087	−	0.881016i	$-0.656860\pi$
$827$	−40.3124	−	14.6725i	−1.40180	−	0.510213i	−0.928712	+	0.370803i	$0.879083\pi$
$828$		0			0
$829$	−13.4165	+	4.88321i	−0.465975	+	0.169601i	−0.564328	−	0.825551i	$-0.690865\pi$
$829$	−13.4165	+	4.88321i	−0.465975	+	0.169601i	0.0983534	+	0.995152i	$0.468642\pi$
$830$	−5.64428	−	7.58158i	−0.195916	−	0.263160i
$831$		0			0
$832$	64.3496	−	15.2511i	2.23092	−	0.528738i
$833$	9.90860	+	22.9707i	0.343312	+	0.795888i
$834$		0			0
$835$	−1.97410	−	1.29839i	−0.0683167	−	0.0449326i
$836$	−10.5221	+	18.2249i	−0.363916	+	0.630321i
$837$		0			0
$838$	21.6341	+	37.4714i	0.747338	+	1.29443i
$839$	1.74775	−	30.0078i	0.0603391	−	1.03598i	−0.823238	−	0.567697i	$-0.807835\pi$
$839$	1.74775	−	30.0078i	0.0603391	−	1.03598i	0.883577	−	0.468286i	$-0.155128\pi$
$840$		0			0
$841$	−5.61087	−	0.655817i	−0.193478	−	0.0226144i
$842$	18.7471	+	19.8707i	0.646067	+	0.684791i
$843$		0			0
$844$	15.4138	−	1.80161i	0.530563	−	0.0620140i
$845$	−7.64942	−	6.41863i	−0.263148	−	0.220807i
$846$		0			0
$847$	13.3637	−	11.2135i	0.459183	−	0.385300i
$848$	11.6551	−	12.3537i	0.400238	−	0.424227i
$849$		0			0
$850$	−61.0038	−	30.6373i	−2.09241	−	1.05085i
$851$	−3.97943	−	1.99855i	−0.136413	−	0.0685093i
$852$		0			0
$853$	−25.0747	+	26.5776i	−0.858542	+	0.910001i	−0.996763	−	0.0804005i	$-0.974380\pi$
$853$	−25.0747	+	26.5776i	−0.858542	+	0.910001i	0.138221	+	0.990401i	$0.455862\pi$
$854$	−10.9463	+	9.18504i	−0.374575	+	0.314306i
$855$		0			0
$856$	−15.8956	−	13.3380i	−0.543299	−	0.455882i
$857$	−45.8475	+	5.35881i	−1.56612	+	0.183053i	−0.854478	−	0.519487i	$-0.826123\pi$
$857$	−45.8475	+	5.35881i	−1.56612	+	0.183053i	−0.711644	+	0.702541i	$0.752049\pi$
$858$		0			0
$859$	0.211808	+	0.224503i	0.00722679	+	0.00765995i	0.730977	−	0.682402i	$-0.239065\pi$
$859$	0.211808	+	0.224503i	0.00722679	+	0.00765995i	−0.723750	+	0.690062i	$0.757583\pi$
$860$	−16.9147	−	1.97704i	−0.576785	−	0.0674165i
$861$		0			0
$862$	2.73299	−	46.9236i	0.0930859	−	1.59822i
$863$	−16.3176	−	28.2630i	−0.555459	−	0.962083i	−0.997868	−	0.0652694i	$-0.979209\pi$
$863$	−16.3176	−	28.2630i	−0.555459	−	0.962083i	0.442409	−	0.896813i	$-0.354124\pi$
$864$		0			0
$865$	−4.29355	+	7.43665i	−0.145985	+	0.252854i
$866$	7.27033	+	4.78177i	0.247056	+	0.162491i
$867$		0			0
$868$	5.49409	+	12.7367i	0.186482	+	0.432313i
$869$	−16.7854	+	3.97821i	−0.569405	+	0.134951i
$870$		0			0
$871$	−3.88488	−	5.21830i	−0.131634	−	0.176816i
$872$	2.66783	−	0.971011i	0.0903441	−	0.0328826i
$873$		0			0
$874$	40.5398	+	14.7553i	1.37128	+	0.499105i
$875$	3.25013	+	10.8562i	0.109874	+	0.367006i
$876$		0			0
$877$	−0.404272	−	6.94107i	−0.0136513	−	0.234383i	−0.998231	−	0.0594489i	$-0.981066\pi$
$877$	−0.404272	−	6.94107i	−0.0136513	−	0.234383i	0.984580	−	0.174935i	$-0.0559714\pi$
$878$	−56.7375	+	37.3168i	−1.91480	+	1.25938i
$879$		0			0
$880$	1.51665	+	0.359453i	0.0511264	+	0.0121172i
$881$	−6.47573	−	36.7257i	−0.218173	−	1.23732i	−0.875315	−	0.483553i	$-0.839346\pi$
$881$	−6.47573	−	36.7257i	−0.218173	−	1.23732i	0.657142	−	0.753767i	$-0.271765\pi$
$882$		0			0
$883$	1.07456	−	6.09412i	0.0361618	−	0.205084i	−0.961374	−	0.275246i	$-0.911241\pi$
$883$	1.07456	−	6.09412i	0.0361618	−	0.205084i	0.997536	+	0.0701625i	$0.0223518\pi$
$884$	39.5484	−	91.6836i	1.33016	−	3.08365i
$885$		0			0
$886$	−0.999804	+	3.33958i	−0.0335891	+	0.112195i
$887$	11.1212	−	14.9384i	0.373413	−	0.501581i	−0.575203	−	0.818011i	$-0.695077\pi$
$887$	11.1212	−	14.9384i	0.373413	−	0.501581i	0.948616	+	0.316430i	$0.102484\pi$
$888$		0			0
$889$	18.6289	−	9.35581i	0.624795	−	0.313784i
$890$	21.9166			0.734646
$891$		0			0
$892$	20.5958			0.689599
$893$	−34.6930	+	17.4235i	−1.16096	+	0.583055i
$894$		0			0
$895$	0.161351	−	0.216732i	0.00539336	−	0.00724454i
$896$	6.25277	−	20.8857i	0.208890	−	0.697742i
$897$		0			0
$898$	9.05303	−	20.9873i	0.302103	−	0.700355i
$899$	−2.83476	+	16.0767i	−0.0945444	+	0.536188i
$900$		0			0
$901$	−10.1337	−	57.4708i	−0.337601	−	1.91463i
$902$	2.85701	+	0.677124i	0.0951280	+	0.0225458i
$903$		0			0
$904$	−18.5343	+	12.1902i	−0.616443	+	0.405441i
$905$	0.783576	+	13.4535i	0.0260469	+	0.447209i
$906$		0			0
$907$	−7.50927	−	25.0827i	−0.249341	−	0.832858i	−0.987417	−	0.158140i	$-0.949450\pi$
$907$	−7.50927	−	25.0827i	−0.249341	−	0.832858i	0.738075	−	0.674718i	$-0.235735\pi$
$908$	−35.0525	−	12.7581i	−1.16326	−	0.423392i
$909$		0			0
$910$	−12.8966	+	4.69396i	−0.427516	+	0.155603i
$911$	−4.75418	−	6.38597i	−0.157513	−	0.211576i	0.716360	−	0.697731i	$-0.245807\pi$
$911$	−4.75418	−	6.38597i	−0.157513	−	0.211576i	−0.873873	+	0.486154i	$0.838399\pi$
$912$		0			0
$913$	−7.91034	+	1.87478i	−0.261794	+	0.0620463i
$914$	−35.4549	−	82.1937i	−1.17274	−	2.71873i
$915$		0			0
$916$	−36.5368	−	24.0306i	−1.20721	−	0.793995i
$917$	13.3366	−	23.0996i	0.440412	−	0.762816i
$918$		0			0
$919$	−27.5324	−	47.6875i	−0.908210	−	1.57307i	−0.816549	−	0.577276i	$-0.804116\pi$
$919$	−27.5324	−	47.6875i	−0.908210	−	1.57307i	−0.0916606	−	0.995790i	$-0.529217\pi$
$920$	−0.187136	+	3.21301i	−0.00616971	+	0.105930i
$921$		0			0
$922$	74.1232	+	8.66376i	2.44112	+	0.285326i
$923$	−29.8304	−	31.6183i	−0.981878	−	1.04073i
$924$		0			0
$925$	−6.50258	+	0.760043i	−0.213804	+	0.0249901i
$926$	55.5581	+	46.6188i	1.82575	+	1.53199i
$927$		0			0
$928$	33.9569	−	28.4932i	1.11469	−	0.935336i
$929$	−30.0976	+	31.9016i	−0.987472	+	1.04666i	0.0114360	+	0.999935i	$0.496360\pi$
$929$	−30.0976	+	31.9016i	−0.987472	+	1.04666i	−0.998908	+	0.0467244i	$0.985122\pi$
$930$		0			0
$931$	−20.7710	−	10.4316i	−0.680741	−	0.341881i
$932$	13.0940	+	6.57607i	0.428909	+	0.215406i
$933$		0			0
$934$	−15.5142	+	16.4441i	−0.507641	+	0.538068i
$935$	4.10265	−	3.44253i	0.134171	−	0.112583i
$936$		0			0
$937$	25.4682	+	21.3704i	0.832010	+	0.698140i	0.955752	−	0.294175i	$-0.0950449\pi$
$937$	25.4682	+	21.3704i	0.832010	+	0.698140i	−0.123741	+	0.992315i	$0.539489\pi$
$938$	−4.82222	+	0.563637i	−0.157451	+	0.0184034i
$939$		0			0
$940$	−7.40214	−	7.84581i	−0.241431	−	0.255902i
$941$	11.1321	+	1.30115i	0.362896	+	0.0424164i	0.295587	−	0.955316i	$-0.404485\pi$
$941$	11.1321	+	1.30115i	0.362896	+	0.0424164i	0.0673085	+	0.997732i	$0.478559\pi$
$942$		0			0
$943$	0.202130	−	3.47044i	0.00658226	−	0.113013i
$944$	−2.08058	−	3.60368i	−0.0677172	−	0.117290i
$945$		0			0
$946$	−12.6807	+	21.9637i	−0.412286	+	0.714101i
$947$	3.95278	+	2.59978i	0.128448	+	0.0844816i	0.612107	−	0.790775i	$-0.290322\pi$
$947$	3.95278	+	2.59978i	0.128448	+	0.0844816i	−0.483659	+	0.875256i	$0.660693\pi$
$948$		0			0
$949$	−13.5671	−	31.4522i	−0.440408	−	1.02098i
$950$	61.7162	−	14.6270i	2.00234	−	0.474563i
$951$		0			0
$952$	−11.9480	−	16.0490i	−0.387238	−	0.520151i
$953$	−1.77553	+	0.646238i	−0.0575149	+	0.0209337i	−0.370617	−	0.928786i	$-0.620854\pi$
$953$	−1.77553	+	0.646238i	−0.0575149	+	0.0209337i	0.313102	+	0.949719i	$0.398632\pi$
$954$		0			0
$955$	−4.18525	−	1.52331i	−0.135432	−	0.0492930i
$956$	−12.6591	−	42.2844i	−0.409425	−	1.36758i
$957$		0			0
$958$	−2.56775	−	44.0865i	−0.0829601	−	1.42437i
$959$	0.566740	−	0.372750i	0.0183010	−	0.0120367i
$960$		0			0
$961$	−22.6804	−	5.37536i	−0.731626	−	0.173399i
$962$	−2.87920	−	16.3288i	−0.0928293	−	0.526461i
$963$		0			0
$964$	−11.1041	+	62.9743i	−0.357638	+	2.02827i
$965$	2.23963	−	5.19204i	0.0720962	−	0.167138i
$966$		0			0
$967$	16.0167	−	53.4996i	0.515064	−	1.72043i	−0.164099	−	0.986444i	$-0.552472\pi$
$967$	16.0167	−	53.4996i	0.515064	−	1.72043i	0.679162	−	0.733988i	$-0.262343\pi$
$968$	9.09626	−	12.2184i	0.292365	−	0.392714i
$969$		0			0
$970$	−4.68781	+	2.35431i	−0.150517	+	0.0755922i
$971$	6.12547			0.196576			0.0982879	−	0.995158i	$-0.468663\pi$
$971$	6.12547			0.196576			0.0982879	+	0.995158i	$0.468663\pi$
$972$		0			0
$973$	−27.3990			−0.878370
$974$	53.6094	−	26.9236i	1.71776	−	0.862689i
$975$		0			0
$976$	4.27219	−	5.73854i	0.136749	−	0.183686i
$977$	8.18742	−	27.3479i	0.261939	−	0.874937i	−0.721301	−	0.692621i	$-0.756456\pi$
$977$	8.18742	−	27.3479i	0.261939	−	0.874937i	0.983240	−	0.182315i	$-0.0583591\pi$
$978$		0			0
$979$	7.46620	−	17.3086i	0.238621	−	0.553185i
$980$	1.12141	−	6.35984i	0.0358222	−	0.203158i
$981$		0			0
$982$	3.86034	+	21.8931i	0.123188	+	0.698636i
$983$	21.4823	+	5.09140i	0.685179	+	0.162390i	0.558439	−	0.829545i	$-0.311400\pi$
$983$	21.4823	+	5.09140i	0.685179	+	0.162390i	0.126740	+	0.991936i	$0.459549\pi$
$984$		0			0
$985$	4.56266	−	3.00091i	0.145378	−	0.0956168i
$986$	−5.09912	−	87.5485i	−0.162389	−	2.78811i
$987$		0			0
$988$	26.6072	+	88.8742i	0.846488	+	2.82747i
$989$	28.2164	+	10.2699i	0.897228	+	0.326564i
$990$		0			0
$991$	33.4354	−	12.1695i	1.06211	−	0.386577i	0.248890	−	0.968532i	$-0.419934\pi$
$991$	33.4354	−	12.1695i	1.06211	−	0.386577i	0.813221	+	0.581955i	$0.197712\pi$
$992$	−12.4715	−	16.7521i	−0.395969	−	0.531879i
$993$		0			0
$994$	−31.5660	+	7.48128i	−1.00121	+	0.237292i
$995$	−3.23166	−	7.49182i	−0.102450	−	0.237507i
$996$		0			0
$997$	−30.7695	−	20.2374i	−0.974479	−	0.640925i	−0.0408497	−	0.999165i	$-0.513006\pi$
$997$	−30.7695	−	20.2374i	−0.974479	−	0.640925i	−0.933629	+	0.358240i	$0.883377\pi$
$998$	−9.51222	+	16.4757i	−0.301104	+	0.521528i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.73.1		144
3.2	odd	2		81.2.g.a.25.8	yes	144
9.2	odd	6		729.2.g.c.703.1		144
9.4	even	3		729.2.g.a.217.8		144
9.5	odd	6		729.2.g.d.217.1		144
9.7	even	3		729.2.g.b.703.8		144
81.13	even	27	inner	243.2.g.a.10.1		144
81.14	odd	54		729.2.g.d.514.1		144
81.16	even	27		6561.2.a.d.1.8		72
81.40	even	27		729.2.g.b.28.8		144
81.41	odd	54		729.2.g.c.28.1		144
81.65	odd	54		6561.2.a.c.1.65		72
81.67	even	27		729.2.g.a.514.8		144
81.68	odd	54		81.2.g.a.13.8	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.8	✓	144	81.68	odd	54
81.2.g.a.25.8	yes	144	3.2	odd	2
243.2.g.a.10.1		144	81.13	even	27	inner
243.2.g.a.73.1		144	1.1	even	1	trivial
729.2.g.a.217.8		144	9.4	even	3
729.2.g.a.514.8		144	81.67	even	27
729.2.g.b.28.8		144	81.40	even	27
729.2.g.b.703.8		144	9.7	even	3
729.2.g.c.28.1		144	81.41	odd	54
729.2.g.c.703.1		144	9.2	odd	6
729.2.g.d.217.1		144	9.5	odd	6
729.2.g.d.514.1		144	81.14	odd	54
6561.2.a.c.1.65		72	81.65	odd	54
6561.2.a.d.1.8		72	81.16	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.94437 + 0.976500i) q^{2} +(1.63271 - 2.19311i) q^{4} +(0.185416 - 0.619334i) q^{5} +(-0.724564 + 1.67973i) q^{7} +(-0.277373 + 1.57306i) q^{8} +(0.244261 + 1.38527i) q^{10} +(1.17723 + 0.279008i) q^{11} +(4.45604 - 2.93078i) q^{13} +(-0.231433 - 3.97355i) q^{14} +(0.571538 + 1.90907i) q^{16} +(6.43434 + 2.34191i) q^{17} +(-5.97823 + 2.17590i) q^{19} +(-1.05554 - 1.41783i) q^{20} +(-2.56142 + 0.607068i) q^{22} +(1.23445 + 2.86177i) q^{23} +(3.82824 + 2.51788i) q^{25} +(-5.80229 + 10.0499i) q^{26} +(2.50083 + 4.33156i) q^{28} +(-0.342261 + 5.87639i) q^{29} +(2.75457 + 0.321963i) q^{31} +(-5.16779 - 5.47754i) q^{32} +(-14.7976 + 1.72959i) q^{34} +(0.905967 + 0.760197i) q^{35} +(-1.09453 + 0.918418i) q^{37} +(9.49913 - 10.0685i) q^{38} +(0.922821 + 0.463458i) q^{40} +(-0.996758 - 0.500591i) q^{41} +(6.61155 - 7.00783i) q^{43} +(2.53397 - 2.12625i) q^{44} +(-5.19473 - 4.35890i) q^{46} +(6.06108 - 0.708439i) q^{47} +(2.50720 + 2.65747i) q^{49} +(-9.90223 - 1.15740i) q^{50} +(0.847890 - 14.5577i) q^{52} +(-4.26135 - 7.38088i) q^{53} +(0.391077 - 0.677365i) q^{55} +(-2.44134 - 1.60569i) q^{56} +(-5.07281 - 11.7601i) q^{58} +(-2.03183 + 0.481552i) q^{59} +(-2.14382 - 2.87965i) q^{61} +(-5.67029 + 2.06382i) q^{62} +(11.6517 + 4.24088i) q^{64} +(-0.988911 - 3.30319i) q^{65} +(-0.0709235 - 1.21771i) q^{67} +(15.6415 - 10.2876i) q^{68} +(-2.50387 - 0.593428i) q^{70} +(-1.41528 - 8.02646i) q^{71} +(1.11524 - 6.32482i) q^{73} +(1.23133 - 2.85455i) q^{74} +(-4.98873 + 16.6635i) q^{76} +(-1.32164 + 1.77527i) q^{77} +(-12.7417 + 6.39915i) q^{79} +1.28832 q^{80} +2.42689 q^{82} +(-6.00472 + 3.01569i) q^{83} +(2.64346 - 3.55078i) q^{85} +(-6.01216 + 20.0820i) q^{86} +(-0.765429 + 1.77446i) q^{88} +(2.70557 - 15.3441i) q^{89} +(1.69423 + 9.60848i) q^{91} +(8.29166 + 1.96516i) q^{92} +(-11.0932 + 7.29611i) q^{94} +(0.239145 + 4.10597i) q^{95} +(1.06957 + 3.57262i) q^{97} +(-7.46994 - 2.71884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 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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