LMFDB - Embedded newform 243.2.g.a.10.1

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			10.1
Character	$\chi$	$=$	243.10
Dual form			243.2.g.a.73.1

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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	−0.400687	−	0.916215i	$-0.631229\pi$
$2$	−1.94437	−	0.976500i	−1.37488	−	0.690490i	−0.974191	+	0.225725i	$0.927525\pi$
$3$		0			0
$3$		0			0
$4$	1.63271	+	2.19311i	0.816355	+	1.09656i
$5$	0.185416	+	0.619334i	0.0829208	+	0.276975i	0.989387	−	0.145303i	$-0.0464158\pi$
$5$	0.185416	+	0.619334i	0.0829208	+	0.276975i	−0.906466	+	0.422278i	$0.861231\pi$
$6$		0			0
$7$	−0.724564	−	1.67973i	−0.273860	−	0.634878i	0.724670	−	0.689097i	$-0.241992\pi$
$7$	−0.724564	−	1.67973i	−0.273860	−	0.634878i	−0.998529	+	0.0542188i	$0.982733\pi$
$8$	−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	−0.0492736	−	0.998785i	$-0.515691\pi$
$11$	1.17723	−	0.279008i	0.354948	−	0.0841242i	0.404222	+	0.914661i	$0.367542\pi$
$12$		0			0
$13$	4.45604	+	2.93078i	1.23588	+	0.812853i	0.987776	−	0.155879i	$-0.0498211\pi$
$13$	4.45604	+	2.93078i	1.23588	+	0.812853i	0.248107	+	0.968733i	$0.420191\pi$
$14$	−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	0.589693	−	0.807628i	$-0.299249\pi$
$17$	6.43434	−	2.34191i	1.56056	−	0.567996i	0.970864	+	0.239631i	$0.0770266\pi$
$18$		0			0
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.451909	−	0.892064i	$-0.649257\pi$
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.919590	+	0.392879i	$0.871479\pi$
$20$	−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	−0.739691	−	0.672947i	$-0.765028\pi$
$23$	1.23445	−	2.86177i	0.257400	−	0.596719i	0.997090	+	0.0762275i	$0.0242875\pi$
$24$		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	−0.867799	−	0.496916i	$-0.834466\pi$
$29$	−0.342261	−	5.87639i	−0.0635562	−	1.09122i	0.804242	−	0.594301i	$-0.202571\pi$
$30$		0			0
$31$	2.75457	−	0.321963i	0.494735	−	0.0578262i	0.134932	−	0.990855i	$-0.456918\pi$
$31$	2.75457	−	0.321963i	0.494735	−	0.0578262i	0.359802	+	0.933029i	$0.382844\pi$
$32$	−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	0.548369	−	0.836236i	$-0.315249\pi$
$37$	−1.09453	−	0.918418i	−0.179939	−	0.150987i	−0.728309	+	0.685249i	$0.759693\pi$
$38$	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	−0.524927	−	0.851147i	$-0.675908\pi$
$41$	−0.996758	+	0.500591i	−0.155667	+	0.0781791i	0.369260	+	0.929326i	$0.379611\pi$
$42$		0			0
$43$	6.61155	+	7.00783i	1.00825	+	1.06868i	0.997635	+	0.0687407i	$0.0218981\pi$
$43$	6.61155	+	7.00783i	1.00825	+	1.06868i	0.0106171	+	0.999944i	$0.496620\pi$
$44$	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	0.546011	−	0.837778i	$-0.316146\pi$
$47$	6.06108	+	0.708439i	0.884099	+	0.103336i	0.338088	+	0.941114i	$0.390220\pi$
$48$		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	0.409491	+	0.912314i	$0.365706\pi$
$53$	−4.26135	+	7.38088i	−0.585342	+	1.01384i	−0.994833	+	0.101528i	$0.967627\pi$
$54$		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	0.0962148	−	0.995361i	$-0.469326\pi$
$59$	−2.03183	−	0.481552i	−0.264521	−	0.0626927i	−0.360736	+	0.932668i	$0.617475\pi$
$60$		0			0
$61$	−2.14382	+	2.87965i	−0.274488	+	0.368702i	−0.917895	−	0.396822i	$-0.870113\pi$
$61$	−2.14382	+	2.87965i	−0.274488	+	0.368702i	0.643407	+	0.765524i	$0.277520\pi$
$62$	−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	0.991201	+	0.132367i	$0.0422576\pi$
$67$	−0.0709235	+	1.21771i	−0.00866469	+	0.148767i	−0.999866	+	0.0164003i	$0.994779\pi$
$68$	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	0.777994	+	0.628272i	$0.216237\pi$
$71$	−1.41528	+	8.02646i	−0.167963	+	0.952565i	−0.945957	+	0.324293i	$0.894874\pi$
$72$		0			0
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	0.977870	+	0.209215i	$0.0670909\pi$
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	−0.847341	+	0.531049i	$0.821798\pi$
$74$	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	−0.448759	−	0.893653i	$-0.648134\pi$
$79$	−12.7417	−	6.39915i	−1.43356	−	0.719960i	−0.984800	+	0.173693i	$0.944430\pi$
$80$	1.28832			0.144039
$81$		0			0
$82$	2.42689			0.268006
$83$	−6.00472	−	3.01569i	−0.659104	−	0.331015i	0.0876146	−	0.996154i	$-0.472076\pi$
$83$	−6.00472	−	3.01569i	−0.659104	−	0.331015i	−0.746719	+	0.665140i	$0.768372\pi$
$84$		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	0.698820	+	0.715297i	$0.253709\pi$
$89$	2.70557	+	15.3441i	0.286790	+	1.62647i	−0.412030	+	0.911170i	$0.635180\pi$
$90$		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	−0.886364	−	0.462989i	$-0.846777\pi$
$97$	1.06957	−	3.57262i	0.108599	−	0.362745i	0.994963	+	0.100244i	$0.0319622\pi$
$98$	−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	−0.642190	−	0.766546i	$-0.721974\pi$
$101$	2.77713	−	3.73034i	0.276335	−	0.371182i	0.918525	+	0.395363i	$0.129381\pi$
$102$		0			0
$103$	5.02919	+	1.19194i	0.495541	+	0.117445i	0.470785	−	0.882248i	$-0.343971\pi$
$103$	5.02919	+	1.19194i	0.495541	+	0.117445i	0.0247562	+	0.999694i	$0.492119\pi$
$104$	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	−0.987968	−	0.154659i	$-0.950572\pi$
$107$	−6.49528	−	11.2502i	−0.627922	−	1.08759i	0.360046	−	0.932935i	$-0.382761\pi$
$108$		0			0
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	−0.905443	−	0.424469i	$-0.860461\pi$
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	0.820322	+	0.571902i	$0.193794\pi$
$110$	−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	−0.102449	−	0.994738i	$-0.532668\pi$
$113$	9.53060	−	10.1018i	0.896563	−	0.950302i	0.999012	+	0.0444366i	$0.0141493\pi$
$114$		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	−0.941887	−	0.335930i	$-0.890949\pi$
$127$	−8.72949	+	7.32491i	−0.774617	+	0.649981i	0.167270	+	0.985911i	$0.446505\pi$
$128$	−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	−0.722151	−	0.691735i	$-0.756847\pi$
$131$	−14.4822	+	1.69272i	−1.26531	+	0.147894i	−0.543160	+	0.839629i	$0.682772\pi$
$132$		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	−0.562674	−	0.826679i	$-0.690227\pi$
$137$	−0.309806	+	0.203762i	−0.0264685	+	0.0174086i	0.536206	+	0.844087i	$0.319857\pi$
$138$		0			0
$139$	5.93229	−	13.7526i	0.503170	−	1.16648i	−0.457606	−	0.889155i	$-0.651293\pi$
$139$	5.93229	−	13.7526i	0.503170	−	1.16648i	0.960776	−	0.277325i	$-0.0894479\pi$
$140$	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	0.514816	−	0.857301i	$-0.327860\pi$
$149$	−0.835701	−	0.549649i	−0.0684633	−	0.0450290i	−0.583279	+	0.812272i	$0.698231\pi$
$150$		0			0
$151$	0.0191032	−	0.00452754i	0.00155460	−	0.000368446i	−0.229838	−	0.973229i	$-0.573820\pi$
$151$	0.0191032	−	0.00452754i	0.00155460	−	0.000368446i	0.231393	+	0.972860i	$0.425672\pi$
$152$	−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	0.999667	+	0.0258129i	$0.00821741\pi$
$157$	2.23838	+	7.47669i	0.178642	+	0.596705i	−0.821025	+	0.570892i	$0.806597\pi$
$158$	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	0.988919	−	0.148453i	$-0.0474293\pi$
$167$	1.04821	+	3.50128i	0.0811132	+	0.270937i	−0.907806	+	0.419390i	$0.862244\pi$
$168$		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	−0.690376	−	0.723450i	$-0.742555\pi$
$173$	−12.9245	+	3.06317i	−0.982635	+	0.232889i	−0.292259	+	0.956339i	$0.594407\pi$
$174$		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	−0.327301	−	0.944920i	$-0.606139\pi$
$179$	0.392738	−	0.142945i	0.0293546	−	0.0106842i	0.356656	+	0.934236i	$0.383917\pi$
$180$		0			0
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.511717	−	0.859154i	$-0.670990\pi$
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.944252	+	0.329225i	$0.893213\pi$
$182$	−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	0.981295	+	0.192512i	$0.0616636\pi$
$191$	0.400574	+	6.87758i	0.0289845	+	0.497645i	−0.952310	+	0.305132i	$0.901299\pi$
$192$		0			0
$193$	8.68725	−	1.01539i	0.625322	−	0.0730897i	0.202470	−	0.979288i	$-0.435103\pi$
$193$	8.68725	−	1.01539i	0.625322	−	0.0730897i	0.422852	+	0.906199i	$0.361029\pi$
$194$	−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	−0.382476	−	0.923965i	$-0.624929\pi$
$197$	6.47094	−	5.42976i	0.461035	−	0.386855i	0.843512	+	0.537111i	$0.180484\pi$
$198$		0			0
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	0.917561	−	0.397595i	$-0.130155\pi$
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	−0.232222	+	0.972663i	$0.574599\pi$
$200$	−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	−0.579283	−	0.815126i	$-0.696668\pi$
$211$	3.89505	−	4.12851i	0.268146	−	0.284218i	0.847429	+	0.530908i	$0.178149\pi$
$212$	−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	−0.625576	−	0.780163i	$-0.715136\pi$
$223$	4.49831	−	6.04228i	0.301229	−	0.404621i	0.926805	+	0.375542i	$0.122543\pi$
$224$	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	0.724319	+	0.689465i	$0.242154\pi$
$227$	−3.91290	+	13.0700i	−0.259708	+	0.867485i	−0.984027	+	0.178020i	$0.943031\pi$
$228$		0			0
$229$	−0.929998	+	15.9675i	−0.0614560	+	1.05516i	0.816785	+	0.576942i	$0.195754\pi$
$229$	−0.929998	+	15.9675i	−0.0614560	+	1.05516i	−0.878241	+	0.478218i	$0.841283\pi$
$230$	−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	−0.939032	−	0.343829i	$-0.888276\pi$
$233$	0.930605	−	5.27772i	0.0609660	−	0.345755i	0.999998	−	0.00192589i	$-0.000613031\pi$
$234$		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	0.995897	−	0.0904942i	$-0.0288447\pi$
$239$	9.64028	+	12.9491i	0.623578	+	0.837611i	−0.372319	+	0.928105i	$0.621437\pi$
$240$		0			0
$241$	−20.9003	−	10.4965i	−1.34630	−	0.676139i	−0.377975	−	0.925816i	$-0.623379\pi$
$241$	−20.9003	−	10.4965i	−1.34630	−	0.676139i	−0.968329	+	0.249677i	$0.919676\pi$
$242$	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	−0.765588	−	0.643331i	$-0.777552\pi$
$251$	−4.21745	−	23.9183i	−0.266203	−	1.50971i	0.499385	−	0.866380i	$-0.333559\pi$
$252$		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	−0.934705	−	0.355423i	$-0.884337\pi$
$257$	0.560163	−	9.61763i	0.0349420	−	0.599931i	0.969647	−	0.244508i	$-0.0786263\pi$
$258$		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	−0.907409	−	0.420249i	$-0.861943\pi$
$263$	−3.96621	+	5.32754i	−0.244567	+	0.328510i	0.662842	+	0.748759i	$0.269350\pi$
$264$		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	0.833494	+	0.552529i	$0.186337\pi$
$269$	14.6832	+	25.4321i	0.895251	+	1.55062i	0.0617568	+	0.998091i	$0.480330\pi$
$270$		0			0
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	−0.422799	−	0.906223i	$-0.638952\pi$
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	0.996212	−	0.0869568i	$-0.0277142\pi$
$272$	−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	−0.313638	−	0.949543i	$-0.601548\pi$
$277$	−13.9438	−	1.62979i	−0.837801	−	0.0979249i	−0.524163	+	0.851618i	$0.675622\pi$
$278$	−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	0.0953791	−	0.995441i	$-0.469594\pi$
$281$	−15.1525	−	16.0607i	−0.903924	−	0.958103i	−0.999303	+	0.0373380i	$0.988112\pi$
$282$		0			0
$283$	3.53563	−	1.77566i	0.210172	−	0.105552i	−0.340599	−	0.940208i	$-0.610630\pi$
$283$	3.53563	−	1.77566i	0.210172	−	0.105552i	0.550771	+	0.834656i	$0.314334\pi$
$284$	−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	0.118546	−	0.992949i	$-0.462177\pi$
$293$	7.92333	−	0.926104i	0.462886	−	0.0541036i	0.344340	+	0.938845i	$0.388103\pi$
$294$		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	−0.285534	−	0.958369i	$-0.592171\pi$
$307$	1.95823	−	0.712736i	0.111762	−	0.0406780i	0.397296	+	0.917691i	$0.369949\pi$
$308$	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	0.141570	−	0.989928i	$-0.454785\pi$
$311$	−12.5444	−	8.25056i	−0.711326	−	0.467846i	−0.852895	+	0.522082i	$0.825155\pi$
$312$		0			0
$313$	4.95368	−	1.17404i	0.279998	−	0.0663608i	−0.0882173	−	0.996101i	$-0.528117\pi$
$313$	4.95368	−	1.17404i	0.279998	−	0.0663608i	0.368216	+	0.929740i	$0.379969\pi$
$314$	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	0.884943	+	0.465700i	$0.154197\pi$
$317$	10.9746	+	25.4420i	0.616396	+	1.42897i	−0.268547	+	0.963267i	$0.586543\pi$
$318$		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	0.904774	+	0.425891i	$0.140039\pi$
$331$	10.8007	+	25.0389i	0.593663	+	1.37626i	−0.311112	+	0.950373i	$0.600701\pi$
$332$	−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	0.804908	−	0.593400i	$-0.202215\pi$
$337$	10.6262	+	6.98897i	0.578846	+	0.380713i	−0.226062	+	0.974113i	$0.572585\pi$
$338$	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	−0.983940	−	0.178497i	$-0.942877\pi$
$347$	−3.33227	+	7.72507i	−0.178886	+	0.414703i	0.805055	+	0.593200i	$0.202136\pi$
$348$		0			0
$349$	−25.1843	+	16.5640i	−1.34808	+	0.886649i	−0.998732	−	0.0503430i	$-0.983969\pi$
$349$	−25.1843	+	16.5640i	−1.34808	+	0.886649i	−0.349352	+	0.936992i	$0.613598\pi$
$350$	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	0.820606	+	0.571494i	$0.193636\pi$
$353$	1.35078	+	23.1921i	0.0718950	+	1.23439i	−0.748711	+	0.662896i	$0.769327\pi$
$354$		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	−0.723145	−	0.690696i	$-0.757304\pi$
$359$	−3.19290	+	2.67916i	−0.168515	+	0.141401i	0.554630	+	0.832097i	$0.312860\pi$
$360$		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	0.902435	−	0.430826i	$-0.141778\pi$
$367$	8.04346	+	8.52557i	0.419865	+	0.445031i	−0.482569	+	0.875858i	$0.660296\pi$
$368$	−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	−0.401313	+	0.915941i	$0.631446\pi$
$373$	−24.9598	+	26.4559i	−1.29237	+	1.36983i	−0.891057	+	0.453891i	$0.850036\pi$
$374$	−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	0.965740	−	0.259513i	$-0.0835620\pi$
$379$	5.02516	+	8.70383i	0.258125	+	0.447086i	−0.707615	+	0.706599i	$0.750229\pi$
$380$	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	0.238132	−	0.971233i	$-0.423465\pi$
$383$	0.294453	+	0.0697866i	0.0150458	+	0.00356593i	−0.223086	+	0.974799i	$0.571613\pi$
$384$		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	−0.885750	−	0.464164i	$-0.846355\pi$
$389$	2.15663	−	7.20364i	0.109345	−	0.365239i	0.995095	+	0.0989244i	$0.0315402\pi$
$390$		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	0.964448	+	0.264271i	$0.0851314\pi$
$397$	2.95983	+	16.7860i	0.148549	+	0.842466i	−0.815899	+	0.578195i	$0.803757\pi$
$398$	−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	0.552179	−	0.833726i	$-0.313797\pi$
$401$	−8.10789	−	10.8908i	−0.404889	−	0.543860i	−0.957067	+	0.289866i	$0.906389\pi$
$402$		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	0.792086	−	0.610410i	$-0.208995\pi$
$409$	−0.401500	−	0.539308i	−0.0198529	−	0.0266671i	−0.811939	+	0.583743i	$0.801588\pi$
$410$	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	0.844376	+	0.535752i	$0.179972\pi$
$419$	−1.15627	+	19.8524i	−0.0564876	+	0.969855i	−0.900863	+	0.434103i	$0.857065\pi$
$420$		0			0
$421$	−3.60098	+	12.0281i	−0.175501	+	0.586214i	0.824298	+	0.566156i	$0.191570\pi$
$421$	−3.60098	+	12.0281i	−0.175501	+	0.586214i	−0.999799	+	0.0200574i	$0.993615\pi$
$422$	−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	−0.999722	−	0.0235787i	$-0.992494\pi$
$431$	−10.8013	−	18.7084i	−0.520281	−	0.901153i	0.479441	−	0.877574i	$-0.340839\pi$
$432$		0			0
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	−0.910067	−	0.414461i	$-0.863970\pi$
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	0.813968	+	0.580910i	$0.197303\pi$
$434$	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	0.817243	−	0.576293i	$-0.195501\pi$
$439$	31.0001	+	3.62339i	1.47955	+	0.172935i	0.662312	+	0.749228i	$0.269575\pi$
$440$	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	0.752966	−	0.658060i	$-0.228623\pi$
$443$	1.09948	+	1.16538i	0.0522379	+	0.0553689i	−0.700728	+	0.713429i	$0.747141\pi$
$444$		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	0.432841	−	0.901470i	$-0.357511\pi$
$449$	−8.04720	−	6.75241i	−0.379771	−	0.318666i	−0.812613	+	0.582804i	$0.801955\pi$
$450$		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	−0.327676	−	0.944790i	$-0.606265\pi$
$457$	−2.39213	−	41.0713i	−0.111899	−	1.92123i	0.215777	−	0.976443i	$-0.430772\pi$
$458$	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	−0.997963	−	0.0637944i	$-0.979680\pi$
$461$	−28.6563	+	18.8476i	−1.33466	+	0.877819i	−0.336696	+	0.941613i	$0.609309\pi$
$462$		0			0
$463$	−13.2025	+	30.6068i	−0.613572	+	1.42242i	0.273990	+	0.961732i	$0.411656\pi$
$463$	−13.2025	+	30.6068i	−0.613572	+	1.42242i	−0.887562	+	0.460688i	$0.847603\pi$
$464$	−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	0.557897	−	0.829910i	$-0.311608\pi$
$467$	9.76380	+	3.55373i	0.451815	+	0.164447i	−0.106082	+	0.994357i	$0.533831\pi$
$468$		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	−0.997196	−	0.0748364i	$-0.976157\pi$
$479$	−8.03903	−	18.6366i	−0.367313	−	0.851526i	0.629883	−	0.776690i	$-0.283103\pi$
$480$		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	0.998304	−	0.0582128i	$-0.0185402\pi$
$491$	2.93035	+	9.78804i	0.132245	+	0.441728i	−0.866059	+	0.499941i	$0.833355\pi$
$492$		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	0.702395	−	0.711787i	$-0.252114\pi$
$499$	7.30520	+	4.80470i	0.327026	+	0.215088i	−0.375370	+	0.926875i	$0.622484\pi$
$500$	−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	−0.0530509	−	0.998592i	$-0.516895\pi$
$503$	12.2947	−	4.47489i	0.548192	−	0.199526i	0.601243	+	0.799066i	$0.294672\pi$
$504$		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	−0.411117	−	0.911583i	$-0.634861\pi$
$509$	12.0492	−	27.9331i	0.534070	−	1.23811i	0.945187	−	0.326530i	$-0.105880\pi$
$510$		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	−0.805525	−	0.592561i	$-0.798117\pi$
$521$	−8.25925	+	6.93034i	−0.361845	+	0.303624i	0.443681	+	0.896185i	$0.353672\pi$
$522$		0			0
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	0.825517	−	0.564377i	$-0.190884\pi$
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	−0.412453	+	0.910979i	$0.635328\pi$
$524$	−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	0.985105	−	0.171953i	$-0.0550078\pi$
$541$	7.99279	+	13.8439i	0.343637	+	0.595196i	−0.641468	+	0.767149i	$0.721674\pi$
$542$	−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	−0.786056	−	0.618155i	$-0.787880\pi$
$547$	0.738452	−	0.991913i	0.0315739	−	0.0424111i	0.817630	+	0.575744i	$0.195288\pi$
$548$	−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	0.897499	+	0.441017i	$0.145382\pi$
$557$	−2.28246	+	12.9445i	−0.0967109	+	0.548475i	−0.994210	+	0.107458i	$0.965729\pi$
$558$		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	0.718873	−	0.695142i	$-0.244658\pi$
$563$	−3.63605	−	4.88406i	−0.153241	−	0.205838i	−0.872114	+	0.489303i	$0.837251\pi$
$564$		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	0.110307	−	0.993898i	$-0.464817\pi$
$569$	−14.8144	−	7.44006i	−0.621051	−	0.311904i	−0.731358	+	0.681994i	$0.761113\pi$
$570$		0			0
$571$	20.8094	+	27.9518i	0.870844	+	1.16975i	0.984353	+	0.176210i	$0.0563838\pi$
$571$	20.8094	+	27.9518i	0.870844	+	1.16975i	−0.113508	+	0.993537i	$0.536209\pi$
$572$	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	−0.639854	−	0.768497i	$-0.721005\pi$
$577$	5.38675	−	30.5498i	0.224254	−	1.27180i	0.864107	−	0.503308i	$-0.167884\pi$
$578$	−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	0.233214	−	0.972425i	$-0.425076\pi$
$587$	26.6000	−	35.7300i	1.09790	−	1.47474i	0.864687	−	0.502311i	$-0.167517\pi$
$588$		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	0.587756	−	0.809038i	$-0.300011\pi$
$593$	−9.90549	−	17.1568i	−0.406770	−	0.704546i	−0.994526	+	0.104493i	$0.966678\pi$
$594$		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	−0.988902	−	0.148570i	$-0.952533\pi$
$599$	−19.1656	+	20.3143i	−0.783084	+	0.830020i	0.205818	+	0.978590i	$0.434014\pi$
$600$		0			0
$601$	10.0762	+	1.17774i	0.411015	+	0.0480408i	0.319088	−	0.947725i	$-0.396623\pi$
$601$	10.0762	+	1.17774i	0.411015	+	0.0480408i	0.0919270	+	0.995766i	$0.470697\pi$
$602$	−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	−0.241690	−	0.970354i	$-0.577702\pi$
$607$	9.66590	−	4.85440i	0.392327	−	0.197034i	0.634016	+	0.773320i	$0.281405\pi$
$608$	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	−0.555372	−	0.831602i	$-0.687424\pi$
$613$	4.13859	−	3.47269i	0.167156	−	0.140261i	0.722528	+	0.691341i	$0.242980\pi$
$614$	−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	−0.600901	−	0.799324i	$-0.705191\pi$
$617$	−24.8710	+	2.90700i	−1.00127	+	0.117031i	−0.400367	+	0.916355i	$0.631117\pi$
$618$		0			0
$619$	−1.48183	−	25.4420i	−0.0595596	−	1.02260i	−0.887213	−	0.461360i	$-0.847362\pi$
$619$	−1.48183	−	25.4420i	−0.0595596	−	1.02260i	0.827654	−	0.561239i	$-0.189675\pi$
$620$	−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	−0.687451	−	0.726231i	$-0.741270\pi$
$631$	−18.7709	+	6.83203i	−0.747256	+	0.271979i	−0.0598054	+	0.998210i	$0.519048\pi$
$632$	−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	0.973674	−	0.227947i	$-0.0732011\pi$
$641$	3.53682	+	8.19927i	0.139696	+	0.323852i	−0.833978	+	0.551798i	$0.813942\pi$
$642$		0			0
$643$	−3.84314	−	12.8370i	−0.151559	−	0.506241i	0.848165	−	0.529731i	$-0.177707\pi$
$643$	−3.84314	−	12.8370i	−0.151559	−	0.506241i	−0.999724	+	0.0234904i	$0.992522\pi$
$644$	−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	0.980710	−	0.195467i	$-0.0626222\pi$
$653$	1.37807	+	4.60307i	0.0539280	+	0.180132i	−0.926782	+	0.375599i	$0.877437\pi$
$654$		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	0.278666	−	0.960388i	$-0.410108\pi$
$659$	24.6111	−	5.83293i	0.958712	−	0.227219i	0.680046	+	0.733169i	$0.261960\pi$
$660$		0			0
$661$	11.8107	+	7.76805i	0.459385	+	0.302142i	0.758027	−	0.652223i	$-0.226163\pi$
$661$	11.8107	+	7.76805i	0.459385	+	0.302142i	−0.298642	+	0.954365i	$0.596534\pi$
$662$	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	−0.591734	−	0.806133i	$-0.701557\pi$
$673$	−2.22854	+	1.46573i	−0.0859039	+	0.0564999i	0.505830	+	0.862633i	$0.331186\pi$
$674$	−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	−0.973790	−	0.227449i	$-0.926961\pi$
$677$	−0.858366	−	14.7376i	−0.0329897	−	0.566411i	0.940800	−	0.338962i	$-0.110076\pi$
$678$		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	−0.281263	−	0.959631i	$-0.590753\pi$
$683$	16.0712	−	13.4854i	0.614948	−	0.516003i	0.896211	+	0.443628i	$0.146309\pi$
$684$		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	0.0901196	−	0.995931i	$-0.471275\pi$
$691$	−23.9044	−	25.3372i	−0.909366	−	0.963872i	−0.999486	+	0.0320589i	$0.989794\pi$
$692$	−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	0.0794276	+	0.996841i	$0.474691\pi$
$701$	−21.8053	+	37.7679i	−0.823576	+	1.42647i	−0.903003	+	0.429634i	$0.858643\pi$
$702$		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	−0.548617	−	0.836074i	$-0.684846\pi$
$709$	10.9085	−	14.6527i	0.409677	−	0.550292i	0.958295	+	0.285781i	$0.0922530\pi$
$710$	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	−0.868018	−	0.496532i	$-0.834607\pi$
$719$	3.15002	−	17.8647i	0.117476	−	0.666240i	0.985494	−	0.169708i	$-0.0542824\pi$
$720$		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	0.751579	−	0.659643i	$-0.229293\pi$
$727$	18.0996	+	9.08994i	0.671276	+	0.337127i	−0.0803032	+	0.996770i	$0.525589\pi$
$728$	−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	0.782198	−	0.623030i	$-0.214099\pi$
$733$	−1.05577	−	1.41814i	−0.0389957	−	0.0523803i	−0.821193	+	0.570650i	$0.806691\pi$
$734$	−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	−0.999982	−	0.00602346i	$-0.998083\pi$
$739$	−1.58340	+	8.97988i	−0.0582461	+	0.330330i	0.941736	+	0.336354i	$0.109194\pi$
$740$	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	0.908018	+	0.418930i	$0.137595\pi$
$743$	−1.15833	+	19.8878i	−0.0424951	+	0.729613i	−0.950514	+	0.310683i	$0.899442\pi$
$744$		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	−0.520591	−	0.853806i	$-0.674289\pi$
$751$	−37.5165	−	8.89157i	−1.36900	−	0.324458i	−0.848405	+	0.529348i	$0.822437\pi$
$752$	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	0.135606	−	0.990763i	$-0.456702\pi$
$757$	25.4729	−	44.1204i	0.925829	−	1.60358i	0.790223	−	0.612820i	$-0.209965\pi$
$758$	−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	−0.0309391	−	0.999521i	$-0.509850\pi$
$761$	26.7225	−	28.3242i	0.968690	−	1.02675i	0.999629	−	0.0272302i	$-0.00866872\pi$
$762$		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	0.196648	−	0.980474i	$-0.436995\pi$
$769$	30.5189	−	15.3272i	1.10054	−	0.552711i	0.903891	+	0.427763i	$0.140698\pi$
$770$	−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	0.683546	−	0.729907i	$-0.260437\pi$
$773$	2.31945	+	1.94625i	0.0834247	+	0.0700016i	−0.600122	+	0.799909i	$0.704881\pi$
$774$		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	−0.901430	−	0.432924i	$-0.857482\pi$
$787$	0.899575	−	2.08545i	0.0320664	−	0.0743382i	0.933497	+	0.358586i	$0.116741\pi$
$788$	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	0.721884	−	0.692014i	$-0.243276\pi$
$797$	10.5130	+	6.91452i	0.372390	+	0.244925i	−0.349494	+	0.936939i	$0.613647\pi$
$798$		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	0.778477	−	0.627673i	$-0.215993\pi$
$821$	50.3105	−	11.9238i	1.75585	−	0.416144i	0.977372	+	0.211530i	$0.0678445\pi$
$822$		0			0
$823$	−17.0312	−	11.2016i	−0.593669	−	0.390463i	0.216824	−	0.976211i	$-0.430430\pi$
$823$	−17.0312	−	11.2016i	−0.593669	−	0.390463i	−0.810493	+	0.585748i	$0.800801\pi$
$824$	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	−0.928712	−	0.370803i	$-0.879083\pi$
$827$	−40.3124	+	14.6725i	−1.40180	+	0.510213i	−0.473087	+	0.881016i	$0.656860\pi$
$828$		0			0
$829$	−13.4165	−	4.88321i	−0.465975	−	0.169601i	0.0983534	−	0.995152i	$-0.468642\pi$
$829$	−13.4165	−	4.88321i	−0.465975	−	0.169601i	−0.564328	+	0.825551i	$0.690865\pi$
$830$	−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	0.883577	+	0.468286i	$0.155128\pi$
$839$	1.74775	+	30.0078i	0.0603391	+	1.03598i	−0.823238	+	0.567697i	$0.807835\pi$
$840$		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	0.138221	−	0.990401i	$-0.455862\pi$
$853$	−25.0747	−	26.5776i	−0.858542	−	0.910001i	−0.996763	+	0.0804005i	$0.974380\pi$
$854$	−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	−0.711644	−	0.702541i	$-0.752049\pi$
$857$	−45.8475	−	5.35881i	−1.56612	−	0.183053i	−0.854478	+	0.519487i	$0.826123\pi$
$858$		0			0
$859$	0.211808	−	0.224503i	0.00722679	−	0.00765995i	−0.723750	−	0.690062i	$-0.757583\pi$
$859$	0.211808	−	0.224503i	0.00722679	−	0.00765995i	0.730977	+	0.682402i	$0.239065\pi$
$860$	−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	0.442409	+	0.896813i	$0.354124\pi$
$863$	−16.3176	+	28.2630i	−0.555459	+	0.962083i	−0.997868	+	0.0652694i	$0.979209\pi$
$864$		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	0.984580	+	0.174935i	$0.0559714\pi$
$877$	−0.404272	+	6.94107i	−0.0136513	+	0.234383i	−0.998231	+	0.0594489i	$0.981066\pi$
$878$	−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	0.657142	+	0.753767i	$0.271765\pi$
$881$	−6.47573	+	36.7257i	−0.218173	+	1.23732i	−0.875315	+	0.483553i	$0.839346\pi$
$882$		0			0
$883$	1.07456	+	6.09412i	0.0361618	+	0.205084i	0.997536	−	0.0701625i	$-0.0223518\pi$
$883$	1.07456	+	6.09412i	0.0361618	+	0.205084i	−0.961374	+	0.275246i	$0.911241\pi$
$884$	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	0.948616	−	0.316430i	$-0.102484\pi$
$887$	11.1212	+	14.9384i	0.373413	+	0.501581i	−0.575203	+	0.818011i	$0.695077\pi$
$888$		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	0.738075	+	0.674718i	$0.235735\pi$
$907$	−7.50927	+	25.0827i	−0.249341	+	0.832858i	−0.987417	+	0.158140i	$0.949450\pi$
$908$	−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	−0.873873	−	0.486154i	$-0.838399\pi$
$911$	−4.75418	+	6.38597i	−0.157513	+	0.211576i	0.716360	+	0.697731i	$0.245807\pi$
$912$		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	−0.0916606	+	0.995790i	$0.529217\pi$
$919$	−27.5324	+	47.6875i	−0.908210	+	1.57307i	−0.816549	+	0.577276i	$0.804116\pi$
$920$	−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	−0.998908	−	0.0467244i	$-0.985122\pi$
$929$	−30.0976	−	31.9016i	−0.987472	−	1.04666i	0.0114360	−	0.999935i	$-0.496360\pi$
$930$		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	−0.123741	−	0.992315i	$-0.539489\pi$
$937$	25.4682	−	21.3704i	0.832010	−	0.698140i	0.955752	+	0.294175i	$0.0950449\pi$
$938$	−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	0.0673085	−	0.997732i	$-0.478559\pi$
$941$	11.1321	−	1.30115i	0.362896	−	0.0424164i	0.295587	+	0.955316i	$0.404485\pi$
$942$		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	−0.483659	−	0.875256i	$-0.660693\pi$
$947$	3.95278	−	2.59978i	0.128448	−	0.0844816i	0.612107	+	0.790775i	$0.290322\pi$
$948$		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	0.313102	−	0.949719i	$-0.398632\pi$
$953$	−1.77553	−	0.646238i	−0.0575149	−	0.0209337i	−0.370617	+	0.928786i	$0.620854\pi$
$954$		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	0.679162	+	0.733988i	$0.262343\pi$
$967$	16.0167	+	53.4996i	0.515064	+	1.72043i	−0.164099	+	0.986444i	$0.552472\pi$
$968$	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	0.983240	+	0.182315i	$0.0583591\pi$
$977$	8.18742	+	27.3479i	0.261939	+	0.874937i	−0.721301	+	0.692621i	$0.756456\pi$
$978$		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	0.126740	−	0.991936i	$-0.459549\pi$
$983$	21.4823	−	5.09140i	0.685179	−	0.162390i	0.558439	+	0.829545i	$0.311400\pi$
$984$		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	0.813221	−	0.581955i	$-0.197712\pi$
$991$	33.4354	+	12.1695i	1.06211	+	0.386577i	0.248890	+	0.968532i	$0.419934\pi$
$992$	−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	−0.933629	−	0.358240i	$-0.883377\pi$
$997$	−30.7695	+	20.2374i	−0.974479	+	0.640925i	−0.0408497	+	0.999165i	$0.513006\pi$
$998$	−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.10.1		144
3.2	odd	2		81.2.g.a.13.8	✓	144
9.2	odd	6		729.2.g.d.514.1		144
9.4	even	3		729.2.g.b.28.8		144
9.5	odd	6		729.2.g.c.28.1		144
9.7	even	3		729.2.g.a.514.8		144
81.2	odd	54		729.2.g.c.703.1		144
81.5	odd	54		6561.2.a.c.1.65		72
81.25	even	27	inner	243.2.g.a.73.1		144
81.29	odd	54		729.2.g.d.217.1		144
81.52	even	27		729.2.g.a.217.8		144
81.56	odd	54		81.2.g.a.25.8	yes	144
81.76	even	27		6561.2.a.d.1.8		72
81.79	even	27		729.2.g.b.703.8		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.8	✓	144	3.2	odd	2
81.2.g.a.25.8	yes	144	81.56	odd	54
243.2.g.a.10.1		144	1.1	even	1	trivial
243.2.g.a.73.1		144	81.25	even	27	inner
729.2.g.a.217.8		144	81.52	even	27
729.2.g.a.514.8		144	9.7	even	3
729.2.g.b.28.8		144	9.4	even	3
729.2.g.b.703.8		144	81.79	even	27
729.2.g.c.28.1		144	9.5	odd	6
729.2.g.c.703.1		144	81.2	odd	54
729.2.g.d.217.1		144	81.29	odd	54
729.2.g.d.514.1		144	9.2	odd	6
6561.2.a.c.1.65		72	81.5	odd	54
6561.2.a.d.1.8		72	81.76	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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