LMFDB - Embedded newform 729.2.i.a.64.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(10,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			64.17
Character	$\chi$	$=$	729.64
Dual form			729.2.i.a.262.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.829136 + 0.0321742i) q^{2} +(-1.30755 - 0.101631i) q^{4} +(1.06671 + 1.32252i) q^{5} +(-2.20706 + 1.00323i) q^{7} +(-2.72917 - 0.318994i) q^{8} +(0.841900 + 1.13087i) q^{10} +(-0.0547589 - 2.82335i) q^{11} +(-5.52920 - 1.77287i) q^{13} +(-1.86223 + 0.760804i) q^{14} +(0.338906 + 0.0530039i) q^{16} +(-0.381447 - 1.27412i) q^{17} +(-3.22382 + 0.764059i) q^{19} +(-1.26038 - 1.83768i) q^{20} +(0.0454367 - 2.34271i) q^{22} +(-1.54117 + 1.10156i) q^{23} +(0.447345 - 2.06517i) q^{25} +(-4.52742 - 1.64785i) q^{26} +(2.98781 - 1.08747i) q^{28} +(0.282681 + 2.06959i) q^{29} +(-3.04514 - 2.98665i) q^{31} +(5.67178 + 1.11390i) q^{32} +(-0.275278 - 1.06869i) q^{34} +(-3.68109 - 1.84871i) q^{35} +(-3.01579 - 1.98352i) q^{37} +(-2.69757 + 0.529785i) q^{38} +(-2.48937 - 3.94965i) q^{40} +(-1.91949 + 3.64407i) q^{41} +(1.79685 - 5.25149i) q^{43} +(-0.215341 + 3.69725i) q^{44} +(-1.31328 + 0.863761i) q^{46} +(-3.87549 + 3.80105i) q^{47} +(-0.738023 + 0.845680i) q^{49} +(0.437355 - 1.69792i) q^{50} +(7.04955 + 2.88006i) q^{52} +(2.96543 + 2.48829i) q^{53} +(3.67552 - 3.08413i) q^{55} +(6.34345 - 2.03395i) q^{56} +(0.167793 + 1.72507i) q^{58} +(-13.1182 + 7.23834i) q^{59} +(3.50428 - 0.272375i) q^{61} +(-2.42874 - 2.57431i) q^{62} +(3.99928 + 0.947846i) q^{64} +(-3.55343 - 9.20361i) q^{65} +(-1.81968 + 13.3224i) q^{67} +(0.369273 + 1.70475i) q^{68} +(-2.99264 - 1.65127i) q^{70} +(0.433406 - 1.00475i) q^{71} +(-3.80885 + 5.11617i) q^{73} +(-2.43669 - 1.74164i) q^{74} +(4.29297 - 0.671408i) q^{76} +(2.95333 + 6.17636i) q^{77} +(8.07966 - 12.8192i) q^{79} +(0.291417 + 0.504749i) q^{80} +(-1.70877 + 2.95967i) q^{82} +(3.14312 + 5.96706i) q^{83} +(1.27816 - 1.86360i) q^{85} +(1.65880 - 4.29639i) q^{86} +(-0.751187 + 7.72288i) q^{88} +(0.186829 + 0.433118i) q^{89} +(13.9818 - 1.63424i) q^{91} +(2.12712 - 1.28373i) q^{92} +(-3.33560 + 3.02690i) q^{94} +(-4.44937 - 3.44852i) q^{95} +(1.41603 - 1.75560i) q^{97} +(-0.639130 + 0.677439i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{81}\right)$

Coefficient data

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

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

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

$2$	0.829136	+	0.0321742i	0.586288	+	0.0227506i	0.330213	−	0.943906i	$-0.392879\pi$
$2$	0.829136	+	0.0321742i	0.586288	+	0.0227506i	0.256075	+	0.966657i	$0.417571\pi$
$3$		0			0
$3$		0			0
$4$	−1.30755	−	0.101631i	−0.653777	−	0.0508156i
$5$	1.06671	+	1.32252i	0.477049	+	0.591448i	0.958524	−	0.285012i	$-0.0919976\pi$
$5$	1.06671	+	1.32252i	0.477049	+	0.591448i	−0.481475	+	0.876460i	$0.659899\pi$
$6$		0			0
$7$	−2.20706	+	1.00323i	−0.834189	+	0.379185i	−0.784918	−	0.619600i	$-0.787295\pi$
$7$	−2.20706	+	1.00323i	−0.834189	+	0.379185i	−0.0492712	+	0.998785i	$0.515690\pi$
$8$	−2.72917	−	0.318994i	−0.964907	−	0.112781i
$9$		0			0
$10$	0.841900	+	1.13087i	0.266232	+	0.357612i
$11$	−0.0547589	−	2.82335i	−0.0165104	−	0.851273i	−0.912942	−	0.408090i	$-0.866195\pi$
$11$	−0.0547589	−	2.82335i	−0.0165104	−	0.851273i	0.896431	−	0.443183i	$-0.146151\pi$
$12$		0			0
$13$	−5.52920	−	1.77287i	−1.53352	−	0.491705i	−0.585708	−	0.810522i	$-0.699183\pi$
$13$	−5.52920	−	1.77287i	−1.53352	−	0.491705i	−0.947816	+	0.318817i	$0.896714\pi$
$14$	−1.86223	+	0.760804i	−0.497701	+	0.203333i
$15$		0			0
$16$	0.338906	+	0.0530039i	0.0847264	+	0.0132510i
$17$	−0.381447	−	1.27412i	−0.0925146	−	0.309020i	0.899190	−	0.437558i	$-0.144157\pi$
$17$	−0.381447	−	1.27412i	−0.0925146	−	0.309020i	−0.991705	+	0.128538i	$0.958972\pi$
$18$		0			0
$19$	−3.22382	+	0.764059i	−0.739594	+	0.175287i	−0.583110	−	0.812393i	$-0.698164\pi$
$19$	−3.22382	+	0.764059i	−0.739594	+	0.175287i	−0.156484	+	0.987680i	$0.550016\pi$
$20$	−1.26038	−	1.83768i	−0.281829	−	0.410917i
$21$		0			0
$22$	0.0454367	−	2.34271i	0.00968714	−	0.499466i
$23$	−1.54117	+	1.10156i	−0.321357	+	0.229692i	−0.730717	−	0.682681i	$-0.760814\pi$
$23$	−1.54117	+	1.10156i	−0.321357	+	0.229692i	0.409360	+	0.912373i	$0.365752\pi$
$24$		0			0
$25$	0.447345	−	2.06517i	0.0894690	−	0.413035i
$26$	−4.52742	−	1.64785i	−0.887900	−	0.323169i
$27$		0			0
$28$	2.98781	−	1.08747i	0.564642	−	0.205513i
$29$	0.282681	+	2.06959i	0.0524925	+	0.384313i	0.998235	+	0.0593949i	$0.0189171\pi$
$29$	0.282681	+	2.06959i	0.0524925	+	0.384313i	−0.945742	+	0.324919i	$0.894663\pi$
$30$		0			0
$31$	−3.04514	−	2.98665i	−0.546923	−	0.536418i	0.373353	−	0.927689i	$-0.378208\pi$
$31$	−3.04514	−	2.98665i	−0.546923	−	0.536418i	−0.920275	+	0.391272i	$0.872035\pi$
$32$	5.67178	+	1.11390i	1.00264	+	0.196912i
$33$		0			0
$34$	−0.275278	−	1.06869i	−0.0472098	−	0.183280i
$35$	−3.68109	−	1.84871i	−0.622217	−	0.312489i
$36$		0			0
$37$	−3.01579	−	1.98352i	−0.495794	−	0.326089i	0.276867	−	0.960908i	$-0.410704\pi$
$37$	−3.01579	−	1.98352i	−0.495794	−	0.326089i	−0.772660	+	0.634820i	$0.781074\pi$
$38$	−2.69757	+	0.529785i	−0.437603	+	0.0859424i
$39$		0			0
$40$	−2.48937	−	3.94965i	−0.393604	−	0.624495i
$41$	−1.91949	+	3.64407i	−0.299774	+	0.569108i	−0.987642	−	0.156729i	$-0.949905\pi$
$41$	−1.91949	+	3.64407i	−0.299774	+	0.569108i	0.687867	+	0.725837i	$0.258547\pi$
$42$		0			0
$43$	1.79685	−	5.25149i	0.274017	−	0.800845i	−0.720230	−	0.693735i	$-0.755964\pi$
$43$	1.79685	−	5.25149i	0.274017	−	0.800845i	0.994247	−	0.107110i	$-0.0341597\pi$
$44$	−0.215341	+	3.69725i	−0.0324638	+	0.557382i
$45$		0			0
$46$	−1.31328	+	0.863761i	−0.193633	+	0.127355i
$47$	−3.87549	+	3.80105i	−0.565298	+	0.554441i	−0.925652	−	0.378375i	$-0.876483\pi$
$47$	−3.87549	+	3.80105i	−0.565298	+	0.554441i	0.360354	+	0.932816i	$0.382656\pi$
$48$		0			0
$49$	−0.738023	+	0.845680i	−0.105432	+	0.120811i
$50$	0.437355	−	1.69792i	0.0618513	−	0.240122i
$51$		0			0
$52$	7.04955	+	2.88006i	0.977597	+	0.399392i
$53$	2.96543	+	2.48829i	0.407333	+	0.341793i	0.823320	−	0.567578i	$-0.192119\pi$
$53$	2.96543	+	2.48829i	0.407333	+	0.341793i	−0.415987	+	0.909371i	$0.636564\pi$
$54$		0			0
$55$	3.67552	−	3.08413i	0.495607	−	0.415864i
$56$	6.34345	−	2.03395i	0.847680	−	0.271798i
$57$		0			0
$58$	0.167793	+	1.72507i	0.0220324	+	0.226512i
$59$	−13.1182	+	7.23834i	−1.70785	+	0.942352i	−0.747196	+	0.664604i	$0.768600\pi$
$59$	−13.1182	+	7.23834i	−1.70785	+	0.942352i	−0.960654	+	0.277748i	$0.910412\pi$
$60$		0			0
$61$	3.50428	−	0.272375i	0.448678	−	0.0348740i	0.148834	−	0.988862i	$-0.452448\pi$
$61$	3.50428	−	0.272375i	0.448678	−	0.0348740i	0.299844	+	0.953988i	$0.403065\pi$
$62$	−2.42874	−	2.57431i	−0.308450	−	0.326938i
$63$		0			0
$64$	3.99928	+	0.947846i	0.499910	+	0.118481i
$65$	−3.55343	−	9.20361i	−0.440748	−	1.14157i
$66$		0			0
$67$	−1.81968	+	13.3224i	−0.222309	+	1.62759i	0.454021	+	0.890991i	$0.349989\pi$
$67$	−1.81968	+	13.3224i	−0.222309	+	1.62759i	−0.676330	+	0.736598i	$0.736431\pi$
$68$	0.369273	+	1.70475i	0.0447809	+	0.206732i
$69$		0			0
$70$	−2.99264	−	1.65127i	−0.357689	−	0.197364i
$71$	0.433406	−	1.00475i	0.0514359	−	0.119242i	−0.890560	−	0.454865i	$-0.849688\pi$
$71$	0.433406	−	1.00475i	0.0514359	−	0.119242i	0.941996	+	0.335623i	$0.108947\pi$
$72$		0			0
$73$	−3.80885	+	5.11617i	−0.445792	+	0.598803i	−0.967047	−	0.254598i	$-0.918057\pi$
$73$	−3.80885	+	5.11617i	−0.445792	+	0.598803i	0.521255	+	0.853401i	$0.325464\pi$
$74$	−2.43669	−	1.74164i	−0.283259	−	0.202461i
$75$		0			0
$76$	4.29297	−	0.671408i	0.492437	−	0.0770158i
$77$	2.95333	+	6.17636i	0.336563	+	0.703862i
$78$		0			0
$79$	8.07966	−	12.8192i	0.909032	−	1.44228i	0.0121908	−	0.999926i	$-0.496119\pi$
$79$	8.07966	−	12.8192i	0.909032	−	1.44228i	0.896841	−	0.442352i	$-0.145856\pi$
$80$	0.291417	+	0.504749i	0.0325814	+	0.0564326i
$81$		0			0
$82$	−1.70877	+	2.95967i	−0.188702	+	0.326841i
$83$	3.14312	+	5.96706i	0.345002	+	0.654970i	0.994424	−	0.105458i	$-0.0336310\pi$
$83$	3.14312	+	5.96706i	0.345002	+	0.654970i	−0.649422	+	0.760428i	$0.724989\pi$
$84$		0			0
$85$	1.27816	−	1.86360i	0.138635	−	0.202135i
$86$	1.65880	−	4.29639i	0.178873	−	0.463292i
$87$		0			0
$88$	−0.751187	+	7.72288i	−0.0800768	+	0.823262i
$89$	0.186829	+	0.433118i	0.0198038	+	0.0459104i	0.927831	−	0.373001i	$-0.121671\pi$
$89$	0.186829	+	0.433118i	0.0198038	+	0.0459104i	−0.908027	+	0.418911i	$0.862412\pi$
$90$		0			0
$91$	13.9818	−	1.63424i	1.46570	−	0.171315i
$92$	2.12712	−	1.28373i	0.221768	−	0.133838i
$93$		0			0
$94$	−3.33560	+	3.02690i	−0.344041	+	0.312201i
$95$	−4.44937	−	3.44852i	−0.456496	−	0.353811i
$96$		0			0
$97$	1.41603	−	1.75560i	0.143776	−	0.178254i	−0.701357	−	0.712810i	$-0.747422\pi$
$97$	1.41603	−	1.75560i	0.143776	−	0.178254i	0.845133	+	0.534556i	$0.179521\pi$
$98$	−0.639130	+	0.677439i	−0.0645619	+	0.0684316i
$99$		0			0
$100$	−0.794814	+	2.65486i	−0.0794814	+	0.265486i
$101$	8.43430	−	17.6388i	0.839244	−	1.75513i	0.210371	−	0.977622i	$-0.432533\pi$
$101$	8.43430	−	17.6388i	0.839244	−	1.75513i	0.628873	−	0.777508i	$-0.283517\pi$
$102$		0			0
$103$	−16.9853	−	10.2507i	−1.67361	−	1.01003i	−0.946067	−	0.323971i	$-0.894982\pi$
$103$	−16.9853	−	10.2507i	−1.67361	−	1.01003i	−0.727545	−	0.686060i	$-0.759339\pi$
$104$	14.5246	+	6.60224i	1.42425	+	0.647403i
$105$		0			0
$106$	2.37869	+	2.15854i	0.231038	+	0.209656i
$107$	−1.24856	−	7.08095i	−0.120703	−	0.684541i	−0.983768	−	0.179447i	$-0.942569\pi$
$107$	−1.24856	−	7.08095i	−0.120703	−	0.684541i	0.863065	−	0.505094i	$-0.168542\pi$
$108$		0			0
$109$	−1.97531	+	11.2026i	−0.189201	+	1.07301i	0.731238	+	0.682123i	$0.238943\pi$
$109$	−1.97531	+	11.2026i	−0.189201	+	1.07301i	−0.920438	+	0.390888i	$0.872168\pi$
$110$	3.14674	−	2.43891i	0.300030	−	0.232541i
$111$		0			0
$112$	−0.801159	+	0.223018i	−0.0757024	+	0.0210732i
$113$	5.97854	+	17.4729i	0.562414	+	1.64372i	0.749977	+	0.661464i	$0.230064\pi$
$113$	5.97854	+	17.4729i	0.562414	+	1.64372i	−0.187563	+	0.982253i	$0.560059\pi$
$114$		0			0
$115$	−3.10083	−	0.863175i	−0.289154	−	0.0804915i
$116$	−0.159286	−	2.73483i	−0.0147893	−	0.253923i
$117$		0			0
$118$	−11.1097	+	5.57950i	−1.02273	+	0.513635i
$119$	2.12011	+	2.42938i	0.194351	+	0.222701i
$120$		0			0
$121$	3.02340	−	0.117322i	0.274855	−	0.0106656i
$122$	2.91429	−	0.113088i	0.263848	−	0.0102385i
$123$		0			0
$124$	3.67815	+	4.21469i	0.330307	+	0.378490i
$125$	10.8003	−	5.42409i	0.966005	−	0.485146i
$126$		0			0
$127$	−0.621306	−	10.6674i	−0.0551320	−	0.946580i	−0.906552	−	0.422095i	$-0.861295\pi$
$127$	−0.621306	−	10.6674i	−0.0551320	−	0.946580i	0.851420	−	0.524485i	$-0.175742\pi$
$128$	−7.85136	−	2.18558i	−0.693969	−	0.193179i
$129$		0			0
$130$	−2.65015	−	7.74537i	−0.232434	−	0.679314i
$131$	11.2629	−	3.13525i	0.984047	−	0.273928i	0.261464	−	0.965213i	$-0.415795\pi$
$131$	11.2629	−	3.13525i	0.984047	−	0.273928i	0.722582	+	0.691285i	$0.242955\pi$
$132$		0			0
$133$	6.34862	−	4.92055i	0.550495	−	0.426666i
$134$	−1.93740	+	10.9875i	−0.167366	+	0.949178i
$135$		0			0
$136$	0.634597	+	3.59898i	0.0544162	+	0.308610i
$137$	7.75634	+	7.03850i	0.662669	+	0.601340i	0.932327	−	0.361616i	$-0.117775\pi$
$137$	7.75634	+	7.03850i	0.662669	+	0.601340i	−0.269658	+	0.962956i	$0.586911\pi$
$138$		0			0
$139$	6.23021	+	2.83198i	0.528439	+	0.240205i	0.660218	−	0.751074i	$-0.270464\pi$
$139$	6.23021	+	2.83198i	0.528439	+	0.240205i	−0.131779	+	0.991279i	$0.542069\pi$
$140$	4.62534	+	2.79140i	0.390912	+	0.235917i
$141$		0			0
$142$	0.391680	−	0.819129i	0.0328690	−	0.0687398i
$143$	−4.70266	+	15.7080i	−0.393256	+	1.31357i
$144$		0			0
$145$	−2.43553	+	2.58151i	−0.202260	+	0.214383i
$146$	−3.32266	+	4.11945i	−0.274985	+	0.340929i
$147$		0			0
$148$	3.74173	+	2.90006i	0.307568	+	0.238383i
$149$	15.1226	−	13.7230i	1.23889	−	1.12423i	0.251178	−	0.967941i	$-0.419182\pi$
$149$	15.1226	−	13.7230i	1.23889	−	1.12423i	0.987711	−	0.156291i	$-0.0499537\pi$
$150$		0			0
$151$	−11.0234	+	6.65265i	−0.897071	+	0.541385i	−0.888654	−	0.458579i	$-0.848359\pi$
$151$	−11.0234	+	6.65265i	−0.897071	+	0.541385i	−0.00841786	+	0.999965i	$0.502680\pi$
$152$	9.04207	−	1.05687i	0.733409	−	0.0857232i
$153$		0			0
$154$	2.24999	+	5.21607i	0.181309	+	0.420323i
$155$	0.701606	−	7.21315i	0.0563544	−	0.579374i
$156$		0			0
$157$	6.49463	−	16.8215i	0.518328	−	1.34250i	−0.388674	−	0.921376i	$-0.627067\pi$
$157$	6.49463	−	16.8215i	0.518328	−	1.34250i	0.907001	−	0.421127i	$-0.138365\pi$
$158$	7.11158	−	10.3689i	0.565767	−	0.824909i
$159$		0			0
$160$	4.57701	+	8.68924i	0.361845	+	0.686945i
$161$	2.29633	−	3.97737i	0.180977	−	0.313461i
$162$		0			0
$163$	7.64208	+	13.2365i	0.598574	+	1.03676i	0.993032	+	0.117846i	$0.0375990\pi$
$163$	7.64208	+	13.2365i	0.598574	+	1.03676i	−0.394458	+	0.918914i	$0.629068\pi$
$164$	2.88019	−	4.56974i	0.224905	−	0.356837i
$165$		0			0
$166$	2.41409	+	5.04863i	0.187369	+	0.391850i
$167$	−18.9291	+	2.96046i	−1.46478	+	0.229087i	−0.836099	−	0.548578i	$-0.815169\pi$
$167$	−18.9291	+	2.96046i	−1.46478	+	0.229087i	−0.628679	+	0.777665i	$0.716404\pi$
$168$		0			0
$169$	16.8528	+	12.0457i	1.29637	+	0.926590i
$170$	1.11972	−	1.50405i	0.0858789	−	0.115355i
$171$		0			0
$172$	−2.88320	+	6.68400i	−0.219842	+	0.509650i
$173$	−5.49832	−	3.03385i	−0.418030	−	0.230659i	0.260130	−	0.965574i	$-0.416235\pi$
$173$	−5.49832	−	3.03385i	−0.418030	−	0.230659i	−0.678160	+	0.734915i	$0.737222\pi$
$174$		0			0
$175$	1.08453	+	5.00674i	0.0819827	+	0.378474i
$176$	0.131091	−	0.959753i	0.00988132	−	0.0723441i
$177$		0			0
$178$	0.140971	+	0.365124i	0.0105662	+	0.0273672i
$179$	−22.5711	−	5.34944i	−1.68704	−	0.399836i	−0.728557	−	0.684985i	$-0.759809\pi$
$179$	−22.5711	−	5.34944i	−1.68704	−	0.399836i	−0.958483	+	0.285149i	$0.907957\pi$
$180$		0			0
$181$	−10.9314	−	11.5866i	−0.812525	−	0.861226i	0.179950	−	0.983676i	$-0.442406\pi$
$181$	−10.9314	−	11.5866i	−0.812525	−	0.861226i	−0.992475	+	0.122450i	$0.960925\pi$
$182$	11.6454	−	0.905155i	0.863217	−	0.0670945i
$183$		0			0
$184$	4.55752	−	2.51473i	0.335985	−	0.185388i
$185$	−0.593751	−	6.10429i	−0.0436534	−	0.448796i
$186$		0			0
$187$	−3.57641	+	1.14673i	−0.261533	+	0.0838572i
$188$	5.45372	−	4.57622i	0.397753	−	0.333755i
$189$		0			0
$190$	−3.57818	−	3.00245i	−0.259588	−	0.217821i
$191$	−7.54340	−	3.08182i	−0.545821	−	0.222993i	0.0884808	−	0.996078i	$-0.471799\pi$
$191$	−7.54340	−	3.08182i	−0.545821	−	0.222993i	−0.634302	+	0.773085i	$0.718712\pi$
$192$		0			0
$193$	−3.54104	+	13.7472i	−0.254890	+	0.989542i	0.705010	+	0.709198i	$0.250943\pi$
$193$	−3.54104	+	13.7472i	−0.254890	+	0.989542i	−0.959899	+	0.280345i	$0.909551\pi$
$194$	1.23057	−	1.41007i	0.0883496	−	0.101237i
$195$		0			0
$196$	1.05095	−	1.03077i	0.0750681	−	0.0736262i
$197$	−13.7129	+	9.01913i	−0.977006	+	0.642587i	−0.934295	−	0.356501i	$-0.883970\pi$
$197$	−13.7129	+	9.01913i	−0.977006	+	0.642587i	−0.0427106	+	0.999087i	$0.513599\pi$
$198$		0			0
$199$	0.111730	−	1.91833i	0.00792032	−	0.135987i	−0.992030	−	0.126003i	$-0.959785\pi$
$199$	0.111730	−	1.91833i	0.00792032	−	0.135987i	0.999950	−	0.00998352i	$-0.00317791\pi$
$200$	−1.87966	+	5.49351i	−0.132912	+	0.388450i
$201$		0			0
$202$	7.56069	−	14.3536i	0.531969	−	1.00992i
$203$	−2.70017	−	4.28411i	−0.189515	−	0.300686i
$204$		0			0
$205$	−6.86689	+	1.34861i	−0.479605	+	0.0941913i
$206$	−13.7533	−	9.04570i	−0.958239	−	0.630244i
$207$		0			0
$208$	−1.77991	−	0.893903i	−0.123414	−	0.0619811i
$209$	2.33374	+	9.06014i	0.161428	+	0.626703i
$210$		0			0
$211$	−2.35475	−	0.462458i	−0.162108	−	0.0318369i	0.111000	−	0.993820i	$-0.464595\pi$
$211$	−2.35475	−	0.462458i	−0.162108	−	0.0318369i	−0.273108	+	0.961984i	$0.588051\pi$
$212$	−3.62457	−	3.55496i	−0.248937	−	0.244156i
$213$		0			0
$214$	−0.807403	−	5.91124i	−0.0551930	−	0.404084i
$215$	8.86192	−	3.22547i	0.604378	−	0.219976i
$216$		0			0
$217$	9.71708	+	3.53673i	0.659639	+	0.240089i
$218$	−1.99824	+	9.22489i	−0.135338	+	0.624788i
$219$		0			0
$220$	−5.11939	+	3.65912i	−0.345149	+	0.246698i
$221$	−0.149751	+	7.72114i	−0.0100734	+	0.519380i
$222$		0			0
$223$	−13.4502	−	19.6109i	−0.900694	−	1.31324i	−0.949282	−	0.314425i	$-0.898188\pi$
$223$	−13.4502	−	19.6109i	−0.900694	−	1.31324i	0.0485882	−	0.998819i	$-0.484528\pi$
$224$	−13.6354	+	3.23166i	−0.911056	+	0.215924i
$225$		0			0
$226$	4.39484	+	14.6798i	0.292341	+	0.976486i
$227$	4.79249	+	0.749531i	0.318089	+	0.0497481i	0.311548	−	0.950230i	$-0.399153\pi$
$227$	4.79249	+	0.749531i	0.318089	+	0.0497481i	0.00654074	+	0.999979i	$0.497918\pi$
$228$		0			0
$229$	−18.1242	+	7.40456i	−1.19768	+	0.489307i	−0.887250	−	0.461289i	$-0.847387\pi$
$229$	−18.1242	+	7.40456i	−1.19768	+	0.489307i	−0.310432	+	0.950596i	$0.600474\pi$
$230$	−2.54324	−	0.815456i	−0.167696	−	0.0537696i
$231$		0			0
$232$	−0.111297	−	5.73844i	−0.00730700	−	0.376747i
$233$	−1.58126	−	2.12400i	−0.103592	−	0.139148i	0.747304	−	0.664482i	$-0.231348\pi$
$233$	−1.58126	−	2.12400i	−0.103592	−	0.139148i	−0.850896	+	0.525334i	$0.823940\pi$
$234$		0			0
$235$	−9.16100	−	1.07077i	−0.597598	−	0.0698492i
$236$	17.8885	−	8.13131i	1.16444	−	0.529303i
$237$		0			0
$238$	1.67970	+	2.08250i	0.108879	+	0.134988i
$239$	−25.3818	−	1.97283i	−1.64181	−	0.127612i	−0.776928	−	0.629589i	$-0.783223\pi$
$239$	−25.3818	−	1.97283i	−1.64181	−	0.127612i	−0.864881	+	0.501977i	$0.832606\pi$
$240$		0			0
$241$	−0.350894	−	0.0136163i	−0.0226031	−	0.000877103i	0.0274713	−	0.999623i	$-0.491254\pi$
$241$	−0.350894	−	0.0136163i	−0.0226031	−	0.000877103i	−0.0500744	+	0.998745i	$0.515946\pi$
$242$	2.51058			0.161387
$243$		0			0
$244$	−4.60973			−0.295107
$245$	−1.90569	−	0.0739493i	−0.121750	−	0.00472445i
$246$		0			0
$247$	19.1797	+	1.49076i	1.22038	+	0.0948551i
$248$	7.35797	+	9.12245i	0.467231	+	0.579276i
$249$		0			0
$250$	9.12940	−	4.14982i	0.577394	−	0.262458i
$251$	−15.4587	−	1.80686i	−0.975742	−	0.114048i	−0.386748	−	0.922185i	$-0.626402\pi$
$251$	−15.4587	−	1.80686i	−0.975742	−	0.114048i	−0.588994	+	0.808138i	$0.700476\pi$
$252$		0			0
$253$	3.19450	+	4.29096i	0.200837	+	0.269770i
$254$	−0.171931	−	8.86472i	−0.0107879	−	0.556222i
$255$		0			0
$256$	−14.2671	−	4.57457i	−0.891696	−	0.285911i
$257$	−8.79401	+	3.59275i	−0.548555	+	0.224109i	−0.635496	−	0.772104i	$-0.719204\pi$
$257$	−8.79401	+	3.59275i	−0.548555	+	0.224109i	0.0869411	+	0.996213i	$0.472291\pi$
$258$		0			0
$259$	8.64595	+	1.35220i	0.537233	+	0.0840218i
$260$	3.71093	+	12.3954i	0.230142	+	0.768728i
$261$		0			0
$262$	9.43937	−	2.23717i	0.583166	−	0.138213i
$263$	10.2397	+	14.9299i	0.631409	+	0.920617i	0.999960	−	0.00899097i	$-0.00286195\pi$
$263$	10.2397	+	14.9299i	0.631409	+	0.920617i	−0.368551	+	0.929608i	$0.620146\pi$
$264$		0			0
$265$	−0.127544	+	6.57613i	−0.00783496	+	0.403968i
$266$	5.42218	−	3.87554i	0.332455	−	0.237625i
$267$		0			0
$268$	3.73330	−	17.2348i	0.228047	−	1.05278i
$269$	26.0104	+	9.46702i	1.58588	+	0.577215i	0.976473	−	0.215640i	$-0.0691837\pi$
$269$	26.0104	+	9.46702i	1.58588	+	0.577215i	0.609411	+	0.792854i	$0.291406\pi$
$270$		0			0
$271$	23.4889	−	8.54924i	1.42685	−	0.519330i	0.490821	−	0.871261i	$-0.336697\pi$
$271$	23.4889	−	8.54924i	1.42685	−	0.519330i	0.936026	+	0.351931i	$0.114475\pi$
$272$	−0.0617412	−	0.452026i	−0.00374361	−	0.0274081i
$273$		0			0
$274$	6.20460	+	6.08543i	0.374834	+	0.367634i
$275$	−5.85521	−	1.14993i	−0.353082	−	0.0693431i
$276$		0			0
$277$	2.99679	+	11.6343i	0.180060	+	0.699035i	0.993145	+	0.116890i	$0.0372925\pi$
$277$	2.99679	+	11.6343i	0.180060	+	0.699035i	−0.813085	+	0.582145i	$0.802214\pi$
$278$	5.07457	+	2.54855i	0.304353	+	0.152852i
$279$		0			0
$280$	9.45658	+	6.21969i	0.565139	+	0.371698i
$281$	16.3492	−	3.21088i	0.975314	−	0.191545i	0.320428	−	0.947273i	$-0.396173\pi$
$281$	16.3492	−	3.21088i	0.975314	−	0.191545i	0.654886	+	0.755728i	$0.272717\pi$
$282$		0			0
$283$	8.06138	+	12.7902i	0.479199	+	0.760301i	0.995363	−	0.0961887i	$-0.0306652\pi$
$283$	8.06138	+	12.7902i	0.479199	+	0.760301i	−0.516164	+	0.856490i	$0.672641\pi$
$284$	−0.668816	+	1.26972i	−0.0396870	+	0.0753438i
$285$		0			0
$286$	−4.40453	+	12.8727i	−0.260446	+	0.761181i
$287$	0.580591	−	9.96835i	0.0342712	−	0.588413i
$288$		0			0
$289$	12.7254	−	8.36963i	0.748553	−	0.492331i
$290$	−2.10244	+	2.06206i	−0.123460	+	0.121089i
$291$		0			0
$292$	5.50024	−	6.30258i	0.321877	−	0.368830i
$293$	1.83587	−	7.12730i	0.107253	−	0.416381i	−0.892120	−	0.451799i	$-0.850782\pi$
$293$	1.83587	−	7.12730i	0.107253	−	0.416381i	0.999373	+	0.0354179i	$0.0112762\pi$
$294$		0			0
$295$	−23.5662	−	9.62787i	−1.37208	−	0.560556i
$296$	7.59788	+	6.37538i	0.441618	+	0.370561i
$297$		0			0
$298$	12.9802	−	10.8917i	0.751922	−	0.630938i
$299$	10.4744	−	3.35848i	0.605749	−	0.194226i
$300$		0			0
$301$	1.30271	+	13.3930i	0.0750868	+	0.771959i
$302$	−9.35394	+	5.16129i	−0.538259	+	0.296999i
$303$		0			0
$304$	−1.13307	+	0.0880690i	−0.0649859	+	0.00505110i
$305$	4.09829	+	4.34393i	0.234667	+	0.248733i
$306$		0			0
$307$	−24.0734	−	5.70551i	−1.37394	−	0.325631i	−0.523648	−	0.851935i	$-0.675429\pi$
$307$	−24.0734	−	5.70551i	−1.37394	−	0.325631i	−0.850296	+	0.526304i	$0.823577\pi$
$308$	−3.23393	−	8.37608i	−0.184270	−	0.477272i
$309$		0			0
$310$	0.813805	−	5.95810i	0.0462210	−	0.338398i
$311$	−5.79765	−	26.7649i	−0.328755	−	1.51770i	−0.780273	−	0.625439i	$-0.784920\pi$
$311$	−5.79765	−	26.7649i	−0.328755	−	1.51770i	0.451519	−	0.892262i	$-0.350882\pi$
$312$		0			0
$313$	−23.9257	−	13.2017i	−1.35236	−	0.746202i	−0.369272	−	0.929321i	$-0.620393\pi$
$313$	−23.9257	−	13.2017i	−1.35236	−	0.746202i	−0.983091	+	0.183119i	$0.941381\pi$
$314$	5.92615	−	13.7384i	0.334432	−	0.775301i
$315$		0			0
$316$	−11.8674	+	15.9407i	−0.667595	+	0.896736i
$317$	−1.64304	−	1.17438i	−0.0922824	−	0.0659595i	0.534415	−	0.845222i	$-0.320532\pi$
$317$	−1.64304	−	1.17438i	−0.0922824	−	0.0659595i	−0.626697	+	0.779263i	$0.715594\pi$
$318$		0			0
$319$	5.82771	−	0.911437i	0.326289	−	0.0510307i
$320$	3.01254	+	6.30020i	0.168406	+	0.352192i
$321$		0			0
$322$	2.03194	−	3.22390i	0.113236	−	0.179661i
$323$	2.20322	+	3.81609i	0.122591	+	0.212333i
$324$		0			0
$325$	−6.13474	+	10.6257i	−0.340294	+	0.589406i
$326$	5.91045	+	11.2207i	0.327349	+	0.621458i
$327$		0			0
$328$	6.40106	−	9.33297i	0.353439	−	0.515327i
$329$	4.74009	−	12.2771i	0.261330	−	0.676861i
$330$		0			0
$331$	−0.324020	+	3.33121i	−0.0178097	+	0.183100i	−0.999988	−	0.00485045i	$-0.998456\pi$
$331$	−0.324020	+	3.33121i	−0.0178097	+	0.183100i	0.982179	+	0.187950i	$0.0601844\pi$
$332$	−3.50336	−	8.12170i	−0.192272	−	0.445736i
$333$		0			0
$334$	−15.7900	+	1.84559i	−0.863993	+	0.100986i
$335$	−19.5602	+	11.8046i	−1.06869	+	0.644956i
$336$		0			0
$337$	11.2759	−	10.2324i	0.614240	−	0.557393i	−0.304372	−	0.952553i	$-0.598447\pi$
$337$	11.2759	−	10.2324i	0.614240	−	0.557393i	0.918612	+	0.395160i	$0.129311\pi$
$338$	13.5857	+	10.5297i	0.738966	+	0.572742i
$339$		0			0
$340$	−1.86066	+	2.30685i	−0.100908	+	0.125107i
$341$	−8.26562	+	8.76104i	−0.447608	+	0.474437i
$342$		0			0
$343$	5.64767	−	18.8645i	0.304945	−	1.01859i
$344$	−6.57910	+	13.7590i	−0.354722	+	0.741837i
$345$		0			0
$346$	−4.46124	−	2.69237i	−0.239838	−	0.144743i
$347$	−14.8576	−	6.75363i	−0.797600	−	0.362554i	−0.0268081	−	0.999641i	$-0.508534\pi$
$347$	−14.8576	−	6.75363i	−0.797600	−	0.362554i	−0.770792	+	0.637087i	$0.780139\pi$
$348$		0			0
$349$	0.841407	+	0.763536i	0.0450395	+	0.0408711i	0.694217	−	0.719766i	$-0.255751\pi$
$349$	0.841407	+	0.763536i	0.0450395	+	0.0408711i	−0.649177	+	0.760637i	$0.724887\pi$
$350$	0.738134	+	4.18616i	0.0394549	+	0.223760i
$351$		0			0
$352$	2.83436	−	16.0744i	0.151072	−	0.856770i
$353$	−21.4933	+	16.6586i	−1.14397	+	0.886647i	−0.994768	−	0.102159i	$-0.967425\pi$
$353$	−21.4933	+	16.6586i	−1.14397	+	0.886647i	−0.149206	+	0.988806i	$0.547672\pi$
$354$		0			0
$355$	1.79112	−	0.498592i	0.0950627	−	0.0264625i
$356$	−0.200270	−	0.585313i	−0.0106143	−	0.0310215i
$357$		0			0
$358$	−18.5424	−	5.16162i	−0.979995	−	0.272800i
$359$	0.388634	+	6.67259i	0.0205113	+	0.352166i	0.992912	+	0.118850i	$0.0379207\pi$
$359$	0.388634	+	6.67259i	0.0205113	+	0.352166i	−0.972401	+	0.233316i	$0.925042\pi$
$360$		0			0
$361$	−7.16981	+	3.60081i	−0.377358	+	0.189517i
$362$	−8.69083	−	9.95858i	−0.456780	−	0.523412i
$363$		0			0
$364$	−18.4481	+	0.715871i	−0.966944	+	0.0375218i
$365$	−10.8292	+	0.420221i	−0.566825	+	0.0219954i
$366$		0			0
$367$	−11.0695	−	12.6842i	−0.577823	−	0.662112i	0.387896	−	0.921703i	$-0.373202\pi$
$367$	−11.0695	−	12.6842i	−0.577823	−	0.662112i	−0.965718	+	0.259592i	$0.916412\pi$
$368$	−0.580700	+	0.291638i	−0.0302711	+	0.0152027i
$369$		0			0
$370$	−0.295899	−	5.08039i	−0.0153831	−	0.264117i
$371$	−9.04120	−	2.51679i	−0.469396	−	0.130665i
$372$		0			0
$373$	−1.53030	−	4.47247i	−0.0792359	−	0.231576i	0.899419	−	0.437088i	$-0.143990\pi$
$373$	−1.53030	−	4.47247i	−0.0792359	−	0.231576i	−0.978654	+	0.205513i	$0.934114\pi$
$374$	−3.00223	+	0.835727i	−0.155241	+	0.0432144i
$375$		0			0
$376$	11.7894	−	9.13746i	0.607991	−	0.471229i
$377$	2.10611	−	11.9443i	0.108470	−	0.615165i
$378$		0			0
$379$	−2.59025	−	14.6901i	−0.133052	−	0.754578i	−0.976196	−	0.216889i	$-0.930409\pi$
$379$	−2.59025	−	14.6901i	−0.133052	−	0.754578i	0.843144	−	0.537688i	$-0.180702\pi$
$380$	5.46732	+	4.96133i	0.280468	+	0.254511i
$381$		0			0
$382$	−6.15535	−	2.79795i	−0.314935	−	0.143156i
$383$	12.6785	+	7.65150i	0.647840	+	0.390973i	0.802212	−	0.597039i	$-0.203656\pi$
$383$	12.6785	+	7.65150i	0.647840	+	0.390973i	−0.154372	+	0.988013i	$0.549335\pi$
$384$		0			0
$385$	−5.01799	+	10.4942i	−0.255741	+	0.534836i
$386$	−3.37831	+	11.2843i	−0.171951	+	0.574358i
$387$		0			0
$388$	−2.02996	+	2.15163i	−0.103056	+	0.109233i
$389$	−14.2403	+	17.6552i	−0.722013	+	0.895156i	−0.997816	−	0.0660585i	$-0.978958\pi$
$389$	−14.2403	+	17.6552i	−0.722013	+	0.895156i	0.275803	+	0.961214i	$0.411056\pi$
$390$		0			0
$391$	1.99141	+	1.54346i	0.100710	+	0.0780560i
$392$	2.28396	−	2.07258i	0.115357	−	0.104681i
$393$		0			0
$394$	−11.6601	+	7.03688i	−0.587426	+	0.354513i
$395$	25.5724	−	2.98898i	1.28669	−	0.150392i
$396$		0			0
$397$	−12.9345	−	29.9856i	−0.649164	−	1.50493i	−0.850810	−	0.525473i	$-0.823888\pi$
$397$	−12.9345	−	29.9856i	−0.649164	−	1.50493i	0.201646	−	0.979458i	$-0.435371\pi$
$398$	0.154360	−	1.58696i	0.00773737	−	0.0795471i
$399$		0			0
$400$	0.261070	−	0.676188i	0.0130535	−	0.0338094i
$401$	2.57215	−	3.75029i	0.128447	−	0.187281i	−0.755118	−	0.655589i	$-0.772420\pi$
$401$	2.57215	−	3.75029i	0.128447	−	0.187281i	0.883565	+	0.468308i	$0.155136\pi$
$402$		0			0
$403$	11.5422	+	21.9124i	0.574960	+	1.09153i
$404$	−12.8210	+	22.2066i	−0.637867	+	1.10482i
$405$		0			0
$406$	−2.10097	−	3.63899i	−0.104269	−	0.180600i
$407$	−5.43503	+	8.62327i	−0.269405	+	0.427440i
$408$		0			0
$409$	1.09353	+	2.28692i	0.0540715	+	0.113081i	0.927430	−	0.373998i	$-0.122013\pi$
$409$	1.09353	+	2.28692i	0.0540715	+	0.113081i	−0.873358	+	0.487078i	$0.838063\pi$
$410$	−5.73698	+	0.897247i	−0.283329	+	0.0443119i
$411$		0			0
$412$	21.1674	+	15.1296i	1.04284	+	0.745381i
$413$	21.6910	−	29.1360i	1.06734	−	1.43369i
$414$		0			0
$415$	−4.53874	+	10.5220i	−0.222798	+	0.516503i
$416$	−29.3856	−	16.2143i	−1.44075	−	0.794971i
$417$		0			0
$418$	1.64348	+	7.58717i	0.0803855	+	0.371101i
$419$	−0.925895	+	6.77875i	−0.0452329	+	0.331164i	0.954250	+	0.299010i	$0.0966564\pi$
$419$	−0.925895	+	6.77875i	−0.0452329	+	0.331164i	−0.999483	+	0.0321538i	$0.989763\pi$
$420$		0			0
$421$	1.35056	+	3.49805i	0.0658224	+	0.170484i	0.961892	−	0.273429i	$-0.0881578\pi$
$421$	1.35056	+	3.49805i	0.0658224	+	0.170484i	−0.896070	+	0.443913i	$0.853590\pi$
$422$	−1.93753	−	0.459203i	−0.0943175	−	0.0223536i
$423$		0			0
$424$	−7.29941	−	7.73692i	−0.354491	−	0.375738i
$425$	−2.80192	+	0.217783i	−0.135913	+	0.0105640i
$426$		0			0
$427$	−7.46090	+	4.11675i	−0.361058	+	0.199223i
$428$	0.912918	+	9.38562i	0.0441276	+	0.453671i
$429$		0			0
$430$	7.45151	−	2.38923i	0.359344	−	0.115219i
$431$	19.3648	−	16.2490i	0.932771	−	0.782688i	−0.0435417	−	0.999052i	$-0.513864\pi$
$431$	19.3648	−	16.2490i	0.932771	−	0.782688i	0.976313	+	0.216364i	$0.0694197\pi$
$432$		0			0
$433$	−18.1533	−	15.2324i	−0.872390	−	0.732022i	0.0922102	−	0.995740i	$-0.470607\pi$
$433$	−18.1533	−	15.2324i	−0.872390	−	0.732022i	−0.964600	+	0.263718i	$0.915051\pi$
$434$	7.94299	+	3.24507i	0.381276	+	0.155768i
$435$		0			0
$436$	3.72136	−	14.4472i	0.178221	−	0.691896i
$437$	4.12680	−	4.72879i	0.197412	−	0.226209i
$438$		0			0
$439$	−6.49561	+	6.37085i	−0.310018	+	0.304064i	−0.838523	−	0.544867i	$-0.816580\pi$
$439$	−6.49561	+	6.37085i	−0.310018	+	0.304064i	0.528504	+	0.848931i	$0.322753\pi$
$440$	−11.0149	+	7.24464i	−0.525117	+	0.345375i
$441$		0			0
$442$	−0.372586	+	6.39705i	−0.0177221	+	0.304277i
$443$	−5.18169	+	15.1441i	−0.246190	+	0.719516i	0.751988	+	0.659176i	$0.229095\pi$
$443$	−5.18169	+	15.1441i	−0.246190	+	0.719516i	−0.998178	+	0.0603398i	$0.980782\pi$
$444$		0			0
$445$	−0.373513	+	0.709097i	−0.0177062	+	0.0336144i
$446$	−10.5211	−	16.6929i	−0.498189	−	0.790430i
$447$		0			0
$448$	−9.77754	+	1.92025i	−0.461945	+	0.0907231i
$449$	−25.1955	−	16.5713i	−1.18905	−	0.782049i	−0.208441	−	0.978035i	$-0.566839\pi$
$449$	−25.1955	−	16.5713i	−1.18905	−	0.782049i	−0.980607	+	0.195986i	$0.937209\pi$
$450$		0			0
$451$	10.3936	+	5.21986i	0.489415	+	0.245794i
$452$	−6.04147	−	23.4544i	−0.284167	−	1.10320i
$453$		0			0
$454$	3.94951	+	0.775658i	0.185360	+	0.0364034i
$455$	17.0759	+	16.7480i	0.800533	+	0.785157i
$456$		0			0
$457$	−0.0172644	−	0.126398i	−0.000807595	−	0.00591264i	0.990392	−	0.138287i	$-0.0441596\pi$
$457$	−0.0172644	−	0.126398i	−0.000807595	−	0.00591264i	−0.991200	+	0.132374i	$0.957740\pi$
$458$	−15.2657	+	5.55625i	−0.713318	+	0.259627i
$459$		0			0
$460$	3.96678	+	1.44379i	0.184952	+	0.0673171i
$461$	−5.12677	+	23.6678i	−0.238777	+	1.10232i	0.687708	+	0.725988i	$0.258617\pi$
$461$	−5.12677	+	23.6678i	−0.238777	+	1.10232i	−0.926485	+	0.376331i	$0.877185\pi$
$462$		0			0
$463$	−7.86262	+	5.61986i	−0.365407	+	0.261177i	−0.749342	−	0.662183i	$-0.769630\pi$
$463$	−7.86262	+	5.61986i	−0.365407	+	0.261177i	0.383936	+	0.923360i	$0.374568\pi$
$464$	−0.0138942	+	0.716379i	−0.000645020	+	0.0332571i
$465$		0			0
$466$	−1.24274	−	1.81196i	−0.0575688	−	0.0839373i
$467$	13.8484	−	3.28214i	0.640829	−	0.151879i	0.102660	−	0.994716i	$-0.467265\pi$
$467$	13.8484	−	3.28214i	0.640829	−	0.151879i	0.538168	+	0.842837i	$0.319116\pi$
$468$		0			0
$469$	−9.34930	−	31.2288i	−0.431710	−	1.44201i
$470$	−7.56126	−	1.18256i	−0.348775	−	0.0545474i
$471$		0			0
$472$	38.1109	−	15.5700i	1.75420	−	0.716668i
$473$	−14.9252	−	4.78558i	−0.686262	−	0.220041i
$474$		0			0
$475$	0.135756	+	6.99954i	0.00622891	+	0.321161i
$476$	−2.52527	−	3.39202i	−0.115745	−	0.155473i
$477$		0			0
$478$	−20.9814	−	2.45238i	−0.959669	−	0.112169i
$479$	−0.699242	+	0.317845i	−0.0319492	+	0.0145227i	−0.429722	−	0.902961i	$-0.641388\pi$
$479$	−0.699242	+	0.317845i	−0.0319492	+	0.0145227i	0.397772	+	0.917484i	$0.369783\pi$
$480$		0			0
$481$	13.1584	+	16.3139i	0.599972	+	0.743849i
$482$	−0.290501	−	0.0225795i	−0.0132320	−	0.00102847i
$483$		0			0
$484$	−3.96519	−	0.153867i	−0.180236	−	0.00699397i
$485$	3.83231			0.174016
$486$		0			0
$487$	20.2541			0.917803			0.458902	−	0.888487i	$-0.348243\pi$
$487$	20.2541			0.917803			0.458902	+	0.888487i	$0.348243\pi$
$488$	−9.65067	−	0.374490i	−0.436865	−	0.0169524i
$489$		0			0
$490$	−1.57769	−	0.122628i	−0.0712729	−	0.00553977i
$491$	−8.57230	−	10.6280i	−0.386862	−	0.479634i	0.547068	−	0.837088i	$-0.315744\pi$
$491$	−8.57230	−	10.6280i	−0.386862	−	0.479634i	−0.933931	+	0.357454i	$0.883645\pi$
$492$		0			0
$493$	2.52909	−	1.14961i	0.113904	−	0.0517759i
$494$	15.8546	+	1.85314i	0.713333	+	0.0833767i
$495$		0			0
$496$	−0.873710	−	1.17360i	−0.0392307	−	0.0526960i
$497$	0.0514422	+	2.65234i	0.00230750	+	0.118974i
$498$		0			0
$499$	−32.1452	−	10.3069i	−1.43901	−	0.461402i	−0.519505	−	0.854468i	$-0.673884\pi$
$499$	−32.1452	−	10.3069i	−1.43901	−	0.461402i	−0.919510	+	0.393066i	$0.871414\pi$
$500$	−14.6732	+	5.99466i	−0.656205	+	0.268089i
$501$		0			0
$502$	−12.7592	−	1.99550i	−0.569471	−	0.0890636i
$503$	5.73460	+	19.1549i	0.255693	+	0.854075i	0.985391	+	0.170306i	$0.0544755\pi$
$503$	5.73460	+	19.1549i	0.255693	+	0.854075i	−0.729698	+	0.683770i	$0.760339\pi$
$504$		0			0
$505$	32.3247	−	7.66108i	1.43843	−	0.340914i
$506$	2.51062	+	3.66057i	0.111611	+	0.162732i
$507$		0			0
$508$	−0.271750	+	14.0114i	−0.0120570	+	0.621654i
$509$	3.97964	−	2.84448i	0.176394	−	0.126079i	−0.489868	−	0.871797i	$-0.662955\pi$
$509$	3.97964	−	2.84448i	0.176394	−	0.126079i	0.666262	+	0.745718i	$0.267893\pi$
$510$		0			0
$511$	3.27365	−	15.1128i	0.144818	−	0.668552i
$512$	3.63457	+	1.32287i	0.160627	+	0.0584633i
$513$		0			0
$514$	−7.40702	+	2.69593i	−0.326710	+	0.118913i
$515$	−4.56175	−	33.3979i	−0.201015	−	1.47169i
$516$		0			0
$517$	10.9439	+	10.7337i	0.481314	+	0.472069i
$518$	7.12517	+	1.39934i	0.313062	+	0.0614833i
$519$		0			0
$520$	6.76201	+	26.2517i	0.296534	+	1.15121i
$521$	17.5217	+	8.79971i	0.767638	+	0.385522i	0.789114	−	0.614247i	$-0.210540\pi$
$521$	17.5217	+	8.79971i	0.767638	+	0.385522i	−0.0214759	+	0.999769i	$0.506837\pi$
$522$		0			0
$523$	−5.03681	−	3.31276i	−0.220244	−	0.144857i	0.434593	−	0.900627i	$-0.356892\pi$
$523$	−5.03681	−	3.31276i	−0.220244	−	0.144857i	−0.654837	+	0.755770i	$0.727263\pi$
$524$	−15.0455	+	2.95485i	−0.657267	+	0.129083i
$525$		0			0
$526$	8.00977	+	12.7084i	0.349243	+	0.554111i
$527$	−2.64380	+	5.01913i	−0.115166	+	0.218637i
$528$		0			0
$529$	−6.28411	+	18.3660i	−0.273222	+	0.798522i
$530$	−0.317333	+	5.44840i	−0.0137841	+	0.236663i
$531$		0			0
$532$	−8.80125	+	5.78867i	−0.381582	+	0.250971i
$533$	17.0737	−	16.7458i	0.739544	−	0.725340i
$534$		0			0
$535$	8.03282	−	9.20459i	0.347289	−	0.397949i
$536$	9.21597	−	35.7786i	0.398069	−	1.54540i
$537$		0			0
$538$	21.2616	+	8.68632i	0.916652	+	0.374494i
$539$	2.42807	+	2.03739i	0.104584	+	0.0877566i
$540$		0			0
$541$	12.3245	−	10.3415i	0.529872	−	0.444615i	−0.338185	−	0.941080i	$-0.609813\pi$
$541$	12.3245	−	10.3415i	0.529872	−	0.444615i	0.868057	+	0.496464i	$0.165369\pi$
$542$	19.7505	−	6.33275i	0.848357	−	0.272015i
$543$		0			0
$544$	−0.744238	−	7.65144i	−0.0319090	−	0.328053i
$545$	−16.9227	+	9.33754i	−0.724888	+	0.399976i
$546$		0			0
$547$	−17.4553	+	1.35673i	−0.746334	+	0.0580096i	−0.445026	−	0.895517i	$-0.646806\pi$
$547$	−17.4553	+	1.35673i	−0.746334	+	0.0580096i	−0.301307	+	0.953527i	$0.597423\pi$
$548$	−9.42651	−	9.99152i	−0.402681	−	0.426816i
$549$		0			0
$550$	−4.81777	−	1.14183i	−0.205430	−	0.0486879i
$551$	−2.49260	−	6.45600i	−0.106188	−	0.275035i
$552$		0			0
$553$	−4.97160	+	36.3986i	−0.211414	+	1.54782i
$554$	2.11042	+	9.74280i	0.0896633	+	0.413932i
$555$		0			0
$556$	−7.85852	−	4.33615i	−0.333276	−	0.183894i
$557$	5.10891	−	11.8438i	0.216472	−	0.501838i	−0.775031	−	0.631923i	$-0.782266\pi$
$557$	5.10891	−	11.8438i	0.216472	−	0.501838i	0.991503	+	0.130085i	$0.0415251\pi$
$558$		0			0
$559$	−19.2453	+	25.8510i	−0.813991	+	1.09338i
$560$	−1.14955	−	0.821651i	−0.0485774	−	0.0347211i
$561$		0			0
$562$	13.6590	−	2.13624i	0.576172	−	0.0901117i
$563$	15.3931	+	32.1919i	0.648741	+	1.35673i	0.919122	+	0.393974i	$0.128900\pi$
$563$	15.3931	+	32.1919i	0.648741	+	1.35673i	−0.270380	+	0.962754i	$0.587149\pi$
$564$		0			0
$565$	−16.7309	+	26.5454i	−0.703874	+	1.11677i
$566$	6.27246	+	10.8642i	0.263651	+	0.456657i
$567$		0			0
$568$	−1.50335	+	2.60388i	−0.0630791	+	0.109256i
$569$	12.3634	+	23.4714i	0.518302	+	0.983972i	0.994510	+	0.104640i	$0.0333690\pi$
$569$	12.3634	+	23.4714i	0.518302	+	0.983972i	−0.476208	+	0.879333i	$0.657989\pi$
$570$		0			0
$571$	15.0871	−	21.9976i	0.631377	−	0.920571i	−0.368582	−	0.929595i	$-0.620157\pi$
$571$	15.0871	−	21.9976i	0.631377	−	0.920571i	0.999959	+	0.00902452i	$0.00287263\pi$
$572$	7.74540	−	20.0611i	0.323851	−	0.838796i
$573$		0			0
$574$	0.802113	−	8.24644i	0.0334795	−	0.344200i
$575$	1.58549	+	3.67557i	0.0661194	+	0.153282i
$576$		0			0
$577$	26.2986	−	3.07386i	1.09482	−	0.127967i	0.450542	−	0.892755i	$-0.351231\pi$
$577$	26.2986	−	3.07386i	1.09482	−	0.127967i	0.644281	+	0.764789i	$0.277157\pi$
$578$	10.8204	−	6.53013i	0.450068	−	0.271618i
$579$		0			0
$580$	3.44695	−	3.12794i	0.143127	−	0.129881i
$581$	−12.9234	−	10.0164i	−0.536152	−	0.415549i
$582$		0			0
$583$	6.86294	−	8.50872i	0.284234	−	0.352395i
$584$	12.0270	−	12.7479i	0.497682	−	0.527512i
$585$		0			0
$586$	1.75150	−	5.85043i	0.0723540	−	0.241679i
$587$	−1.66834	+	3.48904i	−0.0688598	+	0.144008i	−0.933719	−	0.358006i	$-0.883457\pi$
$587$	−1.66834	+	3.48904i	−0.0688598	+	0.144008i	0.864860	+	0.502014i	$0.167407\pi$
$588$		0			0
$589$	12.0989	+	7.30174i	0.498528	+	0.300863i
$590$	−19.2299	−	8.74104i	−0.791681	−	0.359863i
$591$		0			0
$592$	−0.916935	−	0.832075i	−0.0376858	−	0.0341981i
$593$	0.264372	+	1.49933i	0.0108564	+	0.0615700i	0.989755	−	0.142778i	$-0.0456036\pi$
$593$	0.264372	+	1.49933i	0.0108564	+	0.0615700i	−0.978898	+	0.204348i	$0.934492\pi$
$594$		0			0
$595$	−0.951345	+	5.39535i	−0.0390013	+	0.221188i
$596$	−21.1683	+	16.4066i	−0.867086	+	0.672042i
$597$		0			0
$598$	8.79275	−	2.44763i	0.359562	−	0.100091i
$599$	−9.98908	−	29.1942i	−0.408143	−	1.19284i	−0.938563	−	0.345108i	$-0.887842\pi$
$599$	−9.98908	−	29.1942i	−0.408143	−	1.19284i	0.530420	−	0.847735i	$-0.322034\pi$
$600$		0			0
$601$	8.07580	+	2.24805i	0.329419	+	0.0917000i	0.428933	−	0.903336i	$-0.358889\pi$
$601$	8.07580	+	2.24805i	0.329419	+	0.0917000i	−0.0995146	+	0.995036i	$0.531729\pi$
$602$	0.649211	+	11.1465i	0.0264599	+	0.454299i
$603$		0			0
$604$	15.0898	−	7.57839i	0.613996	−	0.308360i
$605$	3.38026	+	3.87335i	0.137427	+	0.157474i
$606$		0			0
$607$	−8.65351	+	0.335796i	−0.351235	+	0.0136295i	−0.213789	−	0.976880i	$-0.568581\pi$
$607$	−8.65351	+	0.335796i	−0.351235	+	0.0136295i	−0.137446	+	0.990509i	$0.543889\pi$
$608$	−19.1359	+	0.742559i	−0.776062	+	0.0301147i
$609$		0			0
$610$	3.25828	+	3.73357i	0.131924	+	0.151168i
$611$	28.1671	−	14.1461i	1.13952	−	0.572288i
$612$		0			0
$613$	0.149667	+	2.56968i	0.00604499	+	0.103789i	0.999981	−	0.00617196i	$-0.00196461\pi$
$613$	0.149667	+	2.56968i	0.00604499	+	0.103789i	−0.993936	+	0.109960i	$0.964928\pi$
$614$	−19.7766	−	5.50519i	−0.798118	−	0.222171i
$615$		0			0
$616$	−6.08991	−	17.7984i	−0.245370	−	0.717120i
$617$	28.6226	−	7.96764i	1.15230	−	0.320765i	0.361223	−	0.932479i	$-0.382359\pi$
$617$	28.6226	−	7.96764i	1.15230	−	0.320765i	0.791079	+	0.611714i	$0.209520\pi$
$618$		0			0
$619$	8.23745	−	6.38451i	0.331091	−	0.256615i	−0.433467	−	0.901169i	$-0.642710\pi$
$619$	8.23745	−	6.38451i	0.331091	−	0.256615i	0.764559	+	0.644554i	$0.222957\pi$
$620$	−1.65047	+	9.36028i	−0.0662844	+	0.375918i
$621$		0			0
$622$	−3.94590	−	22.3783i	−0.158216	−	0.897288i
$623$	−0.846858	−	0.768483i	−0.0339286	−	0.0307886i
$624$		0			0
$625$	9.07595	+	4.12553i	0.363038	+	0.165021i
$626$	−19.4129	−	11.7158i	−0.775897	−	0.468256i
$627$		0			0
$628$	−10.2017	+	21.3350i	−0.407091	+	0.851359i
$629$	−1.37688	+	4.59910i	−0.0548998	+	0.183378i
$630$		0			0
$631$	7.17672	−	7.60688i	0.285701	−	0.302825i	−0.568589	−	0.822621i	$-0.692511\pi$
$631$	7.17672	−	7.60688i	0.285701	−	0.302825i	0.854290	+	0.519796i	$0.173992\pi$
$632$	−26.1400	+	32.4085i	−1.03979	+	1.28914i
$633$		0			0
$634$	−1.32452	−	1.02658i	−0.0526034	−	0.0407707i
$635$	13.4451	−	12.2008i	0.533552	−	0.484173i
$636$		0			0
$637$	5.57996	−	3.36752i	0.221086	−	0.133426i
$638$	4.86129	−	0.568203i	0.192460	−	0.0224954i
$639$		0			0
$640$	−5.48469	−	12.7149i	−0.216802	−	0.502602i
$641$	1.32195	−	13.5909i	0.0522140	−	0.536807i	−0.932322	−	0.361628i	$-0.882221\pi$
$641$	1.32195	−	13.5909i	0.0522140	−	0.536807i	0.984537	−	0.175179i	$-0.0560505\pi$
$642$		0			0
$643$	−1.76665	+	4.57573i	−0.0696697	+	0.180449i	−0.963345	−	0.268265i	$-0.913550\pi$
$643$	−1.76665	+	4.57573i	−0.0696697	+	0.180449i	0.893676	+	0.448714i	$0.148118\pi$
$644$	−3.40681	+	4.96725i	−0.134247	+	0.195737i
$645$		0			0
$646$	1.70399	+	3.23495i	0.0670426	+	0.127277i
$647$	−5.23619	+	9.06935i	−0.205856	+	0.356553i	−0.950405	−	0.311015i	$-0.899331\pi$
$647$	−5.23619	+	9.06935i	−0.205856	+	0.356553i	0.744549	+	0.667568i	$0.232664\pi$
$648$		0			0
$649$	21.1547	+	36.6411i	0.830396	+	1.43829i
$650$	−5.42840	+	8.61275i	−0.212919	+	0.337820i
$651$		0			0
$652$	−8.64720	−	18.0841i	−0.338650	−	0.708227i
$653$	49.7505	−	7.78084i	1.94689	−	0.304488i	0.947027	−	0.321155i	$-0.104071\pi$
$653$	49.7505	−	7.78084i	1.94689	−	0.304488i	0.999861	+	0.0166676i	$0.00530572\pi$
$654$		0			0
$655$	16.1607	+	11.5510i	0.631453	+	0.451335i
$656$	−0.843677	+	1.13325i	−0.0329400	+	0.0442461i
$657$		0			0
$658$	4.32519	−	10.0269i	0.168613	−	0.390890i
$659$	37.0590	+	20.4483i	1.44361	+	0.796553i	0.995255	−	0.0973001i	$-0.0310206\pi$
$659$	37.0590	+	20.4483i	1.44361	+	0.796553i	0.448360	+	0.893853i	$0.352008\pi$
$660$		0			0
$661$	−1.21892	−	5.62718i	−0.0474107	−	0.218872i	0.947482	−	0.319809i	$-0.103619\pi$
$661$	−1.21892	−	5.62718i	−0.0474107	−	0.218872i	−0.994893	+	0.100936i	$0.967816\pi$
$662$	−0.375836	+	2.75160i	−0.0146073	+	0.106944i
$663$		0			0
$664$	−6.67464	−	17.2878i	−0.259026	−	0.670895i
$665$	13.2797	+	3.14734i	0.514964	+	0.122049i
$666$		0			0
$667$	−2.71545	−	2.87821i	−0.105143	−	0.111445i
$668$	25.0517	−	1.94717i	0.969280	−	0.0753384i
$669$		0			0
$670$	−16.5978	+	9.15830i	−0.641231	+	0.353816i
$671$	−0.960900	−	9.87892i	−0.0370951	−	0.381371i
$672$		0			0
$673$	−32.0448	+	10.2747i	−1.23524	+	0.396062i	−0.850013	−	0.526762i	$-0.823406\pi$
$673$	−32.0448	+	10.2747i	−1.23524	+	0.396062i	−0.385222	+	0.922824i	$0.625875\pi$
$674$	9.67851	−	8.12123i	0.372802	−	0.312818i
$675$		0			0
$676$	−20.8118	−	17.4631i	−0.800453	−	0.671660i
$677$	−23.4758	−	9.59093i	−0.902249	−	0.368609i	−0.120872	−	0.992668i	$-0.538569\pi$
$677$	−23.4758	−	9.59093i	−0.902249	−	0.368609i	−0.781377	+	0.624059i	$0.785483\pi$
$678$		0			0
$679$	−1.36399	+	5.29532i	−0.0523450	+	0.203216i
$680$	−4.08278	+	4.67835i	−0.156567	+	0.179406i
$681$		0			0
$682$	−7.13520	+	6.99815i	−0.273221	+	0.267973i
$683$	−12.7392	+	8.37868i	−0.487450	+	0.320601i	−0.769333	−	0.638848i	$-0.779411\pi$
$683$	−12.7392	+	8.37868i	−0.487450	+	0.320601i	0.281883	+	0.959449i	$0.409041\pi$
$684$		0			0
$685$	−1.03475	+	17.7660i	−0.0395358	+	0.678803i
$686$	5.28963	−	15.4595i	0.201959	−	0.590248i
$687$		0			0
$688$	0.887312	−	1.68452i	0.0338285	−	0.0642217i
$689$	−11.9851	−	19.0156i	−0.456594	−	0.724436i
$690$		0			0
$691$	28.6061	−	5.61806i	1.08823	−	0.213721i	0.383743	−	0.923440i	$-0.374635\pi$
$691$	28.6061	−	5.61806i	1.08823	−	0.213721i	0.704485	+	0.709719i	$0.251178\pi$
$692$	6.88102	+	4.52572i	0.261577	+	0.172042i
$693$		0			0
$694$	−12.1017	−	6.07771i	−0.459375	−	0.230707i
$695$	2.90051	+	11.2605i	0.110023	+	0.427134i
$696$		0			0
$697$	5.37518	+	1.05565i	0.203599	+	0.0399856i
$698$	0.673074	+	0.660147i	0.0254762	+	0.0249869i
$699$		0			0
$700$	−0.909240	−	6.65681i	−0.0343660	−	0.251604i
$701$	32.9265	−	11.9843i	1.24362	−	0.452640i	0.365377	−	0.930860i	$-0.380940\pi$
$701$	32.9265	−	11.9843i	1.24362	−	0.452640i	0.878240	+	0.478220i	$0.158718\pi$
$702$		0			0
$703$	11.2379	+	4.09026i	0.423845	+	0.154267i
$704$	2.45711	−	11.3433i	0.0926058	−	0.427516i
$705$		0			0
$706$	−18.3569	+	13.1207i	−0.690870	+	0.493804i
$707$	−0.919156	+	47.3914i	−0.0345684	+	1.78234i
$708$		0			0
$709$	11.7259	+	17.0967i	0.440374	+	0.642082i	0.979807	−	0.199947i	$-0.0640771\pi$
$709$	11.7259	+	17.0967i	0.440374	+	0.642082i	−0.539432	+	0.842029i	$0.681361\pi$
$710$	1.50112	−	0.355773i	0.0563361	−	0.0133519i
$711$		0			0
$712$	−0.371725	−	1.24165i	−0.0139310	−	0.0465327i
$713$	7.98307	+	1.24853i	0.298968	+	0.0467578i
$714$		0			0
$715$	−25.7905	+	10.5366i	−0.964508	+	0.394045i
$716$	28.9692	+	9.28861i	1.08263	+	0.347132i
$717$		0			0
$718$	0.107545	+	5.54499i	0.00401354	+	0.206937i
$719$	−6.43239	−	8.64020i	−0.239888	−	0.322225i	0.665832	−	0.746101i	$-0.268077\pi$
$719$	−6.43239	−	8.64020i	−0.239888	−	0.322225i	−0.905720	+	0.423876i	$0.860669\pi$
$720$		0			0
$721$	47.7713	+	5.58367i	1.77910	+	0.207947i
$722$	−6.06060	+	2.75488i	−0.225552	+	0.102526i
$723$		0			0
$724$	13.1158	+	16.2611i	0.487447	+	0.604339i
$725$	4.40052	+	0.342036i	0.163431	+	0.0127029i
$726$		0			0
$727$	−49.5520	−	1.92284i	−1.83778	−	0.0713144i	−0.903657	−	0.428257i	$-0.859128\pi$
$727$	−49.5520	−	1.92284i	−1.83778	−	0.0713144i	−0.934126	+	0.356942i	$0.883819\pi$
$728$	−38.6801			−1.43358
$729$		0			0
$730$	−8.99238			−0.332823
$731$	−7.37645	−	0.286240i	−0.272828	−	0.0105870i
$732$		0			0
$733$	5.25796	+	0.408681i	0.194207	+	0.0150950i	0.174228	−	0.984705i	$-0.444257\pi$
$733$	5.25796	+	0.408681i	0.194207	+	0.0150950i	0.0199797	+	0.999800i	$0.493640\pi$
$734$	−8.77001	−	10.8731i	−0.323707	−	0.401334i
$735$		0			0
$736$	−9.96823	+	4.53112i	−0.367434	+	0.167019i
$737$	37.7135	+	4.40807i	1.38919	+	0.162373i
$738$		0			0
$739$	27.4491	+	36.8706i	1.00973	+	1.35631i	0.933247	+	0.359235i	$0.116962\pi$
$739$	27.4491	+	36.8706i	1.00973	+	1.35631i	0.0764853	+	0.997071i	$0.475630\pi$
$740$	0.155975	+	8.04204i	0.00573376	+	0.295631i
$741$		0			0
$742$	−7.41541	−	2.37766i	−0.272228	−	0.0872865i
$743$	−10.1345	+	4.14039i	−0.371798	+	0.151896i	−0.556394	−	0.830918i	$-0.687816\pi$
$743$	−10.1345	+	4.14039i	−0.371798	+	0.151896i	0.184597	+	0.982814i	$0.440902\pi$
$744$		0			0
$745$	34.2804	+	5.36135i	1.25594	+	0.196425i
$746$	−1.12493	−	3.75752i	−0.0411865	−	0.137573i
$747$		0			0
$748$	4.79290	−	1.13594i	0.175246	−	0.0415340i
$749$	9.85947	+	14.3755i	0.360257	+	0.525268i
$750$		0			0
$751$	0.0250965	−	1.29397i	0.000915784	−	0.0472176i	−0.999075	−	0.0429947i	$-0.986310\pi$
$751$	0.0250965	−	1.29397i	0.000915784	−	0.0472176i	0.999991	−	0.00422286i	$-0.00134418\pi$
$752$	−1.51490	+	1.08278i	−0.0552426	+	0.0394850i
$753$		0			0
$754$	2.13055	−	9.83572i	0.0775901	−	0.358196i
$755$	−20.5571	−	7.48216i	−0.748148	−	0.272304i
$756$		0			0
$757$	−25.7720	+	9.38023i	−0.936698	+	0.340930i	−0.764861	−	0.644195i	$-0.777192\pi$
$757$	−25.7720	+	9.38023i	−0.936698	+	0.340930i	−0.171837	+	0.985125i	$0.554970\pi$
$758$	−1.67503	−	12.2634i	−0.0608399	−	0.445427i
$759$		0			0
$760$	11.0430	+	10.8309i	0.400573	+	0.392879i
$761$	6.69214	+	1.31429i	0.242590	+	0.0476431i	0.312529	−	0.949908i	$-0.398824\pi$
$761$	6.69214	+	1.31429i	0.242590	+	0.0476431i	−0.0699393	+	0.997551i	$0.522281\pi$
$762$		0			0
$763$	−6.87912	−	26.7064i	−0.249041	−	0.966836i
$764$	9.55020	+	4.79629i	0.345514	+	0.173524i
$765$		0			0
$766$	10.2660	+	6.75205i	0.370926	+	0.243962i
$767$	85.3660	−	16.7653i	3.08239	−	0.605361i
$768$		0			0
$769$	1.22149	+	1.93802i	0.0440480	+	0.0698869i	0.867288	−	0.497806i	$-0.165861\pi$
$769$	1.22149	+	1.93802i	0.0440480	+	0.0698869i	−0.823240	+	0.567693i	$0.807836\pi$
$770$	−4.49824	+	8.53970i	−0.162105	+	0.307750i
$771$		0			0
$772$	6.02725	−	17.6153i	0.216925	−	0.633988i
$773$	0.732487	−	12.5763i	0.0263457	−	0.452339i	−0.959178	−	0.282802i	$-0.908736\pi$
$773$	0.732487	−	12.5763i	0.0263457	−	0.452339i	0.985524	−	0.169536i	$-0.0542270\pi$
$774$		0			0
$775$	−7.53017	+	4.95267i	−0.270492	+	0.177905i
$776$	−4.42461	+	4.33963i	−0.158834	+	0.155784i
$777$		0			0
$778$	−12.3752	+	14.1804i	−0.443673	+	0.508392i
$779$	3.40381	−	13.2144i	0.121954	−	0.473455i
$780$		0			0
$781$	−2.86049	−	1.16864i	−0.102357	−	0.0418172i
$782$	1.60149	+	1.34381i	0.0572691	+	0.0480544i
$783$		0			0
$784$	−0.294944	+	0.247488i	−0.0105337	+	0.00883885i
$785$	29.1747	−	9.35448i	1.04129	−	0.333876i
$786$		0			0
$787$	2.96392	+	30.4718i	0.105652	+	1.08620i	0.886894	+	0.461973i	$0.152858\pi$
$787$	2.96392	+	30.4718i	0.105652	+	1.08620i	−0.781242	+	0.624229i	$0.785413\pi$
$788$	18.8470	−	10.3994i	0.671398	−	0.370462i
$789$		0			0
$790$	21.2991	−	1.65550i	0.757789	−	0.0589000i
$791$	−30.7244	−	32.5659i	−1.09243	−	1.15791i
$792$		0			0
$793$	−19.8588	−	4.70662i	−0.705206	−	0.167137i
$794$	−9.75970	−	25.2783i	−0.346359	−	0.897092i
$795$		0			0
$796$	−0.341055	+	2.49696i	−0.0120884	+	0.0885025i
$797$	2.69653	+	12.4486i	0.0955159	+	0.440951i	0.999899	+	0.0142286i	$0.00452926\pi$
$797$	2.69653	+	12.4486i	0.0955159	+	0.440951i	−0.904383	+	0.426722i	$0.859668\pi$
$798$		0			0
$799$	6.32131	+	3.48795i	0.223632	+	0.123395i
$800$	4.83764	−	11.2149i	0.171036	−	0.396507i
$801$		0			0
$802$	2.25333	−	3.02674i	0.0795678	−	0.106878i
$803$	14.6533	+	10.4736i	0.517105	+	0.369604i
$804$		0			0
$805$	7.70967	−	1.20577i	0.271730	−	0.0424978i
$806$	8.86507	+	18.5397i	0.312259	+	0.653034i
$807$		0			0
$808$	−28.6453	+	45.4489i	−1.00774	+	1.59889i
$809$	−2.00650	−	3.47537i	−0.0705449	−	0.122187i	0.828595	−	0.559848i	$-0.189140\pi$
$809$	−2.00650	−	3.47537i	−0.0705449	−	0.122187i	−0.899140	+	0.437661i	$0.855807\pi$
$810$		0			0
$811$	16.4745	−	28.5346i	0.578497	−	1.00199i	−0.417155	−	0.908835i	$-0.636973\pi$
$811$	16.4745	−	28.5346i	0.578497	−	1.00199i	0.995652	−	0.0931510i	$-0.0296939\pi$
$812$	3.09522	+	5.87613i	0.108621	+	0.206212i
$813$		0			0
$814$	−4.78383	+	6.97499i	−0.167673	+	0.244473i
$815$	−9.35355	+	24.2263i	−0.327641	+	0.848611i
$816$		0			0
$817$	−1.78027	+	18.3028i	−0.0622837	+	0.640332i
$818$	0.833103	+	1.93135i	0.0291288	+	0.0675281i
$819$		0			0
$820$	9.11590	−	1.06550i	0.318341	−	0.0372087i
$821$	−13.9383	+	8.41178i	−0.486448	+	0.293573i	−0.738635	−	0.674105i	$-0.764529\pi$
$821$	−13.9383	+	8.41178i	−0.486448	+	0.293573i	0.252187	+	0.967679i	$0.418850\pi$
$822$		0			0
$823$	2.48296	−	2.25317i	0.0865507	−	0.0785405i	−0.627584	−	0.778549i	$-0.715956\pi$
$823$	2.48296	−	2.25317i	0.0865507	−	0.0785405i	0.714135	+	0.700008i	$0.246820\pi$
$824$	43.0859	+	33.3941i	1.50097	+	1.16334i
$825$		0			0
$826$	18.9222	−	23.4599i	0.658388	−	0.816273i
$827$	−12.6242	+	13.3808i	−0.438985	+	0.465297i	−0.908657	−	0.417544i	$-0.862891\pi$
$827$	−12.6242	+	13.3808i	−0.438985	+	0.465297i	0.469671	+	0.882841i	$0.344372\pi$
$828$		0			0
$829$	−2.90649	+	9.70835i	−0.100947	+	0.337185i	−0.993511	−	0.113735i	$-0.963719\pi$
$829$	−2.90649	+	9.70835i	−0.100947	+	0.337185i	0.892565	+	0.450919i	$0.148904\pi$
$830$	−4.10177	+	8.57812i	−0.142374	+	0.297751i
$831$		0			0
$832$	−20.4324	−	12.3310i	−0.708366	−	0.427501i
$833$	1.35902	+	0.617750i	0.0470872	+	0.0214038i
$834$		0			0
$835$	−24.1072	−	21.8761i	−0.834264	−	0.757054i
$836$	−2.13070	−	12.0838i	−0.0736918	−	0.417927i
$837$		0			0
$838$	−0.985794	+	5.59072i	−0.0340537	+	0.193128i
$839$	−19.1875	+	14.8715i	−0.662427	+	0.513420i	−0.887432	−	0.460938i	$-0.847513\pi$
$839$	−19.1875	+	14.8715i	−0.662427	+	0.513420i	0.225005	+	0.974358i	$0.427760\pi$
$840$		0			0
$841$	23.7345	−	6.60694i	0.818430	−	0.227825i
$842$	1.00725	+	2.94381i	0.0347122	+	0.101450i
$843$		0			0
$844$	3.03197	+	0.844005i	0.104365	+	0.0290519i
$845$	2.04652	+	35.1374i	0.0704025	+	1.20876i
$846$		0			0
$847$	−6.55512	+	3.29210i	−0.225236	+	0.113118i
$848$	0.873112	+	1.00048i	0.0299828	+	0.0343565i
$849$		0			0
$850$	−2.33018	+	0.0904217i	−0.0799246	+	0.00310144i
$851$	6.83284	−	0.265145i	0.234227	−	0.00908906i
$852$		0			0
$853$	22.1129	+	25.3385i	0.757130	+	0.867575i	0.994596	−	0.103821i	$-0.0331068\pi$
$853$	22.1129	+	25.3385i	0.757130	+	0.867575i	−0.237466	+	0.971396i	$0.576317\pi$
$854$	−6.31855	+	3.17330i	−0.216216	+	0.108588i
$855$		0			0
$856$	1.14876	+	19.7234i	0.0392637	+	0.674132i
$857$	−2.16587	−	0.602911i	−0.0739846	−	0.0205950i	0.230983	−	0.972958i	$-0.425806\pi$
$857$	−2.16587	−	0.602911i	−0.0739846	−	0.0205950i	−0.304967	+	0.952363i	$0.598645\pi$
$858$		0			0
$859$	−15.8070	−	46.1976i	−0.539327	−	1.57624i	−0.793172	−	0.608998i	$-0.791572\pi$
$859$	−15.8070	−	46.1976i	−0.539327	−	1.57624i	0.253844	−	0.967245i	$-0.418305\pi$
$860$	−11.9153	+	3.31684i	−0.406307	+	0.113103i
$861$		0			0
$862$	16.5789	−	12.8496i	0.564679	−	0.437659i
$863$	3.21521	−	18.2344i	0.109447	−	0.620706i	−0.879903	−	0.475153i	$-0.842393\pi$
$863$	3.21521	−	18.2344i	0.109447	−	0.620706i	0.989350	−	0.145553i	$-0.0464961\pi$
$864$		0			0
$865$	−1.85282	−	10.5079i	−0.0629978	−	0.357278i
$866$	−14.5614	−	13.2138i	−0.494817	−	0.449023i
$867$		0			0
$868$	−12.3462	−	5.61203i	−0.419056	−	0.190485i
$869$	−36.6357	−	22.1098i	−1.24278	−	0.750022i
$870$		0			0
$871$	33.6802	−	70.4361i	1.14121	−	2.38664i
$872$	8.96452	−	29.9436i	0.303577	−	1.01402i
$873$		0			0
$874$	3.57383	−	3.78803i	0.120886	−	0.128132i
$875$	−18.3952	+	22.8064i	−0.621870	+	0.770998i
$876$		0			0
$877$	26.8867	+	20.8388i	0.907900	+	0.703675i	0.955437	−	0.295194i	$-0.0953843\pi$
$877$	26.8867	+	20.8388i	0.907900	+	0.703675i	−0.0475376	+	0.998869i	$0.515137\pi$
$878$	−5.59072	+	5.07331i	−0.188678	+	0.171216i
$879$		0			0
$880$	1.40913	−	0.850412i	0.0475016	−	0.0286674i
$881$	−10.2578	+	1.19896i	−0.345593	+	0.0403940i	−0.287119	−	0.957895i	$-0.592697\pi$
$881$	−10.2578	+	1.19896i	−0.345593	+	0.0403940i	−0.0584738	+	0.998289i	$0.518623\pi$
$882$		0			0
$883$	−4.16843	−	9.66350i	−0.140279	−	0.325203i	0.833565	−	0.552421i	$-0.186296\pi$
$883$	−4.16843	−	9.66350i	−0.140279	−	0.325203i	−0.973844	+	0.227219i	$0.927037\pi$
$884$	0.980517	−	10.0806i	0.0329783	−	0.339047i
$885$		0			0
$886$	−4.78357	+	12.3898i	−0.160707	+	0.416242i
$887$	−20.1999	+	29.4522i	−0.678247	+	0.988908i	0.320880	+	0.947120i	$0.396021\pi$
$887$	−20.1999	+	29.4522i	−0.678247	+	0.988908i	−0.999127	+	0.0417879i	$0.986695\pi$
$888$		0			0
$889$	12.0731	+	22.9203i	0.404920	+	0.768721i
$890$	−0.332508	+	0.575920i	−0.0111457	+	0.0193049i
$891$		0			0
$892$	15.5938	+	27.0093i	0.522120	+	0.904339i
$893$	9.58964	−	15.2150i	0.320905	−	0.509151i
$894$		0			0
$895$	−17.0021	−	35.5570i	−0.568319	−	1.18854i
$896$	19.5210	−	3.05303i	0.652152	−	0.101995i
$897$		0			0
$898$	−20.3573	−	14.5505i	−0.679332	−	0.485557i
$899$	5.32034	−	7.14646i	0.177443	−	0.238348i
$900$		0			0
$901$	2.03923	−	4.72748i	0.0679368	−	0.157495i
$902$	8.44976	+	4.66238i	0.281346	+	0.155240i
$903$		0			0
$904$	−10.7427	−	49.5937i	−0.357296	−	1.64946i
$905$	3.66282	−	26.8166i	0.121756	−	0.891413i
$906$		0			0
$907$	−5.89714	−	15.2740i	−0.195811	−	0.507164i	0.799852	−	0.600198i	$-0.204912\pi$
$907$	−5.89714	−	15.2740i	−0.195811	−	0.507164i	−0.995663	+	0.0930336i	$0.970344\pi$
$908$	−6.19026	−	1.46712i	−0.205431	−	0.0486881i
$909$		0			0
$910$	13.6194	+	14.4358i	0.451480	+	0.478540i
$911$	−2.12733	+	0.165349i	−0.0704816	+	0.00547826i	−0.112685	−	0.993631i	$-0.535945\pi$
$911$	−2.12733	+	0.165349i	−0.0704816	+	0.00547826i	0.0422032	+	0.999109i	$0.486562\pi$
$912$		0			0
$913$	16.6750	−	9.20088i	0.551862	−	0.304505i
$914$	−0.0102478	−	0.105356i	−0.000338967	−	0.00348488i
$915$		0			0
$916$	24.4509	−	7.83988i	0.807882	−	0.259037i
$917$	−21.7125	+	18.2190i	−0.717011	+	0.601644i
$918$		0			0
$919$	4.76178	+	3.99561i	0.157077	+	0.131803i	0.717939	−	0.696106i	$-0.245086\pi$
$919$	4.76178	+	3.99561i	0.157077	+	0.131803i	−0.560862	+	0.827909i	$0.689530\pi$
$920$	8.18734	+	3.34490i	0.269929	+	0.110278i
$921$		0			0
$922$	−5.01228	+	19.4589i	−0.165071	+	0.640844i
$923$	−4.17768	+	4.78709i	−0.137510	+	0.157569i
$924$		0			0
$925$	−5.44541	+	5.34082i	−0.179044	+	0.175605i
$926$	−6.69999	+	4.40665i	−0.220175	+	0.144812i
$927$		0			0
$928$	−0.702016	+	12.0531i	−0.0230448	+	0.395664i
$929$	−10.2920	+	30.0795i	−0.337669	+	0.986875i	0.638455	+	0.769660i	$0.279574\pi$
$929$	−10.2920	+	30.0795i	−0.337669	+	0.986875i	−0.976124	+	0.217216i	$0.930303\pi$
$930$		0			0
$931$	1.73310	−	3.29021i	0.0568001	−	0.107832i
$932$	1.85172	+	2.93795i	0.0606550	+	0.0962356i
$933$		0			0
$934$	11.5878	−	2.27577i	0.379165	−	0.0744656i
$935$	−5.33158	−	3.50664i	−0.174361	−	0.114679i
$936$		0			0
$937$	38.4912	+	19.3310i	1.25745	+	0.631517i	0.947658	−	0.319287i	$-0.103443\pi$
$937$	38.4912	+	19.3310i	1.25745	+	0.631517i	0.309795	+	0.950803i	$0.399740\pi$
$938$	−6.74707	−	26.1937i	−0.220300	−	0.855256i
$939$		0			0
$940$	11.8697	+	2.33113i	0.387146	+	0.0760331i
$941$	39.1086	+	38.3575i	1.27490	+	1.25042i	0.952759	+	0.303727i	$0.0982311\pi$
$941$	39.1086	+	38.3575i	1.27490	+	1.25042i	0.322145	+	0.946690i	$0.395596\pi$
$942$		0			0
$943$	−1.05590	−	7.73059i	−0.0343850	−	0.251743i
$944$	−4.82951	+	1.75780i	−0.157187	+	0.0572114i
$945$		0			0
$946$	−12.2211	−	4.44810i	−0.397341	−	0.144620i
$947$	11.5150	−	53.1592i	0.374187	−	1.72744i	−0.270256	−	0.962788i	$-0.587108\pi$
$947$	11.5150	−	53.1592i	0.374187	−	1.72744i	0.644443	−	0.764652i	$-0.277089\pi$
$948$		0			0
$949$	30.1302	−	21.5358i	0.978067	−	0.699080i
$950$	−0.112645	+	5.80794i	−0.00365468	+	0.188434i
$951$		0			0
$952$	−5.01119	−	7.30650i	−0.162414	−	0.236805i
$953$	−37.5245	+	8.89347i	−1.21554	+	0.288088i	−0.787866	−	0.615847i	$-0.788814\pi$
$953$	−37.5245	+	8.89347i	−1.21554	+	0.288088i	−0.427671	+	0.903934i	$0.640666\pi$
$954$		0			0
$955$	−3.97089	−	13.2637i	−0.128495	−	0.429203i
$956$	32.9875	+	5.15916i	1.06689	+	0.166859i
$957$		0			0
$958$	−0.589993	+	0.241039i	−0.0190618	+	0.00778761i
$959$	−24.1799	−	7.75298i	−0.780810	−	0.250357i
$960$		0			0
$961$	−0.248346	−	12.8047i	−0.00801117	−	0.413054i
$962$	10.3852	+	13.9498i	0.334833	+	0.449759i
$963$		0			0
$964$	0.457430	+	0.0534659i	0.0147328	+	0.00172202i
$965$	−21.9581	+	9.98120i	−0.706858	+	0.321306i
$966$		0			0
$967$	24.2460	+	30.0603i	0.779699	+	0.966675i	0.999962	−	0.00876583i	$-0.00279029\pi$
$967$	24.2460	+	30.0603i	0.779699	+	0.966675i	−0.220263	+	0.975441i	$0.570692\pi$
$968$	−8.28880	−	0.644256i	−0.266412	−	0.0207072i
$969$		0			0
$970$	3.17751	+	0.123302i	0.102024	+	0.00395898i
$971$	−35.4817			−1.13866			−0.569332	−	0.822108i	$-0.692798\pi$
$971$	−35.4817			−1.13866			−0.569332	+	0.822108i	$0.692798\pi$
$972$		0			0
$973$	−16.5915			−0.531901
$974$	16.7934	+	0.651662i	0.538097	+	0.0208806i
$975$		0			0
$976$	1.20206	+	0.0934314i	0.0384770	+	0.00299067i
$977$	−22.1388	−	27.4478i	−0.708284	−	0.878134i	0.288565	−	0.957460i	$-0.406822\pi$
$977$	−22.1388	−	27.4478i	−0.708284	−	0.878134i	−0.996849	+	0.0793264i	$0.974723\pi$
$978$		0			0
$979$	1.21261	−	0.551200i	0.0387553	−	0.0176164i
$980$	2.48427	+	0.290370i	0.0793572	+	0.00927553i
$981$		0			0
$982$	−6.76565	−	9.08785i	−0.215901	−	0.290005i
$983$	−0.946634	−	48.8082i	−0.0301929	−	1.55674i	−0.642603	−	0.766199i	$-0.722145\pi$
$983$	−0.946634	−	48.8082i	−0.0301929	−	1.55674i	0.612410	−	0.790540i	$-0.290200\pi$
$984$		0			0
$985$	−26.5557	−	8.51475i	−0.846136	−	0.271303i
$986$	2.13394	−	0.871812i	0.0679586	−	0.0277642i
$987$		0			0
$988$	−24.9270	−	3.89851i	−0.793034	−	0.124028i
$989$	3.01560	+	10.0728i	0.0958906	+	0.320297i
$990$		0			0
$991$	0.585153	−	0.138684i	0.0185880	−	0.00440543i	−0.221311	−	0.975203i	$-0.571034\pi$
$991$	0.585153	−	0.138684i	0.0185880	−	0.00440543i	0.239899	+	0.970798i	$0.422886\pi$
$992$	−13.9445	−	20.3316i	−0.442739	−	0.645529i
$993$		0			0
$994$	−0.0426846	+	2.20081i	−0.00135387	+	0.0698054i
$995$	2.65621	−	1.89854i	0.0842074	−	0.0601878i
$996$		0			0
$997$	1.60501	−	7.40957i	0.0508313	−	0.234663i	−0.944850	−	0.327504i	$-0.893792\pi$
$997$	1.60501	−	7.40957i	0.0508313	−	0.234663i	0.995681	+	0.0928410i	$0.0295948\pi$
$998$	−26.3211	−	9.58009i	−0.833179	−	0.303253i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.64.17		1404
3.2	odd	2		243.2.i.a.4.10	✓	1404
243.61	even	81	inner	729.2.i.a.262.17		1404
243.182	odd	162		243.2.i.a.61.10	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.10	✓	1404	3.2	odd	2
243.2.i.a.61.10	yes	1404	243.182	odd	162
729.2.i.a.64.17		1404	1.1	even	1	trivial
729.2.i.a.262.17		1404	243.61	even	81	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.829136 + 0.0321742i) q^{2} +(-1.30755 - 0.101631i) q^{4} +(1.06671 + 1.32252i) q^{5} +(-2.20706 + 1.00323i) q^{7} +(-2.72917 - 0.318994i) q^{8} +(0.841900 + 1.13087i) q^{10} +(-0.0547589 - 2.82335i) q^{11} +(-5.52920 - 1.77287i) q^{13} +(-1.86223 + 0.760804i) q^{14} +(0.338906 + 0.0530039i) q^{16} +(-0.381447 - 1.27412i) q^{17} +(-3.22382 + 0.764059i) q^{19} +(-1.26038 - 1.83768i) q^{20} +(0.0454367 - 2.34271i) q^{22} +(-1.54117 + 1.10156i) q^{23} +(0.447345 - 2.06517i) q^{25} +(-4.52742 - 1.64785i) q^{26} +(2.98781 - 1.08747i) q^{28} +(0.282681 + 2.06959i) q^{29} +(-3.04514 - 2.98665i) q^{31} +(5.67178 + 1.11390i) q^{32} +(-0.275278 - 1.06869i) q^{34} +(-3.68109 - 1.84871i) q^{35} +(-3.01579 - 1.98352i) q^{37} +(-2.69757 + 0.529785i) q^{38} +(-2.48937 - 3.94965i) q^{40} +(-1.91949 + 3.64407i) q^{41} +(1.79685 - 5.25149i) q^{43} +(-0.215341 + 3.69725i) q^{44} +(-1.31328 + 0.863761i) q^{46} +(-3.87549 + 3.80105i) q^{47} +(-0.738023 + 0.845680i) q^{49} +(0.437355 - 1.69792i) q^{50} +(7.04955 + 2.88006i) q^{52} +(2.96543 + 2.48829i) q^{53} +(3.67552 - 3.08413i) q^{55} +(6.34345 - 2.03395i) q^{56} +(0.167793 + 1.72507i) q^{58} +(-13.1182 + 7.23834i) q^{59} +(3.50428 - 0.272375i) q^{61} +(-2.42874 - 2.57431i) q^{62} +(3.99928 + 0.947846i) q^{64} +(-3.55343 - 9.20361i) q^{65} +(-1.81968 + 13.3224i) q^{67} +(0.369273 + 1.70475i) q^{68} +(-2.99264 - 1.65127i) q^{70} +(0.433406 - 1.00475i) q^{71} +(-3.80885 + 5.11617i) q^{73} +(-2.43669 - 1.74164i) q^{74} +(4.29297 - 0.671408i) q^{76} +(2.95333 + 6.17636i) q^{77} +(8.07966 - 12.8192i) q^{79} +(0.291417 + 0.504749i) q^{80} +(-1.70877 + 2.95967i) q^{82} +(3.14312 + 5.96706i) q^{83} +(1.27816 - 1.86360i) q^{85} +(1.65880 - 4.29639i) q^{86} +(-0.751187 + 7.72288i) q^{88} +(0.186829 + 0.433118i) q^{89} +(13.9818 - 1.63424i) q^{91} +(2.12712 - 1.28373i) q^{92} +(-3.33560 + 3.02690i) q^{94} +(-4.44937 - 3.44852i) q^{95} +(1.41603 - 1.75560i) q^{97} +(-0.639130 + 0.677439i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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