LMFDB - Embedded newform 729.2.g.a.541.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] 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("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
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			541.7
Character	$\chi$	$=$	729.541
Dual form			729.2.g.a.190.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03395 + 1.38884i) q^{2} +(-0.286206 + 0.955993i) q^{4} +(-1.15051 + 0.756701i) q^{5} +(-2.25654 + 2.39179i) q^{7} +(1.63042 - 0.593424i) q^{8} +(-2.24050 - 0.815476i) q^{10} +(0.183502 - 0.0921584i) q^{11} +(2.08132 + 4.82504i) q^{13} +(-5.65495 - 0.660968i) q^{14} +(4.17744 + 2.74754i) q^{16} +(-3.88762 + 3.26210i) q^{17} +(-2.25026 - 1.88819i) q^{19} +(-0.394119 - 1.31645i) q^{20} +(0.317725 + 0.159568i) q^{22} +(-2.58175 - 2.73649i) q^{23} +(-1.22933 + 2.84990i) q^{25} +(-4.54921 + 7.87946i) q^{26} +(-1.64070 - 2.84178i) q^{28} +(-6.26558 + 0.732341i) q^{29} +(4.94436 - 1.17183i) q^{31} +(0.301604 + 5.17835i) q^{32} +(-8.55013 - 2.02642i) q^{34} +(0.786294 - 4.45930i) q^{35} +(1.44468 + 8.19321i) q^{37} +(0.295733 - 5.07754i) q^{38} +(-1.42677 + 1.91648i) q^{40} +(1.64966 - 2.21588i) q^{41} +(0.0922521 - 1.58391i) q^{43} +(0.0355834 + 0.201803i) q^{44} +(1.13114 - 6.41502i) q^{46} +(2.02520 + 0.479981i) q^{47} +(-0.221683 - 3.80615i) q^{49} +(-5.22910 + 1.23932i) q^{50} +(-5.20839 + 0.608774i) q^{52} +(-4.51663 - 7.82303i) q^{53} +(-0.141385 + 0.244885i) q^{55} +(-2.25976 + 5.23870i) q^{56} +(-7.49539 - 7.94465i) q^{58} +(13.2668 + 6.66285i) q^{59} +(0.432126 + 1.44340i) q^{61} +(6.73971 + 5.65528i) q^{62} +(0.780406 - 0.654838i) q^{64} +(-6.04569 - 3.97631i) q^{65} +(13.3182 + 1.55668i) q^{67} +(-2.00589 - 4.65018i) q^{68} +(7.00622 - 3.51865i) q^{70} +(-4.39214 - 1.59861i) q^{71} +(15.3008 - 5.56905i) q^{73} +(-9.88529 + 10.4778i) q^{74} +(2.44914 - 1.61082i) q^{76} +(-0.193656 + 0.646857i) q^{77} +(-0.887948 - 1.19272i) q^{79} -6.88524 q^{80} +4.78316 q^{82} +(8.51037 + 11.4314i) q^{83} +(2.00431 - 6.69485i) q^{85} +(2.29517 - 1.50956i) q^{86} +(0.244497 - 0.259152i) q^{88} +(4.83016 - 1.75803i) q^{89} +(-16.2370 - 5.90980i) q^{91} +(3.35498 - 1.68493i) q^{92} +(1.42734 + 3.30895i) q^{94} +(4.01774 + 0.469606i) q^{95} +(1.50005 + 0.986599i) q^{97} +(5.05691 - 4.24325i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	1.03395	+	1.38884i	0.731113	+	0.982055i	0.999823	+	0.0188339i	$0.00599536\pi$
$2$	1.03395	+	1.38884i	0.731113	+	0.982055i	−0.268710	+	0.963221i	$0.586597\pi$
$3$		0			0
$3$		0			0
$4$	−0.286206	+	0.955993i	−0.143103	+	0.477997i
$5$	−1.15051	+	0.756701i	−0.514523	+	0.338407i	−0.780071	−	0.625690i	$-0.784817\pi$
$5$	−1.15051	+	0.756701i	−0.514523	+	0.338407i	0.265548	+	0.964098i	$0.414447\pi$
$6$		0			0
$7$	−2.25654	+	2.39179i	−0.852890	+	0.904011i	−0.996325	−	0.0856487i	$-0.972704\pi$
$7$	−2.25654	+	2.39179i	−0.852890	+	0.904011i	0.143435	+	0.989660i	$0.454185\pi$
$8$	1.63042	−	0.593424i	0.576441	−	0.209807i
$9$		0			0
$10$	−2.24050	−	0.815476i	−0.708509	−	0.257876i
$11$	0.183502	−	0.0921584i	0.0553280	−	0.0277868i	−0.420920	−	0.907098i	$-0.638293\pi$
$11$	0.183502	−	0.0921584i	0.0553280	−	0.0277868i	0.476248	+	0.879311i	$0.341996\pi$
$12$		0			0
$13$	2.08132	+	4.82504i	0.577254	+	1.33823i	0.917443	+	0.397868i	$0.130250\pi$
$13$	2.08132	+	4.82504i	0.577254	+	1.33823i	−0.340189	+	0.940357i	$0.610491\pi$
$14$	−5.65495	−	0.660968i	−1.51135	−	0.176651i
$15$		0			0
$16$	4.17744	+	2.74754i	1.04436	+	0.686886i
$17$	−3.88762	+	3.26210i	−0.942887	+	0.791176i	−0.978085	−	0.208204i	$-0.933238\pi$
$17$	−3.88762	+	3.26210i	−0.942887	+	0.791176i	0.0351981	+	0.999380i	$0.488794\pi$
$18$		0			0
$19$	−2.25026	−	1.88819i	−0.516245	−	0.433181i	0.347075	−	0.937837i	$-0.387175\pi$
$19$	−2.25026	−	1.88819i	−0.516245	−	0.433181i	−0.863320	+	0.504656i	$0.831619\pi$
$20$	−0.394119	−	1.31645i	−0.0881278	−	0.294367i
$21$		0			0
$22$	0.317725	+	0.159568i	0.0677392	+	0.0340199i
$23$	−2.58175	−	2.73649i	−0.538332	−	0.570598i	0.399921	−	0.916550i	$-0.369038\pi$
$23$	−2.58175	−	2.73649i	−0.538332	−	0.570598i	−0.938252	+	0.345952i	$0.887556\pi$
$24$		0			0
$25$	−1.22933	+	2.84990i	−0.245865	+	0.569980i
$26$	−4.54921	+	7.87946i	−0.892173	+	1.54529i
$27$		0			0
$28$	−1.64070	−	2.84178i	−0.310063	−	0.537045i
$29$	−6.26558	+	0.732341i	−1.16349	+	0.135992i	−0.675840	−	0.737048i	$-0.736219\pi$
$29$	−6.26558	+	0.732341i	−1.16349	+	0.135992i	−0.487648	+	0.873040i	$0.662145\pi$
$30$		0			0
$31$	4.94436	−	1.17183i	0.888033	−	0.210468i	0.238811	−	0.971066i	$-0.423242\pi$
$31$	4.94436	−	1.17183i	0.888033	−	0.210468i	0.649223	+	0.760598i	$0.275094\pi$
$32$	0.301604	+	5.17835i	0.0533166	+	0.915411i
$33$		0			0
$34$	−8.55013	−	2.02642i	−1.46634	−	0.347528i
$35$	0.786294	−	4.45930i	0.132908	−	0.753759i
$36$		0			0
$37$	1.44468	+	8.19321i	0.237505	+	1.34696i	0.837274	+	0.546783i	$0.184148\pi$
$37$	1.44468	+	8.19321i	0.237505	+	1.34696i	−0.599770	+	0.800173i	$0.704741\pi$
$38$	0.295733	−	5.07754i	0.0479742	−	0.823685i
$39$		0			0
$40$	−1.42677	+	1.91648i	−0.225592	+	0.303022i
$41$	1.64966	−	2.21588i	0.257634	−	0.346062i	−0.654421	−	0.756130i	$-0.727088\pi$
$41$	1.64966	−	2.21588i	0.257634	−	0.346062i	0.912055	+	0.410068i	$0.134495\pi$
$42$		0			0
$43$	0.0922521	−	1.58391i	0.0140683	−	0.241544i	−0.983942	−	0.178490i	$-0.942879\pi$
$43$	0.0922521	−	1.58391i	0.0140683	−	0.241544i	0.998010	−	0.0630541i	$-0.0200841\pi$
$44$	0.0355834	+	0.201803i	0.00536439	+	0.0304230i
$45$		0			0
$46$	1.13114	−	6.41502i	0.166778	−	0.945843i
$47$	2.02520	+	0.479981i	0.295406	+	0.0700125i	0.375646	−	0.926763i	$-0.377421\pi$
$47$	2.02520	+	0.479981i	0.295406	+	0.0700125i	−0.0802406	+	0.996776i	$0.525569\pi$
$48$		0			0
$49$	−0.221683	−	3.80615i	−0.0316690	−	0.543736i
$50$	−5.22910	+	1.23932i	−0.739507	+	0.175266i
$51$		0			0
$52$	−5.20839	+	0.608774i	−0.722274	+	0.0844217i
$53$	−4.51663	−	7.82303i	−0.620407	−	1.07458i	−0.989410	−	0.145148i	$-0.953634\pi$
$53$	−4.51663	−	7.82303i	−0.620407	−	1.07458i	0.369003	−	0.929428i	$-0.379699\pi$
$54$		0			0
$55$	−0.141385	+	0.244885i	−0.0190643	+	0.0330203i
$56$	−2.25976	+	5.23870i	−0.301973	+	0.700051i
$57$		0			0
$58$	−7.49539	−	7.94465i	−0.984193	−	1.04318i
$59$	13.2668	+	6.66285i	1.72719	+	0.867429i	0.978976	+	0.203976i	$0.0653864\pi$
$59$	13.2668	+	6.66285i	1.72719	+	0.867429i	0.748218	+	0.663453i	$0.230910\pi$
$60$		0			0
$61$	0.432126	+	1.44340i	0.0553281	+	0.184809i	0.981187	−	0.193062i	$-0.0618417\pi$
$61$	0.432126	+	1.44340i	0.0553281	+	0.184809i	−0.925859	+	0.377870i	$0.876657\pi$
$62$	6.73971	+	5.65528i	0.855943	+	0.718222i
$63$		0			0
$64$	0.780406	−	0.654838i	0.0975508	−	0.0818548i
$65$	−6.04569	−	3.97631i	−0.749875	−	0.493201i
$66$		0			0
$67$	13.3182	+	1.55668i	1.62708	+	0.190178i	0.880140	−	0.474715i	$-0.157449\pi$
$67$	13.3182	+	1.55668i	1.62708	+	0.190178i	0.746938	+	0.664893i	$0.231523\pi$
$68$	−2.00589	−	4.65018i	−0.243250	−	0.563917i
$69$		0			0
$70$	7.00622	−	3.51865i	0.837403	−	0.420560i
$71$	−4.39214	−	1.59861i	−0.521252	−	0.189720i	0.0679763	−	0.997687i	$-0.478346\pi$
$71$	−4.39214	−	1.59861i	−0.521252	−	0.189720i	−0.589228	+	0.807967i	$0.700568\pi$
$72$		0			0
$73$	15.3008	−	5.56905i	1.79083	−	0.651808i	0.791662	−	0.610960i	$-0.209216\pi$
$73$	15.3008	−	5.56905i	1.79083	−	0.651808i	0.999165	−	0.0408483i	$-0.0130060\pi$
$74$	−9.88529	+	10.4778i	−1.14914	+	1.21802i
$75$		0			0
$76$	2.44914	−	1.61082i	0.280935	−	0.184774i
$77$	−0.193656	+	0.646857i	−0.0220692	+	0.0737162i
$78$		0			0
$79$	−0.887948	−	1.19272i	−0.0999020	−	0.134192i	0.749361	−	0.662162i	$-0.230361\pi$
$79$	−0.887948	−	1.19272i	−0.0999020	−	0.134192i	−0.849263	+	0.527970i	$0.822953\pi$
$80$	−6.88524			−0.769794
$81$		0			0
$82$	4.78316			0.528211
$83$	8.51037	+	11.4314i	0.934134	+	1.25476i	0.966863	+	0.255296i	$0.0821729\pi$
$83$	8.51037	+	11.4314i	0.934134	+	1.25476i	−0.0327287	+	0.999464i	$0.510420\pi$
$84$		0			0
$85$	2.00431	−	6.69485i	0.217397	−	0.726158i
$86$	2.29517	−	1.50956i	0.247495	−	0.162780i
$87$		0			0
$88$	0.244497	−	0.259152i	0.0260635	−	0.0276257i
$89$	4.83016	−	1.75803i	0.511996	−	0.186351i	−0.0730859	−	0.997326i	$-0.523285\pi$
$89$	4.83016	−	1.75803i	0.511996	−	0.186351i	0.585082	+	0.810974i	$0.301062\pi$
$90$		0			0
$91$	−16.2370	−	5.90980i	−1.70210	−	0.619515i
$92$	3.35498	−	1.68493i	0.349781	−	0.175667i
$93$		0			0
$94$	1.42734	+	3.30895i	0.147219	+	0.341292i
$95$	4.01774	+	0.469606i	0.412211	+	0.0481806i
$96$		0			0
$97$	1.50005	+	0.986599i	0.152307	+	0.100174i	0.623375	−	0.781923i	$-0.285761\pi$
$97$	1.50005	+	0.986599i	0.152307	+	0.100174i	−0.471068	+	0.882097i	$0.656131\pi$
$98$	5.05691	−	4.24325i	0.510825	−	0.428633i
$99$		0			0
$100$	−2.37264	−	1.99088i	−0.237264	−	0.199088i
$101$	−3.29109	−	10.9930i	−0.327475	−	1.09384i	−0.950262	−	0.311452i	$-0.899185\pi$
$101$	−3.29109	−	10.9930i	−0.327475	−	1.09384i	0.622787	−	0.782392i	$-0.286000\pi$
$102$		0			0
$103$	0.446992	+	0.224488i	0.0440434	+	0.0221194i	0.470685	−	0.882302i	$-0.344007\pi$
$103$	0.446992	+	0.224488i	0.0440434	+	0.0221194i	−0.426641	+	0.904421i	$0.640303\pi$
$104$	6.25672	+	6.63174i	0.613522	+	0.650295i
$105$		0			0
$106$	6.19494	−	14.3615i	0.601706	−	1.39491i
$107$	2.72183	−	4.71434i	0.263129	−	0.455752i	−0.703943	−	0.710257i	$-0.748579\pi$
$107$	2.72183	−	4.71434i	0.263129	−	0.455752i	0.967072	+	0.254504i	$0.0819123\pi$
$108$		0			0
$109$	−8.38980	−	14.5316i	−0.803597	−	1.39187i	−0.917234	−	0.398348i	$-0.869584\pi$
$109$	−8.38980	−	14.5316i	−0.803597	−	1.39187i	0.113637	−	0.993522i	$-0.463750\pi$
$110$	−0.486290	+	0.0568392i	−0.0463660	+	0.00541940i
$111$		0			0
$112$	−15.9981	+	3.79161i	−1.51168	+	0.358274i
$113$	−0.513560	−	8.81749i	−0.0483117	−	0.829480i	−0.932236	−	0.361850i	$-0.882145\pi$
$113$	−0.513560	−	8.81749i	−0.0483117	−	0.829480i	0.883925	−	0.467629i	$-0.154892\pi$
$114$		0			0
$115$	5.04103	+	1.19475i	0.470078	+	0.111411i
$116$	1.09313	−	6.19945i	0.101495	−	0.575604i
$117$		0			0
$118$	4.46363	+	25.3145i	0.410910	+	2.33039i
$119$	0.970301	−	16.6594i	0.0889474	−	1.52717i
$120$		0			0
$121$	−6.54356	+	8.78953i	−0.594870	+	0.799048i
$122$	−1.55785	+	2.09256i	−0.141041	+	0.189451i
$123$		0			0
$124$	−0.294837	+	5.06216i	−0.0264772	+	0.454596i
$125$	−1.93778	−	10.9897i	−0.173321	−	0.982950i
$126$		0			0
$127$	−1.21170	+	6.87190i	−0.107521	+	0.609783i	0.882662	+	0.470008i	$0.155749\pi$
$127$	−1.21170	+	6.87190i	−0.107521	+	0.609783i	−0.990183	+	0.139775i	$0.955362\pi$
$128$	11.8110	+	2.79925i	1.04395	+	0.247421i
$129$		0			0
$130$	−0.728495	−	12.5078i	−0.0638932	−	1.09700i
$131$	−5.48768	+	1.30061i	−0.479461	+	0.113634i	−0.463238	−	0.886234i	$-0.653312\pi$
$131$	−5.48768	+	1.30061i	−0.479461	+	0.113634i	−0.0162234	+	0.999868i	$0.505164\pi$
$132$		0			0
$133$	9.59395	−	1.12137i	0.831901	−	0.0972352i
$134$	11.6084	+	20.1063i	1.00281	+	1.73692i
$135$		0			0
$136$	−4.40265	+	7.62561i	−0.377524	+	0.653891i
$137$	0.441416	−	1.02332i	0.0377127	−	0.0874280i	−0.898319	−	0.439345i	$-0.855211\pi$
$137$	0.441416	−	1.02332i	0.0377127	−	0.0874280i	0.936031	+	0.351917i	$0.114470\pi$
$138$		0			0
$139$	3.26512	+	3.46082i	0.276944	+	0.293543i	0.850884	−	0.525354i	$-0.176067\pi$
$139$	3.26512	+	3.46082i	0.276944	+	0.293543i	−0.573940	+	0.818897i	$0.694586\pi$
$140$	4.03802	+	2.02797i	0.341275	+	0.171395i
$141$		0			0
$142$	−2.32105	−	7.75285i	−0.194778	−	0.650605i
$143$	0.826595	+	0.693595i	0.0691233	+	0.0580014i
$144$		0			0
$145$	6.65443	−	5.58373i	0.552621	−	0.463704i
$146$	23.5548	+	15.4922i	1.94941	+	1.28215i
$147$		0			0
$148$	−8.24613	−	0.963835i	−0.677828	−	0.0792267i
$149$	−3.04091	−	7.04963i	−0.249121	−	0.577528i	0.747068	−	0.664748i	$-0.231461\pi$
$149$	−3.04091	−	7.04963i	−0.249121	−	0.577528i	−0.996189	+	0.0872197i	$0.972202\pi$
$150$		0			0
$151$	2.76017	−	1.38621i	0.224620	−	0.112808i	−0.332931	−	0.942951i	$-0.608038\pi$
$151$	2.76017	−	1.38621i	0.224620	−	0.112808i	0.557551	+	0.830143i	$0.311741\pi$
$152$	−4.78937	−	1.74319i	−0.388469	−	0.141391i
$153$		0			0
$154$	−1.09861	+	0.399861i	−0.0885285	+	0.0322217i
$155$	−4.80180	+	5.08961i	−0.385690	+	0.408807i
$156$		0			0
$157$	−5.12220	+	3.36893i	−0.408796	+	0.268870i	−0.737209	−	0.675665i	$-0.763857\pi$
$157$	−5.12220	+	3.36893i	−0.408796	+	0.268870i	0.328413	+	0.944534i	$0.393486\pi$
$158$	0.738400	−	2.46643i	0.0587440	−	0.196219i
$159$		0			0
$160$	−4.26546	−	5.72951i	−0.337214	−	0.452958i
$161$	12.3709			0.974965
$162$		0			0
$163$	−0.171894			−0.0134638			−0.00673188	−	0.999977i	$-0.502143\pi$
$163$	−0.171894			−0.0134638			−0.00673188	+	0.999977i	$0.502143\pi$
$164$	1.64622	+	2.21126i	0.128548	+	0.172670i
$165$		0			0
$166$	−7.07705	+	23.6390i	−0.549286	+	1.83474i
$167$	−0.245915	+	0.161741i	−0.0190295	+	0.0125159i	−0.558988	−	0.829176i	$-0.688810\pi$
$167$	−0.245915	+	0.161741i	−0.0190295	+	0.0125159i	0.539959	+	0.841692i	$0.318440\pi$
$168$		0			0
$169$	−10.0280	+	10.6290i	−0.771383	+	0.817618i
$170$	11.3704	−	4.13849i	0.872069	−	0.317407i
$171$		0			0
$172$	1.48780	+	0.541516i	0.113444	+	0.0412902i
$173$	2.40115	−	1.20590i	0.182556	−	0.0916831i	−0.355174	−	0.934800i	$-0.615578\pi$
$173$	2.40115	−	1.20590i	0.182556	−	0.0916831i	0.537730	+	0.843117i	$0.319282\pi$
$174$		0			0
$175$	−4.04233	−	9.37119i	−0.305572	−	0.708395i
$176$	1.01978	+	0.119195i	0.0768687	+	0.00898466i
$177$		0			0
$178$	7.43576	+	4.89058i	0.557334	+	0.366564i
$179$	1.83356	−	1.53854i	0.137047	−	0.114996i	−0.571687	−	0.820471i	$-0.693711\pi$
$179$	1.83356	−	1.53854i	0.137047	−	0.114996i	0.708734	+	0.705476i	$0.249267\pi$
$180$		0			0
$181$	12.8278	+	10.7638i	0.953481	+	0.800065i	0.979880	−	0.199586i	$-0.0639598\pi$
$181$	12.8278	+	10.7638i	0.953481	+	0.800065i	−0.0263995	+	0.999651i	$0.508404\pi$
$182$	−8.58055	−	28.6610i	−0.636032	−	2.12450i
$183$		0			0
$184$	−5.83323	−	2.92956i	−0.430032	−	0.215970i
$185$	−7.86193	−	8.33316i	−0.578021	−	0.612666i
$186$		0			0
$187$	−0.412758	+	0.956881i	−0.0301839	+	0.0699741i
$188$	−1.03848	+	1.79870i	−0.0757391	+	0.131184i
$189$		0			0
$190$	3.50193	+	6.06553i	0.254057	+	0.440040i
$191$	14.0948	−	1.64745i	1.01987	−	0.119205i	0.410308	−	0.911947i	$-0.365421\pi$
$191$	14.0948	−	1.64745i	1.01987	−	0.119205i	0.609558	+	0.792742i	$0.291347\pi$
$192$		0			0
$193$	−4.06333	+	0.963026i	−0.292485	+	0.0693202i	−0.374239	−	0.927332i	$-0.622096\pi$
$193$	−4.06333	+	0.963026i	−0.292485	+	0.0693202i	0.0817540	+	0.996653i	$0.473948\pi$
$194$	0.180754	+	3.10342i	0.0129774	+	0.222813i
$195$		0			0
$196$	3.70211	+	0.877415i	0.264436	+	0.0626725i
$197$	−3.59768	+	20.4035i	−0.256324	+	1.45369i	0.536326	+	0.844011i	$0.319812\pi$
$197$	−3.59768	+	20.4035i	−0.256324	+	1.45369i	−0.792650	+	0.609677i	$0.791299\pi$
$198$		0			0
$199$	0.499478	+	2.83268i	0.0354071	+	0.200803i	0.997380	−	0.0723417i	$-0.0230472\pi$
$199$	0.499478	+	2.83268i	0.0354071	+	0.200803i	−0.961973	+	0.273145i	$0.911936\pi$
$200$	−0.313119	+	5.37604i	−0.0221408	+	0.380144i
$201$		0			0
$202$	11.8646	−	15.9370i	0.834793	−	1.12132i
$203$	12.3869	−	16.6385i	0.869389	−	1.16779i
$204$		0			0
$205$	−0.221190	+	3.79769i	−0.0154486	+	0.265242i
$206$	0.150390	+	0.852907i	0.0104782	+	0.0594248i
$207$		0			0
$208$	−4.56243	+	25.8748i	−0.316347	+	1.79409i
$209$	−0.586941	−	0.139107i	−0.0405995	−	0.00962227i
$210$		0			0
$211$	0.617143	+	10.5959i	0.0424859	+	0.729454i	0.950540	+	0.310602i	$0.100531\pi$
$211$	0.617143	+	10.5959i	0.0424859	+	0.729454i	−0.908054	+	0.418852i	$0.862432\pi$
$212$	8.77146	−	2.07887i	0.602426	−	0.142778i
$213$		0			0
$214$	9.36167	−	1.09422i	0.639951	−	0.0747995i
$215$	1.09241	+	1.89211i	0.0745016	+	0.129041i
$216$		0			0
$217$	−8.35434	+	14.4701i	−0.567130	+	0.982298i
$218$	11.5073	−	26.6770i	0.779374	−	1.80679i
$219$		0			0
$220$	−0.193644	−	0.205250i	−0.0130555	−	0.0138380i
$221$	−23.8312	−	11.9685i	−1.60306	−	0.805086i
$222$		0			0
$223$	6.79008	+	22.6805i	0.454698	+	1.51880i	0.811351	+	0.584559i	$0.198733\pi$
$223$	6.79008	+	22.6805i	0.454698	+	1.51880i	−0.356653	+	0.934237i	$0.616082\pi$
$224$	−13.0661	−	10.9638i	−0.873015	−	0.732547i
$225$		0			0
$226$	11.7150	−	9.83009i	0.779273	−	0.653888i
$227$	0.383501	+	0.252232i	0.0254538	+	0.0167412i	0.562172	−	0.827020i	$-0.309966\pi$
$227$	0.383501	+	0.252232i	0.0254538	+	0.0167412i	−0.536718	+	0.843761i	$0.680336\pi$
$228$		0			0
$229$	−15.8851	−	1.85670i	−1.04971	−	0.122694i	−0.426297	−	0.904583i	$-0.640182\pi$
$229$	−15.8851	−	1.85670i	−1.04971	−	0.122694i	−0.623417	+	0.781889i	$0.714256\pi$
$230$	3.55287	+	8.23647i	0.234269	+	0.543097i
$231$		0			0
$232$	−9.78093	+	4.91217i	−0.642150	+	0.322500i
$233$	7.46875	+	2.71840i	0.489294	+	0.178089i	0.574873	−	0.818243i	$-0.305052\pi$
$233$	7.46875	+	2.71840i	0.489294	+	0.178089i	−0.0855784	+	0.996331i	$0.527274\pi$
$234$		0			0
$235$	−2.69321	+	0.980249i	−0.175686	+	0.0639444i
$236$	−10.1667	+	10.7761i	−0.661795	+	0.701461i
$237$		0			0
$238$	24.1404	−	15.8774i	1.56479	−	1.02918i
$239$	−6.08524	+	20.3261i	−0.393621	+	1.31479i	0.500023	+	0.866012i	$0.333325\pi$
$239$	−6.08524	+	20.3261i	−0.393621	+	1.31479i	−0.893645	+	0.448775i	$0.851860\pi$
$240$		0			0
$241$	−10.7905	−	14.4942i	−0.695079	−	0.933653i	0.304745	−	0.952434i	$-0.401429\pi$
$241$	−10.7905	−	14.4942i	−0.695079	−	0.933653i	−0.999824	+	0.0187813i	$0.994021\pi$
$242$	−18.9729			−1.21963
$243$		0			0
$244$	−1.50356			−0.0962556
$245$	3.13517	+	4.21127i	0.200299	+	0.269048i
$246$		0			0
$247$	4.42709	−	14.7875i	0.281689	−	0.940907i
$248$	7.36599	−	4.84469i	0.467741	−	0.307638i
$249$		0			0
$250$	13.2593	−	14.0541i	0.838594	−	0.888857i
$251$	−7.58786	+	2.76176i	−0.478942	+	0.174321i	−0.570199	−	0.821507i	$-0.693134\pi$
$251$	−7.58786	+	2.76176i	−0.478942	+	0.174321i	0.0912569	+	0.995827i	$0.470912\pi$
$252$		0			0
$253$	−0.725947	−	0.264223i	−0.0456399	−	0.0166116i
$254$	−10.7968	+	5.42235i	−0.677450	+	0.340228i
$255$		0			0
$256$	7.51724	+	17.4269i	0.469828	+	1.08918i
$257$	16.4217	+	1.91942i	1.02436	+	0.119730i	0.611646	−	0.791132i	$-0.290508\pi$
$257$	16.4217	+	1.91942i	1.02436	+	0.119730i	0.412711	+	0.910862i	$0.364582\pi$
$258$		0			0
$259$	−22.8564	−	15.0329i	−1.42023	−	0.934099i
$260$	5.53164	−	4.64160i	0.343058	−	0.287860i
$261$		0			0
$262$	−7.48032	−	6.27673i	−0.462135	−	0.387778i
$263$	−0.00481531	−	0.0160843i	−0.000296925	−	0.000991797i	0.957841	−	0.287299i	$-0.0927574\pi$
$263$	−0.00481531	−	0.0160843i	−0.000296925	−	0.000991797i	−0.958138	+	0.286307i	$0.907572\pi$
$264$		0			0
$265$	11.1161	+	5.58273i	0.682858	+	0.342944i
$266$	11.4771	+	12.1650i	0.703704	+	0.745882i
$267$		0			0
$268$	−5.29992	+	12.2866i	−0.323744	+	0.750523i
$269$	3.16338	−	5.47913i	0.192874	−	0.334068i	−0.753327	−	0.657646i	$-0.771552\pi$
$269$	3.16338	−	5.47913i	0.192874	−	0.334068i	0.946202	+	0.323578i	$0.104886\pi$
$270$		0			0
$271$	−9.98751	−	17.2989i	−0.606698	−	1.05083i	−0.991781	−	0.127950i	$-0.959160\pi$
$271$	−9.98751	−	17.2989i	−0.606698	−	1.05083i	0.385082	−	0.922882i	$-0.374173\pi$
$272$	−25.2031	+	2.94582i	−1.52816	+	0.178616i
$273$		0			0
$274$	1.87762	−	0.445005i	0.113431	−	0.0268837i
$275$	0.0370577	+	0.636256i	0.00223466	+	0.0383677i
$276$		0			0
$277$	6.08715	+	1.44268i	0.365741	+	0.0866822i	0.409377	−	0.912365i	$-0.365746\pi$
$277$	6.08715	+	1.44268i	0.365741	+	0.0866822i	−0.0436360	+	0.999047i	$0.513894\pi$
$278$	−1.43055	+	8.11303i	−0.0857985	+	0.486587i
$279$		0			0
$280$	−1.36427	−	7.73713i	−0.0815304	−	0.462382i
$281$	−0.338495	+	5.81173i	−0.0201929	+	0.346699i	0.973046	+	0.230611i	$0.0740724\pi$
$281$	−0.338495	+	5.81173i	−0.0201929	+	0.346699i	−0.993239	+	0.116088i	$0.962965\pi$
$282$		0			0
$283$	−5.13375	+	6.89582i	−0.305170	+	0.409914i	−0.928081	−	0.372379i	$-0.878542\pi$
$283$	−5.13375	+	6.89582i	−0.305170	+	0.409914i	0.622911	+	0.782292i	$0.285950\pi$
$284$	2.78532	−	3.74133i	0.165278	−	0.222007i
$285$		0			0
$286$	−0.108632	+	1.86515i	−0.00642357	+	0.110288i
$287$	1.57739	+	8.94585i	0.0931106	+	0.528057i
$288$		0			0
$289$	1.52028	−	8.62194i	0.0894282	−	0.507173i
$290$	14.6352	+	3.46862i	0.859411	+	0.203684i
$291$		0			0
$292$	0.944788	+	16.2214i	0.0552896	+	0.949285i
$293$	−6.26236	+	1.48421i	−0.365851	+	0.0867083i	−0.409430	−	0.912342i	$-0.634272\pi$
$293$	−6.26236	+	1.48421i	−0.365851	+	0.0867083i	0.0435786	+	0.999050i	$0.486124\pi$
$294$		0			0
$295$	−20.3054	+	2.37336i	−1.18222	+	0.138182i
$296$	7.21749	+	12.5011i	0.419508	+	0.726610i
$297$		0			0
$298$	6.64663	−	11.5123i	0.385029	−	0.666889i
$299$	7.83024	−	18.1525i	0.452835	−	1.04979i
$300$		0			0
$301$	3.58020	+	3.79479i	0.206359	+	0.218728i
$302$	4.77910	+	2.40015i	0.275006	+	0.138113i
$303$		0			0
$304$	−4.21243	−	14.0705i	−0.241599	−	0.806998i
$305$	−1.58939	−	1.33366i	−0.0910082	−	0.0763649i
$306$		0			0
$307$	18.8060	−	15.7801i	1.07332	−	0.900619i	0.0779670	−	0.996956i	$-0.475157\pi$
$307$	18.8060	−	15.7801i	1.07332	−	0.900619i	0.995349	+	0.0963370i	$0.0307127\pi$
$308$	−0.562966	−	0.370269i	−0.0320780	−	0.0210980i
$309$		0			0
$310$	−12.0334	−	1.40651i	−0.683454	−	0.0798843i
$311$	5.14380	+	11.9247i	0.291678	+	0.676186i	0.999545	−	0.0301598i	$-0.00960161\pi$
$311$	5.14380	+	11.9247i	0.291678	+	0.676186i	−0.707867	+	0.706346i	$0.750342\pi$
$312$		0			0
$313$	4.67199	−	2.34636i	0.264076	−	0.132624i	−0.311835	−	0.950136i	$-0.600944\pi$
$313$	4.67199	−	2.34636i	0.264076	−	0.132624i	0.575911	+	0.817512i	$0.304647\pi$
$314$	−9.97498	−	3.63060i	−0.562921	−	0.204886i
$315$		0			0
$316$	1.39437	−	0.507509i	0.0784394	−	0.0285496i
$317$	−20.9694	+	22.2263i	−1.17776	+	1.24835i	−0.215412	+	0.976523i	$0.569109\pi$
$317$	−20.9694	+	22.2263i	−1.17776	+	1.24835i	−0.962346	+	0.271827i	$0.912372\pi$
$318$		0			0
$319$	−1.08226	+	0.711811i	−0.0605947	+	0.0398538i
$320$	−0.402347	+	1.34393i	−0.0224919	+	0.0751280i
$321$		0			0
$322$	12.7909	+	17.1812i	0.712809	+	0.957469i
$323$	14.9076			0.829483
$324$		0			0
$325$	−16.3095			−0.904688
$326$	−0.177730	−	0.238732i	−0.00984353	−	0.0132222i
$327$		0			0
$328$	1.37468	−	4.59176i	0.0759042	−	0.253538i
$329$	−5.71795	+	3.76075i	−0.315241	+	0.207337i
$330$		0			0
$331$	−2.18477	+	2.31572i	−0.120086	+	0.127283i	−0.784627	−	0.619968i	$-0.787146\pi$
$331$	−2.18477	+	2.31572i	−0.120086	+	0.127283i	0.664541	+	0.747252i	$0.268627\pi$
$332$	−13.3641	+	4.86412i	−0.733449	+	0.266953i
$333$		0			0
$334$	−0.478896	−	0.174304i	−0.0262040	−	0.00953748i
$335$	−16.5006	+	8.28694i	−0.901527	+	0.452764i
$336$		0			0
$337$	−12.9802	−	30.0915i	−0.707076	−	1.63919i	−0.767528	−	0.641016i	$-0.778513\pi$
$337$	−12.9802	−	30.0915i	−0.707076	−	1.63919i	0.0604518	−	0.998171i	$-0.480746\pi$
$338$	−25.1304	−	2.93732i	−1.36691	−	0.159769i
$339$		0			0
$340$	5.82659	+	3.83221i	0.315991	+	0.207831i
$341$	0.799307	−	0.670699i	0.0432849	−	0.0363204i
$342$		0			0
$343$	−8.02888	−	6.73703i	−0.433519	−	0.363765i
$344$	−0.789520	−	2.63718i	−0.0425681	−	0.142187i
$345$		0			0
$346$	4.15747	+	2.08796i	0.223507	+	0.112249i
$347$	−15.3768	−	16.2984i	−0.825468	−	0.874944i	0.168378	−	0.985723i	$-0.446147\pi$
$347$	−15.3768	−	16.2984i	−0.825468	−	0.874944i	−0.993845	+	0.110778i	$0.964666\pi$
$348$		0			0
$349$	8.74057	−	20.2629i	0.467872	−	1.08465i	−0.507013	−	0.861939i	$-0.669250\pi$
$349$	8.74057	−	20.2629i	0.467872	−	1.08465i	0.974885	−	0.222711i	$-0.0714905\pi$
$350$	8.83546	−	15.3035i	0.472275	−	0.818005i
$351$		0			0
$352$	0.532573	+	0.922444i	0.0283863	+	0.0491664i
$353$	−10.8430	+	1.26736i	−0.577114	+	0.0674550i	−0.399643	−	0.916671i	$-0.630866\pi$
$353$	−10.8430	+	1.26736i	−0.577114	+	0.0674550i	−0.177472	+	0.984126i	$0.556792\pi$
$354$		0			0
$355$	6.26287	−	1.48433i	0.332399	−	0.0787799i
$356$	0.298250	+	5.12076i	0.0158072	+	0.271400i
$357$		0			0
$358$	4.03259	+	0.955741i	0.213129	+	0.0505125i
$359$	4.30460	−	24.4126i	0.227188	−	1.28845i	−0.631269	−	0.775564i	$-0.717466\pi$
$359$	4.30460	−	24.4126i	0.227188	−	1.28845i	0.858457	−	0.512885i	$-0.171423\pi$
$360$		0			0
$361$	−1.80092	−	10.2135i	−0.0947851	−	0.537553i
$362$	−1.68585	+	28.9449i	−0.0886061	+	1.52131i
$363$		0			0
$364$	10.2969	−	13.8311i	0.539702	−	0.724946i
$365$	−13.3896	+	17.9854i	−0.700845	+	0.941399i
$366$		0			0
$367$	0.747077	−	12.8268i	0.0389971	−	0.669555i	−0.921003	−	0.389555i	$-0.872629\pi$
$367$	0.747077	−	12.8268i	0.0389971	−	0.669555i	0.960000	−	0.279999i	$-0.0903343\pi$
$368$	−3.26645	−	18.5250i	−0.170276	−	0.965681i
$369$		0			0
$370$	3.44455	−	19.5350i	0.179074	−	1.01558i
$371$	28.9030	+	6.85013i	1.50057	+	0.355641i
$372$		0			0
$373$	−0.129702	−	2.22690i	−0.00671572	−	0.115304i	0.993284	−	0.115700i	$-0.0369111\pi$
$373$	−0.129702	−	2.22690i	−0.00671572	−	0.115304i	−1.00000		0.000395600i	$0.999874\pi$
$374$	−1.75572	+	0.416114i	−0.0907862	+	0.0215167i
$375$		0			0
$376$	3.58676	−	0.419232i	0.184973	−	0.0216202i
$377$	−16.5742	−	28.7074i	−0.853617	−	1.47851i
$378$		0			0
$379$	3.67947	−	6.37302i	0.189001	−	0.327360i	−0.755916	−	0.654668i	$-0.772808\pi$
$379$	3.67947	−	6.37302i	0.189001	−	0.327360i	0.944918	+	0.327308i	$0.106142\pi$
$380$	−1.59884	+	3.70653i	−0.0820188	+	0.190141i
$381$		0			0
$382$	16.8614	+	17.8720i	0.862703	+	0.914412i
$383$	−12.9185	−	6.48791i	−0.660104	−	0.331517i	0.0870152	−	0.996207i	$-0.472267\pi$
$383$	−12.9185	−	6.48791i	−0.660104	−	0.331517i	−0.747119	+	0.664690i	$0.768563\pi$
$384$		0			0
$385$	−0.266675	−	0.890755i	−0.0135910	−	0.0453971i
$386$	−5.53876	−	4.64757i	−0.281916	−	0.236555i
$387$		0			0
$388$	−1.37251	+	1.15167i	−0.0696784	+	0.0584671i
$389$	−7.10510	−	4.67310i	−0.360243	−	0.236935i	0.356466	−	0.934308i	$-0.383982\pi$
$389$	−7.10510	−	4.67310i	−0.360243	−	0.236935i	−0.716708	+	0.697373i	$0.754352\pi$
$390$		0			0
$391$	18.9636	+	2.21653i	0.959030	+	0.112094i
$392$	−2.62010	−	6.07408i	−0.132335	−	0.306787i
$393$		0			0
$394$	−32.0569	+	16.0996i	−1.61500	+	0.811085i
$395$	1.92413	+	0.700325i	0.0968133	+	0.0352372i
$396$		0			0
$397$	−5.16106	+	1.87847i	−0.259026	+	0.0942779i	−0.468269	−	0.883586i	$-0.655122\pi$
$397$	−5.16106	+	1.87847i	−0.259026	+	0.0942779i	0.209243	+	0.977864i	$0.432900\pi$
$398$	−3.41769	+	3.62254i	−0.171313	+	0.181582i
$399$		0			0
$400$	−12.9656	+	8.52764i	−0.648282	+	0.426382i
$401$	2.69850	−	9.01361i	0.134757	−	0.450118i	−0.863800	−	0.503835i	$-0.831922\pi$
$401$	2.69850	−	9.01361i	0.134757	−	0.450118i	0.998556	+	0.0537173i	$0.0171070\pi$
$402$		0			0
$403$	15.9449	+	21.4178i	0.794274	+	1.06690i
$404$	11.4512			0.569716
$405$		0			0
$406$	35.9155			1.78246
$407$	1.02018	+	1.37033i	0.0505682	+	0.0679249i
$408$		0			0
$409$	4.42300	−	14.7739i	0.218703	−	0.730520i	−0.776272	−	0.630398i	$-0.782892\pi$
$409$	4.42300	−	14.7739i	0.218703	−	0.730520i	0.994975	−	0.100122i	$-0.0319233\pi$
$410$	−5.50306	+	3.61942i	−0.271777	+	0.178750i
$411$		0			0
$412$	−0.342540	+	0.363071i	−0.0168757	+	0.0178872i
$413$	−45.8732	+	16.6965i	−2.25727	+	0.821580i
$414$		0			0
$415$	−18.4414	−	6.71212i	−0.905253	−	0.329485i
$416$	−24.3580	+	12.2331i	−1.19425	+	0.599775i
$417$		0			0
$418$	−0.413670	−	0.958994i	−0.0202332	−	0.0469059i
$419$	24.5377	+	2.86805i	1.19875	+	0.140113i	0.691945	−	0.721950i	$-0.256754\pi$
$419$	24.5377	+	2.86805i	1.19875	+	0.140113i	0.506801	+	0.862063i	$0.330828\pi$
$420$		0			0
$421$	0.155228	+	0.102095i	0.00756535	+	0.00497581i	0.553286	−	0.832991i	$-0.313374\pi$
$421$	0.155228	+	0.102095i	0.00756535	+	0.00497581i	−0.545721	+	0.837967i	$0.683744\pi$
$422$	−14.0779	+	11.8128i	−0.685302	+	0.575037i
$423$		0			0
$424$	−12.0064	−	10.0746i	−0.583082	−	0.489264i
$425$	−4.51751	−	15.0895i	−0.219131	−	0.731949i
$426$		0			0
$427$	−4.42742	−	2.22354i	−0.214258	−	0.107604i
$428$	3.72788	+	3.95132i	0.180194	+	0.190994i
$429$		0			0
$430$	−1.49833	+	3.47352i	−0.0722559	+	0.167508i
$431$	−7.27612	+	12.6026i	−0.350478	+	0.607046i	−0.986333	−	0.164762i	$-0.947314\pi$
$431$	−7.27612	+	12.6026i	−0.350478	+	0.607046i	0.635855	+	0.771808i	$0.280648\pi$
$432$		0			0
$433$	17.3096	+	29.9811i	0.831846	+	1.44080i	0.896573	+	0.442897i	$0.146049\pi$
$433$	17.3096	+	29.9811i	0.831846	+	1.44080i	−0.0647264	+	0.997903i	$0.520617\pi$
$434$	−28.7346	+	3.35860i	−1.37931	+	0.161218i
$435$		0			0
$436$	16.2933	−	3.86158i	0.780307	−	0.184936i
$437$	0.642579	+	11.0327i	0.0307387	+	0.527763i
$438$		0			0
$439$	−1.91282	−	0.453346i	−0.0912937	−	0.0216370i	0.184715	−	0.982792i	$-0.440864\pi$
$439$	−1.91282	−	0.453346i	−0.0912937	−	0.0216370i	−0.276009	+	0.961155i	$0.589012\pi$
$440$	−0.0851954	+	0.483167i	−0.00406153	+	0.0230341i
$441$		0			0
$442$	−8.01800	−	45.4724i	−0.381378	−	2.16290i
$443$	1.84950	−	31.7547i	0.0878725	−	1.50871i	−0.609949	−	0.792441i	$-0.708810\pi$
$443$	1.84950	−	31.7547i	0.0878725	−	1.50871i	0.697821	−	0.716272i	$-0.254153\pi$
$444$		0			0
$445$	−4.22683	+	5.67762i	−0.200371	+	0.269145i
$446$	−24.4788	+	32.8808i	−1.15911	+	1.55695i
$447$		0			0
$448$	−0.194779	+	3.34423i	−0.00920246	+	0.158000i
$449$	5.17251	+	29.3348i	0.244106	+	1.38439i	0.822560	+	0.568679i	$0.192545\pi$
$449$	5.17251	+	29.3348i	0.244106	+	1.38439i	−0.578454	+	0.815715i	$0.696344\pi$
$450$		0			0
$451$	0.0985049	−	0.558649i	0.00463841	−	0.0263057i
$452$	8.57645	+	2.03266i	0.403402	+	0.0956081i
$453$		0			0
$454$	0.0462111	+	0.793415i	0.00216880	+	0.0372368i
$455$	23.1528	−	5.48732i	1.08542	−	0.257249i
$456$		0			0
$457$	−12.6602	+	1.47977i	−0.592220	+	0.0692206i	−0.406924	−	0.913462i	$-0.633399\pi$
$457$	−12.6602	+	1.47977i	−0.592220	+	0.0692206i	−0.185296	+	0.982683i	$0.559325\pi$
$458$	−13.8457	−	23.9815i	−0.646968	−	1.12058i
$459$		0			0
$460$	−2.58494	+	4.47725i	−0.120523	+	0.208753i
$461$	−8.18619	+	18.9777i	−0.381269	+	0.883880i	0.614232	+	0.789126i	$0.289466\pi$
$461$	−8.18619	+	18.9777i	−0.381269	+	0.883880i	−0.995501	+	0.0947547i	$0.969793\pi$
$462$		0			0
$463$	11.4261	+	12.1109i	0.531014	+	0.562842i	0.936234	−	0.351377i	$-0.114286\pi$
$463$	11.4261	+	12.1109i	0.531014	+	0.562842i	−0.405220	+	0.914219i	$0.632805\pi$
$464$	−28.1862	−	14.1556i	−1.30851	−	0.657159i
$465$		0			0
$466$	3.94690	+	13.1836i	0.182837	+	0.610717i
$467$	22.4416	+	18.8308i	1.03848	+	0.871384i	0.991835	−	0.127527i	$-0.0407041\pi$
$467$	22.4416	+	18.8308i	1.03848	+	0.871384i	0.0466403	+	0.998912i	$0.485149\pi$
$468$		0			0
$469$	−33.7762	+	28.3416i	−1.55964	+	1.30870i
$470$	−4.14605	−	2.72690i	−0.191243	−	0.125783i
$471$		0			0
$472$	25.5844	+	2.99039i	1.17762	+	0.137644i
$473$	−0.129042	−	0.299153i	−0.00593335	−	0.0137551i
$474$		0			0
$475$	8.14746	−	4.09181i	0.373831	−	0.187745i
$476$	15.6486	+	5.69562i	0.717252	+	0.261059i
$477$		0			0
$478$	−34.5215	+	12.5648i	−1.57897	+	0.574700i
$479$	15.3457	−	16.2655i	0.701162	−	0.743189i	−0.274711	−	0.961527i	$-0.588582\pi$
$479$	15.3457	−	16.2655i	0.701162	−	0.743189i	0.975873	+	0.218338i	$0.0700636\pi$
$480$		0			0
$481$	−36.5257	+	24.0233i	−1.66543	+	1.09537i
$482$	8.97318	−	29.9725i	0.408717	−	1.36521i
$483$		0			0
$484$	−6.52993	−	8.77122i	−0.296815	−	0.398692i
$485$	−2.47238			−0.112265
$486$		0			0
$487$	3.73936			0.169447			0.0847233	−	0.996405i	$-0.472999\pi$
$487$	3.73936			0.169447			0.0847233	+	0.996405i	$0.472999\pi$
$488$	1.56110	+	2.09692i	0.0706676	+	0.0949230i
$489$		0			0
$490$	−2.60715	+	8.70847i	−0.117779	+	0.393409i
$491$	−1.00818	+	0.663088i	−0.0454984	+	0.0299248i	−0.572054	−	0.820216i	$-0.693853\pi$
$491$	−1.00818	+	0.663088i	−0.0454984	+	0.0299248i	0.526556	+	0.850140i	$0.323483\pi$
$492$		0			0
$493$	21.9692	−	23.2860i	0.989444	−	1.04875i
$494$	25.1148	−	9.14105i	1.12997	−	0.411275i
$495$		0			0
$496$	23.8744	+	8.68957i	1.07199	+	0.390173i
$497$	13.7346	−	6.89776i	0.616079	−	0.309407i
$498$		0			0
$499$	1.32207	+	3.06491i	0.0591842	+	0.137204i	0.945242	−	0.326371i	$-0.105826\pi$
$499$	1.32207	+	3.06491i	0.0591842	+	0.137204i	−0.886058	+	0.463575i	$0.846566\pi$
$500$	11.0607	+	1.29281i	0.494649	+	0.0578162i
$501$		0			0
$502$	−11.6811	−	7.68278i	−0.521353	−	0.342899i
$503$	−18.7108	+	15.7002i	−0.834274	+	0.700039i	−0.956268	−	0.292492i	$-0.905516\pi$
$503$	−18.7108	+	15.7002i	−0.834274	+	0.700039i	0.121994	+	0.992531i	$0.461071\pi$
$504$		0			0
$505$	12.1048	+	10.1572i	0.538658	+	0.451988i
$506$	−0.383630	−	1.28142i	−0.0170545	−	0.0569658i
$507$		0			0
$508$	−6.22270	−	3.12516i	−0.276087	−	0.138656i
$509$	21.2317	+	22.5042i	0.941076	+	0.997483i	1.00000		0.000779780i	$-0.000248212\pi$
$509$	21.2317	+	22.5042i	0.941076	+	0.997483i	−0.0589233	+	0.998263i	$0.518767\pi$
$510$		0			0
$511$	−21.2069	+	49.1631i	−0.938138	+	2.17485i
$512$	−4.29252	+	7.43487i	−0.189705	+	0.328578i
$513$		0			0
$514$	14.3134	+	24.7916i	0.631339	+	1.09351i
$515$	−0.684138	+	0.0799642i	−0.0301467	+	0.00352364i
$516$		0			0
$517$	0.415863	−	0.0985614i	0.0182896	−	0.00433473i
$518$	−2.75416	−	47.2871i	−0.121011	−	2.07767i
$519$		0			0
$520$	−12.2167	−	2.89540i	−0.535736	−	0.126972i
$521$	−2.47495	+	14.0361i	−0.108430	+	0.614934i	0.881365	+	0.472435i	$0.156625\pi$
$521$	−2.47495	+	14.0361i	−0.108430	+	0.614934i	−0.989795	+	0.142499i	$0.954486\pi$
$522$		0			0
$523$	0.234960	+	1.33253i	0.0102741	+	0.0582673i	0.989514	−	0.144439i	$-0.0461376\pi$
$523$	0.234960	+	1.33253i	0.0102741	+	0.0582673i	−0.979240	+	0.202706i	$0.935026\pi$
$524$	0.327236	−	5.61843i	0.0142954	−	0.245442i
$525$		0			0
$526$	0.0173596	−	0.0233180i	0.000756914	−	0.00101671i
$527$	−15.3992	+	20.6847i	−0.670798	+	0.901038i
$528$		0			0
$529$	0.514360	−	8.83122i	0.0223635	−	0.383966i
$530$	3.74002	+	21.2107i	0.162456	+	0.921335i
$531$		0			0
$532$	−1.67382	+	9.49269i	−0.0725692	+	0.411560i
$533$	14.1252	+	3.34773i	0.611829	+	0.145006i
$534$		0			0
$535$	0.435864	+	7.48350i	0.0188440	+	0.323540i
$536$	22.6380	−	5.36531i	0.977814	−	0.231746i
$537$		0			0
$538$	10.8804	−	1.27173i	0.469086	−	0.0548283i
$539$	−0.391448	−	0.678008i	−0.0168609	−	0.0292039i
$540$		0			0
$541$	12.5060	−	21.6611i	0.537676	−	0.931283i	−0.461352	−	0.887217i	$-0.652636\pi$
$541$	12.5060	−	21.6611i	0.537676	−	0.931283i	0.999029	−	0.0440659i	$-0.0140312\pi$
$542$	13.6987	−	31.7572i	0.588410	−	1.36409i
$543$		0			0
$544$	−18.0648	−	19.1476i	−0.774524	−	0.820947i
$545$	20.6486	+	10.3701i	0.884488	+	0.444207i
$546$		0			0
$547$	−8.14494	−	27.2060i	−0.348253	−	1.16325i	−0.935348	−	0.353728i	$-0.884914\pi$
$547$	−8.14494	−	27.2060i	−0.348253	−	1.16325i	0.587096	−	0.809517i	$-0.300271\pi$
$548$	0.851950	+	0.714871i	0.0363935	+	0.0305378i
$549$		0			0
$550$	−0.845339	+	0.709324i	−0.0360454	+	0.0302457i
$551$	15.4820	+	10.1827i	0.659554	+	0.433796i
$552$		0			0
$553$	4.85642	+	0.567635i	0.206516	+	0.0241383i
$554$	4.29016	+	9.94570i	0.182271	+	0.422552i
$555$		0			0
$556$	−4.24302	+	2.13093i	−0.179944	+	0.0903714i
$557$	34.6621	+	12.6160i	1.46868	+	0.534556i	0.947742	−	0.319039i	$-0.103360\pi$
$557$	34.6621	+	12.6160i	1.46868	+	0.534556i	0.520938	+	0.853594i	$0.325582\pi$
$558$		0			0
$559$	7.83442	−	2.85150i	0.331361	−	0.120605i
$560$	15.5368	−	16.4680i	0.656550	−	0.695902i
$561$		0			0
$562$	−8.42152	+	5.53892i	−0.355240	+	0.233645i
$563$	6.35470	−	21.2262i	0.267819	−	0.894576i	−0.713249	−	0.700911i	$-0.752777\pi$
$563$	6.35470	−	21.2262i	0.267819	−	0.894576i	0.981068	−	0.193666i	$-0.0620377\pi$
$564$		0			0
$565$	7.26306	+	9.75598i	0.305559	+	0.410437i
$566$	−14.8852			−0.625671
$567$		0			0
$568$	−8.10969			−0.340275
$569$	−3.82370	−	5.13612i	−0.160298	−	0.215317i	0.714717	−	0.699414i	$-0.246556\pi$
$569$	−3.82370	−	5.13612i	−0.160298	−	0.215317i	−0.875014	+	0.484097i	$0.839148\pi$
$570$		0			0
$571$	1.58425	−	5.29175i	0.0662986	−	0.221453i	−0.918420	−	0.395607i	$-0.870534\pi$
$571$	1.58425	−	5.29175i	0.0662986	−	0.221453i	0.984718	+	0.174155i	$0.0557193\pi$
$572$	−0.899649	+	0.591708i	−0.0376162	+	0.0247406i
$573$		0			0
$574$	−10.7934	+	11.4403i	−0.450506	+	0.477509i
$575$	10.9725	−	3.99368i	0.457586	−	0.166548i
$576$		0			0
$577$	36.7599	+	13.3795i	1.53033	+	0.556996i	0.963703	−	0.266977i	$-0.0860246\pi$
$577$	36.7599	+	13.3795i	1.53033	+	0.556996i	0.566630	+	0.823972i	$0.308247\pi$
$578$	13.5463	−	6.80323i	0.563454	−	0.282977i
$579$		0			0
$580$	3.43348	+	7.95969i	0.142567	+	0.330508i
$581$	−46.5455	−	5.44038i	−1.93103	−	0.225705i
$582$		0			0
$583$	−1.54977	−	1.01930i	−0.0641849	−	0.0422151i
$584$	21.6420	−	18.1598i	0.895551	−	0.751457i
$585$		0			0
$586$	−8.53628	−	7.16279i	−0.352631	−	0.295892i
$587$	3.98891	+	13.3239i	0.164640	+	0.549935i	1.00000		0.000232108i	$7.38823e-5\pi$
$587$	3.98891	+	13.3239i	0.164640	+	0.549935i	−0.835360	+	0.549703i	$0.814741\pi$
$588$		0			0
$589$	−13.3387	−	6.69897i	−0.549613	−	0.276026i
$590$	−24.2909	−	25.7469i	−1.00004	−	1.05998i
$591$		0			0
$592$	−16.4761	+	38.1959i	−0.677164	+	1.56984i
$593$	−8.67989	+	15.0340i	−0.356441	+	0.617373i	−0.987363	−	0.158472i	$-0.949343\pi$
$593$	−8.67989	+	15.0340i	−0.356441	+	0.617373i	0.630923	+	0.775846i	$0.282676\pi$
$594$		0			0
$595$	11.4899	+	19.9010i	0.471039	+	0.815863i
$596$	7.60973	−	0.889450i	0.311707	−	0.0364333i
$597$		0			0
$598$	33.3070	−	7.89390i	1.36202	−	0.322806i
$599$	2.41727	+	41.5029i	0.0987669	+	1.69576i	0.576372	+	0.817187i	$0.304468\pi$
$599$	2.41727	+	41.5029i	0.0987669	+	1.69576i	−0.477606	+	0.878574i	$0.658495\pi$
$600$		0			0
$601$	−8.98563	−	2.12963i	−0.366532	−	0.0868696i	0.0432228	−	0.999065i	$-0.486237\pi$
$601$	−8.98563	−	2.12963i	−0.366532	−	0.0868696i	−0.409754	+	0.912196i	$0.634386\pi$
$602$	−1.56859	+	8.89594i	−0.0639311	+	0.362571i
$603$		0			0
$604$	0.535232	+	3.03545i	0.0217783	+	0.123511i
$605$	0.877375	−	15.0640i	0.0356704	−	0.612437i
$606$		0			0
$607$	−8.05551	+	10.8204i	−0.326963	+	0.439187i	−0.934961	−	0.354751i	$-0.884566\pi$
$607$	−8.05551	+	10.8204i	−0.326963	+	0.439187i	0.607998	+	0.793939i	$0.291973\pi$
$608$	9.09903	−	12.2221i	0.369014	−	0.495672i
$609$		0			0
$610$	0.208880	−	3.58633i	0.00845731	−	0.145206i
$611$	1.89916	+	10.7707i	0.0768317	+	0.435734i
$612$		0			0
$613$	−0.675007	+	3.82815i	−0.0272633	+	0.154618i	−0.995400	−	0.0958034i	$-0.969458\pi$
$613$	−0.675007	+	3.82815i	−0.0272633	+	0.154618i	0.968137	+	0.250421i	$0.0805691\pi$
$614$	41.3605	+	9.80261i	1.66917	+	0.395601i
$615$		0			0
$616$	0.0681197	+	1.16957i	0.00274462	+	0.0471233i
$617$	−23.3671	+	5.53810i	−0.940723	+	0.222956i	−0.672244	−	0.740330i	$-0.734669\pi$
$617$	−23.3671	+	5.53810i	−0.940723	+	0.222956i	−0.268480	+	0.963285i	$0.586521\pi$
$618$		0			0
$619$	10.1098	−	1.18167i	0.406348	−	0.0474953i	0.0895361	−	0.995984i	$-0.471462\pi$
$619$	10.1098	−	1.18167i	0.406348	−	0.0474953i	0.316812	+	0.948488i	$0.397387\pi$
$620$	−3.49133	−	6.04716i	−0.140215	−	0.242860i
$621$		0			0
$622$	−11.2430	+	19.4734i	−0.450802	+	0.780812i
$623$	−6.69458	+	15.5198i	−0.268213	+	0.621787i
$624$		0			0
$625$	−0.104193	−	0.110438i	−0.00416772	−	0.00441753i
$626$	8.08931	+	4.06260i	0.323314	+	0.162374i
$627$		0			0
$628$	−1.75467	−	5.86100i	−0.0700189	−	0.233879i
$629$	−32.3435	−	27.1394i	−1.28962	−	1.08212i
$630$		0			0
$631$	−37.7162	+	31.6476i	−1.50146	+	1.25987i	−0.622836	+	0.782352i	$0.714020\pi$
$631$	−37.7162	+	31.6476i	−1.50146	+	1.25987i	−0.878621	+	0.477520i	$0.841536\pi$
$632$	−2.15552	−	1.41771i	−0.0857419	−	0.0563934i
$633$		0			0
$634$	−52.5499	−	6.14220i	−2.08702	−	0.243938i
$635$	−3.80590	−	8.82307i	−0.151033	−	0.350133i
$636$		0			0
$637$	17.9035	−	8.99145i	0.709361	−	0.356254i
$638$	−2.10759	−	0.767099i	−0.0834402	−	0.0303698i
$639$		0			0
$640$	−15.7068	+	5.71682i	−0.620867	+	0.225977i
$641$	−23.3866	+	24.7883i	−0.923714	+	0.979080i	−0.999838	−	0.0180187i	$-0.994264\pi$
$641$	−23.3866	+	24.7883i	−0.923714	+	0.979080i	0.0761236	+	0.997098i	$0.475746\pi$
$642$		0			0
$643$	16.6064	−	10.9222i	0.654891	−	0.430728i	−0.178102	−	0.984012i	$-0.556996\pi$
$643$	16.6064	−	10.9222i	0.654891	−	0.430728i	0.832993	+	0.553284i	$0.186625\pi$
$644$	−3.54063	+	11.8265i	−0.139520	+	0.466030i
$645$		0			0
$646$	15.4138	+	20.7043i	0.606446	+	0.814598i
$647$	37.1636			1.46105			0.730525	−	0.682886i	$-0.239275\pi$
$647$	37.1636			1.46105			0.730525	+	0.682886i	$0.239275\pi$
$648$		0			0
$649$	3.04853			0.119665
$650$	−16.8632	−	22.6512i	−0.661429	−	0.888453i
$651$		0			0
$652$	0.0491970	−	0.164329i	0.00192670	−	0.00643563i
$653$	−4.60149	+	3.02645i	−0.180070	+	0.118434i	−0.636344	−	0.771405i	$-0.719554\pi$
$653$	−4.60149	+	3.02645i	−0.180070	+	0.118434i	0.456274	+	0.889839i	$0.349184\pi$
$654$		0			0
$655$	5.32946	−	5.64889i	0.208239	−	0.220721i
$656$	12.9796	−	4.72418i	0.506767	−	0.184448i
$657$		0			0
$658$	−11.1351	−	4.05286i	−0.434093	−	0.157997i
$659$	−34.0326	+	17.0918i	−1.32572	+	0.665802i	−0.963855	−	0.266428i	$-0.914156\pi$
$659$	−34.0326	+	17.0918i	−1.32572	+	0.665802i	−0.361866	+	0.932230i	$0.617860\pi$
$660$		0			0
$661$	−11.1606	−	25.8732i	−0.434097	−	1.00635i	−0.985121	−	0.171861i	$-0.945022\pi$
$661$	−11.1606	−	25.8732i	−0.434097	−	1.00635i	0.551024	−	0.834490i	$-0.314237\pi$
$662$	−5.47509	−	0.639947i	−0.212796	−	0.0248722i
$663$		0			0
$664$	20.6592	+	13.5877i	0.801731	+	0.527307i
$665$	−10.1894	+	8.54990i	−0.395127	+	0.331551i
$666$		0			0
$667$	18.1802	+	15.2550i	0.703939	+	0.590675i
$668$	−0.0842410	−	0.281385i	−0.00325938	−	0.0108871i
$669$		0			0
$670$	−28.5700	−	14.3484i	−1.10376	−	0.554327i
$671$	0.212318	+	0.225044i	0.00819644	+	0.00868772i
$672$		0			0
$673$	9.84070	−	22.8133i	0.379331	−	0.879388i	−0.616430	−	0.787410i	$-0.711422\pi$
$673$	9.84070	−	22.8133i	0.379331	−	0.879388i	0.995761	−	0.0919783i	$-0.0293190\pi$
$674$	28.3712	−	49.1404i	1.09282	−	1.89282i
$675$		0			0
$676$	−7.29123	−	12.6288i	−0.280432	−	0.485722i
$677$	35.0463	−	4.09633i	1.34694	−	0.157435i	0.588141	−	0.808759i	$-0.299860\pi$
$677$	35.0463	−	4.09633i	1.34694	−	0.157435i	0.758800	+	0.651324i	$0.225786\pi$
$678$		0			0
$679$	−5.74466	+	1.36151i	−0.220460	+	0.0522499i
$680$	−0.705025	−	12.1048i	−0.0270365	−	0.464199i
$681$		0			0
$682$	1.75793	+	0.416638i	0.0673148	+	0.0159539i
$683$	6.86569	−	38.9372i	0.262708	−	1.48989i	−0.512774	−	0.858523i	$-0.671382\pi$
$683$	6.86569	−	38.9372i	0.262708	−	1.48989i	0.775483	−	0.631369i	$-0.217507\pi$
$684$		0			0
$685$	0.266493	+	1.51136i	0.0101822	+	0.0577460i
$686$	1.05517	−	18.1165i	0.0402865	−	0.691693i
$687$		0			0
$688$	4.73723	−	6.36321i	0.180605	−	0.242595i
$689$	28.3459	−	38.0752i	1.07989	−	1.45055i
$690$		0			0
$691$	0.987935	−	16.9622i	0.0375828	−	0.645272i	−0.925944	−	0.377661i	$-0.876729\pi$
$691$	0.987935	−	16.9622i	0.0375828	−	0.645272i	0.963527	−	0.267612i	$-0.0862344\pi$
$692$	0.465612	+	2.64062i	0.0176999	+	0.100381i
$693$		0			0
$694$	6.73702	−	38.2075i	0.255734	−	1.45034i
$695$	−6.37536	−	1.51099i	−0.241831	−	0.0573150i
$696$		0			0
$697$	0.815166	+	13.9959i	0.0308766	+	0.530131i
$698$	37.1792	−	8.81163i	1.40725	−	0.333525i
$699$		0			0
$700$	10.1157	−	1.18236i	0.382339	−	0.0446890i
$701$	−16.3741	−	28.3608i	−0.618442	−	1.07117i	−0.989770	−	0.142672i	$-0.954431\pi$
$701$	−16.3741	−	28.3608i	−0.618442	−	1.07117i	0.371328	−	0.928502i	$-0.378903\pi$
$702$		0			0
$703$	12.2194	−	21.1647i	0.460865	−	0.798241i
$704$	0.0828575	−	0.192085i	0.00312281	−	0.00723949i
$705$		0			0
$706$	−12.9713	−	13.7487i	−0.488180	−	0.517441i
$707$	33.7194	+	16.9345i	1.26815	+	0.636887i
$708$		0			0
$709$	−9.41268	−	31.4405i	−0.353500	−	1.18077i	−0.931195	−	0.364521i	$-0.881233\pi$
$709$	−9.41268	−	31.4405i	−0.353500	−	1.18077i	0.577695	−	0.816253i	$-0.303952\pi$
$710$	8.53698	+	7.16337i	0.320387	+	0.268837i
$711$		0			0
$712$	6.83193	−	5.73267i	0.256037	−	0.214841i
$713$	−15.9718	−	10.5048i	−0.598149	−	0.393409i
$714$		0			0
$715$	−1.47585	−	0.172502i	−0.0551936	−	0.00645121i
$716$	0.946059	+	2.19321i	0.0353559	+	0.0819641i
$717$		0			0
$718$	38.3559	−	19.2630i	1.43143	−	0.718890i
$719$	15.8250	+	5.75983i	0.590173	+	0.214806i	0.619806	−	0.784755i	$-0.287211\pi$
$719$	15.8250	+	5.75983i	0.590173	+	0.214806i	−0.0296323	+	0.999561i	$0.509434\pi$
$720$		0			0
$721$	−1.54558	+	0.562545i	−0.0575604	+	0.0209503i
$722$	12.3228	−	13.0614i	0.458608	−	0.486096i
$723$		0			0
$724$	−13.9615	+	9.18261i	−0.518874	+	0.341269i
$725$	5.61534	−	18.7565i	0.208548	−	0.696600i
$726$		0			0
$727$	−5.01783	−	6.74011i	−0.186101	−	0.249977i	0.699275	−	0.714853i	$-0.253506\pi$
$727$	−5.01783	−	6.74011i	−0.186101	−	0.249977i	−0.885376	+	0.464876i	$0.846099\pi$
$728$	−29.9802			−1.11114
$729$		0			0
$730$	−38.8230			−1.43690
$731$	4.80823	+	6.45857i	0.177839	+	0.238879i
$732$		0			0
$733$	−3.54104	+	11.8279i	−0.130791	+	0.436874i	−0.998149	−	0.0608113i	$-0.980631\pi$
$733$	−3.54104	+	11.8279i	−0.130791	+	0.436874i	0.867358	+	0.497685i	$0.165816\pi$
$734$	18.5868	−	12.2247i	0.686051	−	0.451223i
$735$		0			0
$736$	13.3918	−	14.1945i	0.493630	−	0.523217i
$737$	2.58738	−	0.941730i	0.0953075	−	0.0346891i
$738$		0			0
$739$	37.3973	+	13.6115i	1.37568	+	0.500707i	0.920866	−	0.389879i	$-0.127483\pi$
$739$	37.3973	+	13.6115i	1.37568	+	0.500707i	0.454815	+	0.890586i	$0.349705\pi$
$740$	10.2166	−	5.13096i	0.375569	−	0.188618i
$741$		0			0
$742$	20.3705	+	47.2242i	0.747826	+	1.73365i
$743$	19.7041	+	2.30308i	0.722873	+	0.0844917i	0.469570	−	0.882895i	$-0.344409\pi$
$743$	19.7041	+	2.30308i	0.722873	+	0.0844917i	0.253303	+	0.967387i	$0.418483\pi$
$744$		0			0
$745$	8.83306	+	5.80960i	0.323618	+	0.212847i
$746$	2.95869	−	2.48263i	0.108325	−	0.0908957i
$747$		0			0
$748$	−0.796638	−	0.668459i	−0.0291280	−	0.0244413i
$749$	5.13381	+	17.1481i	0.187585	+	0.626578i
$750$		0			0
$751$	34.2956	+	17.2239i	1.25146	+	0.628509i	0.946146	−	0.323742i	$-0.104941\pi$
$751$	34.2956	+	17.2239i	1.25146	+	0.628509i	0.305318	+	0.952250i	$0.401237\pi$
$752$	7.14137	+	7.56941i	0.260419	+	0.276028i
$753$		0			0
$754$	22.7330	−	52.7009i	0.827885	−	1.91925i
$755$	−2.12665	+	3.68347i	−0.0773969	+	0.134055i
$756$		0			0
$757$	7.07444	+	12.2533i	0.257125	+	0.445353i	0.965470	−	0.260513i	$-0.0838915\pi$
$757$	7.07444	+	12.2533i	0.257125	+	0.445353i	−0.708346	+	0.705866i	$0.750558\pi$
$758$	12.6555	−	1.47921i	0.459667	−	0.0537274i
$759$		0			0
$760$	6.82928	−	1.61857i	0.247724	−	0.0587117i
$761$	0.551159	+	9.46303i	0.0199795	+	0.343034i	0.993454	+	0.114237i	$0.0364423\pi$
$761$	0.551159	+	9.46303i	0.0199795	+	0.343034i	−0.973474	+	0.228797i	$0.926521\pi$
$762$		0			0
$763$	53.6883	+	12.7244i	1.94365	+	0.460653i
$764$	−2.45907	+	13.9461i	−0.0889660	+	0.504551i
$765$		0			0
$766$	−4.34643	−	24.6498i	−0.157043	−	0.890634i
$767$	−4.53602	+	77.8805i	−0.163786	+	2.81210i
$768$		0			0
$769$	−7.47719	+	10.0436i	−0.269634	+	0.362182i	−0.916231	−	0.400650i	$-0.868784\pi$
$769$	−7.47719	+	10.0436i	−0.269634	+	0.362182i	0.646597	+	0.762832i	$0.276192\pi$
$770$	0.961384	−	1.29136i	0.0346459	−	0.0465375i
$771$		0			0
$772$	0.242300	−	4.16014i	0.00872059	−	0.149727i
$773$	−6.23462	−	35.3583i	−0.224244	−	1.27175i	−0.864125	−	0.503277i	$-0.832128\pi$
$773$	−6.23462	−	35.3583i	−0.224244	−	1.27175i	0.639882	−	0.768474i	$-0.278983\pi$
$774$		0			0
$775$	−2.73862	+	15.5315i	−0.0983742	+	0.557908i
$776$	3.03119	+	0.718404i	0.108813	+	0.0257892i
$777$		0			0
$778$	−0.856152	−	14.6996i	−0.0306945	−	0.527005i
$779$	−7.89617	+	1.87143i	−0.282910	+	0.0670508i
$780$		0			0
$781$	−0.953294	+	0.111424i	−0.0341115	+	0.00398707i
$782$	16.5290	+	28.6291i	0.591076	+	1.02377i
$783$		0			0
$784$	9.53150	−	16.5091i	0.340411	−	0.589609i
$785$	3.34387	−	7.75195i	0.119348	−	0.276679i
$786$		0			0
$787$	−27.4162	−	29.0594i	−0.977281	−	1.03586i	−0.999348	−	0.0361007i	$-0.988506\pi$
$787$	−27.4162	−	29.0594i	−0.977281	−	1.03586i	0.0220673	−	0.999756i	$-0.492975\pi$
$788$	−18.4759	−	9.27895i	−0.658177	−	0.330549i
$789$		0			0
$790$	1.01681	+	3.39639i	0.0361766	+	0.120838i
$791$	22.2484	+	18.6687i	0.791063	+	0.663781i
$792$		0			0
$793$	−6.06508	+	5.08921i	−0.215377	+	0.180723i
$794$	−7.94517	−	5.22562i	−0.281964	−	0.185450i
$795$		0			0
$796$	−2.85098	−	0.333231i	−0.101050	−	0.0118111i
$797$	13.5008	+	31.2984i	0.478224	+	1.10865i	0.971127	+	0.238563i	$0.0766764\pi$
$797$	13.5008	+	31.2984i	0.478224	+	1.10865i	−0.492903	+	0.870084i	$0.664064\pi$
$798$		0			0
$799$	−9.43896	+	4.74043i	−0.333927	+	0.167704i
$800$	−15.1285	−	5.50634i	−0.534875	−	0.194678i
$801$		0			0
$802$	15.3085	−	5.57185i	0.540563	−	0.196749i
$803$	2.29451	−	2.43203i	0.0809713	−	0.0858246i
$804$		0			0
$805$	−14.2328	+	9.36109i	−0.501642	+	0.329935i
$806$	−13.2595	+	44.2898i	−0.467046	+	1.56004i
$807$		0			0
$808$	−11.8894	−	15.9702i	−0.418266	−	0.561829i
$809$	−7.57622			−0.266366			−0.133183	−	0.991091i	$-0.542520\pi$
$809$	−7.57622			−0.266366			−0.133183	+	0.991091i	$0.542520\pi$
$810$		0			0
$811$	20.5558			0.721810			0.360905	−	0.932602i	$-0.382468\pi$
$811$	20.5558			0.721810			0.360905	+	0.932602i	$0.382468\pi$
$812$	12.3611	+	16.6038i	0.433789	+	0.582680i
$813$		0			0
$814$	−0.848358	+	2.83371i	−0.0297349	+	0.0993216i
$815$	0.197765	−	0.130072i	0.00692742	−	0.00455623i
$816$		0			0
$817$	−3.19831	+	3.39001i	−0.111895	+	0.118602i
$818$	25.0916	−	9.13260i	0.877308	−	0.319314i
$819$		0			0
$820$	−3.56726	−	1.29838i	−0.124574	−	0.0453412i
$821$	27.2335	−	13.6772i	0.950455	−	0.477337i	0.0951512	−	0.995463i	$-0.469667\pi$
$821$	27.2335	−	13.6772i	0.950455	−	0.477337i	0.855304	+	0.518126i	$0.173370\pi$
$822$		0			0
$823$	−8.83984	−	20.4930i	−0.308137	−	0.714343i	0.691833	−	0.722058i	$-0.256803\pi$
$823$	−8.83984	−	20.4930i	−0.308137	−	0.714343i	−0.999970	+	0.00771507i	$0.997544\pi$
$824$	0.862001	+	0.100753i	0.0300292	+	0.00350991i
$825$		0			0
$826$	−70.6192	−	46.4470i	−2.45716	−	1.61610i
$827$	27.2509	−	22.8662i	0.947606	−	0.795136i	−0.0312864	−	0.999510i	$-0.509960\pi$
$827$	27.2509	−	22.8662i	0.947606	−	0.795136i	0.978893	+	0.204374i	$0.0655159\pi$
$828$		0			0
$829$	−13.4520	−	11.2875i	−0.467206	−	0.392032i	0.378568	−	0.925573i	$-0.376416\pi$
$829$	−13.4520	−	11.2875i	−0.467206	−	0.392032i	−0.845774	+	0.533541i	$0.820861\pi$
$830$	−9.74546	−	32.5521i	−0.338270	−	1.12990i
$831$		0			0
$832$	4.78390	+	2.40256i	0.165852	+	0.0832939i
$833$	13.2779	+	14.0737i	0.460052	+	0.487626i
$834$		0			0
$835$	0.160538	−	0.372169i	0.00555565	−	0.0128794i
$836$	0.300972	−	0.521298i	0.0104093	−	0.0180295i
$837$		0			0
$838$	21.3875	+	37.0443i	0.738820	+	1.27967i
$839$	−38.0724	+	4.45002i	−1.31440	+	0.153632i	−0.744247	−	0.667904i	$-0.767192\pi$
$839$	−38.0724	+	4.45002i	−1.31440	+	0.153632i	−0.570157	+	0.821536i	$0.693118\pi$
$840$		0			0
$841$	10.5028	−	2.48921i	0.362166	−	0.0858350i
$842$	0.0187047	+	0.321147i	0.000644606	+	0.0110675i
$843$		0			0
$844$	−10.3063	−	2.44263i	−0.354757	−	0.0840789i
$845$	3.49427	−	19.8170i	0.120206	−	0.681725i
$846$		0			0
$847$	−6.25691	−	35.4847i	−0.214990	−	1.21927i
$848$	2.62619	−	45.0899i	0.0901836	−	1.54839i
$849$		0			0
$850$	16.2860	−	21.8759i	0.558605	−	0.750337i
$851$	18.6908	−	25.1062i	0.640714	−	0.860628i
$852$		0			0
$853$	−0.488107	+	8.38047i	−0.0167125	+	0.286942i	0.979589	+	0.201012i	$0.0644231\pi$
$853$	−0.488107	+	8.38047i	−0.0167125	+	0.286942i	−0.996301	+	0.0859296i	$0.972614\pi$
$854$	−1.48961	−	8.44799i	−0.0509733	−	0.289084i
$855$		0			0
$856$	1.64011	−	9.30155i	0.0560580	−	0.317920i
$857$	−46.8244	−	11.0976i	−1.59949	−	0.379087i	−0.668380	−	0.743820i	$-0.733012\pi$
$857$	−46.8244	−	11.0976i	−1.59949	−	0.379087i	−0.931112	+	0.364733i	$0.881160\pi$
$858$		0			0
$859$	−2.97006	−	50.9939i	−0.101337	−	1.73989i	−0.540377	−	0.841423i	$-0.681718\pi$
$859$	−2.97006	−	50.9939i	−0.101337	−	1.73989i	0.439040	−	0.898467i	$-0.355319\pi$
$860$	−2.12149	+	0.502804i	−0.0723424	+	0.0171455i
$861$		0			0
$862$	−25.0261	+	2.92513i	−0.852392	+	0.0996303i
$863$	18.3885	+	31.8499i	0.625953	+	1.08418i	0.988356	+	0.152161i	$0.0486232\pi$
$863$	18.3885	+	31.8499i	0.625953	+	1.08418i	−0.362403	+	0.932022i	$0.618043\pi$
$864$		0			0
$865$	−1.85003	+	3.20435i	−0.0629031	+	0.108951i
$866$	−23.7416	+	55.0391i	−0.806771	+	1.87031i
$867$		0			0
$868$	−11.4423	−	12.1281i	−0.388377	−	0.411656i
$869$	−0.272860	−	0.137035i	−0.00925614	−	0.00464861i
$870$		0			0
$871$	20.2084	+	67.5008i	0.684736	+	2.28718i
$872$	−22.3023	−	18.7138i	−0.755250	−	0.633730i
$873$		0			0
$874$	−14.6581	+	12.2996i	−0.495819	+	0.416042i
$875$	30.6577	+	20.1639i	1.03642	+	0.681665i
$876$		0			0
$877$	4.03239	+	0.471319i	0.136164	+	0.0159153i	0.183902	−	0.982945i	$-0.441127\pi$
$877$	4.03239	+	0.471319i	0.136164	+	0.0159153i	−0.0477378	+	0.998860i	$0.515201\pi$
$878$	−1.34813	−	3.12532i	−0.0454973	−	0.105475i
$879$		0			0
$880$	−1.26346	+	0.634533i	−0.0425912	+	0.0213901i
$881$	−38.2223	−	13.9118i	−1.28774	−	0.468700i	−0.394758	−	0.918785i	$-0.629171\pi$
$881$	−38.2223	−	13.9118i	−1.28774	−	0.468700i	−0.892986	+	0.450085i	$0.851394\pi$
$882$		0			0
$883$	−24.6043	+	8.95523i	−0.828000	+	0.301367i	−0.721038	−	0.692896i	$-0.756335\pi$
$883$	−24.6043	+	8.95523i	−0.828000	+	0.301367i	−0.106962	+	0.994263i	$0.534112\pi$
$884$	18.2624	−	19.3570i	0.614231	−	0.651046i
$885$		0			0
$886$	46.0144	−	30.2641i	1.54588	−	1.01674i
$887$	6.23488	−	20.8260i	0.209347	−	0.699267i	−0.787235	−	0.616654i	$-0.788488\pi$
$887$	6.23488	−	20.8260i	0.209347	−	0.699267i	0.996582	−	0.0826140i	$-0.0263268\pi$
$888$		0			0
$889$	−13.7019	−	18.4048i	−0.459546	−	0.617278i
$890$	−12.2556			−0.410809
$891$		0			0
$892$	−23.6257			−0.791048
$893$	−3.65093	−	4.90405i	−0.122174	−	0.164108i
$894$		0			0
$895$	−0.945312	+	3.15756i	−0.0315983	+	0.105546i
$896$	−33.3471	+	21.9327i	−1.11405	+	0.732721i
$897$		0			0
$898$	−35.3931	+	37.5145i	−1.18108	+	1.25187i
$899$	−30.1211	+	10.9632i	−1.00459	+	0.365642i
$900$		0			0
$901$	43.0785	+	15.6793i	1.43515	+	0.522353i
$902$	0.877720	−	0.440808i	0.0292249	−	0.0146773i
$903$		0			0
$904$	−6.06983	−	14.0715i	−0.201880	−	0.468010i
$905$	−22.9034	−	2.67703i	−0.761336	−	0.0889874i
$906$		0			0
$907$	44.0406	+	28.9659i	1.46234	+	0.961798i	0.997059	+	0.0766368i	$0.0244182\pi$
$907$	44.0406	+	28.9659i	1.46234	+	0.961798i	0.465284	+	0.885161i	$0.345952\pi$
$908$	−0.350892	+	0.294434i	−0.0116448	+	0.00977113i
$909$		0			0
$910$	31.5598	+	26.4818i	1.04620	+	0.877864i
$911$	12.3476	+	41.2438i	0.409094	+	1.36647i	0.876063	+	0.482196i	$0.160161\pi$
$911$	12.3476	+	41.2438i	0.409094	+	1.36647i	−0.466969	+	0.884273i	$0.654654\pi$
$912$		0			0
$913$	2.61517	+	1.31339i	0.0865496	+	0.0434668i
$914$	−15.1452	−	16.0530i	−0.500958	−	0.530985i
$915$		0			0
$916$	6.32139	−	14.6546i	0.208864	−	0.484202i
$917$	9.27238	−	16.0602i	0.306201	−	0.530356i
$918$		0			0
$919$	−25.2136	−	43.6712i	−0.831719	−	1.44058i	−0.896674	−	0.442691i	$-0.854024\pi$
$919$	−25.2136	−	43.6712i	−0.831719	−	1.44058i	0.0649552	−	0.997888i	$-0.479310\pi$
$920$	8.92799	−	1.04353i	0.294347	−	0.0344042i
$921$		0			0
$922$	−34.8210	+	8.25274i	−1.14677	+	0.271789i
$923$	−1.42810	−	24.5195i	−0.0470064	−	0.807069i
$924$		0			0
$925$	−25.1258	−	5.95493i	−0.826131	−	0.195797i
$926$	−5.00610	+	28.3910i	−0.164511	+	0.932987i
$927$		0			0
$928$	−5.68204	−	32.2245i	−0.186522	−	1.05782i
$929$	−0.923930	+	15.8633i	−0.0303132	+	0.520457i	0.948638	+	0.316363i	$0.102462\pi$
$929$	−0.923930	+	15.8633i	−0.0303132	+	0.520457i	−0.978951	+	0.204094i	$0.934575\pi$
$930$		0			0
$931$	−6.68791	+	8.98342i	−0.219187	+	0.294420i
$932$	−4.73638	+	6.36206i	−0.155145	+	0.208396i
$933$		0			0
$934$	−2.94932	+	50.6378i	−0.0965046	+	1.65692i
$935$	−0.249191	−	1.41323i	−0.00814943	−	0.0462177i
$936$		0			0
$937$	3.98093	−	22.5770i	0.130051	−	0.737557i	−0.848128	−	0.529792i	$-0.822270\pi$
$937$	3.98093	−	22.5770i	0.130051	−	0.737557i	0.978179	−	0.207765i	$-0.0666189\pi$
$938$	−74.2848	−	17.6058i	−2.42549	−	0.574851i
$939$		0			0
$940$	−0.166299	−	2.85525i	−0.00542408	−	0.0931278i
$941$	−13.7585	+	3.26083i	−0.448516	+	0.106300i	−0.448665	−	0.893700i	$-0.648100\pi$
$941$	−13.7585	+	3.26083i	−0.448516	+	0.106300i	0.000149695		1.00000i	$0.499952\pi$
$942$		0			0
$943$	−10.3227	+	1.20656i	−0.336155	+	0.0392908i
$944$	37.1148	+	64.2848i	1.20799	+	2.09229i
$945$		0			0
$946$	0.282051	−	0.488527i	0.00917027	−	0.0158834i
$947$	22.6121	−	52.4208i	0.734796	−	1.70345i	0.0243417	−	0.999704i	$-0.492251\pi$
$947$	22.6121	−	52.4208i	0.734796	−	1.70345i	0.710454	−	0.703744i	$-0.248490\pi$
$948$		0			0
$949$	58.7168	+	62.2362i	1.90603	+	2.02027i
$950$	14.1069	+	7.08476i	0.457689	+	0.229860i
$951$		0			0
$952$	−8.30411	−	27.7377i	−0.269138	−	0.898983i
$953$	13.5816	+	11.3963i	0.439951	+	0.369163i	0.835691	−	0.549200i	$-0.185067\pi$
$953$	13.5816	+	11.3963i	0.439951	+	0.369163i	−0.395740	+	0.918363i	$0.629512\pi$
$954$		0			0
$955$	−14.9696	+	12.5610i	−0.484405	+	0.406464i
$956$	−17.6900	−	11.6349i	−0.572136	−	0.376299i
$957$		0			0
$958$	38.4567	+	4.49495i	1.24248	+	0.145225i
$959$	1.45149	+	3.36493i	0.0468710	+	0.108659i
$960$		0			0
$961$	−4.62911	+	2.32483i	−0.149326	+	0.0749945i
$962$	−71.1302	−	25.8893i	−2.29333	−	0.834704i
$963$		0			0
$964$	16.9447	−	6.16735i	0.545751	−	0.198637i
$965$	3.94617	−	4.18270i	0.127032	−	0.134646i
$966$		0			0
$967$	18.4795	−	12.1541i	0.594260	−	0.390851i	−0.216455	−	0.976293i	$-0.569449\pi$
$967$	18.4795	−	12.1541i	0.594260	−	0.390851i	0.810714	+	0.585442i	$0.199079\pi$
$968$	−5.45284	+	18.2137i	−0.175261	+	0.585412i
$969$		0			0
$970$	−2.55632	−	3.43373i	−0.0820785	−	0.110251i
$971$	5.09901			0.163635			0.0818176	−	0.996647i	$-0.473928\pi$
$971$	5.09901			0.163635			0.0818176	+	0.996647i	$0.473928\pi$
$972$		0			0
$973$	−15.6454			−0.501569
$974$	3.86631	+	5.19336i	0.123885	+	0.166406i
$975$		0			0
$976$	−2.16063	+	7.21701i	−0.0691601	+	0.231011i
$977$	19.4106	−	12.7666i	0.621001	−	0.408439i	−0.199651	−	0.979867i	$-0.563981\pi$
$977$	19.4106	−	12.7666i	0.621001	−	0.408439i	0.820652	+	0.571429i	$0.193611\pi$
$978$		0			0
$979$	0.724328	−	0.767743i	0.0231496	−	0.0245372i
$980$	−4.92325	+	1.79191i	−0.157267	+	0.0572406i
$981$		0			0
$982$	−1.96332	−	0.714592i	−0.0626522	−	0.0228035i
$983$	15.0614	−	7.56411i	0.480384	−	0.241258i	−0.192092	−	0.981377i	$-0.561527\pi$
$983$	15.0614	−	7.56411i	0.480384	−	0.241258i	0.672476	+	0.740119i	$0.265231\pi$
$984$		0			0
$985$	−11.3002	−	26.1967i	−0.360053	−	0.834698i
$986$	55.0555	+	6.43507i	1.75333	+	0.204934i
$987$		0			0
$988$	12.8697	+	8.46454i	0.409440	+	0.269293i
$989$	−4.57252	+	3.83680i	−0.145398	+	0.122003i
$990$		0			0
$991$	−0.316451	−	0.265534i	−0.0100524	−	0.00843496i	0.637748	−	0.770245i	$-0.279866\pi$
$991$	−0.316451	−	0.265534i	−0.0100524	−	0.00843496i	−0.647800	+	0.761810i	$0.724311\pi$
$992$	7.55941	+	25.2502i	0.240012	+	0.801694i
$993$		0			0
$994$	23.7807	+	11.9431i	0.754278	+	0.378813i
$995$	−2.71815	−	2.88107i	−0.0861710	−	0.0913360i
$996$		0			0
$997$	2.31383	−	5.36406i	0.0732797	−	0.169882i	−0.877639	−	0.479322i	$-0.840883\pi$
$997$	2.31383	−	5.36406i	0.0732797	−	0.169882i	0.950919	+	0.309441i	$0.100142\pi$
$998$	−2.88970	+	5.00511i	−0.0914719	+	0.158434i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.541.7		144
3.2	odd	2		729.2.g.d.541.2		144
9.2	odd	6		81.2.g.a.34.2	yes	144
9.4	even	3		729.2.g.b.298.2		144
9.5	odd	6		729.2.g.c.298.7		144
9.7	even	3		243.2.g.a.181.7		144
81.4	even	27		243.2.g.a.145.7		144
81.23	odd	54		729.2.g.d.190.2		144
81.25	even	27		6561.2.a.d.1.56		72
81.31	even	27		729.2.g.b.433.2		144
81.50	odd	54		729.2.g.c.433.7		144
81.56	odd	54		6561.2.a.c.1.17		72
81.58	even	27	inner	729.2.g.a.190.7		144
81.77	odd	54		81.2.g.a.31.2	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.31.2	✓	144	81.77	odd	54
81.2.g.a.34.2	yes	144	9.2	odd	6
243.2.g.a.145.7		144	81.4	even	27
243.2.g.a.181.7		144	9.7	even	3
729.2.g.a.190.7		144	81.58	even	27	inner
729.2.g.a.541.7		144	1.1	even	1	trivial
729.2.g.b.298.2		144	9.4	even	3
729.2.g.b.433.2		144	81.31	even	27
729.2.g.c.298.7		144	9.5	odd	6
729.2.g.c.433.7		144	81.50	odd	54
729.2.g.d.190.2		144	81.23	odd	54
729.2.g.d.541.2		144	3.2	odd	2
6561.2.a.c.1.17		72	81.56	odd	54
6561.2.a.d.1.56		72	81.25	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03395 + 1.38884i) q^{2} +(-0.286206 + 0.955993i) q^{4} +(-1.15051 + 0.756701i) q^{5} +(-2.25654 + 2.39179i) q^{7} +(1.63042 - 0.593424i) q^{8} +(-2.24050 - 0.815476i) q^{10} +(0.183502 - 0.0921584i) q^{11} +(2.08132 + 4.82504i) q^{13} +(-5.65495 - 0.660968i) q^{14} +(4.17744 + 2.74754i) q^{16} +(-3.88762 + 3.26210i) q^{17} +(-2.25026 - 1.88819i) q^{19} +(-0.394119 - 1.31645i) q^{20} +(0.317725 + 0.159568i) q^{22} +(-2.58175 - 2.73649i) q^{23} +(-1.22933 + 2.84990i) q^{25} +(-4.54921 + 7.87946i) q^{26} +(-1.64070 - 2.84178i) q^{28} +(-6.26558 + 0.732341i) q^{29} +(4.94436 - 1.17183i) q^{31} +(0.301604 + 5.17835i) q^{32} +(-8.55013 - 2.02642i) q^{34} +(0.786294 - 4.45930i) q^{35} +(1.44468 + 8.19321i) q^{37} +(0.295733 - 5.07754i) q^{38} +(-1.42677 + 1.91648i) q^{40} +(1.64966 - 2.21588i) q^{41} +(0.0922521 - 1.58391i) q^{43} +(0.0355834 + 0.201803i) q^{44} +(1.13114 - 6.41502i) q^{46} +(2.02520 + 0.479981i) q^{47} +(-0.221683 - 3.80615i) q^{49} +(-5.22910 + 1.23932i) q^{50} +(-5.20839 + 0.608774i) q^{52} +(-4.51663 - 7.82303i) q^{53} +(-0.141385 + 0.244885i) q^{55} +(-2.25976 + 5.23870i) q^{56} +(-7.49539 - 7.94465i) q^{58} +(13.2668 + 6.66285i) q^{59} +(0.432126 + 1.44340i) q^{61} +(6.73971 + 5.65528i) q^{62} +(0.780406 - 0.654838i) q^{64} +(-6.04569 - 3.97631i) q^{65} +(13.3182 + 1.55668i) q^{67} +(-2.00589 - 4.65018i) q^{68} +(7.00622 - 3.51865i) q^{70} +(-4.39214 - 1.59861i) q^{71} +(15.3008 - 5.56905i) q^{73} +(-9.88529 + 10.4778i) q^{74} +(2.44914 - 1.61082i) q^{76} +(-0.193656 + 0.646857i) q^{77} +(-0.887948 - 1.19272i) q^{79} -6.88524 q^{80} +4.78316 q^{82} +(8.51037 + 11.4314i) q^{83} +(2.00431 - 6.69485i) q^{85} +(2.29517 - 1.50956i) q^{86} +(0.244497 - 0.259152i) q^{88} +(4.83016 - 1.75803i) q^{89} +(-16.2370 - 5.90980i) q^{91} +(3.35498 - 1.68493i) q^{92} +(1.42734 + 3.30895i) q^{94} +(4.01774 + 0.469606i) q^{95} +(1.50005 + 0.986599i) q^{97} +(5.05691 - 4.24325i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

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