LMFDB - Embedded newform 729.2.g.b.298.2

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,-18,63] 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			298.2
Character	$\chi$	$=$	729.298
Dual form			729.2.g.b.433.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71974 + 0.201009i) q^{2} +(0.971017 - 0.230135i) q^{4} +(1.23058 + 0.618019i) q^{5} +(-0.943081 - 3.15011i) q^{7} +(1.63042 - 0.593424i) q^{8} +(-2.24050 - 0.815476i) q^{10} +(-0.0119397 + 0.204997i) q^{11} +(3.13795 - 4.21500i) q^{13} +(2.25506 + 5.22781i) q^{14} +(-4.46816 + 2.24399i) q^{16} +(-3.88762 + 3.26210i) q^{17} +(-2.25026 - 1.88819i) q^{19} +(1.33714 + 0.316908i) q^{20} +(-0.0206730 - 0.354942i) q^{22} +(-1.07900 + 3.60410i) q^{23} +(-1.85342 - 2.48958i) q^{25} +(-4.54921 + 7.87946i) q^{26} +(-1.64070 - 2.84178i) q^{28} +(2.49856 - 5.79232i) q^{29} +(-3.48702 - 3.69602i) q^{31} +(4.33378 - 2.85037i) q^{32} +(6.03000 - 6.39142i) q^{34} +(0.786294 - 4.45930i) q^{35} +(1.44468 + 8.19321i) q^{37} +(4.24941 + 2.79488i) q^{38} +(2.37310 + 0.277376i) q^{40} +(-2.74384 - 0.320709i) q^{41} +(1.32558 + 0.871847i) q^{43} +(0.0355834 + 0.201803i) q^{44} +(1.13114 - 6.41502i) q^{46} +(-1.42828 + 1.51388i) q^{47} +(-3.18539 + 2.09506i) q^{49} +(3.68783 + 3.90887i) q^{50} +(2.07698 - 4.81499i) q^{52} +(-4.51663 - 7.82303i) q^{53} +(-0.141385 + 0.244885i) q^{55} +(-3.40697 - 4.57636i) q^{56} +(-3.13257 + 10.4635i) q^{58} +(-0.863215 - 14.8208i) q^{59} +(-1.46609 - 0.347469i) q^{61} +(6.73971 + 5.65528i) q^{62} +(0.780406 - 0.654838i) q^{64} +(6.46643 - 3.24756i) q^{65} +(-5.31098 - 12.3122i) q^{67} +(-3.02423 + 4.06224i) q^{68} +(-0.455864 + 7.82689i) q^{70} +(-4.39214 - 1.59861i) q^{71} +(15.3008 - 5.56905i) q^{73} +(-4.13139 - 13.7998i) q^{74} +(-2.61958 - 1.31560i) q^{76} +(0.657023 - 0.155717i) q^{77} +(1.47690 - 0.172625i) q^{79} -6.88524 q^{80} +4.78316 q^{82} +(-14.1551 + 1.65449i) q^{83} +(-6.80006 + 1.61164i) q^{85} +(-2.45490 - 1.23290i) q^{86} +(0.102183 + 0.341316i) q^{88} +(4.83016 - 1.75803i) q^{89} +(-16.2370 - 5.90980i) q^{91} +(-0.218294 + 3.74796i) q^{92} +(2.15196 - 2.89059i) q^{94} +(-1.60218 - 3.71427i) q^{95} +(-1.60445 + 0.805783i) q^{97} +(5.05691 - 4.24325i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 63 q^{20} + 9 q^{22} - 36 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{26}{27}\right)$

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 $

$2$	−1.71974	+	0.201009i	−1.21604	+	0.142135i	−0.699819	−	0.714320i	$-0.746736\pi$
$2$	−1.71974	+	0.201009i	−1.21604	+	0.142135i	−0.516222	+	0.856455i	$0.672662\pi$
$3$		0			0
$3$		0			0
$4$	0.971017	−	0.230135i	0.485509	−	0.115068i
$5$	1.23058	+	0.618019i	0.550331	+	0.276386i	0.702159	−	0.712020i	$-0.252220\pi$
$5$	1.23058	+	0.618019i	0.550331	+	0.276386i	−0.151828	+	0.988407i	$0.548516\pi$
$6$		0			0
$7$	−0.943081	−	3.15011i	−0.356451	−	1.19063i	−0.928788	−	0.370612i	$-0.879148\pi$
$7$	−0.943081	−	3.15011i	−0.356451	−	1.19063i	0.572337	−	0.820019i	$-0.306037\pi$
$8$	1.63042	−	0.593424i	0.576441	−	0.209807i
$9$		0			0
$10$	−2.24050	−	0.815476i	−0.708509	−	0.257876i
$11$	−0.0119397	+	0.204997i	−0.00359996	+	0.0618089i	−0.999630	−	0.0272125i	$-0.991337\pi$
$11$	−0.0119397	+	0.204997i	−0.00359996	+	0.0618089i	0.996030	+	0.0890214i	$0.0283740\pi$
$12$		0			0
$13$	3.13795	−	4.21500i	0.870310	−	1.16903i	−0.114157	−	0.993463i	$-0.536417\pi$
$13$	3.13795	−	4.21500i	0.870310	−	1.16903i	0.984468	−	0.175567i	$-0.0561757\pi$
$14$	2.25506	+	5.22781i	0.602689	+	1.39719i
$15$		0			0
$16$	−4.46816	+	2.24399i	−1.11704	+	0.560998i
$17$	−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	$0.831619\pi$
$20$	1.33714	+	0.316908i	0.298993	+	0.0708628i
$21$		0			0
$22$	−0.0206730	−	0.354942i	−0.00440750	−	0.0756738i
$23$	−1.07900	+	3.60410i	−0.224987	+	0.751508i	0.768729	+	0.639575i	$0.220889\pi$
$23$	−1.07900	+	3.60410i	−0.224987	+	0.751508i	−0.993716	+	0.111933i	$0.964296\pi$
$24$		0			0
$25$	−1.85342	−	2.48958i	−0.370684	−	0.497915i
$26$	−4.54921	+	7.87946i	−0.892173	+	1.54529i
$27$		0			0
$28$	−1.64070	−	2.84178i	−0.310063	−	0.537045i
$29$	2.49856	−	5.79232i	0.463971	−	1.07561i	−0.512251	−	0.858836i	$-0.671188\pi$
$29$	2.49856	−	5.79232i	0.463971	−	1.07561i	0.976223	−	0.216771i	$-0.0695524\pi$
$30$		0			0
$31$	−3.48702	−	3.69602i	−0.626287	−	0.663825i	0.334086	−	0.942543i	$-0.391572\pi$
$31$	−3.48702	−	3.69602i	−0.626287	−	0.663825i	−0.960373	+	0.278717i	$0.910091\pi$
$32$	4.33378	−	2.85037i	0.766111	−	0.503879i
$33$		0			0
$34$	6.03000	−	6.39142i	1.03414	−	1.09612i
$35$	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	$0.704741\pi$
$38$	4.24941	+	2.79488i	0.689345	+	0.453389i
$39$		0			0
$40$	2.37310	+	0.277376i	0.375221	+	0.0438570i
$41$	−2.74384	−	0.320709i	−0.428515	−	0.0500863i	−0.100898	−	0.994897i	$-0.532172\pi$
$41$	−2.74384	−	0.320709i	−0.428515	−	0.0500863i	−0.327617	+	0.944811i	$0.606246\pi$
$42$		0			0
$43$	1.32558	+	0.871847i	0.202149	+	0.132955i	0.646547	−	0.762874i	$-0.276212\pi$
$43$	1.32558	+	0.871847i	0.202149	+	0.132955i	−0.444399	+	0.895829i	$0.646583\pi$
$44$	0.0355834	+	0.201803i	0.00536439	+	0.0304230i
$45$		0			0
$46$	1.13114	−	6.41502i	0.166778	−	0.945843i
$47$	−1.42828	+	1.51388i	−0.208335	+	0.220823i	−0.823113	−	0.567878i	$-0.807764\pi$
$47$	−1.42828	+	1.51388i	−0.208335	+	0.220823i	0.614777	+	0.788701i	$0.289246\pi$
$48$		0			0
$49$	−3.18539	+	2.09506i	−0.455055	+	0.299294i
$50$	3.68783	+	3.90887i	0.521538	+	0.552798i
$51$		0			0
$52$	2.07698	−	4.81499i	0.288026	−	0.667719i
$53$	−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
$56$	−3.40697	−	4.57636i	−0.455276	−	0.611541i
$57$		0			0
$58$	−3.13257	+	10.4635i	−0.411327	+	1.37393i
$59$	−0.863215	−	14.8208i	−0.112381	−	1.92951i	−0.312840	−	0.949806i	$-0.601280\pi$
$59$	−0.863215	−	14.8208i	−0.112381	−	1.92951i	0.200459	−	0.979702i	$-0.435757\pi$
$60$		0			0
$61$	−1.46609	−	0.347469i	−0.187713	−	0.0444888i	0.135684	−	0.990752i	$-0.456677\pi$
$61$	−1.46609	−	0.347469i	−0.187713	−	0.0444888i	−0.323397	+	0.946263i	$0.604825\pi$
$62$	6.73971	+	5.65528i	0.855943	+	0.718222i
$63$		0			0
$64$	0.780406	−	0.654838i	0.0975508	−	0.0818548i
$65$	6.46643	−	3.24756i	0.802062	−	0.402811i
$66$		0			0
$67$	−5.31098	−	12.3122i	−0.648840	−	1.50418i	−0.851185	−	0.524866i	$-0.824116\pi$
$67$	−5.31098	−	12.3122i	−0.648840	−	1.50418i	0.202345	−	0.979314i	$-0.435144\pi$
$68$	−3.02423	+	4.06224i	−0.366741	+	0.492619i
$69$		0			0
$70$	−0.455864	+	7.82689i	−0.0544862	+	0.935492i
$71$	−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	$-0.0130060\pi$
$74$	−4.13139	−	13.7998i	−0.480265	−	1.60420i
$75$		0			0
$76$	−2.61958	−	1.31560i	−0.300487	−	0.150910i
$77$	0.657023	−	0.155717i	0.0748747	−	0.0177456i
$78$		0			0
$79$	1.47690	−	0.172625i	0.166164	−	0.0194218i	−0.0326039	−	0.999468i	$-0.510380\pi$
$79$	1.47690	−	0.172625i	0.166164	−	0.0194218i	0.198768	+	0.980047i	$0.436306\pi$
$80$	−6.88524			−0.769794
$81$		0			0
$82$	4.78316			0.528211
$83$	−14.1551	+	1.65449i	−1.55372	+	0.181604i	−0.849197	−	0.528076i	$-0.822914\pi$
$83$	−14.1551	+	1.65449i	−1.55372	+	0.181604i	−0.704524	+	0.709680i	$0.748840\pi$
$84$		0			0
$85$	−6.80006	+	1.61164i	−0.737570	+	0.174807i
$86$	−2.45490	−	1.23290i	−0.264719	−	0.132947i
$87$		0			0
$88$	0.102183	+	0.341316i	0.0108928	+	0.0363844i
$89$	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
$92$	−0.218294	+	3.74796i	−0.0227587	+	0.390752i
$93$		0			0
$94$	2.15196	−	2.89059i	0.221958	−	0.298141i
$95$	−1.60218	−	3.71427i	−0.164380	−	0.381076i
$96$		0			0
$97$	−1.60445	+	0.805783i	−0.162907	+	0.0818149i	−0.528384	−	0.849005i	$-0.677202\pi$
$97$	−1.60445	+	0.805783i	−0.162907	+	0.0818149i	0.365478	+	0.930820i	$0.380906\pi$
$98$	5.05691	−	4.24325i	0.510825	−	0.428633i
$99$		0			0
$100$	−2.37264	−	1.99088i	−0.237264	−	0.199088i
$101$	11.1658	+	2.64633i	1.11103	+	0.263320i	0.744856	−	0.667225i	$-0.232518\pi$
$101$	11.1658	+	2.64633i	1.11103	+	0.263320i	0.366178	+	0.930545i	$0.380666\pi$
$102$		0			0
$103$	−0.0290838	−	0.499350i	−0.00286571	−	0.0492024i	0.996572	−	0.0827284i	$-0.0263634\pi$
$103$	−0.0290838	−	0.499350i	−0.00286571	−	0.0492024i	−0.999438	+	0.0335260i	$0.989326\pi$
$104$	2.61489	−	8.73435i	0.256411	−	0.856473i
$105$		0			0
$106$	9.33994	+	12.5457i	0.907175	+	1.21855i
$107$	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	$-0.463750\pi$
$110$	0.193921	−	0.449559i	0.0184896	−	0.0428638i
$111$		0			0
$112$	11.2827	+	11.9589i	1.06611	+	1.13001i
$113$	−7.37939	+	4.85350i	−0.694195	+	0.456579i	−0.846941	−	0.531686i	$-0.821559\pi$
$113$	−7.37939	+	4.85350i	−0.694195	+	0.456579i	0.152747	+	0.988265i	$0.451188\pi$
$114$		0			0
$115$	−3.55519	+	3.76829i	−0.331524	+	0.351395i
$116$	1.09313	−	6.19945i	0.101495	−	0.575604i
$117$		0			0
$118$	4.46363	+	25.3145i	0.410910	+	2.33039i
$119$	13.9423	+	9.17002i	1.27809	+	0.840614i
$120$		0			0
$121$	10.8837	+	1.27213i	0.989431	+	0.115648i
$122$	2.59113	+	0.302860i	0.234590	+	0.0274197i
$123$		0			0
$124$	−4.23654	−	2.78642i	−0.380453	−	0.250228i
$125$	−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	$0.955362\pi$
$128$	−8.32971	+	8.82898i	−0.736249	+	0.780379i
$129$		0			0
$130$	−10.4678	+	6.88478i	−0.918087	+	0.603835i
$131$	3.87020	+	4.10217i	0.338141	+	0.358408i	0.874023	−	0.485884i	$-0.161502\pi$
$131$	3.87020	+	4.10217i	0.338141	+	0.358408i	−0.535882	+	0.844293i	$0.680021\pi$
$132$		0			0
$133$	−3.82584	+	8.86929i	−0.331742	+	0.769065i
$134$	11.6084	+	20.1063i	1.00281	+	1.73692i
$135$		0			0
$136$	−4.40265	+	7.62561i	−0.377524	+	0.653891i
$137$	0.665511	+	0.893937i	0.0568585	+	0.0763742i	0.829643	−	0.558294i	$-0.188544\pi$
$137$	0.665511	+	0.893937i	0.0568585	+	0.0763742i	−0.772784	+	0.634669i	$0.781137\pi$
$138$		0			0
$139$	1.36460	−	4.55809i	0.115744	−	0.386612i	−0.880412	−	0.474210i	$-0.842734\pi$
$139$	1.36460	−	4.55809i	0.115744	−	0.386612i	0.996156	+	0.0875977i	$0.0279190\pi$
$140$	−0.262736	−	4.51101i	−0.0222053	−	0.381250i
$141$		0			0
$142$	7.87469	+	1.86634i	0.660829	+	0.156619i
$143$	0.826595	+	0.693595i	0.0691233	+	0.0580014i
$144$		0			0
$145$	6.65443	−	5.58373i	0.552621	−	0.463704i
$146$	−25.1941	+	12.6529i	−2.08507	+	1.04716i
$147$		0			0
$148$	3.28836	+	7.62328i	0.270302	+	0.626630i
$149$	−4.58470	+	6.15832i	−0.375593	+	0.504510i	−0.949222	−	0.314606i	$-0.898128\pi$
$149$	−4.58470	+	6.15832i	−0.375593	+	0.504510i	0.573629	+	0.819115i	$0.305535\pi$
$150$		0			0
$151$	−0.179593	+	3.08349i	−0.0146150	+	0.250930i	0.983085	+	0.183149i	$0.0586291\pi$
$151$	−0.179593	+	3.08349i	−0.0146150	+	0.250930i	−0.997700	+	0.0677814i	$0.978408\pi$
$152$	−4.78937	−	1.74319i	−0.388469	−	0.141391i
$153$		0			0
$154$	−1.09861	+	0.399861i	−0.0885285	+	0.0322217i
$155$	−2.00683	−	6.70328i	−0.161193	−	0.538421i
$156$		0			0
$157$	5.47868	+	2.75149i	0.437246	+	0.219593i	0.653784	−	0.756681i	$-0.273180\pi$
$157$	5.47868	+	2.75149i	0.437246	+	0.219593i	−0.216538	+	0.976274i	$0.569477\pi$
$158$	−2.50519	+	0.593741i	−0.199302	+	0.0472355i
$159$		0			0
$160$	7.09463	−	0.829244i	0.560880	−	0.0655575i
$161$	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	$0.502143\pi$
$164$	−2.73812	+	0.320040i	−0.213811	+	0.0249909i
$165$		0			0
$166$	24.0105	−	5.69059i	1.86358	−	0.441676i
$167$	0.263030	+	0.132098i	0.0203538	+	0.0102221i	0.458947	−	0.888464i	$-0.348227\pi$
$167$	0.263030	+	0.132098i	0.0203538	+	0.0102221i	−0.438593	+	0.898686i	$0.644523\pi$
$168$		0			0
$169$	−4.19103	−	13.9990i	−0.322387	−	1.07685i
$170$	11.3704	−	4.13849i	0.872069	−	0.317407i
$171$		0			0
$172$	1.48780	+	0.541516i	0.113444	+	0.0412902i
$173$	−0.156232	+	2.68241i	−0.0118781	+	0.203940i	0.987148	+	0.159811i	$0.0510883\pi$
$173$	−0.156232	+	2.68241i	−0.0118781	+	0.203940i	−0.999026	+	0.0441291i	$0.985949\pi$
$174$		0			0
$175$	−6.09452	+	8.18636i	−0.460702	+	0.618830i
$176$	−0.406663	−	0.942751i	−0.0306534	−	0.0710626i
$177$		0			0
$178$	−7.95324	+	3.99427i	−0.596121	+	0.299383i
$179$	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	$0.508404\pi$
$182$	29.1114	+	6.89954i	2.15788	+	0.511428i
$183$		0			0
$184$	0.379543	+	6.51651i	0.0279803	+	0.480403i
$185$	−3.28576	+	10.9752i	−0.241574	+	0.806914i
$186$		0			0
$187$	−0.622304	−	0.835899i	−0.0455074	−	0.0611270i
$188$	−1.03848	+	1.79870i	−0.0757391	+	0.131184i
$189$		0			0
$190$	3.50193	+	6.06553i	0.254057	+	0.440040i
$191$	−5.62068	+	13.0302i	−0.406698	+	0.942833i	0.584615	+	0.811311i	$0.301246\pi$
$191$	−5.62068	+	13.0302i	−0.406698	+	0.942833i	−0.991313	+	0.131522i	$0.958014\pi$
$192$		0			0
$193$	2.86567	+	3.03743i	0.206275	+	0.218639i	0.822249	−	0.569127i	$-0.192719\pi$
$193$	2.86567	+	3.03743i	0.206275	+	0.218639i	−0.615974	+	0.787766i	$0.711237\pi$
$194$	2.59726	−	1.70825i	0.186473	−	0.122645i
$195$		0			0
$196$	−2.61092	+	2.76741i	−0.186494	+	0.197672i
$197$	−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	$0.911936\pi$
$200$	−4.49923	−	2.95919i	−0.318144	−	0.209246i
$201$		0			0
$202$	−19.7341	−	2.30659i	−1.38849	−	0.162291i
$203$	−20.6028	−	2.40812i	−1.44603	−	0.169017i
$204$		0			0
$205$	−3.17830	−	2.09040i	−0.221982	−	0.146000i
$206$	0.150390	+	0.852907i	0.0104782	+	0.0594248i
$207$		0			0
$208$	−4.56243	+	25.8748i	−0.316347	+	1.79409i
$209$	0.413941	−	0.438752i	0.0286329	−	0.0303491i
$210$		0			0
$211$	8.86778	−	5.83243i	0.610483	−	0.401521i	−0.206281	−	0.978493i	$-0.566136\pi$
$211$	8.86778	−	5.83243i	0.610483	−	0.401521i	0.816764	+	0.576972i	$0.195766\pi$
$212$	−6.18608	−	6.55687i	−0.424862	−	0.450327i
$213$		0			0
$214$	−3.73321	+	8.65456i	−0.255197	+	0.591613i
$215$	1.09241	+	1.89211i	0.0745016	+	0.129041i
$216$		0			0
$217$	−8.35434	+	14.4701i	−0.567130	+	0.982298i
$218$	17.3493	+	23.3041i	1.17504	+	1.57835i
$219$		0			0
$220$	−0.0809302	+	0.270326i	−0.00545631	+	0.0182254i
$221$	1.55059	+	26.6226i	0.104304	+	1.79083i
$222$		0			0
$223$	−23.0369	−	5.45985i	−1.54266	−	0.365618i	−0.630746	−	0.775989i	$-0.717251\pi$
$223$	−23.0369	−	5.45985i	−1.54266	−	0.365618i	−0.911919	+	0.410371i	$0.865399\pi$
$224$	−13.0661	−	10.9638i	−0.873015	−	0.732547i
$225$		0			0
$226$	11.7150	−	9.83009i	0.779273	−	0.653888i
$227$	−0.410190	+	0.206005i	−0.0272253	+	0.0136730i	−0.462360	−	0.886692i	$-0.652997\pi$
$227$	−0.410190	+	0.206005i	−0.0272253	+	0.0136730i	0.435134	+	0.900365i	$0.356701\pi$
$228$		0			0
$229$	6.33458	+	14.6852i	0.418601	+	0.970426i	0.988845	+	0.148951i	$0.0475896\pi$
$229$	6.33458	+	14.6852i	0.418601	+	0.970426i	−0.570244	+	0.821476i	$0.693151\pi$
$230$	5.35656	−	7.19511i	0.353201	−	0.474431i
$231$		0			0
$232$	0.636403	−	10.9266i	0.0417819	−	0.717368i
$233$	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
$236$	−4.24899	−	14.1926i	−0.276586	−	0.923862i
$237$		0			0
$238$	−25.8205	−	12.9675i	−1.67369	−	0.840560i
$239$	20.6455	−	4.89308i	1.33545	−	0.316507i	0.499977	−	0.866039i	$-0.333342\pi$
$239$	20.6455	−	4.89308i	1.33545	−	0.316507i	0.835473	+	0.549532i	$0.185194\pi$
$240$		0			0
$241$	17.9476	−	2.09777i	1.15611	−	0.135129i	0.483647	−	0.875263i	$-0.339312\pi$
$241$	17.9476	−	2.09777i	1.15611	−	0.135129i	0.672460	+	0.740134i	$0.265238\pi$
$242$	−18.9729			−1.21963
$243$		0			0
$244$	−1.50356			−0.0962556
$245$	−5.21465	+	0.609505i	−0.333152	+	0.0389398i
$246$		0			0
$247$	−15.0199	+	3.55979i	−0.955694	+	0.226504i
$248$	−7.87862	−	3.95679i	−0.500293	−	0.251256i
$249$		0			0
$250$	5.54152	+	18.5100i	0.350476	+	1.17067i
$251$	−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
$254$	0.702500	−	12.0615i	0.0440788	−	0.756803i
$255$		0			0
$256$	11.3335	−	15.2236i	0.708346	−	0.951474i
$257$	−6.54858	−	15.1813i	−0.408489	−	0.946984i	−0.990963	−	0.134135i	$-0.957174\pi$
$257$	−6.54858	−	15.1813i	−0.408489	−	0.946984i	0.582474	−	0.812849i	$-0.302085\pi$
$258$		0			0
$259$	24.4471	−	12.2778i	1.51907	−	0.762904i
$260$	5.53164	−	4.64160i	0.343058	−	0.287860i
$261$		0			0
$262$	−7.48032	−	6.27673i	−0.462135	−	0.387778i
$263$	0.0163370	+	0.00387195i	0.00100738	+	0.000238754i	0.231120	−	0.972925i	$-0.425761\pi$
$263$	0.0163370	+	0.00387195i	0.00100738	+	0.000238754i	−0.230112	+	0.973164i	$0.573909\pi$
$264$		0			0
$265$	−0.723278	−	12.4182i	−0.0444306	−	0.762844i
$266$	4.79665	−	16.0219i	0.294101	−	0.982366i
$267$		0			0
$268$	−7.99054	−	10.7332i	−0.488100	−	0.655632i
$269$	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	$-0.374173\pi$
$272$	10.0504	−	23.2994i	0.609394	−	1.41273i
$273$		0			0
$274$	−1.32420	−	1.40357i	−0.0799977	−	0.0847926i
$275$	0.532485	−	0.350221i	0.0321100	−	0.0211191i
$276$		0			0
$277$	−4.29297	+	4.55028i	−0.257940	+	0.273400i	−0.843383	−	0.537314i	$-0.819439\pi$
$277$	−4.29297	+	4.55028i	−0.257940	+	0.273400i	0.585443	+	0.810714i	$0.300921\pi$
$278$	−1.43055	+	8.11303i	−0.0857985	+	0.486587i
$279$		0			0
$280$	−1.36427	−	7.73713i	−0.0815304	−	0.462382i
$281$	−4.86386	−	3.19901i	−0.290153	−	0.190837i	0.396084	−	0.918214i	$-0.370369\pi$
$281$	−4.86386	−	3.19901i	−0.290153	−	0.190837i	−0.686238	+	0.727377i	$0.740739\pi$
$282$		0			0
$283$	8.53883	+	0.998046i	0.507581	+	0.0593277i	0.366029	−	0.930603i	$-0.380717\pi$
$283$	8.53883	+	0.998046i	0.507581	+	0.0593277i	0.141551	+	0.989931i	$0.454791\pi$
$284$	−4.63274	−	0.541490i	−0.274903	−	0.0321315i
$285$		0			0
$286$	−1.56095	−	1.02665i	−0.0923008	−	0.0607072i
$287$	1.57739	+	8.94585i	0.0931106	+	0.528057i
$288$		0			0
$289$	1.52028	−	8.62194i	0.0894282	−	0.507173i
$290$	−10.3215	+	10.9402i	−0.606101	+	0.642430i
$291$		0			0
$292$	13.5757	−	8.92891i	0.794460	−	0.522525i
$293$	4.41654	+	4.68126i	0.258017	+	0.273482i	0.843413	−	0.537265i	$-0.180543\pi$
$293$	4.41654	+	4.68126i	0.258017	+	0.273482i	−0.585396	+	0.810747i	$0.699061\pi$
$294$		0			0
$295$	8.09730	−	18.7717i	0.471443	−	1.09293i
$296$	7.21749	+	12.5011i	0.419508	+	0.726610i
$297$		0			0
$298$	6.64663	−	11.5123i	0.385029	−	0.666889i
$299$	11.8054	+	15.8575i	0.682726	+	0.917061i
$300$		0			0
$301$	1.49629	−	4.99794i	0.0862445	−	0.288077i
$302$	−0.310955	−	5.33890i	−0.0178935	−	0.307219i
$303$		0			0
$304$	14.2916	+	3.38717i	0.819680	+	0.194268i
$305$	−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	$0.0307127\pi$
$308$	0.602145	−	0.302409i	0.0343104	−	0.0172313i
$309$		0			0
$310$	4.79865	+	11.1245i	0.272545	+	0.631831i
$311$	7.75517	−	10.4170i	0.439755	−	0.590694i	−0.525892	−	0.850552i	$-0.676268\pi$
$311$	7.75517	−	10.4170i	0.439755	−	0.590694i	0.965647	+	0.259858i	$0.0836757\pi$
$312$		0			0
$313$	−0.303986	+	5.21924i	−0.0171823	+	0.295009i	0.978760	+	0.205011i	$0.0657231\pi$
$313$	−0.303986	+	5.21924i	−0.0171823	+	0.295009i	−0.995942	+	0.0899978i	$0.971314\pi$
$314$	−9.97498	−	3.63060i	−0.562921	−	0.204886i
$315$		0			0
$316$	1.39437	−	0.507509i	0.0784394	−	0.0285496i
$317$	−8.76380	−	29.2731i	−0.492224	−	1.64414i	−0.737988	−	0.674814i	$-0.764224\pi$
$317$	−8.76380	−	29.2731i	−0.492224	−	1.64414i	0.245764	−	0.969330i	$-0.420961\pi$
$318$		0			0
$319$	1.15758	+	0.581356i	0.0648118	+	0.0325497i
$320$	1.36505	−	0.323523i	0.0763087	−	0.0180855i
$321$		0			0
$322$	−21.2748	+	2.48667i	−1.18560	+	0.138576i
$323$	14.9076			0.829483
$324$		0			0
$325$	−16.3095			−0.904688
$326$	0.295613	−	0.0345522i	0.0163725	−	0.00191367i
$327$		0			0
$328$	−4.66392	+	1.10537i	−0.257522	+	0.0610338i
$329$	6.11588	+	3.07151i	0.337180	+	0.169338i
$330$		0			0
$331$	−0.913088	−	3.04992i	−0.0501878	−	0.167639i	0.929222	−	0.369523i	$-0.120479\pi$
$331$	−0.913088	−	3.04992i	−0.0501878	−	0.167639i	−0.979409	+	0.201884i	$0.935294\pi$
$332$	−13.3641	+	4.86412i	−0.733449	+	0.266953i
$333$		0			0
$334$	−0.478896	−	0.174304i	−0.0262040	−	0.00953748i
$335$	1.07363	−	18.4334i	0.0586585	−	1.00713i
$336$		0			0
$337$	−19.5699	+	26.2869i	−1.06604	+	1.43194i	−0.171372	+	0.985206i	$0.554820\pi$
$337$	−19.5699	+	26.2869i	−1.06604	+	1.43194i	−0.894667	+	0.446733i	$0.852587\pi$
$338$	10.0214	+	23.2322i	0.545093	+	1.26367i
$339$		0			0
$340$	−6.23208	+	3.12987i	−0.337982	+	0.169741i
$341$	0.799307	−	0.670699i	0.0432849	−	0.0363204i
$342$		0			0
$343$	−8.02888	−	6.73703i	−0.433519	−	0.363765i
$344$	2.67862	+	0.634846i	0.144422	+	0.0342286i
$345$		0			0
$346$	−0.270509	−	4.64445i	−0.0145426	−	0.249687i
$347$	−6.42646	+	21.4659i	−0.344990	+	1.15235i	0.592859	+	0.805306i	$0.297999\pi$
$347$	−6.42646	+	21.4659i	−0.344990	+	1.15235i	−0.937850	+	0.347042i	$0.887186\pi$
$348$		0			0
$349$	13.1779	+	17.7010i	0.705398	+	0.947514i	0.999967	−	0.00811637i	$-0.00258355\pi$
$349$	13.1779	+	17.7010i	0.705398	+	0.947514i	−0.294569	+	0.955630i	$0.595176\pi$
$350$	8.83546	−	15.3035i	0.472275	−	0.818005i
$351$		0			0
$352$	0.532573	+	0.922444i	0.0283863	+	0.0491664i
$353$	4.32393	−	10.0240i	0.230139	−	0.533523i	−0.763542	−	0.645758i	$-0.776542\pi$
$353$	4.32393	−	10.0240i	0.230139	−	0.533523i	0.993682	+	0.112235i	$0.0358008\pi$
$354$		0			0
$355$	−4.41690	−	4.68164i	−0.234425	−	0.248476i
$356$	4.28558	−	2.81867i	0.227135	−	0.149389i
$357$		0			0
$358$	−2.84399	+	3.01445i	−0.150310	+	0.159319i
$359$	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
$362$	−24.2241	−	15.9324i	−1.27319	−	0.837390i
$363$		0			0
$364$	−17.1265	−	2.00180i	−0.897673	−	0.104923i
$365$	22.2706	+	2.60306i	1.16570	+	0.136251i
$366$		0			0
$367$	10.7348	+	7.06040i	0.560353	+	0.368550i	0.797866	−	0.602834i	$-0.205962\pi$
$367$	10.7348	+	7.06040i	0.560353	+	0.368550i	−0.237514	+	0.971384i	$0.576332\pi$
$368$	−3.26645	−	18.5250i	−0.170276	−	0.965681i
$369$		0			0
$370$	3.44455	−	19.5350i	0.179074	−	1.01558i
$371$	−20.3839	+	21.6057i	−1.05828	+	1.12171i
$372$		0			0
$373$	−1.86370	+	1.22577i	−0.0964987	+	0.0634682i	−0.596841	−	0.802359i	$-0.703578\pi$
$373$	−1.86370	+	1.22577i	−0.0964987	+	0.0634682i	0.500343	+	0.865828i	$0.333207\pi$
$374$	1.23823	+	1.31244i	0.0640271	+	0.0678648i
$375$		0			0
$376$	−1.43031	+	3.31584i	−0.0737628	+	0.171001i
$377$	−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	$0.106142\pi$
$380$	−2.41053	−	3.23790i	−0.123657	−	0.166101i
$381$		0			0
$382$	7.04693	−	23.5384i	0.360553	−	1.20433i
$383$	0.840550	+	14.4317i	0.0429501	+	0.737425i	0.949198	+	0.314679i	$0.101897\pi$
$383$	0.840550	+	14.4317i	0.0429501	+	0.737425i	−0.906248	+	0.422746i	$0.861066\pi$
$384$		0			0
$385$	0.904754	+	0.214431i	0.0461105	+	0.0109284i
$386$	−5.53876	−	4.64757i	−0.281916	−	0.236555i
$387$		0			0
$388$	−1.37251	+	1.15167i	−0.0696784	+	0.0584671i
$389$	7.59957	−	3.81665i	0.385314	−	0.193512i	−0.245589	−	0.969374i	$-0.578981\pi$
$389$	7.59957	−	3.81665i	0.385314	−	0.193512i	0.630902	+	0.775862i	$0.282685\pi$
$390$		0			0
$391$	−7.56223	−	17.5312i	−0.382438	−	0.886591i
$392$	−3.95026	+	5.30611i	−0.199518	+	0.267999i
$393$		0			0
$394$	2.08580	−	35.8119i	0.105081	−	1.80418i
$395$	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	$0.432900\pi$
$398$	−1.42837	−	4.77108i	−0.0715976	−	0.239153i
$399$		0			0
$400$	13.8680	+	6.96476i	0.693399	+	0.348238i
$401$	−9.15526	+	2.16984i	−0.457192	+	0.108356i	−0.452758	−	0.891634i	$-0.649560\pi$
$401$	−9.15526	+	2.16984i	−0.457192	+	0.108356i	−0.00443443	+	0.999990i	$0.501412\pi$
$402$		0			0
$403$	−26.5208	+	3.09984i	−1.32110	+	0.154414i
$404$	11.4512			0.569716
$405$		0			0
$406$	35.9155			1.78246
$407$	−1.69683	+	0.198331i	−0.0841088	+	0.00983091i
$408$		0			0
$409$	−15.0060	+	3.55650i	−0.742001	+	0.175857i	−0.584196	−	0.811613i	$-0.698590\pi$
$409$	−15.0060	+	3.55650i	−0.742001	+	0.175857i	−0.157805	+	0.987470i	$0.550442\pi$
$410$	5.88604	+	2.95608i	0.290691	+	0.145990i
$411$		0			0
$412$	−0.143159	−	0.478184i	−0.00705294	−	0.0235584i
$413$	−45.8732	+	16.6965i	−2.25727	+	0.821580i
$414$		0			0
$415$	−18.4414	−	6.71212i	−0.905253	−	0.329485i
$416$	1.58487	−	27.2112i	0.0777047	−	1.33414i
$417$		0			0
$418$	−0.623678	+	0.837746i	−0.0305051	+	0.0409755i
$419$	−9.78506	−	22.6843i	−0.478031	−	1.10820i	−0.971200	−	0.238267i	$-0.923421\pi$
$419$	−9.78506	−	22.6843i	−0.478031	−	1.10820i	0.493168	−	0.869934i	$-0.335839\pi$
$420$		0			0
$421$	−0.166031	+	0.0833838i	−0.00809185	+	0.00406388i	−0.452841	−	0.891592i	$-0.649589\pi$
$421$	−0.166031	+	0.0833838i	−0.00809185	+	0.00406388i	0.444749	+	0.895655i	$0.353293\pi$
$422$	−14.0779	+	11.8128i	−0.685302	+	0.575037i
$423$		0			0
$424$	−12.0064	−	10.0746i	−0.583082	−	0.489264i
$425$	15.3267	+	3.63249i	0.743452	+	0.176201i
$426$		0			0
$427$	0.288073	+	4.94603i	0.0139408	+	0.239355i
$428$	1.55800	−	5.20409i	0.0753089	−	0.251549i
$429$		0			0
$430$	−2.25899	−	3.03435i	−0.108938	−	0.146329i
$431$	−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	$0.520617\pi$
$434$	11.4587	−	26.5642i	0.550034	−	1.27512i
$435$		0			0
$436$	−11.4909	−	12.1796i	−0.550313	−	0.583297i
$437$	9.23327	−	6.07282i	0.441687	−	0.290502i
$438$		0			0
$439$	1.34902	−	1.42987i	0.0643851	−	0.0682442i	−0.694380	−	0.719608i	$-0.744321\pi$
$439$	1.34902	−	1.42987i	0.0643851	−	0.0682442i	0.758765	+	0.651364i	$0.225803\pi$
$440$	−0.0851954	+	0.483167i	−0.00406153	+	0.0230341i
$441$		0			0
$442$	−8.01800	−	45.4724i	−0.381378	−	2.16290i
$443$	26.5757	+	17.4791i	1.26265	+	0.830456i	0.991248	−	0.132010i	$-0.0421433\pi$
$443$	26.5757	+	17.4791i	1.26265	+	0.830456i	0.271399	+	0.962467i	$0.412514\pi$
$444$		0			0
$445$	7.03038	+	0.821733i	0.333272	+	0.0389539i
$446$	40.7150	+	4.75890i	1.92791	+	0.225340i
$447$		0			0
$448$	−2.79880	−	1.84080i	−0.132231	−	0.0869696i
$449$	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
$452$	−6.04855	+	6.41109i	−0.284500	+	0.301552i
$453$		0			0
$454$	0.664012	−	0.436727i	0.0311636	−	0.0204966i
$455$	−16.3286	−	17.3073i	−0.765495	−	0.811377i
$456$		0			0
$457$	5.04859	−	11.7040i	0.236163	−	0.547488i	−0.758380	−	0.651813i	$-0.774009\pi$
$457$	5.04859	−	11.7040i	0.236163	−	0.547488i	0.994543	+	0.104325i	$0.0332681\pi$
$458$	−13.8457	−	23.9815i	−0.646968	−	1.12058i
$459$		0			0
$460$	−2.58494	+	4.47725i	−0.120523	+	0.208753i
$461$	−12.3421	−	16.5783i	−0.574828	−	0.772129i	0.415690	−	0.909506i	$-0.363540\pi$
$461$	−12.3421	−	16.5783i	−0.574828	−	0.772129i	−0.990519	+	0.137378i	$0.956133\pi$
$462$		0			0
$463$	4.77533	−	15.9507i	0.221929	−	0.741293i	−0.772418	−	0.635114i	$-0.780953\pi$
$463$	4.77533	−	15.9507i	0.221929	−	0.741293i	0.994347	−	0.106179i	$-0.0338617\pi$
$464$	1.83395	+	31.4878i	0.0851391	+	1.46178i
$465$		0			0
$466$	−13.3908	−	3.17367i	−0.620315	−	0.147017i
$467$	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
$470$	4.43459	−	2.22713i	0.204552	−	0.102730i
$471$		0			0
$472$	−10.2024	−	23.6519i	−0.469606	−	1.08867i
$473$	−0.194553	+	0.261330i	−0.00894555	+	0.0120160i
$474$		0			0
$475$	−0.530120	+	9.10181i	−0.0243236	+	0.417620i
$476$	15.6486	+	5.69562i	0.717252	+	0.261059i
$477$		0			0
$478$	−34.5215	+	12.5648i	−1.57897	+	0.574700i
$479$	6.41347	+	21.4225i	0.293039	+	0.978819i	0.970062	+	0.242857i	$0.0780845\pi$
$479$	6.41347	+	21.4225i	0.293039	+	0.978819i	−0.677023	+	0.735962i	$0.736730\pi$
$480$		0			0
$481$	39.0677	+	19.6205i	1.78133	+	0.894619i
$482$	−30.4436	+	7.21526i	−1.38667	+	0.328646i
$483$		0			0
$484$	10.8611	−	1.26948i	0.493685	−	0.0577035i
$485$	−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	$0.472999\pi$
$488$	−2.59653	+	0.303491i	−0.117540	+	0.0137384i
$489$		0			0
$490$	8.84533	−	2.09638i	0.399591	−	0.0947049i
$491$	1.07834	+	0.541563i	0.0486648	+	0.0244404i	0.472965	−	0.881081i	$-0.343184\pi$
$491$	1.07834	+	0.541563i	0.0486648	+	0.0244404i	−0.424300	+	0.905521i	$0.639480\pi$
$492$		0			0
$493$	9.18167	+	30.6689i	0.413522	+	1.38126i
$494$	25.1148	−	9.14105i	1.12997	−	0.411275i
$495$		0			0
$496$	23.8744	+	8.68957i	1.07199	+	0.390173i
$497$	−0.893649	+	15.3434i	−0.0400856	+	0.688244i
$498$		0			0
$499$	1.99325	−	2.67741i	0.0892303	−	0.119857i	−0.755266	−	0.655418i	$-0.772492\pi$
$499$	1.99325	−	2.67741i	0.0892303	−	0.119857i	0.844497	+	0.535561i	$0.179900\pi$
$500$	−4.41074	−	10.2252i	−0.197254	−	0.457287i
$501$		0			0
$502$	12.4940	−	6.27474i	0.557636	−	0.280055i
$503$	−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
$506$	1.30155	+	0.308474i	0.0578611	+	0.0137133i
$507$		0			0
$508$	0.404884	+	6.95159i	0.0179638	+	0.308427i
$509$	8.87341	−	29.6393i	0.393307	−	1.31374i	−0.500675	−	0.865635i	$-0.666915\pi$
$509$	8.87341	−	29.6393i	0.393307	−	1.31374i	0.893982	−	0.448102i	$-0.147900\pi$
$510$		0			0
$511$	−31.9731	−	42.9473i	−1.41440	−	1.89988i
$512$	−4.29252	+	7.43487i	−0.189705	+	0.328578i
$513$		0			0
$514$	14.3134	+	24.7916i	0.631339	+	1.09351i
$515$	0.272818	−	0.632463i	0.0120218	−	0.0278696i
$516$		0			0
$517$	−0.293288	−	0.310867i	−0.0128988	−	0.0136719i
$518$	−39.5747	+	26.0287i	−1.73881	+	1.14364i
$519$		0			0
$520$	8.61582	−	9.13223i	0.377829	−	0.400475i
$521$	−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	$0.935026\pi$
$524$	4.70209	+	3.09261i	0.205412	+	0.135101i
$525$		0			0
$526$	−0.0288738	−	0.00337486i	−0.00125896	−	0.000147151i
$527$	25.6130	+	2.99373i	1.11572	+	0.130409i
$528$		0			0
$529$	7.39088	+	4.86106i	0.321343	+	0.211350i
$530$	3.74002	+	21.2107i	0.162456	+	0.921335i
$531$		0			0
$532$	−1.67382	+	9.49269i	−0.0725692	+	0.411560i
$533$	−9.96180	+	10.5589i	−0.431493	+	0.457356i
$534$		0			0
$535$	6.26297	−	4.11922i	0.270772	−	0.178089i
$536$	−15.9655	−	16.9225i	−0.689605	−	0.730939i
$537$		0			0
$538$	−4.33884	+	10.0586i	−0.187060	+	0.433655i
$539$	−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	$-0.0140312\pi$
$542$	20.6532	+	27.7420i	0.887130	+	1.19162i
$543$		0			0
$544$	−7.54990	+	25.2184i	−0.323699	+	1.08123i
$545$	−1.34351	−	23.0672i	−0.0575498	−	0.988092i
$546$		0			0
$547$	27.6336	+	6.54928i	1.18153	+	0.280027i	0.774011	−	0.633172i	$-0.218247\pi$
$547$	27.6336	+	6.54928i	1.18153	+	0.280027i	0.407515	+	0.913199i	$0.366395\pi$
$548$	0.851950	+	0.714871i	0.0363935	+	0.0305378i
$549$		0			0
$550$	−0.845339	+	0.709324i	−0.0360454	+	0.0302457i
$551$	−16.5594	+	8.31645i	−0.705455	+	0.354293i
$552$		0			0
$553$	−1.93663	−	4.48960i	−0.0823537	−	0.190917i
$554$	6.46815	−	8.68824i	0.274805	−	0.369128i
$555$		0			0
$556$	0.276075	−	4.74003i	0.0117082	−	0.201022i
$557$	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
$560$	6.49335	+	21.6893i	0.274394	+	0.916540i
$561$		0			0
$562$	9.00761	+	4.52379i	0.379963	+	0.190825i
$563$	−21.5598	+	5.10976i	−0.908635	+	0.215351i	−0.658253	−	0.752797i	$-0.728704\pi$
$563$	−21.5598	+	5.10976i	−0.908635	+	0.215351i	−0.250382	+	0.968147i	$0.580556\pi$
$564$		0			0
$565$	−12.0805	+	1.41200i	−0.508229	+	0.0594034i
$566$	−14.8852			−0.625671
$567$		0			0
$568$	−8.10969			−0.340275
$569$	6.35985	−	0.743360i	0.266619	−	0.0311633i	0.0182670	−	0.999833i	$-0.494185\pi$
$569$	6.35985	−	0.743360i	0.266619	−	0.0311633i	0.248352	+	0.968670i	$0.420111\pi$
$570$		0			0
$571$	−5.37491	+	1.27388i	−0.224933	+	0.0533101i	−0.341537	−	0.939868i	$-0.610947\pi$
$571$	−5.37491	+	1.27388i	−0.224933	+	0.0533101i	0.116604	+	0.993179i	$0.462799\pi$
$572$	0.962259	+	0.483264i	0.0402341	+	0.0202063i
$573$		0			0
$574$	−4.51091	−	15.0675i	−0.188282	−	0.628904i
$575$	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	$0.308247\pi$
$578$	−0.881402	+	15.1331i	−0.0366615	+	0.629454i
$579$		0			0
$580$	5.17656	−	6.95332i	0.214945	−	0.288721i
$581$	18.5612	+	43.0297i	0.770049	+	1.78517i
$582$		0			0
$583$	1.65763	−	0.832491i	0.0686518	−	0.0344782i
$584$	21.6420	−	18.1598i	0.895551	−	0.751457i
$585$		0			0
$586$	−8.53628	−	7.16279i	−0.352631	−	0.295892i
$587$	−13.5333	−	3.20744i	−0.558578	−	0.132385i	−0.0583765	−	0.998295i	$-0.518592\pi$
$587$	−13.5333	−	3.20744i	−0.558578	−	0.132385i	−0.500201	+	0.865909i	$0.666741\pi$
$588$		0			0
$589$	0.867894	+	14.9012i	0.0357610	+	0.613992i
$590$	−10.1520	+	33.9100i	−0.417951	+	1.39605i
$591$		0			0
$592$	−24.8406	−	33.3667i	−1.02094	−	1.37136i
$593$	−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
$596$	−3.03458	+	7.03494i	−0.124301	+	0.288162i
$597$		0			0
$598$	−23.4898	−	24.8977i	−0.960570	−	1.01814i
$599$	34.7339	−	22.8449i	1.41919	−	0.933415i	0.419519	−	0.907747i	$-0.362199\pi$
$599$	34.7339	−	22.8449i	1.41919	−	0.933415i	0.999671	−	0.0256686i	$-0.00817146\pi$
$600$		0			0
$601$	6.33713	−	6.71697i	0.258497	−	0.273991i	−0.585108	−	0.810956i	$-0.698948\pi$
$601$	6.33713	−	6.71697i	0.258497	−	0.273991i	0.843605	+	0.536965i	$0.180429\pi$
$602$	−1.56859	+	8.89594i	−0.0639311	+	0.362571i
$603$		0			0
$604$	0.535232	+	3.03545i	0.0217783	+	0.123511i
$605$	12.6071	+	8.29181i	0.512551	+	0.337110i
$606$		0			0
$607$	13.3985	+	1.56606i	0.543829	+	0.0635645i	0.383572	−	0.923511i	$-0.374694\pi$
$607$	13.3985	+	1.56606i	0.543829	+	0.0635645i	0.160257	+	0.987075i	$0.448768\pi$
$608$	−15.1342	−	1.76893i	−0.613772	−	0.0717397i
$609$		0			0
$610$	3.00142	+	1.97406i	0.121524	+	0.0799275i
$611$	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	$0.0805691\pi$
$614$	−29.1695	+	30.9179i	−1.17719	+	1.24775i
$615$		0			0
$616$	0.978817	−	0.643778i	0.0394377	−	0.0259386i
$617$	16.4797	+	17.4674i	0.663447	+	0.703212i	0.968469	−	0.249133i	$-0.0801455\pi$
$617$	16.4797	+	17.4674i	0.663447	+	0.703212i	−0.305023	+	0.952345i	$0.598664\pi$
$618$		0			0
$619$	−4.03156	+	9.34620i	−0.162042	+	0.375656i	−0.979821	−	0.199877i	$-0.935946\pi$
$619$	−4.03156	+	9.34620i	−0.162042	+	0.375656i	0.817779	+	0.575532i	$0.195205\pi$
$620$	−3.49133	−	6.04716i	−0.140215	−	0.242860i
$621$		0			0
$622$	−11.2430	+	19.4734i	−0.450802	+	0.780812i
$623$	−10.0932	−	13.5576i	−0.404377	−	0.543172i
$624$		0			0
$625$	−0.0435457	+	0.145453i	−0.00174183	+	0.00581812i
$626$	−0.526337	−	9.03685i	−0.0210366	−	0.361185i
$627$		0			0
$628$	5.95311	+	1.41091i	0.237555	+	0.0563015i
$629$	−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	$0.841536\pi$
$632$	2.30553	−	1.15788i	0.0917090	−	0.0460580i
$633$		0			0
$634$	20.9556	+	48.5806i	0.832255	+	1.92938i
$635$	−5.73806	+	7.70755i	−0.227708	+	0.305865i
$636$		0			0
$637$	−1.16490	+	20.0006i	−0.0461550	+	0.792452i
$638$	−2.10759	−	0.767099i	−0.0834402	−	0.0303698i
$639$		0			0
$640$	−15.7068	+	5.71682i	−0.620867	+	0.225977i
$641$	−9.77403	−	32.6475i	−0.386051	−	1.28950i	−0.901574	−	0.432624i	$-0.857588\pi$
$641$	−9.77403	−	32.6475i	−0.386051	−	1.28950i	0.515524	−	0.856875i	$-0.327597\pi$
$642$		0			0
$643$	−17.7621	−	8.92044i	−0.700467	−	0.351788i	0.0626611	−	0.998035i	$-0.480041\pi$
$643$	−17.7621	−	8.92044i	−0.700467	−	0.351788i	−0.763128	+	0.646247i	$0.776338\pi$
$644$	12.0124	−	2.84699i	0.473354	−	0.112187i
$645$		0			0
$646$	−25.6373	+	2.99657i	−1.00869	+	0.117898i
$647$	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
$650$	28.0481	−	3.27835i	1.10014	−	0.128588i
$651$		0			0
$652$	−0.166912	+	0.0395588i	−0.00653677	+	0.00154924i
$653$	4.92172	+	2.47178i	0.192602	+	0.0967283i	0.542487	−	0.840064i	$-0.317483\pi$
$653$	4.92172	+	2.47178i	0.192602	+	0.0967283i	−0.349885	+	0.936793i	$0.613779\pi$
$654$		0			0
$655$	2.22736	+	7.43989i	0.0870301	+	0.290701i
$656$	12.9796	−	4.72418i	0.506767	−	0.184448i
$657$		0			0
$658$	−11.1351	−	4.05286i	−0.434093	−	0.157997i
$659$	2.21435	−	38.0190i	0.0862589	−	1.48101i	−0.626402	−	0.779500i	$-0.715473\pi$
$659$	2.21435	−	38.0190i	0.0862589	−	1.48101i	0.712661	−	0.701509i	$-0.247490\pi$
$660$		0			0
$661$	−16.8265	+	22.6020i	−0.654477	+	0.879115i	−0.998201	−	0.0599557i	$-0.980904\pi$
$661$	−16.8265	+	22.6020i	−0.654477	+	0.879115i	0.343724	+	0.939071i	$0.388311\pi$
$662$	2.18334	+	5.06154i	0.0848578	+	0.196723i
$663$		0			0
$664$	−22.0969	+	11.0975i	−0.857526	+	0.430666i
$665$	−10.1894	+	8.54990i	−0.395127	+	0.331551i
$666$		0			0
$667$	18.1802	+	15.2550i	0.703939	+	0.590675i
$668$	0.285807	+	0.0677375i	0.0110582	+	0.00262084i
$669$		0			0
$670$	1.85893	+	31.9166i	0.0718167	+	1.23304i
$671$	0.0887347	−	0.296395i	0.00342556	−	0.0114422i
$672$		0			0
$673$	14.8365	+	19.9289i	0.571907	+	0.768204i	0.990132	−	0.140139i	$-0.0447550\pi$
$673$	14.8365	+	19.9289i	0.571907	+	0.768204i	−0.418225	+	0.908343i	$0.637348\pi$
$674$	28.3712	−	49.1404i	1.09282	−	1.89282i
$675$		0			0
$676$	−7.29123	−	12.6288i	−0.280432	−	0.485722i
$677$	−13.9756	+	32.3992i	−0.537128	+	1.24520i	0.406335	+	0.913724i	$0.366806\pi$
$677$	−13.9756	+	32.3992i	−0.537128	+	1.24520i	−0.943463	+	0.331478i	$0.892453\pi$
$678$		0			0
$679$	4.05143	+	4.29426i	0.155480	+	0.164799i
$680$	−10.1306	+	6.66298i	−0.388490	+	0.255514i
$681$		0			0
$682$	−1.23979	+	1.31410i	−0.0474739	+	0.0503193i
$683$	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
$686$	15.1618	+	9.97208i	0.578880	+	0.380736i
$687$		0			0
$688$	−7.87931	−	0.920960i	−0.300396	−	0.0351113i
$689$	−47.1470	−	5.51069i	−1.79616	−	0.209941i
$690$		0			0
$691$	14.1957	+	9.33667i	0.540031	+	0.355184i	0.790036	−	0.613061i	$-0.210062\pi$
$691$	14.1957	+	9.33667i	0.540031	+	0.355184i	−0.250005	+	0.968245i	$0.580432\pi$
$692$	0.465612	+	2.64062i	0.0176999	+	0.100381i
$693$		0			0
$694$	6.73702	−	38.2075i	0.255734	−	1.45034i
$695$	4.49623	−	4.76573i	0.170552	−	0.180774i
$696$		0			0
$697$	11.7132	−	7.70389i	0.443669	−	0.291805i
$698$	−26.2207	−	27.7923i	−0.992468	−	1.05195i
$699$		0			0
$700$	−4.03391	+	9.35166i	−0.152468	+	0.353460i
$701$	−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
$704$	0.124922	+	0.167799i	0.00470818	+	0.00632418i
$705$		0			0
$706$	−5.42113	+	18.1078i	−0.204027	+	0.681497i
$707$	−2.19397	−	37.6691i	−0.0825129	−	1.41669i
$708$		0			0
$709$	31.9346	+	7.56865i	1.19933	+	0.284246i	0.781282	−	0.624178i	$-0.214566\pi$
$709$	31.9346	+	7.56865i	1.19933	+	0.284246i	0.418048	+	0.908425i	$0.362714\pi$
$710$	8.53698	+	7.16337i	0.320387	+	0.268837i
$711$		0			0
$712$	6.83193	−	5.73267i	0.256037	−	0.214841i
$713$	17.0833	−	8.57958i	0.639776	−	0.321308i
$714$		0			0
$715$	0.588533	+	1.36437i	0.0220099	+	0.0510247i
$716$	1.42635	−	1.91592i	0.0533051	−	0.0716012i
$717$		0			0
$718$	−2.49565	+	42.8487i	−0.0931368	+	1.59910i
$719$	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
$722$	5.15012	+	17.2026i	0.191668	+	0.640214i
$723$		0			0
$724$	14.9331	+	7.49969i	0.554985	+	0.278724i
$725$	−19.0513	+	4.51524i	−0.707548	+	0.167692i
$726$		0			0
$727$	8.34602	−	0.975510i	0.309537	−	0.0361797i	0.0400936	−	0.999196i	$-0.487234\pi$
$727$	8.34602	−	0.975510i	0.309537	−	0.0361797i	0.269443	+	0.963016i	$0.413160\pi$
$728$	−29.9802			−1.11114
$729$		0			0
$730$	−38.8230			−1.43690
$731$	−7.99740	+	0.934762i	−0.295795	+	0.0345734i
$732$		0			0
$733$	12.0138	−	2.84732i	0.443739	−	0.105168i	−0.00267116	−	0.999996i	$-0.500850\pi$
$733$	12.0138	−	2.84732i	0.443739	−	0.105168i	0.446411	+	0.894828i	$0.352702\pi$
$734$	−19.8803	−	9.98427i	−0.733796	−	0.368526i
$735$		0			0
$736$	5.59690	+	18.6949i	0.206304	+	0.689105i
$737$	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	$0.349705\pi$
$740$	−0.664749	+	11.4133i	−0.0244367	+	0.419561i
$741$		0			0
$742$	30.7121	−	41.2535i	1.12748	−	1.51446i
$743$	−7.85752	−	18.2158i	−0.288264	−	0.668272i	0.711130	−	0.703060i	$-0.248184\pi$
$743$	−7.85752	−	18.2158i	−0.288264	−	0.668272i	−0.999395	+	0.0347882i	$0.988924\pi$
$744$		0			0
$745$	−9.44779	+	4.74486i	−0.346140	+	0.173838i
$746$	2.95869	−	2.48263i	0.108325	−	0.0908957i
$747$		0			0
$748$	−0.796638	−	0.668459i	−0.0291280	−	0.0244413i
$749$	−17.4176	−	4.12805i	−0.636425	−	0.150836i
$750$		0			0
$751$	−2.23147	−	38.3128i	−0.0814274	−	1.39805i	−0.753441	−	0.657515i	$-0.771607\pi$
$751$	−2.23147	−	38.3128i	−0.0814274	−	1.39805i	0.672014	−	0.740539i	$-0.265430\pi$
$752$	2.98462	−	9.96932i	0.108838	−	0.363544i
$753$		0			0
$754$	34.2739	+	46.0378i	1.24818	+	1.67660i
$755$	−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	$0.750558\pi$
$758$	−5.04670	+	11.6996i	−0.183304	+	0.424947i
$759$		0			0
$760$	−4.81636	−	5.10504i	−0.174708	−	0.185179i
$761$	7.91964	−	5.20883i	0.287087	−	0.188820i	−0.397795	−	0.917474i	$-0.630224\pi$
$761$	7.91964	−	5.20883i	0.287087	−	0.188820i	0.684881	+	0.728655i	$0.259854\pi$
$762$		0			0
$763$	−37.8638	+	40.1332i	−1.37076	+	1.45292i
$764$	−2.45907	+	13.9461i	−0.0889660	+	0.504551i
$765$		0			0
$766$	−4.34643	−	24.6498i	−0.157043	−	0.890634i
$767$	−65.1785	−	42.8685i	−2.35346	−	1.54789i
$768$		0			0
$769$	12.4366	+	1.45363i	0.448476	+	0.0524193i	0.337334	−	0.941385i	$-0.390475\pi$
$769$	12.4366	+	1.45363i	0.448476	+	0.0524193i	0.111142	+	0.993804i	$0.464549\pi$
$770$	−1.59905	−	0.186902i	−0.0576256	−	0.00673547i
$771$		0			0
$772$	3.48164	+	2.28991i	0.125307	+	0.0824156i
$773$	−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
$776$	−2.13775	+	2.26588i	−0.0767407	+	0.0813404i
$777$		0			0
$778$	−12.3021	+	8.09123i	−0.441052	+	0.290085i
$779$	5.56879	+	5.90257i	0.199522	+	0.211481i
$780$		0			0
$781$	0.380151	−	0.881289i	0.0136029	−	0.0315350i
$782$	16.5290	+	28.6291i	0.591076	+	1.02377i
$783$		0			0
$784$	9.53150	−	16.5091i	0.340411	−	0.589609i
$785$	5.04146	+	6.77185i	0.179937	+	0.241698i
$786$		0			0
$787$	−11.4581	+	38.2728i	−0.408438	+	1.36428i	0.468410	+	0.883511i	$0.344827\pi$
$787$	−11.4581	+	38.2728i	−0.408438	+	1.36428i	−0.876848	+	0.480767i	$0.840358\pi$
$788$	1.20215	+	20.6401i	0.0428248	+	0.735273i
$789$		0			0
$790$	−3.44977	−	0.817611i	−0.122737	−	0.0290893i
$791$	22.2484	+	18.6687i	0.791063	+	0.663781i
$792$		0			0
$793$	−6.06508	+	5.08921i	−0.215377	+	0.180723i
$794$	8.49811	−	4.26791i	0.301586	−	0.151462i
$795$		0			0
$796$	1.13690	+	2.63563i	0.0402964	+	0.0934176i
$797$	20.3548	−	27.3413i	0.721005	−	0.968478i	−0.278962	−	0.960302i	$-0.589990\pi$
$797$	20.3548	−	27.3413i	0.721005	−	0.968478i	0.999967	−	0.00817540i	$-0.00260234\pi$
$798$		0			0
$799$	0.614153	−	10.5446i	0.0217272	−	0.373041i
$800$	−15.1285	−	5.50634i	−0.534875	−	0.194678i
$801$		0			0
$802$	15.3085	−	5.57185i	0.540563	−	0.196749i
$803$	0.958950	+	3.20312i	0.0338406	+	0.113036i
$804$		0			0
$805$	15.2234	+	7.64546i	0.536553	+	0.269467i
$806$	44.9858	−	10.6618i	1.58456	−	0.375547i
$807$		0			0
$808$	19.7753	−	2.31140i	0.695691	−	0.0813147i
$809$	−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	$0.382468\pi$
$812$	−20.5599	+	2.40310i	−0.721510	+	0.0843324i
$813$		0			0
$814$	2.87825	−	0.682157i	0.100882	−	0.0239096i
$815$	−0.211529	−	0.106234i	−0.00740952	−	0.00372120i
$816$		0			0
$817$	−1.33668	−	4.46483i	−0.0467646	−	0.156205i
$818$	25.0916	−	9.13260i	0.877308	−	0.319314i
$819$		0			0
$820$	−3.56726	−	1.29838i	−0.124574	−	0.0453412i
$821$	−1.77197	+	30.4235i	−0.0618420	+	1.06179i	0.814520	+	0.580135i	$0.197000\pi$
$821$	−1.77197	+	30.4235i	−0.0618420	+	1.06179i	−0.876363	+	0.481652i	$0.840037\pi$
$822$		0			0
$823$	−13.3276	+	17.9020i	−0.464570	+	0.624026i	−0.971237	−	0.238116i	$-0.923470\pi$
$823$	−13.3276	+	17.9020i	−0.464570	+	0.624026i	0.506667	+	0.862142i	$0.330878\pi$
$824$	−0.343745	−	0.796891i	−0.0119749	−	0.0277610i
$825$		0			0
$826$	75.5339	−	37.9346i	2.62816	−	1.31991i
$827$	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	$0.820861\pi$
$830$	33.0637	+	7.83623i	1.14766	+	0.272000i
$831$		0			0
$832$	−0.311267	−	5.34426i	−0.0107913	−	0.185279i
$833$	5.54927	−	18.5359i	0.192271	−	0.642230i
$834$		0			0
$835$	0.242039	+	0.325114i	0.00837610	+	0.0112510i
$836$	0.300972	−	0.521298i	0.0104093	−	0.0180295i
$837$		0			0
$838$	21.3875	+	37.0443i	0.738820	+	1.27967i
$839$	15.1824	−	35.1966i	0.524153	−	1.21512i	−0.426393	−	0.904538i	$-0.640216\pi$
$839$	15.1824	−	35.1966i	0.524153	−	1.21512i	0.950546	−	0.310585i	$-0.100525\pi$
$840$		0			0
$841$	−7.40713	−	7.85110i	−0.255418	−	0.270728i
$842$	0.268769	−	0.176772i	0.00926240	−	0.00609198i
$843$		0			0
$844$	7.26852	−	7.70418i	0.250193	−	0.265189i
$845$	3.49427	−	19.8170i	0.120206	−	0.681725i
$846$		0			0
$847$	−6.25691	−	35.4847i	−0.214990	−	1.21927i
$848$	37.7359	+	24.8193i	1.29586	+	0.852297i
$849$		0			0
$850$	−27.0881	−	3.16614i	−0.929113	−	0.108598i
$851$	−31.0880	−	3.63367i	−1.06568	−	0.124560i
$852$		0			0
$853$	−7.01364	−	4.61295i	−0.240143	−	0.157944i	0.423733	−	0.905787i	$-0.360719\pi$
$853$	−7.01364	−	4.61295i	−0.240143	−	0.157944i	−0.663876	+	0.747843i	$0.731090\pi$
$854$	−1.48961	−	8.44799i	−0.0509733	−	0.289084i
$855$		0			0
$856$	1.64011	−	9.30155i	0.0560580	−	0.317920i
$857$	33.0230	−	35.0023i	1.12804	−	1.19566i	0.149688	−	0.988733i	$-0.452173\pi$
$857$	33.0230	−	35.0023i	1.12804	−	1.19566i	0.978357	−	0.206924i	$-0.0663453\pi$
$858$		0			0
$859$	−42.6770	+	28.0691i	−1.45612	+	0.957706i	−0.458505	+	0.888692i	$0.651615\pi$
$859$	−42.6770	+	28.0691i	−1.45612	+	0.957706i	−0.997616	+	0.0690137i	$0.978015\pi$
$860$	1.49619	+	1.58587i	0.0510196	+	0.0540776i
$861$		0			0
$862$	9.97981	−	23.1358i	0.339914	−	0.788008i
$863$	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
$866$	−35.7945	−	48.0804i	−1.21635	−	1.63384i
$867$		0			0
$868$	−4.78212	+	15.9734i	−0.162316	+	0.542172i
$869$	0.0177538	+	0.304821i	0.000602257	+	0.0103404i
$870$		0			0
$871$	−68.5616	−	16.2494i	−2.32312	−	0.550590i
$872$	−22.3023	−	18.7138i	−0.755250	−	0.633730i
$873$		0			0
$874$	−14.6581	+	12.2996i	−0.495819	+	0.416042i
$875$	−32.7913	+	16.4684i	−1.10855	+	0.556734i
$876$		0			0
$877$	−1.60802	−	3.72781i	−0.0542990	−	0.125879i	0.888907	−	0.458088i	$-0.151465\pi$
$877$	−1.60802	−	3.72781i	−0.0542990	−	0.125879i	−0.943206	+	0.332209i	$0.892206\pi$
$878$	−2.03254	+	2.73018i	−0.0685950	+	0.0921391i
$879$		0			0
$880$	0.0822078	−	1.41145i	0.00277122	−	0.0475801i
$881$	−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	$0.534112\pi$
$884$	7.63246	+	25.4942i	0.256707	+	0.857462i
$885$		0			0
$886$	−49.2167	−	24.7176i	−1.65347	−	0.830403i
$887$	−21.1533	+	5.01341i	−0.710257	+	0.168334i	−0.569837	−	0.821758i	$-0.692994\pi$
$887$	−21.1533	+	5.01341i	−0.710257	+	0.168334i	−0.140420	+	0.990092i	$0.544845\pi$
$888$		0			0
$889$	22.7900	−	2.66377i	0.764352	−	0.0893399i
$890$	−12.2556			−0.410809
$891$		0			0
$892$	−23.6257			−0.791048
$893$	6.07249	−	0.709773i	0.203208	−	0.0237516i
$894$		0			0
$895$	3.20718	−	0.760117i	0.107204	−	0.0254079i
$896$	35.6679	+	17.9131i	1.19158	+	0.598434i
$897$		0			0
$898$	−14.7919	−	49.4085i	−0.493614	−	1.64878i
$899$	−30.1211	+	10.9632i	−1.00459	+	0.365642i
$900$		0			0
$901$	43.0785	+	15.6793i	1.43515	+	0.522353i
$902$	−0.0571095	+	0.980532i	−0.00190154	+	0.0326481i
$903$		0			0
$904$	−9.15132	+	12.2924i	−0.304368	+	0.408838i
$905$	9.13334	+	21.1735i	0.303602	+	0.703830i
$906$		0			0
$907$	−47.1055	+	23.6573i	−1.56411	+	0.785527i	−0.999214	−	0.0396329i	$-0.987381\pi$
$907$	−47.1055	+	23.6573i	−1.56411	+	0.785527i	−0.564899	+	0.825160i	$0.691085\pi$
$908$	−0.350892	+	0.294434i	−0.0116448	+	0.00977113i
$909$		0			0
$910$	31.5598	+	26.4818i	1.04620	+	0.877864i
$911$	−41.8920	−	9.92859i	−1.38794	−	0.328949i	−0.532319	−	0.846544i	$-0.678679\pi$
$911$	−41.8920	−	9.92859i	−1.38794	−	0.328949i	−0.855626	+	0.517595i	$0.826827\pi$
$912$		0			0
$913$	−0.170158	−	2.92150i	−0.00563141	−	0.0966876i
$914$	−6.32968	+	21.1426i	−0.209367	+	0.699335i
$915$		0			0
$916$	9.53058	+	12.8018i	0.314899	+	0.422983i
$917$	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	$-0.479310\pi$
$920$	−3.56027	+	8.25363i	−0.117379	+	0.272114i
$921$		0			0
$922$	24.5576	+	26.0295i	0.808761	+	0.857237i
$923$	−20.5204	+	13.4965i	−0.675439	+	0.444243i
$924$		0			0
$925$	17.7200	−	18.7821i	0.582631	−	0.617552i
$926$	−5.00610	+	28.3910i	−0.164511	+	0.932987i
$927$		0			0
$928$	−5.68204	−	32.2245i	−0.186522	−	1.05782i
$929$	−13.2760	−	8.73178i	−0.435573	−	0.286481i	0.312725	−	0.949844i	$-0.398758\pi$
$929$	−13.2760	−	8.73178i	−0.435573	−	0.286481i	−0.748298	+	0.663363i	$0.769128\pi$
$930$		0			0
$931$	11.1238	+	1.30019i	0.364568	+	0.0426119i
$932$	7.87789	+	0.920793i	0.258049	+	0.0301616i
$933$		0			0
$934$	−42.3790	−	27.8731i	−1.38668	−	0.912036i
$935$	−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	$-0.0666189\pi$
$938$	52.3895	−	55.5296i	1.71058	−	1.81311i
$939$		0			0
$940$	−2.38957	+	1.57164i	−0.0779390	+	0.0512613i
$941$	9.70324	+	10.2848i	0.316317	+	0.335276i	0.865951	−	0.500130i	$-0.166714\pi$
$941$	9.70324	+	10.2848i	0.316317	+	0.335276i	−0.549634	+	0.835406i	$0.685233\pi$
$942$		0			0
$943$	4.11646	−	9.54303i	0.134050	−	0.310764i
$944$	37.1148	+	64.2848i	1.20799	+	2.09229i
$945$		0			0
$946$	0.282051	−	0.488527i	0.00917027	−	0.0158834i
$947$	34.0917	+	45.7931i	1.10783	+	1.48808i	0.853598	+	0.520932i	$0.174416\pi$
$947$	34.0917	+	45.7931i	1.10783	+	1.48808i	0.254233	+	0.967143i	$0.418177\pi$
$948$		0			0
$949$	24.5397	−	81.9683i	0.796593	−	2.66080i
$950$	−0.917876	−	15.7593i	−0.0297798	−	0.511300i
$951$		0			0
$952$	28.1736	+	6.67726i	0.913111	+	0.216411i
$953$	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
$956$	18.9211	−	9.50254i	0.611953	−	0.307334i
$957$		0			0
$958$	−15.3356	−	35.5520i	−0.495472	−	1.14863i
$959$	2.18837	−	2.93949i	0.0706661	−	0.0949211i
$960$		0			0
$961$	0.301197	−	5.17135i	0.00971602	−	0.166818i
$962$	−71.1302	−	25.8893i	−2.29333	−	0.834704i
$963$		0			0
$964$	16.9447	−	6.16735i	0.545751	−	0.198637i
$965$	1.64924	+	5.50883i	0.0530908	+	0.177336i
$966$		0			0
$967$	−19.7655	−	9.92662i	−0.635617	−	0.319219i	0.101650	−	0.994820i	$-0.467588\pi$
$967$	−19.7655	−	9.92662i	−0.635617	−	0.319219i	−0.737267	+	0.675601i	$0.763884\pi$
$968$	18.5000	−	4.38458i	0.594612	−	0.140926i
$969$		0			0
$970$	4.25186	−	0.496971i	0.136519	−	0.0159568i
$971$	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
$974$	−6.43073	+	0.751645i	−0.206054	+	0.0240843i
$975$		0			0
$976$	7.33043	−	1.73734i	0.234641	−	0.0556110i
$977$	−20.7615	−	10.4268i	−0.664218	−	0.333583i	0.0845457	−	0.996420i	$-0.473056\pi$
$977$	−20.7615	−	10.4268i	−0.664218	−	0.333583i	−0.748764	+	0.662837i	$0.769352\pi$
$978$		0			0
$979$	0.302721	+	1.01116i	0.00967500	+	0.0323167i
$980$	−4.92325	+	1.79191i	−0.157267	+	0.0572406i
$981$		0			0
$982$	−1.96332	−	0.714592i	−0.0626522	−	0.0228035i
$983$	−0.979980	+	16.8256i	−0.0312565	+	0.536653i	0.945943	+	0.324332i	$0.105139\pi$
$983$	−0.979980	+	16.8256i	−0.0312565	+	0.536653i	−0.977200	+	0.212321i	$0.931898\pi$
$984$		0			0
$985$	−17.0370	+	22.8846i	−0.542843	+	0.729164i
$986$	−21.9548	−	50.8970i	−0.699184	−	1.62089i
$987$		0			0
$988$	−13.7654	+	6.91323i	−0.437935	+	0.219939i
$989$	−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	$0.724311\pi$
$992$	−25.6470	−	6.07845i	−0.814293	−	0.192991i
$993$		0			0
$994$	−1.54731	−	26.5663i	−0.0490776	−	0.842630i
$995$	−1.13600	+	3.79452i	−0.0360137	+	0.120294i
$996$		0			0
$997$	3.48850	+	4.68587i	0.110482	+	0.148403i	0.853925	−	0.520397i	$-0.174216\pi$
$997$	3.48850	+	4.68587i	0.110482	+	0.148403i	−0.743443	+	0.668799i	$0.766808\pi$
$998$	−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.b.298.2		144
3.2	odd	2		729.2.g.c.298.7		144
9.2	odd	6		729.2.g.d.541.2		144
9.4	even	3		243.2.g.a.181.7		144
9.5	odd	6		81.2.g.a.34.2	yes	144
9.7	even	3		729.2.g.a.541.7		144
81.2	odd	54		6561.2.a.c.1.17		72
81.4	even	27	inner	729.2.g.b.433.2		144
81.23	odd	54		81.2.g.a.31.2	✓	144
81.31	even	27		729.2.g.a.190.7		144
81.50	odd	54		729.2.g.d.190.2		144
81.58	even	27		243.2.g.a.145.7		144
81.77	odd	54		729.2.g.c.433.7		144
81.79	even	27		6561.2.a.d.1.56		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.31.2	✓	144	81.23	odd	54
81.2.g.a.34.2	yes	144	9.5	odd	6
243.2.g.a.145.7		144	81.58	even	27
243.2.g.a.181.7		144	9.4	even	3
729.2.g.a.190.7		144	81.31	even	27
729.2.g.a.541.7		144	9.7	even	3
729.2.g.b.298.2		144	1.1	even	1	trivial
729.2.g.b.433.2		144	81.4	even	27	inner
729.2.g.c.298.7		144	3.2	odd	2
729.2.g.c.433.7		144	81.77	odd	54
729.2.g.d.190.2		144	81.50	odd	54
729.2.g.d.541.2		144	9.2	odd	6
6561.2.a.c.1.17		72	81.2	odd	54
6561.2.a.d.1.56		72	81.79	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)

\(f(q)\)	\(=\)	\(q+(-1.71974 + 0.201009i) q^{2} +(0.971017 - 0.230135i) q^{4} +(1.23058 + 0.618019i) q^{5} +(-0.943081 - 3.15011i) q^{7} +(1.63042 - 0.593424i) q^{8} +(-2.24050 - 0.815476i) q^{10} +(-0.0119397 + 0.204997i) q^{11} +(3.13795 - 4.21500i) q^{13} +(2.25506 + 5.22781i) q^{14} +(-4.46816 + 2.24399i) q^{16} +(-3.88762 + 3.26210i) q^{17} +(-2.25026 - 1.88819i) q^{19} +(1.33714 + 0.316908i) q^{20} +(-0.0206730 - 0.354942i) q^{22} +(-1.07900 + 3.60410i) q^{23} +(-1.85342 - 2.48958i) q^{25} +(-4.54921 + 7.87946i) q^{26} +(-1.64070 - 2.84178i) q^{28} +(2.49856 - 5.79232i) q^{29} +(-3.48702 - 3.69602i) q^{31} +(4.33378 - 2.85037i) q^{32} +(6.03000 - 6.39142i) q^{34} +(0.786294 - 4.45930i) q^{35} +(1.44468 + 8.19321i) q^{37} +(4.24941 + 2.79488i) q^{38} +(2.37310 + 0.277376i) q^{40} +(-2.74384 - 0.320709i) q^{41} +(1.32558 + 0.871847i) q^{43} +(0.0355834 + 0.201803i) q^{44} +(1.13114 - 6.41502i) q^{46} +(-1.42828 + 1.51388i) q^{47} +(-3.18539 + 2.09506i) q^{49} +(3.68783 + 3.90887i) q^{50} +(2.07698 - 4.81499i) q^{52} +(-4.51663 - 7.82303i) q^{53} +(-0.141385 + 0.244885i) q^{55} +(-3.40697 - 4.57636i) q^{56} +(-3.13257 + 10.4635i) q^{58} +(-0.863215 - 14.8208i) q^{59} +(-1.46609 - 0.347469i) q^{61} +(6.73971 + 5.65528i) q^{62} +(0.780406 - 0.654838i) q^{64} +(6.46643 - 3.24756i) q^{65} +(-5.31098 - 12.3122i) q^{67} +(-3.02423 + 4.06224i) q^{68} +(-0.455864 + 7.82689i) q^{70} +(-4.39214 - 1.59861i) q^{71} +(15.3008 - 5.56905i) q^{73} +(-4.13139 - 13.7998i) q^{74} +(-2.61958 - 1.31560i) q^{76} +(0.657023 - 0.155717i) q^{77} +(1.47690 - 0.172625i) q^{79} -6.88524 q^{80} +4.78316 q^{82} +(-14.1551 + 1.65449i) q^{83} +(-6.80006 + 1.61164i) q^{85} +(-2.45490 - 1.23290i) q^{86} +(0.102183 + 0.341316i) q^{88} +(4.83016 - 1.75803i) q^{89} +(-16.2370 - 5.90980i) q^{91} +(-0.218294 + 3.74796i) q^{92} +(2.15196 - 2.89059i) q^{94} +(-1.60218 - 3.71427i) q^{95} +(-1.60445 + 0.805783i) q^{97} +(5.05691 - 4.24325i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

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