LMFDB - Embedded newform 729.2.g.a.622.4

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			622.4
Character	$\chi$	$=$	729.622
Dual form			729.2.g.a.109.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453861 + 0.481064i) q^{2} +(0.0908564 + 1.55994i) q^{4} +(-2.49650 - 0.291799i) q^{5} +(3.67465 - 1.84548i) q^{7} +(-1.80495 - 1.51453i) q^{8} +(1.27344 - 1.06854i) q^{10} +(-1.17263 + 2.71847i) q^{11} +(-3.15575 + 0.747925i) q^{13} +(-0.779986 + 2.60534i) q^{14} +(-1.55626 + 0.181901i) q^{16} +(0.572741 + 3.24818i) q^{17} +(-0.571121 + 3.23899i) q^{19} +(0.228367 - 3.92091i) q^{20} +(-0.775546 - 1.79792i) q^{22} +(-2.23062 - 1.12026i) q^{23} +(1.28214 + 0.303873i) q^{25} +(1.07247 - 1.85757i) q^{26} +(3.21271 + 5.56458i) q^{28} +(1.59664 + 5.33313i) q^{29} +(-5.36607 + 3.52932i) q^{31} +(3.43286 - 4.61114i) q^{32} +(-1.82253 - 1.19870i) q^{34} +(-9.71228 + 3.53498i) q^{35} +(-2.56937 - 0.935175i) q^{37} +(-1.29895 - 1.74480i) q^{38} +(4.06412 + 4.30771i) q^{40} +(-6.20948 - 6.58166i) q^{41} +(-4.66833 - 6.27065i) q^{43} +(-4.34719 - 1.58225i) q^{44} +(1.55131 - 0.564629i) q^{46} +(-8.45508 - 5.56099i) q^{47} +(5.91716 - 7.94813i) q^{49} +(-0.728095 + 0.478876i) q^{50} +(-1.45344 - 4.85483i) q^{52} +(-0.00494432 - 0.00856381i) q^{53} +(3.72072 - 6.44448i) q^{55} +(-9.42760 - 2.23438i) q^{56} +(-3.29023 - 1.65242i) q^{58} +(4.50463 + 10.4429i) q^{59} +(-0.523995 + 8.99665i) q^{61} +(0.737619 - 4.18325i) q^{62} +(0.116049 + 0.658144i) q^{64} +(8.09656 - 0.946352i) q^{65} +(-1.67644 + 5.59970i) q^{67} +(-5.01494 + 1.18856i) q^{68} +(2.70747 - 6.27662i) q^{70} +(1.81817 - 1.52563i) q^{71} +(3.61987 + 3.03743i) q^{73} +(1.61602 - 0.811594i) q^{74} +(-5.10453 - 0.596634i) q^{76} +(0.707860 + 12.1535i) q^{77} +(-6.17756 + 6.54783i) q^{79} +3.93828 q^{80} +5.98444 q^{82} +(-2.54001 + 2.69226i) q^{83} +(-0.482034 - 8.27620i) q^{85} +(5.13536 + 0.600238i) q^{86} +(6.23375 - 3.13071i) q^{88} +(9.57258 + 8.03235i) q^{89} +(-10.2160 + 8.57223i) q^{91} +(1.54487 - 3.58142i) q^{92} +(6.51263 - 1.54352i) q^{94} +(2.37094 - 7.91949i) q^{95} +(7.10357 - 0.830288i) q^{97} +(1.13799 + 6.45388i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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 $

$2$	−0.453861	+	0.481064i	−0.320928	+	0.340164i	−0.867673	−	0.497135i	$-0.834385\pi$
$2$	−0.453861	+	0.481064i	−0.320928	+	0.340164i	0.546745	+	0.837299i	$0.315867\pi$
$3$		0			0
$3$		0			0
$4$	0.0908564	+	1.55994i	0.0454282	+	0.779972i
$5$	−2.49650	−	0.291799i	−1.11647	−	0.130496i	−0.462212	−	0.886769i	$-0.652944\pi$
$5$	−2.49650	−	0.291799i	−1.11647	−	0.130496i	−0.654256	+	0.756273i	$0.727018\pi$
$6$		0			0
$7$	3.67465	−	1.84548i	1.38889	−	0.697526i	0.411981	−	0.911192i	$-0.364837\pi$
$7$	3.67465	−	1.84548i	1.38889	−	0.697526i	0.976907	+	0.213667i	$0.0685407\pi$
$8$	−1.80495	−	1.51453i	−0.638146	−	0.535468i
$9$		0			0
$10$	1.27344	−	1.06854i	0.402696	−	0.337902i
$11$	−1.17263	+	2.71847i	−0.353562	+	0.819648i	0.644903	+	0.764264i	$0.276898\pi$
$11$	−1.17263	+	2.71847i	−0.353562	+	0.819648i	−0.998465	+	0.0553842i	$0.982362\pi$
$12$		0			0
$13$	−3.15575	+	0.747925i	−0.875246	+	0.207437i	−0.643599	−	0.765363i	$-0.722560\pi$
$13$	−3.15575	+	0.747925i	−0.875246	+	0.207437i	−0.231647	+	0.972800i	$0.574411\pi$
$14$	−0.779986	+	2.60534i	−0.208460	+	0.696305i
$15$		0			0
$16$	−1.55626	+	0.181901i	−0.389065	+	0.0454751i
$17$	0.572741	+	3.24818i	0.138910	+	0.787799i	0.972057	+	0.234746i	$0.0754260\pi$
$17$	0.572741	+	3.24818i	0.138910	+	0.787799i	−0.833146	+	0.553052i	$0.813463\pi$
$18$		0			0
$19$	−0.571121	+	3.23899i	−0.131024	+	0.743075i	0.846522	+	0.532354i	$0.178692\pi$
$19$	−0.571121	+	3.23899i	−0.131024	+	0.743075i	−0.977546	+	0.210722i	$0.932419\pi$
$20$	0.228367	−	3.92091i	0.0510644	−	0.876742i
$21$		0			0
$22$	−0.775546	−	1.79792i	−0.165347	−	0.383317i
$23$	−2.23062	−	1.12026i	−0.465116	−	0.233590i	0.200778	−	0.979637i	$-0.435653\pi$
$23$	−2.23062	−	1.12026i	−0.465116	−	0.233590i	−0.665893	+	0.746047i	$0.731949\pi$
$24$		0			0
$25$	1.28214	+	0.303873i	0.256428	+	0.0607745i
$26$	1.07247	−	1.85757i	0.210329	−	0.364300i
$27$		0			0
$28$	3.21271	+	5.56458i	0.607145	+	1.05161i
$29$	1.59664	+	5.33313i	0.296488	+	0.990338i	0.968336	+	0.249650i	$0.0803154\pi$
$29$	1.59664	+	5.33313i	0.296488	+	0.990338i	−0.671848	+	0.740689i	$0.734499\pi$
$30$		0			0
$31$	−5.36607	+	3.52932i	−0.963775	+	0.633885i	−0.930783	−	0.365571i	$-0.880874\pi$
$31$	−5.36607	+	3.52932i	−0.963775	+	0.633885i	−0.0329913	+	0.999456i	$0.510503\pi$
$32$	3.43286	−	4.61114i	0.606850	−	0.815141i
$33$		0			0
$34$	−1.82253	−	1.19870i	−0.312561	−	0.205575i
$35$	−9.71228	+	3.53498i	−1.64167	+	0.597521i
$36$		0			0
$37$	−2.56937	−	0.935175i	−0.422402	−	0.153742i	0.122069	−	0.992522i	$-0.461047\pi$
$37$	−2.56937	−	0.935175i	−0.422402	−	0.153742i	−0.544471	+	0.838780i	$0.683269\pi$
$38$	−1.29895	−	1.74480i	−0.210718	−	0.283044i
$39$		0			0
$40$	4.06412	+	4.30771i	0.642593	+	0.681109i
$41$	−6.20948	−	6.58166i	−0.969757	−	1.02788i	−0.999599	−	0.0283280i	$-0.990982\pi$
$41$	−6.20948	−	6.58166i	−0.969757	−	1.02788i	0.0298414	−	0.999555i	$-0.490500\pi$
$42$		0			0
$43$	−4.66833	−	6.27065i	−0.711914	−	0.956266i	0.288086	−	0.957605i	$-0.406981\pi$
$43$	−4.66833	−	6.27065i	−0.711914	−	0.956266i	−0.999999	+	0.00133878i	$0.999574\pi$
$44$	−4.34719	−	1.58225i	−0.655364	−	0.238533i
$45$		0			0
$46$	1.55131	−	0.564629i	0.228728	−	0.0832500i
$47$	−8.45508	−	5.56099i	−1.23330	−	0.811154i	−0.245884	−	0.969299i	$-0.579078\pi$
$47$	−8.45508	−	5.56099i	−1.23330	−	0.811154i	−0.987416	+	0.158145i	$0.949449\pi$
$48$		0			0
$49$	5.91716	−	7.94813i	0.845309	−	1.13545i
$50$	−0.728095	+	0.478876i	−0.102968	+	0.0677233i
$51$		0			0
$52$	−1.45344	−	4.85483i	−0.201556	−	0.673244i
$53$	−0.00494432	−	0.00856381i	−0.000679154	−	0.00117633i	0.865686	−	0.500588i	$-0.166883\pi$
$53$	−0.00494432	−	0.00856381i	−0.000679154	−	0.00117633i	−0.866365	+	0.499412i	$0.833550\pi$
$54$		0			0
$55$	3.72072	−	6.44448i	0.501702	−	0.868973i
$56$	−9.42760	−	2.23438i	−1.25982	−	0.298582i
$57$		0			0
$58$	−3.29023	−	1.65242i	−0.432029	−	0.216973i
$59$	4.50463	+	10.4429i	0.586453	+	1.35955i	0.910500	+	0.413509i	$0.135697\pi$
$59$	4.50463	+	10.4429i	0.586453	+	1.35955i	−0.324048	+	0.946041i	$0.605044\pi$
$60$		0			0
$61$	−0.523995	+	8.99665i	−0.0670907	+	1.15190i	0.781868	+	0.623444i	$0.214267\pi$
$61$	−0.523995	+	8.99665i	−0.0670907	+	1.15190i	−0.848959	+	0.528459i	$0.822770\pi$
$62$	0.737619	−	4.18325i	0.0936777	−	0.531273i
$63$		0			0
$64$	0.116049	+	0.658144i	0.0145061	+	0.0822680i
$65$	8.09656	−	0.946352i	1.00425	−	0.117381i
$66$		0			0
$67$	−1.67644	+	5.59970i	−0.204810	+	0.684113i	0.792437	+	0.609954i	$0.208812\pi$
$67$	−1.67644	+	5.59970i	−0.204810	+	0.684113i	−0.997246	+	0.0741583i	$0.976373\pi$
$68$	−5.01494	+	1.18856i	−0.608150	+	0.144134i
$69$		0			0
$70$	2.70747	−	6.27662i	0.323604	−	0.750199i
$71$	1.81817	−	1.52563i	0.215777	−	0.181058i	−0.528492	−	0.848938i	$-0.677242\pi$
$71$	1.81817	−	1.52563i	0.215777	−	0.181058i	0.744269	+	0.667880i	$0.232798\pi$
$72$		0			0
$73$	3.61987	+	3.03743i	0.423674	+	0.355505i	0.829559	−	0.558420i	$-0.188592\pi$
$73$	3.61987	+	3.03743i	0.423674	+	0.355505i	−0.405885	+	0.913924i	$0.633037\pi$
$74$	1.61602	−	0.811594i	0.187858	−	0.0943459i
$75$		0			0
$76$	−5.10453	−	0.596634i	−0.585530	−	0.0684386i
$77$	0.707860	+	12.1535i	0.0806681	+	1.38502i
$78$		0			0
$79$	−6.17756	+	6.54783i	−0.695029	+	0.736688i	−0.974727	−	0.223400i	$-0.928284\pi$
$79$	−6.17756	+	6.54783i	−0.695029	+	0.736688i	0.279698	+	0.960088i	$0.409766\pi$
$80$	3.93828			0.440313
$81$		0			0
$82$	5.98444			0.660871
$83$	−2.54001	+	2.69226i	−0.278803	+	0.295514i	−0.851609	−	0.524177i	$-0.824373\pi$
$83$	−2.54001	+	2.69226i	−0.278803	+	0.295514i	0.572807	+	0.819691i	$0.305855\pi$
$84$		0			0
$85$	−0.482034	−	8.27620i	−0.0522839	−	0.897680i
$86$	5.13536	+	0.600238i	0.553760	+	0.0647253i
$87$		0			0
$88$	6.23375	−	3.13071i	0.664520	−	0.333734i
$89$	9.57258	+	8.03235i	1.01469	+	0.851427i	0.988951	−	0.148242i	$-0.0473614\pi$
$89$	9.57258	+	8.03235i	1.01469	+	0.851427i	0.0257399	+	0.999669i	$0.491806\pi$
$90$		0			0
$91$	−10.2160	+	8.57223i	−1.07093	+	0.898614i
$92$	1.54487	−	3.58142i	0.161064	−	0.373389i
$93$		0			0
$94$	6.51263	−	1.54352i	0.671726	−	0.159202i
$95$	2.37094	−	7.91949i	0.243253	−	0.812522i
$96$		0			0
$97$	7.10357	−	0.830288i	0.721258	−	0.0843030i	0.252459	−	0.967608i	$-0.418761\pi$
$97$	7.10357	−	0.830288i	0.721258	−	0.0843030i	0.468799	+	0.883305i	$0.344687\pi$
$98$	1.13799	+	6.45388i	0.114955	+	0.651940i
$99$		0			0
$100$	−0.357534	+	2.02767i	−0.0357534	+	0.202767i
$101$	−0.122459	+	2.10254i	−0.0121851	+	0.209211i	0.986720	+	0.162430i	$0.0519332\pi$
$101$	−0.122459	+	2.10254i	−0.0121851	+	0.209211i	−0.998905	+	0.0467805i	$0.985104\pi$
$102$		0			0
$103$	−0.818039	−	1.89643i	−0.0806038	−	0.186861i	0.873148	−	0.487454i	$-0.162074\pi$
$103$	−0.818039	−	1.89643i	−0.0806038	−	0.186861i	−0.953752	+	0.300594i	$0.902815\pi$
$104$	6.82872	+	3.42951i	0.669611	+	0.336291i
$105$		0			0
$106$	0.00636378	+	0.00150824i	0.000618105	+	0.000146493i
$107$	7.13179	−	12.3526i	0.689456	−	1.19417i	−0.282558	−	0.959250i	$-0.591183\pi$
$107$	7.13179	−	12.3526i	0.689456	−	1.19417i	0.972014	−	0.234923i	$-0.0754838\pi$
$108$		0			0
$109$	−6.70237	−	11.6088i	−0.641970	−	1.11193i	−0.984992	−	0.172598i	$-0.944784\pi$
$109$	−6.70237	−	11.6088i	−0.641970	−	1.11193i	0.343022	−	0.939327i	$-0.388549\pi$
$110$	1.41152	+	4.71480i	0.134583	+	0.449539i
$111$		0			0
$112$	−5.38302	+	3.54047i	−0.508647	+	0.334543i
$113$	1.76779	−	2.37455i	0.166300	−	0.223379i	−0.711159	−	0.703031i	$-0.751830\pi$
$113$	1.76779	−	2.37455i	0.166300	−	0.223379i	0.877459	+	0.479652i	$0.159237\pi$
$114$		0			0
$115$	5.24184	+	3.44761i	0.488804	+	0.321492i
$116$	−8.17432	+	2.97521i	−0.758967	+	0.276241i
$117$		0			0
$118$	−7.06818	−	2.57261i	−0.650679	−	0.236828i
$119$	8.09907	+	10.8789i	0.742440	+	0.997271i
$120$		0			0
$121$	1.53367	+	1.62559i	0.139424	+	0.147781i
$122$	−4.09015	−	4.33530i	−0.370305	−	0.392500i
$123$		0			0
$124$	−5.99308	−	8.05011i	−0.538195	−	0.722921i
$125$	8.69737	+	3.16558i	0.777917	+	0.283139i
$126$		0			0
$127$	−11.3063	+	4.11514i	−1.00327	+	0.365160i	−0.790844	−	0.612017i	$-0.790358\pi$
$127$	−11.3063	+	4.11514i	−1.00327	+	0.365160i	−0.212425	+	0.977177i	$0.568136\pi$
$128$	9.23660	+	6.07500i	0.816407	+	0.536960i
$129$		0			0
$130$	−3.21946	+	4.32448i	−0.282365	+	0.379282i
$131$	−4.29128	+	2.82242i	−0.374931	+	0.246596i	−0.722963	−	0.690887i	$-0.757220\pi$
$131$	−4.29128	+	2.82242i	−0.374931	+	0.246596i	0.348032	+	0.937483i	$0.386850\pi$
$132$		0			0
$133$	3.87882	+	12.9562i	0.336336	+	1.12344i
$134$	−1.93295	−	3.34796i	−0.166981	−	0.289220i
$135$		0			0
$136$	3.88570	−	6.73023i	0.333196	−	0.577113i
$137$	−1.84980	−	0.438412i	−0.158039	−	0.0374560i	0.150834	−	0.988559i	$-0.451804\pi$
$137$	−1.84980	−	0.438412i	−0.158039	−	0.0374560i	−0.308874	+	0.951103i	$0.599952\pi$
$138$		0			0
$139$	8.36246	+	4.19978i	0.709294	+	0.356221i	0.766591	−	0.642136i	$-0.221952\pi$
$139$	8.36246	+	4.19978i	0.709294	+	0.356221i	−0.0572963	+	0.998357i	$0.518248\pi$
$140$	−6.39679	−	14.8294i	−0.540627	−	1.25332i
$141$		0			0
$142$	−0.0912720	+	1.56708i	−0.00765937	+	0.131506i
$143$	1.66732	−	9.45583i	0.139428	−	0.790736i
$144$		0			0
$145$	−2.42980	−	13.7801i	−0.201784	−	1.14437i
$146$	−3.10412	+	0.362820i	−0.256899	+	0.0300272i
$147$		0			0
$148$	1.22538	−	4.09304i	0.100725	−	0.336446i
$149$	0.864689	−	0.204935i	0.0708381	−	0.0167889i	−0.195044	−	0.980794i	$-0.562485\pi$
$149$	0.864689	−	0.204935i	0.0708381	−	0.0167889i	0.265882	+	0.964006i	$0.414337\pi$
$150$		0			0
$151$	−3.19183	+	7.39949i	−0.259747	+	0.602162i	−0.997325	−	0.0731007i	$-0.976711\pi$
$151$	−3.19183	+	7.39949i	−0.259747	+	0.602162i	0.737577	+	0.675263i	$0.235970\pi$
$152$	5.93640	−	4.98123i	0.481506	−	0.404031i
$153$		0			0
$154$	−6.16788	−	5.17546i	−0.497022	−	0.417051i
$155$	14.4262	−	7.24513i	1.15874	−	0.581943i
$156$		0			0
$157$	14.3727	+	1.67993i	1.14707	+	0.134073i	0.668315	−	0.743878i	$-0.267016\pi$
$157$	14.3727	+	1.67993i	1.14707	+	0.134073i	0.478751	+	0.877951i	$0.341090\pi$
$158$	−0.346176	−	5.94360i	−0.0275402	−	0.472848i
$159$		0			0
$160$	−9.91567	+	10.5100i	−0.783902	+	0.830888i
$161$	−10.2641			−0.808928
$162$		0			0
$163$	8.05495			0.630912			0.315456	−	0.948940i	$-0.397843\pi$
$163$	8.05495			0.630912			0.315456	+	0.948940i	$0.397843\pi$
$164$	9.70285	−	10.2844i	0.757665	−	0.803078i
$165$		0			0
$166$	−0.142336	−	2.44382i	−0.0110474	−	0.189677i
$167$	16.7682	+	1.95992i	1.29756	+	0.151663i	0.736685	−	0.676236i	$-0.236390\pi$
$167$	16.7682	+	1.95992i	1.29756	+	0.151663i	0.560877	+	0.827899i	$0.310464\pi$
$168$		0			0
$169$	−2.21789	+	1.11386i	−0.170607	+	0.0856819i
$170$	4.20016	+	3.52435i	0.322138	+	0.270306i
$171$		0			0
$172$	9.35772	−	7.85206i	0.713520	−	0.598714i
$173$	−2.66291	+	6.17332i	−0.202457	+	0.469349i	−0.988950	−	0.148251i	$-0.952636\pi$
$173$	−2.66291	+	6.17332i	−0.202457	+	0.469349i	0.786492	+	0.617600i	$0.211895\pi$
$174$		0			0
$175$	5.27221	−	1.24954i	0.398541	−	0.0944560i
$176$	1.33043	−	4.44394i	0.100285	−	0.334975i
$177$		0			0
$178$	−8.20869	+	0.959459i	−0.615268	+	0.0719145i
$179$	2.64043	+	14.9746i	0.197355	+	1.11926i	0.909024	+	0.416743i	$0.136828\pi$
$179$	2.64043	+	14.9746i	0.197355	+	1.11926i	−0.711669	+	0.702515i	$0.752060\pi$
$180$		0			0
$181$	−0.973297	+	5.51984i	−0.0723446	+	0.410287i	0.927032	+	0.374982i	$0.122351\pi$
$181$	−0.973297	+	5.51984i	−0.0723446	+	0.410287i	−0.999377	+	0.0353044i	$0.988760\pi$
$182$	0.512841	−	8.80515i	0.0380143	−	0.652681i
$183$		0			0
$184$	2.32948	+	5.40035i	0.171732	+	0.398119i
$185$	6.14155	+	3.08440i	0.451536	+	0.226770i
$186$		0			0
$187$	−9.50168	−	2.25194i	−0.694831	−	0.164678i
$188$	7.90664	−	13.6947i	0.576651	−	0.998788i
$189$		0			0
$190$	2.73371	+	4.73492i	0.198324	+	0.343507i
$191$	−1.23201	−	4.11521i	−0.0891453	−	0.297766i	0.901777	−	0.432202i	$-0.142263\pi$
$191$	−1.23201	−	4.11521i	−0.0891453	−	0.297766i	−0.990922	+	0.134435i	$0.957078\pi$
$192$		0			0
$193$	−2.36750	+	1.55713i	−0.170417	+	0.112085i	−0.631852	−	0.775089i	$-0.717705\pi$
$193$	−2.36750	+	1.55713i	−0.170417	+	0.112085i	0.461435	+	0.887174i	$0.347335\pi$
$194$	−2.82461	+	3.79411i	−0.202795	+	0.272401i
$195$		0			0
$196$	12.9362	+	8.50830i	0.924017	+	0.607736i
$197$	−19.9667	+	7.26729i	−1.42257	+	0.517773i	−0.934792	−	0.355195i	$-0.884414\pi$
$197$	−19.9667	+	7.26729i	−1.42257	+	0.517773i	−0.487777	+	0.872968i	$0.662192\pi$
$198$		0			0
$199$	−9.14529	−	3.32862i	−0.648293	−	0.235959i	−0.00311899	−	0.999995i	$-0.500993\pi$
$199$	−9.14529	−	3.32862i	−0.648293	−	0.235959i	−0.645174	+	0.764036i	$0.723215\pi$
$200$	−1.85397	−	2.49032i	−0.131096	−	0.176092i
$201$		0			0
$202$	−0.955878	−	1.01317i	−0.0672553	−	0.0712865i
$203$	15.7093	+	16.6509i	1.10257	+	1.16866i
$204$		0			0
$205$	13.5814	+	18.2430i	0.948568	+	1.27415i
$206$	1.28358	+	0.467185i	0.0894313	+	0.0325503i
$207$		0			0
$208$	4.77511	−	1.73800i	0.331094	−	0.120508i
$209$	−8.13537	−	5.35072i	−0.562735	−	0.370117i
$210$		0			0
$211$	11.6913	−	15.7041i	0.804861	−	1.08112i	−0.190190	−	0.981747i	$-0.560910\pi$
$211$	11.6913	−	15.7041i	0.804861	−	1.08112i	0.995051	−	0.0993683i	$-0.0316822\pi$
$212$	0.0129098	−	0.00849093i	0.000886651	−	0.000583160i
$213$		0			0
$214$	2.70557	+	9.03722i	0.184949	+	0.617772i
$215$	9.82471	+	17.0169i	0.670040	+	1.16054i
$216$		0			0
$217$	−13.2052	+	22.8720i	−0.896424	+	1.55265i
$218$	8.62654	+	2.04453i	0.584263	+	0.138473i
$219$		0			0
$220$	10.3911	+	5.21859i	0.700566	+	0.351837i
$221$	−4.23682	−	9.82205i	−0.284999	−	0.660703i
$222$		0			0
$223$	0.939986	−	16.1389i	0.0629461	−	1.08074i	−0.807942	−	0.589262i	$-0.799419\pi$
$223$	0.939986	−	16.1389i	0.0629461	−	1.08074i	0.870888	−	0.491481i	$-0.163544\pi$
$224$	4.10482	−	23.2796i	0.274265	−	1.55543i
$225$		0			0
$226$	0.339982	+	1.92814i	0.0226153	+	0.128258i
$227$	21.0869	−	2.46470i	1.39958	−	0.163588i	0.617407	−	0.786644i	$-0.288183\pi$
$227$	21.0869	−	2.46470i	1.39958	−	0.163588i	0.782177	+	0.623056i	$0.214109\pi$
$228$		0			0
$229$	2.47496	−	8.26696i	0.163550	−	0.546296i	−0.836448	−	0.548046i	$-0.815372\pi$
$229$	2.47496	−	8.26696i	0.163550	−	0.546296i	0.999998	+	0.00175006i	$0.000557061\pi$
$230$	−4.03759	+	0.956927i	−0.266231	+	0.0630979i
$231$		0			0
$232$	5.19536	−	12.0442i	0.341092	−	0.790740i
$233$	11.4634	−	9.61890i	0.750989	−	0.630155i	−0.184775	−	0.982781i	$-0.559156\pi$
$233$	11.4634	−	9.61890i	0.750989	−	0.630155i	0.935764	+	0.352626i	$0.114711\pi$
$234$		0			0
$235$	19.4854	+	16.3502i	1.27109	+	1.06657i
$236$	−15.8811	+	7.97577i	−1.03377	+	0.519178i
$237$		0			0
$238$	−8.90932	−	1.04135i	−0.577506	−	0.0675007i
$239$	−0.209933	−	3.60440i	−0.0135794	−	0.233150i	−0.998268	−	0.0588277i	$-0.981264\pi$
$239$	−0.209933	−	3.60440i	−0.0135794	−	0.233150i	0.984689	−	0.174322i	$-0.0557733\pi$
$240$		0			0
$241$	15.7090	−	16.6506i	1.01191	−	1.07256i	0.0145522	−	0.999894i	$-0.495368\pi$
$241$	15.7090	−	16.6506i	1.01191	−	1.07256i	0.997356	−	0.0726662i	$-0.0231508\pi$
$242$	−1.47808			−0.0950149
$243$		0			0
$244$	−14.0819			−0.901500
$245$	−17.0914	+	18.1159i	−1.09193	+	1.15738i
$246$		0			0
$247$	−0.620210	−	10.6486i	−0.0394630	−	0.677553i
$248$	15.0308	+	1.75684i	0.954454	+	0.111560i
$249$		0			0
$250$	−5.47025	+	2.74726i	−0.345969	+	0.173752i
$251$	16.2193	+	13.6096i	1.02375	+	0.859031i	0.990095	−	0.140402i	$-0.0448396\pi$
$251$	16.2193	+	13.6096i	1.02375	+	0.859031i	0.0336587	+	0.999433i	$0.489284\pi$
$252$		0			0
$253$	5.66107	−	4.75020i	0.355909	−	0.298643i
$254$	3.15182	−	7.30675i	0.197763	−	0.458466i
$255$		0			0
$256$	−8.41516	+	1.99443i	−0.525948	+	0.124652i
$257$	−2.23335	+	7.45990i	−0.139312	+	0.465336i	−0.998962	−	0.0455481i	$-0.985497\pi$
$257$	−2.23335	+	7.45990i	−0.139312	+	0.465336i	0.859650	+	0.510884i	$0.170682\pi$
$258$		0			0
$259$	−11.1674	+	1.30528i	−0.693908	+	0.0811062i
$260$	2.21188	+	12.5442i	0.137175	+	0.777958i
$261$		0			0
$262$	0.589879	−	3.34537i	0.0364428	−	0.206678i
$263$	0.0887569	−	1.52390i	0.00547299	−	0.0939675i	−0.994465	−	0.105064i	$-0.966495\pi$
$263$	0.0887569	−	1.52390i	0.00547299	−	0.0939675i	0.999938	+	0.0110966i	$0.00353224\pi$
$264$		0			0
$265$	0.00984458	+	0.0228223i	0.000604747	+	0.00140196i
$266$	−7.99319	−	4.01433i	−0.490094	−	0.246134i
$267$		0			0
$268$	−8.88754	−	2.10638i	−0.542893	−	0.128668i
$269$	−14.7193	+	25.4946i	−0.897454	+	1.55444i	−0.0667154	+	0.997772i	$0.521252\pi$
$269$	−14.7193	+	25.4946i	−0.897454	+	1.55444i	−0.830738	+	0.556663i	$0.812081\pi$
$270$		0			0
$271$	−7.28643	−	12.6205i	−0.442619	−	0.766639i	0.555264	−	0.831674i	$-0.312617\pi$
$271$	−7.28643	−	12.6205i	−0.442619	−	0.766639i	−0.997883	+	0.0650354i	$0.979284\pi$
$272$	−1.48218	−	4.95082i	−0.0898703	−	0.300188i
$273$		0			0
$274$	1.05046	−	0.690897i	0.0634605	−	0.0417386i
$275$	−2.32954	+	3.12912i	−0.140477	+	0.188693i
$276$		0			0
$277$	−8.54418	−	5.61960i	−0.513370	−	0.337649i	0.266247	−	0.963905i	$-0.414216\pi$
$277$	−8.54418	−	5.61960i	−0.513370	−	0.337649i	−0.779618	+	0.626256i	$0.784587\pi$
$278$	−5.81576	+	2.11676i	−0.348806	+	0.126955i
$279$		0			0
$280$	22.8840	+	8.32910i	1.36758	+	0.497759i
$281$	−4.19424	−	5.63385i	−0.250208	−	0.336087i	0.659219	−	0.751951i	$-0.270887\pi$
$281$	−4.19424	−	5.63385i	−0.250208	−	0.336087i	−0.909427	+	0.415863i	$0.863479\pi$
$282$		0			0
$283$	14.8381	+	15.7275i	0.882036	+	0.934904i	0.998298	−	0.0583150i	$-0.0185728\pi$
$283$	14.8381	+	15.7275i	0.882036	+	0.934904i	−0.116262	+	0.993219i	$0.537091\pi$
$284$	2.54508	+	2.69763i	0.151023	+	0.160075i
$285$		0			0
$286$	3.79213	+	5.09372i	0.224234	+	0.301198i
$287$	−34.9640	−	12.7258i	−2.06386	−	0.751183i
$288$		0			0
$289$	5.75215	−	2.09361i	0.338362	−	0.123154i
$290$	7.73189	+	5.08534i	0.454032	+	0.298622i
$291$		0			0
$292$	−4.40934	+	5.92277i	−0.258037	+	0.346604i
$293$	−9.12929	+	6.00443i	−0.533339	+	0.350782i	−0.787436	−	0.616396i	$-0.788592\pi$
$293$	−9.12929	+	6.00443i	−0.533339	+	0.350782i	0.254097	+	0.967179i	$0.418222\pi$
$294$		0			0
$295$	−8.19857	−	27.3851i	−0.477339	−	1.59442i
$296$	3.22124	+	5.57934i	0.187230	+	0.324293i
$297$		0			0
$298$	−0.293862	+	0.508983i	−0.0170229	+	0.0294846i
$299$	7.87713	+	1.86691i	0.455546	+	0.107966i
$300$		0			0
$301$	−28.7268	−	14.4272i	−1.65579	−	0.831568i
$302$	−2.11099	−	4.89382i	−0.121474	−	0.281608i
$303$		0			0
$304$	0.299639	−	5.14460i	0.0171855	−	0.295063i
$305$	3.93337	−	22.3072i	0.225224	−	1.27731i
$306$		0			0
$307$	0.798574	+	4.52894i	0.0455770	+	0.258480i	0.999079	−	0.0429063i	$-0.0136617\pi$
$307$	0.798574	+	4.52894i	0.0455770	+	0.258480i	−0.953502	+	0.301386i	$0.902551\pi$
$308$	−18.8944	+	2.20844i	−1.07661	+	0.125838i
$309$		0			0
$310$	−3.06213	+	10.2282i	−0.173917	+	0.580925i
$311$	16.9690	−	4.02173i	0.962224	−	0.228051i	0.280658	−	0.959808i	$-0.409447\pi$
$311$	16.9690	−	4.02173i	0.962224	−	0.228051i	0.681566	+	0.731756i	$0.261299\pi$
$312$		0			0
$313$	−6.26878	+	14.5327i	−0.354333	+	0.821435i	0.644072	+	0.764965i	$0.277244\pi$
$313$	−6.26878	+	14.5327i	−0.354333	+	0.821435i	−0.998404	+	0.0564701i	$0.982015\pi$
$314$	−7.33136	+	6.15174i	−0.413732	+	0.347163i
$315$		0			0
$316$	−10.7755	−	9.04173i	−0.606170	−	0.508637i
$317$	−17.5175	+	8.79762i	−0.983881	+	0.494124i	−0.866615	−	0.498977i	$-0.833709\pi$
$317$	−17.5175	+	8.79762i	−0.983881	+	0.494124i	−0.117266	+	0.993101i	$0.537413\pi$
$318$		0			0
$319$	−16.3702	−	1.91340i	−0.916556	−	0.107130i
$320$	−0.0976694	−	1.67692i	−0.00545988	−	0.0937426i
$321$		0			0
$322$	4.65850	−	4.93772i	0.259608	−	0.275168i
$323$	−10.8479			−0.603594
$324$		0			0
$325$	−4.27338			−0.237044
$326$	−3.65583	+	3.87495i	−0.202477	+	0.214614i
$327$		0			0
$328$	1.23965	+	21.2840i	0.0684484	+	1.17521i
$329$	−41.3322	−	4.83104i	−2.27872	−	0.266344i
$330$		0			0
$331$	−19.5513	+	9.81905i	−1.07464	+	0.539704i	−0.895929	−	0.444198i	$-0.853489\pi$
$331$	−19.5513	+	9.81905i	−1.07464	+	0.539704i	−0.178710	+	0.983902i	$0.557192\pi$
$332$	−4.43055	−	3.71767i	−0.243158	−	0.204034i
$333$		0			0
$334$	−8.55328	+	7.17706i	−0.468015	+	0.392711i
$335$	5.81922	−	13.4905i	0.317938	−	0.737063i
$336$		0			0
$337$	−8.72133	+	2.06699i	−0.475081	+	0.112596i	−0.461179	−	0.887307i	$-0.652573\pi$
$337$	−8.72133	+	2.06699i	−0.475081	+	0.112596i	−0.0139020	+	0.999903i	$0.504425\pi$
$338$	0.470771	−	1.57249i	0.0256066	−	0.0855320i
$339$		0			0
$340$	12.8666	−	1.50389i	0.697790	−	0.0815599i
$341$	−3.30191	−	18.7261i	−0.178809	−	1.01407i
$342$		0			0
$343$	2.07706	−	11.7796i	0.112151	−	0.636040i
$344$	−1.07101	+	18.3886i	−0.0577451	+	0.991445i
$345$		0			0
$346$	−1.76117	−	4.08286i	−0.0946813	−	0.219496i
$347$	−17.1862	−	8.63124i	−0.922604	−	0.463349i	−0.0769226	−	0.997037i	$-0.524509\pi$
$347$	−17.1862	−	8.63124i	−0.922604	−	0.463349i	−0.845682	+	0.533688i	$0.820806\pi$
$348$		0			0
$349$	20.7785	+	4.92459i	1.11225	+	0.263607i	0.745363	−	0.666659i	$-0.232276\pi$
$349$	20.7785	+	4.92459i	1.11225	+	0.263607i	0.366884	+	0.930267i	$0.380424\pi$
$350$	−1.79174	+	3.10339i	−0.0957726	+	0.165883i
$351$		0			0
$352$	8.50973	+	14.7393i	0.453570	+	0.785607i
$353$	−4.21952	−	14.0942i	−0.224582	−	0.750157i	−0.993801	−	0.111172i	$-0.964540\pi$
$353$	−4.21952	−	14.0942i	−0.224582	−	0.750157i	0.769219	−	0.638985i	$-0.220645\pi$
$354$		0			0
$355$	−4.98424	+	3.27818i	−0.264536	+	0.173988i
$356$	−11.6603	+	15.6625i	−0.617993	+	0.830109i
$357$		0			0
$358$	−8.40216	−	5.52619i	−0.444068	−	0.292068i
$359$	10.0637	−	3.66289i	0.531142	−	0.193320i	−0.0625063	−	0.998045i	$-0.519909\pi$
$359$	10.0637	−	3.66289i	0.531142	−	0.193320i	0.593648	+	0.804725i	$0.297687\pi$
$360$		0			0
$361$	7.68928	+	2.79867i	0.404699	+	0.147298i
$362$	−2.21366	−	2.97346i	−0.116347	−	0.156282i
$363$		0			0
$364$	−14.3004	−	15.1575i	−0.749544	−	0.794470i
$365$	−8.15069	−	8.63923i	−0.426627	−	0.452198i
$366$		0			0
$367$	−2.36813	−	3.18095i	−0.123615	−	0.166044i	0.736007	−	0.676974i	$-0.236709\pi$
$367$	−2.36813	−	3.18095i	−0.123615	−	0.166044i	−0.859623	+	0.510929i	$0.829301\pi$
$368$	3.67519	+	1.33766i	0.191583	+	0.0697304i
$369$		0			0
$370$	−4.27121	+	1.55459i	−0.222050	+	0.0808194i
$371$	−0.0339730	−	0.0223444i	−0.00176379	−	0.00116006i
$372$		0			0
$373$	−14.1663	+	19.0287i	−0.733505	+	0.985268i	0.266267	+	0.963899i	$0.414210\pi$
$373$	−14.1663	+	19.0287i	−0.733505	+	0.985268i	−0.999772	+	0.0213686i	$0.993198\pi$
$374$	5.39577	−	3.54885i	0.279008	−	0.183507i
$375$		0			0
$376$	6.83869	+	22.8428i	0.352678	+	1.17803i
$377$	−9.02736	−	15.6359i	−0.464933	−	0.805287i
$378$		0			0
$379$	13.0094	−	22.5330i	0.668249	−	1.15744i	−0.310145	−	0.950689i	$-0.600377\pi$
$379$	13.0094	−	22.5330i	0.668249	−	1.15744i	0.978393	−	0.206752i	$-0.0662892\pi$
$380$	12.5694	+	2.97899i	0.644795	+	0.152819i
$381$		0			0
$382$	2.53884	+	1.27506i	0.129899	+	0.0652375i
$383$	11.6548	+	27.0188i	0.595530	+	1.38059i	0.903249	+	0.429117i	$0.141175\pi$
$383$	11.6548	+	27.0188i	0.595530	+	1.38059i	−0.307719	+	0.951477i	$0.599566\pi$
$384$		0			0
$385$	1.77920	−	30.5477i	0.0906765	−	1.55686i
$386$	0.325437	−	1.84564i	0.0165643	−	0.0939407i
$387$		0			0
$388$	1.94061	+	11.0057i	0.0985194	+	0.558731i
$389$	−26.3247	+	3.07691i	−1.33471	+	0.156006i	−0.753340	−	0.657631i	$-0.771559\pi$
$389$	−26.3247	+	3.07691i	−1.33471	+	0.156006i	−0.581373	+	0.813637i	$0.697484\pi$
$390$		0			0
$391$	2.36123	−	7.88705i	0.119412	−	0.398865i
$392$	−22.7179	+	5.38424i	−1.14743	+	0.271945i
$393$		0			0
$394$	5.56608	−	12.9036i	0.280415	−	0.650075i
$395$	17.3329	−	14.5440i	0.872114	−	0.731790i
$396$		0			0
$397$	−21.8020	−	18.2941i	−1.09421	−	0.918154i	−0.0971903	−	0.995266i	$-0.530986\pi$
$397$	−21.8020	−	18.2941i	−1.09421	−	0.918154i	−0.997022	+	0.0771123i	$0.975430\pi$
$398$	5.75197	−	2.88875i	0.288320	−	0.144800i
$399$		0			0
$400$	−2.05062	−	0.239683i	−0.102531	−	0.0119841i
$401$	−0.826969	−	14.1985i	−0.0412969	−	0.709040i	−0.953887	−	0.300165i	$-0.902958\pi$
$401$	−0.826969	−	14.1985i	−0.0412969	−	0.709040i	0.912590	−	0.408875i	$-0.134079\pi$
$402$		0			0
$403$	14.2943	−	15.1511i	0.712049	−	0.754728i
$404$	−3.29097			−0.163732
$405$		0			0
$406$	−15.1400			−0.751383
$407$	5.55517	−	5.88814i	0.275360	−	0.291864i
$408$		0			0
$409$	−0.181062	−	3.10871i	−0.00895293	−	0.153716i	−0.999822	−	0.0188857i	$-0.993988\pi$
$409$	−0.181062	−	3.10871i	−0.00895293	−	0.153716i	0.990869	−	0.134830i	$-0.0430489\pi$
$410$	−14.9402	−	1.74625i	−0.737842	−	0.0862413i
$411$		0			0
$412$	2.88400	−	1.44840i	0.142084	−	0.0713574i
$413$	35.8251	+	30.0608i	1.76284	+	1.47920i
$414$		0			0
$415$	7.12674	−	5.98005i	0.349838	−	0.293549i
$416$	−7.38446	+	17.1191i	−0.362053	+	0.839333i
$417$		0			0
$418$	6.26637	−	1.48516i	0.306498	−	0.0726414i
$419$	−1.96491	+	6.56326i	−0.0959921	+	0.320636i	−0.992476	−	0.122441i	$-0.960928\pi$
$419$	−1.96491	+	6.56326i	−0.0959921	+	0.320636i	0.896484	+	0.443077i	$0.146113\pi$
$420$		0			0
$421$	14.8315	−	1.73356i	0.722844	−	0.0844883i	0.253288	−	0.967391i	$-0.418488\pi$
$421$	14.8315	−	1.73356i	0.722844	−	0.0844883i	0.469556	+	0.882903i	$0.344414\pi$
$422$	2.24848	+	12.7517i	0.109454	+	0.620745i
$423$		0			0
$424$	−0.00404592	+	0.0229456i	−0.000196487	+	0.00111434i
$425$	−0.252698	+	4.33866i	−0.0122577	+	0.210456i
$426$		0			0
$427$	14.6776	+	34.0266i	0.710300	+	1.64666i
$428$	19.9174	+	10.0029i	0.962742	+	0.483507i
$429$		0			0
$430$	−12.6453	−	2.99699i	−0.609810	−	0.144528i
$431$	15.4334	−	26.7314i	0.743399	−	1.28760i	−0.207540	−	0.978227i	$-0.566546\pi$
$431$	15.4334	−	26.7314i	0.743399	−	1.28760i	0.950939	−	0.309378i	$-0.100121\pi$
$432$		0			0
$433$	14.3849	+	24.9154i	0.691295	+	1.19736i	0.971414	+	0.237393i	$0.0762928\pi$
$433$	14.3849	+	24.9154i	0.691295	+	1.19736i	−0.280119	+	0.959965i	$0.590374\pi$
$434$	−5.00960	−	16.7332i	−0.240469	−	0.803221i
$435$		0			0
$436$	17.5002	−	11.5101i	0.838107	−	0.551231i
$437$	4.90246	−	6.58514i	0.234516	−	0.315010i
$438$		0			0
$439$	3.69605	+	2.43093i	0.176403	+	0.116022i	0.634640	−	0.772808i	$-0.281149\pi$
$439$	3.69605	+	2.43093i	0.176403	+	0.116022i	−0.458237	+	0.888830i	$0.651519\pi$
$440$	−16.4761	+	5.99681i	−0.785467	+	0.285886i
$441$		0			0
$442$	6.64797	+	2.41966i	0.316212	+	0.115092i
$443$	1.59297	+	2.13973i	0.0756843	+	0.101662i	0.838353	−	0.545128i	$-0.183519\pi$
$443$	1.59297	+	2.13973i	0.0756843	+	0.101662i	−0.762669	+	0.646789i	$0.776111\pi$
$444$		0			0
$445$	−21.5541	−	22.8460i	−1.02176	−	1.08300i
$446$	7.33725	+	7.77703i	0.347429	+	0.368253i
$447$		0			0
$448$	1.64103	+	2.20428i	0.0775313	+	0.104143i
$449$	−39.1256	−	14.2405i	−1.84645	−	0.672053i	−0.986975	−	0.160874i	$-0.948569\pi$
$449$	−39.1256	−	14.2405i	−1.84645	−	0.672053i	−0.859474	−	0.511179i	$-0.829209\pi$
$450$		0			0
$451$	25.1735	−	9.16239i	1.18537	−	0.431440i
$452$	3.86478	+	2.54191i	0.181784	+	0.119561i
$453$		0			0
$454$	−8.38482	+	11.2628i	−0.393519	+	0.528588i
$455$	28.0056	−	18.4196i	1.31292	−	0.863522i
$456$		0			0
$457$	−2.19831	−	7.34286i	−0.102833	−	0.343485i	0.891053	−	0.453899i	$-0.149967\pi$
$457$	−2.19831	−	7.34286i	−0.102833	−	0.343485i	−0.993886	+	0.110414i	$0.964782\pi$
$458$	2.85365	+	4.94267i	0.133342	+	0.230956i
$459$		0			0
$460$	−4.90183	+	8.49022i	−0.228549	+	0.395858i
$461$	−21.4489	−	5.08348i	−0.998974	−	0.236761i	−0.301573	−	0.953443i	$-0.597512\pi$
$461$	−21.4489	−	5.08348i	−0.998974	−	0.236761i	−0.697400	+	0.716682i	$0.745660\pi$
$462$		0			0
$463$	33.2070	+	16.6772i	1.54326	+	0.775054i	0.998000	−	0.0632131i	$-0.0201348\pi$
$463$	33.2070	+	16.6772i	1.54326	+	0.775054i	0.545260	+	0.838267i	$0.316431\pi$
$464$	−3.45488	−	8.00931i	−0.160389	−	0.371823i
$465$		0			0
$466$	−0.575459	+	9.88026i	−0.0266576	+	0.457694i
$467$	−1.44385	+	8.18848i	−0.0668134	+	0.378918i	0.933005	+	0.359863i	$0.117177\pi$
$467$	−1.44385	+	8.18848i	−0.0668134	+	0.378918i	−0.999818	+	0.0190543i	$0.993934\pi$
$468$		0			0
$469$	4.17380	+	23.6708i	0.192728	+	1.09302i
$470$	−16.7092	+	1.95302i	−0.770736	+	0.0900862i
$471$		0			0
$472$	7.68549	−	25.6713i	0.353753	−	1.18162i
$473$	22.5208	−	5.33753i	1.03551	−	0.245420i
$474$		0			0
$475$	−1.71650	+	3.97929i	−0.0787583	+	0.182582i
$476$	−16.2347	+	13.6225i	−0.744115	+	0.624387i
$477$		0			0
$478$	1.82923	+	1.53491i	0.0836671	+	0.0702050i
$479$	−2.28141	+	1.14577i	−0.104240	+	0.0523515i	−0.500155	−	0.865936i	$-0.666724\pi$
$479$	−2.28141	+	1.14577i	−0.104240	+	0.0523515i	0.395915	+	0.918287i	$0.370427\pi$
$480$		0			0
$481$	8.80773	+	1.02948i	0.401598	+	0.0469400i
$482$	0.880298	+	15.1141i	0.0400965	+	0.688430i
$483$		0			0
$484$	−2.39649	+	2.54013i	−0.108931	+	0.115460i
$485$	−17.9763			−0.816263
$486$		0			0
$487$	16.3628			0.741468			0.370734	−	0.928739i	$-0.379106\pi$
$487$	16.3628			0.741468			0.370734	+	0.928739i	$0.379106\pi$
$488$	14.5715	−	15.4449i	0.659621	−	0.699158i
$489$		0			0
$490$	−0.957764	−	16.4442i	−0.0432674	−	0.742872i
$491$	−36.2381	−	4.23562i	−1.63540	−	0.191151i	−0.751800	−	0.659391i	$-0.770814\pi$
$491$	−36.2381	−	4.23562i	−1.63540	−	0.191151i	−0.883601	+	0.468240i	$0.844888\pi$
$492$		0			0
$493$	−16.4085	+	8.24066i	−0.739002	+	0.371141i
$494$	5.40415	+	4.53462i	0.243144	+	0.204022i
$495$		0			0
$496$	7.70901	−	6.46863i	0.346145	−	0.290450i
$497$	3.86563	−	8.96154i	0.173397	−	0.401980i
$498$		0			0
$499$	−30.8822	+	7.31920i	−1.38248	+	0.327653i	−0.853548	−	0.521015i	$-0.825554\pi$
$499$	−30.8822	+	7.31920i	−1.38248	+	0.327653i	−0.528927	+	0.848667i	$0.677406\pi$
$500$	−4.14792	+	13.8550i	−0.185501	+	0.619616i
$501$		0			0
$502$	−13.9084	+	1.62566i	−0.620763	+	0.0725567i
$503$	−1.04817	−	5.94449i	−0.0467358	−	0.265052i	0.952482	−	0.304595i	$-0.0985210\pi$
$503$	−1.04817	−	5.94449i	−0.0467358	−	0.265052i	−0.999218	+	0.0395428i	$0.987410\pi$
$504$		0			0
$505$	0.919238	−	5.21326i	0.0409055	−	0.231987i
$506$	−0.284185	+	4.87927i	−0.0126336	+	0.216910i
$507$		0			0
$508$	−7.44664	−	17.2633i	−0.330391	−	0.765933i
$509$	−23.5056	−	11.8050i	−1.04187	−	0.523246i	−0.156278	−	0.987713i	$-0.549950\pi$
$509$	−23.5056	−	11.8050i	−1.04187	−	0.523246i	−0.885590	+	0.464467i	$0.846246\pi$
$510$		0			0
$511$	18.9073	+	4.48111i	0.836409	+	0.198233i
$512$	−8.19547	+	14.1950i	−0.362192	+	0.627335i
$513$		0			0
$514$	−2.57506	−	4.46014i	−0.113581	−	0.196728i
$515$	1.48886	+	4.97314i	0.0656070	+	0.219143i
$516$		0			0
$517$	25.0321	−	16.4638i	1.10091	−	0.724079i
$518$	4.44052	−	5.96465i	0.195105	−	0.262072i
$519$		0			0
$520$	−16.0472	−	10.5544i	−0.703715	−	0.462841i
$521$	−23.7819	+	8.65589i	−1.04190	+	0.379221i	−0.805601	−	0.592459i	$-0.798157\pi$
$521$	−23.7819	+	8.65589i	−1.04190	+	0.379221i	−0.236301	+	0.971680i	$0.575935\pi$
$522$		0			0
$523$	2.76727	+	1.00720i	0.121004	+	0.0440420i	0.401813	−	0.915722i	$-0.368380\pi$
$523$	2.76727	+	1.00720i	0.121004	+	0.0440420i	−0.280808	+	0.959764i	$0.590603\pi$
$524$	−4.79271	−	6.43772i	−0.209370	−	0.281233i
$525$		0			0
$526$	0.692810	+	0.734335i	0.0302079	+	0.0320185i
$527$	−14.5372	−	15.4086i	−0.633252	−	0.671207i
$528$		0			0
$529$	−10.0140	−	13.4511i	−0.435390	−	0.584831i
$530$	−0.0154471	−	0.00562227i	−0.000670977	−	0.000244216i
$531$		0			0
$532$	−19.8585	+	7.22789i	−0.860973	+	0.313369i
$533$	24.5181	+	16.1258i	1.06200	+	0.698487i
$534$		0			0
$535$	−21.4090	+	28.7573i	−0.925592	+	1.24329i
$536$	11.5068	−	7.56816i	0.497019	−	0.326895i
$537$		0			0
$538$	−5.58403	−	18.6520i	−0.240745	−	0.804143i
$539$	14.6681	+	25.4058i	0.631798	+	1.09431i
$540$		0			0
$541$	−8.84669	+	15.3229i	−0.380349	+	0.658784i	−0.991112	−	0.133030i	$-0.957529\pi$
$541$	−8.84669	+	15.3229i	−0.380349	+	0.658784i	0.610763	+	0.791813i	$0.290863\pi$
$542$	9.37828	+	2.22269i	0.402832	+	0.0954729i
$543$		0			0
$544$	16.9439	+	8.50956i	0.726465	+	0.364844i
$545$	13.3450	+	30.9372i	0.571637	+	1.32520i
$546$		0			0
$547$	−2.36944	+	40.6817i	−0.101310	+	1.73942i	0.439467	+	0.898259i	$0.355167\pi$
$547$	−2.36944	+	40.6817i	−0.101310	+	1.73942i	−0.540777	+	0.841166i	$0.681870\pi$
$548$	0.515831	−	2.92542i	0.0220352	−	0.124968i
$549$		0			0
$550$	−0.448020	−	2.54085i	−0.0191036	−	0.108342i
$551$	−18.1858	+	2.12562i	−0.774743	+	0.0905545i
$552$		0			0
$553$	−10.6165	+	35.4615i	−0.451459	+	1.50798i
$554$	6.58126	−	1.55979i	0.279611	−	0.0662690i
$555$		0			0
$556$	−5.79164	+	13.4265i	−0.245620	+	0.569412i
$557$	23.1644	−	19.4372i	0.981505	−	0.823581i	−0.00281036	−	0.999996i	$-0.500895\pi$
$557$	23.1644	−	19.4372i	0.981505	−	0.823581i	0.984316	+	0.176415i	$0.0564501\pi$
$558$		0			0
$559$	19.4220	+	16.2970i	0.821465	+	0.689291i
$560$	14.4718	−	7.26801i	0.611545	−	0.307130i
$561$		0			0
$562$	4.61385	+	0.539281i	0.194623	+	0.0227482i
$563$	−1.07446	−	18.4478i	−0.0452831	−	0.777480i	−0.942152	−	0.335185i	$-0.891201\pi$
$563$	−1.07446	−	18.4478i	−0.0452831	−	0.777480i	0.896869	−	0.442296i	$-0.145836\pi$
$564$		0			0
$565$	−5.10617	+	5.41223i	−0.214818	+	0.227694i
$566$	−14.3004			−0.601091
$567$		0			0
$568$	−5.59232			−0.234648
$569$	6.17461	−	6.54471i	0.258853	−	0.274368i	−0.584893	−	0.811110i	$-0.698864\pi$
$569$	6.17461	−	6.54471i	0.258853	−	0.274368i	0.843746	+	0.536742i	$0.180345\pi$
$570$		0			0
$571$	0.981371	+	16.8495i	0.0410691	+	0.705129i	0.954514	+	0.298167i	$0.0963751\pi$
$571$	0.981371	+	16.8495i	0.0410691	+	0.705129i	−0.913445	+	0.406963i	$0.866588\pi$
$572$	14.9020	+	1.74180i	0.623086	+	0.0728283i
$573$		0			0
$574$	21.9907	−	11.0442i	0.917876	−	0.460974i
$575$	−2.51954	−	2.11415i	−0.105072	−	0.0881661i
$576$		0			0
$577$	−24.0567	+	20.1860i	−1.00149	+	0.840352i	−0.987191	−	0.159545i	$-0.948997\pi$
$577$	−24.0567	+	20.1860i	−1.00149	+	0.840352i	−0.0143022	+	0.999898i	$0.504553\pi$
$578$	−1.60351	+	3.71736i	−0.0666974	+	0.154622i
$579$		0			0
$580$	21.2754	−	5.04235i	0.883411	−	0.209372i
$581$	−4.36516	+	14.5807i	−0.181097	+	0.604908i
$582$		0			0
$583$	0.0290783	−	0.00339876i	0.00120430	−	0.000140762i
$584$	−1.93340	−	10.9648i	−0.0800045	−	0.453728i
$585$		0			0
$586$	1.25491	−	7.11695i	0.0518399	−	0.293999i
$587$	−0.0800524	+	1.37445i	−0.00330412	+	0.0567295i	−0.999557	−	0.0297566i	$-0.990527\pi$
$587$	−0.0800524	+	1.37445i	−0.00330412	+	0.0567295i	0.996253	+	0.0864861i	$0.0275638\pi$
$588$		0			0
$589$	−8.36676	−	19.3963i	−0.344746	−	0.799212i
$590$	16.8950	+	8.48500i	0.695557	+	0.349322i
$591$		0			0
$592$	4.16872	+	0.988004i	0.171333	+	0.0406067i
$593$	−15.4929	+	26.8346i	−0.636219	+	1.10196i	0.350037	+	0.936736i	$0.386169\pi$
$593$	−15.4929	+	26.8346i	−0.636219	+	1.10196i	−0.986256	+	0.165227i	$0.947164\pi$
$594$		0			0
$595$	−17.0449	−	29.5226i	−0.698771	−	1.21031i
$596$	0.398250	+	1.33025i	0.0163129	+	0.0544890i
$597$		0			0
$598$	−4.47322	+	2.94209i	−0.182924	+	0.120311i
$599$	14.4819	−	19.4526i	0.591715	−	0.794812i	−0.400899	−	0.916122i	$-0.631302\pi$
$599$	14.4819	−	19.4526i	0.591715	−	0.794812i	0.992615	+	0.121310i	$0.0387097\pi$
$600$		0			0
$601$	−6.33832	−	4.16878i	−0.258545	−	0.170048i	0.413619	−	0.910450i	$-0.364265\pi$
$601$	−6.33832	−	4.16878i	−0.258545	−	0.170048i	−0.672164	+	0.740402i	$0.734635\pi$
$602$	19.9784	−	7.27154i	0.814258	−	0.296366i
$603$		0			0
$604$	−11.8328	−	4.30678i	−0.481469	−	0.175241i
$605$	−3.35445	−	4.50581i	−0.136378	−	0.183187i
$606$		0			0
$607$	−20.5630	−	21.7955i	−0.834627	−	0.884653i	0.160111	−	0.987099i	$-0.448815\pi$
$607$	−20.5630	−	21.7955i	−0.834627	−	0.884653i	−0.994739	+	0.102446i	$0.967333\pi$
$608$	12.9748	+	13.7525i	0.526199	+	0.557739i
$609$		0			0
$610$	8.94601	+	12.0166i	0.362214	+	0.486537i
$611$	30.8413	+	11.2253i	1.24770	+	0.454127i
$612$		0			0
$613$	11.4606	−	4.17132i	0.462890	−	0.168478i	−0.100039	−	0.994984i	$-0.531897\pi$
$613$	11.4606	−	4.17132i	0.462890	−	0.168478i	0.562929	+	0.826505i	$0.309675\pi$
$614$	−2.54115	−	1.67134i	−0.102553	−	0.0674499i
$615$		0			0
$616$	17.1292	−	23.0085i	0.690155	−	0.927039i
$617$	−13.2760	+	8.73179i	−0.534474	+	0.351529i	−0.787878	−	0.615832i	$-0.788820\pi$
$617$	−13.2760	+	8.73179i	−0.534474	+	0.351529i	0.253404	+	0.967361i	$0.418450\pi$
$618$		0			0
$619$	−6.67055	−	22.2812i	−0.268112	−	0.895556i	−0.980955	−	0.194233i	$-0.937778\pi$
$619$	−6.67055	−	22.2812i	−0.268112	−	0.895556i	0.712844	−	0.701323i	$-0.247407\pi$
$620$	12.6127	+	21.8459i	0.506539	+	0.877351i
$621$		0			0
$622$	−5.76686	+	9.98849i	−0.231230	+	0.400502i
$623$	49.9994	+	11.8501i	2.00318	+	0.474763i
$624$		0			0
$625$	−26.6768	−	13.3976i	−1.06707	−	0.535903i
$626$	−4.14600	−	9.61150i	−0.165707	−	0.384153i
$627$		0			0
$628$	−1.31474	+	22.5732i	−0.0524639	+	0.900770i
$629$	1.56603	−	8.88139i	0.0624417	−	0.354124i
$630$		0			0
$631$	2.13182	+	12.0902i	0.0848665	+	0.481302i	0.997385	+	0.0722670i	$0.0230234\pi$
$631$	2.13182	+	12.0902i	0.0848665	+	0.481302i	−0.912519	+	0.409035i	$0.865866\pi$
$632$	21.0671	−	2.46239i	0.838003	−	0.0979485i
$633$		0			0
$634$	3.71829	−	12.4199i	0.147672	−	0.493259i
$635$	29.4269	−	6.97430i	1.16777	−	0.276767i
$636$		0			0
$637$	−12.7284	+	29.5079i	−0.504319	+	1.16914i
$638$	8.35027	−	7.00671i	0.330590	−	0.277398i
$639$		0			0
$640$	−21.2865	−	17.8615i	−0.841422	−	0.706037i
$641$	8.36840	−	4.20277i	0.330532	−	0.165999i	−0.275791	−	0.961217i	$-0.588940\pi$
$641$	8.36840	−	4.20277i	0.330532	−	0.165999i	0.606324	+	0.795218i	$0.292644\pi$
$642$		0			0
$643$	19.5316	+	2.28292i	0.770252	+	0.0900295i	0.492136	−	0.870518i	$-0.336216\pi$
$643$	19.5316	+	2.28292i	0.770252	+	0.0900295i	0.278115	+	0.960548i	$0.410290\pi$
$644$	−0.932563	−	16.0115i	−0.0367481	−	0.630941i
$645$		0			0
$646$	4.92345	−	5.21855i	0.193710	−	0.205321i
$647$	14.2593			0.560591			0.280295	−	0.959914i	$-0.409568\pi$
$647$	14.2593			0.560591			0.280295	+	0.959914i	$0.409568\pi$
$648$		0			0
$649$	−33.6709			−1.32170
$650$	1.93952	−	2.05577i	0.0760742	−	0.0806340i
$651$		0			0
$652$	0.731843	+	12.5653i	0.0286612	+	0.492094i
$653$	40.5133	+	4.73532i	1.58541	+	0.185308i	0.862653	−	0.505797i	$-0.168802\pi$
$653$	40.5133	+	4.73532i	1.58541	+	0.185308i	0.722755	+	0.691105i	$0.242876\pi$
$654$		0			0
$655$	11.5368	−	5.79398i	0.450779	−	0.226390i
$656$	10.8608	+	9.11326i	0.424042	+	0.355813i
$657$		0			0
$658$	21.0831	−	17.6908i	0.821905	−	0.689660i
$659$	−1.02550	+	2.37737i	−0.0399477	+	0.0926093i	−0.937022	−	0.349271i	$-0.886429\pi$
$659$	−1.02550	+	2.37737i	−0.0399477	+	0.0926093i	0.897074	+	0.441880i	$0.145688\pi$
$660$		0			0
$661$	29.2233	−	6.92605i	1.13665	−	0.269392i	0.381136	−	0.924519i	$-0.375533\pi$
$661$	29.2233	−	6.92605i	1.13665	−	0.269392i	0.755519	+	0.655127i	$0.227385\pi$
$662$	4.14999	−	13.8619i	0.161294	−	0.538760i
$663$		0			0
$664$	8.66211	−	1.01246i	0.336155	−	0.0392909i
$665$	−5.90288	−	33.4769i	−0.228904	−	1.29818i
$666$		0			0
$667$	2.41300	−	13.6848i	0.0934318	−	0.529878i
$668$	−1.53387	+	26.3355i	−0.0593472	+	1.01895i
$669$		0			0
$670$	3.84867	+	8.92222i	0.148687	+	0.344695i
$671$	−23.8426	−	11.9742i	−0.920435	−	0.462260i
$672$		0			0
$673$	13.4942	+	3.19818i	0.520163	+	0.123281i	0.482307	−	0.876002i	$-0.339799\pi$
$673$	13.4942	+	3.19818i	0.520163	+	0.123281i	0.0378561	+	0.999283i	$0.487947\pi$
$674$	2.96391	−	5.13365i	0.114166	−	0.197741i
$675$		0			0
$676$	−1.93907	−	3.35858i	−0.0745798	−	0.129176i
$677$	5.74687	+	19.1959i	0.220870	+	0.737757i	0.994557	+	0.104190i	$0.0332249\pi$
$677$	5.74687	+	19.1959i	0.220870	+	0.737757i	−0.773687	+	0.633568i	$0.781590\pi$
$678$		0			0
$679$	24.5709	−	16.1605i	0.942943	−	0.620184i
$680$	−11.6645	+	15.6682i	−0.447314	+	0.600847i
$681$		0			0
$682$	10.5071	+	6.91060i	0.402336	+	0.264621i
$683$	29.9877	−	10.9146i	1.14745	−	0.417636i	0.302849	−	0.953039i	$-0.402062\pi$
$683$	29.9877	−	10.9146i	1.14745	−	0.417636i	0.844597	+	0.535402i	$0.179840\pi$
$684$		0			0
$685$	4.49011	+	1.63426i	0.171558	+	0.0624421i
$686$	4.72406	+	6.34551i	0.180365	+	0.242273i
$687$		0			0
$688$	8.40577	+	8.90959i	0.320467	+	0.339675i
$689$	0.0220081	+	0.0233272i	0.000838442	+	0.000888696i
$690$		0			0
$691$	22.3598	+	30.0344i	0.850605	+	1.14256i	0.988366	+	0.152096i	$0.0486022\pi$
$691$	22.3598	+	30.0344i	0.850605	+	1.14256i	−0.137760	+	0.990466i	$0.543990\pi$
$692$	−9.87198	−	3.59311i	−0.375276	−	0.136589i
$693$		0			0
$694$	11.9523	−	4.35029i	0.453704	−	0.165135i
$695$	−19.6514	−	12.9249i	−0.745419	−	0.490270i
$696$		0			0
$697$	17.8220	−	23.9391i	0.675056	−	0.906757i
$698$	−11.7996	+	7.76071i	−0.446621	+	0.293747i
$699$		0			0
$700$	2.42822	+	8.11081i	0.0917780	+	0.306560i
$701$	−11.5923	−	20.0785i	−0.437836	−	0.758355i	0.559686	−	0.828705i	$-0.310922\pi$
$701$	−11.5923	−	20.0785i	−0.437836	−	0.758355i	−0.997522	+	0.0703498i	$0.977588\pi$
$702$		0			0
$703$	4.49645	−	7.78807i	0.169587	−	0.293733i
$704$	−1.92522	−	0.456286i	−0.0725596	−	0.0171969i
$705$		0			0
$706$	8.69527	+	4.36693i	0.327251	+	0.164352i
$707$	3.43020	+	7.95210i	0.129006	+	0.299069i
$708$		0			0
$709$	−0.289566	+	4.97166i	−0.0108749	+	0.186715i	0.988496	+	0.151247i	$0.0483290\pi$
$709$	−0.289566	+	4.97166i	−0.0108749	+	0.186715i	−0.999371	+	0.0354672i	$0.988708\pi$
$710$	0.685132	−	3.88558i	0.0257126	−	0.145823i
$711$		0			0
$712$	−5.11277	−	28.9960i	−0.191609	−	1.08667i
$713$	15.9234	−	1.86118i	0.596336	−	0.0697016i
$714$		0			0
$715$	−6.92166	+	23.1200i	−0.258855	+	0.864637i
$716$	−23.1197	+	5.47947i	−0.864024	+	0.204777i
$717$		0			0
$718$	−2.80544	+	6.50373i	−0.104698	+	0.242717i
$719$	−13.4111	+	11.2533i	−0.500151	+	0.419677i	−0.857648	−	0.514238i	$-0.828075\pi$
$719$	−13.4111	+	11.2533i	−0.500151	+	0.419677i	0.357497	+	0.933914i	$0.383630\pi$
$720$		0			0
$721$	−6.50583	−	5.45904i	−0.242290	−	0.203305i
$722$	−4.83620	+	2.42883i	−0.179985	+	0.0903918i
$723$		0			0
$724$	−8.69907	−	1.01678i	−0.323299	−	0.0377882i
$725$	0.426516	+	7.32299i	0.0158404	+	0.271969i
$726$		0			0
$727$	−5.51070	+	5.84100i	−0.204381	+	0.216631i	−0.821454	−	0.570275i	$-0.806837\pi$
$727$	−5.51070	+	5.84100i	−0.204381	+	0.216631i	0.617073	+	0.786906i	$0.288318\pi$
$728$	31.4223			1.16459
$729$		0			0
$730$	7.85530			0.290738
$731$	17.6945	−	18.7550i	0.654453	−	0.693680i
$732$		0			0
$733$	1.74889	+	30.0273i	0.0645968	+	1.10908i	0.862420	+	0.506193i	$0.168948\pi$
$733$	1.74889	+	30.0273i	0.0645968	+	1.10908i	−0.797823	+	0.602891i	$0.794015\pi$
$734$	2.60505	+	0.304486i	0.0961540	+	0.0112388i
$735$		0			0
$736$	−12.8231	+	6.43998i	−0.472664	+	0.237381i
$737$	−13.2568	−	11.1237i	−0.488319	−	0.409748i
$738$		0			0
$739$	1.84741	−	1.55016i	0.0679580	−	0.0570236i	−0.608176	−	0.793802i	$-0.708098\pi$
$739$	1.84741	−	1.55016i	0.0679580	−	0.0570236i	0.676134	+	0.736779i	$0.263654\pi$
$740$	−4.25350	+	9.86072i	−0.156362	+	0.362487i
$741$		0			0
$742$	0.0261681	−	0.00620195i	0.000960661	−	0.000227681i
$743$	5.63906	−	18.8358i	0.206877	−	0.691018i	−0.790076	−	0.613009i	$-0.789959\pi$
$743$	5.63906	−	18.8358i	0.206877	−	0.691018i	0.996953	−	0.0780084i	$-0.0248561\pi$
$744$		0			0
$745$	−2.21850	+	0.259305i	−0.0812794	+	0.00950020i
$746$	−2.72448	−	15.4513i	−0.0997503	−	0.565712i
$747$		0			0
$748$	2.64961	−	15.0267i	0.0968793	−	0.549430i
$749$	3.41033	−	58.5532i	0.124611	−	2.13949i
$750$		0			0
$751$	−2.72090	−	6.30775i	−0.0992869	−	0.230173i	0.861332	−	0.508043i	$-0.169631\pi$
$751$	−2.72090	−	6.30775i	−0.0992869	−	0.230173i	−0.960619	+	0.277870i	$0.910372\pi$
$752$	14.1698	+	7.11636i	0.516721	+	0.259507i
$753$		0			0
$754$	11.6190	+	2.75376i	0.423140	+	0.100286i
$755$	10.1276	−	17.5415i	0.368580	−	0.638399i
$756$		0			0
$757$	−6.50209	−	11.2620i	−0.236323	−	0.409323i	0.723334	−	0.690499i	$-0.242609\pi$
$757$	−6.50209	−	11.2620i	−0.236323	−	0.409323i	−0.959656	+	0.281176i	$0.909276\pi$
$758$	4.93535	+	16.4852i	0.179260	+	0.598770i
$759$		0			0
$760$	−16.2737	+	10.7034i	−0.590311	+	0.388254i
$761$	−10.3938	+	13.9613i	−0.376775	+	0.506096i	−0.949550	−	0.313616i	$-0.898459\pi$
$761$	−10.3938	+	13.9613i	−0.376775	+	0.506096i	0.572775	+	0.819713i	$0.305867\pi$
$762$		0			0
$763$	−46.0527	−	30.2894i	−1.66722	−	1.09655i
$764$	6.30756	−	2.29576i	0.228200	−	0.0830578i
$765$		0			0
$766$	−18.2874	−	6.65607i	−0.660751	−	0.240494i
$767$	−22.0260	−	29.5860i	−0.795312	−	1.06829i
$768$		0			0
$769$	12.7844	+	13.5507i	0.461018	+	0.488651i	0.915620	−	0.402044i	$-0.131700\pi$
$769$	12.7844	+	13.5507i	0.461018	+	0.488651i	−0.454602	+	0.890695i	$0.650219\pi$
$770$	13.8879	+	14.7203i	0.500486	+	0.530484i
$771$		0			0
$772$	−2.64414	−	3.55170i	−0.0951647	−	0.127828i
$773$	27.2264	+	9.90961i	0.979267	+	0.356424i	0.781555	−	0.623836i	$-0.214427\pi$
$773$	27.2264	+	9.90961i	0.979267	+	0.356424i	0.197712	+	0.980260i	$0.436649\pi$
$774$		0			0
$775$	−7.95251	+	2.89448i	−0.285663	+	0.103973i
$776$	−14.0791	−	9.25996i	−0.505410	−	0.332413i
$777$		0			0
$778$	10.4675	−	14.0604i	0.375280	−	0.504088i
$779$	24.8643	−	16.3535i	0.890856	−	0.585925i
$780$		0			0
$781$	2.01532	+	6.73163i	0.0721138	+	0.240877i
$782$	2.72251	+	4.71553i	0.0973568	+	0.168627i
$783$		0			0
$784$	−7.76286	+	13.4457i	−0.277245	+	0.480203i
$785$	−35.3912	−	8.38787i	−1.26317	−	0.299376i
$786$		0			0
$787$	−13.2388	−	6.64876i	−0.471911	−	0.237003i	0.196916	−	0.980420i	$-0.436907\pi$
$787$	−13.2388	−	6.64876i	−0.471911	−	0.237003i	−0.668828	+	0.743418i	$0.733204\pi$
$788$	−13.1507	−	30.4867i	−0.468473	−	1.08604i
$789$		0			0
$790$	−0.870110	+	14.9392i	−0.0309571	+	0.531514i
$791$	2.11382	−	11.9881i	0.0751588	−	0.426247i
$792$		0			0
$793$	−5.07523	−	28.7830i	−0.180227	−	1.02212i
$794$	18.6957	−	2.18522i	0.663486	−	0.0775504i
$795$		0			0
$796$	4.36154	−	14.5686i	0.154591	−	0.516369i
$797$	−17.1318	+	4.06031i	−0.606840	+	0.143824i	−0.522537	−	0.852617i	$-0.675014\pi$
$797$	−17.1318	+	4.06031i	−0.606840	+	0.143824i	−0.0843026	+	0.996440i	$0.526866\pi$
$798$		0			0
$799$	13.2205	−	30.6486i	0.467708	−	1.08427i
$800$	5.80261	−	4.86896i	0.205153	−	0.172144i
$801$		0			0
$802$	7.20573	+	6.04632i	0.254443	+	0.213503i
$803$	−12.5019	+	6.27871i	−0.441184	+	0.221571i
$804$		0			0
$805$	25.6244	+	2.99507i	0.903143	+	0.105562i
$806$	0.801018	+	13.7529i	0.0282146	+	0.484427i
$807$		0			0
$808$	3.40540	−	3.60951i	0.119802	−	0.126982i
$809$	13.3577			0.469632			0.234816	−	0.972040i	$-0.424551\pi$
$809$	13.3577			0.469632			0.234816	+	0.972040i	$0.424551\pi$
$810$		0			0
$811$	13.6700			0.480017			0.240009	−	0.970771i	$-0.422850\pi$
$811$	13.6700			0.480017			0.240009	+	0.970771i	$0.422850\pi$
$812$	−24.5471	+	26.0184i	−0.861434	+	0.913067i
$813$		0			0
$814$	0.311299	+	5.34479i	0.0109110	+	0.187335i
$815$	−20.1092	−	2.35042i	−0.704393	−	0.0823318i
$816$		0			0
$817$	22.9768	−	11.5394i	0.803856	−	0.403711i
$818$	1.57767	+	1.32382i	0.0551619	+	0.0462863i
$819$		0			0
$820$	−27.2241	+	22.8438i	−0.950708	+	0.797739i
$821$	−3.97678	+	9.21922i	−0.138791	+	0.321753i	−0.973408	−	0.229077i	$-0.926429\pi$
$821$	−3.97678	+	9.21922i	−0.138791	+	0.321753i	0.834618	+	0.550830i	$0.185689\pi$
$822$		0			0
$823$	−29.4335	+	6.97586i	−1.02599	+	0.243163i	−0.708956	−	0.705252i	$-0.750834\pi$
$823$	−29.4335	+	6.97586i	−1.02599	+	0.243163i	−0.317030	+	0.948416i	$0.602686\pi$
$824$	−1.39568	+	4.66191i	−0.0486209	+	0.162405i
$825$		0			0
$826$	−30.7208	+	3.59075i	−1.06891	+	0.124938i
$827$	8.16805	+	46.3233i	0.284031	+	1.61082i	0.708726	+	0.705483i	$0.249270\pi$
$827$	8.16805	+	46.3233i	0.284031	+	1.61082i	−0.424695	+	0.905336i	$0.639619\pi$
$828$		0			0
$829$	−0.608907	+	3.45328i	−0.0211482	+	0.119938i	−0.993554	−	0.113357i	$-0.963840\pi$
$829$	−0.608907	+	3.45328i	−0.0211482	+	0.119938i	0.972406	+	0.233295i	$0.0749507\pi$
$830$	−0.357762	+	6.14253i	−0.0124181	+	0.213210i
$831$		0			0
$832$	−0.858462	−	1.99014i	−0.0297618	−	0.0689956i
$833$	29.2059	+	14.6678i	1.01193	+	0.508208i
$834$		0			0
$835$	−41.2899	−	9.78589i	−1.42890	−	0.338655i
$836$	7.60767	−	13.1769i	0.263117	−	0.455731i
$837$		0			0
$838$	−2.26555	−	3.92405i	−0.0782622	−	0.135554i
$839$	10.5586	+	35.2680i	0.364522	+	1.21759i	0.921932	+	0.387351i	$0.126610\pi$
$839$	10.5586	+	35.2680i	0.364522	+	1.21759i	−0.557411	+	0.830237i	$0.688205\pi$
$840$		0			0
$841$	−1.66393	+	1.09438i	−0.0573768	+	0.0377373i
$842$	−5.89749	+	7.92171i	−0.203241	+	0.273000i
$843$		0			0
$844$	25.5598	+	16.8109i	0.879803	+	0.578656i
$845$	5.86198	−	2.13359i	0.201658	−	0.0733976i
$846$		0			0
$847$	8.63568	+	3.14313i	0.296725	+	0.107999i
$848$	0.00925240	+	0.0124281i	0.000317729	+	0.000426784i
$849$		0			0
$850$	−1.97248	−	2.09071i	−0.0676556	−	0.0717108i
$851$	4.68365	+	4.96437i	0.160553	+	0.170177i
$852$		0			0
$853$	−22.0417	−	29.6072i	−0.754694	−	1.01373i	−0.999030	−	0.0440391i	$-0.985977\pi$
$853$	−22.0417	−	29.6072i	−0.754694	−	1.01373i	0.244336	−	0.969691i	$-0.421430\pi$
$854$	−23.0306	−	8.38245i	−0.788090	−	0.286841i
$855$		0			0
$856$	−31.5810	+	11.4945i	−1.07942	+	0.392875i
$857$	25.1496	+	16.5412i	0.859095	+	0.565035i	0.900869	−	0.434092i	$-0.142931\pi$
$857$	25.1496	+	16.5412i	0.859095	+	0.565035i	−0.0417741	+	0.999127i	$0.513301\pi$
$858$		0			0
$859$	−11.6131	+	15.5991i	−0.396233	+	0.532233i	−0.954809	−	0.297220i	$-0.903940\pi$
$859$	−11.6131	+	15.5991i	−0.396233	+	0.532233i	0.558576	+	0.829453i	$0.311348\pi$
$860$	−25.6528	+	16.8721i	−0.874752	+	0.575334i
$861$		0			0
$862$	5.85491	+	19.5568i	0.199419	+	0.666106i
$863$	−14.3566	−	24.8664i	−0.488706	−	0.846463i	0.511210	−	0.859456i	$-0.329197\pi$
$863$	−14.3566	−	24.8664i	−0.488706	−	0.846463i	−0.999916	+	0.0129930i	$0.995864\pi$
$864$		0			0
$865$	8.44932	−	14.6347i	0.287286	−	0.497593i
$866$	−18.5147	−	4.38806i	−0.629154	−	0.149112i
$867$		0			0
$868$	−36.8788	−	18.5212i	−1.25175	−	0.628651i
$869$	−10.5560	−	24.4717i	−0.358089	−	0.830144i
$870$		0			0
$871$	1.10226	−	18.9251i	0.0373487	−	0.641252i
$872$	−5.48453	+	31.1043i	−0.185730	+	1.05333i
$873$		0			0
$874$	0.942844	+	5.34714i	0.0318922	+	0.180870i
$875$	37.8018	−	4.41840i	1.27794	−	0.149369i
$876$		0			0
$877$	5.48485	−	18.3207i	0.185210	−	0.618646i	−0.814072	−	0.580764i	$-0.802754\pi$
$877$	5.48485	−	18.3207i	0.185210	−	0.618646i	0.999282	−	0.0378815i	$-0.0120609\pi$
$878$	−2.84692	+	0.674733i	−0.0960790	+	0.0227711i
$879$		0			0
$880$	−4.61815	+	10.7061i	−0.155678	+	0.360902i
$881$	−35.7695	+	30.0142i	−1.20510	+	1.01120i	−0.205635	+	0.978629i	$0.565926\pi$
$881$	−35.7695	+	30.0142i	−1.20510	+	1.01120i	−0.999469	+	0.0325741i	$0.989630\pi$
$882$		0			0
$883$	−10.7311	−	9.00449i	−0.361131	−	0.303025i	0.444110	−	0.895972i	$-0.353520\pi$
$883$	−10.7311	−	9.00449i	−0.361131	−	0.303025i	−0.805241	+	0.592947i	$0.797964\pi$
$884$	14.9369	−	7.50160i	0.502383	−	0.252306i
$885$		0			0
$886$	−1.75233	−	0.204819i	−0.0588708	−	0.00688101i
$887$	−0.602791	−	10.3495i	−0.0202397	−	0.347503i	−0.993191	−	0.116494i	$-0.962834\pi$
$887$	−0.602791	−	10.3495i	−0.0202397	−	0.347503i	0.972952	−	0.231009i	$-0.0742027\pi$
$888$		0			0
$889$	−33.9522	+	35.9872i	−1.13872	+	1.20697i
$890$	20.7730			0.696312
$891$		0			0
$892$	25.2612			0.845809
$893$	22.8409	−	24.2099i	0.764341	−	0.810154i
$894$		0			0
$895$	−2.22226	−	38.1547i	−0.0742818	−	1.27537i
$896$	45.1526	+	5.27758i	1.50844	+	0.176312i
$897$		0			0
$898$	24.6082	−	12.3587i	0.821186	−	0.412415i
$899$	−27.3900	−	22.9829i	−0.913508	−	0.766524i
$900$		0			0
$901$	0.0249850	−	0.0209649i	0.000832370	−	0.000698441i
$902$	−7.01755	+	16.2685i	−0.233659	+	0.541682i
$903$		0			0
$904$	−6.78711	+	1.60857i	−0.225736	+	0.0535004i
$905$	4.04052	−	13.4963i	0.134311	−	0.448631i
$906$		0			0
$907$	35.7230	−	4.17542i	1.18616	−	0.138643i	0.499957	−	0.866050i	$-0.333349\pi$
$907$	35.7230	−	4.17542i	1.18616	−	0.138643i	0.686206	+	0.727408i	$0.259275\pi$
$908$	5.76067	+	32.6704i	0.191174	+	1.08420i
$909$		0			0
$910$	−3.84964	+	21.8324i	−0.127614	+	0.723737i
$911$	−0.369861	+	6.35027i	−0.0122541	+	0.210394i	0.986623	+	0.163018i	$0.0521229\pi$
$911$	−0.369861	+	6.35027i	−0.0122541	+	0.210394i	−0.998877	+	0.0473759i	$0.984914\pi$
$912$		0			0
$913$	−4.34031	−	10.0620i	−0.143643	−	0.333003i
$914$	4.53012	+	2.27511i	0.149843	+	0.0752540i
$915$		0			0
$916$	13.1209	+	3.10970i	0.433525	+	0.102747i
$917$	−10.5602	+	18.2909i	−0.348730	+	0.604018i
$918$		0			0
$919$	23.2884	+	40.3367i	0.768213	+	1.33058i	0.938531	+	0.345194i	$0.112187\pi$
$919$	23.2884	+	40.3367i	0.768213	+	1.33058i	−0.170318	+	0.985389i	$0.554480\pi$
$920$	−4.23974	−	14.1617i	−0.139780	−	0.466898i
$921$		0			0
$922$	12.1803	−	8.01110i	0.401136	−	0.263832i
$923$	−4.59663	+	6.17434i	−0.151300	+	0.203231i
$924$		0			0
$925$	−3.01012	−	1.97979i	−0.0989721	−	0.0650950i
$926$	−23.0942	+	8.40558i	−0.758921	+	0.276225i
$927$		0			0
$928$	30.0728	+	10.9456i	0.987189	+	0.359307i
$929$	26.8152	+	36.0191i	0.879779	+	1.18175i	0.982355	+	0.187024i	$0.0598841\pi$
$929$	26.8152	+	36.0191i	0.879779	+	1.18175i	−0.102576	+	0.994725i	$0.532708\pi$
$930$		0			0
$931$	22.3645	+	23.7050i	0.732966	+	0.776899i
$932$	16.0465	+	17.0083i	0.525619	+	0.557124i
$933$		0			0
$934$	−3.28388	−	4.41101i	−0.107452	−	0.144333i
$935$	23.0638	+	8.39454i	0.754267	+	0.274531i
$936$		0			0
$937$	−48.3251	+	17.5889i	−1.57871	+	0.574605i	−0.974924	−	0.222539i	$-0.928565\pi$
$937$	−48.3251	+	17.5889i	−1.57871	+	0.574605i	−0.603790	+	0.797144i	$0.706343\pi$
$938$	−13.2815	−	8.73538i	−0.433656	−	0.285220i
$939$		0			0
$940$	−23.7350	+	31.8817i	−0.774151	+	1.03987i
$941$	8.71156	−	5.72969i	0.283989	−	0.186782i	−0.399520	−	0.916724i	$-0.630823\pi$
$941$	8.71156	−	5.72969i	0.283989	−	0.186782i	0.683509	+	0.729942i	$0.260453\pi$
$942$		0			0
$943$	6.47780	+	21.6374i	0.210946	+	0.704610i
$944$	−8.90994	−	15.4325i	−0.289994	−	0.502284i
$945$		0			0
$946$	−7.65361	+	13.2564i	−0.248840	+	0.431004i
$947$	−43.9305	−	10.4117i	−1.42755	−	0.338335i	−0.557039	−	0.830486i	$-0.688063\pi$
$947$	−43.9305	−	10.4117i	−1.42755	−	0.338335i	−0.870510	+	0.492151i	$0.836211\pi$
$948$		0			0
$949$	−13.6952	−	6.87797i	−0.444564	−	0.223268i
$950$	−1.13524	−	2.63179i	−0.0368322	−	0.0853865i
$951$		0			0
$952$	1.85809	−	31.9022i	0.0602212	−	1.03396i
$953$	−5.08752	+	28.8527i	−0.164801	+	0.934632i	0.784469	+	0.620168i	$0.212936\pi$
$953$	−5.08752	+	28.8527i	−0.164801	+	0.934632i	−0.949270	+	0.314463i	$0.898175\pi$
$954$		0			0
$955$	1.87491	+	10.6331i	0.0606705	+	0.344080i
$956$	5.60359	−	0.654966i	0.181233	−	0.0211831i
$957$		0			0
$958$	0.484256	−	1.61753i	0.0156456	−	0.0522599i
$959$	−7.60646	+	1.80276i	−0.245626	+	0.0582143i
$960$		0			0
$961$	4.06014	−	9.41246i	0.130972	−	0.303628i
$962$	−4.49273	+	3.76985i	−0.144851	+	0.121545i
$963$		0			0
$964$	27.4013	+	22.9924i	0.882536	+	0.740536i
$965$	6.36484	−	3.19654i	0.204891	−	0.102900i
$966$		0			0
$967$	−46.5693	−	5.44317i	−1.49757	−	0.175041i	−0.672510	−	0.740088i	$-0.734784\pi$
$967$	−46.5693	−	5.44317i	−1.49757	−	0.175041i	−0.825059	+	0.565047i	$0.808858\pi$
$968$	−0.306179	−	5.25690i	−0.00984098	−	0.168963i
$969$		0			0
$970$	8.15876	−	8.64778i	0.261962	−	0.277663i
$971$	−45.6691			−1.46559			−0.732795	−	0.680449i	$-0.761785\pi$
$971$	−45.6691			−1.46559			−0.732795	+	0.680449i	$0.761785\pi$
$972$		0			0
$973$	38.4797			1.23360
$974$	−7.42643	+	7.87155i	−0.237958	+	0.252221i
$975$		0			0
$976$	−0.821024	−	14.0964i	−0.0262803	−	0.451216i
$977$	−1.23134	−	0.143923i	−0.0393940	−	0.00460450i	0.0963731	−	0.995345i	$-0.469276\pi$
$977$	−1.23134	−	0.143923i	−0.0393940	−	0.00460450i	−0.135767	+	0.990741i	$0.543350\pi$
$978$		0			0
$979$	−33.0608	+	16.6037i	−1.05663	+	0.530658i
$980$	−29.8126	−	25.0157i	−0.952329	−	0.799099i
$981$		0			0
$982$	18.4847	−	15.5105i	0.589869	−	0.494959i
$983$	14.4907	−	33.5933i	0.462183	−	1.07146i	−0.514639	−	0.857407i	$-0.672074\pi$
$983$	14.4907	−	33.5933i	0.462183	−	1.07146i	0.976822	−	0.214054i	$-0.0686667\pi$
$984$		0			0
$985$	51.9675	−	12.3165i	1.65582	−	0.392437i
$986$	3.48289	−	11.6337i	0.110918	−	0.370491i
$987$		0			0
$988$	16.5548	−	1.93498i	0.526680	−	0.0615600i
$989$	3.38850	+	19.2172i	0.107748	+	0.611070i
$990$		0			0
$991$	−7.21791	+	40.9348i	−0.229285	+	1.30034i	0.625038	+	0.780594i	$0.285083\pi$
$991$	−7.21791	+	40.9348i	−0.229285	+	1.30034i	−0.854323	+	0.519743i	$0.826028\pi$
$992$	−2.14681	+	36.8594i	−0.0681614	+	1.17029i
$993$		0			0
$994$	2.55662	+	5.92691i	0.0810910	+	0.187990i
$995$	21.8599	+	10.9785i	0.693007	+	0.348041i
$996$		0			0
$997$	20.5929	+	4.88061i	0.652185	+	0.154571i	0.543372	−	0.839492i	$-0.317147\pi$
$997$	20.5929	+	4.88061i	0.652185	+	0.154571i	0.108812	+	0.994062i	$0.465295\pi$
$998$	10.4952	−	18.1782i	0.332220	−	0.575421i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.622.4		144
3.2	odd	2		729.2.g.d.622.5		144
9.2	odd	6		81.2.g.a.16.4	✓	144
9.4	even	3		729.2.g.b.379.4		144
9.5	odd	6		729.2.g.c.379.5		144
9.7	even	3		243.2.g.a.208.5		144
81.5	odd	54		729.2.g.c.352.5		144
81.22	even	27	inner	729.2.g.a.109.4		144
81.32	odd	54		81.2.g.a.76.4	yes	144
81.34	even	27		6561.2.a.d.1.42		72
81.47	odd	54		6561.2.a.c.1.31		72
81.49	even	27		243.2.g.a.118.5		144
81.59	odd	54		729.2.g.d.109.5		144
81.76	even	27		729.2.g.b.352.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.4	✓	144	9.2	odd	6
81.2.g.a.76.4	yes	144	81.32	odd	54
243.2.g.a.118.5		144	81.49	even	27
243.2.g.a.208.5		144	9.7	even	3
729.2.g.a.109.4		144	81.22	even	27	inner
729.2.g.a.622.4		144	1.1	even	1	trivial
729.2.g.b.352.4		144	81.76	even	27
729.2.g.b.379.4		144	9.4	even	3
729.2.g.c.352.5		144	81.5	odd	54
729.2.g.c.379.5		144	9.5	odd	6
729.2.g.d.109.5		144	81.59	odd	54
729.2.g.d.622.5		144	3.2	odd	2
6561.2.a.c.1.31		72	81.47	odd	54
6561.2.a.d.1.42		72	81.34	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)

\(f(q)\)	\(=\)	\(q+(-0.453861 + 0.481064i) q^{2} +(0.0908564 + 1.55994i) q^{4} +(-2.49650 - 0.291799i) q^{5} +(3.67465 - 1.84548i) q^{7} +(-1.80495 - 1.51453i) q^{8} +(1.27344 - 1.06854i) q^{10} +(-1.17263 + 2.71847i) q^{11} +(-3.15575 + 0.747925i) q^{13} +(-0.779986 + 2.60534i) q^{14} +(-1.55626 + 0.181901i) q^{16} +(0.572741 + 3.24818i) q^{17} +(-0.571121 + 3.23899i) q^{19} +(0.228367 - 3.92091i) q^{20} +(-0.775546 - 1.79792i) q^{22} +(-2.23062 - 1.12026i) q^{23} +(1.28214 + 0.303873i) q^{25} +(1.07247 - 1.85757i) q^{26} +(3.21271 + 5.56458i) q^{28} +(1.59664 + 5.33313i) q^{29} +(-5.36607 + 3.52932i) q^{31} +(3.43286 - 4.61114i) q^{32} +(-1.82253 - 1.19870i) q^{34} +(-9.71228 + 3.53498i) q^{35} +(-2.56937 - 0.935175i) q^{37} +(-1.29895 - 1.74480i) q^{38} +(4.06412 + 4.30771i) q^{40} +(-6.20948 - 6.58166i) q^{41} +(-4.66833 - 6.27065i) q^{43} +(-4.34719 - 1.58225i) q^{44} +(1.55131 - 0.564629i) q^{46} +(-8.45508 - 5.56099i) q^{47} +(5.91716 - 7.94813i) q^{49} +(-0.728095 + 0.478876i) q^{50} +(-1.45344 - 4.85483i) q^{52} +(-0.00494432 - 0.00856381i) q^{53} +(3.72072 - 6.44448i) q^{55} +(-9.42760 - 2.23438i) q^{56} +(-3.29023 - 1.65242i) q^{58} +(4.50463 + 10.4429i) q^{59} +(-0.523995 + 8.99665i) q^{61} +(0.737619 - 4.18325i) q^{62} +(0.116049 + 0.658144i) q^{64} +(8.09656 - 0.946352i) q^{65} +(-1.67644 + 5.59970i) q^{67} +(-5.01494 + 1.18856i) q^{68} +(2.70747 - 6.27662i) q^{70} +(1.81817 - 1.52563i) q^{71} +(3.61987 + 3.03743i) q^{73} +(1.61602 - 0.811594i) q^{74} +(-5.10453 - 0.596634i) q^{76} +(0.707860 + 12.1535i) q^{77} +(-6.17756 + 6.54783i) q^{79} +3.93828 q^{80} +5.98444 q^{82} +(-2.54001 + 2.69226i) q^{83} +(-0.482034 - 8.27620i) q^{85} +(5.13536 + 0.600238i) q^{86} +(6.23375 - 3.13071i) q^{88} +(9.57258 + 8.03235i) q^{89} +(-10.2160 + 8.57223i) q^{91} +(1.54487 - 3.58142i) q^{92} +(6.51263 - 1.54352i) q^{94} +(2.37094 - 7.91949i) q^{95} +(7.10357 - 0.830288i) q^{97} +(1.13799 + 6.45388i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 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

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