LMFDB - Embedded newform 729.2.g.a.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			109.4
Character	$\chi$	$=$	729.109
Dual form			729.2.g.a.622.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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	0.546745	−	0.837299i	$-0.315867\pi$
$2$	−0.453861	−	0.481064i	−0.320928	−	0.340164i	−0.867673	+	0.497135i	$0.834385\pi$
$3$		0			0
$3$		0			0
$4$	0.0908564	−	1.55994i	0.0454282	−	0.779972i
$5$	−2.49650	+	0.291799i	−1.11647	+	0.130496i	−0.654256	−	0.756273i	$-0.727018\pi$
$5$	−2.49650	+	0.291799i	−1.11647	+	0.130496i	−0.462212	+	0.886769i	$0.652944\pi$
$6$		0			0
$7$	3.67465	+	1.84548i	1.38889	+	0.697526i	0.976907	−	0.213667i	$-0.0685407\pi$
$7$	3.67465	+	1.84548i	1.38889	+	0.697526i	0.411981	+	0.911192i	$0.364837\pi$
$8$	−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	−0.998465	−	0.0553842i	$-0.982362\pi$
$11$	−1.17263	−	2.71847i	−0.353562	−	0.819648i	0.644903	−	0.764264i	$-0.276898\pi$
$12$		0			0
$13$	−3.15575	−	0.747925i	−0.875246	−	0.207437i	−0.231647	−	0.972800i	$-0.574411\pi$
$13$	−3.15575	−	0.747925i	−0.875246	−	0.207437i	−0.643599	+	0.765363i	$0.722560\pi$
$14$	−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	−0.833146	−	0.553052i	$-0.813463\pi$
$17$	0.572741	−	3.24818i	0.138910	−	0.787799i	0.972057	−	0.234746i	$-0.0754260\pi$
$18$		0			0
$19$	−0.571121	−	3.23899i	−0.131024	−	0.743075i	−0.977546	−	0.210722i	$-0.932419\pi$
$19$	−0.571121	−	3.23899i	−0.131024	−	0.743075i	0.846522	−	0.532354i	$-0.178692\pi$
$20$	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	−0.665893	−	0.746047i	$-0.731949\pi$
$23$	−2.23062	+	1.12026i	−0.465116	+	0.233590i	0.200778	+	0.979637i	$0.435653\pi$
$24$		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	−0.671848	−	0.740689i	$-0.734499\pi$
$29$	1.59664	−	5.33313i	0.296488	−	0.990338i	0.968336	−	0.249650i	$-0.0803154\pi$
$30$		0			0
$31$	−5.36607	−	3.52932i	−0.963775	−	0.633885i	−0.0329913	−	0.999456i	$-0.510503\pi$
$31$	−5.36607	−	3.52932i	−0.963775	−	0.633885i	−0.930783	+	0.365571i	$0.880874\pi$
$32$	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	−0.544471	−	0.838780i	$-0.683269\pi$
$37$	−2.56937	+	0.935175i	−0.422402	+	0.153742i	0.122069	+	0.992522i	$0.461047\pi$
$38$	−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	0.0298414	+	0.999555i	$0.490500\pi$
$41$	−6.20948	+	6.58166i	−0.969757	+	1.02788i	−0.999599	+	0.0283280i	$0.990982\pi$
$42$		0			0
$43$	−4.66833	+	6.27065i	−0.711914	+	0.956266i	−0.999999	−	0.00133878i	$-0.999574\pi$
$43$	−4.66833	+	6.27065i	−0.711914	+	0.956266i	0.288086	+	0.957605i	$0.406981\pi$
$44$	−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	−0.987416	−	0.158145i	$-0.949449\pi$
$47$	−8.45508	+	5.56099i	−1.23330	+	0.811154i	−0.245884	+	0.969299i	$0.579078\pi$
$48$		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	−0.866365	−	0.499412i	$-0.833550\pi$
$53$	−0.00494432	+	0.00856381i	−0.000679154	+	0.00117633i	0.865686	+	0.500588i	$0.166883\pi$
$54$		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	−0.324048	−	0.946041i	$-0.605044\pi$
$59$	4.50463	−	10.4429i	0.586453	−	1.35955i	0.910500	−	0.413509i	$-0.135697\pi$
$60$		0			0
$61$	−0.523995	−	8.99665i	−0.0670907	−	1.15190i	−0.848959	−	0.528459i	$-0.822770\pi$
$61$	−0.523995	−	8.99665i	−0.0670907	−	1.15190i	0.781868	−	0.623444i	$-0.214267\pi$
$62$	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	−0.997246	−	0.0741583i	$-0.976373\pi$
$67$	−1.67644	−	5.59970i	−0.204810	−	0.684113i	0.792437	−	0.609954i	$-0.208812\pi$
$68$	−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	0.744269	−	0.667880i	$-0.232798\pi$
$71$	1.81817	+	1.52563i	0.215777	+	0.181058i	−0.528492	+	0.848938i	$0.677242\pi$
$72$		0			0
$73$	3.61987	−	3.03743i	0.423674	−	0.355505i	−0.405885	−	0.913924i	$-0.633037\pi$
$73$	3.61987	−	3.03743i	0.423674	−	0.355505i	0.829559	+	0.558420i	$0.188592\pi$
$74$	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	0.279698	−	0.960088i	$-0.409766\pi$
$79$	−6.17756	−	6.54783i	−0.695029	−	0.736688i	−0.974727	+	0.223400i	$0.928284\pi$
$80$	3.93828			0.440313
$81$		0			0
$82$	5.98444			0.660871
$83$	−2.54001	−	2.69226i	−0.278803	−	0.295514i	0.572807	−	0.819691i	$-0.305855\pi$
$83$	−2.54001	−	2.69226i	−0.278803	−	0.295514i	−0.851609	+	0.524177i	$0.824373\pi$
$84$		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	0.0257399	−	0.999669i	$-0.491806\pi$
$89$	9.57258	−	8.03235i	1.01469	−	0.851427i	0.988951	+	0.148242i	$0.0473614\pi$
$90$		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	0.468799	−	0.883305i	$-0.344687\pi$
$97$	7.10357	+	0.830288i	0.721258	+	0.0843030i	0.252459	+	0.967608i	$0.418761\pi$
$98$	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	−0.998905	−	0.0467805i	$-0.985104\pi$
$101$	−0.122459	−	2.10254i	−0.0121851	−	0.209211i	0.986720	−	0.162430i	$-0.0519332\pi$
$102$		0			0
$103$	−0.818039	+	1.89643i	−0.0806038	+	0.186861i	−0.953752	−	0.300594i	$-0.902815\pi$
$103$	−0.818039	+	1.89643i	−0.0806038	+	0.186861i	0.873148	+	0.487454i	$0.162074\pi$
$104$	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	0.972014	+	0.234923i	$0.0754838\pi$
$107$	7.13179	+	12.3526i	0.689456	+	1.19417i	−0.282558	+	0.959250i	$0.591183\pi$
$108$		0			0
$109$	−6.70237	+	11.6088i	−0.641970	+	1.11193i	0.343022	+	0.939327i	$0.388549\pi$
$109$	−6.70237	+	11.6088i	−0.641970	+	1.11193i	−0.984992	+	0.172598i	$0.944784\pi$
$110$	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	0.877459	−	0.479652i	$-0.159237\pi$
$113$	1.76779	+	2.37455i	0.166300	+	0.223379i	−0.711159	+	0.703031i	$0.751830\pi$
$114$		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	−0.212425	−	0.977177i	$-0.568136\pi$
$127$	−11.3063	−	4.11514i	−1.00327	−	0.365160i	−0.790844	+	0.612017i	$0.790358\pi$
$128$	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	0.348032	−	0.937483i	$-0.386850\pi$
$131$	−4.29128	−	2.82242i	−0.374931	−	0.246596i	−0.722963	+	0.690887i	$0.757220\pi$
$132$		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	−0.308874	−	0.951103i	$-0.599952\pi$
$137$	−1.84980	+	0.438412i	−0.158039	+	0.0374560i	0.150834	+	0.988559i	$0.451804\pi$
$138$		0			0
$139$	8.36246	−	4.19978i	0.709294	−	0.356221i	−0.0572963	−	0.998357i	$-0.518248\pi$
$139$	8.36246	−	4.19978i	0.709294	−	0.356221i	0.766591	+	0.642136i	$0.221952\pi$
$140$	−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	0.265882	−	0.964006i	$-0.414337\pi$
$149$	0.864689	+	0.204935i	0.0708381	+	0.0167889i	−0.195044	+	0.980794i	$0.562485\pi$
$150$		0			0
$151$	−3.19183	−	7.39949i	−0.259747	−	0.602162i	0.737577	−	0.675263i	$-0.235970\pi$
$151$	−3.19183	−	7.39949i	−0.259747	−	0.602162i	−0.997325	+	0.0731007i	$0.976711\pi$
$152$	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	0.478751	−	0.877951i	$-0.341090\pi$
$157$	14.3727	−	1.67993i	1.14707	−	0.134073i	0.668315	+	0.743878i	$0.267016\pi$
$158$	−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	0.560877	−	0.827899i	$-0.310464\pi$
$167$	16.7682	−	1.95992i	1.29756	−	0.151663i	0.736685	+	0.676236i	$0.236390\pi$
$168$		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	0.786492	−	0.617600i	$-0.211895\pi$
$173$	−2.66291	−	6.17332i	−0.202457	−	0.469349i	−0.988950	+	0.148251i	$0.952636\pi$
$174$		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	−0.711669	−	0.702515i	$-0.752060\pi$
$179$	2.64043	−	14.9746i	0.197355	−	1.11926i	0.909024	−	0.416743i	$-0.136828\pi$
$180$		0			0
$181$	−0.973297	−	5.51984i	−0.0723446	−	0.410287i	−0.999377	−	0.0353044i	$-0.988760\pi$
$181$	−0.973297	−	5.51984i	−0.0723446	−	0.410287i	0.927032	−	0.374982i	$-0.122351\pi$
$182$	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	−0.990922	−	0.134435i	$-0.957078\pi$
$191$	−1.23201	+	4.11521i	−0.0891453	+	0.297766i	0.901777	+	0.432202i	$0.142263\pi$
$192$		0			0
$193$	−2.36750	−	1.55713i	−0.170417	−	0.112085i	0.461435	−	0.887174i	$-0.347335\pi$
$193$	−2.36750	−	1.55713i	−0.170417	−	0.112085i	−0.631852	+	0.775089i	$0.717705\pi$
$194$	−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	−0.487777	−	0.872968i	$-0.662192\pi$
$197$	−19.9667	−	7.26729i	−1.42257	−	0.517773i	−0.934792	+	0.355195i	$0.884414\pi$
$198$		0			0
$199$	−9.14529	+	3.32862i	−0.648293	+	0.235959i	−0.645174	−	0.764036i	$-0.723215\pi$
$199$	−9.14529	+	3.32862i	−0.648293	+	0.235959i	−0.00311899	+	0.999995i	$0.500993\pi$
$200$	−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	0.995051	+	0.0993683i	$0.0316822\pi$
$211$	11.6913	+	15.7041i	0.804861	+	1.08112i	−0.190190	+	0.981747i	$0.560910\pi$
$212$	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	0.870888	+	0.491481i	$0.163544\pi$
$223$	0.939986	+	16.1389i	0.0629461	+	1.08074i	−0.807942	+	0.589262i	$0.799419\pi$
$224$	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	0.782177	−	0.623056i	$-0.214109\pi$
$227$	21.0869	+	2.46470i	1.39958	+	0.163588i	0.617407	+	0.786644i	$0.288183\pi$
$228$		0			0
$229$	2.47496	+	8.26696i	0.163550	+	0.546296i	0.999998	−	0.00175006i	$-0.000557061\pi$
$229$	2.47496	+	8.26696i	0.163550	+	0.546296i	−0.836448	+	0.548046i	$0.815372\pi$
$230$	−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	0.935764	−	0.352626i	$-0.114711\pi$
$233$	11.4634	+	9.61890i	0.750989	+	0.630155i	−0.184775	+	0.982781i	$0.559156\pi$
$234$		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	0.984689	+	0.174322i	$0.0557733\pi$
$239$	−0.209933	+	3.60440i	−0.0135794	+	0.233150i	−0.998268	+	0.0588277i	$0.981264\pi$
$240$		0			0
$241$	15.7090	+	16.6506i	1.01191	+	1.07256i	0.997356	+	0.0726662i	$0.0231508\pi$
$241$	15.7090	+	16.6506i	1.01191	+	1.07256i	0.0145522	+	0.999894i	$0.495368\pi$
$242$	−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	0.0336587	−	0.999433i	$-0.489284\pi$
$251$	16.2193	−	13.6096i	1.02375	−	0.859031i	0.990095	+	0.140402i	$0.0448396\pi$
$252$		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	0.859650	−	0.510884i	$-0.170682\pi$
$257$	−2.23335	−	7.45990i	−0.139312	−	0.465336i	−0.998962	+	0.0455481i	$0.985497\pi$
$258$		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	0.999938	−	0.0110966i	$-0.00353224\pi$
$263$	0.0887569	+	1.52390i	0.00547299	+	0.0939675i	−0.994465	+	0.105064i	$0.966495\pi$
$264$		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	−0.830738	−	0.556663i	$-0.812081\pi$
$269$	−14.7193	−	25.4946i	−0.897454	−	1.55444i	−0.0667154	−	0.997772i	$-0.521252\pi$
$270$		0			0
$271$	−7.28643	+	12.6205i	−0.442619	+	0.766639i	−0.997883	−	0.0650354i	$-0.979284\pi$
$271$	−7.28643	+	12.6205i	−0.442619	+	0.766639i	0.555264	+	0.831674i	$0.312617\pi$
$272$	−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	−0.779618	−	0.626256i	$-0.784587\pi$
$277$	−8.54418	+	5.61960i	−0.513370	+	0.337649i	0.266247	+	0.963905i	$0.414216\pi$
$278$	−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	−0.909427	−	0.415863i	$-0.863479\pi$
$281$	−4.19424	+	5.63385i	−0.250208	+	0.336087i	0.659219	+	0.751951i	$0.270887\pi$
$282$		0			0
$283$	14.8381	−	15.7275i	0.882036	−	0.934904i	−0.116262	−	0.993219i	$-0.537091\pi$
$283$	14.8381	−	15.7275i	0.882036	−	0.934904i	0.998298	+	0.0583150i	$0.0185728\pi$
$284$	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	0.254097	−	0.967179i	$-0.418222\pi$
$293$	−9.12929	−	6.00443i	−0.533339	−	0.350782i	−0.787436	+	0.616396i	$0.788592\pi$
$294$		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	−0.953502	−	0.301386i	$-0.902551\pi$
$307$	0.798574	−	4.52894i	0.0455770	−	0.258480i	0.999079	+	0.0429063i	$0.0136617\pi$
$308$	−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	0.681566	−	0.731756i	$-0.261299\pi$
$311$	16.9690	+	4.02173i	0.962224	+	0.228051i	0.280658	+	0.959808i	$0.409447\pi$
$312$		0			0
$313$	−6.26878	−	14.5327i	−0.354333	−	0.821435i	−0.998404	−	0.0564701i	$-0.982015\pi$
$313$	−6.26878	−	14.5327i	−0.354333	−	0.821435i	0.644072	−	0.764965i	$-0.277244\pi$
$314$	−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	−0.117266	−	0.993101i	$-0.537413\pi$
$317$	−17.5175	−	8.79762i	−0.983881	−	0.494124i	−0.866615	+	0.498977i	$0.833709\pi$
$318$		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	−0.178710	−	0.983902i	$-0.557192\pi$
$331$	−19.5513	−	9.81905i	−1.07464	−	0.539704i	−0.895929	+	0.444198i	$0.853489\pi$
$332$	−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	−0.0139020	−	0.999903i	$-0.504425\pi$
$337$	−8.72133	−	2.06699i	−0.475081	−	0.112596i	−0.461179	+	0.887307i	$0.652573\pi$
$338$	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	−0.845682	−	0.533688i	$-0.820806\pi$
$347$	−17.1862	+	8.63124i	−0.922604	+	0.463349i	−0.0769226	+	0.997037i	$0.524509\pi$
$348$		0			0
$349$	20.7785	−	4.92459i	1.11225	−	0.263607i	0.366884	−	0.930267i	$-0.380424\pi$
$349$	20.7785	−	4.92459i	1.11225	−	0.263607i	0.745363	+	0.666659i	$0.232276\pi$
$350$	−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	0.769219	+	0.638985i	$0.220645\pi$
$353$	−4.21952	+	14.0942i	−0.224582	+	0.750157i	−0.993801	+	0.111172i	$0.964540\pi$
$354$		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	0.593648	−	0.804725i	$-0.297687\pi$
$359$	10.0637	+	3.66289i	0.531142	+	0.193320i	−0.0625063	+	0.998045i	$0.519909\pi$
$360$		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	−0.859623	−	0.510929i	$-0.829301\pi$
$367$	−2.36813	+	3.18095i	−0.123615	+	0.166044i	0.736007	+	0.676974i	$0.236709\pi$
$368$	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	−0.999772	−	0.0213686i	$-0.993198\pi$
$373$	−14.1663	−	19.0287i	−0.733505	−	0.985268i	0.266267	−	0.963899i	$-0.414210\pi$
$374$	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	0.978393	+	0.206752i	$0.0662892\pi$
$379$	13.0094	+	22.5330i	0.668249	+	1.15744i	−0.310145	+	0.950689i	$0.600377\pi$
$380$	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	−0.307719	−	0.951477i	$-0.599566\pi$
$383$	11.6548	−	27.0188i	0.595530	−	1.38059i	0.903249	−	0.429117i	$-0.141175\pi$
$384$		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	−0.581373	−	0.813637i	$-0.697484\pi$
$389$	−26.3247	−	3.07691i	−1.33471	−	0.156006i	−0.753340	+	0.657631i	$0.771559\pi$
$390$		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	−0.997022	−	0.0771123i	$-0.975430\pi$
$397$	−21.8020	+	18.2941i	−1.09421	+	0.918154i	−0.0971903	+	0.995266i	$0.530986\pi$
$398$	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	0.912590	+	0.408875i	$0.134079\pi$
$401$	−0.826969	+	14.1985i	−0.0412969	+	0.709040i	−0.953887	+	0.300165i	$0.902958\pi$
$402$		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	0.990869	+	0.134830i	$0.0430489\pi$
$409$	−0.181062	+	3.10871i	−0.00895293	+	0.153716i	−0.999822	+	0.0188857i	$0.993988\pi$
$410$	−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	0.896484	−	0.443077i	$-0.146113\pi$
$419$	−1.96491	−	6.56326i	−0.0959921	−	0.320636i	−0.992476	+	0.122441i	$0.960928\pi$
$420$		0			0
$421$	14.8315	+	1.73356i	0.722844	+	0.0844883i	0.469556	−	0.882903i	$-0.344414\pi$
$421$	14.8315	+	1.73356i	0.722844	+	0.0844883i	0.253288	+	0.967391i	$0.418488\pi$
$422$	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	0.950939	+	0.309378i	$0.100121\pi$
$431$	15.4334	+	26.7314i	0.743399	+	1.28760i	−0.207540	+	0.978227i	$0.566546\pi$
$432$		0			0
$433$	14.3849	−	24.9154i	0.691295	−	1.19736i	−0.280119	−	0.959965i	$-0.590374\pi$
$433$	14.3849	−	24.9154i	0.691295	−	1.19736i	0.971414	−	0.237393i	$-0.0762928\pi$
$434$	−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	−0.458237	−	0.888830i	$-0.651519\pi$
$439$	3.69605	−	2.43093i	0.176403	−	0.116022i	0.634640	+	0.772808i	$0.281149\pi$
$440$	−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	−0.762669	−	0.646789i	$-0.776111\pi$
$443$	1.59297	−	2.13973i	0.0756843	−	0.101662i	0.838353	+	0.545128i	$0.183519\pi$
$444$		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	−0.859474	+	0.511179i	$0.829209\pi$
$449$	−39.1256	+	14.2405i	−1.84645	+	0.672053i	−0.986975	+	0.160874i	$0.948569\pi$
$450$		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	−0.993886	−	0.110414i	$-0.964782\pi$
$457$	−2.19831	+	7.34286i	−0.102833	+	0.343485i	0.891053	+	0.453899i	$0.149967\pi$
$458$	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	−0.697400	−	0.716682i	$-0.745660\pi$
$461$	−21.4489	+	5.08348i	−0.998974	+	0.236761i	−0.301573	+	0.953443i	$0.597512\pi$
$462$		0			0
$463$	33.2070	−	16.6772i	1.54326	−	0.775054i	0.545260	−	0.838267i	$-0.316431\pi$
$463$	33.2070	−	16.6772i	1.54326	−	0.775054i	0.998000	+	0.0632131i	$0.0201348\pi$
$464$	−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	−0.999818	−	0.0190543i	$-0.993934\pi$
$467$	−1.44385	−	8.18848i	−0.0668134	−	0.378918i	0.933005	−	0.359863i	$-0.117177\pi$
$468$		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	0.395915	−	0.918287i	$-0.370427\pi$
$479$	−2.28141	−	1.14577i	−0.104240	−	0.0523515i	−0.500155	+	0.865936i	$0.666724\pi$
$480$		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	−0.883601	−	0.468240i	$-0.844888\pi$
$491$	−36.2381	+	4.23562i	−1.63540	+	0.191151i	−0.751800	+	0.659391i	$0.770814\pi$
$492$		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	−0.528927	−	0.848667i	$-0.677406\pi$
$499$	−30.8822	−	7.31920i	−1.38248	−	0.327653i	−0.853548	+	0.521015i	$0.825554\pi$
$500$	−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	−0.999218	−	0.0395428i	$-0.987410\pi$
$503$	−1.04817	+	5.94449i	−0.0467358	+	0.265052i	0.952482	+	0.304595i	$0.0985210\pi$
$504$		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	−0.885590	−	0.464467i	$-0.846246\pi$
$509$	−23.5056	+	11.8050i	−1.04187	+	0.523246i	−0.156278	+	0.987713i	$0.549950\pi$
$510$		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	−0.236301	−	0.971680i	$-0.575935\pi$
$521$	−23.7819	−	8.65589i	−1.04190	−	0.379221i	−0.805601	+	0.592459i	$0.798157\pi$
$522$		0			0
$523$	2.76727	−	1.00720i	0.121004	−	0.0440420i	−0.280808	−	0.959764i	$-0.590603\pi$
$523$	2.76727	−	1.00720i	0.121004	−	0.0440420i	0.401813	+	0.915722i	$0.368380\pi$
$524$	−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	0.610763	−	0.791813i	$-0.290863\pi$
$541$	−8.84669	−	15.3229i	−0.380349	−	0.658784i	−0.991112	+	0.133030i	$0.957529\pi$
$542$	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	−0.540777	−	0.841166i	$-0.681870\pi$
$547$	−2.36944	−	40.6817i	−0.101310	−	1.73942i	0.439467	−	0.898259i	$-0.355167\pi$
$548$	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	0.984316	−	0.176415i	$-0.0564501\pi$
$557$	23.1644	+	19.4372i	0.981505	+	0.823581i	−0.00281036	+	0.999996i	$0.500895\pi$
$558$		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	0.896869	+	0.442296i	$0.145836\pi$
$563$	−1.07446	+	18.4478i	−0.0452831	+	0.777480i	−0.942152	+	0.335185i	$0.891201\pi$
$564$		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	0.843746	−	0.536742i	$-0.180345\pi$
$569$	6.17461	+	6.54471i	0.258853	+	0.274368i	−0.584893	+	0.811110i	$0.698864\pi$
$570$		0			0
$571$	0.981371	−	16.8495i	0.0410691	−	0.705129i	−0.913445	−	0.406963i	$-0.866588\pi$
$571$	0.981371	−	16.8495i	0.0410691	−	0.705129i	0.954514	−	0.298167i	$-0.0963751\pi$
$572$	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	−0.0143022	−	0.999898i	$-0.504553\pi$
$577$	−24.0567	−	20.1860i	−1.00149	−	0.840352i	−0.987191	+	0.159545i	$0.948997\pi$
$578$	−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	0.996253	−	0.0864861i	$-0.0275638\pi$
$587$	−0.0800524	−	1.37445i	−0.00330412	−	0.0567295i	−0.999557	+	0.0297566i	$0.990527\pi$
$588$		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	−0.986256	−	0.165227i	$-0.947164\pi$
$593$	−15.4929	−	26.8346i	−0.636219	−	1.10196i	0.350037	−	0.936736i	$-0.386169\pi$
$594$		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	0.992615	−	0.121310i	$-0.0387097\pi$
$599$	14.4819	+	19.4526i	0.591715	+	0.794812i	−0.400899	+	0.916122i	$0.631302\pi$
$600$		0			0
$601$	−6.33832	+	4.16878i	−0.258545	+	0.170048i	−0.672164	−	0.740402i	$-0.734635\pi$
$601$	−6.33832	+	4.16878i	−0.258545	+	0.170048i	0.413619	+	0.910450i	$0.364265\pi$
$602$	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	−0.994739	−	0.102446i	$-0.967333\pi$
$607$	−20.5630	+	21.7955i	−0.834627	+	0.884653i	0.160111	+	0.987099i	$0.448815\pi$
$608$	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	0.562929	−	0.826505i	$-0.309675\pi$
$613$	11.4606	+	4.17132i	0.462890	+	0.168478i	−0.100039	+	0.994984i	$0.531897\pi$
$614$	−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	0.253404	−	0.967361i	$-0.418450\pi$
$617$	−13.2760	−	8.73179i	−0.534474	−	0.351529i	−0.787878	+	0.615832i	$0.788820\pi$
$618$		0			0
$619$	−6.67055	+	22.2812i	−0.268112	+	0.895556i	0.712844	+	0.701323i	$0.247407\pi$
$619$	−6.67055	+	22.2812i	−0.268112	+	0.895556i	−0.980955	+	0.194233i	$0.937778\pi$
$620$	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	−0.912519	−	0.409035i	$-0.865866\pi$
$631$	2.13182	−	12.0902i	0.0848665	−	0.481302i	0.997385	−	0.0722670i	$-0.0230234\pi$
$632$	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	0.606324	−	0.795218i	$-0.292644\pi$
$641$	8.36840	+	4.20277i	0.330532	+	0.165999i	−0.275791	+	0.961217i	$0.588940\pi$
$642$		0			0
$643$	19.5316	−	2.28292i	0.770252	−	0.0900295i	0.278115	−	0.960548i	$-0.410290\pi$
$643$	19.5316	−	2.28292i	0.770252	−	0.0900295i	0.492136	+	0.870518i	$0.336216\pi$
$644$	−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	0.722755	−	0.691105i	$-0.242876\pi$
$653$	40.5133	−	4.73532i	1.58541	−	0.185308i	0.862653	+	0.505797i	$0.168802\pi$
$654$		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	0.897074	−	0.441880i	$-0.145688\pi$
$659$	−1.02550	−	2.37737i	−0.0399477	−	0.0926093i	−0.937022	+	0.349271i	$0.886429\pi$
$660$		0			0
$661$	29.2233	+	6.92605i	1.13665	+	0.269392i	0.755519	−	0.655127i	$-0.227385\pi$
$661$	29.2233	+	6.92605i	1.13665	+	0.269392i	0.381136	+	0.924519i	$0.375533\pi$
$662$	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	0.0378561	−	0.999283i	$-0.487947\pi$
$673$	13.4942	−	3.19818i	0.520163	−	0.123281i	0.482307	+	0.876002i	$0.339799\pi$
$674$	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	−0.773687	−	0.633568i	$-0.781590\pi$
$677$	5.74687	−	19.1959i	0.220870	−	0.737757i	0.994557	−	0.104190i	$-0.0332249\pi$
$678$		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	0.844597	−	0.535402i	$-0.179840\pi$
$683$	29.9877	+	10.9146i	1.14745	+	0.417636i	0.302849	+	0.953039i	$0.402062\pi$
$684$		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	−0.137760	−	0.990466i	$-0.543990\pi$
$691$	22.3598	−	30.0344i	0.850605	−	1.14256i	0.988366	−	0.152096i	$-0.0486022\pi$
$692$	−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	−0.997522	−	0.0703498i	$-0.977588\pi$
$701$	−11.5923	+	20.0785i	−0.437836	+	0.758355i	0.559686	+	0.828705i	$0.310922\pi$
$702$		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	−0.999371	−	0.0354672i	$-0.988708\pi$
$709$	−0.289566	−	4.97166i	−0.0108749	−	0.186715i	0.988496	−	0.151247i	$-0.0483290\pi$
$710$	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	0.357497	−	0.933914i	$-0.383630\pi$
$719$	−13.4111	−	11.2533i	−0.500151	−	0.419677i	−0.857648	+	0.514238i	$0.828075\pi$
$720$		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	0.617073	−	0.786906i	$-0.288318\pi$
$727$	−5.51070	−	5.84100i	−0.204381	−	0.216631i	−0.821454	+	0.570275i	$0.806837\pi$
$728$	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	−0.797823	−	0.602891i	$-0.794015\pi$
$733$	1.74889	−	30.0273i	0.0645968	−	1.10908i	0.862420	−	0.506193i	$-0.168948\pi$
$734$	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	0.676134	−	0.736779i	$-0.263654\pi$
$739$	1.84741	+	1.55016i	0.0679580	+	0.0570236i	−0.608176	+	0.793802i	$0.708098\pi$
$740$	−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	0.996953	+	0.0780084i	$0.0248561\pi$
$743$	5.63906	+	18.8358i	0.206877	+	0.691018i	−0.790076	+	0.613009i	$0.789959\pi$
$744$		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	−0.960619	−	0.277870i	$-0.910372\pi$
$751$	−2.72090	+	6.30775i	−0.0992869	+	0.230173i	0.861332	+	0.508043i	$0.169631\pi$
$752$	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	−0.959656	−	0.281176i	$-0.909276\pi$
$757$	−6.50209	+	11.2620i	−0.236323	+	0.409323i	0.723334	+	0.690499i	$0.242609\pi$
$758$	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	0.572775	−	0.819713i	$-0.305867\pi$
$761$	−10.3938	−	13.9613i	−0.376775	−	0.506096i	−0.949550	+	0.313616i	$0.898459\pi$
$762$		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	−0.454602	−	0.890695i	$-0.650219\pi$
$769$	12.7844	−	13.5507i	0.461018	−	0.488651i	0.915620	+	0.402044i	$0.131700\pi$
$770$	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	0.197712	−	0.980260i	$-0.436649\pi$
$773$	27.2264	−	9.90961i	0.979267	−	0.356424i	0.781555	+	0.623836i	$0.214427\pi$
$774$		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

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.453861 - 0.481064i) q^{2} +(0.0908564 - 1.55994i) q^{4} +(-2.49650 + 0.291799i) q^{5} +(3.67465 + 1.84548i) q^{7} +(-1.80495 + 1.51453i) q^{8} +O(q^{10})\)	\(q+(-0.453861 - 0.481064i) q^{2} +(0.0908564 - 1.55994i) q^{4} +(-2.49650 + 0.291799i) q^{5} +(3.67465 + 1.84548i) q^{7} +(-1.80495 + 1.51453i) q^{8} +(1.27344 + 1.06854i) q^{10} +(-1.17263 - 2.71847i) q^{11} +(-3.15575 - 0.747925i) q^{13} +(-0.779986 - 2.60534i) q^{14} +(-1.55626 - 0.181901i) q^{16} +(0.572741 - 3.24818i) q^{17} +(-0.571121 - 3.23899i) q^{19} +(0.228367 + 3.92091i) q^{20} +(-0.775546 + 1.79792i) q^{22} +(-2.23062 + 1.12026i) q^{23} +(1.28214 - 0.303873i) q^{25} +(1.07247 + 1.85757i) q^{26} +(3.21271 - 5.56458i) q^{28} +(1.59664 - 5.33313i) q^{29} +(-5.36607 - 3.52932i) q^{31} +(3.43286 + 4.61114i) q^{32} +(-1.82253 + 1.19870i) q^{34} +(-9.71228 - 3.53498i) q^{35} +(-2.56937 + 0.935175i) q^{37} +(-1.29895 + 1.74480i) q^{38} +(4.06412 - 4.30771i) q^{40} +(-6.20948 + 6.58166i) q^{41} +(-4.66833 + 6.27065i) q^{43} +(-4.34719 + 1.58225i) q^{44} +(1.55131 + 0.564629i) q^{46} +(-8.45508 + 5.56099i) q^{47} +(5.91716 + 7.94813i) q^{49} +(-0.728095 - 0.478876i) q^{50} +(-1.45344 + 4.85483i) q^{52} +(-0.00494432 + 0.00856381i) q^{53} +(3.72072 + 6.44448i) q^{55} +(-9.42760 + 2.23438i) q^{56} +(-3.29023 + 1.65242i) q^{58} +(4.50463 - 10.4429i) q^{59} +(-0.523995 - 8.99665i) q^{61} +(0.737619 + 4.18325i) q^{62} +(0.116049 - 0.658144i) q^{64} +(8.09656 + 0.946352i) q^{65} +(-1.67644 - 5.59970i) q^{67} +(-5.01494 - 1.18856i) q^{68} +(2.70747 + 6.27662i) q^{70} +(1.81817 + 1.52563i) q^{71} +(3.61987 - 3.03743i) q^{73} +(1.61602 + 0.811594i) q^{74} +(-5.10453 + 0.596634i) q^{76} +(0.707860 - 12.1535i) q^{77} +(-6.17756 - 6.54783i) q^{79} +3.93828 q^{80} +5.98444 q^{82} +(-2.54001 - 2.69226i) q^{83} +(-0.482034 + 8.27620i) q^{85} +(5.13536 - 0.600238i) q^{86} +(6.23375 + 3.13071i) q^{88} +(9.57258 - 8.03235i) q^{89} +(-10.2160 - 8.57223i) q^{91} +(1.54487 + 3.58142i) q^{92} +(6.51263 + 1.54352i) q^{94} +(2.37094 + 7.91949i) q^{95} +(7.10357 + 0.830288i) q^{97} +(1.13799 - 6.45388i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

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