LMFDB - Embedded newform 729.2.g.a.109.2

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			109.2
Character	$\chi$	$=$	729.109
Dual form			729.2.g.a.622.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38579 - 1.46885i) q^{2} +(-0.120822 + 2.07444i) q^{4} +(-2.74943 + 0.321362i) q^{5} +(-0.546257 - 0.274341i) q^{7} +(0.120591 - 0.101188i) q^{8} +(4.28217 + 3.59317i) q^{10} +(1.48325 + 3.43857i) q^{11} +(3.32773 + 0.788687i) q^{13} +(0.354033 + 1.18255i) q^{14} +(3.81206 + 0.445566i) q^{16} +(1.31516 - 7.45862i) q^{17} +(0.132568 + 0.751830i) q^{19} +(-0.334454 - 5.74235i) q^{20} +(2.99528 - 6.94383i) q^{22} +(-1.94270 + 0.975661i) q^{23} +(2.59085 - 0.614044i) q^{25} +(-3.45308 - 5.98091i) q^{26} +(0.635103 - 1.10003i) q^{28} +(-1.30287 + 4.35188i) q^{29} +(-6.83895 - 4.49805i) q^{31} +(-4.81627 - 6.46937i) q^{32} +(-12.7782 + 8.40432i) q^{34} +(1.59006 + 0.578734i) q^{35} +(3.96908 - 1.44463i) q^{37} +(0.920617 - 1.23660i) q^{38} +(-0.299038 + 0.316962i) q^{40} +(6.20503 - 6.57695i) q^{41} +(1.04785 - 1.40751i) q^{43} +(-7.31231 + 2.66146i) q^{44} +(4.12528 + 1.50148i) q^{46} +(9.82847 - 6.46428i) q^{47} +(-3.95698 - 5.31514i) q^{49} +(-4.49233 - 2.95465i) q^{50} +(-2.03815 + 6.80788i) q^{52} +(2.80062 - 4.85082i) q^{53} +(-5.18313 - 8.97744i) q^{55} +(-0.0936337 + 0.0221916i) q^{56} +(8.19779 - 4.11708i) q^{58} +(-0.599347 + 1.38944i) q^{59} +(-0.175804 - 3.01844i) q^{61} +(2.87039 + 16.2788i) q^{62} +(-1.49529 + 8.48019i) q^{64} +(-9.40281 - 1.09903i) q^{65} +(2.19466 + 7.33068i) q^{67} +(15.3135 + 3.62938i) q^{68} +(-1.35341 - 3.13757i) q^{70} +(5.19850 + 4.36206i) q^{71} +(0.438511 - 0.367955i) q^{73} +(-7.62227 - 3.82805i) q^{74} +(-1.57564 + 0.184166i) q^{76} +(0.133101 - 2.28526i) q^{77} +(-6.32380 - 6.70284i) q^{79} -10.6242 q^{80} -18.2595 q^{82} +(-4.24676 - 4.50130i) q^{83} +(-1.21901 + 20.9296i) q^{85} +(-3.51954 + 0.411375i) q^{86} +(0.526809 + 0.264573i) q^{88} +(3.52742 - 2.95986i) q^{89} +(-1.60143 - 1.34376i) q^{91} +(-1.78923 - 4.14790i) q^{92} +(-23.1153 - 5.47843i) q^{94} +(-0.606095 - 2.02450i) q^{95} +(10.4458 + 1.22093i) q^{97} +(-2.32362 + 13.1779i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100})$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$ .

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

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

)

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

$2$	−1.38579	−	1.46885i	−0.979903	−	1.03864i	−0.999246	−	0.0388240i	$-0.987639\pi$
$2$	−1.38579	−	1.46885i	−0.979903	−	1.03864i	0.0193427	−	0.999813i	$-0.493843\pi$
$3$		0			0
$3$		0			0
$4$	−0.120822	+	2.07444i	−0.0604111	+	1.03722i
$5$	−2.74943	+	0.321362i	−1.22958	+	0.143717i	−0.705971	−	0.708241i	$-0.749489\pi$
$5$	−2.74943	+	0.321362i	−1.22958	+	0.143717i	−0.523610	+	0.851958i	$0.675415\pi$
$6$		0			0
$7$	−0.546257	−	0.274341i	−0.206466	−	0.103691i	0.342562	−	0.939495i	$-0.388705\pi$
$7$	−0.546257	−	0.274341i	−0.206466	−	0.103691i	−0.549027	+	0.835804i	$0.685002\pi$
$8$	0.120591	−	0.101188i	0.0426353	−	0.0357753i
$9$		0			0
$10$	4.28217	+	3.59317i	1.35414	+	1.13626i
$11$	1.48325	+	3.43857i	0.447218	+	1.03677i	0.981500	+	0.191462i	$0.0613228\pi$
$11$	1.48325	+	3.43857i	0.447218	+	1.03677i	−0.534282	+	0.845306i	$0.679418\pi$
$12$		0			0
$13$	3.32773	+	0.788687i	0.922947	+	0.218742i	0.664504	−	0.747284i	$-0.268643\pi$
$13$	3.32773	+	0.788687i	0.922947	+	0.218742i	0.258442	+	0.966027i	$0.416791\pi$
$14$	0.354033	+	1.18255i	0.0946193	+	0.316050i
$15$		0			0
$16$	3.81206	+	0.445566i	0.953016	+	0.111392i
$17$	1.31516	−	7.45862i	0.318972	−	1.80898i	−0.230058	−	0.973177i	$-0.573891\pi$
$17$	1.31516	−	7.45862i	0.318972	−	1.80898i	0.549030	−	0.835803i	$-0.314997\pi$
$18$		0			0
$19$	0.132568	+	0.751830i	0.0304132	+	0.172482i	0.996231	−	0.0867403i	$-0.0276450\pi$
$19$	0.132568	+	0.751830i	0.0304132	+	0.172482i	−0.965818	+	0.259222i	$0.916534\pi$
$20$	−0.334454	−	5.74235i	−0.0747861	−	1.28403i
$21$		0			0
$22$	2.99528	−	6.94383i	0.638595	−	1.48043i
$23$	−1.94270	+	0.975661i	−0.405081	+	0.203439i	−0.639660	−	0.768658i	$-0.720925\pi$
$23$	−1.94270	+	0.975661i	−0.405081	+	0.203439i	0.234579	+	0.972097i	$0.424629\pi$
$24$		0			0
$25$	2.59085	−	0.614044i	0.518171	−	0.122809i
$26$	−3.45308	−	5.98091i	−0.677205	−	1.17295i
$27$		0			0
$28$	0.635103	−	1.10003i	0.120023	−	0.207886i
$29$	−1.30287	+	4.35188i	−0.241937	+	0.808124i	0.747639	+	0.664106i	$0.231188\pi$
$29$	−1.30287	+	4.35188i	−0.241937	+	0.808124i	−0.989575	+	0.144018i	$0.953998\pi$
$30$		0			0
$31$	−6.83895	−	4.49805i	−1.22831	−	0.807873i	−0.241603	−	0.970375i	$-0.577673\pi$
$31$	−6.83895	−	4.49805i	−1.22831	−	0.807873i	−0.986708	+	0.162502i	$0.948044\pi$
$32$	−4.81627	−	6.46937i	−0.851404	−	1.14363i
$33$		0			0
$34$	−12.7782	+	8.40432i	−2.19143	+	1.44133i
$35$	1.59006	+	0.578734i	0.268769	+	0.0978239i
$36$		0			0
$37$	3.96908	−	1.44463i	0.652513	−	0.237495i	0.00551256	−	0.999985i	$-0.498245\pi$
$37$	3.96908	−	1.44463i	0.652513	−	0.237495i	0.647001	+	0.762489i	$0.276023\pi$
$38$	0.920617	−	1.23660i	0.149344	−	0.200604i
$39$		0			0
$40$	−0.299038	+	0.316962i	−0.0472821	+	0.0501161i
$41$	6.20503	−	6.57695i	0.969063	−	1.02715i	−0.0305559	−	0.999533i	$-0.509728\pi$
$41$	6.20503	−	6.57695i	0.969063	−	1.02715i	0.999619	−	0.0276134i	$-0.00879075\pi$
$42$		0			0
$43$	1.04785	−	1.40751i	0.159796	−	0.214644i	−0.715013	−	0.699111i	$-0.753579\pi$
$43$	1.04785	−	1.40751i	0.159796	−	0.214644i	0.874809	+	0.484468i	$0.160987\pi$
$44$	−7.31231	+	2.66146i	−1.10237	+	0.401231i
$45$		0			0
$46$	4.12528	+	1.50148i	0.608240	+	0.221381i
$47$	9.82847	−	6.46428i	1.43363	−	0.942913i	0.434522	−	0.900661i	$-0.356917\pi$
$47$	9.82847	−	6.46428i	1.43363	−	0.942913i	0.999107	−	0.0422515i	$-0.0134531\pi$
$48$		0			0
$49$	−3.95698	−	5.31514i	−0.565282	−	0.759306i
$50$	−4.49233	−	2.95465i	−0.635311	−	0.417851i
$51$		0			0
$52$	−2.03815	+	6.80788i	−0.282640	+	0.944084i
$53$	2.80062	−	4.85082i	0.384695	−	0.666312i	−0.607032	−	0.794678i	$-0.707640\pi$
$53$	2.80062	−	4.85082i	0.384695	−	0.666312i	0.991727	+	0.128366i	$0.0409732\pi$
$54$		0			0
$55$	−5.18313	−	8.97744i	−0.698893	−	1.21052i
$56$	−0.0936337	+	0.0221916i	−0.0125123	+	0.00296548i
$57$		0			0
$58$	8.19779	−	4.11708i	1.07642	−	0.540599i
$59$	−0.599347	+	1.38944i	−0.0780283	+	0.180890i	−0.952765	−	0.303709i	$-0.901775\pi$
$59$	−0.599347	+	1.38944i	−0.0780283	+	0.180890i	0.874737	+	0.484599i	$0.161034\pi$
$60$		0			0
$61$	−0.175804	−	3.01844i	−0.0225094	−	0.386471i	−0.990683	−	0.136190i	$-0.956514\pi$
$61$	−0.175804	−	3.01844i	−0.0225094	−	0.386471i	0.968173	−	0.250281i	$-0.0805229\pi$
$62$	2.87039	+	16.2788i	0.364540	+	2.06741i
$63$		0			0
$64$	−1.49529	+	8.48019i	−0.186911	+	1.06002i
$65$	−9.40281	−	1.09903i	−1.16628	−	0.136318i
$66$		0			0
$67$	2.19466	+	7.33068i	0.268121	+	0.895585i	0.980952	+	0.194250i	$0.0622272\pi$
$67$	2.19466	+	7.33068i	0.268121	+	0.895585i	−0.712831	+	0.701335i	$0.752588\pi$
$68$	15.3135	+	3.62938i	1.85704	+	0.440126i
$69$		0			0
$70$	−1.35341	−	3.13757i	−0.161764	−	0.375011i
$71$	5.19850	+	4.36206i	0.616948	+	0.517681i	0.896843	−	0.442350i	$-0.145855\pi$
$71$	5.19850	+	4.36206i	0.616948	+	0.517681i	−0.279895	+	0.960031i	$0.590299\pi$
$72$		0			0
$73$	0.438511	−	0.367955i	0.0513238	−	0.0430658i	−0.616765	−	0.787147i	$-0.711557\pi$
$73$	0.438511	−	0.367955i	0.0513238	−	0.0430658i	0.668089	+	0.744082i	$0.267113\pi$
$74$	−7.62227	−	3.82805i	−0.886071	−	0.445002i
$75$		0			0
$76$	−1.57564	+	0.184166i	−0.180739	+	0.0211253i
$77$	0.133101	−	2.28526i	0.0151683	−	0.260430i
$78$		0			0
$79$	−6.32380	−	6.70284i	−0.711483	−	0.754128i	0.266267	−	0.963899i	$-0.414210\pi$
$79$	−6.32380	−	6.70284i	−0.711483	−	0.754128i	−0.977751	+	0.209771i	$0.932728\pi$
$80$	−10.6242			−1.18782
$81$		0			0
$82$	−18.2595			−2.01642
$83$	−4.24676	−	4.50130i	−0.466143	−	0.494082i	0.451065	−	0.892491i	$-0.351044\pi$
$83$	−4.24676	−	4.50130i	−0.466143	−	0.494082i	−0.917208	+	0.398409i	$0.869563\pi$
$84$		0			0
$85$	−1.21901	+	20.9296i	−0.132220	+	2.27013i
$86$	−3.51954	+	0.411375i	−0.379522	+	0.0443597i
$87$		0			0
$88$	0.526809	+	0.264573i	0.0561580	+	0.0282036i
$89$	3.52742	−	2.95986i	0.373906	−	0.313744i	−0.436399	−	0.899753i	$-0.643746\pi$
$89$	3.52742	−	2.95986i	0.373906	−	0.313744i	0.810304	+	0.586009i	$0.199302\pi$
$90$		0			0
$91$	−1.60143	−	1.34376i	−0.167875	−	0.140864i
$92$	−1.78923	−	4.14790i	−0.186540	−	0.432448i
$93$		0			0
$94$	−23.1153	−	5.47843i	−2.38416	−	0.565057i
$95$	−0.606095	−	2.02450i	−0.0621841	−	0.207709i
$96$		0			0
$97$	10.4458	+	1.22093i	1.06061	+	0.123967i	0.628464	−	0.777839i	$-0.283684\pi$
$97$	10.4458	+	1.22093i	1.06061	+	0.123967i	0.432142	+	0.901806i	$0.357758\pi$
$98$	−2.32362	+	13.1779i	−0.234721	+	1.33117i
$99$		0			0
$100$	0.960763	+	5.44876i	0.0960763	+	0.544876i
$101$	0.142370	+	2.44440i	0.0141663	+	0.243227i	0.997956	+	0.0639015i	$0.0203544\pi$
$101$	0.142370	+	2.44440i	0.0141663	+	0.243227i	−0.983790	+	0.179325i	$0.942609\pi$
$102$		0			0
$103$	6.75628	−	15.6628i	0.665716	−	1.54330i	−0.164811	−	0.986325i	$-0.552701\pi$
$103$	6.75628	−	15.6628i	0.665716	−	1.54330i	0.830527	−	0.556978i	$-0.188039\pi$
$104$	0.481100	−	0.241617i	0.0471757	−	0.0236925i
$105$		0			0
$106$	−11.0062	+	2.60853i	−1.06902	+	0.253362i
$107$	−0.402056	−	0.696381i	−0.0388682	−	0.0673217i	0.845937	−	0.533283i	$-0.179042\pi$
$107$	−0.402056	−	0.696381i	−0.0388682	−	0.0673217i	−0.884805	+	0.465961i	$0.845709\pi$
$108$		0			0
$109$	2.11135	−	3.65696i	0.202230	−	0.350273i	−0.747016	−	0.664806i	$-0.768514\pi$
$109$	2.11135	−	3.65696i	0.202230	−	0.350273i	0.949247	+	0.314532i	$0.101848\pi$
$110$	−6.00381	+	20.0541i	−0.572441	+	1.91209i
$111$		0			0
$112$	−1.96013	−	1.28920i	−0.185215	−	0.121818i
$113$	7.37084	+	9.90076i	0.693390	+	0.931385i	0.999789	−	0.0205182i	$-0.00653160\pi$
$113$	7.37084	+	9.90076i	0.693390	+	0.931385i	−0.306399	+	0.951903i	$0.599124\pi$
$114$		0			0
$115$	5.02778	−	3.30682i	0.468842	−	0.308363i
$116$	−8.87030	−	3.22852i	−0.823586	−	0.299761i
$117$		0			0
$118$	2.87146	−	1.04513i	0.264339	−	0.0962116i
$119$	−2.76462	+	3.71352i	−0.253432	+	0.340418i
$120$		0			0
$121$	−2.07506	+	2.19944i	−0.188642	+	0.199949i
$122$	−4.19002	+	4.44116i	−0.379346	+	0.402083i
$123$		0			0
$124$	10.1572	−	13.6435i	0.912145	−	1.22522i
$125$	6.07999	−	2.21294i	0.543811	−	0.197931i
$126$		0			0
$127$	−9.37360	−	3.41171i	−0.831772	−	0.302740i	−0.109186	−	0.994021i	$-0.534824\pi$
$127$	−9.37360	−	3.41171i	−0.831772	−	0.302740i	−0.722586	+	0.691281i	$0.757047\pi$
$128$	1.05138	−	0.691505i	0.0929300	−	0.0611210i
$129$		0			0
$130$	11.4160	+	15.3344i	1.00125	+	1.34491i
$131$	4.58946	+	3.01853i	0.400983	+	0.263731i	0.733944	−	0.679210i	$-0.237677\pi$
$131$	4.58946	+	3.01853i	0.400983	+	0.263731i	−0.332961	+	0.942941i	$0.608048\pi$
$132$		0			0
$133$	0.133841	−	0.447061i	0.0116055	−	0.0387651i
$134$	7.72636	−	13.3824i	0.667456	−	1.15607i
$135$		0			0
$136$	−0.596125	−	1.03252i	−0.0511173	−	0.0885378i
$137$	14.8200	−	3.51241i	1.26616	−	0.300086i	0.457949	−	0.888978i	$-0.348584\pi$
$137$	14.8200	−	3.51241i	1.26616	−	0.300086i	0.808211	+	0.588893i	$0.200436\pi$
$138$		0			0
$139$	14.3127	−	7.18809i	1.21398	−	0.609686i	0.277612	−	0.960693i	$-0.410457\pi$
$139$	14.3127	−	7.18809i	1.21398	−	0.609686i	0.936373	+	0.351008i	$0.114161\pi$
$140$	−1.39266	+	3.22855i	−0.117701	+	0.272863i
$141$		0			0
$142$	−0.796812	−	13.6807i	−0.0668670	−	1.14806i
$143$	2.22392	+	12.6125i	0.185973	+	1.05471i
$144$		0			0
$145$	2.18361	−	12.3839i	0.181339	−	1.02842i
$146$	−1.14816	−	0.134200i	−0.0950222	−	0.0111065i
$147$		0			0
$148$	2.51724	+	8.40816i	0.206916	+	0.691147i
$149$	−8.60207	−	2.03873i	−0.704709	−	0.167019i	−0.137390	−	0.990517i	$-0.543871\pi$
$149$	−8.60207	−	2.03873i	−0.704709	−	0.167019i	−0.567319	+	0.823498i	$0.692019\pi$
$150$		0			0
$151$	0.391266	+	0.907056i	0.0318408	+	0.0738152i	0.933394	−	0.358852i	$-0.116832\pi$
$151$	0.391266	+	0.907056i	0.0318408	+	0.0738152i	−0.901554	+	0.432667i	$0.857572\pi$
$152$	0.0920625	+	0.0772496i	0.00746726	+	0.00626577i
$153$		0			0
$154$	−3.54117	+	2.97139i	−0.285355	+	0.239442i
$155$	20.2487	+	10.1693i	1.62641	+	0.816816i
$156$		0			0
$157$	−18.0755	+	2.11272i	−1.44258	+	0.168613i	−0.801102	−	0.598528i	$-0.795753\pi$
$157$	−18.0755	+	2.11272i	−1.44258	+	0.168613i	−0.641478	+	0.767141i	$0.721679\pi$
$158$	−1.08202	+	18.5775i	−0.0860805	+	1.47795i
$159$		0			0
$160$	15.3210	+	16.2393i	1.21123	+	1.28383i
$161$	1.32888			0.104730
$162$		0			0
$163$	17.1469			1.34305			0.671524	−	0.740983i	$-0.265640\pi$
$163$	17.1469			1.34305			0.671524	+	0.740983i	$0.265640\pi$
$164$	12.8938	+	13.6666i	1.00683	+	1.06718i
$165$		0			0
$166$	−0.726629	+	12.4757i	−0.0563974	+	0.968306i
$167$	5.86126	−	0.685083i	0.453558	−	0.0530133i	0.113753	−	0.993509i	$-0.463713\pi$
$167$	5.86126	−	0.685083i	0.453558	−	0.0530133i	0.339805	+	0.940496i	$0.389639\pi$
$168$		0			0
$169$	−1.16546	−	0.585314i	−0.0896505	−	0.0450242i
$170$	32.4318	−	27.2135i	2.48740	−	2.08718i
$171$		0			0
$172$	2.79319	+	2.34377i	0.212979	+	0.178711i
$173$	−3.56184	−	8.25726i	−0.270801	−	0.627788i	0.727496	−	0.686111i	$-0.240684\pi$
$173$	−3.56184	−	8.25726i	−0.270801	−	0.627788i	−0.998298	+	0.0583234i	$0.981425\pi$
$174$		0			0
$175$	−1.58373	−	0.375351i	−0.119719	−	0.0283739i
$176$	4.12215	+	13.7689i	0.310719	+	1.03787i
$177$		0			0
$178$	−9.23587	−	1.07952i	−0.692258	−	0.0809134i
$179$	−0.223820	+	1.26935i	−0.0167291	+	0.0948754i	−0.992029	−	0.126009i	$-0.959783\pi$
$179$	−0.223820	+	1.26935i	−0.0167291	+	0.0948754i	0.975300	+	0.220884i	$0.0708943\pi$
$180$		0			0
$181$	0.645386	+	3.66017i	0.0479712	+	0.272058i	0.999353	−	0.0359546i	$-0.0114472\pi$
$181$	0.645386	+	3.66017i	0.0479712	+	0.272058i	−0.951382	+	0.308013i	$0.900336\pi$
$182$	0.245463	+	4.21444i	0.0181949	+	0.312395i
$183$		0			0
$184$	−0.135547	+	0.314234i	−0.00999267	+	0.0231656i
$185$	−10.4485	+	5.24741i	−0.768186	+	0.385797i
$186$		0			0
$187$	27.5977	−	6.54077i	2.01814	−	0.478309i
$188$	12.2223	+	21.1696i	0.891400	+	1.54395i
$189$		0			0
$190$	−2.13377	+	3.69580i	−0.154800	+	0.268122i
$191$	2.09081	−	6.98378i	0.151285	−	0.505328i	−0.848427	−	0.529313i	$-0.822450\pi$
$191$	2.09081	−	6.98378i	0.151285	−	0.505328i	0.999712	+	0.0239841i	$0.00763509\pi$
$192$		0			0
$193$	8.04337	+	5.29021i	0.578974	+	0.380797i	0.804956	−	0.593334i	$-0.202189\pi$
$193$	8.04337	+	5.29021i	0.578974	+	0.380797i	−0.225982	+	0.974131i	$0.572559\pi$
$194$	−12.6823	−	17.0352i	−0.910534	−	1.22306i
$195$		0			0
$196$	11.5040	−	7.56632i	0.821716	−	0.540451i
$197$	−4.63898	−	1.68845i	−0.330513	−	0.120297i	0.171433	−	0.985196i	$-0.445160\pi$
$197$	−4.63898	−	1.68845i	−0.330513	−	0.120297i	−0.501946	+	0.864899i	$0.667383\pi$
$198$		0			0
$199$	−2.36550	+	0.860973i	−0.167686	+	0.0610327i	−0.424499	−	0.905428i	$-0.639550\pi$
$199$	−2.36550	+	0.860973i	−0.167686	+	0.0610327i	0.256813	+	0.966461i	$0.417328\pi$
$200$	0.250300	−	0.336211i	0.0176989	−	0.0237737i
$201$		0			0
$202$	3.39317	−	3.59655i	0.238743	−	0.253052i
$203$	1.90560	−	2.01982i	0.133747	−	0.141763i
$204$		0			0
$205$	−14.9467	+	20.0769i	−1.04392	+	1.40223i
$206$	−32.3692	+	11.7814i	−2.25527	+	0.820851i
$207$		0			0
$208$	12.3341	+	4.48925i	0.855217	+	0.311273i
$209$	−2.38859	+	1.57100i	−0.165222	+	0.108668i
$210$		0			0
$211$	4.17283	+	5.60508i	0.287269	+	0.385870i	0.922209	−	0.386692i	$-0.126382\pi$
$211$	4.17283	+	5.60508i	0.287269	+	0.385870i	−0.634939	+	0.772562i	$0.718975\pi$
$212$	9.72436	+	6.39581i	0.667872	+	0.439266i
$213$		0			0
$214$	−0.465716	+	1.55560i	−0.0318357	+	0.106339i
$215$	−2.42868	+	4.20659i	−0.165634	+	0.286887i
$216$		0			0
$217$	2.50183	+	4.33330i	0.169835	+	0.294163i
$218$	−8.29743	+	1.96653i	−0.561973	+	0.133190i
$219$		0			0
$220$	19.2494	−	9.66740i	1.29779	−	0.651776i
$221$	10.2590	−	23.7830i	0.690095	−	1.59982i
$222$		0			0
$223$	1.04650	+	17.9678i	0.0700790	+	1.20321i	0.831714	+	0.555204i	$0.187360\pi$
$223$	1.04650	+	17.9678i	0.0700790	+	1.20321i	−0.761635	+	0.648006i	$0.775603\pi$
$224$	0.856110	+	4.85524i	0.0572012	+	0.324404i
$225$		0			0
$226$	4.32831	−	24.5471i	0.287915	−	1.63285i
$227$	−0.609362	−	0.0712243i	−0.0404448	−	0.00472732i	0.0958464	−	0.995396i	$-0.469444\pi$
$227$	−0.609362	−	0.0712243i	−0.0404448	−	0.00472732i	−0.136291	+	0.990669i	$0.543518\pi$
$228$		0			0
$229$	1.43265	+	4.78538i	0.0946720	+	0.316227i	0.992187	−	0.124757i	$-0.0398150\pi$
$229$	1.43265	+	4.78538i	0.0946720	+	0.316227i	−0.897515	+	0.440983i	$0.854630\pi$
$230$	−11.8247	−	2.80250i	−0.779697	−	0.184792i
$231$		0			0
$232$	0.283243	+	0.656632i	0.0185958	+	0.0431100i
$233$	−10.0792	−	8.45747i	−0.660311	−	0.554067i	0.249869	−	0.968280i	$-0.419613\pi$
$233$	−10.0792	−	8.45747i	−0.660311	−	0.554067i	−0.910180	+	0.414213i	$0.864057\pi$
$234$		0			0
$235$	−24.9453	+	20.9316i	−1.62725	+	1.36543i
$236$	−2.80990	−	1.41118i	−0.182909	−	0.0918603i
$237$		0			0
$238$	9.28581	−	1.08536i	0.601910	−	0.0703531i
$239$	−0.529012	+	9.08278i	−0.0342189	+	0.587517i	0.937000	+	0.349329i	$0.113590\pi$
$239$	−0.529012	+	9.08278i	−0.0342189	+	0.587517i	−0.971219	+	0.238188i	$0.923447\pi$
$240$		0			0
$241$	9.77902	+	10.3652i	0.629922	+	0.667679i	0.961199	−	0.275855i	$-0.0889609\pi$
$241$	9.77902	+	10.3652i	0.629922	+	0.667679i	−0.331277	+	0.943534i	$0.607479\pi$
$242$	6.10626			0.392526
$243$		0			0
$244$	6.28280			0.402215
$245$	12.5875	+	13.3420i	0.804186	+	0.852387i
$246$		0			0
$247$	−0.151808	+	2.60644i	−0.00965931	+	0.165844i
$248$	−1.27986	+	0.149595i	−0.0812714	+	0.00949926i
$249$		0			0
$250$	−11.6761	−	5.86395i	−0.738461	−	0.370869i
$251$	−6.58379	+	5.52445i	−0.415565	+	0.348700i	−0.826473	−	0.562976i	$-0.809656\pi$
$251$	−6.58379	+	5.52445i	−0.415565	+	0.348700i	0.410908	+	0.911677i	$0.365212\pi$
$252$		0			0
$253$	−6.23640	−	5.23296i	−0.392079	−	0.328993i
$254$	7.97856	+	18.4964i	0.500619	+	1.16057i
$255$		0			0
$256$	14.2851	+	3.38562i	0.892817	+	0.211602i
$257$	−6.36608	−	21.2642i	−0.397105	−	1.32642i	−0.889851	−	0.456251i	$-0.849192\pi$
$257$	−6.36608	−	21.2642i	−0.397105	−	1.32642i	0.492746	−	0.870173i	$-0.335993\pi$
$258$		0			0
$259$	−2.56446	−	0.299743i	−0.159348	−	0.0186251i
$260$	3.41594	−	19.3728i	0.211848	−	1.20145i
$261$		0			0
$262$	−1.92625	−	10.9243i	−0.119004	−	0.674906i
$263$	0.305988	+	5.25362i	0.0188681	+	0.323952i	0.994514	+	0.104602i	$0.0333568\pi$
$263$	0.305988	+	5.25362i	0.0188681	+	0.323952i	−0.975646	+	0.219350i	$0.929606\pi$
$264$		0			0
$265$	−6.14124	+	14.2370i	−0.377254	+	0.874572i
$266$	−0.842145	+	0.422941i	−0.0516352	+	0.0259322i
$267$		0			0
$268$	−15.4722	+	3.66698i	−0.945116	+	0.223997i
$269$	3.11423	+	5.39401i	0.189878	+	0.328878i	0.945209	−	0.326465i	$-0.105857\pi$
$269$	3.11423	+	5.39401i	0.189878	+	0.328878i	−0.755331	+	0.655343i	$0.772524\pi$
$270$		0			0
$271$	−3.65935	+	6.33818i	−0.222290	+	0.385017i	−0.955503	−	0.294982i	$-0.904686\pi$
$271$	−3.65935	+	6.33818i	−0.222290	+	0.385017i	0.733213	+	0.679999i	$0.238020\pi$
$272$	8.33676	−	27.8467i	0.505490	−	1.68846i
$273$		0			0
$274$	−25.6967	−	16.9010i	−1.55239	−	1.02103i
$275$	5.95433	+	7.99805i	0.359060	+	0.482301i
$276$		0			0
$277$	15.5663	−	10.2381i	0.935287	−	0.615148i	0.0122776	−	0.999925i	$-0.496092\pi$
$277$	15.5663	−	10.2381i	0.935287	−	0.615148i	0.923010	+	0.384776i	$0.125721\pi$
$278$	−30.3926	−	11.0620i	−1.82283	−	0.663456i
$279$		0			0
$280$	0.250307	−	0.0911045i	0.0149587	−	0.00544453i
$281$	0.610261	−	0.819722i	0.0364051	−	0.0489005i	−0.783548	−	0.621331i	$-0.786592\pi$
$281$	0.610261	−	0.819722i	0.0364051	−	0.0489005i	0.819953	+	0.572431i	$0.193999\pi$
$282$		0			0
$283$	7.52347	−	7.97442i	0.447224	−	0.474030i	−0.464063	−	0.885802i	$-0.653609\pi$
$283$	7.52347	−	7.97442i	0.447224	−	0.474030i	0.911287	+	0.411773i	$0.135090\pi$
$284$	−9.67691	+	10.2569i	−0.574219	+	0.608637i
$285$		0			0
$286$	15.4440	−	20.7449i	0.913222	−	1.22667i
$287$	−5.19387	+	1.89041i	−0.306584	+	0.111588i
$288$		0			0
$289$	−37.9265	−	13.8041i	−2.23097	−	0.812008i
$290$	−21.2161	+	13.9541i	−1.24585	+	0.819412i
$291$		0			0
$292$	0.710317	+	0.954122i	0.0415682	+	0.0558357i
$293$	20.2853	+	13.3418i	1.18508	+	0.779438i	0.979939	−	0.199295i	$-0.0638654\pi$
$293$	20.2853	+	13.3418i	1.18508	+	0.779438i	0.205138	+	0.978733i	$0.434236\pi$
$294$		0			0
$295$	1.20135	−	4.01278i	0.0699451	−	0.233633i
$296$	0.332457	−	0.575832i	0.0193237	−	0.0334696i
$297$		0			0
$298$	8.92609	+	15.4604i	0.517075	+	0.895599i
$299$	−7.23428	+	1.71456i	−0.418369	+	0.0991553i
$300$		0			0
$301$	−0.958536	+	0.481395i	−0.0552491	+	0.0277471i
$302$	0.790120	−	1.83170i	0.0454663	−	0.105403i
$303$		0			0
$304$	0.170367	+	2.92509i	0.00977123	+	0.167765i
$305$	1.45337	+	8.24247i	0.0832198	+	0.471963i
$306$		0			0
$307$	−4.31169	+	24.4528i	−0.246081	+	1.39560i	0.571887	+	0.820333i	$0.306212\pi$
$307$	−4.31169	+	24.4528i	−0.246081	+	1.39560i	−0.817968	+	0.575264i	$0.804899\pi$
$308$	4.72455	+	0.552221i	0.269206	+	0.0314657i
$309$		0			0
$310$	−13.1233	−	43.8349i	−0.745354	−	2.48966i
$311$	−1.80082	−	0.426803i	−0.102115	−	0.0242018i	0.179241	−	0.983805i	$-0.442636\pi$
$311$	−1.80082	−	0.426803i	−0.102115	−	0.0242018i	−0.281356	+	0.959604i	$0.590784\pi$
$312$		0			0
$313$	−2.75336	−	6.38301i	−0.155629	−	0.360789i	0.822507	−	0.568755i	$-0.192575\pi$
$313$	−2.75336	−	6.38301i	−0.155629	−	0.360789i	−0.978136	+	0.207966i	$0.933316\pi$
$314$	28.1521	+	23.6225i	1.58872	+	1.33309i
$315$		0			0
$316$	14.6687	−	12.3085i	0.825178	−	0.692406i
$317$	−23.2678	−	11.6855i	−1.30685	−	0.656324i	−0.347270	−	0.937765i	$-0.612891\pi$
$317$	−23.2678	−	11.6855i	−1.30685	−	0.656324i	−0.959578	+	0.281441i	$0.909188\pi$
$318$		0			0
$319$	−16.8967	+	1.97495i	−0.946036	+	0.110576i
$320$	1.38597	−	23.7962i	0.0774781	−	1.33025i
$321$		0			0
$322$	−1.84155	−	1.95193i	−0.102626	−	0.108777i
$323$	5.78196			0.321717
$324$		0			0
$325$	9.10595			0.505107
$326$	−23.7620	−	25.1863i	−1.31606	−	1.39494i
$327$		0			0
$328$	0.0827635	−	1.42099i	0.00456985	−	0.0784613i
$329$	−7.14229	+	0.834814i	−0.393767	+	0.0460248i
$330$		0			0
$331$	−23.2661	−	11.6847i	−1.27882	−	0.642249i	−0.325884	−	0.945410i	$-0.605662\pi$
$331$	−23.2661	−	11.6847i	−1.27882	−	0.642249i	−0.952939	+	0.303161i	$0.901958\pi$
$332$	9.85078	−	8.26579i	0.540632	−	0.453644i
$333$		0			0
$334$	−9.12878	−	7.65996i	−0.499505	−	0.419134i
$335$	−8.38987	−	19.4499i	−0.458387	−	1.06266i
$336$		0			0
$337$	−14.6259	−	3.46641i	−0.796726	−	0.188828i	−0.187959	−	0.982177i	$-0.560187\pi$
$337$	−14.6259	−	3.46641i	−0.796726	−	0.188828i	−0.608767	+	0.793349i	$0.708335\pi$
$338$	0.755339	+	2.52301i	0.0410850	+	0.137234i
$339$		0			0
$340$	−43.2698	−	5.05752i	−2.34663	−	0.274282i
$341$	5.32295	−	30.1880i	0.288254	−	1.63477i
$342$		0			0
$343$	1.44640	+	8.20293i	0.0780981	+	0.442917i
$344$	−0.0160614	−	0.275763i	−0.000865972	−	0.0148682i
$345$		0			0
$346$	−7.19275	+	16.6747i	−0.386685	+	0.896436i
$347$	22.7180	−	11.4094i	1.21957	−	0.612490i	0.281706	−	0.959501i	$-0.409100\pi$
$347$	22.7180	−	11.4094i	1.21957	−	0.612490i	0.937861	+	0.347011i	$0.112803\pi$
$348$		0			0
$349$	−28.4767	+	6.74910i	−1.52432	+	0.361271i	−0.905530	−	0.424283i	$-0.860526\pi$
$349$	−28.4767	+	6.74910i	−1.52432	+	0.361271i	−0.618793	+	0.785554i	$0.712378\pi$
$350$	1.64339	+	2.84643i	0.0878427	+	0.152148i
$351$		0			0
$352$	15.1016	−	26.1568i	0.804920	−	1.39416i
$353$	8.22886	−	27.4863i	0.437978	−	1.46295i	−0.399629	−	0.916677i	$-0.630861\pi$
$353$	8.22886	−	27.4863i	0.437978	−	1.46295i	0.837608	−	0.546272i	$-0.183954\pi$
$354$		0			0
$355$	−15.6947	−	10.3226i	−0.832988	−	0.547865i
$356$	5.71385	+	7.67504i	0.302834	+	0.406776i
$357$		0			0
$358$	2.17465	−	1.43029i	0.114934	−	0.0755932i
$359$	−19.5984	−	7.13322i	−1.03436	−	0.376477i	−0.231622	−	0.972806i	$-0.574403\pi$
$359$	−19.5984	−	7.13322i	−1.03436	−	0.376477i	−0.802740	+	0.596329i	$0.796625\pi$
$360$		0			0
$361$	17.3065	−	6.29905i	0.910868	−	0.331529i
$362$	4.48188	−	6.02021i	0.235563	−	0.316415i
$363$		0			0
$364$	2.98103	−	3.15971i	0.156249	−	0.165614i
$365$	−1.08741	+	1.15259i	−0.0569175	+	0.0603291i
$366$		0			0
$367$	−20.6418	+	27.7268i	−1.07750	+	1.44733i	−0.192753	+	0.981247i	$0.561742\pi$
$367$	−20.6418	+	27.7268i	−1.07750	+	1.44733i	−0.884742	+	0.466080i	$0.845666\pi$
$368$	−7.84042	+	2.85368i	−0.408710	+	0.148758i
$369$		0			0
$370$	22.1871	+	8.07544i	1.15345	+	0.419822i
$371$	−2.86064	+	1.88147i	−0.148517	+	0.0976812i
$372$		0			0
$373$	−5.59504	−	7.51544i	−0.289700	−	0.389135i	0.633318	−	0.773892i	$-0.281693\pi$
$373$	−5.59504	−	7.51544i	−0.289700	−	0.389135i	−0.923018	+	0.384757i	$0.874285\pi$
$374$	−47.8521	−	31.4728i	−2.47437	−	1.62742i
$375$		0			0
$376$	0.531117	−	1.77406i	0.0273903	−	0.0914899i
$377$	−7.76787	+	13.4543i	−0.400065	+	0.692934i
$378$		0			0
$379$	0.963771	+	1.66930i	0.0495056	+	0.0857462i	0.889716	−	0.456514i	$-0.150902\pi$
$379$	0.963771	+	1.66930i	0.0495056	+	0.0857462i	−0.840211	+	0.542260i	$0.817569\pi$
$380$	4.27293	−	1.01270i	0.219197	−	0.0519506i
$381$		0			0
$382$	−13.1556	+	6.60698i	−0.673098	+	0.338042i
$383$	−7.72041	+	17.8979i	−0.394494	+	0.914541i	0.599010	+	0.800742i	$0.295561\pi$
$383$	−7.72041	+	17.8979i	−0.394494	+	0.914541i	−0.993504	+	0.113799i	$0.963698\pi$
$384$		0			0
$385$	0.368444	+	6.32594i	0.0187776	+	0.322400i
$386$	−3.37590	−	19.1457i	−0.171829	−	0.974489i
$387$		0			0
$388$	−3.79483	+	21.5216i	−0.192653	+	1.09259i
$389$	−9.07811	−	1.06108i	−0.460279	−	0.0537989i	−0.117206	−	0.993108i	$-0.537394\pi$
$389$	−9.07811	−	1.06108i	−0.460279	−	0.0537989i	−0.343073	+	0.939309i	$0.611468\pi$
$390$		0			0
$391$	4.72213	+	15.7730i	0.238808	+	0.797675i
$392$	−1.01500	−	0.240560i	−0.0512654	−	0.0121501i
$393$		0			0
$394$	3.94857	+	9.15382i	0.198926	+	0.461163i
$395$	19.5409	+	16.3967i	0.983208	+	0.825009i
$396$		0			0
$397$	25.5466	−	21.4361i	1.28215	−	1.07585i	0.289202	−	0.957268i	$-0.406610\pi$
$397$	25.5466	−	21.4361i	1.28215	−	1.07585i	0.992944	−	0.118581i	$-0.0378344\pi$
$398$	4.54274	+	2.28145i	0.227707	+	0.114359i
$399$		0			0
$400$	10.1501	−	1.18638i	0.507505	−	0.0593188i
$401$	−0.206340	+	3.54271i	−0.0103041	+	0.176915i	0.989229	+	0.146373i	$0.0467601\pi$
$401$	−0.206340	+	3.54271i	−0.0103041	+	0.176915i	−0.999534	+	0.0305412i	$0.990277\pi$
$402$		0			0
$403$	−19.2106	−	20.3621i	−0.956950	−	1.01431i
$404$	−5.08795			−0.253135
$405$		0			0
$406$	−5.60758			−0.278300
$407$	10.8546	+	11.5052i	0.538043	+	0.570293i
$408$		0			0
$409$	1.86266	−	31.9807i	0.0921027	−	1.58134i	−0.563422	−	0.826169i	$-0.690516\pi$
$409$	1.86266	−	31.9807i	0.0921027	−	1.58134i	0.655525	−	0.755173i	$-0.272447\pi$
$410$	50.2031	−	5.86790i	2.47935	−	0.289795i
$411$		0			0
$412$	31.6752	+	15.9079i	1.56053	+	0.783726i
$413$	0.708579	−	0.594568i	0.0348669	−	0.0292568i
$414$		0			0
$415$	13.1227	+	11.0113i	0.644168	+	0.540522i
$416$	−10.9249	−	25.3268i	−0.535639	−	1.24175i
$417$		0			0
$418$	5.61766	+	1.33141i	0.274769	+	0.0651213i
$419$	−4.25467	−	14.2116i	−0.207854	−	0.694281i	−0.996809	−	0.0798292i	$-0.974563\pi$
$419$	−4.25467	−	14.2116i	−0.207854	−	0.694281i	0.788955	−	0.614452i	$-0.210623\pi$
$420$		0			0
$421$	15.4744	+	1.80870i	0.754176	+	0.0881505i	0.484489	−	0.874798i	$-0.339006\pi$
$421$	15.4744	+	1.80870i	0.754176	+	0.0881505i	0.269687	+	0.962948i	$0.413080\pi$
$422$	2.45037	−	13.8968i	0.119282	−	0.676484i
$423$		0			0
$424$	−0.153114	−	0.868355i	−0.00743589	−	0.0421710i
$425$	−1.17254	−	20.1317i	−0.0568766	−	0.976533i
$426$		0			0
$427$	−0.732046	+	1.69707i	−0.0354262	+	0.0821271i
$428$	1.49318	−	0.749902i	0.0721754	−	0.0362479i
$429$		0			0
$430$	9.54451	−	2.26209i	0.460277	−	0.109088i
$431$	0.648713	+	1.12360i	0.0312474	+	0.0541221i	0.881226	−	0.472695i	$-0.156719\pi$
$431$	0.648713	+	1.12360i	0.0312474	+	0.0541221i	−0.849979	+	0.526817i	$0.823385\pi$
$432$		0			0
$433$	−8.76506	+	15.1815i	−0.421222	+	0.729577i	−0.996059	−	0.0886901i	$-0.971732\pi$
$433$	−8.76506	+	15.1815i	−0.421222	+	0.729577i	0.574838	+	0.818268i	$0.305065\pi$
$434$	2.89796	−	9.67987i	0.139107	−	0.464649i
$435$		0			0
$436$	7.33105	+	4.82170i	0.351093	+	0.230918i
$437$	−0.991071	−	1.33124i	−0.0474094	−	0.0636818i
$438$		0			0
$439$	−18.1453	+	11.9344i	−0.866028	+	0.569596i	−0.902961	−	0.429722i	$-0.858612\pi$
$439$	−18.1453	+	11.9344i	−0.866028	+	0.569596i	0.0369331	+	0.999318i	$0.488241\pi$
$440$	−1.53345	−	0.558129i	−0.0731042	−	0.0266077i
$441$		0			0
$442$	−49.1506	+	17.8894i	−2.33786	+	0.850910i
$443$	−5.46021	+	7.33434i	−0.259422	+	0.348465i	−0.912683	−	0.408668i	$-0.865993\pi$
$443$	−5.46021	+	7.33434i	−0.259422	+	0.348465i	0.653260	+	0.757133i	$0.273401\pi$
$444$		0			0
$445$	−8.74720	+	9.27149i	−0.414657	+	0.439511i
$446$	24.9418	−	26.4367i	1.18103	−	1.25182i
$447$		0			0
$448$	3.14327	−	4.22215i	0.148506	−	0.199478i
$449$	11.6732	−	4.24870i	0.550893	−	0.200509i	−0.0515501	−	0.998670i	$-0.516416\pi$
$449$	11.6732	−	4.24870i	0.550893	−	0.200509i	0.602443	+	0.798162i	$0.294194\pi$
$450$		0			0
$451$	31.8189	+	11.5811i	1.49829	+	0.545335i
$452$	−21.4291	+	14.0941i	−1.00794	+	0.662932i
$453$		0			0
$454$	0.739832	+	0.993767i	0.0347220	+	0.0466398i
$455$	4.83485	+	3.17993i	0.226661	+	0.149077i
$456$		0			0
$457$	5.36176	−	17.9095i	0.250812	−	0.837772i	−0.736150	−	0.676819i	$-0.763358\pi$
$457$	5.36176	−	17.9095i	0.250812	−	0.837772i	0.986962	−	0.160953i	$-0.0514567\pi$
$458$	5.04367	−	8.73589i	0.235675	−	0.408201i
$459$		0			0
$460$	6.25233	+	10.8293i	0.291516	+	0.504921i
$461$	−39.9745	+	9.47414i	−1.86180	+	0.441255i	−0.998036	−	0.0626425i	$-0.980047\pi$
$461$	−39.9745	+	9.47414i	−1.86180	+	0.441255i	−0.863764	+	0.503897i	$0.831899\pi$
$462$		0			0
$463$	−3.69053	+	1.85346i	−0.171514	+	0.0861374i	−0.532485	−	0.846440i	$-0.678742\pi$
$463$	−3.69053	+	1.85346i	−0.171514	+	0.0861374i	0.360971	+	0.932577i	$0.382445\pi$
$464$	−6.90567	+	16.0091i	−0.320588	+	0.743205i
$465$		0			0
$466$	1.54492	+	26.5252i	0.0715669	+	1.22876i
$467$	4.38922	+	24.8925i	0.203109	+	1.15189i	0.900388	+	0.435087i	$0.143283\pi$
$467$	4.38922	+	24.8925i	0.203109	+	1.15189i	−0.697279	+	0.716799i	$0.745606\pi$
$468$		0			0
$469$	0.812254	−	4.60652i	0.0375064	−	0.212710i
$470$	65.3144	+	7.63416i	3.01273	+	0.352138i
$471$		0			0
$472$	0.0683188	+	0.228201i	0.00314463	+	0.0105038i
$473$	6.39406	+	1.51542i	0.293999	+	0.0696791i
$474$		0			0
$475$	0.805121	+	1.86648i	0.0369415	+	0.0856399i
$476$	−7.36945	−	6.18370i	−0.337778	−	0.283430i
$477$		0			0
$478$	14.0744	−	11.8098i	0.643748	−	0.540168i
$479$	18.5894	+	9.33596i	0.849372	+	0.426571i	0.819566	−	0.572985i	$-0.194215\pi$
$479$	18.5894	+	9.33596i	0.849372	+	0.426571i	0.0298064	+	0.999556i	$0.490511\pi$
$480$		0			0
$481$	14.3474	−	1.67697i	0.654185	−	0.0764633i
$482$	1.67321	−	28.7279i	0.0762127	−	1.30852i
$483$		0			0
$484$	−4.31189	−	4.57033i	−0.195995	−	0.207742i
$485$	−29.1122			−1.32192
$486$		0			0
$487$	−6.60060			−0.299102			−0.149551	−	0.988754i	$-0.547783\pi$
$487$	−6.60060			−0.299102			−0.149551	+	0.988754i	$0.547783\pi$
$488$	−0.326629	−	0.346207i	−0.0147858	−	0.0156721i
$489$		0			0
$490$	2.15375	−	36.9784i	0.0972964	−	1.67051i
$491$	−36.2982	+	4.24265i	−1.63811	+	0.191468i	−0.884727	−	0.466109i	$-0.845655\pi$
$491$	−36.2982	+	4.24265i	−1.63811	+	0.191468i	−0.753387	+	0.657577i	$0.771581\pi$
$492$		0			0
$493$	30.7455	+	15.4410i	1.38471	+	0.695427i
$494$	4.03886	−	3.38900i	0.181717	−	0.152479i
$495$		0			0
$496$	−24.0663	−	20.1941i	−1.08061	−	0.906740i
$497$	−1.64303	−	3.80897i	−0.0736998	−	0.170855i
$498$		0			0
$499$	35.4129	+	8.39301i	1.58530	+	0.375723i	0.926410	−	0.376517i	$-0.122878\pi$
$499$	35.4129	+	8.39301i	1.58530	+	0.375723i	0.658890	+	0.752239i	$0.271026\pi$
$500$	3.85600	+	12.8799i	0.172446	+	0.576008i
$501$		0			0
$502$	17.2384	+	2.01488i	0.769387	+	0.0899284i
$503$	−1.38230	+	7.83939i	−0.0616335	+	0.349541i	0.938359	+	0.345662i	$0.112346\pi$
$503$	−1.38230	+	7.83939i	−0.0616335	+	0.349541i	−0.999992	+	0.00387871i	$0.998765\pi$
$504$		0			0
$505$	−1.17697	−	6.67494i	−0.0523746	−	0.297031i
$506$	0.955899	+	16.4122i	0.0424949	+	0.729610i
$507$		0			0
$508$	8.20992	−	19.0327i	0.364256	−	0.844441i
$509$	1.49130	−	0.748960i	0.0661008	−	0.0331971i	−0.415442	−	0.909620i	$-0.636373\pi$
$509$	1.49130	−	0.748960i	0.0661008	−	0.0331971i	0.481543	+	0.876423i	$0.340077\pi$
$510$		0			0
$511$	−0.340485	+	0.0806964i	−0.0150622	+	0.00356980i
$512$	−16.0816	−	27.8541i	−0.710711	−	1.23099i
$513$		0			0
$514$	−22.4119	+	38.8186i	−0.988548	+	1.71221i
$515$	−13.5425	+	45.2350i	−0.596753	+	1.99329i
$516$		0			0
$517$	36.8060	+	24.2077i	1.61873	+	1.06465i
$518$	3.11353	+	4.18220i	0.136801	+	0.183755i
$519$		0			0
$520$	−1.24510	+	0.818917i	−0.0546014	+	0.0359119i
$521$	−32.9725	−	12.0010i	−1.44455	−	0.525773i	−0.503486	−	0.864003i	$-0.667950\pi$
$521$	−32.9725	−	12.0010i	−1.44455	−	0.525773i	−0.941063	+	0.338230i	$0.890172\pi$
$522$		0			0
$523$	11.3086	−	4.11600i	0.494491	−	0.179980i	−0.0827236	−	0.996573i	$-0.526362\pi$
$523$	11.3086	−	4.11600i	0.494491	−	0.179980i	0.577214	+	0.816593i	$0.304140\pi$
$524$	−6.81627	+	9.15584i	−0.297770	+	0.399975i
$525$		0			0
$526$	7.29276	−	7.72988i	0.317980	−	0.337039i
$527$	−42.5435	+	45.0935i	−1.85322	+	1.96430i
$528$		0			0
$529$	−10.9125	+	14.6580i	−0.474455	+	0.637304i
$530$	29.4226	−	10.7089i	1.27803	−	0.465167i
$531$		0			0
$532$	0.911231	+	0.331661i	0.0395069	+	0.0143793i
$533$	25.8358	−	16.9925i	1.11907	−	0.736026i
$534$		0			0
$535$	1.32921	+	1.78544i	0.0574669	+	0.0771915i
$536$	1.00643	+	0.661941i	0.0434712	+	0.0285915i
$537$		0			0
$538$	3.60733	−	12.0493i	0.155523	−	0.519483i
$539$	12.4073	−	21.4900i	0.534420	−	0.925642i
$540$		0			0
$541$	−9.81306	−	16.9967i	−0.421896	−	0.730746i	0.574229	−	0.818695i	$-0.305302\pi$
$541$	−9.81306	−	16.9967i	−0.421896	−	0.730746i	−0.996125	+	0.0879490i	$0.971969\pi$
$542$	14.3810	−	3.40835i	0.617715	−	0.146401i
$543$		0			0
$544$	−54.5867	+	27.4145i	−2.34038	+	1.17539i
$545$	−4.62979	+	10.7331i	−0.198318	+	0.459754i
$546$		0			0
$547$	−0.507250	−	8.70914i	−0.0216884	−	0.372376i	−0.991636	−	0.129063i	$-0.958803\pi$
$547$	−0.507250	−	8.70914i	−0.0216884	−	0.372376i	0.969948	−	0.243313i	$-0.0782341\pi$
$548$	5.49569	+	31.1676i	0.234764	+	1.33141i
$549$		0			0
$550$	3.49651	−	19.8297i	0.149092	−	0.845540i
$551$	−3.44459	−	0.402615i	−0.146745	−	0.0171520i
$552$		0			0
$553$	1.61556	+	5.39635i	0.0687007	+	0.229476i
$554$	−36.6099	−	8.67671i	−1.55541	−	0.368638i
$555$		0			0
$556$	13.1820	+	30.5592i	0.559040	+	1.29600i
$557$	−15.1698	−	12.7290i	−0.642765	−	0.539344i	0.262101	−	0.965041i	$-0.415585\pi$
$557$	−15.1698	−	12.7290i	−0.642765	−	0.539344i	−0.904866	+	0.425696i	$0.860029\pi$
$558$		0			0
$559$	4.59706	−	3.85739i	0.194435	−	0.163150i
$560$	5.80354	+	2.91465i	0.245244	+	0.123166i
$561$		0			0
$562$	−2.04975	+	0.239581i	−0.0864634	+	0.0101061i
$563$	1.97439	−	33.8990i	0.0832108	−	1.42867i	−0.655777	−	0.754955i	$-0.727659\pi$
$563$	1.97439	−	33.8990i	0.0832108	−	1.42867i	0.738987	−	0.673719i	$-0.235304\pi$
$564$		0			0
$565$	−23.4473	−	24.8527i	−0.986436	−	1.04556i
$566$	−22.1392			−0.930581
$567$		0			0
$568$	1.06828			0.0448240
$569$	−13.2027	−	13.9941i	−0.553486	−	0.586661i	0.388861	−	0.921296i	$-0.372868\pi$
$569$	−13.2027	−	13.9941i	−0.553486	−	0.586661i	−0.942348	+	0.334635i	$0.891387\pi$
$570$		0			0
$571$	0.144601	−	2.48271i	0.00605138	−	0.103898i	−0.993930	−	0.110015i	$-0.964910\pi$
$571$	0.144601	−	2.48271i	0.00605138	−	0.103898i	0.999981	+	0.00611695i	$0.00194710\pi$
$572$	−26.4325	+	3.08951i	−1.10520	+	0.129179i
$573$		0			0
$574$	9.97437	+	5.00931i	0.416322	+	0.209085i
$575$	−4.43416	+	3.72070i	−0.184917	+	0.155164i
$576$		0			0
$577$	19.5278	+	16.3857i	0.812951	+	0.682147i	0.951310	−	0.308235i	$-0.0997383\pi$
$577$	19.5278	+	16.3857i	0.812951	+	0.682147i	−0.138359	+	0.990382i	$0.544183\pi$
$578$	32.2821	+	74.8382i	1.34276	+	3.11286i
$579$		0			0
$580$	25.4258	+	6.02602i	1.05575	+	0.250217i
$581$	1.08493	+	3.62393i	0.0450106	+	0.150346i
$582$		0			0
$583$	20.8339	+	2.43514i	0.862854	+	0.100853i
$584$	0.0156480	−	0.0887440i	0.000647517	−	0.00367225i
$585$		0			0
$586$	−8.51396	−	48.2851i	−0.351709	−	1.99464i
$587$	0.0520618	+	0.893866i	0.00214882	+	0.0368938i	0.999212	−	0.0396880i	$-0.0126364\pi$
$587$	0.0520618	+	0.893866i	0.00214882	+	0.0368938i	−0.997063	+	0.0765818i	$0.975599\pi$
$588$		0			0
$589$	2.47514	−	5.73802i	0.101986	−	0.236431i
$590$	−7.55901	+	3.79628i	−0.311199	+	0.156290i
$591$		0			0
$592$	15.7741	−	3.73852i	0.648310	−	0.153652i
$593$	16.2145	+	28.0843i	0.665848	+	1.15328i	0.979055	+	0.203597i	$0.0652634\pi$
$593$	16.2145	+	28.0843i	0.665848	+	1.15328i	−0.313207	+	0.949685i	$0.601403\pi$
$594$		0			0
$595$	6.40773	−	11.0985i	0.262691	−	0.454994i
$596$	5.26854	−	17.5981i	0.215808	−	0.720848i
$597$		0			0
$598$	12.5436	+	8.25008i	0.512948	+	0.337371i
$599$	25.1367	+	33.7644i	1.02706	+	1.37958i	0.922910	+	0.385016i	$0.125804\pi$
$599$	25.1367	+	33.7644i	1.02706	+	1.37958i	0.104148	+	0.994562i	$0.466788\pi$
$600$		0			0
$601$	25.8496	−	17.0016i	1.05443	−	0.693509i	0.100926	−	0.994894i	$-0.467819\pi$
$601$	25.8496	−	17.0016i	1.05443	−	0.693509i	0.953502	+	0.301385i	$0.0974490\pi$
$602$	2.03543	+	0.740836i	0.0829580	+	0.0301942i
$603$		0			0
$604$	−1.92891	+	0.702064i	−0.0784861	+	0.0285666i
$605$	4.99842	−	6.71405i	0.203215	−	0.272965i
$606$		0			0
$607$	10.2760	−	10.8919i	0.417090	−	0.442090i	−0.484428	−	0.874831i	$-0.660972\pi$
$607$	10.2760	−	10.8919i	0.417090	−	0.442090i	0.901518	+	0.432742i	$0.142454\pi$
$608$	4.22538	−	4.47864i	0.171362	−	0.181633i
$609$		0			0
$610$	10.0929	−	13.5572i	0.408651	−	0.548913i
$611$	37.8048	−	13.7598i	1.52942	−	0.556663i
$612$		0			0
$613$	17.2467	+	6.27730i	0.696589	+	0.253538i	0.665954	−	0.745993i	$-0.268025\pi$
$613$	17.2467	+	6.27730i	0.696589	+	0.253538i	0.0306353	+	0.999531i	$0.490247\pi$
$614$	41.8928	−	27.5533i	1.69065	−	1.11196i
$615$		0			0
$616$	−0.215190	−	0.289050i	−0.00867025	−	0.0116462i
$617$	−27.3834	−	18.0103i	−1.10241	−	0.725069i	−0.138255	−	0.990397i	$-0.544149\pi$
$617$	−27.3834	−	18.0103i	−1.10241	−	0.725069i	−0.964158	+	0.265328i	$0.914520\pi$
$618$		0			0
$619$	1.72149	−	5.75017i	0.0691925	−	0.231119i	−0.916398	−	0.400268i	$-0.868917\pi$
$619$	1.72149	−	5.75017i	0.0691925	−	0.231119i	0.985590	+	0.169150i	$0.0541021\pi$
$620$	−23.5420	+	40.7760i	−0.945471	+	1.63760i
$621$		0			0
$622$	1.86865	+	3.23661i	0.0749262	+	0.129776i
$623$	−2.73889	+	0.649129i	−0.109731	+	0.0260068i
$624$		0			0
$625$	−27.9024	+	14.0131i	−1.11610	+	0.560524i
$626$	−5.56013	+	12.8898i	−0.222227	+	0.515181i
$627$		0			0
$628$	−2.19879	−	37.7517i	−0.0877412	−	1.50646i
$629$	−5.55497	−	31.5038i	−0.221491	−	1.25614i
$630$		0			0
$631$	−4.24361	+	24.0667i	−0.168935	+	0.958080i	0.775978	+	0.630760i	$0.217257\pi$
$631$	−4.24361	+	24.0667i	−0.168935	+	0.958080i	−0.944914	+	0.327320i	$0.893854\pi$
$632$	−1.44084	−	0.168410i	−0.0573135	−	0.00669899i
$633$		0			0
$634$	15.0800	+	50.3707i	0.598903	+	2.00048i
$635$	26.8684	+	6.36793i	1.06624	+	0.252704i
$636$		0			0
$637$	−8.97577	−	20.8082i	−0.355633	−	0.824450i
$638$	26.3163	+	22.0820i	1.04187	+	0.874234i
$639$		0			0
$640$	−2.66848	+	2.23912i	−0.105481	+	0.0885089i
$641$	−9.21794	−	4.62942i	−0.364087	−	0.182851i	0.257345	−	0.966320i	$-0.417152\pi$
$641$	−9.21794	−	4.62942i	−0.364087	−	0.182851i	−0.621432	+	0.783468i	$0.713449\pi$
$642$		0			0
$643$	43.0139	−	5.02761i	1.69630	−	0.198270i	0.787738	−	0.616010i	$-0.211252\pi$
$643$	43.0139	−	5.02761i	1.69630	−	0.198270i	0.908566	+	0.417741i	$0.137178\pi$
$644$	−0.160558	+	2.75668i	−0.00632688	+	0.108628i
$645$		0			0
$646$	−8.01259	−	8.49285i	−0.315251	−	0.334147i
$647$	−6.50021			−0.255550			−0.127775	−	0.991803i	$-0.540783\pi$
$647$	−6.50021			−0.255550			−0.127775	+	0.991803i	$0.540783\pi$
$648$		0			0
$649$	−5.66668			−0.222437
$650$	−12.6190	−	13.3753i	−0.494956	−	0.524623i
$651$		0			0
$652$	−2.07173	+	35.5702i	−0.0811350	+	1.39303i
$653$	2.95697	−	0.345620i	0.115715	−	0.0135251i	−0.0580383	−	0.998314i	$-0.518485\pi$
$653$	2.95697	−	0.345620i	0.115715	−	0.0135251i	0.173753	+	0.984789i	$0.444410\pi$
$654$		0			0
$655$	−13.5884	−	6.82436i	−0.530944	−	0.266650i
$656$	26.5844	−	22.3070i	1.03795	−	0.870941i
$657$		0			0
$658$	11.1240	+	9.33410i	0.433657	+	0.363881i
$659$	11.1338	+	25.8110i	0.433710	+	1.00545i	0.985221	+	0.171285i	$0.0547920\pi$
$659$	11.1338	+	25.8110i	0.433710	+	1.00545i	−0.551512	+	0.834167i	$0.685949\pi$
$660$		0			0
$661$	−3.16302	−	0.749650i	−0.123027	−	0.0291580i	0.168641	−	0.985678i	$-0.446062\pi$
$661$	−3.16302	−	0.749650i	−0.123027	−	0.0291580i	−0.291668	+	0.956520i	$0.594210\pi$
$662$	15.0789	+	50.3671i	0.586059	+	1.95757i
$663$		0			0
$664$	−0.967598	−	0.113096i	−0.0375501	−	0.00438898i
$665$	−0.224319	+	1.27217i	−0.00869871	+	0.0493328i
$666$		0			0
$667$	−1.71488	−	9.72556i	−0.0664004	−	0.376575i
$668$	0.712992	+	12.2416i	0.0275865	+	0.473642i
$669$		0			0
$670$	−16.9424	+	39.2770i	−0.654544	+	1.51740i
$671$	10.1183	−	5.08162i	0.390614	−	0.196174i
$672$		0			0
$673$	13.5198	−	3.20426i	0.521152	−	0.123515i	0.0383830	−	0.999263i	$-0.487779\pi$
$673$	13.5198	−	3.20426i	0.521152	−	0.123515i	0.482769	+	0.875748i	$0.339631\pi$
$674$	15.1769	+	26.2871i	0.584591	+	1.01254i
$675$		0			0
$676$	1.35501	−	2.34695i	0.0521158	−	0.0902672i
$677$	−3.11373	+	10.4006i	−0.119670	+	0.399727i	−0.996744	−	0.0806287i	$-0.974307\pi$
$677$	−3.11373	+	10.4006i	−0.119670	+	0.399727i	0.877074	+	0.480356i	$0.159492\pi$
$678$		0			0
$679$	−5.37112	−	3.53264i	−0.206125	−	0.135570i
$680$	1.97082	+	2.64726i	0.0755773	+	0.101518i
$681$		0			0
$682$	−51.7182	+	34.0156i	−1.98039	+	1.30253i
$683$	31.5858	+	11.4963i	1.20860	+	0.439893i	0.866217	−	0.499668i	$-0.166545\pi$
$683$	31.5858	+	11.4963i	1.20860	+	0.439893i	0.342380	+	0.939562i	$0.388767\pi$
$684$		0			0
$685$	−39.6178	+	14.4197i	−1.51372	+	0.550949i
$686$	10.0445	−	13.4921i	0.383501	−	0.515131i
$687$		0			0
$688$	4.62162	−	4.89864i	0.176198	−	0.186759i
$689$	13.1455	−	13.9334i	0.500804	−	0.530821i
$690$		0			0
$691$	−0.267326	+	0.359082i	−0.0101696	+	0.0136601i	−0.807179	−	0.590307i	$-0.799007\pi$
$691$	−0.267326	+	0.359082i	−0.0101696	+	0.0136601i	0.797009	+	0.603967i	$0.206414\pi$
$692$	17.5595	−	6.39115i	0.667513	−	0.242955i
$693$		0			0
$694$	−48.2412	−	17.5584i	−1.83121	−	0.666507i
$695$	−37.0417	+	24.3627i	−1.40507	+	0.924129i
$696$		0			0
$697$	−40.8943	−	54.9306i	−1.54898	−	2.08065i
$698$	49.3762	+	32.4753i	1.86892	+	1.22921i
$699$		0			0
$700$	0.969993	−	3.24000i	0.0366623	−	0.122461i
$701$	−1.94332	+	3.36593i	−0.0733982	+	0.127129i	−0.900389	−	0.435087i	$-0.856718\pi$
$701$	−1.94332	+	3.36593i	−0.0733982	+	0.127129i	0.826990	+	0.562216i	$0.190051\pi$
$702$		0			0
$703$	1.61229	+	2.79256i	0.0608086	+	0.105324i
$704$	−31.3776	+	7.43663i	−1.18259	+	0.280278i
$705$		0			0
$706$	−51.7769	+	26.0033i	−1.94865	+	0.978648i
$707$	0.592827	−	1.37433i	0.0222956	−	0.0516869i
$708$		0			0
$709$	0.857054	+	14.7150i	0.0321873	+	0.552635i	0.975400	+	0.220444i	$0.0707507\pi$
$709$	0.857054	+	14.7150i	0.0321873	+	0.552635i	−0.943212	+	0.332191i	$0.892212\pi$
$710$	6.58725	+	37.3581i	0.247215	+	1.40203i
$711$		0			0
$712$	0.125874	−	0.713864i	0.00471731	−	0.0267532i
$713$	17.6746	+	2.06587i	0.661919	+	0.0773673i
$714$		0			0
$715$	−10.1677	−	33.9624i	−0.380249	−	1.27012i
$716$	−2.60614	−	0.617666i	−0.0973959	−	0.0230833i
$717$		0			0
$718$	16.6816	+	38.6723i	0.622552	+	1.44324i
$719$	−24.7821	−	20.7947i	−0.924218	−	0.775511i	0.0505523	−	0.998721i	$-0.483902\pi$
$719$	−24.7821	−	20.7947i	−0.924218	−	0.775511i	−0.974770	+	0.223210i	$0.928346\pi$
$720$		0			0
$721$	−7.98762	+	6.70241i	−0.297474	+	0.249611i
$722$	−33.2356	−	16.6915i	−1.23690	−	0.621195i
$723$		0			0
$724$	−7.67077	+	0.896585i	−0.285082	+	0.0333213i
$725$	−0.703295	+	12.0751i	−0.0261197	+	0.448458i
$726$		0			0
$727$	6.33415	+	6.71380i	0.234921	+	0.249001i	0.834100	−	0.551614i	$-0.185988\pi$
$727$	6.33415	+	6.71380i	0.234921	+	0.249001i	−0.599179	+	0.800615i	$0.704506\pi$
$728$	−0.329090			−0.0121969
$729$		0			0
$730$	3.19990			0.118434
$731$	−9.12000	−	9.66663i	−0.337315	−	0.357533i
$732$		0			0
$733$	3.08131	−	52.9040i	0.113811	−	1.95405i	−0.148126	−	0.988969i	$-0.547324\pi$
$733$	3.08131	−	52.9040i	0.113811	−	1.95405i	0.261936	−	0.965085i	$-0.415639\pi$
$734$	69.3320	−	8.10374i	2.55909	−	0.299115i
$735$		0			0
$736$	15.6685	+	7.86901i	0.577548	+	0.290055i
$737$	−21.9518	+	18.4198i	−0.808606	+	0.678501i
$738$		0			0
$739$	2.18316	+	1.83188i	0.0803087	+	0.0673870i	0.682058	−	0.731298i	$-0.261085\pi$
$739$	2.18316	+	1.83188i	0.0803087	+	0.0673870i	−0.601750	+	0.798685i	$0.705529\pi$
$740$	−9.62303	−	22.3087i	−0.353750	−	0.820084i
$741$		0			0
$742$	6.72786	+	1.59453i	0.246988	+	0.0585372i
$743$	−8.43563	−	28.1770i	−0.309473	−	1.03371i	−0.961336	−	0.275376i	$-0.911198\pi$
$743$	−8.43563	−	28.1770i	−0.309473	−	1.03371i	0.651863	−	0.758337i	$-0.273988\pi$
$744$		0			0
$745$	24.3059	+	2.84096i	0.890501	+	0.104085i
$746$	−3.28553	+	18.6331i	−0.120292	+	0.682208i
$747$		0			0
$748$	10.2340	+	58.0400i	0.374193	+	2.12215i
$749$	0.0285802	+	0.490704i	0.00104430	+	0.0179299i
$750$		0			0
$751$	−10.8644	+	25.1865i	−0.396447	+	0.919067i	0.596729	+	0.802443i	$0.296467\pi$
$751$	−10.8644	+	25.1865i	−0.396447	+	0.919067i	−0.993176	+	0.116624i	$0.962793\pi$
$752$	40.3470	−	20.2630i	1.47130	−	0.738917i
$753$		0			0
$754$	30.5271	−	7.23506i	1.11173	−	0.263485i
$755$	−1.36725	−	2.36815i	−0.0497593	−	0.0861857i
$756$		0			0
$757$	14.2323	−	24.6511i	0.517282	−	0.895959i	−0.482516	−	0.875887i	$-0.660277\pi$
$757$	14.2323	−	24.6511i	0.517282	−	0.895959i	0.999799	−	0.0200719i	$-0.00638952\pi$
$758$	1.11637	−	3.72894i	0.0405485	−	0.135441i
$759$		0			0
$760$	−0.277944	−	0.182807i	−0.0100821	−	0.00663110i
$761$	−16.7039	−	22.4372i	−0.605514	−	0.813347i	0.388631	−	0.921393i	$-0.372948\pi$
$761$	−16.7039	−	22.4372i	−0.605514	−	0.813347i	−0.994146	+	0.108046i	$0.965541\pi$
$762$		0			0
$763$	−2.15659	+	1.41841i	−0.0780739	+	0.0513500i
$764$	14.2348	+	5.18104i	0.514997	+	0.187444i
$765$		0			0
$766$	36.9883	−	13.4626i	1.33644	−	0.486425i
$767$	−3.09030	+	4.15099i	−0.111584	+	0.149884i
$768$		0			0
$769$	−32.2285	+	34.1602i	−1.16219	+	1.23185i	−0.194169	+	0.980968i	$0.562201\pi$
$769$	−32.2285	+	34.1602i	−1.16219	+	1.23185i	−0.968018	+	0.250879i	$0.919280\pi$
$770$	8.78129	−	9.30762i	0.316456	−	0.335424i
$771$		0			0
$772$	−11.9460	+	16.0463i	−0.429947	+	0.577519i
$773$	−41.5507	+	15.1232i	−1.49447	+	0.543944i	−0.954623	−	0.297816i	$-0.903742\pi$
$773$	−41.5507	+	15.1232i	−1.49447	+	0.543944i	−0.539851	+	0.841761i	$0.681519\pi$
$774$		0			0
$775$	−20.4807	−	7.45437i	−0.735689	−	0.267769i
$776$	1.38321	−	0.909749i	0.0496542	−	0.0326581i
$777$		0			0
$778$	11.0218	+	14.8049i	0.395151	+	0.530780i
$779$	5.76733	+	3.79323i	0.206636	+	0.135907i
$780$		0			0
$781$	−7.28855	+	24.3454i	−0.260805	+	0.871148i
$782$	16.6244	−	28.7942i	0.594486	−	1.02968i
$783$		0			0
$784$	−12.7160	−	22.0247i	−0.454143	−	0.786598i
$785$	49.0183	−	11.6175i	1.74954	−	0.414648i
$786$		0			0
$787$	32.6021	−	16.3734i	1.16214	−	0.583649i	0.240102	−	0.970748i	$-0.422819\pi$
$787$	32.6021	−	16.3734i	1.16214	−	0.583649i	0.922038	+	0.387099i	$0.126523\pi$
$788$	4.06308	−	9.41927i	0.144741	−	0.335548i
$789$		0			0
$790$	−2.99517	−	51.4252i	−0.106564	−	1.82963i
$791$	−1.31019	−	7.43049i	−0.0465852	−	0.264198i
$792$		0			0
$793$	1.79557	−	10.1832i	0.0637627	−	0.361616i
$794$	−66.8888	−	7.81818i	−2.37380	−	0.277457i
$795$		0			0
$796$	−1.50023	−	5.01112i	−0.0531742	−	0.177614i
$797$	14.7098	+	3.48628i	0.521046	+	0.123490i	0.482719	−	0.875775i	$-0.339649\pi$
$797$	14.7098	+	3.48628i	0.521046	+	0.123490i	0.0383267	+	0.999265i	$0.487797\pi$
$798$		0			0
$799$	−35.2886	−	81.8083i	−1.24842	−	2.89417i
$800$	−16.4507	−	13.8038i	−0.581621	−	0.488038i
$801$		0			0
$802$	5.48967	−	4.60638i	0.193847	−	0.162657i
$803$	1.91566	+	0.962081i	0.0676022	+	0.0339511i
$804$		0			0
$805$	−3.65366	+	0.427051i	−0.128774	+	0.0150516i
$806$	−3.28698	+	56.4353i	−0.115779	+	1.98785i
$807$		0			0
$808$	0.264512	+	0.280366i	0.00930549	+	0.00986325i
$809$	49.6978			1.74728			0.873641	−	0.486571i	$-0.161753\pi$
$809$	49.6978			1.74728			0.873641	+	0.486571i	$0.161753\pi$
$810$		0			0
$811$	−8.76133			−0.307652			−0.153826	−	0.988098i	$-0.549159\pi$
$811$	−8.76133			−0.307652			−0.153826	+	0.988098i	$0.549159\pi$
$812$	3.95975	+	4.19709i	0.138960	+	0.147289i
$813$		0			0
$814$	1.85725	−	31.8877i	0.0650965	−	1.11766i
$815$	−47.1441	+	5.51036i	−1.65139	+	0.193019i
$816$		0			0
$817$	1.19712	+	0.601217i	0.0418820	+	0.0210339i
$818$	−49.5562	+	41.5826i	−1.73269	+	1.45390i
$819$		0			0
$820$	−39.8424	−	33.4317i	−1.39136	−	1.16749i
$821$	14.0466	+	32.5637i	0.490230	+	1.13648i	0.966380	+	0.257117i	$0.0827726\pi$
$821$	14.0466	+	32.5637i	0.490230	+	1.13648i	−0.476150	+	0.879364i	$0.657968\pi$
$822$		0			0
$823$	−1.82849	−	0.433361i	−0.0637372	−	0.0151060i	0.198624	−	0.980076i	$-0.436353\pi$
$823$	−1.82849	−	0.433361i	−0.0637372	−	0.0151060i	−0.262361	+	0.964970i	$0.584501\pi$
$824$	−0.770140	−	2.57245i	−0.0268291	−	0.0896155i
$825$		0			0
$826$	−1.85528	−	0.216851i	−0.0645533	−	0.00754520i
$827$	−1.66995	+	9.47075i	−0.0580698	+	0.329330i	−0.999979	−	0.00653851i	$-0.997919\pi$
$827$	−1.66995	+	9.47075i	−0.0580698	+	0.329330i	0.941909	+	0.335869i	$0.109030\pi$
$828$		0			0
$829$	−1.31856	−	7.47791i	−0.0457954	−	0.259719i	0.953311	−	0.301991i	$-0.0976513\pi$
$829$	−1.31856	−	7.47791i	−0.0457954	−	0.259719i	−0.999106	+	0.0422726i	$0.986540\pi$
$830$	−2.01142	−	34.5347i	−0.0698173	−	1.19872i
$831$		0			0
$832$	−11.6641	+	27.0405i	−0.404381	+	0.937460i
$833$	−44.8476	+	22.5233i	−1.55388	+	0.780387i
$834$		0			0
$835$	−15.8950	+	3.76717i	−0.550068	+	0.130368i
$836$	−2.97035	−	5.14479i	−0.102732	−	0.177936i
$837$		0			0
$838$	−14.9786	+	25.9438i	−0.517429	+	0.896213i
$839$	−11.3639	+	37.9580i	−0.392325	+	1.31046i	0.502707	+	0.864457i	$0.332337\pi$
$839$	−11.3639	+	37.9580i	−0.392325	+	1.31046i	−0.895033	+	0.446001i	$0.852848\pi$
$840$		0			0
$841$	6.98773	+	4.59591i	0.240956	+	0.158479i
$842$	−18.7876	−	25.2361i	−0.647463	−	0.869694i
$843$		0			0
$844$	−12.1316	+	7.97906i	−0.417586	+	0.274651i
$845$	3.39243	+	1.23475i	0.116703	+	0.0424765i
$846$		0			0
$847$	1.73692	−	0.632185i	0.0596811	−	0.0217221i
$848$	12.8375	−	17.2438i	0.440842	−	0.592154i
$849$		0			0
$850$	−27.9457	+	29.6207i	−0.958530	+	1.01598i
$851$	−6.30127	+	6.67896i	−0.216005	+	0.228952i
$852$		0			0
$853$	2.05643	−	2.76227i	0.0704110	−	0.0945783i	−0.765523	−	0.643409i	$-0.777519\pi$
$853$	2.05643	−	2.76227i	0.0704110	−	0.0945783i	0.835933	+	0.548831i	$0.184927\pi$
$854$	3.50722	−	1.27652i	0.120015	−	0.0436817i
$855$		0			0
$856$	−0.118950	−	0.0432941i	−0.00406561	−	0.00147976i
$857$	−18.5031	+	12.1697i	−0.632053	+	0.415708i	−0.824708	−	0.565559i	$-0.808661\pi$
$857$	−18.5031	+	12.1697i	−0.632053	+	0.415708i	0.192655	+	0.981267i	$0.438290\pi$
$858$		0			0
$859$	21.2724	+	28.5737i	0.725804	+	0.974924i	0.999913	+	0.0132249i	$0.00420973\pi$
$859$	21.2724	+	28.5737i	0.725804	+	0.974924i	−0.274109	+	0.961699i	$0.588383\pi$
$860$	−8.43288	−	5.54639i	−0.287559	−	0.189130i
$861$		0			0
$862$	0.751429	−	2.50995i	0.0255938	−	0.0854891i
$863$	−10.4873	+	18.1645i	−0.356992	+	0.618328i	−0.987457	−	0.157890i	$-0.949531\pi$
$863$	−10.4873	+	18.1645i	−0.356992	+	0.618328i	0.630465	+	0.776218i	$0.282864\pi$
$864$		0			0
$865$	12.4466	+	21.5581i	0.423196	+	0.732998i
$866$	34.4460	−	8.16385i	1.17052	−	0.277419i
$867$		0			0
$868$	−9.29143	+	4.66633i	−0.315372	+	0.158386i
$869$	13.6684	−	31.6868i	0.463668	−	1.07490i
$870$		0			0
$871$	1.52163	+	26.1254i	0.0515586	+	0.885227i
$872$	−0.115431	−	0.654639i	−0.00390897	−	0.0221689i
$873$		0			0
$874$	−0.581978	+	3.30056i	−0.0196857	+	0.111643i
$875$	−3.92834	−	0.459157i	−0.132802	−	0.0155223i
$876$		0			0
$877$	−12.1070	−	40.4401i	−0.408823	−	1.36556i	−0.876388	−	0.481605i	$-0.840054\pi$
$877$	−12.1070	−	40.4401i	−0.408823	−	1.36556i	0.467565	−	0.883959i	$-0.345131\pi$
$878$	42.6755	+	10.1143i	1.44023	+	0.341340i
$879$		0			0
$880$	−15.7584	−	36.5320i	−0.531214	−	1.23149i
$881$	29.2913	+	24.5783i	0.986848	+	0.828064i	0.985108	−	0.171935i	$-0.0550019\pi$
$881$	29.2913	+	24.5783i	0.986848	+	0.828064i	0.00173943	+	0.999998i	$0.499446\pi$
$882$		0			0
$883$	−22.0694	+	18.5184i	−0.742693	+	0.623194i	−0.933560	−	0.358422i	$-0.883315\pi$
$883$	−22.0694	+	18.5184i	−0.742693	+	0.623194i	0.190866	+	0.981616i	$0.438870\pi$
$884$	48.0969	+	24.1552i	1.61767	+	0.812426i
$885$		0			0
$886$	18.3398	−	2.14361i	0.616137	−	0.0720161i
$887$	−0.797647	+	13.6951i	−0.0267824	+	0.459835i	0.958080	+	0.286500i	$0.0924917\pi$
$887$	−0.797647	+	13.6951i	−0.0267824	+	0.459835i	−0.984863	+	0.173336i	$0.944545\pi$
$888$		0			0
$889$	4.18443	+	4.43523i	0.140341	+	0.148753i
$890$	25.7403			0.862816
$891$		0			0
$892$	−37.3995			−1.25223
$893$	6.16298	+	6.53238i	0.206236	+	0.218598i
$894$		0			0
$895$	0.207457	−	3.56190i	0.00693453	−	0.119061i
$896$	−0.764034	+	0.0893027i	−0.0255246	+	0.00298340i
$897$		0			0
$898$	−22.4174	−	11.2584i	−0.748078	−	0.375699i
$899$	28.4852	−	23.9019i	0.950035	−	0.797174i
$900$		0			0
$901$	−32.4972	−	27.2684i	−1.08264	−	0.908441i
$902$	−27.0834	−	62.7864i	−0.901779	−	2.09056i
$903$		0			0
$904$	1.89069	+	0.448102i	0.0628835	+	0.0149037i
$905$	−2.95068	−	9.85597i	−0.0980840	−	0.327623i
$906$		0			0
$907$	−56.3534	−	6.58677i	−1.87119	−	0.218710i	−0.896618	−	0.442805i	$-0.853984\pi$
$907$	−56.3534	−	6.58677i	−1.87119	−	0.218710i	−0.974567	+	0.224094i	$0.928058\pi$
$908$	0.221375	−	1.25548i	0.00734659	−	0.0416646i
$909$		0			0
$910$	−2.02924	−	11.5084i	−0.0672687	−	0.381500i
$911$	−0.0414988	−	0.712508i	−0.00137492	−	0.0236064i	0.997551	−	0.0699440i	$-0.0222821\pi$
$911$	−0.0414988	−	0.712508i	−0.00137492	−	0.0236064i	−0.998926	+	0.0463376i	$0.985245\pi$
$912$		0			0
$913$	9.17902	−	21.2794i	0.303781	−	0.704244i
$914$	−33.7367	+	16.9432i	−1.11591	+	0.560432i
$915$		0			0
$916$	−10.1001	+	2.39376i	−0.333716	+	0.0790921i
$917$	−1.67892	−	2.90797i	−0.0554428	−	0.0960297i
$918$		0			0
$919$	28.6606	−	49.6416i	0.945425	−	1.63752i	0.190527	−	0.981682i	$-0.438980\pi$
$919$	28.6606	−	49.6416i	0.945425	−	1.63752i	0.754898	−	0.655842i	$-0.227686\pi$
$920$	0.271694	−	0.907522i	0.00895750	−	0.0299201i
$921$		0			0
$922$	69.3125	+	45.5876i	2.28269	+	1.50135i
$923$	13.8589	+	18.6157i	0.456171	+	0.612744i
$924$		0			0
$925$	9.39625	−	6.18001i	0.308947	−	0.203198i
$926$	7.83677	+	2.85235i	0.257532	+	0.0937341i
$927$		0			0
$928$	34.4289	−	12.5311i	1.13018	−	0.411353i
$929$	−8.93536	+	12.0023i	−0.293160	+	0.393782i	−0.924163	−	0.381998i	$-0.875236\pi$
$929$	−8.93536	+	12.0023i	−0.293160	+	0.393782i	0.631003	+	0.775780i	$0.282643\pi$
$930$		0			0
$931$	3.47151	−	3.67959i	0.113774	−	0.120594i
$932$	18.7623	−	19.8869i	0.614579	−	0.651416i
$933$		0			0
$934$	30.4809	−	40.9429i	0.997365	−	1.33969i
$935$	−73.7759	+	26.8522i	−2.41273	+	0.878162i
$936$		0			0
$937$	23.1819	+	8.43751i	0.757319	+	0.275641i	0.691682	−	0.722202i	$-0.256870\pi$
$937$	23.1819	+	8.43751i	0.757319	+	0.275641i	0.0656366	+	0.997844i	$0.479092\pi$
$938$	−7.89193	+	5.19060i	−0.257681	+	0.169479i
$939$		0			0
$940$	−40.4073	−	54.2765i	−1.31794	−	1.77030i
$941$	−19.4338	−	12.7818i	−0.633523	−	0.416675i	0.191722	−	0.981449i	$-0.438593\pi$
$941$	−19.4338	−	12.7818i	−0.633523	−	0.416675i	−0.825245	+	0.564775i	$0.808963\pi$
$942$		0			0
$943$	−5.63765	+	18.8310i	−0.183587	+	0.613223i
$944$	−2.90384	+	5.02959i	−0.0945119	+	0.163699i
$945$		0			0
$946$	−6.63491	−	11.4920i	−0.215720	−	0.373637i
$947$	18.6605	−	4.42261i	0.606384	−	0.143716i	0.0840570	−	0.996461i	$-0.473212\pi$
$947$	18.6605	−	4.42261i	0.606384	−	0.143716i	0.522327	+	0.852745i	$0.325064\pi$
$948$		0			0
$949$	1.74945	−	0.878606i	0.0567895	−	0.0285208i
$950$	1.62586	−	3.76916i	0.0527497	−	0.122288i
$951$		0			0
$952$	0.0423757	+	0.727563i	0.00137340	+	0.0235804i
$953$	−5.37991	−	30.5110i	−0.174272	−	0.988348i	−0.938980	−	0.343971i	$-0.888228\pi$
$953$	−5.37991	−	30.5110i	−0.174272	−	0.988348i	0.764708	−	0.644377i	$-0.222883\pi$
$954$		0			0
$955$	−3.50420	+	19.8733i	−0.113393	+	0.643085i
$956$	−18.7778	−	2.19481i	−0.607316	−	0.0709851i
$957$		0			0
$958$	−12.0479	−	40.2429i	−0.389251	−	1.30019i
$959$	−9.05915	−	2.14706i	−0.292535	−	0.0693321i
$960$		0			0
$961$	14.2603	+	33.0592i	0.460011	+	1.06642i
$962$	−22.3457	−	18.7503i	−0.720456	−	0.604534i
$963$		0			0
$964$	−22.6834	+	19.0336i	−0.730583	+	0.613032i
$965$	−23.8147	−	11.9602i	−0.766623	−	0.385013i
$966$		0			0
$967$	−19.7235	+	2.30534i	−0.634264	+	0.0741348i	−0.427148	−	0.904182i	$-0.640482\pi$
$967$	−19.7235	+	2.30534i	−0.634264	+	0.0741348i	−0.207116	+	0.978316i	$0.566408\pi$
$968$	−0.0276775	+	0.475204i	−0.000889587	+	0.0152736i
$969$		0			0
$970$	40.3435	+	42.7616i	1.29535	+	1.37299i
$971$	3.39436			0.108930			0.0544651	−	0.998516i	$-0.482655\pi$
$971$	3.39436			0.108930			0.0544651	+	0.998516i	$0.482655\pi$
$972$		0			0
$973$	−9.79039			−0.313865
$974$	9.14706	+	9.69532i	0.293091	+	0.310658i
$975$		0			0
$976$	0.674738	−	11.5848i	0.0215978	−	0.370820i
$977$	−53.2053	+	6.21881i	−1.70219	+	0.198957i	−0.910941	−	0.412537i	$-0.864643\pi$
$977$	−53.2053	+	6.21881i	−1.70219	+	0.198957i	−0.791249	+	0.611494i	$0.790569\pi$
$978$		0			0
$979$	15.4097	+	7.73906i	0.492497	+	0.247342i
$980$	−29.1980	+	24.5000i	−0.932694	+	0.782624i
$981$		0			0
$982$	56.5336	+	47.4373i	1.80406	+	1.51379i
$983$	−11.0201	−	25.5474i	−0.351486	−	0.814836i	−0.998623	−	0.0524620i	$-0.983293\pi$
$983$	−11.0201	−	25.5474i	−0.351486	−	0.814836i	0.647137	−	0.762374i	$-0.275966\pi$
$984$		0			0
$985$	13.2971	+	3.15148i	0.423682	+	0.100414i
$986$	−19.9264	−	66.5587i	−0.634585	−	2.11966i
$987$		0			0
$988$	−5.38856	−	0.629833i	−0.171433	−	0.0200376i
$989$	−0.662412	+	3.75672i	−0.0210635	+	0.119457i
$990$		0			0
$991$	2.53438	+	14.3732i	0.0805071	+	0.456579i	0.998236	+	0.0593711i	$0.0189095\pi$
$991$	2.53438	+	14.3732i	0.0805071	+	0.456579i	−0.917729	+	0.397207i	$0.869979\pi$
$992$	3.83867	+	65.9075i	0.121878	+	2.09257i
$993$		0			0
$994$	−3.31792	+	7.69180i	−0.105238	+	0.243969i
$995$	6.22710	−	3.12737i	0.197412	−	0.0991441i
$996$		0			0
$997$	−2.37129	+	0.562006i	−0.0750995	+	0.0177989i	−0.267994	−	0.963421i	$-0.586361\pi$
$997$	−2.37129	+	0.562006i	−0.0750995	+	0.0177989i	0.192894	+	0.981220i	$0.438213\pi$
$998$	−36.7468	−	63.6474i	−1.16320	−	2.01472i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.109.2		144
3.2	odd	2		729.2.g.d.109.7		144
9.2	odd	6		729.2.g.c.352.7		144
9.4	even	3		243.2.g.a.118.7		144
9.5	odd	6		81.2.g.a.76.2	yes	144
9.7	even	3		729.2.g.b.352.2		144
81.11	odd	54		729.2.g.d.622.7		144
81.16	even	27		729.2.g.b.379.2		144
81.31	even	27		6561.2.a.d.1.59		72
81.38	odd	54		81.2.g.a.16.2	✓	144
81.43	even	27		243.2.g.a.208.7		144
81.50	odd	54		6561.2.a.c.1.14		72
81.65	odd	54		729.2.g.c.379.7		144
81.70	even	27	inner	729.2.g.a.622.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.2	✓	144	81.38	odd	54
81.2.g.a.76.2	yes	144	9.5	odd	6
243.2.g.a.118.7		144	9.4	even	3
243.2.g.a.208.7		144	81.43	even	27
729.2.g.a.109.2		144	1.1	even	1	trivial
729.2.g.a.622.2		144	81.70	even	27	inner
729.2.g.b.352.2		144	9.7	even	3
729.2.g.b.379.2		144	81.16	even	27
729.2.g.c.352.7		144	9.2	odd	6
729.2.g.c.379.7		144	81.65	odd	54
729.2.g.d.109.7		144	3.2	odd	2
729.2.g.d.622.7		144	81.11	odd	54
6561.2.a.c.1.14		72	81.50	odd	54
6561.2.a.d.1.59		72	81.31	even	27

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Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	729.2.g.a.109.2

Level	$729$
Weight	$2$
Character	729.109
Analytic conductor	$5.821$
Analytic rank	$0$
Dimension	$144$
Inner twists	$2$