LMFDB - Embedded newform 648.2.t.a.253.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.13
Character	$\chi$	$=$	648.253
Dual form			648.2.t.a.397.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.495022 - 1.32475i) q^{2} +(-1.50991 + 1.31156i) q^{4} +(0.185555 - 0.221136i) q^{5} +(-2.62731 - 0.956263i) q^{7} +(2.48492 + 1.35099i) q^{8} +(-0.384803 - 0.136346i) q^{10} +(-3.08006 - 3.67067i) q^{11} +(3.17478 + 0.559799i) q^{13} +(0.0337716 + 3.95389i) q^{14} +(0.559631 - 3.96066i) q^{16} +(-2.81522 + 4.87610i) q^{17} +(0.00428975 - 0.00247669i) q^{19} +(0.00986189 + 0.577261i) q^{20} +(-3.33801 + 5.89736i) q^{22} +(-1.84294 + 0.670777i) q^{23} +(0.853770 + 4.84197i) q^{25} +(-0.829994 - 4.48289i) q^{26} +(5.22119 - 2.00200i) q^{28} +(-7.88122 + 1.38967i) q^{29} +(-5.45972 + 1.98718i) q^{31} +(-5.52390 + 1.21924i) q^{32} +(7.85319 + 1.31567i) q^{34} +(-0.698975 + 0.403553i) q^{35} +(-8.20717 - 4.73841i) q^{37} +(-0.00540451 - 0.00445682i) q^{38} +(0.759842 - 0.298821i) q^{40} +(-1.69965 + 9.63917i) q^{41} +(3.57494 + 4.26045i) q^{43} +(9.46489 + 1.50269i) q^{44} +(1.80091 + 2.10938i) q^{46} +(-3.48835 - 1.26966i) q^{47} +(0.626015 + 0.525289i) q^{49} +(5.99175 - 3.52791i) q^{50} +(-5.52782 + 3.31866i) q^{52} +0.865665i q^{53} -1.38324 q^{55} +(-5.23675 - 5.92571i) q^{56} +(5.74234 + 9.75270i) q^{58} +(3.57109 - 4.25586i) q^{59} +(2.43327 - 6.68534i) q^{61} +(5.33519 + 6.24905i) q^{62} +(4.34964 + 6.71421i) q^{64} +(0.712888 - 0.598184i) q^{65} +(-0.224950 - 0.0396647i) q^{67} +(-2.14457 - 11.0548i) q^{68} +(0.880614 + 0.726197i) q^{70} +(-0.429923 + 0.744648i) q^{71} +(-2.02670 - 3.51035i) q^{73} +(-2.21446 + 13.2180i) q^{74} +(-0.00322880 + 0.00936583i) q^{76} +(4.58214 + 12.5893i) q^{77} +(-0.797428 - 4.52244i) q^{79} +(-0.772001 - 0.858675i) q^{80} +(13.6108 - 2.52001i) q^{82} +(4.00250 - 0.705749i) q^{83} +(0.555903 + 1.52733i) q^{85} +(3.87434 - 6.84491i) q^{86} +(-2.69465 - 13.2824i) q^{88} +(1.77889 + 3.08112i) q^{89} +(-7.80581 - 4.50669i) q^{91} +(1.90291 - 3.42994i) q^{92} +(0.0448395 + 5.24969i) q^{94} +(0.000248300 - 0.00140818i) q^{95} +(6.04757 - 5.07452i) q^{97} +(0.385983 - 1.08934i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.495022	−	1.32475i	−0.350034	−	0.936737i
$2$	−0.495022	−	1.32475i	−0.350034	−	0.936737i
$3$		0			0
$3$		0			0
$4$	−1.50991	+	1.31156i	−0.754953	+	0.655779i
$5$	0.185555	−	0.221136i	0.0829828	−	0.0988950i	−0.722956	−	0.690895i	$-0.757217\pi$
$5$	0.185555	−	0.221136i	0.0829828	−	0.0988950i	0.805938	+	0.592000i	$0.201661\pi$
$6$		0			0
$7$	−2.62731	−	0.956263i	−0.993030	−	0.361433i	−0.206137	−	0.978523i	$-0.566089\pi$
$7$	−2.62731	−	0.956263i	−0.993030	−	0.361433i	−0.786893	+	0.617090i	$0.788312\pi$
$8$	2.48492	+	1.35099i	0.878551	+	0.477648i
$9$		0			0
$10$	−0.384803	−	0.136346i	−0.121685	−	0.0431165i
$11$	−3.08006	−	3.67067i	−0.928672	−	1.10675i	−0.994054	−	0.108888i	$-0.965271\pi$
$11$	−3.08006	−	3.67067i	−0.928672	−	1.10675i	0.0653817	−	0.997860i	$-0.479174\pi$
$12$		0			0
$13$	3.17478	+	0.559799i	0.880525	+	0.155260i	0.595592	−	0.803287i	$-0.296918\pi$
$13$	3.17478	+	0.559799i	0.880525	+	0.155260i	0.284933	+	0.958547i	$0.408029\pi$
$14$	0.0337716	+	3.95389i	0.00902584	+	1.05672i
$15$		0			0
$16$	0.559631	−	3.96066i	0.139908	−	0.990165i
$17$	−2.81522	+	4.87610i	−0.682791	+	1.18263i	0.291335	+	0.956621i	$0.405901\pi$
$17$	−2.81522	+	4.87610i	−0.682791	+	1.18263i	−0.974126	+	0.226007i	$0.927433\pi$
$18$		0			0
$19$	0.00428975	−	0.00247669i	0.000984137	−	0.000568192i	−0.499508	−	0.866309i	$-0.666486\pi$
$19$	0.00428975	−	0.00247669i	0.000984137	−	0.000568192i	0.500492	+	0.865741i	$0.333152\pi$
$20$	0.00986189	+	0.577261i	0.00220519	+	0.129079i
$21$		0			0
$22$	−3.33801	+	5.89736i	−0.711666	+	1.25732i
$23$	−1.84294	+	0.670777i	−0.384280	+	0.139867i	−0.526934	−	0.849906i	$-0.676659\pi$
$23$	−1.84294	+	0.670777i	−0.384280	+	0.139867i	0.142654	+	0.989773i	$0.454436\pi$
$24$		0			0
$25$	0.853770	+	4.84197i	0.170754	+	0.968395i
$26$	−0.829994	−	4.48289i	−0.162775	−	0.879167i
$27$		0			0
$28$	5.22119	−	2.00200i	0.986712	−	0.378343i
$29$	−7.88122	+	1.38967i	−1.46351	+	0.258056i	−0.847966	−	0.530050i	$-0.822173\pi$
$29$	−7.88122	+	1.38967i	−1.46351	+	0.258056i	−0.615540	+	0.788106i	$0.711062\pi$
$30$		0			0
$31$	−5.45972	+	1.98718i	−0.980595	+	0.356907i	−0.782071	−	0.623189i	$-0.785837\pi$
$31$	−5.45972	+	1.98718i	−0.980595	+	0.356907i	−0.198523	+	0.980096i	$0.563615\pi$
$32$	−5.52390	+	1.21924i	−0.976496	+	0.215534i
$33$		0			0
$34$	7.85319	+	1.31567i	1.34681	+	0.225636i
$35$	−0.698975	+	0.403553i	−0.118148	+	0.0682130i
$36$		0			0
$37$	−8.20717	−	4.73841i	−1.34925	−	0.778990i	−0.361107	−	0.932524i	$-0.617601\pi$
$37$	−8.20717	−	4.73841i	−1.34925	−	0.778990i	−0.988143	+	0.153534i	$0.950934\pi$
$38$	−0.00540451	−	0.00445682i	−0.000876727	−	0.000722991i
$39$		0			0
$40$	0.759842	−	0.298821i	0.120142	−	0.0472478i
$41$	−1.69965	+	9.63917i	−0.265440	+	1.50539i	0.502339	+	0.864671i	$0.332473\pi$
$41$	−1.69965	+	9.63917i	−0.265440	+	1.50539i	−0.767779	+	0.640715i	$0.778638\pi$
$42$		0			0
$43$	3.57494	+	4.26045i	0.545173	+	0.649712i	0.966339	−	0.257271i	$-0.0828234\pi$
$43$	3.57494	+	4.26045i	0.545173	+	0.649712i	−0.421166	+	0.906984i	$0.638379\pi$
$44$	9.46489	+	1.50269i	1.42689	+	0.226539i
$45$		0			0
$46$	1.80091	+	2.10938i	0.265529	+	0.311012i
$47$	−3.48835	−	1.26966i	−0.508829	−	0.185199i	0.0748320	−	0.997196i	$-0.476158\pi$
$47$	−3.48835	−	1.26966i	−0.508829	−	0.185199i	−0.583661	+	0.811998i	$0.698380\pi$
$48$		0			0
$49$	0.626015	+	0.525289i	0.0894307	+	0.0750413i
$50$	5.99175	−	3.52791i	0.847362	−	0.498922i
$51$		0			0
$52$	−5.52782	+	3.31866i	−0.766571	+	0.460215i
$53$			0.865665i			0.118908i	0.998231	+	0.0594541i	$0.0189360\pi$
$53$			0.865665i			0.118908i	−0.998231	+	0.0594541i	$0.981064\pi$
$54$		0			0
$55$	−1.38324			−0.186516
$56$	−5.23675	−	5.92571i	−0.699790	−	0.791857i
$57$		0			0
$58$	5.74234	+	9.75270i	0.754007	+	1.28059i
$59$	3.57109	−	4.25586i	0.464916	−	0.554066i	−0.481739	−	0.876315i	$-0.659995\pi$
$59$	3.57109	−	4.25586i	0.464916	−	0.554066i	0.946655	+	0.322249i	$0.104439\pi$
$60$		0			0
$61$	2.43327	−	6.68534i	0.311548	−	0.855970i	−0.680797	−	0.732472i	$-0.738366\pi$
$61$	2.43327	−	6.68534i	0.311548	−	0.855970i	0.992345	−	0.123498i	$-0.0394113\pi$
$62$	5.33519	+	6.24905i	0.677569	+	0.793630i
$63$		0			0
$64$	4.34964	+	6.71421i	0.543705	+	0.839276i
$65$	0.712888	−	0.598184i	0.0884228	−	0.0741956i
$66$		0			0
$67$	−0.224950	−	0.0396647i	−0.0274820	−	0.00484582i	0.159890	−	0.987135i	$-0.448886\pi$
$67$	−0.224950	−	0.0396647i	−0.0274820	−	0.00484582i	−0.187372	+	0.982289i	$0.559997\pi$
$68$	−2.14457	−	11.0548i	−0.260068	−	1.34059i
$69$		0			0
$70$	0.880614	+	0.726197i	0.105254	+	0.0867971i
$71$	−0.429923	+	0.744648i	−0.0510224	+	0.0883735i	−0.890409	−	0.455162i	$-0.849581\pi$
$71$	−0.429923	+	0.744648i	−0.0510224	+	0.0883735i	0.839386	+	0.543535i	$0.182915\pi$
$72$		0			0
$73$	−2.02670	−	3.51035i	−0.237208	−	0.410856i	0.722704	−	0.691157i	$-0.242899\pi$
$73$	−2.02670	−	3.51035i	−0.237208	−	0.410856i	−0.959912	+	0.280301i	$0.909566\pi$
$74$	−2.21446	+	13.2180i	−0.257426	+	1.53657i
$75$		0			0
$76$	−0.00322880	+	0.00936583i	−0.000370369	+	0.00107433i
$77$	4.58214	+	12.5893i	0.522184	+	1.43469i
$78$		0			0
$79$	−0.797428	−	4.52244i	−0.0897176	−	0.508814i	−0.996239	−	0.0866531i	$-0.972383\pi$
$79$	−0.797428	−	4.52244i	−0.0897176	−	0.508814i	0.906521	−	0.422161i	$-0.138728\pi$
$80$	−0.772001	−	0.858675i	−0.0863124	−	0.0960028i
$81$		0			0
$82$	13.6108	−	2.52001i	1.50306	−	0.278288i
$83$	4.00250	−	0.705749i	0.439332	−	0.0774660i	0.0503925	−	0.998729i	$-0.483953\pi$
$83$	4.00250	−	0.705749i	0.439332	−	0.0774660i	0.388939	+	0.921263i	$0.372842\pi$
$84$		0			0
$85$	0.555903	+	1.52733i	0.0602961	+	0.165662i
$86$	3.87434	−	6.84491i	0.417781	−	0.738105i
$87$		0			0
$88$	−2.69465	−	13.2824i	−0.287250	−	1.41591i
$89$	1.77889	+	3.08112i	0.188562	+	0.326599i	0.944771	−	0.327731i	$-0.106284\pi$
$89$	1.77889	+	3.08112i	0.188562	+	0.326599i	−0.756209	+	0.654330i	$0.772951\pi$
$90$		0			0
$91$	−7.80581	−	4.50669i	−0.818272	−	0.472429i
$92$	1.90291	−	3.42994i	0.198392	−	0.357596i
$93$		0			0
$94$	0.0448395	+	5.24969i	0.00462484	+	0.541464i
$95$	0.000248300	−	0.00140818i	2.54751e−5	−	0.000144476i
$96$		0			0
$97$	6.04757	−	5.07452i	0.614038	−	0.515239i	−0.281885	−	0.959448i	$-0.590960\pi$
$97$	6.04757	−	5.07452i	0.614038	−	0.515239i	0.895923	+	0.444209i	$0.146515\pi$
$98$	0.385983	−	1.08934i	0.0389902	−	0.110040i
$99$		0			0
$100$	−7.63964	−	6.19115i	−0.763964	−	0.619115i
$101$	6.35260	−	17.4536i	0.632107	−	1.73670i	−0.0430976	−	0.999071i	$-0.513723\pi$
$101$	6.35260	−	17.4536i	0.632107	−	1.73670i	0.675205	−	0.737630i	$-0.264055\pi$
$102$		0			0
$103$	−3.47298	−	2.91418i	−0.342203	−	0.287143i	0.455447	−	0.890263i	$-0.349479\pi$
$103$	−3.47298	−	2.91418i	−0.342203	−	0.287143i	−0.797650	+	0.603120i	$0.793924\pi$
$104$	7.13278	+	5.68015i	0.699427	+	0.556985i
$105$		0			0
$106$	1.14679	−	0.428523i	0.111386	−	0.0416219i
$107$			3.74905i			0.362434i	0.983443	+	0.181217i	$0.0580036\pi$
$107$			3.74905i			0.362434i	−0.983443	+	0.181217i	$0.941996\pi$
$108$		0			0
$109$			16.8471i			1.61366i	0.590782	+	0.806831i	$0.298819\pi$
$109$			16.8471i			1.61366i	−0.590782	+	0.806831i	$0.701181\pi$
$110$	0.684733	+	1.83244i	0.0652868	+	0.174716i
$111$		0			0
$112$	−5.25776	+	9.87073i	−0.496811	+	0.932696i
$113$	−4.67369	−	3.92169i	−0.439664	−	0.368921i	0.395920	−	0.918285i	$-0.370426\pi$
$113$	−4.67369	−	3.92169i	−0.439664	−	0.368921i	−0.835583	+	0.549364i	$0.814870\pi$
$114$		0			0
$115$	−0.193635	+	0.532007i	−0.0180565	+	0.0496099i
$116$	10.0773	−	12.4350i	0.935651	−	1.15456i
$117$		0			0
$118$	−7.40570	−	2.62404i	−0.681750	−	0.241563i
$119$	12.0593	−	10.1189i	1.10547	−	0.927602i
$120$		0			0
$121$	−2.07693	+	11.7789i	−0.188812	+	1.07081i
$122$	−10.0609	+	0.0859337i	−0.910871	+	0.00778007i
$123$		0			0
$124$	5.63737	−	10.1612i	0.506250	−	0.912501i
$125$	2.47914	+	1.43133i	0.221741	+	0.128022i
$126$		0			0
$127$	−10.6004	−	18.3604i	−0.940632	−	1.62922i	−0.764270	−	0.644896i	$-0.776901\pi$
$127$	−10.6004	−	18.3604i	−0.940632	−	1.62922i	−0.176362	−	0.984325i	$-0.556433\pi$
$128$	6.74146	−	9.08586i	0.595866	−	0.803084i
$129$		0			0
$130$	−1.14534	−	0.648281i	−0.100453	−	0.0568580i
$131$	3.62600	+	9.96234i	0.316805	+	0.870414i	0.991239	+	0.132079i	$0.0421653\pi$
$131$	3.62600	+	9.96234i	0.316805	+	0.870414i	−0.674435	+	0.738335i	$0.735613\pi$
$132$		0			0
$133$	−0.0136389	+	0.00240490i	−0.00118264	+	0.000208532i
$134$	0.0588095	+	0.317636i	0.00508037	+	0.0274396i
$135$		0			0
$136$	−13.5832	+	8.31338i	−1.16475	+	0.712866i
$137$	2.46640	+	13.9877i	0.210719	+	1.19505i	0.888182	+	0.459491i	$0.151968\pi$
$137$	2.46640	+	13.9877i	0.210719	+	1.19505i	−0.677463	+	0.735557i	$0.736921\pi$
$138$		0			0
$139$	−3.33532	−	9.16372i	−0.282898	−	0.777257i	−0.997013	−	0.0772283i	$-0.975393\pi$
$139$	−3.33532	−	9.16372i	−0.282898	−	0.777257i	0.714115	−	0.700028i	$-0.246829\pi$
$140$	0.526103	−	1.52607i	0.0444638	−	0.128977i
$141$		0			0
$142$	1.19929	+	0.200921i	0.100642	+	0.0168609i
$143$	−7.72366	−	13.3778i	−0.645885	−	1.11871i
$144$		0			0
$145$	−1.15509	+	2.00068i	−0.0959254	+	0.166148i
$146$	−3.64707	+	4.42257i	−0.301833	+	0.366015i
$147$		0			0
$148$	18.6068	−	3.60962i	1.52947	−	0.296709i
$149$	−1.13973	−	0.200964i	−0.0933699	−	0.0164636i	0.126768	−	0.991932i	$-0.459540\pi$
$149$	−1.13973	−	0.200964i	−0.0933699	−	0.0164636i	−0.220138	+	0.975469i	$0.570651\pi$
$150$		0			0
$151$	−15.9973	+	13.4234i	−1.30184	+	1.09238i	−0.312022	+	0.950075i	$0.601006\pi$
$151$	−15.9973	+	13.4234i	−1.30184	+	1.09238i	−0.989823	+	0.142303i	$0.954549\pi$
$152$	0.0140057		0.000358952i	0.00113601		2.91149e-5i
$153$		0			0
$154$	14.4094	−	12.3022i	1.16114	−	0.991338i
$155$	−0.573643	+	1.57607i	−0.0460761	+	0.126593i
$156$		0			0
$157$	12.0447	−	14.3543i	0.961268	−	1.14560i	−0.0280180	−	0.999607i	$-0.508920\pi$
$157$	12.0447	−	14.3543i	0.961268	−	1.14560i	0.989286	−	0.145988i	$-0.0466360\pi$
$158$	−5.59634	+	3.29510i	−0.445221	+	0.262144i
$159$		0			0
$160$	−0.755368	+	1.44777i	−0.0597171	+	0.114456i
$161$	5.48343			0.432155
$162$		0			0
$163$		−	11.5772i		−	0.906795i	−0.891308	−	0.453397i	$-0.850212\pi$
$163$		−	11.5772i		−	0.906795i	0.891308	−	0.453397i	$-0.149788\pi$
$164$	−10.0760	−	16.7834i	−0.786806	−	1.31057i
$165$		0			0
$166$	−2.91627	−	4.95294i	−0.226346	−	0.384422i
$167$	−7.59855	−	6.37594i	−0.587994	−	0.493385i	0.299568	−	0.954075i	$-0.403158\pi$
$167$	−7.59855	−	6.37594i	−0.587994	−	0.493385i	−0.887561	+	0.460690i	$0.847602\pi$
$168$		0			0
$169$	−2.45017	−	0.891789i	−0.188475	−	0.0685991i
$170$	1.74814	−	1.49249i	0.134076	−	0.114469i
$171$		0			0
$172$	−10.9856	−	1.74413i	−0.837648	−	0.132989i
$173$	−12.8453	−	15.3084i	−0.976609	−	1.16388i	−0.986473	−	0.163926i	$-0.947584\pi$
$173$	−12.8453	−	15.3084i	−0.976609	−	1.16388i	0.00986338	−	0.999951i	$-0.496860\pi$
$174$		0			0
$175$	2.38708	−	13.5378i	0.180446	−	1.02336i
$176$	−16.2620	+	10.1448i	−1.22579	+	0.764696i
$177$		0			0
$178$	3.20112	−	3.88180i	0.239934	−	0.290953i
$179$	−18.6622	−	10.7746i	−1.39488	−	0.805335i	−0.401030	−	0.916065i	$-0.631348\pi$
$179$	−18.6622	−	10.7746i	−1.39488	−	0.805335i	−0.993851	+	0.110730i	$0.964681\pi$
$180$		0			0
$181$	−17.9309	+	10.3524i	−1.33280	+	0.769490i	−0.985727	−	0.168350i	$-0.946156\pi$
$181$	−17.9309	+	10.3524i	−1.33280	+	0.769490i	−0.347068	+	0.937840i	$0.612823\pi$
$182$	−2.10617	+	12.5716i	−0.156120	+	0.931871i
$183$		0			0
$184$	−5.48578	−	0.822977i	−0.404417	−	0.0606706i
$185$	−2.57071	+	0.935664i	−0.189003	+	0.0687914i
$186$		0			0
$187$	26.5696	−	4.68494i	1.94296	−	0.342596i
$188$	6.93231	−	2.65812i	0.505591	−	0.193863i
$189$		0			0
$190$	−0.00198840		0.000368146i	−0.000144253		2.67081e-5i
$191$	0.173666	+	0.984911i	0.0125661	+	0.0712657i	0.990446	−	0.137902i	$-0.0440358\pi$
$191$	0.173666	+	0.984911i	0.0125661	+	0.0712657i	−0.977880	+	0.209167i	$0.932925\pi$
$192$		0			0
$193$	18.6207	−	6.77739i	1.34035	−	0.487847i	0.430427	−	0.902625i	$-0.358363\pi$
$193$	18.6207	−	6.77739i	1.34035	−	0.487847i	0.909923	+	0.414778i	$0.136141\pi$
$194$	−9.71613	−	5.49950i	−0.697577	−	0.394841i
$195$		0			0
$196$	−1.63417	+	0.0279181i	−0.116726	+	0.00199415i
$197$	5.14676	−	2.97148i	0.366691	−	0.211709i	−0.305321	−	0.952250i	$-0.598764\pi$
$197$	5.14676	−	2.97148i	0.366691	−	0.211709i	0.672012	+	0.740540i	$0.265430\pi$
$198$		0			0
$199$	−4.22572	+	7.31916i	−0.299553	+	0.518842i	−0.976034	−	0.217619i	$-0.930171\pi$
$199$	−4.22572	+	7.31916i	−0.299553	+	0.518842i	0.676480	+	0.736461i	$0.263504\pi$
$200$	−4.41992	+	13.1853i	−0.312535	+	0.932345i
$201$		0			0
$202$	−26.2663	+	0.224350i	−1.84809	+	0.0157852i
$203$	22.0353	+	3.88542i	1.54658	+	0.272703i
$204$		0			0
$205$	1.81619	+	2.16445i	0.126848	+	0.151172i
$206$	−2.14134	+	6.04341i	−0.149194	+	0.421064i
$207$		0			0
$208$	3.99388	−	12.2609i	0.276926	−	0.850142i
$209$	−0.0223038	−	0.00811792i	−0.00154279	−	0.000561528i
$210$		0			0
$211$	−2.67743	+	3.19083i	−0.184322	+	0.219666i	−0.850291	−	0.526313i	$-0.823574\pi$
$211$	−2.67743	+	3.19083i	−0.184322	+	0.219666i	0.665969	+	0.745980i	$0.268018\pi$
$212$	−1.13537	−	1.30707i	−0.0779775	−	0.0897701i
$213$		0			0
$214$	4.96654	−	1.85586i	0.339505	−	0.126864i
$215$	1.60549			0.109493
$216$		0			0
$217$	16.2446			1.10276
$218$	22.3182	−	8.33971i	1.51158	−	0.564836i
$219$		0			0
$220$	2.08856	−	1.81420i	0.140811	−	0.122313i
$221$	−11.6673	+	13.9046i	−0.784829	+	0.935323i
$222$		0			0
$223$	13.7266	+	4.99606i	0.919198	+	0.334561i	0.757919	−	0.652348i	$-0.226216\pi$
$223$	13.7266	+	4.99606i	0.919198	+	0.334561i	0.161279	+	0.986909i	$0.448438\pi$
$224$	15.6789	+	2.07896i	1.04759	+	0.138907i
$225$		0			0
$226$	−2.88166	+	8.13277i	−0.191685	+	0.540984i
$227$	13.2187	+	15.7535i	0.877359	+	1.04560i	0.998596	+	0.0529722i	$0.0168695\pi$
$227$	13.2187	+	15.7535i	0.877359	+	1.04560i	−0.121237	+	0.992624i	$0.538686\pi$
$228$		0			0
$229$	11.3156	+	1.99525i	0.747759	+	0.131850i	0.534527	−	0.845151i	$-0.320490\pi$
$229$	11.3156	+	1.99525i	0.747759	+	0.131850i	0.213232	+	0.977002i	$0.431601\pi$
$230$	0.800628	−	0.00683845i	0.0527919	−	0.000450914i
$231$		0			0
$232$	−21.4616	−	7.19424i	−1.40903	−	0.472325i
$233$	2.16566	−	3.75103i	0.141877	−	0.245738i	−0.786326	−	0.617811i	$-0.788020\pi$
$233$	2.16566	−	3.75103i	0.141877	−	0.245738i	0.928203	+	0.372073i	$0.121353\pi$
$234$		0			0
$235$	−0.928049	+	0.535809i	−0.0605392	+	0.0349523i
$236$	0.189797	+	11.1096i	0.0123547	+	0.723176i
$237$		0			0
$238$	−19.3747	−	10.9664i	−1.25587	−	0.710846i
$239$	13.2703	−	4.82998i	0.858382	−	0.312426i	0.124929	−	0.992166i	$-0.460130\pi$
$239$	13.2703	−	4.82998i	0.858382	−	0.312426i	0.733453	+	0.679740i	$0.237907\pi$
$240$		0			0
$241$	2.60609	+	14.7799i	0.167873	+	0.952056i	0.946052	+	0.324014i	$0.105032\pi$
$241$	2.60609	+	14.7799i	0.167873	+	0.952056i	−0.778179	+	0.628042i	$0.783856\pi$
$242$	16.6321	−	3.07939i	1.06915	−	0.197951i
$243$		0			0
$244$	5.09421	+	13.2856i	0.326124	+	0.850524i
$245$	0.232321	−	0.0409644i	0.0148424	−	0.00261712i
$246$		0			0
$247$	0.0150055	−	0.00546154i	0.000954774	−	0.000347509i
$248$	−16.2516	−	2.43807i	−1.03198	−	0.154817i
$249$		0			0
$250$	0.668924	−	3.99278i	0.0423064	−	0.252526i
$251$	−26.0768	+	15.0554i	−1.64595	+	0.950290i	−0.667293	+	0.744795i	$0.732547\pi$
$251$	−26.0768	+	15.0554i	−1.64595	+	0.950290i	−0.978658	+	0.205495i	$0.934120\pi$
$252$		0			0
$253$	8.13857	+	4.69881i	0.511668	+	0.295412i
$254$	−19.0754	+	23.1316i	−1.19690	+	1.45141i
$255$		0			0
$256$	−15.3736	−	4.43302i	−0.960852	−	0.277064i
$257$	0.685637	−	3.88844i	0.0427688	−	0.242554i	−0.955927	−	0.293603i	$-0.905145\pi$
$257$	0.685637	−	3.88844i	0.0427688	−	0.242554i	0.998696	+	0.0510494i	$0.0162566\pi$
$258$		0			0
$259$	17.0316	+	20.2975i	1.05829	+	1.26123i
$260$	−0.291841	+	1.83819i	−0.0180992	+	0.114000i
$261$		0			0
$262$	11.4026	−	9.73510i	0.704457	−	0.601437i
$263$	−12.3951	−	4.51144i	−0.764313	−	0.278187i	−0.0696970	−	0.997568i	$-0.522203\pi$
$263$	−12.3951	−	4.51144i	−0.764313	−	0.278187i	−0.694616	+	0.719381i	$0.744425\pi$
$264$		0			0
$265$	0.191430	+	0.160629i	0.0117594	+	0.00986733i
$266$	0.00993744	+	0.0168776i	0.000609303	+	0.00103483i
$267$		0			0
$268$	0.391676	−	0.235145i	0.0239254	−	0.0143638i
$269$			7.68651i			0.468655i	0.972158	+	0.234327i	$0.0752887\pi$
$269$			7.68651i			0.468655i	−0.972158	+	0.234327i	$0.924711\pi$
$270$		0			0
$271$	21.3410			1.29637			0.648187	−	0.761481i	$-0.275528\pi$
$271$	21.3410			1.29637			0.648187	+	0.761481i	$0.275528\pi$
$272$	17.7371	+	13.8789i	1.07547	+	0.841534i
$273$		0			0
$274$	17.3092	−	10.1916i	1.04569	−	0.615695i
$275$	15.1436	−	18.0475i	0.913195	−	1.08830i
$276$		0			0
$277$	−7.73418	+	21.2495i	−0.464702	+	1.27676i	0.457210	+	0.889359i	$0.348849\pi$
$277$	−7.73418	+	21.2495i	−0.464702	+	1.27676i	−0.921912	+	0.387400i	$0.873373\pi$
$278$	−10.4885	+	8.95470i	−0.629061	+	0.537067i
$279$		0			0
$280$	−2.28209	+	0.0584879i	−0.136381	+	0.00349532i
$281$	24.7061	−	20.7308i	1.47384	−	1.23670i	0.561363	−	0.827570i	$-0.310277\pi$
$281$	24.7061	−	20.7308i	1.47384	−	1.23670i	0.912477	−	0.409129i	$-0.134167\pi$
$282$		0			0
$283$	−20.0970	−	3.54364i	−1.19464	−	0.210648i	−0.459261	−	0.888301i	$-0.651886\pi$
$283$	−20.0970	−	3.54364i	−1.19464	−	0.210648i	−0.735381	+	0.677653i	$0.762997\pi$
$284$	−0.327506	−	1.68822i	−0.0194339	−	0.100177i
$285$		0			0
$286$	−13.8988	+	16.8542i	−0.821851	+	0.996609i
$287$	13.6831	−	23.6998i	0.807687	−	1.39896i
$288$		0			0
$289$	−7.35090	−	12.7321i	−0.432406	−	0.748949i
$290$	3.22219	+	0.539825i	0.189214	+	0.0316996i
$291$		0			0
$292$	7.66417	+	2.64217i	0.448511	+	0.154621i
$293$	1.43710	+	3.94839i	0.0839561	+	0.230667i	0.974566	−	0.224101i	$-0.0719444\pi$
$293$	1.43710	+	3.94839i	0.0839561	+	0.230667i	−0.890610	+	0.454768i	$0.849722\pi$
$294$		0			0
$295$	−0.278490	−	1.57939i	−0.0162143	−	0.0919558i
$296$	−13.9926	−	22.8624i	−0.813303	−	1.32885i
$297$		0			0
$298$	0.297963	+	1.60933i	0.0172605	+	0.0932259i
$299$	−6.22644	+	1.09789i	−0.360084	+	0.0634926i
$300$		0			0
$301$	−5.31837	−	14.6121i	−0.306546	−	0.842228i
$302$	25.7016	+	14.5476i	1.47896	+	0.837118i
$303$		0			0
$304$	−0.00740864	−	0.0183763i	−0.000424915	−	0.00105395i
$305$	−1.02686	−	1.77858i	−0.0587981	−	0.101841i
$306$		0			0
$307$	−16.4700	−	9.50896i	−0.939993	−	0.542705i	−0.0500346	−	0.998747i	$-0.515933\pi$
$307$	−16.4700	−	9.50896i	−0.939993	−	0.542705i	−0.889958	+	0.456043i	$0.849266\pi$
$308$	−23.4303	−	12.9990i	−1.33506	−	0.740685i
$309$		0			0
$310$	2.37186	−	0.0202589i	0.134713	−	0.00115063i
$311$	−3.01498	+	17.0988i	−0.170964	+	0.969585i	0.771736	+	0.635943i	$0.219389\pi$
$311$	−3.01498	+	17.0988i	−0.170964	+	0.969585i	−0.942700	+	0.333642i	$0.891722\pi$
$312$		0			0
$313$	0.579959	−	0.486644i	0.0327812	−	0.0275067i	−0.626250	−	0.779622i	$-0.715411\pi$
$313$	0.579959	−	0.486644i	0.0327812	−	0.0275067i	0.659031	+	0.752116i	$0.270967\pi$
$314$	−24.9781	−	8.85044i	−1.40960	−	0.499459i
$315$		0			0
$316$	7.13548	+	5.78258i	0.401402	+	0.325296i
$317$	6.72476	−	18.4761i	0.377700	−	1.03772i	−0.594607	−	0.804016i	$-0.702692\pi$
$317$	6.72476	−	18.4761i	0.377700	−	1.03772i	0.972307	−	0.233706i	$-0.0750853\pi$
$318$		0			0
$319$	29.3756	+	24.6491i	1.64472	+	1.38008i
$320$	2.29185	+	0.283994i	0.128118	+	0.0158757i
$321$		0			0
$322$	−2.71442	−	7.26415i	−0.151269	−	0.404815i
$323$			0.0278897i			0.00155182i
$324$		0			0
$325$			15.8501i			0.879207i
$326$	−15.3368	+	5.73096i	−0.849428	+	0.317409i
$327$		0			0
$328$	−17.2459	+	21.6564i	−0.952247	+	1.19577i
$329$	7.95087	+	6.67157i	0.438345	+	0.367815i
$330$		0			0
$331$	−8.42157	+	23.1381i	−0.462891	+	1.27178i	0.460409	+	0.887707i	$0.347703\pi$
$331$	−8.42157	+	23.1381i	−0.462891	+	1.27178i	−0.923301	+	0.384077i	$0.874520\pi$
$332$	−5.11777	+	6.31513i	−0.280874	+	0.346588i
$333$		0			0
$334$	−4.68505	+	13.2224i	−0.256355	+	0.723497i
$335$	−0.0505119	+	0.0423845i	−0.00275976	+	0.00231571i
$336$		0			0
$337$	−1.71929	+	9.75056i	−0.0936555	+	0.531147i	0.901496	+	0.432788i	$0.142470\pi$
$337$	−1.71929	+	9.75056i	−0.0936555	+	0.531147i	−0.995151	+	0.0983585i	$0.968641\pi$
$338$	0.0314946	+	3.68731i	0.00171308	+	0.200563i
$339$		0			0
$340$	−2.84254	−	1.57703i	−0.154159	−	0.0855263i
$341$	24.1105	+	13.9202i	1.30566	+	0.753822i
$342$		0			0
$343$	8.64332	+	14.9707i	0.466695	+	0.808340i
$344$	3.12761	+	15.4166i	0.168629	+	0.831207i
$345$		0			0
$346$	−13.9211	+	24.5948i	−0.748401	+	1.32222i
$347$	−7.12971	−	19.5887i	−0.382743	−	1.05158i	−0.970196	−	0.242320i	$-0.922092\pi$
$347$	−7.12971	−	19.5887i	−0.382743	−	1.05158i	0.587453	−	0.809258i	$-0.300131\pi$
$348$		0			0
$349$	−14.8725	+	2.62242i	−0.796107	+	0.140375i	−0.556885	−	0.830590i	$-0.688004\pi$
$349$	−14.8725	+	2.62242i	−0.796107	+	0.140375i	−0.239222	+	0.970965i	$0.576892\pi$
$350$	−19.1158	+	3.53924i	−1.02178	+	0.189180i
$351$		0			0
$352$	21.4894	+	16.5211i	1.14539	+	0.880575i
$353$	0.616217	+	3.49474i	0.0327979	+	0.186006i	0.996805	−	0.0798689i	$-0.0254502\pi$
$353$	0.616217	+	3.49474i	0.0327979	+	0.186006i	−0.964007	+	0.265875i	$0.914339\pi$
$354$		0			0
$355$	0.0848941	+	0.233245i	0.00450571	+	0.0123793i
$356$	−6.72703	−	2.31909i	−0.356532	−	0.122912i
$357$		0			0
$358$	−5.03545	+	30.0564i	−0.266132	+	1.58853i
$359$	11.0808	+	19.1925i	0.584823	+	1.01294i	0.994897	+	0.100891i	$0.0321694\pi$
$359$	11.0808	+	19.1925i	0.584823	+	1.01294i	−0.410074	+	0.912052i	$0.634497\pi$
$360$		0			0
$361$	−9.49999	+	16.4545i	−0.499999	+	0.866024i
$362$	22.5905	+	18.6292i	1.18733	+	0.979131i
$363$		0			0
$364$	17.6968	−	3.43310i	0.927566	−	0.179943i
$365$	−1.15233	−	0.203187i	−0.0603158	−	0.0106353i
$366$		0			0
$367$	13.2887	−	11.1505i	0.693664	−	0.582053i	−0.226299	−	0.974058i	$-0.572663\pi$
$367$	13.2887	−	11.1505i	0.693664	−	0.582053i	0.919963	+	0.392005i	$0.128218\pi$
$368$	1.62535	+	7.67466i	0.0847271	+	0.400069i
$369$		0			0
$370$	2.51208	+	2.94237i	0.130597	+	0.152967i
$371$	0.827803	−	2.27437i	0.0429774	−	0.118079i
$372$		0			0
$373$	10.6639	−	12.7087i	0.552156	−	0.658034i	−0.415711	−	0.909497i	$-0.636467\pi$
$373$	10.6639	−	12.7087i	0.552156	−	0.658034i	0.967867	+	0.251463i	$0.0809116\pi$
$374$	−19.3589	−	32.8788i	−1.00102	−	1.70012i
$375$		0			0
$376$	−6.95298	−	7.86773i	−0.358573	−	0.405747i
$377$	−25.7991			−1.32872
$378$		0			0
$379$			9.64915i			0.495644i	0.968806	+	0.247822i	$0.0797148\pi$
$379$			9.64915i			0.495644i	−0.968806	+	0.247822i	$0.920285\pi$
$380$	0.00147200	+	0.00245188i	7.55120e−5	+	0.000125779i
$381$		0			0
$382$	1.21879	−	0.717617i	0.0623586	−	0.0367165i
$383$	9.22574	+	7.74132i	0.471414	+	0.395563i	0.847310	−	0.531099i	$-0.178221\pi$
$383$	9.22574	+	7.74132i	0.471414	+	0.395563i	−0.375896	+	0.926662i	$0.622665\pi$
$384$		0			0
$385$	3.63420	+	1.32274i	0.185216	+	0.0674130i
$386$	−18.1960	−	21.3128i	−0.926152	−	1.08479i
$387$		0			0
$388$	−2.47574	+	15.5938i	−0.125687	+	0.791654i
$389$	1.86623	+	2.22408i	0.0946216	+	0.112766i	0.811277	−	0.584661i	$-0.198773\pi$
$389$	1.86623	+	2.22408i	0.0946216	+	0.112766i	−0.716656	+	0.697427i	$0.754328\pi$
$390$		0			0
$391$	1.91751	−	10.8748i	0.0969729	−	0.549960i
$392$	0.845935	+	2.15104i	0.0427262	+	0.108644i
$393$		0			0
$394$	−6.48422	−	5.34720i	−0.326670	−	0.269388i
$395$	−1.14804	−	0.662821i	−0.0577642	−	0.0333502i
$396$		0			0
$397$	3.53148	−	2.03890i	0.177240	−	0.102330i	−0.408755	−	0.912644i	$-0.634037\pi$
$397$	3.53148	−	2.03890i	0.177240	−	0.102330i	0.585995	+	0.810314i	$0.300704\pi$
$398$	11.7879	+	1.97486i	0.590872	+	0.0989907i
$399$		0			0
$400$	19.6552	−	0.671773i	0.982760	−	0.0335886i
$401$	−2.09322	+	0.761870i	−0.104530	+	0.0380460i	−0.393756	−	0.919215i	$-0.628824\pi$
$401$	−2.09322	+	0.761870i	−0.104530	+	0.0380460i	0.289226	+	0.957261i	$0.406602\pi$
$402$		0			0
$403$	−18.4458	+	3.25249i	−0.918851	+	0.162018i
$404$	13.2996	+	34.6851i	0.661681	+	1.72565i
$405$		0			0
$406$	−5.76078	−	31.1146i	−0.285903	−	1.54419i
$407$	7.88541	+	44.7204i	0.390865	+	2.21671i
$408$		0			0
$409$	17.7345	−	6.45483i	0.876914	−	0.319171i	0.135950	−	0.990716i	$-0.456591\pi$
$409$	17.7345	−	6.45483i	0.876914	−	0.319171i	0.740964	+	0.671545i	$0.234369\pi$
$410$	1.96829	−	3.47744i	0.0972071	−	0.171739i
$411$		0			0
$412$	9.06599	−	0.154883i	0.446649	−	0.00763054i
$413$	−13.4521	+	7.76657i	−0.661934	+	0.382168i
$414$		0			0
$415$	0.586618	−	1.01605i	0.0287959	−	0.0498760i
$416$	−18.2197	+	0.778558i	−0.893293	+	0.0381719i
$417$		0			0
$418$	0.000286694		0.0335654i	1.40227e−5		0.00164174i
$419$	−13.5715	−	2.39303i	−0.663013	−	0.116907i	−0.167992	−	0.985788i	$-0.553728\pi$
$419$	−13.5715	−	2.39303i	−0.663013	−	0.116907i	−0.495021	+	0.868881i	$0.664839\pi$
$420$		0			0
$421$	−23.8985	−	28.4811i	−1.16474	−	1.38809i	−0.906607	−	0.421977i	$-0.861336\pi$
$421$	−23.8985	−	28.4811i	−1.16474	−	1.38809i	−0.258135	−	0.966109i	$-0.583108\pi$
$422$	5.55243	+	1.96738i	0.270288	+	0.0957705i
$423$		0			0
$424$	−1.16951	+	2.15111i	−0.0567962	+	0.104467i
$425$	−26.0135	−	9.46814i	−1.26184	−	0.459272i
$426$		0			0
$427$	−12.7859	+	15.2376i	−0.618753	+	0.737401i
$428$	−4.91709	−	5.66071i	−0.237677	−	0.273621i
$429$		0			0
$430$	−0.794752	−	2.12686i	−0.0383263	−	0.102566i
$431$	−11.4089			−0.549548			−0.274774	−	0.961509i	$-0.588603\pi$
$431$	−11.4089			−0.549548			−0.274774	+	0.961509i	$0.588603\pi$
$432$		0			0
$433$	−7.51420			−0.361109			−0.180555	−	0.983565i	$-0.557789\pi$
$433$	−7.51420			−0.361109			−0.180555	+	0.983565i	$0.557789\pi$
$434$	−8.04146	−	21.5200i	−0.386003	−	1.03299i
$435$		0			0
$436$	−22.0960	−	25.4376i	−1.05821	−	1.21824i
$437$	−0.00624447	+	0.00744187i	−0.000298713	+	0.000355993i
$438$		0			0
$439$	−19.2063	−	6.99052i	−0.916667	−	0.333639i	−0.159755	−	0.987157i	$-0.551070\pi$
$439$	−19.2063	−	6.99052i	−0.916667	−	0.333639i	−0.756912	+	0.653517i	$0.773293\pi$
$440$	−3.43723	−	1.86874i	−0.163864	−	0.0890888i
$441$		0			0
$442$	24.1956	+	8.57317i	1.15087	+	0.407784i
$443$	18.1395	+	21.6178i	0.861832	+	1.02709i	0.999330	+	0.0365893i	$0.0116493\pi$
$443$	18.1395	+	21.6178i	0.861832	+	1.02709i	−0.137498	+	0.990502i	$0.543906\pi$
$444$		0			0
$445$	1.01143	+	0.178342i	0.0479463	+	0.00845423i
$446$	−0.176442	−	20.6574i	−0.00835476	−	0.978154i
$447$		0			0
$448$	−5.00731	−	21.7997i	−0.236573	−	1.02994i
$449$	5.65025	−	9.78653i	0.266652	−	0.461855i	−0.701343	−	0.712824i	$-0.747416\pi$
$449$	5.65025	−	9.78653i	0.266652	−	0.461855i	0.967995	+	0.250969i	$0.0807492\pi$
$450$		0			0
$451$	40.6172	−	23.4504i	1.91259	−	1.10423i
$452$	12.2004	−	0.208430i	0.573856	−	0.00980373i
$453$		0			0
$454$	14.3258	−	25.3098i	0.672343	−	1.18785i
$455$	−2.44500	+	0.889907i	−0.114623	+	0.0417195i
$456$		0			0
$457$	−6.59891	−	37.4243i	−0.308684	−	1.75063i	−0.605636	−	0.795742i	$-0.707081\pi$
$457$	−6.59891	−	37.4243i	−0.308684	−	1.75063i	0.296952	−	0.954892i	$-0.404030\pi$
$458$	−2.95829	−	15.9781i	−0.138232	−	0.746606i
$459$		0			0
$460$	−0.405388	−	1.05724i	−0.0189013	−	0.0492943i
$461$	7.55207	−	1.33163i	0.351735	−	0.0620204i	0.00501063	−	0.999987i	$-0.498405\pi$
$461$	7.55207	−	1.33163i	0.351735	−	0.0620204i	0.346724	+	0.937967i	$0.387294\pi$
$462$		0			0
$463$	−20.5953	+	7.49607i	−0.957144	+	0.348372i	−0.772914	−	0.634511i	$-0.781202\pi$
$463$	−20.5953	+	7.49607i	−0.957144	+	0.348372i	−0.184231	+	0.982883i	$0.558979\pi$
$464$	1.09344	+	31.9925i	0.0507615	+	1.48522i
$465$		0			0
$466$	−6.04121	−	1.01210i	−0.279854	−	0.0468848i
$467$	−2.10941	+	1.21787i	−0.0976119	+	0.0563563i	−0.548011	−	0.836471i	$-0.684615\pi$
$467$	−2.10941	+	1.21787i	−0.0976119	+	0.0563563i	0.450399	+	0.892827i	$0.351282\pi$
$468$		0			0
$469$	0.553083	+	0.319323i	0.0255390	+	0.0147450i
$470$	1.16922	+	0.964192i	0.0539319	+	0.0444748i
$471$		0			0
$472$	14.6235	−	5.75095i	0.673101	−	0.264709i
$473$	4.62768	−	26.2449i	0.212781	−	1.20674i
$474$		0			0
$475$	0.0156545	+	0.0186563i	0.000718279	+	0.000856012i
$476$	−4.93681	+	31.0951i	−0.226278	+	1.42524i
$477$		0			0
$478$	−12.9676	−	15.1888i	−0.593123	−	0.694719i
$479$	−13.6689	−	4.97509i	−0.624550	−	0.227318i	0.0103076	−	0.999947i	$-0.496719\pi$
$479$	−13.6689	−	4.97509i	−0.624550	−	0.227318i	−0.634857	+	0.772629i	$0.718941\pi$
$480$		0			0
$481$	−23.4034	−	19.6378i	−1.06710	−	0.895405i
$482$	18.2895	−	10.7688i	0.833065	−	0.490505i
$483$		0			0
$484$	−12.3127	−	20.5090i	−0.559668	−	0.932227i
$485$		−	2.27894i		−	0.103481i
$486$		0			0
$487$	2.54679			0.115406			0.0577031	−	0.998334i	$-0.481622\pi$
$487$	2.54679			0.115406			0.0577031	+	0.998334i	$0.481622\pi$
$488$	15.0783	−	13.3252i	0.682563	−	0.603204i
$489$		0			0
$490$	−0.169271	−	0.287487i	−0.00764690	−	0.0129874i
$491$	11.6939	−	13.9362i	0.527738	−	0.628933i	−0.434654	−	0.900597i	$-0.643129\pi$
$491$	11.6939	−	13.9362i	0.527738	−	0.628933i	0.962392	+	0.271664i	$0.0875739\pi$
$492$		0			0
$493$	15.4112	−	42.3419i	0.694085	−	1.90698i
$494$	−0.0146632	−	0.0171748i	−0.000659728	−	0.000772733i
$495$		0			0
$496$	4.81509	+	22.7362i	0.216204	+	1.02088i
$497$	1.84162	−	1.54530i	0.0826080	−	0.0693163i
$498$		0			0
$499$	2.03309	+	0.358488i	0.0910134	+	0.0160481i	0.218969	−	0.975732i	$-0.429731\pi$
$499$	2.03309	+	0.358488i	0.0910134	+	0.0160481i	−0.127956	+	0.991780i	$0.540842\pi$
$500$	−5.62055	+	1.09036i	−0.251359	+	0.0487624i
$501$		0			0
$502$	32.8532	+	27.0923i	1.46631	+	1.20919i
$503$	−15.5785	+	26.9828i	−0.694613	+	1.20310i	0.275699	+	0.961244i	$0.411091\pi$
$503$	−15.5785	+	26.9828i	−0.694613	+	1.20310i	−0.970311	+	0.241860i	$0.922242\pi$
$504$		0			0
$505$	−2.68087	−	4.64340i	−0.119297	−	0.206628i
$506$	2.19595	−	13.1076i	0.0976220	−	0.582702i
$507$		0			0
$508$	40.0863	+	13.8195i	1.77854	+	0.613139i
$509$	0.653669	+	1.79594i	0.0289734	+	0.0796037i	0.953336	−	0.301911i	$-0.0976247\pi$
$509$	0.653669	+	1.79594i	0.0289734	+	0.0796037i	−0.924363	+	0.381515i	$0.875402\pi$
$510$		0			0
$511$	1.96796	+	11.1609i	0.0870574	+	0.493727i
$512$	1.73766	+	22.5606i	0.0767946	+	0.997047i
$513$		0			0
$514$	−5.49060	+	1.01657i	−0.242180	+	0.0448389i
$515$	−1.28886	+	0.227261i	−0.0567939	+	0.0100143i
$516$		0			0
$517$	6.08384	+	16.7152i	0.267567	+	0.735134i
$518$	18.4580	−	32.6103i	0.810998	−	1.43281i
$519$		0			0
$520$	2.57961	−	0.523333i	0.113123	−	0.0229497i
$521$	−4.36155	−	7.55442i	−0.191083	−	0.330965i	0.754527	−	0.656269i	$-0.227867\pi$
$521$	−4.36155	−	7.55442i	−0.191083	−	0.330965i	−0.945609	+	0.325304i	$0.894533\pi$
$522$		0			0
$523$	17.9490	+	10.3629i	0.784855	+	0.453136i	0.838148	−	0.545443i	$-0.183638\pi$
$523$	17.9490	+	10.3629i	0.784855	+	0.453136i	−0.0532932	+	0.998579i	$0.516972\pi$
$524$	−18.5411	−	10.2865i	−0.809972	−	0.449367i
$525$		0			0
$526$	0.159327	+	18.6536i	0.00694698	+	0.813335i
$527$	5.68063	−	32.2165i	0.247452	−	1.40337i
$528$		0			0
$529$	−14.6725	+	12.3117i	−0.637936	+	0.535292i
$530$	0.118030	−	0.333110i	0.00512690	−	0.0144694i
$531$		0			0
$532$	0.0174393	−	0.0215194i	0.000756088	−	0.000932983i
$533$	−10.7920	+	29.6508i	−0.467453	+	1.28432i
$534$		0			0
$535$	0.829049	+	0.695655i	0.0358429	+	0.0300758i
$536$	−0.505395	−	0.402469i	−0.0218298	−	0.0173840i
$537$		0			0
$538$	10.1827	−	3.80499i	0.439006	−	0.164045i
$539$		−	3.91581i		−	0.168666i
$540$		0			0
$541$		−	3.63212i		−	0.156157i	−0.996947	−	0.0780785i	$-0.975122\pi$
$541$		−	3.63212i		−	0.156157i	0.996947	−	0.0780785i	$-0.0248785\pi$
$542$	−10.5643	−	28.2714i	−0.453774	−	1.21436i
$543$		0			0
$544$	9.60582	−	30.3675i	0.411846	−	1.30200i
$545$	3.72551	+	3.12607i	0.159583	+	0.133906i
$546$		0			0
$547$	−3.43081	+	9.42608i	−0.146691	+	0.403030i	−0.991177	−	0.132548i	$-0.957684\pi$
$547$	−3.43081	+	9.42608i	−0.146691	+	0.403030i	0.844486	+	0.535578i	$0.179906\pi$
$548$	−22.0697	−	17.8852i	−0.942770	−	0.764019i
$549$		0			0
$550$	−31.4047	−	11.1276i	−1.33910	−	0.474481i
$551$	−0.0303667	+	0.0254807i	−0.00129367	+	0.00108551i
$552$		0			0
$553$	−2.22955	+	12.6444i	−0.0948101	+	0.537695i
$554$	31.9788	−	0.273142i	1.35865	−	0.0116047i
$555$		0			0
$556$	17.0548	+	9.46189i	0.723283	+	0.401273i
$557$	−9.46379	−	5.46392i	−0.400994	−	0.231514i	0.285919	−	0.958254i	$-0.407701\pi$
$557$	−9.46379	−	5.46392i	−0.400994	−	0.231514i	−0.686913	+	0.726740i	$0.741034\pi$
$558$		0			0
$559$	8.96465	+	15.5272i	0.379164	+	0.656732i
$560$	1.20717	+	2.99424i	0.0510122	+	0.126530i
$561$		0			0
$562$	−39.6932	−	22.4670i	−1.67435	−	0.947714i
$563$	−9.70697	−	26.6697i	−0.409100	−	1.12399i	−0.957665	−	0.287885i	$-0.907048\pi$
$563$	−9.70697	−	26.6697i	−0.409100	−	1.12399i	0.548565	−	0.836108i	$-0.315174\pi$
$564$		0			0
$565$	−1.73445	+	0.305831i	−0.0729690	+	0.0128664i
$566$	5.25403	+	28.3776i	0.220844	+	1.19280i
$567$		0			0
$568$	−2.07434	+	1.26957i	−0.0870372	+	0.0532699i
$569$	2.42865	+	13.7735i	0.101814	+	0.577417i	0.992445	+	0.122690i	$0.0391521\pi$
$569$	2.42865	+	13.7735i	0.101814	+	0.577417i	−0.890631	+	0.454727i	$0.849737\pi$
$570$		0			0
$571$	−5.30577	−	14.5775i	−0.222040	−	0.610049i	0.777790	−	0.628525i	$-0.216341\pi$
$571$	−5.30577	−	14.5775i	−0.222040	−	0.610049i	−0.999829	+	0.0184759i	$0.994119\pi$
$572$	29.2077	+	10.0691i	1.22124	+	0.421012i
$573$		0			0
$574$	−38.1697	−	6.39469i	−1.59317	−	0.266909i
$575$	−4.82133	−	8.35080i	−0.201064	−	0.348252i
$576$		0			0
$577$	−0.198083	+	0.343090i	−0.00824632	+	0.0142830i	−0.870119	−	0.492841i	$-0.835958\pi$
$577$	−0.198083	+	0.343090i	−0.00824632	+	0.0142830i	0.861873	+	0.507125i	$0.169292\pi$
$578$	−13.2280	+	16.0408i	−0.550212	+	0.667208i
$579$		0			0
$580$	−0.879927	−	4.53581i	−0.0365370	−	0.188339i
$581$	−11.1907	−	1.97322i	−0.464268	−	0.0818630i
$582$		0			0
$583$	3.17757	−	2.66630i	0.131602	−	0.110427i
$584$	−0.293735	−	11.4610i	−0.0121548	−	0.474260i
$585$		0			0
$586$	4.51922	−	3.85833i	0.186687	−	0.159386i
$587$	4.01994	−	11.0447i	0.165921	−	0.455864i	−0.828670	−	0.559738i	$-0.810902\pi$
$587$	4.01994	−	11.0447i	0.165921	−	0.455864i	0.994590	+	0.103874i	$0.0331240\pi$
$588$		0			0
$589$	−0.0184992	+	0.0220465i	−0.000762247	+	0.000908411i
$590$	−1.95444	+	1.15076i	−0.0804629	+	0.0473761i
$591$		0			0
$592$	−23.3602	+	29.8540i	−0.960099	+	1.22699i
$593$	14.1087			0.579377			0.289688	−	0.957121i	$-0.406448\pi$
$593$	14.1087			0.579377			0.289688	+	0.957121i	$0.406448\pi$
$594$		0			0
$595$		−	4.54436i		−	0.186301i
$596$	1.98445	−	1.19138i	0.0812864	−	0.0488008i
$597$		0			0
$598$	4.53665	+	7.70497i	0.185517	+	0.315080i
$599$	28.5436	+	23.9509i	1.16626	+	0.978607i	0.999972	−	0.00747033i	$-0.00237790\pi$
$599$	28.5436	+	23.9509i	1.16626	+	0.978607i	0.166286	+	0.986077i	$0.446822\pi$
$600$		0			0
$601$	−11.4635	−	4.17236i	−0.467605	−	0.170194i	0.0974622	−	0.995239i	$-0.468927\pi$
$601$	−11.4635	−	4.17236i	−0.467605	−	0.170194i	−0.565067	+	0.825045i	$0.691150\pi$
$602$	−16.7246	+	14.2788i	−0.681645	+	0.581961i
$603$		0			0
$604$	6.54896	−	41.2494i	0.266473	−	1.67842i
$605$	2.21934	+	2.64491i	0.0902292	+	0.107531i
$606$		0			0
$607$	7.57443	−	42.9567i	0.307436	−	1.74356i	−0.304372	−	0.952553i	$-0.598447\pi$
$607$	7.57443	−	42.9567i	0.307436	−	1.74356i	0.611809	−	0.791006i	$-0.290442\pi$
$608$	−0.0206765	+	0.0189112i	−0.000838541	+	0.000766952i
$609$		0			0
$610$	−1.84785	+	2.24077i	−0.0748172	+	0.0907262i
$611$	−10.3640	−	5.98365i	−0.419282	−	0.242073i
$612$		0			0
$613$	24.6408	−	14.2264i	0.995233	−	0.574598i	0.0883987	−	0.996085i	$-0.471825\pi$
$613$	24.6408	−	14.2264i	0.995233	−	0.574598i	0.906834	+	0.421487i	$0.138492\pi$
$614$	−4.44394	+	26.5257i	−0.179343	+	1.07049i
$615$		0			0
$616$	−5.62184	+	37.4739i	−0.226510	+	1.50987i
$617$	6.84389	−	2.49097i	0.275525	−	0.100283i	−0.200562	−	0.979681i	$-0.564277\pi$
$617$	6.84389	−	2.49097i	0.275525	−	0.100283i	0.476087	+	0.879398i	$0.342055\pi$
$618$		0			0
$619$	−4.70638	+	0.829861i	−0.189165	+	0.0333549i	−0.267428	−	0.963578i	$-0.586174\pi$
$619$	−4.70638	+	0.829861i	−0.189165	+	0.0333549i	0.0782628	+	0.996933i	$0.475063\pi$
$620$	−1.20096	−	3.13208i	−0.0482318	−	0.125788i
$621$		0			0
$622$	24.1441	−	4.47021i	0.968089	−	0.179239i
$623$	−1.72733	−	9.79616i	−0.0692039	−	0.392475i
$624$		0			0
$625$	−22.3242	+	8.12536i	−0.892970	+	0.325014i
$626$	−0.931772	−	0.527400i	−0.0372411	−	0.0210791i
$627$		0			0
$628$	0.640150	+	37.4709i	0.0255448	+	1.49525i
$629$	46.2099	−	26.6793i	1.84251	−	1.06377i
$630$		0			0
$631$	−10.2228	+	17.7064i	−0.406964	+	0.704882i	−0.994548	−	0.104281i	$-0.966746\pi$
$631$	−10.2228	+	17.7064i	−0.406964	+	0.704882i	0.587584	+	0.809163i	$0.300079\pi$
$632$	4.12823	−	12.3152i	0.164212	−	0.489873i
$633$		0			0
$634$	−27.8051	+	0.237493i	−1.10428	+	0.00943205i
$635$	−6.02710	−	1.06274i	−0.239178	−	0.0421736i
$636$		0			0
$637$	1.69340	+	2.01812i	0.0670950	+	0.0799607i
$638$	18.1122	−	51.1171i	0.717069	−	2.02375i
$639$		0			0
$640$	−0.758298	−	3.17670i	−0.0299744	−	0.125570i
$641$	−17.9357	−	6.52806i	−0.708417	−	0.257843i	−0.0374167	−	0.999300i	$-0.511913\pi$
$641$	−17.9357	−	6.52806i	−0.708417	−	0.257843i	−0.671000	+	0.741457i	$0.734135\pi$
$642$		0			0
$643$	−11.9937	+	14.2935i	−0.472984	+	0.563680i	−0.948805	−	0.315862i	$-0.897706\pi$
$643$	−11.9937	+	14.2935i	−0.472984	+	0.563680i	0.475821	+	0.879542i	$0.342151\pi$
$644$	−8.27946	+	7.19183i	−0.326256	+	0.283398i
$645$		0			0
$646$	0.0369468	−	0.0138060i	0.00145365	−	0.000543190i
$647$	−1.28685			−0.0505911			−0.0252955	−	0.999680i	$-0.508053\pi$
$647$	−1.28685			−0.0505911			−0.0252955	+	0.999680i	$0.508053\pi$
$648$		0			0
$649$	−26.6210			−1.04497
$650$	20.9974	−	7.84617i	0.823586	−	0.307752i
$651$		0			0
$652$	15.1841	+	17.4805i	0.594657	+	0.684587i
$653$	−4.80662	+	5.72830i	−0.188097	+	0.224166i	−0.851849	−	0.523787i	$-0.824519\pi$
$653$	−4.80662	+	5.72830i	−0.188097	+	0.224166i	0.663752	+	0.747953i	$0.268963\pi$
$654$		0			0
$655$	2.87585	+	1.04672i	0.112369	+	0.0408989i
$656$	37.2263	+	12.1261i	1.45344	+	0.473445i
$657$		0			0
$658$	4.90228	−	13.8355i	0.191111	−	0.539362i
$659$	15.2256	+	18.1451i	0.593104	+	0.706834i	0.976199	−	0.216875i	$-0.0695864\pi$
$659$	15.2256	+	18.1451i	0.593104	+	0.706834i	−0.383095	+	0.923709i	$0.625142\pi$
$660$		0			0
$661$	4.78633	+	0.843960i	0.186167	+	0.0328262i	0.265954	−	0.963986i	$-0.414313\pi$
$661$	4.78633	+	0.843960i	0.186167	+	0.0328262i	−0.0797873	+	0.996812i	$0.525424\pi$
$662$	34.8210	−	0.297418i	1.35335	−	0.0115595i
$663$		0			0
$664$	10.8994	+	3.65362i	0.422977	+	0.141788i
$665$	−0.00199895	+	0.00346229i	−7.75161e−5	+	0.000134262i
$666$		0			0
$667$	13.5925	−	7.84763i	0.526303	−	0.303861i
$668$	19.8355	−	0.338869i	0.767459	−	0.0131112i
$669$		0			0
$670$	0.0811532	+	0.0459342i	0.00313522	+	0.00177459i
$671$	−32.0343	+	11.6595i	−1.23667	+	0.450111i
$672$		0			0
$673$	−6.24184	−	35.3992i	−0.240605	−	1.36454i	−0.830482	−	0.557046i	$-0.811935\pi$
$673$	−6.24184	−	35.3992i	−0.240605	−	1.36454i	0.589876	−	0.807494i	$-0.299176\pi$
$674$	13.7681	−	2.54913i	0.530328	−	0.0981887i
$675$		0			0
$676$	4.86916	−	1.86702i	0.187275	−	0.0718085i
$677$	−17.6982	+	3.12068i	−0.680199	+	0.119937i	−0.503064	−	0.864249i	$-0.667794\pi$
$677$	−17.6982	+	3.12068i	−0.680199	+	0.119937i	−0.177135	+	0.984187i	$0.556683\pi$
$678$		0			0
$679$	−20.7414	+	7.54926i	−0.795983	+	0.289714i
$680$	−0.682038	+	4.54631i	−0.0261550	+	0.174343i
$681$		0			0
$682$	6.50551	−	38.8311i	0.249109	−	1.48692i
$683$	5.01354	−	2.89457i	0.191838	−	0.110758i	−0.401005	−	0.916076i	$-0.631339\pi$
$683$	5.01354	−	2.89457i	0.191838	−	0.110758i	0.592843	+	0.805318i	$0.298006\pi$
$684$		0			0
$685$	3.55083	+	2.05007i	0.135670	+	0.0783293i
$686$	15.5537	−	18.8610i	0.593843	−	0.720117i
$687$		0			0
$688$	18.8748	−	11.7748i	0.719596	−	0.448911i
$689$	−0.484598	+	2.74829i	−0.0184617	+	0.104702i
$690$		0			0
$691$	−8.42802	−	10.0441i	−0.320617	−	0.382097i	0.581530	−	0.813525i	$-0.302454\pi$
$691$	−8.42802	−	10.0441i	−0.320617	−	0.382097i	−0.902147	+	0.431428i	$0.858010\pi$
$692$	39.4731	+	6.26693i	1.50054	+	0.238233i
$693$		0			0
$694$	−22.4207	+	19.1419i	−0.851079	+	0.726617i
$695$	−2.64531	−	0.962815i	−0.100342	−	0.0365217i
$696$		0			0
$697$	−42.2167	−	35.4240i	−1.59907	−	1.34178i
$698$	10.8363	+	18.4041i	0.410159	+	0.696607i
$699$		0			0
$700$	14.1513	+	23.5716i	0.534871	+	0.890923i
$701$		−	3.89204i		−	0.147000i	−0.997295	−	0.0735002i	$-0.976583\pi$
$701$		−	3.89204i		−	0.147000i	0.997295	−	0.0735002i	$-0.0234170\pi$
$702$		0			0
$703$	−0.0469423			−0.00177046
$704$	11.2485	−	36.6463i	0.423944	−	1.38116i
$705$		0			0
$706$	4.32461	−	2.54631i	0.162759	−	0.0958315i
$707$	−33.3805	+	39.7814i	−1.25540	+	1.49613i
$708$		0			0
$709$	−10.4928	+	28.8286i	−0.394064	+	1.08268i	0.571065	+	0.820905i	$0.306531\pi$
$709$	−10.4928	+	28.8286i	−0.394064	+	1.08268i	−0.965128	+	0.261777i	$0.915692\pi$
$710$	0.266965	−	0.227924i	0.0100190	−	0.00855385i
$711$		0			0
$712$	0.257818	+	10.0596i	0.00966214	+	0.377000i
$713$	8.72901	−	7.32451i	0.326904	−	0.274305i
$714$		0			0
$715$	−4.39147	−	0.774335i	−0.164232	−	0.0289585i
$716$	42.3098	−	8.20790i	1.58119	−	0.306744i
$717$		0			0
$718$	19.9400	−	24.1800i	0.744154	−	0.902390i
$719$	−10.3301	+	17.8922i	−0.385246	+	0.667266i	−0.991803	−	0.127774i	$-0.959217\pi$
$719$	−10.3301	+	17.8922i	−0.385246	+	0.667266i	0.606557	+	0.795040i	$0.292550\pi$
$720$		0			0
$721$	6.33789	+	10.9775i	0.236035	+	0.408825i
$722$	26.5007	+	4.43975i	0.986254	+	0.165230i
$723$		0			0
$724$	13.4962	−	39.1486i	0.501582	−	1.45495i
$725$	−13.4575	−	36.9742i	−0.499799	−	1.37319i
$726$		0			0
$727$	5.27477	+	29.9147i	0.195630	+	1.10947i	0.911518	+	0.411259i	$0.134911\pi$
$727$	5.27477	+	29.9147i	0.195630	+	1.10947i	−0.715888	+	0.698215i	$0.753978\pi$
$728$	−13.3083	−	21.7443i	−0.493239	−	0.805899i
$729$		0			0
$730$	0.301258	+	1.62713i	0.0111501	+	0.0602227i
$731$	−30.8386	+	5.43768i	−1.14061	+	0.201120i
$732$		0			0
$733$	12.3847	+	34.0267i	0.457439	+	1.25680i	0.927385	+	0.374108i	$0.122051\pi$
$733$	12.3847	+	34.0267i	0.457439	+	1.25680i	−0.469946	+	0.882695i	$0.655727\pi$
$734$	−21.3498	−	12.0844i	−0.788036	−	0.446042i
$735$		0			0
$736$	9.36239	−	5.95230i	0.345102	−	0.219405i
$737$	0.547262	+	0.947886i	0.0201587	+	0.0349158i
$738$		0			0
$739$	4.81815	+	2.78176i	0.177239	+	0.102329i	0.585995	−	0.810315i	$-0.300704\pi$
$739$	4.81815	+	2.78176i	0.177239	+	0.102329i	−0.408756	+	0.912644i	$0.634037\pi$
$740$	2.65436	−	4.78441i	0.0975762	−	0.175878i
$741$		0			0
$742$	−3.42275	+	0.0292349i	−0.125653	+	0.00107325i
$743$	−6.80955	+	38.6189i	−0.249818	+	1.41679i	0.559214	+	0.829024i	$0.311103\pi$
$743$	−6.80955	+	38.6189i	−0.249818	+	1.41679i	−0.809032	+	0.587765i	$0.800008\pi$
$744$		0			0
$745$	−0.255922	+	0.214744i	−0.00937627	+	0.00786762i
$746$	−22.1147	−	7.83586i	−0.809678	−	0.286891i
$747$		0			0
$748$	−33.9730	+	41.9214i	−1.24218	+	1.53280i
$749$	3.58507	−	9.84991i	0.130996	−	0.359908i
$750$		0			0
$751$	20.3773	+	17.0986i	0.743579	+	0.623937i	0.933796	−	0.357805i	$-0.116475\pi$
$751$	20.3773	+	17.0986i	0.743579	+	0.623937i	−0.190217	+	0.981742i	$0.560919\pi$
$752$	−6.98087	+	13.1056i	−0.254566	+	0.477913i
$753$		0			0
$754$	12.7711	+	34.1772i	0.465096	+	1.24466i
$755$			6.02836i			0.219394i
$756$		0			0
$757$		−	9.99796i		−	0.363382i	−0.983356	−	0.181691i	$-0.941843\pi$
$757$		−	9.99796i		−	0.363382i	0.983356	−	0.181691i	$-0.0581571\pi$
$758$	12.7827	−	4.77655i	0.464288	−	0.173492i
$759$		0			0
$760$	0.00251945	−	0.00316376i	9.13899e−5	−	0.000114762i
$761$	−36.4687	−	30.6009i	−1.32199	−	1.10928i	−0.985879	−	0.167460i	$-0.946444\pi$
$761$	−36.4687	−	30.6009i	−1.32199	−	1.10928i	−0.336112	−	0.941822i	$-0.609112\pi$
$762$		0			0
$763$	16.1103	−	44.2627i	0.583232	−	1.60242i
$764$	−1.55399	−	1.25935i	−0.0562213	−	0.0455617i
$765$		0			0
$766$	5.68833	−	16.0539i	0.205528	−	0.580051i
$767$	13.7198	−	11.5123i	0.495395	−	0.415685i
$768$		0			0
$769$	−7.87549	+	44.6641i	−0.283998	+	1.61063i	0.424847	+	0.905265i	$0.360328\pi$
$769$	−7.87549	+	44.6641i	−0.283998	+	1.61063i	−0.708844	+	0.705365i	$0.750783\pi$
$770$	−0.0467141	−	5.46917i	−0.00168346	−	0.197095i
$771$		0			0
$772$	−19.2266	+	34.6554i	−0.691981	+	1.24728i
$773$	7.37741	+	4.25935i	0.265347	+	0.153198i	0.626771	−	0.779203i	$-0.284376\pi$
$773$	7.37741	+	4.25935i	0.265347	+	0.153198i	−0.361424	+	0.932401i	$0.617709\pi$
$774$		0			0
$775$	−14.2832	−	24.7392i	−0.513068	−	0.888659i
$776$	21.8834	−	4.43954i	0.785567	−	0.159370i
$777$		0			0
$778$	2.02252	−	3.57325i	0.0725110	−	0.128107i
$779$	0.0165822	+	0.0455592i	0.000594118	+	0.00163233i
$780$		0			0
$781$	4.05754	−	0.715454i	0.145190	−	0.0256010i
$782$	−15.3555	+	2.84303i	−0.549112	+	0.101667i
$783$		0			0
$784$	2.43083	−	2.18546i	0.0868153	−	0.0780523i
$785$	−0.939296	−	5.32701i	−0.0335249	−	0.190129i
$786$		0			0
$787$	6.01089	+	16.5148i	0.214265	+	0.588688i	0.999536	−	0.0304642i	$-0.00969856\pi$
$787$	6.01089	+	16.5148i	0.214265	+	0.588688i	−0.785271	+	0.619152i	$0.787476\pi$
$788$	−3.87385	+	11.2369i	−0.138000	+	0.400299i
$789$		0			0
$790$	−0.309765	+	1.84897i	−0.0110209	+	0.0657835i
$791$	8.52906	+	14.7728i	0.303259	+	0.525259i
$792$		0			0
$793$	11.4675	−	19.8623i	0.407224	−	0.705332i
$794$	−4.44919	−	3.66902i	−0.157896	−	0.130208i
$795$		0			0
$796$	−3.21907	−	16.5935i	−0.114097	−	0.588142i
$797$	14.0527	+	2.47787i	0.497773	+	0.0877708i	0.416898	−	0.908953i	$-0.363117\pi$
$797$	14.0527	+	2.47787i	0.497773	+	0.0877708i	0.0808752	+	0.996724i	$0.474228\pi$
$798$		0			0
$799$	16.0115	−	13.4352i	0.566444	−	0.475303i
$800$	−10.6197	−	25.7056i	−0.375463	−	0.908830i
$801$		0			0
$802$	2.04547	+	2.39584i	0.0722282	+	0.0846001i
$803$	−6.64299	+	18.2515i	−0.234426	+	0.644080i
$804$		0			0
$805$	1.01748	−	1.21258i	0.0358614	−	0.0427379i
$806$	13.4398	+	22.8260i	0.473397	+	0.804010i
$807$		0			0
$808$	39.3654	−	34.7885i	1.38487	−	1.22386i
$809$	41.9742			1.47573			0.737867	−	0.674946i	$-0.235833\pi$
$809$	41.9742			1.47573			0.737867	+	0.674946i	$0.235833\pi$
$810$		0			0
$811$		−	34.8911i		−	1.22519i	−0.790397	−	0.612595i	$-0.790125\pi$
$811$		−	34.8911i		−	1.22519i	0.790397	−	0.612595i	$-0.209875\pi$
$812$	−38.3672	+	23.0340i	−1.34643	+	0.808334i
$813$		0			0
$814$	55.3397	−	32.5838i	1.93966	−	1.14206i
$815$	−2.56013	−	2.14820i	−0.0896775	−	0.0752483i
$816$		0			0
$817$	0.0258874	+	0.00942225i	0.000905686	+	0.000329643i
$818$	−17.3300	−	20.2984i	−0.605928	−	0.709718i
$819$		0			0
$820$	−5.58108	−	0.886079i	−0.194900	−	0.0309432i
$821$	−2.36456	−	2.81797i	−0.0825236	−	0.0983478i	0.723203	−	0.690636i	$-0.242669\pi$
$821$	−2.36456	−	2.81797i	−0.0825236	−	0.0983478i	−0.805726	+	0.592288i	$0.798225\pi$
$822$		0			0
$823$	−4.05525	+	22.9985i	−0.141357	+	0.801676i	0.828863	+	0.559452i	$0.188988\pi$
$823$	−4.05525	+	22.9985i	−0.141357	+	0.801676i	−0.970220	+	0.242225i	$0.922123\pi$
$824$	−4.69305	−	11.9335i	−0.163490	−	0.415722i
$825$		0			0
$826$	16.9478	+	13.9760i	0.589690	+	0.486287i
$827$	17.6991	+	10.2186i	0.615456	+	0.355334i	0.775098	−	0.631841i	$-0.217701\pi$
$827$	17.6991	+	10.2186i	0.615456	+	0.355334i	−0.159642	+	0.987175i	$0.551034\pi$
$828$		0			0
$829$	−18.2976	+	10.5641i	−0.635503	+	0.366908i	−0.782880	−	0.622173i	$-0.786250\pi$
$829$	−18.2976	+	10.5641i	−0.635503	+	0.366908i	0.147377	+	0.989080i	$0.452917\pi$
$830$	−1.63640	−	0.274152i	−0.0568003	−	0.00951594i
$831$		0			0
$832$	10.0505	+	23.7510i	0.348440	+	0.823419i
$833$	−4.32373	+	1.57371i	−0.149808	+	0.0545258i
$834$		0			0
$835$	−2.81990	+	0.497224i	−0.0975866	+	0.0172072i
$836$	0.0443238	−	0.0169954i	0.00153297	−	0.000587799i
$837$		0			0
$838$	3.54806	+	19.1634i	0.122566	+	0.661990i
$839$	5.53919	+	31.4143i	0.191234	+	1.08454i	0.917680	+	0.397320i	$0.130060\pi$
$839$	5.53919	+	31.4143i	0.191234	+	1.08454i	−0.726446	+	0.687223i	$0.758829\pi$
$840$		0			0
$841$	32.9314	−	11.9860i	1.13557	−	0.413312i
$842$	−25.9000	+	45.7583i	−0.892572	+	1.57693i
$843$		0			0
$844$	−0.142300	−	8.32946i	−0.00489817	−	0.286712i
$845$	−0.651848	+	0.376345i	−0.0224242	+	0.0129466i
$846$		0			0
$847$	16.7204	−	28.9607i	0.574521	−	0.995100i
$848$	3.42860	+	0.484453i	0.117739	+	0.0166362i
$849$		0			0
$850$	0.334379	+	39.1482i	0.0114691	+	1.34277i
$851$	18.3038	+	3.22745i	0.627445	+	0.110636i
$852$		0			0
$853$	−10.1055	−	12.0433i	−0.346006	−	0.412354i	0.564774	−	0.825246i	$-0.308963\pi$
$853$	−10.1055	−	12.0433i	−0.346006	−	0.412354i	−0.910780	+	0.412891i	$0.864519\pi$
$854$	26.5153	+	9.39510i	0.907335	+	0.321494i
$855$		0			0
$856$	−5.06493	+	9.31608i	−0.173116	+	0.318417i
$857$	−30.3992	−	11.0644i	−1.03842	−	0.377953i	−0.234138	−	0.972203i	$-0.575227\pi$
$857$	−30.3992	−	11.0644i	−1.03842	−	0.377953i	−0.804280	+	0.594250i	$0.797449\pi$
$858$		0			0
$859$	7.62842	−	9.09120i	0.260278	−	0.310188i	−0.620041	−	0.784570i	$-0.712884\pi$
$859$	7.62842	−	9.09120i	0.260278	−	0.310188i	0.880319	+	0.474382i	$0.157328\pi$
$860$	−2.42413	+	2.10569i	−0.0826623	+	0.0718034i
$861$		0			0
$862$	5.64766	+	15.1139i	0.192360	+	0.514782i
$863$	25.9229			0.882426			0.441213	−	0.897402i	$-0.354548\pi$
$863$	25.9229			0.882426			0.441213	+	0.897402i	$0.354548\pi$
$864$		0			0
$865$	−5.76875			−0.196143
$866$	3.71970	+	9.95441i	0.126400	+	0.338265i
$867$		0			0
$868$	−24.5279	+	21.3058i	−0.832531	+	0.723166i
$869$	−14.1443	+	16.8565i	−0.479811	+	0.571816i
$870$		0			0
$871$	−0.691961	−	0.251853i	−0.0234462	−	0.00853373i
$872$	−22.7603	+	41.8637i	−0.770762	+	1.41769i
$873$		0			0
$874$	0.0129497	+	0.00458845i	0.000438031	+	0.000155207i
$875$	−5.14475	−	6.13128i	−0.173924	−	0.207275i
$876$		0			0
$877$	−23.4419	−	4.13345i	−0.791578	−	0.139577i	−0.236782	−	0.971563i	$-0.576093\pi$
$877$	−23.4419	−	4.13345i	−0.791578	−	0.139577i	−0.554796	+	0.831986i	$0.687204\pi$
$878$	0.246879	+	28.9039i	0.00833175	+	0.975461i
$879$		0			0
$880$	−0.774103	+	5.47853i	−0.0260950	+	0.184681i
$881$	−19.7098	+	34.1384i	−0.664040	+	1.15015i	0.315504	+	0.948924i	$0.397826\pi$
$881$	−19.7098	+	34.1384i	−0.664040	+	1.15015i	−0.979545	+	0.201227i	$0.935507\pi$
$882$		0			0
$883$	−39.3493	+	22.7183i	−1.32421	+	0.764533i	−0.984397	−	0.175960i	$-0.943697\pi$
$883$	−39.3493	+	22.7183i	−1.32421	+	0.764533i	−0.339812	+	0.940493i	$0.610364\pi$
$884$	−0.620096	−	36.2970i	−0.0208561	−	1.22080i
$885$		0			0
$886$	19.6586	−	34.7315i	0.660444	−	1.16683i
$887$	3.61326	−	1.31512i	0.121321	−	0.0441573i	−0.280646	−	0.959811i	$-0.590549\pi$
$887$	3.61326	−	1.31512i	0.121321	−	0.0441573i	0.401967	+	0.915654i	$0.368327\pi$
$888$		0			0
$889$	10.2931	+	58.3752i	0.345220	+	1.95784i
$890$	−0.264422	−	1.42817i	−0.00886344	−	0.0478724i
$891$		0			0
$892$	−27.2784	+	10.4596i	−0.913349	+	0.350213i
$893$	−0.0181087	+	0.00319306i	−0.000605985	+	0.000106852i
$894$		0			0
$895$	−5.84553	+	2.12760i	−0.195395	+	0.0711178i
$896$	−26.4004	+	17.4248i	−0.881975	+	0.582121i
$897$		0			0
$898$	−15.7617	−	2.64060i	−0.525974	−	0.0881181i
$899$	40.2677	−	23.2486i	1.34300	−	0.775384i
$900$		0			0
$901$	−4.22107	−	2.43704i	−0.140624	−	0.0811894i
$902$	−51.1722	−	42.1991i	−1.70385	−	1.40508i
$903$		0			0
$904$	−6.31556	−	16.0592i	−0.210052	−	0.534121i
$905$	−1.03788	+	5.88612i	−0.0345003	+	0.195661i
$906$		0			0
$907$	6.16891	+	7.35182i	0.204835	+	0.244113i	0.858676	−	0.512519i	$-0.171288\pi$
$907$	6.16891	+	7.35182i	0.204835	+	0.244113i	−0.653840	+	0.756632i	$0.726843\pi$
$908$	−40.6207	−	6.44913i	−1.34804	−	0.214022i
$909$		0			0
$910$	2.38923	+	2.79848i	0.0792022	+	0.0927687i
$911$	−27.8833	−	10.1487i	−0.923814	−	0.336241i	−0.164059	−	0.986451i	$-0.552459\pi$
$911$	−27.8833	−	10.1487i	−0.923814	−	0.336241i	−0.759755	+	0.650210i	$0.774681\pi$
$912$		0			0
$913$	−14.9185	−	12.5181i	−0.493730	−	0.414289i
$914$	−46.3111	+	27.2677i	−1.53183	+	0.901936i
$915$		0			0
$916$	−19.7025	+	11.8285i	−0.650987	+	0.390824i
$917$		−	29.6416i		−	0.978851i
$918$		0			0
$919$	−18.2259			−0.601217			−0.300608	−	0.953748i	$-0.597190\pi$
$919$	−18.2259			−0.601217			−0.300608	+	0.953748i	$0.597190\pi$
$920$	−1.19990	+	1.06040i	−0.0395597	+	0.0349602i
$921$		0			0
$922$	−5.50252	−	9.34539i	−0.181216	−	0.307774i
$923$	−1.78176	+	2.12342i	−0.0586474	+	0.0698933i
$924$		0			0
$925$	15.9362	−	43.7844i	0.523980	−	1.43962i
$926$	20.1255	+	23.5728i	0.661366	+	0.774651i
$927$		0			0
$928$	41.8407	−	17.2855i	1.37349	−	0.567426i
$929$	1.32347	−	1.11052i	0.0434216	−	0.0364351i	−0.620819	−	0.783954i	$-0.713200\pi$
$929$	1.32347	−	1.11052i	0.0434216	−	0.0364351i	0.664240	+	0.747519i	$0.268755\pi$
$930$		0			0
$931$	0.00398643		0.000702915i	0.000130650		2.30371e-5i
$932$	1.64975	+	8.50409i	0.0540395	+	0.278561i
$933$		0			0
$934$	2.65757	+	2.19156i	0.0869585	+	0.0717101i
$935$	3.89411	−	6.74480i	0.127351	−	0.220579i
$936$		0			0
$937$	−3.54099	−	6.13317i	−0.115679	−	0.200362i	0.802372	−	0.596824i	$-0.203571\pi$
$937$	−3.54099	−	6.13317i	−0.115679	−	0.200362i	−0.918051	+	0.396462i	$0.870238\pi$
$938$	0.149233	−	0.890767i	0.00487264	−	0.0290846i
$939$		0			0
$940$	0.698521	−	2.02621i	0.0227833	−	0.0660877i
$941$	3.52638	+	9.68865i	0.114957	+	0.315841i	0.983806	−	0.179235i	$-0.0573624\pi$
$941$	3.52638	+	9.68865i	0.114957	+	0.315841i	−0.868850	+	0.495076i	$0.835140\pi$
$942$		0			0
$943$	−3.33338	−	18.9045i	−0.108550	−	0.615617i
$944$	−14.8575	−	16.5256i	−0.483571	−	0.537862i
$945$		0			0
$946$	−37.0586	+	6.86129i	−1.20488	+	0.223080i
$947$	10.4361	−	1.84016i	0.339127	−	0.0597973i	−0.00149128	−	0.999999i	$-0.500475\pi$
$947$	10.4361	−	1.84016i	0.339127	−	0.0597973i	0.340618	+	0.940202i	$0.389364\pi$
$948$		0			0
$949$	−4.46924	−	12.2791i	−0.145078	−	0.398598i
$950$	0.0169656	−	0.0299736i	0.000550436	−	0.000972472i
$951$		0			0
$952$	43.6370	−	8.85275i	1.41428	−	0.286919i
$953$	3.01897	+	5.22901i	0.0977940	+	0.169384i	0.910771	−	0.412911i	$-0.135488\pi$
$953$	3.01897	+	5.22901i	0.0977940	+	0.169384i	−0.812977	+	0.582295i	$0.802155\pi$
$954$		0			0
$955$	0.250024	+	0.144351i	0.00809058	+	0.00467110i
$956$	−13.7021	+	24.6975i	−0.443156	+	0.798776i
$957$		0			0
$958$	0.175701	+	20.5707i	0.00567665	+	0.664608i
$959$	6.89588	−	39.1085i	0.222680	−	1.26288i
$960$		0			0
$961$	2.11229	−	1.77242i	0.0681384	−	0.0571749i
$962$	−14.4299	+	40.7247i	−0.465237	+	1.31302i
$963$		0			0
$964$	−23.3196	−	18.8982i	−0.751075	−	0.608670i
$965$	1.95645	−	5.37529i	0.0629802	−	0.173037i
$966$		0			0
$967$	15.4521	+	12.9658i	0.496906	+	0.416954i	0.856494	−	0.516158i	$-0.172638\pi$
$967$	15.4521	+	12.9658i	0.496906	+	0.416954i	−0.359588	+	0.933111i	$0.617083\pi$
$968$	−21.0742	+	26.4636i	−0.677349	+	0.850572i
$969$		0			0
$970$	−3.01901	+	1.12812i	−0.0969347	+	0.0362219i
$971$		−	31.1328i		−	0.999100i	−0.866285	−	0.499550i	$-0.833499\pi$
$971$		−	31.1328i		−	0.999100i	0.866285	−	0.499550i	$-0.166501\pi$
$972$		0			0
$973$			27.2654i			0.874088i
$974$	−1.26072	−	3.37385i	−0.0403961	−	0.108105i
$975$		0			0
$976$	−25.1166	−	13.3787i	−0.803964	−	0.428240i
$977$	14.4476	+	12.1229i	0.462219	+	0.387848i	0.843947	−	0.536427i	$-0.180226\pi$
$977$	14.4476	+	12.1229i	0.462219	+	0.387848i	−0.381728	+	0.924275i	$0.624671\pi$
$978$		0			0
$979$	5.83071	−	16.0198i	0.186350	−	0.511993i
$980$	−0.297055	+	0.366554i	−0.00948907	+	0.0117091i
$981$		0			0
$982$	−24.2507	−	8.59269i	−0.773871	−	0.274204i
$983$	−24.2461	+	20.3449i	−0.773330	+	0.648901i	−0.941559	−	0.336847i	$-0.890639\pi$
$983$	−24.2461	+	20.3449i	−0.773330	+	0.648901i	0.168229	+	0.985748i	$0.446195\pi$
$984$		0			0
$985$	0.297906	−	1.68951i	0.00949206	−	0.0538322i
$986$	−63.7211	+	0.544264i	−2.02929	+	0.0173329i
$987$		0			0
$988$	−0.0154937	+	0.0279269i	−0.000492920	+	0.000888474i
$989$	−9.44623	−	5.45378i	−0.300373	−	0.173420i
$990$		0			0
$991$	22.5906	+	39.1281i	0.717614	+	1.24294i	0.961942	+	0.273252i	$0.0880993\pi$
$991$	22.5906	+	39.1281i	0.717614	+	1.24294i	−0.244328	+	0.969693i	$0.578567\pi$
$992$	27.7361	−	17.6337i	0.880621	−	0.559870i
$993$		0			0
$994$	−2.95878	−	1.67472i	−0.0938467	−	0.0531189i
$995$	0.834426	+	2.29257i	0.0264531	+	0.0726792i
$996$		0			0
$997$	−20.6197	+	3.63580i	−0.653031	+	0.115147i	−0.490342	−	0.871530i	$-0.663128\pi$
$997$	−20.6197	+	3.63580i	−0.653031	+	0.115147i	−0.162689	+	0.986677i	$0.552017\pi$
$998$	−0.531517	−	2.87078i	−0.0168249	−	0.0908730i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.253.13		204
3.2	odd	2		216.2.t.a.13.22	yes	204
8.5	even	2	inner	648.2.t.a.253.18		204
12.11	even	2		864.2.bf.a.337.11		204
24.5	odd	2		216.2.t.a.13.17	✓	204
24.11	even	2		864.2.bf.a.337.24		204
27.2	odd	18		216.2.t.a.133.17	yes	204
27.25	even	9	inner	648.2.t.a.397.18		204
108.83	even	18		864.2.bf.a.241.24		204
216.29	odd	18		216.2.t.a.133.22	yes	204
216.83	even	18		864.2.bf.a.241.11		204
216.133	even	18	inner	648.2.t.a.397.13		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.17	✓	204	24.5	odd	2
216.2.t.a.13.22	yes	204	3.2	odd	2
216.2.t.a.133.17	yes	204	27.2	odd	18
216.2.t.a.133.22	yes	204	216.29	odd	18
648.2.t.a.253.13		204	1.1	even	1	trivial
648.2.t.a.253.18		204	8.5	even	2	inner
648.2.t.a.397.13		204	216.133	even	18	inner
648.2.t.a.397.18		204	27.25	even	9	inner
864.2.bf.a.241.11		204	216.83	even	18
864.2.bf.a.241.24		204	108.83	even	18
864.2.bf.a.337.11		204	12.11	even	2
864.2.bf.a.337.24		204	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.495022 - 1.32475i) q^{2} +(-1.50991 + 1.31156i) q^{4} +(0.185555 - 0.221136i) q^{5} +(-2.62731 - 0.956263i) q^{7} +(2.48492 + 1.35099i) q^{8} +(-0.384803 - 0.136346i) q^{10} +(-3.08006 - 3.67067i) q^{11} +(3.17478 + 0.559799i) q^{13} +(0.0337716 + 3.95389i) q^{14} +(0.559631 - 3.96066i) q^{16} +(-2.81522 + 4.87610i) q^{17} +(0.00428975 - 0.00247669i) q^{19} +(0.00986189 + 0.577261i) q^{20} +(-3.33801 + 5.89736i) q^{22} +(-1.84294 + 0.670777i) q^{23} +(0.853770 + 4.84197i) q^{25} +(-0.829994 - 4.48289i) q^{26} +(5.22119 - 2.00200i) q^{28} +(-7.88122 + 1.38967i) q^{29} +(-5.45972 + 1.98718i) q^{31} +(-5.52390 + 1.21924i) q^{32} +(7.85319 + 1.31567i) q^{34} +(-0.698975 + 0.403553i) q^{35} +(-8.20717 - 4.73841i) q^{37} +(-0.00540451 - 0.00445682i) q^{38} +(0.759842 - 0.298821i) q^{40} +(-1.69965 + 9.63917i) q^{41} +(3.57494 + 4.26045i) q^{43} +(9.46489 + 1.50269i) q^{44} +(1.80091 + 2.10938i) q^{46} +(-3.48835 - 1.26966i) q^{47} +(0.626015 + 0.525289i) q^{49} +(5.99175 - 3.52791i) q^{50} +(-5.52782 + 3.31866i) q^{52} +0.865665i q^{53} -1.38324 q^{55} +(-5.23675 - 5.92571i) q^{56} +(5.74234 + 9.75270i) q^{58} +(3.57109 - 4.25586i) q^{59} +(2.43327 - 6.68534i) q^{61} +(5.33519 + 6.24905i) q^{62} +(4.34964 + 6.71421i) q^{64} +(0.712888 - 0.598184i) q^{65} +(-0.224950 - 0.0396647i) q^{67} +(-2.14457 - 11.0548i) q^{68} +(0.880614 + 0.726197i) q^{70} +(-0.429923 + 0.744648i) q^{71} +(-2.02670 - 3.51035i) q^{73} +(-2.21446 + 13.2180i) q^{74} +(-0.00322880 + 0.00936583i) q^{76} +(4.58214 + 12.5893i) q^{77} +(-0.797428 - 4.52244i) q^{79} +(-0.772001 - 0.858675i) q^{80} +(13.6108 - 2.52001i) q^{82} +(4.00250 - 0.705749i) q^{83} +(0.555903 + 1.52733i) q^{85} +(3.87434 - 6.84491i) q^{86} +(-2.69465 - 13.2824i) q^{88} +(1.77889 + 3.08112i) q^{89} +(-7.80581 - 4.50669i) q^{91} +(1.90291 - 3.42994i) q^{92} +(0.0448395 + 5.24969i) q^{94} +(0.000248300 - 0.00140818i) q^{95} +(6.04757 - 5.07452i) q^{97} +(0.385983 - 1.08934i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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Database

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