LMFDB - Embedded newform 567.2.be.a.62.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] 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("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			62.14
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.234777 + 0.645045i) q^{2} +(1.17113 - 0.982692i) q^{4} +(0.231854 + 1.31491i) q^{5} +(2.46223 + 0.968204i) q^{7} +(2.09779 + 1.21116i) q^{8} +(-0.793741 + 0.458267i) q^{10} +(-0.216508 - 0.0381762i) q^{11} +(-0.673991 + 1.85178i) q^{13} +(-0.0464596 + 1.81556i) q^{14} +(0.242207 - 1.37362i) q^{16} +(-0.469803 - 0.813723i) q^{17} +(-3.04150 - 1.75601i) q^{19} +(1.56368 + 1.31208i) q^{20} +(-0.0262057 - 0.148620i) q^{22} +(-1.17579 - 1.40126i) q^{23} +(3.02323 - 1.10037i) q^{25} -1.35272 q^{26} +(3.83503 - 1.28572i) q^{28} +(1.33239 + 3.66070i) q^{29} +(5.95195 + 7.09326i) q^{31} +(5.71394 - 1.00752i) q^{32} +(0.414589 - 0.494088i) q^{34} +(-0.702223 + 3.46209i) q^{35} +(-1.56504 - 2.71072i) q^{37} +(0.418631 - 2.37418i) q^{38} +(-1.10618 + 3.03921i) q^{40} +(-10.8664 - 3.95506i) q^{41} +(-0.261843 + 1.48498i) q^{43} +(-0.291074 + 0.168051i) q^{44} +(0.627824 - 1.08742i) q^{46} +(5.18484 + 4.35059i) q^{47} +(5.12516 + 4.76788i) q^{49} +(1.41957 + 1.69178i) q^{50} +(1.03040 + 2.83099i) q^{52} -3.77077i q^{53} -0.293540i q^{55} +(3.99259 + 5.01324i) q^{56} +(-2.04850 + 1.71890i) q^{58} +(-1.72130 - 9.76195i) q^{59} +(6.04827 - 7.20805i) q^{61} +(-3.17809 + 5.50461i) q^{62} +(0.596586 + 1.03332i) q^{64} +(-2.59119 - 0.456896i) q^{65} +(-6.36714 - 2.31745i) q^{67} +(-1.34984 - 0.491301i) q^{68} +(-2.39807 + 0.359855i) q^{70} +(-11.8706 + 6.85351i) q^{71} +(-7.68223 - 4.43534i) q^{73} +(1.38110 - 1.64593i) q^{74} +(-5.28760 + 0.932347i) q^{76} +(-0.496130 - 0.303622i) q^{77} +(-7.91776 + 2.88183i) q^{79} +1.86235 q^{80} -7.93789i q^{82} +(16.1714 - 5.88589i) q^{83} +(0.961047 - 0.806414i) q^{85} +(-1.01936 + 0.179740i) q^{86} +(-0.407950 - 0.342311i) q^{88} +(-3.46240 + 5.99705i) q^{89} +(-3.45242 + 3.90694i) q^{91} +(-2.75401 - 0.485606i) q^{92} +(-1.58905 + 4.36587i) q^{94} +(1.60381 - 4.40644i) q^{95} +(4.42872 + 0.780904i) q^{97} +(-1.87223 + 4.42535i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.234777	+	0.645045i	0.166012	+	0.456116i	0.994605	−	0.103737i	$-0.0330800\pi$
$2$	0.234777	+	0.645045i	0.166012	+	0.456116i	−0.828592	+	0.559852i	$0.810858\pi$
$3$		0			0
$3$		0			0
$4$	1.17113	−	0.982692i	0.585563	−	0.491346i
$5$	0.231854	+	1.31491i	0.103688	+	0.588045i	0.991736	+	0.128294i	$0.0409502\pi$
$5$	0.231854	+	1.31491i	0.103688	+	0.588045i	−0.888048	+	0.459751i	$0.847939\pi$
$6$		0			0
$7$	2.46223	+	0.968204i	0.930636	+	0.365947i
$7$	2.46223	+	0.968204i	0.930636	+	0.365947i
$8$	2.09779	+	1.21116i	0.741680	+	0.428209i
$9$		0			0
$10$	−0.793741	+	0.458267i	−0.251003	+	0.144917i
$11$	−0.216508	−	0.0381762i	−0.0652796	−	0.0115106i	0.140913	−	0.990022i	$-0.454996\pi$
$11$	−0.216508	−	0.0381762i	−0.0652796	−	0.0115106i	−0.206193	+	0.978511i	$0.566107\pi$
$12$		0			0
$13$	−0.673991	+	1.85178i	−0.186932	+	0.513590i	−0.997390	−	0.0722062i	$-0.976996\pi$
$13$	−0.673991	+	1.85178i	−0.186932	+	0.513590i	0.810458	+	0.585797i	$0.199218\pi$
$14$	−0.0464596	+	1.81556i	−0.0124169	+	0.485229i
$15$		0			0
$16$	0.242207	−	1.37362i	0.0605517	−	0.343406i
$17$	−0.469803	−	0.813723i	−0.113944	−	0.197357i	0.803413	−	0.595422i	$-0.203015\pi$
$17$	−0.469803	−	0.813723i	−0.113944	−	0.197357i	−0.917357	+	0.398065i	$0.869682\pi$
$18$		0			0
$19$	−3.04150	−	1.75601i	−0.697768	−	0.402857i	0.108747	−	0.994069i	$-0.465316\pi$
$19$	−3.04150	−	1.75601i	−0.697768	−	0.402857i	−0.806516	+	0.591213i	$0.798649\pi$
$20$	1.56368	+	1.31208i	0.349650	+	0.293391i
$21$		0			0
$22$	−0.0262057	−	0.148620i	−0.00558708	−	0.0316859i
$23$	−1.17579	−	1.40126i	−0.245170	−	0.292182i	0.629400	−	0.777082i	$-0.283301\pi$
$23$	−1.17579	−	1.40126i	−0.245170	−	0.292182i	−0.874570	+	0.484899i	$0.838856\pi$
$24$		0			0
$25$	3.02323	−	1.10037i	0.604647	−	0.220073i
$26$	−1.35272			−0.265289
$27$		0			0
$28$	3.83503	−	1.28572i	0.724753	−	0.242979i
$29$	1.33239	+	3.66070i	0.247418	+	0.679776i	0.999779	+	0.0210245i	$0.00669280\pi$
$29$	1.33239	+	3.66070i	0.247418	+	0.679776i	−0.752361	+	0.658751i	$0.771085\pi$
$30$		0			0
$31$	5.95195	+	7.09326i	1.06900	+	1.27399i	0.960017	+	0.279943i	$0.0903156\pi$
$31$	5.95195	+	7.09326i	1.06900	+	1.27399i	0.108985	+	0.994043i	$0.465240\pi$
$32$	5.71394	−	1.00752i	1.01009	−	0.178106i
$33$		0			0
$34$	0.414589	−	0.494088i	0.0711014	−	0.0847353i
$35$	−0.702223	+	3.46209i	−0.118697	+	0.585200i
$36$		0			0
$37$	−1.56504	−	2.71072i	−0.257290	−	0.445640i	0.708225	−	0.705987i	$-0.249496\pi$
$37$	−1.56504	−	2.71072i	−0.257290	−	0.445640i	−0.965515	+	0.260347i	$0.916163\pi$
$38$	0.418631	−	2.37418i	0.0679110	−	0.385142i
$39$		0			0
$40$	−1.10618	+	3.03921i	−0.174903	+	0.480542i
$41$	−10.8664	−	3.95506i	−1.69705	−	0.617676i	−0.701567	−	0.712603i	$-0.747516\pi$
$41$	−10.8664	−	3.95506i	−1.69705	−	0.617676i	−0.995484	+	0.0949267i	$0.969738\pi$
$42$		0			0
$43$	−0.261843	+	1.48498i	−0.0399307	+	0.226458i	−0.998242	−	0.0592676i	$-0.981123\pi$
$43$	−0.261843	+	1.48498i	−0.0399307	+	0.226458i	0.958311	+	0.285726i	$0.0922346\pi$
$44$	−0.291074	+	0.168051i	−0.0438810	+	0.0253347i
$45$		0			0
$46$	0.627824	−	1.08742i	0.0925676	−	0.160332i
$47$	5.18484	+	4.35059i	0.756286	+	0.634599i	0.937157	−	0.348907i	$-0.113447\pi$
$47$	5.18484	+	4.35059i	0.756286	+	0.634599i	−0.180871	+	0.983507i	$0.557892\pi$
$48$		0			0
$49$	5.12516	+	4.76788i	0.732166	+	0.681126i
$50$	1.41957	+	1.69178i	0.200758	+	0.239254i
$51$		0			0
$52$	1.03040	+	2.83099i	0.142890	+	0.392588i
$53$		−	3.77077i		−	0.517954i	−0.965883	−	0.258977i	$-0.916615\pi$
$53$		−	3.77077i		−	0.517954i	0.965883	−	0.258977i	$-0.0833855\pi$
$54$		0			0
$55$		−	0.293540i		−	0.0395809i
$56$	3.99259	+	5.01324i	0.533532	+	0.669922i
$57$		0			0
$58$	−2.04850	+	1.71890i	−0.268982	+	0.225703i
$59$	−1.72130	−	9.76195i	−0.224094	−	1.27090i	−0.864410	−	0.502787i	$-0.832308\pi$
$59$	−1.72130	−	9.76195i	−0.224094	−	1.27090i	0.640317	−	0.768111i	$-0.278803\pi$
$60$		0			0
$61$	6.04827	−	7.20805i	0.774402	−	0.922896i	−0.224264	−	0.974528i	$-0.571998\pi$
$61$	6.04827	−	7.20805i	0.774402	−	0.922896i	0.998666	+	0.0516319i	$0.0164423\pi$
$62$	−3.17809	+	5.50461i	−0.403617	+	0.699086i
$63$		0			0
$64$	0.596586	+	1.03332i	0.0745733	+	0.129165i
$65$	−2.59119	−	0.456896i	−0.321397	−	0.0566710i
$66$		0			0
$67$	−6.36714	−	2.31745i	−0.777871	−	0.283122i	−0.0775861	−	0.996986i	$-0.524721\pi$
$67$	−6.36714	−	2.31745i	−0.777871	−	0.283122i	−0.700284	+	0.713864i	$0.746943\pi$
$68$	−1.34984	−	0.491301i	−0.163692	−	0.0595790i
$69$		0			0
$70$	−2.39807	+	0.359855i	−0.286624	+	0.0430109i
$71$	−11.8706	+	6.85351i	−1.40879	+	0.813362i	−0.995271	−	0.0971354i	$-0.969032\pi$
$71$	−11.8706	+	6.85351i	−1.40879	+	0.813362i	−0.413514	+	0.910498i	$0.635699\pi$
$72$		0			0
$73$	−7.68223	−	4.43534i	−0.899137	−	0.519117i	−0.0222170	−	0.999753i	$-0.507072\pi$
$73$	−7.68223	−	4.43534i	−0.899137	−	0.519117i	−0.876920	+	0.480636i	$0.840406\pi$
$74$	1.38110	−	1.64593i	0.160550	−	0.191336i
$75$		0			0
$76$	−5.28760	+	0.932347i	−0.606529	+	0.106948i
$77$	−0.496130	−	0.303622i	−0.0565393	−	0.0346010i
$78$		0			0
$79$	−7.91776	+	2.88183i	−0.890818	+	0.324231i	−0.746567	−	0.665310i	$-0.768299\pi$
$79$	−7.91776	+	2.88183i	−0.890818	+	0.324231i	−0.144251	+	0.989541i	$0.546077\pi$
$80$	1.86235			0.208217
$81$		0			0
$82$		−	7.93789i		−	0.876594i
$83$	16.1714	−	5.88589i	1.77504	−	0.646061i	0.775139	−	0.631791i	$-0.217680\pi$
$83$	16.1714	−	5.88589i	1.77504	−	0.646061i	0.999898	−	0.0142697i	$-0.00454236\pi$
$84$		0			0
$85$	0.961047	−	0.806414i	0.104240	−	0.0874679i
$86$	−1.01936	+	0.179740i	−0.109920	+	0.0193819i
$87$		0			0
$88$	−0.407950	−	0.342311i	−0.0434876	−	0.0364904i
$89$	−3.46240	+	5.99705i	−0.367014	+	0.635686i	−0.989097	−	0.147265i	$-0.952953\pi$
$89$	−3.46240	+	5.99705i	−0.367014	+	0.635686i	0.622084	+	0.782951i	$0.286286\pi$
$90$		0			0
$91$	−3.45242	+	3.90694i	−0.361912	+	0.409559i
$92$	−2.75401	−	0.485606i	−0.287125	−	0.0506279i
$93$		0			0
$94$	−1.58905	+	4.36587i	−0.163898	+	0.450305i
$95$	1.60381	−	4.40644i	0.164548	−	0.452091i
$96$		0			0
$97$	4.42872	+	0.780904i	0.449669	+	0.0792887i	0.393897	−	0.919155i	$-0.371127\pi$
$97$	4.42872	+	0.780904i	0.449669	+	0.0792887i	0.0557722	+	0.998444i	$0.482238\pi$
$98$	−1.87223	+	4.42535i	−0.189124	+	0.447028i
$99$		0			0
$100$	2.45927	−	4.25957i	0.245927	−	0.425957i
$101$	0.750944	+	0.630116i	0.0747217	+	0.0626989i	0.679384	−	0.733783i	$-0.262247\pi$
$101$	0.750944	+	0.630116i	0.0747217	+	0.0626989i	−0.604662	+	0.796482i	$0.706692\pi$
$102$		0			0
$103$	−13.1659	+	2.32150i	−1.29727	+	0.228744i	−0.779299	−	0.626652i	$-0.784425\pi$
$103$	−13.1659	+	2.32150i	−1.29727	+	0.228744i	−0.517974	+	0.855396i	$0.673314\pi$
$104$	−3.65668	+	3.06832i	−0.358567	+	0.300874i
$105$		0			0
$106$	2.43231	−	0.885289i	0.236247	−	0.0859869i
$107$		−	18.7220i		−	1.80992i	−0.425496	−	0.904960i	$-0.639900\pi$
$107$		−	18.7220i		−	1.80992i	0.425496	−	0.904960i	$-0.360100\pi$
$108$		0			0
$109$	−5.24050			−0.501949			−0.250975	−	0.967994i	$-0.580751\pi$
$109$	−5.24050			−0.501949			−0.250975	+	0.967994i	$0.580751\pi$
$110$	0.189346	−	0.0689164i	0.0180534	−	0.00657092i
$111$		0			0
$112$	1.92632	−	3.14767i	0.182020	−	0.297427i
$113$	−8.07557	+	1.42394i	−0.759686	+	0.133953i	−0.540055	−	0.841630i	$-0.681596\pi$
$113$	−8.07557	+	1.42394i	−0.759686	+	0.133953i	−0.219631	+	0.975583i	$0.570485\pi$
$114$		0			0
$115$	1.56991	−	1.87095i	0.146395	−	0.174467i
$116$	5.15774	+	2.97782i	0.478884	+	0.276484i
$117$		0			0
$118$	5.89278	−	3.40220i	0.542474	−	0.313198i
$119$	−0.368914	−	2.45844i	−0.0338183	−	0.225365i
$120$		0			0
$121$	−10.2912	−	3.74569i	−0.935564	−	0.340517i
$122$	6.06951	+	2.20912i	0.549508	+	0.200004i
$123$		0			0
$124$	13.9410	+	2.45817i	1.25194	+	0.220750i
$125$	5.48582	+	9.50171i	0.490666	+	0.849859i
$126$		0			0
$127$	−0.479905	+	0.831220i	−0.0425847	+	0.0737588i	−0.886532	−	0.462667i	$-0.846893\pi$
$127$	−0.479905	+	0.831220i	−0.0425847	+	0.0737588i	0.843947	+	0.536426i	$0.180226\pi$
$128$	6.93255	−	8.26189i	0.612757	−	0.730255i
$129$		0			0
$130$	−0.313633	−	1.77870i	−0.0275074	−	0.156002i
$131$	3.74843	−	3.14531i	0.327502	−	0.274807i	−0.464179	−	0.885741i	$-0.653651\pi$
$131$	3.74843	−	3.14531i	0.327502	−	0.274807i	0.791681	+	0.610935i	$0.209206\pi$
$132$		0			0
$133$	−5.78870	−	7.26850i	−0.501944	−	0.630259i
$134$		−	4.65118i		−	0.401801i
$135$		0			0
$136$		−	2.27602i		−	0.195167i
$137$	−3.97977	−	10.9343i	−0.340015	−	0.934183i	−0.985389	−	0.170317i	$-0.945521\pi$
$137$	−3.97977	−	10.9343i	−0.340015	−	0.934183i	0.645375	−	0.763866i	$-0.276701\pi$
$138$		0			0
$139$	−5.90509	−	7.03742i	−0.500864	−	0.596906i	0.455082	−	0.890449i	$-0.349610\pi$
$139$	−5.90509	−	7.03742i	−0.500864	−	0.596906i	−0.955946	+	0.293544i	$0.905165\pi$
$140$	2.57978	+	4.74462i	0.218031	+	0.400993i
$141$		0			0
$142$	−7.20778	−	6.04804i	−0.604863	−	0.507540i
$143$	0.216618	−	0.375194i	0.0181145	−	0.0313753i
$144$		0			0
$145$	−4.50458	+	2.60072i	−0.374085	+	0.215978i
$146$	1.05738	−	5.99670i	0.0875094	−	0.496290i
$147$		0			0
$148$	−4.49666	−	1.63665i	−0.369623	−	0.134532i
$149$	5.20678	−	14.3055i	0.426556	−	1.17195i	−0.521333	−	0.853353i	$-0.674565\pi$
$149$	5.20678	−	14.3055i	0.426556	−	1.17195i	0.947889	−	0.318600i	$-0.103213\pi$
$150$		0			0
$151$	−1.95736	+	11.1008i	−0.159288	+	0.903366i	0.795472	+	0.605990i	$0.207223\pi$
$151$	−1.95736	+	11.1008i	−0.159288	+	0.903366i	−0.954760	+	0.297376i	$0.903888\pi$
$152$	−4.25361	−	7.36748i	−0.345014	−	0.597581i
$153$		0			0
$154$	0.0793701	−	0.391310i	0.00639582	−	0.0315326i
$155$	−7.94701	+	9.47087i	−0.638319	+	0.760719i
$156$		0			0
$157$	12.3894	−	2.18459i	0.988784	−	0.174349i	0.344211	−	0.938892i	$-0.388146\pi$
$157$	12.3894	−	2.18459i	0.988784	−	0.174349i	0.644573	+	0.764543i	$0.277035\pi$
$158$	−3.71782	−	4.43072i	−0.295774	−	0.352489i
$159$		0			0
$160$	2.64960	+	7.27972i	0.209469	+	0.575512i
$161$	−1.53837	−	4.58863i	−0.121241	−	0.361635i
$162$		0			0
$163$	−15.4955			−1.21370			−0.606850	−	0.794816i	$-0.707567\pi$
$163$	−15.4955			−1.21370			−0.606850	+	0.794816i	$0.707567\pi$
$164$	−16.6126	+	6.04648i	−1.29722	+	0.472151i
$165$		0			0
$166$	7.59333	+	9.04938i	0.589357	+	0.702368i
$167$	−3.86013	−	21.8919i	−0.298706	−	1.69405i	−0.651746	−	0.758437i	$-0.725963\pi$
$167$	−3.86013	−	21.8919i	−0.298706	−	1.69405i	0.353040	−	0.935608i	$-0.385148\pi$
$168$		0			0
$169$	6.98377	+	5.86008i	0.537213	+	0.450775i
$170$	0.745805	+	0.430591i	0.0572006	+	0.0330248i
$171$		0			0
$172$	1.15263	+	1.99642i	0.0878873	+	0.152225i
$173$	0.814058	−	4.61675i	0.0618917	−	0.351005i	−0.938098	−	0.346371i	$-0.887414\pi$
$173$	0.814058	−	4.61675i	0.0618917	−	0.351005i	0.999989	−	0.00463414i	$-0.00147510\pi$
$174$		0			0
$175$	8.50928	+	0.217750i	0.643241	+	0.0164603i
$176$	−0.104879	+	0.288154i	−0.00790558	+	0.0217204i
$177$		0			0
$178$	−4.68126	−	0.825432i	−0.350875	−	0.0618688i
$179$	−13.7669	+	7.94833i	−1.02899	+	0.594086i	−0.916694	−	0.399589i	$-0.869153\pi$
$179$	−13.7669	+	7.94833i	−1.02899	+	0.594086i	−0.112293	+	0.993675i	$0.535820\pi$
$180$		0			0
$181$	4.81888	+	2.78218i	0.358185	+	0.206798i	0.668284	−	0.743906i	$-0.267029\pi$
$181$	4.81888	+	2.78218i	0.358185	+	0.206798i	−0.310100	+	0.950704i	$0.600362\pi$
$182$	−3.33070	−	1.30971i	−0.246888	−	0.0970818i
$183$		0			0
$184$	−0.769423	−	4.36361i	−0.0567226	−	0.321690i
$185$	3.20150	−	2.68637i	0.235379	−	0.197506i
$186$		0			0
$187$	0.0706513	+	0.194113i	0.00516653	+	0.0141949i
$188$	10.3474			0.754661
$189$		0			0
$190$	3.21889			0.233523
$191$	−0.626662	−	1.72174i	−0.0453437	−	0.124581i	0.914954	−	0.403558i	$-0.132227\pi$
$191$	−0.626662	−	1.72174i	−0.0453437	−	0.124581i	−0.960298	+	0.278978i	$0.910004\pi$
$192$		0			0
$193$	0.0889424	−	0.0746315i	0.00640221	−	0.00537209i	−0.639581	−	0.768724i	$-0.720892\pi$
$193$	0.0889424	−	0.0746315i	0.00640221	−	0.00537209i	0.645983	+	0.763352i	$0.276448\pi$
$194$	0.536045	+	3.04006i	0.0384858	+	0.218264i
$195$		0			0
$196$	10.6876	+	0.547341i	0.763398	+	0.0390958i
$197$	13.5481	+	7.82201i	0.965264	+	0.557295i	0.897789	−	0.440425i	$-0.145172\pi$
$197$	13.5481	+	7.82201i	0.965264	+	0.557295i	0.0674749	+	0.997721i	$0.478506\pi$
$198$		0			0
$199$	−8.33355	+	4.81138i	−0.590750	+	0.341069i	−0.765394	−	0.643562i	$-0.777456\pi$
$199$	−8.33355	+	4.81138i	−0.590750	+	0.341069i	0.174644	+	0.984632i	$0.444122\pi$
$200$	7.67481	+	1.35328i	0.542691	+	0.0956911i
$201$		0			0
$202$	−0.230149	+	0.632329i	−0.0161932	+	0.0444905i
$203$	−0.263664	+	10.3035i	−0.0185056	+	0.723166i
$204$		0			0
$205$	2.68112	−	15.2054i	0.187257	−	1.06199i
$206$	−4.58852	−	7.94755i	−0.319697	−	0.553732i
$207$		0			0
$208$	2.38040	+	1.37432i	0.165051	+	0.0952922i
$209$	0.591471	+	0.496303i	0.0409129	+	0.0343300i
$210$		0			0
$211$	2.41262	+	13.6827i	0.166092	+	0.941954i	0.947932	+	0.318474i	$0.103170\pi$
$211$	2.41262	+	13.6827i	0.166092	+	0.941954i	−0.781840	+	0.623479i	$0.785719\pi$
$212$	−3.70550	−	4.41604i	−0.254495	−	0.303295i
$213$		0			0
$214$	12.0765	−	4.39549i	0.825533	−	0.300469i
$215$	−2.01333			−0.137308
$216$		0			0
$217$	7.78735	+	23.2279i	0.528640	+	1.57682i
$218$	−1.23035	−	3.38036i	−0.0833298	−	0.228947i
$219$		0			0
$220$	−0.288459	−	0.343772i	−0.0194479	−	0.0231771i
$221$	1.82348	−	0.321528i	0.122660	−	0.0216283i
$222$		0			0
$223$	−11.6645	+	13.9012i	−0.781115	+	0.930896i	−0.998983	−	0.0450820i	$-0.985645\pi$
$223$	−11.6645	+	13.9012i	−0.781115	+	0.930896i	0.217869	+	0.975978i	$0.430090\pi$
$224$	15.0445	+	3.05151i	1.00521	+	0.203888i
$225$		0			0
$226$	−2.81446	−	4.87479i	−0.187215	−	0.324267i
$227$	−4.49086	+	25.4689i	−0.298069	+	1.69043i	0.356393	+	0.934336i	$0.384006\pi$
$227$	−4.49086	+	25.4689i	−0.298069	+	1.69043i	−0.654462	+	0.756095i	$0.727105\pi$
$228$		0			0
$229$	3.70816	−	10.1881i	0.245042	−	0.673247i	−0.754809	−	0.655945i	$-0.772270\pi$
$229$	3.70816	−	10.1881i	0.245042	−	0.673247i	0.999850	−	0.0173016i	$-0.00550755\pi$
$230$	1.57543	+	0.573409i	0.103881	+	0.0378094i
$231$		0			0
$232$	−1.63863	+	9.29311i	−0.107581	+	0.610122i
$233$	−2.36196	+	1.36368i	−0.154737	+	0.0893375i	−0.575369	−	0.817894i	$-0.695142\pi$
$233$	−2.36196	+	1.36368i	−0.154737	+	0.0893375i	0.420632	+	0.907231i	$0.361808\pi$
$234$		0			0
$235$	−4.51851	+	7.82629i	−0.294755	+	0.510531i
$236$	−11.6088	−	9.74098i	−0.755672	−	0.634084i
$237$		0			0
$238$	1.49919	−	0.815151i	0.0971781	−	0.0528384i
$239$	19.4562	+	23.1870i	1.25852	+	1.49984i	0.785599	+	0.618736i	$0.212355\pi$
$239$	19.4562	+	23.1870i	1.25852	+	1.49984i	0.472919	+	0.881106i	$0.343200\pi$
$240$		0			0
$241$	−8.39131	−	23.0549i	−0.540531	−	1.48510i	−0.846150	−	0.532944i	$-0.821086\pi$
$241$	−8.39131	−	23.0549i	−0.540531	−	1.48510i	0.305619	−	0.952154i	$-0.401137\pi$
$242$		−	7.51769i		−	0.483255i
$243$		0			0
$244$		−	14.3851i		−	0.920914i
$245$	−5.08105	+	7.84458i	−0.324616	+	0.501172i
$246$		0			0
$247$	5.30169	−	4.44864i	0.337338	−	0.283060i
$248$	3.89487	+	22.0889i	0.247324	+	1.40265i
$249$		0			0
$250$	−4.84109	+	5.76938i	−0.306177	+	0.364888i
$251$	−12.0630	+	20.8937i	−0.761409	+	1.31880i	0.180715	+	0.983536i	$0.442159\pi$
$251$	−12.0630	+	20.8937i	−0.761409	+	1.31880i	−0.942124	+	0.335264i	$0.891174\pi$
$252$		0			0
$253$	0.201074	+	0.348271i	0.0126414	+	0.0218956i
$254$	−0.648845	−	0.114409i	−0.0407121	−	0.00717865i
$255$		0			0
$256$	9.19933	+	3.34828i	0.574958	+	0.209268i
$257$	11.0337	+	4.01595i	0.688265	+	0.250508i	0.662392	−	0.749157i	$-0.269541\pi$
$257$	11.0337	+	4.01595i	0.688265	+	0.250508i	0.0258727	+	0.999665i	$0.491764\pi$
$258$		0			0
$259$	−1.22895	−	8.18970i	−0.0763631	−	0.508883i
$260$	−3.48359	+	2.01125i	−0.216043	+	0.124733i
$261$		0			0
$262$	2.90891	+	1.67946i	0.179713	+	0.103757i
$263$	−12.7126	+	15.1503i	−0.783891	+	0.934205i	−0.999102	−	0.0423623i	$-0.986512\pi$
$263$	−12.7126	+	15.1503i	−0.783891	+	0.934205i	0.215211	+	0.976568i	$0.430956\pi$
$264$		0			0
$265$	4.95821	−	0.874267i	0.304581	−	0.0537058i
$266$	3.32945	−	5.44045i	0.204142	−	0.333575i
$267$		0			0
$268$	−9.73407	+	3.54291i	−0.594603	+	0.216418i
$269$	17.1269			1.04424			0.522122	−	0.852871i	$-0.325141\pi$
$269$	17.1269			1.04424			0.522122	+	0.852871i	$0.325141\pi$
$270$		0			0
$271$			16.5484i			1.00525i	0.864506	+	0.502623i	$0.167632\pi$
$271$			16.5484i			1.00525i	−0.864506	+	0.502623i	$0.832368\pi$
$272$	−1.23154	+	0.448244i	−0.0746730	+	0.0271788i
$273$		0			0
$274$	6.11877	−	5.13426i	0.369649	−	0.310172i
$275$	−0.696561	+	0.122823i	−0.0420042	+	0.00740648i
$276$		0			0
$277$	−13.1995	−	11.0757i	−0.793078	−	0.665472i	0.153427	−	0.988160i	$-0.450969\pi$
$277$	−13.1995	−	11.0757i	−0.793078	−	0.665472i	−0.946505	+	0.322688i	$0.895413\pi$
$278$	3.15307	−	5.46127i	0.189108	−	0.327545i
$279$		0			0
$280$	−5.66625	+	6.41223i	−0.338623	+	0.383204i
$281$	14.1177	+	2.48933i	0.842190	+	0.148501i	0.578068	−	0.815988i	$-0.303807\pi$
$281$	14.1177	+	2.48933i	0.842190	+	0.148501i	0.264122	+	0.964489i	$0.414918\pi$
$282$		0			0
$283$	4.76130	−	13.0816i	0.283030	−	0.777618i	−0.713967	−	0.700179i	$-0.753103\pi$
$283$	4.76130	−	13.0816i	0.283030	−	0.777618i	0.996997	−	0.0774390i	$-0.0246743\pi$
$284$	−7.16712	+	19.6915i	−0.425290	+	1.16848i
$285$		0			0
$286$	0.292874	+	0.0516415i	0.0173180	+	0.00305363i
$287$	−22.9264	−	20.2592i	−1.35330	−	1.19586i
$288$		0			0
$289$	8.05857	−	13.9579i	0.474034	−	0.821050i
$290$	−2.73515	−	2.29506i	−0.160614	−	0.134771i
$291$		0			0
$292$	−13.3554	+	2.35492i	−0.781568	+	0.137811i
$293$	−9.24858	+	7.76048i	−0.540308	+	0.453372i	−0.871643	−	0.490141i	$-0.836945\pi$
$293$	−9.24858	+	7.76048i	−0.540308	+	0.453372i	0.331335	+	0.943513i	$0.392501\pi$
$294$		0			0
$295$	12.4370	−	4.52670i	0.724110	−	0.263554i
$296$		−	7.58203i		−	0.440696i
$297$		0			0
$298$	10.4501			0.605359
$299$	3.38729	−	1.23287i	0.195892	−	0.0712989i
$300$		0			0
$301$	−2.08249	+	3.40286i	−0.120032	+	0.196137i
$302$	−7.62002	+	1.34362i	−0.438483	+	0.0773164i
$303$		0			0
$304$	−3.14877	+	3.75256i	−0.180594	+	0.215224i
$305$	10.8803	+	6.28172i	0.623001	+	0.359690i
$306$		0			0
$307$	19.5181	−	11.2688i	1.11396	−	0.643144i	0.174107	−	0.984727i	$-0.444296\pi$
$307$	19.5181	−	11.2688i	1.11396	−	0.643144i	0.939852	+	0.341583i	$0.110963\pi$
$308$	−0.879398	+	0.131963i	−0.0501084	+	0.00751927i
$309$		0			0
$310$	−7.97491	−	2.90263i	−0.452945	−	0.164858i
$311$	2.46202	+	0.896103i	0.139608	+	0.0508133i	0.410879	−	0.911690i	$-0.365222\pi$
$311$	2.46202	+	0.896103i	0.139608	+	0.0508133i	−0.271271	+	0.962503i	$0.587444\pi$
$312$		0			0
$313$	−5.70705	−	1.00631i	−0.322582	−	0.0568798i	0.0100126	−	0.999950i	$-0.496813\pi$
$313$	−5.70705	−	1.00631i	−0.322582	−	0.0568798i	−0.332594	+	0.943070i	$0.607924\pi$
$314$	4.31791	+	7.47885i	0.243674	+	0.422056i
$315$		0			0
$316$	−6.44075	+	11.1557i	−0.362320	+	0.627557i
$317$	9.51195	−	11.3359i	0.534244	−	0.636687i	−0.429643	−	0.902999i	$-0.641361\pi$
$317$	9.51195	−	11.3359i	0.534244	−	0.636687i	0.963887	+	0.266312i	$0.0858050\pi$
$318$		0			0
$319$	−0.148721	−	0.843437i	−0.00832676	−	0.0472234i
$320$	−1.22040	+	1.02404i	−0.0682223	+	0.0572453i
$321$		0			0
$322$	2.59870	−	2.06963i	0.144820	−	0.115336i
$323$			3.29992i			0.183612i
$324$		0			0
$325$			6.33999i			0.351679i
$326$	−3.63798	−	9.99528i	−0.201489	−	0.553587i
$327$		0			0
$328$	−18.0053	−	21.4578i	−0.994174	−	1.18481i
$329$	8.55400	+	15.7321i	0.471597	+	0.867341i
$330$		0			0
$331$	7.87879	+	6.61109i	0.433057	+	0.363378i	0.833104	−	0.553117i	$-0.186562\pi$
$331$	7.87879	+	6.61109i	0.433057	+	0.363378i	−0.400047	+	0.916495i	$0.631006\pi$
$332$	13.1547	−	22.7846i	0.721957	−	1.25047i
$333$		0			0
$334$	13.2150	−	7.62967i	0.723092	−	0.417477i
$335$	1.57099	−	8.90953i	0.0858324	−	0.486780i
$336$		0			0
$337$	25.9383	+	9.44078i	1.41295	+	0.514272i	0.931995	−	0.362472i	$-0.118067\pi$
$337$	25.9383	+	9.44078i	1.41295	+	0.514272i	0.480957	+	0.876744i	$0.340289\pi$
$338$	−2.14038	+	5.88065i	−0.116421	+	0.319865i
$339$		0			0
$340$	0.333051	−	1.88883i	0.0180622	−	0.102436i
$341$	−1.01785	−	1.76297i	−0.0551197	−	0.0954701i
$342$		0			0
$343$	8.00305	+	16.7018i	0.432124	+	0.901814i
$344$	−2.34784	+	2.79805i	−0.126587	+	0.150861i
$345$		0			0
$346$	3.16913	−	0.558804i	0.170374	−	0.0300415i
$347$	−4.96950	−	5.92242i	−0.266777	−	0.317932i	0.615981	−	0.787761i	$-0.288760\pi$
$347$	−4.96950	−	5.92242i	−0.266777	−	0.317932i	−0.882757	+	0.469829i	$0.844316\pi$
$348$		0			0
$349$	10.3198	+	28.3535i	0.552407	+	1.51773i	0.830414	+	0.557147i	$0.188104\pi$
$349$	10.3198	+	28.3535i	0.552407	+	1.51773i	−0.278007	+	0.960579i	$0.589674\pi$
$350$	1.85732	+	5.53999i	0.0992782	+	0.296125i
$351$		0			0
$352$	−1.27558			−0.0679885
$353$	−13.2988	+	4.84037i	−0.707824	+	0.257627i	−0.670748	−	0.741685i	$-0.734027\pi$
$353$	−13.2988	+	4.84037i	−0.707824	+	0.257627i	−0.0370764	+	0.999312i	$0.511804\pi$
$354$		0			0
$355$	−11.7640	−	14.0198i	−0.624369	−	0.744093i
$356$	1.83835	+	10.4258i	0.0974321	+	0.552565i
$357$		0			0
$358$	−8.35919	−	7.01419i	−0.441797	−	0.370711i
$359$	22.1647	+	12.7968i	1.16981	+	0.675389i	0.953635	−	0.300966i	$-0.0973089\pi$
$359$	22.1647	+	12.7968i	1.16981	+	0.675389i	0.216174	+	0.976355i	$0.430642\pi$
$360$		0			0
$361$	−3.33285	−	5.77266i	−0.175413	−	0.303824i
$362$	−0.663269	+	3.76159i	−0.0348607	+	0.197705i
$363$		0			0
$364$	−0.203903	+	7.96818i	−0.0106874	+	0.417646i
$365$	4.05091	−	11.1298i	0.212034	−	0.582560i
$366$		0			0
$367$	−17.3863	−	3.06568i	−0.907559	−	0.160027i	−0.299664	−	0.954045i	$-0.596875\pi$
$367$	−17.3863	−	3.06568i	−0.907559	−	0.160027i	−0.607895	+	0.794017i	$0.707986\pi$
$368$	−2.20959	+	1.27571i	−0.115183	+	0.0665007i
$369$		0			0
$370$	2.48447	+	1.43441i	0.129161	+	0.0745714i
$371$	3.65087	−	9.28449i	0.189544	−	0.482027i
$372$		0			0
$373$	−1.01057	−	5.73121i	−0.0523252	−	0.296751i	0.947404	−	0.320041i	$-0.103697\pi$
$373$	−1.01057	−	5.73121i	−0.0523252	−	0.296751i	−0.999729	+	0.0232906i	$0.992586\pi$
$374$	−0.108624	+	0.0911465i	−0.00561682	+	0.00471307i
$375$		0			0
$376$	5.60743	+	15.4063i	0.289181	+	0.794518i
$377$	−7.67682			−0.395377
$378$		0			0
$379$	28.0324			1.43993			0.719964	−	0.694011i	$-0.244158\pi$
$379$	28.0324			1.43993			0.719964	+	0.694011i	$0.244158\pi$
$380$	−2.45190	−	6.73655i	−0.125780	−	0.345578i
$381$		0			0
$382$	0.963473	−	0.808450i	0.0492956	−	0.0413639i
$383$	0.202834	+	1.15033i	0.0103643	+	0.0587790i	0.989551	−	0.144181i	$-0.0460549\pi$
$383$	0.202834	+	1.15033i	0.0103643	+	0.0587790i	−0.979187	+	0.202960i	$0.934944\pi$
$384$		0			0
$385$	0.284206	−	0.722762i	0.0144845	−	0.0368354i
$386$	0.0690223	+	0.0398500i	0.00351314	+	0.00202831i
$387$		0			0
$388$	5.95398	−	3.43753i	0.302268	−	0.174514i
$389$	22.4622	+	3.96069i	1.13888	+	0.200815i	0.711115	−	0.703076i	$-0.248191\pi$
$389$	22.4622	+	3.96069i	1.13888	+	0.200815i	0.427763	+	0.903891i	$0.359302\pi$
$390$		0			0
$391$	−0.587844	+	1.61509i	−0.0297285	+	0.0816785i
$392$	4.97684	+	16.2094i	0.251368	+	0.818698i
$393$		0			0
$394$	−1.86476	+	10.5756i	−0.0939452	+	0.532790i
$395$	−5.62511	−	9.74298i	−0.283030	−	0.490222i
$396$		0			0
$397$	13.0866	+	7.55554i	0.656797	+	0.379202i	0.791055	−	0.611745i	$-0.209532\pi$
$397$	13.0866	+	7.55554i	0.656797	+	0.379202i	−0.134259	+	0.990946i	$0.542865\pi$
$398$	−5.06008	−	4.24591i	−0.253639	−	0.212828i
$399$		0			0
$400$	−0.779242	−	4.41930i	−0.0389621	−	0.220965i
$401$	2.49029	+	2.96781i	0.124359	+	0.148205i	0.824631	−	0.565670i	$-0.191383\pi$
$401$	2.49029	+	2.96781i	0.124359	+	0.148205i	−0.700272	+	0.713876i	$0.746938\pi$
$402$		0			0
$403$	−17.1467	+	6.24088i	−0.854137	+	0.310881i
$404$	1.49866			0.0745611
$405$		0			0
$406$	−6.70814	+	2.24896i	−0.332919	+	0.111614i
$407$	0.235358	+	0.646640i	0.0116663	+	0.0320528i
$408$		0			0
$409$	15.1865	+	18.0986i	0.750926	+	0.894919i	0.997238	−	0.0742715i	$-0.0236631\pi$
$409$	15.1865	+	18.0986i	0.750926	+	0.894919i	−0.246312	+	0.969191i	$0.579219\pi$
$410$	10.4376	−	1.84043i	0.515477	−	0.0908925i
$411$		0			0
$412$	−13.1376	+	15.6568i	−0.647243	+	0.771354i
$413$	5.21334	−	25.7027i	0.256532	−	1.26475i
$414$		0			0
$415$	11.4888	+	19.8992i	0.563963	+	0.976813i
$416$	−1.98544	+	11.2600i	−0.0973443	+	0.552067i
$417$		0			0
$418$	−0.181274	+	0.498046i	−0.00886640	+	0.0243602i
$419$	−19.8064	−	7.20893i	−0.967605	−	0.352179i	−0.190596	−	0.981669i	$-0.561042\pi$
$419$	−19.8064	−	7.20893i	−0.967605	−	0.352179i	−0.777009	+	0.629489i	$0.783264\pi$
$420$		0			0
$421$	2.68706	−	15.2391i	0.130959	−	0.742708i	−0.846629	−	0.532183i	$-0.821372\pi$
$421$	2.68706	−	15.2391i	0.130959	−	0.742708i	0.977589	−	0.210524i	$-0.0675172\pi$
$422$	−8.25950	+	4.76863i	−0.402066	+	0.232133i
$423$		0			0
$424$	4.56699	−	7.91026i	0.221793	−	0.384156i
$425$	−2.31572	−	1.94312i	−0.112329	−	0.0942551i
$426$		0			0
$427$	21.8711	−	11.8919i	1.05842	−	0.575491i
$428$	−18.3979	−	21.9258i	−0.889297	−	1.05982i
$429$		0			0
$430$	−0.472684	−	1.29869i	−0.0227948	−	0.0626283i
$431$		−	22.9807i		−	1.10694i	−0.832868	−	0.553472i	$-0.813303\pi$
$431$		−	22.9807i		−	1.10694i	0.832868	−	0.553472i	$-0.186697\pi$
$432$		0			0
$433$		−	24.6163i		−	1.18299i	−0.806310	−	0.591493i	$-0.798539\pi$
$433$		−	24.6163i		−	1.18299i	0.806310	−	0.591493i	$-0.201461\pi$
$434$	−13.1548	+	10.4766i	−0.631449	+	0.502892i
$435$		0			0
$436$	−6.13729	+	5.14980i	−0.293923	+	0.246631i
$437$	1.11556	+	6.32664i	0.0533643	+	0.302644i
$438$		0			0
$439$	−12.4166	+	14.7975i	−0.592613	+	0.706248i	−0.976106	−	0.217296i	$-0.930276\pi$
$439$	−12.4166	+	14.7975i	−0.592613	+	0.706248i	0.383493	+	0.923544i	$0.374721\pi$
$440$	0.355523	−	0.615783i	0.0169489	−	0.0293563i
$441$		0			0
$442$	0.635511	+	1.10074i	0.0302282	+	0.0523567i
$443$	−19.7211	−	3.47737i	−0.936980	−	0.165215i	−0.315749	−	0.948843i	$-0.602256\pi$
$443$	−19.7211	−	3.47737i	−0.936980	−	0.165215i	−0.621231	+	0.783628i	$0.713367\pi$
$444$		0			0
$445$	−8.68835	−	3.16230i	−0.411867	−	0.149907i
$446$	−11.7055	−	4.26045i	−0.554271	−	0.201738i
$447$		0			0
$448$	0.468471	+	3.12188i	0.0221332	+	0.147495i
$449$	10.4575	−	6.03767i	0.493522	−	0.284935i	−0.232512	−	0.972593i	$-0.574695\pi$
$449$	10.4575	−	6.03767i	0.493522	−	0.284935i	0.726034	+	0.687658i	$0.241361\pi$
$450$		0			0
$451$	2.20168	+	1.27114i	0.103673	+	0.0598557i
$452$	−8.05822	+	9.60341i	−0.379027	+	0.451706i
$453$		0			0
$454$	−17.4829	+	3.08271i	−0.820515	+	0.144679i
$455$	−5.93773	−	3.63378i	−0.278365	−	0.170354i
$456$		0			0
$457$	16.7442	−	6.09438i	0.783259	−	0.285083i	0.0807282	−	0.996736i	$-0.474275\pi$
$457$	16.7442	−	6.09438i	0.783259	−	0.285083i	0.702531	+	0.711653i	$0.252053\pi$
$458$	7.44235			0.347758
$459$		0			0
$460$		−	3.73386i		−	0.174092i
$461$	11.0937	−	4.03778i	0.516685	−	0.188058i	−0.0704983	−	0.997512i	$-0.522459\pi$
$461$	11.0937	−	4.03778i	0.516685	−	0.188058i	0.587183	+	0.809454i	$0.300237\pi$
$462$		0			0
$463$	−5.77577	+	4.84645i	−0.268423	+	0.225234i	−0.767057	−	0.641579i	$-0.778280\pi$
$463$	−5.77577	+	4.84645i	−0.268423	+	0.225234i	0.498634	+	0.866813i	$0.333835\pi$
$464$	5.35114	−	0.943551i	0.248421	−	0.0438033i
$465$		0			0
$466$	−1.43417	−	1.20341i	−0.0664365	−	0.0557468i
$467$	−5.54773	+	9.60896i	−0.256719	+	0.444650i	−0.965361	−	0.260918i	$-0.915975\pi$
$467$	−5.54773	+	9.60896i	−0.256719	+	0.444650i	0.708642	+	0.705568i	$0.249308\pi$
$468$		0			0
$469$	−13.4336	−	11.8708i	−0.620307	−	0.548142i
$470$	−6.10915	−	1.07721i	−0.281794	−	0.0496879i
$471$		0			0
$472$	8.21235	−	22.5633i	0.378004	−	1.03856i
$473$	0.113382	−	0.311515i	0.00521331	−	0.0143235i
$474$		0			0
$475$	−11.1274	−	1.96206i	−0.510561	−	0.0900257i
$476$	−2.84793	−	2.51662i	−0.130535	−	0.115349i
$477$		0			0
$478$	−10.3888	+	17.9939i	−0.475172	+	0.823022i
$479$	0.344634	+	0.289182i	0.0157467	+	0.0132131i	0.650627	−	0.759397i	$-0.274506\pi$
$479$	0.344634	+	0.289182i	0.0157467	+	0.0132131i	−0.634880	+	0.772611i	$0.718951\pi$
$480$		0			0
$481$	6.07448	−	1.07109i	0.276972	−	0.0488377i
$482$	12.9014	−	10.8255i	0.587641	−	0.493090i
$483$		0			0
$484$	−15.7332	+	5.72640i	−0.715143	+	0.260291i
$485$			6.00443i			0.272647i
$486$		0			0
$487$	−24.3678			−1.10421			−0.552105	−	0.833774i	$-0.686175\pi$
$487$	−24.3678			−1.10421			−0.552105	+	0.833774i	$0.686175\pi$
$488$	21.4181	−	7.79554i	0.969551	−	0.352888i
$489$		0			0
$490$	−6.25302	−	1.43578i	−0.282482	−	0.0648617i
$491$	−12.6614	+	2.23255i	−0.571402	+	0.100754i	−0.451881	−	0.892078i	$-0.649247\pi$
$491$	−12.6614	+	2.23255i	−0.571402	+	0.100754i	−0.119521	+	0.992832i	$0.538136\pi$
$492$		0			0
$493$	2.35284	−	2.80401i	0.105967	−	0.126286i
$494$	4.11429	+	2.37539i	0.185111	+	0.106874i
$495$		0			0
$496$	11.1851	−	6.45770i	0.502224	−	0.289959i
$497$	−35.8638	+	5.38174i	−1.60871	+	0.241404i
$498$		0			0
$499$	27.7006	+	10.0822i	1.24005	+	0.451341i	0.877028	−	0.480439i	$-0.159523\pi$
$499$	27.7006	+	10.0822i	1.24005	+	0.451341i	0.363022	+	0.931781i	$0.381745\pi$
$500$	15.7618	+	5.73684i	0.704891	+	0.256559i
$501$		0			0
$502$	−16.3095	−	2.87580i	−0.727929	−	0.128353i
$503$	6.61558	+	11.4585i	0.294974	+	0.510910i	0.974979	−	0.222298i	$-0.0713557\pi$
$503$	6.61558	+	11.4585i	0.294974	+	0.510910i	−0.680005	+	0.733208i	$0.738022\pi$
$504$		0			0
$505$	−0.654437	+	1.13352i	−0.0291221	+	0.0504409i
$506$	−0.177443	+	0.211468i	−0.00788829	+	0.00940089i
$507$		0			0
$508$	0.254803	+	1.44506i	0.0113051	+	0.0641143i
$509$	−10.7916	+	9.05526i	−0.478331	+	0.401367i	−0.849823	−	0.527069i	$-0.823291\pi$
$509$	−10.7916	+	9.05526i	−0.478331	+	0.401367i	0.371491	+	0.928436i	$0.378847\pi$
$510$		0			0
$511$	−14.6211	−	18.3588i	−0.646800	−	0.812145i
$512$		−	14.8502i		−	0.656292i
$513$		0			0
$514$			8.06010i			0.355516i
$515$	−6.10512	−	16.7737i	−0.269024	−	0.739137i
$516$		0			0
$517$	−0.956469	−	1.13988i	−0.0420655	−	0.0501317i
$518$	4.99420	−	2.71548i	0.219432	−	0.119311i
$519$		0			0
$520$	−4.88238	−	4.09680i	−0.214107	−	0.179657i
$521$	4.03394	−	6.98699i	0.176730	−	0.306105i	−0.764029	−	0.645182i	$-0.776781\pi$
$521$	4.03394	−	6.98699i	0.176730	−	0.306105i	0.940759	+	0.339077i	$0.110115\pi$
$522$		0			0
$523$	10.5643	−	6.09931i	0.461945	−	0.266704i	−0.250917	−	0.968009i	$-0.580732\pi$
$523$	10.5643	−	6.09931i	0.461945	−	0.266704i	0.712862	+	0.701305i	$0.247399\pi$
$524$	1.29902	−	7.36711i	0.0567479	−	0.321833i
$525$		0			0
$526$	−12.7572	−	4.64325i	−0.556241	−	0.202455i
$527$	2.97570	−	8.17568i	0.129624	−	0.356138i
$528$		0			0
$529$	3.41288	−	19.3554i	0.148386	−	0.841539i
$530$	1.72802	+	2.99301i	0.0750602	+	0.130008i
$531$		0			0
$532$	−13.9220	−	2.82382i	−0.603595	−	0.122428i
$533$	14.6478	−	17.4565i	0.634465	−	0.756126i
$534$		0			0
$535$	24.6177	−	4.34076i	1.06432	−	0.187668i
$536$	−10.5501	−	12.5731i	−0.455695	−	0.543077i
$537$		0			0
$538$	4.02100	+	11.0476i	0.173357	+	0.476296i
$539$	−0.927618	−	1.22794i	−0.0399553	−	0.0528913i
$540$		0			0
$541$	−17.3576			−0.746264			−0.373132	−	0.927778i	$-0.621716\pi$
$541$	−17.3576			−0.746264			−0.373132	+	0.927778i	$0.621716\pi$
$542$	−10.6745	+	3.88519i	−0.458508	+	0.166883i
$543$		0			0
$544$	−3.50427	−	4.17623i	−0.150245	−	0.179054i
$545$	−1.21503	−	6.89079i	−0.0520462	−	0.295169i
$546$		0			0
$547$	5.51648	+	4.62888i	0.235868	+	0.197916i	0.753058	−	0.657954i	$-0.228578\pi$
$547$	5.51648	+	4.62888i	0.235868	+	0.197916i	−0.517191	+	0.855870i	$0.673022\pi$
$548$	−15.4059	−	8.89460i	−0.658107	−	0.379958i
$549$		0			0
$550$	−0.242763	−	0.420477i	−0.0103514	−	0.0179292i
$551$	2.37578	−	13.4737i	0.101212	−	0.574000i
$552$		0			0
$553$	−22.2856	−	0.570280i	−0.947678	−	0.0242508i
$554$	4.04537	−	11.1145i	0.171871	−	0.472212i
$555$		0			0
$556$	−13.8312	−	2.43882i	−0.586575	−	0.103429i
$557$	15.7336	−	9.08382i	0.666655	−	0.384894i	−0.128153	−	0.991754i	$-0.540905\pi$
$557$	15.7336	−	9.08382i	0.666655	−	0.384894i	0.794808	+	0.606861i	$0.207571\pi$
$558$		0			0
$559$	−2.57338	−	1.48574i	−0.108842	−	0.0628402i
$560$	4.58553	+	1.80313i	0.193774	+	0.0761963i
$561$		0			0
$562$	1.70878	+	9.69097i	0.0720805	+	0.408789i
$563$	6.45074	−	5.41282i	0.271866	−	0.228123i	−0.496653	−	0.867949i	$-0.665438\pi$
$563$	6.45074	−	5.41282i	0.271866	−	0.228123i	0.768520	+	0.639826i	$0.220994\pi$
$564$		0			0
$565$	−3.74471	−	10.2885i	−0.157541	−	0.432840i
$566$	9.55604			0.401670
$567$		0			0
$568$	−33.2027			−1.39316
$569$	13.8694	+	38.1057i	0.581434	+	1.59748i	0.785732	+	0.618567i	$0.212286\pi$
$569$	13.8694	+	38.1057i	0.581434	+	1.59748i	−0.204298	+	0.978909i	$0.565491\pi$
$570$		0			0
$571$	−15.0780	+	12.6519i	−0.630994	+	0.529467i	−0.901238	−	0.433325i	$-0.857340\pi$
$571$	−15.0780	+	12.6519i	−0.630994	+	0.529467i	0.270244	+	0.962792i	$0.412896\pi$
$572$	−0.115012	−	0.652268i	−0.00480891	−	0.0272727i
$573$		0			0
$574$	7.68550	−	19.5449i	0.320787	−	0.815789i
$575$	−5.09660	−	2.94252i	−0.212543	−	0.122712i
$576$		0			0
$577$	−33.4084	+	19.2884i	−1.39081	+	0.802985i	−0.993405	−	0.114658i	$-0.963423\pi$
$577$	−33.4084	+	19.2884i	−1.39081	+	0.802985i	−0.397405	+	0.917643i	$0.630089\pi$
$578$	10.8954	+	1.92115i	0.453189	+	0.0799095i
$579$		0			0
$580$	−2.71972	+	7.47238i	−0.112930	+	0.310274i
$581$	45.5164	+	1.16475i	1.88834	+	0.0483219i
$582$		0			0
$583$	−0.143953	+	0.816400i	−0.00596194	+	0.0338118i
$584$	−10.7438	−	18.6088i	−0.444581	−	0.770037i
$585$		0			0
$586$	−7.17721	−	4.14376i	−0.296488	−	0.171177i
$587$	26.1514	+	21.9436i	1.07938	+	0.905710i	0.995869	−	0.0907969i	$-0.0289414\pi$
$587$	26.1514	+	21.9436i	1.07938	+	0.905710i	0.0835134	+	0.996507i	$0.473386\pi$
$588$		0			0
$589$	−5.64702	−	32.0258i	−0.232681	−	1.31960i
$590$	5.83984	+	6.95965i	0.240423	+	0.286524i
$591$		0			0
$592$	−4.10258	+	1.49322i	−0.168615	+	0.0613708i
$593$	6.67349			0.274048			0.137024	−	0.990568i	$-0.456246\pi$
$593$	6.67349			0.274048			0.137024	+	0.990568i	$0.456246\pi$
$594$		0			0
$595$	3.14709	−	1.05509i	0.129018	−	0.0432544i
$596$	−7.96011	−	21.8702i	−0.326059	−	0.895839i
$597$		0			0
$598$	1.59052	+	1.89550i	0.0650411	+	0.0775129i
$599$	−25.4041	+	4.47942i	−1.03798	+	0.183024i	−0.666569	−	0.745443i	$-0.732238\pi$
$599$	−25.4041	+	4.47942i	−1.03798	+	0.183024i	−0.371413	+	0.928468i	$0.621127\pi$
$600$		0			0
$601$	12.8387	−	15.3005i	0.523699	−	0.624121i	−0.437752	−	0.899096i	$-0.644225\pi$
$601$	12.8387	−	15.3005i	0.523699	−	0.624121i	0.961451	+	0.274975i	$0.0886696\pi$
$602$	−2.68392	−	0.544384i	−0.109388	−	0.0221874i
$603$		0			0
$604$	8.61630	+	14.9239i	0.350592	+	0.607243i
$605$	2.53919	−	14.4005i	0.103233	−	0.585462i
$606$		0			0
$607$	11.2649	−	30.9501i	0.457228	−	1.25622i	−0.470312	−	0.882500i	$-0.655859\pi$
$607$	11.2649	−	30.9501i	0.457228	−	1.25622i	0.927540	−	0.373724i	$-0.121919\pi$
$608$	−19.1482	−	6.96937i	−0.776562	−	0.282645i
$609$		0			0
$610$	−1.49755	+	8.49305i	−0.0606342	+	0.343874i
$611$	−11.5509	+	6.66889i	−0.467298	+	0.269795i
$612$		0			0
$613$	15.5747	−	26.9761i	0.629055	−	1.08956i	−0.358687	−	0.933458i	$-0.616775\pi$
$613$	15.5747	−	26.9761i	0.629055	−	1.08956i	0.987742	−	0.156097i	$-0.0498913\pi$
$614$	11.8513	+	9.94441i	0.478279	+	0.401324i
$615$		0			0
$616$	−0.673040	−	1.23783i	−0.0271176	−	0.0498735i
$617$	21.5216	+	25.6485i	0.866428	+	1.03257i	0.999142	+	0.0414139i	$0.0131862\pi$
$617$	21.5216	+	25.6485i	0.866428	+	1.03257i	−0.132714	+	0.991154i	$0.542369\pi$
$618$		0			0
$619$	−1.15081	−	3.16183i	−0.0462550	−	0.127085i	0.914414	−	0.404780i	$-0.132652\pi$
$619$	−1.15081	−	3.16183i	−0.0462550	−	0.127085i	−0.960669	+	0.277695i	$0.910430\pi$
$620$			18.9011i			0.759084i
$621$		0			0
$622$			1.79850i			0.0721132i
$623$	−14.3316	+	11.4138i	−0.574183	+	0.457285i
$624$		0			0
$625$	1.10083	−	0.923703i	0.0440330	−	0.0369481i
$626$	−0.690772	−	3.91756i	−0.0276088	−	0.156577i
$627$		0			0
$628$	12.3628	−	14.7334i	0.493330	−	0.587928i
$629$	−1.47052	+	2.54701i	−0.0586334	+	0.101556i
$630$		0			0
$631$	−9.48269	−	16.4245i	−0.377500	−	0.653849i	0.613198	−	0.789929i	$-0.289883\pi$
$631$	−9.48269	−	16.4245i	−0.377500	−	0.653849i	−0.990698	+	0.136080i	$0.956549\pi$
$632$	−20.1001	−	3.54419i	−0.799540	−	0.140980i
$633$		0			0
$634$	9.54535	+	3.47422i	0.379094	+	0.137979i
$635$	−1.20425	−	0.438310i	−0.0477891	−	0.0173938i
$636$		0			0
$637$	−12.2834	+	6.27714i	−0.486685	+	0.248709i
$638$	0.509138	−	0.293951i	0.0201570	−	0.0116376i
$639$		0			0
$640$	12.4710	+	7.20013i	0.492959	+	0.284610i
$641$	−12.8204	+	15.2788i	−0.506376	+	0.603475i	−0.957303	−	0.289085i	$-0.906649\pi$
$641$	−12.8204	+	15.2788i	−0.506376	+	0.603475i	0.450927	+	0.892561i	$0.351093\pi$
$642$		0			0
$643$	−32.5518	+	5.73976i	−1.28372	+	0.226354i	−0.773558	−	0.633726i	$-0.781525\pi$
$643$	−32.5518	+	5.73976i	−1.28372	+	0.226354i	−0.510160	+	0.860080i	$0.670414\pi$
$644$	−6.31084	−	3.86212i	−0.248682	−	0.152189i
$645$		0			0
$646$	−2.12860	+	0.774746i	−0.0837485	+	0.0304820i
$647$	−22.6934			−0.892168			−0.446084	−	0.894991i	$-0.647182\pi$
$647$	−22.6934			−0.892168			−0.446084	+	0.894991i	$0.647182\pi$
$648$		0			0
$649$			2.17925i			0.0855431i
$650$	−4.08958	+	1.48848i	−0.160406	+	0.0583831i
$651$		0			0
$652$	−18.1472	+	15.2273i	−0.710698	+	0.596346i
$653$	−17.5842	+	3.10057i	−0.688122	+	0.121335i	−0.506767	−	0.862083i	$-0.669160\pi$
$653$	−17.5842	+	3.10057i	−0.688122	+	0.121335i	−0.181355	+	0.983418i	$0.558048\pi$
$654$		0			0
$655$	5.00488	+	4.19960i	0.195557	+	0.164092i
$656$	−8.06469	+	13.9684i	−0.314873	+	0.545376i
$657$		0			0
$658$	−8.13966	+	9.21126i	−0.317317	+	0.359092i
$659$	15.8260	+	2.79056i	0.616495	+	0.108705i	0.473170	−	0.880971i	$-0.343109\pi$
$659$	15.8260	+	2.79056i	0.616495	+	0.108705i	0.143325	+	0.989676i	$0.454221\pi$
$660$		0			0
$661$	−14.4940	+	39.8218i	−0.563750	+	1.54889i	0.250344	+	0.968157i	$0.419456\pi$
$661$	−14.4940	+	39.8218i	−0.563750	+	1.54889i	−0.814094	+	0.580733i	$0.802766\pi$
$662$	−2.41469	+	6.63430i	−0.0938495	+	0.257849i
$663$		0			0
$664$	41.0528	+	7.23872i	1.59316	+	0.280917i
$665$	8.21529	−	9.29685i	0.318575	−	0.360516i
$666$		0			0
$667$	3.56298	−	6.17126i	0.137959	−	0.238952i
$668$	−26.0337	−	21.8449i	−1.00727	−	0.845203i
$669$		0			0
$670$	6.11588	−	1.07839i	0.236277	−	0.0416620i
$671$	−1.58467	+	1.32970i	−0.0611757	+	0.0513325i
$672$		0			0
$673$	−10.5299	+	3.83256i	−0.405897	+	0.147734i	−0.536897	−	0.843648i	$-0.680403\pi$
$673$	−10.5299	+	3.83256i	−0.405897	+	0.147734i	0.131000	+	0.991382i	$0.458181\pi$
$674$			18.9479i			0.729845i
$675$		0			0
$676$	13.9375			0.536059
$677$	−4.46954	+	1.62678i	−0.171778	+	0.0625222i	−0.426478	−	0.904498i	$-0.640246\pi$
$677$	−4.46954	+	1.62678i	−0.171778	+	0.0625222i	0.254699	+	0.967020i	$0.418024\pi$
$678$		0			0
$679$	10.1485	+	6.21067i	0.389462	+	0.238344i
$680$	2.99277	−	0.527705i	0.114767	−	0.0202366i
$681$		0			0
$682$	0.898226	−	1.07046i	0.0343948	−	0.0409902i
$683$	−22.2708	−	12.8581i	−0.852170	−	0.492001i	0.00921244	−	0.999958i	$-0.497068\pi$
$683$	−22.2708	−	12.8581i	−0.852170	−	0.492001i	−0.861382	+	0.507957i	$0.830401\pi$
$684$		0			0
$685$	13.4549	−	7.76821i	0.514086	−	0.296808i
$686$	−8.89450	+	9.08353i	−0.339594	+	0.346811i
$687$		0			0
$688$	1.97639	+	0.719347i	0.0753492	+	0.0274248i
$689$	6.98261	+	2.54146i	0.266016	+	0.0968220i
$690$		0			0
$691$	6.87549	+	1.21234i	0.261556	+	0.0461194i	0.302888	−	0.953026i	$-0.402049\pi$
$691$	6.87549	+	1.21234i	0.261556	+	0.0461194i	−0.0413322	+	0.999145i	$0.513160\pi$
$692$	−3.58348	−	6.20677i	−0.136223	−	0.235946i
$693$		0			0
$694$	2.65350	−	4.59600i	0.100726	−	0.174462i
$695$	7.88445	−	9.39632i	0.299074	−	0.356423i
$696$		0			0
$697$	1.88676	+	10.7004i	0.0714663	+	0.405305i
$698$	−15.8664	+	13.3135i	−0.600552	+	0.503923i
$699$		0			0
$700$	10.1794	−	8.10698i	0.384746	−	0.306415i
$701$			4.24261i			0.160241i	0.996785	+	0.0801206i	$0.0255305\pi$
$701$			4.24261i			0.160241i	−0.996785	+	0.0801206i	$0.974469\pi$
$702$		0			0
$703$			10.9929i			0.414605i
$704$	−0.0897175	−	0.246497i	−0.00338135	−	0.00929020i
$705$		0			0
$706$	−6.24451	−	7.44192i	−0.235015	−	0.280080i
$707$	1.23892	+	2.27856i	0.0465942	+	0.0856940i
$708$		0			0
$709$	20.5679	+	17.2586i	0.772445	+	0.648159i	0.941334	−	0.337477i	$-0.109573\pi$
$709$	20.5679	+	17.2586i	0.772445	+	0.648159i	−0.168889	+	0.985635i	$0.554018\pi$
$710$	6.28148	−	10.8798i	0.235740	−	0.408313i
$711$		0			0
$712$	−14.5268	+	8.38702i	−0.544413	+	0.314317i
$713$	2.94121	−	16.6804i	0.110149	−	0.624687i
$714$		0			0
$715$	0.543570	+	0.197843i	0.0203283	+	0.00739891i
$716$	−8.31204	+	22.8371i	−0.310635	+	0.853464i
$717$		0			0
$718$	−3.05074	+	17.3016i	−0.113853	+	0.645691i
$719$	18.0874	+	31.3282i	0.674545	+	1.16835i	0.976602	+	0.215057i	$0.0689936\pi$
$719$	18.0874	+	31.3282i	0.674545	+	1.16835i	−0.302056	+	0.953290i	$0.597673\pi$
$720$		0			0
$721$	−34.6651	−	7.03119i	−1.29100	−	0.261855i
$722$	2.94115	−	3.50512i	0.109458	−	0.130447i
$723$		0			0
$724$	8.37755	−	1.47719i	0.311349	−	0.0548992i
$725$	8.05623	+	9.60105i	0.299201	+	0.356574i
$726$		0			0
$727$	6.90637	+	18.9751i	0.256143	+	0.703748i	0.999396	+	0.0347375i	$0.0110595\pi$
$727$	6.90637	+	18.9751i	0.256143	+	0.703748i	−0.743253	+	0.669010i	$0.766718\pi$
$728$	−11.9744	+	4.01450i	−0.443799	+	0.148787i
$729$		0			0
$730$	8.13027			0.300915
$731$	1.33138	−	0.484583i	0.0492429	−	0.0179230i
$732$		0			0
$733$	0.867738	+	1.03413i	0.0320506	+	0.0381965i	0.781832	−	0.623490i	$-0.214286\pi$
$733$	0.867738	+	1.03413i	0.0320506	+	0.0381965i	−0.749781	+	0.661686i	$0.769841\pi$
$734$	−2.10441	−	11.9347i	−0.0776753	−	0.440518i
$735$		0			0
$736$	−8.13022	−	6.82207i	−0.299684	−	0.251465i
$737$	1.29007	+	0.744820i	0.0475202	+	0.0274358i
$738$		0			0
$739$	8.05469	+	13.9511i	0.296297	+	0.513201i	0.975286	−	0.220948i	$-0.0709150\pi$
$739$	8.05469	+	13.9511i	0.296297	+	0.513201i	−0.678989	+	0.734148i	$0.737582\pi$
$740$	1.10948	−	6.29217i	0.0407853	−	0.231305i
$741$		0			0
$742$	6.84606	+	0.175188i	0.251327	+	0.00643136i
$743$	10.0891	−	27.7195i	0.370132	−	1.01693i	−0.605178	−	0.796090i	$-0.706898\pi$
$743$	10.0891	−	27.7195i	0.370132	−	1.01693i	0.975310	−	0.220840i	$-0.0708798\pi$
$744$		0			0
$745$	20.0177	+	3.52965i	0.733390	+	0.129316i
$746$	3.45963	−	1.99742i	0.126666	−	0.0731307i
$747$		0			0
$748$	0.273495	+	0.157902i	0.00999995	+	0.00577348i
$749$	18.1267	−	46.0978i	0.662335	−	1.68438i
$750$		0			0
$751$	−1.81313	−	10.2828i	−0.0661622	−	0.375224i	−0.999853	−	0.0171442i	$-0.994543\pi$
$751$	−1.81313	−	10.2828i	−0.0661622	−	0.375224i	0.933691	−	0.358080i	$-0.116569\pi$
$752$	7.23188	−	6.06827i	0.263720	−	0.221287i
$753$		0			0
$754$	−1.80234	−	4.95189i	−0.0656374	−	0.180337i
$755$	−15.0503			−0.547737
$756$		0			0
$757$	28.0501			1.01950			0.509749	−	0.860323i	$-0.329738\pi$
$757$	28.0501			1.01950			0.509749	+	0.860323i	$0.329738\pi$
$758$	6.58137	+	18.0822i	0.239046	+	0.656774i
$759$		0			0
$760$	8.70135	−	7.30130i	0.315631	−	0.264846i
$761$	−4.79778	−	27.2096i	−0.173919	−	0.986346i	−0.939384	−	0.342867i	$-0.888602\pi$
$761$	−4.79778	−	27.2096i	−0.173919	−	0.986346i	0.765464	−	0.643478i	$-0.222509\pi$
$762$		0			0
$763$	−12.9033	−	5.07388i	−0.467132	−	0.183687i
$764$	−2.42584	−	1.40056i	−0.0877638	−	0.0506704i
$765$		0			0
$766$	−0.694392	+	0.400908i	−0.0250894	+	0.0144854i
$767$	19.2371	+	3.39202i	0.694611	+	0.122479i
$768$		0			0
$769$	−13.9253	+	38.2594i	−0.502159	+	1.37967i	0.387004	+	0.922078i	$0.373510\pi$
$769$	−13.9253	+	38.2594i	−0.502159	+	1.37967i	−0.889162	+	0.457592i	$0.848712\pi$
$770$	0.532939	+	0.0136377i	0.0192058	+	0.000491470i
$771$		0			0
$772$	0.0308230	−	0.174806i	0.00110934	−	0.00629140i
$773$	10.5422	+	18.2596i	0.379176	+	0.656752i	0.990943	−	0.134286i	$-0.0428742\pi$
$773$	10.5422	+	18.2596i	0.379176	+	0.656752i	−0.611767	+	0.791038i	$0.709541\pi$
$774$		0			0
$775$	25.7993	+	14.8952i	0.926739	+	0.535053i
$776$	8.34472	+	7.00205i	0.299558	+	0.251359i
$777$		0			0
$778$	2.71878	+	15.4190i	0.0974732	+	0.552798i
$779$	26.1051	+	31.1109i	0.935314	+	1.11466i
$780$		0			0
$781$	2.83173	−	1.03066i	0.101327	−	0.0368801i
$782$	−1.17982			−0.0421901
$783$		0			0
$784$	7.79063	−	5.88523i	0.278237	−	0.210187i
$785$	5.74508	+	15.7845i	0.205051	+	0.563372i
$786$		0			0
$787$	9.72249	+	11.5868i	0.346569	+	0.413025i	0.910968	−	0.412477i	$-0.135336\pi$
$787$	9.72249	+	11.5868i	0.346569	+	0.413025i	−0.564399	+	0.825502i	$0.690892\pi$
$788$	23.5532	−	4.15306i	0.839048	−	0.147947i
$789$		0			0
$790$	4.96401	−	5.91588i	0.176612	−	0.210477i
$791$	−21.2626	−	4.31273i	−0.756010	−	0.153343i
$792$		0			0
$793$	9.27121	+	16.0582i	0.329230	+	0.570244i
$794$	−1.80123	+	10.2153i	−0.0639234	+	0.362527i
$795$		0			0
$796$	−5.03154	+	13.8240i	−0.178338	+	0.489980i
$797$	−21.7035	−	7.89942i	−0.768776	−	0.279812i	−0.0722918	−	0.997384i	$-0.523031\pi$
$797$	−21.7035	−	7.89942i	−0.768776	−	0.279812i	−0.696484	+	0.717572i	$0.745254\pi$
$798$		0			0
$799$	1.10433	−	6.26295i	0.0390683	−	0.221567i
$800$	16.1659	−	9.33341i	0.571552	−	0.329986i
$801$		0			0
$802$	−1.32971	+	2.30312i	−0.0469536	+	0.0813260i
$803$	1.49394	+	1.25356i	0.0527200	+	0.0442373i
$804$		0			0
$805$	5.67695	−	3.08672i	0.200086	−	0.108792i
$806$	−8.05130	−	9.59516i	−0.283595	−	0.337975i
$807$		0			0
$808$	0.812149	+	2.23136i	0.0285713	+	0.0784990i
$809$			28.4204i			0.999209i	0.866254	+	0.499604i	$0.166521\pi$
$809$			28.4204i			0.999209i	−0.866254	+	0.499604i	$0.833479\pi$
$810$		0			0
$811$		−	19.4101i		−	0.681580i	−0.940139	−	0.340790i	$-0.889305\pi$
$811$		−	19.4101i		−	0.681580i	0.940139	−	0.340790i	$-0.110695\pi$
$812$	9.81640	+	12.3258i	0.344488	+	0.432552i
$813$		0			0
$814$	−0.361855	+	0.303633i	−0.0126830	+	0.0106423i
$815$	−3.59269	−	20.3752i	−0.125846	−	0.713711i
$816$		0			0
$817$	3.40405	−	4.05678i	0.119092	−	0.141929i
$818$	−8.10897	+	14.0451i	−0.283523	+	0.491077i
$819$		0			0
$820$	−11.8023	−	20.4421i	−0.412153	−	0.713870i
$821$	−20.0727	−	3.53937i	−0.700544	−	0.123525i	−0.187979	−	0.982173i	$-0.560194\pi$
$821$	−20.0727	−	3.53937i	−0.700544	−	0.123525i	−0.512565	+	0.858648i	$0.671305\pi$
$822$		0			0
$823$	16.5465	+	6.02243i	0.576774	+	0.209929i	0.613903	−	0.789382i	$-0.289599\pi$
$823$	16.5465	+	6.02243i	0.576774	+	0.209929i	−0.0371281	+	0.999311i	$0.511821\pi$
$824$	−30.4309	−	11.0759i	−1.06011	−	0.385849i
$825$		0			0
$826$	17.8034	−	2.67158i	0.619459	−	0.0929562i
$827$	15.2517	−	8.80555i	0.530352	−	0.306199i	−0.210808	−	0.977528i	$-0.567609\pi$
$827$	15.2517	−	8.80555i	0.530352	−	0.306199i	0.741160	+	0.671329i	$0.234276\pi$
$828$		0			0
$829$	−35.2758	−	20.3665i	−1.22518	−	0.707357i	−0.259161	−	0.965834i	$-0.583446\pi$
$829$	−35.2758	−	20.3665i	−1.22518	−	0.707357i	−0.966017	+	0.258477i	$0.916779\pi$
$830$	−10.1386	+	12.0827i	−0.351915	+	0.419396i
$831$		0			0
$832$	−2.31557	+	0.408297i	−0.0802778	+	0.0141551i
$833$	1.47192	−	6.41043i	0.0509990	−	0.222108i
$834$		0			0
$835$	27.8909	−	10.1514i	0.965203	−	0.351305i
$836$	1.18040			0.0408250
$837$		0			0
$838$		−	14.4685i		−	0.499806i
$839$	48.4147	−	17.6215i	1.67146	−	0.608362i	0.679361	−	0.733804i	$-0.262257\pi$
$839$	48.4147	−	17.6215i	1.67146	−	0.608362i	0.992101	+	0.125442i	$0.0400348\pi$
$840$		0			0
$841$	10.5898	−	8.88589i	0.365165	−	0.306410i
$842$	10.4608	−	1.84451i	0.360501	−	0.0635661i
$843$		0			0
$844$	16.2713	+	13.6533i	0.560082	+	0.469965i
$845$	−6.08626	+	10.5417i	−0.209374	+	0.362646i
$846$		0			0
$847$	−21.7127	−	19.1867i	−0.746058	−	0.659264i
$848$	−5.17961	−	0.913305i	−0.177869	−	0.0313630i
$849$		0			0
$850$	0.709721	−	1.94994i	0.0243432	−	0.0668825i
$851$	−1.95826	+	5.38028i	−0.0671283	+	0.184433i
$852$		0			0
$853$	34.7100	+	6.12032i	1.18845	+	0.209556i	0.732700	−	0.680552i	$-0.238260\pi$
$853$	34.7100	+	6.12032i	1.18845	+	0.209556i	0.455750	+	0.890108i	$0.349371\pi$
$854$	12.8057	+	11.3159i	0.438201	+	0.387222i
$855$		0			0
$856$	22.6753	−	39.2747i	0.775024	−	1.34238i
$857$	11.0923	+	9.30753i	0.378905	+	0.317939i	0.812272	−	0.583278i	$-0.198230\pi$
$857$	11.0923	+	9.30753i	0.378905	+	0.317939i	−0.433367	+	0.901217i	$0.642675\pi$
$858$		0			0
$859$	−25.8833	+	4.56392i	−0.883125	+	0.155719i	−0.596777	−	0.802407i	$-0.703552\pi$
$859$	−25.8833	+	4.56392i	−0.883125	+	0.155719i	−0.286348	+	0.958126i	$0.592441\pi$
$860$	−2.35786	+	1.97848i	−0.0804025	+	0.0674657i
$861$		0			0
$862$	14.8236	−	5.39535i	0.504894	−	0.183766i
$863$			30.3370i			1.03269i	0.856382	+	0.516343i	$0.172707\pi$
$863$			30.3370i			1.03269i	−0.856382	+	0.516343i	$0.827293\pi$
$864$		0			0
$865$	6.25936			0.212824
$866$	15.8786	−	5.77935i	0.539578	−	0.196390i
$867$		0			0
$868$	31.9459	+	19.5503i	1.08431	+	0.663580i
$869$	1.82428	−	0.321669i	0.0618843	−	0.0109119i
$870$		0			0
$871$	8.58280	−	10.2286i	0.290817	−	0.346582i
$872$	−10.9935	−	6.34707i	−0.372285	−	0.214939i
$873$		0			0
$874$	−3.81906	+	2.20493i	−0.129182	+	0.0745830i
$875$	4.30775	+	28.7068i	0.145628	+	0.970467i
$876$		0			0
$877$	9.84932	+	3.58486i	0.332588	+	0.121052i	0.502916	−	0.864335i	$-0.332261\pi$
$877$	9.84932	+	3.58486i	0.332588	+	0.121052i	−0.170328	+	0.985387i	$0.554483\pi$
$878$	−12.4602	−	4.53515i	−0.420512	−	0.153054i
$879$		0			0
$880$	−0.403213	−	0.0710973i	−0.0135923	−	0.00239669i
$881$	11.9814	+	20.7524i	0.403664	+	0.699166i	0.994165	−	0.107871i	$-0.0344033\pi$
$881$	11.9814	+	20.7524i	0.403664	+	0.699166i	−0.590501	+	0.807037i	$0.701070\pi$
$882$		0			0
$883$	−4.74787	+	8.22356i	−0.159779	+	0.276745i	−0.934789	−	0.355204i	$-0.884411\pi$
$883$	−4.74787	+	8.22356i	−0.159779	+	0.276745i	0.775010	+	0.631949i	$0.217745\pi$
$884$	1.81956	−	2.16847i	0.0611984	−	0.0729334i
$885$		0			0
$886$	−2.38701	−	13.5374i	−0.0801933	−	0.454799i
$887$	7.75777	−	6.50955i	0.260481	−	0.218569i	−0.503189	−	0.864176i	$-0.667840\pi$
$887$	7.75777	−	6.50955i	0.260481	−	0.218569i	0.763670	+	0.645607i	$0.223396\pi$
$888$		0			0
$889$	−1.98643	+	1.58201i	−0.0666226	+	0.0530589i
$890$		−	6.34681i		−	0.212746i
$891$		0			0
$892$			27.7427i			0.928896i
$893$	−8.12999	−	22.3370i	−0.272060	−	0.747478i
$894$		0			0
$895$	−13.6433	−	16.2594i	−0.456044	−	0.543492i
$896$	25.0687	−	13.6306i	0.837488	−	0.455365i
$897$		0			0
$898$	6.34976	+	5.32808i	0.211894	+	0.177800i
$899$	−18.0360	+	31.2393i	−0.601535	+	1.04189i
$900$		0			0
$901$	−3.06836	+	1.77152i	−0.102222	+	0.0590178i
$902$	−0.303038	+	1.71862i	−0.0100901	+	0.0572237i
$903$		0			0
$904$	−18.6654	−	6.79366i	−0.620803	−	0.225954i
$905$	−2.54104	+	6.98145i	−0.0844671	+	0.232071i
$906$		0			0
$907$	1.43669	−	8.14786i	0.0477044	−	0.270545i	−0.951621	−	0.307275i	$-0.900583\pi$
$907$	1.43669	−	8.14786i	0.0477044	−	0.270545i	0.999325	+	0.0367297i	$0.0116940\pi$
$908$	19.7687	+	34.2405i	0.656048	+	1.13631i
$909$		0			0
$910$	0.949908	−	4.68323i	0.0314891	−	0.155248i
$911$	−29.3546	+	34.9835i	−0.972562	+	1.15905i	0.0146900	+	0.999892i	$0.495324\pi$
$911$	−29.3546	+	34.9835i	−0.972562	+	1.15905i	−0.987252	+	0.159163i	$0.949121\pi$
$912$		0			0
$913$	−3.72593	+	0.656981i	−0.123310	+	0.0217429i
$914$	7.86230	+	9.36992i	0.260062	+	0.309929i
$915$		0			0
$916$	−5.66902	−	15.5755i	−0.187310	−	0.514629i
$917$	12.2748	−	4.11523i	0.405350	−	0.135897i
$918$		0			0
$919$	30.8173			1.01657			0.508285	−	0.861189i	$-0.330280\pi$
$919$	30.8173			1.01657			0.508285	+	0.861189i	$0.330280\pi$
$920$	5.55936	−	2.02344i	0.183287	−	0.0667109i
$921$		0			0
$922$	5.20909	+	6.20796i	0.171552	+	0.204448i
$923$	−4.69047	−	26.6010i	−0.154389	−	0.875582i
$924$		0			0
$925$	−7.71426	−	6.47303i	−0.253643	−	0.212832i
$926$	−4.48220	−	2.58780i	−0.147294	−	0.0850403i
$927$		0			0
$928$	11.3014	+	19.5746i	0.370988	+	0.642569i
$929$	2.61616	−	14.8370i	0.0858334	−	0.486786i	−0.911340	−	0.411654i	$-0.864951\pi$
$929$	2.61616	−	14.8370i	0.0858334	−	0.486786i	0.997174	−	0.0751316i	$-0.0239377\pi$
$930$		0			0
$931$	−7.21573	−	23.5014i	−0.236486	−	0.770226i
$932$	−1.42608	+	3.91812i	−0.0467127	+	0.128342i
$933$		0			0
$934$	−7.50069	−	1.32257i	−0.245430	−	0.0432759i
$935$	−0.238860	+	0.137906i	−0.00781156	+	0.00451000i
$936$		0			0
$937$	−3.52097	−	2.03283i	−0.115025	−	0.0664097i	0.441384	−	0.897318i	$-0.354488\pi$
$937$	−3.52097	−	2.03283i	−0.115025	−	0.0664097i	−0.556409	+	0.830909i	$0.687821\pi$
$938$	4.50329	−	11.4523i	0.147038	−	0.373930i
$939$		0			0
$940$	2.39908	+	13.6059i	0.0782495	+	0.443775i
$941$	7.66760	−	6.43388i	0.249957	−	0.209738i	−0.509197	−	0.860650i	$-0.670058\pi$
$941$	7.66760	−	6.43388i	0.249957	−	0.209738i	0.759154	+	0.650912i	$0.225613\pi$
$942$		0			0
$943$	7.23464	+	19.8770i	0.235592	+	0.647285i
$944$	−13.8262			−0.450003
$945$		0			0
$946$	0.227560			0.00739863
$947$	17.9748	+	49.3853i	0.584102	+	1.60481i	0.781102	+	0.624403i	$0.214658\pi$
$947$	17.9748	+	49.3853i	0.584102	+	1.60481i	−0.197001	+	0.980403i	$0.563120\pi$
$948$		0			0
$949$	13.3910	−	11.2364i	0.434691	−	0.364749i
$950$	−1.34684	−	7.63833i	−0.0436974	−	0.247820i
$951$		0			0
$952$	2.20366	−	5.60410i	0.0714209	−	0.181630i
$953$	−40.6849	−	23.4895i	−1.31791	−	0.760898i	−0.334521	−	0.942388i	$-0.608575\pi$
$953$	−40.6849	−	23.4895i	−1.31791	−	0.760898i	−0.983393	+	0.181490i	$0.941908\pi$
$954$		0			0
$955$	2.11864	−	1.22320i	0.0685575	−	0.0395817i
$956$	45.5714	+	8.03546i	1.47388	+	0.259885i
$957$		0			0
$958$	−0.105623	+	0.290197i	−0.00341253	+	0.00937585i
$959$	0.787550	−	30.7761i	0.0254313	−	0.993811i
$960$		0			0
$961$	−9.50550	+	53.9084i	−0.306629	+	1.73898i
$962$	2.11705	+	3.66684i	0.0682565	+	0.118224i
$963$		0			0
$964$	−32.4832	−	18.7542i	−1.04621	−	0.604031i
$965$	0.118755	+	0.0996476i	0.00382287	+	0.00320777i
$966$		0			0
$967$	1.24818	+	7.07876i	0.0401386	+	0.227638i	0.998278	−	0.0586658i	$-0.0186846\pi$
$967$	1.24818	+	7.07876i	0.0401386	+	0.227638i	−0.958139	+	0.286303i	$0.907574\pi$
$968$	−17.0521	−	20.3219i	−0.548076	−	0.653172i
$969$		0			0
$970$	−3.87312	+	1.40970i	−0.124359	+	0.0452628i
$971$	−13.7938			−0.442663			−0.221331	−	0.975199i	$-0.571040\pi$
$971$	−13.7938			−0.442663			−0.221331	+	0.975199i	$0.571040\pi$
$972$		0			0
$973$	−7.72605	−	23.0451i	−0.247686	−	0.738791i
$974$	−5.72100	−	15.7183i	−0.183313	−	0.503648i
$975$		0			0
$976$	−8.43622	−	10.0539i	−0.270037	−	0.321817i
$977$	12.3023	−	2.16922i	0.393584	−	0.0693996i	0.0266464	−	0.999645i	$-0.491517\pi$
$977$	12.3023	−	2.16922i	0.393584	−	0.0693996i	0.366938	+	0.930245i	$0.380406\pi$
$978$		0			0
$979$	0.978581	−	1.16623i	0.0312756	−	0.0372728i
$980$	1.75825	+	14.1801i	0.0561653	+	0.452966i
$981$		0			0
$982$	−4.41271	−	7.64304i	−0.140815	−	0.243899i
$983$	5.29506	−	30.0298i	0.168886	−	0.957801i	−0.776081	−	0.630634i	$-0.782795\pi$
$983$	5.29506	−	30.0298i	0.168886	−	0.957801i	0.944967	−	0.327167i	$-0.106094\pi$
$984$		0			0
$985$	−7.14405	+	19.6281i	−0.227628	+	0.625404i
$986$	2.36110	+	0.859371i	0.0751928	+	0.0273679i
$987$		0			0
$988$	1.83730	−	10.4198i	0.0584523	−	0.331500i
$989$	2.38872	−	1.37913i	0.0759569	−	0.0438537i
$990$		0			0
$991$	−26.4504	+	45.8134i	−0.840224	+	1.45531i	0.0494806	+	0.998775i	$0.484243\pi$
$991$	−26.4504	+	45.8134i	−0.840224	+	1.45531i	−0.889705	+	0.456536i	$0.849090\pi$
$992$	41.1557	+	34.5337i	1.30670	+	1.09645i
$993$		0			0
$994$	−11.8915	−	21.8703i	−0.377175	−	0.693683i
$995$	−8.25869	−	9.84233i	−0.261818	−	0.312023i
$996$		0			0
$997$	−12.3634	−	33.9682i	−0.391553	−	1.07578i	−0.966293	−	0.257446i	$-0.917119\pi$
$997$	−12.3634	−	33.9682i	−0.391553	−	1.07578i	0.574740	−	0.818336i	$-0.305103\pi$
$998$			20.2352i			0.640534i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.62.14		132
3.2	odd	2		189.2.be.a.20.9	✓	132
7.6	odd	2	inner	567.2.be.a.62.13		132
21.20	even	2		189.2.be.a.20.10	yes	132
27.4	even	9		189.2.be.a.104.10	yes	132
27.23	odd	18	inner	567.2.be.a.503.13		132
189.104	even	18	inner	567.2.be.a.503.14		132
189.139	odd	18		189.2.be.a.104.9	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.9	✓	132	3.2	odd	2
189.2.be.a.20.10	yes	132	21.20	even	2
189.2.be.a.104.9	yes	132	189.139	odd	18
189.2.be.a.104.10	yes	132	27.4	even	9
567.2.be.a.62.13		132	7.6	odd	2	inner
567.2.be.a.62.14		132	1.1	even	1	trivial
567.2.be.a.503.13		132	27.23	odd	18	inner
567.2.be.a.503.14		132	189.104	even	18	inner

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.234777 + 0.645045i) q^{2} +(1.17113 - 0.982692i) q^{4} +(0.231854 + 1.31491i) q^{5} +(2.46223 + 0.968204i) q^{7} +(2.09779 + 1.21116i) q^{8} +(-0.793741 + 0.458267i) q^{10} +(-0.216508 - 0.0381762i) q^{11} +(-0.673991 + 1.85178i) q^{13} +(-0.0464596 + 1.81556i) q^{14} +(0.242207 - 1.37362i) q^{16} +(-0.469803 - 0.813723i) q^{17} +(-3.04150 - 1.75601i) q^{19} +(1.56368 + 1.31208i) q^{20} +(-0.0262057 - 0.148620i) q^{22} +(-1.17579 - 1.40126i) q^{23} +(3.02323 - 1.10037i) q^{25} -1.35272 q^{26} +(3.83503 - 1.28572i) q^{28} +(1.33239 + 3.66070i) q^{29} +(5.95195 + 7.09326i) q^{31} +(5.71394 - 1.00752i) q^{32} +(0.414589 - 0.494088i) q^{34} +(-0.702223 + 3.46209i) q^{35} +(-1.56504 - 2.71072i) q^{37} +(0.418631 - 2.37418i) q^{38} +(-1.10618 + 3.03921i) q^{40} +(-10.8664 - 3.95506i) q^{41} +(-0.261843 + 1.48498i) q^{43} +(-0.291074 + 0.168051i) q^{44} +(0.627824 - 1.08742i) q^{46} +(5.18484 + 4.35059i) q^{47} +(5.12516 + 4.76788i) q^{49} +(1.41957 + 1.69178i) q^{50} +(1.03040 + 2.83099i) q^{52} -3.77077i q^{53} -0.293540i q^{55} +(3.99259 + 5.01324i) q^{56} +(-2.04850 + 1.71890i) q^{58} +(-1.72130 - 9.76195i) q^{59} +(6.04827 - 7.20805i) q^{61} +(-3.17809 + 5.50461i) q^{62} +(0.596586 + 1.03332i) q^{64} +(-2.59119 - 0.456896i) q^{65} +(-6.36714 - 2.31745i) q^{67} +(-1.34984 - 0.491301i) q^{68} +(-2.39807 + 0.359855i) q^{70} +(-11.8706 + 6.85351i) q^{71} +(-7.68223 - 4.43534i) q^{73} +(1.38110 - 1.64593i) q^{74} +(-5.28760 + 0.932347i) q^{76} +(-0.496130 - 0.303622i) q^{77} +(-7.91776 + 2.88183i) q^{79} +1.86235 q^{80} -7.93789i q^{82} +(16.1714 - 5.88589i) q^{83} +(0.961047 - 0.806414i) q^{85} +(-1.01936 + 0.179740i) q^{86} +(-0.407950 - 0.342311i) q^{88} +(-3.46240 + 5.99705i) q^{89} +(-3.45242 + 3.90694i) q^{91} +(-2.75401 - 0.485606i) q^{92} +(-1.58905 + 4.36587i) q^{94} +(1.60381 - 4.40644i) q^{95} +(4.42872 + 0.780904i) q^{97} +(-1.87223 + 4.42535i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

L-functions

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