LMFDB - Embedded newform 684.2.ce.a.215.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(35,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("684.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.ce (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.8
Character	$\chi$	$=$	684.215
Dual form			684.2.ce.a.35.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12762 + 0.853506i) q^{2} +(0.543054 - 1.92486i) q^{4} +(4.17116 - 0.735488i) q^{5} +(2.05168 + 1.18454i) q^{7} +(1.03052 + 2.63401i) q^{8} +O(q^{10})$	\(q+(-1.12762 + 0.853506i) q^{2} +(0.543054 - 1.92486i) q^{4} +(4.17116 - 0.735488i) q^{5} +(2.05168 + 1.18454i) q^{7} +(1.03052 + 2.63401i) q^{8} +(-4.07574 + 4.38947i) q^{10} +(2.46013 + 4.26108i) q^{11} +(-3.96446 + 1.44294i) q^{13} +(-3.32452 + 0.415413i) q^{14} +(-3.41019 - 2.09061i) q^{16} +(2.78144 + 3.31479i) q^{17} +(-4.10988 + 1.45220i) q^{19} +(0.849452 - 8.42832i) q^{20} +(-6.41095 - 2.70514i) q^{22} +(0.671956 - 3.81085i) q^{23} +(12.1592 - 4.42558i) q^{25} +(3.23884 - 5.01078i) q^{26} +(3.39424 - 3.30593i) q^{28} +(-2.73073 + 3.25435i) q^{29} +(-4.29690 - 2.48082i) q^{31} +(5.62974 - 0.553205i) q^{32} +(-5.96560 - 1.36385i) q^{34} +(9.42909 + 3.43191i) q^{35} +4.93259 q^{37} +(3.39492 - 5.14534i) q^{38} +(6.23577 + 10.2290i) q^{40} +(0.564228 - 1.55020i) q^{41} +(-8.22562 + 1.45040i) q^{43} +(9.53797 - 2.42142i) q^{44} +(2.49487 + 4.87071i) q^{46} +(-6.63122 - 5.56426i) q^{47} +(-0.693747 - 1.20160i) q^{49} +(-9.93368 + 15.3683i) q^{50} +(0.624555 + 8.41462i) q^{52} +(-2.44391 - 0.430928i) q^{53} +(13.3956 + 15.9642i) q^{55} +(-1.00578 + 6.62484i) q^{56} +(0.301611 - 6.00037i) q^{58} +(3.10160 - 2.60255i) q^{59} +(0.847176 - 4.80457i) q^{61} +(6.96267 - 0.870014i) q^{62} +(-5.87604 + 5.42882i) q^{64} +(-15.4751 + 8.93456i) q^{65} +(8.57119 - 10.2147i) q^{67} +(7.89099 - 3.55378i) q^{68} +(-13.5616 + 4.17790i) q^{70} +(1.59125 + 9.02445i) q^{71} +(-0.973188 - 0.354212i) q^{73} +(-5.56208 + 4.20999i) q^{74} +(0.563407 + 8.69957i) q^{76} +11.6565i q^{77} +(0.557573 - 1.53192i) q^{79} +(-15.7621 - 6.21211i) q^{80} +(0.686873 + 2.22961i) q^{82} +(-2.35877 + 4.08551i) q^{83} +(14.0398 + 11.7808i) q^{85} +(8.03745 - 8.65612i) q^{86} +(-8.68851 + 10.8712i) q^{88} +(-0.0667092 - 0.183282i) q^{89} +(-9.84300 - 1.73559i) q^{91} +(-6.97045 - 3.36292i) q^{92} +(12.2266 + 0.614576i) q^{94} +(-16.0749 + 9.08015i) q^{95} +(14.7227 - 12.3538i) q^{97} +(1.80786 + 0.762836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{4}+O(q^{10}) $ 240 * q + 12 * q^4	$ 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) $ 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.12762	+	0.853506i	−0.797348	+	0.603520i
$2$	−1.12762	+	0.853506i	−0.797348	+	0.603520i
$3$		0			0
$3$		0			0
$4$	0.543054	−	1.92486i	0.271527	−	0.962431i
$5$	4.17116	−	0.735488i	1.86540	−	0.328920i	0.876964	−	0.480556i	$-0.159565\pi$
$5$	4.17116	−	0.735488i	1.86540	−	0.328920i	0.988436	+	0.151635i	$0.0484540\pi$
$6$		0			0
$7$	2.05168	+	1.18454i	0.775461	+	0.447713i	0.834819	−	0.550524i	$-0.185572\pi$
$7$	2.05168	+	1.18454i	0.775461	+	0.447713i	−0.0593582	+	0.998237i	$0.518905\pi$
$8$	1.03052	+	2.63401i	0.364345	+	0.931264i
$9$		0			0
$10$	−4.07574	+	4.38947i	−1.28886	+	1.38807i
$11$	2.46013	+	4.26108i	0.741758	+	1.28476i	0.951694	+	0.307048i	$0.0993412\pi$
$11$	2.46013	+	4.26108i	0.741758	+	1.28476i	−0.209936	+	0.977715i	$0.567325\pi$
$12$		0			0
$13$	−3.96446	+	1.44294i	−1.09954	+	0.400201i	−0.827147	−	0.561985i	$-0.810038\pi$
$13$	−3.96446	+	1.44294i	−1.09954	+	0.400201i	−0.272395	+	0.962186i	$0.587816\pi$
$14$	−3.32452	+	0.415413i	−0.888516	+	0.111024i
$15$		0			0
$16$	−3.41019	−	2.09061i	−0.852546	−	0.522652i
$17$	2.78144	+	3.31479i	0.674598	+	0.803955i	0.989402	−	0.145202i	$-0.0463831\pi$
$17$	2.78144	+	3.31479i	0.674598	+	0.803955i	−0.314804	+	0.949157i	$0.601939\pi$
$18$		0			0
$19$	−4.10988	+	1.45220i	−0.942871	+	0.333158i
$19$	−4.10988	+	1.45220i	−0.942871	+	0.333158i
$20$	0.849452	−	8.42832i	0.189943	−	1.88463i
$21$		0			0
$22$	−6.41095	−	2.70514i	−1.36682	−	0.576737i
$23$	0.671956	−	3.81085i	0.140112	−	0.794617i	−0.831050	−	0.556198i	$-0.812260\pi$
$23$	0.671956	−	3.81085i	0.140112	−	0.794617i	0.971162	−	0.238419i	$-0.0766292\pi$
$24$		0			0
$25$	12.1592	−	4.42558i	2.43184	−	0.885117i
$26$	3.23884	−	5.01078i	0.635188	−	0.982695i
$27$		0			0
$28$	3.39424	−	3.30593i	0.641451	−	0.624762i
$29$	−2.73073	+	3.25435i	−0.507083	+	0.604318i	−0.957476	−	0.288512i	$-0.906839\pi$
$29$	−2.73073	+	3.25435i	−0.507083	+	0.604318i	0.450393	+	0.892830i	$0.351284\pi$
$30$		0			0
$31$	−4.29690	−	2.48082i	−0.771747	−	0.445568i	0.0617507	−	0.998092i	$-0.480332\pi$
$31$	−4.29690	−	2.48082i	−0.771747	−	0.445568i	−0.833497	+	0.552523i	$0.813665\pi$
$32$	5.62974	−	0.553205i	0.995207	−	0.0977937i
$33$		0			0
$34$	−5.96560	−	1.36385i	−1.02309	−	0.233898i
$35$	9.42909	+	3.43191i	1.59381	+	0.580098i
$36$		0			0
$37$	4.93259			0.810912			0.405456	−	0.914114i	$-0.367113\pi$
$37$	4.93259			0.810912			0.405456	+	0.914114i	$0.367113\pi$
$38$	3.39492	−	5.14534i	0.550728	−	0.834685i
$39$		0			0
$40$	6.23577	+	10.2290i	0.985961	+	1.61734i
$41$	0.564228	−	1.55020i	0.0881175	−	0.242101i	−0.887804	−	0.460221i	$-0.847770\pi$
$41$	0.564228	−	1.55020i	0.0881175	−	0.242101i	0.975922	+	0.218120i	$0.0699924\pi$
$42$		0			0
$43$	−8.22562	+	1.45040i	−1.25440	+	0.221184i	−0.761075	−	0.648664i	$-0.775328\pi$
$43$	−8.22562	+	1.45040i	−1.25440	+	0.221184i	−0.493321	+	0.869848i	$0.664217\pi$
$44$	9.53797	−	2.42142i	1.43790	−	0.365043i
$45$		0			0
$46$	2.49487	+	4.87071i	0.367849	+	0.718147i
$47$	−6.63122	−	5.56426i	−0.967263	−	0.811630i	0.0148563	−	0.999890i	$-0.495271\pi$
$47$	−6.63122	−	5.56426i	−0.967263	−	0.811630i	−0.982119	+	0.188260i	$0.939715\pi$
$48$		0			0
$49$	−0.693747	−	1.20160i	−0.0991067	−	0.171658i
$50$	−9.93368	+	15.3683i	−1.40483	+	2.17341i
$51$		0			0
$52$	0.624555	+	8.41462i	0.0866102	+	1.16690i
$53$	−2.44391	−	0.430928i	−0.335697	−	0.0591925i	0.00325877	−	0.999995i	$-0.498963\pi$
$53$	−2.44391	−	0.430928i	−0.335697	−	0.0591925i	−0.338956	+	0.940802i	$0.610074\pi$
$54$		0			0
$55$	13.3956	+	15.9642i	1.80626	+	2.15262i
$56$	−1.00578	+	6.62484i	−0.134403	+	0.885281i
$57$		0			0
$58$	0.301611	−	6.00037i	0.0396034	−	0.787887i
$59$	3.10160	−	2.60255i	0.403794	−	0.338823i	−0.418164	−	0.908371i	$-0.637326\pi$
$59$	3.10160	−	2.60255i	0.403794	−	0.338823i	0.821958	+	0.569548i	$0.192882\pi$
$60$		0			0
$61$	0.847176	−	4.80457i	0.108470	−	0.615162i	−0.881308	−	0.472543i	$-0.843336\pi$
$61$	0.847176	−	4.80457i	0.108470	−	0.615162i	0.989778	−	0.142620i	$-0.0455526\pi$
$62$	6.96267	−	0.870014i	0.884260	−	0.110492i
$63$		0			0
$64$	−5.87604	+	5.42882i	−0.734505	+	0.678603i
$65$	−15.4751	+	8.93456i	−1.91945	+	1.10820i
$66$		0			0
$67$	8.57119	−	10.2147i	1.04714	−	1.24793i	0.0791678	−	0.996861i	$-0.474774\pi$
$67$	8.57119	−	10.2147i	1.04714	−	1.24793i	0.967969	−	0.251068i	$-0.0807819\pi$
$68$	7.89099	−	3.55378i	0.956923	−	0.430959i
$69$		0			0
$70$	−13.5616	+	4.17790i	−1.62092	+	0.499355i
$71$	1.59125	+	9.02445i	0.188847	+	1.07101i	0.920912	+	0.389770i	$0.127446\pi$
$71$	1.59125	+	9.02445i	0.188847	+	1.07101i	−0.732065	+	0.681235i	$0.761443\pi$
$72$		0			0
$73$	−0.973188	−	0.354212i	−0.113903	−	0.0414573i	0.284440	−	0.958694i	$-0.408192\pi$
$73$	−0.973188	−	0.354212i	−0.113903	−	0.0414573i	−0.398343	+	0.917237i	$0.630415\pi$
$74$	−5.56208	+	4.20999i	−0.646579	+	0.489402i
$75$		0			0
$76$	0.563407	+	8.69957i	0.0646272	+	0.997909i
$77$			11.6565i			1.32838i
$78$		0			0
$79$	0.557573	−	1.53192i	0.0627319	−	0.172355i	−0.904367	−	0.426756i	$-0.859656\pi$
$79$	0.557573	−	1.53192i	0.0627319	−	0.172355i	0.967099	+	0.254402i	$0.0818785\pi$
$80$	−15.7621	−	6.21211i	−1.76225	−	0.694535i
$81$		0			0
$82$	0.686873	+	2.22961i	0.0758525	+	0.246219i
$83$	−2.35877	+	4.08551i	−0.258909	+	0.448443i	−0.965950	−	0.258729i	$-0.916696\pi$
$83$	−2.35877	+	4.08551i	−0.258909	+	0.448443i	0.707041	+	0.707172i	$0.250030\pi$
$84$		0			0
$85$	14.0398	+	11.7808i	1.52283	+	1.27781i
$86$	8.03745	−	8.65612i	0.866701	−	0.933413i
$87$		0			0
$88$	−8.68851	+	10.8712i	−0.926198	+	1.15887i
$89$	−0.0667092	−	0.183282i	−0.00707117	−	0.0194279i	0.936107	−	0.351716i	$-0.114402\pi$
$89$	−0.0667092	−	0.183282i	−0.00707117	−	0.0194279i	−0.943178	+	0.332288i	$0.892179\pi$
$90$		0			0
$91$	−9.84300	−	1.73559i	−1.03183	−	0.181939i
$92$	−6.97045	−	3.36292i	−0.726720	−	0.350608i
$93$		0			0
$94$	12.2266	+	0.614576i	1.26108	+	0.0633887i
$95$	−16.0749	+	9.08015i	−1.64925	+	0.931603i
$96$		0			0
$97$	14.7227	−	12.3538i	1.49487	−	1.25434i	0.606609	−	0.795000i	$-0.292529\pi$
$97$	14.7227	−	12.3538i	1.49487	−	1.25434i	0.888259	−	0.459343i	$-0.151915\pi$
$98$	1.80786	+	0.762836i	0.182621	+	0.0770581i
$99$		0			0
$100$	−1.91554	−	25.8081i	−0.191554	−	2.58081i
$101$	−0.213461	−	0.586480i	−0.0212402	−	0.0583569i	0.928619	−	0.371034i	$-0.120997\pi$
$101$	−0.213461	−	0.586480i	−0.0212402	−	0.0583569i	−0.949860	+	0.312677i	$0.898774\pi$
$102$		0			0
$103$	0.867609	−	0.500914i	0.0854881	−	0.0493566i	−0.456647	−	0.889648i	$-0.650950\pi$
$103$	0.867609	−	0.500914i	0.0854881	−	0.0493566i	0.542135	+	0.840292i	$0.317616\pi$
$104$	−7.88620	−	8.95544i	−0.773305	−	0.878153i
$105$		0			0
$106$	3.12361	−	1.59997i	0.303391	−	0.155403i
$107$	8.77073	−	15.1913i	0.847898	−	1.46860i	−0.0351824	−	0.999381i	$-0.511201\pi$
$107$	8.77073	−	15.1913i	0.847898	−	1.46860i	0.883080	−	0.469222i	$-0.155465\pi$
$108$		0			0
$109$	0.547450	+	3.10474i	0.0524362	+	0.297381i	0.999736	−	0.0229672i	$-0.00731134\pi$
$109$	0.547450	+	3.10474i	0.0524362	+	0.297381i	−0.947300	+	0.320348i	$0.896200\pi$
$110$	−28.7307	−	6.56838i	−2.73937	−	0.626270i
$111$		0			0
$112$	−4.52020	−	8.32874i	−0.427119	−	0.786992i
$113$			2.93545i			0.276144i	0.990422	+	0.138072i	$0.0440905\pi$
$113$			2.93545i			0.276144i	−0.990422	+	0.138072i	$0.955909\pi$
$114$		0			0
$115$		−	16.3899i		−	1.52836i
$116$	4.78125	+	7.02356i	0.443928	+	0.652121i
$117$		0			0
$118$	−1.27613	+	5.58192i	−0.117477	+	0.513858i
$119$	1.78013	+	10.0956i	0.163184	+	0.925462i
$120$		0			0
$121$	−6.60452	+	11.4394i	−0.600411	+	1.03994i
$122$	3.14544	+	6.14080i	0.284775	+	0.555962i
$123$		0			0
$124$	−7.10868	+	6.92373i	−0.638379	+	0.621769i
$125$	29.1227	−	16.8140i	2.60481	−	1.50389i
$126$		0			0
$127$	−1.70038	−	4.67176i	−0.150884	−	0.414551i	0.841105	−	0.540872i	$-0.181906\pi$
$127$	−1.70038	−	4.67176i	−0.150884	−	0.414551i	−0.991990	+	0.126320i	$0.959683\pi$
$128$	1.99241	−	11.1369i	0.176106	−	0.984371i
$129$		0			0
$130$	9.82435	−	23.2829i	0.861652	−	2.04205i
$131$	7.62616	−	6.39911i	0.666301	−	0.559093i	−0.245667	−	0.969354i	$-0.579007\pi$
$131$	7.62616	−	6.39911i	0.666301	−	0.559093i	0.911968	+	0.410262i	$0.134563\pi$
$132$		0			0
$133$	−10.1523	−	1.88885i	−0.880319	−	0.163784i
$134$	−0.946694	+	18.8339i	−0.0817819	+	1.62700i
$135$		0			0
$136$	−5.86486	+	10.7423i	−0.502908	+	0.921146i
$137$	6.82117	+	1.20276i	0.582772	+	0.102758i	0.457259	−	0.889334i	$-0.348831\pi$
$137$	6.82117	+	1.20276i	0.582772	+	0.102758i	0.125513	+	0.992092i	$0.459942\pi$
$138$		0			0
$139$	−1.85427	−	5.09456i	−0.157277	−	0.432115i	0.835878	−	0.548915i	$-0.184959\pi$
$139$	−1.85427	−	5.09456i	−0.157277	−	0.432115i	−0.993156	+	0.116799i	$0.962737\pi$
$140$	11.7265	−	16.2860i	0.991066	−	1.37642i
$141$		0			0
$142$	−9.49676	−	8.81801i	−0.796950	−	0.739991i
$143$	−15.9016	−	13.3430i	−1.32976	−	1.11580i
$144$		0			0
$145$	−8.99676	+	15.5829i	−0.747141	+	1.29409i
$146$	1.39971	−	0.431206i	0.115841	−	0.0356869i
$147$		0			0
$148$	2.67866	−	9.49455i	0.220184	−	0.780447i
$149$	−5.56930	+	15.3015i	−0.456255	+	1.25355i	0.471997	+	0.881600i	$0.343533\pi$
$149$	−5.56930	+	15.3015i	−0.456255	+	1.25355i	−0.928252	+	0.371951i	$0.878689\pi$
$150$		0			0
$151$			0.224746i			0.0182896i	0.999958	+	0.00914478i	$0.00291091\pi$
$151$			0.224746i			0.0182896i	−0.999958	+	0.00914478i	$0.997089\pi$
$152$	−8.06045	−	9.32894i	−0.653789	−	0.756677i
$153$		0			0
$154$	−9.94888	−	13.1441i	−0.801703	−	1.05918i
$155$	−19.7477	−	7.18757i	−1.58617	−	0.577320i
$156$		0			0
$157$	−2.09430	−	11.8774i	−0.167143	−	0.947917i	−0.946827	−	0.321743i	$-0.895731\pi$
$157$	−2.09430	−	11.8774i	−0.167143	−	0.947917i	0.779684	−	0.626174i	$-0.215380\pi$
$158$	0.678773	+	2.20332i	0.0540003	+	0.175286i
$159$		0			0
$160$	23.0757	−	6.44812i	1.82429	−	0.509768i
$161$	5.89273	−	7.02268i	0.464412	−	0.553464i
$162$		0			0
$163$	−3.80807	+	2.19859i	−0.298271	+	0.172207i	−0.641666	−	0.766984i	$-0.721756\pi$
$163$	−3.80807	+	2.19859i	−0.298271	+	0.172207i	0.343395	+	0.939191i	$0.388423\pi$
$164$	−2.67752	−	1.92790i	−0.209079	−	0.150544i
$165$		0			0
$166$	−0.827212	−	6.62013i	−0.0642041	−	0.513821i
$167$	3.56050	−	20.1926i	0.275520	−	1.56255i	−0.461786	−	0.886991i	$-0.652791\pi$
$167$	3.56050	−	20.1926i	0.275520	−	1.56255i	0.737306	−	0.675559i	$-0.236098\pi$
$168$		0			0
$169$	3.67624	−	3.08473i	0.282788	−	0.237287i
$170$	−25.8866	−	1.30120i	−1.98541	−	0.0997975i
$171$		0			0
$172$	−1.67514	+	16.6208i	−0.127728	+	1.26733i
$173$	2.73872	+	3.26387i	0.208221	+	0.248148i	0.860040	−	0.510226i	$-0.170438\pi$
$173$	2.73872	+	3.26387i	0.208221	+	0.248148i	−0.651819	+	0.758374i	$0.725994\pi$
$174$		0			0
$175$	30.1890	+	5.32314i	2.28207	+	0.402391i
$176$	0.518724	−	19.6742i	0.0391003	−	1.48300i
$177$		0			0
$178$	0.231655	+	0.149736i	0.0173633	+	0.0112232i
$179$	4.10247	+	7.10569i	0.306633	+	0.531104i	0.977624	−	0.210362i	$-0.0674642\pi$
$179$	4.10247	+	7.10569i	0.306633	+	0.531104i	−0.670991	+	0.741466i	$0.734131\pi$
$180$		0			0
$181$	−3.61966	−	3.03726i	−0.269047	−	0.225757i	0.498275	−	0.867019i	$-0.333967\pi$
$181$	−3.61966	−	3.03726i	−0.269047	−	0.225757i	−0.767322	+	0.641261i	$0.778411\pi$
$182$	12.5805	−	6.44398i	0.932529	−	0.477660i
$183$		0			0
$184$	10.7303	−	2.15723i	0.791047	−	0.159033i
$185$	20.5746	−	3.62786i	1.51268	−	0.266726i
$186$		0			0
$187$	−7.28187	+	20.0068i	−0.532503	+	1.46304i
$188$	−14.3115	+	9.74249i	−1.04378	+	0.710544i
$189$		0			0
$190$	10.3764	−	23.9590i	0.752784	−	1.73817i
$191$	16.4905			1.19321			0.596604	−	0.802536i	$-0.296516\pi$
$191$	16.4905			1.19321			0.596604	+	0.802536i	$0.296516\pi$
$192$		0			0
$193$	−13.8738	−	5.04966i	−0.998660	−	0.363482i	−0.209592	−	0.977789i	$-0.567214\pi$
$193$	−13.8738	−	5.04966i	−0.998660	−	0.363482i	−0.789068	+	0.614306i	$0.789436\pi$
$194$	−6.05757	+	26.4964i	−0.434908	+	1.90233i
$195$		0			0
$196$	−2.68967	+	0.682831i	−0.192119	+	0.0487736i
$197$	−20.2363	−	11.6835i	−1.44178	−	0.832412i	−0.443811	−	0.896120i	$-0.646374\pi$
$197$	−20.2363	−	11.6835i	−1.44178	−	0.832412i	−0.997969	+	0.0637088i	$0.979707\pi$
$198$		0			0
$199$	7.86734	−	9.37593i	0.557701	−	0.664642i	−0.411358	−	0.911474i	$-0.634945\pi$
$199$	7.86734	−	9.37593i	0.557701	−	0.664642i	0.969058	+	0.246832i	$0.0793897\pi$
$200$	24.1874	+	27.4668i	1.71031	+	1.94220i
$201$		0			0
$202$	0.741267	+	0.479136i	0.0521554	+	0.0337119i
$203$	−9.45747	+	3.44224i	−0.663784	+	0.241598i
$204$		0			0
$205$	1.21333	−	6.88113i	0.0847426	−	0.480599i
$206$	−0.550800	+	1.30535i	−0.0383760	+	0.0909481i
$207$		0			0
$208$	16.5362	+	3.36741i	1.14658	+	0.233488i
$209$	−16.2988	−	13.9399i	−1.12741	−	0.964243i
$210$		0			0
$211$	11.1716	+	13.3137i	0.769082	+	0.916556i	0.998386	−	0.0567987i	$-0.0180893\pi$
$211$	11.1716	+	13.3137i	0.769082	+	0.916556i	−0.229304	+	0.973355i	$0.573645\pi$
$212$	−2.15665	+	4.47018i	−0.148120	+	0.307013i
$213$		0			0
$214$	3.07586	+	24.6159i	0.210262	+	1.68271i
$215$	−33.2437	+	12.0997i	−2.26720	+	0.825193i
$216$		0			0
$217$	−5.87724	−	10.1797i	−0.398973	−	0.691042i
$218$	−3.26723	−	3.03372i	−0.221285	−	0.205469i
$219$		0			0
$220$	38.0035	−	17.1152i	2.56220	−	1.15391i
$221$	−15.8100	−	9.12788i	−1.06349	−	0.614008i
$222$		0			0
$223$	−17.2507	+	3.04177i	−1.15519	+	0.203692i	−0.718242	−	0.695793i	$-0.755053\pi$
$223$	−17.2507	+	3.04177i	−1.15519	+	0.203692i	−0.436951	+	0.899485i	$0.643942\pi$
$224$	12.2057	+	5.53363i	0.815528	+	0.369731i
$225$		0			0
$226$	−2.50543	−	3.31007i	−0.166658	−	0.220183i
$227$	14.1929			0.942018			0.471009	−	0.882128i	$-0.343890\pi$
$227$	14.1929			0.942018			0.471009	+	0.882128i	$0.343890\pi$
$228$		0			0
$229$	0.146313			0.00966863			0.00483432	−	0.999988i	$-0.498461\pi$
$229$	0.146313			0.00966863			0.00483432	+	0.999988i	$0.498461\pi$
$230$	13.9889	+	18.4816i	0.922399	+	1.21864i
$231$		0			0
$232$	−11.3861	−	3.83908i	−0.747533	−	0.252048i
$233$	6.57849	−	1.15996i	0.430971	−	0.0759918i	0.0460453	−	0.998939i	$-0.485338\pi$
$233$	6.57849	−	1.15996i	0.430971	−	0.0759918i	0.384926	+	0.922948i	$0.374227\pi$
$234$		0			0
$235$	−31.7523	−	18.3322i	−2.07129	−	1.19586i
$236$	−3.32521	−	7.38347i	−0.216453	−	0.480623i
$237$		0			0
$238$	−10.6240	−	9.86465i	−0.688649	−	0.639430i
$239$	−9.01958	−	15.6224i	−0.583428	−	1.01053i	−0.995069	−	0.0991812i	$-0.968378\pi$
$239$	−9.01958	−	15.6224i	−0.583428	−	1.01053i	0.411641	−	0.911346i	$-0.364956\pi$
$240$		0			0
$241$	−24.2234	+	8.81659i	−1.56037	+	0.567927i	−0.970820	−	0.239809i	$-0.922915\pi$
$241$	−24.2234	+	8.81659i	−1.56037	+	0.567927i	−0.589545	+	0.807735i	$0.700693\pi$
$242$	−2.31618	−	18.5363i	−0.148890	−	1.19156i
$243$		0			0
$244$	−8.78807	−	4.23984i	−0.562599	−	0.271428i
$245$	−3.77750	−	4.50185i	−0.241335	−	0.287612i
$246$		0			0
$247$	14.1980	−	11.6875i	0.903396	−	0.743659i
$248$	2.10645	−	13.8746i	0.133759	−	0.881040i
$249$		0			0
$250$	−18.4885	+	43.8162i	−1.16931	+	2.77118i
$251$	−2.36645	+	13.4208i	−0.149369	+	0.847115i	0.814385	+	0.580324i	$0.197074\pi$
$251$	−2.36645	+	13.4208i	−0.149369	+	0.847115i	−0.963755	+	0.266790i	$0.914037\pi$
$252$		0			0
$253$	17.8914	−	6.51195i	1.12482	−	0.409403i
$254$	5.90476	+	3.81668i	0.370497	+	0.239480i
$255$		0			0
$256$	7.25873	+	14.2587i	0.453670	+	0.891170i
$257$	−7.01354	+	8.35841i	−0.437493	+	0.521384i	−0.939068	−	0.343730i	$-0.888309\pi$
$257$	−7.01354	+	8.35841i	−0.437493	+	0.521384i	0.501576	+	0.865114i	$0.332754\pi$
$258$		0			0
$259$	10.1201	+	5.84283i	0.628831	+	0.363056i
$260$	8.79398	+	34.6394i	0.545379	+	2.14825i
$261$		0			0
$262$	−3.13773	+	13.7247i	−0.193850	+	0.847917i
$263$	0.651063	+	0.236968i	0.0401463	+	0.0146120i	0.362015	−	0.932172i	$-0.382089\pi$
$263$	0.651063	+	0.236968i	0.0401463	+	0.0146120i	−0.321869	+	0.946784i	$0.604311\pi$
$264$		0			0
$265$	−10.5109			−0.645680
$266$	13.0601	−	6.53518i	0.800767	−	0.400698i
$267$		0			0
$268$	−15.0074	−	22.0455i	−0.916720	−	1.34664i
$269$	−7.26990	+	19.9739i	−0.443253	+	1.21783i	0.494086	+	0.869413i	$0.335503\pi$
$269$	−7.26990	+	19.9739i	−0.443253	+	1.21783i	−0.937340	+	0.348416i	$0.886720\pi$
$270$		0			0
$271$	−19.5639	+	3.44964i	−1.18842	+	0.209551i	−0.732688	−	0.680565i	$-0.761734\pi$
$271$	−19.5639	+	3.44964i	−1.18842	+	0.209551i	−0.455734	+	0.890116i	$0.650623\pi$
$272$	−2.55530	−	17.1190i	−0.154938	−	1.03799i
$273$		0			0
$274$	−8.71825	+	4.46566i	−0.526689	+	0.269780i
$275$	48.7710	+	40.9237i	2.94100	+	2.46779i
$276$		0			0
$277$	8.11262	+	14.0515i	0.487440	+	0.844271i	0.999896	−	0.0144429i	$-0.00459749\pi$
$277$	8.11262	+	14.0515i	0.487440	+	0.844271i	−0.512456	+	0.858714i	$0.671264\pi$
$278$	6.43915	+	4.16210i	0.386195	+	0.249626i
$279$		0			0
$280$	0.677210	+	28.3730i	0.0404711	+	1.69561i
$281$	−21.1699	−	3.73283i	−1.26289	−	0.222682i	−0.498191	−	0.867067i	$-0.666002\pi$
$281$	−21.1699	−	3.73283i	−1.26289	−	0.222682i	−0.764701	+	0.644385i	$0.777113\pi$
$282$		0			0
$283$	1.89394	+	2.25711i	0.112583	+	0.134171i	0.819393	−	0.573232i	$-0.194311\pi$
$283$	1.89394	+	2.25711i	0.112583	+	0.134171i	−0.706810	+	0.707404i	$0.749866\pi$
$284$	18.2350	+	1.83782i	1.08205	+	0.109054i
$285$		0			0
$286$	29.3193	+	1.47375i	1.73369	+	0.0871444i
$287$	2.99388	−	2.51217i	0.176723	−	0.148289i
$288$		0			0
$289$	−0.299414	+	1.69806i	−0.0176126	+	0.0998858i
$290$	−3.15513	−	25.2503i	−0.185276	−	1.48275i
$291$		0			0
$292$	−1.21030	+	1.68090i	−0.0708275	+	0.0983670i
$293$	9.55476	−	5.51644i	0.558195	−	0.322274i	−0.194226	−	0.980957i	$-0.562219\pi$
$293$	9.55476	−	5.51644i	0.558195	−	0.322274i	0.752421	+	0.658683i	$0.228886\pi$
$294$		0			0
$295$	11.0231	−	13.1368i	0.641791	−	0.764857i
$296$	5.08315	+	12.9925i	0.295452	+	0.755173i
$297$		0			0
$298$	−6.77990	−	22.0078i	−0.392749	−	1.27488i
$299$	2.83490	+	16.0775i	0.163947	+	0.929788i
$300$		0			0
$301$	−18.5944	−	6.76780i	−1.07176	−	0.390089i
$302$	−0.191822	−	0.253428i	−0.0110381	−	0.0145831i
$303$		0			0
$304$	17.0514	+	3.63986i	0.977967	+	0.208760i
$305$		−	20.6637i		−	1.18320i
$306$		0			0
$307$	−3.92839	+	10.7932i	−0.224205	+	0.615999i	−0.999886	−	0.0151271i	$-0.995185\pi$
$307$	−3.92839	+	10.7932i	−0.224205	+	0.615999i	0.775680	+	0.631126i	$0.217407\pi$
$308$	22.4371	+	6.33009i	1.27847	+	0.360690i
$309$		0			0
$310$	28.4025	−	8.74993i	1.61316	−	0.496963i
$311$	−3.18725	+	5.52048i	−0.180732	+	0.313038i	−0.942130	−	0.335247i	$-0.891180\pi$
$311$	−3.18725	+	5.52048i	−0.180732	+	0.313038i	0.761398	+	0.648285i	$0.224513\pi$
$312$		0			0
$313$	−9.60754	−	8.06168i	−0.543050	−	0.455673i	0.329529	−	0.944145i	$-0.393110\pi$
$313$	−9.60754	−	8.06168i	−0.543050	−	0.455673i	−0.872580	+	0.488472i	$0.837554\pi$
$314$	12.4990	+	11.6057i	0.705358	+	0.654945i
$315$		0			0
$316$	−2.64594	−	1.90517i	−0.148846	−	0.107174i
$317$	1.37807	+	3.78621i	0.0774000	+	0.212655i	0.972358	−	0.233496i	$-0.0750167\pi$
$317$	1.37807	+	3.78621i	0.0774000	+	0.212655i	−0.894958	+	0.446151i	$0.852794\pi$
$318$		0			0
$319$	−20.5850	−	3.62969i	−1.15254	−	0.203224i
$320$	−20.5171	+	26.9663i	−1.14694	+	1.50746i
$321$		0			0
$322$	−0.650856	+	12.9484i	−0.0362708	+	0.721586i
$323$	−16.2451	−	9.58417i	−0.903904	−	0.533278i
$324$		0			0
$325$	−41.8187	+	35.0901i	−2.31968	+	1.94645i
$326$	2.41754	−	5.72938i	0.133895	−	0.317321i
$327$		0			0
$328$	4.66470	−	0.111338i	0.257565	−	0.00614759i
$329$	−7.01406	−	19.2710i	−0.386698	−	1.06244i
$330$		0			0
$331$	−0.202955	+	0.117176i	−0.0111554	+	0.00644059i	−0.505567	−	0.862787i	$-0.668717\pi$
$331$	−0.202955	+	0.117176i	−0.0111554	+	0.00644059i	0.494412	+	0.869228i	$0.335383\pi$
$332$	6.58310	+	6.75896i	0.361295	+	0.370946i
$333$		0			0
$334$	13.2196	+	25.8085i	0.723345	+	1.41218i
$335$	28.2390	−	48.9114i	1.54286	−	2.67231i
$336$		0			0
$337$	1.32528	+	7.51605i	0.0721927	+	0.409425i	0.999392	+	0.0348576i	$0.0110978\pi$
$337$	1.32528	+	7.51605i	0.0721927	+	0.409425i	−0.927200	+	0.374568i	$0.877791\pi$
$338$	−1.51256	+	6.61610i	−0.0822726	+	0.359868i
$339$		0			0
$340$	30.3008	−	20.6271i	1.64329	−	1.11866i
$341$		−	24.4126i		−	1.32202i
$342$		0			0
$343$		−	19.8706i		−	1.07291i
$344$	−12.2971	−	20.1717i	−0.663013	−	1.08759i
$345$		0			0
$346$	−5.87397	−	1.34290i	−0.315786	−	0.0721947i
$347$	3.09850	+	17.5725i	0.166336	+	0.943339i	0.947676	+	0.319234i	$0.103425\pi$
$347$	3.09850	+	17.5725i	0.166336	+	0.943339i	−0.781340	+	0.624106i	$0.785463\pi$
$348$		0			0
$349$	−3.25938	+	5.64541i	−0.174471	+	0.302192i	−0.939978	−	0.341235i	$-0.889155\pi$
$349$	−3.25938	+	5.64541i	−0.174471	+	0.302192i	0.765507	+	0.643427i	$0.222488\pi$
$350$	−38.5850	+	19.7640i	−2.06246	+	1.05643i
$351$		0			0
$352$	16.2072	+	22.6278i	0.863845	+	1.20607i
$353$	−4.43020	+	2.55777i	−0.235796	+	0.136137i	−0.613243	−	0.789894i	$-0.710135\pi$
$353$	−4.43020	+	2.55777i	−0.235796	+	0.136137i	0.377447	+	0.926031i	$0.376802\pi$
$354$		0			0
$355$	13.2748	+	36.4721i	0.704551	+	1.93574i
$356$	−0.389019	+	0.0288740i	−0.0206180	+	0.00153032i
$357$		0			0
$358$	−10.6908	−	4.51103i	−0.565025	−	0.238415i
$359$	11.7130	−	9.82840i	0.618190	−	0.518723i	−0.279044	−	0.960278i	$-0.590018\pi$
$359$	11.7130	−	9.82840i	0.618190	−	0.518723i	0.897234	+	0.441555i	$0.145573\pi$
$360$		0			0
$361$	14.7822	−	11.9368i	0.778011	−	0.628251i
$362$	6.67392	+	0.335467i	0.350773	+	0.0176318i
$363$		0			0
$364$	−8.68604	+	18.0039i	−0.455272	+	0.943661i
$365$	−4.31984	−	0.761705i	−0.226111	−	0.0398695i
$366$		0			0
$367$	4.55658	+	12.5191i	0.237851	+	0.653491i	0.999982	+	0.00606742i	$0.00193133\pi$
$367$	4.55658	+	12.5191i	0.237851	+	0.653491i	−0.762130	+	0.647424i	$0.775846\pi$
$368$	−10.2585	+	11.5909i	−0.534760	+	0.604218i
$369$		0			0
$370$	−20.1040	+	21.6514i	−1.04515	+	1.12560i
$371$	−4.50367	−	3.77903i	−0.233819	−	0.196197i
$372$		0			0
$373$	12.1873	−	21.1090i	0.631035	−	1.09298i	−0.356306	−	0.934369i	$-0.615964\pi$
$373$	12.1873	−	21.1090i	0.631035	−	1.09298i	0.987341	−	0.158615i	$-0.0507028\pi$
$374$	−8.86472	−	28.7751i	−0.458384	−	1.48793i
$375$		0			0
$376$	7.82269	−	23.2008i	0.403424	−	1.19649i
$377$	6.12999	−	16.8420i	0.315711	−	0.867408i
$378$		0			0
$379$			30.0944i			1.54585i	0.634499	+	0.772924i	$0.281206\pi$
$379$			30.0944i			1.54585i	−0.634499	+	0.772924i	$0.718794\pi$
$380$	8.74850	+	35.8730i	0.448788	+	1.84024i
$381$		0			0
$382$	−18.5950	+	14.0747i	−0.951402	+	0.720125i
$383$	−3.41839	−	1.24419i	−0.174671	−	0.0635752i	0.253204	−	0.967413i	$-0.418516\pi$
$383$	−3.41839	−	1.24419i	−0.174671	−	0.0635752i	−0.427875	+	0.903838i	$0.640738\pi$
$384$		0			0
$385$	8.57320	+	48.6211i	0.436931	+	2.47796i
$386$	19.9543	−	6.14730i	1.01565	−	0.312889i
$387$		0			0
$388$	−15.7842	−	35.0481i	−0.801322	−	1.77930i
$389$	−4.00467	+	4.77258i	−0.203045	+	0.241980i	−0.857952	−	0.513730i	$-0.828263\pi$
$389$	−4.00467	+	4.77258i	−0.203045	+	0.241980i	0.654907	+	0.755709i	$0.272708\pi$
$390$		0			0
$391$	14.5012	−	8.37226i	0.733356	−	0.423403i
$392$	2.45012	−	3.06562i	0.123750	−	0.154837i
$393$		0			0
$394$	32.7908	−	4.09735i	1.65198	−	0.206421i
$395$	1.19902	−	6.79998i	0.0603292	−	0.342144i
$396$		0			0
$397$	−9.93552	+	8.33689i	−0.498649	+	0.418416i	−0.857114	−	0.515127i	$-0.827745\pi$
$397$	−9.93552	+	8.33689i	−0.498649	+	0.418416i	0.358465	+	0.933543i	$0.383300\pi$
$398$	−0.868953	+	17.2873i	−0.0435567	+	0.866534i
$399$		0			0
$400$	−50.7172	−	10.3280i	−2.53586	−	0.516401i
$401$	16.6333	+	19.8227i	0.830625	+	0.989901i	0.999991	+	0.00434722i	$0.00138377\pi$
$401$	16.6333	+	19.8227i	0.830625	+	0.989901i	−0.169365	+	0.985553i	$0.554172\pi$
$402$		0			0
$403$	20.6146	+	3.63490i	1.02688	+	0.181067i
$404$	−1.24481	+	0.0923932i	−0.0619318	+	0.00459673i
$405$		0			0
$406$	7.72646	−	11.9535i	0.383458	−	0.593244i
$407$	12.1348	+	21.0181i	0.601501	+	1.04183i
$408$		0			0
$409$	22.8428	+	19.1674i	1.12951	+	0.947768i	0.999045	−	0.0436860i	$-0.0139101\pi$
$409$	22.8428	+	19.1674i	1.12951	+	0.947768i	0.130460	+	0.991454i	$0.458355\pi$
$410$	4.50491	+	8.79488i	0.222482	+	0.434348i
$411$		0			0
$412$	−0.493033	−	1.94205i	−0.0242900	−	0.0956780i
$413$	9.44629	−	1.66564i	0.464822	−	0.0819606i
$414$		0			0
$415$	−6.83397	+	18.7762i	−0.335466	+	0.921686i
$416$	−21.5206	+	10.3166i	−1.05513	+	0.505811i
$417$		0			0
$418$	30.2767	+	1.80777i	1.48088	+	0.0884209i
$419$	6.12219			0.299089			0.149544	−	0.988755i	$-0.452219\pi$
$419$	6.12219			0.299089			0.149544	+	0.988755i	$0.452219\pi$
$420$		0			0
$421$	−6.83129	−	2.48639i	−0.332937	−	0.121179i	0.170142	−	0.985420i	$-0.445577\pi$
$421$	−6.83129	−	2.48639i	−0.332937	−	0.121179i	−0.503079	+	0.864240i	$0.667800\pi$
$422$	−23.9606	−	5.47785i	−1.16639	−	0.266658i
$423$		0			0
$424$	−1.38344	−	6.88138i	−0.0671858	−	0.334189i
$425$	48.4900	+	27.9957i	2.35211	+	1.35799i
$426$		0			0
$427$	7.42932	−	8.85392i	0.359530	−	0.428471i
$428$	−24.4783	−	25.1322i	−1.18320	−	1.21481i
$429$		0			0
$430$	27.1590	−	42.0175i	1.30973	−	2.02627i
$431$	13.8715	−	5.04883i	0.668168	−	0.243193i	0.0144094	−	0.999896i	$-0.495413\pi$
$431$	13.8715	−	5.04883i	0.668168	−	0.243193i	0.653759	+	0.756703i	$0.273191\pi$
$432$		0			0
$433$	4.63194	−	26.2691i	0.222597	−	1.26241i	−0.644629	−	0.764495i	$-0.722988\pi$
$433$	4.63194	−	26.2691i	0.222597	−	1.26241i	0.867226	−	0.497915i	$-0.165901\pi$
$434$	15.3157	+	6.46255i	0.735178	+	0.310212i
$435$		0			0
$436$	6.27350	+	0.632277i	0.300446	+	0.0302806i
$437$	2.77247	+	16.6379i	0.132625	+	0.795901i
$438$		0			0
$439$	−11.2411	−	13.3966i	−0.536508	−	0.639385i	0.427893	−	0.903829i	$-0.359256\pi$
$439$	−11.2411	−	13.3966i	−0.536508	−	0.639385i	−0.964401	+	0.264444i	$0.914811\pi$
$440$	−28.2456	+	51.7357i	−1.34655	+	2.46640i
$441$		0			0
$442$	25.6183	−	3.20111i	1.21854	−	0.152262i
$443$	−31.0821	+	11.3129i	−1.47675	+	0.537494i	−0.949925	−	0.312477i	$-0.898841\pi$
$443$	−31.0821	+	11.3129i	−1.47675	+	0.537494i	−0.526828	+	0.849972i	$0.676619\pi$
$444$		0			0
$445$	−0.413057	−	0.715436i	−0.0195808	−	0.0339149i
$446$	16.8561	−	18.1535i	0.798159	−	0.859595i
$447$		0			0
$448$	−18.4864	+	4.17781i	−0.873399	+	0.197383i
$449$	25.3686	+	14.6466i	1.19722	+	0.691215i	0.959934	−	0.280225i	$-0.0904090\pi$
$449$	25.3686	+	14.6466i	1.19722	+	0.691215i	0.237286	+	0.971440i	$0.423742\pi$
$450$		0			0
$451$	7.99361	−	1.40949i	0.376404	−	0.0663702i
$452$	5.65034	+	1.59411i	0.265769	+	0.0749805i
$453$		0			0
$454$	−16.0042	+	12.1138i	−0.751116	+	0.568527i
$455$	−42.3333			−1.98461
$456$		0			0
$457$	−23.9763			−1.12157			−0.560783	−	0.827963i	$-0.689500\pi$
$457$	−23.9763			−1.12157			−0.560783	+	0.827963i	$0.689500\pi$
$458$	−0.164985	+	0.124879i	−0.00770926	+	0.00583522i
$459$		0			0
$460$	−31.5483	−	8.90059i	−1.47095	−	0.414992i
$461$	−19.2838	+	3.40025i	−0.898134	+	0.158365i	−0.603611	−	0.797279i	$-0.706272\pi$
$461$	−19.2838	+	3.40025i	−0.898134	+	0.158365i	−0.294523	+	0.955644i	$0.595161\pi$
$462$		0			0
$463$	−0.803683	−	0.464006i	−0.0373503	−	0.0215642i	0.481209	−	0.876606i	$-0.340198\pi$
$463$	−0.803683	−	0.464006i	−0.0373503	−	0.0215642i	−0.518559	+	0.855042i	$0.673531\pi$
$464$	16.1159	−	5.38907i	0.748160	−	0.250181i
$465$		0			0
$466$	−6.42800	+	6.92278i	−0.297771	+	0.320692i
$467$	15.9239	+	27.5810i	0.736869	+	1.27630i	0.953898	+	0.300130i	$0.0970301\pi$
$467$	15.9239	+	27.5810i	0.736869	+	1.27630i	−0.217029	+	0.976165i	$0.569637\pi$
$468$		0			0
$469$	29.6850	−	10.8045i	1.37073	−	0.498904i
$470$	51.4513	−	6.42905i	2.37327	−	0.296550i
$471$		0			0
$472$	10.0514	+	5.48766i	0.462654	+	0.252590i
$473$	−26.4164	−	31.4818i	−1.21463	−	1.44754i
$474$		0			0
$475$	−43.5460	+	35.8462i	−1.99803	+	1.64474i
$476$	20.3993	+	2.05596i	0.935002	+	0.0942346i
$477$		0			0
$478$	23.5045	+	9.91783i	1.07507	+	0.453631i
$479$	−0.747358	+	4.23848i	−0.0341476	+	0.193661i	−0.997110	−	0.0759763i	$-0.975793\pi$
$479$	−0.747358	+	4.23848i	−0.0341476	+	0.193661i	0.962962	+	0.269637i	$0.0869038\pi$
$480$		0			0
$481$	−19.5550	+	7.11745i	−0.891632	+	0.324528i
$482$	19.7898	−	30.6166i	0.901399	−	1.39455i
$483$		0			0
$484$	18.4326	+	18.9250i	0.837845	+	0.860226i
$485$	52.3248	−	62.3583i	2.37595	−	2.83155i
$486$		0			0
$487$	−31.4925	−	18.1822i	−1.42706	−	0.823915i	−0.430175	−	0.902745i	$-0.641548\pi$
$487$	−31.4925	−	18.1822i	−1.42706	−	0.823915i	−0.996888	+	0.0788302i	$0.974882\pi$
$488$	13.5283	−	2.71975i	0.612399	−	0.123117i
$489$		0			0
$490$	8.10194	+	1.85225i	0.366008	+	0.0836763i
$491$	12.1750	+	4.43132i	0.549448	+	0.199983i	0.601801	−	0.798646i	$-0.294450\pi$
$491$	12.1750	+	4.43132i	0.549448	+	0.199983i	−0.0523531	+	0.998629i	$0.516672\pi$
$492$		0			0
$493$	−18.3829			−0.827922
$494$	−6.03455	+	25.2972i	−0.271507	+	1.13817i
$495$		0			0
$496$	9.46682	+	17.4432i	0.425073	+	0.783222i
$497$	−7.42505	+	20.4002i	−0.333059	+	0.915072i
$498$		0			0
$499$	−33.5963	+	5.92393i	−1.50398	+	0.265192i	−0.864113	−	0.503297i	$-0.832120\pi$
$499$	−33.5963	+	5.92393i	−1.50398	+	0.265192i	−0.639863	+	0.768489i	$0.721009\pi$
$500$	−16.5494	−	65.1881i	−0.740113	−	2.91530i
$501$		0			0
$502$	−8.78630	−	17.1534i	−0.392152	−	0.765592i
$503$	−1.18149	−	0.991387i	−0.0526800	−	0.0442037i	0.616068	−	0.787693i	$-0.288725\pi$
$503$	−1.18149	−	0.991387i	−0.0526800	−	0.0442037i	−0.668748	+	0.743490i	$0.733169\pi$
$504$		0			0
$505$	−1.32173	−	2.28930i	−0.0588162	−	0.101873i
$506$	−14.6167	+	22.6134i	−0.649793	+	1.00529i
$507$		0			0
$508$	−9.91588	+	0.735982i	−0.439946	+	0.0326539i
$509$	−31.1834	−	5.49847i	−1.38218	−	0.243716i	−0.567379	−	0.823457i	$-0.692042\pi$
$509$	−31.1834	−	5.49847i	−1.38218	−	0.243716i	−0.814801	+	0.579741i	$0.803154\pi$
$510$		0			0
$511$	−1.57709	−	1.87950i	−0.0697664	−	0.0831444i
$512$	−20.3550	−	9.88304i	−0.899572	−	0.436773i
$513$		0			0
$514$	0.774651	−	15.4112i	0.0341684	−	0.679760i
$515$	3.25052	−	2.72751i	0.143235	−	0.120189i
$516$		0			0
$517$	7.39603	−	41.9450i	0.325277	−	1.84474i
$518$	−16.3985	+	2.04906i	−0.720508	+	0.0900305i
$519$		0			0
$520$	−39.4812	−	31.5544i	−1.73137	−	1.38375i
$521$	−6.05147	+	3.49382i	−0.265120	+	0.153067i	−0.626668	−	0.779287i	$-0.715582\pi$
$521$	−6.05147	+	3.49382i	−0.265120	+	0.153067i	0.361548	+	0.932353i	$0.382248\pi$
$522$		0			0
$523$	19.2320	−	22.9198i	0.840957	−	1.00221i	−0.158932	−	0.987290i	$-0.550805\pi$
$523$	19.2320	−	22.9198i	0.840957	−	1.00221i	0.999889	−	0.0149239i	$-0.00475060\pi$
$524$	−8.17598	−	18.1544i	−0.357169	−	0.793077i
$525$		0			0
$526$	−0.936405	+	0.288477i	−0.0408292	+	0.0125782i
$527$	−3.72819	−	21.1436i	−0.162402	−	0.921029i
$528$		0			0
$529$	7.54188	+	2.74502i	0.327908	+	0.119349i
$530$	11.8523	−	8.97112i	0.514831	−	0.389681i
$531$		0			0
$532$	−9.14903	+	18.5161i	−0.396661	+	0.802774i
$533$			6.95986i			0.301465i
$534$		0			0
$535$	25.4111	−	69.8163i	1.09862	−	3.01842i
$536$	35.7386	+	12.0501i	1.54367	+	0.520484i
$537$		0			0
$538$	−8.85015	−	28.7279i	−0.381557	−	1.23855i
$539$	3.41342	−	5.91222i	0.147026	−	0.254657i
$540$		0			0
$541$	−17.0748	−	14.3275i	−0.734103	−	0.615985i	0.197144	−	0.980375i	$-0.436833\pi$
$541$	−17.0748	−	14.3275i	−0.734103	−	0.615985i	−0.931247	+	0.364389i	$0.881278\pi$
$542$	19.1163	−	20.5878i	0.821117	−	0.884322i
$543$		0			0
$544$	17.4925	+	17.1227i	0.749987	+	0.734130i
$545$	4.56701	+	12.5477i	0.195629	+	0.537487i
$546$		0			0
$547$	−5.39427	−	0.951155i	−0.230642	−	0.0406684i	0.0571324	−	0.998367i	$-0.481804\pi$
$547$	−5.39427	−	0.951155i	−0.230642	−	0.0406684i	−0.287775	+	0.957698i	$0.592915\pi$
$548$	6.01940	−	12.4767i	0.257136	−	0.532976i
$549$		0			0
$550$	−89.9238	−	4.52005i	−3.83436	−	0.192736i
$551$	6.49697	−	17.3406i	0.276780	−	0.738733i
$552$		0			0
$553$	2.95858	−	2.48254i	0.125811	−	0.105568i
$554$	−21.1410	−	8.92054i	−0.898193	−	0.378998i
$555$		0			0
$556$	−10.8133	+	0.802591i	−0.458586	+	0.0340374i
$557$	−10.2490	−	28.1589i	−0.434263	−	1.19313i	−0.943171	−	0.332308i	$-0.892173\pi$
$557$	−10.2490	−	28.1589i	−0.434263	−	1.19313i	0.508908	−	0.860821i	$-0.330049\pi$
$558$		0			0
$559$	30.5173	−	17.6192i	1.29074	−	0.745211i
$560$	−24.9802	−	31.4160i	−1.05561	−	1.32757i
$561$		0			0
$562$	27.0576	−	13.8595i	1.14136	−	0.584626i
$563$	−8.98365	+	15.5601i	−0.378616	+	0.655782i	−0.990861	−	0.134886i	$-0.956933\pi$
$563$	−8.98365	+	15.5601i	−0.378616	+	0.655782i	0.612245	+	0.790668i	$0.290267\pi$
$564$		0			0
$565$	2.15899	+	12.2442i	0.0908294	+	0.515119i
$566$	−4.06211	−	0.928674i	−0.170743	−	0.0390351i
$567$		0			0
$568$	−22.1307	+	13.4913i	−0.928583	+	0.566082i
$569$			41.6349i			1.74543i	0.488233	+	0.872713i	$0.337642\pi$
$569$			41.6349i			1.74543i	−0.488233	+	0.872713i	$0.662358\pi$
$570$		0			0
$571$		−	1.68623i		−	0.0705664i	−0.999377	−	0.0352832i	$-0.988767\pi$
$571$		−	1.68623i		−	0.0705664i	0.999377	−	0.0352832i	$-0.0112333\pi$
$572$	−34.3189	+	23.3624i	−1.43494	+	0.976830i
$573$		0			0
$574$	−1.23181	+	5.38807i	−0.0514149	+	0.224894i
$575$	−8.69480	−	49.3106i	−0.362598	−	2.05640i
$576$		0			0
$577$	5.96096	−	10.3247i	0.248158	−	0.429822i	−0.714857	−	0.699271i	$-0.753508\pi$
$577$	5.96096	−	10.3247i	0.248158	−	0.429822i	0.963015	+	0.269449i	$0.0868414\pi$
$578$	−1.11168	−	2.17032i	−0.0462398	−	0.0902733i
$579$		0			0
$580$	25.1091	+	25.7799i	1.04260	+	1.07045i
$581$	−9.67887	+	5.58810i	−0.401547	+	0.231833i
$582$		0			0
$583$	−4.17614	−	11.4738i	−0.172958	−	0.475198i
$584$	−0.0698957	−	2.92841i	−0.00289230	−	0.121179i
$585$		0			0
$586$	−6.06582	+	14.3755i	−0.250577	+	0.593846i
$587$	−26.5994	+	22.3195i	−1.09787	+	0.921226i	−0.997280	−	0.0737013i	$-0.976519\pi$
$587$	−26.5994	+	22.3195i	−1.09787	+	0.921226i	−0.100594	+	0.994928i	$0.532074\pi$
$588$		0			0
$589$	21.2624	+	3.95588i	0.876102	+	0.162999i
$590$	−1.21751	+	24.2217i	−0.0501242	+	0.997191i
$591$		0			0
$592$	−16.8210	−	10.3121i	−0.691340	−	0.423825i
$593$	−37.9041	−	6.68351i	−1.55653	−	0.274459i	−0.671863	−	0.740676i	$-0.734506\pi$
$593$	−37.9041	−	6.68351i	−1.55653	−	0.274459i	−0.884671	+	0.466217i	$0.845617\pi$
$594$		0			0
$595$	14.8504	+	40.8011i	0.608807	+	1.67268i
$596$	26.4289	+	19.0297i	1.08257	+	0.779487i
$597$		0			0
$598$	−16.9190	−	15.7097i	−0.691868	−	0.642419i
$599$	−2.51107	−	2.10703i	−0.102599	−	0.0860911i	0.590045	−	0.807370i	$-0.299110\pi$
$599$	−2.51107	−	2.10703i	−0.102599	−	0.0860911i	−0.692644	+	0.721279i	$0.743554\pi$
$600$		0			0
$601$	15.2155	−	26.3540i	0.620652	−	1.07500i	−0.368713	−	0.929543i	$-0.620201\pi$
$601$	15.2155	−	26.3540i	0.620652	−	1.07500i	0.989365	−	0.145457i	$-0.0464653\pi$
$602$	26.7437	−	8.23891i	1.08999	−	0.335793i
$603$		0			0
$604$	0.432605	+	0.122049i	0.0176024	+	0.00496611i
$605$	−19.1350	+	52.5730i	−0.777949	+	2.13740i
$606$		0			0
$607$			22.1799i			0.900254i	0.892965	+	0.450127i	$0.148621\pi$
$607$			22.1799i			0.900254i	−0.892965	+	0.450127i	$0.851379\pi$
$608$	−22.3342	+	10.4491i	−0.905771	+	0.423768i
$609$		0			0
$610$	17.6366	+	23.3008i	0.714086	+	0.943423i
$611$	34.3181	+	12.4908i	1.38836	+	0.505322i
$612$		0			0
$613$	−0.903611	−	5.12463i	−0.0364965	−	0.206982i	0.961107	−	0.276178i	$-0.0890678\pi$
$613$	−0.903611	−	5.12463i	−0.0364965	−	0.206982i	−0.997603	+	0.0691957i	$0.977957\pi$
$614$	−4.78231	−	15.5235i	−0.192998	−	0.626478i
$615$		0			0
$616$	−30.7033	+	12.0123i	−1.23707	+	0.483988i
$617$	−5.84795	+	6.96932i	−0.235430	+	0.280574i	−0.870804	−	0.491630i	$-0.836401\pi$
$617$	−5.84795	+	6.96932i	−0.235430	+	0.280574i	0.635375	+	0.772204i	$0.280846\pi$
$618$		0			0
$619$	−20.0116	+	11.5537i	−0.804335	+	0.464383i	−0.844985	−	0.534790i	$-0.820391\pi$
$619$	−20.0116	+	11.5537i	−0.804335	+	0.464383i	0.0406494	+	0.999173i	$0.487057\pi$
$620$	−24.5591	+	34.1083i	−0.986319	+	1.36982i
$621$		0			0
$622$	−1.11776	−	8.94534i	−0.0448180	−	0.358675i
$623$	0.0802385	−	0.455055i	0.00321469	−	0.0182314i
$624$		0			0
$625$	59.5477	−	49.9665i	2.38191	−	1.99866i
$626$	17.7144	+	0.890419i	0.708008	+	0.0355883i
$627$		0			0
$628$	−23.9996	−	2.41881i	−0.957688	−	0.0965210i
$629$	13.7197	+	16.3505i	0.547040	+	0.651937i
$630$		0			0
$631$	19.1908	+	3.38385i	0.763972	+	0.134709i	0.542039	−	0.840353i	$-0.317652\pi$
$631$	19.1908	+	3.38385i	0.763972	+	0.134709i	0.221933	+	0.975062i	$0.428763\pi$
$632$	4.60969	−	0.110025i	0.183364	−	0.00437654i
$633$		0			0
$634$	−4.78549	−	3.09322i	−0.190056	−	0.122847i
$635$	−10.5286	−	18.2360i	−0.417814	−	0.723675i
$636$		0			0
$637$	4.48418	+	3.76267i	0.177670	+	0.149082i
$638$	26.3100	−	13.4765i	1.04162	−	0.533541i
$639$		0			0
$640$	0.119604	−	47.9192i	0.00472776	−	1.89417i
$641$	21.0061	−	3.70394i	0.829691	−	0.146297i	0.257356	−	0.966317i	$-0.417149\pi$
$641$	21.0061	−	3.70394i	0.829691	−	0.146297i	0.572335	+	0.820020i	$0.306038\pi$
$642$		0			0
$643$	9.01221	−	24.7608i	0.355407	−	0.976472i	−0.625196	−	0.780468i	$-0.714981\pi$
$643$	9.01221	−	24.7608i	0.355407	−	0.976472i	0.980603	−	0.196005i	$-0.0627968\pi$
$644$	−10.3176	−	15.1564i	−0.406571	−	0.597245i
$645$		0			0
$646$	26.4985	−	3.05802i	1.04257	−	0.120316i
$647$	−24.9968			−0.982727			−0.491363	−	0.870955i	$-0.663501\pi$
$647$	−24.9968			−0.982727			−0.491363	+	0.870955i	$0.663501\pi$
$648$		0			0
$649$	18.7200	+	6.81353i	0.734825	+	0.267454i
$650$	17.2060	−	75.2608i	0.674875	−	2.95197i
$651$		0			0
$652$	2.16399	+	8.52395i	0.0847485	+	0.333824i
$653$	21.3431	+	12.3224i	0.835220	+	0.482214i	0.855636	−	0.517577i	$-0.173166\pi$
$653$	21.3431	+	12.3224i	0.835220	+	0.482214i	−0.0204168	+	0.999792i	$0.506499\pi$
$654$		0			0
$655$	27.1035	−	32.3007i	1.05902	−	1.26209i
$656$	−5.16498	+	4.10690i	−0.201659	+	0.160347i
$657$		0			0
$658$	24.3571	+	15.7438i	0.949539	+	0.613757i
$659$	−32.4811	+	11.8221i	−1.26528	+	0.460525i	−0.885538	−	0.464566i	$-0.846210\pi$
$659$	−32.4811	+	11.8221i	−1.26528	+	0.460525i	−0.379744	+	0.925092i	$0.623988\pi$
$660$		0			0
$661$	−4.61468	+	26.1712i	−0.179490	+	1.01794i	0.753342	+	0.657629i	$0.228441\pi$
$661$	−4.61468	+	26.1712i	−0.179490	+	1.01794i	−0.932832	+	0.360311i	$0.882670\pi$
$662$	0.128846	−	0.305354i	0.00500773	−	0.0118679i
$663$		0			0
$664$	−13.1920	−	2.00282i	−0.511951	−	0.0777243i
$665$	−43.7363	−	0.411765i	−1.69602	−	0.0159676i
$666$		0			0
$667$	10.5669	+	12.5932i	0.409153	+	0.487609i
$668$	−36.9344	−	17.8191i	−1.42904	−	0.689443i
$669$		0			0
$670$	9.90331	+	79.2556i	0.382598	+	3.06191i
$671$	22.5568	−	8.21001i	0.870796	−	0.316944i
$672$		0			0
$673$	−10.0909	−	17.4780i	−0.388977	−	0.673727i	0.603336	−	0.797487i	$-0.293838\pi$
$673$	−10.0909	−	17.4780i	−0.388977	−	0.673727i	−0.992312	+	0.123760i	$0.960505\pi$
$674$	−7.90941	−	7.34411i	−0.304659	−	0.282885i
$675$		0			0
$676$	−3.94129	−	8.75143i	−0.151588	−	0.336593i
$677$	−7.97495	−	4.60434i	−0.306502	−	0.176959i	0.338858	−	0.940838i	$-0.389959\pi$
$677$	−7.97495	−	4.60434i	−0.306502	−	0.176959i	−0.645360	+	0.763878i	$0.723293\pi$
$678$		0			0
$679$	44.8399	−	7.90648i	1.72080	−	0.303423i
$680$	−16.5624	+	49.1215i	−0.635141	+	1.88372i
$681$		0			0
$682$	20.8363	+	27.5281i	0.797863	+	1.05411i
$683$	26.2485			1.00437			0.502186	−	0.864760i	$-0.332529\pi$
$683$	26.2485			1.00437			0.502186	+	0.864760i	$0.332529\pi$
$684$		0			0
$685$	29.3368			1.12090
$686$	16.9597	+	22.4065i	0.647523	+	0.855483i
$687$		0			0
$688$	31.0831	+	12.2504i	1.18503	+	0.467043i
$689$	10.3106	−	1.81804i	0.392802	−	0.0692616i
$690$		0			0
$691$	43.4628	+	25.0933i	1.65340	+	0.954593i	0.975658	+	0.219296i	$0.0703760\pi$
$691$	43.4628	+	25.0933i	1.65340	+	0.954593i	0.677745	+	0.735297i	$0.262957\pi$
$692$	7.76978	−	3.49919i	0.295363	−	0.133019i
$693$		0			0
$694$	−18.4921	−	17.1705i	−0.701952	−	0.651782i
$695$	−11.4815	−	19.8865i	−0.435516	−	0.754336i
$696$		0			0
$697$	6.70796	−	2.44150i	0.254082	−	0.0924784i
$698$	−1.14305	−	9.14778i	−0.0432652	−	0.346249i
$699$		0			0
$700$	26.6405	−	55.2189i	1.00692	−	2.08708i
$701$	−20.3775	−	24.2850i	−0.769649	−	0.917231i	0.228768	−	0.973481i	$-0.426530\pi$
$701$	−20.3775	−	24.2850i	−0.769649	−	0.917231i	−0.998417	+	0.0562494i	$0.982086\pi$
$702$		0			0
$703$	−20.2723	+	7.16312i	−0.764586	+	0.270162i
$704$	−37.5885	−	11.6826i	−1.41667	−	0.440306i
$705$		0			0
$706$	2.81250	−	6.66540i	0.105850	−	0.250856i
$707$	0.256753	−	1.45612i	0.00965620	−	0.0547630i
$708$		0			0
$709$	−0.480967	+	0.175058i	−0.0180631	+	0.00657443i	−0.351036	−	0.936362i	$-0.614170\pi$
$709$	−0.480967	+	0.175058i	−0.0180631	+	0.00657443i	0.332973	+	0.942936i	$0.391948\pi$
$710$	−46.0981	−	29.7966i	−1.73003	−	1.11825i
$711$		0			0
$712$	0.414022	−	0.364590i	0.0155161	−	0.0136636i
$713$	−12.3414	+	14.7079i	−0.462187	+	0.550813i
$714$		0			0
$715$	−76.1417	−	43.9605i	−2.84754	−	1.64403i
$716$	15.9053	−	4.03792i	0.594410	−	0.150904i
$717$		0			0
$718$	−4.81924	+	21.0798i	−0.179853	+	0.786693i
$719$	−17.6720	−	6.43209i	−0.659055	−	0.239876i	−0.00922653	−	0.999957i	$-0.502937\pi$
$719$	−17.6720	−	6.43209i	−0.659055	−	0.239876i	−0.649828	+	0.760081i	$0.725159\pi$
$720$		0			0
$721$	2.37341			0.0883902
$722$	−6.48061	+	26.0768i	−0.241183	+	0.970480i
$723$		0			0
$724$	−7.81197	+	5.31795i	−0.290330	+	0.197640i
$725$	−18.8010	+	51.6554i	−0.698252	+	1.91843i
$726$		0			0
$727$	38.2376	−	6.74232i	1.41815	−	0.250059i	0.588573	−	0.808444i	$-0.299690\pi$
$727$	38.2376	−	6.74232i	1.41815	−	0.250059i	0.829582	+	0.558385i	$0.188579\pi$
$728$	−5.57189	−	27.7152i	−0.206508	−	1.02719i
$729$		0			0
$730$	5.52126	−	2.82810i	0.204351	−	0.104673i
$731$	−27.6868	−	23.2320i	−1.02404	−	0.859268i
$732$		0			0
$733$	24.0421	+	41.6422i	0.888017	+	1.53809i	0.842216	+	0.539140i	$0.181250\pi$
$733$	24.0421	+	41.6422i	0.888017	+	1.53809i	0.0458003	+	0.998951i	$0.485416\pi$
$734$	−15.8232	−	10.2277i	−0.584045	−	0.377512i
$735$		0			0
$736$	1.67475	−	21.8258i	0.0617323	−	0.804510i
$737$	64.6121	+	11.3929i	2.38002	+	0.419661i
$738$		0			0
$739$	16.1794	+	19.2819i	0.595170	+	0.709297i	0.976591	−	0.215105i	$-0.0690094\pi$
$739$	16.1794	+	19.2819i	0.595170	+	0.709297i	−0.381420	+	0.924402i	$0.624565\pi$
$740$	4.18999	−	41.5734i	0.154027	−	1.52827i
$741$		0			0
$742$	8.30386	+	0.417397i	0.304844	+	0.0153231i
$743$	−20.5179	+	17.2165i	−0.752727	+	0.631613i	−0.936223	−	0.351408i	$-0.885703\pi$
$743$	−20.5179	+	17.2165i	−0.752727	+	0.631613i	0.183496	+	0.983021i	$0.441259\pi$
$744$		0			0
$745$	−11.9764	+	67.9214i	−0.438780	+	2.48845i
$746$	4.27404	+	34.2049i	0.156484	+	1.25233i
$747$		0			0
$748$	34.5558	+	24.8813i	1.26349	+	0.909752i
$749$	35.9894	−	20.7785i	1.31502	−	0.759229i
$750$		0			0
$751$	−27.5600	+	32.8447i	−1.00568	+	1.19852i	−0.0256472	+	0.999671i	$0.508165\pi$
$751$	−27.5600	+	32.8447i	−1.00568	+	1.19852i	−0.980030	+	0.198849i	$0.936280\pi$
$752$	10.9810	+	32.8384i	0.400437	+	1.19749i
$753$		0			0
$754$	7.46247	+	24.2234i	0.271767	+	0.882164i
$755$	0.165298	+	0.937452i	0.00601581	+	0.0341174i
$756$		0			0
$757$	27.6260	+	10.0550i	1.00408	+	0.365456i	0.791158	−	0.611612i	$-0.209479\pi$
$757$	27.6260	+	10.0550i	1.00408	+	0.365456i	0.212925	+	0.977068i	$0.431701\pi$
$758$	−25.6858	−	33.9351i	−0.932950	−	1.23258i
$759$		0			0
$760$	−40.4828	−	32.9842i	−1.46846	−	1.19646i
$761$		−	12.6138i		−	0.457251i	−0.973514	−	0.228625i	$-0.926577\pi$
$761$		−	12.6138i		−	0.457251i	0.973514	−	0.228625i	$-0.0734231\pi$
$762$		0			0
$763$	−2.55449	+	7.01841i	−0.0924788	+	0.254083i
$764$	8.95521	−	31.7419i	0.323988	−	1.14838i
$765$		0			0
$766$	4.91656	−	1.51464i	0.177643	−	0.0547262i
$767$	−8.54081	+	14.7931i	−0.308391	+	0.534149i
$768$		0			0
$769$	−13.4964	−	11.3248i	−0.486693	−	0.408384i	0.366147	−	0.930557i	$-0.380677\pi$
$769$	−13.4964	−	11.3248i	−0.486693	−	0.408384i	−0.852839	+	0.522173i	$0.825121\pi$
$770$	−51.1657	−	47.5088i	−1.84388	−	1.71210i
$771$		0			0
$772$	−17.2541	+	23.9630i	−0.620990	+	0.862446i
$773$	15.9489	+	43.8192i	0.573642	+	1.57607i	0.798704	+	0.601723i	$0.205519\pi$
$773$	15.9489	+	43.8192i	0.573642	+	1.57607i	−0.225063	+	0.974344i	$0.572259\pi$
$774$		0			0
$775$	−63.2259	−	11.1484i	−2.27114	−	0.400464i
$776$	47.7123	+	26.0490i	1.71277	+	0.935103i
$777$		0			0
$778$	0.442319	−	8.79967i	0.0158579	−	0.315484i
$779$	−0.0676968	+	7.19052i	−0.00242549	+	0.257627i
$780$		0			0
$781$	−34.5392	+	28.9818i	−1.23591	+	1.03705i
$782$	−9.20604	+	21.8176i	−0.329207	+	0.780195i
$783$		0			0
$784$	−0.146278	+	5.54805i	−0.00522421	+	0.198145i
$785$	−17.4713	−	48.0021i	−0.623578	−	1.71327i
$786$		0			0
$787$	−25.8761	+	14.9395i	−0.922382	+	0.532537i	−0.884394	−	0.466741i	$-0.845428\pi$
$787$	−25.8761	+	14.9395i	−0.922382	+	0.532537i	−0.0379877	+	0.999278i	$0.512095\pi$
$788$	−33.4785	+	32.6074i	−1.19262	+	1.16159i
$789$		0			0
$790$	4.45179	+	8.69116i	0.158387	+	0.309218i
$791$	−3.47715	+	6.02260i	−0.123633	+	0.214139i
$792$		0			0
$793$	3.57414	+	20.2699i	0.126921	+	0.719806i
$794$	4.08790	−	17.8809i	0.145074	−	0.634568i
$795$		0			0
$796$	−13.7750	−	20.2352i	−0.488241	−	0.717216i
$797$			20.4097i			0.722950i	0.932382	+	0.361475i	$0.117727\pi$
$797$			20.4097i			0.722950i	−0.932382	+	0.361475i	$0.882273\pi$
$798$		0			0
$799$		−	37.4578i		−	1.32516i
$800$	66.0048	−	31.6414i	2.33362	−	1.11869i
$801$		0			0
$802$	−35.6748	−	8.15593i	−1.25972	−	0.287996i
$803$	−0.884851	−	5.01824i	−0.0312257	−	0.177090i
$804$		0			0
$805$	19.4144	−	33.6268i	0.684268	−	1.18519i
$806$	−26.3478	+	13.4959i	−0.928062	+	0.475372i
$807$		0			0
$808$	1.32482	−	1.16664i	0.0466069	−	0.0410423i
$809$	−18.5251	+	10.6955i	−0.651309	+	0.376033i	−0.788957	−	0.614448i	$-0.789379\pi$
$809$	−18.5251	+	10.6955i	−0.651309	+	0.376033i	0.137649	+	0.990481i	$0.456046\pi$
$810$		0			0
$811$	2.15199	+	5.91254i	0.0755665	+	0.207617i	0.971724	−	0.236118i	$-0.0758752\pi$
$811$	2.15199	+	5.91254i	0.0755665	+	0.207617i	−0.896158	+	0.443735i	$0.853653\pi$
$812$	1.48992	+	20.0736i	0.0522858	+	0.704447i
$813$		0			0
$814$	−31.6226	−	13.3433i	−1.10837	−	0.467683i
$815$	−14.2670	+	11.9715i	−0.499752	+	0.419342i
$816$		0			0
$817$	31.7000	−	17.9062i	1.10904	−	0.626460i
$818$	−42.1175	−	2.11705i	−1.47261	−	0.0740211i
$819$		0			0
$820$	−12.5863	−	6.07231i	−0.439533	−	0.212054i
$821$	42.5399	+	7.50093i	1.48465	+	0.261784i	0.856435	−	0.516255i	$-0.172674\pi$
$821$	42.5399	+	7.50093i	1.48465	+	0.261784i	0.628216	+	0.778039i	$0.283785\pi$
$822$		0			0
$823$	6.72283	+	18.4708i	0.234343	+	0.643852i	1.00000		0.000602960i	$0.000191928\pi$
$823$	6.72283	+	18.4708i	0.234343	+	0.643852i	−0.765657	+	0.643249i	$0.777586\pi$
$824$	2.21351	+	1.76909i	0.0771112	+	0.0616292i
$825$		0			0
$826$	−9.23020	+	9.94068i	−0.321160	+	0.345880i
$827$	34.7622	+	29.1689i	1.20880	+	1.01430i	0.999334	+	0.0364873i	$0.0116168\pi$
$827$	34.7622	+	29.1689i	1.20880	+	1.01430i	0.209466	+	0.977816i	$0.432828\pi$
$828$		0			0
$829$	−8.49047	+	14.7059i	−0.294886	+	0.510758i	−0.974958	−	0.222387i	$-0.928615\pi$
$829$	−8.49047	+	14.7059i	−0.294886	+	0.510758i	0.680072	+	0.733145i	$0.261948\pi$
$830$	−8.31946	−	27.0052i	−0.288773	−	0.937365i
$831$		0			0
$832$	15.4618	−	30.0011i	0.536042	−	1.04010i
$833$	2.05345	−	5.64182i	0.0711480	−	0.195477i
$834$		0			0
$835$		−	86.8453i		−	3.00541i
$836$	−35.6835	+	23.8028i	−1.23414	+	0.823238i
$837$		0			0
$838$	−6.90351	+	5.22533i	−0.238478	+	0.180506i
$839$	31.7940	+	11.5721i	1.09765	+	0.399512i	0.826450	−	0.563010i	$-0.190357\pi$
$839$	31.7940	+	11.5721i	1.09765	+	0.399512i	0.271201	+	0.962523i	$0.412579\pi$
$840$		0			0
$841$	1.90185	+	10.7859i	0.0655811	+	0.371929i
$842$	9.82525	−	3.02685i	0.338600	−	0.104312i
$843$		0			0
$844$	31.6939	−	14.2736i	1.09095	−	0.491319i
$845$	13.0654	−	15.5708i	0.449464	−	0.535650i
$846$		0			0
$847$	−27.1007	+	15.6466i	−0.931191	+	0.537623i
$848$	7.43330	+	6.57881i	0.255260	+	0.225917i
$849$		0			0
$850$	−78.5727	+	9.81799i	−2.69502	+	0.336754i
$851$	3.31448	−	18.7973i	0.113619	−	0.644365i
$852$		0			0
$853$	0.214013	−	0.179578i	0.00732767	−	0.00614864i	−0.639116	−	0.769110i	$-0.720700\pi$
$853$	0.214013	−	0.179578i	0.00732767	−	0.00614864i	0.646444	+	0.762961i	$0.276255\pi$
$854$	−0.820574	+	16.3248i	−0.0280795	+	0.558624i
$855$		0			0
$856$	49.0526	+	7.44717i	1.67658	+	0.254539i
$857$	25.5799	+	30.4849i	0.873792	+	1.04135i	0.998790	+	0.0491882i	$0.0156634\pi$
$857$	25.5799	+	30.4849i	0.873792	+	1.04135i	−0.124997	+	0.992157i	$0.539892\pi$
$858$		0			0
$859$	−4.77072	−	0.841208i	−0.162775	−	0.0287016i	0.0916666	−	0.995790i	$-0.470781\pi$
$859$	−4.77072	−	0.841208i	−0.162775	−	0.0287016i	−0.254442	+	0.967088i	$0.581892\pi$
$860$	5.23716	+	70.5602i	0.178586	+	2.40608i
$861$		0			0
$862$	−11.3326	+	17.5326i	−0.385990	+	0.597163i
$863$	−17.4697	−	30.2584i	−0.594675	−	1.03001i	−0.993593	−	0.113020i	$-0.963947\pi$
$863$	−17.4697	−	30.2584i	−0.594675	−	1.03001i	0.398918	−	0.916987i	$-0.369386\pi$
$864$		0			0
$865$	13.8242	+	11.5999i	0.470036	+	0.394407i
$866$	17.1977	+	33.5749i	0.584403	+	1.14092i
$867$		0			0
$868$	−22.7861	+	5.78476i	−0.773412	+	0.196348i
$869$	7.89934	−	1.39287i	0.267967	−	0.0472498i
$870$		0			0
$871$	−19.2408	+	52.8636i	−0.651949	+	1.79122i
$872$	−7.61377	+	4.64150i	−0.257835	+	0.157181i
$873$		0			0
$874$	−17.3269	−	16.3950i	−0.586091	−	0.554568i
$875$	79.6672			2.69324
$876$		0			0
$877$	−16.6231	−	6.05032i	−0.561322	−	0.204305i	0.0457475	−	0.998953i	$-0.485433\pi$
$877$	−16.6231	−	6.05032i	−0.561322	−	0.204305i	−0.607070	+	0.794648i	$0.707655\pi$
$878$	24.1098	+	5.51194i	0.813665	+	0.186019i
$879$		0			0
$880$	−12.3065	−	82.4460i	−0.414852	−	2.77925i
$881$	−32.5283	−	18.7802i	−1.09591	−	0.632721i	−0.160763	−	0.986993i	$-0.551396\pi$
$881$	−32.5283	−	18.7802i	−1.09591	−	0.632721i	−0.935143	+	0.354272i	$0.884729\pi$
$882$		0			0
$883$	27.4909	−	32.7623i	0.925141	−	1.10254i	−0.0693368	−	0.997593i	$-0.522088\pi$
$883$	27.4909	−	32.7623i	0.925141	−	1.10254i	0.994478	−	0.104947i	$-0.0334672\pi$
$884$	−26.1556	+	25.4750i	−0.879707	+	0.856818i
$885$		0			0
$886$	25.3931	−	39.2854i	0.853098	−	1.31982i
$887$	2.31077	−	0.841050i	0.0775879	−	0.0282397i	−0.302935	−	0.953011i	$-0.597966\pi$
$887$	2.31077	−	0.841050i	0.0775879	−	0.0282397i	0.380523	+	0.924772i	$0.375744\pi$
$888$		0			0
$889$	2.04523	−	11.5991i	0.0685950	−	0.389021i
$890$	1.07640	+	0.454193i	0.0360810	+	0.0152246i
$891$		0			0
$892$	−3.51309	+	34.8571i	−0.117627	+	1.16710i
$893$	35.3339	+	13.2385i	1.18241	+	0.443010i
$894$		0			0
$895$	22.3382	+	26.6217i	0.746684	+	0.889864i
$896$	17.2798	−	20.4892i	0.577279	−	0.684497i
$897$		0			0
$898$	−41.1071	+	5.13651i	−1.37176	+	0.171407i
$899$	19.8071	−	7.20920i	0.660605	−	0.240440i
$900$		0			0
$901$	−5.36916	−	9.29966i	−0.178873	−	0.309817i
$902$	−7.81075	+	8.41196i	−0.260069	+	0.280088i
$903$		0			0
$904$	−7.73201	+	3.02505i	−0.257163	+	0.100612i
$905$	−17.3321	−	10.0067i	−0.576137	−	0.332633i
$906$		0			0
$907$	−24.9369	+	4.39705i	−0.828016	+	0.146002i	−0.571566	−	0.820556i	$-0.693664\pi$
$907$	−24.9369	+	4.39705i	−0.828016	+	0.146002i	−0.256450	+	0.966558i	$0.582553\pi$
$908$	7.70752	−	27.3194i	0.255783	−	0.906627i
$909$		0			0
$910$	47.7358	−	36.1317i	1.58243	−	1.19775i
$911$	19.4697			0.645058			0.322529	−	0.946560i	$-0.395467\pi$
$911$	19.4697			0.645058			0.322529	+	0.946560i	$0.395467\pi$
$912$		0			0
$913$	−23.2116			−0.768190
$914$	27.0362	−	20.4639i	0.894277	−	0.676887i
$915$		0			0
$916$	0.0794558	−	0.281632i	0.00262529	−	0.00930539i
$917$	23.2264	−	4.09544i	0.767003	−	0.135243i
$918$		0			0
$919$	27.6842	+	15.9835i	0.913219	+	0.527247i	0.881465	−	0.472249i	$-0.156558\pi$
$919$	27.6842	+	15.9835i	0.913219	+	0.527247i	0.0317534	+	0.999496i	$0.489891\pi$
$920$	43.1712	−	16.8902i	1.42331	−	0.556852i
$921$		0			0
$922$	18.8426	−	20.2930i	0.620549	−	0.668314i
$923$	−19.3302	−	33.4809i	−0.636262	−	1.10204i
$924$		0			0
$925$	59.9763	−	21.8296i	1.97201	−	0.717752i
$926$	1.30228	−	0.162725i	0.0427956	−	0.00534749i
$927$		0			0
$928$	−13.5730	+	19.8318i	−0.445554	+	0.651011i
$929$	17.3537	+	20.6813i	0.569357	+	0.678533i	0.971499	−	0.237044i	$-0.0761787\pi$
$929$	17.3537	+	20.6813i	0.569357	+	0.678533i	−0.402142	+	0.915577i	$0.631734\pi$
$930$		0			0
$931$	4.59619	+	3.93099i	0.150634	+	0.128833i
$932$	1.33970	−	13.2926i	0.0438833	−	0.435414i
$933$		0			0
$934$	−41.4966	−	17.5097i	−1.35781	−	0.572936i
$935$	−15.6591	+	88.8072i	−0.512108	+	2.90431i
$936$		0			0
$937$	28.7346	−	10.4586i	0.938720	−	0.341666i	0.173060	−	0.984911i	$-0.444635\pi$
$937$	28.7346	−	10.4586i	0.938720	−	0.341666i	0.765660	+	0.643245i	$0.222412\pi$
$938$	−24.2518	+	37.5197i	−0.791848	+	1.22506i
$939$		0			0
$940$	−52.5302	+	51.1635i	−1.71335	+	1.66877i
$941$	−10.6636	+	12.7084i	−0.347624	+	0.414282i	−0.911319	−	0.411701i	$-0.864935\pi$
$941$	−10.6636	+	12.7084i	−0.347624	+	0.414282i	0.563695	+	0.825983i	$0.309379\pi$
$942$		0			0
$943$	−5.52845	−	3.19185i	−0.180031	−	0.103941i
$944$	−16.0179	+	2.39096i	−0.521339	+	0.0778190i
$945$		0			0
$946$	56.6576	+	12.9530i	1.84210	+	0.421138i
$947$	−44.4089	−	16.1635i	−1.44309	−	0.525244i	−0.502441	−	0.864611i	$-0.667565\pi$
$947$	−44.4089	−	16.1635i	−1.44309	−	0.525244i	−0.940654	+	0.339368i	$0.889787\pi$
$948$		0			0
$949$	4.36927			0.141832
$950$	18.5083	−	77.5877i	0.600488	−	2.51728i
$951$		0			0
$952$	−24.7575	+	15.0926i	−0.802394	+	0.489155i
$953$	13.8733	−	38.1165i	0.449399	−	1.23471i	−0.483744	−	0.875209i	$-0.660724\pi$
$953$	13.8733	−	38.1165i	0.449399	−	1.23471i	0.933143	−	0.359504i	$-0.117054\pi$
$954$		0			0
$955$	68.7844	−	12.1285i	2.22581	−	0.392471i
$956$	−34.9690	+	8.87766i	−1.13098	+	0.287124i
$957$		0			0
$958$	−2.77483	−	5.41726i	−0.0896507	−	0.175024i
$959$	12.5701	+	10.5476i	0.405911	+	0.340600i
$960$		0			0
$961$	−3.19108	−	5.52711i	−0.102938	−	0.178294i
$962$	15.9758	−	24.7161i	0.515082	−	0.796879i
$963$		0			0
$964$	3.81612	+	51.4145i	0.122909	+	1.65595i
$965$	−61.5840	−	10.8589i	−1.98246	−	0.349561i
$966$		0			0
$967$	−8.64232	−	10.2995i	−0.277918	−	0.331210i	0.608971	−	0.793193i	$-0.291583\pi$
$967$	−8.64232	−	10.2995i	−0.277918	−	0.331210i	−0.886889	+	0.461983i	$0.847138\pi$
$968$	−36.9375	−	5.60786i	−1.18722	−	0.180243i
$969$		0			0
$970$	−5.77932	+	114.976i	−0.185563	+	3.69166i
$971$	−1.57017	+	1.31753i	−0.0503890	+	0.0422814i	−0.667634	−	0.744489i	$-0.732693\pi$
$971$	−1.57017	+	1.31753i	−0.0503890	+	0.0422814i	0.617245	+	0.786771i	$0.288249\pi$
$972$		0			0
$973$	2.23033	−	12.6489i	0.0715012	−	0.405504i
$974$	51.0303	−	6.37644i	1.63512	−	0.204314i
$975$		0			0
$976$	−12.9335	+	14.6134i	−0.413991	+	0.467762i
$977$	−38.4227	+	22.1834i	−1.22925	+	0.709709i	−0.966874	−	0.255256i	$-0.917840\pi$
$977$	−38.4227	+	22.1834i	−1.22925	+	0.709709i	−0.262379	+	0.964965i	$0.584507\pi$
$978$		0			0
$979$	0.616866	−	0.735152i	0.0197151	−	0.0234956i
$980$	−10.7168	+	4.82642i	−0.342336	+	0.154174i
$981$		0			0
$982$	−17.5109	+	5.39456i	−0.558795	+	0.172147i
$983$	−2.37730	−	13.4823i	−0.0758241	−	0.430020i	−0.998962	−	0.0455508i	$-0.985496\pi$
$983$	−2.37730	−	13.4823i	−0.0758241	−	0.430020i	0.923138	−	0.384469i	$-0.125615\pi$
$984$		0			0
$985$	−93.0021	−	33.8500i	−2.96329	−	1.07855i
$986$	20.7289	−	15.6899i	0.660142	−	0.499668i
$987$		0			0
$988$	−14.7866	−	33.6761i	−0.470424	−	1.07138i
$989$			32.3212i			1.02775i
$990$		0			0
$991$	−3.62582	+	9.96186i	−0.115178	+	0.316449i	−0.983865	−	0.178912i	$-0.942742\pi$
$991$	−3.62582	+	9.96186i	−0.115178	+	0.316449i	0.868687	+	0.495361i	$0.164964\pi$
$992$	−25.5628	−	11.5893i	−0.811621	−	0.367960i
$993$		0			0
$994$	−9.03903	−	29.3410i	−0.286701	−	0.930639i
$995$	25.9201	−	44.8948i	0.821721	−	1.42326i
$996$		0			0
$997$	19.5916	+	16.4393i	0.620473	+	0.520639i	0.897952	−	0.440093i	$-0.145054\pi$
$997$	19.5916	+	16.4393i	0.620473	+	0.520639i	−0.277479	+	0.960732i	$0.589499\pi$
$998$	32.8277	−	35.3546i	1.03914	−	1.11913i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.ce.a.215.8	yes	240
3.2	odd	2	inner	684.2.ce.a.215.33	yes	240
4.3	odd	2	inner	684.2.ce.a.215.29	yes	240
12.11	even	2	inner	684.2.ce.a.215.12	yes	240
19.16	even	9	inner	684.2.ce.a.35.12	yes	240
57.35	odd	18	inner	684.2.ce.a.35.29	yes	240
76.35	odd	18	inner	684.2.ce.a.35.33	yes	240
228.35	even	18	inner	684.2.ce.a.35.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.ce.a.35.8	✓	240	228.35	even	18	inner
684.2.ce.a.35.12	yes	240	19.16	even	9	inner
684.2.ce.a.35.29	yes	240	57.35	odd	18	inner
684.2.ce.a.35.33	yes	240	76.35	odd	18	inner
684.2.ce.a.215.8	yes	240	1.1	even	1	trivial
684.2.ce.a.215.12	yes	240	12.11	even	2	inner
684.2.ce.a.215.29	yes	240	4.3	odd	2	inner
684.2.ce.a.215.33	yes	240	3.2	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.ce (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12762 + 0.853506i) q^{2} +(0.543054 - 1.92486i) q^{4} +(4.17116 - 0.735488i) q^{5} +(2.05168 + 1.18454i) q^{7} +(1.03052 + 2.63401i) q^{8} +O(q^{10})\)	\(q+(-1.12762 + 0.853506i) q^{2} +(0.543054 - 1.92486i) q^{4} +(4.17116 - 0.735488i) q^{5} +(2.05168 + 1.18454i) q^{7} +(1.03052 + 2.63401i) q^{8} +(-4.07574 + 4.38947i) q^{10} +(2.46013 + 4.26108i) q^{11} +(-3.96446 + 1.44294i) q^{13} +(-3.32452 + 0.415413i) q^{14} +(-3.41019 - 2.09061i) q^{16} +(2.78144 + 3.31479i) q^{17} +(-4.10988 + 1.45220i) q^{19} +(0.849452 - 8.42832i) q^{20} +(-6.41095 - 2.70514i) q^{22} +(0.671956 - 3.81085i) q^{23} +(12.1592 - 4.42558i) q^{25} +(3.23884 - 5.01078i) q^{26} +(3.39424 - 3.30593i) q^{28} +(-2.73073 + 3.25435i) q^{29} +(-4.29690 - 2.48082i) q^{31} +(5.62974 - 0.553205i) q^{32} +(-5.96560 - 1.36385i) q^{34} +(9.42909 + 3.43191i) q^{35} +4.93259 q^{37} +(3.39492 - 5.14534i) q^{38} +(6.23577 + 10.2290i) q^{40} +(0.564228 - 1.55020i) q^{41} +(-8.22562 + 1.45040i) q^{43} +(9.53797 - 2.42142i) q^{44} +(2.49487 + 4.87071i) q^{46} +(-6.63122 - 5.56426i) q^{47} +(-0.693747 - 1.20160i) q^{49} +(-9.93368 + 15.3683i) q^{50} +(0.624555 + 8.41462i) q^{52} +(-2.44391 - 0.430928i) q^{53} +(13.3956 + 15.9642i) q^{55} +(-1.00578 + 6.62484i) q^{56} +(0.301611 - 6.00037i) q^{58} +(3.10160 - 2.60255i) q^{59} +(0.847176 - 4.80457i) q^{61} +(6.96267 - 0.870014i) q^{62} +(-5.87604 + 5.42882i) q^{64} +(-15.4751 + 8.93456i) q^{65} +(8.57119 - 10.2147i) q^{67} +(7.89099 - 3.55378i) q^{68} +(-13.5616 + 4.17790i) q^{70} +(1.59125 + 9.02445i) q^{71} +(-0.973188 - 0.354212i) q^{73} +(-5.56208 + 4.20999i) q^{74} +(0.563407 + 8.69957i) q^{76} +11.6565i q^{77} +(0.557573 - 1.53192i) q^{79} +(-15.7621 - 6.21211i) q^{80} +(0.686873 + 2.22961i) q^{82} +(-2.35877 + 4.08551i) q^{83} +(14.0398 + 11.7808i) q^{85} +(8.03745 - 8.65612i) q^{86} +(-8.68851 + 10.8712i) q^{88} +(-0.0667092 - 0.183282i) q^{89} +(-9.84300 - 1.73559i) q^{91} +(-6.97045 - 3.36292i) q^{92} +(12.2266 + 0.614576i) q^{94} +(-16.0749 + 9.08015i) q^{95} +(14.7227 - 12.3538i) q^{97} +(1.80786 + 0.762836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{4}+O(q^{10}) \) 240 * q + 12 * q^4	\( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Introduction

L-functions

Modular forms

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Database

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