LMFDB - Embedded newform 684.2.ce.a.215.12

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			215.12
Character	$\chi$	$=$	684.215
Dual form			684.2.ce.a.35.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03635 + 0.962279i) q^{2} +(0.148038 - 1.99451i) q^{4} +(-4.17116 + 0.735488i) q^{5} +(-2.05168 - 1.18454i) q^{7} +(1.76586 + 2.20947i) q^{8} +O(q^{10})$	\(q+(-1.03635 + 0.962279i) q^{2} +(0.148038 - 1.99451i) q^{4} +(-4.17116 + 0.735488i) q^{5} +(-2.05168 - 1.18454i) q^{7} +(1.76586 + 2.20947i) q^{8} +(3.61503 - 4.77605i) q^{10} +(2.46013 + 4.26108i) q^{11} +(-3.96446 + 1.44294i) q^{13} +(3.26611 - 0.746693i) q^{14} +(-3.95617 - 0.590527i) q^{16} +(-2.78144 - 3.31479i) q^{17} +(4.10988 - 1.45220i) q^{19} +(0.849452 + 8.42832i) q^{20} +(-6.64990 - 2.04863i) q^{22} +(0.671956 - 3.81085i) q^{23} +(12.1592 - 4.42558i) q^{25} +(2.72004 - 5.31031i) q^{26} +(-2.66630 + 3.91674i) q^{28} +(2.73073 - 3.25435i) q^{29} +(4.29690 + 2.48082i) q^{31} +(4.66822 - 3.19495i) q^{32} +(6.07230 + 0.758759i) q^{34} +(9.42909 + 3.43191i) q^{35} +4.93259 q^{37} +(-2.86184 + 5.45984i) q^{38} +(-8.99073 - 7.91727i) q^{40} +(-0.564228 + 1.55020i) q^{41} +(8.22562 - 1.45040i) q^{43} +(8.86297 - 4.27597i) q^{44} +(2.97072 + 4.59598i) q^{46} +(-6.63122 - 5.56426i) q^{47} +(-0.693747 - 1.20160i) q^{49} +(-8.34252 + 16.2870i) q^{50} +(2.29108 + 8.12077i) q^{52} +(2.44391 + 0.430928i) q^{53} +(-13.3956 - 15.9642i) q^{55} +(-1.00578 - 6.62484i) q^{56} +(0.301611 + 6.00037i) q^{58} +(3.10160 - 2.60255i) q^{59} +(0.847176 - 4.80457i) q^{61} +(-6.84033 + 1.56383i) q^{62} +(-1.76348 + 7.80321i) q^{64} +(15.4751 - 8.93456i) q^{65} +(-8.57119 + 10.2147i) q^{67} +(-7.02316 + 5.05691i) q^{68} +(-13.0743 + 5.51676i) q^{70} +(1.59125 + 9.02445i) q^{71} +(-0.973188 - 0.354212i) q^{73} +(-5.11188 + 4.74653i) q^{74} +(-2.28802 - 8.41219i) q^{76} -11.6565i q^{77} +(-0.557573 + 1.53192i) q^{79} +(16.9362 - 0.446532i) q^{80} +(-0.906991 - 2.14949i) q^{82} +(-2.35877 + 4.08551i) q^{83} +(14.0398 + 11.7808i) q^{85} +(-7.12893 + 9.41846i) q^{86} +(-5.07045 + 12.9600i) q^{88} +(0.0667092 + 0.183282i) q^{89} +(9.84300 + 1.73559i) q^{91} +(-7.50132 - 1.90437i) q^{92} +(12.2266 - 0.614576i) q^{94} +(-16.0749 + 9.08015i) q^{95} +(14.7227 - 12.3538i) q^{97} +(1.87524 + 0.577704i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.03635	+	0.962279i	−0.732809	+	0.680434i
$2$	−1.03635	+	0.962279i	−0.732809	+	0.680434i
$3$		0			0
$3$		0			0
$4$	0.148038	−	1.99451i	0.0740189	−	0.997257i
$5$	−4.17116	+	0.735488i	−1.86540	+	0.328920i	−0.988436	−	0.151635i	$-0.951546\pi$
$5$	−4.17116	+	0.735488i	−1.86540	+	0.328920i	−0.876964	+	0.480556i	$0.840435\pi$
$6$		0			0
$7$	−2.05168	−	1.18454i	−0.775461	−	0.447713i	0.0593582	−	0.998237i	$-0.481095\pi$
$7$	−2.05168	−	1.18454i	−0.775461	−	0.447713i	−0.834819	+	0.550524i	$0.814428\pi$
$8$	1.76586	+	2.20947i	0.624326	+	0.781164i
$9$		0			0
$10$	3.61503	−	4.77605i	1.14317	−	1.51032i
$11$	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	$0.587816\pi$
$14$	3.26611	−	0.746693i	0.872904	−	0.199562i
$15$		0			0
$16$	−3.95617	−	0.590527i	−0.989042	−	0.147632i
$17$	−2.78144	−	3.31479i	−0.674598	−	0.803955i	0.314804	−	0.949157i	$-0.398061\pi$
$17$	−2.78144	−	3.31479i	−0.674598	−	0.803955i	−0.989402	+	0.145202i	$0.953617\pi$
$18$		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
$22$	−6.64990	−	2.04863i	−1.41776	−	0.436769i
$23$	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
$26$	2.72004	−	5.31031i	0.533445	−	1.04144i
$27$		0			0
$28$	−2.66630	+	3.91674i	−0.503883	+	0.740195i
$29$	2.73073	−	3.25435i	0.507083	−	0.604318i	−0.450393	−	0.892830i	$-0.648716\pi$
$29$	2.73073	−	3.25435i	0.507083	−	0.604318i	0.957476	+	0.288512i	$0.0931606\pi$
$30$		0			0
$31$	4.29690	+	2.48082i	0.771747	+	0.445568i	0.833497	−	0.552523i	$-0.186335\pi$
$31$	4.29690	+	2.48082i	0.771747	+	0.445568i	−0.0617507	+	0.998092i	$0.519668\pi$
$32$	4.66822	−	3.19495i	0.825233	−	0.564792i
$33$		0			0
$34$	6.07230	+	0.758759i	1.04139	+	0.130126i
$35$	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	$0.367113\pi$
$38$	−2.86184	+	5.45984i	−0.464252	+	0.885703i
$39$		0			0
$40$	−8.99073	−	7.91727i	−1.42156	−	1.25183i
$41$	−0.564228	+	1.55020i	−0.0881175	+	0.242101i	−0.975922	−	0.218120i	$-0.930008\pi$
$41$	−0.564228	+	1.55020i	−0.0881175	+	0.242101i	0.887804	+	0.460221i	$0.152230\pi$
$42$		0			0
$43$	8.22562	−	1.45040i	1.25440	−	0.221184i	0.493321	−	0.869848i	$-0.335783\pi$
$43$	8.22562	−	1.45040i	1.25440	−	0.221184i	0.761075	+	0.648664i	$0.224672\pi$
$44$	8.86297	−	4.27597i	1.33614	−	0.644627i
$45$		0			0
$46$	2.97072	+	4.59598i	0.438009	+	0.677640i
$47$	−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
$50$	−8.34252	+	16.2870i	−1.17981	+	2.30333i
$51$		0			0
$52$	2.29108	+	8.12077i	0.317716	+	1.12615i
$53$	2.44391	+	0.430928i	0.335697	+	0.0591925i	0.338956	−	0.940802i	$-0.389926\pi$
$53$	2.44391	+	0.430928i	0.335697	+	0.0591925i	−0.00325877	+	0.999995i	$0.501037\pi$
$54$		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	$-0.0455526\pi$
$62$	−6.84033	+	1.56383i	−0.868723	+	0.198606i
$63$		0			0
$64$	−1.76348	+	7.80321i	−0.220435	+	0.975402i
$65$	15.4751	−	8.93456i	1.91945	−	1.10820i
$66$		0			0
$67$	−8.57119	+	10.2147i	−1.04714	+	1.24793i	−0.0791678	+	0.996861i	$0.525226\pi$
$67$	−8.57119	+	10.2147i	−1.04714	+	1.24793i	−0.967969	+	0.251068i	$0.919218\pi$
$68$	−7.02316	+	5.05691i	−0.851683	+	0.613240i
$69$		0			0
$70$	−13.0743	+	5.51676i	−1.56268	+	0.659379i
$71$	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	$0.630415\pi$
$74$	−5.11188	+	4.74653i	−0.594244	+	0.551772i
$75$		0			0
$76$	−2.28802	−	8.41219i	−0.262454	−	0.964944i
$77$		−	11.6565i		−	1.32838i
$78$		0			0
$79$	−0.557573	+	1.53192i	−0.0627319	+	0.172355i	−0.967099	−	0.254402i	$-0.918122\pi$
$79$	−0.557573	+	1.53192i	−0.0627319	+	0.172355i	0.904367	+	0.426756i	$0.140344\pi$
$80$	16.9362	−	0.446532i	1.89352	−	0.0499238i
$81$		0			0
$82$	−0.906991	−	2.14949i	−0.100160	−	0.237372i
$83$	−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
$86$	−7.12893	+	9.41846i	−0.768732	+	1.01562i
$87$		0			0
$88$	−5.07045	+	12.9600i	−0.540512	+	1.38155i
$89$	0.0667092	+	0.183282i	0.00707117	+	0.0194279i	0.943178	−	0.332288i	$-0.107821\pi$
$89$	0.0667092	+	0.183282i	0.00707117	+	0.0194279i	−0.936107	+	0.351716i	$0.885598\pi$
$90$		0			0
$91$	9.84300	+	1.73559i	1.03183	+	0.181939i
$92$	−7.50132	−	1.90437i	−0.782066	−	0.198545i
$93$		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	$-0.151915\pi$
$98$	1.87524	+	0.577704i	0.189428	+	0.0583569i
$99$		0			0
$100$	−7.02687	−	24.9068i	−0.702687	−	2.49068i
$101$	0.213461	+	0.586480i	0.0212402	+	0.0583569i	0.949860	−	0.312677i	$-0.101226\pi$
$101$	0.213461	+	0.586480i	0.0212402	+	0.0583569i	−0.928619	+	0.371034i	$0.879003\pi$
$102$		0			0
$103$	−0.867609	+	0.500914i	−0.0854881	+	0.0493566i	−0.542135	−	0.840292i	$-0.682384\pi$
$103$	−0.867609	+	0.500914i	−0.0854881	+	0.0493566i	0.456647	+	0.889648i	$0.349050\pi$
$104$	−10.1888	−	6.21129i	−0.999095	−	0.609067i
$105$		0			0
$106$	−2.94742	+	1.90514i	−0.286279	+	0.185043i
$107$	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	$0.896200\pi$
$110$	29.2446	+	3.65423i	2.78836	+	0.348417i
$111$		0			0
$112$	7.41728	+	5.89780i	0.700867	+	0.557290i
$113$		−	2.93545i		−	0.276144i	−0.990422	−	0.138072i	$-0.955909\pi$
$113$		−	2.93545i		−	0.276144i	0.990422	−	0.138072i	$-0.0440905\pi$
$114$		0			0
$115$			16.3899i			1.52836i
$116$	−6.08660	−	5.92824i	−0.565127	−	0.550423i
$117$		0			0
$118$	−0.709958	+	5.68175i	−0.0653570	+	0.523048i
$119$	1.78013	+	10.0956i	0.163184	+	0.925462i
$120$		0			0
$121$	−6.60452	+	11.4394i	−0.600411	+	1.03994i
$122$	3.74537	+	5.79443i	0.339090	+	0.524603i
$123$		0			0
$124$	5.58413	−	8.20298i	0.501470	−	0.736649i
$125$	−29.1227	+	16.8140i	−2.60481	+	1.50389i
$126$		0			0
$127$	1.70038	+	4.67176i	0.150884	+	0.414551i	0.991990	−	0.126320i	$-0.0403167\pi$
$127$	1.70038	+	4.67176i	0.150884	+	0.414551i	−0.841105	+	0.540872i	$0.818094\pi$
$128$	−5.68129	−	9.78381i	−0.502160	−	0.864775i
$129$		0			0
$130$	−7.44008	+	24.1507i	−0.652538	+	2.11816i
$131$	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
$136$	2.41228	−	11.9990i	0.206852	−	1.02890i
$137$	−6.82117	−	1.20276i	−0.582772	−	0.102758i	−0.125513	−	0.992092i	$-0.540058\pi$
$137$	−6.82117	−	1.20276i	−0.582772	−	0.102758i	−0.457259	+	0.889334i	$0.651169\pi$
$138$		0			0
$139$	1.85427	+	5.09456i	0.157277	+	0.432115i	0.993156	−	0.116799i	$-0.0372634\pi$
$139$	1.85427	+	5.09456i	0.157277	+	0.432115i	−0.835878	+	0.548915i	$0.815041\pi$
$140$	8.24085	−	18.2984i	0.696479	−	1.54650i
$141$		0			0
$142$	−10.3331	−	7.82125i	−0.867137	−	0.656345i
$143$	−15.9016	−	13.3430i	−1.32976	−	1.11580i
$144$		0			0
$145$	−8.99676	+	15.5829i	−0.747141	+	1.29409i
$146$	1.34941	−	0.569392i	0.111678	−	0.0471232i
$147$		0			0
$148$	0.730210	−	9.83811i	0.0600229	−	0.808688i
$149$	5.56930	−	15.3015i	0.456255	−	1.25355i	−0.471997	−	0.881600i	$-0.656467\pi$
$149$	5.56930	−	15.3015i	0.456255	−	1.25355i	0.928252	−	0.371951i	$-0.121311\pi$
$150$		0			0
$151$		−	0.224746i		−	0.0182896i	−0.999958	−	0.00914478i	$-0.997089\pi$
$151$		−	0.224746i		−	0.0182896i	0.999958	−	0.00914478i	$-0.00291091\pi$
$152$	10.4661	+	6.51625i	0.848910	+	0.528537i
$153$		0			0
$154$	11.2168	+	12.0802i	0.903874	+	0.973448i
$155$	−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	$-0.215380\pi$
$158$	−0.896294	−	2.12415i	−0.0713054	−	0.168988i
$159$		0			0
$160$	−17.1221	+	16.7601i	−1.35362	+	1.32500i
$161$	−5.89273	+	7.02268i	−0.464412	+	0.553464i
$162$		0			0
$163$	3.80807	−	2.19859i	0.298271	−	0.172207i	−0.343395	−	0.939191i	$-0.611577\pi$
$163$	3.80807	−	2.19859i	0.298271	−	0.172207i	0.641666	+	0.766984i	$0.278244\pi$
$164$	3.00837	+	1.35485i	0.234914	+	0.105796i
$165$		0			0
$166$	−1.48689	−	6.50381i	−0.115405	−	0.504793i
$167$	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	0.651819	−	0.758374i	$-0.274006\pi$
$173$	−2.73872	−	3.26387i	−0.208221	−	0.248148i	−0.860040	+	0.510226i	$0.829562\pi$
$174$		0			0
$175$	−30.1890	−	5.32314i	−2.28207	−	0.402391i
$176$	−7.21643	−	18.3103i	−0.543959	−	1.38019i
$177$		0			0
$178$	−0.245503	−	0.125751i	−0.0184012	−	0.00942546i
$179$	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	$0.778411\pi$
$182$	−11.8709	+	7.67304i	−0.879930	+	0.568764i
$183$		0			0
$184$	9.60652	−	5.24476i	0.708202	−	0.386649i
$185$	−20.5746	+	3.62786i	−1.51268	+	0.266726i
$186$		0			0
$187$	7.28187	−	20.0068i	0.532503	−	1.46304i
$188$	−12.0797	+	12.4023i	−0.880999	+	0.904534i
$189$		0			0
$190$	7.92156	−	24.8787i	0.574690	−	1.80489i
$191$	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	$0.789436\pi$
$194$	−3.37005	+	26.9703i	−0.241955	+	1.93635i
$195$		0			0
$196$	−2.49932	+	1.20580i	−0.178523	+	0.0861289i
$197$	20.2363	+	11.6835i	1.44178	+	0.832412i	0.997969	−	0.0637088i	$-0.0202929\pi$
$197$	20.2363	+	11.6835i	1.44178	+	0.832412i	0.443811	+	0.896120i	$0.353626\pi$
$198$		0			0
$199$	−7.86734	+	9.37593i	−0.557701	+	0.664642i	−0.969058	−	0.246832i	$-0.920610\pi$
$199$	−7.86734	+	9.37593i	−0.557701	+	0.664642i	0.411358	+	0.911474i	$0.365055\pi$
$200$	31.2496	+	19.0504i	2.20968	+	1.34706i
$201$		0			0
$202$	−0.785577	−	0.402388i	−0.0552730	−	0.0283119i
$203$	−9.45747	+	3.44224i	−0.663784	+	0.241598i
$204$		0			0
$205$	1.21333	−	6.88113i	0.0847426	−	0.480599i
$206$	0.417126	−	1.35400i	0.0290626	−	0.0943380i
$207$		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	0.229304	−	0.973355i	$-0.426355\pi$
$211$	−11.1716	−	13.3137i	−0.769082	−	0.916556i	−0.998386	+	0.0567987i	$0.981911\pi$
$212$	1.22128	−	4.81062i	0.0838781	−	0.330395i
$213$		0			0
$214$	5.52878	+	24.1834i	0.377940	+	1.65314i
$215$	−33.2437	+	12.0997i	−2.26720	+	0.825193i
$216$		0			0
$217$	−5.87724	−	10.1797i	−0.398973	−	0.691042i
$218$	−3.55498	−	2.69080i	−0.240774	−	0.182244i
$219$		0			0
$220$	−33.8240	+	24.3544i	−2.28041	+	1.64197i
$221$	15.8100	+	9.12788i	1.06349	+	0.614008i
$222$		0			0
$223$	17.2507	−	3.04177i	1.15519	−	0.203692i	0.436951	−	0.899485i	$-0.356058\pi$
$223$	17.2507	−	3.04177i	1.15519	−	0.203692i	0.718242	+	0.695793i	$0.244947\pi$
$224$	−13.3622	+	1.02532i	−0.892801	+	0.0685070i
$225$		0			0
$226$	2.82472	+	3.04215i	0.187898	+	0.202361i
$227$	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	$0.498461\pi$
$230$	−15.7716	−	16.9856i	−1.03995	−	1.12000i
$231$		0			0
$232$	12.0125	+	0.286715i	0.788657	+	0.0188237i
$233$	−6.57849	+	1.15996i	−0.430971	+	0.0759918i	−0.384926	−	0.922948i	$-0.625773\pi$
$233$	−6.57849	+	1.15996i	−0.430971	+	0.0759918i	−0.0460453	+	0.998939i	$0.514662\pi$
$234$		0			0
$235$	31.7523	+	18.3322i	2.07129	+	1.19586i
$236$	−4.73167	−	6.57146i	−0.308005	−	0.427765i
$237$		0			0
$238$	−11.5596	−	8.74958i	−0.749299	−	0.567151i
$239$	−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	$0.700693\pi$
$242$	−4.16328	−	18.2106i	−0.267625	−	1.17062i
$243$		0			0
$244$	−9.45737	−	2.40096i	−0.605446	−	0.153706i
$245$	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
$250$	14.0015	−	45.4493i	0.885534	−	2.87447i
$251$	−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
$254$	−6.25772	−	3.20533i	−0.392644	−	0.201120i
$255$		0			0
$256$	15.3026	+	4.67245i	0.956410	+	0.292028i
$257$	7.01354	−	8.35841i	0.437493	−	0.521384i	−0.501576	−	0.865114i	$-0.667246\pi$
$257$	7.01354	−	8.35841i	0.437493	−	0.521384i	0.939068	+	0.343730i	$0.111691\pi$
$258$		0			0
$259$	−10.1201	−	5.84283i	−0.628831	−	0.363056i
$260$	−15.5292	−	32.1880i	−0.963080	−	1.99621i
$261$		0			0
$262$	−1.74563	+	13.9702i	−0.107846	+	0.863082i
$263$	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
$266$	12.3390	−	7.81187i	0.756550	−	0.478977i
$267$		0			0
$268$	19.1046	+	18.6075i	1.16700	+	1.13664i
$269$	7.26990	−	19.9739i	0.443253	−	1.21783i	−0.494086	−	0.869413i	$-0.664497\pi$
$269$	7.26990	−	19.9739i	0.443253	−	1.21783i	0.937340	−	0.348416i	$-0.113280\pi$
$270$		0			0
$271$	19.5639	−	3.44964i	1.18842	−	0.209551i	0.455734	−	0.890116i	$-0.349377\pi$
$271$	19.5639	−	3.44964i	1.18842	−	0.209551i	0.732688	+	0.680565i	$0.238266\pi$
$272$	9.04638	+	14.7564i	0.548517	+	0.894738i
$273$		0			0
$274$	8.22650	−	5.31740i	0.496981	−	0.321236i
$275$	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	$0.671264\pi$
$278$	−6.82406	−	3.49542i	−0.409280	−	0.209641i
$279$		0			0
$280$	9.06777	+	26.8935i	0.541903	+	1.60720i
$281$	21.1699	+	3.73283i	1.26289	+	0.222682i	0.764701	−	0.644385i	$-0.222887\pi$
$281$	21.1699	+	3.73283i	1.26289	+	0.222682i	0.498191	+	0.867067i	$0.333998\pi$
$282$		0			0
$283$	−1.89394	−	2.25711i	−0.112583	−	0.134171i	0.706810	−	0.707404i	$-0.250134\pi$
$283$	−1.89394	−	2.25711i	−0.112583	−	0.134171i	−0.819393	+	0.573232i	$0.805689\pi$
$284$	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
$290$	−5.67127	−	24.8067i	−0.333028	−	1.45670i
$291$		0			0
$292$	−0.850548	+	1.88860i	−0.0497746	+	0.110522i
$293$	−9.55476	+	5.51644i	−0.558195	+	0.322274i	−0.752421	−	0.658683i	$-0.771114\pi$
$293$	−9.55476	+	5.51644i	−0.558195	+	0.322274i	0.194226	+	0.980957i	$0.437781\pi$
$294$		0			0
$295$	−11.0231	+	13.1368i	−0.641791	+	0.764857i
$296$	8.71026	+	10.8984i	0.506273	+	0.633456i
$297$		0			0
$298$	8.95261	+	21.2170i	0.518611	+	1.22907i
$299$	2.83490	+	16.0775i	0.163947	+	0.929788i
$300$		0			0
$301$	−18.5944	−	6.76780i	−1.07176	−	0.390089i
$302$	0.216268	+	0.232915i	0.0124448	+	0.0134028i
$303$		0			0
$304$	−17.1169	+	3.31817i	−0.981724	+	0.190310i
$305$			20.6637i			1.18320i
$306$		0			0
$307$	3.92839	−	10.7932i	0.224205	−	0.615999i	−0.775680	−	0.631126i	$-0.782593\pi$
$307$	3.92839	−	10.7932i	0.224205	−	0.615999i	0.999886	+	0.0151271i	$0.00481529\pi$
$308$	−23.2490	−	1.72560i	−1.32473	−	0.0983252i
$309$		0			0
$310$	27.3820	−	11.5540i	1.55519	−	0.656221i
$311$	−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	$0.837554\pi$
$314$	13.5998	+	10.2938i	0.767479	+	0.580912i
$315$		0			0
$316$	2.97289	+	1.33887i	0.167238	+	0.0753173i
$317$	−1.37807	−	3.78621i	−0.0774000	−	0.212655i	0.894958	−	0.446151i	$-0.147206\pi$
$317$	−1.37807	−	3.78621i	−0.0774000	−	0.212655i	−0.972358	+	0.233496i	$0.924983\pi$
$318$		0			0
$319$	20.5850	+	3.62969i	1.15254	+	0.203224i
$320$	1.61658	−	33.8455i	0.0903694	−	1.89202i
$321$		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
$326$	−1.83083	+	5.94293i	−0.101400	+	0.329148i
$327$		0			0
$328$	−4.42147	+	1.49080i	−0.244135	+	0.0823156i
$329$	7.01406	+	19.2710i	0.386698	+	1.06244i
$330$		0			0
$331$	0.202955	−	0.117176i	0.0111554	−	0.00644059i	−0.494412	−	0.869228i	$-0.664617\pi$
$331$	0.202955	−	0.117176i	0.0111554	−	0.00644059i	0.505567	+	0.862787i	$0.331283\pi$
$332$	7.79942	+	5.30941i	0.428049	+	0.291392i
$333$		0			0
$334$	15.7410	+	24.3528i	0.861309	+	1.33252i
$335$	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	$0.877791\pi$
$338$	−0.841495	+	6.73443i	−0.0457713	+	0.366305i
$339$		0			0
$340$	25.5754	−	26.2586i	1.38702	−	1.42407i
$341$			24.4126i			1.32202i
$342$		0			0
$343$			19.8706i			1.07291i
$344$	17.7299	+	15.6130i	0.955932	+	0.841798i
$345$		0			0
$346$	5.97902	+	0.747103i	0.321434	+	0.0401645i
$347$	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	$0.222488\pi$
$350$	36.4087	−	23.5336i	1.94613	−	1.25792i
$351$		0			0
$352$	25.0984	+	12.0317i	1.33775	+	0.641290i
$353$	4.43020	−	2.55777i	0.235796	−	0.136137i	−0.377447	−	0.926031i	$-0.623198\pi$
$353$	4.43020	−	2.55777i	0.235796	−	0.136137i	0.613243	+	0.789894i	$0.289865\pi$
$354$		0			0
$355$	−13.2748	−	36.4721i	−0.704551	−	1.93574i
$356$	0.375434	−	0.105920i	0.0198980	−	0.00561374i
$357$		0			0
$358$	−11.0892	−	3.41625i	−0.586085	−	0.180554i
$359$	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
$364$	4.91879	−	19.3751i	0.257815	−	1.01553i
$365$	4.31984	+	0.761705i	0.226111	+	0.0398695i
$366$		0			0
$367$	−4.55658	−	12.5191i	−0.237851	−	0.653491i	−0.999982	−	0.00606742i	$-0.998069\pi$
$367$	−4.55658	−	12.5191i	−0.237851	−	0.653491i	0.762130	−	0.647424i	$-0.224154\pi$
$368$	−4.90878	+	14.6796i	−0.255888	+	0.765225i
$369$		0			0
$370$	17.8315	−	23.5583i	0.927014	−	1.22474i
$371$	−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	$-0.0507028\pi$
$374$	11.7055	+	27.7412i	0.605279	+	1.43446i
$375$		0			0
$376$	0.584223	−	24.4772i	0.0301290	−	1.26231i
$377$	−6.12999	+	16.8420i	−0.315711	+	0.867408i
$378$		0			0
$379$		−	30.0944i		−	1.54585i	−0.634499	−	0.772924i	$-0.718794\pi$
$379$		−	30.0944i		−	1.54585i	0.634499	−	0.772924i	$-0.281206\pi$
$380$	15.7308	+	33.4058i	0.806972	+	1.71368i
$381$		0			0
$382$	−17.0899	+	15.8684i	−0.874394	+	0.811900i
$383$	−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
$386$	19.2373	−	8.11728i	0.979153	−	0.413159i
$387$		0			0
$388$	−22.4604	−	31.1936i	−1.14025	−	1.58361i
$389$	4.00467	−	4.77258i	0.203045	−	0.241980i	−0.654907	−	0.755709i	$-0.727292\pi$
$389$	4.00467	−	4.77258i	0.203045	−	0.241980i	0.857952	+	0.513730i	$0.171737\pi$
$390$		0			0
$391$	−14.5012	+	8.37226i	−0.733356	+	0.423403i
$392$	1.42984	−	3.65468i	0.0722181	−	0.184589i
$393$		0			0
$394$	−32.2147	+	7.36487i	−1.62295	+	0.371037i
$395$	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	$-0.998616\pi$
$401$	−16.6333	−	19.8227i	−0.830625	−	0.989901i	0.169365	−	0.985553i	$-0.445828\pi$
$402$		0			0
$403$	−20.6146	−	3.63490i	−1.02688	−	0.181067i
$404$	1.20134	−	0.338930i	0.0597690	−	0.0168624i
$405$		0			0
$406$	6.48884	−	12.6681i	0.322036	−	0.628706i
$407$	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	$0.458355\pi$
$410$	5.36414	+	8.29881i	0.264916	+	0.409849i
$411$		0			0
$412$	0.870642	+	1.80461i	0.0428934	+	0.0889069i
$413$	−9.44629	+	1.66564i	−0.464822	+	0.0819606i
$414$		0			0
$415$	6.83397	−	18.7762i	0.335466	−	0.921686i
$416$	−13.8968	+	19.4022i	−0.681348	+	0.951272i
$417$		0			0
$418$	−30.3053	+	1.23741i	−1.48228	+	0.0605235i
$419$	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	$0.667800\pi$
$422$	24.3892	+	3.04753i	1.18725	+	0.148351i
$423$		0			0
$424$	3.36349	+	6.16070i	0.163345	+	0.299190i
$425$	−48.4900	−	27.9957i	−2.35211	−	1.35799i
$426$		0			0
$427$	−7.42932	+	8.85392i	−0.359530	+	0.428471i
$428$	−29.0009	−	19.7422i	−1.40181	−	0.954277i
$429$		0			0
$430$	22.8087	−	44.5292i	1.09993	−	2.14739i
$431$	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	$-0.165901\pi$
$434$	15.8866	+	4.89415i	0.762579	+	0.234927i
$435$		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	0.964401	−	0.264444i	$-0.0851886\pi$
$439$	11.2411	+	13.3966i	0.536508	+	0.639385i	−0.427893	+	0.903829i	$0.640744\pi$
$440$	11.6177	−	57.7877i	0.553853	−	2.75492i
$441$		0			0
$442$	−25.1682	+	5.75392i	−1.19713	+	0.273686i
$443$	−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
$446$	−14.9507	+	19.7523i	−0.707938	+	0.935300i
$447$		0			0
$448$	12.8613	−	13.9208i	0.607638	−	0.657695i
$449$	−25.3686	−	14.6466i	−1.19722	−	0.691215i	−0.237286	−	0.971440i	$-0.576258\pi$
$449$	−25.3686	−	14.6466i	−1.19722	−	0.691215i	−0.959934	+	0.280225i	$0.909591\pi$
$450$		0			0
$451$	−7.99361	+	1.40949i	−0.376404	+	0.0663702i
$452$	−5.85480	−	0.434558i	−0.275386	−	0.0204399i
$453$		0			0
$454$	−14.7088	+	13.6576i	−0.690319	+	0.640981i
$455$	−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	$0.689500\pi$
$458$	−0.151631	+	0.140794i	−0.00708527	+	0.00657887i
$459$		0			0
$460$	32.6899	+	2.42632i	1.52417	+	0.113128i
$461$	19.2838	−	3.40025i	0.898134	−	0.158365i	0.294523	−	0.955644i	$-0.404839\pi$
$461$	19.2838	−	3.40025i	0.898134	−	0.158365i	0.603611	+	0.797279i	$0.293728\pi$
$462$		0			0
$463$	0.803683	+	0.464006i	0.0373503	+	0.0215642i	0.518559	−	0.855042i	$-0.326469\pi$
$463$	0.803683	+	0.464006i	0.0373503	+	0.0215642i	−0.481209	+	0.876606i	$0.659802\pi$
$464$	−12.7250	+	11.2622i	−0.590743	+	0.522835i
$465$		0			0
$466$	5.70140	−	7.53247i	0.264112	−	0.348935i
$467$	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
$470$	−50.5472	+	11.5560i	−2.33157	+	0.533040i
$471$		0			0
$472$	11.2272	+	2.25714i	0.516775	+	0.103893i
$473$	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
$478$	24.3805	+	7.51087i	1.11514	+	0.343539i
$479$	−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
$482$	16.6199	−	32.4467i	0.757014	−	1.47791i
$483$		0			0
$484$	21.8383	+	14.8663i	0.992648	+	0.675739i
$485$	−52.3248	+	62.3583i	−2.37595	+	2.83155i
$486$		0			0
$487$	31.4925	+	18.1822i	1.42706	+	0.823915i	0.996888	−	0.0788302i	$-0.0251185\pi$
$487$	31.4925	+	18.1822i	1.42706	+	0.823915i	0.430175	+	0.902745i	$0.358452\pi$
$488$	12.1115	−	6.61239i	0.548263	−	0.299329i
$489$		0			0
$490$	−8.24684	−	1.03048i	−0.372554	−	0.0465522i
$491$	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
$494$	3.46741	−	25.7748i	0.156006	−	1.15966i
$495$		0			0
$496$	−15.5343	−	12.3520i	−0.697510	−	0.554620i
$497$	7.42505	−	20.4002i	0.333059	−	0.915072i
$498$		0			0
$499$	33.5963	−	5.92393i	1.50398	−	0.265192i	0.639863	−	0.768489i	$-0.278991\pi$
$499$	33.5963	−	5.92393i	1.50398	−	0.265192i	0.864113	+	0.503297i	$0.167880\pi$
$500$	29.2245	+	60.5747i	1.30696	+	2.70898i
$501$		0			0
$502$	−10.4621	−	16.1858i	−0.466947	−	0.722409i
$503$	−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
$506$	−12.2754	+	23.9652i	−0.545710	+	1.06538i
$507$		0			0
$508$	9.56960	−	2.69983i	0.424582	−	0.119786i
$509$	31.1834	+	5.49847i	1.38218	+	0.243716i	0.814801	−	0.579741i	$-0.196846\pi$
$509$	31.1834	+	5.49847i	1.38218	+	0.243716i	0.567379	+	0.823457i	$0.307958\pi$
$510$		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
$518$	16.1104	−	3.68313i	0.707849	−	0.161827i
$519$		0			0
$520$	47.0675	+	18.4146i	2.06405	+	0.807532i
$521$	6.05147	−	3.49382i	0.265120	−	0.153067i	−0.361548	−	0.932353i	$-0.617752\pi$
$521$	6.05147	−	3.49382i	0.265120	−	0.153067i	0.626668	+	0.779287i	$0.284418\pi$
$522$		0			0
$523$	−19.2320	+	22.9198i	−0.840957	+	1.00221i	0.158932	+	0.987290i	$0.449195\pi$
$523$	−19.2320	+	22.9198i	−0.840957	+	1.00221i	−0.999889	+	0.0149239i	$0.995249\pi$
$524$	−11.6341	−	16.1578i	−0.508240	−	0.705856i
$525$		0			0
$526$	−0.902757	+	0.380923i	−0.0393621	+	0.0166090i
$527$	−3.72819	−	21.1436i	−0.162402	−	0.921029i
$528$		0			0
$529$	7.54188	+	2.74502i	0.327908	+	0.119349i
$530$	10.8930	−	10.1144i	0.473160	−	0.439342i
$531$		0			0
$532$	−5.27026	+	19.9693i	−0.228495	+	0.865781i
$533$		−	6.95986i		−	0.301465i
$534$		0			0
$535$	−25.4111	+	69.8163i	−1.09862	+	3.01842i
$536$	−37.7046	−	0.899939i	−1.62859	−	0.0388714i
$537$		0			0
$538$	11.6863	+	27.6956i	0.503832	+	1.19404i
$539$	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	$0.881278\pi$
$542$	−16.9555	+	22.4010i	−0.728301	+	0.962204i
$543$		0			0
$544$	−23.5750	−	6.58763i	−1.01077	−	0.282442i
$545$	−4.56701	−	12.5477i	−0.195629	−	0.537487i
$546$		0			0
$547$	5.39427	+	0.951155i	0.230642	+	0.0406684i	0.287775	−	0.957698i	$-0.407085\pi$
$547$	5.39427	+	0.951155i	0.230642	+	0.0406684i	−0.0571324	+	0.998367i	$0.518196\pi$
$548$	−3.40871	+	13.4269i	−0.145613	+	0.573567i
$549$		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
$554$	−21.9289	−	6.75562i	−0.931671	−	0.287019i
$555$		0			0
$556$	10.4357	−	2.94418i	0.442571	−	0.124861i
$557$	10.2490	+	28.1589i	0.434263	+	1.19313i	0.943171	+	0.332308i	$0.107827\pi$
$557$	10.2490	+	28.1589i	0.434263	+	1.19313i	−0.508908	+	0.860821i	$0.669951\pi$
$558$		0			0
$559$	−30.5173	+	17.6192i	−1.29074	+	0.745211i
$560$	−35.2765	−	19.1453i	−1.49070	−	0.809039i
$561$		0			0
$562$	−25.5315	+	16.5029i	−1.07698	+	0.696131i
$563$	−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
$566$	4.13476	+	0.516655i	0.173797	+	0.0217166i
$567$		0			0
$568$	−17.1293	+	19.4517i	−0.718729	+	0.816177i
$569$		−	41.6349i		−	1.74543i	−0.488233	−	0.872713i	$-0.662358\pi$
$569$		−	41.6349i		−	1.74543i	0.488233	−	0.872713i	$-0.337642\pi$
$570$		0			0
$571$			1.68623i			0.0705664i	0.999377	+	0.0352832i	$0.0112333\pi$
$571$			1.68623i			0.0705664i	−0.999377	+	0.0352832i	$0.988767\pi$
$572$	−28.9669	+	29.7407i	−1.21117	+	1.24352i
$573$		0			0
$574$	−0.685303	+	5.48443i	−0.0286040	+	0.228916i
$575$	−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	$0.0868414\pi$
$578$	−1.32371	−	2.04790i	−0.0550591	−	0.0851814i
$579$		0			0
$580$	29.7484	+	20.2510i	1.23523	+	0.840878i
$581$	9.67887	−	5.58810i	0.401547	−	0.231833i
$582$		0			0
$583$	4.17614	+	11.4738i	0.172958	+	0.475198i
$584$	−0.935896	−	2.77571i	−0.0387276	−	0.114860i
$585$		0			0
$586$	4.59371	−	14.9113i	0.189764	−	0.615980i
$587$	−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
$592$	−19.5142	−	2.91283i	−0.802027	−	0.119716i
$593$	37.9041	+	6.68351i	1.55653	+	0.274459i	0.884671	−	0.466217i	$-0.154383\pi$
$593$	37.9041	+	6.68351i	1.55653	+	0.274459i	0.671863	+	0.740676i	$0.265494\pi$
$594$		0			0
$595$	−14.8504	−	40.8011i	−0.608807	−	1.67268i
$596$	−29.6947	−	13.3733i	−1.21634	−	0.547790i
$597$		0			0
$598$	−18.4090	−	13.9340i	−0.752801	−	0.569802i
$599$	−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	$-0.0464653\pi$
$602$	25.7828	−	10.8792i	1.05083	−	0.443402i
$603$		0			0
$604$	−0.448259	−	0.0332709i	−0.0182394	−	0.00135377i
$605$	19.1350	−	52.5730i	0.777949	−	2.13740i
$606$		0			0
$607$		−	22.1799i		−	0.900254i	−0.892965	−	0.450127i	$-0.851379\pi$
$607$		−	22.1799i		−	0.900254i	0.892965	−	0.450127i	$-0.148621\pi$
$608$	14.5461	−	19.9101i	0.589923	−	0.807459i
$609$		0			0
$610$	−19.8843	−	21.4148i	−0.805091	−	0.867061i
$611$	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	$0.977957\pi$
$614$	6.31486	+	14.9657i	0.254847	+	0.603967i
$615$		0			0
$616$	25.7546	−	20.5837i	1.03768	−	0.829341i
$617$	5.84795	−	6.96932i	0.235430	−	0.280574i	−0.635375	−	0.772204i	$-0.719154\pi$
$617$	5.84795	−	6.96932i	0.235430	−	0.280574i	0.870804	+	0.491630i	$0.163599\pi$
$618$		0			0
$619$	20.0116	−	11.5537i	0.804335	−	0.464383i	−0.0406494	−	0.999173i	$-0.512943\pi$
$619$	20.0116	−	11.5537i	0.804335	−	0.464383i	0.844985	+	0.534790i	$0.179609\pi$
$620$	−17.2591	+	38.3230i	−0.693143	+	1.53909i
$621$		0			0
$622$	−2.00914	−	8.78817i	−0.0805591	−	0.352373i
$623$	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	−0.221933	−	0.975062i	$-0.571237\pi$
$631$	−19.1908	−	3.38385i	−0.763972	−	0.134709i	−0.542039	+	0.840353i	$0.682348\pi$
$632$	−4.36932	+	1.47322i	−0.173802	+	0.0586014i
$633$		0			0
$634$	5.07155	+	2.59775i	0.201417	+	0.103170i
$635$	−10.5286	−	18.2360i	−0.417814	−	0.723675i
$636$		0			0
$637$	4.48418	+	3.76267i	0.177670	+	0.149082i
$638$	−24.8260	+	16.0469i	−0.982872	+	0.635303i
$639$		0			0
$640$	30.8935	+	36.6313i	1.22117	+	1.44798i
$641$	−21.0061	+	3.70394i	−0.829691	+	0.146297i	−0.572335	−	0.820020i	$-0.693962\pi$
$641$	−21.0061	+	3.70394i	−0.829691	+	0.146297i	−0.257356	+	0.966317i	$0.582851\pi$
$642$		0			0
$643$	−9.01221	+	24.7608i	−0.355407	+	0.976472i	0.625196	+	0.780468i	$0.285019\pi$
$643$	−9.01221	+	24.7608i	−0.355407	+	0.976472i	−0.980603	+	0.196005i	$0.937203\pi$
$644$	13.1345	+	12.7927i	0.517571	+	0.504105i
$645$		0			0
$646$	26.0583	−	5.69981i	1.02525	−	0.224256i
$647$	−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
$650$	9.57233	−	76.6068i	0.375458	−	3.00477i
$651$		0			0
$652$	−3.82138	−	7.92071i	−0.149657	−	0.310199i
$653$	−21.3431	−	12.3224i	−0.835220	−	0.482214i	0.0204168	−	0.999792i	$-0.493501\pi$
$653$	−21.3431	−	12.3224i	−0.835220	−	0.482214i	−0.855636	+	0.517577i	$0.826834\pi$
$654$		0			0
$655$	−27.1035	+	32.3007i	−1.05902	+	1.26209i
$656$	3.14762	−	5.79967i	0.122894	−	0.226439i
$657$		0			0
$658$	−25.8131	−	13.2220i	−1.00630	−	0.515446i
$659$	−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	$0.882670\pi$
$662$	−0.0975762	+	0.316735i	−0.00379241	+	0.0123103i
$663$		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
$668$	−39.7473	−	10.0907i	−1.53787	−	0.390422i
$669$		0			0
$670$	17.8009	+	77.8630i	0.687710	+	3.00811i
$671$	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	$0.960505\pi$
$674$	−8.60599	−	6.51396i	−0.331490	−	0.250908i
$675$		0			0
$676$	−5.60832	−	7.78897i	−0.215705	−	0.299576i
$677$	7.97495	+	4.60434i	0.306502	+	0.176959i	0.645360	−	0.763878i	$-0.276707\pi$
$677$	7.97495	+	4.60434i	0.306502	+	0.176959i	−0.338858	+	0.940838i	$0.610041\pi$
$678$		0			0
$679$	−44.8399	+	7.90648i	−1.72080	+	0.303423i
$680$	−1.23694	+	51.8238i	−0.0474343	+	1.98735i
$681$		0			0
$682$	−23.4917	−	25.3000i	−0.899545	−	0.968785i
$683$	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
$686$	−19.1210	−	20.5929i	−0.730045	−	0.786239i
$687$		0			0
$688$	−33.3985	+	0.880572i	−1.27330	+	0.0335715i
$689$	−10.3106	+	1.81804i	−0.392802	+	0.0692616i
$690$		0			0
$691$	−43.4628	−	25.0933i	−1.65340	−	0.954593i	−0.975658	−	0.219296i	$-0.929624\pi$
$691$	−43.4628	−	25.0933i	−1.65340	−	0.954593i	−0.677745	−	0.735297i	$-0.737043\pi$
$692$	−6.91528	+	4.97923i	−0.262879	+	0.189282i
$693$		0			0
$694$	−20.1207	−	15.2296i	−0.763773	−	0.578107i
$695$	−11.4815	−	19.8865i	−0.435516	−	0.754336i
$696$		0			0
$697$	6.70796	−	2.44150i	0.254082	−	0.0924784i
$698$	−2.05461	−	8.98705i	−0.0777680	−	0.340165i
$699$		0			0
$700$	−15.0862	+	59.4243i	−0.570204	+	2.24603i
$701$	20.3775	+	24.2850i	0.769649	+	0.917231i	0.998417	−	0.0562494i	$-0.0179142\pi$
$701$	20.3775	+	24.2850i	0.769649	+	0.917231i	−0.228768	+	0.973481i	$0.573470\pi$
$702$		0			0
$703$	20.2723	−	7.16312i	0.764586	−	0.270162i
$704$	−37.5885	+	11.6826i	−1.41667	+	0.440306i
$705$		0			0
$706$	−2.12994	+	6.91383i	−0.0801612	+	0.260205i
$707$	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	$0.391948\pi$
$710$	48.8536	+	25.0238i	1.83344	+	0.939126i
$711$		0			0
$712$	−0.287156	+	0.471042i	−0.0107616	+	0.0176531i
$713$	12.3414	−	14.7079i	0.462187	−	0.550813i
$714$		0			0
$715$	76.1417	+	43.9605i	2.84754	+	1.64403i
$716$	14.7797	−	7.13052i	0.552344	−	0.266480i
$717$		0			0
$718$	−2.68112	+	21.4568i	−0.100059	+	0.800762i
$719$	−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
$722$	−3.83303	+	26.5953i	−0.142650	+	0.989773i
$723$		0			0
$724$	−6.59370	+	6.76983i	−0.245053	+	0.251599i
$725$	18.8010	−	51.6554i	0.698252	−	1.91843i
$726$		0			0
$727$	−38.2376	+	6.74232i	−1.41815	+	0.250059i	−0.829582	−	0.558385i	$-0.811421\pi$
$727$	−38.2376	+	6.74232i	−1.41815	+	0.250059i	−0.588573	+	0.808444i	$0.700310\pi$
$728$	13.5466	+	24.8126i	0.502072	+	0.919615i
$729$		0			0
$730$	−5.20984	+	3.36750i	−0.192825	+	0.124637i
$731$	−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	$0.485416\pi$
$734$	16.7691	+	8.58945i	0.618957	+	0.317042i
$735$		0			0
$736$	−9.03862	−	19.9368i	−0.333168	−	0.734879i
$737$	−64.6121	−	11.3929i	−2.38002	−	0.419661i
$738$		0			0
$739$	−16.1794	−	19.2819i	−0.595170	−	0.709297i	0.381420	−	0.924402i	$-0.375435\pi$
$739$	−16.1794	−	19.2819i	−0.595170	−	0.709297i	−0.976591	+	0.215105i	$0.930991\pi$
$740$	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
$746$	7.68248	+	33.6039i	0.281276	+	1.23033i
$747$		0			0
$748$	−38.8258	−	17.4855i	−1.41961	−	0.639335i
$749$	−35.9894	+	20.7785i	−1.31502	+	0.759229i
$750$		0			0
$751$	27.5600	−	32.8447i	1.00568	−	1.19852i	0.0256472	−	0.999671i	$-0.491835\pi$
$751$	27.5600	−	32.8447i	1.00568	−	1.19852i	0.980030	−	0.198849i	$-0.0637202\pi$
$752$	22.9484	+	25.9291i	0.836842	+	0.945535i
$753$		0			0
$754$	−9.85391	−	23.3530i	−0.358858	−	0.850465i
$755$	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	$0.431701\pi$
$758$	28.9592	+	31.1883i	1.05185	+	1.13281i
$759$		0			0
$760$	−48.4483	−	19.4827i	−1.75740	−	0.706710i
$761$			12.6138i			0.457251i	0.973514	+	0.228625i	$0.0734231\pi$
$761$			12.6138i			0.457251i	−0.973514	+	0.228625i	$0.926577\pi$
$762$		0			0
$763$	2.55449	−	7.01841i	0.0924788	−	0.254083i
$764$	2.44121	−	32.8905i	0.0883200	−	1.18994i
$765$		0			0
$766$	4.73990	−	2.00003i	0.171260	−	0.0722639i
$767$	−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	$0.825121\pi$
$770$	−55.6719	−	42.1386i	−2.00627	−	1.51857i
$771$		0			0
$772$	−12.1255	+	26.9240i	−0.436405	+	0.969016i
$773$	−15.9489	−	43.8192i	−0.573642	−	1.57607i	−0.798704	−	0.601723i	$-0.794481\pi$
$773$	−15.9489	−	43.8192i	−0.573642	−	1.57607i	0.225063	−	0.974344i	$-0.427741\pi$
$774$		0			0
$775$	63.2259	+	11.1484i	2.27114	+	0.400464i
$776$	53.2937	+	10.7142i	1.91313	+	0.384618i
$777$		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
$782$	6.97183	−	22.6308i	0.249312	−	0.809274i
$783$		0			0
$784$	2.03500	+	5.16343i	0.0726786	+	0.184408i
$785$	17.4713	+	48.0021i	0.623578	+	1.71327i
$786$		0			0
$787$	25.8761	−	14.9395i	0.922382	−	0.532537i	0.0379877	−	0.999278i	$-0.487905\pi$
$787$	25.8761	−	14.9395i	0.922382	−	0.532537i	0.884394	+	0.466741i	$0.154572\pi$
$788$	26.2986	−	38.6321i	0.936847	−	1.37621i
$789$		0			0
$790$	5.30087	+	8.20094i	0.188597	+	0.291776i
$791$	−3.47715	+	6.02260i	−0.123633	+	0.214139i
$792$		0			0
$793$	3.57414	+	20.2699i	0.126921	+	0.719806i
$794$	2.27425	−	18.2007i	0.0807100	−	0.645917i
$795$		0			0
$796$	17.5357	+	17.0795i	0.621538	+	0.605367i
$797$		−	20.4097i		−	0.722950i	−0.932382	−	0.361475i	$-0.882273\pi$
$797$		−	20.4097i		−	0.722950i	0.932382	−	0.361475i	$-0.117727\pi$
$798$		0			0
$799$			37.4578i			1.32516i
$800$	42.6223	−	59.5076i	1.50693	−	2.10391i
$801$		0			0
$802$	36.3129	+	4.53744i	1.28225	+	0.160223i
$803$	−0.884851	−	5.01824i	−0.0312257	−	0.177090i
$804$		0			0
$805$	19.4144	−	33.6268i	0.684268	−	1.18519i
$806$	24.8617	−	16.0699i	0.875715	−	0.566039i
$807$		0			0
$808$	−0.918864	+	1.50728i	−0.0323255	+	0.0530258i
$809$	18.5251	−	10.6955i	0.651309	−	0.376033i	−0.137649	−	0.990481i	$-0.543954\pi$
$809$	18.5251	−	10.6955i	0.651309	−	0.376033i	0.788957	+	0.614448i	$0.210621\pi$
$810$		0			0
$811$	−2.15199	−	5.91254i	−0.0755665	−	0.207617i	0.896158	−	0.443735i	$-0.146347\pi$
$811$	−2.15199	−	5.91254i	−0.0755665	−	0.207617i	−0.971724	+	0.236118i	$0.924125\pi$
$812$	5.46553	+	19.3726i	0.191802	+	0.679846i
$813$		0			0
$814$	−32.8012	−	10.1050i	−1.14968	−	0.354181i
$815$	−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
$820$	−13.5449	−	3.43867i	−0.473008	−	0.120084i
$821$	−42.5399	−	7.50093i	−1.48465	−	0.261784i	−0.628216	−	0.778039i	$-0.716215\pi$
$821$	−42.5399	−	7.50093i	−1.48465	−	0.261784i	−0.856435	+	0.516255i	$0.827326\pi$
$822$		0			0
$823$	−6.72283	−	18.4708i	−0.234343	−	0.643852i	−1.00000		0.000602960i	$-0.999808\pi$
$823$	−6.72283	−	18.4708i	−0.234343	−	0.643852i	0.765657	−	0.643249i	$-0.222414\pi$
$824$	−2.63883	−	1.03241i	−0.0919280	−	0.0359656i
$825$		0			0
$826$	8.18685	−	10.8162i	0.284857	−	0.376342i
$827$	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	$0.261948\pi$
$830$	10.9855	+	26.0348i	0.381314	+	0.903683i
$831$		0			0
$832$	−4.26837	−	33.4801i	−0.147979	−	1.16071i
$833$	−2.05345	+	5.64182i	−0.0711480	+	0.195477i
$834$		0			0
$835$			86.8453i			3.00541i
$836$	30.2162	−	30.4446i	1.04505	−	1.05295i
$837$		0			0
$838$	−6.34473	+	5.89126i	−0.219175	+	0.203510i
$839$	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
$842$	9.47220	−	3.99684i	0.326433	−	0.137740i
$843$		0			0
$844$	−28.2083	+	20.3109i	−0.970969	+	0.699130i
$845$	−13.0654	+	15.5708i	−0.449464	+	0.535650i
$846$		0			0
$847$	27.1007	−	15.6466i	0.931191	−	0.537623i
$848$	−9.41406	−	3.14802i	−0.323280	−	0.108103i
$849$		0			0
$850$	77.1922	−	17.6476i	2.64767	−	0.605307i
$851$	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	$-0.984337\pi$
$857$	−25.5799	−	30.4849i	−0.873792	−	1.04135i	0.124997	−	0.992157i	$-0.460108\pi$
$858$		0			0
$859$	4.77072	+	0.841208i	0.162775	+	0.0287016i	0.254442	−	0.967088i	$-0.418108\pi$
$859$	4.77072	+	0.841208i	0.162775	+	0.0287016i	−0.0916666	+	0.995790i	$0.529219\pi$
$860$	19.2117	+	68.0961i	0.655114	+	2.32206i
$861$		0			0
$862$	−9.51737	+	18.5806i	−0.324163	+	0.632859i
$863$	−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
$866$	20.4779	+	31.6811i	0.695866	+	1.07657i
$867$		0			0
$868$	−21.1736	+	10.2153i	−0.718677	+	0.346728i
$869$	−7.89934	+	1.39287i	−0.267967	+	0.0472498i
$870$		0			0
$871$	19.2408	−	52.8636i	0.651949	−	1.79122i
$872$	−5.89311	+	6.69212i	−0.199566	+	0.226624i
$873$		0			0
$874$	18.8836	+	14.5748i	0.638747	+	0.493001i
$875$	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	$0.707655\pi$
$878$	−24.5410	−	3.06649i	−0.828217	−	0.103489i
$879$		0			0
$880$	43.5679	+	71.0677i	1.46867	+	2.39569i
$881$	32.5283	+	18.7802i	1.09591	+	0.632721i	0.935143	−	0.354272i	$-0.115271\pi$
$881$	32.5283	+	18.7802i	1.09591	+	0.632721i	0.160763	+	0.986993i	$0.448604\pi$
$882$		0			0
$883$	−27.4909	+	32.7623i	−0.925141	+	1.10254i	0.0693368	+	0.997593i	$0.477912\pi$
$883$	−27.4909	+	32.7623i	−0.925141	+	1.10254i	−0.994478	+	0.104947i	$0.966533\pi$
$884$	20.5462	−	30.1819i	0.691042	−	1.01513i
$885$		0			0
$886$	21.3257	−	41.6338i	0.716449	−	1.39871i
$887$	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
$890$	1.11652	+	0.343965i	0.0374258	+	0.0115297i
$891$		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
$896$	0.0668988	+	26.8029i	0.00223493	+	0.895423i
$897$		0			0
$898$	40.3849	−	9.23273i	1.34766	−	0.308100i
$899$	19.8071	−	7.20920i	0.660605	−	0.240440i
$900$		0			0
$901$	−5.36916	−	9.29966i	−0.178873	−	0.309817i
$902$	6.92785	−	9.15280i	0.230672	−	0.304755i
$903$		0			0
$904$	6.48578	−	5.18359i	0.215714	−	0.172404i
$905$	17.3321	+	10.0067i	0.576137	+	0.332633i
$906$		0			0
$907$	24.9369	−	4.39705i	0.828016	−	0.146002i	0.256450	−	0.966558i	$-0.417447\pi$
$907$	24.9369	−	4.39705i	0.828016	−	0.146002i	0.571566	+	0.820556i	$0.306336\pi$
$908$	2.10109	−	28.3080i	0.0697272	−	0.939434i
$909$		0			0
$910$	43.8720	−	40.7364i	1.45434	−	1.35040i
$911$	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
$914$	24.8478	−	23.0719i	0.821893	−	0.763151i
$915$		0			0
$916$	0.0216599	−	0.291823i	0.000715662	−	0.00964211i
$917$	−23.2264	+	4.09544i	−0.767003	+	0.135243i
$918$		0			0
$919$	−27.6842	−	15.9835i	−0.913219	−	0.527247i	−0.0317534	−	0.999496i	$-0.510109\pi$
$919$	−27.6842	−	15.9835i	−0.913219	−	0.527247i	−0.881465	+	0.472249i	$0.843442\pi$
$920$	−36.2129	+	28.9422i	−1.19390	+	0.954198i
$921$		0			0
$922$	−16.7127	+	22.0802i	−0.550404	+	0.727173i
$923$	−19.3302	−	33.4809i	−0.636262	−	1.10204i
$924$		0			0
$925$	59.9763	−	21.8296i	1.97201	−	0.717752i
$926$	−1.27940	+	0.292495i	−0.0420437	+	0.00961197i
$927$		0			0
$928$	2.35016	−	23.9166i	0.0771476	−	0.785100i
$929$	−17.3537	−	20.6813i	−0.569357	−	0.678533i	0.402142	−	0.915577i	$-0.368266\pi$
$929$	−17.3537	−	20.6813i	−0.569357	−	0.678533i	−0.971499	+	0.237044i	$0.923821\pi$
$930$		0			0
$931$	−4.59619	−	3.93099i	−0.150634	−	0.128833i
$932$	1.33970	+	13.2926i	0.0438833	+	0.435414i
$933$		0			0
$934$	−43.0433	−	13.2603i	−1.40842	−	0.433890i
$935$	−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	$0.222412\pi$
$938$	−20.3671	+	39.7625i	−0.665011	+	1.29829i
$939$		0			0
$940$	41.2644	−	60.6166i	1.34590	−	1.97710i
$941$	10.6636	−	12.7084i	0.347624	−	0.414282i	−0.563695	−	0.825983i	$-0.690621\pi$
$941$	10.6636	−	12.7084i	0.347624	−	0.414282i	0.911319	+	0.411701i	$0.135065\pi$
$942$		0			0
$943$	5.52845	+	3.19185i	0.180031	+	0.103941i
$944$	−13.8073	+	8.46455i	−0.449390	+	0.275498i
$945$		0			0
$946$	−57.6709	−	7.20622i	−1.87504	−	0.234294i
$947$	−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
$950$	−10.6347	+	79.0526i	−0.345036	+	2.56480i
$951$		0			0
$952$	−19.1624	+	21.7605i	−0.621058	+	0.705263i
$953$	−13.8733	+	38.1165i	−0.449399	+	1.23471i	0.483744	+	0.875209i	$0.339276\pi$
$953$	−13.8733	+	38.1165i	−0.449399	+	1.23471i	−0.933143	+	0.359504i	$0.882946\pi$
$954$		0			0
$955$	−68.7844	+	12.1285i	−2.22581	+	0.392471i
$956$	−32.4943	+	15.6770i	−1.05094	+	0.507030i
$957$		0			0
$958$	−3.30407	−	5.11171i	−0.106750	−	0.165152i
$959$	12.5701	+	10.5476i	0.405911	+	0.340600i
$960$		0			0
$961$	−3.19108	−	5.52711i	−0.102938	−	0.178294i
$962$	13.4169	−	26.1935i	0.432577	−	0.844514i
$963$		0			0
$964$	13.9988	+	49.6191i	0.450872	+	1.59812i
$965$	61.5840	+	10.8589i	1.98246	+	0.349561i
$966$		0			0
$967$	8.64232	+	10.2995i	0.277918	+	0.331210i	0.886889	−	0.461983i	$-0.152862\pi$
$967$	8.64232	+	10.2995i	0.277918	+	0.331210i	−0.608971	+	0.793193i	$0.708417\pi$
$968$	−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
$974$	−50.1336	+	11.4615i	−1.60639	+	0.367250i
$975$		0			0
$976$	−6.18880	+	18.5074i	−0.198099	+	0.592408i
$977$	38.4227	−	22.1834i	1.22925	−	0.709709i	0.262379	−	0.964965i	$-0.415493\pi$
$977$	38.4227	−	22.1834i	1.22925	−	0.709709i	0.966874	+	0.255256i	$0.0821597\pi$
$978$		0			0
$979$	−0.616866	+	0.735152i	−0.0197151	+	0.0234956i
$980$	9.53821	−	6.86783i	0.304687	−	0.219385i
$981$		0			0
$982$	−16.8817	+	7.12331i	−0.538716	+	0.227314i
$983$	−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
$986$	19.0511	−	17.6894i	0.606709	−	0.563346i
$987$		0			0
$988$	21.2091	+	30.0483i	0.674751	+	0.955963i
$989$		−	32.3212i		−	1.02775i
$990$		0			0
$991$	3.62582	−	9.96186i	0.115178	−	0.316449i	−0.868687	−	0.495361i	$-0.835036\pi$
$991$	3.62582	−	9.96186i	0.115178	−	0.316449i	0.983865	+	0.178912i	$0.0572579\pi$
$992$	27.9850	−	2.14736i	0.888524	−	0.0681789i
$993$		0			0
$994$	11.9357	+	28.2867i	0.378578	+	0.897198i
$995$	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	$0.589499\pi$
$998$	−29.1170	+	38.4683i	−0.921683	+	1.21769i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.03635 + 0.962279i) q^{2} +(0.148038 - 1.99451i) q^{4} +(-4.17116 + 0.735488i) q^{5} +(-2.05168 - 1.18454i) q^{7} +(1.76586 + 2.20947i) q^{8} +O(q^{10})\)	\(q+(-1.03635 + 0.962279i) q^{2} +(0.148038 - 1.99451i) q^{4} +(-4.17116 + 0.735488i) q^{5} +(-2.05168 - 1.18454i) q^{7} +(1.76586 + 2.20947i) q^{8} +(3.61503 - 4.77605i) q^{10} +(2.46013 + 4.26108i) q^{11} +(-3.96446 + 1.44294i) q^{13} +(3.26611 - 0.746693i) q^{14} +(-3.95617 - 0.590527i) q^{16} +(-2.78144 - 3.31479i) q^{17} +(4.10988 - 1.45220i) q^{19} +(0.849452 + 8.42832i) q^{20} +(-6.64990 - 2.04863i) q^{22} +(0.671956 - 3.81085i) q^{23} +(12.1592 - 4.42558i) q^{25} +(2.72004 - 5.31031i) q^{26} +(-2.66630 + 3.91674i) q^{28} +(2.73073 - 3.25435i) q^{29} +(4.29690 + 2.48082i) q^{31} +(4.66822 - 3.19495i) q^{32} +(6.07230 + 0.758759i) q^{34} +(9.42909 + 3.43191i) q^{35} +4.93259 q^{37} +(-2.86184 + 5.45984i) q^{38} +(-8.99073 - 7.91727i) q^{40} +(-0.564228 + 1.55020i) q^{41} +(8.22562 - 1.45040i) q^{43} +(8.86297 - 4.27597i) q^{44} +(2.97072 + 4.59598i) q^{46} +(-6.63122 - 5.56426i) q^{47} +(-0.693747 - 1.20160i) q^{49} +(-8.34252 + 16.2870i) q^{50} +(2.29108 + 8.12077i) q^{52} +(2.44391 + 0.430928i) q^{53} +(-13.3956 - 15.9642i) q^{55} +(-1.00578 - 6.62484i) q^{56} +(0.301611 + 6.00037i) q^{58} +(3.10160 - 2.60255i) q^{59} +(0.847176 - 4.80457i) q^{61} +(-6.84033 + 1.56383i) q^{62} +(-1.76348 + 7.80321i) q^{64} +(15.4751 - 8.93456i) q^{65} +(-8.57119 + 10.2147i) q^{67} +(-7.02316 + 5.05691i) q^{68} +(-13.0743 + 5.51676i) q^{70} +(1.59125 + 9.02445i) q^{71} +(-0.973188 - 0.354212i) q^{73} +(-5.11188 + 4.74653i) q^{74} +(-2.28802 - 8.41219i) q^{76} -11.6565i q^{77} +(-0.557573 + 1.53192i) q^{79} +(16.9362 - 0.446532i) q^{80} +(-0.906991 - 2.14949i) q^{82} +(-2.35877 + 4.08551i) q^{83} +(14.0398 + 11.7808i) q^{85} +(-7.12893 + 9.41846i) q^{86} +(-5.07045 + 12.9600i) q^{88} +(0.0667092 + 0.183282i) q^{89} +(9.84300 + 1.73559i) q^{91} +(-7.50132 - 1.90437i) q^{92} +(12.2266 - 0.614576i) q^{94} +(-16.0749 + 9.08015i) q^{95} +(14.7227 - 12.3538i) q^{97} +(1.87524 + 0.577704i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{4}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more