LMFDB - Embedded newform 342.2.bb.b.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(53,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 11]))

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

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

chi := DirichletCharacter("342.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.bb (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.1
Character	$\chi$	$=$	342.143
Dual form			342.2.bb.b.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.835315 + 2.29501i) q^{5} +(-0.0101738 + 0.0176215i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.835315 + 2.29501i) q^{5} +(-0.0101738 + 0.0176215i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.40519 + 0.424100i) q^{10} +(-5.28395 + 3.05069i) q^{11} +(-0.818782 + 0.975787i) q^{13} +(0.0191205 + 0.00695929i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-2.82716 + 0.498505i) q^{17} +(2.36132 + 3.66390i) q^{19} -2.44230i q^{20} +(3.92189 + 4.67393i) q^{22} +(2.62758 + 7.21921i) q^{23} +(-0.739090 - 0.620170i) q^{25} +(1.10314 + 0.636900i) q^{26} +(0.00353332 - 0.0200385i) q^{28} +(1.12823 - 6.39853i) q^{29} +(-1.25553 - 0.724880i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.981864 + 2.69765i) q^{34} +(-0.0319433 - 0.0380685i) q^{35} -2.98930i q^{37} +(3.19820 - 2.96167i) q^{38} +(-2.40519 + 0.424100i) q^{40} +(5.87990 - 4.93382i) q^{41} +(-1.45096 - 0.528107i) q^{43} +(3.92189 - 4.67393i) q^{44} +(6.65326 - 3.84126i) q^{46} +(-1.71246 - 0.301952i) q^{47} +(3.49979 + 6.06182i) q^{49} +(-0.482407 + 0.835553i) q^{50} +(0.435665 - 1.19698i) q^{52} +(-3.51814 + 1.28050i) q^{53} +(-2.58760 - 14.6750i) q^{55} -0.0203476 q^{56} -6.49724 q^{58} +(0.986296 + 5.59356i) q^{59} +(-11.9082 + 4.33425i) q^{61} +(-0.495847 + 1.36233i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.55550 - 2.69420i) q^{65} +(-11.6339 - 2.05137i) q^{67} +(2.48617 - 1.43539i) q^{68} +(-0.0319433 + 0.0380685i) q^{70} +(9.36760 + 3.40953i) q^{71} +(5.93403 - 4.97924i) q^{73} +(-2.94388 + 0.519086i) q^{74} +(-3.47204 - 2.63532i) q^{76} -0.124148i q^{77} +(1.78876 + 2.13176i) q^{79} +(0.835315 + 2.29501i) q^{80} +(-5.87990 - 4.93382i) q^{82} +(-4.68738 - 2.70626i) q^{83} +(1.21750 - 6.90477i) q^{85} +(-0.268127 + 1.52062i) q^{86} +(-5.28395 - 3.05069i) q^{88} +(-3.15178 - 2.64466i) q^{89} +(-0.00886474 - 0.0243557i) q^{91} +(-4.93823 - 5.88515i) q^{92} +1.73887i q^{94} +(-10.3811 + 2.35873i) q^{95} +(13.5064 - 2.38154i) q^{97} +(5.36199 - 4.49925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} + 36 q^{26} - 12 q^{29} + 12 q^{34} - 48 q^{35} - 12 q^{38} - 12 q^{41} + 12 q^{44} - 36 q^{46} + 60 q^{47} - 36 q^{49} - 24 q^{50} - 48 q^{53} - 60 q^{55} - 24 q^{58} + 24 q^{59} - 60 q^{61} + 24 q^{62} - 12 q^{64} - 24 q^{65} - 48 q^{70} - 36 q^{71} + 24 q^{79} + 12 q^{82} + 72 q^{83} - 36 q^{86} - 120 q^{89} - 24 q^{91} + 12 q^{95}+O(q^{100}) $ 24 * q + 12 * q^8 + 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 + 36 * q^26 - 12 * q^29 + 12 * q^34 - 48 * q^35 - 12 * q^38 - 12 * q^41 + 12 * q^44 - 36 * q^46 + 60 * q^47 - 36 * q^49 - 24 * q^50 - 48 * q^53 - 60 * q^55 - 24 * q^58 + 24 * q^59 - 60 * q^61 + 24 * q^62 - 12 * q^64 - 24 * q^65 - 48 * q^70 - 36 * q^71 + 24 * q^79 + 12 * q^82 + 72 * q^83 - 36 * q^86 - 120 * q^89 - 24 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.835315	+	2.29501i	−0.373564	+	1.02636i	0.600409	+	0.799693i	$0.295005\pi$
$5$	−0.835315	+	2.29501i	−0.373564	+	1.02636i	−0.973973	+	0.226665i	$0.927218\pi$
$6$		0			0
$7$	−0.0101738	+	0.0176215i	−0.00384534	+	0.00666032i	−0.867942	−	0.496666i	$-0.834557\pi$
$7$	−0.0101738	+	0.0176215i	−0.00384534	+	0.00666032i	0.864096	+	0.503326i	$0.167891\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	2.40519	+	0.424100i	0.760589	+	0.134112i
$11$	−5.28395	+	3.05069i	−1.59317	+	0.919818i	−0.600413	+	0.799690i	$0.704997\pi$
$11$	−5.28395	+	3.05069i	−1.59317	+	0.919818i	−0.992759	+	0.120127i	$0.961670\pi$
$12$		0			0
$13$	−0.818782	+	0.975787i	−0.227089	+	0.270635i	−0.867543	−	0.497362i	$-0.834302\pi$
$13$	−0.818782	+	0.975787i	−0.227089	+	0.270635i	0.640454	+	0.767997i	$0.278746\pi$
$14$	0.0191205	+	0.00695929i	0.00511017	+	0.00185995i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−2.82716	+	0.498505i	−0.685688	+	0.120905i	−0.505630	−	0.862751i	$-0.668740\pi$
$17$	−2.82716	+	0.498505i	−0.685688	+	0.120905i	−0.180058	+	0.983656i	$0.557629\pi$
$18$		0			0
$19$	2.36132	+	3.66390i	0.541724	+	0.840557i
$19$	2.36132	+	3.66390i	0.541724	+	0.840557i
$20$		−	2.44230i		−	0.546114i
$21$		0			0
$22$	3.92189	+	4.67393i	0.836150	+	0.996485i
$23$	2.62758	+	7.21921i	0.547887	+	1.50531i	0.836557	+	0.547880i	$0.184565\pi$
$23$	2.62758	+	7.21921i	0.547887	+	1.50531i	−0.288670	+	0.957429i	$0.593213\pi$
$24$		0			0
$25$	−0.739090	−	0.620170i	−0.147818	−	0.124034i
$26$	1.10314	+	0.636900i	0.216344	+	0.124906i
$27$		0			0
$28$	0.00353332	−	0.0200385i	0.000667735	−	0.00378692i
$29$	1.12823	−	6.39853i	0.209508	−	1.18818i	−0.680679	−	0.732582i	$-0.738315\pi$
$29$	1.12823	−	6.39853i	0.209508	−	1.18818i	0.890187	−	0.455596i	$-0.150574\pi$
$30$		0			0
$31$	−1.25553	−	0.724880i	−0.225500	−	0.130192i	0.382994	−	0.923751i	$-0.374893\pi$
$31$	−1.25553	−	0.724880i	−0.225500	−	0.130192i	−0.608494	+	0.793558i	$0.708226\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$		0			0
$34$	0.981864	+	2.69765i	0.168388	+	0.462643i
$35$	−0.0319433	−	0.0380685i	−0.00539940	−	0.00643475i
$36$		0			0
$37$		−	2.98930i		−	0.491437i	−0.969341	−	0.245719i	$-0.920976\pi$
$37$		−	2.98930i		−	0.491437i	0.969341	−	0.245719i	$-0.0790239\pi$
$38$	3.19820	−	2.96167i	0.518817	−	0.480447i
$39$		0			0
$40$	−2.40519	+	0.424100i	−0.380294	+	0.0670562i
$41$	5.87990	−	4.93382i	0.918286	−	0.770533i	−0.0553914	−	0.998465i	$-0.517641\pi$
$41$	5.87990	−	4.93382i	0.918286	−	0.770533i	0.973677	+	0.227931i	$0.0731962\pi$
$42$		0			0
$43$	−1.45096	−	0.528107i	−0.221269	−	0.0805355i	0.229007	−	0.973425i	$-0.426452\pi$
$43$	−1.45096	−	0.528107i	−0.221269	−	0.0805355i	−0.450276	+	0.892889i	$0.648674\pi$
$44$	3.92189	−	4.67393i	0.591247	−	0.704621i
$45$		0			0
$46$	6.65326	−	3.84126i	0.980969	−	0.566363i
$47$	−1.71246	−	0.301952i	−0.249787	−	0.0440442i	0.0473524	−	0.998878i	$-0.484922\pi$
$47$	−1.71246	−	0.301952i	−0.249787	−	0.0440442i	−0.297140	+	0.954834i	$0.596033\pi$
$48$		0			0
$49$	3.49979	+	6.06182i	0.499970	+	0.865974i
$50$	−0.482407	+	0.835553i	−0.0682226	+	0.118165i
$51$		0			0
$52$	0.435665	−	1.19698i	0.0604159	−	0.165991i
$53$	−3.51814	+	1.28050i	−0.483254	+	0.175890i	−0.572147	−	0.820151i	$-0.693889\pi$
$53$	−3.51814	+	1.28050i	−0.483254	+	0.175890i	0.0888928	+	0.996041i	$0.471667\pi$
$54$		0			0
$55$	−2.58760	−	14.6750i	−0.348912	−	1.97878i
$56$	−0.0203476			−0.00271906
$57$		0			0
$58$	−6.49724			−0.853129
$59$	0.986296	+	5.59356i	0.128405	+	0.728220i	0.979227	+	0.202766i	$0.0649932\pi$
$59$	0.986296	+	5.59356i	0.128405	+	0.728220i	−0.850822	+	0.525453i	$0.823896\pi$
$60$		0			0
$61$	−11.9082	+	4.33425i	−1.52469	+	0.554943i	−0.962315	−	0.271936i	$-0.912336\pi$
$61$	−11.9082	+	4.33425i	−1.52469	+	0.554943i	−0.562379	+	0.826880i	$0.690114\pi$
$62$	−0.495847	+	1.36233i	−0.0629727	+	0.173016i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.55550	−	2.69420i	−0.192936	−	0.334175i
$66$		0			0
$67$	−11.6339	−	2.05137i	−1.42131	−	0.250615i	−0.590437	−	0.807083i	$-0.701045\pi$
$67$	−11.6339	−	2.05137i	−1.42131	−	0.250615i	−0.830869	+	0.556469i	$0.812156\pi$
$68$	2.48617	−	1.43539i	0.301492	−	0.174066i
$69$		0			0
$70$	−0.0319433	+	0.0380685i	−0.00381795	+	0.00455005i
$71$	9.36760	+	3.40953i	1.11173	+	0.404637i	0.831628	−	0.555334i	$-0.187409\pi$
$71$	9.36760	+	3.40953i	1.11173	+	0.404637i	0.280102	+	0.959970i	$0.409632\pi$
$72$		0			0
$73$	5.93403	−	4.97924i	0.694526	−	0.582776i	−0.225685	−	0.974200i	$-0.572462\pi$
$73$	5.93403	−	4.97924i	0.694526	−	0.582776i	0.920210	+	0.391424i	$0.128018\pi$
$74$	−2.94388	+	0.519086i	−0.342219	+	0.0603425i
$75$		0			0
$76$	−3.47204	−	2.63532i	−0.398270	−	0.302292i
$77$		−	0.124148i		−	0.0141480i
$78$		0			0
$79$	1.78876	+	2.13176i	0.201251	+	0.239842i	0.857225	−	0.514942i	$-0.172186\pi$
$79$	1.78876	+	2.13176i	0.201251	+	0.239842i	−0.655974	+	0.754783i	$0.727742\pi$
$80$	0.835315	+	2.29501i	0.0933910	+	0.256590i
$81$		0			0
$82$	−5.87990	−	4.93382i	−0.649326	−	0.544849i
$83$	−4.68738	−	2.70626i	−0.514507	−	0.297051i	0.220177	−	0.975460i	$-0.429336\pi$
$83$	−4.68738	−	2.70626i	−0.514507	−	0.297051i	−0.734684	+	0.678409i	$0.762670\pi$
$84$		0			0
$85$	1.21750	−	6.90477i	0.132056	−	0.748928i
$86$	−0.268127	+	1.52062i	−0.0289128	+	0.163973i
$87$		0			0
$88$	−5.28395	−	3.05069i	−0.563271	−	0.325205i
$89$	−3.15178	−	2.64466i	−0.334088	−	0.280333i	0.460275	−	0.887776i	$-0.347751\pi$
$89$	−3.15178	−	2.64466i	−0.334088	−	0.280333i	−0.794363	+	0.607443i	$0.792195\pi$
$90$		0			0
$91$	−0.00886474	−	0.0243557i	−0.000929277	−	0.00255317i
$92$	−4.93823	−	5.88515i	−0.514846	−	0.613569i
$93$		0			0
$94$			1.73887i			0.179351i
$95$	−10.3811	+	2.35873i	−1.06508	+	0.242001i
$96$		0			0
$97$	13.5064	−	2.38154i	1.37137	−	0.241809i	0.561040	−	0.827789i	$-0.310401\pi$
$97$	13.5064	−	2.38154i	1.37137	−	0.241809i	0.810326	+	0.585980i	$0.199290\pi$
$98$	5.36199	−	4.49925i	0.541643	−	0.454493i
$99$		0			0
$100$	0.906628	+	0.329986i	0.0906628	+	0.0329986i
$101$	9.76870	−	11.6419i	0.972022	−	1.15841i	−0.0153330	−	0.999882i	$-0.504881\pi$
$101$	9.76870	−	11.6419i	0.972022	−	1.15841i	0.987355	−	0.158528i	$-0.0506747\pi$
$102$		0			0
$103$	4.45621	−	2.57279i	0.439083	−	0.253505i	−0.264125	−	0.964488i	$-0.585083\pi$
$103$	4.45621	−	2.57279i	0.439083	−	0.253505i	0.703209	+	0.710983i	$0.251750\pi$
$104$	−1.25445	−	0.221193i	−0.123009	−	0.0216898i
$105$		0			0
$106$	1.87197	+	3.24234i	0.181821	+	0.314924i
$107$	2.01814	−	3.49553i	0.195101	−	0.337926i	−0.751832	−	0.659354i	$-0.770830\pi$
$107$	2.01814	−	3.49553i	0.195101	−	0.337926i	0.946934	+	0.321429i	$0.104163\pi$
$108$		0			0
$109$	−5.67998	+	15.6056i	−0.544044	+	1.49475i	0.297587	+	0.954695i	$0.403818\pi$
$109$	−5.67998	+	15.6056i	−0.544044	+	1.49475i	−0.841631	+	0.540053i	$0.818404\pi$
$110$	−14.0027	+	5.09657i	−1.33511	+	0.485939i
$111$		0			0
$112$	0.00353332	+	0.0200385i	0.000333868	+	0.00189346i
$113$	18.3468			1.72592			0.862961	−	0.505271i	$-0.168607\pi$
$113$	18.3468			1.72592			0.862961	+	0.505271i	$0.168607\pi$
$114$		0			0
$115$	−18.7630			−1.74966
$116$	1.12823	+	6.39853i	0.104754	+	0.594089i
$117$		0			0
$118$	5.33731	−	1.94262i	0.491340	−	0.178833i
$119$	0.0199786	−	0.0548907i	0.00183143	−	0.00503182i
$120$		0			0
$121$	13.1134	−	22.7131i	1.19213	−	2.06483i
$122$	6.33624	+	10.9747i	0.573657	+	0.993602i
$123$		0			0
$124$	1.42774	+	0.251748i	0.128214	+	0.0226077i
$125$	−8.53479	+	4.92756i	−0.763375	+	0.440735i
$126$		0			0
$127$	−13.2600	+	15.8027i	−1.17664	+	1.40226i	−0.279705	+	0.960086i	$0.590237\pi$
$127$	−13.2600	+	15.8027i	−1.17664	+	1.40226i	−0.896930	+	0.442173i	$0.854208\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$		0			0
$130$	−2.38316	+	1.99971i	−0.209017	+	0.175386i
$131$	5.42540	−	0.956644i	0.474019	−	0.0835824i	0.0684654	−	0.997653i	$-0.478190\pi$
$131$	5.42540	−	0.956644i	0.474019	−	0.0835824i	0.405554	+	0.914071i	$0.367079\pi$
$132$		0			0
$133$	−0.0885872	+	0.00433426i	−0.00768148	+	0.000375828i
$134$			11.8134i			1.02052i
$135$		0			0
$136$	−1.84530	−	2.19914i	−0.158233	−	0.188575i
$137$	−4.59284	−	12.6187i	−0.392393	−	1.07809i	−0.965906	−	0.258894i	$-0.916642\pi$
$137$	−4.59284	−	12.6187i	−0.392393	−	1.07809i	0.573513	−	0.819196i	$-0.305580\pi$
$138$		0			0
$139$	1.80525	+	1.51479i	0.153120	+	0.128483i	0.716129	−	0.697968i	$-0.245912\pi$
$139$	1.80525	+	1.51479i	0.153120	+	0.128483i	−0.563010	+	0.826450i	$0.690357\pi$
$140$	0.0430370	+	0.0248474i	0.00363729	+	0.00209999i
$141$		0			0
$142$	1.73106	−	9.81735i	0.145268	−	0.823853i
$143$	1.34958	−	7.65386i	0.112858	−	0.640048i
$144$		0			0
$145$	13.7422	+	7.93409i	1.14123	+	0.658890i
$146$	−5.93403	−	4.97924i	−0.491104	−	0.412085i
$147$		0			0
$148$	1.02240	+	2.80902i	0.0840407	+	0.230900i
$149$	2.57443	+	3.06809i	0.210906	+	0.251347i	0.861118	−	0.508405i	$-0.169765\pi$
$149$	2.57443	+	3.06809i	0.210906	+	0.251347i	−0.650213	+	0.759752i	$0.725320\pi$
$150$		0			0
$151$			7.46625i			0.607595i	0.952737	+	0.303797i	$0.0982546\pi$
$151$			7.46625i			0.607595i	−0.952737	+	0.303797i	$0.901745\pi$
$152$	−1.99237	+	3.87691i	−0.161603	+	0.314459i
$153$		0			0
$154$	−0.122262	+	0.0215582i	−0.00985218	+	0.00173721i
$155$	2.71237	−	2.27595i	0.217863	−	0.182809i
$156$		0			0
$157$	18.0585	+	6.57274i	1.44122	+	0.524562i	0.940125	−	0.340829i	$-0.110708\pi$
$157$	18.0585	+	6.57274i	1.44122	+	0.524562i	0.501097	+	0.865391i	$0.332930\pi$
$158$	1.78876	−	2.13176i	0.142306	−	0.169594i
$159$		0			0
$160$	2.11509	−	1.22115i	0.167213	−	0.0965403i
$161$	−0.153946	−	0.0271448i	−0.0121326	−	0.00213931i
$162$		0			0
$163$	4.88906	+	8.46811i	0.382941	+	0.663273i	0.991481	−	0.130250i	$-0.0415779\pi$
$163$	4.88906	+	8.46811i	0.382941	+	0.663273i	−0.608540	+	0.793523i	$0.708245\pi$
$164$	−3.83783	+	6.64732i	−0.299684	+	0.519068i
$165$		0			0
$166$	−1.85119	+	5.08611i	−0.143680	+	0.394758i
$167$	−19.8427	+	7.22217i	−1.53548	+	0.558868i	−0.964955	−	0.262414i	$-0.915481\pi$
$167$	−19.8427	+	7.22217i	−1.53548	+	0.558868i	−0.570522	+	0.821282i	$0.693259\pi$
$168$		0			0
$169$	1.97567	+	11.2046i	0.151975	+	0.861891i
$170$	−7.01129			−0.537742
$171$		0			0
$172$	1.54408			0.117735
$173$	−0.737151	−	4.18059i	−0.0560446	−	0.317845i	0.943878	−	0.330294i	$-0.107148\pi$
$173$	−0.737151	−	4.18059i	−0.0560446	−	0.317845i	−0.999922	+	0.0124500i	$0.996037\pi$
$174$		0			0
$175$	0.0184477	−	0.00671441i	0.00139452	−	0.000507562i
$176$	−2.08680	+	5.73342i	−0.157298	+	0.432173i
$177$		0			0
$178$	−2.05718	+	3.56314i	−0.154192	+	0.267068i
$179$	10.9342	+	18.9387i	0.817263	+	1.41554i	0.907691	+	0.419639i	$0.137843\pi$
$179$	10.9342	+	18.9387i	0.817263	+	1.41554i	−0.0904279	+	0.995903i	$0.528823\pi$
$180$		0			0
$181$	7.61863	+	1.34337i	0.566289	+	0.0998520i	0.449461	−	0.893300i	$-0.351616\pi$
$181$	7.61863	+	1.34337i	0.566289	+	0.0998520i	0.116828	+	0.993152i	$0.462727\pi$
$182$	−0.0224463	+	0.0129594i	−0.00166383	+	0.000960613i
$183$		0			0
$184$	−4.93823	+	5.88515i	−0.364051	+	0.433859i
$185$	6.86046	+	2.49700i	0.504391	+	0.183583i
$186$		0			0
$187$	13.4178	−	11.2589i	0.981208	−	0.823331i
$188$	1.71246	−	0.301952i	0.124894	−	0.0220221i
$189$		0			0
$190$	4.12556	+	9.81383i	0.299300	+	0.711970i
$191$		−	2.10883i		−	0.152589i	−0.997085	−	0.0762947i	$-0.975691\pi$
$191$		−	2.10883i		−	0.152589i	0.997085	−	0.0762947i	$-0.0243090\pi$
$192$		0			0
$193$	3.66151	+	4.36361i	0.263561	+	0.314100i	0.881553	−	0.472084i	$-0.156498\pi$
$193$	3.66151	+	4.36361i	0.263561	+	0.314100i	−0.617992	+	0.786184i	$0.712054\pi$
$194$	−4.69072	−	12.8876i	−0.336774	−	0.925279i
$195$		0			0
$196$	−5.36199	−	4.49925i	−0.383000	−	0.321375i
$197$	15.0936	+	8.71428i	1.07537	+	0.620867i	0.929645	−	0.368458i	$-0.120114\pi$
$197$	15.0936	+	8.71428i	1.07537	+	0.620867i	0.145729	+	0.989325i	$0.453447\pi$
$198$		0			0
$199$	−2.22462	+	12.6164i	−0.157699	+	0.894356i	0.798577	+	0.601892i	$0.205586\pi$
$199$	−2.22462	+	12.6164i	−0.157699	+	0.894356i	−0.956277	+	0.292464i	$0.905525\pi$
$200$	0.167538	−	0.950156i	0.0118467	−	0.0671861i
$201$		0			0
$202$	−13.1613	−	7.59870i	−0.926028	−	0.534642i
$203$	0.101274	+	0.0849786i	0.00710801	+	0.00596433i
$204$		0			0
$205$	6.41159	+	17.6157i	0.447805	+	1.23033i
$206$	−3.30752	−	3.94175i	−0.230446	−	0.274635i
$207$		0			0
$208$			1.27380i			0.0883221i
$209$	−23.6545	−	12.1562i	−1.63622	−	0.840864i
$210$		0			0
$211$	22.1504	−	3.90571i	1.52490	−	0.268880i	0.652541	−	0.757753i	$-0.273703\pi$
$211$	22.1504	−	3.90571i	1.52490	−	0.268880i	0.872355	+	0.488873i	$0.162592\pi$
$212$	2.86802	−	2.40655i	0.196976	−	0.165283i
$213$		0			0
$214$	−3.79287	−	1.38049i	−0.259275	−	0.0943685i
$215$	2.42402	−	2.88883i	0.165317	−	0.197017i
$216$		0			0
$217$	0.0255470	−	0.0147496i	0.00173424	−	0.00100127i
$218$	16.3549	+	2.88380i	1.10769	+	0.195316i
$219$		0			0
$220$	7.45069	+	12.9050i	0.502325	+	0.870053i
$221$	1.82840	−	3.16688i	0.122991	−	0.213027i
$222$		0			0
$223$	6.46120	−	17.7520i	0.432674	−	1.18876i	−0.511491	−	0.859289i	$-0.670907\pi$
$223$	6.46120	−	17.7520i	0.432674	−	1.18876i	0.944165	−	0.329473i	$-0.106871\pi$
$224$	0.0191205	−	0.00695929i	0.00127754	−	0.000464987i
$225$		0			0
$226$	−3.18589	−	18.0681i	−0.211922	−	1.20187i
$227$	−16.7947			−1.11470			−0.557352	−	0.830277i	$-0.688182\pi$
$227$	−16.7947			−1.11470			−0.557352	+	0.830277i	$0.688182\pi$
$228$		0			0
$229$	−17.4594			−1.15375			−0.576875	−	0.816833i	$-0.695728\pi$
$229$	−17.4594			−1.15375			−0.576875	+	0.816833i	$0.695728\pi$
$230$	3.25816	+	18.4779i	0.214837	+	1.21840i
$231$		0			0
$232$	6.10541	−	2.22219i	0.400840	−	0.145894i
$233$	4.59539	−	12.6257i	0.301054	−	0.827139i	−0.693263	−	0.720684i	$-0.743828\pi$
$233$	4.59539	−	12.6257i	0.301054	−	0.827139i	0.994318	−	0.106455i	$-0.0339501\pi$
$234$		0			0
$235$	2.12342	−	3.67787i	0.138517	−	0.239918i
$236$	−2.83993	−	4.91889i	−0.184863	−	0.320193i
$237$		0			0
$238$	−0.0575260	−	0.0101434i	−0.00372886	−	0.000657498i
$239$	−3.16499	+	1.82731i	−0.204726	+	0.118199i	−0.598858	−	0.800855i	$-0.704379\pi$
$239$	−3.16499	+	1.82731i	−0.204726	+	0.118199i	0.394132	+	0.919054i	$0.371045\pi$
$240$		0			0
$241$	−14.2707	+	17.0072i	−0.919258	+	1.09553i	0.0758877	+	0.997116i	$0.475821\pi$
$241$	−14.2707	+	17.0072i	−0.919258	+	1.09553i	−0.995146	+	0.0984126i	$0.968624\pi$
$242$	−24.6452	−	8.97011i	−1.58425	−	0.576620i
$243$		0			0
$244$	9.70769	−	8.14572i	0.621471	−	0.521476i
$245$	−16.8354	+	2.96853i	−1.07557	+	0.189652i
$246$		0			0
$247$	−5.50859	−	0.695795i	−0.350503	−	0.0442724i
$248$		−	1.44976i		−	0.0920599i
$249$		0			0
$250$	6.33475	+	7.54946i	0.400645	+	0.477470i
$251$	9.50884	+	26.1253i	0.600193	+	1.64902i	0.750883	+	0.660435i	$0.229628\pi$
$251$	9.50884	+	26.1253i	0.600193	+	1.64902i	−0.150690	+	0.988581i	$0.548150\pi$
$252$		0			0
$253$	−35.9075	−	30.1300i	−2.25749	−	1.89426i
$254$	17.8652	+	10.3145i	1.12096	+	0.647186i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.21104	−	12.5394i	0.137921	−	0.782188i	−0.834860	−	0.550462i	$-0.814452\pi$
$257$	2.21104	−	12.5394i	0.137921	−	0.782188i	0.972781	−	0.231726i	$-0.0744372\pi$
$258$		0			0
$259$	0.0526760	+	0.0304125i	0.00327313	+	0.00188974i
$260$	2.38316	+	1.99971i	0.147797	+	0.124017i
$261$		0			0
$262$	−1.88422	−	5.17686i	−0.116408	−	0.319827i
$263$	11.2636	+	13.4234i	0.694543	+	0.827724i	0.991897	−	0.127043i	$-0.0405487\pi$
$263$	11.2636	+	13.4234i	0.694543	+	0.827724i	−0.297354	+	0.954767i	$0.596104\pi$
$264$		0			0
$265$		−	9.14379i		−	0.561699i
$266$	0.0196514	+	0.0864887i	0.00120491	+	0.00530296i
$267$		0			0
$268$	11.6339	−	2.05137i	0.710653	−	0.125307i
$269$	−14.6834	+	12.3208i	−0.895260	+	0.751213i	−0.969258	−	0.246046i	$-0.920869\pi$
$269$	−14.6834	+	12.3208i	−0.895260	+	0.751213i	0.0739977	+	0.997258i	$0.476424\pi$
$270$		0			0
$271$	−9.56064	−	3.47979i	−0.580767	−	0.211382i	0.0348964	−	0.999391i	$-0.488890\pi$
$271$	−9.56064	−	3.47979i	−0.580767	−	0.211382i	−0.615664	+	0.788009i	$0.711112\pi$
$272$	−1.84530	+	2.19914i	−0.111888	+	0.133343i
$273$		0			0
$274$	−11.6295	+	6.71428i	−0.702562	+	0.405625i
$275$	5.79726	+	1.02221i	0.349588	+	0.0616418i
$276$		0			0
$277$	−2.96103	−	5.12865i	−0.177911	−	0.308151i	0.763254	−	0.646099i	$-0.223601\pi$
$277$	−2.96103	−	5.12865i	−0.177911	−	0.308151i	−0.941165	+	0.337948i	$0.890267\pi$
$278$	1.17830	−	2.04087i	0.0706695	−	0.122403i
$279$		0			0
$280$	0.0169967	−	0.0466979i	0.00101574	−	0.00279073i
$281$	3.58403	−	1.30448i	0.213805	−	0.0778188i	−0.232897	−	0.972501i	$-0.574820\pi$
$281$	3.58403	−	1.30448i	0.213805	−	0.0778188i	0.446702	+	0.894683i	$0.352598\pi$
$282$		0			0
$283$	−3.22679	−	18.3000i	−0.191813	−	1.08782i	−0.916885	−	0.399152i	$-0.869305\pi$
$283$	−3.22679	−	18.3000i	−0.191813	−	1.08782i	0.725072	−	0.688673i	$-0.241806\pi$
$284$	−9.96879			−0.591539
$285$		0			0
$286$	−7.77193			−0.459564
$287$	0.0271206	+	0.153809i	0.00160088	+	0.00907903i
$288$		0			0
$289$	−8.23042	+	2.99563i	−0.484143	+	0.176213i
$290$	5.42724	−	14.9112i	0.318698	−	0.875617i
$291$		0			0
$292$	−3.87316	+	6.70851i	−0.226660	+	0.392586i
$293$	5.70300	+	9.87789i	0.333173	+	0.577072i	0.983132	−	0.182897i	$-0.0585474\pi$
$293$	5.70300	+	9.87789i	0.333173	+	0.577072i	−0.649959	+	0.759969i	$0.725214\pi$
$294$		0			0
$295$	−13.6611	−	2.40883i	−0.795382	−	0.140247i
$296$	2.58881	−	1.49465i	0.150471	−	0.0868746i
$297$		0			0
$298$	2.57443	−	3.06809i	0.149133	−	0.177730i
$299$	−9.19582	−	3.34700i	−0.531808	−	0.193562i
$300$		0			0
$301$	0.0240678	−	0.0201953i	0.00138725	−	0.00116404i
$302$	7.35282	−	1.29650i	0.423107	−	0.0746052i
$303$		0			0
$304$	4.16399	+	1.28889i	0.238821	+	0.0739227i
$305$		−	30.9500i		−	1.77219i
$306$		0			0
$307$	−16.7089	−	19.9128i	−0.953625	−	1.13649i	−0.990548	−	0.137168i	$-0.956200\pi$
$307$	−16.7089	−	19.9128i	−0.953625	−	1.13649i	0.0369228	−	0.999318i	$-0.488244\pi$
$308$	0.0424613	+	0.116661i	0.00241946	+	0.00664740i
$309$		0			0
$310$	−2.71237	−	2.27595i	−0.154052	−	0.129265i
$311$	−0.750899	−	0.433532i	−0.0425796	−	0.0245833i	0.478559	−	0.878055i	$-0.341159\pi$
$311$	−0.750899	−	0.433532i	−0.0425796	−	0.0245833i	−0.521139	+	0.853472i	$0.674493\pi$
$312$		0			0
$313$	2.58238	−	14.6454i	0.145965	−	0.827808i	−0.820623	−	0.571471i	$-0.806373\pi$
$313$	2.58238	−	14.6454i	0.145965	−	0.827808i	0.966587	−	0.256337i	$-0.0825158\pi$
$314$	3.33707	−	18.9255i	0.188322	−	1.06803i
$315$		0			0
$316$	−2.40999	−	1.39141i	−0.135572	−	0.0782727i
$317$	16.4493	+	13.8026i	0.923884	+	0.775231i	0.974709	−	0.223477i	$-0.0717407\pi$
$317$	16.4493	+	13.8026i	0.923884	+	0.775231i	−0.0508253	+	0.998708i	$0.516185\pi$
$318$		0			0
$319$	13.5584	+	37.2514i	0.759125	+	2.08568i
$320$	−1.56988	−	1.87091i	−0.0877589	−	0.104587i
$321$		0			0
$322$			0.156321i			0.00871142i
$323$	−8.50231	−	9.18132i	−0.473081	−	0.510862i
$324$		0			0
$325$	1.21031	−	0.213410i	0.0671358	−	0.0118378i
$326$	7.49048	−	6.28526i	0.414859	−	0.348108i
$327$		0			0
$328$	7.21276	+	2.62523i	0.398258	+	0.144954i
$329$	0.0227430	−	0.0271041i	0.00125386	−	0.00149430i
$330$		0			0
$331$	13.9946	−	8.07981i	0.769215	−	0.444106i	−0.0633796	−	0.997989i	$-0.520188\pi$
$331$	13.9946	−	8.07981i	0.769215	−	0.444106i	0.832594	+	0.553883i	$0.186855\pi$
$332$	5.33029	+	0.939874i	0.292538	+	0.0515823i
$333$		0			0
$334$	10.5581	+	18.2872i	0.577714	+	1.00063i
$335$	14.4259	−	24.9863i	0.788169	−	1.36515i
$336$		0			0
$337$	7.70971	−	21.1822i	0.419974	−	1.15387i	−0.531746	−	0.846904i	$-0.678464\pi$
$337$	7.70971	−	21.1822i	0.419974	−	1.15387i	0.951720	−	0.306966i	$-0.0993139\pi$
$338$	10.6913	−	3.89131i	0.581530	−	0.211659i
$339$		0			0
$340$	1.21750	+	6.90477i	0.0660281	+	0.374464i
$341$	8.84554			0.479013
$342$		0			0
$343$	−0.284858			−0.0153809
$344$	−0.268127	−	1.52062i	−0.0144564	−	0.0819865i
$345$		0			0
$346$	−3.98907	+	1.45190i	−0.214454	+	0.0780549i
$347$	8.98746	−	24.6928i	0.482472	−	1.32558i	−0.424895	−	0.905243i	$-0.639689\pi$
$347$	8.98746	−	24.6928i	0.482472	−	1.32558i	0.907367	−	0.420339i	$-0.138089\pi$
$348$		0			0
$349$	2.77887	−	4.81314i	0.148749	−	0.257642i	−0.782016	−	0.623258i	$-0.785809\pi$
$349$	2.77887	−	4.81314i	0.148749	−	0.257642i	0.930766	+	0.365617i	$0.119142\pi$
$350$	−0.00981582	−	0.0170015i	−0.000524678	−	0.000908768i
$351$		0			0
$352$	6.00869	+	1.05949i	0.320264	+	0.0564712i
$353$	−25.7793	+	14.8837i	−1.37209	+	0.792178i	−0.991191	−	0.132437i	$-0.957720\pi$
$353$	−25.7793	+	14.8837i	−1.37209	+	0.792178i	−0.380902	+	0.924616i	$0.624386\pi$
$354$		0			0
$355$	−15.6498	+	18.6507i	−0.830605	+	0.989876i
$356$	3.86623	+	1.40719i	0.204910	+	0.0745810i
$357$		0			0
$358$	16.7522	−	14.0568i	0.885383	−	0.742924i
$359$	7.94709	−	1.40129i	0.419431	−	0.0739571i	0.0400505	−	0.999198i	$-0.487248\pi$
$359$	7.94709	−	1.40129i	0.419431	−	0.0739571i	0.379381	+	0.925241i	$0.376137\pi$
$360$		0			0
$361$	−7.84835	+	17.3033i	−0.413071	+	0.910699i
$362$		−	7.73616i		−	0.406604i
$363$		0			0
$364$	0.0166603	+	0.0198549i	0.000873235	+	0.00104068i
$365$	6.47062	+	17.7779i	0.338688	+	0.930537i
$366$		0			0
$367$	−8.73891	−	7.33281i	−0.456167	−	0.382770i	0.385551	−	0.922686i	$-0.374011\pi$
$367$	−8.73891	−	7.33281i	−0.456167	−	0.382770i	−0.841718	+	0.539917i	$0.818456\pi$
$368$	6.65326	+	3.84126i	0.346825	+	0.200239i
$369$		0			0
$370$	1.26776	−	7.18983i	0.0659078	−	0.373782i
$371$	0.0132285	−	0.0750227i	0.000686791	−	0.00389498i
$372$		0			0
$373$	−28.0662	−	16.2040i	−1.45321	−	0.839013i	−0.454552	−	0.890720i	$-0.650200\pi$
$373$	−28.0662	−	16.2040i	−1.45321	−	0.839013i	−0.998662	+	0.0517071i	$0.983534\pi$
$374$	−13.4178	−	11.2589i	−0.693818	−	0.582183i
$375$		0			0
$376$	−0.594730	−	1.63401i	−0.0306708	−	0.0842674i
$377$	5.31982	+	6.33992i	0.273985	+	0.326522i
$378$		0			0
$379$			18.5750i			0.954135i	0.878867	+	0.477067i	$0.158300\pi$
$379$			18.5750i			0.954135i	−0.878867	+	0.477067i	$0.841700\pi$
$380$	8.94834	−	5.76704i	0.459040	−	0.295843i
$381$		0			0
$382$	−2.07679	+	0.366194i	−0.106258	+	0.0187361i
$383$	−21.6354	+	18.1543i	−1.10552	+	0.927640i	−0.997784	−	0.0665398i	$-0.978804\pi$
$383$	−21.6354	+	18.1543i	−1.10552	+	0.927640i	−0.107734	+	0.994180i	$0.534360\pi$
$384$		0			0
$385$	0.284922	+	0.103703i	0.0145210	+	0.00528520i
$386$	3.66151	−	4.36361i	0.186366	−	0.222102i
$387$		0			0
$388$	−11.8773	+	6.85737i	−0.602979	+	0.348130i
$389$	15.9183	+	2.80682i	0.807088	+	0.142311i	0.561944	−	0.827175i	$-0.310054\pi$
$389$	15.9183	+	2.80682i	0.807088	+	0.142311i	0.245144	+	0.969487i	$0.421165\pi$
$390$		0			0
$391$	−11.0274	−	19.1000i	−0.557680	−	0.965930i
$392$	−3.49979	+	6.06182i	−0.176766	+	0.306168i
$393$		0			0
$394$	5.96092	−	16.3775i	0.300307	−	0.825086i
$395$	−6.38658	+	2.32452i	−0.321344	+	0.116959i
$396$		0			0
$397$	2.84571	+	16.1388i	0.142822	+	0.809986i	0.969090	+	0.246708i	$0.0793488\pi$
$397$	2.84571	+	16.1388i	0.142822	+	0.809986i	−0.826268	+	0.563278i	$0.809540\pi$
$398$	12.8111			0.642161
$399$		0			0
$400$	−0.964813			−0.0482407
$401$	−1.08648	−	6.16175i	−0.0542564	−	0.307703i	0.945588	−	0.325368i	$-0.105488\pi$
$401$	−1.08648	−	6.16175i	−0.0542564	−	0.307703i	−0.999844	+	0.0176644i	$0.994377\pi$
$402$		0			0
$403$	1.73533	−	0.631610i	0.0864432	−	0.0314627i
$404$	−5.19781	+	14.2809i	−0.258601	+	0.710500i
$405$		0			0
$406$	0.0661016	−	0.114491i	0.00328057	−	0.00568211i
$407$	9.11941	+	15.7953i	0.452033	+	0.782943i
$408$		0			0
$409$	25.1955	+	4.44265i	1.24584	+	0.219675i	0.757416	−	0.652932i	$-0.226461\pi$
$409$	25.1955	+	4.44265i	1.24584	+	0.219675i	0.488422	+	0.872607i	$0.337573\pi$
$410$	16.2347	−	9.37312i	0.801776	−	0.462905i
$411$		0			0
$412$	−3.30752	+	3.94175i	−0.162950	+	0.194196i
$413$	−0.108602	−	0.0395277i	−0.00534393	−	0.00194503i
$414$		0			0
$415$	10.1263	−	8.49700i	0.497082	−	0.417101i
$416$	1.25445	−	0.221193i	0.0615043	−	0.0108449i
$417$		0			0
$418$	−7.86398	+	25.4061i	−0.384640	+	1.24265i
$419$		−	10.5624i		−	0.516008i	−0.966144	−	0.258004i	$-0.916935\pi$
$419$		−	10.5624i		−	0.516008i	0.966144	−	0.258004i	$-0.0830647\pi$
$420$		0			0
$421$	−2.78319	−	3.31687i	−0.135644	−	0.161654i	0.693946	−	0.720027i	$-0.255871\pi$
$421$	−2.78319	−	3.31687i	−0.135644	−	0.161654i	−0.829590	+	0.558372i	$0.811426\pi$
$422$	−7.69275	−	21.1357i	−0.374477	−	1.02887i
$423$		0			0
$424$	−2.86802	−	2.40655i	−0.139283	−	0.116873i
$425$	2.39869	+	1.38488i	0.116353	+	0.0671767i
$426$		0			0
$427$	0.0447760	−	0.253937i	0.00216686	−	0.0122889i
$428$	−0.700894	+	3.97497i	−0.0338790	+	0.192137i
$429$		0			0
$430$	−3.26587	−	1.88555i	−0.157494	−	0.0909293i
$431$	−16.2265	−	13.6157i	−0.781604	−	0.655843i	0.162048	−	0.986783i	$-0.448190\pi$
$431$	−16.2265	−	13.6157i	−0.781604	−	0.655843i	−0.943652	+	0.330939i	$0.892634\pi$
$432$		0			0
$433$	−5.84623	−	16.0624i	−0.280952	−	0.771908i	−0.997250	−	0.0741140i	$-0.976387\pi$
$433$	−5.84623	−	16.0624i	−0.280952	−	0.771908i	0.716298	−	0.697794i	$-0.245835\pi$
$434$	−0.0189617	−	0.0225977i	−0.000910190	−	0.00108472i
$435$		0			0
$436$		−	16.6072i		−	0.795339i
$437$	−20.2459	+	26.6740i	−0.968494	+	1.27599i
$438$		0			0
$439$	31.6170	−	5.57492i	1.50900	−	0.266077i	0.642898	−	0.765952i	$-0.277732\pi$
$439$	31.6170	−	5.57492i	1.50900	−	0.266077i	0.866097	+	0.499875i	$0.166621\pi$
$440$	11.4151	−	9.57842i	0.544195	−	0.456633i
$441$		0			0
$442$	−3.43626	−	1.25070i	−0.163446	−	0.0594896i
$443$	7.04087	−	8.39098i	0.334522	−	0.398668i	−0.572394	−	0.819978i	$-0.693985\pi$
$443$	7.04087	−	8.39098i	0.334522	−	0.398668i	0.906916	+	0.421311i	$0.138430\pi$
$444$		0			0
$445$	8.70224	−	5.02424i	0.412526	−	0.238172i
$446$	−18.6043	−	3.28044i	−0.880938	−	0.155333i
$447$		0			0
$448$	−0.0101738	−	0.0176215i	−0.000480667	−	0.000832540i
$449$	1.67766	−	2.90580i	0.0791738	−	0.137133i	−0.823720	−	0.566997i	$-0.808105\pi$
$449$	1.67766	−	2.90580i	0.0791738	−	0.137133i	0.902894	+	0.429864i	$0.141438\pi$
$450$		0			0
$451$	−16.0175	+	44.0078i	−0.754236	+	2.07225i
$452$	−17.2403	+	6.27497i	−0.810918	+	0.295150i
$453$		0			0
$454$	2.91637	+	16.5395i	0.136872	+	0.776239i
$455$	0.0633013			0.00296761
$456$		0			0
$457$	−12.7981			−0.598671			−0.299336	−	0.954148i	$-0.596765\pi$
$457$	−12.7981			−0.598671			−0.299336	+	0.954148i	$0.596765\pi$
$458$	3.03179	+	17.1942i	0.141666	+	0.803430i
$459$		0			0
$460$	17.6314	−	6.41732i	0.822070	−	0.299209i
$461$	−13.8786	+	38.1313i	−0.646393	+	1.77595i	−0.0157503	+	0.999876i	$0.505014\pi$
$461$	−13.8786	+	38.1313i	−0.646393	+	1.77595i	−0.630642	+	0.776074i	$0.717209\pi$
$462$		0			0
$463$	13.6991	−	23.7275i	0.636649	−	1.10271i	−0.349514	−	0.936931i	$-0.613653\pi$
$463$	13.6991	−	23.7275i	0.636649	−	1.10271i	0.986163	−	0.165778i	$-0.0530135\pi$
$464$	−3.24862	−	5.62677i	−0.150813	−	0.261216i
$465$		0			0
$466$	−13.2319	−	2.33314i	−0.612956	−	0.108081i
$467$	−10.1512	+	5.86079i	−0.469741	+	0.271205i	−0.716131	−	0.697966i	$-0.754089\pi$
$467$	−10.1512	+	5.86079i	−0.469741	+	0.271205i	0.246390	+	0.969171i	$0.420755\pi$
$468$		0			0
$469$	0.154509	−	0.184137i	0.00713457	−	0.00850265i
$470$	−3.99073	−	1.45251i	−0.184079	−	0.0669991i
$471$		0			0
$472$	−4.35102	+	3.65094i	−0.200272	+	0.168048i
$473$	9.27789	−	1.63594i	0.426598	−	0.0752207i
$474$		0			0
$475$	0.527016	−	4.17237i	0.0241811	−	0.191442i
$476$			0.0584134i			0.00267738i
$477$		0			0
$478$	2.34914	+	2.79959i	0.107447	+	0.128050i
$479$	−6.75889	−	18.5699i	−0.308822	−	0.848480i	−0.992887	−	0.119060i	$-0.962012\pi$
$479$	−6.75889	−	18.5699i	−0.308822	−	0.848480i	0.684065	−	0.729421i	$-0.260210\pi$
$480$		0			0
$481$	2.91692	+	2.44758i	0.133000	+	0.111600i
$482$	19.2269	+	11.1007i	0.875761	+	0.505621i
$483$		0			0
$484$	−4.55424	+	25.8284i	−0.207011	+	1.17402i
$485$	−5.81643	+	32.9866i	−0.264110	+	1.49784i
$486$		0			0
$487$	19.6656	+	11.3539i	0.891132	+	0.514495i	0.874313	−	0.485363i	$-0.161313\pi$
$487$	19.6656	+	11.3539i	0.891132	+	0.514495i	0.0168195	+	0.999859i	$0.494646\pi$
$488$	−9.70769	−	8.14572i	−0.439446	−	0.368739i
$489$		0			0
$490$	5.84686	+	16.0641i	0.264134	+	0.725702i
$491$	−0.0135702	−	0.0161723i	−0.000612414	−	0.000729847i	0.765738	−	0.643152i	$-0.222374\pi$
$491$	−0.0135702	−	0.0161723i	−0.000612414	−	0.000729847i	−0.766351	+	0.642423i	$0.777929\pi$
$492$		0			0
$493$			18.6521i			0.840050i
$494$	0.271333	+	5.54573i	0.0122078	+	0.249514i
$495$		0			0
$496$	−1.42774	+	0.251748i	−0.0641072	+	0.0113038i
$497$	−0.155385	+	0.130384i	−0.00696998	+	0.00584851i
$498$		0			0
$499$	10.8850	+	3.96180i	0.487277	+	0.177354i	0.573963	−	0.818881i	$-0.305405\pi$
$499$	10.8850	+	3.96180i	0.487277	+	0.177354i	−0.0866856	+	0.996236i	$0.527628\pi$
$500$	6.33475	−	7.54946i	0.283299	−	0.337622i
$501$		0			0
$502$	24.0772	−	13.9010i	1.07462	−	0.620432i
$503$	13.2239	+	2.33174i	0.589626	+	0.103967i	0.460498	−	0.887661i	$-0.347671\pi$
$503$	13.2239	+	2.33174i	0.589626	+	0.103967i	0.129128	+	0.991628i	$0.458782\pi$
$504$		0			0
$505$	18.5583	+	32.1439i	0.825832	+	1.43038i
$506$	−23.4370	+	40.5940i	−1.04190	+	1.80463i
$507$		0			0
$508$	7.05550	−	19.3848i	0.313037	−	0.860063i
$509$	−8.88464	+	3.23375i	−0.393805	+	0.143333i	−0.531330	−	0.847165i	$-0.678307\pi$
$509$	−8.88464	+	3.23375i	−0.393805	+	0.143333i	0.137525	+	0.990498i	$0.456085\pi$
$510$		0			0
$511$	0.0273703	+	0.155225i	0.00121079	+	0.00686673i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−12.7329			−0.561623
$515$	2.18225	+	12.3761i	0.0961612	+	0.545357i
$516$		0			0
$517$	9.96969	−	3.62867i	0.438467	−	0.159589i
$518$	0.0208034	−	0.0571568i	0.000914048	−	0.00251133i
$519$		0			0
$520$	1.55550	−	2.69420i	0.0682131	−	0.118149i
$521$	−14.8897	−	25.7897i	−0.652329	−	1.12987i	−0.982556	−	0.185965i	$-0.940459\pi$
$521$	−14.8897	−	25.7897i	−0.652329	−	1.12987i	0.330228	−	0.943901i	$-0.392875\pi$
$522$		0			0
$523$	−24.2618	−	4.27802i	−1.06090	−	0.187065i	−0.384142	−	0.923274i	$-0.625503\pi$
$523$	−24.2618	−	4.27802i	−1.06090	−	0.187065i	−0.676754	+	0.736209i	$0.736614\pi$
$524$	−4.77102	+	2.75455i	−0.208423	+	0.120333i
$525$		0			0
$526$	11.2636	−	13.4234i	0.491116	−	0.585289i
$527$	3.91095	+	1.42347i	0.170363	+	0.0620072i
$528$		0			0
$529$	−27.5938	+	23.1539i	−1.19973	+	1.00669i
$530$	−9.00488	+	1.58780i	−0.391147	+	0.0689697i
$531$		0			0
$532$	0.0817623	−	0.0343715i	0.00354485	−	0.00149019i
$533$			9.77725i			0.423500i
$534$		0			0
$535$	6.33648	+	7.55153i	0.273950	+	0.326481i
$536$	−4.04041	−	11.1009i	−0.174519	−	0.479487i
$537$		0			0
$538$	14.6834	+	12.3208i	0.633045	+	0.531188i
$539$	−36.9855	−	21.3536i	−1.59308	−	0.919763i
$540$		0			0
$541$	7.68683	−	43.5942i	0.330482	−	1.87426i	−0.137471	−	0.990506i	$-0.543897\pi$
$541$	7.68683	−	43.5942i	0.330482	−	1.87426i	0.467953	−	0.883753i	$-0.344992\pi$
$542$	−1.76673	+	10.0196i	−0.0758877	+	0.430381i
$543$		0			0
$544$	2.48617	+	1.43539i	0.106594	+	0.0615418i
$545$	−31.0705	−	26.0712i	−1.33091	−	1.11677i
$546$		0			0
$547$	2.87573	+	7.90099i	0.122957	+	0.337822i	0.985866	−	0.167538i	$-0.0535818\pi$
$547$	2.87573	+	7.90099i	0.122957	+	0.337822i	−0.862908	+	0.505360i	$0.831360\pi$
$548$	8.63171	+	10.2869i	0.368729	+	0.439434i
$549$		0			0
$550$		−	5.88669i		−	0.251009i
$551$	26.1077	−	10.9752i	1.11223	−	0.467560i
$552$		0			0
$553$	−0.0557633	+	0.00983258i	−0.00237130	+	0.000418124i
$554$	−4.53656	+	3.80662i	−0.192740	+	0.161728i
$555$		0			0
$556$	−2.21447	−	0.806001i	−0.0939145	−	0.0341821i
$557$	−3.05066	+	3.63563i	−0.129261	+	0.154047i	−0.826793	−	0.562507i	$-0.809837\pi$
$557$	−3.05066	+	3.63563i	−0.129261	+	0.154047i	0.697532	+	0.716554i	$0.254281\pi$
$558$		0			0
$559$	1.70334	−	0.983424i	0.0720436	−	0.0415944i
$560$	−0.0489399	−	0.00862943i	−0.00206809	−	0.000364660i
$561$		0			0
$562$	−1.90702	−	3.30306i	−0.0804429	−	0.139331i
$563$	13.1641	−	22.8009i	0.554801	−	0.960943i	−0.443118	−	0.896463i	$-0.646128\pi$
$563$	13.1641	−	22.8009i	0.554801	−	0.960943i	0.997919	−	0.0644797i	$-0.0205388\pi$
$564$		0			0
$565$	−15.3253	+	42.1060i	−0.644742	+	1.77141i
$566$	−17.4617	+	6.35554i	−0.733970	+	0.267143i
$567$		0			0
$568$	1.73106	+	9.81735i	0.0726338	+	0.411927i
$569$	−7.96586			−0.333946			−0.166973	−	0.985961i	$-0.553399\pi$
$569$	−7.96586			−0.333946			−0.166973	+	0.985961i	$0.553399\pi$
$570$		0			0
$571$	30.6064			1.28084			0.640420	−	0.768025i	$-0.278760\pi$
$571$	30.6064			1.28084			0.640420	+	0.768025i	$0.278760\pi$
$572$	1.34958	+	7.65386i	0.0564289	+	0.320024i
$573$		0			0
$574$	0.146762	−	0.0534172i	0.00612575	−	0.00222959i
$575$	2.53512	−	6.96519i	0.105722	−	0.290468i
$576$		0			0
$577$	−0.694063	+	1.20215i	−0.0288942	+	0.0500463i	−0.880111	−	0.474768i	$-0.842532\pi$
$577$	−0.694063	+	1.20215i	−0.0288942	+	0.0500463i	0.851217	+	0.524814i	$0.175865\pi$
$578$	4.37932	+	7.58520i	0.182156	+	0.315503i
$579$		0			0
$580$	−15.6271	−	2.75548i	−0.648880	−	0.114415i
$581$	0.0953770	−	0.0550659i	0.00395690	−	0.00228452i
$582$		0			0
$583$	14.6833	−	17.4989i	0.608120	−	0.724729i
$584$	7.27916	+	2.64940i	0.301214	+	0.109633i
$585$		0			0
$586$	8.73750	−	7.33164i	0.360943	−	0.302867i
$587$	33.7351	−	5.94841i	1.39240	−	0.245517i	0.573381	−	0.819289i	$-0.305631\pi$
$587$	33.7351	−	5.94841i	1.39240	−	0.245517i	0.819015	+	0.573772i	$0.194520\pi$
$588$		0			0
$589$	−0.308814	−	6.31181i	−0.0127245	−	0.260074i
$590$			13.8719i			0.571096i
$591$		0			0
$592$	−1.92148	−	2.28993i	−0.0789724	−	0.0941157i
$593$	0.566476	+	1.55638i	0.0232624	+	0.0639128i	0.950780	−	0.309866i	$-0.100284\pi$
$593$	0.566476	+	1.55638i	0.0232624	+	0.0639128i	−0.927518	+	0.373779i	$0.878062\pi$
$594$		0			0
$595$	0.109286	+	0.0917020i	0.00448030	+	0.00375941i
$596$	−3.46852	−	2.00255i	−0.142076	−	0.0820277i
$597$		0			0
$598$	−1.69932	+	9.63732i	−0.0694903	+	0.394099i
$599$	−5.67102	+	32.1620i	−0.231712	+	1.31410i	0.617718	+	0.786400i	$0.288057\pi$
$599$	−5.67102	+	32.1620i	−0.231712	+	1.31410i	−0.849429	+	0.527702i	$0.823054\pi$
$600$		0			0
$601$	14.9612	+	8.63787i	0.610281	+	0.352346i	0.773076	−	0.634314i	$-0.218717\pi$
$601$	14.9612	+	8.63787i	0.610281	+	0.352346i	−0.162794	+	0.986660i	$0.552051\pi$
$602$	−0.0240678	−	0.0201953i	−0.000980932	−	0.000823100i
$603$		0			0
$604$	−2.55361	−	7.01598i	−0.103905	−	0.285476i
$605$	41.1729	+	49.0680i	1.67392	+	1.99490i
$606$		0			0
$607$			6.78195i			0.275271i	0.990483	+	0.137635i	$0.0439503\pi$
$607$			6.78195i			0.275271i	−0.990483	+	0.137635i	$0.956050\pi$
$608$	0.546236	−	4.32454i	0.0221528	−	0.175383i
$609$		0			0
$610$	−30.4798	+	5.37441i	−1.23409	+	0.217603i
$611$	1.69677	−	1.42376i	0.0686439	−	0.0575991i
$612$		0			0
$613$	−1.20794	−	0.439656i	−0.0487884	−	0.0177575i	0.317511	−	0.948255i	$-0.397153\pi$
$613$	−1.20794	−	0.439656i	−0.0487884	−	0.0177575i	−0.366299	+	0.930497i	$0.619375\pi$
$614$	−16.7089	+	19.9128i	−0.674315	+	0.803617i
$615$		0			0
$616$	0.107516	−	0.0620742i	0.00433193	−	0.00250104i
$617$	−14.4229	−	2.54315i	−0.580644	−	0.102383i	−0.124391	−	0.992233i	$-0.539698\pi$
$617$	−14.4229	−	2.54315i	−0.580644	−	0.102383i	−0.456253	+	0.889850i	$0.650809\pi$
$618$		0			0
$619$	2.89004	+	5.00570i	0.116161	+	0.201196i	0.918243	−	0.396017i	$-0.129608\pi$
$619$	2.89004	+	5.00570i	0.116161	+	0.201196i	−0.802083	+	0.597213i	$0.796275\pi$
$620$	−1.77037	+	3.06638i	−0.0710999	+	0.123149i
$621$		0			0
$622$	−0.296553	+	0.814773i	−0.0118907	+	0.0326694i
$623$	0.0786685	−	0.0286330i	0.00315179	−	0.00114716i
$624$		0			0
$625$	−5.01725	−	28.4542i	−0.200690	−	1.13817i
$626$	−14.8713			−0.594378
$627$		0			0
$628$	−19.2174			−0.766858
$629$	1.49018	+	8.45123i	0.0594174	+	0.336973i
$630$		0			0
$631$	−16.9376	+	6.16479i	−0.674276	+	0.245416i	−0.656388	−	0.754424i	$-0.727917\pi$
$631$	−16.9376	+	6.16479i	−0.674276	+	0.245416i	−0.0178881	+	0.999840i	$0.505694\pi$
$632$	−0.951778	+	2.61499i	−0.0378597	+	0.104019i
$633$		0			0
$634$	10.7365	−	18.5962i	0.426401	−	0.738549i
$635$	−25.1910	−	43.6320i	−0.999672	−	1.73148i
$636$		0			0
$637$	−8.78061	−	1.54826i	−0.347901	−	0.0613443i
$638$	34.3311	−	19.8211i	1.35918	−	0.784723i
$639$		0			0
$640$	−1.56988	+	1.87091i	−0.0620549	+	0.0739541i
$641$	41.8885	+	15.2462i	1.65450	+	0.602187i	0.989484	−	0.144645i	$-0.0462041\pi$
$641$	41.8885	+	15.2462i	1.65450	+	0.602187i	0.665012	+	0.746833i	$0.268426\pi$
$642$		0			0
$643$	−21.4718	+	18.0170i	−0.846766	+	0.710521i	−0.959075	−	0.283152i	$-0.908620\pi$
$643$	−21.4718	+	18.0170i	−0.846766	+	0.710521i	0.112309	+	0.993673i	$0.464175\pi$
$644$	0.153946	−	0.0271448i	0.00606632	−	0.00106966i
$645$		0			0
$646$	−7.56543	+	9.96746i	−0.297658	+	0.392164i
$647$		−	19.0706i		−	0.749741i	−0.927077	−	0.374871i	$-0.877687\pi$
$647$		−	19.0706i		−	0.749741i	0.927077	−	0.374871i	$-0.122313\pi$
$648$		0			0
$649$	−22.2758	−	26.5472i	−0.874400	−	1.04207i
$650$	−0.420335	−	1.15486i	−0.0164869	−	0.0452974i
$651$		0			0
$652$	−7.49048	−	6.28526i	−0.293350	−	0.246150i
$653$	−22.8083	−	13.1684i	−0.892558	−	0.515318i	−0.0177795	−	0.999842i	$-0.505660\pi$
$653$	−22.8083	−	13.1684i	−0.892558	−	0.515318i	−0.874778	+	0.484523i	$0.838993\pi$
$654$		0			0
$655$	−2.33641	+	13.2504i	−0.0912911	+	0.517737i
$656$	1.33286	−	7.55905i	0.0520396	−	0.295131i
$657$		0			0
$658$	−0.0306416	−	0.0176909i	−0.00119453	−	0.000689665i
$659$	22.7353	+	19.0771i	0.885640	+	0.743140i	0.967331	−	0.253518i	$-0.0815876\pi$
$659$	22.7353	+	19.0771i	0.885640	+	0.743140i	−0.0816908	+	0.996658i	$0.526032\pi$
$660$		0			0
$661$	8.23095	+	22.6144i	0.320147	+	0.879597i	0.990495	+	0.137550i	$0.0439227\pi$
$661$	8.23095	+	22.6144i	0.320147	+	0.879597i	−0.670348	+	0.742047i	$0.733855\pi$
$662$	−10.3872	−	12.3790i	−0.403710	−	0.481123i
$663$		0			0
$664$		−	5.41252i		−	0.210047i
$665$	0.0640510	−	0.206929i	0.00248379	−	0.00802435i
$666$		0			0
$667$	49.1568	−	8.66767i	1.90336	−	0.335614i
$668$	16.1759	−	13.5732i	0.625866	−	0.525164i
$669$		0			0
$670$	−27.1118	−	9.86788i	−1.04742	−	0.381229i
$671$	49.7001	−	59.2303i	1.91865	−	2.28656i
$672$		0			0
$673$	35.6937	−	20.6078i	1.37589	−	0.794372i	0.384230	−	0.923237i	$-0.374467\pi$
$673$	35.6937	−	20.6078i	1.37589	−	0.794372i	0.991662	+	0.128866i	$0.0411337\pi$
$674$	−22.1992	−	3.91432i	−0.855082	−	0.150774i
$675$		0			0
$676$	−5.68872	−	9.85315i	−0.218797	−	0.378967i
$677$	13.5658	−	23.4966i	0.521375	−	0.903047i	−0.478316	−	0.878188i	$-0.658753\pi$
$677$	13.5658	−	23.4966i	0.521375	−	0.903047i	0.999691	−	0.0248597i	$-0.00791391\pi$
$678$		0			0
$679$	−0.0954449	+	0.262233i	−0.00366284	+	0.0100636i
$680$	6.58846	−	2.39800i	0.252656	−	0.0919592i
$681$		0			0
$682$	−1.53601	−	8.71116i	−0.0588170	−	0.333568i
$683$	3.44331			0.131754			0.0658772	−	0.997828i	$-0.479015\pi$
$683$	3.44331			0.131754			0.0658772	+	0.997828i	$0.479015\pi$
$684$		0			0
$685$	32.7965			1.25309
$686$	0.0494651	+	0.280530i	0.00188859	+	0.0107107i
$687$		0			0
$688$	−1.45096	+	0.528107i	−0.0553174	+	0.0201339i
$689$	1.63110	−	4.48141i	0.0621400	−	0.170728i
$690$		0			0
$691$	3.20635	−	5.55356i	0.121975	−	0.211267i	−0.798571	−	0.601900i	$-0.794410\pi$
$691$	3.20635	−	5.55356i	0.121975	−	0.211267i	0.920547	+	0.390633i	$0.127744\pi$
$692$	2.12254	+	3.67635i	0.0806869	+	0.139754i
$693$		0			0
$694$	−25.8784	−	4.56305i	−0.982329	−	0.173211i
$695$	−4.98440	+	2.87775i	−0.189069	+	0.109159i
$696$		0			0
$697$	−14.1639	+	16.8799i	−0.536496	+	0.639371i
$698$	−5.22256	−	1.90086i	−0.197677	−	0.0719485i
$699$		0			0
$700$	−0.0150387	+	0.0126190i	−0.000568410	+	0.000476952i
$701$	9.07247	−	1.59972i	0.342662	−	0.0604206i	0.000331154	−	1.00000i	$-0.499895\pi$
$701$	9.07247	−	1.59972i	0.342662	−	0.0604206i	0.342331	+	0.939579i	$0.388783\pi$
$702$		0			0
$703$	10.9525	−	7.05868i	0.413081	−	0.266223i
$704$		−	6.10138i		−	0.229954i
$705$		0			0
$706$	19.1341	+	22.8031i	0.720121	+	0.858207i
$707$	0.105763	+	0.290582i	0.00397763	+	0.0109284i
$708$		0			0
$709$	−17.3395	−	14.5496i	−0.651199	−	0.546421i	0.256236	−	0.966614i	$-0.417518\pi$
$709$	−17.3395	−	14.5496i	−0.651199	−	0.546421i	−0.907434	+	0.420194i	$0.861962\pi$
$710$	21.0849	+	12.1734i	0.791302	+	0.456859i
$711$		0			0
$712$	0.714450	−	4.05185i	0.0267752	−	0.151849i
$713$	1.93406	−	10.9686i	0.0724312	−	0.410778i
$714$		0			0
$715$	16.4383	+	9.49069i	0.614759	+	0.354932i
$716$	−16.7522	−	14.0568i	−0.626060	−	0.525327i
$717$		0			0
$718$	−2.76000	−	7.58302i	−0.103002	−	0.282996i
$719$	−24.6339	−	29.3575i	−0.918690	−	1.09485i	−0.995208	−	0.0977835i	$-0.968825\pi$
$719$	−24.6339	−	29.3575i	−0.918690	−	1.09485i	0.0765181	−	0.997068i	$-0.475620\pi$
$720$		0			0
$721$			0.104700i			0.00389925i
$722$	18.4033	+	4.72444i	0.684898	+	0.175825i
$723$		0			0
$724$	−7.61863	+	1.34337i	−0.283144	+	0.0499260i
$725$	−4.80204	+	4.02939i	−0.178343	+	0.149648i
$726$		0			0
$727$	−19.1993	−	6.98799i	−0.712064	−	0.259170i	−0.0395110	−	0.999219i	$-0.512580\pi$
$727$	−19.1993	−	6.98799i	−0.712064	−	0.259170i	−0.672553	+	0.740049i	$0.734802\pi$
$728$	0.0166603	−	0.0198549i	0.000617470	−	0.000735872i
$729$		0			0
$730$	16.3842	−	9.45941i	0.606406	−	0.350109i
$731$	4.36537	+	0.769732i	0.161459	+	0.0284696i
$732$		0			0
$733$	−17.7516	−	30.7467i	−0.655671	−	1.13566i	−0.981725	−	0.190305i	$-0.939052\pi$
$733$	−17.7516	−	30.7467i	−0.655671	−	1.13566i	0.326054	−	0.945351i	$-0.394281\pi$
$734$	−5.70392	+	9.87947i	−0.210535	+	0.364658i
$735$		0			0
$736$	2.62758	−	7.21921i	0.0968537	−	0.266103i
$737$	67.7310	−	24.6521i	2.49490	−	0.908071i
$738$		0			0
$739$	2.82554	+	16.0245i	0.103939	+	0.589469i	0.991639	+	0.129046i	$0.0411913\pi$
$739$	2.82554	+	16.0245i	0.103939	+	0.589469i	−0.887699	+	0.460424i	$0.847698\pi$
$740$	−7.30075			−0.268381
$741$		0			0
$742$	−0.0761800			−0.00279666
$743$	−2.27791	−	12.9187i	−0.0835683	−	0.473939i	−0.997656	−	0.0684236i	$-0.978203\pi$
$743$	−2.27791	−	12.9187i	−0.0835683	−	0.473939i	0.914088	−	0.405516i	$-0.132908\pi$
$744$		0			0
$745$	−9.19174	+	3.34552i	−0.336759	+	0.122570i
$746$	−11.0842	+	30.4536i	−0.405822	+	1.11499i
$747$		0			0
$748$	−8.75785	+	15.1690i	−0.320219	+	0.554635i
$749$	0.0410644	+	0.0711256i	0.00150046	+	0.00259887i
$750$		0			0
$751$	−13.1476	−	2.31827i	−0.479761	−	0.0845948i	−0.0714626	−	0.997443i	$-0.522767\pi$
$751$	−13.1476	−	2.31827i	−0.479761	−	0.0845948i	−0.408299	+	0.912848i	$0.633878\pi$
$752$	−1.50591	+	0.869436i	−0.0549148	+	0.0317051i
$753$		0			0
$754$	5.31982	−	6.33992i	0.193737	−	0.230886i
$755$	−17.1351	−	6.23667i	−0.623610	−	0.226976i
$756$		0			0
$757$	−21.2678	+	17.8458i	−0.772993	+	0.648618i	−0.941474	−	0.337087i	$-0.890558\pi$
$757$	−21.2678	+	17.8458i	−0.772993	+	0.648618i	0.168481	+	0.985705i	$0.446114\pi$
$758$	18.2928	−	3.22552i	0.664425	−	0.117156i
$759$		0			0
$760$	−7.23329	−	7.81095i	−0.262379	−	0.283333i
$761$		−	7.21941i		−	0.261703i	−0.991402	−	0.130852i	$-0.958229\pi$
$761$		−	7.21941i		−	0.261703i	0.991402	−	0.130852i	$-0.0417712\pi$
$762$		0			0
$763$	−0.217208	−	0.258859i	−0.00786346	−	0.00937131i
$764$	0.721262	+	1.98165i	0.0260943	+	0.0716936i
$765$		0			0
$766$	21.6354	+	18.1543i	0.781719	+	0.655941i
$767$	−6.26569	−	3.61750i	−0.226241	−	0.130620i
$768$		0			0
$769$	1.19345	−	6.76838i	0.0430368	−	0.244074i	−0.955699	−	0.294347i	$-0.904898\pi$
$769$	1.19345	−	6.76838i	0.0430368	−	0.244074i	0.998736	+	0.0502727i	$0.0160091\pi$
$770$	0.0526514	−	0.298601i	0.00189743	−	0.0107608i
$771$		0			0
$772$	−4.93314	−	2.84815i	−0.177547	−	0.102507i
$773$	−6.97998	−	5.85689i	−0.251052	−	0.210658i	0.508573	−	0.861019i	$-0.330173\pi$
$773$	−6.97998	−	5.85689i	−0.251052	−	0.210658i	−0.759625	+	0.650361i	$0.774618\pi$
$774$		0			0
$775$	0.478400	+	1.31439i	0.0171846	+	0.0472144i
$776$	8.81567	+	10.5061i	0.316464	+	0.377147i
$777$		0			0
$778$		−	16.1638i		−	0.579501i
$779$	31.9613	+	9.89305i	1.14513	+	0.354455i
$780$		0			0
$781$	−59.8994	+	10.5619i	−2.14337	+	0.377934i
$782$	−16.8950	+	14.1766i	−0.604163	+	0.506953i
$783$		0			0
$784$	6.57746	+	2.39400i	0.234909	+	0.0855000i
$785$	−30.1690	+	35.9540i	−1.07678	+	1.28325i
$786$		0			0
$787$	−31.4055	+	18.1320i	−1.11948	+	0.646334i	−0.941269	−	0.337657i	$-0.890365\pi$
$787$	−31.4055	+	18.1320i	−1.11948	+	0.646334i	−0.178215	+	0.983992i	$0.557032\pi$
$788$	−17.1638	−	3.02644i	−0.611435	−	0.107812i
$789$		0			0
$790$	3.39823	+	5.88590i	0.120903	+	0.209411i
$791$	−0.186657	+	0.323299i	−0.00663675	+	0.0114952i
$792$		0			0
$793$	5.52096	−	15.1687i	0.196055	−	0.538657i
$794$	15.3995	−	5.60496i	0.546508	−	0.198913i
$795$		0			0
$796$	−2.22462	−	12.6164i	−0.0788496	−	0.447178i
$797$	31.1778			1.10438			0.552188	−	0.833720i	$-0.313793\pi$
$797$	31.1778			1.10438			0.552188	+	0.833720i	$0.313793\pi$
$798$		0			0
$799$	4.99192			0.176601
$800$	0.167538	+	0.950156i	0.00592336	+	0.0335931i
$801$		0			0
$802$	−5.87948	+	2.13996i	−0.207612	+	0.0755644i
$803$	−16.1650	+	44.4129i	−0.570450	+	1.56730i
$804$		0			0
$805$	0.190891	−	0.330633i	0.00672802	−	0.0116533i
$806$	−0.923352	−	1.59929i	−0.0325237	−	0.0563327i
$807$		0			0
$808$	14.9665	+	2.63900i	0.526520	+	0.0928397i
$809$	−37.5328	+	21.6696i	−1.31958	+	0.761861i	−0.983661	−	0.180029i	$-0.942381\pi$
$809$	−37.5328	+	21.6696i	−1.31958	+	0.761861i	−0.335921	+	0.941890i	$0.609047\pi$
$810$		0			0
$811$	30.9034	−	36.8293i	1.08517	−	1.29325i	0.131853	−	0.991269i	$-0.457907\pi$
$811$	30.9034	−	36.8293i	1.08517	−	1.29325i	0.953314	−	0.301982i	$-0.0976482\pi$
$812$	−0.124230	−	0.0452162i	−0.00435963	−	0.00158678i
$813$		0			0
$814$	13.9718	−	11.7237i	0.489710	−	0.410915i
$815$	−23.5183	+	4.14691i	−0.823809	+	0.145260i
$816$		0			0
$817$	−1.49125	−	6.56321i	−0.0521722	−	0.229618i
$818$		−	25.5842i		−	0.894531i
$819$		0			0
$820$	−12.0499	−	14.3605i	−0.420799	−	0.501489i
$821$	6.43212	+	17.6721i	0.224483	+	0.616761i	0.999892	−	0.0146979i	$-0.00467864\pi$
$821$	6.43212	+	17.6721i	0.224483	+	0.616761i	−0.775409	+	0.631459i	$0.782456\pi$
$822$		0			0
$823$	7.73878	+	6.49360i	0.269757	+	0.226353i	0.767624	−	0.640900i	$-0.221439\pi$
$823$	7.73878	+	6.49360i	0.269757	+	0.226353i	−0.497867	+	0.867253i	$0.665883\pi$
$824$	4.45621	+	2.57279i	0.155239	+	0.0896275i
$825$		0			0
$826$	−0.0200688	+	0.113816i	−0.000698281	+	0.00396015i
$827$	3.71209	−	21.0523i	0.129082	−	0.732061i	−0.849717	−	0.527239i	$-0.823227\pi$
$827$	3.71209	−	21.0523i	0.129082	−	0.732061i	0.978799	−	0.204822i	$-0.0656616\pi$
$828$		0			0
$829$	−36.8912	−	21.2992i	−1.28128	−	0.739750i	−0.304202	−	0.952608i	$-0.598390\pi$
$829$	−36.8912	−	21.2992i	−1.28128	−	0.739750i	−0.977083	+	0.212858i	$0.931723\pi$
$830$	−10.1263	−	8.49700i	−0.351490	−	0.294935i
$831$		0			0
$832$	−0.435665	−	1.19698i	−0.0151040	−	0.0414978i
$833$	−12.9163	−	15.3931i	−0.447525	−	0.533339i
$834$		0			0
$835$		−	51.5720i		−	1.78472i
$836$	26.3856	+	3.33279i	0.912567	+	0.115267i
$837$		0			0
$838$	−10.4019	+	1.83414i	−0.359329	+	0.0633595i
$839$	−9.37593	+	7.86734i	−0.323693	+	0.271611i	−0.790124	−	0.612947i	$-0.789984\pi$
$839$	−9.37593	+	7.86734i	−0.323693	+	0.271611i	0.466431	+	0.884557i	$0.345540\pi$
$840$		0			0
$841$	−12.4172	−	4.51949i	−0.428179	−	0.155844i
$842$	−2.78319	+	3.31687i	−0.0959149	+	0.114307i
$843$		0			0
$844$	−19.4787	+	11.2460i	−0.670486	+	0.387105i
$845$	−27.3649	−	4.82517i	−0.941382	−	0.165991i
$846$		0			0
$847$	0.266827	+	0.462157i	0.00916827	+	0.0158799i
$848$	−1.87197	+	3.24234i	−0.0642836	+	0.111342i
$849$		0			0
$850$	0.947315	−	2.60273i	0.0324926	−	0.0892728i
$851$	21.5803	−	7.85460i	0.739765	−	0.269252i
$852$		0			0
$853$	3.01259	+	17.0853i	0.103149	+	0.584989i	0.991943	+	0.126682i	$0.0404327\pi$
$853$	3.01259	+	17.0853i	0.103149	+	0.584989i	−0.888794	+	0.458307i	$0.848456\pi$
$854$	−0.257855			−0.00882361
$855$		0			0
$856$	4.03629			0.137958
$857$	−7.19347	−	40.7962i	−0.245724	−	1.39357i	−0.818805	−	0.574072i	$-0.805363\pi$
$857$	−7.19347	−	40.7962i	−0.245724	−	1.39357i	0.573081	−	0.819499i	$-0.305748\pi$
$858$		0			0
$859$	−12.2167	+	4.44651i	−0.416828	+	0.151713i	−0.541916	−	0.840433i	$-0.682301\pi$
$859$	−12.2167	+	4.44651i	−0.416828	+	0.151713i	0.125088	+	0.992146i	$0.460079\pi$
$860$	−1.28979	+	3.54368i	−0.0439816	+	0.120838i
$861$		0			0
$862$	−10.5911	+	18.3443i	−0.360734	+	0.624810i
$863$	14.2592	+	24.6977i	0.485390	+	0.840720i	0.999859	−	0.0167889i	$-0.00534432\pi$
$863$	14.2592	+	24.6977i	0.485390	+	0.840720i	−0.514469	+	0.857509i	$0.672011\pi$
$864$		0			0
$865$	10.2102	+	1.80034i	0.347159	+	0.0612135i
$866$	−14.8032	+	8.54661i	−0.503032	+	0.290426i
$867$		0			0
$868$	−0.0189617	+	0.0225977i	−0.000643602	+	0.000767015i
$869$	−15.9550	−	5.80716i	−0.541238	−	0.196994i
$870$		0			0
$871$	11.5273	−	9.67257i	0.390589	−	0.327743i
$872$	−16.3549	+	2.88380i	−0.553845	+	0.0976579i
$873$		0			0
$874$	29.7845	+	15.3064i	1.00747	+	0.517748i
$875$		−	0.200528i		−	0.00677909i
$876$		0			0
$877$	−7.99554	−	9.52871i	−0.269990	−	0.321762i	0.613965	−	0.789333i	$-0.289574\pi$
$877$	−7.99554	−	9.52871i	−0.269990	−	0.321762i	−0.883955	+	0.467571i	$0.845129\pi$
$878$	−10.9805	−	30.1685i	−0.370572	−	1.01814i
$879$		0			0
$880$	−11.4151	−	9.57842i	−0.384804	−	0.322889i
$881$	20.9577	+	12.0999i	0.706082	+	0.407657i	0.809609	−	0.586970i	$-0.199679\pi$
$881$	20.9577	+	12.0999i	0.706082	+	0.407657i	−0.103527	+	0.994627i	$0.533013\pi$
$882$		0			0
$883$	6.05843	−	34.3591i	0.203882	−	1.15627i	−0.695306	−	0.718713i	$-0.744731\pi$
$883$	6.05843	−	34.3591i	0.203882	−	1.15627i	0.899189	−	0.437561i	$-0.144158\pi$
$884$	−0.634996	+	3.60124i	−0.0213572	+	0.121123i
$885$		0			0
$886$	−9.48614	−	5.47683i	−0.318693	−	0.183998i
$887$	25.5673	+	21.4535i	0.858467	+	0.720339i	0.961637	−	0.274324i	$-0.0884542\pi$
$887$	25.5673	+	21.4535i	0.858467	+	0.720339i	−0.103170	+	0.994664i	$0.532899\pi$
$888$		0			0
$889$	−0.143563	−	0.394435i	−0.00481493	−	0.0132289i
$890$	−6.45904	−	7.69758i	−0.216507	−	0.258023i
$891$		0			0
$892$			18.8913i			0.632527i
$893$	−2.93733	−	6.98727i	−0.0982940	−	0.233820i
$894$		0			0
$895$	−52.5979	+	9.27443i	−1.75815	+	0.310010i
$896$	−0.0155872	+	0.0130792i	−0.000520731	+	0.000436945i
$897$		0			0
$898$	−3.15298	−	1.14759i	−0.105216	−	0.0382955i
$899$	−6.05470	+	7.21571i	−0.201936	+	0.240657i
$900$		0			0
$901$	9.30804	−	5.37400i	0.310096	−	0.179034i
$902$	46.1206	+	8.13231i	1.53565	+	0.270776i
$903$		0			0
$904$	9.17340	+	15.8888i	0.305103	+	0.528453i
$905$	−9.44700	+	16.3627i	−0.314029	+	0.543914i
$906$		0			0
$907$	13.4568	−	36.9722i	0.446825	−	1.22764i	−0.488097	−	0.872789i	$-0.662309\pi$
$907$	13.4568	−	36.9722i	0.446825	−	1.22764i	0.934922	−	0.354852i	$-0.115469\pi$
$908$	15.7819	−	5.74412i	0.523739	−	0.190625i
$909$		0			0
$910$	−0.0109922	−	0.0623396i	−0.000364386	−	0.00206654i
$911$	−35.7150			−1.18329			−0.591646	−	0.806198i	$-0.701522\pi$
$911$	−35.7150			−1.18329			−0.591646	+	0.806198i	$0.701522\pi$
$912$		0			0
$913$	33.0239			1.09293
$914$	2.22237	+	12.6037i	0.0735095	+	0.416893i
$915$		0			0
$916$	16.4065	−	5.97147i	0.542085	−	0.197303i
$917$	−0.0383394	+	0.105337i	−0.00126608	+	0.00347852i
$918$		0			0
$919$	−17.5138	+	30.3349i	−0.577728	+	1.00065i	0.418011	+	0.908442i	$0.362727\pi$
$919$	−17.5138	+	30.3349i	−0.577728	+	1.00065i	−0.995739	+	0.0922128i	$0.970606\pi$
$920$	−9.38149	−	16.2492i	−0.309299	−	0.535721i
$921$		0			0
$922$	39.9620	+	7.04637i	1.31608	+	0.232060i
$923$	−10.9970	+	6.34912i	−0.361971	+	0.208984i
$924$		0			0
$925$	−1.85387	+	2.20936i	−0.0609549	+	0.0726432i
$926$	−25.7458	−	9.37071i	−0.846060	−	0.307941i
$927$		0			0
$928$	−4.97717	+	4.17634i	−0.163384	+	0.137095i
$929$	−4.98540	+	0.879060i	−0.163566	+	0.0288410i	−0.254831	−	0.966986i	$-0.582020\pi$
$929$	−4.98540	+	0.879060i	−0.163566	+	0.0288410i	0.0912656	+	0.995827i	$0.470909\pi$
$930$		0			0
$931$	−13.9458	+	27.1368i	−0.457055	+	0.889372i
$932$			13.4360i			0.440112i
$933$		0			0
$934$	7.53448	+	8.97925i	0.246536	+	0.293810i
$935$	14.6311	+	40.1987i	0.478489	+	1.31464i
$936$		0			0
$937$	42.9782	+	36.0630i	1.40404	+	1.17813i	0.959273	+	0.282480i	$0.0911569\pi$
$937$	42.9782	+	36.0630i	1.40404	+	1.17813i	0.444764	+	0.895648i	$0.353288\pi$
$938$	−0.208170	−	0.120187i	−0.00679698	−	0.00392424i
$939$		0			0
$940$	−0.737457	+	4.18232i	−0.0240532	+	0.136412i
$941$	2.68497	−	15.2272i	0.0875277	−	0.496394i	−0.909255	−	0.416240i	$-0.863348\pi$
$941$	2.68497	−	15.2272i	0.0875277	−	0.496394i	0.996782	−	0.0801542i	$-0.0255413\pi$
$942$		0			0
$943$	51.0681	+	29.4842i	1.66301	+	0.960138i
$944$	4.35102	+	3.65094i	0.141614	+	0.118828i
$945$		0			0
$946$	−3.22218	−	8.85286i	−0.104762	−	0.287831i
$947$	19.1052	+	22.7687i	0.620836	+	0.739883i	0.981214	−	0.192923i	$-0.0617968\pi$
$947$	19.1052	+	22.7687i	0.620836	+	0.739883i	−0.360378	+	0.932806i	$0.617352\pi$
$948$		0			0
$949$			9.86726i			0.320305i
$950$	−4.20050	+	0.205515i	−0.136282	+	0.00666780i
$951$		0			0
$952$	0.0575260	−	0.0101434i	0.00186443	−	0.000328749i
$953$	−16.0967	+	13.5068i	−0.521424	+	0.437527i	−0.865128	−	0.501551i	$-0.832763\pi$
$953$	−16.0967	+	13.5068i	−0.521424	+	0.437527i	0.343704	+	0.939078i	$0.388318\pi$
$954$		0			0
$955$	4.83978	+	1.76154i	0.156612	+	0.0570019i
$956$	2.34914	−	2.79959i	0.0759766	−	0.0905454i
$957$		0			0
$958$	−17.1141	+	9.88084i	−0.552932	+	0.319235i
$959$	0.269088	+	0.0474475i	0.00868930	+	0.00153216i
$960$		0			0
$961$	−14.4491	−	25.0266i	−0.466100	−	0.807309i
$962$	1.90388	−	3.29762i	0.0613836	−	0.106320i
$963$		0			0
$964$	7.59329	−	20.8624i	0.244563	−	0.671933i
$965$	−13.0730	+	4.75820i	−0.420836	+	0.153172i
$966$		0			0
$967$	4.91881	+	27.8960i	0.158178	+	0.897074i	0.955822	+	0.293945i	$0.0949683\pi$
$967$	4.91881	+	27.8960i	0.158178	+	0.897074i	−0.797644	+	0.603129i	$0.793921\pi$
$968$	26.2268			0.842963
$969$		0			0
$970$	33.4955			1.07547
$971$	−1.16663	−	6.61629i	−0.0374389	−	0.212327i	0.960349	−	0.278800i	$-0.0899365\pi$
$971$	−1.16663	−	6.61629i	−0.0374389	−	0.212327i	−0.997788	+	0.0664728i	$0.978825\pi$
$972$		0			0
$973$	−0.0450592	+	0.0164002i	−0.00144453	+	0.000525766i
$974$	7.76654	−	21.3384i	0.248856	−	0.683726i
$975$		0			0
$976$	−6.33624	+	10.9747i	−0.202818	+	0.351291i
$977$	6.57515	+	11.3885i	0.210358	+	0.364350i	0.951826	−	0.306637i	$-0.0992038\pi$
$977$	6.57515	+	11.3885i	0.210358	+	0.364350i	−0.741469	+	0.670987i	$0.765870\pi$
$978$		0			0
$979$	24.7219	+	4.35913i	0.790114	+	0.139318i
$980$	14.8048	−	8.54753i	0.472921	−	0.273041i
$981$		0			0
$982$	−0.0135702	+	0.0161723i	−0.000433042	+	0.000516080i
$983$	−9.18945	−	3.34469i	−0.293098	−	0.106679i	0.191286	−	0.981534i	$-0.438734\pi$
$983$	−9.18945	−	3.34469i	−0.293098	−	0.106679i	−0.484384	+	0.874855i	$0.660956\pi$
$984$		0			0
$985$	−32.6072	+	27.3607i	−1.03895	+	0.871785i
$986$	18.3688	−	3.23891i	0.584980	−	0.103148i
$987$		0			0
$988$	5.41436	−	1.23022i	0.172254	−	0.0391384i
$989$		−	11.8624i		−	0.377203i
$990$		0			0
$991$	11.6632	+	13.8996i	0.370493	+	0.441537i	0.918790	−	0.394747i	$-0.129168\pi$
$991$	11.6632	+	13.8996i	0.370493	+	0.441537i	−0.548296	+	0.836284i	$0.684723\pi$
$992$	0.495847	+	1.36233i	0.0157432	+	0.0432540i
$993$		0			0
$994$	0.155385	+	0.130384i	0.00492852	+	0.00413552i
$995$	−27.0966	−	15.6442i	−0.859020	−	0.495955i
$996$		0			0
$997$	−10.3352	+	58.6141i	−0.327321	+	1.85633i	0.165518	+	0.986207i	$0.447070\pi$
$997$	−10.3352	+	58.6141i	−0.327321	+	1.85633i	−0.492839	+	0.870121i	$0.664041\pi$
$998$	2.01146	−	11.4075i	0.0636716	−	0.361100i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.bb.b.143.1	yes	24
3.2	odd	2		342.2.bb.a.143.4	✓	24
19.2	odd	18		342.2.bb.a.287.4	yes	24
57.2	even	18	inner	342.2.bb.b.287.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.bb.a.143.4	✓	24	3.2	odd	2
342.2.bb.a.287.4	yes	24	19.2	odd	18
342.2.bb.b.143.1	yes	24	1.1	even	1	trivial
342.2.bb.b.287.1	yes	24	57.2	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.835315 + 2.29501i) q^{5} +(-0.0101738 + 0.0176215i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.835315 + 2.29501i) q^{5} +(-0.0101738 + 0.0176215i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.40519 + 0.424100i) q^{10} +(-5.28395 + 3.05069i) q^{11} +(-0.818782 + 0.975787i) q^{13} +(0.0191205 + 0.00695929i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-2.82716 + 0.498505i) q^{17} +(2.36132 + 3.66390i) q^{19} -2.44230i q^{20} +(3.92189 + 4.67393i) q^{22} +(2.62758 + 7.21921i) q^{23} +(-0.739090 - 0.620170i) q^{25} +(1.10314 + 0.636900i) q^{26} +(0.00353332 - 0.0200385i) q^{28} +(1.12823 - 6.39853i) q^{29} +(-1.25553 - 0.724880i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.981864 + 2.69765i) q^{34} +(-0.0319433 - 0.0380685i) q^{35} -2.98930i q^{37} +(3.19820 - 2.96167i) q^{38} +(-2.40519 + 0.424100i) q^{40} +(5.87990 - 4.93382i) q^{41} +(-1.45096 - 0.528107i) q^{43} +(3.92189 - 4.67393i) q^{44} +(6.65326 - 3.84126i) q^{46} +(-1.71246 - 0.301952i) q^{47} +(3.49979 + 6.06182i) q^{49} +(-0.482407 + 0.835553i) q^{50} +(0.435665 - 1.19698i) q^{52} +(-3.51814 + 1.28050i) q^{53} +(-2.58760 - 14.6750i) q^{55} -0.0203476 q^{56} -6.49724 q^{58} +(0.986296 + 5.59356i) q^{59} +(-11.9082 + 4.33425i) q^{61} +(-0.495847 + 1.36233i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.55550 - 2.69420i) q^{65} +(-11.6339 - 2.05137i) q^{67} +(2.48617 - 1.43539i) q^{68} +(-0.0319433 + 0.0380685i) q^{70} +(9.36760 + 3.40953i) q^{71} +(5.93403 - 4.97924i) q^{73} +(-2.94388 + 0.519086i) q^{74} +(-3.47204 - 2.63532i) q^{76} -0.124148i q^{77} +(1.78876 + 2.13176i) q^{79} +(0.835315 + 2.29501i) q^{80} +(-5.87990 - 4.93382i) q^{82} +(-4.68738 - 2.70626i) q^{83} +(1.21750 - 6.90477i) q^{85} +(-0.268127 + 1.52062i) q^{86} +(-5.28395 - 3.05069i) q^{88} +(-3.15178 - 2.64466i) q^{89} +(-0.00886474 - 0.0243557i) q^{91} +(-4.93823 - 5.88515i) q^{92} +1.73887i q^{94} +(-10.3811 + 2.35873i) q^{95} +(13.5064 - 2.38154i) q^{97} +(5.36199 - 4.49925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 12 q^{17} + 24 q^{19} + 12 q^{22} + 36 q^{25} + 36 q^{26} - 12 q^{29} + 12 q^{34} - 48 q^{35} - 12 q^{38} - 12 q^{41} + 12 q^{44} - 36 q^{46} + 60 q^{47} - 36 q^{49} - 24 q^{50} - 48 q^{53} - 60 q^{55} - 24 q^{58} + 24 q^{59} - 60 q^{61} + 24 q^{62} - 12 q^{64} - 24 q^{65} - 48 q^{70} - 36 q^{71} + 24 q^{79} + 12 q^{82} + 72 q^{83} - 36 q^{86} - 120 q^{89} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) 24 * q + 12 * q^8 + 12 * q^17 + 24 * q^19 + 12 * q^22 + 36 * q^25 + 36 * q^26 - 12 * q^29 + 12 * q^34 - 48 * q^35 - 12 * q^38 - 12 * q^41 + 12 * q^44 - 36 * q^46 + 60 * q^47 - 36 * q^49 - 24 * q^50 - 48 * q^53 - 60 * q^55 - 24 * q^58 + 24 * q^59 - 60 * q^61 + 24 * q^62 - 12 * q^64 - 24 * q^65 - 48 * q^70 - 36 * q^71 + 24 * q^79 + 12 * q^82 + 72 * q^83 - 36 * q^86 - 120 * q^89 - 24 * q^91 + 12 * q^95

Introduction

L-functions

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