LMFDB - Embedded newform 2070.2.h.b.2069.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(2069,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("2070.2069");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.h (of order $2$, degree $1$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2069.4
Character	$\chi$	$=$	2070.2069
Dual form			2070.2.h.b.2069.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-2.15114 + 0.610392i) q^{5} -4.98705 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.15114 + 0.610392i) q^{5} -4.98705 q^{7} +1.00000 q^{8} +(-2.15114 + 0.610392i) q^{10} +2.47913 q^{11} +3.76528i q^{13} -4.98705 q^{14} +1.00000 q^{16} +1.23834i q^{17} -7.97179i q^{19} +(-2.15114 + 0.610392i) q^{20} +2.47913 q^{22} +(2.46795 - 4.11208i) q^{23} +(4.25484 - 2.62608i) q^{25} +3.76528i q^{26} -4.98705 q^{28} -6.53426i q^{29} +1.26885 q^{31} +1.00000 q^{32} +1.23834i q^{34} +(10.7279 - 3.04406i) q^{35} +10.7699 q^{37} -7.97179i q^{38} +(-2.15114 + 0.610392i) q^{40} +4.87196i q^{41} +3.98846 q^{43} +2.47913 q^{44} +(2.46795 - 4.11208i) q^{46} -10.2769 q^{47} +17.8707 q^{49} +(4.25484 - 2.62608i) q^{50} +3.76528i q^{52} -2.28524i q^{53} +(-5.33298 + 1.51324i) q^{55} -4.98705 q^{56} -6.53426i q^{58} -10.2995i q^{59} +11.6057i q^{61} +1.26885 q^{62} +1.00000 q^{64} +(-2.29830 - 8.09966i) q^{65} +8.76589 q^{67} +1.23834i q^{68} +(10.7279 - 3.04406i) q^{70} -11.7864i q^{71} -12.1450i q^{73} +10.7699 q^{74} -7.97179i q^{76} -12.3636 q^{77} +0.127873i q^{79} +(-2.15114 + 0.610392i) q^{80} +4.87196i q^{82} +3.92699i q^{83} +(-0.755873 - 2.66385i) q^{85} +3.98846 q^{86} +2.47913 q^{88} -4.67322 q^{89} -18.7776i q^{91} +(2.46795 - 4.11208i) q^{92} -10.2769 q^{94} +(4.86591 + 17.1485i) q^{95} +8.10991 q^{97} +17.8707 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q + 24 * q^2 + 24 * q^4 + 24 * q^8	$ 24 q + 24 q^{2} + 24 q^{4} + 24 q^{8} + 24 q^{16} + 4 q^{23} + 8 q^{31} + 24 q^{32} + 16 q^{35} + 4 q^{46} - 16 q^{47} + 56 q^{49} - 8 q^{55} + 8 q^{62} + 24 q^{64} + 16 q^{70} + 40 q^{77} + 64 q^{85} + 4 q^{92} - 16 q^{94} + 8 q^{95} + 56 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 + 24 * q^4 + 24 * q^8 + 24 * q^16 + 4 * q^23 + 8 * q^31 + 24 * q^32 + 16 * q^35 + 4 * q^46 - 16 * q^47 + 56 * q^49 - 8 * q^55 + 8 * q^62 + 24 * q^64 + 16 * q^70 + 40 * q^77 + 64 * q^85 + 4 * q^92 - 16 * q^94 + 8 * q^95 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.15114	+	0.610392i	−0.962021	+	0.272975i
$5$	−2.15114	+	0.610392i	−0.962021	+	0.272975i
$6$		0			0
$7$	−4.98705			−1.88493			−0.942464	−	0.334306i	$-0.891498\pi$
$7$	−4.98705			−1.88493			−0.942464	+	0.334306i	$0.891498\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.15114	+	0.610392i	−0.680252	+	0.193023i
$11$	2.47913			0.747487			0.373744	−	0.927532i	$-0.378074\pi$
$11$	2.47913			0.747487			0.373744	+	0.927532i	$0.378074\pi$
$12$		0			0
$13$			3.76528i			1.04430i	0.852853	+	0.522150i	$0.174870\pi$
$13$			3.76528i			1.04430i	−0.852853	+	0.522150i	$0.825130\pi$
$14$	−4.98705			−1.33285
$15$		0			0
$16$	1.00000			0.250000
$17$			1.23834i			0.300342i	0.988660	+	0.150171i	$0.0479824\pi$
$17$			1.23834i			0.300342i	−0.988660	+	0.150171i	$0.952018\pi$
$18$		0			0
$19$		−	7.97179i		−	1.82885i	−0.404752	−	0.914427i	$-0.632642\pi$
$19$		−	7.97179i		−	1.82885i	0.404752	−	0.914427i	$-0.367358\pi$
$20$	−2.15114	+	0.610392i	−0.481010	+	0.136488i
$21$		0			0
$22$	2.47913			0.528553
$23$	2.46795	−	4.11208i	0.514603	−	0.857429i
$23$	2.46795	−	4.11208i	0.514603	−	0.857429i
$24$		0			0
$25$	4.25484	−	2.62608i	0.850969	−	0.525216i
$26$			3.76528i			0.738432i
$27$		0			0
$28$	−4.98705			−0.942464
$29$		−	6.53426i		−	1.21338i	−0.794938	−	0.606691i	$-0.792497\pi$
$29$		−	6.53426i		−	1.21338i	0.794938	−	0.606691i	$-0.207503\pi$
$30$		0			0
$31$	1.26885			0.227891			0.113946	−	0.993487i	$-0.463651\pi$
$31$	1.26885			0.227891			0.113946	+	0.993487i	$0.463651\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$			1.23834i			0.212374i
$35$	10.7279	−	3.04406i	1.81334	−	0.514539i
$36$		0			0
$37$	10.7699			1.77056			0.885279	−	0.465060i	$-0.153967\pi$
$37$	10.7699			1.77056			0.885279	+	0.465060i	$0.153967\pi$
$38$		−	7.97179i		−	1.29319i
$39$		0			0
$40$	−2.15114	+	0.610392i	−0.340126	+	0.0965114i
$41$			4.87196i			0.760872i	0.924807	+	0.380436i	$0.124226\pi$
$41$			4.87196i			0.760872i	−0.924807	+	0.380436i	$0.875774\pi$
$42$		0			0
$43$	3.98846			0.608234			0.304117	−	0.952635i	$-0.401639\pi$
$43$	3.98846			0.608234			0.304117	+	0.952635i	$0.401639\pi$
$44$	2.47913			0.373744
$45$		0			0
$46$	2.46795	−	4.11208i	0.363879	−	0.606294i
$47$	−10.2769			−1.49905			−0.749523	−	0.661978i	$-0.769717\pi$
$47$	−10.2769			−1.49905			−0.749523	+	0.661978i	$0.769717\pi$
$48$		0			0
$49$	17.8707			2.55296
$50$	4.25484	−	2.62608i	0.601726	−	0.371384i
$51$		0			0
$52$			3.76528i			0.522150i
$53$		−	2.28524i		−	0.313902i	−0.987606	−	0.156951i	$-0.949833\pi$
$53$		−	2.28524i		−	0.313902i	0.987606	−	0.156951i	$-0.0501665\pi$
$54$		0			0
$55$	−5.33298	+	1.51324i	−0.719098	+	0.204046i
$56$	−4.98705			−0.666423
$57$		0			0
$58$		−	6.53426i		−	0.857991i
$59$		−	10.2995i		−	1.34089i	−0.741961	−	0.670443i	$-0.766104\pi$
$59$		−	10.2995i		−	1.34089i	0.741961	−	0.670443i	$-0.233896\pi$
$60$		0			0
$61$			11.6057i			1.48596i	0.669316	+	0.742978i	$0.266587\pi$
$61$			11.6057i			1.48596i	−0.669316	+	0.742978i	$0.733413\pi$
$62$	1.26885			0.161144
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.29830	−	8.09966i	−0.285068	−	1.00464i
$66$		0			0
$67$	8.76589			1.07092			0.535462	−	0.844559i	$-0.320138\pi$
$67$	8.76589			1.07092			0.535462	+	0.844559i	$0.320138\pi$
$68$			1.23834i			0.150171i
$69$		0			0
$70$	10.7279	−	3.04406i	1.28223	−	0.363834i
$71$		−	11.7864i		−	1.39879i	−0.714735	−	0.699396i	$-0.753453\pi$
$71$		−	11.7864i		−	1.39879i	0.714735	−	0.699396i	$-0.246547\pi$
$72$		0			0
$73$		−	12.1450i		−	1.42147i	−0.703462	−	0.710733i	$-0.748363\pi$
$73$		−	12.1450i		−	1.42147i	0.703462	−	0.710733i	$-0.251637\pi$
$74$	10.7699			1.25197
$75$		0			0
$76$		−	7.97179i		−	0.914427i
$77$	−12.3636			−1.40896
$78$		0			0
$79$			0.127873i			0.0143868i	0.999974	+	0.00719341i	$0.00228975\pi$
$79$			0.127873i			0.0143868i	−0.999974	+	0.00719341i	$0.997710\pi$
$80$	−2.15114	+	0.610392i	−0.240505	+	0.0682439i
$81$		0			0
$82$			4.87196i			0.538018i
$83$			3.92699i			0.431043i	0.976499	+	0.215521i	$0.0691451\pi$
$83$			3.92699i			0.431043i	−0.976499	+	0.215521i	$0.930855\pi$
$84$		0			0
$85$	−0.755873	−	2.66385i	−0.0819860	−	0.288935i
$86$	3.98846			0.430087
$87$		0			0
$88$	2.47913			0.264277
$89$	−4.67322			−0.495361			−0.247680	−	0.968842i	$-0.579668\pi$
$89$	−4.67322			−0.495361			−0.247680	+	0.968842i	$0.579668\pi$
$90$		0			0
$91$		−	18.7776i		−	1.96843i
$92$	2.46795	−	4.11208i	0.257301	−	0.428714i
$93$		0			0
$94$	−10.2769			−1.05999
$95$	4.86591	+	17.1485i	0.499232	+	1.75940i
$96$		0			0
$97$	8.10991			0.823436			0.411718	−	0.911311i	$-0.364929\pi$
$97$	8.10991			0.823436			0.411718	+	0.911311i	$0.364929\pi$
$98$	17.8707			1.80521
$99$		0			0
$100$	4.25484	−	2.62608i	0.425484	−	0.262608i
$101$		−	7.17197i		−	0.713638i	−0.934174	−	0.356819i	$-0.883861\pi$
$101$		−	7.17197i		−	0.713638i	0.934174	−	0.356819i	$-0.116139\pi$
$102$		0			0
$103$	−13.5916			−1.33922			−0.669612	−	0.742711i	$-0.733539\pi$
$103$	−13.5916			−1.33922			−0.669612	+	0.742711i	$0.733539\pi$
$104$			3.76528i			0.369216i
$105$		0			0
$106$		−	2.28524i		−	0.221962i
$107$			5.95985i			0.576160i	0.957606	+	0.288080i	$0.0930169\pi$
$107$			5.95985i			0.576160i	−0.957606	+	0.288080i	$0.906983\pi$
$108$		0			0
$109$		−	16.7623i		−	1.60554i	−0.596288	−	0.802771i	$-0.703358\pi$
$109$		−	16.7623i		−	1.60554i	0.596288	−	0.802771i	$-0.296642\pi$
$110$	−5.33298	+	1.51324i	−0.508479	+	0.144282i
$111$		0			0
$112$	−4.98705			−0.471232
$113$			2.98034i			0.280367i	0.990126	+	0.140183i	$0.0447692\pi$
$113$			2.98034i			0.280367i	−0.990126	+	0.140183i	$0.955231\pi$
$114$		0			0
$115$	−2.79893	+	10.3521i	−0.261002	+	0.965338i
$116$		−	6.53426i		−	0.606691i
$117$		0			0
$118$		−	10.2995i		−	0.948150i
$119$		−	6.17567i		−	0.566123i
$120$		0			0
$121$	−4.85389			−0.441263
$122$			11.6057i			1.05073i
$123$		0			0
$124$	1.26885			0.113946
$125$	−7.54984	+	8.24620i	−0.675279	+	0.737563i
$126$		0			0
$127$			11.9564i			1.06096i	0.847699	+	0.530478i	$0.177988\pi$
$127$			11.9564i			1.06096i	−0.847699	+	0.530478i	$0.822012\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−2.29830	−	8.09966i	−0.201574	−	0.710387i
$131$		−	15.6272i		−	1.36536i	−0.730718	−	0.682679i	$-0.760815\pi$
$131$		−	15.6272i		−	1.36536i	0.730718	−	0.682679i	$-0.239185\pi$
$132$		0			0
$133$			39.7557i			3.44726i
$134$	8.76589			0.757258
$135$		0			0
$136$			1.23834i			0.106187i
$137$		−	5.77371i		−	0.493281i	−0.969107	−	0.246641i	$-0.920673\pi$
$137$		−	5.77371i		−	0.493281i	0.969107	−	0.246641i	$-0.0793268\pi$
$138$		0			0
$139$	5.56508			0.472024			0.236012	−	0.971750i	$-0.424160\pi$
$139$	5.56508			0.472024			0.236012	+	0.971750i	$0.424160\pi$
$140$	10.7279	−	3.04406i	0.906671	−	0.257270i
$141$		0			0
$142$		−	11.7864i		−	0.989095i
$143$			9.33464i			0.780601i
$144$		0			0
$145$	3.98846	+	14.0561i	0.331224	+	1.16730i
$146$		−	12.1450i		−	1.00513i
$147$		0			0
$148$	10.7699			0.885279
$149$	4.52336			0.370568			0.185284	−	0.982685i	$-0.440679\pi$
$149$	4.52336			0.370568			0.185284	+	0.982685i	$0.440679\pi$
$150$		0			0
$151$	12.0748			0.982631			0.491315	−	0.870982i	$-0.336516\pi$
$151$	12.0748			0.982631			0.491315	+	0.870982i	$0.336516\pi$
$152$		−	7.97179i		−	0.646597i
$153$		0			0
$154$	−12.3636			−0.996285
$155$	−2.72947	+	0.774493i	−0.219236	+	0.0622088i
$156$		0			0
$157$	−0.865604			−0.0690827			−0.0345414	−	0.999403i	$-0.510997\pi$
$157$	−0.865604			−0.0690827			−0.0345414	+	0.999403i	$0.510997\pi$
$158$			0.127873i			0.0101730i
$159$		0			0
$160$	−2.15114	+	0.610392i	−0.170063	+	0.0482557i
$161$	−12.3078	+	20.5072i	−0.969990	+	1.61619i
$162$		0			0
$163$		−	17.3972i		−	1.36265i	−0.731980	−	0.681326i	$-0.761404\pi$
$163$		−	17.3972i		−	1.36265i	0.731980	−	0.681326i	$-0.238596\pi$
$164$			4.87196i			0.380436i
$165$		0			0
$166$			3.92699i			0.304793i
$167$	12.7687			0.988074			0.494037	−	0.869441i	$-0.335521\pi$
$167$	12.7687			0.988074			0.494037	+	0.869441i	$0.335521\pi$
$168$		0			0
$169$	−1.17733			−0.0905637
$170$	−0.755873	−	2.66385i	−0.0579728	−	0.204308i
$171$		0			0
$172$	3.98846			0.304117
$173$	−1.33089			−0.101186			−0.0505928	−	0.998719i	$-0.516111\pi$
$173$	−1.33089			−0.101186			−0.0505928	+	0.998719i	$0.516111\pi$
$174$		0			0
$175$	−21.2191	+	13.0964i	−1.60402	+	0.989995i
$176$	2.47913			0.186872
$177$		0			0
$178$	−4.67322			−0.350273
$179$			13.0630i			0.976378i	0.872738	+	0.488189i	$0.162342\pi$
$179$			13.0630i			0.976378i	−0.872738	+	0.488189i	$0.837658\pi$
$180$		0			0
$181$			17.6900i			1.31489i	0.753502	+	0.657445i	$0.228363\pi$
$181$			17.6900i			1.31489i	−0.753502	+	0.657445i	$0.771637\pi$
$182$		−	18.7776i		−	1.39189i
$183$		0			0
$184$	2.46795	−	4.11208i	0.181940	−	0.303147i
$185$	−23.1676	+	6.57385i	−1.70331	+	0.483319i
$186$		0			0
$187$			3.07002i			0.224502i
$188$	−10.2769			−0.749523
$189$		0			0
$190$	4.86591	+	17.1485i	0.353010	+	1.24408i
$191$	−17.7702			−1.28581			−0.642903	−	0.765948i	$-0.722270\pi$
$191$	−17.7702			−1.28581			−0.642903	+	0.765948i	$0.722270\pi$
$192$		0			0
$193$			22.1519i			1.59453i	0.603630	+	0.797265i	$0.293721\pi$
$193$			22.1519i			1.59453i	−0.603630	+	0.797265i	$0.706279\pi$
$194$	8.10991			0.582258
$195$		0			0
$196$	17.8707			1.27648
$197$	−13.6945			−0.975690			−0.487845	−	0.872930i	$-0.662217\pi$
$197$	−13.6945			−0.975690			−0.487845	+	0.872930i	$0.662217\pi$
$198$		0			0
$199$		−	19.0529i		−	1.35062i	−0.737532	−	0.675312i	$-0.764009\pi$
$199$		−	19.0529i		−	1.35062i	0.737532	−	0.675312i	$-0.235991\pi$
$200$	4.25484	−	2.62608i	0.300863	−	0.185692i
$201$		0			0
$202$		−	7.17197i		−	0.504618i
$203$			32.5867i			2.28714i
$204$		0			0
$205$	−2.97380	−	10.4803i	−0.207699	−	0.731975i
$206$	−13.5916			−0.946974
$207$		0			0
$208$			3.76528i			0.261075i
$209$		−	19.7631i		−	1.36704i
$210$		0			0
$211$	12.4476			0.856931			0.428466	−	0.903558i	$-0.359054\pi$
$211$	12.4476			0.856931			0.428466	+	0.903558i	$0.359054\pi$
$212$		−	2.28524i		−	0.156951i
$213$		0			0
$214$			5.95985i			0.407407i
$215$	−8.57975	+	2.43452i	−0.585134	+	0.166033i
$216$		0			0
$217$	−6.32780			−0.429559
$218$		−	16.7623i		−	1.13529i
$219$		0			0
$220$	−5.33298	+	1.51324i	−0.359549	+	0.102023i
$221$	−4.66270			−0.313647
$222$		0			0
$223$			10.0324i			0.671822i	0.941894	+	0.335911i	$0.109044\pi$
$223$			10.0324i			0.671822i	−0.941894	+	0.335911i	$0.890956\pi$
$224$	−4.98705			−0.333211
$225$		0			0
$226$			2.98034i			0.198249i
$227$		−	9.16942i		−	0.608596i	−0.952577	−	0.304298i	$-0.901578\pi$
$227$		−	9.16942i		−	0.608596i	0.952577	−	0.304298i	$-0.0984219\pi$
$228$		0			0
$229$			14.7086i			0.971971i	0.873967	+	0.485986i	$0.161539\pi$
$229$			14.7086i			0.971971i	−0.873967	+	0.485986i	$0.838461\pi$
$230$	−2.79893	+	10.3521i	−0.184556	+	0.682597i
$231$		0			0
$232$		−	6.53426i		−	0.428995i
$233$	−24.0936			−1.57843			−0.789213	−	0.614119i	$-0.789511\pi$
$233$	−24.0936			−1.57843			−0.789213	+	0.614119i	$0.789511\pi$
$234$		0			0
$235$	22.1072	−	6.27296i	1.44211	−	0.409203i
$236$		−	10.2995i		−	0.670443i
$237$		0			0
$238$		−	6.17567i		−	0.400310i
$239$		−	10.9948i		−	0.711195i	−0.934639	−	0.355597i	$-0.884277\pi$
$239$		−	10.9948i		−	0.711195i	0.934639	−	0.355597i	$-0.115723\pi$
$240$		0			0
$241$		−	14.3516i		−	0.924470i	−0.886757	−	0.462235i	$-0.847048\pi$
$241$		−	14.3516i		−	0.924470i	0.886757	−	0.462235i	$-0.152952\pi$
$242$	−4.85389			−0.312020
$243$		0			0
$244$			11.6057i			0.742978i
$245$	−38.4424	+	10.9081i	−2.45600	+	0.696895i
$246$		0			0
$247$	30.0160			1.90987
$248$	1.26885			0.0805718
$249$		0			0
$250$	−7.54984	+	8.24620i	−0.477494	+	0.521536i
$251$	20.6512			1.30349			0.651747	−	0.758436i	$-0.274036\pi$
$251$	20.6512			1.30349			0.651747	+	0.758436i	$0.274036\pi$
$252$		0			0
$253$	6.11838	−	10.1944i	0.384659	−	0.640917i
$254$			11.9564i			0.750209i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.21345			−0.512341			−0.256171	−	0.966632i	$-0.582461\pi$
$257$	−8.21345			−0.512341			−0.256171	+	0.966632i	$0.582461\pi$
$258$		0			0
$259$	−53.7100			−3.33738
$260$	−2.29830	−	8.09966i	−0.142534	−	0.502320i
$261$		0			0
$262$		−	15.6272i		−	0.965454i
$263$			8.92373i			0.550261i	0.961407	+	0.275130i	$0.0887211\pi$
$263$			8.92373i			0.550261i	−0.961407	+	0.275130i	$0.911279\pi$
$264$		0			0
$265$	1.39489	+	4.91589i	0.0856876	+	0.301981i
$266$			39.7557i			2.43758i
$267$		0			0
$268$	8.76589			0.535462
$269$		−	27.0106i		−	1.64687i	−0.567412	−	0.823434i	$-0.692055\pi$
$269$		−	27.0106i		−	1.64687i	0.567412	−	0.823434i	$-0.307945\pi$
$270$		0			0
$271$	10.0281			0.609161			0.304581	−	0.952487i	$-0.401484\pi$
$271$	10.0281			0.609161			0.304581	+	0.952487i	$0.401484\pi$
$272$			1.23834i			0.0750855i
$273$		0			0
$274$		−	5.77371i		−	0.348803i
$275$	10.5483	−	6.51041i	0.636088	−	0.392593i
$276$		0			0
$277$		−	15.1187i		−	0.908393i	−0.890902	−	0.454196i	$-0.849926\pi$
$277$		−	15.1187i		−	0.908393i	0.890902	−	0.454196i	$-0.150074\pi$
$278$	5.56508			0.333771
$279$		0			0
$280$	10.7279	−	3.04406i	0.641113	−	0.181917i
$281$	13.7542			0.820507			0.410254	−	0.911971i	$-0.365440\pi$
$281$	13.7542			0.820507			0.410254	+	0.911971i	$0.365440\pi$
$282$		0			0
$283$	2.17583			0.129340			0.0646698	−	0.997907i	$-0.479401\pi$
$283$	2.17583			0.129340			0.0646698	+	0.997907i	$0.479401\pi$
$284$		−	11.7864i		−	0.699396i
$285$		0			0
$286$			9.33464i			0.551969i
$287$		−	24.2967i		−	1.43419i
$288$		0			0
$289$	15.4665			0.909795
$290$	3.98846	+	14.0561i	0.234210	+	0.825405i
$291$		0			0
$292$		−	12.1450i		−	0.710733i
$293$		−	2.69105i		−	0.157213i	−0.996906	−	0.0786064i	$-0.974953\pi$
$293$		−	2.69105i		−	0.157213i	0.996906	−	0.0786064i	$-0.0250470\pi$
$294$		0			0
$295$	6.28676	+	22.1558i	0.366029	+	1.28996i
$296$	10.7699			0.625987
$297$		0			0
$298$	4.52336			0.262031
$299$	15.4831	+	9.29252i	0.895413	+	0.537400i
$300$		0			0
$301$	−19.8907			−1.14648
$302$	12.0748			0.694825
$303$		0			0
$304$		−	7.97179i		−	0.457213i
$305$	−7.08401	−	24.9655i	−0.405630	−	1.42952i
$306$		0			0
$307$		−	8.54556i		−	0.487721i	−0.969810	−	0.243860i	$-0.921586\pi$
$307$		−	8.54556i		−	0.487721i	0.969810	−	0.243860i	$-0.0784139\pi$
$308$	−12.3636			−0.704480
$309$		0			0
$310$	−2.72947	+	0.774493i	−0.155023	+	0.0439882i
$311$			23.4652i			1.33059i	0.746580	+	0.665295i	$0.231694\pi$
$311$			23.4652i			1.33059i	−0.746580	+	0.665295i	$0.768306\pi$
$312$		0			0
$313$	26.3565			1.48976			0.744879	−	0.667200i	$-0.232507\pi$
$313$	26.3565			1.48976			0.744879	+	0.667200i	$0.232507\pi$
$314$	−0.865604			−0.0488488
$315$		0			0
$316$			0.127873i			0.00719341i
$317$	17.0134			0.955567			0.477784	−	0.878477i	$-0.341440\pi$
$317$	17.0134			0.955567			0.477784	+	0.878477i	$0.341440\pi$
$318$		0			0
$319$		−	16.1993i		−	0.906988i
$320$	−2.15114	+	0.610392i	−0.120253	+	0.0341219i
$321$		0			0
$322$	−12.3078	+	20.5072i	−0.685886	+	1.14282i
$323$	9.87179			0.549281
$324$		0			0
$325$	9.88793	+	16.0207i	0.548484	+	0.888667i
$326$		−	17.3972i		−	0.963540i
$327$		0			0
$328$			4.87196i			0.269009i
$329$	51.2517			2.82560
$330$		0			0
$331$	−6.49178			−0.356821			−0.178410	−	0.983956i	$-0.557095\pi$
$331$	−6.49178			−0.356821			−0.178410	+	0.983956i	$0.557095\pi$
$332$			3.92699i			0.215521i
$333$		0			0
$334$	12.7687			0.698674
$335$	−18.8567	+	5.35063i	−1.03025	+	0.292336i
$336$		0			0
$337$	2.19629			0.119639			0.0598197	−	0.998209i	$-0.480947\pi$
$337$	2.19629			0.119639			0.0598197	+	0.998209i	$0.480947\pi$
$338$	−1.17733			−0.0640382
$339$		0			0
$340$	−0.755873	−	2.66385i	−0.0409930	−	0.144468i
$341$	3.14564			0.170346
$342$		0			0
$343$	−54.2127			−2.92721
$344$	3.98846			0.215043
$345$		0			0
$346$	−1.33089			−0.0715490
$347$	−18.3082			−0.982834			−0.491417	−	0.870925i	$-0.663521\pi$
$347$	−18.3082			−0.982834			−0.491417	+	0.870925i	$0.663521\pi$
$348$		0			0
$349$	−18.8138			−1.00708			−0.503541	−	0.863972i	$-0.667970\pi$
$349$	−18.8138			−1.00708			−0.503541	+	0.863972i	$0.667970\pi$
$350$	−21.2191	+	13.0964i	−1.13421	+	0.700032i
$351$		0			0
$352$	2.47913			0.132138
$353$	−2.76173			−0.146992			−0.0734959	−	0.997296i	$-0.523416\pi$
$353$	−2.76173			−0.146992			−0.0734959	+	0.997296i	$0.523416\pi$
$354$		0			0
$355$	7.19434	+	25.3543i	0.381836	+	1.34567i
$356$	−4.67322			−0.247680
$357$		0			0
$358$			13.0630i			0.690403i
$359$	5.23786			0.276444			0.138222	−	0.990401i	$-0.455861\pi$
$359$	5.23786			0.276444			0.138222	+	0.990401i	$0.455861\pi$
$360$		0			0
$361$	−44.5494			−2.34470
$362$			17.6900i			0.929768i
$363$		0			0
$364$		−	18.7776i		−	0.984216i
$365$	7.41322	+	26.1257i	0.388025	+	1.36748i
$366$		0			0
$367$	10.1541			0.530042			0.265021	−	0.964243i	$-0.414621\pi$
$367$	10.1541			0.530042			0.265021	+	0.964243i	$0.414621\pi$
$368$	2.46795	−	4.11208i	0.128651	−	0.214357i
$369$		0			0
$370$	−23.1676	+	6.57385i	−1.20442	+	0.341758i
$371$			11.3966i			0.591683i
$372$		0			0
$373$	−28.0098			−1.45029			−0.725147	−	0.688595i	$-0.758228\pi$
$373$	−28.0098			−1.45029			−0.725147	+	0.688595i	$0.758228\pi$
$374$			3.07002i			0.158747i
$375$		0			0
$376$	−10.2769			−0.529993
$377$	24.6033			1.26714
$378$		0			0
$379$			2.15806i			0.110852i	0.998463	+	0.0554260i	$0.0176517\pi$
$379$			2.15806i			0.110852i	−0.998463	+	0.0554260i	$0.982348\pi$
$380$	4.86591	+	17.1485i	0.249616	+	0.879698i
$381$		0			0
$382$	−17.7702			−0.909202
$383$		−	31.7631i		−	1.62302i	−0.584341	−	0.811508i	$-0.698647\pi$
$383$		−	31.7631i		−	1.62302i	0.584341	−	0.811508i	$-0.301353\pi$
$384$		0			0
$385$	26.5958	−	7.54663i	1.35545	−	0.384612i
$386$			22.1519i			1.12750i
$387$		0			0
$388$	8.10991			0.411718
$389$	20.1944			1.02390			0.511949	−	0.859016i	$-0.328924\pi$
$389$	20.1944			1.02390			0.511949	+	0.859016i	$0.328924\pi$
$390$		0			0
$391$	5.09216	+	3.05616i	0.257522	+	0.154557i
$392$	17.8707			0.902606
$393$		0			0
$394$	−13.6945			−0.689917
$395$	−0.0780525	−	0.275073i	−0.00392725	−	0.0138404i
$396$		0			0
$397$		−	2.83784i		−	0.142427i	−0.997461	−	0.0712136i	$-0.977313\pi$
$397$		−	2.83784i		−	0.142427i	0.997461	−	0.0712136i	$-0.0226872\pi$
$398$		−	19.0529i		−	0.955035i
$399$		0			0
$400$	4.25484	−	2.62608i	0.212742	−	0.131304i
$401$	−13.5683			−0.677569			−0.338784	−	0.940864i	$-0.610016\pi$
$401$	−13.5683			−0.677569			−0.338784	+	0.940864i	$0.610016\pi$
$402$		0			0
$403$			4.77756i			0.237987i
$404$		−	7.17197i		−	0.356819i
$405$		0			0
$406$			32.5867i			1.61725i
$407$	26.7000			1.32347
$408$		0			0
$409$	−4.25145			−0.210221			−0.105110	−	0.994461i	$-0.533520\pi$
$409$	−4.25145			−0.210221			−0.105110	+	0.994461i	$0.533520\pi$
$410$	−2.97380	−	10.4803i	−0.146866	−	0.517584i
$411$		0			0
$412$	−13.5916			−0.669612
$413$			51.3644i			2.52747i
$414$		0			0
$415$	−2.39700	−	8.44751i	−0.117664	−	0.414672i
$416$			3.76528i			0.184608i
$417$		0			0
$418$		−	19.7631i		−	0.966646i
$419$	5.06628			0.247504			0.123752	−	0.992313i	$-0.460507\pi$
$419$	5.06628			0.247504			0.123752	+	0.992313i	$0.460507\pi$
$420$		0			0
$421$		−	2.85433i		−	0.139111i	−0.997578	−	0.0695556i	$-0.977842\pi$
$421$		−	2.85433i		−	0.139111i	0.997578	−	0.0695556i	$-0.0221581\pi$
$422$	12.4476			0.605942
$423$		0			0
$424$		−	2.28524i		−	0.110981i
$425$	3.25199	+	5.26895i	0.157744	+	0.255582i
$426$		0			0
$427$		−	57.8782i		−	2.80092i
$428$			5.95985i			0.288080i
$429$		0			0
$430$	−8.57975	+	2.43452i	−0.413752	+	0.117403i
$431$	−38.9161			−1.87452			−0.937262	−	0.348625i	$-0.886649\pi$
$431$	−38.9161			−1.87452			−0.937262	+	0.348625i	$0.886649\pi$
$432$		0			0
$433$	−7.06301			−0.339426			−0.169713	−	0.985493i	$-0.554284\pi$
$433$	−7.06301			−0.339426			−0.169713	+	0.985493i	$0.554284\pi$
$434$	−6.32780			−0.303744
$435$		0			0
$436$		−	16.7623i		−	0.802771i
$437$	−32.7807	−	19.6740i	−1.56811	−	0.941133i
$438$		0			0
$439$	26.7409			1.27627			0.638136	−	0.769923i	$-0.279706\pi$
$439$	26.7409			1.27627			0.638136	+	0.769923i	$0.279706\pi$
$440$	−5.33298	+	1.51324i	−0.254240	+	0.0721411i
$441$		0			0
$442$	−4.66270			−0.221782
$443$	14.3696			0.682718			0.341359	−	0.939933i	$-0.389113\pi$
$443$	14.3696			0.682718			0.341359	+	0.939933i	$0.389113\pi$
$444$		0			0
$445$	10.0528	−	2.85250i	0.476547	−	0.135221i
$446$			10.0324i			0.475050i
$447$		0			0
$448$	−4.98705			−0.235616
$449$		−	11.3145i		−	0.533966i	−0.963701	−	0.266983i	$-0.913973\pi$
$449$		−	11.3145i		−	0.533966i	0.963701	−	0.266983i	$-0.0860268\pi$
$450$		0			0
$451$			12.0782i			0.568742i
$452$			2.98034i			0.140183i
$453$		0			0
$454$		−	9.16942i		−	0.430342i
$455$	11.4617	+	40.3934i	0.537334	+	1.89367i
$456$		0			0
$457$	7.45519			0.348739			0.174370	−	0.984680i	$-0.444211\pi$
$457$	7.45519			0.348739			0.174370	+	0.984680i	$0.444211\pi$
$458$			14.7086i			0.687288i
$459$		0			0
$460$	−2.79893	+	10.3521i	−0.130501	+	0.482669i
$461$			24.8237i			1.15616i	0.815981	+	0.578078i	$0.196197\pi$
$461$			24.8237i			1.15616i	−0.815981	+	0.578078i	$0.803803\pi$
$462$		0			0
$463$			12.1270i			0.563591i	0.959475	+	0.281795i	$0.0909299\pi$
$463$			12.1270i			0.563591i	−0.959475	+	0.281795i	$0.909070\pi$
$464$		−	6.53426i		−	0.303346i
$465$		0			0
$466$	−24.0936			−1.11612
$467$		−	37.8573i		−	1.75183i	−0.482470	−	0.875913i	$-0.660260\pi$
$467$		−	37.8573i		−	1.75183i	0.482470	−	0.875913i	$-0.339740\pi$
$468$		0			0
$469$	−43.7160			−2.01862
$470$	22.1072	−	6.27296i	1.01973	−	0.289350i
$471$		0			0
$472$		−	10.2995i		−	0.474075i
$473$	9.88793			0.454648
$474$		0			0
$475$	−20.9346	−	33.9187i	−0.960544	−	1.55630i
$476$		−	6.17567i		−	0.283062i
$477$		0			0
$478$		−	10.9948i		−	0.502891i
$479$	0.0987532			0.00451215			0.00225607	−	0.999997i	$-0.499282\pi$
$479$	0.0987532			0.00451215			0.00225607	+	0.999997i	$0.499282\pi$
$480$		0			0
$481$			40.5516i			1.84899i
$482$		−	14.3516i		−	0.653699i
$483$		0			0
$484$	−4.85389			−0.220631
$485$	−17.4456	+	4.95022i	−0.792163	+	0.224778i
$486$		0			0
$487$		−	7.96068i		−	0.360733i	−0.983599	−	0.180366i	$-0.942272\pi$
$487$		−	7.96068i		−	0.360733i	0.983599	−	0.180366i	$-0.0577283\pi$
$488$			11.6057i			0.525365i
$489$		0			0
$490$	−38.4424	+	10.9081i	−1.73665	+	0.492779i
$491$			22.1094i			0.997785i	0.866664	+	0.498892i	$0.166260\pi$
$491$			22.1094i			0.997785i	−0.866664	+	0.498892i	$0.833740\pi$
$492$		0			0
$493$	8.09165			0.364430
$494$	30.0160			1.35048
$495$		0			0
$496$	1.26885			0.0569728
$497$			58.7795i			2.63662i
$498$		0			0
$499$	−9.48101			−0.424428			−0.212214	−	0.977223i	$-0.568067\pi$
$499$	−9.48101			−0.424428			−0.212214	+	0.977223i	$0.568067\pi$
$500$	−7.54984	+	8.24620i	−0.337639	+	0.368781i
$501$		0			0
$502$	20.6512			0.921710
$503$		−	6.87247i		−	0.306428i	−0.988193	−	0.153214i	$-0.951038\pi$
$503$		−	6.87247i		−	0.306428i	0.988193	−	0.153214i	$-0.0489624\pi$
$504$		0			0
$505$	4.37771	+	15.4279i	0.194806	+	0.686535i
$506$	6.11838	−	10.1944i	0.271995	−	0.453197i
$507$		0			0
$508$			11.9564i			0.530478i
$509$			30.1695i			1.33724i	0.743604	+	0.668621i	$0.233115\pi$
$509$			30.1695i			1.33724i	−0.743604	+	0.668621i	$0.766885\pi$
$510$		0			0
$511$			60.5678i			2.67936i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−8.21345			−0.362280
$515$	29.2376	−	8.29622i	1.28836	−	0.365575i
$516$		0			0
$517$	−25.4779			−1.12052
$518$	−53.7100			−2.35988
$519$		0			0
$520$	−2.29830	−	8.09966i	−0.100787	−	0.355194i
$521$	35.9075			1.57314			0.786568	−	0.617503i	$-0.211856\pi$
$521$	35.9075			1.57314			0.786568	+	0.617503i	$0.211856\pi$
$522$		0			0
$523$	−36.1083			−1.57890			−0.789452	−	0.613812i	$-0.789635\pi$
$523$	−36.1083			−1.57890			−0.789452	+	0.613812i	$0.789635\pi$
$524$		−	15.6272i		−	0.682679i
$525$		0			0
$526$			8.92373i			0.389093i
$527$			1.57126i			0.0684453i
$528$		0			0
$529$	−10.8185	−	20.2968i	−0.470368	−	0.882470i
$530$	1.39489	+	4.91589i	0.0605903	+	0.213532i
$531$		0			0
$532$			39.7557i			1.72363i
$533$	−18.3443			−0.794579
$534$		0			0
$535$	−3.63784	−	12.8205i	−0.157278	−	0.554278i
$536$	8.76589			0.378629
$537$		0			0
$538$		−	27.0106i		−	1.16451i
$539$	44.3039			1.90830
$540$		0			0
$541$	0.466937			0.0200752			0.0100376	−	0.999950i	$-0.496805\pi$
$541$	0.466937			0.0200752			0.0100376	+	0.999950i	$0.496805\pi$
$542$	10.0281			0.430742
$543$		0			0
$544$			1.23834i			0.0530935i
$545$	10.2316	+	36.0582i	0.438273	+	1.54456i
$546$		0			0
$547$		−	5.51151i		−	0.235655i	−0.993034	−	0.117828i	$-0.962407\pi$
$547$		−	5.51151i		−	0.235655i	0.993034	−	0.117828i	$-0.0375930\pi$
$548$		−	5.77371i		−	0.246641i
$549$		0			0
$550$	10.5483	−	6.51041i	0.449782	−	0.277605i
$551$	−52.0897			−2.21910
$552$		0			0
$553$		−	0.637709i		−	0.0271181i
$554$		−	15.1187i		−	0.642331i
$555$		0			0
$556$	5.56508			0.236012
$557$		−	5.88264i		−	0.249255i	−0.992204	−	0.124628i	$-0.960226\pi$
$557$		−	5.88264i		−	0.249255i	0.992204	−	0.124628i	$-0.0397736\pi$
$558$		0			0
$559$			15.0177i			0.635180i
$560$	10.7279	−	3.04406i	0.453335	−	0.128635i
$561$		0			0
$562$	13.7542			0.580186
$563$		−	37.7385i		−	1.59049i	−0.606290	−	0.795244i	$-0.707343\pi$
$563$		−	37.7385i		−	1.59049i	0.606290	−	0.795244i	$-0.292657\pi$
$564$		0			0
$565$	−1.81918	−	6.41115i	−0.0765333	−	0.269719i
$566$	2.17583			0.0914569
$567$		0			0
$568$		−	11.7864i		−	0.494547i
$569$	−6.23306			−0.261303			−0.130652	−	0.991428i	$-0.541707\pi$
$569$	−6.23306			−0.261303			−0.130652	+	0.991428i	$0.541707\pi$
$570$		0			0
$571$		−	7.40339i		−	0.309822i	−0.987928	−	0.154911i	$-0.950491\pi$
$571$		−	7.40339i		−	0.309822i	0.987928	−	0.154911i	$-0.0495091\pi$
$572$			9.33464i			0.390301i
$573$		0			0
$574$		−	24.2967i		−	1.01413i
$575$	−0.297931	−	23.9773i	−0.0124246	−	0.999923i
$576$		0			0
$577$			4.29744i			0.178905i	0.995991	+	0.0894524i	$0.0285117\pi$
$577$			4.29744i			0.178905i	−0.995991	+	0.0894524i	$0.971488\pi$
$578$	15.4665			0.643322
$579$		0			0
$580$	3.98846	+	14.0561i	0.165612	+	0.583649i
$581$		−	19.5841i		−	0.812485i
$582$		0			0
$583$		−	5.66543i		−	0.234638i
$584$		−	12.1450i		−	0.502564i
$585$		0			0
$586$		−	2.69105i		−	0.111166i
$587$	−20.3978			−0.841906			−0.420953	−	0.907082i	$-0.638304\pi$
$587$	−20.3978			−0.841906			−0.420953	+	0.907082i	$0.638304\pi$
$588$		0			0
$589$		−	10.1150i		−	0.416780i
$590$	6.28676	+	22.1558i	0.258822	+	0.912140i
$591$		0			0
$592$	10.7699			0.442639
$593$	23.2995			0.956795			0.478397	−	0.878143i	$-0.341218\pi$
$593$	23.2995			0.956795			0.478397	+	0.878143i	$0.341218\pi$
$594$		0			0
$595$	3.76958	+	13.2848i	0.154538	+	0.544622i
$596$	4.52336			0.185284
$597$		0			0
$598$	15.4831	+	9.29252i	0.633153	+	0.379999i
$599$			32.3903i			1.32343i	0.749755	+	0.661715i	$0.230171\pi$
$599$			32.3903i			1.32343i	−0.749755	+	0.661715i	$0.769829\pi$
$600$		0			0
$601$	−11.9628			−0.487973			−0.243986	−	0.969779i	$-0.578455\pi$
$601$	−11.9628			−0.487973			−0.243986	+	0.969779i	$0.578455\pi$
$602$	−19.8907			−0.810683
$603$		0			0
$604$	12.0748			0.491315
$605$	10.4414	−	2.96277i	0.424504	−	0.120454i
$606$		0			0
$607$		−	0.105548i		−	0.00428405i	−0.999998	−	0.00214203i	$-0.999318\pi$
$607$		−	0.105548i		−	0.00428405i	0.999998	−	0.00214203i	$-0.000681829\pi$
$608$		−	7.97179i		−	0.323299i
$609$		0			0
$610$	−7.08401	−	24.9655i	−0.286823	−	1.01082i
$611$		−	38.6956i		−	1.56545i
$612$		0			0
$613$	9.65220			0.389849			0.194924	−	0.980818i	$-0.437554\pi$
$613$	9.65220			0.389849			0.194924	+	0.980818i	$0.437554\pi$
$614$		−	8.54556i		−	0.344871i
$615$		0			0
$616$	−12.3636			−0.498143
$617$		−	21.4993i		−	0.865531i	−0.901507	−	0.432766i	$-0.857538\pi$
$617$		−	21.4993i		−	0.865531i	0.901507	−	0.432766i	$-0.142462\pi$
$618$		0			0
$619$			16.5776i			0.666309i	0.942872	+	0.333154i	$0.108113\pi$
$619$			16.5776i			0.666309i	−0.942872	+	0.333154i	$0.891887\pi$
$620$	−2.72947	+	0.774493i	−0.109618	+	0.0311044i
$621$		0			0
$622$			23.4652i			0.940870i
$623$	23.3056			0.933720
$624$		0			0
$625$	11.2074	−	22.3471i	0.448296	−	0.893885i
$626$	26.3565			1.05342
$627$		0			0
$628$	−0.865604			−0.0345414
$629$			13.3368i			0.531773i
$630$		0			0
$631$		−	23.8769i		−	0.950525i	−0.879844	−	0.475263i	$-0.842353\pi$
$631$		−	23.8769i		−	0.950525i	0.879844	−	0.475263i	$-0.157647\pi$
$632$			0.127873i			0.00508651i
$633$		0			0
$634$	17.0134			0.675688
$635$	−7.29807	−	25.7199i	−0.289615	−	1.02066i
$636$		0			0
$637$			67.2882i			2.66605i
$638$		−	16.1993i		−	0.641337i
$639$		0			0
$640$	−2.15114	+	0.610392i	−0.0850314	+	0.0241279i
$641$	1.78292			0.0704210			0.0352105	−	0.999380i	$-0.488790\pi$
$641$	1.78292			0.0704210			0.0352105	+	0.999380i	$0.488790\pi$
$642$		0			0
$643$	12.8560			0.506990			0.253495	−	0.967337i	$-0.418420\pi$
$643$	12.8560			0.506990			0.253495	+	0.967337i	$0.418420\pi$
$644$	−12.3078	+	20.5072i	−0.484995	+	0.808096i
$645$		0			0
$646$	9.87179			0.388401
$647$	−26.6314			−1.04699			−0.523494	−	0.852029i	$-0.675372\pi$
$647$	−26.6314			−1.04699			−0.523494	+	0.852029i	$0.675372\pi$
$648$		0			0
$649$		−	25.5340i		−	1.00230i
$650$	9.88793	+	16.0207i	0.387837	+	0.628383i
$651$		0			0
$652$		−	17.3972i		−	0.681326i
$653$	3.53045			0.138157			0.0690786	−	0.997611i	$-0.477994\pi$
$653$	3.53045			0.138157			0.0690786	+	0.997611i	$0.477994\pi$
$654$		0			0
$655$	9.53874	+	33.6165i	0.372709	+	1.31350i
$656$			4.87196i			0.190218i
$657$		0			0
$658$	51.2517			1.99800
$659$	−1.64358			−0.0640248			−0.0320124	−	0.999487i	$-0.510192\pi$
$659$	−1.64358			−0.0640248			−0.0320124	+	0.999487i	$0.510192\pi$
$660$		0			0
$661$		−	12.3155i		−	0.479019i	−0.970894	−	0.239509i	$-0.923013\pi$
$661$		−	12.3155i		−	0.479019i	0.970894	−	0.239509i	$-0.0769865\pi$
$662$	−6.49178			−0.252310
$663$		0			0
$664$			3.92699i			0.152397i
$665$	−24.2666	−	85.5203i	−0.941017	−	3.31633i
$666$		0			0
$667$	−26.8694	−	16.1262i	−1.04039	−	0.624410i
$668$	12.7687			0.494037
$669$		0			0
$670$	−18.8567	+	5.35063i	−0.728498	+	0.206713i
$671$			28.7721i			1.11073i
$672$		0			0
$673$		−	17.9266i		−	0.691020i	−0.938415	−	0.345510i	$-0.887706\pi$
$673$		−	17.9266i		−	0.691020i	0.938415	−	0.345510i	$-0.112294\pi$
$674$	2.19629			0.0845978
$675$		0			0
$676$	−1.17733			−0.0452818
$677$			19.2181i			0.738612i	0.929308	+	0.369306i	$0.120405\pi$
$677$			19.2181i			0.738612i	−0.929308	+	0.369306i	$0.879595\pi$
$678$		0			0
$679$	−40.4445			−1.55212
$680$	−0.755873	−	2.66385i	−0.0289864	−	0.102154i
$681$		0			0
$682$	3.14564			0.120453
$683$	20.5216			0.785238			0.392619	−	0.919701i	$-0.371569\pi$
$683$	20.5216			0.785238			0.392619	+	0.919701i	$0.371569\pi$
$684$		0			0
$685$	3.52423	+	12.4201i	0.134654	+	0.474547i
$686$	−54.2127			−2.06985
$687$		0			0
$688$	3.98846			0.152059
$689$	8.60458			0.327808
$690$		0			0
$691$	50.4117			1.91775			0.958875	−	0.283827i	$-0.0916042\pi$
$691$	50.4117			1.91775			0.958875	+	0.283827i	$0.0916042\pi$
$692$	−1.33089			−0.0505928
$693$		0			0
$694$	−18.3082			−0.694968
$695$	−11.9713	+	3.39688i	−0.454097	+	0.128851i
$696$		0			0
$697$	−6.03315			−0.228522
$698$	−18.8138			−0.712114
$699$		0			0
$700$	−21.2191	+	13.0964i	−0.802008	+	0.494998i
$701$	−32.1749			−1.21523			−0.607615	−	0.794232i	$-0.707874\pi$
$701$	−32.1749			−1.21523			−0.607615	+	0.794232i	$0.707874\pi$
$702$		0			0
$703$		−	85.8552i		−	3.23809i
$704$	2.47913			0.0934359
$705$		0			0
$706$	−2.76173			−0.103939
$707$			35.7670i			1.34516i
$708$		0			0
$709$		−	7.57508i		−	0.284488i	−0.989832	−	0.142244i	$-0.954568\pi$
$709$		−	7.57508i		−	0.284488i	0.989832	−	0.142244i	$-0.0454318\pi$
$710$	7.19434	+	25.3543i	0.269999	+	0.951530i
$711$		0			0
$712$	−4.67322			−0.175136
$713$	3.13144	−	5.21760i	0.117274	−	0.195401i
$714$		0			0
$715$	−5.69778	−	20.0801i	−0.213085	−	0.750955i
$716$			13.0630i			0.488189i
$717$		0			0
$718$	5.23786			0.195475
$719$		−	7.86628i		−	0.293363i	−0.989184	−	0.146681i	$-0.953141\pi$
$719$		−	7.86628i		−	0.293363i	0.989184	−	0.146681i	$-0.0468592\pi$
$720$		0			0
$721$	67.7822			2.52434
$722$	−44.5494			−1.65796
$723$		0			0
$724$			17.6900i			0.657445i
$725$	−17.1595	−	27.8023i	−0.637288	−	1.03255i
$726$		0			0
$727$	−0.770654			−0.0285820			−0.0142910	−	0.999898i	$-0.504549\pi$
$727$	−0.770654			−0.0285820			−0.0142910	+	0.999898i	$0.504549\pi$
$728$		−	18.7776i		−	0.695946i
$729$		0			0
$730$	7.41322	+	26.1257i	0.274375	+	0.966955i
$731$			4.93908i			0.182678i
$732$		0			0
$733$	3.50991			0.129642			0.0648208	−	0.997897i	$-0.479352\pi$
$733$	3.50991			0.129642			0.0648208	+	0.997897i	$0.479352\pi$
$734$	10.1541			0.374796
$735$		0			0
$736$	2.46795	−	4.11208i	0.0909698	−	0.151573i
$737$	21.7318			0.800502
$738$		0			0
$739$	18.9666			0.697699			0.348849	−	0.937179i	$-0.386572\pi$
$739$	18.9666			0.697699			0.348849	+	0.937179i	$0.386572\pi$
$740$	−23.1676	+	6.57385i	−0.851657	+	0.241659i
$741$		0			0
$742$			11.3966i			0.418383i
$743$			21.6530i			0.794373i	0.917738	+	0.397187i	$0.130013\pi$
$743$			21.6530i			0.794373i	−0.917738	+	0.397187i	$0.869987\pi$
$744$		0			0
$745$	−9.73041	+	2.76102i	−0.356495	+	0.101156i
$746$	−28.0098			−1.02551
$747$		0			0
$748$			3.07002i			0.112251i
$749$		−	29.7221i		−	1.08602i
$750$		0			0
$751$			2.16343i			0.0789446i	0.999221	+	0.0394723i	$0.0125677\pi$
$751$			2.16343i			0.0789446i	−0.999221	+	0.0394723i	$0.987432\pi$
$752$	−10.2769			−0.374762
$753$		0			0
$754$	24.6033			0.896000
$755$	−25.9746	+	7.37034i	−0.945311	+	0.268234i
$756$		0			0
$757$	−1.79576			−0.0652680			−0.0326340	−	0.999467i	$-0.510390\pi$
$757$	−1.79576			−0.0652680			−0.0326340	+	0.999467i	$0.510390\pi$
$758$			2.15806i			0.0783842i
$759$		0			0
$760$	4.86591	+	17.1485i	0.176505	+	0.622040i
$761$			29.4682i			1.06822i	0.845415	+	0.534111i	$0.179353\pi$
$761$			29.4682i			1.06822i	−0.845415	+	0.534111i	$0.820647\pi$
$762$		0			0
$763$			83.5947i			3.02633i
$764$	−17.7702			−0.642903
$765$		0			0
$766$		−	31.7631i		−	1.14765i
$767$	38.7807			1.40029
$768$		0			0
$769$			45.2831i			1.63295i	0.577380	+	0.816475i	$0.304075\pi$
$769$			45.2831i			1.63295i	−0.577380	+	0.816475i	$0.695925\pi$
$770$	26.5958	−	7.54663i	0.958448	−	0.271962i
$771$		0			0
$772$			22.1519i			0.797265i
$773$		−	11.5070i		−	0.413877i	−0.978354	−	0.206939i	$-0.933650\pi$
$773$		−	11.5070i		−	0.413877i	0.978354	−	0.206939i	$-0.0663500\pi$
$774$		0			0
$775$	5.39874	−	3.33209i	0.193928	−	0.119692i
$776$	8.10991			0.291129
$777$		0			0
$778$	20.1944			0.724005
$779$	38.8382			1.39152
$780$		0			0
$781$		−	29.2201i		−	1.04558i
$782$	5.09216	+	3.05616i	0.182095	+	0.109288i
$783$		0			0
$784$	17.8707			0.638239
$785$	1.86204	−	0.528357i	0.0664590	−	0.0188579i
$786$		0			0
$787$	17.6627			0.629608			0.314804	−	0.949157i	$-0.398061\pi$
$787$	17.6627			0.629608			0.314804	+	0.949157i	$0.398061\pi$
$788$	−13.6945			−0.487845
$789$		0			0
$790$	−0.0780525	−	0.275073i	−0.00277698	−	0.00978666i
$791$		−	14.8631i		−	0.528472i
$792$		0			0
$793$	−43.6986			−1.55178
$794$		−	2.83784i		−	0.100711i
$795$		0			0
$796$		−	19.0529i		−	0.675312i
$797$			12.9476i			0.458627i	0.973353	+	0.229313i	$0.0736481\pi$
$797$			12.9476i			0.458627i	−0.973353	+	0.229313i	$0.926352\pi$
$798$		0			0
$799$		−	12.7264i		−	0.450226i
$800$	4.25484	−	2.62608i	0.150431	−	0.0928460i
$801$		0			0
$802$	−13.5683			−0.479113
$803$		−	30.1091i		−	1.06253i
$804$		0			0
$805$	13.9584	−	51.6265i	0.491970	−	1.81959i
$806$			4.77756i			0.168282i
$807$		0			0
$808$		−	7.17197i		−	0.252309i
$809$		−	31.8846i		−	1.12100i	−0.828154	−	0.560501i	$-0.810609\pi$
$809$		−	31.8846i		−	1.12100i	0.828154	−	0.560501i	$-0.189391\pi$
$810$		0			0
$811$	32.7747			1.15087			0.575437	−	0.817846i	$-0.304832\pi$
$811$	32.7747			1.15087			0.575437	+	0.817846i	$0.304832\pi$
$812$			32.5867i			1.14357i
$813$		0			0
$814$	26.7000			0.935834
$815$	10.6191	+	37.4238i	0.371971	+	1.31090i
$816$		0			0
$817$		−	31.7951i		−	1.11237i
$818$	−4.25145			−0.148648
$819$		0			0
$820$	−2.97380	−	10.4803i	−0.103850	−	0.365987i
$821$			26.9939i			0.942092i	0.882109	+	0.471046i	$0.156123\pi$
$821$			26.9939i			0.942092i	−0.882109	+	0.471046i	$0.843877\pi$
$822$		0			0
$823$		−	6.69974i		−	0.233538i	−0.993159	−	0.116769i	$-0.962746\pi$
$823$		−	6.69974i		−	0.233538i	0.993159	−	0.116769i	$-0.0372538\pi$
$824$	−13.5916			−0.473487
$825$		0			0
$826$			51.3644i			1.78719i
$827$		−	30.7794i		−	1.07030i	−0.844756	−	0.535151i	$-0.820255\pi$
$827$		−	30.7794i		−	1.07030i	0.844756	−	0.535151i	$-0.179745\pi$
$828$		0			0
$829$	−38.8486			−1.34927			−0.674634	−	0.738152i	$-0.735699\pi$
$829$	−38.8486			−1.34927			−0.674634	+	0.738152i	$0.735699\pi$
$830$	−2.39700	−	8.44751i	−0.0832011	−	0.293217i
$831$		0			0
$832$			3.76528i			0.130538i
$833$			22.1300i			0.766760i
$834$		0			0
$835$	−27.4674	+	7.79392i	−0.950548	+	0.269720i
$836$		−	19.7631i		−	0.683522i
$837$		0			0
$838$	5.06628			0.175012
$839$	15.8780			0.548169			0.274085	−	0.961706i	$-0.411625\pi$
$839$	15.8780			0.548169			0.274085	+	0.961706i	$0.411625\pi$
$840$		0			0
$841$	−13.6966			−0.472296
$842$		−	2.85433i		−	0.0983665i
$843$		0			0
$844$	12.4476			0.428466
$845$	2.53260	−	0.718631i	0.0871242	−	0.0247217i
$846$		0			0
$847$	24.2066			0.831749
$848$		−	2.28524i		−	0.0784756i
$849$		0			0
$850$	3.25199	+	5.26895i	0.111542	+	0.180723i
$851$	26.5795	−	44.2867i	0.911134	−	1.51813i
$852$		0			0
$853$			16.1791i			0.553960i	0.960876	+	0.276980i	$0.0893336\pi$
$853$			16.1791i			0.553960i	−0.960876	+	0.276980i	$0.910666\pi$
$854$		−	57.8782i		−	1.98055i
$855$		0			0
$856$			5.95985i			0.203703i
$857$	−46.4835			−1.58785			−0.793923	−	0.608018i	$-0.791965\pi$
$857$	−46.4835			−1.58785			−0.793923	+	0.608018i	$0.791965\pi$
$858$		0			0
$859$	−52.7684			−1.80043			−0.900217	−	0.435443i	$-0.856592\pi$
$859$	−52.7684			−1.80043			−0.900217	+	0.435443i	$0.856592\pi$
$860$	−8.57975	+	2.43452i	−0.292567	+	0.0830165i
$861$		0			0
$862$	−38.9161			−1.32549
$863$	55.0222			1.87298			0.936488	−	0.350699i	$-0.114056\pi$
$863$	55.0222			1.87298			0.936488	+	0.350699i	$0.114056\pi$
$864$		0			0
$865$	2.86293	−	0.812364i	0.0973427	−	0.0276212i
$866$	−7.06301			−0.240011
$867$		0			0
$868$	−6.32780			−0.214779
$869$			0.317014i			0.0107540i
$870$		0			0
$871$			33.0060i			1.11837i
$872$		−	16.7623i		−	0.567645i
$873$		0			0
$874$	−32.7807	−	19.6740i	−1.10882	−	0.665482i
$875$	37.6515	−	41.1242i	1.27285	−	1.39025i
$876$		0			0
$877$			36.7430i			1.24072i	0.784316	+	0.620361i	$0.213014\pi$
$877$			36.7430i			1.24072i	−0.784316	+	0.620361i	$0.786986\pi$
$878$	26.7409			0.902461
$879$		0			0
$880$	−5.33298	+	1.51324i	−0.179775	+	0.0510114i
$881$	−22.1689			−0.746889			−0.373444	−	0.927653i	$-0.621823\pi$
$881$	−22.1689			−0.746889			−0.373444	+	0.927653i	$0.621823\pi$
$882$		0			0
$883$		−	3.92849i		−	0.132204i	−0.997813	−	0.0661021i	$-0.978944\pi$
$883$		−	3.92849i		−	0.132204i	0.997813	−	0.0661021i	$-0.0210563\pi$
$884$	−4.66270			−0.156824
$885$		0			0
$886$	14.3696			0.482755
$887$	−9.18286			−0.308330			−0.154165	−	0.988045i	$-0.549269\pi$
$887$	−9.18286			−0.308330			−0.154165	+	0.988045i	$0.549269\pi$
$888$		0			0
$889$		−	59.6270i		−	1.99983i
$890$	10.0528	−	2.85250i	0.336970	−	0.0956159i
$891$		0			0
$892$			10.0324i			0.335911i
$893$			81.9256i			2.74154i
$894$		0			0
$895$	−7.97358	−	28.1005i	−0.266527	−	0.939296i
$896$	−4.98705			−0.166606
$897$		0			0
$898$		−	11.3145i		−	0.377571i
$899$		−	8.29097i		−	0.276519i
$900$		0			0
$901$	2.82991			0.0942780
$902$			12.0782i			0.402161i
$903$		0			0
$904$			2.98034i			0.0991247i
$905$	−10.7979	−	38.0538i	−0.358933	−	1.26495i
$906$		0			0
$907$	−8.38475			−0.278411			−0.139205	−	0.990264i	$-0.544455\pi$
$907$	−8.38475			−0.278411			−0.139205	+	0.990264i	$0.544455\pi$
$908$		−	9.16942i		−	0.304298i
$909$		0			0
$910$	11.4617	+	40.3934i	0.379952	+	1.33903i
$911$	34.6193			1.14699			0.573494	−	0.819210i	$-0.305588\pi$
$911$	34.6193			1.14699			0.573494	+	0.819210i	$0.305588\pi$
$912$		0			0
$913$			9.73553i			0.322199i
$914$	7.45519			0.246596
$915$		0			0
$916$			14.7086i			0.485986i
$917$			77.9339i			2.57360i
$918$		0			0
$919$		−	20.4975i		−	0.676149i	−0.941119	−	0.338074i	$-0.890224\pi$
$919$		−	20.4975i		−	0.676149i	0.941119	−	0.338074i	$-0.109776\pi$
$920$	−2.79893	+	10.3521i	−0.0922780	+	0.341299i
$921$		0			0
$922$			24.8237i			0.817526i
$923$	44.3792			1.46076
$924$		0			0
$925$	45.8242	−	28.2826i	1.50669	−	0.929926i
$926$			12.1270i			0.398519i
$927$		0			0
$928$		−	6.53426i		−	0.214498i
$929$			1.54372i			0.0506478i	0.999679	+	0.0253239i	$0.00806170\pi$
$929$			1.54372i			0.0506478i	−0.999679	+	0.0253239i	$0.991938\pi$
$930$		0			0
$931$		−	142.461i		−	4.66898i
$932$	−24.0936			−0.789213
$933$		0			0
$934$		−	37.8573i		−	1.23873i
$935$	−1.87391	−	6.60405i	−0.0612835	−	0.215975i
$936$		0			0
$937$	29.0424			0.948773			0.474387	−	0.880317i	$-0.342670\pi$
$937$	29.0424			0.948773			0.474387	+	0.880317i	$0.342670\pi$
$938$	−43.7160			−1.42738
$939$		0			0
$940$	22.1072	−	6.27296i	0.721057	−	0.204601i
$941$	45.3795			1.47933			0.739665	−	0.672975i	$-0.234984\pi$
$941$	45.3795			1.47933			0.739665	+	0.672975i	$0.234984\pi$
$942$		0			0
$943$	20.0339	+	12.0237i	0.652394	+	0.391547i
$944$		−	10.2995i		−	0.335222i
$945$		0			0
$946$	9.88793			0.321484
$947$	34.6112			1.12471			0.562357	−	0.826895i	$-0.309895\pi$
$947$	34.6112			1.12471			0.562357	+	0.826895i	$0.309895\pi$
$948$		0			0
$949$	45.7294			1.48444
$950$	−20.9346	−	33.9187i	−0.679207	−	1.10047i
$951$		0			0
$952$		−	6.17567i		−	0.200155i
$953$			34.6425i			1.12218i	0.827755	+	0.561090i	$0.189618\pi$
$953$			34.6425i			1.12218i	−0.827755	+	0.561090i	$0.810382\pi$
$954$		0			0
$955$	38.2262	−	10.8468i	1.23697	−	0.350993i
$956$		−	10.9948i		−	0.355597i
$957$		0			0
$958$	0.0987532			0.00319057
$959$			28.7938i			0.929800i
$960$		0			0
$961$	−29.3900			−0.948066
$962$			40.5516i			1.30744i
$963$		0			0
$964$		−	14.3516i		−	0.462235i
$965$	−13.5213	−	47.6520i	−0.435267	−	1.53397i
$966$		0			0
$967$			44.7844i			1.44017i	0.693886	+	0.720084i	$0.255897\pi$
$967$			44.7844i			1.44017i	−0.693886	+	0.720084i	$0.744103\pi$
$968$	−4.85389			−0.156010
$969$		0			0
$970$	−17.4456	+	4.95022i	−0.560144	+	0.158942i
$971$	−32.2046			−1.03350			−0.516748	−	0.856138i	$-0.672858\pi$
$971$	−32.2046			−1.03350			−0.516748	+	0.856138i	$0.672858\pi$
$972$		0			0
$973$	−27.7534			−0.889732
$974$		−	7.96068i		−	0.255077i
$975$		0			0
$976$			11.6057i			0.371489i
$977$		−	49.2919i		−	1.57699i	−0.615043	−	0.788494i	$-0.710861\pi$
$977$		−	49.2919i		−	1.57699i	0.615043	−	0.788494i	$-0.289139\pi$
$978$		0			0
$979$	−11.5856			−0.370276
$980$	−38.4424	+	10.9081i	−1.22800	+	0.348447i
$981$		0			0
$982$			22.1094i			0.705540i
$983$			2.17961i			0.0695189i	0.999396	+	0.0347595i	$0.0110665\pi$
$983$			2.17961i			0.0695189i	−0.999396	+	0.0347595i	$0.988933\pi$
$984$		0			0
$985$	29.4588	−	8.35899i	0.938635	−	0.266340i
$986$	8.09165			0.257691
$987$		0			0
$988$	30.0160			0.954936
$989$	9.84331	−	16.4009i	0.312999	−	0.521518i
$990$		0			0
$991$	16.4164			0.521485			0.260742	−	0.965408i	$-0.416033\pi$
$991$	16.4164			0.521485			0.260742	+	0.965408i	$0.416033\pi$
$992$	1.26885			0.0402859
$993$		0			0
$994$			58.7795i			1.86437i
$995$	11.6297	+	40.9855i	0.368687	+	1.29933i
$996$		0			0
$997$			45.3848i			1.43735i	0.695346	+	0.718676i	$0.255251\pi$
$997$			45.3848i			1.43735i	−0.695346	+	0.718676i	$0.744749\pi$
$998$	−9.48101			−0.300116
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.h.b.2069.4	yes	24
3.2	odd	2		2070.2.h.a.2069.21	yes	24
5.4	even	2		2070.2.h.a.2069.3	✓	24
15.14	odd	2	inner	2070.2.h.b.2069.22	yes	24
23.22	odd	2	inner	2070.2.h.b.2069.21	yes	24
69.68	even	2		2070.2.h.a.2069.4	yes	24
115.114	odd	2		2070.2.h.a.2069.22	yes	24
345.344	even	2	inner	2070.2.h.b.2069.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.h.a.2069.3	✓	24	5.4	even	2
2070.2.h.a.2069.4	yes	24	69.68	even	2
2070.2.h.a.2069.21	yes	24	3.2	odd	2
2070.2.h.a.2069.22	yes	24	115.114	odd	2
2070.2.h.b.2069.3	yes	24	345.344	even	2	inner
2070.2.h.b.2069.4	yes	24	1.1	even	1	trivial
2070.2.h.b.2069.21	yes	24	23.22	odd	2	inner
2070.2.h.b.2069.22	yes	24	15.14	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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.15114 + 0.610392i) q^{5} -4.98705 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.15114 + 0.610392i) q^{5} -4.98705 q^{7} +1.00000 q^{8} +(-2.15114 + 0.610392i) q^{10} +2.47913 q^{11} +3.76528i q^{13} -4.98705 q^{14} +1.00000 q^{16} +1.23834i q^{17} -7.97179i q^{19} +(-2.15114 + 0.610392i) q^{20} +2.47913 q^{22} +(2.46795 - 4.11208i) q^{23} +(4.25484 - 2.62608i) q^{25} +3.76528i q^{26} -4.98705 q^{28} -6.53426i q^{29} +1.26885 q^{31} +1.00000 q^{32} +1.23834i q^{34} +(10.7279 - 3.04406i) q^{35} +10.7699 q^{37} -7.97179i q^{38} +(-2.15114 + 0.610392i) q^{40} +4.87196i q^{41} +3.98846 q^{43} +2.47913 q^{44} +(2.46795 - 4.11208i) q^{46} -10.2769 q^{47} +17.8707 q^{49} +(4.25484 - 2.62608i) q^{50} +3.76528i q^{52} -2.28524i q^{53} +(-5.33298 + 1.51324i) q^{55} -4.98705 q^{56} -6.53426i q^{58} -10.2995i q^{59} +11.6057i q^{61} +1.26885 q^{62} +1.00000 q^{64} +(-2.29830 - 8.09966i) q^{65} +8.76589 q^{67} +1.23834i q^{68} +(10.7279 - 3.04406i) q^{70} -11.7864i q^{71} -12.1450i q^{73} +10.7699 q^{74} -7.97179i q^{76} -12.3636 q^{77} +0.127873i q^{79} +(-2.15114 + 0.610392i) q^{80} +4.87196i q^{82} +3.92699i q^{83} +(-0.755873 - 2.66385i) q^{85} +3.98846 q^{86} +2.47913 q^{88} -4.67322 q^{89} -18.7776i q^{91} +(2.46795 - 4.11208i) q^{92} -10.2769 q^{94} +(4.86591 + 17.1485i) q^{95} +8.10991 q^{97} +17.8707 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q + 24 * q^2 + 24 * q^4 + 24 * q^8	\( 24 q + 24 q^{2} + 24 q^{4} + 24 q^{8} + 24 q^{16} + 4 q^{23} + 8 q^{31} + 24 q^{32} + 16 q^{35} + 4 q^{46} - 16 q^{47} + 56 q^{49} - 8 q^{55} + 8 q^{62} + 24 q^{64} + 16 q^{70} + 40 q^{77} + 64 q^{85} + 4 q^{92} - 16 q^{94} + 8 q^{95} + 56 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 + 24 * q^4 + 24 * q^8 + 24 * q^16 + 4 * q^23 + 8 * q^31 + 24 * q^32 + 16 * q^35 + 4 * q^46 - 16 * q^47 + 56 * q^49 - 8 * q^55 + 8 * q^62 + 24 * q^64 + 16 * q^70 + 40 * q^77 + 64 * q^85 + 4 * q^92 - 16 * q^94 + 8 * q^95 + 56 * q^98

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