LMFDB - Embedded newform 2268.2.k.c.1621.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1297,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("2268.1297");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.k (of order $3$, degree $2$, 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.3
Root			$-0.198169 - 0.343239i$ of defining polynomial
Character	$\chi$	$=$	2268.1621
Dual form			2268.2.k.c.1297.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.705299 + 1.22161i) q^{5} +(2.57934 - 0.589053i) q^{7} +O(q^{10})$	$q+(0.705299 + 1.22161i) q^{5} +(2.57934 - 0.589053i) q^{7} +(2.48484 - 4.30386i) q^{11} -2.96967 q^{13} +(-1.29981 + 2.25133i) q^{17} +(-3.76437 - 6.52009i) q^{19} +(-4.06418 - 7.03937i) q^{23} +(1.50511 - 2.60692i) q^{25} -6.93935 q^{29} +(5.26948 - 9.12701i) q^{31} +(2.53880 + 2.73550i) q^{35} +(-0.0945078 - 0.163692i) q^{37} +2.04054 q^{41} -4.38027 q^{43} +(4.69014 + 8.12355i) q^{47} +(6.30603 - 3.03874i) q^{49} +(-6.95339 + 12.0436i) q^{53} +7.01021 q^{55} +(3.39431 - 5.87913i) q^{59} +(-2.94828 - 5.10658i) q^{61} +(-2.09451 - 3.62779i) q^{65} +(-5.00623 + 8.67104i) q^{67} -7.86174 q^{71} +(0.894315 - 1.54900i) q^{73} +(3.87405 - 12.5648i) q^{77} +(-0.853775 - 1.47878i) q^{79} -0.0201149 q^{83} -3.66701 q^{85} +(7.33366 + 12.7023i) q^{89} +(-7.65981 + 1.74929i) q^{91} +(5.31002 - 9.19722i) q^{95} +8.67272 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} + q^{7}+O(q^{10}) $ 8 * q - 2 * q^5 + q^7	$ 8 q - 2 q^{5} + q^{7} + 5 q^{11} + 6 q^{13} + 2 q^{17} - 8 q^{19} + 2 q^{23} - 8 q^{25} + 4 q^{29} + 11 q^{35} + 4 q^{37} + 6 q^{41} + 10 q^{43} + 15 q^{47} + 5 q^{49} - 24 q^{53} + 16 q^{55} + 10 q^{59} - 12 q^{61} - 12 q^{65} - 7 q^{67} - 22 q^{71} - 10 q^{73} + 19 q^{77} - 70 q^{83} - 26 q^{85} - 18 q^{89} - 9 q^{91} - 10 q^{95} + 38 q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 + q^7 + 5 * q^11 + 6 * q^13 + 2 * q^17 - 8 * q^19 + 2 * q^23 - 8 * q^25 + 4 * q^29 + 11 * q^35 + 4 * q^37 + 6 * q^41 + 10 * q^43 + 15 * q^47 + 5 * q^49 - 24 * q^53 + 16 * q^55 + 10 * q^59 - 12 * q^61 - 12 * q^65 - 7 * q^67 - 22 * q^71 - 10 * q^73 + 19 * q^77 - 70 * q^83 - 26 * q^85 - 18 * q^89 - 9 * q^91 - 10 * q^95 + 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.705299	+	1.22161i	0.315419	+	0.546322i	0.979527	−	0.201315i	$-0.0645215\pi$
$5$	0.705299	+	1.22161i	0.315419	+	0.546322i	−0.664107	+	0.747637i	$0.731188\pi$
$6$		0			0
$7$	2.57934	−	0.589053i	0.974900	−	0.222641i
$7$	2.57934	−	0.589053i	0.974900	−	0.222641i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.48484	−	4.30386i	0.749206	−	1.29766i	−0.198997	−	0.980000i	$-0.563768\pi$
$11$	2.48484	−	4.30386i	0.749206	−	1.29766i	0.948204	−	0.317663i	$-0.102898\pi$
$12$		0			0
$13$	−2.96967			−0.823639			−0.411820	−	0.911265i	$-0.635107\pi$
$13$	−2.96967			−0.823639			−0.411820	+	0.911265i	$0.635107\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.29981	+	2.25133i	−0.315249	+	0.546028i	−0.979491	−	0.201490i	$-0.935422\pi$
$17$	−1.29981	+	2.25133i	−0.315249	+	0.546028i	0.664241	+	0.747518i	$0.268755\pi$
$18$		0			0
$19$	−3.76437	−	6.52009i	−0.863607	−	1.49581i	−0.868424	−	0.495822i	$-0.834867\pi$
$19$	−3.76437	−	6.52009i	−0.863607	−	1.49581i	0.00481762	−	0.999988i	$-0.498466\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.06418	−	7.03937i	−0.847440	−	1.46781i	−0.883485	−	0.468459i	$-0.844809\pi$
$23$	−4.06418	−	7.03937i	−0.847440	−	1.46781i	0.0360448	−	0.999350i	$-0.488524\pi$
$24$		0			0
$25$	1.50511	−	2.60692i	0.301021	−	0.521384i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.93935			−1.28860			−0.644302	−	0.764771i	$-0.722852\pi$
$29$	−6.93935			−1.28860			−0.644302	+	0.764771i	$0.722852\pi$
$30$		0			0
$31$	5.26948	−	9.12701i	0.946427	−	1.63926i	0.193557	−	0.981089i	$-0.437998\pi$
$31$	5.26948	−	9.12701i	0.946427	−	1.63926i	0.752870	−	0.658170i	$-0.228669\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.53880	+	2.73550i	0.429136	+	0.462385i
$36$		0			0
$37$	−0.0945078	−	0.163692i	−0.0155370	−	0.0269108i	0.858152	−	0.513395i	$-0.171612\pi$
$37$	−0.0945078	−	0.163692i	−0.0155370	−	0.0269108i	−0.873689	+	0.486484i	$0.838279\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.04054			0.318679			0.159339	−	0.987224i	$-0.449064\pi$
$41$	2.04054			0.318679			0.159339	+	0.987224i	$0.449064\pi$
$42$		0			0
$43$	−4.38027			−0.667985			−0.333993	−	0.942576i	$-0.608396\pi$
$43$	−4.38027			−0.667985			−0.333993	+	0.942576i	$0.608396\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.69014	+	8.12355i	0.684127	+	1.18494i	0.973710	+	0.227789i	$0.0731498\pi$
$47$	4.69014	+	8.12355i	0.684127	+	1.18494i	−0.289584	+	0.957153i	$0.593517\pi$
$48$		0			0
$49$	6.30603	−	3.03874i	0.900862	−	0.434106i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.95339	+	12.0436i	−0.955121	+	1.65432i	−0.221032	+	0.975267i	$0.570942\pi$
$53$	−6.95339	+	12.0436i	−0.955121	+	1.65432i	−0.734090	+	0.679052i	$0.762391\pi$
$54$		0			0
$55$	7.01021			0.945257
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.39431	−	5.87913i	0.441902	−	0.765397i	−0.555929	−	0.831230i	$-0.687637\pi$
$59$	3.39431	−	5.87913i	0.441902	−	0.765397i	0.997831	+	0.0658331i	$0.0209705\pi$
$60$		0			0
$61$	−2.94828	−	5.10658i	−0.377489	−	0.653830i	0.613207	−	0.789922i	$-0.289879\pi$
$61$	−2.94828	−	5.10658i	−0.377489	−	0.653830i	−0.990696	+	0.136092i	$0.956546\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.09451	−	3.62779i	−0.259792	−	0.449972i
$66$		0			0
$67$	−5.00623	+	8.67104i	−0.611608	+	1.05934i	0.379362	+	0.925248i	$0.376144\pi$
$67$	−5.00623	+	8.67104i	−0.611608	+	1.05934i	−0.990970	+	0.134087i	$0.957190\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.86174			−0.933016			−0.466508	−	0.884517i	$-0.654488\pi$
$71$	−7.86174			−0.933016			−0.466508	+	0.884517i	$0.654488\pi$
$72$		0			0
$73$	0.894315	−	1.54900i	0.104672	−	0.181297i	−0.808932	−	0.587902i	$-0.799954\pi$
$73$	0.894315	−	1.54900i	0.104672	−	0.181297i	0.913604	+	0.406605i	$0.133288\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.87405	−	12.5648i	0.441488	−	1.43190i
$78$		0			0
$79$	−0.853775	−	1.47878i	−0.0960572	−	0.166376i	0.813992	−	0.580876i	$-0.197290\pi$
$79$	−0.853775	−	1.47878i	−0.0960572	−	0.166376i	−0.910049	+	0.414500i	$0.863957\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.0201149			−0.00220789			−0.00110395	−	0.999999i	$-0.500351\pi$
$83$	−0.0201149			−0.00220789			−0.00110395	+	0.999999i	$0.500351\pi$
$84$		0			0
$85$	−3.66701			−0.397743
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.33366	+	12.7023i	0.777366	+	1.34644i	0.933455	+	0.358695i	$0.116778\pi$
$89$	7.33366	+	12.7023i	0.777366	+	1.34644i	−0.156088	+	0.987743i	$0.549888\pi$
$90$		0			0
$91$	−7.65981	+	1.74929i	−0.802966	+	0.183376i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.31002	−	9.19722i	0.544796	−	0.943615i
$96$		0			0
$97$	8.67272			0.880581			0.440291	−	0.897855i	$-0.354875\pi$
$97$	8.67272			0.880581			0.440291	+	0.897855i	$0.354875\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.56418	−	9.63744i	0.553657	−	0.958961i	−0.444350	−	0.895853i	$-0.646565\pi$
$101$	5.56418	−	9.63744i	0.553657	−	0.958961i	0.998007	−	0.0631082i	$-0.0201013\pi$
$102$		0			0
$103$	−5.40054	−	9.35401i	−0.532131	−	0.921678i	−0.999296	−	0.0375081i	$-0.988058\pi$
$103$	−5.40054	−	9.35401i	−0.532131	−	0.921678i	0.467165	−	0.884170i	$-0.345275\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.21776	+	14.2336i	0.794441	+	1.37601i	0.923193	+	0.384336i	$0.125569\pi$
$107$	8.21776	+	14.2336i	0.794441	+	1.37601i	−0.128752	+	0.991677i	$0.541097\pi$
$108$		0			0
$109$	5.77459	−	10.0019i	0.553105	−	0.958006i	−0.444943	−	0.895559i	$-0.646776\pi$
$109$	5.77459	−	10.0019i	0.553105	−	0.958006i	0.998048	−	0.0624472i	$-0.0198905\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.18104			−0.111103			−0.0555516	−	0.998456i	$-0.517692\pi$
$113$	−1.18104			−0.111103			−0.0555516	+	0.998456i	$0.517692\pi$
$114$		0			0
$115$	5.73293	−	9.92972i	0.534598	−	0.925951i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.02650	+	6.57261i	−0.185769	+	0.602511i
$120$		0			0
$121$	−6.84882	−	11.8625i	−0.622620	−	1.07841i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.2992			1.01063
$126$		0			0
$127$	9.16890			0.813608			0.406804	−	0.913515i	$-0.366643\pi$
$127$	9.16890			0.813608			0.406804	+	0.913515i	$0.366643\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.84260	−	6.65557i	−0.335729	−	0.581500i	0.647895	−	0.761729i	$-0.275649\pi$
$131$	−3.84260	−	6.65557i	−0.335729	−	0.581500i	−0.983625	+	0.180229i	$0.942316\pi$
$132$		0			0
$133$	−13.5503	−	14.6001i	−1.17496	−	1.26599i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.38696	−	4.13433i	0.203932	−	0.353220i	−0.745860	−	0.666102i	$-0.767961\pi$
$137$	2.38696	−	4.13433i	0.203932	−	0.353220i	0.949792	+	0.312883i	$0.101295\pi$
$138$		0			0
$139$	20.8765			1.77072			0.885359	−	0.464908i	$-0.153913\pi$
$139$	20.8765			1.77072			0.885359	+	0.464908i	$0.153913\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.37915	+	12.7811i	−0.617076	+	1.06881i
$144$		0			0
$145$	−4.89431	−	8.47720i	−0.406451	−	0.703993i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.90054	+	10.2200i	0.483391	+	0.837258i	0.999818	−	0.0190732i	$-0.00607156\pi$
$149$	5.90054	+	10.2200i	0.483391	+	0.837258i	−0.516427	+	0.856331i	$0.672738\pi$
$150$		0			0
$151$	3.51133	−	6.08181i	0.285748	−	0.494930i	−0.687042	−	0.726618i	$-0.741091\pi$
$151$	3.51133	−	6.08181i	0.285748	−	0.494930i	0.972790	+	0.231687i	$0.0744246\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	14.8662			1.19409
$156$		0			0
$157$	−3.33861	+	5.78265i	−0.266450	+	0.461505i	−0.967943	−	0.251172i	$-0.919184\pi$
$157$	−3.33861	+	5.78265i	−0.266450	+	0.461505i	0.701492	+	0.712677i	$0.252517\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−14.6295	−	15.7629i	−1.15296	−	1.24229i
$162$		0			0
$163$	−0.169866	−	0.294216i	−0.0133049	−	0.0230448i	0.859296	−	0.511478i	$-0.170902\pi$
$163$	−0.169866	−	0.294216i	−0.0133049	−	0.0230448i	−0.872601	+	0.488433i	$0.837569\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.896566			−0.0693784			−0.0346892	−	0.999398i	$-0.511044\pi$
$167$	−0.896566			−0.0693784			−0.0346892	+	0.999398i	$0.511044\pi$
$168$		0			0
$169$	−4.18104			−0.321619
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.41796	−	4.18802i	−0.183834	−	0.318409i	0.759349	−	0.650683i	$-0.225517\pi$
$173$	−2.41796	−	4.18802i	−0.183834	−	0.318409i	−0.943183	+	0.332274i	$0.892184\pi$
$174$		0			0
$175$	2.34657	−	7.61073i	0.177384	−	0.575317i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.42464	+	2.46755i	−0.106483	+	0.184434i	−0.914343	−	0.404941i	$-0.867292\pi$
$179$	−1.42464	+	2.46755i	−0.106483	+	0.184434i	0.807860	+	0.589374i	$0.200626\pi$
$180$		0			0
$181$	1.46104			0.108598			0.0542991	−	0.998525i	$-0.482708\pi$
$181$	1.46104			0.108598			0.0542991	+	0.998525i	$0.482708\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.133313	−	0.230904i	0.00980133	−	0.0169764i
$186$		0			0
$187$	6.45962	+	11.1884i	0.472374	+	0.818176i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.29071	−	3.96763i	−0.165750	−	0.287088i	0.771171	−	0.636628i	$-0.219671\pi$
$191$	−2.29071	−	3.96763i	−0.165750	−	0.287088i	−0.936921	+	0.349540i	$0.886338\pi$
$192$		0			0
$193$	6.79200	−	11.7641i	0.488899	−	0.846798i	−0.511020	−	0.859569i	$-0.670732\pi$
$193$	6.79200	−	11.7641i	0.488899	−	0.846798i	0.999918	+	0.0127713i	$0.00406535\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−13.3905			−0.954032			−0.477016	−	0.878894i	$-0.658282\pi$
$197$	−13.3905			−0.954032			−0.477016	+	0.878894i	$0.658282\pi$
$198$		0			0
$199$	0.385222	−	0.667225i	0.0273077	−	0.0472983i	−0.852049	−	0.523463i	$-0.824640\pi$
$199$	0.385222	−	0.667225i	0.0273077	−	0.0472983i	0.879356	+	0.476164i	$0.157973\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−17.8990	+	4.08764i	−1.25626	+	0.286896i
$204$		0			0
$205$	1.43919	+	2.49275i	0.100517	+	0.174101i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−37.4154			−2.58808
$210$		0			0
$211$	4.57153			0.314717			0.157358	−	0.987542i	$-0.449702\pi$
$211$	4.57153			0.314717			0.157358	+	0.987542i	$0.449702\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.08940	−	5.35100i	−0.210695	−	0.364935i
$216$		0			0
$217$	8.21551	−	26.6457i	0.557705	−	1.80883i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.86000	−	6.68572i	0.259652	−	0.449730i
$222$		0			0
$223$	11.5670			0.774587			0.387293	−	0.921957i	$-0.373410\pi$
$223$	11.5670			0.774587			0.387293	+	0.921957i	$0.373410\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.90054	+	5.02388i	−0.192516	+	0.333447i	−0.946083	−	0.323923i	$-0.894998\pi$
$227$	−2.90054	+	5.02388i	−0.192516	+	0.333447i	0.753568	+	0.657370i	$0.228331\pi$
$228$		0			0
$229$	−6.43087	−	11.1386i	−0.424964	−	0.736059i	0.571453	−	0.820635i	$-0.306380\pi$
$229$	−6.43087	−	11.1386i	−0.424964	−	0.736059i	−0.996417	+	0.0845758i	$0.973046\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.33636	+	10.9749i	0.415109	+	0.718989i	0.995440	−	0.0953912i	$-0.0304102\pi$
$233$	6.33636	+	10.9749i	0.415109	+	0.718989i	−0.580331	+	0.814381i	$0.697077\pi$
$234$		0			0
$235$	−6.61590	+	11.4591i	−0.431574	+	0.747507i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.28705			−0.536045			−0.268022	−	0.963413i	$-0.586370\pi$
$239$	−8.28705			−0.536045			−0.268022	+	0.963413i	$0.586370\pi$
$240$		0			0
$241$	−8.50848	+	14.7371i	−0.548079	+	0.949301i	0.450327	+	0.892864i	$0.351307\pi$
$241$	−8.50848	+	14.7371i	−0.548079	+	0.949301i	−0.998406	+	0.0564373i	$0.982026\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.15981	+	5.56032i	0.521311	+	0.355236i
$246$		0			0
$247$	11.1790	+	19.3625i	0.711300	+	1.23201i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.3228			0.840926			0.420463	−	0.907310i	$-0.361868\pi$
$251$	13.3228			0.840926			0.420463	+	0.907310i	$0.361868\pi$
$252$		0			0
$253$	−40.3953			−2.53963
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.196207	−	0.339840i	−0.0122390	−	0.0211987i	0.859841	−	0.510562i	$-0.170563\pi$
$257$	−0.196207	−	0.339840i	−0.0122390	−	0.0211987i	−0.872080	+	0.489363i	$0.837229\pi$
$258$		0			0
$259$	−0.340192	−	0.366549i	−0.0211385	−	0.0227762i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.4342	−	21.5367i	0.766728	−	1.32801i	−0.172600	−	0.984992i	$-0.555217\pi$
$263$	12.4342	−	21.5367i	0.766728	−	1.32801i	0.939328	−	0.343020i	$-0.111450\pi$
$264$		0			0
$265$	−19.6169			−1.20506
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.60073	+	2.77255i	−0.0975985	+	0.169046i	−0.910690	−	0.413090i	$-0.864449\pi$
$269$	−1.60073	+	2.77255i	−0.0975985	+	0.169046i	0.813092	+	0.582136i	$0.197783\pi$
$270$		0			0
$271$	12.2443	+	21.2077i	0.743786	+	1.28827i	0.950760	+	0.309928i	$0.100305\pi$
$271$	12.2443	+	21.2077i	0.743786	+	1.28827i	−0.206974	+	0.978346i	$0.566362\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.47989	−	12.9555i	−0.451054	−	0.781249i
$276$		0			0
$277$	−4.42576	+	7.66564i	−0.265918	+	0.460584i	−0.967804	−	0.251706i	$-0.919008\pi$
$277$	−4.42576	+	7.66564i	−0.265918	+	0.460584i	0.701886	+	0.712290i	$0.252342\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.9416			1.01065			0.505325	−	0.862929i	$-0.331373\pi$
$281$	16.9416			1.01065			0.505325	+	0.862929i	$0.331373\pi$
$282$		0			0
$283$	−7.26948	+	12.5911i	−0.432126	+	0.748464i	−0.997056	−	0.0766748i	$-0.975570\pi$
$283$	−7.26948	+	12.5911i	−0.432126	+	0.748464i	0.564930	+	0.825139i	$0.308903\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.26325	−	1.20199i	0.310680	−	0.0709510i
$288$		0			0
$289$	5.12100	+	8.86984i	0.301236	+	0.521755i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	25.9237			1.51448			0.757240	−	0.653136i	$-0.226547\pi$
$293$	25.9237			1.51448			0.757240	+	0.653136i	$0.226547\pi$
$294$		0			0
$295$	9.57603			0.557538
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.0693	+	20.9046i	0.697985	+	1.20895i
$300$		0			0
$301$	−11.2982	+	2.58021i	−0.651219	+	0.148721i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.15884	−	7.20333i	0.238135	−	0.412461i
$306$		0			0
$307$	13.1204			0.748820			0.374410	−	0.927263i	$-0.377845\pi$
$307$	13.1204			0.748820			0.374410	+	0.927263i	$0.377845\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.15245	−	7.19226i	0.235464	−	0.407835i	−0.723944	−	0.689859i	$-0.757672\pi$
$311$	4.15245	−	7.19226i	0.235464	−	0.407835i	0.959407	+	0.282024i	$0.0910057\pi$
$312$		0			0
$313$	−11.5793	−	20.0560i	−0.654503	−	1.13363i	−0.982018	−	0.188787i	$-0.939544\pi$
$313$	−11.5793	−	20.0560i	−0.654503	−	1.13363i	0.327515	−	0.944846i	$-0.393789\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.85776	−	10.1459i	−0.329005	−	0.569853i	0.653310	−	0.757091i	$-0.273380\pi$
$317$	−5.85776	−	10.1459i	−0.329005	−	0.569853i	−0.982315	+	0.187238i	$0.940047\pi$
$318$		0			0
$319$	−17.2431	+	29.8660i	−0.965430	+	1.67217i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.5718			1.08901
$324$		0			0
$325$	−4.46967	+	7.74170i	−0.247933	+	0.429432i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	16.8827	+	18.1907i	0.930772	+	1.00289i
$330$		0			0
$331$	8.25094	+	14.2911i	0.453513	+	0.785507i	0.998601	−	0.0528711i	$-0.0168373\pi$
$331$	8.25094	+	14.2911i	0.453513	+	0.785507i	−0.545088	+	0.838379i	$0.683504\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−14.1235			−0.771652
$336$		0			0
$337$	17.9563			0.978142			0.489071	−	0.872244i	$-0.337336\pi$
$337$	17.9563			0.978142			0.489071	+	0.872244i	$0.337336\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−26.1876	−	45.3582i	−1.41814	−	2.45629i
$342$		0			0
$343$	14.4755	−	11.5525i	0.781601	−	0.623779i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.3539	+	19.6656i	−0.609511	+	1.05570i	0.381810	+	0.924241i	$0.375301\pi$
$347$	−11.3539	+	19.6656i	−0.609511	+	1.05570i	−0.991321	+	0.131463i	$0.958033\pi$
$348$		0			0
$349$	18.7829			1.00543			0.502713	−	0.864454i	$-0.332335\pi$
$349$	18.7829			1.00543			0.502713	+	0.864454i	$0.332335\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.8421	+	25.7073i	−0.789967	+	1.36826i	0.136019	+	0.990706i	$0.456569\pi$
$353$	−14.8421	+	25.7073i	−0.789967	+	1.36826i	−0.925986	+	0.377557i	$0.876764\pi$
$354$		0			0
$355$	−5.54488	−	9.60401i	−0.294291	−	0.509728i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.5829	−	21.7942i	−0.664099	−	1.15025i	−0.979529	−	0.201304i	$-0.935482\pi$
$359$	−12.5829	−	21.7942i	−0.664099	−	1.15025i	0.315430	−	0.948949i	$-0.397851\pi$
$360$		0			0
$361$	−18.8410	+	32.6336i	−0.991633	+	1.71756i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.52304			0.132062
$366$		0			0
$367$	−13.2534	+	22.9555i	−0.691819	+	1.19827i	0.279422	+	0.960168i	$0.409857\pi$
$367$	−13.2534	+	22.9555i	−0.691819	+	1.19827i	−0.971241	+	0.238098i	$0.923476\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.8409	+	35.1606i	−0.562829	+	1.82545i
$372$		0			0
$373$	6.97815	+	12.0865i	0.361315	+	0.625816i	0.988178	−	0.153314i	$-0.0489946\pi$
$373$	6.97815	+	12.0865i	0.361315	+	0.625816i	−0.626863	+	0.779130i	$0.715661\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.6076			1.06134
$378$		0			0
$379$	10.5537			0.542106			0.271053	−	0.962564i	$-0.412628\pi$
$379$	10.5537			0.542106			0.271053	+	0.962564i	$0.412628\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.72557	−	8.18493i	−0.241465	−	0.418230i	0.719667	−	0.694320i	$-0.244295\pi$
$383$	−4.72557	−	8.18493i	−0.241465	−	0.418230i	−0.961132	+	0.276090i	$0.910961\pi$
$384$		0			0
$385$	18.0818	−	4.12939i	0.921531	−	0.210453i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.3740	−	24.8966i	0.728793	−	1.26231i	−0.228601	−	0.973520i	$-0.573415\pi$
$389$	14.3740	−	24.8966i	0.728793	−	1.26231i	0.957394	−	0.288786i	$-0.0932517\pi$
$390$		0			0
$391$	21.1306			1.06862
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.20433	−	2.08597i	0.0605966	−	0.104956i
$396$		0			0
$397$	−4.34642	−	7.52822i	−0.218140	−	0.377830i	0.736099	−	0.676874i	$-0.236666\pi$
$397$	−4.34642	−	7.52822i	−0.218140	−	0.377830i	−0.954239	+	0.299044i	$0.903332\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	17.0514	+	29.5339i	0.851507	+	1.47485i	0.879848	+	0.475256i	$0.157644\pi$
$401$	17.0514	+	29.5339i	0.851507	+	1.47485i	−0.0283402	+	0.999598i	$0.509022\pi$
$402$		0			0
$403$	−15.6486	+	27.1042i	−0.779514	+	1.35016i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.939346			−0.0465616
$408$		0			0
$409$	3.98214	−	6.89726i	0.196904	−	0.341048i	−0.750619	−	0.660735i	$-0.770245\pi$
$409$	3.98214	−	6.89726i	0.196904	−	0.341048i	0.947523	+	0.319688i	$0.103578\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.29199	−	17.1637i	0.260402	−	0.844571i
$414$		0			0
$415$	−0.0141870	−	0.0245726i	−0.000696413	−	0.00120622i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−22.4355			−1.09605			−0.548024	−	0.836463i	$-0.684620\pi$
$419$	−22.4355			−1.09605			−0.548024	+	0.836463i	$0.684620\pi$
$420$		0			0
$421$	−32.5821			−1.58795			−0.793977	−	0.607948i	$-0.791993\pi$
$421$	−32.5821			−1.58795			−0.793977	+	0.607948i	$0.791993\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.91269	+	6.77699i	0.189794	+	0.328732i
$426$		0			0
$427$	−10.6127	−	11.4349i	−0.513584	−	0.553375i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.2666	+	19.5143i	−0.542694	+	0.939973i	0.456054	+	0.889952i	$0.349262\pi$
$431$	−11.2666	+	19.5143i	−0.542694	+	0.939973i	−0.998748	+	0.0500212i	$0.984071\pi$
$432$		0			0
$433$	11.1868			0.537602			0.268801	−	0.963196i	$-0.413373\pi$
$433$	11.1868			0.537602			0.268801	+	0.963196i	$0.413373\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.5982	+	52.9976i	−1.46371	+	2.53522i
$438$		0			0
$439$	−3.78178	−	6.55023i	−0.180494	−	0.312625i	0.761555	−	0.648101i	$-0.224436\pi$
$439$	−3.78178	−	6.55023i	−0.180494	−	0.312625i	−0.942049	+	0.335475i	$0.891103\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.81384	−	3.14166i	−0.0861781	−	0.149265i	0.819715	−	0.572772i	$-0.194132\pi$
$443$	−1.81384	−	3.14166i	−0.0861781	−	0.149265i	−0.905893	+	0.423507i	$0.860799\pi$
$444$		0			0
$445$	−10.3448	+	17.9178i	−0.490393	+	0.849385i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	5.04851			0.238254			0.119127	−	0.992879i	$-0.461990\pi$
$449$	5.04851			0.238254			0.119127	+	0.992879i	$0.461990\pi$
$450$		0			0
$451$	5.07041	−	8.78220i	0.238756	−	0.413538i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.53942	−	8.12355i	−0.353453	−	0.380838i
$456$		0			0
$457$	−12.0564	−	20.8822i	−0.563973	−	0.976830i	−0.997144	−	0.0755182i	$-0.975939\pi$
$457$	−12.0564	−	20.8822i	−0.563973	−	0.976830i	0.433172	−	0.901311i	$-0.357394\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.5032			0.489184			0.244592	−	0.969626i	$-0.421346\pi$
$461$	10.5032			0.489184			0.244592	+	0.969626i	$0.421346\pi$
$462$		0			0
$463$	3.64242			0.169277			0.0846387	−	0.996412i	$-0.473026\pi$
$463$	3.64242			0.169277			0.0846387	+	0.996412i	$0.473026\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.9933	−	27.7012i	−0.740082	−	1.28186i	−0.952457	−	0.304672i	$-0.901453\pi$
$467$	−15.9933	−	27.7012i	−0.740082	−	1.28186i	0.212375	−	0.977188i	$-0.431880\pi$
$468$		0			0
$469$	−7.80508	+	25.3145i	−0.360405	+	1.16892i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.8843	+	18.8521i	−0.500459	+	0.866820i
$474$		0			0
$475$	−22.6631			−1.03986
$476$		0			0
$477$		0			0
$478$		0			0
$479$	17.3613	−	30.0706i	0.793257	−	1.37396i	−0.130683	−	0.991424i	$-0.541717\pi$
$479$	17.3613	−	30.0706i	0.793257	−	1.37396i	0.923940	−	0.382537i	$-0.124950\pi$
$480$		0			0
$481$	0.280657	+	0.486113i	0.0127969	+	0.0221648i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.11686	+	10.5947i	0.277752	+	0.481081i
$486$		0			0
$487$	−17.9411	+	31.0749i	−0.812988	+	1.40814i	0.0977757	+	0.995208i	$0.468827\pi$
$487$	−17.9411	+	31.0749i	−0.812988	+	1.40814i	−0.910764	+	0.412928i	$0.864506\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.0855589			0.00386122			0.00193061	−	0.999998i	$-0.499385\pi$
$491$	0.0855589			0.00386122			0.00193061	+	0.999998i	$0.499385\pi$
$492$		0			0
$493$	9.01981	−	15.6228i	0.406232	−	0.703614i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−20.2781	+	4.63098i	−0.909598	+	0.207728i
$498$		0			0
$499$	6.27842	+	10.8745i	0.281061	+	0.486811i	0.971646	−	0.236439i	$-0.0759805\pi$
$499$	6.27842	+	10.8745i	0.281061	+	0.486811i	−0.690586	+	0.723251i	$0.742647\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	42.8822			1.91202			0.956011	−	0.293332i	$-0.0947643\pi$
$503$	42.8822			1.91202			0.956011	+	0.293332i	$0.0947643\pi$
$504$		0			0
$505$	15.6976			0.698536
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.48102	+	12.9575i	0.331590	+	0.574331i	0.982824	−	0.184546i	$-0.0590815\pi$
$509$	7.48102	+	12.9575i	0.331590	+	0.574331i	−0.651234	+	0.758877i	$0.725748\pi$
$510$		0			0
$511$	1.39430	−	4.52220i	0.0616803	−	0.200050i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.61799	−	13.1948i	0.335689	−	0.581430i
$516$		0			0
$517$	46.6169			2.05021
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.8479	−	32.6454i	0.825740	−	1.43022i	−0.0756130	−	0.997137i	$-0.524091\pi$
$521$	18.8479	−	32.6454i	0.825740	−	1.43022i	0.901353	−	0.433086i	$-0.142575\pi$
$522$		0			0
$523$	−0.707999	−	1.22629i	−0.0309586	−	0.0536219i	0.850131	−	0.526571i	$-0.176523\pi$
$523$	−0.707999	−	1.22629i	−0.0309586	−	0.0536219i	−0.881090	+	0.472949i	$0.843189\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.6986	+	23.7267i	0.596721	+	1.03355i
$528$		0			0
$529$	−21.5351	+	37.2999i	−0.936310	+	1.62174i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.05973			−0.262476
$534$		0			0
$535$	−11.5920	+	20.0779i	−0.501164	+	0.868042i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.59114	−	34.6911i	0.111608	−	1.49425i
$540$		0			0
$541$	−3.35266	−	5.80697i	−0.144142	−	0.249661i	0.784911	−	0.619609i	$-0.212709\pi$
$541$	−3.35266	−	5.80697i	−0.144142	−	0.249661i	−0.929052	+	0.369948i	$0.879376\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.2912			0.697840
$546$		0			0
$547$	31.6351			1.35262			0.676309	−	0.736618i	$-0.263578\pi$
$547$	31.6351			1.35262			0.676309	+	0.736618i	$0.263578\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	26.1223	+	45.2451i	1.11285	+	1.92751i
$552$		0			0
$553$	−3.07326	−	3.31137i	−0.130688	−	0.140814i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.6007	+	23.5572i	−0.576282	+	0.998149i	0.419620	+	0.907700i	$0.362164\pi$
$557$	−13.6007	+	23.5572i	−0.576282	+	0.998149i	−0.995901	+	0.0904489i	$0.971170\pi$
$558$		0			0
$559$	13.0080			0.550179
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.15118	−	1.99390i	0.0485163	−	0.0840327i	−0.840747	−	0.541428i	$-0.817884\pi$
$563$	1.15118	−	1.99390i	0.0485163	−	0.0840327i	0.889264	+	0.457395i	$0.151217\pi$
$564$		0			0
$565$	−0.832989	−	1.44278i	−0.0350441	−	0.0606982i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.9737	−	29.3992i	−0.711573	−	1.23248i	−0.964267	−	0.264934i	$-0.914650\pi$
$569$	−16.9737	−	29.3992i	−0.711573	−	1.23248i	0.252694	−	0.967546i	$-0.418683\pi$
$570$		0			0
$571$	−0.114623	+	0.198532i	−0.00479681	+	0.00830832i	−0.868414	−	0.495840i	$-0.834860\pi$
$571$	−0.114623	+	0.198532i	−0.00479681	+	0.00830832i	0.863617	+	0.504148i	$0.168194\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−24.4681			−1.02039
$576$		0			0
$577$	−11.5733	+	20.0455i	−0.481802	+	0.834505i	−0.999782	−	0.0208877i	$-0.993351\pi$
$577$	−11.5733	+	20.0455i	−0.481802	+	0.834505i	0.517980	+	0.855393i	$0.326684\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.0518832	+	0.0118487i	−0.00215248	+	0.000491568i
$582$		0			0
$583$	34.5561	+	59.8529i	1.43117	+	2.47885i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−37.3477			−1.54150			−0.770752	−	0.637135i	$-0.780119\pi$
$587$	−37.3477			−1.54150			−0.770752	+	0.637135i	$0.780119\pi$
$588$		0			0
$589$	−79.3452			−3.26936
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.1975	−	17.6626i	−0.418761	−	0.725315i	0.577054	−	0.816706i	$-0.304202\pi$
$593$	−10.1975	−	17.6626i	−0.418761	−	0.725315i	−0.995815	+	0.0913907i	$0.970869\pi$
$594$		0			0
$595$	−9.45848	+	2.16006i	−0.387760	+	0.0885540i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.3956	+	21.4698i	−0.506470	+	0.877232i	0.493502	+	0.869745i	$0.335717\pi$
$599$	−12.3956	+	21.4698i	−0.506470	+	0.877232i	−0.999972	+	0.00748717i	$0.997617\pi$
$600$		0			0
$601$	46.0881			1.87997			0.939987	−	0.341210i	$-0.110837\pi$
$601$	46.0881			1.87997			0.939987	+	0.341210i	$0.110837\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.66094	−	16.7332i	0.392773	−	0.680303i
$606$		0			0
$607$	11.8399	+	20.5073i	0.480566	+	0.832365i	0.999751	−	0.0222967i	$-0.00709786\pi$
$607$	11.8399	+	20.5073i	0.480566	+	0.832365i	−0.519185	+	0.854662i	$0.673765\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.9282	−	24.1243i	−0.563473	−	0.975965i
$612$		0			0
$613$	11.2993	−	19.5710i	0.456376	−	0.790467i	−0.542390	−	0.840127i	$-0.682480\pi$
$613$	11.2993	−	19.5710i	0.456376	−	0.790467i	0.998766	+	0.0496599i	$0.0158138\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.2593			0.775349			0.387675	−	0.921796i	$-0.373278\pi$
$617$	19.2593			0.775349			0.387675	+	0.921796i	$0.373278\pi$
$618$		0			0
$619$	1.28066	−	2.21816i	0.0514740	−	0.0891555i	−0.839140	−	0.543915i	$-0.816941\pi$
$619$	1.28066	−	2.21816i	0.0514740	−	0.0891555i	0.890614	+	0.454759i	$0.150275\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	26.3983	+	28.4436i	1.05763	+	1.13957i
$624$		0			0
$625$	0.443780	+	0.768650i	0.0177512	+	0.0307460i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.491368			0.0195921
$630$		0			0
$631$	−23.3806			−0.930767			−0.465384	−	0.885109i	$-0.654084\pi$
$631$	−23.3806			−0.930767			−0.465384	+	0.885109i	$0.654084\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.46682	+	11.2009i	0.256628	+	0.444492i
$636$		0			0
$637$	−18.7269	+	9.02407i	−0.741985	+	0.357547i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.39784	+	9.34933i	−0.213202	+	0.369277i	−0.952715	−	0.303866i	$-0.901723\pi$
$641$	−5.39784	+	9.34933i	−0.213202	+	0.369277i	0.739513	+	0.673142i	$0.235056\pi$
$642$		0			0
$643$	−1.56705			−0.0617983			−0.0308991	−	0.999523i	$-0.509837\pi$
$643$	−1.56705			−0.0617983			−0.0308991	+	0.999523i	$0.509837\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.7966	−	25.6285i	0.581716	−	1.00756i	−0.413560	−	0.910477i	$-0.635715\pi$
$647$	14.7966	−	25.6285i	0.581716	−	1.00756i	0.995276	−	0.0970851i	$-0.0309519\pi$
$648$		0			0
$649$	−16.8686	−	29.2173i	−0.662152	−	1.14688i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.3696	−	33.5491i	−0.757991	−	1.31288i	−0.943874	−	0.330307i	$-0.892848\pi$
$653$	−19.3696	−	33.5491i	−0.757991	−	1.31288i	0.185883	−	0.982572i	$-0.440486\pi$
$654$		0			0
$655$	5.42036	−	9.38834i	0.211791	−	0.366833i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.1465			1.09643			0.548216	−	0.836337i	$-0.315307\pi$
$659$	28.1465			1.09643			0.548216	+	0.836337i	$0.315307\pi$
$660$		0			0
$661$	−13.7431	+	23.8038i	−0.534546	+	0.925861i	0.464639	+	0.885500i	$0.346184\pi$
$661$	−13.7431	+	23.8038i	−0.534546	+	0.925861i	−0.999185	+	0.0403609i	$0.987149\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.27872	−	26.8507i	0.321035	−	1.04122i
$666$		0			0
$667$	28.2028	+	48.8486i	1.09202	+	1.89143i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−29.3040			−1.13127
$672$		0			0
$673$	−10.9167			−0.420807			−0.210404	−	0.977615i	$-0.567478\pi$
$673$	−10.9167			−0.420807			−0.210404	+	0.977615i	$0.567478\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.57281	−	16.5806i	−0.367913	−	0.637244i	0.621326	−	0.783552i	$-0.286594\pi$
$677$	−9.57281	−	16.5806i	−0.367913	−	0.637244i	−0.989239	+	0.146308i	$0.953261\pi$
$678$		0			0
$679$	22.3699	−	5.10869i	0.858479	−	0.196054i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.60854	+	4.51812i	−0.0998130	+	0.172881i	−0.911607	−	0.411063i	$-0.865158\pi$
$683$	−2.60854	+	4.51812i	−0.0998130	+	0.172881i	0.811794	+	0.583944i	$0.198491\pi$
$684$		0			0
$685$	6.73408			0.257296
$686$		0			0
$687$		0			0
$688$		0			0
$689$	20.6493	−	35.7656i	0.786675	−	1.36256i
$690$		0			0
$691$	−16.2184	−	28.0910i	−0.616976	−	1.06863i	−0.990034	−	0.140826i	$-0.955024\pi$
$691$	−16.2184	−	28.0910i	−0.616976	−	1.06863i	0.373059	−	0.927808i	$-0.378309\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.7241	+	25.5030i	0.558519	+	0.967383i
$696$		0			0
$697$	−2.65231	+	4.59393i	−0.100463	+	0.174008i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−15.0981			−0.570246			−0.285123	−	0.958491i	$-0.592034\pi$
$701$	−15.0981			−0.570246			−0.285123	+	0.958491i	$0.592034\pi$
$702$		0			0
$703$	−0.711525	+	1.23240i	−0.0268357	+	0.0464808i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.67497	−	28.1359i	0.326256	−	1.05816i
$708$		0			0
$709$	4.50736	+	7.80697i	0.169277	+	0.293197i	0.938166	−	0.346186i	$-0.112523\pi$
$709$	4.50736	+	7.80697i	0.169277	+	0.293197i	−0.768889	+	0.639383i	$0.779190\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−85.6645			−3.20816
$714$		0			0
$715$	−20.8180			−0.778550
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.2753	+	22.9934i	0.495084	+	0.857510i	0.999984	−	0.00566774i	$-0.00180411\pi$
$719$	13.2753	+	22.9934i	0.495084	+	0.857510i	−0.504900	+	0.863178i	$0.668471\pi$
$720$		0			0
$721$	−19.4399	−	20.9460i	−0.723978	−	0.780070i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.4445	+	18.0903i	−0.387897	+	0.671858i
$726$		0			0
$727$	−9.68517			−0.359203			−0.179602	−	0.983739i	$-0.557481\pi$
$727$	−9.68517			−0.359203			−0.179602	+	0.983739i	$0.557481\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.69351	−	9.86144i	0.210582	−	0.364739i
$732$		0			0
$733$	−4.23676	−	7.33828i	−0.156488	−	0.271046i	0.777112	−	0.629363i	$-0.216684\pi$
$733$	−4.23676	−	7.33828i	−0.156488	−	0.271046i	−0.933600	+	0.358317i	$0.883351\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.8793	+	43.0922i	0.916441	+	1.58732i
$738$		0			0
$739$	−4.58445	+	7.94050i	−0.168642	+	0.292096i	−0.937943	−	0.346791i	$-0.887271\pi$
$739$	−4.58445	+	7.94050i	−0.168642	+	0.292096i	0.769301	+	0.638887i	$0.220605\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.6022			−0.425642			−0.212821	−	0.977091i	$-0.568265\pi$
$743$	−11.6022			−0.425642			−0.212821	+	0.977091i	$0.568265\pi$
$744$		0			0
$745$	−8.32329	+	14.4164i	−0.304942	+	0.528175i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	29.5808	+	31.8726i	1.08086	+	1.16460i
$750$		0			0
$751$	1.92515	+	3.33445i	0.0702496	+	0.121676i	0.899011	−	0.437927i	$-0.144287\pi$
$751$	1.92515	+	3.33445i	0.0702496	+	0.121676i	−0.828761	+	0.559603i	$0.810954\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.90616			0.360522
$756$		0			0
$757$	2.92720			0.106391			0.0531955	−	0.998584i	$-0.483059\pi$
$757$	2.92720			0.106391			0.0531955	+	0.998584i	$0.483059\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.15470	+	5.46410i	0.114358	+	0.198074i	0.917523	−	0.397683i	$-0.130186\pi$
$761$	3.15470	+	5.46410i	0.114358	+	0.198074i	−0.803165	+	0.595757i	$0.796852\pi$
$762$		0			0
$763$	9.00301	−	29.1998i	0.325931	−	1.05710i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.0800	+	17.4591i	−0.363968	+	0.630411i
$768$		0			0
$769$	24.8617			0.896537			0.448269	−	0.893899i	$-0.352041\pi$
$769$	24.8617			0.896537			0.448269	+	0.893899i	$0.352041\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.01982	+	12.1587i	−0.252485	+	0.437318i	−0.964209	−	0.265142i	$-0.914581\pi$
$773$	−7.01982	+	12.1587i	−0.252485	+	0.437318i	0.711724	+	0.702459i	$0.247915\pi$
$774$		0			0
$775$	−15.8623	−	27.4742i	−0.569789	−	0.986903i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.68135	−	13.3045i	−0.275213	−	0.476683i
$780$		0			0
$781$	−19.5351	+	33.8358i	−0.699022	+	1.21074i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.41888			−0.336174
$786$		0			0
$787$	12.6897	−	21.9792i	0.452338	−	0.783473i	−0.546192	−	0.837660i	$-0.683923\pi$
$787$	12.6897	−	21.9792i	0.452338	−	0.783473i	0.998531	+	0.0541865i	$0.0172566\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.04632	+	0.695697i	−0.108315	+	0.0247361i
$792$		0			0
$793$	8.75544	+	15.1649i	0.310915	+	0.538520i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19.1890			0.679710			0.339855	−	0.940478i	$-0.389622\pi$
$797$	19.1890			0.679710			0.339855	+	0.940478i	$0.389622\pi$
$798$		0			0
$799$	−24.3851			−0.862682
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.44445	−	7.69802i	−0.156841	−	0.271657i
$804$		0			0
$805$	8.93806	−	28.9892i	0.315025	−	1.02173i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.221134	−	0.383016i	0.00777467	−	0.0134661i	−0.862112	−	0.506718i	$-0.830859\pi$
$809$	0.221134	−	0.383016i	0.00777467	−	0.0134661i	0.869887	+	0.493252i	$0.164192\pi$
$810$		0			0
$811$	28.1510			0.988516			0.494258	−	0.869315i	$-0.335440\pi$
$811$	28.1510			0.988516			0.494258	+	0.869315i	$0.335440\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.239612	−	0.415021i	0.00839326	−	0.0145376i
$816$		0			0
$817$	16.4890	+	28.5597i	0.576876	+	0.999179i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.26646	−	7.38972i	−0.148900	−	0.257903i	0.781921	−	0.623378i	$-0.214240\pi$
$821$	−4.26646	−	7.38972i	−0.148900	−	0.257903i	−0.930821	+	0.365475i	$0.880907\pi$
$822$		0			0
$823$	14.7590	−	25.5633i	0.514465	−	0.891080i	−0.485394	−	0.874296i	$-0.661324\pi$
$823$	14.7590	−	25.5633i	0.514465	−	0.891080i	0.999859	−	0.0167842i	$-0.00534282\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−35.7222			−1.24218			−0.621092	−	0.783738i	$-0.713311\pi$
$827$	−35.7222			−1.24218			−0.621092	+	0.783738i	$0.713311\pi$
$828$		0			0
$829$	−25.8399	+	44.7560i	−0.897456	+	1.55444i	−0.0667215	+	0.997772i	$0.521254\pi$
$829$	−25.8399	+	44.7560i	−0.897456	+	1.55444i	−0.830735	+	0.556668i	$0.812079\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.35541	+	18.1467i	−0.0469622	+	0.628748i
$834$		0			0
$835$	−0.632347	−	1.09526i	−0.0218833	−	0.0379030i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−37.2567			−1.28624			−0.643122	−	0.765763i	$-0.722361\pi$
$839$	−37.2567			−1.28624			−0.643122	+	0.765763i	$0.722361\pi$
$840$		0			0
$841$	19.1545			0.660501
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.94889	−	5.10762i	−0.101445	−	0.175708i
$846$		0			0
$847$	−24.6531	−	26.5632i	−0.847091	−	0.912722i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.768194	+	1.33055i	−0.0263333	+	0.0456107i
$852$		0			0
$853$	−12.0623			−0.413006			−0.206503	−	0.978446i	$-0.566208\pi$
$853$	−12.0623			−0.413006			−0.206503	+	0.978446i	$0.566208\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.1047	−	24.4301i	0.481808	−	0.834515i	−0.517974	−	0.855396i	$-0.673314\pi$
$857$	14.1047	−	24.4301i	0.481808	−	0.834515i	0.999782	+	0.0208808i	$0.00664705\pi$
$858$		0			0
$859$	25.7641	+	44.6247i	0.879059	+	1.52257i	0.852375	+	0.522930i	$0.175161\pi$
$859$	25.7641	+	44.6247i	0.879059	+	1.52257i	0.0266833	+	0.999644i	$0.491505\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.57423	−	2.72664i	−0.0535873	−	0.0928159i	0.837987	−	0.545690i	$-0.183732\pi$
$863$	−1.57423	−	2.72664i	−0.0535873	−	0.0928159i	−0.891575	+	0.452874i	$0.850399\pi$
$864$		0			0
$865$	3.41076	−	5.90762i	0.115969	−	0.200865i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.48597			−0.287867
$870$		0			0
$871$	14.8669	−	25.7501i	0.503744	−	0.872510i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	29.1445	−	6.65582i	0.985264	−	0.225008i
$876$		0			0
$877$	−1.27555	−	2.20932i	−0.0430723	−	0.0746034i	0.843686	−	0.536838i	$-0.180381\pi$
$877$	−1.27555	−	2.20932i	−0.0430723	−	0.0746034i	−0.886758	+	0.462234i	$0.847048\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−14.4378			−0.486421			−0.243210	−	0.969974i	$-0.578201\pi$
$881$	−14.4378			−0.486421			−0.243210	+	0.969974i	$0.578201\pi$
$882$		0			0
$883$	0.478915			0.0161168			0.00805839	−	0.999968i	$-0.497435\pi$
$883$	0.478915			0.0161168			0.00805839	+	0.999968i	$0.497435\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.62821	−	9.74834i	−0.188977	−	0.327317i	0.755933	−	0.654649i	$-0.227184\pi$
$887$	−5.62821	−	9.74834i	−0.188977	−	0.327317i	−0.944909	+	0.327332i	$0.893850\pi$
$888$		0			0
$889$	23.6498	−	5.40097i	0.793187	−	0.181143i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	35.3108	−	61.1602i	1.18163	−	2.04665i
$894$		0			0
$895$	−4.01920			−0.134347
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−36.5667	+	63.3355i	−1.21957	+	2.11236i
$900$		0			0
$901$	−18.0761	−	31.3088i	−0.602203	−	1.04305i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.03047	+	1.78483i	0.0342540	+	0.0593297i
$906$		0			0
$907$	−0.359496	+	0.622666i	−0.0119369	+	0.0206753i	−0.871932	−	0.489627i	$-0.837133\pi$
$907$	−0.359496	+	0.622666i	−0.0119369	+	0.0206753i	0.859995	+	0.510302i	$0.170466\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	21.1779			0.701655			0.350828	−	0.936440i	$-0.385900\pi$
$911$	21.1779			0.701655			0.350828	+	0.936440i	$0.385900\pi$
$912$		0			0
$913$	−0.0499822	+	0.0865717i	−0.00165417	+	0.00286510i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.8319	−	14.9035i	−0.456769	−	0.492158i
$918$		0			0
$919$	7.17784	+	12.4324i	0.236775	+	0.410106i	0.959787	−	0.280729i	$-0.0905762\pi$
$919$	7.17784	+	12.4324i	0.236775	+	0.410106i	−0.723012	+	0.690835i	$0.757243\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	23.3468			0.768469
$924$		0			0
$925$	−0.568977			−0.0187079
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.6542	+	32.3101i	0.612026	+	1.06006i	0.990899	+	0.134611i	$0.0429785\pi$
$929$	18.6542	+	32.3101i	0.612026	+	1.06006i	−0.378873	+	0.925449i	$0.623688\pi$
$930$		0			0
$931$	−43.5511	−	29.6769i	−1.42733	−	0.972622i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.11192	+	15.7823i	−0.297992	+	0.516137i
$936$		0			0
$937$	50.9094			1.66314			0.831568	−	0.555423i	$-0.187444\pi$
$937$	50.9094			1.66314			0.831568	+	0.555423i	$0.187444\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.9251	+	20.6550i	−0.388749	+	0.673332i	−0.992282	−	0.124006i	$-0.960426\pi$
$941$	−11.9251	+	20.6550i	−0.388749	+	0.673332i	0.603533	+	0.797338i	$0.293759\pi$
$942$		0			0
$943$	−8.29312	−	14.3641i	−0.270061	−	0.467760i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.3576	−	50.8489i	−0.953994	−	1.65237i	−0.736653	−	0.676271i	$-0.763595\pi$
$947$	−29.3576	−	50.8489i	−0.953994	−	1.65237i	−0.217341	−	0.976096i	$-0.569738\pi$
$948$		0			0
$949$	−2.65582	+	4.60002i	−0.0862116	+	0.149323i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	28.4324			0.921015			0.460507	−	0.887656i	$-0.347667\pi$
$953$	28.4324			0.921015			0.460507	+	0.887656i	$0.347667\pi$
$954$		0			0
$955$	3.23128	−	5.59674i	0.104562	−	0.181106i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.72144	−	12.0699i	0.120172	−	0.389758i
$960$		0			0
$961$	−40.0348	−	69.3424i	−1.29145	−	2.23685i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	19.1616			0.616833
$966$		0			0
$967$	−27.6931			−0.890552			−0.445276	−	0.895393i	$-0.646894\pi$
$967$	−27.6931			−0.890552			−0.445276	+	0.895393i	$0.646894\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.510672	−	0.884510i	−0.0163882	−	0.0283853i	0.857715	−	0.514125i	$-0.171883\pi$
$971$	−0.510672	−	0.884510i	−0.0163882	−	0.0283853i	−0.874103	+	0.485740i	$0.838550\pi$
$972$		0			0
$973$	53.8476	−	12.2973i	1.72627	−	0.394235i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.9018	−	32.7389i	0.604723	−	1.04741i	−0.387372	−	0.921923i	$-0.626617\pi$
$977$	18.9018	−	32.7389i	0.604723	−	1.04741i	0.992095	−	0.125488i	$-0.0400495\pi$
$978$		0			0
$979$	72.8918			2.32963
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−8.19366	+	14.1918i	−0.261337	+	0.452649i	−0.966598	−	0.256299i	$-0.917497\pi$
$983$	−8.19366	+	14.1918i	−0.261337	+	0.452649i	0.705260	+	0.708948i	$0.250830\pi$
$984$		0			0
$985$	−9.44430	−	16.3580i	−0.300920	−	0.521209i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	17.8022	+	30.8343i	0.566077	+	0.980475i
$990$		0			0
$991$	13.7067	−	23.7408i	0.435409	−	0.754150i	−0.561920	−	0.827192i	$-0.689937\pi$
$991$	13.7067	−	23.7408i	0.435409	−	0.754150i	0.997329	+	0.0730412i	$0.0232704\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.08679			0.0344535
$996$		0			0
$997$	7.67099	−	13.2865i	0.242943	−	0.420789i	−0.718609	−	0.695415i	$-0.755221\pi$
$997$	7.67099	−	13.2865i	0.242943	−	0.420789i	0.961551	+	0.274626i	$0.0885540\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.k.c.1621.3	yes	8
3.2	odd	2		2268.2.k.d.1621.2	yes	8
7.2	even	3	inner	2268.2.k.c.1297.3	✓	8
9.2	odd	6		2268.2.l.l.109.3		8
9.4	even	3		2268.2.i.l.865.3		8
9.5	odd	6		2268.2.i.m.865.2		8
9.7	even	3		2268.2.l.m.109.2		8
21.2	odd	6		2268.2.k.d.1297.2	yes	8
63.2	odd	6		2268.2.i.m.2053.2		8
63.16	even	3		2268.2.i.l.2053.3		8
63.23	odd	6		2268.2.l.l.541.3		8
63.58	even	3		2268.2.l.m.541.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.l.865.3		8	9.4	even	3
2268.2.i.l.2053.3		8	63.16	even	3
2268.2.i.m.865.2		8	9.5	odd	6
2268.2.i.m.2053.2		8	63.2	odd	6
2268.2.k.c.1297.3	✓	8	7.2	even	3	inner
2268.2.k.c.1621.3	yes	8	1.1	even	1	trivial
2268.2.k.d.1297.2	yes	8	21.2	odd	6
2268.2.k.d.1621.2	yes	8	3.2	odd	2
2268.2.l.l.109.3		8	9.2	odd	6
2268.2.l.l.541.3		8	63.23	odd	6
2268.2.l.m.109.2		8	9.7	even	3
2268.2.l.m.541.2		8	63.58	even	3

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.705299 + 1.22161i) q^{5} +(2.57934 - 0.589053i) q^{7} +O(q^{10})\)	\(q+(0.705299 + 1.22161i) q^{5} +(2.57934 - 0.589053i) q^{7} +(2.48484 - 4.30386i) q^{11} -2.96967 q^{13} +(-1.29981 + 2.25133i) q^{17} +(-3.76437 - 6.52009i) q^{19} +(-4.06418 - 7.03937i) q^{23} +(1.50511 - 2.60692i) q^{25} -6.93935 q^{29} +(5.26948 - 9.12701i) q^{31} +(2.53880 + 2.73550i) q^{35} +(-0.0945078 - 0.163692i) q^{37} +2.04054 q^{41} -4.38027 q^{43} +(4.69014 + 8.12355i) q^{47} +(6.30603 - 3.03874i) q^{49} +(-6.95339 + 12.0436i) q^{53} +7.01021 q^{55} +(3.39431 - 5.87913i) q^{59} +(-2.94828 - 5.10658i) q^{61} +(-2.09451 - 3.62779i) q^{65} +(-5.00623 + 8.67104i) q^{67} -7.86174 q^{71} +(0.894315 - 1.54900i) q^{73} +(3.87405 - 12.5648i) q^{77} +(-0.853775 - 1.47878i) q^{79} -0.0201149 q^{83} -3.66701 q^{85} +(7.33366 + 12.7023i) q^{89} +(-7.65981 + 1.74929i) q^{91} +(5.31002 - 9.19722i) q^{95} +8.67272 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} + q^{7}+O(q^{10}) \) 8 * q - 2 * q^5 + q^7	\( 8 q - 2 q^{5} + q^{7} + 5 q^{11} + 6 q^{13} + 2 q^{17} - 8 q^{19} + 2 q^{23} - 8 q^{25} + 4 q^{29} + 11 q^{35} + 4 q^{37} + 6 q^{41} + 10 q^{43} + 15 q^{47} + 5 q^{49} - 24 q^{53} + 16 q^{55} + 10 q^{59} - 12 q^{61} - 12 q^{65} - 7 q^{67} - 22 q^{71} - 10 q^{73} + 19 q^{77} - 70 q^{83} - 26 q^{85} - 18 q^{89} - 9 q^{91} - 10 q^{95} + 38 q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 + q^7 + 5 * q^11 + 6 * q^13 + 2 * q^17 - 8 * q^19 + 2 * q^23 - 8 * q^25 + 4 * q^29 + 11 * q^35 + 4 * q^37 + 6 * q^41 + 10 * q^43 + 15 * q^47 + 5 * q^49 - 24 * q^53 + 16 * q^55 + 10 * q^59 - 12 * q^61 - 12 * q^65 - 7 * q^67 - 22 * q^71 - 10 * q^73 + 19 * q^77 - 70 * q^83 - 26 * q^85 - 18 * q^89 - 9 * q^91 - 10 * q^95 + 38 * q^97

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