LMFDB - Embedded newform 2268.2.l.j.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(109,2268)]

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, 2, 4]))

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

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

chi := DirichletCharacter("2268.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.l (of order $3$, degree $2$, not 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	2268.109
Dual form			2268.2.l.j.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.28799 q^{5} +(-2.64400 - 0.0963576i) q^{7} +O(q^{10})$	$q-4.28799 q^{5} +(-2.64400 - 0.0963576i) q^{7} -3.81089 q^{11} +(-1.64400 + 2.84748i) q^{13} +(0.405446 - 0.702253i) q^{17} +(-3.54944 - 6.14781i) q^{19} -6.47710 q^{23} +13.3869 q^{25} +(-1.90545 - 3.30033i) q^{29} +(-1.64400 - 2.84748i) q^{31} +(11.3374 + 0.413181i) q^{35} +(2.88255 + 4.99272i) q^{37} +(-1.04944 + 1.81769i) q^{41} +(4.38255 + 7.59079i) q^{43} +(-1.66690 + 2.88715i) q^{47} +(6.98143 + 0.509538i) q^{49} +(-4.93199 + 8.54245i) q^{53} +16.3411 q^{55} +(-1.73855 - 3.01126i) q^{59} +(-2.97710 + 5.15649i) q^{61} +(7.04944 - 12.2100i) q^{65} +(1.76145 + 3.05092i) q^{67} +6.05308 q^{71} +(5.19344 - 8.99530i) q^{73} +(10.0760 + 0.367208i) q^{77} +(2.57234 - 4.45543i) q^{79} +(0.856004 + 1.48264i) q^{83} +(-1.73855 + 3.01126i) q^{85} +(-6.26509 - 10.8515i) q^{89} +(4.62110 - 7.37033i) q^{91} +(15.2200 + 26.3618i) q^{95} +(-0.522900 - 0.905690i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q - 2 * q^5 - 4 * q^7	$ 6 q - 2 q^{5} - 4 q^{7} - 10 q^{11} + 2 q^{13} - 4 q^{17} - 3 q^{19} - 28 q^{23} + 20 q^{25} - 5 q^{29} + 2 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} - 9 q^{47} - 12 q^{49} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 13 q^{77} + 8 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} - 14 q^{97}+O(q^{100}) $ 6 * q - 2 * q^5 - 4 * q^7 - 10 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 - 28 * q^23 + 20 * q^25 - 5 * q^29 + 2 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 - 9 * q^47 - 12 * q^49 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 13 * q^77 + 8 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−4.28799			−1.91765			−0.958824	−	0.284000i	$-0.908338\pi$
$5$	−4.28799			−1.91765			−0.958824	+	0.284000i	$0.908338\pi$
$6$		0			0
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.81089			−1.14903			−0.574514	−	0.818495i	$-0.694809\pi$
$11$	−3.81089			−1.14903			−0.574514	+	0.818495i	$0.694809\pi$
$12$		0			0
$13$	−1.64400	+	2.84748i	−0.455962	+	0.789750i	−0.998743	−	0.0501244i	$-0.984038\pi$
$13$	−1.64400	+	2.84748i	−0.455962	+	0.789750i	0.542781	+	0.839875i	$0.317372\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.405446	−	0.702253i	0.0983351	−	0.170321i	−0.812661	−	0.582737i	$-0.801982\pi$
$17$	0.405446	−	0.702253i	0.0983351	−	0.170321i	0.910996	+	0.412416i	$0.135315\pi$
$18$		0			0
$19$	−3.54944	−	6.14781i	−0.814298	−	1.41041i	−0.909831	−	0.414979i	$-0.863789\pi$
$19$	−3.54944	−	6.14781i	−0.814298	−	1.41041i	0.0955331	−	0.995426i	$-0.469544\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.47710			−1.35057			−0.675284	−	0.737557i	$-0.735979\pi$
$23$	−6.47710			−1.35057			−0.675284	+	0.737557i	$0.735979\pi$
$24$		0			0
$25$	13.3869			2.67738
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.90545	−	3.30033i	−0.353832	−	0.612856i	0.633085	−	0.774082i	$-0.281788\pi$
$29$	−1.90545	−	3.30033i	−0.353832	−	0.612856i	−0.986917	+	0.161227i	$0.948455\pi$
$30$		0			0
$31$	−1.64400	−	2.84748i	−0.295270	−	0.511423i	0.679777	−	0.733419i	$-0.262076\pi$
$31$	−1.64400	−	2.84748i	−0.295270	−	0.511423i	−0.975048	+	0.221995i	$0.928743\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	11.3374	+	0.413181i	1.91638	+	0.0698403i
$36$		0			0
$37$	2.88255	+	4.99272i	0.473888	+	0.820797i	0.999553	−	0.0298939i	$-0.00951695\pi$
$37$	2.88255	+	4.99272i	0.473888	+	0.820797i	−0.525665	+	0.850691i	$0.676184\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.04944	+	1.81769i	−0.163895	+	0.283875i	−0.936262	−	0.351301i	$-0.885739\pi$
$41$	−1.04944	+	1.81769i	−0.163895	+	0.283875i	0.772367	+	0.635176i	$0.219073\pi$
$42$		0			0
$43$	4.38255	+	7.59079i	0.668332	+	1.15758i	0.978370	+	0.206861i	$0.0663248\pi$
$43$	4.38255	+	7.59079i	0.668332	+	1.15758i	−0.310038	+	0.950724i	$0.600342\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.66690	+	2.88715i	−0.243142	+	0.421134i	−0.961608	−	0.274428i	$-0.911511\pi$
$47$	−1.66690	+	2.88715i	−0.243142	+	0.421134i	0.718466	+	0.695562i	$0.244845\pi$
$48$		0			0
$49$	6.98143	+	0.509538i	0.997347	+	0.0727912i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.93199	+	8.54245i	−0.677461	+	1.17340i	0.298282	+	0.954478i	$0.403586\pi$
$53$	−4.93199	+	8.54245i	−0.677461	+	1.17340i	−0.975743	+	0.218919i	$0.929747\pi$
$54$		0			0
$55$	16.3411			2.20343
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.73855	−	3.01126i	−0.226340	−	0.392032i	0.730381	−	0.683040i	$-0.239343\pi$
$59$	−1.73855	−	3.01126i	−0.226340	−	0.392032i	−0.956721	+	0.291008i	$0.906009\pi$
$60$		0			0
$61$	−2.97710	+	5.15649i	−0.381179	+	0.660221i	−0.991231	−	0.132140i	$-0.957815\pi$
$61$	−2.97710	+	5.15649i	−0.381179	+	0.660221i	0.610052	+	0.792361i	$0.291148\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.04944	−	12.2100i	0.874376	−	1.51446i
$66$		0			0
$67$	1.76145	+	3.05092i	0.215195	+	0.372729i	0.953333	−	0.301921i	$-0.0976278\pi$
$67$	1.76145	+	3.05092i	0.215195	+	0.372729i	−0.738138	+	0.674650i	$0.764295\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.05308			0.718369			0.359184	−	0.933267i	$-0.383055\pi$
$71$	6.05308			0.718369			0.359184	+	0.933267i	$0.383055\pi$
$72$		0			0
$73$	5.19344	−	8.99530i	0.607846	−	1.05282i	−0.383749	−	0.923438i	$-0.625367\pi$
$73$	5.19344	−	8.99530i	0.607846	−	1.05282i	0.991595	−	0.129383i	$-0.0412995\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.0760	+	0.367208i	1.14826	+	0.0418473i
$78$		0			0
$79$	2.57234	−	4.45543i	0.289411	−	0.501275i	−0.684258	−	0.729240i	$-0.739874\pi$
$79$	2.57234	−	4.45543i	0.289411	−	0.501275i	0.973669	+	0.227965i	$0.0732072\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.856004	+	1.48264i	0.0939586	+	0.162741i	0.909174	−	0.416417i	$-0.136715\pi$
$83$	0.856004	+	1.48264i	0.0939586	+	0.162741i	−0.815215	+	0.579159i	$0.803381\pi$
$84$		0			0
$85$	−1.73855	+	3.01126i	−0.188572	+	0.326617i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.26509	−	10.8515i	−0.664098	−	1.15025i	−0.979529	−	0.201304i	$-0.935482\pi$
$89$	−6.26509	−	10.8515i	−0.664098	−	1.15025i	0.315430	−	0.948949i	$-0.397851\pi$
$90$		0			0
$91$	4.62110	−	7.37033i	0.484422	−	0.772620i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.2200	+	26.3618i	1.56154	+	2.70466i
$96$		0			0
$97$	−0.522900	−	0.905690i	−0.0530925	−	0.0919589i	0.838258	−	0.545274i	$-0.183574\pi$
$97$	−0.522900	−	0.905690i	−0.0530925	−	0.0919589i	−0.891350	+	0.453315i	$0.850241\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	17.9098			1.78209			0.891045	−	0.453916i	$-0.149973\pi$
$101$	17.9098			1.78209			0.891045	+	0.453916i	$0.149973\pi$
$102$		0			0
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.45056	+	5.97654i	0.333578	+	0.577774i	0.983211	−	0.182474i	$-0.0584106\pi$
$107$	3.45056	+	5.97654i	0.333578	+	0.577774i	−0.649633	+	0.760248i	$0.725077\pi$
$108$		0			0
$109$	2.81089	−	4.86861i	0.269235	−	0.466328i	−0.699430	−	0.714701i	$-0.746563\pi$
$109$	2.81089	−	4.86861i	0.269235	−	0.466328i	0.968664	+	0.248373i	$0.0798959\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10.0760	−	17.4521i	0.947869	−	1.64176i	0.197966	−	0.980209i	$-0.436566\pi$
$113$	10.0760	−	17.4521i	0.947869	−	1.64176i	0.749903	−	0.661548i	$-0.230100\pi$
$114$		0			0
$115$	27.7738			2.58992
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.13967	+	1.81769i	−0.104473	+	0.166627i
$120$		0			0
$121$	3.52290			0.320264
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−35.9629			−3.21662
$126$		0			0
$127$	−2.14468			−0.190310			−0.0951550	−	0.995462i	$-0.530335\pi$
$127$	−2.14468			−0.190310			−0.0951550	+	0.995462i	$0.530335\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.38688			−0.295913			−0.147956	−	0.988994i	$-0.547270\pi$
$131$	−3.38688			−0.295913			−0.147956	+	0.988994i	$0.547270\pi$
$132$		0			0
$133$	8.79232	+	16.5968i	0.762391	+	1.43913i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.9542			−1.10675			−0.553376	−	0.832932i	$-0.686661\pi$
$137$	−12.9542			−1.10675			−0.553376	+	0.832932i	$0.686661\pi$
$138$		0			0
$139$	8.64400	−	14.9718i	0.733174	−	1.26989i	−0.222346	−	0.974968i	$-0.571371\pi$
$139$	8.64400	−	14.9718i	0.733174	−	1.26989i	0.955520	−	0.294927i	$-0.0952953\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.26509	−	10.8515i	0.523913	−	0.907444i
$144$		0			0
$145$	8.17054	+	14.1518i	0.678526	+	1.17524i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.56870			−0.128513			−0.0642565	−	0.997933i	$-0.520468\pi$
$149$	−1.56870			−0.128513			−0.0642565	+	0.997933i	$0.520468\pi$
$150$		0			0
$151$	−1.38688			−0.112862			−0.0564312	−	0.998406i	$-0.517972\pi$
$151$	−1.38688			−0.112862			−0.0564312	+	0.998406i	$0.517972\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.04944	+	12.2100i	0.566225	+	0.980730i
$156$		0			0
$157$	8.43199	+	14.6046i	0.672946	+	1.16558i	0.977065	+	0.212942i	$0.0683047\pi$
$157$	8.43199	+	14.6046i	0.672946	+	1.16558i	−0.304119	+	0.952634i	$0.598362\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	17.1254	+	0.624118i	1.34967	+	0.0491874i
$162$		0			0
$163$	−8.64833	−	14.9793i	−0.677389	−	1.17327i	−0.975764	−	0.218824i	$-0.929778\pi$
$163$	−8.64833	−	14.9793i	−0.677389	−	1.17327i	0.298375	−	0.954449i	$-0.403555\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.97779	−	12.0859i	0.539957	−	0.935234i	−0.458948	−	0.888463i	$-0.651774\pi$
$167$	6.97779	−	12.0859i	0.539957	−	0.935234i	0.998906	−	0.0467708i	$-0.0148930\pi$
$168$		0			0
$169$	1.09455	+	1.89582i	0.0841964	+	0.145833i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.57165	+	7.91834i	−0.347576	+	0.602020i	−0.985818	−	0.167816i	$-0.946329\pi$
$173$	−4.57165	+	7.91834i	−0.347576	+	0.602020i	0.638242	+	0.769836i	$0.279662\pi$
$174$		0			0
$175$	−35.3948	−	1.28993i	−2.67560	−	0.0975093i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.53087	+	14.7759i	−0.637627	+	1.10440i	0.348325	+	0.937374i	$0.386751\pi$
$179$	−8.53087	+	14.7759i	−0.637627	+	1.10440i	−0.985952	+	0.167029i	$0.946583\pi$
$180$		0			0
$181$	−16.4400			−1.22197			−0.610986	−	0.791641i	$-0.709227\pi$
$181$	−16.4400			−1.22197			−0.610986	+	0.791641i	$0.709227\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.3603	−	21.4087i	−0.908750	−	1.57400i
$186$		0			0
$187$	−1.54511	+	2.67621i	−0.112990	+	0.195704i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.48143	+	2.56591i	−0.107193	+	0.185663i	−0.914632	−	0.404288i	$-0.867519\pi$
$191$	−1.48143	+	2.56591i	−0.107193	+	0.185663i	0.807439	+	0.589951i	$0.200853\pi$
$192$		0			0
$193$	8.71565	+	15.0959i	0.627366	+	1.08663i	0.988078	+	0.153953i	$0.0492004\pi$
$193$	8.71565	+	15.0959i	0.627366	+	1.08663i	−0.360712	+	0.932677i	$0.617466\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.2880			0.732989			0.366495	−	0.930420i	$-0.380558\pi$
$197$	10.2880			0.732989			0.366495	+	0.930420i	$0.380558\pi$
$198$		0			0
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.71998	+	8.90966i	0.331278	+	0.625336i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	13.5265	+	23.4287i	0.935650	+	1.62059i
$210$		0			0
$211$	−8.21634	+	14.2311i	−0.565636	+	0.979710i	0.431354	+	0.902183i	$0.358036\pi$
$211$	−8.21634	+	14.2311i	−0.565636	+	0.979710i	−0.996990	+	0.0775277i	$0.975297\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−18.7923	−	32.5493i	−1.28163	−	2.21984i
$216$		0			0
$217$	4.07234	+	7.68715i	0.276449	+	0.521838i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.33310	+	2.30900i	0.0896743	+	0.155320i
$222$		0			0
$223$	−2.06801	−	3.58190i	−0.138484	−	0.239862i	0.788439	−	0.615113i	$-0.210890\pi$
$223$	−2.06801	−	3.58190i	−0.138484	−	0.239862i	−0.926923	+	0.375251i	$0.877556\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−21.2967			−1.41351			−0.706754	−	0.707459i	$-0.749841\pi$
$227$	−21.2967			−1.41351			−0.706754	+	0.707459i	$0.749841\pi$
$228$		0			0
$229$	−5.85532			−0.386930			−0.193465	−	0.981107i	$-0.561973\pi$
$229$	−5.85532			−0.386930			−0.193465	+	0.981107i	$0.561973\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.02290	+	6.96787i	0.263549	+	0.456480i	0.967182	−	0.254083i	$-0.0817736\pi$
$233$	4.02290	+	6.96787i	0.263549	+	0.456480i	−0.703633	+	0.710563i	$0.748440\pi$
$234$		0			0
$235$	7.14764	−	12.3801i	0.466260	−	0.807587i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.04944	−	12.2100i	0.455991	−	0.789799i	−0.542754	−	0.839892i	$-0.682618\pi$
$239$	7.04944	−	12.2100i	0.455991	−	0.789799i	0.998745	+	0.0500930i	$0.0159518\pi$
$240$		0			0
$241$	−26.7280			−1.72170			−0.860849	−	0.508860i	$-0.830067\pi$
$241$	−26.7280			−1.72170			−0.860849	+	0.508860i	$0.830067\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−29.9363	−	2.18490i	−1.91256	−	0.139588i
$246$		0			0
$247$	23.3411			1.48516
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.43268			0.153549			0.0767746	−	0.997048i	$-0.475538\pi$
$251$	2.43268			0.153549			0.0767746	+	0.997048i	$0.475538\pi$
$252$		0			0
$253$	24.6835			1.55184
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.5302			−0.781611			−0.390806	−	0.920473i	$-0.627804\pi$
$257$	−12.5302			−0.781611			−0.390806	+	0.920473i	$0.627804\pi$
$258$		0			0
$259$	−7.14035	−	13.4785i	−0.443680	−	0.837512i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.90112			−0.425541			−0.212771	−	0.977102i	$-0.568249\pi$
$263$	−6.90112			−0.425541			−0.212771	+	0.977102i	$0.568249\pi$
$264$		0			0
$265$	21.1483	−	36.6300i	1.29913	−	2.25016i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.9054	+	18.8888i	−0.664917	+	1.15167i	0.314391	+	0.949294i	$0.398200\pi$
$269$	−10.9054	+	18.8888i	−0.664917	+	1.15167i	−0.979308	+	0.202376i	$0.935134\pi$
$270$		0			0
$271$	−3.76145	−	6.51502i	−0.228492	−	0.395759i	0.728870	−	0.684653i	$-0.240046\pi$
$271$	−3.76145	−	6.51502i	−0.228492	−	0.395759i	−0.957361	+	0.288893i	$0.906713\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−51.0159			−3.07638
$276$		0			0
$277$	9.23491			0.554872			0.277436	−	0.960744i	$-0.410515\pi$
$277$	9.23491			0.554872			0.277436	+	0.960744i	$0.410515\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.83743	+	11.8428i	0.407887	+	0.706481i	0.994653	−	0.103276i	$-0.0329323\pi$
$281$	6.83743	+	11.8428i	0.407887	+	0.706481i	−0.586766	+	0.809757i	$0.699599\pi$
$282$		0			0
$283$	−1.07165	−	1.85616i	−0.0637032	−	0.110337i	0.832415	−	0.554153i	$-0.186958\pi$
$283$	−1.07165	−	1.85616i	−0.0637032	−	0.110337i	−0.896118	+	0.443816i	$0.853624\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.94987	−	4.70484i	0.174125	−	0.277718i
$288$		0			0
$289$	8.17123	+	14.1530i	0.480660	+	0.832528i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.64833	+	8.05114i	−0.271558	+	0.470353i	−0.969261	−	0.246035i	$-0.920872\pi$
$293$	−4.64833	+	8.05114i	−0.271558	+	0.470353i	0.697703	+	0.716387i	$0.254206\pi$
$294$		0			0
$295$	7.45489	+	12.9122i	0.434040	+	0.751780i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.6483	−	18.4434i	0.615809	−	1.06661i
$300$		0			0
$301$	−10.8560	−	20.4923i	−0.625730	−	1.18116i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.7658	−	22.1110i	0.730966	−	1.26607i
$306$		0			0
$307$	−10.3869			−0.592810			−0.296405	−	0.955062i	$-0.595788\pi$
$307$	−10.3869			−0.592810			−0.296405	+	0.955062i	$0.595788\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.28799	−	2.23087i	−0.0730353	−	0.126501i	0.827195	−	0.561915i	$-0.189935\pi$
$311$	−1.28799	−	2.23087i	−0.0730353	−	0.126501i	−0.900230	+	0.435414i	$0.856602\pi$
$312$		0			0
$313$	5.74219	−	9.94577i	0.324568	−	0.562168i	−0.656857	−	0.754015i	$-0.728114\pi$
$313$	5.74219	−	9.94577i	0.324568	−	0.562168i	0.981425	+	0.191847i	$0.0614478\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.59820	−	13.1605i	0.426757	−	0.739165i	−0.569826	−	0.821766i	$-0.692989\pi$
$317$	7.59820	−	13.1605i	0.426757	−	0.739165i	0.996583	+	0.0826006i	$0.0263226\pi$
$318$		0			0
$319$	7.26145	+	12.5772i	0.406563	+	0.704188i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.75643			−0.320296
$324$		0			0
$325$	−22.0080	+	38.1189i	−1.22078	+	2.11446i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.68547	−	7.47299i	0.258318	−	0.411999i
$330$		0			0
$331$	−7.76578	+	13.4507i	−0.426846	+	0.739319i	−0.996591	−	0.0825028i	$-0.973709\pi$
$331$	−7.76578	+	13.4507i	−0.426846	+	0.739319i	0.569745	+	0.821822i	$0.307042\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.55308	−	13.0823i	−0.412669	−	0.714764i
$336$		0			0
$337$	1.50433	−	2.60558i	0.0819461	−	0.141935i	−0.822140	−	0.569286i	$-0.807220\pi$
$337$	1.50433	−	2.60558i	0.0819461	−	0.141935i	0.904086	+	0.427351i	$0.140553\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.26509	+	10.8515i	0.339274	+	0.587639i
$342$		0			0
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.4327	+	19.8020i	0.613738	+	1.06303i	0.990604	+	0.136758i	$0.0436683\pi$
$347$	11.4327	+	19.8020i	0.613738	+	1.06303i	−0.376866	+	0.926268i	$0.622998\pi$
$348$		0			0
$349$	−4.52221	−	7.83270i	−0.242068	−	0.419275i	0.719235	−	0.694767i	$-0.244493\pi$
$349$	−4.52221	−	7.83270i	−0.242068	−	0.419275i	−0.961303	+	0.275492i	$0.911159\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.1964			0.968496			0.484248	−	0.874931i	$-0.339093\pi$
$353$	18.1964			0.968496			0.484248	+	0.874931i	$0.339093\pi$
$354$		0			0
$355$	−25.9556			−1.37758
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.1934	+	21.1197i	0.643545	+	1.11465i	0.984636	+	0.174622i	$0.0558704\pi$
$359$	12.1934	+	21.1197i	0.643545	+	1.11465i	−0.341090	+	0.940030i	$0.610796\pi$
$360$		0			0
$361$	−15.6971	+	27.1881i	−0.826162	+	1.43095i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−22.2694	+	38.5718i	−1.16563	+	2.01894i
$366$		0			0
$367$	−8.86535			−0.462768			−0.231384	−	0.972863i	$-0.574325\pi$
$367$	−8.86535			−0.462768			−0.231384	+	0.972863i	$0.574325\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.8633	−	22.1110i	0.719746	−	1.14794i
$372$		0			0
$373$	−3.15197			−0.163203			−0.0816014	−	0.996665i	$-0.526003\pi$
$373$	−3.15197			−0.163203			−0.0816014	+	0.996665i	$0.526003\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.5302			0.645337
$378$		0			0
$379$	−2.28799			−0.117526			−0.0587631	−	0.998272i	$-0.518716\pi$
$379$	−2.28799			−0.117526			−0.0587631	+	0.998272i	$0.518716\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	28.2509			1.44355			0.721776	−	0.692127i	$-0.243326\pi$
$383$	28.2509			1.44355			0.721776	+	0.692127i	$0.243326\pi$
$384$		0			0
$385$	−43.2057	−	1.57459i	−2.20197	−	0.0802484i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.720669			−0.0365394			−0.0182697	−	0.999833i	$-0.505816\pi$
$389$	−0.720669			−0.0365394			−0.0182697	+	0.999833i	$0.505816\pi$
$390$		0			0
$391$	−2.62612	+	4.54856i	−0.132808	+	0.230031i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11.0302	+	19.1048i	−0.554989	+	0.961269i
$396$		0			0
$397$	−10.5753	−	18.3169i	−0.530759	−	0.919301i	−0.999356	−	0.0358892i	$-0.988574\pi$
$397$	−10.5753	−	18.3169i	−0.530759	−	0.919301i	0.468597	−	0.883412i	$-0.344760\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	28.4944			1.42294			0.711472	−	0.702715i	$-0.248029\pi$
$401$	28.4944			1.42294			0.711472	+	0.702715i	$0.248029\pi$
$402$		0			0
$403$	10.8109			0.538529
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.9851	−	19.0267i	−0.544510	−	0.943119i
$408$		0			0
$409$	5.38186	+	9.32165i	0.266116	+	0.460926i	0.967855	−	0.251508i	$-0.0809263\pi$
$409$	5.38186	+	9.32165i	0.266116	+	0.460926i	−0.701740	+	0.712434i	$0.747593\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.30656	+	8.12927i	0.211912	+	0.400015i
$414$		0			0
$415$	−3.67054	−	6.35756i	−0.180180	−	0.312080i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.0302	−	29.4971i	0.831979	−	1.44103i	−0.0644877	−	0.997919i	$-0.520541\pi$
$419$	17.0302	−	29.4971i	0.831979	−	1.44103i	0.896467	−	0.443111i	$-0.146125\pi$
$420$		0			0
$421$	−10.2916	−	17.8256i	−0.501584	−	0.868768i	−0.999998	−	0.00182949i	$-0.999418\pi$
$421$	−10.2916	−	17.8256i	−0.501584	−	0.868768i	0.498415	−	0.866939i	$-0.333916\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.42766	−	9.40098i	0.263280	−	0.456014i
$426$		0			0
$427$	8.36831	−	13.3469i	0.404971	−	0.645900i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.9814	−	20.7524i	0.577125	−	0.999610i	−0.418682	−	0.908133i	$-0.637508\pi$
$431$	11.9814	−	20.7524i	0.577125	−	0.999610i	0.995807	−	0.0914772i	$-0.0291589\pi$
$432$		0			0
$433$	29.9642			1.43999			0.719995	−	0.693980i	$-0.244144\pi$
$433$	29.9642			1.43999			0.719995	+	0.693980i	$0.244144\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.9901	+	39.8200i	1.09977	+	1.90485i
$438$		0			0
$439$	−14.4098	+	24.9585i	−0.687741	+	1.19120i	0.284826	+	0.958579i	$0.408064\pi$
$439$	−14.4098	+	24.9585i	−0.687741	+	1.19120i	−0.972567	+	0.232623i	$0.925269\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.0043	−	27.7203i	0.760389	−	1.31703i	−0.182262	−	0.983250i	$-0.558342\pi$
$443$	16.0043	−	27.7203i	0.760389	−	1.31703i	0.942650	−	0.333782i	$-0.108325\pi$
$444$		0			0
$445$	26.8647	+	46.5310i	1.27351	+	2.20578i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	32.0087			1.51058			0.755291	−	0.655390i	$-0.227496\pi$
$449$	32.0087			1.51058			0.755291	+	0.655390i	$0.227496\pi$
$450$		0			0
$451$	3.99931	−	6.92701i	0.188320	−	0.326180i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−19.8152	+	31.6039i	−0.928952	+	1.48161i
$456$		0			0
$457$	10.4277	−	18.0612i	0.487785	−	0.844869i	−0.512116	−	0.858916i	$-0.671138\pi$
$457$	10.4277	−	18.0612i	0.487785	−	0.844869i	0.999901	+	0.0140474i	$0.00447158\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.6254	+	21.8679i	0.588025	+	1.01849i	0.994491	+	0.104823i	$0.0334276\pi$
$461$	12.6254	+	21.8679i	0.588025	+	1.01849i	−0.406466	+	0.913666i	$0.633239\pi$
$462$		0			0
$463$	10.5760	−	18.3181i	0.491508	−	0.851316i	−0.508445	−	0.861095i	$-0.669779\pi$
$463$	10.5760	−	18.3181i	0.491508	−	0.851316i	0.999952	+	0.00977849i	$0.00311264\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.95853	+	13.7846i	0.368277	+	0.637874i	0.989296	−	0.145921i	$-0.0466145\pi$
$467$	7.95853	+	13.7846i	0.368277	+	0.637874i	−0.621019	+	0.783795i	$0.713281\pi$
$468$		0			0
$469$	−4.36329	−	8.23635i	−0.201478	−	0.380319i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−16.7014	−	28.9277i	−0.767932	−	1.33010i
$474$		0			0
$475$	−47.5159	−	82.3000i	−2.18018	−	3.77618i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.95558			0.0893526			0.0446763	−	0.999002i	$-0.485774\pi$
$479$	1.95558			0.0893526			0.0446763	+	0.999002i	$0.485774\pi$
$480$		0			0
$481$	−18.9556			−0.864300
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.24219	+	3.88359i	0.101813	+	0.176345i
$486$		0			0
$487$	−9.98143	+	17.2883i	−0.452302	+	0.783410i	−0.998529	−	0.0542276i	$-0.982730\pi$
$487$	−9.98143	+	17.2883i	−0.452302	+	0.783410i	0.546227	+	0.837637i	$0.316064\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.0488	−	19.1370i	0.498623	−	0.863641i	−0.501375	−	0.865230i	$-0.667172\pi$
$491$	11.0488	−	19.1370i	0.498623	−	0.863641i	0.999999	+	0.00158899i	$0.000505790\pi$
$492$		0			0
$493$	−3.09022			−0.139177
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.0043	−	0.583261i	−0.717892	−	0.0261628i
$498$		0			0
$499$	−33.1148			−1.48242			−0.741212	−	0.671271i	$-0.765749\pi$
$499$	−33.1148			−1.48242			−0.741212	+	0.671271i	$0.765749\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.76509			0.212465			0.106232	−	0.994341i	$-0.466121\pi$
$503$	4.76509			0.212465			0.106232	+	0.994341i	$0.466121\pi$
$504$		0			0
$505$	−76.7970			−3.41742
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.7651			0.477154			0.238577	−	0.971124i	$-0.423319\pi$
$509$	10.7651			0.477154			0.238577	+	0.971124i	$0.423319\pi$
$510$		0			0
$511$	−14.5982	+	23.2831i	−0.645786	+	1.02998i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	30.0159			1.32266
$516$		0			0
$517$	6.35236	−	11.0026i	0.279377	−	0.483894i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.617454	+	1.06946i	−0.0270512	+	0.0468540i	−0.879234	−	0.476390i	$-0.841945\pi$
$521$	−0.617454	+	1.06946i	−0.0270512	+	0.0468540i	0.852183	+	0.523244i	$0.175278\pi$
$522$		0			0
$523$	4.28435	+	7.42071i	0.187342	+	0.324485i	0.944363	−	0.328905i	$-0.106680\pi$
$523$	4.28435	+	7.42071i	0.187342	+	0.324485i	−0.757022	+	0.653390i	$0.773346\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.66621			−0.116142
$528$		0			0
$529$	18.9528			0.824036
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.45056	−	5.97654i	−0.149460	−	0.258873i
$534$		0			0
$535$	−14.7960	−	25.6274i	−0.639685	−	1.10797i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−26.6055	−	1.94180i	−1.14598	−	0.0836390i
$540$		0			0
$541$	7.50433	+	12.9979i	0.322636	+	0.558823i	0.981031	−	0.193850i	$-0.0620976\pi$
$541$	7.50433	+	12.9979i	0.322636	+	0.558823i	−0.658395	+	0.752673i	$0.728764\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.0531	+	20.8766i	−0.516297	+	0.894253i
$546$		0			0
$547$	−6.12543	−	10.6095i	−0.261904	−	0.453632i	0.704844	−	0.709363i	$-0.251017\pi$
$547$	−6.12543	−	10.6095i	−0.261904	−	0.453632i	−0.966748	+	0.255731i	$0.917684\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.5265	+	23.4287i	−0.576250	+	0.998094i
$552$		0			0
$553$	−7.23058	+	11.5323i	−0.307475	+	0.490402i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.8905	−	22.3270i	0.546189	−	0.946027i	−0.452342	−	0.891844i	$-0.649411\pi$
$557$	12.8905	−	22.3270i	0.546189	−	0.946027i	0.998531	−	0.0541823i	$-0.0172552\pi$
$558$		0			0
$559$	−28.8196			−1.21894
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.3418	−	21.3766i	−0.520143	−	0.900915i	−0.999726	−	0.0234179i	$-0.992545\pi$
$563$	−12.3418	−	21.3766i	−0.520143	−	0.900915i	0.479582	−	0.877497i	$-0.340788\pi$
$564$		0			0
$565$	−43.2057	+	74.8345i	−1.81768	+	3.14831i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.11677	+	10.5945i	−0.256428	+	0.444147i	−0.965282	−	0.261208i	$-0.915879\pi$
$569$	−6.11677	+	10.5945i	−0.256428	+	0.444147i	0.708854	+	0.705355i	$0.249212\pi$
$570$		0			0
$571$	−17.6563	−	30.5816i	−0.738893	−	1.27980i	−0.952994	−	0.302989i	$-0.902015\pi$
$571$	−17.6563	−	30.5816i	−0.738893	−	1.27980i	0.214101	−	0.976812i	$-0.431318\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−86.7081			−3.61598
$576$		0			0
$577$	−4.52221	+	7.83270i	−0.188262	+	0.326080i	−0.944671	−	0.328020i	$-0.893619\pi$
$577$	−4.52221	+	7.83270i	−0.188262	+	0.326080i	0.756409	+	0.654099i	$0.226952\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.12041	−	4.00258i	−0.0879693	−	0.166055i
$582$		0			0
$583$	18.7953	−	32.5544i	0.778421	−	1.34826i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.9098	−	31.0206i	−0.739216	−	1.28036i	−0.952849	−	0.303445i	$-0.901863\pi$
$587$	−17.9098	−	31.0206i	−0.739216	−	1.28036i	0.213633	−	0.976914i	$-0.431470\pi$
$588$		0			0
$589$	−11.6705	+	20.2140i	−0.480876	+	0.832902i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	22.0309	+	38.1586i	0.904700	+	1.56699i	0.821320	+	0.570468i	$0.193238\pi$
$593$	22.0309	+	38.1586i	0.904700	+	1.56699i	0.0833794	+	0.996518i	$0.473429\pi$
$594$		0			0
$595$	4.88688	−	7.79423i	0.200342	−	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−15.0316	−	26.0354i	−0.614173	−	1.06378i	−0.990529	−	0.137304i	$-0.956156\pi$
$599$	−15.0316	−	26.0354i	−0.614173	−	1.06378i	0.376356	−	0.926475i	$-0.377177\pi$
$600$		0			0
$601$	−14.5982	−	25.2848i	−0.595473	−	1.03139i	−0.993480	−	0.114007i	$-0.963631\pi$
$601$	−14.5982	−	25.2848i	−0.595473	−	1.03139i	0.398007	−	0.917382i	$-0.369702\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−15.1062			−0.614153
$606$		0			0
$607$	−16.1433			−0.655237			−0.327618	−	0.944810i	$-0.606246\pi$
$607$	−16.1433			−0.655237			−0.327618	+	0.944810i	$0.606246\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.48074	−	9.49292i	−0.221727	−	0.384043i
$612$		0			0
$613$	−23.5581	+	40.8038i	−0.951503	+	1.64805i	−0.209327	+	0.977846i	$0.567127\pi$
$613$	−23.5581	+	40.8038i	−0.951503	+	1.64805i	−0.742175	+	0.670206i	$0.766206\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−19.0073	+	32.9216i	−0.765204	+	1.32537i	0.174934	+	0.984580i	$0.444029\pi$
$617$	−19.0073	+	32.9216i	−0.765204	+	1.32537i	−0.940138	+	0.340793i	$0.889305\pi$
$618$		0			0
$619$	12.1818			0.489629			0.244814	−	0.969570i	$-0.421273\pi$
$619$	12.1818			0.489629			0.244814	+	0.969570i	$0.421273\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	15.5193	+	29.2949i	0.621766	+	1.17368i
$624$		0			0
$625$	87.2741			3.49096
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4.67487			0.186399
$630$		0			0
$631$	−10.8640			−0.432488			−0.216244	−	0.976339i	$-0.569381\pi$
$631$	−10.8640			−0.432488			−0.216244	+	0.976339i	$0.569381\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.19639			0.364948
$636$		0			0
$637$	−12.9283	+	19.0418i	−0.512240	+	0.754465i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−30.4400			−1.20231			−0.601153	−	0.799134i	$-0.705292\pi$
$641$	−30.4400			−1.20231			−0.601153	+	0.799134i	$0.705292\pi$
$642$		0			0
$643$	18.9320	−	32.7912i	0.746605	−	1.29316i	−0.202837	−	0.979213i	$-0.565016\pi$
$643$	18.9320	−	32.7912i	0.746605	−	1.29316i	0.949441	−	0.313945i	$-0.101651\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.0982	−	31.3470i	0.711513	−	1.23238i	−0.252775	−	0.967525i	$-0.581343\pi$
$647$	18.0982	−	31.3470i	0.711513	−	1.23238i	0.964289	−	0.264853i	$-0.0853233\pi$
$648$		0			0
$649$	6.62543	+	11.4756i	0.260071	+	0.450456i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.0975			0.864742			0.432371	−	0.901696i	$-0.357677\pi$
$653$	22.0975			0.864742			0.432371	+	0.901696i	$0.357677\pi$
$654$		0			0
$655$	14.5229			0.567457
$656$		0			0
$657$		0			0
$658$		0			0
$659$	22.0338	+	38.1637i	0.858316	+	1.48665i	0.873534	+	0.486763i	$0.161822\pi$
$659$	22.0338	+	38.1637i	0.858316	+	1.48665i	−0.0152182	+	0.999884i	$0.504844\pi$
$660$		0			0
$661$	−2.95351	−	5.11563i	−0.114878	−	0.198975i	0.802853	−	0.596177i	$-0.203314\pi$
$661$	−2.95351	−	5.11563i	−0.114878	−	0.198975i	−0.917731	+	0.397202i	$0.869981\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−37.7014	−	71.1670i	−1.46200	−	2.75974i
$666$		0			0
$667$	12.3418	+	21.3766i	0.477875	+	0.827704i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.3454	−	19.6508i	0.437985	−	0.758612i
$672$		0			0
$673$	1.09888	+	1.90332i	0.0423589	+	0.0733677i	0.886428	−	0.462867i	$-0.153179\pi$
$673$	1.09888	+	1.90332i	0.0423589	+	0.0733677i	−0.844069	+	0.536235i	$0.819846\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.0316	+	26.0354i	−0.577710	+	1.00062i	0.418032	+	0.908432i	$0.362720\pi$
$677$	−15.0316	+	26.0354i	−0.577710	+	1.00062i	−0.995741	+	0.0921903i	$0.970613\pi$
$678$		0			0
$679$	1.29528	+	2.44503i	0.0497081	+	0.0938315i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.14764	−	7.18392i	0.158705	−	0.274885i	−0.775697	−	0.631106i	$-0.782601\pi$
$683$	4.14764	−	7.18392i	0.158705	−	0.274885i	0.934402	+	0.356221i	$0.115935\pi$
$684$		0			0
$685$	55.5475			2.12236
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−16.2163	−	28.0875i	−0.617793	−	1.07005i
$690$		0			0
$691$	0.598196	−	1.03611i	0.0227564	−	0.0394153i	−0.854423	−	0.519578i	$-0.826089\pi$
$691$	0.598196	−	1.03611i	0.0227564	−	0.0394153i	0.877179	+	0.480163i	$0.159422\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−37.0654	+	64.1991i	−1.40597	+	2.43521i
$696$		0			0
$697$	0.850985	+	1.47395i	0.0322333	+	0.0558298i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−31.8813			−1.20414			−0.602070	−	0.798443i	$-0.705657\pi$
$701$	−31.8813			−1.20414			−0.602070	+	0.798443i	$0.705657\pi$
$702$		0			0
$703$	20.4629	−	35.4427i	0.771771	−	1.33675i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−47.3534	−	1.72574i	−1.78091	−	0.0649032i
$708$		0			0
$709$	10.7163	−	18.5612i	0.402461	−	0.697082i	−0.591562	−	0.806260i	$-0.701488\pi$
$709$	10.7163	−	18.5612i	0.402461	−	0.697082i	0.994022	+	0.109178i	$0.0348217\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.6483	+	18.4434i	0.398783	+	0.690712i
$714$		0			0
$715$	−26.8647	+	46.5310i	−1.00468	+	1.74016i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.6304	+	37.4650i	0.806680	+	1.39721i	0.915151	+	0.403110i	$0.132071\pi$
$719$	21.6304	+	37.4650i	0.806680	+	1.39721i	−0.108472	+	0.994100i	$0.534596\pi$
$720$		0			0
$721$	18.5080	+	0.674503i	0.689273	+	0.0251198i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−25.5080	−	44.1811i	−0.947342	−	1.64085i
$726$		0			0
$727$	−6.09091	−	10.5498i	−0.225899	−	0.391269i	0.730689	−	0.682710i	$-0.239199\pi$
$727$	−6.09091	−	10.5498i	−0.225899	−	0.391269i	−0.956589	+	0.291441i	$0.905865\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.10755			0.262882
$732$		0			0
$733$	13.4486			0.496736			0.248368	−	0.968666i	$-0.420106\pi$
$733$	13.4486			0.496736			0.248368	+	0.968666i	$0.420106\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.71270	−	11.6267i	−0.247265	−	0.428276i
$738$		0			0
$739$	4.93632	−	8.54995i	0.181585	−	0.314515i	−0.760835	−	0.648945i	$-0.775210\pi$
$739$	4.93632	−	8.54995i	0.181585	−	0.314515i	0.942421	+	0.334430i	$0.108544\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.2844	−	19.5451i	0.413983	−	0.717039i	−0.581338	−	0.813662i	$-0.697471\pi$
$743$	11.2844	−	19.5451i	0.413983	−	0.717039i	0.995321	+	0.0966229i	$0.0308041\pi$
$744$		0			0
$745$	6.72658			0.246443
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.54738	−	16.1344i	−0.312314	−	0.589540i
$750$		0			0
$751$	−0.575984			−0.0210180			−0.0105090	−	0.999945i	$-0.503345\pi$
$751$	−0.575984			−0.0210180			−0.0105090	+	0.999945i	$0.503345\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.94692			0.216430
$756$		0			0
$757$	22.8196			0.829391			0.414695	−	0.909960i	$-0.363888\pi$
$757$	22.8196			0.829391			0.414695	+	0.909960i	$0.363888\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.7810			0.717062			0.358531	−	0.933518i	$-0.383278\pi$
$761$	19.7810			0.717062			0.358531	+	0.933518i	$0.383278\pi$
$762$		0			0
$763$	−7.90112	+	12.6017i	−0.286040	+	0.456213i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	11.4327			0.412810
$768$		0			0
$769$	14.3603	−	24.8728i	0.517847	−	0.896937i	−0.481938	−	0.876205i	$-0.660067\pi$
$769$	14.3603	−	24.8728i	0.517847	−	0.896937i	0.999785	−	0.0207319i	$-0.00659965\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.10253	+	7.10578i	−0.147558	+	0.255577i	−0.930324	−	0.366738i	$-0.880475\pi$
$773$	−4.10253	+	7.10578i	−0.147558	+	0.255577i	0.782767	+	0.622315i	$0.213808\pi$
$774$		0			0
$775$	−22.0080	−	38.1189i	−0.790550	−	1.36927i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.8997			0.533839
$780$		0			0
$781$	−23.0677			−0.825425
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−36.1563	−	62.6245i	−1.29047	−	2.23517i
$786$		0			0
$787$	26.3182	+	45.5844i	0.938142	+	1.62491i	0.768934	+	0.639329i	$0.220788\pi$
$787$	26.3182	+	45.5844i	0.938142	+	1.62491i	0.169208	+	0.985580i	$0.445879\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−28.3225	+	45.1724i	−1.00703	+	1.60615i
$792$		0			0
$793$	−9.78868	−	16.9545i	−0.347606	−	0.602072i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.76647	−	15.1840i	0.310524	−	0.537844i	−0.667952	−	0.744205i	$-0.732829\pi$
$797$	8.76647	−	15.1840i	0.310524	−	0.537844i	0.978476	+	0.206361i	$0.0661621\pi$
$798$		0			0
$799$	1.35167	+	2.34117i	0.0478188	+	0.0828245i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.7916	+	34.2801i	−0.698432	+	1.20972i
$804$		0			0
$805$	−73.4337	−	2.67621i	−2.58820	−	0.0943241i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.57530	−	6.19259i	0.125701	−	0.217720i	−0.796306	−	0.604894i	$-0.793215\pi$
$809$	3.57530	−	6.19259i	0.125701	−	0.217720i	0.922007	+	0.387174i	$0.126549\pi$
$810$		0			0
$811$	−31.6835			−1.11256			−0.556280	−	0.830995i	$-0.687772\pi$
$811$	−31.6835			−1.11256			−0.556280	+	0.830995i	$0.687772\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	37.0840	+	64.2313i	1.29899	+	2.24992i
$816$		0			0
$817$	31.1112	−	53.8862i	1.08844	−	1.88524i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.53451	−	13.0502i	0.262956	−	0.455454i	−0.704070	−	0.710131i	$-0.748636\pi$
$821$	7.53451	−	13.0502i	0.262956	−	0.455454i	0.967026	+	0.254677i	$0.0819691\pi$
$822$		0			0
$823$	10.4778	+	18.1481i	0.365233	+	0.632602i	0.988813	−	0.149157i	$-0.0476561\pi$
$823$	10.4778	+	18.1481i	0.365233	+	0.632602i	−0.623581	+	0.781759i	$0.714323\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.7897			1.27930			0.639652	−	0.768665i	$-0.279079\pi$
$827$	36.7897			1.27930			0.639652	+	0.768665i	$0.279079\pi$
$828$		0			0
$829$	−23.1527	+	40.1016i	−0.804125	+	1.39279i	0.112755	+	0.993623i	$0.464032\pi$
$829$	−23.1527	+	40.1016i	−0.804125	+	1.39279i	−0.916880	+	0.399163i	$0.869301\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.18842	−	4.69614i	0.110472	−	0.162712i
$834$		0			0
$835$	−29.9207	+	51.8242i	−1.03545	+	1.79345i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.8189	+	22.2029i	0.442556	+	0.766530i	0.997878	−	0.0651053i	$-0.0207383\pi$
$839$	12.8189	+	22.2029i	0.442556	+	0.766530i	−0.555322	+	0.831635i	$0.687405\pi$
$840$		0			0
$841$	7.23855	−	12.5375i	0.249605	−	0.432329i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.69344	−	8.12927i	−0.161459	−	0.279656i
$846$		0			0
$847$	−9.31453	−	0.339458i	−0.320051	−	0.0116639i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−18.6705	−	32.3383i	−0.640018	−	1.10854i
$852$		0			0
$853$	2.71565	+	4.70364i	0.0929821	+	0.161050i	0.908765	−	0.417309i	$-0.137027\pi$
$853$	2.71565	+	4.70364i	0.0929821	+	0.161050i	−0.815783	+	0.578359i	$0.803693\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.23491			0.247140			0.123570	−	0.992336i	$-0.460566\pi$
$857$	7.23491			0.247140			0.123570	+	0.992336i	$0.460566\pi$
$858$		0			0
$859$	−5.43130			−0.185314			−0.0926568	−	0.995698i	$-0.529536\pi$
$859$	−5.43130			−0.185314			−0.0926568	+	0.995698i	$0.529536\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.35600	−	9.27687i	−0.182320	−	0.315788i	0.760350	−	0.649514i	$-0.225028\pi$
$863$	−5.35600	−	9.27687i	−0.182320	−	0.315788i	−0.942670	+	0.333725i	$0.891694\pi$
$864$		0			0
$865$	19.6032	−	33.9538i	0.666529	−	1.15446i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.80292	+	16.9792i	−0.332541	+	0.575978i
$870$		0			0
$871$	−11.5833			−0.392484
$872$		0			0
$873$		0			0
$874$		0			0
$875$	95.0857	+	3.46529i	3.21448	+	0.117148i
$876$		0			0
$877$	−13.8168			−0.466560			−0.233280	−	0.972410i	$-0.574946\pi$
$877$	−13.8168			−0.466560			−0.233280	+	0.972410i	$0.574946\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.6662			0.797335			0.398667	−	0.917096i	$-0.369473\pi$
$881$	23.6662			0.797335			0.398667	+	0.917096i	$0.369473\pi$
$882$		0			0
$883$	18.9615			0.638105			0.319052	−	0.947737i	$-0.396635\pi$
$883$	18.9615			0.638105			0.319052	+	0.947737i	$0.396635\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.3955			0.684815			0.342408	−	0.939552i	$-0.388758\pi$
$887$	20.3955			0.684815			0.342408	+	0.939552i	$0.388758\pi$
$888$		0			0
$889$	5.67054	+	0.206657i	0.190184	+	0.00693104i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	23.6662			0.791959
$894$		0			0
$895$	36.5803	−	63.3590i	1.22275	−	2.11786i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.26509	+	10.8515i	−0.208953	+	0.361916i
$900$		0			0
$901$	3.99931	+	6.92701i	0.133236	+	0.230772i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	70.4944			2.34331
$906$		0			0
$907$	40.0146			1.32866			0.664331	−	0.747439i	$-0.268717\pi$
$907$	40.0146			1.32866			0.664331	+	0.747439i	$0.268717\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.41342	−	11.1084i	−0.212486	−	0.368037i	0.740006	−	0.672600i	$-0.234823\pi$
$911$	−6.41342	−	11.1084i	−0.212486	−	0.368037i	−0.952492	+	0.304564i	$0.901489\pi$
$912$		0			0
$913$	−3.26214	−	5.65019i	−0.107961	−	0.186994i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.95489	+	0.326351i	0.295716	+	0.0107771i
$918$		0			0
$919$	21.9771	+	38.0655i	0.724958	+	1.25566i	0.958991	+	0.283435i	$0.0914740\pi$
$919$	21.9771	+	38.0655i	0.724958	+	1.25566i	−0.234034	+	0.972228i	$0.575193\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.95125	+	17.2361i	−0.327549	+	0.567332i
$924$		0			0
$925$	38.5883	+	66.8369i	1.26878	+	2.19758i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	20.1175	−	34.8445i	0.660032	−	1.14321i	−0.320574	−	0.947223i	$-0.603876\pi$
$929$	20.1175	−	34.8445i	0.660032	−	1.14321i	0.980607	−	0.195986i	$-0.0627907\pi$
$930$		0			0
$931$	−21.6476	−	44.7291i	−0.709473	−	1.46594i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.62543	−	11.4756i	0.216675	−	0.375291i
$936$		0			0
$937$	−3.06175			−0.100023			−0.0500114	−	0.998749i	$-0.515926\pi$
$937$	−3.06175			−0.100023			−0.0500114	+	0.998749i	$0.515926\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.0946	+	17.4843i	0.329073	+	0.569971i	0.982328	−	0.187167i	$-0.0599304\pi$
$941$	10.0946	+	17.4843i	0.329073	+	0.569971i	−0.653255	+	0.757138i	$0.726597\pi$
$942$		0			0
$943$	6.79734	−	11.7733i	0.221352	−	0.383393i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.572342	+	0.991326i	−0.0185986	+	0.0322138i	−0.875175	−	0.483807i	$-0.839254\pi$
$947$	−0.572342	+	0.991326i	−0.0185986	+	0.0322138i	0.856576	+	0.516020i	$0.172587\pi$
$948$		0			0
$949$	17.0760	+	29.5765i	0.554310	+	0.960093i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−42.9701			−1.39194			−0.695970	−	0.718071i	$-0.745025\pi$
$953$	−42.9701			−1.39194			−0.695970	+	0.718071i	$0.745025\pi$
$954$		0			0
$955$	6.35236	−	11.0026i	0.205558	−	0.356036i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	34.2509	+	1.24824i	1.10602	+	0.0403076i
$960$		0			0
$961$	10.0946	−	17.4843i	0.325631	−	0.564009i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−37.3726	−	64.7313i	−1.20307	−	2.08377i
$966$		0			0
$967$	−4.99931	+	8.65906i	−0.160767	+	0.278457i	−0.935144	−	0.354268i	$-0.884730\pi$
$967$	−4.99931	+	8.65906i	−0.160767	+	0.278457i	0.774377	+	0.632725i	$0.218063\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	16.3145	+	28.2576i	0.523558	+	0.906830i	0.999624	+	0.0274199i	$0.00872911\pi$
$971$	16.3145	+	28.2576i	0.523558	+	0.906830i	−0.476066	+	0.879410i	$0.657938\pi$
$972$		0			0
$973$	−24.2973	+	38.7526i	−0.778937	+	1.24235i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.7479	+	35.9364i	0.663784	+	1.14971i	0.979613	+	0.200892i	$0.0643840\pi$
$977$	20.7479	+	35.9364i	0.663784	+	1.14971i	−0.315829	+	0.948816i	$0.602283\pi$
$978$		0			0
$979$	23.8756	+	41.3537i	0.763067	+	1.32167i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−35.4327			−1.13013			−0.565063	−	0.825047i	$-0.691148\pi$
$983$	−35.4327			−1.13013			−0.565063	+	0.825047i	$0.691148\pi$
$984$		0			0
$985$	−44.1148			−1.40562
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−28.3862	−	49.1663i	−0.902628	−	1.56340i
$990$		0			0
$991$	24.2960	−	42.0818i	0.771787	−	1.33677i	−0.164796	−	0.986328i	$-0.552697\pi$
$991$	24.2960	−	42.0818i	0.771787	−	1.33677i	0.936583	−	0.350446i	$-0.113970\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−15.0080	+	25.9946i	−0.475785	+	0.824083i
$996$		0			0
$997$	47.0260			1.48933			0.744664	−	0.667440i	$-0.232610\pi$
$997$	47.0260			1.48933			0.744664	+	0.667440i	$0.232610\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.l.j.109.1		6
3.2	odd	2		2268.2.l.k.109.3		6
7.2	even	3		2268.2.i.k.2053.3		6
9.2	odd	6		2268.2.i.j.865.1		6
9.4	even	3		756.2.k.f.109.3	yes	6
9.5	odd	6		756.2.k.e.109.1	✓	6
9.7	even	3		2268.2.i.k.865.3		6
21.2	odd	6		2268.2.i.j.2053.1		6
63.2	odd	6		2268.2.l.k.541.3		6
63.4	even	3		5292.2.a.u.1.1		3
63.16	even	3	inner	2268.2.l.j.541.1		6
63.23	odd	6		756.2.k.e.541.1	yes	6
63.31	odd	6		5292.2.a.w.1.3		3
63.32	odd	6		5292.2.a.x.1.3		3
63.58	even	3		756.2.k.f.541.3	yes	6
63.59	even	6		5292.2.a.v.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.1	✓	6	9.5	odd	6
756.2.k.e.541.1	yes	6	63.23	odd	6
756.2.k.f.109.3	yes	6	9.4	even	3
756.2.k.f.541.3	yes	6	63.58	even	3
2268.2.i.j.865.1		6	9.2	odd	6
2268.2.i.j.2053.1		6	21.2	odd	6
2268.2.i.k.865.3		6	9.7	even	3
2268.2.i.k.2053.3		6	7.2	even	3
2268.2.l.j.109.1		6	1.1	even	1	trivial
2268.2.l.j.541.1		6	63.16	even	3	inner
2268.2.l.k.109.3		6	3.2	odd	2
2268.2.l.k.541.3		6	63.2	odd	6
5292.2.a.u.1.1		3	63.4	even	3
5292.2.a.v.1.1		3	63.59	even	6
5292.2.a.w.1.3		3	63.31	odd	6
5292.2.a.x.1.3		3	63.32	odd	6

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.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-4.28799 q^{5} +(-2.64400 - 0.0963576i) q^{7} +O(q^{10})\)	\(q-4.28799 q^{5} +(-2.64400 - 0.0963576i) q^{7} -3.81089 q^{11} +(-1.64400 + 2.84748i) q^{13} +(0.405446 - 0.702253i) q^{17} +(-3.54944 - 6.14781i) q^{19} -6.47710 q^{23} +13.3869 q^{25} +(-1.90545 - 3.30033i) q^{29} +(-1.64400 - 2.84748i) q^{31} +(11.3374 + 0.413181i) q^{35} +(2.88255 + 4.99272i) q^{37} +(-1.04944 + 1.81769i) q^{41} +(4.38255 + 7.59079i) q^{43} +(-1.66690 + 2.88715i) q^{47} +(6.98143 + 0.509538i) q^{49} +(-4.93199 + 8.54245i) q^{53} +16.3411 q^{55} +(-1.73855 - 3.01126i) q^{59} +(-2.97710 + 5.15649i) q^{61} +(7.04944 - 12.2100i) q^{65} +(1.76145 + 3.05092i) q^{67} +6.05308 q^{71} +(5.19344 - 8.99530i) q^{73} +(10.0760 + 0.367208i) q^{77} +(2.57234 - 4.45543i) q^{79} +(0.856004 + 1.48264i) q^{83} +(-1.73855 + 3.01126i) q^{85} +(-6.26509 - 10.8515i) q^{89} +(4.62110 - 7.37033i) q^{91} +(15.2200 + 26.3618i) q^{95} +(-0.522900 - 0.905690i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q - 2 * q^5 - 4 * q^7	\( 6 q - 2 q^{5} - 4 q^{7} - 10 q^{11} + 2 q^{13} - 4 q^{17} - 3 q^{19} - 28 q^{23} + 20 q^{25} - 5 q^{29} + 2 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} - 9 q^{47} - 12 q^{49} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 13 q^{77} + 8 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} - 14 q^{97}+O(q^{100}) \) 6 * q - 2 * q^5 - 4 * q^7 - 10 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 - 28 * q^23 + 20 * q^25 - 5 * q^29 + 2 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 - 9 * q^47 - 12 * q^49 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 13 * q^77 + 8 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 - 14 * q^97

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