LMFDB - Embedded newform 2268.2.i.j.2053.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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, 4, 4]))

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.i (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			2053.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	2268.2053
Dual form			2268.2.i.j.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14400 - 3.71351i) q^{5} +(1.23855 - 2.33795i) q^{7} +O(q^{10})$	$q+(-2.14400 - 3.71351i) q^{5} +(1.23855 - 2.33795i) q^{7} +(-1.90545 + 3.30033i) q^{11} +(-1.64400 + 2.84748i) q^{13} +(-0.405446 - 0.702253i) q^{17} +(-3.54944 + 6.14781i) q^{19} +(-3.23855 - 5.60933i) q^{23} +(-6.69344 + 11.5934i) q^{25} +(1.90545 + 3.30033i) q^{29} +3.28799 q^{31} +(-11.3374 + 0.413181i) q^{35} +(2.88255 - 4.99272i) q^{37} +(1.04944 - 1.81769i) q^{41} +(4.38255 + 7.59079i) q^{43} -3.33379 q^{47} +(-3.93199 - 5.79133i) q^{49} +(4.93199 + 8.54245i) q^{53} +16.3411 q^{55} -3.47710 q^{59} +5.95420 q^{61} +14.0989 q^{65} -3.52290 q^{67} -6.05308 q^{71} +(5.19344 + 8.99530i) q^{73} +(5.35600 + 8.54245i) q^{77} -5.14468 q^{79} +(-0.856004 - 1.48264i) q^{83} +(-1.73855 + 3.01126i) q^{85} +(6.26509 - 10.8515i) q^{89} +(4.62110 + 7.37033i) q^{91} +30.4400 q^{95} +(-0.522900 - 0.905690i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{5} + 2 q^{7}+O(q^{10}) $ 6 * q - q^5 + 2 * q^7	$ 6 q - q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} + 4 q^{17} - 3 q^{19} - 14 q^{23} - 10 q^{25} + 5 q^{29} - 4 q^{31} - 26 q^{35} - 12 q^{41} + 9 q^{43} - 18 q^{47} + 12 q^{49} - 6 q^{53} + 16 q^{55} - 10 q^{59} + 14 q^{61} + 48 q^{65} - 32 q^{67} + 22 q^{71} + q^{73} + 44 q^{77} - 16 q^{79} - 17 q^{83} - 5 q^{85} + 3 q^{89} + 5 q^{91} + 64 q^{95} - 14 q^{97}+O(q^{100}) $ 6 * q - q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 + 4 * q^17 - 3 * q^19 - 14 * q^23 - 10 * q^25 + 5 * q^29 - 4 * q^31 - 26 * q^35 - 12 * q^41 + 9 * q^43 - 18 * q^47 + 12 * q^49 - 6 * q^53 + 16 * q^55 - 10 * q^59 + 14 * q^61 + 48 * q^65 - 32 * q^67 + 22 * q^71 + q^73 + 44 * q^77 - 16 * q^79 - 17 * q^83 - 5 * q^85 + 3 * q^89 + 5 * q^91 + 64 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−2.14400	−	3.71351i	−0.958824	−	1.66073i	−0.725364	−	0.688366i	$-0.758328\pi$
$5$	−2.14400	−	3.71351i	−0.958824	−	1.66073i	−0.233461	−	0.972366i	$-0.575005\pi$
$6$		0			0
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.90545	+	3.30033i	−0.574514	+	0.995087i	0.421581	+	0.906791i	$0.361475\pi$
$11$	−1.90545	+	3.30033i	−0.574514	+	0.995087i	−0.996094	+	0.0882959i	$0.971858\pi$
$12$		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	$-0.198018\pi$
$17$	−0.405446	−	0.702253i	−0.0983351	−	0.170321i	−0.910996	+	0.412416i	$0.864685\pi$
$18$		0			0
$19$	−3.54944	+	6.14781i	−0.814298	+	1.41041i	0.0955331	+	0.995426i	$0.469544\pi$
$19$	−3.54944	+	6.14781i	−0.814298	+	1.41041i	−0.909831	+	0.414979i	$0.863789\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.23855	−	5.60933i	−0.675284	−	1.16963i	−0.976386	−	0.216035i	$-0.930688\pi$
$23$	−3.23855	−	5.60933i	−0.675284	−	1.16963i	0.301101	−	0.953592i	$-0.402646\pi$
$24$		0			0
$25$	−6.69344	+	11.5934i	−1.33869	+	2.31868i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.90545	+	3.30033i	0.353832	+	0.612856i	0.986917	−	0.161227i	$-0.0515450\pi$
$29$	1.90545	+	3.30033i	0.353832	+	0.612856i	−0.633085	+	0.774082i	$0.718212\pi$
$30$		0			0
$31$	3.28799			0.590541			0.295270	−	0.955414i	$-0.404590\pi$
$31$	3.28799			0.590541			0.295270	+	0.955414i	$0.404590\pi$
$32$		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	−0.525665	−	0.850691i	$-0.676184\pi$
$37$	2.88255	−	4.99272i	0.473888	−	0.820797i	0.999553	+	0.0298939i	$0.00951695\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.04944	−	1.81769i	0.163895	−	0.283875i	−0.772367	−	0.635176i	$-0.780927\pi$
$41$	1.04944	−	1.81769i	0.163895	−	0.283875i	0.936262	+	0.351301i	$0.114261\pi$
$42$		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
$47$	−3.33379			−0.486284			−0.243142	−	0.969991i	$-0.578178\pi$
$47$	−3.33379			−0.486284			−0.243142	+	0.969991i	$0.578178\pi$
$48$		0			0
$49$	−3.93199	−	5.79133i	−0.561713	−	0.827332i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.93199	+	8.54245i	0.677461	+	1.17340i	0.975743	+	0.218919i	$0.0702529\pi$
$53$	4.93199	+	8.54245i	0.677461	+	1.17340i	−0.298282	+	0.954478i	$0.596414\pi$
$54$		0			0
$55$	16.3411			2.20343
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.47710			−0.452680			−0.226340	−	0.974048i	$-0.572676\pi$
$59$	−3.47710			−0.452680			−0.226340	+	0.974048i	$0.572676\pi$
$60$		0			0
$61$	5.95420			0.762357			0.381179	−	0.924501i	$-0.375518\pi$
$61$	5.95420			0.762357			0.381179	+	0.924501i	$0.375518\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	14.0989			1.74875
$66$		0			0
$67$	−3.52290			−0.430391			−0.215195	−	0.976571i	$-0.569039\pi$
$67$	−3.52290			−0.430391			−0.215195	+	0.976571i	$0.569039\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.05308			−0.718369			−0.359184	−	0.933267i	$-0.616945\pi$
$71$	−6.05308			−0.718369			−0.359184	+	0.933267i	$0.616945\pi$
$72$		0			0
$73$	5.19344	+	8.99530i	0.607846	+	1.05282i	0.991595	+	0.129383i	$0.0412995\pi$
$73$	5.19344	+	8.99530i	0.607846	+	1.05282i	−0.383749	+	0.923438i	$0.625367\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.35600	+	8.54245i	0.610373	+	0.973503i
$78$		0			0
$79$	−5.14468			−0.578822			−0.289411	−	0.957205i	$-0.593459\pi$
$79$	−5.14468			−0.578822			−0.289411	+	0.957205i	$0.593459\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.856004	−	1.48264i	−0.0939586	−	0.162741i	0.815215	−	0.579159i	$-0.196619\pi$
$83$	−0.856004	−	1.48264i	−0.0939586	−	0.162741i	−0.909174	+	0.416417i	$0.863285\pi$
$84$		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	−0.315430	−	0.948949i	$-0.602149\pi$
$89$	6.26509	−	10.8515i	0.664098	−	1.15025i	0.979529	−	0.201304i	$-0.0645178\pi$
$90$		0			0
$91$	4.62110	+	7.37033i	0.484422	+	0.772620i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	30.4400			3.12307
$96$		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
$101$	8.95489	−	15.5103i	0.891045	−	1.54333i	0.0524199	−	0.998625i	$-0.483307\pi$
$101$	8.95489	−	15.5103i	0.891045	−	1.54333i	0.838625	−	0.544710i	$-0.183360\pi$
$102$		0			0
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.45056	+	5.97654i	−0.333578	+	0.577774i	−0.983211	−	0.182474i	$-0.941589\pi$
$107$	−3.45056	+	5.97654i	−0.333578	+	0.577774i	0.649633	+	0.760248i	$0.274923\pi$
$108$		0			0
$109$	2.81089	+	4.86861i	0.269235	+	0.466328i	0.968664	−	0.248373i	$-0.0798959\pi$
$109$	2.81089	+	4.86861i	0.269235	+	0.466328i	−0.699430	+	0.714701i	$0.746563\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.0760	+	17.4521i	−0.947869	+	1.64176i	−0.197966	+	0.980209i	$0.563434\pi$
$113$	−10.0760	+	17.4521i	−0.947869	+	1.64176i	−0.749903	+	0.661548i	$0.769900\pi$
$114$		0			0
$115$	−13.8869	+	24.0528i	−1.29496	+	2.24293i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.14400	+	0.0781356i	−0.196540	+	0.00716268i
$120$		0			0
$121$	−1.76145	−	3.05092i	−0.160132	−	0.277356i
$122$		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
$131$	−1.69344	−	2.93312i	−0.147956	−	0.256268i	0.782516	−	0.622631i	$-0.213936\pi$
$131$	−1.69344	−	2.93312i	−0.147956	−	0.256268i	−0.930472	+	0.366363i	$0.880603\pi$
$132$		0			0
$133$	9.97710	+	15.9128i	0.865124	+	1.37981i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.47710	+	11.2187i	−0.553376	+	0.958475i	0.444652	+	0.895703i	$0.353327\pi$
$137$	−6.47710	+	11.2187i	−0.553376	+	0.958475i	−0.998028	+	0.0627719i	$0.980006\pi$
$138$		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
$149$	−0.784350	−	1.35853i	−0.0642565	−	0.111295i	0.832107	−	0.554614i	$-0.187134\pi$
$149$	−0.784350	−	1.35853i	−0.0642565	−	0.111295i	−0.896364	+	0.443319i	$0.853801\pi$
$150$		0			0
$151$	0.693438	−	1.20107i	0.0564312	−	0.0977417i	−0.836430	−	0.548074i	$-0.815361\pi$
$151$	0.693438	−	1.20107i	0.0564312	−	0.0977417i	0.892861	+	0.450332i	$0.148695\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.04944	−	12.2100i	−0.566225	−	0.980730i
$156$		0			0
$157$	−16.8640			−1.34589			−0.672946	−	0.739692i	$-0.734971\pi$
$157$	−16.8640			−1.34589			−0.672946	+	0.739692i	$0.734971\pi$
$158$		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	0.298375	+	0.954449i	$0.403555\pi$
$163$	−8.64833	+	14.9793i	−0.677389	+	1.17327i	−0.975764	+	0.218824i	$0.929778\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.97779	+	12.0859i	−0.539957	+	0.935234i	0.458948	+	0.888463i	$0.348226\pi$
$167$	−6.97779	+	12.0859i	−0.539957	+	0.935234i	−0.998906	+	0.0467708i	$0.985107\pi$
$168$		0			0
$169$	1.09455	+	1.89582i	0.0841964	+	0.145833i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.14331			−0.695153			−0.347576	−	0.937652i	$-0.612995\pi$
$173$	−9.14331			−0.695153			−0.347576	+	0.937652i	$0.612995\pi$
$174$		0			0
$175$	18.8145	+	30.0079i	1.42225	+	2.26838i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.53087	+	14.7759i	0.637627	+	1.10440i	0.985952	+	0.167029i	$0.0534174\pi$
$179$	8.53087	+	14.7759i	0.637627	+	1.10440i	−0.348325	+	0.937374i	$0.613249\pi$
$180$		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
$185$	−24.7207			−1.81750
$186$		0			0
$187$	3.09022			0.225980
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.96286			−0.214385			−0.107193	−	0.994238i	$-0.534186\pi$
$191$	−2.96286			−0.214385			−0.107193	+	0.994238i	$0.534186\pi$
$192$		0			0
$193$	−17.4313			−1.25473			−0.627366	−	0.778724i	$-0.715867\pi$
$193$	−17.4313			−1.25473			−0.627366	+	0.778724i	$0.715867\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.2880			−0.732989			−0.366495	−	0.930420i	$-0.619442\pi$
$197$	−10.2880			−0.732989			−0.366495	+	0.930420i	$0.619442\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.0760	−	0.367208i	0.707195	−	0.0257730i
$204$		0			0
$205$	−9.00000			−0.628587
$206$		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
$221$	2.66621			0.179349
$222$		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
$227$	−10.6483	+	18.4434i	−0.706754	+	1.22413i	0.259300	+	0.965797i	$0.416508\pi$
$227$	−10.6483	+	18.4434i	−0.706754	+	1.22413i	−0.966055	+	0.258338i	$0.916825\pi$
$228$		0			0
$229$	2.92766	+	5.07085i	0.193465	+	0.335091i	0.946396	−	0.323008i	$-0.104694\pi$
$229$	2.92766	+	5.07085i	0.193465	+	0.335091i	−0.752931	+	0.658099i	$0.771361\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.02290	+	6.96787i	−0.263549	+	0.456480i	−0.967182	−	0.254083i	$-0.918226\pi$
$233$	−4.02290	+	6.96787i	−0.263549	+	0.456480i	0.703633	+	0.710563i	$0.251560\pi$
$234$		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	−0.998745	−	0.0500930i	$-0.984048\pi$
$239$	−7.04944	+	12.2100i	−0.455991	+	0.789799i	0.542754	+	0.839892i	$0.317382\pi$
$240$		0			0
$241$	13.3640	−	23.1471i	0.860849	−	1.49103i	−0.0102608	−	0.999947i	$-0.503266\pi$
$241$	13.3640	−	23.1471i	0.860849	−	1.49103i	0.871110	−	0.491088i	$-0.163400\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.0760	+	27.0181i	−0.835394	+	1.72612i
$246$		0			0
$247$	−11.6705	−	20.2140i	−0.742579	−	1.28618i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.43268			−0.153549			−0.0767746	−	0.997048i	$-0.524462\pi$
$251$	−2.43268			−0.153549			−0.0767746	+	0.997048i	$0.524462\pi$
$252$		0			0
$253$	24.6835			1.55184
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.26509	−	10.8515i	−0.390806	−	0.676895i	0.601750	−	0.798684i	$-0.294470\pi$
$257$	−6.26509	−	10.8515i	−0.390806	−	0.676895i	−0.992556	+	0.121789i	$0.961137\pi$
$258$		0			0
$259$	−8.10253	−	12.9230i	−0.503466	−	0.802994i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.45056	+	5.97654i	−0.212771	+	0.368529i	−0.952581	−	0.304286i	$-0.901582\pi$
$263$	−3.45056	+	5.97654i	−0.212771	+	0.368529i	0.739810	+	0.672816i	$0.234915\pi$
$264$		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	0.979308	+	0.202376i	$0.0648663\pi$
$269$	10.9054	+	18.8888i	0.664917	+	1.15167i	−0.314391	+	0.949294i	$0.601800\pi$
$270$		0			0
$271$	−3.76145	+	6.51502i	−0.228492	+	0.395759i	−0.957361	−	0.288893i	$-0.906713\pi$
$271$	−3.76145	+	6.51502i	−0.228492	+	0.395759i	0.728870	+	0.684653i	$0.240046\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−25.5080	−	44.1811i	−1.53819	−	2.66422i
$276$		0			0
$277$	−4.61745	+	7.99766i	−0.277436	+	0.480533i	−0.970747	−	0.240106i	$-0.922818\pi$
$277$	−4.61745	+	7.99766i	−0.277436	+	0.480533i	0.693311	+	0.720639i	$0.256151\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.83743	−	11.8428i	−0.407887	−	0.706481i	0.586766	−	0.809757i	$-0.300401\pi$
$281$	−6.83743	−	11.8428i	−0.407887	−	0.706481i	−0.994653	+	0.103276i	$0.967068\pi$
$282$		0			0
$283$	2.14331			0.127406			0.0637032	−	0.997969i	$-0.479709\pi$
$283$	2.14331			0.127406			0.0637032	+	0.997969i	$0.479709\pi$
$284$		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	−0.697703	−	0.716387i	$-0.745794\pi$
$293$	4.64833	−	8.05114i	0.271558	−	0.470353i	0.969261	+	0.246035i	$0.0791277\pi$
$294$		0			0
$295$	7.45489	+	12.9122i	0.434040	+	0.751780i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	21.2967			1.23162
$300$		0			0
$301$	23.1749	−	0.844583i	1.33578	−	0.0486810i
$302$		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
$311$	−2.57598			−0.146071			−0.0730353	−	0.997329i	$-0.523269\pi$
$311$	−2.57598			−0.146071			−0.0730353	+	0.997329i	$0.523269\pi$
$312$		0			0
$313$	−11.4844			−0.649136			−0.324568	−	0.945862i	$-0.605219\pi$
$313$	−11.4844			−0.649136			−0.324568	+	0.945862i	$0.605219\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.1964			0.853514			0.426757	−	0.904366i	$-0.359656\pi$
$317$	15.1964			0.853514			0.426757	+	0.904366i	$0.359656\pi$
$318$		0			0
$319$	−14.5229			−0.813126
$320$		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
$329$	−4.12907	+	7.79423i	−0.227643	+	0.429710i
$330$		0			0
$331$	15.5316			0.853692			0.426846	−	0.904324i	$-0.359625\pi$
$331$	15.5316			0.853692			0.426846	+	0.904324i	$0.359625\pi$
$332$		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
$347$	22.8654			1.22748			0.613738	−	0.789510i	$-0.289665\pi$
$347$	22.8654			1.22748			0.613738	+	0.789510i	$0.289665\pi$
$348$		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
$353$	9.09820	−	15.7585i	0.484248	−	0.838742i	−0.515588	−	0.856837i	$-0.672427\pi$
$353$	9.09820	−	15.7585i	0.484248	−	0.838742i	0.999836	+	0.0180942i	$0.00575988\pi$
$354$		0			0
$355$	12.9778	+	22.4782i	0.688789	+	1.19302i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.1934	+	21.1197i	−0.643545	+	1.11465i	0.341090	+	0.940030i	$0.389204\pi$
$359$	−12.1934	+	21.1197i	−0.643545	+	1.11465i	−0.984636	+	0.174622i	$0.944130\pi$
$360$		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
$367$	4.43268	−	7.67762i	0.231384	−	0.400769i	−0.726832	−	0.686816i	$-0.759008\pi$
$367$	4.43268	−	7.67762i	0.231384	−	0.400769i	0.958216	+	0.286047i	$0.0923413\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	26.0803	−	0.950469i	1.35402	−	0.0493459i
$372$		0			0
$373$	1.57598	+	2.72968i	0.0816014	+	0.141338i	0.903938	−	0.427664i	$-0.140663\pi$
$373$	1.57598	+	2.72968i	0.0816014	+	0.141338i	−0.822337	+	0.569001i	$0.807330\pi$
$374$		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
$383$	14.1254	+	24.4660i	0.721776	+	1.25015i	0.960287	+	0.279012i	$0.0900071\pi$
$383$	14.1254	+	24.4660i	0.721776	+	1.25015i	−0.238512	+	0.971140i	$0.576660\pi$
$384$		0			0
$385$	20.2392	−	38.2046i	1.03149	−	1.94708i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.360335	+	0.624118i	−0.0182697	+	0.0316440i	−0.875016	−	0.484095i	$-0.839149\pi$
$389$	−0.360335	+	0.624118i	−0.0182697	+	0.0316440i	0.856746	+	0.515739i	$0.172482\pi$
$390$		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	0.468597	+	0.883412i	$0.344760\pi$
$397$	−10.5753	+	18.3169i	−0.530759	+	0.919301i	−0.999356	+	0.0358892i	$0.988574\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.2472	+	24.6769i	0.711472	+	1.23231i	0.964305	+	0.264795i	$0.0853044\pi$
$401$	14.2472	+	24.6769i	0.711472	+	1.23231i	−0.252833	+	0.967510i	$0.581362\pi$
$402$		0			0
$403$	−5.40545	+	9.36251i	−0.269264	+	0.466380i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	10.9851	+	19.0267i	0.544510	+	0.943119i
$408$		0			0
$409$	−10.7637			−0.532231			−0.266116	−	0.963941i	$-0.585740\pi$
$409$	−10.7637			−0.532231			−0.266116	+	0.963941i	$0.585740\pi$
$410$		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	$0.479459\pi$
$419$	−17.0302	+	29.4971i	−0.831979	+	1.44103i	−0.896467	+	0.443111i	$0.853875\pi$
$420$		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
$425$	10.8553			0.526560
$426$		0			0
$427$	7.37457	−	13.9206i	0.356881	−	0.673665i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.9814	−	20.7524i	−0.577125	−	0.999610i	−0.995807	−	0.0914772i	$-0.970841\pi$
$431$	−11.9814	−	20.7524i	−0.577125	−	0.999610i	0.418682	−	0.908133i	$-0.362492\pi$
$432$		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
$437$	45.9802			2.19953
$438$		0			0
$439$	28.8196			1.37548			0.687741	−	0.725956i	$-0.258602\pi$
$439$	28.8196			1.37548			0.687741	+	0.725956i	$0.258602\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	32.0087			1.52078			0.760389	−	0.649468i	$-0.225008\pi$
$443$	32.0087			1.52078			0.760389	+	0.649468i	$0.225008\pi$
$444$		0			0
$445$	−53.7293			−2.54701
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−32.0087			−1.51058			−0.755291	−	0.655390i	$-0.772504\pi$
$449$	−32.0087			−1.51058			−0.755291	+	0.655390i	$0.772504\pi$
$450$		0			0
$451$	3.99931	+	6.92701i	0.188320	+	0.326180i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	17.4622	−	32.9624i	0.818639	−	1.54530i
$456$		0			0
$457$	−20.8553			−0.975570			−0.487785	−	0.872964i	$-0.662195\pi$
$457$	−20.8553			−0.975570			−0.487785	+	0.872964i	$0.662195\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.6254	−	21.8679i	−0.588025	−	1.01849i	−0.994491	−	0.104823i	$-0.966572\pi$
$461$	−12.6254	−	21.8679i	−0.588025	−	1.01849i	0.406466	−	0.913666i	$-0.366761\pi$
$462$		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	$-0.953385\pi$
$467$	−7.95853	+	13.7846i	−0.368277	+	0.637874i	0.621019	+	0.783795i	$0.286719\pi$
$468$		0			0
$469$	−4.36329	+	8.23635i	−0.201478	+	0.380319i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−33.4028			−1.53586
$474$		0			0
$475$	−47.5159	−	82.3000i	−2.18018	−	3.77618i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.977789	−	1.69358i	0.0446763	−	0.0773816i	−0.842823	−	0.538192i	$-0.819108\pi$
$479$	0.977789	−	1.69358i	0.0446763	−	0.0773816i	0.887499	+	0.460810i	$0.152441\pi$
$480$		0			0
$481$	9.47779	+	16.4160i	0.432150	+	0.748506i
$482$		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	0.546227	−	0.837637i	$-0.316064\pi$
$487$	−9.98143	−	17.2883i	−0.452302	−	0.783410i	−0.998529	+	0.0542276i	$0.982730\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.0488	+	19.1370i	−0.498623	+	0.863641i	−0.999999	−	0.00158899i	$-0.999494\pi$
$491$	−11.0488	+	19.1370i	−0.498623	+	0.863641i	0.501375	+	0.865230i	$0.332828\pi$
$492$		0			0
$493$	1.54511	−	2.67621i	0.0695883	−	0.120531i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.49705	+	14.1518i	−0.336289	+	0.634794i
$498$		0			0
$499$	16.5574	+	28.6783i	0.741212	+	1.28382i	0.951944	+	0.306272i	$0.0990819\pi$
$499$	16.5574	+	28.6783i	0.741212	+	1.28382i	−0.210732	+	0.977544i	$0.567585\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.76509			−0.212465			−0.106232	−	0.994341i	$-0.533879\pi$
$503$	−4.76509			−0.212465			−0.106232	+	0.994341i	$0.533879\pi$
$504$		0			0
$505$	−76.7970			−3.41742
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.38255	+	9.32284i	0.238577	+	0.413228i	0.960306	−	0.278948i	$-0.0899857\pi$
$509$	5.38255	+	9.32284i	0.238577	+	0.413228i	−0.721729	+	0.692176i	$0.756652\pi$
$510$		0			0
$511$	27.4629	−	1.00085i	1.21489	−	0.0442752i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.0080	−	25.9946i	0.661330	−	1.14546i
$516$		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	$-0.158055\pi$
$521$	0.617454	+	1.06946i	0.0270512	+	0.0468540i	−0.852183	+	0.523244i	$0.824722\pi$
$522$		0			0
$523$	4.28435	−	7.42071i	0.187342	−	0.324485i	−0.757022	−	0.653390i	$-0.773346\pi$
$523$	4.28435	−	7.42071i	0.187342	−	0.324485i	0.944363	+	0.328905i	$0.106680\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.33310	−	2.30900i	−0.0580709	−	0.100582i
$528$		0			0
$529$	−9.47641	+	16.4136i	−0.412018	+	0.713636i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.45056	+	5.97654i	0.149460	+	0.258873i
$534$		0			0
$535$	29.5919			1.27937
$536$		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	−0.658395	−	0.752673i	$-0.728764\pi$
$541$	7.50433	−	12.9979i	0.322636	−	0.558823i	0.981031	+	0.193850i	$0.0620976\pi$
$542$		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
$551$	−27.0531			−1.15250
$552$		0			0
$553$	−6.37195	+	12.0280i	−0.270963	+	0.511483i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.8905	−	22.3270i	−0.546189	−	0.946027i	−0.998531	−	0.0541823i	$-0.982745\pi$
$557$	−12.8905	−	22.3270i	−0.546189	−	0.946027i	0.452342	−	0.891844i	$-0.350589\pi$
$558$		0			0
$559$	−28.8196			−1.21894
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−24.6835			−1.04029			−0.520143	−	0.854079i	$-0.674121\pi$
$563$	−24.6835			−1.04029			−0.520143	+	0.854079i	$0.674121\pi$
$564$		0			0
$565$	86.4115			3.63536
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.2335			−0.512856			−0.256428	−	0.966563i	$-0.582546\pi$
$569$	−12.2335			−0.512856			−0.256428	+	0.966563i	$0.582546\pi$
$570$		0			0
$571$	35.3126			1.47779			0.738893	−	0.673823i	$-0.235349\pi$
$571$	35.3126			1.47779			0.738893	+	0.673823i	$0.235349\pi$
$572$		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	0.756409	−	0.654099i	$-0.226952\pi$
$577$	−4.52221	−	7.83270i	−0.188262	−	0.326080i	−0.944671	+	0.328020i	$0.893619\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.52654	+	0.164965i	−0.187793	+	0.00684390i
$582$		0			0
$583$	−37.5906			−1.55684
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.9098	+	31.0206i	0.739216	+	1.28036i	0.952849	+	0.303445i	$0.0981369\pi$
$587$	17.9098	+	31.0206i	0.739216	+	1.28036i	−0.213633	+	0.976914i	$0.568530\pi$
$588$		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	−0.0833794	+	0.996518i	$0.526571\pi$
$593$	−22.0309	+	38.1586i	−0.904700	+	1.56699i	−0.821320	+	0.570468i	$0.806762\pi$
$594$		0			0
$595$	4.88688	+	7.79423i	0.200342	+	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−30.0631			−1.22835			−0.614173	−	0.789171i	$-0.710510\pi$
$599$	−30.0631			−1.22835			−0.614173	+	0.789171i	$0.710510\pi$
$600$		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
$605$	−7.55308	+	13.0823i	−0.307077	+	0.531872i
$606$		0			0
$607$	8.07165	+	13.9805i	0.327618	+	0.567452i	0.982039	−	0.188679i	$-0.0604207\pi$
$607$	8.07165	+	13.9805i	0.327618	+	0.567452i	−0.654420	+	0.756131i	$0.727087\pi$
$608$		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	−0.742175	−	0.670206i	$-0.766206\pi$
$613$	−23.5581	−	40.8038i	−0.951503	−	1.64805i	−0.209327	−	0.977846i	$-0.567127\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.0073	−	32.9216i	0.765204	−	1.32537i	−0.174934	−	0.984580i	$-0.555971\pi$
$617$	19.0073	−	32.9216i	0.765204	−	1.32537i	0.940138	−	0.340793i	$-0.110695\pi$
$618$		0			0
$619$	−6.09091	+	10.5498i	−0.244814	+	0.424031i	−0.962079	−	0.272769i	$-0.912060\pi$
$619$	−6.09091	+	10.5498i	−0.244814	+	0.424031i	0.717265	+	0.696800i	$0.245394\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−17.6105	−	28.0875i	−0.705550	−	1.12530i
$624$		0			0
$625$	−43.6370	−	75.5816i	−1.74548	−	3.02326i
$626$		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
$635$	4.59820	+	7.96431i	0.182474	+	0.316054i
$636$		0			0
$637$	22.9549	−	1.67536i	0.909506	−	0.0663801i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.2200	+	26.3618i	−0.601153	+	1.04123i	0.391494	+	0.920181i	$0.371958\pi$
$641$	−15.2200	+	26.3618i	−0.601153	+	1.04123i	−0.992647	+	0.121047i	$0.961375\pi$
$642$		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	−0.964289	−	0.264853i	$-0.914677\pi$
$647$	−18.0982	−	31.3470i	−0.711513	−	1.23238i	0.252775	−	0.967525i	$-0.418657\pi$
$648$		0			0
$649$	6.62543	−	11.4756i	0.260071	−	0.450456i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.0488	+	19.1370i	0.432371	+	0.748889i	0.997077	−	0.0764035i	$-0.0243437\pi$
$653$	11.0488	+	19.1370i	0.432371	+	0.748889i	−0.564706	+	0.825292i	$0.691010\pi$
$654$		0			0
$655$	−7.26145	+	12.5772i	−0.283728	+	0.491432i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−22.0338	−	38.1637i	−0.858316	−	1.48665i	−0.873534	−	0.486763i	$-0.838178\pi$
$659$	−22.0338	−	38.1637i	−0.858316	−	1.48665i	0.0152182	−	0.999884i	$-0.495156\pi$
$660$		0			0
$661$	5.90702			0.229757			0.114878	−	0.993380i	$-0.463352\pi$
$661$	5.90702			0.229757			0.114878	+	0.993380i	$0.463352\pi$
$662$		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
$677$	−30.0631			−1.15542			−0.577710	−	0.816242i	$-0.696053\pi$
$677$	−30.0631			−1.15542			−0.577710	+	0.816242i	$0.696053\pi$
$678$		0			0
$679$	−2.76509	+	0.100771i	−0.106114	+	0.00386723i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.14764	−	7.18392i	−0.158705	−	0.274885i	0.775697	−	0.631106i	$-0.217399\pi$
$683$	−4.14764	−	7.18392i	−0.158705	−	0.274885i	−0.934402	+	0.356221i	$0.884065\pi$
$684$		0			0
$685$	55.5475			2.12236
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−32.4327			−1.23559
$690$		0			0
$691$	−1.19639			−0.0455129			−0.0227564	−	0.999741i	$-0.507244\pi$
$691$	−1.19639			−0.0455129			−0.0227564	+	0.999741i	$0.507244\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−74.1308			−2.81194
$696$		0			0
$697$	−1.70197			−0.0644667
$698$		0			0
$699$		0			0
$700$		0			0
$701$	31.8813			1.20414			0.602070	−	0.798443i	$-0.294343\pi$
$701$	31.8813			1.20414			0.602070	+	0.798443i	$0.294343\pi$
$702$		0			0
$703$	20.4629	+	35.4427i	0.771771	+	1.33675i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−25.1712	−	40.1464i	−0.946661	−	1.50986i
$708$		0			0
$709$	−21.4327			−0.804921			−0.402461	−	0.915437i	$-0.631845\pi$
$709$	−21.4327			−0.804921			−0.402461	+	0.915437i	$0.631845\pi$
$710$		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	0.108472	+	0.994100i	$0.465404\pi$
$719$	−21.6304	+	37.4650i	−0.806680	+	1.39721i	−0.915151	+	0.403110i	$0.867929\pi$
$720$		0			0
$721$	18.5080	−	0.674503i	0.689273	−	0.0251198i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−51.0159			−1.89468
$726$		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
$731$	3.55377	−	6.15532i	0.131441	−	0.227663i
$732$		0			0
$733$	−6.72431	−	11.6468i	−0.248368	−	0.430186i	0.714705	−	0.699426i	$-0.246561\pi$
$733$	−6.72431	−	11.6468i	−0.248368	−	0.430186i	−0.963073	+	0.269240i	$0.913228\pi$
$734$		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	0.942421	−	0.334430i	$-0.108544\pi$
$739$	4.93632	+	8.54995i	0.181585	+	0.314515i	−0.760835	+	0.648945i	$0.775210\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.2844	+	19.5451i	−0.413983	+	0.717039i	−0.995321	−	0.0966229i	$-0.969196\pi$
$743$	−11.2844	+	19.5451i	−0.413983	+	0.717039i	0.581338	+	0.813662i	$0.302529\pi$
$744$		0			0
$745$	−3.36329	+	5.82539i	−0.123221	+	0.213426i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.69915	+	15.4695i	0.354399	+	0.565242i
$750$		0			0
$751$	0.287992	+	0.498817i	0.0105090	+	0.0182021i	0.871232	−	0.490871i	$-0.163321\pi$
$751$	0.287992	+	0.498817i	0.0105090	+	0.0182021i	−0.860723	+	0.509073i	$0.829988\pi$
$752$		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
$761$	9.89052	+	17.1309i	0.358531	+	0.620994i	0.987716	−	0.156262i	$-0.0499444\pi$
$761$	9.89052	+	17.1309i	0.358531	+	0.620994i	−0.629185	+	0.777256i	$0.716611\pi$
$762$		0			0
$763$	14.8640	−	0.541702i	0.538112	−	0.0196109i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.71634	−	9.90099i	0.206405	−	0.357504i
$768$		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	$-0.119525\pi$
$773$	4.10253	+	7.10578i	0.147558	+	0.255577i	−0.782767	+	0.622315i	$0.786192\pi$
$774$		0			0
$775$	−22.0080	+	38.1189i	−0.790550	+	1.36927i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.44987	+	12.9036i	0.266919	+	0.462318i
$780$		0			0
$781$	11.5338	−	19.9772i	0.412713	−	0.714839i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	36.1563	+	62.6245i	1.29047	+	2.23517i
$786$		0			0
$787$	−52.6364			−1.87628			−0.938142	−	0.346252i	$-0.887454\pi$
$787$	−52.6364			−1.87628			−0.938142	+	0.346252i	$0.887454\pi$
$788$		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	−0.978476	−	0.206361i	$-0.933838\pi$
$797$	−8.76647	+	15.1840i	−0.310524	+	0.537844i	0.667952	+	0.744205i	$0.267171\pi$
$798$		0			0
$799$	1.35167	+	2.34117i	0.0478188	+	0.0828245i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−39.5833			−1.39686
$804$		0			0
$805$	39.0345	+	62.2573i	1.37579	+	2.19428i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.57530	−	6.19259i	−0.125701	−	0.217720i	0.796306	−	0.604894i	$-0.206785\pi$
$809$	−3.57530	−	6.19259i	−0.125701	−	0.217720i	−0.922007	+	0.387174i	$0.873451\pi$
$810$		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
$815$	74.1679			2.59799
$816$		0			0
$817$	−62.2224			−2.17689
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.0690			0.525913			0.262956	−	0.964808i	$-0.415302\pi$
$821$	15.0690			0.525913			0.262956	+	0.964808i	$0.415302\pi$
$822$		0			0
$823$	−20.9556			−0.730465			−0.365233	−	0.930916i	$-0.619011\pi$
$823$	−20.9556			−0.730465			−0.365233	+	0.930916i	$0.619011\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36.7897			−1.27930			−0.639652	−	0.768665i	$-0.720921\pi$
$827$	−36.7897			−1.27930			−0.639652	+	0.768665i	$0.720921\pi$
$828$		0			0
$829$	−23.1527	−	40.1016i	−0.804125	−	1.39279i	−0.916880	−	0.399163i	$-0.869301\pi$
$829$	−23.1527	−	40.1016i	−0.804125	−	1.39279i	0.112755	−	0.993623i	$-0.464032\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.47277	+	5.10932i	−0.0856764	+	0.177028i
$834$		0			0
$835$	59.8414			2.07090
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.8189	−	22.2029i	−0.442556	−	0.766530i	0.555322	−	0.831635i	$-0.312595\pi$
$839$	−12.8189	−	22.2029i	−0.442556	−	0.766530i	−0.997878	+	0.0651053i	$0.979262\pi$
$840$		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
$851$	−37.3411			−1.28004
$852$		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
$857$	3.61745	−	6.26561i	0.123570	−	0.214029i	−0.797603	−	0.603183i	$-0.793899\pi$
$857$	3.61745	−	6.26561i	0.123570	−	0.214029i	0.921173	+	0.389153i	$0.127232\pi$
$858$		0			0
$859$	2.71565	+	4.70364i	0.0926568	+	0.160486i	0.908628	−	0.417606i	$-0.137131\pi$
$859$	2.71565	+	4.70364i	0.0926568	+	0.160486i	−0.815971	+	0.578092i	$0.803797\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.35600	−	9.27687i	0.182320	−	0.315788i	−0.760350	−	0.649514i	$-0.774972\pi$
$863$	5.35600	−	9.27687i	0.182320	−	0.315788i	0.942670	+	0.333725i	$0.108306\pi$
$864$		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
$871$	5.79163	−	10.0314i	0.196242	−	0.339901i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	44.5418	−	84.0792i	1.50579	−	2.84240i
$876$		0			0
$877$	6.90840	+	11.9657i	0.233280	+	0.404053i	0.958771	−	0.284178i	$-0.0917208\pi$
$877$	6.90840	+	11.9657i	0.233280	+	0.404053i	−0.725491	+	0.688231i	$0.758387\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−23.6662			−0.797335			−0.398667	−	0.917096i	$-0.630527\pi$
$881$	−23.6662			−0.797335			−0.398667	+	0.917096i	$0.630527\pi$
$882$		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
$887$	10.1978	+	17.6631i	0.342408	+	0.593067i	0.984879	−	0.173242i	$-0.0554243\pi$
$887$	10.1978	+	17.6631i	0.342408	+	0.593067i	−0.642472	+	0.766309i	$0.722091\pi$
$888$		0			0
$889$	−2.65630	+	5.01416i	−0.0890894	+	0.168169i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11.8331	−	20.4955i	0.395980	−	0.685857i
$894$		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
$905$	35.2472	+	61.0500i	1.17166	+	2.02937i
$906$		0			0
$907$	−20.0073	+	34.6536i	−0.664331	+	1.15065i	0.315135	+	0.949047i	$0.397950\pi$
$907$	−20.0073	+	34.6536i	−0.664331	+	1.15065i	−0.979466	+	0.201608i	$0.935383\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.41342	+	11.1084i	0.212486	+	0.368037i	0.952492	−	0.304564i	$-0.0985107\pi$
$911$	6.41342	+	11.1084i	0.212486	+	0.368037i	−0.740006	+	0.672600i	$0.765177\pi$
$912$		0			0
$913$	6.52428			0.215922
$914$		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	−0.234034	−	0.972228i	$-0.575193\pi$
$919$	21.9771	−	38.0655i	0.724958	−	1.25566i	0.958991	−	0.283435i	$-0.0914740\pi$
$920$		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
$929$	40.2349			1.32006			0.660032	−	0.751237i	$-0.270543\pi$
$929$	40.2349			1.32006			0.660032	+	0.751237i	$0.270543\pi$
$930$		0			0
$931$	49.5604	−	3.61715i	1.62428	−	0.118547i
$932$		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
$941$	20.1891			0.658146			0.329073	−	0.944304i	$-0.393264\pi$
$941$	20.1891			0.658146			0.329073	+	0.944304i	$0.393264\pi$
$942$		0			0
$943$	−13.5947			−0.442704
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.14468			−0.0371973			−0.0185986	−	0.999827i	$-0.505920\pi$
$947$	−1.14468			−0.0371973			−0.0185986	+	0.999827i	$0.505920\pi$
$948$		0			0
$949$	−34.1520			−1.10862
$950$		0			0
$951$		0			0
$952$		0			0
$953$	42.9701			1.39194			0.695970	−	0.718071i	$-0.254975\pi$
$953$	42.9701			1.39194			0.695970	+	0.718071i	$0.254975\pi$
$954$		0			0
$955$	6.35236	+	11.0026i	0.205558	+	0.356036i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.2064	+	29.0380i	0.587916	+	0.937686i
$960$		0			0
$961$	−20.1891			−0.651262
$962$		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	0.476066	+	0.879410i	$0.342062\pi$
$971$	−16.3145	+	28.2576i	−0.523558	+	0.906830i	−0.999624	+	0.0274199i	$0.991271\pi$
$972$		0			0
$973$	−24.2973	−	38.7526i	−0.778937	−	1.24235i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	41.4958			1.32757			0.663784	−	0.747924i	$-0.268949\pi$
$977$	41.4958			1.32757			0.663784	+	0.747924i	$0.268949\pi$
$978$		0			0
$979$	23.8756	+	41.3537i	0.763067	+	1.32167i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.7163	+	30.6856i	−0.565063	+	0.978719i	0.431980	+	0.901883i	$0.357815\pi$
$983$	−17.7163	+	30.6856i	−0.565063	+	0.978719i	−0.997044	+	0.0768356i	$0.975518\pi$
$984$		0			0
$985$	22.0574	+	38.2046i	0.702808	+	1.21730i
$986$		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	0.936583	+	0.350446i	$0.113970\pi$
$991$	24.2960	+	42.0818i	0.771787	+	1.33677i	−0.164796	+	0.986328i	$0.552697\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	15.0080	−	25.9946i	0.475785	−	0.824083i
$996$		0			0
$997$	−23.5130	+	40.7257i	−0.744664	+	1.28980i	0.205688	+	0.978618i	$0.434057\pi$
$997$	−23.5130	+	40.7257i	−0.744664	+	1.28980i	−0.950352	+	0.311178i	$0.899276\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.1	✓	6	63.4	even	3
756.2.k.e.541.1	yes	6	9.4	even	3
756.2.k.f.109.3	yes	6	63.32	odd	6
756.2.k.f.541.3	yes	6	9.5	odd	6
2268.2.i.j.865.1		6	63.25	even	3	inner
2268.2.i.j.2053.1		6	1.1	even	1	trivial
2268.2.i.k.865.3		6	63.11	odd	6
2268.2.i.k.2053.3		6	3.2	odd	2
2268.2.l.j.109.1		6	21.11	odd	6
2268.2.l.j.541.1		6	9.2	odd	6
2268.2.l.k.109.3		6	7.4	even	3
2268.2.l.k.541.3		6	9.7	even	3
5292.2.a.u.1.1		3	63.23	odd	6
5292.2.a.v.1.1		3	63.40	odd	6
5292.2.a.w.1.3		3	63.5	even	6
5292.2.a.x.1.3		3	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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.14400 - 3.71351i) q^{5} +(1.23855 - 2.33795i) q^{7} +O(q^{10})\)	\(q+(-2.14400 - 3.71351i) q^{5} +(1.23855 - 2.33795i) q^{7} +(-1.90545 + 3.30033i) q^{11} +(-1.64400 + 2.84748i) q^{13} +(-0.405446 - 0.702253i) q^{17} +(-3.54944 + 6.14781i) q^{19} +(-3.23855 - 5.60933i) q^{23} +(-6.69344 + 11.5934i) q^{25} +(1.90545 + 3.30033i) q^{29} +3.28799 q^{31} +(-11.3374 + 0.413181i) q^{35} +(2.88255 - 4.99272i) q^{37} +(1.04944 - 1.81769i) q^{41} +(4.38255 + 7.59079i) q^{43} -3.33379 q^{47} +(-3.93199 - 5.79133i) q^{49} +(4.93199 + 8.54245i) q^{53} +16.3411 q^{55} -3.47710 q^{59} +5.95420 q^{61} +14.0989 q^{65} -3.52290 q^{67} -6.05308 q^{71} +(5.19344 + 8.99530i) q^{73} +(5.35600 + 8.54245i) q^{77} -5.14468 q^{79} +(-0.856004 - 1.48264i) q^{83} +(-1.73855 + 3.01126i) q^{85} +(6.26509 - 10.8515i) q^{89} +(4.62110 + 7.37033i) q^{91} +30.4400 q^{95} +(-0.522900 - 0.905690i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{5} + 2 q^{7}+O(q^{10}) \) 6 * q - q^5 + 2 * q^7	\( 6 q - q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} + 4 q^{17} - 3 q^{19} - 14 q^{23} - 10 q^{25} + 5 q^{29} - 4 q^{31} - 26 q^{35} - 12 q^{41} + 9 q^{43} - 18 q^{47} + 12 q^{49} - 6 q^{53} + 16 q^{55} - 10 q^{59} + 14 q^{61} + 48 q^{65} - 32 q^{67} + 22 q^{71} + q^{73} + 44 q^{77} - 16 q^{79} - 17 q^{83} - 5 q^{85} + 3 q^{89} + 5 q^{91} + 64 q^{95} - 14 q^{97}+O(q^{100}) \) 6 * q - q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 + 4 * q^17 - 3 * q^19 - 14 * q^23 - 10 * q^25 + 5 * q^29 - 4 * q^31 - 26 * q^35 - 12 * q^41 + 9 * q^43 - 18 * q^47 + 12 * q^49 - 6 * q^53 + 16 * q^55 - 10 * q^59 + 14 * q^61 + 48 * q^65 - 32 * q^67 + 22 * q^71 + q^73 + 44 * q^77 - 16 * q^79 - 17 * q^83 - 5 * q^85 + 3 * q^89 + 5 * q^91 + 64 * q^95 - 14 * q^97

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