LMFDB - Embedded newform 2268.2.k.f.1297.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(1297,2268)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.1297"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1297.1
Root			$-1.58203 - 0.705117i$ of defining polynomial
Character	$\chi$	$=$	2268.1297
Dual form			2268.2.k.f.1621.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26013 + 2.18261i) q^{5} +(-2.50909 - 0.839338i) q^{7} +(-0.687041 - 1.18999i) q^{11} +5.60017 q^{13} +(2.69613 + 4.66983i) q^{17} +(2.44717 - 4.23863i) q^{19} +(2.08765 - 3.61591i) q^{23} +(-0.675864 - 1.17063i) q^{25} -3.13521 q^{29} +(-2.40060 - 4.15797i) q^{31} +(4.99373 - 4.41869i) q^{35} +(-2.69839 + 4.67374i) q^{37} -6.05983 q^{41} -4.89435 q^{43} +(-2.82774 + 4.89779i) q^{47} +(5.59102 + 4.21194i) q^{49} +(7.00281 + 12.1292i) q^{53} +3.46305 q^{55} +(7.13442 + 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(-7.05695 + 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +2.25704 q^{71} +(3.51456 + 6.08739i) q^{73} +(0.725042 + 3.56245i) q^{77} +(-1.37843 + 2.38750i) q^{79} +14.9775 q^{83} -13.5899 q^{85} +(-2.75804 + 4.77707i) q^{89} +(-14.0513 - 4.70043i) q^{91} +(6.16752 + 10.6825i) q^{95} -1.78801 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} - 3 q^{7} - 2 q^{11} - 4 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} + 2 q^{29} - q^{31} + 19 q^{35} + 10 q^{37} - 66 q^{41} - 14 q^{43} + 3 q^{47} + 17 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots + 36 q^{97}+O(q^{100}) $ 14 * q + 2 * q^5 - 3 * q^7 - 2 * q^11 - 4 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 + 2 * q^29 - q^31 + 19 * q^35 + 10 * q^37 - 66 * q^41 - 14 * q^43 + 3 * q^47 + 17 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 28 * q^77 - 10 * q^79 - 50 * q^83 - 16 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 + 36 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.26013	+	2.18261i	−0.563548	+	0.976094i	0.433635	+	0.901089i	$0.357231\pi$
$5$	−1.26013	+	2.18261i	−0.563548	+	0.976094i	−0.997183	+	0.0750053i	$0.976103\pi$
$6$		0			0
$7$	−2.50909	−	0.839338i	−0.948345	−	0.317240i
$7$	−2.50909	−	0.839338i	−0.948345	−	0.317240i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.687041	−	1.18999i	−0.207151	−	0.358796i	0.743665	−	0.668552i	$-0.233086\pi$
$11$	−0.687041	−	1.18999i	−0.207151	−	0.358796i	−0.950816	+	0.309757i	$0.899752\pi$
$12$		0			0
$13$	5.60017			1.55321			0.776603	−	0.629990i	$-0.216941\pi$
$13$	5.60017			1.55321			0.776603	+	0.629990i	$0.216941\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.69613	+	4.66983i	0.653907	+	1.13260i	0.982167	+	0.188013i	$0.0602046\pi$
$17$	2.69613	+	4.66983i	0.653907	+	1.13260i	−0.328260	+	0.944588i	$0.606462\pi$
$18$		0			0
$19$	2.44717	−	4.23863i	0.561420	−	0.972408i	−0.435953	−	0.899969i	$-0.643589\pi$
$19$	2.44717	−	4.23863i	0.561420	−	0.972408i	0.997373	−	0.0724385i	$-0.0230781\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.08765	−	3.61591i	0.435304	−	0.753969i	−0.562016	−	0.827126i	$-0.689974\pi$
$23$	2.08765	−	3.61591i	0.435304	−	0.753969i	0.997320	+	0.0731570i	$0.0233074\pi$
$24$		0			0
$25$	−0.675864	−	1.17063i	−0.135173	−	0.234126i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.13521			−0.582195			−0.291097	−	0.956693i	$-0.594020\pi$
$29$	−3.13521			−0.582195			−0.291097	+	0.956693i	$0.594020\pi$
$30$		0			0
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	0.565812	−	0.824534i	$-0.308563\pi$
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	−0.996974	+	0.0777407i	$0.975229\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.99373	−	4.41869i	0.844094	−	0.746894i
$36$		0			0
$37$	−2.69839	+	4.67374i	−0.443612	+	0.768359i	−0.997954	−	0.0639302i	$-0.979637\pi$
$37$	−2.69839	+	4.67374i	−0.443612	+	0.768359i	0.554342	+	0.832289i	$0.312970\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.05983			−0.946386			−0.473193	−	0.880959i	$-0.656899\pi$
$41$	−6.05983			−0.946386			−0.473193	+	0.880959i	$0.656899\pi$
$42$		0			0
$43$	−4.89435			−0.746381			−0.373190	−	0.927755i	$-0.621736\pi$
$43$	−4.89435			−0.746381			−0.373190	+	0.927755i	$0.621736\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.82774	+	4.89779i	−0.412468	+	0.714416i	−0.995159	−	0.0982782i	$-0.968667\pi$
$47$	−2.82774	+	4.89779i	−0.412468	+	0.714416i	0.582691	+	0.812694i	$0.302000\pi$
$48$		0			0
$49$	5.59102	+	4.21194i	0.798718	+	0.601706i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.00281	+	12.1292i	0.961910	+	1.66608i	0.717696	+	0.696356i	$0.245197\pi$
$53$	7.00281	+	12.1292i	0.961910	+	1.66608i	0.244214	+	0.969721i	$0.421470\pi$
$54$		0			0
$55$	3.46305			0.466958
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.13442	+	12.3572i	0.928823	+	1.60877i	0.785294	+	0.619122i	$0.212512\pi$
$59$	7.13442	+	12.3572i	0.928823	+	1.60877i	0.143529	+	0.989646i	$0.454155\pi$
$60$		0			0
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	−0.558624	−	0.829421i	$-0.688670\pi$
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	0.997612	+	0.0690720i	$0.0220038\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.05695	+	12.2230i	−0.875307	+	1.51608i
$66$		0			0
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	0.999987	−	0.00505643i	$-0.00160952\pi$
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	−0.504373	+	0.863486i	$0.668276\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.25704			0.267861			0.133931	−	0.990991i	$-0.457240\pi$
$71$	2.25704			0.267861			0.133931	+	0.990991i	$0.457240\pi$
$72$		0			0
$73$	3.51456	+	6.08739i	0.411348	+	0.712475i	0.995037	−	0.0995017i	$-0.0317249\pi$
$73$	3.51456	+	6.08739i	0.411348	+	0.712475i	−0.583690	+	0.811977i	$0.698392\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.725042	+	3.56245i	0.0826262	+	0.405979i
$78$		0			0
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	−0.933090	−	0.359643i	$-0.882898\pi$
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	0.778005	+	0.628258i	$0.216232\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	14.9775			1.64400			0.821998	−	0.569490i	$-0.192859\pi$
$83$	14.9775			1.64400			0.821998	+	0.569490i	$0.192859\pi$
$84$		0			0
$85$	−13.5899			−1.47403
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.75804	+	4.77707i	−0.292352	+	0.506368i	−0.974365	−	0.224971i	$-0.927771\pi$
$89$	−2.75804	+	4.77707i	−0.292352	+	0.506368i	0.682014	+	0.731339i	$0.261104\pi$
$90$		0			0
$91$	−14.0513	−	4.70043i	−1.47298	−	0.492739i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.16752	+	10.6825i	0.632774	+	1.09600i
$96$		0			0
$97$	−1.78801			−0.181544			−0.0907722	−	0.995872i	$-0.528934\pi$
$97$	−1.78801			−0.181544			−0.0907722	+	0.995872i	$0.528934\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.69534	+	11.5967i	0.666211	+	1.15391i	0.978955	+	0.204074i	$0.0654183\pi$
$101$	6.69534	+	11.5967i	0.666211	+	1.15391i	−0.312744	+	0.949837i	$0.601248\pi$
$102$		0			0
$103$	−1.10164	+	1.90810i	−0.108548	+	0.188010i	−0.915182	−	0.403040i	$-0.867953\pi$
$103$	−1.10164	+	1.90810i	−0.108548	+	0.188010i	0.806634	+	0.591051i	$0.201287\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.93284	+	8.54392i	−0.476875	+	0.825972i	−0.999649	−	0.0264995i	$-0.991564\pi$
$107$	−4.93284	+	8.54392i	−0.476875	+	0.825972i	0.522774	+	0.852472i	$0.324897\pi$
$108$		0			0
$109$	1.54340	+	2.67325i	0.147831	+	0.256051i	0.930426	−	0.366481i	$-0.119438\pi$
$109$	1.54340	+	2.67325i	0.147831	+	0.256051i	−0.782595	+	0.622532i	$0.786104\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.437630			0.0411688			0.0205844	−	0.999788i	$-0.493447\pi$
$113$	0.437630			0.0411688			0.0205844	+	0.999788i	$0.493447\pi$
$114$		0			0
$115$	5.26142	+	9.11304i	0.490630	+	0.849796i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.84525	−	13.9800i	−0.260824	−	1.28154i
$120$		0			0
$121$	4.55595	−	7.89113i	0.414177	−	0.717376i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.19461			−0.822391
$126$		0			0
$127$	−5.75958			−0.511080			−0.255540	−	0.966798i	$-0.582253\pi$
$127$	−5.75958			−0.511080			−0.255540	+	0.966798i	$0.582253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.714865	+	1.23818i	−0.0624580	+	0.108180i	−0.895564	−	0.444934i	$-0.853227\pi$
$131$	−0.714865	+	1.23818i	−0.0624580	+	0.108180i	0.833106	+	0.553114i	$0.186561\pi$
$132$		0			0
$133$	−9.69781	+	8.58108i	−0.840907	+	0.744074i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.59335	+	9.68796i	0.477872	+	0.827698i	0.999678	−	0.0253656i	$-0.00807500\pi$
$137$	5.59335	+	9.68796i	0.477872	+	0.827698i	−0.521806	+	0.853064i	$0.674742\pi$
$138$		0			0
$139$	−15.7405			−1.33509			−0.667545	−	0.744570i	$-0.732655\pi$
$139$	−15.7405			−1.33509			−0.667545	+	0.744570i	$0.732655\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.84755	−	6.66415i	−0.321748	−	0.557284i
$144$		0			0
$145$	3.95078	−	6.84296i	0.328095	−	0.568277i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.96513	−	6.86780i	0.324836	−	0.562632i	−0.656643	−	0.754201i	$-0.728024\pi$
$149$	3.96513	−	6.86780i	0.324836	−	0.562632i	0.981479	+	0.191569i	$0.0613576\pi$
$150$		0			0
$151$	5.39683	+	9.34758i	0.439188	+	0.760696i	0.997627	−	0.0688499i	$-0.0219329\pi$
$151$	5.39683	+	9.34758i	0.439188	+	0.760696i	−0.558439	+	0.829545i	$0.688600\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	12.1003			0.971921
$156$		0			0
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	−0.885582	−	0.464483i	$-0.846240\pi$
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	0.0405373	−	0.999178i	$-0.487093\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.27305	+	7.32039i	−0.652008	+	0.576927i
$162$		0			0
$163$	0.536552	−	0.929336i	0.0420260	−	0.0727912i	−0.844247	−	0.535954i	$-0.819952\pi$
$163$	0.536552	−	0.929336i	0.0420260	−	0.0727912i	0.886273	+	0.463163i	$0.153285\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−15.4328			−1.19422			−0.597112	−	0.802158i	$-0.703685\pi$
$167$	−15.4328			−1.19422			−0.597112	+	0.802158i	$0.703685\pi$
$168$		0			0
$169$	18.3619			1.41245
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.1810	−	17.6340i	0.774046	−	1.34069i	−0.161283	−	0.986908i	$-0.551563\pi$
$173$	10.1810	−	17.6340i	0.774046	−	1.34069i	0.935329	−	0.353779i	$-0.115103\pi$
$174$		0			0
$175$	0.713246	+	3.50449i	0.0539164	+	0.264915i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.04960	−	5.28206i	−0.227938	−	0.394800i	0.729259	−	0.684238i	$-0.239865\pi$
$179$	−3.04960	−	5.28206i	−0.227938	−	0.394800i	−0.957197	+	0.289438i	$0.906532\pi$
$180$		0			0
$181$	10.0056			0.743714			0.371857	−	0.928290i	$-0.378721\pi$
$181$	10.0056			0.743714			0.371857	+	0.928290i	$0.378721\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.80065	−	11.7791i	−0.499993	−	0.866014i
$186$		0			0
$187$	3.70470	−	6.41673i	0.270915	−	0.469238i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.0993	+	19.2246i	−0.803120	+	1.39104i	0.114433	+	0.993431i	$0.463495\pi$
$191$	−11.0993	+	19.2246i	−0.803120	+	1.39104i	−0.917553	+	0.397613i	$0.869839\pi$
$192$		0			0
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.727516	+	0.686091i	$0.240675\pi$
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.230414	+	0.973093i	$0.425992\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.1696			−0.724551			−0.362276	−	0.932071i	$-0.618000\pi$
$197$	−10.1696			−0.724551			−0.362276	+	0.932071i	$0.618000\pi$
$198$		0			0
$199$	−1.66243	−	2.87941i	−0.117846	−	0.204116i	0.801068	−	0.598574i	$-0.204266\pi$
$199$	−1.66243	−	2.87941i	−0.117846	−	0.204116i	−0.918914	+	0.394458i	$0.870932\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.86652	+	2.63150i	0.552122	+	0.184695i
$204$		0			0
$205$	7.63618	−	13.2263i	0.533334	−	0.923762i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.72524			−0.465194
$210$		0			0
$211$	2.59070			0.178351			0.0891755	−	0.996016i	$-0.471577\pi$
$211$	2.59070			0.178351			0.0891755	+	0.996016i	$0.471577\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.16752	−	10.6825i	0.420621	−	0.728538i
$216$		0			0
$217$	2.53338	+	12.4476i	0.171977	+	0.845000i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.0988	+	26.1518i	1.01565	+	1.75916i
$222$		0			0
$223$	24.8057			1.66111			0.830556	−	0.556934i	$-0.188023\pi$
$223$	24.8057			1.66111			0.830556	+	0.556934i	$0.188023\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.55125	+	6.15095i	0.235705	+	0.408253i	0.959477	−	0.281786i	$-0.0909267\pi$
$227$	3.55125	+	6.15095i	0.235705	+	0.408253i	−0.723772	+	0.690039i	$0.757593\pi$
$228$		0			0
$229$	3.23252	−	5.59889i	0.213611	−	0.369985i	−0.739231	−	0.673452i	$-0.764811\pi$
$229$	3.23252	−	5.59889i	0.213611	−	0.369985i	0.952842	+	0.303467i	$0.0981442\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.42950	−	7.67212i	0.290186	−	0.502617i	−0.683667	−	0.729794i	$-0.739616\pi$
$233$	4.42950	−	7.67212i	0.290186	−	0.502617i	0.973854	+	0.227177i	$0.0729495\pi$
$234$		0			0
$235$	−7.12665	−	12.3437i	−0.464891	−	0.805215i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	17.2167			1.11366			0.556828	−	0.830628i	$-0.312018\pi$
$239$	17.2167			1.11366			0.556828	+	0.830628i	$0.312018\pi$
$240$		0			0
$241$	−10.1106	−	17.5120i	−0.651279	−	1.12805i	−0.982813	−	0.184604i	$-0.940900\pi$
$241$	−10.1106	−	17.5120i	−0.651279	−	1.12805i	0.331534	−	0.943443i	$-0.392434\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−16.2385	+	6.89544i	−1.03744	+	0.440533i
$246$		0			0
$247$	13.7046	−	23.7370i	0.872001	−	1.51035i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.32214			−0.462169			−0.231085	−	0.972934i	$-0.574227\pi$
$251$	−7.32214			−0.462169			−0.231085	+	0.972934i	$0.574227\pi$
$252$		0			0
$253$	−5.73720			−0.360695
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.07308	−	5.32274i	0.191694	−	0.332023i	−0.754118	−	0.656739i	$-0.771935\pi$
$257$	3.07308	−	5.32274i	0.191694	−	0.332023i	0.945812	+	0.324716i	$0.105269\pi$
$258$		0			0
$259$	10.6933	−	9.46197i	0.664451	−	0.587938i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.0824634	−	0.142831i	−0.00508491	−	0.00880732i	0.863472	−	0.504397i	$-0.168285\pi$
$263$	−0.0824634	−	0.142831i	−0.00508491	−	0.00880732i	−0.868557	+	0.495590i	$0.834952\pi$
$264$		0			0
$265$	−35.2979			−2.16833
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.86477	+	3.22988i	0.113697	+	0.196929i	0.917258	−	0.398293i	$-0.130397\pi$
$269$	1.86477	+	3.22988i	0.113697	+	0.196929i	−0.803561	+	0.595222i	$0.797064\pi$
$270$		0			0
$271$	−0.393652	+	0.681825i	−0.0239127	+	0.0414179i	−0.877734	−	0.479148i	$-0.840946\pi$
$271$	−0.393652	+	0.681825i	−0.0239127	+	0.0414179i	0.853821	+	0.520566i	$0.174279\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.928693	+	1.60854i	−0.0560023	+	0.0969988i
$276$		0			0
$277$	1.62954	+	2.82245i	0.0979096	+	0.169584i	0.910819	−	0.412805i	$-0.135451\pi$
$277$	1.62954	+	2.82245i	0.0979096	+	0.169584i	−0.812910	+	0.582390i	$0.802118\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	18.7829			1.12050			0.560248	−	0.828325i	$-0.310706\pi$
$281$	18.7829			1.12050			0.560248	+	0.828325i	$0.310706\pi$
$282$		0			0
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	0.991282	−	0.131754i	$-0.0420608\pi$
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	−0.609743	+	0.792599i	$0.708727\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.2046	+	5.08624i	0.897501	+	0.300231i
$288$		0			0
$289$	−6.03821	+	10.4585i	−0.355189	+	0.615205i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−27.2585			−1.59246			−0.796230	−	0.604994i	$-0.793176\pi$
$293$	−27.2585			−1.59246			−0.796230	+	0.604994i	$0.793176\pi$
$294$		0			0
$295$	−35.9613			−2.09375
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.6912	−	20.2497i	0.676118	−	1.17107i
$300$		0			0
$301$	12.2803	+	4.10801i	0.707827	+	0.236782i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.64098	+	14.9666i	0.494781	+	0.856986i
$306$		0			0
$307$	24.4623			1.39614			0.698069	−	0.716030i	$-0.254043\pi$
$307$	24.4623			1.39614			0.698069	+	0.716030i	$0.254043\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.58916	−	14.8769i	−0.487047	−	0.843590i	0.512842	−	0.858483i	$-0.328593\pi$
$311$	−8.58916	−	14.8769i	−0.487047	−	0.843590i	−0.999889	+	0.0148930i	$0.995259\pi$
$312$		0			0
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	−0.998279	−	0.0586380i	$-0.981324\pi$
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	0.549922	+	0.835216i	$0.314658\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.3626	+	19.6806i	−0.638188	+	1.10537i	0.347642	+	0.937627i	$0.386983\pi$
$317$	−11.3626	+	19.6806i	−0.638188	+	1.10537i	−0.985830	+	0.167747i	$0.946351\pi$
$318$		0			0
$319$	2.15402	+	3.73088i	0.120602	+	0.208889i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	26.3916			1.46847
$324$		0			0
$325$	−3.78495	−	6.55573i	−0.209951	−	0.363646i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.2059	−	9.91554i	0.617803	−	0.546662i
$330$		0			0
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	0.313207	+	0.949685i	$0.398597\pi$
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	−0.979055	+	0.203597i	$0.934737\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−20.4483			−1.11721
$336$		0			0
$337$	4.40363			0.239881			0.119940	−	0.992781i	$-0.461730\pi$
$337$	4.40363			0.239881			0.119940	+	0.992781i	$0.461730\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.29863	+	5.71339i	−0.178631	+	0.309398i
$342$		0			0
$343$	−10.4931	−	15.2609i	−0.566575	−	0.824010i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.12528	−	10.6093i	−0.328823	−	0.569537i	0.653456	−	0.756965i	$-0.273318\pi$
$347$	−6.12528	−	10.6093i	−0.328823	−	0.569537i	−0.982278	+	0.187427i	$0.939985\pi$
$348$		0			0
$349$	−14.3889			−0.770219			−0.385110	−	0.922871i	$-0.625836\pi$
$349$	−14.3889			−0.770219			−0.385110	+	0.922871i	$0.625836\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.40835	−	7.63549i	−0.234633	−	0.406396i	0.724533	−	0.689240i	$-0.242055\pi$
$353$	−4.40835	−	7.63549i	−0.234633	−	0.406396i	−0.959166	+	0.282844i	$0.908722\pi$
$354$		0			0
$355$	−2.84417	+	4.92624i	−0.150953	+	0.261458i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.04909	−	5.28118i	0.160925	−	0.278730i	−0.774276	−	0.632848i	$-0.781886\pi$
$359$	3.04909	−	5.28118i	0.160925	−	0.278730i	0.935201	+	0.354118i	$0.115219\pi$
$360$		0			0
$361$	−2.47731	−	4.29083i	−0.130385	−	0.225833i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−17.7152			−0.927257
$366$		0			0
$367$	3.45814	+	5.98967i	0.180513	+	0.312658i	0.942055	−	0.335457i	$-0.108891\pi$
$367$	3.45814	+	5.98967i	0.180513	+	0.312658i	−0.761542	+	0.648115i	$0.775557\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.39014	−	36.3110i	−0.383677	−	1.88517i
$372$		0			0
$373$	11.9489	−	20.6961i	0.618691	−	1.07160i	−0.371034	−	0.928619i	$-0.620997\pi$
$373$	11.9489	−	20.6961i	0.618691	−	1.07160i	0.989725	−	0.142985i	$-0.0456701\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.5577			−0.904269
$378$		0			0
$379$	34.6719			1.78097			0.890487	−	0.455008i	$-0.150364\pi$
$379$	34.6719			1.78097			0.890487	+	0.455008i	$0.150364\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.71507	−	16.8270i	0.496417	−	0.859820i	−0.503574	−	0.863952i	$-0.667982\pi$
$383$	9.71507	−	16.8270i	0.496417	−	0.859820i	0.999991	+	0.00413220i	$0.00131532\pi$
$384$		0			0
$385$	−8.68909	−	2.90667i	−0.442837	−	0.148138i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.3172	−	28.2623i	−0.827317	−	1.43295i	−0.900136	−	0.435610i	$-0.856533\pi$
$389$	−16.3172	−	28.2623i	−0.827317	−	1.43295i	0.0728190	−	0.997345i	$-0.476800\pi$
$390$		0			0
$391$	22.5142			1.13859
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.47400	−	6.01714i	−0.174796	−	0.302755i
$396$		0			0
$397$	−3.11807	+	5.40065i	−0.156491	+	0.271051i	−0.933601	−	0.358314i	$-0.883352\pi$
$397$	−3.11807	+	5.40065i	−0.156491	+	0.271051i	0.777110	+	0.629365i	$0.216685\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.3672	+	21.4207i	−0.617591	+	1.06970i	0.372333	+	0.928099i	$0.378558\pi$
$401$	−12.3672	+	21.4207i	−0.617591	+	1.06970i	−0.989924	+	0.141599i	$0.954776\pi$
$402$		0			0
$403$	−13.4438	−	23.2853i	−0.669683	−	1.15992i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.41561			0.367578
$408$		0			0
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	0.996325	+	0.0856575i	$0.0272991\pi$
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	−0.423981	+	0.905671i	$0.639368\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.52903	−	36.9934i	−0.370480	−	1.82033i
$414$		0			0
$415$	−18.8737	+	32.6901i	−0.926471	+	1.60470i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.40652			−0.0687130			−0.0343565	−	0.999410i	$-0.510938\pi$
$419$	−1.40652			−0.0687130			−0.0343565	+	0.999410i	$0.510938\pi$
$420$		0			0
$421$	1.32781			0.0647134			0.0323567	−	0.999476i	$-0.489699\pi$
$421$	1.32781			0.0647134			0.0323567	+	0.999476i	$0.489699\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.64443	−	6.31234i	0.176781	−	0.306193i
$426$		0			0
$427$	−13.5871	+	12.0225i	−0.657525	+	0.581809i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.83378	+	4.90825i	0.136498	+	0.236422i	0.926169	−	0.377109i	$-0.123082\pi$
$431$	2.83378	+	4.90825i	0.136498	+	0.236422i	−0.789670	+	0.613531i	$0.789748\pi$
$432$		0			0
$433$	1.60371			0.0770696			0.0385348	−	0.999257i	$-0.487731\pi$
$433$	1.60371			0.0770696			0.0385348	+	0.999257i	$0.487731\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.2177	−	17.6975i	−0.488777	−	0.846587i
$438$		0			0
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	−0.860550	−	0.509367i	$-0.829880\pi$
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	0.871399	+	0.490575i	$0.163213\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.31442	−	16.1331i	0.442542	−	0.766505i	−0.555336	−	0.831626i	$-0.687410\pi$
$443$	9.31442	−	16.1331i	0.442542	−	0.766505i	0.997877	+	0.0651217i	$0.0207436\pi$
$444$		0			0
$445$	−6.95099	−	12.0395i	−0.329508	−	0.570725i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.2330			0.671696			0.335848	−	0.941916i	$-0.390977\pi$
$449$	14.2330			0.671696			0.335848	+	0.941916i	$0.390977\pi$
$450$		0			0
$451$	4.16335	+	7.21114i	0.196045	+	0.339559i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	27.9657	−	24.7454i	1.31105	−	1.16008i
$456$		0			0
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	0.286634	+	0.958040i	$0.407464\pi$
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	−0.973004	+	0.230788i	$0.925870\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−25.3173			−1.17914			−0.589572	−	0.807715i	$-0.700704\pi$
$461$	−25.3173			−1.17914			−0.589572	+	0.807715i	$0.700704\pi$
$462$		0			0
$463$	23.3006			1.08287			0.541435	−	0.840743i	$-0.317881\pi$
$463$	23.3006			1.08287			0.541435	+	0.840743i	$0.317881\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.8409	−	36.0976i	0.964403	−	1.67040i	0.253194	−	0.967416i	$-0.418519\pi$
$467$	20.8409	−	36.0976i	0.964403	−	1.67040i	0.711210	−	0.702980i	$-0.248148\pi$
$468$		0			0
$469$	−4.28116	−	21.0352i	−0.197686	−	0.971316i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.36262	+	5.82423i	0.154613	+	0.267798i
$474$		0			0
$475$	−6.61582			−0.303555
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.76946	+	4.79684i	0.126540	+	0.219173i	0.922334	−	0.386394i	$-0.126280\pi$
$479$	2.76946	+	4.79684i	0.126540	+	0.219173i	−0.795794	+	0.605567i	$0.792946\pi$
$480$		0			0
$481$	−15.1114	+	26.1737i	−0.689021	+	1.19342i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.25312	−	3.90252i	0.102309	−	0.177204i
$486$		0			0
$487$	12.3357	+	21.3661i	0.558985	+	0.968190i	0.997582	+	0.0695061i	$0.0221423\pi$
$487$	12.3357	+	21.3661i	0.558985	+	0.968190i	−0.438597	+	0.898684i	$0.644524\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−20.1018			−0.907181			−0.453590	−	0.891210i	$-0.649857\pi$
$491$	−20.1018			−0.907181			−0.453590	+	0.891210i	$0.649857\pi$
$492$		0			0
$493$	−8.45294	−	14.6409i	−0.380701	−	0.659394i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.66311	−	1.89442i	−0.254025	−	0.0849763i
$498$		0			0
$499$	−17.7587	+	30.7589i	−0.794987	+	1.37696i	0.127861	+	0.991792i	$0.459189\pi$
$499$	−17.7587	+	30.7589i	−0.794987	+	1.37696i	−0.922848	+	0.385166i	$0.874144\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.2236			−1.08008			−0.540039	−	0.841640i	$-0.681590\pi$
$503$	−24.2236			−1.08008			−0.540039	+	0.841640i	$0.681590\pi$
$504$		0			0
$505$	−33.7480			−1.50177
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.86723	+	6.69824i	−0.171412	+	0.296894i	−0.938914	−	0.344153i	$-0.888166\pi$
$509$	−3.86723	+	6.69824i	−0.171412	+	0.296894i	0.767502	+	0.641047i	$0.221500\pi$
$510$		0			0
$511$	−3.70895	−	18.2237i	−0.164074	−	0.806168i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.77642	−	4.80891i	−0.122344	−	0.211906i
$516$		0			0
$517$	7.77109			0.341772
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.9050	+	25.8161i	0.652998	+	1.13103i	0.982392	+	0.186833i	$0.0598223\pi$
$521$	14.9050	+	25.8161i	0.652998	+	1.13103i	−0.329394	+	0.944193i	$0.606844\pi$
$522$		0			0
$523$	−1.76218	+	3.05219i	−0.0770547	+	0.133463i	−0.901978	−	0.431782i	$-0.857885\pi$
$523$	−1.76218	+	3.05219i	−0.0770547	+	0.133463i	0.824923	+	0.565245i	$0.191218\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.9447	−	22.4208i	0.563879	−	0.976667i
$528$		0			0
$529$	2.78347	+	4.82110i	0.121020	+	0.209613i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−33.9361			−1.46993
$534$		0			0
$535$	−12.4320	−	21.5329i	−0.537484	−	0.930950i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.17090	−	9.54704i	0.0504344	−	0.411220i
$540$		0			0
$541$	13.8435	−	23.9777i	0.595180	−	1.03088i	−0.398342	−	0.917237i	$-0.630414\pi$
$541$	13.8435	−	23.9777i	0.595180	−	1.03088i	0.993521	−	0.113645i	$-0.0362525\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.77955			−0.333239
$546$		0			0
$547$	33.2272			1.42069			0.710347	−	0.703852i	$-0.248538\pi$
$547$	33.2272			1.42069			0.710347	+	0.703852i	$0.248538\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.67241	+	13.2890i	−0.326856	+	0.566131i
$552$		0			0
$553$	5.46251	−	4.83349i	0.232290	−	0.205541i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.80873	−	13.5251i	−0.330866	−	0.573078i	0.651816	−	0.758378i	$-0.274008\pi$
$557$	−7.80873	−	13.5251i	−0.330866	−	0.573078i	−0.982682	+	0.185300i	$0.940674\pi$
$558$		0			0
$559$	−27.4092			−1.15928
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.75592	−	16.8977i	−0.411163	−	0.712155i	0.583854	−	0.811858i	$-0.301544\pi$
$563$	−9.75592	−	16.8977i	−0.411163	−	0.712155i	−0.995017	+	0.0997034i	$0.968211\pi$
$564$		0			0
$565$	−0.551472	+	0.955177i	−0.0232006	+	0.0401846i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.59181	−	6.22119i	0.150576	−	0.260806i	−0.780863	−	0.624702i	$-0.785220\pi$
$569$	3.59181	−	6.22119i	0.150576	−	0.260806i	0.931439	+	0.363896i	$0.118554\pi$
$570$		0			0
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	−0.989689	−	0.143230i	$-0.954251\pi$
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	0.370804	−	0.928711i	$-0.379082\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.64386			−0.235365
$576$		0			0
$577$	5.18911	+	8.98780i	0.216025	+	0.374167i	0.953589	−	0.301110i	$-0.0973573\pi$
$577$	5.18911	+	8.98780i	0.216025	+	0.374167i	−0.737564	+	0.675277i	$0.764024\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−37.5799	−	12.5712i	−1.55908	−	0.521541i
$582$		0			0
$583$	9.62244	−	16.6666i	0.398521	−	0.690259i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	28.9127			1.19335			0.596677	−	0.802481i	$-0.296487\pi$
$587$	28.9127			1.19335			0.596677	+	0.802481i	$0.296487\pi$
$588$		0			0
$589$	−23.4988			−0.968251
$590$		0			0
$591$		0			0
$592$		0			0
$593$	10.2645	−	17.7786i	0.421512	−	0.730080i	−0.574576	−	0.818451i	$-0.694833\pi$
$593$	10.2645	−	17.7786i	0.421512	−	0.730080i	0.996088	+	0.0883714i	$0.0281662\pi$
$594$		0			0
$595$	34.0982	+	11.4065i	1.39789	+	0.467622i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.91652	+	6.78361i	0.160025	+	0.277171i	0.934877	−	0.354971i	$-0.115509\pi$
$599$	3.91652	+	6.78361i	0.160025	+	0.277171i	−0.774853	+	0.632142i	$0.782176\pi$
$600$		0			0
$601$	14.5404			0.593116			0.296558	−	0.955015i	$-0.404161\pi$
$601$	14.5404			0.593116			0.296558	+	0.955015i	$0.404161\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	11.4822	+	19.8877i	0.466817	+	0.808551i
$606$		0			0
$607$	15.2755	−	26.4579i	0.620013	−	1.07389i	−0.369470	−	0.929243i	$-0.620461\pi$
$607$	15.2755	−	26.4579i	0.620013	−	1.07389i	0.989483	−	0.144651i	$-0.0462060\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.8358	+	27.4284i	−0.640648	+	1.10964i
$612$		0			0
$613$	−14.4646	−	25.0534i	−0.584220	−	1.01190i	−0.994972	−	0.100152i	$-0.968067\pi$
$613$	−14.4646	−	25.0534i	−0.584220	−	1.01190i	0.410752	−	0.911747i	$-0.365266\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	40.4213			1.62730			0.813650	−	0.581355i	$-0.197477\pi$
$617$	40.4213			1.62730			0.813650	+	0.581355i	$0.197477\pi$
$618$		0			0
$619$	9.05857	+	15.6899i	0.364095	+	0.630631i	0.988630	−	0.150366i	$-0.0480451\pi$
$619$	9.05857	+	15.6899i	0.364095	+	0.630631i	−0.624536	+	0.780996i	$0.714712\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.9297	−	9.67114i	0.437890	−	0.387466i
$624$		0			0
$625$	14.9657	−	25.9214i	0.598629	−	1.03686i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−29.1008			−1.16032
$630$		0			0
$631$	8.50373			0.338528			0.169264	−	0.985571i	$-0.445861\pi$
$631$	8.50373			0.338528			0.169264	+	0.985571i	$0.445861\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.25783	−	12.5709i	0.288018	−	0.498862i
$636$		0			0
$637$	31.3107	+	23.5876i	1.24057	+	0.934574i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.0020	+	19.0561i	0.434554	+	0.752669i	0.997259	−	0.0739883i	$-0.0235727\pi$
$641$	11.0020	+	19.0561i	0.434554	+	0.752669i	−0.562705	+	0.826658i	$0.690239\pi$
$642$		0			0
$643$	−26.2313			−1.03446			−0.517230	−	0.855846i	$-0.673037\pi$
$643$	−26.2313			−1.03446			−0.517230	+	0.855846i	$0.673037\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.5845	−	33.9214i	−0.769946	−	1.33359i	−0.937591	−	0.347739i	$-0.886950\pi$
$647$	−19.5845	−	33.9214i	−0.769946	−	1.33359i	0.167645	−	0.985847i	$-0.446384\pi$
$648$		0			0
$649$	9.80329	−	16.9798i	0.384813	−	0.666515i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.83467	−	11.8380i	0.267461	−	0.463257i	−0.700744	−	0.713413i	$-0.747149\pi$
$653$	6.83467	−	11.8380i	0.267461	−	0.463257i	0.968206	+	0.250156i	$0.0804819\pi$
$654$		0			0
$655$	−1.80165	−	3.12054i	−0.0703962	−	0.121930i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6.13367			−0.238934			−0.119467	−	0.992838i	$-0.538119\pi$
$659$	−6.13367			−0.238934			−0.119467	+	0.992838i	$0.538119\pi$
$660$		0			0
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.864212	+	0.503128i	$0.167818\pi$
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.00361604	+	0.999993i	$0.498849\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.50865	−	31.9798i	−0.252395	−	1.24013i
$666$		0			0
$667$	−6.54522	+	11.3367i	−0.253432	+	0.438957i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.42237			−0.363747
$672$		0			0
$673$	32.7666			1.26306			0.631531	−	0.775351i	$-0.282427\pi$
$673$	32.7666			1.26306			0.631531	+	0.775351i	$0.282427\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.5764	−	23.5150i	0.521782	−	0.903753i	−0.477897	−	0.878416i	$-0.658601\pi$
$677$	13.5764	−	23.5150i	0.521782	−	0.903753i	0.999679	−	0.0253373i	$-0.00806596\pi$
$678$		0			0
$679$	4.48626	+	1.50074i	0.172167	+	0.0575931i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.0334	+	32.9668i	0.728293	+	1.26144i	0.957604	+	0.288087i	$0.0930192\pi$
$683$	19.0334	+	32.9668i	0.728293	+	1.26144i	−0.229312	+	0.973353i	$0.573647\pi$
$684$		0			0
$685$	−28.1934			−1.07721
$686$		0			0
$687$		0			0
$688$		0			0
$689$	39.2169	+	67.9257i	1.49405	+	2.58776i
$690$		0			0
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	−0.718819	−	0.695197i	$-0.755317\pi$
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	0.961468	+	0.274917i	$0.0886504\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	19.8351	−	34.3554i	0.752387	−	1.30317i
$696$		0			0
$697$	−16.3381	−	28.2984i	−0.618849	−	1.07188i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−40.6428			−1.53506			−0.767528	−	0.641015i	$-0.778514\pi$
$701$	−40.6428			−1.53506			−0.767528	+	0.641015i	$0.778514\pi$
$702$		0			0
$703$	13.2068	+	22.8749i	0.498105	+	0.862744i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.06566	−	34.7167i	−0.265732	−	1.30566i
$708$		0			0
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	−0.787082	−	0.616849i	$-0.788409\pi$
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	0.927748	+	0.373208i	$0.121742\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−20.0465			−0.750746
$714$		0			0
$715$	19.3937			0.725282
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.64056	−	2.84154i	0.0611827	−	0.105972i	−0.833812	−	0.552049i	$-0.813846\pi$
$719$	1.64056	−	2.84154i	0.0611827	−	0.105972i	0.894994	+	0.446078i	$0.147179\pi$
$720$		0			0
$721$	4.36565	−	3.86293i	0.162585	−	0.143863i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.11898	+	3.67018i	0.0786969	+	0.136307i
$726$		0			0
$727$	−16.0218			−0.594214			−0.297107	−	0.954844i	$-0.596022\pi$
$727$	−16.0218			−0.594214			−0.297107	+	0.954844i	$0.596022\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.1958	−	22.8558i	−0.488064	−	0.845351i
$732$		0			0
$733$	−14.8123	+	25.6556i	−0.547104	+	0.947611i	0.451368	+	0.892338i	$0.350936\pi$
$733$	−14.8123	+	25.6556i	−0.547104	+	0.947611i	−0.998471	+	0.0552733i	$0.982397\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.57435	−	9.65506i	0.205334	−	0.355649i
$738$		0			0
$739$	−22.2867	−	38.6017i	−0.819829	−	1.41998i	−0.905808	−	0.423688i	$-0.860735\pi$
$739$	−22.2867	−	38.6017i	−0.819829	−	1.41998i	0.0859797	−	0.996297i	$-0.472598\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.3473			−0.416292			−0.208146	−	0.978098i	$-0.566743\pi$
$743$	−11.3473			−0.416292			−0.208146	+	0.978098i	$0.566743\pi$
$744$		0			0
$745$	9.99317	+	17.3087i	0.366121	+	0.634141i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	19.5481	−	17.2971i	0.714274	−	0.632023i
$750$		0			0
$751$	−17.5928	+	30.4716i	−0.641970	+	1.11192i	0.343023	+	0.939327i	$0.388549\pi$
$751$	−17.5928	+	30.4716i	−0.641970	+	1.11192i	−0.984992	+	0.172597i	$0.944784\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−27.2029			−0.990014
$756$		0			0
$757$	40.9186			1.48721			0.743605	−	0.668619i	$-0.233114\pi$
$757$	40.9186			1.48721			0.743605	+	0.668619i	$0.233114\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.72243	−	9.91155i	0.207438	−	0.359293i	−0.743469	−	0.668771i	$-0.766821\pi$
$761$	5.72243	−	9.91155i	0.207438	−	0.359293i	0.950907	+	0.309477i	$0.100154\pi$
$762$		0			0
$763$	−1.62877	−	8.00284i	−0.0589653	−	0.289722i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	39.9540	+	69.2023i	1.44265	+	2.49875i
$768$		0			0
$769$	29.9447			1.07983			0.539916	−	0.841719i	$-0.318456\pi$
$769$	29.9447			1.07983			0.539916	+	0.841719i	$0.318456\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.96578	+	6.86893i	0.142639	+	0.247058i	0.928490	−	0.371358i	$-0.121108\pi$
$773$	3.96578	+	6.86893i	0.142639	+	0.247058i	−0.785851	+	0.618416i	$0.787775\pi$
$774$		0			0
$775$	−3.24496	+	5.62044i	−0.116563	+	0.201892i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−14.8295	+	25.6854i	−0.531320	+	0.920274i
$780$		0			0
$781$	−1.55068	−	2.68586i	−0.0554877	−	0.0961075i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	53.3710			1.90489
$786$		0			0
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	−0.937514	−	0.347949i	$-0.886878\pi$
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	0.167425	−	0.985885i	$-0.446455\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.09805	−	0.367320i	−0.0390422	−	0.0130604i
$792$		0			0
$793$	19.2008	−	33.2567i	0.681839	−	1.18098i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.6877			−0.591108			−0.295554	−	0.955326i	$-0.595504\pi$
$797$	−16.6877			−0.591108			−0.295554	+	0.955326i	$0.595504\pi$
$798$		0			0
$799$	−30.4958			−1.07886
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.82929	−	8.36458i	0.170422	−	0.295180i
$804$		0			0
$805$	−5.55243	−	27.2815i	−0.195697	−	0.961547i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.54846	+	4.41407i	0.0895992	+	0.155190i	0.907342	−	0.420394i	$-0.138108\pi$
$809$	2.54846	+	4.41407i	0.0895992	+	0.155190i	−0.817743	+	0.575584i	$0.804775\pi$
$810$		0			0
$811$	10.2996			0.361666			0.180833	−	0.983514i	$-0.442121\pi$
$811$	10.2996			0.361666			0.180833	+	0.983514i	$0.442121\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.35225	+	2.34217i	0.0473674	+	0.0820427i
$816$		0			0
$817$	−11.9773	+	20.7453i	−0.419033	+	0.725787i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.6369	+	21.8878i	−0.441031	+	0.763889i	−0.997766	−	0.0668013i	$-0.978721\pi$
$821$	−12.6369	+	21.8878i	−0.441031	+	0.763889i	0.556735	+	0.830690i	$0.312054\pi$
$822$		0			0
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	0.778120	−	0.628116i	$-0.216174\pi$
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	−0.933024	+	0.359813i	$0.882840\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.1680			0.457895			0.228947	−	0.973439i	$-0.426472\pi$
$827$	13.1680			0.457895			0.228947	+	0.973439i	$0.426472\pi$
$828$		0			0
$829$	−11.3459	−	19.6516i	−0.394058	−	0.682529i	0.598922	−	0.800807i	$-0.295596\pi$
$829$	−11.3459	−	19.6516i	−0.394058	−	0.682529i	−0.992981	+	0.118278i	$0.962263\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.59493	+	37.4651i	−0.159205	+	1.29809i
$834$		0			0
$835$	19.4473	−	33.6838i	0.673002	−	1.16567i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−29.9265			−1.03318			−0.516588	−	0.856234i	$-0.672798\pi$
$839$	−29.9265			−1.03318			−0.516588	+	0.856234i	$0.672798\pi$
$840$		0			0
$841$	−19.1704			−0.661049
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−23.1384	+	40.0768i	−0.795984	+	1.37869i
$846$		0			0
$847$	−18.0546	+	15.9756i	−0.620363	+	0.548927i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.2666	+	19.5142i	0.386213	+	0.668940i
$852$		0			0
$853$	−12.9386			−0.443009			−0.221504	−	0.975159i	$-0.571097\pi$
$853$	−12.9386			−0.443009			−0.221504	+	0.975159i	$0.571097\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.12252	−	7.14042i	−0.140823	−	0.243912i	0.786984	−	0.616973i	$-0.211641\pi$
$857$	−4.12252	−	7.14042i	−0.140823	−	0.243912i	−0.927807	+	0.373061i	$0.878308\pi$
$858$		0			0
$859$	−1.73399	+	3.00336i	−0.0591630	+	0.102473i	−0.894090	−	0.447888i	$-0.852177\pi$
$859$	−1.73399	+	3.00336i	−0.0591630	+	0.102473i	0.834927	+	0.550361i	$0.185510\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.256394	−	0.444087i	0.00872775	−	0.0151169i	−0.861629	−	0.507539i	$-0.830555\pi$
$863$	0.256394	−	0.444087i	0.00872775	−	0.0151169i	0.870356	+	0.492423i	$0.163889\pi$
$864$		0			0
$865$	25.6588	+	44.4423i	0.872424	+	1.51108i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.78814			0.128504
$870$		0			0
$871$	22.7186	+	39.3499i	0.769792	+	1.33332i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	23.0701	+	7.71738i	0.779910	+	0.260895i
$876$		0			0
$877$	−18.1880	+	31.5026i	−0.614166	+	1.06377i	0.376365	+	0.926472i	$0.377174\pi$
$877$	−18.1880	+	31.5026i	−0.614166	+	1.06377i	−0.990530	+	0.137295i	$0.956159\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.3999			0.788363			0.394181	−	0.919033i	$-0.371028\pi$
$881$	23.3999			0.788363			0.394181	+	0.919033i	$0.371028\pi$
$882$		0			0
$883$	−22.8345			−0.768442			−0.384221	−	0.923241i	$-0.625530\pi$
$883$	−22.8345			−0.768442			−0.384221	+	0.923241i	$0.625530\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.0791	−	38.2421i	0.741344	−	1.28405i	−0.210539	−	0.977585i	$-0.567522\pi$
$887$	22.0791	−	38.2421i	0.741344	−	1.28405i	0.951883	−	0.306460i	$-0.0991446\pi$
$888$		0			0
$889$	14.4513	+	4.83423i	0.484680	+	0.162135i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.8399	+	23.9715i	0.463136	+	0.802175i
$894$		0			0
$895$	15.3716			0.513816
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.52641	+	13.0361i	0.251020	+	0.434779i
$900$		0			0
$901$	−37.7610	+	65.4039i	−1.25800	+	2.17892i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.6084	+	21.8384i	−0.419118	+	0.725934i
$906$		0			0
$907$	−3.53884	−	6.12946i	−0.117505	−	0.203525i	0.801273	−	0.598299i	$-0.204156\pi$
$907$	−3.53884	−	6.12946i	−0.117505	−	0.203525i	−0.918778	+	0.394773i	$0.870823\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−47.3529			−1.56887			−0.784435	−	0.620211i	$-0.787047\pi$
$911$	−47.3529			−1.56887			−0.784435	+	0.620211i	$0.787047\pi$
$912$		0			0
$913$	−10.2902	−	17.8231i	−0.340555	−	0.589859i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.83291	−	2.50669i	0.0935509	−	0.0827783i
$918$		0			0
$919$	12.9752	−	22.4736i	0.428011	−	0.741337i	−0.568685	−	0.822555i	$-0.692548\pi$
$919$	12.9752	−	22.4736i	0.428011	−	0.741337i	0.996696	+	0.0812182i	$0.0258811\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	12.6398			0.416044
$924$		0			0
$925$	7.29497			0.239857
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.66110	+	4.60917i	−0.0873080	+	0.151222i	−0.906372	−	0.422480i	$-0.861160\pi$
$929$	−2.66110	+	4.60917i	−0.0873080	+	0.151222i	0.819064	+	0.573702i	$0.194493\pi$
$930$		0			0
$931$	31.5351	−	13.3909i	1.03352	−	0.438870i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.33682	+	16.1719i	0.305347	+	0.528876i
$936$		0			0
$937$	−30.4266			−0.993994			−0.496997	−	0.867752i	$-0.665564\pi$
$937$	−30.4266			−0.993994			−0.496997	+	0.867752i	$0.665564\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.8818	+	18.8479i	0.354738	+	0.614424i	0.987073	−	0.160271i	$-0.0512368\pi$
$941$	10.8818	+	18.8479i	0.354738	+	0.614424i	−0.632335	+	0.774695i	$0.717903\pi$
$942$		0			0
$943$	−12.6508	+	21.9118i	−0.411966	+	0.713546i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.4392	+	30.2055i	−0.566697	+	0.981548i	0.430192	+	0.902737i	$0.358446\pi$
$947$	−17.4392	+	30.2055i	−0.566697	+	0.981548i	−0.996890	+	0.0788112i	$0.974888\pi$
$948$		0			0
$949$	19.6821	+	34.0904i	0.638908	+	1.10662i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.3744			−0.886742			−0.443371	−	0.896338i	$-0.646218\pi$
$953$	−27.3744			−0.886742			−0.443371	+	0.896338i	$0.646218\pi$
$954$		0			0
$955$	−27.9732	−	48.4511i	−0.905193	−	1.56784i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.90272	−	29.0026i	−0.190609	−	0.936544i
$960$		0			0
$961$	3.97419	−	6.88350i	0.128200	−	0.222048i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−67.0793			−2.15936
$966$		0			0
$967$	−14.4265			−0.463926			−0.231963	−	0.972725i	$-0.574515\pi$
$967$	−14.4265			−0.463926			−0.231963	+	0.972725i	$0.574515\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.2592	−	22.9657i	0.425509	−	0.737004i	−0.570959	−	0.820979i	$-0.693428\pi$
$971$	13.2592	−	22.9657i	0.425509	−	0.737004i	0.996468	+	0.0839752i	$0.0267617\pi$
$972$		0			0
$973$	39.4942	+	13.2116i	1.26613	+	0.423544i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.1867	−	34.9643i	−0.645829	−	1.11861i	−0.984109	−	0.177563i	$-0.943179\pi$
$977$	−20.1867	−	34.9643i	−0.645829	−	1.11861i	0.338281	−	0.941045i	$-0.390155\pi$
$978$		0			0
$979$	7.57955			0.242243
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−10.7299	−	18.5847i	−0.342230	−	0.592759i	0.642617	−	0.766188i	$-0.277849\pi$
$983$	−10.7299	−	18.5847i	−0.342230	−	0.592759i	−0.984846	+	0.173429i	$0.944515\pi$
$984$		0			0
$985$	12.8150	−	22.1962i	0.408319	−	0.707230i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−10.2177	+	17.6975i	−0.324903	+	0.562748i
$990$		0			0
$991$	7.25341	+	12.5633i	0.230412	+	0.399085i	0.957929	−	0.287004i	$-0.0926593\pi$
$991$	7.25341	+	12.5633i	0.230412	+	0.399085i	−0.727517	+	0.686089i	$0.759326\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.37951			0.265648
$996$		0			0
$997$	−18.2204	−	31.5587i	−0.577047	−	0.999475i	−0.995816	−	0.0913822i	$-0.970871\pi$
$997$	−18.2204	−	31.5587i	−0.577047	−	0.999475i	0.418769	−	0.908093i	$-0.362462\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.k.f.1297.1		14
3.2	odd	2		2268.2.k.e.1297.7		14
7.4	even	3	inner	2268.2.k.f.1621.1		14
9.2	odd	6		252.2.i.b.121.6	yes	14
9.4	even	3		756.2.l.b.289.7		14
9.5	odd	6		252.2.l.b.205.2	yes	14
9.7	even	3		756.2.i.b.37.1		14
21.11	odd	6		2268.2.k.e.1621.7		14
36.7	odd	6		3024.2.q.j.2305.1		14
36.11	even	6		1008.2.q.j.625.2		14
36.23	even	6		1008.2.t.j.961.6		14
36.31	odd	6		3024.2.t.j.289.7		14
63.2	odd	6		1764.2.j.g.589.5		14
63.4	even	3		756.2.i.b.613.1		14
63.5	even	6		1764.2.j.h.1177.3		14
63.11	odd	6		252.2.l.b.193.2	yes	14
63.13	odd	6		5292.2.l.i.3313.1		14
63.16	even	3		5292.2.j.h.1765.1		14
63.20	even	6		1764.2.i.i.373.2		14
63.23	odd	6		1764.2.j.g.1177.5		14
63.25	even	3		756.2.l.b.361.7		14
63.31	odd	6		5292.2.i.i.2125.7		14
63.32	odd	6		252.2.i.b.25.6	✓	14
63.34	odd	6		5292.2.i.i.1549.7		14
63.38	even	6		1764.2.l.i.949.6		14
63.40	odd	6		5292.2.j.g.3529.7		14
63.41	even	6		1764.2.l.i.961.6		14
63.47	even	6		1764.2.j.h.589.3		14
63.52	odd	6		5292.2.l.i.361.1		14
63.58	even	3		5292.2.j.h.3529.1		14
63.59	even	6		1764.2.i.i.1537.2		14
63.61	odd	6		5292.2.j.g.1765.7		14
252.11	even	6		1008.2.t.j.193.6		14
252.67	odd	6		3024.2.q.j.2881.1		14
252.95	even	6		1008.2.q.j.529.2		14
252.151	odd	6		3024.2.t.j.1873.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.6	✓	14	63.32	odd	6
252.2.i.b.121.6	yes	14	9.2	odd	6
252.2.l.b.193.2	yes	14	63.11	odd	6
252.2.l.b.205.2	yes	14	9.5	odd	6
756.2.i.b.37.1		14	9.7	even	3
756.2.i.b.613.1		14	63.4	even	3
756.2.l.b.289.7		14	9.4	even	3
756.2.l.b.361.7		14	63.25	even	3
1008.2.q.j.529.2		14	252.95	even	6
1008.2.q.j.625.2		14	36.11	even	6
1008.2.t.j.193.6		14	252.11	even	6
1008.2.t.j.961.6		14	36.23	even	6
1764.2.i.i.373.2		14	63.20	even	6
1764.2.i.i.1537.2		14	63.59	even	6
1764.2.j.g.589.5		14	63.2	odd	6
1764.2.j.g.1177.5		14	63.23	odd	6
1764.2.j.h.589.3		14	63.47	even	6
1764.2.j.h.1177.3		14	63.5	even	6
1764.2.l.i.949.6		14	63.38	even	6
1764.2.l.i.961.6		14	63.41	even	6
2268.2.k.e.1297.7		14	3.2	odd	2
2268.2.k.e.1621.7		14	21.11	odd	6
2268.2.k.f.1297.1		14	1.1	even	1	trivial
2268.2.k.f.1621.1		14	7.4	even	3	inner
3024.2.q.j.2305.1		14	36.7	odd	6
3024.2.q.j.2881.1		14	252.67	odd	6
3024.2.t.j.289.7		14	36.31	odd	6
3024.2.t.j.1873.7		14	252.151	odd	6
5292.2.i.i.1549.7		14	63.34	odd	6
5292.2.i.i.2125.7		14	63.31	odd	6
5292.2.j.g.1765.7		14	63.61	odd	6
5292.2.j.g.3529.7		14	63.40	odd	6
5292.2.j.h.1765.1		14	63.16	even	3
5292.2.j.h.3529.1		14	63.58	even	3
5292.2.l.i.361.1		14	63.52	odd	6
5292.2.l.i.3313.1		14	63.13	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.26013 + 2.18261i) q^{5} +(-2.50909 - 0.839338i) q^{7} +(-0.687041 - 1.18999i) q^{11} +5.60017 q^{13} +(2.69613 + 4.66983i) q^{17} +(2.44717 - 4.23863i) q^{19} +(2.08765 - 3.61591i) q^{23} +(-0.675864 - 1.17063i) q^{25} -3.13521 q^{29} +(-2.40060 - 4.15797i) q^{31} +(4.99373 - 4.41869i) q^{35} +(-2.69839 + 4.67374i) q^{37} -6.05983 q^{41} -4.89435 q^{43} +(-2.82774 + 4.89779i) q^{47} +(5.59102 + 4.21194i) q^{49} +(7.00281 + 12.1292i) q^{53} +3.46305 q^{55} +(7.13442 + 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(-7.05695 + 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +2.25704 q^{71} +(3.51456 + 6.08739i) q^{73} +(0.725042 + 3.56245i) q^{77} +(-1.37843 + 2.38750i) q^{79} +14.9775 q^{83} -13.5899 q^{85} +(-2.75804 + 4.77707i) q^{89} +(-14.0513 - 4.70043i) q^{91} +(6.16752 + 10.6825i) q^{95} -1.78801 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} - 3 q^{7} - 2 q^{11} - 4 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} + 2 q^{29} - q^{31} + 19 q^{35} + 10 q^{37} - 66 q^{41} - 14 q^{43} + 3 q^{47} + 17 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots + 36 q^{97}+O(q^{100}) \) 14 * q + 2 * q^5 - 3 * q^7 - 2 * q^11 - 4 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 + 2 * q^29 - q^31 + 19 * q^35 + 10 * q^37 - 66 * q^41 - 14 * q^43 + 3 * q^47 + 17 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 28 * q^77 - 10 * q^79 - 50 * q^83 - 16 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 + 36 * q^97

Introduction

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