LMFDB - Embedded newform 1044.2.z.c.325.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1044,2,Mod(109,1044)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1044, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("1044.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1044 = 2^{2} \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1044.z (of order $14$, degree $6$, 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:	$8.33638197102$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			325.4
Character	$\chi$	$=$	1044.325
Dual form			1044.2.z.c.469.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81616 - 2.27739i) q^{5} +(-0.620985 + 2.72071i) q^{7} +O(q^{10})$	$q+(1.81616 - 2.27739i) q^{5} +(-0.620985 + 2.72071i) q^{7} +(1.64877 + 3.42372i) q^{11} +(-5.43161 + 2.61573i) q^{13} +6.61615i q^{17} +(2.85782 - 0.652279i) q^{19} +(1.28906 + 1.61643i) q^{23} +(-0.775470 - 3.39756i) q^{25} +(-2.03013 + 4.98784i) q^{29} +(0.575797 + 0.459183i) q^{31} +(5.06832 + 6.35547i) q^{35} +(2.51293 - 5.21815i) q^{37} -1.73867i q^{41} +(6.44955 - 5.14334i) q^{43} +(-1.54934 - 3.21723i) q^{47} +(-0.709874 - 0.341857i) q^{49} +(-1.36151 + 1.70728i) q^{53} +(10.7916 + 2.46310i) q^{55} +13.5683 q^{59} +(-13.3338 - 3.04336i) q^{61} +(-3.90763 + 17.1205i) q^{65} +(-4.97479 - 2.39573i) q^{67} +(12.2131 - 5.88150i) q^{71} +(0.225677 - 0.179972i) q^{73} +(-10.3388 + 2.35977i) q^{77} +(-5.36045 + 11.1311i) q^{79} +(1.98190 + 8.68327i) q^{83} +(15.0676 + 12.0160i) q^{85} +(7.73977 + 6.17226i) q^{89} +(-3.74369 - 16.4022i) q^{91} +(3.70476 - 7.69302i) q^{95} +(0.521674 - 0.119069i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1044\mathbb{Z}\right)^\times$.

$n$	$523$	$901$	$929$
$\chi(n)$	$1$	$e\left(\frac{3}{14}\right)$	$1$

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
$5$	1.81616	−	2.27739i	0.812210	−	1.01848i	−0.187136	−	0.982334i	$-0.559921\pi$
$5$	1.81616	−	2.27739i	0.812210	−	1.01848i	0.999347	−	0.0361456i	$-0.0115080\pi$
$6$		0			0
$7$	−0.620985	+	2.72071i	−0.234710	+	1.02833i	0.710967	+	0.703225i	$0.248258\pi$
$7$	−0.620985	+	2.72071i	−0.234710	+	1.02833i	−0.945677	+	0.325107i	$0.894600\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.64877	+	3.42372i	0.497124	+	1.03229i	0.987033	+	0.160515i	$0.0513156\pi$
$11$	1.64877	+	3.42372i	0.497124	+	1.03229i	−0.489909	+	0.871773i	$0.662970\pi$
$12$		0			0
$13$	−5.43161	+	2.61573i	−1.50646	+	0.725472i	−0.991300	−	0.131623i	$-0.957981\pi$
$13$	−5.43161	+	2.61573i	−1.50646	+	0.725472i	−0.515158	+	0.857095i	$0.672267\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			6.61615i			1.60465i	0.596886	+	0.802326i	$0.296404\pi$
$17$			6.61615i			1.60465i	−0.596886	+	0.802326i	$0.703596\pi$
$18$		0			0
$19$	2.85782	−	0.652279i	0.655629	−	0.149643i	0.118250	−	0.992984i	$-0.462272\pi$
$19$	2.85782	−	0.652279i	0.655629	−	0.149643i	0.537379	+	0.843341i	$0.319414\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.28906	+	1.61643i	0.268788	+	0.337049i	0.897847	−	0.440308i	$-0.145131\pi$
$23$	1.28906	+	1.61643i	0.268788	+	0.337049i	−0.629059	+	0.777358i	$0.716559\pi$
$24$		0			0
$25$	−0.775470	−	3.39756i	−0.155094	−	0.679512i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.03013	+	4.98784i	−0.376986	+	0.926219i
$29$	−2.03013	+	4.98784i	−0.376986	+	0.926219i
$30$		0			0
$31$	0.575797	+	0.459183i	0.103416	+	0.0824717i	0.673833	−	0.738884i	$-0.264647\pi$
$31$	0.575797	+	0.459183i	0.103416	+	0.0824717i	−0.570417	+	0.821356i	$0.693218\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.06832	+	6.35547i	0.856702	+	1.07427i
$36$		0			0
$37$	2.51293	−	5.21815i	0.413123	−	0.857858i	−0.585755	−	0.810488i	$-0.699202\pi$
$37$	2.51293	−	5.21815i	0.413123	−	0.857858i	0.998877	−	0.0473696i	$-0.0150839\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	1.73867i		−	0.271534i	−0.990741	−	0.135767i	$-0.956650\pi$
$41$		−	1.73867i		−	0.271534i	0.990741	−	0.135767i	$-0.0433499\pi$
$42$		0			0
$43$	6.44955	−	5.14334i	0.983547	−	0.784352i	0.00707001	−	0.999975i	$-0.497750\pi$
$43$	6.44955	−	5.14334i	0.983547	−	0.784352i	0.976477	+	0.215623i	$0.0691781\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.54934	−	3.21723i	−0.225994	−	0.469281i	0.756882	−	0.653552i	$-0.226722\pi$
$47$	−1.54934	−	3.21723i	−0.225994	−	0.469281i	−0.982876	+	0.184271i	$0.941008\pi$
$48$		0			0
$49$	−0.709874	−	0.341857i	−0.101411	−	0.0488368i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.36151	+	1.70728i	−0.187018	+	0.234513i	−0.866497	−	0.499182i	$-0.833634\pi$
$53$	−1.36151	+	1.70728i	−0.187018	+	0.234513i	0.679480	+	0.733694i	$0.262206\pi$
$54$		0			0
$55$	10.7916	+	2.46310i	1.45513	+	0.332125i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	13.5683			1.76644			0.883218	−	0.468963i	$-0.155372\pi$
$59$	13.5683			1.76644			0.883218	+	0.468963i	$0.155372\pi$
$60$		0			0
$61$	−13.3338	−	3.04336i	−1.70722	−	0.389663i	−0.746111	−	0.665822i	$-0.768081\pi$
$61$	−13.3338	−	3.04336i	−1.70722	−	0.389663i	−0.961112	+	0.276159i	$0.910938\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.90763	+	17.1205i	−0.484682	+	2.12353i
$66$		0			0
$67$	−4.97479	−	2.39573i	−0.607767	−	0.292685i	0.104576	−	0.994517i	$-0.466652\pi$
$67$	−4.97479	−	2.39573i	−0.607767	−	0.292685i	−0.712343	+	0.701832i	$0.752366\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.2131	−	5.88150i	1.44942	−	0.698006i	0.466929	−	0.884295i	$-0.345360\pi$
$71$	12.2131	−	5.88150i	1.44942	−	0.698006i	0.982495	+	0.186289i	$0.0596460\pi$
$72$		0			0
$73$	0.225677	−	0.179972i	0.0264135	−	0.0210641i	−0.610194	−	0.792252i	$-0.708909\pi$
$73$	0.225677	−	0.179972i	0.0264135	−	0.0210641i	0.636608	+	0.771188i	$0.280337\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.3388	+	2.35977i	−1.17822	+	0.268920i
$78$		0			0
$79$	−5.36045	+	11.1311i	−0.603098	+	1.25235i	0.346257	+	0.938140i	$0.387453\pi$
$79$	−5.36045	+	11.1311i	−0.603098	+	1.25235i	−0.949355	+	0.314206i	$0.898262\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.98190	+	8.68327i	0.217542	+	0.953113i	0.959287	+	0.282432i	$0.0911411\pi$
$83$	1.98190	+	8.68327i	0.217542	+	0.953113i	−0.741746	+	0.670681i	$0.766002\pi$
$84$		0			0
$85$	15.0676	+	12.0160i	1.63431	+	1.30332i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.73977	+	6.17226i	0.820414	+	0.654258i	0.940986	−	0.338446i	$-0.109901\pi$
$89$	7.73977	+	6.17226i	0.820414	+	0.654258i	−0.120572	+	0.992705i	$0.538473\pi$
$90$		0			0
$91$	−3.74369	−	16.4022i	−0.392445	−	1.71942i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.70476	−	7.69302i	0.380101	−	0.789287i
$96$		0			0
$97$	0.521674	−	0.119069i	0.0529680	−	0.0120896i	−0.195955	−	0.980613i	$-0.562781\pi$
$97$	0.521674	−	0.119069i	0.0529680	−	0.0120896i	0.248923	+	0.968523i	$0.419923\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.5426	−	10.0024i	1.24803	−	0.995273i	0.248388	−	0.968661i	$-0.420099\pi$
$101$	12.5426	−	10.0024i	1.24803	−	0.995273i	0.999646	−	0.0266128i	$-0.00847211\pi$
$102$		0			0
$103$	−16.6734	+	8.02948i	−1.64288	+	0.791168i	−0.643202	+	0.765697i	$0.722394\pi$
$103$	−16.6734	+	8.02948i	−1.64288	+	0.791168i	−0.999676	+	0.0254715i	$0.991891\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.31214	−	3.03977i	−0.610217	−	0.293865i	0.103139	−	0.994667i	$-0.467111\pi$
$107$	−6.31214	−	3.03977i	−0.610217	−	0.293865i	−0.713356	+	0.700802i	$0.752826\pi$
$108$		0			0
$109$	−1.93207	+	8.46497i	−0.185059	+	0.810797i	0.794114	+	0.607769i	$0.207935\pi$
$109$	−1.93207	+	8.46497i	−0.185059	+	0.810797i	−0.979173	+	0.203028i	$0.934922\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.1630	−	3.68910i	−1.52049	−	0.347041i	−0.620938	−	0.783860i	$-0.713248\pi$
$113$	−16.1630	−	3.68910i	−1.52049	−	0.347041i	−0.899550	+	0.436818i	$0.856105\pi$
$114$		0			0
$115$	6.02239			0.561590
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−18.0006	−	4.10853i	−1.65012	−	0.376628i
$120$		0			0
$121$	−2.14498	+	2.68972i	−0.194998	+	0.244520i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.97618	+	1.91483i	0.355640	+	0.171267i
$126$		0			0
$127$	−0.603036	−	1.25222i	−0.0535108	−	0.111116i	0.872499	−	0.488616i	$-0.162498\pi$
$127$	−0.603036	−	1.25222i	−0.0535108	−	0.111116i	−0.926010	+	0.377500i	$0.876784\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.92580	−	7.11809i	0.779851	−	0.621910i	−0.150488	−	0.988612i	$-0.548084\pi$
$131$	8.92580	−	7.11809i	0.779851	−	0.621910i	0.930339	+	0.366701i	$0.119513\pi$
$132$		0			0
$133$			8.18037i			0.709328i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.62496	+	5.45078i	−0.224265	+	0.465692i	−0.982493	−	0.186298i	$-0.940351\pi$
$137$	−2.62496	+	5.45078i	−0.224265	+	0.465692i	0.758228	+	0.651989i	$0.226065\pi$
$138$		0			0
$139$	−1.31641	−	1.65073i	−0.111656	−	0.140013i	0.722863	−	0.690992i	$-0.242826\pi$
$139$	−1.31641	−	1.65073i	−0.111656	−	0.140013i	−0.834519	+	0.550979i	$0.814254\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−17.9110	−	14.2835i	−1.49779	−	1.19445i
$144$		0			0
$145$	7.67222	+	13.6821i	0.637143	+	1.13624i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.68306	+	16.1366i	0.301728	+	1.32196i	0.867517	+	0.497408i	$0.165715\pi$
$149$	3.68306	+	16.1366i	0.301728	+	1.32196i	−0.565788	+	0.824550i	$0.691428\pi$
$150$		0			0
$151$	4.31660	+	5.41284i	0.351280	+	0.440491i	0.925808	−	0.377994i	$-0.123386\pi$
$151$	4.31660	+	5.41284i	0.351280	+	0.440491i	−0.574528	+	0.818485i	$0.694815\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.09148	−	0.477366i	0.167991	−	0.0383430i
$156$		0			0
$157$		−	20.1376i		−	1.60716i	−0.595198	−	0.803579i	$-0.702927\pi$
$157$		−	20.1376i		−	1.60716i	0.595198	−	0.803579i	$-0.297073\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.19834	+	2.50339i	−0.409686	+	0.197295i
$162$		0			0
$163$	−4.12740	−	8.57063i	−0.323283	−	0.671303i	0.674470	−	0.738302i	$-0.264372\pi$
$163$	−4.12740	−	8.57063i	−0.323283	−	0.671303i	−0.997753	+	0.0669984i	$0.978658\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.479060	+	2.09890i	−0.0370707	+	0.162418i	−0.990075	−	0.140539i	$-0.955117\pi$
$167$	−0.479060	+	2.09890i	−0.0370707	+	0.162418i	0.953004	+	0.302956i	$0.0979737\pi$
$168$		0			0
$169$	14.5550	−	18.2514i	1.11962	−	1.40395i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.33313			−0.481499			−0.240749	−	0.970587i	$-0.577393\pi$
$173$	−6.33313			−0.481499			−0.240749	+	0.970587i	$0.577393\pi$
$174$		0			0
$175$	9.72533			0.735166
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0764	−	15.1434i	0.902634	−	1.13187i	−0.0881078	−	0.996111i	$-0.528082\pi$
$179$	12.0764	−	15.1434i	0.902634	−	1.13187i	0.990742	−	0.135757i	$-0.0433466\pi$
$180$		0			0
$181$	2.43046	−	10.6486i	0.180655	−	0.791501i	−0.800664	−	0.599114i	$-0.795520\pi$
$181$	2.43046	−	10.6486i	0.180655	−	0.791501i	0.981319	−	0.192387i	$-0.0616230\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.31988	−	15.1999i	−0.538168	−	1.11752i
$186$		0			0
$187$	−22.6518	+	10.9085i	−1.65646	+	0.797711i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			15.0422i			1.08842i	0.838950	+	0.544208i	$0.183170\pi$
$191$			15.0422i			1.08842i	−0.838950	+	0.544208i	$0.816830\pi$
$192$		0			0
$193$	7.25071	−	1.65493i	0.521917	−	0.119124i	0.0465574	−	0.998916i	$-0.485175\pi$
$193$	7.25071	−	1.65493i	0.521917	−	0.119124i	0.475360	+	0.879791i	$0.342318\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.08478	−	3.86819i	−0.219781	−	0.275597i	0.659702	−	0.751528i	$-0.270683\pi$
$197$	−3.08478	−	3.86819i	−0.219781	−	0.275597i	−0.879483	+	0.475931i	$0.842111\pi$
$198$		0			0
$199$	−3.32601	−	14.5722i	−0.235774	−	1.03299i	−0.944758	−	0.327770i	$-0.893703\pi$
$199$	−3.32601	−	14.5722i	−0.235774	−	1.03299i	0.708983	−	0.705225i	$-0.249154\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12.3098	−	8.62078i	−0.863979	−	0.605060i
$204$		0			0
$205$	−3.95962	−	3.15769i	−0.276552	−	0.220543i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.94512	+	8.70891i	0.480404	+	0.602408i
$210$		0			0
$211$	0.892716	−	1.85374i	0.0614571	−	0.127617i	−0.867978	−	0.496603i	$-0.834581\pi$
$211$	0.892716	−	1.85374i	0.0614571	−	0.127617i	0.929435	+	0.368986i	$0.120295\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	24.0293i		−	1.63878i
$216$		0			0
$217$	−1.60687	+	1.28143i	−0.109081	+	0.0869894i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−17.3060	−	35.9364i	−1.16413	−	2.41734i
$222$		0			0
$223$	16.2247	+	7.81341i	1.08649	+	0.523225i	0.889385	−	0.457158i	$-0.151133\pi$
$223$	16.2247	+	7.81341i	1.08649	+	0.523225i	0.197102	+	0.980383i	$0.436847\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	16.8582	−	21.1395i	1.11892	−	1.40308i	0.214341	−	0.976759i	$-0.431240\pi$
$227$	16.8582	−	21.1395i	1.11892	−	1.40308i	0.904574	−	0.426317i	$-0.140189\pi$
$228$		0			0
$229$	−0.950174	−	0.216871i	−0.0627893	−	0.0143312i	0.191011	−	0.981588i	$-0.438823\pi$
$229$	−0.950174	−	0.216871i	−0.0627893	−	0.0143312i	−0.253800	+	0.967257i	$0.581681\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.10163			−0.465244			−0.232622	−	0.972567i	$-0.574730\pi$
$233$	−7.10163			−0.465244			−0.232622	+	0.972567i	$0.574730\pi$
$234$		0			0
$235$	−10.1407	−	2.31455i	−0.661508	−	0.150985i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.75600	−	20.8374i	0.307640	−	1.34786i	−0.550668	−	0.834724i	$-0.685627\pi$
$239$	4.75600	−	20.8374i	0.307640	−	1.34786i	0.858308	−	0.513134i	$-0.171516\pi$
$240$		0			0
$241$	−12.0959	−	5.82510i	−0.779168	−	0.375228i	0.00163978	−	0.999999i	$-0.499478\pi$
$241$	−12.0959	−	5.82510i	−0.779168	−	0.375228i	−0.780808	+	0.624771i	$0.785192\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.06779	+	0.995793i	−0.132106	+	0.0636189i
$246$		0			0
$247$	−13.8164	+	11.0182i	−0.879116	+	0.701072i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.5962	+	2.64675i	−0.731945	+	0.167062i	−0.572220	−	0.820100i	$-0.693918\pi$
$251$	−11.5962	+	2.64675i	−0.731945	+	0.167062i	−0.159724	+	0.987162i	$0.551061\pi$
$252$		0			0
$253$	−3.40883	+	7.07851i	−0.214311	+	0.445022i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.76912	−	16.5136i	−0.235111	−	1.03009i	−0.945332	−	0.326110i	$-0.894262\pi$
$257$	−3.76912	−	16.5136i	−0.235111	−	1.03009i	0.710221	−	0.703979i	$-0.248595\pi$
$258$		0			0
$259$	12.6366	+	10.0773i	0.785199	+	0.626176i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.2876	+	17.7738i	1.37431	+	1.09598i	0.984557	+	0.175062i	$0.0560126\pi$
$263$	22.2876	+	17.7738i	1.37431	+	1.09598i	0.389757	+	0.920918i	$0.372559\pi$
$264$		0			0
$265$	1.41542	+	6.20137i	0.0869487	+	0.380947i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.39969	+	17.4421i	−0.512138	+	1.06347i	0.471258	+	0.881995i	$0.343800\pi$
$269$	−8.39969	+	17.4421i	−0.512138	+	1.06347i	−0.983396	+	0.181471i	$0.941914\pi$
$270$		0			0
$271$	3.67042	−	0.837749i	0.222962	−	0.0508896i	−0.109580	−	0.993978i	$-0.534951\pi$
$271$	3.67042	−	0.837749i	0.222962	−	0.0508896i	0.332542	+	0.943088i	$0.392094\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.3537	−	8.25679i	0.624351	−	0.497903i
$276$		0			0
$277$	21.3812	−	10.2967i	1.28467	−	0.618667i	0.338087	−	0.941115i	$-0.390220\pi$
$277$	21.3812	−	10.2967i	1.28467	−	0.618667i	0.946587	+	0.322448i	$0.104506\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.61080	−	3.18359i	−0.394367	−	0.189917i	0.226182	−	0.974085i	$-0.427376\pi$
$281$	−6.61080	−	3.18359i	−0.394367	−	0.189917i	−0.620549	+	0.784168i	$0.713090\pi$
$282$		0			0
$283$	0.753102	−	3.29956i	0.0447673	−	0.196138i	−0.947599	−	0.319461i	$-0.896498\pi$
$283$	0.753102	−	3.29956i	0.0447673	−	0.196138i	0.992367	+	0.123323i	$0.0393552\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.73041	+	1.07969i	0.279227	+	0.0637318i
$288$		0			0
$289$	−26.7734			−1.57491
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−23.2501	−	5.30667i	−1.35828	−	0.310019i	−0.519493	−	0.854475i	$-0.673879\pi$
$293$	−23.2501	−	5.30667i	−1.35828	−	0.310019i	−0.838790	+	0.544455i	$0.816736\pi$
$294$		0			0
$295$	24.6421	−	30.9002i	1.43472	−	1.79908i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.2298	−	5.40800i	−0.649438	−	0.312753i
$300$		0			0
$301$	9.98849	+	20.7413i	0.575727	+	1.19551i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−31.1473	+	24.8391i	−1.78349	+	1.42228i
$306$		0			0
$307$			29.7787i			1.69956i	0.527138	+	0.849780i	$0.323265\pi$
$307$			29.7787i			1.69956i	−0.527138	+	0.849780i	$0.676735\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.435163	−	0.903625i	0.0246758	−	0.0512399i	−0.888267	−	0.459328i	$-0.848090\pi$
$311$	0.435163	−	0.903625i	0.0246758	−	0.0512399i	0.912942	+	0.408088i	$0.133804\pi$
$312$		0			0
$313$	8.54595	+	10.7163i	0.483046	+	0.605720i	0.962311	−	0.271950i	$-0.0876685\pi$
$313$	8.54595	+	10.7163i	0.483046	+	0.605720i	−0.479266	+	0.877670i	$0.659097\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.08869	+	5.65304i	0.398140	+	0.317506i	0.802010	−	0.597310i	$-0.203764\pi$
$317$	7.08869	+	5.65304i	0.398140	+	0.317506i	−0.403870	+	0.914816i	$0.632335\pi$
$318$		0			0
$319$	−20.4242	+	1.27323i	−1.14353	+	0.0712873i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.31558	+	18.9078i	0.240125	+	1.05206i
$324$		0			0
$325$	13.0991	+	16.4258i	0.726609	+	0.911139i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.71527	−	2.21745i	0.535620	−	0.122252i
$330$		0			0
$331$			10.0766i			0.553861i	0.960890	+	0.276930i	$0.0893172\pi$
$331$			10.0766i			0.553861i	−0.960890	+	0.276930i	$0.910683\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−14.4910	+	6.97851i	−0.791729	+	0.381277i
$336$		0			0
$337$	−2.47151	−	5.13215i	−0.134632	−	0.279566i	0.822743	−	0.568413i	$-0.192442\pi$
$337$	−2.47151	−	5.13215i	−0.134632	−	0.279566i	−0.957375	+	0.288847i	$0.906728\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.622752	+	2.72845i	−0.0337239	+	0.147754i
$342$		0			0
$343$	−10.8088	+	13.5538i	−0.583621	+	0.731838i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	29.1636			1.56558			0.782792	−	0.622283i	$-0.213795\pi$
$347$	29.1636			1.56558			0.782792	+	0.622283i	$0.213795\pi$
$348$		0			0
$349$	−32.5973			−1.74489			−0.872447	−	0.488708i	$-0.837468\pi$
$349$	−32.5973			−1.74489			−0.872447	+	0.488708i	$0.837468\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.65086	+	4.57804i	−0.194316	+	0.243664i	−0.869439	−	0.494041i	$-0.835519\pi$
$353$	−3.65086	+	4.57804i	−0.194316	+	0.243664i	0.675123	+	0.737705i	$0.264091\pi$
$354$		0			0
$355$	8.78638	−	38.4956i	0.466333	−	2.04314i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.675138	−	1.40194i	−0.0356324	−	0.0739915i	0.882393	−	0.470514i	$-0.155931\pi$
$359$	−0.675138	−	1.40194i	−0.0356324	−	0.0739915i	−0.918025	+	0.396522i	$0.870217\pi$
$360$		0			0
$361$	−9.37673	+	4.51559i	−0.493512	+	0.237663i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	0.840812i		−	0.0440101i
$366$		0			0
$367$	−9.37679	+	2.14019i	−0.489464	+	0.111717i	−0.460128	−	0.887853i	$-0.652197\pi$
$367$	−9.37679	+	2.14019i	−0.489464	+	0.111717i	−0.0293363	+	0.999570i	$0.509339\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.79954	−	4.76447i	−0.197262	−	0.247359i
$372$		0			0
$373$	−5.38729	−	23.6032i	−0.278943	−	1.22213i	−0.899132	−	0.437677i	$-0.855801\pi$
$373$	−5.38729	−	23.6032i	−0.278943	−	1.22213i	0.620189	−	0.784452i	$-0.287056\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.01994	−	32.4023i	−0.104032	−	1.66880i
$378$		0			0
$379$	1.34965	+	1.07631i	0.0693266	+	0.0552861i	0.657540	−	0.753420i	$-0.271597\pi$
$379$	1.34965	+	1.07631i	0.0693266	+	0.0552861i	−0.588213	+	0.808706i	$0.700168\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−22.0312	−	27.6262i	−1.12574	−	1.41163i	−0.899149	−	0.437642i	$-0.855814\pi$
$383$	−22.0312	−	27.6262i	−1.12574	−	1.41163i	−0.226590	−	0.973990i	$-0.572758\pi$
$384$		0			0
$385$	−13.4028	+	27.8312i	−0.683070	+	1.41841i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			9.84239i			0.499029i	0.968371	+	0.249514i	$0.0802710\pi$
$389$			9.84239i			0.499029i	−0.968371	+	0.249514i	$0.919729\pi$
$390$		0			0
$391$	−10.6946	+	8.52863i	−0.540847	+	0.431311i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	15.6144	+	32.4237i	0.785646	+	1.63141i
$396$		0			0
$397$	6.30676	+	3.03718i	0.316527	+	0.152431i	0.585401	−	0.810744i	$-0.300937\pi$
$397$	6.30676	+	3.03718i	0.316527	+	0.152431i	−0.268874	+	0.963175i	$0.586651\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.2986	−	16.6759i	0.664100	−	0.832755i	−0.329683	−	0.944092i	$-0.606942\pi$
$401$	13.2986	−	16.6759i	0.664100	−	0.832755i	0.993783	+	0.111337i	$0.0355133\pi$
$402$		0			0
$403$	−4.32860	−	0.987975i	−0.215623	−	0.0492146i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	22.0087			1.09093
$408$		0			0
$409$	7.30188	+	1.66661i	0.361055	+	0.0824084i	0.399200	−	0.916864i	$-0.369288\pi$
$409$	7.30188	+	1.66661i	0.361055	+	0.0824084i	−0.0381454	+	0.999272i	$0.512145\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.42568	+	36.9153i	−0.414601	+	1.81648i
$414$		0			0
$415$	23.3746	+	11.2566i	1.14742	+	0.552566i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.0611	−	7.25304i	0.735783	−	0.354334i	−0.0281729	−	0.999603i	$-0.508969\pi$
$419$	15.0611	−	7.25304i	0.735783	−	0.354334i	0.763956	+	0.645269i	$0.223255\pi$
$420$		0			0
$421$	14.5208	−	11.5799i	0.707699	−	0.564371i	−0.202128	−	0.979359i	$-0.564786\pi$
$421$	14.5208	−	11.5799i	0.707699	−	0.564371i	0.909827	+	0.414988i	$0.136214\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	22.4788	−	5.13063i	1.09038	−	0.248872i
$426$		0			0
$427$	16.5602	−	34.3877i	0.801405	−	1.66414i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.459881	+	2.01487i	0.0221517	+	0.0970528i	0.984795	−	0.173719i	$-0.0555784\pi$
$431$	0.459881	+	2.01487i	0.0221517	+	0.0970528i	−0.962644	+	0.270772i	$0.912721\pi$
$432$		0			0
$433$	−15.3543	−	12.2447i	−0.737883	−	0.588442i	0.180762	−	0.983527i	$-0.442144\pi$
$433$	−15.3543	−	12.2447i	−0.737883	−	0.588442i	−0.918645	+	0.395085i	$0.870715\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.73828	+	3.77865i	0.226662	+	0.180757i
$438$		0			0
$439$	−9.07736	−	39.7705i	−0.433239	−	1.89814i	−0.439662	−	0.898163i	$-0.644902\pi$
$439$	−9.07736	−	39.7705i	−0.433239	−	1.89814i	0.00642294	−	0.999979i	$-0.497956\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.8958	+	22.6254i	−0.517676	+	1.07497i	0.464250	+	0.885704i	$0.346324\pi$
$443$	−10.8958	+	22.6254i	−0.517676	+	1.07497i	−0.981927	+	0.189262i	$0.939391\pi$
$444$		0			0
$445$	28.1133	−	6.41667i	1.33270	−	0.304180i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	3.40119	−	2.71236i	0.160512	−	0.128004i	−0.539940	−	0.841703i	$-0.681553\pi$
$449$	3.40119	−	2.71236i	0.160512	−	0.128004i	0.700452	+	0.713699i	$0.252982\pi$
$450$		0			0
$451$	5.95270	−	2.86667i	0.280302	−	0.134986i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−44.1533	−	21.2631i	−2.06994	−	0.996830i
$456$		0			0
$457$	−1.56895	+	6.87400i	−0.0733922	+	0.321552i	−0.998276	−	0.0586982i	$-0.981305\pi$
$457$	−1.56895	+	6.87400i	−0.0733922	+	0.321552i	0.924884	+	0.380250i	$0.124162\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	29.7762	+	6.79622i	1.38682	+	0.316532i	0.849829	−	0.527059i	$-0.176705\pi$
$461$	29.7762	+	6.79622i	1.38682	+	0.316532i	0.536987	+	0.843590i	$0.319562\pi$
$462$		0			0
$463$	37.0839			1.72344			0.861718	−	0.507387i	$-0.169388\pi$
$463$	37.0839			1.72344			0.861718	+	0.507387i	$0.169388\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	31.6548	+	7.22501i	1.46481	+	0.334333i	0.879275	−	0.476314i	$-0.158027\pi$
$467$	31.6548	+	7.22501i	1.46481	+	0.334333i	0.585535	+	0.810647i	$0.300884\pi$
$468$		0			0
$469$	9.60737	−	12.0473i	0.443627	−	0.556291i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	28.2432	+	13.6012i	1.29862	+	0.625384i
$474$		0			0
$475$	−4.43231	−	9.20379i	−0.203368	−	0.422299i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.3383	+	11.4344i	−0.655134	+	0.522452i	−0.893695	−	0.448676i	$-0.851896\pi$
$479$	−14.3383	+	11.4344i	−0.655134	+	0.522452i	0.238561	+	0.971128i	$0.423324\pi$
$480$		0			0
$481$			34.9161i			1.59204i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.676276	−	1.40430i	0.0307081	−	0.0637661i
$486$		0			0
$487$	12.0513	+	15.1118i	0.546096	+	0.684783i	0.975920	−	0.218130i	$-0.0699958\pi$
$487$	12.0513	+	15.1118i	0.546096	+	0.684783i	−0.429824	+	0.902913i	$0.641424\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.31621	+	4.23953i	0.239917	+	0.191328i	0.736066	−	0.676910i	$-0.236681\pi$
$491$	5.31621	+	4.23953i	0.239917	+	0.191328i	−0.496149	+	0.868238i	$0.665253\pi$
$492$		0			0
$493$	−33.0003	−	13.4317i	−1.48626	−	0.604931i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.41775	+	36.8806i	0.377588	+	1.65432i
$498$		0			0
$499$	13.2589	+	16.6261i	0.593550	+	0.744288i	0.984357	−	0.176184i	$-0.0563755\pi$
$499$	13.2589	+	16.6261i	0.593550	+	0.744288i	−0.390807	+	0.920473i	$0.627804\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−5.21440	+	1.19015i	−0.232499	+	0.0530663i	−0.337183	−	0.941439i	$-0.609474\pi$
$503$	−5.21440	+	1.19015i	−0.232499	+	0.0530663i	0.104684	+	0.994506i	$0.466617\pi$
$504$		0			0
$505$		−	46.7302i		−	2.07947i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	19.0726	−	9.18489i	0.845379	−	0.407113i	0.0395190	−	0.999219i	$-0.487417\pi$
$509$	19.0726	−	9.18489i	0.845379	−	0.407113i	0.805860	+	0.592106i	$0.201703\pi$
$510$		0			0
$511$	0.349509	+	0.725763i	0.0154614	+	0.0321059i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.9952	+	52.5546i	−0.528574	+	2.31583i
$516$		0			0
$517$	8.46037	−	10.6090i	0.372087	−	0.466582i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.731059			0.0320283			0.0160141	−	0.999872i	$-0.494902\pi$
$521$	0.731059			0.0320283			0.0160141	+	0.999872i	$0.494902\pi$
$522$		0			0
$523$	11.2257			0.490867			0.245433	−	0.969413i	$-0.421070\pi$
$523$	11.2257			0.490867			0.245433	+	0.969413i	$0.421070\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.03802	+	3.80956i	−0.132338	+	0.165947i
$528$		0			0
$529$	4.16681	−	18.2560i	0.181166	−	0.793738i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.54787	+	9.44376i	0.196990	+	0.409055i
$534$		0			0
$535$	−18.3866	+	8.85450i	−0.794921	+	0.382814i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	2.99405i		−	0.128963i
$540$		0			0
$541$	−29.1334	+	6.64951i	−1.25254	+	0.285885i	−0.796809	−	0.604231i	$-0.793480\pi$
$541$	−29.1334	+	6.64951i	−1.25254	+	0.285885i	−0.455734	+	0.890116i	$0.650623\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	15.7691	+	19.7738i	0.675473	+	0.847017i
$546$		0			0
$547$	9.14511	+	40.0673i	0.391017	+	1.71316i	0.661082	+	0.750313i	$0.270097\pi$
$547$	9.14511	+	40.0673i	0.391017	+	1.71316i	−0.270066	+	0.962842i	$0.587045\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.54829	+	15.5786i	−0.108561	+	0.663670i
$552$		0			0
$553$	−26.9557	−	21.4965i	−1.14628	−	0.914124i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.25163	−	5.33138i	−0.180148	−	0.225898i	0.683556	−	0.729898i	$-0.260433\pi$
$557$	−4.25163	−	5.33138i	−0.180148	−	0.225898i	−0.863704	+	0.504000i	$0.831861\pi$
$558$		0			0
$559$	−21.5779	+	44.8069i	−0.912646	+	1.89513i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			37.7443i			1.59073i	0.606128	+	0.795367i	$0.292722\pi$
$563$			37.7443i			1.59073i	−0.606128	+	0.795367i	$0.707278\pi$
$564$		0			0
$565$	−37.7561	+	30.1095i	−1.58841	+	1.26671i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.98503	−	20.7341i	−0.418594	−	0.869220i	−0.998511	−	0.0545444i	$-0.982629\pi$
$569$	−9.98503	−	20.7341i	−0.418594	−	0.869220i	0.579917	−	0.814676i	$-0.303085\pi$
$570$		0			0
$571$	29.0138	+	13.9723i	1.21419	+	0.584723i	0.927688	−	0.373357i	$-0.121793\pi$
$571$	29.0138	+	13.9723i	1.21419	+	0.584723i	0.286502	+	0.958080i	$0.407508\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.49229	−	5.63316i	0.187342	−	0.234919i
$576$		0			0
$577$	−3.86922	−	0.883124i	−0.161078	−	0.0367649i	0.141222	−	0.989978i	$-0.454897\pi$
$577$	−3.86922	−	0.883124i	−0.161078	−	0.0367649i	−0.302299	+	0.953213i	$0.597754\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.8554			−1.03118
$582$		0			0
$583$	−8.09005	−	1.84650i	−0.335056	−	0.0764743i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.83792	−	34.3402i	0.323506	−	1.41737i	−0.507762	−	0.861498i	$-0.669527\pi$
$587$	7.83792	−	34.3402i	0.323506	−	1.41737i	0.831267	−	0.555873i	$-0.187616\pi$
$588$		0			0
$589$	1.94504	+	0.936683i	0.0801441	+	0.0385953i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.33717	−	0.643949i	0.0549112	−	0.0264438i	−0.406227	−	0.913772i	$-0.633156\pi$
$593$	1.33717	−	0.643949i	0.0549112	−	0.0264438i	0.461138	+	0.887329i	$0.347441\pi$
$594$		0			0
$595$	−42.0487	+	33.5327i	−1.72383	+	1.37471i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.8564	+	3.39088i	−0.607016	+	0.138547i	−0.514971	−	0.857207i	$-0.672197\pi$
$599$	−14.8564	+	3.39088i	−0.607016	+	0.138547i	−0.0920448	+	0.995755i	$0.529340\pi$
$600$		0			0
$601$	2.81976	−	5.85529i	0.115020	−	0.238842i	−0.835509	−	0.549477i	$-0.814827\pi$
$601$	2.81976	−	5.85529i	0.115020	−	0.238842i	0.950529	+	0.310634i	$0.100541\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.22992	+	9.76991i	0.0906591	+	0.397203i
$606$		0			0
$607$	−15.4468	−	12.3184i	−0.626967	−	0.499990i	0.257692	−	0.966227i	$-0.417038\pi$
$607$	−15.4468	−	12.3184i	−0.626967	−	0.499990i	−0.884660	+	0.466237i	$0.845609\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.8308	+	13.4221i	0.680901	+	0.543000i
$612$		0			0
$613$	−0.991589	−	4.34443i	−0.0400499	−	0.175470i	0.950947	−	0.309353i	$-0.100112\pi$
$613$	−0.991589	−	4.34443i	−0.0400499	−	0.175470i	−0.990997	+	0.133883i	$0.957255\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.19271	−	2.47669i	0.0480167	−	0.0997077i	−0.875580	−	0.483073i	$-0.839521\pi$
$617$	1.19271	−	2.47669i	0.0480167	−	0.0997077i	0.923597	+	0.383365i	$0.125235\pi$
$618$		0			0
$619$	25.6750	−	5.86014i	1.03196	−	0.235539i	0.327181	−	0.944962i	$-0.393901\pi$
$619$	25.6750	−	5.86014i	1.03196	−	0.235539i	0.704783	+	0.709423i	$0.251044\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.5992	+	17.2248i	−0.865355	+	0.690098i
$624$		0			0
$625$	27.2813	−	13.1380i	1.09125	−	0.525518i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	34.5240	+	16.6259i	1.37656	+	0.662918i
$630$		0			0
$631$	7.40829	−	32.4578i	0.294919	−	1.29213i	−0.582669	−	0.812710i	$-0.697991\pi$
$631$	7.40829	−	32.4578i	0.294919	−	1.29213i	0.877588	−	0.479416i	$-0.159151\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.94700	−	0.900876i	−0.156632	−	0.0357502i
$636$		0			0
$637$	4.74997			0.188201
$638$		0			0
$639$		0			0
$640$		0			0
$641$	30.3209	+	6.92054i	1.19760	+	0.273345i	0.774404	−	0.632692i	$-0.218050\pi$
$641$	30.3209	+	6.92054i	1.19760	+	0.273345i	0.423199	+	0.906037i	$0.360907\pi$
$642$		0			0
$643$	1.45823	−	1.82856i	0.0575069	−	0.0721114i	−0.752246	−	0.658882i	$-0.771030\pi$
$643$	1.45823	−	1.82856i	0.0575069	−	0.0721114i	0.809753	+	0.586771i	$0.199601\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.03444	−	4.35075i	−0.355180	−	0.171046i	0.247781	−	0.968816i	$-0.420299\pi$
$647$	−9.03444	−	4.35075i	−0.355180	−	0.171046i	−0.602962	+	0.797770i	$0.706013\pi$
$648$		0			0
$649$	22.3710	+	46.4538i	0.878138	+	1.82347i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.46804	+	4.36062i	−0.213981	+	0.170644i	−0.724615	−	0.689154i	$-0.757982\pi$
$653$	−5.46804	+	4.36062i	−0.213981	+	0.170644i	0.510634	+	0.859798i	$0.329411\pi$
$654$		0			0
$655$		−	33.2551i		−	1.29938i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.39394	+	11.2006i	−0.210118	+	0.436314i	−0.979217	−	0.202815i	$-0.934991\pi$
$659$	−5.39394	+	11.2006i	−0.210118	+	0.436314i	0.769099	+	0.639130i	$0.220705\pi$
$660$		0			0
$661$	23.6568	+	29.6647i	0.920143	+	1.15382i	0.987740	+	0.156110i	$0.0498955\pi$
$661$	23.6568	+	29.6647i	0.920143	+	1.15382i	−0.0675967	+	0.997713i	$0.521533\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	18.6299	+	14.8568i	0.722436	+	0.576124i
$666$		0			0
$667$	−10.6795	+	3.14807i	−0.413511	+	0.121894i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.5649	−	50.6691i	−0.446457	−	1.95606i
$672$		0			0
$673$	14.1911	+	17.7951i	0.547028	+	0.685952i	0.976101	−	0.217318i	$-0.0697309\pi$
$673$	14.1911	+	17.7951i	0.547028	+	0.685952i	−0.429072	+	0.903270i	$0.641159\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.1036	+	6.41446i	−1.08011	+	0.246528i	−0.725315	−	0.688417i	$-0.758306\pi$
$677$	−28.1036	+	6.41446i	−1.08011	+	0.246528i	−0.354793	+	0.934945i	$0.615449\pi$
$678$		0			0
$679$			1.49326i			0.0573062i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.1569	−	5.85447i	0.465172	−	0.224015i	−0.186591	−	0.982438i	$-0.559744\pi$
$683$	12.1569	−	5.85447i	0.465172	−	0.224015i	0.651763	+	0.758423i	$0.274030\pi$
$684$		0			0
$685$	7.64622	+	15.8775i	0.292147	+	0.606649i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.92941	−	12.8346i	0.111602	−	0.488960i
$690$		0			0
$691$	−11.0186	+	13.8169i	−0.419167	+	0.525619i	−0.945920	−	0.324399i	$-0.894838\pi$
$691$	−11.0186	+	13.8169i	−0.419167	+	0.525619i	0.526753	+	0.850018i	$0.323409\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.15015			−0.233289
$696$		0			0
$697$	11.5033			0.435718
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.0012	−	12.5411i	0.377740	−	0.473671i	−0.556227	−	0.831030i	$-0.687752\pi$
$701$	10.0012	−	12.5411i	0.377740	−	0.473671i	0.933967	+	0.357360i	$0.116323\pi$
$702$		0			0
$703$	3.77781	−	16.5517i	0.142483	−	0.624258i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	19.4248	+	40.3361i	0.730546	+	1.51699i
$708$		0			0
$709$	6.26187	−	3.01556i	0.235169	−	0.113252i	−0.312588	−	0.949889i	$-0.601196\pi$
$709$	6.26187	−	3.01556i	0.235169	−	0.113252i	0.547758	+	0.836637i	$0.315482\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			1.52265i			0.0570238i
$714$		0			0
$715$	−65.0584	+	14.8492i	−2.43305	+	0.555327i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.21879	−	11.5600i	−0.343803	−	0.431115i	0.579627	−	0.814882i	$-0.303198\pi$
$719$	−9.21879	−	11.5600i	−0.343803	−	0.431115i	−0.923430	+	0.383767i	$0.874627\pi$
$720$		0			0
$721$	−11.4920	−	50.3497i	−0.427984	−	1.87512i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	18.5208	+	3.02957i	0.687845	+	0.112515i
$726$		0			0
$727$	1.14782	+	0.915356i	0.0425703	+	0.0339487i	0.644544	−	0.764567i	$-0.277047\pi$
$727$	1.14782	+	0.915356i	0.0425703	+	0.0339487i	−0.601974	+	0.798516i	$0.705619\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	34.0291	+	42.6712i	1.25861	+	1.57825i
$732$		0			0
$733$	−3.39961	+	7.05937i	−0.125568	+	0.260744i	−0.954270	−	0.298945i	$-0.903365\pi$
$733$	−3.39961	+	7.05937i	−0.125568	+	0.260744i	0.828703	+	0.559689i	$0.189079\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	20.9823i		−	0.772892i
$738$		0			0
$739$	37.8651	−	30.1964i	1.39289	−	1.11079i	0.413120	−	0.910677i	$-0.364439\pi$
$739$	37.8651	−	30.1964i	1.39289	−	1.11079i	0.979772	−	0.200117i	$-0.0641323\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.51983	+	13.5386i	0.239189	+	0.496682i	0.985661	−	0.168735i	$-0.0539681\pi$
$743$	6.51983	+	13.5386i	0.239189	+	0.496682i	−0.746472	+	0.665417i	$0.768254\pi$
$744$		0			0
$745$	43.4383	+	20.9188i	1.59145	+	0.766404i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	12.1901	−	15.2859i	0.445415	−	0.558533i
$750$		0			0
$751$	−36.0306	−	8.22374i	−1.31477	−	0.300089i	−0.493063	−	0.869993i	$-0.664123\pi$
$751$	−36.0306	−	8.22374i	−1.31477	−	0.300089i	−0.821711	+	0.569905i	$0.806980\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.1668			0.733944
$756$		0			0
$757$	−41.5654	−	9.48703i	−1.51072	−	0.344812i	−0.614677	−	0.788779i	$-0.710714\pi$
$757$	−41.5654	−	9.48703i	−1.51072	−	0.344812i	−0.896043	+	0.443967i	$0.853571\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.50046	−	37.2430i	0.308142	−	1.35006i	−0.549365	−	0.835583i	$-0.685130\pi$
$761$	8.50046	−	37.2430i	0.308142	−	1.35006i	0.857506	−	0.514474i	$-0.172013\pi$
$762$		0			0
$763$	−21.8310	−	10.5132i	−0.790334	−	0.380605i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−73.6975	+	35.4908i	−2.66106	+	1.28150i
$768$		0			0
$769$	−32.3543	+	25.8017i	−1.16673	+	0.930432i	−0.998469	−	0.0553110i	$-0.982385\pi$
$769$	−32.3543	+	25.8017i	−1.16673	+	0.930432i	−0.168256	+	0.985743i	$0.553814\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−38.6055	+	8.81146i	−1.38854	+	0.316926i	−0.850493	−	0.525986i	$-0.823696\pi$
$773$	−38.6055	+	8.81146i	−1.38854	+	0.316926i	−0.538051	+	0.842912i	$0.680839\pi$
$774$		0			0
$775$	1.11359	−	2.31239i	0.0400012	−	0.0830634i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.13410	−	4.96880i	−0.0406332	−	0.178026i
$780$		0			0
$781$	40.2732	+	32.1168i	1.44109	+	1.14923i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−45.8612	−	36.5731i	−1.63686	−	1.30535i
$786$		0			0
$787$	−7.46773	−	32.7183i	−0.266196	−	1.16628i	−0.914399	−	0.404813i	$-0.867336\pi$
$787$	−7.46773	−	32.7183i	−0.266196	−	1.16628i	0.648203	−	0.761467i	$-0.275521\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	20.0740	−	41.6840i	0.713748	−	1.48211i
$792$		0			0
$793$	80.3848	−	18.3473i	2.85455	−	0.651532i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	29.4111	−	23.4545i	1.04179	−	0.830802i	0.0559434	−	0.998434i	$-0.482183\pi$
$797$	29.4111	−	23.4545i	1.04179	−	0.830802i	0.985850	+	0.167632i	$0.0536119\pi$
$798$		0			0
$799$	21.2857	−	10.2506i	0.753033	−	0.362642i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.988262	+	0.475922i	0.0348750	+	0.0167949i
$804$		0			0
$805$	−3.73981	+	16.3852i	−0.131811	+	0.577502i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.31102	−	0.299232i	−0.0460931	−	0.0105204i	0.199412	−	0.979916i	$-0.436097\pi$
$809$	−1.31102	−	0.299232i	−0.0460931	−	0.0105204i	−0.245505	+	0.969395i	$0.578954\pi$
$810$		0			0
$811$	−4.06614			−0.142781			−0.0713907	−	0.997448i	$-0.522744\pi$
$811$	−4.06614			−0.142781			−0.0713907	+	0.997448i	$0.522744\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−27.0147	−	6.16592i	−0.946282	−	0.215983i
$816$		0			0
$817$	15.0768	−	18.9057i	0.527469	−	0.661426i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	44.4095	+	21.3865i	1.54990	+	0.746394i	0.996264	−	0.0863616i	$-0.0275241\pi$
$821$	44.4095	+	21.3865i	1.54990	+	0.746394i	0.553640	+	0.832756i	$0.313238\pi$
$822$		0			0
$823$	−17.1881	−	35.6915i	−0.599140	−	1.24413i	−0.951323	−	0.308195i	$-0.900275\pi$
$823$	−17.1881	−	35.6915i	−0.599140	−	1.24413i	0.352183	−	0.935931i	$-0.385439\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.2991	−	20.9728i	0.914508	−	0.729296i	−0.0484842	−	0.998824i	$-0.515439\pi$
$827$	26.2991	−	20.9728i	0.914508	−	0.729296i	0.962993	+	0.269528i	$0.0868676\pi$
$828$		0			0
$829$		−	45.1571i		−	1.56837i	−0.620527	−	0.784185i	$-0.713081\pi$
$829$		−	45.1571i		−	1.56837i	0.620527	−	0.784185i	$-0.286919\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.26178	−	4.69663i	0.0783660	−	0.162729i
$834$		0			0
$835$	3.90996	+	4.90293i	0.135310	+	0.169673i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−25.3666	−	20.2292i	−0.875753	−	0.698390i	0.0786529	−	0.996902i	$-0.474938\pi$
$839$	−25.3666	−	20.2292i	−0.875753	−	0.698390i	−0.954406	+	0.298512i	$0.903510\pi$
$840$		0			0
$841$	−20.7571	−	20.2520i	−0.715763	−	0.698343i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−15.1314	−	66.2949i	−0.520535	−	2.28061i
$846$		0			0
$847$	−5.98596	−	7.50615i	−0.205680	−	0.257914i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.6741	−	2.66454i	0.400183	−	0.0913392i
$852$		0			0
$853$		−	37.4830i		−	1.28339i	−0.766958	−	0.641697i	$-0.778231\pi$
$853$		−	37.4830i		−	1.28339i	0.766958	−	0.641697i	$-0.221769\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.5905	+	5.58171i	−0.395925	+	0.190668i	−0.621243	−	0.783618i	$-0.713372\pi$
$857$	−11.5905	+	5.58171i	−0.395925	+	0.190668i	0.225318	+	0.974285i	$0.427658\pi$
$858$		0			0
$859$	20.1229	+	41.7857i	0.686586	+	1.42571i	0.894276	+	0.447516i	$0.147691\pi$
$859$	20.1229	+	41.7857i	0.686586	+	1.42571i	−0.207690	+	0.978195i	$0.566595\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.27892	+	18.7472i	−0.145656	+	0.638161i	0.848406	+	0.529346i	$0.177563\pi$
$863$	−4.27892	+	18.7472i	−0.145656	+	0.638161i	−0.994062	+	0.108815i	$0.965295\pi$
$864$		0			0
$865$	−11.5020	+	14.4230i	−0.391078	+	0.490397i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−46.9479			−1.59260
$870$		0			0
$871$	33.2877			1.12791
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.67884	+	9.62897i	−0.259592	+	0.325518i
$876$		0			0
$877$	−8.16720	+	35.7828i	−0.275787	+	1.20830i	0.627278	+	0.778796i	$0.284169\pi$
$877$	−8.16720	+	35.7828i	−0.275787	+	1.20830i	−0.903064	+	0.429505i	$0.858688\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−14.1873	−	29.4602i	−0.477981	−	0.992538i	−0.990963	−	0.134138i	$-0.957173\pi$
$881$	−14.1873	−	29.4602i	−0.477981	−	0.992538i	0.512982	−	0.858400i	$-0.328541\pi$
$882$		0			0
$883$	−29.4062	+	14.1613i	−0.989596	+	0.476564i	−0.857395	−	0.514659i	$-0.827919\pi$
$883$	−29.4062	+	14.1613i	−0.989596	+	0.476564i	−0.132201	+	0.991223i	$0.542204\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	55.8120i		−	1.87398i	−0.349350	−	0.936992i	$-0.613598\pi$
$887$		−	55.8120i		−	1.87398i	0.349350	−	0.936992i	$-0.386402\pi$
$888$		0			0
$889$	3.78140	−	0.863080i	0.126824	−	0.0289468i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.52626	−	8.18367i	−0.218393	−	0.273856i
$894$		0			0
$895$	−12.5546	−	55.0055i	−0.419655	−	1.83863i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.45928	+	1.93978i	−0.115373	+	0.0646954i
$900$		0			0
$901$	−11.2956	−	9.00795i	−0.376311	−	0.300098i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−19.8368	−	24.8746i	−0.659398	−	0.826859i
$906$		0			0
$907$	−15.8304	+	32.8722i	−0.525641	+	1.09150i	0.454048	+	0.890977i	$0.349980\pi$
$907$	−15.8304	+	32.8722i	−0.525641	+	1.09150i	−0.979688	+	0.200526i	$0.935735\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	19.7316i		−	0.653736i	−0.945070	−	0.326868i	$-0.894007\pi$
$911$		−	19.7316i		−	0.653736i	0.945070	−	0.326868i	$-0.105993\pi$
$912$		0			0
$913$	−26.4613	+	21.1022i	−0.875743	+	0.698382i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.8235	+	28.7048i	0.456492	+	0.947915i
$918$		0			0
$919$	4.08361	+	1.96656i	0.134706	+	0.0648709i	0.500023	−	0.866012i	$-0.333325\pi$
$919$	4.08361	+	1.96656i	0.134706	+	0.0648709i	−0.365317	+	0.930883i	$0.619039\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−50.9522	+	63.8921i	−1.67711	+	2.10303i
$924$		0			0
$925$	−19.6777	−	4.49130i	−0.646997	−	0.147673i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−27.6884			−0.908426			−0.454213	−	0.890893i	$-0.650080\pi$
$929$	−27.6884			−0.908426			−0.454213	+	0.890893i	$0.650080\pi$
$930$		0			0
$931$	−2.25168	−	0.513932i	−0.0737959	−	0.0168434i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.2963	+	71.3986i	−0.532945	+	2.33498i
$936$		0			0
$937$	35.5916	+	17.1400i	1.16273	+	0.559940i	0.912833	−	0.408333i	$-0.133890\pi$
$937$	35.5916	+	17.1400i	1.16273	+	0.559940i	0.249894	+	0.968273i	$0.419604\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	33.0837	−	15.9323i	1.07850	−	0.519378i	0.191663	−	0.981461i	$-0.438612\pi$
$941$	33.0837	−	15.9323i	1.07850	−	0.519378i	0.886837	+	0.462083i	$0.152898\pi$
$942$		0			0
$943$	2.81044	−	2.24125i	0.0915204	−	0.0729851i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.37996	−	0.314967i	0.0448427	−	0.0102350i	−0.200041	−	0.979788i	$-0.564107\pi$
$947$	1.37996	−	0.314967i	0.0448427	−	0.0102350i	0.244883	+	0.969553i	$0.421250\pi$
$948$		0			0
$949$	−0.755035	+	1.56785i	−0.0245095	+	0.0508944i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.192647	+	0.844042i	0.00624045	+	0.0273412i	0.977952	−	0.208828i	$-0.0669650\pi$
$953$	0.192647	+	0.844042i	0.00624045	+	0.0273412i	−0.971712	+	0.236170i	$0.924108\pi$
$954$		0			0
$955$	34.2570	+	27.3190i	1.10853	+	0.884023i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−13.2000	−	10.5266i	−0.426249	−	0.339922i
$960$		0			0
$961$	−6.77746	−	29.6940i	−0.218628	−	0.957870i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.39952	−	19.5183i	0.302581	−	0.628316i
$966$		0			0
$967$	50.3935	−	11.5020i	1.62055	−	0.369879i	0.686528	−	0.727103i	$-0.259134\pi$
$967$	50.3935	−	11.5020i	1.62055	−	0.369879i	0.934019	+	0.357224i	$0.116277\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−41.0067	+	32.7017i	−1.31597	+	1.04945i	−0.321229	+	0.947002i	$0.604096\pi$
$971$	−41.0067	+	32.7017i	−1.31597	+	1.04945i	−0.994738	+	0.102447i	$0.967333\pi$
$972$		0			0
$973$	5.30862	−	2.55650i	0.170187	−	0.0819575i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.8957	+	5.72866i	0.380577	+	0.183276i	0.614385	−	0.789007i	$-0.289404\pi$
$977$	11.8957	+	5.72866i	0.380577	+	0.183276i	−0.233808	+	0.972283i	$0.575119\pi$
$978$		0			0
$979$	−8.37093	+	36.6754i	−0.267536	+	1.17215i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.84891	−	1.79146i	−0.250341	−	0.0571388i	0.0955086	−	0.995429i	$-0.469552\pi$
$983$	−7.84891	−	1.79146i	−0.250341	−	0.0571388i	−0.345850	+	0.938290i	$0.612409\pi$
$984$		0			0
$985$	−14.4118			−0.459198
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16.6277	+	3.79517i	0.528731	+	0.120679i
$990$		0			0
$991$	−16.0918	+	20.1784i	−0.511172	+	0.640989i	−0.968708	−	0.248202i	$-0.920160\pi$
$991$	−16.0918	+	20.1784i	−0.511172	+	0.640989i	0.457537	+	0.889191i	$0.348732\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−39.2271	−	18.8908i	−1.24358	−	0.598878i
$996$		0			0
$997$	−5.22270	−	10.8451i	−0.165405	−	0.343466i	0.801748	−	0.597662i	$-0.203904\pi$
$997$	−5.22270	−	10.8451i	−0.165405	−	0.343466i	−0.967153	+	0.254196i	$0.918189\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1044.2.z.c.325.4	yes	24
3.2	odd	2	inner	1044.2.z.c.325.1	✓	24
29.5	even	14	inner	1044.2.z.c.469.4	yes	24
87.5	odd	14	inner	1044.2.z.c.469.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1044.2.z.c.325.1	✓	24	3.2	odd	2	inner
1044.2.z.c.325.4	yes	24	1.1	even	1	trivial
1044.2.z.c.469.1	yes	24	87.5	odd	14	inner
1044.2.z.c.469.4	yes	24	29.5	even	14	inner

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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:	\( N \)	\(=\)	\( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1044.z (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81616 - 2.27739i) q^{5} +(-0.620985 + 2.72071i) q^{7} +O(q^{10})\)	\(q+(1.81616 - 2.27739i) q^{5} +(-0.620985 + 2.72071i) q^{7} +(1.64877 + 3.42372i) q^{11} +(-5.43161 + 2.61573i) q^{13} +6.61615i q^{17} +(2.85782 - 0.652279i) q^{19} +(1.28906 + 1.61643i) q^{23} +(-0.775470 - 3.39756i) q^{25} +(-2.03013 + 4.98784i) q^{29} +(0.575797 + 0.459183i) q^{31} +(5.06832 + 6.35547i) q^{35} +(2.51293 - 5.21815i) q^{37} -1.73867i q^{41} +(6.44955 - 5.14334i) q^{43} +(-1.54934 - 3.21723i) q^{47} +(-0.709874 - 0.341857i) q^{49} +(-1.36151 + 1.70728i) q^{53} +(10.7916 + 2.46310i) q^{55} +13.5683 q^{59} +(-13.3338 - 3.04336i) q^{61} +(-3.90763 + 17.1205i) q^{65} +(-4.97479 - 2.39573i) q^{67} +(12.2131 - 5.88150i) q^{71} +(0.225677 - 0.179972i) q^{73} +(-10.3388 + 2.35977i) q^{77} +(-5.36045 + 11.1311i) q^{79} +(1.98190 + 8.68327i) q^{83} +(15.0676 + 12.0160i) q^{85} +(7.73977 + 6.17226i) q^{89} +(-3.74369 - 16.4022i) q^{91} +(3.70476 - 7.69302i) q^{95} +(0.521674 - 0.119069i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

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