LMFDB - Embedded newform 396.2.j.d.181.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [396,2,Mod(37,396)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(396, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("396.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.6
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + 16x^{4} - 66x^{2} + 121 $ x^8 - x^6 + 16x^4 - 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-1.26313 - 1.73855i$ of defining polynomial
Character	$\chi$	$=$	396.181
Dual form			396.2.j.d.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780656 + 2.40261i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-2.82444 + 1.73855i) q^{11} +(-0.0729490 - 0.224514i) q^{13} +(-2.04378 + 6.29012i) q^{17} +(-3.11803 - 2.26538i) q^{19} +0.964944 q^{23} +(-1.11803 - 0.812299i) q^{25} +(-2.52626 + 1.83543i) q^{29} +(2.11803 + 6.51864i) q^{31} +(-0.780656 - 2.40261i) q^{35} +(5.42705 - 3.94298i) q^{37} +(7.39448 + 5.37240i) q^{41} +3.00000 q^{43} +(-7.87695 - 5.72294i) q^{47} +(-1.85410 + 5.70634i) q^{49} +(-0.482472 - 1.48490i) q^{53} +(-1.97214 - 8.14324i) q^{55} +(8.65761 - 6.29012i) q^{59} +(0.281153 - 0.865300i) q^{61} +0.596368 q^{65} +4.32624 q^{67} +(3.30691 - 10.1776i) q^{71} +(-11.7082 + 8.50651i) q^{73} +(1.26313 - 3.06668i) q^{77} +(-0.218847 - 0.673542i) q^{79} +(1.85950 - 5.72294i) q^{83} +(-13.5172 - 9.82084i) q^{85} +7.21019 q^{89} +(0.190983 + 0.138757i) q^{91} +(7.87695 - 5.72294i) q^{95} +(3.57295 + 10.9964i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{7} - 14 q^{13} - 16 q^{19} + 8 q^{31} + 30 q^{37} + 24 q^{43} + 12 q^{49} + 20 q^{55} - 38 q^{61} - 28 q^{67} - 40 q^{73} - 42 q^{79} - 50 q^{85} + 6 q^{91} + 42 q^{97}+O(q^{100}) $ 8 * q - 2 * q^7 - 14 * q^13 - 16 * q^19 + 8 * q^31 + 30 * q^37 + 24 * q^43 + 12 * q^49 + 20 * q^55 - 38 * q^61 - 28 * q^67 - 40 * q^73 - 42 * q^79 - 50 * q^85 + 6 * q^91 + 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.780656	+	2.40261i	−0.349120	+	1.07448i	0.610221	+	0.792231i	$0.291081\pi$
$5$	−0.780656	+	2.40261i	−0.349120	+	1.07448i	−0.959341	+	0.282249i	$0.908919\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i	−0.730084	−	0.683358i	$-0.760519\pi$
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i	0.424304	+	0.905520i	$0.360519\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.82444	+	1.73855i	−0.851600	+	0.524191i
$11$	−2.82444	+	1.73855i	−0.851600	+	0.524191i
$12$		0			0
$13$	−0.0729490	−	0.224514i	−0.0202324	−	0.0622690i	0.940431	−	0.339986i	$-0.110422\pi$
$13$	−0.0729490	−	0.224514i	−0.0202324	−	0.0622690i	−0.960663	+	0.277717i	$0.910422\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.04378	+	6.29012i	−0.495690	+	1.52558i	0.320188	+	0.947354i	$0.396254\pi$
$17$	−2.04378	+	6.29012i	−0.495690	+	1.52558i	−0.815878	+	0.578224i	$0.803746\pi$
$18$		0			0
$19$	−3.11803	−	2.26538i	−0.715326	−	0.519715i	0.169561	−	0.985520i	$-0.445765\pi$
$19$	−3.11803	−	2.26538i	−0.715326	−	0.519715i	−0.884887	+	0.465805i	$0.845765\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.964944			0.201205			0.100602	−	0.994927i	$-0.467923\pi$
$23$	0.964944			0.201205			0.100602	+	0.994927i	$0.467923\pi$
$24$		0			0
$25$	−1.11803	−	0.812299i	−0.223607	−	0.162460i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.52626	+	1.83543i	−0.469114	+	0.340831i	−0.797096	−	0.603853i	$-0.793631\pi$
$29$	−2.52626	+	1.83543i	−0.469114	+	0.340831i	0.327982	+	0.944684i	$0.393631\pi$
$30$		0			0
$31$	2.11803	+	6.51864i	0.380410	+	1.17078i	0.939756	+	0.341847i	$0.111053\pi$
$31$	2.11803	+	6.51864i	0.380410	+	1.17078i	−0.559345	+	0.828935i	$0.688947\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.780656	−	2.40261i	−0.131955	−	0.406115i
$36$		0			0
$37$	5.42705	−	3.94298i	0.892202	−	0.648222i	−0.0442495	−	0.999021i	$-0.514090\pi$
$37$	5.42705	−	3.94298i	0.892202	−	0.648222i	0.936451	+	0.350798i	$0.114090\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.39448	+	5.37240i	1.15482	+	0.839028i	0.989115	−	0.147146i	$-0.0470088\pi$
$41$	7.39448	+	5.37240i	1.15482	+	0.839028i	0.165709	+	0.986175i	$0.447009\pi$
$42$		0			0
$43$	3.00000			0.457496			0.228748	−	0.973486i	$-0.426537\pi$
$43$	3.00000			0.457496			0.228748	+	0.973486i	$0.426537\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.87695	−	5.72294i	−1.14897	−	0.834776i	−0.160627	−	0.987015i	$-0.551352\pi$
$47$	−7.87695	−	5.72294i	−1.14897	−	0.834776i	−0.988344	+	0.152239i	$0.951352\pi$
$48$		0			0
$49$	−1.85410	+	5.70634i	−0.264872	+	0.815191i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.482472	−	1.48490i	−0.0662726	−	0.203966i	0.912437	−	0.409218i	$-0.134199\pi$
$53$	−0.482472	−	1.48490i	−0.0662726	−	0.203966i	−0.978709	+	0.205252i	$0.934199\pi$
$54$		0			0
$55$	−1.97214	−	8.14324i	−0.265923	−	1.09803i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.65761	−	6.29012i	1.12712	−	0.818904i	0.141851	−	0.989888i	$-0.454695\pi$
$59$	8.65761	−	6.29012i	1.12712	−	0.818904i	0.985274	+	0.170984i	$0.0546948\pi$
$60$		0			0
$61$	0.281153	−	0.865300i	0.0359979	−	0.110790i	−0.931443	−	0.363888i	$-0.881449\pi$
$61$	0.281153	−	0.865300i	0.0359979	−	0.110790i	0.967441	+	0.253097i	$0.0814493\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.596368			0.0739703
$66$		0			0
$67$	4.32624			0.528534			0.264267	−	0.964450i	$-0.414870\pi$
$67$	4.32624			0.528534			0.264267	+	0.964450i	$0.414870\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.30691	−	10.1776i	0.392458	−	1.20786i	−0.538465	−	0.842648i	$-0.680996\pi$
$71$	3.30691	−	10.1776i	0.392458	−	1.20786i	0.930923	−	0.365214i	$-0.119004\pi$
$72$		0			0
$73$	−11.7082	+	8.50651i	−1.37034	+	0.995611i	−0.372631	+	0.927979i	$0.621544\pi$
$73$	−11.7082	+	8.50651i	−1.37034	+	0.995611i	−0.997710	+	0.0676320i	$0.978456\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.26313	−	3.06668i	0.143947	−	0.349480i
$78$		0			0
$79$	−0.218847	−	0.673542i	−0.0246222	−	0.0757794i	0.937990	−	0.346661i	$-0.112685\pi$
$79$	−0.218847	−	0.673542i	−0.0246222	−	0.0757794i	−0.962613	+	0.270882i	$0.912685\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.85950	−	5.72294i	0.204106	−	0.628174i	−0.795643	−	0.605766i	$-0.792867\pi$
$83$	1.85950	−	5.72294i	0.204106	−	0.628174i	0.999749	−	0.0224080i	$-0.00713330\pi$
$84$		0			0
$85$	−13.5172	−	9.82084i	−1.46615	−	1.06522i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.21019			0.764279			0.382139	−	0.924105i	$-0.375187\pi$
$89$	7.21019			0.764279			0.382139	+	0.924105i	$0.375187\pi$
$90$		0			0
$91$	0.190983	+	0.138757i	0.0200205	+	0.0145457i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.87695	−	5.72294i	0.808158	−	0.587161i
$96$		0			0
$97$	3.57295	+	10.9964i	0.362778	+	1.11652i	0.951361	+	0.308079i	$0.0996861\pi$
$97$	3.57295	+	10.9964i	0.362778	+	1.11652i	−0.588583	+	0.808437i	$0.700314\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.22807	−	6.85730i	−0.221701	−	0.682327i	−0.998610	−	0.0527130i	$-0.983213\pi$
$101$	−2.22807	−	6.85730i	−0.221701	−	0.682327i	0.776908	−	0.629614i	$-0.216787\pi$
$102$		0			0
$103$	10.8541	−	7.88597i	1.06949	−	0.777027i	0.0936666	−	0.995604i	$-0.470141\pi$
$103$	10.8541	−	7.88597i	1.06949	−	0.777027i	0.975820	+	0.218576i	$0.0701412\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.92073	−	7.20783i	−0.959074	−	0.696808i	−0.00613812	−	0.999981i	$-0.501954\pi$
$107$	−9.92073	−	7.20783i	−0.959074	−	0.696808i	−0.952935	+	0.303173i	$0.901954\pi$
$108$		0			0
$109$	18.1803			1.74136			0.870680	−	0.491849i	$-0.163679\pi$
$109$	18.1803			1.74136			0.870680	+	0.491849i	$0.163679\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.92073	+	7.20783i	0.933264	+	0.678056i	0.946790	−	0.321852i	$-0.104306\pi$
$113$	9.92073	+	7.20783i	0.933264	+	0.678056i	−0.0135257	+	0.999909i	$0.504306\pi$
$114$		0			0
$115$	−0.753289	+	2.31838i	−0.0702446	+	0.216191i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.04378	−	6.29012i	−0.187353	−	0.576614i
$120$		0			0
$121$	4.95492	−	9.82084i	0.450447	−	0.892803i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.39448	+	5.37240i	−0.661382	+	0.480522i
$126$		0			0
$127$	−5.00000	+	15.3884i	−0.443678	+	1.36550i	0.440249	+	0.897876i	$0.354890\pi$
$127$	−5.00000	+	15.3884i	−0.443678	+	1.36550i	−0.883927	+	0.467625i	$0.845110\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.54371			0.746467			0.373234	−	0.927737i	$-0.378249\pi$
$131$	8.54371			0.746467			0.373234	+	0.927737i	$0.378249\pi$
$132$		0			0
$133$	3.85410			0.334193
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.75433	+	14.6323i	−0.406190	+	1.25012i	0.513708	+	0.857965i	$0.328271\pi$
$137$	−4.75433	+	14.6323i	−0.406190	+	1.25012i	−0.919898	+	0.392158i	$0.871729\pi$
$138$		0			0
$139$	−10.6353	+	7.72696i	−0.902071	+	0.655393i	−0.938997	−	0.343925i	$-0.888243\pi$
$139$	−10.6353	+	7.72696i	−0.902071	+	0.655393i	0.0369264	+	0.999318i	$0.488243\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.596368	+	0.507301i	0.0498708	+	0.0424226i
$144$		0			0
$145$	−2.43769	−	7.50245i	−0.202439	−	0.623045i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.19302	−	9.82709i	0.261582	−	0.805067i	−0.730879	−	0.682507i	$-0.760890\pi$
$149$	3.19302	−	9.82709i	0.261582	−	0.805067i	0.992461	−	0.122560i	$-0.0391103\pi$
$150$		0			0
$151$	−17.0902	−	12.4167i	−1.39078	−	1.01046i	−0.995779	−	0.0917780i	$-0.970745\pi$
$151$	−17.0902	−	12.4167i	−1.39078	−	1.01046i	−0.394999	−	0.918682i	$-0.629255\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−17.3152			−1.39079
$156$		0			0
$157$	−1.85410	−	1.34708i	−0.147973	−	0.107509i	0.511335	−	0.859381i	$-0.329151\pi$
$157$	−1.85410	−	1.34708i	−0.147973	−	0.107509i	−0.659309	+	0.751872i	$0.729151\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.780656	+	0.567180i	−0.0615243	+	0.0447000i
$162$		0			0
$163$	4.44427	+	13.6781i	0.348102	+	1.07135i	0.959902	+	0.280336i	$0.0904458\pi$
$163$	4.44427	+	13.6781i	0.348102	+	1.07135i	−0.611800	+	0.791013i	$0.709554\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.79811	+	20.9224i	0.526054	+	1.61903i	0.762223	+	0.647314i	$0.224108\pi$
$167$	6.79811	+	20.9224i	0.526054	+	1.61903i	−0.236169	+	0.971712i	$0.575892\pi$
$168$		0			0
$169$	10.4721	−	7.60845i	0.805549	−	0.585266i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.69266	−	5.58905i	−0.584862	−	0.424927i	0.255611	−	0.966780i	$-0.417723\pi$
$173$	−7.69266	−	5.58905i	−0.584862	−	0.424927i	−0.840474	+	0.541852i	$0.817723\pi$
$174$		0			0
$175$	1.38197			0.104467
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.4470	+	9.04327i	0.930332	+	0.675925i	0.946074	−	0.323951i	$-0.105011\pi$
$179$	12.4470	+	9.04327i	0.930332	+	0.675925i	−0.0157424	+	0.999876i	$0.505011\pi$
$180$		0			0
$181$	−5.01722	+	15.4414i	−0.372927	+	1.14775i	0.571939	+	0.820296i	$0.306191\pi$
$181$	−5.01722	+	15.4414i	−0.372927	+	1.14775i	−0.944867	+	0.327456i	$0.893809\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.23680	+	16.1172i	0.385017	+	1.18496i
$186$		0			0
$187$	−5.16312	−	21.3193i	−0.377565	−	1.55902i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−19.0608	+	13.8485i	−1.37919	+	1.00204i	−0.382237	+	0.924064i	$0.624846\pi$
$191$	−19.0608	+	13.8485i	−1.37919	+	1.00204i	−0.996955	+	0.0779771i	$0.975154\pi$
$192$		0			0
$193$	3.44427	−	10.6004i	0.247924	−	0.763032i	−0.747218	−	0.664579i	$-0.768611\pi$
$193$	3.44427	−	10.6004i	0.247924	−	0.763032i	0.995142	−	0.0984525i	$-0.0313893\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−26.0867			−1.85860			−0.929301	−	0.369324i	$-0.879589\pi$
$197$	−26.0867			−1.85860			−0.929301	+	0.369324i	$0.879589\pi$
$198$		0			0
$199$	4.23607			0.300287			0.150143	−	0.988664i	$-0.452026\pi$
$199$	4.23607			0.300287			0.150143	+	0.988664i	$0.452026\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.964944	−	2.96979i	0.0677258	−	0.208438i
$204$		0			0
$205$	−18.6803	+	13.5721i	−1.30469	+	0.947914i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	12.7452	+	0.977595i	0.881602	+	0.0676216i
$210$		0			0
$211$	3.20820	+	9.87384i	0.220862	+	0.679743i	0.998685	+	0.0512601i	$0.0163238\pi$
$211$	3.20820	+	9.87384i	0.220862	+	0.679743i	−0.777823	+	0.628483i	$0.783676\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.34197	+	7.20783i	−0.159721	+	0.491570i
$216$		0			0
$217$	−5.54508	−	4.02874i	−0.376425	−	0.273489i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.56131			0.105025
$222$		0			0
$223$	5.19098	+	3.77147i	0.347614	+	0.252556i	0.747867	−	0.663848i	$-0.231078\pi$
$223$	5.19098	+	3.77147i	0.347614	+	0.252556i	−0.400253	+	0.916404i	$0.631078\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.6572	+	14.2818i	−1.30469	+	0.947915i	−0.999990	−	0.00453258i	$-0.998557\pi$
$227$	−19.6572	+	14.2818i	−1.30469	+	0.947915i	−0.304703	+	0.952447i	$0.598557\pi$
$228$		0			0
$229$	3.52786	+	10.8576i	0.233128	+	0.717494i	0.997364	+	0.0725574i	$0.0231161\pi$
$229$	3.52786	+	10.8576i	0.233128	+	0.717494i	−0.764236	+	0.644936i	$0.776884\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.74560	+	5.37240i	0.114358	+	0.351958i	0.991813	−	0.127702i	$-0.0407601\pi$
$233$	1.74560	+	5.37240i	0.114358	+	0.351958i	−0.877455	+	0.479660i	$0.840760\pi$
$234$		0			0
$235$	19.8992	−	14.4576i	1.29808	−	0.943110i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.78938	+	2.75315i	0.245115	+	0.178086i	0.703559	−	0.710637i	$-0.251593\pi$
$239$	3.78938	+	2.75315i	0.245115	+	0.178086i	−0.458444	+	0.888723i	$0.651593\pi$
$240$		0			0
$241$	22.9443			1.47797			0.738985	−	0.673722i	$-0.235305\pi$
$241$	22.9443			1.47797			0.738985	+	0.673722i	$0.235305\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.2627	−	8.90937i	−0.783435	−	0.569199i
$246$		0			0
$247$	−0.281153	+	0.865300i	−0.0178893	+	0.0550577i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.16641	+	15.9006i	0.326101	+	1.00363i	0.970941	+	0.239318i	$0.0769237\pi$
$251$	5.16641	+	15.9006i	0.326101	+	1.00363i	−0.644841	+	0.764317i	$0.723076\pi$
$252$		0			0
$253$	−2.72542	+	1.67760i	−0.171346	+	0.105470i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.60510	+	2.61925i	−0.224880	+	0.163385i	−0.694520	−	0.719473i	$-0.744383\pi$
$257$	−3.60510	+	2.61925i	−0.224880	+	0.163385i	0.469641	+	0.882858i	$0.344383\pi$
$258$		0			0
$259$	−2.07295	+	6.37988i	−0.128807	+	0.396427i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.7014			0.659876			0.329938	−	0.944003i	$-0.392972\pi$
$263$	10.7014			0.659876			0.329938	+	0.944003i	$0.392972\pi$
$264$		0			0
$265$	3.94427			0.242295
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.49120	−	10.7448i	0.212862	−	0.655122i	−0.786436	−	0.617671i	$-0.788076\pi$
$269$	3.49120	−	10.7448i	0.212862	−	0.655122i	0.999298	−	0.0374510i	$-0.0119238\pi$
$270$		0			0
$271$	1.73607	−	1.26133i	0.105459	−	0.0766202i	−0.533806	−	0.845607i	$-0.679239\pi$
$271$	1.73607	−	1.26133i	0.105459	−	0.0766202i	0.639265	+	0.768987i	$0.279239\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.57004	+	0.350536i	0.275584	+	0.0211381i
$276$		0			0
$277$	−2.55573	−	7.86572i	−0.153559	−	0.472605i	0.844453	−	0.535629i	$-0.179926\pi$
$277$	−2.55573	−	7.86572i	−0.153559	−	0.472605i	−0.998012	+	0.0630239i	$0.979926\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.64888	−	17.3855i	0.336984	−	1.03713i	−0.628753	−	0.777605i	$-0.716434\pi$
$281$	5.64888	−	17.3855i	0.336984	−	1.03713i	0.965737	−	0.259524i	$-0.0835658\pi$
$282$		0			0
$283$	−20.5623	−	14.9394i	−1.22230	−	0.888055i	−0.226013	−	0.974124i	$-0.572569\pi$
$283$	−20.5623	−	14.9394i	−1.22230	−	0.888055i	−0.996289	+	0.0860697i	$0.972569\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.14008			−0.539522
$288$		0			0
$289$	−21.6353	−	15.7189i	−1.27266	−	0.924643i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.39448	−	5.37240i	0.431990	−	0.313859i	−0.350454	−	0.936580i	$-0.613973\pi$
$293$	7.39448	−	5.37240i	0.431990	−	0.313859i	0.782444	+	0.622721i	$0.213973\pi$
$294$		0			0
$295$	8.35410	+	25.7113i	0.486395	+	1.49697i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0703917	−	0.216643i	−0.00407086	−	0.0125288i
$300$		0			0
$301$	−2.42705	+	1.76336i	−0.139893	+	0.101638i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.85950	+	1.35100i	0.106474	+	0.0773582i
$306$		0			0
$307$	−14.0902			−0.804168			−0.402084	−	0.915603i	$-0.631714\pi$
$307$	−14.0902			−0.804168			−0.402084	+	0.915603i	$0.631714\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.86822	+	3.53697i	0.276052	+	0.200563i	0.717193	−	0.696874i	$-0.245426\pi$
$311$	4.86822	+	3.53697i	0.276052	+	0.200563i	−0.441142	+	0.897437i	$0.645426\pi$
$312$		0			0
$313$	−4.07295	+	12.5352i	−0.230217	+	0.708534i	0.767503	+	0.641045i	$0.221499\pi$
$313$	−4.07295	+	12.5352i	−0.230217	+	0.708534i	−0.997720	+	0.0674891i	$0.978501\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.47332	−	26.0782i	−0.475909	−	1.46470i	−0.844728	−	0.535196i	$-0.820238\pi$
$317$	−8.47332	−	26.0782i	−0.475909	−	1.46470i	0.368819	−	0.929501i	$-0.379762\pi$
$318$		0			0
$319$	3.94427	−	9.57608i	0.220837	−	0.536157i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	20.6221	−	14.9828i	1.14745	−	0.833668i
$324$		0			0
$325$	−0.100813	+	0.310271i	−0.00559210	+	0.0172107i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.73645			0.536788
$330$		0			0
$331$	10.4164			0.572538			0.286269	−	0.958149i	$-0.407585\pi$
$331$	10.4164			0.572538			0.286269	+	0.958149i	$0.407585\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.37730	+	10.3943i	−0.184522	+	0.567900i
$336$		0			0
$337$	−10.7082	+	7.77997i	−0.583313	+	0.423802i	−0.839917	−	0.542715i	$-0.817396\pi$
$337$	−10.7082	+	7.77997i	−0.583313	+	0.423802i	0.256604	+	0.966517i	$0.417396\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−17.3152	−	14.7292i	−0.937671	−	0.797631i
$342$		0			0
$343$	−4.01722	−	12.3637i	−0.216910	−	0.667579i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.45614	+	13.7146i	−0.239218	+	0.736238i	0.757316	+	0.653049i	$0.226511\pi$
$347$	−4.45614	+	13.7146i	−0.239218	+	0.736238i	−0.996534	+	0.0831890i	$0.973489\pi$
$348$		0			0
$349$	−9.51722	−	6.91467i	−0.509445	−	0.370134i	0.303168	−	0.952937i	$-0.401956\pi$
$349$	−9.51722	−	6.91467i	−0.509445	−	0.370134i	−0.812613	+	0.582804i	$0.801956\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.2802			0.972954			0.486477	−	0.873693i	$-0.338282\pi$
$353$	18.2802			0.972954			0.486477	+	0.873693i	$0.338282\pi$
$354$		0			0
$355$	21.8713	+	15.8904i	1.16081	+	0.843377i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.5254	−	17.8187i	1.29440	−	0.940438i	0.294517	−	0.955646i	$-0.404841\pi$
$359$	24.5254	−	17.8187i	1.29440	−	0.940438i	0.999884	+	0.0152088i	$0.00484128\pi$
$360$		0			0
$361$	−1.28115	−	3.94298i	−0.0674291	−	0.207525i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−11.2978	−	34.7709i	−0.591352	−	1.81999i
$366$		0			0
$367$	1.26393	−	0.918300i	0.0659767	−	0.0479349i	−0.554308	−	0.832312i	$-0.687017\pi$
$367$	1.26393	−	0.918300i	0.0659767	−	0.0479349i	0.620285	+	0.784377i	$0.287017\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.26313	+	0.917716i	0.0655783	+	0.0476454i
$372$		0			0
$373$	13.0000			0.673114			0.336557	−	0.941663i	$-0.390737\pi$
$373$	13.0000			0.673114			0.336557	+	0.941663i	$0.390737\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.596368	+	0.433287i	0.0307145	+	0.0223154i
$378$		0			0
$379$	6.12868	−	18.8621i	0.314809	−	0.968882i	−0.661024	−	0.750365i	$-0.729878\pi$
$379$	6.12868	−	18.8621i	0.314809	−	0.968882i	0.975833	−	0.218518i	$-0.0701221\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.71927	−	17.6021i	−0.292241	−	0.899426i	−0.984134	−	0.177426i	$-0.943223\pi$
$383$	−5.71927	−	17.6021i	−0.292241	−	0.899426i	0.691893	−	0.722000i	$-0.256777\pi$
$384$		0			0
$385$	6.38197	+	5.42882i	0.325255	+	0.276679i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	20.1397	−	14.6323i	1.02112	−	0.741888i	0.0546085	−	0.998508i	$-0.482609\pi$
$389$	20.1397	−	14.6323i	1.02112	−	0.741888i	0.966512	+	0.256620i	$0.0826089\pi$
$390$		0			0
$391$	−1.97214	+	6.06961i	−0.0997352	+	0.306953i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.78910			0.0900196
$396$		0			0
$397$	21.0000			1.05396			0.526980	−	0.849878i	$-0.323324\pi$
$397$	21.0000			1.05396			0.526980	+	0.849878i	$0.323324\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.57004	−	14.0651i	0.228217	−	0.702379i	−0.769732	−	0.638367i	$-0.779610\pi$
$401$	4.57004	−	14.0651i	0.228217	−	0.702379i	0.997949	−	0.0640124i	$-0.0203897\pi$
$402$		0			0
$403$	1.30902	−	0.951057i	0.0652068	−	0.0473755i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.47332	+	20.5719i	−0.420007	+	1.01971i
$408$		0			0
$409$	5.56231	+	17.1190i	0.275038	+	0.846481i	0.989209	+	0.146510i	$0.0468039\pi$
$409$	5.56231	+	17.1190i	0.275038	+	0.846481i	−0.714171	+	0.699971i	$0.753196\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.30691	+	10.1776i	−0.162722	+	0.500808i
$414$		0			0
$415$	12.2984	+	8.93529i	0.603703	+	0.438616i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	32.1042			1.56839			0.784196	−	0.620514i	$-0.213076\pi$
$419$	32.1042			1.56839			0.784196	+	0.620514i	$0.213076\pi$
$420$		0			0
$421$	−11.2082	−	8.14324i	−0.546254	−	0.396877i	0.280148	−	0.959957i	$-0.409616\pi$
$421$	−11.2082	−	8.14324i	−0.546254	−	0.396877i	−0.826403	+	0.563080i	$0.809616\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.39448	−	5.37240i	0.358685	−	0.260600i
$426$		0			0
$427$	0.281153	+	0.865300i	0.0136059	+	0.0418748i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.64015	−	8.12555i	−0.127172	−	0.391394i	0.867119	−	0.498101i	$-0.165969\pi$
$431$	−2.64015	−	8.12555i	−0.127172	−	0.391394i	−0.994290	+	0.106707i	$0.965969\pi$
$432$		0			0
$433$	8.70820	−	6.32688i	0.418490	−	0.304050i	−0.358540	−	0.933514i	$-0.616725\pi$
$433$	8.70820	−	6.32688i	0.418490	−	0.304050i	0.777030	+	0.629464i	$0.216725\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.00873	−	2.18597i	−0.143927	−	0.104569i
$438$		0			0
$439$	−14.7082			−0.701984			−0.350992	−	0.936378i	$-0.614156\pi$
$439$	−14.7082			−0.701984			−0.350992	+	0.936378i	$0.614156\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.8415	−	14.4157i	−0.942697	−	0.684909i	0.00637170	−	0.999980i	$-0.497972\pi$
$443$	−19.8415	−	14.4157i	−0.942697	−	0.684909i	−0.949068	+	0.315071i	$0.897972\pi$
$444$		0			0
$445$	−5.62868	+	17.3233i	−0.266825	+	0.821203i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.89483	−	8.90937i	−0.136616	−	0.420459i	0.859222	−	0.511602i	$-0.170948\pi$
$449$	−2.89483	−	8.90937i	−0.136616	−	0.420459i	−0.995838	+	0.0911431i	$0.970948\pi$
$450$		0			0
$451$	−30.2254	−	2.31838i	−1.42326	−	0.109168i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.482472	+	0.350536i	−0.0226186	+	0.0164334i
$456$		0			0
$457$	7.50000	−	23.0826i	0.350835	−	1.07976i	−0.607550	−	0.794281i	$-0.707848\pi$
$457$	7.50000	−	23.0826i	0.350835	−	1.07976i	0.958385	−	0.285478i	$-0.0921524\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	27.0517			1.25992			0.629961	−	0.776627i	$-0.283071\pi$
$461$	27.0517			1.25992			0.629961	+	0.776627i	$0.283071\pi$
$462$		0			0
$463$	−32.5623			−1.51330			−0.756649	−	0.653821i	$-0.773165\pi$
$463$	−32.5623			−1.51330			−0.756649	+	0.653821i	$0.773165\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.01718	+	12.3636i	−0.185893	+	0.572119i	−0.999963	−	0.00864799i	$-0.997247\pi$
$467$	−4.01718	+	12.3636i	−0.185893	+	0.572119i	0.814070	+	0.580767i	$0.197247\pi$
$468$		0			0
$469$	−3.50000	+	2.54290i	−0.161615	+	0.117420i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.47332	+	5.21564i	−0.389604	+	0.239815i
$474$		0			0
$475$	1.64590	+	5.06555i	0.0755190	+	0.232424i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.482472	−	1.48490i	0.0220447	−	0.0678466i	−0.939429	−	0.342744i	$-0.888644\pi$
$479$	0.482472	−	1.48490i	0.0220447	−	0.0678466i	0.961474	+	0.274897i	$0.0886438\pi$
$480$		0			0
$481$	−1.28115	−	0.930812i	−0.0584155	−	0.0424414i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−29.2093			−1.32633
$486$		0			0
$487$	−1.42705	−	1.03681i	−0.0646659	−	0.0469825i	0.554983	−	0.831862i	$-0.312725\pi$
$487$	−1.42705	−	1.03681i	−0.0646659	−	0.0469825i	−0.619649	+	0.784879i	$0.712725\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−23.6308	+	17.1688i	−1.06645	+	0.774818i	−0.975270	−	0.221017i	$-0.929062\pi$
$491$	−23.6308	+	17.1688i	−1.06645	+	0.774818i	−0.0911754	+	0.995835i	$0.529062\pi$
$492$		0			0
$493$	−6.38197	−	19.6417i	−0.287429	−	0.884616i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.30691	+	10.1776i	0.148335	+	0.456529i
$498$		0			0
$499$	−7.73607	+	5.62058i	−0.346314	+	0.251612i	−0.747321	−	0.664463i	$-0.768660\pi$
$499$	−7.73607	+	5.62058i	−0.346314	+	0.251612i	0.401007	+	0.916075i	$0.368660\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	36.1917	+	26.2948i	1.61371	+	1.17243i	0.849799	+	0.527106i	$0.176723\pi$
$503$	36.1917	+	26.2948i	1.61371	+	1.17243i	0.763910	+	0.645322i	$0.223277\pi$
$504$		0			0
$505$	18.2148			0.810547
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.0521	−	11.6625i	−0.711496	−	0.516932i	0.172160	−	0.985069i	$-0.444925\pi$
$509$	−16.0521	−	11.6625i	−0.711496	−	0.516932i	−0.883656	+	0.468137i	$0.844925\pi$
$510$		0			0
$511$	4.47214	−	13.7638i	0.197836	−	0.608876i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.4736	+	32.2344i	0.461522	+	1.42042i
$516$		0			0
$517$	32.1976	+	2.46965i	1.41605	+	0.108615i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.14008	−	6.64066i	0.400434	−	0.290932i	−0.369284	−	0.929317i	$-0.620397\pi$
$521$	9.14008	−	6.64066i	0.400434	−	0.290932i	0.769718	+	0.638384i	$0.220397\pi$
$522$		0			0
$523$	−8.97214	+	27.6134i	−0.392324	+	1.20745i	0.538702	+	0.842496i	$0.318915\pi$
$523$	−8.97214	+	27.6134i	−0.392324	+	1.20745i	−0.931026	+	0.364953i	$0.881085\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−45.3318			−1.97468
$528$		0			0
$529$	−22.0689			−0.959517
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.666760	−	2.05208i	0.0288806	−	0.0888852i
$534$		0			0
$535$	25.0623	−	18.2088i	1.08354	−	0.787236i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.68393	−	19.3407i	−0.201751	−	0.833061i
$540$		0			0
$541$	−3.66312	−	11.2739i	−0.157490	−	0.484704i	0.840915	−	0.541167i	$-0.182017\pi$
$541$	−3.66312	−	11.2739i	−0.157490	−	0.484704i	−0.998405	+	0.0564637i	$0.982017\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.1926	+	43.6803i	−0.607944	+	1.87106i
$546$		0			0
$547$	20.4894	+	14.8864i	0.876062	+	0.636496i	0.932207	−	0.361927i	$-0.117881\pi$
$547$	20.4894	+	14.8864i	0.876062	+	0.636496i	−0.0561450	+	0.998423i	$0.517881\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.0349			0.512704
$552$		0			0
$553$	0.572949	+	0.416272i	0.0243643	+	0.0177017i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−23.4466	+	17.0349i	−0.993463	+	0.721793i	−0.960677	−	0.277669i	$-0.910438\pi$
$557$	−23.4466	+	17.0349i	−0.993463	+	0.721793i	−0.0327861	+	0.999462i	$0.510438\pi$
$558$		0			0
$559$	−0.218847	−	0.673542i	−0.00925624	−	0.0284878i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.0703917	−	0.216643i	−0.00296666	−	0.00913043i	0.949562	−	0.313579i	$-0.101528\pi$
$563$	−0.0703917	−	0.216643i	−0.00296666	−	0.00913043i	−0.952529	+	0.304448i	$0.901528\pi$
$564$		0			0
$565$	−25.0623	+	18.2088i	−1.05438	+	0.766051i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.7188	+	12.1470i	0.700890	+	0.509227i	0.880222	−	0.474562i	$-0.157394\pi$
$569$	16.7188	+	12.1470i	0.700890	+	0.509227i	−0.179332	+	0.983789i	$0.557394\pi$
$570$		0			0
$571$	−25.9230			−1.08484			−0.542422	−	0.840106i	$-0.682492\pi$
$571$	−25.9230			−1.08484			−0.542422	+	0.840106i	$0.682492\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.07884	−	0.783823i	−0.0449907	−	0.0326877i
$576$		0			0
$577$	−6.85410	+	21.0948i	−0.285340	+	0.878186i	0.700957	+	0.713204i	$0.252757\pi$
$577$	−6.85410	+	21.0948i	−0.285340	+	0.878186i	−0.986297	+	0.164982i	$0.947243\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.85950	+	5.72294i	0.0771449	+	0.237428i
$582$		0			0
$583$	3.94427	+	3.35520i	0.163355	+	0.138958i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.6047	+	10.6109i	−0.602799	+	0.437959i	−0.846871	−	0.531798i	$-0.821517\pi$
$587$	−14.6047	+	10.6109i	−0.602799	+	0.437959i	0.244072	+	0.969757i	$0.421517\pi$
$588$		0			0
$589$	8.16312	−	25.1235i	0.336355	−	1.03520i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.78910			−0.0734697			−0.0367348	−	0.999325i	$-0.511696\pi$
$593$	−1.78910			−0.0734697			−0.0367348	+	0.999325i	$0.511696\pi$
$594$		0			0
$595$	16.7082			0.684970
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$599$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$600$		0			0
$601$	10.0451	−	7.29818i	0.409748	−	0.297699i	−0.363752	−	0.931496i	$-0.618504\pi$
$601$	10.0451	−	7.29818i	0.409748	−	0.297699i	0.773500	+	0.633797i	$0.218504\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	19.7276	+	19.5714i	0.802040	+	0.795692i
$606$		0			0
$607$	−1.77051	−	5.44907i	−0.0718628	−	0.221171i	0.908674	−	0.417506i	$-0.137096\pi$
$607$	−1.77051	−	5.44907i	−0.0718628	−	0.221171i	−0.980537	+	0.196335i	$0.937096\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.710264	+	2.18597i	−0.0287342	+	0.0884348i
$612$		0			0
$613$	29.7984	+	21.6498i	1.20354	+	0.874427i	0.994629	−	0.103507i	$-0.0330064\pi$
$613$	29.7984	+	21.6498i	1.20354	+	0.874427i	0.208916	+	0.977934i	$0.433006\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−33.6655			−1.35532			−0.677661	−	0.735375i	$-0.737006\pi$
$617$	−33.6655			−1.35532			−0.677661	+	0.735375i	$0.737006\pi$
$618$		0			0
$619$	28.9336	+	21.0215i	1.16294	+	0.844926i	0.990147	−	0.140032i	$-0.0447206\pi$
$619$	28.9336	+	21.0215i	1.16294	+	0.844926i	0.172794	+	0.984958i	$0.444721\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5.83317	+	4.23804i	−0.233701	+	0.169794i
$624$		0			0
$625$	−9.27051	−	28.5317i	−0.370820	−	1.14127i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	13.7101	+	42.1954i	0.546658	+	1.68244i
$630$		0			0
$631$	10.8713	−	7.89848i	0.432781	−	0.314433i	−0.349979	−	0.936757i	$-0.613811\pi$
$631$	10.8713	−	7.89848i	0.432781	−	0.314433i	0.782760	+	0.622324i	$0.213811\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−33.0691	−	24.0261i	−1.31231	−	0.953447i
$636$		0			0
$637$	1.41641			0.0561201
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.2714	+	11.0953i	0.603185	+	0.438240i	0.847008	−	0.531580i	$-0.178402\pi$
$641$	15.2714	+	11.0953i	0.603185	+	0.438240i	−0.243823	+	0.969820i	$0.578402\pi$
$642$		0			0
$643$	14.2082	−	43.7284i	0.560317	−	1.72448i	−0.121155	−	0.992634i	$-0.538660\pi$
$643$	14.2082	−	43.7284i	0.560317	−	1.72448i	0.681472	−	0.731844i	$-0.261340\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.113896	−	0.350536i	−0.00447772	−	0.0137810i	0.948793	−	0.315899i	$-0.102306\pi$
$647$	−0.113896	−	0.350536i	−0.00447772	−	0.0137810i	−0.953270	+	0.302118i	$0.902306\pi$
$648$		0			0
$649$	−13.5172	+	32.8177i	−0.530597	+	1.28821i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.0695	+	16.0345i	−0.863648	+	0.627477i	−0.928875	−	0.370394i	$-0.879223\pi$
$653$	−22.0695	+	16.0345i	−0.863648	+	0.627477i	0.0652271	+	0.997870i	$0.479223\pi$
$654$		0			0
$655$	−6.66970	+	20.5272i	−0.260607	+	0.802065i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.0349			0.468813			0.234407	−	0.972139i	$-0.424685\pi$
$659$	12.0349			0.468813			0.234407	+	0.972139i	$0.424685\pi$
$660$		0			0
$661$	−3.90983			−0.152075			−0.0760374	−	0.997105i	$-0.524227\pi$
$661$	−3.90983			−0.152075			−0.0760374	+	0.997105i	$0.524227\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.00873	+	9.25991i	−0.116673	+	0.359084i
$666$		0			0
$667$	−2.43769	+	1.77109i	−0.0943879	+	0.0685768i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.710264	+	2.93278i	0.0274194	+	0.113219i
$672$		0			0
$673$	3.12868	+	9.62908i	0.120602	+	0.371174i	0.993074	−	0.117490i	$-0.0374847\pi$
$673$	3.12868	+	9.62908i	0.120602	+	0.371174i	−0.872472	+	0.488663i	$0.837485\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.12262	−	9.61045i	0.120012	−	0.369359i	−0.872947	−	0.487815i	$-0.837794\pi$
$677$	3.12262	−	9.61045i	0.120012	−	0.369359i	0.992959	+	0.118455i	$0.0377942\pi$
$678$		0			0
$679$	−9.35410	−	6.79615i	−0.358977	−	0.260812i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.5781			0.634342			0.317171	−	0.948368i	$-0.397267\pi$
$683$	16.5781			0.634342			0.317171	+	0.948368i	$0.397267\pi$
$684$		0			0
$685$	−31.4443	−	22.8456i	−1.20142	−	0.872886i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.298184	+	0.216643i	−0.0113599	+	0.00825345i
$690$		0			0
$691$	−10.2918	−	31.6749i	−0.391518	−	1.20497i	−0.931640	−	0.363383i	$-0.881622\pi$
$691$	−10.2918	−	31.6749i	−0.391518	−	1.20497i	0.540122	−	0.841587i	$-0.318378\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.2624	−	31.5845i	−0.389276	−	1.19807i
$696$		0			0
$697$	−48.9058	+	35.5321i	−1.85244	+	1.34587i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.3941	−	13.3641i	−0.694734	−	0.504754i	0.183479	−	0.983024i	$-0.441264\pi$
$701$	−18.3941	−	13.3641i	−0.694734	−	0.504754i	−0.878213	+	0.478270i	$0.841264\pi$
$702$		0			0
$703$	−25.8541			−0.975106
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.83317	+	4.23804i	0.219379	+	0.159388i
$708$		0			0
$709$	7.00658	−	21.5640i	0.263138	−	0.809854i	−0.728979	−	0.684536i	$-0.760005\pi$
$709$	7.00658	−	21.5640i	0.263138	−	0.809854i	0.992117	−	0.125318i	$-0.0399951\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.04378	+	6.29012i	0.0765403	+	0.235567i
$714$		0			0
$715$	−1.68441	+	1.03681i	−0.0629932	+	0.0387746i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.92073	+	7.20783i	−0.369981	+	0.268807i	−0.757203	−	0.653180i	$-0.773435\pi$
$719$	−9.92073	+	7.20783i	−0.369981	+	0.268807i	0.387222	+	0.921986i	$0.373435\pi$
$720$		0			0
$721$	−4.14590	+	12.7598i	−0.154401	+	0.475198i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.31536			0.160268
$726$		0			0
$727$	−13.4377			−0.498376			−0.249188	−	0.968455i	$-0.580164\pi$
$727$	−13.4377			−0.498376			−0.249188	+	0.968455i	$0.580164\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.13135	+	18.8704i	−0.226776	+	0.697945i
$732$		0			0
$733$	9.47214	−	6.88191i	0.349861	−	0.254189i	−0.398950	−	0.916973i	$-0.630625\pi$
$733$	9.47214	−	6.88191i	0.349861	−	0.254189i	0.748811	+	0.662784i	$0.230625\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.2192	+	7.52136i	−0.450100	+	0.277053i
$738$		0			0
$739$	4.89261	+	15.0579i	0.179978	+	0.553914i	0.999826	−	0.0186670i	$-0.00594224\pi$
$739$	4.89261	+	15.0579i	0.179978	+	0.553914i	−0.819848	+	0.572581i	$0.805942\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.8243	−	48.7022i	0.580537	−	1.78671i	−0.0359618	−	0.999353i	$-0.511449\pi$
$743$	15.8243	−	48.7022i	0.580537	−	1.78671i	0.616499	−	0.787356i	$-0.288551\pi$
$744$		0			0
$745$	21.1180	+	15.3431i	0.773705	+	0.562130i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	12.2627			0.448069
$750$		0			0
$751$	28.9164	+	21.0090i	1.05517	+	0.766629i	0.973190	−	0.230004i	$-0.0738740\pi$
$751$	28.9164	+	21.0090i	1.05517	+	0.766629i	0.0819851	+	0.996634i	$0.473874\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	43.1741	−	31.3678i	1.57127	−	1.14159i
$756$		0			0
$757$	−10.3435	−	31.8339i	−0.375939	−	1.15702i	−0.942843	−	0.333238i	$-0.891859\pi$
$757$	−10.3435	−	31.8339i	−0.375939	−	1.15702i	0.566903	−	0.823784i	$-0.308141\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.54343	+	20.1386i	0.237199	+	0.730024i	0.996822	+	0.0796602i	$0.0253835\pi$
$761$	6.54343	+	20.1386i	0.237199	+	0.730024i	−0.759623	+	0.650364i	$0.774616\pi$
$762$		0			0
$763$	−14.7082	+	10.6861i	−0.532473	+	0.386864i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.04378	−	1.48490i	−0.0737967	−	0.0536165i
$768$		0			0
$769$	7.85410			0.283226			0.141613	−	0.989922i	$-0.454771\pi$
$769$	7.85410			0.283226			0.141613	+	0.989922i	$0.454771\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	31.3235	+	22.7579i	1.12663	+	0.818543i	0.985201	−	0.171405i	$-0.0548307\pi$
$773$	31.3235	+	22.7579i	1.12663	+	0.818543i	0.141428	+	0.989949i	$0.454831\pi$
$774$		0			0
$775$	2.92705	−	9.00854i	0.105143	−	0.323596i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.8857	−	33.5027i	−0.390020	−	1.20036i
$780$		0			0
$781$	8.35410	+	34.4953i	0.298933	+	1.23434i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.68393	−	3.40308i	0.167177	−	0.121461i
$786$		0			0
$787$	12.5836	−	38.7283i	0.448557	−	1.38052i	−0.429979	−	0.902839i	$-0.641479\pi$
$787$	12.5836	−	38.7283i	0.448557	−	1.38052i	0.878536	−	0.477677i	$-0.158521\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.2627			−0.436011
$792$		0			0
$793$	−0.214782			−0.00762712
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.824160	−	2.53650i	0.0291933	−	0.0898476i	−0.935398	−	0.353596i	$-0.884959\pi$
$797$	0.824160	−	2.53650i	0.0291933	−	0.0898476i	0.964592	+	0.263748i	$0.0849588\pi$
$798$		0			0
$799$	52.0967	−	37.8505i	1.84305	−	1.33905i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	18.2802	−	44.3814i	0.645093	−	1.56618i
$804$		0			0
$805$	−0.753289	−	2.31838i	−0.0265499	−	0.0817123i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.6748	−	39.0090i	0.445622	−	1.37148i	−0.436179	−	0.899860i	$-0.643669\pi$
$809$	12.6748	−	39.0090i	0.445622	−	1.37148i	0.881801	−	0.471622i	$-0.156331\pi$
$810$		0			0
$811$	43.5238	+	31.6219i	1.52833	+	1.11039i	0.957159	+	0.289561i	$0.0935095\pi$
$811$	43.5238	+	31.6219i	1.52833	+	1.11039i	0.571168	+	0.820833i	$0.306491\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−36.3325			−1.27267
$816$		0			0
$817$	−9.35410	−	6.79615i	−0.327259	−	0.237767i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	29.7622	−	21.6235i	1.03871	−	0.754666i	0.0686751	−	0.997639i	$-0.478123\pi$
$821$	29.7622	−	21.6235i	1.03871	−	0.754666i	0.970033	+	0.242974i	$0.0781228\pi$
$822$		0			0
$823$	7.30902	+	22.4948i	0.254776	+	0.784121i	0.993874	+	0.110522i	$0.0352523\pi$
$823$	7.30902	+	22.4948i	0.254776	+	0.784121i	−0.739097	+	0.673599i	$0.764748\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.54371	−	26.2948i	−0.297094	−	0.914361i	−0.982510	−	0.186209i	$-0.940380\pi$
$827$	−8.54371	−	26.2948i	−0.297094	−	0.914361i	0.685416	−	0.728152i	$-0.259620\pi$
$828$		0			0
$829$	5.01722	−	3.64522i	0.174255	−	0.126604i	−0.497239	−	0.867614i	$-0.665653\pi$
$829$	5.01722	−	3.64522i	0.174255	−	0.126604i	0.671494	+	0.741010i	$0.265653\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−32.1042	−	23.3250i	−1.11234	−	0.808165i
$834$		0			0
$835$	−55.5755			−1.92327
$836$		0			0
$837$		0			0
$838$		0			0
$839$	36.9724	+	26.8620i	1.27643	+	0.927380i	0.999439	−	0.0334932i	$-0.0106632\pi$
$839$	36.9724	+	26.8620i	1.27643	+	0.927380i	0.276990	+	0.960873i	$0.410663\pi$
$840$		0			0
$841$	−5.94834	+	18.3071i	−0.205115	+	0.631279i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.1050	+	31.1001i	0.347623	+	1.06987i
$846$		0			0
$847$	1.76393	+	10.8576i	0.0606094	+	0.373073i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.23680	−	3.80476i	0.179515	−	0.130425i
$852$		0			0
$853$	10.2533	−	31.5564i	0.351066	−	1.08047i	−0.607190	−	0.794557i	$-0.707703\pi$
$853$	10.2533	−	31.5564i	0.351066	−	1.08047i	0.958256	−	0.285913i	$-0.0922968\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.2976			0.829991			0.414995	−	0.909824i	$-0.363783\pi$
$857$	24.2976			0.829991			0.414995	+	0.909824i	$0.363783\pi$
$858$		0			0
$859$	−19.6525			−0.670534			−0.335267	−	0.942123i	$-0.608826\pi$
$859$	−19.6525			−0.670534			−0.335267	+	0.942123i	$0.608826\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	12.4905	−	38.4418i	0.425181	−	1.30857i	−0.477639	−	0.878556i	$-0.658507\pi$
$863$	12.4905	−	38.4418i	0.425181	−	1.30857i	0.902821	−	0.430018i	$-0.141493\pi$
$864$		0			0
$865$	19.4336	−	14.1194i	0.660763	−	0.480073i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.78910	+	1.52190i	0.0606912	+	0.0516270i
$870$		0			0
$871$	−0.315595	−	0.971301i	−0.0106935	−	0.0329113i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.82444	−	8.69273i	0.0954835	−	0.293868i
$876$		0			0
$877$	28.1353	+	20.4415i	0.950060	+	0.690259i	0.950821	−	0.309741i	$-0.100242\pi$
$877$	28.1353	+	20.4415i	0.950060	+	0.690259i	−0.000761020		1.00000i	$0.500242\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.9817			0.538437			0.269218	−	0.963079i	$-0.413235\pi$
$881$	15.9817			0.538437			0.269218	+	0.963079i	$0.413235\pi$
$882$		0			0
$883$	−12.0000	−	8.71851i	−0.403832	−	0.293401i	0.367268	−	0.930115i	$-0.380293\pi$
$883$	−12.0000	−	8.71851i	−0.403832	−	0.293401i	−0.771100	+	0.636714i	$0.780293\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.4820	+	8.34219i	−0.385529	+	0.280103i	−0.763621	−	0.645665i	$-0.776580\pi$
$887$	−11.4820	+	8.34219i	−0.385529	+	0.280103i	0.378092	+	0.925768i	$0.376580\pi$
$888$		0			0
$889$	−5.00000	−	15.3884i	−0.167695	−	0.516111i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11.5959	+	35.6886i	0.388043	+	1.19427i
$894$		0			0
$895$	−31.4443	+	22.8456i	−1.05107	+	0.763644i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−17.3152	−	12.5802i	−0.577495	−	0.419574i
$900$		0			0
$901$	10.3262			0.344017
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−33.1830	−	24.1089i	−1.10304	−	0.801406i
$906$		0			0
$907$	0.225425	−	0.693786i	0.00748511	−	0.0230368i	−0.947244	−	0.320513i	$-0.896145\pi$
$907$	0.225425	−	0.693786i	0.00748511	−	0.0230368i	0.954729	+	0.297476i	$0.0961448\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.5609	−	38.6584i	−0.416161	−	1.28081i	−0.911209	−	0.411945i	$-0.864850\pi$
$911$	−12.5609	−	38.6584i	−0.416161	−	1.28081i	0.495048	−	0.868866i	$-0.335150\pi$
$912$		0			0
$913$	4.69756	+	19.3969i	0.155467	+	0.641944i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.91201	+	5.02187i	−0.228255	+	0.165837i
$918$		0			0
$919$	−16.6353	+	51.1981i	−0.548746	+	1.68887i	0.163165	+	0.986599i	$0.447830\pi$
$919$	−16.6353	+	51.1981i	−0.548746	+	1.68887i	−0.711912	+	0.702269i	$0.752170\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.52626			−0.0831527
$924$		0			0
$925$	−9.27051			−0.304812
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.3331	−	37.9574i	0.404636	−	1.24534i	−0.516563	−	0.856249i	$-0.672789\pi$
$929$	12.3331	−	37.9574i	0.404636	−	1.24534i	0.921199	−	0.389092i	$-0.127211\pi$
$930$		0			0
$931$	18.7082	−	13.5923i	0.613137	−	0.445470i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	55.2525	+	4.23804i	1.80695	+	0.138599i
$936$		0			0
$937$	−13.6353	−	41.9650i	−0.445444	−	1.37094i	−0.881996	−	0.471257i	$-0.843800\pi$
$937$	−13.6353	−	41.9650i	−0.445444	−	1.37094i	0.436551	−	0.899679i	$-0.356200\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.83289	−	11.7964i	0.124949	−	0.384552i	−0.868943	−	0.494912i	$-0.835200\pi$
$941$	3.83289	−	11.7964i	0.124949	−	0.384552i	0.993892	+	0.110360i	$0.0352003\pi$
$942$		0			0
$943$	7.13525	+	5.18407i	0.232356	+	0.168816i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.7014			0.347748			0.173874	−	0.984768i	$-0.444371\pi$
$947$	10.7014			0.347748			0.173874	+	0.984768i	$0.444371\pi$
$948$		0			0
$949$	2.76393	+	2.00811i	0.0897210	+	0.0651861i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−23.9290	+	17.3855i	−0.775137	+	0.563170i	−0.903516	−	0.428555i	$-0.859023\pi$
$953$	−23.9290	+	17.3855i	−0.775137	+	0.563170i	0.128378	+	0.991725i	$0.459023\pi$
$954$		0			0
$955$	−18.3926	−	56.6066i	−0.595171	−	1.83175i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.75433	−	14.6323i	−0.153525	−	0.472502i
$960$		0			0
$961$	−12.9271	+	9.39205i	−0.417002	+	0.302969i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.7798	+	16.5505i	0.733308	+	0.532779i
$966$		0			0
$967$	−57.5623			−1.85108			−0.925539	−	0.378651i	$-0.876388\pi$
$967$	−57.5623			−1.85108			−0.925539	+	0.378651i	$0.876388\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−20.4378	−	14.8490i	−0.655881	−	0.476526i	0.209388	−	0.977833i	$-0.432853\pi$
$971$	−20.4378	−	14.8490i	−0.655881	−	0.476526i	−0.865270	+	0.501307i	$0.832853\pi$
$972$		0			0
$973$	4.06231	−	12.5025i	0.130232	−	0.400811i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.50837	+	23.1084i	0.240214	+	0.739303i	0.996387	+	0.0849311i	$0.0270670\pi$
$977$	7.50837	+	23.1084i	0.240214	+	0.739303i	−0.756173	+	0.654372i	$0.772933\pi$
$978$		0			0
$979$	−20.3647	+	12.5352i	−0.650860	+	0.400628i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.57877	−	5.50630i	0.241725	−	0.175624i	−0.460326	−	0.887750i	$-0.652268\pi$
$983$	7.57877	−	5.50630i	0.241725	−	0.175624i	0.702051	+	0.712126i	$0.252268\pi$
$984$		0			0
$985$	20.3647	−	62.6762i	0.648875	−	1.99703i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.89483			0.0920503
$990$		0			0
$991$	−20.3951			−0.647872			−0.323936	−	0.946079i	$-0.605006\pi$
$991$	−20.3951			−0.647872			−0.323936	+	0.946079i	$0.605006\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.30691	+	10.1776i	−0.104836	+	0.322652i
$996$		0			0
$997$	−9.73607	+	7.07367i	−0.308344	+	0.224025i	−0.731186	−	0.682178i	$-0.761033\pi$
$997$	−9.73607	+	7.07367i	−0.308344	+	0.224025i	0.422841	+	0.906204i	$0.361033\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.j.d.181.1	✓	8
3.2	odd	2	inner	396.2.j.d.181.2	yes	8
11.3	even	5		4356.2.a.z.1.2		4
11.8	odd	10		4356.2.a.x.1.2		4
11.9	even	5	inner	396.2.j.d.361.1	yes	8
33.8	even	10		4356.2.a.x.1.3		4
33.14	odd	10		4356.2.a.z.1.3		4
33.20	odd	10	inner	396.2.j.d.361.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.j.d.181.1	✓	8	1.1	even	1	trivial
396.2.j.d.181.2	yes	8	3.2	odd	2	inner
396.2.j.d.361.1	yes	8	11.9	even	5	inner
396.2.j.d.361.2	yes	8	33.20	odd	10	inner
4356.2.a.x.1.2		4	11.8	odd	10
4356.2.a.x.1.3		4	33.8	even	10
4356.2.a.z.1.2		4	11.3	even	5
4356.2.a.z.1.3		4	33.14	odd	10

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780656 + 2.40261i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-2.82444 + 1.73855i) q^{11} +(-0.0729490 - 0.224514i) q^{13} +(-2.04378 + 6.29012i) q^{17} +(-3.11803 - 2.26538i) q^{19} +0.964944 q^{23} +(-1.11803 - 0.812299i) q^{25} +(-2.52626 + 1.83543i) q^{29} +(2.11803 + 6.51864i) q^{31} +(-0.780656 - 2.40261i) q^{35} +(5.42705 - 3.94298i) q^{37} +(7.39448 + 5.37240i) q^{41} +3.00000 q^{43} +(-7.87695 - 5.72294i) q^{47} +(-1.85410 + 5.70634i) q^{49} +(-0.482472 - 1.48490i) q^{53} +(-1.97214 - 8.14324i) q^{55} +(8.65761 - 6.29012i) q^{59} +(0.281153 - 0.865300i) q^{61} +0.596368 q^{65} +4.32624 q^{67} +(3.30691 - 10.1776i) q^{71} +(-11.7082 + 8.50651i) q^{73} +(1.26313 - 3.06668i) q^{77} +(-0.218847 - 0.673542i) q^{79} +(1.85950 - 5.72294i) q^{83} +(-13.5172 - 9.82084i) q^{85} +7.21019 q^{89} +(0.190983 + 0.138757i) q^{91} +(7.87695 - 5.72294i) q^{95} +(3.57295 + 10.9964i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{7} - 14 q^{13} - 16 q^{19} + 8 q^{31} + 30 q^{37} + 24 q^{43} + 12 q^{49} + 20 q^{55} - 38 q^{61} - 28 q^{67} - 40 q^{73} - 42 q^{79} - 50 q^{85} + 6 q^{91} + 42 q^{97}+O(q^{100}) \) 8 * q - 2 * q^7 - 14 * q^13 - 16 * q^19 + 8 * q^31 + 30 * q^37 + 24 * q^43 + 12 * q^49 + 20 * q^55 - 38 * q^61 - 28 * q^67 - 40 * q^73 - 42 * q^79 - 50 * q^85 + 6 * q^91 + 42 * q^97

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