LMFDB - Embedded newform 315.3.e.d.244.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,3,Mod(244,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.244"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-32,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 76 x^{14} + 336 x^{13} + 2593 x^{12} - 8066 x^{11} - 46400 x^{10} + 130882 x^{9} + \cdots + 31397100 $ x^16 - 4x^15 - 76x^14 + 336x^13 + 2593x^12 - 8066x^11 - 46400x^10 + 130882x^9 + 482347x^8 - 1462818x^7 - 443896x^6 - 16494592x^5 - 6620606x^4 + 183639960x^3 + 285498360x^2 + 87465000*x + 31397100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{22}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			244.13
Root			$3.96507 + 0.339479i$ of defining polynomial
Character	$\chi$	$=$	315.244
Dual form			315.3.e.d.244.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.25309i q^{2} -6.58258 q^{4} +(-4.09772 - 2.86509i) q^{5} +(2.45837 - 6.55412i) q^{7} -8.40134i q^{8} +(9.32037 - 13.3302i) q^{10} -11.2474 q^{11} +23.5575 q^{13} +(21.3211 + 7.99728i) q^{14} +1.00000 q^{16} +22.8758 q^{17} -21.0961i q^{19} +(26.9735 + 18.8596i) q^{20} -36.5888i q^{22} +1.35792i q^{23} +(8.58258 + 23.4806i) q^{25} +76.6345i q^{26} +(-16.1824 + 43.1430i) q^{28} +31.3948 q^{29} -26.6605i q^{31} -30.3523i q^{32} +74.4170i q^{34} +(-28.8518 + 19.8135i) q^{35} -49.6971i q^{37} +68.6275 q^{38} +(-24.0706 + 34.4263i) q^{40} -44.6454i q^{41} +15.8441i q^{43} +74.0370 q^{44} -4.41742 q^{46} -63.8530 q^{47} +(-36.9129 - 32.2248i) q^{49} +(-76.3845 + 27.9199i) q^{50} -155.069 q^{52} +34.9633i q^{53} +(46.0888 + 32.2248i) q^{55} +(-55.0634 - 20.6536i) q^{56} +102.130i q^{58} -79.9728i q^{59} +47.7566i q^{61} +86.7288 q^{62} +102.739 q^{64} +(-96.5319 - 67.4942i) q^{65} -15.8441i q^{67} -150.582 q^{68} +(-64.4550 - 93.8574i) q^{70} +47.3372 q^{71} +30.5266 q^{73} +161.669 q^{74} +138.867i q^{76} +(-27.6503 + 73.7169i) q^{77} +35.4955 q^{79} +(-4.09772 - 2.86509i) q^{80} +145.235 q^{82} -9.54892 q^{83} +(-93.7386 - 65.5412i) q^{85} -51.5422 q^{86} +94.4935i q^{88} +37.9689i q^{89} +(57.9129 - 154.398i) q^{91} -8.93860i q^{92} -207.719i q^{94} +(-60.4421 + 86.4459i) q^{95} +91.1513 q^{97} +(104.830 - 120.081i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 16 q^{16} + 64 q^{25} - 144 q^{46} - 224 q^{49} + 544 q^{64} + 128 q^{79} - 400 q^{85} + 560 q^{91}+O(q^{100}) $ 16 * q - 32 * q^4 + 16 * q^16 + 64 * q^25 - 144 * q^46 - 224 * q^49 + 544 * q^64 + 128 * q^79 - 400 * q^85 + 560 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			3.25309i			1.62654i	0.581884	+	0.813272i	$0.302316\pi$
$2$			3.25309i			1.62654i	−0.581884	+	0.813272i	$0.697684\pi$
$3$		0			0
$3$		0			0
$4$	−6.58258			−1.64564
$5$	−4.09772	−	2.86509i	−0.819543	−	0.573017i
$5$	−4.09772	−	2.86509i	−0.819543	−	0.573017i
$6$		0			0
$7$	2.45837	−	6.55412i	0.351195	−	0.936302i
$7$	2.45837	−	6.55412i	0.351195	−	0.936302i
$8$		−	8.40134i		−	1.05017i
$9$		0			0
$10$	9.32037	−	13.3302i	0.932037	−	1.33302i
$11$	−11.2474			−1.02249			−0.511247	−	0.859434i	$-0.670816\pi$
$11$	−11.2474			−1.02249			−0.511247	+	0.859434i	$0.670816\pi$
$12$		0			0
$13$	23.5575			1.81211			0.906057	−	0.423156i	$-0.139078\pi$
$13$	23.5575			1.81211			0.906057	+	0.423156i	$0.139078\pi$
$14$	21.3211	+	7.99728i	1.52294	+	0.571234i
$15$		0			0
$16$	1.00000			0.0625000
$17$	22.8758			1.34564			0.672818	−	0.739808i	$-0.265084\pi$
$17$	22.8758			1.34564			0.672818	+	0.739808i	$0.265084\pi$
$18$		0			0
$19$		−	21.0961i		−	1.11032i	−0.831743	−	0.555161i	$-0.812657\pi$
$19$		−	21.0961i		−	1.11032i	0.831743	−	0.555161i	$-0.187343\pi$
$20$	26.9735	+	18.8596i	1.34868	+	0.942982i
$21$		0			0
$22$		−	36.5888i		−	1.66313i
$23$			1.35792i			0.0590399i	0.999564	+	0.0295199i	$0.00939786\pi$
$23$			1.35792i			0.0590399i	−0.999564	+	0.0295199i	$0.990602\pi$
$24$		0			0
$25$	8.58258	+	23.4806i	0.343303	+	0.939225i
$26$			76.6345i			2.94748i
$27$		0			0
$28$	−16.1824	+	43.1430i	−0.577942	+	1.54082i
$29$	31.3948			1.08258			0.541290	−	0.840836i	$-0.317936\pi$
$29$	31.3948			1.08258			0.541290	+	0.840836i	$0.317936\pi$
$30$		0			0
$31$		−	26.6605i		−	0.860015i	−0.902825	−	0.430007i	$-0.858511\pi$
$31$		−	26.6605i		−	0.860015i	0.902825	−	0.430007i	$-0.141489\pi$
$32$		−	30.3523i		−	0.948509i
$33$		0			0
$34$			74.4170i			2.18874i
$35$	−28.8518	+	19.8135i	−0.824337	+	0.566100i
$36$		0			0
$37$		−	49.6971i		−	1.34316i	−0.740930	−	0.671582i	$-0.765615\pi$
$37$		−	49.6971i		−	1.34316i	0.740930	−	0.671582i	$-0.234385\pi$
$38$	68.6275			1.80599
$39$		0			0
$40$	−24.0706	+	34.4263i	−0.601764	+	0.860658i
$41$		−	44.6454i		−	1.08891i	−0.838789	−	0.544456i	$-0.816736\pi$
$41$		−	44.6454i		−	1.08891i	0.838789	−	0.544456i	$-0.183264\pi$
$42$		0			0
$43$			15.8441i			0.368467i	0.982883	+	0.184233i	$0.0589803\pi$
$43$			15.8441i			0.368467i	−0.982883	+	0.184233i	$0.941020\pi$
$44$	74.0370			1.68266
$45$		0			0
$46$	−4.41742			−0.0960310
$47$	−63.8530			−1.35857			−0.679287	−	0.733873i	$-0.737711\pi$
$47$	−63.8530			−1.35857			−0.679287	+	0.733873i	$0.737711\pi$
$48$		0			0
$49$	−36.9129	−	32.2248i	−0.753324	−	0.657650i
$50$	−76.3845	+	27.9199i	−1.52769	+	0.558397i
$51$		0			0
$52$	−155.069			−2.98209
$53$			34.9633i			0.659685i	0.944036	+	0.329842i	$0.106996\pi$
$53$			34.9633i			0.659685i	−0.944036	+	0.329842i	$0.893004\pi$
$54$		0			0
$55$	46.0888	+	32.2248i	0.837978	+	0.585906i
$56$	−55.0634	−	20.6536i	−0.983275	−	0.368814i
$57$		0			0
$58$			102.130i			1.76086i
$59$		−	79.9728i		−	1.35547i	−0.735306	−	0.677735i	$-0.762962\pi$
$59$		−	79.9728i		−	1.35547i	0.735306	−	0.677735i	$-0.237038\pi$
$60$		0			0
$61$			47.7566i			0.782894i	0.920201	+	0.391447i	$0.128025\pi$
$61$			47.7566i			0.782894i	−0.920201	+	0.391447i	$0.871975\pi$
$62$	86.7288			1.39885
$63$		0			0
$64$	102.739			1.60529
$65$	−96.5319	−	67.4942i	−1.48511	−	1.03837i
$66$		0			0
$67$		−	15.8441i		−	0.236479i	−0.992985	−	0.118239i	$-0.962275\pi$
$67$		−	15.8441i		−	0.236479i	0.992985	−	0.118239i	$-0.0377250\pi$
$68$	−150.582			−2.21444
$69$		0			0
$70$	−64.4550	−	93.8574i	−0.920786	−	1.34082i
$71$	47.3372			0.666721			0.333360	−	0.942799i	$-0.391817\pi$
$71$	47.3372			0.666721			0.333360	+	0.942799i	$0.391817\pi$
$72$		0			0
$73$	30.5266			0.418172			0.209086	−	0.977897i	$-0.432951\pi$
$73$	30.5266			0.418172			0.209086	+	0.977897i	$0.432951\pi$
$74$	161.669			2.18472
$75$		0			0
$76$			138.867i			1.82719i
$77$	−27.6503	+	73.7169i	−0.359095	+	0.957363i
$78$		0			0
$79$	35.4955			0.449310			0.224655	−	0.974438i	$-0.427875\pi$
$79$	35.4955			0.449310			0.224655	+	0.974438i	$0.427875\pi$
$80$	−4.09772	−	2.86509i	−0.0512215	−	0.0358136i
$81$		0			0
$82$	145.235			1.77116
$83$	−9.54892			−0.115047			−0.0575236	−	0.998344i	$-0.518320\pi$
$83$	−9.54892			−0.115047			−0.0575236	+	0.998344i	$0.518320\pi$
$84$		0			0
$85$	−93.7386	−	65.5412i	−1.10281	−	0.771072i
$86$	−51.5422			−0.599328
$87$		0			0
$88$			94.4935i			1.07379i
$89$			37.9689i			0.426617i	0.976985	+	0.213308i	$0.0684239\pi$
$89$			37.9689i			0.426617i	−0.976985	+	0.213308i	$0.931576\pi$
$90$		0			0
$91$	57.9129	−	154.398i	0.636405	−	1.69669i
$92$		−	8.93860i		−	0.0971586i
$93$		0			0
$94$		−	207.719i		−	2.20978i
$95$	−60.4421	+	86.4459i	−0.636233	+	0.909956i
$96$		0			0
$97$	91.1513			0.939705			0.469852	−	0.882745i	$-0.344307\pi$
$97$	91.1513			0.939705			0.469852	+	0.882745i	$0.344307\pi$
$98$	104.830	−	120.081i	1.06970	−	1.22531i
$99$		0			0
$100$	−56.4955	−	154.563i	−0.564955	−	1.54563i
$101$		−	3.33826i		−	0.0330521i	−0.999863	−	0.0165260i	$-0.994739\pi$
$101$		−	3.33826i		−	0.0330521i	0.999863	−	0.0165260i	$-0.00526064\pi$
$102$		0			0
$103$	63.9175			0.620558			0.310279	−	0.950645i	$-0.399577\pi$
$103$	63.9175			0.620558			0.310279	+	0.950645i	$0.399577\pi$
$104$		−	197.914i		−	1.90302i
$105$		0			0
$106$	−113.739			−1.07301
$107$			68.0018i			0.635531i	0.948169	+	0.317766i	$0.102933\pi$
$107$			68.0018i			0.635531i	−0.948169	+	0.317766i	$0.897067\pi$
$108$		0			0
$109$	−147.147			−1.34997			−0.674986	−	0.737830i	$-0.735850\pi$
$109$	−147.147			−1.34997			−0.674986	+	0.737830i	$0.735850\pi$
$110$	−104.830	+	149.931i	−0.953002	+	1.36301i
$111$		0			0
$112$	2.45837	−	6.55412i	0.0219497	−	0.0585189i
$113$		−	53.9741i		−	0.477647i	−0.971063	−	0.238824i	$-0.923238\pi$
$113$		−	53.9741i		−	0.477647i	0.971063	−	0.238824i	$-0.0767618\pi$
$114$		0			0
$115$	3.89055	−	5.56436i	0.0338309	−	0.0483858i
$116$	−206.659			−1.78154
$117$		0			0
$118$	260.158			2.20473
$119$	56.2371	−	149.931i	0.472581	−	1.25992i
$120$		0			0
$121$	5.50455			0.0454921
$122$	−155.356			−1.27341
$123$		0			0
$124$			175.495i			1.41528i
$125$	32.1050	−	120.807i	0.256840	−	0.966454i
$126$		0			0
$127$			101.559i			0.799677i	0.916586	+	0.399839i	$0.130934\pi$
$127$			101.559i			0.799677i	−0.916586	+	0.399839i	$0.869066\pi$
$128$			212.809i			1.66257i
$129$		0			0
$130$	219.564	−	314.027i	1.68896	−	2.41559i
$131$		−	150.628i		−	1.14983i	−0.818214	−	0.574914i	$-0.805035\pi$
$131$		−	150.628i		−	1.14983i	0.818214	−	0.574914i	$-0.194965\pi$
$132$		0			0
$133$	−138.266	−	51.8619i	−1.03960	−	0.389939i
$134$	51.5422			0.384643
$135$		0			0
$136$		−	192.188i		−	1.41314i
$137$		−	221.434i		−	1.61631i	−0.588971	−	0.808154i	$-0.700467\pi$
$137$		−	221.434i		−	1.61631i	0.588971	−	0.808154i	$-0.299533\pi$
$138$		0			0
$139$			149.995i			1.07910i	0.841952	+	0.539552i	$0.181406\pi$
$139$			149.995i			1.07910i	−0.841952	+	0.539552i	$0.818594\pi$
$140$	189.919	−	130.424i	1.35656	−	0.931599i
$141$		0			0
$142$			153.992i			1.08445i
$143$	−264.961			−1.85287
$144$		0			0
$145$	−128.647	−	89.9488i	−0.887221	−	0.620336i
$146$			99.3056i			0.680175i
$147$		0			0
$148$			327.135i			2.21037i
$149$	−71.6895			−0.481138			−0.240569	−	0.970632i	$-0.577334\pi$
$149$	−71.6895			−0.481138			−0.240569	+	0.970632i	$0.577334\pi$
$150$		0			0
$151$	51.9818			0.344250			0.172125	−	0.985075i	$-0.444937\pi$
$151$	51.9818			0.344250			0.172125	+	0.985075i	$0.444937\pi$
$152$	−177.236			−1.16602
$153$		0			0
$154$	−239.808	−	89.9488i	−1.55719	−	0.584083i
$155$	−76.3845	+	109.247i	−0.492803	+	0.704820i
$156$		0			0
$157$	−35.4433			−0.225753			−0.112877	−	0.993609i	$-0.536007\pi$
$157$	−35.4433			−0.225753			−0.112877	+	0.993609i	$0.536007\pi$
$158$			115.470i			0.730822i
$159$		0			0
$160$	−86.9619	+	124.375i	−0.543512	+	0.777344i
$161$	8.89995	+	3.33826i	0.0552792	+	0.0207345i
$162$		0			0
$163$			26.7875i			0.164340i	0.996618	+	0.0821702i	$0.0261851\pi$
$163$			26.7875i			0.164340i	−0.996618	+	0.0821702i	$0.973815\pi$
$164$			293.882i			1.79196i
$165$		0			0
$166$		−	31.0635i		−	0.187129i
$167$	44.7551			0.267995			0.133997	−	0.990982i	$-0.457219\pi$
$167$	44.7551			0.267995			0.133997	+	0.990982i	$0.457219\pi$
$168$		0			0
$169$	385.955			2.28375
$170$	213.211	−	304.940i	1.25418	−	1.79376i
$171$		0			0
$172$		−	104.295i		−	0.606365i
$173$	69.6239			0.402451			0.201225	−	0.979545i	$-0.435508\pi$
$173$	69.6239			0.402451			0.201225	+	0.979545i	$0.435508\pi$
$174$		0			0
$175$	174.994	+	1.47274i	0.999965	+	0.00841566i
$176$	−11.2474			−0.0639058
$177$		0			0
$178$	−123.516			−0.693911
$179$	−249.301			−1.39274			−0.696371	−	0.717682i	$-0.745203\pi$
$179$	−249.301			−1.39274			−0.696371	+	0.717682i	$0.745203\pi$
$180$		0			0
$181$			185.462i			1.02465i	0.858791	+	0.512326i	$0.171216\pi$
$181$			185.462i			1.02465i	−0.858791	+	0.512326i	$0.828784\pi$
$182$	502.271	+	188.396i	2.75973	+	1.03514i
$183$		0			0
$184$	11.4083			0.0620018
$185$	−142.386	+	203.645i	−0.769656	+	1.10078i
$186$		0			0
$187$	−257.294			−1.37590
$188$	420.317			2.23573
$189$		0			0
$190$	−281.216	−	196.623i	−1.48008	−	1.03486i
$191$	253.506			1.32726			0.663628	−	0.748063i	$-0.269016\pi$
$191$	253.506			1.32726			0.663628	+	0.748063i	$0.269016\pi$
$192$		0			0
$193$			329.871i			1.70917i	0.519308	+	0.854587i	$0.326190\pi$
$193$			329.871i			1.70917i	−0.519308	+	0.854587i	$0.673810\pi$
$194$			296.523i			1.52847i
$195$		0			0
$196$	242.982	+	212.122i	1.23970	+	1.08226i
$197$			119.036i			0.604243i	0.953269	+	0.302122i	$0.0976948\pi$
$197$			119.036i			0.604243i	−0.953269	+	0.302122i	$0.902305\pi$
$198$		0			0
$199$			324.329i			1.62979i	0.579607	+	0.814896i	$0.303206\pi$
$199$			324.329i			1.62979i	−0.579607	+	0.814896i	$0.696794\pi$
$200$	197.269	−	72.1052i	0.986344	−	0.360526i
$201$		0			0
$202$	10.8596			0.0537606
$203$	77.1799	−	205.765i	0.380196	−	1.01362i
$204$		0			0
$205$	−127.913	+	182.944i	−0.623965	+	0.892411i
$206$			207.929i			1.00937i
$207$		0			0
$208$	23.5575			0.113257
$209$			237.277i			1.13530i
$210$		0			0
$211$	−249.477			−1.18236			−0.591178	−	0.806541i	$-0.701337\pi$
$211$	−249.477			−1.18236			−0.591178	+	0.806541i	$0.701337\pi$
$212$		−	230.149i		−	1.08561i
$213$		0			0
$214$	−221.216			−1.03372
$215$	45.3946	−	64.9246i	0.211138	−	0.301975i
$216$		0			0
$217$	−174.736	−	65.5412i	−0.805234	−	0.302033i
$218$		−	478.682i		−	2.19579i
$219$		0			0
$220$	−303.383	−	212.122i	−1.37901	−	0.964193i
$221$	538.896			2.43845
$222$		0			0
$223$	−226.553			−1.01593			−0.507967	−	0.861377i	$-0.669603\pi$
$223$	−226.553			−1.01593			−0.507967	+	0.861377i	$0.669603\pi$
$224$	−198.932	−	74.6170i	−0.888091	−	0.333112i
$225$		0			0
$226$	175.583			0.776914
$227$	19.0978			0.0841315			0.0420657	−	0.999115i	$-0.486606\pi$
$227$	19.0978			0.0841315			0.0420657	+	0.999115i	$0.486606\pi$
$228$		0			0
$229$		−	241.106i		−	1.05286i	−0.850218	−	0.526431i	$-0.823530\pi$
$229$		−	241.106i		−	1.05286i	0.850218	−	0.526431i	$-0.176470\pi$
$230$	18.1014	+	12.6563i	0.0787015	+	0.0550274i
$231$		0			0
$232$		−	263.758i		−	1.13689i
$233$			369.553i			1.58607i	0.609179	+	0.793033i	$0.291499\pi$
$233$			369.553i			1.58607i	−0.609179	+	0.793033i	$0.708501\pi$
$234$		0			0
$235$	261.652	+	182.944i	1.11341	+	0.778486i
$236$			526.427i			2.23062i
$237$		0			0
$238$	487.738	+	182.944i	2.04932	+	0.768673i
$239$	−446.570			−1.86849			−0.934246	−	0.356629i	$-0.883926\pi$
$239$	−446.570			−1.86849			−0.934246	+	0.356629i	$0.883926\pi$
$240$		0			0
$241$			299.991i			1.24478i	0.782709	+	0.622388i	$0.213837\pi$
$241$			299.991i			1.24478i	−0.782709	+	0.622388i	$0.786163\pi$
$242$			17.9068i			0.0739949i
$243$		0			0
$244$		−	314.361i		−	1.28837i
$245$	58.9317	+	237.807i	0.240537	+	0.970640i
$246$		0			0
$247$		−	496.971i		−	2.01203i
$248$	−223.984			−0.903160
$249$		0			0
$250$	392.995	+	104.440i	1.57198	+	0.417761i
$251$		−	462.449i		−	1.84242i	−0.389060	−	0.921212i	$-0.627200\pi$
$251$		−	462.449i		−	1.84242i	0.389060	−	0.921212i	$-0.372800\pi$
$252$		0			0
$253$		−	15.2731i		−	0.0603679i
$254$	−330.380			−1.30071
$255$		0			0
$256$	−281.330			−1.09895
$257$	−49.5296			−0.192722			−0.0963611	−	0.995346i	$-0.530720\pi$
$257$	−49.5296			−0.192722			−0.0963611	+	0.995346i	$0.530720\pi$
$258$		0			0
$259$	−325.720	−	122.174i	−1.25761	−	0.471713i
$260$	635.428	+	444.285i	2.44396	+	1.70879i
$261$		0			0
$262$	490.004			1.87025
$263$			212.271i			0.807115i	0.914954	+	0.403558i	$0.132227\pi$
$263$			212.271i			0.807115i	−0.914954	+	0.403558i	$0.867773\pi$
$264$		0			0
$265$	100.173	−	143.270i	0.378011	−	0.540640i
$266$	168.711	−	449.792i	0.634253	−	1.69095i
$267$		0			0
$268$			104.295i			0.389160i
$269$			156.607i			0.582183i	0.956695	+	0.291092i	$0.0940184\pi$
$269$			156.607i			0.582183i	−0.956695	+	0.291092i	$0.905982\pi$
$270$		0			0
$271$		−	197.752i		−	0.729712i	−0.931064	−	0.364856i	$-0.881118\pi$
$271$		−	197.752i		−	0.729712i	0.931064	−	0.364856i	$-0.118882\pi$
$272$	22.8758			0.0841023
$273$		0			0
$274$	720.345			2.62900
$275$	−96.5319	−	264.096i	−0.351025	−	0.960351i
$276$		0			0
$277$		−	197.194i		−	0.711893i	−0.934506	−	0.355947i	$-0.884158\pi$
$277$		−	197.194i		−	0.711893i	0.934506	−	0.355947i	$-0.115842\pi$
$278$	−487.948			−1.75521
$279$		0			0
$280$	166.460	+	242.394i	0.594500	+	0.865692i
$281$	196.779			0.700280			0.350140	−	0.936697i	$-0.386134\pi$
$281$	196.779			0.700280			0.350140	+	0.936697i	$0.386134\pi$
$282$		0			0
$283$	400.263			1.41436			0.707178	−	0.707035i	$-0.249968\pi$
$283$	400.263			1.41436			0.707178	+	0.707035i	$0.249968\pi$
$284$	−311.601			−1.09718
$285$		0			0
$286$		−	861.941i		−	3.01378i
$287$	−292.611	−	109.755i	−1.01955	−	0.382421i
$288$		0			0
$289$	234.303			0.810737
$290$	292.611	−	418.500i	1.00900	−	1.44310i
$291$		0			0
$292$	−200.943			−0.688162
$293$	286.840			0.978977			0.489488	−	0.872010i	$-0.337184\pi$
$293$	286.840			0.978977			0.489488	+	0.872010i	$0.337184\pi$
$294$		0			0
$295$	−229.129	+	327.706i	−0.776708	+	1.11087i
$296$	−417.522			−1.41055
$297$		0			0
$298$		−	233.212i		−	0.782592i
$299$			31.9891i			0.106987i
$300$		0			0
$301$	103.844	+	38.9505i	0.344996	+	0.129404i
$302$			169.101i			0.559938i
$303$		0			0
$304$		−	21.0961i		−	0.0693951i
$305$	136.827	−	195.693i	0.448612	−	0.641616i
$306$		0			0
$307$	−308.085			−1.00354			−0.501768	−	0.865002i	$-0.667317\pi$
$307$	−308.085			−1.00354			−0.501768	+	0.865002i	$0.667317\pi$
$308$	182.010	−	485.247i	0.590942	−	1.57548i
$309$		0			0
$310$	−355.390	−	248.485i	−1.14642	−	0.801566i
$311$		−	26.7061i		−	0.0858716i	−0.999078	−	0.0429358i	$-0.986329\pi$
$311$		−	26.7061i		−	0.0858716i	0.999078	−	0.0429358i	$-0.0136711\pi$
$312$		0			0
$313$	275.935			0.881581			0.440790	−	0.897610i	$-0.354698\pi$
$313$	275.935			0.881581			0.440790	+	0.897610i	$0.354698\pi$
$314$		−	115.300i		−	0.367198i
$315$		0			0
$316$	−233.652			−0.739404
$317$		−	299.508i		−	0.944821i	−0.881379	−	0.472411i	$-0.843384\pi$
$317$		−	299.508i		−	0.944821i	0.881379	−	0.472411i	$-0.156616\pi$
$318$		0			0
$319$	−353.111			−1.10693
$320$	−420.994	−	294.355i	−1.31561	−	0.919859i
$321$		0			0
$322$	−10.8596	+	28.9523i	−0.0337256	+	0.0899140i
$323$		−	482.591i		−	1.49409i
$324$		0			0
$325$	202.184	+	553.144i	0.622104	+	1.70198i
$326$	−87.1420			−0.267307
$327$		0			0
$328$	−375.081			−1.14354
$329$	−156.974	+	418.500i	−0.477125	+	1.27204i
$330$		0			0
$331$	17.0273			0.0514419			0.0257210	−	0.999669i	$-0.491812\pi$
$331$	17.0273			0.0514419			0.0257210	+	0.999669i	$0.491812\pi$
$332$	62.8565			0.189327
$333$		0			0
$334$			145.592i			0.435905i
$335$	−45.3946	+	64.9246i	−0.135506	+	0.193805i
$336$		0			0
$337$		−	444.538i		−	1.31910i	−0.751659	−	0.659552i	$-0.770746\pi$
$337$		−	444.538i		−	1.31910i	0.751659	−	0.659552i	$-0.229254\pi$
$338$			1255.54i			3.71463i
$339$		0			0
$340$	617.042	+	431.430i	1.81483	+	1.26891i
$341$			299.862i			0.879359i
$342$		0			0
$343$	−301.951	+	162.711i	−0.880322	+	0.474376i
$344$	133.112			0.386952
$345$		0			0
$346$			226.493i			0.654603i
$347$			221.883i			0.639431i	0.947514	+	0.319716i	$0.103587\pi$
$347$			221.883i			0.639431i	−0.947514	+	0.319716i	$0.896413\pi$
$348$		0			0
$349$		−	507.710i		−	1.45476i	−0.686237	−	0.727378i	$-0.740739\pi$
$349$		−	507.710i		−	1.45476i	0.686237	−	0.727378i	$-0.259261\pi$
$350$	−4.79095	+	569.270i	−0.0136884	+	1.62649i
$351$		0			0
$352$			341.385i			0.969844i
$353$	535.693			1.51754			0.758772	−	0.651357i	$-0.225800\pi$
$353$	535.693			1.51754			0.758772	+	0.651357i	$0.225800\pi$
$354$		0			0
$355$	−193.974	−	135.625i	−0.546407	−	0.382042i
$356$		−	249.933i		−	0.702059i
$357$		0			0
$358$		−	810.997i		−	2.26536i
$359$	231.991			0.646214			0.323107	−	0.946362i	$-0.395273\pi$
$359$	231.991			0.646214			0.323107	+	0.946362i	$0.395273\pi$
$360$		0			0
$361$	−84.0455			−0.232813
$362$	−603.324			−1.66664
$363$		0			0
$364$	−381.216	+	1016.34i	−1.04730	+	2.79214i
$365$	−125.089	−	87.4612i	−0.342710	−	0.239620i
$366$		0			0
$367$	662.045			1.80394			0.901969	−	0.431801i	$-0.142122\pi$
$367$	662.045			1.80394			0.901969	+	0.431801i	$0.142122\pi$
$368$			1.35792i			0.00368999i
$369$		0			0
$370$	−662.474	−	463.195i	−1.79047	−	1.25188i
$371$	229.153	+	85.9526i	0.617664	+	0.231678i
$372$		0			0
$373$			284.503i			0.762743i	0.924422	+	0.381372i	$0.124548\pi$
$373$			284.503i			0.762743i	−0.924422	+	0.381372i	$0.875452\pi$
$374$		−	837.000i		−	2.23797i
$375$		0			0
$376$			536.451i			1.42673i
$377$	739.582			1.96176
$378$		0			0
$379$	187.808			0.495534			0.247767	−	0.968820i	$-0.420303\pi$
$379$	187.808			0.495534			0.247767	+	0.968820i	$0.420303\pi$
$380$	397.865	−	569.036i	1.04701	−	1.49746i
$381$		0			0
$382$			824.677i			2.15884i
$383$	−229.755			−0.599882			−0.299941	−	0.953958i	$-0.596967\pi$
$383$	−229.755			−0.599882			−0.299941	+	0.953958i	$0.596967\pi$
$384$		0			0
$385$	324.508	−	222.851i	0.842879	−	0.578833i
$386$	−1073.10			−2.78005
$387$		0			0
$388$	−600.011			−1.54642
$389$	−288.228			−0.740946			−0.370473	−	0.928843i	$-0.620804\pi$
$389$	−288.228			−0.740946			−0.370473	+	0.928843i	$0.620804\pi$
$390$		0			0
$391$			31.0635i			0.0794462i
$392$	−270.732	+	310.118i	−0.690642	+	0.791117i
$393$		0			0
$394$	−387.234			−0.982828
$395$	−145.450	−	101.697i	−0.368229	−	0.257462i
$396$		0			0
$397$	−370.977			−0.934450			−0.467225	−	0.884138i	$-0.654746\pi$
$397$	−370.977			−0.934450			−0.467225	+	0.884138i	$0.654746\pi$
$398$	−1055.07			−2.65093
$399$		0			0
$400$	8.58258	+	23.4806i	0.0214564	+	0.0587015i
$401$	381.433			0.951203			0.475602	−	0.879661i	$-0.342230\pi$
$401$	381.433			0.951203			0.475602	+	0.879661i	$0.342230\pi$
$402$		0			0
$403$		−	628.053i		−	1.55844i
$404$			21.9743i			0.0543919i
$405$		0			0
$406$	669.372	+	251.073i	1.64870	+	0.618406i
$407$			558.964i			1.37338i
$408$		0			0
$409$			280.056i			0.684734i	0.939566	+	0.342367i	$0.111229\pi$
$409$			280.056i			0.684734i	−0.939566	+	0.342367i	$0.888771\pi$
$410$	−595.134	−	416.112i	−1.45155	−	1.01491i
$411$		0			0
$412$	−420.742			−1.02122
$413$	−524.151	−	196.602i	−1.26913	−	0.476035i
$414$		0			0
$415$	39.1288	+	27.3585i	0.0942862	+	0.0659240i
$416$		−	715.023i		−	1.71881i
$417$		0			0
$418$	−771.882			−1.84661
$419$		−	565.092i		−	1.34867i	−0.738426	−	0.674335i	$-0.764431\pi$
$419$		−	565.092i		−	1.34867i	0.738426	−	0.674335i	$-0.235569\pi$
$420$		0			0
$421$	−24.5045			−0.0582056			−0.0291028	−	0.999576i	$-0.509265\pi$
$421$	−24.5045			−0.0582056			−0.0291028	+	0.999576i	$0.509265\pi$
$422$		−	811.571i		−	1.92315i
$423$		0			0
$424$	293.739			0.692780
$425$	196.333	+	537.138i	0.461961	+	1.26385i
$426$		0			0
$427$	313.002	+	117.403i	0.733026	+	0.274949i
$428$		−	447.627i		−	1.04586i
$429$		0			0
$430$	211.205	+	147.673i	0.491175	+	0.343425i
$431$	−141.032			−0.327220			−0.163610	−	0.986525i	$-0.552314\pi$
$431$	−141.032			−0.327220			−0.163610	+	0.986525i	$0.552314\pi$
$432$		0			0
$433$	−162.038			−0.374222			−0.187111	−	0.982339i	$-0.559912\pi$
$433$	−162.038			−0.374222			−0.187111	+	0.982339i	$0.559912\pi$
$434$	213.211	−	568.431i	0.491270	−	1.30975i
$435$		0			0
$436$	968.606			2.22157
$437$	28.6468			0.0655532
$438$		0			0
$439$		−	310.877i		−	0.708148i	−0.935217	−	0.354074i	$-0.884796\pi$
$439$		−	310.877i		−	0.708148i	0.935217	−	0.354074i	$-0.115204\pi$
$440$	270.732	−	387.208i	0.615300	−	0.880017i
$441$		0			0
$442$			1753.08i			3.96624i
$443$			703.009i			1.58693i	0.608617	+	0.793464i	$0.291725\pi$
$443$			703.009i			1.58693i	−0.608617	+	0.793464i	$0.708275\pi$
$444$		0			0
$445$	108.784	−	155.586i	0.244459	−	0.349631i
$446$		−	736.998i		−	1.65246i
$447$		0			0
$448$	252.569	−	673.361i	0.563770	−	1.50304i
$449$	520.117			1.15839			0.579195	−	0.815189i	$-0.303367\pi$
$449$	520.117			1.15839			0.579195	+	0.815189i	$0.303367\pi$
$450$		0			0
$451$			502.146i			1.11341i
$452$			355.289i			0.786037i
$453$		0			0
$454$			62.1270i			0.136844i
$455$	−679.675	+	466.756i	−1.49379	+	1.02584i
$456$		0			0
$457$			275.154i			0.602087i	0.953610	+	0.301043i	$0.0973349\pi$
$457$			275.154i			0.602087i	−0.953610	+	0.301043i	$0.902665\pi$
$458$	784.337			1.71253
$459$		0			0
$460$	−25.6098	+	36.6278i	−0.0556736	+	0.0796257i
$461$			597.778i			1.29670i	0.761343	+	0.648350i	$0.224540\pi$
$461$			597.778i			1.29670i	−0.761343	+	0.648350i	$0.775460\pi$
$462$		0			0
$463$			220.556i			0.476363i	0.971221	+	0.238181i	$0.0765513\pi$
$463$			220.556i			0.476363i	−0.971221	+	0.238181i	$0.923449\pi$
$464$	31.3948			0.0676612
$465$		0			0
$466$	−1202.19			−2.57980
$467$	200.111			0.428504			0.214252	−	0.976778i	$-0.431269\pi$
$467$	200.111			0.428504			0.214252	+	0.976778i	$0.431269\pi$
$468$		0			0
$469$	−103.844	−	38.9505i	−0.221416	−	0.0830502i
$470$	−595.134	+	851.175i	−1.26624	+	1.81101i
$471$		0			0
$472$	−671.879			−1.42347
$473$		−	178.205i		−	0.376755i
$474$		0			0
$475$	495.349	−	181.059i	1.04284	−	0.381177i
$476$	−370.185	+	986.931i	−0.777700	+	2.07338i
$477$		0			0
$478$		−	1452.73i		−	3.03918i
$479$			497.079i			1.03774i	0.854852	+	0.518872i	$0.173648\pi$
$479$			497.079i			1.03774i	−0.854852	+	0.518872i	$0.826352\pi$
$480$		0			0
$481$		−	1170.74i		−	2.43397i
$482$	−975.896			−2.02468
$483$		0			0
$484$	−36.2341			−0.0748638
$485$	−373.512	−	261.156i	−0.770129	−	0.538467i
$486$		0			0
$487$		−	205.283i		−	0.421525i	−0.977537	−	0.210763i	$-0.932405\pi$
$487$		−	205.283i		−	0.421525i	0.977537	−	0.210763i	$-0.0675947\pi$
$488$	401.219			0.822171
$489$		0			0
$490$	−773.606	+	191.710i	−1.57879	+	0.391245i
$491$	702.913			1.43159			0.715797	−	0.698308i	$-0.246063\pi$
$491$	702.913			1.43159			0.715797	+	0.698308i	$0.246063\pi$
$492$		0			0
$493$	718.182			1.45676
$494$	1616.69			3.27265
$495$		0			0
$496$		−	26.6605i		−	0.0537509i
$497$	116.372	−	310.253i	0.234149	−	0.624252i
$498$		0			0
$499$	−22.0000			−0.0440882			−0.0220441	−	0.999757i	$-0.507017\pi$
$499$	−22.0000			−0.0440882			−0.0220441	+	0.999757i	$0.507017\pi$
$500$	−211.334	+	795.220i	−0.422667	+	1.59044i
$501$		0			0
$502$	1504.39			2.99678
$503$	456.520			0.907594			0.453797	−	0.891105i	$-0.350069\pi$
$503$	456.520			0.907594			0.453797	+	0.891105i	$0.350069\pi$
$504$		0			0
$505$	−9.56439	+	13.6792i	−0.0189394	+	0.0270876i
$506$	49.6846			0.0981910
$507$		0			0
$508$		−	668.520i		−	1.31598i
$509$		−	1.94479i		−	0.00382080i	−0.999998	−	0.00191040i	$-0.999392\pi$
$509$		−	1.94479i		−	0.00382080i	0.999998	−	0.00191040i	$-0.000608100\pi$
$510$		0			0
$511$	75.0455	−	200.075i	0.146860	−	0.391536i
$512$		−	63.9577i		−	0.124917i
$513$		0			0
$514$		−	161.124i		−	0.313471i
$515$	−261.916	−	183.129i	−0.508574	−	0.355590i
$516$		0			0
$517$	718.182			1.38913
$518$	397.441	−	1059.60i	0.767261	−	2.04555i
$519$		0			0
$520$	−567.042	+	810.997i	−1.09046	+	1.55961i
$521$			295.275i			0.566747i	0.959010	+	0.283374i	$0.0914536\pi$
$521$			295.275i			0.566747i	−0.959010	+	0.283374i	$0.908546\pi$
$522$		0			0
$523$	−149.554			−0.285955			−0.142977	−	0.989726i	$-0.545668\pi$
$523$	−149.554			−0.285955			−0.142977	+	0.989726i	$0.545668\pi$
$524$			991.517i			1.89221i
$525$		0			0
$526$	−690.537			−1.31281
$527$		−	609.880i		−	1.15727i
$528$		0			0
$529$	527.156			0.996514
$530$	466.069	+	325.871i	0.879375	+	0.614851i
$531$		0			0
$532$	910.148	+	341.385i	1.71081	+	0.641701i
$533$		−	1051.73i		−	1.97323i
$534$		0			0
$535$	194.831	−	278.652i	0.364170	−	0.520845i
$536$	−133.112			−0.248342
$537$		0			0
$538$	−509.457			−0.946946
$539$	415.175	+	362.446i	0.770269	+	0.672442i
$540$		0			0
$541$	−426.065			−0.787551			−0.393776	−	0.919207i	$-0.628831\pi$
$541$	−426.065			−0.787551			−0.393776	+	0.919207i	$0.628831\pi$
$542$	643.304			1.18691
$543$		0			0
$544$		−	694.333i		−	1.27635i
$545$	602.967	+	421.589i	1.10636	+	0.773557i
$546$		0			0
$547$		−	671.256i		−	1.22716i	−0.789633	−	0.613579i	$-0.789729\pi$
$547$		−	671.256i		−	1.22716i	0.789633	−	0.613579i	$-0.210271\pi$
$548$			1457.61i			2.65987i
$549$		0			0
$550$	859.129	−	314.027i	1.56205	−	0.570957i
$551$		−	662.308i		−	1.20201i
$552$		0			0
$553$	87.2608	−	232.641i	0.157795	−	0.420690i
$554$	641.491			1.15793
$555$		0			0
$556$		−	987.356i		−	1.77582i
$557$			57.7053i			0.103600i	0.998657	+	0.0518001i	$0.0164959\pi$
$557$			57.7053i			0.103600i	−0.998657	+	0.0518001i	$0.983504\pi$
$558$		0			0
$559$			373.246i			0.667704i
$560$	−28.8518	+	19.8135i	−0.0515210	+	0.0353812i
$561$		0			0
$562$			640.139i			1.13904i
$563$	−1021.65			−1.81465			−0.907325	−	0.420430i	$-0.861879\pi$
$563$	−1021.65			−1.81465			−0.907325	+	0.420430i	$0.861879\pi$
$564$		0			0
$565$	−154.640	+	221.171i	−0.273700	+	0.391453i
$566$			1302.09i			2.30051i
$567$		0			0
$568$		−	397.696i		−	0.700169i
$569$	438.547			0.770733			0.385367	−	0.922764i	$-0.374075\pi$
$569$	438.547			0.770733			0.385367	+	0.922764i	$0.374075\pi$
$570$		0			0
$571$	45.4045			0.0795176			0.0397588	−	0.999209i	$-0.487341\pi$
$571$	45.4045			0.0795176			0.0397588	+	0.999209i	$0.487341\pi$
$572$	1744.13			3.04917
$573$		0			0
$574$	357.042	−	951.890i	0.622024	−	1.65834i
$575$	−31.8847	+	11.6544i	−0.0554517	+	0.0202686i
$576$		0			0
$577$	−735.198			−1.27417			−0.637087	−	0.770792i	$-0.719861\pi$
$577$	−735.198			−1.27417			−0.637087	+	0.770792i	$0.719861\pi$
$578$			762.208i			1.31870i
$579$		0			0
$580$	846.829	+	592.095i	1.46005	+	1.02085i
$581$	−23.4747	+	62.5847i	−0.0404040	+	0.107719i
$582$		0			0
$583$		−	393.247i		−	0.674523i
$584$		−	256.464i		−	0.439151i
$585$		0			0
$586$			933.116i			1.59235i
$587$	−219.209			−0.373440			−0.186720	−	0.982413i	$-0.559786\pi$
$587$	−219.209			−0.373440			−0.186720	+	0.982413i	$0.559786\pi$
$588$		0			0
$589$	−562.432			−0.954893
$590$	−1066.06	−	745.376i	−1.80687	−	1.26335i
$591$		0			0
$592$		−	49.6971i		−	0.0839478i
$593$	853.961			1.44007			0.720035	−	0.693938i	$-0.244126\pi$
$593$	853.961			1.44007			0.720035	+	0.693938i	$0.244126\pi$
$594$		0			0
$595$	−660.008	+	453.250i	−1.10926	+	0.761764i
$596$	471.902			0.791782
$597$		0			0
$598$	−104.063			−0.174019
$599$	338.790			0.565593			0.282797	−	0.959180i	$-0.408738\pi$
$599$	338.790			0.565593			0.282797	+	0.959180i	$0.408738\pi$
$600$		0			0
$601$		−	62.1270i		−	0.103373i	−0.998663	−	0.0516863i	$-0.983540\pi$
$601$		−	62.1270i		−	0.103373i	0.998663	−	0.0516863i	$-0.0164596\pi$
$602$	−126.709	+	337.813i	−0.210481	+	0.561152i
$603$		0			0
$604$	−342.174			−0.566514
$605$	−22.5561	−	15.7710i	−0.0372828	−	0.0260678i
$606$		0			0
$607$	−383.460			−0.631730			−0.315865	−	0.948804i	$-0.602295\pi$
$607$	−383.460			−0.631730			−0.315865	+	0.948804i	$0.602295\pi$
$608$	−640.315			−1.05315
$609$		0			0
$610$	636.606	+	445.109i	1.04362	+	0.729687i
$611$	−1504.22			−2.46189
$612$		0			0
$613$			546.668i			0.891791i	0.895085	+	0.445896i	$0.147115\pi$
$613$			546.668i			0.891791i	−0.895085	+	0.445896i	$0.852885\pi$
$614$		−	1002.23i		−	1.63229i
$615$		0			0
$616$	619.321	+	232.299i	1.00539	+	0.377110i
$617$			734.466i			1.19038i	0.803584	+	0.595191i	$0.202924\pi$
$617$			734.466i			1.19038i	−0.803584	+	0.595191i	$0.797076\pi$
$618$		0			0
$619$			549.660i			0.887981i	0.896032	+	0.443990i	$0.146438\pi$
$619$			549.660i			0.887981i	−0.896032	+	0.443990i	$0.853562\pi$
$620$	502.807	−	719.127i	0.810979	−	1.15988i
$621$		0			0
$622$	86.8771			0.139674
$623$	248.853	+	93.3414i	0.399442	+	0.149826i
$624$		0			0
$625$	−477.679	+	403.048i	−0.764286	+	0.644877i
$626$			897.640i			1.43393i
$627$		0			0
$628$	233.308			0.371510
$629$		−	1136.86i		−	1.80741i
$630$		0			0
$631$	661.230			1.04791			0.523954	−	0.851746i	$-0.324456\pi$
$631$	661.230			1.04791			0.523954	+	0.851746i	$0.324456\pi$
$632$		−	298.210i		−	0.471850i
$633$		0			0
$634$	974.327			1.53679
$635$	290.975	−	416.160i	0.458229	−	0.655370i
$636$		0			0
$637$	−869.574	−	759.135i	−1.36511	−	1.19174i
$638$		−	1148.70i		−	1.80047i
$639$		0			0
$640$	609.715	−	872.029i	0.952679	−	1.36255i
$641$	−211.844			−0.330489			−0.165245	−	0.986253i	$-0.552841\pi$
$641$	−211.844			−0.330489			−0.165245	+	0.986253i	$0.552841\pi$
$642$		0			0
$643$	693.982			1.07929			0.539644	−	0.841894i	$-0.318559\pi$
$643$	693.982			1.07929			0.539644	+	0.841894i	$0.318559\pi$
$644$	−58.5846	−	21.9743i	−0.0909699	−	0.0341216i
$645$		0			0
$646$	1569.91			2.43020
$647$	−1161.89			−1.79581			−0.897907	−	0.440184i	$-0.854913\pi$
$647$	−1161.89			−1.79581			−0.897907	+	0.440184i	$0.854913\pi$
$648$		0			0
$649$			899.488i			1.38596i
$650$	−1799.43	+	657.722i	−2.76835	+	1.01188i
$651$		0			0
$652$		−	176.331i		−	0.270446i
$653$			516.538i			0.791024i	0.918461	+	0.395512i	$0.129433\pi$
$653$			516.538i			0.791024i	−0.918461	+	0.395512i	$0.870567\pi$
$654$		0			0
$655$	−431.561	+	617.229i	−0.658871	+	0.942334i
$656$		−	44.6454i		−	0.0680570i
$657$		0			0
$658$	−1361.42	−	510.650i	−2.06902	−	0.776064i
$659$	−64.6471			−0.0980988			−0.0490494	−	0.998796i	$-0.515619\pi$
$659$	−64.6471			−0.0980988			−0.0490494	+	0.998796i	$0.515619\pi$
$660$		0			0
$661$			147.430i			0.223041i	0.993762	+	0.111521i	$0.0355721\pi$
$661$			147.430i			0.223041i	−0.993762	+	0.111521i	$0.964428\pi$
$662$			55.3912i			0.0836725i
$663$		0			0
$664$			80.2238i			0.120819i
$665$	417.987	+	608.660i	0.628552	+	0.915278i
$666$		0			0
$667$			42.6315i			0.0639154i
$668$	−294.604			−0.441024
$669$		0			0
$670$	−211.205	−	147.673i	−0.315232	−	0.220407i
$671$		−	537.138i		−	0.800504i
$672$		0			0
$673$			473.038i			0.702880i	0.936210	+	0.351440i	$0.114308\pi$
$673$			473.038i			0.702880i	−0.936210	+	0.351440i	$0.885692\pi$
$674$	1446.12			2.14558
$675$		0			0
$676$	−2540.57			−3.75825
$677$	330.599			0.488329			0.244165	−	0.969734i	$-0.421486\pi$
$677$	330.599			0.488329			0.244165	+	0.969734i	$0.421486\pi$
$678$		0			0
$679$	224.083	−	597.417i	0.330020	−	0.879848i
$680$	−550.634	+	787.530i	−0.809756	+	1.15813i
$681$		0			0
$682$	−975.476			−1.43032
$683$			407.338i			0.596396i	0.954504	+	0.298198i	$0.0963855\pi$
$683$			407.338i			0.596396i	−0.954504	+	0.298198i	$0.903614\pi$
$684$		0			0
$685$	−634.428	+	907.375i	−0.926172	+	1.32463i
$686$	−529.313	−	982.272i	−0.771593	−	1.43188i
$687$		0			0
$688$			15.8441i			0.0230292i
$689$			823.647i			1.19542i
$690$		0			0
$691$			1011.94i			1.46445i	0.681062	+	0.732226i	$0.261518\pi$
$691$			1011.94i			1.46445i	−0.681062	+	0.732226i	$0.738482\pi$
$692$	−458.305			−0.662290
$693$		0			0
$694$	−721.804			−1.04006
$695$	429.750	−	614.639i	0.618345	−	0.884372i
$696$		0			0
$697$		−	1021.30i		−	1.46528i
$698$	1651.63			2.36623
$699$		0			0
$700$	−1151.91	−	9.69443i	−1.64559	−	0.0138492i
$701$	−793.280			−1.13164			−0.565820	−	0.824529i	$-0.691440\pi$
$701$	−793.280			−1.13164			−0.565820	+	0.824529i	$0.691440\pi$
$702$		0			0
$703$	−1048.41			−1.49134
$704$	−1155.54			−1.64140
$705$		0			0
$706$			1742.66i			2.46835i
$707$	−21.8793	−	8.20666i	−0.0309467	−	0.0116077i
$708$		0			0
$709$	−385.303			−0.543446			−0.271723	−	0.962376i	$-0.587593\pi$
$709$	−385.303			−0.543446			−0.271723	+	0.962376i	$0.587593\pi$
$710$	441.200	−	631.015i	0.621408	−	0.888754i
$711$		0			0
$712$	318.990			0.448019
$713$	36.2027			0.0507752
$714$		0			0
$715$	1085.73	+	759.135i	1.51851	+	1.06173i
$716$	1641.04			2.29196
$717$		0			0
$718$			754.687i			1.05110i
$719$		−	1091.52i		−	1.51811i	−0.651028	−	0.759054i	$-0.725662\pi$
$719$		−	1091.52i		−	1.51811i	0.651028	−	0.759054i	$-0.274338\pi$
$720$		0			0
$721$	157.133	−	418.923i	0.217937	−	0.581030i
$722$		−	273.407i		−	0.378680i
$723$		0			0
$724$		−	1220.82i		−	1.68621i
$725$	269.448	+	737.169i	0.371653	+	1.01679i
$726$		0			0
$727$	−1040.25			−1.43088			−0.715440	−	0.698674i	$-0.753774\pi$
$727$	−1040.25			−1.43088			−0.715440	+	0.698674i	$0.753774\pi$
$728$	−1297.15	−	486.546i	−1.78181	−	0.668332i
$729$		0			0
$730$	284.519	−	406.926i	0.389752	−	0.557433i
$731$			362.446i			0.495823i
$732$		0			0
$733$	−633.571			−0.864353			−0.432177	−	0.901789i	$-0.642254\pi$
$733$	−633.571			−0.864353			−0.432177	+	0.901789i	$0.642254\pi$
$734$			2153.69i			2.93418i
$735$		0			0
$736$	41.2159			0.0559999
$737$			178.205i			0.241798i
$738$		0			0
$739$	910.450			1.23200			0.616001	−	0.787745i	$-0.288752\pi$
$739$	910.450			1.23200			0.616001	+	0.787745i	$0.288752\pi$
$740$	937.269	−	1340.51i	1.26658	−	1.81149i
$741$		0			0
$742$	−279.611	+	745.456i	−0.376834	+	1.00466i
$743$			327.445i			0.440707i	0.975420	+	0.220354i	$0.0707211\pi$
$743$			327.445i			0.440707i	−0.975420	+	0.220354i	$0.929279\pi$
$744$		0			0
$745$	293.763	+	205.397i	0.394313	+	0.275700i
$746$	−925.514			−1.24064
$747$		0			0
$748$	1693.66			2.26425
$749$	445.692	+	167.173i	0.595049	+	0.223195i
$750$		0			0
$751$	1017.13			1.35437			0.677183	−	0.735815i	$-0.263201\pi$
$751$	1017.13			1.35437			0.677183	+	0.735815i	$0.263201\pi$
$752$	−63.8530			−0.0849109
$753$		0			0
$754$			2405.93i			3.19088i
$755$	−213.007	−	148.932i	−0.282128	−	0.197261i
$756$		0			0
$757$		−	754.116i		−	0.996190i	−0.867123	−	0.498095i	$-0.834033\pi$
$757$		−	754.116i		−	0.996190i	0.867123	−	0.498095i	$-0.165967\pi$
$758$			610.954i			0.806008i
$759$		0			0
$760$	726.261	+	507.795i	0.955607	+	0.668151i
$761$			333.941i			0.438818i	0.975633	+	0.219409i	$0.0704130\pi$
$761$			333.941i			0.438818i	−0.975633	+	0.219409i	$0.929587\pi$
$762$		0			0
$763$	−361.741	+	964.418i	−0.474104	+	1.26398i
$764$	−1668.72			−2.18419
$765$		0			0
$766$		−	747.412i		−	0.975734i
$767$		−	1883.96i		−	2.45627i
$768$		0			0
$769$			1315.41i			1.71055i	0.518176	+	0.855274i	$0.326611\pi$
$769$			1315.41i			1.71055i	−0.518176	+	0.855274i	$0.673389\pi$
$770$	724.953	+	1055.65i	0.941497	+	1.37098i
$771$		0			0
$772$		−	2171.40i		−	2.81269i
$773$	−391.878			−0.506958			−0.253479	−	0.967341i	$-0.581575\pi$
$773$	−391.878			−0.506958			−0.253479	+	0.967341i	$0.581575\pi$
$774$		0			0
$775$	626.004	−	228.815i	0.807747	−	0.295246i
$776$		−	765.794i		−	0.986848i
$777$		0			0
$778$		−	937.631i		−	1.20518i
$779$	−941.844			−1.20904
$780$		0			0
$781$	−532.421			−0.681717
$782$	−101.052			−0.129223
$783$		0			0
$784$	−36.9129	−	32.2248i	−0.0470828	−	0.0411031i
$785$	145.237	+	101.548i	0.185015	+	0.129361i
$786$		0			0
$787$	−93.8015			−0.119189			−0.0595944	−	0.998223i	$-0.518981\pi$
$787$	−93.8015			−0.119189			−0.0595944	+	0.998223i	$0.518981\pi$
$788$		−	783.563i		−	0.994369i
$789$		0			0
$790$	330.831	−	473.163i	0.418773	−	0.598940i
$791$	−353.753	−	132.688i	−0.447222	−	0.167747i
$792$		0			0
$793$			1125.02i			1.41869i
$794$		−	1206.82i		−	1.51992i
$795$		0			0
$796$		−	2134.92i		−	2.68206i
$797$	−23.8723			−0.0299527			−0.0149764	−	0.999888i	$-0.504767\pi$
$797$	−23.8723			−0.0299527			−0.0149764	+	0.999888i	$0.504767\pi$
$798$		0			0
$799$	−1460.69			−1.82815
$800$	712.690	−	260.501i	0.890863	−	0.325626i
$801$		0			0
$802$			1240.83i			1.54717i
$803$	−343.345			−0.427578
$804$		0			0
$805$	−26.9051	−	39.1784i	−0.0334225	−	0.0486688i
$806$	2043.11			2.53488
$807$		0			0
$808$	−28.0459			−0.0347102
$809$	−375.758			−0.464472			−0.232236	−	0.972659i	$-0.574604\pi$
$809$	−375.758			−0.464472			−0.232236	+	0.972659i	$0.574604\pi$
$810$		0			0
$811$		−	174.091i		−	0.214662i	−0.994223	−	0.107331i	$-0.965770\pi$
$811$		−	174.091i		−	0.214662i	0.994223	−	0.107331i	$-0.0342304\pi$
$812$	−508.042	+	1354.46i	−0.625668	+	1.66806i
$813$		0			0
$814$	−1818.36			−2.23386
$815$	76.7484	−	109.767i	0.0941698	−	0.134684i
$816$		0			0
$817$	334.248			0.409117
$818$	−911.047			−1.11375
$819$		0			0
$820$	841.996	−	1204.24i	1.02682	−	1.46859i
$821$	549.756			0.669618			0.334809	−	0.942286i	$-0.391328\pi$
$821$	549.756			0.669618			0.334809	+	0.942286i	$0.391328\pi$
$822$		0			0
$823$		−	368.053i		−	0.447209i	−0.974680	−	0.223605i	$-0.928218\pi$
$823$		−	368.053i		−	0.447209i	0.974680	−	0.223605i	$-0.0717825\pi$
$824$		−	536.993i		−	0.651690i
$825$		0			0
$826$	639.564	−	1705.11i	0.774291	−	2.06430i
$827$			998.892i			1.20785i	0.797041	+	0.603925i	$0.206397\pi$
$827$			998.892i			1.20785i	−0.797041	+	0.603925i	$0.793603\pi$
$828$		0			0
$829$		−	1575.97i		−	1.90105i	−0.310655	−	0.950523i	$-0.600548\pi$
$829$		−	1575.97i		−	1.90105i	0.310655	−	0.950523i	$-0.399452\pi$
$830$	−88.9995	+	127.289i	−0.107228	+	0.153361i
$831$		0			0
$832$	2420.26			2.90897
$833$	−844.412	−	737.169i	−1.01370	−	0.884957i
$834$		0			0
$835$	−183.394	−	128.227i	−0.219633	−	0.153566i
$836$		−	1561.89i		−	1.86829i
$837$		0			0
$838$	1838.29			2.19367
$839$		−	331.851i		−	0.395531i	−0.980249	−	0.197766i	$-0.936632\pi$
$839$		−	331.851i		−	0.395531i	0.980249	−	0.197766i	$-0.0633685\pi$
$840$		0			0
$841$	144.633			0.171978
$842$		−	79.7154i		−	0.0946739i
$843$		0			0
$844$	1642.20			1.94574
$845$	−1581.53	−	1105.79i	−1.87164	−	1.30863i
$846$		0			0
$847$	13.5322	−	36.0774i	0.0159766	−	0.0425944i
$848$			34.9633i			0.0412303i
$849$		0			0
$850$	−1747.36	+	638.690i	−2.05571	+	0.751400i
$851$	67.4845			0.0793003
$852$		0			0
$853$	−55.8775			−0.0655071			−0.0327535	−	0.999463i	$-0.510428\pi$
$853$	−55.8775			−0.0655071			−0.0327535	+	0.999463i	$0.510428\pi$
$854$	−381.922	+	1018.22i	−0.447216	+	1.19230i
$855$		0			0
$856$	571.307			0.667415
$857$	−78.1764			−0.0912210			−0.0456105	−	0.998959i	$-0.514523\pi$
$857$	−78.1764			−0.0912210			−0.0456105	+	0.998959i	$0.514523\pi$
$858$		0			0
$859$		−	1425.05i		−	1.65897i	−0.558532	−	0.829483i	$-0.688635\pi$
$859$		−	1425.05i		−	1.65897i	0.558532	−	0.829483i	$-0.311365\pi$
$860$	−298.814	+	427.371i	−0.347458	+	0.496943i
$861$		0			0
$862$		−	458.788i		−	0.532237i
$863$			255.040i			0.295527i	0.989023	+	0.147763i	$0.0472074\pi$
$863$			255.040i			0.295527i	−0.989023	+	0.147763i	$0.952793\pi$
$864$		0			0
$865$	−285.299	−	199.479i	−0.329826	−	0.230611i
$866$		−	527.124i		−	0.608688i
$867$		0			0
$868$	1150.21	+	431.430i	1.32513	+	0.497039i
$869$	−399.232			−0.459416
$870$		0			0
$871$		−	373.246i		−	0.428526i
$872$			1236.23i			1.41770i
$873$		0			0
$874$			93.1904i			0.106625i
$875$	−712.856	−	507.407i	−0.814692	−	0.579894i
$876$		0			0
$877$			272.418i			0.310625i	0.987865	+	0.155312i	$0.0496384\pi$
$877$			272.418i			0.310625i	−0.987865	+	0.155312i	$0.950362\pi$
$878$	1011.31			1.15183
$879$		0			0
$880$	46.0888	+	32.2248i	0.0523736	+	0.0366191i
$881$		−	1033.52i		−	1.17312i	−0.809905	−	0.586561i	$-0.800481\pi$
$881$		−	1033.52i		−	1.17312i	0.809905	−	0.586561i	$-0.199519\pi$
$882$		0			0
$883$		−	847.015i		−	0.959247i	−0.877474	−	0.479624i	$-0.840773\pi$
$883$		−	847.015i		−	0.959247i	0.877474	−	0.479624i	$-0.159227\pi$
$884$	−3547.33			−4.01281
$885$		0			0
$886$	−2286.95			−2.58121
$887$	818.547			0.922826			0.461413	−	0.887185i	$-0.347343\pi$
$887$	818.547			0.922826			0.461413	+	0.887185i	$0.347343\pi$
$888$		0			0
$889$	665.630	+	249.669i	0.748740	+	0.280843i
$890$	506.134	+	353.884i	0.568690	+	0.397623i
$891$		0			0
$892$	1491.30			1.67187
$893$			1347.05i			1.50845i
$894$		0			0
$895$	1021.56	+	714.268i	1.14141	+	0.798065i
$896$	1394.77	+	523.161i	1.55667	+	0.583885i
$897$		0			0
$898$			1691.98i			1.88417i
$899$		−	837.000i		−	0.931034i
$900$		0			0
$901$			799.814i			0.887696i
$902$	−1633.52			−1.81100
$903$		0			0
$904$	−453.455			−0.501610
$905$	531.364	−	759.970i	0.587143	−	0.839746i
$906$		0			0
$907$			49.5779i			0.0546614i	0.999626	+	0.0273307i	$0.00870072\pi$
$907$			49.5779i			0.0546614i	−0.999626	+	0.0273307i	$0.991299\pi$
$908$	−125.713			−0.138450
$909$		0			0
$910$	−1518.40	−	2211.04i	−1.66857	−	2.42972i
$911$	−1061.36			−1.16505			−0.582525	−	0.812813i	$-0.697935\pi$
$911$	−1061.36			−1.16505			−0.582525	+	0.812813i	$0.697935\pi$
$912$		0			0
$913$	107.401			0.117635
$914$	−895.099			−0.979321
$915$		0			0
$916$			1587.10i			1.73264i
$917$	−987.230	−	370.297i	−1.07659	−	0.403814i
$918$		0			0
$919$	914.414			0.995009			0.497505	−	0.867461i	$-0.334250\pi$
$919$	914.414			0.995009			0.497505	+	0.867461i	$0.334250\pi$
$920$	−46.7481	−	32.6858i	−0.0508132	−	0.0355281i
$921$		0			0
$922$	−1944.62			−2.10914
$923$	1115.14			1.20817
$924$		0			0
$925$	1166.92	−	426.529i	1.26153	−	0.461112i
$926$	−717.488			−0.774825
$927$		0			0
$928$		−	952.904i		−	1.02684i
$929$			1125.60i			1.21162i	0.795608	+	0.605812i	$0.207152\pi$
$929$			1125.60i			1.21162i	−0.795608	+	0.605812i	$0.792848\pi$
$930$		0			0
$931$	−679.818	+	778.718i	−0.730202	+	0.836432i
$932$		−	2432.61i		−	2.61010i
$933$		0			0
$934$			650.980i			0.696981i
$935$	1054.32	+	737.169i	1.12761	+	0.788416i
$936$		0			0
$937$	625.406			0.667456			0.333728	−	0.942669i	$-0.391693\pi$
$937$	625.406			0.667456			0.333728	+	0.942669i	$0.391693\pi$
$938$	126.709	−	337.813i	0.135085	−	0.360142i
$939$		0			0
$940$	−1722.34	−	1204.24i	−1.83228	−	1.28111i
$941$		−	784.430i		−	0.833613i	−0.908995	−	0.416807i	$-0.863149\pi$
$941$		−	784.430i		−	0.833613i	0.908995	−	0.416807i	$-0.136851\pi$
$942$		0			0
$943$	60.6248			0.0642893
$944$		−	79.9728i		−	0.0847169i
$945$		0			0
$946$	579.717			0.612808
$947$			1851.02i			1.95462i	0.211817	+	0.977309i	$0.432062\pi$
$947$			1851.02i			1.95462i	−0.211817	+	0.977309i	$0.567938\pi$
$948$		0			0
$949$	719.129			0.757775
$950$	589.000	+	1611.41i	0.620000	+	1.69623i
$951$		0			0
$952$	−1259.62	−	472.467i	−1.32313	−	0.496289i
$953$		−	332.665i		−	0.349071i	−0.984651	−	0.174536i	$-0.944158\pi$
$953$		−	332.665i		−	0.349071i	0.984651	−	0.174536i	$-0.0558425\pi$
$954$		0			0
$955$	−1038.80	−	726.316i	−1.08774	−	0.760540i
$956$	2939.58			3.07487
$957$		0			0
$958$	−1617.04			−1.68794
$959$	−1451.31	−	544.366i	−1.51335	−	0.567639i
$960$		0			0
$961$	250.220			0.260374
$962$	3808.51			3.95895
$963$		0			0
$964$		−	1974.71i		−	2.04846i
$965$	945.107	−	1351.72i	0.979386	−	1.40074i
$966$		0			0
$967$			1711.47i			1.76987i	0.465711	+	0.884937i	$0.345799\pi$
$967$			1711.47i			1.76987i	−0.465711	+	0.884937i	$0.654201\pi$
$968$		−	46.2456i		−	0.0477744i
$969$		0			0
$970$	849.564	−	1215.07i	0.875840	−	1.25265i
$971$			285.260i			0.293780i	0.989153	+	0.146890i	$0.0469263\pi$
$971$			285.260i			0.293780i	−0.989153	+	0.146890i	$0.953074\pi$
$972$		0			0
$973$	983.087	+	368.744i	1.01037	+	0.378976i
$974$	667.803			0.685629
$975$		0			0
$976$			47.7566i			0.0489309i
$977$		−	1059.99i		−	1.08494i	−0.840075	−	0.542470i	$-0.817489\pi$
$977$		−	1059.99i		−	1.08494i	0.840075	−	0.542470i	$-0.182511\pi$
$978$		0			0
$979$		−	427.052i		−	0.436213i
$980$	−387.922	−	1565.38i	−0.395839	−	1.59733i
$981$		0			0
$982$			2286.64i			2.32855i
$983$	−115.168			−0.117159			−0.0585797	−	0.998283i	$-0.518657\pi$
$983$	−115.168			−0.117159			−0.0585797	+	0.998283i	$0.518657\pi$
$984$		0			0
$985$	341.048	−	487.775i	0.346242	−	0.495203i
$986$			2336.31i			2.36948i
$987$		0			0
$988$			3271.35i			3.31108i
$989$	−21.5150			−0.0217543
$990$		0			0
$991$	−1012.19			−1.02138			−0.510692	−	0.859763i	$-0.670611\pi$
$991$	−1012.19			−1.02138			−0.510692	+	0.859763i	$0.670611\pi$
$992$	−809.206			−0.815732
$993$		0			0
$994$	1009.28	+	378.568i	1.01537	+	0.380854i
$995$	929.229	−	1329.01i	0.933898	−	1.33569i
$996$		0			0
$997$	−28.9473			−0.0290344			−0.0145172	−	0.999895i	$-0.504621\pi$
$997$	−28.9473			−0.0290344			−0.0145172	+	0.999895i	$0.504621\pi$
$998$		−	71.5679i		−	0.0717113i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.e.d.244.13	yes	16
3.2	odd	2	inner	315.3.e.d.244.4	yes	16
5.4	even	2	inner	315.3.e.d.244.3	yes	16
7.6	odd	2	inner	315.3.e.d.244.16	yes	16
15.14	odd	2	inner	315.3.e.d.244.14	yes	16
21.20	even	2	inner	315.3.e.d.244.1	✓	16
35.34	odd	2	inner	315.3.e.d.244.2	yes	16
105.104	even	2	inner	315.3.e.d.244.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.3.e.d.244.1	✓	16	21.20	even	2	inner
315.3.e.d.244.2	yes	16	35.34	odd	2	inner
315.3.e.d.244.3	yes	16	5.4	even	2	inner
315.3.e.d.244.4	yes	16	3.2	odd	2	inner
315.3.e.d.244.13	yes	16	1.1	even	1	trivial
315.3.e.d.244.14	yes	16	15.14	odd	2	inner
315.3.e.d.244.15	yes	16	105.104	even	2	inner
315.3.e.d.244.16	yes	16	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.25309i q^{2} -6.58258 q^{4} +(-4.09772 - 2.86509i) q^{5} +(2.45837 - 6.55412i) q^{7} -8.40134i q^{8} +(9.32037 - 13.3302i) q^{10} -11.2474 q^{11} +23.5575 q^{13} +(21.3211 + 7.99728i) q^{14} +1.00000 q^{16} +22.8758 q^{17} -21.0961i q^{19} +(26.9735 + 18.8596i) q^{20} -36.5888i q^{22} +1.35792i q^{23} +(8.58258 + 23.4806i) q^{25} +76.6345i q^{26} +(-16.1824 + 43.1430i) q^{28} +31.3948 q^{29} -26.6605i q^{31} -30.3523i q^{32} +74.4170i q^{34} +(-28.8518 + 19.8135i) q^{35} -49.6971i q^{37} +68.6275 q^{38} +(-24.0706 + 34.4263i) q^{40} -44.6454i q^{41} +15.8441i q^{43} +74.0370 q^{44} -4.41742 q^{46} -63.8530 q^{47} +(-36.9129 - 32.2248i) q^{49} +(-76.3845 + 27.9199i) q^{50} -155.069 q^{52} +34.9633i q^{53} +(46.0888 + 32.2248i) q^{55} +(-55.0634 - 20.6536i) q^{56} +102.130i q^{58} -79.9728i q^{59} +47.7566i q^{61} +86.7288 q^{62} +102.739 q^{64} +(-96.5319 - 67.4942i) q^{65} -15.8441i q^{67} -150.582 q^{68} +(-64.4550 - 93.8574i) q^{70} +47.3372 q^{71} +30.5266 q^{73} +161.669 q^{74} +138.867i q^{76} +(-27.6503 + 73.7169i) q^{77} +35.4955 q^{79} +(-4.09772 - 2.86509i) q^{80} +145.235 q^{82} -9.54892 q^{83} +(-93.7386 - 65.5412i) q^{85} -51.5422 q^{86} +94.4935i q^{88} +37.9689i q^{89} +(57.9129 - 154.398i) q^{91} -8.93860i q^{92} -207.719i q^{94} +(-60.4421 + 86.4459i) q^{95} +91.1513 q^{97} +(104.830 - 120.081i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 16 q^{16} + 64 q^{25} - 144 q^{46} - 224 q^{49} + 544 q^{64} + 128 q^{79} - 400 q^{85} + 560 q^{91}+O(q^{100}) \) 16 * q - 32 * q^4 + 16 * q^16 + 64 * q^25 - 144 * q^46 - 224 * q^49 + 544 * q^64 + 128 * q^79 - 400 * q^85 + 560 * q^91

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