LMFDB - Embedded newform 120.9.l.a.41.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [120,9,Mod(41,120)] 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("120.41"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(120, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 0])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	120.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$48.8854332073$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	120.41
Dual form			120.9.l.a.41.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-74.5360 - 31.7078i) q^{3} +279.508i q^{5} -171.670 q^{7} +(4550.23 + 4726.74i) q^{9} +6473.42i q^{11} -13007.6 q^{13} +(8862.59 - 20833.4i) q^{15} -90002.6i q^{17} +209646. q^{19} +(12795.6 + 5443.26i) q^{21} +142496. i q^{23} -78125.0 q^{25} +(-189282. - 496590. i) q^{27} -214871. i q^{29} +624531. q^{31} +(205258. - 482503. i) q^{33} -47983.1i q^{35} -1.54483e6 q^{37} +(969536. + 412443. i) q^{39} -716603. i q^{41} -2.19014e6 q^{43} +(-1.32116e6 + 1.27183e6i) q^{45} +4.57901e6i q^{47} -5.73533e6 q^{49} +(-2.85378e6 + 6.70844e6i) q^{51} +6.30043e6i q^{53} -1.80938e6 q^{55} +(-1.56261e7 - 6.64739e6i) q^{57} +1.68574e7i q^{59} -9.90116e6 q^{61} +(-781137. - 811438. i) q^{63} -3.63574e6i q^{65} -1.04269e7 q^{67} +(4.51822e6 - 1.06211e7i) q^{69} -2.23330e6i q^{71} -3.07135e7 q^{73} +(5.82313e6 + 2.47717e6i) q^{75} -1.11129e6i q^{77} -5.95888e7 q^{79} +(-1.63746e6 + 4.30156e7i) q^{81} -901913. i q^{83} +2.51565e7 q^{85} +(-6.81307e6 + 1.60156e7i) q^{87} -6.13760e7i q^{89} +2.23301e6 q^{91} +(-4.65500e7 - 1.98025e7i) q^{93} +5.85977e7i q^{95} -2.96725e7 q^{97} +(-3.05982e7 + 2.94556e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 112 q^{3} - 3008 q^{7} - 3184 q^{9} + 25696 q^{13} - 315872 q^{19} + 55216 q^{21} - 2500000 q^{25} + 605360 q^{27} - 1668576 q^{31} + 567104 q^{33} - 982624 q^{37} + 6709536 q^{39} - 13925344 q^{43}+ \cdots + 369200768 q^{99}+O(q^{100}) $ 32 * q - 112 * q^3 - 3008 * q^7 - 3184 * q^9 + 25696 * q^13 - 315872 * q^19 + 55216 * q^21 - 2500000 * q^25 + 605360 * q^27 - 1668576 * q^31 + 567104 * q^33 - 982624 * q^37 + 6709536 * q^39 - 13925344 * q^43 + 2370000 * q^45 + 44885632 * q^49 + 5870080 * q^51 - 2380000 * q^55 - 18347616 * q^57 + 43722656 * q^61 + 49774624 * q^63 - 28637536 * q^67 - 117303344 * q^69 + 133552256 * q^73 + 8750000 * q^75 - 68622944 * q^79 - 206826112 * q^81 + 392120416 * q^87 - 489280960 * q^91 - 242074304 * q^93 + 532016448 * q^97 + 369200768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−74.5360	−	31.7078i	−0.920198	−	0.391454i
$3$	−74.5360	−	31.7078i	−0.920198	−	0.391454i
$4$		0			0
$5$			279.508i			0.447214i
$5$			279.508i			0.447214i
$6$		0			0
$7$	−171.670			−0.0714992			−0.0357496	−	0.999361i	$-0.511382\pi$
$7$	−171.670			−0.0714992			−0.0357496	+	0.999361i	$0.511382\pi$
$8$		0			0
$9$	4550.23	+	4726.74i	0.693528	+	0.720430i
$10$		0			0
$11$			6473.42i			0.442143i	0.975258	+	0.221072i	$0.0709555\pi$
$11$			6473.42i			0.442143i	−0.975258	+	0.221072i	$0.929045\pi$
$12$		0			0
$13$	−13007.6			−0.455433			−0.227716	−	0.973728i	$-0.573126\pi$
$13$	−13007.6			−0.455433			−0.227716	+	0.973728i	$0.573126\pi$
$14$		0			0
$15$	8862.59	−	20833.4i	0.175064	−	0.411525i
$16$		0			0
$17$		−	90002.6i		−	1.07760i	−0.842432	−	0.538802i	$-0.818877\pi$
$17$		−	90002.6i		−	1.07760i	0.842432	−	0.538802i	$-0.181123\pi$
$18$		0			0
$19$	209646.			1.60869			0.804343	−	0.594165i	$-0.202517\pi$
$19$	209646.			1.60869			0.804343	+	0.594165i	$0.202517\pi$
$20$		0			0
$21$	12795.6	+	5443.26i	0.0657934	+	0.0279887i
$22$		0			0
$23$			142496.i			0.509203i	0.967046	+	0.254601i	$0.0819442\pi$
$23$			142496.i			0.509203i	−0.967046	+	0.254601i	$0.918056\pi$
$24$		0			0
$25$	−78125.0			−0.200000
$26$		0			0
$27$	−189282.	−	496590.i	−0.356167	−	0.934422i
$28$		0			0
$29$		−	214871.i		−	0.303798i	−0.988396	−	0.151899i	$-0.951461\pi$
$29$		−	214871.i		−	0.303798i	0.988396	−	0.151899i	$-0.0485389\pi$
$30$		0			0
$31$	624531.			0.676249			0.338125	−	0.941101i	$-0.390207\pi$
$31$	624531.			0.676249			0.338125	+	0.941101i	$0.390207\pi$
$32$		0			0
$33$	205258.	−	482503.i	0.173079	−	0.406859i
$34$		0			0
$35$		−	47983.1i		−	0.0319754i
$36$		0			0
$37$	−1.54483e6			−0.824276			−0.412138	−	0.911122i	$-0.635218\pi$
$37$	−1.54483e6			−0.824276			−0.412138	+	0.911122i	$0.635218\pi$
$38$		0			0
$39$	969536.	+	412443.i	0.419088	+	0.178281i
$40$		0			0
$41$		−	716603.i		−	0.253596i	−0.991929	−	0.126798i	$-0.959530\pi$
$41$		−	716603.i		−	0.253596i	0.991929	−	0.126798i	$-0.0404701\pi$
$42$		0			0
$43$	−2.19014e6			−0.640618			−0.320309	−	0.947313i	$-0.603787\pi$
$43$	−2.19014e6			−0.640618			−0.320309	+	0.947313i	$0.603787\pi$
$44$		0			0
$45$	−1.32116e6	+	1.27183e6i	−0.322186	+	0.310155i
$46$		0			0
$47$			4.57901e6i			0.938382i	0.883097	+	0.469191i	$0.155454\pi$
$47$			4.57901e6i			0.938382i	−0.883097	+	0.469191i	$0.844546\pi$
$48$		0			0
$49$	−5.73533e6			−0.994888
$50$		0			0
$51$	−2.85378e6	+	6.70844e6i	−0.421833	+	0.991609i
$52$		0			0
$53$			6.30043e6i			0.798484i	0.916846	+	0.399242i	$0.130727\pi$
$53$			6.30043e6i			0.798484i	−0.916846	+	0.399242i	$0.869273\pi$
$54$		0			0
$55$	−1.80938e6			−0.197732
$56$		0			0
$57$	−1.56261e7	−	6.64739e6i	−1.48031	−	0.629727i
$58$		0			0
$59$			1.68574e7i			1.39118i	0.718439	+	0.695590i	$0.244857\pi$
$59$			1.68574e7i			1.39118i	−0.718439	+	0.695590i	$0.755143\pi$
$60$		0			0
$61$	−9.90116e6			−0.715100			−0.357550	−	0.933894i	$-0.616388\pi$
$61$	−9.90116e6			−0.715100			−0.357550	+	0.933894i	$0.616388\pi$
$62$		0			0
$63$	−781137.	−	811438.i	−0.0495867	−	0.0515102i
$64$		0			0
$65$		−	3.63574e6i		−	0.203676i
$66$		0			0
$67$	−1.04269e7			−0.517437			−0.258719	−	0.965953i	$-0.583300\pi$
$67$	−1.04269e7			−0.517437			−0.258719	+	0.965953i	$0.583300\pi$
$68$		0			0
$69$	4.51822e6	−	1.06211e7i	0.199329	−	0.468567i
$70$		0			0
$71$		−	2.23330e6i		−	0.0878847i	−0.999034	−	0.0439424i	$-0.986008\pi$
$71$		−	2.23330e6i		−	0.0878847i	0.999034	−	0.0439424i	$-0.0139918\pi$
$72$		0			0
$73$	−3.07135e7			−1.08153			−0.540764	−	0.841174i	$-0.681865\pi$
$73$	−3.07135e7			−1.08153			−0.540764	+	0.841174i	$0.681865\pi$
$74$		0			0
$75$	5.82313e6	+	2.47717e6i	0.184040	+	0.0782908i
$76$		0			0
$77$		−	1.11129e6i		−	0.0316129i
$78$		0			0
$79$	−5.95888e7			−1.52988			−0.764938	−	0.644104i	$-0.777230\pi$
$79$	−5.95888e7			−1.52988			−0.764938	+	0.644104i	$0.777230\pi$
$80$		0			0
$81$	−1.63746e6	+	4.30156e7i	−0.0380392	+	0.999276i
$82$		0			0
$83$		−	901913.i		−	0.0190043i	−0.999955	−	0.00950216i	$-0.996975\pi$
$83$		−	901913.i		−	0.0190043i	0.999955	−	0.00950216i	$-0.00302468\pi$
$84$		0			0
$85$	2.51565e7			0.481919
$86$		0			0
$87$	−6.81307e6	+	1.60156e7i	−0.118923	+	0.279554i
$88$		0			0
$89$		−	6.13760e7i		−	0.978225i	−0.872221	−	0.489113i	$-0.837321\pi$
$89$		−	6.13760e7i		−	0.978225i	0.872221	−	0.489113i	$-0.162679\pi$
$90$		0			0
$91$	2.23301e6			0.0325631
$92$		0			0
$93$	−4.65500e7	−	1.98025e7i	−0.622283	−	0.264721i
$94$		0			0
$95$			5.85977e7i			0.719426i
$96$		0			0
$97$	−2.96725e7			−0.335171			−0.167586	−	0.985858i	$-0.553597\pi$
$97$	−2.96725e7			−0.335171			−0.167586	+	0.985858i	$0.553597\pi$
$98$		0			0
$99$	−3.05982e7	+	2.94556e7i	−0.318533	+	0.306638i
$100$		0			0
$101$			8.54439e7i			0.821099i	0.911838	+	0.410549i	$0.134663\pi$
$101$			8.54439e7i			0.821099i	−0.911838	+	0.410549i	$0.865337\pi$
$102$		0			0
$103$	−1.21936e7			−0.108338			−0.0541691	−	0.998532i	$-0.517251\pi$
$103$	−1.21936e7			−0.108338			−0.0541691	+	0.998532i	$0.517251\pi$
$104$		0			0
$105$	−1.52144e6	+	3.57647e6i	−0.0125169	+	0.0294237i
$106$		0			0
$107$		−	5.20836e7i		−	0.397343i	−0.980066	−	0.198672i	$-0.936337\pi$
$107$		−	5.20836e7i		−	0.397343i	0.980066	−	0.198672i	$-0.0636627\pi$
$108$		0			0
$109$	−2.09207e8			−1.48208			−0.741039	−	0.671462i	$-0.765667\pi$
$109$	−2.09207e8			−1.48208			−0.741039	+	0.671462i	$0.765667\pi$
$110$		0			0
$111$	1.15145e8	+	4.89830e7i	0.758497	+	0.322666i
$112$		0			0
$113$			1.77766e7i			0.109027i	0.998513	+	0.0545136i	$0.0173608\pi$
$113$			1.77766e7i			0.109027i	−0.998513	+	0.0545136i	$0.982639\pi$
$114$		0			0
$115$	−3.98288e7			−0.227722
$116$		0			0
$117$	−5.91877e7	−	6.14836e7i	−0.315855	−	0.328108i
$118$		0			0
$119$			1.54507e7i			0.0770479i
$120$		0			0
$121$	1.72454e8			0.804509
$122$		0			0
$123$	−2.27219e7	+	5.34127e7i	−0.0992714	+	0.233359i
$124$		0			0
$125$		−	2.18366e7i		−	0.0894427i
$126$		0			0
$127$	−4.57135e8			−1.75723			−0.878616	−	0.477528i	$-0.841533\pi$
$127$	−4.57135e8			−1.75723			−0.878616	+	0.477528i	$0.841533\pi$
$128$		0			0
$129$	1.63245e8	+	6.94446e7i	0.589495	+	0.250772i
$130$		0			0
$131$			4.95158e8i			1.68135i	0.541537	+	0.840677i	$0.317842\pi$
$131$			4.95158e8i			1.68135i	−0.541537	+	0.840677i	$0.682158\pi$
$132$		0			0
$133$	−3.59898e7			−0.115020
$134$		0			0
$135$	1.38801e8	−	5.29059e7i	0.417886	−	0.159283i
$136$		0			0
$137$		−	5.97473e8i		−	1.69604i	−0.529965	−	0.848020i	$-0.677795\pi$
$137$		−	5.97473e8i		−	1.69604i	0.529965	−	0.848020i	$-0.322205\pi$
$138$		0			0
$139$	5.92301e8			1.58666			0.793329	−	0.608794i	$-0.208346\pi$
$139$	5.92301e8			1.58666			0.793329	+	0.608794i	$0.208346\pi$
$140$		0			0
$141$	1.45190e8	−	3.41301e8i	0.367334	−	0.863497i
$142$		0			0
$143$		−	8.42037e7i		−	0.201367i
$144$		0			0
$145$	6.00582e7			0.135863
$146$		0			0
$147$	4.27489e8	+	1.81855e8i	0.915493	+	0.389453i
$148$		0			0
$149$		−	3.91213e8i		−	0.793722i	−0.917879	−	0.396861i	$-0.870099\pi$
$149$		−	3.91213e8i		−	0.793722i	0.917879	−	0.396861i	$-0.129901\pi$
$150$		0			0
$151$	6.44987e8			1.24063			0.620316	−	0.784352i	$-0.287004\pi$
$151$	6.44987e8			1.24063			0.620316	+	0.784352i	$0.287004\pi$
$152$		0			0
$153$	4.25419e8	−	4.09533e8i	0.776339	−	0.747349i
$154$		0			0
$155$			1.74562e8i			0.302428i
$156$		0			0
$157$	−1.47952e8			−0.243513			−0.121757	−	0.992560i	$-0.538853\pi$
$157$	−1.47952e8			−0.243513			−0.121757	+	0.992560i	$0.538853\pi$
$158$		0			0
$159$	1.99772e8	−	4.69609e8i	0.312570	−	0.734763i
$160$		0			0
$161$		−	2.44622e7i		−	0.0364076i
$162$		0			0
$163$	5.42924e8			0.769111			0.384555	−	0.923102i	$-0.374355\pi$
$163$	5.42924e8			0.769111			0.384555	+	0.923102i	$0.374355\pi$
$164$		0			0
$165$	1.34864e8	+	5.73713e7i	0.181953	+	0.0774032i
$166$		0			0
$167$			4.70654e8i			0.605113i	0.953132	+	0.302556i	$0.0978400\pi$
$167$			4.70654e8i			0.605113i	−0.953132	+	0.302556i	$0.902160\pi$
$168$		0			0
$169$	−6.46533e8			−0.792581
$170$		0			0
$171$	9.53936e8	+	9.90941e8i	1.11567	+	1.15895i
$172$		0			0
$173$		−	1.34866e9i		−	1.50563i	−0.658232	−	0.752815i	$-0.728696\pi$
$173$		−	1.34866e9i		−	1.50563i	0.658232	−	0.752815i	$-0.271304\pi$
$174$		0			0
$175$	1.34117e7			0.0142998
$176$		0			0
$177$	5.34511e8	−	1.25649e9i	0.544583	−	1.28016i
$178$		0			0
$179$			1.37350e8i			0.133788i	0.997760	+	0.0668939i	$0.0213089\pi$
$179$			1.37350e8i			0.133788i	−0.997760	+	0.0668939i	$0.978691\pi$
$180$		0			0
$181$	−1.14873e8			−0.107030			−0.0535150	−	0.998567i	$-0.517042\pi$
$181$	−1.14873e8			−0.107030			−0.0535150	+	0.998567i	$0.517042\pi$
$182$		0			0
$183$	7.37993e8	+	3.13944e8i	0.658033	+	0.279929i
$184$		0			0
$185$		−	4.31792e8i		−	0.368627i
$186$		0			0
$187$	5.82625e8			0.476456
$188$		0			0
$189$	3.24939e7	+	8.52495e7i	0.0254657	+	0.0668105i
$190$		0			0
$191$		−	9.26491e7i		−	0.0696158i	−0.999394	−	0.0348079i	$-0.988918\pi$
$191$		−	9.26491e7i		−	0.0696158i	0.999394	−	0.0348079i	$-0.0110819\pi$
$192$		0			0
$193$	−2.15772e9			−1.55512			−0.777562	−	0.628806i	$-0.783544\pi$
$193$	−2.15772e9			−1.55512			−0.777562	+	0.628806i	$0.783544\pi$
$194$		0			0
$195$	−1.15281e8	+	2.70993e8i	−0.0797297	+	0.187422i
$196$		0			0
$197$			4.88154e8i			0.324110i	0.986782	+	0.162055i	$0.0518122\pi$
$197$			4.88154e8i			0.324110i	−0.986782	+	0.162055i	$0.948188\pi$
$198$		0			0
$199$	−8.37599e8			−0.534102			−0.267051	−	0.963682i	$-0.586049\pi$
$199$	−8.37599e8			−0.534102			−0.267051	+	0.963682i	$0.586049\pi$
$200$		0			0
$201$	7.77183e8	+	3.30615e8i	0.476145	+	0.202553i
$202$		0			0
$203$			3.68868e7i			0.0217213i
$204$		0			0
$205$	2.00297e8			0.113412
$206$		0			0
$207$	−6.73541e8	+	6.48389e8i	−0.366845	+	0.353146i
$208$		0			0
$209$			1.35712e9i			0.711270i
$210$		0			0
$211$	−2.32062e9			−1.17078			−0.585390	−	0.810752i	$-0.699058\pi$
$211$	−2.32062e9			−1.17078			−0.585390	+	0.810752i	$0.699058\pi$
$212$		0			0
$213$	−7.08129e7	+	1.66461e8i	−0.0344028	+	0.0808713i
$214$		0			0
$215$		−	6.12164e8i		−	0.286493i
$216$		0			0
$217$	−1.07213e8			−0.0483513
$218$		0			0
$219$	2.28926e9	+	9.73856e8i	0.995219	+	0.423368i
$220$		0			0
$221$			1.17072e9i			0.490777i
$222$		0			0
$223$	−3.72404e9			−1.50590			−0.752948	−	0.658080i	$-0.771369\pi$
$223$	−3.72404e9			−1.50590			−0.752948	+	0.658080i	$0.771369\pi$
$224$		0			0
$225$	−3.55487e8	−	3.69277e8i	−0.138706	−	0.144086i
$226$		0			0
$227$			3.77637e9i			1.42223i	0.703074	+	0.711117i	$0.251810\pi$
$227$			3.77637e9i			1.42223i	−0.703074	+	0.711117i	$0.748190\pi$
$228$		0			0
$229$	−2.18662e9			−0.795116			−0.397558	−	0.917577i	$-0.630142\pi$
$229$	−2.18662e9			−0.795116			−0.397558	+	0.917577i	$0.630142\pi$
$230$		0			0
$231$	−3.52365e7	+	8.28311e7i	−0.0123750	+	0.0290901i
$232$		0			0
$233$		−	1.55999e8i		−	0.0529296i	−0.999650	−	0.0264648i	$-0.991575\pi$
$233$		−	1.55999e8i		−	0.0529296i	0.999650	−	0.0264648i	$-0.00842499\pi$
$234$		0			0
$235$	−1.27987e9			−0.419657
$236$		0			0
$237$	4.44151e9	+	1.88943e9i	1.40779	+	0.598876i
$238$		0			0
$239$		−	2.95576e9i		−	0.905895i	−0.891537	−	0.452948i	$-0.850372\pi$
$239$		−	2.95576e9i		−	0.905895i	0.891537	−	0.452948i	$-0.149628\pi$
$240$		0			0
$241$	−2.98059e9			−0.883557			−0.441778	−	0.897124i	$-0.645652\pi$
$241$	−2.98059e9			−0.883557			−0.441778	+	0.897124i	$0.645652\pi$
$242$		0			0
$243$	1.48598e9	−	3.15429e9i	0.426174	−	0.904641i
$244$		0			0
$245$		−	1.60307e9i		−	0.444927i
$246$		0			0
$247$	−2.72699e9			−0.732648
$248$		0			0
$249$	−2.85977e7	+	6.72250e7i	−0.00743932	+	0.0174877i
$250$		0			0
$251$		−	1.27947e9i		−	0.322357i	−0.986925	−	0.161178i	$-0.948471\pi$
$251$		−	1.27947e9i		−	0.322357i	0.986925	−	0.161178i	$-0.0515294\pi$
$252$		0			0
$253$	−9.22435e8			−0.225140
$254$		0			0
$255$	−1.87507e9	−	7.97657e8i	−0.443461	−	0.188649i
$256$		0			0
$257$		−	6.71890e8i		−	0.154016i	−0.997030	−	0.0770080i	$-0.975463\pi$
$257$		−	6.71890e8i		−	0.154016i	0.997030	−	0.0770080i	$-0.0245367\pi$
$258$		0			0
$259$	2.65200e8			0.0589351
$260$		0			0
$261$	1.01564e9	−	9.77712e8i	0.218865	−	0.210692i
$262$		0			0
$263$		−	6.42461e9i		−	1.34284i	−0.741078	−	0.671419i	$-0.765685\pi$
$263$		−	6.42461e9i		−	1.34284i	0.741078	−	0.671419i	$-0.234315\pi$
$264$		0			0
$265$	−1.76102e9			−0.357093
$266$		0			0
$267$	−1.94610e9	+	4.57473e9i	−0.382930	+	0.900161i
$268$		0			0
$269$			8.73020e9i			1.66730i	0.552289	+	0.833652i	$0.313754\pi$
$269$			8.73020e9i			1.66730i	−0.552289	+	0.833652i	$0.686246\pi$
$270$		0			0
$271$	−5.68086e9			−1.05326			−0.526631	−	0.850094i	$-0.676545\pi$
$271$	−5.68086e9			−1.05326			−0.526631	+	0.850094i	$0.676545\pi$
$272$		0			0
$273$	−1.66440e8	−	7.08039e7i	−0.0299645	−	0.0127470i
$274$		0			0
$275$		−	5.05736e8i		−	0.0884286i
$276$		0			0
$277$	−1.15644e9			−0.196429			−0.0982145	−	0.995165i	$-0.531313\pi$
$277$	−1.15644e9			−0.196429			−0.0982145	+	0.995165i	$0.531313\pi$
$278$		0			0
$279$	2.84176e9	+	2.95199e9i	0.468998	+	0.487190i
$280$		0			0
$281$			8.38190e9i			1.34437i	0.740385	+	0.672183i	$0.234643\pi$
$281$			8.38190e9i			1.34437i	−0.740385	+	0.672183i	$0.765357\pi$
$282$		0			0
$283$	−2.84371e9			−0.443343			−0.221672	−	0.975121i	$-0.571151\pi$
$283$	−2.84371e9			−0.443343			−0.221672	+	0.975121i	$0.571151\pi$
$284$		0			0
$285$	1.85800e9	−	4.36764e9i	0.281622	−	0.662014i
$286$		0			0
$287$			1.23019e8i			0.0181320i
$288$		0			0
$289$	−1.12471e9			−0.161232
$290$		0			0
$291$	2.21167e9	+	9.40848e8i	0.308424	+	0.131204i
$292$		0			0
$293$			3.40005e9i			0.461333i	0.973033	+	0.230666i	$0.0740906\pi$
$293$			3.40005e9i			0.461333i	−0.973033	+	0.230666i	$0.925909\pi$
$294$		0			0
$295$	−4.71179e9			−0.622154
$296$		0			0
$297$	3.21464e9	−	1.22530e9i	0.413148	−	0.157477i
$298$		0			0
$299$		−	1.85353e9i		−	0.231908i
$300$		0			0
$301$	3.75981e8			0.0458037
$302$		0			0
$303$	2.70923e9	−	6.36865e9i	0.321422	−	0.755573i
$304$		0			0
$305$		−	2.76746e9i		−	0.319802i
$306$		0			0
$307$	−2.61177e9			−0.294023			−0.147011	−	0.989135i	$-0.546965\pi$
$307$	−2.61177e9			−0.294023			−0.147011	+	0.989135i	$0.546965\pi$
$308$		0			0
$309$	9.08860e8	+	3.86631e8i	0.0996926	+	0.0424094i
$310$		0			0
$311$			6.14252e9i			0.656606i	0.944572	+	0.328303i	$0.106477\pi$
$311$			6.14252e9i			0.656606i	−0.944572	+	0.328303i	$0.893523\pi$
$312$		0			0
$313$	−1.03834e10			−1.08183			−0.540917	−	0.841076i	$-0.681923\pi$
$313$	−1.03834e10			−1.08183			−0.540917	+	0.841076i	$0.681923\pi$
$314$		0			0
$315$	2.26804e8	−	2.18334e8i	0.0230361	−	0.0221758i
$316$		0			0
$317$			1.49393e10i			1.47942i	0.672924	+	0.739712i	$0.265038\pi$
$317$			1.49393e10i			1.47942i	−0.672924	+	0.739712i	$0.734962\pi$
$318$		0			0
$319$	1.39095e9			0.134322
$320$		0			0
$321$	−1.65145e9	+	3.88210e9i	−0.155542	+	0.365634i
$322$		0			0
$323$		−	1.88687e10i		−	1.73353i
$324$		0			0
$325$	1.01622e9			0.0910866
$326$		0			0
$327$	1.55935e10	+	6.63350e9i	1.36380	+	0.580165i
$328$		0			0
$329$		−	7.86077e8i		−	0.0670936i
$330$		0			0
$331$	1.04730e10			0.872487			0.436244	−	0.899829i	$-0.356309\pi$
$331$	1.04730e10			0.872487			0.436244	+	0.899829i	$0.356309\pi$
$332$		0			0
$333$	−7.02932e9	−	7.30199e9i	−0.571658	−	0.593833i
$334$		0			0
$335$		−	2.91442e9i		−	0.231405i
$336$		0			0
$337$	2.08868e10			1.61939			0.809696	−	0.586849i	$-0.199632\pi$
$337$	2.08868e10			1.61939			0.809696	+	0.586849i	$0.199632\pi$
$338$		0			0
$339$	5.63656e8	−	1.32500e9i	0.0426791	−	0.100327i
$340$		0			0
$341$			4.04285e9i			0.298999i
$342$		0			0
$343$	1.97422e9			0.142633
$344$		0			0
$345$	2.96868e9	+	1.26288e9i	0.209550	+	0.0891428i
$346$		0			0
$347$		−	4.58221e9i		−	0.316051i	−0.987435	−	0.158026i	$-0.949487\pi$
$347$		−	4.58221e9i		−	0.316051i	0.987435	−	0.158026i	$-0.0505129\pi$
$348$		0			0
$349$	4.22524e9			0.284806			0.142403	−	0.989809i	$-0.454517\pi$
$349$	4.22524e9			0.284806			0.142403	+	0.989809i	$0.454517\pi$
$350$		0			0
$351$	2.46211e9	+	6.45946e9i	0.162210	+	0.425567i
$352$		0			0
$353$		−	2.14402e10i		−	1.38080i	−0.723428	−	0.690399i	$-0.757435\pi$
$353$		−	2.14402e10i		−	1.38080i	0.723428	−	0.690399i	$-0.242565\pi$
$354$		0			0
$355$	6.24226e8			0.0393032
$356$		0			0
$357$	4.89908e8	−	1.15164e9i	0.0301607	−	0.0708993i
$358$		0			0
$359$		−	2.43580e10i		−	1.46644i	−0.679992	−	0.733220i	$-0.738017\pi$
$359$		−	2.43580e10i		−	1.46644i	0.679992	−	0.733220i	$-0.261983\pi$
$360$		0			0
$361$	2.69677e10			1.58787
$362$		0			0
$363$	−1.28540e10	−	5.46812e9i	−0.740308	−	0.314928i
$364$		0			0
$365$		−	8.58468e9i		−	0.483674i
$366$		0			0
$367$	5.32515e9			0.293540			0.146770	−	0.989171i	$-0.453112\pi$
$367$	5.32515e9			0.293540			0.146770	+	0.989171i	$0.453112\pi$
$368$		0			0
$369$	3.38720e9	−	3.26071e9i	0.182699	−	0.175876i
$370$		0			0
$371$		−	1.08159e9i		−	0.0570910i
$372$		0			0
$373$	1.55435e10			0.802994			0.401497	−	0.915860i	$-0.368490\pi$
$373$	1.55435e10			0.802994			0.401497	+	0.915860i	$0.368490\pi$
$374$		0			0
$375$	−6.92390e8	+	1.62761e9i	−0.0350127	+	0.0823050i
$376$		0			0
$377$			2.79496e9i			0.138360i
$378$		0			0
$379$	9.25639e9			0.448626			0.224313	−	0.974517i	$-0.427986\pi$
$379$	9.25639e9			0.448626			0.224313	+	0.974517i	$0.427986\pi$
$380$		0			0
$381$	3.40730e10	+	1.44947e10i	1.61700	+	0.687876i
$382$		0			0
$383$		−	2.09394e10i		−	0.973128i	−0.873645	−	0.486564i	$-0.838250\pi$
$383$		−	2.09394e10i		−	0.973128i	0.873645	−	0.486564i	$-0.161750\pi$
$384$		0			0
$385$	3.10615e8			0.0141377
$386$		0			0
$387$	−9.96567e9	−	1.03522e10i	−0.444286	−	0.461520i
$388$		0			0
$389$			4.05460e10i			1.77072i	0.464907	+	0.885359i	$0.346088\pi$
$389$			4.05460e10i			1.77072i	−0.464907	+	0.885359i	$0.653912\pi$
$390$		0			0
$391$	1.28250e10			0.548719
$392$		0			0
$393$	1.57004e10	−	3.69071e10i	0.658172	−	1.54718i
$394$		0			0
$395$		−	1.66556e10i		−	0.684181i
$396$		0			0
$397$	−1.21222e10			−0.488001			−0.244001	−	0.969775i	$-0.578460\pi$
$397$	−1.21222e10			−0.488001			−0.244001	+	0.969775i	$0.578460\pi$
$398$		0			0
$399$	2.68254e9	+	1.14116e9i	0.105841	+	0.0450250i
$400$		0			0
$401$			4.59483e10i			1.77702i	0.458857	+	0.888510i	$0.348259\pi$
$401$			4.59483e10i			1.77702i	−0.458857	+	0.888510i	$0.651741\pi$
$402$		0			0
$403$	−8.12365e9			−0.307986
$404$		0			0
$405$	−1.20232e10	−	4.57684e8i	−0.446890	−	0.0170116i
$406$		0			0
$407$		−	1.00003e10i		−	0.364448i
$408$		0			0
$409$	−1.98882e10			−0.710725			−0.355363	−	0.934728i	$-0.615643\pi$
$409$	−1.98882e10			−0.710725			−0.355363	+	0.934728i	$0.615643\pi$
$410$		0			0
$411$	−1.89445e10	+	4.45332e10i	−0.663921	+	1.56069i
$412$		0			0
$413$		−	2.89391e9i		−	0.0994683i
$414$		0			0
$415$	2.52092e8			0.00849899
$416$		0			0
$417$	−4.41477e10	−	1.87805e10i	−1.46004	−	0.621103i
$418$		0			0
$419$		−	3.82490e9i		−	0.124098i	−0.998073	−	0.0620490i	$-0.980237\pi$
$419$		−	3.82490e9i		−	0.124098i	0.998073	−	0.0620490i	$-0.0197635\pi$
$420$		0			0
$421$	3.10997e10			0.989983			0.494991	−	0.868898i	$-0.335171\pi$
$421$	3.10997e10			0.989983			0.494991	+	0.868898i	$0.335171\pi$
$422$		0			0
$423$	−2.16438e10	+	2.08356e10i	−0.676039	+	0.650794i
$424$		0			0
$425$			7.03145e9i			0.215521i
$426$		0			0
$427$	1.69973e9			0.0511291
$428$		0			0
$429$	−2.66991e9	+	6.27621e9i	−0.0788257	+	0.185297i
$430$		0			0
$431$			6.64386e10i			1.92536i	0.270648	+	0.962678i	$0.412762\pi$
$431$			6.64386e10i			1.92536i	−0.270648	+	0.962678i	$0.587238\pi$
$432$		0			0
$433$	−3.41384e10			−0.971161			−0.485581	−	0.874192i	$-0.661392\pi$
$433$	−3.41384e10			−0.971161			−0.485581	+	0.874192i	$0.661392\pi$
$434$		0			0
$435$	−4.47650e9	−	1.90431e9i	−0.125021	−	0.0531840i
$436$		0			0
$437$			2.98736e10i			0.819147i
$438$		0			0
$439$	2.13285e10			0.574253			0.287126	−	0.957893i	$-0.407300\pi$
$439$	2.13285e10			0.574253			0.287126	+	0.957893i	$0.407300\pi$
$440$		0			0
$441$	−2.60971e10	−	2.71094e10i	−0.689982	−	0.716747i
$442$		0			0
$443$		−	6.09380e10i		−	1.58224i	−0.611658	−	0.791122i	$-0.709497\pi$
$443$		−	6.09380e10i		−	1.58224i	0.611658	−	0.791122i	$-0.290503\pi$
$444$		0			0
$445$	1.71551e10			0.437476
$446$		0			0
$447$	−1.24045e10	+	2.91595e10i	−0.310706	+	0.730381i
$448$		0			0
$449$		−	6.72168e10i		−	1.65384i	−0.562323	−	0.826918i	$-0.690092\pi$
$449$		−	6.72168e10i		−	1.65384i	0.562323	−	0.826918i	$-0.309908\pi$
$450$		0			0
$451$	4.63887e9			0.112126
$452$		0			0
$453$	−4.80747e10	−	2.04511e10i	−1.14163	−	0.485650i
$454$		0			0
$455$			6.24146e8i			0.0145627i
$456$		0			0
$457$	−3.19081e10			−0.731536			−0.365768	−	0.930706i	$-0.619194\pi$
$457$	−3.19081e10			−0.731536			−0.365768	+	0.930706i	$0.619194\pi$
$458$		0			0
$459$	−4.46944e10	+	1.70359e10i	−1.00694	+	0.383807i
$460$		0			0
$461$			5.46837e10i			1.21075i	0.795940	+	0.605375i	$0.206977\pi$
$461$			5.46837e10i			1.21075i	−0.795940	+	0.605375i	$0.793023\pi$
$462$		0			0
$463$	−2.01111e10			−0.437634			−0.218817	−	0.975766i	$-0.570220\pi$
$463$	−2.01111e10			−0.437634			−0.218817	+	0.975766i	$0.570220\pi$
$464$		0			0
$465$	5.53496e9	−	1.30111e10i	0.118387	−	0.278293i
$466$		0			0
$467$			7.69028e9i			0.161687i	0.996727	+	0.0808434i	$0.0257614\pi$
$467$			7.69028e9i			0.161687i	−0.996727	+	0.0808434i	$0.974239\pi$
$468$		0			0
$469$	1.78999e9			0.0369964
$470$		0			0
$471$	1.10278e10	+	4.69124e9i	0.224081	+	0.0953243i
$472$		0			0
$473$		−	1.41777e10i		−	0.283245i
$474$		0			0
$475$	−1.63786e10			−0.321737
$476$		0			0
$477$	−2.97805e10	+	2.86684e10i	−0.575252	+	0.553771i
$478$		0			0
$479$			7.15869e10i			1.35985i	0.733281	+	0.679925i	$0.237988\pi$
$479$			7.15869e10i			1.35985i	−0.733281	+	0.679925i	$0.762012\pi$
$480$		0			0
$481$	2.00945e10			0.375402
$482$		0			0
$483$	−7.75642e8	+	1.82332e9i	−0.0142519	+	0.0335022i
$484$		0			0
$485$		−	8.29371e9i		−	0.149893i
$486$		0			0
$487$	7.70589e10			1.36996			0.684978	−	0.728564i	$-0.259812\pi$
$487$	7.70589e10			1.36996			0.684978	+	0.728564i	$0.259812\pi$
$488$		0			0
$489$	−4.04674e10	−	1.72149e10i	−0.707734	−	0.301071i
$490$		0			0
$491$			5.00758e10i			0.861592i	0.902449	+	0.430796i	$0.141767\pi$
$491$			5.00758e10i			0.861592i	−0.902449	+	0.430796i	$0.858233\pi$
$492$		0			0
$493$	−1.93389e10			−0.327374
$494$		0			0
$495$	−8.23308e9	−	8.55245e9i	−0.137133	−	0.142452i
$496$		0			0
$497$			3.83390e8i			0.00628369i
$498$		0			0
$499$	−1.20598e10			−0.194507			−0.0972537	−	0.995260i	$-0.531006\pi$
$499$	−1.20598e10			−0.194507			−0.0972537	+	0.995260i	$0.531006\pi$
$500$		0			0
$501$	1.49234e10	−	3.50807e10i	0.236874	−	0.556823i
$502$		0			0
$503$			6.52535e9i			0.101937i	0.998700	+	0.0509685i	$0.0162308\pi$
$503$			6.52535e9i			0.101937i	−0.998700	+	0.0509685i	$0.983769\pi$
$504$		0			0
$505$	−2.38823e10			−0.367207
$506$		0			0
$507$	4.81900e10	+	2.05001e10i	0.729331	+	0.310259i
$508$		0			0
$509$		−	2.77909e10i		−	0.414030i	−0.978338	−	0.207015i	$-0.933625\pi$
$509$		−	2.77909e10i		−	0.414030i	0.978338	−	0.207015i	$-0.0663748\pi$
$510$		0			0
$511$	5.27257e9			0.0773284
$512$		0			0
$513$	−3.96821e10	−	1.04108e11i	−0.572961	−	1.50319i
$514$		0			0
$515$		−	3.40820e9i		−	0.0484503i
$516$		0			0
$517$	−2.96418e10			−0.414899
$518$		0			0
$519$	−4.27630e10	+	1.00524e11i	−0.589385	+	1.38548i
$520$		0			0
$521$		−	7.02333e10i		−	0.953218i	−0.879116	−	0.476609i	$-0.841866\pi$
$521$		−	7.02333e10i		−	0.953218i	0.879116	−	0.476609i	$-0.158134\pi$
$522$		0			0
$523$	3.64311e10			0.486929			0.243464	−	0.969910i	$-0.421716\pi$
$523$	3.64311e10			0.486929			0.243464	+	0.969910i	$0.421716\pi$
$524$		0			0
$525$	−9.99654e8	−	4.25255e8i	−0.0131587	−	0.00559773i
$526$		0			0
$527$		−	5.62094e10i		−	0.728730i
$528$		0			0
$529$	5.80059e10			0.740713
$530$		0			0
$531$	−7.96807e10	+	7.67052e10i	−1.00225	+	0.964821i
$532$		0			0
$533$			9.32130e9i			0.115496i
$534$		0			0
$535$	1.45578e10			0.177697
$536$		0			0
$537$	4.35506e9	−	1.02375e10i	0.0523718	−	0.123111i
$538$		0			0
$539$		−	3.71272e10i		−	0.439883i
$540$		0			0
$541$	5.72377e10			0.668180			0.334090	−	0.942541i	$-0.391571\pi$
$541$	5.72377e10			0.668180			0.334090	+	0.942541i	$0.391571\pi$
$542$		0			0
$543$	8.56221e9	+	3.64238e9i	0.0984887	+	0.0418973i
$544$		0			0
$545$		−	5.84752e10i		−	0.662805i
$546$		0			0
$547$	1.62638e11			1.81665			0.908327	−	0.418262i	$-0.137361\pi$
$547$	1.62638e11			1.81665			0.908327	+	0.418262i	$0.137361\pi$
$548$		0			0
$549$	−4.50526e10	−	4.68002e10i	−0.495941	−	0.515179i
$550$		0			0
$551$		−	4.50467e10i		−	0.488716i
$552$		0			0
$553$	1.02296e10			0.109385
$554$		0			0
$555$	−1.36912e10	+	3.21840e10i	−0.144301	+	0.339210i
$556$		0			0
$557$			1.76310e11i			1.83170i	0.401516	+	0.915852i	$0.368483\pi$
$557$			1.76310e11i			1.83170i	−0.401516	+	0.915852i	$0.631517\pi$
$558$		0			0
$559$	2.84886e10			0.291758
$560$		0			0
$561$	−4.34265e10	−	1.84737e10i	−0.438433	−	0.186510i
$562$		0			0
$563$			5.08629e10i			0.506253i	0.967433	+	0.253127i	$0.0814589\pi$
$563$			5.08629e10i			0.506253i	−0.967433	+	0.253127i	$0.918541\pi$
$564$		0			0
$565$	−4.96871e9			−0.0487584
$566$		0			0
$567$	2.81103e8	−	7.38447e9i	0.00271977	−	0.0714475i
$568$		0			0
$569$			1.16156e10i			0.110813i	0.998464	+	0.0554065i	$0.0176455\pi$
$569$			1.16156e10i			0.110813i	−0.998464	+	0.0554065i	$0.982355\pi$
$570$		0			0
$571$	−1.60785e11			−1.51252			−0.756259	−	0.654272i	$-0.772975\pi$
$571$	−1.60785e11			−1.51252			−0.756259	+	0.654272i	$0.772975\pi$
$572$		0			0
$573$	−2.93770e9	+	6.90569e9i	−0.0272514	+	0.0640603i
$574$		0			0
$575$		−	1.11325e10i		−	0.101841i
$576$		0			0
$577$	−1.68755e11			−1.52248			−0.761242	−	0.648468i	$-0.775410\pi$
$577$	−1.68755e11			−1.52248			−0.761242	+	0.648468i	$0.775410\pi$
$578$		0			0
$579$	1.60828e11	+	6.84164e10i	1.43102	+	0.608760i
$580$		0			0
$581$			1.54831e8i			0.00135879i
$582$		0			0
$583$	−4.07853e10			−0.353044
$584$		0			0
$585$	1.71852e10	−	1.65435e10i	0.146734	−	0.141255i
$586$		0			0
$587$		−	5.48415e9i		−	0.0461909i	−0.999733	−	0.0230955i	$-0.992648\pi$
$587$		−	5.48415e9i		−	0.0461909i	0.999733	−	0.0230955i	$-0.00735217\pi$
$588$		0			0
$589$	1.30930e11			1.08787
$590$		0			0
$591$	1.54783e10	−	3.63851e10i	0.126874	−	0.298245i
$592$		0			0
$593$		−	4.89042e10i		−	0.395483i	−0.980254	−	0.197741i	$-0.936639\pi$
$593$		−	4.89042e10i		−	0.395483i	0.980254	−	0.197741i	$-0.0633606\pi$
$594$		0			0
$595$	−4.31861e9			−0.0344569
$596$		0			0
$597$	6.24313e10	+	2.65584e10i	0.491479	+	0.209076i
$598$		0			0
$599$		−	1.15033e11i		−	0.893540i	−0.894649	−	0.446770i	$-0.852574\pi$
$599$		−	1.15033e11i		−	0.893540i	0.894649	−	0.446770i	$-0.147426\pi$
$600$		0			0
$601$	1.45871e11			1.11807			0.559036	−	0.829143i	$-0.311171\pi$
$601$	1.45871e11			1.11807			0.559036	+	0.829143i	$0.311171\pi$
$602$		0			0
$603$	−4.74450e10	−	4.92855e10i	−0.358857	−	0.372778i
$604$		0			0
$605$			4.82023e10i			0.359788i
$606$		0			0
$607$	1.39678e11			1.02890			0.514451	−	0.857520i	$-0.327996\pi$
$607$	1.39678e11			1.02890			0.514451	+	0.857520i	$0.327996\pi$
$608$		0			0
$609$	1.16960e9	−	2.74939e9i	0.00850291	−	0.0199879i
$610$		0			0
$611$		−	5.95620e10i		−	0.427370i
$612$		0			0
$613$	2.36975e11			1.67826			0.839132	−	0.543929i	$-0.183064\pi$
$613$	2.36975e11			1.67826			0.839132	+	0.543929i	$0.183064\pi$
$614$		0			0
$615$	−1.49293e10	−	6.35096e9i	−0.104361	−	0.0443955i
$616$		0			0
$617$			9.46540e10i			0.653128i	0.945175	+	0.326564i	$0.105891\pi$
$617$			9.46540e10i			0.653128i	−0.945175	+	0.326564i	$0.894109\pi$
$618$		0			0
$619$	1.58887e10			0.108224			0.0541122	−	0.998535i	$-0.482767\pi$
$619$	1.58887e10			0.108224			0.0541122	+	0.998535i	$0.482767\pi$
$620$		0			0
$621$	7.07620e10	−	2.69719e10i	0.475810	−	0.181361i
$622$		0			0
$623$			1.05364e10i			0.0699424i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$		0			0
$627$	4.30314e10	−	1.01155e11i	0.278429	−	0.654509i
$628$		0			0
$629$			1.39038e11i			0.888243i
$630$		0			0
$631$	−1.76082e11			−1.11070			−0.555352	−	0.831615i	$-0.687417\pi$
$631$	−1.76082e11			−1.11070			−0.555352	+	0.831615i	$0.687417\pi$
$632$		0			0
$633$	1.72970e11	+	7.35818e10i	1.07735	+	0.458306i
$634$		0			0
$635$		−	1.27773e11i		−	0.785858i
$636$		0			0
$637$	7.46030e10			0.453105
$638$		0			0
$639$	1.05562e10	−	1.01620e10i	0.0633148	−	0.0609505i
$640$		0			0
$641$		−	3.17452e11i		−	1.88038i	−0.340645	−	0.940192i	$-0.610646\pi$
$641$		−	3.17452e11i		−	1.88038i	0.340645	−	0.940192i	$-0.389354\pi$
$642$		0			0
$643$	2.56942e11			1.50311			0.751556	−	0.659670i	$-0.229304\pi$
$643$	2.56942e11			1.50311			0.751556	+	0.659670i	$0.229304\pi$
$644$		0			0
$645$	−1.94104e10	+	4.56283e10i	−0.112149	+	0.263630i
$646$		0			0
$647$		−	2.10683e11i		−	1.20230i	−0.799137	−	0.601150i	$-0.794710\pi$
$647$		−	2.10683e11i		−	1.20230i	0.799137	−	0.601150i	$-0.205290\pi$
$648$		0			0
$649$	−1.09125e11			−0.615101
$650$		0			0
$651$	7.99123e9	+	3.39948e9i	0.0444928	+	0.0189273i
$652$		0			0
$653$			2.94654e11i			1.62054i	0.586056	+	0.810271i	$0.300680\pi$
$653$			2.94654e11i			1.62054i	−0.586056	+	0.810271i	$0.699320\pi$
$654$		0			0
$655$	−1.38401e11			−0.751924
$656$		0			0
$657$	−1.39754e11	−	1.45175e11i	−0.750069	−	0.779165i
$658$		0			0
$659$		−	8.29850e10i		−	0.440005i	−0.975499	−	0.220003i	$-0.929393\pi$
$659$		−	8.29850e10i		−	0.440005i	0.975499	−	0.220003i	$-0.0706066\pi$
$660$		0			0
$661$	5.70901e10			0.299058			0.149529	−	0.988757i	$-0.452224\pi$
$661$	5.70901e10			0.299058			0.149529	+	0.988757i	$0.452224\pi$
$662$		0			0
$663$	3.71209e10	−	8.72608e10i	0.192116	−	0.451611i
$664$		0			0
$665$		−	1.00595e10i		−	0.0514384i
$666$		0			0
$667$	3.06182e10			0.154695
$668$		0			0
$669$	2.77575e11	+	1.18081e11i	1.38572	+	0.589489i
$670$		0			0
$671$		−	6.40943e10i		−	0.316176i
$672$		0			0
$673$	−2.61393e11			−1.27419			−0.637094	−	0.770787i	$-0.719864\pi$
$673$	−2.61393e11			−1.27419			−0.637094	+	0.770787i	$0.719864\pi$
$674$		0			0
$675$	1.47876e10	+	3.87961e10i	0.0712334	+	0.186884i
$676$		0			0
$677$			1.30471e10i			0.0621098i	0.999518	+	0.0310549i	$0.00988668\pi$
$677$			1.30471e10i			0.0621098i	−0.999518	+	0.0310549i	$0.990113\pi$
$678$		0			0
$679$	5.09387e9			0.0239645
$680$		0			0
$681$	1.19740e11	−	2.81475e11i	0.556739	−	1.30874i
$682$		0			0
$683$			1.50022e11i			0.689402i	0.938713	+	0.344701i	$0.112020\pi$
$683$			1.50022e11i			0.689402i	−0.938713	+	0.344701i	$0.887980\pi$
$684$		0			0
$685$	1.66999e11			0.758492
$686$		0			0
$687$	1.62982e11	+	6.93327e10i	0.731664	+	0.311251i
$688$		0			0
$689$		−	8.19535e10i		−	0.363656i
$690$		0			0
$691$	−1.92476e11			−0.844239			−0.422119	−	0.906540i	$-0.638714\pi$
$691$	−1.92476e11			−0.844239			−0.422119	+	0.906540i	$0.638714\pi$
$692$		0			0
$693$	5.25278e9	−	5.05663e9i	0.0227749	−	0.0219244i
$694$		0			0
$695$			1.65553e11i			0.709575i
$696$		0			0
$697$	−6.44961e10			−0.273277
$698$		0			0
$699$	−4.94639e9	+	1.16276e10i	−0.0207195	+	0.0487057i
$700$		0			0
$701$			3.50902e11i			1.45316i	0.687081	+	0.726581i	$0.258892\pi$
$701$			3.50902e11i			1.45316i	−0.687081	+	0.726581i	$0.741108\pi$
$702$		0			0
$703$	−3.23866e11			−1.32600
$704$		0			0
$705$	9.53965e10	+	4.05819e10i	0.386168	+	0.164277i
$706$		0			0
$707$		−	1.46681e10i		−	0.0587079i
$708$		0			0
$709$	−4.83201e11			−1.91224			−0.956122	−	0.292969i	$-0.905357\pi$
$709$	−4.83201e11			−1.91224			−0.956122	+	0.292969i	$0.905357\pi$
$710$		0			0
$711$	−2.71143e11	−	2.81661e11i	−1.06101	−	1.10217i
$712$		0			0
$713$			8.89930e10i			0.344348i
$714$		0			0
$715$	2.35357e10			0.0900538
$716$		0			0
$717$	−9.37207e10	+	2.20311e11i	−0.354616	+	0.833603i
$718$		0			0
$719$		−	4.66620e11i		−	1.74601i	−0.487707	−	0.873007i	$-0.662167\pi$
$719$		−	4.66620e11i		−	1.74601i	0.487707	−	0.873007i	$-0.337833\pi$
$720$		0			0
$721$	2.09326e9			0.00774610
$722$		0			0
$723$	2.22161e11	+	9.45079e10i	0.813047	+	0.345872i
$724$		0			0
$725$			1.67868e10i			0.0607596i
$726$		0			0
$727$	−1.26030e11			−0.451167			−0.225584	−	0.974224i	$-0.572429\pi$
$727$	−1.26030e11			−0.451167			−0.225584	+	0.974224i	$0.572429\pi$
$728$		0			0
$729$	−2.10774e11	+	1.87991e11i	−0.746290	+	0.665621i
$730$		0			0
$731$			1.97119e11i			0.690333i
$732$		0			0
$733$	−1.62979e11			−0.564568			−0.282284	−	0.959331i	$-0.591092\pi$
$733$	−1.62979e11			−0.564568			−0.282284	+	0.959331i	$0.591092\pi$
$734$		0			0
$735$	−5.08299e10	+	1.19487e11i	−0.174169	+	0.409421i
$736$		0			0
$737$		−	6.74980e10i		−	0.228781i
$738$		0			0
$739$	−1.24100e11			−0.416096			−0.208048	−	0.978119i	$-0.566711\pi$
$739$	−1.24100e11			−0.416096			−0.208048	+	0.978119i	$0.566711\pi$
$740$		0			0
$741$	2.03259e11	+	8.64668e10i	0.674181	+	0.286798i
$742$		0			0
$743$			5.23314e11i			1.71715i	0.512691	+	0.858573i	$0.328649\pi$
$743$			5.23314e11i			1.71715i	−0.512691	+	0.858573i	$0.671351\pi$
$744$		0			0
$745$	1.09347e11			0.354963
$746$		0			0
$747$	4.26311e9	−	4.10392e9i	0.0136913	−	0.0131800i
$748$		0			0
$749$			8.94117e9i			0.0284097i
$750$		0			0
$751$	−3.61299e11			−1.13581			−0.567907	−	0.823093i	$-0.692247\pi$
$751$	−3.61299e11			−1.13581			−0.567907	+	0.823093i	$0.692247\pi$
$752$		0			0
$753$	−4.05693e10	+	9.53669e10i	−0.126188	+	0.296632i
$754$		0			0
$755$			1.80279e11i			0.554828i
$756$		0			0
$757$	−5.00926e11			−1.52542			−0.762711	−	0.646740i	$-0.776132\pi$
$757$	−5.00926e11			−1.52542			−0.762711	+	0.646740i	$0.776132\pi$
$758$		0			0
$759$	6.87546e10	+	2.92484e10i	0.207174	+	0.0881321i
$760$		0			0
$761$		−	7.17674e10i		−	0.213988i	−0.994260	−	0.106994i	$-0.965877\pi$
$761$		−	7.17674e10i		−	0.213988i	0.994260	−	0.106994i	$-0.0341225\pi$
$762$		0			0
$763$	3.59146e10			0.105967
$764$		0			0
$765$	1.14468e11	+	1.18908e11i	0.334224	+	0.347189i
$766$		0			0
$767$		−	2.19275e11i		−	0.633589i
$768$		0			0
$769$	−4.37235e11			−1.25029			−0.625144	−	0.780509i	$-0.714960\pi$
$769$	−4.37235e11			−1.25029			−0.625144	+	0.780509i	$0.714960\pi$
$770$		0			0
$771$	−2.13042e10	+	5.00800e10i	−0.0602902	+	0.141725i
$772$		0			0
$773$			5.36529e11i			1.50271i	0.659898	+	0.751355i	$0.270599\pi$
$773$			5.36529e11i			1.50271i	−0.659898	+	0.751355i	$0.729401\pi$
$774$		0			0
$775$	−4.87914e10			−0.135250
$776$		0			0
$777$	−1.97669e10	−	8.40889e9i	−0.0542319	−	0.0230704i
$778$		0			0
$779$		−	1.50233e11i		−	0.407957i
$780$		0			0
$781$	1.44571e10			0.0388576
$782$		0			0
$783$	−1.06703e11	+	4.06711e10i	−0.283876	+	0.108203i
$784$		0			0
$785$		−	4.13539e10i		−	0.108903i
$786$		0			0
$787$	−6.69453e11			−1.74510			−0.872551	−	0.488523i	$-0.837536\pi$
$787$	−6.69453e11			−1.74510			−0.872551	+	0.488523i	$0.837536\pi$
$788$		0			0
$789$	−2.03710e11	+	4.78865e11i	−0.525659	+	1.23568i
$790$		0			0
$791$		−	3.05170e9i		−	0.00779536i
$792$		0			0
$793$	1.28790e11			0.325680
$794$		0			0
$795$	1.31260e11	+	5.58381e10i	0.328596	+	0.139786i
$796$		0			0
$797$		−	5.50542e11i		−	1.36445i	−0.731143	−	0.682225i	$-0.761013\pi$
$797$		−	5.50542e11i		−	1.36445i	0.731143	−	0.682225i	$-0.238987\pi$
$798$		0			0
$799$	4.12123e11			1.01121
$800$		0			0
$801$	2.90109e11	−	2.79275e11i	0.704743	−	0.678426i
$802$		0			0
$803$		−	1.98821e11i		−	0.478190i
$804$		0			0
$805$	6.83739e9			0.0162820
$806$		0			0
$807$	2.76815e11	−	6.50714e11i	0.652673	−	1.53425i
$808$		0			0
$809$		−	3.06384e11i		−	0.715274i	−0.933861	−	0.357637i	$-0.883583\pi$
$809$		−	3.06384e11i		−	0.715274i	0.933861	−	0.357637i	$-0.116417\pi$
$810$		0			0
$811$	−4.43688e11			−1.02564			−0.512819	−	0.858497i	$-0.671399\pi$
$811$	−4.43688e11			−1.02564			−0.512819	+	0.858497i	$0.671399\pi$
$812$		0			0
$813$	4.23429e11	+	1.80127e11i	0.969210	+	0.412304i
$814$		0			0
$815$			1.51752e11i			0.343957i
$816$		0			0
$817$	−4.59154e11			−1.03055
$818$		0			0
$819$	1.01607e10	+	1.05549e10i	0.0225834	+	0.0234594i
$820$		0			0
$821$		−	2.98689e11i		−	0.657426i	−0.944430	−	0.328713i	$-0.893385\pi$
$821$		−	2.98689e11i		−	0.657426i	0.944430	−	0.328713i	$-0.106615\pi$
$822$		0			0
$823$	5.31239e11			1.15795			0.578976	−	0.815344i	$-0.303452\pi$
$823$	5.31239e11			1.15795			0.578976	+	0.815344i	$0.303452\pi$
$824$		0			0
$825$	−1.60358e10	+	3.76955e10i	−0.0346157	+	0.0813718i
$826$		0			0
$827$		−	3.61075e10i		−	0.0771926i	−0.999255	−	0.0385963i	$-0.987711\pi$
$827$		−	3.61075e10i		−	0.0771926i	0.999255	−	0.0385963i	$-0.0122886\pi$
$828$		0			0
$829$	1.86943e11			0.395815			0.197907	−	0.980221i	$-0.436585\pi$
$829$	1.86943e11			0.395815			0.197907	+	0.980221i	$0.436585\pi$
$830$		0			0
$831$	8.61968e10	+	3.66683e10i	0.180754	+	0.0768929i
$832$		0			0
$833$			5.16195e11i			1.07210i
$834$		0			0
$835$	−1.31552e11			−0.270615
$836$		0			0
$837$	−1.18212e11	−	3.10136e11i	−0.240858	−	0.631902i
$838$		0			0
$839$			6.44305e9i			0.0130030i	0.999979	+	0.00650150i	$0.00206951\pi$
$839$			6.44305e9i			0.0130030i	−0.999979	+	0.00650150i	$0.997930\pi$
$840$		0			0
$841$	4.54077e11			0.907707
$842$		0			0
$843$	2.65771e11	−	6.24753e11i	0.526257	−	1.23708i
$844$		0			0
$845$		−	1.80711e11i		−	0.354453i
$846$		0			0
$847$	−2.96051e10			−0.0575218
$848$		0			0
$849$	2.11959e11	+	9.01679e10i	0.407964	+	0.173549i
$850$		0			0
$851$		−	2.20131e11i		−	0.419723i
$852$		0			0
$853$	−1.72700e11			−0.326209			−0.163105	−	0.986609i	$-0.552151\pi$
$853$	−1.72700e11			−0.326209			−0.163105	+	0.986609i	$0.552151\pi$
$854$		0			0
$855$	−2.76976e11	+	2.66633e11i	−0.518296	+	0.498942i
$856$		0			0
$857$			7.95922e10i			0.147553i	0.997275	+	0.0737763i	$0.0235051\pi$
$857$			7.95922e10i			0.147553i	−0.997275	+	0.0737763i	$0.976495\pi$
$858$		0			0
$859$	8.64486e10			0.158776			0.0793881	−	0.996844i	$-0.474703\pi$
$859$	8.64486e10			0.158776			0.0793881	+	0.996844i	$0.474703\pi$
$860$		0			0
$861$	3.90066e9	−	9.16935e9i	0.00709783	−	0.0166850i
$862$		0			0
$863$			9.99047e11i			1.80112i	0.434731	+	0.900560i	$0.356843\pi$
$863$			9.99047e11i			1.80112i	−0.434731	+	0.900560i	$0.643157\pi$
$864$		0			0
$865$	3.76962e11			0.673338
$866$		0			0
$867$	8.38318e10	+	3.56622e10i	0.148365	+	0.0631149i
$868$		0			0
$869$		−	3.85743e11i		−	0.676424i
$870$		0			0
$871$	1.35630e11			0.235658
$872$		0			0
$873$	−1.35017e11	−	1.40254e11i	−0.232451	−	0.241468i
$874$		0			0
$875$			3.74868e9i			0.00639509i
$876$		0			0
$877$	2.38490e11			0.403155			0.201578	−	0.979473i	$-0.435393\pi$
$877$	2.38490e11			0.403155			0.201578	+	0.979473i	$0.435393\pi$
$878$		0			0
$879$	1.07808e11	−	2.53426e11i	0.180591	−	0.424518i
$880$		0			0
$881$		−	1.03350e12i		−	1.71556i	−0.514016	−	0.857781i	$-0.671843\pi$
$881$		−	1.03350e12i		−	1.71556i	0.514016	−	0.857781i	$-0.328157\pi$
$882$		0			0
$883$	2.82764e11			0.465137			0.232569	−	0.972580i	$-0.425287\pi$
$883$	2.82764e11			0.465137			0.232569	+	0.972580i	$0.425287\pi$
$884$		0			0
$885$	3.51198e11	+	1.49400e11i	0.572505	+	0.243545i
$886$		0			0
$887$			3.71450e11i			0.600075i	0.953927	+	0.300038i	$0.0969992\pi$
$887$			3.71450e11i			0.600075i	−0.953927	+	0.300038i	$0.903001\pi$
$888$		0			0
$889$	7.84762e10			0.125641
$890$		0			0
$891$	−2.78458e11	−	1.06000e10i	−0.441823	−	0.0168188i
$892$		0			0
$893$			9.59968e11i			1.50956i
$894$		0			0
$895$	−3.83905e10			−0.0598317
$896$		0			0
$897$	−5.87713e10	+	1.38155e11i	−0.0907812	+	0.213401i
$898$		0			0
$899$		−	1.34193e11i		−	0.205443i
$900$		0			0
$901$	5.67055e11			0.860450
$902$		0			0
$903$	−2.80241e10	−	1.19215e10i	−0.0421484	−	0.0179300i
$904$		0			0
$905$		−	3.21081e10i		−	0.0478653i
$906$		0			0
$907$	8.73952e11			1.29139			0.645697	−	0.763594i	$-0.276567\pi$
$907$	8.73952e11			1.29139			0.645697	+	0.763594i	$0.276567\pi$
$908$		0			0
$909$	−4.03871e11	+	3.88790e11i	−0.591544	+	0.569455i
$910$		0			0
$911$			3.02963e11i			0.439862i	0.975515	+	0.219931i	$0.0705832\pi$
$911$			3.02963e11i			0.439862i	−0.975515	+	0.219931i	$0.929417\pi$
$912$		0			0
$913$	5.83846e9			0.00840263
$914$		0			0
$915$	−8.77499e10	+	2.06275e11i	−0.125188	+	0.294281i
$916$		0			0
$917$		−	8.50037e10i		−	0.120215i
$918$		0			0
$919$	−6.44252e10			−0.0903220			−0.0451610	−	0.998980i	$-0.514380\pi$
$919$	−6.44252e10			−0.0903220			−0.0451610	+	0.998980i	$0.514380\pi$
$920$		0			0
$921$	1.94671e11	+	8.28134e10i	0.270559	+	0.115096i
$922$		0			0
$923$			2.90499e10i			0.0400256i
$924$		0			0
$925$	1.20689e11			0.164855
$926$		0			0
$927$	−5.54836e10	−	5.76358e10i	−0.0751355	−	0.0780501i
$928$		0			0
$929$		−	1.28458e12i		−	1.72464i	−0.506363	−	0.862320i	$-0.669010\pi$
$929$		−	1.28458e12i		−	1.72464i	0.506363	−	0.862320i	$-0.330990\pi$
$930$		0			0
$931$	−1.20239e12			−1.60046
$932$		0			0
$933$	1.94766e11	−	4.57839e11i	0.257031	−	0.604207i
$934$		0			0
$935$			1.62849e11i			0.213077i
$936$		0			0
$937$	1.51713e11			0.196818			0.0984091	−	0.995146i	$-0.468625\pi$
$937$	1.51713e11			0.196818			0.0984091	+	0.995146i	$0.468625\pi$
$938$		0			0
$939$	7.73934e11	+	3.29233e11i	0.995501	+	0.423488i
$940$		0			0
$941$		−	5.73298e11i		−	0.731176i	−0.930777	−	0.365588i	$-0.880868\pi$
$941$		−	5.73298e11i		−	0.731176i	0.930777	−	0.365588i	$-0.119132\pi$
$942$		0			0
$943$	1.02113e11			0.129132
$944$		0			0
$945$	−2.38280e10	+	9.08233e9i	−0.0298786	+	0.0113886i
$946$		0			0
$947$			1.42399e11i			0.177055i	0.996074	+	0.0885273i	$0.0282161\pi$
$947$			1.42399e11i			0.177055i	−0.996074	+	0.0885273i	$0.971784\pi$
$948$		0			0
$949$	3.99509e11			0.492563
$950$		0			0
$951$	4.73691e11	−	1.11351e12i	0.579126	−	1.36136i
$952$		0			0
$953$		−	2.81542e11i		−	0.341327i	−0.985329	−	0.170664i	$-0.945409\pi$
$953$		−	2.81542e11i		−	0.341327i	0.985329	−	0.170664i	$-0.0545912\pi$
$954$		0			0
$955$	2.58962e10			0.0311331
$956$		0			0
$957$	−1.03676e11	−	4.41039e10i	−0.123603	−	0.0525810i
$958$		0			0
$959$			1.02568e11i			0.121266i
$960$		0			0
$961$	−4.62853e11			−0.542687
$962$		0			0
$963$	2.46186e11	−	2.36993e11i	0.286258	−	0.275568i
$964$		0			0
$965$		−	6.03100e11i		−	0.695473i
$966$		0			0
$967$	1.59050e12			1.81898			0.909488	−	0.415729i	$-0.136474\pi$
$967$	1.59050e12			1.81898			0.909488	+	0.415729i	$0.136474\pi$
$968$		0			0
$969$	−5.98283e11	+	1.40639e12i	−0.678596	+	1.59519i
$970$		0			0
$971$			1.52892e12i			1.71992i	0.510365	+	0.859958i	$0.329510\pi$
$971$			1.52892e12i			1.71992i	−0.510365	+	0.859958i	$0.670490\pi$
$972$		0			0
$973$	−1.01680e11			−0.113445
$974$		0			0
$975$	−7.57450e10	−	3.22221e10i	−0.0838176	−	0.0356562i
$976$		0			0
$977$		−	1.07377e12i		−	1.17851i	−0.807947	−	0.589255i	$-0.799421\pi$
$977$		−	1.07377e12i		−	1.17851i	0.807947	−	0.589255i	$-0.200579\pi$
$978$		0			0
$979$	3.97313e11			0.432516
$980$		0			0
$981$	−9.51943e11	−	9.88869e11i	−1.02786	−	1.06773i
$982$		0			0
$983$			1.76471e12i			1.88998i	0.327093	+	0.944992i	$0.393931\pi$
$983$			1.76471e12i			1.88998i	−0.327093	+	0.944992i	$0.606069\pi$
$984$		0			0
$985$	−1.36443e11			−0.144946
$986$		0			0
$987$	−2.49247e10	+	5.85910e10i	−0.0262641	+	0.0617394i
$988$		0			0
$989$		−	3.12086e11i		−	0.326204i
$990$		0			0
$991$	7.95898e11			0.825206			0.412603	−	0.910911i	$-0.364620\pi$
$991$	7.95898e11			0.825206			0.412603	+	0.910911i	$0.364620\pi$
$992$		0			0
$993$	−7.80615e11	−	3.32075e11i	−0.802861	−	0.341539i
$994$		0			0
$995$		−	2.34116e11i		−	0.238858i
$996$		0			0
$997$	−1.04577e11			−0.105842			−0.0529209	−	0.998599i	$-0.516853\pi$
$997$	−1.04577e11			−0.105842			−0.0529209	+	0.998599i	$0.516853\pi$
$998$		0			0
$999$	2.92407e11	+	7.67145e11i	0.293580	+	0.770222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.9.l.a.41.3	✓	32
3.2	odd	2	inner	120.9.l.a.41.4	yes	32
4.3	odd	2		240.9.l.d.161.30		32
12.11	even	2		240.9.l.d.161.29		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.9.l.a.41.3	✓	32	1.1	even	1	trivial
120.9.l.a.41.4	yes	32	3.2	odd	2	inner
240.9.l.d.161.29		32	12.11	even	2
240.9.l.d.161.30		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	120.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-74.5360 - 31.7078i) q^{3} +279.508i q^{5} -171.670 q^{7} +(4550.23 + 4726.74i) q^{9} +6473.42i q^{11} -13007.6 q^{13} +(8862.59 - 20833.4i) q^{15} -90002.6i q^{17} +209646. q^{19} +(12795.6 + 5443.26i) q^{21} +142496. i q^{23} -78125.0 q^{25} +(-189282. - 496590. i) q^{27} -214871. i q^{29} +624531. q^{31} +(205258. - 482503. i) q^{33} -47983.1i q^{35} -1.54483e6 q^{37} +(969536. + 412443. i) q^{39} -716603. i q^{41} -2.19014e6 q^{43} +(-1.32116e6 + 1.27183e6i) q^{45} +4.57901e6i q^{47} -5.73533e6 q^{49} +(-2.85378e6 + 6.70844e6i) q^{51} +6.30043e6i q^{53} -1.80938e6 q^{55} +(-1.56261e7 - 6.64739e6i) q^{57} +1.68574e7i q^{59} -9.90116e6 q^{61} +(-781137. - 811438. i) q^{63} -3.63574e6i q^{65} -1.04269e7 q^{67} +(4.51822e6 - 1.06211e7i) q^{69} -2.23330e6i q^{71} -3.07135e7 q^{73} +(5.82313e6 + 2.47717e6i) q^{75} -1.11129e6i q^{77} -5.95888e7 q^{79} +(-1.63746e6 + 4.30156e7i) q^{81} -901913. i q^{83} +2.51565e7 q^{85} +(-6.81307e6 + 1.60156e7i) q^{87} -6.13760e7i q^{89} +2.23301e6 q^{91} +(-4.65500e7 - 1.98025e7i) q^{93} +5.85977e7i q^{95} -2.96725e7 q^{97} +(-3.05982e7 + 2.94556e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 112 q^{3} - 3008 q^{7} - 3184 q^{9} + 25696 q^{13} - 315872 q^{19} + 55216 q^{21} - 2500000 q^{25} + 605360 q^{27} - 1668576 q^{31} + 567104 q^{33} - 982624 q^{37} + 6709536 q^{39} - 13925344 q^{43}+ \cdots + 369200768 q^{99}+O(q^{100}) \) 32 * q - 112 * q^3 - 3008 * q^7 - 3184 * q^9 + 25696 * q^13 - 315872 * q^19 + 55216 * q^21 - 2500000 * q^25 + 605360 * q^27 - 1668576 * q^31 + 567104 * q^33 - 982624 * q^37 + 6709536 * q^39 - 13925344 * q^43 + 2370000 * q^45 + 44885632 * q^49 + 5870080 * q^51 - 2380000 * q^55 - 18347616 * q^57 + 43722656 * q^61 + 49774624 * q^63 - 28637536 * q^67 - 117303344 * q^69 + 133552256 * q^73 + 8750000 * q^75 - 68622944 * q^79 - 206826112 * q^81 + 392120416 * q^87 - 489280960 * q^91 - 242074304 * q^93 + 532016448 * q^97 + 369200768 * q^99

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