LMFDB - Embedded newform 1470.2.m.e.1273.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1470,2,Mod(97,1470)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1470, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1470.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1273.4
Root			$-0.709944 + 0.925217i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.e.97.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(2.17041 - 0.537883i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-1.15437 + 1.91505i) q^{10} -1.16579 q^{11} +(0.707107 + 0.707107i) q^{12} +(1.92501 - 1.92501i) q^{13} +(-1.15437 + 1.91505i) q^{15} -1.00000 q^{16} +(-0.0153229 - 0.0153229i) q^{17} +(0.707107 + 0.707107i) q^{18} -1.97873 q^{19} +(-0.537883 - 2.17041i) q^{20} +(0.824341 - 0.824341i) q^{22} +(5.07695 + 5.07695i) q^{23} -1.00000 q^{24} +(4.42136 - 2.33485i) q^{25} +2.72238i q^{26} +(0.707107 + 0.707107i) q^{27} -5.60604i q^{29} +(-0.537883 - 2.17041i) q^{30} +7.93107i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.824341 - 0.824341i) q^{33} +0.0216699 q^{34} -1.00000 q^{36} +(7.51026 - 7.51026i) q^{37} +(1.39917 - 1.39917i) q^{38} +2.72238i q^{39} +(1.91505 + 1.15437i) q^{40} -2.48977i q^{41} +(-7.87756 - 7.87756i) q^{43} +1.16579i q^{44} +(-0.537883 - 2.17041i) q^{45} -7.17989 q^{46} +(2.88977 + 2.88977i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-1.47539 + 4.77737i) q^{50} +0.0216699 q^{51} +(-1.92501 - 1.92501i) q^{52} +(-2.06984 - 2.06984i) q^{53} -1.00000 q^{54} +(-2.53025 + 0.627061i) q^{55} +(1.39917 - 1.39917i) q^{57} +(3.96407 + 3.96407i) q^{58} +10.6925 q^{59} +(1.91505 + 1.15437i) q^{60} +3.64649i q^{61} +(-5.60811 - 5.60811i) q^{62} +1.00000i q^{64} +(3.14264 - 5.21350i) q^{65} +1.16579i q^{66} +(10.2942 - 10.2942i) q^{67} +(-0.0153229 + 0.0153229i) q^{68} -7.17989 q^{69} +7.51848 q^{71} +(0.707107 - 0.707107i) q^{72} +(-2.64838 + 2.64838i) q^{73} +10.6211i q^{74} +(-1.47539 + 4.77737i) q^{75} +1.97873i q^{76} +(-1.92501 - 1.92501i) q^{78} -1.61039i q^{79} +(-2.17041 + 0.537883i) q^{80} -1.00000 q^{81} +(1.76053 + 1.76053i) q^{82} +(9.74815 - 9.74815i) q^{83} +(-0.0414990 - 0.0250151i) q^{85} +11.1406 q^{86} +(3.96407 + 3.96407i) q^{87} +(-0.824341 - 0.824341i) q^{88} +3.60510 q^{89} +(1.91505 + 1.15437i) q^{90} +(5.07695 - 5.07695i) q^{92} +(-5.60811 - 5.60811i) q^{93} -4.08675 q^{94} +(-4.29465 + 1.06432i) q^{95} +1.00000i q^{96} +(0.265501 + 0.265501i) q^{97} +1.16579i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38}+ \cdots - 44 q^{97}+O(q^{100}) $ 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	2.17041	−	0.537883i	0.970637	−	0.240548i
$5$	2.17041	−	0.537883i	0.970637	−	0.240548i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−1.15437	+	1.91505i	−0.365044	+	0.605593i
$11$	−1.16579			−0.351500			−0.175750	−	0.984435i	$-0.556235\pi$
$11$	−1.16579			−0.351500			−0.175750	+	0.984435i	$0.556235\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	1.92501	−	1.92501i	0.533903	−	0.533903i	−0.387829	−	0.921731i	$-0.626775\pi$
$13$	1.92501	−	1.92501i	0.533903	−	0.533903i	0.921731	+	0.387829i	$0.126775\pi$
$14$		0			0
$15$	−1.15437	+	1.91505i	−0.298057	+	0.494464i
$16$	−1.00000			−0.250000
$17$	−0.0153229	−	0.0153229i	−0.00371636	−	0.00371636i	0.705246	−	0.708963i	$-0.250836\pi$
$17$	−0.0153229	−	0.0153229i	−0.00371636	−	0.00371636i	−0.708963	+	0.705246i	$0.750836\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−1.97873			−0.453951			−0.226976	−	0.973900i	$-0.572884\pi$
$19$	−1.97873			−0.453951			−0.226976	+	0.973900i	$0.572884\pi$
$20$	−0.537883	−	2.17041i	−0.120274	−	0.485319i
$21$		0			0
$22$	0.824341	−	0.824341i	0.175750	−	0.175750i
$23$	5.07695	+	5.07695i	1.05862	+	1.05862i	0.998171	+	0.0604462i	$0.0192524\pi$
$23$	5.07695	+	5.07695i	1.05862	+	1.05862i	0.0604462	+	0.998171i	$0.480748\pi$
$24$	−1.00000			−0.204124
$25$	4.42136	−	2.33485i	0.884273	−	0.466971i
$26$			2.72238i			0.533903i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	5.60604i		−	1.04102i	−0.853857	−	0.520508i	$-0.825743\pi$
$29$		−	5.60604i		−	1.04102i	0.853857	−	0.520508i	$-0.174257\pi$
$30$	−0.537883	−	2.17041i	−0.0982035	−	0.396261i
$31$			7.93107i			1.42446i	0.701945	+	0.712231i	$0.252315\pi$
$31$			7.93107i			1.42446i	−0.701945	+	0.712231i	$0.747685\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.824341	−	0.824341i	0.143499	−	0.143499i
$34$	0.0216699			0.00371636
$35$		0			0
$36$	−1.00000			−0.166667
$37$	7.51026	−	7.51026i	1.23468	−	1.23468i	0.272532	−	0.962147i	$-0.412139\pi$
$37$	7.51026	−	7.51026i	1.23468	−	1.23468i	0.962147	−	0.272532i	$-0.0878610\pi$
$38$	1.39917	−	1.39917i	0.226976	−	0.226976i
$39$			2.72238i			0.435930i
$40$	1.91505	+	1.15437i	0.302796	+	0.182522i
$41$		−	2.48977i		−	0.388837i	−0.980919	−	0.194418i	$-0.937718\pi$
$41$		−	2.48977i		−	0.388837i	0.980919	−	0.194418i	$-0.0622819\pi$
$42$		0			0
$43$	−7.87756	−	7.87756i	−1.20132	−	1.20132i	−0.973766	−	0.227550i	$-0.926928\pi$
$43$	−7.87756	−	7.87756i	−1.20132	−	1.20132i	−0.227550	−	0.973766i	$-0.573072\pi$
$44$			1.16579i			0.175750i
$45$	−0.537883	−	2.17041i	−0.0801828	−	0.323546i
$46$	−7.17989			−1.05862
$47$	2.88977	+	2.88977i	0.421516	+	0.421516i	0.885726	−	0.464209i	$-0.153661\pi$
$47$	2.88977	+	2.88977i	0.421516	+	0.421516i	−0.464209	+	0.885726i	$0.653661\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		0			0
$50$	−1.47539	+	4.77737i	−0.208651	+	0.675622i
$51$	0.0216699			0.00303439
$52$	−1.92501	−	1.92501i	−0.266951	−	0.266951i
$53$	−2.06984	−	2.06984i	−0.284314	−	0.284314i	0.550513	−	0.834827i	$-0.314432\pi$
$53$	−2.06984	−	2.06984i	−0.284314	−	0.284314i	−0.834827	+	0.550513i	$0.814432\pi$
$54$	−1.00000			−0.136083
$55$	−2.53025	+	0.627061i	−0.341179	+	0.0845529i
$56$		0			0
$57$	1.39917	−	1.39917i	0.185325	−	0.185325i
$58$	3.96407	+	3.96407i	0.520508	+	0.520508i
$59$	10.6925			1.39204			0.696020	−	0.718022i	$-0.254952\pi$
$59$	10.6925			1.39204			0.696020	+	0.718022i	$0.254952\pi$
$60$	1.91505	+	1.15437i	0.247232	+	0.149029i
$61$			3.64649i			0.466885i	0.972371	+	0.233442i	$0.0749991\pi$
$61$			3.64649i			0.466885i	−0.972371	+	0.233442i	$0.925001\pi$
$62$	−5.60811	−	5.60811i	−0.712231	−	0.712231i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	3.14264	−	5.21350i	0.389796	−	0.646655i
$66$			1.16579i			0.143499i
$67$	10.2942	−	10.2942i	1.25764	−	1.25764i	0.305420	−	0.952218i	$-0.401203\pi$
$67$	10.2942	−	10.2942i	1.25764	−	1.25764i	0.952218	−	0.305420i	$-0.0987968\pi$
$68$	−0.0153229	+	0.0153229i	−0.00185818	+	0.00185818i
$69$	−7.17989			−0.864358
$70$		0			0
$71$	7.51848			0.892280			0.446140	−	0.894963i	$-0.352798\pi$
$71$	7.51848			0.892280			0.446140	+	0.894963i	$0.352798\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−2.64838	+	2.64838i	−0.309970	+	0.309970i	−0.844898	−	0.534928i	$-0.820339\pi$
$73$	−2.64838	+	2.64838i	−0.309970	+	0.309970i	0.534928	+	0.844898i	$0.320339\pi$
$74$			10.6211i			1.23468i
$75$	−1.47539	+	4.77737i	−0.170363	+	0.551643i
$76$			1.97873i			0.226976i
$77$		0			0
$78$	−1.92501	−	1.92501i	−0.217965	−	0.217965i
$79$		−	1.61039i		−	0.181184i	−0.995888	−	0.0905918i	$-0.971124\pi$
$79$		−	1.61039i		−	0.181184i	0.995888	−	0.0905918i	$-0.0288759\pi$
$80$	−2.17041	+	0.537883i	−0.242659	+	0.0601371i
$81$	−1.00000			−0.111111
$82$	1.76053	+	1.76053i	0.194418	+	0.194418i
$83$	9.74815	−	9.74815i	1.07000	−	1.07000i	0.0726405	−	0.997358i	$-0.476857\pi$
$83$	9.74815	−	9.74815i	1.07000	−	1.07000i	0.997358	−	0.0726405i	$-0.0231426\pi$
$84$		0			0
$85$	−0.0414990	−	0.0250151i	−0.00450120	−	0.00271327i
$86$	11.1406			1.20132
$87$	3.96407	+	3.96407i	0.424993	+	0.424993i
$88$	−0.824341	−	0.824341i	−0.0878751	−	0.0878751i
$89$	3.60510			0.382140			0.191070	−	0.981576i	$-0.438804\pi$
$89$	3.60510			0.382140			0.191070	+	0.981576i	$0.438804\pi$
$90$	1.91505	+	1.15437i	0.201864	+	0.121681i
$91$		0			0
$92$	5.07695	−	5.07695i	0.529309	−	0.529309i
$93$	−5.60811	−	5.60811i	−0.581534	−	0.581534i
$94$	−4.08675			−0.421516
$95$	−4.29465	+	1.06432i	−0.440622	+	0.109197i
$96$			1.00000i			0.102062i
$97$	0.265501	+	0.265501i	0.0269575	+	0.0269575i	0.720457	−	0.693500i	$-0.243932\pi$
$97$	0.265501	+	0.265501i	0.0269575	+	0.0269575i	−0.693500	+	0.720457i	$0.743932\pi$
$98$		0			0
$99$			1.16579i			0.117167i
$100$	−2.33485	−	4.42136i	−0.233485	−	0.442136i
$101$			13.9159i			1.38469i	0.721569	+	0.692343i	$0.243421\pi$
$101$			13.9159i			1.38469i	−0.721569	+	0.692343i	$0.756579\pi$
$102$	−0.0153229	+	0.0153229i	−0.00151720	+	0.00151720i
$103$	−8.47403	+	8.47403i	−0.834971	+	0.834971i	−0.988192	−	0.153221i	$-0.951035\pi$
$103$	−8.47403	+	8.47403i	−0.834971	+	0.834971i	0.153221	+	0.988192i	$0.451035\pi$
$104$	2.72238			0.266951
$105$		0			0
$106$	2.92719			0.284314
$107$	4.88300	−	4.88300i	0.472058	−	0.472058i	−0.430522	−	0.902580i	$-0.641671\pi$
$107$	4.88300	−	4.88300i	0.472058	−	0.472058i	0.902580	+	0.430522i	$0.141671\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$			0.577314i			0.0552967i	0.999618	+	0.0276483i	$0.00880186\pi$
$109$			0.577314i			0.0552967i	−0.999618	+	0.0276483i	$0.991198\pi$
$110$	1.34576	−	2.23256i	0.128313	−	0.212866i
$111$			10.6211i			1.00811i
$112$		0			0
$113$	13.2689	+	13.2689i	1.24823	+	1.24823i	0.956501	+	0.291728i	$0.0942301\pi$
$113$	13.2689	+	13.2689i	1.24823	+	1.24823i	0.291728	+	0.956501i	$0.405770\pi$
$114$			1.97873i			0.185325i
$115$	13.7499	+	8.28827i	1.28218	+	0.772885i
$116$	−5.60604			−0.520508
$117$	−1.92501	−	1.92501i	−0.177968	−	0.177968i
$118$	−7.56072	+	7.56072i	−0.696020	+	0.696020i
$119$		0			0
$120$	−2.17041	+	0.537883i	−0.198130	+	0.0491018i
$121$	−9.64092			−0.876447
$122$	−2.57846	−	2.57846i	−0.233442	−	0.233442i
$123$	1.76053	+	1.76053i	0.158742	+	0.158742i
$124$	7.93107			0.712231
$125$	8.34030	−	7.44577i	0.745979	−	0.665969i
$126$		0			0
$127$	1.36110	−	1.36110i	0.120778	−	0.120778i	−0.644134	−	0.764912i	$-0.722782\pi$
$127$	1.36110	−	1.36110i	0.120778	−	0.120778i	0.764912	+	0.644134i	$0.222782\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	11.1406			0.980871
$130$	1.46432	+	5.90868i	0.128429	+	0.518226i
$131$			17.1498i			1.49838i	0.662353	+	0.749192i	$0.269558\pi$
$131$			17.1498i			1.49838i	−0.662353	+	0.749192i	$0.730442\pi$
$132$	−0.824341	−	0.824341i	−0.0717497	−	0.0717497i
$133$		0			0
$134$			14.5582i			1.25764i
$135$	1.91505	+	1.15437i	0.164821	+	0.0993525i
$136$		−	0.0216699i		−	0.00185818i
$137$	7.23778	−	7.23778i	0.618365	−	0.618365i	−0.326747	−	0.945112i	$-0.605952\pi$
$137$	7.23778	−	7.23778i	0.618365	−	0.618365i	0.945112	+	0.326747i	$0.105952\pi$
$138$	5.07695	−	5.07695i	0.432179	−	0.432179i
$139$	−5.65119			−0.479327			−0.239664	−	0.970856i	$-0.577037\pi$
$139$	−5.65119			−0.479327			−0.239664	+	0.970856i	$0.577037\pi$
$140$		0			0
$141$	−4.08675			−0.344166
$142$	−5.31637	+	5.31637i	−0.446140	+	0.446140i
$143$	−2.24417	+	2.24417i	−0.187667	+	0.187667i
$144$			1.00000i			0.0833333i
$145$	−3.01539	−	12.1674i	−0.250415	−	1.01045i
$146$		−	3.74538i		−	0.309970i
$147$		0			0
$148$	−7.51026	−	7.51026i	−0.617339	−	0.617339i
$149$			0.220803i			0.0180889i	0.999959	+	0.00904446i	$0.00287898\pi$
$149$			0.220803i			0.0180889i	−0.999959	+	0.00904446i	$0.997121\pi$
$150$	−2.33485	−	4.42136i	−0.190640	−	0.361003i
$151$	−6.36885			−0.518290			−0.259145	−	0.965838i	$-0.583441\pi$
$151$	−6.36885			−0.518290			−0.259145	+	0.965838i	$0.583441\pi$
$152$	−1.39917	−	1.39917i	−0.113488	−	0.113488i
$153$	−0.0153229	+	0.0153229i	−0.00123879	+	0.00123879i
$154$		0			0
$155$	4.26598	+	17.2137i	0.342652	+	1.38264i
$156$	2.72238			0.217965
$157$	−10.2363	−	10.2363i	−0.816943	−	0.816943i	0.168721	−	0.985664i	$-0.446036\pi$
$157$	−10.2363	−	10.2363i	−0.816943	−	0.816943i	−0.985664	+	0.168721i	$0.946036\pi$
$158$	1.13872	+	1.13872i	0.0905918	+	0.0905918i
$159$	2.92719			0.232141
$160$	1.15437	−	1.91505i	0.0912611	−	0.151398i
$161$		0			0
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	15.4896	+	15.4896i	1.21324	+	1.21324i	0.969954	+	0.243289i	$0.0782263\pi$
$163$	15.4896	+	15.4896i	1.21324	+	1.21324i	0.243289	+	0.969954i	$0.421774\pi$
$164$	−2.48977			−0.194418
$165$	1.34576	−	2.23256i	0.104767	−	0.173804i
$166$			13.7860i			1.07000i
$167$	11.3917	+	11.3917i	0.881515	+	0.881515i	0.993689	−	0.112174i	$-0.0357814\pi$
$167$	11.3917	+	11.3917i	0.881515	+	0.881515i	−0.112174	+	0.993689i	$0.535781\pi$
$168$		0			0
$169$			5.58865i			0.429896i
$170$	0.0470326	−	0.0116559i	0.00360723	−	0.000893964i
$171$			1.97873i			0.151317i
$172$	−7.87756	+	7.87756i	−0.600658	+	0.600658i
$173$	7.38450	−	7.38450i	0.561433	−	0.561433i	−0.368281	−	0.929714i	$-0.620054\pi$
$173$	7.38450	−	7.38450i	0.561433	−	0.561433i	0.929714	+	0.368281i	$0.120054\pi$
$174$	−5.60604			−0.424993
$175$		0			0
$176$	1.16579			0.0878751
$177$	−7.56072	+	7.56072i	−0.568298	+	0.568298i
$178$	−2.54919	+	2.54919i	−0.191070	+	0.191070i
$179$		−	1.50703i		−	0.112641i	−0.998413	−	0.0563204i	$-0.982063\pi$
$179$		−	1.50703i		−	0.112641i	0.998413	−	0.0563204i	$-0.0179368\pi$
$180$	−2.17041	+	0.537883i	−0.161773	+	0.0400914i
$181$			21.3457i			1.58662i	0.608821	+	0.793308i	$0.291643\pi$
$181$			21.3457i			1.58662i	−0.608821	+	0.793308i	$0.708357\pi$
$182$		0			0
$183$	−2.57846	−	2.57846i	−0.190605	−	0.190605i
$184$			7.17989i			0.529309i
$185$	12.2607	−	20.3400i	0.901425	−	1.49542i
$186$	7.93107			0.581534
$187$	0.0178634	+	0.0178634i	0.00130630	+	0.00130630i
$188$	2.88977	−	2.88977i	0.210758	−	0.210758i
$189$		0			0
$190$	2.28419	−	3.78937i	0.165712	−	0.274909i
$191$	6.45086			0.466768			0.233384	−	0.972385i	$-0.425020\pi$
$191$	6.45086			0.466768			0.233384	+	0.972385i	$0.425020\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−3.63352	−	3.63352i	−0.261547	−	0.261547i	0.564135	−	0.825682i	$-0.309210\pi$
$193$	−3.63352	−	3.63352i	−0.261547	−	0.261547i	−0.825682	+	0.564135i	$0.809210\pi$
$194$	−0.375475			−0.0269575
$195$	1.46432	+	5.90868i	0.104862	+	0.423129i
$196$		0			0
$197$	17.8347	−	17.8347i	1.27067	−	1.27067i	0.324931	−	0.945738i	$-0.394659\pi$
$197$	17.8347	−	17.8347i	1.27067	−	1.27067i	0.945738	−	0.324931i	$-0.105341\pi$
$198$	−0.824341	−	0.824341i	−0.0585834	−	0.0585834i
$199$	−4.94197			−0.350327			−0.175163	−	0.984539i	$-0.556045\pi$
$199$	−4.94197			−0.350327			−0.175163	+	0.984539i	$0.556045\pi$
$200$	4.77737	+	1.47539i	0.337811	+	0.104326i
$201$			14.5582i			1.02686i
$202$	−9.84004	−	9.84004i	−0.692343	−	0.692343i
$203$		0			0
$204$		−	0.0216699i		−	0.00151720i
$205$	−1.33920	−	5.40382i	−0.0935340	−	0.377419i
$206$		−	11.9841i		−	0.834971i
$207$	5.07695	−	5.07695i	0.352873	−	0.352873i
$208$	−1.92501	+	1.92501i	−0.133476	+	0.133476i
$209$	2.30679			0.159564
$210$		0			0
$211$	−19.0455			−1.31115			−0.655574	−	0.755131i	$-0.727573\pi$
$211$	−19.0455			−1.31115			−0.655574	+	0.755131i	$0.727573\pi$
$212$	−2.06984	+	2.06984i	−0.142157	+	0.142157i
$213$	−5.31637	+	5.31637i	−0.364272	+	0.364272i
$214$			6.90561i			0.472058i
$215$	−21.3347	−	12.8603i	−1.45502	−	0.877068i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	−0.408223	−	0.408223i	−0.0276483	−	0.0276483i
$219$		−	3.74538i		−	0.253089i
$220$	0.627061	+	2.53025i	0.0422764	+	0.170590i
$221$	−0.0589937			−0.00396834
$222$	−7.51026	−	7.51026i	−0.504055	−	0.504055i
$223$	−2.94490	+	2.94490i	−0.197205	+	0.197205i	−0.798801	−	0.601596i	$-0.794532\pi$
$223$	−2.94490	+	2.94490i	−0.197205	+	0.197205i	0.601596	+	0.798801i	$0.294532\pi$
$224$		0			0
$225$	−2.33485	−	4.42136i	−0.155657	−	0.294758i
$226$	−18.7650			−1.24823
$227$	−13.0383	−	13.0383i	−0.865381	−	0.865381i	0.126576	−	0.991957i	$-0.459601\pi$
$227$	−13.0383	−	13.0383i	−0.865381	−	0.865381i	−0.991957	+	0.126576i	$0.959601\pi$
$228$	−1.39917	−	1.39917i	−0.0926624	−	0.0926624i
$229$	−5.91011			−0.390551			−0.195276	−	0.980748i	$-0.562560\pi$
$229$	−5.91011			−0.390551			−0.195276	+	0.980748i	$0.562560\pi$
$230$	−15.5833	+	3.86194i	−1.02753	+	0.254649i
$231$		0			0
$232$	3.96407	−	3.96407i	0.260254	−	0.260254i
$233$	5.11615	+	5.11615i	0.335170	+	0.335170i	0.854546	−	0.519376i	$-0.173835\pi$
$233$	5.11615	+	5.11615i	0.335170	+	0.335170i	−0.519376	+	0.854546i	$0.673835\pi$
$234$	2.72238			0.177968
$235$	7.82634	+	4.71763i	0.510534	+	0.307744i
$236$		−	10.6925i		−	0.696020i
$237$	1.13872	+	1.13872i	0.0739679	+	0.0739679i
$238$		0			0
$239$			4.20172i			0.271787i	0.990723	+	0.135893i	$0.0433904\pi$
$239$			4.20172i			0.271787i	−0.990723	+	0.135893i	$0.956610\pi$
$240$	1.15437	−	1.91505i	0.0745144	−	0.123616i
$241$		−	21.9359i		−	1.41301i	−0.707706	−	0.706507i	$-0.750270\pi$
$241$		−	21.9359i		−	1.41301i	0.707706	−	0.706507i	$-0.249730\pi$
$242$	6.81716	−	6.81716i	0.438224	−	0.438224i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	3.64649			0.233442
$245$		0			0
$246$	−2.48977			−0.158742
$247$	−3.80907	+	3.80907i	−0.242366	+	0.242366i
$248$	−5.60811	+	5.60811i	−0.356115	+	0.356115i
$249$			13.7860i			0.873650i
$250$	−0.632531	+	11.1624i	−0.0400048	+	0.705974i
$251$		−	15.1293i		−	0.954952i	−0.878645	−	0.477476i	$-0.841552\pi$
$251$		−	15.1293i		−	0.954952i	0.878645	−	0.477476i	$-0.158448\pi$
$252$		0			0
$253$	−5.91868	−	5.91868i	−0.372105	−	0.372105i
$254$			1.92488i			0.120778i
$255$	0.0470326	−	0.0116559i	0.00294529	−	0.000729918i
$256$	1.00000			0.0625000
$257$	−16.2735	−	16.2735i	−1.01512	−	1.01512i	−0.999884	−	0.0152320i	$-0.995151\pi$
$257$	−16.2735	−	16.2735i	−1.01512	−	1.01512i	−0.0152320	−	0.999884i	$-0.504849\pi$
$258$	−7.87756	+	7.87756i	−0.490435	+	0.490435i
$259$		0			0
$260$	−5.21350	−	3.14264i	−0.323328	−	0.194898i
$261$	−5.60604			−0.347005
$262$	−12.1267	−	12.1267i	−0.749192	−	0.749192i
$263$	−14.2273	−	14.2273i	−0.877294	−	0.877294i	0.115960	−	0.993254i	$-0.463006\pi$
$263$	−14.2273	−	14.2273i	−0.877294	−	0.877294i	−0.993254	+	0.115960i	$0.963006\pi$
$264$	1.16579			0.0717497
$265$	−5.60573	−	3.37907i	−0.344357	−	0.207574i
$266$		0			0
$267$	−2.54919	+	2.54919i	−0.156008	+	0.156008i
$268$	−10.2942	−	10.2942i	−0.628819	−	0.628819i
$269$	9.26959			0.565177			0.282588	−	0.959241i	$-0.408807\pi$
$269$	9.26959			0.565177			0.282588	+	0.959241i	$0.408807\pi$
$270$	−2.17041	+	0.537883i	−0.132087	+	0.0327345i
$271$		−	26.2298i		−	1.59335i	−0.604410	−	0.796673i	$-0.706591\pi$
$271$		−	26.2298i		−	1.59335i	0.604410	−	0.796673i	$-0.293409\pi$
$272$	0.0153229	+	0.0153229i	0.000929089	+	0.000929089i
$273$		0			0
$274$			10.2358i			0.618365i
$275$	−5.15440	+	2.72196i	−0.310822	+	0.164140i
$276$			7.17989i			0.432179i
$277$	9.40415	−	9.40415i	0.565040	−	0.565040i	−0.365695	−	0.930735i	$-0.619169\pi$
$277$	9.40415	−	9.40415i	0.565040	−	0.565040i	0.930735	+	0.365695i	$0.119169\pi$
$278$	3.99599	−	3.99599i	0.239664	−	0.239664i
$279$	7.93107			0.474821
$280$		0			0
$281$	−13.5101			−0.805944			−0.402972	−	0.915212i	$-0.632023\pi$
$281$	−13.5101			−0.805944			−0.402972	+	0.915212i	$0.632023\pi$
$282$	2.88977	−	2.88977i	0.172083	−	0.172083i
$283$	−14.0651	+	14.0651i	−0.836085	+	0.836085i	−0.988341	−	0.152256i	$-0.951346\pi$
$283$	−14.0651	+	14.0651i	−0.836085	+	0.836085i	0.152256	+	0.988341i	$0.451346\pi$
$284$		−	7.51848i		−	0.446140i
$285$	2.28419	−	3.78937i	0.135303	−	0.224463i
$286$		−	3.17374i		−	0.187667i
$287$		0			0
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	16.9995i		−	0.999972i
$290$	10.7359	+	6.47146i	0.630432	+	0.380017i
$291$	−0.375475			−0.0220107
$292$	2.64838	+	2.64838i	0.154985	+	0.154985i
$293$	−17.4044	+	17.4044i	−1.01677	+	1.01677i	−0.0169176	+	0.999857i	$0.505385\pi$
$293$	−17.4044	+	17.4044i	−1.01677	+	1.01677i	−0.999857	+	0.0169176i	$0.994615\pi$
$294$		0			0
$295$	23.2070	−	5.75129i	1.35117	−	0.334853i
$296$	10.6211			0.617339
$297$	−0.824341	−	0.824341i	−0.0478331	−	0.0478331i
$298$	−0.156132	−	0.156132i	−0.00904446	−	0.00904446i
$299$	19.5464			1.13040
$300$	4.77737	+	1.47539i	0.275821	+	0.0851815i
$301$		0			0
$302$	4.50346	−	4.50346i	0.259145	−	0.259145i
$303$	−9.84004	−	9.84004i	−0.565296	−	0.565296i
$304$	1.97873			0.113488
$305$	1.96138	+	7.91438i	0.112308	+	0.453176i
$306$		−	0.0216699i		−	0.00123879i
$307$	0.566349	+	0.566349i	0.0323232	+	0.0323232i	0.723084	−	0.690760i	$-0.242724\pi$
$307$	0.566349	+	0.566349i	0.0323232	+	0.0323232i	−0.690760	+	0.723084i	$0.742724\pi$
$308$		0			0
$309$		−	11.9841i		−	0.681751i
$310$	−15.1884	−	9.15540i	−0.862644	−	0.519992i
$311$			13.3972i			0.759687i	0.925051	+	0.379844i	$0.124022\pi$
$311$			13.3972i			0.759687i	−0.925051	+	0.379844i	$0.875978\pi$
$312$	−1.92501	+	1.92501i	−0.108982	+	0.108982i
$313$	20.3350	−	20.3350i	1.14940	−	1.14940i	0.162730	−	0.986671i	$-0.447970\pi$
$313$	20.3350	−	20.3350i	1.14940	−	1.14940i	0.986671	−	0.162730i	$-0.0520299\pi$
$314$	14.4763			0.816943
$315$		0			0
$316$	−1.61039			−0.0905918
$317$	−23.8542	+	23.8542i	−1.33979	+	1.33979i	−0.443521	+	0.896264i	$0.646271\pi$
$317$	−23.8542	+	23.8542i	−1.33979	+	1.33979i	−0.896264	+	0.443521i	$0.853729\pi$
$318$	−2.06984	+	2.06984i	−0.116071	+	0.116071i
$319$			6.53550i			0.365918i
$320$	0.537883	+	2.17041i	0.0300686	+	0.121330i
$321$			6.90561i			0.385434i
$322$		0			0
$323$	0.0303199	+	0.0303199i	0.00168704	+	0.00168704i
$324$			1.00000i			0.0555556i
$325$	4.01656	−	13.0058i	0.222799	−	0.721432i
$326$	−21.9057			−1.21324
$327$	−0.408223	−	0.408223i	−0.0225748	−	0.0225748i
$328$	1.76053	−	1.76053i	0.0972091	−	0.0972091i
$329$		0			0
$330$	0.627061	+	2.53025i	0.0345186	+	0.139286i
$331$	−10.9356			−0.601076			−0.300538	−	0.953770i	$-0.597166\pi$
$331$	−10.9356			−0.601076			−0.300538	+	0.953770i	$0.597166\pi$
$332$	−9.74815	−	9.74815i	−0.534999	−	0.534999i
$333$	−7.51026	−	7.51026i	−0.411560	−	0.411560i
$334$	−16.1103			−0.881515
$335$	16.8056	−	27.8797i	0.918187	−	1.52323i
$336$		0			0
$337$	−10.2916	+	10.2916i	−0.560617	+	0.560617i	−0.929483	−	0.368866i	$-0.879746\pi$
$337$	−10.2916	+	10.2916i	−0.560617	+	0.560617i	0.368866	+	0.929483i	$0.379746\pi$
$338$	−3.95177	−	3.95177i	−0.214948	−	0.214948i
$339$	−18.7650			−1.01917
$340$	−0.0250151	+	0.0414990i	−0.00135663	+	0.00225060i
$341$		−	9.24600i		−	0.500699i
$342$	−1.39917	−	1.39917i	−0.0756585	−	0.0756585i
$343$		0			0
$344$		−	11.1406i		−	0.600658i
$345$	−15.5833	+	3.86194i	−0.838978	+	0.207920i
$346$			10.4433i			0.561433i
$347$	−1.80636	+	1.80636i	−0.0969703	+	0.0969703i	−0.753928	−	0.656957i	$-0.771843\pi$
$347$	−1.80636	+	1.80636i	−0.0969703	+	0.0969703i	0.656957	+	0.753928i	$0.271843\pi$
$348$	3.96407	−	3.96407i	0.212497	−	0.212497i
$349$	18.6079			0.996058			0.498029	−	0.867160i	$-0.334057\pi$
$349$	18.6079			0.996058			0.498029	+	0.867160i	$0.334057\pi$
$350$		0			0
$351$	2.72238			0.145310
$352$	−0.824341	+	0.824341i	−0.0439375	+	0.0439375i
$353$	11.1944	−	11.1944i	0.595816	−	0.595816i	−0.343381	−	0.939196i	$-0.611572\pi$
$353$	11.1944	−	11.1944i	0.595816	−	0.595816i	0.939196	+	0.343381i	$0.111572\pi$
$354$		−	10.6925i		−	0.568298i
$355$	16.3182	−	4.04406i	0.866080	−	0.214637i
$356$		−	3.60510i		−	0.191070i
$357$		0			0
$358$	1.06563	+	1.06563i	0.0563204	+	0.0563204i
$359$			7.50618i			0.396161i	0.980186	+	0.198081i	$0.0634708\pi$
$359$			7.50618i			0.396161i	−0.980186	+	0.198081i	$0.936529\pi$
$360$	1.15437	−	1.91505i	0.0608407	−	0.100932i
$361$	−15.0846			−0.793928
$362$	−15.0937	−	15.0937i	−0.793308	−	0.793308i
$363$	6.81716	−	6.81716i	0.357808	−	0.357808i
$364$		0			0
$365$	−4.32356	+	7.17260i	−0.226306	+	0.375431i
$366$	3.64649			0.190605
$367$	2.79163	+	2.79163i	0.145722	+	0.145722i	0.776204	−	0.630482i	$-0.217143\pi$
$367$	2.79163	+	2.79163i	0.145722	+	0.145722i	−0.630482	+	0.776204i	$0.717143\pi$
$368$	−5.07695	−	5.07695i	−0.264654	−	0.264654i
$369$	−2.48977			−0.129612
$370$	5.71291	+	23.0522i	0.297000	+	1.19842i
$371$		0			0
$372$	−5.60811	+	5.60811i	−0.290767	+	0.290767i
$373$	3.81421	+	3.81421i	0.197492	+	0.197492i	0.798924	−	0.601432i	$-0.205403\pi$
$373$	3.81421	+	3.81421i	0.197492	+	0.197492i	−0.601432	+	0.798924i	$0.705403\pi$
$374$	−0.0252626			−0.00130630
$375$	−0.632531	+	11.1624i	−0.0326637	+	0.576426i
$376$			4.08675i			0.210758i
$377$	−10.7917	−	10.7917i	−0.555801	−	0.555801i
$378$		0			0
$379$			2.47403i			0.127082i	0.997979	+	0.0635411i	$0.0202394\pi$
$379$			2.47403i			0.127082i	−0.997979	+	0.0635411i	$0.979761\pi$
$380$	1.06432	+	4.29465i	0.0545986	+	0.220311i
$381$			1.92488i			0.0986148i
$382$	−4.56144	+	4.56144i	−0.233384	+	0.233384i
$383$	−17.0474	+	17.0474i	−0.871083	+	0.871083i	−0.992591	−	0.121507i	$-0.961227\pi$
$383$	−17.0474	+	17.0474i	−0.871083	+	0.871083i	0.121507	+	0.992591i	$0.461227\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	5.13858			0.261547
$387$	−7.87756	+	7.87756i	−0.400439	+	0.400439i
$388$	0.265501	−	0.265501i	0.0134788	−	0.0134788i
$389$		−	6.45060i		−	0.327058i	−0.986539	−	0.163529i	$-0.947712\pi$
$389$		−	6.45060i		−	0.327058i	0.986539	−	0.163529i	$-0.0522878\pi$
$390$	−5.21350	−	3.14264i	−0.263996	−	0.159134i
$391$		−	0.155588i		−	0.00786840i
$392$		0			0
$393$	−12.1267	−	12.1267i	−0.611713	−	0.611713i
$394$			25.2221i			1.27067i
$395$	−0.866204	−	3.49522i	−0.0435834	−	0.175864i
$396$	1.16579			0.0585834
$397$	−13.2347	−	13.2347i	−0.664230	−	0.664230i	0.292145	−	0.956374i	$-0.405631\pi$
$397$	−13.2347	−	13.2347i	−0.664230	−	0.664230i	−0.956374	+	0.292145i	$0.905631\pi$
$398$	3.49450	−	3.49450i	0.175163	−	0.175163i
$399$		0			0
$400$	−4.42136	+	2.33485i	−0.221068	+	0.116743i
$401$	−18.7394			−0.935799			−0.467900	−	0.883782i	$-0.654989\pi$
$401$	−18.7394			−0.935799			−0.467900	+	0.883782i	$0.654989\pi$
$402$	−10.2942	−	10.2942i	−0.513428	−	0.513428i
$403$	15.2674	+	15.2674i	0.760524	+	0.760524i
$404$	13.9159			0.692343
$405$	−2.17041	+	0.537883i	−0.107849	+	0.0267276i
$406$		0			0
$407$	−8.75542	+	8.75542i	−0.433990	+	0.433990i
$408$	0.0153229	+	0.0153229i	0.000758598	+	0.000758598i
$409$	23.3536			1.15476			0.577381	−	0.816475i	$-0.304075\pi$
$409$	23.3536			1.15476			0.577381	+	0.816475i	$0.304075\pi$
$410$	4.76804	+	2.87412i	0.235477	+	0.141943i
$411$			10.2358i			0.504893i
$412$	8.47403	+	8.47403i	0.417485	+	0.417485i
$413$		0			0
$414$			7.17989i			0.352873i
$415$	15.9141	−	26.4009i	0.781194	−	1.29597i
$416$		−	2.72238i		−	0.133476i
$417$	3.99599	−	3.99599i	0.195685	−	0.195685i
$418$	−1.63115	+	1.63115i	−0.0797820	+	0.0797820i
$419$	−8.27092			−0.404061			−0.202030	−	0.979379i	$-0.564754\pi$
$419$	−8.27092			−0.404061			−0.202030	+	0.979379i	$0.564754\pi$
$420$		0			0
$421$	−33.3728			−1.62649			−0.813246	−	0.581920i	$-0.802302\pi$
$421$	−33.3728			−1.62649			−0.813246	+	0.581920i	$0.802302\pi$
$422$	13.4672	−	13.4672i	0.655574	−	0.655574i
$423$	2.88977	−	2.88977i	0.140505	−	0.140505i
$424$		−	2.92719i		−	0.142157i
$425$	−0.103525	−	0.0319715i	−0.00502170	−	0.00155084i
$426$		−	7.51848i		−	0.364272i
$427$		0			0
$428$	−4.88300	−	4.88300i	−0.236029	−	0.236029i
$429$		−	3.17374i		−	0.153229i
$430$	24.1796	−	5.99231i	1.16604	−	0.288975i
$431$	−24.3467			−1.17274			−0.586369	−	0.810044i	$-0.699443\pi$
$431$	−24.3467			−1.17274			−0.586369	+	0.810044i	$0.699443\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	18.0803	−	18.0803i	0.868885	−	0.868885i	−0.123464	−	0.992349i	$-0.539400\pi$
$433$	18.0803	−	18.0803i	0.868885	−	0.868885i	0.992349	+	0.123464i	$0.0394002\pi$
$434$		0			0
$435$	10.7359	+	6.47146i	0.514746	+	0.310283i
$436$	0.577314			0.0276483
$437$	−10.0459	−	10.0459i	−0.480561	−	0.480561i
$438$	2.64838	+	2.64838i	0.126545	+	0.126545i
$439$	−16.2202			−0.774150			−0.387075	−	0.922048i	$-0.626514\pi$
$439$	−16.2202			−0.774150			−0.387075	+	0.922048i	$0.626514\pi$
$440$	−2.23256	−	1.34576i	−0.106433	−	0.0641566i
$441$		0			0
$442$	0.0417148	−	0.0417148i	0.00198417	−	0.00198417i
$443$	15.4050	+	15.4050i	0.731911	+	0.731911i	0.970998	−	0.239087i	$-0.0768480\pi$
$443$	15.4050	+	15.4050i	0.731911	+	0.731911i	−0.239087	+	0.970998i	$0.576848\pi$
$444$	10.6211			0.504055
$445$	7.82455	−	1.93912i	0.370919	−	0.0919231i
$446$		−	4.16472i		−	0.197205i
$447$	−0.156132	−	0.156132i	−0.00738477	−	0.00738477i
$448$		0			0
$449$		−	10.1648i		−	0.479708i	−0.970809	−	0.239854i	$-0.922900\pi$
$449$		−	10.1648i		−	0.479708i	0.970809	−	0.239854i	$-0.0770996\pi$
$450$	4.77737	+	1.47539i	0.225207	+	0.0695504i
$451$			2.90256i			0.136676i
$452$	13.2689	−	13.2689i	0.624115	−	0.624115i
$453$	4.50346	−	4.50346i	0.211591	−	0.211591i
$454$	18.4389			0.865381
$455$		0			0
$456$	1.97873			0.0926624
$457$	−20.1699	+	20.1699i	−0.943509	+	0.943509i	−0.998488	−	0.0549784i	$-0.982491\pi$
$457$	−20.1699	+	20.1699i	−0.943509	+	0.943509i	0.0549784	+	0.998488i	$0.482491\pi$
$458$	4.17908	−	4.17908i	0.195276	−	0.195276i
$459$		−	0.0216699i		−	0.00101146i
$460$	8.28827	−	13.7499i	0.386442	−	0.641091i
$461$			20.0972i			0.936022i	0.883723	+	0.468011i	$0.155029\pi$
$461$			20.0972i			0.936022i	−0.883723	+	0.468011i	$0.844971\pi$
$462$		0			0
$463$	−7.34462	−	7.34462i	−0.341334	−	0.341334i	0.515535	−	0.856869i	$-0.327593\pi$
$463$	−7.34462	−	7.34462i	−0.341334	−	0.341334i	−0.856869	+	0.515535i	$0.827593\pi$
$464$			5.60604i			0.260254i
$465$	−15.1884	−	9.15540i	−0.704346	−	0.424571i
$466$	−7.23533			−0.335170
$467$	16.6908	+	16.6908i	0.772359	+	0.772359i	0.978518	−	0.206160i	$-0.0660966\pi$
$467$	16.6908	+	16.6908i	0.772359	+	0.772359i	−0.206160	+	0.978518i	$0.566097\pi$
$468$	−1.92501	+	1.92501i	−0.0889838	+	0.0889838i
$469$		0			0
$470$	−8.86993	+	2.19819i	−0.409139	+	0.101395i
$471$	14.4763			0.667031
$472$	7.56072	+	7.56072i	0.348010	+	0.348010i
$473$	9.18362	+	9.18362i	0.422263	+	0.422263i
$474$	−1.61039			−0.0739679
$475$	−8.74867	+	4.62004i	−0.401417	+	0.211982i
$476$		0			0
$477$	−2.06984	+	2.06984i	−0.0947714	+	0.0947714i
$478$	−2.97106	−	2.97106i	−0.135893	−	0.135893i
$479$	−24.7785			−1.13216			−0.566079	−	0.824351i	$-0.691540\pi$
$479$	−24.7785			−1.13216			−0.566079	+	0.824351i	$0.691540\pi$
$480$	0.537883	+	2.17041i	0.0245509	+	0.0990652i
$481$		−	28.9147i		−	1.31840i
$482$	15.5110	+	15.5110i	0.706507	+	0.706507i
$483$		0			0
$484$			9.64092i			0.438224i
$485$	0.719054	+	0.433437i	0.0326506	+	0.0196814i
$486$			1.00000i			0.0453609i
$487$	16.8056	−	16.8056i	0.761536	−	0.761536i	−0.215064	−	0.976600i	$-0.568996\pi$
$487$	16.8056	−	16.8056i	0.761536	−	0.761536i	0.976600	+	0.215064i	$0.0689960\pi$
$488$	−2.57846	+	2.57846i	−0.116721	+	0.116721i
$489$	−21.9057			−0.990608
$490$		0			0
$491$	−0.386093			−0.0174242			−0.00871208	−	0.999962i	$-0.502773\pi$
$491$	−0.386093			−0.0174242			−0.00871208	+	0.999962i	$0.502773\pi$
$492$	1.76053	−	1.76053i	0.0793709	−	0.0793709i
$493$	−0.0859010	+	0.0859010i	−0.00386879	+	0.00386879i
$494$		−	5.38685i		−	0.242366i
$495$	0.627061	+	2.53025i	0.0281843	+	0.113726i
$496$		−	7.93107i		−	0.356115i
$497$		0			0
$498$	−9.74815	−	9.74815i	−0.436825	−	0.436825i
$499$		−	8.02507i		−	0.359252i	−0.983735	−	0.179626i	$-0.942511\pi$
$499$		−	8.02507i		−	0.359252i	0.983735	−	0.179626i	$-0.0574887\pi$
$500$	−7.44577	−	8.34030i	−0.332985	−	0.372989i
$501$	−16.1103			−0.719754
$502$	10.6980	+	10.6980i	0.477476	+	0.477476i
$503$	−11.5901	+	11.5901i	−0.516775	+	0.516775i	−0.916594	−	0.399819i	$-0.869073\pi$
$503$	−11.5901	+	11.5901i	−0.516775	+	0.516775i	0.399819	+	0.916594i	$0.369073\pi$
$504$		0			0
$505$	7.48513	+	30.2033i	0.333084	+	1.34403i
$506$	8.37028			0.372105
$507$	−3.95177	−	3.95177i	−0.175504	−	0.175504i
$508$	−1.36110	−	1.36110i	−0.0603890	−	0.0603890i
$509$	15.5484			0.689173			0.344586	−	0.938755i	$-0.388019\pi$
$509$	15.5484			0.689173			0.344586	+	0.938755i	$0.388019\pi$
$510$	−0.0250151	+	0.0414990i	−0.00110769	+	0.00183761i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.39917	−	1.39917i	−0.0617749	−	0.0617749i
$514$	23.0143			1.01512
$515$	−13.8341	+	22.9502i	−0.609603	+	1.01130i
$516$		−	11.1406i		−	0.490435i
$517$	−3.36888	−	3.36888i	−0.148163	−	0.148163i
$518$		0			0
$519$			10.4433i			0.458408i
$520$	5.90868	−	1.46432i	0.259113	−	0.0642147i
$521$			26.3933i			1.15631i	0.815926	+	0.578156i	$0.196228\pi$
$521$			26.3933i			1.15631i	−0.815926	+	0.578156i	$0.803772\pi$
$522$	3.96407	−	3.96407i	0.173503	−	0.173503i
$523$	−27.9009	+	27.9009i	−1.22002	+	1.22002i	−0.252400	+	0.967623i	$0.581220\pi$
$523$	−27.9009	+	27.9009i	−1.22002	+	1.22002i	−0.967623	+	0.252400i	$0.918780\pi$
$524$	17.1498			0.749192
$525$		0			0
$526$	20.1205			0.877294
$527$	0.121527	−	0.121527i	0.00529381	−	0.00529381i
$528$	−0.824341	+	0.824341i	−0.0358749	+	0.0358749i
$529$			28.5509i			1.24134i
$530$	6.35321	−	1.57449i	0.275966	−	0.0683913i
$531$		−	10.6925i		−	0.464014i
$532$		0			0
$533$	−4.79284	−	4.79284i	−0.207601	−	0.207601i
$534$		−	3.60510i		−	0.156008i
$535$	7.97164	−	13.2246i	0.344644	−	0.571750i
$536$	14.5582			0.628819
$537$	1.06563	+	1.06563i	0.0459854	+	0.0459854i
$538$	−6.55459	+	6.55459i	−0.282588	+	0.282588i
$539$		0			0
$540$	1.15437	−	1.91505i	0.0496762	−	0.0824107i
$541$	8.13698			0.349836			0.174918	−	0.984583i	$-0.444034\pi$
$541$	8.13698			0.349836			0.174918	+	0.984583i	$0.444034\pi$
$542$	18.5473	+	18.5473i	0.796673	+	0.796673i
$543$	−15.0937	−	15.0937i	−0.647733	−	0.647733i
$544$	−0.0216699			−0.000929089
$545$	0.310527	+	1.25301i	0.0133015	+	0.0536730i
$546$		0			0
$547$	12.5204	−	12.5204i	0.535335	−	0.535335i	−0.386820	−	0.922155i	$-0.626427\pi$
$547$	12.5204	−	12.5204i	0.535335	−	0.535335i	0.922155	+	0.386820i	$0.126427\pi$
$548$	−7.23778	−	7.23778i	−0.309182	−	0.309182i
$549$	3.64649			0.155628
$550$	1.72000	−	5.56943i	0.0733410	−	0.237481i
$551$			11.0928i			0.472570i
$552$	−5.07695	−	5.07695i	−0.216089	−	0.216089i
$553$		0			0
$554$			13.2995i			0.565040i
$555$	5.71291	+	23.0522i	0.242500	+	0.978510i
$556$			5.65119i			0.239664i
$557$	−11.4507	+	11.4507i	−0.485180	+	0.485180i	−0.906781	−	0.421601i	$-0.861468\pi$
$557$	−11.4507	+	11.4507i	−0.485180	+	0.485180i	0.421601	+	0.906781i	$0.361468\pi$
$558$	−5.60811	+	5.60811i	−0.237410	+	0.237410i
$559$	−30.3288			−1.28277
$560$		0			0
$561$	−0.0252626			−0.00106659
$562$	9.55307	−	9.55307i	0.402972	−	0.402972i
$563$	−6.19009	+	6.19009i	−0.260881	+	0.260881i	−0.825412	−	0.564531i	$-0.809057\pi$
$563$	−6.19009	+	6.19009i	−0.260881	+	0.260881i	0.564531	+	0.825412i	$0.309057\pi$
$564$			4.08675i			0.172083i
$565$	35.9360	+	21.6618i	1.51184	+	0.911318i
$566$		−	19.8911i		−	0.836085i
$567$		0			0
$568$	5.31637	+	5.31637i	0.223070	+	0.223070i
$569$		−	41.5454i		−	1.74168i	−0.491571	−	0.870838i	$-0.663577\pi$
$569$		−	41.5454i		−	1.74168i	0.491571	−	0.870838i	$-0.336423\pi$
$570$	1.06432	+	4.29465i	0.0445796	+	0.179883i
$571$	13.1852			0.551782			0.275891	−	0.961189i	$-0.411027\pi$
$571$	13.1852			0.551782			0.275891	+	0.961189i	$0.411027\pi$
$572$	2.24417	+	2.24417i	0.0938335	+	0.0938335i
$573$	−4.56144	+	4.56144i	−0.190557	+	0.190557i
$574$		0			0
$575$	34.3010	+	10.5931i	1.43045	+	0.441764i
$576$	1.00000			0.0416667
$577$	12.6878	+	12.6878i	0.528201	+	0.528201i	0.920036	−	0.391835i	$-0.128160\pi$
$577$	12.6878	+	12.6878i	0.528201	+	0.528201i	−0.391835	+	0.920036i	$0.628160\pi$
$578$	12.0205	+	12.0205i	0.499986	+	0.499986i
$579$	5.13858			0.213552
$580$	−12.1674	+	3.01539i	−0.505225	+	0.125207i
$581$		0			0
$582$	0.265501	−	0.265501i	0.0110054	−	0.0110054i
$583$	2.41301	+	2.41301i	0.0999365	+	0.0999365i
$584$	−3.74538			−0.154985
$585$	−5.21350	−	3.14264i	−0.215552	−	0.129932i
$586$		−	24.6135i		−	1.01677i
$587$	−7.68342	−	7.68342i	−0.317129	−	0.317129i	0.530535	−	0.847663i	$-0.321991\pi$
$587$	−7.68342	−	7.68342i	−0.317129	−	0.317129i	−0.847663	+	0.530535i	$0.821991\pi$
$588$		0			0
$589$		−	15.6934i		−	0.646636i
$590$	−12.3431	+	20.4766i	−0.508157	+	0.843010i
$591$			25.2221i			1.03750i
$592$	−7.51026	+	7.51026i	−0.308670	+	0.308670i
$593$	−5.55504	+	5.55504i	−0.228118	+	0.228118i	−0.811906	−	0.583788i	$-0.801570\pi$
$593$	−5.55504	+	5.55504i	−0.228118	+	0.228118i	0.583788	+	0.811906i	$0.301570\pi$
$594$	1.16579			0.0478331
$595$		0			0
$596$	0.220803			0.00904446
$597$	3.49450	−	3.49450i	0.143020	−	0.143020i
$598$	−13.8214	+	13.8214i	−0.565199	+	0.565199i
$599$			23.7314i			0.969638i	0.874615	+	0.484819i	$0.161114\pi$
$599$			23.7314i			0.969638i	−0.874615	+	0.484819i	$0.838886\pi$
$600$	−4.42136	+	2.33485i	−0.180501	+	0.0953200i
$601$			14.4348i			0.588806i	0.955681	+	0.294403i	$0.0951208\pi$
$601$			14.4348i			0.588806i	−0.955681	+	0.294403i	$0.904879\pi$
$602$		0			0
$603$	−10.2942	−	10.2942i	−0.419213	−	0.419213i
$604$			6.36885i			0.259145i
$605$	−20.9248	+	5.18569i	−0.850712	+	0.210828i
$606$	13.9159			0.565296
$607$	−0.472022	−	0.472022i	−0.0191588	−	0.0191588i	0.697462	−	0.716621i	$-0.254312\pi$
$607$	−0.472022	−	0.472022i	−0.0191588	−	0.0191588i	−0.716621	+	0.697462i	$0.754312\pi$
$608$	−1.39917	+	1.39917i	−0.0567439	+	0.0567439i
$609$		0			0
$610$	−6.98322	−	4.20940i	−0.282742	−	0.170434i
$611$	11.1257			0.450097
$612$	0.0153229	+	0.0153229i	0.000619393	+	0.000619393i
$613$	−10.4369	−	10.4369i	−0.421544	−	0.421544i	0.464191	−	0.885735i	$-0.346345\pi$
$613$	−10.4369	−	10.4369i	−0.421544	−	0.421544i	−0.885735	+	0.464191i	$0.846345\pi$
$614$	−0.800938			−0.0323232
$615$	4.76804	+	2.87412i	0.192266	+	0.115896i
$616$		0			0
$617$	−4.88322	+	4.88322i	−0.196591	+	0.196591i	−0.798537	−	0.601946i	$-0.794392\pi$
$617$	−4.88322	+	4.88322i	−0.196591	+	0.196591i	0.601946	+	0.798537i	$0.294392\pi$
$618$	8.47403	+	8.47403i	0.340875	+	0.340875i
$619$	−27.7950			−1.11718			−0.558589	−	0.829445i	$-0.688657\pi$
$619$	−27.7950			−1.11718			−0.558589	+	0.829445i	$0.688657\pi$
$620$	17.2137	−	4.26598i	0.691318	−	0.171326i
$621$			7.17989i			0.288119i
$622$	−9.47327	−	9.47327i	−0.379844	−	0.379844i
$623$		0			0
$624$		−	2.72238i		−	0.108982i
$625$	14.0969	−	20.6465i	0.563877	−	0.825859i
$626$			28.7580i			1.14940i
$627$	−1.63115	+	1.63115i	−0.0651417	+	0.0651417i
$628$	−10.2363	+	10.2363i	−0.408471	+	0.408471i
$629$	−0.230158			−0.00917701
$630$		0			0
$631$	6.30112			0.250844			0.125422	−	0.992104i	$-0.459972\pi$
$631$	6.30112			0.250844			0.125422	+	0.992104i	$0.459972\pi$
$632$	1.13872	−	1.13872i	0.0452959	−	0.0452959i
$633$	13.4672	−	13.4672i	0.535274	−	0.535274i
$634$		−	33.7349i		−	1.33979i
$635$	2.22203	−	3.68625i	0.0881786	−	0.146284i
$636$		−	2.92719i		−	0.116071i
$637$		0			0
$638$	−4.62129	−	4.62129i	−0.182959	−	0.182959i
$639$		−	7.51848i		−	0.297427i
$640$	−1.91505	−	1.15437i	−0.0756991	−	0.0456305i
$641$	5.27369			0.208298			0.104149	−	0.994562i	$-0.466788\pi$
$641$	5.27369			0.208298			0.104149	+	0.994562i	$0.466788\pi$
$642$	−4.88300	−	4.88300i	−0.192717	−	0.192717i
$643$	5.34948	−	5.34948i	0.210963	−	0.210963i	−0.593714	−	0.804677i	$-0.702339\pi$
$643$	5.34948	−	5.34948i	0.210963	−	0.210963i	0.804677	+	0.593714i	$0.202339\pi$
$644$		0			0
$645$	24.1796	−	5.99231i	0.952070	−	0.235947i
$646$	−0.0428788			−0.00168704
$647$	−15.6685	−	15.6685i	−0.615992	−	0.615992i	0.328509	−	0.944501i	$-0.393454\pi$
$647$	−15.6685	−	15.6685i	−0.615992	−	0.615992i	−0.944501	+	0.328509i	$0.893454\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−12.4652			−0.489303
$650$	6.35636	+	12.0366i	0.249317	+	0.472116i
$651$		0			0
$652$	15.4896	−	15.4896i	0.606621	−	0.606621i
$653$	−31.3513	−	31.3513i	−1.22687	−	1.22687i	−0.965141	−	0.261729i	$-0.915707\pi$
$653$	−31.3513	−	31.3513i	−1.22687	−	1.22687i	−0.261729	−	0.965141i	$-0.584293\pi$
$654$	0.577314			0.0225748
$655$	9.22458	+	37.2221i	0.360434	+	1.45439i
$656$			2.48977i			0.0972091i
$657$	2.64838	+	2.64838i	0.103323	+	0.103323i
$658$		0			0
$659$		−	38.6387i		−	1.50515i	−0.658507	−	0.752575i	$-0.728812\pi$
$659$		−	38.6387i		−	1.50515i	0.658507	−	0.752575i	$-0.271188\pi$
$660$	−2.23256	−	1.34576i	−0.0869022	−	0.0523837i
$661$		−	28.6063i		−	1.11265i	−0.830963	−	0.556327i	$-0.812210\pi$
$661$		−	28.6063i		−	1.11265i	0.830963	−	0.556327i	$-0.187790\pi$
$662$	7.73266	−	7.73266i	0.300538	−	0.300538i
$663$	0.0417148	−	0.0417148i	0.00162007	−	0.00162007i
$664$	13.7860			0.534999
$665$		0			0
$666$	10.6211			0.411560
$667$	28.4616	−	28.4616i	1.10204	−	1.10204i
$668$	11.3917	−	11.3917i	0.440757	−	0.440757i
$669$		−	4.16472i		−	0.161018i
$670$	7.83061	+	31.5973i	0.302523	+	1.22071i
$671$		−	4.25106i		−	0.164110i
$672$		0			0
$673$	36.6126	+	36.6126i	1.41131	+	1.41131i	0.750932	+	0.660379i	$0.229604\pi$
$673$	36.6126	+	36.6126i	1.41131	+	1.41131i	0.660379	+	0.750932i	$0.270396\pi$
$674$		−	14.5545i		−	0.560617i
$675$	4.77737	+	1.47539i	0.183881	+	0.0567876i
$676$	5.58865			0.214948
$677$	18.9864	+	18.9864i	0.729707	+	0.729707i	0.970561	−	0.240854i	$-0.0774276\pi$
$677$	18.9864	+	18.9864i	0.729707	+	0.729707i	−0.240854	+	0.970561i	$0.577428\pi$
$678$	13.2689	−	13.2689i	0.509587	−	0.509587i
$679$		0			0
$680$	−0.0116559	−	0.0470326i	−0.000446982	−	0.00180362i
$681$	18.4389			0.706580
$682$	6.53791	+	6.53791i	0.250349	+	0.250349i
$683$	−1.40553	−	1.40553i	−0.0537811	−	0.0537811i	0.679705	−	0.733486i	$-0.262108\pi$
$683$	−1.40553	−	1.40553i	−0.0537811	−	0.0537811i	−0.733486	+	0.679705i	$0.762108\pi$
$684$	1.97873			0.0756585
$685$	11.8159	−	19.6020i	0.451461	−	0.748955i
$686$		0			0
$687$	4.17908	−	4.17908i	0.159442	−	0.159442i
$688$	7.87756	+	7.87756i	0.300329	+	0.300329i
$689$	−7.96893			−0.303592
$690$	8.28827	−	13.7499i	0.315529	−	0.523449i
$691$			9.62525i			0.366162i	0.983098	+	0.183081i	$0.0586070\pi$
$691$			9.62525i			0.366162i	−0.983098	+	0.183081i	$0.941393\pi$
$692$	−7.38450	−	7.38450i	−0.280717	−	0.280717i
$693$		0			0
$694$		−	2.55458i		−	0.0969703i
$695$	−12.2654	+	3.03968i	−0.465253	+	0.115301i
$696$			5.60604i			0.212497i
$697$	−0.0381505	+	0.0381505i	−0.00144505	+	0.00144505i
$698$	−13.1578	+	13.1578i	−0.498029	+	0.498029i
$699$	−7.23533			−0.273665
$700$		0			0
$701$	−12.4958			−0.471959			−0.235980	−	0.971758i	$-0.575830\pi$
$701$	−12.4958			−0.471959			−0.235980	+	0.971758i	$0.575830\pi$
$702$	−1.92501	+	1.92501i	−0.0726549	+	0.0726549i
$703$	−14.8607	+	14.8607i	−0.560484	+	0.560484i
$704$		−	1.16579i		−	0.0439375i
$705$	−8.86993	+	2.19819i	−0.334061	+	0.0827887i
$706$			15.8312i			0.595816i
$707$		0			0
$708$	7.56072	+	7.56072i	0.284149	+	0.284149i
$709$			45.7462i			1.71804i	0.511946	+	0.859018i	$0.328925\pi$
$709$			45.7462i			1.71804i	−0.511946	+	0.859018i	$0.671075\pi$
$710$	−8.67912	+	14.3983i	−0.325722	+	0.540358i
$711$	−1.61039			−0.0603945
$712$	2.54919	+	2.54919i	0.0955349	+	0.0955349i
$713$	−40.2656	+	40.2656i	−1.50796	+	1.50796i
$714$		0			0
$715$	−3.66367	+	6.07787i	−0.137014	+	0.227300i
$716$	−1.50703			−0.0563204
$717$	−2.97106	−	2.97106i	−0.110956	−	0.110956i
$718$	−5.30767	−	5.30767i	−0.198081	−	0.198081i
$719$	−16.1088			−0.600756			−0.300378	−	0.953820i	$-0.597113\pi$
$719$	−16.1088			−0.600756			−0.300378	+	0.953820i	$0.597113\pi$
$720$	0.537883	+	2.17041i	0.0200457	+	0.0808864i
$721$		0			0
$722$	10.6665	−	10.6665i	0.396964	−	0.396964i
$723$	15.5110	+	15.5110i	0.576861	+	0.576861i
$724$	21.3457			0.793308
$725$	−13.0893	−	24.7864i	−0.486124	−	0.920542i
$726$			9.64092i			0.357808i
$727$	−26.7345	−	26.7345i	−0.991528	−	0.991528i	0.00843633	−	0.999964i	$-0.497315\pi$
$727$	−26.7345	−	26.7345i	−0.991528	−	0.991528i	−0.999964	+	0.00843633i	$0.997315\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−2.01458	−	8.12901i	−0.0745628	−	0.300868i
$731$			0.241415i			0.00892904i
$732$	−2.57846	+	2.57846i	−0.0953025	+	0.0953025i
$733$	−7.18611	+	7.18611i	−0.265425	+	0.265425i	−0.827254	−	0.561829i	$-0.810098\pi$
$733$	−7.18611	+	7.18611i	−0.265425	+	0.265425i	0.561829	+	0.827254i	$0.310098\pi$
$734$	−3.94796			−0.145722
$735$		0			0
$736$	7.17989			0.264654
$737$	−12.0009	+	12.0009i	−0.442060	+	0.442060i
$738$	1.76053	−	1.76053i	0.0648061	−	0.0648061i
$739$		−	1.74772i		−	0.0642908i	−0.999483	−	0.0321454i	$-0.989766\pi$
$739$		−	1.74772i		−	0.0642908i	0.999483	−	0.0321454i	$-0.0102340\pi$
$740$	−20.3400	−	12.2607i	−0.747712	−	0.450712i
$741$		−	5.38685i		−	0.197891i
$742$		0			0
$743$	4.26452	+	4.26452i	0.156450	+	0.156450i	0.780992	−	0.624542i	$-0.214714\pi$
$743$	4.26452	+	4.26452i	0.156450	+	0.156450i	−0.624542	+	0.780992i	$0.714714\pi$
$744$		−	7.93107i		−	0.290767i
$745$	0.118766	+	0.479234i	0.00435126	+	0.0175578i
$746$	−5.39411			−0.197492
$747$	−9.74815	−	9.74815i	−0.356666	−	0.356666i
$748$	0.0178634	−	0.0178634i	0.000653150	−	0.000653150i
$749$		0			0
$750$	−7.44577	−	8.34030i	−0.271881	−	0.304545i
$751$	15.0871			0.550535			0.275268	−	0.961368i	$-0.411234\pi$
$751$	15.0871			0.550535			0.275268	+	0.961368i	$0.411234\pi$
$752$	−2.88977	−	2.88977i	−0.105379	−	0.105379i
$753$	10.6980	+	10.6980i	0.389858	+	0.389858i
$754$	15.2618			0.555801
$755$	−13.8230	+	3.42569i	−0.503071	+	0.124674i
$756$		0			0
$757$	−7.26095	+	7.26095i	−0.263904	+	0.263904i	−0.826638	−	0.562734i	$-0.809749\pi$
$757$	−7.26095	+	7.26095i	−0.263904	+	0.263904i	0.562734	+	0.826638i	$0.309749\pi$
$758$	−1.74940	−	1.74940i	−0.0635411	−	0.0635411i
$759$	8.37028			0.303822
$760$	−3.78937	−	2.28419i	−0.137455	−	0.0828561i
$761$			12.3608i			0.448079i	0.974580	+	0.224040i	$0.0719245\pi$
$761$			12.3608i			0.448079i	−0.974580	+	0.224040i	$0.928076\pi$
$762$	−1.36110	−	1.36110i	−0.0493074	−	0.0493074i
$763$		0			0
$764$		−	6.45086i		−	0.233384i
$765$	−0.0250151	+	0.0414990i	−0.000904423	+	0.00150040i
$766$		−	24.1087i		−	0.871083i
$767$	20.5831	−	20.5831i	0.743214	−	0.743214i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−17.1708			−0.619196			−0.309598	−	0.950867i	$-0.600195\pi$
$769$	−17.1708			−0.619196			−0.309598	+	0.950867i	$0.600195\pi$
$770$		0			0
$771$	23.0143			0.828839
$772$	−3.63352	+	3.63352i	−0.130773	+	0.130773i
$773$	0.895237	−	0.895237i	0.0321994	−	0.0321994i	−0.690824	−	0.723023i	$-0.742752\pi$
$773$	0.895237	−	0.895237i	0.0321994	−	0.0321994i	0.723023	+	0.690824i	$0.242752\pi$
$774$		−	11.1406i		−	0.400439i
$775$	18.5179	+	35.0661i	0.665182	+	1.25961i
$776$			0.375475i			0.0134788i
$777$		0			0
$778$	4.56126	+	4.56126i	0.163529	+	0.163529i
$779$			4.92657i			0.176513i
$780$	5.90868	−	1.46432i	0.211565	−	0.0524311i
$781$	−8.76501			−0.313637
$782$	0.110017	+	0.110017i	0.00393420	+	0.00393420i
$783$	3.96407	−	3.96407i	0.141664	−	0.141664i
$784$		0			0
$785$	−27.7228	−	16.7110i	−0.989469	−	0.596441i
$786$	17.1498			0.611713
$787$	10.8355	+	10.8355i	0.386243	+	0.386243i	0.873345	−	0.487102i	$-0.161946\pi$
$787$	10.8355	+	10.8355i	0.386243	+	0.386243i	−0.487102	+	0.873345i	$0.661946\pi$
$788$	−17.8347	−	17.8347i	−0.635334	−	0.635334i
$789$	20.1205			0.716308
$790$	3.08399	+	1.85899i	0.109723	+	0.0661400i
$791$		0			0
$792$	−0.824341	+	0.824341i	−0.0292917	+	0.0292917i
$793$	7.01954	+	7.01954i	0.249271	+	0.249271i
$794$	18.7167			0.664230
$795$	6.35321	−	1.57449i	0.225325	−	0.0558413i
$796$			4.94197i			0.175163i
$797$	36.4737	+	36.4737i	1.29197	+	1.29197i	0.933570	+	0.358396i	$0.116676\pi$
$797$	36.4737	+	36.4737i	1.29197	+	1.29197i	0.358396	+	0.933570i	$0.383324\pi$
$798$		0			0
$799$		−	0.0885594i		−	0.00313301i
$800$	1.47539	−	4.77737i	0.0521628	−	0.168905i
$801$		−	3.60510i		−	0.127380i
$802$	13.2507	−	13.2507i	0.467900	−	0.467900i
$803$	3.08747	−	3.08747i	0.108955	−	0.108955i
$804$	14.5582			0.513428
$805$		0			0
$806$	−21.5914			−0.760524
$807$	−6.55459	+	6.55459i	−0.230732	+	0.230732i
$808$	−9.84004	+	9.84004i	−0.346171	+	0.346171i
$809$			13.8746i			0.487806i	0.969800	+	0.243903i	$0.0784278\pi$
$809$			13.8746i			0.487806i	−0.969800	+	0.243903i	$0.921572\pi$
$810$	1.15437	−	1.91505i	0.0405605	−	0.0672881i
$811$		−	18.4047i		−	0.646275i	−0.946352	−	0.323137i	$-0.895262\pi$
$811$		−	18.4047i		−	0.646275i	0.946352	−	0.323137i	$-0.104738\pi$
$812$		0			0
$813$	18.5473	+	18.5473i	0.650481	+	0.650481i
$814$		−	12.3820i		−	0.433990i
$815$	41.9505	+	25.2873i	1.46946	+	0.885775i
$816$	−0.0216699			−0.000758598
$817$	15.5875	+	15.5875i	0.545339	+	0.545339i
$818$	−16.5135	+	16.5135i	−0.577381	+	0.577381i
$819$		0			0
$820$	−5.40382	+	1.33920i	−0.188710	+	0.0467670i
$821$	32.8805			1.14754			0.573768	−	0.819018i	$-0.305481\pi$
$821$	32.8805			1.14754			0.573768	+	0.819018i	$0.305481\pi$
$822$	−7.23778	−	7.23778i	−0.252446	−	0.252446i
$823$	−17.2643	−	17.2643i	−0.601796	−	0.601796i	0.338993	−	0.940789i	$-0.389914\pi$
$823$	−17.2643	−	17.2643i	−0.601796	−	0.601796i	−0.940789	+	0.338993i	$0.889914\pi$
$824$	−11.9841			−0.417485
$825$	1.72000	−	5.56943i	0.0598826	−	0.193903i
$826$		0			0
$827$	1.94367	−	1.94367i	0.0675881	−	0.0675881i	−0.672505	−	0.740093i	$-0.734782\pi$
$827$	1.94367	−	1.94367i	0.0675881	−	0.0675881i	0.740093	+	0.672505i	$0.234782\pi$
$828$	−5.07695	−	5.07695i	−0.176436	−	0.176436i
$829$	−17.9832			−0.624583			−0.312291	−	0.949986i	$-0.601097\pi$
$829$	−17.9832			−0.624583			−0.312291	+	0.949986i	$0.601097\pi$
$830$	7.41524	+	29.9212i	0.257387	+	1.03858i
$831$			13.2995i			0.461354i
$832$	1.92501	+	1.92501i	0.0667378	+	0.0667378i
$833$		0			0
$834$			5.65119i			0.195685i
$835$	30.8520	+	18.5972i	1.06768	+	0.643584i
$836$		−	2.30679i		−	0.0797820i
$837$	−5.60811	+	5.60811i	−0.193845	+	0.193845i
$838$	5.84842	−	5.84842i	0.202030	−	0.202030i
$839$	4.25819			0.147009			0.0735045	−	0.997295i	$-0.476582\pi$
$839$	4.25819			0.147009			0.0735045	+	0.997295i	$0.476582\pi$
$840$		0			0
$841$	−2.42773			−0.0837148
$842$	23.5982	−	23.5982i	0.813246	−	0.813246i
$843$	9.55307	−	9.55307i	0.329025	−	0.329025i
$844$			19.0455i			0.655574i
$845$	3.00604	+	12.1297i	0.103411	+	0.417273i
$846$			4.08675i			0.140505i
$847$		0			0
$848$	2.06984	+	2.06984i	0.0710785	+	0.0710785i
$849$		−	19.8911i		−	0.682660i
$850$	0.0958105	−	0.0505960i	0.00328627	−	0.00173543i
$851$	76.2584			2.61411
$852$	5.31637	+	5.31637i	0.182136	+	0.182136i
$853$	36.5310	−	36.5310i	1.25080	−	1.25080i	0.295436	−	0.955362i	$-0.404535\pi$
$853$	36.5310	−	36.5310i	1.25080	−	1.25080i	0.955362	−	0.295436i	$-0.0954650\pi$
$854$		0			0
$855$	1.06432	+	4.29465i	0.0363991	+	0.146874i
$856$	6.90561			0.236029
$857$	−2.24292	−	2.24292i	−0.0766167	−	0.0766167i	0.667760	−	0.744377i	$-0.267253\pi$
$857$	−2.24292	−	2.24292i	−0.0766167	−	0.0766167i	−0.744377	+	0.667760i	$0.767253\pi$
$858$	2.24417	+	2.24417i	0.0766147	+	0.0766147i
$859$	−29.8751			−1.01933			−0.509663	−	0.860374i	$-0.670230\pi$
$859$	−29.8751			−1.01933			−0.509663	+	0.860374i	$0.670230\pi$
$860$	−12.8603	+	21.3347i	−0.438534	+	0.727509i
$861$		0			0
$862$	17.2157	−	17.2157i	0.586369	−	0.586369i
$863$	22.8475	+	22.8475i	0.777738	+	0.777738i	0.979446	−	0.201708i	$-0.0646491\pi$
$863$	22.8475	+	22.8475i	0.777738	+	0.777738i	−0.201708	+	0.979446i	$0.564649\pi$
$864$	1.00000			0.0340207
$865$	12.0554	−	19.9994i	0.409896	−	0.680000i
$866$			25.5695i			0.868885i
$867$	12.0205	+	12.0205i	0.408237	+	0.408237i
$868$		0			0
$869$			1.87739i			0.0636861i
$870$	−12.1674	+	3.01539i	−0.412514	+	0.102231i
$871$		−	39.6330i		−	1.34291i
$872$	−0.408223	+	0.408223i	−0.0138242	+	0.0138242i
$873$	0.265501	−	0.265501i	0.00898584	−	0.00898584i
$874$	14.2070			0.480561
$875$		0			0
$876$	−3.74538			−0.126545
$877$	2.88138	−	2.88138i	0.0972971	−	0.0972971i	−0.656783	−	0.754080i	$-0.728083\pi$
$877$	2.88138	−	2.88138i	0.0972971	−	0.0972971i	0.754080	+	0.656783i	$0.228083\pi$
$878$	11.4694	−	11.4694i	0.387075	−	0.387075i
$879$		−	24.6135i		−	0.830193i
$880$	2.53025	−	0.627061i	0.0852948	−	0.0211382i
$881$		−	19.0783i		−	0.642764i	−0.946950	−	0.321382i	$-0.895853\pi$
$881$		−	19.0783i		−	0.642764i	0.946950	−	0.321382i	$-0.104147\pi$
$882$		0			0
$883$	6.02976	+	6.02976i	0.202918	+	0.202918i	0.801249	−	0.598331i	$-0.204169\pi$
$883$	6.02976	+	6.02976i	0.202918	+	0.202918i	−0.598331	+	0.801249i	$0.704169\pi$
$884$			0.0589937i			0.00198417i
$885$	−12.3431	+	20.4766i	−0.414908	+	0.688315i
$886$	−21.7859			−0.731911
$887$	30.7970	+	30.7970i	1.03406	+	1.03406i	0.999399	+	0.0346645i	$0.0110363\pi$
$887$	30.7970	+	30.7970i	1.03406	+	1.03406i	0.0346645	+	0.999399i	$0.488964\pi$
$888$	−7.51026	+	7.51026i	−0.252028	+	0.252028i
$889$		0			0
$890$	−4.16162	+	6.90395i	−0.139498	+	0.231421i
$891$	1.16579			0.0390556
$892$	2.94490	+	2.94490i	0.0986027	+	0.0986027i
$893$	−5.71806	−	5.71806i	−0.191348	−	0.191348i
$894$	0.220803			0.00738477
$895$	−0.810606	−	3.27088i	−0.0270956	−	0.109333i
$896$		0			0
$897$	−13.8214	+	13.8214i	−0.461483	+	0.461483i
$898$	7.18762	+	7.18762i	0.239854	+	0.239854i
$899$	44.4619			1.48289
$900$	−4.42136	+	2.33485i	−0.147379	+	0.0778284i
$901$			0.0634319i			0.00211322i
$902$	−2.05242	−	2.05242i	−0.0683381	−	0.0683381i
$903$		0			0
$904$			18.7650i			0.624115i
$905$	11.4815	+	46.3290i	0.381658	+	1.54003i
$906$			6.36885i			0.211591i
$907$	−40.3409	+	40.3409i	−1.33950	+	1.33950i	−0.442950	+	0.896546i	$0.646068\pi$
$907$	−40.3409	+	40.3409i	−1.33950	+	1.33950i	−0.896546	+	0.442950i	$0.853932\pi$
$908$	−13.0383	+	13.0383i	−0.432690	+	0.432690i
$909$	13.9159			0.461562
$910$		0			0
$911$	−32.4993			−1.07675			−0.538375	−	0.842705i	$-0.680962\pi$
$911$	−32.4993			−1.07675			−0.538375	+	0.842705i	$0.680962\pi$
$912$	−1.39917	+	1.39917i	−0.0463312	+	0.0463312i
$913$	−11.3643	+	11.3643i	−0.376105	+	0.376105i
$914$		−	28.5246i		−	0.943509i
$915$	−6.98322	−	4.20940i	−0.230858	−	0.139159i
$916$			5.91011i			0.195276i
$917$		0			0
$918$	0.0153229	+	0.0153229i	0.000505732	+	0.000505732i
$919$		−	2.22330i		−	0.0733400i	−0.999327	−	0.0366700i	$-0.988325\pi$
$919$		−	2.22330i		−	0.0733400i	0.999327	−	0.0366700i	$-0.0116750\pi$
$920$	3.86194	+	15.5833i	0.127324	+	0.513767i
$921$	−0.800938			−0.0263918
$922$	−14.2109	−	14.2109i	−0.468011	−	0.468011i
$923$	14.4732	−	14.4732i	0.476391	−	0.476391i
$924$		0			0
$925$	15.6702	−	50.7409i	0.515234	−	1.66835i
$926$	10.3869			0.341334
$927$	8.47403	+	8.47403i	0.278324	+	0.278324i
$928$	−3.96407	−	3.96407i	−0.130127	−	0.130127i
$929$	−0.716611			−0.0235112			−0.0117556	−	0.999931i	$-0.503742\pi$
$929$	−0.716611			−0.0235112			−0.0117556	+	0.999931i	$0.503742\pi$
$930$	17.2137	−	4.26598i	0.564458	−	0.139887i
$931$		0			0
$932$	5.11615	−	5.11615i	0.167585	−	0.167585i
$933$	−9.47327	−	9.47327i	−0.310141	−	0.310141i
$934$	−23.6044			−0.772359
$935$	0.0483793	+	0.0291625i	0.00158217	+	0.000953715i
$936$		−	2.72238i		−	0.0889838i
$937$	−11.6639	−	11.6639i	−0.381042	−	0.381042i	0.490435	−	0.871478i	$-0.336838\pi$
$937$	−11.6639	−	11.6639i	−0.381042	−	0.381042i	−0.871478	+	0.490435i	$0.836838\pi$
$938$		0			0
$939$			28.7580i			0.938481i
$940$	4.71763	−	7.82634i	0.153872	−	0.255267i
$941$			30.9242i			1.00810i	0.863674	+	0.504051i	$0.168158\pi$
$941$			30.9242i			1.00810i	−0.863674	+	0.504051i	$0.831842\pi$
$942$	−10.2363	+	10.2363i	−0.333515	+	0.333515i
$943$	12.6404	−	12.6404i	0.411629	−	0.411629i
$944$	−10.6925			−0.348010
$945$		0			0
$946$	−12.9876			−0.422263
$947$	−11.5507	+	11.5507i	−0.375348	+	0.375348i	−0.869421	−	0.494073i	$-0.835508\pi$
$947$	−11.5507	+	11.5507i	−0.375348	+	0.375348i	0.494073	+	0.869421i	$0.335508\pi$
$948$	1.13872	−	1.13872i	0.0369839	−	0.0369839i
$949$			10.1963i			0.330988i
$950$	2.91939	−	9.45310i	0.0947174	−	0.306699i
$951$		−	33.7349i		−	1.09393i
$952$		0			0
$953$	−8.22927	−	8.22927i	−0.266572	−	0.266572i	0.561145	−	0.827717i	$-0.310361\pi$
$953$	−8.22927	−	8.22927i	−0.266572	−	0.266572i	−0.827717	+	0.561145i	$0.810361\pi$
$954$		−	2.92719i		−	0.0947714i
$955$	14.0010	−	3.46980i	0.453062	−	0.112280i
$956$	4.20172			0.135893
$957$	−4.62129	−	4.62129i	−0.149385	−	0.149385i
$958$	17.5210	−	17.5210i	0.566079	−	0.566079i
$959$		0			0
$960$	−1.91505	−	1.15437i	−0.0618081	−	0.0372572i
$961$	−31.9018			−1.02909
$962$	20.4458	+	20.4458i	0.659198	+	0.659198i
$963$	−4.88300	−	4.88300i	−0.157353	−	0.157353i
$964$	−21.9359			−0.706507
$965$	−9.84065	−	5.93183i	−0.316782	−	0.190952i
$966$		0			0
$967$	1.15164	−	1.15164i	0.0370342	−	0.0370342i	−0.688347	−	0.725381i	$-0.741663\pi$
$967$	1.15164	−	1.15164i	0.0370342	−	0.0370342i	0.725381	+	0.688347i	$0.241663\pi$
$968$	−6.81716	−	6.81716i	−0.219112	−	0.219112i
$969$	−0.0428788			−0.00137747
$970$	−0.814935	+	0.201961i	−0.0261660	+	0.00648459i
$971$		−	14.4046i		−	0.462265i	−0.972922	−	0.231133i	$-0.925757\pi$
$971$		−	14.4046i		−	0.462265i	0.972922	−	0.231133i	$-0.0742431\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$		0			0
$974$			23.7668i			0.761536i
$975$	6.35636	+	12.0366i	0.203566	+	0.385481i
$976$		−	3.64649i		−	0.116721i
$977$	−26.3118	+	26.3118i	−0.841788	+	0.841788i	−0.989091	−	0.147303i	$-0.952941\pi$
$977$	−26.3118	+	26.3118i	−0.841788	+	0.841788i	0.147303	+	0.989091i	$0.452941\pi$
$978$	15.4896	−	15.4896i	0.495304	−	0.495304i
$979$	−4.20281			−0.134322
$980$		0			0
$981$	0.577314			0.0184322
$982$	0.273009	−	0.273009i	0.00871208	−	0.00871208i
$983$	−20.0064	+	20.0064i	−0.638106	+	0.638106i	−0.950088	−	0.311982i	$-0.899007\pi$
$983$	−20.0064	+	20.0064i	−0.638106	+	0.638106i	0.311982	+	0.950088i	$0.399007\pi$
$984$			2.48977i			0.0793709i
$985$	29.1156	−	48.3016i	0.927701	−	1.53902i
$986$		−	0.121482i		−	0.00386879i
$987$		0			0
$988$	3.80907	+	3.80907i	0.121183	+	0.121183i
$989$		−	79.9880i		−	2.54347i
$990$	−2.23256	−	1.34576i	−0.0709554	−	0.0427711i
$991$	37.3450			1.18630			0.593151	−	0.805091i	$-0.297884\pi$
$991$	37.3450			1.18630			0.593151	+	0.805091i	$0.297884\pi$
$992$	5.60811	+	5.60811i	0.178058	+	0.178058i
$993$	7.73266	−	7.73266i	0.245388	−	0.245388i
$994$		0			0
$995$	−10.7261	+	2.65820i	−0.340040	+	0.0842706i
$996$	13.7860			0.436825
$997$	26.2047	+	26.2047i	0.829913	+	0.829913i	0.987504	−	0.157592i	$-0.0503730\pi$
$997$	26.2047	+	26.2047i	0.829913	+	0.829913i	−0.157592	+	0.987504i	$0.550373\pi$
$998$	5.67458	+	5.67458i	0.179626	+	0.179626i
$999$	10.6211			0.336037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.e.1273.4		16
5.2	odd	4		1470.2.m.d.97.1		16
7.4	even	3		210.2.u.b.103.1	yes	16
7.5	odd	6		210.2.u.a.73.4	✓	16
7.6	odd	2		1470.2.m.d.1273.1		16
21.5	even	6		630.2.bv.a.73.1		16
21.11	odd	6		630.2.bv.b.523.4		16
35.4	even	6		1050.2.bc.g.943.3		16
35.12	even	12		210.2.u.b.157.1	yes	16
35.18	odd	12		1050.2.bc.h.607.2		16
35.19	odd	6		1050.2.bc.h.493.2		16
35.27	even	4	inner	1470.2.m.e.97.4		16
35.32	odd	12		210.2.u.a.187.4	yes	16
35.33	even	12		1050.2.bc.g.157.3		16
105.32	even	12		630.2.bv.a.397.1		16
105.47	odd	12		630.2.bv.b.577.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.4	✓	16	7.5	odd	6
210.2.u.a.187.4	yes	16	35.32	odd	12
210.2.u.b.103.1	yes	16	7.4	even	3
210.2.u.b.157.1	yes	16	35.12	even	12
630.2.bv.a.73.1		16	21.5	even	6
630.2.bv.a.397.1		16	105.32	even	12
630.2.bv.b.523.4		16	21.11	odd	6
630.2.bv.b.577.4		16	105.47	odd	12
1050.2.bc.g.157.3		16	35.33	even	12
1050.2.bc.g.943.3		16	35.4	even	6
1050.2.bc.h.493.2		16	35.19	odd	6
1050.2.bc.h.607.2		16	35.18	odd	12
1470.2.m.d.97.1		16	5.2	odd	4
1470.2.m.d.1273.1		16	7.6	odd	2
1470.2.m.e.97.4		16	35.27	even	4	inner
1470.2.m.e.1273.4		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(2.17041 - 0.537883i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-1.15437 + 1.91505i) q^{10} -1.16579 q^{11} +(0.707107 + 0.707107i) q^{12} +(1.92501 - 1.92501i) q^{13} +(-1.15437 + 1.91505i) q^{15} -1.00000 q^{16} +(-0.0153229 - 0.0153229i) q^{17} +(0.707107 + 0.707107i) q^{18} -1.97873 q^{19} +(-0.537883 - 2.17041i) q^{20} +(0.824341 - 0.824341i) q^{22} +(5.07695 + 5.07695i) q^{23} -1.00000 q^{24} +(4.42136 - 2.33485i) q^{25} +2.72238i q^{26} +(0.707107 + 0.707107i) q^{27} -5.60604i q^{29} +(-0.537883 - 2.17041i) q^{30} +7.93107i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.824341 - 0.824341i) q^{33} +0.0216699 q^{34} -1.00000 q^{36} +(7.51026 - 7.51026i) q^{37} +(1.39917 - 1.39917i) q^{38} +2.72238i q^{39} +(1.91505 + 1.15437i) q^{40} -2.48977i q^{41} +(-7.87756 - 7.87756i) q^{43} +1.16579i q^{44} +(-0.537883 - 2.17041i) q^{45} -7.17989 q^{46} +(2.88977 + 2.88977i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-1.47539 + 4.77737i) q^{50} +0.0216699 q^{51} +(-1.92501 - 1.92501i) q^{52} +(-2.06984 - 2.06984i) q^{53} -1.00000 q^{54} +(-2.53025 + 0.627061i) q^{55} +(1.39917 - 1.39917i) q^{57} +(3.96407 + 3.96407i) q^{58} +10.6925 q^{59} +(1.91505 + 1.15437i) q^{60} +3.64649i q^{61} +(-5.60811 - 5.60811i) q^{62} +1.00000i q^{64} +(3.14264 - 5.21350i) q^{65} +1.16579i q^{66} +(10.2942 - 10.2942i) q^{67} +(-0.0153229 + 0.0153229i) q^{68} -7.17989 q^{69} +7.51848 q^{71} +(0.707107 - 0.707107i) q^{72} +(-2.64838 + 2.64838i) q^{73} +10.6211i q^{74} +(-1.47539 + 4.77737i) q^{75} +1.97873i q^{76} +(-1.92501 - 1.92501i) q^{78} -1.61039i q^{79} +(-2.17041 + 0.537883i) q^{80} -1.00000 q^{81} +(1.76053 + 1.76053i) q^{82} +(9.74815 - 9.74815i) q^{83} +(-0.0414990 - 0.0250151i) q^{85} +11.1406 q^{86} +(3.96407 + 3.96407i) q^{87} +(-0.824341 - 0.824341i) q^{88} +3.60510 q^{89} +(1.91505 + 1.15437i) q^{90} +(5.07695 - 5.07695i) q^{92} +(-5.60811 - 5.60811i) q^{93} -4.08675 q^{94} +(-4.29465 + 1.06432i) q^{95} +1.00000i q^{96} +(0.265501 + 0.265501i) q^{97} +1.16579i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38}+ \cdots - 44 q^{97}+O(q^{100}) \) 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

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