LMFDB - Embedded newform 312.2.g.a.157.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(157,312)] 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("312.157"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			157.4
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	312.157
Dual form			312.2.g.a.157.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.221232 + 1.39680i) q^{2} -1.00000i q^{3} +(-1.90211 + 0.618034i) q^{4} +2.52015i q^{5} +(1.39680 - 0.221232i) q^{6} +2.79360 q^{7} +(-1.28408 - 2.52015i) q^{8} -1.00000 q^{9} +(-3.52015 + 0.557537i) q^{10} +5.31375i q^{11} +(0.618034 + 1.90211i) q^{12} -1.00000i q^{13} +(0.618034 + 3.90211i) q^{14} +2.52015 q^{15} +(3.23607 - 2.35114i) q^{16} -4.35114 q^{17} +(-0.221232 - 1.39680i) q^{18} +6.02967i q^{19} +(-1.55754 - 4.79360i) q^{20} -2.79360i q^{21} +(-7.42226 + 1.17557i) q^{22} +0.568158 q^{23} +(-2.52015 + 1.28408i) q^{24} -1.35114 q^{25} +(1.39680 - 0.221232i) q^{26} +1.00000i q^{27} +(-5.31375 + 1.72654i) q^{28} +2.68915i q^{29} +(0.557537 + 3.52015i) q^{30} +1.90868 q^{31} +(4.00000 + 4.00000i) q^{32} +5.31375 q^{33} +(-0.962611 - 6.07768i) q^{34} +7.04029i q^{35} +(1.90211 - 0.618034i) q^{36} -9.60845i q^{37} +(-8.42226 + 1.33395i) q^{38} -1.00000 q^{39} +(6.35114 - 3.23607i) q^{40} +11.2093 q^{41} +(3.90211 - 0.618034i) q^{42} -9.48746i q^{43} +(-3.28408 - 10.1074i) q^{44} -2.52015i q^{45} +(0.125695 + 0.793604i) q^{46} +3.95669 q^{47} +(-2.35114 - 3.23607i) q^{48} +0.804226 q^{49} +(-0.298915 - 1.88728i) q^{50} +4.35114i q^{51} +(0.618034 + 1.90211i) q^{52} -8.05934i q^{53} +(-1.39680 + 0.221232i) q^{54} -13.3914 q^{55} +(-3.58721 - 7.04029i) q^{56} +6.02967 q^{57} +(-3.75621 + 0.594926i) q^{58} -6.19868i q^{59} +(-4.79360 + 1.55754i) q^{60} -7.23607i q^{61} +(0.422260 + 2.66605i) q^{62} -2.79360 q^{63} +(-4.70228 + 6.47214i) q^{64} +2.52015 q^{65} +(1.17557 + 7.42226i) q^{66} +10.0297i q^{67} +(8.27636 - 2.68915i) q^{68} -0.568158i q^{69} +(-9.83390 + 1.55754i) q^{70} -1.63052 q^{71} +(1.28408 + 2.52015i) q^{72} -5.17442 q^{73} +(13.4211 - 2.12569i) q^{74} +1.35114i q^{75} +(-3.72654 - 11.4691i) q^{76} +14.8445i q^{77} +(-0.221232 - 1.39680i) q^{78} +9.17442 q^{79} +(5.92522 + 8.15537i) q^{80} +1.00000 q^{81} +(2.47985 + 15.6572i) q^{82} -4.61147i q^{83} +(1.72654 + 5.31375i) q^{84} -10.9655i q^{85} +(13.2521 - 2.09893i) q^{86} +2.68915 q^{87} +(13.3914 - 6.82328i) q^{88} +11.4182 q^{89} +(3.52015 - 0.557537i) q^{90} -2.79360i q^{91} +(-1.08070 + 0.351141i) q^{92} -1.90868i q^{93} +(0.875345 + 5.52671i) q^{94} -15.1957 q^{95} +(4.00000 - 4.00000i) q^{96} -10.2514 q^{97} +(0.177920 + 1.12334i) q^{98} -5.31375i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{6} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{10} - 4 q^{12} - 4 q^{14} - 4 q^{15} + 8 q^{16} - 16 q^{17} - 2 q^{18} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 4 q^{24} + 8 q^{25} + 2 q^{26} + 4 q^{30}+ \cdots - 6 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^6 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^10 - 4 * q^12 - 4 * q^14 - 4 * q^15 + 8 * q^16 - 16 * q^17 - 2 * q^18 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 4 * q^24 + 8 * q^25 + 2 * q^26 + 4 * q^30 - 4 * q^31 + 32 * q^32 + 16 * q^34 - 28 * q^38 - 8 * q^39 + 32 * q^40 + 36 * q^41 + 16 * q^42 - 20 * q^44 - 12 * q^46 + 24 * q^47 - 24 * q^49 + 22 * q^50 - 4 * q^52 - 2 * q^54 - 40 * q^55 + 8 * q^56 + 12 * q^57 + 12 * q^58 - 20 * q^60 - 36 * q^62 - 4 * q^63 - 4 * q^65 - 12 * q^70 + 16 * q^71 + 4 * q^72 + 32 * q^73 + 4 * q^74 - 24 * q^76 - 2 * q^78 + 8 * q^81 + 44 * q^82 + 8 * q^84 + 8 * q^86 - 8 * q^87 + 40 * q^88 + 60 * q^89 + 4 * q^90 - 40 * q^92 - 44 * q^94 - 24 * q^95 + 32 * q^96 - 56 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$			2.52015i			1.12704i	0.826101	+	0.563522i	$0.190554\pi$
$5$			2.52015i			1.12704i	−0.826101	+	0.563522i	$0.809446\pi$
$6$	1.39680	−	0.221232i	0.570242	−	0.0903175i
$7$	2.79360			1.05588			0.527942	−	0.849281i	$-0.322964\pi$
$7$	2.79360			1.05588			0.527942	+	0.849281i	$0.322964\pi$
$8$	−1.28408	−	2.52015i	−0.453990	−	0.891007i
$9$	−1.00000			−0.333333
$10$	−3.52015	+	0.557537i	−1.11317	+	0.176309i
$11$			5.31375i			1.60216i	0.598560	+	0.801078i	$0.295740\pi$
$11$			5.31375i			1.60216i	−0.598560	+	0.801078i	$0.704260\pi$
$12$	0.618034	+	1.90211i	0.178411	+	0.549093i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.618034	+	3.90211i	0.165177	+	1.04288i
$15$	2.52015			0.650699
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	−4.35114			−1.05531			−0.527653	−	0.849460i	$-0.676928\pi$
$17$	−4.35114			−1.05531			−0.527653	+	0.849460i	$0.676928\pi$
$18$	−0.221232	−	1.39680i	−0.0521448	−	0.329229i
$19$			6.02967i			1.38330i	0.722232	+	0.691651i	$0.243116\pi$
$19$			6.02967i			1.38330i	−0.722232	+	0.691651i	$0.756884\pi$
$20$	−1.55754	−	4.79360i	−0.348276	−	1.07188i
$21$		−	2.79360i		−	0.609614i
$22$	−7.42226	+	1.17557i	−1.58243	+	0.250632i
$23$	0.568158			0.118469			0.0592346	−	0.998244i	$-0.481134\pi$
$23$	0.568158			0.118469			0.0592346	+	0.998244i	$0.481134\pi$
$24$	−2.52015	+	1.28408i	−0.514423	+	0.262112i
$25$	−1.35114			−0.270228
$26$	1.39680	−	0.221232i	0.273935	−	0.0433871i
$27$			1.00000i			0.192450i
$28$	−5.31375	+	1.72654i	−1.00420	+	0.326286i
$29$			2.68915i			0.499363i	0.968328	+	0.249682i	$0.0803260\pi$
$29$			2.68915i			0.499363i	−0.968328	+	0.249682i	$0.919674\pi$
$30$	0.557537	+	3.52015i	0.101792	+	0.642688i
$31$	1.90868			0.342809			0.171404	−	0.985201i	$-0.445170\pi$
$31$	1.90868			0.342809			0.171404	+	0.985201i	$0.445170\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	5.31375			0.925005
$34$	−0.962611	−	6.07768i	−0.165086	−	1.04231i
$35$			7.04029i			1.19003i
$36$	1.90211	−	0.618034i	0.317019	−	0.103006i
$37$		−	9.60845i		−	1.57962i	−0.613352	−	0.789810i	$-0.710179\pi$
$37$		−	9.60845i		−	1.57962i	0.613352	−	0.789810i	$-0.289821\pi$
$38$	−8.42226	+	1.33395i	−1.36627	+	0.216396i
$39$	−1.00000			−0.160128
$40$	6.35114	−	3.23607i	1.00420	−	0.511667i
$41$	11.2093			1.75060			0.875299	−	0.483582i	$-0.160664\pi$
$41$	11.2093			1.75060			0.875299	+	0.483582i	$0.160664\pi$
$42$	3.90211	−	0.618034i	0.602109	−	0.0953647i
$43$		−	9.48746i		−	1.44682i	−0.690417	−	0.723412i	$-0.742573\pi$
$43$		−	9.48746i		−	1.44682i	0.690417	−	0.723412i	$-0.257427\pi$
$44$	−3.28408	−	10.1074i	−0.495094	−	1.52374i
$45$		−	2.52015i		−	0.375681i
$46$	0.125695	+	0.793604i	0.0185327	+	0.117011i
$47$	3.95669			0.577142			0.288571	−	0.957458i	$-0.406820\pi$
$47$	3.95669			0.577142			0.288571	+	0.957458i	$0.406820\pi$
$48$	−2.35114	−	3.23607i	−0.339358	−	0.467086i
$49$	0.804226			0.114889
$50$	−0.298915	−	1.88728i	−0.0422730	−	0.266901i
$51$			4.35114i			0.609282i
$52$	0.618034	+	1.90211i	0.0857059	+	0.263776i
$53$		−	8.05934i		−	1.10704i	−0.832837	−	0.553518i	$-0.813285\pi$
$53$		−	8.05934i		−	1.10704i	0.832837	−	0.553518i	$-0.186715\pi$
$54$	−1.39680	+	0.221232i	−0.190081	+	0.0301058i
$55$	−13.3914			−1.80570
$56$	−3.58721	−	7.04029i	−0.479361	−	0.940799i
$57$	6.02967			0.798650
$58$	−3.75621	+	0.594926i	−0.493215	+	0.0781176i
$59$		−	6.19868i		−	0.806999i	−0.914980	−	0.403500i	$-0.867794\pi$
$59$		−	6.19868i		−	0.806999i	0.914980	−	0.403500i	$-0.132206\pi$
$60$	−4.79360	+	1.55754i	−0.618852	+	0.201077i
$61$		−	7.23607i		−	0.926484i	−0.886232	−	0.463242i	$-0.846686\pi$
$61$		−	7.23607i		−	0.926484i	0.886232	−	0.463242i	$-0.153314\pi$
$62$	0.422260	+	2.66605i	0.0536271	+	0.338588i
$63$	−2.79360			−0.351961
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$	2.52015			0.312586
$66$	1.17557	+	7.42226i	0.144703	+	0.913617i
$67$			10.0297i			1.22532i	0.790347	+	0.612660i	$0.209900\pi$
$67$			10.0297i			1.22532i	−0.790347	+	0.612660i	$0.790100\pi$
$68$	8.27636	−	2.68915i	1.00366	−	0.326108i
$69$		−	0.568158i		−	0.0683982i
$70$	−9.83390	+	1.55754i	−1.17538	+	0.186161i
$71$	−1.63052			−0.193507			−0.0967536	−	0.995308i	$-0.530846\pi$
$71$	−1.63052			−0.193507			−0.0967536	+	0.995308i	$0.530846\pi$
$72$	1.28408	+	2.52015i	0.151330	+	0.297002i
$73$	−5.17442			−0.605620			−0.302810	−	0.953051i	$-0.597925\pi$
$73$	−5.17442			−0.605620			−0.302810	+	0.953051i	$0.597925\pi$
$74$	13.4211	−	2.12569i	1.56017	−	0.247107i
$75$			1.35114i			0.156016i
$76$	−3.72654	−	11.4691i	−0.427464	−	1.31560i
$77$			14.8445i			1.69169i
$78$	−0.221232	−	1.39680i	−0.0250496	−	0.158157i
$79$	9.17442			1.03220			0.516101	−	0.856528i	$-0.327383\pi$
$79$	9.17442			1.03220			0.516101	+	0.856528i	$0.327383\pi$
$80$	5.92522	+	8.15537i	0.662460	+	0.911798i
$81$	1.00000			0.111111
$82$	2.47985	+	15.6572i	0.273854	+	1.72905i
$83$		−	4.61147i		−	0.506175i	−0.967443	−	0.253087i	$-0.918554\pi$
$83$		−	4.61147i		−	0.506175i	0.967443	−	0.253087i	$-0.0814460\pi$
$84$	1.72654	+	5.31375i	0.188381	+	0.579778i
$85$		−	10.9655i		−	1.18938i
$86$	13.2521	−	2.09893i	1.42901	−	0.226333i
$87$	2.68915			0.288307
$88$	13.3914	−	6.82328i	1.42753	−	0.727364i
$89$	11.4182			1.21033			0.605164	−	0.796101i	$-0.293108\pi$
$89$	11.4182			1.21033			0.605164	+	0.796101i	$0.293108\pi$
$90$	3.52015	−	0.557537i	0.371056	−	0.0587695i
$91$		−	2.79360i		−	0.292849i
$92$	−1.08070	+	0.351141i	−0.112671	+	0.0366090i
$93$		−	1.90868i		−	0.197921i
$94$	0.875345	+	5.52671i	0.0902850	+	0.570037i
$95$	−15.1957			−1.55904
$96$	4.00000	−	4.00000i	0.408248	−	0.408248i
$97$	−10.2514			−1.04087			−0.520435	−	0.853901i	$-0.674230\pi$
$97$	−10.2514			−1.04087			−0.520435	+	0.853901i	$0.674230\pi$
$98$	0.177920	+	1.12334i	0.0179727	+	0.113475i
$99$		−	5.31375i		−	0.534052i
$100$	2.57002	−	0.835051i	0.257002	−	0.0835051i
$101$		−	3.01905i		−	0.300407i	−0.988655	−	0.150203i	$-0.952007\pi$
$101$		−	3.01905i		−	0.300407i	0.988655	−	0.150203i	$-0.0479929\pi$
$102$	−6.07768	+	0.962611i	−0.601780	+	0.0953126i
$103$	12.9193			1.27298			0.636488	−	0.771286i	$-0.280386\pi$
$103$	12.9193			1.27298			0.636488	+	0.771286i	$0.280386\pi$
$104$	−2.52015	+	1.28408i	−0.247121	+	0.125914i
$105$	7.04029			0.687062
$106$	11.2573	−	1.78298i	1.09341	−	0.173179i
$107$			10.9537i			1.05893i	0.848331	+	0.529466i	$0.177608\pi$
$107$			10.9537i			1.05893i	−0.848331	+	0.529466i	$0.822392\pi$
$108$	−0.618034	−	1.90211i	−0.0594703	−	0.183031i
$109$			5.45309i			0.522311i	0.965297	+	0.261155i	$0.0841035\pi$
$109$			5.45309i			0.522311i	−0.965297	+	0.261155i	$0.915896\pi$
$110$	−2.96261	−	18.7052i	−0.282474	−	1.78347i
$111$	−9.60845			−0.911994
$112$	9.04029	−	6.56816i	0.854227	−	0.620633i
$113$	−13.6334			−1.28252			−0.641262	−	0.767322i	$-0.721589\pi$
$113$	−13.6334			−1.28252			−0.641262	+	0.767322i	$0.721589\pi$
$114$	1.33395	+	8.42226i	0.124936	+	0.788817i
$115$			1.43184i			0.133520i
$116$	−1.66199	−	5.11507i	−0.154312	−	0.474923i
$117$			1.00000i			0.0924500i
$118$	8.65833	−	1.37134i	0.797064	−	0.126242i
$119$	−12.1554			−1.11428
$120$	−3.23607	−	6.35114i	−0.295411	−	0.579777i
$121$	−17.2360			−1.56691
$122$	10.1074	−	1.60085i	0.915077	−	0.144934i
$123$		−	11.2093i		−	1.01071i
$124$	−3.63052	+	1.17963i	−0.326030	+	0.105934i
$125$			9.19566i			0.822485i
$126$	−0.618034	−	3.90211i	−0.0550588	−	0.347628i
$127$	19.4377			1.72481			0.862406	−	0.506217i	$-0.168956\pi$
$127$	19.4377			1.72481			0.862406	+	0.506217i	$0.168956\pi$
$128$	−10.0806	−	5.13632i	−0.891007	−	0.453990i
$129$	−9.48746			−0.835324
$130$	0.557537	+	3.52015i	0.0488992	+	0.308737i
$131$			12.7235i			1.11166i	0.831296	+	0.555830i	$0.187599\pi$
$131$			12.7235i			1.11166i	−0.831296	+	0.555830i	$0.812401\pi$
$132$	−10.1074	+	3.28408i	−0.879732	+	0.285842i
$133$			16.8445i			1.46061i
$134$	−14.0095	+	2.21888i	−1.21023	+	0.191682i
$135$	−2.52015			−0.216900
$136$	5.58721	+	10.9655i	0.479099	+	0.940285i
$137$	−9.23054			−0.788619			−0.394309	−	0.918978i	$-0.629016\pi$
$137$	−9.23054			−0.788619			−0.394309	+	0.918978i	$0.629016\pi$
$138$	0.793604	−	0.125695i	0.0675561	−	0.0106998i
$139$			11.7507i			0.996681i	0.866982	+	0.498340i	$0.166057\pi$
$139$			11.7507i			0.996681i	−0.866982	+	0.498340i	$0.833943\pi$
$140$	−4.35114	−	13.3914i	−0.367739	−	1.13178i
$141$		−	3.95669i		−	0.333213i
$142$	−0.360723	−	2.27751i	−0.0302712	−	0.191125i
$143$	5.31375			0.444358
$144$	−3.23607	+	2.35114i	−0.269672	+	0.195928i
$145$	−6.77706			−0.562804
$146$	−1.14475	−	7.22764i	−0.0947398	−	0.598164i
$147$		−	0.804226i		−	0.0663314i
$148$	5.93835	+	18.2764i	0.488129	+	1.50231i
$149$		−	17.6079i		−	1.44250i	−0.692675	−	0.721249i	$-0.743568\pi$
$149$		−	17.6079i		−	1.44250i	0.692675	−	0.721249i	$-0.256432\pi$
$150$	−1.88728	+	0.298915i	−0.154096	+	0.0244063i
$151$	−11.6250			−0.946029			−0.473014	−	0.881055i	$-0.656834\pi$
$151$	−11.6250			−0.946029			−0.473014	+	0.881055i	$0.656834\pi$
$152$	15.1957	−	7.74258i	1.23253	−	0.628006i
$153$	4.35114			0.351769
$154$	−20.7349	+	3.28408i	−1.67086	+	0.264639i
$155$			4.81015i			0.386360i
$156$	1.90211	−	0.618034i	0.152291	−	0.0494823i
$157$		−	13.4781i		−	1.07567i	−0.843051	−	0.537833i	$-0.819243\pi$
$157$		−	13.4781i		−	1.07567i	0.843051	−	0.537833i	$-0.180757\pi$
$158$	2.02967	+	12.8148i	0.161472	+	1.01949i
$159$	−8.05934			−0.639148
$160$	−10.0806	+	10.0806i	−0.796940	+	0.796940i
$161$	1.58721			0.125090
$162$	0.221232	+	1.39680i	0.0173816	+	0.109743i
$163$		−	9.79349i		−	0.767085i	−0.923523	−	0.383543i	$-0.874704\pi$
$163$		−	9.79349i		−	0.767085i	0.923523	−	0.383543i	$-0.125296\pi$
$164$	−21.3214	+	6.92773i	−1.66492	+	0.540965i
$165$			13.3914i			1.04252i
$166$	6.44131	−	1.02020i	0.499943	−	0.0791831i
$167$	−16.6054			−1.28497			−0.642484	−	0.766299i	$-0.722096\pi$
$167$	−16.6054			−1.28497			−0.642484	+	0.766299i	$0.722096\pi$
$168$	−7.04029	+	3.58721i	−0.543170	+	0.276759i
$169$	−1.00000			−0.0769231
$170$	15.3167	−	2.42592i	1.17473	−	0.186060i
$171$		−	6.02967i		−	0.461101i
$172$	5.86357	+	18.0462i	0.447093	+	1.37601i
$173$		−	16.1979i		−	1.23150i	−0.787942	−	0.615750i	$-0.788853\pi$
$173$		−	16.1979i		−	1.23150i	0.787942	−	0.615750i	$-0.211147\pi$
$174$	0.594926	+	3.75621i	0.0451012	+	0.284758i
$175$	−3.77455			−0.285329
$176$	12.4934	+	17.1957i	0.941724	+	1.29617i
$177$	−6.19868			−0.465921
$178$	2.52607	+	15.9490i	0.189337	+	1.19543i
$179$		−	1.22795i		−	0.0917816i	−0.998946	−	0.0458908i	$-0.985387\pi$
$179$		−	1.22795i		−	0.0917816i	0.998946	−	0.0458908i	$-0.0146126\pi$
$180$	1.55754	+	4.79360i	0.116092	+	0.357294i
$181$		−	7.00592i		−	0.520746i	−0.965508	−	0.260373i	$-0.916154\pi$
$181$		−	7.00592i		−	0.520746i	0.965508	−	0.260373i	$-0.0838455\pi$
$182$	3.90211	−	0.618034i	0.289244	−	0.0458117i
$183$	−7.23607			−0.534906
$184$	−0.729560	−	1.43184i	−0.0537839	−	0.105557i
$185$	24.2147			1.78030
$186$	2.66605	−	0.422260i	0.195484	−	0.0309616i
$187$		−	23.1209i		−	1.69077i
$188$	−7.52607	+	2.44537i	−0.548895	+	0.178347i
$189$			2.79360i			0.203205i
$190$	−3.36176	−	21.2253i	−0.243888	−	1.53985i
$191$	−14.3701			−1.03978			−0.519891	−	0.854232i	$-0.674028\pi$
$191$	−14.3701			−1.03978			−0.519891	+	0.854232i	$0.674028\pi$
$192$	6.47214	+	4.70228i	0.467086	+	0.339358i
$193$	−3.67383			−0.264448			−0.132224	−	0.991220i	$-0.542212\pi$
$193$	−3.67383			−0.264448			−0.132224	+	0.991220i	$0.542212\pi$
$194$	−2.26793	−	14.3192i	−0.162828	−	1.02806i
$195$		−	2.52015i		−	0.180471i
$196$	−1.52973	+	0.497039i	−0.109266	+	0.0355028i
$197$			6.88442i			0.490494i	0.969461	+	0.245247i	$0.0788691\pi$
$197$			6.88442i			0.490494i	−0.969461	+	0.245247i	$0.921131\pi$
$198$	7.42226	−	1.17557i	0.527477	−	0.0835442i
$199$	15.3952			1.09133			0.545667	−	0.838002i	$-0.316276\pi$
$199$	15.3952			1.09133			0.545667	+	0.838002i	$0.316276\pi$
$200$	1.73497	+	3.40507i	0.122681	+	0.240775i
$201$	10.0297			0.707439
$202$	4.21702	−	0.667910i	0.296708	−	0.0469940i
$203$			7.51243i			0.527269i
$204$	−2.68915	−	8.27636i	−0.188278	−	0.579461i
$205$			28.2491i			1.97300i
$206$	2.85816	+	18.0457i	0.199137	+	1.25730i
$207$	−0.568158			−0.0394897
$208$	−2.35114	−	3.23607i	−0.163022	−	0.224381i
$209$	−32.0402			−2.21627
$210$	1.55754	+	9.83390i	0.107480	+	0.678603i
$211$			1.57035i			0.108107i	0.998538	+	0.0540537i	$0.0172142\pi$
$211$			1.57035i			0.108107i	−0.998538	+	0.0540537i	$0.982786\pi$
$212$	4.98095	+	15.3298i	0.342093	+	1.05285i
$213$			1.63052i			0.111721i
$214$	−15.3001	+	2.42330i	−1.04589	+	0.165653i
$215$	23.9098			1.63063
$216$	2.52015	−	1.28408i	0.171474	−	0.0873705i
$217$	5.33209			0.361966
$218$	−7.61688	+	1.20640i	−0.515880	+	0.0817074i
$219$			5.17442i			0.349655i
$220$	25.4720	−	8.27636i	1.71732	−	0.557992i
$221$			4.35114i			0.292689i
$222$	−2.12569	−	13.4211i	−0.142667	−	0.900766i
$223$	27.6571			1.85205			0.926027	−	0.377457i	$-0.123202\pi$
$223$	27.6571			1.85205			0.926027	+	0.377457i	$0.123202\pi$
$224$	11.1744	+	11.1744i	0.746622	+	0.746622i
$225$	1.35114			0.0900761
$226$	−3.01615	−	19.0432i	−0.200631	−	1.26673i
$227$		−	22.9434i		−	1.52281i	−0.648276	−	0.761405i	$-0.724510\pi$
$227$		−	22.9434i		−	1.52281i	0.648276	−	0.761405i	$-0.275490\pi$
$228$	−11.4691	+	3.72654i	−0.759561	+	0.246796i
$229$			23.5064i			1.55335i	0.629904	+	0.776673i	$0.283094\pi$
$229$			23.5064i			1.55335i	−0.629904	+	0.776673i	$0.716906\pi$
$230$	−2.00000	+	0.316769i	−0.131876	+	0.0208871i
$231$	14.8445			0.976698
$232$	6.77706	−	3.45309i	0.444936	−	0.226706i
$233$	3.47433			0.227611			0.113805	−	0.993503i	$-0.463696\pi$
$233$	3.47433			0.227611			0.113805	+	0.993503i	$0.463696\pi$
$234$	−1.39680	+	0.221232i	−0.0913118	+	0.0144624i
$235$			9.97144i			0.650465i
$236$	3.83099	+	11.7906i	0.249376	+	0.767502i
$237$		−	9.17442i		−	0.595942i
$238$	−2.68915	−	16.9786i	−0.174312	−	1.10056i
$239$	−11.5820			−0.749177			−0.374589	−	0.927191i	$-0.622216\pi$
$239$	−11.5820			−0.749177			−0.374589	+	0.927191i	$0.622216\pi$
$240$	8.15537	−	5.92522i	0.526427	−	0.382471i
$241$	10.0058			0.644531			0.322265	−	0.946649i	$-0.395556\pi$
$241$	10.0058			0.644531			0.322265	+	0.946649i	$0.395556\pi$
$242$	−3.81314	−	24.0752i	−0.245118	−	1.54761i
$243$		−	1.00000i		−	0.0641500i
$244$	4.47214	+	13.7638i	0.286299	+	0.881138i
$245$			2.02677i			0.129485i
$246$	15.6572	−	2.47985i	0.998265	−	0.158110i
$247$	6.02967			0.383659
$248$	−2.45089	−	4.81015i	−0.155632	−	0.305445i
$249$	−4.61147			−0.292240
$250$	−12.8445	+	2.03437i	−0.812359	+	0.128665i
$251$		−	11.3723i		−	0.717811i	−0.933374	−	0.358906i	$-0.883150\pi$
$251$		−	11.3723i		−	0.717811i	0.933374	−	0.358906i	$-0.116850\pi$
$252$	5.31375	−	1.72654i	0.334735	−	0.108762i
$253$			3.01905i			0.189806i
$254$	4.30023	+	27.1506i	0.269820	+	1.70358i
$255$	−10.9655			−0.686687
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	11.3510			0.708058			0.354029	−	0.935235i	$-0.384811\pi$
$257$	11.3510			0.708058			0.354029	+	0.935235i	$0.384811\pi$
$258$	−2.09893	−	13.2521i	−0.130673	−	0.825040i
$259$		−	26.8422i		−	1.66789i
$260$	−4.79360	+	1.55754i	−0.297287	+	0.0965943i
$261$		−	2.68915i		−	0.166454i
$262$	−17.7722	+	2.81485i	−1.09797	+	0.173902i
$263$	3.88712			0.239690			0.119845	−	0.992793i	$-0.461760\pi$
$263$	3.88712			0.239690			0.119845	+	0.992793i	$0.461760\pi$
$264$	−6.82328	−	13.3914i	−0.419944	−	0.824186i
$265$	20.3107			1.24768
$266$	−23.5285	+	3.72654i	−1.44262	+	0.228489i
$267$		−	11.4182i		−	0.698783i
$268$	−6.19868	−	19.0776i	−0.378645	−	1.16535i
$269$			25.2300i			1.53830i	0.639067	+	0.769151i	$0.279321\pi$
$269$			25.2300i			1.53830i	−0.639067	+	0.769151i	$0.720679\pi$
$270$	−0.557537	−	3.52015i	−0.0339306	−	0.214229i
$271$	−2.90649			−0.176556			−0.0882782	−	0.996096i	$-0.528136\pi$
$271$	−2.90649			−0.176556			−0.0882782	+	0.996096i	$0.528136\pi$
$272$	−14.0806	+	10.2301i	−0.853761	+	0.620294i
$273$	−2.79360			−0.169077
$274$	−2.04209	−	12.8932i	−0.123367	−	0.778909i
$275$		−	7.17963i		−	0.432948i
$276$	0.351141	+	1.08070i	0.0211362	+	0.0650506i
$277$			4.26825i			0.256454i	0.991745	+	0.128227i	$0.0409286\pi$
$277$			4.26825i			0.256454i	−0.991745	+	0.128227i	$0.959071\pi$
$278$	−16.4134	+	2.59963i	−0.984410	+	0.155915i
$279$	−1.90868			−0.114270
$280$	17.7426	−	9.04029i	1.06032	−	0.540261i
$281$	−18.9900			−1.13285			−0.566424	−	0.824114i	$-0.691673\pi$
$281$	−18.9900			−1.13285			−0.566424	+	0.824114i	$0.691673\pi$
$282$	5.52671	−	0.875345i	0.329111	−	0.0521260i
$283$			13.1957i			0.784401i	0.919880	+	0.392200i	$0.128286\pi$
$283$			13.1957i			0.784401i	−0.919880	+	0.392200i	$0.871714\pi$
$284$	3.10143	−	1.00772i	0.184036	−	0.0597970i
$285$			15.1957i			0.900113i
$286$	1.17557	+	7.42226i	0.0695129	+	0.438887i
$287$	31.3144			1.84843
$288$	−4.00000	−	4.00000i	−0.235702	−	0.235702i
$289$	1.93243			0.113672
$290$	−1.49930	−	9.46621i	−0.0880420	−	0.555875i
$291$			10.2514i			0.600947i
$292$	9.84233	−	3.19797i	0.575979	−	0.187147i
$293$			12.0980i			0.706770i	0.935478	+	0.353385i	$0.114969\pi$
$293$			12.0980i			0.706770i	−0.935478	+	0.353385i	$0.885031\pi$
$294$	1.12334	−	0.177920i	0.0655148	−	0.0103765i
$295$	15.6216			0.909524
$296$	−24.2147	+	12.3380i	−1.40745	+	0.717132i
$297$	−5.31375			−0.308335
$298$	24.5948	−	3.89544i	1.42474	−	0.225657i
$299$		−	0.568158i		−	0.0328574i
$300$	−0.835051	−	2.57002i	−0.0482117	−	0.148380i
$301$		−	26.5042i		−	1.52768i
$302$	−2.57182	−	16.2378i	−0.147991	−	0.934382i
$303$	−3.01905			−0.173440
$304$	14.1766	+	19.5124i	0.813084	+	1.11911i
$305$	18.2360			1.04419
$306$	0.962611	+	6.07768i	0.0550288	+	0.347438i
$307$			24.7863i			1.41463i	0.706900	+	0.707314i	$0.250093\pi$
$307$			24.7863i			1.41463i	−0.706900	+	0.707314i	$0.749907\pi$
$308$	−9.17442	−	28.2360i	−0.522761	−	1.60889i
$309$		−	12.9193i		−	0.734953i
$310$	−6.71883	+	1.06416i	−0.381604	+	0.0604401i
$311$	−6.72956			−0.381598			−0.190799	−	0.981629i	$-0.561108\pi$
$311$	−6.72956			−0.381598			−0.190799	+	0.981629i	$0.561108\pi$
$312$	1.28408	+	2.52015i	0.0726967	+	0.142675i
$313$	11.4956			0.649768			0.324884	−	0.945754i	$-0.394675\pi$
$313$	11.4956			0.649768			0.324884	+	0.945754i	$0.394675\pi$
$314$	18.8262	−	2.98177i	1.06242	−	0.168271i
$315$		−	7.04029i		−	0.396676i
$316$	−17.4508	+	5.67010i	−0.981683	+	0.318968i
$317$		−	2.86756i		−	0.161058i	−0.996752	−	0.0805291i	$-0.974339\pi$
$317$		−	2.86756i		−	0.161058i	0.996752	−	0.0805291i	$-0.0256610\pi$
$318$	−1.78298	−	11.2573i	−0.0999847	−	0.631279i
$319$	−14.2895			−0.800058
$320$	−16.3107	−	11.8504i	−0.911798	−	0.662460i
$321$	10.9537			0.611374
$322$	0.351141	+	2.21702i	0.0195683	+	0.123550i
$323$		−	26.2360i		−	1.45981i
$324$	−1.90211	+	0.618034i	−0.105673	+	0.0343352i
$325$			1.35114i			0.0749478i
$326$	13.6796	−	2.16663i	0.757641	−	0.119999i
$327$	5.45309			0.301556
$328$	−14.3936	−	28.2491i	−0.794755	−	1.55979i
$329$	11.0534			0.609395
$330$	−18.7052	+	2.96261i	−1.02969	+	0.163086i
$331$			1.44967i			0.0796811i	0.999206	+	0.0398405i	$0.0126850\pi$
$331$			1.44967i			0.0796811i	−0.999206	+	0.0398405i	$0.987315\pi$
$332$	2.85004	+	8.77154i	0.156417	+	0.481401i
$333$			9.60845i			0.526540i
$334$	−3.67365	−	23.1945i	−0.201013	−	1.26915i
$335$	−25.2762			−1.38099
$336$	−6.56816	−	9.04029i	−0.358322	−	0.493188i
$337$	−22.6774			−1.23532			−0.617660	−	0.786446i	$-0.711919\pi$
$337$	−22.6774			−1.23532			−0.617660	+	0.786446i	$0.711919\pi$
$338$	−0.221232	−	1.39680i	−0.0120334	−	0.0759760i
$339$			13.6334i			0.740466i
$340$	6.77706	+	20.8576i	0.367538	+	1.13116i
$341$			10.1422i			0.549233i
$342$	8.42226	−	1.33395i	0.455424	−	0.0721320i
$343$	−17.3085			−0.934573
$344$	−23.9098	+	12.1826i	−1.28913	+	0.656844i
$345$	1.43184			0.0770878
$346$	22.6252	−	3.58348i	1.21634	−	0.192649i
$347$		−	33.7652i		−	1.81261i	−0.422621	−	0.906307i	$-0.638890\pi$
$347$		−	33.7652i		−	1.81261i	0.422621	−	0.906307i	$-0.361110\pi$
$348$	−5.11507	+	1.66199i	−0.274197	+	0.0890919i
$349$		−	6.34741i		−	0.339769i	−0.985464	−	0.169885i	$-0.945661\pi$
$349$		−	6.34741i		−	0.339769i	0.985464	−	0.169885i	$-0.0543395\pi$
$350$	−0.835051	−	5.27230i	−0.0446354	−	0.281817i
$351$	1.00000			0.0533761
$352$	−21.2550	+	21.2550i	−1.13290	+	1.13290i
$353$	32.1856			1.71307			0.856534	−	0.516090i	$-0.172613\pi$
$353$	32.1856			1.71307			0.856534	+	0.516090i	$0.172613\pi$
$354$	−1.37134	−	8.65833i	−0.0728861	−	0.460185i
$355$		−	4.10915i		−	0.218091i
$356$	−21.7187	+	7.05684i	−1.15109	+	0.374012i
$357$			12.1554i			0.643330i
$358$	1.71521	−	0.271662i	0.0906516	−	0.0143578i
$359$	22.9222			1.20979			0.604894	−	0.796306i	$-0.293216\pi$
$359$	22.9222			1.20979			0.604894	+	0.796306i	$0.293216\pi$
$360$	−6.35114	+	3.23607i	−0.334735	+	0.170556i
$361$	−17.3570			−0.913524
$362$	9.78589	−	1.54993i	0.514335	−	0.0814626i
$363$			17.2360i			0.904653i
$364$	1.72654	+	5.31375i	0.0904954	+	0.278516i
$365$		−	13.0403i		−	0.682560i
$366$	−1.60085	−	10.1074i	−0.0836777	−	0.528320i
$367$	−9.68093			−0.505340			−0.252670	−	0.967552i	$-0.581309\pi$
$367$	−9.68093			−0.505340			−0.252670	+	0.967552i	$0.581309\pi$
$368$	1.83860	−	1.33582i	0.0958436	−	0.0696344i
$369$	−11.2093			−0.583533
$370$	5.35706	+	33.8232i	0.278500	+	1.75838i
$371$		−	22.5146i		−	1.16890i
$372$	1.17963	+	3.63052i	0.0611608	+	0.188234i
$373$			23.2975i			1.20630i	0.797628	+	0.603149i	$0.206088\pi$
$373$			23.2975i			1.20630i	−0.797628	+	0.603149i	$0.793912\pi$
$374$	32.2953	−	5.11507i	1.66995	−	0.264494i
$375$	9.19566			0.474862
$376$	−5.08070	−	9.97144i	−0.262017	−	0.514238i
$377$	2.68915			0.138498
$378$	−3.90211	+	0.618034i	−0.200703	+	0.0317882i
$379$		−	9.48276i		−	0.487097i	−0.969889	−	0.243548i	$-0.921689\pi$
$379$		−	9.48276i		−	0.487097i	0.969889	−	0.243548i	$-0.0783114\pi$
$380$	28.9039	−	9.39144i	1.48274	−	0.481770i
$381$		−	19.4377i		−	0.995821i
$382$	−3.17912	−	20.0722i	−0.162658	−	1.02698i
$383$	−5.68406			−0.290442			−0.145221	−	0.989399i	$-0.546389\pi$
$383$	−5.68406			−0.290442			−0.145221	+	0.989399i	$0.546389\pi$
$384$	−5.13632	+	10.0806i	−0.262112	+	0.514423i
$385$	−37.4104			−1.90661
$386$	−0.812768	−	5.13162i	−0.0413688	−	0.261192i
$387$			9.48746i			0.482275i
$388$	19.4993	−	6.33571i	0.989927	−	0.321647i
$389$		−	1.79842i		−	0.0911834i	−0.998960	−	0.0455917i	$-0.985483\pi$
$389$		−	1.79842i		−	0.0911834i	0.998960	−	0.0455917i	$-0.0145173\pi$
$390$	3.52015	−	0.557537i	0.178250	−	0.0282320i
$391$	−2.47214			−0.125021
$392$	−1.03269	−	2.02677i	−0.0521587	−	0.102367i
$393$	12.7235			0.641817
$394$	−9.61617	+	1.52305i	−0.484456	+	0.0767302i
$395$			23.1209i			1.16334i
$396$	3.28408	+	10.1074i	0.165031	+	0.507914i
$397$		−	4.61064i		−	0.231402i	−0.993284	−	0.115701i	$-0.963089\pi$
$397$		−	4.61064i		−	0.231402i	0.993284	−	0.115701i	$-0.0369114\pi$
$398$	3.40590	+	21.5040i	0.170722	+	1.07790i
$399$	16.8445			0.843281
$400$	−4.37238	+	3.17672i	−0.218619	+	0.158836i
$401$	−19.4701			−0.972290			−0.486145	−	0.873878i	$-0.661597\pi$
$401$	−19.4701			−0.972290			−0.486145	+	0.873878i	$0.661597\pi$
$402$	2.21888	+	14.0095i	0.110668	+	0.698729i
$403$		−	1.90868i		−	0.0950780i
$404$	1.86588	+	5.74258i	0.0928308	+	0.285704i
$405$			2.52015i			0.125227i
$406$	−10.4934	+	1.66199i	−0.520778	+	0.0824831i
$407$	51.0569			2.53080
$408$	10.9655	−	5.58721i	0.542874	−	0.276608i
$409$	34.5696			1.70936			0.854678	−	0.519159i	$-0.173755\pi$
$409$	34.5696			1.70936			0.854678	+	0.519159i	$0.173755\pi$
$410$	−39.4584	+	6.24959i	−1.94871	+	0.308645i
$411$			9.23054i			0.455309i
$412$	−24.5740	+	7.98457i	−1.21067	+	0.393371i
$413$		−	17.3167i		−	0.852097i
$414$	−0.125695	−	0.793604i	−0.00617755	−	0.0390035i
$415$	11.6216			0.570481
$416$	4.00000	−	4.00000i	0.196116	−	0.196116i
$417$	11.7507			0.575434
$418$	−7.08831	−	44.7538i	−0.346700	−	2.18898i
$419$		−	5.72235i		−	0.279555i	−0.990183	−	0.139778i	$-0.955361\pi$
$419$		−	5.72235i		−	0.279555i	0.990183	−	0.139778i	$-0.0446388\pi$
$420$	−13.3914	+	4.35114i	−0.653435	+	0.212314i
$421$		−	30.8897i		−	1.50547i	−0.658322	−	0.752736i	$-0.728734\pi$
$421$		−	30.8897i		−	1.50547i	0.658322	−	0.752736i	$-0.271266\pi$
$422$	−2.19347	+	0.347411i	−0.106776	+	0.0169117i
$423$	−3.95669			−0.192381
$424$	−20.3107	+	10.3488i	−0.986376	+	0.502584i
$425$	5.87901			0.285174
$426$	−2.27751	+	0.360723i	−0.110346	+	0.0174771i
$427$		−	20.2147i		−	0.978258i
$428$	−6.76974	−	20.8351i	−0.327228	−	1.00710i
$429$		−	5.31375i		−	0.256550i
$430$	5.28960	+	33.3972i	0.255087	+	1.61056i
$431$	16.3709			0.788559			0.394279	−	0.918991i	$-0.370994\pi$
$431$	16.3709			0.788559			0.394279	+	0.918991i	$0.370994\pi$
$432$	2.35114	+	3.23607i	0.113119	+	0.155695i
$433$	−9.17672			−0.441005			−0.220503	−	0.975386i	$-0.570770\pi$
$433$	−9.17672			−0.441005			−0.220503	+	0.975386i	$0.570770\pi$
$434$	1.17963	+	7.44788i	0.0566239	+	0.357509i
$435$			6.77706i			0.324935i
$436$	−3.37019	−	10.3724i	−0.161403	−	0.496747i
$437$			3.42581i			0.163879i
$438$	−7.22764	+	1.14475i	−0.345350	+	0.0546981i
$439$	−19.1494			−0.913953			−0.456977	−	0.889479i	$-0.651068\pi$
$439$	−19.1494			−0.913953			−0.456977	+	0.889479i	$0.651068\pi$
$440$	17.1957	+	33.7484i	0.819771	+	1.60889i
$441$	−0.804226			−0.0382965
$442$	−6.07768	+	0.962611i	−0.289086	+	0.0457867i
$443$			5.89817i			0.280230i	0.990135	+	0.140115i	$0.0447473\pi$
$443$			5.89817i			0.280230i	−0.990135	+	0.140115i	$0.955253\pi$
$444$	18.2764	−	5.93835i	0.867358	−	0.281822i
$445$			28.7756i			1.36409i
$446$	6.11862	+	38.6314i	0.289725	+	1.82925i
$447$	−17.6079			−0.832827
$448$	−13.1363	+	18.0806i	−0.620633	+	0.854227i
$449$	−21.8310			−1.03027			−0.515134	−	0.857110i	$-0.672258\pi$
$449$	−21.8310			−1.03027			−0.515134	+	0.857110i	$0.672258\pi$
$450$	0.298915	+	1.88728i	0.0140910	+	0.0889671i
$451$			59.5634i			2.80473i
$452$	25.9323	−	8.42592i	1.21975	−	0.396322i
$453$			11.6250i			0.546190i
$454$	32.0475	−	5.07582i	1.50406	−	0.238220i
$455$	7.04029			0.330054
$456$	−7.74258	−	15.1957i	−0.362579	−	0.711602i
$457$	6.84244			0.320076			0.160038	−	0.987111i	$-0.448838\pi$
$457$	6.84244			0.320076			0.160038	+	0.987111i	$0.448838\pi$
$458$	−32.8338	+	5.20036i	−1.53422	+	0.242997i
$459$		−	4.35114i		−	0.203094i
$460$	−0.884927	−	2.72353i	−0.0412599	−	0.126985i
$461$			22.2688i			1.03716i	0.855029	+	0.518580i	$0.173539\pi$
$461$			22.2688i			1.03716i	−0.855029	+	0.518580i	$0.826461\pi$
$462$	3.28408	+	20.7349i	0.152789	+	0.964673i
$463$	26.4021			1.22701			0.613504	−	0.789692i	$-0.289760\pi$
$463$	26.4021			1.22701			0.613504	+	0.789692i	$0.289760\pi$
$464$	6.32258	+	8.70228i	0.293518	+	0.403993i
$465$	4.81015			0.223065
$466$	0.768632	+	4.85295i	0.0356062	+	0.224809i
$467$			11.3035i			0.523065i	0.965195	+	0.261532i	$0.0842278\pi$
$467$			11.3035i			0.523065i	−0.965195	+	0.261532i	$0.915772\pi$
$468$	−0.618034	−	1.90211i	−0.0285686	−	0.0879252i
$469$			28.0189i			1.29379i
$470$	−13.9281	+	2.20600i	−0.642457	+	0.101755i
$471$	−13.4781			−0.621036
$472$	−15.6216	+	7.95959i	−0.719042	+	0.366370i
$473$	50.4140			2.31804
$474$	12.8148	−	2.02967i	0.588605	−	0.0932259i
$475$		−	8.14694i		−	0.373807i
$476$	23.1209	−	7.51243i	1.05974	−	0.344332i
$477$			8.05934i			0.369012i
$478$	−2.56231	−	16.1778i	−0.117197	−	0.739954i
$479$	−40.4023			−1.84603			−0.923015	−	0.384764i	$-0.874283\pi$
$479$	−40.4023			−1.84603			−0.923015	+	0.384764i	$0.874283\pi$
$480$	10.0806	+	10.0806i	0.460114	+	0.460114i
$481$	−9.60845			−0.438108
$482$	2.21360	+	13.9761i	0.100827	+	0.636596i
$483$		−	1.58721i		−	0.0722205i
$484$	32.7847	−	10.6524i	1.49022	−	0.484200i
$485$		−	25.8350i		−	1.17311i
$486$	1.39680	−	0.221232i	0.0633602	−	0.0100353i
$487$	−36.4018			−1.64952			−0.824762	−	0.565480i	$-0.808691\pi$
$487$	−36.4018			−1.64952			−0.824762	+	0.565480i	$0.808691\pi$
$488$	−18.2360	+	9.29168i	−0.825503	+	0.420615i
$489$	−9.79349			−0.442877
$490$	−2.83099	+	0.448385i	−0.127891	+	0.0202560i
$491$		−	3.76382i		−	0.169859i	−0.996387	−	0.0849294i	$-0.972934\pi$
$491$		−	3.76382i		−	0.169859i	0.996387	−	0.0849294i	$-0.0270665\pi$
$492$	6.92773	+	21.3214i	0.312326	+	0.961241i
$493$		−	11.7009i		−	0.526981i
$494$	1.33395	+	8.42226i	0.0600175	+	0.378935i
$495$	13.3914			0.601900
$496$	6.17661	−	4.48757i	0.277338	−	0.201498i
$497$	−4.55503			−0.204321
$498$	−1.02020	−	6.44131i	−0.0457164	−	0.288642i
$499$			16.9348i			0.758107i	0.925375	+	0.379053i	$0.123750\pi$
$499$			16.9348i			0.758107i	−0.925375	+	0.379053i	$0.876250\pi$
$500$	−5.68323	−	17.4912i	−0.254162	−	0.782230i
$501$			16.6054i			0.741876i
$502$	15.8848	−	2.51591i	0.708974	−	0.112290i
$503$	−12.9809			−0.578792			−0.289396	−	0.957209i	$-0.593454\pi$
$503$	−12.9809			−0.578792			−0.289396	+	0.957209i	$0.593454\pi$
$504$	3.58721	+	7.04029i	0.159787	+	0.313600i
$505$	7.60845			0.338572
$506$	−4.21702	+	0.667910i	−0.187469	+	0.0296922i
$507$			1.00000i			0.0444116i
$508$	−36.9726	+	12.0131i	−1.64039	+	0.532996i
$509$		−	13.4857i		−	0.597741i	−0.954294	−	0.298871i	$-0.903390\pi$
$509$		−	13.4857i		−	0.597741i	0.954294	−	0.298871i	$-0.0966099\pi$
$510$	−2.42592	−	15.3167i	−0.107422	−	0.678233i
$511$	−14.4553			−0.639464
$512$	22.3488	+	3.53971i	0.987688	+	0.156434i
$513$	−6.02967			−0.266217
$514$	2.51121	+	15.8551i	0.110765	+	0.699340i
$515$			32.5585i			1.43470i
$516$	18.0462	−	5.86357i	0.794440	−	0.258129i
$517$			21.0249i			0.924672i
$518$	37.4933	−	5.93835i	1.64736	−	0.260916i
$519$	−16.1979			−0.711007
$520$	−3.23607	−	6.35114i	−0.141911	−	0.278516i
$521$	−35.4175			−1.55167			−0.775834	−	0.630937i	$-0.782670\pi$
$521$	−35.4175			−1.55167			−0.775834	+	0.630937i	$0.782670\pi$
$522$	3.75621	−	0.594926i	0.164405	−	0.0260392i
$523$			4.72122i			0.206445i	0.994658	+	0.103222i	$0.0329153\pi$
$523$			4.72122i			0.206445i	−0.994658	+	0.103222i	$0.967085\pi$
$524$	−7.86357	−	24.2016i	−0.343522	−	1.05725i
$525$			3.77455i			0.164735i
$526$	0.859954	+	5.42954i	0.0374958	+	0.236739i
$527$	−8.30493			−0.361768
$528$	17.1957	−	12.4934i	0.748345	−	0.543705i
$529$	−22.6772			−0.985965
$530$	4.49338	+	28.3701i	0.195180	+	1.23232i
$531$			6.19868i			0.269000i
$532$	−10.4105	−	32.0402i	−0.451352	−	1.38912i
$533$		−	11.2093i		−	0.485529i
$534$	15.9490	−	2.52607i	0.690179	−	0.109314i
$535$	−27.6049			−1.19346
$536$	25.2762	−	12.8789i	1.09177	−	0.556283i
$537$	−1.22795			−0.0529901
$538$	−35.2414	+	5.58168i	−1.51936	+	0.240643i
$539$			4.27346i			0.184071i
$540$	4.79360	−	1.55754i	0.206284	−	0.0670257i
$541$		−	26.4200i		−	1.13589i	−0.823068	−	0.567943i	$-0.807739\pi$
$541$		−	26.4200i		−	1.13589i	0.823068	−	0.567943i	$-0.192261\pi$
$542$	−0.643007	−	4.05979i	−0.0276195	−	0.174383i
$543$	−7.00592			−0.300653
$544$	−17.4046	−	17.4046i	−0.746215	−	0.746215i
$545$	−13.7426			−0.588667
$546$	−0.618034	−	3.90211i	−0.0264494	−	0.166995i
$547$		−	26.9939i		−	1.15417i	−0.816683	−	0.577087i	$-0.804189\pi$
$547$		−	26.9939i		−	1.15417i	0.816683	−	0.577087i	$-0.195811\pi$
$548$	17.5575	−	5.70479i	0.750021	−	0.243697i
$549$			7.23607i			0.308828i
$550$	10.0285	−	1.58836i	0.427618	−	0.0677280i
$551$	−16.2147			−0.690770
$552$	−1.43184	+	0.729560i	−0.0609432	+	0.0310521i
$553$	25.6297			1.08989
$554$	−5.96190	+	0.944272i	−0.253297	+	0.0401183i
$555$		−	24.2147i		−	1.02786i
$556$	−7.26233	−	22.3511i	−0.307991	−	0.947900i
$557$		−	24.7636i		−	1.04927i	−0.851329	−	0.524633i	$-0.824203\pi$
$557$		−	24.7636i		−	1.04927i	0.851329	−	0.524633i	$-0.175797\pi$
$558$	−0.422260	−	2.66605i	−0.0178757	−	0.112863i
$559$	−9.48746			−0.401277
$560$	16.5527	+	22.7829i	0.699480	+	0.962752i
$561$	−23.1209			−0.976164
$562$	−4.20119	−	26.5252i	−0.177216	−	1.11890i
$563$		−	19.7426i		−	0.832050i	−0.909353	−	0.416025i	$-0.863423\pi$
$563$		−	19.7426i		−	0.832050i	0.909353	−	0.416025i	$-0.136577\pi$
$564$	2.44537	+	7.52607i	0.102969	+	0.316905i
$565$		−	34.3582i		−	1.44546i
$566$	−18.4317	+	2.91930i	−0.774743	+	0.122707i
$567$	2.79360			0.117320
$568$	2.09372	+	4.10915i	0.0878504	+	0.172416i
$569$	2.17684			0.0912577			0.0456289	−	0.998958i	$-0.485471\pi$
$569$	2.17684			0.0912577			0.0456289	+	0.998958i	$0.485471\pi$
$570$	−21.2253	+	3.36176i	−0.889031	+	0.140809i
$571$		−	4.05934i		−	0.169878i	−0.996386	−	0.0849391i	$-0.972930\pi$
$571$		−	4.05934i		−	0.169878i	0.996386	−	0.0849391i	$-0.0270696\pi$
$572$	−10.1074	+	3.28408i	−0.422610	+	0.137314i
$573$			14.3701i			0.600319i
$574$	6.92773	+	43.7400i	0.289158	+	1.82567i
$575$	−0.767662			−0.0320137
$576$	4.70228	−	6.47214i	0.195928	−	0.269672i
$577$	−27.5489			−1.14687			−0.573437	−	0.819249i	$-0.694390\pi$
$577$	−27.5489			−1.14687			−0.573437	+	0.819249i	$0.694390\pi$
$578$	0.427514	+	2.69922i	0.0177823	+	0.112273i
$579$			3.67383i			0.152679i
$580$	12.8907	−	4.18845i	0.535259	−	0.173916i
$581$		−	12.8826i		−	0.534461i
$582$	−14.3192	+	2.26793i	−0.593548	+	0.0940088i
$583$	42.8254			1.77365
$584$	6.64436	+	13.0403i	0.274946	+	0.539611i
$585$	−2.52015			−0.104195
$586$	−16.8985	+	2.67645i	−0.698069	+	0.110563i
$587$		−	14.3268i		−	0.591329i	−0.955292	−	0.295664i	$-0.904459\pi$
$587$		−	14.3268i		−	0.591329i	0.955292	−	0.295664i	$-0.0955410\pi$
$588$	0.497039	+	1.52973i	0.0204975	+	0.0630850i
$589$			11.5087i			0.474208i
$590$	3.45599	+	21.8203i	0.142281	+	0.898326i
$591$	6.88442			0.283187
$592$	−22.5908	−	31.0936i	−0.928477	−	1.27794i
$593$	27.6050			1.13360			0.566801	−	0.823855i	$-0.308181\pi$
$593$	27.6050			1.13360			0.566801	+	0.823855i	$0.308181\pi$
$594$	−1.17557	−	7.42226i	−0.0482342	−	0.304539i
$595$		−	30.6333i		−	1.25584i
$596$	10.8823	+	33.4923i	0.445757	+	1.37190i
$597$		−	15.3952i		−	0.630082i
$598$	0.793604	−	0.125695i	0.0324529	−	0.00514003i
$599$	−18.5204			−0.756724			−0.378362	−	0.925658i	$-0.623513\pi$
$599$	−18.5204			−0.756724			−0.378362	+	0.925658i	$0.623513\pi$
$600$	3.40507	−	1.73497i	0.139012	−	0.0708299i
$601$	35.1640			1.43437			0.717185	−	0.696883i	$-0.245430\pi$
$601$	35.1640			1.43437			0.717185	+	0.696883i	$0.245430\pi$
$602$	37.0211	−	5.86357i	1.50887	−	0.238981i
$603$		−	10.0297i		−	0.408440i
$604$	22.1121	−	7.18464i	0.899727	−	0.292339i
$605$		−	43.4371i		−	1.76597i
$606$	−0.667910	−	4.21702i	−0.0271320	−	0.171305i
$607$	−35.5432			−1.44265			−0.721327	−	0.692594i	$-0.756468\pi$
$607$	−35.5432			−1.44265			−0.721327	+	0.692594i	$0.756468\pi$
$608$	−24.1187	+	24.1187i	−0.978142	+	0.978142i
$609$	7.51243			0.304419
$610$	4.03437	+	25.4720i	0.163347	+	1.03133i
$611$		−	3.95669i		−	0.160070i
$612$	−8.27636	+	2.68915i	−0.334552	+	0.108703i
$613$		−	37.3356i		−	1.50797i	−0.656891	−	0.753985i	$-0.728129\pi$
$613$		−	37.3356i		−	1.50797i	0.656891	−	0.753985i	$-0.271871\pi$
$614$	−34.6215	+	5.48351i	−1.39721	+	0.221297i
$615$	28.2491			1.13911
$616$	37.4104	−	19.0615i	1.50731	−	0.768011i
$617$	20.1630			0.811731			0.405865	−	0.913933i	$-0.366970\pi$
$617$	20.1630			0.811731			0.405865	+	0.913933i	$0.366970\pi$
$618$	18.0457	−	2.85816i	0.725905	−	0.114972i
$619$			15.1066i			0.607187i	0.952802	+	0.303594i	$0.0981865\pi$
$619$			15.1066i			0.607187i	−0.952802	+	0.303594i	$0.901813\pi$
$620$	−2.97283	−	9.14945i	−0.119392	−	0.367451i
$621$			0.568158i			0.0227994i
$622$	−1.48879	−	9.39986i	−0.0596951	−	0.376900i
$623$	31.8979			1.27796
$624$	−3.23607	+	2.35114i	−0.129546	+	0.0941210i
$625$	−29.9301			−1.19720
$626$	2.54319	+	16.0570i	0.101646	+	0.641768i
$627$			32.0402i			1.27956i
$628$	8.32990	+	25.6368i	0.332399	+	1.02302i
$629$			41.8077i			1.66698i
$630$	9.83390	−	1.55754i	0.391792	−	0.0620537i
$631$	0.390213			0.0155341			0.00776706	−	0.999970i	$-0.497528\pi$
$631$	0.390213			0.0155341			0.00776706	+	0.999970i	$0.497528\pi$
$632$	−11.7807	−	23.1209i	−0.468610	−	0.919699i
$633$	1.57035			0.0624158
$634$	4.00541	−	0.634395i	0.159075	−	0.0251950i
$635$			48.9857i			1.94394i
$636$	15.3298	−	4.98095i	0.607866	−	0.197507i
$637$		−	0.804226i		−	0.0318646i
$638$	−3.16129	−	19.9596i	−0.125157	−	0.790208i
$639$	1.63052			0.0645024
$640$	12.9443	−	25.4046i	0.511667	−	1.00420i
$641$	−36.5386			−1.44319			−0.721593	−	0.692317i	$-0.756590\pi$
$641$	−36.5386			−1.44319			−0.721593	+	0.692317i	$0.756590\pi$
$642$	2.42330	+	15.3001i	0.0956400	+	0.603847i
$643$			29.1064i			1.14785i	0.818910	+	0.573923i	$0.194579\pi$
$643$			29.1064i			1.14785i	−0.818910	+	0.573923i	$0.805421\pi$
$644$	−3.01905	+	0.980949i	−0.118967	+	0.0386548i
$645$		−	23.9098i		−	0.941447i
$646$	36.6464	−	5.80423i	1.44183	−	0.228364i
$647$	−15.1906			−0.597206			−0.298603	−	0.954377i	$-0.596521\pi$
$647$	−15.1906			−0.597206			−0.298603	+	0.954377i	$0.596521\pi$
$648$	−1.28408	−	2.52015i	−0.0504434	−	0.0990007i
$649$	32.9382			1.29294
$650$	−1.88728	+	0.298915i	−0.0740251	+	0.0117244i
$651$		−	5.33209i		−	0.208981i
$652$	6.05271	+	18.6283i	0.237042	+	0.729542i
$653$		−	15.9205i		−	0.623016i	−0.950243	−	0.311508i	$-0.899166\pi$
$653$		−	15.9205i		−	0.623016i	0.950243	−	0.311508i	$-0.100834\pi$
$654$	1.20640	+	7.61688i	0.0471738	+	0.297844i
$655$	−32.0652			−1.25289
$656$	36.2741	−	26.3546i	1.41626	−	1.02898i
$657$	5.17442			0.201873
$658$	2.44537	+	15.4394i	0.0953304	+	0.601892i
$659$		−	7.56597i		−	0.294728i	−0.989082	−	0.147364i	$-0.952921\pi$
$659$		−	7.56597i		−	0.294728i	0.989082	−	0.147364i	$-0.0470789\pi$
$660$	−8.27636	−	25.4720i	−0.322157	−	0.991497i
$661$			32.0806i			1.24779i	0.781508	+	0.623895i	$0.214451\pi$
$661$			32.0806i			1.24779i	−0.781508	+	0.623895i	$0.785549\pi$
$662$	−2.02490	+	0.320713i	−0.0787001	+	0.0124649i
$663$	4.35114			0.168984
$664$	−11.6216	+	5.92149i	−0.451005	+	0.229798i
$665$	−42.4507			−1.64617
$666$	−13.4211	+	2.12569i	−0.520057	+	0.0823690i
$667$			1.52786i			0.0591591i
$668$	31.5854	−	10.2627i	1.22208	−	0.397077i
$669$		−	27.6571i		−	1.06928i
$670$	−5.59191	−	35.3059i	−0.216034	−	1.36399i
$671$	38.4507			1.48437
$672$	11.1744	−	11.1744i	0.431063	−	0.431063i
$673$	19.0592			0.734679			0.367340	−	0.930087i	$-0.380269\pi$
$673$	19.0592			0.734679			0.367340	+	0.930087i	$0.380269\pi$
$674$	−5.01697	−	31.6759i	−0.193247	−	1.22011i
$675$		−	1.35114i		−	0.0520054i
$676$	1.90211	−	0.618034i	0.0731582	−	0.0237705i
$677$			4.40095i			0.169142i	0.996417	+	0.0845711i	$0.0269520\pi$
$677$			4.40095i			0.169142i	−0.996417	+	0.0845711i	$0.973048\pi$
$678$	−19.0432	+	3.01615i	−0.731350	+	0.115834i
$679$	−28.6383			−1.09904
$680$	−27.6347	+	14.0806i	−1.05974	+	0.539966i
$681$	−22.9434			−0.879195
$682$	−14.1667	+	2.24379i	−0.542471	+	0.0859190i
$683$			33.8071i			1.29359i	0.762662	+	0.646797i	$0.223892\pi$
$683$			33.8071i			1.29359i	−0.762662	+	0.646797i	$0.776108\pi$
$684$	3.72654	+	11.4691i	0.142488	+	0.438533i
$685$		−	23.2623i		−	0.888808i
$686$	−3.82920	−	24.1766i	−0.146199	−	0.923067i
$687$	23.5064			0.896825
$688$	−22.3063	−	30.7021i	−0.850422	−	1.17050i
$689$	−8.05934			−0.307037
$690$	0.316769	+	2.00000i	0.0120592	+	0.0761387i
$691$			12.4856i			0.474974i	0.971391	+	0.237487i	$0.0763237\pi$
$691$			12.4856i			0.474974i	−0.971391	+	0.237487i	$0.923676\pi$
$692$	10.0108	+	30.8101i	0.380554	+	1.17123i
$693$		−	14.8445i		−	0.563897i
$694$	47.1634	−	7.46994i	1.79030	−	0.283555i
$695$	−29.6135			−1.12330
$696$	−3.45309	−	6.77706i	−0.130889	−	0.256884i
$697$	−48.7732			−1.84742
$698$	8.86608	−	1.40425i	0.335586	−	0.0531516i
$699$		−	3.47433i		−	0.131411i
$700$	7.17963	−	2.33280i	0.271364	−	0.0881716i
$701$		−	34.2016i		−	1.29178i	−0.763432	−	0.645888i	$-0.776487\pi$
$701$		−	34.2016i		−	1.29178i	0.763432	−	0.645888i	$-0.223513\pi$
$702$	0.221232	+	1.39680i	0.00834985	+	0.0527189i
$703$	57.9358			2.18509
$704$	−34.3913	−	24.9868i	−1.29617	−	0.941724i
$705$	9.97144			0.375546
$706$	7.12048	+	44.9570i	0.267983	+	1.69198i
$707$		−	8.43403i		−	0.317195i
$708$	11.7906	−	3.83099i	0.443117	−	0.143978i
$709$		−	41.6463i		−	1.56406i	−0.623240	−	0.782030i	$-0.714184\pi$
$709$		−	41.6463i		−	1.56406i	0.623240	−	0.782030i	$-0.285816\pi$
$710$	5.73967	−	0.909075i	0.215406	−	0.0341170i
$711$	−9.17442			−0.344068
$712$	−14.6619	−	28.7756i	−0.549477	−	1.07841i
$713$	1.08443			0.0406122
$714$	−16.9786	+	2.68915i	−0.635410	+	0.100639i
$715$			13.3914i			0.500811i
$716$	0.758917	+	2.33571i	0.0283621	+	0.0872895i
$717$			11.5820i			0.432538i
$718$	5.07112	+	32.0178i	0.189252	+	1.19489i
$719$	33.0401			1.23219			0.616093	−	0.787673i	$-0.288714\pi$
$719$	33.0401			1.23219			0.616093	+	0.787673i	$0.288714\pi$
$720$	−5.92522	−	8.15537i	−0.220820	−	0.303933i
$721$	36.0914			1.34411
$722$	−3.83991	−	24.2442i	−0.142907	−	0.902277i
$723$		−	10.0058i		−	0.372120i
$724$	4.32990	+	13.3261i	0.160919	+	0.495259i
$725$		−	3.63342i		−	0.134942i
$726$	−24.0752	+	3.81314i	−0.893515	+	0.141519i
$727$	−7.80551			−0.289490			−0.144745	−	0.989469i	$-0.546236\pi$
$727$	−7.80551			−0.289490			−0.144745	+	0.989469i	$0.546236\pi$
$728$	−7.04029	+	3.58721i	−0.260931	+	0.132951i
$729$	−1.00000			−0.0370370
$730$	18.2147	−	2.88493i	0.674157	−	0.106776i
$731$			41.2813i			1.52684i
$732$	13.7638	−	4.47214i	0.508725	−	0.165295i
$733$			29.3035i			1.08235i	0.840910	+	0.541175i	$0.182020\pi$
$733$			29.3035i			1.08235i	−0.840910	+	0.541175i	$0.817980\pi$
$734$	−2.14173	−	13.5223i	−0.0790526	−	0.499119i
$735$	2.02677			0.0747585
$736$	2.27263	+	2.27263i	0.0837703	+	0.0837703i
$737$	−53.2952			−1.96315
$738$	−2.47985	−	15.6572i	−0.0912846	−	0.576349i
$739$		−	42.2408i		−	1.55385i	−0.629591	−	0.776926i	$-0.716778\pi$
$739$		−	42.2408i		−	1.55385i	0.629591	−	0.776926i	$-0.283222\pi$
$740$	−46.0591	+	14.9655i	−1.69317	+	0.550143i
$741$		−	6.02967i		−	0.221506i
$742$	31.4485	−	4.98095i	1.15451	−	0.182856i
$743$	19.3835			0.711112			0.355556	−	0.934655i	$-0.384291\pi$
$743$	19.3835			0.711112			0.355556	+	0.934655i	$0.384291\pi$
$744$	−4.81015	+	2.45089i	−0.176349	+	0.0898541i
$745$	44.3746			1.62576
$746$	−32.5420	+	5.15414i	−1.19145	+	0.188707i
$747$			4.61147i			0.168725i
$748$	14.2895	+	43.9785i	0.522476	+	1.60801i
$749$			30.6002i			1.11811i
$750$	2.03437	+	12.8445i	0.0742848	+	0.469016i
$751$	9.06886			0.330927			0.165464	−	0.986216i	$-0.447088\pi$
$751$	9.06886			0.330927			0.165464	+	0.986216i	$0.447088\pi$
$752$	12.8041	−	9.30273i	0.466918	−	0.339236i
$753$	−11.3723			−0.414429
$754$	0.594926	+	3.75621i	0.0216659	+	0.136793i
$755$		−	29.2967i		−	1.06622i
$756$	−1.72654	−	5.31375i	−0.0627937	−	0.193259i
$757$			6.34174i			0.230495i	0.993337	+	0.115247i	$0.0367660\pi$
$757$			6.34174i			0.230495i	−0.993337	+	0.115247i	$0.963234\pi$
$758$	13.2455	−	2.09789i	0.481100	−	0.0761987i
$759$	3.01905			0.109585
$760$	19.5124	+	38.2953i	0.707790	+	1.38912i
$761$	19.1133			0.692856			0.346428	−	0.938077i	$-0.387395\pi$
$761$	19.1133			0.692856			0.346428	+	0.938077i	$0.387395\pi$
$762$	27.1506	−	4.30023i	0.983561	−	0.155781i
$763$			15.2338i			0.551499i
$764$	27.3335	−	8.88120i	0.988892	−	0.321310i
$765$			10.9655i			0.396459i
$766$	−1.25749	−	7.93950i	−0.0454351	−	0.286866i
$767$	−6.19868			−0.223821
$768$	−15.2169	−	4.94427i	−0.549093	−	0.178411i
$769$	−5.22795			−0.188525			−0.0942624	−	0.995547i	$-0.530049\pi$
$769$	−5.22795			−0.188525			−0.0942624	+	0.995547i	$0.530049\pi$
$770$	−8.27636	−	52.2549i	−0.298259	−	1.88314i
$771$		−	11.3510i		−	0.408797i
$772$	6.98804	−	2.27055i	0.251505	−	0.0817190i
$773$		−	32.5414i		−	1.17043i	−0.810877	−	0.585216i	$-0.801010\pi$
$773$		−	32.5414i		−	1.17043i	0.810877	−	0.585216i	$-0.198990\pi$
$774$	−13.2521	+	2.09893i	−0.476337	+	0.0754444i
$775$	−2.57889			−0.0926366
$776$	13.1636	+	25.8350i	0.472545	+	0.927423i
$777$	−26.8422			−0.962959
$778$	2.51203	−	0.397867i	0.0900607	−	0.0142642i
$779$			67.5884i			2.42161i
$780$	1.55754	+	4.79360i	0.0557688	+	0.171639i
$781$		−	8.66418i		−	0.310029i
$782$	−0.546915	−	3.45309i	−0.0195576	−	0.123482i
$783$	−2.68915			−0.0961025
$784$	2.60253	−	1.89085i	0.0929475	−	0.0675303i
$785$	33.9667			1.21232
$786$	2.81485	+	17.7722i	0.100402	+	0.633915i
$787$			8.62409i			0.307416i	0.988116	+	0.153708i	$0.0491214\pi$
$787$			8.62409i			0.307416i	−0.988116	+	0.153708i	$0.950879\pi$
$788$	−4.25480	−	13.0949i	−0.151571	−	0.466488i
$789$		−	3.88712i		−	0.138385i
$790$	−32.2953	+	5.11507i	−1.14902	+	0.181986i
$791$	−38.0864			−1.35420
$792$	−13.3914	+	6.82328i	−0.475844	+	0.242455i
$793$	−7.23607			−0.256960
$794$	6.44016	−	1.02002i	0.228553	−	0.0361992i
$795$		−	20.3107i		−	0.720348i
$796$	−29.2833	+	9.51474i	−1.03792	+	0.337241i
$797$			27.6486i			0.979365i	0.871901	+	0.489682i	$0.162887\pi$
$797$			27.6486i			0.979365i	−0.871901	+	0.489682i	$0.837113\pi$
$798$	3.72654	+	23.5285i	0.131918	+	0.832899i
$799$	−17.2161			−0.609062
$800$	−5.40456	−	5.40456i	−0.191080	−	0.191080i
$801$	−11.4182			−0.403442
$802$	−4.30740	−	27.1959i	−0.152100	−	0.960319i
$803$		−	27.4956i		−	0.970298i
$804$	−19.0776	+	6.19868i	−0.672814	+	0.218611i
$805$			4.00000i			0.140981i
$806$	2.66605	−	0.422260i	0.0939074	−	0.0148735i
$807$	25.2300			0.888139
$808$	−7.60845	+	3.87670i	−0.267664	+	0.136382i
$809$	−24.4163			−0.858431			−0.429216	−	0.903202i	$-0.641210\pi$
$809$	−24.4163			−0.858431			−0.429216	+	0.903202i	$0.641210\pi$
$810$	−3.52015	+	0.557537i	−0.123685	+	0.0195898i
$811$		−	9.54312i		−	0.335104i	−0.985863	−	0.167552i	$-0.946414\pi$
$811$		−	9.54312i		−	0.335104i	0.985863	−	0.167552i	$-0.0535863\pi$
$812$	−4.64294	−	14.2895i	−0.162935	−	0.501463i
$813$			2.90649i			0.101935i
$814$	11.2954	+	71.3164i	0.395904	+	2.49964i
$815$	24.6810			0.864539
$816$	10.2301	+	14.0806i	0.358127	+	0.492919i
$817$	57.2063			2.00139
$818$	7.64789	+	48.2869i	0.267402	+	1.68831i
$819$			2.79360i			0.0976164i
$820$	−17.4589	−	53.7330i	−0.609691	−	1.87644i
$821$			2.26876i			0.0791802i	0.999216	+	0.0395901i	$0.0126052\pi$
$821$			2.26876i			0.0791802i	−0.999216	+	0.0395901i	$0.987395\pi$
$822$	−12.8932	+	2.04209i	−0.449704	+	0.0712260i
$823$	−14.4047			−0.502115			−0.251058	−	0.967972i	$-0.580778\pi$
$823$	−14.4047			−0.502115			−0.251058	+	0.967972i	$0.580778\pi$
$824$	−16.5894	−	32.5585i	−0.577919	−	1.13423i
$825$	−7.17963			−0.249963
$826$	24.1879	−	3.83099i	0.841606	−	0.133297i
$827$			15.2993i			0.532010i	0.963972	+	0.266005i	$0.0857038\pi$
$827$			15.2993i			0.532010i	−0.963972	+	0.266005i	$0.914296\pi$
$828$	1.08070	−	0.351141i	0.0375570	−	0.0122030i
$829$		−	21.5350i		−	0.747940i	−0.927441	−	0.373970i	$-0.877996\pi$
$829$		−	21.5350i		−	0.747940i	0.927441	−	0.373970i	$-0.122004\pi$
$830$	2.57106	+	16.2331i	0.0892429	+	0.563457i
$831$	4.26825			0.148064
$832$	6.47214	+	4.70228i	0.224381	+	0.163022i
$833$	−3.49930			−0.121244
$834$	2.59963	+	16.4134i	0.0900177	+	0.568349i
$835$		−	41.8481i		−	1.44821i
$836$	60.9440	−	19.8019i	2.10779	−	0.684864i
$837$			1.90868i			0.0659735i
$838$	7.99300	−	1.26597i	0.276113	−	0.0437321i
$839$	47.6245			1.64418			0.822090	−	0.569358i	$-0.192808\pi$
$839$	47.6245			1.64418			0.822090	+	0.569358i	$0.192808\pi$
$840$	−9.04029	−	17.7426i	−0.311920	−	0.612177i
$841$	21.7685			0.750636
$842$	43.1468	−	6.83379i	1.48694	−	0.235508i
$843$			18.9900i			0.654050i
$844$	−0.970530	−	2.98698i	−0.0334070	−	0.102816i
$845$		−	2.52015i		−	0.0866957i
$846$	−0.875345	−	5.52671i	−0.0300950	−	0.190012i
$847$	−48.1504			−1.65447
$848$	−18.9487	−	26.0806i	−0.650700	−	0.895611i
$849$	13.1957			0.452874
$850$	1.30062	+	8.21181i	0.0446110	+	0.281663i
$851$		−	5.45912i		−	0.187136i
$852$	−1.00772	−	3.10143i	−0.0345238	−	0.106253i
$853$		−	15.3358i		−	0.525088i	−0.964920	−	0.262544i	$-0.915438\pi$
$853$		−	15.3358i		−	0.525088i	0.964920	−	0.262544i	$-0.0845616\pi$
$854$	28.2360	−	4.47214i	0.966214	−	0.153033i
$855$	15.1957			0.519681
$856$	27.6049	−	14.0654i	0.943515	−	0.480745i
$857$	15.0828			0.515218			0.257609	−	0.966249i	$-0.417065\pi$
$857$	15.0828			0.515218			0.257609	+	0.966249i	$0.417065\pi$
$858$	7.42226	−	1.17557i	0.253392	−	0.0401333i
$859$			15.0249i			0.512642i	0.966592	+	0.256321i	$0.0825104\pi$
$859$			15.0249i			0.512642i	−0.966592	+	0.256321i	$0.917490\pi$
$860$	−45.4791	+	14.7771i	−1.55083	+	0.503894i
$861$		−	31.3144i		−	1.06719i
$862$	3.62176	+	22.8669i	0.123358	+	0.778850i
$863$	−1.32919			−0.0452460			−0.0226230	−	0.999744i	$-0.507202\pi$
$863$	−1.32919			−0.0452460			−0.0226230	+	0.999744i	$0.507202\pi$
$864$	−4.00000	+	4.00000i	−0.136083	+	0.136083i
$865$	40.8210			1.38795
$866$	−2.03018	−	12.8181i	−0.0689884	−	0.435576i
$867$		−	1.93243i		−	0.0656287i
$868$	−10.1422	+	3.29541i	−0.344250	+	0.111854i
$869$			48.7506i			1.65375i
$870$	−9.46621	+	1.49930i	−0.320935	+	0.0508311i
$871$	10.0297			0.339842
$872$	13.7426	−	7.00219i	0.465382	−	0.237124i
$873$	10.2514			0.346957
$874$	−4.78518	+	0.757897i	−0.161861	+	0.0256363i
$875$			25.6890i			0.868448i
$876$	−3.19797	−	9.84233i	−0.108049	−	0.332541i
$877$			44.4244i			1.50011i	0.661378	+	0.750053i	$0.269972\pi$
$877$			44.4244i			1.50011i	−0.661378	+	0.750053i	$0.730028\pi$
$878$	−4.23647	−	26.7480i	−0.142974	−	0.902701i
$879$	12.0980			0.408054
$880$	−43.3356	+	31.4852i	−1.46084	+	1.06136i
$881$	−36.5136			−1.23017			−0.615087	−	0.788459i	$-0.710879\pi$
$881$	−36.5136			−1.23017			−0.615087	+	0.788459i	$0.710879\pi$
$882$	−0.177920	−	1.12334i	−0.00599089	−	0.0378250i
$883$			6.77808i			0.228101i	0.993475	+	0.114050i	$0.0363825\pi$
$883$			6.77808i			0.228101i	−0.993475	+	0.114050i	$0.963617\pi$
$884$	−2.68915	−	8.27636i	−0.0904460	−	0.278364i
$885$		−	15.6216i		−	0.525114i
$886$	−8.23858	+	1.30486i	−0.276780	+	0.0438377i
$887$	−48.6502			−1.63351			−0.816756	−	0.576983i	$-0.804230\pi$
$887$	−48.6502			−1.63351			−0.816756	+	0.576983i	$0.804230\pi$
$888$	12.3380	+	24.2147i	0.414037	+	0.812593i
$889$	54.3011			1.82120
$890$	−40.1938	+	6.36607i	−1.34730	+	0.213391i
$891$			5.31375i			0.178017i
$892$	−52.6069	+	17.0930i	−1.76141	+	0.572316i
$893$			23.8575i			0.798362i
$894$	−3.89544	−	24.5948i	−0.130283	−	0.822574i
$895$	3.09462			0.103442
$896$	−28.1612	−	14.3488i	−0.940799	−	0.479361i
$897$	−0.568158			−0.0189702
$898$	−4.82971	−	30.4936i	−0.161169	−	1.01758i
$899$			5.13273i			0.171186i
$900$	−2.57002	+	0.835051i	−0.0856674	+	0.0278350i
$901$			35.0673i			1.16826i
$902$	−83.1983	+	13.1773i	−2.77020	+	0.438757i
$903$	−26.5042			−0.882005
$904$	17.5064	+	34.3582i	0.582254	+	1.14274i
$905$	17.6560			0.586904
$906$	−16.2378	+	2.57182i	−0.539465	+	0.0854429i
$907$		−	36.5196i		−	1.21261i	−0.795230	−	0.606307i	$-0.792650\pi$
$907$		−	36.5196i		−	1.21261i	0.795230	−	0.606307i	$-0.207350\pi$
$908$	14.1798	+	43.6410i	0.470574	+	1.44828i
$909$			3.01905i			0.100136i
$910$	1.55754	+	9.83390i	0.0516318	+	0.325991i
$911$	−23.9142			−0.792312			−0.396156	−	0.918183i	$-0.629656\pi$
$911$	−23.9142			−0.792312			−0.396156	+	0.918183i	$0.629656\pi$
$912$	19.5124	−	14.1766i	0.646121	−	0.469434i
$913$	24.5042			0.810971
$914$	1.51377	+	9.55754i	0.0500709	+	0.316135i
$915$		−	18.2360i		−	0.602862i
$916$	−14.5278	−	44.7118i	−0.480010	−	1.47732i
$917$			35.5445i			1.17378i
$918$	6.07768	−	0.962611i	0.200593	−	0.0317709i
$919$	18.4982			0.610198			0.305099	−	0.952321i	$-0.401310\pi$
$919$	18.4982			0.610198			0.305099	+	0.952321i	$0.401310\pi$
$920$	3.60845	−	1.83860i	0.118967	−	0.0606168i
$921$	24.7863			0.816736
$922$	−31.1051	+	4.92656i	−1.02439	+	0.162247i
$923$			1.63052i			0.0536692i
$924$	−28.2360	+	9.17442i	−0.928895	+	0.301816i
$925$			12.9824i			0.426858i
$926$	5.84097	+	36.8785i	0.191946	+	1.21190i
$927$	−12.9193			−0.424325
$928$	−10.7566	+	10.7566i	−0.353103	+	0.353103i
$929$	31.5521			1.03519			0.517595	−	0.855625i	$-0.326827\pi$
$929$	31.5521			1.03519			0.517595	+	0.855625i	$0.326827\pi$
$930$	1.06416	+	6.71883i	0.0348951	+	0.220319i
$931$			4.84922i			0.158927i
$932$	−6.60856	+	2.14725i	−0.216471	+	0.0703356i
$933$			6.72956i			0.220316i
$934$	−15.7888	+	2.50070i	−0.516625	+	0.0818254i
$935$	58.2680			1.90557
$936$	2.52015	−	1.28408i	0.0823736	−	0.0419714i
$937$	−5.54201			−0.181050			−0.0905248	−	0.995894i	$-0.528854\pi$
$937$	−5.54201			−0.181050			−0.0905248	+	0.995894i	$0.528854\pi$
$938$	−39.1369	+	6.19868i	−1.27787	+	0.202394i
$939$		−	11.4956i		−	0.375144i
$940$	−6.16269	−	18.9668i	−0.201005	−	0.618629i
$941$		−	9.62480i		−	0.313760i	−0.987618	−	0.156880i	$-0.949856\pi$
$941$		−	9.62480i		−	0.313760i	0.987618	−	0.156880i	$-0.0501435\pi$
$942$	−2.98177	−	18.8262i	−0.0971515	−	0.613390i
$943$	6.36865			0.207392
$944$	−14.5740	−	20.0593i	−0.474342	−	0.652876i
$945$	−7.04029			−0.229021
$946$	11.1532	+	70.4184i	0.362621	+	2.28950i
$947$		−	31.1231i		−	1.01137i	−0.862719	−	0.505683i	$-0.831241\pi$
$947$		−	31.1231i		−	1.01137i	0.862719	−	0.505683i	$-0.168759\pi$
$948$	5.67010	+	17.4508i	0.184156	+	0.566775i
$949$			5.17442i			0.167969i
$950$	11.3797	−	1.80236i	0.369205	−	0.0584763i
$951$	−2.86756			−0.0929870
$952$	15.6085	+	30.6333i	0.505873	+	0.992831i
$953$	−17.0359			−0.551847			−0.275924	−	0.961180i	$-0.588984\pi$
$953$	−17.0359			−0.551847			−0.275924	+	0.961180i	$0.588984\pi$
$954$	−11.2573	+	1.78298i	−0.364469	+	0.0577262i
$955$		−	36.2147i		−	1.17188i
$956$	22.0303	−	7.15807i	0.712510	−	0.231509i
$957$			14.2895i			0.461914i
$958$	−8.93828	−	56.4341i	−0.288783	−	1.82330i
$959$	−25.7865			−0.832689
$960$	−11.8504	+	16.3107i	−0.382471	+	0.526427i
$961$	−27.3570			−0.882482
$962$	−2.12569	−	13.4211i	−0.0685351	−	0.432714i
$963$		−	10.9537i		−	0.352977i
$964$	−19.0322	+	6.18393i	−0.612985	+	0.199171i
$965$		−	9.25860i		−	0.298045i
$966$	2.21702	−	0.351141i	0.0713314	−	0.0112978i
$967$	7.56565			0.243295			0.121647	−	0.992573i	$-0.461182\pi$
$967$	7.56565			0.243295			0.121647	+	0.992573i	$0.461182\pi$
$968$	22.1323	+	43.4371i	0.711360	+	1.39612i
$969$	−26.2360			−0.842820
$970$	36.0864	−	5.71552i	1.15866	−	0.183514i
$971$			25.0676i			0.804457i	0.915539	+	0.402228i	$0.131764\pi$
$971$			25.0676i			0.804457i	−0.915539	+	0.402228i	$0.868236\pi$
$972$	0.618034	+	1.90211i	0.0198234	+	0.0610103i
$973$			32.8268i			1.05238i
$974$	−8.05324	−	50.8462i	−0.258042	−	1.62922i
$975$	1.35114			0.0432711
$976$	−17.0130	−	23.4164i	−0.544573	−	0.749541i
$977$	−37.9292			−1.21346			−0.606732	−	0.794907i	$-0.707520\pi$
$977$	−37.9292			−1.21346			−0.606732	+	0.794907i	$0.707520\pi$
$978$	−2.16663	−	13.6796i	−0.0692812	−	0.437424i
$979$			60.6735i			1.93913i
$980$	−1.25261	−	3.85514i	−0.0400132	−	0.123148i
$981$		−	5.45309i		−	0.174104i
$982$	5.25731	−	0.832676i	0.167768	−	0.0265718i
$983$	−10.3543			−0.330250			−0.165125	−	0.986273i	$-0.552803\pi$
$983$	−10.3543			−0.330250			−0.165125	+	0.986273i	$0.552803\pi$
$984$	−28.2491	+	14.3936i	−0.900548	+	0.458852i
$985$	−17.3497			−0.552809
$986$	16.3438	−	2.58861i	0.520493	−	0.0824380i
$987$		−	11.0534i		−	0.351834i
$988$	−11.4691	+	3.72654i	−0.364881	+	0.118557i
$989$		−	5.39038i		−	0.171404i
$990$	2.96261	+	18.7052i	0.0941579	+	0.594490i
$991$	−45.2348			−1.43693			−0.718466	−	0.695562i	$-0.755155\pi$
$991$	−45.2348			−1.43693			−0.718466	+	0.695562i	$0.755155\pi$
$992$	7.63471	+	7.63471i	0.242402	+	0.242402i
$993$	1.44967			0.0460039
$994$	−1.00772	−	6.36247i	−0.0319628	−	0.201805i
$995$			38.7981i			1.22998i
$996$	8.77154	−	2.85004i	0.277937	−	0.0903071i
$997$		−	24.7402i		−	0.783529i	−0.920066	−	0.391764i	$-0.871865\pi$
$997$		−	24.7402i		−	0.783529i	0.920066	−	0.391764i	$-0.128135\pi$
$998$	−23.6546	+	3.74652i	−0.748773	+	0.118594i
$999$	9.60845			0.303998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.g.a.157.4	yes	8
3.2	odd	2		936.2.g.d.469.5		8
4.3	odd	2		1248.2.g.a.625.8		8
8.3	odd	2		1248.2.g.a.625.1		8
8.5	even	2	inner	312.2.g.a.157.3	✓	8
12.11	even	2		3744.2.g.d.1873.2		8
16.3	odd	4		9984.2.a.s.1.4		4
16.5	even	4		9984.2.a.y.1.1		4
16.11	odd	4		9984.2.a.bh.1.1		4
16.13	even	4		9984.2.a.bb.1.4		4
24.5	odd	2		936.2.g.d.469.6		8
24.11	even	2		3744.2.g.d.1873.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.g.a.157.3	✓	8	8.5	even	2	inner
312.2.g.a.157.4	yes	8	1.1	even	1	trivial
936.2.g.d.469.5		8	3.2	odd	2
936.2.g.d.469.6		8	24.5	odd	2
1248.2.g.a.625.1		8	8.3	odd	2
1248.2.g.a.625.8		8	4.3	odd	2
3744.2.g.d.1873.2		8	12.11	even	2
3744.2.g.d.1873.7		8	24.11	even	2
9984.2.a.s.1.4		4	16.3	odd	4
9984.2.a.y.1.1		4	16.5	even	4
9984.2.a.bb.1.4		4	16.13	even	4
9984.2.a.bh.1.1		4	16.11	odd	4

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221232 + 1.39680i) q^{2} -1.00000i q^{3} +(-1.90211 + 0.618034i) q^{4} +2.52015i q^{5} +(1.39680 - 0.221232i) q^{6} +2.79360 q^{7} +(-1.28408 - 2.52015i) q^{8} -1.00000 q^{9} +(-3.52015 + 0.557537i) q^{10} +5.31375i q^{11} +(0.618034 + 1.90211i) q^{12} -1.00000i q^{13} +(0.618034 + 3.90211i) q^{14} +2.52015 q^{15} +(3.23607 - 2.35114i) q^{16} -4.35114 q^{17} +(-0.221232 - 1.39680i) q^{18} +6.02967i q^{19} +(-1.55754 - 4.79360i) q^{20} -2.79360i q^{21} +(-7.42226 + 1.17557i) q^{22} +0.568158 q^{23} +(-2.52015 + 1.28408i) q^{24} -1.35114 q^{25} +(1.39680 - 0.221232i) q^{26} +1.00000i q^{27} +(-5.31375 + 1.72654i) q^{28} +2.68915i q^{29} +(0.557537 + 3.52015i) q^{30} +1.90868 q^{31} +(4.00000 + 4.00000i) q^{32} +5.31375 q^{33} +(-0.962611 - 6.07768i) q^{34} +7.04029i q^{35} +(1.90211 - 0.618034i) q^{36} -9.60845i q^{37} +(-8.42226 + 1.33395i) q^{38} -1.00000 q^{39} +(6.35114 - 3.23607i) q^{40} +11.2093 q^{41} +(3.90211 - 0.618034i) q^{42} -9.48746i q^{43} +(-3.28408 - 10.1074i) q^{44} -2.52015i q^{45} +(0.125695 + 0.793604i) q^{46} +3.95669 q^{47} +(-2.35114 - 3.23607i) q^{48} +0.804226 q^{49} +(-0.298915 - 1.88728i) q^{50} +4.35114i q^{51} +(0.618034 + 1.90211i) q^{52} -8.05934i q^{53} +(-1.39680 + 0.221232i) q^{54} -13.3914 q^{55} +(-3.58721 - 7.04029i) q^{56} +6.02967 q^{57} +(-3.75621 + 0.594926i) q^{58} -6.19868i q^{59} +(-4.79360 + 1.55754i) q^{60} -7.23607i q^{61} +(0.422260 + 2.66605i) q^{62} -2.79360 q^{63} +(-4.70228 + 6.47214i) q^{64} +2.52015 q^{65} +(1.17557 + 7.42226i) q^{66} +10.0297i q^{67} +(8.27636 - 2.68915i) q^{68} -0.568158i q^{69} +(-9.83390 + 1.55754i) q^{70} -1.63052 q^{71} +(1.28408 + 2.52015i) q^{72} -5.17442 q^{73} +(13.4211 - 2.12569i) q^{74} +1.35114i q^{75} +(-3.72654 - 11.4691i) q^{76} +14.8445i q^{77} +(-0.221232 - 1.39680i) q^{78} +9.17442 q^{79} +(5.92522 + 8.15537i) q^{80} +1.00000 q^{81} +(2.47985 + 15.6572i) q^{82} -4.61147i q^{83} +(1.72654 + 5.31375i) q^{84} -10.9655i q^{85} +(13.2521 - 2.09893i) q^{86} +2.68915 q^{87} +(13.3914 - 6.82328i) q^{88} +11.4182 q^{89} +(3.52015 - 0.557537i) q^{90} -2.79360i q^{91} +(-1.08070 + 0.351141i) q^{92} -1.90868i q^{93} +(0.875345 + 5.52671i) q^{94} -15.1957 q^{95} +(4.00000 - 4.00000i) q^{96} -10.2514 q^{97} +(0.177920 + 1.12334i) q^{98} -5.31375i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{6} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{10} - 4 q^{12} - 4 q^{14} - 4 q^{15} + 8 q^{16} - 16 q^{17} - 2 q^{18} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 4 q^{24} + 8 q^{25} + 2 q^{26} + 4 q^{30}+ \cdots - 6 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^6 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^10 - 4 * q^12 - 4 * q^14 - 4 * q^15 + 8 * q^16 - 16 * q^17 - 2 * q^18 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 4 * q^24 + 8 * q^25 + 2 * q^26 + 4 * q^30 - 4 * q^31 + 32 * q^32 + 16 * q^34 - 28 * q^38 - 8 * q^39 + 32 * q^40 + 36 * q^41 + 16 * q^42 - 20 * q^44 - 12 * q^46 + 24 * q^47 - 24 * q^49 + 22 * q^50 - 4 * q^52 - 2 * q^54 - 40 * q^55 + 8 * q^56 + 12 * q^57 + 12 * q^58 - 20 * q^60 - 36 * q^62 - 4 * q^63 - 4 * q^65 - 12 * q^70 + 16 * q^71 + 4 * q^72 + 32 * q^73 + 4 * q^74 - 24 * q^76 - 2 * q^78 + 8 * q^81 + 44 * q^82 + 8 * q^84 + 8 * q^86 - 8 * q^87 + 40 * q^88 + 60 * q^89 + 4 * q^90 - 40 * q^92 - 44 * q^94 - 24 * q^95 + 32 * q^96 - 56 * q^97 - 6 * q^98

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