LMFDB - Embedded newform 1470.2.m.f.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 $ x^16 - 32x^13 + 2x^12 + 352x^10 - 288x^9 + 2x^8 - 1440x^7 + 8800x^6 + 1250x^4 - 100000*x^3 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.8
Root			$-1.07534 + 1.96052i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.f.1273.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.22280 + 0.243230i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.22280 + 0.243230i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.39977 + 1.74375i) q^{10} -5.33525 q^{11} +(0.707107 - 0.707107i) q^{12} +(3.82733 + 3.82733i) q^{13} +(-1.39977 - 1.74375i) q^{15} -1.00000 q^{16} +(-5.19896 + 5.19896i) q^{17} +(-0.707107 + 0.707107i) q^{18} -3.04189 q^{19} +(-0.243230 + 2.22280i) q^{20} +(-3.77259 - 3.77259i) q^{22} +(-1.63559 + 1.63559i) q^{23} +1.00000 q^{24} +(4.88168 + 1.08130i) q^{25} +5.41266i q^{26} +(0.707107 - 0.707107i) q^{27} -4.97911i q^{29} +(0.243230 - 2.22280i) q^{30} +6.37678i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.77259 + 3.77259i) q^{33} -7.35245 q^{34} -1.00000 q^{36} +(2.11124 + 2.11124i) q^{37} +(-2.15094 - 2.15094i) q^{38} -5.41266i q^{39} +(-1.74375 + 1.39977i) q^{40} +10.4281i q^{41} +(1.27961 - 1.27961i) q^{43} -5.33525i q^{44} +(-0.243230 + 2.22280i) q^{45} -2.31307 q^{46} +(8.75513 - 8.75513i) q^{47} +(0.707107 + 0.707107i) q^{48} +(2.68727 + 4.21646i) q^{50} +7.35245 q^{51} +(-3.82733 + 3.82733i) q^{52} +(-4.91277 + 4.91277i) q^{53} +1.00000 q^{54} +(-11.8592 - 1.29769i) q^{55} +(2.15094 + 2.15094i) q^{57} +(3.52077 - 3.52077i) q^{58} +6.15893 q^{59} +(1.74375 - 1.39977i) q^{60} -0.777764i q^{61} +(-4.50907 + 4.50907i) q^{62} -1.00000i q^{64} +(7.57646 + 9.43831i) q^{65} +5.33525i q^{66} +(-5.72162 - 5.72162i) q^{67} +(-5.19896 - 5.19896i) q^{68} +2.31307 q^{69} -5.85378 q^{71} +(-0.707107 - 0.707107i) q^{72} +(5.03959 + 5.03959i) q^{73} +2.98575i q^{74} +(-2.68727 - 4.21646i) q^{75} -3.04189i q^{76} +(3.82733 - 3.82733i) q^{78} +11.3463i q^{79} +(-2.22280 - 0.243230i) q^{80} -1.00000 q^{81} +(-7.37381 + 7.37381i) q^{82} +(2.41890 + 2.41890i) q^{83} +(-12.8208 + 10.2917i) q^{85} +1.80964 q^{86} +(-3.52077 + 3.52077i) q^{87} +(3.77259 - 3.77259i) q^{88} +3.19810 q^{89} +(-1.74375 + 1.39977i) q^{90} +(-1.63559 - 1.63559i) q^{92} +(4.50907 - 4.50907i) q^{93} +12.3816 q^{94} +(-6.76152 - 0.739880i) q^{95} +1.00000i q^{96} +(-4.72414 + 4.72414i) q^{97} -5.33525i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5}+O(q^{10}) $ 16 * q + 8 * q^5	$ 16 q + 8 q^{5} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 48 q^{19} - 8 q^{22} - 8 q^{23} + 16 q^{24} + 8 q^{25} + 8 q^{33} - 16 q^{36} + 8 q^{37} - 8 q^{38} + 16 q^{47} - 8 q^{52} + 8 q^{53} + 16 q^{54} + 8 q^{57} + 24 q^{58} + 48 q^{59} - 8 q^{62} + 72 q^{65} - 48 q^{67} - 8 q^{68} + 16 q^{73} + 8 q^{78} - 8 q^{80} - 16 q^{81} - 16 q^{82} - 72 q^{85} - 24 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{92} + 8 q^{93} + 64 q^{94} + 48 q^{95} - 64 q^{97}+O(q^{100}) $ 16 * q + 8 * q^5 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 48 * q^19 - 8 * q^22 - 8 * q^23 + 16 * q^24 + 8 * q^25 + 8 * q^33 - 16 * q^36 + 8 * q^37 - 8 * q^38 + 16 * q^47 - 8 * q^52 + 8 * q^53 + 16 * q^54 + 8 * q^57 + 24 * q^58 + 48 * q^59 - 8 * q^62 + 72 * q^65 - 48 * q^67 - 8 * q^68 + 16 * q^73 + 8 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 72 * q^85 - 24 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^92 + 8 * q^93 + 64 * q^94 + 48 * q^95 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.22280	+	0.243230i	0.994066	+	0.108776i
$5$	2.22280	+	0.243230i	0.994066	+	0.108776i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	1.39977	+	1.74375i	0.442645	+	0.551421i
$11$	−5.33525			−1.60864			−0.804319	−	0.594197i	$-0.797470\pi$
$11$	−5.33525			−1.60864			−0.804319	+	0.594197i	$0.797470\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	3.82733	+	3.82733i	1.06151	+	1.06151i	0.997980	+	0.0635301i	$0.0202359\pi$
$13$	3.82733	+	3.82733i	1.06151	+	1.06151i	0.0635301	+	0.997980i	$0.479764\pi$
$14$		0			0
$15$	−1.39977	−	1.74375i	−0.361418	−	0.450233i
$16$	−1.00000			−0.250000
$17$	−5.19896	+	5.19896i	−1.26093	+	1.26093i	−0.310293	+	0.950641i	$0.600427\pi$
$17$	−5.19896	+	5.19896i	−1.26093	+	1.26093i	−0.950641	+	0.310293i	$0.899573\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−3.04189			−0.697858			−0.348929	−	0.937149i	$-0.613455\pi$
$19$	−3.04189			−0.697858			−0.348929	+	0.937149i	$0.613455\pi$
$20$	−0.243230	+	2.22280i	−0.0543879	+	0.497033i
$21$		0			0
$22$	−3.77259	−	3.77259i	−0.804319	−	0.804319i
$23$	−1.63559	+	1.63559i	−0.341044	+	0.341044i	−0.856760	−	0.515716i	$-0.827526\pi$
$23$	−1.63559	+	1.63559i	−0.341044	+	0.341044i	0.515716	+	0.856760i	$0.327526\pi$
$24$	1.00000			0.204124
$25$	4.88168	+	1.08130i	0.976336	+	0.216261i
$26$			5.41266i			1.06151i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	4.97911i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$29$		−	4.97911i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$30$	0.243230	−	2.22280i	0.0444075	−	0.405826i
$31$			6.37678i			1.14530i	0.819799	+	0.572652i	$0.194085\pi$
$31$			6.37678i			1.14530i	−0.819799	+	0.572652i	$0.805915\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	3.77259	+	3.77259i	0.656724	+	0.656724i
$34$	−7.35245			−1.26093
$35$		0			0
$36$	−1.00000			−0.166667
$37$	2.11124	+	2.11124i	0.347086	+	0.347086i	0.859023	−	0.511937i	$-0.171072\pi$
$37$	2.11124	+	2.11124i	0.347086	+	0.347086i	−0.511937	+	0.859023i	$0.671072\pi$
$38$	−2.15094	−	2.15094i	−0.348929	−	0.348929i
$39$		−	5.41266i		−	0.866719i
$40$	−1.74375	+	1.39977i	−0.275711	+	0.221323i
$41$			10.4281i			1.62860i	0.580442	+	0.814301i	$0.302880\pi$
$41$			10.4281i			1.62860i	−0.580442	+	0.814301i	$0.697120\pi$
$42$		0			0
$43$	1.27961	−	1.27961i	0.195139	−	0.195139i	−0.602774	−	0.797912i	$-0.705938\pi$
$43$	1.27961	−	1.27961i	0.195139	−	0.195139i	0.797912	+	0.602774i	$0.205938\pi$
$44$		−	5.33525i		−	0.804319i
$45$	−0.243230	+	2.22280i	−0.0362586	+	0.331355i
$46$	−2.31307			−0.341044
$47$	8.75513	−	8.75513i	1.27707	−	1.27707i	0.334766	−	0.942301i	$-0.391343\pi$
$47$	8.75513	−	8.75513i	1.27707	−	1.27707i	0.942301	−	0.334766i	$-0.108657\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		0			0
$50$	2.68727	+	4.21646i	0.380038	+	0.596298i
$51$	7.35245			1.02955
$52$	−3.82733	+	3.82733i	−0.530755	+	0.530755i
$53$	−4.91277	+	4.91277i	−0.674820	+	0.674820i	−0.958823	−	0.284003i	$-0.908337\pi$
$53$	−4.91277	+	4.91277i	−0.674820	+	0.674820i	0.284003	+	0.958823i	$0.408337\pi$
$54$	1.00000			0.136083
$55$	−11.8592	−	1.29769i	−1.59909	−	0.174981i
$56$		0			0
$57$	2.15094	+	2.15094i	0.284899	+	0.284899i
$58$	3.52077	−	3.52077i	0.462299	−	0.462299i
$59$	6.15893			0.801824			0.400912	−	0.916117i	$-0.368693\pi$
$59$	6.15893			0.801824			0.400912	+	0.916117i	$0.368693\pi$
$60$	1.74375	−	1.39977i	0.225117	−	0.180709i
$61$		−	0.777764i		−	0.0995824i	−0.998760	−	0.0497912i	$-0.984144\pi$
$61$		−	0.777764i		−	0.0995824i	0.998760	−	0.0497912i	$-0.0158556\pi$
$62$	−4.50907	+	4.50907i	−0.572652	+	0.572652i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	7.57646	+	9.43831i	0.939745	+	1.17068i
$66$			5.33525i			0.656724i
$67$	−5.72162	−	5.72162i	−0.699007	−	0.699007i	0.265189	−	0.964196i	$-0.414566\pi$
$67$	−5.72162	−	5.72162i	−0.699007	−	0.699007i	−0.964196	+	0.265189i	$0.914566\pi$
$68$	−5.19896	−	5.19896i	−0.630467	−	0.630467i
$69$	2.31307			0.278461
$70$		0			0
$71$	−5.85378			−0.694715			−0.347358	−	0.937733i	$-0.612921\pi$
$71$	−5.85378			−0.694715			−0.347358	+	0.937733i	$0.612921\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	5.03959	+	5.03959i	0.589840	+	0.589840i	0.937588	−	0.347748i	$-0.113054\pi$
$73$	5.03959	+	5.03959i	0.589840	+	0.589840i	−0.347748	+	0.937588i	$0.613054\pi$
$74$			2.98575i			0.347086i
$75$	−2.68727	−	4.21646i	−0.310299	−	0.486875i
$76$		−	3.04189i		−	0.348929i
$77$		0			0
$78$	3.82733	−	3.82733i	0.433360	−	0.433360i
$79$			11.3463i			1.27656i	0.769805	+	0.638279i	$0.220353\pi$
$79$			11.3463i			1.27656i	−0.769805	+	0.638279i	$0.779647\pi$
$80$	−2.22280	−	0.243230i	−0.248517	−	0.0271939i
$81$	−1.00000			−0.111111
$82$	−7.37381	+	7.37381i	−0.814301	+	0.814301i
$83$	2.41890	+	2.41890i	0.265509	+	0.265509i	0.827288	−	0.561779i	$-0.189883\pi$
$83$	2.41890	+	2.41890i	0.265509	+	0.265509i	−0.561779	+	0.827288i	$0.689883\pi$
$84$		0			0
$85$	−12.8208	+	10.2917i	−1.39061	+	1.11629i
$86$	1.80964			0.195139
$87$	−3.52077	+	3.52077i	−0.377466	+	0.377466i
$88$	3.77259	−	3.77259i	0.402160	−	0.402160i
$89$	3.19810			0.338998			0.169499	−	0.985530i	$-0.445785\pi$
$89$	3.19810			0.338998			0.169499	+	0.985530i	$0.445785\pi$
$90$	−1.74375	+	1.39977i	−0.183807	+	0.147548i
$91$		0			0
$92$	−1.63559	−	1.63559i	−0.170522	−	0.170522i
$93$	4.50907	−	4.50907i	0.467568	−	0.467568i
$94$	12.3816			1.27707
$95$	−6.76152	−	0.739880i	−0.693717	−	0.0759101i
$96$			1.00000i			0.102062i
$97$	−4.72414	+	4.72414i	−0.479664	+	0.479664i	−0.905024	−	0.425360i	$-0.860147\pi$
$97$	−4.72414	+	4.72414i	−0.479664	+	0.479664i	0.425360	+	0.905024i	$0.360147\pi$
$98$		0			0
$99$		−	5.33525i		−	0.536213i
$100$	−1.08130	+	4.88168i	−0.108130	+	0.488168i
$101$		−	10.2204i		−	1.01697i	−0.861072	−	0.508483i	$-0.830206\pi$
$101$		−	10.2204i		−	1.01697i	0.861072	−	0.508483i	$-0.169794\pi$
$102$	5.19896	+	5.19896i	0.514774	+	0.514774i
$103$	0.809817	+	0.809817i	0.0797936	+	0.0797936i	0.745877	−	0.666084i	$-0.232031\pi$
$103$	0.809817	+	0.809817i	0.0797936	+	0.0797936i	−0.666084	+	0.745877i	$0.732031\pi$
$104$	−5.41266			−0.530755
$105$		0			0
$106$	−6.94770			−0.674820
$107$	−10.1474	−	10.1474i	−0.980991	−	0.980991i	0.0188320	−	0.999823i	$-0.494005\pi$
$107$	−10.1474	−	10.1474i	−0.980991	−	0.980991i	−0.999823	+	0.0188320i	$0.994005\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	2.97059i		−	0.284531i	−0.989829	−	0.142265i	$-0.954561\pi$
$109$		−	2.97059i		−	0.284531i	0.989829	−	0.142265i	$-0.0454386\pi$
$110$	−7.46811	−	9.30333i	−0.712056	−	0.887037i
$111$		−	2.98575i		−	0.283395i
$112$		0			0
$113$	5.14988	−	5.14988i	0.484460	−	0.484460i	−0.422093	−	0.906553i	$-0.638704\pi$
$113$	5.14988	−	5.14988i	0.484460	−	0.484460i	0.906553	+	0.422093i	$0.138704\pi$
$114$			3.04189i			0.284899i
$115$	−4.03342	+	3.23777i	−0.376118	+	0.301923i
$116$	4.97911			0.462299
$117$	−3.82733	+	3.82733i	−0.353837	+	0.353837i
$118$	4.35502	+	4.35502i	0.400912	+	0.400912i
$119$		0			0
$120$	2.22280	+	0.243230i	0.202913	+	0.0222038i
$121$	17.4649			1.58772
$122$	0.549962	−	0.549962i	0.0497912	−	0.0497912i
$123$	7.37381	−	7.37381i	0.664874	−	0.664874i
$124$	−6.37678			−0.572652
$125$	10.5880	+	3.59089i	0.947018	+	0.321179i
$126$		0			0
$127$	−1.20668	−	1.20668i	−0.107075	−	0.107075i	0.651539	−	0.758615i	$-0.274124\pi$
$127$	−1.20668	−	1.20668i	−0.107075	−	0.107075i	−0.758615	+	0.651539i	$0.774124\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−1.80964			−0.159330
$130$	−1.31652	+	12.0313i	−0.115467	+	1.05521i
$131$			19.4185i			1.69660i	0.529516	+	0.848300i	$0.322374\pi$
$131$			19.4185i			1.69660i	−0.529516	+	0.848300i	$0.677626\pi$
$132$	−3.77259	+	3.77259i	−0.328362	+	0.328362i
$133$		0			0
$134$		−	8.09159i		−	0.699007i
$135$	1.74375	−	1.39977i	0.150078	−	0.120473i
$136$		−	7.35245i		−	0.630467i
$137$	−7.80852	−	7.80852i	−0.667127	−	0.667127i	0.289923	−	0.957050i	$-0.406370\pi$
$137$	−7.80852	−	7.80852i	−0.667127	−	0.667127i	−0.957050	+	0.289923i	$0.906370\pi$
$138$	1.63559	+	1.63559i	0.139231	+	0.139231i
$139$	11.7913			1.00013			0.500064	−	0.865989i	$-0.333310\pi$
$139$	11.7913			1.00013			0.500064	+	0.865989i	$0.333310\pi$
$140$		0			0
$141$	−12.3816			−1.04272
$142$	−4.13924	−	4.13924i	−0.347358	−	0.347358i
$143$	−20.4198	−	20.4198i	−1.70759	−	1.70759i
$144$		−	1.00000i		−	0.0833333i
$145$	1.21107	−	11.0676i	0.100574	−	0.919112i
$146$			7.12706i			0.589840i
$147$		0			0
$148$	−2.11124	+	2.11124i	−0.173543	+	0.173543i
$149$			21.3443i			1.74860i	0.485390	+	0.874298i	$0.338678\pi$
$149$			21.3443i			1.74860i	−0.485390	+	0.874298i	$0.661322\pi$
$150$	1.08130	−	4.88168i	0.0882880	−	0.398587i
$151$	6.89343			0.560980			0.280490	−	0.959857i	$-0.409503\pi$
$151$	6.89343			0.560980			0.280490	+	0.959857i	$0.409503\pi$
$152$	2.15094	−	2.15094i	0.174465	−	0.174465i
$153$	−5.19896	−	5.19896i	−0.420311	−	0.420311i
$154$		0			0
$155$	−1.55103	+	14.1743i	−0.124581	+	1.13851i
$156$	5.41266			0.433360
$157$	−5.07142	+	5.07142i	−0.404744	+	0.404744i	−0.879901	−	0.475157i	$-0.842391\pi$
$157$	−5.07142	+	5.07142i	−0.404744	+	0.404744i	0.475157	+	0.879901i	$0.342391\pi$
$158$	−8.02304	+	8.02304i	−0.638279	+	0.638279i
$159$	6.94770			0.550988
$160$	−1.39977	−	1.74375i	−0.110661	−	0.137855i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−3.30725	+	3.30725i	−0.259044	+	0.259044i	−0.824665	−	0.565621i	$-0.808636\pi$
$163$	−3.30725	+	3.30725i	−0.259044	+	0.259044i	0.565621	+	0.824665i	$0.308636\pi$
$164$	−10.4281			−0.814301
$165$	7.46811	+	9.30333i	0.581392	+	0.724263i
$166$			3.42085i			0.265509i
$167$	−5.19936	+	5.19936i	−0.402338	+	0.402338i	−0.879056	−	0.476718i	$-0.841826\pi$
$167$	−5.19936	+	5.19936i	−0.402338	+	0.402338i	0.476718	+	0.879056i	$0.341826\pi$
$168$		0			0
$169$			16.2969i			1.25361i
$170$	−16.3430	−	1.78834i	−1.25345	−	0.137159i
$171$		−	3.04189i		−	0.232619i
$172$	1.27961	+	1.27961i	0.0975693	+	0.0975693i
$173$	−9.04482	−	9.04482i	−0.687665	−	0.687665i	0.274050	−	0.961715i	$-0.411637\pi$
$173$	−9.04482	−	9.04482i	−0.687665	−	0.687665i	−0.961715	+	0.274050i	$0.911637\pi$
$174$	−4.97911			−0.377466
$175$		0			0
$176$	5.33525			0.402160
$177$	−4.35502	−	4.35502i	−0.327343	−	0.327343i
$178$	2.26140	+	2.26140i	0.169499	+	0.169499i
$179$			9.80725i			0.733028i	0.930412	+	0.366514i	$0.119449\pi$
$179$			9.80725i			0.733028i	−0.930412	+	0.366514i	$0.880551\pi$
$180$	−2.22280	−	0.243230i	−0.165678	−	0.0181293i
$181$		−	14.3346i		−	1.06548i	−0.846278	−	0.532741i	$-0.821162\pi$
$181$		−	14.3346i		−	1.06548i	0.846278	−	0.532741i	$-0.178838\pi$
$182$		0			0
$183$	−0.549962	+	0.549962i	−0.0406544	+	0.0406544i
$184$		−	2.31307i		−	0.170522i
$185$	4.17935	+	5.20639i	0.307272	+	0.382781i
$186$	6.37678			0.467568
$187$	27.7378	−	27.7378i	2.02839	−	2.02839i
$188$	8.75513	+	8.75513i	0.638534	+	0.638534i
$189$		0			0
$190$	−4.25794	−	5.30429i	−0.308904	−	0.384814i
$191$	−6.50768			−0.470879			−0.235439	−	0.971889i	$-0.575653\pi$
$191$	−6.50768			−0.470879			−0.235439	+	0.971889i	$0.575653\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	16.0866	−	16.0866i	1.15794	−	1.15794i	0.173019	−	0.984919i	$-0.444648\pi$
$193$	16.0866	−	16.0866i	1.15794	−	1.15794i	0.984919	−	0.173019i	$-0.0553521\pi$
$194$	−6.68094			−0.479664
$195$	1.31652	−	12.0313i	0.0942781	−	0.861576i
$196$		0			0
$197$	−8.52204	−	8.52204i	−0.607170	−	0.607170i	0.335035	−	0.942206i	$-0.391252\pi$
$197$	−8.52204	−	8.52204i	−0.607170	−	0.607170i	−0.942206	+	0.335035i	$0.891252\pi$
$198$	3.77259	−	3.77259i	0.268106	−	0.268106i
$199$	5.68230			0.402808			0.201404	−	0.979508i	$-0.435450\pi$
$199$	5.68230			0.402808			0.201404	+	0.979508i	$0.435450\pi$
$200$	−4.21646	+	2.68727i	−0.298149	+	0.190019i
$201$			8.09159i			0.570737i
$202$	7.22690	−	7.22690i	0.508483	−	0.508483i
$203$		0			0
$204$			7.35245i			0.514774i
$205$	−2.53644	+	23.1797i	−0.177153	+	1.61894i
$206$			1.14525i			0.0797936i
$207$	−1.63559	−	1.63559i	−0.113681	−	0.113681i
$208$	−3.82733	−	3.82733i	−0.265378	−	0.265378i
$209$	16.2293			1.12260
$210$		0			0
$211$	27.9905			1.92695			0.963474	−	0.267803i	$-0.0862978\pi$
$211$	27.9905			1.92695			0.963474	+	0.267803i	$0.0862978\pi$
$212$	−4.91277	−	4.91277i	−0.337410	−	0.337410i
$213$	4.13924	+	4.13924i	0.283616	+	0.283616i
$214$		−	14.3507i		−	0.980991i
$215$	3.15555	−	2.53308i	0.215207	−	0.172754i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	2.10052	−	2.10052i	0.142265	−	0.142265i
$219$		−	7.12706i		−	0.481602i
$220$	1.29769	−	11.8592i	0.0874905	−	0.799547i
$221$	−39.7963			−2.67699
$222$	2.11124	−	2.11124i	0.141697	−	0.141697i
$223$	−0.994508	−	0.994508i	−0.0665972	−	0.0665972i	0.673024	−	0.739621i	$-0.264995\pi$
$223$	−0.994508	−	0.994508i	−0.0665972	−	0.0665972i	−0.739621	+	0.673024i	$0.764995\pi$
$224$		0			0
$225$	−1.08130	+	4.88168i	−0.0720869	+	0.325445i
$226$	7.28303			0.484460
$227$	11.7968	−	11.7968i	0.782980	−	0.782980i	−0.197352	−	0.980333i	$-0.563234\pi$
$227$	11.7968	−	11.7968i	0.782980	−	0.782980i	0.980333	+	0.197352i	$0.0632343\pi$
$228$	−2.15094	+	2.15094i	−0.142450	+	0.142450i
$229$	−0.535959			−0.0354172			−0.0177086	−	0.999843i	$-0.505637\pi$
$229$	−0.535959			−0.0354172			−0.0177086	+	0.999843i	$0.505637\pi$
$230$	−5.14150	−	0.562609i	−0.339021	−	0.0370973i
$231$		0			0
$232$	3.52077	+	3.52077i	0.231150	+	0.231150i
$233$	15.3761	−	15.3761i	1.00732	−	1.00732i	0.00734582	−	0.999973i	$-0.497662\pi$
$233$	15.3761	−	15.3761i	1.00732	−	1.00732i	0.999973	−	0.00734582i	$-0.00233827\pi$
$234$	−5.41266			−0.353837
$235$	21.5904	−	17.3314i	1.40840	−	1.13058i
$236$			6.15893i			0.400912i
$237$	8.02304	−	8.02304i	0.521153	−	0.521153i
$238$		0			0
$239$		−	3.25205i		−	0.210357i	−0.994453	−	0.105179i	$-0.966459\pi$
$239$		−	3.25205i		−	0.210357i	0.994453	−	0.105179i	$-0.0335415\pi$
$240$	1.39977	+	1.74375i	0.0903546	+	0.112558i
$241$		−	13.7283i		−	0.884316i	−0.896937	−	0.442158i	$-0.854213\pi$
$241$		−	13.7283i		−	0.884316i	0.896937	−	0.442158i	$-0.145787\pi$
$242$	12.3496	+	12.3496i	0.793860	+	0.793860i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	0.777764			0.0497912
$245$		0			0
$246$	10.4281			0.664874
$247$	−11.6423	−	11.6423i	−0.740783	−	0.740783i
$248$	−4.50907	−	4.50907i	−0.286326	−	0.286326i
$249$		−	3.42085i		−	0.216787i
$250$	4.94769	+	10.0260i	0.312920	+	0.634099i
$251$		−	10.6569i		−	0.672656i	−0.941745	−	0.336328i	$-0.890815\pi$
$251$		−	10.6569i		−	0.672656i	0.941745	−	0.336328i	$-0.109185\pi$
$252$		0			0
$253$	8.72629	−	8.72629i	0.548617	−	0.548617i
$254$		−	1.70650i		−	0.107075i
$255$	16.3430	+	1.78834i	1.02344	+	0.111990i
$256$	1.00000			0.0625000
$257$	−1.53556	+	1.53556i	−0.0957858	+	0.0957858i	−0.753376	−	0.657590i	$-0.771576\pi$
$257$	−1.53556	+	1.53556i	−0.0957858	+	0.0957858i	0.657590	+	0.753376i	$0.271576\pi$
$258$	−1.27961	−	1.27961i	−0.0796650	−	0.0796650i
$259$		0			0
$260$	−9.43831	+	7.57646i	−0.585339	+	0.469872i
$261$	4.97911			0.308199
$262$	−13.7309	+	13.7309i	−0.848300	+	0.848300i
$263$	13.9959	−	13.9959i	0.863025	−	0.863025i	−0.128664	−	0.991688i	$-0.541069\pi$
$263$	13.9959	−	13.9959i	0.863025	−	0.863025i	0.991688	+	0.128664i	$0.0410687\pi$
$264$	−5.33525			−0.328362
$265$	−12.1150	+	9.72516i	−0.744220	+	0.597412i
$266$		0			0
$267$	−2.26140	−	2.26140i	−0.138395	−	0.138395i
$268$	5.72162	−	5.72162i	0.349504	−	0.349504i
$269$	11.6671			0.711353			0.355677	−	0.934609i	$-0.384250\pi$
$269$	11.6671			0.711353			0.355677	+	0.934609i	$0.384250\pi$
$270$	2.22280	+	0.243230i	0.135275	+	0.0148025i
$271$			11.2204i			0.681588i	0.940138	+	0.340794i	$0.110696\pi$
$271$			11.2204i			0.681588i	−0.940138	+	0.340794i	$0.889304\pi$
$272$	5.19896	−	5.19896i	0.315234	−	0.315234i
$273$		0			0
$274$		−	11.0429i		−	0.667127i
$275$	−26.0450	−	5.76903i	−1.57057	−	0.347885i
$276$			2.31307i			0.139231i
$277$	14.5443	+	14.5443i	0.873881	+	0.873881i	0.992893	−	0.119012i	$-0.0379726\pi$
$277$	14.5443	+	14.5443i	0.873881	+	0.873881i	−0.119012	+	0.992893i	$0.537973\pi$
$278$	8.33773	+	8.33773i	0.500064	+	0.500064i
$279$	−6.37678			−0.381768
$280$		0			0
$281$	0.810507			0.0483508			0.0241754	−	0.999708i	$-0.492304\pi$
$281$	0.810507			0.0483508			0.0241754	+	0.999708i	$0.492304\pi$
$282$	−8.75513	−	8.75513i	−0.521361	−	0.521361i
$283$	2.35075	+	2.35075i	0.139738	+	0.139738i	0.773515	−	0.633778i	$-0.218497\pi$
$283$	2.35075	+	2.35075i	0.139738	+	0.139738i	−0.633778	+	0.773515i	$0.718497\pi$
$284$		−	5.85378i		−	0.347358i
$285$	4.25794	+	5.30429i	0.252219	+	0.314199i
$286$		−	28.8779i		−	1.70759i
$287$		0			0
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$		−	37.0585i		−	2.17991i
$290$	8.68231	−	6.96960i	0.509843	−	0.409269i
$291$	6.68094			0.391644
$292$	−5.03959	+	5.03959i	−0.294920	+	0.294920i
$293$	5.05031	+	5.05031i	0.295042	+	0.295042i	0.839068	−	0.544026i	$-0.183101\pi$
$293$	5.05031	+	5.05031i	0.295042	+	0.295042i	−0.544026	+	0.839068i	$0.683101\pi$
$294$		0			0
$295$	13.6901	+	1.49804i	0.797066	+	0.0872190i
$296$	−2.98575			−0.173543
$297$	−3.77259	+	3.77259i	−0.218908	+	0.218908i
$298$	−15.0927	+	15.0927i	−0.874298	+	0.874298i
$299$	−12.5199			−0.724044
$300$	4.21646	−	2.68727i	0.243438	−	0.155150i
$301$		0			0
$302$	4.87439	+	4.87439i	0.280490	+	0.280490i
$303$	−7.22690	+	7.22690i	−0.415175	+	0.415175i
$304$	3.04189			0.174465
$305$	0.189175	−	1.72881i	0.0108322	−	0.0989916i
$306$		−	7.35245i		−	0.420311i
$307$	19.1533	−	19.1533i	1.09314	−	1.09314i	0.0979470	−	0.995192i	$-0.468772\pi$
$307$	19.1533	−	19.1533i	1.09314	−	1.09314i	0.995192	−	0.0979470i	$-0.0312276\pi$
$308$		0			0
$309$		−	1.14525i		−	0.0651512i
$310$	−11.1195	+	8.92601i	−0.631545	+	0.506963i
$311$		−	16.8569i		−	0.955868i	−0.878396	−	0.477934i	$-0.841386\pi$
$311$		−	16.8569i		−	0.955868i	0.878396	−	0.477934i	$-0.158614\pi$
$312$	3.82733	+	3.82733i	0.216680	+	0.216680i
$313$	19.5236	+	19.5236i	1.10354	+	1.10354i	0.993980	+	0.109558i	$0.0349436\pi$
$313$	19.5236	+	19.5236i	1.10354	+	1.10354i	0.109558	+	0.993980i	$0.465056\pi$
$314$	−7.17208			−0.404744
$315$		0			0
$316$	−11.3463			−0.638279
$317$	−20.6732	−	20.6732i	−1.16112	−	1.16112i	−0.984230	−	0.176892i	$-0.943396\pi$
$317$	−20.6732	−	20.6732i	−1.16112	−	1.16112i	−0.176892	−	0.984230i	$-0.556604\pi$
$318$	4.91277	+	4.91277i	0.275494	+	0.275494i
$319$			26.5648i			1.48735i
$320$	0.243230	−	2.22280i	0.0135970	−	0.124258i
$321$			14.3507i			0.800976i
$322$		0			0
$323$	15.8147	−	15.8147i	0.879953	−	0.879953i
$324$		−	1.00000i		−	0.0555556i
$325$	14.5453	+	22.8223i	0.806827	+	1.26595i
$326$	−4.67716			−0.259044
$327$	−2.10052	+	2.10052i	−0.116159	+	0.116159i
$328$	−7.37381	−	7.37381i	−0.407151	−	0.407151i
$329$		0			0
$330$	−1.29769	+	11.8592i	−0.0714357	+	0.652827i
$331$	−18.3302			−1.00752			−0.503759	−	0.863844i	$-0.668050\pi$
$331$	−18.3302			−1.00752			−0.503759	+	0.863844i	$0.668050\pi$
$332$	−2.41890	+	2.41890i	−0.132755	+	0.132755i
$333$	−2.11124	+	2.11124i	−0.115695	+	0.115695i
$334$	−7.35300			−0.402338
$335$	−11.3263	−	14.1097i	−0.618824	−	0.770894i
$336$		0			0
$337$	11.8410	+	11.8410i	0.645021	+	0.645021i	0.951785	−	0.306765i	$-0.0992465\pi$
$337$	11.8410	+	11.8410i	0.645021	+	0.645021i	−0.306765	+	0.951785i	$0.599246\pi$
$338$	−11.5236	+	11.5236i	−0.626804	+	0.626804i
$339$	−7.28303			−0.395560
$340$	−10.2917	−	12.8208i	−0.558146	−	0.695306i
$341$		−	34.0217i		−	1.84238i
$342$	2.15094	−	2.15094i	0.116310	−	0.116310i
$343$		0			0
$344$			1.80964i			0.0975693i
$345$	5.14150	+	0.562609i	0.276809	+	0.0302899i
$346$		−	12.7913i		−	0.687665i
$347$	3.71384	+	3.71384i	0.199370	+	0.199370i	0.799730	−	0.600360i	$-0.204976\pi$
$347$	3.71384	+	3.71384i	0.199370	+	0.199370i	−0.600360	+	0.799730i	$0.704976\pi$
$348$	−3.52077	−	3.52077i	−0.188733	−	0.188733i
$349$	−0.367827			−0.0196893			−0.00984466	−	0.999952i	$-0.503134\pi$
$349$	−0.367827			−0.0196893			−0.00984466	+	0.999952i	$0.503134\pi$
$350$		0			0
$351$	5.41266			0.288906
$352$	3.77259	+	3.77259i	0.201080	+	0.201080i
$353$	−19.3859	−	19.3859i	−1.03181	−	1.03181i	−0.999477	−	0.0323299i	$-0.989707\pi$
$353$	−19.3859	−	19.3859i	−1.03181	−	1.03181i	−0.0323299	−	0.999477i	$-0.510293\pi$
$354$		−	6.15893i		−	0.327343i
$355$	−13.0118	−	1.42381i	−0.690593	−	0.0755682i
$356$			3.19810i			0.169499i
$357$		0			0
$358$	−6.93477	+	6.93477i	−0.366514	+	0.366514i
$359$			32.5796i			1.71948i	0.510728	+	0.859742i	$0.329376\pi$
$359$			32.5796i			1.71948i	−0.510728	+	0.859742i	$0.670624\pi$
$360$	−1.39977	−	1.74375i	−0.0737742	−	0.0919035i
$361$	−9.74689			−0.512994
$362$	10.1361	−	10.1361i	0.532741	−	0.532741i
$363$	−12.3496	−	12.3496i	−0.648184	−	0.648184i
$364$		0			0
$365$	9.97623	+	12.4278i	0.522180	+	0.650500i
$366$	−0.777764			−0.0406544
$367$	−11.4724	+	11.4724i	−0.598852	+	0.598852i	−0.940007	−	0.341155i	$-0.889182\pi$
$367$	−11.4724	+	11.4724i	−0.598852	+	0.598852i	0.341155	+	0.940007i	$0.389182\pi$
$368$	1.63559	−	1.63559i	0.0852611	−	0.0852611i
$369$	−10.4281			−0.542868
$370$	−0.726223	+	6.63672i	−0.0377546	+	0.345027i
$371$		0			0
$372$	4.50907	+	4.50907i	0.233784	+	0.233784i
$373$	27.2609	−	27.2609i	1.41151	−	1.41151i	0.662093	−	0.749422i	$-0.269668\pi$
$373$	27.2609	−	27.2609i	1.41151	−	1.41151i	0.749422	−	0.662093i	$-0.230332\pi$
$374$	39.2272			2.02839
$375$	−4.94769	−	10.0260i	−0.255498	−	0.517739i
$376$			12.3816i			0.638534i
$377$	19.0567	−	19.0567i	0.981471	−	0.981471i
$378$		0			0
$379$			9.65378i			0.495881i	0.968775	+	0.247941i	$0.0797538\pi$
$379$			9.65378i			0.495881i	−0.968775	+	0.247941i	$0.920246\pi$
$380$	0.739880	−	6.76152i	0.0379550	−	0.346859i
$381$			1.70650i			0.0874266i
$382$	−4.60162	−	4.60162i	−0.235439	−	0.235439i
$383$	6.93385	+	6.93385i	0.354303	+	0.354303i	0.861708	−	0.507405i	$-0.169395\pi$
$383$	6.93385	+	6.93385i	0.354303	+	0.354303i	−0.507405	+	0.861708i	$0.669395\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	22.7499			1.15794
$387$	1.27961	+	1.27961i	0.0650462	+	0.0650462i
$388$	−4.72414	−	4.72414i	−0.239832	−	0.239832i
$389$			4.84222i			0.245510i	0.992437	+	0.122755i	$0.0391730\pi$
$389$			4.84222i			0.245510i	−0.992437	+	0.122755i	$0.960827\pi$
$390$	9.43831	−	7.57646i	0.477927	−	0.383649i
$391$		−	17.0068i		−	0.860069i
$392$		0			0
$393$	13.7309	−	13.7309i	0.692634	−	0.692634i
$394$		−	12.0520i		−	0.607170i
$395$	−2.75976	+	25.2206i	−0.138859	+	1.26898i
$396$	5.33525			0.268106
$397$	0.741854	−	0.741854i	0.0372326	−	0.0372326i	−0.688245	−	0.725478i	$-0.741619\pi$
$397$	0.741854	−	0.741854i	0.0372326	−	0.0372326i	0.725478	+	0.688245i	$0.241619\pi$
$398$	4.01799	+	4.01799i	0.201404	+	0.201404i
$399$		0			0
$400$	−4.88168	−	1.08130i	−0.244084	−	0.0540652i
$401$	8.86775			0.442834			0.221417	−	0.975179i	$-0.428932\pi$
$401$	8.86775			0.442834			0.221417	+	0.975179i	$0.428932\pi$
$402$	−5.72162	+	5.72162i	−0.285368	+	0.285368i
$403$	−24.4060	+	24.4060i	−1.21575	+	1.21575i
$404$	10.2204			0.508483
$405$	−2.22280	−	0.243230i	−0.110452	−	0.0120862i
$406$		0			0
$407$	−11.2640	−	11.2640i	−0.558336	−	0.558336i
$408$	−5.19896	+	5.19896i	−0.257387	+	0.257387i
$409$	2.81754			0.139318			0.0696592	−	0.997571i	$-0.477809\pi$
$409$	2.81754			0.139318			0.0696592	+	0.997571i	$0.477809\pi$
$410$	−18.1840	+	14.5970i	−0.898046	+	0.720893i
$411$			11.0429i			0.544707i
$412$	−0.809817	+	0.809817i	−0.0398968	+	0.0398968i
$413$		0			0
$414$		−	2.31307i		−	0.113681i
$415$	4.78839	+	5.96509i	0.235053	+	0.292815i
$416$		−	5.41266i		−	0.265378i
$417$	−8.33773	−	8.33773i	−0.408300	−	0.408300i
$418$	11.4758	+	11.4758i	0.561301	+	0.561301i
$419$	14.8943			0.727633			0.363817	−	0.931471i	$-0.381473\pi$
$419$	14.8943			0.727633			0.363817	+	0.931471i	$0.381473\pi$
$420$		0			0
$421$	9.95472			0.485163			0.242582	−	0.970131i	$-0.422006\pi$
$421$	9.95472			0.485163			0.242582	+	0.970131i	$0.422006\pi$
$422$	19.7923	+	19.7923i	0.963474	+	0.963474i
$423$	8.75513	+	8.75513i	0.425689	+	0.425689i
$424$		−	6.94770i		−	0.337410i
$425$	−31.0013	+	19.7580i	−1.50379	+	0.958404i
$426$			5.85378i			0.283616i
$427$		0			0
$428$	10.1474	−	10.1474i	0.490495	−	0.490495i
$429$			28.8779i			1.39424i
$430$	4.02247	+	0.440159i	0.193981	+	0.0212263i
$431$	−9.34070			−0.449926			−0.224963	−	0.974367i	$-0.572226\pi$
$431$	−9.34070			−0.449926			−0.224963	+	0.974367i	$0.572226\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	13.5192	+	13.5192i	0.649693	+	0.649693i	0.952919	−	0.303226i	$-0.0980636\pi$
$433$	13.5192	+	13.5192i	0.649693	+	0.649693i	−0.303226	+	0.952919i	$0.598064\pi$
$434$		0			0
$435$	−8.68231	+	6.96960i	−0.416285	+	0.334167i
$436$	2.97059			0.142265
$437$	4.97529	−	4.97529i	0.238000	−	0.238000i
$438$	5.03959	−	5.03959i	0.240801	−	0.240801i
$439$	−29.1942			−1.39337			−0.696683	−	0.717380i	$-0.745341\pi$
$439$	−29.1942			−1.39337			−0.696683	+	0.717380i	$0.745341\pi$
$440$	9.30333	−	7.46811i	0.443519	−	0.356028i
$441$		0			0
$442$	−28.1402	−	28.1402i	−1.33849	−	1.33849i
$443$	−18.2503	+	18.2503i	−0.867098	+	0.867098i	−0.992150	−	0.125052i	$-0.960090\pi$
$443$	−18.2503	+	18.2503i	−0.867098	+	0.867098i	0.125052	+	0.992150i	$0.460090\pi$
$444$	2.98575			0.141697
$445$	7.10874	+	0.777874i	0.336986	+	0.0368748i
$446$		−	1.40645i		−	0.0665972i
$447$	15.0927	−	15.0927i	0.713861	−	0.713861i
$448$		0			0
$449$			28.0929i			1.32579i	0.748714	+	0.662893i	$0.230672\pi$
$449$			28.0929i			1.32579i	−0.748714	+	0.662893i	$0.769328\pi$
$450$	−4.21646	+	2.68727i	−0.198766	+	0.126679i
$451$		−	55.6368i		−	2.61983i
$452$	5.14988	+	5.14988i	0.242230	+	0.242230i
$453$	−4.87439	−	4.87439i	−0.229019	−	0.229019i
$454$	16.6832			0.782980
$455$		0			0
$456$	−3.04189			−0.142450
$457$	−13.0173	−	13.0173i	−0.608922	−	0.608922i	0.333742	−	0.942664i	$-0.391688\pi$
$457$	−13.0173	−	13.0173i	−0.608922	−	0.608922i	−0.942664	+	0.333742i	$0.891688\pi$
$458$	−0.378980	−	0.378980i	−0.0177086	−	0.0177086i
$459$			7.35245i			0.343183i
$460$	−3.23777	−	4.03342i	−0.150962	−	0.188059i
$461$			33.1391i			1.54344i	0.635962	+	0.771720i	$0.280604\pi$
$461$			33.1391i			1.54344i	−0.635962	+	0.771720i	$0.719396\pi$
$462$		0			0
$463$	11.6083	−	11.6083i	0.539484	−	0.539484i	−0.383893	−	0.923377i	$-0.625417\pi$
$463$	11.6083	−	11.6083i	0.539484	−	0.539484i	0.923377	+	0.383893i	$0.125417\pi$
$464$			4.97911i			0.231150i
$465$	11.1195	−	8.92601i	0.515654	−	0.413934i
$466$	21.7450			1.00732
$467$	−17.7072	+	17.7072i	−0.819394	+	0.819394i	−0.986020	−	0.166626i	$-0.946713\pi$
$467$	−17.7072	+	17.7072i	−0.819394	+	0.819394i	0.166626	+	0.986020i	$0.446713\pi$
$468$	−3.82733	−	3.82733i	−0.176918	−	0.176918i
$469$		0			0
$470$	27.5219	+	3.01158i	1.26949	+	0.138914i
$471$	7.17208			0.330472
$472$	−4.35502	+	4.35502i	−0.200456	+	0.200456i
$473$	−6.82704	+	6.82704i	−0.313907	+	0.313907i
$474$	11.3463			0.521153
$475$	−14.8495	−	3.28921i	−0.681344	−	0.150919i
$476$		0			0
$477$	−4.91277	−	4.91277i	−0.224940	−	0.224940i
$478$	2.29954	−	2.29954i	0.105179	−	0.105179i
$479$	−22.1797			−1.01341			−0.506707	−	0.862118i	$-0.669137\pi$
$479$	−22.1797			−1.01341			−0.506707	+	0.862118i	$0.669137\pi$
$480$	−0.243230	+	2.22280i	−0.0111019	+	0.101456i
$481$			16.1608i			0.736871i
$482$	9.70736	−	9.70736i	0.442158	−	0.442158i
$483$		0			0
$484$			17.4649i			0.793860i
$485$	−11.6499	+	9.35176i	−0.528993	+	0.424642i
$486$			1.00000i			0.0453609i
$487$	8.53994	+	8.53994i	0.386982	+	0.386982i	0.873609	−	0.486628i	$-0.161773\pi$
$487$	8.53994	+	8.53994i	0.386982	+	0.386982i	−0.486628	+	0.873609i	$0.661773\pi$
$488$	0.549962	+	0.549962i	0.0248956	+	0.0248956i
$489$	4.67716			0.211508
$490$		0			0
$491$	14.4241			0.650953			0.325476	−	0.945550i	$-0.394475\pi$
$491$	14.4241			0.650953			0.325476	+	0.945550i	$0.394475\pi$
$492$	7.37381	+	7.37381i	0.332437	+	0.332437i
$493$	25.8862	+	25.8862i	1.16586	+	1.16586i
$494$		−	16.4647i		−	0.740783i
$495$	1.29769	−	11.8592i	0.0583270	−	0.533031i
$496$		−	6.37678i		−	0.286326i
$497$		0			0
$498$	2.41890	−	2.41890i	0.108394	−	0.108394i
$499$			26.3989i			1.18178i	0.806753	+	0.590889i	$0.201223\pi$
$499$			26.3989i			1.18178i	−0.806753	+	0.590889i	$0.798777\pi$
$500$	−3.59089	+	10.5880i	−0.160590	+	0.473509i
$501$	7.35300			0.328508
$502$	7.53555	−	7.53555i	0.336328	−	0.336328i
$503$	−28.1311	−	28.1311i	−1.25430	−	1.25430i	−0.953773	−	0.300529i	$-0.902837\pi$
$503$	−28.1311	−	28.1311i	−1.25430	−	1.25430i	−0.300529	−	0.953773i	$-0.597163\pi$
$504$		0			0
$505$	2.48590	−	22.7179i	0.110621	−	1.01093i
$506$	12.3408			0.548617
$507$	11.5236	−	11.5236i	0.511783	−	0.511783i
$508$	1.20668	−	1.20668i	0.0535377	−	0.0535377i
$509$	25.6304			1.13605			0.568024	−	0.823012i	$-0.307708\pi$
$509$	25.6304			1.13605			0.568024	+	0.823012i	$0.307708\pi$
$510$	10.2917	+	12.8208i	0.455725	+	0.567715i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.15094	+	2.15094i	−0.0949665	+	0.0949665i
$514$	−2.17162			−0.0957858
$515$	1.60309	+	1.99703i	0.0706405	+	0.0879998i
$516$		−	1.80964i		−	0.0796650i
$517$	−46.7108	+	46.7108i	−2.05434	+	2.05434i
$518$		0			0
$519$			12.7913i			0.561476i
$520$	−12.0313	−	1.31652i	−0.527606	−	0.0577333i
$521$			24.5533i			1.07570i	0.843041	+	0.537849i	$0.180763\pi$
$521$			24.5533i			1.07570i	−0.843041	+	0.537849i	$0.819237\pi$
$522$	3.52077	+	3.52077i	0.154100	+	0.154100i
$523$	2.18151	+	2.18151i	0.0953909	+	0.0953909i	0.753192	−	0.657801i	$-0.228513\pi$
$523$	2.18151	+	2.18151i	0.0953909	+	0.0953909i	−0.657801	+	0.753192i	$0.728513\pi$
$524$	−19.4185			−0.848300
$525$		0			0
$526$	19.7932			0.863025
$527$	−33.1527	−	33.1527i	−1.44415	−	1.44415i
$528$	−3.77259	−	3.77259i	−0.164181	−	0.164181i
$529$			17.6497i			0.767378i
$530$	−15.4433	−	1.68989i	−0.670816	−	0.0734041i
$531$			6.15893i			0.267275i
$532$		0			0
$533$	−39.9119	+	39.9119i	−1.72878	+	1.72878i
$534$		−	3.19810i		−	0.138395i
$535$	−20.0876	−	25.0239i	−0.868462	−	1.08188i
$536$	8.09159			0.349504
$537$	6.93477	−	6.93477i	0.299258	−	0.299258i
$538$	8.24986	+	8.24986i	0.355677	+	0.355677i
$539$		0			0
$540$	1.39977	+	1.74375i	0.0602364	+	0.0750389i
$541$	−32.9933			−1.41849			−0.709247	−	0.704961i	$-0.750965\pi$
$541$	−32.9933			−1.41849			−0.709247	+	0.704961i	$0.750965\pi$
$542$	−7.93399	+	7.93399i	−0.340794	+	0.340794i
$543$	−10.1361	+	10.1361i	−0.434981	+	0.434981i
$544$	7.35245			0.315234
$545$	0.722536	−	6.60302i	0.0309500	−	0.282842i
$546$		0			0
$547$	−3.66749	−	3.66749i	−0.156811	−	0.156811i	0.624341	−	0.781152i	$-0.285368\pi$
$547$	−3.66749	−	3.66749i	−0.156811	−	0.156811i	−0.781152	+	0.624341i	$0.785368\pi$
$548$	7.80852	−	7.80852i	0.333563	−	0.333563i
$549$	0.777764			0.0331941
$550$	−14.3373	−	22.4959i	−0.611343	−	0.959228i
$551$			15.1459i			0.645239i
$552$	−1.63559	+	1.63559i	−0.0696154	+	0.0696154i
$553$		0			0
$554$			20.5687i			0.873881i
$555$	0.726223	−	6.63672i	0.0308265	−	0.281713i
$556$			11.7913i			0.500064i
$557$	11.5358	+	11.5358i	0.488786	+	0.488786i	0.907923	−	0.419137i	$-0.137667\pi$
$557$	11.5358	+	11.5358i	0.488786	+	0.488786i	−0.419137	+	0.907923i	$0.637667\pi$
$558$	−4.50907	−	4.50907i	−0.190884	−	0.190884i
$559$	9.79497			0.414283
$560$		0			0
$561$	−39.2272			−1.65617
$562$	0.573115	+	0.573115i	0.0241754	+	0.0241754i
$563$	10.8772	+	10.8772i	0.458419	+	0.458419i	0.898136	−	0.439717i	$-0.144921\pi$
$563$	10.8772	+	10.8772i	0.458419	+	0.458419i	−0.439717	+	0.898136i	$0.644921\pi$
$564$		−	12.3816i		−	0.521361i
$565$	12.6998	−	10.1945i	0.534283	−	0.428888i
$566$			3.32447i			0.139738i
$567$		0			0
$568$	4.13924	−	4.13924i	0.173679	−	0.173679i
$569$			3.64304i			0.152724i	0.997080	+	0.0763620i	$0.0243305\pi$
$569$			3.64304i			0.152724i	−0.997080	+	0.0763620i	$0.975670\pi$
$570$	−0.739880	+	6.76152i	−0.0309902	+	0.283209i
$571$	23.8194			0.996810			0.498405	−	0.866944i	$-0.333919\pi$
$571$	23.8194			0.996810			0.498405	+	0.866944i	$0.333919\pi$
$572$	20.4198	−	20.4198i	0.853793	−	0.853793i
$573$	4.60162	+	4.60162i	0.192236	+	0.192236i
$574$		0			0
$575$	−9.75300	+	6.21586i	−0.406728	+	0.259219i
$576$	1.00000			0.0416667
$577$	−7.24788	+	7.24788i	−0.301733	+	0.301733i	−0.841692	−	0.539959i	$-0.818440\pi$
$577$	−7.24788	+	7.24788i	−0.301733	+	0.301733i	0.539959	+	0.841692i	$0.318440\pi$
$578$	26.2043	−	26.2043i	1.08995	−	1.08995i
$579$	−22.7499			−0.945452
$580$	11.0676	+	1.21107i	0.459556	+	0.0502870i
$581$		0			0
$582$	4.72414	+	4.72414i	0.195822	+	0.195822i
$583$	26.2108	−	26.2108i	1.08554	−	1.08554i
$584$	−7.12706			−0.294920
$585$	−9.43831	+	7.57646i	−0.390226	+	0.313248i
$586$			7.14222i			0.295042i
$587$	−11.2912	+	11.2912i	−0.466037	+	0.466037i	−0.900628	−	0.434591i	$-0.856893\pi$
$587$	−11.2912	+	11.2912i	−0.466037	+	0.466037i	0.434591	+	0.900628i	$0.356893\pi$
$588$		0			0
$589$		−	19.3975i		−	0.799260i
$590$	8.62106	+	10.7396i	0.354923	+	0.442142i
$591$			12.0520i			0.495753i
$592$	−2.11124	−	2.11124i	−0.0867715	−	0.0867715i
$593$	3.12947	+	3.12947i	0.128512	+	0.128512i	0.768437	−	0.639925i	$-0.221035\pi$
$593$	3.12947	+	3.12947i	0.128512	+	0.128512i	−0.639925	+	0.768437i	$0.721035\pi$
$594$	−5.33525			−0.218908
$595$		0			0
$596$	−21.3443			−0.874298
$597$	−4.01799	−	4.01799i	−0.164445	−	0.164445i
$598$	−8.85290	−	8.85290i	−0.362022	−	0.362022i
$599$		−	6.34083i		−	0.259079i	−0.991574	−	0.129540i	$-0.958650\pi$
$599$		−	6.34083i		−	0.259079i	0.991574	−	0.129540i	$-0.0413499\pi$
$600$	4.88168	+	1.08130i	0.199294	+	0.0441440i
$601$			44.8871i			1.83098i	0.402338	+	0.915491i	$0.368198\pi$
$601$			44.8871i			1.83098i	−0.402338	+	0.915491i	$0.631802\pi$
$602$		0			0
$603$	5.72162	−	5.72162i	0.233002	−	0.233002i
$604$			6.89343i			0.280490i
$605$	38.8210	+	4.24799i	1.57830	+	0.172705i
$606$	−10.2204			−0.415175
$607$	15.6974	−	15.6974i	0.637139	−	0.637139i	−0.312710	−	0.949849i	$-0.601237\pi$
$607$	15.6974	−	15.6974i	0.637139	−	0.637139i	0.949849	+	0.312710i	$0.101237\pi$
$608$	2.15094	+	2.15094i	0.0872323	+	0.0872323i
$609$		0			0
$610$	1.35622	−	1.08869i	0.0549119	−	0.0440797i
$611$	67.0176			2.71124
$612$	5.19896	−	5.19896i	0.210156	−	0.210156i
$613$	20.9439	−	20.9439i	0.845918	−	0.845918i	−0.143703	−	0.989621i	$-0.545901\pi$
$613$	20.9439	−	20.9439i	0.845918	−	0.845918i	0.989621	+	0.143703i	$0.0459009\pi$
$614$	27.0869			1.09314
$615$	18.1840	−	14.5970i	0.733251	−	0.588607i
$616$		0			0
$617$	−19.6484	−	19.6484i	−0.791014	−	0.791014i	0.190645	−	0.981659i	$-0.438942\pi$
$617$	−19.6484	−	19.6484i	−0.791014	−	0.791014i	−0.981659	+	0.190645i	$0.938942\pi$
$618$	0.809817	−	0.809817i	0.0325756	−	0.0325756i
$619$	−45.4316			−1.82605			−0.913026	−	0.407902i	$-0.866260\pi$
$619$	−45.4316			−1.82605			−0.913026	+	0.407902i	$0.866260\pi$
$620$	−14.1743	−	1.55103i	−0.569254	−	0.0622907i
$621$			2.31307i			0.0928205i
$622$	11.9196	−	11.9196i	0.477934	−	0.477934i
$623$		0			0
$624$			5.41266i			0.216680i
$625$	22.6616	+	10.5571i	0.906463	+	0.422286i
$626$			27.6105i			1.10354i
$627$	−11.4758	−	11.4758i	−0.458300	−	0.458300i
$628$	−5.07142	−	5.07142i	−0.202372	−	0.202372i
$629$	−21.9525			−0.875305
$630$		0			0
$631$	31.1912			1.24170			0.620851	−	0.783928i	$-0.286787\pi$
$631$	31.1912			1.24170			0.620851	+	0.783928i	$0.286787\pi$
$632$	−8.02304	−	8.02304i	−0.319140	−	0.319140i
$633$	−19.7923	−	19.7923i	−0.786673	−	0.786673i
$634$		−	29.2363i		−	1.16112i
$635$	−2.38870	−	2.97570i	−0.0947928	−	0.118087i
$636$			6.94770i			0.275494i
$637$		0			0
$638$	−18.7842	+	18.7842i	−0.743673	+	0.743673i
$639$		−	5.85378i		−	0.231572i
$640$	1.74375	−	1.39977i	0.0689276	−	0.0553307i
$641$	20.2641			0.800383			0.400191	−	0.916432i	$-0.368944\pi$
$641$	20.2641			0.800383			0.400191	+	0.916432i	$0.368944\pi$
$642$	−10.1474	+	10.1474i	−0.400488	+	0.400488i
$643$	2.85809	+	2.85809i	0.112712	+	0.112712i	0.761213	−	0.648501i	$-0.224604\pi$
$643$	2.85809	+	2.85809i	0.112712	+	0.112712i	−0.648501	+	0.761213i	$0.724604\pi$
$644$		0			0
$645$	−4.02247	−	0.440159i	−0.158385	−	0.0173312i
$646$	22.3654			0.879953
$647$	16.7153	−	16.7153i	0.657147	−	0.657147i	−0.297557	−	0.954704i	$-0.596172\pi$
$647$	16.7153	−	16.7153i	0.657147	−	0.657147i	0.954704	+	0.297557i	$0.0961719\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−32.8594			−1.28984
$650$	−5.85273	+	26.4229i	−0.229563	+	1.03639i
$651$		0			0
$652$	−3.30725	−	3.30725i	−0.129522	−	0.129522i
$653$	25.7755	−	25.7755i	1.00867	−	1.00867i	0.00871283	−	0.999962i	$-0.497227\pi$
$653$	25.7755	−	25.7755i	1.00867	−	1.00867i	0.999962	−	0.00871283i	$-0.00277342\pi$
$654$	−2.97059			−0.116159
$655$	−4.72316	+	43.1634i	−0.184549	+	1.68653i
$656$		−	10.4281i		−	0.407151i
$657$	−5.03959	+	5.03959i	−0.196613	+	0.196613i
$658$		0			0
$659$		−	43.0330i		−	1.67633i	−0.545420	−	0.838163i	$-0.683630\pi$
$659$		−	43.0330i		−	1.67633i	0.545420	−	0.838163i	$-0.316370\pi$
$660$	−9.30333	+	7.46811i	−0.362131	+	0.290696i
$661$		−	2.77875i		−	0.108081i	−0.998539	−	0.0540404i	$-0.982790\pi$
$661$		−	2.77875i		−	0.108081i	0.998539	−	0.0540404i	$-0.0172100\pi$
$662$	−12.9614	−	12.9614i	−0.503759	−	0.503759i
$663$	28.1402	+	28.1402i	1.09288	+	1.09288i
$664$	−3.42085			−0.132755
$665$		0			0
$666$	−2.98575			−0.115695
$667$	8.14379	+	8.14379i	0.315329	+	0.315329i
$668$	−5.19936	−	5.19936i	−0.201169	−	0.201169i
$669$			1.40645i			0.0543764i
$670$	1.96812	−	17.9860i	0.0760350	−	0.694859i
$671$			4.14957i			0.160192i
$672$		0			0
$673$	−25.5371	+	25.5371i	−0.984384	+	0.984384i	−0.999880	−	0.0154963i	$-0.995067\pi$
$673$	−25.5371	+	25.5371i	−0.984384	+	0.984384i	0.0154963	+	0.999880i	$0.495067\pi$
$674$			16.7457i			0.645021i
$675$	4.21646	−	2.68727i	0.162292	−	0.103433i
$676$	−16.2969			−0.626804
$677$	13.3443	−	13.3443i	0.512862	−	0.512862i	−0.402540	−	0.915402i	$-0.631873\pi$
$677$	13.3443	−	13.3443i	0.512862	−	0.512862i	0.915402	+	0.402540i	$0.131873\pi$
$678$	−5.14988	−	5.14988i	−0.197780	−	0.197780i
$679$		0			0
$680$	1.78834	−	16.3430i	0.0685795	−	0.626726i
$681$	−16.6832			−0.639301
$682$	24.0570	−	24.0570i	0.921190	−	0.921190i
$683$	20.7449	−	20.7449i	0.793783	−	0.793783i	−0.188324	−	0.982107i	$-0.560305\pi$
$683$	20.7449	−	20.7449i	0.793783	−	0.793783i	0.982107	+	0.188324i	$0.0603055\pi$
$684$	3.04189			0.116310
$685$	−15.4575	−	19.2560i	−0.590601	−	0.735736i
$686$		0			0
$687$	0.378980	+	0.378980i	0.0144590	+	0.0144590i
$688$	−1.27961	+	1.27961i	−0.0487846	+	0.0487846i
$689$	−37.6055			−1.43266
$690$	3.23777	+	4.03342i	0.123260	+	0.153549i
$691$		−	41.1414i		−	1.56509i	−0.622592	−	0.782546i	$-0.713920\pi$
$691$		−	41.1414i		−	1.56509i	0.622592	−	0.782546i	$-0.286080\pi$
$692$	9.04482	−	9.04482i	0.343833	−	0.343833i
$693$		0			0
$694$			5.25217i			0.199370i
$695$	26.2098	+	2.86801i	0.994193	+	0.108790i
$696$		−	4.97911i		−	0.188733i
$697$	−54.2156	−	54.2156i	−2.05356	−	2.05356i
$698$	−0.260093	−	0.260093i	−0.00984466	−	0.00984466i
$699$	−21.7450			−0.822472
$700$		0			0
$701$	−23.4144			−0.884350			−0.442175	−	0.896929i	$-0.645793\pi$
$701$	−23.4144			−0.884350			−0.442175	+	0.896929i	$0.645793\pi$
$702$	3.82733	+	3.82733i	0.144453	+	0.144453i
$703$	−6.42217	−	6.42217i	−0.242217	−	0.242217i
$704$			5.33525i			0.201080i
$705$	−27.5219	−	3.01158i	−1.03653	−	0.113423i
$706$		−	27.4158i		−	1.03181i
$707$		0			0
$708$	4.35502	−	4.35502i	0.163672	−	0.163672i
$709$		−	37.4403i		−	1.40610i	−0.711141	−	0.703049i	$-0.751821\pi$
$709$		−	37.4403i		−	1.40610i	0.711141	−	0.703049i	$-0.248179\pi$
$710$	−8.19392	−	10.2075i	−0.307512	−	0.383081i
$711$	−11.3463			−0.425519
$712$	−2.26140	+	2.26140i	−0.0847495	+	0.0847495i
$713$	−10.4298	−	10.4298i	−0.390599	−	0.390599i
$714$		0			0
$715$	−40.4223	−	50.3557i	−1.51171	−	1.88320i
$716$	−9.80725			−0.366514
$717$	−2.29954	+	2.29954i	−0.0858781	+	0.0858781i
$718$	−23.0372	+	23.0372i	−0.859742	+	0.859742i
$719$	−29.0630			−1.08387			−0.541934	−	0.840421i	$-0.682308\pi$
$719$	−29.0630			−1.08387			−0.541934	+	0.840421i	$0.682308\pi$
$720$	0.243230	−	2.22280i	0.00906465	−	0.0828389i
$721$		0			0
$722$	−6.89209	−	6.89209i	−0.256497	−	0.256497i
$723$	−9.70736	+	9.70736i	−0.361020	+	0.361020i
$724$	14.3346			0.532741
$725$	5.38393	−	24.3064i	0.199954	−	0.902718i
$726$		−	17.4649i		−	0.648184i
$727$	−17.1526	+	17.1526i	−0.636155	+	0.636155i	−0.949605	−	0.313450i	$-0.898515\pi$
$727$	−17.1526	+	17.1526i	−0.636155	+	0.636155i	0.313450	+	0.949605i	$0.398515\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−1.73352	+	15.8420i	−0.0641603	+	0.586340i
$731$			13.3053i			0.492114i
$732$	−0.549962	−	0.549962i	−0.0203272	−	0.0203272i
$733$	2.53448	+	2.53448i	0.0936132	+	0.0936132i	0.752362	−	0.658749i	$-0.228914\pi$
$733$	2.53448	+	2.53448i	0.0936132	+	0.0936132i	−0.658749	+	0.752362i	$0.728914\pi$
$734$	−16.2244			−0.598852
$735$		0			0
$736$	2.31307			0.0852611
$737$	30.5263	+	30.5263i	1.12445	+	1.12445i
$738$	−7.37381	−	7.37381i	−0.271434	−	0.271434i
$739$		−	5.57298i		−	0.205006i	−0.994733	−	0.102503i	$-0.967315\pi$
$739$		−	5.57298i		−	0.205006i	0.994733	−	0.102503i	$-0.0326851\pi$
$740$	−5.20639	+	4.17935i	−0.191391	+	0.153636i
$741$			16.4647i			0.604847i
$742$		0			0
$743$	5.16576	−	5.16576i	0.189513	−	0.189513i	−0.605972	−	0.795486i	$-0.707216\pi$
$743$	5.16576	−	5.16576i	0.189513	−	0.189513i	0.795486	+	0.605972i	$0.207216\pi$
$744$			6.37678i			0.233784i
$745$	−5.19158	+	47.4442i	−0.190205	+	1.73822i
$746$	38.5527			1.41151
$747$	−2.41890	+	2.41890i	−0.0885031	+	0.0885031i
$748$	27.7378	+	27.7378i	1.01419	+	1.01419i
$749$		0			0
$750$	3.59089	−	10.5880i	0.131121	−	0.386619i
$751$	−27.2758			−0.995308			−0.497654	−	0.867376i	$-0.665805\pi$
$751$	−27.2758			−0.995308			−0.497654	+	0.867376i	$0.665805\pi$
$752$	−8.75513	+	8.75513i	−0.319267	+	0.319267i
$753$	−7.53555	+	7.53555i	−0.274611	+	0.274611i
$754$	26.9503			0.981471
$755$	15.3227	+	1.67669i	0.557651	+	0.0610210i
$756$		0			0
$757$	−27.6453	−	27.6453i	−1.00479	−	1.00479i	−0.999988	−	0.00479880i	$-0.998472\pi$
$757$	−27.6453	−	27.6453i	−1.00479	−	1.00479i	−0.00479880	−	0.999988i	$-0.501528\pi$
$758$	−6.82625	+	6.82625i	−0.247941	+	0.247941i
$759$	−12.3408			−0.447944
$760$	5.30429	−	4.25794i	0.192407	−	0.154452i
$761$			1.08093i			0.0391837i	0.999808	+	0.0195919i	$0.00623668\pi$
$761$			1.08093i			0.0391837i	−0.999808	+	0.0195919i	$0.993763\pi$
$762$	−1.20668	+	1.20668i	−0.0437133	+	0.0437133i
$763$		0			0
$764$		−	6.50768i		−	0.235439i
$765$	−10.2917	−	12.8208i	−0.372098	−	0.463537i
$766$			9.80594i			0.354303i
$767$	23.5722	+	23.5722i	0.851144	+	0.851144i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	20.8561			0.752092			0.376046	−	0.926601i	$-0.377283\pi$
$769$	20.8561			0.752092			0.376046	+	0.926601i	$0.377283\pi$
$770$		0			0
$771$	2.17162			0.0782088
$772$	16.0866	+	16.0866i	0.578969	+	0.578969i
$773$	4.97179	+	4.97179i	0.178823	+	0.178823i	0.790842	−	0.612020i	$-0.209643\pi$
$773$	4.97179	+	4.97179i	0.178823	+	0.178823i	−0.612020	+	0.790842i	$0.709643\pi$
$774$			1.80964i			0.0650462i
$775$	−6.89524	+	31.1294i	−0.247684	+	1.11820i
$776$		−	6.68094i		−	0.239832i
$777$		0			0
$778$	−3.42397	+	3.42397i	−0.122755	+	0.122755i
$779$		−	31.7213i		−	1.13653i
$780$	12.0313	+	1.31652i	0.430788	+	0.0471390i
$781$	31.2314			1.11755
$782$	12.0256	−	12.0256i	0.430034	−	0.430034i
$783$	−3.52077	−	3.52077i	−0.125822	−	0.125822i
$784$		0			0
$785$	−12.5063	+	10.0392i	−0.446368	+	0.358316i
$786$	19.4185			0.692634
$787$	−28.5800	+	28.5800i	−1.01877	+	1.01877i	−0.0189465	+	0.999820i	$0.506031\pi$
$787$	−28.5800	+	28.5800i	−1.01877	+	1.01877i	−0.999820	+	0.0189465i	$0.993969\pi$
$788$	8.52204	−	8.52204i	0.303585	−	0.303585i
$789$	−19.7932			−0.704657
$790$	−19.7851	+	15.8822i	−0.703921	+	0.565062i
$791$		0			0
$792$	3.77259	+	3.77259i	0.134053	+	0.134053i
$793$	2.97676	−	2.97676i	0.105708	−	0.105708i
$794$	1.04914			0.0372326
$795$	15.4433	+	1.68989i	0.547719	+	0.0599342i
$796$			5.68230i			0.201404i
$797$	−38.2383	+	38.2383i	−1.35447	+	1.35447i	−0.473881	+	0.880589i	$0.657147\pi$
$797$	−38.2383	+	38.2383i	−1.35447	+	1.35447i	−0.880589	+	0.473881i	$0.842853\pi$
$798$		0			0
$799$			91.0353i			3.22060i
$800$	−2.68727	−	4.21646i	−0.0950094	−	0.149075i
$801$			3.19810i			0.112999i
$802$	6.27044	+	6.27044i	0.221417	+	0.221417i
$803$	−26.8875	−	26.8875i	−0.948839	−	0.948839i
$804$	−8.09159			−0.285368
$805$		0			0
$806$	−34.5154			−1.21575
$807$	−8.24986	−	8.24986i	−0.290409	−	0.290409i
$808$	7.22690	+	7.22690i	0.254241	+	0.254241i
$809$			51.5137i			1.81113i	0.424212	+	0.905563i	$0.360551\pi$
$809$			51.5137i			1.81113i	−0.424212	+	0.905563i	$0.639449\pi$
$810$	−1.39977	−	1.74375i	−0.0491828	−	0.0612690i
$811$			23.8786i			0.838490i	0.907873	+	0.419245i	$0.137705\pi$
$811$			23.8786i			0.838490i	−0.907873	+	0.419245i	$0.862295\pi$
$812$		0			0
$813$	7.93399	−	7.93399i	0.278257	−	0.278257i
$814$		−	15.9297i		−	0.558336i
$815$	−8.15578	+	6.54693i	−0.285684	+	0.229329i
$816$	−7.35245			−0.257387
$817$	−3.89243	+	3.89243i	−0.136179	+	0.136179i
$818$	1.99230	+	1.99230i	0.0696592	+	0.0696592i
$819$		0			0
$820$	−23.1797	−	2.53644i	−0.809470	−	0.0885763i
$821$	12.9714			0.452703			0.226352	−	0.974046i	$-0.427320\pi$
$821$	12.9714			0.452703			0.226352	+	0.974046i	$0.427320\pi$
$822$	−7.80852	+	7.80852i	−0.272353	+	0.272353i
$823$	−21.6334	+	21.6334i	−0.754092	+	0.754092i	−0.975240	−	0.221148i	$-0.929019\pi$
$823$	−21.6334	+	21.6334i	−0.754092	+	0.754092i	0.221148	+	0.975240i	$0.429019\pi$
$824$	−1.14525			−0.0398968
$825$	14.3373	+	22.4959i	0.499160	+	0.783207i
$826$		0			0
$827$	8.17418	+	8.17418i	0.284244	+	0.284244i	0.834799	−	0.550555i	$-0.185584\pi$
$827$	8.17418	+	8.17418i	0.284244	+	0.284244i	−0.550555	+	0.834799i	$0.685584\pi$
$828$	1.63559	−	1.63559i	0.0568407	−	0.0568407i
$829$	33.1649			1.15186			0.575932	−	0.817497i	$-0.304639\pi$
$829$	33.1649			1.15186			0.575932	+	0.817497i	$0.304639\pi$
$830$	−0.832052	+	7.60386i	−0.0288810	+	0.263934i
$831$		−	20.5687i		−	0.713521i
$832$	3.82733	−	3.82733i	0.132689	−	0.132689i
$833$		0			0
$834$		−	11.7913i		−	0.408300i
$835$	−12.8218	+	10.2925i	−0.443715	+	0.356186i
$836$			16.2293i			0.561301i
$837$	4.50907	+	4.50907i	0.155856	+	0.155856i
$838$	10.5318	+	10.5318i	0.363817	+	0.363817i
$839$	−31.4195			−1.08472			−0.542360	−	0.840146i	$-0.682469\pi$
$839$	−31.4195			−1.08472			−0.542360	+	0.840146i	$0.682469\pi$
$840$		0			0
$841$	4.20841			0.145118
$842$	7.03905	+	7.03905i	0.242582	+	0.242582i
$843$	−0.573115	−	0.573115i	−0.0197391	−	0.0197391i
$844$			27.9905i			0.963474i
$845$	−3.96389	+	36.2247i	−0.136362	+	1.24617i
$846$			12.3816i			0.425689i
$847$		0			0
$848$	4.91277	−	4.91277i	0.168705	−	0.168705i
$849$		−	3.32447i		−	0.114095i
$850$	−35.8923	−	7.95022i	−1.23109	−	0.272690i
$851$	−6.90626			−0.236743
$852$	−4.13924	+	4.13924i	−0.141808	+	0.141808i
$853$	14.5233	+	14.5233i	0.497267	+	0.497267i	0.910586	−	0.413319i	$-0.135631\pi$
$853$	14.5233	+	14.5233i	0.497267	+	0.497267i	−0.413319	+	0.910586i	$0.635631\pi$
$854$		0			0
$855$	0.739880	−	6.76152i	0.0253034	−	0.231239i
$856$	14.3507			0.490495
$857$	−8.27080	+	8.27080i	−0.282525	+	0.282525i	−0.834115	−	0.551590i	$-0.814021\pi$
$857$	−8.27080	+	8.27080i	−0.282525	+	0.282525i	0.551590	+	0.834115i	$0.314021\pi$
$858$	−20.4198	+	20.4198i	−0.697119	+	0.697119i
$859$	36.0902			1.23138			0.615691	−	0.787988i	$-0.288877\pi$
$859$	36.0902			1.23138			0.615691	+	0.787988i	$0.288877\pi$
$860$	2.53308	+	3.15555i	0.0863772	+	0.107604i
$861$		0			0
$862$	−6.60487	−	6.60487i	−0.224963	−	0.224963i
$863$	−3.80716	+	3.80716i	−0.129597	+	0.129597i	−0.768930	−	0.639333i	$-0.779211\pi$
$863$	−3.80716	+	3.80716i	−0.129597	+	0.129597i	0.639333	+	0.768930i	$0.279211\pi$
$864$	−1.00000			−0.0340207
$865$	−17.9049	−	22.3048i	−0.608783	−	0.758386i
$866$			19.1191i			0.649693i
$867$	−26.2043	+	26.2043i	−0.889944	+	0.889944i
$868$		0			0
$869$		−	60.5354i		−	2.05352i
$870$	−11.0676	−	1.21107i	−0.375226	−	0.0410591i
$871$		−	43.7970i		−	1.48401i
$872$	2.10052	+	2.10052i	0.0711327	+	0.0711327i
$873$	−4.72414	−	4.72414i	−0.159888	−	0.159888i
$874$	7.03613			0.238000
$875$		0			0
$876$	7.12706			0.240801
$877$	21.5744	+	21.5744i	0.728515	+	0.728515i	0.970324	−	0.241809i	$-0.0777407\pi$
$877$	21.5744	+	21.5744i	0.728515	+	0.728515i	−0.241809	+	0.970324i	$0.577741\pi$
$878$	−20.6434	−	20.6434i	−0.696683	−	0.696683i
$879$		−	7.14222i		−	0.240901i
$880$	11.8592	+	1.29769i	0.399773	+	0.0437452i
$881$			3.63544i			0.122481i	0.998123	+	0.0612405i	$0.0195057\pi$
$881$			3.63544i			0.122481i	−0.998123	+	0.0612405i	$0.980494\pi$
$882$		0			0
$883$	−6.17107	+	6.17107i	−0.207673	+	0.207673i	−0.803278	−	0.595605i	$-0.796913\pi$
$883$	−6.17107	+	6.17107i	−0.207673	+	0.207673i	0.595605	+	0.803278i	$0.296913\pi$
$884$		−	39.7963i		−	1.33849i
$885$	−8.62106	−	10.7396i	−0.289794	−	0.361008i
$886$	−25.8098			−0.867098
$887$	−8.29549	+	8.29549i	−0.278535	+	0.278535i	−0.832524	−	0.553989i	$-0.813105\pi$
$887$	−8.29549	+	8.29549i	−0.278535	+	0.278535i	0.553989	+	0.832524i	$0.313105\pi$
$888$	2.11124	+	2.11124i	0.0708487	+	0.0708487i
$889$		0			0
$890$	4.47660	+	5.57668i	0.150056	+	0.186931i
$891$	5.33525			0.178738
$892$	0.994508	−	0.994508i	0.0332986	−	0.0332986i
$893$	−26.6322	+	26.6322i	−0.891212	+	0.891212i
$894$	21.3443			0.713861
$895$	−2.38542	+	21.7996i	−0.0797357	+	0.728679i
$896$		0			0
$897$	8.85290	+	8.85290i	0.295590	+	0.295590i
$898$	−19.8647	+	19.8647i	−0.662893	+	0.662893i
$899$	31.7507			1.05895
$900$	−4.88168	−	1.08130i	−0.162723	−	0.0360434i
$901$		−	51.0826i		−	1.70181i
$902$	39.3411	−	39.3411i	1.30992	−	1.30992i
$903$		0			0
$904$			7.28303i			0.242230i
$905$	3.48660	−	31.8629i	0.115899	−	1.05916i
$906$		−	6.89343i		−	0.229019i
$907$	−4.22039	−	4.22039i	−0.140136	−	0.140136i	0.633559	−	0.773695i	$-0.281593\pi$
$907$	−4.22039	−	4.22039i	−0.140136	−	0.140136i	−0.773695	+	0.633559i	$0.781593\pi$
$908$	11.7968	+	11.7968i	0.391490	+	0.391490i
$909$	10.2204			0.338989
$910$		0			0
$911$	35.5780			1.17875			0.589376	−	0.807859i	$-0.299374\pi$
$911$	35.5780			1.17875			0.589376	+	0.807859i	$0.299374\pi$
$912$	−2.15094	−	2.15094i	−0.0712248	−	0.0712248i
$913$	−12.9055	−	12.9055i	−0.427108	−	0.427108i
$914$		−	18.4092i		−	0.608922i
$915$	−1.35622	+	1.08869i	−0.0448353	+	0.0359909i
$916$		−	0.535959i		−	0.0177086i
$917$		0			0
$918$	−5.19896	+	5.19896i	−0.171591	+	0.171591i
$919$			44.3793i			1.46394i	0.681338	+	0.731968i	$0.261398\pi$
$919$			44.3793i			1.46394i	−0.681338	+	0.731968i	$0.738602\pi$
$920$	0.562609	−	5.14150i	0.0185487	−	0.169510i
$921$	−27.0869			−0.892544
$922$	−23.4329	+	23.4329i	−0.771720	+	0.771720i
$923$	−22.4043	−	22.4043i	−0.737447	−	0.737447i
$924$		0			0
$925$	8.02351	+	12.5893i	0.263811	+	0.413934i
$926$	16.4166			0.539484
$927$	−0.809817	+	0.809817i	−0.0265979	+	0.0265979i
$928$	−3.52077	+	3.52077i	−0.115575	+	0.115575i
$929$	9.12123			0.299258			0.149629	−	0.988742i	$-0.452192\pi$
$929$	9.12123			0.299258			0.149629	+	0.988742i	$0.452192\pi$
$930$	14.1743	+	1.55103i	0.464794	+	0.0508601i
$931$		0			0
$932$	15.3761	+	15.3761i	0.503659	+	0.503659i
$933$	−11.9196	+	11.9196i	−0.390232	+	0.390232i
$934$	−25.0418			−0.819394
$935$	68.4022	−	54.9089i	2.23699	−	1.79571i
$936$		−	5.41266i		−	0.176918i
$937$	20.3769	−	20.3769i	0.665686	−	0.665686i	−0.291028	−	0.956714i	$-0.593997\pi$
$937$	20.3769	−	20.3769i	0.665686	−	0.665686i	0.956714	+	0.291028i	$0.0939974\pi$
$938$		0			0
$939$		−	27.6105i		−	0.901035i
$940$	17.3314	+	21.5904i	0.565288	+	0.704202i
$941$			36.1182i			1.17742i	0.808345	+	0.588709i	$0.200364\pi$
$941$			36.1182i			1.17742i	−0.808345	+	0.588709i	$0.799636\pi$
$942$	5.07142	+	5.07142i	0.165236	+	0.165236i
$943$	−17.0562	−	17.0562i	−0.555426	−	0.555426i
$944$	−6.15893			−0.200456
$945$		0			0
$946$	−9.65489			−0.313907
$947$	8.15755	+	8.15755i	0.265085	+	0.265085i	0.827116	−	0.562031i	$-0.189980\pi$
$947$	8.15755	+	8.15755i	0.265085	+	0.265085i	−0.562031	+	0.827116i	$0.689980\pi$
$948$	8.02304	+	8.02304i	0.260576	+	0.260576i
$949$			38.5764i			1.25224i
$950$	−8.17439	−	12.8260i	−0.265212	−	0.416132i
$951$			29.2363i			0.948053i
$952$		0			0
$953$	10.8236	−	10.8236i	0.350610	−	0.350610i	−0.509727	−	0.860336i	$-0.670254\pi$
$953$	10.8236	−	10.8236i	0.350610	−	0.350610i	0.860336	+	0.509727i	$0.170254\pi$
$954$		−	6.94770i		−	0.224940i
$955$	−14.4653	−	1.58286i	−0.468085	−	0.0512202i
$956$	3.25205			0.105179
$957$	18.7842	−	18.7842i	0.607206	−	0.607206i
$958$	−15.6834	−	15.6834i	−0.506707	−	0.506707i
$959$		0			0
$960$	−1.74375	+	1.39977i	−0.0562792	+	0.0451773i
$961$	−9.66337			−0.311722
$962$	−11.4274	+	11.4274i	−0.368435	+	0.368435i
$963$	10.1474	−	10.1474i	0.326997	−	0.326997i
$964$	13.7283			0.442158
$965$	39.6700	−	31.8445i	1.27702	−	1.02511i
$966$		0			0
$967$	−14.2750	−	14.2750i	−0.459055	−	0.459055i	0.439290	−	0.898345i	$-0.355230\pi$
$967$	−14.2750	−	14.2750i	−0.459055	−	0.459055i	−0.898345	+	0.439290i	$0.855230\pi$
$968$	−12.3496	+	12.3496i	−0.396930	+	0.396930i
$969$	−22.3654			−0.718479
$970$	−14.8504	−	1.62501i	−0.476817	−	0.0521758i
$971$			23.4515i			0.752593i	0.926499	+	0.376296i	$0.122803\pi$
$971$			23.4515i			0.752593i	−0.926499	+	0.376296i	$0.877197\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		0			0
$974$			12.0773i			0.386982i
$975$	5.85273	−	26.4229i	0.187437	−	0.846209i
$976$			0.777764i			0.0248956i
$977$	−7.46754	−	7.46754i	−0.238908	−	0.238908i	0.577490	−	0.816398i	$-0.304032\pi$
$977$	−7.46754	−	7.46754i	−0.238908	−	0.238908i	−0.816398	+	0.577490i	$0.804032\pi$
$978$	3.30725	+	3.30725i	0.105754	+	0.105754i
$979$	−17.0627			−0.545325
$980$		0			0
$981$	2.97059			0.0948435
$982$	10.1994	+	10.1994i	0.325476	+	0.325476i
$983$	43.8301	+	43.8301i	1.39796	+	1.39796i	0.805873	+	0.592089i	$0.201697\pi$
$983$	43.8301	+	43.8301i	1.39796	+	1.39796i	0.592089	+	0.805873i	$0.298303\pi$
$984$			10.4281i			0.332437i
$985$	−16.8700	−	21.0156i	−0.537522	−	0.669613i
$986$			36.6087i			1.16586i
$987$		0			0
$988$	11.6423	−	11.6423i	0.370392	−	0.370392i
$989$			4.18583i			0.133102i
$990$	9.30333	−	7.46811i	0.295679	−	0.237352i
$991$	−32.0101			−1.01684			−0.508418	−	0.861110i	$-0.669769\pi$
$991$	−32.0101			−1.01684			−0.508418	+	0.861110i	$0.669769\pi$
$992$	4.50907	−	4.50907i	0.143163	−	0.143163i
$993$	12.9614	+	12.9614i	0.411317	+	0.411317i
$994$		0			0
$995$	12.6306	+	1.38211i	0.400417	+	0.0438157i
$996$	3.42085			0.108394
$997$	12.4334	−	12.4334i	0.393768	−	0.393768i	−0.482260	−	0.876028i	$-0.660184\pi$
$997$	12.4334	−	12.4334i	0.393768	−	0.393768i	0.876028	+	0.482260i	$0.160184\pi$
$998$	−18.6669	+	18.6669i	−0.590889	+	0.590889i
$999$	2.98575			0.0944649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.f.97.8	yes	16
5.3	odd	4		1470.2.m.c.1273.5	yes	16
7.6	odd	2		1470.2.m.c.97.5	✓	16
35.13	even	4	inner	1470.2.m.f.1273.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.5	✓	16	7.6	odd	2
1470.2.m.c.1273.5	yes	16	5.3	odd	4
1470.2.m.f.97.8	yes	16	1.1	even	1	trivial
1470.2.m.f.1273.8	yes	16	35.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.22280 + 0.243230i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.22280 + 0.243230i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.39977 + 1.74375i) q^{10} -5.33525 q^{11} +(0.707107 - 0.707107i) q^{12} +(3.82733 + 3.82733i) q^{13} +(-1.39977 - 1.74375i) q^{15} -1.00000 q^{16} +(-5.19896 + 5.19896i) q^{17} +(-0.707107 + 0.707107i) q^{18} -3.04189 q^{19} +(-0.243230 + 2.22280i) q^{20} +(-3.77259 - 3.77259i) q^{22} +(-1.63559 + 1.63559i) q^{23} +1.00000 q^{24} +(4.88168 + 1.08130i) q^{25} +5.41266i q^{26} +(0.707107 - 0.707107i) q^{27} -4.97911i q^{29} +(0.243230 - 2.22280i) q^{30} +6.37678i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.77259 + 3.77259i) q^{33} -7.35245 q^{34} -1.00000 q^{36} +(2.11124 + 2.11124i) q^{37} +(-2.15094 - 2.15094i) q^{38} -5.41266i q^{39} +(-1.74375 + 1.39977i) q^{40} +10.4281i q^{41} +(1.27961 - 1.27961i) q^{43} -5.33525i q^{44} +(-0.243230 + 2.22280i) q^{45} -2.31307 q^{46} +(8.75513 - 8.75513i) q^{47} +(0.707107 + 0.707107i) q^{48} +(2.68727 + 4.21646i) q^{50} +7.35245 q^{51} +(-3.82733 + 3.82733i) q^{52} +(-4.91277 + 4.91277i) q^{53} +1.00000 q^{54} +(-11.8592 - 1.29769i) q^{55} +(2.15094 + 2.15094i) q^{57} +(3.52077 - 3.52077i) q^{58} +6.15893 q^{59} +(1.74375 - 1.39977i) q^{60} -0.777764i q^{61} +(-4.50907 + 4.50907i) q^{62} -1.00000i q^{64} +(7.57646 + 9.43831i) q^{65} +5.33525i q^{66} +(-5.72162 - 5.72162i) q^{67} +(-5.19896 - 5.19896i) q^{68} +2.31307 q^{69} -5.85378 q^{71} +(-0.707107 - 0.707107i) q^{72} +(5.03959 + 5.03959i) q^{73} +2.98575i q^{74} +(-2.68727 - 4.21646i) q^{75} -3.04189i q^{76} +(3.82733 - 3.82733i) q^{78} +11.3463i q^{79} +(-2.22280 - 0.243230i) q^{80} -1.00000 q^{81} +(-7.37381 + 7.37381i) q^{82} +(2.41890 + 2.41890i) q^{83} +(-12.8208 + 10.2917i) q^{85} +1.80964 q^{86} +(-3.52077 + 3.52077i) q^{87} +(3.77259 - 3.77259i) q^{88} +3.19810 q^{89} +(-1.74375 + 1.39977i) q^{90} +(-1.63559 - 1.63559i) q^{92} +(4.50907 - 4.50907i) q^{93} +12.3816 q^{94} +(-6.76152 - 0.739880i) q^{95} +1.00000i q^{96} +(-4.72414 + 4.72414i) q^{97} -5.33525i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5}+O(q^{10}) \) 16 * q + 8 * q^5	\( 16 q + 8 q^{5} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 48 q^{19} - 8 q^{22} - 8 q^{23} + 16 q^{24} + 8 q^{25} + 8 q^{33} - 16 q^{36} + 8 q^{37} - 8 q^{38} + 16 q^{47} - 8 q^{52} + 8 q^{53} + 16 q^{54} + 8 q^{57} + 24 q^{58} + 48 q^{59} - 8 q^{62} + 72 q^{65} - 48 q^{67} - 8 q^{68} + 16 q^{73} + 8 q^{78} - 8 q^{80} - 16 q^{81} - 16 q^{82} - 72 q^{85} - 24 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{92} + 8 q^{93} + 64 q^{94} + 48 q^{95} - 64 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 48 * q^19 - 8 * q^22 - 8 * q^23 + 16 * q^24 + 8 * q^25 + 8 * q^33 - 16 * q^36 + 8 * q^37 - 8 * q^38 + 16 * q^47 - 8 * q^52 + 8 * q^53 + 16 * q^54 + 8 * q^57 + 24 * q^58 + 48 * q^59 - 8 * q^62 + 72 * q^65 - 48 * q^67 - 8 * q^68 + 16 * q^73 + 8 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 72 * q^85 - 24 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^92 + 8 * q^93 + 64 * q^94 + 48 * q^95 - 64 * q^97

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