LMFDB - Embedded newform 1470.2.m.c.1273.1

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			1273.1
Root			$2.23272 - 0.122339i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.c.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.10958 - 0.741398i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.10958 - 0.741398i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(2.01595 - 0.967451i) q^{10} +1.16954 q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.61635 + 3.61635i) q^{13} +(2.01595 - 0.967451i) q^{15} -1.00000 q^{16} +(4.48861 + 4.48861i) q^{17} +(0.707107 + 0.707107i) q^{18} -2.15406 q^{19} +(-0.741398 + 2.10958i) q^{20} +(-0.826986 + 0.826986i) q^{22} +(-1.80248 - 1.80248i) q^{23} -1.00000 q^{24} +(3.90066 + 3.12808i) q^{25} -5.11428i q^{26} +(0.707107 + 0.707107i) q^{27} -7.29386i q^{29} +(-0.741398 + 2.10958i) q^{30} +3.14555i q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.826986 + 0.826986i) q^{33} -6.34785 q^{34} -1.00000 q^{36} +(-2.88788 + 2.88788i) q^{37} +(1.52315 - 1.52315i) q^{38} -5.11428i q^{39} +(-0.967451 - 2.01595i) q^{40} -4.21690i q^{41} +(2.87119 + 2.87119i) q^{43} -1.16954i q^{44} +(-0.741398 + 2.10958i) q^{45} +2.54910 q^{46} +(-7.84171 - 7.84171i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-4.97007 + 0.546298i) q^{50} -6.34785 q^{51} +(3.61635 + 3.61635i) q^{52} +(-7.17149 - 7.17149i) q^{53} -1.00000 q^{54} +(-2.46723 - 0.867091i) q^{55} +(1.52315 - 1.52315i) q^{57} +(5.15754 + 5.15754i) q^{58} -2.85840 q^{59} +(-0.967451 - 2.01595i) q^{60} -10.0946i q^{61} +(-2.22424 - 2.22424i) q^{62} +1.00000i q^{64} +(10.3101 - 4.94782i) q^{65} -1.16954i q^{66} +(10.3888 - 10.3888i) q^{67} +(4.48861 - 4.48861i) q^{68} +2.54910 q^{69} -6.87114 q^{71} +(0.707107 - 0.707107i) q^{72} +(-3.69923 + 3.69923i) q^{73} -4.08408i q^{74} +(-4.97007 + 0.546298i) q^{75} +2.15406i q^{76} +(3.61635 + 3.61635i) q^{78} +0.468286i q^{79} +(2.10958 + 0.741398i) q^{80} -1.00000 q^{81} +(2.98180 + 2.98180i) q^{82} +(9.87385 - 9.87385i) q^{83} +(-6.14123 - 12.7969i) q^{85} -4.06048 q^{86} +(5.15754 + 5.15754i) q^{87} +(0.826986 + 0.826986i) q^{88} -2.12512 q^{89} +(-0.967451 - 2.01595i) q^{90} +(-1.80248 + 1.80248i) q^{92} +(-2.22424 - 2.22424i) q^{93} +11.0899 q^{94} +(4.54417 + 1.59702i) q^{95} +1.00000i q^{96} +(6.30698 + 6.30698i) q^{97} -1.16954i 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 $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−2.10958	−	0.741398i	−0.943433	−	0.331563i
$5$	−2.10958	−	0.741398i	−0.943433	−	0.331563i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	2.01595	−	0.967451i	0.637498	−	0.305935i
$11$	1.16954			0.352628			0.176314	−	0.984334i	$-0.443583\pi$
$11$	1.16954			0.352628			0.176314	+	0.984334i	$0.443583\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−3.61635	+	3.61635i	−1.00299	+	1.00299i	−0.00299816	+	0.999996i	$0.500954\pi$
$13$	−3.61635	+	3.61635i	−1.00299	+	1.00299i	−0.999996	+	0.00299816i	$0.999046\pi$
$14$		0			0
$15$	2.01595	−	0.967451i	0.520515	−	0.249795i
$16$	−1.00000			−0.250000
$17$	4.48861	+	4.48861i	1.08865	+	1.08865i	0.995668	+	0.0929791i	$0.0296390\pi$
$17$	4.48861	+	4.48861i	1.08865	+	1.08865i	0.0929791	+	0.995668i	$0.470361\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−2.15406			−0.494176			−0.247088	−	0.968993i	$-0.579474\pi$
$19$	−2.15406			−0.494176			−0.247088	+	0.968993i	$0.579474\pi$
$20$	−0.741398	+	2.10958i	−0.165782	+	0.471717i
$21$		0			0
$22$	−0.826986	+	0.826986i	−0.176314	+	0.176314i
$23$	−1.80248	−	1.80248i	−0.375844	−	0.375844i	0.493756	−	0.869600i	$-0.335623\pi$
$23$	−1.80248	−	1.80248i	−0.375844	−	0.375844i	−0.869600	+	0.493756i	$0.835623\pi$
$24$	−1.00000			−0.204124
$25$	3.90066	+	3.12808i	0.780132	+	0.625615i
$26$		−	5.11428i		−	1.00299i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	7.29386i		−	1.35444i	−0.735782	−	0.677218i	$-0.763185\pi$
$29$		−	7.29386i		−	1.35444i	0.735782	−	0.677218i	$-0.236815\pi$
$30$	−0.741398	+	2.10958i	−0.135360	+	0.385155i
$31$			3.14555i			0.564957i	0.959274	+	0.282478i	$0.0911566\pi$
$31$			3.14555i			0.564957i	−0.959274	+	0.282478i	$0.908843\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.826986	+	0.826986i	−0.143960	+	0.143960i
$34$	−6.34785			−1.08865
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.88788	+	2.88788i	−0.474765	+	0.474765i	−0.903453	−	0.428688i	$-0.858976\pi$
$37$	−2.88788	+	2.88788i	−0.474765	+	0.474765i	0.428688	+	0.903453i	$0.358976\pi$
$38$	1.52315	−	1.52315i	0.247088	−	0.247088i
$39$		−	5.11428i		−	0.818941i
$40$	−0.967451	−	2.01595i	−0.152967	−	0.318749i
$41$		−	4.21690i		−	0.658569i	−0.944231	−	0.329285i	$-0.893192\pi$
$41$		−	4.21690i		−	0.658569i	0.944231	−	0.329285i	$-0.106808\pi$
$42$		0			0
$43$	2.87119	+	2.87119i	0.437853	+	0.437853i	0.891289	−	0.453436i	$-0.149802\pi$
$43$	2.87119	+	2.87119i	0.437853	+	0.437853i	−0.453436	+	0.891289i	$0.649802\pi$
$44$		−	1.16954i		−	0.176314i
$45$	−0.741398	+	2.10958i	−0.110521	+	0.314478i
$46$	2.54910			0.375844
$47$	−7.84171	−	7.84171i	−1.14383	−	1.14383i	−0.987743	−	0.156088i	$-0.950112\pi$
$47$	−7.84171	−	7.84171i	−1.14383	−	1.14383i	−0.156088	−	0.987743i	$-0.549888\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		0			0
$50$	−4.97007	+	0.546298i	−0.702874	+	0.0772582i
$51$	−6.34785			−0.888877
$52$	3.61635	+	3.61635i	0.501497	+	0.501497i
$53$	−7.17149	−	7.17149i	−0.985080	−	0.985080i	0.0148103	−	0.999890i	$-0.495286\pi$
$53$	−7.17149	−	7.17149i	−0.985080	−	0.985080i	−0.999890	+	0.0148103i	$0.995286\pi$
$54$	−1.00000			−0.136083
$55$	−2.46723	−	0.867091i	−0.332681	−	0.116919i
$56$		0			0
$57$	1.52315	−	1.52315i	0.201746	−	0.201746i
$58$	5.15754	+	5.15754i	0.677218	+	0.677218i
$59$	−2.85840			−0.372132			−0.186066	−	0.982537i	$-0.559574\pi$
$59$	−2.85840			−0.372132			−0.186066	+	0.982537i	$0.559574\pi$
$60$	−0.967451	−	2.01595i	−0.124897	−	0.260258i
$61$		−	10.0946i		−	1.29248i	−0.763132	−	0.646242i	$-0.776340\pi$
$61$		−	10.0946i		−	1.29248i	0.763132	−	0.646242i	$-0.223660\pi$
$62$	−2.22424	−	2.22424i	−0.282478	−	0.282478i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	10.3101	−	4.94782i	1.27881	−	0.613702i
$66$		−	1.16954i		−	0.143960i
$67$	10.3888	−	10.3888i	1.26919	−	1.26919i	0.322684	−	0.946507i	$-0.395415\pi$
$67$	10.3888	−	10.3888i	1.26919	−	1.26919i	0.946507	−	0.322684i	$-0.104585\pi$
$68$	4.48861	−	4.48861i	0.544324	−	0.544324i
$69$	2.54910			0.306875
$70$		0			0
$71$	−6.87114			−0.815454			−0.407727	−	0.913104i	$-0.633678\pi$
$71$	−6.87114			−0.815454			−0.407727	+	0.913104i	$0.633678\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−3.69923	+	3.69923i	−0.432962	+	0.432962i	−0.889635	−	0.456673i	$-0.849041\pi$
$73$	−3.69923	+	3.69923i	−0.432962	+	0.432962i	0.456673	+	0.889635i	$0.349041\pi$
$74$		−	4.08408i		−	0.474765i
$75$	−4.97007	+	0.546298i	−0.573894	+	0.0630810i
$76$			2.15406i			0.247088i
$77$		0			0
$78$	3.61635	+	3.61635i	0.409470	+	0.409470i
$79$			0.468286i			0.0526863i	0.999653	+	0.0263432i	$0.00838626\pi$
$79$			0.468286i			0.0526863i	−0.999653	+	0.0263432i	$0.991614\pi$
$80$	2.10958	+	0.741398i	0.235858	+	0.0828908i
$81$	−1.00000			−0.111111
$82$	2.98180	+	2.98180i	0.329285	+	0.329285i
$83$	9.87385	−	9.87385i	1.08380	−	1.08380i	0.0876438	−	0.996152i	$-0.472066\pi$
$83$	9.87385	−	9.87385i	1.08380	−	1.08380i	0.996152	−	0.0876438i	$-0.0279337\pi$
$84$		0			0
$85$	−6.14123	−	12.7969i	−0.666110	−	1.38802i
$86$	−4.06048			−0.437853
$87$	5.15754	+	5.15754i	0.552946	+	0.552946i
$88$	0.826986	+	0.826986i	0.0881570	+	0.0881570i
$89$	−2.12512			−0.225262			−0.112631	−	0.993637i	$-0.535928\pi$
$89$	−2.12512			−0.225262			−0.112631	+	0.993637i	$0.535928\pi$
$90$	−0.967451	−	2.01595i	−0.101978	−	0.212499i
$91$		0			0
$92$	−1.80248	+	1.80248i	−0.187922	+	0.187922i
$93$	−2.22424	−	2.22424i	−0.230643	−	0.230643i
$94$	11.0899			1.14383
$95$	4.54417	+	1.59702i	0.466222	+	0.163851i
$96$			1.00000i			0.102062i
$97$	6.30698	+	6.30698i	0.640377	+	0.640377i	0.950648	−	0.310271i	$-0.100420\pi$
$97$	6.30698	+	6.30698i	0.640377	+	0.640377i	−0.310271	+	0.950648i	$0.600420\pi$
$98$		0			0
$99$		−	1.16954i		−	0.117543i
$100$	3.12808	−	3.90066i	0.312808	−	0.390066i
$101$		−	13.9318i		−	1.38627i	−0.720808	−	0.693135i	$-0.756229\pi$
$101$		−	13.9318i		−	1.38627i	0.720808	−	0.693135i	$-0.243771\pi$
$102$	4.48861	−	4.48861i	0.444438	−	0.444438i
$103$	−13.9294	+	13.9294i	−1.37251	+	1.37251i	−0.515792	+	0.856714i	$0.672502\pi$
$103$	−13.9294	+	13.9294i	−1.37251	+	1.37251i	−0.856714	+	0.515792i	$0.827498\pi$
$104$	−5.11428			−0.501497
$105$		0			0
$106$	10.1420			0.985080
$107$	11.6959	−	11.6959i	1.13068	−	1.13068i	0.140619	−	0.990064i	$-0.455091\pi$
$107$	11.6959	−	11.6959i	1.13068	−	1.13068i	0.990064	−	0.140619i	$-0.0449093\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$		−	9.35564i		−	0.896108i	−0.894006	−	0.448054i	$-0.852117\pi$
$109$		−	9.35564i		−	0.896108i	0.894006	−	0.448054i	$-0.147883\pi$
$110$	2.35772	−	1.13147i	0.224800	−	0.107881i
$111$		−	4.08408i		−	0.387644i
$112$		0			0
$113$	0.775120	+	0.775120i	0.0729172	+	0.0729172i	0.742625	−	0.669708i	$-0.233581\pi$
$113$	0.775120	+	0.775120i	0.0729172	+	0.0729172i	−0.669708	+	0.742625i	$0.733581\pi$
$114$			2.15406i			0.201746i
$115$	2.46613	+	5.13884i	0.229967	+	0.479199i
$116$	−7.29386			−0.677218
$117$	3.61635	+	3.61635i	0.334331	+	0.334331i
$118$	2.02119	−	2.02119i	0.186066	−	0.186066i
$119$		0			0
$120$	2.10958	+	0.741398i	0.192577	+	0.0676801i
$121$	−9.63219			−0.875653
$122$	7.13798	+	7.13798i	0.646242	+	0.646242i
$123$	2.98180	+	2.98180i	0.268860	+	0.268860i
$124$	3.14555			0.282478
$125$	−5.90960	−	9.49087i	−0.528571	−	0.848889i
$126$		0			0
$127$	0.927811	−	0.927811i	0.0823299	−	0.0823299i	−0.664743	−	0.747072i	$-0.731459\pi$
$127$	0.927811	−	0.927811i	0.0823299	−	0.0823299i	0.747072	+	0.664743i	$0.231459\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−4.06048			−0.357505
$130$	−3.79172	+	10.7890i	−0.332556	+	0.946257i
$131$		−	14.3865i		−	1.25695i	−0.777828	−	0.628477i	$-0.783679\pi$
$131$		−	14.3865i		−	1.25695i	0.777828	−	0.628477i	$-0.216321\pi$
$132$	0.826986	+	0.826986i	0.0719799	+	0.0719799i
$133$		0			0
$134$			14.6919i			1.26919i
$135$	−0.967451	−	2.01595i	−0.0832649	−	0.173505i
$136$			6.34785i			0.544324i
$137$	−0.319881	+	0.319881i	−0.0273293	+	0.0273293i	−0.720639	−	0.693310i	$-0.756152\pi$
$137$	−0.319881	+	0.319881i	−0.0273293	+	0.0273293i	0.693310	+	0.720639i	$0.256152\pi$
$138$	−1.80248	+	1.80248i	−0.153438	+	0.153438i
$139$	−13.9455			−1.18284			−0.591419	−	0.806364i	$-0.701432\pi$
$139$	−13.9455			−1.18284			−0.591419	+	0.806364i	$0.701432\pi$
$140$		0			0
$141$	11.0899			0.933934
$142$	4.85863	−	4.85863i	0.407727	−	0.407727i
$143$	−4.22944	+	4.22944i	−0.353684	+	0.353684i
$144$			1.00000i			0.0833333i
$145$	−5.40766	+	15.3870i	−0.449081	+	1.27782i
$146$		−	5.23150i		−	0.432962i
$147$		0			0
$148$	2.88788	+	2.88788i	0.237382	+	0.237382i
$149$			11.8494i			0.970743i	0.874308	+	0.485372i	$0.161316\pi$
$149$			11.8494i			0.970743i	−0.874308	+	0.485372i	$0.838684\pi$
$150$	3.12808	−	3.90066i	0.255406	−	0.318487i
$151$	18.3304			1.49171			0.745855	−	0.666109i	$-0.232041\pi$
$151$	18.3304			1.49171			0.745855	+	0.666109i	$0.232041\pi$
$152$	−1.52315	−	1.52315i	−0.123544	−	0.123544i
$153$	4.48861	−	4.48861i	0.362882	−	0.362882i
$154$		0			0
$155$	2.33210	−	6.63578i	0.187319	−	0.532999i
$156$	−5.11428			−0.409470
$157$	−12.6906	−	12.6906i	−1.01282	−	1.01282i	−0.999917	−	0.0129021i	$-0.995893\pi$
$157$	−12.6906	−	12.6906i	−1.01282	−	1.01282i	−0.0129021	−	0.999917i	$-0.504107\pi$
$158$	−0.331128	−	0.331128i	−0.0263432	−	0.0263432i
$159$	10.1420			0.804314
$160$	−2.01595	+	0.967451i	−0.159375	+	0.0764837i
$161$		0			0
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−0.801211	−	0.801211i	−0.0627557	−	0.0627557i	0.675032	−	0.737788i	$-0.264130\pi$
$163$	−0.801211	−	0.801211i	−0.0627557	−	0.0627557i	−0.737788	+	0.675032i	$0.764130\pi$
$164$	−4.21690			−0.329285
$165$	2.35772	−	1.13147i	0.183548	−	0.0880847i
$166$			13.9637i			1.08380i
$167$	17.0302	+	17.0302i	1.31783	+	1.31783i	0.915487	+	0.402348i	$0.131806\pi$
$167$	17.0302	+	17.0302i	1.31783	+	1.31783i	0.402348	+	0.915487i	$0.368194\pi$
$168$		0			0
$169$		−	13.1559i		−	1.01199i
$170$	13.3913	+	4.70628i	1.02707	+	0.360955i
$171$			2.15406i			0.164725i
$172$	2.87119	−	2.87119i	0.218926	−	0.218926i
$173$	5.87360	−	5.87360i	0.446561	−	0.446561i	−0.447648	−	0.894210i	$-0.647738\pi$
$173$	5.87360	−	5.87360i	0.446561	−	0.446561i	0.894210	+	0.447648i	$0.147738\pi$
$174$	−7.29386			−0.552946
$175$		0			0
$176$	−1.16954			−0.0881570
$177$	2.02119	−	2.02119i	0.151922	−	0.151922i
$178$	1.50268	−	1.50268i	0.112631	−	0.112631i
$179$			4.86023i			0.363271i	0.983366	+	0.181635i	$0.0581391\pi$
$179$			4.86023i			0.363271i	−0.983366	+	0.181635i	$0.941861\pi$
$180$	2.10958	+	0.741398i	0.157239	+	0.0552605i
$181$		−	13.0480i		−	0.969849i	−0.874556	−	0.484925i	$-0.838847\pi$
$181$		−	13.0480i		−	0.969849i	0.874556	−	0.484925i	$-0.161153\pi$
$182$		0			0
$183$	7.13798	+	7.13798i	0.527655	+	0.527655i
$184$		−	2.54910i		−	0.187922i
$185$	8.23328	−	3.95115i	0.605323	−	0.290494i
$186$	3.14555			0.230643
$187$	5.24958	+	5.24958i	0.383888	+	0.383888i
$188$	−7.84171	+	7.84171i	−0.571916	+	0.571916i
$189$		0			0
$190$	−4.34247	+	2.08395i	−0.315036	+	0.151186i
$191$	13.3222			0.963957			0.481979	−	0.876183i	$-0.339918\pi$
$191$	13.3222			0.963957			0.481979	+	0.876183i	$0.339918\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−8.96412	−	8.96412i	−0.645252	−	0.645252i	0.306590	−	0.951842i	$-0.400812\pi$
$193$	−8.96412	−	8.96412i	−0.645252	−	0.645252i	−0.951842	+	0.306590i	$0.900812\pi$
$194$	−8.91942			−0.640377
$195$	−3.79172	+	10.7890i	−0.271531	+	0.772616i
$196$		0			0
$197$	−17.2907	+	17.2907i	−1.23191	+	1.23191i	−0.268686	+	0.963228i	$0.586590\pi$
$197$	−17.2907	+	17.2907i	−1.23191	+	1.23191i	−0.963228	+	0.268686i	$0.913410\pi$
$198$	0.826986	+	0.826986i	0.0587714	+	0.0587714i
$199$	−20.6120			−1.46115			−0.730573	−	0.682834i	$-0.760747\pi$
$199$	−20.6120			−1.46115			−0.730573	+	0.682834i	$0.760747\pi$
$200$	0.546298	+	4.97007i	0.0386291	+	0.351437i
$201$			14.6919i			1.03629i
$202$	9.85130	+	9.85130i	0.693135	+	0.693135i
$203$		0			0
$204$			6.34785i			0.444438i
$205$	−3.12640	+	8.89589i	−0.218357	+	0.621316i
$206$		−	19.6992i		−	1.37251i
$207$	−1.80248	+	1.80248i	−0.125281	+	0.125281i
$208$	3.61635	−	3.61635i	0.250748	−	0.250748i
$209$	−2.51925			−0.174260
$210$		0			0
$211$	0.258759			0.0178137			0.00890685	−	0.999960i	$-0.497165\pi$
$211$	0.258759			0.0178137			0.00890685	+	0.999960i	$0.497165\pi$
$212$	−7.17149	+	7.17149i	−0.492540	+	0.492540i
$213$	4.85863	−	4.85863i	0.332908	−	0.332908i
$214$			16.5405i			1.13068i
$215$	−3.92832	−	8.18571i	−0.267909	−	0.558261i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	6.61544	+	6.61544i	0.448054	+	0.448054i
$219$		−	5.23150i		−	0.353512i
$220$	−0.867091	+	2.46723i	−0.0584593	+	0.166341i
$221$	−32.4647			−2.18381
$222$	2.88788	+	2.88788i	0.193822	+	0.193822i
$223$	13.8620	−	13.8620i	0.928271	−	0.928271i	−0.0693236	−	0.997594i	$-0.522084\pi$
$223$	13.8620	−	13.8620i	0.928271	−	0.928271i	0.997594	+	0.0693236i	$0.0220841\pi$
$224$		0			0
$225$	3.12808	−	3.90066i	0.208538	−	0.260044i
$226$	−1.09619			−0.0729172
$227$	−5.18875	−	5.18875i	−0.344389	−	0.344389i	0.513625	−	0.858015i	$-0.328302\pi$
$227$	−5.18875	−	5.18875i	−0.344389	−	0.344389i	−0.858015	+	0.513625i	$0.828302\pi$
$228$	−1.52315	−	1.52315i	−0.100873	−	0.100873i
$229$	9.92964			0.656169			0.328084	−	0.944648i	$-0.393597\pi$
$229$	9.92964			0.656169			0.328084	+	0.944648i	$0.393597\pi$
$230$	−5.37752	−	1.88989i	−0.354583	−	0.124616i
$231$		0			0
$232$	5.15754	−	5.15754i	0.338609	−	0.338609i
$233$	1.38480	+	1.38480i	0.0907214	+	0.0907214i	0.751011	−	0.660290i	$-0.229566\pi$
$233$	1.38480	+	1.38480i	0.0907214	+	0.0907214i	−0.660290	+	0.751011i	$0.729566\pi$
$234$	−5.11428			−0.334331
$235$	10.7289	+	22.3566i	0.699876	+	1.45838i
$236$			2.85840i			0.186066i
$237$	−0.331128	−	0.331128i	−0.0215091	−	0.0215091i
$238$		0			0
$239$		−	11.5030i		−	0.744070i	−0.928219	−	0.372035i	$-0.878660\pi$
$239$		−	11.5030i		−	0.744070i	0.928219	−	0.372035i	$-0.121340\pi$
$240$	−2.01595	+	0.967451i	−0.130129	+	0.0624487i
$241$		−	15.4652i		−	0.996199i	−0.867120	−	0.498100i	$-0.834031\pi$
$241$		−	15.4652i		−	0.996199i	0.867120	−	0.498100i	$-0.165969\pi$
$242$	6.81098	−	6.81098i	0.437827	−	0.437827i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−10.0946			−0.646242
$245$		0			0
$246$	−4.21690			−0.268860
$247$	7.78983	−	7.78983i	0.495655	−	0.495655i
$248$	−2.22424	+	2.22424i	−0.141239	+	0.141239i
$249$			13.9637i			0.884915i
$250$	10.8898	+	2.53234i	0.688730	+	0.160159i
$251$		−	19.2786i		−	1.21685i	−0.793610	−	0.608427i	$-0.791801\pi$
$251$		−	19.2786i		−	1.21685i	0.793610	−	0.608427i	$-0.208199\pi$
$252$		0			0
$253$	−2.10807	−	2.10807i	−0.132533	−	0.132533i
$254$			1.31212i			0.0823299i
$255$	13.3913	+	4.70628i	0.838596	+	0.294719i
$256$	1.00000			0.0625000
$257$	−0.287481	−	0.287481i	−0.0179326	−	0.0179326i	0.698084	−	0.716016i	$-0.254036\pi$
$257$	−0.287481	−	0.287481i	−0.0179326	−	0.0179326i	−0.716016	+	0.698084i	$0.754036\pi$
$258$	2.87119	−	2.87119i	0.178753	−	0.178753i
$259$		0			0
$260$	−4.94782	−	10.3101i	−0.306851	−	0.639407i
$261$	−7.29386			−0.451479
$262$	10.1728	+	10.1728i	0.628477	+	0.628477i
$263$	−10.4661	−	10.4661i	−0.645365	−	0.645365i	0.306504	−	0.951869i	$-0.400841\pi$
$263$	−10.4661	−	10.4661i	−0.645365	−	0.645365i	−0.951869	+	0.306504i	$0.900841\pi$
$264$	−1.16954			−0.0719799
$265$	9.81191	+	20.4458i	0.602741	+	1.25597i
$266$		0			0
$267$	1.50268	−	1.50268i	0.0919628	−	0.0919628i
$268$	−10.3888	−	10.3888i	−0.634595	−	0.634595i
$269$	−11.5210			−0.702445			−0.351223	−	0.936292i	$-0.614234\pi$
$269$	−11.5210			−0.702445			−0.351223	+	0.936292i	$0.614234\pi$
$270$	2.10958	+	0.741398i	0.128385	+	0.0451200i
$271$		−	14.0088i		−	0.850975i	−0.904964	−	0.425488i	$-0.860103\pi$
$271$		−	14.0088i		−	0.850975i	0.904964	−	0.425488i	$-0.139897\pi$
$272$	−4.48861	−	4.48861i	−0.272162	−	0.272162i
$273$		0			0
$274$		−	0.452380i		−	0.0273293i
$275$	4.56196	+	3.65840i	0.275096	+	0.220610i
$276$		−	2.54910i		−	0.153438i
$277$	−16.1177	+	16.1177i	−0.968418	+	0.968418i	−0.999516	−	0.0310981i	$-0.990100\pi$
$277$	−16.1177	+	16.1177i	−0.968418	+	0.968418i	0.0310981	+	0.999516i	$0.490100\pi$
$278$	9.86093	−	9.86093i	0.591419	−	0.591419i
$279$	3.14555			0.188319
$280$		0			0
$281$	−21.9749			−1.31091			−0.655456	−	0.755233i	$-0.727524\pi$
$281$	−21.9749			−1.31091			−0.655456	+	0.755233i	$0.727524\pi$
$282$	−7.84171	+	7.84171i	−0.466967	+	0.466967i
$283$	2.42743	−	2.42743i	0.144296	−	0.144296i	−0.631269	−	0.775564i	$-0.717465\pi$
$283$	2.42743	−	2.42743i	0.144296	−	0.144296i	0.775564	+	0.631269i	$0.217465\pi$
$284$			6.87114i			0.407727i
$285$	−4.34247	+	2.08395i	−0.257226	+	0.123443i
$286$		−	5.98134i		−	0.353684i
$287$		0			0
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$			23.2952i			1.37031i
$290$	−7.05646	−	14.7040i	−0.414369	−	0.863451i
$291$	−8.91942			−0.522866
$292$	3.69923	+	3.69923i	0.216481	+	0.216481i
$293$	−12.1647	+	12.1647i	−0.710670	+	0.710670i	−0.966675	−	0.256005i	$-0.917594\pi$
$293$	−12.1647	+	12.1647i	−0.710670	+	0.710670i	0.256005	+	0.966675i	$0.417594\pi$
$294$		0			0
$295$	6.03002	+	2.11921i	0.351081	+	0.123385i
$296$	−4.08408			−0.237382
$297$	0.826986	+	0.826986i	0.0479866	+	0.0479866i
$298$	−8.37881	−	8.37881i	−0.485372	−	0.485372i
$299$	13.0368			0.753938
$300$	0.546298	+	4.97007i	0.0315405	+	0.286947i
$301$		0			0
$302$	−12.9616	+	12.9616i	−0.745855	+	0.745855i
$303$	9.85130	+	9.85130i	0.565942	+	0.565942i
$304$	2.15406			0.123544
$305$	−7.48413	+	21.2954i	−0.428540	+	1.21937i
$306$			6.34785i			0.362882i
$307$	14.6908	+	14.6908i	0.838447	+	0.838447i	0.988654	−	0.150208i	$-0.0479943\pi$
$307$	14.6908	+	14.6908i	0.838447	+	0.838447i	−0.150208	+	0.988654i	$0.547994\pi$
$308$		0			0
$309$		−	19.6992i		−	1.12065i
$310$	3.04316	+	6.34125i	0.172840	+	0.360159i
$311$			11.8795i			0.673622i	0.941572	+	0.336811i	$0.109348\pi$
$311$			11.8795i			0.673622i	−0.941572	+	0.336811i	$0.890652\pi$
$312$	3.61635	−	3.61635i	0.204735	−	0.204735i
$313$	−7.63841	+	7.63841i	−0.431748	+	0.431748i	−0.889223	−	0.457474i	$-0.848754\pi$
$313$	−7.63841	+	7.63841i	−0.431748	+	0.431748i	0.457474	+	0.889223i	$0.348754\pi$
$314$	17.9472			1.01282
$315$		0			0
$316$	0.468286			0.0263432
$317$	14.2030	−	14.2030i	0.797718	−	0.797718i	−0.185018	−	0.982735i	$-0.559234\pi$
$317$	14.2030	−	14.2030i	0.797718	−	0.797718i	0.982735	+	0.185018i	$0.0592342\pi$
$318$	−7.17149	+	7.17149i	−0.402157	+	0.402157i
$319$		−	8.53043i		−	0.477613i
$320$	0.741398	−	2.10958i	0.0414454	−	0.117929i
$321$			16.5405i			0.923199i
$322$		0			0
$323$	−9.66874	−	9.66874i	−0.537983	−	0.537983i
$324$			1.00000i			0.0555556i
$325$	−25.4183	+	2.79392i	−1.40996	+	0.154979i
$326$	1.13308			0.0627557
$327$	6.61544	+	6.61544i	0.365835	+	0.365835i
$328$	2.98180	−	2.98180i	0.164642	−	0.164642i
$329$		0			0
$330$	−0.867091	+	2.46723i	−0.0477318	+	0.135816i
$331$	−22.9107			−1.25929			−0.629644	−	0.776884i	$-0.716799\pi$
$331$	−22.9107			−1.25929			−0.629644	+	0.776884i	$0.716799\pi$
$332$	−9.87385	−	9.87385i	−0.541898	−	0.541898i
$333$	2.88788	+	2.88788i	0.158255	+	0.158255i
$334$	−24.0843			−1.31783
$335$	−29.6182	+	14.2137i	−1.61821	+	0.776579i
$336$		0			0
$337$	−19.9855	+	19.9855i	−1.08868	+	1.08868i	−0.0930152	+	0.995665i	$0.529651\pi$
$337$	−19.9855	+	19.9855i	−1.08868	+	1.08868i	−0.995665	+	0.0930152i	$0.970349\pi$
$338$	9.30263	+	9.30263i	0.505996	+	0.505996i
$339$	−1.09619			−0.0595366
$340$	−12.7969	+	6.14123i	−0.694011	+	0.333055i
$341$			3.67883i			0.199220i
$342$	−1.52315	−	1.52315i	−0.0823627	−	0.0823627i
$343$		0			0
$344$			4.06048i			0.218926i
$345$	−5.37752	−	1.88989i	−0.289516	−	0.101749i
$346$			8.30652i			0.446561i
$347$	0.0255303	−	0.0255303i	0.00137054	−	0.00137054i	−0.706421	−	0.707792i	$-0.749692\pi$
$347$	0.0255303	−	0.0255303i	0.00137054	−	0.00137054i	0.707792	+	0.706421i	$0.249692\pi$
$348$	5.15754	−	5.15754i	0.276473	−	0.276473i
$349$	−5.64651			−0.302251			−0.151125	−	0.988515i	$-0.548290\pi$
$349$	−5.64651			−0.302251			−0.151125	+	0.988515i	$0.548290\pi$
$350$		0			0
$351$	−5.11428			−0.272980
$352$	0.826986	−	0.826986i	0.0440785	−	0.0440785i
$353$	−8.84624	+	8.84624i	−0.470838	+	0.470838i	−0.902186	−	0.431348i	$-0.858038\pi$
$353$	−8.84624	+	8.84624i	−0.470838	+	0.470838i	0.431348	+	0.902186i	$0.358038\pi$
$354$			2.85840i			0.151922i
$355$	14.4952	+	5.09425i	0.769326	+	0.270374i
$356$			2.12512i			0.112631i
$357$		0			0
$358$	−3.43670	−	3.43670i	−0.181635	−	0.181635i
$359$			6.02161i			0.317808i	0.987294	+	0.158904i	$0.0507961\pi$
$359$			6.02161i			0.317808i	−0.987294	+	0.158904i	$0.949204\pi$
$360$	−2.01595	+	0.967451i	−0.106250	+	0.0509891i
$361$	−14.3600			−0.755790
$362$	9.22632	+	9.22632i	0.484925	+	0.484925i
$363$	6.81098	−	6.81098i	0.357484	−	0.357484i
$364$		0			0
$365$	10.5464	−	5.06122i	0.552025	−	0.264916i
$366$	−10.0946			−0.527655
$367$	0.650518	+	0.650518i	0.0339567	+	0.0339567i	0.723881	−	0.689925i	$-0.242356\pi$
$367$	0.650518	+	0.650518i	0.0339567	+	0.0339567i	−0.689925	+	0.723881i	$0.742356\pi$
$368$	1.80248	+	1.80248i	0.0939609	+	0.0939609i
$369$	−4.21690			−0.219523
$370$	−3.02793	+	8.61569i	−0.157414	+	0.447909i
$371$		0			0
$372$	−2.22424	+	2.22424i	−0.115321	+	0.115321i
$373$	−9.69257	−	9.69257i	−0.501862	−	0.501862i	0.410154	−	0.912016i	$-0.365475\pi$
$373$	−9.69257	−	9.69257i	−0.501862	−	0.501862i	−0.912016	+	0.410154i	$0.865475\pi$
$374$	−7.42403			−0.383888
$375$	10.8898	+	2.53234i	0.562346	+	0.130769i
$376$		−	11.0899i		−	0.571916i
$377$	26.3771	+	26.3771i	1.35849	+	1.35849i
$378$		0			0
$379$			21.3559i			1.09698i	0.836157	+	0.548489i	$0.184797\pi$
$379$			21.3559i			1.09698i	−0.836157	+	0.548489i	$0.815203\pi$
$380$	1.59702	−	4.54417i	0.0819253	−	0.233111i
$381$			1.31212i			0.0672221i
$382$	−9.42019	+	9.42019i	−0.481979	+	0.481979i
$383$	19.3348	−	19.3348i	0.987963	−	0.987963i	−0.0119658	−	0.999928i	$-0.503809\pi$
$383$	19.3348	−	19.3348i	0.987963	−	0.987963i	0.999928	+	0.0119658i	$0.00380892\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	12.6772			0.645252
$387$	2.87119	−	2.87119i	0.145951	−	0.145951i
$388$	6.30698	−	6.30698i	0.320189	−	0.320189i
$389$			38.4244i			1.94819i	0.226131	+	0.974097i	$0.427392\pi$
$389$			38.4244i			1.94819i	−0.226131	+	0.974097i	$0.572608\pi$
$390$	−4.94782	−	10.3101i	−0.250543	−	0.522073i
$391$		−	16.1813i		−	0.818322i
$392$		0			0
$393$	10.1728	+	10.1728i	0.513149	+	0.513149i
$394$		−	24.4528i		−	1.23191i
$395$	0.347186	−	0.987887i	0.0174688	−	0.0497060i
$396$	−1.16954			−0.0587714
$397$	23.1431	+	23.1431i	1.16152	+	1.16152i	0.984143	+	0.177375i	$0.0567605\pi$
$397$	23.1431	+	23.1431i	1.16152	+	1.16152i	0.177375	+	0.984143i	$0.443239\pi$
$398$	14.5749	−	14.5749i	0.730573	−	0.730573i
$399$		0			0
$400$	−3.90066	−	3.12808i	−0.195033	−	0.156404i
$401$	−22.2823			−1.11272			−0.556362	−	0.830940i	$-0.687803\pi$
$401$	−22.2823			−1.11272			−0.556362	+	0.830940i	$0.687803\pi$
$402$	−10.3888	−	10.3888i	−0.518145	−	0.518145i
$403$	−11.3754	−	11.3754i	−0.566648	−	0.566648i
$404$	−13.9318			−0.693135
$405$	2.10958	+	0.741398i	0.104826	+	0.0368404i
$406$		0			0
$407$	−3.37748	+	3.37748i	−0.167415	+	0.167415i
$408$	−4.48861	−	4.48861i	−0.222219	−	0.222219i
$409$	16.3375			0.807838			0.403919	−	0.914795i	$-0.367648\pi$
$409$	16.3375			0.807838			0.403919	+	0.914795i	$0.367648\pi$
$410$	−4.07964	−	8.50104i	−0.201479	−	0.419837i
$411$		−	0.452380i		−	0.0223143i
$412$	13.9294	+	13.9294i	0.686253	+	0.686253i
$413$		0			0
$414$		−	2.54910i		−	0.125281i
$415$	−28.1501	+	13.5092i	−1.38184	+	0.663142i
$416$			5.11428i			0.250748i
$417$	9.86093	−	9.86093i	0.482892	−	0.482892i
$418$	1.78138	−	1.78138i	0.0871302	−	0.0871302i
$419$	29.3057			1.43168			0.715839	−	0.698265i	$-0.246044\pi$
$419$	29.3057			1.43168			0.715839	+	0.698265i	$0.246044\pi$
$420$		0			0
$421$	32.5881			1.58825			0.794123	−	0.607758i	$-0.207931\pi$
$421$	32.5881			1.58825			0.794123	+	0.607758i	$0.207931\pi$
$422$	−0.182970	+	0.182970i	−0.00890685	+	0.00890685i
$423$	−7.84171	+	7.84171i	−0.381277	+	0.381277i
$424$		−	10.1420i		−	0.492540i
$425$	3.46782	+	31.5492i	0.168214	+	1.53036i
$426$			6.87114i			0.332908i
$427$		0			0
$428$	−11.6959	−	11.6959i	−0.565341	−	0.565341i
$429$		−	5.98134i		−	0.288782i
$430$	8.56591	+	3.01043i	0.413085	+	0.145176i
$431$	−19.1308			−0.921499			−0.460749	−	0.887530i	$-0.652419\pi$
$431$	−19.1308			−0.921499			−0.460749	+	0.887530i	$0.652419\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−0.414118	+	0.414118i	−0.0199012	+	0.0199012i	−0.716987	−	0.697086i	$-0.754479\pi$
$433$	−0.414118	+	0.414118i	−0.0199012	+	0.0199012i	0.697086	+	0.716987i	$0.254479\pi$
$434$		0			0
$435$	−7.05646	−	14.7040i	−0.338331	−	0.705005i
$436$	−9.35564			−0.448054
$437$	3.88266	+	3.88266i	0.185733	+	0.185733i
$438$	3.69923	+	3.69923i	0.176756	+	0.176756i
$439$	1.62250			0.0774379			0.0387189	−	0.999250i	$-0.487672\pi$
$439$	1.62250			0.0774379			0.0387189	+	0.999250i	$0.487672\pi$
$440$	−1.13147	−	2.35772i	−0.0539406	−	0.112400i
$441$		0			0
$442$	22.9560	−	22.9560i	1.09191	−	1.09191i
$443$	−16.8370	−	16.8370i	−0.799949	−	0.799949i	0.183138	−	0.983087i	$-0.441375\pi$
$443$	−16.8370	−	16.8370i	−0.799949	−	0.799949i	−0.983087	+	0.183138i	$0.941375\pi$
$444$	−4.08408			−0.193822
$445$	4.48311	+	1.57556i	0.212520	+	0.0746886i
$446$			19.6039i			0.928271i
$447$	−8.37881	−	8.37881i	−0.396304	−	0.396304i
$448$		0			0
$449$			19.6138i			0.925631i	0.886455	+	0.462816i	$0.153161\pi$
$449$			19.6138i			0.925631i	−0.886455	+	0.462816i	$0.846839\pi$
$450$	0.546298	+	4.97007i	0.0257527	+	0.234291i
$451$		−	4.93181i		−	0.232230i
$452$	0.775120	−	0.775120i	0.0364586	−	0.0364586i
$453$	−12.9616	+	12.9616i	−0.608988	+	0.608988i
$454$	7.33800			0.344389
$455$		0			0
$456$	2.15406			0.100873
$457$	12.9126	−	12.9126i	0.604025	−	0.604025i	−0.337354	−	0.941378i	$-0.609532\pi$
$457$	12.9126	−	12.9126i	0.604025	−	0.604025i	0.941378	+	0.337354i	$0.109532\pi$
$458$	−7.02131	+	7.02131i	−0.328084	+	0.328084i
$459$			6.34785i			0.296292i
$460$	5.13884	−	2.46613i	0.239600	−	0.114984i
$461$			0.778831i			0.0362738i	0.999836	+	0.0181369i	$0.00577347\pi$
$461$			0.778831i			0.0362738i	−0.999836	+	0.0181369i	$0.994227\pi$
$462$		0			0
$463$	25.9903	+	25.9903i	1.20787	+	1.20787i	0.971716	+	0.236154i	$0.0758870\pi$
$463$	25.9903	+	25.9903i	1.20787	+	1.20787i	0.236154	+	0.971716i	$0.424113\pi$
$464$			7.29386i			0.338609i
$465$	3.04316	+	6.34125i	0.141123	+	0.294069i
$466$	−1.95841			−0.0907214
$467$	−27.5454	−	27.5454i	−1.27465	−	1.27465i	−0.943621	−	0.331027i	$-0.892605\pi$
$467$	−27.5454	−	27.5454i	−1.27465	−	1.27465i	−0.331027	−	0.943621i	$-0.607395\pi$
$468$	3.61635	−	3.61635i	0.167166	−	0.167166i
$469$		0			0
$470$	−23.3949	−	8.22200i	−1.07913	−	0.379252i
$471$	17.9472			0.826963
$472$	−2.02119	−	2.02119i	−0.0930329	−	0.0930329i
$473$	3.35796	+	3.35796i	0.154399	+	0.154399i
$474$	0.468286			0.0215091
$475$	−8.40226	−	6.73807i	−0.385522	−	0.309164i
$476$		0			0
$477$	−7.17149	+	7.17149i	−0.328360	+	0.328360i
$478$	8.13388	+	8.13388i	0.372035	+	0.372035i
$479$	23.4155			1.06988			0.534941	−	0.844889i	$-0.320334\pi$
$479$	23.4155			1.06988			0.534941	+	0.844889i	$0.320334\pi$
$480$	0.741398	−	2.10958i	0.0338400	−	0.0962887i
$481$		−	20.8871i		−	0.952372i
$482$	10.9355	+	10.9355i	0.498100	+	0.498100i
$483$		0			0
$484$			9.63219i			0.437827i
$485$	−8.62910	−	17.9811i	−0.391827	−	0.816478i
$486$			1.00000i			0.0453609i
$487$	14.0720	−	14.0720i	0.637662	−	0.637662i	−0.312316	−	0.949978i	$-0.601105\pi$
$487$	14.0720	−	14.0720i	0.637662	−	0.637662i	0.949978	+	0.312316i	$0.101105\pi$
$488$	7.13798	−	7.13798i	0.323121	−	0.323121i
$489$	1.13308			0.0512398
$490$		0			0
$491$	10.1674			0.458848			0.229424	−	0.973327i	$-0.426316\pi$
$491$	10.1674			0.458848			0.229424	+	0.973327i	$0.426316\pi$
$492$	2.98180	−	2.98180i	0.134430	−	0.134430i
$493$	32.7393	−	32.7393i	1.47450	−	1.47450i
$494$			11.0165i			0.495655i
$495$	−0.867091	+	2.46723i	−0.0389728	+	0.110894i
$496$		−	3.14555i		−	0.141239i
$497$		0			0
$498$	−9.87385	−	9.87385i	−0.442458	−	0.442458i
$499$			22.0376i			0.986537i	0.869877	+	0.493268i	$0.164198\pi$
$499$			22.0376i			0.986537i	−0.869877	+	0.493268i	$0.835802\pi$
$500$	−9.49087	+	5.90960i	−0.424445	+	0.264285i
$501$	−24.0843			−1.07601
$502$	13.6320	+	13.6320i	0.608427	+	0.608427i
$503$	−2.86588	+	2.86588i	−0.127783	+	0.127783i	−0.768106	−	0.640323i	$-0.778801\pi$
$503$	−2.86588	+	2.86588i	−0.127783	+	0.127783i	0.640323	+	0.768106i	$0.278801\pi$
$504$		0			0
$505$	−10.3290	+	29.3903i	−0.459636	+	1.30785i
$506$	2.98126			0.132533
$507$	9.30263	+	9.30263i	0.413144	+	0.413144i
$508$	−0.927811	−	0.927811i	−0.0411650	−	0.0411650i
$509$	5.80907			0.257483			0.128741	−	0.991678i	$-0.458906\pi$
$509$	5.80907			0.257483			0.128741	+	0.991678i	$0.458906\pi$
$510$	−12.7969	+	6.14123i	−0.566657	+	0.271938i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.52315	−	1.52315i	−0.0672488	−	0.0672488i
$514$	0.406560			0.0179326
$515$	39.7124	−	19.0580i	1.74994	−	0.839795i
$516$			4.06048i			0.178753i
$517$	−9.17116	−	9.17116i	−0.403347	−	0.403347i
$518$		0			0
$519$			8.30652i			0.364616i
$520$	10.7890	+	3.79172i	0.473129	+	0.166278i
$521$		−	19.2396i		−	0.842903i	−0.906851	−	0.421452i	$-0.861521\pi$
$521$		−	19.2396i		−	0.842903i	0.906851	−	0.421452i	$-0.138479\pi$
$522$	5.15754	−	5.15754i	0.225739	−	0.225739i
$523$	7.54922	−	7.54922i	0.330104	−	0.330104i	−0.522522	−	0.852626i	$-0.675009\pi$
$523$	7.54922	−	7.54922i	0.330104	−	0.330104i	0.852626	+	0.522522i	$0.175009\pi$
$524$	−14.3865			−0.628477
$525$		0			0
$526$	14.8012			0.645365
$527$	−14.1191	+	14.1191i	−0.615039	+	0.615039i
$528$	0.826986	−	0.826986i	0.0359900	−	0.0359900i
$529$		−	16.5021i		−	0.717483i
$530$	−21.3954	−	7.51927i	−0.929357	−	0.326616i
$531$			2.85840i			0.124044i
$532$		0			0
$533$	15.2498	+	15.2498i	0.660541	+	0.660541i
$534$			2.12512i			0.0919628i
$535$	−33.3447	+	16.0021i	−1.44162	+	0.691831i
$536$	14.6919			0.634595
$537$	−3.43670	−	3.43670i	−0.148305	−	0.148305i
$538$	8.14655	−	8.14655i	0.351223	−	0.351223i
$539$		0			0
$540$	−2.01595	+	0.967451i	−0.0867525	+	0.0416325i
$541$	10.0051			0.430151			0.215076	−	0.976597i	$-0.431000\pi$
$541$	10.0051			0.430151			0.215076	+	0.976597i	$0.431000\pi$
$542$	9.90573	+	9.90573i	0.425488	+	0.425488i
$543$	9.22632	+	9.22632i	0.395939	+	0.395939i
$544$	6.34785			0.272162
$545$	−6.93625	+	19.7365i	−0.297116	+	0.845418i
$546$		0			0
$547$	−24.0578	+	24.0578i	−1.02864	+	1.02864i	−0.0290596	+	0.999578i	$0.509251\pi$
$547$	−24.0578	+	24.0578i	−1.02864	+	1.02864i	−0.999578	+	0.0290596i	$0.990749\pi$
$548$	0.319881	+	0.319881i	0.0136646	+	0.0136646i
$549$	−10.0946			−0.430828
$550$	−5.81267	+	0.638914i	−0.247853	+	0.0272434i
$551$			15.7114i			0.669330i
$552$	1.80248	+	1.80248i	0.0767188	+	0.0767188i
$553$		0			0
$554$		−	22.7939i		−	0.968418i
$555$	−3.02793	+	8.61569i	−0.128528	+	0.365716i
$556$			13.9455i			0.591419i
$557$	0.107225	−	0.107225i	0.00454326	−	0.00454326i	−0.704832	−	0.709375i	$-0.748977\pi$
$557$	0.107225	−	0.107225i	0.00454326	−	0.00454326i	0.709375	+	0.704832i	$0.248977\pi$
$558$	−2.22424	+	2.22424i	−0.0941595	+	0.0941595i
$559$	−20.7665			−0.878328
$560$		0			0
$561$	−7.42403			−0.313443
$562$	15.5386	−	15.5386i	0.655456	−	0.655456i
$563$	−2.04028	+	2.04028i	−0.0859876	+	0.0859876i	−0.748792	−	0.662805i	$-0.769366\pi$
$563$	−2.04028	+	2.04028i	−0.0859876	+	0.0859876i	0.662805	+	0.748792i	$0.269366\pi$
$564$		−	11.0899i		−	0.466967i
$565$	−1.06051	−	2.20985i	−0.0446158	−	0.0929691i
$566$			3.43290i			0.144296i
$567$		0			0
$568$	−4.85863	−	4.85863i	−0.203863	−	0.203863i
$569$			32.4544i			1.36056i	0.732953	+	0.680279i	$0.238141\pi$
$569$			32.4544i			1.36056i	−0.732953	+	0.680279i	$0.761859\pi$
$570$	1.59702	−	4.54417i	0.0668917	−	0.190334i
$571$	44.8446			1.87669			0.938343	−	0.345706i	$-0.112360\pi$
$571$	44.8446			1.87669			0.938343	+	0.345706i	$0.112360\pi$
$572$	4.22944	+	4.22944i	0.176842	+	0.176842i
$573$	−9.42019	+	9.42019i	−0.393534	+	0.393534i
$574$		0			0
$575$	−1.39257	−	12.6692i	−0.0580740	−	0.528341i
$576$	1.00000			0.0416667
$577$	−25.1807	−	25.1807i	−1.04829	−	1.04829i	−0.998773	−	0.0495146i	$-0.984233\pi$
$577$	−25.1807	−	25.1807i	−1.04829	−	1.04829i	−0.0495146	−	0.998773i	$-0.515767\pi$
$578$	−16.4722	−	16.4722i	−0.685153	−	0.685153i
$579$	12.6772			0.526846
$580$	15.3870	+	5.40766i	0.638910	+	0.224541i
$581$		0			0
$582$	6.30698	−	6.30698i	0.261433	−	0.261433i
$583$	−8.38731	−	8.38731i	−0.347367	−	0.347367i
$584$	−5.23150			−0.216481
$585$	−4.94782	−	10.3101i	−0.204567	−	0.426271i
$586$		−	17.2035i		−	0.710670i
$587$	−21.9203	−	21.9203i	−0.904749	−	0.904749i	0.0910934	−	0.995842i	$-0.470964\pi$
$587$	−21.9203	−	21.9203i	−0.904749	−	0.904749i	−0.995842	+	0.0910934i	$0.970964\pi$
$588$		0			0
$589$		−	6.77571i		−	0.279188i
$590$	−5.76238	+	2.76536i	−0.237233	+	0.113848i
$591$		−	24.4528i		−	1.00585i
$592$	2.88788	−	2.88788i	0.118691	−	0.118691i
$593$	−2.86095	+	2.86095i	−0.117485	+	0.117485i	−0.763405	−	0.645920i	$-0.776474\pi$
$593$	−2.86095	+	2.86095i	−0.117485	+	0.117485i	0.645920	+	0.763405i	$0.276474\pi$
$594$	−1.16954			−0.0479866
$595$		0			0
$596$	11.8494			0.485372
$597$	14.5749	−	14.5749i	0.596510	−	0.596510i
$598$	−9.21841	+	9.21841i	−0.376969	+	0.376969i
$599$		−	9.64419i		−	0.394051i	−0.980398	−	0.197026i	$-0.936872\pi$
$599$		−	9.64419i		−	0.394051i	0.980398	−	0.197026i	$-0.0631282\pi$
$600$	−3.90066	−	3.12808i	−0.159244	−	0.127703i
$601$		−	29.7149i		−	1.21210i	−0.795428	−	0.606048i	$-0.792754\pi$
$601$		−	29.7149i		−	1.21210i	0.795428	−	0.606048i	$-0.207246\pi$
$602$		0			0
$603$	−10.3888	−	10.3888i	−0.423063	−	0.423063i
$604$		−	18.3304i		−	0.745855i
$605$	20.3199	+	7.14128i	0.826120	+	0.290334i
$606$	−13.9318			−0.565942
$607$	−23.4795	−	23.4795i	−0.953003	−	0.953003i	0.0459409	−	0.998944i	$-0.485371\pi$
$607$	−23.4795	−	23.4795i	−0.953003	−	0.953003i	−0.998944	+	0.0459409i	$0.985371\pi$
$608$	−1.52315	+	1.52315i	−0.0617720	+	0.0617720i
$609$		0			0
$610$	−9.76606	−	20.3502i	−0.395416	−	0.823956i
$611$	56.7167			2.29451
$612$	−4.48861	−	4.48861i	−0.181441	−	0.181441i
$613$	−28.4522	−	28.4522i	−1.14917	−	1.14917i	−0.986716	−	0.162457i	$-0.948058\pi$
$613$	−28.4522	−	28.4522i	−1.14917	−	1.14917i	−0.162457	−	0.986716i	$-0.551942\pi$
$614$	−20.7759			−0.838447
$615$	−4.07964	−	8.50104i	−0.164507	−	0.342795i
$616$		0			0
$617$	8.45912	−	8.45912i	0.340551	−	0.340551i	−0.516023	−	0.856575i	$-0.672588\pi$
$617$	8.45912	−	8.45912i	0.340551	−	0.340551i	0.856575	+	0.516023i	$0.172588\pi$
$618$	13.9294	+	13.9294i	0.560323	+	0.560323i
$619$	44.3961			1.78443			0.892215	−	0.451610i	$-0.149150\pi$
$619$	44.3961			1.78443			0.892215	+	0.451610i	$0.149150\pi$
$620$	−6.63578	−	2.33210i	−0.266500	−	0.0936595i
$621$		−	2.54910i		−	0.102292i
$622$	−8.40005	−	8.40005i	−0.336811	−	0.336811i
$623$		0			0
$624$			5.11428i			0.204735i
$625$	5.43027	+	24.4031i	0.217211	+	0.976125i
$626$		−	10.8023i		−	0.431748i
$627$	1.78138	−	1.78138i	0.0711415	−	0.0711415i
$628$	−12.6906	+	12.6906i	−0.506409	+	0.506409i
$629$	−25.9251			−1.03370
$630$		0			0
$631$	15.7488			0.626951			0.313475	−	0.949596i	$-0.398507\pi$
$631$	15.7488			0.626951			0.313475	+	0.949596i	$0.398507\pi$
$632$	−0.331128	+	0.331128i	−0.0131716	+	0.0131716i
$633$	−0.182970	+	0.182970i	−0.00727241	+	0.00727241i
$634$			20.0860i			0.797718i
$635$	−2.64517	+	1.26941i	−0.104970	+	0.0503752i
$636$		−	10.1420i		−	0.402157i
$637$		0			0
$638$	6.03193	+	6.03193i	0.238806	+	0.238806i
$639$			6.87114i			0.271818i
$640$	0.967451	+	2.01595i	0.0382419	+	0.0796873i
$641$	−4.36993			−0.172602			−0.0863010	−	0.996269i	$-0.527505\pi$
$641$	−4.36993			−0.172602			−0.0863010	+	0.996269i	$0.527505\pi$
$642$	−11.6959	−	11.6959i	−0.461599	−	0.461599i
$643$	−5.95934	+	5.95934i	−0.235013	+	0.235013i	−0.814781	−	0.579768i	$-0.803143\pi$
$643$	−5.95934	+	5.95934i	−0.235013	+	0.235013i	0.579768	+	0.814781i	$0.303143\pi$
$644$		0			0
$645$	8.56591	+	3.01043i	0.337282	+	0.118536i
$646$	13.6737			0.537983
$647$	10.8598	+	10.8598i	0.426941	+	0.426941i	0.887585	−	0.460644i	$-0.152382\pi$
$647$	10.8598	+	10.8598i	0.426941	+	0.426941i	−0.460644	+	0.887585i	$0.652382\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−3.34300			−0.131224
$650$	15.9979	−	19.9491i	0.627488	−	0.782467i
$651$		0			0
$652$	−0.801211	+	0.801211i	−0.0313778	+	0.0313778i
$653$	−33.1191	−	33.1191i	−1.29605	−	1.29605i	−0.930981	−	0.365068i	$-0.881046\pi$
$653$	−33.1191	−	33.1191i	−1.29605	−	1.29605i	−0.365068	−	0.930981i	$-0.618954\pi$
$654$	−9.35564			−0.365835
$655$	−10.6661	+	30.3495i	−0.416760	+	1.18585i
$656$			4.21690i			0.164642i
$657$	3.69923	+	3.69923i	0.144321	+	0.144321i
$658$		0			0
$659$		−	23.2624i		−	0.906176i	−0.891466	−	0.453088i	$-0.850322\pi$
$659$		−	23.2624i		−	0.906176i	0.891466	−	0.453088i	$-0.149678\pi$
$660$	−1.13147	−	2.35772i	−0.0440423	−	0.0917741i
$661$			13.3959i			0.521041i	0.965468	+	0.260521i	$0.0838942\pi$
$661$			13.3959i			0.521041i	−0.965468	+	0.260521i	$0.916106\pi$
$662$	16.2003	−	16.2003i	0.629644	−	0.629644i
$663$	22.9560	−	22.9560i	0.891538	−	0.891538i
$664$	13.9637			0.541898
$665$		0			0
$666$	−4.08408			−0.158255
$667$	−13.1471	+	13.1471i	−0.509057	+	0.509057i
$668$	17.0302	−	17.0302i	0.658917	−	0.658917i
$669$			19.6039i			0.757930i
$670$	10.8926	−	30.9938i	0.420817	−	1.19740i
$671$		−	11.8060i		−	0.455766i
$672$		0			0
$673$	−26.2079	−	26.2079i	−1.01024	−	1.01024i	−0.999947	−	0.0102944i	$-0.996723\pi$
$673$	−26.2079	−	26.2079i	−1.01024	−	1.01024i	−0.0102944	−	0.999947i	$-0.503277\pi$
$674$		−	28.2638i		−	1.08868i
$675$	0.546298	+	4.97007i	0.0210270	+	0.191298i
$676$	−13.1559			−0.505996
$677$	13.1542	+	13.1542i	0.505557	+	0.505557i	0.913159	−	0.407603i	$-0.133635\pi$
$677$	13.1542	+	13.1542i	0.505557	+	0.505557i	−0.407603	+	0.913159i	$0.633635\pi$
$678$	0.775120	−	0.775120i	0.0297683	−	0.0297683i
$679$		0			0
$680$	4.70628	−	13.3913i	0.180478	−	0.513533i
$681$	7.33800			0.281193
$682$	−2.60132	−	2.60132i	−0.0996099	−	0.0996099i
$683$	36.1197	+	36.1197i	1.38208	+	1.38208i	0.840918	+	0.541163i	$0.182016\pi$
$683$	36.1197	+	36.1197i	1.38208	+	1.38208i	0.541163	+	0.840918i	$0.317984\pi$
$684$	2.15406			0.0823627
$685$	0.911973	−	0.437655i	0.0348447	−	0.0167220i
$686$		0			0
$687$	−7.02131	+	7.02131i	−0.267880	+	0.267880i
$688$	−2.87119	−	2.87119i	−0.109463	−	0.109463i
$689$	51.8692			1.97606
$690$	5.13884	−	2.46613i	0.195632	−	0.0938838i
$691$		−	19.8996i		−	0.757016i	−0.925598	−	0.378508i	$-0.876437\pi$
$691$		−	19.8996i		−	0.757016i	0.925598	−	0.378508i	$-0.123563\pi$
$692$	−5.87360	−	5.87360i	−0.223281	−	0.223281i
$693$		0			0
$694$			0.0361053i			0.00137054i
$695$	29.4191	+	10.3391i	1.11593	+	0.392186i
$696$			7.29386i			0.276473i
$697$	18.9280	−	18.9280i	0.716949	−	0.716949i
$698$	3.99269	−	3.99269i	0.151125	−	0.151125i
$699$	−1.95841			−0.0740737
$700$		0			0
$701$	10.4696			0.395431			0.197715	−	0.980259i	$-0.436648\pi$
$701$	10.4696			0.395431			0.197715	+	0.980259i	$0.436648\pi$
$702$	3.61635	−	3.61635i	0.136490	−	0.136490i
$703$	6.22068	−	6.22068i	0.234617	−	0.234617i
$704$			1.16954i			0.0440785i
$705$	−23.3949	−	8.22200i	−0.881105	−	0.309658i
$706$		−	12.5105i		−	0.470838i
$707$		0			0
$708$	−2.02119	−	2.02119i	−0.0759611	−	0.0759611i
$709$		−	29.2000i		−	1.09663i	−0.836272	−	0.548315i	$-0.815270\pi$
$709$		−	29.2000i		−	1.09663i	0.836272	−	0.548315i	$-0.184730\pi$
$710$	−13.8518	+	6.64749i	−0.519850	+	0.249476i
$711$	0.468286			0.0175621
$712$	−1.50268	−	1.50268i	−0.0563155	−	0.0563155i
$713$	5.66980	−	5.66980i	0.212336	−	0.212336i
$714$		0			0
$715$	12.0581	−	5.78665i	0.450946	−	0.216408i
$716$	4.86023			0.181635
$717$	8.13388	+	8.13388i	0.303765	+	0.303765i
$718$	−4.25792	−	4.25792i	−0.158904	−	0.158904i
$719$	8.92100			0.332697			0.166349	−	0.986067i	$-0.446802\pi$
$719$	8.92100			0.332697			0.166349	+	0.986067i	$0.446802\pi$
$720$	0.741398	−	2.10958i	0.0276303	−	0.0786194i
$721$		0			0
$722$	10.1541	−	10.1541i	0.377895	−	0.377895i
$723$	10.9355	+	10.9355i	0.406697	+	0.406697i
$724$	−13.0480			−0.484925
$725$	22.8158	−	28.4509i	0.847356	−	1.05664i
$726$			9.63219i			0.357484i
$727$	−18.4955	−	18.4955i	−0.685958	−	0.685958i	0.275378	−	0.961336i	$-0.411197\pi$
$727$	−18.4955	−	18.4955i	−0.685958	−	0.685958i	−0.961336	+	0.275378i	$0.911197\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−3.87862	+	11.0363i	−0.143554	+	0.408470i
$731$			25.7753i			0.953335i
$732$	7.13798	−	7.13798i	0.263827	−	0.263827i
$733$	−10.8123	+	10.8123i	−0.399362	+	0.399362i	−0.878008	−	0.478646i	$-0.841128\pi$
$733$	−10.8123	+	10.8123i	−0.399362	+	0.399362i	0.478646	+	0.878008i	$0.341128\pi$
$734$	−0.919971			−0.0339567
$735$		0			0
$736$	−2.54910			−0.0939609
$737$	12.1500	−	12.1500i	0.447552	−	0.447552i
$738$	2.98180	−	2.98180i	0.109762	−	0.109762i
$739$		−	38.2631i		−	1.40753i	−0.710432	−	0.703766i	$-0.751500\pi$
$739$		−	38.2631i		−	1.40753i	0.710432	−	0.703766i	$-0.248500\pi$
$740$	−3.95115	−	8.23328i	−0.145247	−	0.302662i
$741$			11.0165i			0.404701i
$742$		0			0
$743$	17.5430	+	17.5430i	0.643589	+	0.643589i	0.951436	−	0.307847i	$-0.0996085\pi$
$743$	17.5430	+	17.5430i	0.643589	+	0.643589i	−0.307847	+	0.951436i	$0.599608\pi$
$744$		−	3.14555i		−	0.115321i
$745$	8.78514	−	24.9973i	0.321863	−	0.915831i
$746$	13.7074			0.501862
$747$	−9.87385	−	9.87385i	−0.361265	−	0.361265i
$748$	5.24958	−	5.24958i	0.191944	−	0.191944i
$749$		0			0
$750$	−9.49087	+	5.90960i	−0.346558	+	0.215788i
$751$	39.9959			1.45947			0.729736	−	0.683729i	$-0.239643\pi$
$751$	39.9959			1.45947			0.729736	+	0.683729i	$0.239643\pi$
$752$	7.84171	+	7.84171i	0.285958	+	0.285958i
$753$	13.6320	+	13.6320i	0.496778	+	0.496778i
$754$	−37.3029			−1.35849
$755$	−38.6695	−	13.5901i	−1.40733	−	0.494596i
$756$		0			0
$757$	−24.4907	+	24.4907i	−0.890129	+	0.890129i	−0.994535	−	0.104405i	$-0.966706\pi$
$757$	−24.4907	+	24.4907i	−0.890129	+	0.890129i	0.104405	+	0.994535i	$0.466706\pi$
$758$	−15.1009	−	15.1009i	−0.548489	−	0.548489i
$759$	2.98126			0.108213
$760$	2.08395	+	4.34247i	0.0755928	+	0.157518i
$761$			42.4551i			1.53900i	0.638648	+	0.769499i	$0.279494\pi$
$761$			42.4551i			1.53900i	−0.638648	+	0.769499i	$0.720506\pi$
$762$	−0.927811	−	0.927811i	−0.0336110	−	0.0336110i
$763$		0			0
$764$		−	13.3222i		−	0.481979i
$765$	−12.7969	+	6.14123i	−0.462674	+	0.222037i
$766$			27.3435i			0.987963i
$767$	10.3370	−	10.3370i	0.373246	−	0.373246i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	6.19909			0.223545			0.111773	−	0.993734i	$-0.464347\pi$
$769$	6.19909			0.223545			0.111773	+	0.993734i	$0.464347\pi$
$770$		0			0
$771$	0.406560			0.0146419
$772$	−8.96412	+	8.96412i	−0.322626	+	0.322626i
$773$	−16.9371	+	16.9371i	−0.609185	+	0.609185i	−0.942733	−	0.333548i	$-0.891754\pi$
$773$	−16.9371	+	16.9371i	−0.609185	+	0.609185i	0.333548	+	0.942733i	$0.391754\pi$
$774$			4.06048i			0.145951i
$775$	−9.83951	+	12.2697i	−0.353446	+	0.440741i
$776$			8.91942i			0.320189i
$777$		0			0
$778$	−27.1701	−	27.1701i	−0.974097	−	0.974097i
$779$			9.08347i			0.325449i
$780$	10.7890	+	3.79172i	0.386308	+	0.135765i
$781$	−8.03604			−0.287552
$782$	11.4419	+	11.4419i	0.409161	+	0.409161i
$783$	5.15754	−	5.15754i	0.184315	−	0.184315i
$784$		0			0
$785$	17.3630	+	36.1806i	0.619713	+	1.29134i
$786$	−14.3865			−0.513149
$787$	16.4803	+	16.4803i	0.587460	+	0.587460i	0.936943	−	0.349483i	$-0.113643\pi$
$787$	16.4803	+	16.4803i	0.587460	+	0.587460i	−0.349483	+	0.936943i	$0.613643\pi$
$788$	17.2907	+	17.2907i	0.615957	+	0.615957i
$789$	14.8012			0.526938
$790$	0.453044	+	0.944040i	0.0161186	+	0.0335874i
$791$		0			0
$792$	0.826986	−	0.826986i	0.0293857	−	0.0293857i
$793$	36.5057	+	36.5057i	1.29635	+	1.29635i
$794$	−32.7293			−1.16152
$795$	−21.3954	−	7.51927i	−0.758817	−	0.266681i
$796$			20.6120i			0.730573i
$797$	−13.9779	−	13.9779i	−0.495124	−	0.495124i	0.414792	−	0.909916i	$-0.363854\pi$
$797$	−13.9779	−	13.9779i	−0.495124	−	0.495124i	−0.909916	+	0.414792i	$0.863854\pi$
$798$		0			0
$799$		−	70.3967i		−	2.49046i
$800$	4.97007	−	0.546298i	0.175718	−	0.0193145i
$801$			2.12512i			0.0750873i
$802$	15.7560	−	15.7560i	0.556362	−	0.556362i
$803$	−4.32638	+	4.32638i	−0.152675	+	0.152675i
$804$	14.6919			0.518145
$805$		0			0
$806$	16.0872			0.566648
$807$	8.14655	−	8.14655i	0.286772	−	0.286772i
$808$	9.85130	−	9.85130i	0.346567	−	0.346567i
$809$		−	23.2598i		−	0.817772i	−0.912585	−	0.408886i	$-0.865917\pi$
$809$		−	23.2598i		−	0.817772i	0.912585	−	0.408886i	$-0.134083\pi$
$810$	−2.01595	+	0.967451i	−0.0708331	+	0.0339928i
$811$		−	0.121247i		−	0.00425757i	−0.999998	−	0.00212879i	$-0.999322\pi$
$811$		−	0.121247i		−	0.00425757i	0.999998	−	0.00212879i	$-0.000677614\pi$
$812$		0			0
$813$	9.90573	+	9.90573i	0.347409	+	0.347409i
$814$		−	4.77648i		−	0.167415i
$815$	1.09620	+	2.28423i	0.0383983	+	0.0800132i
$816$	6.34785			0.222219
$817$	−6.18473	−	6.18473i	−0.216376	−	0.216376i
$818$	−11.5524	+	11.5524i	−0.403919	+	0.403919i
$819$		0			0
$820$	8.89589	+	3.12640i	0.310658	+	0.109179i
$821$	−23.7218			−0.827898			−0.413949	−	0.910300i	$-0.635851\pi$
$821$	−23.7218			−0.827898			−0.413949	+	0.910300i	$0.635851\pi$
$822$	0.319881	+	0.319881i	0.0111571	+	0.0111571i
$823$	7.15889	+	7.15889i	0.249543	+	0.249543i	0.820783	−	0.571240i	$-0.193537\pi$
$823$	7.15889	+	7.15889i	0.249543	+	0.249543i	−0.571240	+	0.820783i	$0.693537\pi$
$824$	−19.6992			−0.686253
$825$	−5.81267	+	0.638914i	−0.202371	+	0.0222441i
$826$		0			0
$827$	17.4450	−	17.4450i	0.606621	−	0.606621i	−0.335441	−	0.942061i	$-0.608885\pi$
$827$	17.4450	−	17.4450i	0.606621	−	0.606621i	0.942061	+	0.335441i	$0.108885\pi$
$828$	1.80248	+	1.80248i	0.0626406	+	0.0626406i
$829$	−18.8711			−0.655421			−0.327710	−	0.944778i	$-0.606277\pi$
$829$	−18.8711			−0.655421			−0.327710	+	0.944778i	$0.606277\pi$
$830$	10.3527	−	29.4576i	0.359347	−	1.02249i
$831$		−	22.7939i		−	0.790710i
$832$	−3.61635	−	3.61635i	−0.125374	−	0.125374i
$833$		0			0
$834$			13.9455i			0.482892i
$835$	−23.3004	−	48.5527i	−0.806343	−	1.68023i
$836$			2.51925i			0.0871302i
$837$	−2.22424	+	2.22424i	−0.0768809	+	0.0768809i
$838$	−20.7223	+	20.7223i	−0.715839	+	0.715839i
$839$	7.62589			0.263275			0.131637	−	0.991298i	$-0.457977\pi$
$839$	7.62589			0.263275			0.131637	+	0.991298i	$0.457977\pi$
$840$		0			0
$841$	−24.2005			−0.834499
$842$	−23.0432	+	23.0432i	−0.794123	+	0.794123i
$843$	15.5386	−	15.5386i	0.535178	−	0.535178i
$844$		−	0.258759i		−	0.00890685i
$845$	−9.75376	+	27.7534i	−0.335540	+	0.954747i
$846$		−	11.0899i		−	0.381277i
$847$		0			0
$848$	7.17149	+	7.17149i	0.246270	+	0.246270i
$849$			3.43290i			0.117817i
$850$	−24.7608	−	19.8566i	−0.849288	−	0.681074i
$851$	10.4107			0.356875
$852$	−4.85863	−	4.85863i	−0.166454	−	0.166454i
$853$	−17.4463	+	17.4463i	−0.597350	+	0.597350i	−0.939607	−	0.342256i	$-0.888809\pi$
$853$	−17.4463	+	17.4463i	−0.597350	+	0.597350i	0.342256	+	0.939607i	$0.388809\pi$
$854$		0			0
$855$	1.59702	−	4.54417i	0.0546169	−	0.155407i
$856$	16.5405			0.565341
$857$	−8.57759	−	8.57759i	−0.293005	−	0.293005i	0.545261	−	0.838266i	$-0.316430\pi$
$857$	−8.57759	−	8.57759i	−0.293005	−	0.293005i	−0.838266	+	0.545261i	$0.816430\pi$
$858$	4.22944	+	4.22944i	0.144391	+	0.144391i
$859$	−41.9829			−1.43244			−0.716219	−	0.697875i	$-0.754129\pi$
$859$	−41.9829			−1.43244			−0.716219	+	0.697875i	$0.754129\pi$
$860$	−8.18571	+	3.92832i	−0.279130	+	0.133955i
$861$		0			0
$862$	13.5275	−	13.5275i	0.460749	−	0.460749i
$863$	−14.7762	−	14.7762i	−0.502989	−	0.502989i	0.409377	−	0.912365i	$-0.365746\pi$
$863$	−14.7762	−	14.7762i	−0.502989	−	0.502989i	−0.912365	+	0.409377i	$0.865746\pi$
$864$	1.00000			0.0340207
$865$	−16.7455	+	8.03615i	−0.569364	+	0.273237i
$866$		−	0.585651i		−	0.0199012i
$867$	−16.4722	−	16.4722i	−0.559425	−	0.559425i
$868$		0			0
$869$			0.547677i			0.0185787i
$870$	15.3870	+	5.40766i	0.521668	+	0.183337i
$871$			75.1388i			2.54598i
$872$	6.61544	−	6.61544i	0.224027	−	0.224027i
$873$	6.30698	−	6.30698i	0.213459	−	0.213459i
$874$	−5.49091			−0.185733
$875$		0			0
$876$	−5.23150			−0.176756
$877$	1.70077	−	1.70077i	0.0574310	−	0.0574310i	−0.677808	−	0.735239i	$-0.737070\pi$
$877$	1.70077	−	1.70077i	0.0574310	−	0.0574310i	0.735239	+	0.677808i	$0.237070\pi$
$878$	−1.14728	+	1.14728i	−0.0387189	+	0.0387189i
$879$		−	17.2035i		−	0.580260i
$880$	2.46723	+	0.867091i	0.0831703	+	0.0292296i
$881$		−	6.85789i		−	0.231048i	−0.993305	−	0.115524i	$-0.963145\pi$
$881$		−	6.85789i		−	0.231048i	0.993305	−	0.115524i	$-0.0368548\pi$
$882$		0			0
$883$	35.6889	+	35.6889i	1.20103	+	1.20103i	0.973854	+	0.227174i	$0.0729484\pi$
$883$	35.6889	+	35.6889i	1.20103	+	1.20103i	0.227174	+	0.973854i	$0.427052\pi$
$884$			32.4647i			1.09191i
$885$	−5.76238	+	2.76536i	−0.193700	+	0.0929566i
$886$	23.8111			0.799949
$887$	10.9315	+	10.9315i	0.367042	+	0.367042i	0.866397	−	0.499355i	$-0.166430\pi$
$887$	10.9315	+	10.9315i	0.367042	+	0.367042i	−0.499355	+	0.866397i	$0.666430\pi$
$888$	2.88788	−	2.88788i	0.0969109	−	0.0969109i
$889$		0			0
$890$	−4.28412	+	2.05595i	−0.143604	+	0.0689155i
$891$	−1.16954			−0.0391809
$892$	−13.8620	−	13.8620i	−0.464135	−	0.464135i
$893$	16.8915	+	16.8915i	0.565254	+	0.565254i
$894$	11.8494			0.396304
$895$	3.60337	−	10.2531i	0.120447	−	0.342722i
$896$		0			0
$897$	−9.21841	+	9.21841i	−0.307794	+	0.307794i
$898$	−13.8690	−	13.8690i	−0.462816	−	0.462816i
$899$	22.9432			0.765198
$900$	−3.90066	−	3.12808i	−0.130022	−	0.104269i
$901$		−	64.3800i		−	2.14481i
$902$	3.48732	+	3.48732i	0.116115	+	0.116115i
$903$		0			0
$904$			1.09619i			0.0364586i
$905$	−9.67375	+	27.5258i	−0.321566	+	0.914988i
$906$		−	18.3304i		−	0.608988i
$907$	−25.7869	+	25.7869i	−0.856238	+	0.856238i	−0.990893	−	0.134654i	$-0.957008\pi$
$907$	−25.7869	+	25.7869i	−0.856238	+	0.856238i	0.134654	+	0.990893i	$0.457008\pi$
$908$	−5.18875	+	5.18875i	−0.172195	+	0.172195i
$909$	−13.9318			−0.462090
$910$		0			0
$911$	3.16845			0.104976			0.0524878	−	0.998622i	$-0.483285\pi$
$911$	3.16845			0.104976			0.0524878	+	0.998622i	$0.483285\pi$
$912$	−1.52315	+	1.52315i	−0.0504366	+	0.0504366i
$913$	11.5478	−	11.5478i	0.382177	−	0.382177i
$914$			18.2611i			0.604025i
$915$	−9.76606	−	20.3502i	−0.322856	−	0.672758i
$916$		−	9.92964i		−	0.328084i
$917$		0			0
$918$	−4.48861	−	4.48861i	−0.148146	−	0.148146i
$919$		−	4.95462i		−	0.163438i	−0.996655	−	0.0817189i	$-0.973959\pi$
$919$		−	4.95462i		−	0.163438i	0.996655	−	0.0817189i	$-0.0260410\pi$
$920$	−1.88989	+	5.37752i	−0.0623080	+	0.177292i
$921$	−20.7759			−0.684589
$922$	−0.550717	−	0.550717i	−0.0181369	−	0.0181369i
$923$	24.8484	−	24.8484i	0.817895	−	0.817895i
$924$		0			0
$925$	−20.2981	+	2.23112i	−0.667399	+	0.0733589i
$926$	−36.7558			−1.20787
$927$	13.9294	+	13.9294i	0.457502	+	0.457502i
$928$	−5.15754	−	5.15754i	−0.169305	−	0.169305i
$929$	−6.99153			−0.229385			−0.114692	−	0.993401i	$-0.536588\pi$
$929$	−6.99153			−0.229385			−0.114692	+	0.993401i	$0.536588\pi$
$930$	−6.63578	−	2.33210i	−0.217596	−	0.0764726i
$931$		0			0
$932$	1.38480	−	1.38480i	0.0453607	−	0.0453607i
$933$	−8.40005	−	8.40005i	−0.275005	−	0.275005i
$934$	38.9551			1.27465
$935$	−7.18239	−	14.9665i	−0.234889	−	0.489455i
$936$			5.11428i			0.167166i
$937$	1.17791	+	1.17791i	0.0384806	+	0.0384806i	0.726085	−	0.687605i	$-0.241338\pi$
$937$	1.17791	+	1.17791i	0.0384806	+	0.0384806i	−0.687605	+	0.726085i	$0.741338\pi$
$938$		0			0
$939$		−	10.8023i		−	0.352521i
$940$	22.3566	−	10.7289i	0.729190	−	0.349938i
$941$			10.4808i			0.341663i	0.985300	+	0.170832i	$0.0546454\pi$
$941$			10.4808i			0.341663i	−0.985300	+	0.170832i	$0.945355\pi$
$942$	−12.6906	+	12.6906i	−0.413482	+	0.413482i
$943$	−7.60089	+	7.60089i	−0.247519	+	0.247519i
$944$	2.85840			0.0930329
$945$		0			0
$946$	−4.74888			−0.154399
$947$	−28.1616	+	28.1616i	−0.915128	+	0.915128i	−0.996670	−	0.0815421i	$-0.974016\pi$
$947$	−28.1616	+	28.1616i	−0.915128	+	0.915128i	0.0815421	+	0.996670i	$0.474016\pi$
$948$	−0.331128	+	0.331128i	−0.0107545	+	0.0107545i
$949$		−	26.7554i		−	0.868516i
$950$	10.7058	−	1.17676i	0.347343	−	0.0381791i
$951$			20.0860i			0.651334i
$952$		0			0
$953$	−6.03816	−	6.03816i	−0.195595	−	0.195595i	0.602513	−	0.798109i	$-0.294166\pi$
$953$	−6.03816	−	6.03816i	−0.195595	−	0.195595i	−0.798109	+	0.602513i	$0.794166\pi$
$954$		−	10.1420i		−	0.328360i
$955$	−28.1042	−	9.87702i	−0.909429	−	0.319613i
$956$	−11.5030			−0.372035
$957$	6.03193	+	6.03193i	0.194984	+	0.194984i
$958$	−16.5573	+	16.5573i	−0.534941	+	0.534941i
$959$		0			0
$960$	0.967451	+	2.01595i	0.0312243	+	0.0650644i
$961$	21.1055			0.680824
$962$	14.7694	+	14.7694i	0.476186	+	0.476186i
$963$	−11.6959	−	11.6959i	−0.376894	−	0.376894i
$964$	−15.4652			−0.498100
$965$	12.2646	+	25.5565i	0.394810	+	0.822693i
$966$		0			0
$967$	−7.44311	+	7.44311i	−0.239354	+	0.239354i	−0.816583	−	0.577228i	$-0.804134\pi$
$967$	−7.44311	+	7.44311i	−0.239354	+	0.239354i	0.577228	+	0.816583i	$0.304134\pi$
$968$	−6.81098	−	6.81098i	−0.218913	−	0.218913i
$969$	13.6737			0.439261
$970$	18.8162	+	6.61284i	0.604153	+	0.212325i
$971$		−	5.29938i		−	0.170065i	−0.996378	−	0.0850326i	$-0.972901\pi$
$971$		−	5.29938i		−	0.170065i	0.996378	−	0.0850326i	$-0.0270995\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$		0			0
$974$			19.9008i			0.637662i
$975$	15.9979	−	19.9491i	0.512342	−	0.638882i
$976$			10.0946i			0.323121i
$977$	22.1876	−	22.1876i	0.709845	−	0.709845i	−0.256658	−	0.966502i	$-0.582621\pi$
$977$	22.1876	−	22.1876i	0.709845	−	0.709845i	0.966502	+	0.256658i	$0.0826213\pi$
$978$	−0.801211	+	0.801211i	−0.0256199	+	0.0256199i
$979$	−2.48540			−0.0794337
$980$		0			0
$981$	−9.35564			−0.298703
$982$	−7.18943	+	7.18943i	−0.229424	+	0.229424i
$983$	2.55977	−	2.55977i	0.0816441	−	0.0816441i	−0.665105	−	0.746749i	$-0.731613\pi$
$983$	2.55977	−	2.55977i	0.0816441	−	0.0816441i	0.746749	+	0.665105i	$0.231613\pi$
$984$			4.21690i			0.134430i
$985$	49.2955	−	23.6569i	1.57069	−	0.753771i
$986$			46.3004i			1.47450i
$987$		0			0
$988$	−7.78983	−	7.78983i	−0.247828	−	0.247828i
$989$		−	10.3506i		−	0.329129i
$990$	−1.13147	−	2.35772i	−0.0359604	−	0.0749333i
$991$	38.0909			1.21000			0.604998	−	0.796227i	$-0.293174\pi$
$991$	38.0909			1.21000			0.604998	+	0.796227i	$0.293174\pi$
$992$	2.22424	+	2.22424i	0.0706196	+	0.0706196i
$993$	16.2003	−	16.2003i	0.514102	−	0.514102i
$994$		0			0
$995$	43.4827	+	15.2817i	1.37849	+	0.484462i
$996$	13.9637			0.442458
$997$	−0.946124	−	0.946124i	−0.0299640	−	0.0299640i	0.691966	−	0.721930i	$-0.256745\pi$
$997$	−0.946124	−	0.946124i	−0.0299640	−	0.0299640i	−0.721930	+	0.691966i	$0.756745\pi$
$998$	−15.5829	−	15.5829i	−0.493268	−	0.493268i
$999$	−4.08408			−0.129215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.c.1273.1	yes	16
5.2	odd	4		1470.2.m.f.97.4	yes	16
7.6	odd	2		1470.2.m.f.1273.4	yes	16
35.27	even	4	inner	1470.2.m.c.97.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.1	✓	16	35.27	even	4	inner
1470.2.m.c.1273.1	yes	16	1.1	even	1	trivial
1470.2.m.f.97.4	yes	16	5.2	odd	4
1470.2.m.f.1273.4	yes	16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.10958 - 0.741398i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.10958 - 0.741398i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(2.01595 - 0.967451i) q^{10} +1.16954 q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.61635 + 3.61635i) q^{13} +(2.01595 - 0.967451i) q^{15} -1.00000 q^{16} +(4.48861 + 4.48861i) q^{17} +(0.707107 + 0.707107i) q^{18} -2.15406 q^{19} +(-0.741398 + 2.10958i) q^{20} +(-0.826986 + 0.826986i) q^{22} +(-1.80248 - 1.80248i) q^{23} -1.00000 q^{24} +(3.90066 + 3.12808i) q^{25} -5.11428i q^{26} +(0.707107 + 0.707107i) q^{27} -7.29386i q^{29} +(-0.741398 + 2.10958i) q^{30} +3.14555i q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.826986 + 0.826986i) q^{33} -6.34785 q^{34} -1.00000 q^{36} +(-2.88788 + 2.88788i) q^{37} +(1.52315 - 1.52315i) q^{38} -5.11428i q^{39} +(-0.967451 - 2.01595i) q^{40} -4.21690i q^{41} +(2.87119 + 2.87119i) q^{43} -1.16954i q^{44} +(-0.741398 + 2.10958i) q^{45} +2.54910 q^{46} +(-7.84171 - 7.84171i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-4.97007 + 0.546298i) q^{50} -6.34785 q^{51} +(3.61635 + 3.61635i) q^{52} +(-7.17149 - 7.17149i) q^{53} -1.00000 q^{54} +(-2.46723 - 0.867091i) q^{55} +(1.52315 - 1.52315i) q^{57} +(5.15754 + 5.15754i) q^{58} -2.85840 q^{59} +(-0.967451 - 2.01595i) q^{60} -10.0946i q^{61} +(-2.22424 - 2.22424i) q^{62} +1.00000i q^{64} +(10.3101 - 4.94782i) q^{65} -1.16954i q^{66} +(10.3888 - 10.3888i) q^{67} +(4.48861 - 4.48861i) q^{68} +2.54910 q^{69} -6.87114 q^{71} +(0.707107 - 0.707107i) q^{72} +(-3.69923 + 3.69923i) q^{73} -4.08408i q^{74} +(-4.97007 + 0.546298i) q^{75} +2.15406i q^{76} +(3.61635 + 3.61635i) q^{78} +0.468286i q^{79} +(2.10958 + 0.741398i) q^{80} -1.00000 q^{81} +(2.98180 + 2.98180i) q^{82} +(9.87385 - 9.87385i) q^{83} +(-6.14123 - 12.7969i) q^{85} -4.06048 q^{86} +(5.15754 + 5.15754i) q^{87} +(0.826986 + 0.826986i) q^{88} -2.12512 q^{89} +(-0.967451 - 2.01595i) q^{90} +(-1.80248 + 1.80248i) q^{92} +(-2.22424 - 2.22424i) q^{93} +11.0899 q^{94} +(4.54417 + 1.59702i) q^{95} +1.00000i q^{96} +(6.30698 + 6.30698i) q^{97} -1.16954i 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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