LMFDB - Embedded newform 1470.2.m.c.97.1

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			97.1
Root			$2.23272 + 0.122339i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.c.1273.1

$q$-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 $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

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

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
$5$	−2.10958	+	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	−0.999996	−	0.00299816i	$-0.999046\pi$
$13$	−3.61635	−	3.61635i	−1.00299	−	1.00299i	−0.00299816	−	0.999996i	$-0.500954\pi$
$14$		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	0.0929791	−	0.995668i	$-0.470361\pi$
$17$	4.48861	−	4.48861i	1.08865	−	1.08865i	0.995668	−	0.0929791i	$-0.0296390\pi$
$18$	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	−0.869600	−	0.493756i	$-0.835623\pi$
$23$	−1.80248	+	1.80248i	−0.375844	+	0.375844i	0.493756	+	0.869600i	$0.335623\pi$
$24$	−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	$0.236815\pi$
$29$			7.29386i			1.35444i	−0.735782	+	0.677218i	$0.763185\pi$
$30$	−0.741398	−	2.10958i	−0.135360	−	0.385155i
$31$		−	3.14555i		−	0.564957i	−0.959274	−	0.282478i	$-0.908843\pi$
$31$		−	3.14555i		−	0.564957i	0.959274	−	0.282478i	$-0.0911566\pi$
$32$	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	0.428688	−	0.903453i	$-0.358976\pi$
$37$	−2.88788	−	2.88788i	−0.474765	−	0.474765i	−0.903453	+	0.428688i	$0.858976\pi$
$38$	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	$0.106808\pi$
$41$			4.21690i			0.658569i	−0.944231	+	0.329285i	$0.893192\pi$
$42$		0			0
$43$	2.87119	−	2.87119i	0.437853	−	0.437853i	−0.453436	−	0.891289i	$-0.649802\pi$
$43$	2.87119	−	2.87119i	0.437853	−	0.437853i	0.891289	+	0.453436i	$0.149802\pi$
$44$			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	−0.156088	+	0.987743i	$0.549888\pi$
$47$	−7.84171	+	7.84171i	−1.14383	+	1.14383i	−0.987743	+	0.156088i	$0.950112\pi$
$48$	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	−0.999890	−	0.0148103i	$-0.995286\pi$
$53$	−7.17149	+	7.17149i	−0.985080	+	0.985080i	0.0148103	+	0.999890i	$0.495286\pi$
$54$	−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	$0.223660\pi$
$61$			10.0946i			1.29248i	−0.763132	+	0.646242i	$0.776340\pi$
$62$	−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	0.946507	+	0.322684i	$0.104585\pi$
$67$	10.3888	+	10.3888i	1.26919	+	1.26919i	0.322684	+	0.946507i	$0.395415\pi$
$68$	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	0.456673	−	0.889635i	$-0.349041\pi$
$73$	−3.69923	−	3.69923i	−0.432962	−	0.432962i	−0.889635	+	0.456673i	$0.849041\pi$
$74$			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	$-0.991614\pi$
$79$		−	0.468286i		−	0.0526863i	0.999653	−	0.0263432i	$-0.00838626\pi$
$80$	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	0.996152	+	0.0876438i	$0.0279337\pi$
$83$	9.87385	+	9.87385i	1.08380	+	1.08380i	0.0876438	+	0.996152i	$0.472066\pi$
$84$		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	−0.310271	−	0.950648i	$-0.600420\pi$
$97$	6.30698	−	6.30698i	0.640377	−	0.640377i	0.950648	+	0.310271i	$0.100420\pi$
$98$		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	$0.243771\pi$
$101$			13.9318i			1.38627i	−0.720808	+	0.693135i	$0.756229\pi$
$102$	4.48861	+	4.48861i	0.444438	+	0.444438i
$103$	−13.9294	−	13.9294i	−1.37251	−	1.37251i	−0.856714	−	0.515792i	$-0.827498\pi$
$103$	−13.9294	−	13.9294i	−1.37251	−	1.37251i	−0.515792	−	0.856714i	$-0.672502\pi$
$104$	−5.11428			−0.501497
$105$		0			0
$106$	10.1420			0.985080
$107$	11.6959	+	11.6959i	1.13068	+	1.13068i	0.990064	+	0.140619i	$0.0449093\pi$
$107$	11.6959	+	11.6959i	1.13068	+	1.13068i	0.140619	+	0.990064i	$0.455091\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			9.35564i			0.896108i	0.894006	+	0.448054i	$0.147883\pi$
$109$			9.35564i			0.896108i	−0.894006	+	0.448054i	$0.852117\pi$
$110$	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	−0.669708	−	0.742625i	$-0.733581\pi$
$113$	0.775120	−	0.775120i	0.0729172	−	0.0729172i	0.742625	+	0.669708i	$0.233581\pi$
$114$		−	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	0.747072	−	0.664743i	$-0.231459\pi$
$127$	0.927811	+	0.927811i	0.0823299	+	0.0823299i	−0.664743	+	0.747072i	$0.731459\pi$
$128$	−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	$0.216321\pi$
$131$			14.3865i			1.25695i	−0.777828	+	0.628477i	$0.783679\pi$
$132$	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	0.693310	−	0.720639i	$-0.256152\pi$
$137$	−0.319881	−	0.319881i	−0.0273293	−	0.0273293i	−0.720639	+	0.693310i	$0.756152\pi$
$138$	−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	$-0.838684\pi$
$149$		−	11.8494i		−	0.970743i	0.874308	−	0.485372i	$-0.161316\pi$
$150$	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	−0.0129021	+	0.999917i	$0.504107\pi$
$157$	−12.6906	+	12.6906i	−1.01282	+	1.01282i	−0.999917	+	0.0129021i	$0.995893\pi$
$158$	−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	−0.737788	−	0.675032i	$-0.764130\pi$
$163$	−0.801211	+	0.801211i	−0.0627557	+	0.0627557i	0.675032	+	0.737788i	$0.264130\pi$
$164$	−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	0.402348	−	0.915487i	$-0.368194\pi$
$167$	17.0302	−	17.0302i	1.31783	−	1.31783i	0.915487	−	0.402348i	$-0.131806\pi$
$168$		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	0.894210	−	0.447648i	$-0.147738\pi$
$173$	5.87360	+	5.87360i	0.446561	+	0.446561i	−0.447648	+	0.894210i	$0.647738\pi$
$174$	−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	$-0.941861\pi$
$179$		−	4.86023i		−	0.363271i	0.983366	−	0.181635i	$-0.0581391\pi$
$180$	2.10958	−	0.741398i	0.157239	−	0.0552605i
$181$			13.0480i			0.969849i	0.874556	+	0.484925i	$0.161153\pi$
$181$			13.0480i			0.969849i	−0.874556	+	0.484925i	$0.838847\pi$
$182$		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	−0.951842	−	0.306590i	$-0.900812\pi$
$193$	−8.96412	+	8.96412i	−0.645252	+	0.645252i	0.306590	+	0.951842i	$0.400812\pi$
$194$	−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	−0.963228	−	0.268686i	$-0.913410\pi$
$197$	−17.2907	−	17.2907i	−1.23191	−	1.23191i	−0.268686	−	0.963228i	$-0.586590\pi$
$198$	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	0.997594	−	0.0693236i	$-0.0220841\pi$
$223$	13.8620	+	13.8620i	0.928271	+	0.928271i	−0.0693236	+	0.997594i	$0.522084\pi$
$224$		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	−0.858015	−	0.513625i	$-0.828302\pi$
$227$	−5.18875	+	5.18875i	−0.344389	+	0.344389i	0.513625	+	0.858015i	$0.328302\pi$
$228$	−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	−0.660290	−	0.751011i	$-0.729566\pi$
$233$	1.38480	−	1.38480i	0.0907214	−	0.0907214i	0.751011	+	0.660290i	$0.229566\pi$
$234$	−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	$0.121340\pi$
$239$			11.5030i			0.744070i	−0.928219	+	0.372035i	$0.878660\pi$
$240$	−2.01595	−	0.967451i	−0.130129	−	0.0624487i
$241$			15.4652i			0.996199i	0.867120	+	0.498100i	$0.165969\pi$
$241$			15.4652i			0.996199i	−0.867120	+	0.498100i	$0.834031\pi$
$242$	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	$0.208199\pi$
$251$			19.2786i			1.21685i	−0.793610	+	0.608427i	$0.791801\pi$
$252$		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	−0.716016	−	0.698084i	$-0.754036\pi$
$257$	−0.287481	+	0.287481i	−0.0179326	+	0.0179326i	0.698084	+	0.716016i	$0.254036\pi$
$258$	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	−0.951869	−	0.306504i	$-0.900841\pi$
$263$	−10.4661	+	10.4661i	−0.645365	+	0.645365i	0.306504	+	0.951869i	$0.400841\pi$
$264$	−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	$0.139897\pi$
$271$			14.0088i			0.850975i	−0.904964	+	0.425488i	$0.860103\pi$
$272$	−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	0.0310981	−	0.999516i	$-0.490100\pi$
$277$	−16.1177	−	16.1177i	−0.968418	−	0.968418i	−0.999516	+	0.0310981i	$0.990100\pi$
$278$	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	0.775564	−	0.631269i	$-0.217465\pi$
$283$	2.42743	+	2.42743i	0.144296	+	0.144296i	−0.631269	+	0.775564i	$0.717465\pi$
$284$		−	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	0.256005	−	0.966675i	$-0.417594\pi$
$293$	−12.1647	−	12.1647i	−0.710670	−	0.710670i	−0.966675	+	0.256005i	$0.917594\pi$
$294$		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	−0.150208	−	0.988654i	$-0.547994\pi$
$307$	14.6908	−	14.6908i	0.838447	−	0.838447i	0.988654	+	0.150208i	$0.0479943\pi$
$308$		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	$-0.890652\pi$
$311$		−	11.8795i		−	0.673622i	0.941572	−	0.336811i	$-0.109348\pi$
$312$	3.61635	+	3.61635i	0.204735	+	0.204735i
$313$	−7.63841	−	7.63841i	−0.431748	−	0.431748i	0.457474	−	0.889223i	$-0.348754\pi$
$313$	−7.63841	−	7.63841i	−0.431748	−	0.431748i	−0.889223	+	0.457474i	$0.848754\pi$
$314$	17.9472			1.01282
$315$		0			0
$316$	0.468286			0.0263432
$317$	14.2030	+	14.2030i	0.797718	+	0.797718i	0.982735	−	0.185018i	$-0.0592342\pi$
$317$	14.2030	+	14.2030i	0.797718	+	0.797718i	−0.185018	+	0.982735i	$0.559234\pi$
$318$	−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	−0.995665	−	0.0930152i	$-0.970349\pi$
$337$	−19.9855	−	19.9855i	−1.08868	−	1.08868i	−0.0930152	−	0.995665i	$-0.529651\pi$
$338$	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	0.707792	−	0.706421i	$-0.249692\pi$
$347$	0.0255303	+	0.0255303i	0.00137054	+	0.00137054i	−0.706421	+	0.707792i	$0.749692\pi$
$348$	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	0.431348	−	0.902186i	$-0.358038\pi$
$353$	−8.84624	−	8.84624i	−0.470838	−	0.470838i	−0.902186	+	0.431348i	$0.858038\pi$
$354$		−	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	$-0.949204\pi$
$359$		−	6.02161i		−	0.317808i	0.987294	−	0.158904i	$-0.0507961\pi$
$360$	−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	−0.689925	−	0.723881i	$-0.742356\pi$
$367$	0.650518	−	0.650518i	0.0339567	−	0.0339567i	0.723881	+	0.689925i	$0.242356\pi$
$368$	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	−0.912016	−	0.410154i	$-0.865475\pi$
$373$	−9.69257	+	9.69257i	−0.501862	+	0.501862i	0.410154	+	0.912016i	$0.365475\pi$
$374$	−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	$-0.815203\pi$
$379$		−	21.3559i		−	1.09698i	0.836157	−	0.548489i	$-0.184797\pi$
$380$	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	0.999928	−	0.0119658i	$-0.00380892\pi$
$383$	19.3348	+	19.3348i	0.987963	+	0.987963i	−0.0119658	+	0.999928i	$0.503809\pi$
$384$	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	$-0.572608\pi$
$389$		−	38.4244i		−	1.94819i	0.226131	−	0.974097i	$-0.427392\pi$
$390$	−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	0.177375	−	0.984143i	$-0.443239\pi$
$397$	23.1431	−	23.1431i	1.16152	−	1.16152i	0.984143	−	0.177375i	$-0.0567605\pi$
$398$	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	0.697086	−	0.716987i	$-0.254479\pi$
$433$	−0.414118	−	0.414118i	−0.0199012	−	0.0199012i	−0.716987	+	0.697086i	$0.754479\pi$
$434$		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	−0.983087	−	0.183138i	$-0.941375\pi$
$443$	−16.8370	+	16.8370i	−0.799949	+	0.799949i	0.183138	+	0.983087i	$0.441375\pi$
$444$	−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	$-0.846839\pi$
$449$		−	19.6138i		−	0.925631i	0.886455	−	0.462816i	$-0.153161\pi$
$450$	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	0.941378	−	0.337354i	$-0.109532\pi$
$457$	12.9126	+	12.9126i	0.604025	+	0.604025i	−0.337354	+	0.941378i	$0.609532\pi$
$458$	−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	$-0.994227\pi$
$461$		−	0.778831i		−	0.0362738i	0.999836	−	0.0181369i	$-0.00577347\pi$
$462$		0			0
$463$	25.9903	−	25.9903i	1.20787	−	1.20787i	0.236154	−	0.971716i	$-0.424113\pi$
$463$	25.9903	−	25.9903i	1.20787	−	1.20787i	0.971716	−	0.236154i	$-0.0758870\pi$
$464$		−	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	−0.331027	+	0.943621i	$0.607395\pi$
$467$	−27.5454	+	27.5454i	−1.27465	+	1.27465i	−0.943621	+	0.331027i	$0.892605\pi$
$468$	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	0.949978	−	0.312316i	$-0.101105\pi$
$487$	14.0720	+	14.0720i	0.637662	+	0.637662i	−0.312316	+	0.949978i	$0.601105\pi$
$488$	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	$-0.835802\pi$
$499$		−	22.0376i		−	0.986537i	0.869877	−	0.493268i	$-0.164198\pi$
$500$	−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	0.640323	−	0.768106i	$-0.278801\pi$
$503$	−2.86588	−	2.86588i	−0.127783	−	0.127783i	−0.768106	+	0.640323i	$0.778801\pi$
$504$		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	$0.138479\pi$
$521$			19.2396i			0.842903i	−0.906851	+	0.421452i	$0.861521\pi$
$522$	5.15754	+	5.15754i	0.225739	+	0.225739i
$523$	7.54922	+	7.54922i	0.330104	+	0.330104i	0.852626	−	0.522522i	$-0.175009\pi$
$523$	7.54922	+	7.54922i	0.330104	+	0.330104i	−0.522522	+	0.852626i	$0.675009\pi$
$524$	−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	−0.999578	−	0.0290596i	$-0.990749\pi$
$547$	−24.0578	−	24.0578i	−1.02864	−	1.02864i	−0.0290596	−	0.999578i	$-0.509251\pi$
$548$	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	0.709375	−	0.704832i	$-0.248977\pi$
$557$	0.107225	+	0.107225i	0.00454326	+	0.00454326i	−0.704832	+	0.709375i	$0.748977\pi$
$558$	−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	0.662805	−	0.748792i	$-0.269366\pi$
$563$	−2.04028	−	2.04028i	−0.0859876	−	0.0859876i	−0.748792	+	0.662805i	$0.769366\pi$
$564$			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	$-0.761859\pi$
$569$		−	32.4544i		−	1.36056i	0.732953	−	0.680279i	$-0.238141\pi$
$570$	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	−0.0495146	+	0.998773i	$0.515767\pi$
$577$	−25.1807	+	25.1807i	−1.04829	+	1.04829i	−0.998773	+	0.0495146i	$0.984233\pi$
$578$	−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	−0.995842	−	0.0910934i	$-0.970964\pi$
$587$	−21.9203	+	21.9203i	−0.904749	+	0.904749i	0.0910934	+	0.995842i	$0.470964\pi$
$588$		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	0.645920	−	0.763405i	$-0.276474\pi$
$593$	−2.86095	−	2.86095i	−0.117485	−	0.117485i	−0.763405	+	0.645920i	$0.776474\pi$
$594$	−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	$0.0631282\pi$
$599$			9.64419i			0.394051i	−0.980398	+	0.197026i	$0.936872\pi$
$600$	−3.90066	+	3.12808i	−0.159244	+	0.127703i
$601$			29.7149i			1.21210i	0.795428	+	0.606048i	$0.207246\pi$
$601$			29.7149i			1.21210i	−0.795428	+	0.606048i	$0.792754\pi$
$602$		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	−0.998944	−	0.0459409i	$-0.985371\pi$
$607$	−23.4795	+	23.4795i	−0.953003	+	0.953003i	0.0459409	+	0.998944i	$0.485371\pi$
$608$	−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	−0.162457	+	0.986716i	$0.551942\pi$
$613$	−28.4522	+	28.4522i	−1.14917	+	1.14917i	−0.986716	+	0.162457i	$0.948058\pi$
$614$	−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	0.856575	−	0.516023i	$-0.172588\pi$
$617$	8.45912	+	8.45912i	0.340551	+	0.340551i	−0.516023	+	0.856575i	$0.672588\pi$
$618$	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	0.579768	−	0.814781i	$-0.303143\pi$
$643$	−5.95934	−	5.95934i	−0.235013	−	0.235013i	−0.814781	+	0.579768i	$0.803143\pi$
$644$		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	−0.460644	−	0.887585i	$-0.652382\pi$
$647$	10.8598	−	10.8598i	0.426941	−	0.426941i	0.887585	+	0.460644i	$0.152382\pi$
$648$	−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	−0.365068	+	0.930981i	$0.618954\pi$
$653$	−33.1191	+	33.1191i	−1.29605	+	1.29605i	−0.930981	+	0.365068i	$0.881046\pi$
$654$	−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	$0.149678\pi$
$659$			23.2624i			0.906176i	−0.891466	+	0.453088i	$0.850322\pi$
$660$	−1.13147	+	2.35772i	−0.0440423	+	0.0917741i
$661$		−	13.3959i		−	0.521041i	−0.965468	−	0.260521i	$-0.916106\pi$
$661$		−	13.3959i		−	0.521041i	0.965468	−	0.260521i	$-0.0838942\pi$
$662$	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	−0.0102944	+	0.999947i	$0.503277\pi$
$673$	−26.2079	+	26.2079i	−1.01024	+	1.01024i	−0.999947	+	0.0102944i	$0.996723\pi$
$674$			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	−0.407603	−	0.913159i	$-0.633635\pi$
$677$	13.1542	−	13.1542i	0.505557	−	0.505557i	0.913159	+	0.407603i	$0.133635\pi$
$678$	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	0.541163	−	0.840918i	$-0.317984\pi$
$683$	36.1197	−	36.1197i	1.38208	−	1.38208i	0.840918	−	0.541163i	$-0.182016\pi$
$684$	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	$0.123563\pi$
$691$			19.8996i			0.757016i	−0.925598	+	0.378508i	$0.876437\pi$
$692$	−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	$0.184730\pi$
$709$			29.2000i			1.09663i	−0.836272	+	0.548315i	$0.815270\pi$
$710$	−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	−0.961336	−	0.275378i	$-0.911197\pi$
$727$	−18.4955	+	18.4955i	−0.685958	+	0.685958i	0.275378	+	0.961336i	$0.411197\pi$
$728$		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	0.478646	−	0.878008i	$-0.341128\pi$
$733$	−10.8123	−	10.8123i	−0.399362	−	0.399362i	−0.878008	+	0.478646i	$0.841128\pi$
$734$	−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	$0.248500\pi$
$739$			38.2631i			1.40753i	−0.710432	+	0.703766i	$0.751500\pi$
$740$	−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	−0.307847	−	0.951436i	$-0.599608\pi$
$743$	17.5430	−	17.5430i	0.643589	−	0.643589i	0.951436	+	0.307847i	$0.0996085\pi$
$744$			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	0.104405	−	0.994535i	$-0.466706\pi$
$757$	−24.4907	−	24.4907i	−0.890129	−	0.890129i	−0.994535	+	0.104405i	$0.966706\pi$
$758$	−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	$-0.720506\pi$
$761$		−	42.4551i		−	1.53900i	0.638648	−	0.769499i	$-0.279494\pi$
$762$	−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	0.333548	−	0.942733i	$-0.391754\pi$
$773$	−16.9371	−	16.9371i	−0.609185	−	0.609185i	−0.942733	+	0.333548i	$0.891754\pi$
$774$		−	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	−0.349483	−	0.936943i	$-0.613643\pi$
$787$	16.4803	−	16.4803i	0.587460	−	0.587460i	0.936943	+	0.349483i	$0.113643\pi$
$788$	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	−0.909916	−	0.414792i	$-0.863854\pi$
$797$	−13.9779	+	13.9779i	−0.495124	+	0.495124i	0.414792	+	0.909916i	$0.363854\pi$
$798$		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	$0.134083\pi$
$809$			23.2598i			0.817772i	−0.912585	+	0.408886i	$0.865917\pi$
$810$	−2.01595	−	0.967451i	−0.0708331	−	0.0339928i
$811$			0.121247i			0.00425757i	0.999998	+	0.00212879i	$0.000677614\pi$
$811$			0.121247i			0.00425757i	−0.999998	+	0.00212879i	$0.999322\pi$
$812$		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	−0.571240	−	0.820783i	$-0.693537\pi$
$823$	7.15889	−	7.15889i	0.249543	−	0.249543i	0.820783	+	0.571240i	$0.193537\pi$
$824$	−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	0.942061	−	0.335441i	$-0.108885\pi$
$827$	17.4450	+	17.4450i	0.606621	+	0.606621i	−0.335441	+	0.942061i	$0.608885\pi$
$828$	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	0.342256	−	0.939607i	$-0.388809\pi$
$853$	−17.4463	−	17.4463i	−0.597350	−	0.597350i	−0.939607	+	0.342256i	$0.888809\pi$
$854$		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	−0.838266	−	0.545261i	$-0.816430\pi$
$857$	−8.57759	+	8.57759i	−0.293005	+	0.293005i	0.545261	+	0.838266i	$0.316430\pi$
$858$	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	−0.912365	−	0.409377i	$-0.865746\pi$
$863$	−14.7762	+	14.7762i	−0.502989	+	0.502989i	0.409377	+	0.912365i	$0.365746\pi$
$864$	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	0.735239	−	0.677808i	$-0.237070\pi$
$877$	1.70077	+	1.70077i	0.0574310	+	0.0574310i	−0.677808	+	0.735239i	$0.737070\pi$
$878$	−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	$0.0368548\pi$
$881$			6.85789i			0.231048i	−0.993305	+	0.115524i	$0.963145\pi$
$882$		0			0
$883$	35.6889	−	35.6889i	1.20103	−	1.20103i	0.227174	−	0.973854i	$-0.427052\pi$
$883$	35.6889	−	35.6889i	1.20103	−	1.20103i	0.973854	−	0.227174i	$-0.0729484\pi$
$884$		−	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	−0.499355	−	0.866397i	$-0.666430\pi$
$887$	10.9315	−	10.9315i	0.367042	−	0.367042i	0.866397	+	0.499355i	$0.166430\pi$
$888$	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	0.134654	−	0.990893i	$-0.457008\pi$
$907$	−25.7869	−	25.7869i	−0.856238	−	0.856238i	−0.990893	+	0.134654i	$0.957008\pi$
$908$	−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	$0.0260410\pi$
$919$			4.95462i			0.163438i	−0.996655	+	0.0817189i	$0.973959\pi$
$920$	−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	−0.687605	−	0.726085i	$-0.741338\pi$
$937$	1.17791	−	1.17791i	0.0384806	−	0.0384806i	0.726085	+	0.687605i	$0.241338\pi$
$938$		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	$-0.945355\pi$
$941$		−	10.4808i		−	0.341663i	0.985300	−	0.170832i	$-0.0546454\pi$
$942$	−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	0.0815421	−	0.996670i	$-0.474016\pi$
$947$	−28.1616	−	28.1616i	−0.915128	−	0.915128i	−0.996670	+	0.0815421i	$0.974016\pi$
$948$	−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	−0.798109	−	0.602513i	$-0.794166\pi$
$953$	−6.03816	+	6.03816i	−0.195595	+	0.195595i	0.602513	+	0.798109i	$0.294166\pi$
$954$			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	0.577228	−	0.816583i	$-0.304134\pi$
$967$	−7.44311	−	7.44311i	−0.239354	−	0.239354i	−0.816583	+	0.577228i	$0.804134\pi$
$968$	−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	$0.0270995\pi$
$971$			5.29938i			0.170065i	−0.996378	+	0.0850326i	$0.972901\pi$
$972$	−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	0.966502	−	0.256658i	$-0.0826213\pi$
$977$	22.1876	+	22.1876i	0.709845	+	0.709845i	−0.256658	+	0.966502i	$0.582621\pi$
$978$	−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	0.746749	−	0.665105i	$-0.231613\pi$
$983$	2.55977	+	2.55977i	0.0816441	+	0.0816441i	−0.665105	+	0.746749i	$0.731613\pi$
$984$		−	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	−0.721930	−	0.691966i	$-0.756745\pi$
$997$	−0.946124	+	0.946124i	−0.0299640	+	0.0299640i	0.691966	+	0.721930i	$0.256745\pi$
$998$	−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.97.1	✓	16
5.3	odd	4		1470.2.m.f.1273.4	yes	16
7.6	odd	2		1470.2.m.f.97.4	yes	16
35.13	even	4	inner	1470.2.m.c.1273.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.1	✓	16	1.1	even	1	trivial
1470.2.m.c.1273.1	yes	16	35.13	even	4	inner
1470.2.m.f.97.4	yes	16	7.6	odd	2
1470.2.m.f.1273.4	yes	16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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