LMFDB - Embedded newform 1470.2.m.f.97.5

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			97.5
Root			$1.39977 - 1.74375i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.f.1273.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-2.14668 - 0.625913i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-2.14668 - 0.625913i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.07534 - 1.96052i) q^{10} +2.07328 q^{11} +(0.707107 - 0.707107i) q^{12} +(0.326993 + 0.326993i) q^{13} +(1.07534 + 1.96052i) q^{15} -1.00000 q^{16} +(1.26881 - 1.26881i) q^{17} +(-0.707107 + 0.707107i) q^{18} -4.37232 q^{19} +(0.625913 - 2.14668i) q^{20} +(1.46603 + 1.46603i) q^{22} +(0.635591 - 0.635591i) q^{23} +1.00000 q^{24} +(4.21646 + 2.68727i) q^{25} +0.462438i q^{26} +(0.707107 - 0.707107i) q^{27} -0.0288926i q^{29} +(-0.625913 + 2.14668i) q^{30} -8.03242i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.46603 - 1.46603i) q^{33} +1.79437 q^{34} -1.00000 q^{36} +(-8.07760 - 8.07760i) q^{37} +(-3.09170 - 3.09170i) q^{38} -0.462438i q^{39} +(1.96052 - 1.07534i) q^{40} -10.6696i q^{41} +(2.50876 - 2.50876i) q^{43} +2.07328i q^{44} +(0.625913 - 2.14668i) q^{45} +0.898861 q^{46} +(0.525308 - 0.525308i) q^{47} +(0.707107 + 0.707107i) q^{48} +(1.08130 + 4.88168i) q^{50} -1.79437 q^{51} +(-0.326993 + 0.326993i) q^{52} +(7.22526 - 7.22526i) q^{53} +1.00000 q^{54} +(-4.45067 - 1.29769i) q^{55} +(3.09170 + 3.09170i) q^{57} +(0.0204302 - 0.0204302i) q^{58} +13.4242 q^{59} +(-1.96052 + 1.07534i) q^{60} +9.84270i q^{61} +(5.67978 - 5.67978i) q^{62} -1.00000i q^{64} +(-0.497280 - 0.906619i) q^{65} -2.07328i q^{66} +(-3.33098 - 3.33098i) q^{67} +(1.26881 + 1.26881i) q^{68} -0.898861 q^{69} +2.27478 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-8.14046 - 8.14046i) q^{73} -11.4235i q^{74} +(-1.08130 - 4.88168i) q^{75} -4.37232i q^{76} +(0.326993 - 0.326993i) q^{78} -8.01313i q^{79} +(2.14668 + 0.625913i) q^{80} -1.00000 q^{81} +(7.54452 - 7.54452i) q^{82} +(-4.26961 - 4.26961i) q^{83} +(-3.51790 + 1.92957i) q^{85} +3.54793 q^{86} +(-0.0204302 + 0.0204302i) q^{87} +(-1.46603 + 1.46603i) q^{88} +0.0197698 q^{89} +(1.96052 - 1.07534i) q^{90} +(0.635591 + 0.635591i) q^{92} +(-5.67978 + 5.67978i) q^{93} +0.742898 q^{94} +(9.38597 + 2.73669i) q^{95} +1.00000i q^{96} +(5.65183 - 5.65183i) q^{97} +2.07328i 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
$5$	−2.14668	−	0.625913i	−0.960024	−	0.279917i
$5$	−2.14668	−	0.625913i	−0.960024	−	0.279917i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−1.07534	−	1.96052i	−0.340054	−	0.619971i
$11$	2.07328			0.625117			0.312559	−	0.949898i	$-0.398814\pi$
$11$	2.07328			0.625117			0.312559	+	0.949898i	$0.398814\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	0.326993	+	0.326993i	0.0906916	+	0.0906916i	0.750997	−	0.660306i	$-0.229573\pi$
$13$	0.326993	+	0.326993i	0.0906916	+	0.0906916i	−0.660306	+	0.750997i	$0.729573\pi$
$14$		0			0
$15$	1.07534	+	1.96052i	0.277653	+	0.506204i
$16$	−1.00000			−0.250000
$17$	1.26881	−	1.26881i	0.307732	−	0.307732i	−0.536297	−	0.844029i	$-0.680177\pi$
$17$	1.26881	−	1.26881i	0.307732	−	0.307732i	0.844029	+	0.536297i	$0.180177\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−4.37232			−1.00308			−0.501540	−	0.865135i	$-0.667233\pi$
$19$	−4.37232			−1.00308			−0.501540	+	0.865135i	$0.667233\pi$
$20$	0.625913	−	2.14668i	0.139959	−	0.480012i
$21$		0			0
$22$	1.46603	+	1.46603i	0.312559	+	0.312559i
$23$	0.635591	−	0.635591i	0.132530	−	0.132530i	−0.637730	−	0.770260i	$-0.720126\pi$
$23$	0.635591	−	0.635591i	0.132530	−	0.132530i	0.770260	+	0.637730i	$0.220126\pi$
$24$	1.00000			0.204124
$25$	4.21646	+	2.68727i	0.843293	+	0.537454i
$26$			0.462438i			0.0906916i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	0.0288926i		−	0.00536522i	−0.999996	−	0.00268261i	$-0.999146\pi$
$29$		−	0.0288926i		−	0.00536522i	0.999996	−	0.00268261i	$-0.000853903\pi$
$30$	−0.625913	+	2.14668i	−0.114276	+	0.391928i
$31$		−	8.03242i		−	1.44267i	−0.692589	−	0.721333i	$-0.743530\pi$
$31$		−	8.03242i		−	1.44267i	0.692589	−	0.721333i	$-0.256470\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.46603	−	1.46603i	−0.255203	−	0.255203i
$34$	1.79437			0.307732
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−8.07760	−	8.07760i	−1.32795	−	1.32795i	−0.907157	−	0.420793i	$-0.861752\pi$
$37$	−8.07760	−	8.07760i	−1.32795	−	1.32795i	−0.420793	−	0.907157i	$-0.638248\pi$
$38$	−3.09170	−	3.09170i	−0.501540	−	0.501540i
$39$		−	0.462438i		−	0.0740494i
$40$	1.96052	−	1.07534i	0.309985	−	0.170027i
$41$		−	10.6696i		−	1.66631i	−0.553042	−	0.833153i	$-0.686533\pi$
$41$		−	10.6696i		−	1.66631i	0.553042	−	0.833153i	$-0.313467\pi$
$42$		0			0
$43$	2.50876	−	2.50876i	0.382583	−	0.382583i	−0.489449	−	0.872032i	$-0.662802\pi$
$43$	2.50876	−	2.50876i	0.382583	−	0.382583i	0.872032	+	0.489449i	$0.162802\pi$
$44$			2.07328i			0.312559i
$45$	0.625913	−	2.14668i	0.0933057	−	0.320008i
$46$	0.898861			0.132530
$47$	0.525308	−	0.525308i	0.0766241	−	0.0766241i	−0.667756	−	0.744380i	$-0.732745\pi$
$47$	0.525308	−	0.525308i	0.0766241	−	0.0766241i	0.744380	+	0.667756i	$0.232745\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		0			0
$50$	1.08130	+	4.88168i	0.152919	+	0.690374i
$51$	−1.79437			−0.251262
$52$	−0.326993	+	0.326993i	−0.0453458	+	0.0453458i
$53$	7.22526	−	7.22526i	0.992465	−	0.992465i	−0.00750666	−	0.999972i	$-0.502389\pi$
$53$	7.22526	−	7.22526i	0.992465	−	0.992465i	0.999972	+	0.00750666i	$0.00238947\pi$
$54$	1.00000			0.136083
$55$	−4.45067	−	1.29769i	−0.600128	−	0.174981i
$56$		0			0
$57$	3.09170	+	3.09170i	0.409505	+	0.409505i
$58$	0.0204302	−	0.0204302i	0.00268261	−	0.00268261i
$59$	13.4242			1.74769			0.873843	−	0.486208i	$-0.161620\pi$
$59$	13.4242			1.74769			0.873843	+	0.486208i	$0.161620\pi$
$60$	−1.96052	+	1.07534i	−0.253102	+	0.138826i
$61$			9.84270i			1.26023i	0.776502	+	0.630114i	$0.216992\pi$
$61$			9.84270i			1.26023i	−0.776502	+	0.630114i	$0.783008\pi$
$62$	5.67978	−	5.67978i	0.721333	−	0.721333i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.497280	−	0.906619i	−0.0616800	−	0.112452i
$66$		−	2.07328i		−	0.255203i
$67$	−3.33098	−	3.33098i	−0.406944	−	0.406944i	0.473728	−	0.880671i	$-0.342908\pi$
$67$	−3.33098	−	3.33098i	−0.406944	−	0.406944i	−0.880671	+	0.473728i	$0.842908\pi$
$68$	1.26881	+	1.26881i	0.153866	+	0.153866i
$69$	−0.898861			−0.108210
$70$		0			0
$71$	2.27478			0.269966			0.134983	−	0.990848i	$-0.456902\pi$
$71$	2.27478			0.269966			0.134983	+	0.990848i	$0.456902\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−8.14046	−	8.14046i	−0.952768	−	0.952768i	0.0461656	−	0.998934i	$-0.485300\pi$
$73$	−8.14046	−	8.14046i	−0.952768	−	0.952768i	−0.998934	+	0.0461656i	$0.985300\pi$
$74$		−	11.4235i		−	1.32795i
$75$	−1.08130	−	4.88168i	−0.124858	−	0.563688i
$76$		−	4.37232i		−	0.501540i
$77$		0			0
$78$	0.326993	−	0.326993i	0.0370247	−	0.0370247i
$79$		−	8.01313i		−	0.901547i	−0.892638	−	0.450774i	$-0.851148\pi$
$79$		−	8.01313i		−	0.901547i	0.892638	−	0.450774i	$-0.148852\pi$
$80$	2.14668	+	0.625913i	0.240006	+	0.0699793i
$81$	−1.00000			−0.111111
$82$	7.54452	−	7.54452i	0.833153	−	0.833153i
$83$	−4.26961	−	4.26961i	−0.468650	−	0.468650i	0.432827	−	0.901477i	$-0.357516\pi$
$83$	−4.26961	−	4.26961i	−0.468650	−	0.468650i	−0.901477	+	0.432827i	$0.857516\pi$
$84$		0			0
$85$	−3.51790	+	1.92957i	−0.381570	+	0.209291i
$86$	3.54793			0.382583
$87$	−0.0204302	+	0.0204302i	−0.00219034	+	0.00219034i
$88$	−1.46603	+	1.46603i	−0.156279	+	0.156279i
$89$	0.0197698			0.00209560			0.00104780	−	0.999999i	$-0.499666\pi$
$89$	0.0197698			0.00209560			0.00104780	+	0.999999i	$0.499666\pi$
$90$	1.96052	−	1.07534i	0.206657	−	0.113351i
$91$		0			0
$92$	0.635591	+	0.635591i	0.0662649	+	0.0662649i
$93$	−5.67978	+	5.67978i	−0.588966	+	0.588966i
$94$	0.742898			0.0766241
$95$	9.38597	+	2.73669i	0.962980	+	0.280779i
$96$			1.00000i			0.102062i
$97$	5.65183	−	5.65183i	0.573857	−	0.573857i	−0.359347	−	0.933204i	$-0.617001\pi$
$97$	5.65183	−	5.65183i	0.573857	−	0.573857i	0.933204	+	0.359347i	$0.117001\pi$
$98$		0			0
$99$			2.07328i			0.208372i
$100$	−2.68727	+	4.21646i	−0.268727	+	0.421646i
$101$			4.18882i			0.416803i	0.978043	+	0.208402i	$0.0668261\pi$
$101$			4.18882i			0.416803i	−0.978043	+	0.208402i	$0.933174\pi$
$102$	−1.26881	−	1.26881i	−0.125631	−	0.125631i
$103$	2.69132	+	2.69132i	0.265184	+	0.265184i	0.827156	−	0.561972i	$-0.189957\pi$
$103$	2.69132	+	2.69132i	0.265184	+	0.265184i	−0.561972	+	0.827156i	$0.689957\pi$
$104$	−0.462438			−0.0453458
$105$		0			0
$106$	10.2181			0.992465
$107$	−12.1979	−	12.1979i	−1.17922	−	1.17922i	−0.979945	−	0.199271i	$-0.936143\pi$
$107$	−12.1979	−	12.1979i	−1.17922	−	1.17922i	−0.199271	−	0.979945i	$-0.563857\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			12.6001i			1.20687i	0.797412	+	0.603435i	$0.206202\pi$
$109$			12.6001i			1.20687i	−0.797412	+	0.603435i	$0.793798\pi$
$110$	−2.22949	−	4.06470i	−0.212573	−	0.387554i
$111$			11.4235i			1.08427i
$112$		0			0
$113$	9.87937	−	9.87937i	0.929373	−	0.929373i	−0.0682924	−	0.997665i	$-0.521755\pi$
$113$	9.87937	−	9.87937i	0.929373	−	0.929373i	0.997665	+	0.0682924i	$0.0217551\pi$
$114$			4.37232i			0.409505i
$115$	−1.76223	+	0.966585i	−0.164329	+	0.0901345i
$116$	0.0288926			0.00268261
$117$	−0.326993	+	0.326993i	−0.0302305	+	0.0302305i
$118$	9.49237	+	9.49237i	0.873843	+	0.873843i
$119$		0			0
$120$	−2.14668	−	0.625913i	−0.195964	−	0.0571378i
$121$	−6.70151			−0.609228
$122$	−6.95984	+	6.95984i	−0.630114	+	0.630114i
$123$	−7.54452	+	7.54452i	−0.680267	+	0.680267i
$124$	8.03242			0.721333
$125$	−7.36940	−	8.40785i	−0.659139	−	0.752021i
$126$		0			0
$127$	−2.53710	−	2.53710i	−0.225132	−	0.225132i	0.585524	−	0.810655i	$-0.300889\pi$
$127$	−2.53710	−	2.53710i	−0.225132	−	0.225132i	−0.810655	+	0.585524i	$0.800889\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.54793			−0.312378
$130$	0.289446	−	0.992706i	0.0253861	−	0.0870661i
$131$			19.7306i			1.72387i	0.507016	+	0.861937i	$0.330749\pi$
$131$			19.7306i			1.72387i	−0.507016	+	0.861937i	$0.669251\pi$
$132$	1.46603	−	1.46603i	0.127602	−	0.127602i
$133$		0			0
$134$		−	4.71072i		−	0.406944i
$135$	−1.96052	+	1.07534i	−0.168735	+	0.0925509i
$136$			1.79437i			0.153866i
$137$	11.5948	+	11.5948i	0.990612	+	0.990612i	0.999956	−	0.00934474i	$-0.00297456\pi$
$137$	11.5948	+	11.5948i	0.990612	+	0.990612i	−0.00934474	+	0.999956i	$0.502975\pi$
$138$	−0.635591	−	0.635591i	−0.0541051	−	0.0541051i
$139$	6.98433			0.592403			0.296202	−	0.955125i	$-0.404280\pi$
$139$	6.98433			0.592403			0.296202	+	0.955125i	$0.404280\pi$
$140$		0			0
$141$	−0.742898			−0.0625633
$142$	1.60851	+	1.60851i	0.134983	+	0.134983i
$143$	0.677948	+	0.677948i	0.0566929	+	0.0566929i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.0180843	+	0.0620232i	−0.00150182	+	0.00515075i
$146$		−	11.5123i		−	0.952768i
$147$		0			0
$148$	8.07760	−	8.07760i	0.663975	−	0.663975i
$149$			8.06301i			0.660547i	0.943885	+	0.330274i	$0.107141\pi$
$149$			8.06301i			0.660547i	−0.943885	+	0.330274i	$0.892859\pi$
$150$	2.68727	−	4.21646i	0.219415	−	0.344273i
$151$	−20.7971			−1.69244			−0.846222	−	0.532831i	$-0.821128\pi$
$151$	−20.7971			−1.69244			−0.846222	+	0.532831i	$0.821128\pi$
$152$	3.09170	−	3.09170i	0.250770	−	0.250770i
$153$	1.26881	+	1.26881i	0.102577	+	0.102577i
$154$		0			0
$155$	−5.02760	+	17.2430i	−0.403826	+	1.38499i
$156$	0.462438			0.0370247
$157$	−10.0893	+	10.0893i	−0.805215	+	0.805215i	−0.983905	−	0.178690i	$-0.942814\pi$
$157$	−10.0893	+	10.0893i	−0.805215	+	0.805215i	0.178690	+	0.983905i	$0.442814\pi$
$158$	5.66614	−	5.66614i	0.450774	−	0.450774i
$159$	−10.2181			−0.810344
$160$	1.07534	+	1.96052i	0.0850134	+	0.154993i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	8.54237	−	8.54237i	0.669090	−	0.669090i	−0.288415	−	0.957505i	$-0.593128\pi$
$163$	8.54237	−	8.54237i	0.669090	−	0.669090i	0.957505	+	0.288415i	$0.0931284\pi$
$164$	10.6696			0.833153
$165$	2.22949	+	4.06470i	0.173565	+	0.316437i
$166$		−	6.03813i		−	0.468650i
$167$	−8.16680	+	8.16680i	−0.631966	+	0.631966i	−0.948561	−	0.316595i	$-0.897460\pi$
$167$	−8.16680	+	8.16680i	−0.631966	+	0.631966i	0.316595	+	0.948561i	$0.397460\pi$
$168$		0			0
$169$		−	12.7862i		−	0.983550i
$170$	−3.85194	−	1.12312i	−0.295430	−	0.0861395i
$171$		−	4.37232i		−	0.334360i
$172$	2.50876	+	2.50876i	0.191291	+	0.191291i
$173$	−4.93408	−	4.93408i	−0.375131	−	0.375131i	0.494211	−	0.869342i	$-0.335457\pi$
$173$	−4.93408	−	4.93408i	−0.375131	−	0.375131i	−0.869342	+	0.494211i	$0.835457\pi$
$174$	−0.0288926			−0.00219034
$175$		0			0
$176$	−2.07328			−0.156279
$177$	−9.49237	−	9.49237i	−0.713490	−	0.713490i
$178$	0.0139794	+	0.0139794i	0.00104780	+	0.00104780i
$179$			6.45209i			0.482252i	0.970494	+	0.241126i	$0.0775167\pi$
$179$			6.45209i			0.482252i	−0.970494	+	0.241126i	$0.922483\pi$
$180$	2.14668	+	0.625913i	0.160004	+	0.0466528i
$181$		−	10.5123i		−	0.781370i	−0.920524	−	0.390685i	$-0.872238\pi$
$181$		−	10.5123i		−	0.781370i	0.920524	−	0.390685i	$-0.127762\pi$
$182$		0			0
$183$	6.95984	−	6.95984i	0.514486	−	0.514486i
$184$			0.898861i			0.0662649i
$185$	12.2841	+	22.3959i	0.903148	+	1.64658i
$186$	−8.03242			−0.588966
$187$	2.63060	−	2.63060i	0.192369	−	0.192369i
$188$	0.525308	+	0.525308i	0.0383120	+	0.0383120i
$189$		0			0
$190$	4.70175	+	8.57202i	0.341101	+	0.621880i
$191$	24.8983			1.80158			0.900790	−	0.434254i	$-0.142988\pi$
$191$	24.8983			1.80158			0.900790	+	0.434254i	$0.142988\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−8.94309	+	8.94309i	−0.643738	+	0.643738i	−0.951472	−	0.307734i	$-0.900429\pi$
$193$	−8.94309	+	8.94309i	−0.643738	+	0.643738i	0.307734	+	0.951472i	$0.400429\pi$
$194$	7.99290			0.573857
$195$	−0.289446	+	0.992706i	−0.0207277	+	0.0710892i
$196$		0			0
$197$	−2.46213	−	2.46213i	−0.175419	−	0.175419i	0.613936	−	0.789356i	$-0.289585\pi$
$197$	−2.46213	−	2.46213i	−0.175419	−	0.175419i	−0.789356	+	0.613936i	$0.789585\pi$
$198$	−1.46603	+	1.46603i	−0.104186	+	0.104186i
$199$	7.59741			0.538566			0.269283	−	0.963061i	$-0.413213\pi$
$199$	7.59741			0.538566			0.269283	+	0.963061i	$0.413213\pi$
$200$	−4.88168	+	1.08130i	−0.345187	+	0.0764597i
$201$			4.71072i			0.332268i
$202$	−2.96194	+	2.96194i	−0.208402	+	0.208402i
$203$		0			0
$204$		−	1.79437i		−	0.125631i
$205$	−6.67823	+	22.9041i	−0.466427	+	1.59969i
$206$			3.80611i			0.265184i
$207$	0.635591	+	0.635591i	0.0441766	+	0.0441766i
$208$	−0.326993	−	0.326993i	−0.0226729	−	0.0226729i
$209$	−9.06504			−0.627042
$210$		0			0
$211$	−5.32272			−0.366431			−0.183216	−	0.983073i	$-0.558651\pi$
$211$	−5.32272			−0.366431			−0.183216	+	0.983073i	$0.558651\pi$
$212$	7.22526	+	7.22526i	0.496233	+	0.496233i
$213$	−1.60851	−	1.60851i	−0.110213	−	0.110213i
$214$		−	17.2504i		−	1.17922i
$215$	−6.95578	+	3.81524i	−0.474380	+	0.260197i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	−8.90962	+	8.90962i	−0.603435	+	0.603435i
$219$			11.5123i			0.777932i
$220$	1.29769	−	4.45067i	0.0874905	−	0.300064i
$221$	0.829786			0.0558175
$222$	−8.07760	+	8.07760i	−0.542133	+	0.542133i
$223$	15.4987	+	15.4987i	1.03787	+	1.03787i	0.999254	+	0.0386189i	$0.0122958\pi$
$223$	15.4987	+	15.4987i	1.03787	+	1.03787i	0.0386189	+	0.999254i	$0.487704\pi$
$224$		0			0
$225$	−2.68727	+	4.21646i	−0.179151	+	0.281098i
$226$	13.9715			0.929373
$227$	−6.80901	+	6.80901i	−0.451930	+	0.451930i	−0.895995	−	0.444065i	$-0.853536\pi$
$227$	−6.80901	+	6.80901i	−0.451930	+	0.451930i	0.444065	+	0.895995i	$0.353536\pi$
$228$	−3.09170	+	3.09170i	−0.204753	+	0.204753i
$229$	−18.9728			−1.25376			−0.626880	−	0.779116i	$-0.715668\pi$
$229$	−18.9728			−1.25376			−0.626880	+	0.779116i	$0.715668\pi$
$230$	−1.92957	−	0.562609i	−0.127232	−	0.0370973i
$231$		0			0
$232$	0.0204302	+	0.0204302i	0.00134131	+	0.00134131i
$233$	16.3943	−	16.3943i	1.07403	−	1.07403i	0.0769962	−	0.997031i	$-0.475467\pi$
$233$	16.3943	−	16.3943i	1.07403	−	1.07403i	0.997031	−	0.0769962i	$-0.0245329\pi$
$234$	−0.462438			−0.0302305
$235$	−1.45647	+	0.798871i	−0.0950094	+	0.0521126i
$236$			13.4242i			0.873843i
$237$	−5.66614	+	5.66614i	−0.368055	+	0.368055i
$238$		0			0
$239$		−	2.98741i		−	0.193239i	−0.995321	−	0.0966197i	$-0.969197\pi$
$239$		−	2.98741i		−	0.193239i	0.995321	−	0.0966197i	$-0.0308031\pi$
$240$	−1.07534	−	1.96052i	−0.0694132	−	0.126551i
$241$		−	27.1053i		−	1.74601i	−0.487715	−	0.873003i	$-0.662170\pi$
$241$		−	27.1053i		−	1.74601i	0.487715	−	0.873003i	$-0.337830\pi$
$242$	−4.73869	−	4.73869i	−0.304614	−	0.304614i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−9.84270			−0.630114
$245$		0			0
$246$	−10.6696			−0.680267
$247$	−1.42972	−	1.42972i	−0.0909708	−	0.0909708i
$248$	5.67978	+	5.67978i	0.360666	+	0.360666i
$249$			6.03813i			0.382651i
$250$	0.734297	−	11.1562i	0.0464410	−	0.705580i
$251$			29.6570i			1.87194i	0.352086	+	0.935968i	$0.385473\pi$
$251$			29.6570i			1.87194i	−0.352086	+	0.935968i	$0.614527\pi$
$252$		0			0
$253$	1.31776	−	1.31776i	0.0828467	−	0.0828467i
$254$		−	3.58801i		−	0.225132i
$255$	3.85194	+	1.12312i	0.241218	+	0.0703326i
$256$	1.00000			0.0625000
$257$	6.26264	−	6.26264i	0.390653	−	0.390653i	−0.484267	−	0.874920i	$-0.660914\pi$
$257$	6.26264	−	6.26264i	0.390653	−	0.390653i	0.874920	+	0.484267i	$0.160914\pi$
$258$	−2.50876	−	2.50876i	−0.156189	−	0.156189i
$259$		0			0
$260$	0.906619	−	0.497280i	0.0562261	−	0.0308400i
$261$	0.0288926			0.00178841
$262$	−13.9517	+	13.9517i	−0.861937	+	0.861937i
$263$	19.4790	−	19.4790i	1.20113	−	1.20113i	0.227304	−	0.973824i	$-0.427009\pi$
$263$	19.4790	−	19.4790i	1.20113	−	1.20113i	0.973824	−	0.227304i	$-0.0729912\pi$
$264$	2.07328			0.127602
$265$	−20.0327	+	10.9879i	−1.23060	+	0.674983i
$266$		0			0
$267$	−0.0139794	−	0.0139794i	−0.000855524	−	0.000855524i
$268$	3.33098	−	3.33098i	0.203472	−	0.203472i
$269$	−2.19106			−0.133591			−0.0667957	−	0.997767i	$-0.521278\pi$
$269$	−2.19106			−0.133591			−0.0667957	+	0.997767i	$0.521278\pi$
$270$	−2.14668	−	0.625913i	−0.130643	−	0.0380919i
$271$			7.28839i			0.442738i	0.975190	+	0.221369i	$0.0710526\pi$
$271$			7.28839i			0.442738i	−0.975190	+	0.221369i	$0.928947\pi$
$272$	−1.26881	+	1.26881i	−0.0769331	+	0.0769331i
$273$		0			0
$274$			16.3975i			0.990612i
$275$	8.74191	+	5.57146i	0.527157	+	0.335972i
$276$		−	0.898861i		−	0.0541051i
$277$	−16.6172	−	16.6172i	−0.998433	−	0.998433i	0.00156542	−	0.999999i	$-0.499502\pi$
$277$	−16.6172	−	16.6172i	−0.998433	−	0.998433i	−0.999999	+	0.00156542i	$0.999502\pi$
$278$	4.93867	+	4.93867i	0.296202	+	0.296202i
$279$	8.03242			0.480888
$280$		0			0
$281$	1.32521			0.0790557			0.0395278	−	0.999218i	$-0.487415\pi$
$281$	1.32521			0.0790557			0.0395278	+	0.999218i	$0.487415\pi$
$282$	−0.525308	−	0.525308i	−0.0312817	−	0.0312817i
$283$	14.5224	+	14.5224i	0.863266	+	0.863266i	0.991716	−	0.128450i	$-0.0410002\pi$
$283$	14.5224	+	14.5224i	0.863266	+	0.863266i	−0.128450	+	0.991716i	$0.541000\pi$
$284$			2.27478i			0.134983i
$285$	−4.70175	−	8.57202i	−0.278508	−	0.507763i
$286$			0.958763i			0.0566929i
$287$		0			0
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			13.7802i			0.810602i
$290$	−0.0566445	+	0.0310695i	−0.00332628	+	0.00182446i
$291$	−7.99290			−0.468552
$292$	8.14046	−	8.14046i	0.476384	−	0.476384i
$293$	−15.7254	−	15.7254i	−0.918687	−	0.918687i	0.0782467	−	0.996934i	$-0.475068\pi$
$293$	−15.7254	−	15.7254i	−0.918687	−	0.918687i	−0.996934	+	0.0782467i	$0.975068\pi$
$294$		0			0
$295$	−28.8175	−	8.40241i	−1.67782	−	0.489207i
$296$	11.4235			0.663975
$297$	1.46603	−	1.46603i	0.0850677	−	0.0850677i
$298$	−5.70141	+	5.70141i	−0.330274	+	0.330274i
$299$	0.415668			0.0240387
$300$	4.88168	−	1.08130i	0.281844	−	0.0624291i
$301$		0			0
$302$	−14.7058	−	14.7058i	−0.846222	−	0.846222i
$303$	2.96194	−	2.96194i	0.170159	−	0.170159i
$304$	4.37232			0.250770
$305$	6.16068	−	21.1291i	0.352760	−	1.20985i
$306$			1.79437i			0.102577i
$307$	−12.0759	+	12.0759i	−0.689205	+	0.689205i	−0.962056	−	0.272851i	$-0.912033\pi$
$307$	−12.0759	+	12.0759i	−0.689205	+	0.689205i	0.272851	+	0.962056i	$0.412033\pi$
$308$		0			0
$309$		−	3.80611i		−	0.216522i
$310$	−15.7477	+	8.63761i	−0.894410	+	0.490583i
$311$			20.2193i			1.14653i	0.819369	+	0.573267i	$0.194324\pi$
$311$			20.2193i			1.14653i	−0.819369	+	0.573267i	$0.805676\pi$
$312$	0.326993	+	0.326993i	0.0185123	+	0.0185123i
$313$	8.65863	+	8.65863i	0.489415	+	0.489415i	0.908121	−	0.418707i	$-0.137516\pi$
$313$	8.65863	+	8.65863i	0.489415	+	0.489415i	−0.418707	+	0.908121i	$0.637516\pi$
$314$	−14.2684			−0.805215
$315$		0			0
$316$	8.01313			0.450774
$317$	−11.3393	−	11.3393i	−0.636876	−	0.636876i	0.312908	−	0.949784i	$-0.398697\pi$
$317$	−11.3393	−	11.3393i	−0.636876	−	0.636876i	−0.949784	+	0.312908i	$0.898697\pi$
$318$	−7.22526	−	7.22526i	−0.405172	−	0.405172i
$319$		−	0.0599025i		−	0.00335389i
$320$	−0.625913	+	2.14668i	−0.0349896	+	0.120003i
$321$			17.2504i			0.962825i
$322$		0			0
$323$	−5.54766	+	5.54766i	−0.308680	+	0.308680i
$324$		−	1.00000i		−	0.0555556i
$325$	0.500036	+	2.25747i	0.0277370	+	0.125222i
$326$	12.0807			0.669090
$327$	8.90962	−	8.90962i	0.492703	−	0.492703i
$328$	7.54452	+	7.54452i	0.416577	+	0.416577i
$329$		0			0
$330$	−1.29769	+	4.45067i	−0.0714357	+	0.245001i
$331$	21.7448			1.19520			0.597602	−	0.801793i	$-0.296120\pi$
$331$	21.7448			1.19520			0.597602	+	0.801793i	$0.296120\pi$
$332$	4.26961	−	4.26961i	0.234325	−	0.234325i
$333$	8.07760	−	8.07760i	0.442650	−	0.442650i
$334$	−11.5496			−0.631966
$335$	5.06564	+	9.23545i	0.276765	+	0.504586i
$336$		0			0
$337$	−17.8706	−	17.8706i	−0.973475	−	0.973475i	0.0261820	−	0.999657i	$-0.491665\pi$
$337$	−17.8706	−	17.8706i	−0.973475	−	0.973475i	−0.999657	+	0.0261820i	$0.991665\pi$
$338$	9.04117	−	9.04117i	0.491775	−	0.491775i
$339$	−13.9715			−0.758830
$340$	−1.92957	−	3.51790i	−0.104645	−	0.190785i
$341$		−	16.6534i		−	0.901835i
$342$	3.09170	−	3.09170i	0.167180	−	0.167180i
$343$		0			0
$344$			3.54793i			0.191291i
$345$	1.92957	+	0.562609i	0.103884	+	0.0302899i
$346$		−	6.97784i		−	0.375131i
$347$	14.1911	+	14.1911i	0.761818	+	0.761818i	0.976651	−	0.214833i	$-0.0689208\pi$
$347$	14.1911	+	14.1911i	0.761818	+	0.761818i	−0.214833	+	0.976651i	$0.568921\pi$
$348$	−0.0204302	−	0.0204302i	−0.00109517	−	0.00109517i
$349$	24.9858			1.33746			0.668730	−	0.743506i	$-0.266838\pi$
$349$	24.9858			1.33746			0.668730	+	0.743506i	$0.266838\pi$
$350$		0			0
$351$	0.462438			0.0246831
$352$	−1.46603	−	1.46603i	−0.0781397	−	0.0781397i
$353$	−19.1988	−	19.1988i	−1.02185	−	1.02185i	−0.999756	−	0.0220914i	$-0.992968\pi$
$353$	−19.1988	−	19.1988i	−1.02185	−	1.02185i	−0.0220914	−	0.999756i	$-0.507032\pi$
$354$		−	13.4242i		−	0.713490i
$355$	−4.88322	−	1.42381i	−0.259174	−	0.0755682i
$356$			0.0197698i			0.00104780i
$357$		0			0
$358$	−4.56232	+	4.56232i	−0.241126	+	0.241126i
$359$			16.7185i			0.882370i	0.897416	+	0.441185i	$0.145442\pi$
$359$			16.7185i			0.882370i	−0.897416	+	0.441185i	$0.854558\pi$
$360$	1.07534	+	1.96052i	0.0566756	+	0.103328i
$361$	0.117186			0.00616766
$362$	7.43329	−	7.43329i	0.390685	−	0.390685i
$363$	4.73869	+	4.73869i	0.248716	+	0.248716i
$364$		0			0
$365$	12.3797	+	22.5702i	0.647985	+	1.18138i
$366$	9.84270			0.514486
$367$	−5.94533	+	5.94533i	−0.310344	+	0.310344i	−0.845043	−	0.534699i	$-0.820425\pi$
$367$	−5.94533	+	5.94533i	−0.310344	+	0.310344i	0.534699	+	0.845043i	$0.320425\pi$
$368$	−0.635591	+	0.635591i	−0.0331325	+	0.0331325i
$369$	10.6696			0.555435
$370$	−7.15009	+	24.5225i	−0.371716	+	1.27486i
$371$		0			0
$372$	−5.67978	−	5.67978i	−0.294483	−	0.294483i
$373$	−0.0162120	+	0.0162120i	−0.000839423	+	0.000839423i	−0.707526	−	0.706687i	$-0.750189\pi$
$373$	−0.0162120	+	0.0162120i	−0.000839423	+	0.000839423i	0.706687	+	0.707526i	$0.250189\pi$
$374$	3.72024			0.192369
$375$	−0.734297	+	11.1562i	−0.0379189	+	0.576104i
$376$			0.742898i			0.0383120i
$377$	0.00944769	−	0.00944769i	0.000486581	−	0.000486581i
$378$		0			0
$379$			31.0300i			1.59391i	0.604041	+	0.796953i	$0.293556\pi$
$379$			31.0300i			1.59391i	−0.604041	+	0.796953i	$0.706444\pi$
$380$	−2.73669	+	9.38597i	−0.140389	+	0.481490i
$381$			3.58801i			0.183819i
$382$	17.6058	+	17.6058i	0.900790	+	0.900790i
$383$	−3.47573	−	3.47573i	−0.177602	−	0.177602i	0.612708	−	0.790309i	$-0.290080\pi$
$383$	−3.47573	−	3.47573i	−0.177602	−	0.177602i	−0.790309	+	0.612708i	$0.790080\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−12.6474			−0.643738
$387$	2.50876	+	2.50876i	0.127528	+	0.127528i
$388$	5.65183	+	5.65183i	0.286928	+	0.286928i
$389$		−	11.0267i		−	0.559076i	−0.960135	−	0.279538i	$-0.909819\pi$
$389$		−	11.0267i		−	0.559076i	0.960135	−	0.279538i	$-0.0901814\pi$
$390$	−0.906619	+	0.497280i	−0.0459084	+	0.0251808i
$391$		−	1.61289i		−	0.0815674i
$392$		0			0
$393$	13.9517	−	13.9517i	0.703768	−	0.703768i
$394$		−	3.48197i		−	0.175419i
$395$	−5.01552	+	17.2016i	−0.252358	+	0.865507i
$396$	−2.07328			−0.104186
$397$	5.75974	−	5.75974i	0.289073	−	0.289073i	−0.547640	−	0.836714i	$-0.684474\pi$
$397$	5.75974	−	5.75974i	0.289073	−	0.289073i	0.836714	+	0.547640i	$0.184474\pi$
$398$	5.37218	+	5.37218i	0.269283	+	0.269283i
$399$		0			0
$400$	−4.21646	−	2.68727i	−0.210823	−	0.134364i
$401$	11.7932			0.588926			0.294463	−	0.955663i	$-0.404859\pi$
$401$	11.7932			0.588926			0.294463	+	0.955663i	$0.404859\pi$
$402$	−3.33098	+	3.33098i	−0.166134	+	0.166134i
$403$	2.62655	−	2.62655i	0.130838	−	0.130838i
$404$	−4.18882			−0.208402
$405$	2.14668	+	0.625913i	0.106669	+	0.0311019i
$406$		0			0
$407$	−16.7471	−	16.7471i	−0.830124	−	0.830124i
$408$	1.26881	−	1.26881i	0.0628156	−	0.0628156i
$409$	−6.26719			−0.309892			−0.154946	−	0.987923i	$-0.549520\pi$
$409$	−6.26719			−0.309892			−0.154946	+	0.987923i	$0.549520\pi$
$410$	−20.9179	+	11.4735i	−1.03306	+	0.566633i
$411$		−	16.3975i		−	0.808831i
$412$	−2.69132	+	2.69132i	−0.132592	+	0.132592i
$413$		0			0
$414$			0.898861i			0.0441766i
$415$	6.49307	+	11.8379i	0.318732	+	0.581099i
$416$		−	0.462438i		−	0.0226729i
$417$	−4.93867	−	4.93867i	−0.241848	−	0.241848i
$418$	−6.40995	−	6.40995i	−0.313521	−	0.313521i
$419$	23.9790			1.17145			0.585726	−	0.810509i	$-0.300810\pi$
$419$	23.9790			1.17145			0.585726	+	0.810509i	$0.300810\pi$
$420$		0			0
$421$	−8.01218			−0.390490			−0.195245	−	0.980755i	$-0.562550\pi$
$421$	−8.01218			−0.390490			−0.195245	+	0.980755i	$0.562550\pi$
$422$	−3.76373	−	3.76373i	−0.183216	−	0.183216i
$423$	0.525308	+	0.525308i	0.0255414	+	0.0255414i
$424$			10.2181i			0.496233i
$425$	8.75955	−	1.94026i	0.424901	−	0.0941165i
$426$		−	2.27478i		−	0.110213i
$427$		0			0
$428$	12.1979	−	12.1979i	0.589608	−	0.589608i
$429$		−	0.958763i		−	0.0462895i
$430$	−7.61626	−	2.22070i	−0.367289	−	0.107091i
$431$	−17.0950			−0.823437			−0.411719	−	0.911311i	$-0.635071\pi$
$431$	−17.0950			−0.823437			−0.411719	+	0.911311i	$0.635071\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−3.28061	−	3.28061i	−0.157656	−	0.157656i	0.623871	−	0.781527i	$-0.285559\pi$
$433$	−3.28061	−	3.28061i	−0.157656	−	0.157656i	−0.781527	+	0.623871i	$0.785559\pi$
$434$		0			0
$435$	0.0566445	−	0.0310695i	0.00271590	−	0.00148967i
$436$	−12.6001			−0.603435
$437$	−2.77901	+	2.77901i	−0.132938	+	0.132938i
$438$	−8.14046	+	8.14046i	−0.388966	+	0.388966i
$439$	−34.3470			−1.63929			−0.819647	−	0.572869i	$-0.805830\pi$
$439$	−34.3470			−1.63929			−0.819647	+	0.572869i	$0.805830\pi$
$440$	4.06470	−	2.22949i	0.193777	−	0.106287i
$441$		0			0
$442$	0.586747	+	0.586747i	0.0279087	+	0.0279087i
$443$	19.9796	−	19.9796i	0.949258	−	0.949258i	−0.0495155	−	0.998773i	$-0.515768\pi$
$443$	19.9796	−	19.9796i	0.949258	−	0.949258i	0.998773	+	0.0495155i	$0.0157677\pi$
$444$	−11.4235			−0.542133
$445$	−0.0424395	−	0.0123742i	−0.00201182	−	0.000586593i
$446$			21.9185i			1.03787i
$447$	5.70141	−	5.70141i	0.269667	−	0.269667i
$448$		0			0
$449$		−	10.0016i		−	0.472006i	−0.971752	−	0.236003i	$-0.924163\pi$
$449$		−	10.0016i		−	0.472006i	0.971752	−	0.236003i	$-0.0758375\pi$
$450$	−4.88168	+	1.08130i	−0.230125	+	0.0509731i
$451$		−	22.1210i		−	1.04164i
$452$	9.87937	+	9.87937i	0.464686	+	0.464686i
$453$	14.7058	+	14.7058i	0.690937	+	0.690937i
$454$	−9.62940			−0.451930
$455$		0			0
$456$	−4.37232			−0.204753
$457$	−1.20959	−	1.20959i	−0.0565823	−	0.0565823i	0.678249	−	0.734832i	$-0.262739\pi$
$457$	−1.20959	−	1.20959i	−0.0565823	−	0.0565823i	−0.734832	+	0.678249i	$0.762739\pi$
$458$	−13.4158	−	13.4158i	−0.626880	−	0.626880i
$459$		−	1.79437i		−	0.0837541i
$460$	−0.966585	−	1.76223i	−0.0450672	−	0.0821646i
$461$			8.80371i			0.410030i	0.978759	+	0.205015i	$0.0657243\pi$
$461$			8.80371i			0.410030i	−0.978759	+	0.205015i	$0.934276\pi$
$462$		0			0
$463$	−19.8709	+	19.8709i	−0.923481	+	0.923481i	−0.997274	−	0.0737924i	$-0.976490\pi$
$463$	−19.8709	+	19.8709i	−0.923481	+	0.923481i	0.0737924	+	0.997274i	$0.476490\pi$
$464$			0.0288926i			0.00134131i
$465$	15.7477	−	8.63761i	0.730283	−	0.400560i
$466$	23.1851			1.07403
$467$	19.3690	−	19.3690i	0.896291	−	0.896291i	−0.0988148	−	0.995106i	$-0.531505\pi$
$467$	19.3690	−	19.3690i	0.896291	−	0.896291i	0.995106	+	0.0988148i	$0.0315052\pi$
$468$	−0.326993	−	0.326993i	−0.0151153	−	0.0151153i
$469$		0			0
$470$	−1.59476	−	0.464990i	−0.0735610	−	0.0214484i
$471$	14.2684			0.657455
$472$	−9.49237	+	9.49237i	−0.436922	+	0.436922i
$473$	5.20137	−	5.20137i	0.239159	−	0.239159i
$474$	−8.01313			−0.368055
$475$	−18.4357	−	11.7496i	−0.845890	−	0.539109i
$476$		0			0
$477$	7.22526	+	7.22526i	0.330822	+	0.330822i
$478$	2.11242	−	2.11242i	0.0966197	−	0.0966197i
$479$	−24.0136			−1.09721			−0.548605	−	0.836081i	$-0.684841\pi$
$479$	−24.0136			−1.09721			−0.548605	+	0.836081i	$0.684841\pi$
$480$	0.625913	−	2.14668i	0.0285689	−	0.0979821i
$481$		−	5.28264i		−	0.240868i
$482$	19.1663	−	19.1663i	0.873003	−	0.873003i
$483$		0			0
$484$		−	6.70151i		−	0.304614i
$485$	−15.6702	+	8.59512i	−0.711549	+	0.390284i
$486$			1.00000i			0.0453609i
$487$	−6.32464	−	6.32464i	−0.286597	−	0.286597i	0.549136	−	0.835733i	$-0.314957\pi$
$487$	−6.32464	−	6.32464i	−0.286597	−	0.286597i	−0.835733	+	0.549136i	$0.814957\pi$
$488$	−6.95984	−	6.95984i	−0.315057	−	0.315057i
$489$	−12.0807			−0.546310
$490$		0			0
$491$	2.05148			0.0925818			0.0462909	−	0.998928i	$-0.485260\pi$
$491$	2.05148			0.0925818			0.0462909	+	0.998928i	$0.485260\pi$
$492$	−7.54452	−	7.54452i	−0.340133	−	0.340133i
$493$	−0.0366593	−	0.0366593i	−0.00165105	−	0.00165105i
$494$		−	2.02193i		−	0.0909708i
$495$	1.29769	−	4.45067i	0.0583270	−	0.200043i
$496$			8.03242i			0.360666i
$497$		0			0
$498$	−4.26961	+	4.26961i	−0.191326	+	0.191326i
$499$			5.36056i			0.239971i	0.992776	+	0.119986i	$0.0382849\pi$
$499$			5.36056i			0.239971i	−0.992776	+	0.119986i	$0.961715\pi$
$500$	8.40785	−	7.36940i	0.376011	−	0.329570i
$501$	11.5496			0.515998
$502$	−20.9707	+	20.9707i	−0.935968	+	0.935968i
$503$	3.75049	+	3.75049i	0.167226	+	0.167226i	0.785759	−	0.618533i	$-0.212273\pi$
$503$	3.75049	+	3.75049i	0.167226	+	0.167226i	−0.618533	+	0.785759i	$0.712273\pi$
$504$		0			0
$505$	2.62184	−	8.99206i	0.116670	−	0.400141i
$506$	1.86359			0.0828467
$507$	−9.04117	+	9.04117i	−0.401533	+	0.401533i
$508$	2.53710	−	2.53710i	0.112566	−	0.112566i
$509$	9.76149			0.432670			0.216335	−	0.976319i	$-0.430590\pi$
$509$	9.76149			0.432670			0.216335	+	0.976319i	$0.430590\pi$
$510$	1.92957	+	3.51790i	0.0854427	+	0.155775i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.09170	+	3.09170i	−0.136502	+	0.136502i
$514$	8.85671			0.390653
$515$	−4.09288	−	7.46195i	−0.180354	−	0.328813i
$516$		−	3.54793i		−	0.156189i
$517$	1.08911	−	1.08911i	0.0478990	−	0.0478990i
$518$		0			0
$519$			6.97784i			0.306293i
$520$	0.992706	+	0.289446i	0.0435331	+	0.0126931i
$521$		−	23.1435i		−	1.01393i	−0.861966	−	0.506967i	$-0.830767\pi$
$521$		−	23.1435i		−	1.01393i	0.861966	−	0.506967i	$-0.169233\pi$
$522$	0.0204302	+	0.0204302i	0.000894204	+	0.000894204i
$523$	20.6002	+	20.6002i	0.900783	+	0.900783i	0.995504	−	0.0947207i	$-0.0301958\pi$
$523$	20.6002	+	20.6002i	0.900783	+	0.900783i	−0.0947207	+	0.995504i	$0.530196\pi$
$524$	−19.7306			−0.861937
$525$		0			0
$526$	27.5475			1.20113
$527$	−10.1916	−	10.1916i	−0.443955	−	0.443955i
$528$	1.46603	+	1.46603i	0.0638008	+	0.0638008i
$529$			22.1920i			0.964872i
$530$	−21.9349	−	6.39562i	−0.952791	−	0.277808i
$531$			13.4242i			0.582562i
$532$		0			0
$533$	3.48888	−	3.48888i	0.151120	−	0.151120i
$534$		−	0.0197698i		−	0.000855524i
$535$	18.5501	+	33.8198i	0.801993	+	1.46216i
$536$	4.71072			0.203472
$537$	4.56232	−	4.56232i	0.196879	−	0.196879i
$538$	−1.54931	−	1.54931i	−0.0667957	−	0.0667957i
$539$		0			0
$540$	−1.07534	−	1.96052i	−0.0462754	−	0.0843673i
$541$	−40.7258			−1.75094			−0.875469	−	0.483273i	$-0.839448\pi$
$541$	−40.7258			−1.75094			−0.875469	+	0.483273i	$0.839448\pi$
$542$	−5.15367	+	5.15367i	−0.221369	+	0.221369i
$543$	−7.43329	+	7.43329i	−0.318993	+	0.318993i
$544$	−1.79437			−0.0769331
$545$	7.88657	−	27.0484i	0.337824	−	1.15863i
$546$		0			0
$547$	−24.2561	−	24.2561i	−1.03711	−	1.03711i	−0.999284	−	0.0378306i	$-0.987955\pi$
$547$	−24.2561	−	24.2561i	−1.03711	−	1.03711i	−0.0378306	−	0.999284i	$-0.512045\pi$
$548$	−11.5948	+	11.5948i	−0.495306	+	0.495306i
$549$	−9.84270			−0.420076
$550$	2.24184	+	10.1211i	0.0955925	+	0.431564i
$551$			0.126328i			0.00538174i
$552$	0.635591	−	0.635591i	0.0270525	−	0.0270525i
$553$		0			0
$554$		−	23.5003i		−	0.998433i
$555$	7.15009	−	24.5225i	0.303505	−	1.04092i
$556$			6.98433i			0.296202i
$557$	−24.3133	−	24.3133i	−1.03019	−	1.03019i	−0.999530	−	0.0306577i	$-0.990240\pi$
$557$	−24.3133	−	24.3133i	−1.03019	−	1.03019i	−0.0306577	−	0.999530i	$-0.509760\pi$
$558$	5.67978	+	5.67978i	0.240444	+	0.240444i
$559$	1.64070			0.0693941
$560$		0			0
$561$	−3.72024			−0.157068
$562$	0.937068	+	0.937068i	0.0395278	+	0.0395278i
$563$	2.30717	+	2.30717i	0.0972357	+	0.0972357i	0.754051	−	0.656816i	$-0.228097\pi$
$563$	2.30717	+	2.30717i	0.0972357	+	0.0972357i	−0.656816	+	0.754051i	$0.728097\pi$
$564$		−	0.742898i		−	0.0312817i
$565$	−27.3915	+	15.0242i	−1.15237	+	0.632073i
$566$			20.5377i			0.863266i
$567$		0			0
$568$	−1.60851	+	1.60851i	−0.0674916	+	0.0674916i
$569$			11.4851i			0.481482i	0.970589	+	0.240741i	$0.0773905\pi$
$569$			11.4851i			0.481482i	−0.970589	+	0.240741i	$0.922609\pi$
$570$	2.73669	−	9.38597i	0.114628	−	0.393135i
$571$	2.24056			0.0937644			0.0468822	−	0.998900i	$-0.485071\pi$
$571$	2.24056			0.0937644			0.0468822	+	0.998900i	$0.485071\pi$
$572$	−0.677948	+	0.677948i	−0.0283464	+	0.0283464i
$573$	−17.6058	−	17.6058i	−0.735492	−	0.735492i
$574$		0			0
$575$	4.38795	−	0.971941i	0.182990	−	0.0405328i
$576$	1.00000			0.0416667
$577$	5.15283	−	5.15283i	0.214515	−	0.214515i	−0.591667	−	0.806182i	$-0.701530\pi$
$577$	5.15283	−	5.15283i	0.214515	−	0.214515i	0.806182	+	0.591667i	$0.201530\pi$
$578$	−9.74409	+	9.74409i	−0.405301	+	0.405301i
$579$	12.6474			0.525610
$580$	−0.0620232	−	0.0180843i	−0.00257537	−	0.000750909i
$581$		0			0
$582$	−5.65183	−	5.65183i	−0.234276	−	0.234276i
$583$	14.9800	−	14.9800i	0.620407	−	0.620407i
$584$	11.5123			0.476384
$585$	0.906619	−	0.497280i	0.0374841	−	0.0205600i
$586$		−	22.2391i		−	0.918687i
$587$	15.5725	−	15.5725i	0.642745	−	0.642745i	−0.308484	−	0.951229i	$-0.599822\pi$
$587$	15.5725	−	15.5725i	0.642745	−	0.642745i	0.951229	+	0.308484i	$0.0998218\pi$
$588$		0			0
$589$			35.1203i			1.44711i
$590$	−14.4357	−	26.3185i	−0.594307	−	1.08351i
$591$			3.48197i			0.143229i
$592$	8.07760	+	8.07760i	0.331987	+	0.331987i
$593$	11.1666	+	11.1666i	0.458557	+	0.458557i	0.898182	−	0.439625i	$-0.144888\pi$
$593$	11.1666	+	11.1666i	0.458557	+	0.458557i	−0.439625	+	0.898182i	$0.644888\pi$
$594$	2.07328			0.0850677
$595$		0			0
$596$	−8.06301			−0.330274
$597$	−5.37218	−	5.37218i	−0.219869	−	0.219869i
$598$	0.293921	+	0.293921i	0.0120193	+	0.0120193i
$599$			13.7247i			0.560776i	0.959887	+	0.280388i	$0.0904631\pi$
$599$			13.7247i			0.560776i	−0.959887	+	0.280388i	$0.909537\pi$
$600$	4.21646	+	2.68727i	0.172136	+	0.109707i
$601$		−	36.5565i		−	1.49117i	−0.666411	−	0.745585i	$-0.732170\pi$
$601$		−	36.5565i		−	1.49117i	0.666411	−	0.745585i	$-0.267830\pi$
$602$		0			0
$603$	3.33098	−	3.33098i	0.135648	−	0.135648i
$604$		−	20.7971i		−	0.846222i
$605$	14.3860	+	4.19457i	0.584874	+	0.170533i
$606$	4.18882			0.170159
$607$	22.5291	−	22.5291i	0.914430	−	0.914430i	−0.0821870	−	0.996617i	$-0.526190\pi$
$607$	22.5291	−	22.5291i	0.914430	−	0.914430i	0.996617	+	0.0821870i	$0.0261905\pi$
$608$	3.09170	+	3.09170i	0.125385	+	0.125385i
$609$		0			0
$610$	19.2968	−	10.5843i	0.781305	−	0.428545i
$611$	0.343544			0.0138983
$612$	−1.26881	+	1.26881i	−0.0512887	+	0.0512887i
$613$	2.84302	−	2.84302i	0.114828	−	0.114828i	−0.647358	−	0.762186i	$-0.724126\pi$
$613$	2.84302	−	2.84302i	0.114828	−	0.114828i	0.762186	+	0.647358i	$0.224126\pi$
$614$	−17.0778			−0.689205
$615$	20.9179	−	11.4735i	0.843491	−	0.462654i
$616$		0			0
$617$	5.28987	+	5.28987i	0.212962	+	0.212962i	0.805525	−	0.592562i	$-0.201884\pi$
$617$	5.28987	+	5.28987i	0.212962	+	0.212962i	−0.592562	+	0.805525i	$0.701884\pi$
$618$	2.69132	−	2.69132i	0.108261	−	0.108261i
$619$	16.3515			0.657222			0.328611	−	0.944465i	$-0.393420\pi$
$619$	16.3515			0.657222			0.328611	+	0.944465i	$0.393420\pi$
$620$	−17.2430	−	5.02760i	−0.692497	−	0.201913i
$621$		−	0.898861i		−	0.0360700i
$622$	−14.2972	+	14.2972i	−0.573267	+	0.573267i
$623$		0			0
$624$			0.462438i			0.0185123i
$625$	10.5571	+	22.6616i	0.422286	+	0.906463i
$626$			12.2452i			0.489415i
$627$	6.40995	+	6.40995i	0.255989	+	0.255989i
$628$	−10.0893	−	10.0893i	−0.402607	−	0.402607i
$629$	−20.4979			−0.817306
$630$		0			0
$631$	43.7268			1.74074			0.870368	−	0.492401i	$-0.163881\pi$
$631$	43.7268			1.74074			0.870368	+	0.492401i	$0.163881\pi$
$632$	5.66614	+	5.66614i	0.225387	+	0.225387i
$633$	3.76373	+	3.76373i	0.149595	+	0.149595i
$634$		−	16.0361i		−	0.636876i
$635$	3.85834	+	7.03436i	0.153114	+	0.279150i
$636$		−	10.2181i		−	0.405172i
$637$		0			0
$638$	0.0423574	−	0.0423574i	0.00167695	−	0.00167695i
$639$			2.27478i			0.0899888i
$640$	−1.96052	+	1.07534i	−0.0774963	+	0.0425067i
$641$	−16.0222			−0.632838			−0.316419	−	0.948619i	$-0.602481\pi$
$641$	−16.0222			−0.632838			−0.316419	+	0.948619i	$0.602481\pi$
$642$	−12.1979	+	12.1979i	−0.481413	+	0.481413i
$643$	−5.28588	−	5.28588i	−0.208455	−	0.208455i	0.595156	−	0.803610i	$-0.297090\pi$
$643$	−5.28588	−	5.28588i	−0.208455	−	0.208455i	−0.803610	+	0.595156i	$0.797090\pi$
$644$		0			0
$645$	7.61626	+	2.22070i	0.299890	+	0.0874398i
$646$	−7.84557			−0.308680
$647$	28.4692	−	28.4692i	1.11924	−	1.11924i	0.127388	−	0.991853i	$-0.459341\pi$
$647$	28.4692	−	28.4692i	1.11924	−	1.11924i	0.991853	−	0.127388i	$-0.0406594\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	27.8322			1.09251
$650$	−1.24270	+	1.94985i	−0.0487426	+	0.0764796i
$651$		0			0
$652$	8.54237	+	8.54237i	0.334545	+	0.334545i
$653$	−5.75189	+	5.75189i	−0.225089	+	0.225089i	−0.810637	−	0.585548i	$-0.800879\pi$
$653$	−5.75189	+	5.75189i	−0.225089	+	0.225089i	0.585548	+	0.810637i	$0.300879\pi$
$654$	12.6001			0.492703
$655$	12.3497	−	42.3553i	0.482542	−	1.65496i
$656$			10.6696i			0.416577i
$657$	8.14046	−	8.14046i	0.317589	−	0.317589i
$658$		0			0
$659$			15.0314i			0.585540i	0.956183	+	0.292770i	$0.0945770\pi$
$659$			15.0314i			0.585540i	−0.956183	+	0.292770i	$0.905423\pi$
$660$	−4.06470	+	2.22949i	−0.158218	+	0.0867827i
$661$		−	25.7580i		−	1.00187i	−0.865485	−	0.500934i	$-0.832990\pi$
$661$		−	25.7580i		−	1.00187i	0.865485	−	0.500934i	$-0.167010\pi$
$662$	15.3759	+	15.3759i	0.597602	+	0.597602i
$663$	−0.586747	−	0.586747i	−0.0227874	−	0.0227874i
$664$	6.03813			0.234325
$665$		0			0
$666$	11.4235			0.442650
$667$	−0.0183639	−	0.0183639i	−0.000711052	−	0.000711052i
$668$	−8.16680	−	8.16680i	−0.315983	−	0.315983i
$669$		−	21.9185i		−	0.847420i
$670$	−2.94850	+	10.1124i	−0.113910	+	0.390676i
$671$			20.4067i			0.787791i
$672$		0			0
$673$	15.5407	−	15.5407i	0.599051	−	0.599051i	−0.341009	−	0.940060i	$-0.610769\pi$
$673$	15.5407	−	15.5407i	0.599051	−	0.599051i	0.940060	+	0.341009i	$0.110769\pi$
$674$		−	25.2729i		−	0.973475i
$675$	4.88168	−	1.08130i	0.187896	−	0.0416194i
$676$	12.7862			0.491775
$677$	−5.67922	+	5.67922i	−0.218270	+	0.218270i	−0.807769	−	0.589499i	$-0.799325\pi$
$677$	−5.67922	+	5.67922i	−0.218270	+	0.218270i	0.589499	+	0.807769i	$0.299325\pi$
$678$	−9.87937	−	9.87937i	−0.379415	−	0.379415i
$679$		0			0
$680$	1.12312	−	3.85194i	0.0430698	−	0.147715i
$681$	9.62940			0.368999
$682$	11.7758	−	11.7758i	0.450917	−	0.450917i
$683$	−27.3490	+	27.3490i	−1.04648	+	1.04648i	−0.0476144	+	0.998866i	$0.515162\pi$
$683$	−27.3490	+	27.3490i	−1.04648	+	1.04648i	−0.998866	+	0.0476144i	$0.984838\pi$
$684$	4.37232			0.167180
$685$	−17.6330	−	32.1477i	−0.673722	−	1.22830i
$686$		0			0
$687$	13.4158	+	13.4158i	0.511845	+	0.511845i
$688$	−2.50876	+	2.50876i	−0.0956457	+	0.0956457i
$689$	4.72522			0.180016
$690$	0.966585	+	1.76223i	0.0367972	+	0.0670871i
$691$			25.5947i			0.973668i	0.873494	+	0.486834i	$0.161848\pi$
$691$			25.5947i			0.973668i	−0.873494	+	0.486834i	$0.838152\pi$
$692$	4.93408	−	4.93408i	0.187566	−	0.187566i
$693$		0			0
$694$			20.0692i			0.761818i
$695$	−14.9931	−	4.37159i	−0.568721	−	0.165824i
$696$		−	0.0288926i		−	0.00109517i
$697$	−13.5377	−	13.5377i	−0.512776	−	0.512776i
$698$	17.6676	+	17.6676i	0.668730	+	0.668730i
$699$	−23.1851			−0.876940
$700$		0			0
$701$	41.0066			1.54880			0.774399	−	0.632698i	$-0.218052\pi$
$701$	41.0066			1.54880			0.774399	+	0.632698i	$0.218052\pi$
$702$	0.326993	+	0.326993i	0.0123416	+	0.0123416i
$703$	35.3179	+	35.3179i	1.33204	+	1.33204i
$704$		−	2.07328i		−	0.0781397i
$705$	1.59476	+	0.464990i	0.0600623	+	0.0175125i
$706$		−	27.1512i		−	1.02185i
$707$		0			0
$708$	9.49237	−	9.49237i	0.356745	−	0.356745i
$709$			15.5334i			0.583370i	0.956514	+	0.291685i	$0.0942159\pi$
$709$			15.5334i			0.583370i	−0.956514	+	0.291685i	$0.905784\pi$
$710$	−2.44617	−	4.45975i	−0.0918031	−	0.167371i
$711$	8.01313			0.300516
$712$	−0.0139794	+	0.0139794i	−0.000523899	+	0.000523899i
$713$	−5.10533	−	5.10533i	−0.191196	−	0.191196i
$714$		0			0
$715$	−1.03100	−	1.87967i	−0.0385572	−	0.0702958i
$716$	−6.45209			−0.241126
$717$	−2.11242	+	2.11242i	−0.0788896	+	0.0788896i
$718$	−11.8218	+	11.8218i	−0.441185	+	0.441185i
$719$	−0.379933			−0.0141691			−0.00708455	−	0.999975i	$-0.502255\pi$
$719$	−0.379933			−0.0141691			−0.00708455	+	0.999975i	$0.502255\pi$
$720$	−0.625913	+	2.14668i	−0.0233264	+	0.0800020i
$721$		0			0
$722$	0.0828627	+	0.0828627i	0.00308383	+	0.00308383i
$723$	−19.1663	+	19.1663i	−0.712804	+	0.712804i
$724$	10.5123			0.390685
$725$	0.0776423	−	0.121825i	0.00288356	−	0.00452446i
$726$			6.70151i			0.248716i
$727$	27.3322	−	27.3322i	1.01369	−	1.01369i	0.0137898	−	0.999905i	$-0.495610\pi$
$727$	27.3322	−	27.3322i	1.01369	−	1.01369i	0.999905	−	0.0137898i	$-0.00438956\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−7.20573	+	24.7133i	−0.266696	+	0.914681i
$731$		−	6.36630i		−	0.235466i
$732$	6.95984	+	6.95984i	0.257243	+	0.257243i
$733$	6.42449	+	6.42449i	0.237294	+	0.237294i	0.815729	−	0.578435i	$-0.196336\pi$
$733$	6.42449	+	6.42449i	0.237294	+	0.237294i	−0.578435	+	0.815729i	$0.696336\pi$
$734$	−8.40797			−0.310344
$735$		0			0
$736$	−0.898861			−0.0331325
$737$	−6.90605	−	6.90605i	−0.254388	−	0.254388i
$738$	7.54452	+	7.54452i	0.277718	+	0.277718i
$739$		−	3.73900i		−	0.137541i	−0.997632	−	0.0687707i	$-0.978092\pi$
$739$		−	3.73900i		−	0.137541i	0.997632	−	0.0687707i	$-0.0219077\pi$
$740$	−22.3959	+	12.2841i	−0.823290	+	0.451574i
$741$			2.02193i			0.0742774i
$742$		0			0
$743$	1.84421	−	1.84421i	0.0676575	−	0.0676575i	−0.672468	−	0.740126i	$-0.734766\pi$
$743$	1.84421	−	1.84421i	0.0676575	−	0.0676575i	0.740126	+	0.672468i	$0.234766\pi$
$744$		−	8.03242i		−	0.294483i
$745$	5.04675	−	17.3087i	0.184898	−	0.634141i
$746$	−0.0229272			−0.000839423
$747$	4.26961	−	4.26961i	0.156217	−	0.156217i
$748$	2.63060	+	2.63060i	0.0961844	+	0.0961844i
$749$		0			0
$750$	−8.40785	+	7.36940i	−0.307011	+	0.269092i
$751$	−18.9083			−0.689974			−0.344987	−	0.938607i	$-0.612117\pi$
$751$	−18.9083			−0.689974			−0.344987	+	0.938607i	$0.612117\pi$
$752$	−0.525308	+	0.525308i	−0.0191560	+	0.0191560i
$753$	20.9707	−	20.9707i	0.764214	−	0.764214i
$754$	0.0133610			0.000486581
$755$	44.6447	+	13.0172i	1.62479	+	0.473744i
$756$		0			0
$757$	36.1051	+	36.1051i	1.31226	+	1.31226i	0.919744	+	0.392520i	$0.128396\pi$
$757$	36.1051	+	36.1051i	1.31226	+	1.31226i	0.392520	+	0.919744i	$0.371604\pi$
$758$	−21.9416	+	21.9416i	−0.796953	+	0.796953i
$759$	−1.86359			−0.0676440
$760$	−8.57202	+	4.70175i	−0.310940	+	0.170550i
$761$		−	24.5228i		−	0.888950i	−0.895791	−	0.444475i	$-0.853390\pi$
$761$		−	24.5228i		−	0.888950i	0.895791	−	0.444475i	$-0.146610\pi$
$762$	−2.53710	+	2.53710i	−0.0919096	+	0.0919096i
$763$		0			0
$764$			24.8983i			0.900790i
$765$	−1.92957	−	3.51790i	−0.0697637	−	0.127190i
$766$		−	4.91543i		−	0.177602i
$767$	4.38963	+	4.38963i	0.158500	+	0.158500i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	41.6081			1.50043			0.750213	−	0.661196i	$-0.229951\pi$
$769$	41.6081			1.50043			0.750213	+	0.661196i	$0.229951\pi$
$770$		0			0
$771$	−8.85671			−0.318967
$772$	−8.94309	−	8.94309i	−0.321869	−	0.321869i
$773$	−26.5458	−	26.5458i	−0.954786	−	0.954786i	0.0442349	−	0.999021i	$-0.485915\pi$
$773$	−26.5458	−	26.5458i	−0.954786	−	0.954786i	−0.999021	+	0.0442349i	$0.985915\pi$
$774$			3.54793i			0.127528i
$775$	21.5853	−	33.8684i	0.775366	−	1.21659i
$776$			7.99290i			0.286928i
$777$		0			0
$778$	7.79706	−	7.79706i	0.279538	−	0.279538i
$779$			46.6508i			1.67144i
$780$	−0.992706	−	0.289446i	−0.0355446	−	0.0103638i
$781$	4.71625			0.168761
$782$	1.14049	−	1.14049i	0.0407837	−	0.0407837i
$783$	−0.0204302	−	0.0204302i	−0.000730115	−	0.000730115i
$784$		0			0
$785$	27.9736	−	15.3435i	0.998419	−	0.547632i
$786$	19.7306			0.703768
$787$	3.71498	−	3.71498i	0.132425	−	0.132425i	−0.637788	−	0.770212i	$-0.720150\pi$
$787$	3.71498	−	3.71498i	0.132425	−	0.132425i	0.770212	+	0.637788i	$0.220150\pi$
$788$	2.46213	−	2.46213i	0.0877096	−	0.0877096i
$789$	−27.5475			−0.980717
$790$	−15.7099	+	8.61687i	−0.558933	+	0.306574i
$791$		0			0
$792$	−1.46603	−	1.46603i	−0.0520931	−	0.0520931i
$793$	−3.21850	+	3.21850i	−0.114292	+	0.114292i
$794$	8.14551			0.289073
$795$	21.9349	+	6.39562i	0.777950	+	0.226829i
$796$			7.59741i			0.269283i
$797$	−0.406449	+	0.406449i	−0.0143971	+	0.0143971i	−0.714269	−	0.699872i	$-0.753241\pi$
$797$	−0.406449	+	0.406449i	−0.0143971	+	0.0143971i	0.699872	+	0.714269i	$0.253241\pi$
$798$		0			0
$799$		−	1.33304i		−	0.0471594i
$800$	−1.08130	−	4.88168i	−0.0382298	−	0.172593i
$801$			0.0197698i			0.000698532i
$802$	8.33908	+	8.33908i	0.294463	+	0.294463i
$803$	−16.8774	−	16.8774i	−0.595592	−	0.595592i
$804$	−4.71072			−0.166134
$805$		0			0
$806$	3.71450			0.130838
$807$	1.54931	+	1.54931i	0.0545385	+	0.0545385i
$808$	−2.96194	−	2.96194i	−0.104201	−	0.104201i
$809$			35.8295i			1.25970i	0.776718	+	0.629849i	$0.216883\pi$
$809$			35.8295i			1.25970i	−0.776718	+	0.629849i	$0.783117\pi$
$810$	1.07534	+	1.96052i	0.0377837	+	0.0688856i
$811$		−	30.6135i		−	1.07499i	−0.843268	−	0.537493i	$-0.819372\pi$
$811$		−	30.6135i		−	1.07499i	0.843268	−	0.537493i	$-0.180628\pi$
$812$		0			0
$813$	5.15367	−	5.15367i	0.180747	−	0.180747i
$814$		−	23.6840i		−	0.830124i
$815$	−23.6845	+	12.9909i	−0.829632	+	0.455053i
$816$	1.79437			0.0628156
$817$	−10.9691	+	10.9691i	−0.383761	+	0.383761i
$818$	−4.43157	−	4.43157i	−0.154946	−	0.154946i
$819$		0			0
$820$	−22.9041	−	6.67823i	−0.799847	−	0.233214i
$821$	−26.8615			−0.937471			−0.468736	−	0.883338i	$-0.655290\pi$
$821$	−26.8615			−0.937471			−0.468736	+	0.883338i	$0.655290\pi$
$822$	11.5948	−	11.5948i	0.404415	−	0.404415i
$823$	−3.80691	+	3.80691i	−0.132701	+	0.132701i	−0.770337	−	0.637637i	$-0.779912\pi$
$823$	−3.80691	+	3.80691i	−0.132701	+	0.132701i	0.637637	+	0.770337i	$0.279912\pi$
$824$	−3.80611			−0.132592
$825$	−2.24184	−	10.1211i	−0.0780510	−	0.352371i
$826$		0			0
$827$	5.30801	+	5.30801i	0.184578	+	0.184578i	0.793347	−	0.608770i	$-0.208337\pi$
$827$	5.30801	+	5.30801i	0.184578	+	0.184578i	−0.608770	+	0.793347i	$0.708337\pi$
$828$	−0.635591	+	0.635591i	−0.0220883	+	0.0220883i
$829$	−42.2481			−1.46734			−0.733668	−	0.679508i	$-0.762193\pi$
$829$	−42.2481			−1.46734			−0.733668	+	0.679508i	$0.762193\pi$
$830$	−3.77935	+	12.9619i	−0.131183	+	0.449915i
$831$			23.5003i			0.815217i
$832$	0.326993	−	0.326993i	0.0113364	−	0.0113364i
$833$		0			0
$834$		−	6.98433i		−	0.241848i
$835$	22.6432	−	12.4198i	0.783600	−	0.429804i
$836$		−	9.06504i		−	0.313521i
$837$	−5.67978	−	5.67978i	−0.196322	−	0.196322i
$838$	16.9557	+	16.9557i	0.585726	+	0.585726i
$839$	31.3254			1.08147			0.540736	−	0.841192i	$-0.318146\pi$
$839$	31.3254			1.08147			0.540736	+	0.841192i	$0.318146\pi$
$840$		0			0
$841$	28.9992			0.999971
$842$	−5.66547	−	5.66547i	−0.195245	−	0.195245i
$843$	−0.937068	−	0.937068i	−0.0322743	−	0.0322743i
$844$		−	5.32272i		−	0.183216i
$845$	−8.00302	+	27.4478i	−0.275312	+	0.944232i
$846$			0.742898i			0.0255414i
$847$		0			0
$848$	−7.22526	+	7.22526i	−0.248116	+	0.248116i
$849$		−	20.5377i		−	0.704854i
$850$	7.56591	+	4.82197i	0.259509	+	0.165392i
$851$	−10.2681			−0.351986
$852$	1.60851	−	1.60851i	0.0551067	−	0.0551067i
$853$	17.7771	+	17.7771i	0.608678	+	0.608678i	0.942600	−	0.333923i	$-0.108372\pi$
$853$	17.7771	+	17.7771i	0.608678	+	0.608678i	−0.333923	+	0.942600i	$0.608372\pi$
$854$		0			0
$855$	−2.73669	+	9.38597i	−0.0935930	+	0.320993i
$856$	17.2504			0.589608
$857$	30.2273	−	30.2273i	1.03255	−	1.03255i	0.0330932	−	0.999452i	$-0.489464\pi$
$857$	30.2273	−	30.2273i	1.03255	−	1.03255i	0.999452	−	0.0330932i	$-0.0105358\pi$
$858$	0.677948	−	0.677948i	0.0231448	−	0.0231448i
$859$	16.6575			0.568348			0.284174	−	0.958773i	$-0.408281\pi$
$859$	16.6575			0.568348			0.284174	+	0.958773i	$0.408281\pi$
$860$	−3.81524	−	6.95578i	−0.130099	−	0.237190i
$861$		0			0
$862$	−12.0880	−	12.0880i	−0.411719	−	0.411719i
$863$	−39.3141	+	39.3141i	−1.33827	+	1.33827i	−0.440528	+	0.897739i	$0.645209\pi$
$863$	−39.3141	+	39.3141i	−1.33827	+	1.33827i	−0.897739	+	0.440528i	$0.854791\pi$
$864$	−1.00000			−0.0340207
$865$	7.50358	+	13.6802i	0.255129	+	0.465141i
$866$		−	4.63948i		−	0.157656i
$867$	9.74409	−	9.74409i	0.330927	−	0.330927i
$868$		0			0
$869$		−	16.6134i		−	0.563573i
$870$	0.0620232	+	0.0180843i	0.00210278	+	0.000613114i
$871$		−	2.17841i		−	0.0738128i
$872$	−8.90962	−	8.90962i	−0.301718	−	0.301718i
$873$	5.65183	+	5.65183i	0.191286	+	0.191286i
$874$	−3.93011			−0.132938
$875$		0			0
$876$	−11.5123			−0.388966
$877$	32.6886	+	32.6886i	1.10381	+	1.10381i	0.993946	+	0.109868i	$0.0350428\pi$
$877$	32.6886	+	32.6886i	1.10381	+	1.10381i	0.109868	+	0.993946i	$0.464957\pi$
$878$	−24.2870	−	24.2870i	−0.819647	−	0.819647i
$879$			22.2391i			0.750105i
$880$	4.45067	+	1.29769i	0.150032	+	0.0437452i
$881$			1.61071i			0.0542661i	0.999632	+	0.0271330i	$0.00863778\pi$
$881$			1.61071i			0.0542661i	−0.999632	+	0.0271330i	$0.991362\pi$
$882$		0			0
$883$	−35.7890	+	35.7890i	−1.20439	+	1.20439i	−0.231579	+	0.972816i	$0.574389\pi$
$883$	−35.7890	+	35.7890i	−1.20439	+	1.20439i	−0.972816	+	0.231579i	$0.925611\pi$
$884$			0.829786i			0.0279087i
$885$	14.4357	+	26.3185i	0.485250	+	0.884686i
$886$	28.2554			0.949258
$887$	−14.1627	+	14.1627i	−0.475537	+	0.475537i	−0.903701	−	0.428164i	$-0.859161\pi$
$887$	−14.1627	+	14.1627i	−0.475537	+	0.475537i	0.428164	+	0.903701i	$0.359161\pi$
$888$	−8.07760	−	8.07760i	−0.271067	−	0.271067i
$889$		0			0
$890$	−0.0212594	−	0.0387591i	−0.000712615	−	0.00129921i
$891$	−2.07328			−0.0694575
$892$	−15.4987	+	15.4987i	−0.518936	+	0.518936i
$893$	−2.29682	+	2.29682i	−0.0768600	+	0.0768600i
$894$	8.06301			0.269667
$895$	4.03845	−	13.8506i	0.134991	−	0.462974i
$896$		0			0
$897$	−0.293921	−	0.293921i	−0.00981375	−	0.00981375i
$898$	7.07222	−	7.07222i	0.236003	−	0.236003i
$899$	−0.232078			−0.00774022
$900$	−4.21646	−	2.68727i	−0.140549	−	0.0895757i
$901$		−	18.3350i		−	0.610827i
$902$	15.6419	−	15.6419i	0.520818	−	0.520818i
$903$		0			0
$904$			13.9715i			0.464686i
$905$	−6.57976	+	22.5664i	−0.218719	+	0.750134i
$906$			20.7971i			0.690937i
$907$	−36.8528	−	36.8528i	−1.22368	−	1.22368i	−0.966315	−	0.257362i	$-0.917147\pi$
$907$	−36.8528	−	36.8528i	−1.22368	−	1.22368i	−0.257362	−	0.966315i	$-0.582853\pi$
$908$	−6.80901	−	6.80901i	−0.225965	−	0.225965i
$909$	−4.18882			−0.138934
$910$		0			0
$911$	14.6381			0.484981			0.242490	−	0.970154i	$-0.422036\pi$
$911$	14.6381			0.484981			0.242490	+	0.970154i	$0.422036\pi$
$912$	−3.09170	−	3.09170i	−0.102376	−	0.102376i
$913$	−8.85209	−	8.85209i	−0.292961	−	0.292961i
$914$		−	1.71062i		−	0.0565823i
$915$	−19.2968	+	10.5843i	−0.637933	+	0.349906i
$916$		−	18.9728i		−	0.626880i
$917$		0			0
$918$	1.26881	−	1.26881i	0.0418771	−	0.0418771i
$919$		−	49.3134i		−	1.62670i	−0.581775	−	0.813350i	$-0.697642\pi$
$919$		−	49.3134i		−	1.62670i	0.581775	−	0.813350i	$-0.302358\pi$
$920$	0.562609	−	1.92957i	0.0185487	−	0.0636159i
$921$	17.0778			0.562734
$922$	−6.22516	+	6.22516i	−0.205015	+	0.205015i
$923$	0.743837	+	0.743837i	0.0244837	+	0.0244837i
$924$		0			0
$925$	−12.3522	−	55.7656i	−0.406138	−	1.83356i
$926$	−28.1018			−0.923481
$927$	−2.69132	+	2.69132i	−0.0883947	+	0.0883947i
$928$	−0.0204302	+	0.0204302i	−0.000670653	+	0.000670653i
$929$	50.7683			1.66566			0.832828	−	0.553532i	$-0.186720\pi$
$929$	50.7683			1.66566			0.832828	+	0.553532i	$0.186720\pi$
$930$	17.2430	+	5.02760i	0.565421	+	0.164861i
$931$		0			0
$932$	16.3943	+	16.3943i	0.537014	+	0.537014i
$933$	14.2972	−	14.2972i	0.468070	−	0.468070i
$934$	27.3919			0.896291
$935$	−7.29359	+	4.00053i	−0.238526	+	0.130831i
$936$		−	0.462438i		−	0.0151153i
$937$	−6.18012	+	6.18012i	−0.201896	+	0.201896i	−0.800812	−	0.598916i	$-0.795598\pi$
$937$	−6.18012	+	6.18012i	−0.201896	+	0.201896i	0.598916	+	0.800812i	$0.295598\pi$
$938$		0			0
$939$		−	12.2452i		−	0.399605i
$940$	−0.798871	−	1.45647i	−0.0260563	−	0.0475047i
$941$			11.7207i			0.382084i	0.981582	+	0.191042i	$0.0611867\pi$
$941$			11.7207i			0.382084i	−0.981582	+	0.191042i	$0.938813\pi$
$942$	10.0893	+	10.0893i	0.328728	+	0.328728i
$943$	−6.78148	−	6.78148i	−0.220835	−	0.220835i
$944$	−13.4242			−0.436922
$945$		0			0
$946$	7.35584			0.239159
$947$	−23.5131	−	23.5131i	−0.764073	−	0.764073i	0.212983	−	0.977056i	$-0.431682\pi$
$947$	−23.5131	−	23.5131i	−0.764073	−	0.764073i	−0.977056	+	0.212983i	$0.931682\pi$
$948$	−5.66614	−	5.66614i	−0.184028	−	0.184028i
$949$		−	5.32375i		−	0.172816i
$950$	−4.72780	−	21.3443i	−0.153390	−	0.692499i
$951$			16.0361i			0.520007i
$952$		0			0
$953$	−7.37438	+	7.37438i	−0.238879	+	0.238879i	−0.816386	−	0.577507i	$-0.804026\pi$
$953$	−7.37438	+	7.37438i	−0.238879	+	0.238879i	0.577507	+	0.816386i	$0.304026\pi$
$954$			10.2181i			0.330822i
$955$	−53.4488	−	15.5842i	−1.72956	−	0.504293i
$956$	2.98741			0.0966197
$957$	−0.0423574	+	0.0423574i	−0.00136922	+	0.00136922i
$958$	−16.9802	−	16.9802i	−0.548605	−	0.548605i
$959$		0			0
$960$	1.96052	−	1.07534i	0.0632755	−	0.0347066i
$961$	−33.5198			−1.08128
$962$	3.73539	−	3.73539i	0.120434	−	0.120434i
$963$	12.1979	−	12.1979i	0.393072	−	0.393072i
$964$	27.1053			0.873003
$965$	24.7956	−	13.6003i	0.798197	−	0.437811i
$966$		0			0
$967$	−25.7706	−	25.7706i	−0.828725	−	0.828725i	0.158615	−	0.987340i	$-0.449297\pi$
$967$	−25.7706	−	25.7706i	−0.828725	−	0.828725i	−0.987340	+	0.158615i	$0.949297\pi$
$968$	4.73869	−	4.73869i	0.152307	−	0.152307i
$969$	7.84557			0.252036
$970$	−17.1582	−	5.00286i	−0.550916	−	0.160632i
$971$		−	54.9570i		−	1.76365i	−0.471573	−	0.881827i	$-0.656314\pi$
$971$		−	54.9570i		−	1.76365i	0.471573	−	0.881827i	$-0.343686\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		0			0
$974$		−	8.94440i		−	0.286597i
$975$	1.24270	−	1.94985i	0.0397981	−	0.0624453i
$976$		−	9.84270i		−	0.315057i
$977$	12.0469	+	12.0469i	0.385415	+	0.385415i	0.873048	−	0.487634i	$-0.162140\pi$
$977$	12.0469	+	12.0469i	0.385415	+	0.385415i	−0.487634	+	0.873048i	$0.662140\pi$
$978$	−8.54237	−	8.54237i	−0.273155	−	0.273155i
$979$	0.0409884			0.00130999
$980$		0			0
$981$	−12.6001			−0.402290
$982$	1.45061	+	1.45061i	0.0462909	+	0.0462909i
$983$	−17.2157	−	17.2157i	−0.549094	−	0.549094i	0.377084	−	0.926179i	$-0.376927\pi$
$983$	−17.2157	−	17.2157i	−0.549094	−	0.549094i	−0.926179	+	0.377084i	$0.876927\pi$
$984$		−	10.6696i		−	0.340133i
$985$	3.74432	+	6.82647i	0.119304	+	0.217510i
$986$		−	0.0518441i		−	0.00165105i
$987$		0			0
$988$	1.42972	−	1.42972i	0.0454854	−	0.0454854i
$989$		−	3.18909i		−	0.101407i
$990$	4.06470	−	2.22949i	0.129185	−	0.0708578i
$991$	52.6929			1.67384			0.836922	−	0.547322i	$-0.184353\pi$
$991$	52.6929			1.67384			0.836922	+	0.547322i	$0.184353\pi$
$992$	−5.67978	+	5.67978i	−0.180333	+	0.180333i
$993$	−15.3759	−	15.3759i	−0.487940	−	0.487940i
$994$		0			0
$995$	−16.3092	−	4.75532i	−0.517037	−	0.150754i
$996$	−6.03813			−0.191326
$997$	−10.7568	+	10.7568i	−0.340670	+	0.340670i	−0.856619	−	0.515949i	$-0.827439\pi$
$997$	−10.7568	+	10.7568i	−0.340670	+	0.340670i	0.515949	+	0.856619i	$0.327439\pi$
$998$	−3.79048	+	3.79048i	−0.119986	+	0.119986i
$999$	−11.4235			−0.361422

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-2.14668 - 0.625913i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-2.14668 - 0.625913i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.07534 - 1.96052i) q^{10} +2.07328 q^{11} +(0.707107 - 0.707107i) q^{12} +(0.326993 + 0.326993i) q^{13} +(1.07534 + 1.96052i) q^{15} -1.00000 q^{16} +(1.26881 - 1.26881i) q^{17} +(-0.707107 + 0.707107i) q^{18} -4.37232 q^{19} +(0.625913 - 2.14668i) q^{20} +(1.46603 + 1.46603i) q^{22} +(0.635591 - 0.635591i) q^{23} +1.00000 q^{24} +(4.21646 + 2.68727i) q^{25} +0.462438i q^{26} +(0.707107 - 0.707107i) q^{27} -0.0288926i q^{29} +(-0.625913 + 2.14668i) q^{30} -8.03242i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.46603 - 1.46603i) q^{33} +1.79437 q^{34} -1.00000 q^{36} +(-8.07760 - 8.07760i) q^{37} +(-3.09170 - 3.09170i) q^{38} -0.462438i q^{39} +(1.96052 - 1.07534i) q^{40} -10.6696i q^{41} +(2.50876 - 2.50876i) q^{43} +2.07328i q^{44} +(0.625913 - 2.14668i) q^{45} +0.898861 q^{46} +(0.525308 - 0.525308i) q^{47} +(0.707107 + 0.707107i) q^{48} +(1.08130 + 4.88168i) q^{50} -1.79437 q^{51} +(-0.326993 + 0.326993i) q^{52} +(7.22526 - 7.22526i) q^{53} +1.00000 q^{54} +(-4.45067 - 1.29769i) q^{55} +(3.09170 + 3.09170i) q^{57} +(0.0204302 - 0.0204302i) q^{58} +13.4242 q^{59} +(-1.96052 + 1.07534i) q^{60} +9.84270i q^{61} +(5.67978 - 5.67978i) q^{62} -1.00000i q^{64} +(-0.497280 - 0.906619i) q^{65} -2.07328i q^{66} +(-3.33098 - 3.33098i) q^{67} +(1.26881 + 1.26881i) q^{68} -0.898861 q^{69} +2.27478 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-8.14046 - 8.14046i) q^{73} -11.4235i q^{74} +(-1.08130 - 4.88168i) q^{75} -4.37232i q^{76} +(0.326993 - 0.326993i) q^{78} -8.01313i q^{79} +(2.14668 + 0.625913i) q^{80} -1.00000 q^{81} +(7.54452 - 7.54452i) q^{82} +(-4.26961 - 4.26961i) q^{83} +(-3.51790 + 1.92957i) q^{85} +3.54793 q^{86} +(-0.0204302 + 0.0204302i) q^{87} +(-1.46603 + 1.46603i) q^{88} +0.0197698 q^{89} +(1.96052 - 1.07534i) q^{90} +(0.635591 + 0.635591i) q^{92} +(-5.67978 + 5.67978i) q^{93} +0.742898 q^{94} +(9.38597 + 2.73669i) q^{95} +1.00000i q^{96} +(5.65183 - 5.65183i) q^{97} +2.07328i 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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