LMFDB - Embedded newform 1470.2.m.c.1273.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625$ x^16 - 32x^13 + 2x^12 + 352x^10 - 288x^9 + 2x^8 - 1440x^7 + 8800x^6 + 1250x^4 - 100000*x^3 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1273.8
Root			$1.39977 + 1.74375i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.c.97.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.14668 - 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})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57}+ \cdots + 64 q^{97}+O(q^{100})$ 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

Character values

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

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

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	2.14668	−	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	$-0.770427\pi$
$13$	−0.326993	+	0.326993i	−0.0906916	+	0.0906916i	0.660306	+	0.750997i	$0.270427\pi$
$14$		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	$-0.319823\pi$
$17$	−1.26881	−	1.26881i	−0.307732	−	0.307732i	−0.844029	+	0.536297i	$0.819823\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	4.37232			1.00308			0.501540	−	0.865135i	$-0.332767\pi$
$19$	4.37232			1.00308			0.501540	+	0.865135i	$0.332767\pi$
$20$	−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	0.770260	−	0.637730i	$-0.220126\pi$
$23$	0.635591	+	0.635591i	0.132530	+	0.132530i	−0.637730	+	0.770260i	$0.720126\pi$
$24$	−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	$0.000853903\pi$
$29$			0.0288926i			0.00536522i	−0.999996	+	0.00268261i	$0.999146\pi$
$30$	−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	−0.420793	+	0.907157i	$0.638248\pi$
$37$	−8.07760	+	8.07760i	−1.32795	+	1.32795i	−0.907157	+	0.420793i	$0.861752\pi$
$38$	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	0.872032	−	0.489449i	$-0.162802\pi$
$43$	2.50876	+	2.50876i	0.382583	+	0.382583i	−0.489449	+	0.872032i	$0.662802\pi$
$44$		−	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	$-0.267255\pi$
$47$	−0.525308	−	0.525308i	−0.0766241	−	0.0766241i	−0.744380	+	0.667756i	$0.767255\pi$
$48$	−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	0.999972	−	0.00750666i	$-0.00238947\pi$
$53$	7.22526	+	7.22526i	0.992465	+	0.992465i	−0.00750666	+	0.999972i	$0.502389\pi$
$54$	−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	$-0.838380\pi$
$59$	−13.4242			−1.74769			−0.873843	+	0.486208i	$0.838380\pi$
$60$	−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	−0.880671	−	0.473728i	$-0.842908\pi$
$67$	−3.33098	+	3.33098i	−0.406944	+	0.406944i	0.473728	+	0.880671i	$0.342908\pi$
$68$	−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	$-0.514700\pi$
$73$	8.14046	−	8.14046i	0.952768	−	0.952768i	0.998934	+	0.0461656i	$0.0147002\pi$
$74$			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	$0.148852\pi$
$79$			8.01313i			0.901547i	−0.892638	+	0.450774i	$0.851148\pi$
$80$	−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	$-0.642484\pi$
$83$	4.26961	−	4.26961i	0.468650	−	0.468650i	0.901477	+	0.432827i	$0.142484\pi$
$84$		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	$-0.500334\pi$
$89$	−0.0197698			−0.00209560			−0.00104780	+	0.999999i	$0.500334\pi$
$90$	−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	$-0.382999\pi$
$97$	−5.65183	−	5.65183i	−0.573857	−	0.573857i	−0.933204	+	0.359347i	$0.882999\pi$
$98$		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	$-0.810043\pi$
$103$	−2.69132	+	2.69132i	−0.265184	+	0.265184i	0.561972	+	0.827156i	$0.310043\pi$
$104$	0.462438			0.0453458
$105$		0			0
$106$	10.2181			0.992465
$107$	−12.1979	+	12.1979i	−1.17922	+	1.17922i	−0.199271	+	0.979945i	$0.563857\pi$
$107$	−12.1979	+	12.1979i	−1.17922	+	1.17922i	−0.979945	+	0.199271i	$0.936143\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	12.6001i		−	1.20687i	−0.797412	−	0.603435i	$-0.793798\pi$
$109$		−	12.6001i		−	1.20687i	0.797412	−	0.603435i	$-0.206202\pi$
$110$	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	0.997665	−	0.0682924i	$-0.0217551\pi$
$113$	9.87937	+	9.87937i	0.929373	+	0.929373i	−0.0682924	+	0.997665i	$0.521755\pi$
$114$		−	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	−0.810655	−	0.585524i	$-0.800889\pi$
$127$	−2.53710	+	2.53710i	−0.225132	+	0.225132i	0.585524	+	0.810655i	$0.300889\pi$
$128$	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	−0.00934474	−	0.999956i	$-0.502975\pi$
$137$	11.5948	−	11.5948i	0.990612	−	0.990612i	0.999956	+	0.00934474i	$0.00297456\pi$
$138$	0.635591	−	0.635591i	0.0541051	−	0.0541051i
$139$	−6.98433			−0.592403			−0.296202	−	0.955125i	$-0.595720\pi$
$139$	−6.98433			−0.592403			−0.296202	+	0.955125i	$0.595720\pi$
$140$		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	$-0.892859\pi$
$149$		−	8.06301i		−	0.660547i	0.943885	−	0.330274i	$-0.107141\pi$
$150$	−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	$-0.0571861\pi$
$157$	10.0893	+	10.0893i	0.805215	+	0.805215i	−0.178690	+	0.983905i	$0.557186\pi$
$158$	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	0.957505	−	0.288415i	$-0.0931284\pi$
$163$	8.54237	+	8.54237i	0.669090	+	0.669090i	−0.288415	+	0.957505i	$0.593128\pi$
$164$	−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	$-0.102540\pi$
$167$	8.16680	+	8.16680i	0.631966	+	0.631966i	−0.316595	+	0.948561i	$0.602540\pi$
$168$		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	$-0.664543\pi$
$173$	4.93408	−	4.93408i	0.375131	−	0.375131i	0.869342	+	0.494211i	$0.164543\pi$
$174$	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	$-0.922483\pi$
$179$		−	6.45209i		−	0.482252i	0.970494	−	0.241126i	$-0.0775167\pi$
$180$	−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	0.307734	−	0.951472i	$-0.400429\pi$
$193$	−8.94309	−	8.94309i	−0.643738	−	0.643738i	−0.951472	+	0.307734i	$0.900429\pi$
$194$	−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	−0.789356	−	0.613936i	$-0.789585\pi$
$197$	−2.46213	+	2.46213i	−0.175419	+	0.175419i	0.613936	+	0.789356i	$0.289585\pi$
$198$	−1.46603	−	1.46603i	−0.104186	−	0.104186i
$199$	−7.59741			−0.538566			−0.269283	−	0.963061i	$-0.586787\pi$
$199$	−7.59741			−0.538566			−0.269283	+	0.963061i	$0.586787\pi$
$200$	−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	−0.0386189	+	0.999254i	$0.512296\pi$
$223$	−15.4987	+	15.4987i	−1.03787	+	1.03787i	−0.999254	+	0.0386189i	$0.987704\pi$
$224$		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	$-0.146464\pi$
$227$	6.80901	+	6.80901i	0.451930	+	0.451930i	−0.444065	+	0.895995i	$0.646464\pi$
$228$	−3.09170	−	3.09170i	−0.204753	−	0.204753i
$229$	18.9728			1.25376			0.626880	−	0.779116i	$-0.284332\pi$
$229$	18.9728			1.25376			0.626880	+	0.779116i	$0.284332\pi$
$230$	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	0.997031	+	0.0769962i	$0.0245329\pi$
$233$	16.3943	+	16.3943i	1.07403	+	1.07403i	0.0769962	+	0.997031i	$0.475467\pi$
$234$	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	$0.0308031\pi$
$239$			2.98741i			0.193239i	−0.995321	+	0.0966197i	$0.969197\pi$
$240$	−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	$-0.339086\pi$
$257$	−6.26264	−	6.26264i	−0.390653	−	0.390653i	−0.874920	+	0.484267i	$0.839086\pi$
$258$	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	0.973824	+	0.227304i	$0.0729912\pi$
$263$	19.4790	+	19.4790i	1.20113	+	1.20113i	0.227304	+	0.973824i	$0.427009\pi$
$264$	−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	$-0.478722\pi$
$269$	2.19106			0.133591			0.0667957	+	0.997767i	$0.478722\pi$
$270$	−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	−0.999999	−	0.00156542i	$-0.999502\pi$
$277$	−16.6172	+	16.6172i	−0.998433	+	0.998433i	0.00156542	+	0.999999i	$0.499502\pi$
$278$	−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	$-0.959000\pi$
$283$	−14.5224	+	14.5224i	−0.863266	+	0.863266i	0.128450	+	0.991716i	$0.459000\pi$
$284$		−	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	$-0.524932\pi$
$293$	15.7254	−	15.7254i	0.918687	−	0.918687i	0.996934	+	0.0782467i	$0.0249322\pi$
$294$		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	$-0.0879666\pi$
$307$	12.0759	+	12.0759i	0.689205	+	0.689205i	−0.272851	+	0.962056i	$0.587967\pi$
$308$		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	$-0.862484\pi$
$313$	−8.65863	+	8.65863i	−0.489415	+	0.489415i	0.418707	+	0.908121i	$0.362484\pi$
$314$	14.2684			0.805215
$315$		0			0
$316$	8.01313			0.450774
$317$	−11.3393	+	11.3393i	−0.636876	+	0.636876i	−0.949784	−	0.312908i	$-0.898697\pi$
$317$	−11.3393	+	11.3393i	−0.636876	+	0.636876i	0.312908	+	0.949784i	$0.398697\pi$
$318$	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	−0.999657	−	0.0261820i	$-0.991665\pi$
$337$	−17.8706	+	17.8706i	−0.973475	+	0.973475i	0.0261820	+	0.999657i	$0.491665\pi$
$338$	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	−0.214833	−	0.976651i	$-0.568921\pi$
$347$	14.1911	−	14.1911i	0.761818	−	0.761818i	0.976651	+	0.214833i	$0.0689208\pi$
$348$	0.0204302	−	0.0204302i	0.00109517	−	0.00109517i
$349$	−24.9858			−1.33746			−0.668730	−	0.743506i	$-0.733162\pi$
$349$	−24.9858			−1.33746			−0.668730	+	0.743506i	$0.733162\pi$
$350$		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	0.0220914	−	0.999756i	$-0.492968\pi$
$353$	19.1988	−	19.1988i	1.02185	−	1.02185i	0.999756	−	0.0220914i	$-0.00703248\pi$
$354$			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	$-0.854558\pi$
$359$		−	16.7185i		−	0.882370i	0.897416	−	0.441185i	$-0.145442\pi$
$360$	−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	$-0.179575\pi$
$367$	5.94533	+	5.94533i	0.310344	+	0.310344i	−0.534699	+	0.845043i	$0.679575\pi$
$368$	−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	0.706687	−	0.707526i	$-0.250189\pi$
$373$	−0.0162120	−	0.0162120i	−0.000839423	−	0.000839423i	−0.707526	+	0.706687i	$0.750189\pi$
$374$	−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	$-0.706444\pi$
$379$		−	31.0300i		−	1.59391i	0.604041	−	0.796953i	$-0.293556\pi$
$380$	−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	$-0.709920\pi$
$383$	3.47573	−	3.47573i	0.177602	−	0.177602i	0.790309	+	0.612708i	$0.209920\pi$
$384$	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	$0.0901814\pi$
$389$			11.0267i			0.559076i	−0.960135	+	0.279538i	$0.909819\pi$
$390$	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	$-0.315526\pi$
$397$	−5.75974	−	5.75974i	−0.289073	−	0.289073i	−0.836714	+	0.547640i	$0.815526\pi$
$398$	−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	$-0.450480\pi$
$409$	6.26719			0.309892			0.154946	+	0.987923i	$0.450480\pi$
$410$	−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	$-0.699190\pi$
$419$	−23.9790			−1.17145			−0.585726	+	0.810509i	$0.699190\pi$
$420$		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	$-0.714441\pi$
$433$	3.28061	−	3.28061i	0.157656	−	0.157656i	0.781527	+	0.623871i	$0.214441\pi$
$434$		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	$-0.194170\pi$
$439$	34.3470			1.63929			0.819647	+	0.572869i	$0.194170\pi$
$440$	−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	0.998773	−	0.0495155i	$-0.0157677\pi$
$443$	19.9796	+	19.9796i	0.949258	+	0.949258i	−0.0495155	+	0.998773i	$0.515768\pi$
$444$	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	$0.0758375\pi$
$449$			10.0016i			0.472006i	−0.971752	+	0.236003i	$0.924163\pi$
$450$	−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	−0.734832	−	0.678249i	$-0.762739\pi$
$457$	−1.20959	+	1.20959i	−0.0565823	+	0.0565823i	0.678249	+	0.734832i	$0.262739\pi$
$458$	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	0.0737924	−	0.997274i	$-0.476490\pi$
$463$	−19.8709	−	19.8709i	−0.923481	−	0.923481i	−0.997274	+	0.0737924i	$0.976490\pi$
$464$		−	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	$-0.468495\pi$
$467$	−19.3690	−	19.3690i	−0.896291	−	0.896291i	−0.995106	+	0.0988148i	$0.968495\pi$
$468$	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	$-0.315159\pi$
$479$	24.0136			1.09721			0.548605	+	0.836081i	$0.315159\pi$
$480$	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	−0.835733	−	0.549136i	$-0.814957\pi$
$487$	−6.32464	+	6.32464i	−0.286597	+	0.286597i	0.549136	+	0.835733i	$0.314957\pi$
$488$	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	$-0.961715\pi$
$499$		−	5.36056i		−	0.239971i	0.992776	−	0.119986i	$-0.0382849\pi$
$500$	−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	$-0.787727\pi$
$503$	−3.75049	+	3.75049i	−0.167226	+	0.167226i	0.618533	+	0.785759i	$0.287727\pi$
$504$		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	$-0.569410\pi$
$509$	−9.76149			−0.432670			−0.216335	+	0.976319i	$0.569410\pi$
$510$	−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	$-0.969804\pi$
$523$	−20.6002	+	20.6002i	−0.900783	+	0.900783i	0.0947207	+	0.995504i	$0.469804\pi$
$524$	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	−0.0378306	+	0.999284i	$0.512045\pi$
$547$	−24.2561	+	24.2561i	−1.03711	+	1.03711i	−0.999284	+	0.0378306i	$0.987955\pi$
$548$	−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	−0.0306577	+	0.999530i	$0.509760\pi$
$557$	−24.3133	+	24.3133i	−1.03019	+	1.03019i	−0.999530	+	0.0306577i	$0.990240\pi$
$558$	−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	$-0.771903\pi$
$563$	−2.30717	+	2.30717i	−0.0972357	+	0.0972357i	0.656816	+	0.754051i	$0.271903\pi$
$564$			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	$-0.922609\pi$
$569$		−	11.4851i		−	0.481482i	0.970589	−	0.240741i	$-0.0773905\pi$
$570$	−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	$-0.298470\pi$
$577$	−5.15283	−	5.15283i	−0.214515	−	0.214515i	−0.806182	+	0.591667i	$0.798470\pi$
$578$	−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	$-0.400178\pi$
$587$	−15.5725	−	15.5725i	−0.642745	−	0.642745i	−0.951229	+	0.308484i	$0.900178\pi$
$588$		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	$-0.855112\pi$
$593$	−11.1666	+	11.1666i	−0.458557	+	0.458557i	0.439625	+	0.898182i	$0.355112\pi$
$594$	−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	$-0.909537\pi$
$599$		−	13.7247i		−	0.560776i	0.959887	−	0.280388i	$-0.0904631\pi$
$600$	−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	$-0.473810\pi$
$607$	−22.5291	−	22.5291i	−0.914430	−	0.914430i	−0.996617	+	0.0821870i	$0.973810\pi$
$608$	−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	0.762186	−	0.647358i	$-0.224126\pi$
$613$	2.84302	+	2.84302i	0.114828	+	0.114828i	−0.647358	+	0.762186i	$0.724126\pi$
$614$	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	−0.592562	−	0.805525i	$-0.701884\pi$
$617$	5.28987	−	5.28987i	0.212962	−	0.212962i	0.805525	+	0.592562i	$0.201884\pi$
$618$	2.69132	+	2.69132i	0.108261	+	0.108261i
$619$	−16.3515			−0.657222			−0.328611	−	0.944465i	$-0.606580\pi$
$619$	−16.3515			−0.657222			−0.328611	+	0.944465i	$0.606580\pi$
$620$	−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	$-0.702910\pi$
$643$	5.28588	−	5.28588i	0.208455	−	0.208455i	0.803610	+	0.595156i	$0.202910\pi$
$644$		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	−0.991853	−	0.127388i	$-0.959341\pi$
$647$	−28.4692	−	28.4692i	−1.11924	−	1.11924i	−0.127388	−	0.991853i	$-0.540659\pi$
$648$	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	0.585548	−	0.810637i	$-0.300879\pi$
$653$	−5.75189	−	5.75189i	−0.225089	−	0.225089i	−0.810637	+	0.585548i	$0.800879\pi$
$654$	−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	$-0.905423\pi$
$659$		−	15.0314i		−	0.585540i	0.956183	−	0.292770i	$-0.0945770\pi$
$660$	−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	0.940060	−	0.341009i	$-0.110769\pi$
$673$	15.5407	+	15.5407i	0.599051	+	0.599051i	−0.341009	+	0.940060i	$0.610769\pi$
$674$			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	$-0.200675\pi$
$677$	5.67922	+	5.67922i	0.218270	+	0.218270i	−0.589499	+	0.807769i	$0.700675\pi$
$678$	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	−0.998866	−	0.0476144i	$-0.984838\pi$
$683$	−27.3490	−	27.3490i	−1.04648	−	1.04648i	−0.0476144	−	0.998866i	$-0.515162\pi$
$684$	−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	$-0.905784\pi$
$709$		−	15.5334i		−	0.583370i	0.956514	−	0.291685i	$-0.0942159\pi$
$710$	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	$-0.497745\pi$
$719$	0.379933			0.0141691			0.00708455	+	0.999975i	$0.497745\pi$
$720$	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	−0.999905	−	0.0137898i	$-0.995610\pi$
$727$	−27.3322	−	27.3322i	−1.01369	−	1.01369i	−0.0137898	−	0.999905i	$-0.504390\pi$
$728$		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	$-0.803664\pi$
$733$	−6.42449	+	6.42449i	−0.237294	+	0.237294i	0.578435	+	0.815729i	$0.303664\pi$
$734$	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	$0.0219077\pi$
$739$			3.73900i			0.137541i	−0.997632	+	0.0687707i	$0.978092\pi$
$740$	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	0.740126	−	0.672468i	$-0.234766\pi$
$743$	1.84421	+	1.84421i	0.0676575	+	0.0676575i	−0.672468	+	0.740126i	$0.734766\pi$
$744$			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	0.392520	−	0.919744i	$-0.371604\pi$
$757$	36.1051	−	36.1051i	1.31226	−	1.31226i	0.919744	−	0.392520i	$-0.128396\pi$
$758$	−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	$-0.770049\pi$
$769$	−41.6081			−1.50043			−0.750213	+	0.661196i	$0.770049\pi$
$770$		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	$-0.514085\pi$
$773$	26.5458	−	26.5458i	0.954786	−	0.954786i	0.999021	+	0.0442349i	$0.0140850\pi$
$774$		−	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	$-0.279850\pi$
$787$	−3.71498	−	3.71498i	−0.132425	−	0.132425i	−0.770212	+	0.637788i	$0.779850\pi$
$788$	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	$-0.246759\pi$
$797$	0.406449	+	0.406449i	0.0143971	+	0.0143971i	−0.699872	+	0.714269i	$0.746759\pi$
$798$		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	$-0.783117\pi$
$809$		−	35.8295i		−	1.25970i	0.776718	−	0.629849i	$-0.216883\pi$
$810$	−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	0.637637	−	0.770337i	$-0.279912\pi$
$823$	−3.80691	−	3.80691i	−0.132701	−	0.132701i	−0.770337	+	0.637637i	$0.779912\pi$
$824$	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	−0.608770	−	0.793347i	$-0.708337\pi$
$827$	5.30801	−	5.30801i	0.184578	−	0.184578i	0.793347	+	0.608770i	$0.208337\pi$
$828$	−0.635591	−	0.635591i	−0.0220883	−	0.0220883i
$829$	42.2481			1.46734			0.733668	−	0.679508i	$-0.237807\pi$
$829$	42.2481			1.46734			0.733668	+	0.679508i	$0.237807\pi$
$830$	−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	$-0.681854\pi$
$839$	−31.3254			−1.08147			−0.540736	+	0.841192i	$0.681854\pi$
$840$		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	$-0.891628\pi$
$853$	−17.7771	+	17.7771i	−0.608678	+	0.608678i	0.333923	+	0.942600i	$0.391628\pi$
$854$		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	−0.999452	−	0.0330932i	$-0.989464\pi$
$857$	−30.2273	−	30.2273i	−1.03255	−	1.03255i	−0.0330932	−	0.999452i	$-0.510536\pi$
$858$	0.677948	+	0.677948i	0.0231448	+	0.0231448i
$859$	−16.6575			−0.568348			−0.284174	−	0.958773i	$-0.591719\pi$
$859$	−16.6575			−0.568348			−0.284174	+	0.958773i	$0.591719\pi$
$860$	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	−0.897739	−	0.440528i	$-0.854791\pi$
$863$	−39.3141	−	39.3141i	−1.33827	−	1.33827i	−0.440528	−	0.897739i	$-0.645209\pi$
$864$	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	0.109868	−	0.993946i	$-0.464957\pi$
$877$	32.6886	−	32.6886i	1.10381	−	1.10381i	0.993946	−	0.109868i	$-0.0350428\pi$
$878$	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	−0.972816	−	0.231579i	$-0.925611\pi$
$883$	−35.7890	−	35.7890i	−1.20439	−	1.20439i	−0.231579	−	0.972816i	$-0.574389\pi$
$884$		−	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	$-0.140839\pi$
$887$	14.1627	+	14.1627i	0.475537	+	0.475537i	−0.428164	+	0.903701i	$0.640839\pi$
$888$	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	−0.257362	+	0.966315i	$0.582853\pi$
$907$	−36.8528	+	36.8528i	−1.22368	+	1.22368i	−0.966315	+	0.257362i	$0.917147\pi$
$908$	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	$0.302358\pi$
$919$			49.3134i			1.62670i	−0.581775	+	0.813350i	$0.697642\pi$
$920$	−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	$-0.813280\pi$
$929$	−50.7683			−1.66566			−0.832828	+	0.553532i	$0.813280\pi$
$930$	−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	$-0.204402\pi$
$937$	6.18012	+	6.18012i	0.201896	+	0.201896i	−0.598916	+	0.800812i	$0.704402\pi$
$938$		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	−0.977056	−	0.212983i	$-0.931682\pi$
$947$	−23.5131	+	23.5131i	−0.764073	+	0.764073i	0.212983	+	0.977056i	$0.431682\pi$
$948$	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	0.577507	−	0.816386i	$-0.304026\pi$
$953$	−7.37438	−	7.37438i	−0.238879	−	0.238879i	−0.816386	+	0.577507i	$0.804026\pi$
$954$		−	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	−0.987340	−	0.158615i	$-0.949297\pi$
$967$	−25.7706	+	25.7706i	−0.828725	+	0.828725i	0.158615	+	0.987340i	$0.449297\pi$
$968$	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	−0.487634	−	0.873048i	$-0.662140\pi$
$977$	12.0469	−	12.0469i	0.385415	−	0.385415i	0.873048	+	0.487634i	$0.162140\pi$
$978$	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	$-0.623073\pi$
$983$	17.2157	−	17.2157i	0.549094	−	0.549094i	0.926179	+	0.377084i	$0.123073\pi$
$984$			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	$-0.172561\pi$
$997$	10.7568	+	10.7568i	0.340670	+	0.340670i	−0.515949	+	0.856619i	$0.672561\pi$
$998$	−3.79048	−	3.79048i	−0.119986	−	0.119986i
$999$	11.4235			0.361422

Display

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.8	✓	16	35.27	even	4	inner
1470.2.m.c.1273.8	yes	16	1.1	even	1	trivial
1470.2.m.f.97.5	yes	16	5.2	odd	4
1470.2.m.f.1273.5	yes	16	7.6	odd	2

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

Newform invariants

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1470.2.m.c.1273.8

Level	$1470$
Weight	$2$
Character	1470.1273
Analytic conductor	$11.738$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$