LMFDB - Embedded newform 702.2.bb.a.71.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("702.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.8
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-3.83221 + 1.02684i) q^{5} +(-1.55176 + 0.415793i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-3.83221 + 1.02684i) q^{5} +(-1.55176 + 0.415793i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-3.43586 - 1.98370i) q^{10} +(3.50976 - 3.50976i) q^{11} +(-1.03908 - 3.45258i) q^{13} +(-1.39127 - 0.803251i) q^{14} -1.00000 q^{16} +(-0.584080 - 1.01166i) q^{17} +(-4.16646 - 1.11640i) q^{19} +(-1.02684 - 3.83221i) q^{20} +4.96355 q^{22} +(-1.63500 - 2.83190i) q^{23} +(9.30128 - 5.37010i) q^{25} +(1.70661 - 3.17608i) q^{26} +(-0.415793 - 1.55176i) q^{28} +7.50570i q^{29} +(-1.94388 - 7.25468i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.302342 - 1.12836i) q^{34} +(5.51972 - 3.18681i) q^{35} +(-4.28775 + 1.14890i) q^{37} +(-2.15672 - 3.73555i) q^{38} +(1.98370 - 3.43586i) q^{40} +(1.44991 - 5.41115i) q^{41} +(-0.770434 - 0.444811i) q^{43} +(3.50976 + 3.50976i) q^{44} +(0.846338 - 3.15858i) q^{46} +(-2.43773 - 0.653187i) q^{47} +(-3.82710 + 2.20958i) q^{49} +(10.3742 + 2.77977i) q^{50} +(3.45258 - 1.03908i) q^{52} -6.60181i q^{53} +(-9.84618 + 17.0541i) q^{55} +(0.803251 - 1.39127i) q^{56} +(-5.30733 + 5.30733i) q^{58} +(-5.81273 + 5.81273i) q^{59} +(-7.05927 + 12.2270i) q^{61} +(3.75530 - 6.50436i) q^{62} -1.00000i q^{64} +(7.52719 + 12.1640i) q^{65} +(-3.19229 - 0.855370i) q^{67} +(1.01166 - 0.584080i) q^{68} +(6.15644 + 1.64961i) q^{70} +(-0.942701 + 3.51821i) q^{71} +(-3.33343 - 3.33343i) q^{73} +(-3.84429 - 2.21950i) q^{74} +(1.11640 - 4.16646i) q^{76} +(-3.98698 + 6.90565i) q^{77} +(-1.16902 - 2.02480i) q^{79} +(3.83221 - 1.02684i) q^{80} +(4.85151 - 2.80102i) q^{82} +(2.82772 - 10.5532i) q^{83} +(3.27712 + 3.27712i) q^{85} +(-0.230251 - 0.859308i) q^{86} +4.96355i q^{88} +(1.78297 + 6.65415i) q^{89} +(3.04796 + 4.92554i) q^{91} +(2.83190 - 1.63500i) q^{92} +(-1.26186 - 2.18561i) q^{94} +17.1131 q^{95} +(-1.65585 - 6.17970i) q^{97} +(-4.26857 - 1.14376i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−3.83221	+	1.02684i	−1.71381	+	0.459215i	−0.976354	−	0.216176i	$-0.930642\pi$
$5$	−3.83221	+	1.02684i	−1.71381	+	0.459215i	−0.737460	+	0.675391i	$0.763975\pi$
$6$		0			0
$7$	−1.55176	+	0.415793i	−0.586511	+	0.157155i	−0.539858	−	0.841756i	$-0.681522\pi$
$7$	−1.55176	+	0.415793i	−0.586511	+	0.157155i	−0.0466526	+	0.998911i	$0.514855\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−3.43586	−	1.98370i	−1.08651	−	0.627300i
$11$	3.50976	−	3.50976i	1.05823	−	1.05823i	0.0600368	−	0.998196i	$-0.480878\pi$
$11$	3.50976	−	3.50976i	1.05823	−	1.05823i	0.998196	−	0.0600368i	$-0.0191218\pi$
$12$		0			0
$13$	−1.03908	−	3.45258i	−0.288188	−	0.957574i
$13$	−1.03908	−	3.45258i	−0.288188	−	0.957574i
$14$	−1.39127	−	0.803251i	−0.371833	−	0.214678i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.584080	−	1.01166i	−0.141660	−	0.245363i	0.786462	−	0.617639i	$-0.211911\pi$
$17$	−0.584080	−	1.01166i	−0.141660	−	0.245363i	−0.928122	+	0.372276i	$0.878577\pi$
$18$		0			0
$19$	−4.16646	−	1.11640i	−0.955853	−	0.256120i	−0.253009	−	0.967464i	$-0.581420\pi$
$19$	−4.16646	−	1.11640i	−0.955853	−	0.256120i	−0.702844	+	0.711344i	$0.748087\pi$
$20$	−1.02684	−	3.83221i	−0.229608	−	0.856907i
$21$		0			0
$22$	4.96355			1.05823
$23$	−1.63500	−	2.83190i	−0.340921	−	0.590492i	0.643683	−	0.765292i	$-0.277406\pi$
$23$	−1.63500	−	2.83190i	−0.340921	−	0.590492i	−0.984604	+	0.174800i	$0.944072\pi$
$24$		0			0
$25$	9.30128	−	5.37010i	1.86026	−	1.07402i
$26$	1.70661	−	3.17608i	0.334693	−	0.622881i
$27$		0			0
$28$	−0.415793	−	1.55176i	−0.0785775	−	0.293255i
$29$			7.50570i			1.39377i	0.717182	+	0.696886i	$0.245432\pi$
$29$			7.50570i			1.39377i	−0.717182	+	0.696886i	$0.754568\pi$
$30$		0			0
$31$	−1.94388	−	7.25468i	−0.349132	−	1.30298i	−0.887710	−	0.460403i	$-0.847705\pi$
$31$	−1.94388	−	7.25468i	−0.349132	−	1.30298i	0.538578	−	0.842576i	$-0.318962\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	0.302342	−	1.12836i	0.0518513	−	0.193512i
$35$	5.51972	−	3.18681i	0.933002	−	0.538669i
$36$		0			0
$37$	−4.28775	+	1.14890i	−0.704902	+	0.188878i	−0.593425	−	0.804889i	$-0.702225\pi$
$37$	−4.28775	+	1.14890i	−0.704902	+	0.188878i	−0.111477	+	0.993767i	$0.535558\pi$
$38$	−2.15672	−	3.73555i	−0.349866	−	0.605986i
$39$		0			0
$40$	1.98370	−	3.43586i	0.313650	−	0.543257i
$41$	1.44991	−	5.41115i	0.226439	−	0.845080i	−0.755384	−	0.655282i	$-0.772550\pi$
$41$	1.44991	−	5.41115i	0.226439	−	0.845080i	0.981823	−	0.189799i	$-0.0607835\pi$
$42$		0			0
$43$	−0.770434	−	0.444811i	−0.117490	−	0.0678330i	0.440103	−	0.897947i	$-0.354942\pi$
$43$	−0.770434	−	0.444811i	−0.117490	−	0.0678330i	−0.557593	+	0.830114i	$0.688275\pi$
$44$	3.50976	+	3.50976i	0.529116	+	0.529116i
$45$		0			0
$46$	0.846338	−	3.15858i	0.124786	−	0.465707i
$47$	−2.43773	−	0.653187i	−0.355579	−	0.0952772i	0.0766074	−	0.997061i	$-0.475591\pi$
$47$	−2.43773	−	0.653187i	−0.355579	−	0.0952772i	−0.432187	+	0.901784i	$0.642258\pi$
$48$		0			0
$49$	−3.82710	+	2.20958i	−0.546728	+	0.315654i
$50$	10.3742	+	2.77977i	1.46714	+	0.393118i
$51$		0			0
$52$	3.45258	−	1.03908i	0.478787	−	0.144094i
$53$		−	6.60181i		−	0.906828i	−0.891300	−	0.453414i	$-0.850206\pi$
$53$		−	6.60181i		−	0.906828i	0.891300	−	0.453414i	$-0.149794\pi$
$54$		0			0
$55$	−9.84618	+	17.0541i	−1.32766	+	2.29957i
$56$	0.803251	−	1.39127i	0.107339	−	0.185916i
$57$		0			0
$58$	−5.30733	+	5.30733i	−0.696886	+	0.696886i
$59$	−5.81273	+	5.81273i	−0.756753	+	0.756753i	−0.975730	−	0.218977i	$-0.929728\pi$
$59$	−5.81273	+	5.81273i	−0.756753	+	0.756753i	0.218977	+	0.975730i	$0.429728\pi$
$60$		0			0
$61$	−7.05927	+	12.2270i	−0.903847	+	1.56551i	−0.0813898	+	0.996682i	$0.525936\pi$
$61$	−7.05927	+	12.2270i	−0.903847	+	1.56551i	−0.822457	+	0.568827i	$0.807397\pi$
$62$	3.75530	−	6.50436i	0.476923	−	0.826055i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	7.52719	+	12.1640i	0.933633	+	1.50876i
$66$		0			0
$67$	−3.19229	−	0.855370i	−0.390000	−	0.104500i	0.0584902	−	0.998288i	$-0.481371\pi$
$67$	−3.19229	−	0.855370i	−0.390000	−	0.104500i	−0.448490	+	0.893788i	$0.648038\pi$
$68$	1.01166	−	0.584080i	0.122681	−	0.0708301i
$69$		0			0
$70$	6.15644	+	1.64961i	0.735836	+	0.197167i
$71$	−0.942701	+	3.51821i	−0.111878	+	0.417534i	−0.999034	−	0.0439344i	$-0.986011\pi$
$71$	−0.942701	+	3.51821i	−0.111878	+	0.417534i	0.887156	+	0.461469i	$0.152677\pi$
$72$		0			0
$73$	−3.33343	−	3.33343i	−0.390149	−	0.390149i	0.484592	−	0.874741i	$-0.338968\pi$
$73$	−3.33343	−	3.33343i	−0.390149	−	0.390149i	−0.874741	+	0.484592i	$0.838968\pi$
$74$	−3.84429	−	2.21950i	−0.446890	−	0.258012i
$75$		0			0
$76$	1.11640	−	4.16646i	0.128060	−	0.477926i
$77$	−3.98698	+	6.90565i	−0.454358	+	0.786971i
$78$		0			0
$79$	−1.16902	−	2.02480i	−0.131525	−	0.227808i	0.792740	−	0.609560i	$-0.208654\pi$
$79$	−1.16902	−	2.02480i	−0.131525	−	0.227808i	−0.924265	+	0.381753i	$0.875321\pi$
$80$	3.83221	−	1.02684i	0.428454	−	0.114804i
$81$		0			0
$82$	4.85151	−	2.80102i	0.535760	−	0.309321i
$83$	2.82772	−	10.5532i	0.310383	−	1.15837i	−0.617829	−	0.786313i	$-0.711988\pi$
$83$	2.82772	−	10.5532i	0.310383	−	1.15837i	0.928212	−	0.372052i	$-0.121346\pi$
$84$		0			0
$85$	3.27712	+	3.27712i	0.355454	+	0.355454i
$86$	−0.230251	−	0.859308i	−0.0248286	−	0.0926616i
$87$		0			0
$88$			4.96355i			0.529116i
$89$	1.78297	+	6.65415i	0.188995	+	0.705338i	0.993740	+	0.111718i	$0.0356352\pi$
$89$	1.78297	+	6.65415i	0.188995	+	0.705338i	−0.804745	+	0.593620i	$0.797698\pi$
$90$		0			0
$91$	3.04796	+	4.92554i	0.319513	+	0.516337i
$92$	2.83190	−	1.63500i	0.295246	−	0.170460i
$93$		0			0
$94$	−1.26186	−	2.18561i	−0.130151	−	0.225428i
$95$	17.1131			1.75577
$96$		0			0
$97$	−1.65585	−	6.17970i	−0.168126	−	0.627453i	−0.997621	−	0.0689395i	$-0.978038\pi$
$97$	−1.65585	−	6.17970i	−0.168126	−	0.627453i	0.829495	−	0.558514i	$-0.188628\pi$
$98$	−4.26857	−	1.14376i	−0.431191	−	0.115537i
$99$		0			0
$100$	5.37010	+	9.30128i	0.537010	+	0.930128i
$101$	−16.2961			−1.62152			−0.810762	−	0.585375i	$-0.800947\pi$
$101$	−16.2961			−1.62152			−0.810762	+	0.585375i	$0.800947\pi$
$102$		0			0
$103$	2.00231	+	1.15604i	0.197294	+	0.113908i	0.595393	−	0.803435i	$-0.296997\pi$
$103$	2.00231	+	1.15604i	0.197294	+	0.113908i	−0.398099	+	0.917343i	$0.630330\pi$
$104$	3.17608	+	1.70661i	0.311440	+	0.167346i
$105$		0			0
$106$	4.66818	−	4.66818i	0.453414	−	0.453414i
$107$	8.90852	+	5.14333i	0.861219	+	0.497225i	0.864420	−	0.502770i	$-0.167686\pi$
$107$	8.90852	+	5.14333i	0.861219	+	0.497225i	−0.00320143	+	0.999995i	$0.501019\pi$
$108$		0			0
$109$	5.93227	−	5.93227i	0.568208	−	0.568208i	−0.363418	−	0.931626i	$-0.618390\pi$
$109$	5.93227	−	5.93227i	0.568208	−	0.568208i	0.931626	+	0.363418i	$0.118390\pi$
$110$	−19.0214	+	5.09676i	−1.81361	+	0.485957i
$111$		0			0
$112$	1.55176	−	0.415793i	0.146628	−	0.0392888i
$113$			3.52980i			0.332055i	0.986121	+	0.166028i	$0.0530941\pi$
$113$			3.52980i			0.332055i	−0.986121	+	0.166028i	$0.946906\pi$
$114$		0			0
$115$	9.17355	+	9.17355i	0.855438	+	0.855438i
$116$	−7.50570			−0.696886
$117$		0			0
$118$	−8.22044			−0.756753
$119$	1.32699	+	1.32699i	0.121645	+	0.121645i
$120$		0			0
$121$		−	13.6369i		−	1.23971i
$122$	−13.6375	+	3.65415i	−1.23468	+	0.330831i
$123$		0			0
$124$	7.25468	−	1.94388i	0.651489	−	0.174566i
$125$	−16.1034	+	16.1034i	−1.44033	+	1.44033i
$126$		0			0
$127$	11.2191	+	6.47732i	0.995530	+	0.574769i	0.906923	−	0.421297i	$-0.138425\pi$
$127$	11.2191	+	6.47732i	0.995530	+	0.574769i	0.0886073	+	0.996067i	$0.471758\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−3.27875	+	13.9238i	−0.287565	+	1.22120i
$131$	−1.69814	−	0.980422i	−0.148367	−	0.0856599i	0.423979	−	0.905672i	$-0.360633\pi$
$131$	−1.69814	−	0.980422i	−0.148367	−	0.0856599i	−0.572346	+	0.820012i	$0.693967\pi$
$132$		0			0
$133$	6.92955			0.600868
$134$	−1.65245	−	2.86212i	−0.142750	−	0.247250i
$135$		0			0
$136$	1.12836	+	0.302342i	0.0967558	+	0.0259256i
$137$	−4.35359	−	16.2478i	−0.371953	−	1.38815i	−0.857747	−	0.514073i	$-0.828136\pi$
$137$	−4.35359	−	16.2478i	−0.371953	−	1.38815i	0.485794	−	0.874073i	$-0.338530\pi$
$138$		0			0
$139$	16.0718			1.36319			0.681597	−	0.731728i	$-0.261286\pi$
$139$	16.0718			1.36319			0.681597	+	0.731728i	$0.261286\pi$
$140$	3.18681	+	5.51972i	0.269335	+	0.466501i
$141$		0			0
$142$	−3.15434	+	1.82116i	−0.264706	+	0.152828i
$143$	−15.7647	−	8.47083i	−1.31831	−	0.708366i
$144$		0			0
$145$	−7.70712	−	28.7634i	−0.640042	−	2.38867i
$146$		−	4.71419i		−	0.390149i
$147$		0			0
$148$	−1.14890	−	4.28775i	−0.0944390	−	0.352451i
$149$	2.01440	+	2.01440i	0.165026	+	0.165026i	0.784789	−	0.619763i	$-0.212771\pi$
$149$	2.01440	+	2.01440i	0.165026	+	0.165026i	−0.619763	+	0.784789i	$0.712771\pi$
$150$		0			0
$151$	−1.23214	+	4.59840i	−0.100270	+	0.374213i	−0.997766	−	0.0668104i	$-0.978718\pi$
$151$	−1.23214	+	4.59840i	−0.100270	+	0.374213i	0.897496	+	0.441023i	$0.145384\pi$
$152$	3.73555	−	2.15672i	0.302993	−	0.174933i
$153$		0			0
$154$	−7.70225	+	2.06381i	−0.620665	+	0.166307i
$155$	14.8987	+	25.8054i	1.19669	+	2.07274i
$156$		0			0
$157$	3.96212	−	6.86259i	0.316211	−	0.547694i	−0.663483	−	0.748192i	$-0.730922\pi$
$157$	3.96212	−	6.86259i	0.316211	−	0.547694i	0.979694	+	0.200497i	$0.0642558\pi$
$158$	0.605128	−	2.25837i	0.0481414	−	0.179666i
$159$		0			0
$160$	3.43586	+	1.98370i	0.271629	+	0.156825i
$161$	3.71461	+	3.71461i	0.292753	+	0.292753i
$162$		0			0
$163$	−4.59427	+	17.1461i	−0.359851	+	1.34298i	0.514417	+	0.857540i	$0.328008\pi$
$163$	−4.59427	+	17.1461i	−0.359851	+	1.34298i	−0.874268	+	0.485443i	$0.838658\pi$
$164$	5.41115	+	1.44991i	0.422540	+	0.113219i
$165$		0			0
$166$	9.46175	−	5.46274i	0.734374	−	0.423991i
$167$	−10.9578	−	2.93613i	−0.847938	−	0.227204i	−0.191414	−	0.981509i	$-0.561307\pi$
$167$	−10.9578	−	2.93613i	−0.847938	−	0.227204i	−0.656524	+	0.754305i	$0.727974\pi$
$168$		0			0
$169$	−10.8406	+	7.17499i	−0.833895	+	0.551923i
$170$			4.63455i			0.355454i
$171$		0			0
$172$	0.444811	−	0.770434i	0.0339165	−	0.0587451i
$173$	8.37298	−	14.5024i	0.636586	−	1.10260i	−0.349591	−	0.936903i	$-0.613679\pi$
$173$	8.37298	−	14.5024i	0.636586	−	1.10260i	0.986177	−	0.165697i	$-0.0529874\pi$
$174$		0			0
$175$	−12.2005	+	12.2005i	−0.922272	+	0.922272i
$176$	−3.50976	+	3.50976i	−0.264558	+	0.264558i
$177$		0			0
$178$	−3.44444	+	5.96594i	−0.258172	+	0.447166i
$179$	−2.08607	+	3.61317i	−0.155920	+	0.270061i	−0.933394	−	0.358854i	$-0.883168\pi$
$179$	−2.08607	+	3.61317i	−0.155920	+	0.270061i	0.777474	+	0.628916i	$0.216501\pi$
$180$		0			0
$181$			7.52589i			0.559395i	0.960088	+	0.279698i	$0.0902342\pi$
$181$			7.52589i			0.559395i	−0.960088	+	0.279698i	$0.909766\pi$
$182$	−1.32765	+	5.63812i	−0.0984120	+	0.417925i
$183$		0			0
$184$	3.15858	+	0.846338i	0.232853	+	0.0623929i
$185$	15.2518	−	8.80564i	1.12134	−	0.647404i
$186$		0			0
$187$	−5.60066	−	1.50069i	−0.409561	−	0.109741i
$188$	0.653187	−	2.43773i	0.0476386	−	0.177790i
$189$		0			0
$190$	12.1008	+	12.1008i	0.877884	+	0.877884i
$191$	10.4815	+	6.05149i	0.758414	+	0.437871i	0.828726	−	0.559655i	$-0.189066\pi$
$191$	10.4815	+	6.05149i	0.758414	+	0.437871i	−0.0703120	+	0.997525i	$0.522399\pi$
$192$		0			0
$193$	4.12614	−	15.3990i	0.297006	−	1.10844i	−0.642605	−	0.766197i	$-0.722146\pi$
$193$	4.12614	−	15.3990i	0.297006	−	1.10844i	0.939611	−	0.342244i	$-0.111187\pi$
$194$	3.19885	−	5.54057i	0.229664	−	0.397789i
$195$		0			0
$196$	−2.20958	−	3.82710i	−0.157827	−	0.273364i
$197$	−12.3667	+	3.31364i	−0.881090	+	0.236087i	−0.670877	−	0.741568i	$-0.734082\pi$
$197$	−12.3667	+	3.31364i	−0.881090	+	0.236087i	−0.210212	+	0.977656i	$0.567416\pi$
$198$		0			0
$199$	11.0194	−	6.36204i	0.781143	−	0.450993i	−0.0556924	−	0.998448i	$-0.517737\pi$
$199$	11.0194	−	6.36204i	0.781143	−	0.450993i	0.836835	+	0.547455i	$0.184403\pi$
$200$	−2.77977	+	10.3742i	−0.196559	+	0.733569i
$201$		0			0
$202$	−11.5231	−	11.5231i	−0.810762	−	0.810762i
$203$	−3.12082	−	11.6470i	−0.219038	−	0.817462i
$204$		0			0
$205$			22.2255i			1.55230i
$206$	0.598408	+	2.23329i	0.0416931	+	0.155601i
$207$		0			0
$208$	1.03908	+	3.45258i	0.0720470	+	0.239393i
$209$	−18.5416	+	10.7050i	−1.28255	+	0.740480i
$210$		0			0
$211$	−7.86486	−	13.6223i	−0.541439	−	0.937800i	−0.998822	−	0.0485301i	$-0.984546\pi$
$211$	−7.86486	−	13.6223i	−0.541439	−	0.937800i	0.457383	−	0.889270i	$-0.348787\pi$
$212$	6.60181			0.453414
$213$		0			0
$214$	2.66239	+	9.93616i	0.181997	+	0.679222i
$215$	3.40921	+	0.913495i	0.232506	+	0.0622999i
$216$		0			0
$217$	6.03289	+	10.4493i	0.409539	+	0.709343i
$218$	8.38949			0.568208
$219$		0			0
$220$	−17.0541	−	9.84618i	−1.14979	−	0.663829i
$221$	−2.88592	+	3.06777i	−0.194128	+	0.206361i
$222$		0			0
$223$	0.129240	−	0.129240i	0.00865452	−	0.00865452i	−0.702766	−	0.711421i	$-0.748052\pi$
$223$	0.129240	−	0.129240i	0.00865452	−	0.00865452i	0.711421	+	0.702766i	$0.248052\pi$
$224$	1.39127	+	0.803251i	0.0929582	+	0.0536694i
$225$		0			0
$226$	−2.49594	+	2.49594i	−0.166028	+	0.166028i
$227$	12.8172	−	3.43437i	0.850710	−	0.227947i	0.192982	−	0.981202i	$-0.438184\pi$
$227$	12.8172	−	3.43437i	0.850710	−	0.227947i	0.657728	+	0.753255i	$0.271517\pi$
$228$		0			0
$229$	−8.72905	+	2.33894i	−0.576832	+	0.154562i	−0.535428	−	0.844581i	$-0.679850\pi$
$229$	−8.72905	+	2.33894i	−0.576832	+	0.154562i	−0.0414037	+	0.999142i	$0.513183\pi$
$230$			12.9734i			0.855438i
$231$		0			0
$232$	−5.30733	−	5.30733i	−0.348443	−	0.348443i
$233$	−5.07704			−0.332608			−0.166304	−	0.986075i	$-0.553183\pi$
$233$	−5.07704			−0.332608			−0.166304	+	0.986075i	$0.553183\pi$
$234$		0			0
$235$	10.0126			0.653150
$236$	−5.81273	−	5.81273i	−0.378377	−	0.378377i
$237$		0			0
$238$			1.87665i			0.121645i
$239$	−29.0366	+	7.78032i	−1.87822	+	0.503267i	−0.878547	+	0.477657i	$0.841486\pi$
$239$	−29.0366	+	7.78032i	−1.87822	+	0.503267i	−0.999672	+	0.0256107i	$0.991847\pi$
$240$		0			0
$241$	16.9189	−	4.53340i	1.08984	−	0.292022i	0.331219	−	0.943554i	$-0.392540\pi$
$241$	16.9189	−	4.53340i	1.08984	−	0.292022i	0.758621	+	0.651532i	$0.225874\pi$
$242$	9.64271	−	9.64271i	0.619857	−	0.619857i
$243$		0			0
$244$	−12.2270	−	7.05927i	−0.782755	−	0.451924i
$245$	12.3974	−	12.3974i	0.792038	−	0.792038i
$246$		0			0
$247$	0.474812	+	15.5451i	0.0302116	+	0.989110i
$248$	6.50436	+	3.75530i	0.413028	+	0.238462i
$249$		0			0
$250$	−22.7736			−1.44033
$251$	12.2713	+	21.2544i	0.774555	+	1.34157i	0.935044	+	0.354531i	$0.115360\pi$
$251$	12.2713	+	21.2544i	0.774555	+	1.34157i	−0.160489	+	0.987038i	$0.551307\pi$
$252$		0			0
$253$	−15.6778	−	4.20084i	−0.985652	−	0.264105i
$254$	3.35291	+	12.5132i	0.210380	+	0.785150i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.5671	−	18.3027i	−0.659156	−	1.14169i	−0.980834	−	0.194843i	$-0.937580\pi$
$257$	−10.5671	−	18.3027i	−0.659156	−	1.14169i	0.321678	−	0.946849i	$-0.395753\pi$
$258$		0			0
$259$	6.17586	−	3.56564i	0.383750	−	0.221558i
$260$	−12.1640	+	7.52719i	−0.754382	+	0.466817i
$261$		0			0
$262$	−0.507504	−	1.89403i	−0.0313537	−	0.117014i
$263$			1.30808i			0.0806599i	0.999186	+	0.0403299i	$0.0128409\pi$
$263$			1.30808i			0.0806599i	−0.999186	+	0.0403299i	$0.987159\pi$
$264$		0			0
$265$	6.77898	+	25.2995i	0.416429	+	1.55413i
$266$	4.89993	+	4.89993i	0.300434	+	0.300434i
$267$		0			0
$268$	0.855370	−	3.19229i	0.0522501	−	0.195000i
$269$	−24.6923	+	14.2561i	−1.50552	+	0.869210i	−0.505536	+	0.862805i	$0.668705\pi$
$269$	−24.6923	+	14.2561i	−1.50552	+	0.869210i	−0.999979	+	0.00640436i	$0.997961\pi$
$270$		0			0
$271$	1.05690	−	0.283196i	0.0642021	−	0.0172029i	−0.226575	−	0.973994i	$-0.572753\pi$
$271$	1.05690	−	0.283196i	0.0642021	−	0.0172029i	0.290777	+	0.956791i	$0.406086\pi$
$272$	0.584080	+	1.01166i	0.0354151	+	0.0613407i
$273$		0			0
$274$	8.41050	−	14.5674i	0.508097	−	0.880049i
$275$	13.7975	−	51.4930i	0.832021	−	3.10515i
$276$		0			0
$277$	−11.9296	−	6.88754i	−0.716779	−	0.413832i	0.0967872	−	0.995305i	$-0.469143\pi$
$277$	−11.9296	−	6.88754i	−0.716779	−	0.413832i	−0.813566	+	0.581473i	$0.802477\pi$
$278$	11.3645	+	11.3645i	0.681597	+	0.681597i
$279$		0			0
$280$	−1.64961	+	6.15644i	−0.0985833	+	0.367918i
$281$	4.37098	+	1.17120i	0.260751	+	0.0698680i	0.386826	−	0.922153i	$-0.373571\pi$
$281$	4.37098	+	1.17120i	0.260751	+	0.0698680i	−0.126075	+	0.992021i	$0.540238\pi$
$282$		0			0
$283$	−3.36340	+	1.94186i	−0.199933	+	0.115432i	−0.596624	−	0.802521i	$-0.703492\pi$
$283$	−3.36340	+	1.94186i	−0.199933	+	0.115432i	0.396691	+	0.917952i	$0.370158\pi$
$284$	−3.51821	−	0.942701i	−0.208767	−	0.0559390i
$285$		0			0
$286$	−5.15751	−	17.1371i	−0.304970	−	1.01334i
$287$			8.99968i			0.531235i
$288$		0			0
$289$	7.81770	−	13.5407i	0.459865	−	0.796509i
$290$	14.8890	−	25.7885i	0.874313	−	1.51435i
$291$		0			0
$292$	3.33343	−	3.33343i	0.195074	−	0.195074i
$293$	3.87378	−	3.87378i	0.226309	−	0.226309i	−0.584840	−	0.811149i	$-0.698843\pi$
$293$	3.87378	−	3.87378i	0.226309	−	0.226309i	0.811149	+	0.584840i	$0.198843\pi$
$294$		0			0
$295$	16.3069	−	28.2443i	0.949422	−	1.64445i
$296$	2.21950	−	3.84429i	0.129006	−	0.223445i
$297$		0			0
$298$			2.84880i			0.165026i
$299$	−8.07848	+	8.58753i	−0.467191	+	0.496630i
$300$		0			0
$301$	1.38048	+	0.369898i	0.0795695	+	0.0213206i
$302$	−4.12282	+	2.38031i	−0.237241	+	0.136971i
$303$		0			0
$304$	4.16646	+	1.11640i	0.238963	+	0.0640300i
$305$	14.4974	−	54.1052i	0.830121	−	3.09805i
$306$		0			0
$307$	0.236798	+	0.236798i	0.0135148	+	0.0135148i	0.713832	−	0.700317i	$-0.246958\pi$
$307$	0.236798	+	0.236798i	0.0135148	+	0.0135148i	−0.700317	+	0.713832i	$0.746958\pi$
$308$	−6.90565	−	3.98698i	−0.393486	−	0.227179i
$309$		0			0
$310$	−7.71215	+	28.7821i	−0.438021	+	1.63472i
$311$	7.57359	−	13.1178i	0.429459	−	0.743844i	−0.567366	−	0.823465i	$-0.692038\pi$
$311$	7.57359	−	13.1178i	0.429459	−	0.743844i	0.996825	+	0.0796211i	$0.0253710\pi$
$312$		0			0
$313$	−6.19713	−	10.7337i	−0.350282	−	0.606707i	0.636016	−	0.771675i	$-0.280581\pi$
$313$	−6.19713	−	10.7337i	−0.350282	−	0.606707i	−0.986299	+	0.164969i	$0.947248\pi$
$314$	7.65422	−	2.05094i	0.431953	−	0.115741i
$315$		0			0
$316$	2.02480	−	1.16902i	0.113904	−	0.0657624i
$317$	3.26964	−	12.2024i	0.183641	−	0.685358i	−0.811276	−	0.584663i	$-0.801227\pi$
$317$	3.26964	−	12.2024i	0.183641	−	0.685358i	0.994917	−	0.100695i	$-0.0321066\pi$
$318$		0			0
$319$	26.3432	+	26.3432i	1.47494	+	1.47494i
$320$	1.02684	+	3.83221i	0.0574019	+	0.214227i
$321$		0			0
$322$			5.25326i			0.292753i
$323$	1.30414	+	4.86710i	0.0725640	+	0.270813i
$324$		0			0
$325$	−28.2054	−	26.5335i	−1.56456	−	1.47181i
$326$	−15.3727	+	8.87545i	−0.851417	+	0.491566i
$327$		0			0
$328$	2.80102	+	4.85151i	0.154660	+	0.267880i
$329$	4.05436			0.223524
$330$		0			0
$331$	−0.372128	−	1.38880i	−0.0204540	−	0.0763353i	0.954944	−	0.296785i	$-0.0959143\pi$
$331$	−0.372128	−	1.38880i	−0.0204540	−	0.0763353i	−0.975398	+	0.220449i	$0.929248\pi$
$332$	10.5532	+	2.82772i	0.579183	+	0.155191i
$333$		0			0
$334$	−5.67216	−	9.82447i	−0.310367	−	0.537571i
$335$	13.1118			0.716375
$336$		0			0
$337$	16.5630	+	9.56266i	0.902245	+	0.520911i	0.877928	−	0.478793i	$-0.158926\pi$
$337$	16.5630	+	9.56266i	0.902245	+	0.520911i	0.0243169	+	0.999704i	$0.492259\pi$
$338$	−12.7390	−	2.59200i	−0.692909	−	0.140986i
$339$		0			0
$340$	−3.27712	+	3.27712i	−0.177727	+	0.177727i
$341$	−32.2848	−	18.6396i	−1.74832	−	1.00939i
$342$		0			0
$343$	12.9718	−	12.9718i	0.700411	−	0.700411i
$344$	0.859308	−	0.230251i	0.0463308	−	0.0124143i
$345$		0			0
$346$	16.1754	−	4.33418i	0.869593	−	0.233007i
$347$			30.2389i			1.62331i	0.584137	+	0.811655i	$0.301433\pi$
$347$			30.2389i			1.62331i	−0.584137	+	0.811655i	$0.698567\pi$
$348$		0			0
$349$	13.0186	+	13.0186i	0.696868	+	0.696868i	0.963734	−	0.266865i	$-0.0859879\pi$
$349$	13.0186	+	13.0186i	0.696868	+	0.696868i	−0.266865	+	0.963734i	$0.585988\pi$
$350$	−17.2541			−0.922272
$351$		0			0
$352$	−4.96355			−0.264558
$353$	−13.6207	−	13.6207i	−0.724955	−	0.724955i	0.244655	−	0.969610i	$-0.421325\pi$
$353$	−13.6207	−	13.6207i	−0.724955	−	0.724955i	−0.969610	+	0.244655i	$0.921325\pi$
$354$		0			0
$355$		−	14.4505i		−	0.766953i
$356$	−6.65415	+	1.78297i	−0.352669	+	0.0944974i
$357$		0			0
$358$	−4.02997	+	1.07983i	−0.212991	+	0.0570707i
$359$	14.9056	−	14.9056i	0.786685	−	0.786685i	−0.194264	−	0.980949i	$-0.562232\pi$
$359$	14.9056	−	14.9056i	0.786685	−	0.786685i	0.980949	+	0.194264i	$0.0622319\pi$
$360$		0			0
$361$	−0.341404	−	0.197110i	−0.0179686	−	0.0103742i
$362$	−5.32161	+	5.32161i	−0.279698	+	0.279698i
$363$		0			0
$364$	−4.92554	+	3.04796i	−0.258168	+	0.159756i
$365$	16.1973	+	9.35151i	0.847805	+	0.489480i
$366$		0			0
$367$	21.2676			1.11016			0.555079	−	0.831798i	$-0.312688\pi$
$367$	21.2676			1.11016			0.555079	+	0.831798i	$0.312688\pi$
$368$	1.63500	+	2.83190i	0.0852302	+	0.147623i
$369$		0			0
$370$	17.0112	+	4.55814i	0.884370	+	0.236966i
$371$	2.74499	+	10.2444i	0.142513	+	0.531864i
$372$		0			0
$373$	−19.9407			−1.03249			−0.516246	−	0.856440i	$-0.672671\pi$
$373$	−19.9407			−1.03249			−0.516246	+	0.856440i	$0.672671\pi$
$374$	−2.89911	−	5.02141i	−0.149910	−	0.259651i
$375$		0			0
$376$	2.18561	−	1.26186i	0.112714	−	0.0650755i
$377$	25.9140	−	7.79899i	1.33464	−	0.401669i
$378$		0			0
$379$	−7.46317	−	27.8529i	−0.383357	−	1.43071i	−0.840740	−	0.541439i	$-0.817880\pi$
$379$	−7.46317	−	27.8529i	−0.383357	−	1.43071i	0.457383	−	0.889270i	$-0.348787\pi$
$380$			17.1131i			0.877884i
$381$		0			0
$382$	3.13248	+	11.6906i	0.160272	+	0.598142i
$383$	13.9292	+	13.9292i	0.711750	+	0.711750i	0.966901	−	0.255151i	$-0.0821253\pi$
$383$	13.9292	+	13.9292i	0.711750	+	0.711750i	−0.255151	+	0.966901i	$0.582125\pi$
$384$		0			0
$385$	8.18795	−	30.5578i	0.417296	−	1.55737i
$386$	13.8063	−	7.97109i	0.702724	−	0.405718i
$387$		0			0
$388$	6.17970	−	1.65585i	0.313727	−	0.0840628i
$389$	−1.75344	−	3.03705i	−0.0889030	−	0.153984i	0.818145	−	0.575012i	$-0.195003\pi$
$389$	−1.75344	−	3.03705i	−0.0889030	−	0.153984i	−0.907048	+	0.421028i	$0.861669\pi$
$390$		0			0
$391$	−1.90994	+	3.30812i	−0.0965899	+	0.167299i
$392$	1.14376	−	4.26857i	0.0577687	−	0.215596i
$393$		0			0
$394$	−11.0877	−	6.40147i	−0.558588	−	0.322501i
$395$	6.55906	+	6.55906i	0.330022	+	0.330022i
$396$		0			0
$397$	−3.67258	+	13.7062i	−0.184321	+	0.687896i	0.810454	+	0.585803i	$0.199221\pi$
$397$	−3.67258	+	13.7062i	−0.184321	+	0.687896i	−0.994775	+	0.102093i	$0.967446\pi$
$398$	12.2905	+	3.29323i	0.616068	+	0.165075i
$399$		0			0
$400$	−9.30128	+	5.37010i	−0.465064	+	0.268505i
$401$	29.5314	+	7.91291i	1.47473	+	0.395152i	0.904549	−	0.426370i	$-0.140208\pi$
$401$	29.5314	+	7.91291i	1.47473	+	0.395152i	0.570177	+	0.821522i	$0.306875\pi$
$402$		0			0
$403$	−23.0275	+	14.2496i	−1.14708	+	0.709822i
$404$		−	16.2961i		−	0.810762i
$405$		0			0
$406$	6.02895	−	10.4425i	0.299212	−	0.518250i
$407$	−11.0166	+	19.0814i	−0.546074	+	0.945828i
$408$		0			0
$409$	−13.2956	+	13.2956i	−0.657426	+	0.657426i	−0.954770	−	0.297344i	$-0.903899\pi$
$409$	−13.2956	+	13.2956i	−0.657426	+	0.657426i	0.297344	+	0.954770i	$0.403899\pi$
$410$	−15.7158	+	15.7158i	−0.776148	+	0.776148i
$411$		0			0
$412$	−1.15604	+	2.00231i	−0.0569538	+	0.0986469i
$413$	6.60308	−	11.4369i	0.324916	−	0.562771i
$414$		0			0
$415$			43.3457i			2.12776i
$416$	−1.70661	+	3.17608i	−0.0836732	+	0.155720i
$417$		0			0
$418$	−20.6805	−	5.54131i	−1.01151	−	0.271035i
$419$	−3.91273	+	2.25902i	−0.191149	+	0.110360i	−0.592520	−	0.805555i	$-0.701867\pi$
$419$	−3.91273	+	2.25902i	−0.191149	+	0.110360i	0.401371	+	0.915915i	$0.368534\pi$
$420$		0			0
$421$	−31.8142	−	8.52459i	−1.55053	−	0.415463i	−0.620879	−	0.783907i	$-0.713224\pi$
$421$	−31.8142	−	8.52459i	−1.55053	−	0.415463i	−0.929650	+	0.368444i	$0.879891\pi$
$422$	4.07115	−	15.1937i	0.198180	−	0.739620i
$423$		0			0
$424$	4.66818	+	4.66818i	0.226707	+	0.226707i
$425$	−10.8654	−	6.27313i	−0.527049	−	0.304292i
$426$		0			0
$427$	5.87039	−	21.9086i	0.284088	−	1.06023i
$428$	−5.14333	+	8.90852i	−0.248612	+	0.430609i
$429$		0			0
$430$	1.76474	+	3.05661i	0.0851032	+	0.147403i
$431$	−10.5837	+	2.83588i	−0.509797	+	0.136600i	−0.504543	−	0.863386i	$-0.668339\pi$
$431$	−10.5837	+	2.83588i	−0.509797	+	0.136600i	−0.00525390	+	0.999986i	$0.501672\pi$
$432$		0			0
$433$	−7.59434	+	4.38459i	−0.364960	+	0.210710i	−0.671255	−	0.741227i	$-0.734244\pi$
$433$	−7.59434	+	4.38459i	−0.364960	+	0.210710i	0.306294	+	0.951937i	$0.400911\pi$
$434$	−3.12285	+	11.6546i	−0.149902	+	0.559441i
$435$		0			0
$436$	5.93227	+	5.93227i	0.284104	+	0.284104i
$437$	3.65063	+	13.6243i	0.174633	+	0.651740i
$438$		0			0
$439$		−	32.7658i		−	1.56383i	−0.623387	−	0.781913i	$-0.714244\pi$
$439$		−	32.7658i		−	1.56383i	0.623387	−	0.781913i	$-0.285756\pi$
$440$	−5.09676	−	19.0214i	−0.242978	−	0.906807i
$441$		0			0
$442$	−4.20990	+	0.128588i	−0.200245	+	0.00611630i
$443$	25.8748	−	14.9388i	1.22935	−	0.709766i	0.262457	−	0.964944i	$-0.415467\pi$
$443$	25.8748	−	14.9388i	1.22935	−	0.709766i	0.966894	+	0.255178i	$0.0821340\pi$
$444$		0			0
$445$	−13.6654	−	23.6692i	−0.647804	−	1.12203i
$446$	0.182772			0.00865452
$447$		0			0
$448$	0.415793	+	1.55176i	0.0196444	+	0.0733138i
$449$	14.4946	+	3.88382i	0.684043	+	0.183289i	0.584072	−	0.811702i	$-0.301458\pi$
$449$	14.4946	+	3.88382i	0.684043	+	0.183289i	0.0999708	+	0.994990i	$0.468125\pi$
$450$		0			0
$451$	−13.9030	−	24.0807i	−0.654667	−	1.13392i
$452$	−3.52980			−0.166028
$453$		0			0
$454$	11.4916	+	6.63469i	0.539329	+	0.311382i
$455$	−16.7381	−	15.7459i	−0.784696	−	0.738181i
$456$		0			0
$457$	2.55074	−	2.55074i	0.119318	−	0.119318i	−0.644926	−	0.764245i	$-0.723112\pi$
$457$	2.55074	−	2.55074i	0.119318	−	0.119318i	0.764245	+	0.644926i	$0.223112\pi$
$458$	−7.82625	−	4.51849i	−0.365697	−	0.211135i
$459$		0			0
$460$	−9.17355	+	9.17355i	−0.427719	+	0.427719i
$461$	−32.0555	+	8.58926i	−1.49298	+	0.400042i	−0.910741	−	0.412979i	$-0.864488\pi$
$461$	−32.0555	+	8.58926i	−1.49298	+	0.400042i	−0.582235	+	0.813021i	$0.697822\pi$
$462$		0			0
$463$	3.54265	−	0.949249i	0.164641	−	0.0441154i	−0.175557	−	0.984469i	$-0.556173\pi$
$463$	3.54265	−	0.949249i	0.164641	−	0.0441154i	0.340198	+	0.940354i	$0.389506\pi$
$464$		−	7.50570i		−	0.348443i
$465$		0			0
$466$	−3.59001	−	3.59001i	−0.166304	−	0.166304i
$467$	5.90589			0.273292			0.136646	−	0.990620i	$-0.456368\pi$
$467$	5.90589			0.273292			0.136646	+	0.990620i	$0.456368\pi$
$468$		0			0
$469$	5.30932			0.245162
$470$	7.07997	+	7.07997i	0.326575	+	0.326575i
$471$		0			0
$472$		−	8.22044i		−	0.378377i
$473$	−4.26522	+	1.14286i	−0.196115	+	0.0525489i
$474$		0			0
$475$	−44.7486	+	11.9904i	−2.05321	+	0.550155i
$476$	−1.32699	+	1.32699i	−0.0608226	+	0.0608226i
$477$		0			0
$478$	−26.0335	−	15.0304i	−1.19074	−	0.687476i
$479$	15.1937	−	15.1937i	0.694217	−	0.694217i	−0.268940	−	0.963157i	$-0.586673\pi$
$479$	15.1937	−	15.1937i	0.694217	−	0.694217i	0.963157	+	0.268940i	$0.0866734\pi$
$480$		0			0
$481$	8.42198	+	13.6100i	0.384009	+	0.620564i
$482$	15.1690	+	8.75785i	0.690931	+	0.398909i
$483$		0			0
$484$	13.6369			0.619857
$485$	12.6911	+	21.9816i	0.576272	+	0.998133i
$486$		0			0
$487$	41.0392	+	10.9964i	1.85966	+	0.498295i	0.999923	−	0.0124347i	$-0.00395819\pi$
$487$	41.0392	+	10.9964i	1.85966	+	0.498295i	0.859741	+	0.510730i	$0.170625\pi$
$488$	−3.65415	−	13.6375i	−0.165416	−	0.617339i
$489$		0			0
$490$	17.5325			0.792038
$491$	−10.2924	−	17.8270i	−0.464490	−	0.804521i	0.534688	−	0.845050i	$-0.320429\pi$
$491$	−10.2924	−	17.8270i	−0.464490	−	0.804521i	−0.999178	+	0.0405286i	$0.987096\pi$
$492$		0			0
$493$	7.59319	−	4.38393i	0.341980	−	0.197442i
$494$	−10.6563	+	11.3278i	−0.479449	+	0.509661i
$495$		0			0
$496$	1.94388	+	7.25468i	0.0872830	+	0.325745i
$497$		−	5.85139i		−	0.262471i
$498$		0			0
$499$	5.19060	+	19.3716i	0.232363	+	0.867190i	0.979320	+	0.202318i	$0.0648474\pi$
$499$	5.19060	+	19.3716i	0.232363	+	0.867190i	−0.746957	+	0.664872i	$0.768486\pi$
$500$	−16.1034	−	16.1034i	−0.720164	−	0.720164i
$501$		0			0
$502$	−6.35207	+	23.7063i	−0.283507	+	1.05806i
$503$	12.7223	−	7.34523i	0.567260	−	0.327508i	−0.188794	−	0.982017i	$-0.560458\pi$
$503$	12.7223	−	7.34523i	0.567260	−	0.327508i	0.756054	+	0.654509i	$0.227125\pi$
$504$		0			0
$505$	62.4501	−	16.7335i	2.77899	−	0.744629i
$506$	−8.11541	−	14.0563i	−0.360774	−	0.624879i
$507$		0			0
$508$	−6.47732	+	11.2191i	−0.287385	+	0.497765i
$509$	2.01708	−	7.52784i	0.0894055	−	0.333666i	−0.906706	−	0.421762i	$-0.861412\pi$
$509$	2.01708	−	7.52784i	0.0894055	−	0.333666i	0.996112	+	0.0880964i	$0.0280784\pi$
$510$		0			0
$511$	6.55871	+	3.78667i	0.290140	+	0.167513i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	5.46992	−	20.4140i	0.241268	−	0.900424i
$515$	−8.86034	−	2.37412i	−0.390433	−	0.104616i
$516$		0			0
$517$	−10.8484	+	6.26331i	−0.477111	+	0.275460i
$518$	6.88828	+	1.84571i	0.302654	+	0.0810958i
$519$		0			0
$520$	−13.9238	−	3.27875i	−0.610599	−	0.143783i
$521$		−	2.05915i		−	0.0902131i	−0.998982	−	0.0451065i	$-0.985637\pi$
$521$		−	2.05915i		−	0.0902131i	0.998982	−	0.0451065i	$-0.0143627\pi$
$522$		0			0
$523$	−10.5734	+	18.3136i	−0.462342	+	0.800800i	−0.999077	−	0.0429511i	$-0.986324\pi$
$523$	−10.5734	+	18.3136i	−0.462342	+	0.800800i	0.536735	+	0.843751i	$0.319657\pi$
$524$	0.980422	−	1.69814i	0.0428299	−	0.0741836i
$525$		0			0
$526$	−0.924955	+	0.924955i	−0.0403299	+	0.0403299i
$527$	−6.20386	+	6.20386i	−0.270244	+	0.270244i
$528$		0			0
$529$	6.15355	−	10.6583i	0.267546	−	0.463403i
$530$	−13.0960	+	22.6829i	−0.568853	+	0.985282i
$531$		0			0
$532$			6.92955i			0.300434i
$533$	−20.1890	+	0.616657i	−0.874484	+	0.0267104i
$534$		0			0
$535$	−39.4206	−	10.5627i	−1.70430	−	0.456666i
$536$	2.86212	−	1.65245i	0.123625	−	0.0713749i
$537$		0			0
$538$	−27.5407	−	7.37950i	−1.18736	−	0.318153i
$539$	−5.67712	+	21.1873i	−0.244531	+	0.912601i
$540$		0			0
$541$	−5.41302	−	5.41302i	−0.232724	−	0.232724i	0.581105	−	0.813829i	$-0.302621\pi$
$541$	−5.41302	−	5.41302i	−0.232724	−	0.232724i	−0.813829	+	0.581105i	$0.802621\pi$
$542$	0.947591	+	0.547092i	0.0407025	+	0.0234996i
$543$		0			0
$544$	−0.302342	+	1.12836i	−0.0129628	+	0.0483779i
$545$	−16.6422	+	28.8251i	−0.712873	+	1.23473i
$546$		0			0
$547$	10.3483	+	17.9238i	0.442461	+	0.766365i	0.997871	−	0.0652117i	$-0.0207723\pi$
$547$	10.3483	+	17.9238i	0.442461	+	0.766365i	−0.555411	+	0.831576i	$0.687439\pi$
$548$	16.2478	−	4.35359i	0.694073	−	0.185976i
$549$		0			0
$550$	46.1674	−	26.6548i	1.96858	−	1.13656i
$551$	8.37937	−	31.2722i	0.356973	−	1.33224i
$552$		0			0
$553$	2.65593	+	2.65593i	0.112942	+	0.112942i
$554$	−3.56526	−	13.3057i	−0.151473	−	0.565306i
$555$		0			0
$556$			16.0718i			0.681597i
$557$	2.69183	+	10.0460i	0.114056	+	0.425664i	0.999215	−	0.0396260i	$-0.0126167\pi$
$557$	2.69183	+	10.0460i	0.114056	+	0.425664i	−0.885158	+	0.465290i	$0.845950\pi$
$558$		0			0
$559$	−0.735204	+	3.12218i	−0.0310958	+	0.132054i
$560$	−5.51972	+	3.18681i	−0.233251	+	0.134667i
$561$		0			0
$562$	2.26259	+	3.91892i	0.0954415	+	0.165310i
$563$	−12.0716			−0.508759			−0.254379	−	0.967104i	$-0.581871\pi$
$563$	−12.0716			−0.508759			−0.254379	+	0.967104i	$0.581871\pi$
$564$		0			0
$565$	−3.62452	−	13.5269i	−0.152485	−	0.569081i
$566$	−3.75139	−	1.00518i	−0.157683	−	0.0422509i
$567$		0			0
$568$	−1.82116	−	3.15434i	−0.0764141	−	0.132353i
$569$	−3.09992			−0.129955			−0.0649777	−	0.997887i	$-0.520698\pi$
$569$	−3.09992			−0.129955			−0.0649777	+	0.997887i	$0.520698\pi$
$570$		0			0
$571$	−16.8061	−	9.70302i	−0.703314	−	0.406059i	0.105266	−	0.994444i	$-0.466431\pi$
$571$	−16.8061	−	9.70302i	−0.703314	−	0.406059i	−0.808581	+	0.588385i	$0.799764\pi$
$572$	8.47083	−	15.7647i	0.354183	−	0.659153i
$573$		0			0
$574$	−6.36374	+	6.36374i	−0.265617	+	0.265617i
$575$	−30.4152	−	17.5602i	−1.26840	−	0.732311i
$576$		0			0
$577$	−13.0940	+	13.0940i	−0.545109	+	0.545109i	−0.925022	−	0.379913i	$-0.875954\pi$
$577$	−13.0940	+	13.0940i	−0.545109	+	0.545109i	0.379913	+	0.925022i	$0.375954\pi$
$578$	15.1026	−	4.04674i	0.628187	−	0.168322i
$579$		0			0
$580$	28.7634	−	7.70712i	1.19433	−	0.320021i
$581$			17.5518i			0.728172i
$582$		0			0
$583$	−23.1708	−	23.1708i	−0.959635	−	0.959635i
$584$	4.71419			0.195074
$585$		0			0
$586$	5.47836			0.226309
$587$	−3.53264	−	3.53264i	−0.145808	−	0.145808i	0.630435	−	0.776242i	$-0.282877\pi$
$587$	−3.53264	−	3.53264i	−0.145808	−	0.145808i	−0.776242	+	0.630435i	$0.782877\pi$
$588$		0			0
$589$			32.3965i			1.33487i
$590$	31.5024	−	8.44105i	1.29693	−	0.347513i
$591$		0			0
$592$	4.28775	−	1.14890i	0.176226	−	0.0472195i
$593$	6.13688	−	6.13688i	0.252012	−	0.252012i	−0.569783	−	0.821795i	$-0.692973\pi$
$593$	6.13688	−	6.13688i	0.252012	−	0.252012i	0.821795	+	0.569783i	$0.192973\pi$
$594$		0			0
$595$	−6.44792	−	3.72271i	−0.264339	−	0.152616i
$596$	−2.01440	+	2.01440i	−0.0825132	+	0.0825132i
$597$		0			0
$598$	−11.7847	+	0.359953i	−0.481910	+	0.0147196i
$599$	14.0676	+	8.12194i	0.574787	+	0.331853i	0.759059	−	0.651022i	$-0.225659\pi$
$599$	14.0676	+	8.12194i	0.574787	+	0.331853i	−0.184272	+	0.982875i	$0.558993\pi$
$600$		0			0
$601$	−12.6796			−0.517213			−0.258607	−	0.965983i	$-0.583263\pi$
$601$	−12.6796			−0.517213			−0.258607	+	0.965983i	$0.583263\pi$
$602$	0.714589	+	1.23770i	0.0291245	+	0.0504450i
$603$		0			0
$604$	−4.59840	−	1.23214i	−0.187106	−	0.0501350i
$605$	14.0028	+	52.2592i	0.569296	+	2.12464i
$606$		0			0
$607$	10.0497			0.407903			0.203951	−	0.978981i	$-0.434622\pi$
$607$	10.0497			0.407903			0.203951	+	0.978981i	$0.434622\pi$
$608$	2.15672	+	3.73555i	0.0874666	+	0.151497i
$609$		0			0
$610$	48.5094	−	28.0069i	1.96409	−	1.13397i
$611$	0.277804	+	9.09517i	0.0112388	+	0.367951i
$612$		0			0
$613$	−1.97714	−	7.37880i	−0.0798561	−	0.298027i	0.914434	−	0.404734i	$-0.132636\pi$
$613$	−1.97714	−	7.37880i	−0.0798561	−	0.298027i	−0.994290	+	0.106707i	$0.965969\pi$
$614$			0.334882i			0.0135148i
$615$		0			0
$616$	−2.06381	−	7.70225i	−0.0831533	−	0.310332i
$617$	−25.8657	−	25.8657i	−1.04131	−	1.04131i	−0.999109	−	0.0422041i	$-0.986562\pi$
$617$	−25.8657	−	25.8657i	−1.04131	−	1.04131i	−0.0422041	−	0.999109i	$-0.513438\pi$
$618$		0			0
$619$	−11.4452	+	42.7139i	−0.460020	+	1.71682i	0.212877	+	0.977079i	$0.431717\pi$
$619$	−11.4452	+	42.7139i	−0.460020	+	1.71682i	−0.672896	+	0.739737i	$0.734950\pi$
$620$	−25.8054	+	14.8987i	−1.03637	+	0.598347i
$621$		0			0
$622$	14.6310	−	3.92038i	0.586652	−	0.157193i
$623$	−5.53350	−	9.58430i	−0.221695	−	0.383987i
$624$		0			0
$625$	18.3254	−	31.7405i	0.733015	−	1.26962i
$626$	3.20787	−	11.9719i	0.128212	−	0.478495i
$627$		0			0
$628$	6.86259	+	3.96212i	0.273847	+	0.158106i
$629$	3.66669	+	3.66669i	0.146200	+	0.146200i
$630$		0			0
$631$	5.78419	−	21.5869i	0.230265	−	0.859360i	−0.749962	−	0.661481i	$-0.769928\pi$
$631$	5.78419	−	21.5869i	0.230265	−	0.859360i	0.980226	−	0.197879i	$-0.0634053\pi$
$632$	2.25837	+	0.605128i	0.0898331	+	0.0240707i
$633$		0			0
$634$	10.9404	−	6.31645i	0.434499	−	0.250858i
$635$	−49.6449	−	13.3023i	−1.97010	−	0.527886i
$636$		0			0
$637$	11.6054	+	10.9175i	0.459822	+	0.432565i
$638$			37.2549i			1.47494i
$639$		0			0
$640$	−1.98370	+	3.43586i	−0.0784124	+	0.135814i
$641$	−1.06735	+	1.84870i	−0.0421577	+	0.0730192i	−0.886334	−	0.463046i	$-0.846757\pi$
$641$	−1.06735	+	1.84870i	−0.0421577	+	0.0730192i	0.844177	+	0.536065i	$0.180090\pi$
$642$		0			0
$643$	−8.55199	+	8.55199i	−0.337258	+	0.337258i	−0.855334	−	0.518077i	$-0.826648\pi$
$643$	−8.55199	+	8.55199i	−0.337258	+	0.337258i	0.518077	+	0.855334i	$0.326648\pi$
$644$	−3.71461	+	3.71461i	−0.146376	+	0.146376i
$645$		0			0
$646$	−2.51940	+	4.36372i	−0.0991243	+	0.171688i
$647$	0.758934	−	1.31451i	0.0298368	−	0.0516788i	−0.850721	−	0.525617i	$-0.823835\pi$
$647$	0.758934	−	1.31451i	0.0298368	−	0.0516788i	0.880558	+	0.473938i	$0.157168\pi$
$648$		0			0
$649$			40.8026i			1.60164i
$650$	−1.18225	−	38.7063i	−0.0463717	−	1.51818i
$651$		0			0
$652$	−17.1461	−	4.59427i	−0.671492	−	0.179926i
$653$	−4.79770	+	2.76995i	−0.187748	+	0.108397i	−0.590928	−	0.806724i	$-0.701238\pi$
$653$	−4.79770	+	2.76995i	−0.187748	+	0.108397i	0.403180	+	0.915121i	$0.367905\pi$
$654$		0			0
$655$	7.51436	+	2.01347i	0.293610	+	0.0786726i
$656$	−1.44991	+	5.41115i	−0.0566097	+	0.211270i
$657$		0			0
$658$	2.86687	+	2.86687i	0.111762	+	0.111762i
$659$	26.0385	+	15.0334i	1.01432	+	0.585616i	0.912453	−	0.409182i	$-0.134186\pi$
$659$	26.0385	+	15.0334i	1.01432	+	0.585616i	0.101865	+	0.994798i	$0.467519\pi$
$660$		0			0
$661$	−7.83198	+	29.2293i	−0.304629	+	1.13689i	0.628636	+	0.777700i	$0.283614\pi$
$661$	−7.83198	+	29.2293i	−0.304629	+	1.13689i	−0.933264	+	0.359190i	$0.883053\pi$
$662$	0.718896	−	1.24516i	0.0279407	−	0.0483947i
$663$		0			0
$664$	5.46274	+	9.46175i	0.211996	+	0.367187i
$665$	−26.5555	+	7.11551i	−1.02978	+	0.275928i
$666$		0			0
$667$	21.2554	−	12.2718i	0.823012	−	0.475166i
$668$	2.93613	−	10.9578i	0.113602	−	0.423969i
$669$		0			0
$670$	9.27146	+	9.27146i	0.358188	+	0.358188i
$671$	18.1376	+	67.6903i	0.700193	+	2.61315i
$672$		0			0
$673$			27.8812i			1.07474i	0.843346	+	0.537371i	$0.180582\pi$
$673$			27.8812i			1.07474i	−0.843346	+	0.537371i	$0.819418\pi$
$674$	4.95000	+	18.4736i	0.190667	+	0.711578i
$675$		0			0
$676$	−7.17499	−	10.8406i	−0.275961	−	0.416948i
$677$	33.3037	−	19.2279i	1.27997	−	0.738989i	0.303124	−	0.952951i	$-0.401970\pi$
$677$	33.3037	−	19.2279i	1.27997	−	0.738989i	0.976842	+	0.213962i	$0.0686369\pi$
$678$		0			0
$679$	5.13895	+	8.90093i	0.197215	+	0.341586i
$680$	−4.63455			−0.177727
$681$		0			0
$682$	−9.64857	−	36.0090i	−0.369463	−	1.37885i
$683$	−27.1625	−	7.27817i	−1.03934	−	0.278491i	−0.301502	−	0.953465i	$-0.597488\pi$
$683$	−27.1625	−	7.27817i	−1.03934	−	0.278491i	−0.737841	+	0.674974i	$0.764155\pi$
$684$		0			0
$685$	33.3677	+	57.7946i	1.27492	+	2.20822i
$686$	18.3449			0.700411
$687$		0			0
$688$	0.770434	+	0.444811i	0.0293725	+	0.0169582i
$689$	−22.7933	+	6.85979i	−0.868355	+	0.261337i
$690$		0			0
$691$	−20.5446	+	20.5446i	−0.781554	+	0.781554i	−0.980093	−	0.198539i	$-0.936380\pi$
$691$	−20.5446	+	20.5446i	−0.781554	+	0.781554i	0.198539	+	0.980093i	$0.436380\pi$
$692$	14.5024	+	8.37298i	0.551300	+	0.318293i
$693$		0			0
$694$	−21.3821	+	21.3821i	−0.811655	+	0.811655i
$695$	−61.5905	+	16.5031i	−2.33626	+	0.625999i
$696$		0			0
$697$	−6.32110	+	1.69373i	−0.239429	+	0.0641547i
$698$			18.4110i			0.696868i
$699$		0			0
$700$	−12.2005	−	12.2005i	−0.461136	−	0.461136i
$701$	24.1668			0.912769			0.456384	−	0.889783i	$-0.349144\pi$
$701$	24.1668			0.912769			0.456384	+	0.889783i	$0.349144\pi$
$702$		0			0
$703$	19.1474			0.722158
$704$	−3.50976	−	3.50976i	−0.132279	−	0.132279i
$705$		0			0
$706$		−	19.2625i		−	0.724955i
$707$	25.2877	−	6.77582i	0.951041	−	0.254831i
$708$		0			0
$709$	46.0830	−	12.3479i	1.73068	−	0.463735i	0.750342	−	0.661050i	$-0.229889\pi$
$709$	46.0830	−	12.3479i	1.73068	−	0.463735i	0.980340	+	0.197316i	$0.0632224\pi$
$710$	10.2180	−	10.2180i	0.383476	−	0.383476i
$711$		0			0
$712$	−5.96594	−	3.44444i	−0.223583	−	0.129086i
$713$	−17.3663	+	17.3663i	−0.650372	+	0.650372i
$714$		0			0
$715$	69.1115	+	16.2742i	2.58462	+	0.608622i
$716$	−3.61317	−	2.08607i	−0.135031	−	0.0779600i
$717$		0			0
$718$	21.0796			0.786685
$719$	22.5283	+	39.0202i	0.840165	+	1.45521i	0.889755	+	0.456438i	$0.150875\pi$
$719$	22.5283	+	39.0202i	0.840165	+	1.45521i	−0.0495902	+	0.998770i	$0.515792\pi$
$720$		0			0
$721$	−3.58778	−	0.961344i	−0.133616	−	0.0358023i
$722$	−0.102031	−	0.380787i	−0.00379722	−	0.0141714i
$723$		0			0
$724$	−7.52589			−0.279698
$725$	40.3063	+	69.8126i	1.49694	+	2.59277i
$726$		0			0
$727$	−41.1027	+	23.7307i	−1.52442	+	0.880122i	−0.524834	+	0.851205i	$0.675872\pi$
$727$	−41.1027	+	23.7307i	−1.52442	+	0.880122i	−0.999582	+	0.0289169i	$0.990794\pi$
$728$	−5.63812	−	1.32765i	−0.208962	−	0.0492060i
$729$		0			0
$730$	4.84070	+	18.0657i	0.179162	+	0.668643i
$731$			1.03922i			0.0384370i
$732$		0			0
$733$	−3.96299	−	14.7901i	−0.146377	−	0.546285i	−0.999690	−	0.0248869i	$-0.992077\pi$
$733$	−3.96299	−	14.7901i	−0.146377	−	0.546285i	0.853314	−	0.521398i	$-0.174589\pi$
$734$	15.0384	+	15.0384i	0.555079	+	0.555079i
$735$		0			0
$736$	−0.846338	+	3.15858i	−0.0311964	+	0.116427i
$737$	−14.2063	+	8.20202i	−0.523296	+	0.302125i
$738$		0			0
$739$	−39.2148	+	10.5076i	−1.44254	+	0.386527i	−0.893422	−	0.449218i	$-0.851702\pi$
$739$	−39.2148	+	10.5076i	−1.44254	+	0.386527i	−0.549117	+	0.835746i	$0.685036\pi$
$740$	8.80564	+	15.2518i	0.323702	+	0.560668i
$741$		0			0
$742$	−5.30291	+	9.18490i	−0.194676	+	0.337188i
$743$	5.31877	−	19.8499i	0.195127	−	0.728223i	−0.797107	−	0.603838i	$-0.793637\pi$
$743$	5.31877	−	19.8499i	0.195127	−	0.728223i	0.992234	−	0.124385i	$-0.0396959\pi$
$744$		0			0
$745$	−9.78808	−	5.65115i	−0.358607	−	0.207042i
$746$	−14.1002	−	14.1002i	−0.516246	−	0.516246i
$747$		0			0
$748$	1.50069	−	5.60066i	0.0548707	−	0.204780i
$749$	−15.9625	−	4.27713i	−0.583255	−	0.156283i
$750$		0			0
$751$	2.70228	−	1.56016i	0.0986078	−	0.0569312i	−0.449885	−	0.893086i	$-0.648535\pi$
$751$	2.70228	−	1.56016i	0.0986078	−	0.0569312i	0.548493	+	0.836155i	$0.315202\pi$
$752$	2.43773	+	0.653187i	0.0888948	+	0.0238193i
$753$		0			0
$754$	23.8387	+	12.8093i	0.868154	+	0.466486i
$755$		−	18.8872i		−	0.687377i
$756$		0			0
$757$	16.5089	−	28.5942i	0.600026	−	1.03928i	−0.392791	−	0.919628i	$-0.628490\pi$
$757$	16.5089	−	28.5942i	0.600026	−	1.03928i	0.992816	−	0.119647i	$-0.0381764\pi$
$758$	14.4177	−	24.9723i	0.523676	−	0.907033i
$759$		0			0
$760$	−12.1008	+	12.1008i	−0.438942	+	0.438942i
$761$	1.09462	−	1.09462i	0.0396798	−	0.0396798i	−0.686988	−	0.726668i	$-0.741068\pi$
$761$	1.09462	−	1.09462i	0.0396798	−	0.0396798i	0.726668	+	0.686988i	$0.241068\pi$
$762$		0			0
$763$	−6.73886	+	11.6721i	−0.243963	+	0.422557i
$764$	−6.05149	+	10.4815i	−0.218935	+	0.379207i
$765$		0			0
$766$			19.6989i			0.711750i
$767$	26.1088	+	14.0291i	0.942734	+	0.506560i
$768$		0			0
$769$	41.6581	+	11.1623i	1.50223	+	0.402522i	0.913847	−	0.406060i	$-0.133097\pi$
$769$	41.6581	+	11.1623i	1.50223	+	0.402522i	0.588385	+	0.808581i	$0.299764\pi$
$770$	27.3974	−	15.8179i	0.987334	−	0.570037i
$771$		0			0
$772$	15.3990	+	4.12614i	0.554221	+	0.148503i
$773$	−1.57719	+	5.88615i	−0.0567275	+	0.211710i	−0.988472	−	0.151405i	$-0.951620\pi$
$773$	−1.57719	+	5.88615i	−0.0567275	+	0.211710i	0.931744	+	0.363115i	$0.118287\pi$
$774$		0			0
$775$	−57.0389	−	57.0389i	−2.04890	−	2.04890i
$776$	5.54057	+	3.19885i	0.198895	+	0.114832i
$777$		0			0
$778$	0.907648	−	3.38739i	0.0325407	−	0.121444i
$779$	−12.0820	+	20.9267i	−0.432884	+	0.749777i
$780$		0			0
$781$	9.03942	+	15.6567i	0.323456	+	0.560242i
$782$	−3.68972	+	0.988659i	−0.131944	+	0.0353544i
$783$		0			0
$784$	3.82710	−	2.20958i	0.136682	−	0.0789135i

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-3.83221 + 1.02684i) q^{5} +(-1.55176 + 0.415793i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-3.83221 + 1.02684i) q^{5} +(-1.55176 + 0.415793i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-3.43586 - 1.98370i) q^{10} +(3.50976 - 3.50976i) q^{11} +(-1.03908 - 3.45258i) q^{13} +(-1.39127 - 0.803251i) q^{14} -1.00000 q^{16} +(-0.584080 - 1.01166i) q^{17} +(-4.16646 - 1.11640i) q^{19} +(-1.02684 - 3.83221i) q^{20} +4.96355 q^{22} +(-1.63500 - 2.83190i) q^{23} +(9.30128 - 5.37010i) q^{25} +(1.70661 - 3.17608i) q^{26} +(-0.415793 - 1.55176i) q^{28} +7.50570i q^{29} +(-1.94388 - 7.25468i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.302342 - 1.12836i) q^{34} +(5.51972 - 3.18681i) q^{35} +(-4.28775 + 1.14890i) q^{37} +(-2.15672 - 3.73555i) q^{38} +(1.98370 - 3.43586i) q^{40} +(1.44991 - 5.41115i) q^{41} +(-0.770434 - 0.444811i) q^{43} +(3.50976 + 3.50976i) q^{44} +(0.846338 - 3.15858i) q^{46} +(-2.43773 - 0.653187i) q^{47} +(-3.82710 + 2.20958i) q^{49} +(10.3742 + 2.77977i) q^{50} +(3.45258 - 1.03908i) q^{52} -6.60181i q^{53} +(-9.84618 + 17.0541i) q^{55} +(0.803251 - 1.39127i) q^{56} +(-5.30733 + 5.30733i) q^{58} +(-5.81273 + 5.81273i) q^{59} +(-7.05927 + 12.2270i) q^{61} +(3.75530 - 6.50436i) q^{62} -1.00000i q^{64} +(7.52719 + 12.1640i) q^{65} +(-3.19229 - 0.855370i) q^{67} +(1.01166 - 0.584080i) q^{68} +(6.15644 + 1.64961i) q^{70} +(-0.942701 + 3.51821i) q^{71} +(-3.33343 - 3.33343i) q^{73} +(-3.84429 - 2.21950i) q^{74} +(1.11640 - 4.16646i) q^{76} +(-3.98698 + 6.90565i) q^{77} +(-1.16902 - 2.02480i) q^{79} +(3.83221 - 1.02684i) q^{80} +(4.85151 - 2.80102i) q^{82} +(2.82772 - 10.5532i) q^{83} +(3.27712 + 3.27712i) q^{85} +(-0.230251 - 0.859308i) q^{86} +4.96355i q^{88} +(1.78297 + 6.65415i) q^{89} +(3.04796 + 4.92554i) q^{91} +(2.83190 - 1.63500i) q^{92} +(-1.26186 - 2.18561i) q^{94} +17.1131 q^{95} +(-1.65585 - 6.17970i) q^{97} +(-4.26857 - 1.14376i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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