LMFDB - Embedded newform 702.2.bb.a.71.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			71.10
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.994452 + 0.266463i) q^{5} +(0.339163 - 0.0908784i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.891601 - 0.514766i) q^{10} +(-2.56893 + 2.56893i) q^{11} +(0.0241746 + 3.60547i) q^{13} +(0.304085 + 0.175564i) q^{14} -1.00000 q^{16} +(1.67236 + 2.89660i) q^{17} +(-0.969723 - 0.259837i) q^{19} +(-0.266463 - 0.994452i) q^{20} -3.63301 q^{22} +(-0.735260 - 1.27351i) q^{23} +(-3.41219 + 1.97003i) q^{25} +(-2.53236 + 2.56655i) q^{26} +(0.0908784 + 0.339163i) q^{28} +5.82075i q^{29} +(1.48558 + 5.54424i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.865675 + 3.23074i) q^{34} +(-0.313065 + 0.180748i) q^{35} +(4.96682 - 1.33085i) q^{37} +(-0.501966 - 0.869430i) q^{38} +(0.514766 - 0.891601i) q^{40} +(2.41936 - 9.02916i) q^{41} +(2.37192 + 1.36943i) q^{43} +(-2.56893 - 2.56893i) q^{44} +(0.380599 - 1.42041i) q^{46} +(-8.18256 - 2.19251i) q^{47} +(-5.95541 + 3.43835i) q^{49} +(-3.80581 - 1.01976i) q^{50} +(-3.60547 + 0.0241746i) q^{52} -2.67501i q^{53} +(1.87015 - 3.23920i) q^{55} +(-0.175564 + 0.304085i) q^{56} +(-4.11589 + 4.11589i) q^{58} +(3.42622 - 3.42622i) q^{59} +(-2.86325 + 4.95929i) q^{61} +(-2.86991 + 4.97083i) q^{62} -1.00000i q^{64} +(-0.984764 - 3.57903i) q^{65} +(14.5603 + 3.90143i) q^{67} +(-2.89660 + 1.67236i) q^{68} +(-0.349179 - 0.0935622i) q^{70} +(1.53985 - 5.74681i) q^{71} +(2.47165 + 2.47165i) q^{73} +(4.45313 + 2.57101i) q^{74} +(0.259837 - 0.969723i) q^{76} +(-0.637824 + 1.10474i) q^{77} +(-1.76544 - 3.05783i) q^{79} +(0.994452 - 0.266463i) q^{80} +(8.09532 - 4.67384i) q^{82} +(2.23652 - 8.34680i) q^{83} +(-2.43491 - 2.43491i) q^{85} +(0.708868 + 2.64553i) q^{86} -3.63301i q^{88} +(2.68520 + 10.0213i) q^{89} +(0.335858 + 1.22064i) q^{91} +(1.27351 - 0.735260i) q^{92} +(-4.23561 - 7.33629i) q^{94} +1.03358 q^{95} +(-3.82280 - 14.2669i) q^{97} +(-6.64239 - 1.77982i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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
$5$	−0.994452	+	0.266463i	−0.444732	+	0.119166i	−0.474234	−	0.880399i	$-0.657275\pi$
$5$	−0.994452	+	0.266463i	−0.444732	+	0.119166i	0.0295011	+	0.999565i	$0.490608\pi$
$6$		0			0
$7$	0.339163	−	0.0908784i	0.128191	−	0.0343488i	−0.194153	−	0.980971i	$-0.562196\pi$
$7$	0.339163	−	0.0908784i	0.128191	−	0.0343488i	0.322344	+	0.946622i	$0.395529\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−0.891601	−	0.514766i	−0.281949	−	0.162783i
$11$	−2.56893	+	2.56893i	−0.774560	+	0.774560i	−0.978900	−	0.204340i	$-0.934495\pi$
$11$	−2.56893	+	2.56893i	−0.774560	+	0.774560i	0.204340	+	0.978900i	$0.434495\pi$
$12$		0			0
$13$	0.0241746	+	3.60547i	0.00670484	+	0.999978i
$13$	0.0241746	+	3.60547i	0.00670484	+	0.999978i
$14$	0.304085	+	0.175564i	0.0812701	+	0.0469213i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.67236	+	2.89660i	0.405606	+	0.702530i	0.994392	−	0.105759i	$-0.0337273\pi$
$17$	1.67236	+	2.89660i	0.405606	+	0.702530i	−0.588786	+	0.808289i	$0.700394\pi$
$18$		0			0
$19$	−0.969723	−	0.259837i	−0.222470	−	0.0596106i	0.145862	−	0.989305i	$-0.453404\pi$
$19$	−0.969723	−	0.259837i	−0.222470	−	0.0596106i	−0.368332	+	0.929694i	$0.620071\pi$
$20$	−0.266463	−	0.994452i	−0.0595829	−	0.222366i
$21$		0			0
$22$	−3.63301			−0.774560
$23$	−0.735260	−	1.27351i	−0.153312	−	0.265545i	0.779131	−	0.626861i	$-0.215661\pi$
$23$	−0.735260	−	1.27351i	−0.153312	−	0.265545i	−0.932443	+	0.361317i	$0.882327\pi$
$24$		0			0
$25$	−3.41219	+	1.97003i	−0.682439	+	0.394006i
$26$	−2.53236	+	2.56655i	−0.496636	+	0.503341i
$27$		0			0
$28$	0.0908784	+	0.339163i	0.0171744	+	0.0640957i
$29$			5.82075i			1.08089i	0.841380	+	0.540443i	$0.181743\pi$
$29$			5.82075i			1.08089i	−0.841380	+	0.540443i	$0.818257\pi$
$30$		0			0
$31$	1.48558	+	5.54424i	0.266817	+	0.995775i	0.961129	+	0.276101i	$0.0890423\pi$
$31$	1.48558	+	5.54424i	0.266817	+	0.995775i	−0.694312	+	0.719675i	$0.744291\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	−0.865675	+	3.23074i	−0.148462	+	0.554068i
$35$	−0.313065	+	0.180748i	−0.0529177	+	0.0305520i
$36$		0			0
$37$	4.96682	−	1.33085i	0.816540	−	0.218791i	0.173707	−	0.984797i	$-0.444426\pi$
$37$	4.96682	−	1.33085i	0.816540	−	0.218791i	0.642833	+	0.766006i	$0.277759\pi$
$38$	−0.501966	−	0.869430i	−0.0814296	−	0.141040i
$39$		0			0
$40$	0.514766	−	0.891601i	0.0813917	−	0.140975i
$41$	2.41936	−	9.02916i	0.377840	−	1.41012i	−0.471311	−	0.881967i	$-0.656219\pi$
$41$	2.41936	−	9.02916i	0.377840	−	1.41012i	0.849151	−	0.528151i	$-0.177114\pi$
$42$		0			0
$43$	2.37192	+	1.36943i	0.361714	+	0.208836i	0.669833	−	0.742512i	$-0.266366\pi$
$43$	2.37192	+	1.36943i	0.361714	+	0.208836i	−0.308118	+	0.951348i	$0.599699\pi$
$44$	−2.56893	−	2.56893i	−0.387280	−	0.387280i
$45$		0			0
$46$	0.380599	−	1.42041i	0.0561162	−	0.209429i
$47$	−8.18256	−	2.19251i	−1.19355	−	0.319811i	−0.393262	−	0.919427i	$-0.628653\pi$
$47$	−8.18256	−	2.19251i	−1.19355	−	0.319811i	−0.800288	+	0.599616i	$0.795320\pi$
$48$		0			0
$49$	−5.95541	+	3.43835i	−0.850772	+	0.491194i
$50$	−3.80581	−	1.01976i	−0.538223	−	0.144216i
$51$		0			0
$52$	−3.60547	+	0.0241746i	−0.499989	+	0.00335242i
$53$		−	2.67501i		−	0.367442i	−0.982978	−	0.183721i	$-0.941186\pi$
$53$		−	2.67501i		−	0.367442i	0.982978	−	0.183721i	$-0.0588142\pi$
$54$		0			0
$55$	1.87015	−	3.23920i	0.252171	−	0.436773i
$56$	−0.175564	+	0.304085i	−0.0234607	+	0.0406351i
$57$		0			0
$58$	−4.11589	+	4.11589i	−0.540443	+	0.540443i
$59$	3.42622	−	3.42622i	0.446055	−	0.446055i	−0.447985	−	0.894041i	$-0.647858\pi$
$59$	3.42622	−	3.42622i	0.446055	−	0.446055i	0.894041	+	0.447985i	$0.147858\pi$
$60$		0			0
$61$	−2.86325	+	4.95929i	−0.366601	+	0.634972i	−0.989032	−	0.147703i	$-0.952812\pi$
$61$	−2.86325	+	4.95929i	−0.366601	+	0.634972i	0.622431	+	0.782675i	$0.286145\pi$
$62$	−2.86991	+	4.97083i	−0.364479	+	0.631296i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.984764	−	3.57903i	−0.122145	−	0.443924i
$66$		0			0
$67$	14.5603	+	3.90143i	1.77883	+	0.476636i	0.990369	−	0.138451i	$-0.0442125\pi$
$67$	14.5603	+	3.90143i	1.77883	+	0.476636i	0.788459	+	0.615087i	$0.210879\pi$
$68$	−2.89660	+	1.67236i	−0.351265	+	0.202803i
$69$		0			0
$70$	−0.349179	−	0.0935622i	−0.0417349	−	0.0111828i
$71$	1.53985	−	5.74681i	0.182747	−	0.682021i	−0.812355	−	0.583164i	$-0.801815\pi$
$71$	1.53985	−	5.74681i	0.182747	−	0.682021i	0.995102	−	0.0988571i	$-0.0315187\pi$
$72$		0			0
$73$	2.47165	+	2.47165i	0.289285	+	0.289285i	0.836797	−	0.547513i	$-0.184425\pi$
$73$	2.47165	+	2.47165i	0.289285	+	0.289285i	−0.547513	+	0.836797i	$0.684425\pi$
$74$	4.45313	+	2.57101i	0.517665	+	0.298874i
$75$		0			0
$76$	0.259837	−	0.969723i	0.0298053	−	0.111235i
$77$	−0.637824	+	1.10474i	−0.0726868	+	0.125897i
$78$		0			0
$79$	−1.76544	−	3.05783i	−0.198627	−	0.344033i	0.749456	−	0.662054i	$-0.230315\pi$
$79$	−1.76544	−	3.05783i	−0.198627	−	0.344033i	−0.948084	+	0.318021i	$0.896982\pi$
$80$	0.994452	−	0.266463i	0.111183	−	0.0297914i
$81$		0			0
$82$	8.09532	−	4.67384i	0.893979	−	0.516139i
$83$	2.23652	−	8.34680i	0.245490	−	0.916181i	−0.727647	−	0.685952i	$-0.759386\pi$
$83$	2.23652	−	8.34680i	0.245490	−	0.916181i	0.973137	−	0.230228i	$-0.0739474\pi$
$84$		0			0
$85$	−2.43491	−	2.43491i	−0.264103	−	0.264103i
$86$	0.708868	+	2.64553i	0.0764392	+	0.285275i
$87$		0			0
$88$		−	3.63301i		−	0.387280i
$89$	2.68520	+	10.0213i	0.284630	+	1.06225i	0.949109	+	0.314947i	$0.101987\pi$
$89$	2.68520	+	10.0213i	0.284630	+	1.06225i	−0.664479	+	0.747307i	$0.731347\pi$
$90$		0			0
$91$	0.335858	+	1.22064i	0.0352075	+	0.127958i
$92$	1.27351	−	0.735260i	0.132772	−	0.0766562i
$93$		0			0
$94$	−4.23561	−	7.33629i	−0.436869	−	0.756680i
$95$	1.03358			0.106043
$96$		0			0
$97$	−3.82280	−	14.2669i	−0.388147	−	1.44858i	−0.833146	−	0.553053i	$-0.813463\pi$
$97$	−3.82280	−	14.2669i	−0.388147	−	1.44858i	0.444999	−	0.895531i	$-0.353204\pi$
$98$	−6.64239	−	1.77982i	−0.670983	−	0.179789i
$99$		0			0
$100$	−1.97003	−	3.41219i	−0.197003	−	0.341219i
$101$	17.3422			1.72561			0.862804	−	0.505538i	$-0.168706\pi$
$101$	17.3422			1.72561			0.862804	+	0.505538i	$0.168706\pi$
$102$		0			0
$103$	9.22402	+	5.32549i	0.908870	+	0.524736i	0.880067	−	0.474849i	$-0.157497\pi$
$103$	9.22402	+	5.32549i	0.908870	+	0.524736i	0.0288023	+	0.999585i	$0.490831\pi$
$104$	−2.56655	−	2.53236i	−0.251671	−	0.248318i
$105$		0			0
$106$	1.89152	−	1.89152i	0.183721	−	0.183721i
$107$	−0.693025	−	0.400118i	−0.0669973	−	0.0386809i	0.466127	−	0.884718i	$-0.345649\pi$
$107$	−0.693025	−	0.400118i	−0.0669973	−	0.0386809i	−0.533124	+	0.846037i	$0.678982\pi$
$108$		0			0
$109$	5.83921	−	5.83921i	0.559294	−	0.559294i	−0.369812	−	0.929107i	$-0.620578\pi$
$109$	5.83921	−	5.83921i	0.559294	−	0.559294i	0.929107	+	0.369812i	$0.120578\pi$
$110$	3.61285	−	0.968061i	0.344472	−	0.0923010i
$111$		0			0
$112$	−0.339163	+	0.0908784i	−0.0320479	+	0.00858720i
$113$			13.4923i			1.26925i	0.772822	+	0.634623i	$0.218844\pi$
$113$			13.4923i			1.26925i	−0.772822	+	0.634623i	$0.781156\pi$
$114$		0			0
$115$	1.07052	+	1.07052i	0.0998268	+	0.0998268i
$116$	−5.82075			−0.540443
$117$		0			0
$118$	4.84540			0.446055
$119$	0.830439	+	0.830439i	0.0761262	+	0.0761262i
$120$		0			0
$121$		−	2.19876i		−	0.199887i
$122$	−5.53137	+	1.48213i	−0.500787	+	0.134185i
$123$		0			0
$124$	−5.54424	+	1.48558i	−0.497888	+	0.133409i
$125$	6.50827	−	6.50827i	0.582117	−	0.582117i
$126$		0			0
$127$	−16.2637	−	9.38987i	−1.44317	−	0.833216i	−0.445112	−	0.895475i	$-0.646836\pi$
$127$	−16.2637	−	9.38987i	−1.44317	−	0.833216i	−0.998060	+	0.0622590i	$0.980170\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	1.83442	−	3.22709i	0.160889	−	0.283034i
$131$	2.91497	+	1.68296i	0.254682	+	0.147041i	0.621906	−	0.783092i	$-0.286358\pi$
$131$	2.91497	+	1.68296i	0.254682	+	0.147041i	−0.367224	+	0.930133i	$0.619692\pi$
$132$		0			0
$133$	−0.352507			−0.0305663
$134$	7.53699	+	13.0544i	0.651096	+	1.12773i
$135$		0			0
$136$	−3.23074	−	0.865675i	−0.277034	−	0.0742310i
$137$	1.00768	+	3.76073i	0.0860923	+	0.321301i	0.995519	−	0.0945638i	$-0.0301456\pi$
$137$	1.00768	+	3.76073i	0.0860923	+	0.321301i	−0.909426	+	0.415865i	$0.863479\pi$
$138$		0			0
$139$	0.552490			0.0468616			0.0234308	−	0.999725i	$-0.492541\pi$
$139$	0.552490			0.0468616			0.0234308	+	0.999725i	$0.492541\pi$
$140$	−0.180748	−	0.313065i	−0.0152760	−	0.0264588i
$141$		0			0
$142$	5.15245	−	2.97477i	0.432384	−	0.249637i
$143$	−9.32429	−	9.20008i	−0.779736	−	0.769350i
$144$		0			0
$145$	−1.55101	−	5.78846i	−0.128805	−	0.480705i
$146$			3.49544i			0.289285i
$147$		0			0
$148$	1.33085	+	4.96682i	0.109396	+	0.408270i
$149$	9.15442	+	9.15442i	0.749960	+	0.749960i	0.974471	−	0.224512i	$-0.0720787\pi$
$149$	9.15442	+	9.15442i	0.749960	+	0.749960i	−0.224512	+	0.974471i	$0.572079\pi$
$150$		0			0
$151$	2.33886	−	8.72875i	0.190334	−	0.710336i	−0.803092	−	0.595856i	$-0.796813\pi$
$151$	2.33886	−	8.72875i	0.190334	−	0.710336i	0.993426	−	0.114480i	$-0.0365203\pi$
$152$	0.869430	−	0.501966i	0.0705201	−	0.0407148i
$153$		0			0
$154$	−1.23218	+	0.330162i	−0.0992920	+	0.0266052i
$155$	−2.95467	−	5.11763i	−0.237325	−	0.411058i
$156$		0			0
$157$	5.60064	−	9.70059i	0.446980	−	0.774191i	−0.551208	−	0.834368i	$-0.685833\pi$
$157$	5.60064	−	9.70059i	0.446980	−	0.774191i	0.998188	+	0.0601763i	$0.0191663\pi$
$158$	0.913858	−	3.41056i	0.0727026	−	0.271330i
$159$		0			0
$160$	0.891601	+	0.514766i	0.0704873	+	0.0406958i
$161$	−0.365107	−	0.365107i	−0.0287745	−	0.0287745i
$162$		0			0
$163$	−2.29883	+	8.57937i	−0.180059	+	0.671988i	0.815576	+	0.578650i	$0.196420\pi$
$163$	−2.29883	+	8.57937i	−0.180059	+	0.671988i	−0.995635	+	0.0933377i	$0.970246\pi$
$164$	9.02916	+	2.41936i	0.705059	+	0.188920i
$165$		0			0
$166$	7.48354	−	4.32062i	0.580835	−	0.335345i
$167$	8.97462	+	2.40474i	0.694477	+	0.186084i	0.588755	−	0.808311i	$-0.299618\pi$
$167$	8.97462	+	2.40474i	0.694477	+	0.186084i	0.105721	+	0.994396i	$0.466285\pi$
$168$		0			0
$169$	−12.9988	+	0.174322i	−0.999910	+	0.0134094i
$170$		−	3.44349i		−	0.264103i
$171$		0			0
$172$	−1.36943	+	2.37192i	−0.104418	+	0.180857i
$173$	−5.29421	+	9.16985i	−0.402512	+	0.697171i	−0.994028	−	0.109122i	$-0.965196\pi$
$173$	−5.29421	+	9.16985i	−0.402512	+	0.697171i	0.591517	+	0.806293i	$0.298529\pi$
$174$		0			0
$175$	−0.978256	+	0.978256i	−0.0739492	+	0.0739492i
$176$	2.56893	−	2.56893i	0.193640	−	0.193640i
$177$		0			0
$178$	−5.18740	+	8.98484i	−0.388812	+	0.673442i
$179$	12.5097	−	21.6674i	0.935018	−	1.61950i	0.160417	−	0.987049i	$-0.448716\pi$
$179$	12.5097	−	21.6674i	0.935018	−	1.61950i	0.774601	−	0.632450i	$-0.217951\pi$
$180$		0			0
$181$			23.3875i			1.73838i	0.494482	+	0.869188i	$0.335358\pi$
$181$			23.3875i			1.73838i	−0.494482	+	0.869188i	$0.664642\pi$
$182$	−0.625638	+	1.10061i	−0.0463754	+	0.0815829i
$183$		0			0
$184$	1.42041	+	0.380599i	0.104714	+	0.0280581i
$185$	−4.58464	+	2.64694i	−0.337069	+	0.194607i
$186$		0			0
$187$	−11.7373	−	3.14500i	−0.858318	−	0.229986i
$188$	2.19251	−	8.18256i	0.159905	−	0.596775i
$189$		0			0
$190$	0.730852	+	0.730852i	0.0530215	+	0.0530215i
$191$	−10.6625	−	6.15600i	−0.771512	−	0.445432i	0.0619020	−	0.998082i	$-0.480283\pi$
$191$	−10.6625	−	6.15600i	−0.771512	−	0.445432i	−0.833414	+	0.552650i	$0.813617\pi$
$192$		0			0
$193$	−3.34912	+	12.4991i	−0.241075	+	0.899704i	0.734241	+	0.678889i	$0.237538\pi$
$193$	−3.34912	+	12.4991i	−0.241075	+	0.899704i	−0.975316	+	0.220815i	$0.929128\pi$
$194$	7.38509	−	12.7913i	0.530218	−	0.918365i
$195$		0			0
$196$	−3.43835	−	5.95541i	−0.245597	−	0.425386i
$197$	20.6372	−	5.52972i	1.47034	−	0.393976i	0.567292	−	0.823517i	$-0.307991\pi$
$197$	20.6372	−	5.52972i	1.47034	−	0.393976i	0.903048	+	0.429540i	$0.141324\pi$
$198$		0			0
$199$	19.2376	−	11.1069i	1.36372	−	0.787344i	0.373603	−	0.927589i	$-0.378122\pi$
$199$	19.2376	−	11.1069i	1.36372	−	0.787344i	0.990117	+	0.140245i	$0.0447889\pi$
$200$	1.01976	−	3.80581i	0.0721082	−	0.269111i
$201$		0			0
$202$	12.2628	+	12.2628i	0.862804	+	0.862804i
$203$	0.528980	+	1.97418i	0.0371271	+	0.138560i
$204$		0			0
$205$			9.62373i			0.672151i
$206$	2.75668	+	10.2881i	0.192067	+	0.716803i
$207$		0			0
$208$	−0.0241746	−	3.60547i	−0.00167621	−	0.249994i
$209$	3.15865	−	1.82365i	0.218488	−	0.126144i
$210$		0			0
$211$	−9.17554	−	15.8925i	−0.631670	−	1.09408i	−0.987210	−	0.159424i	$-0.949036\pi$
$211$	−9.17554	−	15.8925i	−0.631670	−	1.09408i	0.355540	−	0.934661i	$-0.384297\pi$
$212$	2.67501			0.183721
$213$		0			0
$214$	−0.207116	−	0.772969i	−0.0141582	−	0.0528391i
$215$	−2.72366	−	0.729803i	−0.185752	−	0.0497722i
$216$		0			0
$217$	1.00770	+	1.74539i	0.0684073	+	0.118485i
$218$	8.25788			0.559294
$219$		0			0
$220$	3.23920	+	1.87015i	0.218387	+	0.126086i
$221$	−10.4032	+	6.09965i	−0.699794	+	0.410307i
$222$		0			0
$223$	17.9280	−	17.9280i	1.20055	−	1.20055i	0.226550	−	0.974000i	$-0.427255\pi$
$223$	17.9280	−	17.9280i	1.20055	−	1.20055i	0.974000	−	0.226550i	$-0.0727446\pi$
$224$	−0.304085	−	0.175564i	−0.0203175	−	0.0117303i
$225$		0			0
$226$	−9.54047	+	9.54047i	−0.634623	+	0.634623i
$227$	−24.0759	+	6.45111i	−1.59797	+	0.428175i	−0.944429	−	0.328715i	$-0.893384\pi$
$227$	−24.0759	+	6.45111i	−1.59797	+	0.428175i	−0.653542	+	0.756890i	$0.726718\pi$
$228$		0			0
$229$	−1.49912	+	0.401688i	−0.0990647	+	0.0265443i	−0.308011	−	0.951383i	$-0.599663\pi$
$229$	−1.49912	+	0.401688i	−0.0990647	+	0.0265443i	0.208946	+	0.977927i	$0.432997\pi$
$230$			1.51395i			0.0998268i
$231$		0			0
$232$	−4.11589	−	4.11589i	−0.270222	−	0.270222i
$233$	−9.96467			−0.652807			−0.326403	−	0.945231i	$-0.605837\pi$
$233$	−9.96467			−0.652807			−0.326403	+	0.945231i	$0.605837\pi$
$234$		0			0
$235$	8.72139			0.568921
$236$	3.42622	+	3.42622i	0.223028	+	0.223028i
$237$		0			0
$238$			1.17442i			0.0761262i
$239$	0.0697473	−	0.0186887i	0.00451158	−	0.00120887i	−0.256563	−	0.966528i	$-0.582590\pi$
$239$	0.0697473	−	0.0186887i	0.00451158	−	0.00120887i	0.261074	+	0.965319i	$0.415923\pi$
$240$		0			0
$241$	−18.0719	+	4.84236i	−1.16412	+	0.311924i	−0.788609	−	0.614895i	$-0.789198\pi$
$241$	−18.0719	+	4.84236i	−1.16412	+	0.311924i	−0.375507	+	0.926819i	$0.622532\pi$
$242$	1.55476	−	1.55476i	0.0999436	−	0.0999436i
$243$		0			0
$244$	−4.95929	−	2.86325i	−0.317486	−	0.183301i
$245$	5.00617	−	5.00617i	0.319833	−	0.319833i
$246$		0			0
$247$	0.913390	−	3.50259i	0.0581176	−	0.222864i
$248$	−4.97083	−	2.86991i	−0.315648	−	0.182240i
$249$		0			0
$250$	9.20409			0.582117
$251$	10.5789	+	18.3232i	0.667735	+	1.15655i	0.978536	+	0.206075i	$0.0660692\pi$
$251$	10.5789	+	18.3232i	0.667735	+	1.15655i	−0.310802	+	0.950475i	$0.600597\pi$
$252$		0			0
$253$	5.16037	+	1.38272i	0.324430	+	0.0869308i
$254$	−4.86055	−	18.1398i	−0.304978	−	1.13819i
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.32194	+	12.6820i	0.456730	+	0.791079i	0.998786	−	0.0492631i	$-0.0156873\pi$
$257$	7.32194	+	12.6820i	0.456730	+	0.791079i	−0.542056	+	0.840342i	$0.682354\pi$
$258$		0			0
$259$	1.56361	−	0.902752i	0.0971582	−	0.0560943i
$260$	3.57903	−	0.984764i	0.221962	−	0.0610724i
$261$		0			0
$262$	0.871165	+	3.25123i	0.0538207	+	0.200862i
$263$			11.5254i			0.710686i	0.934736	+	0.355343i	$0.115636\pi$
$263$			11.5254i			0.710686i	−0.934736	+	0.355343i	$0.884364\pi$
$264$		0			0
$265$	0.712791	+	2.66017i	0.0437864	+	0.163413i
$266$	−0.249260	−	0.249260i	−0.0152831	−	0.0152831i
$267$		0			0
$268$	−3.90143	+	14.5603i	−0.238318	+	0.889414i
$269$	−17.7279	+	10.2352i	−1.08089	+	0.624052i	−0.931136	−	0.364671i	$-0.881182\pi$
$269$	−17.7279	+	10.2352i	−1.08089	+	0.624052i	−0.149754	+	0.988723i	$0.547848\pi$
$270$		0			0
$271$	0.537040	−	0.143899i	0.0326229	−	0.00874127i	−0.242471	−	0.970159i	$-0.577958\pi$
$271$	0.537040	−	0.143899i	0.0326229	−	0.00874127i	0.275094	+	0.961417i	$0.411291\pi$
$272$	−1.67236	−	2.89660i	−0.101401	−	0.175632i
$273$		0			0
$274$	−1.94670	+	3.37178i	−0.117604	+	0.203697i
$275$	3.70481	−	13.8265i	0.223408	−	0.833772i
$276$		0			0
$277$	10.4571	+	6.03744i	0.628309	+	0.362754i	0.780097	−	0.625659i	$-0.215170\pi$
$277$	10.4571	+	6.03744i	0.628309	+	0.362754i	−0.151788	+	0.988413i	$0.548503\pi$
$278$	0.390670	+	0.390670i	0.0234308	+	0.0234308i
$279$		0			0
$280$	0.0935622	−	0.349179i	0.00559141	−	0.0208674i
$281$	−14.0707	−	3.77024i	−0.839388	−	0.224913i	−0.186583	−	0.982439i	$-0.559741\pi$
$281$	−14.0707	−	3.77024i	−0.839388	−	0.224913i	−0.652805	+	0.757526i	$0.726408\pi$
$282$		0			0
$283$	−11.5559	+	6.67178i	−0.686925	+	0.396596i	−0.802459	−	0.596707i	$-0.796475\pi$
$283$	−11.5559	+	6.67178i	−0.686925	+	0.396596i	0.115534	+	0.993304i	$0.463142\pi$
$284$	5.74681	+	1.53985i	0.341010	+	0.0913735i
$285$		0			0
$286$	−0.0878267	−	13.0987i	−0.00519330	−	0.774543i
$287$		−	3.28222i		−	0.193743i
$288$		0			0
$289$	2.90646	−	5.03413i	0.170968	−	0.296125i
$290$	2.99633	−	5.18979i	0.175950	−	0.304755i
$291$		0			0
$292$	−2.47165	+	2.47165i	−0.144642	+	0.144642i
$293$	−14.9275	+	14.9275i	−0.872071	+	0.872071i	−0.992698	−	0.120627i	$-0.961510\pi$
$293$	−14.9275	+	14.9275i	−0.872071	+	0.872071i	0.120627	+	0.992698i	$0.461510\pi$
$294$		0			0
$295$	−2.49425	+	4.32017i	−0.145221	+	0.251530i
$296$	−2.57101	+	4.45313i	−0.149437	+	0.258833i
$297$		0			0
$298$			12.9463i			0.749960i
$299$	4.57382	−	2.68174i	0.264511	−	0.155089i
$300$		0			0
$301$	0.928918	+	0.248903i	0.0535419	+	0.0143465i
$302$	7.82599	−	4.51833i	0.450335	−	0.260001i
$303$		0			0
$304$	0.969723	+	0.259837i	0.0556174	+	0.0149027i
$305$	1.52590	−	5.69472i	0.0873726	−	0.326079i
$306$		0			0
$307$	−10.9437	−	10.9437i	−0.624590	−	0.624590i	0.322111	−	0.946702i	$-0.395607\pi$
$307$	−10.9437	−	10.9437i	−0.624590	−	0.624590i	−0.946702	+	0.322111i	$0.895607\pi$
$308$	−1.10474	−	0.637824i	−0.0629486	−	0.0363434i
$309$		0			0
$310$	1.52945	−	5.70798i	0.0868668	−	0.324191i
$311$	−12.9553	+	22.4392i	−0.734626	+	1.27241i	0.220262	+	0.975441i	$0.429309\pi$
$311$	−12.9553	+	22.4392i	−0.734626	+	1.27241i	−0.954887	+	0.296968i	$0.904024\pi$
$312$		0			0
$313$	17.6482	+	30.5676i	0.997537	+	1.72779i	0.559509	+	0.828824i	$0.310990\pi$
$313$	17.6482	+	30.5676i	0.997537	+	1.72779i	0.438028	+	0.898961i	$0.355677\pi$
$314$	10.8196	−	2.89910i	0.610586	−	0.163606i
$315$		0			0
$316$	3.05783	−	1.76544i	0.172016	−	0.0993137i
$317$	3.27025	−	12.2048i	0.183676	−	0.685487i	−0.811234	−	0.584721i	$-0.801204\pi$
$317$	3.27025	−	12.2048i	0.183676	−	0.685487i	0.994910	−	0.100766i	$-0.0321294\pi$
$318$		0			0
$319$	−14.9531	−	14.9531i	−0.837212	−	0.837212i
$320$	0.266463	+	0.994452i	0.0148957	+	0.0555916i
$321$		0			0
$322$		−	0.516339i		−	0.0287745i
$323$	−0.869078	−	3.24344i	−0.0483568	−	0.180470i
$324$		0			0
$325$	−7.18538	−	12.2549i	−0.398573	−	0.679782i
$326$	−7.69205	+	4.44101i	−0.426023	+	0.245965i
$327$		0			0
$328$	4.67384	+	8.09532i	0.258069	+	0.446989i
$329$	−2.97447			−0.163988
$330$		0			0
$331$	−2.57987	−	9.62819i	−0.141802	−	0.529213i	−0.999877	−	0.0156883i	$-0.995006\pi$
$331$	−2.57987	−	9.62819i	−0.141802	−	0.529213i	0.858075	−	0.513525i	$-0.171661\pi$
$332$	8.34680	+	2.23652i	0.458090	+	0.122745i
$333$		0			0
$334$	4.64560	+	8.04642i	0.254196	+	0.440281i
$335$	−15.5191			−0.847901
$336$		0			0
$337$	−25.2475	−	14.5766i	−1.37532	−	0.794040i	−0.383727	−	0.923447i	$-0.625360\pi$
$337$	−25.2475	−	14.5766i	−1.37532	−	0.794040i	−0.991592	+	0.129406i	$0.958693\pi$
$338$	−9.31483	−	9.06830i	−0.506660	−	0.493250i
$339$		0			0
$340$	2.43491	−	2.43491i	0.132052	−	0.132052i
$341$	−18.0591	−	10.4264i	−0.977954	−	0.564622i
$342$		0			0
$343$	−3.44537	+	3.44537i	−0.186032	+	0.186032i
$344$	−2.64553	+	0.708868i	−0.142638	+	0.0382196i
$345$		0			0
$346$	−10.2276	+	2.74049i	−0.549841	+	0.147329i
$347$		−	14.3451i		−	0.770084i	−0.922899	−	0.385042i	$-0.874187\pi$
$347$		−	14.3451i		−	0.770084i	0.922899	−	0.385042i	$-0.125813\pi$
$348$		0			0
$349$	18.7095	+	18.7095i	1.00150	+	1.00150i	0.999999	+	0.00149761i	$0.000476704\pi$
$349$	18.7095	+	18.7095i	1.00150	+	1.00150i	0.00149761	+	0.999999i	$0.499523\pi$
$350$	−1.38346			−0.0739492
$351$		0			0
$352$	3.63301			0.193640
$353$	8.42845	+	8.42845i	0.448601	+	0.448601i	0.894889	−	0.446288i	$-0.147254\pi$
$353$	8.42845	+	8.42845i	0.448601	+	0.448601i	−0.446288	+	0.894889i	$0.647254\pi$
$354$		0			0
$355$			6.12524i			0.325094i
$356$	−10.0213	+	2.68520i	−0.531127	+	0.142315i
$357$		0			0
$358$	24.1669	−	6.47549i	1.27726	−	0.342240i
$359$	−13.9898	+	13.9898i	−0.738351	+	0.738351i	−0.972259	−	0.233907i	$-0.924849\pi$
$359$	−13.9898	+	13.9898i	−0.738351	+	0.738351i	0.233907	+	0.972259i	$0.424849\pi$
$360$		0			0
$361$	−15.5816	−	8.99606i	−0.820086	−	0.473477i
$362$	−16.5374	+	16.5374i	−0.869188	+	0.869188i
$363$		0			0
$364$	−1.22064	+	0.335858i	−0.0639791	+	0.0176038i
$365$	−3.11654	−	1.79934i	−0.163127	−	0.0941815i
$366$		0			0
$367$	16.6794			0.870658			0.435329	−	0.900271i	$-0.356632\pi$
$367$	16.6794			0.870658			0.435329	+	0.900271i	$0.356632\pi$
$368$	0.735260	+	1.27351i	0.0383281	+	0.0663862i
$369$		0			0
$370$	−5.11350	−	1.37016i	−0.265838	−	0.0712311i
$371$	−0.243101	−	0.907265i	−0.0126212	−	0.0471029i
$372$		0			0
$373$	−0.533360			−0.0276163			−0.0138082	−	0.999905i	$-0.504395\pi$
$373$	−0.533360			−0.0276163			−0.0138082	+	0.999905i	$0.504395\pi$
$374$	−6.07568	−	10.5234i	−0.314166	−	0.544152i
$375$		0			0
$376$	7.33629	−	4.23561i	0.378340	−	0.218435i
$377$	−20.9865	+	0.140715i	−1.08086	+	0.00724717i
$378$		0			0
$379$	−8.93403	−	33.3422i	−0.458910	−	1.71268i	−0.676331	−	0.736598i	$-0.736431\pi$
$379$	−8.93403	−	33.3422i	−0.458910	−	1.71268i	0.217421	−	0.976078i	$-0.430236\pi$
$380$			1.03358i			0.0530215i
$381$		0			0
$382$	−3.18658	−	11.8925i	−0.163040	−	0.608472i
$383$	−1.42871	−	1.42871i	−0.0730038	−	0.0730038i	0.669662	−	0.742666i	$-0.266439\pi$
$383$	−1.42871	−	1.42871i	−0.0730038	−	0.0730038i	−0.742666	+	0.669662i	$0.766439\pi$
$384$		0			0
$385$	0.339912	−	1.26857i	0.0173235	−	0.0646523i
$386$	−11.2064	+	6.47000i	−0.570389	+	0.329314i
$387$		0			0
$388$	14.2669	−	3.82280i	0.724292	−	0.194073i
$389$	−0.968658	−	1.67777i	−0.0491129	−	0.0850661i	0.840424	−	0.541930i	$-0.182306\pi$
$389$	−0.968658	−	1.67777i	−0.0491129	−	0.0850661i	−0.889537	+	0.456864i	$0.848973\pi$
$390$		0			0
$391$	2.45923	−	4.25951i	0.124369	−	0.215413i
$392$	1.77982	−	6.64239i	0.0898947	−	0.335491i
$393$		0			0
$394$	18.5028	+	10.6826i	0.932158	+	0.538182i
$395$	2.57044	+	2.57044i	0.129333	+	0.129333i
$396$		0			0
$397$	−8.86089	+	33.0693i	−0.444716	+	1.65970i	0.271971	+	0.962305i	$0.412324\pi$
$397$	−8.86089	+	33.0693i	−0.444716	+	1.65970i	−0.716687	+	0.697395i	$0.754342\pi$
$398$	21.4568	+	5.74933i	1.07553	+	0.288188i
$399$		0			0
$400$	3.41219	−	1.97003i	0.170610	−	0.0985016i
$401$	−8.68363	−	2.32677i	−0.433640	−	0.116193i	0.0353944	−	0.999373i	$-0.488731\pi$
$401$	−8.68363	−	2.32677i	−0.433640	−	0.116193i	−0.469034	+	0.883180i	$0.655398\pi$
$402$		0			0
$403$	−19.9537	+	5.49023i	−0.993964	+	0.273488i
$404$			17.3422i			0.862804i
$405$		0			0
$406$	−1.02191	+	1.77000i	−0.0507166	+	0.0878438i
$407$	−9.34052	+	16.1783i	−0.462992	+	0.801926i
$408$		0			0
$409$	−10.4309	+	10.4309i	−0.515772	+	0.515772i	−0.916289	−	0.400517i	$-0.868831\pi$
$409$	−10.4309	+	10.4309i	−0.515772	+	0.515772i	0.400517	+	0.916289i	$0.368831\pi$
$410$	−6.80501	+	6.80501i	−0.336075	+	0.336075i
$411$		0			0
$412$	−5.32549	+	9.22402i	−0.262368	+	0.454435i
$413$	0.850676	−	1.47341i	0.0418590	−	0.0725019i
$414$		0			0
$415$			8.89644i			0.436709i
$416$	2.53236	−	2.56655i	0.124159	−	0.125835i
$417$		0			0
$418$	3.52301	+	0.943989i	0.172316	+	0.0461720i
$419$	30.2692	−	17.4759i	1.47875	−	0.853755i	0.479036	−	0.877795i	$-0.340986\pi$
$419$	30.2692	−	17.4759i	1.47875	−	0.853755i	0.999711	+	0.0240402i	$0.00765296\pi$
$420$		0			0
$421$	2.55665	+	0.685052i	0.124603	+	0.0333874i	0.320582	−	0.947221i	$-0.396122\pi$
$421$	2.55665	+	0.685052i	0.124603	+	0.0333874i	−0.195978	+	0.980608i	$0.562788\pi$
$422$	4.74961	−	17.7258i	0.231207	−	0.862878i
$423$		0			0
$424$	1.89152	+	1.89152i	0.0918604	+	0.0918604i
$425$	−11.4128	−	6.58918i	−0.553602	−	0.319622i
$426$		0			0
$427$	−0.520414	+	1.94221i	−0.0251846	+	0.0939903i
$428$	0.400118	−	0.693025i	0.0193404	−	0.0334986i
$429$		0			0
$430$	−1.40987	−	2.44197i	−0.0679900	−	0.117762i
$431$	14.1857	−	3.80104i	0.683301	−	0.183090i	0.0995618	−	0.995031i	$-0.468256\pi$
$431$	14.1857	−	3.80104i	0.683301	−	0.183090i	0.583739	+	0.811942i	$0.301589\pi$
$432$		0			0
$433$	−13.2828	+	7.66884i	−0.638332	+	0.368541i	−0.783972	−	0.620797i	$-0.786809\pi$
$433$	−13.2828	+	7.66884i	−0.638332	+	0.368541i	0.145640	+	0.989338i	$0.453476\pi$
$434$	−0.521626	+	1.94673i	−0.0250388	+	0.0934462i
$435$		0			0
$436$	5.83921	+	5.83921i	0.279647	+	0.279647i
$437$	0.382095	+	1.42600i	0.0182781	+	0.0682147i
$438$		0			0
$439$			10.8523i			0.517952i	0.965884	+	0.258976i	$0.0833851\pi$
$439$			10.8523i			0.517952i	−0.965884	+	0.258976i	$0.916615\pi$
$440$	0.968061	+	3.61285i	0.0461505	+	0.172236i
$441$		0			0
$442$	−11.6693	−	3.04306i	−0.555051	−	0.144744i
$443$	−28.8694	+	16.6678i	−1.37163	+	0.791909i	−0.991133	−	0.132874i	$-0.957579\pi$
$443$	−28.8694	+	16.6678i	−1.37163	+	0.791909i	−0.380494	+	0.924783i	$0.624246\pi$
$444$		0			0
$445$	−5.34060	−	9.25018i	−0.253169	−	0.438501i
$446$	25.3541			1.20055
$447$		0			0
$448$	−0.0908784	−	0.339163i	−0.00429360	−	0.0160239i
$449$	17.6413	+	4.72697i	0.832543	+	0.223079i	0.649823	−	0.760086i	$-0.274843\pi$
$449$	17.6413	+	4.72697i	0.832543	+	0.223079i	0.182720	+	0.983165i	$0.441510\pi$
$450$		0			0
$451$	16.9801	+	29.4104i	0.799561	+	1.38488i
$452$	−13.4923			−0.634623
$453$		0			0
$454$	−21.5858	−	12.4626i	−1.01307	−	0.584898i
$455$	−0.659251	−	1.12438i	−0.0309062	−	0.0527117i
$456$		0			0
$457$	4.51133	−	4.51133i	0.211031	−	0.211031i	−0.593674	−	0.804705i	$-0.702323\pi$
$457$	4.51133	−	4.51133i	0.211031	−	0.211031i	0.804705	+	0.593674i	$0.202323\pi$
$458$	−1.34408	−	0.776002i	−0.0628045	−	0.0362602i
$459$		0			0
$460$	−1.07052	+	1.07052i	−0.0499134	+	0.0499134i
$461$	34.7844	−	9.32045i	1.62007	−	0.434097i	0.669049	−	0.743219i	$-0.266702\pi$
$461$	34.7844	−	9.32045i	1.62007	−	0.434097i	0.951022	+	0.309122i	$0.100035\pi$
$462$		0			0
$463$	21.6855	−	5.81062i	1.00781	−	0.270042i	0.283097	−	0.959091i	$-0.408638\pi$
$463$	21.6855	−	5.81062i	1.00781	−	0.270042i	0.724715	+	0.689049i	$0.241972\pi$
$464$		−	5.82075i		−	0.270222i
$465$		0			0
$466$	−7.04608	−	7.04608i	−0.326403	−	0.326403i
$467$	−14.0000			−0.647843			−0.323921	−	0.946084i	$-0.605001\pi$
$467$	−14.0000			−0.647843			−0.323921	+	0.946084i	$0.605001\pi$
$468$		0			0
$469$	5.29288			0.244402
$470$	6.16695	+	6.16695i	0.284460	+	0.284460i
$471$		0			0
$472$			4.84540i			0.223028i
$473$	−9.61125	+	2.57533i	−0.441926	+	0.118414i
$474$		0			0
$475$	3.82077	−	1.02377i	0.175309	−	0.0469739i
$476$	−0.830439	+	0.830439i	−0.0380631	+	0.0380631i
$477$		0			0
$478$	0.0625337	+	0.0361039i	0.00286023	+	0.00165135i
$479$	18.8236	−	18.8236i	0.860073	−	0.860073i	−0.131273	−	0.991346i	$-0.541907\pi$
$479$	18.8236	−	18.8236i	0.860073	−	0.860073i	0.991346	+	0.131273i	$0.0419065\pi$
$480$		0			0
$481$	4.91843	+	17.8755i	0.224261	+	0.815054i
$482$	−16.2029	−	9.35472i	−0.738020	−	0.426096i
$483$		0			0
$484$	2.19876			0.0999436
$485$	7.60319	+	13.1691i	0.345243	+	0.597978i
$486$		0			0
$487$	−14.7534	−	3.95317i	−0.668542	−	0.179135i	−0.0914441	−	0.995810i	$-0.529148\pi$
$487$	−14.7534	−	3.95317i	−0.668542	−	0.179135i	−0.577098	+	0.816675i	$0.695815\pi$
$488$	−1.48213	−	5.53137i	−0.0670927	−	0.250393i
$489$		0			0
$490$	7.07980			0.319833
$491$	0.935816	+	1.62088i	0.0422328	+	0.0731493i	0.886369	−	0.462979i	$-0.153220\pi$
$491$	0.935816	+	1.62088i	0.0422328	+	0.0731493i	−0.844136	+	0.536129i	$0.819886\pi$
$492$		0			0
$493$	−16.8604	+	9.73437i	−0.759355	+	0.438414i
$494$	3.12257	−	1.83084i	0.140491	−	0.0823734i
$495$		0			0
$496$	−1.48558	−	5.54424i	−0.0667043	−	0.248944i
$497$		−	2.08904i		−	0.0937064i
$498$		0			0
$499$	−2.93283	−	10.9455i	−0.131291	−	0.489986i	0.868694	−	0.495349i	$-0.164960\pi$
$499$	−2.93283	−	10.9455i	−0.131291	−	0.489986i	−0.999986	+	0.00536247i	$0.998293\pi$
$500$	6.50827	+	6.50827i	0.291059	+	0.291059i
$501$		0			0
$502$	−5.47604	+	20.4369i	−0.244408	+	0.912142i
$503$	−0.311572	+	0.179886i	−0.0138923	+	0.00802072i	−0.506930	−	0.861987i	$-0.669220\pi$
$503$	−0.311572	+	0.179886i	−0.0138923	+	0.00802072i	0.493038	+	0.870008i	$0.335886\pi$
$504$		0			0
$505$	−17.2459	+	4.62104i	−0.767434	+	0.205633i
$506$	2.67121	+	4.62667i	0.118750	+	0.205680i
$507$		0			0
$508$	9.38987	−	16.2637i	0.416608	−	0.721586i
$509$	11.1705	−	41.6889i	0.495124	−	1.84783i	−0.0342084	−	0.999415i	$-0.510891\pi$
$509$	11.1705	−	41.6889i	0.495124	−	1.84783i	0.529333	−	0.848414i	$-0.322442\pi$
$510$		0			0
$511$	1.06291	+	0.613672i	0.0470204	+	0.0271472i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−3.79011	+	14.1449i	−0.167175	+	0.623905i
$515$	−10.5919	−	2.83809i	−0.466734	−	0.125061i
$516$		0			0
$517$	26.6528	−	15.3880i	1.17219	−	0.676763i
$518$	1.74398	+	0.467299i	0.0766262	+	0.0205319i
$519$		0			0
$520$	3.22709	+	1.83442i	0.141517	+	0.0804447i
$521$			39.0644i			1.71144i	0.517436	+	0.855722i	$0.326887\pi$
$521$			39.0644i			1.71144i	−0.517436	+	0.855722i	$0.673113\pi$
$522$		0			0
$523$	−22.3670	+	38.7408i	−0.978041	+	1.69402i	−0.308529	+	0.951215i	$0.599837\pi$
$523$	−22.3670	+	38.7408i	−0.978041	+	1.69402i	−0.669512	+	0.742801i	$0.733497\pi$
$524$	−1.68296	+	2.91497i	−0.0735205	+	0.127341i
$525$		0			0
$526$	−8.14968	+	8.14968i	−0.355343	+	0.355343i
$527$	−13.5751	+	13.5751i	−0.591339	+	0.591339i
$528$		0			0
$529$	10.4188	−	18.0459i	0.452991	−	0.784603i
$530$	−1.37701	+	2.38505i	−0.0598134	+	0.103600i
$531$		0			0
$532$		−	0.352507i		−	0.0152831i
$533$	32.6128	+	8.50464i	1.41262	+	0.368377i
$534$		0			0
$535$	0.795797	+	0.213233i	0.0344053	+	0.00921887i
$536$	−13.0544	+	7.53699i	−0.563866	+	0.325548i
$537$		0			0
$538$	−19.7729	−	5.29814i	−0.852471	−	0.228419i
$539$	6.46612	−	24.1319i	0.278515	−	1.03943i
$540$		0			0
$541$	20.3887	+	20.3887i	0.876580	+	0.876580i	0.993179	−	0.116599i	$-0.0371993\pi$
$541$	20.3887	+	20.3887i	0.876580	+	0.876580i	−0.116599	+	0.993179i	$0.537199\pi$
$542$	0.481497	+	0.277992i	0.0206821	+	0.0119408i
$543$		0			0
$544$	0.865675	−	3.23074i	0.0371155	−	0.138517i
$545$	−4.25088	+	7.36274i	−0.182088	+	0.315385i
$546$		0			0
$547$	9.46079	+	16.3866i	0.404514	+	0.700639i	0.994265	−	0.106947i	$-0.0341074\pi$
$547$	9.46079	+	16.3866i	0.404514	+	0.700639i	−0.589751	+	0.807585i	$0.700774\pi$
$548$	−3.76073	+	1.00768i	−0.160650	+	0.0430462i
$549$		0			0
$550$	12.3965	−	7.15714i	0.528590	−	0.305182i
$551$	1.51244	−	5.64452i	0.0644323	−	0.240465i
$552$		0			0
$553$	−0.876661	−	0.876661i	−0.0372794	−	0.0372794i
$554$	3.12521	+	11.6634i	0.132777	+	0.495532i
$555$		0			0
$556$			0.552490i			0.0234308i
$557$	−0.839623	−	3.13351i	−0.0355760	−	0.132771i	0.945854	−	0.324593i	$-0.105227\pi$
$557$	−0.839623	−	3.13351i	−0.0355760	−	0.132771i	−0.981430	+	0.191821i	$0.938561\pi$
$558$		0			0
$559$	−4.88009	+	8.58499i	−0.206406	+	0.363106i
$560$	0.313065	−	0.180748i	0.0132294	−	0.00763801i
$561$		0			0
$562$	−7.28354	−	12.6155i	−0.307237	−	0.532151i
$563$	−2.30675			−0.0972180			−0.0486090	−	0.998818i	$-0.515479\pi$
$563$	−2.30675			−0.0972180			−0.0486090	+	0.998818i	$0.515479\pi$
$564$		0			0
$565$	−3.59518	−	13.4174i	−0.151251	−	0.564475i
$566$	−12.8889	−	3.45357i	−0.541761	−	0.145164i
$567$		0			0
$568$	2.97477	+	5.15245i	0.124818	+	0.216192i
$569$	−9.50229			−0.398357			−0.199178	−	0.979963i	$-0.563827\pi$
$569$	−9.50229			−0.398357			−0.199178	+	0.979963i	$0.563827\pi$
$570$		0			0
$571$	−22.0695	−	12.7418i	−0.923578	−	0.533228i	−0.0388033	−	0.999247i	$-0.512355\pi$
$571$	−22.0695	−	12.7418i	−0.923578	−	0.533228i	−0.884775	+	0.466019i	$0.845688\pi$
$572$	9.20008	−	9.32429i	0.384675	−	0.389868i
$573$		0			0
$574$	2.32088	−	2.32088i	0.0968717	−	0.0968717i
$575$	5.01770	+	2.89697i	0.209253	+	0.120812i
$576$		0			0
$577$	17.9008	−	17.9008i	0.745221	−	0.745221i	−0.228357	−	0.973577i	$-0.573335\pi$
$577$	17.9008	−	17.9008i	0.745221	−	0.745221i	0.973577	+	0.228357i	$0.0733353\pi$
$578$	5.61484	−	1.50449i	0.233547	−	0.0625786i
$579$		0			0
$580$	5.78846	−	1.55101i	0.240353	−	0.0644023i
$581$		−	3.03417i		−	0.125879i
$582$		0			0
$583$	6.87191	+	6.87191i	0.284606	+	0.284606i
$584$	−3.49544			−0.144642
$585$		0			0
$586$	−21.1106			−0.872071
$587$	21.8482	+	21.8482i	0.901773	+	0.901773i	0.995590	−	0.0938164i	$-0.0299067\pi$
$587$	21.8482	+	21.8482i	0.901773	+	0.901773i	−0.0938164	+	0.995590i	$0.529907\pi$
$588$		0			0
$589$		−	5.76239i		−	0.237435i
$590$	−4.81852	+	1.29112i	−0.198375	+	0.0531545i
$591$		0			0
$592$	−4.96682	+	1.33085i	−0.204135	+	0.0546978i
$593$	−1.91150	+	1.91150i	−0.0784959	+	0.0784959i	−0.745265	−	0.666769i	$-0.767677\pi$
$593$	−1.91150	+	1.91150i	−0.0784959	+	0.0784959i	0.666769	+	0.745265i	$0.267677\pi$
$594$		0			0
$595$	−1.04711	−	0.604551i	−0.0429274	−	0.0247842i
$596$	−9.15442	+	9.15442i	−0.374980	+	0.374980i
$597$		0			0
$598$	5.13046	+	1.33790i	0.209800	+	0.0547108i
$599$	24.8798	+	14.3643i	1.01656	+	0.586911i	0.913105	−	0.407723i	$-0.133677\pi$
$599$	24.8798	+	14.3643i	1.01656	+	0.586911i	0.103454	+	0.994634i	$0.467011\pi$
$600$		0			0
$601$	30.9870			1.26399			0.631993	−	0.774974i	$-0.282237\pi$
$601$	30.9870			1.26399			0.631993	+	0.774974i	$0.282237\pi$
$602$	0.480843	+	0.832845i	0.0195977	+	0.0339442i
$603$		0			0
$604$	8.72875	+	2.33886i	0.355168	+	0.0951670i
$605$	0.585887	+	2.18656i	0.0238197	+	0.0888963i
$606$		0			0
$607$	10.0680			0.408647			0.204323	−	0.978903i	$-0.434501\pi$
$607$	10.0680			0.408647			0.204323	+	0.978903i	$0.434501\pi$
$608$	0.501966	+	0.869430i	0.0203574	+	0.0352600i
$609$		0			0
$610$	5.10575	−	2.94781i	0.206726	−	0.119353i
$611$	7.70722	−	29.5550i	0.311801	−	1.19567i
$612$		0			0
$613$	−5.97413	−	22.2957i	−0.241293	−	0.900516i	−0.975211	−	0.221278i	$-0.928977\pi$
$613$	−5.97413	−	22.2957i	−0.241293	−	0.900516i	0.733918	−	0.679238i	$-0.237690\pi$
$614$		−	15.4767i		−	0.624590i
$615$		0			0
$616$	−0.330162	−	1.23218i	−0.0133026	−	0.0496460i
$617$	−18.5480	−	18.5480i	−0.746714	−	0.746714i	0.227146	−	0.973861i	$-0.427060\pi$
$617$	−18.5480	−	18.5480i	−0.746714	−	0.746714i	−0.973861	+	0.227146i	$0.927060\pi$
$618$		0			0
$619$	5.49310	−	20.5005i	0.220786	−	0.823985i	−0.763263	−	0.646088i	$-0.776404\pi$
$619$	5.49310	−	20.5005i	0.220786	−	0.823985i	0.984049	−	0.177897i	$-0.0569295\pi$
$620$	5.11763	−	2.95467i	0.205529	−	0.118662i
$621$		0			0
$622$	−25.0277	+	6.70614i	−1.00352	+	0.268892i
$623$	1.82144	+	3.15482i	0.0729743	+	0.126395i
$624$		0			0
$625$	5.11220	−	8.85460i	0.204488	−	0.354184i
$626$	−9.13540	+	34.0938i	−0.365124	+	1.36266i
$627$		0			0
$628$	9.70059	+	5.60064i	0.387096	+	0.223490i
$629$	12.1612	+	12.1612i	0.484900	+	0.484900i
$630$		0			0
$631$	2.60255	−	9.71284i	0.103606	−	0.386662i	−0.894578	−	0.446913i	$-0.852523\pi$
$631$	2.60255	−	9.71284i	0.103606	−	0.386662i	0.998183	+	0.0602509i	$0.0191901\pi$
$632$	3.41056	+	0.913858i	0.135665	+	0.0363513i
$633$		0			0
$634$	10.9425	−	6.31764i	0.434581	−	0.250906i
$635$	18.6755	+	5.00410i	0.741116	+	0.198582i
$636$		0			0
$637$	−12.5409	−	21.3889i	−0.496887	−	0.847460i
$638$		−	21.1468i		−	0.837212i
$639$		0			0
$640$	−0.514766	+	0.891601i	−0.0203479	+	0.0352436i
$641$	3.23854	−	5.60931i	0.127915	−	0.221555i	−0.794954	−	0.606670i	$-0.792505\pi$
$641$	3.23854	−	5.60931i	0.127915	−	0.221555i	0.922868	+	0.385115i	$0.125838\pi$
$642$		0			0
$643$	−5.14668	+	5.14668i	−0.202965	+	0.202965i	−0.801269	−	0.598304i	$-0.795841\pi$
$643$	−5.14668	+	5.14668i	−0.202965	+	0.202965i	0.598304	+	0.801269i	$0.295841\pi$
$644$	0.365107	−	0.365107i	0.0143872	−	0.0143872i
$645$		0			0
$646$	1.67893	−	2.90799i	0.0660566	−	0.114413i
$647$	2.67717	−	4.63699i	0.105250	−	0.182299i	−0.808590	−	0.588372i	$-0.799769\pi$
$647$	2.67717	−	4.63699i	0.105250	−	0.182299i	0.913840	+	0.406073i	$0.133102\pi$
$648$		0			0
$649$			17.6034i			0.690993i
$650$	3.58472	−	13.7464i	0.140604	−	0.539177i
$651$		0			0
$652$	−8.57937	−	2.29883i	−0.335994	−	0.0900293i
$653$	11.7085	−	6.75992i	0.458190	−	0.264536i	−0.253093	−	0.967442i	$-0.581448\pi$
$653$	11.7085	−	6.75992i	0.458190	−	0.264536i	0.711283	+	0.702906i	$0.248114\pi$
$654$		0			0
$655$	−3.34725	−	0.896892i	−0.130788	−	0.0350445i
$656$	−2.41936	+	9.02916i	−0.0944600	+	0.352529i
$657$		0			0
$658$	−2.10327	−	2.10327i	−0.0819940	−	0.0819940i
$659$	22.4923	+	12.9859i	0.876176	+	0.505861i	0.869396	−	0.494116i	$-0.164508\pi$
$659$	22.4923	+	12.9859i	0.876176	+	0.505861i	0.00678051	+	0.999977i	$0.497842\pi$
$660$		0			0
$661$	3.57302	−	13.3347i	0.138975	−	0.518660i	−0.860975	−	0.508647i	$-0.830146\pi$
$661$	3.57302	−	13.3347i	0.138975	−	0.518660i	0.999950	−	0.0100133i	$-0.00318737\pi$
$662$	4.98392	−	8.63240i	0.193706	−	0.335508i
$663$		0			0
$664$	4.32062	+	7.48354i	0.167673	+	0.290418i
$665$	0.350552	−	0.0939301i	0.0135938	−	0.00364245i
$666$		0			0
$667$	7.41277	−	4.27977i	0.287024	−	0.165713i
$668$	−2.40474	+	8.97462i	−0.0930422	+	0.347238i
$669$		0			0
$670$	−10.9737	−	10.9737i	−0.423951	−	0.423951i
$671$	−5.38458	−	20.0955i	−0.207869	−	0.775779i
$672$		0			0
$673$		−	28.2814i		−	1.09017i	−0.838382	−	0.545083i	$-0.816498\pi$
$673$		−	28.2814i		−	1.09017i	0.838382	−	0.545083i	$-0.183502\pi$
$674$	−7.54543	−	28.1599i	−0.290639	−	1.08468i
$675$		0			0
$676$	−0.174322	−	12.9988i	−0.00670468	−	0.499955i
$677$	34.1714	−	19.7289i	1.31331	−	0.758242i	0.330671	−	0.943746i	$-0.392725\pi$
$677$	34.1714	−	19.7289i	1.31331	−	0.758242i	0.982644	+	0.185504i	$0.0593917\pi$
$678$		0			0
$679$	−2.59310	−	4.49139i	−0.0995142	−	0.172364i
$680$	3.44349			0.132052
$681$		0			0
$682$	−5.39711	−	20.1423i	−0.206666	−	0.771288i
$683$	−25.3130	−	6.78259i	−0.968574	−	0.259529i	−0.260348	−	0.965515i	$-0.583837\pi$
$683$	−25.3130	−	6.78259i	−0.968574	−	0.259529i	−0.708226	+	0.705986i	$0.750504\pi$
$684$		0			0
$685$	−2.00419	−	3.47136i	−0.0765761	−	0.132634i
$686$	−4.87249			−0.186032
$687$		0			0
$688$	−2.37192	−	1.36943i	−0.0904286	−	0.0522090i
$689$	9.64469	−	0.0646675i	0.367433	−	0.00246363i
$690$		0			0
$691$	8.34355	−	8.34355i	0.317404	−	0.317404i	−0.530366	−	0.847769i	$-0.677945\pi$
$691$	8.34355	−	8.34355i	0.317404	−	0.317404i	0.847769	+	0.530366i	$0.177945\pi$
$692$	−9.16985	−	5.29421i	−0.348585	−	0.201256i
$693$		0			0
$694$	10.1435	−	10.1435i	0.385042	−	0.385042i
$695$	−0.549425	+	0.147218i	−0.0208409	+	0.00558430i
$696$		0			0
$697$	30.1999	−	8.09204i	1.14390	−	0.306508i
$698$			26.4592i			1.00150i
$699$		0			0
$700$	−0.978256	−	0.978256i	−0.0369746	−	0.0369746i
$701$	32.2520			1.21814			0.609071	−	0.793115i	$-0.291542\pi$
$701$	32.2520			1.21814			0.609071	+	0.793115i	$0.291542\pi$
$702$		0			0
$703$	−5.16224			−0.194698
$704$	2.56893	+	2.56893i	0.0968200	+	0.0968200i
$705$		0			0
$706$			11.9196i			0.448601i
$707$	5.88181	−	1.57603i	0.221208	−	0.0592726i
$708$		0			0
$709$	−13.0734	+	3.50300i	−0.490981	+	0.131558i	−0.495811	−	0.868430i	$-0.665129\pi$
$709$	−13.0734	+	3.50300i	−0.490981	+	0.131558i	0.00482996	+	0.999988i	$0.498463\pi$
$710$	−4.33120	+	4.33120i	−0.162547	+	0.162547i
$711$		0			0
$712$	−8.98484	−	5.18740i	−0.336721	−	0.194406i
$713$	5.96835	−	5.96835i	0.223516	−	0.223516i
$714$		0			0
$715$	11.7240	+	6.66447i	0.438454	+	0.249237i
$716$	21.6674	+	12.5097i	0.809750	+	0.467509i
$717$		0			0
$718$	−19.7845			−0.738351
$719$	−5.20762	−	9.01985i	−0.194211	−	0.336384i	0.752430	−	0.658672i	$-0.228881\pi$
$719$	−5.20762	−	9.01985i	−0.194211	−	0.336384i	−0.946642	+	0.322288i	$0.895548\pi$
$720$		0			0
$721$	3.61241	+	0.967944i	0.134533	+	0.0360481i
$722$	−4.65670	−	17.3791i	−0.173305	−	0.646781i
$723$		0			0
$724$	−23.3875			−0.869188
$725$	−11.4671	−	19.8615i	−0.425876	−	0.737639i
$726$		0			0
$727$	20.0010	−	11.5476i	0.741796	−	0.428276i	−0.0809260	−	0.996720i	$-0.525788\pi$
$727$	20.0010	−	11.5476i	0.741796	−	0.428276i	0.822722	+	0.568444i	$0.192454\pi$
$728$	−1.10061	−	0.625638i	−0.0407914	−	0.0231877i
$729$		0			0
$730$	−0.931405	−	3.47605i	−0.0344728	−	0.128654i
$731$			9.16068i			0.338820i
$732$		0			0
$733$	6.58200	+	24.5643i	0.243112	+	0.907305i	0.974323	+	0.225154i	$0.0722885\pi$
$733$	6.58200	+	24.5643i	0.243112	+	0.907305i	−0.731212	+	0.682151i	$0.761045\pi$
$734$	11.7941	+	11.7941i	0.435329	+	0.435329i
$735$		0			0
$736$	−0.380599	+	1.42041i	−0.0140290	+	0.0523571i
$737$	−47.4269	+	27.3819i	−1.74699	+	1.00863i
$738$		0			0
$739$	23.9997	−	6.43070i	0.882843	−	0.236557i	0.211209	−	0.977441i	$-0.432260\pi$
$739$	23.9997	−	6.43070i	0.882843	−	0.236557i	0.671633	+	0.740884i	$0.265593\pi$
$740$	−2.64694	−	4.58464i	−0.0973035	−	0.168535i
$741$		0			0
$742$	0.469635	−	0.813432i	0.0172408	−	0.0298620i
$743$	−5.53701	+	20.6644i	−0.203133	+	0.758104i	0.786877	+	0.617110i	$0.211697\pi$
$743$	−5.53701	+	20.6644i	−0.203133	+	0.758104i	−0.990010	+	0.140994i	$0.954970\pi$
$744$		0			0
$745$	−11.5429	−	6.66432i	−0.422901	−	0.244162i
$746$	−0.377142	−	0.377142i	−0.0138082	−	0.0138082i
$747$		0			0
$748$	3.14500	−	11.7373i	0.114993	−	0.429159i
$749$	−0.271410	−	0.0727242i	−0.00991712	−	0.00265728i
$750$		0			0
$751$	36.9669	−	21.3428i	1.34894	−	0.778812i	0.360842	−	0.932627i	$-0.382490\pi$
$751$	36.9669	−	21.3428i	1.34894	−	0.778812i	0.988100	+	0.153816i	$0.0491562\pi$
$752$	8.18256	+	2.19251i	0.298387	+	0.0799527i
$753$		0			0
$754$	−14.9392	−	14.7402i	−0.544055	−	0.536808i
$755$			9.30355i			0.338591i
$756$		0			0
$757$	8.17298	−	14.1560i	0.297052	−	0.514509i	−0.678408	−	0.734685i	$-0.737330\pi$
$757$	8.17298	−	14.1560i	0.297052	−	0.514509i	0.975460	+	0.220176i	$0.0706632\pi$
$758$	17.2592	−	29.8938i	0.626883	−	1.08579i
$759$		0			0
$760$	−0.730852	+	0.730852i	−0.0265108	+	0.0265108i
$761$	4.38948	−	4.38948i	0.159119	−	0.159119i	−0.623057	−	0.782176i	$-0.714110\pi$
$761$	4.38948	−	4.38948i	0.159119	−	0.159119i	0.782176	+	0.623057i	$0.214110\pi$
$762$		0			0
$763$	1.44978	−	2.51110i	0.0524857	−	0.0909078i
$764$	6.15600	−	10.6625i	0.222716	−	0.385756i
$765$		0			0
$766$		−	2.02050i		−	0.0730038i
$767$	12.4359	+	12.2703i	0.449036	+	0.443055i
$768$		0			0
$769$	−22.4859	−	6.02508i	−0.810863	−	0.217270i	−0.170515	−	0.985355i	$-0.554543\pi$
$769$	−22.4859	−	6.02508i	−0.810863	−	0.217270i	−0.640348	+	0.768085i	$0.721210\pi$
$770$	1.13737	−	0.656660i	0.0409879	−	0.0236644i
$771$		0			0
$772$	−12.4991	−	3.34912i	−0.449852	−	0.120537i
$773$	2.25389	−	8.41164i	0.0810668	−	0.302546i	−0.913474	−	0.406898i	$-0.866610\pi$
$773$	2.25389	−	8.41164i	0.0810668	−	0.302546i	0.994540	+	0.104353i	$0.0332770\pi$
$774$		0			0
$775$	−15.9914	−	15.9914i	−0.574428	−	0.574428i
$776$	12.7913	+	7.38509i	0.459183	+	0.265109i
$777$		0			0
$778$	0.501414	−	1.87130i	0.0179766	−	0.0670895i
$779$	−4.69221	+	8.12715i	−0.168116	+	0.291185i
$780$		0			0
$781$	10.8074	+	18.7189i	0.386718	+	0.669815i
$782$	4.75087	−	1.27299i	0.169891	−	0.0455221i
$783$		0			0
$784$	5.95541	−	3.43835i	0.212693	−	0.122798i
$785$	−2.98472	+	11.1391i	−0.106529	+	0.397573i
$786$		0			0
$787$	5.48176	+	5.48176i	0.195404	+	0.195404i	0.798026	−	0.602623i	$-0.205878\pi$
$787$	5.48176	+	5.48176i	0.195404	+	0.195404i	−0.602623	+	0.798026i	$0.705878\pi$
$788$	5.52972	+	20.6372i	0.196988	+	0.735170i
$789$		0			0
$790$			3.63515i			0.129333i
$791$	1.22615	+	4.57607i	0.0435970	+	0.162706i
$792$		0			0
$793$	−17.9498	−	10.2035i	−0.637416	−	0.362336i
$794$	−29.6491	+	17.1179i	−1.05221	+	0.607493i
$795$		0			0
$796$	11.1069	+	19.2376i	0.393672	+	0.681860i
$797$	−18.7264			−0.663325			−0.331662	−	0.943398i	$-0.607609\pi$
$797$	−18.7264			−0.663325			−0.331662	+	0.943398i	$0.607609\pi$
$798$		0			0
$799$	−7.33332	−	27.3683i	−0.259434	−	0.968221i
$800$	3.80581	+	1.01976i	0.134556	+	0.0360541i
$801$		0			0
$802$	−4.49498	−	7.78553i	−0.158723	−	0.274917i
$803$	−12.6990			−0.448137
$804$		0			0
$805$	0.460369	+	0.265794i	0.0162259	+	0.00936801i
$806$	−17.9916	−	10.2272i	−0.633726	−	0.360238i
$807$		0			0
$808$	−12.2628	+	12.2628i	−0.431402	+	0.431402i
$809$	−8.00375	−	4.62097i	−0.281397	−	0.162465i	0.352659	−	0.935752i	$-0.385278\pi$
$809$	−8.00375	−	4.62097i	−0.281397	−	0.162465i	−0.634056	+	0.773287i	$0.718611\pi$
$810$		0			0
$811$	27.8829	−	27.8829i	0.979100	−	0.979100i	−0.0206860	−	0.999786i	$-0.506585\pi$
$811$	27.8829	−	27.8829i	0.979100	−	0.979100i	0.999786	+	0.0206860i	$0.00658503\pi$
$812$	−1.97418	+	0.528980i	−0.0692802	+	0.0185636i
$813$		0			0
$814$	−18.0445	+	4.83501i	−0.632459	+	0.169467i
$815$		−	9.14432i		−	0.320312i
$816$		0			0
$817$	−1.94428	−	1.94428i	−0.0680217	−	0.0680217i
$818$	−14.7515			−0.515772
$819$		0			0
$820$	−9.62373			−0.336075
$821$	−6.26653	−	6.26653i	−0.218704	−	0.218704i	0.589248	−	0.807952i	$-0.299424\pi$
$821$	−6.26653	−	6.26653i	−0.218704	−	0.218704i	−0.807952	+	0.589248i	$0.799424\pi$
$822$		0			0
$823$			9.65676i			0.336614i	0.985735	+	0.168307i	$0.0538299\pi$
$823$			9.65676i			0.336614i	−0.985735	+	0.168307i	$0.946170\pi$
$824$	−10.2881	+	2.75668i	−0.358401	+	0.0960334i
$825$		0			0
$826$	1.64338	−	0.440342i	0.0571805	−	0.0153215i
$827$	16.2044	−	16.2044i	0.563482	−	0.563482i	−0.366813	−	0.930295i	$-0.619551\pi$
$827$	16.2044	−	16.2044i	0.563482	−	0.563482i	0.930295	+	0.366813i	$0.119551\pi$
$828$		0			0
$829$	39.4372	+	22.7691i	1.36971	+	0.790802i	0.990891	−	0.134668i	$-0.0429969\pi$
$829$	39.4372	+	22.7691i	1.36971	+	0.790802i	0.378819	+	0.925471i	$0.376330\pi$
$830$	−6.29074	+	6.29074i	−0.218355	+	0.218355i
$831$		0			0
$832$	3.60547	−	0.0241746i	0.124997	−	0.000838104i
$833$	−19.9191	−	11.5003i	−0.690156	−	0.398462i
$834$		0			0
$835$	−9.56560			−0.331031
$836$	1.82365	+	3.15865i	0.0630721	+	0.109244i
$837$		0			0
$838$	33.7609	+	9.04621i	1.16625	+	0.312496i
$839$	−8.23770	−	30.7435i	−0.284397	−	1.06138i	−0.949279	−	0.314435i	$-0.898185\pi$
$839$	−8.23770	−	30.7435i	−0.284397	−	1.06138i	0.664882	−	0.746948i	$-0.268482\pi$
$840$		0			0
$841$	−4.88116			−0.168316
$842$	1.32342	+	2.29223i	0.0456080	+	0.0789954i
$843$		0			0
$844$	15.8925	−	9.17554i	0.547042	−	0.315835i
$845$	12.8803	−	3.63706i	0.443095	−	0.125119i
$846$		0			0
$847$	−0.199820	−	0.745737i	−0.00686588	−	0.0256238i
$848$			2.67501i			0.0918604i
$849$		0			0
$850$	−3.41081	−	12.7293i	−0.116990	−	0.436612i
$851$	−5.34676	−	5.34676i	−0.183284	−	0.183284i
$852$		0			0
$853$	−0.534054	+	1.99312i	−0.0182857	+	0.0682430i	−0.974466	−	0.224536i	$-0.927913\pi$
$853$	−0.534054	+	1.99312i	−0.0182857	+	0.0682430i	0.956180	+	0.292779i	$0.0945800\pi$
$854$	−1.74134	+	1.00536i	−0.0595874	+	0.0344028i
$855$		0			0
$856$	0.772969	−	0.207116i	0.0264195	−	0.00707910i
$857$	−7.56394	−	13.1011i	−0.258379	−	0.447526i	0.707429	−	0.706785i	$-0.249855\pi$
$857$	−7.56394	−	13.1011i	−0.258379	−	0.447526i	−0.965808	+	0.259259i	$0.916522\pi$
$858$		0			0
$859$	−15.4894	+	26.8284i	−0.528492	+	0.915375i	0.470956	+	0.882156i	$0.343909\pi$
$859$	−15.4894	+	26.8284i	−0.528492	+	0.915375i	−0.999448	+	0.0332181i	$0.989424\pi$
$860$	0.729803	−	2.72366i	0.0248861	−	0.0928761i
$861$		0			0
$862$	12.7185	+	7.34305i	0.433195	+	0.250105i
$863$	14.4513	+	14.4513i	0.491927	+	0.491927i	0.908913	−	0.416986i	$-0.136914\pi$
$863$	14.4513	+	14.4513i	0.491927	+	0.491927i	−0.416986	+	0.908913i	$0.636914\pi$
$864$		0			0
$865$	2.82142	−	10.5297i	0.0959312	−	0.358020i
$866$	−14.8151	−	3.96968i	−0.503436	−	0.134895i
$867$		0			0
$868$	−1.74539	+	1.00770i	−0.0592425	+	0.0342037i
$869$	12.3906	+	3.32005i	0.420323	+	0.112625i
$870$		0			0
$871$	−13.7145	+	52.5912i	−0.464698	+	1.78198i
$872$			8.25788i			0.279647i
$873$		0			0
$874$	−0.738151	+	1.27851i	−0.0249683	+	0.0432464i
$875$	1.61590	−	2.79882i	0.0546274	−	0.0946175i
$876$		0			0
$877$	5.75998	−	5.75998i	0.194501	−	0.194501i	−0.603137	−	0.797638i	$-0.706083\pi$
$877$	5.75998	−	5.75998i	0.194501	−	0.194501i	0.797638	+	0.603137i	$0.206083\pi$
$878$	−7.67374	+	7.67374i	−0.258976	+	0.258976i
$879$		0			0
$880$	−1.87015	+	3.23920i	−0.0630428	+	0.109193i
$881$	7.84542	−	13.5887i	0.264319	−	0.457814i	−0.703066	−	0.711125i	$-0.748186\pi$
$881$	7.84542	−	13.5887i	0.264319	−	0.457814i	0.967385	+	0.253311i	$0.0815195\pi$
$882$		0			0
$883$			49.4553i			1.66430i	0.554549	+	0.832151i	$0.312891\pi$
$883$			49.4553i			1.66430i	−0.554549	+	0.832151i	$0.687109\pi$
$884$	−6.09965	−	10.4032i	−0.205153	−	0.349897i
$885$		0			0
$886$	−32.1996	−	8.62787i	−1.08177	−	0.289859i
$887$	22.9994	−	13.2787i	0.772243	−	0.445855i	−0.0614312	−	0.998111i	$-0.519566\pi$
$887$	22.9994	−	13.2787i	0.772243	−	0.445855i	0.833674	+	0.552257i	$0.186233\pi$
$888$		0			0
$889$	−6.36938	−	1.70667i	−0.213622	−	0.0572399i
$890$	2.76450	−	10.3172i	0.0926661	−	0.345835i
$891$		0			0
$892$	17.9280	+	17.9280i	0.600275	+	0.600275i
$893$	7.36513	+	4.25226i	0.246465	+	0.142296i
$894$		0			0
$895$	−6.66673	+	24.8806i	−0.222844	+	0.831666i
$896$	0.175564	−	0.304085i	0.00586516	−	0.0101588i
$897$		0			0
$898$	9.13180	+	15.8167i	0.304732	+	0.527811i
$899$	−32.2717	+	8.64716i	−1.07632	+	0.288399i
$900$		0			0
$901$	7.74846	−	4.47357i	0.258139	−	0.149036i
$902$	−8.78954	+	32.8030i	−0.292660	+	1.09222i
$903$		0			0
$904$	−9.54047	−	9.54047i	−0.317311	−	0.317311i
$905$	−6.23188	−	23.2577i	−0.207155	−	0.773112i
$906$		0			0
$907$			9.77194i			0.324472i	0.986752	+	0.162236i	$0.0518706\pi$
$907$			9.77194i			0.324472i	−0.986752	+	0.162236i	$0.948129\pi$
$908$	−6.45111	−	24.0759i	−0.214088	−	0.798986i
$909$		0			0
$910$	0.328895	−	1.26122i	0.0109027	−	0.0418089i
$911$	35.0988	−	20.2643i	1.16288	−	0.671387i	0.210884	−	0.977511i	$-0.432366\pi$
$911$	35.0988	−	20.2643i	1.16288	−	0.671387i	0.951992	+	0.306124i	$0.0990323\pi$
$912$		0			0
$913$	15.6969	+	27.1878i	0.519490	+	0.899784i
$914$	6.37999			0.211031
$915$		0			0
$916$	−0.401688	−	1.49912i	−0.0132722	−	0.0495324i
$917$	1.14159	+	0.305889i	0.0376988	+	0.0101014i
$918$		0			0
$919$	5.97895	+	10.3558i	0.197227	+	0.341608i	0.947628	−	0.319375i	$-0.103473\pi$
$919$	5.97895	+	10.3558i	0.197227	+	0.341608i	−0.750401	+	0.660983i	$0.770140\pi$
$920$	−1.51395			−0.0499134
$921$		0			0
$922$	31.1868	+	18.0057i	1.02708	+	0.592987i
$923$	20.7572	+	5.41297i	0.683231	+	0.178170i
$924$		0			0
$925$	−14.3259	+	14.3259i	−0.471033	+	0.471033i
$926$	19.4427	+	11.2253i	0.638927	+	0.368885i
$927$		0			0
$928$	4.11589	−	4.11589i	0.135111	−	0.135111i
$929$	−17.9546	+	4.81092i	−0.589071	+	0.157841i	−0.541028	−	0.841004i	$-0.681965\pi$
$929$	−17.9546	+	4.81092i	−0.589071	+	0.157841i	−0.0480422	+	0.998845i	$0.515298\pi$
$930$		0			0
$931$	6.66851	−	1.78682i	0.218551	−	0.0585607i
$932$		−	9.96467i		−	0.326403i
$933$		0			0
$934$	−9.89950	−	9.89950i	−0.323921	−	0.323921i
$935$	12.5102			0.409128
$936$		0			0
$937$	−28.4270			−0.928669			−0.464335	−	0.885660i	$-0.653706\pi$
$937$	−28.4270			−0.928669			−0.464335	+	0.885660i	$0.653706\pi$
$938$	3.74263	+	3.74263i	0.122201	+	0.122201i
$939$		0			0
$940$			8.72139i			0.284460i
$941$	−9.21859	+	2.47011i	−0.300518	+	0.0805234i	−0.405927	−	0.913905i	$-0.633051\pi$
$941$	−9.21859	+	2.47011i	−0.300518	+	0.0805234i	0.105410	+	0.994429i	$0.466385\pi$
$942$		0			0
$943$	−13.2776	+	3.55771i	−0.432377	+	0.115855i
$944$	−3.42622	+	3.42622i	−0.111514	+	0.111514i
$945$		0			0
$946$	−8.61721	−	4.97515i	−0.280170	−	0.161756i
$947$	−14.2847	+	14.2847i	−0.464189	+	0.464189i	−0.900026	−	0.435837i	$-0.856453\pi$
$947$	−14.2847	+	14.2847i	−0.464189	+	0.464189i	0.435837	+	0.900026i	$0.356453\pi$
$948$		0			0
$949$	−8.85171	+	8.97121i	−0.287339	+	0.291218i
$950$	3.42561	+	1.97778i	0.111141	+	0.0641675i
$951$		0			0
$952$	−1.17442			−0.0380631
$953$	28.6270	+	49.5834i	0.927319	+	1.60616i	0.787788	+	0.615947i	$0.211226\pi$
$953$	28.6270	+	49.5834i	0.927319	+	1.60616i	0.139532	+	0.990218i	$0.455440\pi$
$954$		0			0
$955$	12.2437	+	3.28069i	0.396197	+	0.106161i
$956$	0.0186887	+	0.0697473i	0.000604437	+	0.00225579i
$957$		0			0
$958$	26.6206			0.860073
$959$	0.683538	+	1.18392i	0.0220726	+	0.0382309i
$960$		0			0
$961$	−1.68490	+	0.972775i	−0.0543515	+	0.0313798i
$962$	−9.16206	+	16.1178i	−0.295397	+	0.519658i
$963$		0			0
$964$	−4.84236	−	18.0719i	−0.155962	−	0.582058i
$965$		−	13.3222i		−	0.428855i
$966$		0			0
$967$	9.89640	+	36.9339i	0.318247	+	1.18771i	0.920929	+	0.389732i	$0.127432\pi$
$967$	9.89640	+	36.9339i	0.318247	+	1.18771i	−0.602682	+	0.797982i	$0.705901\pi$
$968$	1.55476	+	1.55476i	0.0499718	+	0.0499718i
$969$		0			0
$970$	−3.93570	+	14.6882i	−0.126368	+	0.471611i
$971$	−0.712957	+	0.411626i	−0.0228799	+	0.0132097i	−0.511396	−	0.859345i	$-0.670872\pi$
$971$	−0.712957	+	0.411626i	−0.0228799	+	0.0132097i	0.488516	+	0.872555i	$0.337538\pi$
$972$		0			0
$973$	0.187384	−	0.0502094i	0.00600726	−	0.00160964i
$974$	−7.63694	−	13.2276i	−0.244703	−	0.423839i
$975$		0			0
$976$	2.86325	−	4.95929i	0.0916503	−	0.158743i
$977$	0.814302	−	3.03902i	0.0260518	−	0.0972268i	−0.951676	−	0.307104i	$-0.900640\pi$
$977$	0.814302	−	3.03902i	0.0260518	−	0.0972268i	0.977728	+	0.209878i	$0.0673066\pi$
$978$		0			0
$979$	−32.6420	−	18.8459i	−1.04324	−	0.602317i
$980$	5.00617	+	5.00617i	0.159916	+	0.159916i
$981$		0			0
$982$	−0.484414	+	1.80786i	−0.0154583	+	0.0576911i
$983$	−50.1857	−	13.4472i	−1.60068	−	0.428900i	−0.655429	−	0.755256i	$-0.727512\pi$
$983$	−50.1857	−	13.4472i	−1.60068	−	0.428900i	−0.945247	+	0.326357i	$0.894179\pi$
$984$		0			0
$985$	−19.0492	+	10.9981i	−0.606959	+	0.350428i
$986$	−18.8053	−	5.03888i	−0.598884	−	0.160471i
$987$		0			0
$988$	3.50259	+	0.913390i	0.111432	+	0.0290588i
$989$		−	4.02754i		−	0.128068i
$990$		0			0
$991$	−20.4564	+	35.4315i	−0.649818	+	1.12552i	0.333348	+	0.942804i	$0.391822\pi$
$991$	−20.4564	+	35.4315i	−0.649818	+	1.12552i	−0.983166	+	0.182714i	$0.941512\pi$
$992$	2.86991	−	4.97083i	0.0911198	−	0.157824i
$993$		0			0
$994$	1.47718	−	1.47718i	0.0468532	−	0.0468532i
$995$	−16.1713	+	16.1713i	−0.512666	+	0.512666i
$996$		0			0
$997$	−15.4647	+	26.7856i	−0.489771	+	0.848308i	−0.999931	−	0.0117714i	$-0.996253\pi$
$997$	−15.4647	+	26.7856i	−0.489771	+	0.848308i	0.510160	+	0.860080i	$0.329586\pi$
$998$	5.66579	−	9.81344i	0.179347	−	0.310639i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.71.10		56
3.2	odd	2		234.2.y.a.149.5	yes	56
9.2	odd	6		702.2.bc.a.305.3		56
9.7	even	3		234.2.z.a.227.12	yes	56
13.11	odd	12		702.2.bc.a.557.3		56
39.11	even	12		234.2.z.a.167.12	yes	56
117.11	even	12	inner	702.2.bb.a.89.10		56
117.115	odd	12		234.2.y.a.11.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.5	✓	56	117.115	odd	12
234.2.y.a.149.5	yes	56	3.2	odd	2
234.2.z.a.167.12	yes	56	39.11	even	12
234.2.z.a.227.12	yes	56	9.7	even	3
702.2.bb.a.71.10		56	1.1	even	1	trivial
702.2.bb.a.89.10		56	117.11	even	12	inner
702.2.bc.a.305.3		56	9.2	odd	6
702.2.bc.a.557.3		56	13.11	odd	12

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.994452 + 0.266463i) q^{5} +(0.339163 - 0.0908784i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.891601 - 0.514766i) q^{10} +(-2.56893 + 2.56893i) q^{11} +(0.0241746 + 3.60547i) q^{13} +(0.304085 + 0.175564i) q^{14} -1.00000 q^{16} +(1.67236 + 2.89660i) q^{17} +(-0.969723 - 0.259837i) q^{19} +(-0.266463 - 0.994452i) q^{20} -3.63301 q^{22} +(-0.735260 - 1.27351i) q^{23} +(-3.41219 + 1.97003i) q^{25} +(-2.53236 + 2.56655i) q^{26} +(0.0908784 + 0.339163i) q^{28} +5.82075i q^{29} +(1.48558 + 5.54424i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.865675 + 3.23074i) q^{34} +(-0.313065 + 0.180748i) q^{35} +(4.96682 - 1.33085i) q^{37} +(-0.501966 - 0.869430i) q^{38} +(0.514766 - 0.891601i) q^{40} +(2.41936 - 9.02916i) q^{41} +(2.37192 + 1.36943i) q^{43} +(-2.56893 - 2.56893i) q^{44} +(0.380599 - 1.42041i) q^{46} +(-8.18256 - 2.19251i) q^{47} +(-5.95541 + 3.43835i) q^{49} +(-3.80581 - 1.01976i) q^{50} +(-3.60547 + 0.0241746i) q^{52} -2.67501i q^{53} +(1.87015 - 3.23920i) q^{55} +(-0.175564 + 0.304085i) q^{56} +(-4.11589 + 4.11589i) q^{58} +(3.42622 - 3.42622i) q^{59} +(-2.86325 + 4.95929i) q^{61} +(-2.86991 + 4.97083i) q^{62} -1.00000i q^{64} +(-0.984764 - 3.57903i) q^{65} +(14.5603 + 3.90143i) q^{67} +(-2.89660 + 1.67236i) q^{68} +(-0.349179 - 0.0935622i) q^{70} +(1.53985 - 5.74681i) q^{71} +(2.47165 + 2.47165i) q^{73} +(4.45313 + 2.57101i) q^{74} +(0.259837 - 0.969723i) q^{76} +(-0.637824 + 1.10474i) q^{77} +(-1.76544 - 3.05783i) q^{79} +(0.994452 - 0.266463i) q^{80} +(8.09532 - 4.67384i) q^{82} +(2.23652 - 8.34680i) q^{83} +(-2.43491 - 2.43491i) q^{85} +(0.708868 + 2.64553i) q^{86} -3.63301i q^{88} +(2.68520 + 10.0213i) q^{89} +(0.335858 + 1.22064i) q^{91} +(1.27351 - 0.735260i) q^{92} +(-4.23561 - 7.33629i) q^{94} +1.03358 q^{95} +(-3.82280 - 14.2669i) q^{97} +(-6.64239 - 1.77982i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 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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