LMFDB - Embedded newform 828.2.u.a.199.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,2,Mod(19,828)] 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("828.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 0, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.u (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [100,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 92)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			199.8
Character	$\chi$	$=$	828.199
Dual form			828.2.u.a.595.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19684 - 0.753380i) q^{2} +(0.864836 - 1.80335i) q^{4} +(-1.65610 + 1.43502i) q^{5} +(3.14077 + 2.01845i) q^{7} +(-0.323539 - 2.80986i) q^{8} +(-0.900968 + 2.96516i) q^{10} +(0.162776 + 1.13213i) q^{11} +(2.71951 - 1.74772i) q^{13} +(5.27965 + 0.0495605i) q^{14} +(-2.50412 - 3.11920i) q^{16} +(1.03533 + 3.52600i) q^{17} +(1.68979 + 0.496168i) q^{19} +(1.15559 + 4.22759i) q^{20} +(1.04775 + 1.23235i) q^{22} +(4.46833 - 1.74184i) q^{23} +(-0.0281822 + 0.196011i) q^{25} +(1.93811 - 4.14056i) q^{26} +(6.35622 - 3.91827i) q^{28} +(8.53724 - 2.50676i) q^{29} +(-9.07531 - 4.14456i) q^{31} +(-5.34696 - 1.84662i) q^{32} +(3.89553 + 3.44005i) q^{34} +(-8.09797 + 1.16431i) q^{35} +(4.67281 + 4.04902i) q^{37} +(2.39621 - 0.679225i) q^{38} +(4.56803 + 4.18914i) q^{40} +(0.800388 + 0.923697i) q^{41} +(-1.14894 - 2.51582i) q^{43} +(2.18241 + 0.685568i) q^{44} +(4.03559 - 5.45106i) q^{46} +2.26417i q^{47} +(2.88240 + 6.31158i) q^{49} +(0.113942 + 0.255825i) q^{50} +(-0.799821 - 6.41571i) q^{52} +(-0.401905 + 0.625377i) q^{53} +(-1.89421 - 1.64135i) q^{55} +(4.65541 - 9.47819i) q^{56} +(8.32913 - 9.43197i) q^{58} +(-5.02299 - 7.81592i) q^{59} +(-3.25979 - 1.48870i) q^{61} +(-13.9841 + 1.87681i) q^{62} +(-7.79064 + 1.81820i) q^{64} +(-1.99577 + 6.79697i) q^{65} +(1.45310 - 10.1065i) q^{67} +(7.25398 + 1.18236i) q^{68} +(-8.81478 + 7.49435i) q^{70} +(-9.06545 - 1.30341i) q^{71} +(4.26223 + 1.25150i) q^{73} +(8.64304 + 1.32560i) q^{74} +(2.35616 - 2.61818i) q^{76} +(-1.77392 + 3.88434i) q^{77} +(-13.6810 + 8.79222i) q^{79} +(8.62320 + 1.57225i) q^{80} +(1.65383 + 0.502518i) q^{82} +(-3.52806 + 4.07160i) q^{83} +(-6.77449 - 4.35370i) q^{85} +(-3.27047 - 2.14544i) q^{86} +(3.12848 - 0.823669i) q^{88} +(5.59347 - 2.55445i) q^{89} +12.0691 q^{91} +(0.723225 - 9.56436i) q^{92} +(1.70578 + 2.70984i) q^{94} +(-3.51049 + 1.60318i) q^{95} +(-6.04072 + 5.23431i) q^{97} +(8.20478 + 5.38238i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 7 q^{2} - 11 q^{4} + 22 q^{5} + 10 q^{8} - 11 q^{10} - 18 q^{13} + 11 q^{14} + 5 q^{16} + 22 q^{17} + 11 q^{20} - 16 q^{25} - 12 q^{26} - 11 q^{28} + 42 q^{29} + 27 q^{32} + 11 q^{34} - 22 q^{37}+ \cdots + 71 q^{98}+O(q^{100}) $ 100 * q + 7 * q^2 - 11 * q^4 + 22 * q^5 + 10 * q^8 - 11 * q^10 - 18 * q^13 + 11 * q^14 + 5 * q^16 + 22 * q^17 + 11 * q^20 - 16 * q^25 - 12 * q^26 - 11 * q^28 + 42 * q^29 + 27 * q^32 + 11 * q^34 - 22 * q^37 - 44 * q^38 + 77 * q^40 + 10 * q^41 - 66 * q^44 + 65 * q^46 - 8 * q^49 - 30 * q^50 + 96 * q^52 + 22 * q^53 - 44 * q^56 + 79 * q^58 - 22 * q^61 + 36 * q^62 + 10 * q^64 + 22 * q^65 + 34 * q^70 - 18 * q^73 + 22 * q^74 - 66 * q^76 - 122 * q^77 + 110 * q^80 - 122 * q^82 + 54 * q^85 + 121 * q^86 - 99 * q^88 - 22 * q^89 + 86 * q^92 - 61 * q^94 + 22 * q^97 + 71 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	1.19684	−	0.753380i	0.846291	−	0.532720i
$2$	1.19684	−	0.753380i	0.846291	−	0.532720i
$3$		0			0
$3$		0			0
$4$	0.864836	−	1.80335i	0.432418	−	0.901673i
$5$	−1.65610	+	1.43502i	−0.740633	+	0.641762i	−0.941174	−	0.337924i	$-0.890275\pi$
$5$	−1.65610	+	1.43502i	−0.740633	+	0.641762i	0.200541	+	0.979685i	$0.435730\pi$
$6$		0			0
$7$	3.14077	+	2.01845i	1.18710	+	0.762903i	0.976678	−	0.214707i	$-0.0688798\pi$
$7$	3.14077	+	2.01845i	1.18710	+	0.762903i	0.210422	+	0.977611i	$0.432516\pi$
$8$	−0.323539	−	2.80986i	−0.114388	−	0.993436i
$9$		0			0
$10$	−0.900968	+	2.96516i	−0.284911	+	0.937667i
$11$	0.162776	+	1.13213i	0.0490789	+	0.341352i	0.999535	+	0.0304926i	$0.00970759\pi$
$11$	0.162776	+	1.13213i	0.0490789	+	0.341352i	−0.950456	+	0.310859i	$0.899383\pi$
$12$		0			0
$13$	2.71951	−	1.74772i	0.754256	−	0.484731i	−0.106143	−	0.994351i	$-0.533850\pi$
$13$	2.71951	−	1.74772i	0.754256	−	0.484731i	0.860400	+	0.509620i	$0.170214\pi$
$14$	5.27965	+	0.0495605i	1.41105	+	0.0132456i
$15$		0			0
$16$	−2.50412	−	3.11920i	−0.626030	−	0.779799i
$17$	1.03533	+	3.52600i	0.251103	+	0.855180i	0.984501	+	0.175380i	$0.0561153\pi$
$17$	1.03533	+	3.52600i	0.251103	+	0.855180i	−0.733397	+	0.679800i	$0.762067\pi$
$18$		0			0
$19$	1.68979	+	0.496168i	0.387665	+	0.113829i	0.469756	−	0.882796i	$-0.344342\pi$
$19$	1.68979	+	0.496168i	0.387665	+	0.113829i	−0.0820914	+	0.996625i	$0.526160\pi$
$20$	1.15559	+	4.22759i	0.258397	+	0.945318i
$21$		0			0
$22$	1.04775	+	1.23235i	0.223380	+	0.262737i
$23$	4.46833	−	1.74184i	0.931711	−	0.363199i
$23$	4.46833	−	1.74184i	0.931711	−	0.363199i
$24$		0			0
$25$	−0.0281822	+	0.196011i	−0.00563644	+	0.0392023i
$26$	1.93811	−	4.14056i	0.380094	−	0.812031i
$27$		0			0
$28$	6.35622	−	3.91827i	1.20121	−	0.740484i
$29$	8.53724	−	2.50676i	1.58532	−	0.465493i	0.633910	−	0.773407i	$-0.281449\pi$
$29$	8.53724	−	2.50676i	1.58532	−	0.465493i	0.951414	+	0.307913i	$0.0996306\pi$
$30$		0			0
$31$	−9.07531	−	4.14456i	−1.62997	−	0.744384i	−0.630480	−	0.776205i	$-0.717142\pi$
$31$	−9.07531	−	4.14456i	−1.62997	−	0.744384i	−0.999494	+	0.0318213i	$0.989869\pi$
$32$	−5.34696	−	1.84662i	−0.945218	−	0.326439i
$33$		0			0
$34$	3.89553	+	3.44005i	0.668078	+	0.589963i
$35$	−8.09797	+	1.16431i	−1.36881	+	0.196805i
$36$		0			0
$37$	4.67281	+	4.04902i	0.768206	+	0.665654i	0.948079	−	0.318036i	$-0.103023\pi$
$37$	4.67281	+	4.04902i	0.768206	+	0.665654i	−0.179873	+	0.983690i	$0.557569\pi$
$38$	2.39621	−	0.679225i	0.388716	−	0.110185i
$39$		0			0
$40$	4.56803	+	4.18914i	0.722269	+	0.662361i
$41$	0.800388	+	0.923697i	0.125000	+	0.144257i	0.814800	−	0.579743i	$-0.196847\pi$
$41$	0.800388	+	0.923697i	0.125000	+	0.144257i	−0.689800	+	0.724000i	$0.742302\pi$
$42$		0			0
$43$	−1.14894	−	2.51582i	−0.175212	−	0.383660i	0.801569	−	0.597902i	$-0.203999\pi$
$43$	−1.14894	−	2.51582i	−0.175212	−	0.383660i	−0.976780	+	0.214243i	$0.931272\pi$
$44$	2.18241	+	0.685568i	0.329010	+	0.103353i
$45$		0			0
$46$	4.03559	−	5.45106i	0.595015	−	0.803714i
$47$			2.26417i			0.330263i	0.986272	+	0.165131i	$0.0528048\pi$
$47$			2.26417i			0.330263i	−0.986272	+	0.165131i	$0.947195\pi$
$48$		0			0
$49$	2.88240	+	6.31158i	0.411771	+	0.901654i
$50$	0.113942	+	0.255825i	0.0161138	+	0.0361792i
$51$		0			0
$52$	−0.799821	−	6.41571i	−0.110915	−	0.889699i
$53$	−0.401905	+	0.625377i	−0.0552060	+	0.0859021i	−0.867759	−	0.496985i	$-0.834441\pi$
$53$	−0.401905	+	0.625377i	−0.0552060	+	0.0859021i	0.812553	+	0.582887i	$0.198077\pi$
$54$		0			0
$55$	−1.89421	−	1.64135i	−0.255416	−	0.221319i
$56$	4.65541	−	9.47819i	0.622105	−	1.26658i
$57$		0			0
$58$	8.32913	−	9.43197i	1.09367	−	1.23848i
$59$	−5.02299	−	7.81592i	−0.653937	−	1.01755i	−0.996937	−	0.0782107i	$-0.975079\pi$
$59$	−5.02299	−	7.81592i	−0.653937	−	1.01755i	0.343000	−	0.939336i	$-0.388557\pi$
$60$		0			0
$61$	−3.25979	−	1.48870i	−0.417374	−	0.190608i	0.195648	−	0.980674i	$-0.437319\pi$
$61$	−3.25979	−	1.48870i	−0.417374	−	0.190608i	−0.613022	+	0.790066i	$0.710046\pi$
$62$	−13.9841	+	1.87681i	−1.77598	+	0.238355i
$63$		0			0
$64$	−7.79064	+	1.81820i	−0.973831	+	0.227275i
$65$	−1.99577	+	6.79697i	−0.247545	+	0.843060i
$66$		0			0
$67$	1.45310	−	10.1065i	0.177525	−	1.23471i	−0.684943	−	0.728597i	$-0.740173\pi$
$67$	1.45310	−	10.1065i	0.177525	−	1.23471i	0.862467	−	0.506113i	$-0.168918\pi$
$68$	7.25398	+	1.18236i	0.879674	+	0.143382i
$69$		0			0
$70$	−8.81478	+	7.49435i	−1.05357	+	0.895746i
$71$	−9.06545	−	1.30341i	−1.07587	−	0.154687i	−0.418472	−	0.908230i	$-0.637434\pi$
$71$	−9.06545	−	1.30341i	−1.07587	−	0.154687i	−0.657399	+	0.753543i	$0.728343\pi$
$72$		0			0
$73$	4.26223	+	1.25150i	0.498857	+	0.146478i	0.521475	−	0.853267i	$-0.325382\pi$
$73$	4.26223	+	1.25150i	0.498857	+	0.146478i	−0.0226182	+	0.999744i	$0.507200\pi$
$74$	8.64304	+	1.32560i	1.00473	+	0.154098i
$75$		0			0
$76$	2.35616	−	2.61818i	0.270270	−	0.300326i
$77$	−1.77392	+	3.88434i	−0.202157	+	0.442661i
$78$		0			0
$79$	−13.6810	+	8.79222i	−1.53923	+	0.989202i	−0.551296	+	0.834310i	$0.685867\pi$
$79$	−13.6810	+	8.79222i	−1.53923	+	0.989202i	−0.987931	+	0.154892i	$0.950497\pi$
$80$	8.62320	+	1.57225i	0.964103	+	0.175783i
$81$		0			0
$82$	1.65383	+	0.502518i	0.182635	+	0.0554938i
$83$	−3.52806	+	4.07160i	−0.387255	+	0.446916i	−0.915586	−	0.402123i	$-0.868273\pi$
$83$	−3.52806	+	4.07160i	−0.387255	+	0.446916i	0.528331	+	0.849038i	$0.322818\pi$
$84$		0			0
$85$	−6.77449	−	4.35370i	−0.734797	−	0.472225i
$86$	−3.27047	−	2.14544i	−0.352663	−	0.231349i
$87$		0			0
$88$	3.12848	−	0.823669i	0.333497	−	0.0878034i
$89$	5.59347	−	2.55445i	0.592907	−	0.270772i	−0.0962809	−	0.995354i	$-0.530695\pi$
$89$	5.59347	−	2.55445i	0.592907	−	0.270772i	0.689188	+	0.724583i	$0.257967\pi$
$90$		0			0
$91$	12.0691			1.26518
$92$	0.723225	−	9.56436i	0.0754014	−	0.997153i
$93$		0			0
$94$	1.70578	+	2.70984i	0.175938	+	0.279499i
$95$	−3.51049	+	1.60318i	−0.360168	+	0.164483i
$96$		0			0
$97$	−6.04072	+	5.23431i	−0.613342	+	0.531464i	−0.905193	−	0.425000i	$-0.860274\pi$
$97$	−6.04072	+	5.23431i	−0.613342	+	0.531464i	0.291852	+	0.956464i	$0.405729\pi$
$98$	8.20478	+	5.38238i	0.828808	+	0.543703i
$99$		0			0
$100$	0.329103	+	0.220340i	0.0329103	+	0.0220340i
$101$	−10.4416	+	12.0503i	−1.03898	+	1.19905i	−0.0593535	+	0.998237i	$0.518904\pi$
$101$	−10.4416	+	12.0503i	−1.03898	+	1.19905i	−0.979630	+	0.200813i	$0.935642\pi$
$102$		0			0
$103$	2.55830	+	17.7934i	0.252077	+	1.75323i	0.585701	+	0.810527i	$0.300819\pi$
$103$	2.55830	+	17.7934i	0.252077	+	1.75323i	−0.333624	+	0.942706i	$0.608272\pi$
$104$	−5.79073	−	7.07599i	−0.567828	−	0.693858i
$105$		0			0
$106$	−0.00986828	+	1.05126i	−0.000958492	+	0.102108i
$107$	3.56732	−	7.81135i	0.344866	−	0.755151i	−0.655134	−	0.755513i	$-0.727388\pi$
$107$	3.56732	−	7.81135i	0.344866	−	0.755151i	1.00000		0.000361420i	$0.000115044\pi$
$108$		0			0
$109$	−2.90209	−	9.88360i	−0.277970	−	0.946677i	−0.973597	−	0.228274i	$-0.926692\pi$
$109$	−2.90209	−	9.88360i	−0.277970	−	0.946677i	0.695627	−	0.718403i	$-0.255127\pi$
$110$	−3.50362	−	0.537359i	−0.334057	−	0.0512352i
$111$		0			0
$112$	−1.56892	−	14.8511i	−0.148249	−	1.40330i
$113$	−10.1971	−	1.46612i	−0.959260	−	0.137921i	−0.355139	−	0.934813i	$-0.615567\pi$
$113$	−10.1971	−	1.46612i	−0.959260	−	0.137921i	−0.604121	+	0.796893i	$0.706476\pi$
$114$		0			0
$115$	−4.90044	+	9.29683i	−0.456968	+	0.866934i
$116$	2.86275	−	17.5635i	0.265800	−	1.63073i
$117$		0			0
$118$	−11.9001	−	5.57016i	−1.09549	−	0.512775i
$119$	−3.86533	+	13.1641i	−0.354334	+	1.20675i
$120$		0			0
$121$	9.29919	−	2.73049i	0.845381	−	0.248226i
$122$	−5.02300	+	0.674137i	−0.454761	+	0.0610335i
$123$		0			0
$124$	−15.3227	+	12.7816i	−1.37602	+	1.14782i
$125$	−6.15825	−	9.58242i	−0.550811	−	0.857078i
$126$		0			0
$127$	−2.28895	+	0.329102i	−0.203112	+	0.0292031i	−0.243120	−	0.969996i	$-0.578171\pi$
$127$	−2.28895	+	0.329102i	−0.203112	+	0.0292031i	0.0400079	+	0.999199i	$0.487262\pi$
$128$	−7.95433	+	8.04541i	−0.703070	+	0.711120i
$129$		0			0
$130$	2.73209	+	9.63844i	0.239620	+	0.845347i
$131$	−6.69494	+	10.4175i	−0.584940	+	0.910184i	0.415060	+	0.909794i	$0.363761\pi$
$131$	−6.69494	+	10.4175i	−0.584940	+	0.910184i	−1.00000		0.000390307i	$0.999876\pi$
$132$		0			0
$133$	4.30576	+	4.96912i	0.373357	+	0.430877i
$134$	−5.87494	−	13.1906i	−0.507518	−	1.13950i
$135$		0			0
$136$	9.57260	−	4.04992i	0.820843	−	0.347278i
$137$			9.53713i			0.814812i	0.913247	+	0.407406i	$0.133567\pi$
$137$			9.53713i			0.814812i	−0.913247	+	0.407406i	$0.866433\pi$
$138$		0			0
$139$		−	14.8214i		−	1.25713i	−0.777755	−	0.628567i	$-0.783642\pi$
$139$		−	14.8214i		−	1.25713i	0.777755	−	0.628567i	$-0.216358\pi$
$140$	−4.90376	+	15.6104i	−0.414443	+	1.31932i
$141$		0			0
$142$	−11.8318	+	5.26976i	−0.992905	+	0.442228i
$143$	2.42133	+	2.79436i	0.202482	+	0.233676i
$144$		0			0
$145$	−10.5413	+	16.4026i	−0.875407	+	1.36216i
$146$	6.04406	−	1.71324i	0.500210	−	0.141789i
$147$		0			0
$148$	11.3430	−	4.92497i	0.932389	−	0.404830i
$149$	11.6451	−	1.67432i	0.954006	−	0.137165i	0.352304	−	0.935886i	$-0.385398\pi$
$149$	11.6451	−	1.67432i	0.954006	−	0.137165i	0.601703	+	0.798720i	$0.294489\pi$
$150$		0			0
$151$	−0.682332	−	1.06173i	−0.0555274	−	0.0864023i	0.812380	−	0.583129i	$-0.198172\pi$
$151$	−0.682332	−	1.06173i	−0.0555274	−	0.0864023i	−0.867907	+	0.496726i	$0.834535\pi$
$152$	0.847449	−	4.90861i	0.0687372	−	0.398141i
$153$		0			0
$154$	0.803294	+	5.98535i	0.0647313	+	0.482313i
$155$	20.9772	−	6.15946i	1.68493	−	0.494740i
$156$		0			0
$157$	1.44386	−	4.91732i	0.115232	−	0.392445i	−0.881598	−	0.472001i	$-0.843532\pi$
$157$	1.44386	−	4.91732i	0.115232	−	0.392445i	0.996830	+	0.0795558i	$0.0253502\pi$
$158$	−9.74998	+	20.8298i	−0.775667	+	1.65713i
$159$		0			0
$160$	11.5051	−	4.61482i	0.909555	−	0.364834i
$161$	17.5498	+	3.54838i	1.38312	+	0.279651i
$162$		0			0
$163$	9.67641	+	1.39126i	0.757915	+	0.108972i	0.510429	−	0.859920i	$-0.329487\pi$
$163$	9.67641	+	1.39126i	0.757915	+	0.108972i	0.247486	+	0.968892i	$0.420396\pi$
$164$	2.35795	−	0.644531i	0.184125	−	0.0503294i
$165$		0			0
$166$	−1.15505	+	7.53101i	−0.0896491	+	0.584519i
$167$	−1.03844	−	3.53662i	−0.0803572	−	0.273672i	0.909507	−	0.415689i	$-0.136459\pi$
$167$	−1.03844	−	3.53662i	−0.0803572	−	0.273672i	−0.989864	+	0.142017i	$0.954641\pi$
$168$		0			0
$169$	−1.05920	+	2.31932i	−0.0814766	+	0.178409i
$170$	−11.3880	−	0.106900i	−0.873416	−	0.00819883i
$171$		0			0
$172$	−5.53055	−	0.103841i	−0.421700	−	0.00791776i
$173$	−0.724466	−	5.03877i	−0.0550801	−	0.383091i	−0.998651	−	0.0519206i	$-0.983466\pi$
$173$	−0.724466	−	5.03877i	−0.0550801	−	0.383091i	0.943571	−	0.331170i	$-0.107443\pi$
$174$		0			0
$175$	−0.484153	+	0.558743i	−0.0365986	+	0.0422370i
$176$	3.12374	−	3.34273i	0.235461	−	0.251968i
$177$		0			0
$178$	4.77000	−	7.27128i	0.357526	−	0.545005i
$179$	1.34857	−	1.16854i	0.100797	−	0.0873407i	−0.603005	−	0.797738i	$-0.706030\pi$
$179$	1.34857	−	1.16854i	0.100797	−	0.0873407i	0.703801	+	0.710397i	$0.251485\pi$
$180$		0			0
$181$	−19.2255	+	8.77998i	−1.42902	+	0.652611i	−0.971598	−	0.236639i	$-0.923954\pi$
$181$	−19.2255	+	8.77998i	−1.42902	+	0.652611i	−0.457421	+	0.889250i	$0.651227\pi$
$182$	14.4447	−	9.09259i	1.07071	−	0.673988i
$183$		0			0
$184$	−6.34002	−	11.9918i	−0.467392	−	0.884050i
$185$	−13.5491			−0.996150
$186$		0			0
$187$	−3.82338	+	1.74608i	−0.279593	+	0.127686i
$188$	4.08308	+	1.95813i	0.297789	+	0.142812i
$189$		0			0
$190$	−2.99367	+	4.56348i	−0.217184	+	0.331070i
$191$	−17.7180	−	11.3867i	−1.28203	−	0.823911i	−0.290893	−	0.956756i	$-0.593952\pi$
$191$	−17.7180	−	11.3867i	−1.28203	−	0.823911i	−0.991137	+	0.132845i	$0.957589\pi$
$192$		0			0
$193$	0.606229	−	0.699625i	0.0436373	−	0.0503601i	−0.733511	−	0.679677i	$-0.762120\pi$
$193$	0.606229	−	0.699625i	0.0436373	−	0.0503601i	0.777149	+	0.629317i	$0.216665\pi$
$194$	−3.28632	+	10.8156i	−0.235944	+	0.776513i
$195$		0			0
$196$	13.8748	+	0.260510i	0.991054	+	0.0186078i
$197$	7.17132	−	4.60873i	0.510936	−	0.328358i	−0.259642	−	0.965705i	$-0.583604\pi$
$197$	7.17132	−	4.60873i	0.510936	−	0.328358i	0.770577	+	0.637347i	$0.219968\pi$
$198$		0			0
$199$	4.93644	−	10.8093i	0.349935	−	0.766250i	−0.650045	−	0.759896i	$-0.725250\pi$
$199$	4.93644	−	10.8093i	0.349935	−	0.766250i	0.999980	−	0.00635466i	$-0.00202276\pi$
$200$	0.559883	+	0.0157707i	0.0395897	+	0.00111516i
$201$		0			0
$202$	−3.41848	+	22.2888i	−0.240524	+	1.56823i
$203$	31.8733	+	9.35884i	2.23707	+	0.656862i
$204$		0			0
$205$	−2.65105	−	0.381164i	−0.185158	−	0.0266216i
$206$	16.4671	+	19.3684i	1.14731	+	1.34946i
$207$		0			0
$208$	−12.2615	−	4.10618i	−0.850180	−	0.284713i
$209$	−0.286671	+	1.99384i	−0.0198294	+	0.137917i
$210$		0			0
$211$	5.81597	−	19.8074i	0.400388	−	1.36360i	−0.474919	−	0.880030i	$-0.657523\pi$
$211$	5.81597	−	19.8074i	0.400388	−	1.36360i	0.875307	−	0.483567i	$-0.160659\pi$
$212$	0.780189	+	1.26562i	0.0535836	+	0.0869234i
$213$		0			0
$214$	−1.61541	−	12.0365i	−0.110427	−	0.822795i
$215$	5.51303	+	2.51772i	0.375985	+	0.171707i
$216$		0			0
$217$	−20.1379	−	31.3352i	−1.36705	−	2.12717i
$218$	−10.9194	−	9.64268i	−0.739558	−	0.653085i
$219$		0			0
$220$	−4.59810	+	1.99643i	−0.310004	+	0.134599i
$221$	8.97805	+	7.77952i	0.603929	+	0.523307i
$222$		0			0
$223$	−7.55708	+	11.7591i	−0.506060	+	0.787444i	−0.996461	−	0.0840523i	$-0.973214\pi$
$223$	−7.55708	+	11.7591i	−0.506060	+	0.787444i	0.490402	+	0.871497i	$0.336850\pi$
$224$	−13.0663	−	16.5924i	−0.873028	−	1.10863i
$225$		0			0
$226$	−13.3088	+	5.92757i	−0.885287	+	0.394296i
$227$	−11.7401	−	25.7073i	−0.779220	−	1.70625i	−0.705212	−	0.708996i	$-0.749148\pi$
$227$	−11.7401	−	25.7073i	−0.779220	−	1.70625i	−0.0740076	−	0.997258i	$-0.523579\pi$
$228$		0			0
$229$			10.5591i			0.697763i	0.937167	+	0.348882i	$0.113438\pi$
$229$			10.5591i			0.697763i	−0.937167	+	0.348882i	$0.886562\pi$
$230$	1.13903	+	14.8187i	0.0751052	+	0.977115i
$231$		0			0
$232$	−9.80577	−	23.1774i	−0.643781	−	1.52167i
$233$	−3.77738	−	8.27132i	−0.247465	−	0.541872i	0.744613	−	0.667496i	$-0.232634\pi$
$233$	−3.77738	−	8.27132i	−0.247465	−	0.541872i	−0.992078	+	0.125624i	$0.959907\pi$
$234$		0			0
$235$	−3.24913	−	3.74970i	−0.211950	−	0.244603i
$236$	−18.4389	+	2.29870i	−1.20027	+	0.149633i
$237$		0			0
$238$	5.29141	+	18.6674i	0.342991	+	1.21002i
$239$	3.93558	+	3.41020i	0.254572	+	0.220588i	0.772792	−	0.634660i	$-0.218860\pi$
$239$	3.93558	+	3.41020i	0.254572	+	0.220588i	−0.518220	+	0.855247i	$0.673405\pi$
$240$		0			0
$241$	14.9668	−	2.15190i	0.964097	−	0.138616i	0.357751	−	0.933817i	$-0.383544\pi$
$241$	14.9668	−	2.15190i	0.964097	−	0.138616i	0.606346	+	0.795201i	$0.292635\pi$
$242$	9.07251	−	10.2738i	0.583203	−	0.660423i
$243$		0			0
$244$	−5.50382	+	4.59106i	−0.352346	+	0.293912i
$245$	−13.8308	−	6.31632i	−0.883618	−	0.403535i
$246$		0			0
$247$	5.46257	−	1.60396i	0.347575	−	0.102057i
$248$	−8.70941	+	26.8413i	−0.553048	+	1.70442i
$249$		0			0
$250$	−14.5896	−	6.82909i	−0.922729	−	0.431910i
$251$	−0.300202	+	2.08795i	−0.0189486	+	0.131790i	−0.997100	−	0.0761039i	$-0.975752\pi$
$251$	−0.300202	+	2.08795i	−0.0189486	+	0.131790i	0.978151	+	0.207894i	$0.0666610\pi$
$252$		0			0
$253$	2.69934	+	4.77522i	0.169706	+	0.300216i
$254$	−2.49156	+	2.11833i	−0.156335	+	0.132916i
$255$		0			0
$256$	−3.45878	+	15.6217i	−0.216174	+	0.976355i
$257$	−17.6327	−	5.17743i	−1.09990	−	0.322959i	−0.319087	−	0.947725i	$-0.603376\pi$
$257$	−17.6327	−	5.17743i	−1.09990	−	0.322959i	−0.780812	+	0.624766i	$0.785194\pi$
$258$		0			0
$259$	6.50350	+	22.1489i	0.404108	+	1.37627i
$260$	10.5313	+	9.47733i	0.653122	+	0.587759i
$261$		0			0
$262$	−0.164386	+	17.5119i	−0.0101558	+	1.08189i
$263$	−8.46337	+	5.43908i	−0.521874	+	0.335388i	−0.774913	−	0.632068i	$-0.782206\pi$
$263$	−8.46337	+	5.43908i	−0.521874	+	0.335388i	0.253039	+	0.967456i	$0.418570\pi$
$264$		0			0
$265$	−0.231833	−	1.61243i	−0.0142414	−	0.0990510i
$266$	8.89693	+	2.70334i	0.545506	+	0.165753i
$267$		0			0
$268$	−16.9689	−	11.3609i	−1.03654	−	0.693980i
$269$	−17.0822	−	10.9781i	−1.04152	−	0.669346i	−0.0961596	−	0.995366i	$-0.530656\pi$
$269$	−17.0822	−	10.9781i	−1.04152	−	0.669346i	−0.945363	+	0.326020i	$0.894292\pi$
$270$		0			0
$271$	−4.88932	+	4.23662i	−0.297005	+	0.257356i	−0.790596	−	0.612338i	$-0.790229\pi$
$271$	−4.88932	+	4.23662i	−0.297005	+	0.257356i	0.493591	+	0.869694i	$0.335684\pi$
$272$	8.40570	−	12.0589i	0.509670	−	0.731178i
$273$		0			0
$274$	7.18509	+	11.4144i	0.434067	+	0.689568i
$275$	−0.226499			−0.0136584
$276$		0			0
$277$	20.6386			1.24005			0.620026	−	0.784582i	$-0.287122\pi$
$277$	20.6386			1.24005			0.620026	+	0.784582i	$0.287122\pi$
$278$	−11.1661	−	17.7388i	−0.669701	−	1.06390i
$279$		0			0
$280$	5.89157	+	22.3775i	0.352089	+	1.33731i
$281$	13.0739	−	11.3286i	0.779923	−	0.675807i	−0.170987	−	0.985273i	$-0.554696\pi$
$281$	13.0739	−	11.3286i	0.779923	−	0.675807i	0.950911	+	0.309466i	$0.100150\pi$
$282$		0			0
$283$	−1.50653	−	0.968186i	−0.0895537	−	0.0575527i	0.495098	−	0.868837i	$-0.335132\pi$
$283$	−1.50653	−	0.968186i	−0.0895537	−	0.0575527i	−0.584651	+	0.811285i	$0.698769\pi$
$284$	−10.1906	+	15.2209i	−0.604703	+	0.903195i
$285$		0			0
$286$	5.00316	+	1.52021i	0.295843	+	0.0898922i
$287$	0.649399	+	4.51667i	0.0383328	+	0.266610i
$288$		0			0
$289$	2.94056	−	1.88978i	0.172974	−	0.111164i
$290$	−0.258828	+	27.5728i	−0.0151989	+	1.61913i
$291$		0			0
$292$	5.94303	−	6.60394i	0.347789	−	0.386466i
$293$	4.05277	+	13.8025i	0.236765	+	0.806349i	0.989059	+	0.147521i	$0.0471294\pi$
$293$	4.05277	+	13.8025i	0.236765	+	0.806349i	−0.752294	+	0.658828i	$0.771052\pi$
$294$		0			0
$295$	19.5346	+	5.73588i	1.13735	+	0.333956i
$296$	9.86534	−	14.4400i	0.573411	−	0.839307i
$297$		0			0
$298$	12.6759	−	10.7771i	0.734296	−	0.624301i
$299$	9.10741	−	12.5464i	0.526695	−	0.725575i
$300$		0			0
$301$	1.46952	−	10.2207i	0.0847015	−	0.589112i
$302$	−1.61653	−	0.756661i	−0.0930206	−	0.0435409i
$303$		0			0
$304$	−2.68379	−	6.51326i	−0.153926	−	0.373561i
$305$	7.53487	−	2.21244i	0.431446	−	0.126684i
$306$		0			0
$307$	0.0421634	+	0.0192554i	0.00240639	+	0.00109896i	0.416618	−	0.909082i	$-0.363215\pi$
$307$	0.0421634	+	0.0192554i	0.00240639	+	0.00109896i	−0.414211	+	0.910181i	$0.635943\pi$
$308$	5.47066	+	6.55830i	0.311720	+	0.373694i
$309$		0			0
$310$	20.4659	−	23.1757i	1.16238	−	1.31629i
$311$	7.22360	−	1.03860i	0.409613	−	0.0588934i	0.0655712	−	0.997848i	$-0.479113\pi$
$311$	7.22360	−	1.03860i	0.409613	−	0.0588934i	0.344041	+	0.938954i	$0.388204\pi$
$312$		0			0
$313$	16.9083	+	14.6511i	0.955713	+	0.828130i	0.985195	−	0.171435i	$-0.0548405\pi$
$313$	16.9083	+	14.6511i	0.955713	+	0.828130i	−0.0294826	+	0.999565i	$0.509386\pi$
$314$	−1.97655	−	6.97300i	−0.111543	−	0.393509i
$315$		0			0
$316$	4.02363	+	32.2753i	0.226347	+	1.81563i
$317$	4.71950	+	5.44659i	0.265074	+	0.305911i	0.872646	−	0.488353i	$-0.162402\pi$
$317$	4.71950	+	5.44659i	0.265074	+	0.305911i	−0.607573	+	0.794264i	$0.707857\pi$
$318$		0			0
$319$	4.22765	+	9.25726i	0.236703	+	0.518307i
$320$	10.2930	−	14.1909i	0.575394	−	0.793294i
$321$		0			0
$322$	23.6776	−	8.97488i	1.31950	−	0.500150i
$323$			6.47190i			0.360106i
$324$		0			0
$325$	0.265932	+	0.582309i	0.0147512	+	0.0323007i
$326$	12.6292	−	5.62491i	0.699468	−	0.311535i
$327$		0			0
$328$	2.33650	−	2.54783i	0.129012	−	0.140680i
$329$	−4.57012	+	7.11124i	−0.251959	+	0.392055i
$330$		0			0
$331$	−15.8808	−	13.7608i	−0.872886	−	0.756360i	0.0981803	−	0.995169i	$-0.468698\pi$
$331$	−15.8808	−	13.7608i	−0.872886	−	0.756360i	−0.971067	+	0.238808i	$0.923243\pi$
$332$	4.29131	+	9.88357i	0.235516	+	0.542432i
$333$		0			0
$334$	−3.90727	−	3.45041i	−0.213796	−	0.188798i
$335$	12.0966	+	18.8227i	0.660909	+	1.02839i
$336$		0			0
$337$	−21.0240	−	9.60132i	−1.14525	−	0.523017i	−0.249850	−	0.968284i	$-0.580381\pi$
$337$	−21.0240	−	9.60132i	−1.14525	−	0.523017i	−0.895398	+	0.445267i	$0.853109\pi$
$338$	0.479643	+	3.57382i	0.0260891	+	0.194390i
$339$		0			0
$340$	−13.7101	+	8.45152i	−0.743532	+	0.458348i
$341$	3.21495	−	10.9491i	0.174099	−	0.592928i
$342$		0			0
$343$	0.0326215	−	0.226887i	0.00176139	−	0.0122508i
$344$	−6.69739	+	4.04233i	−0.361099	+	0.217948i
$345$		0			0
$346$	−4.66318	−	5.48479i	−0.250694	−	0.294864i
$347$	13.8830	+	1.99607i	0.745277	+	0.107155i	0.504483	−	0.863422i	$-0.331683\pi$
$347$	13.8830	+	1.99607i	0.745277	+	0.107155i	0.240794	+	0.970576i	$0.422592\pi$
$348$		0			0
$349$	−5.34964	−	1.57080i	−0.286360	−	0.0840828i	0.135398	−	0.990791i	$-0.456769\pi$
$349$	−5.34964	−	1.57080i	−0.286360	−	0.0840828i	−0.421758	+	0.906708i	$0.638587\pi$
$350$	−0.158507	+	1.03348i	−0.00847253	+	0.0552416i
$351$		0			0
$352$	1.22026	−	6.35407i	0.0650400	−	0.338673i
$353$	0.464795	−	1.01776i	0.0247385	−	0.0541699i	−0.896859	−	0.442316i	$-0.854157\pi$
$353$	0.464795	−	1.01776i	0.0247385	−	0.0541699i	0.921598	+	0.388146i	$0.126884\pi$
$354$		0			0
$355$	16.8838	−	10.8505i	0.896097	−	0.575887i
$356$	0.230870	−	12.2962i	0.0122361	−	0.651695i
$357$		0			0
$358$	0.733658	−	2.41453i	0.0387750	−	0.127612i
$359$	−10.1453	+	11.7083i	−0.535451	+	0.617943i	−0.957431	−	0.288662i	$-0.906790\pi$
$359$	−10.1453	+	11.7083i	−0.535451	+	0.617943i	0.421980	+	0.906605i	$0.361335\pi$
$360$		0			0
$361$	−13.3746	−	8.59533i	−0.703926	−	0.452386i
$362$	−16.3951	+	24.9923i	−0.861707	+	1.31357i
$363$		0			0
$364$	10.4378	−	21.7647i	0.547087	−	1.14078i
$365$	−8.85464	+	4.04378i	−0.463473	+	0.211661i
$366$		0			0
$367$	−0.817746			−0.0426860			−0.0213430	−	0.999772i	$-0.506794\pi$
$367$	−0.817746			−0.0426860			−0.0213430	+	0.999772i	$0.506794\pi$
$368$	−16.6224	−	9.57582i	−0.866502	−	0.499174i
$369$		0			0
$370$	−16.2161	+	10.2076i	−0.843033	+	0.530669i
$371$	−2.52459	+	1.15294i	−0.131070	+	0.0598577i
$372$		0			0
$373$	6.00992	−	5.20762i	0.311182	−	0.269641i	−0.485241	−	0.874380i	$-0.661268\pi$
$373$	6.00992	−	5.20762i	0.311182	−	0.269641i	0.796423	+	0.604740i	$0.206723\pi$
$374$	−3.26050	+	4.97023i	−0.168596	+	0.257004i
$375$		0			0
$376$	6.36200	−	0.732547i	0.328095	−	0.0377782i
$377$	18.8360	−	21.7379i	0.970102	−	1.11956i
$378$		0			0
$379$	−2.85196	−	19.8358i	−0.146495	−	1.01890i	−0.921899	−	0.387431i	$-0.873362\pi$
$379$	−2.85196	−	19.8358i	−0.146495	−	1.01890i	0.775403	−	0.631467i	$-0.217547\pi$
$380$	−0.144895	+	7.71711i	−0.00743296	+	0.395880i
$381$		0			0
$382$	−29.7841	−	0.279585i	−1.52388	−	0.0143048i
$383$	0.939261	−	2.05669i	0.0479940	−	0.105092i	−0.884116	−	0.467267i	$-0.845239\pi$
$383$	0.939261	−	2.05669i	0.0479940	−	0.105092i	0.932110	+	0.362175i	$0.117966\pi$
$384$		0			0
$385$	−2.63632	−	8.97848i	−0.134359	−	0.457586i
$386$	0.198473	−	1.29406i	0.0101020	−	0.0658658i
$387$		0			0
$388$	4.21505	+	15.4203i	0.213987	+	0.782848i
$389$	8.33260	+	1.19805i	0.422480	+	0.0607434i	0.350276	−	0.936646i	$-0.386088\pi$
$389$	8.33260	+	1.19805i	0.422480	+	0.0607434i	0.0722037	+	0.997390i	$0.476997\pi$
$390$		0			0
$391$	10.7679	+	13.9519i	0.544557	+	0.705580i
$392$	16.8021	−	10.1412i	0.848633	−	0.512207i
$393$		0			0
$394$	5.11078	−	10.9186i	0.257477	−	0.550073i
$395$	10.0401	−	34.1933i	0.505170	−	1.72045i
$396$		0			0
$397$	−3.23260	+	0.949177i	−0.162239	+	0.0476378i	−0.361844	−	0.932239i	$-0.617853\pi$
$397$	−3.23260	+	0.949177i	−0.162239	+	0.0476378i	0.199604	+	0.979877i	$0.436034\pi$
$398$	−2.23540	−	16.6560i	−0.112050	−	0.834888i
$399$		0			0
$400$	0.681970	−	0.402930i	0.0340985	−	0.0201465i
$401$	−8.46186	−	13.1669i	−0.422565	−	0.657525i	0.563071	−	0.826409i	$-0.309620\pi$
$401$	−8.46186	−	13.1669i	−0.422565	−	0.657525i	−0.985636	+	0.168884i	$0.945984\pi$
$402$		0			0
$403$	−31.9239	+	4.58997i	−1.59024	+	0.228643i
$404$	12.7006	+	29.2515i	0.631877	+	1.45531i
$405$		0			0
$406$	45.1979	−	12.8117i	2.24313	−	0.635834i
$407$	−3.82341	+	5.94934i	−0.189519	+	0.294898i
$408$		0			0
$409$	13.5096	+	15.5909i	0.668008	+	0.770923i	0.984063	−	0.177818i	$-0.0569039\pi$
$409$	13.5096	+	15.5909i	0.668008	+	0.770923i	−0.316055	+	0.948741i	$0.602358\pi$
$410$	−3.46004	+	1.54106i	−0.170879	+	0.0761075i
$411$		0			0
$412$	34.3001	+	10.7748i	1.68985	+	0.530838i
$413$		−	34.6867i		−	1.70682i
$414$		0			0
$415$		−	11.8058i		−	0.579526i
$416$	−17.7685	+	4.32312i	−0.871172	+	0.211958i
$417$		0			0
$418$	1.15902	+	2.60227i	0.0566895	+	0.127281i
$419$	−6.55475	−	7.56458i	−0.320220	−	0.369554i	0.572703	−	0.819763i	$-0.305895\pi$
$419$	−6.55475	−	7.56458i	−0.320220	−	0.369554i	−0.892923	+	0.450209i	$0.851349\pi$
$420$		0			0
$421$	−10.1364	+	15.7726i	−0.494020	+	0.768710i	−0.995327	−	0.0965595i	$-0.969216\pi$
$421$	−10.1364	+	15.7726i	−0.494020	+	0.768710i	0.501307	+	0.865269i	$0.332853\pi$
$422$	−7.96173	−	28.0879i	−0.387571	−	1.36730i
$423$		0			0
$424$	1.88725	+	0.926965i	0.0916532	+	0.0450174i
$425$	−0.720313	+	0.103565i	−0.0349403	+	0.00502366i
$426$		0			0
$427$	−7.23340	−	11.2554i	−0.350049	−	0.544687i
$428$	−11.0014	−	13.1887i	−0.531774	−	0.637498i
$429$		0			0
$430$	8.49499	−	1.14011i	0.409665	−	0.0549812i
$431$	−2.71944	+	0.798501i	−0.130991	+	0.0384624i	−0.346571	−	0.938024i	$-0.612654\pi$
$431$	−2.71944	+	0.798501i	−0.130991	+	0.0384624i	0.215580	+	0.976486i	$0.430836\pi$
$432$		0			0
$433$	5.21341	−	17.7552i	0.250540	−	0.853262i	−0.734156	−	0.678981i	$-0.762422\pi$
$433$	5.21341	−	17.7552i	0.250540	−	0.853262i	0.984696	−	0.174281i	$-0.0557600\pi$
$434$	−47.7091	−	22.3316i	−2.29011	−	1.07195i
$435$		0			0
$436$	−20.3334	−	3.31422i	−0.973793	−	0.158722i
$437$	8.41480	−	0.726312i	0.402534	−	0.0347442i
$438$		0			0
$439$	3.02122	+	0.434385i	0.144195	+	0.0207321i	0.214034	−	0.976826i	$-0.431340\pi$
$439$	3.02122	+	0.434385i	0.144195	+	0.0207321i	−0.0698394	+	0.997558i	$0.522249\pi$
$440$	−3.99910	+	5.85352i	−0.190650	+	0.279056i
$441$		0			0
$442$	16.6062	+	2.54693i	0.789876	+	0.121145i
$443$	4.88374	+	16.6325i	0.232034	+	0.790234i	0.990379	+	0.138381i	$0.0441899\pi$
$443$	4.88374	+	16.6325i	0.232034	+	0.790234i	−0.758345	+	0.651853i	$0.773992\pi$
$444$		0			0
$445$	−5.59768	+	12.2572i	−0.265355	+	0.581047i
$446$	−0.185555	+	19.7670i	−0.00878626	+	0.935996i
$447$		0			0
$448$	−28.1386	−	10.0145i	−1.32942	−	0.473140i
$449$	−0.0379424	−	0.263895i	−0.00179061	−	0.0124540i	0.988907	−	0.148539i	$-0.0474571\pi$
$449$	−0.0379424	−	0.263895i	−0.00179061	−	0.0124540i	−0.990697	+	0.136085i	$0.956548\pi$
$450$		0			0
$451$	−0.915465	+	1.05650i	−0.0431076	+	0.0497488i
$452$	−11.4627	+	17.1209i	−0.539161	+	0.805300i
$453$		0			0
$454$	−33.4184	−	21.9227i	−1.56840	−	1.02888i
$455$	−19.9876	+	17.3194i	−0.937034	+	0.811945i
$456$		0			0
$457$	26.5005	−	12.1024i	1.23964	−	0.566124i	0.315771	−	0.948835i	$-0.397737\pi$
$457$	26.5005	−	12.1024i	1.23964	−	0.566124i	0.923868	+	0.382711i	$0.125010\pi$
$458$	7.95500	+	12.6375i	0.371713	+	0.590511i
$459$		0			0
$460$	12.5273	+	16.8774i	0.584090	+	0.786914i
$461$	8.90884			0.414926			0.207463	−	0.978243i	$-0.433479\pi$
$461$	8.90884			0.414926			0.207463	+	0.978243i	$0.433479\pi$
$462$		0			0
$463$	10.0885	−	4.60724i	0.468850	−	0.214117i	−0.166958	−	0.985964i	$-0.553394\pi$
$463$	10.0885	−	4.60724i	0.468850	−	0.214117i	0.635808	+	0.771847i	$0.280667\pi$
$464$	−29.1973	−	20.3521i	−1.35545	−	0.944823i
$465$		0			0
$466$	−10.7524	−	7.05361i	−0.498093	−	0.326752i
$467$	29.0694	+	18.6818i	1.34517	+	0.864489i	0.997327	−	0.0730634i	$-0.0232775\pi$
$467$	29.0694	+	18.6818i	1.34517	+	0.864489i	0.347844	+	0.937552i	$0.386914\pi$
$468$		0			0
$469$	24.9634	−	28.8093i	1.15270	−	1.33029i
$470$	−6.71363	−	2.03994i	−0.309677	−	0.0940956i
$471$		0			0
$472$	−20.3365	+	16.6427i	−0.936064	+	0.766040i
$473$	2.66123	−	1.71027i	0.122364	−	0.0786383i
$474$		0			0
$475$	−0.144877	+	0.317235i	−0.00664739	+	0.0145558i
$476$	20.3966	+	18.3553i	0.934876	+	0.841315i
$477$		0			0
$478$	7.27943	+	1.11646i	0.332953	+	0.0510658i
$479$	27.9632	+	8.21073i	1.27767	+	0.375158i	0.849043	−	0.528323i	$-0.177179\pi$
$479$	27.9632	+	8.21073i	1.27767	+	0.375158i	0.428627	+	0.903481i	$0.358997\pi$
$480$		0			0
$481$	19.7843	+	2.84456i	0.902087	+	0.129701i
$482$	16.2916	−	13.8512i	0.742063	−	0.630904i
$483$		0			0
$484$	3.11825	−	19.1311i	0.141739	−	0.869595i
$485$	2.49270	−	17.3371i	0.113188	−	0.787239i
$486$		0			0
$487$	−5.43992	+	18.5267i	−0.246506	+	0.839523i	0.739549	+	0.673103i	$0.235039\pi$
$487$	−5.43992	+	18.5267i	−0.246506	+	0.839523i	−0.986055	+	0.166420i	$0.946779\pi$
$488$	−3.12836	+	9.64122i	−0.141614	+	0.436437i
$489$		0			0
$490$	−21.3118	+	2.86026i	−0.962770	+	0.129213i
$491$	−9.74561	−	4.45067i	−0.439813	−	0.200856i	0.183186	−	0.983078i	$-0.441359\pi$
$491$	−9.74561	−	4.45067i	−0.439813	−	0.200856i	−0.622999	+	0.782222i	$0.714086\pi$
$492$		0			0
$493$	17.6776	+	27.5070i	0.796161	+	1.23885i
$494$	5.32942	−	6.03507i	0.239782	−	0.271531i
$495$		0			0
$496$	9.79796	+	38.6861i	0.439942	+	1.73706i
$497$	−25.8416	−	22.3919i	−1.15916	−	1.00441i
$498$		0			0
$499$	−4.94897	+	7.70075i	−0.221546	+	0.344733i	−0.934179	−	0.356804i	$-0.883866\pi$
$499$	−4.94897	+	7.70075i	−0.221546	+	0.344733i	0.712633	+	0.701537i	$0.247503\pi$
$500$	−22.6063	+	2.81824i	−1.01098	+	0.126035i
$501$		0			0
$502$	1.21373	+	2.72510i	0.0541714	+	0.121627i
$503$	−10.3583	−	22.6815i	−0.461853	−	1.01132i	−0.987061	−	0.160344i	$-0.948740\pi$
$503$	−10.3583	−	22.6815i	−0.461853	−	1.01132i	0.525208	−	0.850974i	$-0.323987\pi$
$504$		0			0
$505$		−	34.9406i		−	1.55484i
$506$	6.82823	+	3.68153i	0.303552	+	0.163664i
$507$		0			0
$508$	−1.38608	+	4.41240i	−0.0614975	+	0.195768i
$509$	14.7254	+	32.2441i	0.652691	+	1.42919i	0.889179	+	0.457559i	$0.151276\pi$
$509$	14.7254	+	32.2441i	0.652691	+	1.42919i	−0.236488	+	0.971634i	$0.575997\pi$
$510$		0			0
$511$	10.8606	+	12.5338i	0.480445	+	0.554463i
$512$	7.62947	+	21.3024i	0.337178	+	0.941441i
$513$		0			0
$514$	−25.0041	+	7.08761i	−1.10288	+	0.312621i
$515$	−29.7707	−	25.7965i	−1.31185	−	1.13673i
$516$		0			0
$517$	−2.56334	+	0.368553i	−0.112736	+	0.0162090i
$518$	24.4702	+	21.6090i	1.07516	+	0.949445i
$519$		0			0
$520$	19.7443	+	3.40875i	0.865843	+	0.149484i
$521$	−0.527552	−	0.240925i	−0.0231125	−	0.0105551i	0.403825	−	0.914836i	$-0.367680\pi$
$521$	−0.527552	−	0.240925i	−0.0231125	−	0.0105551i	−0.426938	+	0.904281i	$0.640408\pi$
$522$		0			0
$523$	16.1023	−	4.72806i	0.704104	−	0.206744i	0.0899692	−	0.995945i	$-0.471323\pi$
$523$	16.1023	−	4.72806i	0.704104	−	0.206744i	0.614135	+	0.789201i	$0.289505\pi$
$524$	12.9964	+	21.0828i	0.567750	+	0.921005i
$525$		0			0
$526$	−6.03158	+	12.8858i	−0.262989	+	0.561849i
$527$	5.21778	−	36.2905i	0.227290	−	1.58084i
$528$		0			0
$529$	16.9320	−	15.5663i	0.736172	−	0.676794i
$530$	−1.49224	−	1.75516i	−0.0648188	−	0.0762393i
$531$		0			0
$532$	12.6848	−	3.46731i	0.549957	−	0.150327i
$533$	3.79103	+	1.11315i	0.164208	+	0.0482157i
$534$		0			0
$535$	5.30160	+	18.0556i	0.229208	+	0.780612i
$536$	−28.8681	−	0.813153i	−1.24691	−	0.0351228i
$537$		0			0
$538$	−28.7153	−	0.269553i	−1.23801	−	0.0116213i
$539$	−6.67637	+	4.29064i	−0.287572	+	0.184811i
$540$		0			0
$541$	−1.23736	−	8.60605i	−0.0531984	−	0.370003i	−0.998978	−	0.0451944i	$-0.985609\pi$
$541$	−1.23736	−	8.60605i	−0.0531984	−	0.370003i	0.945780	−	0.324808i	$-0.105300\pi$
$542$	−2.65993	+	8.75405i	−0.114254	+	0.376019i
$543$		0			0
$544$	0.975311	−	20.7652i	0.0418161	−	0.890302i
$545$	18.9894	+	12.2037i	0.813415	+	0.522750i
$546$		0			0
$547$	16.9263	−	14.6667i	0.723717	−	0.627104i	−0.213057	−	0.977040i	$-0.568342\pi$
$547$	16.9263	−	14.6667i	0.723717	−	0.627104i	0.936774	+	0.349936i	$0.113797\pi$
$548$	17.1988	+	8.24805i	0.734694	+	0.352339i
$549$		0			0
$550$	−0.271082	+	0.170640i	−0.0115590	+	0.00727610i
$551$	15.6699			0.667561
$552$		0			0
$553$	−60.7154			−2.58188
$554$	24.7010	−	15.5487i	1.04944	−	0.660601i
$555$		0			0
$556$	−26.7281	−	12.8181i	−1.13352	−	0.543607i
$557$	1.28707	−	1.11525i	0.0545347	−	0.0472546i	−0.627167	−	0.778885i	$-0.715786\pi$
$557$	1.28707	−	1.11525i	0.0545347	−	0.0472546i	0.681702	+	0.731630i	$0.261240\pi$
$558$		0			0
$559$	−7.52152	−	4.83378i	−0.318126	−	0.204447i
$560$	23.9100	+	22.3436i	1.01038	+	0.944189i
$561$		0			0
$562$	7.11258	−	23.4081i	0.300026	−	0.987411i
$563$	−0.711102	−	4.94582i	−0.0299694	−	0.208442i	0.969335	−	0.245745i	$-0.0790324\pi$
$563$	−0.711102	−	4.94582i	−0.0299694	−	0.208442i	−0.999304	+	0.0373029i	$0.988123\pi$
$564$		0			0
$565$	18.9913	−	12.2050i	0.798972	−	0.513468i
$566$	−2.53248	−	0.0237726i	−0.106448	−	0.000999236i
$567$		0			0
$568$	−0.729388	+	25.8944i	−0.0306045	+	1.08650i
$569$	−1.02167	−	3.47948i	−0.0428305	−	0.145867i	0.935302	−	0.353851i	$-0.115128\pi$
$569$	−1.02167	−	3.47948i	−0.0428305	−	0.145867i	−0.978132	+	0.207984i	$0.933310\pi$
$570$		0			0
$571$	32.1866	+	9.45084i	1.34697	+	0.395506i	0.874151	−	0.485655i	$-0.161419\pi$
$571$	32.1866	+	9.45084i	1.34697	+	0.395506i	0.472817	+	0.881160i	$0.343237\pi$
$572$	7.13326	−	1.94983i	0.298257	−	0.0815266i
$573$		0			0
$574$	4.17999	+	4.91647i	0.174470	+	0.205209i
$575$	0.215494	+	0.924932i	0.00898671	+	0.0385724i
$576$		0			0
$577$	−2.41627	+	16.8056i	−0.100591	+	0.699625i	0.875652	+	0.482943i	$0.160432\pi$
$577$	−2.41627	+	16.8056i	−0.100591	+	0.699625i	−0.976242	+	0.216681i	$0.930477\pi$
$578$	2.09564	−	4.47712i	0.0871672	−	0.186223i
$579$		0			0
$580$	20.4630	+	33.1952i	0.849682	+	1.37835i
$581$	−19.2992	+	5.66674i	−0.800664	+	0.235096i
$582$		0			0
$583$	−0.773432	−	0.353215i	−0.0320323	−	0.0146287i
$584$	2.13756	−	12.3812i	0.0884527	−	0.512338i
$585$		0			0
$586$	15.2490	+	13.4660i	0.629931	+	0.556276i
$587$	−19.9892	+	2.87401i	−0.825041	+	0.118623i	−0.541887	−	0.840451i	$-0.682290\pi$
$587$	−19.9892	+	2.87401i	−0.825041	+	0.118623i	−0.283154	+	0.959074i	$0.591381\pi$
$588$		0			0
$589$	−13.2790	−	11.5063i	−0.547151	−	0.474109i
$590$	27.7010	−	7.85209i	1.14043	−	0.323265i
$591$		0			0
$592$	0.928402	−	24.7146i	0.0381571	−	1.01577i
$593$	17.7814	+	20.5208i	0.730193	+	0.842688i	0.992493	−	0.122298i	$-0.0390265\pi$
$593$	17.7814	+	20.5208i	0.730193	+	0.842688i	−0.262300	+	0.964986i	$0.584481\pi$
$594$		0			0
$595$	−12.4894	−	27.3480i	−0.512016	−	1.12116i
$596$	7.05175	−	22.4482i	0.288851	−	0.919515i
$597$		0			0
$598$	1.44790	−	21.8773i	0.0592089	−	0.894629i
$599$			4.57335i			0.186862i	0.995626	+	0.0934309i	$0.0297834\pi$
$599$			4.57335i			0.186862i	−0.995626	+	0.0934309i	$0.970217\pi$
$600$		0			0
$601$	7.98506	+	17.4848i	0.325717	+	0.713221i	0.999674	−	0.0255499i	$-0.00813368\pi$
$601$	7.98506	+	17.4848i	0.325717	+	0.713221i	−0.673956	+	0.738771i	$0.735406\pi$
$602$	−5.94131	−	13.3396i	−0.242150	−	0.543683i
$603$		0			0
$604$	−2.50477	+	0.312260i	−0.101918	+	0.0127057i
$605$	−11.4821	+	17.8665i	−0.466814	+	0.726377i
$606$		0			0
$607$	−16.2200	−	14.0547i	−0.658350	−	0.570464i	0.260304	−	0.965527i	$-0.416177\pi$
$607$	−16.2200	−	14.0547i	−0.658350	−	0.570464i	−0.918654	+	0.395063i	$0.870723\pi$
$608$	−8.11903	−	5.77339i	−0.329270	−	0.234142i
$609$		0			0
$610$	7.35120	−	8.32455i	0.297642	−	0.337051i
$611$	3.95714	+	6.15743i	0.160089	+	0.249103i
$612$		0			0
$613$	−23.9891	−	10.9555i	−0.968912	−	0.442487i	−0.132858	−	0.991135i	$-0.542416\pi$
$613$	−23.9891	−	10.9555i	−0.968912	−	0.442487i	−0.836054	+	0.548648i	$0.815143\pi$
$614$	0.0649693	−	0.00871954i	0.00262195	−	0.000351892i
$615$		0			0
$616$	11.4884	+	3.72773i	0.462880	+	0.150194i
$617$	−2.46606	+	8.39862i	−0.0992797	+	0.338116i	−0.994122	−	0.108267i	$-0.965470\pi$
$617$	−2.46606	+	8.39862i	−0.0992797	+	0.338116i	0.894842	+	0.446383i	$0.147288\pi$
$618$		0			0
$619$	−5.92703	+	41.2234i	−0.238227	+	1.65691i	0.422560	+	0.906335i	$0.361132\pi$
$619$	−5.92703	+	41.2234i	−0.238227	+	1.65691i	−0.660788	+	0.750573i	$0.729778\pi$
$620$	7.03419	−	43.1561i	0.282500	−	1.73319i
$621$		0			0
$622$	7.86301	−	6.68515i	0.315278	−	0.268050i
$623$	22.7239	+	3.26720i	0.910413	+	0.130898i
$624$		0			0
$625$	22.9997	+	6.75331i	0.919987	+	0.270133i
$626$	31.2743	+	4.79662i	1.24997	+	0.191711i
$627$		0			0
$628$	−7.61893	−	6.85645i	−0.304029	−	0.273602i
$629$	−9.43893	+	20.6684i	−0.376355	+	0.824102i
$630$		0			0
$631$	−11.5707	+	7.43606i	−0.460624	+	0.296025i	−0.750297	−	0.661101i	$-0.770090\pi$
$631$	−11.5707	+	7.43606i	−0.460624	+	0.296025i	0.289674	+	0.957126i	$0.406453\pi$
$632$	29.1312	+	35.5970i	1.15878	+	1.41597i
$633$		0			0
$634$	9.75183	+	2.96310i	0.387295	+	0.117680i
$635$	3.31848	−	3.82973i	0.131690	−	0.151978i
$636$		0			0
$637$	18.8696	+	12.1268i	0.747641	+	0.480480i
$638$	12.0340	+	7.89440i	0.476432	+	0.312542i
$639$		0			0
$640$	1.62786	−	24.7387i	0.0643470	−	0.977882i
$641$	22.0233	−	10.0577i	0.869868	−	0.397255i	0.0700824	−	0.997541i	$-0.477674\pi$
$641$	22.0233	−	10.0577i	0.869868	−	0.397255i	0.799786	+	0.600286i	$0.204946\pi$
$642$		0			0
$643$	2.43251			0.0959288			0.0479644	−	0.998849i	$-0.484727\pi$
$643$	2.43251			0.0959288			0.0479644	+	0.998849i	$0.484727\pi$
$644$	21.5767	−	28.5797i	0.850241	−	1.12620i
$645$		0			0
$646$	4.87580	+	7.74581i	0.191836	+	0.304755i
$647$	44.7251	−	20.4253i	1.75833	−	0.803001i	0.772547	−	0.634958i	$-0.218983\pi$
$647$	44.7251	−	20.4253i	1.75833	−	0.803001i	0.985780	−	0.168043i	$-0.0537446\pi$
$648$		0			0
$649$	8.03105	−	6.95895i	0.315246	−	0.273163i
$650$	0.756977	+	0.496581i	0.0296911	+	0.0194775i
$651$		0			0
$652$	10.8774	−	16.2467i	0.425993	−	0.636270i
$653$	1.36207	−	1.57192i	0.0533021	−	0.0615139i	−0.728472	−	0.685075i	$-0.759769\pi$
$653$	1.36207	−	1.57192i	0.0533021	−	0.0615139i	0.781775	+	0.623561i	$0.214315\pi$
$654$		0			0
$655$	−3.86187	−	26.8599i	−0.150896	−	1.04950i
$656$	0.876927	−	4.80961i	0.0342382	−	0.187784i
$657$		0			0
$658$	−0.112213	+	11.9540i	−0.00437453	+	0.466017i
$659$	−7.38557	+	16.1722i	−0.287701	+	0.629978i	−0.997204	−	0.0747248i	$-0.976192\pi$
$659$	−7.38557	+	16.1722i	−0.287701	+	0.629978i	0.709503	+	0.704702i	$0.248919\pi$
$660$		0			0
$661$	10.9719	+	37.3667i	0.426756	+	1.45340i	0.839905	+	0.542734i	$0.182611\pi$
$661$	10.9719	+	37.3667i	0.426756	+	1.45340i	−0.413149	+	0.910663i	$0.635571\pi$
$662$	−29.3738	−	4.50513i	−1.14164	−	0.175097i
$663$		0			0
$664$	12.5821	+	8.59603i	0.488280	+	0.333591i
$665$	−14.2616	−	2.05051i	−0.553041	−	0.0795153i
$666$		0			0
$667$	33.7808	−	26.0716i	1.30800	−	1.00949i
$668$	−7.27583	−	1.18592i	−0.281510	−	0.0458845i
$669$		0			0
$670$	28.6584	+	13.4144i	1.10717	+	0.518242i
$671$	1.15479	−	3.93285i	0.0445801	−	0.151826i
$672$		0			0
$673$	−33.1659	+	9.73838i	−1.27845	+	0.375387i	−0.849331	−	0.527860i	$-0.822994\pi$
$673$	−33.1659	+	9.73838i	−1.27845	+	0.375387i	−0.429120	+	0.903248i	$0.641176\pi$
$674$	−32.3957	+	4.34783i	−1.24784	+	0.167472i
$675$		0			0
$676$	3.26650	+	3.91593i	0.125635	+	0.150613i
$677$	5.84218	+	9.09061i	0.224533	+	0.349380i	0.935183	−	0.354166i	$-0.115235\pi$
$677$	5.84218	+	9.09061i	0.224533	+	0.349380i	−0.710649	+	0.703546i	$0.751599\pi$
$678$		0			0
$679$	−29.5377	+	4.24688i	−1.13355	+	0.162980i
$680$	−10.0415	+	20.4440i	−0.385074	+	0.783991i
$681$		0			0
$682$	−4.40108	−	15.5264i	−0.168526	−	0.594536i
$683$	−15.2977	+	23.8036i	−0.585349	+	0.910821i	0.414651	+	0.909981i	$0.363904\pi$
$683$	−15.2977	+	23.8036i	−0.585349	+	0.910821i	−1.00000		0.000840079i	$0.999733\pi$
$684$		0			0
$685$	−13.6860	−	15.7945i	−0.522915	−	0.603476i
$686$	−0.131890	−	0.296123i	−0.00503558	−	0.0113060i
$687$		0			0
$688$	−4.97028	+	9.88369i	−0.189490	+	0.376812i
$689$			2.40314i			0.0915523i
$690$		0			0
$691$			13.6014i			0.517422i	0.965955	+	0.258711i	$0.0832977\pi$
$691$			13.6014i			0.517422i	−0.965955	+	0.258711i	$0.916702\pi$
$692$	−9.71319	−	3.05125i	−0.369240	−	0.115991i
$693$		0			0
$694$	18.1194	−	8.07019i	0.687805	−	0.306340i
$695$	21.2690	+	24.5458i	0.806780	+	0.931074i
$696$		0			0
$697$	−2.42829	+	3.77849i	−0.0919780	+	0.143121i
$698$	−7.58605	+	2.15033i	−0.287136	+	0.0813911i
$699$		0			0
$700$	0.588894	+	1.35632i	0.0222581	+	0.0512640i
$701$	−20.6692	+	2.97178i	−0.780664	+	0.112243i	−0.521114	−	0.853487i	$-0.674483\pi$
$701$	−20.6692	+	2.97178i	−0.780664	+	0.112243i	−0.259550	+	0.965730i	$0.583574\pi$
$702$		0			0
$703$	5.88709	+	9.16050i	0.222036	+	0.345495i
$704$	−3.32658	−	8.52410i	−0.125375	−	0.321264i
$705$		0			0
$706$	−0.210476	−	1.56826i	−0.00792138	−	0.0590222i
$707$	−57.1178	+	16.7713i	−2.14814	+	0.630750i
$708$		0			0
$709$	−14.6578	+	49.9199i	−0.550486	+	1.87478i	−0.0704858	+	0.997513i	$0.522455\pi$
$709$	−14.6578	+	49.9199i	−0.550486	+	1.87478i	−0.480000	+	0.877269i	$0.659363\pi$
$710$	12.0325	−	25.7062i	0.451572	−	0.964737i
$711$		0			0
$712$	−8.98737	−	14.8904i	−0.336816	−	0.558042i
$713$	−47.7707	−	2.71148i	−1.78903	−	0.101546i
$714$		0			0
$715$	−8.01995	−	1.15310i	−0.299929	−	0.0431233i
$716$	−0.940993	−	3.44252i	−0.0351665	−	0.128653i
$717$		0			0
$718$	−3.32148	+	21.6563i	−0.123956	+	0.808205i
$719$	4.77265	+	16.2541i	0.177990	+	0.606177i	0.999360	+	0.0357815i	$0.0113920\pi$
$719$	4.77265	+	16.2541i	0.177990	+	0.606177i	−0.821370	+	0.570396i	$0.806790\pi$
$720$		0			0
$721$	−27.8800	+	61.0488i	−1.03831	+	2.27357i
$722$	−22.4828	−	0.211047i	−0.836722	−	0.00785437i
$723$		0			0
$724$	−0.793531	+	42.2635i	−0.0294913	+	1.57071i
$725$	0.250755	+	1.74404i	0.00931281	+	0.0647721i
$726$		0			0
$727$	−21.5901	+	24.9163i	−0.800731	+	0.924093i	−0.998421	−	0.0561715i	$-0.982111\pi$
$727$	−21.5901	+	24.9163i	−0.800731	+	0.924093i	0.197690	+	0.980265i	$0.436656\pi$
$728$	−3.90481	−	33.9124i	−0.144722	−	1.25688i
$729$		0			0
$730$	−7.55106	+	11.5107i	−0.279477	+	0.426029i
$731$	7.68126	−	6.65585i	0.284102	−	0.246176i
$732$		0			0
$733$	7.07169	−	3.22953i	0.261199	−	0.119286i	−0.280512	−	0.959851i	$-0.590504\pi$
$733$	7.07169	−	3.22953i	0.261199	−	0.119286i	0.541711	+	0.840565i	$0.317777\pi$
$734$	−0.978709	+	0.616074i	−0.0361248	+	0.0227397i
$735$		0			0
$736$	−27.1085	+	1.06228i	−0.999233	+	0.0391562i
$737$	11.6785			0.430183
$738$		0			0
$739$	0.342533	−	0.156430i	0.0126003	−	0.00575436i	−0.409105	−	0.912487i	$-0.634159\pi$
$739$	0.342533	−	0.156430i	0.0126003	−	0.00575436i	0.421705	+	0.906733i	$0.361432\pi$
$740$	−11.7177	+	24.4337i	−0.430753	+	0.898202i
$741$		0			0
$742$	−2.15292	+	3.28186i	−0.0790360	+	0.120481i
$743$	2.19442	+	1.41027i	0.0805055	+	0.0517377i	0.580274	−	0.814421i	$-0.302945\pi$
$743$	2.19442	+	1.41027i	0.0805055	+	0.0517377i	−0.499769	+	0.866159i	$0.666582\pi$
$744$		0			0
$745$	−16.8829	+	19.4839i	−0.618541	+	0.713834i
$746$	3.26957	−	10.7604i	0.119707	−	0.393967i
$747$		0			0
$748$	−0.157810	+	8.40495i	−0.00577009	+	0.307315i
$749$	26.9710	−	17.3332i	0.985498	−	0.633341i
$750$		0			0
$751$	−16.6578	+	36.4756i	−0.607853	+	1.33101i	0.316180	+	0.948699i	$0.397600\pi$
$751$	−16.6578	+	36.4756i	−0.607853	+	1.33101i	−0.924033	+	0.382313i	$0.875128\pi$
$752$	7.06239	−	5.66975i	0.257539	−	0.206754i
$753$		0			0
$754$	6.16670	−	40.2073i	0.224578	−	1.46427i
$755$	2.65362	+	0.779172i	0.0965750	+	0.0283570i
$756$		0			0
$757$	−26.3015	−	3.78158i	−0.955943	−	0.137444i	−0.353349	−	0.935492i	$-0.614957\pi$
$757$	−26.3015	−	3.78158i	−0.955943	−	0.137444i	−0.602594	+	0.798048i	$0.705866\pi$
$758$	−18.3573	−	21.5916i	−0.666766	−	0.784243i
$759$		0			0
$760$	5.64051	+	9.34529i	0.204603	+	0.338989i
$761$	−6.22185	+	43.2739i	−0.225542	+	1.56868i	0.491017	+	0.871150i	$0.336625\pi$
$761$	−6.22185	+	43.2739i	−0.225542	+	1.56868i	−0.716559	+	0.697527i	$0.754284\pi$
$762$		0			0
$763$	10.8348	−	36.8999i	0.392245	−	1.33587i
$764$	−35.8573	+	22.1041i	−1.29727	+	0.799699i
$765$		0			0
$766$	−0.425332	−	3.16915i	−0.0153679	−	0.114506i
$767$	−27.3201	−	12.4767i	−0.986473	−	0.450507i
$768$		0			0
$769$	−18.0559	−	28.0956i	−0.651113	−	1.01315i	−0.997188	−	0.0749451i	$-0.976122\pi$
$769$	−18.0559	−	28.0956i	−0.651113	−	1.01315i	0.346074	−	0.938207i	$-0.387515\pi$
$770$	−9.91945	−	8.75962i	−0.357472	−	0.315675i
$771$		0			0
$772$	−0.737379	−	1.69830i	−0.0265388	−	0.0611232i
$773$	29.6254	+	25.6706i	1.06555	+	0.923306i	0.997232	−	0.0743579i	$-0.0236907\pi$
$773$	29.6254	+	25.6706i	1.06555	+	0.923306i	0.0683198	+	0.997663i	$0.478236\pi$
$774$		0			0
$775$	1.06814	−	1.66206i	0.0383688	−	0.0597030i
$776$	16.6621	+	15.2801i	0.598134	+	0.548523i
$777$		0			0
$778$	10.8754	−	4.84375i	0.389900	−	0.173657i
$779$	0.894181	+	1.95798i	0.0320374	+	0.0701520i
$780$		0			0
$781$		−	10.4755i		−	0.374842i
$782$	23.3986	+	8.58586i	0.836731	+	0.307030i
$783$		0			0
$784$	12.4692	−	24.7957i	0.445328	−	0.885561i
$785$	4.66529	+	10.2156i	0.166511	+	0.364609i
$786$		0			0
$787$	−24.5886	−	28.3768i	−0.876490	−	1.01152i	−0.999816	−	0.0191574i	$-0.993902\pi$
$787$	−24.5886	−	28.3768i	−0.876490	−	1.01152i	0.123326	−	0.992366i	$-0.460644\pi$
$788$	−2.10912	−	16.9182i	−0.0751343	−	0.602685i
$789$		0			0
$790$	−13.7443	−	48.4878i	−0.488999	−	1.72512i
$791$	−29.0674	−	25.1871i	−1.03352	−	0.895549i
$792$		0			0
$793$	−11.4669	+	1.64869i	−0.407200	+	0.0585466i
$794$	−3.15380	+	3.57139i	−0.111924	+	0.126744i
$795$		0			0
$796$	−15.2237	−	18.2504i	−0.539589	−	0.646867i
$797$	−30.2453	−	13.8126i	−1.07134	−	0.489266i	−0.199927	−	0.979811i	$-0.564070\pi$
$797$	−30.2453	−	13.8126i	−1.07134	−	0.489266i	−0.871416	+	0.490545i	$0.836798\pi$
$798$		0			0
$799$	−7.98345	+	2.34415i	−0.282434	+	0.0829302i
$800$	0.512647	−	0.996024i	0.0181248	−	0.0352148i
$801$		0			0
$802$	−20.0472	−	9.38365i	−0.707890	−	0.331348i
$803$	−0.723081	+	5.02914i	−0.0255170	+	0.177474i
$804$		0			0
$805$	−34.1564	+	19.3079i	−1.20385	+	0.680515i
$806$	−34.7497	+	29.5443i	−1.22401	+	1.04065i
$807$		0			0
$808$	37.2380	+	25.4408i	1.31003	+	0.895006i
$809$	21.3600	+	6.27186i	0.750977	+	0.220507i	0.634752	−	0.772716i	$-0.281102\pi$
$809$	21.3600	+	6.27186i	0.750977	+	0.220507i	0.116225	+	0.993223i	$0.462921\pi$
$810$		0			0
$811$	−10.2056	−	34.7572i	−0.358368	−	1.22049i	−0.919608	−	0.392837i	$-0.871494\pi$
$811$	−10.2056	−	34.7572i	−0.358368	−	1.22049i	0.561240	−	0.827653i	$-0.310324\pi$
$812$	44.4424	−	49.3847i	1.55962	−	1.73306i
$813$		0			0
$814$	−0.0938789	+	10.0009i	−0.00329046	+	0.350530i
$815$	−18.0216	+	11.5818i	−0.631270	+	0.405693i
$816$		0			0
$817$	−0.693197	−	4.82129i	−0.0242519	−	0.168676i
$818$	27.9147	+	8.48192i	0.976016	+	0.296563i
$819$		0			0
$820$	−2.98010	+	4.45112i	−0.104069	+	0.155440i
$821$	−8.19631	−	5.26745i	−0.286053	−	0.183835i	0.389743	−	0.920924i	$-0.372564\pi$
$821$	−8.19631	−	5.26745i	−0.286053	−	0.183835i	−0.675796	+	0.737088i	$0.736200\pi$
$822$		0			0
$823$	−28.9373	+	25.0743i	−1.00869	+	0.874036i	−0.992052	−	0.125825i	$-0.959842\pi$
$823$	−28.9373	+	25.0743i	−1.00869	+	0.874036i	−0.0166394	+	0.999862i	$0.505297\pi$
$824$	49.1692	−	12.9453i	1.71289	−	0.450972i
$825$		0			0
$826$	−26.1323	−	41.5143i	−0.909258	−	1.44447i
$827$	14.2948			0.497077			0.248539	−	0.968622i	$-0.420050\pi$
$827$	14.2948			0.497077			0.248539	+	0.968622i	$0.420050\pi$
$828$		0			0
$829$	17.8480			0.619887			0.309944	−	0.950755i	$-0.399690\pi$
$829$	17.8480			0.619887			0.309944	+	0.950755i	$0.399690\pi$
$830$	−8.89428	−	14.1297i	−0.308725	−	0.490447i
$831$		0			0
$832$	−18.0090	+	18.5605i	−0.624351	+	0.643470i
$833$	−19.2704	+	16.6979i	−0.667679	+	0.578547i
$834$		0			0
$835$	6.79490	+	4.36682i	0.235147	+	0.151120i
$836$	3.34766	+	2.24131i	0.115781	+	0.0775173i
$837$		0			0
$838$	−13.5440	−	4.11535i	−0.467869	−	0.142162i
$839$	2.11741	+	14.7269i	0.0731011	+	0.508430i	0.993170	+	0.116674i	$0.0372232\pi$
$839$	2.11741	+	14.7269i	0.0731011	+	0.508430i	−0.920069	+	0.391756i	$0.871868\pi$
$840$		0			0
$841$	42.2042	−	27.1230i	1.45532	−	0.935276i
$842$	−0.248887	+	26.5138i	−0.00857722	+	0.913727i
$843$		0			0
$844$	−30.6897	−	27.6184i	−1.05638	−	0.950663i
$845$	−1.57413	−	5.36100i	−0.0541518	−	0.184424i
$846$		0			0
$847$	34.7180	+	10.1941i	1.19292	+	0.350274i
$848$	2.95709	−	0.312396i	0.101547	−	0.0107277i
$849$		0			0
$850$	−0.784073	+	0.666621i	−0.0268935	+	0.0228649i
$851$	27.9324	+	9.95304i	0.957511	+	0.341186i
$852$		0			0
$853$	2.41211	−	16.7766i	0.0825892	−	0.574421i	−0.905942	−	0.423402i	$-0.860836\pi$
$853$	2.41211	−	16.7766i	0.0825892	−	0.574421i	0.988531	−	0.151018i	$-0.0482552\pi$
$854$	−17.1368	−	8.02137i	−0.586409	−	0.274485i
$855$		0			0
$856$	−23.1030	−	7.49641i	−0.789643	−	0.256222i
$857$	−29.5877	+	8.68772i	−1.01070	+	0.296767i	−0.744838	−	0.667246i	$-0.767473\pi$
$857$	−29.5877	+	8.68772i	−1.01070	+	0.296767i	−0.265857	+	0.964012i	$0.585655\pi$
$858$		0			0
$859$	25.1115	+	11.4680i	0.856792	+	0.391284i	0.794857	−	0.606797i	$-0.207546\pi$
$859$	25.1115	+	11.4680i	0.856792	+	0.391284i	0.0619346	+	0.998080i	$0.480273\pi$
$860$	9.30818	−	7.76449i	0.317406	−	0.264767i
$861$		0			0
$862$	−2.65315	+	3.00445i	−0.0903668	+	0.102332i
$863$	−43.5095	+	6.25573i	−1.48108	+	0.212947i	−0.834970	−	0.550296i	$-0.814515\pi$
$863$	−43.5095	+	6.25573i	−1.48108	+	0.212947i	−0.646112	+	0.763243i	$0.723606\pi$
$864$		0			0
$865$	8.43054	+	7.30511i	0.286647	+	0.248381i
$866$	−7.13685	−	25.1778i	−0.242520	−	0.855576i
$867$		0			0
$868$	−73.9242	+	9.21583i	−2.50915	+	0.312806i
$869$	−12.1809	−	14.0575i	−0.413209	−	0.476869i
$870$		0			0
$871$	−13.7117	−	30.0245i	−0.464603	−	1.01734i
$872$	−26.8326	+	11.3522i	−0.908667	+	0.384434i
$873$		0			0
$874$	9.52395	−	7.20882i	0.322152	−	0.243842i
$875$		−	42.5263i		−	1.43765i
$876$		0			0
$877$	−20.7018	−	45.3307i	−0.699051	−	1.53071i	−0.841118	−	0.540852i	$-0.818102\pi$
$877$	−20.7018	−	45.3307i	−0.699051	−	1.53071i	0.142066	−	0.989857i	$-0.454625\pi$
$878$	3.94316	−	1.75624i	0.133075	−	0.0592701i
$879$		0			0
$880$	−0.376346	+	10.0186i	−0.0126866	+	0.337725i
$881$	−7.62978	+	11.8722i	−0.257054	+	0.399984i	−0.945663	−	0.325149i	$-0.894585\pi$
$881$	−7.62978	+	11.8722i	−0.257054	+	0.399984i	0.688609	+	0.725133i	$0.258222\pi$
$882$		0			0
$883$	−17.3903	−	15.0687i	−0.585229	−	0.507104i	0.311169	−	0.950355i	$-0.399280\pi$
$883$	−17.3903	−	15.0687i	−0.585229	−	0.507104i	−0.896397	+	0.443251i	$0.853825\pi$
$884$	21.7937	−	9.46252i	0.733002	−	0.318259i
$885$		0			0
$886$	18.3757	+	16.2271i	0.617342	+	0.545159i
$887$	−10.8614	−	16.9006i	−0.364689	−	0.567468i	0.609616	−	0.792697i	$-0.291323\pi$
$887$	−10.8614	−	16.9006i	−0.364689	−	0.567468i	−0.974306	+	0.225229i	$0.927687\pi$
$888$		0			0
$889$	−7.85336	−	3.58651i	−0.263393	−	0.120288i
$890$	2.53483	+	18.8871i	0.0849678	+	0.633095i
$891$		0			0
$892$	14.6700	+	23.7977i	0.491188	+	0.796805i
$893$	−1.12341	+	3.82598i	−0.0375934	+	0.128031i
$894$		0			0
$895$	−0.556486	+	3.87044i	−0.0186013	+	0.129375i
$896$	−41.2220	+	9.21336i	−1.37713	+	0.307797i
$897$		0			0
$898$	−0.244224	−	0.287255i	−0.00814988	−	0.00958581i
$899$	−87.8675	−	12.6334i	−2.93054	−	0.421349i
$900$		0			0
$901$	−2.62118	−	0.769648i	−0.0873242	−	0.0256407i
$902$	−0.299713	+	1.95416i	−0.00997937	+	0.0650663i
$903$		0			0
$904$	−0.820437	+	29.1267i	−0.0272873	+	0.968740i
$905$	19.2399	−	42.1296i	0.639557	−	1.40043i
$906$		0			0
$907$	−3.20468	+	2.05952i	−0.106410	+	0.0683853i	−0.592763	−	0.805377i	$-0.701963\pi$
$907$	−3.20468	+	2.05952i	−0.106410	+	0.0683853i	0.486354	+	0.873762i	$0.338327\pi$
$908$	−56.5125	−	1.06107i	−1.87543	−	0.0352128i
$909$		0			0
$910$	−10.8738	+	35.7867i	−0.360464	+	1.18632i
$911$	13.7808	−	15.9039i	0.456580	−	0.526921i	−0.480050	−	0.877241i	$-0.659382\pi$
$911$	13.7808	−	15.9039i	0.456580	−	0.526921i	0.936630	+	0.350320i	$0.113927\pi$
$912$		0			0
$913$	−5.18388	−	3.33148i	−0.171561	−	0.110256i
$914$	22.5990	−	34.4495i	0.747510	−	1.13949i
$915$		0			0
$916$	19.0417	+	9.13187i	0.629155	+	0.301725i
$917$	−42.0546	+	19.2057i	−1.38877	+	0.634228i
$918$		0			0
$919$	5.41672			0.178681			0.0893406	−	0.996001i	$-0.471524\pi$
$919$	5.41672			0.178681			0.0893406	+	0.996001i	$0.471524\pi$
$920$	27.7083	+	10.7617i	0.913515	+	0.354802i
$921$		0			0
$922$	10.6624	−	6.71175i	0.351148	−	0.221040i
$923$	−26.9316	+	12.2992i	−0.886464	+	0.404834i
$924$		0			0
$925$	−0.925343	+	0.801814i	−0.0304251	+	0.0263635i
$926$	8.60323	−	13.1146i	0.282720	−	0.430971i
$927$		0			0
$928$	−50.2773	−	2.36145i	−1.65043	−	0.0775184i
$929$	7.06195	−	8.14992i	0.231695	−	0.267390i	−0.627983	−	0.778227i	$-0.716119\pi$
$929$	7.06195	−	8.14992i	0.231695	−	0.267390i	0.859677	+	0.510837i	$0.170665\pi$
$930$		0			0
$931$	1.73906	+	12.0954i	0.0569953	+	0.396411i
$932$	−18.1829	−	0.341398i	−0.595600	−	0.0111829i
$933$		0			0
$934$	48.8658	+	0.458707i	1.59894	+	0.0150094i
$935$	3.82625	−	8.37832i	0.125132	−	0.274000i
$936$		0			0
$937$	10.1361	+	34.5205i	0.331133	+	1.12773i	0.941891	+	0.335917i	$0.109046\pi$
$937$	10.1361	+	34.5205i	0.331133	+	1.12773i	−0.610759	+	0.791817i	$0.709136\pi$
$938$	8.17276	−	53.2870i	0.266850	−	1.73988i
$939$		0			0
$940$	−9.57198	+	2.61644i	−0.312203	+	0.0853388i
$941$	38.2159	+	5.49462i	1.24580	+	0.179120i	0.733503	−	0.679687i	$-0.237884\pi$
$941$	38.2159	+	5.49462i	1.24580	+	0.179120i	0.512301	+	0.858806i	$0.328793\pi$
$942$		0			0
$943$	5.18533	+	2.73323i	0.168858	+	0.0890063i
$944$	−11.8012	+	35.2397i	−0.384098	+	1.14695i
$945$		0			0
$946$	1.89658	−	4.05184i	0.0616630	−	0.131737i
$947$	14.4334	−	49.1557i	0.469023	−	1.59735i	−0.297229	−	0.954806i	$-0.596062\pi$
$947$	14.4334	−	49.1557i	0.469023	−	1.59735i	0.766252	−	0.642540i	$-0.222119\pi$
$948$		0			0
$949$	13.7785	−	4.04572i	0.447268	−	0.131330i
$950$	0.0656054	+	0.488826i	0.00212852	+	0.0158596i
$951$		0			0
$952$	38.2399	+	6.60194i	1.23936	+	0.213970i
$953$	11.8788	+	18.4837i	0.384790	+	0.598746i	0.978578	−	0.205876i	$-0.0660044\pi$
$953$	11.8788	+	18.4837i	0.384790	+	0.598746i	−0.593788	+	0.804622i	$0.702368\pi$
$954$		0			0
$955$	45.6830	−	6.56823i	1.47827	−	0.212543i
$956$	9.55341	−	4.14795i	0.308979	−	0.134154i
$957$		0			0
$958$	39.6532	−	11.2400i	1.28114	−	0.363148i
$959$	−19.2502	+	29.9540i	−0.621623	+	0.967264i
$960$		0			0
$961$	44.8832	+	51.7980i	1.44785	+	1.67090i
$962$	25.8216	−	11.5007i	0.832523	−	0.370796i
$963$		0			0
$964$	9.06320	−	28.8514i	0.291906	−	0.929240i
$965$			2.02860i			0.0653031i
$966$		0			0
$967$			57.4779i			1.84836i	0.381952	+	0.924182i	$0.375252\pi$
$967$			57.4779i			1.84836i	−0.381952	+	0.924182i	$0.624748\pi$
$968$	−10.6809	−	25.2460i	−0.343299	−	0.811438i
$969$		0			0
$970$	−10.0781	−	22.6277i	−0.323588	−	0.726531i
$971$	14.7913	+	17.0701i	0.474675	+	0.547804i	0.941706	−	0.336437i	$-0.109222\pi$
$971$	14.7913	+	17.0701i	0.474675	+	0.547804i	−0.467031	+	0.884241i	$0.654676\pi$
$972$		0			0
$973$	29.9163	−	46.5506i	0.959072	−	1.49234i
$974$	7.44693	+	26.2717i	0.238615	+	0.841800i
$975$		0			0
$976$	3.51937	+	13.8958i	0.112652	+	0.444794i
$977$	−11.7808	+	1.69383i	−0.376903	+	0.0541904i	−0.328163	−	0.944621i	$-0.606430\pi$
$977$	−11.7808	+	1.69383i	−0.376903	+	0.0541904i	−0.0487397	+	0.998812i	$0.515520\pi$
$978$		0			0
$979$	3.80247	+	5.91676i	0.121528	+	0.189101i
$980$	−23.3519	+	19.4792i	−0.745949	+	0.622239i
$981$		0			0
$982$	−15.0169	+	2.01543i	−0.479210	+	0.0643148i
$983$	−36.5695	+	10.7378i	−1.16639	+	0.342482i	−0.806911	−	0.590673i	$-0.798862\pi$
$983$	−36.5695	+	10.7378i	−1.16639	+	0.342482i	−0.359475	+	0.933155i	$0.617044\pi$
$984$		0			0
$985$	−5.26283	+	17.9236i	−0.167688	+	0.571092i
$986$	41.8805	+	19.6033i	1.33375	+	0.624297i
$987$		0			0
$988$	1.83174	−	11.2381i	0.0582754	−	0.357531i
$989$	−9.51601	−	9.24027i	−0.302592	−	0.293823i
$990$		0			0
$991$	−11.4588	−	1.64753i	−0.364002	−	0.0523356i	−0.0421126	−	0.999113i	$-0.513409\pi$
$991$	−11.4588	−	1.64753i	−0.364002	−	0.0523356i	−0.321889	+	0.946777i	$0.604318\pi$
$992$	40.8719	+	38.9194i	1.29769	+	1.23569i
$993$		0			0
$994$	−47.7978	−	7.33087i	−1.51606	−	0.232521i
$995$	7.33632	+	24.9852i	0.232577	+	0.792085i
$996$		0			0
$997$	16.0331	−	35.1076i	0.507773	−	1.11187i	−0.466091	−	0.884737i	$-0.654338\pi$
$997$	16.0331	−	35.1076i	0.507773	−	1.11187i	0.973864	−	0.227132i	$-0.0729348\pi$
$998$	−0.121516	+	12.9450i	−0.00384651	+	0.409767i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.u.a.199.8		100
3.2	odd	2		92.2.h.a.15.3	✓	100
4.3	odd	2	inner	828.2.u.a.199.4		100
12.11	even	2		92.2.h.a.15.7	yes	100
23.20	odd	22	inner	828.2.u.a.595.4		100
69.20	even	22		92.2.h.a.43.7	yes	100
92.43	even	22	inner	828.2.u.a.595.8		100
276.227	odd	22		92.2.h.a.43.3	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.h.a.15.3	✓	100	3.2	odd	2
92.2.h.a.15.7	yes	100	12.11	even	2
92.2.h.a.43.3	yes	100	276.227	odd	22
92.2.h.a.43.7	yes	100	69.20	even	22
828.2.u.a.199.4		100	4.3	odd	2	inner
828.2.u.a.199.8		100	1.1	even	1	trivial
828.2.u.a.595.4		100	23.20	odd	22	inner
828.2.u.a.595.8		100	92.43	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19684 - 0.753380i) q^{2} +(0.864836 - 1.80335i) q^{4} +(-1.65610 + 1.43502i) q^{5} +(3.14077 + 2.01845i) q^{7} +(-0.323539 - 2.80986i) q^{8} +(-0.900968 + 2.96516i) q^{10} +(0.162776 + 1.13213i) q^{11} +(2.71951 - 1.74772i) q^{13} +(5.27965 + 0.0495605i) q^{14} +(-2.50412 - 3.11920i) q^{16} +(1.03533 + 3.52600i) q^{17} +(1.68979 + 0.496168i) q^{19} +(1.15559 + 4.22759i) q^{20} +(1.04775 + 1.23235i) q^{22} +(4.46833 - 1.74184i) q^{23} +(-0.0281822 + 0.196011i) q^{25} +(1.93811 - 4.14056i) q^{26} +(6.35622 - 3.91827i) q^{28} +(8.53724 - 2.50676i) q^{29} +(-9.07531 - 4.14456i) q^{31} +(-5.34696 - 1.84662i) q^{32} +(3.89553 + 3.44005i) q^{34} +(-8.09797 + 1.16431i) q^{35} +(4.67281 + 4.04902i) q^{37} +(2.39621 - 0.679225i) q^{38} +(4.56803 + 4.18914i) q^{40} +(0.800388 + 0.923697i) q^{41} +(-1.14894 - 2.51582i) q^{43} +(2.18241 + 0.685568i) q^{44} +(4.03559 - 5.45106i) q^{46} +2.26417i q^{47} +(2.88240 + 6.31158i) q^{49} +(0.113942 + 0.255825i) q^{50} +(-0.799821 - 6.41571i) q^{52} +(-0.401905 + 0.625377i) q^{53} +(-1.89421 - 1.64135i) q^{55} +(4.65541 - 9.47819i) q^{56} +(8.32913 - 9.43197i) q^{58} +(-5.02299 - 7.81592i) q^{59} +(-3.25979 - 1.48870i) q^{61} +(-13.9841 + 1.87681i) q^{62} +(-7.79064 + 1.81820i) q^{64} +(-1.99577 + 6.79697i) q^{65} +(1.45310 - 10.1065i) q^{67} +(7.25398 + 1.18236i) q^{68} +(-8.81478 + 7.49435i) q^{70} +(-9.06545 - 1.30341i) q^{71} +(4.26223 + 1.25150i) q^{73} +(8.64304 + 1.32560i) q^{74} +(2.35616 - 2.61818i) q^{76} +(-1.77392 + 3.88434i) q^{77} +(-13.6810 + 8.79222i) q^{79} +(8.62320 + 1.57225i) q^{80} +(1.65383 + 0.502518i) q^{82} +(-3.52806 + 4.07160i) q^{83} +(-6.77449 - 4.35370i) q^{85} +(-3.27047 - 2.14544i) q^{86} +(3.12848 - 0.823669i) q^{88} +(5.59347 - 2.55445i) q^{89} +12.0691 q^{91} +(0.723225 - 9.56436i) q^{92} +(1.70578 + 2.70984i) q^{94} +(-3.51049 + 1.60318i) q^{95} +(-6.04072 + 5.23431i) q^{97} +(8.20478 + 5.38238i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 7 q^{2} - 11 q^{4} + 22 q^{5} + 10 q^{8} - 11 q^{10} - 18 q^{13} + 11 q^{14} + 5 q^{16} + 22 q^{17} + 11 q^{20} - 16 q^{25} - 12 q^{26} - 11 q^{28} + 42 q^{29} + 27 q^{32} + 11 q^{34} - 22 q^{37}+ \cdots + 71 q^{98}+O(q^{100}) \) 100 * q + 7 * q^2 - 11 * q^4 + 22 * q^5 + 10 * q^8 - 11 * q^10 - 18 * q^13 + 11 * q^14 + 5 * q^16 + 22 * q^17 + 11 * q^20 - 16 * q^25 - 12 * q^26 - 11 * q^28 + 42 * q^29 + 27 * q^32 + 11 * q^34 - 22 * q^37 - 44 * q^38 + 77 * q^40 + 10 * q^41 - 66 * q^44 + 65 * q^46 - 8 * q^49 - 30 * q^50 + 96 * q^52 + 22 * q^53 - 44 * q^56 + 79 * q^58 - 22 * q^61 + 36 * q^62 + 10 * q^64 + 22 * q^65 + 34 * q^70 - 18 * q^73 + 22 * q^74 - 66 * q^76 - 122 * q^77 + 110 * q^80 - 122 * q^82 + 54 * q^85 + 121 * q^86 - 99 * q^88 - 22 * q^89 + 86 * q^92 - 61 * q^94 + 22 * q^97 + 71 * q^98

Introduction

L-functions

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