LMFDB - Embedded newform 819.2.et.c.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.3
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09987 - 1.09987i) q^{2} +0.419447i q^{4} +(-0.745735 - 2.78312i) q^{5} +(-1.80794 - 1.93167i) q^{7} +(-1.73841 + 1.73841i) q^{8} +O(q^{10})$	\(q+(-1.09987 - 1.09987i) q^{2} +0.419447i q^{4} +(-0.745735 - 2.78312i) q^{5} +(-1.80794 - 1.93167i) q^{7} +(-1.73841 + 1.73841i) q^{8} +(-2.24087 + 3.88130i) q^{10} +(-1.41711 - 5.28871i) q^{11} +(-0.662549 - 3.54415i) q^{13} +(-0.136094 + 4.11310i) q^{14} +4.66296 q^{16} +4.36465 q^{17} +(-1.39486 - 0.373751i) q^{19} +(1.16737 - 0.312796i) q^{20} +(-4.25828 + 7.37555i) q^{22} +8.37225i q^{23} +(-2.85951 + 1.65094i) q^{25} +(-3.16940 + 4.62684i) q^{26} +(0.810234 - 0.758334i) q^{28} +(-0.882488 - 1.52851i) q^{29} +(0.770818 + 0.206540i) q^{31} +(-1.65185 - 1.65185i) q^{32} +(-4.80057 - 4.80057i) q^{34} +(-4.02784 + 6.47222i) q^{35} +(3.86358 - 3.86358i) q^{37} +(1.12309 + 1.94525i) q^{38} +(6.13459 + 3.54181i) q^{40} +(-3.88124 - 1.03997i) q^{41} +(-5.58033 - 3.22180i) q^{43} +(2.21833 - 0.594400i) q^{44} +(9.20842 - 9.20842i) q^{46} +(8.52304 - 2.28374i) q^{47} +(-0.462723 + 6.98469i) q^{49} +(4.96092 + 1.32927i) q^{50} +(1.48658 - 0.277904i) q^{52} +(-0.139208 - 0.241116i) q^{53} +(-13.6623 + 7.88795i) q^{55} +(6.50098 + 0.215103i) q^{56} +(-0.710548 + 2.65180i) q^{58} +(5.16369 + 5.16369i) q^{59} +(4.10703 - 2.37119i) q^{61} +(-0.620634 - 1.07497i) q^{62} -5.69226i q^{64} +(-9.36972 + 4.48695i) q^{65} +(1.87565 - 0.502580i) q^{67} +1.83074i q^{68} +(11.5487 - 2.68852i) q^{70} +(-11.3490 + 3.04095i) q^{71} +(-3.72736 + 13.9107i) q^{73} -8.49891 q^{74} +(0.156769 - 0.585069i) q^{76} +(-7.65402 + 12.2990i) q^{77} +(-0.431242 + 0.746933i) q^{79} +(-3.47733 - 12.9776i) q^{80} +(3.12503 + 5.41271i) q^{82} +(-4.29551 + 4.29551i) q^{83} +(-3.25487 - 12.1473i) q^{85} +(2.59408 + 9.68124i) q^{86} +(11.6575 + 6.73043i) q^{88} +(-4.21484 - 4.21484i) q^{89} +(-5.64830 + 7.68744i) q^{91} -3.51171 q^{92} +(-11.8861 - 6.86245i) q^{94} +4.16078i q^{95} +(-0.575652 - 2.14836i) q^{97} +(8.19122 - 7.17334i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.09987	−	1.09987i	−0.777729	−	0.777729i	0.201716	−	0.979444i	$-0.435348\pi$
$2$	−1.09987	−	1.09987i	−0.777729	−	0.777729i	−0.979444	+	0.201716i	$0.935348\pi$
$3$		0			0
$3$		0			0
$4$			0.419447i			0.209723i
$5$	−0.745735	−	2.78312i	−0.333503	−	1.24465i	−0.905483	−	0.424382i	$-0.860491\pi$
$5$	−0.745735	−	2.78312i	−0.333503	−	1.24465i	0.571981	−	0.820267i	$-0.306175\pi$
$6$		0			0
$7$	−1.80794	−	1.93167i	−0.683336	−	0.730104i
$7$	−1.80794	−	1.93167i	−0.683336	−	0.730104i
$8$	−1.73841	+	1.73841i	−0.614621	+	0.614621i
$9$		0			0
$10$	−2.24087	+	3.88130i	−0.708624	+	1.22737i
$11$	−1.41711	−	5.28871i	−0.427273	−	1.59461i	−0.758908	−	0.651198i	$-0.774267\pi$
$11$	−1.41711	−	5.28871i	−0.427273	−	1.59461i	0.331635	−	0.943408i	$-0.392400\pi$
$12$		0			0
$13$	−0.662549	−	3.54415i	−0.183758	−	0.982972i
$13$	−0.662549	−	3.54415i	−0.183758	−	0.982972i
$14$	−0.136094	+	4.11310i	−0.0363725	+	1.09927i
$15$		0			0
$16$	4.66296			1.16574
$17$	4.36465			1.05858			0.529292	−	0.848440i	$-0.322458\pi$
$17$	4.36465			1.05858			0.529292	+	0.848440i	$0.322458\pi$
$18$		0			0
$19$	−1.39486	−	0.373751i	−0.320003	−	0.0857444i	0.0952423	−	0.995454i	$-0.469637\pi$
$19$	−1.39486	−	0.373751i	−0.320003	−	0.0857444i	−0.415245	+	0.909710i	$0.636304\pi$
$20$	1.16737	−	0.312796i	0.261032	−	0.0699433i
$21$		0			0
$22$	−4.25828	+	7.37555i	−0.907868	+	1.57247i
$23$			8.37225i			1.74573i	0.487958	+	0.872867i	$0.337742\pi$
$23$			8.37225i			1.74573i	−0.487958	+	0.872867i	$0.662258\pi$
$24$		0			0
$25$	−2.85951	+	1.65094i	−0.571901	+	0.330187i
$26$	−3.16940	+	4.62684i	−0.621571	+	0.907399i
$27$		0			0
$28$	0.810234	−	0.758334i	0.153120	−	0.143312i
$29$	−0.882488	−	1.52851i	−0.163874	−	0.283838i	0.772381	−	0.635160i	$-0.219066\pi$
$29$	−0.882488	−	1.52851i	−0.163874	−	0.283838i	−0.936255	+	0.351322i	$0.885732\pi$
$30$		0			0
$31$	0.770818	+	0.206540i	0.138443	+	0.0370957i	0.327375	−	0.944894i	$-0.393836\pi$
$31$	0.770818	+	0.206540i	0.138443	+	0.0370957i	−0.188932	+	0.981990i	$0.560503\pi$
$32$	−1.65185	−	1.65185i	−0.292008	−	0.292008i
$33$		0			0
$34$	−4.80057	−	4.80057i	−0.823290	−	0.823290i
$35$	−4.02784	+	6.47222i	−0.680829	+	1.09401i
$36$		0			0
$37$	3.86358	−	3.86358i	0.635169	−	0.635169i	−0.314191	−	0.949360i	$-0.601733\pi$
$37$	3.86358	−	3.86358i	0.635169	−	0.635169i	0.949360	+	0.314191i	$0.101733\pi$
$38$	1.12309	+	1.94525i	0.182189	+	0.315561i
$39$		0			0
$40$	6.13459	+	3.54181i	0.969965	+	0.560009i
$41$	−3.88124	−	1.03997i	−0.606147	−	0.162417i	−0.0573248	−	0.998356i	$-0.518257\pi$
$41$	−3.88124	−	1.03997i	−0.606147	−	0.162417i	−0.548823	+	0.835939i	$0.684924\pi$
$42$		0			0
$43$	−5.58033	−	3.22180i	−0.850992	−	0.491320i	0.00999354	−	0.999950i	$-0.496819\pi$
$43$	−5.58033	−	3.22180i	−0.850992	−	0.491320i	−0.860985	+	0.508630i	$0.830152\pi$
$44$	2.21833	−	0.594400i	0.334426	−	0.0896092i
$45$		0			0
$46$	9.20842	−	9.20842i	1.35771	−	1.35771i
$47$	8.52304	−	2.28374i	1.24321	−	0.333118i	0.423502	−	0.905895i	$-0.360800\pi$
$47$	8.52304	−	2.28374i	1.24321	−	0.333118i	0.819711	+	0.572777i	$0.194134\pi$
$48$		0			0
$49$	−0.462723	+	6.98469i	−0.0661033	+	0.997813i
$50$	4.96092	+	1.32927i	0.701580	+	0.187988i
$51$		0			0
$52$	1.48658	−	0.277904i	0.206152	−	0.0385384i
$53$	−0.139208	−	0.241116i	−0.0191217	−	0.0331198i	0.856306	−	0.516468i	$-0.172754\pi$
$53$	−0.139208	−	0.241116i	−0.0191217	−	0.0331198i	−0.875428	+	0.483349i	$0.839420\pi$
$54$		0			0
$55$	−13.6623	+	7.88795i	−1.84223	+	1.06361i
$56$	6.50098	+	0.215103i	0.868729	+	0.0287444i
$57$		0			0
$58$	−0.710548	+	2.65180i	−0.0932995	+	0.348198i
$59$	5.16369	+	5.16369i	0.672255	+	0.672255i	0.958235	−	0.285980i	$-0.0923192\pi$
$59$	5.16369	+	5.16369i	0.672255	+	0.672255i	−0.285980	+	0.958235i	$0.592319\pi$
$60$		0			0
$61$	4.10703	−	2.37119i	0.525851	−	0.303600i	−0.213474	−	0.976949i	$-0.568478\pi$
$61$	4.10703	−	2.37119i	0.525851	−	0.303600i	0.739325	+	0.673348i	$0.235145\pi$
$62$	−0.620634	−	1.07497i	−0.0788207	−	0.136521i
$63$		0			0
$64$		−	5.69226i		−	0.711533i
$65$	−9.36972	+	4.48695i	−1.16217	+	0.556538i
$66$		0			0
$67$	1.87565	−	0.502580i	0.229148	−	0.0613999i	−0.142418	−	0.989807i	$-0.545488\pi$
$67$	1.87565	−	0.502580i	0.229148	−	0.0613999i	0.371566	+	0.928407i	$0.378821\pi$
$68$			1.83074i			0.222010i
$69$		0			0
$70$	11.5487	−	2.68852i	1.38034	−	0.321339i
$71$	−11.3490	+	3.04095i	−1.34688	+	0.360894i	−0.858981	−	0.512008i	$-0.828902\pi$
$71$	−11.3490	+	3.04095i	−1.34688	+	0.360894i	−0.487895	+	0.872902i	$0.662235\pi$
$72$		0			0
$73$	−3.72736	+	13.9107i	−0.436254	+	1.62812i	0.301793	+	0.953373i	$0.402415\pi$
$73$	−3.72736	+	13.9107i	−0.436254	+	1.62812i	−0.738047	+	0.674749i	$0.764252\pi$
$74$	−8.49891			−0.987978
$75$		0			0
$76$	0.156769	−	0.585069i	0.0179826	−	0.0671121i
$77$	−7.65402	+	12.2990i	−0.872256	+	1.40161i
$78$		0			0
$79$	−0.431242	+	0.746933i	−0.0485185	+	0.0840365i	−0.889265	−	0.457393i	$-0.848783\pi$
$79$	−0.431242	+	0.746933i	−0.0485185	+	0.0840365i	0.840746	+	0.541429i	$0.182117\pi$
$80$	−3.47733	−	12.9776i	−0.388777	−	1.45094i
$81$		0			0
$82$	3.12503	+	5.41271i	0.345102	+	0.597734i
$83$	−4.29551	+	4.29551i	−0.471494	+	0.471494i	−0.902398	−	0.430904i	$-0.858195\pi$
$83$	−4.29551	+	4.29551i	−0.471494	+	0.471494i	0.430904	+	0.902398i	$0.358195\pi$
$84$		0			0
$85$	−3.25487	−	12.1473i	−0.353040	−	1.31756i
$86$	2.59408	+	9.68124i	0.279727	+	1.04395i
$87$		0			0
$88$	11.6575	+	6.73043i	1.24269	+	0.717467i
$89$	−4.21484	−	4.21484i	−0.446772	−	0.446772i	0.447508	−	0.894280i	$-0.352312\pi$
$89$	−4.21484	−	4.21484i	−0.446772	−	0.446772i	−0.894280	+	0.447508i	$0.852312\pi$
$90$		0			0
$91$	−5.64830	+	7.68744i	−0.592103	+	0.805862i
$92$	−3.51171			−0.366121
$93$		0			0
$94$	−11.8861	−	6.86245i	−1.22596	−	0.707807i
$95$			4.16078i			0.426887i
$96$		0			0
$97$	−0.575652	−	2.14836i	−0.0584486	−	0.218133i	0.930524	−	0.366230i	$-0.119352\pi$
$97$	−0.575652	−	2.14836i	−0.0584486	−	0.218133i	−0.988973	+	0.148097i	$0.952685\pi$
$98$	8.19122	−	7.17334i	0.827438	−	0.724617i
$99$		0			0
$100$	−0.692481	−	1.19941i	−0.0692481	−	0.119941i
$101$	7.92218	−	13.7216i	0.788287	−	1.36535i	−0.138729	−	0.990330i	$-0.544302\pi$
$101$	7.92218	−	13.7216i	0.788287	−	1.36535i	0.927016	−	0.375023i	$-0.122365\pi$
$102$		0			0
$103$	−5.32654	+	9.22583i	−0.524839	+	0.909048i	0.474742	+	0.880125i	$0.342541\pi$
$103$	−5.32654	+	9.22583i	−0.524839	+	0.909048i	−0.999582	+	0.0289234i	$0.990792\pi$
$104$	7.31297	+	5.00941i	0.717096	+	0.491213i
$105$		0			0
$106$	−0.112085	+	0.418309i	−0.0108867	+	0.0406297i
$107$	14.5513			1.40672			0.703361	−	0.710833i	$-0.251682\pi$
$107$	14.5513			1.40672			0.703361	+	0.710833i	$0.251682\pi$
$108$		0			0
$109$	−2.22729	+	8.31237i	−0.213336	+	0.796181i	0.773410	+	0.633906i	$0.218550\pi$
$109$	−2.22729	+	8.31237i	−0.213336	+	0.796181i	−0.986746	+	0.162274i	$0.948117\pi$
$110$	23.7026	+	6.35109i	2.25995	+	0.605553i
$111$		0			0
$112$	−8.43034	−	9.00731i	−0.796592	−	0.851111i
$113$	6.81406	−	11.8023i	0.641013	−	1.11027i	−0.344195	−	0.938898i	$-0.611848\pi$
$113$	6.81406	−	11.8023i	0.641013	−	1.11027i	0.985207	−	0.171368i	$-0.0548187\pi$
$114$		0			0
$115$	23.3010	−	6.24347i	2.17283	−	0.582207i
$116$	0.641131	−	0.370157i	0.0595275	−	0.0343682i
$117$		0			0
$118$		−	11.3588i		−	1.04566i
$119$	−7.89102	−	8.43108i	−0.723368	−	0.772876i
$120$		0			0
$121$	−16.4360	+	9.48931i	−1.49418	+	0.862665i
$122$	−7.12523	−	1.90920i	−0.645088	−	0.172851i
$123$		0			0
$124$	−0.0866325	+	0.323317i	−0.00777983	+	0.0290347i
$125$	−3.45974	−	3.45974i	−0.309448	−	0.309448i
$126$		0			0
$127$	3.01715	−	1.74195i	0.267728	−	0.154573i	−0.360126	−	0.932904i	$-0.617266\pi$
$127$	3.01715	−	1.74195i	0.267728	−	0.154573i	0.627855	+	0.778330i	$0.283933\pi$
$128$	−9.56447	+	9.56447i	−0.845388	+	0.845388i
$129$		0			0
$130$	15.2406	+	5.37043i	1.33669	+	0.471018i
$131$	5.01539	+	2.89564i	0.438197	+	0.252993i	0.702832	−	0.711356i	$-0.251918\pi$
$131$	5.01539	+	2.89564i	0.438197	+	0.252993i	−0.264636	+	0.964348i	$0.585252\pi$
$132$		0			0
$133$	1.79985	+	3.37013i	0.156067	+	0.292227i
$134$	−2.61576	−	1.51021i	−0.225967	−	0.130462i
$135$		0			0
$136$	−7.58755	+	7.58755i	−0.650627	+	0.650627i
$137$	2.42365	−	2.42365i	0.207067	−	0.207067i	−0.595953	−	0.803019i	$-0.703226\pi$
$137$	2.42365	−	2.42365i	0.207067	−	0.207067i	0.803019	+	0.595953i	$0.203226\pi$
$138$		0			0
$139$	−16.1580	−	9.32882i	−1.37050	−	0.791260i	−0.379512	−	0.925187i	$-0.623908\pi$
$139$	−16.1580	−	9.32882i	−1.37050	−	0.791260i	−0.990991	+	0.133927i	$0.957241\pi$
$140$	−2.71475	−	1.68946i	−0.229439	−	0.142786i
$141$		0			0
$142$	15.8271	+	9.13779i	1.32818	+	0.766826i
$143$	−17.8051	+	8.52647i	−1.48894	+	0.713019i
$144$		0			0
$145$	−3.59594	+	3.59594i	−0.298626	+	0.298626i
$146$	19.3996	−	11.2004i	1.60552	−	0.926950i
$147$		0			0
$148$	1.62057	+	1.62057i	0.133210	+	0.133210i
$149$	3.69990	−	13.8082i	0.303108	−	1.13121i	−0.631454	−	0.775413i	$-0.717542\pi$
$149$	3.69990	−	13.8082i	0.303108	−	1.13121i	0.934562	−	0.355801i	$-0.115792\pi$
$150$		0			0
$151$	−0.0198676	−	0.00532352i	−0.00161681	−	0.000433222i	0.258011	−	0.966142i	$-0.416933\pi$
$151$	−0.0198676	−	0.00532352i	−0.00161681	−	0.000433222i	−0.259627	+	0.965709i	$0.583600\pi$
$152$	3.07457	−	1.77510i	0.249381	−	0.143980i
$153$		0			0
$154$	21.9459	−	5.10894i	1.76845	−	0.411690i
$155$		−	2.29930i		−	0.184684i
$156$		0			0
$157$	5.26575	−	3.04018i	0.420253	−	0.242633i	−0.274933	−	0.961463i	$-0.588656\pi$
$157$	5.26575	−	3.04018i	0.420253	−	0.242633i	0.695185	+	0.718830i	$0.255322\pi$
$158$	1.29584	−	0.347220i	0.103092	−	0.0276234i
$159$		0			0
$160$	−3.36545	+	5.82913i	−0.266062	+	0.460833i
$161$	16.1724	−	15.1365i	1.27457	−	1.19292i
$162$		0			0
$163$	13.7573	+	3.68627i	1.07756	+	0.288731i	0.753595	−	0.657339i	$-0.228318\pi$
$163$	13.7573	+	3.68627i	1.07756	+	0.288731i	0.323963	+	0.946070i	$0.394985\pi$
$164$	0.436214	−	1.62797i	0.0340626	−	0.127123i
$165$		0			0
$166$	9.44905			0.733388
$167$	0.579671	−	2.16336i	0.0448563	−	0.167406i	−0.939864	−	0.341548i	$-0.889049\pi$
$167$	0.579671	−	2.16336i	0.0448563	−	0.167406i	0.984720	+	0.174142i	$0.0557153\pi$
$168$		0			0
$169$	−12.1221	+	4.69635i	−0.932466	+	0.361258i
$170$	−9.78060	+	16.9405i	−0.750138	+	1.29928i
$171$		0			0
$172$	1.35138	−	2.34065i	0.103041	−	0.178473i
$173$	1.62494	+	2.81448i	0.123542	+	0.213981i	0.921162	−	0.389179i	$-0.127241\pi$
$173$	1.62494	+	2.81448i	0.123542	+	0.213981i	−0.797620	+	0.603160i	$0.793908\pi$
$174$		0			0
$175$	8.35888	+	2.53884i	0.631872	+	0.191918i
$176$	−6.60790	−	24.6610i	−0.498089	−	1.85889i
$177$		0			0
$178$			9.27158i			0.694934i
$179$	−18.3339	−	10.5851i	−1.37034	−	0.791165i	−0.379367	−	0.925246i	$-0.623858\pi$
$179$	−18.3339	−	10.5851i	−1.37034	−	0.791165i	−0.990970	+	0.134081i	$0.957192\pi$
$180$		0			0
$181$	18.5217			1.37671			0.688353	−	0.725376i	$-0.258334\pi$
$181$	18.5217			1.37671			0.688353	+	0.725376i	$0.258334\pi$
$182$	14.6676	−	2.24279i	1.08724	−	0.166247i
$183$		0			0
$184$	−14.5544	−	14.5544i	−1.07296	−	1.07296i
$185$	−13.6340	−	7.87160i	−1.00239	−	0.578732i
$186$		0			0
$187$	−6.18517	−	23.0834i	−0.452304	−	1.68802i
$188$	0.957909	+	3.57496i	0.0698627	+	0.260731i
$189$		0			0
$190$	4.57633	−	4.57633i	0.332002	−	0.332002i
$191$	−13.7090	−	23.7447i	−0.991948	−	1.71810i	−0.605655	−	0.795727i	$-0.707089\pi$
$191$	−13.7090	−	23.7447i	−0.991948	−	1.71810i	−0.386292	−	0.922376i	$-0.626244\pi$
$192$		0			0
$193$	−4.93597	−	18.4213i	−0.355299	−	1.32599i	−0.880108	−	0.474774i	$-0.842530\pi$
$193$	−4.93597	−	18.4213i	−0.355299	−	1.32599i	0.524809	−	0.851220i	$-0.324137\pi$
$194$	−1.72978	+	2.99607i	−0.124191	+	0.215105i
$195$		0			0
$196$	−2.92971	−	0.194088i	−0.209265	−	0.0138634i
$197$	−1.20155	+	4.48424i	−0.0856068	+	0.319489i	−0.995428	−	0.0955106i	$-0.969552\pi$
$197$	−1.20155	+	4.48424i	−0.0856068	+	0.319489i	0.909822	+	0.415000i	$0.136218\pi$
$198$		0			0
$199$	−0.447121			−0.0316956			−0.0158478	−	0.999874i	$-0.505045\pi$
$199$	−0.447121			−0.0316956			−0.0158478	+	0.999874i	$0.505045\pi$
$200$	2.10099	−	7.84100i	0.148562	−	0.554442i
$201$		0			0
$202$	−23.8055	+	6.37866i	−1.67495	+	0.448801i
$203$	−1.35711	+	4.46814i	−0.0952502	+	0.313602i
$204$		0			0
$205$			11.5775i			0.808607i
$206$	16.0058	−	4.28873i	1.11518	−	0.298810i
$207$		0			0
$208$	−3.08944	−	16.5262i	−0.214214	−	1.14589i
$209$			7.90665i			0.546914i
$210$		0			0
$211$	−14.3795	−	24.9060i	−0.989924	−	1.71460i	−0.617592	−	0.786498i	$-0.711892\pi$
$211$	−14.3795	−	24.9060i	−0.989924	−	1.71460i	−0.372331	−	0.928100i	$-0.621442\pi$
$212$	0.101135	−	0.0583905i	0.00694600	−	0.00401028i
$213$		0			0
$214$	−16.0045	−	16.0045i	−1.09405	−	1.09405i
$215$	−4.80522	+	17.9333i	−0.327713	+	1.22304i
$216$		0			0
$217$	−0.994622	−	1.86238i	−0.0675194	−	0.126427i
$218$	11.5923	−	6.69282i	0.785130	−	0.453295i
$219$		0			0
$220$	−3.30857	−	5.73062i	−0.223064	−	0.386358i
$221$	−2.89179	−	15.4690i	−0.194523	−	1.04056i
$222$		0			0
$223$	14.0758	+	3.77160i	0.942586	+	0.252565i	0.697213	−	0.716864i	$-0.254423\pi$
$223$	14.0758	+	3.77160i	0.942586	+	0.252565i	0.245372	+	0.969429i	$0.421090\pi$
$224$	−0.204392	+	6.17727i	−0.0136565	+	0.412736i
$225$		0			0
$226$	−20.4756	+	5.48643i	−1.36202	+	0.364952i
$227$	−12.6759	+	12.6759i	−0.841326	+	0.841326i	−0.989031	−	0.147705i	$-0.952811\pi$
$227$	−12.6759	+	12.6759i	−0.841326	+	0.841326i	0.147705	+	0.989031i	$0.452811\pi$
$228$		0			0
$229$	−6.61427	+	1.77229i	−0.437083	+	0.117116i	−0.470649	−	0.882320i	$-0.655980\pi$
$229$	−6.61427	+	1.77229i	−0.437083	+	0.117116i	0.0335661	+	0.999437i	$0.489314\pi$
$230$	−32.4952	−	18.7611i	−2.14267	−	1.23707i
$231$		0			0
$232$	4.19131	+	1.12306i	0.275173	+	0.0737324i
$233$	−6.74247	−	3.89276i	−0.441714	−	0.255023i	0.262611	−	0.964902i	$-0.415417\pi$
$233$	−6.74247	−	3.89276i	−0.441714	−	0.255023i	−0.704324	+	0.709878i	$0.748750\pi$
$234$		0			0
$235$	−12.7119	−	22.0176i	−0.829230	−	1.43627i
$236$	−2.16589	+	2.16589i	−0.140988	+	0.140988i
$237$		0			0
$238$	−0.594001	+	17.9523i	−0.0385034	+	1.16367i
$239$	2.22428	+	2.22428i	0.143877	+	0.143877i	0.775376	−	0.631499i	$-0.217560\pi$
$239$	2.22428	+	2.22428i	0.143877	+	0.143877i	−0.631499	+	0.775376i	$0.717560\pi$
$240$		0			0
$241$	6.34946	+	6.34946i	0.409005	+	0.409005i	0.881391	−	0.472387i	$-0.156607\pi$
$241$	6.34946	+	6.34946i	0.409005	+	0.409005i	−0.472387	+	0.881391i	$0.656607\pi$
$242$	28.5146	+	7.64045i	1.83298	+	0.491147i
$243$		0			0
$244$	0.994590	+	1.72268i	0.0636721	+	0.110283i
$245$	19.7843	−	3.92091i	1.26397	−	0.250498i
$246$		0			0
$247$	−0.400470	+	5.19122i	−0.0254813	+	0.330310i
$248$	−1.69905	+	0.980946i	−0.107890	+	0.0622901i
$249$		0			0
$250$			7.61055i			0.481333i
$251$	−12.3486	+	21.3883i	−0.779434	+	1.35002i	0.152835	+	0.988252i	$0.451160\pi$
$251$	−12.3486	+	21.3883i	−0.779434	+	1.35002i	−0.932269	+	0.361767i	$0.882174\pi$
$252$		0			0
$253$	44.2784	−	11.8644i	2.78376	−	0.745905i
$254$	−5.23441	−	1.40256i	−0.328436	−	0.0880042i
$255$		0			0
$256$	9.65491			0.603432
$257$	6.15108			0.383694			0.191847	−	0.981425i	$-0.438552\pi$
$257$	6.15108			0.383694			0.191847	+	0.981425i	$0.438552\pi$
$258$		0			0
$259$	−14.4483	−	0.478063i	−0.897773	−	0.0297054i
$260$	−1.88204	−	3.93010i	−0.116719	−	0.243734i
$261$		0			0
$262$	−2.33146	−	8.70113i	−0.144038	−	0.537558i
$263$	8.57461	−	14.8517i	0.528733	−	0.915792i	−0.470706	−	0.882290i	$-0.656001\pi$
$263$	8.57461	−	14.8517i	0.528733	−	0.915792i	0.999439	−	0.0335020i	$-0.0106660\pi$
$264$		0			0
$265$	−0.567242	+	0.567242i	−0.0348454	+	0.0348454i
$266$	1.72711	−	5.68633i	0.105896	−	0.348651i
$267$		0			0
$268$	0.210806	+	0.786737i	0.0128770	+	0.0480576i
$269$			2.31154i			0.140937i	0.997514	+	0.0704685i	$0.0224494\pi$
$269$			2.31154i			0.140937i	−0.997514	+	0.0704685i	$0.977551\pi$
$270$		0			0
$271$	−4.58217	−	4.58217i	−0.278347	−	0.278347i	0.554102	−	0.832449i	$-0.313062\pi$
$271$	−4.58217	−	4.58217i	−0.278347	−	0.278347i	−0.832449	+	0.554102i	$0.813062\pi$
$272$	20.3522			1.23403
$273$		0			0
$274$	−5.33142			−0.322083
$275$	12.7835	+	12.7835i	0.770877	+	0.770877i
$276$		0			0
$277$		−	24.1768i		−	1.45265i	−0.687354	−	0.726323i	$-0.741228\pi$
$277$		−	24.1768i		−	1.45265i	0.687354	−	0.726323i	$-0.258772\pi$
$278$	7.51123	+	28.0323i	0.450494	+	1.68127i
$279$		0			0
$280$	−4.24934	−	18.2534i	−0.253947	−	1.09085i
$281$	−18.6196	+	18.6196i	−1.11075	+	1.11075i	−0.117703	+	0.993049i	$0.537553\pi$
$281$	−18.6196	+	18.6196i	−1.11075	+	1.11075i	−0.993049	+	0.117703i	$0.962447\pi$
$282$		0			0
$283$	−6.25230	+	10.8293i	−0.371661	+	0.643736i	−0.989821	−	0.142317i	$-0.954545\pi$
$283$	−6.25230	+	10.8293i	−0.371661	+	0.643736i	0.618160	+	0.786052i	$0.287878\pi$
$284$	−1.27552	−	4.76029i	−0.0756880	−	0.282472i
$285$		0			0
$286$	28.9614	+	10.2053i	1.71252	+	0.603454i
$287$	5.00814	+	9.37749i	0.295621	+	0.553536i
$288$		0			0
$289$	2.05017			0.120598
$290$	7.91016			0.464500
$291$		0			0
$292$	−5.83479	−	1.56343i	−0.341455	−	0.0914927i
$293$	0.0851383	−	0.0228127i	0.00497383	−	0.00133274i	−0.256331	−	0.966589i	$-0.582514\pi$
$293$	0.0851383	−	0.0228127i	0.00497383	−	0.00133274i	0.261305	+	0.965256i	$0.415847\pi$
$294$		0			0
$295$	10.5204	−	18.2219i	0.612523	−	1.06092i
$296$			13.4330i			0.780776i
$297$		0			0
$298$	−19.2567	+	11.1179i	−1.11551	+	0.644042i
$299$	29.6725	−	5.54702i	1.71601	−	0.320793i
$300$		0			0
$301$	3.86541	+	16.6042i	0.222799	+	0.957049i
$302$	0.0159967	+	0.0277071i	0.000920507	+	0.00159436i
$303$		0			0
$304$	−6.50417	−	1.74279i	−0.373040	−	0.0999557i
$305$	−9.66207	−	9.66207i	−0.553248	−	0.553248i
$306$		0			0
$307$	−7.58728	−	7.58728i	−0.433029	−	0.433029i	0.456628	−	0.889658i	$-0.349057\pi$
$307$	−7.58728	−	7.58728i	−0.433029	−	0.433029i	−0.889658	+	0.456628i	$0.849057\pi$
$308$	−5.15879	−	3.21045i	−0.293950	−	0.182933i
$309$		0			0
$310$	−2.52894	+	2.52894i	−0.143634	+	0.143634i
$311$	15.1148	+	26.1796i	0.857082	+	1.48451i	0.874700	+	0.484665i	$0.161059\pi$
$311$	15.1148	+	26.1796i	0.857082	+	1.48451i	−0.0176172	+	0.999845i	$0.505608\pi$
$312$		0			0
$313$	24.9891	+	14.4275i	1.41247	+	0.815489i	0.995621	−	0.0934866i	$-0.0298012\pi$
$313$	24.9891	+	14.4275i	1.41247	+	0.815489i	0.416849	+	0.908976i	$0.363135\pi$
$314$	−9.13548	−	2.44784i	−0.515545	−	0.138140i
$315$		0			0
$316$	−0.313299	−	0.180883i	−0.0176244	−	0.0101755i
$317$	−16.2082	+	4.34297i	−0.910343	+	0.243926i	−0.683453	−	0.729995i	$-0.739523\pi$
$317$	−16.2082	+	4.34297i	−0.910343	+	0.243926i	−0.226890	+	0.973920i	$0.572856\pi$
$318$		0			0
$319$	−6.83329	+	6.83329i	−0.382591	+	0.382591i
$320$	−15.8423	+	4.24492i	−0.885609	+	0.237298i
$321$		0			0
$322$	−34.4359	−	1.13941i	−1.91904	−	0.0634968i
$323$	−6.08807	−	1.63129i	−0.338749	−	0.0907676i
$324$		0			0
$325$	7.74574	+	9.04071i	0.429656	+	0.501488i
$326$	−11.0769	−	19.1858i	−0.613493	−	1.06260i
$327$		0			0
$328$	8.55508	−	4.93928i	0.472375	−	0.272726i
$329$	−19.8206	−	12.3349i	−1.09274	−	0.680044i
$330$		0			0
$331$	1.62870	−	6.07840i	0.0895215	−	0.334099i	−0.906610	−	0.421969i	$-0.861339\pi$
$331$	1.62870	−	6.07840i	0.0895215	−	0.334099i	0.996132	+	0.0878697i	$0.0280059\pi$
$332$	−1.80174	−	1.80174i	−0.0988833	−	0.0988833i
$333$		0			0
$334$	−3.01699	+	1.74186i	−0.165083	+	0.0953104i
$335$	−2.79748	−	4.84538i	−0.152843	−	0.264731i
$336$		0			0
$337$			17.1415i			0.933758i	0.884321	+	0.466879i	$0.154622\pi$
$337$			17.1415i			0.933758i	−0.884321	+	0.466879i	$0.845378\pi$
$338$	18.4981	+	8.16734i	1.00617	+	0.444245i
$339$		0			0
$340$	5.09517	−	1.36525i	0.276324	−	0.0740408i
$341$		−	4.36932i		−	0.236612i
$342$		0			0
$343$	14.3287	−	11.7341i	0.773678	−	0.633579i
$344$	15.3017	−	4.10008i	0.825013	−	0.221062i
$345$		0			0
$346$	1.30834	−	4.88281i	0.0703370	−	0.262501i
$347$	−4.22975			−0.227065			−0.113532	−	0.993534i	$-0.536217\pi$
$347$	−4.22975			−0.227065			−0.113532	+	0.993534i	$0.536217\pi$
$348$		0			0
$349$	4.82352	−	18.0016i	0.258197	−	0.963605i	−0.708087	−	0.706125i	$-0.750441\pi$
$349$	4.82352	−	18.0016i	0.258197	−	0.963605i	0.966284	−	0.257479i	$-0.0828919\pi$
$350$	−6.40131	−	11.9861i	−0.342165	−	0.640685i
$351$		0			0
$352$	−6.39530	+	11.0770i	−0.340871	+	0.590405i
$353$	1.15293	+	4.30278i	0.0613641	+	0.229014i	0.989797	−	0.142487i	$-0.0455099\pi$
$353$	1.15293	+	4.30278i	0.0613641	+	0.229014i	−0.928433	+	0.371501i	$0.878843\pi$
$354$		0			0
$355$	16.9267	+	29.3178i	0.898373	+	1.55603i
$356$	1.76790	−	1.76790i	0.0936985	−	0.0936985i
$357$		0			0
$358$	8.52271	+	31.8072i	0.450439	+	1.68106i
$359$	4.24764	+	15.8524i	0.224182	+	0.836657i	0.982731	+	0.185041i	$0.0592420\pi$
$359$	4.24764	+	15.8524i	0.224182	+	0.836657i	−0.758549	+	0.651616i	$0.774091\pi$
$360$		0			0
$361$	−14.6485	−	8.45734i	−0.770976	−	0.445123i
$362$	−20.3715	−	20.3715i	−1.07070	−	1.07070i
$363$		0			0
$364$	−3.22447	−	2.36916i	−0.169008	−	0.124178i
$365$	41.4947			2.17193
$366$		0			0
$367$	−24.1880	−	13.9650i	−1.26260	−	0.728964i	−0.289026	−	0.957321i	$-0.593331\pi$
$367$	−24.1880	−	13.9650i	−1.26260	−	0.728964i	−0.973578	+	0.228357i	$0.926665\pi$
$368$			39.0394i			2.03507i
$369$		0			0
$370$	6.33793	+	23.6535i	0.329493	+	1.22969i
$371$	−0.214077	+	0.704827i	−0.0111143	+	0.0365928i
$372$		0			0
$373$	2.92406	+	5.06463i	0.151402	+	0.262237i	0.931743	−	0.363118i	$-0.118288\pi$
$373$	2.92406	+	5.06463i	0.151402	+	0.262237i	−0.780341	+	0.625354i	$0.784954\pi$
$374$	−18.5859	+	32.1917i	−0.961054	+	1.66459i
$375$		0			0
$376$	−10.8465	+	18.7866i	−0.559364	+	0.968846i
$377$	−4.83260	+	4.14039i	−0.248892	+	0.213241i
$378$		0			0
$379$	−0.411597	+	1.53610i	−0.0211423	+	0.0789043i	−0.975691	−	0.219151i	$-0.929671\pi$
$379$	−0.411597	+	1.53610i	−0.0211423	+	0.0789043i	0.954549	+	0.298055i	$0.0963380\pi$
$380$	−1.74523			−0.0895282
$381$		0			0
$382$	−11.0380	+	41.1943i	−0.564752	+	2.10768i
$383$	13.6049	+	3.64543i	0.695179	+	0.186273i	0.589070	−	0.808082i	$-0.299494\pi$
$383$	13.6049	+	3.64543i	0.695179	+	0.186273i	0.106109	+	0.994355i	$0.466161\pi$
$384$		0			0
$385$	39.9376	+	12.1302i	2.03541	+	0.618214i
$386$	−14.8322	+	25.6901i	−0.754937	+	1.30759i
$387$		0			0
$388$	0.901124	−	0.241455i	0.0457476	−	0.0122580i
$389$	−0.216783	+	0.125160i	−0.0109913	+	0.00634584i	−0.505486	−	0.862835i	$-0.668687\pi$
$389$	−0.216783	+	0.125160i	−0.0109913	+	0.00634584i	0.494494	+	0.869181i	$0.335353\pi$
$390$		0			0
$391$			36.5419i			1.84800i
$392$	−11.3378	−	12.9467i	−0.572648	−	0.653905i
$393$		0			0
$394$	6.25365	−	3.61055i	0.315055	−	0.181897i
$395$	2.40040	+	0.643184i	0.120777	+	0.0323621i
$396$		0			0
$397$	1.74276	−	6.50408i	0.0874668	−	0.326430i	−0.908303	−	0.418313i	$-0.862622\pi$
$397$	1.74276	−	6.50408i	0.0874668	−	0.326430i	0.995770	+	0.0918822i	$0.0292883\pi$
$398$	0.491777	+	0.491777i	0.0246505	+	0.0246505i
$399$		0			0
$400$	−13.3338	+	7.69825i	−0.666688	+	0.384913i
$401$	20.3892	−	20.3892i	1.01819	−	1.01819i	0.0183568	−	0.999831i	$-0.494157\pi$
$401$	20.3892	−	20.3892i	1.01819	−	1.01819i	0.999831	−	0.0183568i	$-0.00584349\pi$
$402$		0			0
$403$	0.221305	−	2.86874i	0.0110240	−	0.142902i
$404$	5.75549	+	3.32294i	0.286347	+	0.165322i
$405$		0			0
$406$	6.40704	−	3.42174i	0.317976	−	0.169818i
$407$	−25.9085	−	14.9583i	−1.28423	−	0.741453i
$408$		0			0
$409$	19.0625	−	19.0625i	0.942582	−	0.942582i	−0.0558573	−	0.998439i	$-0.517789\pi$
$409$	19.0625	−	19.0625i	0.942582	−	0.942582i	0.998439	+	0.0558573i	$0.0177892\pi$
$410$	12.7338	−	12.7338i	0.628877	−	0.628877i
$411$		0			0
$412$	−3.86975	−	2.23420i	−0.190649	−	0.110071i
$413$	0.638932	−	19.3102i	0.0314398	−	0.950192i
$414$		0			0
$415$	15.1582	+	8.75161i	0.744089	+	0.429600i
$416$	−4.75998	+	6.94884i	−0.233377	+	0.340695i
$417$		0			0
$418$	8.69632	−	8.69632i	0.425351	−	0.425351i
$419$	−12.0707	+	6.96900i	−0.589691	+	0.340458i	−0.764975	−	0.644060i	$-0.777249\pi$
$419$	−12.0707	+	6.96900i	−0.589691	+	0.340458i	0.175284	+	0.984518i	$0.443916\pi$
$420$		0			0
$421$	15.9864	+	15.9864i	0.779131	+	0.779131i	0.979683	−	0.200552i	$-0.0642735\pi$
$421$	15.9864	+	15.9864i	0.779131	+	0.779131i	−0.200552	+	0.979683i	$0.564274\pi$
$422$	−11.5778	+	43.2091i	−0.563600	+	2.10338i
$423$		0			0
$424$	0.661159	+	0.177157i	0.0321087	+	0.00860351i
$425$	−12.4807	+	7.20576i	−0.605405	+	0.349531i
$426$		0			0
$427$	−12.0056	−	3.64647i	−0.580993	−	0.176465i
$428$			6.10348i			0.295023i
$429$		0			0
$430$	25.0095	−	14.4393i	1.20607	−	0.696323i
$431$	−3.10956	+	0.833204i	−0.149782	+	0.0401340i	−0.332931	−	0.942951i	$-0.608038\pi$
$431$	−3.10956	+	0.833204i	−0.149782	+	0.0401340i	0.183149	+	0.983085i	$0.441371\pi$
$432$		0			0
$433$	−5.34137	+	9.25152i	−0.256690	+	0.444600i	−0.965353	−	0.260947i	$-0.915965\pi$
$433$	−5.34137	+	9.25152i	−0.256690	+	0.444600i	0.708663	+	0.705547i	$0.249299\pi$
$434$	−0.954423	+	3.14234i	−0.0458138	+	0.150837i
$435$		0			0
$436$	−3.48660	−	0.934231i	−0.166978	−	0.0447416i
$437$	3.12914	−	11.6781i	0.149687	−	0.558639i
$438$		0			0
$439$	14.5610			0.694961			0.347480	−	0.937687i	$-0.387037\pi$
$439$	14.5610			0.694961			0.347480	+	0.937687i	$0.387037\pi$
$440$	10.0382	−	37.4632i	0.478554	−	1.78599i
$441$		0			0
$442$	−13.8333	+	20.1946i	−0.657985	+	0.960557i
$443$	2.49941	−	4.32911i	0.118751	−	0.205682i	−0.800522	−	0.599303i	$-0.795444\pi$
$443$	2.49941	−	4.32911i	0.118751	−	0.205682i	0.919273	+	0.393621i	$0.128778\pi$
$444$		0			0
$445$	−8.58724	+	14.8735i	−0.407074	+	0.705073i
$446$	−11.3333	−	19.6299i	−0.536649	−	0.929503i
$447$		0			0
$448$	−10.9956	+	10.2913i	−0.519493	+	0.486216i
$449$	−6.89362	−	25.7273i	−0.325330	−	1.21415i	−0.913980	−	0.405760i	$-0.867007\pi$
$449$	−6.89362	−	25.7273i	−0.325330	−	1.21415i	0.588650	−	0.808388i	$-0.299660\pi$
$450$		0			0
$451$			22.0005i			1.03596i
$452$	4.95044	+	2.85814i	0.232849	+	0.134435i
$453$		0			0
$454$	27.8837			1.30865
$455$	25.6072	+	9.98711i	1.20048	+	0.468203i
$456$		0			0
$457$	−8.85252	−	8.85252i	−0.414103	−	0.414103i	0.469062	−	0.883165i	$-0.344592\pi$
$457$	−8.85252	−	8.85252i	−0.414103	−	0.414103i	−0.883165	+	0.469062i	$0.844592\pi$
$458$	9.22416	+	5.32557i	0.431017	+	0.248848i
$459$		0			0
$460$	2.61881	+	9.77352i	0.122102	+	0.455693i
$461$	−2.58295	−	9.63971i	−0.120300	−	0.448966i	0.879329	−	0.476216i	$-0.157992\pi$
$461$	−2.58295	−	9.63971i	−0.120300	−	0.448966i	−0.999629	+	0.0272495i	$0.991325\pi$
$462$		0			0
$463$	−8.87215	+	8.87215i	−0.412324	+	0.412324i	−0.882547	−	0.470224i	$-0.844173\pi$
$463$	−8.87215	+	8.87215i	−0.412324	+	0.412324i	0.470224	+	0.882547i	$0.344173\pi$
$464$	−4.11501	−	7.12740i	−0.191034	−	0.330881i
$465$		0			0
$466$	3.13431	+	11.6974i	0.145194	+	0.541872i
$467$	−7.33629	+	12.7068i	−0.339483	+	0.588002i	−0.984336	−	0.176305i	$-0.943585\pi$
$467$	−7.33629	+	12.7068i	−0.339483	+	0.588002i	0.644853	+	0.764307i	$0.276919\pi$
$468$		0			0
$469$	−4.36188	−	2.71452i	−0.201413	−	0.125345i
$470$	−10.2351	+	38.1980i	−0.472111	+	1.76194i
$471$		0			0
$472$	−17.9532			−0.826364
$473$	−9.13127	+	34.0784i	−0.419856	+	1.56692i
$474$		0			0
$475$	4.60565	−	1.23408i	0.211322	−	0.0566235i
$476$	3.53639	−	3.30986i	0.162090	−	0.151707i
$477$		0			0
$478$		−	4.89286i		−	0.223794i
$479$	−13.3439	+	3.57549i	−0.609699	+	0.163368i	−0.550441	−	0.834874i	$-0.685540\pi$
$479$	−13.3439	+	3.57549i	−0.609699	+	0.163368i	−0.0592583	+	0.998243i	$0.518874\pi$
$480$		0			0
$481$	−16.2529	−	11.1333i	−0.741070	−	0.507636i
$482$		−	13.9672i		−	0.636189i
$483$		0			0
$484$	−3.98026	−	6.89402i	−0.180921	−	0.313364i
$485$	−5.54986	+	3.20421i	−0.252006	+	0.145496i
$486$		0			0
$487$	21.2572	+	21.2572i	0.963257	+	0.963257i	0.999348	−	0.0360915i	$-0.0114908\pi$
$487$	21.2572	+	21.2572i	0.963257	+	0.963257i	−0.0360915	+	0.999348i	$0.511491\pi$
$488$	−3.01759	+	11.2618i	−0.136600	+	0.509798i
$489$		0			0
$490$	−26.0727	−	17.4477i	−1.17785	−	0.788208i
$491$	−27.2827	+	15.7517i	−1.23125	+	0.710863i	−0.967291	−	0.253670i	$-0.918362\pi$
$491$	−27.2827	+	15.7517i	−1.23125	+	0.710863i	−0.263961	+	0.964533i	$0.585029\pi$
$492$		0			0
$493$	−3.85175	−	6.67143i	−0.173474	−	0.300466i
$494$	6.15016	−	5.26923i	0.276709	−	0.237074i
$495$		0			0
$496$	3.59429	+	0.963087i	0.161388	+	0.0432439i
$497$	26.3924	+	16.4247i	1.18386	+	0.736747i
$498$		0			0
$499$	−22.5875	+	6.05231i	−1.01116	+	0.270938i	−0.726112	−	0.687576i	$-0.758675\pi$
$499$	−22.5875	+	6.05231i	−1.01116	+	0.270938i	−0.285044	+	0.958515i	$0.592008\pi$
$500$	1.45118	−	1.45118i	0.0648985	−	0.0648985i
$501$		0			0
$502$	37.1063	−	9.94261i	1.65614	−	0.443760i
$503$	7.16456	+	4.13646i	0.319452	+	0.184436i	0.651148	−	0.758951i	$-0.274288\pi$
$503$	7.16456	+	4.13646i	0.319452	+	0.184436i	−0.331696	+	0.943386i	$0.607621\pi$
$504$		0			0
$505$	−44.0968	−	11.8157i	−1.96228	−	0.525792i
$506$	−61.7499	−	35.6513i	−2.74512	−	1.58490i
$507$		0			0
$508$	0.730656	+	1.26553i	0.0324176	+	0.0561489i
$509$	6.51433	−	6.51433i	0.288742	−	0.288742i	−0.547840	−	0.836583i	$-0.684550\pi$
$509$	6.51433	−	6.51433i	0.288742	−	0.288742i	0.836583	+	0.547840i	$0.184550\pi$
$510$		0			0
$511$	33.6097	−	17.9496i	1.48681	−	0.794044i
$512$	8.50976	+	8.50976i	0.376082	+	0.376082i
$513$		0			0
$514$	−6.76541	−	6.76541i	−0.298409	−	0.298409i
$515$	29.6488	+	7.94436i	1.30648	+	0.350071i
$516$		0			0
$517$	−24.1561	−	41.8396i	−1.06238	−	1.84010i
$518$	15.3655	+	16.4171i	0.675121	+	0.721326i
$519$		0			0
$520$	8.48825	−	24.0886i	0.372234	−	1.05635i
$521$	−5.78613	+	3.34062i	−0.253495	+	0.146355i	−0.621364	−	0.783522i	$-0.713421\pi$
$521$	−5.78613	+	3.34062i	−0.253495	+	0.146355i	0.367869	+	0.929878i	$0.380088\pi$
$522$		0			0
$523$			32.1180i			1.40442i	0.711969	+	0.702211i	$0.247804\pi$
$523$			32.1180i			1.40442i	−0.711969	+	0.702211i	$0.752196\pi$
$524$	−1.21457	+	2.10369i	−0.0530586	+	0.0919001i
$525$		0			0
$526$	−25.7659	+	6.90396i	−1.12345	+	0.301027i
$527$	3.36435	+	0.901475i	0.146553	+	0.0392689i
$528$		0			0
$529$	−47.0945			−2.04759
$530$	1.24779			0.0542005
$531$		0			0
$532$	−1.41359	+	0.754943i	−0.0612869	+	0.0327309i
$533$	−1.11432	+	14.4447i	−0.0482665	+	0.625671i
$534$		0			0
$535$	−10.8514	−	40.4979i	−0.469146	−	1.75088i
$536$	−2.38696	+	4.13434i	−0.103101	+	0.178576i
$537$		0			0
$538$	2.54240	−	2.54240i	0.109611	−	0.109611i
$539$	37.5957	−	7.45083i	1.61936	−	0.320930i
$540$		0			0
$541$	−1.62221	−	6.05418i	−0.0697443	−	0.260289i	0.922246	−	0.386604i	$-0.126352\pi$
$541$	−1.62221	−	6.05418i	−0.0697443	−	0.260289i	−0.991990	+	0.126314i	$0.959685\pi$
$542$			10.0796i			0.432957i
$543$		0			0
$544$	−7.20974	−	7.20974i	−0.309115	−	0.309115i
$545$	24.7953			1.06211
$546$		0			0
$547$	−17.9848			−0.768973			−0.384487	−	0.923131i	$-0.625622\pi$
$547$	−17.9848			−0.768973			−0.384487	+	0.923131i	$0.625622\pi$
$548$	1.01659	+	1.01659i	0.0434267	+	0.0434267i
$549$		0			0
$550$		−	28.1206i		−	1.19907i
$551$	0.659662	+	2.46189i	0.0281026	+	0.104880i
$552$		0			0
$553$	2.22249	−	0.517390i	0.0945099	−	0.0220017i
$554$	−26.5915	+	26.5915i	−1.12976	+	1.12976i
$555$		0			0
$556$	3.91295	−	6.77742i	0.165946	−	0.287427i
$557$	−9.77773	−	36.4910i	−0.414296	−	1.54617i	−0.786242	−	0.617919i	$-0.787976\pi$
$557$	−9.77773	−	36.4910i	−0.414296	−	1.54617i	0.371946	−	0.928254i	$-0.378691\pi$
$558$		0			0
$559$	−7.72133	+	21.9121i	−0.326577	+	0.926785i
$560$	−18.7816	+	30.1797i	−0.793669	+	1.27533i
$561$		0			0
$562$	40.9584			1.72773
$563$	6.37316			0.268596			0.134298	−	0.990941i	$-0.457122\pi$
$563$	6.37316			0.268596			0.134298	+	0.990941i	$0.457122\pi$
$564$		0			0
$565$	−37.9287	−	10.1630i	−1.59567	−	0.427559i
$566$	18.7876	−	5.03413i	0.789703	−	0.211600i
$567$		0			0
$568$	14.4428	−	25.0156i	0.606005	−	1.04963i
$569$		−	4.40653i		−	0.184731i	−0.995725	−	0.0923657i	$-0.970557\pi$
$569$		−	4.40653i		−	0.184731i	0.995725	−	0.0923657i	$-0.0294429\pi$
$570$		0			0
$571$	12.2682	−	7.08302i	0.513406	−	0.296415i	−0.220826	−	0.975313i	$-0.570875\pi$
$571$	12.2682	−	7.08302i	0.513406	−	0.296415i	0.734233	+	0.678898i	$0.237542\pi$
$572$	−3.57640	−	7.46829i	−0.149537	−	0.312265i
$573$		0			0
$574$	4.80573	−	15.8224i	0.200587	−	0.660414i
$575$	−13.8221	−	23.9405i	−0.576419	−	0.998388i
$576$		0			0
$577$	8.98371	+	2.40718i	0.373997	+	0.100212i	0.440921	−	0.897546i	$-0.354652\pi$
$577$	8.98371	+	2.40718i	0.373997	+	0.100212i	−0.0669241	+	0.997758i	$0.521319\pi$
$578$	−2.25493	−	2.25493i	−0.0937929	−	0.0937929i
$579$		0			0
$580$	−1.50830	−	1.50830i	−0.0626289	−	0.0626289i
$581$	16.0635	+	0.531508i	0.666428	+	0.0220507i
$582$		0			0
$583$	−1.07792	+	1.07792i	−0.0446428	+	0.0446428i
$584$	−17.7028	−	30.6621i	−0.732547	−	1.26881i
$585$		0			0
$586$	−0.118733	−	0.0685503i	−0.00490480	−	0.00283179i
$587$	10.0172	+	2.68411i	0.413455	+	0.110785i	0.459550	−	0.888152i	$-0.348011\pi$
$587$	10.0172	+	2.68411i	0.413455	+	0.110785i	−0.0460944	+	0.998937i	$0.514678\pi$
$588$		0			0
$589$	−0.997987	−	0.576188i	−0.0411213	−	0.0237414i
$590$	−31.6130	+	8.47066i	−1.30148	+	0.348732i
$591$		0			0
$592$	18.0157	−	18.0157i	0.740441	−	0.740441i
$593$	−11.6126	+	3.11158i	−0.476871	+	0.127777i	−0.489245	−	0.872146i	$-0.662728\pi$
$593$	−11.6126	+	3.11158i	−0.476871	+	0.127777i	0.0123741	+	0.999923i	$0.496061\pi$
$594$		0			0
$595$	−17.5801	+	28.2490i	−0.720714	+	1.15810i
$596$	5.79182	+	1.55191i	0.237242	+	0.0635688i
$597$		0			0
$598$	−38.7371	−	26.5350i	−1.58408	−	1.08510i
$599$	9.16962	+	15.8822i	0.374660	+	0.648931i	0.990276	−	0.139116i	$-0.0444260\pi$
$599$	9.16962	+	15.8822i	0.374660	+	0.648931i	−0.615616	+	0.788046i	$0.711093\pi$
$600$		0			0
$601$	29.4396	−	16.9969i	1.20086	−	0.693319i	0.240117	−	0.970744i	$-0.422814\pi$
$601$	29.4396	−	16.9969i	1.20086	−	0.693319i	0.960747	+	0.277424i	$0.0894808\pi$
$602$	14.0111	−	22.5140i	0.571048	−	0.917602i
$603$		0			0
$604$	0.00223293	−	0.00833342i	9.08568e−5	−	0.000339082i
$605$	38.6668	+	38.6668i	1.57203	+	1.57203i
$606$		0			0
$607$	35.5453	−	20.5221i	1.44274	−	0.832965i	0.444707	−	0.895676i	$-0.353308\pi$
$607$	35.5453	−	20.5221i	1.44274	−	0.832965i	0.998032	+	0.0627107i	$0.0199745\pi$
$608$	1.68672	+	2.92148i	0.0684053	+	0.118482i
$609$		0			0
$610$			21.2541i			0.860554i
$611$	−13.7409	−	28.6939i	−0.555896	−	1.16083i
$612$		0			0
$613$	−25.8999	+	6.93987i	−1.04609	+	0.280299i	−0.740635	−	0.671908i	$-0.765475\pi$
$613$	−25.8999	+	6.93987i	−1.04609	+	0.280299i	−0.305454	+	0.952207i	$0.598808\pi$
$614$			16.6901i			0.673558i
$615$		0			0
$616$	−8.07495	−	34.6866i	−0.325349	−	1.39756i
$617$	10.2681	−	2.75133i	0.413378	−	0.110764i	−0.0461351	−	0.998935i	$-0.514690\pi$
$617$	10.2681	−	2.75133i	0.413378	−	0.110764i	0.459513	+	0.888171i	$0.348024\pi$
$618$		0			0
$619$	−7.23874	+	27.0153i	−0.290949	+	1.08584i	0.653432	+	0.756985i	$0.273329\pi$
$619$	−7.23874	+	27.0153i	−0.290949	+	1.08584i	−0.944381	+	0.328853i	$0.893338\pi$
$620$	0.964435			0.0387326
$621$		0			0
$622$	12.1699	−	45.4187i	0.487969	−	1.82112i
$623$	−0.521525	+	15.7618i	−0.0208945	+	0.631485i
$624$		0			0
$625$	−15.3035	+	26.5064i	−0.612140	+	1.06026i
$626$	−11.6165	−	43.3533i	−0.464288	−	1.73275i
$627$		0			0
$628$	1.27520	+	2.20870i	0.0508858	+	0.0881368i
$629$	16.8632	−	16.8632i	0.672379	−	0.672379i
$630$		0			0
$631$	−0.748324	−	2.79278i	−0.0297903	−	0.111179i	0.949430	−	0.313980i	$-0.101662\pi$
$631$	−0.748324	−	2.79278i	−0.0297903	−	0.111179i	−0.979220	+	0.202801i	$0.934996\pi$
$632$	−0.548800	−	2.04815i	−0.0218301	−	0.0814711i
$633$		0			0
$634$	22.6037	+	13.0503i	0.897708	+	0.518292i
$635$	−7.09805	−	7.09805i	−0.281677	−	0.281677i
$636$		0			0
$637$	25.0614	−	2.98774i	0.992969	−	0.118378i
$638$	15.0315			0.595103
$639$		0			0
$640$	33.7516	+	19.4865i	1.33415	+	0.770272i
$641$			15.0751i			0.595431i	0.954655	+	0.297715i	$0.0962246\pi$
$641$			15.0751i			0.595431i	−0.954655	+	0.297715i	$0.903775\pi$
$642$		0			0
$643$	10.7996	+	40.3048i	0.425896	+	1.58946i	0.761959	+	0.647625i	$0.224238\pi$
$643$	10.7996	+	40.3048i	0.425896	+	1.58946i	−0.336063	+	0.941839i	$0.609096\pi$
$644$	6.34896	+	6.78348i	0.250184	+	0.267307i
$645$		0			0
$646$	4.90190	+	8.49033i	0.192863	+	0.334048i
$647$	0.214109	−	0.370847i	0.00841747	−	0.0145795i	−0.861786	−	0.507272i	$-0.830654\pi$
$647$	0.214109	−	0.370847i	0.00841747	−	0.0145795i	0.870203	+	0.492693i	$0.163987\pi$
$648$		0			0
$649$	19.9918	−	34.6267i	0.784745	−	1.35922i
$650$	1.42430	−	18.4630i	0.0558657	−	0.724178i
$651$		0			0
$652$	−1.54619	+	5.77047i	−0.0605536	+	0.225989i
$653$	16.3850			0.641195			0.320597	−	0.947216i	$-0.396116\pi$
$653$	16.3850			0.641195			0.320597	+	0.947216i	$0.396116\pi$
$654$		0			0
$655$	4.31875	−	16.1178i	0.168748	−	0.629775i
$656$	−18.0980	−	4.84936i	−0.706610	−	0.189336i
$657$		0			0
$658$	8.23334	+	35.3670i	0.320969	+	1.37875i
$659$	13.2020	−	22.8666i	0.514278	−	0.890755i	−0.485585	−	0.874190i	$-0.661393\pi$
$659$	13.2020	−	22.8666i	0.514278	−	0.890755i	0.999863	−	0.0165659i	$-0.00527333\pi$
$660$		0			0
$661$	26.7452	−	7.16635i	1.04027	−	0.278739i	0.302043	−	0.953294i	$-0.402331\pi$
$661$	26.7452	−	7.16635i	1.04027	−	0.278739i	0.738224	+	0.674555i	$0.235665\pi$
$662$	−8.47684	+	4.89411i	−0.329462	+	0.190215i
$663$		0			0
$664$		−	14.9347i		−	0.579580i
$665$	8.03726	−	7.52243i	0.311672	−	0.291707i
$666$		0			0
$667$	12.7971	−	7.38841i	0.495506	−	0.286080i
$668$	0.907416	+	0.243141i	0.0351090	+	0.00940742i
$669$		0			0
$670$	−2.25243	+	8.40618i	−0.0870189	+	0.324759i
$671$	−18.3606	−	18.3606i	−0.708805	−	0.708805i
$672$		0			0
$673$	−16.8918	+	9.75249i	−0.651131	+	0.375931i	−0.788889	−	0.614535i	$-0.789344\pi$
$673$	−16.8918	+	9.75249i	−0.651131	+	0.375931i	0.137758	+	0.990466i	$0.456010\pi$
$674$	18.8535	−	18.8535i	0.726210	−	0.726210i
$675$		0			0
$676$	−1.96987	−	5.08456i	−0.0757642	−	0.195560i
$677$	1.91182	+	1.10379i	0.0734772	+	0.0424221i	0.536288	−	0.844035i	$-0.319826\pi$
$677$	1.91182	+	1.10379i	0.0734772	+	0.0424221i	−0.462811	+	0.886457i	$0.653159\pi$
$678$		0			0
$679$	−3.10919	+	4.99607i	−0.119320	+	0.191732i
$680$	26.7754	+	15.4588i	1.02679	+	0.592816i
$681$		0			0
$682$	−4.80570	+	4.80570i	−0.184020	+	0.184020i
$683$	9.24232	−	9.24232i	0.353647	−	0.353647i	−0.507817	−	0.861465i	$-0.669548\pi$
$683$	9.24232	−	9.24232i	0.353647	−	0.353647i	0.861465	+	0.507817i	$0.169548\pi$
$684$		0			0
$685$	−8.55271	−	4.93791i	−0.326782	−	0.188668i
$686$	−28.6658	−	2.85380i	−1.09446	−	0.108959i
$687$		0			0
$688$	−26.0208	−	15.0231i	−0.992035	−	0.572752i
$689$	−0.762319	+	0.653127i	−0.0290421	+	0.0248821i
$690$		0			0
$691$	−35.9312	+	35.9312i	−1.36689	+	1.36689i	−0.502045	+	0.864842i	$0.667419\pi$
$691$	−35.9312	+	35.9312i	−1.36689	+	1.36689i	−0.864842	+	0.502045i	$0.832581\pi$
$692$	−1.18053	+	0.681577i	−0.0448768	+	0.0259097i
$693$		0			0
$694$	4.65219	+	4.65219i	0.176595	+	0.176595i
$695$	−13.9137	+	51.9265i	−0.527775	+	1.96968i
$696$		0			0
$697$	−16.9402	−	4.53912i	−0.641657	−	0.171932i
$698$	−25.1048	+	14.4943i	−0.950230	+	0.548616i
$699$		0			0
$700$	−1.06491	+	3.50611i	−0.0402498	+	0.132518i
$701$		−	12.9407i		−	0.488765i	−0.969679	−	0.244383i	$-0.921415\pi$
$701$		−	12.9407i		−	0.488765i	0.969679	−	0.244383i	$-0.0785853\pi$
$702$		0			0
$703$	−6.83317	+	3.94513i	−0.257718	+	0.148793i
$704$	−30.1047	+	8.06654i	−1.13461	+	0.304019i
$705$		0			0
$706$	3.46444	−	6.00059i	0.130386	−	0.225835i
$707$	−40.8285	+	9.50477i	−1.53551	+	0.357464i
$708$		0			0
$709$	−23.8425	−	6.38859i	−0.895426	−	0.239929i	−0.218375	−	0.975865i	$-0.570076\pi$
$709$	−23.8425	−	6.38859i	−0.895426	−	0.239929i	−0.677051	+	0.735936i	$0.736742\pi$
$710$	13.6287	−	50.8631i	0.511477	−	1.90886i
$711$		0			0
$712$	14.6542			0.549190
$713$	−1.72920	+	6.45347i	−0.0647592	+	0.241684i
$714$		0			0
$715$	37.0081	+	43.1952i	1.38402	+	1.61541i
$716$	4.43987	−	7.69008i	0.165926	−	0.287392i
$717$		0			0
$718$	12.7638	−	22.1075i	0.476340	−	0.825045i
$719$	7.46614	+	12.9317i	0.278440	+	0.482273i	0.970997	−	0.239091i	$-0.0768493\pi$
$719$	7.46614	+	12.9317i	0.278440	+	0.482273i	−0.692557	+	0.721363i	$0.743516\pi$
$720$		0			0
$721$	27.4513	−	6.39060i	1.02234	−	0.237998i
$722$	6.80954	+	25.4136i	0.253425	+	0.945795i
$723$		0			0
$724$			7.76886i			0.288727i
$725$	5.04696	+	2.91387i	0.187439	+	0.108218i
$726$		0			0
$727$	8.06701			0.299189			0.149595	−	0.988747i	$-0.452203\pi$
$727$	8.06701			0.299189			0.149595	+	0.988747i	$0.452203\pi$
$728$	−3.54486	−	23.1830i	−0.131381	−	0.859218i
$729$		0			0
$730$	−45.6390	−	45.6390i	−1.68917	−	1.68917i
$731$	−24.3562	−	14.0620i	−0.900846	−	0.520104i
$732$		0			0
$733$	0.991378	+	3.69987i	0.0366174	+	0.136658i	0.981815	−	0.189842i	$-0.0607975\pi$
$733$	0.991378	+	3.69987i	0.0366174	+	0.136658i	−0.945197	+	0.326500i	$0.894131\pi$
$734$	11.2441	+	41.9635i	0.415026	+	1.54890i
$735$		0			0
$736$	13.8297	−	13.8297i	0.509769	−	0.509769i
$737$	−5.31600	−	9.20757i	−0.195817	−	0.339165i
$738$		0			0
$739$	4.96535	+	18.5309i	0.182653	+	0.681671i	0.995121	+	0.0986647i	$0.0314571\pi$
$739$	4.96535	+	18.5309i	0.182653	+	0.681671i	−0.812467	+	0.583007i	$0.801876\pi$
$740$	3.30172	−	5.71875i	0.121374	−	0.210225i
$741$		0			0
$742$	1.01068	−	0.539764i	0.0371032	−	0.0198153i
$743$	−2.24541	+	8.37997i	−0.0823759	+	0.307431i	−0.994804	−	0.101805i	$-0.967538\pi$
$743$	−2.24541	+	8.37997i	−0.0823759	+	0.307431i	0.912428	+	0.409236i	$0.134205\pi$
$744$		0			0
$745$	−41.1891			−1.50905
$746$	2.35435	−	8.78656i	0.0861989	−	0.321699i
$747$		0			0
$748$	9.68225	−	2.59435i	0.354018	−	0.0948588i
$749$	−26.3078	−	28.1083i	−0.961264	−	1.02705i
$750$		0			0
$751$		−	30.1279i		−	1.09938i	−0.835367	−	0.549692i	$-0.814745\pi$
$751$		−	30.1279i		−	1.09938i	0.835367	−	0.549692i	$-0.185255\pi$
$752$	39.7426	−	10.6490i	1.44926	−	0.388329i
$753$		0			0
$754$	9.86916	+	0.761343i	0.359414	+	0.0277265i
$755$			0.0592640i			0.00215684i
$756$		0			0
$757$	−0.444897	−	0.770584i	−0.0161700	−	0.0280073i	0.857827	−	0.513938i	$-0.171814\pi$
$757$	−0.444897	−	0.770584i	−0.0161700	−	0.0280073i	−0.873997	+	0.485931i	$0.838481\pi$
$758$	2.14223	−	1.23681i	0.0778091	−	0.0449231i
$759$		0			0
$760$	−7.23314	−	7.23314i	−0.262373	−	0.262373i
$761$	12.4145	−	46.3316i	0.450026	−	1.67952i	−0.252288	−	0.967652i	$-0.581183\pi$
$761$	12.4145	−	46.3316i	0.450026	−	1.67952i	0.702314	−	0.711867i	$-0.252150\pi$
$762$		0			0
$763$	20.0836	−	10.7258i	0.727075	−	0.388302i
$764$	9.95963	−	5.75019i	0.360327	−	0.208035i
$765$		0			0
$766$	−10.9542	−	18.9732i	−0.395791	−	0.685530i
$767$	14.8797	−	21.7221i	0.537275	−	0.784340i
$768$		0			0
$769$	4.85396	+	1.30061i	0.175038	+	0.0469013i	0.345274	−	0.938502i	$-0.387786\pi$
$769$	4.85396	+	1.30061i	0.175038	+	0.0469013i	−0.170235	+	0.985403i	$0.554453\pi$
$770$	−30.5846	−	57.2680i	−1.10219	−	2.06380i
$771$		0			0
$772$	7.72676	−	2.07038i	0.278092	−	0.0745146i
$773$	−9.15642	+	9.15642i	−0.329333	+	0.329333i	−0.852333	−	0.523000i	$-0.824813\pi$
$773$	−9.15642	+	9.15642i	−0.329333	+	0.329333i	0.523000	+	0.852333i	$0.324813\pi$
$774$		0			0
$775$	−2.54514	+	0.681969i	−0.0914242	+	0.0244970i
$776$	4.73545	+	2.73401i	0.169993	+	0.0981454i
$777$		0			0
$778$	0.376093	+	0.100774i	0.0134836	+	0.00361292i
$779$	5.02509	+	2.90123i	0.180042	+	0.103948i
$780$		0			0
$781$	32.1654	+	55.7121i	1.15097	+	1.99354i
$782$	40.1915	−	40.1915i	1.43725	−	1.43725i
$783$		0			0
$784$	−2.15766	+	32.5693i	−0.0770592	+	1.16319i
$785$	−12.3880	−	12.3880i	−0.442148	−	0.442148i
$786$		0			0
$787$	1.63546	+	1.63546i	0.0582978	+	0.0582978i	0.735655	−	0.677357i	$-0.236875\pi$
$787$	1.63546	+	1.63546i	0.0582978	+	0.0582978i	−0.677357	+	0.735655i	$0.736875\pi$
$788$	−1.88090	−	0.503986i	−0.0670043	−	0.0179538i
$789$		0			0
$790$	−1.93271	−	3.34756i	−0.0687628	−	0.119101i
$791$	−35.1176	+	8.17528i	−1.24864	+	0.290679i
$792$		0			0
$793$	−11.1250	−	12.9849i	−0.395060	−	0.461108i
$794$	−9.07049	+	5.23685i	−0.321900	+	0.185849i
$795$		0			0
$796$		−	0.187543i		−	0.00664730i
$797$	−22.4781	+	38.9332i	−0.796216	+	1.37909i	0.125848	+	0.992049i	$0.459835\pi$
$797$	−22.4781	+	38.9332i	−0.796216	+	1.37909i	−0.922064	+	0.387037i	$0.873499\pi$
$798$		0			0
$799$	37.2001	−	9.96774i	1.31605	−	0.352633i
$800$	7.45057	+	1.99637i	0.263417	+	0.0705825i
$801$		0			0
$802$	−44.8511			−1.58375
$803$	78.8516			2.78261
$804$		0			0
$805$	−54.1870	−	33.7220i	−1.90984	−	1.18855i
$806$	−3.39866	+	2.91184i	−0.119713	+	0.102565i
$807$		0			0
$808$	10.0818	+	37.6258i	0.354677	+	1.32367i
$809$	−7.19827	+	12.4678i	−0.253078	+	0.438343i	−0.964372	−	0.264551i	$-0.914776\pi$
$809$	−7.19827	+	12.4678i	−0.253078	+	0.438343i	0.711294	+	0.702895i	$0.248109\pi$
$810$		0			0
$811$	15.3043	−	15.3043i	0.537406	−	0.537406i	−0.385360	−	0.922766i	$-0.625923\pi$
$811$	15.3043	−	15.3043i	0.537406	−	0.537406i	0.922766	+	0.385360i	$0.125923\pi$
$812$	−1.87415	−	0.569234i	−0.0657697	−	0.0199762i
$813$		0			0
$814$	12.0438	+	44.9482i	0.422137	+	1.57544i
$815$		−	41.0373i		−	1.43747i
$816$		0			0
$817$	6.57962	+	6.57962i	0.230192	+	0.230192i
$818$	−41.9328			−1.46615
$819$		0			0
$820$	−4.85614			−0.169584
$821$	25.9843	+	25.9843i	0.906858	+	0.906858i	0.996017	−	0.0891592i	$-0.0284180\pi$
$821$	25.9843	+	25.9843i	0.906858	+	0.906858i	−0.0891592	+	0.996017i	$0.528418\pi$
$822$		0			0
$823$		−	32.4449i		−	1.13096i	−0.824762	−	0.565480i	$-0.808691\pi$
$823$		−	32.4449i		−	1.13096i	0.824762	−	0.565480i	$-0.191309\pi$
$824$	−6.77857	−	25.2980i	−0.236143	−	0.881297i
$825$		0			0
$826$	−21.9415	+	20.5360i	−0.763443	+	0.714540i
$827$	32.5966	−	32.5966i	1.13349	−	1.13349i	0.143901	−	0.989592i	$-0.454035\pi$
$827$	32.5966	−	32.5966i	1.13349	−	1.13349i	0.989592	−	0.143901i	$-0.0459647\pi$
$828$		0			0
$829$	23.7107	−	41.0681i	0.823507	−	1.42636i	−0.0795487	−	0.996831i	$-0.525348\pi$
$829$	23.7107	−	41.0681i	0.823507	−	1.42636i	0.903055	−	0.429524i	$-0.141319\pi$
$830$	−7.04648	−	26.2978i	−0.244587	−	0.912811i
$831$		0			0
$832$	−20.1743	+	3.77140i	−0.699417	+	0.130750i
$833$	−2.01962	+	30.4857i	−0.0699758	+	1.05627i
$834$		0			0
$835$	−6.45318			−0.223321
$836$	−3.31642			−0.114701
$837$		0			0
$838$	20.9412	+	5.61119i	0.723403	+	0.193835i
$839$	3.74709	−	1.00403i	0.129364	−	0.0346629i	−0.193556	−	0.981089i	$-0.562002\pi$
$839$	3.74709	−	1.00403i	0.129364	−	0.0346629i	0.322920	+	0.946426i	$0.395336\pi$
$840$		0			0
$841$	12.9424	−	22.4169i	0.446291	−	0.772998i
$842$		−	35.1661i		−	1.21191i
$843$		0			0
$844$	10.4467	−	6.03143i	0.359591	−	0.207610i
$845$	22.1103	+	30.2349i	0.760619	+	1.04011i
$846$		0			0
$847$	48.0455	+	14.5928i	1.65086	+	0.501416i
$848$	−0.649122	−	1.12431i	−0.0222910	−	0.0386091i
$849$		0			0
$850$	21.6527	+	5.80182i	0.742681	+	0.199001i
$851$	32.3469	+	32.3469i	1.10884	+	1.10884i
$852$		0			0
$853$	−23.3977	−	23.3977i	−0.801122	−	0.801122i	0.182149	−	0.983271i	$-0.441695\pi$
$853$	−23.3977	−	23.3977i	−0.801122	−	0.801122i	−0.983271	+	0.182149i	$0.941695\pi$
$854$	9.19402	+	17.2153i	0.314613	+	0.589096i
$855$		0			0
$856$	−25.2960	+	25.2960i	−0.864601	+	0.864601i
$857$	7.09899	+	12.2958i	0.242497	+	0.420017i	0.961425	−	0.275068i	$-0.0887003\pi$
$857$	7.09899	+	12.2958i	0.242497	+	0.420017i	−0.718928	+	0.695084i	$0.755367\pi$
$858$		0			0
$859$	−41.7926	−	24.1290i	−1.42595	−	0.823270i	−0.429148	−	0.903234i	$-0.641186\pi$
$859$	−41.7926	−	24.1290i	−1.42595	−	0.823270i	−0.996798	+	0.0799637i	$0.974520\pi$
$860$	−7.52208	−	2.01553i	−0.256501	−	0.0687292i
$861$		0			0
$862$	4.33655	+	2.50371i	0.147703	+	0.0852766i
$863$	39.8830	−	10.6866i	1.35763	−	0.363776i	0.494686	−	0.869072i	$-0.335283\pi$
$863$	39.8830	−	10.6866i	1.35763	−	0.363776i	0.862946	+	0.505296i	$0.168617\pi$
$864$		0			0
$865$	6.62126	−	6.62126i	0.225130	−	0.225130i
$866$	16.0503	−	4.30068i	0.545413	−	0.146143i
$867$		0			0
$868$	0.781169	−	0.417191i	0.0265146	−	0.0141604i
$869$	4.56143	+	1.22223i	0.154736	+	0.0414613i
$870$		0			0
$871$	−3.02393	−	6.31462i	−0.102462	−	0.213963i
$872$	−10.5784	−	18.3223i	−0.358228	−	0.620470i
$873$		0			0
$874$	−16.2861	+	9.40279i	−0.550886	+	0.318054i
$875$	−0.428092	+	12.9381i	−0.0144722	+	0.437386i
$876$		0			0
$877$	5.12324	−	19.1202i	0.173000	−	0.645643i	−0.823884	−	0.566758i	$-0.808197\pi$
$877$	5.12324	−	19.1202i	0.173000	−	0.645643i	0.996884	−	0.0788850i	$-0.0251360\pi$
$878$	−16.0153	−	16.0153i	−0.540491	−	0.540491i
$879$		0			0
$880$	−63.7068	+	36.7812i	−2.14756	+	1.23989i
$881$	−4.58892	−	7.94824i	−0.154605	−	0.267783i	0.778310	−	0.627880i	$-0.216077\pi$
$881$	−4.58892	−	7.94824i	−0.154605	−	0.267783i	−0.932915	+	0.360097i	$0.882744\pi$
$882$		0			0
$883$		−	2.23790i		−	0.0753113i	−0.999291	−	0.0376556i	$-0.988011\pi$
$883$		−	2.23790i		−	0.0753113i	0.999291	−	0.0376556i	$-0.0119890\pi$
$884$	6.48842	−	1.21295i	0.218229	−	0.0407961i
$885$		0			0
$886$	−7.51051	+	2.01244i	−0.252321	+	0.0676091i
$887$			10.1980i			0.342415i	0.985235	+	0.171207i	$0.0547668\pi$
$887$			10.1980i			0.342415i	−0.985235	+	0.171207i	$0.945233\pi$
$888$		0			0
$889$	−8.81969	−	2.67880i	−0.295803	−	0.0898442i
$890$	25.8039	−	6.91414i	0.864949	−	0.231762i
$891$		0			0
$892$	−1.58199	+	5.90405i	−0.0529688	+	0.197682i
$893$	−12.7420			−0.426395
$894$		0			0
$895$	−15.7873	+	58.9190i	−0.527711	+	1.96944i
$896$	35.7674	+	1.18347i	1.19491	+	0.0395368i
$897$		0			0
$898$	−20.7147	+	35.8790i	−0.691259	+	1.19730i
$899$	−0.364538	−	1.36047i	−0.0121580	−	0.0453744i
$900$		0			0
$901$	−0.607596	−	1.05239i	−0.0202419	−	0.0350601i
$902$	24.1978	−	24.1978i	0.805697	−	0.805697i
$903$		0			0
$904$	8.67160	+	32.3628i	0.288413	+	1.07637i
$905$	−13.8123	−	51.5480i	−0.459135	−	1.71351i
$906$		0			0
$907$	35.4824	+	20.4858i	1.17817	+	0.680219i	0.955591	−	0.294695i	$-0.0952181\pi$
$907$	35.4824	+	20.4858i	1.17817	+	0.680219i	0.222582	+	0.974914i	$0.428551\pi$
$908$	−5.31685	−	5.31685i	−0.176446	−	0.176446i
$909$		0			0
$910$	−17.1801	−	39.1493i	−0.569516	−	1.29779i
$911$	−45.1869			−1.49711			−0.748554	−	0.663074i	$-0.769252\pi$
$911$	−45.1869			−1.49711			−0.748554	+	0.663074i	$0.769252\pi$
$912$		0			0
$913$	28.8049	+	16.6305i	0.953303	+	0.550390i
$914$			19.4733i			0.644120i
$915$		0			0
$916$	−0.743381	−	2.77433i	−0.0245620	−	0.0916666i
$917$	−3.47409	−	14.9232i	−0.114724	−	0.492808i
$918$		0			0
$919$	−10.4121	−	18.0342i	−0.343463	−	0.594895i	0.641611	−	0.767030i	$-0.278267\pi$
$919$	−10.4121	−	18.0342i	−0.343463	−	0.594895i	−0.985073	+	0.172136i	$0.944933\pi$
$920$	−29.6529	+	51.3603i	−0.977627	+	1.69330i
$921$		0			0
$922$	−7.76155	+	13.4434i	−0.255613	+	0.442735i
$923$	18.2968	+	38.2078i	0.602248	+	1.25762i
$924$		0			0
$925$	−4.66941	+	17.4265i	−0.153529	+	0.572979i
$926$	19.5165			0.641352
$927$		0			0
$928$	−1.06714	+	3.98261i	−0.0350305	+	0.130736i
$929$	−54.2535	−	14.5372i	−1.78000	−	0.476949i	−0.789416	−	0.613859i	$-0.789616\pi$
$929$	−54.2535	−	14.5372i	−1.78000	−	0.476949i	−0.990584	+	0.136910i	$0.956283\pi$
$930$		0			0
$931$	3.25597	−	9.56971i	0.106710	−	0.313635i
$932$	1.63281	−	2.82811i	0.0534844	−	0.0926377i
$933$		0			0
$934$	22.0449	−	5.90691i	0.721331	−	0.193280i
$935$	−59.6313	+	34.4281i	−1.95015	+	1.12592i
$936$		0			0
$937$		−	12.6449i		−	0.413092i	−0.978437	−	0.206546i	$-0.933778\pi$
$937$		−	12.6449i		−	0.413092i	0.978437	−	0.206546i	$-0.0662223\pi$
$938$	1.81190	+	7.78315i	0.0591605	+	0.254129i
$939$		0			0
$940$	9.23521	−	5.33195i	0.301219	−	0.173909i
$941$	1.15761	+	0.310180i	0.0377369	+	0.0101116i	0.277638	−	0.960686i	$-0.410448\pi$
$941$	1.15761	+	0.310180i	0.0377369	+	0.0101116i	−0.239901	+	0.970797i	$0.577115\pi$
$942$		0			0
$943$	8.70692	−	32.4947i	0.283536	−	1.05817i
$944$	24.0781	+	24.0781i	0.783674	+	0.783674i
$945$		0			0
$946$	47.5252	−	27.4387i	1.54518	−	0.892108i
$947$	−22.5630	+	22.5630i	−0.733199	+	0.733199i	−0.971252	−	0.238053i	$-0.923491\pi$
$947$	−22.5630	+	22.5630i	−0.733199	+	0.733199i	0.238053	+	0.971252i	$0.423491\pi$
$948$		0			0
$949$	51.7712	+	3.99382i	1.68056	+	0.129645i
$950$	−6.42297	−	3.70830i	−0.208389	−	0.120313i
$951$		0			0
$952$	28.3745	+	0.938850i	0.919622	+	0.0304283i
$953$	−9.16224	−	5.28982i	−0.296794	−	0.171354i	0.344208	−	0.938894i	$-0.388148\pi$
$953$	−9.16224	−	5.28982i	−0.296794	−	0.171354i	−0.641002	+	0.767539i	$0.721481\pi$
$954$		0			0
$955$	−55.8610	+	55.8610i	−1.80762	+	1.80762i
$956$	−0.932968	+	0.932968i	−0.0301743	+	0.0301743i
$957$		0			0
$958$	18.6092	+	10.7440i	0.601236	+	0.347124i
$959$	−9.06351	−	0.299892i	−0.292676	−	0.00968402i
$960$		0			0
$961$	−26.2953	−	15.1816i	−0.848235	−	0.489729i
$962$	5.63094	+	30.1214i	0.181549	+	0.971154i
$963$		0			0
$964$	−2.66326	+	2.66326i	−0.0857779	+	0.0857779i
$965$	−47.5878	+	27.4748i	−1.53190	+	0.884445i
$966$		0			0
$967$	23.9761	+	23.9761i	0.771021	+	0.771021i	0.978285	−	0.207264i	$-0.0664560\pi$
$967$	23.9761	+	23.9761i	0.771021	+	0.771021i	−0.207264	+	0.978285i	$0.566456\pi$
$968$	12.0761	−	45.0688i	0.388142	−	1.44856i
$969$		0			0
$970$	9.62838	+	2.57992i	0.309149	+	0.0828362i
$971$	−21.6257	+	12.4856i	−0.694002	+	0.400682i	−0.805109	−	0.593126i	$-0.797893\pi$
$971$	−21.6257	+	12.4856i	−0.694002	+	0.400682i	0.111108	+	0.993808i	$0.464560\pi$
$972$		0			0
$973$	11.1924	+	48.0779i	0.358812	+	1.54131i
$974$		−	46.7606i		−	1.49831i
$975$		0			0
$976$	19.1509	−	11.0568i	0.613005	−	0.353919i
$977$	−16.3501	+	4.38099i	−0.523085	+	0.140160i	−0.510693	−	0.859763i	$-0.670611\pi$
$977$	−16.3501	+	4.38099i	−0.523085	+	0.140160i	−0.0123917	+	0.999923i	$0.503945\pi$
$978$		0			0
$979$	−16.3182	+	28.2639i	−0.521531	+	0.903318i
$980$	1.64461	+	8.29846i	0.0525353	+	0.265085i
$981$		0			0
$982$	47.3324	+	12.6827i	1.51044	+	0.404721i
$983$	7.16888	−	26.7546i	0.228652	−	0.853340i	−0.752257	−	0.658870i	$-0.771035\pi$
$983$	7.16888	−	26.7546i	0.228652	−	0.853340i	0.980908	−	0.194470i	$-0.0622987\pi$
$984$		0			0
$985$	13.3762			0.426202
$986$	−3.10129	+	11.5742i	−0.0987653	+	0.368597i
$987$		0			0
$988$	−2.17744	−	0.167976i	−0.0692737	−	0.00534403i
$989$	26.9737	−	46.7199i	0.857715	−	1.48561i
$990$		0			0
$991$	−6.15625	+	10.6629i	−0.195560	+	0.338720i	−0.947084	−	0.320986i	$-0.895986\pi$
$991$	−6.15625	+	10.6629i	−0.195560	+	0.338720i	0.751524	+	0.659706i	$0.229319\pi$
$992$	−0.932101	−	1.61445i	−0.0295942	−	0.0512587i
$993$		0			0
$994$	−10.9632	−	47.0934i	−0.347732	−	1.49371i
$995$	0.333433	+	1.24439i	0.0105706	+	0.0394498i
$996$		0			0
$997$		−	12.5696i		−	0.398082i	−0.979991	−	0.199041i	$-0.936217\pi$
$997$		−	12.5696i		−	0.398082i	0.979991	−	0.199041i	$-0.0637827\pi$
$998$	31.5002	+	18.1866i	0.997121	+	0.575688i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.271.3		36
3.2	odd	2		273.2.bt.a.271.7	yes	36
7.3	odd	6		819.2.gh.c.388.7		36
13.6	odd	12		819.2.gh.c.19.7		36
21.17	even	6		273.2.cg.a.115.3	yes	36
39.32	even	12		273.2.cg.a.19.3	yes	36
91.45	even	12	inner	819.2.et.c.136.3		36
273.227	odd	12		273.2.bt.a.136.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.7	✓	36	273.227	odd	12
273.2.bt.a.271.7	yes	36	3.2	odd	2
273.2.cg.a.19.3	yes	36	39.32	even	12
273.2.cg.a.115.3	yes	36	21.17	even	6
819.2.et.c.136.3		36	91.45	even	12	inner
819.2.et.c.271.3		36	1.1	even	1	trivial
819.2.gh.c.19.7		36	13.6	odd	12
819.2.gh.c.388.7		36	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09987 - 1.09987i) q^{2} +0.419447i q^{4} +(-0.745735 - 2.78312i) q^{5} +(-1.80794 - 1.93167i) q^{7} +(-1.73841 + 1.73841i) q^{8} +O(q^{10})\)	\(q+(-1.09987 - 1.09987i) q^{2} +0.419447i q^{4} +(-0.745735 - 2.78312i) q^{5} +(-1.80794 - 1.93167i) q^{7} +(-1.73841 + 1.73841i) q^{8} +(-2.24087 + 3.88130i) q^{10} +(-1.41711 - 5.28871i) q^{11} +(-0.662549 - 3.54415i) q^{13} +(-0.136094 + 4.11310i) q^{14} +4.66296 q^{16} +4.36465 q^{17} +(-1.39486 - 0.373751i) q^{19} +(1.16737 - 0.312796i) q^{20} +(-4.25828 + 7.37555i) q^{22} +8.37225i q^{23} +(-2.85951 + 1.65094i) q^{25} +(-3.16940 + 4.62684i) q^{26} +(0.810234 - 0.758334i) q^{28} +(-0.882488 - 1.52851i) q^{29} +(0.770818 + 0.206540i) q^{31} +(-1.65185 - 1.65185i) q^{32} +(-4.80057 - 4.80057i) q^{34} +(-4.02784 + 6.47222i) q^{35} +(3.86358 - 3.86358i) q^{37} +(1.12309 + 1.94525i) q^{38} +(6.13459 + 3.54181i) q^{40} +(-3.88124 - 1.03997i) q^{41} +(-5.58033 - 3.22180i) q^{43} +(2.21833 - 0.594400i) q^{44} +(9.20842 - 9.20842i) q^{46} +(8.52304 - 2.28374i) q^{47} +(-0.462723 + 6.98469i) q^{49} +(4.96092 + 1.32927i) q^{50} +(1.48658 - 0.277904i) q^{52} +(-0.139208 - 0.241116i) q^{53} +(-13.6623 + 7.88795i) q^{55} +(6.50098 + 0.215103i) q^{56} +(-0.710548 + 2.65180i) q^{58} +(5.16369 + 5.16369i) q^{59} +(4.10703 - 2.37119i) q^{61} +(-0.620634 - 1.07497i) q^{62} -5.69226i q^{64} +(-9.36972 + 4.48695i) q^{65} +(1.87565 - 0.502580i) q^{67} +1.83074i q^{68} +(11.5487 - 2.68852i) q^{70} +(-11.3490 + 3.04095i) q^{71} +(-3.72736 + 13.9107i) q^{73} -8.49891 q^{74} +(0.156769 - 0.585069i) q^{76} +(-7.65402 + 12.2990i) q^{77} +(-0.431242 + 0.746933i) q^{79} +(-3.47733 - 12.9776i) q^{80} +(3.12503 + 5.41271i) q^{82} +(-4.29551 + 4.29551i) q^{83} +(-3.25487 - 12.1473i) q^{85} +(2.59408 + 9.68124i) q^{86} +(11.6575 + 6.73043i) q^{88} +(-4.21484 - 4.21484i) q^{89} +(-5.64830 + 7.68744i) q^{91} -3.51171 q^{92} +(-11.8861 - 6.86245i) q^{94} +4.16078i q^{95} +(-0.575652 - 2.14836i) q^{97} +(8.19122 - 7.17334i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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