LMFDB - Embedded newform 324.2.l.a.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.608544 - 1.27659i) q^{2} +(-1.25935 + 1.55372i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(-1.81474 - 0.319988i) q^{7} +(2.74983 + 0.662160i) q^{8} +O(q^{10})$	\(q+(-0.608544 - 1.27659i) q^{2} +(-1.25935 + 1.55372i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(-1.81474 - 0.319988i) q^{7} +(2.74983 + 0.662160i) q^{8} +(1.73207 - 0.166382i) q^{10} +(5.09161 - 1.85319i) q^{11} +(2.61776 - 2.19656i) q^{13} +(0.695857 + 2.51140i) q^{14} +(-0.828087 - 3.91335i) q^{16} +(4.18778 - 2.41782i) q^{17} +(3.42957 + 1.98006i) q^{19} +(-1.26644 - 2.10989i) q^{20} +(-5.46423 - 5.37213i) q^{22} +(0.674078 + 3.82288i) q^{23} +(2.67053 + 2.24084i) q^{25} +(-4.39712 - 2.00509i) q^{26} +(2.78256 - 2.41662i) q^{28} +(-1.76149 + 2.09927i) q^{29} +(-0.190727 + 0.0336302i) q^{31} +(-4.49180 + 3.43857i) q^{32} +(-5.63501 - 3.87472i) q^{34} +(1.13365 - 1.96353i) q^{35} +(-3.47493 - 6.01875i) q^{37} +(0.440678 - 5.58310i) q^{38} +(-1.92277 + 2.90068i) q^{40} +(-2.51742 - 3.00014i) q^{41} +(2.57902 + 7.08581i) q^{43} +(-3.53276 + 10.2447i) q^{44} +(4.47004 - 3.18691i) q^{46} +(0.343697 - 1.94920i) q^{47} +(-3.38696 - 1.23275i) q^{49} +(1.23549 - 4.77281i) q^{50} +(0.116170 + 6.83349i) q^{52} -11.2308i q^{53} +6.66675i q^{55} +(-4.77834 - 2.08156i) q^{56} +(3.75184 + 0.971203i) q^{58} +(-3.62667 - 1.32000i) q^{59} +(-2.54693 + 14.4444i) q^{61} +(0.158997 + 0.223013i) q^{62} +(7.12309 + 3.64165i) q^{64} +(1.43804 + 3.95099i) q^{65} +(-1.34096 - 1.59809i) q^{67} +(-1.51727 + 9.55151i) q^{68} +(-3.19649 - 0.252301i) q^{70} +(4.41692 + 7.65033i) q^{71} +(2.62025 - 4.53841i) q^{73} +(-5.56881 + 8.09872i) q^{74} +(-7.39549 + 2.83500i) q^{76} +(-9.83294 + 1.73381i) q^{77} +(5.09766 - 6.07516i) q^{79} +(4.87306 + 0.689385i) q^{80} +(-2.29798 + 5.03942i) q^{82} +(1.39029 + 1.16659i) q^{83} +(1.03316 + 5.85935i) q^{85} +(7.47620 - 7.60437i) q^{86} +(15.2282 - 1.72450i) q^{88} +(14.2059 + 8.20179i) q^{89} +(-5.45341 + 3.14853i) q^{91} +(-6.78859 - 3.76701i) q^{92} +(-2.69748 + 0.747418i) q^{94} +(-3.73257 + 3.13200i) q^{95} +(0.0876267 - 0.0318935i) q^{97} +(0.487400 + 5.07393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.608544	−	1.27659i	−0.430306	−	0.902683i
$2$	−0.608544	−	1.27659i	−0.430306	−	0.902683i
$3$		0			0
$3$		0			0
$4$	−1.25935	+	1.55372i	−0.629674	+	0.776860i
$5$	−0.420820	+	1.15619i	−0.188196	+	0.517065i	−0.997527	−	0.0702884i	$-0.977608\pi$
$5$	−0.420820	+	1.15619i	−0.188196	+	0.517065i	0.809330	+	0.587354i	$0.199830\pi$
$6$		0			0
$7$	−1.81474	−	0.319988i	−0.685907	−	0.120944i	−0.180175	−	0.983635i	$-0.557666\pi$
$7$	−1.81474	−	0.319988i	−0.685907	−	0.120944i	−0.505732	+	0.862691i	$0.668778\pi$
$8$	2.74983	+	0.662160i	0.972210	+	0.234109i
$9$		0			0
$10$	1.73207	−	0.166382i	0.547728	−	0.0526145i
$11$	5.09161	−	1.85319i	1.53518	−	0.558759i	0.570295	−	0.821440i	$-0.306829\pi$
$11$	5.09161	−	1.85319i	1.53518	−	0.558759i	0.964883	+	0.262681i	$0.0846066\pi$
$12$		0			0
$13$	2.61776	−	2.19656i	0.726035	−	0.609215i	−0.203013	−	0.979176i	$-0.565073\pi$
$13$	2.61776	−	2.19656i	0.726035	−	0.609215i	0.929047	+	0.369961i	$0.120629\pi$
$14$	0.695857	+	2.51140i	0.185976	+	0.671200i
$15$		0			0
$16$	−0.828087	−	3.91335i	−0.207022	−	0.978336i
$17$	4.18778	−	2.41782i	1.01569	−	0.586407i	0.102835	−	0.994698i	$-0.467209\pi$
$17$	4.18778	−	2.41782i	1.01569	−	0.586407i	0.912852	+	0.408291i	$0.133875\pi$
$18$		0			0
$19$	3.42957	+	1.98006i	0.786798	+	0.454258i	0.838834	−	0.544387i	$-0.183238\pi$
$19$	3.42957	+	1.98006i	0.786798	+	0.454258i	−0.0520361	+	0.998645i	$0.516571\pi$
$20$	−1.26644	−	2.10989i	−0.283185	−	0.471785i
$21$		0			0
$22$	−5.46423	−	5.37213i	−1.16498	−	1.14534i
$23$	0.674078	+	3.82288i	0.140555	+	0.797126i	0.970829	+	0.239772i	$0.0770725\pi$
$23$	0.674078	+	3.82288i	0.140555	+	0.797126i	−0.830274	+	0.557355i	$0.811816\pi$
$24$		0			0
$25$	2.67053	+	2.24084i	0.534106	+	0.448168i
$26$	−4.39712	−	2.00509i	−0.862345	−	0.393230i
$27$		0			0
$28$	2.78256	−	2.41662i	0.525854	−	0.456698i
$29$	−1.76149	+	2.09927i	−0.327101	+	0.389824i	−0.904384	−	0.426721i	$-0.859669\pi$
$29$	−1.76149	+	2.09927i	−0.327101	+	0.389824i	0.577282	+	0.816545i	$0.304113\pi$
$30$		0			0
$31$	−0.190727	+	0.0336302i	−0.0342555	+	0.00604017i	−0.190750	−	0.981639i	$-0.561092\pi$
$31$	−0.190727	+	0.0336302i	−0.0342555	+	0.00604017i	0.156494	+	0.987679i	$0.449981\pi$
$32$	−4.49180	+	3.43857i	−0.794045	+	0.607859i
$33$		0			0
$34$	−5.63501	−	3.87472i	−0.966396	−	0.664509i
$35$	1.13365	−	1.96353i	0.191621	−	0.331898i
$36$		0			0
$37$	−3.47493	−	6.01875i	−0.571274	−	0.989476i	−0.996435	−	0.0843584i	$-0.973116\pi$
$37$	−3.47493	−	6.01875i	−0.571274	−	0.989476i	0.425161	−	0.905118i	$-0.360217\pi$
$38$	0.440678	−	5.58310i	0.0714873	−	0.905699i
$39$		0			0
$40$	−1.92277	+	2.90068i	−0.304016	+	0.458638i
$41$	−2.51742	−	3.00014i	−0.393154	−	0.468543i	0.532766	−	0.846263i	$-0.321153\pi$
$41$	−2.51742	−	3.00014i	−0.393154	−	0.468543i	−0.925920	+	0.377720i	$0.876708\pi$
$42$		0			0
$43$	2.57902	+	7.08581i	0.393297	+	1.08058i	0.965486	+	0.260454i	$0.0838721\pi$
$43$	2.57902	+	7.08581i	0.393297	+	1.08058i	−0.572189	+	0.820122i	$0.693906\pi$
$44$	−3.53276	+	10.2447i	−0.532584	+	1.54445i
$45$		0			0
$46$	4.47004	−	3.18691i	0.659071	−	0.469885i
$47$	0.343697	−	1.94920i	0.0501334	−	0.284321i	−0.949426	−	0.313990i	$-0.898334\pi$
$47$	0.343697	−	1.94920i	0.0501334	−	0.284321i	0.999560	+	0.0296691i	$0.00944536\pi$
$48$		0			0
$49$	−3.38696	−	1.23275i	−0.483852	−	0.176108i
$50$	1.23549	−	4.77281i	0.174725	−	0.674977i
$51$		0			0
$52$	0.116170	+	6.83349i	0.0161098	+	0.947634i
$53$		−	11.2308i		−	1.54267i	−0.636432	−	0.771333i	$-0.719590\pi$
$53$		−	11.2308i		−	1.54267i	0.636432	−	0.771333i	$-0.280410\pi$
$54$		0			0
$55$			6.66675i			0.898944i
$56$	−4.77834	−	2.08156i	−0.638532	−	0.278160i
$57$		0			0
$58$	3.75184	+	0.971203i	0.492641	+	0.127525i
$59$	−3.62667	−	1.32000i	−0.472152	−	0.171849i	0.0949749	−	0.995480i	$-0.469723\pi$
$59$	−3.62667	−	1.32000i	−0.472152	−	0.171849i	−0.567127	+	0.823630i	$0.691945\pi$
$60$		0			0
$61$	−2.54693	+	14.4444i	−0.326101	+	1.84941i	0.175719	+	0.984440i	$0.443775\pi$
$61$	−2.54693	+	14.4444i	−0.326101	+	1.84941i	−0.501820	+	0.864972i	$0.667336\pi$
$62$	0.158997	+	0.223013i	0.0201927	+	0.0283227i
$63$		0			0
$64$	7.12309	+	3.64165i	0.890386	+	0.455206i
$65$	1.43804	+	3.95099i	0.178367	+	0.490060i
$66$		0			0
$67$	−1.34096	−	1.59809i	−0.163824	−	0.195238i	0.677887	−	0.735166i	$-0.262896\pi$
$67$	−1.34096	−	1.59809i	−0.163824	−	0.195238i	−0.841711	+	0.539928i	$0.818451\pi$
$68$	−1.51727	+	9.55151i	−0.183995	+	1.15829i
$69$		0			0
$70$	−3.19649	−	0.252301i	−0.382054	−	0.0301557i
$71$	4.41692	+	7.65033i	0.524192	+	0.907927i	0.999603	+	0.0281636i	$0.00896593\pi$
$71$	4.41692	+	7.65033i	0.524192	+	0.907927i	−0.475411	+	0.879764i	$0.657701\pi$
$72$		0			0
$73$	2.62025	−	4.53841i	0.306677	−	0.531180i	−0.670956	−	0.741497i	$-0.734116\pi$
$73$	2.62025	−	4.53841i	0.306677	−	0.531180i	0.977633	+	0.210317i	$0.0674495\pi$
$74$	−5.56881	+	8.09872i	−0.647361	+	0.941457i
$75$		0			0
$76$	−7.39549	+	2.83500i	−0.848321	+	0.325197i
$77$	−9.83294	+	1.73381i	−1.12057	+	0.197586i
$78$		0			0
$79$	5.09766	−	6.07516i	0.573532	−	0.683508i	−0.398820	−	0.917029i	$-0.630580\pi$
$79$	5.09766	−	6.07516i	0.573532	−	0.683508i	0.972352	+	0.233521i	$0.0750247\pi$
$80$	4.87306	+	0.689385i	0.544825	+	0.0770756i
$81$		0			0
$82$	−2.29798	+	5.03942i	−0.253769	+	0.556510i
$83$	1.39029	+	1.16659i	0.152604	+	0.128050i	0.715893	−	0.698210i	$-0.246020\pi$
$83$	1.39029	+	1.16659i	0.152604	+	0.128050i	−0.563289	+	0.826260i	$0.690464\pi$
$84$		0			0
$85$	1.03316	+	5.85935i	0.112062	+	0.635536i
$86$	7.47620	−	7.60437i	0.806179	−	0.820001i
$87$		0			0
$88$	15.2282	−	1.72450i	1.62333	−	0.183833i
$89$	14.2059	+	8.20179i	1.50582	+	0.869388i	0.999977	+	0.00676565i	$0.00215359\pi$
$89$	14.2059	+	8.20179i	1.50582	+	0.869388i	0.505848	+	0.862623i	$0.331180\pi$
$90$		0			0
$91$	−5.45341	+	3.14853i	−0.571673	+	0.330056i
$92$	−6.78859	−	3.76701i	−0.707759	−	0.392738i
$93$		0			0
$94$	−2.69748	+	0.747418i	−0.278224	+	0.0770902i
$95$	−3.73257	+	3.13200i	−0.382954	+	0.321336i
$96$		0			0
$97$	0.0876267	−	0.0318935i	0.00889714	−	0.00323830i	−0.337568	−	0.941301i	$-0.609604\pi$
$97$	0.0876267	−	0.0318935i	0.00889714	−	0.00323830i	0.346465	+	0.938063i	$0.387382\pi$
$98$	0.487400	+	5.07393i	0.0492348	+	0.512545i
$99$		0			0
$100$	−6.84476	+	1.32726i	−0.684476	+	0.132726i
$101$	−1.18836	−	0.209540i	−0.118246	−	0.0208500i	0.114212	−	0.993456i	$-0.463566\pi$
$101$	−1.18836	−	0.209540i	−0.118246	−	0.0208500i	−0.232458	+	0.972606i	$0.574677\pi$
$102$		0			0
$103$	5.38263	−	14.7887i	0.530366	−	1.45717i	−0.328270	−	0.944584i	$-0.606466\pi$
$103$	5.38263	−	14.7887i	0.530366	−	1.45717i	0.858636	−	0.512586i	$-0.171312\pi$
$104$	8.65284	−	4.30678i	0.848481	−	0.422315i
$105$		0			0
$106$	−14.3371	+	6.83442i	−1.39254	+	0.663818i
$107$	−15.2848			−1.47764			−0.738820	−	0.673903i	$-0.764616\pi$
$107$	−15.2848			−1.47764			−0.738820	+	0.673903i	$0.764616\pi$
$108$		0			0
$109$	−12.4401			−1.19154			−0.595772	−	0.803154i	$-0.703154\pi$
$109$	−12.4401			−1.19154			−0.595772	+	0.803154i	$0.703154\pi$
$110$	8.51068	−	4.05701i	0.811462	−	0.386821i
$111$		0			0
$112$	0.250540	+	7.36668i	0.0236738	+	0.696086i
$113$	−1.29655	+	3.56224i	−0.121969	+	0.335107i	−0.985619	−	0.168986i	$-0.945951\pi$
$113$	−1.29655	+	3.56224i	−0.121969	+	0.335107i	0.863649	+	0.504093i	$0.168173\pi$
$114$		0			0
$115$	−4.70366	−	0.829382i	−0.438618	−	0.0773403i
$116$	−1.04334	−	5.38057i	−0.0968715	−	0.499574i
$117$		0			0
$118$	0.521895	+	5.43304i	0.0480443	+	0.500152i
$119$	−8.37341	+	3.04767i	−0.767589	+	0.279380i
$120$		0			0
$121$	14.0637	−	11.8008i	1.27852	−	1.07280i
$122$	19.9894	−	5.53866i	1.80976	−	0.501447i
$123$		0			0
$124$	0.187939	−	0.338688i	0.0168774	−	0.0304150i
$125$	−9.04242	+	5.22065i	−0.808779	+	0.466949i
$126$		0			0
$127$	−10.8485	−	6.26340i	−0.962651	−	0.555787i	−0.0656631	−	0.997842i	$-0.520916\pi$
$127$	−10.8485	−	6.26340i	−0.962651	−	0.555787i	−0.896988	+	0.442055i	$0.854250\pi$
$128$	0.314164	−	11.3093i	0.0277684	−	0.999614i
$129$		0			0
$130$	4.16867	−	4.24014i	0.365616	−	0.371884i
$131$	−0.603670	−	3.42359i	−0.0527429	−	0.299120i	0.947013	−	0.321194i	$-0.104084\pi$
$131$	−0.603670	−	3.42359i	−0.0527429	−	0.299120i	−0.999756	+	0.0220740i	$0.992973\pi$
$132$		0			0
$133$	−5.59018	−	4.69072i	−0.484731	−	0.406737i
$134$	−1.22407	+	2.68436i	−0.105744	+	0.231893i
$135$		0			0
$136$	13.1167	−	3.87560i	1.12474	−	0.332330i
$137$	−3.24936	+	3.87244i	−0.277612	+	0.330845i	−0.886776	−	0.462199i	$-0.847061\pi$
$137$	−3.24936	+	3.87244i	−0.277612	+	0.330845i	0.609164	+	0.793044i	$0.291505\pi$
$138$		0			0
$139$	−6.37891	+	1.12477i	−0.541052	+	0.0954022i	−0.437494	−	0.899221i	$-0.644134\pi$
$139$	−6.37891	+	1.12477i	−0.541052	+	0.0954022i	−0.103558	+	0.994623i	$0.533023\pi$
$140$	1.62312	+	4.23414i	0.137179	+	0.357850i
$141$		0			0
$142$	7.07842	−	10.2941i	0.594008	−	0.863866i
$143$	9.25794	−	16.0352i	0.774188	−	1.34093i
$144$		0			0
$145$	−1.68589	−	2.92004i	−0.140005	−	0.242496i
$146$	−7.38821	−	0.583155i	−0.611452	−	0.0482623i
$147$		0			0
$148$	13.7276	+	2.18064i	1.12840	+	0.179247i
$149$	−3.39500	−	4.04600i	−0.278129	−	0.331461i	0.608837	−	0.793295i	$-0.291636\pi$
$149$	−3.39500	−	4.04600i	−0.278129	−	0.331461i	−0.886967	+	0.461834i	$0.847192\pi$
$150$		0			0
$151$	3.02704	+	8.31673i	0.246337	+	0.676806i	0.999813	+	0.0193304i	$0.00615346\pi$
$151$	3.02704	+	8.31673i	0.246337	+	0.676806i	−0.753476	+	0.657475i	$0.771624\pi$
$152$	8.11961	+	7.71576i	0.658587	+	0.625831i
$153$		0			0
$154$	8.19715	+	11.4975i	0.660545	+	0.926495i
$155$	0.0413785	−	0.234669i	0.00332360	−	0.0188491i
$156$		0			0
$157$	9.32232	+	3.39305i	0.744002	+	0.270795i	0.686079	−	0.727527i	$-0.259330\pi$
$157$	9.32232	+	3.39305i	0.744002	+	0.270795i	0.0579223	+	0.998321i	$0.481552\pi$
$158$	−10.8576	−	2.81061i	−0.863786	−	0.223600i
$159$		0			0
$160$	−2.08541	−	6.64041i	−0.164866	−	0.524970i
$161$		−	7.15323i		−	0.563754i
$162$		0			0
$163$		−	16.2908i		−	1.27600i	−0.770038	−	0.637998i	$-0.779763\pi$
$163$		−	16.2908i		−	1.27600i	0.770038	−	0.637998i	$-0.220237\pi$
$164$	7.83167	−	0.133139i	0.611551	−	0.0103964i
$165$		0			0
$166$	0.643202	−	2.48475i	0.0499221	−	0.192854i
$167$	1.16436	+	0.423791i	0.0901007	+	0.0327940i	0.386677	−	0.922215i	$-0.373623\pi$
$167$	1.16436	+	0.423791i	0.0901007	+	0.0327940i	−0.296577	+	0.955009i	$0.595845\pi$
$168$		0			0
$169$	−0.229648	+	1.30240i	−0.0176653	+	0.100185i
$170$	6.85125	−	4.88460i	0.525467	−	0.374632i
$171$		0			0
$172$	−14.2572	−	4.91642i	−1.08710	−	0.374873i
$173$	4.93959	+	13.5714i	0.375550	+	1.03181i	0.973180	+	0.230043i	$0.0738866\pi$
$173$	4.93959	+	13.5714i	0.375550	+	1.03181i	−0.597631	+	0.801771i	$0.703891\pi$
$174$		0			0
$175$	−4.12927	−	4.92108i	−0.312144	−	0.371998i
$176$	−11.4685	−	18.3906i	−0.864470	−	1.38625i
$177$		0			0
$178$	1.82537	−	23.1262i	0.136817	−	1.73339i
$179$	−4.99509	−	8.65175i	−0.373351	−	0.646662i	0.616728	−	0.787176i	$-0.288458\pi$
$179$	−4.99509	−	8.65175i	−0.373351	−	0.646662i	−0.990079	+	0.140514i	$0.955124\pi$
$180$		0			0
$181$	−5.92900	+	10.2693i	−0.440699	+	0.763314i	−0.997742	−	0.0671706i	$-0.978603\pi$
$181$	−5.92900	+	10.2693i	−0.440699	+	0.763314i	0.557042	+	0.830484i	$0.311936\pi$
$182$	7.33802	+	5.04574i	0.543930	+	0.374015i
$183$		0			0
$184$	−0.677763	+	10.9586i	−0.0499654	+	0.807880i
$185$	8.42116	−	1.48488i	0.619136	−	0.109170i
$186$		0			0
$187$	16.8419	−	20.0714i	1.23160	−	1.46776i
$188$	2.59568	+	2.98873i	0.189310	+	0.217976i
$189$		0			0
$190$	6.26970	+	2.85899i	0.454852	+	0.207413i
$191$	−0.136281	−	0.114354i	−0.00986096	−	0.00827433i	0.637844	−	0.770166i	$-0.279827\pi$
$191$	−0.136281	−	0.114354i	−0.00986096	−	0.00827433i	−0.647705	+	0.761891i	$0.724271\pi$
$192$		0			0
$193$	−1.20989	−	6.86163i	−0.0870899	−	0.493911i	−0.996886	−	0.0788559i	$-0.974873\pi$
$193$	−1.20989	−	6.86163i	−0.0870899	−	0.493911i	0.909796	−	0.415055i	$-0.136238\pi$
$194$	−0.0940396	−	0.0924545i	−0.00675165	−	0.00663785i
$195$		0			0
$196$	6.18071	−	3.70992i	0.441480	−	0.264994i
$197$	−4.71520	−	2.72232i	−0.335944	−	0.193957i	0.322533	−	0.946558i	$-0.395466\pi$
$197$	−4.71520	−	2.72232i	−0.335944	−	0.193957i	−0.658477	+	0.752601i	$0.728799\pi$
$198$		0			0
$199$	5.18692	−	2.99467i	0.367691	−	0.212287i	−0.304758	−	0.952430i	$-0.598576\pi$
$199$	5.18692	−	2.99467i	0.367691	−	0.212287i	0.672449	+	0.740143i	$0.265242\pi$
$200$	5.85970	+	7.93024i	0.414343	+	0.560752i
$201$		0			0
$202$	0.455674	+	1.64456i	0.0320611	+	0.115711i
$203$	3.86839	−	3.24597i	0.271508	−	0.227822i
$204$		0			0
$205$	4.52812	−	1.64810i	0.316258	−	0.115108i
$206$	−22.1546	+	2.12816i	−1.54358	+	0.148276i
$207$		0			0
$208$	−10.7636	−	8.42524i	−0.746323	−	0.584185i
$209$	21.1315	+	3.72605i	1.46170	+	0.257736i
$210$		0			0
$211$	−8.87740	+	24.3905i	−0.611145	+	1.67911i	0.116531	+	0.993187i	$0.462823\pi$
$211$	−8.87740	+	24.3905i	−0.611145	+	1.67911i	−0.727676	+	0.685921i	$0.759400\pi$
$212$	17.4495	+	14.1434i	1.19843	+	0.971376i
$213$		0			0
$214$	9.30149	+	19.5124i	0.635837	+	1.33384i
$215$	−9.27787			−0.632745
$216$		0			0
$217$	0.356880			0.0242266
$218$	7.57034	+	15.8808i	0.512728	+	1.07559i
$219$		0			0
$220$	−10.3583	−	8.39575i	−0.698353	−	0.566041i
$221$	5.65172	−	15.5280i	0.380176	−	1.04452i
$222$		0			0
$223$	−22.0110	−	3.88113i	−1.47396	−	0.259900i	−0.621801	−	0.783175i	$-0.713599\pi$
$223$	−22.0110	−	3.88113i	−1.47396	−	0.259900i	−0.852164	+	0.523275i	$0.824710\pi$
$224$	9.25174	−	4.80279i	0.618158	−	0.320900i
$225$		0			0
$226$	5.33651	−	0.512623i	0.354980	−	0.0340992i
$227$	1.58931	−	0.578461i	0.105486	−	0.0383938i	−0.288738	−	0.957408i	$-0.593236\pi$
$227$	1.58931	−	0.578461i	0.105486	−	0.0383938i	0.394224	+	0.919014i	$0.371013\pi$
$228$		0			0
$229$	−20.3257	+	17.0553i	−1.34316	+	1.12704i	−0.362355	+	0.932040i	$0.618027\pi$
$229$	−20.3257	+	17.0553i	−1.34316	+	1.12704i	−0.980803	+	0.195003i	$0.937528\pi$
$230$	1.80361	+	6.50934i	0.118926	+	0.429213i
$231$		0			0
$232$	−6.23385	+	4.60623i	−0.409272	+	0.302414i
$233$	−4.08160	+	2.35651i	−0.267395	+	0.154380i	−0.627703	−	0.778453i	$-0.716005\pi$
$233$	−4.08160	+	2.35651i	−0.267395	+	0.154380i	0.360308	+	0.932833i	$0.382671\pi$
$234$		0			0
$235$	2.10902	+	1.21764i	0.137577	+	0.0794304i
$236$	6.61815	−	3.97249i	0.430805	−	0.258587i
$237$		0			0
$238$	8.98621	+	8.83474i	0.582489	+	0.572671i
$239$	0.585031	+	3.31788i	0.0378425	+	0.214616i	0.997865	−	0.0653065i	$-0.0208025\pi$
$239$	0.585031	+	3.31788i	0.0378425	+	0.214616i	−0.960023	+	0.279922i	$0.909691\pi$
$240$		0			0
$241$	−12.2315	−	10.2635i	−0.787901	−	0.661127i	0.157324	−	0.987547i	$-0.449713\pi$
$241$	−12.2315	−	10.2635i	−0.787901	−	0.661127i	−0.945225	+	0.326420i	$0.894158\pi$
$242$	−23.6231	−	10.7722i	−1.51855	−	0.692462i
$243$		0			0
$244$	−19.2350	−	22.1477i	−1.23140	−	1.41786i
$245$	2.85060	−	3.39722i	0.182118	−	0.217040i
$246$		0			0
$247$	13.3271	−	2.34993i	0.847984	−	0.149522i
$248$	−0.546733	−	0.0338141i	−0.0347176	−	0.00214720i
$249$		0			0
$250$	12.1673	+	8.36644i	0.769529	+	0.529140i
$251$	−8.45736	+	14.6486i	−0.533824	+	0.924610i	0.465396	+	0.885103i	$0.345912\pi$
$251$	−8.45736	+	14.6486i	−0.533824	+	0.924610i	−0.999219	+	0.0395068i	$0.987421\pi$
$252$		0			0
$253$	10.5167	+	18.2154i	0.661178	+	1.14519i
$254$	−1.39396	+	17.6606i	−0.0874651	+	1.10813i
$255$		0			0
$256$	−14.6285	+	6.48118i	−0.914284	+	0.405074i
$257$	1.87760	+	2.23763i	0.117121	+	0.139580i	0.821419	−	0.570325i	$-0.193183\pi$
$257$	1.87760	+	2.23763i	0.117121	+	0.139580i	−0.704298	+	0.709904i	$0.748738\pi$
$258$		0			0
$259$	4.38016	+	12.0344i	0.272170	+	0.747781i
$260$	−7.94972	−	2.74135i	−0.493021	−	0.170012i
$261$		0			0
$262$	−4.00314	+	2.85404i	−0.247315	+	0.176323i
$263$	0.00324687	−	0.0184139i	0.000200211	−	0.00113545i	−0.984707	−	0.174216i	$-0.944261\pi$
$263$	0.00324687	−	0.0184139i	0.000200211	−	0.00113545i	0.984908	+	0.173080i	$0.0553721\pi$
$264$		0			0
$265$	12.9849	+	4.72613i	0.797659	+	0.290324i
$266$	−2.58624	+	9.99087i	−0.158572	+	0.612579i
$267$		0			0
$268$	4.17172	−	0.0709195i	0.254828	−	0.00433210i
$269$			16.1328i			0.983634i	0.870699	+	0.491817i	$0.163667\pi$
$269$			16.1328i			0.983634i	−0.870699	+	0.491817i	$0.836333\pi$
$270$		0			0
$271$			22.8808i			1.38991i	0.719053	+	0.694955i	$0.244576\pi$
$271$			22.8808i			1.38991i	−0.719053	+	0.694955i	$0.755424\pi$
$272$	−12.9296	−	14.3861i	−0.783973	−	0.872284i
$273$		0			0
$274$	6.92088	+	1.79154i	0.418106	+	0.108231i
$275$	17.7500	+	6.46047i	1.07037	+	0.389581i
$276$		0			0
$277$	1.19415	−	6.77238i	0.0717497	−	0.406913i	−0.927687	−	0.373358i	$-0.878206\pi$
$277$	1.19415	−	6.77238i	0.0717497	−	0.406913i	0.999437	−	0.0335545i	$-0.0106827\pi$
$278$	5.31772	+	7.45876i	0.318936	+	0.447347i
$279$		0			0
$280$	4.41750	−	4.64872i	0.263996	−	0.277814i
$281$	−4.84953	−	13.3240i	−0.289298	−	0.794841i	−0.996165	−	0.0874941i	$-0.972114\pi$
$281$	−4.84953	−	13.3240i	−0.289298	−	0.794841i	0.706867	−	0.707347i	$-0.250108\pi$
$282$		0			0
$283$	7.76714	+	9.25651i	0.461708	+	0.550243i	0.945789	−	0.324781i	$-0.105290\pi$
$283$	7.76714	+	9.25651i	0.461708	+	0.550243i	−0.484081	+	0.875023i	$0.660846\pi$
$284$	−17.4489	−	2.77177i	−1.03540	−	0.164474i
$285$		0			0
$286$	−26.1042	−	2.06042i	−1.54357	−	0.121835i
$287$	3.60845	+	6.25001i	0.213000	+	0.368927i
$288$		0			0
$289$	3.19169	−	5.52817i	0.187747	−	0.325187i
$290$	−2.70175	+	3.92915i	−0.158652	+	0.230728i
$291$		0			0
$292$	3.75160	+	9.78656i	0.219546	+	0.572715i
$293$	−5.78523	+	1.02009i	−0.337977	+	0.0595944i	−0.340061	−	0.940403i	$-0.610448\pi$
$293$	−5.78523	+	1.02009i	−0.337977	+	0.0595944i	0.00208409	+	0.999998i	$0.499337\pi$
$294$		0			0
$295$	3.05235	−	3.63765i	0.177715	−	0.211792i
$296$	−5.57007	−	18.8515i	−0.323754	−	1.09572i
$297$		0			0
$298$	−3.09907	+	6.79618i	−0.179524	+	0.393692i
$299$	10.1618	+	8.52672i	0.587669	+	0.493113i
$300$		0			0
$301$	−2.41288	−	13.6841i	−0.139076	−	0.788741i
$302$	8.77494	−	8.92538i	0.504941	−	0.513598i
$303$		0			0
$304$	4.90869	−	15.0608i	0.281533	−	0.863794i
$305$	−15.6287	−	9.02323i	−0.894896	−	0.516668i
$306$		0			0
$307$	3.55307	−	2.05137i	0.202784	−	0.117078i	−0.395169	−	0.918608i	$-0.629314\pi$
$307$	3.55307	−	2.05137i	0.202784	−	0.117078i	0.597954	+	0.801531i	$0.295981\pi$
$308$	9.68924	−	17.4611i	0.552095	−	0.994939i
$309$		0			0
$310$	−0.324756	+	0.0899833i	−0.0184449	+	0.00511071i
$311$	−2.76079	+	2.31658i	−0.156550	+	0.131361i	−0.717698	−	0.696354i	$-0.754804\pi$
$311$	−2.76079	+	2.31658i	−0.156550	+	0.131361i	0.561148	+	0.827715i	$0.310360\pi$
$312$		0			0
$313$	20.0330	−	7.29141i	1.13233	−	0.412135i	0.293193	−	0.956053i	$-0.405282\pi$
$313$	20.0330	−	7.29141i	1.13233	−	0.412135i	0.839138	+	0.543919i	$0.183060\pi$
$314$	−1.34153	−	13.9656i	−0.0757066	−	0.788122i
$315$		0			0
$316$	3.01936	+	15.5711i	0.169852	+	0.875941i
$317$	−34.5729	−	6.09614i	−1.94181	−	0.342393i	−0.999980	−	0.00629824i	$-0.997995\pi$
$317$	−34.5729	−	6.09614i	−1.94181	−	0.342393i	−0.941828	−	0.336095i	$-0.890894\pi$
$318$		0			0
$319$	−5.07849	+	13.9530i	−0.284341	+	0.781220i
$320$	−7.20799	+	6.70319i	−0.402939	+	0.374720i
$321$		0			0
$322$	−9.13172	+	4.35306i	−0.508891	+	0.242587i
$323$	19.1497			1.06552
$324$		0			0
$325$	11.9129			0.660810
$326$	−20.7966	+	9.91369i	−1.15182	+	0.549068i
$327$		0			0
$328$	−4.93588	−	9.91679i	−0.272539	−	0.547563i
$329$	−1.24744	+	3.42732i	−0.0687737	+	0.188954i
$330$		0			0
$331$	−0.234592	−	0.0413648i	−0.0128943	−	0.00227362i	0.167197	−	0.985923i	$-0.446528\pi$
$331$	−0.234592	−	0.0413648i	−0.0128943	−	0.00227362i	−0.180092	+	0.983650i	$0.557639\pi$
$332$	−3.56341	+	0.690975i	−0.195568	+	0.0379222i
$333$		0			0
$334$	−0.167556	−	1.74430i	−0.00916828	−	0.0954438i
$335$	2.41201	−	0.877898i	0.131782	−	0.0479647i
$336$		0			0
$337$	−5.13534	+	4.30906i	−0.279740	+	0.234729i	−0.771852	−	0.635802i	$-0.780669\pi$
$337$	−5.13534	+	4.30906i	−0.279740	+	0.234729i	0.492112	+	0.870532i	$0.336225\pi$
$338$	1.80238	−	0.499402i	0.0980364	−	0.0271639i
$339$		0			0
$340$	−10.4049	−	5.77372i	−0.564285	−	0.313124i
$341$	−0.908782	+	0.524685i	−0.0492133	+	0.0284133i
$342$		0			0
$343$	16.9230	+	9.77048i	0.913755	+	0.527556i
$344$	2.39993	+	21.1925i	0.129396	+	1.14262i
$345$		0			0
$346$	14.3191	−	14.5646i	0.769800	−	0.782998i
$347$	−1.22136	−	6.92666i	−0.0655659	−	0.371843i	−0.999881	−	0.0153957i	$-0.995099\pi$
$347$	−1.22136	−	6.92666i	−0.0655659	−	0.371843i	0.934316	−	0.356447i	$-0.116012\pi$
$348$		0			0
$349$	−5.45858	−	4.58030i	−0.292191	−	0.245178i	0.484894	−	0.874573i	$-0.338858\pi$
$349$	−5.45858	−	4.58030i	−0.292191	−	0.245178i	−0.777085	+	0.629395i	$0.783303\pi$
$350$	−3.76933	+	8.26607i	−0.201479	+	0.441840i
$351$		0			0
$352$	−16.4981	+	25.8320i	−0.879354	+	1.37685i
$353$	10.1110	−	12.0498i	0.538152	−	0.641344i	−0.426620	−	0.904431i	$-0.640296\pi$
$353$	10.1110	−	12.0498i	0.538152	−	0.641344i	0.964772	+	0.263086i	$0.0847404\pi$
$354$		0			0
$355$	−10.7040	+	1.88740i	−0.568109	+	0.100173i
$356$	−30.6335	+	11.7431i	−1.62357	+	0.622383i
$357$		0			0
$358$	−8.00498	+	11.6416i	−0.423076	+	0.615280i
$359$	6.28667	−	10.8888i	0.331798	−	0.574691i	−0.651067	−	0.759021i	$-0.725678\pi$
$359$	6.28667	−	10.8888i	0.331798	−	0.574691i	0.982864	+	0.184330i	$0.0590115\pi$
$360$		0			0
$361$	−1.65869	−	2.87293i	−0.0872993	−	0.151207i
$362$	16.7178	+	1.31954i	0.878666	+	0.0693536i
$363$		0			0
$364$	1.97581	−	12.4382i	0.103561	−	0.651937i
$365$	4.14462	+	4.93937i	0.216939	+	0.258538i
$366$		0			0
$367$	7.46561	+	20.5116i	0.389702	+	1.07070i	0.967136	+	0.254260i	$0.0818318\pi$
$367$	7.46561	+	20.5116i	0.389702	+	1.07070i	−0.577434	+	0.816437i	$0.695946\pi$
$368$	14.4021	−	5.80358i	0.750760	−	0.302532i
$369$		0			0
$370$	−7.02022	−	9.84672i	−0.364964	−	0.511907i
$371$	−3.59371	+	20.3809i	−0.186576	+	1.05813i
$372$		0			0
$373$	−14.2207	−	5.17591i	−0.736320	−	0.267999i	−0.0534826	−	0.998569i	$-0.517032\pi$
$373$	−14.2207	−	5.17591i	−0.736320	−	0.267999i	−0.682838	+	0.730570i	$0.739254\pi$
$374$	−35.8719	−	9.28580i	−1.85489	−	0.480157i
$375$		0			0
$376$	2.23579	−	5.13239i	0.115302	−	0.264683i
$377$			9.36459i			0.482301i
$378$		0			0
$379$		−	25.8363i		−	1.32712i	−0.748122	−	0.663561i	$-0.769044\pi$
$379$		−	25.8363i		−	1.32712i	0.748122	−	0.663561i	$-0.230956\pi$
$380$	−0.165642	−	9.74364i	−0.00849728	−	0.499838i
$381$		0			0
$382$	−0.0630490	+	0.243564i	−0.00322587	+	0.0124618i
$383$	4.37364	+	1.59187i	0.223482	+	0.0813410i	0.451335	−	0.892355i	$-0.350948\pi$
$383$	4.37364	+	1.59187i	0.223482	+	0.0813410i	−0.227852	+	0.973696i	$0.573170\pi$
$384$		0			0
$385$	2.13328	−	12.0984i	0.108722	−	0.616592i
$386$	−8.02320	+	5.72014i	−0.408370	+	0.291147i
$387$		0			0
$388$	−0.0607989	+	0.176312i	−0.00308660	+	0.00895090i
$389$	−9.75902	−	26.8127i	−0.494802	−	1.35946i	−0.896239	−	0.443571i	$-0.853712\pi$
$389$	−9.75902	−	26.8127i	−0.494802	−	1.35946i	0.401438	−	0.915886i	$-0.368511\pi$
$390$		0			0
$391$	12.0659	+	14.3796i	0.610200	+	0.727208i
$392$	−8.49728	−	5.63257i	−0.429177	−	0.284488i
$393$		0			0
$394$	−0.605872	+	7.67601i	−0.0305234	+	0.386712i
$395$	4.87886	+	8.45043i	0.245482	+	0.425187i
$396$		0			0
$397$	−0.983521	+	1.70351i	−0.0493615	+	0.0854966i	−0.889650	−	0.456642i	$-0.849052\pi$
$397$	−0.983521	+	1.70351i	−0.0493615	+	0.0854966i	0.840289	+	0.542139i	$0.182385\pi$
$398$	−6.97943	−	4.79917i	−0.349847	−	0.240561i
$399$		0			0
$400$	6.55775	−	12.3063i	0.327887	−	0.615315i
$401$	18.7451	−	3.30527i	0.936087	−	0.165057i	0.315260	−	0.949005i	$-0.397908\pi$
$401$	18.7451	−	3.30527i	0.936087	−	0.165057i	0.620827	+	0.783948i	$0.286797\pi$
$402$		0			0
$403$	−0.425405	+	0.506978i	−0.0211909	+	0.0252544i
$404$	1.82213	−	1.58250i	0.0906542	−	0.0787321i
$405$		0			0
$406$	−6.49784	−	2.96302i	−0.322483	−	0.147052i
$407$	−28.8469	−	24.2054i	−1.42989	−	1.19982i
$408$		0			0
$409$	2.54702	+	14.4449i	0.125942	+	0.714252i	0.980744	+	0.195298i	$0.0625674\pi$
$409$	2.54702	+	14.4449i	0.125942	+	0.714252i	−0.854802	+	0.518954i	$0.826322\pi$
$410$	−4.85950	−	4.77760i	−0.239994	−	0.235949i
$411$		0			0
$412$	16.1988	+	26.9872i	0.798058	+	1.32956i
$413$	6.15908	+	3.55594i	0.303068	+	0.174977i
$414$		0			0
$415$	−1.93387	+	1.11652i	−0.0949297	+	0.0548077i
$416$	−4.20541	+	18.8678i	−0.206187	+	0.925071i
$417$		0			0
$418$	−8.10282	−	29.2436i	−0.396322	−	1.43035i
$419$	8.87113	−	7.44376i	0.433383	−	0.363651i	−0.399843	−	0.916583i	$-0.630936\pi$
$419$	8.87113	−	7.44376i	0.433383	−	0.363651i	0.833226	+	0.552932i	$0.186491\pi$
$420$		0			0
$421$	1.16623	−	0.424473i	0.0568386	−	0.0206876i	−0.313444	−	0.949607i	$-0.601483\pi$
$421$	1.16623	−	0.424473i	0.0568386	−	0.0206876i	0.370283	+	0.928919i	$0.379261\pi$
$422$	36.5388	−	3.50990i	1.77868	−	0.170859i
$423$		0			0
$424$	7.43657	−	30.8827i	0.361152	−	1.49980i
$425$	16.6015	+	2.92730i	0.805293	+	0.141995i
$426$		0			0
$427$	9.24404	−	25.3978i	0.447350	−	1.22908i
$428$	19.2489	−	23.7483i	0.930431	−	1.14792i
$429$		0			0
$430$	5.64599	+	11.8440i	0.272274	+	0.571169i
$431$	33.8486			1.63043			0.815214	−	0.579159i	$-0.196619\pi$
$431$	33.8486			1.63043			0.815214	+	0.579159i	$0.196619\pi$
$432$		0			0
$433$	21.7047			1.04306			0.521531	−	0.853232i	$-0.325361\pi$
$433$	21.7047			1.04306			0.521531	+	0.853232i	$0.325361\pi$
$434$	−0.217177	−	0.455589i	−0.0104249	−	0.0218690i
$435$		0			0
$436$	15.6664	−	19.3284i	0.750283	−	0.925662i
$437$	−5.25776	+	14.4456i	−0.251513	+	0.691026i
$438$		0			0
$439$	−36.8270	−	6.49360i	−1.75766	−	0.309923i	−0.800467	−	0.599377i	$-0.795415\pi$
$439$	−36.8270	−	6.49360i	−1.75766	−	0.309923i	−0.957192	+	0.289454i	$0.906526\pi$
$440$	−4.41445	+	18.3324i	−0.210451	+	0.873963i
$441$		0			0
$442$	−23.2621	+	2.23455i	−1.10647	+	0.106287i
$443$	5.77721	−	2.10273i	0.274484	−	0.0999039i	−0.201111	−	0.979568i	$-0.564455\pi$
$443$	5.77721	−	2.10273i	0.274484	−	0.0999039i	0.475595	+	0.879665i	$0.342233\pi$
$444$		0			0
$445$	−15.4610	+	12.9733i	−0.732922	+	0.614994i
$446$	8.44006	+	30.4608i	0.399649	+	1.44236i
$447$		0			0
$448$	−11.7613	−	8.88794i	−0.555668	−	0.419916i
$449$	−4.30776	+	2.48709i	−0.203296	+	0.117373i	−0.598192	−	0.801353i	$-0.704114\pi$
$449$	−4.30776	+	2.48709i	−0.203296	+	0.117373i	0.394896	+	0.918726i	$0.370781\pi$
$450$		0			0
$451$	−18.3775	−	10.6103i	−0.865364	−	0.499618i
$452$	−3.90191	−	6.50057i	−0.183531	−	0.305761i
$453$		0			0
$454$	−1.70562	−	1.67687i	−0.0800487	−	0.0786995i
$455$	−1.34540	−	7.63017i	−0.0630735	−	0.357708i
$456$		0			0
$457$	8.14455	+	6.83409i	0.380986	+	0.319685i	0.813089	−	0.582139i	$-0.197784\pi$
$457$	8.14455	+	6.83409i	0.380986	+	0.319685i	−0.432103	+	0.901824i	$0.642228\pi$
$458$	34.1416	+	15.5686i	1.59533	+	0.727473i
$459$		0			0
$460$	7.21217	−	6.26368i	0.336269	−	0.292046i
$461$	9.23017	−	11.0001i	0.429892	−	0.512325i	−0.506999	−	0.861946i	$-0.669245\pi$
$461$	9.23017	−	11.0001i	0.429892	−	0.512325i	0.936891	+	0.349621i	$0.113690\pi$
$462$		0			0
$463$	17.9752	−	3.16951i	0.835377	−	0.147300i	0.260433	−	0.965492i	$-0.416135\pi$
$463$	17.9752	−	3.16951i	0.835377	−	0.147300i	0.574944	+	0.818192i	$0.305024\pi$
$464$	9.67383	+	5.15496i	0.449096	+	0.239313i
$465$		0			0
$466$	5.49213	+	3.77648i	0.254418	+	0.174942i
$467$	−11.4763	+	19.8775i	−0.531060	+	0.919823i	0.468283	+	0.883579i	$0.344873\pi$
$467$	−11.4763	+	19.8775i	−0.531060	+	0.919823i	−0.999343	+	0.0362446i	$0.988460\pi$
$468$		0			0
$469$	1.92212	+	3.32921i	0.0887553	+	0.153729i
$470$	0.270995	−	3.43334i	0.0125001	−	0.158368i
$471$		0			0
$472$	−9.09866	−	6.03120i	−0.418800	−	0.277609i
$473$	26.2628	+	31.2987i	1.20756	+	1.43912i
$474$		0			0
$475$	4.72176	+	12.9729i	0.216649	+	0.595239i
$476$	5.80981	−	16.8480i	0.266292	−	0.772227i
$477$		0			0
$478$	3.87954	−	2.76592i	0.177446	−	0.126510i
$479$	3.05382	−	17.3191i	0.139533	−	0.791329i	−0.832063	−	0.554681i	$-0.812840\pi$
$479$	3.05382	−	17.3191i	0.139533	−	0.791329i	0.971596	−	0.236648i	$-0.0760487\pi$
$480$		0			0
$481$	−22.3170	−	8.12274i	−1.01757	−	0.370365i
$482$	−5.65878	+	21.8604i	−0.257750	+	0.995712i
$483$		0			0
$484$	0.624111	+	36.7123i	0.0283687	+	1.66874i
$485$			0.114735i			0.00520984i
$486$		0			0
$487$			15.6716i			0.710147i	0.934838	+	0.355073i	$0.115544\pi$
$487$			15.6716i			0.710147i	−0.934838	+	0.355073i	$0.884456\pi$
$488$	−16.5681	+	38.0330i	−0.750003	+	1.72167i
$489$		0			0
$490$	−6.07156	−	1.57168i	−0.274285	−	0.0710015i
$491$	−37.6017	−	13.6859i	−1.69694	−	0.617636i	−0.701469	−	0.712700i	$-0.747472\pi$
$491$	−37.6017	−	13.6859i	−1.69694	−	0.617636i	−0.995471	+	0.0950638i	$0.969694\pi$
$492$		0			0
$493$	−2.30111	+	13.0502i	−0.103637	+	0.587754i
$494$	−11.1100	−	15.5832i	−0.499864	−	0.701120i
$495$		0			0
$496$	0.289545	+	0.718530i	0.0130009	+	0.0322630i
$497$	−5.56755	−	15.2967i	−0.249739	−	0.686152i
$498$		0			0
$499$	−13.3375	−	15.8950i	−0.597067	−	0.711556i	0.379881	−	0.925035i	$-0.375965\pi$
$499$	−13.3375	−	15.8950i	−0.597067	−	0.711556i	−0.976948	+	0.213479i	$0.931521\pi$
$500$	3.27614	−	20.6240i	0.146513	−	0.922333i
$501$		0			0
$502$	23.8468	+	1.88224i	1.06434	+	0.0840087i
$503$	2.51174	+	4.35046i	0.111993	+	0.193977i	0.916574	−	0.399866i	$-0.130943\pi$
$503$	2.51174	+	4.35046i	0.111993	+	0.193977i	−0.804581	+	0.593843i	$0.797610\pi$
$504$		0			0
$505$	0.742355	−	1.28580i	0.0330344	−	0.0572172i
$506$	16.8537	−	24.5104i	0.749239	−	1.08962i
$507$		0			0
$508$	23.3936	−	8.96777i	1.03792	−	0.397880i
$509$	21.4633	−	3.78456i	0.951344	−	0.167748i	0.323623	−	0.946186i	$-0.395099\pi$
$509$	21.4633	−	3.78456i	0.951344	−	0.167748i	0.627721	+	0.778438i	$0.283988\pi$
$510$		0			0
$511$	−6.20730	+	7.39758i	−0.274595	+	0.327250i
$512$	17.1759	+	14.7305i	0.759075	+	0.651003i
$513$		0			0
$514$	1.71393	−	3.75862i	0.0755983	−	0.165785i
$515$	14.8334	+	12.4467i	0.653639	+	0.548468i
$516$		0			0
$517$	−1.86228	−	10.5615i	−0.0819030	−	0.464495i
$518$	12.6974	−	12.9151i	0.557893	−	0.567458i
$519$		0			0
$520$	1.33818	+	11.8167i	0.0586831	+	0.518198i
$521$	8.39768	+	4.84840i	0.367909	+	0.212412i	0.672545	−	0.740057i	$-0.265201\pi$
$521$	8.39768	+	4.84840i	0.367909	+	0.212412i	−0.304635	+	0.952469i	$0.598535\pi$
$522$		0			0
$523$	3.03420	−	1.75180i	0.132676	−	0.0766007i	−0.432193	−	0.901781i	$-0.642260\pi$
$523$	3.03420	−	1.75180i	0.132676	−	0.0766007i	0.564869	+	0.825181i	$0.308927\pi$
$524$	6.07952	+	3.37355i	0.265585	+	0.147374i
$525$		0			0
$526$	−0.0254828	+	0.00706078i	−0.00111110	+	0.000307864i
$527$	−0.717410	+	0.601978i	−0.0312509	+	0.0262226i
$528$		0			0
$529$	7.45287	−	2.71262i	0.324038	−	0.117940i
$530$	−1.86860	−	19.4525i	−0.0811666	−	0.844962i
$531$		0			0
$532$	14.3281	−	2.77833i	0.621200	−	0.120456i
$533$	−13.1800	−	2.32398i	−0.570887	−	0.100663i
$534$		0			0
$535$	6.43216	−	17.6722i	0.278086	−	0.764036i
$536$	−2.62921	−	5.28241i	−0.113565	−	0.228165i
$537$		0			0
$538$	20.5949	−	9.81752i	0.887910	−	0.423263i
$539$	−19.5296			−0.841200
$540$		0			0
$541$	25.3365			1.08930			0.544652	−	0.838662i	$-0.316662\pi$
$541$	25.3365			1.08930			0.544652	+	0.838662i	$0.316662\pi$
$542$	29.2093	−	13.9240i	1.25465	−	0.598086i
$543$		0			0
$544$	−10.4968	+	25.2603i	−0.450048	+	1.08303i
$545$	5.23503	−	14.3831i	0.224244	−	0.616106i
$546$		0			0
$547$	6.82129	+	1.20278i	0.291657	+	0.0514270i	0.317562	−	0.948237i	$-0.397136\pi$
$547$	6.82129	+	1.20278i	0.291657	+	0.0514270i	−0.0259052	+	0.999664i	$0.508247\pi$
$548$	−1.92461	−	9.92534i	−0.0822151	−	0.423990i
$549$		0			0
$550$	−2.55431	−	26.5909i	−0.108916	−	1.13384i
$551$	−10.1979	+	3.71172i	−0.434443	+	0.158124i
$552$		0			0
$553$	−11.1949	+	9.39364i	−0.476056	+	0.399458i
$554$	−9.37223	+	2.59685i	−0.398188	+	0.110330i
$555$		0			0
$556$	6.28569	−	11.3275i	0.266573	−	0.480394i
$557$	1.26444	−	0.730025i	0.0535761	−	0.0309322i	−0.472973	−	0.881077i	$-0.656819\pi$
$557$	1.26444	−	0.730025i	0.0535761	−	0.0309322i	0.526549	+	0.850145i	$0.323486\pi$
$558$		0			0
$559$	22.3156	+	12.8839i	0.943851	+	0.544932i
$560$	−8.62274	−	2.81037i	−0.364377	−	0.118760i
$561$		0			0
$562$	−14.0580	+	14.2991i	−0.593003	+	0.603170i
$563$	−5.77946	−	32.7770i	−0.243575	−	1.38138i	−0.823778	−	0.566912i	$-0.808138\pi$
$563$	−5.77946	−	32.7770i	−0.243575	−	1.38138i	0.580203	−	0.814472i	$-0.302973\pi$
$564$		0			0
$565$	−3.57302	−	2.99812i	−0.150318	−	0.126132i
$566$	7.09010	−	15.5484i	0.298019	−	0.653549i
$567$		0			0
$568$	7.08002	+	23.9618i	0.297071	+	1.00541i
$569$	−27.7062	+	33.0189i	−1.16150	+	1.38423i	−0.252417	+	0.967619i	$0.581225\pi$
$569$	−27.7062	+	33.0189i	−1.16150	+	1.38423i	−0.909087	+	0.416607i	$0.863219\pi$
$570$		0			0
$571$	−8.94615	+	1.57745i	−0.374385	+	0.0660141i	−0.357675	−	0.933846i	$-0.616430\pi$
$571$	−8.94615	+	1.57745i	−0.374385	+	0.0660141i	−0.0167100	+	0.999860i	$0.505319\pi$
$572$	13.2553	+	34.5782i	0.554231	+	1.44579i
$573$		0			0
$574$	5.78278	−	8.40990i	0.241369	−	0.351023i
$575$	−6.76632	+	11.7196i	−0.282175	+	0.488742i
$576$		0			0
$577$	−1.27460	−	2.20767i	−0.0530622	−	0.0919064i	0.838274	−	0.545249i	$-0.183565\pi$
$577$	−1.27460	−	2.20767i	−0.0530622	−	0.0919064i	−0.891336	+	0.453342i	$0.850231\pi$
$578$	−8.99948	−	0.710334i	−0.374329	−	0.0295460i
$579$		0			0
$580$	6.66004	+	1.05795i	0.276543	+	0.0439291i
$581$	−2.14972	−	2.56193i	−0.0891853	−	0.106287i
$582$		0			0
$583$	−20.8128	−	57.1827i	−0.861978	−	2.36827i
$584$	10.2104	−	10.7448i	0.422509	−	0.444623i
$585$		0			0
$586$	4.82281	+	6.76458i	0.199228	+	0.279442i
$587$	0.223906	−	1.26984i	0.00924160	−	0.0524117i	−0.979838	−	0.199793i	$-0.935973\pi$
$587$	0.223906	−	1.26984i	0.00924160	−	0.0524117i	0.989080	+	0.147381i	$0.0470843\pi$
$588$		0			0
$589$	−0.720701	−	0.262314i	−0.0296959	−	0.0108084i
$590$	−6.50127	−	1.68292i	−0.267653	−	0.0692847i
$591$		0			0
$592$	−20.6759	+	18.5826i	−0.849774	+	0.763741i
$593$			10.8961i			0.447448i	0.974652	+	0.223724i	$0.0718215\pi$
$593$			10.8961i			0.447448i	−0.974652	+	0.223724i	$0.928179\pi$
$594$		0			0
$595$		−	10.9638i		−	0.449472i
$596$	10.5618	−	0.179552i	0.432630	−	0.00735472i
$597$		0			0
$598$	4.70123	−	18.1612i	0.192247	−	0.742669i
$599$	−9.33315	−	3.39699i	−0.381342	−	0.138797i	0.144234	−	0.989544i	$-0.453928\pi$
$599$	−9.33315	−	3.39699i	−0.381342	−	0.138797i	−0.525576	+	0.850746i	$0.676150\pi$
$600$		0			0
$601$	−1.10305	+	6.25571i	−0.0449943	+	0.255176i	−0.999005	−	0.0445969i	$-0.985800\pi$
$601$	−1.10305	+	6.25571i	−0.0449943	+	0.255176i	0.954011	+	0.299772i	$0.0969108\pi$
$602$	−16.0007	+	11.4077i	−0.652138	+	0.464942i
$603$		0			0
$604$	−16.7340	−	5.77048i	−0.680895	−	0.234798i
$605$	7.72576	+	21.2263i	0.314097	+	0.862974i
$606$		0			0
$607$	−20.0100	−	23.8470i	−0.812182	−	0.967921i	0.187715	−	0.982223i	$-0.439892\pi$
$607$	−20.0100	−	23.8470i	−0.812182	−	0.967921i	−0.999898	+	0.0143022i	$0.995447\pi$
$608$	−22.2135	+	2.89877i	−0.900878	+	0.117561i
$609$		0			0
$610$	−2.00818	+	25.4424i	−0.0813090	+	1.03013i
$611$	−3.38182	−	5.85749i	−0.136814	−	0.236969i
$612$		0			0
$613$	5.32449	−	9.22228i	0.215054	−	0.372484i	−0.738235	−	0.674543i	$-0.764341\pi$
$613$	5.32449	−	9.22228i	0.215054	−	0.372484i	0.953289	+	0.302059i	$0.0976739\pi$
$614$	−4.78095	−	3.28745i	−0.192943	−	0.132671i
$615$		0			0
$616$	−28.1869	−	1.74329i	−1.13568	−	0.0702393i
$617$	−12.1176	+	2.13666i	−0.487835	+	0.0860185i	−0.412155	−	0.911114i	$-0.635224\pi$
$617$	−12.1176	+	2.13666i	−0.487835	+	0.0860185i	−0.0756800	+	0.997132i	$0.524113\pi$
$618$		0			0
$619$	2.32369	−	2.76926i	0.0933968	−	0.111306i	−0.717322	−	0.696742i	$-0.754632\pi$
$619$	2.32369	−	2.76926i	0.0933968	−	0.111306i	0.810719	+	0.585436i	$0.199077\pi$
$620$	0.312500	+	0.359820i	0.0125503	+	0.0144507i
$621$		0			0
$622$	4.63738	+	2.11465i	0.185942	+	0.0847897i
$623$	−23.1556	−	19.4298i	−0.927709	−	0.778440i
$624$		0			0
$625$	0.795955	+	4.51408i	0.0318382	+	0.180563i
$626$	−21.4991	−	21.1367i	−0.859275	−	0.844792i
$627$		0			0
$628$	−17.0119	+	10.2112i	−0.678848	+	0.407473i
$629$	−29.1045	−	16.8035i	−1.16047	−	0.669999i
$630$		0			0
$631$	−0.363542	+	0.209891i	−0.0144724	+	0.00835562i	−0.507219	−	0.861817i	$-0.669326\pi$
$631$	−0.363542	+	0.209891i	−0.0144724	+	0.00835562i	0.492746	+	0.870173i	$0.335993\pi$
$632$	18.0404	−	13.3302i	0.717609	−	0.530245i
$633$		0			0
$634$	13.2569	+	47.8451i	0.526499	+	1.90017i
$635$	11.8070	−	9.90723i	0.468546	−	0.393156i
$636$		0			0
$637$	−11.5740	+	4.21261i	−0.458581	+	0.166910i
$638$	20.9027	−	2.00791i	0.827548	−	0.0794938i
$639$		0			0
$640$	12.9436	+	5.12243i	0.511640	+	0.202482i
$641$	−27.4445	−	4.83920i	−1.08399	−	0.191137i	−0.397012	−	0.917813i	$-0.629953\pi$
$641$	−27.4445	−	4.83920i	−1.08399	−	0.191137i	−0.686980	+	0.726676i	$0.741064\pi$
$642$		0			0
$643$	−9.89822	+	27.1951i	−0.390348	+	1.07247i	0.576495	+	0.817100i	$0.304420\pi$
$643$	−9.89822	+	27.1951i	−0.390348	+	1.07247i	−0.966843	+	0.255371i	$0.917802\pi$
$644$	11.1141	+	9.00841i	0.437958	+	0.354981i
$645$		0			0
$646$	−11.6535	−	24.4463i	−0.458500	−	0.961827i
$647$	20.3805			0.801241			0.400620	−	0.916244i	$-0.368795\pi$
$647$	20.3805			0.801241			0.400620	+	0.916244i	$0.368795\pi$
$648$		0			0
$649$	−20.9118			−0.820860
$650$	−7.24954	−	15.2079i	−0.284350	−	0.596502i
$651$		0			0
$652$	25.3114	+	20.5158i	0.991269	+	0.803461i
$653$	−14.1421	+	38.8551i	−0.553424	+	1.52052i	0.275581	+	0.961278i	$0.411130\pi$
$653$	−14.1421	+	38.8551i	−0.553424	+	1.52052i	−0.829005	+	0.559241i	$0.811093\pi$
$654$		0			0
$655$	4.21236	+	0.742753i	0.164591	+	0.0290218i
$656$	−9.65594	+	12.3359i	−0.377001	+	0.481636i
$657$		0			0
$658$	5.13439	−	0.493207i	0.200159	−	0.0192272i
$659$	−14.0070	+	5.09812i	−0.545634	+	0.198595i	−0.600106	−	0.799921i	$-0.704875\pi$
$659$	−14.0070	+	5.09812i	−0.545634	+	0.198595i	0.0544714	+	0.998515i	$0.482653\pi$
$660$		0			0
$661$	17.3934	−	14.5948i	0.676525	−	0.567672i	−0.238463	−	0.971151i	$-0.576644\pi$
$661$	17.3934	−	14.5948i	0.676525	−	0.567672i	0.914989	+	0.403479i	$0.132199\pi$
$662$	0.0899536	+	0.324649i	0.00349614	+	0.0126178i
$663$		0			0
$664$	3.05058	+	4.12851i	0.118386	+	0.160217i
$665$	7.77584	−	4.48939i	0.301534	−	0.174091i
$666$		0			0
$667$	−9.21264	−	5.31892i	−0.356715	−	0.205949i
$668$	−2.12478	+	1.27538i	−0.0822103	+	0.0493461i
$669$		0			0
$670$	−2.58853	−	2.54490i	−0.100003	−	0.0983179i
$671$	13.8002	+	78.2651i	0.532752	+	3.02139i
$672$		0			0
$673$	−25.8262	−	21.6708i	−0.995527	−	0.835346i	−0.00916851	−	0.999958i	$-0.502918\pi$
$673$	−25.8262	−	21.6708i	−0.995527	−	0.835346i	−0.986358	+	0.164612i	$0.947363\pi$
$674$	8.62597	+	3.93345i	0.332260	+	0.151511i
$675$		0			0
$676$	−1.73436	−	1.99698i	−0.0667060	−	0.0768071i
$677$	21.5588	−	25.6927i	0.828571	−	0.987452i	−0.171427	−	0.985197i	$-0.554838\pi$
$677$	21.5588	−	25.6927i	0.828571	−	0.987452i	0.999997	−	0.00225532i	$-0.000717892\pi$
$678$		0			0
$679$	−0.169225	+	0.0298390i	−0.00649427	+	0.00114511i
$680$	−1.03881	+	16.7963i	−0.0398366	+	0.644110i
$681$		0			0
$682$	1.22284	+	0.840844i	0.0468250	+	0.0321976i
$683$	−13.6418	+	23.6283i	−0.521989	+	0.904112i	0.477684	+	0.878532i	$0.341477\pi$
$683$	−13.6418	+	23.6283i	−0.521989	+	0.904112i	−0.999673	+	0.0255798i	$0.991857\pi$
$684$		0			0
$685$	−3.10989	−	5.38649i	−0.118823	−	0.205807i
$686$	2.17449	−	27.5494i	0.0830224	−	1.05184i
$687$		0			0
$688$	25.5936	−	15.9603i	0.975745	−	0.608480i
$689$	−24.6690	−	29.3994i	−0.939816	−	1.12003i
$690$		0			0
$691$	7.43220	+	20.4198i	0.282734	+	0.776806i	0.997034	+	0.0769659i	$0.0245232\pi$
$691$	7.43220	+	20.4198i	0.282734	+	0.776806i	−0.714299	+	0.699840i	$0.753255\pi$
$692$	−27.3068	−	9.41638i	−1.03805	−	0.357957i
$693$		0			0
$694$	−8.09923	+	5.77435i	−0.307443	+	0.219191i
$695$	1.38392	−	7.84859i	0.0524950	−	0.297714i
$696$		0			0
$697$	−17.7962	−	6.47728i	−0.674079	−	0.245345i
$698$	−2.52536	+	9.75567i	−0.0955861	+	0.369258i
$699$		0			0
$700$	12.8462	−	0.218385i	0.485539	−	0.00825419i
$701$			16.5491i			0.625051i	0.949909	+	0.312526i	$0.101175\pi$
$701$			16.5491i			0.625051i	−0.949909	+	0.312526i	$0.898825\pi$
$702$		0			0
$703$		−	27.5223i		−	1.03802i
$704$	43.0167	+	5.34138i	1.62125	+	0.201311i
$705$		0			0
$706$	−21.5355	−	5.57469i	−0.810501	−	0.209806i
$707$	2.08952	+	0.760521i	0.0785843	+	0.0286023i
$708$		0			0
$709$	4.05285	−	22.9848i	0.152208	−	0.863214i	−0.809086	−	0.587690i	$-0.800038\pi$
$709$	4.05285	−	22.9848i	0.152208	−	0.863214i	0.961294	−	0.275524i	$-0.0888514\pi$
$710$	8.92329	+	12.5160i	0.334885	+	0.469717i
$711$		0			0
$712$	33.6329	+	31.9601i	1.26045	+	1.19776i
$713$	−0.257129	−	0.706456i	−0.00962955	−	0.0264570i
$714$		0			0
$715$	14.6439	+	17.4519i	0.547651	+	0.652665i
$716$	19.7329	+	3.13459i	0.737455	+	0.117145i
$717$		0			0
$718$	−17.7263	−	1.39914i	−0.661538	−	0.0522156i
$719$	−25.8381	−	44.7529i	−0.963599	−	1.66900i	−0.713334	−	0.700825i	$-0.752816\pi$
$719$	−25.8381	−	44.7529i	−0.963599	−	1.66900i	−0.250265	−	0.968177i	$-0.580518\pi$
$720$		0			0
$721$	−14.5003	+	25.1152i	−0.540018	+	0.935338i
$722$	−2.65816	+	3.86576i	−0.0989265	+	0.143869i
$723$		0			0
$724$	−8.48899	−	22.1447i	−0.315491	−	0.823000i
$725$	−9.40824	+	1.65893i	−0.349413	+	0.0616110i
$726$		0			0
$727$	−7.38738	+	8.80393i	−0.273983	+	0.326520i	−0.885437	−	0.464760i	$-0.846141\pi$
$727$	−7.38738	+	8.80393i	−0.273983	+	0.326520i	0.611454	+	0.791280i	$0.290585\pi$
$728$	−17.0808	+	5.04688i	−0.633056	+	0.187050i
$729$		0			0
$730$	3.78335	−	8.29679i	0.140028	−	0.307078i
$731$	27.9326	+	23.4382i	1.03312	+	0.866894i
$732$		0			0
$733$	4.49588	+	25.4974i	0.166059	+	0.941768i	0.947966	+	0.318373i	$0.103136\pi$
$733$	4.49588	+	25.4974i	0.166059	+	0.941768i	−0.781906	+	0.623396i	$0.785753\pi$
$734$	21.6417	−	22.0127i	0.798809	−	0.812504i
$735$		0			0
$736$	−16.1731	−	14.8538i	−0.596147	−	0.547517i
$737$	−9.78921	−	5.65181i	−0.360590	−	0.208187i
$738$		0			0
$739$	27.0700	−	15.6289i	0.995786	−	0.574917i	0.0887874	−	0.996051i	$-0.471701\pi$
$739$	27.0700	−	15.6289i	0.995786	−	0.574917i	0.906999	+	0.421133i	$0.138367\pi$
$740$	−8.29808	+	14.9541i	−0.305044	+	0.549723i
$741$		0			0
$742$	28.2050	−	7.81502i	1.03544	−	0.286898i
$743$	−36.0136	+	30.2190i	−1.32121	+	1.10863i	−0.335166	+	0.942159i	$0.608792\pi$
$743$	−36.0136	+	30.2190i	−1.32121	+	1.10863i	−0.986047	+	0.166470i	$0.946763\pi$
$744$		0			0
$745$	6.10664	−	2.22264i	0.223730	−	0.0814311i
$746$	2.04643	+	21.3037i	0.0749250	+	0.779985i
$747$		0			0
$748$	9.97549	+	51.4444i	0.364740	+	1.88099i
$749$	27.7380	+	4.89095i	1.01352	+	0.178711i
$750$		0			0
$751$	3.24256	−	8.90885i	0.118323	−	0.325089i	−0.866366	−	0.499409i	$-0.833551\pi$
$751$	3.24256	−	8.90885i	0.118323	−	0.325089i	0.984689	+	0.174320i	$0.0557728\pi$
$752$	−7.91252	+	0.269104i	−0.288540	+	0.00981322i
$753$		0			0
$754$	11.9547	−	5.69877i	0.435365	−	0.207537i
$755$	−10.8896			−0.396313
$756$		0			0
$757$	−46.0979			−1.67546			−0.837728	−	0.546087i	$-0.816117\pi$
$757$	−46.0979			−1.67546			−0.837728	+	0.546087i	$0.816117\pi$
$758$	−32.9823	+	15.7225i	−1.19797	+	0.571068i
$759$		0			0
$760$	−12.3378	+	6.14089i	−0.447539	+	0.222754i
$761$	1.59797	−	4.39038i	0.0579263	−	0.159151i	−0.907354	−	0.420367i	$-0.861901\pi$
$761$	1.59797	−	4.39038i	0.0579263	−	0.159151i	0.965280	+	0.261216i	$0.0841235\pi$
$762$		0			0
$763$	22.5755	+	3.98067i	0.817288	+	0.144110i
$764$	0.349299	−	0.0677319i	0.0126372	−	0.00245045i
$765$		0			0
$766$	−0.629387	−	6.55206i	−0.0227407	−	0.236735i
$767$	−12.3932	+	4.51075i	−0.447492	+	0.162874i
$768$		0			0
$769$	18.4826	−	15.5088i	0.666501	−	0.559261i	−0.245526	−	0.969390i	$-0.578961\pi$
$769$	18.4826	−	15.5088i	0.666501	−	0.559261i	0.912028	+	0.410129i	$0.134516\pi$
$770$	−16.7429	+	4.63911i	−0.603371	+	0.167182i
$771$		0			0
$772$	12.1847	+	6.76135i	0.438538	+	0.243346i
$773$	37.2078	−	21.4820i	1.33827	−	0.772652i	0.351722	−	0.936105i	$-0.385596\pi$
$773$	37.2078	−	21.4820i	1.33827	−	0.772652i	0.986551	+	0.163452i	$0.0522630\pi$
$774$		0			0
$775$	−0.584701	−	0.337577i	−0.0210031	−	0.0121261i
$776$	0.262077	−	0.0296788i	0.00940801	−	0.00106541i
$777$		0			0
$778$	−28.2899	+	28.7749i	−1.01424	+	1.03163i
$779$	−2.69319	−	15.2738i	−0.0964935	−	0.547242i
$780$		0			0
$781$	36.6668	+	30.7671i	1.31204	+	1.10093i
$782$	11.0142	−	24.1538i	0.393866	−	0.863739i
$783$		0			0
$784$	−2.01949	+	14.2752i	−0.0721247	+	0.509828i
$785$	−7.84603	+	9.35054i	−0.280037	+	0.333735i
$786$		0			0
$787$	−19.5797	+	3.45243i	−0.697940	+	0.123066i	−0.511350	−	0.859372i	$-0.670855\pi$
$787$	−19.5797	+	3.45243i	−0.697940	+	0.123066i	−0.186590	+	0.982438i	$0.559743\pi$
$788$	10.1678	−	3.89775i	0.362213	−	0.138851i
$789$		0			0
$790$	7.81871	−	11.3707i	0.278177	−	0.404553i
$791$	3.49277	−	6.04966i	0.124189	−	0.215101i
$792$		0			0
$793$	25.0606	+	43.4063i	0.889930	+	1.54140i
$794$	2.77319	+	0.218890i	0.0984169	+	0.00776810i
$795$		0			0
$796$	−1.87926	+	11.8304i	−0.0666086	+	0.419316i
$797$	−0.657198	−	0.783218i	−0.0232792	−	0.0277430i	0.754279	−	0.656554i	$-0.227986\pi$
$797$	−0.657198	−	0.783218i	−0.0232792	−	0.0277430i	−0.777558	+	0.628811i	$0.783542\pi$
$798$		0			0
$799$	−3.27349	−	8.99384i	−0.115808	−	0.318179i
$800$	−19.7008	−	0.882601i	−0.696527	−	0.0312047i
$801$		0			0
$802$	−15.6267	−	21.9184i	−0.551798	−	0.773965i
$803$	4.93074	−	27.9636i	0.174002	−	0.986815i
$804$		0			0
$805$	8.27052	+	3.01022i	0.291498	+	0.106096i
$806$	0.906078	+	0.234548i	0.0319153	+	0.00826159i
$807$		0			0
$808$	−3.12904	−	1.36308i	−0.110079	−	0.0479531i
$809$			7.34131i			0.258107i	0.991638	+	0.129053i	$0.0411938\pi$
$809$			7.34131i			0.258107i	−0.991638	+	0.129053i	$0.958806\pi$
$810$		0			0
$811$			51.3514i			1.80319i	0.432581	+	0.901595i	$0.357603\pi$
$811$			51.3514i			1.80319i	−0.432581	+	0.901595i	$0.642397\pi$
$812$	0.171670	+	10.0982i	0.00602443	+	0.354377i
$813$		0			0
$814$	−13.3457	+	51.5556i	−0.467766	+	1.80702i
$815$	18.8353	+	6.85550i	0.659773	+	0.240138i
$816$		0			0
$817$	−5.18541	+	29.4079i	−0.181415	+	1.02885i
$818$	16.8901	−	12.0418i	0.590550	−	0.421032i
$819$		0			0
$820$	−3.14179	+	9.11096i	−0.109716	+	0.318168i
$821$	11.7882	+	32.3878i	0.411411	+	1.13034i	0.956441	+	0.291926i	$0.0942960\pi$
$821$	11.7882	+	32.3878i	0.411411	+	1.13034i	−0.545030	+	0.838416i	$0.683482\pi$
$822$		0			0
$823$	30.1050	+	35.8777i	1.04939	+	1.25062i	0.967204	+	0.254001i	$0.0817468\pi$
$823$	30.1050	+	35.8777i	1.04939	+	1.25062i	0.0821894	+	0.996617i	$0.473809\pi$
$824$	24.5938	−	37.1021i	0.856764	−	1.29251i
$825$		0			0
$826$	0.791401	−	10.0265i	0.0275364	−	0.348868i
$827$	−19.3141	−	33.4530i	−0.671616	−	1.16327i	−0.977446	−	0.211187i	$-0.932267\pi$
$827$	−19.3141	−	33.4530i	−0.671616	−	1.16327i	0.305830	−	0.952086i	$-0.401066\pi$
$828$		0			0
$829$	13.2958	−	23.0290i	0.461782	−	0.799830i	−0.537268	−	0.843412i	$-0.680543\pi$
$829$	13.2958	−	23.0290i	0.461782	−	0.799830i	0.999050	+	0.0435815i	$0.0138768\pi$
$830$	2.60217	+	1.78930i	0.0903228	+	0.0621074i
$831$		0			0
$832$	26.6456	−	6.11333i	0.923770	−	0.211942i
$833$	−17.1644	+	3.02655i	−0.594712	+	0.104864i
$834$		0			0
$835$	−0.979970	+	1.16788i	−0.0339132	+	0.0404162i
$836$	−32.4011	+	28.1400i	−1.12062	+	0.973243i
$837$		0			0
$838$	−14.9011	−	6.79491i	−0.514749	−	0.234726i
$839$	38.1735	+	32.0314i	1.31790	+	1.10585i	0.986747	+	0.162268i	$0.0518811\pi$
$839$	38.1735	+	32.0314i	1.31790	+	1.10585i	0.331150	+	0.943578i	$0.392563\pi$
$840$		0			0
$841$	3.73174	+	21.1637i	0.128681	+	0.729784i
$842$	−1.25158	−	1.23048i	−0.0431323	−	0.0424053i
$843$		0			0
$844$	−26.7162	−	44.5090i	−0.919609	−	1.53206i
$845$	−1.40919	−	0.813594i	−0.0484775	−	0.0279885i
$846$		0			0
$847$	−29.2980	+	16.9152i	−1.00669	+	0.581214i
$848$	−43.9499	+	9.30006i	−1.50925	+	0.319365i
$849$		0			0
$850$	−6.36582	−	22.9747i	−0.218346	−	0.788026i
$851$	20.6666	−	17.3413i	0.708442	−	0.594453i
$852$		0			0
$853$	−34.7953	+	12.6644i	−1.19137	+	0.433622i	−0.860203	−	0.509951i	$-0.829664\pi$
$853$	−34.7953	+	12.6644i	−1.19137	+	0.433622i	−0.331164	+	0.943573i	$0.607441\pi$
$854$	−38.0479	+	3.65486i	−1.30197	+	0.125067i
$855$		0			0
$856$	−42.0306	−	10.1210i	−1.43658	−	0.345928i
$857$	30.2150	+	5.32771i	1.03212	+	0.181991i	0.663959	−	0.747769i	$-0.268875\pi$
$857$	30.2150	+	5.32771i	1.03212	+	0.181991i	0.368165	+	0.929761i	$0.379986\pi$
$858$		0			0
$859$	−6.72321	+	18.4719i	−0.229393	+	0.630252i	−0.999975	−	0.00708895i	$-0.997743\pi$
$859$	−6.72321	+	18.4719i	−0.229393	+	0.630252i	0.770582	+	0.637341i	$0.219966\pi$
$860$	11.6841	−	14.4152i	0.398423	−	0.491554i
$861$		0			0
$862$	−20.5984	−	43.2107i	−0.701583	−	1.47176i
$863$	5.14051			0.174985			0.0874925	−	0.996165i	$-0.472115\pi$
$863$	5.14051			0.174985			0.0874925	+	0.996165i	$0.472115\pi$
$864$		0			0
$865$	−17.7698			−0.604193
$866$	−13.2083	−	27.7080i	−0.448836	−	0.941555i
$867$		0			0
$868$	−0.449436	+	0.554492i	−0.0152549	+	0.0188207i
$869$	14.6969	−	40.3793i	0.498557	−	1.36977i
$870$		0			0
$871$	−7.02060	−	1.23792i	−0.237884	−	0.0419454i
$872$	−34.2080	−	8.23731i	−1.15843	−	0.278951i
$873$		0			0
$874$	21.6406	−	2.07879i	0.732004	−	0.0703160i
$875$	18.0802	−	6.58065i	0.611222	−	0.222467i
$876$		0			0
$877$	39.7096	−	33.3203i	1.34090	−	1.12515i	0.359504	−	0.933143i	$-0.382946\pi$
$877$	39.7096	−	33.3203i	1.34090	−	1.12515i	0.981394	−	0.192004i	$-0.0614986\pi$
$878$	14.1212	+	50.9646i	0.476569	+	1.71997i
$879$		0			0
$880$	26.0893	−	5.52065i	0.879470	−	0.186101i
$881$	28.7442	−	16.5955i	0.968418	−	0.559116i	0.0696643	−	0.997570i	$-0.477807\pi$
$881$	28.7442	−	16.5955i	0.968418	−	0.559116i	0.898754	+	0.438454i	$0.144474\pi$
$882$		0			0
$883$	−31.2856	−	18.0627i	−1.05284	−	0.607859i	−0.129399	−	0.991593i	$-0.541305\pi$
$883$	−31.2856	−	18.0627i	−1.05284	−	0.607859i	−0.923444	+	0.383733i	$0.874638\pi$
$884$	17.0086	+	28.3363i	0.572062	+	0.953053i
$885$		0			0
$886$	−6.20001	−	6.09551i	−0.208293	−	0.204783i
$887$	−4.04900	−	22.9630i	−0.135952	−	0.771023i	−0.974192	−	0.225721i	$-0.927526\pi$
$887$	−4.04900	−	22.9630i	−0.135952	−	0.771023i	0.838240	−	0.545302i	$-0.183585\pi$
$888$		0			0
$889$	17.6830	+	14.8378i	0.593070	+	0.497645i
$890$	25.9703	+	11.8425i	0.870525	+	0.396960i
$891$		0			0
$892$	33.7497	−	29.3112i	1.13002	−	0.981412i
$893$	5.03828	−	6.00439i	0.168600	−	0.200929i
$894$		0			0
$895$	12.1051	−	2.13446i	0.404630	−	0.0713472i
$896$	−4.18898	+	20.4230i	−0.139944	+	0.682284i
$897$		0			0
$898$	5.79645	+	3.98573i	0.193430	+	0.133005i
$899$	0.265365	−	0.459625i	0.00885041	−	0.0153294i
$900$		0			0
$901$	−27.1540	−	47.0321i	−0.904630	−	1.56687i
$902$	−2.36139	+	29.9173i	−0.0786258	+	0.996139i
$903$		0			0
$904$	−5.92405	+	8.93701i	−0.197031	+	0.297241i
$905$	−9.37829	−	11.1766i	−0.311745	−	0.371523i
$906$		0			0
$907$	−4.67374	−	12.8410i	−0.155189	−	0.426379i	0.837595	−	0.546291i	$-0.183961\pi$
$907$	−4.67374	−	12.8410i	−0.155189	−	0.426379i	−0.992784	+	0.119913i	$0.961739\pi$
$908$	−1.10273	+	3.19782i	−0.0365953	+	0.106123i
$909$		0			0
$910$	−8.92183	+	6.36082i	−0.295756	+	0.210859i
$911$	−4.68110	+	26.5479i	−0.155092	+	0.879570i	0.803610	+	0.595156i	$0.202910\pi$
$911$	−4.68110	+	26.5479i	−0.155092	+	0.879570i	−0.958702	+	0.284413i	$0.908201\pi$
$912$		0			0
$913$	9.24072	+	3.36335i	0.305823	+	0.111311i
$914$	3.76799	−	14.5561i	0.124634	−	0.481472i
$915$		0			0
$916$	−0.902003	−	53.0589i	−0.0298030	−	1.75311i
$917$			6.40608i			0.211547i
$918$		0			0
$919$			10.8263i			0.357127i	0.983928	+	0.178563i	$0.0571449\pi$
$919$			10.8263i			0.357127i	−0.983928	+	0.178563i	$0.942855\pi$
$920$	−12.3851	−	5.39523i	−0.408323	−	0.177875i
$921$		0			0
$922$	−19.6595	−	5.08907i	−0.647452	−	0.167600i
$923$	28.3668	+	10.3247i	0.933705	+	0.339841i
$924$		0			0
$925$	4.20716	−	23.8600i	0.138331	−	0.784512i
$926$	−14.9848	−	21.0181i	−0.492432	−	0.690697i
$927$		0			0
$928$	0.693801	−	15.4865i	0.0227751	−	0.508369i
$929$	−5.88119	−	16.1584i	−0.192956	−	0.530141i	0.805054	−	0.593201i	$-0.202136\pi$
$929$	−5.88119	−	16.1584i	−0.192956	−	0.530141i	−0.998010	+	0.0630604i	$0.979914\pi$
$930$		0			0
$931$	−9.17490	−	10.9342i	−0.300695	−	0.358355i
$932$	1.47880	−	9.30934i	0.0484395	−	0.304937i
$933$		0			0
$934$	32.3593	+	2.55413i	1.05883	+	0.0835738i
$935$	16.1190	+	27.9189i	0.527147	+	0.913046i
$936$		0			0
$937$	9.74943	−	16.8865i	0.318500	−	0.551658i	−0.661675	−	0.749791i	$-0.730154\pi$
$937$	9.74943	−	16.8865i	0.318500	−	0.551658i	0.980175	+	0.198132i	$0.0634876\pi$
$938$	3.08033	−	4.47973i	0.100576	−	0.146268i
$939$		0			0
$940$	−4.54787	+	1.74339i	−0.148335	+	0.0568631i
$941$	2.10956	−	0.371973i	0.0687698	−	0.0121260i	−0.139157	−	0.990270i	$-0.544439\pi$
$941$	2.10956	−	0.371973i	0.0687698	−	0.0121260i	0.207927	+	0.978144i	$0.433328\pi$
$942$		0			0
$943$	9.77225	−	11.6461i	0.318228	−	0.379250i
$944$	−2.16242	+	15.2855i	−0.0703807	+	0.497500i
$945$		0			0
$946$	23.9735	−	52.5733i	0.779446	−	1.70931i
$947$	−32.2731	−	27.0803i	−1.04873	−	0.879992i	−0.0557737	−	0.998443i	$-0.517763\pi$
$947$	−32.2731	−	27.0803i	−1.04873	−	0.879992i	−0.992960	+	0.118452i	$0.962207\pi$
$948$		0			0
$949$	−3.10970	−	17.6360i	−0.100945	−	0.572488i
$950$	13.6877	−	13.9224i	0.444087	−	0.451701i
$951$		0			0
$952$	−25.0435	+	2.83603i	−0.811663	+	0.0919164i
$953$	−19.8498	−	11.4603i	−0.642999	−	0.371236i	0.142770	−	0.989756i	$-0.454399\pi$
$953$	−19.8498	−	11.4603i	−0.642999	−	0.371236i	−0.785769	+	0.618520i	$0.787732\pi$
$954$		0			0
$955$	0.189565	−	0.109445i	0.00613417	−	0.00354156i
$956$	−5.89180	−	3.26939i	−0.190555	−	0.105739i
$957$		0			0
$958$	−23.9677	+	6.64096i	−0.774361	+	0.214560i
$959$	7.13588	−	5.98771i	0.230430	−	0.193353i
$960$		0			0
$961$	−29.0952	+	10.5898i	−0.938556	+	0.341606i
$962$	3.21153	+	33.4327i	0.103544	+	1.07791i
$963$		0			0
$964$	31.3503	−	6.07907i	1.00972	−	0.195794i
$965$	8.44252	+	1.48864i	0.271774	+	0.0479212i
$966$		0			0
$967$	14.1549	−	38.8902i	0.455190	−	1.25062i	−0.473837	−	0.880613i	$-0.657131\pi$
$967$	14.1549	−	38.8902i	0.455190	−	1.25062i	0.929027	−	0.370012i	$-0.120646\pi$
$968$	46.4867	−	23.1378i	1.49414	−	0.743677i
$969$		0			0
$970$	0.146469	−	0.0698212i	0.00470284	−	0.00224183i
$971$	14.7098			0.472061			0.236030	−	0.971746i	$-0.424153\pi$
$971$	14.7098			0.472061			0.236030	+	0.971746i	$0.424153\pi$
$972$		0			0
$973$	11.9360			0.382650
$974$	20.0061	−	9.53684i	0.641037	−	0.305580i
$975$		0			0
$976$	58.6349	−	1.99417i	1.87686	−	0.0638318i
$977$	11.1196	−	30.5509i	0.355748	−	0.977409i	−0.624741	−	0.780832i	$-0.714795\pi$
$977$	11.1196	−	30.5509i	0.355748	−	0.977409i	0.980488	−	0.196577i	$-0.0629825\pi$
$978$		0			0
$979$	87.5305	+	15.4340i	2.79749	+	0.493273i
$980$	1.68842	+	8.70731i	0.0539346	+	0.278145i
$981$		0			0
$982$	5.41106	+	56.3303i	0.172674	+	1.79757i
$983$	49.0400	−	17.8491i	1.56413	−	0.569298i	0.592455	−	0.805604i	$-0.298159\pi$
$983$	49.0400	−	17.8491i	1.56413	−	0.569298i	0.971679	+	0.236306i	$0.0759367\pi$
$984$		0			0
$985$	5.13178	−	4.30607i	0.163512	−	0.137203i
$986$	18.0601	−	5.00409i	0.575151	−	0.159363i
$987$		0			0
$988$	−13.1323	+	23.6660i	−0.417795	+	0.752915i
$989$	−25.3498	+	14.6357i	−0.806075	+	0.465388i
$990$		0			0
$991$	17.1645	+	9.90990i	0.545247	+	0.314798i	0.747203	−	0.664596i	$-0.231396\pi$
$991$	17.1645	+	9.90990i	0.545247	+	0.314798i	−0.201956	+	0.979395i	$0.564730\pi$
$992$	0.741065	−	0.806887i	0.0235288	−	0.0256187i
$993$		0			0
$994$	−16.1395	+	16.4162i	−0.511913	+	0.520690i
$995$	1.27966	+	7.25731i	0.0405679	+	0.230072i
$996$		0			0
$997$	1.62058	+	1.35983i	0.0513244	+	0.0430663i	0.668089	−	0.744081i	$-0.267113\pi$
$997$	1.62058	+	1.35983i	0.0513244	+	0.0430663i	−0.616765	+	0.787148i	$0.711557\pi$
$998$	−12.1749	+	26.6992i	−0.385389	+	0.845149i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.5		96
3.2	odd	2		108.2.l.a.11.12	yes	96
4.3	odd	2	inner	324.2.l.a.35.15		96
9.2	odd	6		972.2.l.d.755.11		96
9.4	even	3		972.2.l.b.431.16		96
9.5	odd	6		972.2.l.c.431.1		96
9.7	even	3		972.2.l.a.755.6		96
12.11	even	2		108.2.l.a.11.2	✓	96
27.4	even	9		972.2.l.d.215.9		96
27.5	odd	18	inner	324.2.l.a.287.15		96
27.13	even	9		972.2.l.c.539.13		96
27.14	odd	18		972.2.l.b.539.4		96
27.22	even	9		108.2.l.a.59.2	yes	96
27.23	odd	18		972.2.l.a.215.8		96
36.7	odd	6		972.2.l.a.755.8		96
36.11	even	6		972.2.l.d.755.9		96
36.23	even	6		972.2.l.c.431.13		96
36.31	odd	6		972.2.l.b.431.4		96
108.23	even	18		972.2.l.a.215.6		96
108.31	odd	18		972.2.l.d.215.11		96
108.59	even	18	inner	324.2.l.a.287.5		96
108.67	odd	18		972.2.l.c.539.1		96
108.95	even	18		972.2.l.b.539.16		96
108.103	odd	18		108.2.l.a.59.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.2	✓	96	12.11	even	2
108.2.l.a.11.12	yes	96	3.2	odd	2
108.2.l.a.59.2	yes	96	27.22	even	9
108.2.l.a.59.12	yes	96	108.103	odd	18
324.2.l.a.35.5		96	1.1	even	1	trivial
324.2.l.a.35.15		96	4.3	odd	2	inner
324.2.l.a.287.5		96	108.59	even	18	inner
324.2.l.a.287.15		96	27.5	odd	18	inner
972.2.l.a.215.6		96	108.23	even	18
972.2.l.a.215.8		96	27.23	odd	18
972.2.l.a.755.6		96	9.7	even	3
972.2.l.a.755.8		96	36.7	odd	6
972.2.l.b.431.4		96	36.31	odd	6
972.2.l.b.431.16		96	9.4	even	3
972.2.l.b.539.4		96	27.14	odd	18
972.2.l.b.539.16		96	108.95	even	18
972.2.l.c.431.1		96	9.5	odd	6
972.2.l.c.431.13		96	36.23	even	6
972.2.l.c.539.1		96	108.67	odd	18
972.2.l.c.539.13		96	27.13	even	9
972.2.l.d.215.9		96	27.4	even	9
972.2.l.d.215.11		96	108.31	odd	18
972.2.l.d.755.9		96	36.11	even	6
972.2.l.d.755.11		96	9.2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.608544 - 1.27659i) q^{2} +(-1.25935 + 1.55372i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(-1.81474 - 0.319988i) q^{7} +(2.74983 + 0.662160i) q^{8} +O(q^{10})\)	\(q+(-0.608544 - 1.27659i) q^{2} +(-1.25935 + 1.55372i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(-1.81474 - 0.319988i) q^{7} +(2.74983 + 0.662160i) q^{8} +(1.73207 - 0.166382i) q^{10} +(5.09161 - 1.85319i) q^{11} +(2.61776 - 2.19656i) q^{13} +(0.695857 + 2.51140i) q^{14} +(-0.828087 - 3.91335i) q^{16} +(4.18778 - 2.41782i) q^{17} +(3.42957 + 1.98006i) q^{19} +(-1.26644 - 2.10989i) q^{20} +(-5.46423 - 5.37213i) q^{22} +(0.674078 + 3.82288i) q^{23} +(2.67053 + 2.24084i) q^{25} +(-4.39712 - 2.00509i) q^{26} +(2.78256 - 2.41662i) q^{28} +(-1.76149 + 2.09927i) q^{29} +(-0.190727 + 0.0336302i) q^{31} +(-4.49180 + 3.43857i) q^{32} +(-5.63501 - 3.87472i) q^{34} +(1.13365 - 1.96353i) q^{35} +(-3.47493 - 6.01875i) q^{37} +(0.440678 - 5.58310i) q^{38} +(-1.92277 + 2.90068i) q^{40} +(-2.51742 - 3.00014i) q^{41} +(2.57902 + 7.08581i) q^{43} +(-3.53276 + 10.2447i) q^{44} +(4.47004 - 3.18691i) q^{46} +(0.343697 - 1.94920i) q^{47} +(-3.38696 - 1.23275i) q^{49} +(1.23549 - 4.77281i) q^{50} +(0.116170 + 6.83349i) q^{52} -11.2308i q^{53} +6.66675i q^{55} +(-4.77834 - 2.08156i) q^{56} +(3.75184 + 0.971203i) q^{58} +(-3.62667 - 1.32000i) q^{59} +(-2.54693 + 14.4444i) q^{61} +(0.158997 + 0.223013i) q^{62} +(7.12309 + 3.64165i) q^{64} +(1.43804 + 3.95099i) q^{65} +(-1.34096 - 1.59809i) q^{67} +(-1.51727 + 9.55151i) q^{68} +(-3.19649 - 0.252301i) q^{70} +(4.41692 + 7.65033i) q^{71} +(2.62025 - 4.53841i) q^{73} +(-5.56881 + 8.09872i) q^{74} +(-7.39549 + 2.83500i) q^{76} +(-9.83294 + 1.73381i) q^{77} +(5.09766 - 6.07516i) q^{79} +(4.87306 + 0.689385i) q^{80} +(-2.29798 + 5.03942i) q^{82} +(1.39029 + 1.16659i) q^{83} +(1.03316 + 5.85935i) q^{85} +(7.47620 - 7.60437i) q^{86} +(15.2282 - 1.72450i) q^{88} +(14.2059 + 8.20179i) q^{89} +(-5.45341 + 3.14853i) q^{91} +(-6.78859 - 3.76701i) q^{92} +(-2.69748 + 0.747418i) q^{94} +(-3.73257 + 3.13200i) q^{95} +(0.0876267 - 0.0318935i) q^{97} +(0.487400 + 5.07393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

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