LMFDB - Embedded newform 324.2.l.a.35.15

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			35.15
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36287 + 0.377622i) q^{2} +(1.71480 + 1.02930i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(1.81474 + 0.319988i) q^{7} +(1.94836 + 2.05034i) q^{8} +O(q^{10})$	\(q+(1.36287 + 0.377622i) q^{2} +(1.71480 + 1.02930i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(1.81474 + 0.319988i) q^{7} +(1.94836 + 2.05034i) q^{8} +(-1.01013 + 1.41682i) q^{10} +(-5.09161 + 1.85319i) q^{11} +(2.61776 - 2.19656i) q^{13} +(2.35241 + 1.12139i) q^{14} +(1.88110 + 3.53008i) q^{16} +(4.18778 - 2.41782i) q^{17} +(-3.42957 - 1.98006i) q^{19} +(-1.91169 + 1.54950i) q^{20} +(-7.63898 + 0.602949i) q^{22} +(-0.674078 - 3.82288i) q^{23} +(2.67053 + 2.24084i) q^{25} +(4.39712 - 2.00509i) q^{26} +(2.78256 + 2.41662i) q^{28} +(-1.76149 + 2.09927i) q^{29} +(0.190727 - 0.0336302i) q^{31} +(1.23065 + 5.52137i) q^{32} +(6.62041 - 1.71376i) q^{34} +(-1.13365 + 1.96353i) q^{35} +(-3.47493 - 6.01875i) q^{37} +(-3.92633 - 3.99364i) q^{38} +(-3.19050 + 1.38986i) q^{40} +(-2.51742 - 3.00014i) q^{41} +(-2.57902 - 7.08581i) q^{43} +(-10.6386 - 2.06291i) q^{44} +(0.524929 - 5.46462i) q^{46} +(-0.343697 + 1.94920i) q^{47} +(-3.38696 - 1.23275i) q^{49} +(2.79338 + 4.06241i) q^{50} +(6.74984 - 1.07222i) q^{52} -11.2308i q^{53} -6.66675i q^{55} +(2.87968 + 4.34428i) q^{56} +(-3.19341 + 2.19584i) q^{58} +(3.62667 + 1.32000i) q^{59} +(-2.54693 + 14.4444i) q^{61} +(0.272634 + 0.0261891i) q^{62} +(-0.407785 + 7.98960i) q^{64} +(1.43804 + 3.95099i) q^{65} +(1.34096 + 1.59809i) q^{67} +(9.66988 + 0.164388i) q^{68} +(-2.28648 + 2.24794i) q^{70} +(-4.41692 - 7.65033i) q^{71} +(2.62025 - 4.53841i) q^{73} +(-2.46304 - 9.51495i) q^{74} +(-3.84297 - 6.92547i) q^{76} +(-9.83294 + 1.73381i) q^{77} +(-5.09766 + 6.07516i) q^{79} +(-4.87306 + 0.689385i) q^{80} +(-2.29798 - 5.03942i) q^{82} +(-1.39029 - 1.16659i) q^{83} +(1.03316 + 5.85935i) q^{85} +(-0.839103 - 10.6309i) q^{86} +(-13.7200 - 6.82884i) q^{88} +(14.2059 + 8.20179i) q^{89} +(5.45341 - 3.14853i) q^{91} +(2.77897 - 7.24932i) q^{92} +(-1.20448 + 2.52671i) q^{94} +(3.73257 - 3.13200i) q^{95} +(0.0876267 - 0.0318935i) q^{97} +(-4.15046 - 2.95907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.36287	+	0.377622i	0.963691	+	0.267019i
$2$	1.36287	+	0.377622i	0.963691	+	0.267019i
$3$		0			0
$3$		0			0
$4$	1.71480	+	1.02930i	0.857401	+	0.514648i
$5$	−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	0.505732	−	0.862691i	$-0.331222\pi$
$7$	1.81474	+	0.319988i	0.685907	+	0.120944i	0.180175	+	0.983635i	$0.442334\pi$
$8$	1.94836	+	2.05034i	0.688849	+	0.724905i
$9$		0			0
$10$	−1.01013	+	1.41682i	−0.319430	+	0.448039i
$11$	−5.09161	+	1.85319i	−1.53518	+	0.558759i	−0.964883	−	0.262681i	$-0.915393\pi$
$11$	−5.09161	+	1.85319i	−1.53518	+	0.558759i	−0.570295	+	0.821440i	$0.693171\pi$
$12$		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	$0.120629\pi$
$14$	2.35241	+	1.12139i	0.628708	+	0.299703i
$15$		0			0
$16$	1.88110	+	3.53008i	0.470275	+	0.882520i
$17$	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	0.0520361	−	0.998645i	$-0.483429\pi$
$19$	−3.42957	−	1.98006i	−0.786798	−	0.454258i	−0.838834	+	0.544387i	$0.816762\pi$
$20$	−1.91169	+	1.54950i	−0.427467	+	0.346478i
$21$		0			0
$22$	−7.63898	+	0.602949i	−1.62864	+	0.128549i
$23$	−0.674078	−	3.82288i	−0.140555	−	0.797126i	−0.970829	−	0.239772i	$-0.922927\pi$
$23$	−0.674078	−	3.82288i	−0.140555	−	0.797126i	0.830274	−	0.557355i	$-0.188184\pi$
$24$		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	−0.156494	−	0.987679i	$-0.550019\pi$
$31$	0.190727	−	0.0336302i	0.0342555	−	0.00604017i	0.190750	+	0.981639i	$0.438908\pi$
$32$	1.23065	+	5.52137i	0.217550	+	0.976049i
$33$		0			0
$34$	6.62041	−	1.71376i	1.13539	−	0.293907i
$35$	−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	$-0.360217\pi$
$38$	−3.92633	−	3.99364i	−0.636935	−	0.647855i
$39$		0			0
$40$	−3.19050	+	1.38986i	−0.504462	+	0.219756i
$41$	−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	$-0.916128\pi$
$43$	−2.57902	−	7.08581i	−0.393297	−	1.08058i	0.572189	−	0.820122i	$-0.306094\pi$
$44$	−10.6386	−	2.06291i	−1.60383	−	0.310996i
$45$		0			0
$46$	0.524929	−	5.46462i	0.0773965	−	0.805714i
$47$	−0.343697	+	1.94920i	−0.0501334	+	0.284321i	−0.999560	−	0.0296691i	$-0.990555\pi$
$47$	−0.343697	+	1.94920i	−0.0501334	+	0.284321i	0.949426	+	0.313990i	$0.101666\pi$
$48$		0			0
$49$	−3.38696	−	1.23275i	−0.483852	−	0.176108i
$50$	2.79338	+	4.06241i	0.395044	+	0.574512i
$51$		0			0
$52$	6.74984	−	1.07222i	0.936035	−	0.148690i
$53$		−	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
$56$	2.87968	+	4.34428i	0.384814	+	0.580529i
$57$		0			0
$58$	−3.19341	+	2.19584i	−0.419315	+	0.288328i
$59$	3.62667	+	1.32000i	0.472152	+	0.171849i	0.567127	−	0.823630i	$-0.308055\pi$
$59$	3.62667	+	1.32000i	0.472152	+	0.171849i	−0.0949749	+	0.995480i	$0.530277\pi$
$60$		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	$0.667336\pi$
$62$	0.272634	+	0.0261891i	0.0346246	+	0.00332602i
$63$		0			0
$64$	−0.407785	+	7.98960i	−0.0509731	+	0.998700i
$65$	1.43804	+	3.95099i	0.178367	+	0.490060i
$66$		0			0
$67$	1.34096	+	1.59809i	0.163824	+	0.195238i	0.841711	−	0.539928i	$-0.181549\pi$
$67$	1.34096	+	1.59809i	0.163824	+	0.195238i	−0.677887	+	0.735166i	$0.737104\pi$
$68$	9.66988	+	0.164388i	1.17264	+	0.0199350i
$69$		0			0
$70$	−2.28648	+	2.24794i	−0.273287	+	0.268680i
$71$	−4.41692	−	7.65033i	−0.524192	−	0.907927i	−0.999603	−	0.0281636i	$-0.991034\pi$
$71$	−4.41692	−	7.65033i	−0.524192	−	0.907927i	0.475411	−	0.879764i	$-0.342299\pi$
$72$		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	$0.0674495\pi$
$74$	−2.46304	−	9.51495i	−0.286323	−	1.10609i
$75$		0			0
$76$	−3.84297	−	6.92547i	−0.440819	−	0.794406i
$77$	−9.83294	+	1.73381i	−1.12057	+	0.197586i
$78$		0			0
$79$	−5.09766	+	6.07516i	−0.573532	+	0.683508i	−0.972352	−	0.233521i	$-0.924975\pi$
$79$	−5.09766	+	6.07516i	−0.573532	+	0.683508i	0.398820	+	0.917029i	$0.369420\pi$
$80$	−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	0.563289	−	0.826260i	$-0.309536\pi$
$83$	−1.39029	−	1.16659i	−0.152604	−	0.128050i	−0.715893	+	0.698210i	$0.753980\pi$
$84$		0			0
$85$	1.03316	+	5.85935i	0.112062	+	0.635536i
$86$	−0.839103	−	10.6309i	−0.0904828	−	1.14636i
$87$		0			0
$88$	−13.7200	−	6.82884i	−1.46255	−	0.727957i
$89$	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
$92$	2.77897	−	7.24932i	0.289728	−	0.755794i
$93$		0			0
$94$	−1.20448	+	2.52671i	−0.124232	+	0.260611i
$95$	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	$0.387382\pi$
$98$	−4.15046	−	2.95907i	−0.419259	−	0.298911i
$99$		0			0
$100$	2.27294	+	6.59136i	0.227294	+	0.659136i
$101$	−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	$0.393534\pi$
$103$	−5.38263	+	14.7887i	−0.530366	+	1.45717i	−0.858636	+	0.512586i	$0.828688\pi$
$104$	9.60402	+	1.08760i	0.941752	+	0.106648i
$105$		0			0
$106$	4.24099	−	15.3060i	0.411921	−	1.48665i
$107$	15.2848			1.47764			0.738820	−	0.673903i	$-0.235384\pi$
$107$	15.2848			1.47764			0.738820	+	0.673903i	$0.235384\pi$
$108$		0			0
$109$	−12.4401			−1.19154			−0.595772	−	0.803154i	$-0.703154\pi$
$109$	−12.4401			−1.19154			−0.595772	+	0.803154i	$0.703154\pi$
$110$	2.51751	−	9.08588i	0.240035	−	0.866304i
$111$		0			0
$112$	2.28412	+	7.00810i	0.215829	+	0.662204i
$113$	−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
$116$	−5.18138	+	1.78673i	−0.481079	+	0.165894i
$117$		0			0
$118$	4.44420	+	3.16849i	0.409122	+	0.291683i
$119$	8.37341	−	3.04767i	0.767589	−	0.279380i
$120$		0			0
$121$	14.0637	−	11.8008i	1.27852	−	1.07280i
$122$	−8.92564	+	18.7240i	−0.808090	+	1.69519i
$123$		0			0
$124$	0.361674	+	0.138645i	0.0324793	+	0.0124507i
$125$	−9.04242	+	5.22065i	−0.808779	+	0.466949i
$126$		0			0
$127$	10.8485	+	6.26340i	0.962651	+	0.555787i	0.896988	−	0.442055i	$-0.145750\pi$
$127$	10.8485	+	6.26340i	0.962651	+	0.555787i	0.0656631	+	0.997842i	$0.479084\pi$
$128$	−3.57281	+	10.7348i	−0.315794	+	0.948828i
$129$		0			0
$130$	0.467877	+	5.92770i	0.0410355	+	0.519894i
$131$	0.603670	+	3.42359i	0.0527429	+	0.299120i	0.999756	−	0.0220740i	$-0.00702694\pi$
$131$	0.603670	+	3.42359i	0.0527429	+	0.299120i	−0.947013	+	0.321194i	$0.895916\pi$
$132$		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	0.103558	−	0.994623i	$-0.466977\pi$
$139$	6.37891	−	1.12477i	0.541052	−	0.0954022i	0.437494	+	0.899221i	$0.355866\pi$
$140$	−3.96504	+	2.20021i	−0.335107	+	0.185952i
$141$		0			0
$142$	−3.13073	−	12.0943i	−0.262725	−	1.01493i
$143$	−9.25794	+	16.0352i	−0.774188	+	1.34093i
$144$		0			0
$145$	−1.68589	−	2.92004i	−0.140005	−	0.242496i
$146$	5.28485	−	5.19577i	0.437377	−	0.430005i
$147$		0			0
$148$	0.236262	−	13.8977i	0.0194206	−	1.14238i
$149$	−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	$-0.993847\pi$
$151$	−3.02704	−	8.31673i	−0.246337	−	0.676806i	0.753476	−	0.657475i	$-0.228376\pi$
$152$	−2.62224	−	10.8897i	−0.212692	−	0.883269i
$153$		0			0
$154$	−14.0557	−	1.35018i	−1.13264	−	0.108801i
$155$	−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	$0.481552\pi$
$158$	−9.24154	+	6.35463i	−0.735217	+	0.505547i
$159$		0			0
$160$	−6.90165	−	0.900636i	−0.545623	−	0.0712015i
$161$		−	7.15323i		−	0.563754i
$162$		0			0
$163$			16.2908i			1.27600i	0.770038	+	0.637998i	$0.220237\pi$
$163$			16.2908i			1.27600i	−0.770038	+	0.637998i	$0.779763\pi$
$164$	−1.22884	−	7.73581i	−0.0959563	−	0.604066i
$165$		0			0
$166$	−1.45425	−	2.11491i	−0.112871	−	0.164149i
$167$	−1.16436	−	0.423791i	−0.0901007	−	0.0327940i	0.296577	−	0.955009i	$-0.404155\pi$
$167$	−1.16436	−	0.423791i	−0.0901007	−	0.0327940i	−0.386677	+	0.922215i	$0.626377\pi$
$168$		0			0
$169$	−0.229648	+	1.30240i	−0.0176653	+	0.100185i
$170$	−0.804561	+	8.37566i	−0.0617070	+	0.642383i
$171$		0			0
$172$	2.87088	−	14.8053i	0.218902	−	1.12890i
$173$	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
$176$	−16.1197	−	14.4878i	−1.21507	−	1.09206i
$177$		0			0
$178$	16.2636	+	16.5424i	1.21901	+	1.23991i
$179$	4.99509	+	8.65175i	0.373351	+	0.646662i	0.990079	−	0.140514i	$-0.0448755\pi$
$179$	4.99509	+	8.65175i	0.373351	+	0.646662i	−0.616728	+	0.787176i	$0.711542\pi$
$180$		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	$0.311936\pi$
$182$	8.62122	−	2.23169i	0.639048	−	0.165424i
$183$		0			0
$184$	6.52486	−	8.83044i	0.481019	−	0.650989i
$185$	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	0.647705	−	0.761891i	$-0.275729\pi$
$191$	0.136281	+	0.114354i	0.00986096	+	0.00827433i	−0.637844	+	0.770166i	$0.720173\pi$
$192$		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	$-0.136238\pi$
$194$	0.131467	−	0.0103768i	0.00943879	−	0.000745009i
$195$		0			0
$196$	−4.53910	−	5.60011i	−0.324222	−	0.400008i
$197$	−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	−0.672449	−	0.740143i	$-0.734758\pi$
$199$	−5.18692	+	2.99467i	−0.367691	+	0.212287i	0.304758	+	0.952430i	$0.401424\pi$
$200$	0.608669	+	9.84145i	0.0430394	+	0.695896i
$201$		0			0
$202$	−1.54045	−	0.734326i	−0.108386	−	0.0516670i
$203$	−3.86839	+	3.24597i	−0.271508	+	0.227822i
$204$		0			0
$205$	4.52812	−	1.64810i	0.316258	−	0.115108i
$206$	−12.9203	+	18.1223i	−0.900202	+	1.26264i
$207$		0			0
$208$	12.6783	+	5.10895i	0.879081	+	0.354242i
$209$	21.1315	+	3.72605i	1.46170	+	0.257736i
$210$		0			0
$211$	8.87740	−	24.3905i	0.611145	−	1.67911i	−0.116531	−	0.993187i	$-0.537177\pi$
$211$	8.87740	−	24.3905i	0.611145	−	1.67911i	0.727676	−	0.685921i	$-0.240600\pi$
$212$	11.5598	−	19.2586i	0.793930	−	1.32268i
$213$		0			0
$214$	20.8311	+	5.77189i	1.42399	+	0.394558i
$215$	9.27787			0.632745
$216$		0			0
$217$	0.356880			0.0242266
$218$	−16.9541	−	4.69765i	−1.14828	−	0.318165i
$219$		0			0
$220$	6.86206	−	11.4322i	0.462640	−	0.770756i
$221$	5.65172	−	15.5280i	0.380176	−	1.04452i
$222$		0			0
$223$	22.0110	+	3.88113i	1.47396	+	0.259900i	0.852164	−	0.523275i	$-0.175290\pi$
$223$	22.0110	+	3.88113i	1.47396	+	0.259900i	0.621801	+	0.783175i	$0.286401\pi$
$224$	0.466535	+	10.4136i	0.0311717	+	0.695790i
$225$		0			0
$226$	−3.11220	+	4.36525i	−0.207021	+	0.290372i
$227$	−1.58931	+	0.578461i	−0.105486	+	0.0383938i	−0.394224	−	0.919014i	$-0.628987\pi$
$227$	−1.58931	+	0.578461i	−0.105486	+	0.0383938i	0.288738	+	0.957408i	$0.406764\pi$
$228$		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	$0.937528\pi$
$230$	6.09726	+	2.90654i	0.402041	+	0.191652i
$231$		0			0
$232$	−7.73623	+	0.478467i	−0.507909	+	0.0314129i
$233$	−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
$236$	4.86035	+	5.99646i	0.316382	+	0.390336i
$237$		0			0
$238$	12.5627	−	0.991581i	0.814319	−	0.0642746i
$239$	−0.585031	−	3.31788i	−0.0378425	−	0.214616i	0.960023	−	0.279922i	$-0.0903086\pi$
$239$	−0.585031	−	3.31788i	−0.0378425	−	0.214616i	−0.997865	+	0.0653065i	$0.979197\pi$
$240$		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
$248$	0.440557	+	0.325530i	0.0279754	+	0.0206712i
$249$		0			0
$250$	−14.2950	+	3.70042i	−0.904097	+	0.234035i
$251$	8.45736	−	14.6486i	0.533824	−	0.924610i	−0.465396	−	0.885103i	$-0.654088\pi$
$251$	8.45736	−	14.6486i	0.533824	−	0.924610i	0.999219	−	0.0395068i	$-0.0125787\pi$
$252$		0			0
$253$	10.5167	+	18.2154i	0.661178	+	1.14519i
$254$	12.4199	+	12.6328i	0.779293	+	0.792653i
$255$		0			0
$256$	−8.92294	+	13.2809i	−0.557684	+	0.830054i
$257$	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
$260$	−1.60078	+	8.25533i	−0.0992760	+	0.511974i
$261$		0			0
$262$	−0.470100	+	4.89384i	−0.0290429	+	0.302343i
$263$	−0.00324687	+	0.0184139i	−0.000200211	+	0.00113545i	−0.984908	−	0.173080i	$-0.944628\pi$
$263$	−0.00324687	+	0.0184139i	−0.000200211	+	0.00113545i	0.984707	+	0.174216i	$0.0557391\pi$
$264$		0			0
$265$	12.9849	+	4.72613i	0.797659	+	0.290324i
$266$	−5.84735	−	8.50380i	−0.358524	−	0.521401i
$267$		0			0
$268$	0.654570	+	4.12066i	0.0399842	+	0.251709i
$269$			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	$-0.755424\pi$
$271$		−	22.8808i		−	1.38991i	0.719053	−	0.694955i	$-0.244576\pi$
$272$	16.4127	+	10.2351i	0.995168	+	0.620592i
$273$		0			0
$274$	−5.89076	+	4.05058i	−0.355874	+	0.244705i
$275$	−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	$-0.0106827\pi$
$278$	9.11834	+	0.875903i	0.546882	+	0.0525332i
$279$		0			0
$280$	−6.23466	+	1.50131i	−0.372592	+	0.0897204i
$281$	−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	0.484081	−	0.875023i	$-0.339154\pi$
$283$	−7.76714	−	9.25651i	−0.461708	−	0.550243i	−0.945789	+	0.324781i	$0.894710\pi$
$284$	0.300308	−	17.6651i	0.0178200	−	1.04823i
$285$		0			0
$286$	−18.6726	+	18.3578i	−1.10413	+	1.08552i
$287$	−3.60845	−	6.25001i	−0.213000	−	0.368927i
$288$		0			0
$289$	3.19169	−	5.52817i	0.187747	−	0.325187i
$290$	−1.19496	−	4.61625i	−0.0701707	−	0.271076i
$291$		0			0
$292$	9.16458	−	5.08546i	0.536316	−	0.297604i
$293$	−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
$302$	−0.984869	−	12.4777i	−0.0566728	−	0.718009i
$303$		0			0
$304$	0.538424	−	15.8314i	0.0308807	−	0.907991i
$305$	−15.6287	−	9.02323i	−0.894896	−	0.516668i
$306$		0			0
$307$	−3.55307	+	2.05137i	−0.202784	+	0.117078i	−0.597954	−	0.801531i	$-0.704019\pi$
$307$	−3.55307	+	2.05137i	−0.202784	+	0.117078i	0.395169	+	0.918608i	$0.370686\pi$
$308$	−18.6462	−	7.14786i	−1.06246	−	0.407287i
$309$		0			0
$310$	−0.145010	+	0.304197i	−0.00823599	+	0.0172772i
$311$	2.76079	−	2.31658i	0.156550	−	0.131361i	−0.561148	−	0.827715i	$-0.689640\pi$
$311$	2.76079	−	2.31658i	0.156550	−	0.131361i	0.717698	+	0.696354i	$0.245196\pi$
$312$		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	$0.183060\pi$
$314$	11.4238	+	8.14458i	0.644681	+	0.459625i
$315$		0			0
$316$	−14.9946	+	5.17069i	−0.843513	+	0.290874i
$317$	−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
$320$	−9.06592	−	3.83366i	−0.506800	−	0.214308i
$321$		0			0
$322$	2.70122	−	9.74889i	0.150533	−	0.543285i
$323$	−19.1497			−1.06552
$324$		0			0
$325$	11.9129			0.660810
$326$	−6.15178	+	22.2022i	−0.340715	+	1.22967i
$327$		0			0
$328$	1.24647	−	11.0069i	0.0688249	−	0.607755i
$329$	−1.24744	+	3.42732i	−0.0687737	+	0.188954i
$330$		0			0
$331$	0.234592	+	0.0413648i	0.0128943	+	0.00227362i	0.180092	−	0.983650i	$-0.442361\pi$
$331$	0.234592	+	0.0413648i	0.0128943	+	0.00227362i	−0.167197	+	0.985923i	$0.553472\pi$
$332$	−1.18330	−	3.43149i	−0.0649422	−	0.188328i
$333$		0			0
$334$	−1.42683	−	1.01726i	−0.0780726	−	0.0556619i
$335$	−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	$0.336225\pi$
$338$	−0.804795	+	1.68828i	−0.0437751	+	0.0918301i
$339$		0			0
$340$	−4.25934	+	11.1111i	−0.230995	+	0.602582i
$341$	−0.908782	+	0.524685i	−0.0492133	+	0.0284133i
$342$		0			0
$343$	−16.9230	−	9.77048i	−0.913755	−	0.527556i
$344$	9.50345	−	19.0936i	0.512391	−	1.02946i
$345$		0			0
$346$	1.60713	+	20.3613i	0.0863997	+	1.09463i
$347$	1.22136	+	6.92666i	0.0655659	+	0.371843i	0.999881	+	0.0153957i	$0.00490079\pi$
$347$	1.22136	+	6.92666i	0.0655659	+	0.371843i	−0.934316	+	0.356447i	$0.883988\pi$
$348$		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
$356$	15.9183	+	28.6866i	0.843667	+	1.52038i
$357$		0			0
$358$	3.54054	+	13.6774i	0.187123	+	0.722874i
$359$	−6.28667	+	10.8888i	−0.331798	+	0.574691i	−0.982864	−	0.184330i	$-0.940988\pi$
$359$	−6.28667	+	10.8888i	−0.331798	+	0.574691i	0.651067	+	0.759021i	$0.274322\pi$
$360$		0			0
$361$	−1.65869	−	2.87293i	−0.0872993	−	0.151207i
$362$	−11.9584	+	11.7568i	−0.628517	+	0.617923i
$363$		0			0
$364$	12.5923	+	0.214070i	0.660016	+	0.0112203i
$365$	4.14462	+	4.93937i	0.216939	+	0.258538i
$366$		0			0
$367$	−7.46561	−	20.5116i	−0.389702	−	1.07070i	−0.967136	−	0.254260i	$-0.918168\pi$
$367$	−7.46561	−	20.5116i	−0.389702	−	1.07070i	0.577434	−	0.816437i	$-0.304054\pi$
$368$	12.2271	−	9.57077i	0.637381	−	0.498911i
$369$		0			0
$370$	12.0376	+	1.15633i	0.625806	+	0.0601146i
$371$	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	$0.739254\pi$
$374$	−30.5326	+	20.9947i	−1.57880	+	1.08561i
$375$		0			0
$376$	−4.66618	+	3.09306i	−0.240640	+	0.159512i
$377$			9.36459i			0.482301i
$378$		0			0
$379$			25.8363i			1.32712i	0.748122	+	0.663561i	$0.230956\pi$
$379$			25.8363i			1.32712i	−0.748122	+	0.663561i	$0.769044\pi$
$380$	9.62438	−	1.52884i	0.493720	−	0.0784278i
$381$		0			0
$382$	0.142550	+	0.207311i	0.00729352	+	0.0106070i
$383$	−4.37364	−	1.59187i	−0.223482	−	0.0813410i	0.227852	−	0.973696i	$-0.426830\pi$
$383$	−4.37364	−	1.59187i	−0.223482	−	0.0813410i	−0.451335	+	0.892355i	$0.649052\pi$
$384$		0			0
$385$	2.13328	−	12.0984i	0.108722	−	0.616592i
$386$	0.942187	−	9.80836i	0.0479560	−	0.499233i
$387$		0			0
$388$	0.183090	+	0.0355027i	0.00929501	+	0.00180238i
$389$	−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
$392$	−4.07146	−	9.34627i	−0.205640	−	0.472058i
$393$		0			0
$394$	−5.39817	−	5.49072i	−0.271956	−	0.276619i
$395$	−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	$0.182385\pi$
$398$	−8.19993	+	2.12264i	−0.411025	+	0.106398i
$399$		0			0
$400$	−2.88682	+	13.6424i	−0.144341	+	0.682121i
$401$	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	$0.826322\pi$
$410$	6.79358	−	0.536221i	0.335511	−	0.0264821i
$411$		0			0
$412$	−24.4521	+	19.8193i	−1.20467	+	0.976427i
$413$	6.15908	+	3.55594i	0.303068	+	0.174977i
$414$		0			0
$415$	1.93387	−	1.11652i	0.0949297	−	0.0548077i
$416$	15.3495	+	11.7504i	0.752573	+	0.576111i
$417$		0			0
$418$	27.3923	+	13.0578i	1.33980	+	0.638679i
$419$	−8.87113	+	7.44376i	−0.433383	+	0.363651i	−0.833226	−	0.552932i	$-0.813509\pi$
$419$	−8.87113	+	7.44376i	−0.433383	+	0.363651i	0.399843	+	0.916583i	$0.369064\pi$
$420$		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	$0.379261\pi$
$422$	21.3091	−	29.8886i	1.03731	−	1.45495i
$423$		0			0
$424$	23.0269	−	21.8816i	1.11829	−	1.06266i
$425$	16.6015	+	2.92730i	0.805293	+	0.141995i
$426$		0			0
$427$	−9.24404	+	25.3978i	−0.447350	+	1.22908i
$428$	26.2105	+	15.7326i	1.26693	+	0.760464i
$429$		0			0
$430$	12.6445	+	3.50353i	0.609771	+	0.168955i
$431$	−33.8486			−1.63043			−0.815214	−	0.579159i	$-0.803381\pi$
$431$	−33.8486			−1.63043			−0.815214	+	0.579159i	$0.803381\pi$
$432$		0			0
$433$	21.7047			1.04306			0.521531	−	0.853232i	$-0.325361\pi$
$433$	21.7047			1.04306			0.521531	+	0.853232i	$0.325361\pi$
$434$	0.486380	+	0.134766i	0.0233470	+	0.00646897i
$435$		0			0
$436$	−21.3323	−	12.8045i	−1.02163	−	0.613225i
$437$	−5.25776	+	14.4456i	−0.251513	+	0.691026i
$438$		0			0
$439$	36.8270	+	6.49360i	1.75766	+	0.309923i	0.957192	−	0.289454i	$-0.0934737\pi$
$439$	36.8270	+	6.49360i	1.75766	+	0.309923i	0.800467	+	0.599377i	$0.204585\pi$
$440$	13.6691	−	12.9892i	0.651649	−	0.619237i
$441$		0			0
$442$	13.5662	−	19.0283i	0.645280	−	0.905084i
$443$	−5.77721	+	2.10273i	−0.274484	+	0.0999039i	−0.475595	−	0.879665i	$-0.657767\pi$
$443$	−5.77721	+	2.10273i	−0.274484	+	0.0999039i	0.201111	+	0.979568i	$0.435545\pi$
$444$		0			0
$445$	−15.4610	+	12.9733i	−0.732922	+	0.614994i
$446$	28.5324	+	13.6013i	1.35105	+	0.644040i
$447$		0			0
$448$	−3.29660	+	14.3686i	−0.155750	+	0.678850i
$449$	−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
$452$	−5.88992	+	4.77400i	−0.277039	+	0.224550i
$453$		0			0
$454$	−2.38445	+	0.188206i	−0.111908	+	0.00883296i
$455$	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	−0.574944	−	0.818192i	$-0.694976\pi$
$463$	−17.9752	+	3.16951i	−0.835377	+	0.147300i	−0.260433	+	0.965492i	$0.583865\pi$
$464$	−10.7241	−	2.26929i	−0.497855	−	0.105349i
$465$		0			0
$466$	−6.45255	+	1.67031i	−0.298908	+	0.0773755i
$467$	11.4763	−	19.8775i	0.531060	−	0.919823i	−0.468283	−	0.883579i	$-0.655127\pi$
$467$	11.4763	−	19.8775i	0.531060	−	0.919823i	0.999343	−	0.0362446i	$-0.0115395\pi$
$468$		0			0
$469$	1.92212	+	3.32921i	0.0887553	+	0.153729i
$470$	−2.41450	−	2.45590i	−0.111373	−	0.113282i
$471$		0			0
$472$	4.35961	+	10.0077i	0.200667	+	0.460644i
$473$	26.2628	+	31.2987i	1.20756	+	1.43912i
$474$		0			0
$475$	−4.72176	−	12.9729i	−0.216649	−	0.595239i
$476$	17.4957	+	3.39256i	0.801914	+	0.155498i
$477$		0			0
$478$	0.455585	−	4.74274i	0.0208380	−	0.216928i
$479$	−3.05382	+	17.3191i	−0.139533	+	0.791329i	0.832063	+	0.554681i	$0.187160\pi$
$479$	−3.05382	+	17.3191i	−0.139533	+	0.791329i	−0.971596	+	0.236648i	$0.923951\pi$
$480$		0			0
$481$	−22.3170	−	8.12274i	−1.01757	−	0.370365i
$482$	−12.7942	−	18.6066i	−0.582759	−	0.847507i
$483$		0			0
$484$	36.2630	−	5.76040i	1.64832	−	0.261836i
$485$			0.114735i			0.00520984i
$486$		0			0
$487$		−	15.6716i		−	0.710147i	−0.934838	−	0.355073i	$-0.884456\pi$
$487$		−	15.6716i		−	0.710147i	0.934838	−	0.355073i	$-0.115544\pi$
$488$	−34.5782	+	22.9208i	−1.56528	+	1.03757i
$489$		0			0
$490$	5.16785	−	3.55350i	0.233460	−	0.160531i
$491$	37.6017	+	13.6859i	1.69694	+	0.617636i	0.995471	−	0.0950638i	$-0.0303055\pi$
$491$	37.6017	+	13.6859i	1.69694	+	0.617636i	0.701469	+	0.712700i	$0.252528\pi$
$492$		0			0
$493$	−2.30111	+	13.0502i	−0.103637	+	0.587754i
$494$	−19.0504	−	1.82998i	−0.857120	−	0.0823345i
$495$		0			0
$496$	0.477493	+	0.610018i	0.0214401	+	0.0273906i
$497$	−5.56755	−	15.2967i	−0.249739	−	0.686152i
$498$		0			0
$499$	13.3375	+	15.8950i	0.597067	+	0.711556i	0.976948	−	0.213479i	$-0.0684795\pi$
$499$	13.3375	+	15.8950i	0.597067	+	0.711556i	−0.379881	+	0.925035i	$0.624035\pi$
$500$	−20.8796	−	0.354954i	−0.933763	−	0.0158740i
$501$		0			0
$502$	17.0579	−	16.7703i	0.761330	−	0.748497i
$503$	−2.51174	−	4.35046i	−0.111993	−	0.193977i	0.804581	−	0.593843i	$-0.202390\pi$
$503$	−2.51174	−	4.35046i	−0.111993	−	0.193977i	−0.916574	+	0.399866i	$0.869057\pi$
$504$		0			0
$505$	0.742355	−	1.28580i	0.0330344	−	0.0572172i
$506$	7.45427	+	28.7965i	0.331383	+	1.28016i
$507$		0			0
$508$	12.1562	+	21.9068i	0.539344	+	0.971959i
$509$	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
$518$	−1.42511	−	18.0553i	−0.0626160	−	0.793304i
$519$		0			0
$520$	−5.29904	+	10.6464i	−0.232378	+	0.466876i
$521$	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	−0.564869	−	0.825181i	$-0.691073\pi$
$523$	−3.03420	+	1.75180i	−0.132676	+	0.0766007i	0.432193	+	0.901781i	$0.357740\pi$
$524$	−2.48871	+	6.49213i	−0.108720	+	0.283610i
$525$		0			0
$526$	−0.0113786	+	0.0238696i	−0.000496129	+	0.00104076i
$527$	0.717410	−	0.601978i	0.0312509	−	0.0262226i
$528$		0			0
$529$	7.45287	−	2.71262i	0.324038	−	0.117940i
$530$	15.9120	+	11.3445i	0.691175	+	0.492773i
$531$		0			0
$532$	−4.75792	−	13.7976i	−0.206282	−	0.598203i
$533$	−13.1800	−	2.32398i	−0.570887	−	0.100663i
$534$		0			0
$535$	−6.43216	+	17.6722i	−0.278086	+	0.764036i
$536$	−0.663962	+	5.86308i	−0.0286788	+	0.253247i
$537$		0			0
$538$	−6.09210	+	21.9868i	−0.262649	+	0.947919i
$539$	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	$0.316662\pi$
$542$	8.64030	−	31.1835i	0.371133	−	1.33944i
$543$		0			0
$544$	18.5033	+	20.1468i	0.793325	+	0.863788i
$545$	5.23503	−	14.3831i	0.224244	−	0.616106i
$546$		0			0
$547$	−6.82129	−	1.20278i	−0.291657	−	0.0514270i	0.0259052	−	0.999664i	$-0.491753\pi$
$547$	−6.82129	−	1.20278i	−0.291657	−	0.0514270i	−0.317562	+	0.948237i	$0.602864\pi$
$548$	−9.55790	+	3.29591i	−0.408293	+	0.140794i
$549$		0			0
$550$	−21.7512	−	15.5075i	−0.927476	−	0.661244i
$551$	10.1979	−	3.71172i	0.434443	−	0.158124i
$552$		0			0
$553$	−11.1949	+	9.39364i	−0.476056	+	0.399458i
$554$	4.18487	−	8.77890i	0.177798	−	0.372980i
$555$		0			0
$556$	12.0963	+	4.63703i	0.512998	+	0.196654i
$557$	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
$560$	−9.06393	−	0.308264i	−0.383021	−	0.0130265i
$561$		0			0
$562$	−1.57783	−	19.9901i	−0.0665566	−	0.843229i
$563$	5.77946	+	32.7770i	0.243575	+	1.38138i	0.823778	+	0.566912i	$0.191862\pi$
$563$	5.77946	+	32.7770i	0.243575	+	1.38138i	−0.580203	+	0.814472i	$0.697027\pi$
$564$		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	0.0167100	−	0.999860i	$-0.494681\pi$
$571$	8.94615	−	1.57745i	0.374385	−	0.0660141i	0.357675	+	0.933846i	$0.383570\pi$
$572$	−32.3805	+	17.9681i	−1.35390	+	0.751283i
$573$		0			0
$574$	−2.55768	−	9.88055i	−0.106756	−	0.412406i
$575$	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	$0.850231\pi$
$578$	6.43740	−	6.32890i	0.267761	−	0.263247i
$579$		0			0
$580$	0.114624	−	6.74257i	0.00475950	−	0.279970i
$581$	−2.14972	−	2.56193i	−0.0891853	−	0.106287i
$582$		0			0
$583$	20.8128	+	57.1827i	0.861978	+	2.36827i
$584$	14.4105	−	3.47005i	0.596309	−	0.143592i
$585$		0			0
$586$	−8.26970	−	0.794383i	−0.341618	−	0.0328157i
$587$	−0.223906	+	1.26984i	−0.00924160	+	0.0524117i	−0.989080	−	0.147381i	$-0.952916\pi$
$587$	−0.223906	+	1.26984i	−0.00924160	+	0.0524117i	0.979838	+	0.199793i	$0.0640268\pi$
$588$		0			0
$589$	−0.720701	−	0.262314i	−0.0296959	−	0.0108084i
$590$	−5.53360	+	3.80499i	−0.227815	+	0.156649i
$591$		0			0
$592$	14.7100	−	23.5886i	0.604577	−	0.969487i
$593$			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
$596$	−1.65722	−	10.4326i	−0.0678823	−	0.427334i
$597$		0			0
$598$	−10.6292	−	15.4581i	−0.434661	−	0.632128i
$599$	9.33315	+	3.39699i	0.381342	+	0.138797i	0.525576	−	0.850746i	$-0.323850\pi$
$599$	9.33315	+	3.39699i	0.381342	+	0.138797i	−0.144234	+	0.989544i	$0.546072\pi$
$600$		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	$0.0969108\pi$
$602$	1.87900	−	19.5608i	0.0765824	−	0.797239i
$603$		0			0
$604$	3.36960	−	17.3773i	0.137107	−	0.707071i
$605$	7.72576	+	21.2263i	0.314097	+	0.862974i
$606$		0			0
$607$	20.0100	+	23.8470i	0.812182	+	0.967921i	0.999898	−	0.0143022i	$-0.00455270\pi$
$607$	20.0100	+	23.8470i	0.812182	+	0.967921i	−0.187715	+	0.982223i	$0.560108\pi$
$608$	6.71207	−	21.3727i	0.272211	−	0.866777i
$609$		0			0
$610$	−17.8924	−	18.1992i	−0.724443	−	0.736863i
$611$	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	$0.0976739\pi$
$614$	−5.61700	+	1.45402i	−0.226683	+	0.0586793i
$615$		0			0
$616$	−22.7130	−	16.7828i	−0.915134	−	0.676198i
$617$	−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	−0.810719	−	0.585436i	$-0.800923\pi$
$619$	−2.32369	+	2.76926i	−0.0933968	+	0.111306i	0.717322	+	0.696742i	$0.245368\pi$
$620$	−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
$626$	30.0556	−	2.37231i	1.20126	−	0.0948165i
$627$		0			0
$628$	12.4935	+	15.4138i	0.498544	+	0.615079i
$629$	−29.1045	−	16.8035i	−1.16047	−	0.669999i
$630$		0			0
$631$	0.363542	−	0.209891i	0.0144724	−	0.00835562i	−0.492746	−	0.870173i	$-0.664007\pi$
$631$	0.363542	−	0.209891i	0.0144724	−	0.00835562i	0.507219	+	0.861817i	$0.330674\pi$
$632$	−22.3882	+	1.38466i	−0.890555	+	0.0550786i
$633$		0			0
$634$	−44.8162	−	21.3637i	−1.77988	−	0.848461i
$635$	−11.8070	+	9.90723i	−0.468546	+	0.393156i
$636$		0			0
$637$	−11.5740	+	4.21261i	−0.458581	+	0.166910i
$638$	12.1903	−	17.0984i	0.482618	−	0.676930i
$639$		0			0
$640$	−10.9079	−	8.64826i	−0.431175	−	0.341852i
$641$	−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	$-0.695580\pi$
$643$	9.89822	−	27.1951i	0.390348	−	1.07247i	0.966843	−	0.255371i	$-0.0821977\pi$
$644$	7.36280	−	12.2664i	0.290135	−	0.483363i
$645$		0			0
$646$	−26.0985	−	7.23137i	−1.02683	−	0.284514i
$647$	−20.3805			−0.801241			−0.400620	−	0.916244i	$-0.631205\pi$
$647$	−20.3805			−0.801241			−0.400620	+	0.916244i	$0.631205\pi$
$648$		0			0
$649$	−20.9118			−0.820860
$650$	16.2357	+	4.49858i	0.636817	+	0.176449i
$651$		0			0
$652$	−16.7681	+	27.9355i	−0.656689	+	1.09404i
$653$	−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
$656$	5.85523	−	14.5302i	0.228608	−	0.567310i
$657$		0			0
$658$	−2.99433	+	4.19991i	−0.116731	+	0.163730i
$659$	14.0070	−	5.09812i	0.545634	−	0.198595i	−0.0544714	−	0.998515i	$-0.517347\pi$
$659$	14.0070	−	5.09812i	0.545634	−	0.198595i	0.600106	+	0.799921i	$0.295125\pi$
$660$		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	$0.132199\pi$
$662$	0.304096	+	0.144962i	0.0118190	+	0.00563409i
$663$		0			0
$664$	−0.316876	−	5.12350i	−0.0122972	−	0.198830i
$665$	7.77584	−	4.48939i	0.301534	−	0.174091i
$666$		0			0
$667$	9.21264	+	5.31892i	0.356715	+	0.205949i
$668$	−1.56044	−	1.92519i	−0.0603751	−	0.0744877i
$669$		0			0
$670$	−3.61875	+	0.285630i	−0.139805	+	0.0110349i
$671$	−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
$680$	−10.0007	+	13.5345i	−0.383509	+	0.519023i
$681$		0			0
$682$	−1.43668	+	0.371899i	−0.0550133	+	0.0142408i
$683$	13.6418	−	23.6283i	0.521989	−	0.904112i	−0.477684	−	0.878532i	$-0.658523\pi$
$683$	13.6418	−	23.6283i	0.521989	−	0.904112i	0.999673	−	0.0255798i	$-0.00814320\pi$
$684$		0			0
$685$	−3.10989	−	5.38649i	−0.118823	−	0.205807i
$686$	−19.3742	−	19.7063i	−0.739710	−	0.752392i
$687$		0			0
$688$	20.1621	−	22.4333i	0.768672	−	0.855260i
$689$	−24.6690	−	29.3994i	−0.939816	−	1.12003i
$690$		0			0
$691$	−7.43220	−	20.4198i	−0.282734	−	0.776806i	−0.997034	−	0.0769659i	$-0.975477\pi$
$691$	−7.43220	−	20.4198i	−0.282734	−	0.776806i	0.714299	−	0.699840i	$-0.246745\pi$
$692$	−5.49857	+	28.3566i	−0.209024	+	1.07796i
$693$		0			0
$694$	−0.951115	+	9.90131i	−0.0361038	+	0.375849i
$695$	−1.38392	+	7.84859i	−0.0524950	+	0.297714i
$696$		0			0
$697$	−17.7962	−	6.47728i	−0.674079	−	0.245345i
$698$	−5.70969	−	8.30361i	−0.216115	−	0.314296i
$699$		0			0
$700$	2.01564	+	12.6889i	0.0761842	+	0.479596i
$701$			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
$704$	−12.7300	−	41.4356i	−0.479780	−	1.56166i
$705$		0			0
$706$	18.3301	−	12.6041i	0.689863	−	0.474361i
$707$	−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	$-0.0888514\pi$
$710$	15.3008	+	1.46979i	0.574230	+	0.0551602i
$711$		0			0
$712$	10.8618	+	45.1070i	0.407063	+	1.69046i
$713$	−0.257129	−	0.706456i	−0.00962955	−	0.0264570i
$714$		0			0
$715$	−14.6439	−	17.4519i	−0.547651	−	0.652665i
$716$	−0.339618	+	19.9775i	−0.0126921	+	0.746593i
$717$		0			0
$718$	−12.6797	+	12.4660i	−0.473204	+	0.465228i
$719$	25.8381	+	44.7529i	0.963599	+	1.66900i	0.713334	+	0.700825i	$0.247184\pi$
$719$	25.8381	+	44.7529i	0.963599	+	1.66900i	0.250265	+	0.968177i	$0.419482\pi$
$720$		0			0
$721$	−14.5003	+	25.1152i	−0.540018	+	0.935338i
$722$	−1.17568	−	4.54177i	−0.0437545	−	0.169027i
$723$		0			0
$724$	−20.7373	+	11.5072i	−0.770694	+	0.427661i
$725$	−9.40824	+	1.65893i	−0.349413	+	0.0616110i
$726$		0			0
$727$	7.38738	−	8.80393i	0.273983	−	0.326520i	−0.611454	−	0.791280i	$-0.709415\pi$
$727$	7.38738	−	8.80393i	0.273983	−	0.326520i	0.885437	+	0.464760i	$0.153859\pi$
$728$	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	$0.785753\pi$
$734$	−2.42899	−	30.7737i	−0.0896556	−	1.13588i
$735$		0			0
$736$	20.2780	−	8.42645i	0.747457	−	0.310603i
$737$	−9.78921	−	5.65181i	−0.360590	−	0.208187i
$738$		0			0
$739$	−27.0700	+	15.6289i	−0.995786	+	0.574917i	−0.906999	−	0.421133i	$-0.861633\pi$
$739$	−27.0700	+	15.6289i	−0.995786	+	0.574917i	−0.0887874	+	0.996051i	$0.528299\pi$
$740$	15.9690	+	6.12159i	0.587032	+	0.225034i
$741$		0			0
$742$	12.5940	−	26.4194i	0.462341	−	0.969887i
$743$	36.0136	−	30.2190i	1.32121	−	1.10863i	0.335166	−	0.942159i	$-0.391208\pi$
$743$	36.0136	−	30.2190i	1.32121	−	1.10863i	0.986047	−	0.166470i	$-0.0532368\pi$
$744$		0			0
$745$	6.10664	−	2.22264i	0.223730	−	0.0814311i
$746$	−17.4264	−	12.4241i	−0.638025	−	0.454880i
$747$		0			0
$748$	−49.5399	+	17.0832i	−1.81136	+	0.624622i
$749$	27.7380	+	4.89095i	1.01352	+	0.178711i
$750$		0			0
$751$	−3.24256	+	8.90885i	−0.118323	+	0.325089i	−0.984689	−	0.174320i	$-0.944227\pi$
$751$	−3.24256	+	8.90885i	−0.118323	+	0.325089i	0.866366	+	0.499409i	$0.166449\pi$
$752$	−7.52738	+	2.45337i	−0.274495	+	0.0894650i
$753$		0			0
$754$	−3.53628	+	12.7627i	−0.128784	+	0.464789i
$755$	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	$0.816117\pi$
$758$	−9.75636	+	35.2114i	−0.354367	+	1.27894i
$759$		0			0
$760$	13.6941	+	1.55078i	0.496736	+	0.0562526i
$761$	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
$764$	0.115992	+	0.336367i	0.00419644	+	0.0121693i
$765$		0			0
$766$	−5.35955	−	3.82109i	−0.193649	−	0.138062i
$767$	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	$0.134516\pi$
$770$	7.47599	−	15.6829i	0.269416	−	0.565173i
$771$		0			0
$772$	4.98793	−	13.0117i	0.179519	−	0.468301i
$773$	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
$776$	0.236121	+	0.117524i	0.00847625	+	0.00421888i
$777$		0			0
$778$	−3.17516	−	40.2273i	−0.113835	−	1.44222i
$779$	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	0.186590	−	0.982438i	$-0.440257\pi$
$787$	19.5797	−	3.45243i	0.697940	−	0.123066i	0.511350	+	0.859372i	$0.329145\pi$
$788$	−5.28356	−	9.52158i	−0.188219	−	0.339192i
$789$		0			0
$790$	−3.45816	−	13.3592i	−0.123036	−	0.475298i
$791$	−3.49277	+	6.04966i	−0.124189	+	0.215101i
$792$		0			0
$793$	25.0606	+	43.4063i	0.889930	+	1.54140i
$794$	−1.98369	+	1.95025i	−0.0703985	+	0.0692119i
$795$		0			0
$796$	−11.9770	−	0.203609i	−0.424512	−	0.00721673i
$797$	−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
$800$	−9.08602	+	17.5027i	−0.321239	+	0.618812i
$801$		0			0
$802$	26.7952	+	2.57394i	0.946172	+	0.0908888i
$803$	−4.93074	+	27.9636i	−0.174002	+	0.986815i
$804$		0			0
$805$	8.27052	+	3.01022i	0.291498	+	0.106096i
$806$	0.771215	−	0.530300i	0.0271649	−	0.0186790i
$807$		0			0
$808$	−1.88573	−	2.84480i	−0.0663396	−	0.100080i
$809$			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	$-0.642397\pi$
$811$		−	51.3514i		−	1.80319i	0.432581	−	0.901595i	$-0.357603\pi$
$812$	−9.97459	+	1.58447i	−0.350039	+	0.0556040i
$813$		0			0
$814$	30.1739	+	43.8819i	1.05759	+	1.53806i
$815$	−18.8353	−	6.85550i	−0.659773	−	0.240138i
$816$		0			0
$817$	−5.18541	+	29.4079i	−0.181415	+	1.02885i
$818$	−1.98346	+	20.6482i	−0.0693499	+	0.721947i
$819$		0			0
$820$	9.46122	+	1.83461i	0.330400	+	0.0640673i
$821$	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	$-0.918253\pi$
$823$	−30.1050	−	35.8777i	−1.04939	−	1.25062i	−0.0821894	−	0.996617i	$-0.526191\pi$
$824$	−40.8091	+	17.7774i	−1.42165	+	0.619305i
$825$		0			0
$826$	7.05119	+	7.17208i	0.245342	+	0.249548i
$827$	19.3141	+	33.4530i	0.671616	+	1.16327i	0.977446	+	0.211187i	$0.0677329\pi$
$827$	19.3141	+	33.4530i	0.671616	+	1.16327i	−0.305830	+	0.952086i	$0.598934\pi$
$828$		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	$0.0138768\pi$
$830$	3.05722	−	0.791393i	0.106118	−	0.0274696i
$831$		0			0
$832$	16.4821	+	21.8105i	0.571415	+	0.756145i
$833$	−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	$-0.948119\pi$
$839$	−38.1735	−	32.0314i	−1.31790	−	1.10585i	−0.331150	−	0.943578i	$-0.607437\pi$
$840$		0			0
$841$	3.73174	+	21.1637i	0.128681	+	0.729784i
$842$	1.74971	−	0.138105i	0.0602988	−	0.00475942i
$843$		0			0
$844$	40.3280	−	32.6873i	1.38815	−	1.12514i
$845$	−1.40919	−	0.813594i	−0.0484775	−	0.0279885i
$846$		0			0
$847$	29.2980	−	16.9152i	1.00669	−	0.581214i
$848$	39.6455	−	21.1262i	1.36143	−	0.725476i
$849$		0			0
$850$	21.5202	+	10.2586i	0.738138	+	0.351868i
$851$	−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	$0.607441\pi$
$854$	−22.1891	+	31.1230i	−0.759297	+	1.06501i
$855$		0			0
$856$	29.7803	+	31.3391i	1.01787	+	1.07115i
$857$	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	−0.770582	−	0.637341i	$-0.780034\pi$
$859$	6.72321	−	18.4719i	0.229393	−	0.630252i	0.999975	+	0.00708895i	$0.00225650\pi$
$860$	15.9097	+	9.54967i	0.542517	+	0.325641i
$861$		0			0
$862$	−46.1311	−	12.7820i	−1.57123	−	0.435356i
$863$	−5.14051			−0.174985			−0.0874925	−	0.996165i	$-0.527885\pi$
$863$	−5.14051			−0.174985			−0.0874925	+	0.996165i	$0.527885\pi$
$864$		0			0
$865$	−17.7698			−0.604193
$866$	29.5806	+	8.19618i	1.00519	+	0.278518i
$867$		0			0
$868$	0.611979	+	0.367335i	0.0207719	+	0.0124682i
$869$	14.6969	−	40.3793i	0.498557	−	1.36977i
$870$		0			0
$871$	7.02060	+	1.23792i	0.237884	+	0.0419454i
$872$	−24.2377	−	25.5064i	−0.820794	−	0.863755i
$873$		0			0
$874$	−12.6206	+	17.7019i	−0.426898	+	0.598776i
$875$	−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	$-0.0614986\pi$
$878$	47.7382	+	22.7566i	1.61109	+	0.767999i
$879$		0			0
$880$	23.5342	−	12.5408i	0.793336	−	0.422751i
$881$	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	0.923444	−	0.383733i	$-0.125362\pi$
$883$	31.2856	+	18.0627i	1.05284	+	0.607859i	0.129399	+	0.991593i	$0.458695\pi$
$884$	25.6745	−	20.8101i	0.863525	−	0.699920i
$885$		0			0
$886$	−8.66760	+	0.684138i	−0.291194	+	0.0229841i
$887$	4.04900	+	22.9630i	0.135952	+	0.771023i	0.974192	+	0.225721i	$0.0724739\pi$
$887$	4.04900	+	22.9630i	0.135952	+	0.771023i	−0.838240	+	0.545302i	$0.816415\pi$
$888$		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
$896$	−9.91870	+	18.3375i	−0.331361	+	0.612614i
$897$		0			0
$898$	−6.81008	+	1.76286i	−0.227255	+	0.0588273i
$899$	−0.265365	+	0.459625i	−0.00885041	+	0.0153294i
$900$		0			0
$901$	−27.1540	−	47.0321i	−0.904630	−	1.56687i
$902$	21.0394	+	21.4001i	0.700536	+	0.712547i
$903$		0			0
$904$	−9.82994	+	4.28216i	−0.326939	+	0.142422i
$905$	−9.37829	−	11.1766i	−0.311745	−	0.371523i
$906$		0			0
$907$	4.67374	+	12.8410i	0.155189	+	0.426379i	0.992784	−	0.119913i	$-0.0382614\pi$
$907$	4.67374	+	12.8410i	0.155189	+	0.426379i	−0.837595	+	0.546291i	$0.816039\pi$
$908$	−3.32076	−	0.643923i	−0.110203	−	0.0213693i
$909$		0			0
$910$	−1.04772	+	10.9069i	−0.0347314	+	0.361562i
$911$	4.68110	−	26.5479i	0.155092	−	0.879570i	−0.803610	−	0.595156i	$-0.797090\pi$
$911$	4.68110	−	26.5479i	0.155092	−	0.879570i	0.958702	−	0.284413i	$-0.0917988\pi$
$912$		0			0
$913$	9.24072	+	3.36335i	0.305823	+	0.111311i
$914$	8.51922	+	12.3895i	0.281791	+	0.409808i
$915$		0			0
$916$	−52.4094	+	8.32528i	−1.73166	+	0.275075i
$917$			6.40608i			0.211547i
$918$		0			0
$919$		−	10.8263i		−	0.357127i	−0.983928	−	0.178563i	$-0.942855\pi$
$919$		−	10.8263i		−	0.357127i	0.983928	−	0.178563i	$-0.0571449\pi$
$920$	7.46391	+	11.2600i	0.246078	+	0.371232i
$921$		0			0
$922$	16.7334	−	11.5061i	0.551084	−	0.378934i
$923$	−28.3668	−	10.3247i	−0.933705	−	0.339841i
$924$		0			0
$925$	4.20716	−	23.8600i	0.138331	−	0.784512i
$926$	−25.6946	−	2.46821i	−0.844377	−	0.0811105i
$927$		0			0
$928$	−13.7586	−	7.14240i	−0.451648	−	0.234461i
$929$	−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
$932$	−9.42470	−	0.160220i	−0.308716	−	0.00524819i
$933$		0			0
$934$	23.1469	−	22.7567i	0.757389	−	0.744622i
$935$	−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	$0.0634876\pi$
$938$	1.36241	+	5.26310i	0.0444842	+	0.171846i
$939$		0			0
$940$	−2.36324	−	4.25883i	−0.0770804	−	0.138908i
$941$	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	0.992960	−	0.118452i	$-0.0377930\pi$
$947$	32.2731	+	27.0803i	1.04873	+	0.879992i	0.0557737	+	0.998443i	$0.482237\pi$
$948$		0			0
$949$	−3.10970	−	17.6360i	−0.100945	−	0.572488i
$950$	−1.53626	−	19.4634i	−0.0498428	−	0.631476i
$951$		0			0
$952$	22.5632	+	11.2304i	0.731277	+	0.363978i
$953$	−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
$956$	2.41186	−	6.29167i	0.0780053	−	0.203487i
$957$		0			0
$958$	−10.7020	+	22.4504i	−0.345766	+	0.725339i
$959$	−7.13588	+	5.98771i	−0.230430	+	0.193353i
$960$		0			0
$961$	−29.0952	+	10.5898i	−0.938556	+	0.341606i
$962$	−27.3478	−	19.4976i	−0.881728	−	0.628628i
$963$		0			0
$964$	−10.4105	−	30.1897i	−0.335299	−	0.972343i
$965$	8.44252	+	1.48864i	0.271774	+	0.0479212i
$966$		0			0
$967$	−14.1549	+	38.8902i	−0.455190	+	1.25062i	0.473837	+	0.880613i	$0.342869\pi$
$967$	−14.1549	+	38.8902i	−0.455190	+	1.25062i	−0.929027	+	0.370012i	$0.879354\pi$
$968$	51.5968	+	5.84305i	1.65838	+	0.187803i
$969$		0			0
$970$	−0.0433264	+	0.156368i	−0.00139113	+	0.00502068i
$971$	−14.7098			−0.472061			−0.236030	−	0.971746i	$-0.575847\pi$
$971$	−14.7098			−0.472061			−0.236030	+	0.971746i	$0.575847\pi$
$972$		0			0
$973$	11.9360			0.382650
$974$	5.91793	−	21.3582i	0.189623	−	0.684362i
$975$		0			0
$976$	−55.7808	+	18.1804i	−1.78550	+	0.581941i
$977$	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
$980$	8.38496	−	2.89144i	0.267848	−	0.0923637i
$981$		0			0
$982$	46.0779	+	32.8513i	1.47041	+	1.04833i
$983$	−49.0400	+	17.8491i	−1.56413	+	0.569298i	−0.971679	−	0.236306i	$-0.924063\pi$
$983$	−49.0400	+	17.8491i	−1.56413	+	0.569298i	−0.592455	+	0.805604i	$0.701841\pi$
$984$		0			0
$985$	5.13178	−	4.30607i	0.163512	−	0.137203i
$986$	−8.06417	+	16.9168i	−0.256815	+	0.538740i
$987$		0			0
$988$	−25.2721	−	9.68788i	−0.804014	−	0.308212i
$989$	−25.3498	+	14.6357i	−0.806075	+	0.465388i
$990$		0			0
$991$	−17.1645	−	9.90990i	−0.545247	−	0.314798i	0.201956	−	0.979395i	$-0.435270\pi$
$991$	−17.1645	−	9.90990i	−0.545247	−	0.314798i	−0.747203	+	0.664596i	$0.768604\pi$
$992$	0.420402	+	1.01168i	0.0133478	+	0.0321210i
$993$		0			0
$994$	−1.81144	−	22.9498i	−0.0574554	−	0.727923i
$995$	−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.35.15		96
3.2	odd	2		108.2.l.a.11.2	✓	96
4.3	odd	2	inner	324.2.l.a.35.5		96
9.2	odd	6		972.2.l.d.755.9		96
9.4	even	3		972.2.l.b.431.4		96
9.5	odd	6		972.2.l.c.431.13		96
9.7	even	3		972.2.l.a.755.8		96
12.11	even	2		108.2.l.a.11.12	yes	96
27.4	even	9		972.2.l.d.215.11		96
27.5	odd	18	inner	324.2.l.a.287.5		96
27.13	even	9		972.2.l.c.539.1		96
27.14	odd	18		972.2.l.b.539.16		96
27.22	even	9		108.2.l.a.59.12	yes	96
27.23	odd	18		972.2.l.a.215.6		96
36.7	odd	6		972.2.l.a.755.6		96
36.11	even	6		972.2.l.d.755.11		96
36.23	even	6		972.2.l.c.431.1		96
36.31	odd	6		972.2.l.b.431.16		96
108.23	even	18		972.2.l.a.215.8		96
108.31	odd	18		972.2.l.d.215.9		96
108.59	even	18	inner	324.2.l.a.287.15		96
108.67	odd	18		972.2.l.c.539.13		96
108.95	even	18		972.2.l.b.539.4		96
108.103	odd	18		108.2.l.a.59.2	yes	96

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

\(f(q)\)	\(=\)	\(q+(1.36287 + 0.377622i) q^{2} +(1.71480 + 1.02930i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(1.81474 + 0.319988i) q^{7} +(1.94836 + 2.05034i) q^{8} +O(q^{10})\)	\(q+(1.36287 + 0.377622i) q^{2} +(1.71480 + 1.02930i) q^{4} +(-0.420820 + 1.15619i) q^{5} +(1.81474 + 0.319988i) q^{7} +(1.94836 + 2.05034i) q^{8} +(-1.01013 + 1.41682i) q^{10} +(-5.09161 + 1.85319i) q^{11} +(2.61776 - 2.19656i) q^{13} +(2.35241 + 1.12139i) q^{14} +(1.88110 + 3.53008i) q^{16} +(4.18778 - 2.41782i) q^{17} +(-3.42957 - 1.98006i) q^{19} +(-1.91169 + 1.54950i) q^{20} +(-7.63898 + 0.602949i) q^{22} +(-0.674078 - 3.82288i) q^{23} +(2.67053 + 2.24084i) q^{25} +(4.39712 - 2.00509i) q^{26} +(2.78256 + 2.41662i) q^{28} +(-1.76149 + 2.09927i) q^{29} +(0.190727 - 0.0336302i) q^{31} +(1.23065 + 5.52137i) q^{32} +(6.62041 - 1.71376i) q^{34} +(-1.13365 + 1.96353i) q^{35} +(-3.47493 - 6.01875i) q^{37} +(-3.92633 - 3.99364i) q^{38} +(-3.19050 + 1.38986i) q^{40} +(-2.51742 - 3.00014i) q^{41} +(-2.57902 - 7.08581i) q^{43} +(-10.6386 - 2.06291i) q^{44} +(0.524929 - 5.46462i) q^{46} +(-0.343697 + 1.94920i) q^{47} +(-3.38696 - 1.23275i) q^{49} +(2.79338 + 4.06241i) q^{50} +(6.74984 - 1.07222i) q^{52} -11.2308i q^{53} -6.66675i q^{55} +(2.87968 + 4.34428i) q^{56} +(-3.19341 + 2.19584i) q^{58} +(3.62667 + 1.32000i) q^{59} +(-2.54693 + 14.4444i) q^{61} +(0.272634 + 0.0261891i) q^{62} +(-0.407785 + 7.98960i) q^{64} +(1.43804 + 3.95099i) q^{65} +(1.34096 + 1.59809i) q^{67} +(9.66988 + 0.164388i) q^{68} +(-2.28648 + 2.24794i) q^{70} +(-4.41692 - 7.65033i) q^{71} +(2.62025 - 4.53841i) q^{73} +(-2.46304 - 9.51495i) q^{74} +(-3.84297 - 6.92547i) q^{76} +(-9.83294 + 1.73381i) q^{77} +(-5.09766 + 6.07516i) q^{79} +(-4.87306 + 0.689385i) q^{80} +(-2.29798 - 5.03942i) q^{82} +(-1.39029 - 1.16659i) q^{83} +(1.03316 + 5.85935i) q^{85} +(-0.839103 - 10.6309i) q^{86} +(-13.7200 - 6.82884i) q^{88} +(14.2059 + 8.20179i) q^{89} +(5.45341 - 3.14853i) q^{91} +(2.77897 - 7.24932i) q^{92} +(-1.20448 + 2.52671i) q^{94} +(3.73257 - 3.13200i) q^{95} +(0.0876267 - 0.0318935i) q^{97} +(-4.15046 - 2.95907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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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