LMFDB - Embedded newform 927.2.ba.e.28.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(19,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(102))

chi = DirichletCharacter(H, H._module([0, 80]))

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

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

chi := DirichletCharacter("927.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.ba (of order $51$, degree $32$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$16$ over $\Q(\zeta_{51})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{51}]$

Embedding invariants

Embedding label			28.4
Character	$\chi$	$=$	927.28
Dual form			927.2.ba.e.298.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14375 + 1.72609i) q^{2} +(-0.891651 - 2.10661i) q^{4} +(0.0369533 - 0.0117557i) q^{5} +(-1.22063 + 3.46389i) q^{7} +(0.585256 + 0.109403i) q^{8} +O(q^{10})$	\(q+(-1.14375 + 1.72609i) q^{2} +(-0.891651 - 2.10661i) q^{4} +(0.0369533 - 0.0117557i) q^{5} +(-1.22063 + 3.46389i) q^{7} +(0.585256 + 0.109403i) q^{8} +(-0.0219739 + 0.0772301i) q^{10} +(-4.28077 - 0.264029i) q^{11} +(1.53716 - 0.287345i) q^{13} +(-4.58289 - 6.06872i) q^{14} +(2.32665 - 2.39943i) q^{16} +(-1.81012 - 0.832787i) q^{17} +(2.73266 + 1.46741i) q^{19} +(-0.0577140 - 0.0673641i) q^{20} +(5.35186 - 7.08701i) q^{22} +(-0.414368 + 0.832164i) q^{23} +(-4.07976 + 2.88800i) q^{25} +(-1.26214 + 2.98193i) q^{26} +(8.38543 - 0.517196i) q^{28} +(-0.0516503 + 0.235843i) q^{29} +(-2.05456 - 7.22102i) q^{31} +(1.73529 + 7.92356i) q^{32} +(3.50778 - 2.17193i) q^{34} +(-0.00438579 + 0.142351i) q^{35} +(0.645829 - 0.250195i) q^{37} +(-5.65835 + 3.03847i) q^{38} +(0.0229132 - 0.00283727i) q^{40} +(-7.17640 - 2.28298i) q^{41} +(-1.10533 - 7.12063i) q^{43} +(3.26075 + 9.25333i) q^{44} +(-0.962455 - 1.66702i) q^{46} +(4.32679 - 7.49422i) q^{47} +(-5.05502 - 4.06776i) q^{49} +(-0.318731 - 10.3452i) q^{50} +(-1.97593 - 2.98198i) q^{52} +(0.104419 + 3.38915i) q^{53} +(-0.161292 + 0.0405666i) q^{55} +(-1.09334 + 1.89372i) q^{56} +(-0.348010 - 0.358897i) q^{58} +(-3.68357 - 10.4532i) q^{59} +(0.0782765 + 0.844738i) q^{61} +(14.8140 + 4.71268i) q^{62} +(-9.42841 - 3.65259i) q^{64} +(0.0534251 - 0.0286887i) q^{65} +(7.07547 - 8.25852i) q^{67} +(-0.140362 + 4.55577i) q^{68} +(-0.240695 - 0.170384i) q^{70} +(-1.95278 - 8.91668i) q^{71} +(-10.7581 + 9.80732i) q^{73} +(-0.306806 + 1.40092i) q^{74} +(0.654675 - 7.06506i) q^{76} +(6.13979 - 14.5058i) q^{77} +(0.194927 + 0.177699i) q^{79} +(0.0577702 - 0.116018i) q^{80} +(12.1486 - 9.77596i) q^{82} +(3.75688 + 4.38505i) q^{83} +(-0.0766798 - 0.00949501i) q^{85} +(13.5550 + 6.23631i) q^{86} +(-2.47646 - 0.622855i) q^{88} +(6.33239 + 8.38544i) q^{89} +(-0.880968 + 5.67529i) q^{91} +(2.12252 + 0.130912i) q^{92} +(7.98693 + 16.0399i) q^{94} +(0.118231 + 0.0221012i) q^{95} +(-6.71789 + 3.09072i) q^{97} +(12.8030 - 4.07292i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 18 q^{4} - 8 q^{7}+O(q^{10}) $ 512 * q + 18 * q^4 - 8 * q^7	$ 512 q + 18 q^{4} - 8 q^{7} - 36 q^{10} + 4 q^{13} + 18 q^{16} + 30 q^{19} + 40 q^{22} - 42 q^{25} - 110 q^{28} - 32 q^{31} - 110 q^{34} + 48 q^{37} - 22 q^{40} - 2 q^{43} + 152 q^{46} + 76 q^{49} + 68 q^{52} + 32 q^{55} - 44 q^{58} + 20 q^{61} - 170 q^{64} - 8 q^{67} - 38 q^{70} - 4 q^{73} + 188 q^{76} + 20 q^{79} + 212 q^{82} + 60 q^{85} + 164 q^{88} - 310 q^{91} + 228 q^{94} - 100 q^{97}+O(q^{100}) $ 512 * q + 18 * q^4 - 8 * q^7 - 36 * q^10 + 4 * q^13 + 18 * q^16 + 30 * q^19 + 40 * q^22 - 42 * q^25 - 110 * q^28 - 32 * q^31 - 110 * q^34 + 48 * q^37 - 22 * q^40 - 2 * q^43 + 152 * q^46 + 76 * q^49 + 68 * q^52 + 32 * q^55 - 44 * q^58 + 20 * q^61 - 170 * q^64 - 8 * q^67 - 38 * q^70 - 4 * q^73 + 188 * q^76 + 20 * q^79 + 212 * q^82 + 60 * q^85 + 164 * q^88 - 310 * q^91 + 228 * q^94 - 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{46}{51}\right)$

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 $

$2$	−1.14375	+	1.72609i	−0.808752	+	1.22053i	0.163489	+	0.986545i	$0.447725\pi$
$2$	−1.14375	+	1.72609i	−0.808752	+	1.22053i	−0.972240	+	0.233984i	$0.924824\pi$
$3$		0			0
$3$		0			0
$4$	−0.891651	−	2.10661i	−0.445826	−	1.05330i
$5$	0.0369533	−	0.0117557i	0.0165260	−	0.00525730i	−0.294878	−	0.955535i	$-0.595279\pi$
$5$	0.0369533	−	0.0117557i	0.0165260	−	0.00525730i	0.311404	+	0.950278i	$0.399201\pi$
$6$		0			0
$7$	−1.22063	+	3.46389i	−0.461354	+	1.30923i	0.448309	+	0.893879i	$0.352026\pi$
$7$	−1.22063	+	3.46389i	−0.461354	+	1.30923i	−0.909663	+	0.415348i	$0.863660\pi$
$8$	0.585256	+	0.109403i	0.206919	+	0.0386799i
$9$		0			0
$10$	−0.0219739	+	0.0772301i	−0.00694875	+	0.0244223i
$11$	−4.28077	−	0.264029i	−1.29070	−	0.0796077i	−0.598389	−	0.801206i	$-0.704192\pi$
$11$	−4.28077	−	0.264029i	−1.29070	−	0.0796077i	−0.692312	+	0.721598i	$0.743408\pi$
$12$		0			0
$13$	1.53716	−	0.287345i	0.426332	−	0.0796952i	0.0337889	−	0.999429i	$-0.489243\pi$
$13$	1.53716	−	0.287345i	0.426332	−	0.0796952i	0.392543	+	0.919734i	$0.371596\pi$
$14$	−4.58289	−	6.06872i	−1.22483	−	1.62193i
$15$		0			0
$16$	2.32665	−	2.39943i	0.581661	−	0.599858i
$17$	−1.81012	−	0.832787i	−0.439018	−	0.201980i	0.186067	−	0.982537i	$-0.440426\pi$
$17$	−1.81012	−	0.832787i	−0.439018	−	0.201980i	−0.625085	+	0.780557i	$0.714936\pi$
$18$		0			0
$19$	2.73266	+	1.46741i	0.626915	+	0.336646i	0.755594	−	0.655040i	$-0.227348\pi$
$19$	2.73266	+	1.46741i	0.626915	+	0.336646i	−0.128679	+	0.991686i	$0.541074\pi$
$20$	−0.0577140	−	0.0673641i	−0.0129053	−	0.0150631i
$21$		0			0
$22$	5.35186	−	7.08701i	1.14102	−	1.51095i
$23$	−0.414368	+	0.832164i	−0.0864018	+	0.173518i	−0.934150	−	0.356881i	$-0.883840\pi$
$23$	−0.414368	+	0.832164i	−0.0864018	+	0.173518i	0.847748	+	0.530399i	$0.177958\pi$
$24$		0			0
$25$	−4.07976	+	2.88800i	−0.815951	+	0.577600i
$26$	−1.26214	+	2.98193i	−0.247526	+	0.584804i
$27$		0			0
$28$	8.38543	−	0.517196i	1.58470	−	0.0977408i
$29$	−0.0516503	+	0.235843i	−0.00959122	+	0.0437949i	−0.981398	−	0.191982i	$-0.938509\pi$
$29$	−0.0516503	+	0.235843i	−0.00959122	+	0.0437949i	0.971807	+	0.235777i	$0.0757634\pi$
$30$		0			0
$31$	−2.05456	−	7.22102i	−0.369009	−	1.29693i	−0.894856	−	0.446354i	$-0.852722\pi$
$31$	−2.05456	−	7.22102i	−0.369009	−	1.29693i	0.525847	−	0.850579i	$-0.323748\pi$
$32$	1.73529	+	7.92356i	0.306758	+	1.40070i
$33$		0			0
$34$	3.50778	−	2.17193i	0.601580	−	0.372482i
$35$	−0.00438579	+	0.142351i	−0.000741334	+	0.0240617i
$36$		0			0
$37$	0.645829	−	0.250195i	0.106174	−	0.0411319i	−0.307569	−	0.951526i	$-0.599515\pi$
$37$	0.645829	−	0.250195i	0.106174	−	0.0411319i	0.413743	+	0.910394i	$0.364221\pi$
$38$	−5.65835	+	3.03847i	−0.917906	+	0.492905i
$39$		0			0
$40$	0.0229132	−	0.00283727i	0.00362290	−	0.000448612i
$41$	−7.17640	−	2.28298i	−1.12077	−	0.356541i	−0.315187	−	0.949030i	$-0.602067\pi$
$41$	−7.17640	−	2.28298i	−1.12077	−	0.356541i	−0.805579	+	0.592488i	$0.798146\pi$
$42$		0			0
$43$	−1.10533	−	7.12063i	−0.168561	−	1.08589i	−0.909922	−	0.414779i	$-0.863859\pi$
$43$	−1.10533	−	7.12063i	−0.168561	−	1.08589i	0.741361	−	0.671106i	$-0.234180\pi$
$44$	3.26075	+	9.25333i	0.491576	+	1.39499i
$45$		0			0
$46$	−0.962455	−	1.66702i	−0.141906	−	0.245789i
$47$	4.32679	−	7.49422i	0.631127	−	1.09314i	−0.356194	−	0.934412i	$-0.615926\pi$
$47$	4.32679	−	7.49422i	0.631127	−	1.09314i	0.987322	−	0.158733i	$-0.0507408\pi$
$48$		0			0
$49$	−5.05502	−	4.06776i	−0.722146	−	0.581109i
$50$	−0.318731	−	10.3452i	−0.0450754	−	1.46303i
$51$		0			0
$52$	−1.97593	−	2.98198i	−0.274013	−	0.413527i
$53$	0.104419	+	3.38915i	0.0143430	+	0.465536i	0.979216	+	0.202820i	$0.0650105\pi$
$53$	0.104419	+	3.38915i	0.0143430	+	0.465536i	−0.964873	+	0.262716i	$0.915382\pi$
$54$		0			0
$55$	−0.161292	+	0.0405666i	−0.0217486	+	0.00547000i
$56$	−1.09334	+	1.89372i	−0.146104	+	0.253059i
$57$		0			0
$58$	−0.348010	−	0.358897i	−0.0456960	−	0.0471255i
$59$	−3.68357	−	10.4532i	−0.479560	−	1.36089i	−0.892875	−	0.450304i	$-0.851316\pi$
$59$	−3.68357	−	10.4532i	−0.479560	−	1.36089i	0.413315	−	0.910588i	$-0.364371\pi$
$60$		0			0
$61$	0.0782765	+	0.844738i	0.0100223	+	0.108158i	0.999276	−	0.0380534i	$-0.0121157\pi$
$61$	0.0782765	+	0.844738i	0.0100223	+	0.108158i	−0.989253	+	0.146211i	$0.953292\pi$
$62$	14.8140	+	4.71268i	1.88138	+	0.598510i
$63$		0			0
$64$	−9.42841	−	3.65259i	−1.17855	−	0.456573i
$65$	0.0534251	−	0.0286887i	0.00662657	−	0.00355839i
$66$		0			0
$67$	7.07547	−	8.25852i	0.864406	−	1.00894i	−0.135429	−	0.990787i	$-0.543241\pi$
$67$	7.07547	−	8.25852i	0.864406	−	1.00894i	0.999835	−	0.0181523i	$-0.00577837\pi$
$68$	−0.140362	+	4.55577i	−0.0170214	+	0.552468i
$69$		0			0
$70$	−0.240695	−	0.170384i	−0.0287685	−	0.0203648i
$71$	−1.95278	−	8.91668i	−0.231753	−	1.05821i	−0.937021	−	0.349274i	$-0.886428\pi$
$71$	−1.95278	−	8.91668i	−0.231753	−	1.05821i	0.705268	−	0.708941i	$-0.250827\pi$
$72$		0			0
$73$	−10.7581	+	9.80732i	−1.25914	+	1.14786i	−0.276767	+	0.960937i	$0.589263\pi$
$73$	−10.7581	+	9.80732i	−1.25914	+	1.14786i	−0.982375	+	0.186923i	$0.940149\pi$
$74$	−0.306806	+	1.40092i	−0.0356654	+	0.162853i
$75$		0			0
$76$	0.654675	−	7.06506i	0.0750963	−	0.810418i
$77$	6.13979	−	14.5058i	0.699694	−	1.65309i
$78$		0			0
$79$	0.194927	+	0.177699i	0.0219310	+	0.0199927i	0.684587	−	0.728931i	$-0.259983\pi$
$79$	0.194927	+	0.177699i	0.0219310	+	0.0199927i	−0.662656	+	0.748924i	$0.730571\pi$
$80$	0.0577702	−	0.116018i	0.00645890	−	0.0129712i
$81$		0			0
$82$	12.1486	−	9.77596i	1.34159	−	1.07957i
$83$	3.75688	+	4.38505i	0.412372	+	0.481322i	0.926448	−	0.376422i	$-0.122846\pi$
$83$	3.75688	+	4.38505i	0.412372	+	0.481322i	−0.514077	+	0.857744i	$0.671865\pi$
$84$		0			0
$85$	−0.0766798	−	0.00949501i	−0.00831709	−	0.00102988i
$86$	13.5550	+	6.23631i	1.46168	+	0.672479i
$87$		0			0
$88$	−2.47646	−	0.622855i	−0.263992	−	0.0663966i
$89$	6.33239	+	8.38544i	0.671232	+	0.888855i	0.998425	−	0.0561027i	$-0.0178674\pi$
$89$	6.33239	+	8.38544i	0.671232	+	0.888855i	−0.327193	+	0.944958i	$0.606103\pi$
$90$		0			0
$91$	−0.880968	+	5.67529i	−0.0923506	+	0.594932i
$92$	2.12252	+	0.130912i	0.221288	+	0.0136485i
$93$		0			0
$94$	7.98693	+	16.0399i	0.823789	+	1.65439i
$95$	0.118231	+	0.0221012i	0.0121303	+	0.00226754i
$96$		0			0
$97$	−6.71789	+	3.09072i	−0.682098	+	0.313815i	−0.728439	−	0.685111i	$-0.759754\pi$
$97$	−6.71789	+	3.09072i	−0.682098	+	0.313815i	0.0463408	+	0.998926i	$0.485244\pi$
$98$	12.8030	−	4.07292i	1.29330	−	0.411427i
$99$		0			0
$100$	9.72161	+	6.01937i	0.972161	+	0.601937i
$101$	−0.920291	+	1.38886i	−0.0915724	+	0.138197i	−0.876520	−	0.481366i	$-0.840141\pi$
$101$	−0.920291	+	1.38886i	−0.0915724	+	0.138197i	0.784947	+	0.619562i	$0.212690\pi$
$102$		0			0
$103$	0.762657	−	10.1202i	0.0751468	−	0.997172i
$103$	0.762657	−	10.1202i	0.0751468	−	0.997172i
$104$	0.931069			0.0912988
$105$		0			0
$106$	−5.96940	−	3.69610i	−0.579800	−	0.358997i
$107$	0.396138	+	0.935914i	0.0382961	+	0.0904782i	0.938942	−	0.344076i	$-0.111808\pi$
$107$	0.396138	+	0.935914i	0.0382961	+	0.0904782i	−0.900646	+	0.434554i	$0.856906\pi$
$108$		0			0
$109$	−4.14141	+	1.90535i	−0.396675	+	0.182499i	−0.606215	−	0.795301i	$-0.707313\pi$
$109$	−4.14141	+	1.90535i	−0.396675	+	0.182499i	0.209540	+	0.977800i	$0.432803\pi$
$110$	0.114456	−	0.324803i	0.0109130	−	0.0309687i
$111$		0			0
$112$	5.47140	+	10.9880i	0.516998	+	1.03827i
$113$	−4.84969	+	17.0449i	−0.456221	+	1.60345i	0.303252	+	0.952910i	$0.401928\pi$
$113$	−4.84969	+	17.0449i	−0.456221	+	1.60345i	−0.759473	+	0.650539i	$0.774543\pi$
$114$		0			0
$115$	−0.00552961	+	0.0356223i	−0.000515639	+	0.00332180i
$116$	0.542882	−	0.101482i	0.0504053	−	0.00942239i
$117$		0			0
$118$	22.2562	+	5.59767i	2.04885	+	0.515307i
$119$	5.09416	−	5.25353i	0.466981	−	0.481590i
$120$		0			0
$121$	7.33866	+	0.908723i	0.667151	+	0.0826112i
$122$	−1.54762	−	0.831055i	−0.140115	−	0.0752402i
$123$		0			0
$124$	−13.3799	+	10.7668i	−1.20155	+	0.966885i
$125$	−0.233655	+	0.309409i	−0.0208987	+	0.0276744i
$126$		0			0
$127$	1.68779	+	1.53862i	0.149767	+	0.136530i	0.745111	−	0.666940i	$-0.232396\pi$
$127$	1.68779	+	1.53862i	0.149767	+	0.136530i	−0.595345	+	0.803470i	$0.702984\pi$
$128$	3.84749	−	2.72358i	0.340073	−	0.240733i
$129$		0			0
$130$	−0.0115857	+	0.125029i	−0.00101613	+	0.0109658i
$131$	−10.6870	+	0.659152i	−0.933728	+	0.0575904i	−0.521275	−	0.853389i	$-0.674544\pi$
$131$	−10.6870	+	0.659152i	−0.933728	+	0.0575904i	−0.412453	+	0.910979i	$0.635328\pi$
$132$		0			0
$133$	−8.41849	+	7.67447i	−0.729976	+	0.665461i
$134$	6.16239	+	21.6586i	0.532350	+	1.87101i
$135$		0			0
$136$	−0.968273	−	0.685426i	−0.0830287	−	0.0587748i
$137$	16.9748	−	10.5103i	1.45025	−	0.897958i	0.450264	−	0.892895i	$-0.351330\pi$
$137$	16.9748	−	10.5103i	1.45025	−	0.897958i	0.999987	−	0.00506239i	$-0.00161142\pi$
$138$		0			0
$139$	3.61130	−	4.21512i	0.306306	−	0.357522i	−0.584912	−	0.811097i	$-0.698871\pi$
$139$	3.61130	−	4.21512i	0.306306	−	0.357522i	0.891218	+	0.453575i	$0.149851\pi$
$140$	0.303789	−	0.117688i	0.0256749	−	0.00994649i
$141$		0			0
$142$	17.6245	+	6.82775i	1.47901	+	0.572972i
$143$	−6.65610	+	0.824204i	−0.556611	+	0.0689234i
$144$		0			0
$145$	0.000863842		0.00932234i	7.17381e−5		0.000774178i
$146$	−4.62373	−	29.7866i	−0.382663	−	2.46515i
$147$		0			0
$148$	−1.10292	−	1.13742i	−0.0906593	−	0.0934955i
$149$	−10.5815	−	18.3277i	−0.866871	−	1.50146i	−0.865177	−	0.501466i	$-0.832794\pi$
$149$	−10.5815	−	18.3277i	−0.866871	−	1.50146i	−0.00169364	−	0.999999i	$-0.500539\pi$
$150$		0			0
$151$	−18.3977	+	4.62722i	−1.49719	+	0.376558i	−0.903658	−	0.428255i	$-0.859129\pi$
$151$	−18.3977	+	4.62722i	−1.49719	+	0.376558i	−0.593529	+	0.804813i	$0.702266\pi$
$152$	1.43877	+	1.15777i	0.116699	+	0.0939076i
$153$		0			0
$154$	18.0160	+	27.1888i	1.45177	+	2.19094i
$155$	−0.160811	−	0.242687i	−0.0129166	−	0.0194931i
$156$		0			0
$157$	1.07823	+	0.867648i	0.0860521	+	0.0692459i	0.668993	−	0.743269i	$-0.266726\pi$
$157$	1.07823	+	0.867648i	0.0860521	+	0.0692459i	−0.582941	+	0.812515i	$0.698098\pi$
$158$	−0.529671	+	0.133218i	−0.0421384	+	0.0105982i
$159$		0			0
$160$	0.157271	+	0.272402i	0.0124334	+	0.0215353i
$161$	−2.37673	−	2.45109i	−0.187313	−	0.193173i
$162$		0			0
$163$	−3.53306	−	22.7603i	−0.276730	−	1.78273i	−0.564913	−	0.825151i	$-0.691090\pi$
$163$	−3.53306	−	22.7603i	−0.276730	−	1.78273i	0.288182	−	0.957576i	$-0.406949\pi$
$164$	1.58951	+	17.1535i	0.124120	+	1.33946i
$165$		0			0
$166$	−11.8659	+	1.46932i	−0.920974	+	0.114041i
$167$	4.93458	+	1.91167i	0.381850	+	0.147929i	0.544513	−	0.838752i	$-0.316714\pi$
$167$	4.93458	+	1.91167i	0.381850	+	0.147929i	−0.162664	+	0.986682i	$0.552009\pi$
$168$		0			0
$169$	−9.84184	+	3.81275i	−0.757065	+	0.293289i
$170$	0.104092	−	0.121496i	0.00798346	−	0.00931833i
$171$		0			0
$172$	−14.0148	+	8.67760i	−1.06862	+	0.661661i
$173$	8.08129	+	5.72063i	0.614409	+	0.434931i	0.842491	−	0.538711i	$-0.181088\pi$
$173$	8.08129	+	5.72063i	0.614409	+	0.434931i	−0.228081	+	0.973642i	$0.573245\pi$
$174$		0			0
$175$	−5.02385	−	17.6570i	−0.379767	−	1.33474i
$176$	−10.5934	+	9.65712i	−0.798504	+	0.727933i
$177$		0			0
$178$	−21.7167	+	1.33944i	−1.62773	+	0.100395i
$179$	−0.926197	+	9.99526i	−0.0692272	+	0.747081i	0.888400	+	0.459070i	$0.151817\pi$
$179$	−0.926197	+	9.99526i	−0.0692272	+	0.747081i	−0.957627	+	0.288011i	$0.907006\pi$
$180$		0			0
$181$	−8.20452	+	5.80786i	−0.609837	+	0.431695i	−0.840859	−	0.541254i	$-0.817950\pi$
$181$	−8.20452	+	5.80786i	−0.609837	+	0.431695i	0.231022	+	0.972948i	$0.425793\pi$
$182$	−8.78845	−	8.01173i	−0.651443	−	0.593869i
$183$		0			0
$184$	−0.333553	+	0.441695i	−0.0245898	+	0.0325622i
$185$	0.0209243	−	0.0168377i	0.00153838	−	0.00123793i
$186$		0			0
$187$	7.52882	+	4.04289i	0.550562	+	0.295646i
$188$	−19.6454	−	2.43263i	−1.43279	−	0.177417i
$189$		0			0
$190$	−0.173375	+	0.178799i	−0.0125780	+	0.0129714i
$191$	7.53409	+	1.89490i	0.545148	+	0.137110i	0.506655	−	0.862149i	$-0.330882\pi$
$191$	7.53409	+	1.89490i	0.545148	+	0.137110i	0.0384923	+	0.999259i	$0.487744\pi$
$192$		0			0
$193$	−6.11100	+	1.14234i	−0.439879	+	0.0822277i	−0.399031	−	0.916938i	$-0.630653\pi$
$193$	−6.11100	+	1.14234i	−0.439879	+	0.0822277i	−0.0408489	+	0.999165i	$0.513006\pi$
$194$	2.34871	−	15.1307i	0.168628	−	1.08632i
$195$		0			0
$196$	−4.06187	+	14.2760i	−0.290133	+	1.01971i
$197$	1.94919	+	3.91451i	0.138874	+	0.278897i	0.953672	−	0.300848i	$-0.0972697\pi$
$197$	1.94919	+	3.91451i	0.138874	+	0.278897i	−0.814798	+	0.579745i	$0.803152\pi$
$198$		0			0
$199$	−1.99742	+	5.66827i	−0.141593	+	0.401813i	−0.992305	−	0.123820i	$-0.960485\pi$
$199$	−1.99742	+	5.66827i	−0.141593	+	0.401813i	0.850711	+	0.525633i	$0.176172\pi$
$200$	−2.70366	+	1.24388i	−0.191178	+	0.0879556i
$201$		0			0
$202$	−1.34471	−	3.17701i	−0.0946136	−	0.223534i
$203$	−0.753886	−	0.466787i	−0.0529124	−	0.0327620i
$204$		0			0
$205$	−0.292029			−0.0203962
$206$	16.5961	+	12.8914i	1.15630	+	0.898184i
$207$		0			0
$208$	2.88696	−	4.35686i	0.200175	−	0.302094i
$209$	−11.3105	−	7.00314i	−0.782360	−	0.484417i
$210$		0			0
$211$	−12.2665	+	3.90227i	−0.844463	+	0.268643i	−0.694002	−	0.719973i	$-0.744154\pi$
$211$	−12.2665	+	3.90227i	−0.844463	+	0.268643i	−0.150461	+	0.988616i	$0.548076\pi$
$212$	7.04651	−	3.24191i	0.483957	−	0.222655i
$213$		0			0
$214$	−2.06855	−	0.386680i	−0.141403	−	0.0264329i
$215$	−0.124553	−	0.250136i	−0.00849445	−	0.0170592i
$216$		0			0
$217$	27.5206	+	1.69741i	1.86822	+	0.115228i
$218$	1.44792	−	9.32767i	0.0980657	−	0.631750i
$219$		0			0
$220$	0.229274	+	0.303608i	0.0154577	+	0.0204693i
$221$	−3.02174	−	0.759998i	−0.203264	−	0.0511230i
$222$		0			0
$223$	−16.6956	−	7.68118i	−1.11802	−	0.514370i	−0.229544	−	0.973298i	$-0.573724\pi$
$223$	−16.6956	−	7.68118i	−1.11802	−	0.514370i	−0.888473	+	0.458929i	$0.848233\pi$
$224$	−29.5645	−	3.66087i	−1.97536	−	0.244602i
$225$		0			0
$226$	−23.8742	−	27.8661i	−1.58809	−	1.85362i
$227$	−19.2557	+	15.4950i	−1.27805	+	1.02844i	−0.280400	+	0.959883i	$0.590467\pi$
$227$	−19.2557	+	15.4950i	−1.27805	+	1.02844i	−0.997647	+	0.0685578i	$0.978160\pi$
$228$		0			0
$229$	−8.78308	+	17.6388i	−0.580402	+	1.16560i	0.389254	+	0.921131i	$0.372733\pi$
$229$	−8.78308	+	17.6388i	−0.580402	+	1.16560i	−0.969656	+	0.244474i	$0.921385\pi$
$230$	−0.0551628	−	0.0502876i	−0.00363733	−	0.00331586i
$231$		0			0
$232$	−0.0560306	+	0.132378i	−0.00367859	+	0.00869101i
$233$	0.341433	−	3.68465i	0.0223680	−	0.241389i	−0.977208	−	0.212283i	$-0.931910\pi$
$233$	0.341433	−	3.68465i	0.0223680	−	0.241389i	0.999576	−	0.0291066i	$-0.00926624\pi$
$234$		0			0
$235$	0.0717894	−	0.327800i	0.00468302	−	0.0213833i
$236$	−18.7364	+	17.0805i	−1.21963	+	1.11184i
$237$		0			0
$238$	3.24162	+	14.8017i	0.210123	+	0.959450i
$239$	−14.3223	−	10.1385i	−0.926432	−	0.655808i	0.0124956	−	0.999922i	$-0.496022\pi$
$239$	−14.3223	−	10.1385i	−0.926432	−	0.655808i	−0.938928	+	0.344114i	$0.888179\pi$
$240$		0			0
$241$	0.0251115	−	0.815052i	0.00161757	−	0.0525021i	−0.998372	−	0.0570355i	$-0.981835\pi$
$241$	0.0251115	−	0.815052i	0.00161757	−	0.0525021i	0.999990	+	0.00453337i	$0.00144302\pi$
$242$	−9.96211	+	11.6278i	−0.640389	+	0.747465i
$243$		0			0
$244$	1.70974	−	0.918109i	0.109455	−	0.0587759i
$245$	−0.234619	−	0.0908918i	−0.0149892	−	0.00580686i
$246$		0			0
$247$	4.62219	+	1.47042i	0.294103	+	0.0935609i
$248$	−0.412438	−	4.45092i	−0.0261899	−	0.282634i
$249$		0			0
$250$	−0.266825	−	0.757195i	−0.0168755	−	0.0478892i
$251$	13.3348	+	13.7519i	0.841683	+	0.868014i	0.992711	−	0.120515i	$-0.0384546\pi$
$251$	13.3348	+	13.7519i	0.841683	+	0.868014i	−0.151029	+	0.988529i	$0.548259\pi$
$252$		0			0
$253$	1.99353	−	3.45290i	0.125332	−	0.217082i
$254$	−4.58620	+	1.15347i	−0.287764	+	0.0723755i
$255$		0			0
$256$	−0.322165	−	10.4566i	−0.0201353	−	0.653538i
$257$	−6.26081	−	9.44851i	−0.390539	−	0.589382i	0.584506	−	0.811389i	$-0.301288\pi$
$257$	−6.26081	−	9.44851i	−0.390539	−	0.589382i	−0.975045	+	0.222007i	$0.928739\pi$
$258$		0			0
$259$	0.0783328	+	2.54247i	0.00486736	+	0.157982i
$260$	−0.108072	−	0.0869656i	−0.00670237	−	0.00539338i
$261$		0			0
$262$	11.0855	−	19.2006i	0.684864	−	1.18622i
$263$	7.55597	+	13.0873i	0.465921	+	0.806999i	0.999243	−	0.0389136i	$-0.0123897\pi$
$263$	7.55597	+	13.0873i	0.465921	+	0.806999i	−0.533321	+	0.845913i	$0.679056\pi$
$264$		0			0
$265$	0.0437004	+	0.124013i	0.00268449	+	0.00761804i
$266$	−3.61818	−	23.3087i	−0.221845	−	1.42915i
$267$		0			0
$268$	−23.7063	−	7.54153i	−1.44810	−	0.460672i
$269$	−20.6334	+	2.55497i	−1.25804	+	0.155779i	−0.724072	−	0.689724i	$-0.757732\pi$
$269$	−20.6334	+	2.55497i	−1.25804	+	0.155779i	−0.533970	+	0.845503i	$0.679301\pi$
$270$		0			0
$271$	−14.8607	+	7.98004i	−0.902724	+	0.484753i	−0.857652	−	0.514231i	$-0.828077\pi$
$271$	−14.8607	+	7.98004i	−0.902724	+	0.484753i	−0.0450726	+	0.998984i	$0.514352\pi$
$272$	−6.20972	+	2.40566i	−0.376520	+	0.145864i
$273$		0			0
$274$	−1.27309	+	41.3211i	−0.0769101	+	2.49630i
$275$	18.2270	−	11.2857i	1.09913	−	0.680553i
$276$		0			0
$277$	1.71955	+	7.85168i	0.103317	+	0.471762i	0.999600	+	0.0282786i	$0.00900257\pi$
$277$	1.71955	+	7.85168i	0.103317	+	0.471762i	−0.896283	+	0.443483i	$0.853743\pi$
$278$	3.14526	+	11.0545i	0.188640	+	0.663002i
$279$		0			0
$280$	−0.0181405	+	0.0828321i	−0.00108410	+	0.00495016i
$281$	−6.44008	+	0.397210i	−0.384183	+	0.0236956i	−0.252501	−	0.967597i	$-0.581253\pi$
$281$	−6.44008	+	0.397210i	−0.384183	+	0.0236956i	−0.131681	+	0.991292i	$0.542038\pi$
$282$		0			0
$283$	−9.86590	+	23.3091i	−0.586467	+	1.38558i	0.313485	+	0.949593i	$0.398504\pi$
$283$	−9.86590	+	23.3091i	−0.586467	+	1.38558i	−0.899952	+	0.435990i	$0.856398\pi$
$284$	−17.0428	+	12.0643i	−1.01130	+	0.715885i
$285$		0			0
$286$	6.19025	−	12.4317i	0.366037	−	0.735102i
$287$	16.6677	−	22.0716i	0.983863	−	1.30284i
$288$		0			0
$289$	−8.47751	−	9.89500i	−0.498677	−	0.582059i
$290$	−0.0170792	−	0.00917133i	−0.00100292	−	0.000538559i
$291$		0			0
$292$	30.2527	+	13.9184i	1.77040	+	0.814515i
$293$	−15.3365	+	15.8163i	−0.895970	+	0.923999i	−0.997488	−	0.0708344i	$-0.977434\pi$
$293$	−15.3365	+	15.8163i	−0.895970	+	0.923999i	0.101519	+	0.994834i	$0.467630\pi$
$294$		0			0
$295$	−0.259004	−	0.342977i	−0.0150798	−	0.0199689i
$296$	0.405347	−	0.0757725i	0.0235603	−	0.00440419i
$297$		0			0
$298$	43.7378	+	2.69766i	2.53366	+	0.156271i
$299$	−0.397832	+	1.39824i	−0.0230072	+	0.0808621i
$300$		0			0
$301$	26.0142	+	4.86290i	1.49944	+	0.280293i
$302$	13.0554	−	37.0485i	0.751253	−	2.13190i
$303$		0			0
$304$	9.87888	−	3.14270i	0.566592	−	0.180246i
$305$	0.0128230	+	0.0302956i	0.000734245	+	0.00173472i
$306$		0			0
$307$	1.96468	−	2.96500i	0.112130	−	0.169221i	−0.773232	−	0.634123i	$-0.781361\pi$
$307$	1.96468	−	2.96500i	0.112130	−	0.169221i	0.885362	+	0.464902i	$0.153910\pi$
$308$	−36.0327			−2.05315
$309$		0			0
$310$	0.602827			0.0342383
$311$	−5.60173	+	8.45385i	−0.317645	+	0.479374i	−0.957223	−	0.289352i	$-0.906560\pi$
$311$	−5.60173	+	8.45385i	−0.317645	+	0.479374i	0.639578	+	0.768726i	$0.279109\pi$
$312$		0			0
$313$	5.33283	+	12.5993i	0.301429	+	0.712155i	0.999994	−	0.00339159i	$-0.00107958\pi$
$313$	5.33283	+	12.5993i	0.301429	+	0.712155i	−0.698565	+	0.715547i	$0.746178\pi$
$314$	−2.73086	+	0.868750i	−0.154111	+	0.0490264i
$315$		0			0
$316$	0.200536	−	0.569080i	0.0112810	−	0.0320132i
$317$	18.2358	+	3.40887i	1.02423	+	0.191461i	0.668956	−	0.743302i	$-0.266742\pi$
$317$	18.2358	+	3.40887i	1.02423	+	0.191461i	0.355271	+	0.934763i	$0.384389\pi$
$318$		0			0
$319$	0.283372	−	0.995951i	0.0158658	−	0.0557625i
$320$	−0.391349	−	0.0241376i	−0.0218771	−	0.00134933i
$321$		0			0
$322$	6.94917	−	1.29903i	0.387262	−	0.0723919i
$323$	−3.72440	−	4.93191i	−0.207231	−	0.274419i
$324$		0			0
$325$	−5.44139	+	5.61162i	−0.301834	+	0.311277i
$326$	43.3273	+	19.9337i	2.39968	+	1.10403i
$327$		0			0
$328$	−3.95027	−	2.12125i	−0.218117	−	0.117126i
$329$	20.6777	+	24.1352i	1.14000	+	1.33061i
$330$		0			0
$331$	2.95884	−	3.91813i	0.162632	−	0.215360i	−0.709403	−	0.704803i	$-0.751035\pi$
$331$	2.95884	−	3.91813i	0.162632	−	0.215360i	0.872035	+	0.489443i	$0.162800\pi$
$332$	5.88776	−	11.8242i	0.323133	−	0.648939i
$333$		0			0
$334$	−8.94363	+	6.33106i	−0.489373	+	0.346420i
$335$	0.164377	−	0.388356i	0.00898088	−	0.0212182i
$336$		0			0
$337$	19.8912	−	1.22685i	1.08354	−	0.0668306i	0.490068	−	0.871684i	$-0.336972\pi$
$337$	19.8912	−	1.22685i	1.08354	−	0.0668306i	0.593474	+	0.804853i	$0.297756\pi$
$338$	4.67544	−	21.3487i	0.254311	−	1.16122i
$339$		0			0
$340$	0.0483693	+	0.170001i	0.00262319	+	0.00921957i
$341$	6.88853	+	31.4540i	0.373035	+	1.70333i
$342$		0			0
$343$	−1.59736	+	0.989044i	−0.0862494	+	0.0534033i
$344$	0.132122	−	4.28831i	0.00712352	−	0.231210i
$345$		0			0
$346$	−19.1173	+	7.40607i	−1.02775	+	0.398153i
$347$	−5.72986	+	3.07687i	−0.307595	+	0.165175i	−0.619627	−	0.784897i	$-0.712716\pi$
$347$	−5.72986	+	3.07687i	−0.307595	+	0.165175i	0.312032	+	0.950072i	$0.398990\pi$
$348$		0			0
$349$	10.2904	−	1.27423i	0.550833	−	0.0682079i	0.157355	−	0.987542i	$-0.449703\pi$
$349$	10.2904	−	1.27423i	0.550833	−	0.0682079i	0.393478	+	0.919334i	$0.371272\pi$
$350$	36.2235	+	11.5235i	1.93623	+	0.615959i
$351$		0			0
$352$	−5.33631	−	34.3771i	−0.284426	−	1.83231i
$353$	−11.9775	−	33.9898i	−0.637500	−	1.80909i	−0.585838	−	0.810428i	$-0.699235\pi$
$353$	−11.9775	−	33.9898i	−0.637500	−	1.80909i	−0.0516614	−	0.998665i	$-0.516452\pi$
$354$		0			0
$355$	−0.176983	−	0.306544i	−0.00939329	−	0.0162697i
$356$	12.0186	−	20.8168i	0.636983	−	1.10329i
$357$		0			0
$358$	−16.1934	−	13.0308i	−0.855846	−	0.688697i
$359$	0.764871	+	24.8257i	0.0403683	+	1.31025i	0.775077	+	0.631866i	$0.217711\pi$
$359$	0.764871	+	24.8257i	0.0403683	+	1.31025i	−0.734709	+	0.678382i	$0.762681\pi$
$360$		0			0
$361$	−5.18079	−	7.81859i	−0.272673	−	0.411505i
$362$	−0.640978	−	20.8045i	−0.0336891	−	1.09346i
$363$		0			0
$364$	12.7411	−	3.20452i	0.667817	−	0.167963i
$365$	−0.282256	+	0.488881i	−0.0147739	+	0.0255892i
$366$		0			0
$367$	−6.57271	−	6.77833i	−0.343093	−	0.353826i	0.524226	−	0.851579i	$-0.324355\pi$
$367$	−6.57271	−	6.77833i	−0.343093	−	0.353826i	−0.867319	+	0.497753i	$0.834159\pi$
$368$	1.03263	+	2.93040i	0.0538297	+	0.152758i
$369$		0			0
$370$	0.00513127	+	0.0553752i	0.000266762	+	0.00287882i
$371$	−11.8671	−	3.77519i	−0.616109	−	0.195998i
$372$		0			0
$373$	−26.5005	−	10.2663i	−1.37214	−	0.531571i	−0.441421	−	0.897300i	$-0.645525\pi$
$373$	−26.5005	−	10.2663i	−1.37214	−	0.531571i	−0.930721	+	0.365729i	$0.880820\pi$
$374$	−15.5895	+	8.37137i	−0.806112	+	0.432873i
$375$		0			0
$376$	3.35217	−	3.91267i	0.172875	−	0.201781i
$377$	−0.0116266	+	0.377369i	−0.000598802	+	0.0194355i
$378$		0			0
$379$	10.1366	+	7.17553i	0.520681	+	0.368582i	0.807935	−	0.589272i	$-0.200585\pi$
$379$	10.1366	+	7.17553i	0.520681	+	0.368582i	−0.287254	+	0.957855i	$0.592742\pi$
$380$	−0.0588622	−	0.268773i	−0.00301957	−	0.0137878i
$381$		0			0
$382$	−11.8879	+	10.8372i	−0.608236	+	0.554480i
$383$	−4.08833	+	18.6679i	−0.208904	+	0.953884i	0.748050	+	0.663643i	$0.230990\pi$
$383$	−4.08833	+	18.6679i	−0.208904	+	0.953884i	−0.956954	+	0.290241i	$0.906264\pi$
$384$		0			0
$385$	0.0563594	−	0.608215i	0.00287234	−	0.0309975i
$386$	5.01766	−	11.8547i	0.255392	−	0.603388i
$387$		0			0
$388$	12.5010	+	11.3961i	0.634640	+	0.578550i
$389$	11.4622	−	23.0191i	0.581155	−	1.16712i	−0.388228	−	0.921563i	$-0.626913\pi$
$389$	11.4622	−	23.0191i	0.581155	−	1.16712i	0.969383	−	0.245553i	$-0.0789697\pi$
$390$		0			0
$391$	1.44307	−	1.16123i	0.0729792	−	0.0587262i
$392$	−2.51346	−	2.93372i	−0.126949	−	0.148175i
$393$		0			0
$394$	−8.98618	−	1.11273i	−0.452717	−	0.0560585i
$395$	0.00929215	+	0.00427507i	0.000467539	+	0.000215102i
$396$		0			0
$397$	1.43413	+	0.360699i	0.0719771	+	0.0181030i	0.279734	−	0.960077i	$-0.409754\pi$
$397$	1.43413	+	0.360699i	0.0719771	+	0.0181030i	−0.207757	+	0.978180i	$0.566616\pi$
$398$	−7.49939	−	9.93080i	−0.375910	−	0.497786i
$399$		0			0
$400$	−2.56259	+	16.5085i	−0.128129	+	0.825423i
$401$	−2.14567	−	0.132340i	−0.107150	−	0.00660877i	0.00789730	−	0.999969i	$-0.497486\pi$
$401$	−2.14567	−	0.132340i	−0.107150	−	0.00660877i	−0.115047	+	0.993360i	$0.536702\pi$
$402$		0			0
$403$	−5.23311	−	10.5095i	−0.260680	−	0.523515i
$404$	3.74636	+	0.700316i	0.186388	+	0.0348420i
$405$		0			0
$406$	1.66797	−	0.767388i	0.0827800	−	0.0380848i
$407$	−2.83070	+	0.900511i	−0.140313	+	0.0446367i
$408$		0			0
$409$	5.88526	+	3.64400i	0.291007	+	0.180184i	0.664170	−	0.747582i	$-0.268785\pi$
$409$	5.88526	+	3.64400i	0.291007	+	0.180184i	−0.373162	+	0.927766i	$0.621726\pi$
$410$	0.334008	−	0.504069i	0.0164955	−	0.0248942i
$411$		0			0
$412$	−21.9993	+	7.41706i	−1.08383	+	0.365413i
$413$	40.7050			2.00296
$414$		0			0
$415$	0.190378	+	0.117877i	0.00934531	+	0.00578637i
$416$	4.94421	+	11.6812i	0.242410	+	0.572716i
$417$		0			0
$418$	25.0243	−	11.5130i	1.22398	−	0.563120i
$419$	−5.24676	+	14.8892i	−0.256321	+	0.727386i	0.742051	+	0.670344i	$0.233853\pi$
$419$	−5.24676	+	14.8892i	−0.256321	+	0.727386i	−0.998372	+	0.0570425i	$0.981833\pi$
$420$		0			0
$421$	−4.40776	−	8.85198i	−0.214821	−	0.431419i	0.761374	−	0.648313i	$-0.224525\pi$
$421$	−4.40776	−	8.85198i	−0.214821	−	0.431419i	−0.976195	+	0.216894i	$0.930407\pi$
$422$	7.29417	−	25.6363i	0.355075	−	1.24796i
$423$		0			0
$424$	−0.309673	+	1.99494i	−0.0150390	+	0.0968831i
$425$	9.78993	−	1.83006i	0.474882	−	0.0887707i
$426$		0			0
$427$	−3.02162	−	0.759969i	−0.146227	−	0.0367775i
$428$	1.61839	−	1.66902i	0.0782277	−	0.0806750i
$429$		0			0
$430$	0.574215	+	0.0711032i	0.0276911	+	0.00342890i
$431$	22.4262	+	12.0426i	1.08023	+	0.580072i	0.913876	−	0.405993i	$-0.133074\pi$
$431$	22.4262	+	12.0426i	1.08023	+	0.580072i	0.166356	+	0.986066i	$0.446800\pi$
$432$		0			0
$433$	17.8446	−	14.3595i	0.857559	−	0.690075i	−0.0946539	−	0.995510i	$-0.530174\pi$
$433$	17.8446	−	14.3595i	0.857559	−	0.690075i	0.952213	+	0.305435i	$0.0988019\pi$
$434$	−34.4066	+	45.5616i	−1.65157	+	2.18703i
$435$		0			0
$436$	7.70652	+	7.02542i	0.369075	+	0.336457i
$437$	−2.35345	+	1.66597i	−0.112581	+	0.0796943i
$438$		0			0
$439$	2.52841	−	27.2859i	0.120675	−	1.30229i	−0.692988	−	0.720949i	$-0.743706\pi$
$439$	2.52841	−	27.2859i	0.120675	−	1.30229i	0.813663	−	0.581337i	$-0.197470\pi$
$440$	−0.0988354	+	0.00609596i	−0.00471179	+	0.000290613i
$441$		0			0
$442$	4.76793	−	4.34654i	0.226787	−	0.206744i
$443$	9.35409	+	32.8762i	0.444426	+	1.56200i	0.783596	+	0.621271i	$0.213383\pi$
$443$	9.35409	+	32.8762i	0.444426	+	1.56200i	−0.339169	+	0.940725i	$0.610146\pi$
$444$		0			0
$445$	0.332579	+	0.235428i	0.0157658	+	0.0111603i
$446$	32.3539	−	20.0327i	1.53200	−	0.948575i
$447$		0			0
$448$	24.1607	−	28.2005i	1.14149	−	1.33235i
$449$	−10.2456	+	3.96917i	−0.483521	+	0.187317i	−0.590649	−	0.806928i	$-0.701128\pi$
$449$	−10.2456	+	3.96917i	−0.483521	+	0.187317i	0.107129	+	0.994245i	$0.465834\pi$
$450$		0			0
$451$	30.1178	+	11.6677i	1.41819	+	0.549410i
$452$	40.2312	−	4.98170i	1.89232	−	0.234319i
$453$		0			0
$454$	−4.72209	−	50.9595i	−0.221619	−	2.39165i
$455$	0.0341622	+	0.220077i	0.00160155	+	0.0103174i
$456$		0			0
$457$	−7.62427	−	7.86279i	−0.356648	−	0.367806i	0.515634	−	0.856809i	$-0.327557\pi$
$457$	−7.62427	−	7.86279i	−0.356648	−	0.367806i	−0.872282	+	0.489004i	$0.837360\pi$
$458$	−20.4005	−	35.3347i	−0.953253	−	1.65108i
$459$		0			0
$460$	0.0799728	−	0.0201140i	0.00372875	−	0.000937819i
$461$	−7.48779	−	6.02540i	−0.348741	−	0.280631i	0.436649	−	0.899632i	$-0.356165\pi$
$461$	−7.48779	−	6.02540i	−0.348741	−	0.280631i	−0.785390	+	0.619001i	$0.787538\pi$
$462$		0			0
$463$	−16.5784	−	25.0193i	−0.770463	−	1.16275i	−0.982642	−	0.185515i	$-0.940605\pi$
$463$	−16.5784	−	25.0193i	−0.770463	−	1.16275i	0.212178	−	0.977231i	$-0.431944\pi$
$464$	0.445716	+	0.672653i	0.0206919	+	0.0312271i
$465$		0			0
$466$	5.96952	+	4.80365i	0.276533	+	0.222525i
$467$	17.9519	−	4.51508i	0.830715	−	0.208933i	0.194947	−	0.980814i	$-0.437546\pi$
$467$	17.9519	−	4.51508i	0.830715	−	0.208933i	0.635768	+	0.771881i	$0.280684\pi$
$468$		0			0
$469$	19.9701	+	34.5892i	0.922133	+	1.59718i
$470$	0.483703	+	0.498836i	0.0223116	+	0.0230096i
$471$		0			0
$472$	−1.01222	−	6.52080i	−0.0465910	−	0.300144i
$473$	2.85159	+	30.7736i	0.131116	+	1.41497i
$474$		0			0
$475$	−15.3865	+	1.90526i	−0.705979	+	0.0874192i
$476$	−15.6093	−	6.04709i	−0.715453	−	0.277168i
$477$		0			0
$478$	33.8811	−	13.1256i	1.54969	−	0.600352i
$479$	20.1768	−	23.5505i	0.921903	−	1.07605i	−0.0749825	−	0.997185i	$-0.523890\pi$
$479$	20.1768	−	23.5505i	0.921903	−	1.07605i	0.996885	−	0.0788647i	$-0.0251295\pi$
$480$		0			0
$481$	0.920850	−	0.570166i	0.0419871	−	0.0259973i
$482$	1.37813	+	0.975559i	0.0627722	+	0.0444355i
$483$		0			0
$484$	−4.62920	−	16.2700i	−0.210418	−	0.739543i
$485$	−0.211914	+	0.193185i	−0.00962253	+	0.00877210i
$486$		0			0
$487$	−15.5536	+	0.959310i	−0.704799	+	0.0434705i	−0.409996	−	0.912088i	$-0.634470\pi$
$487$	−15.5536	+	0.959310i	−0.704799	+	0.0434705i	−0.294803	+	0.955558i	$0.595254\pi$
$488$	−0.0466053	+	0.502951i	−0.00210972	+	0.0227675i
$489$		0			0
$490$	0.425232	−	0.301016i	0.0192100	−	0.0135985i
$491$	−0.237629	−	0.216627i	−0.0107240	−	0.00977626i	0.668316	−	0.743878i	$-0.267015\pi$
$491$	−0.237629	−	0.216627i	−0.0107240	−	0.00977626i	−0.679040	+	0.734101i	$0.737604\pi$
$492$		0			0
$493$	0.289900	−	0.383889i	0.0130564	−	0.0172895i
$494$	−7.82470	+	6.29651i	−0.352050	+	0.283294i
$495$		0			0
$496$	−22.1066	−	11.8710i	−0.992614	−	0.533023i
$497$	33.2700	+	4.11972i	1.49236	+	0.184795i
$498$		0			0
$499$	12.1023	−	12.4809i	0.541773	−	0.558721i	−0.390442	−	0.920628i	$-0.627678\pi$
$499$	12.1023	−	12.4809i	0.541773	−	0.558721i	0.932215	+	0.361906i	$0.117874\pi$
$500$	0.860143	+	0.216335i	0.0384668	+	0.00967478i
$501$		0			0
$502$	−38.9887	+	7.28824i	−1.74015	+	0.325290i
$503$	4.09450	−	26.3772i	0.182565	−	1.17610i	−0.702863	−	0.711325i	$-0.748095\pi$
$503$	4.09450	−	26.3772i	0.182565	−	1.17610i	0.885428	−	0.464777i	$-0.153865\pi$
$504$		0			0
$505$	−0.0176808	+	0.0621415i	−0.000786785	+	0.00276526i
$506$	3.67991	+	7.39025i	0.163592	+	0.328537i
$507$		0			0
$508$	1.73636	−	4.92742i	0.0770383	−	0.218619i
$509$	−0.495449	+	0.227943i	−0.0219604	+	0.0101034i	−0.428910	−	0.903347i	$-0.641102\pi$
$509$	−0.495449	+	0.227943i	−0.0219604	+	0.0101034i	0.406950	+	0.913451i	$0.366592\pi$
$510$		0			0
$511$	−20.8398	−	49.2360i	−0.921898	−	2.17807i
$512$	26.4332	+	16.3668i	1.16819	+	0.723315i
$513$		0			0
$514$	23.4698			1.03521
$515$	−0.0907871	−	0.382940i	−0.00400056	−	0.0168743i
$516$		0			0
$517$	−20.5007	+	30.9386i	−0.901619	+	1.36068i
$518$	−4.47813	−	2.77274i	−0.196758	−	0.121827i
$519$		0			0
$520$	0.0344060	−	0.0109453i	0.00150880	−	0.000479985i
$521$	−13.8692	+	6.38087i	−0.607623	+	0.279551i	−0.697707	−	0.716383i	$-0.745796\pi$
$521$	−13.8692	+	6.38087i	−0.607623	+	0.279551i	0.0900841	+	0.995934i	$0.471286\pi$
$522$		0			0
$523$	28.6361	+	5.35301i	1.25217	+	0.234071i	0.767741	−	0.640761i	$-0.221381\pi$
$523$	28.6361	+	5.35301i	1.25217	+	0.234071i	0.484427	+	0.874832i	$0.339028\pi$
$524$	10.9177	+	21.9256i	0.476940	+	0.957825i
$525$		0			0
$526$	−31.2320	−	1.92632i	−1.36178	−	0.0839917i
$527$	−2.29458	+	14.7819i	−0.0999533	+	0.643910i
$528$		0			0
$529$	13.3398	+	17.6648i	0.579991	+	0.768033i
$530$	−0.264039	−	0.0664085i	−0.0114691	−	0.00288460i
$531$		0			0
$532$	23.6735	+	10.8915i	1.02638	+	0.472207i
$533$	−11.6873	−	1.44720i	−0.506232	−	0.0626852i
$534$		0			0
$535$	0.0256409	+	0.0299282i	0.00110855	+	0.00129391i
$536$	5.04447	−	4.05927i	0.217888	−	0.175334i
$537$		0			0
$538$	19.1893	−	38.5374i	0.827311	−	1.66146i
$539$	20.5654	+	18.7478i	0.885814	+	0.807526i
$540$		0			0
$541$	12.5254	−	29.5924i	0.538509	−	1.27228i	−0.396624	−	0.917981i	$-0.629818\pi$
$541$	12.5254	−	29.5924i	0.538509	−	1.27228i	0.935133	−	0.354297i	$-0.115280\pi$
$542$	3.22266	−	34.7781i	0.138425	−	1.49385i
$543$		0			0
$544$	3.45756	−	15.7877i	0.148242	−	0.676892i
$545$	−0.130640	+	0.119094i	−0.00559599	+	0.00510142i
$546$		0			0
$547$	3.27038	+	14.9330i	0.139831	+	0.638490i	0.993125	+	0.117059i	$0.0373466\pi$
$547$	3.27038	+	14.9330i	0.139831	+	0.638490i	−0.853294	+	0.521431i	$0.825398\pi$
$548$	−37.2767	−	26.3876i	−1.59238	−	1.12722i
$549$		0			0
$550$	−1.36701	+	44.3694i	−0.0582894	+	1.89192i
$551$	−0.487220	+	0.568686i	−0.0207563	+	0.0242268i
$552$		0			0
$553$	−0.853462	+	0.458300i	−0.0362929	+	0.0194889i
$554$	−15.5194	−	6.01226i	−0.659357	−	0.255436i
$555$		0			0
$556$	−12.0996	−	3.84917i	−0.513139	−	0.163241i
$557$	−0.786713	−	8.48999i	−0.0333341	−	0.359732i	−0.996021	−	0.0891156i	$-0.971596\pi$
$557$	−0.786713	−	8.48999i	−0.0333341	−	0.359732i	0.962687	−	0.270617i	$-0.0872276\pi$
$558$		0			0
$559$	−3.74514	−	10.6279i	−0.158403	−	0.449514i
$560$	0.331358	+	0.341724i	0.0140024	+	0.0144405i
$561$		0			0
$562$	6.68020	−	11.5705i	0.281787	−	0.488070i
$563$	7.24611	−	1.82247i	0.305387	−	0.0768080i	−0.0881778	−	0.996105i	$-0.528104\pi$
$563$	7.24611	−	1.82247i	0.305387	−	0.0768080i	0.393565	+	0.919297i	$0.371242\pi$
$564$		0			0
$565$	0.0211624	+	0.686876i	0.000890310	+	0.0288971i
$566$	−28.9495	−	43.6892i	−1.21684	−	1.83639i
$567$		0			0
$568$	−0.167364	−	5.43218i	−0.00702242	−	0.227929i
$569$	−16.2645	−	13.0880i	−0.681842	−	0.548676i	0.222792	−	0.974866i	$-0.428483\pi$
$569$	−16.2645	−	13.0880i	−0.681842	−	0.548676i	−0.904634	+	0.426190i	$0.859856\pi$
$570$		0			0
$571$	13.7091	−	23.7448i	0.573707	−	0.993689i	−0.422474	−	0.906375i	$-0.638838\pi$
$571$	13.7091	−	23.7448i	0.573707	−	0.993689i	0.996181	−	0.0873141i	$-0.0278284\pi$
$572$	7.67119	+	13.2869i	0.320749	+	0.555553i
$573$		0			0
$574$	19.0339	+	54.0142i	0.794459	+	2.25451i
$575$	−0.712767	−	4.59172i	−0.0297244	−	0.191488i
$576$		0			0
$577$	1.93657	+	0.616066i	0.0806203	+	0.0256472i	0.343191	−	0.939265i	$-0.388492\pi$
$577$	1.93657	+	0.616066i	0.0806203	+	0.0256472i	−0.262571	+	0.964913i	$0.584570\pi$
$578$	26.7758	−	3.31556i	1.11373	−	0.137909i
$579$		0			0
$580$	0.0188683	−	0.0101320i	0.000783462	−	0.000420710i
$581$	−19.7751	+	7.66091i	−0.820409	+	0.317828i
$582$		0			0
$583$	0.447842	−	14.5357i	0.0185477	−	0.602009i
$584$	−7.36920	+	4.56282i	−0.304940	+	0.188811i
$585$		0			0
$586$	−9.75925	−	44.5621i	−0.403151	−	1.84084i
$587$	−9.26873	−	32.5762i	−0.382562	−	1.34456i	−0.879136	−	0.476571i	$-0.841880\pi$
$587$	−9.26873	−	32.5762i	−0.382562	−	1.34456i	0.496575	−	0.867994i	$-0.334591\pi$
$588$		0			0
$589$	4.98177	−	22.7475i	0.205270	−	0.937293i
$590$	0.888245	−	0.0547851i	0.0365685	−	0.00225547i
$591$		0			0
$592$	0.902287	−	2.13174i	0.0370838	−	0.0876139i
$593$	19.1553	−	13.5597i	0.786612	−	0.556831i	−0.112962	−	0.993599i	$-0.536034\pi$
$593$	19.1553	−	13.5597i	0.786612	−	0.556831i	0.899574	+	0.436768i	$0.143877\pi$
$594$		0			0
$595$	0.126487	−	0.254020i	0.00518546	−	0.0104138i
$596$	−29.1743	+	38.6330i	−1.19503	+	1.58247i
$597$		0			0
$598$	−1.95846	−	2.28592i	−0.0800873	−	0.0934783i
$599$	22.2668	+	11.9570i	0.909795	+	0.488550i	0.860049	−	0.510212i	$-0.170433\pi$
$599$	22.2668	+	11.9570i	0.909795	+	0.488550i	0.0497468	+	0.998762i	$0.484159\pi$
$600$		0			0
$601$	36.5417	+	16.8119i	1.49057	+	0.685770i	0.984283	−	0.176596i	$-0.0565087\pi$
$601$	36.5417	+	16.8119i	1.49057	+	0.685770i	0.506285	+	0.862366i	$0.331018\pi$
$602$	−38.1475	+	39.3409i	−1.55478	+	1.60342i
$603$		0			0
$604$	26.1521	+	34.6310i	1.06411	+	1.40912i
$605$	0.281870	−	0.0526906i	0.0114596	−	0.00214218i
$606$		0			0
$607$	7.47792	+	0.461222i	0.303519	+	0.0187204i	0.212605	−	0.977138i	$-0.431805\pi$
$607$	7.47792	+	0.461222i	0.303519	+	0.0187204i	0.0909145	+	0.995859i	$0.471021\pi$
$608$	−6.88514	+	24.1988i	−0.279229	+	0.981390i
$609$		0			0
$610$	−0.0669592	−	0.0125168i	−0.00271110	−	0.000506792i
$611$	4.49754	−	12.7631i	0.181951	−	0.516340i
$612$		0			0
$613$	5.53565	−	1.76102i	0.223583	−	0.0711268i	−0.189268	−	0.981925i	$-0.560612\pi$
$613$	5.53565	−	1.76102i	0.223583	−	0.0711268i	0.412851	+	0.910799i	$0.364533\pi$
$614$	2.87075	+	6.78242i	0.115854	+	0.273716i
$615$		0			0
$616$	5.18033	−	7.81791i	0.208722	−	0.314992i
$617$	16.9175			0.681072			0.340536	−	0.940232i	$-0.389392\pi$
$617$	16.9175			0.681072			0.340536	+	0.940232i	$0.389392\pi$
$618$		0			0
$619$	1.01264			0.0407013			0.0203506	−	0.999793i	$-0.493522\pi$
$619$	1.01264			0.0407013			0.0203506	+	0.999793i	$0.493522\pi$
$620$	−0.367861	+	0.555157i	−0.0147736	+	0.0222957i
$621$		0			0
$622$	−8.18514	−	19.3382i	−0.328194	−	0.775389i
$623$	−36.7757	+	11.6992i	−1.47339	+	0.468718i
$624$		0			0
$625$	8.30137	−	23.5576i	0.332055	−	0.942304i
$626$	−27.8469	−	5.20550i	−1.11299	−	0.208053i
$627$		0			0
$628$	0.866391	−	3.04505i	0.0345728	−	0.121511i
$629$	−1.37739	−	0.0849543i	−0.0549200	−	0.00338735i
$630$		0			0
$631$	−47.7872	+	8.93297i	−1.90238	+	0.355616i	−0.997537	−	0.0701366i	$-0.977656\pi$
$631$	−47.7872	+	8.93297i	−1.90238	+	0.355616i	−0.904840	+	0.425752i	$0.860009\pi$
$632$	0.0946411	+	0.125325i	0.00376462	+	0.00498516i
$633$		0			0
$634$	−26.7412	+	27.5778i	−1.06203	+	1.09525i
$635$	0.0804567	+	0.0370160i	0.00319283	+	0.00146893i
$636$		0			0
$637$	−8.93923	−	4.80026i	−0.354185	−	0.190193i
$638$	1.39499	+	1.62824i	0.0552283	+	0.0644627i
$639$		0			0
$640$	0.110160	−	0.145875i	0.00435444	−	0.00576622i
$641$	−4.15708	+	8.34853i	−0.164195	+	0.329747i	−0.961946	−	0.273239i	$-0.911905\pi$
$641$	−4.15708	+	8.34853i	−0.164195	+	0.329747i	0.797752	+	0.602986i	$0.206023\pi$
$642$		0			0
$643$	−32.3941	+	22.9313i	−1.27750	+	0.904323i	−0.998434	−	0.0559497i	$-0.982181\pi$
$643$	−32.3941	+	22.9313i	−1.27750	+	0.904323i	−0.279065	+	0.960272i	$0.590024\pi$
$644$	−3.04426	+	7.19236i	−0.119961	+	0.283419i
$645$		0			0
$646$	12.7727	−	0.787792i	0.502534	−	0.0309953i
$647$	10.4374	−	47.6585i	0.410335	−	1.87365i	−0.0715881	−	0.997434i	$-0.522807\pi$
$647$	10.4374	−	47.6585i	0.410335	−	1.87365i	0.481923	−	0.876213i	$-0.339938\pi$
$648$		0			0
$649$	13.0086	+	45.7204i	0.510631	+	1.79468i
$650$	−3.46257	−	15.8106i	−0.135813	−	0.620143i
$651$		0			0
$652$	−44.7969	+	27.7370i	−1.75438	+	1.08627i
$653$	−1.03884	+	33.7181i	−0.0406531	+	1.31949i	0.730532	+	0.682879i	$0.239272\pi$
$653$	−1.03884	+	33.7181i	−0.0406531	+	1.31949i	−0.771185	+	0.636611i	$0.780336\pi$
$654$		0			0
$655$	−0.387171	+	0.149991i	−0.0151280	+	0.00586063i
$656$	−22.1748	+	11.9076i	−0.865780	+	0.464914i
$657$		0			0
$658$	−65.3096	+	8.08708i	−2.54603	+	0.315267i
$659$	−46.5782	−	14.8176i	−1.81443	−	0.577211i	−0.814432	−	0.580258i	$-0.802952\pi$
$659$	−46.5782	−	14.8176i	−1.81443	−	0.577211i	−0.999995	+	0.00304739i	$0.999030\pi$
$660$		0			0
$661$	5.82378	+	37.5174i	0.226519	+	1.45926i	0.779677	+	0.626182i	$0.215383\pi$
$661$	5.82378	+	37.5174i	0.226519	+	1.45926i	−0.553158	+	0.833077i	$0.686577\pi$
$662$	3.37888	+	9.58857i	0.131324	+	0.372670i
$663$		0			0
$664$	1.71900	+	2.97739i	0.0667101	+	0.115545i
$665$	−0.220872	+	0.382562i	−0.00856505	+	0.0148351i
$666$		0			0
$667$	−0.174857	−	0.140707i	−0.00677050	−	0.00544820i
$668$	−0.372790	−	12.0998i	−0.0144237	−	0.468155i
$669$		0			0
$670$	0.482331	+	0.727911i	0.0186341	+	0.0281217i
$671$	−0.112048	−	3.63680i	−0.00432558	−	0.140397i
$672$		0			0
$673$	47.5286	−	11.9539i	1.83209	−	0.460790i	0.835972	−	0.548772i	$-0.184905\pi$
$673$	47.5286	−	11.9539i	1.83209	−	0.460790i	0.996122	+	0.0879820i	$0.0280418\pi$
$674$	−20.6329	+	35.7372i	−0.794748	+	1.37654i
$675$		0			0
$676$	16.8075	+	17.3333i	0.646441	+	0.666664i
$677$	−2.75456	−	7.81688i	−0.105866	−	0.300427i	0.878182	−	0.478326i	$-0.158756\pi$
$677$	−2.75456	−	7.81688i	−0.105866	−	0.300427i	−0.984049	+	0.177899i	$0.943070\pi$
$678$		0			0
$679$	−2.50587	−	27.0426i	−0.0961664	−	1.03780i
$680$	−0.0438385	−	0.0139460i	−0.00168113	−	0.000534806i
$681$		0			0
$682$	−62.1711	−	24.0852i	−2.38065	−	0.922270i
$683$	−27.8127	+	14.9351i	−1.06422	+	0.571477i	−0.909168	−	0.416429i	$-0.863281\pi$
$683$	−27.8127	+	14.9351i	−1.06422	+	0.571477i	−0.155056	+	0.987906i	$0.549556\pi$
$684$		0			0
$685$	0.503717	−	0.587941i	0.0192460	−	0.0224641i
$686$	0.119800	−	3.88840i	0.00457400	−	0.148460i
$687$		0			0
$688$	−19.6572	−	13.9150i	−0.749422	−	0.530505i
$689$	1.13436	+	5.17967i	0.0432158	+	0.197330i
$690$		0			0
$691$	−7.09172	+	6.46496i	−0.269782	+	0.245939i	−0.797269	−	0.603625i	$-0.793723\pi$
$691$	−7.09172	+	6.46496i	−0.269782	+	0.245939i	0.527487	+	0.849563i	$0.323134\pi$
$692$	4.84544	−	22.1249i	0.184196	−	0.841064i
$693$		0			0
$694$	1.24256	−	13.4094i	0.0471671	−	0.509014i
$695$	0.0838975	−	0.198216i	0.00318241	−	0.00751875i
$696$		0			0
$697$	11.0889	+	10.1089i	0.420022	+	0.382901i
$698$	−9.57021	+	19.2196i	−0.362238	+	0.727471i
$699$		0			0
$700$	−32.7169	+	26.3272i	−1.23658	+	0.995073i
$701$	−12.1621	−	14.1956i	−0.459354	−	0.536161i	0.480836	−	0.876811i	$-0.340333\pi$
$701$	−12.1621	−	14.1956i	−0.459354	−	0.536161i	−0.940190	+	0.340650i	$0.889353\pi$
$702$		0			0
$703$	2.13197	+	0.263995i	0.0804087	+	0.00995676i
$704$	39.3965	+	18.1253i	1.48481	+	0.683121i
$705$		0			0
$706$	72.3686	+	18.2014i	2.72363	+	0.685020i
$707$	−3.68752	−	4.88306i	−0.138683	−	0.183647i
$708$		0			0
$709$	−6.93215	+	44.6577i	−0.260342	+	1.67715i	0.392571	+	0.919722i	$0.371586\pi$
$709$	−6.93215	+	44.6577i	−0.260342	+	1.67715i	−0.652914	+	0.757432i	$0.726454\pi$
$710$	0.731546	+	0.0451202i	0.0274544	+	0.00169333i
$711$		0			0
$712$	2.78867	+	5.60041i	0.104510	+	0.209884i
$713$	6.86041	+	1.28243i	0.256924	+	0.0480275i
$714$		0			0
$715$	−0.236275	+	0.108704i	−0.00883620	+	0.00406530i
$716$	21.8820	−	6.96115i	0.817767	−	0.260150i
$717$		0			0
$718$	−43.7261	−	27.0741i	−1.63184	−	1.01040i
$719$	−19.9612	+	30.1245i	−0.744427	+	1.12345i	0.243705	+	0.969849i	$0.421637\pi$
$719$	−19.9612	+	30.1245i	−0.744427	+	1.12345i	−0.988132	+	0.153604i	$0.950912\pi$
$720$		0			0
$721$	34.1243	+	14.9947i	1.27086	+	0.558433i
$722$	19.4211			0.722778
$723$		0			0
$724$	19.5505	+	12.1051i	0.726587	+	0.449884i
$725$	−0.470393	−	1.11135i	−0.0174699	−	0.0412744i
$726$		0			0
$727$	28.3181	−	13.0284i	1.05026	−	0.483196i	0.184071	−	0.982913i	$-0.441072\pi$
$727$	28.3181	−	13.0284i	1.05026	−	0.483196i	0.866189	+	0.499717i	$0.166563\pi$
$728$	−1.13649	+	3.22512i	−0.0421210	+	0.119531i
$729$		0			0
$730$	−0.521023	−	1.04636i	−0.0192839	−	0.0387273i
$731$	−3.92919	+	13.8097i	−0.145326	+	0.510769i
$732$		0			0
$733$	−1.23215	+	7.93762i	−0.0455104	+	0.293183i	−0.999987	−	0.00510301i	$-0.998376\pi$
$733$	−1.23215	+	7.93762i	−0.0455104	+	0.293183i	0.954477	+	0.298286i	$0.0964149\pi$
$734$	19.2175	−	3.59238i	0.709332	−	0.132597i
$735$		0			0
$736$	−7.31275	−	1.83923i	−0.269551	−	0.0677949i
$737$	−32.4690	+	33.4847i	−1.19601	+	1.23343i
$738$		0			0
$739$	33.5780	+	4.15786i	1.23519	+	0.152949i	0.713787	−	0.700363i	$-0.246979\pi$
$739$	33.5780	+	4.15786i	1.23519	+	0.152949i	0.521400	+	0.853313i	$0.325410\pi$
$740$	−0.0541276	−	0.0290659i	−0.00198977	−	0.00106848i
$741$		0			0
$742$	20.0893	−	16.1658i	0.737501	−	0.593465i
$743$	−10.6060	+	14.0446i	−0.389096	+	0.515247i	−0.949837	−	0.312745i	$-0.898752\pi$
$743$	−10.6060	+	14.0446i	−0.389096	+	0.515247i	0.560741	+	0.827991i	$0.310516\pi$
$744$		0			0
$745$	−0.606476	−	0.552876i	−0.0222196	−	0.0202558i
$746$	48.0305	−	34.0001i	1.75852	−	1.24483i
$747$		0			0
$748$	1.80371	−	19.4651i	0.0659502	−	0.711716i
$749$	−3.72544	+	0.229777i	−0.136125	+	0.00839587i
$750$		0			0
$751$	15.8688	−	14.4663i	0.579061	−	0.527884i	−0.330308	−	0.943873i	$-0.607153\pi$
$751$	15.8688	−	14.4663i	0.579061	−	0.527884i	0.909370	+	0.415989i	$0.136565\pi$
$752$	−7.91497	−	27.8182i	−0.288629	−	1.01443i
$753$		0			0
$754$	−0.638075	−	0.451684i	−0.0232373	−	0.0164494i
$755$	−0.625460	+	0.387269i	−0.0227628	+	0.0140942i
$756$		0			0
$757$	−24.8705	+	29.0289i	−0.903933	+	1.05507i	0.0942937	+	0.995544i	$0.469941\pi$
$757$	−24.8705	+	29.0289i	−0.903933	+	1.05507i	−0.998226	+	0.0595304i	$0.981040\pi$
$758$	−23.9793	+	9.28963i	−0.870967	+	0.337414i
$759$		0			0
$760$	0.0667775	+	0.0258697i	0.00242227	+	0.000938394i
$761$	−14.9351	+	1.84937i	−0.541398	+	0.0670397i	−0.388928	−	0.921268i	$-0.627154\pi$
$761$	−14.9351	+	1.84937i	−0.541398	+	0.0670397i	−0.152471	+	0.988308i	$0.548723\pi$
$762$		0			0
$763$	−1.54480	−	16.6711i	−0.0559257	−	0.603534i
$764$	−2.72597	−	17.5610i	−0.0986220	−	0.635334i
$765$		0			0
$766$	−27.5464	−	28.4082i	−0.995292	−	1.02643i
$767$	−8.66592	−	15.0098i	−0.312908	−	0.541973i
$768$		0			0
$769$	4.02628	−	1.01265i	0.145191	−	0.0365171i	−0.170634	−	0.985335i	$-0.554581\pi$
$769$	4.02628	−	1.01265i	0.145191	−	0.0365171i	0.315825	+	0.948817i	$0.397719\pi$
$770$	0.985372	+	0.792926i	0.0355103	+	0.0285751i
$771$		0			0
$772$	7.85535	+	11.8549i	0.282720	+	0.426668i
$773$	−21.6742	−	32.7096i	−0.779565	−	1.17648i	−0.980431	−	0.196863i	$-0.936924\pi$
$773$	−21.6742	−	32.7096i	−0.779565	−	1.17648i	0.200866	−	0.979619i	$-0.435625\pi$
$774$		0			0
$775$	29.2364	+	23.5264i	1.05020	+	0.845095i
$776$	−4.26982	+	1.07390i	−0.153278	+	0.0385509i
$777$		0			0
$778$	26.6232	+	46.1128i	0.954490	+	1.65322i
$779$	−16.2606	−	16.7693i	−0.582597	−	0.600823i
$780$		0			0
$781$	6.00515	+	38.6858i	0.214881	+	1.38429i
$782$	0.353885	+	3.81903i	0.0126549	+	0.136568i
$783$		0			0
$784$	−21.5216	+	2.66495i	−0.768627	+	0.0951767i
$785$	0.0500439	+	0.0193871i	0.00178614	+	0.000691956i
$786$		0			0
$787$	−23.0301	+	8.92191i	−0.820934	+	0.318032i	−0.734827	−	0.678254i	$-0.762737\pi$
$787$	−23.0301	+	8.92191i	−0.820934	+	0.318032i	−0.0861070	+	0.996286i	$0.527443\pi$
$788$	6.50834	−	7.59657i	0.231850	−	0.270617i
$789$		0			0
$790$	−0.0180070	+	0.0111495i	−0.000640661	+	0.000396680i
$791$	−53.1220	−	37.6043i	−1.88880	−	1.33705i
$792$		0			0
$793$	0.363055	+	1.27600i	0.0128924	+	0.0453123i
$794$	−2.26288	+	2.06289i	−0.0803068	+	0.0732093i
$795$		0			0
$796$	13.7218	−	0.846334i	0.486357	−	0.0299975i
$797$	−2.68977	+	29.0272i	−0.0952765	+	1.02820i	0.805116	+	0.593118i	$0.202103\pi$
$797$	−2.68977	+	29.0272i	−0.0952765	+	1.02820i	−0.900392	+	0.435079i	$0.856720\pi$
$798$		0			0
$799$	−14.0731	+	9.96214i	−0.497870	+	0.352435i
$800$	−29.9628	−	27.3147i	−1.05934	−	0.965720i
$801$		0			0
$802$	2.68254	−	3.55225i	0.0947237	−	0.125434i
$803$	48.6424	−	39.1424i	1.71655	−	1.38131i
$804$		0			0
$805$	−0.116642	−	0.0626355i	−0.00411110	−	0.00220761i
$806$	24.1257	+	2.98741i	0.849791	+	0.105227i
$807$		0			0
$808$	−0.690552	+	0.712155i	−0.0242935	+	0.0250535i
$809$	0.447242	+	0.112486i	0.0157242	+	0.00395479i	0.251768	−	0.967788i	$-0.418988\pi$
$809$	0.447242	+	0.112486i	0.0157242	+	0.00395479i	−0.236044	+	0.971742i	$0.575851\pi$
$810$		0			0
$811$	14.7728	−	2.76151i	0.518742	−	0.0969697i	0.0821335	−	0.996621i	$-0.473827\pi$
$811$	14.7728	−	2.76151i	0.518742	−	0.0969697i	0.436608	+	0.899652i	$0.356180\pi$
$812$	−0.311133	+	2.00435i	−0.0109186	+	0.0703391i
$813$		0			0
$814$	1.68325	−	5.91600i	0.0589978	−	0.207356i
$815$	−0.398121	−	0.799535i	−0.0139456	−	0.0280065i
$816$		0			0
$817$	7.42838	−	21.0802i	0.259886	−	0.737503i
$818$	−13.0211	+	5.99067i	−0.455273	+	0.209459i
$819$		0			0
$820$	0.260388	+	0.615192i	0.00909316	+	0.0214834i
$821$	28.2832	+	17.5122i	0.987091	+	0.611181i	0.922201	−	0.386712i	$-0.126389\pi$
$821$	28.2832	+	17.5122i	0.987091	+	0.611181i	0.0648902	+	0.997892i	$0.479330\pi$
$822$		0			0
$823$	36.0973			1.25827			0.629136	−	0.777295i	$-0.283409\pi$
$823$	36.0973			1.25827			0.629136	+	0.777295i	$0.283409\pi$
$824$	1.55353	−	5.83947i	0.0541199	−	0.203427i
$825$		0			0
$826$	−46.5563	+	70.2605i	−1.61990	+	2.44467i
$827$	−36.3362	−	22.4984i	−1.26353	−	0.782347i	−0.279469	−	0.960155i	$-0.590158\pi$
$827$	−36.3362	−	22.4984i	−1.26353	−	0.782347i	−0.984065	+	0.177808i	$0.943099\pi$
$828$		0			0
$829$	−52.0775	+	16.5670i	−1.80873	+	0.575397i	−0.999920	−	0.0126774i	$-0.995965\pi$
$829$	−52.0775	+	16.5670i	−1.80873	+	0.575397i	−0.808807	+	0.588075i	$0.799886\pi$
$830$	−0.421211	+	0.193788i	−0.0146205	+	0.00672648i
$831$		0			0
$832$	−15.5425	−	2.90540i	−0.538840	−	0.100727i
$833$	5.76261	+	11.5729i	0.199663	+	0.400977i
$834$		0			0
$835$	0.204822	+	0.0126330i	0.00708815	+	0.000437182i
$836$	−4.66789	+	30.0711i	−0.161442	+	1.04003i
$837$		0			0
$838$	−19.6991	−	26.0859i	−0.680496	−	0.901122i
$839$	−20.5266	−	5.16265i	−0.708657	−	0.178234i	−0.127278	−	0.991867i	$-0.540624\pi$
$839$	−20.5266	−	5.16265i	−0.708657	−	0.178234i	−0.581379	+	0.813633i	$0.697487\pi$
$840$		0			0
$841$	26.2925	+	12.0965i	0.906639	+	0.417120i
$842$	20.3207	+	2.51625i	0.700297	+	0.0867155i
$843$		0			0
$844$	19.1580	+	22.3613i	0.659446	+	0.769709i
$845$	−0.318867	+	0.256591i	−0.0109693	+	0.00882700i
$846$		0			0
$847$	−12.1055	+	24.3111i	−0.415949	+	0.835338i
$848$	8.37498	+	7.63481i	0.287598	+	0.262180i
$849$		0			0
$850$	−8.03838	+	18.9914i	−0.275714	+	0.651400i
$851$	−0.0594074	+	0.641108i	−0.00203646	+	0.0219769i
$852$		0			0
$853$	1.87656	−	8.56862i	0.0642521	−	0.293384i	−0.933645	−	0.358199i	$-0.883391\pi$
$853$	1.87656	−	8.56862i	0.0642521	−	0.293384i	0.997897	+	0.0648151i	$0.0206458\pi$
$854$	4.76775	−	4.34638i	0.163149	−	0.148730i
$855$		0			0
$856$	0.129450	+	0.591088i	0.00442452	+	0.0202030i
$857$	23.8985	+	16.9174i	0.816356	+	0.577887i	0.908512	−	0.417858i	$-0.137219\pi$
$857$	23.8985	+	16.9174i	0.816356	+	0.577887i	−0.0921561	+	0.995745i	$0.529376\pi$
$858$		0			0
$859$	−0.570947	+	18.5314i	−0.0194805	+	0.632284i	0.938472	+	0.345356i	$0.112242\pi$
$859$	−0.570947	+	18.5314i	−0.0194805	+	0.632284i	−0.957952	+	0.286928i	$0.907366\pi$
$860$	−0.415882	+	0.485419i	−0.0141815	+	0.0165527i
$861$		0			0
$862$	−46.4365	+	24.9359i	−1.58163	+	0.849320i
$863$	14.1087	+	5.46574i	0.480266	+	0.186056i	0.589191	−	0.807994i	$-0.299447\pi$
$863$	14.1087	+	5.46574i	0.480266	+	0.186056i	−0.108925	+	0.994050i	$0.534741\pi$
$864$		0			0
$865$	0.365880	+	0.116395i	0.0124403	+	0.00395754i
$866$	4.37605	+	47.2251i	0.148704	+	1.60478i
$867$		0			0
$868$	−20.9630	−	59.4887i	−0.711531	−	2.01918i
$869$	−0.787519	−	0.812155i	−0.0267147	−	0.0275505i
$870$		0			0
$871$	8.50309	−	14.7278i	0.288116	−	0.499032i
$872$	−2.63223	+	0.662034i	−0.0891387	+	0.0224193i
$873$		0			0
$874$	−0.183863	−	5.96772i	−0.00621927	−	0.201861i
$875$	−0.786553	−	1.18703i	−0.0265903	−	0.0401289i
$876$		0			0
$877$	−0.366012	−	11.8798i	−0.0123593	−	0.401151i	−0.985374	−	0.170407i	$-0.945492\pi$
$877$	−0.366012	−	11.8798i	−0.0123593	−	0.401151i	0.973014	−	0.230744i	$-0.0741161\pi$
$878$	44.2061	+	35.5725i	1.49188	+	1.20051i
$879$		0			0
$880$	−0.277933	+	0.481394i	−0.00936912	+	0.0162278i
$881$	−20.7944	−	36.0170i	−0.700582	−	1.21344i	−0.968262	−	0.249936i	$-0.919591\pi$
$881$	−20.7944	−	36.0170i	−0.700582	−	1.21344i	0.267681	−	0.963508i	$-0.413743\pi$
$882$		0			0
$883$	−13.4780	−	38.2478i	−0.453571	−	1.28714i	−0.916247	−	0.400613i	$-0.868797\pi$
$883$	−13.4780	−	38.2478i	−0.453571	−	1.28714i	0.462677	−	0.886527i	$-0.346889\pi$
$884$	1.09332	+	7.04328i	0.0367723	+	0.236891i
$885$		0			0
$886$	−67.4460	−	21.4561i	−2.26589	−	0.720832i
$887$	55.0942	−	6.82214i	1.84988	−	0.229065i	0.880401	−	0.474229i	$-0.157273\pi$
$887$	55.0942	−	6.82214i	1.84988	−	0.229065i	0.969482	+	0.245164i	$0.0788418\pi$
$888$		0			0
$889$	−7.38977	+	3.96822i	−0.247845	+	0.133090i
$890$	−0.786756	+	0.304791i	−0.0263721	+	0.0102166i
$891$		0			0
$892$	−1.29462	+	42.0200i	−0.0433471	+	1.40693i
$893$	22.8207	−	14.1300i	0.763666	−	0.472842i
$894$		0			0
$895$	0.0832750	+	0.380245i	0.00278358	+	0.0127102i
$896$	4.73783	+	16.6517i	0.158280	+	0.556296i
$897$		0			0
$898$	4.86726	−	22.2246i	0.162423	−	0.741644i
$899$	1.80914	−	0.111584i	0.0603383	−	0.00372154i
$900$		0			0
$901$	2.63343	−	6.22173i	0.0877323	−	0.207276i
$902$	−54.5866	+	38.6410i	−1.81753	+	1.28661i
$903$		0			0
$904$	−4.70308	+	9.44506i	−0.156422	+	0.314138i
$905$	−0.234908	+	0.311069i	−0.00780862	+	0.0103403i
$906$		0			0
$907$	−26.7739	−	31.2507i	−0.889014	−	1.03766i	−0.999043	−	0.0437329i	$-0.986075\pi$
$907$	−26.7739	−	31.2507i	−0.889014	−	1.03766i	0.110030	−	0.993928i	$-0.464905\pi$
$908$	49.8114	+	26.7481i	1.65305	+	0.887668i
$909$		0			0
$910$	−0.418945	−	0.192745i	−0.0138879	−	0.00638945i
$911$	6.08406	−	6.27439i	0.201574	−	0.207880i	−0.609561	−	0.792739i	$-0.708654\pi$
$911$	6.08406	−	6.27439i	0.201574	−	0.207880i	0.811135	+	0.584859i	$0.198850\pi$
$912$		0			0
$913$	−14.9246	−	19.7633i	−0.493931	−	0.654071i
$914$	22.2921	−	4.16712i	0.737357	−	0.137836i
$915$		0			0
$916$	44.9895	+	2.77486i	1.48649	+	0.0916839i
$917$	10.7616	−	37.8232i	0.355380	−	1.24903i
$918$		0			0
$919$	56.2040	+	10.5063i	1.85400	+	0.346572i	0.988120	−	0.153683i	$-0.0491136\pi$
$919$	56.2040	+	10.5063i	1.85400	+	0.346572i	0.865878	+	0.500256i	$0.166761\pi$
$920$	−0.00713344	+	0.0202432i	−0.000235182	+	0.000667399i
$921$		0			0
$922$	18.9645	−	6.03305i	0.624563	−	0.198688i
$923$	−5.56390	−	13.1452i	−0.183138	−	0.432681i
$924$		0			0
$925$	−1.91226	+	2.88589i	−0.0628747	+	0.0948875i
$926$	62.1470			2.04228
$927$		0			0
$928$	−1.95834			−0.0642857
$929$	−6.85741	+	10.3489i	−0.224984	+	0.339535i	−0.928624	−	0.371021i	$-0.879008\pi$
$929$	−6.85741	+	10.3489i	−0.224984	+	0.339535i	0.703640	+	0.710557i	$0.251557\pi$
$930$		0			0
$931$	−7.84459	−	18.5336i	−0.257096	−	0.607414i
$932$	−8.06655	+	2.56616i	−0.264229	+	0.0840572i
$933$		0			0
$934$	−12.7390	+	36.1507i	−0.416833	+	1.18289i
$935$	0.325741	+	0.0608916i	0.0106529	+	0.00199137i
$936$		0			0
$937$	2.20259	−	7.74130i	0.0719555	−	0.252897i	−0.917500	−	0.397736i	$-0.869796\pi$
$937$	2.20259	−	7.74130i	0.0719555	−	0.252897i	0.989455	+	0.144839i	$0.0462665\pi$
$938$	−82.5448	−	5.09119i	−2.69518	−	0.166233i
$939$		0			0
$940$	−0.754558	+	0.141051i	−0.0246110	+	0.00460059i
$941$	9.23052	+	12.2232i	0.300906	+	0.398465i	0.923200	−	0.384319i	$-0.125564\pi$
$941$	9.23052	+	12.2232i	0.300906	+	0.398465i	−0.622294	+	0.782784i	$0.713799\pi$
$942$		0			0
$943$	4.87348	−	5.02595i	0.158703	−	0.163667i
$944$	−33.6521	−	15.4824i	−1.09528	−	0.503910i
$945$		0			0
$946$	−56.3795	−	30.2751i	−1.83305	−	0.984330i
$947$	31.1893	+	36.4043i	1.01351	+	1.18298i	0.983030	+	0.183444i	$0.0587246\pi$
$947$	31.1893	+	36.4043i	1.01351	+	1.18298i	0.0304844	+	0.999535i	$0.490295\pi$
$948$		0			0
$949$	−13.7189	+	18.1667i	−0.445333	+	0.589716i
$950$	14.3096	−	28.7375i	0.464264	−	0.932369i
$951$		0			0
$952$	3.55614	−	2.51734i	0.115255	−	0.0815874i
$953$	4.71767	−	11.1459i	0.152820	−	0.361052i	−0.826628	−	0.562749i	$-0.809744\pi$
$953$	4.71767	−	11.1459i	0.152820	−	0.361052i	0.979448	+	0.201697i	$0.0646456\pi$
$954$		0			0
$955$	0.300685	−	0.0185456i	0.00972994	−	0.000600122i
$956$	−8.58746	+	39.2115i	−0.277738	+	1.26819i
$957$		0			0
$958$	17.5730	+	61.7628i	0.567759	+	1.99547i
$959$	15.6867	+	71.6278i	0.506551	+	2.31298i
$960$		0			0
$961$	−21.5652	+	13.3526i	−0.695650	+	0.430729i
$962$	−0.0690628	+	2.24159i	−0.00222667	+	0.0722719i
$963$		0			0
$964$	−1.73939	+	0.673842i	−0.0560219	+	0.0217030i
$965$	−0.212392	+	0.114052i	−0.00683715	+	0.00367147i
$966$		0			0
$967$	−22.5031	+	2.78649i	−0.723652	+	0.0896076i	−0.476256	−	0.879307i	$-0.658006\pi$
$967$	−22.5031	+	2.78649i	−0.723652	+	0.0896076i	−0.247397	+	0.968914i	$0.579575\pi$
$968$	4.19558	+	1.33471i	0.134851	+	0.0428992i
$969$		0			0
$970$	−0.0910786	−	0.586738i	−0.00292436	−	0.0188390i
$971$	−12.8760	−	36.5395i	−0.413211	−	1.17261i	−0.945380	−	0.325970i	$-0.894309\pi$
$971$	−12.8760	−	36.5395i	−0.413211	−	1.17261i	0.532169	−	0.846638i	$-0.321377\pi$
$972$		0			0
$973$	10.1927	+	17.6542i	0.326762	+	0.565968i
$974$	16.1335	−	27.9440i	0.516950	−	0.895384i
$975$		0			0
$976$	2.20901	+	1.77759i	0.0707088	+	0.0568991i
$977$	−1.19161	−	38.6764i	−0.0381229	−	1.23737i	−0.804098	−	0.594496i	$-0.797351\pi$
$977$	−1.19161	−	38.6764i	−0.0381229	−	1.23737i	0.765975	−	0.642870i	$-0.222256\pi$
$978$		0			0
$979$	−24.8935	−	37.5681i	−0.795600	−	1.20068i
$980$	0.0177246	+	0.575294i	0.000566192	+	0.0183771i
$981$		0			0
$982$	0.645706	−	0.162402i	0.0206053	−	0.00518244i
$983$	7.05878	−	12.2262i	0.225140	−	0.389954i	−0.731221	−	0.682140i	$-0.761049\pi$
$983$	7.05878	−	12.2262i	0.225140	−	0.389954i	0.956361	+	0.292186i	$0.0943827\pi$
$984$		0			0
$985$	0.118047	+	0.121740i	0.00376128	+	0.00387895i
$986$	0.331055	+	0.939465i	0.0105429	+	0.0299187i
$987$		0			0
$988$	−1.02377	−	11.0483i	−0.0325705	−	0.351492i
$989$	6.38354	+	2.03075i	0.202985	+	0.0645741i
$990$		0			0
$991$	−6.93522	−	2.68672i	−0.220305	−	0.0853465i	0.248560	−	0.968616i	$-0.420043\pi$
$991$	−6.93522	−	2.68672i	−0.220305	−	0.0853465i	−0.468865	+	0.883270i	$0.655337\pi$
$992$	53.6509	−	28.8099i	1.70342	−	0.914716i
$993$		0			0
$994$	−45.1635	+	52.7150i	−1.43250	+	1.67202i
$995$	−0.00717687	+	0.232942i	−0.000227522	+	0.00738476i
$996$		0			0
$997$	25.0315	+	17.7194i	0.792756	+	0.561180i	0.901444	−	0.432895i	$-0.142508\pi$
$997$	25.0315	+	17.7194i	0.792756	+	0.561180i	−0.108688	+	0.994076i	$0.534665\pi$
$998$	7.70117	+	35.1646i	0.243776	+	1.11312i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.ba.e.28.4	✓	512
3.2	odd	2	inner	927.2.ba.e.28.13	yes	512
103.92	even	51	inner	927.2.ba.e.298.4	yes	512
309.92	odd	102	inner	927.2.ba.e.298.13	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.ba.e.28.4	✓	512	1.1	even	1	trivial
927.2.ba.e.28.13	yes	512	3.2	odd	2	inner
927.2.ba.e.298.4	yes	512	103.92	even	51	inner
927.2.ba.e.298.13	yes	512	309.92	odd	102	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.ba (of order \(51\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14375 + 1.72609i) q^{2} +(-0.891651 - 2.10661i) q^{4} +(0.0369533 - 0.0117557i) q^{5} +(-1.22063 + 3.46389i) q^{7} +(0.585256 + 0.109403i) q^{8} +O(q^{10})\)	\(q+(-1.14375 + 1.72609i) q^{2} +(-0.891651 - 2.10661i) q^{4} +(0.0369533 - 0.0117557i) q^{5} +(-1.22063 + 3.46389i) q^{7} +(0.585256 + 0.109403i) q^{8} +(-0.0219739 + 0.0772301i) q^{10} +(-4.28077 - 0.264029i) q^{11} +(1.53716 - 0.287345i) q^{13} +(-4.58289 - 6.06872i) q^{14} +(2.32665 - 2.39943i) q^{16} +(-1.81012 - 0.832787i) q^{17} +(2.73266 + 1.46741i) q^{19} +(-0.0577140 - 0.0673641i) q^{20} +(5.35186 - 7.08701i) q^{22} +(-0.414368 + 0.832164i) q^{23} +(-4.07976 + 2.88800i) q^{25} +(-1.26214 + 2.98193i) q^{26} +(8.38543 - 0.517196i) q^{28} +(-0.0516503 + 0.235843i) q^{29} +(-2.05456 - 7.22102i) q^{31} +(1.73529 + 7.92356i) q^{32} +(3.50778 - 2.17193i) q^{34} +(-0.00438579 + 0.142351i) q^{35} +(0.645829 - 0.250195i) q^{37} +(-5.65835 + 3.03847i) q^{38} +(0.0229132 - 0.00283727i) q^{40} +(-7.17640 - 2.28298i) q^{41} +(-1.10533 - 7.12063i) q^{43} +(3.26075 + 9.25333i) q^{44} +(-0.962455 - 1.66702i) q^{46} +(4.32679 - 7.49422i) q^{47} +(-5.05502 - 4.06776i) q^{49} +(-0.318731 - 10.3452i) q^{50} +(-1.97593 - 2.98198i) q^{52} +(0.104419 + 3.38915i) q^{53} +(-0.161292 + 0.0405666i) q^{55} +(-1.09334 + 1.89372i) q^{56} +(-0.348010 - 0.358897i) q^{58} +(-3.68357 - 10.4532i) q^{59} +(0.0782765 + 0.844738i) q^{61} +(14.8140 + 4.71268i) q^{62} +(-9.42841 - 3.65259i) q^{64} +(0.0534251 - 0.0286887i) q^{65} +(7.07547 - 8.25852i) q^{67} +(-0.140362 + 4.55577i) q^{68} +(-0.240695 - 0.170384i) q^{70} +(-1.95278 - 8.91668i) q^{71} +(-10.7581 + 9.80732i) q^{73} +(-0.306806 + 1.40092i) q^{74} +(0.654675 - 7.06506i) q^{76} +(6.13979 - 14.5058i) q^{77} +(0.194927 + 0.177699i) q^{79} +(0.0577702 - 0.116018i) q^{80} +(12.1486 - 9.77596i) q^{82} +(3.75688 + 4.38505i) q^{83} +(-0.0766798 - 0.00949501i) q^{85} +(13.5550 + 6.23631i) q^{86} +(-2.47646 - 0.622855i) q^{88} +(6.33239 + 8.38544i) q^{89} +(-0.880968 + 5.67529i) q^{91} +(2.12252 + 0.130912i) q^{92} +(7.98693 + 16.0399i) q^{94} +(0.118231 + 0.0221012i) q^{95} +(-6.71789 + 3.09072i) q^{97} +(12.8030 - 4.07292i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 18 q^{4} - 8 q^{7}+O(q^{10}) \) 512 * q + 18 * q^4 - 8 * q^7	\( 512 q + 18 q^{4} - 8 q^{7} - 36 q^{10} + 4 q^{13} + 18 q^{16} + 30 q^{19} + 40 q^{22} - 42 q^{25} - 110 q^{28} - 32 q^{31} - 110 q^{34} + 48 q^{37} - 22 q^{40} - 2 q^{43} + 152 q^{46} + 76 q^{49} + 68 q^{52} + 32 q^{55} - 44 q^{58} + 20 q^{61} - 170 q^{64} - 8 q^{67} - 38 q^{70} - 4 q^{73} + 188 q^{76} + 20 q^{79} + 212 q^{82} + 60 q^{85} + 164 q^{88} - 310 q^{91} + 228 q^{94} - 100 q^{97}+O(q^{100}) \) 512 * q + 18 * q^4 - 8 * q^7 - 36 * q^10 + 4 * q^13 + 18 * q^16 + 30 * q^19 + 40 * q^22 - 42 * q^25 - 110 * q^28 - 32 * q^31 - 110 * q^34 + 48 * q^37 - 22 * q^40 - 2 * q^43 + 152 * q^46 + 76 * q^49 + 68 * q^52 + 32 * q^55 - 44 * q^58 + 20 * q^61 - 170 * q^64 - 8 * q^67 - 38 * q^70 - 4 * q^73 + 188 * q^76 + 20 * q^79 + 212 * q^82 + 60 * q^85 + 164 * q^88 - 310 * q^91 + 228 * q^94 - 100 * q^97

Introduction

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