LMFDB - Embedded newform 864.2.w.a.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37973 - 0.310377i) q^{2} +(1.80733 + 0.856477i) q^{4} +(-1.77643 - 0.735821i) q^{5} +(2.53483 - 2.53483i) q^{7} +(-2.22781 - 1.74266i) q^{8} +O(q^{10})$	\(q+(-1.37973 - 0.310377i) q^{2} +(1.80733 + 0.856477i) q^{4} +(-1.77643 - 0.735821i) q^{5} +(2.53483 - 2.53483i) q^{7} +(-2.22781 - 1.74266i) q^{8} +(2.22262 + 1.56660i) q^{10} +(-1.34921 - 0.558859i) q^{11} +(-1.41905 - 3.42590i) q^{13} +(-4.28414 + 2.71064i) q^{14} +(2.53290 + 3.09587i) q^{16} +2.46530 q^{17} +(-5.69490 + 2.35890i) q^{19} +(-2.58038 - 2.85134i) q^{20} +(1.68809 + 1.18984i) q^{22} +(0.300908 - 0.300908i) q^{23} +(-0.921266 - 0.921266i) q^{25} +(0.894594 + 5.16727i) q^{26} +(6.75230 - 2.41026i) q^{28} +(2.59237 + 6.25853i) q^{29} -1.18242i q^{31} +(-2.53383 - 5.05764i) q^{32} +(-3.40146 - 0.765174i) q^{34} +(-6.36813 + 2.63776i) q^{35} +(-0.336213 + 0.811690i) q^{37} +(8.58960 - 1.48709i) q^{38} +(2.67525 + 4.73499i) q^{40} +(-8.31394 - 8.31394i) q^{41} +(-3.84352 + 9.27907i) q^{43} +(-1.95981 - 2.16561i) q^{44} +(-0.508568 + 0.321778i) q^{46} -10.1733i q^{47} -5.85072i q^{49} +(0.985162 + 1.55704i) q^{50} +(0.369501 - 7.40712i) q^{52} +(-1.71262 + 4.13464i) q^{53} +(1.98555 + 1.98555i) q^{55} +(-10.0645 + 1.22975i) q^{56} +(-1.63427 - 9.43971i) q^{58} +(2.58441 - 6.23932i) q^{59} +(-5.00176 + 2.07179i) q^{61} +(-0.366998 + 1.63143i) q^{62} +(1.92624 + 7.76464i) q^{64} +7.13003i q^{65} +(-5.31529 - 12.8322i) q^{67} +(4.45562 + 2.11147i) q^{68} +(9.60502 - 1.66289i) q^{70} +(1.36432 + 1.36432i) q^{71} +(-0.326237 + 0.326237i) q^{73} +(0.715815 - 1.01556i) q^{74} +(-12.3129 - 0.614225i) q^{76} +(-4.83662 + 2.00339i) q^{77} -0.284754 q^{79} +(-2.22150 - 7.36336i) q^{80} +(8.89056 + 14.0515i) q^{82} +(-3.81580 - 9.21215i) q^{83} +(-4.37943 - 1.81402i) q^{85} +(8.18304 - 11.6097i) q^{86} +(2.03186 + 3.59624i) q^{88} +(-10.1828 + 10.1828i) q^{89} +(-12.2811 - 5.08701i) q^{91} +(0.801562 - 0.286120i) q^{92} +(-3.15755 + 14.0364i) q^{94} +11.8523 q^{95} -5.40113 q^{97} +(-1.81593 + 8.07244i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.37973	−	0.310377i	−0.975619	−	0.219470i
$2$	−1.37973	−	0.310377i	−0.975619	−	0.219470i
$3$		0			0
$3$		0			0
$4$	1.80733	+	0.856477i	0.903666	+	0.428238i
$5$	−1.77643	−	0.735821i	−0.794443	−	0.329069i	−0.0517148	−	0.998662i	$-0.516469\pi$
$5$	−1.77643	−	0.735821i	−0.794443	−	0.329069i	−0.742728	+	0.669593i	$0.766469\pi$
$6$		0			0
$7$	2.53483	−	2.53483i	0.958076	−	0.958076i	−0.0410803	−	0.999156i	$-0.513080\pi$
$7$	2.53483	−	2.53483i	0.958076	−	0.958076i	0.999156	+	0.0410803i	$0.0130799\pi$
$8$	−2.22781	−	1.74266i	−0.787648	−	0.616125i
$9$		0			0
$10$	2.22262	+	1.56660i	0.702853	+	0.495403i
$11$	−1.34921	−	0.558859i	−0.406801	−	0.168502i	0.169894	−	0.985462i	$-0.445658\pi$
$11$	−1.34921	−	0.558859i	−0.406801	−	0.168502i	−0.576694	+	0.816960i	$0.695658\pi$
$12$		0			0
$13$	−1.41905	−	3.42590i	−0.393574	−	0.950173i	−0.989155	−	0.146877i	$-0.953078\pi$
$13$	−1.41905	−	3.42590i	−0.393574	−	0.950173i	0.595580	−	0.803296i	$-0.296922\pi$
$14$	−4.28414	+	2.71064i	−1.14499	+	0.724448i
$15$		0			0
$16$	2.53290	+	3.09587i	0.633224	+	0.773969i
$17$	2.46530			0.597924			0.298962	−	0.954265i	$-0.403360\pi$
$17$	2.46530			0.597924			0.298962	+	0.954265i	$0.403360\pi$
$18$		0			0
$19$	−5.69490	+	2.35890i	−1.30650	+	0.541170i	−0.923861	−	0.382728i	$-0.874985\pi$
$19$	−5.69490	+	2.35890i	−1.30650	+	0.541170i	−0.382639	+	0.923898i	$0.624985\pi$
$20$	−2.58038	−	2.85134i	−0.576991	−	0.637580i
$21$		0			0
$22$	1.68809	+	1.18984i	0.359901	+	0.253675i
$23$	0.300908	−	0.300908i	0.0627437	−	0.0627437i	−0.675039	−	0.737782i	$-0.735873\pi$
$23$	0.300908	−	0.300908i	0.0627437	−	0.0627437i	0.737782	+	0.675039i	$0.235873\pi$
$24$		0			0
$25$	−0.921266	−	0.921266i	−0.184253	−	0.184253i
$26$	0.894594	+	5.16727i	0.175444	+	1.01338i
$27$		0			0
$28$	6.75230	−	2.41026i	1.27606	−	0.455496i
$29$	2.59237	+	6.25853i	0.481390	+	1.16218i	0.958949	+	0.283579i	$0.0915219\pi$
$29$	2.59237	+	6.25853i	0.481390	+	1.16218i	−0.477558	+	0.878600i	$0.658478\pi$
$30$		0			0
$31$		−	1.18242i		−	0.212370i	−0.994346	−	0.106185i	$-0.966136\pi$
$31$		−	1.18242i		−	0.212370i	0.994346	−	0.106185i	$-0.0338635\pi$
$32$	−2.53383	−	5.05764i	−0.447923	−	0.894072i
$33$		0			0
$34$	−3.40146	−	0.765174i	−0.583346	−	0.131226i
$35$	−6.36813	+	2.63776i	−1.07641	+	0.445864i
$36$		0			0
$37$	−0.336213	+	0.811690i	−0.0552731	+	0.133441i	−0.949104	−	0.314964i	$-0.898008\pi$
$37$	−0.336213	+	0.811690i	−0.0552731	+	0.133441i	0.893831	+	0.448405i	$0.148008\pi$
$38$	8.58960	−	1.48709i	1.39342	−	0.241238i
$39$		0			0
$40$	2.67525	+	4.73499i	0.422994	+	0.748667i
$41$	−8.31394	−	8.31394i	−1.29842	−	1.29842i	−0.929436	−	0.368983i	$-0.879706\pi$
$41$	−8.31394	−	8.31394i	−1.29842	−	1.29842i	−0.368983	−	0.929436i	$-0.620294\pi$
$42$		0			0
$43$	−3.84352	+	9.27907i	−0.586131	+	1.41504i	0.301044	+	0.953610i	$0.402665\pi$
$43$	−3.84352	+	9.27907i	−0.586131	+	1.41504i	−0.887174	+	0.461434i	$0.847335\pi$
$44$	−1.95981	−	2.16561i	−0.295453	−	0.326478i
$45$		0			0
$46$	−0.508568	+	0.321778i	−0.0749843	+	0.0474436i
$47$		−	10.1733i		−	1.48392i	−0.670443	−	0.741961i	$-0.733896\pi$
$47$		−	10.1733i		−	1.48392i	0.670443	−	0.741961i	$-0.266104\pi$
$48$		0			0
$49$		−	5.85072i		−	0.835818i
$50$	0.985162	+	1.55704i	0.139323	+	0.220199i
$51$		0			0
$52$	0.369501	−	7.40712i	0.0512406	−	1.02718i
$53$	−1.71262	+	4.13464i	−0.235247	+	0.567936i	−0.996780	−	0.0801902i	$-0.974447\pi$
$53$	−1.71262	+	4.13464i	−0.235247	+	0.567936i	0.761533	+	0.648127i	$0.224447\pi$
$54$		0			0
$55$	1.98555	+	1.98555i	0.267731	+	0.267731i
$56$	−10.0645	+	1.22975i	−1.34492	+	0.164332i
$57$		0			0
$58$	−1.63427	−	9.43971i	−0.214590	−	1.23950i
$59$	2.58441	−	6.23932i	0.336461	−	0.812290i	−0.661588	−	0.749867i	$-0.730117\pi$
$59$	2.58441	−	6.23932i	0.336461	−	0.812290i	0.998050	−	0.0624225i	$-0.0198826\pi$
$60$		0			0
$61$	−5.00176	+	2.07179i	−0.640409	+	0.265266i	−0.679168	−	0.733982i	$-0.737659\pi$
$61$	−5.00176	+	2.07179i	−0.640409	+	0.265266i	0.0387593	+	0.999249i	$0.487659\pi$
$62$	−0.366998	+	1.63143i	−0.0466088	+	0.207192i
$63$		0			0
$64$	1.92624	+	7.76464i	0.240780	+	0.970580i
$65$			7.13003i			0.884372i
$66$		0			0
$67$	−5.31529	−	12.8322i	−0.649366	−	1.56771i	−0.813689	−	0.581301i	$-0.802544\pi$
$67$	−5.31529	−	12.8322i	−0.649366	−	1.56771i	0.164323	−	0.986407i	$-0.447456\pi$
$68$	4.45562	+	2.11147i	0.540323	+	0.256054i
$69$		0			0
$70$	9.60502	−	1.66289i	1.14802	−	0.198753i
$71$	1.36432	+	1.36432i	0.161915	+	0.161915i	0.783415	−	0.621499i	$-0.213476\pi$
$71$	1.36432	+	1.36432i	0.161915	+	0.161915i	−0.621499	+	0.783415i	$0.713476\pi$
$72$		0			0
$73$	−0.326237	+	0.326237i	−0.0381831	+	0.0381831i	−0.725941	−	0.687757i	$-0.758595\pi$
$73$	−0.326237	+	0.326237i	−0.0381831	+	0.0381831i	0.687757	+	0.725941i	$0.258595\pi$
$74$	0.715815	−	1.01556i	0.0832118	−	0.118057i
$75$		0			0
$76$	−12.3129	−	0.614225i	−1.41239	−	0.0704565i
$77$	−4.83662	+	2.00339i	−0.551184	+	0.228308i
$78$		0			0
$79$	−0.284754			−0.0320373			−0.0160187	−	0.999872i	$-0.505099\pi$
$79$	−0.284754			−0.0320373			−0.0160187	+	0.999872i	$0.505099\pi$
$80$	−2.22150	−	7.36336i	−0.248371	−	0.823249i
$81$		0			0
$82$	8.89056	+	14.0515i	0.981799	+	1.55173i
$83$	−3.81580	−	9.21215i	−0.418838	−	1.01116i	−0.982685	−	0.185285i	$-0.940679\pi$
$83$	−3.81580	−	9.21215i	−0.418838	−	1.01116i	0.563847	−	0.825879i	$-0.309321\pi$
$84$		0			0
$85$	−4.37943	−	1.81402i	−0.475016	−	0.196758i
$86$	8.18304	−	11.6097i	0.882400	−	1.25191i
$87$		0			0
$88$	2.03186	+	3.59624i	0.216597	+	0.383361i
$89$	−10.1828	+	10.1828i	−1.07938	+	1.07938i	−0.0828120	+	0.996565i	$0.526390\pi$
$89$	−10.1828	+	10.1828i	−1.07938	+	1.07938i	−0.996565	+	0.0828120i	$0.973610\pi$
$90$		0			0
$91$	−12.2811	−	5.08701i	−1.28741	−	0.533263i
$92$	0.801562	−	0.286120i	0.0835686	−	0.0298301i
$93$		0			0
$94$	−3.15755	+	14.0364i	−0.325676	+	1.44774i
$95$	11.8523			1.21602
$96$		0			0
$97$	−5.40113			−0.548402			−0.274201	−	0.961672i	$-0.588413\pi$
$97$	−5.40113			−0.548402			−0.274201	+	0.961672i	$0.588413\pi$
$98$	−1.81593	+	8.07244i	−0.183437	+	0.815440i
$99$		0			0
$100$	−0.875991	−	2.45408i	−0.0875991	−	0.245408i
$101$	−17.8941	−	7.41196i	−1.78053	−	0.737518i	−0.992554	−	0.121806i	$-0.961131\pi$
$101$	−17.8941	−	7.41196i	−1.78053	−	0.737518i	−0.787972	−	0.615711i	$-0.788869\pi$
$102$		0			0
$103$	−2.32725	+	2.32725i	−0.229311	+	0.229311i	−0.812405	−	0.583094i	$-0.801842\pi$
$103$	−2.32725	+	2.32725i	−0.229311	+	0.229311i	0.583094	+	0.812405i	$0.301842\pi$
$104$	−2.80882	+	10.1052i	−0.275427	+	0.990893i
$105$		0			0
$106$	3.64626	−	5.17314i	0.354156	−	0.502460i
$107$	17.6706	+	7.31940i	1.70828	+	0.707593i	0.999999	+	0.00166443i	$0.000529805\pi$
$107$	17.6706	+	7.31940i	1.70828	+	0.707593i	0.708283	+	0.705929i	$0.249470\pi$
$108$		0			0
$109$	−2.19722	−	5.30457i	−0.210456	−	0.508085i	0.783038	−	0.621974i	$-0.213669\pi$
$109$	−2.19722	−	5.30457i	−0.210456	−	0.508085i	−0.993493	+	0.113889i	$0.963669\pi$
$110$	−2.12326	−	3.35580i	−0.202445	−	0.319963i
$111$		0			0
$112$	14.2680	+	1.42706i	1.34820	+	0.134844i
$113$	−3.95250			−0.371819			−0.185910	−	0.982567i	$-0.559523\pi$
$113$	−3.95250			−0.371819			−0.185910	+	0.982567i	$0.559523\pi$
$114$		0			0
$115$	−0.755957	+	0.313127i	−0.0704933	+	0.0291993i
$116$	−0.675015	+	13.5315i	−0.0626736	+	1.25637i
$117$		0			0
$118$	−5.50234	+	7.80645i	−0.506531	+	0.718642i
$119$	6.24912	−	6.24912i	0.572856	−	0.572856i
$120$		0			0
$121$	−6.27014	−	6.27014i	−0.570013	−	0.570013i
$122$	7.54413	−	1.30609i	0.683013	−	0.118248i
$123$		0			0
$124$	1.01272	−	2.13703i	0.0909449	−	0.191911i
$125$	4.63778	+	11.1966i	0.414816	+	1.00145i
$126$		0			0
$127$		−	6.50250i		−	0.577004i	−0.957479	−	0.288502i	$-0.906843\pi$
$127$		−	6.50250i		−	0.577004i	0.957479	−	0.288502i	$-0.0931571\pi$
$128$	−0.247728	−	11.3110i	−0.0218963	−	0.999760i
$129$		0			0
$130$	2.21300	−	9.83755i	0.194093	−	0.862810i
$131$	7.63076	−	3.16077i	0.666703	−	0.276157i	−0.0235531	−	0.999723i	$-0.507498\pi$
$131$	7.63076	−	3.16077i	0.666703	−	0.276157i	0.690256	+	0.723565i	$0.257498\pi$
$132$		0			0
$133$	−8.45618	+	20.4150i	−0.733244	+	1.77021i
$134$	3.35085	+	19.3548i	0.289469	+	1.67200i
$135$		0			0
$136$	−5.49221	−	4.29620i	−0.470954	−	0.368396i
$137$	0.678788	+	0.678788i	0.0579928	+	0.0579928i	0.735508	−	0.677516i	$-0.236943\pi$
$137$	0.678788	+	0.678788i	0.0579928	+	0.0579928i	−0.677516	+	0.735508i	$0.736943\pi$
$138$		0			0
$139$	4.75170	−	11.4716i	0.403034	−	0.973010i	−0.583892	−	0.811832i	$-0.698471\pi$
$139$	4.75170	−	11.4716i	0.403034	−	0.973010i	0.986925	−	0.161178i	$-0.0515293\pi$
$140$	−13.7685	−	0.686836i	−1.16365	−	0.0580482i
$141$		0			0
$142$	−1.45895	−	2.30586i	−0.122432	−	0.193503i
$143$			5.41529i			0.452849i
$144$		0			0
$145$		−	13.0253i		−	1.08170i
$146$	0.551376	−	0.348863i	0.0456322	−	0.0288721i
$147$		0			0
$148$	−1.30284	+	1.17903i	−0.107093	+	0.0969161i
$149$	−5.02178	+	12.1236i	−0.411400	+	0.993208i	0.573362	+	0.819302i	$0.305639\pi$
$149$	−5.02178	+	12.1236i	−0.411400	+	0.993208i	−0.984762	+	0.173906i	$0.944361\pi$
$150$		0			0
$151$	3.83062	+	3.83062i	0.311731	+	0.311731i	0.845580	−	0.533849i	$-0.179255\pi$
$151$	3.83062	+	3.83062i	0.311731	+	0.311731i	−0.533849	+	0.845580i	$0.679255\pi$
$152$	16.7979	+	4.66912i	1.36249	+	0.378716i
$153$		0			0
$154$	7.29506	−	1.26297i	0.587852	−	0.101773i
$155$	−0.870053	+	2.10049i	−0.0698843	+	0.168716i
$156$		0			0
$157$	−11.8338	+	4.90173i	−0.944442	+	0.391201i	−0.801139	−	0.598478i	$-0.795772\pi$
$157$	−11.8338	+	4.90173i	−0.944442	+	0.391201i	−0.143303	+	0.989679i	$0.545772\pi$
$158$	0.392885	+	0.0883812i	0.0312562	+	0.00703123i
$159$		0			0
$160$	0.779658	+	10.8490i	0.0616374	+	0.857687i
$161$		−	1.52550i		−	0.120226i
$162$		0			0
$163$	−2.14153	−	5.17012i	−0.167738	−	0.404955i	0.817550	−	0.575857i	$-0.195332\pi$
$163$	−2.14153	−	5.17012i	−0.167738	−	0.404955i	−0.985288	+	0.170903i	$0.945332\pi$
$164$	−7.90535	−	22.1467i	−0.617304	−	1.72937i
$165$		0			0
$166$	2.40554	+	13.8946i	0.186706	+	1.07843i
$167$	0.258461	+	0.258461i	0.0200003	+	0.0200003i	0.717036	−	0.697036i	$-0.245498\pi$
$167$	0.258461	+	0.258461i	0.0200003	+	0.0200003i	−0.697036	+	0.717036i	$0.745498\pi$
$168$		0			0
$169$	−0.530670	+	0.530670i	−0.0408208	+	0.0408208i
$170$	5.47942	+	3.86214i	0.420253	+	0.296213i
$171$		0			0
$172$	−14.8938	+	13.4785i	−1.13564	+	1.02772i
$173$	20.2376	−	8.38269i	1.53864	−	0.637324i	0.557420	−	0.830231i	$-0.311792\pi$
$173$	20.2376	−	8.38269i	1.53864	−	0.637324i	0.981217	+	0.192907i	$0.0617915\pi$
$174$		0			0
$175$	−4.67051			−0.353057
$176$	−1.68724	−	5.59250i	−0.127180	−	0.421551i
$177$		0			0
$178$	17.2101	−	10.8891i	1.28995	−	0.816170i
$179$	−8.48809	−	20.4921i	−0.634430	−	1.53165i	−0.834000	−	0.551765i	$-0.813955\pi$
$179$	−8.48809	−	20.4921i	−0.634430	−	1.53165i	0.199570	−	0.979884i	$-0.436045\pi$
$180$		0			0
$181$	18.2561	+	7.56193i	1.35697	+	0.562074i	0.938223	−	0.346031i	$-0.112471\pi$
$181$	18.2561	+	7.56193i	1.35697	+	0.562074i	0.418743	+	0.908105i	$0.362471\pi$
$182$	15.3658	+	10.8305i	1.13899	+	0.802810i
$183$		0			0
$184$	−1.19475	+	0.145983i	−0.0880779	+	0.0107620i
$185$	1.19452	−	1.19452i	0.0878227	−	0.0878227i
$186$		0			0
$187$	−3.32620	−	1.37776i	−0.243236	−	0.100752i
$188$	8.71315	−	18.3864i	0.635472	−	1.34097i
$189$		0			0
$190$	−16.3530	−	3.67869i	−1.18637	−	0.266880i
$191$	9.99346			0.723102			0.361551	−	0.932352i	$-0.382247\pi$
$191$	9.99346			0.723102			0.361551	+	0.932352i	$0.382247\pi$
$192$		0			0
$193$	18.6589			1.34310			0.671550	−	0.740959i	$-0.265629\pi$
$193$	18.6589			1.34310			0.671550	+	0.740959i	$0.265629\pi$
$194$	7.45212	+	1.67639i	0.535031	+	0.120358i
$195$		0			0
$196$	5.01101	−	10.5742i	0.357929	−	0.755300i
$197$	14.1714	+	5.86997i	1.00967	+	0.418218i	0.825333	−	0.564646i	$-0.190987\pi$
$197$	14.1714	+	5.86997i	1.00967	+	0.418218i	0.184334	+	0.982864i	$0.440987\pi$
$198$		0			0
$199$	19.8170	−	19.8170i	1.40479	−	1.40479i	0.620917	−	0.783876i	$-0.286760\pi$
$199$	19.8170	−	19.8170i	1.40479	−	1.40479i	0.783876	−	0.620917i	$-0.213240\pi$
$200$	0.446944	+	3.65786i	0.0316037	+	0.258650i
$201$		0			0
$202$	22.3885	+	15.7804i	1.57525	+	1.11031i
$203$	22.4355	+	9.29309i	1.57466	+	0.652247i
$204$		0			0
$205$	8.65155	+	20.8867i	0.604250	+	1.45879i
$206$	3.93332	−	2.48867i	0.274047	−	0.173394i
$207$		0			0
$208$	7.01183	−	13.0706i	0.486183	−	0.906286i
$209$	9.00189			0.622673
$210$		0			0
$211$	0.109282	−	0.0452661i	0.00752329	−	0.00311625i	−0.378919	−	0.925430i	$-0.623704\pi$
$211$	0.109282	−	0.0452661i	0.00752329	−	0.00311625i	0.386442	+	0.922314i	$0.373704\pi$
$212$	−6.63650	+	6.00584i	−0.455797	+	0.412483i
$213$		0			0
$214$	−22.1089	−	15.5834i	−1.51134	−	1.06526i
$215$	13.6555	−	13.6555i	0.931295	−	0.931295i
$216$		0			0
$217$	−2.99725	−	2.99725i	−0.203466	−	0.203466i
$218$	1.38517	+	8.00086i	0.0938153	+	0.541886i
$219$		0			0
$220$	1.88797	+	5.28912i	0.127287	+	0.356592i
$221$	−3.49839	−	8.44587i	−0.235327	−	0.568131i
$222$		0			0
$223$			21.2945i			1.42599i	0.701171	+	0.712993i	$0.252661\pi$
$223$			21.2945i			1.42599i	−0.701171	+	0.712993i	$0.747339\pi$
$224$	−19.2431	−	6.39741i	−1.28573	−	0.427445i
$225$		0			0
$226$	5.45339	+	1.22677i	0.362754	+	0.0816032i
$227$	−2.30237	+	0.953673i	−0.152814	+	0.0632975i	−0.457779	−	0.889066i	$-0.651355\pi$
$227$	−2.30237	+	0.953673i	−0.152814	+	0.0632975i	0.304966	+	0.952363i	$0.401355\pi$
$228$		0			0
$229$	1.17483	−	2.83630i	0.0776353	−	0.187428i	−0.880297	−	0.474424i	$-0.842656\pi$
$229$	1.17483	−	2.83630i	0.0776353	−	0.187428i	0.957932	+	0.286996i	$0.0926565\pi$
$230$	1.14021	−	0.197401i	0.0751830	−	0.0130162i
$231$		0			0
$232$	5.13122	−	18.4604i	0.336881	−	1.21199i
$233$	10.3239	+	10.3239i	0.676341	+	0.676341i	0.959170	−	0.282829i	$-0.0912730\pi$
$233$	10.3239	+	10.3239i	0.676341	+	0.676341i	−0.282829	+	0.959170i	$0.591273\pi$
$234$		0			0
$235$	−7.48569	+	18.0721i	−0.488313	+	1.17889i
$236$	10.0147	−	9.06303i	0.651902	−	0.589953i
$237$		0			0
$238$	−10.5617	+	6.68254i	−0.684614	+	0.433165i
$239$			12.7213i			0.822873i	0.911438	+	0.411437i	$0.134973\pi$
$239$			12.7213i			0.822873i	−0.911438	+	0.411437i	$0.865027\pi$
$240$		0			0
$241$		−	17.1173i		−	1.10262i	−0.834300	−	0.551311i	$-0.814128\pi$
$241$		−	17.1173i		−	1.10262i	0.834300	−	0.551311i	$-0.185872\pi$
$242$	6.70502	+	10.5972i	0.431015	+	0.681216i
$243$		0			0
$244$	−10.8143	−	0.539466i	−0.692313	−	0.0345358i
$245$	−4.30508	+	10.3934i	−0.275042	+	0.664010i
$246$		0			0
$247$	16.1627	+	16.1627i	1.02841	+	1.02841i
$248$	−2.06057	+	2.63421i	−0.130846	+	0.167273i
$249$		0			0
$250$	−2.92373	−	16.8878i	−0.184913	−	1.06808i
$251$	3.56293	−	8.60168i	0.224890	−	0.542933i	−0.770651	−	0.637257i	$-0.780069\pi$
$251$	3.56293	−	8.60168i	0.224890	−	0.542933i	0.995542	+	0.0943239i	$0.0300689\pi$
$252$		0			0
$253$	−0.574152	+	0.237822i	−0.0360966	+	0.0149517i
$254$	−2.01823	+	8.97172i	−0.126635	+	0.562936i
$255$		0			0
$256$	−3.16888	+	15.6831i	−0.198055	+	0.980191i
$257$			30.8853i			1.92657i	0.268476	+	0.963286i	$0.413480\pi$
$257$			30.8853i			1.92657i	−0.268476	+	0.963286i	$0.586520\pi$
$258$		0			0
$259$	1.20525	+	2.90974i	0.0748908	+	0.180802i
$260$	−6.10671	+	12.8863i	−0.378722	+	0.799176i
$261$		0			0
$262$	−11.5095	+	1.99260i	−0.711057	+	0.123103i
$263$	−12.2047	−	12.2047i	−0.752576	−	0.752576i	0.222383	−	0.974959i	$-0.428616\pi$
$263$	−12.2047	−	12.2047i	−0.752576	−	0.752576i	−0.974959	+	0.222383i	$0.928616\pi$
$264$		0			0
$265$	6.08471	−	6.08471i	0.373781	−	0.373781i
$266$	18.0036	−	25.5427i	1.10387	−	1.56612i
$267$		0			0
$268$	1.38403	−	27.7445i	0.0845428	−	1.69477i
$269$	−7.95018	+	3.29307i	−0.484731	+	0.200782i	−0.611646	−	0.791131i	$-0.709492\pi$
$269$	−7.95018	+	3.29307i	−0.484731	+	0.200782i	0.126915	+	0.991914i	$0.459492\pi$
$270$		0			0
$271$	27.3953			1.66415			0.832073	−	0.554666i	$-0.187154\pi$
$271$	27.3953			1.66415			0.832073	+	0.554666i	$0.187154\pi$
$272$	6.24435	+	7.63227i	0.378620	+	0.462774i
$273$		0			0
$274$	−0.725866	−	1.14723i	−0.0438512	−	0.0693065i
$275$	0.728119	+	1.75784i	0.0439073	+	0.106001i
$276$		0			0
$277$	19.3675	+	8.02230i	1.16368	+	0.482013i	0.879099	−	0.476638i	$-0.158145\pi$
$277$	19.3675	+	8.02230i	1.16368	+	0.482013i	0.284583	+	0.958651i	$0.408145\pi$
$278$	−10.1166	+	14.3530i	−0.606754	+	0.860833i
$279$		0			0
$280$	18.7837	+	5.22108i	1.12254	+	0.312019i
$281$	−1.32581	+	1.32581i	−0.0790911	+	0.0790911i	−0.745546	−	0.666455i	$-0.767811\pi$
$281$	−1.32581	+	1.32581i	−0.0790911	+	0.0790911i	0.666455	+	0.745546i	$0.267811\pi$
$282$		0			0
$283$	9.84238	+	4.07685i	0.585068	+	0.242343i	0.655527	−	0.755171i	$-0.272446\pi$
$283$	9.84238	+	4.07685i	0.585068	+	0.242343i	−0.0704589	+	0.997515i	$0.522446\pi$
$284$	1.29727	+	3.63429i	0.0769790	+	0.215656i
$285$		0			0
$286$	1.68078	−	7.47166i	0.0993868	−	0.441808i
$287$	−42.1488			−2.48797
$288$		0			0
$289$	−10.9223			−0.642487
$290$	−4.04277	+	17.9715i	−0.237400	+	1.05532i
$291$		0			0
$292$	−0.869032	+	0.310204i	−0.0508562	+	0.0181533i
$293$	−9.16465	−	3.79612i	−0.535405	−	0.221772i	0.0985639	−	0.995131i	$-0.468575\pi$
$293$	−9.16465	−	3.79612i	−0.535405	−	0.221772i	−0.633968	+	0.773359i	$0.718575\pi$
$294$		0			0
$295$	−9.18204	+	9.18204i	−0.534599	+	0.534599i
$296$	2.16352	−	1.22238i	0.125752	−	0.0710495i
$297$		0			0
$298$	10.6916	−	15.1688i	0.619349	−	0.878703i
$299$	−1.45788	−	0.603876i	−0.0843117	−	0.0349230i
$300$		0			0
$301$	13.7782	+	33.2635i	0.794162	+	1.91728i
$302$	−4.09630	−	6.47417i	−0.235715	−	0.372547i
$303$		0			0
$304$	−21.7275	−	11.6558i	−1.24616	−	0.668508i
$305$	10.4097			0.596060
$306$		0			0
$307$	−7.74141	+	3.20660i	−0.441825	+	0.183010i	−0.592495	−	0.805574i	$-0.701857\pi$
$307$	−7.74141	+	3.20660i	−0.441825	+	0.183010i	0.150670	+	0.988584i	$0.451857\pi$
$308$	−10.4572	−	0.521655i	−0.595856	−	0.0297241i
$309$		0			0
$310$	1.85239	−	2.62808i	0.105209	−	0.149265i
$311$	18.0906	−	18.0906i	1.02583	−	1.02583i	0.0261675	−	0.999658i	$-0.491670\pi$
$311$	18.0906	−	18.0906i	1.02583	−	1.02583i	0.999658	−	0.0261675i	$-0.00833032\pi$
$312$		0			0
$313$	−7.79907	−	7.79907i	−0.440829	−	0.440829i	0.451461	−	0.892291i	$-0.350903\pi$
$313$	−7.79907	−	7.79907i	−0.440829	−	0.440829i	−0.892291	+	0.451461i	$0.850903\pi$
$314$	17.8489	−	3.09013i	1.00727	−	0.174386i
$315$		0			0
$316$	−0.514645	−	0.243885i	−0.0289510	−	0.0137196i
$317$	−5.12469	−	12.3721i	−0.287832	−	0.694887i	0.712143	−	0.702034i	$-0.247725\pi$
$317$	−5.12469	−	12.3721i	−0.287832	−	0.694887i	−0.999974	+	0.00714775i	$0.997725\pi$
$318$		0			0
$319$		−	9.89281i		−	0.553891i
$320$	2.29156	−	15.2107i	0.128102	−	0.850304i
$321$		0			0
$322$	−0.473481	+	2.10479i	−0.0263861	+	0.117295i
$323$	−14.0396	+	5.81541i	−0.781187	+	0.323578i
$324$		0			0
$325$	−1.84884	+	4.46349i	−0.102555	+	0.247590i
$326$	1.35006	+	7.79807i	0.0747728	+	0.431895i
$327$		0			0
$328$	4.03343	+	33.0102i	0.222709	+	1.82269i
$329$	−25.7875	−	25.7875i	−1.42171	−	1.42171i
$330$		0			0
$331$	4.07715	−	9.84312i	0.224101	−	0.541027i	−0.771339	−	0.636425i	$-0.780412\pi$
$331$	4.07715	−	9.84312i	0.224101	−	0.541027i	0.995439	+	0.0953982i	$0.0304124\pi$
$332$	0.993579	−	19.9175i	0.0545297	−	1.09312i
$333$		0			0
$334$	−0.276387	−	0.436827i	−0.0151232	−	0.0239021i
$335$			26.7067i			1.45914i
$336$		0			0
$337$		−	25.3029i		−	1.37834i	−0.724600	−	0.689169i	$-0.757976\pi$
$337$		−	25.3029i		−	1.37834i	0.724600	−	0.689169i	$-0.242024\pi$
$338$	0.896892	−	0.567476i	0.0487845	−	0.0308666i
$339$		0			0
$340$	−6.36142	−	7.02942i	−0.344997	−	0.381224i
$341$	−0.660809	+	1.59533i	−0.0357848	+	0.0863922i
$342$		0			0
$343$	2.91322	+	2.91322i	0.157299	+	0.157299i
$344$	24.7329	−	13.9740i	1.33351	−	0.753428i
$345$		0			0
$346$	−30.5243	+	5.28459i	−1.64100	+	0.284101i
$347$	5.72321	−	13.8170i	0.307238	−	0.741738i	−0.692555	−	0.721365i	$-0.743515\pi$
$347$	5.72321	−	13.8170i	0.307238	−	0.741738i	0.999792	−	0.0203722i	$-0.00648513\pi$
$348$		0			0
$349$	2.74117	−	1.13543i	0.146731	−	0.0607781i	−0.308109	−	0.951351i	$-0.599696\pi$
$349$	2.74117	−	1.13543i	0.146731	−	0.0607781i	0.454841	+	0.890573i	$0.349696\pi$
$350$	6.44406	+	1.44962i	0.344449	+	0.0774854i
$351$		0			0
$352$	0.592154	+	8.23985i	0.0315619	+	0.439185i
$353$			18.2490i			0.971297i	0.874154	+	0.485649i	$0.161417\pi$
$353$			18.2490i			0.971297i	−0.874154	+	0.485649i	$0.838583\pi$
$354$		0			0
$355$	−1.41972	−	3.42752i	−0.0753512	−	0.181914i
$356$	−27.1251	+	9.68239i	−1.43763	+	0.513166i
$357$		0			0
$358$	5.35103	+	30.9081i	0.282811	+	1.63354i
$359$	−14.6191	−	14.6191i	−0.771568	−	0.771568i	0.206813	−	0.978381i	$-0.433691\pi$
$359$	−14.6191	−	14.6191i	−0.771568	−	0.771568i	−0.978381	+	0.206813i	$0.933691\pi$
$360$		0			0
$361$	13.4324	−	13.4324i	0.706970	−	0.706970i
$362$	−22.8415	−	16.0997i	−1.20052	−	0.846184i
$363$		0			0
$364$	−17.8392	−	19.7124i	−0.935026	−	1.03321i
$365$	0.819588	−	0.339484i	0.0428992	−	0.0177694i
$366$		0			0
$367$	−2.08043			−0.108598			−0.0542988	−	0.998525i	$-0.517292\pi$
$367$	−2.08043			−0.108598			−0.0542988	+	0.998525i	$0.517292\pi$
$368$	1.69374	+	0.169405i	0.0882924	+	0.00883084i
$369$		0			0
$370$	−2.01887	+	1.27737i	−0.104956	+	0.0664070i
$371$	6.13940	+	14.8218i	0.318742	+	0.769510i
$372$		0			0
$373$	−5.91341	−	2.44941i	−0.306185	−	0.126826i	0.224301	−	0.974520i	$-0.427990\pi$
$373$	−5.91341	−	2.44941i	−0.306185	−	0.126826i	−0.530485	+	0.847694i	$0.677990\pi$
$374$	4.16165	+	2.93332i	0.215194	+	0.151678i
$375$		0			0
$376$	−17.7286	+	22.6640i	−0.914281	+	1.16881i
$377$	17.7624	−	17.7624i	0.914808	−	0.914808i
$378$		0			0
$379$	−31.5285	−	13.0595i	−1.61951	−	0.670822i	−0.625510	−	0.780216i	$-0.715109\pi$
$379$	−31.5285	−	13.0595i	−1.61951	−	0.670822i	−0.993998	+	0.109394i	$0.965109\pi$
$380$	21.4211	+	10.1512i	1.09888	+	0.520747i
$381$		0			0
$382$	−13.7883	−	3.10175i	−0.705472	−	0.158699i
$383$	−21.6081			−1.10412			−0.552061	−	0.833804i	$-0.686159\pi$
$383$	−21.6081			−1.10412			−0.552061	+	0.833804i	$0.686159\pi$
$384$		0			0
$385$	10.0660			0.513013
$386$	−25.7444	−	5.79131i	−1.31035	−	0.294770i
$387$		0			0
$388$	−9.76163	−	4.62594i	−0.495572	−	0.234847i
$389$	−23.5877	−	9.77033i	−1.19594	−	0.495375i	−0.306256	−	0.951949i	$-0.599076\pi$
$389$	−23.5877	−	9.77033i	−1.19594	−	0.495375i	−0.889685	+	0.456574i	$0.849076\pi$
$390$		0			0
$391$	0.741830	−	0.741830i	0.0375159	−	0.0375159i
$392$	−10.1958	+	13.0343i	−0.514968	+	0.658330i
$393$		0			0
$394$	−17.7308	−	12.4975i	−0.893265	−	0.629613i
$395$	0.505845	+	0.209528i	0.0254518	+	0.0105425i
$396$		0			0
$397$	−9.27785	−	22.3987i	−0.465642	−	1.12416i	−0.966047	−	0.258367i	$-0.916816\pi$
$397$	−9.27785	−	22.3987i	−0.465642	−	1.12416i	0.500405	−	0.865792i	$-0.333184\pi$
$398$	−33.4930	+	21.1915i	−1.67885	+	1.06223i
$399$		0			0
$400$	0.518654	−	5.18560i	0.0259327	−	0.259280i
$401$	−26.8222			−1.33944			−0.669718	−	0.742616i	$-0.733585\pi$
$401$	−26.8222			−1.33944			−0.669718	+	0.742616i	$0.733585\pi$
$402$		0			0
$403$	−4.05087	+	1.67792i	−0.201788	+	0.0835833i
$404$	−25.9923	−	28.7217i	−1.29317	−	1.42896i
$405$		0			0
$406$	−28.0707	−	19.7855i	−1.39312	−	0.981936i
$407$	0.907241	−	0.907241i	0.0449703	−	0.0449703i
$408$		0			0
$409$	−3.69700	−	3.69700i	−0.182805	−	0.182805i	0.609772	−	0.792577i	$-0.291261\pi$
$409$	−3.69700	−	3.69700i	−0.182805	−	0.182805i	−0.792577	+	0.609772i	$0.791261\pi$
$410$	−5.45408	−	31.5033i	−0.269358	−	1.55584i
$411$		0			0
$412$	−6.19936	+	2.21288i	−0.305421	+	0.109021i
$413$	−9.26457	−	22.3666i	−0.455879	−	1.10059i
$414$		0			0
$415$			19.1725i			0.941139i
$416$	−13.7313	+	15.8577i	−0.673232	+	0.777488i
$417$		0			0
$418$	−12.4202	−	2.79398i	−0.607492	−	0.136658i
$419$	5.39550	−	2.23489i	0.263588	−	0.109182i	−0.246976	−	0.969022i	$-0.579437\pi$
$419$	5.39550	−	2.23489i	0.263588	−	0.109182i	0.510563	+	0.859840i	$0.329437\pi$
$420$		0			0
$421$	−6.19635	+	14.9593i	−0.301992	+	0.729072i	0.697925	+	0.716171i	$0.254107\pi$
$421$	−6.19635	+	14.9593i	−0.301992	+	0.729072i	−0.999917	+	0.0129014i	$0.995893\pi$
$422$	−0.164830	+	0.0285365i	−0.00802379	+	0.00138914i
$423$		0			0
$424$	11.0207	−	6.22664i	0.535212	−	0.302393i
$425$	−2.27120	−	2.27120i	−0.110169	−	0.110169i
$426$		0			0
$427$	−7.42695	+	17.9302i	−0.359415	+	0.867705i
$428$	25.6677	+	28.3630i	1.24070	+	1.37098i
$429$		0			0
$430$	−23.0793	+	14.6026i	−1.11298	+	0.704198i
$431$			26.6626i			1.28429i	0.766582	+	0.642147i	$0.221956\pi$
$431$			26.6626i			1.28429i	−0.766582	+	0.642147i	$0.778044\pi$
$432$		0			0
$433$			40.8027i			1.96085i	0.196892	+	0.980425i	$0.436915\pi$
$433$			40.8027i			1.96085i	−0.196892	+	0.980425i	$0.563085\pi$
$434$	3.20512	+	5.06568i	0.153851	+	0.243160i
$435$		0			0
$436$	0.572125	−	11.4690i	0.0273998	−	0.549264i
$437$	−1.00383	+	2.42346i	−0.0480196	+	0.115930i
$438$		0			0
$439$	12.8695	+	12.8695i	0.614229	+	0.614229i	0.944045	−	0.329816i	$-0.106987\pi$
$439$	12.8695	+	12.8695i	0.614229	+	0.614229i	−0.329816	+	0.944045i	$0.606987\pi$
$440$	−0.963271	−	7.88356i	−0.0459221	−	0.375834i
$441$		0			0
$442$	2.20545	+	12.7389i	0.104902	+	0.605927i
$443$	−5.51165	+	13.3063i	−0.261866	+	0.632201i	−0.999054	−	0.0434868i	$-0.986153\pi$
$443$	−5.51165	+	13.3063i	−0.261866	+	0.632201i	0.737188	+	0.675688i	$0.236153\pi$
$444$		0			0
$445$	25.5818	−	10.5963i	1.21269	−	0.502314i
$446$	6.60934	−	29.3808i	0.312961	−	1.39122i
$447$		0			0
$448$	24.5647	+	14.7993i	1.16057	+	0.699203i
$449$			21.2509i			1.00289i	0.865188	+	0.501447i	$0.167199\pi$
$449$			21.2509i			1.00289i	−0.865188	+	0.501447i	$0.832801\pi$
$450$		0			0
$451$	6.57089	+	15.8635i	0.309411	+	0.746984i
$452$	−7.14347	−	3.38522i	−0.336001	−	0.159227i
$453$		0			0
$454$	3.47266	−	0.601211i	0.162980	−	0.0282162i
$455$	18.0734	+	18.0734i	0.847295	+	0.847295i
$456$		0			0
$457$	19.3016	−	19.3016i	0.902892	−	0.902892i	−0.0927935	−	0.995685i	$-0.529580\pi$
$457$	19.3016	−	19.3016i	0.902892	−	0.902892i	0.995685	+	0.0927935i	$0.0295797\pi$
$458$	−2.50128	+	3.54870i	−0.116877	+	0.165820i
$459$		0			0
$460$	−1.63445	−	0.0815339i	−0.0762066	−	0.00380154i
$461$	27.3491	−	11.3284i	1.27377	−	0.527614i	0.359663	−	0.933082i	$-0.382892\pi$
$461$	27.3491	−	11.3284i	1.27377	−	0.527614i	0.914109	+	0.405468i	$0.132892\pi$
$462$		0			0
$463$	38.8911			1.80742			0.903711	−	0.428144i	$-0.140832\pi$
$463$	38.8911			1.80742			0.903711	+	0.428144i	$0.140832\pi$
$464$	−12.8094	+	23.8778i	−0.594662	+	1.10850i
$465$		0			0
$466$	−11.0399	−	17.4485i	−0.511415	−	0.808288i
$467$	−7.15356	−	17.2702i	−0.331027	−	0.799170i	−0.998511	−	0.0545463i	$-0.982629\pi$
$467$	−7.15356	−	17.2702i	−0.331027	−	0.799170i	0.667484	−	0.744624i	$-0.267371\pi$
$468$		0			0
$469$	−46.0009	−	19.0542i	−2.12412	−	0.879841i
$470$	15.9374	−	22.6113i	0.735139	−	1.04298i
$471$		0			0
$472$	−16.6306	+	9.39623i	−0.765485	+	0.432496i
$473$	10.3714	−	10.3714i	0.476877	−	0.476877i
$474$		0			0
$475$	7.41970	+	3.07334i	0.340439	+	0.141015i
$476$	16.6465	−	5.94201i	0.762989	−	0.272352i
$477$		0			0
$478$	3.94841	−	17.5520i	0.180596	−	0.802811i
$479$	14.1110			0.644746			0.322373	−	0.946613i	$-0.395519\pi$
$479$	14.1110			0.644746			0.322373	+	0.946613i	$0.395519\pi$
$480$		0			0
$481$	3.25787			0.148546
$482$	−5.31282	+	23.6173i	−0.241992	+	1.07574i
$483$		0			0
$484$	−5.96200	−	16.7025i	−0.271000	−	0.759203i
$485$	9.59472	+	3.97426i	0.435674	+	0.180462i
$486$		0			0
$487$	13.4305	−	13.4305i	0.608594	−	0.608594i	−0.333984	−	0.942579i	$-0.608393\pi$
$487$	13.4305	−	13.4305i	0.608594	−	0.608594i	0.942579	+	0.333984i	$0.108393\pi$
$488$	14.7534	+	4.10083i	0.667854	+	0.185636i
$489$		0			0
$490$	9.16575	−	13.0039i	0.414066	−	0.587457i
$491$	6.20425	+	2.56989i	0.279994	+	0.115977i	0.518261	−	0.855222i	$-0.326579\pi$
$491$	6.20425	+	2.56989i	0.279994	+	0.115977i	−0.238267	+	0.971200i	$0.576579\pi$
$492$		0			0
$493$	6.39097	+	15.4292i	0.287835	+	0.694894i
$494$	−17.2837	−	27.3168i	−0.777631	−	1.22904i
$495$		0			0
$496$	3.66064	−	2.99496i	0.164368	−	0.134478i
$497$	6.91665			0.310254
$498$		0			0
$499$	−27.7903	+	11.5111i	−1.24406	+	0.515308i	−0.904982	−	0.425449i	$-0.860116\pi$
$499$	−27.7903	+	11.5111i	−1.24406	+	0.515308i	−0.339081	+	0.940757i	$0.610116\pi$
$500$	−1.20761	+	24.2081i	−0.0540061	+	1.08262i
$501$		0			0
$502$	−7.58567	+	10.7622i	−0.338565	+	0.480339i
$503$	19.3465	−	19.3465i	0.862617	−	0.862617i	−0.129024	−	0.991641i	$-0.541185\pi$
$503$	19.3465	−	19.3465i	0.862617	−	0.862617i	0.991641	+	0.129024i	$0.0411846\pi$
$504$		0			0
$505$	26.3337	+	26.3337i	1.17183	+	1.17183i
$506$	0.865992	−	0.149927i	0.0384980	−	0.00666505i
$507$		0			0
$508$	5.56924	−	11.7522i	0.247095	−	0.521418i
$509$	−0.598618	−	1.44519i	−0.0265333	−	0.0640570i	0.910058	−	0.414482i	$-0.136037\pi$
$509$	−0.598618	−	1.44519i	−0.0265333	−	0.0640570i	−0.936591	+	0.350425i	$0.886037\pi$
$510$		0			0
$511$			1.65391i			0.0731646i
$512$	9.23988	−	20.6549i	0.408349	−	0.912826i
$513$		0			0
$514$	9.58610	−	42.6135i	0.422825	−	1.87960i
$515$	5.84665	−	2.42176i	0.257634	−	0.106715i
$516$		0			0
$517$	−5.68542	+	13.7258i	−0.250044	+	0.603660i
$518$	−0.759812	−	4.38875i	−0.0333842	−	0.192831i
$519$		0			0
$520$	12.4253	−	15.8843i	0.544884	−	0.696574i
$521$	−26.3086	−	26.3086i	−1.15260	−	1.15260i	−0.986029	−	0.166572i	$-0.946730\pi$
$521$	−26.3086	−	26.3086i	−1.15260	−	1.15260i	−0.166572	−	0.986029i	$-0.553270\pi$
$522$		0			0
$523$	9.75858	−	23.5593i	0.426713	−	1.03018i	−0.553610	−	0.832776i	$-0.686750\pi$
$523$	9.75858	−	23.5593i	0.426713	−	1.03018i	0.980323	−	0.197400i	$-0.0632497\pi$
$524$	16.4984	+	0.823018i	0.720738	+	0.0359537i
$525$		0			0
$526$	13.0512	+	20.6274i	0.569060	+	0.899396i
$527$		−	2.91503i		−	0.126981i
$528$		0			0
$529$			22.8189i			0.992126i
$530$	−10.2838	+	6.50672i	−0.446701	+	0.282634i
$531$		0			0
$532$	−32.7681	+	29.6542i	−1.42068	+	1.28567i
$533$	−16.6848	+	40.2806i	−0.722698	+	1.74475i
$534$		0			0
$535$	−26.0048	−	26.0048i	−1.12429	−	1.12429i
$536$	−10.5209	+	37.8505i	−0.454432	+	1.63489i
$537$		0			0
$538$	11.9912	−	2.07601i	0.516979	−	0.0895030i
$539$	−3.26973	+	7.89383i	−0.140837	+	0.340011i
$540$		0			0
$541$	−19.5295	+	8.08940i	−0.839641	+	0.347791i	−0.760712	−	0.649090i	$-0.775150\pi$
$541$	−19.5295	+	8.08940i	−0.839641	+	0.347791i	−0.0789289	+	0.996880i	$0.525150\pi$
$542$	−37.7982	−	8.50289i	−1.62357	−	0.365230i
$543$		0			0
$544$	−6.24666	−	12.4686i	−0.267823	−	0.534587i
$545$			11.0399i			0.472899i
$546$		0			0
$547$	4.17842	+	10.0876i	0.178656	+	0.431315i	0.987685	−	0.156454i	$-0.0500064\pi$
$547$	4.17842	+	10.0876i	0.178656	+	0.431315i	−0.809029	+	0.587769i	$0.800006\pi$
$548$	0.645429	+	1.80816i	0.0275714	+	0.0772408i
$549$		0			0
$550$	−0.459019	−	2.65134i	−0.0195726	−	0.113053i
$551$	−29.5265	−	29.5265i	−1.25787	−	1.25787i
$552$		0			0
$553$	−0.721803	+	0.721803i	−0.0306942	+	0.0306942i
$554$	−24.2321	−	17.0799i	−1.02952	−	0.725655i
$555$		0			0
$556$	18.4131	−	16.6633i	0.780888	−	0.706681i
$557$	38.3158	−	15.8709i	1.62349	−	0.672473i	0.629013	−	0.777394i	$-0.283459\pi$
$557$	38.3158	−	15.8709i	1.62349	−	0.672473i	0.994481	+	0.104921i	$0.0334591\pi$
$558$		0			0
$559$	37.2433			1.57522
$560$	−24.2960	−	13.0337i	−1.02669	−	0.550776i
$561$		0			0
$562$	2.24077	−	1.41776i	0.0945210	−	0.0598047i
$563$	8.24322	+	19.9009i	0.347410	+	0.838723i	0.996924	+	0.0783730i	$0.0249725\pi$
$563$	8.24322	+	19.9009i	0.347410	+	0.838723i	−0.649514	+	0.760350i	$0.725027\pi$
$564$		0			0
$565$	7.02133	+	2.90833i	0.295389	+	0.122354i
$566$	−12.3145	−	8.67981i	−0.517617	−	0.364840i
$567$		0			0
$568$	−0.661889	−	5.41700i	−0.0277722	−	0.227292i
$569$	9.06238	−	9.06238i	0.379915	−	0.379915i	−0.491157	−	0.871071i	$-0.663426\pi$
$569$	9.06238	−	9.06238i	0.379915	−	0.379915i	0.871071	+	0.491157i	$0.163426\pi$
$570$		0			0
$571$	−5.65894	−	2.34401i	−0.236819	−	0.0980938i	0.261118	−	0.965307i	$-0.415909\pi$
$571$	−5.65894	−	2.34401i	−0.236819	−	0.0980938i	−0.497937	+	0.867213i	$0.665909\pi$
$572$	−4.63807	+	9.78722i	−0.193927	+	0.409224i
$573$		0			0
$574$	58.1542	+	13.0820i	2.42731	+	0.546034i
$575$	−0.554433			−0.0231215
$576$		0			0
$577$	30.3808			1.26477			0.632384	−	0.774655i	$-0.282076\pi$
$577$	30.3808			1.26477			0.632384	+	0.774655i	$0.282076\pi$
$578$	15.0698	+	3.39003i	0.626823	+	0.141007i
$579$		0			0
$580$	11.1559	−	23.5411i	0.463224	−	0.977492i
$581$	−33.0236	−	13.6788i	−1.37005	−	0.567493i
$582$		0			0
$583$	4.62136	−	4.62136i	0.191397	−	0.191397i
$584$	1.29531	−	0.158271i	0.0536004	−	0.00654929i
$585$		0			0
$586$	11.4665	+	8.08214i	0.473679	+	0.333870i
$587$	−19.7971	−	8.20022i	−0.817113	−	0.338459i	−0.0653251	−	0.997864i	$-0.520808\pi$
$587$	−19.7971	−	8.20022i	−0.817113	−	0.338459i	−0.751788	+	0.659405i	$0.770808\pi$
$588$		0			0
$589$	2.78923	+	6.73379i	0.114928	+	0.277461i
$590$	15.5187	−	9.81887i	0.638894	−	0.404237i
$591$		0			0
$592$	−3.36448	+	1.01505i	−0.138279	+	0.0417184i
$593$	6.72563			0.276189			0.138094	−	0.990419i	$-0.455902\pi$
$593$	6.72563			0.276189			0.138094	+	0.990419i	$0.455902\pi$
$594$		0			0
$595$	−15.6994	+	6.50289i	−0.643611	+	0.266592i
$596$	−19.4596	+	17.6104i	−0.797098	+	0.721351i
$597$		0			0
$598$	1.82406	+	1.28568i	0.0745915	+	0.0525755i
$599$	−1.29750	+	1.29750i	−0.0530145	+	0.0530145i	−0.733117	−	0.680103i	$-0.761935\pi$
$599$	−1.29750	+	1.29750i	−0.0530145	+	0.0530145i	0.680103	+	0.733117i	$0.261935\pi$
$600$		0			0
$601$	−0.182275	−	0.182275i	−0.00743515	−	0.00743515i	0.703379	−	0.710815i	$-0.251674\pi$
$601$	−0.182275	−	0.182275i	−0.00743515	−	0.00743515i	−0.710815	+	0.703379i	$0.751674\pi$
$602$	−8.68601	−	50.1712i	−0.354015	−	2.04483i
$603$		0			0
$604$	3.64236	+	10.2040i	0.148206	+	0.415196i
$605$	6.52476	+	15.7522i	0.265269	+	0.640417i
$606$		0			0
$607$		−	29.4713i		−	1.19620i	−0.801420	−	0.598102i	$-0.795922\pi$
$607$		−	29.4713i		−	1.19620i	0.801420	−	0.598102i	$-0.204078\pi$
$608$	26.3604	+	22.8257i	1.06906	+	0.925703i
$609$		0			0
$610$	−14.3627	−	3.23095i	−0.581527	−	0.130817i
$611$	−34.8525	+	14.4364i	−1.40998	+	0.584034i
$612$		0			0
$613$	9.91046	−	23.9260i	0.400280	−	0.966361i	−0.587318	−	0.809356i	$-0.699816\pi$
$613$	9.91046	−	23.9260i	0.400280	−	0.966361i	0.987598	−	0.157004i	$-0.0501837\pi$
$614$	11.6763	−	2.02149i	0.471219	−	0.0815807i
$615$		0			0
$616$	14.2663	+	3.96543i	0.574805	+	0.159772i
$617$	−7.14566	−	7.14566i	−0.287674	−	0.287674i	0.548486	−	0.836160i	$-0.315204\pi$
$617$	−7.14566	−	7.14566i	−0.287674	−	0.287674i	−0.836160	+	0.548486i	$0.815204\pi$
$618$		0			0
$619$	0.670855	−	1.61959i	0.0269639	−	0.0650967i	−0.909824	−	0.414994i	$-0.863784\pi$
$619$	0.670855	−	1.61959i	0.0269639	−	0.0650967i	0.936788	+	0.349898i	$0.113784\pi$
$620$	−3.37150	+	3.05111i	−0.135403	+	0.122535i
$621$		0			0
$622$	−30.5752	+	19.3453i	−1.22595	+	0.775677i
$623$			51.6234i			2.06825i
$624$		0			0
$625$		−	16.7882i		−	0.671528i
$626$	8.33999	+	13.1813i	0.333333	+	0.526831i
$627$		0			0
$628$	−25.5859	−	1.27634i	−1.02099	−	0.0509316i
$629$	−0.828867	+	2.00106i	−0.0330491	+	0.0797876i
$630$		0			0
$631$	28.3494	+	28.3494i	1.12857	+	1.12857i	0.990410	+	0.138163i	$0.0441198\pi$
$631$	28.3494	+	28.3494i	1.12857	+	1.12857i	0.138163	+	0.990410i	$0.455880\pi$
$632$	0.634377	+	0.496231i	0.0252341	+	0.0197390i
$633$		0			0
$634$	3.23069	+	18.6608i	0.128307	+	0.741115i
$635$	−4.78468	+	11.5512i	−0.189874	+	0.458397i
$636$		0			0
$637$	−20.0440	+	8.30249i	−0.794171	+	0.328956i
$638$	−3.07050	+	13.6494i	−0.121562	+	0.540387i
$639$		0			0
$640$	−7.88280	+	20.2755i	−0.311595	+	0.801458i
$641$		−	28.2618i		−	1.11627i	−0.829749	−	0.558137i	$-0.811516\pi$
$641$		−	28.2618i		−	1.11627i	0.829749	−	0.558137i	$-0.188484\pi$
$642$		0			0
$643$	−0.417300	−	1.00745i	−0.0164567	−	0.0397300i	0.915438	−	0.402460i	$-0.131845\pi$
$643$	−0.417300	−	1.00745i	−0.0164567	−	0.0397300i	−0.931894	+	0.362730i	$0.881845\pi$
$644$	1.30656	−	2.75709i	0.0514855	−	0.108644i
$645$		0			0
$646$	21.1760	−	3.66613i	0.833157	−	0.144242i
$647$	−4.57952	−	4.57952i	−0.180039	−	0.180039i	0.611334	−	0.791373i	$-0.290633\pi$
$647$	−4.57952	−	4.57952i	−0.180039	−	0.180039i	−0.791373	+	0.611334i	$0.790633\pi$
$648$		0			0
$649$	−6.97380	+	6.97380i	−0.273746	+	0.273746i
$650$	3.93627	−	5.58459i	0.154393	−	0.219046i
$651$		0			0
$652$	0.557625	−	11.1783i	0.0218383	−	0.437776i
$653$	12.3794	−	5.12770i	0.484442	−	0.200663i	−0.127076	−	0.991893i	$-0.540559\pi$
$653$	12.3794	−	5.12770i	0.484442	−	0.200663i	0.611518	+	0.791230i	$0.290559\pi$
$654$		0			0
$655$	−15.8813			−0.620533
$656$	4.68057	−	46.7972i	0.182746	−	1.82713i
$657$		0			0
$658$	27.5760	+	43.5837i	1.07502	+	1.69907i
$659$	−13.7055	−	33.0880i	−0.533890	−	1.28892i	−0.928928	−	0.370259i	$-0.879269\pi$
$659$	−13.7055	−	33.0880i	−0.533890	−	1.28892i	0.395039	−	0.918664i	$-0.370731\pi$
$660$		0			0
$661$	20.3845	+	8.44353i	0.792865	+	0.328415i	0.742095	−	0.670295i	$-0.233832\pi$
$661$	20.3845	+	8.44353i	0.792865	+	0.328415i	0.0507700	+	0.998710i	$0.483832\pi$
$662$	−8.68047	+	12.3154i	−0.337376	+	0.478653i
$663$		0			0
$664$	−7.55283	+	27.1725i	−0.293107	+	1.05450i
$665$	30.0436	−	30.0436i	1.16504	−	1.16504i
$666$		0			0
$667$	2.66331	+	1.10318i	0.103124	+	0.0427152i
$668$	0.245759	+	0.688490i	0.00950869	+	0.0266385i
$669$		0			0
$670$	8.28915	−	36.8481i	0.320238	−	1.42357i
$671$	7.90624			0.305217
$672$		0			0
$673$	−36.2413			−1.39700			−0.698500	−	0.715610i	$-0.746149\pi$
$673$	−36.2413			−1.39700			−0.698500	+	0.715610i	$0.746149\pi$
$674$	−7.85346	+	34.9113i	−0.302504	+	1.34473i
$675$		0			0
$676$	−1.41360	+	0.504591i	−0.0543694	+	0.0194073i
$677$	29.3501	+	12.1572i	1.12802	+	0.467239i	0.867106	−	0.498124i	$-0.165978\pi$
$677$	29.3501	+	12.1572i	1.12802	+	0.467239i	0.260910	+	0.965363i	$0.415978\pi$
$678$		0			0
$679$	−13.6909	+	13.6909i	−0.525410	+	0.525410i
$680$	6.59530	+	11.6732i	0.252918	+	0.447646i
$681$		0			0
$682$	1.40690	−	1.99604i	0.0538728	−	0.0764322i
$683$	−11.1133	−	4.60326i	−0.425237	−	0.176139i	0.159793	−	0.987151i	$-0.448917\pi$
$683$	−11.1133	−	4.60326i	−0.425237	−	0.176139i	−0.585030	+	0.811012i	$0.698917\pi$
$684$		0			0
$685$	−0.706352	−	1.70529i	−0.0269883	−	0.0651556i
$686$	−3.11527	−	4.92367i	−0.118942	−	0.187987i
$687$		0			0
$688$	−38.4621	+	11.6039i	−1.46635	+	0.442393i
$689$	16.5952			0.632225
$690$		0			0
$691$	23.3035	−	9.65261i	0.886505	−	0.367203i	0.107489	−	0.994206i	$-0.465719\pi$
$691$	23.3035	−	9.65261i	0.886505	−	0.367203i	0.779016	+	0.627004i	$0.215719\pi$
$692$	43.7556	+	2.18273i	1.66334	+	0.0829751i
$693$		0			0
$694$	−12.1850	+	17.2875i	−0.462536	+	0.656224i
$695$	−16.8821	+	16.8821i	−0.640375	+	0.640375i
$696$		0			0
$697$	−20.4964	−	20.4964i	−0.776355	−	0.776355i
$698$	−4.13450	+	0.715793i	−0.156493	+	0.0270932i
$699$		0			0
$700$	−8.44115	−	4.00018i	−0.319046	−	0.151193i
$701$	0.346071	+	0.835489i	0.0130709	+	0.0315560i	0.930280	−	0.366850i	$-0.119564\pi$
$701$	0.346071	+	0.835489i	0.0130709	+	0.0315560i	−0.917209	+	0.398406i	$0.869564\pi$
$702$		0			0
$703$		−	5.41559i		−	0.204253i
$704$	1.74045	−	11.5526i	0.0655956	−	0.435405i
$705$		0			0
$706$	5.66408	−	25.1788i	0.213171	−	0.947616i
$707$	−64.1465	+	26.5703i	−2.41248	+	0.999280i
$708$		0			0
$709$	4.27421	−	10.3189i	0.160521	−	0.387533i	−0.823071	−	0.567939i	$-0.807741\pi$
$709$	4.27421	−	10.3189i	0.160521	−	0.387533i	0.983592	+	0.180406i	$0.0577411\pi$
$710$	0.895018	+	5.16971i	0.0335894	+	0.194016i
$711$		0			0
$712$	40.4306	−	4.94011i	1.51520	−	0.185138i
$713$	−0.355801	−	0.355801i	−0.0133249	−	0.0133249i
$714$		0			0
$715$	3.98468	−	9.61988i	0.149019	−	0.359763i
$716$	2.21018	−	44.3058i	0.0825982	−	1.65579i
$717$		0			0
$718$	15.6331	+	24.7079i	0.583420	+	0.922092i
$719$		−	4.15441i		−	0.154933i	−0.996995	−	0.0774667i	$-0.975317\pi$
$719$		−	4.15441i		−	0.154933i	0.996995	−	0.0774667i	$-0.0246831\pi$
$720$		0			0
$721$			11.7984i			0.439395i
$722$	−22.7023	+	14.3641i	−0.844892	+	0.534575i
$723$		0			0
$724$	26.5182	+	29.3029i	0.985543	+	1.08903i
$725$	3.37751	−	8.15403i	0.125438	−	0.302833i
$726$		0			0
$727$	−29.4907	−	29.4907i	−1.09375	−	1.09375i	−0.995125	−	0.0986243i	$-0.968556\pi$
$727$	−29.4907	−	29.4907i	−1.09375	−	1.09375i	−0.0986243	−	0.995125i	$-0.531444\pi$
$728$	18.4950	+	32.7347i	0.685471	+	1.21323i
$729$		0			0
$730$	−1.23618	+	0.214017i	−0.0457531	+	0.00792111i
$731$	−9.47543	+	22.8757i	−0.350461	+	0.846089i
$732$		0			0
$733$	−11.3075	+	4.68372i	−0.417652	+	0.172997i	−0.581606	−	0.813471i	$-0.697575\pi$
$733$	−11.3075	+	4.68372i	−0.417652	+	0.172997i	0.163954	+	0.986468i	$0.447575\pi$
$734$	2.87044	+	0.645719i	0.105950	+	0.0238339i
$735$		0			0
$736$	−2.28434	−	0.759433i	−0.0842017	−	0.0279931i
$737$			20.2838i			0.747164i
$738$		0			0
$739$	−13.2382	−	31.9598i	−0.486975	−	1.17566i	−0.956235	−	0.292601i	$-0.905479\pi$
$739$	−13.2382	−	31.9598i	−0.486975	−	1.17566i	0.469260	−	0.883060i	$-0.344521\pi$
$740$	3.18197	−	1.13581i	0.116971	−	0.0417533i
$741$		0			0
$742$	−3.87038	−	22.3557i	−0.142086	−	0.820703i
$743$	33.1432	+	33.1432i	1.21591	+	1.21591i	0.969053	+	0.246854i	$0.0793967\pi$
$743$	33.1432	+	33.1432i	1.21591	+	1.21591i	0.246854	+	0.969053i	$0.420603\pi$
$744$		0			0
$745$	17.8417	−	17.8417i	0.653668	−	0.653668i
$746$	7.39869	+	5.21493i	0.270885	+	0.190932i
$747$		0			0
$748$	−4.83153	−	5.33888i	−0.176658	−	0.195209i
$749$	63.3454	−	26.2385i	2.31459	−	0.958735i
$750$		0			0
$751$	−10.1264			−0.369518			−0.184759	−	0.982784i	$-0.559150\pi$
$751$	−10.1264			−0.369518			−0.184759	+	0.982784i	$0.559150\pi$
$752$	31.4951	−	25.7678i	1.14851	−	0.939655i
$753$		0			0
$754$	−30.0204	+	18.9943i	−1.09328	+	0.691731i
$755$	−3.98617	−	9.62347i	−0.145072	−	0.350234i
$756$		0			0
$757$	−3.42020	−	1.41669i	−0.124309	−	0.0514906i	0.319662	−	0.947532i	$-0.396431\pi$
$757$	−3.42020	−	1.41669i	−0.124309	−	0.0514906i	−0.443971	+	0.896041i	$0.646431\pi$
$758$	39.4475	+	27.8044i	1.43280	+	1.00990i
$759$		0			0
$760$	−26.4047	−	20.6546i	−0.957798	−	0.749222i
$761$	21.5698	−	21.5698i	0.781906	−	0.781906i	−0.198247	−	0.980152i	$-0.563525\pi$
$761$	21.5698	−	21.5698i	0.781906	−	0.781906i	0.980152	+	0.198247i	$0.0635247\pi$
$762$		0			0
$763$	−19.0158	−	7.87658i	−0.688417	−	0.285151i
$764$	18.0615	+	8.55917i	0.653442	+	0.309660i
$765$		0			0
$766$	29.8134	+	6.70667i	1.07720	+	0.242322i
$767$	−25.0427			−0.904238
$768$		0			0
$769$	−50.4552			−1.81946			−0.909731	−	0.415197i	$-0.863713\pi$
$769$	−50.4552			−1.81946			−0.909731	+	0.415197i	$0.863713\pi$
$770$	−13.8885	−	3.12427i	−0.500506	−	0.112591i
$771$		0			0
$772$	33.7229	+	15.9809i	1.21371	+	0.575167i
$773$	−4.35448	−	1.80369i	−0.156620	−	0.0648740i	0.302996	−	0.952992i	$-0.402013\pi$
$773$	−4.35448	−	1.80369i	−0.156620	−	0.0648740i	−0.459616	+	0.888118i	$0.652013\pi$
$774$		0			0
$775$	−1.08933	+	1.08933i	−0.0391298	+	0.0391298i
$776$	12.0327	+	9.41236i	0.431948	+	0.337884i
$777$		0			0
$778$	29.5122	+	20.8015i	1.05806	+	0.745771i
$779$	66.9588	+	27.7353i	2.39905	+	0.993719i
$780$		0			0
$781$	−1.07829	−	2.60322i	−0.0385841	−	0.0931504i
$782$	−1.25377	+	0.793280i	−0.0448349	+	0.0283676i
$783$		0			0
$784$	18.1131	−	14.8193i	0.646897	−	0.529260i
$785$	24.6288			0.879038
$786$		0			0
$787$	17.4964	−	7.24727i	0.623681	−	0.258337i	−0.0483845	−	0.998829i	$-0.515407\pi$
$787$	17.4964	−	7.24727i	0.623681	−	0.258337i	0.672066	+	0.740492i	$0.265407\pi$
$788$	20.5848	+	22.7464i	0.733305	+	0.810307i
$789$		0			0
$790$	−0.632899	−	0.446096i	−0.0225175	−	0.0158714i
$791$	−10.0189	+	10.0189i	−0.356231	+	0.356231i
$792$		0			0
$793$	14.1955	+	14.1955i	0.504097	+	0.504097i
$794$	5.84891	+	33.7839i	0.207570	+	1.19895i
$795$		0			0
$796$	52.7888	−	18.8431i	1.87105	−	0.667877i
$797$	−11.4321	−	27.5996i	−0.404947	−	0.977629i	−0.986447	−	0.164082i	$-0.947534\pi$
$797$	−11.4321	−	27.5996i	−0.404947	−	0.977629i	0.581500	−	0.813547i	$-0.302466\pi$
$798$		0			0
$799$		−	25.0801i		−	0.887272i
$800$	−2.32510	+	6.99377i	−0.0822046	+	0.247267i
$801$		0			0
$802$	37.0075	+	8.32500i	1.30678	+	0.293966i
$803$	0.622481	−	0.257840i	0.0219669	−	0.00909897i
$804$		0			0
$805$	−1.12250	+	2.70995i	−0.0395628	+	0.0955130i
$806$	6.10991	−	1.05779i	0.215212	−	0.0372591i
$807$		0			0
$808$	26.9479	+	47.6958i	0.948025	+	1.67793i
$809$	1.55374	+	1.55374i	0.0546264	+	0.0546264i	0.733892	−	0.679266i	$-0.237702\pi$
$809$	1.55374	+	1.55374i	0.0546264	+	0.0546264i	−0.679266	+	0.733892i	$0.737702\pi$
$810$		0			0
$811$	−10.6167	+	25.6310i	−0.372803	+	0.900027i	0.620470	+	0.784230i	$0.286942\pi$
$811$	−10.6167	+	25.6310i	−0.372803	+	0.900027i	−0.993273	+	0.115796i	$0.963058\pi$
$812$	32.5891	+	36.0112i	1.14365	+	1.26374i
$813$		0			0
$814$	−1.53334	+	0.970164i	−0.0537435	+	0.0340042i
$815$			10.7601i			0.376911i
$816$		0			0
$817$		−	61.9099i		−	2.16595i
$818$	3.95341	+	6.24834i	0.138228	+	0.218468i
$819$		0			0
$820$	−2.25274	+	45.1590i	−0.0786691	+	1.57702i
$821$	−1.59820	+	3.85839i	−0.0557774	+	0.134659i	−0.949312	−	0.314337i	$-0.898218\pi$
$821$	−1.59820	+	3.85839i	−0.0557774	+	0.134659i	0.893534	+	0.448995i	$0.148218\pi$
$822$		0			0
$823$	0.231053	+	0.231053i	0.00805399	+	0.00805399i	0.711122	−	0.703068i	$-0.248187\pi$
$823$	0.231053	+	0.231053i	0.00805399	+	0.00805399i	−0.703068	+	0.711122i	$0.748187\pi$
$824$	9.24030	−	1.12905i	0.321901	−	0.0393322i
$825$		0			0
$826$	5.84054	+	33.7355i	0.203218	+	1.17381i
$827$	−5.75161	+	13.8856i	−0.200003	+	0.482850i	−0.991779	−	0.127962i	$-0.959157\pi$
$827$	−5.75161	+	13.8856i	−0.200003	+	0.482850i	0.791776	+	0.610811i	$0.209157\pi$
$828$		0			0
$829$	44.6027	−	18.4750i	1.54911	−	0.641664i	0.565959	−	0.824433i	$-0.308506\pi$
$829$	44.6027	−	18.4750i	1.54911	−	0.641664i	0.983156	+	0.182769i	$0.0585061\pi$
$830$	5.95070	−	26.4529i	0.206552	−	0.918194i
$831$		0			0
$832$	23.8674	−	17.6175i	0.827454	−	0.610778i
$833$		−	14.4238i		−	0.499755i
$834$		0			0
$835$	−0.268956	−	0.649318i	−0.00930762	−	0.0224706i
$836$	16.2694	+	7.70990i	0.562689	+	0.266653i
$837$		0			0
$838$	−8.13802	+	1.40891i	−0.281123	+	0.0486701i
$839$	−22.8280	−	22.8280i	−0.788112	−	0.788112i	0.193073	−	0.981184i	$-0.438155\pi$
$839$	−22.8280	−	22.8280i	−0.788112	−	0.788112i	−0.981184	+	0.193073i	$0.938155\pi$
$840$		0			0
$841$	−11.9427	+	11.9427i	−0.411817	+	0.411817i
$842$	13.1923	−	18.7167i	0.454638	−	0.645019i
$843$		0			0
$844$	0.236278	+	0.0117867i	0.00813304	+	0.000405713i
$845$	1.33318	−	0.552220i	0.0458627	−	0.0189969i
$846$		0			0
$847$	−31.7875			−1.09223
$848$	−17.1382	+	5.17054i	−0.588529	+	0.177557i
$849$		0			0
$850$	2.42872	+	3.83858i	0.0833045	+	0.131662i
$851$	0.143075	+	0.345413i	0.00490455	+	0.0118406i
$852$		0			0
$853$	−15.9555	−	6.60898i	−0.546306	−	0.226287i	0.0924222	−	0.995720i	$-0.470539\pi$
$853$	−15.9555	−	6.60898i	−0.546306	−	0.226287i	−0.638728	+	0.769433i	$0.720539\pi$
$854$	15.8124	−	22.4338i	0.541088	−	0.767669i
$855$		0			0
$856$	−26.6114	−	47.1001i	−0.909559	−	1.60985i
$857$	−21.0080	+	21.0080i	−0.717620	+	0.717620i	−0.968117	−	0.250497i	$-0.919406\pi$
$857$	−21.0080	+	21.0080i	−0.717620	+	0.717620i	0.250497	+	0.968117i	$0.419406\pi$
$858$		0			0
$859$	8.25768	+	3.42044i	0.281748	+	0.116704i	0.519083	−	0.854724i	$-0.326274\pi$
$859$	8.25768	+	3.42044i	0.281748	+	0.116704i	−0.237334	+	0.971428i	$0.576274\pi$
$860$	36.3755	−	12.9844i	1.24040	−	0.442763i
$861$		0			0
$862$	8.27548	−	36.7873i	0.281864	−	1.25298i
$863$	3.79935			0.129332			0.0646658	−	0.997907i	$-0.479402\pi$
$863$	3.79935			0.129332			0.0646658	+	0.997907i	$0.479402\pi$
$864$		0			0
$865$	−42.1188			−1.43208
$866$	12.6642	−	56.2968i	0.430348	−	1.91304i
$867$		0			0
$868$	−2.84995	−	7.98409i	−0.0967335	−	0.270998i
$869$	0.384192	+	0.159137i	0.0130328	+	0.00539837i
$870$		0			0
$871$	−36.4193	+	36.4193i	−1.23402	+	1.23402i
$872$	−4.34909	+	15.6466i	−0.147279	+	0.529860i
$873$		0			0
$874$	2.13720	−	3.03216i	0.0722919	−	0.102564i
$875$	40.1375	+	16.6255i	1.35689	+	0.562044i
$876$		0			0
$877$	12.0336	+	29.0517i	0.406346	+	0.981007i	0.986091	+	0.166208i	$0.0531524\pi$
$877$	12.0336	+	29.0517i	0.406346	+	0.981007i	−0.579744	+	0.814798i	$0.696848\pi$
$878$	−13.7621	−	21.7509i	−0.464449	−	0.734058i
$879$		0			0
$880$	−1.11782	+	11.1762i	−0.0376817	+	0.376749i
$881$	30.5471			1.02916			0.514579	−	0.857443i	$-0.327948\pi$
$881$	30.5471			1.02916			0.514579	+	0.857443i	$0.327948\pi$
$882$		0			0
$883$	−17.9705	+	7.44363i	−0.604756	+	0.250498i	−0.663984	−	0.747746i	$-0.731136\pi$
$883$	−17.9705	+	7.44363i	−0.604756	+	0.250498i	0.0592288	+	0.998244i	$0.481136\pi$
$884$	0.910932	−	18.2608i	0.0306380	−	0.614177i
$885$		0			0
$886$	11.7346	−	16.6485i	0.394231	−	0.559316i
$887$	17.4616	−	17.4616i	0.586302	−	0.586302i	−0.350326	−	0.936628i	$-0.613929\pi$
$887$	17.4616	−	17.4616i	0.586302	−	0.586302i	0.936628	+	0.350326i	$0.113929\pi$
$888$		0			0
$889$	−16.4827	−	16.4827i	−0.552813	−	0.552813i
$890$	−38.5849	+	6.68010i	−1.29337	+	0.223917i
$891$		0			0
$892$	−18.2383	+	38.4863i	−0.610662	+	1.28862i
$893$	23.9977	+	57.9357i	0.803054	+	1.93874i
$894$		0			0
$895$			42.6484i			1.42558i
$896$	−29.2994	−	28.0435i	−0.978824	−	0.936868i
$897$		0			0
$898$	6.59581	−	29.3207i	0.220105	−	0.978443i
$899$	7.40024	−	3.06528i	0.246812	−	0.102233i
$900$		0			0
$901$	−4.22213	+	10.1931i	−0.140660	+	0.339583i
$902$	−4.14240	−	23.9269i	−0.137927	−	0.796679i
$903$		0			0
$904$	8.80539	+	6.88787i	0.292863	+	0.229087i
$905$	−26.8665	−	26.8665i	−0.893072	−	0.893072i
$906$		0			0
$907$	17.7327	−	42.8104i	0.588804	−	1.42150i	−0.295844	−	0.955236i	$-0.595601\pi$
$907$	17.7327	−	42.8104i	0.588804	−	1.42150i	0.884647	−	0.466261i	$-0.154399\pi$
$908$	−4.97794	−	0.248323i	−0.165199	−	0.00824088i
$909$		0			0
$910$	−19.3269	−	30.5461i	−0.640681	−	1.01259i
$911$			23.7577i			0.787126i	0.919298	+	0.393563i	$0.128758\pi$
$911$			23.7577i			0.787126i	−0.919298	+	0.393563i	$0.871242\pi$
$912$		0			0
$913$			14.5616i			0.481918i
$914$	−32.6219	+	20.6403i	−1.07904	+	0.682721i
$915$		0			0
$916$	4.55254	−	4.11992i	0.150420	−	0.136126i
$917$	11.3307	−	27.3547i	0.374172	−	0.903332i
$918$		0			0
$919$	−20.6882	−	20.6882i	−0.682442	−	0.682442i	0.278108	−	0.960550i	$-0.410293\pi$
$919$	−20.6882	−	20.6882i	−0.682442	−	0.682442i	−0.960550	+	0.278108i	$0.910293\pi$
$920$	2.22980	+	0.619792i	0.0735143	+	0.0204339i
$921$		0			0
$922$	−41.2505	+	7.14158i	−1.35851	+	0.235195i
$923$	2.73798	−	6.61007i	0.0901218	−	0.217573i
$924$		0			0
$925$	1.05752	−	0.438041i	0.0347712	−	0.0144027i
$926$	−53.6593	−	12.0709i	−1.76336	−	0.396675i
$927$		0			0
$928$	25.0847	−	28.9693i	0.823447	−	0.950964i
$929$		−	29.6246i		−	0.971953i	−0.873972	−	0.485976i	$-0.838464\pi$
$929$		−	29.6246i		−	0.971953i	0.873972	−	0.485976i	$-0.161536\pi$
$930$		0			0
$931$	13.8013	+	33.3193i	0.452319	+	1.09200i
$932$	9.81653	+	27.5009i	0.321551	+	0.900821i
$933$		0			0
$934$	4.50972	+	26.0486i	0.147563	+	0.852337i
$935$	4.89497	+	4.89497i	0.160083	+	0.160083i
$936$		0			0
$937$	−24.1201	+	24.1201i	−0.787970	+	0.787970i	−0.981161	−	0.193191i	$-0.938116\pi$
$937$	−24.1201	+	24.1201i	−0.787970	+	0.787970i	0.193191	+	0.981161i	$0.438116\pi$
$938$	57.5550	+	40.5674i	1.87924	+	1.32457i
$939$		0			0
$940$	−29.0074	+	26.2509i	−0.946118	+	0.856210i
$941$	−8.70707	+	3.60659i	−0.283842	+	0.117571i	−0.520063	−	0.854128i	$-0.674091\pi$
$941$	−8.70707	+	3.60659i	−0.283842	+	0.117571i	0.236220	+	0.971700i	$0.424091\pi$
$942$		0			0
$943$	−5.00346			−0.162935
$944$	25.8622	−	7.80253i	0.841742	−	0.253951i
$945$		0			0
$946$	−17.5288	+	11.0907i	−0.569910	+	0.360590i
$947$	−16.4900	−	39.8103i	−0.535853	−	1.29366i	−0.927595	−	0.373588i	$-0.878128\pi$
$947$	−16.4900	−	39.8103i	−0.535853	−	1.29366i	0.391742	−	0.920075i	$-0.371872\pi$
$948$		0			0
$949$	1.58060	+	0.654706i	0.0513085	+	0.0212527i
$950$	−9.28332	−	6.54330i	−0.301191	−	0.212293i
$951$		0			0
$952$	−24.8120	+	3.03171i	−0.804160	+	0.0982581i
$953$	0.729891	−	0.729891i	0.0236435	−	0.0236435i	−0.695186	−	0.718830i	$-0.744678\pi$
$953$	0.729891	−	0.729891i	0.0236435	−	0.0236435i	0.718830	+	0.695186i	$0.244678\pi$
$954$		0			0
$955$	−17.7527	−	7.35340i	−0.574463	−	0.237950i
$956$	−10.8955	+	22.9916i	−0.352386	+	0.743602i
$957$		0			0
$958$	−19.4694	−	4.37972i	−0.629027	−	0.141502i
$959$	3.44122			0.111123
$960$		0			0
$961$	29.6019			0.954899
$962$	−4.49500	−	1.01117i	−0.144924	−	0.0326014i
$963$		0			0
$964$	14.6606	−	30.9366i	0.472185	−	0.996402i
$965$	−33.1463	−	13.7296i	−1.06702	−	0.441973i
$966$		0			0
$967$	−4.04809	+	4.04809i	−0.130178	+	0.130178i	−0.769194	−	0.639016i	$-0.779342\pi$
$967$	−4.04809	+	4.04809i	−0.130178	+	0.130178i	0.639016	+	0.769194i	$0.279342\pi$
$968$	3.04190	+	24.8954i	0.0977705	+	0.800169i
$969$		0			0
$970$	−12.0046	−	8.46141i	−0.385446	−	0.271680i
$971$	5.50766	+	2.28135i	0.176749	+	0.0732119i	0.469303	−	0.883037i	$-0.344505\pi$
$971$	5.50766	+	2.28135i	0.176749	+	0.0732119i	−0.292554	+	0.956249i	$0.594505\pi$
$972$		0			0
$973$	−17.0338	−	41.1233i	−0.546080	−	1.31835i
$974$	−22.6990	+	14.3620i	−0.727324	+	0.460188i
$975$		0			0
$976$	−19.0829	−	10.2372i	−0.610830	−	0.327684i
$977$	47.1149			1.50734			0.753669	−	0.657254i	$-0.228282\pi$
$977$	47.1149			1.50734			0.753669	+	0.657254i	$0.228282\pi$
$978$		0			0
$979$	19.4295	−	8.04796i	0.620969	−	0.257214i
$980$	−16.6824	+	15.0971i	−0.532900	+	0.482259i
$981$		0			0
$982$	−7.76259	−	5.47142i	−0.247714	−	0.174600i
$983$	37.5894	−	37.5894i	1.19892	−	1.19892i	0.224425	−	0.974491i	$-0.427950\pi$
$983$	37.5894	−	37.5894i	1.19892	−	1.19892i	0.974491	−	0.224425i	$-0.0720503\pi$
$984$		0			0
$985$	−20.8552	−	20.8552i	−0.664501	−	0.664501i
$986$	−4.02897	−	23.2717i	−0.128309	−	0.741123i
$987$		0			0
$988$	15.3684	+	43.0544i	0.488934	+	1.36974i
$989$	1.63560	+	3.94869i	0.0520091	+	0.125561i
$990$		0			0
$991$		−	4.83775i		−	0.153676i	−0.997044	−	0.0768381i	$-0.975518\pi$
$991$		−	4.83775i		−	0.153676i	0.997044	−	0.0768381i	$-0.0244825\pi$
$992$	−5.98027	+	2.99607i	−0.189874	+	0.0951252i
$993$		0			0
$994$	−9.54314	−	2.14677i	−0.302690	−	0.0680915i
$995$	−49.7854	+	20.6218i	−1.57830	+	0.653754i
$996$		0			0
$997$	−7.20786	+	17.4013i	−0.228275	+	0.551105i	−0.995968	−	0.0897134i	$-0.971405\pi$
$997$	−7.20786	+	17.4013i	−0.228275	+	0.551105i	0.767692	+	0.640819i	$0.221405\pi$
$998$	41.9160	−	7.25679i	1.32683	−	0.229710i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.107.3	✓	128
3.2	odd	2	inner	864.2.w.a.107.30	yes	128
32.3	odd	8	inner	864.2.w.a.323.30	yes	128
96.35	even	8	inner	864.2.w.a.323.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.3	✓	128	1.1	even	1	trivial
864.2.w.a.107.30	yes	128	3.2	odd	2	inner
864.2.w.a.323.3	yes	128	96.35	even	8	inner
864.2.w.a.323.30	yes	128	32.3	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37973 - 0.310377i) q^{2} +(1.80733 + 0.856477i) q^{4} +(-1.77643 - 0.735821i) q^{5} +(2.53483 - 2.53483i) q^{7} +(-2.22781 - 1.74266i) q^{8} +O(q^{10})\)	\(q+(-1.37973 - 0.310377i) q^{2} +(1.80733 + 0.856477i) q^{4} +(-1.77643 - 0.735821i) q^{5} +(2.53483 - 2.53483i) q^{7} +(-2.22781 - 1.74266i) q^{8} +(2.22262 + 1.56660i) q^{10} +(-1.34921 - 0.558859i) q^{11} +(-1.41905 - 3.42590i) q^{13} +(-4.28414 + 2.71064i) q^{14} +(2.53290 + 3.09587i) q^{16} +2.46530 q^{17} +(-5.69490 + 2.35890i) q^{19} +(-2.58038 - 2.85134i) q^{20} +(1.68809 + 1.18984i) q^{22} +(0.300908 - 0.300908i) q^{23} +(-0.921266 - 0.921266i) q^{25} +(0.894594 + 5.16727i) q^{26} +(6.75230 - 2.41026i) q^{28} +(2.59237 + 6.25853i) q^{29} -1.18242i q^{31} +(-2.53383 - 5.05764i) q^{32} +(-3.40146 - 0.765174i) q^{34} +(-6.36813 + 2.63776i) q^{35} +(-0.336213 + 0.811690i) q^{37} +(8.58960 - 1.48709i) q^{38} +(2.67525 + 4.73499i) q^{40} +(-8.31394 - 8.31394i) q^{41} +(-3.84352 + 9.27907i) q^{43} +(-1.95981 - 2.16561i) q^{44} +(-0.508568 + 0.321778i) q^{46} -10.1733i q^{47} -5.85072i q^{49} +(0.985162 + 1.55704i) q^{50} +(0.369501 - 7.40712i) q^{52} +(-1.71262 + 4.13464i) q^{53} +(1.98555 + 1.98555i) q^{55} +(-10.0645 + 1.22975i) q^{56} +(-1.63427 - 9.43971i) q^{58} +(2.58441 - 6.23932i) q^{59} +(-5.00176 + 2.07179i) q^{61} +(-0.366998 + 1.63143i) q^{62} +(1.92624 + 7.76464i) q^{64} +7.13003i q^{65} +(-5.31529 - 12.8322i) q^{67} +(4.45562 + 2.11147i) q^{68} +(9.60502 - 1.66289i) q^{70} +(1.36432 + 1.36432i) q^{71} +(-0.326237 + 0.326237i) q^{73} +(0.715815 - 1.01556i) q^{74} +(-12.3129 - 0.614225i) q^{76} +(-4.83662 + 2.00339i) q^{77} -0.284754 q^{79} +(-2.22150 - 7.36336i) q^{80} +(8.89056 + 14.0515i) q^{82} +(-3.81580 - 9.21215i) q^{83} +(-4.37943 - 1.81402i) q^{85} +(8.18304 - 11.6097i) q^{86} +(2.03186 + 3.59624i) q^{88} +(-10.1828 + 10.1828i) q^{89} +(-12.2811 - 5.08701i) q^{91} +(0.801562 - 0.286120i) q^{92} +(-3.15755 + 14.0364i) q^{94} +11.8523 q^{95} -5.40113 q^{97} +(-1.81593 + 8.07244i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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