LMFDB - Embedded newform 864.2.v.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (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			109.2
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39831 + 0.211463i) q^{2} +(1.91057 - 0.591382i) q^{4} +(-1.77214 + 0.734044i) q^{5} +(-0.0355868 + 0.0355868i) q^{7} +(-2.54652 + 1.23095i) q^{8} +O(q^{10})$	\(q+(-1.39831 + 0.211463i) q^{2} +(1.91057 - 0.591382i) q^{4} +(-1.77214 + 0.734044i) q^{5} +(-0.0355868 + 0.0355868i) q^{7} +(-2.54652 + 1.23095i) q^{8} +(2.32278 - 1.40116i) q^{10} +(1.04798 + 2.53004i) q^{11} +(1.82513 + 0.755995i) q^{13} +(0.0422362 - 0.0572867i) q^{14} +(3.30053 - 2.25975i) q^{16} -2.92843i q^{17} +(-1.55044 - 0.642214i) q^{19} +(-2.95169 + 2.45045i) q^{20} +(-2.00041 - 3.31619i) q^{22} +(-0.146574 - 0.146574i) q^{23} +(-0.933880 + 0.933880i) q^{25} +(-2.71198 - 0.671172i) q^{26} +(-0.0469455 + 0.0890363i) q^{28} +(-2.17892 + 5.26037i) q^{29} -4.28852 q^{31} +(-4.13733 + 3.85778i) q^{32} +(0.619253 + 4.09486i) q^{34} +(0.0369424 - 0.0891869i) q^{35} +(-1.92396 + 0.796930i) q^{37} +(2.30381 + 0.570157i) q^{38} +(3.60921 - 4.05067i) q^{40} +(-4.22763 - 4.22763i) q^{41} +(1.29855 + 3.13498i) q^{43} +(3.49846 + 4.21406i) q^{44} +(0.235952 + 0.173962i) q^{46} +5.33727i q^{47} +6.99747i q^{49} +(1.10838 - 1.50334i) q^{50} +(3.93412 + 0.365028i) q^{52} +(-1.48773 - 3.59170i) q^{53} +(-3.71433 - 3.71433i) q^{55} +(0.0468168 - 0.134428i) q^{56} +(1.93444 - 7.81641i) q^{58} +(-1.27834 + 0.529507i) q^{59} +(-5.58246 + 13.4772i) q^{61} +(5.99670 - 0.906861i) q^{62} +(4.96952 - 6.26928i) q^{64} -3.78932 q^{65} +(1.11670 - 2.69596i) q^{67} +(-1.73182 - 5.59496i) q^{68} +(-0.0327974 + 0.132523i) q^{70} +(-3.73700 + 3.73700i) q^{71} +(-10.8405 - 10.8405i) q^{73} +(2.52178 - 1.52120i) q^{74} +(-3.34202 - 0.310089i) q^{76} +(-0.127330 - 0.0527419i) q^{77} +9.94610i q^{79} +(-4.19025 + 6.42733i) q^{80} +(6.80554 + 5.01757i) q^{82} +(11.2462 + 4.65832i) q^{83} +(2.14959 + 5.18958i) q^{85} +(-2.47871 - 4.10909i) q^{86} +(-5.78306 - 5.15279i) q^{88} +(-6.00227 + 6.00227i) q^{89} +(-0.0918540 + 0.0380472i) q^{91} +(-0.366721 - 0.193358i) q^{92} +(-1.12863 - 7.46318i) q^{94} +3.21901 q^{95} -3.69111 q^{97} +(-1.47970 - 9.78466i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.39831	+	0.211463i	−0.988758	+	0.149527i
$2$	−1.39831	+	0.211463i	−0.988758	+	0.149527i
$3$		0			0
$3$		0			0
$4$	1.91057	−	0.591382i	0.955284	−	0.295691i
$5$	−1.77214	+	0.734044i	−0.792524	+	0.328274i	−0.741958	−	0.670446i	$-0.766103\pi$
$5$	−1.77214	+	0.734044i	−0.792524	+	0.328274i	−0.0505664	+	0.998721i	$0.516103\pi$
$6$		0			0
$7$	−0.0355868	+	0.0355868i	−0.0134505	+	0.0134505i	−0.713800	−	0.700350i	$-0.753027\pi$
$7$	−0.0355868	+	0.0355868i	−0.0134505	+	0.0134505i	0.700350	+	0.713800i	$0.253027\pi$
$8$	−2.54652	+	1.23095i	−0.900330	+	0.435207i
$9$		0			0
$10$	2.32278	−	1.40116i	0.734529	−	0.443087i
$11$	1.04798	+	2.53004i	0.315977	+	0.762837i	0.999460	+	0.0328698i	$0.0104647\pi$
$11$	1.04798	+	2.53004i	0.315977	+	0.762837i	−0.683482	+	0.729967i	$0.739535\pi$
$12$		0			0
$13$	1.82513	+	0.755995i	0.506201	+	0.209675i	0.621144	−	0.783697i	$-0.286668\pi$
$13$	1.82513	+	0.755995i	0.506201	+	0.209675i	−0.114942	+	0.993372i	$0.536668\pi$
$14$	0.0422362	−	0.0572867i	0.0112881	−	0.0153105i
$15$		0			0
$16$	3.30053	−	2.25975i	0.825134	−	0.564938i
$17$		−	2.92843i		−	0.710248i	−0.934819	−	0.355124i	$-0.884439\pi$
$17$		−	2.92843i		−	0.710248i	0.934819	−	0.355124i	$-0.115561\pi$
$18$		0			0
$19$	−1.55044	−	0.642214i	−0.355696	−	0.147334i	0.197678	−	0.980267i	$-0.436660\pi$
$19$	−1.55044	−	0.642214i	−0.355696	−	0.147334i	−0.553374	+	0.832933i	$0.686660\pi$
$20$	−2.95169	+	2.45045i	−0.660018	+	0.547937i
$21$		0			0
$22$	−2.00041	−	3.31619i	−0.426490	−	0.707014i
$23$	−0.146574	−	0.146574i	−0.0305628	−	0.0305628i	0.691660	−	0.722223i	$-0.256880\pi$
$23$	−0.146574	−	0.146574i	−0.0305628	−	0.0305628i	−0.722223	+	0.691660i	$0.756880\pi$
$24$		0			0
$25$	−0.933880	+	0.933880i	−0.186776	+	0.186776i
$26$	−2.71198	−	0.671172i	−0.531862	−	0.131628i
$27$		0			0
$28$	−0.0469455	+	0.0890363i	−0.00887187	+	0.0168263i
$29$	−2.17892	+	5.26037i	−0.404614	+	0.976826i	0.581916	+	0.813249i	$0.302303\pi$
$29$	−2.17892	+	5.26037i	−0.404614	+	0.976826i	−0.986531	+	0.163577i	$0.947697\pi$
$30$		0			0
$31$	−4.28852			−0.770241			−0.385120	−	0.922866i	$-0.625840\pi$
$31$	−4.28852			−0.770241			−0.385120	+	0.922866i	$0.625840\pi$
$32$	−4.13733	+	3.85778i	−0.731384	+	0.681966i
$33$		0			0
$34$	0.619253	+	4.09486i	0.106201	+	0.702263i
$35$	0.0369424	−	0.0891869i	0.00624441	−	0.0150753i
$36$		0			0
$37$	−1.92396	+	0.796930i	−0.316297	+	0.131014i	−0.535183	−	0.844736i	$-0.679758\pi$
$37$	−1.92396	+	0.796930i	−0.316297	+	0.131014i	0.218887	+	0.975750i	$0.429758\pi$
$38$	2.30381	+	0.570157i	0.373727	+	0.0924916i
$39$		0			0
$40$	3.60921	−	4.05067i	0.570666	−	0.640468i
$41$	−4.22763	−	4.22763i	−0.660244	−	0.660244i	0.295193	−	0.955438i	$-0.404616\pi$
$41$	−4.22763	−	4.22763i	−0.660244	−	0.660244i	−0.955438	+	0.295193i	$0.904616\pi$
$42$		0			0
$43$	1.29855	+	3.13498i	0.198027	+	0.478080i	0.991433	−	0.130613i	$-0.0416944\pi$
$43$	1.29855	+	3.13498i	0.198027	+	0.478080i	−0.793406	+	0.608692i	$0.791694\pi$
$44$	3.49846	+	4.21406i	0.527412	+	0.635294i
$45$		0			0
$46$	0.235952	+	0.173962i	0.0347892	+	0.0256493i
$47$			5.33727i			0.778520i	0.921128	+	0.389260i	$0.127269\pi$
$47$			5.33727i			0.778520i	−0.921128	+	0.389260i	$0.872731\pi$
$48$		0			0
$49$			6.99747i			0.999638i
$50$	1.10838	−	1.50334i	0.156748	−	0.212604i
$51$		0			0
$52$	3.93412	+	0.365028i	0.545565	+	0.0506203i
$53$	−1.48773	−	3.59170i	−0.204355	−	0.493357i	0.788161	−	0.615469i	$-0.211033\pi$
$53$	−1.48773	−	3.59170i	−0.204355	−	0.493357i	−0.992516	+	0.122112i	$0.961033\pi$
$54$		0			0
$55$	−3.71433	−	3.71433i	−0.500840	−	0.500840i
$56$	0.0468168	−	0.134428i	0.00625615	−	0.0179637i
$57$		0			0
$58$	1.93444	−	7.81641i	0.254004	−	1.02634i
$59$	−1.27834	+	0.529507i	−0.166426	+	0.0689359i	−0.464341	−	0.885657i	$-0.653709\pi$
$59$	−1.27834	+	0.529507i	−0.166426	+	0.0689359i	0.297915	+	0.954592i	$0.403709\pi$
$60$		0			0
$61$	−5.58246	+	13.4772i	−0.714761	+	1.72558i	−0.0270124	+	0.999635i	$0.508599\pi$
$61$	−5.58246	+	13.4772i	−0.714761	+	1.72558i	−0.687748	+	0.725949i	$0.741401\pi$
$62$	5.99670	−	0.906861i	0.761581	−	0.115171i
$63$		0			0
$64$	4.96952	−	6.26928i	0.621190	−	0.783660i
$65$	−3.78932			−0.470008
$66$		0			0
$67$	1.11670	−	2.69596i	0.136427	−	0.329364i	−0.840870	−	0.541237i	$-0.817956\pi$
$67$	1.11670	−	2.69596i	0.136427	−	0.329364i	0.977297	+	0.211873i	$0.0679562\pi$
$68$	−1.73182	−	5.59496i	−0.210014	−	0.678488i
$69$		0			0
$70$	−0.0327974	+	0.132523i	−0.00392004	+	0.0158396i
$71$	−3.73700	+	3.73700i	−0.443501	+	0.443501i	−0.893187	−	0.449686i	$-0.851536\pi$
$71$	−3.73700	+	3.73700i	−0.443501	+	0.443501i	0.449686	+	0.893187i	$0.351536\pi$
$72$		0			0
$73$	−10.8405	−	10.8405i	−1.26878	−	1.26878i	−0.946718	−	0.322065i	$-0.895623\pi$
$73$	−10.8405	−	10.8405i	−1.26878	−	1.26878i	−0.322065	−	0.946718i	$-0.604377\pi$
$74$	2.52178	−	1.52120i	0.293151	−	0.176836i
$75$		0			0
$76$	−3.34202	−	0.310089i	−0.383355	−	0.0355697i
$77$	−0.127330	−	0.0527419i	−0.0145106	−	0.00601050i
$78$		0			0
$79$			9.94610i			1.11902i	0.828822	+	0.559512i	$0.189011\pi$
$79$			9.94610i			1.11902i	−0.828822	+	0.559512i	$0.810989\pi$
$80$	−4.19025	+	6.42733i	−0.468484	+	0.718597i
$81$		0			0
$82$	6.80554	+	5.01757i	0.751546	+	0.554098i
$83$	11.2462	+	4.65832i	1.23443	+	0.511318i	0.901970	−	0.431800i	$-0.142121\pi$
$83$	11.2462	+	4.65832i	1.23443	+	0.511318i	0.332460	+	0.943117i	$0.392121\pi$
$84$		0			0
$85$	2.14959	+	5.18958i	0.233156	+	0.562889i
$86$	−2.47871	−	4.10909i	−0.267286	−	0.443095i
$87$		0			0
$88$	−5.78306	−	5.15279i	−0.616476	−	0.549290i
$89$	−6.00227	+	6.00227i	−0.636239	+	0.636239i	−0.949626	−	0.313386i	$-0.898537\pi$
$89$	−6.00227	+	6.00227i	−0.636239	+	0.636239i	0.313386	+	0.949626i	$0.398537\pi$
$90$		0			0
$91$	−0.0918540	+	0.0380472i	−0.00962892	+	0.00398843i
$92$	−0.366721	−	0.193358i	−0.0382333	−	0.0201590i
$93$		0			0
$94$	−1.12863	−	7.46318i	−0.116409	−	0.769768i
$95$	3.21901			0.330263
$96$		0			0
$97$	−3.69111			−0.374776			−0.187388	−	0.982286i	$-0.560002\pi$
$97$	−3.69111			−0.374776			−0.187388	+	0.982286i	$0.560002\pi$
$98$	−1.47970	−	9.78466i	−0.149472	−	0.988400i
$99$		0			0
$100$	−1.23196	+	2.33652i	−0.123196	+	0.233652i
$101$	−13.0062	+	5.38735i	−1.29417	+	0.536062i	−0.920225	−	0.391390i	$-0.871994\pi$
$101$	−13.0062	+	5.38735i	−1.29417	+	0.536062i	−0.373943	+	0.927452i	$0.621994\pi$
$102$		0			0
$103$	−14.1391	+	14.1391i	−1.39317	+	1.39317i	−0.575041	+	0.818124i	$0.695014\pi$
$103$	−14.1391	+	14.1391i	−1.39317	+	1.39317i	−0.818124	+	0.575041i	$0.804986\pi$
$104$	−5.57833	+	0.321496i	−0.547000	+	0.0315252i
$105$		0			0
$106$	2.83982	+	4.70772i	0.275828	+	0.457254i
$107$	3.17772	+	7.67170i	0.307202	+	0.741652i	0.999793	+	0.0203215i	$0.00646897\pi$
$107$	3.17772	+	7.67170i	0.307202	+	0.741652i	−0.692591	+	0.721330i	$0.743531\pi$
$108$		0			0
$109$	−2.82294	−	1.16930i	−0.270388	−	0.111999i	0.243370	−	0.969934i	$-0.421747\pi$
$109$	−2.82294	−	1.16930i	−0.270388	−	0.111999i	−0.513758	+	0.857935i	$0.671747\pi$
$110$	5.97924	+	4.40836i	0.570098	+	0.420320i
$111$		0			0
$112$	−0.0370381	+	0.197873i	−0.00349977	+	0.0186972i
$113$		−	13.9959i		−	1.31662i	−0.752745	−	0.658312i	$-0.771271\pi$
$113$		−	13.9959i		−	1.31662i	0.752745	−	0.658312i	$-0.228729\pi$
$114$		0			0
$115$	0.367342	+	0.152158i	0.0342548	+	0.0141888i
$116$	−1.05208	+	11.3389i	−0.0976829	+	1.05279i
$117$		0			0
$118$	1.67555	−	1.01074i	0.154247	−	0.0930460i
$119$	0.104213	+	0.104213i	0.00955321	+	0.00955321i
$120$		0			0
$121$	2.47531	−	2.47531i	0.225028	−	0.225028i
$122$	4.95610	−	20.0259i	0.448704	−	1.81306i
$123$		0			0
$124$	−8.19350	+	2.53615i	−0.735798	+	0.227753i
$125$	4.63967	−	11.2012i	0.414985	−	1.00186i
$126$		0			0
$127$	−3.85566			−0.342135			−0.171067	−	0.985259i	$-0.554722\pi$
$127$	−3.85566			−0.342135			−0.171067	+	0.985259i	$0.554722\pi$
$128$	−5.62323	+	9.81730i	−0.497028	+	0.867735i
$129$		0			0
$130$	5.29867	−	0.801300i	0.464724	−	0.0702786i
$131$	2.42590	−	5.85663i	0.211952	−	0.511697i	−0.781771	−	0.623565i	$-0.785684\pi$
$131$	2.42590	−	5.85663i	0.211952	−	0.511697i	0.993723	+	0.111869i	$0.0356836\pi$
$132$		0			0
$133$	0.0780295	−	0.0323209i	0.00676601	−	0.00280257i
$134$	−0.991409	+	4.00595i	−0.0856447	+	0.346061i
$135$		0			0
$136$	3.60475	+	7.45730i	0.309105	+	0.639458i
$137$	−1.91013	−	1.91013i	−0.163193	−	0.163193i	0.620786	−	0.783980i	$-0.286813\pi$
$137$	−1.91013	−	1.91013i	−0.163193	−	0.163193i	−0.783980	+	0.620786i	$0.786813\pi$
$138$		0			0
$139$	6.94133	+	16.7578i	0.588756	+	1.42138i	0.884693	+	0.466175i	$0.154368\pi$
$139$	6.94133	+	16.7578i	0.588756	+	1.42138i	−0.295937	+	0.955207i	$0.595632\pi$
$140$	0.0178374	−	0.192245i	0.00150754	−	0.0162476i
$141$		0			0
$142$	4.43527	−	6.01574i	0.372200	−	0.504830i
$143$			5.40994i			0.452402i
$144$		0			0
$145$		−	10.9215i		−	0.906983i
$146$	17.4508	+	12.8660i	1.44424	+	1.06480i
$147$		0			0
$148$	−3.20456	+	2.66038i	−0.263413	+	0.218682i
$149$	−5.07715	−	12.2573i	−0.415937	−	1.00416i	−0.983513	−	0.180839i	$-0.942119\pi$
$149$	−5.07715	−	12.2573i	−0.415937	−	1.00416i	0.567576	−	0.823321i	$-0.307881\pi$
$150$		0			0
$151$	−5.21158	−	5.21158i	−0.424112	−	0.424112i	0.462505	−	0.886617i	$-0.346951\pi$
$151$	−5.21158	−	5.21158i	−0.424112	−	0.424112i	−0.886617	+	0.462505i	$0.846951\pi$
$152$	4.73876	−	0.273109i	0.384364	−	0.0221520i
$153$		0			0
$154$	0.189201	+	0.0468242i	0.0152462	+	0.00377320i
$155$	7.59985	−	3.14796i	0.610434	−	0.252850i
$156$		0			0
$157$	−1.66632	+	4.02285i	−0.132987	+	0.321059i	−0.976320	−	0.216333i	$-0.930590\pi$
$157$	−1.66632	+	4.02285i	−0.132987	+	0.321059i	0.843333	+	0.537392i	$0.180590\pi$
$158$	−2.10323	−	13.9078i	−0.167324	−	1.10644i
$159$		0			0
$160$	4.50014	−	9.87351i	0.355768	−	0.780569i
$161$	0.0104322			0.000822173
$162$		0			0
$163$	5.91014	−	14.2683i	0.462918	−	1.11758i	−0.504276	−	0.863542i	$-0.668241\pi$
$163$	5.91014	−	14.2683i	0.462918	−	1.11758i	0.967194	−	0.254039i	$-0.0817593\pi$
$164$	−10.5773	−	5.57702i	−0.825949	−	0.435492i
$165$		0			0
$166$	−16.7108	−	4.13566i	−1.29701	−	0.320989i
$167$	9.14462	−	9.14462i	0.707632	−	0.707632i	−0.258405	−	0.966037i	$-0.583197\pi$
$167$	9.14462	−	9.14462i	0.707632	−	0.707632i	0.966037	+	0.258405i	$0.0831969\pi$
$168$		0			0
$169$	−6.43280	−	6.43280i	−0.494831	−	0.494831i
$170$	−4.10321	−	6.80210i	−0.314702	−	0.521698i
$171$		0			0
$172$	4.33494	+	5.22165i	0.330536	+	0.398147i
$173$	1.32896	+	0.550474i	0.101039	+	0.0418518i	0.432630	−	0.901571i	$-0.357585\pi$
$173$	1.32896	+	0.550474i	0.101039	+	0.0418518i	−0.331591	+	0.943423i	$0.607585\pi$
$174$		0			0
$175$		−	0.0664675i		−	0.00502447i
$176$	9.17616	+	5.98233i	0.691679	+	0.450935i
$177$		0			0
$178$	7.12381	−	9.66232i	0.533952	−	0.724221i
$179$	18.9912	+	7.86639i	1.41947	+	0.587962i	0.954726	−	0.297486i	$-0.0961481\pi$
$179$	18.9912	+	7.86639i	1.41947	+	0.587962i	0.464739	+	0.885448i	$0.346148\pi$
$180$		0			0
$181$	3.31249	+	7.99706i	0.246215	+	0.594417i	0.997877	−	0.0651328i	$-0.0207471\pi$
$181$	3.31249	+	7.99706i	0.246215	+	0.594417i	−0.751661	+	0.659549i	$0.770747\pi$
$182$	0.120395	−	0.0726256i	0.00892429	−	0.00538337i
$183$		0			0
$184$	0.553680	+	0.192828i	0.0408178	+	0.0142155i
$185$	2.82454	−	2.82454i	0.207664	−	0.207664i
$186$		0			0
$187$	7.40905	−	3.06893i	0.541803	−	0.224422i
$188$	3.15636	+	10.1972i	0.230202	+	0.743708i
$189$		0			0
$190$	−4.50119	+	0.680700i	−0.326550	+	0.0493831i
$191$	23.4508			1.69684			0.848422	−	0.529321i	$-0.177553\pi$
$191$	23.4508			1.69684			0.848422	+	0.529321i	$0.177553\pi$
$192$		0			0
$193$	−2.58287			−0.185919			−0.0929594	−	0.995670i	$-0.529633\pi$
$193$	−2.58287			−0.185919			−0.0929594	+	0.995670i	$0.529633\pi$
$194$	5.16134	−	0.780532i	0.370563	−	0.0560390i
$195$		0			0
$196$	4.13818	+	13.3691i	0.295584	+	0.954938i
$197$	11.6273	−	4.81619i	0.828412	−	0.343139i	0.0721379	−	0.997395i	$-0.477018\pi$
$197$	11.6273	−	4.81619i	0.828412	−	0.343139i	0.756274	+	0.654255i	$0.227018\pi$
$198$		0			0
$199$	−7.74779	+	7.74779i	−0.549226	+	0.549226i	−0.926217	−	0.376991i	$-0.876959\pi$
$199$	−7.74779	+	7.74779i	−0.549226	+	0.549226i	0.376991	+	0.926217i	$0.376959\pi$
$200$	1.22858	−	3.52770i	0.0868738	−	0.249446i
$201$		0			0
$202$	17.0476	−	10.2835i	1.19946	−	0.723548i
$203$	−0.109659	−	0.264740i	−0.00769655	−	0.0185811i
$204$		0			0
$205$	10.5952	+	4.38868i	0.740001	+	0.306518i
$206$	16.7810	−	22.7608i	1.16919	−	1.58582i
$207$		0			0
$208$	7.73228	−	1.62916i	0.536137	−	0.112962i
$209$		−	4.59571i		−	0.317892i
$210$		0			0
$211$	14.7043	+	6.09070i	1.01228	+	0.419301i	0.826287	−	0.563249i	$-0.190449\pi$
$211$	14.7043	+	6.09070i	1.01228	+	0.419301i	0.185996	+	0.982551i	$0.440449\pi$
$212$	−4.96647	−	5.98236i	−0.341099	−	0.410870i
$213$		0			0
$214$	−6.06574	−	10.0555i	−0.414645	−	0.687379i
$215$	−4.60242	−	4.60242i	−0.313883	−	0.313883i
$216$		0			0
$217$	0.152614	−	0.152614i	0.0103601	−	0.0103601i
$218$	4.19462	+	1.03810i	0.284095	+	0.0703092i
$219$		0			0
$220$	−9.29306	−	4.89988i	−0.626538	−	0.330350i
$221$	2.21388	−	5.34477i	0.148922	−	0.359528i
$222$		0			0
$223$	8.09618			0.542160			0.271080	−	0.962557i	$-0.412619\pi$
$223$	8.09618			0.542160			0.271080	+	0.962557i	$0.412619\pi$
$224$	0.00994830	−	0.284520i	0.000664699	−	0.0190103i
$225$		0			0
$226$	2.95961	+	19.5707i	0.196870	+	1.30182i
$227$	3.70788	−	8.95160i	0.246100	−	0.594139i	−0.751766	−	0.659430i	$-0.770798\pi$
$227$	3.70788	−	8.95160i	0.246100	−	0.594139i	0.997866	+	0.0652913i	$0.0207977\pi$
$228$		0			0
$229$	11.3986	−	4.72144i	0.753238	−	0.312002i	0.0271762	−	0.999631i	$-0.491348\pi$
$229$	11.3986	−	4.72144i	0.753238	−	0.312002i	0.726062	+	0.687629i	$0.241348\pi$
$230$	−0.545835	−	0.135086i	−0.0359913	−	0.00890728i
$231$		0			0
$232$	−0.926609	−	16.0778i	−0.0608348	−	1.05556i
$233$	8.59855	+	8.59855i	0.563310	+	0.563310i	0.930246	−	0.366936i	$-0.119593\pi$
$233$	8.59855	+	8.59855i	0.563310	+	0.563310i	−0.366936	+	0.930246i	$0.619593\pi$
$234$		0			0
$235$	−3.91779	−	9.45837i	−0.255568	−	0.616996i
$236$	−2.12922	+	1.76765i	−0.138600	+	0.115064i
$237$		0			0
$238$	−0.167760	−	0.123686i	−0.0108743	−	0.00801735i
$239$			25.8457i			1.67182i	0.548868	+	0.835909i	$0.315059\pi$
$239$			25.8457i			1.67182i	−0.548868	+	0.835909i	$0.684941\pi$
$240$		0			0
$241$		−	25.5757i		−	1.64748i	−0.566971	−	0.823738i	$-0.691885\pi$
$241$		−	25.5757i		−	1.64748i	0.566971	−	0.823738i	$-0.308115\pi$
$242$	−2.93783	+	3.98470i	−0.188851	+	0.256146i
$243$		0			0
$244$	−2.69546	+	29.0506i	−0.172559	+	1.85977i
$245$	−5.13645	−	12.4005i	−0.328156	−	0.792238i
$246$		0			0
$247$	−2.34425	−	2.34425i	−0.149161	−	0.149161i
$248$	10.9208	−	5.27896i	0.693471	−	0.335214i
$249$		0			0
$250$	−4.11910	+	16.6439i	−0.260515	+	1.05265i
$251$	−25.5297	+	10.5748i	−1.61142	+	0.667473i	−0.992972	−	0.118350i	$-0.962240\pi$
$251$	−25.5297	+	10.5748i	−1.61142	+	0.667473i	−0.618451	+	0.785823i	$0.712240\pi$
$252$		0			0
$253$	0.217233	−	0.524446i	0.0136573	−	0.0329716i
$254$	5.39143	−	0.815328i	0.338288	−	0.0511582i
$255$		0			0
$256$	5.78705	−	14.9168i	0.361691	−	0.932298i
$257$	6.54897			0.408513			0.204257	−	0.978917i	$-0.434522\pi$
$257$	6.54897			0.408513			0.204257	+	0.978917i	$0.434522\pi$
$258$		0			0
$259$	0.0401073	−	0.0968276i	0.00249215	−	0.00601657i
$260$	−7.23976	+	2.24094i	−0.448991	+	0.138977i
$261$		0			0
$262$	−2.15371	+	8.70240i	−0.133057	+	0.537636i
$263$	17.3589	−	17.3589i	1.07040	−	1.07040i	0.0730702	−	0.997327i	$-0.476720\pi$
$263$	17.3589	−	17.3589i	1.07040	−	1.07040i	0.997327	−	0.0730702i	$-0.0232797\pi$
$264$		0			0
$265$	5.27292	+	5.27292i	0.323913	+	0.323913i
$266$	−0.102275	+	0.0616950i	−0.00627089	+	0.00378277i
$267$		0			0
$268$	0.539194	−	5.81122i	0.0329365	−	0.354977i
$269$	1.98257	+	0.821205i	0.120879	+	0.0500698i	0.442303	−	0.896866i	$-0.354162\pi$
$269$	1.98257	+	0.821205i	0.120879	+	0.0500698i	−0.321424	+	0.946935i	$0.604162\pi$
$270$		0			0
$271$		−	19.0040i		−	1.15441i	−0.816600	−	0.577204i	$-0.804144\pi$
$271$		−	19.0040i		−	1.15441i	0.816600	−	0.577204i	$-0.195856\pi$
$272$	−6.61752	−	9.66537i	−0.401246	−	0.586049i
$273$		0			0
$274$	3.07488	+	2.26704i	0.185760	+	0.136957i
$275$	−3.34144	−	1.38407i	−0.201497	−	0.0834626i
$276$		0			0
$277$	2.76578	+	6.67719i	0.166180	+	0.401193i	0.984929	−	0.172957i	$-0.0553323\pi$
$277$	2.76578	+	6.67719i	0.166180	+	0.401193i	−0.818750	+	0.574151i	$0.805332\pi$
$278$	−13.2498	−	21.9649i	−0.794671	−	1.31737i
$279$		0			0
$280$	0.0157102	+	0.272590i	0.000938863	+	0.0162904i
$281$	−20.5080	+	20.5080i	−1.22341	+	1.22341i	−0.256992	+	0.966413i	$0.582732\pi$
$281$	−20.5080	+	20.5080i	−1.22341	+	1.22341i	−0.966413	+	0.256992i	$0.917268\pi$
$282$		0			0
$283$	26.5696	−	11.0055i	1.57940	−	0.654209i	0.591082	−	0.806612i	$-0.298701\pi$
$283$	26.5696	−	11.0055i	1.57940	−	0.654209i	0.988319	+	0.152403i	$0.0487010\pi$
$284$	−4.92980	+	9.34979i	−0.292530	+	0.554808i
$285$		0			0
$286$	−1.14400	−	7.56479i	−0.0676461	−	0.447316i
$287$	0.300895			0.0177613
$288$		0			0
$289$	8.42431			0.495548
$290$	2.30949	+	15.2717i	0.135618	+	0.896786i
$291$		0			0
$292$	−27.1223	−	14.3006i	−1.58721	−	0.836879i
$293$	−25.9576	+	10.7520i	−1.51646	+	0.628138i	−0.976878	−	0.213797i	$-0.931417\pi$
$293$	−25.9576	+	10.7520i	−1.51646	+	0.628138i	−0.539580	+	0.841934i	$0.681417\pi$
$294$		0			0
$295$	1.87672	−	1.87672i	0.109267	−	0.109267i
$296$	3.91841	−	4.39770i	0.227753	−	0.255611i
$297$		0			0
$298$	9.69143	+	16.0660i	0.561409	+	0.930677i
$299$	−0.156708	−	0.378327i	−0.00906267	−	0.0218792i
$300$		0			0
$301$	−0.157775	−	0.0653525i	−0.00909399	−	0.00376686i
$302$	8.38948	+	6.18538i	0.482761	+	0.355928i
$303$		0			0
$304$	−6.56853	+	1.38396i	−0.376731	+	0.0793757i
$305$		−	27.9813i		−	1.60221i
$306$		0			0
$307$	14.8458	+	6.14934i	0.847296	+	0.350961i	0.763726	−	0.645540i	$-0.223368\pi$
$307$	14.8458	+	6.14934i	0.847296	+	0.350961i	0.0835699	+	0.996502i	$0.473368\pi$
$308$	−0.274464	−	0.0254661i	−0.0156390	−	0.00145107i
$309$		0			0
$310$	−9.96130	+	6.00892i	−0.565764	+	0.341284i
$311$	−0.108964	−	0.108964i	−0.00617877	−	0.00617877i	0.704011	−	0.710189i	$-0.251391\pi$
$311$	−0.108964	−	0.108964i	−0.00617877	−	0.00617877i	−0.710189	+	0.704011i	$0.751391\pi$
$312$		0			0
$313$	17.7967	−	17.7967i	1.00593	−	1.00593i	0.00594408	−	0.999982i	$-0.498108\pi$
$313$	17.7967	−	17.7967i	1.00593	−	1.00593i	0.999982	−	0.00594408i	$-0.00189207\pi$
$314$	1.47936	−	5.97758i	0.0834850	−	0.337334i
$315$		0			0
$316$	5.88195	+	19.0027i	0.330885	+	1.06898i
$317$	−0.847035	+	2.04492i	−0.0475742	+	0.114854i	−0.945880	−	0.324516i	$-0.894798\pi$
$317$	−0.847035	+	2.04492i	−0.0475742	+	0.114854i	0.898306	+	0.439371i	$0.144798\pi$
$318$		0			0
$319$	−15.5924			−0.873008
$320$	−4.20474	+	14.7579i	−0.235052	+	0.824991i
$321$		0			0
$322$	−0.0145875	+	0.00220602i	−0.000812929	+	0.000122937i
$323$	−1.88068	+	4.54035i	−0.104644	+	0.252632i
$324$		0			0
$325$	−2.41046	+	0.998447i	−0.133709	+	0.0553839i
$326$	−5.24701	+	21.2014i	−0.290605	+	1.17424i
$327$		0			0
$328$	15.9697	+	5.56173i	0.881781	+	0.307095i
$329$	−0.189936	−	0.189936i	−0.0104715	−	0.0104715i
$330$		0			0
$331$	−8.40430	−	20.2898i	−0.461942	−	1.11523i	−0.967599	−	0.252492i	$-0.918750\pi$
$331$	−8.40430	−	20.2898i	−0.461942	−	1.11523i	0.505657	−	0.862735i	$-0.331250\pi$
$332$	24.2415	+	2.24925i	1.33042	+	0.123443i
$333$		0			0
$334$	−10.8533	+	14.7208i	−0.593867	+	0.805486i
$335$			5.59733i			0.305815i
$336$		0			0
$337$			0.515293i			0.0280698i	0.999902	+	0.0140349i	$0.00446760\pi$
$337$			0.515293i			0.0280698i	−0.999902	+	0.0140349i	$0.995532\pi$
$338$	10.3554	+	7.63479i	0.563258	+	0.415278i
$339$		0			0
$340$	7.17597	+	8.64381i	0.389171	+	0.468776i
$341$	−4.49428	−	10.8501i	−0.243379	−	0.587568i
$342$		0			0
$343$	−0.498124	−	0.498124i	−0.0268962	−	0.0268962i
$344$	−7.16579	−	6.38483i	−0.386353	−	0.344247i
$345$		0			0
$346$	−1.97471	−	0.488711i	−0.106161	−	0.0262732i
$347$	−21.0299	+	8.71086i	−1.12894	+	0.467623i	−0.867421	−	0.497574i	$-0.834224\pi$
$347$	−21.0299	+	8.71086i	−1.12894	+	0.467623i	−0.261521	+	0.965198i	$0.584224\pi$
$348$		0			0
$349$	−9.27157	+	22.3835i	−0.496296	+	1.19816i	0.455169	+	0.890405i	$0.349579\pi$
$349$	−9.27157	+	22.3835i	−0.496296	+	1.19816i	−0.951465	+	0.307758i	$0.900421\pi$
$350$	0.0140554	+	0.0929425i	0.000751292	+	0.00496798i
$351$		0			0
$352$	−14.0962	−	6.42476i	−0.751330	−	0.342441i
$353$	−19.4215			−1.03370			−0.516851	−	0.856076i	$-0.672896\pi$
$353$	−19.4215			−1.03370			−0.516851	+	0.856076i	$0.672896\pi$
$354$		0			0
$355$	3.87936	−	9.36561i	0.205895	−	0.497075i
$356$	−7.91811	+	15.0174i	−0.419659	+	0.795920i
$357$		0			0
$358$	−28.2191	−	6.98378i	−1.49142	−	0.369104i
$359$	−11.9259	+	11.9259i	−0.629423	+	0.629423i	−0.947923	−	0.318500i	$-0.896821\pi$
$359$	−11.9259	+	11.9259i	−0.629423	+	0.629423i	0.318500	+	0.947923i	$0.396821\pi$
$360$		0			0
$361$	−11.4436	−	11.4436i	−0.602295	−	0.602295i
$362$	−6.32298	−	10.4819i	−0.332328	−	0.550918i
$363$		0			0
$364$	−0.152993	+	0.127013i	−0.00801901	+	0.00665727i
$365$	27.1682	+	11.2534i	1.42205	+	0.589032i
$366$		0			0
$367$			6.36872i			0.332445i	0.986088	+	0.166222i	$0.0531569\pi$
$367$			6.36872i			0.332445i	−0.986088	+	0.166222i	$0.946843\pi$
$368$	−0.814994	−	0.152552i	−0.0424845	−	0.00795232i
$369$		0			0
$370$	−3.35231	+	4.54688i	−0.174278	+	0.236381i
$371$	0.180760	+	0.0748733i	0.00938460	+	0.00388723i
$372$		0			0
$373$	6.20853	+	14.9887i	0.321465	+	0.776086i	0.999169	+	0.0407511i	$0.0129751\pi$
$373$	6.20853	+	14.9887i	0.321465	+	0.776086i	−0.677704	+	0.735335i	$0.737025\pi$
$374$	−9.71122	+	5.85806i	−0.502155	+	0.302913i
$375$		0			0
$376$	−6.56992	−	13.5914i	−0.338818	−	0.700925i
$377$	−7.95363	+	7.95363i	−0.409633	+	0.409633i
$378$		0			0
$379$	−0.643556	+	0.266570i	−0.0330573	+	0.0136928i	−0.399151	−	0.916885i	$-0.630695\pi$
$379$	−0.643556	+	0.266570i	−0.0330573	+	0.0136928i	0.366094	+	0.930578i	$0.380695\pi$
$380$	6.15013	−	1.90366i	0.315495	−	0.0976559i
$381$		0			0
$382$	−32.7917	+	4.95897i	−1.67777	+	0.253723i
$383$	5.97320			0.305216			0.152608	−	0.988287i	$-0.451233\pi$
$383$	5.97320			0.305216			0.152608	+	0.988287i	$0.451233\pi$
$384$		0			0
$385$	0.264362			0.0134731
$386$	3.61166	−	0.546179i	0.183829	−	0.0277998i
$387$		0			0
$388$	−7.05212	+	2.18286i	−0.358017	+	0.110818i
$389$	−17.5487	+	7.26889i	−0.889752	+	0.368547i	−0.780271	−	0.625441i	$-0.784919\pi$
$389$	−17.5487	+	7.26889i	−0.889752	+	0.368547i	−0.109481	+	0.993989i	$0.534919\pi$
$390$		0			0
$391$	−0.429232	+	0.429232i	−0.0217072	+	0.0217072i
$392$	−8.61354	−	17.8192i	−0.435050	−	0.900005i
$393$		0			0
$394$	−15.2402	+	9.19329i	−0.767790	+	0.463151i
$395$	−7.30087	−	17.6259i	−0.367347	−	0.886854i
$396$		0			0
$397$	9.55093	+	3.95613i	0.479348	+	0.198552i	0.609256	−	0.792974i	$-0.291468\pi$
$397$	9.55093	+	3.95613i	0.479348	+	0.198552i	−0.129908	+	0.991526i	$0.541468\pi$
$398$	9.19548	−	12.4722i	0.460928	−	0.625176i
$399$		0			0
$400$	−0.971967	+	5.19264i	−0.0485983	+	0.259632i
$401$			16.0262i			0.800308i	0.916448	+	0.400154i	$0.131043\pi$
$401$			16.0262i			0.800308i	−0.916448	+	0.400154i	$0.868957\pi$
$402$		0			0
$403$	−7.82712	−	3.24210i	−0.389897	−	0.161500i
$404$	−21.6633	+	17.9846i	−1.07779	+	0.894765i
$405$		0			0
$406$	0.209320	+	0.347001i	0.0103884	+	0.0172214i
$407$	−4.03253	−	4.03253i	−0.199885	−	0.199885i
$408$		0			0
$409$	−14.9468	+	14.9468i	−0.739071	+	0.739071i	−0.972398	−	0.233327i	$-0.925039\pi$
$409$	−14.9468	+	14.9468i	−0.739071	+	0.739071i	0.233327	+	0.972398i	$0.425039\pi$
$410$	−15.7435	−	3.89626i	−0.777514	−	0.192423i
$411$		0			0
$412$	−18.6521	+	35.3753i	−0.918922	+	1.74282i
$413$	0.0266486	−	0.0643355i	0.00131129	−	0.00316574i
$414$		0			0
$415$	−23.3492			−1.14617
$416$	−10.4677	+	3.91317i	−0.513219	+	0.191859i
$417$		0			0
$418$	0.971820	+	6.42625i	0.0475333	+	0.314318i
$419$	5.09708	−	12.3054i	0.249009	−	0.601160i	−0.749112	−	0.662444i	$-0.769519\pi$
$419$	5.09708	−	12.3054i	0.249009	−	0.601160i	0.998120	+	0.0612837i	$0.0195194\pi$
$420$		0			0
$421$	12.6398	−	5.23558i	0.616027	−	0.255167i	−0.0527763	−	0.998606i	$-0.516807\pi$
$421$	12.6398	−	5.23558i	0.616027	−	0.255167i	0.668803	+	0.743440i	$0.266807\pi$
$422$	−21.8491	−	5.40732i	−1.06360	−	0.263224i
$423$		0			0
$424$	8.20973	+	7.31500i	0.398700	+	0.355248i
$425$	2.73480	+	2.73480i	0.132657	+	0.132657i
$426$		0			0
$427$	−0.280950	−	0.678273i	−0.0135961	−	0.0328239i
$428$	10.6082	+	12.7781i	0.512765	+	0.617651i
$429$		0			0
$430$	7.40887	+	5.46239i	0.357288	+	0.263420i
$431$			10.9212i			0.526058i	0.964788	+	0.263029i	$0.0847215\pi$
$431$			10.9212i			0.526058i	−0.964788	+	0.263029i	$0.915279\pi$
$432$		0			0
$433$		−	15.4198i		−	0.741030i	−0.928826	−	0.370515i	$-0.879181\pi$
$433$		−	15.4198i		−	0.741030i	0.928826	−	0.370515i	$-0.120819\pi$
$434$	−0.181131	+	0.245675i	−0.00869456	+	0.0117928i
$435$		0			0
$436$	−6.08491	−	0.564589i	−0.291415	−	0.0270389i
$437$	0.133123	+	0.321387i	0.00636812	+	0.0153740i
$438$		0			0
$439$	−2.51199	−	2.51199i	−0.119891	−	0.119891i	0.644616	−	0.764507i	$-0.277017\pi$
$439$	−2.51199	−	2.51199i	−0.119891	−	0.119891i	−0.764507	+	0.644616i	$0.777017\pi$
$440$	14.0308	+	4.88645i	0.668890	+	0.232952i
$441$		0			0
$442$	−1.96548	+	7.94183i	−0.0934882	+	0.377754i
$443$	−17.3256	+	7.17648i	−0.823162	+	0.340965i	−0.754192	−	0.656654i	$-0.771971\pi$
$443$	−17.3256	+	7.17648i	−0.823162	+	0.340965i	−0.0689698	+	0.997619i	$0.521971\pi$
$444$		0			0
$445$	6.23093	−	15.0428i	0.295374	−	0.713096i
$446$	−11.3210	+	1.71204i	−0.536065	+	0.0810674i
$447$		0			0
$448$	0.0462545	+	0.399952i	0.00218532	+	0.0188960i
$449$	28.5759			1.34858			0.674291	−	0.738466i	$-0.264449\pi$
$449$	28.5759			1.34858			0.674291	+	0.738466i	$0.264449\pi$
$450$		0			0
$451$	6.26562	−	15.1265i	0.295036	−	0.712281i
$452$	−8.27693	−	26.7401i	−0.389314	−	1.25775i
$453$		0			0
$454$	−3.29185	+	13.3012i	−0.154494	+	0.624258i
$455$	0.134850	−	0.134850i	0.00632185	−	0.00632185i
$456$		0			0
$457$	−0.438434	−	0.438434i	−0.0205091	−	0.0205091i	0.696778	−	0.717287i	$-0.254616\pi$
$457$	−0.438434	−	0.438434i	−0.0205091	−	0.0205091i	−0.717287	+	0.696778i	$0.754616\pi$
$458$	−14.9404	+	9.01243i	−0.698118	+	0.421123i
$459$		0			0
$460$	0.791814	+	0.0734686i	0.0369185	+	0.00342549i
$461$	11.9681	+	4.95734i	0.557409	+	0.230886i	0.643560	−	0.765396i	$-0.277457\pi$
$461$	11.9681	+	4.95734i	0.557409	+	0.230886i	−0.0861508	+	0.996282i	$0.527457\pi$
$462$		0			0
$463$			7.85370i			0.364993i	0.983207	+	0.182496i	$0.0584178\pi$
$463$			7.85370i			0.364993i	−0.983207	+	0.182496i	$0.941582\pi$
$464$	4.69553	+	22.2858i	0.217985	+	1.03459i
$465$		0			0
$466$	−13.8417	−	10.2052i	−0.641206	−	0.472747i
$467$	5.86660	+	2.43003i	0.271474	+	0.112448i	0.514268	−	0.857630i	$-0.328064\pi$
$467$	5.86660	+	2.43003i	0.271474	+	0.112448i	−0.242794	+	0.970078i	$0.578064\pi$
$468$		0			0
$469$	0.0562007	+	0.135680i	0.00259511	+	0.00626514i
$470$	7.47839	+	12.3973i	0.344952	+	0.571846i
$471$		0			0
$472$	2.60352	−	2.92198i	0.119837	−	0.134495i
$473$	−6.57078	+	6.57078i	−0.302125	+	0.302125i
$474$		0			0
$475$	2.04768	−	0.848175i	0.0939538	−	0.0389169i
$476$	0.260736	+	0.137477i	0.0119508	+	0.00630123i
$477$		0			0
$478$	−5.46539	−	36.1404i	−0.249981	−	1.65302i
$479$	1.98328			0.0906184			0.0453092	−	0.998973i	$-0.485573\pi$
$479$	1.98328			0.0906184			0.0453092	+	0.998973i	$0.485573\pi$
$480$		0			0
$481$	−4.11396			−0.187580
$482$	5.40830	+	35.7629i	0.246341	+	1.62895i
$483$		0			0
$484$	3.26539	−	6.19310i	0.148427	−	0.281505i
$485$	6.54117	−	2.70944i	0.297019	−	0.123029i
$486$		0			0
$487$	4.91751	−	4.91751i	0.222834	−	0.222834i	−0.586857	−	0.809691i	$-0.699635\pi$
$487$	4.91751	−	4.91751i	0.222834	−	0.222834i	0.809691	+	0.586857i	$0.199635\pi$
$488$	−2.37400	−	41.1918i	−0.107466	−	1.86466i
$489$		0			0
$490$	9.80461	+	16.2536i	0.442927	+	0.734263i
$491$	12.9562	+	31.2791i	0.584706	+	1.41160i	0.888504	+	0.458868i	$0.151745\pi$
$491$	12.9562	+	31.2791i	0.584706	+	1.41160i	−0.303798	+	0.952736i	$0.598255\pi$
$492$		0			0
$493$	15.4046	+	6.38080i	0.693789	+	0.287377i
$494$	3.77372	+	2.78228i	0.169788	+	0.125181i
$495$		0			0
$496$	−14.1544	+	9.69098i	−0.635551	+	0.435138i
$497$		−	0.265976i		−	0.0119306i
$498$		0			0
$499$	33.8042	+	14.0021i	1.51328	+	0.626822i	0.976232	−	0.216728i	$-0.0695384\pi$
$499$	33.8042	+	14.0021i	1.51328	+	0.626822i	0.537051	+	0.843550i	$0.319538\pi$
$500$	2.24024	−	24.1444i	0.100187	−	1.07977i
$501$		0			0
$502$	33.4624	−	20.1854i	1.49350	−	0.900920i
$503$	−27.9286	−	27.9286i	−1.24528	−	1.24528i	−0.957782	−	0.287494i	$-0.907178\pi$
$503$	−27.9286	−	27.9286i	−1.24528	−	1.24528i	−0.287494	−	0.957782i	$-0.592822\pi$
$504$		0			0
$505$	19.0943	−	19.0943i	0.849684	−	0.849684i
$506$	−0.192859	+	0.779277i	−0.00857362	+	0.0346431i
$507$		0			0
$508$	−7.36650	+	2.28017i	−0.326836	+	0.101166i
$509$	−2.11556	+	5.10740i	−0.0937704	+	0.226382i	−0.963805	−	0.266610i	$-0.914097\pi$
$509$	−2.11556	+	5.10740i	−0.0937704	+	0.226382i	0.870034	+	0.492991i	$0.164097\pi$
$510$		0			0
$511$	0.771555			0.0341316
$512$	−4.93778	+	22.0821i	−0.218221	+	0.975899i
$513$		0			0
$514$	−9.15752	+	1.38486i	−0.403921	+	0.0610836i
$515$	14.6777	−	35.4351i	0.646777	−	1.56146i
$516$		0			0
$517$	−13.5035	+	5.59334i	−0.593884	+	0.245995i
$518$	−0.0356072	+	0.143877i	−0.00156449	+	0.00632157i
$519$		0			0
$520$	9.64958	−	4.66447i	0.423162	−	0.204551i
$521$	13.8505	+	13.8505i	0.606802	+	0.606802i	0.942109	−	0.335307i	$-0.108840\pi$
$521$	13.8505	+	13.8505i	0.606802	+	0.606802i	−0.335307	+	0.942109i	$0.608840\pi$
$522$		0			0
$523$	−0.594708	−	1.43575i	−0.0260048	−	0.0627810i	0.910344	−	0.413853i	$-0.135817\pi$
$523$	−0.594708	−	1.43575i	−0.0260048	−	0.0627810i	−0.936348	+	0.351072i	$0.885817\pi$
$524$	1.17133	−	12.6241i	0.0511698	−	0.551488i
$525$		0			0
$526$	−20.6025	+	27.9440i	−0.898311	+	1.21842i
$527$			12.5586i			0.547062i
$528$		0			0
$529$		−	22.9570i		−	0.998132i
$530$	−8.48823	−	6.25818i	−0.368705	−	0.271838i
$531$		0			0
$532$	0.129967	−	0.107896i	0.00563477	−	0.00467790i
$533$	−4.51992	−	10.9120i	−0.195779	−	0.472653i
$534$		0			0
$535$	−11.2627	−	11.2627i	−0.486930	−	0.486930i
$536$	0.474891	+	8.23993i	0.0205122	+	0.355911i
$537$		0			0
$538$	−2.94590	−	0.729065i	−0.127007	−	0.0314322i
$539$	−17.7039	+	7.33320i	−0.762561	+	0.315863i
$540$		0			0
$541$	7.61913	−	18.3942i	0.327572	−	0.790829i	−0.671199	−	0.741277i	$-0.734221\pi$
$541$	7.61913	−	18.3942i	0.327572	−	0.790829i	0.998772	−	0.0495523i	$-0.0157795\pi$
$542$	4.01863	+	26.5735i	0.172615	+	1.14143i
$543$		0			0
$544$	11.2972	+	12.1159i	0.484365	+	0.519464i
$545$	5.86095			0.251056
$546$		0			0
$547$	−6.58120	+	15.8884i	−0.281392	+	0.679340i	−0.999869	−	0.0162112i	$-0.994840\pi$
$547$	−6.58120	+	15.8884i	−0.281392	+	0.679340i	0.718477	+	0.695551i	$0.244840\pi$
$548$	−4.77904	−	2.51981i	−0.204151	−	0.107641i
$549$		0			0
$550$	4.96507	+	1.22878i	0.211711	+	0.0523952i
$551$	6.75656	−	6.75656i	0.287839	−	0.287839i
$552$		0			0
$553$	−0.353949	−	0.353949i	−0.0150515	−	0.0150515i
$554$	−5.27941	−	8.75195i	−0.224301	−	0.371835i
$555$		0			0
$556$	23.1722	+	27.9120i	0.982719	+	1.18373i
$557$	15.9135	+	6.59160i	0.674278	+	0.279295i	0.693433	−	0.720521i	$-0.256097\pi$
$557$	15.9135	+	6.59160i	0.674278	+	0.279295i	−0.0191546	+	0.999817i	$0.506097\pi$
$558$		0			0
$559$			6.70345i			0.283526i
$560$	−0.0796104	−	0.377845i	−0.00336416	−	0.0159669i
$561$		0			0
$562$	24.3400	−	33.0133i	1.02672	−	1.39258i
$563$	−6.34626	−	2.62871i	−0.267463	−	0.110787i	0.244922	−	0.969543i	$-0.421238\pi$
$563$	−6.34626	−	2.62871i	−0.267463	−	0.110787i	−0.512385	+	0.858756i	$0.671238\pi$
$564$		0			0
$565$	10.2736	+	24.8027i	0.432214	+	1.04346i
$566$	−34.8254	+	21.0076i	−1.46382	+	0.883017i
$567$		0			0
$568$	4.91628	−	14.1164i	0.206282	−	0.592312i
$569$	−19.2504	+	19.2504i	−0.807017	+	0.807017i	−0.984181	−	0.177164i	$-0.943308\pi$
$569$	−19.2504	+	19.2504i	−0.807017	+	0.807017i	0.177164	+	0.984181i	$0.443308\pi$
$570$		0			0
$571$	30.2725	−	12.5393i	1.26686	−	0.524752i	0.354855	−	0.934921i	$-0.384530\pi$
$571$	30.2725	−	12.5393i	1.26686	−	0.524752i	0.912010	+	0.410169i	$0.134530\pi$
$572$	3.19934	+	10.3360i	0.133771	+	0.432172i
$573$		0			0
$574$	−0.420746	+	0.0636280i	−0.0175616	+	0.00265578i
$575$	0.273765			0.0114168
$576$		0			0
$577$	−11.8128			−0.491775			−0.245887	−	0.969298i	$-0.579079\pi$
$577$	−11.8128			−0.491775			−0.245887	+	0.969298i	$0.579079\pi$
$578$	−11.7798	+	1.78143i	−0.489977	+	0.0740976i
$579$		0			0
$580$	−6.45879	−	20.8663i	−0.268187	−	0.866426i
$581$	−0.565990	+	0.234441i	−0.0234812	+	0.00972624i
$582$		0			0
$583$	7.52804	−	7.52804i	0.311780	−	0.311780i
$584$	40.9496	+	14.2614i	1.69451	+	0.590140i
$585$		0			0
$586$	34.0232	−	20.5237i	1.40549	−	0.847827i
$587$	−4.40174	−	10.6267i	−0.181679	−	0.438613i	0.806634	−	0.591052i	$-0.201287\pi$
$587$	−4.40174	−	10.6267i	−0.181679	−	0.438613i	−0.988313	+	0.152439i	$0.951287\pi$
$588$		0			0
$589$	6.64909	+	2.75415i	0.273971	+	0.113483i
$590$	−2.22739	+	3.02110i	−0.0917000	+	0.124377i
$591$		0			0
$592$	−4.54923	+	6.97796i	−0.186972	+	0.286792i
$593$		−	39.4599i		−	1.62042i	−0.586138	−	0.810211i	$-0.699352\pi$
$593$		−	39.4599i		−	1.62042i	0.586138	−	0.810211i	$-0.300648\pi$
$594$		0			0
$595$	−0.261177	−	0.108183i	−0.0107072	−	0.00443508i
$596$	−16.9490	−	20.4159i	−0.694259	−	0.836269i
$597$		0			0
$598$	0.299129	+	0.495882i	0.0122323	+	0.0202781i
$599$	−28.7816	−	28.7816i	−1.17598	−	1.17598i	−0.980758	−	0.195226i	$-0.937456\pi$
$599$	−28.7816	−	28.7816i	−1.17598	−	1.17598i	−0.195226	−	0.980758i	$-0.562544\pi$
$600$		0			0
$601$	15.1839	−	15.1839i	0.619365	−	0.619365i	−0.326003	−	0.945369i	$-0.605702\pi$
$601$	15.1839	−	15.1839i	0.619365	−	0.619365i	0.945369	+	0.326003i	$0.105702\pi$
$602$	0.234439	+	0.0580199i	0.00955500	+	0.00236471i
$603$		0			0
$604$	−13.0391	−	6.87504i	−0.530554	−	0.279741i
$605$	−2.56961	+	6.20358i	−0.104469	+	0.252211i
$606$		0			0
$607$	−26.6639			−1.08226			−0.541128	−	0.840940i	$-0.682002\pi$
$607$	−26.6639			−1.08226			−0.541128	+	0.840940i	$0.682002\pi$
$608$	8.89221	−	3.32421i	0.360627	−	0.134815i
$609$		0			0
$610$	5.91700	+	39.1267i	0.239572	+	1.58419i
$611$	−4.03495	+	9.74123i	−0.163237	+	0.394088i
$612$		0			0
$613$	−14.1048	+	5.84240i	−0.569687	+	0.235972i	−0.648885	−	0.760887i	$-0.724764\pi$
$613$	−14.1048	+	5.84240i	−0.569687	+	0.235972i	0.0791973	+	0.996859i	$0.474764\pi$
$614$	−22.0595	−	5.45938i	−0.890249	−	0.220323i
$615$		0			0
$616$	0.389172	−	0.0224291i	0.0156802	−	0.000903694i
$617$	14.1525	+	14.1525i	0.569758	+	0.569758i	0.932061	−	0.362302i	$-0.118009\pi$
$617$	14.1525	+	14.1525i	0.569758	+	0.569758i	−0.362302	+	0.932061i	$0.618009\pi$
$618$		0			0
$619$	5.05235	+	12.1975i	0.203071	+	0.490257i	0.992302	−	0.123839i	$-0.0395206\pi$
$619$	5.05235	+	12.1975i	0.203071	+	0.490257i	−0.789231	+	0.614096i	$0.789521\pi$
$620$	12.6584	−	10.5088i	0.508372	−	0.422044i
$621$		0			0
$622$	0.175407	+	0.129324i	0.00703319	+	0.00518541i
$623$		−	0.427203i		−	0.0171155i
$624$		0			0
$625$			16.6522i			0.666088i
$626$	−21.1220	+	28.6486i	−0.844205	+	1.14503i
$627$		0			0
$628$	−0.804574	+	8.67137i	−0.0321060	+	0.346025i
$629$	2.33375	+	5.63417i	0.0930527	+	0.224649i
$630$		0			0
$631$	23.2407	+	23.2407i	0.925199	+	0.925199i	0.997391	−	0.0721919i	$-0.0229994\pi$
$631$	23.2407	+	23.2407i	0.925199	+	0.925199i	−0.0721919	+	0.997391i	$0.522999\pi$
$632$	−12.2432	−	25.3279i	−0.487007	−	1.00749i
$633$		0			0
$634$	0.751997	−	3.03856i	0.0298656	−	0.120677i
$635$	6.83277	−	2.83023i	0.271150	−	0.112314i
$636$		0			0
$637$	−5.29005	+	12.7713i	−0.209599	+	0.506018i
$638$	21.8031	−	3.29721i	0.863193	−	0.130538i
$639$		0			0
$640$	2.75881	−	21.5253i	0.109052	−	0.850862i
$641$	33.3063			1.31552			0.657760	−	0.753227i	$-0.271504\pi$
$641$	33.3063			1.31552			0.657760	+	0.753227i	$0.271504\pi$
$642$		0			0
$643$	−1.26433	+	3.05237i	−0.0498605	+	0.120374i	−0.946847	−	0.321684i	$-0.895751\pi$
$643$	−1.26433	+	3.05237i	−0.0498605	+	0.120374i	0.896987	+	0.442057i	$0.145751\pi$
$644$	0.0199314	−	0.00616942i	0.000785408	−	0.000243109i
$645$		0			0
$646$	1.66966	−	6.74654i	0.0656920	−	0.265439i
$647$	−22.1668	+	22.1668i	−0.871465	+	0.871465i	−0.992632	−	0.121167i	$-0.961336\pi$
$647$	−22.1668	+	22.1668i	−0.871465	+	0.871465i	0.121167	+	0.992632i	$0.461336\pi$
$648$		0			0
$649$	−2.67935	−	2.67935i	−0.105174	−	0.105174i
$650$	3.15945	−	1.90587i	0.123924	−	0.0747542i
$651$		0			0
$652$	2.85368	−	30.7558i	0.111759	−	1.20449i
$653$	43.2891	+	17.9309i	1.69403	+	0.701692i	0.999836	−	0.0180930i	$-0.00575950\pi$
$653$	43.2891	+	17.9309i	1.69403	+	0.701692i	0.694197	+	0.719785i	$0.255759\pi$
$654$		0			0
$655$			12.1595i			0.475110i
$656$	−23.5068	−	4.40004i	−0.917787	−	0.171793i
$657$		0			0
$658$	0.305755	+	0.225426i	0.0119196	+	0.00878802i
$659$	17.3613	+	7.19128i	0.676299	+	0.280132i	0.694279	−	0.719706i	$-0.255723\pi$
$659$	17.3613	+	7.19128i	0.676299	+	0.280132i	−0.0179797	+	0.999838i	$0.505723\pi$
$660$		0			0
$661$	−19.0882	−	46.0829i	−0.742444	−	1.79242i	−0.595637	−	0.803254i	$-0.703100\pi$
$661$	−19.0882	−	46.0829i	−0.742444	−	1.79242i	−0.146807	−	0.989165i	$-0.546900\pi$
$662$	16.0424	+	26.5943i	0.623505	+	1.03362i
$663$		0			0
$664$	−34.3728	+	1.98101i	−1.33392	+	0.0768779i
$665$	−0.114554	+	0.114554i	−0.00444222	+	0.00444222i
$666$		0			0
$667$	1.09041	−	0.451661i	0.0422207	−	0.0174884i
$668$	12.0634	−	22.8794i	0.466749	−	0.885229i
$669$		0			0
$670$	−1.18363	−	7.82683i	−0.0457274	−	0.302377i
$671$	−39.9483			−1.54219
$672$		0			0
$673$	−26.2374			−1.01138			−0.505689	−	0.862716i	$-0.668762\pi$
$673$	−26.2374			−1.01138			−0.505689	+	0.862716i	$0.668762\pi$
$674$	−0.108965	−	0.720542i	−0.00419718	−	0.0277543i
$675$		0			0
$676$	−16.0945	−	8.48606i	−0.619021	−	0.326387i
$677$	−28.0984	+	11.6387i	−1.07991	+	0.447313i	−0.850477	−	0.526012i	$-0.823687\pi$
$677$	−28.0984	+	11.6387i	−1.07991	+	0.447313i	−0.229432	+	0.973325i	$0.573687\pi$
$678$		0			0
$679$	0.131355	−	0.131355i	0.00504093	−	0.00504093i
$680$	−11.8621	−	10.5693i	−0.454891	−	0.405315i
$681$		0			0
$682$	8.57881	+	14.2215i	0.328500	+	0.544571i
$683$	−11.2340	−	27.1214i	−0.429859	−	1.03777i	−0.979332	−	0.202259i	$-0.935172\pi$
$683$	−11.2340	−	27.1214i	−0.429859	−	1.03777i	0.549473	−	0.835511i	$-0.314828\pi$
$684$		0			0
$685$	4.78713	+	1.98289i	0.182907	+	0.0757625i
$686$	0.801869	+	0.591200i	0.0306155	+	0.0225721i
$687$		0			0
$688$	11.3702	+	7.41270i	0.433484	+	0.282607i
$689$		−	7.68004i		−	0.292586i
$690$		0			0
$691$	−35.4669	−	14.6909i	−1.34922	−	0.558867i	−0.413148	−	0.910664i	$-0.635571\pi$
$691$	−35.4669	−	14.6909i	−1.34922	−	0.558867i	−0.936076	+	0.351797i	$0.885571\pi$
$692$	2.86461	+	0.265793i	0.108896	+	0.0101039i
$693$		0			0
$694$	27.5644	−	16.6275i	1.04633	−	0.631173i
$695$	−24.6020	−	24.6020i	−0.933207	−	0.933207i
$696$		0			0
$697$	−12.3803	+	12.3803i	−0.468937	+	0.468937i
$698$	8.23129	−	33.2598i	0.311559	−	1.25890i
$699$		0			0
$700$	−0.0393077	−	0.126991i	−0.00148569	−	0.00479980i
$701$	−12.8945	+	31.1300i	−0.487017	+	1.17576i	0.469197	+	0.883094i	$0.344543\pi$
$701$	−12.8945	+	31.1300i	−0.487017	+	1.17576i	−0.956214	+	0.292669i	$0.905457\pi$
$702$		0			0
$703$	3.49478			0.131808
$704$	21.0695	+	6.00302i	0.794087	+	0.226247i
$705$		0			0
$706$	27.1573	−	4.10692i	1.02208	−	0.154566i
$707$	0.271131	−	0.654568i	0.0101969	−	0.0246176i
$708$		0			0
$709$	−37.5458	+	15.5520i	−1.41006	+	0.584067i	−0.952343	−	0.305029i	$-0.901334\pi$
$709$	−37.5458	+	15.5520i	−1.41006	+	0.584067i	−0.457720	+	0.889096i	$0.651334\pi$
$710$	−3.44409	+	13.9164i	−0.129255	+	0.522274i
$711$		0			0
$712$	7.89639	−	22.6734i	0.295930	−	0.849722i
$713$	0.628586	+	0.628586i	0.0235407	+	0.0235407i
$714$		0			0
$715$	−3.97113	−	9.58716i	−0.148512	−	0.358539i
$716$	40.9359	+	3.79824i	1.52985	+	0.141947i
$717$		0			0
$718$	14.1542	−	19.1980i	0.528231	−	0.716462i
$719$		−	17.6448i		−	0.658041i	−0.944323	−	0.329020i	$-0.893282\pi$
$719$		−	17.6448i		−	0.658041i	0.944323	−	0.329020i	$-0.106718\pi$
$720$		0			0
$721$		−	1.00633i		−	0.0374776i
$722$	18.4216	+	13.5819i	0.685583	+	0.505464i
$723$		0			0
$724$	11.0581	+	13.3200i	0.410969	+	0.495033i
$725$	−2.87771	−	6.94740i	−0.106875	−	0.258020i
$726$		0			0
$727$	22.5497	+	22.5497i	0.836323	+	0.836323i	0.988373	−	0.152050i	$-0.0485874\pi$
$727$	22.5497	+	22.5497i	0.836323	+	0.836323i	−0.152050	+	0.988373i	$0.548587\pi$
$728$	0.187074	−	0.209956i	0.00693341	−	0.00778148i
$729$		0			0
$730$	−40.3694	−	9.99080i	−1.49414	−	0.369776i
$731$	9.18055	−	3.80271i	0.339555	−	0.140648i
$732$		0			0
$733$	16.6634	−	40.2290i	0.615476	−	1.48589i	−0.241430	−	0.970418i	$-0.577616\pi$
$733$	16.6634	−	40.2290i	0.615476	−	1.48589i	0.856906	−	0.515473i	$-0.172384\pi$
$734$	−1.34675	−	8.90548i	−0.0497093	−	0.328707i
$735$		0			0
$736$	1.17188	+	0.0409749i	0.0431960	+	0.00151036i
$737$	7.99119			0.294359
$738$		0			0
$739$	−8.54690	+	20.6340i	−0.314403	+	0.759036i	0.685128	+	0.728422i	$0.259746\pi$
$739$	−8.54690	+	20.6340i	−0.314403	+	0.759036i	−0.999531	+	0.0306134i	$0.990254\pi$
$740$	3.72609	−	7.06685i	0.136974	−	0.259783i
$741$		0			0
$742$	−0.268593	−	0.0664725i	−0.00986034	−	0.00244028i
$743$	15.7640	−	15.7640i	0.578324	−	0.578324i	−0.356118	−	0.934441i	$-0.615900\pi$
$743$	15.7640	−	15.7640i	0.578324	−	0.578324i	0.934441	+	0.356118i	$0.115900\pi$
$744$		0			0
$745$	17.9948	+	17.9948i	0.659280	+	0.659280i
$746$	−11.8510	−	19.6461i	−0.433897	−	0.719293i
$747$		0			0
$748$	12.3406	−	10.2450i	0.451216	−	0.374593i
$749$	−0.386096	−	0.159926i	−0.0141076	−	0.00584358i
$750$		0			0
$751$		−	6.97779i		−	0.254623i	−0.991863	−	0.127312i	$-0.959365\pi$
$751$		−	6.97779i		−	0.254623i	0.991863	−	0.127312i	$-0.0406348\pi$
$752$	12.0609	+	17.6158i	0.439815	+	0.642383i
$753$		0			0
$754$	9.43978	−	12.8036i	0.343776	−	0.466278i
$755$	13.0612	+	5.41011i	0.475345	+	0.196894i
$756$		0			0
$757$	10.7333	+	25.9125i	0.390108	+	0.941805i	0.989915	+	0.141660i	$0.0452440\pi$
$757$	10.7333	+	25.9125i	0.390108	+	0.941805i	−0.599807	+	0.800145i	$0.704756\pi$
$758$	0.843525	−	0.508836i	0.0306382	−	0.0184818i
$759$		0			0
$760$	−8.19727	+	3.96244i	−0.297346	+	0.143733i
$761$	−6.32305	+	6.32305i	−0.229210	+	0.229210i	−0.812363	−	0.583152i	$-0.801819\pi$
$761$	−6.32305	+	6.32305i	−0.229210	+	0.229210i	0.583152	+	0.812363i	$0.301819\pi$
$762$		0			0
$763$	0.142071	−	0.0588476i	0.00514331	−	0.00213043i
$764$	44.8044	−	13.8684i	1.62097	−	0.501742i
$765$		0			0
$766$	−8.35241	+	1.26311i	−0.301785	+	0.0456379i
$767$	−2.73345			−0.0986992
$768$		0			0
$769$	9.25313			0.333676			0.166838	−	0.985984i	$-0.446644\pi$
$769$	9.25313			0.333676			0.166838	+	0.985984i	$0.446644\pi$
$770$	−0.369661	+	0.0559026i	−0.0133216	+	0.00201459i
$771$		0			0
$772$	−4.93474	+	1.52746i	−0.177605	+	0.0549745i
$773$	31.3565	−	12.9883i	1.12782	−	0.467157i	0.260778	−	0.965399i	$-0.416021\pi$
$773$	31.3565	−	12.9883i	1.12782	−	0.467157i	0.867038	+	0.498242i	$0.166021\pi$
$774$		0			0
$775$	4.00496	−	4.00496i	0.143862	−	0.143862i
$776$	9.39949	−	4.54358i	0.337422	−	0.163105i
$777$		0			0
$778$	23.0014	−	13.8751i	0.824642	−	0.497446i
$779$	3.83965	+	9.26972i	0.137570	+	0.332122i
$780$		0			0
$781$	−13.3711	−	5.53848i	−0.478455	−	0.198183i
$782$	0.509435	−	0.690968i	0.0182173	−	0.0247090i
$783$		0			0
$784$	15.8125	+	23.0954i	0.564733	+	0.824835i
$785$		−	8.35221i		−	0.298103i
$786$		0			0
$787$	16.1053	+	6.67103i	0.574092	+	0.237797i	0.650790	−	0.759258i	$-0.274438\pi$
$787$	16.1053	+	6.67103i	0.574092	+	0.237797i	−0.0766981	+	0.997054i	$0.524438\pi$
$788$	19.3666	−	16.0778i	0.689905	−	0.572749i
$789$		0			0
$790$	13.9361	+	23.1026i	0.495825	+	0.821955i
$791$	0.498069	+	0.498069i	0.0177093	+	0.0177093i
$792$		0			0
$793$	−20.3775	+	20.3775i	−0.723625	+	0.723625i
$794$	−14.1918	−	3.51224i	−0.503647	−	0.124645i
$795$		0			0
$796$	−10.2208	+	19.3846i	−0.362266	+	0.687068i
$797$	11.5489	−	27.8816i	0.409084	−	0.987616i	−0.576296	−	0.817241i	$-0.695502\pi$
$797$	11.5489	−	27.8816i	0.409084	−	0.987616i	0.985379	−	0.170374i	$-0.0544977\pi$
$798$		0			0
$799$	15.6298			0.552942
$800$	0.261067	−	7.46648i	0.00923010	−	0.263980i
$801$		0			0
$802$	−3.38893	−	22.4096i	−0.119667	−	0.791311i
$803$	16.0663	−	38.7875i	0.566968	−	1.36878i
$804$		0			0
$805$	−0.0184873	+	0.00765769i	−0.000651592	+	0.000269898i
$806$	11.6304	+	2.87833i	0.409662	+	0.101385i
$807$		0			0
$808$	26.4890	−	29.7290i	0.931881	−	1.04586i
$809$	25.3927	+	25.3927i	0.892761	+	0.892761i	0.994782	−	0.102021i	$-0.0325309\pi$
$809$	25.3927	+	25.3927i	0.892761	+	0.892761i	−0.102021	+	0.994782i	$0.532531\pi$
$810$		0			0
$811$	5.55699	+	13.4158i	0.195132	+	0.471091i	0.990915	−	0.134492i	$-0.0429402\pi$
$811$	5.55699	+	13.4158i	0.195132	+	0.471091i	−0.795783	+	0.605583i	$0.792940\pi$
$812$	−0.366073	−	0.440953i	−0.0128467	−	0.0154744i
$813$		0			0
$814$	6.49148	+	4.78602i	0.227526	+	0.167750i
$815$			29.6238i			1.03767i
$816$		0			0
$817$		−	5.69455i		−	0.199227i
$818$	17.7396	−	24.0610i	0.620252	−	0.841273i
$819$		0			0
$820$	22.8382	+	2.11905i	0.797546	+	0.0740003i
$821$	14.1598	+	34.1848i	0.494181	+	1.19306i	0.952574	+	0.304308i	$0.0984252\pi$
$821$	14.1598	+	34.1848i	0.494181	+	1.19306i	−0.458393	+	0.888749i	$0.651575\pi$
$822$		0			0
$823$	−17.3917	−	17.3917i	−0.606237	−	0.606237i	0.335724	−	0.941961i	$-0.391019\pi$
$823$	−17.3917	−	17.3917i	−0.606237	−	0.606237i	−0.941961	+	0.335724i	$0.891019\pi$
$824$	18.6009	−	53.4100i	0.647994	−	1.86063i
$825$		0			0
$826$	−0.0236586	+	0.0955964i	−0.000823189	+	0.00332622i
$827$	−48.7594	+	20.1968i	−1.69553	+	0.702312i	−0.999871	−	0.0160601i	$-0.994888\pi$
$827$	−48.7594	+	20.1968i	−1.69553	+	0.702312i	−0.695659	+	0.718372i	$0.744888\pi$
$828$		0			0
$829$	−11.7739	+	28.4248i	−0.408926	+	0.987235i	0.576495	+	0.817101i	$0.304420\pi$
$829$	−11.7739	+	28.4248i	−0.408926	+	0.987235i	−0.985421	+	0.170134i	$0.945580\pi$
$830$	32.6496	−	4.93748i	1.13328	−	0.171383i
$831$		0			0
$832$	13.8096	−	7.68535i	0.478761	−	0.266442i
$833$	20.4916			0.709991
$834$		0			0
$835$	−9.49298	+	22.9181i	−0.328518	+	0.793113i
$836$	−2.71782	−	8.78041i	−0.0939978	−	0.303677i
$837$		0			0
$838$	−4.52518	+	18.2847i	−0.156320	+	0.631635i
$839$	20.8789	−	20.8789i	0.720821	−	0.720821i	−0.247951	−	0.968772i	$-0.579757\pi$
$839$	20.8789	−	20.8789i	0.720821	−	0.720821i	0.968772	+	0.247951i	$0.0797573\pi$
$840$		0			0
$841$	−2.41770	−	2.41770i	−0.0833689	−	0.0833689i
$842$	−16.5673	+	9.99383i	−0.570947	+	0.344410i
$843$		0			0
$844$	31.6954	+	2.94086i	1.09100	+	0.101229i
$845$	16.1218	+	6.67786i	0.554606	+	0.229725i
$846$		0			0
$847$			0.176177i			0.00605350i
$848$	−13.0266	−	8.49262i	−0.447337	−	0.291638i
$849$		0			0
$850$	−4.40242	−	3.24580i	−0.151002	−	0.111330i
$851$	0.398812	+	0.165193i	0.0136711	+	0.00566275i
$852$		0			0
$853$	6.22774	+	15.0351i	0.213234	+	0.514791i	0.993917	−	0.110136i	$-0.0351286\pi$
$853$	6.22774	+	15.0351i	0.213234	+	0.514791i	−0.780683	+	0.624927i	$0.785129\pi$
$854$	0.536286	+	0.889029i	0.0183513	+	0.0304219i
$855$		0			0
$856$	−17.5356	−	15.6245i	−0.599356	−	0.534035i
$857$	14.5062	−	14.5062i	0.495522	−	0.495522i	−0.414519	−	0.910041i	$-0.636050\pi$
$857$	14.5062	−	14.5062i	0.495522	−	0.495522i	0.910041	+	0.414519i	$0.136050\pi$
$858$		0			0
$859$	−34.7675	+	14.4012i	−1.18625	+	0.491362i	−0.886533	−	0.462665i	$-0.846893\pi$
$859$	−34.7675	+	14.4012i	−1.18625	+	0.491362i	−0.299720	+	0.954027i	$0.596893\pi$
$860$	−11.5150	−	6.07145i	−0.392659	−	0.207035i
$861$		0			0
$862$	−2.30943	−	15.2713i	−0.0786596	−	0.520144i
$863$	49.6363			1.68964			0.844820	−	0.535051i	$-0.179708\pi$
$863$	49.6363			1.68964			0.844820	+	0.535051i	$0.179708\pi$
$864$		0			0
$865$	−2.75918			−0.0938149
$866$	3.26072	+	21.5618i	0.110804	+	0.732699i
$867$		0			0
$868$	0.201327	−	0.381834i	0.00683347	−	0.0129603i
$869$	−25.1641	+	10.4233i	−0.853633	+	0.353586i
$870$		0			0
$871$	4.07627	−	4.07627i	0.138119	−	0.138119i
$872$	8.62801	−	0.497258i	0.292181	−	0.0168393i
$873$		0			0
$874$	−0.254109	−	0.421249i	−0.00859535	−	0.0142490i
$875$	0.233502	+	0.563724i	0.00789381	+	0.0190574i
$876$		0			0
$877$	−13.2325	−	5.48109i	−0.446831	−	0.185083i	0.147910	−	0.989001i	$-0.452745\pi$
$877$	−13.2325	−	5.48109i	−0.446831	−	0.185083i	−0.594741	+	0.803917i	$0.702745\pi$
$878$	4.04375	+	2.98136i	0.136470	+	0.100616i
$879$		0			0
$880$	−20.6527	−	3.86581i	−0.696203	−	0.130316i
$881$		−	49.3124i		−	1.66138i	−0.556738	−	0.830688i	$-0.687947\pi$
$881$		−	49.3124i		−	1.66138i	0.556738	−	0.830688i	$-0.312053\pi$
$882$		0			0
$883$	−24.8481	−	10.2924i	−0.836204	−	0.346367i	−0.0768485	−	0.997043i	$-0.524486\pi$
$883$	−24.8481	−	10.2924i	−0.836204	−	0.346367i	−0.759356	+	0.650676i	$0.774486\pi$
$884$	1.06896	−	11.5208i	0.0359530	−	0.387486i
$885$		0			0
$886$	22.7090	−	13.6987i	0.762924	−	0.460216i
$887$	−12.9644	−	12.9644i	−0.435303	−	0.435303i	0.455124	−	0.890428i	$-0.349595\pi$
$887$	−12.9644	−	12.9644i	−0.435303	−	0.435303i	−0.890428	+	0.455124i	$0.849595\pi$
$888$		0			0
$889$	0.137211	−	0.137211i	0.00460189	−	0.00460189i
$890$	−5.53181	+	22.3522i	−0.185427	+	0.749246i
$891$		0			0
$892$	15.4683	−	4.78794i	0.517917	−	0.160312i
$893$	3.42767	−	8.27512i	0.114702	−	0.276916i
$894$		0			0
$895$	−39.4292			−1.31797
$896$	−0.149253	−	0.549478i	−0.00498620	−	0.0183568i
$897$		0			0
$898$	−39.9581	+	6.04274i	−1.33342	+	0.201649i
$899$	9.34432	−	22.5592i	0.311650	−	0.752391i
$900$		0			0
$901$	−10.5180	+	4.35671i	−0.350406	+	0.145143i
$902$	−5.56261	+	22.4766i	−0.185215	+	0.748389i
$903$		0			0
$904$	17.2283	+	35.6408i	0.573004	+	1.18540i
$905$	−11.7404	−	11.7404i	−0.390263	−	0.390263i
$906$		0			0
$907$	−0.243212	−	0.587166i	−0.00807573	−	0.0194965i	0.919790	−	0.392410i	$-0.128359\pi$
$907$	−0.243212	−	0.587166i	−0.00807573	−	0.0194965i	−0.927866	+	0.372914i	$0.878359\pi$
$908$	1.79033	−	19.2954i	0.0594141	−	0.640341i
$909$		0			0
$910$	−0.160047	+	0.217078i	−0.00530550	+	0.00719607i
$911$			6.49860i			0.215308i	0.994188	+	0.107654i	$0.0343339\pi$
$911$			6.49860i			0.215308i	−0.994188	+	0.107654i	$0.965666\pi$
$912$		0			0
$913$			33.3352i			1.10323i
$914$	0.705780	+	0.520356i	0.0233451	+	0.0172118i
$915$		0			0
$916$	18.9855	−	15.7615i	0.627300	−	0.520776i
$917$	0.122089	+	0.294748i	0.00403173	+	0.00973345i
$918$		0			0
$919$	−3.69820	−	3.69820i	−0.121992	−	0.121992i	0.643475	−	0.765467i	$-0.277492\pi$
$919$	−3.69820	−	3.69820i	−0.121992	−	0.121992i	−0.765467	+	0.643475i	$0.777492\pi$
$920$	−1.12274	+	0.0647069i	−0.0370157	+	0.00213332i
$921$		0			0
$922$	−17.7834	−	4.40112i	−0.585666	−	0.144943i
$923$	−9.64569	+	3.99538i	−0.317492	+	0.131509i
$924$		0			0
$925$	1.05251	−	2.54098i	0.0346063	−	0.0835470i
$926$	−1.66076	−	10.9819i	−0.0545761	−	0.360889i
$927$		0			0
$928$	−11.2785	−	30.1697i	−0.370233	−	0.990368i
$929$	−15.4821			−0.507951			−0.253976	−	0.967211i	$-0.581738\pi$
$929$	−15.4821			−0.507951			−0.253976	+	0.967211i	$0.581738\pi$
$930$		0			0
$931$	4.49387	−	10.8492i	0.147281	−	0.355567i
$932$	21.5131	+	11.3431i	0.704686	+	0.371555i
$933$		0			0
$934$	−8.71721	−	2.15737i	−0.285236	−	0.0705914i
$935$	−10.8771	+	10.8771i	−0.355720	+	0.355720i
$936$		0			0
$937$	34.9932	+	34.9932i	1.14318	+	1.14318i	0.987865	+	0.155312i	$0.0496384\pi$
$937$	34.9932	+	34.9932i	1.14318	+	1.14318i	0.155312	+	0.987865i	$0.450362\pi$
$938$	−0.107278	−	0.177840i	−0.00350274	−	0.00580667i
$939$		0			0
$940$	−13.0787	−	15.7539i	−0.426580	−	0.513837i
$941$	47.1330	+	19.5231i	1.53649	+	0.636435i	0.980811	−	0.194961i	$-0.0624580\pi$
$941$	47.1330	+	19.5231i	1.53649	+	0.636435i	0.555680	+	0.831396i	$0.312458\pi$
$942$		0			0
$943$			1.23932i			0.0403579i
$944$	−3.02266	+	4.63639i	−0.0983791	+	0.150902i
$945$		0			0
$946$	7.79854	−	10.5775i	0.253552	−	0.343904i
$947$	−6.54208	−	2.70982i	−0.212589	−	0.0880573i	0.273848	−	0.961773i	$-0.411704\pi$
$947$	−6.54208	−	2.70982i	−0.212589	−	0.0880573i	−0.486437	+	0.873716i	$0.661704\pi$
$948$		0			0
$949$	−11.5900	−	27.9807i	−0.376227	−	0.908292i
$950$	−2.68394	+	1.61902i	−0.0870784	+	0.0525280i
$951$		0			0
$952$	−0.393662	−	0.137100i	−0.0127587	−	0.00444342i
$953$	−7.54332	+	7.54332i	−0.244352	+	0.244352i	−0.818648	−	0.574296i	$-0.805276\pi$
$953$	−7.54332	+	7.54332i	−0.244352	+	0.244352i	0.574296	+	0.818648i	$0.305276\pi$
$954$		0			0
$955$	−41.5581	+	17.2139i	−1.34479	+	0.557030i
$956$	15.2847	+	49.3799i	0.494342	+	1.59706i
$957$		0			0
$958$	−2.77325	+	0.419390i	−0.0895997	+	0.0135499i
$959$	0.135951			0.00439007
$960$		0			0
$961$	−12.6086			−0.406729
$962$	5.75260	−	0.869947i	0.185471	−	0.0280482i
$963$		0			0
$964$	−15.1250	−	48.8641i	−0.487144	−	1.57381i
$965$	4.57720	−	1.89594i	0.147345	−	0.0610324i
$966$		0			0
$967$	−30.2181	+	30.2181i	−0.971749	+	0.971749i	−0.999612	−	0.0278625i	$-0.991130\pi$
$967$	−30.2181	+	30.2181i	−0.971749	+	0.971749i	0.0278625	+	0.999612i	$0.491130\pi$
$968$	−3.25644	+	9.35041i	−0.104666	+	0.300534i
$969$		0			0
$970$	−8.57366	+	5.17186i	−0.275284	+	0.166058i
$971$	−19.3720	−	46.7681i	−0.621676	−	1.50086i	−0.849734	−	0.527212i	$-0.823238\pi$
$971$	−19.3720	−	46.7681i	−0.621676	−	1.50086i	0.228058	−	0.973648i	$-0.426762\pi$
$972$		0			0
$973$	−0.843377	−	0.349338i	−0.0270374	−	0.0111993i
$974$	−5.83636	+	7.91609i	−0.187009	+	0.253648i
$975$		0			0
$976$	12.0301	+	57.0971i	0.385075	+	1.82763i
$977$			51.3451i			1.64267i	0.570443	+	0.821337i	$0.306772\pi$
$977$			51.3451i			1.64267i	−0.570443	+	0.821337i	$0.693228\pi$
$978$		0			0
$979$	−21.4763	−	8.89576i	−0.686384	−	0.284310i
$980$	−17.1470	−	20.6543i	−0.547739	−	0.659779i
$981$		0			0
$982$	−24.7312	−	40.9982i	−0.789205	−	1.30831i
$983$	−15.1725	−	15.1725i	−0.483928	−	0.483928i	0.422456	−	0.906383i	$-0.361168\pi$
$983$	−15.1725	−	15.1725i	−0.483928	−	0.483928i	−0.906383	+	0.422456i	$0.861168\pi$
$984$		0			0
$985$	−17.0699	+	17.0699i	−0.543893	+	0.543893i
$986$	−22.8898	−	5.66486i	−0.728959	−	0.180406i
$987$		0			0
$988$	−5.86520	−	3.09250i	−0.186597	−	0.0983856i
$989$	0.269173	−	0.649841i	0.00855920	−	0.0206637i
$990$		0			0
$991$	27.0706			0.859925			0.429962	−	0.902847i	$-0.358527\pi$
$991$	27.0706			0.859925			0.429962	+	0.902847i	$0.358527\pi$
$992$	17.7430	−	16.5442i	0.563342	−	0.525278i
$993$		0			0
$994$	0.0562439	+	0.371918i	0.00178395	+	0.0117965i
$995$	8.04294	−	19.4174i	0.254978	−	0.615572i
$996$		0			0
$997$	6.99450	−	2.89722i	0.221518	−	0.0917557i	−0.269164	−	0.963094i	$-0.586748\pi$
$997$	6.99450	−	2.89722i	0.221518	−	0.0917557i	0.490682	+	0.871338i	$0.336748\pi$
$998$	−50.2298	−	12.4311i	−1.59000	−	0.393499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.2	✓	128
3.2	odd	2	inner	864.2.v.b.109.31	yes	128
32.5	even	8	inner	864.2.v.b.325.2	yes	128
96.5	odd	8	inner	864.2.v.b.325.31	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.2	✓	128	1.1	even	1	trivial
864.2.v.b.109.31	yes	128	3.2	odd	2	inner
864.2.v.b.325.2	yes	128	32.5	even	8	inner
864.2.v.b.325.31	yes	128	96.5	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39831 + 0.211463i) q^{2} +(1.91057 - 0.591382i) q^{4} +(-1.77214 + 0.734044i) q^{5} +(-0.0355868 + 0.0355868i) q^{7} +(-2.54652 + 1.23095i) q^{8} +O(q^{10})\)	\(q+(-1.39831 + 0.211463i) q^{2} +(1.91057 - 0.591382i) q^{4} +(-1.77214 + 0.734044i) q^{5} +(-0.0355868 + 0.0355868i) q^{7} +(-2.54652 + 1.23095i) q^{8} +(2.32278 - 1.40116i) q^{10} +(1.04798 + 2.53004i) q^{11} +(1.82513 + 0.755995i) q^{13} +(0.0422362 - 0.0572867i) q^{14} +(3.30053 - 2.25975i) q^{16} -2.92843i q^{17} +(-1.55044 - 0.642214i) q^{19} +(-2.95169 + 2.45045i) q^{20} +(-2.00041 - 3.31619i) q^{22} +(-0.146574 - 0.146574i) q^{23} +(-0.933880 + 0.933880i) q^{25} +(-2.71198 - 0.671172i) q^{26} +(-0.0469455 + 0.0890363i) q^{28} +(-2.17892 + 5.26037i) q^{29} -4.28852 q^{31} +(-4.13733 + 3.85778i) q^{32} +(0.619253 + 4.09486i) q^{34} +(0.0369424 - 0.0891869i) q^{35} +(-1.92396 + 0.796930i) q^{37} +(2.30381 + 0.570157i) q^{38} +(3.60921 - 4.05067i) q^{40} +(-4.22763 - 4.22763i) q^{41} +(1.29855 + 3.13498i) q^{43} +(3.49846 + 4.21406i) q^{44} +(0.235952 + 0.173962i) q^{46} +5.33727i q^{47} +6.99747i q^{49} +(1.10838 - 1.50334i) q^{50} +(3.93412 + 0.365028i) q^{52} +(-1.48773 - 3.59170i) q^{53} +(-3.71433 - 3.71433i) q^{55} +(0.0468168 - 0.134428i) q^{56} +(1.93444 - 7.81641i) q^{58} +(-1.27834 + 0.529507i) q^{59} +(-5.58246 + 13.4772i) q^{61} +(5.99670 - 0.906861i) q^{62} +(4.96952 - 6.26928i) q^{64} -3.78932 q^{65} +(1.11670 - 2.69596i) q^{67} +(-1.73182 - 5.59496i) q^{68} +(-0.0327974 + 0.132523i) q^{70} +(-3.73700 + 3.73700i) q^{71} +(-10.8405 - 10.8405i) q^{73} +(2.52178 - 1.52120i) q^{74} +(-3.34202 - 0.310089i) q^{76} +(-0.127330 - 0.0527419i) q^{77} +9.94610i q^{79} +(-4.19025 + 6.42733i) q^{80} +(6.80554 + 5.01757i) q^{82} +(11.2462 + 4.65832i) q^{83} +(2.14959 + 5.18958i) q^{85} +(-2.47871 - 4.10909i) q^{86} +(-5.78306 - 5.15279i) q^{88} +(-6.00227 + 6.00227i) q^{89} +(-0.0918540 + 0.0380472i) q^{91} +(-0.366721 - 0.193358i) q^{92} +(-1.12863 - 7.46318i) q^{94} +3.21901 q^{95} -3.69111 q^{97} +(-1.47970 - 9.78466i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Introduction

L-functions

Modular forms

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Database

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