LMFDB - Embedded newform 896.2.bn.a.533.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			533.33
Character	$\chi$	$=$	896.533
Dual form			896.2.bn.a.701.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780122 - 1.17958i) q^{2} +(-2.05240 - 1.68436i) q^{3} +(-0.782820 - 1.84043i) q^{4} +(0.935806 + 3.08494i) q^{5} +(-3.58797 + 1.10697i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-2.78163 - 0.512363i) q^{8} +(0.790006 + 3.97163i) q^{9} +O(q^{10})$	\(q+(0.780122 - 1.17958i) q^{2} +(-2.05240 - 1.68436i) q^{3} +(-0.782820 - 1.84043i) q^{4} +(0.935806 + 3.08494i) q^{5} +(-3.58797 + 1.10697i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-2.78163 - 0.512363i) q^{8} +(0.790006 + 3.97163i) q^{9} +(4.36898 + 1.30277i) q^{10} +(-0.108975 + 1.10644i) q^{11} +(-1.49330 + 5.09586i) q^{12} +(-0.228184 - 0.0692188i) q^{13} +(-0.995257 + 1.00472i) q^{14} +(3.27551 - 7.90778i) q^{15} +(-2.77439 + 2.88145i) q^{16} +(2.83004 + 6.83233i) q^{17} +(5.30115 + 2.16648i) q^{18} +(0.240654 + 0.450231i) q^{19} +(4.94506 - 4.13724i) q^{20} +(1.68436 + 2.05240i) q^{21} +(1.22012 + 0.991700i) q^{22} +(2.73135 - 4.08775i) q^{23} +(4.84602 + 5.73686i) q^{24} +(-4.48377 + 2.99596i) q^{25} +(-0.259660 + 0.215162i) q^{26} +(1.31347 - 2.45733i) q^{27} +(0.408727 + 1.95779i) q^{28} +(3.86465 - 0.380634i) q^{29} +(-6.77256 - 10.0328i) q^{30} +(4.85055 + 4.85055i) q^{31} +(1.23455 + 5.52050i) q^{32} +(2.08730 - 2.08730i) q^{33} +(10.2671 + 1.99178i) q^{34} +(-0.315983 - 3.20823i) q^{35} +(6.69108 - 4.56302i) q^{36} +(3.38748 + 1.81065i) q^{37} +(0.718823 + 0.0673650i) q^{38} +(0.351736 + 0.526410i) q^{39} +(-1.02246 - 9.06064i) q^{40} +(-4.05457 - 2.70918i) q^{41} +(3.73498 - 0.385718i) q^{42} +(-5.01910 + 4.11907i) q^{43} +(2.12163 - 0.665580i) q^{44} +(-11.5129 + 6.15379i) q^{45} +(-2.69104 - 6.41078i) q^{46} +(5.66264 - 2.34554i) q^{47} +(10.5476 - 1.24083i) q^{48} +(0.923880 + 0.382683i) q^{49} +(0.0360876 + 7.62618i) q^{50} +(5.69973 - 18.7895i) q^{51} +(0.0512342 + 0.474143i) q^{52} +(-9.00762 - 0.887173i) q^{53} +(-1.87395 - 3.46635i) q^{54} +(-3.51527 + 0.699231i) q^{55} +(2.62823 + 1.04519i) q^{56} +(0.264435 - 1.32940i) q^{57} +(2.56591 - 4.85560i) q^{58} +(4.12119 - 1.25015i) q^{59} +(-17.1179 + 0.162009i) q^{60} +(0.821257 - 1.00071i) q^{61} +(9.50564 - 1.93759i) q^{62} -4.04944i q^{63} +(7.47497 + 2.85041i) q^{64} -0.768709i q^{65} +(-0.833790 - 4.09049i) q^{66} +(-9.43657 + 11.4985i) q^{67} +(10.3590 - 10.5570i) q^{68} +(-12.4911 + 3.78913i) q^{69} +(-4.03087 - 2.13008i) q^{70} +(-0.396757 + 1.99463i) q^{71} +(-0.162590 - 11.4524i) q^{72} +(6.48751 - 1.29045i) q^{73} +(4.77845 - 2.58328i) q^{74} +(14.2488 + 1.40338i) q^{75} +(0.640232 - 0.795356i) q^{76} +(0.322736 - 1.06392i) q^{77} +(0.895339 - 0.00423680i) q^{78} +(-2.77013 - 1.14743i) q^{79} +(-11.4854 - 5.86233i) q^{80} +(4.38878 - 1.81789i) q^{81} +(-6.35875 + 2.66920i) q^{82} +(5.54771 - 2.96531i) q^{83} +(2.45876 - 4.70662i) q^{84} +(-18.4289 + 15.1242i) q^{85} +(0.943262 + 9.13380i) q^{86} +(-8.57294 - 5.72825i) q^{87} +(0.870025 - 3.02187i) q^{88} +(5.44352 + 8.14681i) q^{89} +(-1.72260 + 18.3811i) q^{90} +(0.210296 + 0.112405i) q^{91} +(-9.66138 - 1.82689i) q^{92} +(-1.78519 - 18.1254i) q^{93} +(1.65079 - 8.50935i) q^{94} +(-1.16373 + 1.16373i) q^{95} +(6.76474 - 13.4097i) q^{96} +(6.79018 + 6.79018i) q^{97} +(1.17214 - 0.791250i) q^{98} +(-4.48045 + 0.441285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q+O(q^{10}) $ 752 * q	$ 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) $ 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{32}\right)$

Coefficient data

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

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

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

$2$	0.780122	−	1.17958i	0.551629	−	0.834089i
$2$	0.780122	−	1.17958i	0.551629	−	0.834089i
$3$	−2.05240	−	1.68436i	−1.18496	−	0.972468i	−0.185008	−	0.982737i	$-0.559231\pi$
$3$	−2.05240	−	1.68436i	−1.18496	−	0.972468i	−0.999947	+	0.0102695i	$0.996731\pi$
$4$	−0.782820	−	1.84043i	−0.391410	−	0.920216i
$5$	0.935806	+	3.08494i	0.418505	+	1.37963i	0.872496	+	0.488621i	$0.162500\pi$
$5$	0.935806	+	3.08494i	0.418505	+	1.37963i	−0.453991	+	0.891006i	$0.650000\pi$
$6$	−3.58797	+	1.10697i	−1.46478	+	0.451917i
$7$	−0.980785	−	0.195090i	−0.370702	−	0.0737372i
$7$	−0.980785	−	0.195090i	−0.370702	−	0.0737372i
$8$	−2.78163	−	0.512363i	−0.983456	−	0.181148i
$9$	0.790006	+	3.97163i	0.263335	+	1.32388i
$10$	4.36898	+	1.30277i	1.38159	+	0.411972i
$11$	−0.108975	+	1.10644i	−0.0328571	+	0.333603i	0.964678	+	0.263432i	$0.0848545\pi$
$11$	−0.108975	+	1.10644i	−0.0328571	+	0.333603i	−0.997535	+	0.0701711i	$0.977645\pi$
$12$	−1.49330	+	5.09586i	−0.431078	+	1.47105i
$13$	−0.228184	−	0.0692188i	−0.0632868	−	0.0191979i	0.258483	−	0.966016i	$-0.416778\pi$
$13$	−0.228184	−	0.0692188i	−0.0632868	−	0.0191979i	−0.321769	+	0.946818i	$0.604278\pi$
$14$	−0.995257	+	1.00472i	−0.265994	+	0.268523i
$15$	3.27551	−	7.90778i	0.845732	−	2.04178i
$16$	−2.77439	+	2.88145i	−0.693597	+	0.720364i
$17$	2.83004	+	6.83233i	0.686386	+	1.65708i	0.751939	+	0.659233i	$0.229119\pi$
$17$	2.83004	+	6.83233i	0.686386	+	1.65708i	−0.0655526	+	0.997849i	$0.520881\pi$
$18$	5.30115	+	2.16648i	1.24949	+	0.510644i
$19$	0.240654	+	0.450231i	0.0552097	+	0.103290i	0.908013	−	0.418943i	$-0.137599\pi$
$19$	0.240654	+	0.450231i	0.0552097	+	0.103290i	−0.852803	+	0.522233i	$0.825099\pi$
$20$	4.94506	−	4.13724i	1.10575	−	0.925115i
$21$	1.68436	+	2.05240i	0.367558	+	0.447871i
$22$	1.22012	+	0.991700i	0.260130	+	0.211431i
$23$	2.73135	−	4.08775i	0.569525	−	0.852354i	−0.429181	−	0.903219i	$-0.641198\pi$
$23$	2.73135	−	4.08775i	0.569525	−	0.852354i	0.998706	+	0.0508644i	$0.0161976\pi$
$24$	4.84602	+	5.73686i	0.989191	+	1.17103i
$25$	−4.48377	+	2.99596i	−0.896754	+	0.599192i
$26$	−0.259660	+	0.215162i	−0.0509236	+	0.0421968i
$27$	1.31347	−	2.45733i	0.252777	−	0.472912i
$28$	0.408727	+	1.95779i	0.0772422	+	0.369988i
$29$	3.86465	−	0.380634i	0.717647	−	0.0706820i	0.267399	−	0.963586i	$-0.413836\pi$
$29$	3.86465	−	0.380634i	0.717647	−	0.0706820i	0.450248	+	0.892904i	$0.351336\pi$
$30$	−6.77256	−	10.0328i	−1.23649	−	1.83172i
$31$	4.85055	+	4.85055i	0.871185	+	0.871185i	0.992602	−	0.121417i	$-0.0387437\pi$
$31$	4.85055	+	4.85055i	0.871185	+	0.871185i	−0.121417	+	0.992602i	$0.538744\pi$
$32$	1.23455	+	5.52050i	0.218239	+	0.975895i
$33$	2.08730	−	2.08730i	0.363353	−	0.363353i
$34$	10.2671	+	1.99178i	1.76079	+	0.341588i
$35$	−0.315983	−	3.20823i	−0.0534109	−	0.542290i
$36$	6.69108	−	4.56302i	1.11518	−	0.760503i
$37$	3.38748	+	1.81065i	0.556899	+	0.297669i	0.725734	−	0.687976i	$-0.241500\pi$
$37$	3.38748	+	1.81065i	0.556899	+	0.297669i	−0.168835	+	0.985644i	$0.554000\pi$
$38$	0.718823	+	0.0673650i	0.116608	+	0.0109280i
$39$	0.351736	+	0.526410i	0.0563228	+	0.0842930i
$40$	−1.02246	−	9.06064i	−0.161665	−	1.43261i
$41$	−4.05457	−	2.70918i	−0.633218	−	0.423103i	0.197107	−	0.980382i	$-0.436845\pi$
$41$	−4.05457	−	2.70918i	−0.633218	−	0.423103i	−0.830325	+	0.557279i	$0.811845\pi$
$42$	3.73498	−	0.385718i	0.576320	−	0.0595175i
$43$	−5.01910	+	4.11907i	−0.765405	+	0.628152i	−0.933893	−	0.357552i	$-0.883611\pi$
$43$	−5.01910	+	4.11907i	−0.765405	+	0.628152i	0.168488	+	0.985704i	$0.446111\pi$
$44$	2.12163	−	0.665580i	0.319848	−	0.100340i
$45$	−11.5129	+	6.15379i	−1.71625	+	0.917353i
$46$	−2.69104	−	6.41078i	−0.396773	−	0.945218i
$47$	5.66264	−	2.34554i	0.825981	−	0.342133i	0.0706707	−	0.997500i	$-0.477486\pi$
$47$	5.66264	−	2.34554i	0.825981	−	0.342133i	0.755311	+	0.655367i	$0.227486\pi$
$48$	10.5476	−	1.24083i	1.52241	−	0.179098i
$49$	0.923880	+	0.382683i	0.131983	+	0.0546691i
$50$	0.0360876	+	7.62618i	0.00510356	+	1.07851i
$51$	5.69973	−	18.7895i	0.798122	−	2.63106i
$52$	0.0512342	+	0.474143i	0.00710491	+	0.0657518i
$53$	−9.00762	−	0.887173i	−1.23729	−	0.121863i	−0.541868	−	0.840463i	$-0.682283\pi$
$53$	−9.00762	−	0.887173i	−1.23729	−	0.121863i	−0.695423	+	0.718601i	$0.744783\pi$
$54$	−1.87395	−	3.46635i	−0.255012	−	0.471711i
$55$	−3.51527	+	0.699231i	−0.473999	+	0.0942843i
$56$	2.62823	+	1.04519i	0.351212	+	0.139669i
$57$	0.264435	−	1.32940i	0.0350252	−	0.176084i
$58$	2.56591	−	4.85560i	0.336920	−	0.637572i
$59$	4.12119	−	1.25015i	0.536533	−	0.162755i	−0.0103782	−	0.999946i	$-0.503304\pi$
$59$	4.12119	−	1.25015i	0.536533	−	0.162755i	0.546911	+	0.837191i	$0.315804\pi$
$60$	−17.1179	+	0.162009i	−2.20991	+	0.0209153i
$61$	0.821257	−	1.00071i	0.105151	−	0.128127i	−0.717776	−	0.696274i	$-0.754840\pi$
$61$	0.821257	−	1.00071i	0.105151	−	0.128127i	0.822927	+	0.568147i	$0.192340\pi$
$62$	9.50564	−	1.93759i	1.20722	−	0.246075i
$63$		−	4.04944i		−	0.510181i
$64$	7.47497	+	2.85041i	0.934371	+	0.356302i
$65$		−	0.768709i		−	0.0953466i
$66$	−0.833790	−	4.09049i	−0.102632	−	0.503504i
$67$	−9.43657	+	11.4985i	−1.15286	+	1.40477i	−0.253624	+	0.967303i	$0.581623\pi$
$67$	−9.43657	+	11.4985i	−1.15286	+	1.40477i	−0.899237	+	0.437462i	$0.855877\pi$
$68$	10.3590	−	10.5570i	1.25622	−	1.28022i
$69$	−12.4911	+	3.78913i	−1.50375	+	0.456157i
$70$	−4.03087	−	2.13008i	−0.481781	−	0.254594i
$71$	−0.396757	+	1.99463i	−0.0470863	+	0.236719i	−0.997161	−	0.0753050i	$-0.976007\pi$
$71$	−0.396757	+	1.99463i	−0.0470863	+	0.236719i	0.950074	+	0.312024i	$0.101007\pi$
$72$	−0.162590	−	11.4524i	−0.0191614	−	1.34968i
$73$	6.48751	−	1.29045i	0.759306	−	0.151035i	0.199771	−	0.979843i	$-0.435980\pi$
$73$	6.48751	−	1.29045i	0.759306	−	0.151035i	0.559534	+	0.828807i	$0.310980\pi$
$74$	4.77845	−	2.58328i	0.555484	−	0.300301i
$75$	14.2488	+	1.40338i	1.64531	+	0.162049i
$76$	0.640232	−	0.795356i	0.0734396	−	0.0912336i
$77$	0.322736	−	1.06392i	0.0367792	−	0.121245i
$78$	0.895339	−	0.00423680i	0.101377	−	0.000479723i
$79$	−2.77013	−	1.14743i	−0.311664	−	0.129095i	0.221368	−	0.975190i	$-0.428948\pi$
$79$	−2.77013	−	1.14743i	−0.311664	−	0.129095i	−0.533033	+	0.846095i	$0.678948\pi$
$80$	−11.4854	−	5.86233i	−1.28411	−	0.655429i
$81$	4.38878	−	1.81789i	0.487642	−	0.201988i
$82$	−6.35875	+	2.66920i	−0.702207	+	0.294764i
$83$	5.54771	−	2.96531i	0.608940	−	0.325485i	−0.137943	−	0.990440i	$-0.544049\pi$
$83$	5.54771	−	2.96531i	0.608940	−	0.325485i	0.746884	+	0.664955i	$0.231549\pi$
$84$	2.45876	−	4.70662i	0.268272	−	0.513534i
$85$	−18.4289	+	15.1242i	−1.99890	+	1.64045i
$86$	0.943262	+	9.13380i	0.101715	+	0.984923i
$87$	−8.57294	−	5.72825i	−0.919115	−	0.614133i
$88$	0.870025	−	3.02187i	0.0927450	−	0.322132i
$89$	5.44352	+	8.14681i	0.577012	+	0.863560i	0.999075	−	0.0430069i	$-0.0136937\pi$
$89$	5.44352	+	8.14681i	0.577012	+	0.863560i	−0.422063	+	0.906567i	$0.638694\pi$
$90$	−1.72260	+	18.3811i	−0.181578	+	1.93754i
$91$	0.210296	+	0.112405i	0.0220450	+	0.0117833i
$92$	−9.66138	−	1.82689i	−1.00727	−	0.190466i
$93$	−1.78519	−	18.1254i	−0.185116	−	1.87951i
$94$	1.65079	−	8.50935i	0.170266	−	0.877673i
$95$	−1.16373	+	1.16373i	−0.119396	+	0.119396i
$96$	6.76474	−	13.4097i	0.690423	−	1.36862i
$97$	6.79018	+	6.79018i	0.689439	+	0.689439i	0.962108	−	0.272669i	$-0.0879064\pi$
$97$	6.79018	+	6.79018i	0.689439	+	0.689439i	−0.272669	+	0.962108i	$0.587906\pi$
$98$	1.17214	−	0.791250i	0.118404	−	0.0799284i
$99$	−4.48045	+	0.441285i	−0.450302	+	0.0443508i
$100$	9.02385	+	5.90678i	0.902385	+	0.590678i
$101$	−6.40676	+	11.9862i	−0.637497	+	1.19267i	0.330997	+	0.943632i	$0.392615\pi$
$101$	−6.40676	+	11.9862i	−0.637497	+	1.19267i	−0.968493	+	0.249040i	$0.919885\pi$
$102$	−17.7172	−	21.3814i	−1.75427	−	2.11707i
$103$	−13.7238	+	9.16992i	−1.35224	+	0.903539i	−0.999482	−	0.0321750i	$-0.989757\pi$
$103$	−13.7238	+	9.16992i	−1.35224	+	0.903539i	−0.352759	+	0.935714i	$0.614757\pi$
$104$	0.599259	+	0.309455i	0.0587622	+	0.0303445i
$105$	−4.75530	+	7.11681i	−0.464070	+	0.694530i
$106$	−8.07353	+	9.93310i	−0.784171	+	0.964788i
$107$	−7.27076	−	8.85945i	−0.702891	−	0.856475i	0.292105	−	0.956386i	$-0.405644\pi$
$107$	−7.27076	−	8.85945i	−0.702891	−	0.856475i	−0.994996	+	0.0999110i	$0.968144\pi$
$108$	−5.55075	−	0.493707i	−0.534121	−	0.0475070i
$109$	6.84910	+	12.8138i	0.656025	+	1.22734i	0.961413	+	0.275108i	$0.0887136\pi$
$109$	6.84910	+	12.8138i	0.656025	+	1.22734i	−0.305389	+	0.952228i	$0.598786\pi$
$110$	−1.91754	+	4.69203i	−0.182830	+	0.447367i
$111$	−3.90269	−	9.42193i	−0.370427	−	0.894290i
$112$	3.28322	−	2.28483i	0.310235	−	0.215896i
$113$	3.48411	−	8.41139i	0.327758	−	0.791277i	−0.671000	−	0.741457i	$-0.734135\pi$
$113$	3.48411	−	8.41139i	0.327758	−	0.791277i	0.998758	−	0.0498203i	$-0.0158649\pi$
$114$	−1.36185	−	1.34902i	−0.127549	−	0.126347i
$115$	15.1665	+	4.60070i	1.41428	+	0.429017i
$116$	−3.72585	−	6.81465i	−0.345937	−	0.632725i
$117$	0.0946448	−	0.960945i	0.00874991	−	0.0888394i
$118$	1.74038	−	5.83654i	0.160215	−	0.537297i
$119$	−1.44274	−	7.25316i	−0.132256	−	0.664896i
$120$	−13.1629	+	20.3183i	−1.20160	+	1.85480i
$121$	9.57631	+	1.90485i	0.870574	+	0.173168i
$122$	−0.539731	−	1.74941i	−0.0488650	−	0.158384i
$123$	3.75837	+	12.3897i	0.338881	+	1.11714i
$124$	5.13001	−	12.7242i	0.460688	−	1.14267i
$125$	−0.978323	−	0.802889i	−0.0875038	−	0.0718126i
$126$	−4.77663	−	3.15905i	−0.425536	−	0.281431i
$127$	11.3618			1.00819			0.504097	−	0.863647i	$-0.331826\pi$
$127$	11.3618			1.00819			0.504097	+	0.863647i	$0.331826\pi$
$128$	9.19368	−	6.59365i	0.812614	−	0.582802i
$129$	17.2392			1.51783
$130$	−0.906754	−	0.599687i	−0.0795276	−	0.0525960i
$131$	16.3399	+	13.4098i	1.42762	+	1.17162i	0.957290	+	0.289129i	$0.0933658\pi$
$131$	16.3399	+	13.4098i	1.42762	+	1.17162i	0.470332	+	0.882490i	$0.344134\pi$
$132$	−5.47552	−	2.20756i	−0.476583	−	0.192143i
$133$	−0.148194	−	0.488529i	−0.0128500	−	0.0423609i
$134$	6.20173	+	20.1014i	0.535747	+	1.73650i
$135$	8.80985	+	1.75239i	0.758231	+	0.150822i
$136$	−4.37151	−	20.4550i	−0.374853	−	1.75400i
$137$	−2.51809	−	12.6593i	−0.215135	−	1.08156i	−0.925796	−	0.378023i	$-0.876604\pi$
$137$	−2.51809	−	12.6593i	−0.215135	−	1.08156i	0.710661	−	0.703535i	$-0.248396\pi$
$138$	−5.27498	+	17.6902i	−0.449036	+	1.50589i
$139$	0.267308	−	2.71402i	0.0226727	−	0.230200i	−0.977170	−	0.212459i	$-0.931853\pi$
$139$	0.267308	−	2.71402i	0.0226727	−	0.230200i	0.999843	−	0.0177407i	$-0.00564734\pi$
$140$	−5.65717	+	3.09301i	−0.478119	+	0.261407i
$141$	−15.5728	−	4.72395i	−1.31146	−	0.397828i
$142$	2.04331	+	2.02406i	0.171471	+	0.169855i
$143$	0.101453	−	0.244928i	0.00848389	−	0.0204819i
$144$	−13.6358	−	8.74246i	−1.13632	−	0.728539i
$145$	4.79079	+	11.5660i	0.397854	+	0.960504i
$146$	3.53886	−	8.65924i	0.292878	−	0.716644i
$147$	−1.25159	−	2.34157i	−0.103230	−	0.193129i
$148$	0.680587	−	7.65185i	0.0559439	−	0.628978i
$149$	1.67594	+	2.04214i	0.137298	+	0.167298i	0.837120	−	0.547019i	$-0.184237\pi$
$149$	1.67594	+	2.04214i	0.137298	+	0.167298i	−0.699822	+	0.714317i	$0.746737\pi$
$150$	12.7712	−	15.7128i	1.04276	−	1.28294i
$151$	−9.28800	+	13.9005i	−0.755847	+	1.13120i	0.231532	+	0.972827i	$0.425626\pi$
$151$	−9.28800	+	13.9005i	−0.755847	+	1.13120i	−0.987379	+	0.158377i	$0.949374\pi$
$152$	−0.438728	−	1.37568i	−0.0355855	−	0.111582i
$153$	−24.8997	+	16.6374i	−2.01302	+	1.34506i
$154$	−1.00320	−	1.21068i	−0.0808404	−	0.0975592i
$155$	−10.4245	+	19.5028i	−0.837315	+	1.56651i
$156$	0.693476	−	1.05943i	0.0555225	−	0.0848222i
$157$	−12.3540	+	1.21676i	−0.985954	+	0.0971080i	−0.578123	−	0.815950i	$-0.696215\pi$
$157$	−12.3540	+	1.21676i	−0.985954	+	0.0971080i	−0.407831	+	0.913058i	$0.633715\pi$
$158$	−3.51452	+	2.37246i	−0.279600	+	0.188743i
$159$	16.9929	+	16.9929i	1.34763	+	1.34763i
$160$	−15.8751	+	8.97462i	−1.25504	+	0.709506i
$161$	−3.47634	+	3.47634i	−0.273974	+	0.273974i
$162$	1.27943	−	6.59509i	0.100522	−	0.518160i
$163$	−0.810536	−	8.22951i	−0.0634861	−	0.644585i	−0.973295	−	0.229558i	$-0.926272\pi$
$163$	−0.810536	−	8.22951i	−0.0634861	−	0.644585i	0.909809	−	0.415027i	$-0.136228\pi$
$164$	−1.81206	+	9.58296i	−0.141498	+	0.748304i
$165$	8.39251	+	4.48589i	0.653356	+	0.349226i
$166$	0.830065	−	8.85728i	0.0644256	−	0.687458i
$167$	7.91466	+	11.8451i	0.612455	+	0.916604i	0.999986	−	0.00525285i	$-0.00167204\pi$
$167$	7.91466	+	11.8451i	0.612455	+	0.916604i	−0.387531	+	0.921857i	$0.626672\pi$
$168$	−3.63370	−	6.57204i	−0.280346	−	0.507044i
$169$	−10.7618	−	7.19082i	−0.827833	−	0.553140i
$170$	3.46344	+	33.5372i	0.265633	+	2.57218i
$171$	−1.59803	+	1.31147i	−0.122205	+	0.100291i
$172$	11.5099	+	6.01282i	0.877623	+	0.458474i
$173$	−21.0763	+	11.2655i	−1.60240	+	0.856503i	−0.604186	+	0.796843i	$0.706502\pi$
$173$	−21.0763	+	11.2655i	−1.60240	+	0.856503i	−0.998219	+	0.0596596i	$0.980998\pi$
$174$	−13.4449	+	5.64373i	−1.01925	+	0.427850i
$175$	4.98210	−	2.06365i	0.376611	−	0.155998i
$176$	−2.88581	−	3.38369i	−0.217526	−	0.255055i
$177$	−10.5640	−	4.37577i	−0.794042	−	0.328903i
$178$	13.8564	−	0.0655695i	1.03858	−	0.00491464i
$179$	−3.84500	+	12.6753i	−0.287389	+	0.947395i	0.687777	+	0.725922i	$0.258587\pi$
$179$	−3.84500	+	12.6753i	−0.287389	+	0.947395i	−0.975166	+	0.221473i	$0.928913\pi$
$180$	20.3382	+	16.3715i	1.51592	+	1.22026i
$181$	10.6533	+	1.04926i	0.791852	+	0.0779906i	0.485852	−	0.874041i	$-0.338509\pi$
$181$	10.6533	+	1.04926i	0.791852	+	0.0779906i	0.306000	+	0.952032i	$0.401009\pi$
$182$	0.296647	−	0.160371i	0.0219890	−	0.0118875i
$183$	−3.37110	+	0.670554i	−0.249199	+	0.0495688i
$184$	−9.69201	+	9.97117i	−0.714505	+	0.735085i
$185$	−2.41571	+	12.1446i	−0.177607	+	0.892888i
$186$	−22.7730	−	12.0342i	−1.66980	−	0.882392i
$187$	−7.86794	+	2.38671i	−0.575361	+	0.174534i
$188$	−8.74964	−	8.58558i	−0.638133	−	0.626167i
$189$	−1.76763	+	2.15386i	−0.128576	+	0.156671i
$190$	0.464862	+	2.28057i	0.0337246	+	0.165450i
$191$		−	3.73904i		−	0.270547i	−0.990808	−	0.135274i	$-0.956809\pi$
$191$		−	3.73904i		−	0.270547i	0.990808	−	0.135274i	$-0.0431913\pi$
$192$	−10.5405	−	18.4408i	−0.760696	−	1.33085i
$193$		−	10.2980i		−	0.741265i	−0.928780	−	0.370632i	$-0.879141\pi$
$193$		−	10.2980i		−	0.741265i	0.928780	−	0.370632i	$-0.120859\pi$
$194$	13.3067	−	2.71240i	0.955368	−	0.194739i
$195$	−1.29479	+	1.57770i	−0.0927215	+	0.112981i
$196$	−0.0189278	−	1.99991i	−0.00135199	−	0.142851i
$197$	−22.5244	+	6.83270i	−1.60480	+	0.486809i	−0.960573	−	0.278028i	$-0.910319\pi$
$197$	−22.5244	+	6.83270i	−1.60480	+	0.486809i	−0.644223	+	0.764838i	$0.722819\pi$
$198$	−2.97476	+	5.62930i	−0.211407	+	0.400057i
$199$	−1.70964	+	8.59493i	−0.121193	+	0.609278i	0.871677	+	0.490080i	$0.163032\pi$
$199$	−1.70964	+	8.59493i	−0.121193	+	0.609278i	−0.992870	+	0.119198i	$0.961968\pi$
$200$	14.0072	−	6.03634i	0.990461	−	0.426834i
$201$	38.7353	−	7.70493i	2.73218	−	0.543464i
$202$	9.14064	+	16.9080i	0.643133	+	1.18964i
$203$	−3.86465	−	0.380634i	−0.271245	−	0.0267153i
$204$	−39.0427	+	4.21881i	−2.73353	+	0.295376i
$205$	4.56336	−	15.0434i	0.318719	−	1.05067i
$206$	0.110456	+	23.3419i	0.00769580	+	1.62631i
$207$	18.3928	+	7.61854i	1.27839	+	0.529525i
$208$	0.832521	−	0.465462i	0.0577250	−	0.0322740i
$209$	−0.524377	+	0.217204i	−0.0362719	+	0.0150243i
$210$	4.68514	+	11.1612i	0.323305	+	0.770199i
$211$	−0.185827	+	0.0993265i	−0.0127928	+	0.00683792i	−0.477781	−	0.878479i	$-0.658559\pi$
$211$	−0.185827	+	0.0993265i	−0.0127928	+	0.00683792i	0.464988	+	0.885317i	$0.346059\pi$
$212$	5.41856	+	17.2724i	0.372148	+	1.18627i
$213$	4.17399	−	3.42550i	0.285997	−	0.234711i
$214$	−16.1225	+	1.66500i	−1.10211	+	0.113817i
$215$	−17.4040	−	11.6290i	−1.18694	−	0.793089i
$216$	−4.91263	+	6.16240i	−0.334262	+	0.419299i
$217$	−3.81105	−	5.70365i	−0.258711	−	0.387189i
$218$	20.4580	+	1.91723i	1.38559	+	0.129851i
$219$	−15.4886	−	8.27881i	−1.04662	−	0.559430i
$220$	4.03871	+	5.92225i	0.272290	+	0.399278i
$221$	−0.172844	−	1.75492i	−0.0116268	−	0.118049i
$222$	−14.1585	−	2.74672i	−0.950256	−	0.184347i
$223$	9.20298	−	9.20298i	0.616277	−	0.616277i	−0.328297	−	0.944574i	$-0.606475\pi$
$223$	9.20298	−	9.20298i	0.616277	−	0.616277i	0.944574	+	0.328297i	$0.106475\pi$
$224$	−0.133830	−	5.65527i	−0.00894186	−	0.377859i
$225$	−15.4410	−	15.4410i	−1.02940	−	1.02940i
$226$	−7.20388	−	10.6717i	−0.479195	−	0.709871i
$227$	−14.8474	+	1.46234i	−0.985457	+	0.0970590i	−0.577889	−	0.816116i	$-0.696123\pi$
$227$	−14.8474	+	1.46234i	−0.985457	+	0.0970590i	−0.407568	+	0.913175i	$0.633623\pi$
$228$	−2.65368	+	0.554009i	−0.175744	+	0.0366901i
$229$	4.20813	−	7.87287i	0.278081	−	0.520254i	−0.703645	−	0.710552i	$-0.748445\pi$
$229$	4.20813	−	7.87287i	0.278081	−	0.520254i	0.981726	+	0.190298i	$0.0609454\pi$
$230$	17.2586	−	14.3010i	1.13800	−	0.942977i
$231$	−2.45441	+	1.63998i	−0.161488	+	0.107903i
$232$	−10.9451	−	0.921318i	−0.718578	−	0.0604875i
$233$	−1.16376	+	1.74168i	−0.0762401	+	0.114101i	−0.867630	−	0.497210i	$-0.834358\pi$
$233$	−1.16376	+	1.74168i	−0.0762401	+	0.114101i	0.791390	+	0.611312i	$0.209358\pi$
$234$	−1.05968	−	0.861295i	−0.0692732	−	0.0563046i
$235$	12.5350	+	15.2739i	0.817693	+	0.996362i
$236$	−5.52696	−	6.60613i	−0.359775	−	0.430022i
$237$	3.75274	+	7.02089i	0.243767	+	0.456056i
$238$	−9.68120	−	3.95652i	−0.627539	−	0.256463i
$239$	−4.42408	−	10.6807i	−0.286170	−	0.690875i	0.713785	−	0.700365i	$-0.246979\pi$
$239$	−4.42408	−	10.6807i	−0.286170	−	0.690875i	−0.999955	+	0.00948965i	$0.996979\pi$
$240$	13.6984	+	31.3775i	0.884226	+	2.02541i
$241$	6.46143	−	15.5993i	0.416217	−	1.00484i	−0.567216	−	0.823569i	$-0.691980\pi$
$241$	6.46143	−	15.5993i	0.416217	−	1.00484i	0.983434	−	0.181269i	$-0.0580203\pi$
$242$	9.71761	−	9.81002i	0.624672	−	0.630612i
$243$	−20.0686	−	6.08774i	−1.28740	−	0.390529i
$244$	−2.48463	−	0.728098i	−0.159062	−	0.0466117i
$245$	−0.315983	+	3.20823i	−0.0201874	+	0.204966i
$246$	17.5466	+	5.23217i	1.11873	+	0.333591i
$247$	−0.0237488	−	0.119393i	−0.00151110	−	0.00759681i
$248$	−11.0072	−	15.9777i	−0.698959	−	1.01459i
$249$	−16.3808	−	3.25834i	−1.03809	−	0.206489i
$250$	−1.71028	+	0.527659i	−0.108168	+	0.0333721i
$251$	−6.59463	−	21.7396i	−0.416250	−	1.37219i	−0.875214	−	0.483736i	$-0.839279\pi$
$251$	−6.59463	−	21.7396i	−0.416250	−	1.37219i	0.458964	−	0.888455i	$-0.348221\pi$
$252$	−7.45271	+	3.16998i	−0.469477	+	0.199690i
$253$	4.22519	+	3.46752i	0.265635	+	0.218001i
$254$	8.86356	−	13.4021i	0.556149	−	0.840923i
$255$	63.2983			3.96389
$256$	−0.605555	−	15.9885i	−0.0378472	−	0.999284i
$257$	25.1608			1.56948			0.784742	−	0.619822i	$-0.212795\pi$
$257$	25.1608			1.56948			0.784742	+	0.619822i	$0.212795\pi$
$258$	13.4487	−	20.3350i	0.837279	−	1.26600i
$259$	−2.96915	−	2.43672i	−0.184494	−	0.151410i
$260$	−1.41476	+	0.601761i	−0.0877395	+	0.0373196i
$261$	4.56483	+	15.0482i	0.282556	+	0.931462i
$262$	28.5650	−	8.81293i	1.76475	−	0.544465i
$263$	21.2595	+	4.22878i	1.31092	+	0.260758i	0.800585	−	0.599220i	$-0.204522\pi$
$263$	21.2595	+	4.22878i	1.31092	+	0.260758i	0.510332	+	0.859977i	$0.329522\pi$
$264$	−6.87556	+	4.73665i	−0.423162	+	0.291521i
$265$	−5.69251	−	28.6182i	−0.349688	−	1.75800i
$266$	−0.691869	−	0.206306i	−0.0424212	−	0.0126494i
$267$	2.54988	−	25.8894i	0.156050	−	1.58441i
$268$	28.5494	+	8.36613i	1.74393	+	0.511043i
$269$	−8.35728	−	2.53515i	−0.509552	−	0.154571i	0.0250313	−	0.999687i	$-0.492031\pi$
$269$	−8.35728	−	2.53515i	−0.509552	−	0.154571i	−0.534583	+	0.845116i	$0.679531\pi$
$270$	8.93984	−	9.02485i	0.544061	−	0.549235i
$271$	6.68560	−	16.1405i	0.406121	−	0.980463i	−0.580027	−	0.814597i	$-0.696958\pi$
$271$	6.68560	−	16.1405i	0.406121	−	0.980463i	0.986148	−	0.165866i	$-0.0530420\pi$
$272$	−27.5387	−	10.8009i	−1.66978	−	0.654899i
$273$	−0.242280	−	0.584915i	−0.0146634	−	0.0354007i
$274$	−16.8971	−	6.90551i	−1.02079	−	0.417177i
$275$	−2.82622	−	5.28749i	−0.170428	−	0.318848i
$276$	16.7519	+	20.0228i	1.00835	+	1.20523i
$277$	−17.7379	−	21.6137i	−1.06577	−	1.29864i	−0.952320	−	0.305100i	$-0.901310\pi$
$277$	−17.7379	−	21.6137i	−1.06577	−	1.29864i	−0.113449	−	0.993544i	$-0.536190\pi$
$278$	−2.99287	−	2.43258i	−0.179501	−	0.145896i
$279$	−15.4326	+	23.0965i	−0.923927	+	1.38275i
$280$	−0.764831	+	9.08602i	−0.0457074	+	0.542993i
$281$	27.1867	−	18.1656i	1.62182	−	1.08367i	0.688135	−	0.725583i	$-0.258430\pi$
$281$	27.1867	−	18.1656i	1.62182	−	1.08367i	0.933689	−	0.358085i	$-0.116570\pi$
$282$	−17.7209	+	14.6841i	−1.05527	+	0.874424i
$283$	7.98130	−	14.9320i	0.474439	−	0.887613i	−0.524897	−	0.851166i	$-0.675896\pi$
$283$	7.98130	−	14.9320i	0.474439	−	0.887613i	0.999336	−	0.0364467i	$-0.0116039\pi$
$284$	3.98157	−	0.831232i	0.236263	−	0.0493245i
$285$	4.34859	−	0.428299i	0.257588	−	0.0253702i
$286$	−0.209767	−	0.310745i	−0.0124038	−	0.0183747i
$287$	3.44813	+	3.44813i	0.203537	+	0.203537i
$288$	−20.9501	+	9.26438i	−1.23449	+	0.545909i
$289$	−26.6507	+	26.6507i	−1.56769	+	1.56769i
$290$	17.3804	+	3.37176i	1.02061	+	0.197997i
$291$	−2.49905	−	25.3733i	−0.146497	−	1.48741i
$292$	−7.45353	−	10.9296i	−0.436185	−	0.639609i
$293$	−12.3722	−	6.61306i	−0.722789	−	0.386339i	0.0686058	−	0.997644i	$-0.478145\pi$
$293$	−12.3722	−	6.61306i	−0.722789	−	0.386339i	−0.791395	+	0.611305i	$0.790645\pi$
$294$	−3.73847	−	0.350353i	−0.218032	−	0.0204330i
$295$	7.71327	+	11.5437i	0.449084	+	0.672101i
$296$	−8.49503	−	6.77218i	−0.493763	−	0.393625i
$297$	2.57574	+	1.72106i	0.149460	+	0.0998658i
$298$	3.71630	−	0.383788i	0.215280	−	0.0222323i
$299$	−0.906198	+	0.743698i	−0.0524068	+	0.0430092i
$300$	−8.57140	−	27.3225i	−0.494870	−	1.57747i
$301$	5.72625	−	3.06074i	0.330055	−	0.176418i
$302$	9.15096	+	21.8000i	0.526578	+	1.25445i
$303$	33.3384	−	13.8092i	1.91524	−	0.793318i
$304$	−1.96499	−	0.555683i	−0.112700	−	0.0318706i
$305$	3.85565	+	1.59706i	0.220774	+	0.0914476i
$306$	0.200405	+	42.3504i	0.0114564	+	2.42101i
$307$	−7.66317	+	25.2621i	−0.437360	+	1.44178i	0.410645	+	0.911795i	$0.365303\pi$
$307$	−7.66317	+	25.2621i	−0.437360	+	1.44178i	−0.848005	+	0.529988i	$0.822197\pi$
$308$	−2.21071	+	0.238882i	−0.125967	+	0.0136116i
$309$	43.6121	+	4.29542i	2.48101	+	0.244358i
$310$	14.8728	+	27.5111i	0.844718	+	1.56253i
$311$	−14.2223	+	2.82898i	−0.806471	+	0.160417i	−0.581075	−	0.813850i	$-0.697368\pi$
$311$	−14.2223	+	2.82898i	−0.806471	+	0.160417i	−0.225396	+	0.974267i	$0.572368\pi$
$312$	−0.708686	−	1.64449i	−0.0401215	−	0.0931012i
$313$	−1.59526	+	8.01990i	−0.0901693	+	0.453312i	0.909152	+	0.416465i	$0.136731\pi$
$313$	−1.59526	+	8.01990i	−0.0901693	+	0.453312i	−0.999321	+	0.0368464i	$0.988269\pi$
$314$	−8.20233	+	15.5217i	−0.462884	+	0.875941i
$315$	12.4923	−	3.78949i	0.703859	−	0.213513i
$316$	0.0567526	+	5.99647i	0.00319258	+	0.337328i
$317$	12.0737	−	14.7119i	0.678127	−	0.826300i	−0.314276	−	0.949332i	$-0.601762\pi$
$317$	12.0737	−	14.7119i	0.678127	−	0.826300i	0.992403	+	0.123032i	$0.0392617\pi$
$318$	33.3011	−	6.78797i	1.86743	−	0.380650i
$319$			4.31747i			0.241732i
$320$	−1.79823	+	25.7273i	−0.100524	+	1.43820i
$321$			30.4298i			1.69842i
$322$	1.38865	+	6.81260i	0.0773867	+	0.379651i
$323$	−2.39507	+	2.91840i	−0.133265	+	0.162384i
$324$	−6.78133	−	6.65417i	−0.376741	−	0.369676i
$325$	1.23050	−	0.373269i	0.0682559	−	0.0207052i
$326$	−10.3397	−	5.46393i	−0.572662	−	0.302619i
$327$	7.52592	−	37.8354i	0.416184	−	2.09230i
$328$	9.89025	+	9.61335i	0.546098	+	0.530809i
$329$	−6.01143	+	1.19575i	−0.331421	+	0.0659237i
$330$	11.8386	−	6.40010i	0.651696	−	0.352314i
$331$	15.3713	+	1.51394i	0.844884	+	0.0832138i	0.511190	−	0.859468i	$-0.329205\pi$
$331$	15.3713	+	1.51394i	0.844884	+	0.0832138i	0.333694	+	0.942681i	$0.391705\pi$
$332$	−9.80032	−	7.88888i	−0.537862	−	0.432959i
$333$	−4.51508	+	14.8842i	−0.247425	+	0.815651i
$334$	20.1467	−	0.0953354i	1.10238	−	0.00521652i
$335$	−44.3030	−	18.3509i	−2.42053	−	1.00262i
$336$	−10.5870	−	0.840743i	−0.577567	−	0.0458663i
$337$	14.7244	−	6.09906i	0.802091	−	0.332237i	0.0562971	−	0.998414i	$-0.482071\pi$
$337$	14.7244	−	6.09906i	0.802091	−	0.332237i	0.745793	+	0.666177i	$0.232071\pi$
$338$	−16.8777	+	7.08472i	−0.918025	+	0.385358i
$339$	−21.3186	+	11.3951i	−1.15787	+	0.618894i
$340$	42.2617	+	22.0777i	2.29196	+	1.19733i
$341$	−5.89542	+	4.83824i	−0.319255	+	0.262006i
$342$	0.300326	+	2.90811i	0.0162397	+	0.157253i
$343$	−0.831470	−	0.555570i	−0.0448951	−	0.0299980i
$344$	16.0717	−	8.88613i	0.866530	−	0.479108i
$345$	−23.3784	−	34.9883i	−1.25865	−	1.88371i
$346$	−3.15351	+	33.6497i	−0.169534	+	1.80902i
$347$	−23.8837	−	12.7661i	−1.28214	−	0.685321i	−0.317346	−	0.948310i	$-0.602792\pi$
$347$	−23.8837	−	12.7661i	−1.28214	−	0.685321i	−0.964799	+	0.262989i	$0.915292\pi$
$348$	−3.83140	+	20.2621i	−0.205385	+	1.08616i
$349$	1.58475	+	16.0902i	0.0848298	+	0.861291i	0.939598	+	0.342281i	$0.111199\pi$
$349$	1.58475	+	16.0902i	0.0848298	+	0.861291i	−0.854768	+	0.519010i	$0.826301\pi$
$350$	1.45240	−	7.48669i	0.0776341	−	0.400180i
$351$	−0.469805	+	0.469805i	−0.0250764	+	0.0250764i
$352$	−6.24262	+	0.764355i	−0.332733	+	0.0407402i
$353$	−24.5040	−	24.5040i	−1.30422	−	1.30422i	−0.925521	−	0.378695i	$-0.876373\pi$
$353$	−24.5040	−	24.5040i	−1.30422	−	1.30422i	−0.378695	−	0.925521i	$-0.623627\pi$
$354$	−13.4028	+	9.04750i	−0.712351	+	0.480869i
$355$	−6.52460	+	0.642617i	−0.346290	+	0.0341066i
$356$	10.7324	−	16.3959i	0.568814	−	0.868982i
$357$	−9.25586	+	17.3165i	−0.489872	+	0.916486i
$358$	11.9519	+	14.4238i	0.631680	+	0.762319i
$359$	−12.4021	+	8.28679i	−0.654556	+	0.437360i	−0.838000	−	0.545670i	$-0.816275\pi$
$359$	−12.4021	+	8.28679i	−0.654556	+	0.437360i	0.183444	+	0.983030i	$0.441275\pi$
$360$	35.1777	−	11.2188i	1.85403	−	0.591282i
$361$	10.4110	−	15.5812i	0.547950	−	0.820064i
$362$	9.54854	−	11.7478i	0.501860	−	0.617453i
$363$	−16.4460	−	20.0395i	−0.863191	−	1.05180i
$364$	0.0422510	−	0.475028i	0.00221455	−	0.0248982i
$365$	10.0520	+	18.8060i	0.526146	+	0.984349i
$366$	−1.83890	+	4.49960i	−0.0961207	+	0.235198i
$367$	−11.2210	−	27.0899i	−0.585731	−	1.41408i	−0.887548	−	0.460714i	$-0.847593\pi$
$367$	−11.2210	−	27.0899i	−0.585731	−	1.41408i	0.301817	−	0.953366i	$-0.402407\pi$
$368$	4.20085	+	19.2112i	0.218984	+	1.00146i
$369$	7.55671	−	18.2435i	0.393387	−	0.949719i
$370$	12.4410	+	12.3238i	0.646776	+	0.640683i
$371$	8.66146	+	2.62742i	0.449681	+	0.136409i
$372$	−31.9611	+	17.4744i	−1.65710	+	0.906007i
$373$	2.22035	−	22.5436i	0.114965	−	1.16726i	−0.748598	−	0.663024i	$-0.769273\pi$
$373$	2.22035	−	22.5436i	0.114965	−	1.16726i	0.863564	−	0.504240i	$-0.168227\pi$
$374$	−3.32263	+	11.1428i	−0.171809	+	0.576180i
$375$	0.655556	+	3.29570i	0.0338528	+	0.170189i
$376$	−16.9532	+	3.62311i	−0.874293	+	0.186848i
$377$	−0.908197	−	0.180652i	−0.0467745	−	0.00930403i
$378$	1.16169	+	3.76534i	0.0597508	+	0.193668i
$379$	6.45152	+	21.2678i	0.331392	+	1.09245i	0.951426	+	0.307878i	$0.0996190\pi$
$379$	6.45152	+	21.2678i	0.331392	+	1.09245i	−0.620033	+	0.784575i	$0.712881\pi$
$380$	3.05276	+	1.23078i	0.156603	+	0.0631375i
$381$	−23.3189	−	19.1373i	−1.19466	−	0.980435i
$382$	−4.41049	−	2.91690i	−0.225660	−	0.149242i
$383$	−32.8208			−1.67707			−0.838533	−	0.544851i	$-0.816586\pi$
$383$	−32.8208			−1.67707			−0.838533	+	0.544851i	$0.816586\pi$
$384$	−29.9752	−	1.95266i	−1.52967	−	0.0996463i
$385$	3.58414			0.182665
$386$	−12.1473	−	8.03368i	−0.618281	−	0.408904i
$387$	−20.3245	−	16.6799i	−1.03315	−	0.847887i
$388$	7.18139	−	17.8124i	0.364580	−	0.904286i
$389$	1.71977	+	5.66933i	0.0871960	+	0.287447i	0.989684	−	0.143269i	$-0.0457613\pi$
$389$	1.71977	+	5.66933i	0.0871960	+	0.287447i	−0.902488	+	0.430715i	$0.858261\pi$
$390$	0.850934	+	2.75810i	0.0430887	+	0.139662i
$391$	35.6586	+	7.09294i	1.80334	+	0.358706i
$392$	−2.37382	−	1.53785i	−0.119896	−	0.0776730i
$393$	−10.9490	−	55.0446i	−0.552306	−	2.77663i
$394$	−9.51205	+	31.8997i	−0.479210	+	1.60708i
$395$	0.947434	−	9.61946i	0.0476706	−	0.484007i
$396$	4.31954	+	7.90051i	0.217065	+	0.397016i
$397$	1.81974	+	0.552013i	0.0913304	+	0.0277048i	0.335619	−	0.941998i	$-0.391054\pi$
$397$	1.81974	+	0.552013i	0.0913304	+	0.0277048i	−0.244289	+	0.969703i	$0.578554\pi$
$398$	8.80468	+	8.72175i	0.441339	+	0.437182i
$399$	−0.518707	+	1.25227i	−0.0259679	+	0.0626919i
$400$	3.80699	−	21.2317i	0.190350	−	1.06159i
$401$	3.75838	+	9.07354i	0.187685	+	0.453111i	0.989513	−	0.144444i	$-0.0461392\pi$
$401$	3.75838	+	9.07354i	0.187685	+	0.453111i	−0.801828	+	0.597554i	$0.796139\pi$
$402$	21.1297	−	51.7022i	1.05385	−	2.57867i
$403$	−0.771069	−	1.44257i	−0.0384097	−	0.0718594i
$404$	27.0752	+	2.40818i	1.34704	+	0.119811i
$405$	9.71513	+	11.8379i	0.482749	+	0.588231i
$406$	−3.46388	+	4.26172i	−0.171910	+	0.211506i
$407$	−2.37252	+	3.55072i	−0.117601	+	0.176003i
$408$	−25.4816	+	49.3452i	−1.26153	+	2.44295i
$409$	−15.0779	+	10.0747i	−0.745555	+	0.498164i	−0.869382	−	0.494140i	$-0.835483\pi$
$409$	−15.0779	+	10.0747i	−0.745555	+	0.498164i	0.123828	+	0.992304i	$0.460483\pi$
$410$	−14.1849	−	17.1185i	−0.700542	−	0.845423i
$411$	−16.1547	+	30.2234i	−0.796854	+	1.49081i
$412$	27.6198	+	18.0793i	1.36073	+	0.890701i
$413$	−4.28589	+	0.422123i	−0.210895	+	0.0207713i
$414$	23.3353	−	15.7524i	1.14687	−	0.774187i
$415$	14.3394	+	14.3394i	0.703893	+	0.703893i
$416$	0.100419	−	1.34514i	0.00492343	−	0.0659511i
$417$	−5.12002	+	5.12002i	−0.250728	+	0.250728i
$418$	−0.152868	+	0.787991i	−0.00747704	+	0.0385419i
$419$	−1.99555	−	20.2611i	−0.0974889	−	0.989822i	−0.912142	−	0.409874i	$-0.865573\pi$
$419$	−1.99555	−	20.2611i	−0.0974889	−	0.989822i	0.814653	−	0.579948i	$-0.196927\pi$
$420$	16.8206	+	3.18063i	0.820759	+	0.155199i
$421$	33.4575	+	17.8834i	1.63062	+	0.871585i	0.995032	+	0.0995579i	$0.0317428\pi$
$421$	33.4575	+	17.8834i	1.63062	+	0.871585i	0.635589	+	0.772027i	$0.280757\pi$
$422$	−0.0278040	+	0.296684i	−0.00135348	+	0.0144424i
$423$	13.7891	+	20.6369i	0.670451	+	1.00340i
$424$	24.6013	+	7.08296i	1.19475	+	0.343979i
$425$	−33.1586	−	22.1559i	−1.60843	−	1.07472i
$426$	−0.784437	−	7.59586i	−0.0380061	−	0.368021i
$427$	−1.00071	+	0.821257i	−0.0484275	+	0.0397434i
$428$	−10.6135	+	20.3167i	−0.513024	+	0.982045i
$429$	−0.620769	+	0.331808i	−0.0299710	+	0.0160198i
$430$	−27.2945	+	11.4574i	−1.31626	+	0.552524i
$431$	−13.9326	+	5.77108i	−0.671111	+	0.277983i	−0.692105	−	0.721796i	$-0.743317\pi$
$431$	−13.9326	+	5.77108i	−0.671111	+	0.277983i	0.0209947	+	0.999780i	$0.493317\pi$
$432$	3.43660	+	10.6023i	0.165344	+	0.510102i
$433$	20.8452	+	8.63437i	1.00176	+	0.414941i	0.822441	−	0.568850i	$-0.192612\pi$
$433$	20.8452	+	8.63437i	1.00176	+	0.414941i	0.179316	+	0.983792i	$0.442612\pi$
$434$	−9.70100	+	0.0459057i	−0.465663	+	0.00220355i
$435$	9.64871	−	31.8075i	0.462620	−	1.52505i
$436$	18.2213	−	22.6362i	0.872640	−	1.08408i
$437$	2.49774	+	0.246006i	0.119483	+	0.0117681i
$438$	−21.8485	+	11.8115i	−1.04396	+	0.564376i
$439$	−33.4860	+	6.66078i	−1.59820	+	0.317902i	−0.912214	−	0.409713i	$-0.865629\pi$
$439$	−33.4860	+	6.66078i	−1.59820	+	0.317902i	−0.685986	+	0.727615i	$0.740629\pi$
$440$	10.1365	−	0.143908i	0.483237	−	0.00686053i
$441$	−0.790006	+	3.97163i	−0.0376193	+	0.189125i
$442$	−2.20491	−	1.16517i	−0.104877	−	0.0554213i
$443$	21.6595	−	6.57033i	1.02907	−	0.312166i	0.269785	−	0.962921i	$-0.413048\pi$
$443$	21.6595	−	6.57033i	1.02907	−	0.312166i	0.759288	+	0.650755i	$0.225548\pi$
$444$	−14.2853	+	14.5583i	−0.677952	+	0.690907i
$445$	−20.0383	+	24.4168i	−0.949908	+	1.15747i
$446$	−3.67621	−	18.0351i	−0.174073	−	0.853987i
$447$		−	7.01418i		−	0.331759i
$448$	−6.77525	−	4.25394i	−0.320100	−	0.200980i
$449$			16.2071i			0.764858i	0.923985	+	0.382429i	$0.124912\pi$
$449$			16.2071i			0.764858i	−0.923985	+	0.382429i	$0.875088\pi$
$450$	−30.2598	+	6.16805i	−1.42646	+	0.290765i
$451$	3.43938	−	4.19090i	0.161954	−	0.197342i
$452$	−18.2080	+	0.172327i	−0.856434	+	0.00810558i
$453$	42.4762	−	12.8850i	1.99570	−	0.605390i
$454$	−9.85784	+	18.6545i	−0.462651	+	0.875500i
$455$	−0.149968	+	0.753939i	−0.00703059	+	0.0353452i
$456$	−1.41670	+	3.56243i	−0.0663430	+	0.166826i
$457$	13.1505	−	2.61579i	0.615153	−	0.122361i	0.122327	−	0.992490i	$-0.460964\pi$
$457$	13.1505	−	2.61579i	0.615153	−	0.122361i	0.492825	+	0.870128i	$0.335964\pi$
$458$	−6.00382	−	11.1056i	−0.280540	−	0.518932i
$459$	20.5064	+	2.01971i	0.957157	+	0.0942718i
$460$	−3.40533	−	31.5144i	−0.158774	−	1.46937i
$461$	−0.793631	+	2.61625i	−0.0369631	+	0.121851i	−0.973480	−	0.228770i	$-0.926530\pi$
$461$	−0.793631	+	2.61625i	−0.0369631	+	0.121851i	0.936517	+	0.350621i	$0.114030\pi$
$462$	0.0197543	+	4.17456i	0.000919052	+	0.194218i
$463$	10.0043	+	4.14393i	0.464941	+	0.192585i	0.602841	−	0.797861i	$-0.294035\pi$
$463$	10.0043	+	4.14393i	0.464941	+	0.192585i	−0.137900	+	0.990446i	$0.544035\pi$
$464$	−9.62524	+	12.1918i	−0.446841	+	0.565991i
$465$	54.2451	−	22.4691i	2.51556	−	1.04198i
$466$	1.14658	+	2.73147i	0.0531145	+	0.126533i
$467$	6.45746	−	3.45159i	0.298816	−	0.159720i	−0.315175	−	0.949034i	$-0.602063\pi$
$467$	6.45746	−	3.45159i	0.298816	−	0.159720i	0.613991	+	0.789313i	$0.289563\pi$
$468$	−1.84264	+	0.578059i	−0.0851762	+	0.0267208i
$469$	11.4985	−	9.43657i	0.530951	−	0.435741i
$470$	27.7957	−	2.87050i	1.28212	−	0.132406i
$471$	27.4048	+	18.3113i	1.26275	+	0.843739i
$472$	−12.1042	+	1.36591i	−0.557139	+	0.0628711i
$473$	−4.01053	−	6.00219i	−0.184405	−	0.275981i
$474$	11.2093	+	1.05049i	0.514860	+	0.0482504i
$475$	−2.42791	−	1.29774i	−0.111400	−	0.0595446i
$476$	−12.2195	+	8.33319i	−0.560082	+	0.381951i
$477$	−3.59255	−	36.4758i	−0.164492	−	1.67011i
$478$	−16.0500	−	3.11367i	−0.734111	−	0.142416i
$479$	24.1299	−	24.1299i	1.10252	−	1.10252i	0.108418	−	0.994105i	$-0.465421\pi$
$479$	24.1299	−	24.1299i	1.10252	−	1.10252i	0.994105	−	0.108418i	$-0.0345786\pi$
$480$	47.6986	+	8.31992i	2.17713	+	0.379750i
$481$	−0.647638	−	0.647638i	−0.0295298	−	0.0295298i
$482$	−13.3599	−	19.7911i	−0.608526	−	0.901460i
$483$	12.9903	−	1.27943i	0.591078	−	0.0582161i
$484$	−3.99078	−	19.1157i	−0.181399	−	0.868896i
$485$	−14.5930	+	27.3016i	−0.662634	+	1.23970i
$486$	−22.8369	+	18.9233i	−1.03590	+	0.858380i
$487$	−17.2072	+	11.4975i	−0.779731	+	0.521000i	−0.880577	−	0.473902i	$-0.842845\pi$
$487$	−17.2072	+	11.4975i	−0.779731	+	0.521000i	0.100846	+	0.994902i	$0.467845\pi$
$488$	−2.79716	+	2.36281i	−0.126622	+	0.106959i
$489$	−12.1979	+	18.2555i	−0.551610	+	0.825542i
$490$	3.53786	+	2.87554i	0.159824	+	0.129904i
$491$	−20.6781	−	25.1964i	−0.933191	−	1.13710i	−0.990330	−	0.138730i	$-0.955698\pi$
$491$	−20.6781	−	25.1964i	−0.933191	−	1.13710i	0.0571391	−	0.998366i	$-0.481802\pi$
$492$	19.8603	−	16.6159i	0.895370	−	0.749104i
$493$	13.5377	+	25.3273i	0.609709	+	1.14068i
$494$	−0.159361	−	0.0651277i	−0.00716999	−	0.00293023i
$495$	−5.55417	−	13.4089i	−0.249641	−	0.602687i
$496$	−27.4340	+	0.519335i	−1.23182	+	0.0233188i
$497$	0.778266	−	1.87890i	0.0349100	−	0.0842802i
$498$	−16.6225	+	16.7806i	−0.744872	+	0.751955i
$499$	19.0939	+	5.79206i	0.854759	+	0.259288i	0.687105	−	0.726558i	$-0.258881\pi$
$499$	19.0939	+	5.79206i	0.854759	+	0.259288i	0.167653	+	0.985846i	$0.446381\pi$
$500$	−0.711813	+	2.42905i	−0.0318332	+	0.108631i
$501$	3.70743	−	37.6421i	0.165636	−	1.68173i
$502$	−30.7882	−	9.18063i	−1.37415	−	0.409752i
$503$	3.33580	+	16.7702i	0.148736	+	0.747747i	0.981098	+	0.193514i	$0.0619884\pi$
$503$	3.33580	+	16.7702i	0.148736	+	0.747747i	−0.832362	+	0.554233i	$0.813012\pi$
$504$	−2.07478	+	11.2640i	−0.0924182	+	0.501740i
$505$	−42.9722	−	8.54770i	−1.91224	−	0.380368i
$506$	7.38638	−	2.27886i	0.328365	−	0.101308i
$507$	9.97564	+	32.8853i	0.443034	+	1.46049i
$508$	−8.89421	−	20.9106i	−0.394617	−	0.927756i
$509$	−4.14309	−	3.40014i	−0.183639	−	0.150709i	0.538082	−	0.842892i	$-0.319149\pi$
$509$	−4.14309	−	3.40014i	−0.183639	−	0.150709i	−0.721722	+	0.692183i	$0.756649\pi$
$510$	49.3804	−	74.6655i	2.18660	−	3.30624i
$511$	−6.61461			−0.292613
$512$	−19.3322	−	11.7587i	−0.854369	−	0.519666i
$513$	1.42245			0.0628029
$514$	19.6285	−	29.6791i	0.865774	−	1.30909i
$515$	−41.1314	−	33.7557i	−1.81247	−	1.48745i
$516$	−13.4952	−	31.7276i	−0.594093	−	1.39673i
$517$	1.97811	+	6.52096i	0.0869973	+	0.286792i
$518$	−5.19061	+	1.60142i	−0.228062	+	0.0703622i
$519$	62.2324	+	12.3788i	2.73170	+	0.543369i
$520$	−0.393858	+	2.13827i	−0.0172718	+	0.0937692i
$521$	5.12656	+	25.7729i	0.224599	+	1.12913i	0.914299	+	0.405039i	$0.132742\pi$
$521$	5.12656	+	25.7729i	0.224599	+	1.12913i	−0.689701	+	0.724094i	$0.742258\pi$
$522$	21.3117	+	6.35487i	0.932789	+	0.278145i
$523$	0.516774	−	5.24690i	0.0225970	−	0.229431i	−0.977252	−	0.212079i	$-0.931977\pi$
$523$	0.516774	−	5.24690i	0.0225970	−	0.229431i	0.999849	−	0.0173517i	$-0.00552348\pi$
$524$	11.8886	−	40.5699i	0.519358	−	1.77230i
$525$	−13.7012	−	4.15622i	−0.597970	−	0.181392i
$526$	21.5732	−	21.7783i	0.940635	−	0.949580i
$527$	−19.4133	+	46.8678i	−0.845656	+	2.04159i
$528$	0.223482	+	11.8054i	0.00972579	+	0.513766i
$529$	−0.447712	−	1.08087i	−0.0194657	−	0.0469944i
$530$	−38.1983	−	15.6109i	−1.65923	−	0.678094i
$531$	8.22088	+	15.3802i	0.356756	+	0.667443i
$532$	−0.783096	+	0.655171i	−0.0339515	+	0.0284053i
$533$	0.737662	+	0.898844i	0.0319517	+	0.0389332i
$534$	−28.5494	−	23.2047i	−1.23545	−	1.00416i
$535$	20.5268	−	30.7206i	0.887453	−	1.32817i
$536$	32.1405	−	27.1497i	1.38826	−	1.17269i
$537$	29.2413	−	19.5384i	1.26185	−	0.843144i
$538$	−9.51011	+	7.88035i	−0.410010	+	0.339746i
$539$	−0.524095	+	0.980512i	−0.0225743	+	0.0422336i
$540$	−3.67137	−	17.5857i	−0.157991	−	0.756770i
$541$	18.1234	−	1.78499i	0.779184	−	0.0767429i	0.299398	−	0.954128i	$-0.403214\pi$
$541$	18.1234	−	1.78499i	0.779184	−	0.0767429i	0.479786	+	0.877385i	$0.340714\pi$
$542$	−13.8234	−	20.4777i	−0.593765	−	0.879594i
$543$	−20.0975	−	20.0975i	−0.862466	−	0.862466i
$544$	−34.2240	+	24.0581i	−1.46734	+	1.03148i
$545$	−33.1202	+	33.1202i	−1.41872	+	1.41872i
$546$	−0.878962	−	0.170517i	−0.0376161	−	0.00729744i
$547$	−0.506145	−	5.13898i	−0.0216412	−	0.219727i	−0.999923	−	0.0124454i	$-0.996038\pi$
$547$	−0.506145	−	5.13898i	−0.0216412	−	0.219727i	0.978281	−	0.207281i	$-0.0664616\pi$
$548$	−21.3274	+	14.5443i	−0.911061	+	0.621303i
$549$	4.62322	+	2.47117i	0.197314	+	0.105467i
$550$	−8.44182	−	0.791131i	−0.359961	−	0.0337339i
$551$	1.10141	+	1.64838i	0.0469218	+	0.0702235i
$552$	36.6870	−	4.13999i	1.56150	−	0.176210i
$553$	2.49305	+	1.66580i	0.106015	+	0.0708372i
$554$	−39.3329	+	4.06197i	−1.67109	+	0.172577i
$555$	25.4139	−	20.8567i	1.07876	−	0.885316i
$556$	−5.20423	+	1.63263i	−0.220708	+	0.0692388i
$557$	24.0737	−	12.8676i	1.02003	−	0.545219i	0.125441	−	0.992101i	$-0.459966\pi$
$557$	24.0737	−	12.8676i	1.02003	−	0.545219i	0.894593	+	0.446882i	$0.147466\pi$
$558$	15.2049	+	36.2221i	0.643675	+	1.53341i
$559$	1.43039	−	0.592489i	0.0604992	−	0.0250596i
$560$	10.1210	+	7.99038i	0.427691	+	0.337655i
$561$	20.1683	+	8.35397i	0.851505	+	0.352705i
$562$	−0.218812	−	46.2403i	−0.00923003	−	1.95053i
$563$	5.45405	−	17.9796i	0.229861	−	0.757750i	−0.763812	−	0.645439i	$-0.776675\pi$
$563$	5.45405	−	17.9796i	0.229861	−	0.757750i	0.993673	−	0.112311i	$-0.0358254\pi$
$564$	3.49656	+	32.3586i	0.147232	+	1.36254i
$565$	29.2091	+	2.87684i	1.22884	+	0.121030i
$566$	−11.3871	−	21.0633i	−0.478634	−	0.885358i
$567$	−4.65910	+	0.926753i	−0.195664	+	0.0389200i
$568$	2.12561	−	5.34505i	0.0891885	−	0.224273i
$569$	5.13985	−	25.8398i	0.215474	−	1.08326i	−0.709929	−	0.704273i	$-0.751273\pi$
$569$	5.13985	−	25.8398i	0.215474	−	1.08326i	0.925403	−	0.378986i	$-0.123727\pi$
$570$	2.88722	−	5.46363i	0.120932	−	0.228846i
$571$	−4.14083	+	1.25611i	−0.173288	+	0.0525664i	−0.375737	−	0.926727i	$-0.622610\pi$
$571$	−4.14083	+	1.25611i	−0.173288	+	0.0525664i	0.202448	+	0.979293i	$0.435110\pi$
$572$	−0.530193	+	0.00501793i	−0.0221685	+	0.000209810i
$573$	−6.29789	+	7.67401i	−0.263098	+	0.320586i
$574$	6.75731	−	1.37738i	0.282045	−	0.0574909i
$575$			26.5115i			1.10561i
$576$	−5.41551	+	31.9396i	−0.225646	+	1.33082i
$577$			35.6211i			1.48293i	0.670994	+	0.741463i	$0.265868\pi$
$577$			35.6211i			1.48293i	−0.670994	+	0.741463i	$0.734132\pi$
$578$	10.6459	+	52.2275i	0.442809	+	2.17238i
$579$	−17.3455	+	21.1356i	−0.720856	+	0.878366i
$580$	17.5361	−	17.8712i	0.728148	−	0.742062i
$581$	−6.01962	+	1.82603i	−0.249736	+	0.0757565i
$582$	−31.8794	−	16.8465i	−1.32145	−	0.698308i
$583$	1.96320	−	9.86968i	0.0813075	−	0.408760i
$584$	−18.7071	+	0.265585i	−0.774103	+	0.0109900i
$585$	3.05303	−	0.607285i	0.126227	−	0.0251081i
$586$	−17.4524	+	9.43497i	−0.720953	+	0.389755i
$587$	22.8353	+	2.24908i	0.942513	+	0.0928294i	0.557587	−	0.830118i	$-0.311727\pi$
$587$	22.8353	+	2.24908i	0.942513	+	0.0928294i	0.384925	+	0.922948i	$0.374227\pi$
$588$	−3.32973	+	4.13650i	−0.137316	+	0.170586i
$589$	−1.01657	+	3.35117i	−0.0418869	+	0.138083i
$590$	19.6340	−	0.0929095i	0.808320	−	0.00382502i
$591$	57.7378	+	23.9158i	2.37502	+	0.983764i
$592$	−14.6155	+	4.73744i	−0.600693	+	0.194708i
$593$	−16.2463	+	6.72945i	−0.667157	+	0.276346i	−0.690447	−	0.723383i	$-0.742586\pi$
$593$	−16.2463	+	6.72945i	−0.667157	+	0.276346i	0.0232896	+	0.999729i	$0.492586\pi$
$594$	4.03951	−	1.69566i	0.165743	−	0.0695738i
$595$	21.0254	−	11.2383i	0.861958	−	0.460726i
$596$	2.44646	−	4.68308i	0.100211	−	0.191826i
$597$	17.9858	−	14.7606i	0.736112	−	0.604111i
$598$	0.170306	+	1.64911i	0.00696433	+	0.0674371i
$599$	17.4123	+	11.6345i	0.711447	+	0.475374i	0.857882	−	0.513846i	$-0.171780\pi$
$599$	17.4123	+	11.6345i	0.711447	+	0.475374i	−0.146435	+	0.989220i	$0.546780\pi$
$600$	−38.9159	−	11.2043i	−1.58873	−	0.457412i
$601$	3.21702	+	4.81462i	0.131225	+	0.196392i	0.891263	−	0.453486i	$-0.149820\pi$
$601$	3.21702	+	4.81462i	0.131225	+	0.196392i	−0.760038	+	0.649878i	$0.774820\pi$
$602$	0.856778	−	9.14232i	0.0349197	−	0.372613i
$603$	−53.1227	−	28.3947i	−2.16332	−	1.15632i
$604$	32.8537	+	6.21238i	1.33680	+	0.252778i
$605$	3.08523	+	31.3249i	0.125433	+	1.27354i
$606$	9.71893	−	50.0982i	0.394804	−	2.03510i
$607$	−10.1075	+	10.1075i	−0.410250	+	0.410250i	−0.881826	−	0.471576i	$-0.843685\pi$
$607$	−10.1075	+	10.1075i	−0.410250	+	0.410250i	0.471576	+	0.881826i	$0.343685\pi$
$608$	−2.18840	+	1.88436i	−0.0887514	+	0.0764208i
$609$	7.29068	+	7.29068i	0.295433	+	0.295433i
$610$	4.89174	−	3.30215i	0.198061	−	0.133700i
$611$	−1.45448	+	0.143254i	−0.0588419	+	0.00579543i
$612$	50.1121	+	32.8021i	2.02566	+	1.32595i
$613$	−6.57686	+	12.3044i	−0.265637	+	0.496972i	−0.979010	−	0.203813i	$-0.934667\pi$
$613$	−6.57686	+	12.3044i	−0.265637	+	0.496972i	0.713373	+	0.700785i	$0.247167\pi$
$614$	23.8204	+	28.7468i	0.961315	+	1.16013i
$615$	−34.7044	+	23.1887i	−1.39941	+	0.935059i
$616$	−1.44285	+	2.79407i	−0.0581339	+	0.112576i
$617$	21.4443	−	32.0937i	0.863317	−	1.29204i	−0.0917887	−	0.995779i	$-0.529258\pi$
$617$	21.4443	−	32.0937i	0.863317	−	1.29204i	0.955105	−	0.296266i	$-0.0957416\pi$
$618$	39.0896	−	48.0931i	1.57241	−	1.93459i
$619$	7.33898	+	8.94257i	0.294978	+	0.359432i	0.899318	−	0.437294i	$-0.144063\pi$
$619$	7.33898	+	8.94257i	0.294978	+	0.359432i	−0.604340	+	0.796726i	$0.706563\pi$
$620$	44.0542	+	3.91836i	1.76926	+	0.157365i
$621$	−6.45739	−	12.0809i	−0.259126	−	0.484791i
$622$	−7.75809	+	18.9833i	−0.311071	+	0.761159i
$623$	−3.74956	−	9.05225i	−0.150223	−	0.362671i
$624$	−2.49268	−	0.446954i	−0.0997869	−	0.0178925i
$625$	−8.75692	+	21.1411i	−0.350277	+	0.845643i
$626$	8.21562	+	8.13824i	0.328362	+	0.325269i
$627$	1.44208	+	0.437452i	0.0575913	+	0.0174701i
$628$	11.9103	+	21.7841i	0.475272	+	0.869282i
$629$	−2.78421	+	28.2686i	−0.111014	+	1.12714i
$630$	5.27548	−	17.6919i	0.210180	−	0.704862i
$631$	−3.63938	−	18.2964i	−0.144881	−	0.728368i	−0.983105	−	0.183042i	$-0.941406\pi$
$631$	−3.63938	−	18.2964i	−0.144881	−	0.728368i	0.838224	−	0.545327i	$-0.183594\pi$
$632$	7.11759	+	4.61103i	0.283123	+	0.183417i
$633$	0.548693	+	0.109142i	0.0218086	+	0.00433800i
$634$	−7.93485	−	25.7189i	−0.315133	−	1.02143i
$635$	10.6324	+	35.0503i	0.421934	+	1.39093i
$636$	17.9720	−	44.5768i	0.712634	−	1.76758i
$637$	−0.184326	−	0.151272i	−0.00730324	−	0.00599362i
$638$	5.09280	+	3.36815i	0.201626	+	0.133346i
$639$	−8.23536			−0.325786
$640$	28.9445	+	22.1916i	1.14413	+	0.877198i
$641$	−20.4306			−0.806958			−0.403479	−	0.914989i	$-0.632199\pi$
$641$	−20.4306			−0.806958			−0.403479	+	0.914989i	$0.632199\pi$
$642$	35.8943	+	23.7389i	1.41664	+	0.936900i
$643$	15.8944	+	13.0442i	0.626815	+	0.514413i	0.893321	−	0.449420i	$-0.148369\pi$
$643$	15.8944	+	13.0442i	0.626815	+	0.514413i	−0.266506	+	0.963833i	$0.585869\pi$
$644$	9.11933	+	3.67663i	0.359352	+	0.144879i
$645$	16.1326	+	53.1819i	0.635219	+	2.09404i
$646$	1.57404	+	5.10188i	0.0619297	+	0.200731i
$647$	−11.3413	−	2.25593i	−0.445873	−	0.0886896i	−0.0329527	−	0.999457i	$-0.510491\pi$
$647$	−11.3413	−	2.25593i	−0.445873	−	0.0886896i	−0.412920	+	0.910767i	$0.635491\pi$
$648$	−13.1394	+	2.80806i	−0.516164	+	0.110311i
$649$	0.934106	+	4.69607i	0.0366669	+	0.184337i
$650$	0.519641	−	1.74267i	0.0203820	−	0.0683532i
$651$	−1.78519	+	18.1254i	−0.0699673	+	0.710390i
$652$	−14.5114	+	7.93396i	−0.568308	+	0.310718i
$653$	−12.6554	−	3.83896i	−0.495243	−	0.150230i	0.0327763	−	0.999463i	$-0.489565\pi$
$653$	−12.6554	−	3.83896i	−0.495243	−	0.150230i	−0.528019	+	0.849232i	$0.677065\pi$
$654$	−38.7587	−	38.3936i	−1.51559	−	1.50131i
$655$	−26.0774	+	62.9565i	−1.01893	+	2.45991i
$656$	19.0553	−	4.16675i	0.743985	−	0.162684i
$657$	10.2503	+	24.7465i	0.399904	+	0.965453i
$658$	−3.27917	+	8.02379i	−0.127835	+	0.312800i
$659$	−10.1593	−	19.0067i	−0.395750	−	0.740396i	0.602586	−	0.798054i	$-0.294137\pi$
$659$	−10.1593	−	19.0067i	−0.395750	−	0.740396i	−0.998336	+	0.0576573i	$0.981637\pi$
$660$	1.68616	−	18.9575i	0.0656336	−	0.737919i
$661$	7.12530	+	8.68220i	0.277142	+	0.337699i	0.892915	−	0.450225i	$-0.148656\pi$
$661$	7.12530	+	8.68220i	0.277142	+	0.337699i	−0.615773	+	0.787924i	$0.711156\pi$
$662$	13.7773	−	16.9506i	0.535471	−	0.658806i
$663$	−2.60117	+	3.89293i	−0.101021	+	0.151189i
$664$	−16.9510	+	5.40597i	−0.657827	+	0.209792i
$665$	1.36840	−	0.914337i	0.0530644	−	0.0354565i
$666$	14.0348	+	16.9374i	0.543839	+	0.656312i
$667$	8.99975	−	16.8373i	0.348472	−	0.651944i
$668$	15.6044	−	23.8390i	0.603753	−	0.922359i
$669$	−34.3894	+	3.38706i	−1.32957	+	0.130951i
$670$	−56.2081	+	37.9430i	−2.17151	+	1.46587i
$671$	1.01772	+	1.01772i	0.0392887	+	0.0392887i
$672$	−9.25086	+	11.8323i	−0.356860	+	0.456441i
$673$	−8.80438	+	8.80438i	−0.339384	+	0.339384i	−0.856135	−	0.516751i	$-0.827141\pi$
$673$	−8.80438	+	8.80438i	−0.339384	+	0.339384i	0.516751	+	0.856135i	$0.327141\pi$
$674$	4.29252	−	22.1266i	0.165342	−	0.852287i
$675$	1.47276	+	14.9532i	0.0566865	+	0.575548i
$676$	−4.80966	+	25.4355i	−0.184987	+	0.978290i
$677$	−19.6952	−	10.5273i	−0.756946	−	0.404596i	0.0473090	−	0.998880i	$-0.484935\pi$
$677$	−19.6952	−	10.5273i	−0.756946	−	0.404596i	−0.804255	+	0.594284i	$0.797435\pi$
$678$	−3.18976	+	34.0366i	−0.122502	+	1.30717i
$679$	−5.33501	−	7.98441i	−0.204739	−	0.306414i
$680$	59.0117	−	32.6278i	2.26299	−	1.25122i
$681$	32.9360	+	22.0071i	1.26211	+	0.843314i
$682$	1.10795	+	10.7285i	0.0424257	+	0.410817i
$683$	39.2188	−	32.1860i	1.50066	−	1.23156i	0.597796	−	0.801648i	$-0.296043\pi$
$683$	39.2188	−	32.1860i	1.50066	−	1.23156i	0.902869	−	0.429916i	$-0.141457\pi$
$684$	3.66465	+	1.91443i	0.140121	+	0.0731999i
$685$	36.6968	−	19.6148i	1.40211	−	0.749444i
$686$	−1.30399	+	0.547373i	−0.0497865	+	0.0208988i
$687$	−21.8976	+	9.07026i	−0.835444	+	0.346052i
$688$	2.05602	−	25.8902i	0.0783849	−	0.987054i
$689$	1.99398	+	0.825935i	0.0759648	+	0.0314656i
$690$	−59.5096	+	0.281603i	−2.26549	+	0.0107204i
$691$	9.59316	−	31.6244i	0.364941	−	1.20305i	−0.561776	−	0.827289i	$-0.689882\pi$
$691$	9.59316	−	31.6244i	0.364941	−	1.20305i	0.926717	−	0.375760i	$-0.122618\pi$
$692$	37.2324	+	29.9707i	1.41537	+	1.13932i
$693$	4.48045	+	0.441285i	0.170198	+	0.0167630i
$694$	−33.6909	+	18.2136i	−1.27889	+	0.691380i
$695$	8.62274	−	1.71517i	0.327079	−	0.0650601i
$696$	20.9118	+	20.3264i	0.792660	+	0.770469i
$697$	7.03538	−	35.3692i	0.266484	−	1.33971i
$698$	20.2160	+	10.6830i	0.765188	+	0.404358i
$699$	5.32212	−	1.61445i	0.201301	−	0.0610640i
$700$	−7.69810	−	7.55375i	−0.290961	−	0.285505i
$701$	23.5818	−	28.7345i	0.890672	−	1.08529i	−0.105194	−	0.994452i	$-0.533546\pi$
$701$	23.5818	−	28.7345i	0.890672	−	1.08529i	0.995866	−	0.0908348i	$-0.0289535\pi$
$702$	0.187668	+	0.920679i	0.00708306	+	0.0347488i
$703$			1.96089i			0.0739563i
$704$	−3.96839	+	7.95996i	−0.149564	+	0.300002i
$705$		−	52.4617i		−	1.97582i
$706$	−48.0206	+	9.78833i	−1.80728	+	0.368389i
$707$	8.62205	−	10.5060i	0.324266	−	0.395119i
$708$	0.216429	+	22.8678i	0.00813390	+	0.859426i
$709$	36.4019	−	11.0424i	1.36710	−	0.414706i	0.480402	−	0.877049i	$-0.340491\pi$
$709$	36.4019	−	11.0424i	1.36710	−	0.414706i	0.886701	+	0.462342i	$0.152991\pi$
$710$	−4.33197	+	8.19761i	−0.162576	+	0.307651i
$711$	2.36873	−	11.9084i	0.0888342	−	0.446600i
$712$	−10.9678	−	25.4505i	−0.411034	−	0.953798i
$713$	33.0764	−	6.57930i	1.23872	−	0.246397i
$714$	13.2055	+	24.4270i	0.494204	+	0.914158i
$715$	0.850528	+	0.0837697i	0.0318080	+	0.00313281i
$716$	26.3379	−	2.84599i	0.984295	−	0.106359i
$717$	−8.91014	+	29.3728i	−0.332755	+	1.09695i
$718$	0.0998179	+	21.0939i	0.00372517	+	0.787219i
$719$	−13.9609	−	5.78280i	−0.520654	−	0.215662i	0.106850	−	0.994275i	$-0.465923\pi$
$719$	−13.9609	−	5.78280i	−0.520654	−	0.215662i	−0.627504	+	0.778613i	$0.715923\pi$
$720$	14.2095	−	50.2470i	0.529556	−	1.87259i
$721$	15.2490	−	6.31635i	0.567903	−	0.235233i
$722$	−10.2574	−	24.4359i	−0.381742	−	0.909410i
$723$	−39.5363	+	21.1326i	−1.47037	+	0.785929i
$724$	−6.40851	−	20.4280i	−0.238170	−	0.759201i
$725$	−16.1878	+	13.2850i	−0.601201	+	0.493393i
$726$	−36.4681	+	3.76612i	−1.35346	+	0.139774i
$727$	−7.94367	−	5.30779i	−0.294614	−	0.196855i	0.399475	−	0.916744i	$-0.369193\pi$
$727$	−7.94367	−	5.30779i	−0.294614	−	0.196855i	−0.694089	+	0.719889i	$0.744193\pi$
$728$	−0.527373	−	0.420418i	−0.0195457	−	0.0155817i
$729$	23.0173	+	34.4479i	0.852494	+	1.27585i
$730$	30.0249	+	2.81381i	1.11127	+	0.104144i
$731$	−42.3471	−	22.6350i	−1.56626	−	0.837185i
$732$	3.87307	+	5.67936i	0.143153	+	0.209915i
$733$	−2.03089	−	20.6199i	−0.0750125	−	0.761615i	−0.956951	−	0.290250i	$-0.906262\pi$
$733$	−2.03089	−	20.6199i	−0.0750125	−	0.761615i	0.881938	−	0.471365i	$-0.156238\pi$
$734$	−40.7084	−	7.89734i	−1.50258	−	0.291496i
$735$	6.05235	−	6.05235i	0.223244	−	0.223244i
$736$	25.9384	+	10.0319i	0.956101	+	0.369780i
$737$	−11.6940	−	11.6940i	−0.430755	−	0.430755i
$738$	−15.6245	−	23.1459i	−0.575147	−	0.852013i
$739$	13.2955	−	1.30949i	0.489081	−	0.0481703i	0.149529	−	0.988757i	$-0.452224\pi$
$739$	13.2955	−	1.30949i	0.489081	−	0.0481703i	0.339553	+	0.940587i	$0.389724\pi$
$740$	24.2424	−	5.06107i	0.891168	−	0.186049i
$741$	−0.152360	+	0.285045i	−0.00559707	+	0.0104714i
$742$	9.85625	−	8.16717i	0.361834	−	0.299826i
$743$	−31.9217	+	21.3294i	−1.17110	+	0.782501i	−0.979986	−	0.199068i	$-0.936209\pi$
$743$	−31.9217	+	21.3294i	−1.17110	+	0.782501i	−0.191109	+	0.981569i	$0.561209\pi$
$744$	−4.32103	+	51.3328i	−0.158416	+	1.88195i
$745$	−4.73152	+	7.08121i	−0.173349	+	0.259436i
$746$	−24.8598	−	20.2058i	−0.910184	−	0.739788i
$747$	16.1598	+	19.6908i	0.591258	+	0.720449i
$748$	10.5518	+	12.6121i	0.385811	+	0.461142i
$749$	5.40266	+	10.1077i	0.197409	+	0.369326i
$750$	4.39896	+	1.79777i	0.160627	+	0.0656452i
$751$	−17.8703	−	43.1427i	−0.652096	−	1.57430i	−0.809730	−	0.586802i	$-0.800387\pi$
$751$	−17.8703	−	43.1427i	−0.652096	−	1.57430i	0.157634	−	0.987498i	$-0.449613\pi$
$752$	−8.95178	+	22.8241i	−0.326438	+	0.832309i
$753$	−23.0825	+	55.7262i	−0.841174	+	2.03077i
$754$	−0.921598	+	0.930361i	−0.0335626	+	0.0338818i
$755$	−51.5739	−	15.6448i	−1.87697	−	0.569372i
$756$	5.34778	+	1.56712i	0.194497	+	0.0569955i
$757$	2.68046	−	27.2152i	0.0974229	−	0.989152i	−0.814878	−	0.579632i	$-0.803196\pi$
$757$	2.68046	−	27.2152i	0.0974229	−	0.989152i	0.912301	−	0.409520i	$-0.134304\pi$
$758$	30.1201	+	8.98140i	1.09401	+	0.326219i
$759$	−2.83122	−	14.2335i	−0.102767	−	0.516643i
$760$	3.83332	−	2.64082i	0.139049	−	0.0957926i
$761$	43.8068	+	8.71371i	1.58799	+	0.315872i	0.908524	−	0.417832i	$-0.137210\pi$
$761$	43.8068	+	8.71371i	1.58799	+	0.315872i	0.679470	+	0.733704i	$0.262210\pi$
$762$	−40.7656	+	12.5771i	−1.47678	+	0.455619i
$763$	−4.21765	−	13.9037i	−0.152689	−	0.503349i
$764$	−6.88144	+	2.92699i	−0.248962	+	0.105895i
$765$	−74.6268	−	61.2446i	−2.69814	−	2.21430i
$766$	−25.6043	+	38.7148i	−0.925119	+	1.39882i
$767$	−1.02692			−0.0370800
$768$	−25.6877	+	33.8349i	−0.926924	+	1.22091i
$769$	−23.3905			−0.843483			−0.421742	−	0.906716i	$-0.638581\pi$
$769$	−23.3905			−0.843483			−0.421742	+	0.906716i	$0.638581\pi$
$770$	2.79607	−	4.22778i	0.100763	−	0.152359i
$771$	−51.6400	−	42.3798i	−1.85977	−	1.52627i
$772$	−18.9527	+	8.06146i	−0.682124	+	0.290138i
$773$	2.44475	+	8.05925i	0.0879315	+	0.289871i	0.989867	−	0.142000i	$-0.0453534\pi$
$773$	2.44475	+	8.05925i	0.0879315	+	0.289871i	−0.901935	+	0.431871i	$0.857853\pi$
$774$	−35.5309	+	10.9620i	−1.27713	+	0.394022i
$775$	−36.2808	−	7.21671i	−1.30325	−	0.259232i
$776$	−15.4088	−	22.3668i	−0.553142	−	0.802923i
$777$	1.98957	+	10.0023i	0.0713756	+	0.358829i
$778$	8.02907	+	2.39416i	0.287856	+	0.0858348i
$779$	0.244009	−	2.47747i	0.00874254	−	0.0887645i
$780$	3.91724	+	1.14791i	0.140260	+	0.0411018i
$781$	−2.16370	−	0.656350i	−0.0774231	−	0.0234861i
$782$	36.1848	−	36.5289i	1.29397	−	1.30627i
$783$	4.14075	−	9.99664i	0.147978	−	0.357251i
$784$	−3.66588	+	1.60040i	−0.130924	+	0.0571573i
$785$	−15.3145	−	36.9726i	−0.546600	−	1.31961i
$786$	−73.4711	−	30.0262i	−2.62063	−	1.07100i
$787$	18.7483	+	35.0756i	0.668305	+	1.25031i	0.956218	+	0.292654i	$0.0945386\pi$
$787$	18.7483	+	35.0756i	0.668305	+	1.25031i	−0.287913	+	0.957657i	$0.592961\pi$
$788$	30.2076	+	36.1058i	1.07610	+	1.28622i
$789$	−36.5102	−	44.4879i	−1.29980	−	1.58381i
$790$	−10.6078	−	8.62192i	−0.377409	−	0.306754i
$791$	−5.05815	+	7.57005i	−0.179847	+	0.269160i
$792$	12.6891	+	1.06812i	0.450886	+	0.0379541i
$793$	−0.256665	+	0.171498i	−0.00911446	+	0.00609008i
$794$	2.07077	−	1.71590i	0.0734888	−	0.0608949i
$795$	−36.5201	+	68.3243i	−1.29523	+	2.42321i
$796$	17.1567	−	3.58181i	0.608104	−	0.126954i
$797$	−15.8318	+	1.55929i	−0.560790	+	0.0552330i	−0.374441	−	0.927251i	$-0.622165\pi$
$797$	−15.8318	+	1.55929i	−0.560790	+	0.0552330i	−0.186349	+	0.982484i	$0.559665\pi$
$798$	1.07250	+	1.58878i	0.0379660	+	0.0562422i
$799$	32.0510	+	32.0510i	1.13388	+	1.13388i
$800$	−22.0746	−	21.0540i	−0.780456	−	0.744371i
$801$	−28.0557	+	28.0557i	−0.991298	+	0.991298i
$802$	13.6350	+	2.64515i	0.481467	+	0.0934035i
$803$	0.720824	+	7.31865i	0.0254373	+	0.258269i
$804$	−44.5032	−	65.2581i	−1.56951	−	2.30148i
$805$	−13.9775	−	7.47113i	−0.492642	−	0.263323i
$806$	−2.30315	−	0.215841i	−0.0811251	−	0.00760269i
$807$	12.8824	+	19.2798i	0.453481	+	0.678682i
$808$	23.9626	−	30.0586i	0.843000	−	1.05746i
$809$	23.6935	+	15.8315i	0.833018	+	0.556605i	0.897348	−	0.441324i	$-0.145491\pi$
$809$	23.6935	+	15.8315i	0.833018	+	0.556605i	−0.0643300	+	0.997929i	$0.520491\pi$
$810$	21.5428	−	2.22476i	0.756936	−	0.0781700i
$811$	−17.2375	+	14.1464i	−0.605289	+	0.496748i	−0.886395	−	0.462929i	$-0.846799\pi$
$811$	−17.2375	+	14.1464i	−0.605289	+	0.496748i	0.281107	+	0.959677i	$0.409299\pi$
$812$	2.32479	+	7.41059i	0.0815841	+	0.260061i
$813$	−40.9079	+	21.8657i	−1.43470	+	0.766865i
$814$	2.33751	+	5.56857i	0.0819297	+	0.195178i
$815$	24.6290	−	10.2017i	0.862717	−	0.357349i
$816$	38.3278	+	68.5529i	1.34174	+	2.39983i
$817$	−3.06239	−	1.26849i	−0.107140	−	0.0443787i
$818$	0.121354	+	25.6451i	0.00424306	+	0.896661i
$819$	−0.280297	+	0.924016i	−0.00979438	+	0.0322877i
$820$	−31.2586	+	3.37769i	−1.09160	+	0.117954i
$821$	34.0740	+	3.35600i	1.18919	+	0.117125i	0.673195	−	0.739465i	$-0.264922\pi$
$821$	34.0740	+	3.35600i	1.18919	+	0.117125i	0.515997	+	0.856591i	$0.327422\pi$
$822$	23.0482	+	42.6337i	0.803900	+	1.48702i
$823$	−17.3543	+	3.45198i	−0.604932	+	0.120328i	−0.488047	−	0.872817i	$-0.662291\pi$
$823$	−17.3543	+	3.45198i	−0.604932	+	0.120328i	−0.116884	+	0.993146i	$0.537291\pi$
$824$	42.8728	−	18.4758i	1.49354	−	0.643635i
$825$	−3.10551	+	15.6125i	−0.108120	+	0.543556i
$826$	−2.84559	+	5.38486i	−0.0990107	+	0.187363i
$827$	36.8930	−	11.1914i	1.28290	−	0.389162i	0.426034	−	0.904707i	$-0.359910\pi$
$827$	36.8930	−	11.1914i	1.28290	−	0.389162i	0.856863	+	0.515545i	$0.172410\pi$
$828$	−0.376819	−	39.8146i	−0.0130954	−	1.38365i
$829$	7.79839	−	9.50236i	0.270849	−	0.330031i	−0.619768	−	0.784785i	$-0.712773\pi$
$829$	7.79839	−	9.50236i	0.270849	−	0.330031i	0.890617	+	0.454755i	$0.150273\pi$
$830$	28.1009	−	5.72799i	0.975398	−	0.198821i
$831$			74.2372i			2.57526i
$832$	−1.50837	−	1.16783i	−0.0522932	−	0.0404871i
$833$			7.39526i			0.256230i
$834$	2.04523	+	10.0337i	0.0708207	+	0.347439i
$835$	−29.1349	+	35.5010i	−1.00826	+	1.22856i
$836$	0.810243	+	0.795050i	0.0280228	+	0.0274974i
$837$	18.2904	−	5.54834i	0.632210	−	0.191779i
$838$	−25.4564	−	13.4523i	−0.879377	−	0.464700i
$839$	−7.77642	+	39.0947i	−0.268472	+	1.34970i	0.577464	+	0.816416i	$0.304042\pi$
$839$	−7.77642	+	39.0947i	−0.268472	+	1.34970i	−0.845936	+	0.533284i	$0.820958\pi$
$840$	16.8739	−	17.3599i	0.582205	−	0.598974i
$841$	−13.6522	+	2.71558i	−0.470764	+	0.0936408i
$842$	47.1959	−	25.5146i	1.62648	−	0.879292i
$843$	−86.3955	−	8.50922i	−2.97562	−	0.293073i
$844$	0.328273	+	0.264247i	0.0112996	+	0.00909576i
$845$	12.1123	−	39.9288i	0.416675	−	1.37359i
$846$	35.1001	−	0.166096i	1.20677	−	0.00571050i
$847$	−9.02069	−	3.73649i	−0.309954	−	0.128387i
$848$	27.5470	−	23.4937i	0.945966	−	0.806776i
$849$	−41.5317	+	17.2030i	−1.42536	+	0.590405i
$850$	−52.0024	+	21.8290i	−1.78367	+	0.748728i
$851$	16.6539	−	8.90167i	0.570887	−	0.305145i
$852$	−9.57188	−	5.00039i	−0.327927	−	0.171311i
$853$	11.6131	−	9.53062i	0.397625	−	0.326322i	−0.414240	−	0.910168i	$-0.635953\pi$
$853$	11.6131	−	9.53062i	0.397625	−	0.326322i	0.811865	+	0.583845i	$0.198453\pi$
$854$	0.188067	+	1.82109i	0.00643553	+	0.0623165i
$855$	−5.54126	−	3.70255i	−0.189507	−	0.126625i
$856$	15.6853	+	28.3690i	0.536114	+	0.969633i
$857$	−11.1782	−	16.7294i	−0.381841	−	0.571465i	0.589912	−	0.807468i	$-0.299163\pi$
$857$	−11.1782	−	16.7294i	−0.381841	−	0.571465i	−0.971752	+	0.236003i	$0.924163\pi$
$858$	−0.0928814	+	0.991098i	−0.00317092	+	0.0338355i
$859$	26.4847	+	14.1564i	0.903647	+	0.483009i	0.856657	−	0.515886i	$-0.172537\pi$
$859$	26.4847	+	14.1564i	0.903647	+	0.483009i	0.0469898	+	0.998895i	$0.485037\pi$
$860$	−7.77815	+	41.1342i	−0.265233	+	1.40267i
$861$	−1.26905	−	12.8849i	−0.0432490	−	0.439115i
$862$	−4.06169	+	20.9368i	−0.138342	+	0.713110i
$863$	−5.75090	+	5.75090i	−0.195763	+	0.195763i	−0.798181	−	0.602418i	$-0.794204\pi$
$863$	−5.75090	+	5.75090i	−0.195763	+	0.195763i	0.602418	+	0.798181i	$0.294204\pi$
$864$	15.1872	+	4.21731i	0.516679	+	0.143476i
$865$	−54.4769	−	54.4769i	−1.85227	−	1.85227i
$866$	26.4467	−	17.8527i	0.898697	−	0.606661i
$867$	99.5875	−	9.80851i	3.38217	−	0.333114i
$868$	−7.51381	+	11.4789i	−0.255035	+	0.389620i
$869$	1.57143	−	2.93994i	0.0533071	−	0.0997305i
$870$	−29.9924	−	36.1952i	−1.01684	−	1.22713i
$871$	2.94919	−	1.97058i	0.0999294	−	0.0667707i
$872$	−12.4864	−	39.1524i	−0.422842	−	1.32587i
$873$	−21.6038	+	32.3324i	−0.731177	+	1.09428i
$874$	2.23872	−	2.75437i	0.0757260	−	0.0931679i
$875$	0.802889	+	0.978323i	0.0271426	+	0.0330733i
$876$	−3.11184	+	34.9865i	−0.105139	+	1.18208i
$877$	−17.1698	−	32.1224i	−0.579782	−	1.08470i	−0.985336	−	0.170625i	$-0.945421\pi$
$877$	−17.1698	−	32.1224i	−0.579782	−	1.08470i	0.405554	−	0.914071i	$-0.367079\pi$
$878$	−18.2662	+	44.6957i	−0.616456	+	1.50841i
$879$	14.2539	+	34.4119i	0.480771	+	1.16068i
$880$	7.73792	−	12.0690i	0.260845	−	0.406847i
$881$	−9.24428	+	22.3177i	−0.311448	+	0.751901i	0.688204	+	0.725517i	$0.258399\pi$
$881$	−9.24428	+	22.3177i	−0.311448	+	0.751901i	−0.999652	+	0.0263841i	$0.991601\pi$
$882$	4.06855	+	4.03023i	0.136995	+	0.135705i
$883$	16.2412	+	4.92672i	0.546560	+	0.165797i	0.551476	−	0.834191i	$-0.314065\pi$
$883$	16.2412	+	4.92672i	0.546560	+	0.165797i	−0.00491592	+	0.999988i	$0.501565\pi$
$884$	−3.09450	+	1.69189i	−0.104079	+	0.0569045i
$885$	3.61309	−	36.6843i	0.121453	−	1.23313i
$886$	9.14679	−	30.6747i	0.307293	−	1.03054i
$887$	0.319119	+	1.60432i	0.0107150	+	0.0538679i	0.985773	−	0.168083i	$-0.0537576\pi$
$887$	0.319119	+	1.60432i	0.0107150	+	0.0538679i	−0.975058	+	0.221951i	$0.928758\pi$
$888$	6.02840	+	28.2079i	0.202300	+	0.946597i
$889$	−11.1434	−	2.21657i	−0.373739	−	0.0743413i
$890$	13.1692	+	42.6849i	0.441433	+	1.43080i
$891$	1.53312	+	5.05401i	0.0513614	+	0.169316i
$892$	−24.1417	−	9.73319i	−0.808325	−	0.325891i
$893$	2.41877	+	1.98503i	0.0809411	+	0.0664266i
$894$	−8.27379	−	5.47191i	−0.276717	−	0.183008i
$895$	−42.7006			−1.42733
$896$	−10.3034	+	4.67336i	−0.344212	+	0.156126i
$897$	3.11254			0.103925
$898$	19.1175	+	12.6435i	0.637960	+	0.421918i
$899$	20.5920	+	16.8994i	0.686780	+	0.563626i
$900$	−16.3306	+	40.5057i	−0.544355	+	1.35019i
$901$	−19.4305	−	64.0537i	−0.647323	−	2.13394i
$902$	−2.26036	−	7.32644i	−0.0752619	−	0.243944i
$903$	−16.9080	−	3.36320i	−0.562662	−	0.111920i
$904$	−14.0012	+	21.6123i	−0.465673	+	0.718814i
$905$	6.73251	+	33.8466i	0.223796	+	1.12510i
$906$	17.9377	−	60.1559i	0.595940	−	1.99855i
$907$	−2.47433	+	25.1223i	−0.0821589	+	0.834173i	0.862487	+	0.506080i	$0.168906\pi$
$907$	−2.47433	+	25.1223i	−0.0821589	+	0.834173i	−0.944645	+	0.328093i	$0.893594\pi$
$908$	14.3142	+	26.1809i	0.475033	+	0.868844i
$909$	−52.6661	−	15.9761i	−1.74682	−	0.529894i
$910$	0.772338	+	0.765063i	0.0256028	+	0.0253616i
$911$	−2.04324	+	4.93282i	−0.0676956	+	0.163432i	−0.954106	−	0.299468i	$-0.903191\pi$
$911$	−2.04324	+	4.93282i	−0.0676956	+	0.163432i	0.886411	+	0.462899i	$0.153191\pi$
$912$	3.09697	+	4.45024i	0.102551	+	0.147362i
$913$	2.67637	+	6.46134i	0.0885750	+	0.213839i
$914$	7.17343	−	17.5527i	0.237276	−	0.580590i
$915$	−5.22332	−	9.77214i	−0.172678	−	0.323057i
$916$	−17.7837	−	1.58176i	−0.587590	−	0.0522627i
$917$	−13.4098	−	16.3399i	−0.442830	−	0.539590i
$918$	18.3799	−	22.6133i	0.606627	−	0.746352i
$919$	28.6278	−	42.8445i	0.944343	−	1.41331i	0.0340144	−	0.999421i	$-0.489171\pi$
$919$	28.6278	−	42.8445i	0.944343	−	1.41331i	0.910328	−	0.413887i	$-0.135829\pi$
$920$	−39.8303	−	20.5682i	−1.31317	−	0.678113i
$921$	58.2784	−	38.9404i	1.92034	−	1.28313i
$922$	2.46695	+	2.97715i	0.0812447	+	0.0980471i
$923$	0.228599	−	0.427679i	0.00752444	−	0.0140772i
$924$	4.93964	+	3.23336i	0.162502	+	0.106370i
$925$	−20.6133	+	2.03024i	−0.677762	+	0.0667537i
$926$	12.6927	−	8.56815i	0.417108	−	0.281567i
$927$	−47.2613	−	47.2613i	−1.55227	−	1.55227i
$928$	6.87238	+	20.8649i	0.225597	+	0.684923i
$929$	4.03077	−	4.03077i	0.132245	−	0.132245i	−0.637886	−	0.770131i	$-0.720191\pi$
$929$	4.03077	−	4.03077i	0.132245	−	0.132245i	0.770131	+	0.637886i	$0.220191\pi$
$930$	15.8137	−	81.5151i	0.518553	−	2.67298i
$931$	0.0500389	+	0.508053i	0.00163996	+	0.0166508i
$932$	4.11646	+	0.778390i	0.134839	+	0.0254970i
$933$	33.9549	+	18.1492i	1.11163	+	0.594180i
$934$	0.966186	−	10.3098i	0.0316146	−	0.337346i
$935$	−14.7257	−	22.0386i	−0.481583	−	0.720740i
$936$	−0.755620	+	2.62450i	−0.0246982	+	0.0857846i
$937$	21.8800	+	14.6198i	0.714789	+	0.477606i	0.859023	−	0.511937i	$-0.171072\pi$
$937$	21.8800	+	14.6198i	0.714789	+	0.477606i	−0.144234	+	0.989544i	$0.546072\pi$
$938$	−2.16097	−	20.9251i	−0.0705581	−	0.683228i
$939$	16.7825	−	13.7731i	0.547677	−	0.449467i
$940$	18.2980	−	35.0266i	0.596815	−	1.14244i
$941$	−46.8218	+	25.0268i	−1.52635	+	0.815850i	−0.999420	−	0.0340605i	$-0.989156\pi$
$941$	−46.8218	+	25.0268i	−1.52635	+	0.815850i	−0.526928	+	0.849910i	$0.676656\pi$
$942$	42.9787	−	18.0411i	1.40032	−	0.587811i
$943$	−22.1489	+	9.17436i	−0.721266	+	0.298758i
$944$	−7.83152	+	15.3434i	−0.254894	+	0.499385i
$945$	−8.29870	−	3.43743i	−0.269957	−	0.111820i
$946$	−10.2088	+	0.0483086i	−0.331916	+	0.00157065i
$947$	−1.65665	+	5.46125i	−0.0538340	+	0.177467i	−0.979734	−	0.200301i	$-0.935808\pi$
$947$	−1.65665	+	5.46125i	−0.0538340	+	0.177467i	0.925901	+	0.377767i	$0.123308\pi$
$948$	9.98375	−	12.4028i	0.324257	−	0.402823i
$949$	−1.56967	−	0.154599i	−0.0509536	−	0.00501849i
$950$	−3.42486	+	1.85152i	−0.111117	+	0.0600711i
$951$	−49.5602	+	9.85814i	−1.60710	+	0.319672i
$952$	0.296929	+	20.9148i	0.00962352	+	0.677854i
$953$	2.63470	−	13.2455i	0.0853462	−	0.429064i	−0.914362	−	0.404898i	$-0.867307\pi$
$953$	2.63470	−	13.2455i	0.0853462	−	0.429064i	0.999708	−	0.0241660i	$-0.00769302\pi$
$954$	−45.8287	−	24.2178i	−1.48376	−	0.784081i
$955$	11.5347	−	3.49901i	0.373254	−	0.113225i
$956$	−16.1938	+	16.5033i	−0.523745	+	0.533753i
$957$	7.27218	−	8.86118i	0.235076	−	0.286441i
$958$	−9.63890	−	47.2874i	−0.311419	−	1.52779i
$959$			12.9073i			0.416799i
$960$	47.0247	−	49.7738i	1.51772	−	1.60644i
$961$			16.0557i			0.517926i
$962$	−1.26918	+	0.258705i	−0.0409199	+	0.00834097i
$963$	29.4425	−	35.8758i	0.948770	−	1.15608i
$964$	−33.7675	+	0.319588i	−1.08758	+	0.0102932i
$965$	31.7687	−	9.63692i	1.02267	−	0.310223i
$966$	8.62481	−	16.3212i	0.277499	−	0.525126i
$967$	−8.53314	+	42.8990i	−0.274407	+	1.37954i	0.560047	+	0.828461i	$0.310783\pi$
$967$	−8.53314	+	42.8990i	−0.274407	+	1.37954i	−0.834454	+	0.551078i	$0.814217\pi$
$968$	−25.6618	−	10.2051i	−0.824802	−	0.328005i
$969$	9.83128	−	1.95556i	0.315826	−	0.0628217i
$970$	20.8201	+	38.5122i	0.668493	+	1.23655i
$971$	17.3172	+	1.70560i	0.555736	+	0.0547352i	0.371987	−	0.928238i	$-0.378677\pi$
$971$	17.3172	+	1.70560i	0.555736	+	0.0547352i	0.183749	+	0.982973i	$0.441177\pi$
$972$	4.50601	+	41.7005i	0.144530	+	1.33754i
$973$	−0.791650	+	2.60972i	−0.0253791	+	0.0836638i
$974$	0.138492	+	29.2666i	0.00443756	+	0.937764i
$975$	−3.15420	−	1.30651i	−0.101015	−	0.0418419i
$976$	0.605000	+	5.14276i	0.0193656	+	0.164616i
$977$	23.4691	−	9.72123i	0.750844	−	0.311010i	0.0257581	−	0.999668i	$-0.491800\pi$
$977$	23.4691	−	9.72123i	0.750844	−	0.311010i	0.725086	+	0.688658i	$0.241800\pi$
$978$	12.0180	+	28.6300i	0.384292	+	0.915485i
$979$	−9.60714	+	5.13512i	−0.307045	+	0.164119i
$980$	6.15189	−	1.92992i	0.196515	−	0.0616490i
$981$	−45.4806	+	37.3250i	−1.45209	+	1.19170i
$982$	−45.8526	+	4.73527i	−1.46322	+	0.151109i
$983$	−38.8128	−	25.9339i	−1.23794	−	0.827162i	−0.248011	−	0.968757i	$-0.579777\pi$
$983$	−38.8128	−	25.9339i	−1.23794	−	0.827162i	−0.989925	+	0.141595i	$0.954777\pi$
$984$	−4.10639	−	36.3892i	−0.130907	−	1.16005i
$985$	−42.1569	−	63.0923i	−1.34323	−	2.01029i
$986$	40.4367	+	3.78955i	1.28777	+	0.120684i
$987$	14.3519	+	7.67127i	0.456827	+	0.244179i
$988$	−0.201144	+	0.137171i	−0.00639925	+	0.00436401i
$989$	3.12882	+	31.7674i	0.0994905	+	1.01014i
$990$	−20.1499	−	3.90903i	−0.640405	−	0.124237i
$991$	29.9907	−	29.9907i	0.952687	−	0.952687i	−0.0462436	−	0.998930i	$-0.514725\pi$
$991$	29.9907	−	29.9907i	0.952687	−	0.952687i	0.998930	+	0.0462436i	$0.0147250\pi$
$992$	−20.7892	+	32.7657i	−0.660059	+	1.04031i
$993$	−28.9981	−	28.9981i	−0.920227	−	0.920227i
$994$	−1.60917	−	2.38380i	−0.0510398	−	0.0756095i
$995$	−28.1147	+	2.76906i	−0.891297	+	0.0877851i
$996$	6.82645	+	32.6985i	0.216304	+	1.03609i
$997$	−3.06629	+	5.73662i	−0.0971103	+	0.181681i	−0.925786	−	0.378049i	$-0.876595\pi$
$997$	−3.06629	+	5.73662i	−0.0971103	+	0.181681i	0.828675	+	0.559730i	$0.189095\pi$
$998$	21.7277	−	18.0042i	0.687780	−	0.569914i
$999$	8.89870	−	5.94592i	0.281542	−	0.188121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.a.533.33	✓	752
128.61	even	32	inner	896.2.bn.a.701.33	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.a.533.33	✓	752	1.1	even	1	trivial
896.2.bn.a.701.33	yes	752	128.61	even	32	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.780122 - 1.17958i) q^{2} +(-2.05240 - 1.68436i) q^{3} +(-0.782820 - 1.84043i) q^{4} +(0.935806 + 3.08494i) q^{5} +(-3.58797 + 1.10697i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-2.78163 - 0.512363i) q^{8} +(0.790006 + 3.97163i) q^{9} +O(q^{10})\)	\(q+(0.780122 - 1.17958i) q^{2} +(-2.05240 - 1.68436i) q^{3} +(-0.782820 - 1.84043i) q^{4} +(0.935806 + 3.08494i) q^{5} +(-3.58797 + 1.10697i) q^{6} +(-0.980785 - 0.195090i) q^{7} +(-2.78163 - 0.512363i) q^{8} +(0.790006 + 3.97163i) q^{9} +(4.36898 + 1.30277i) q^{10} +(-0.108975 + 1.10644i) q^{11} +(-1.49330 + 5.09586i) q^{12} +(-0.228184 - 0.0692188i) q^{13} +(-0.995257 + 1.00472i) q^{14} +(3.27551 - 7.90778i) q^{15} +(-2.77439 + 2.88145i) q^{16} +(2.83004 + 6.83233i) q^{17} +(5.30115 + 2.16648i) q^{18} +(0.240654 + 0.450231i) q^{19} +(4.94506 - 4.13724i) q^{20} +(1.68436 + 2.05240i) q^{21} +(1.22012 + 0.991700i) q^{22} +(2.73135 - 4.08775i) q^{23} +(4.84602 + 5.73686i) q^{24} +(-4.48377 + 2.99596i) q^{25} +(-0.259660 + 0.215162i) q^{26} +(1.31347 - 2.45733i) q^{27} +(0.408727 + 1.95779i) q^{28} +(3.86465 - 0.380634i) q^{29} +(-6.77256 - 10.0328i) q^{30} +(4.85055 + 4.85055i) q^{31} +(1.23455 + 5.52050i) q^{32} +(2.08730 - 2.08730i) q^{33} +(10.2671 + 1.99178i) q^{34} +(-0.315983 - 3.20823i) q^{35} +(6.69108 - 4.56302i) q^{36} +(3.38748 + 1.81065i) q^{37} +(0.718823 + 0.0673650i) q^{38} +(0.351736 + 0.526410i) q^{39} +(-1.02246 - 9.06064i) q^{40} +(-4.05457 - 2.70918i) q^{41} +(3.73498 - 0.385718i) q^{42} +(-5.01910 + 4.11907i) q^{43} +(2.12163 - 0.665580i) q^{44} +(-11.5129 + 6.15379i) q^{45} +(-2.69104 - 6.41078i) q^{46} +(5.66264 - 2.34554i) q^{47} +(10.5476 - 1.24083i) q^{48} +(0.923880 + 0.382683i) q^{49} +(0.0360876 + 7.62618i) q^{50} +(5.69973 - 18.7895i) q^{51} +(0.0512342 + 0.474143i) q^{52} +(-9.00762 - 0.887173i) q^{53} +(-1.87395 - 3.46635i) q^{54} +(-3.51527 + 0.699231i) q^{55} +(2.62823 + 1.04519i) q^{56} +(0.264435 - 1.32940i) q^{57} +(2.56591 - 4.85560i) q^{58} +(4.12119 - 1.25015i) q^{59} +(-17.1179 + 0.162009i) q^{60} +(0.821257 - 1.00071i) q^{61} +(9.50564 - 1.93759i) q^{62} -4.04944i q^{63} +(7.47497 + 2.85041i) q^{64} -0.768709i q^{65} +(-0.833790 - 4.09049i) q^{66} +(-9.43657 + 11.4985i) q^{67} +(10.3590 - 10.5570i) q^{68} +(-12.4911 + 3.78913i) q^{69} +(-4.03087 - 2.13008i) q^{70} +(-0.396757 + 1.99463i) q^{71} +(-0.162590 - 11.4524i) q^{72} +(6.48751 - 1.29045i) q^{73} +(4.77845 - 2.58328i) q^{74} +(14.2488 + 1.40338i) q^{75} +(0.640232 - 0.795356i) q^{76} +(0.322736 - 1.06392i) q^{77} +(0.895339 - 0.00423680i) q^{78} +(-2.77013 - 1.14743i) q^{79} +(-11.4854 - 5.86233i) q^{80} +(4.38878 - 1.81789i) q^{81} +(-6.35875 + 2.66920i) q^{82} +(5.54771 - 2.96531i) q^{83} +(2.45876 - 4.70662i) q^{84} +(-18.4289 + 15.1242i) q^{85} +(0.943262 + 9.13380i) q^{86} +(-8.57294 - 5.72825i) q^{87} +(0.870025 - 3.02187i) q^{88} +(5.44352 + 8.14681i) q^{89} +(-1.72260 + 18.3811i) q^{90} +(0.210296 + 0.112405i) q^{91} +(-9.66138 - 1.82689i) q^{92} +(-1.78519 - 18.1254i) q^{93} +(1.65079 - 8.50935i) q^{94} +(-1.16373 + 1.16373i) q^{95} +(6.76474 - 13.4097i) q^{96} +(6.79018 + 6.79018i) q^{97} +(1.17214 - 0.791250i) q^{98} +(-4.48045 + 0.441285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q+O(q^{10}) \) 752 * q	\( 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) \) 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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