LMFDB - Embedded newform 990.2.o.a.329.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.10
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.13835 + 1.30543i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.78534 + 1.34631i) q^{5} +(0.333128 - 1.69971i) q^{6} +(-2.44430 - 4.23366i) q^{7} +1.00000i q^{8} +(-0.408300 - 2.97209i) q^{9} +(-2.21931 - 0.273267i) q^{10} +(-2.51818 - 2.15842i) q^{11} +(0.561359 + 1.63856i) q^{12} +(1.35370 - 2.34467i) q^{13} +(4.23366 + 2.44430i) q^{14} +(-3.78987 + 0.798065i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.38880i q^{17} +(1.83964 + 2.36975i) q^{18} +3.67973i q^{19} +(2.05861 - 0.872998i) q^{20} +(8.30923 + 1.62853i) q^{21} +(3.26002 + 0.610161i) q^{22} +(-3.74187 + 6.48110i) q^{23} +(-1.30543 - 1.13835i) q^{24} +(1.37490 + 4.80725i) q^{25} +2.70739i q^{26} +(4.34464 + 2.85028i) q^{27} -4.88861 q^{28} +(3.92934 + 6.80582i) q^{29} +(2.88309 - 2.58608i) q^{30} +(0.544335 - 0.942817i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.68425 - 0.830254i) q^{33} +(-2.69440 - 4.66684i) q^{34} +(1.33589 - 10.8493i) q^{35} +(-2.77805 - 1.13244i) q^{36} +3.51348i q^{37} +(-1.83986 - 3.18674i) q^{38} +(1.51982 + 4.43622i) q^{39} +(-1.34631 + 1.78534i) q^{40} +(-1.01361 + 1.75563i) q^{41} +(-8.01027 + 2.74427i) q^{42} +(1.53113 + 2.65199i) q^{43} +(-3.12834 + 1.10159i) q^{44} +(3.27239 - 5.85589i) q^{45} -7.48373i q^{46} +(-0.934774 - 1.61908i) q^{47} +(1.69971 + 0.333128i) q^{48} +(-8.44925 + 14.6345i) q^{49} +(-3.59432 - 3.47575i) q^{50} +(-7.03471 - 6.13437i) q^{51} +(-1.35370 - 2.34467i) q^{52} +13.2351 q^{53} +(-5.18771 - 0.296093i) q^{54} +(-1.58990 - 7.24377i) q^{55} +(4.23366 - 2.44430i) q^{56} +(-4.80363 - 4.18883i) q^{57} +(-6.80582 - 3.92934i) q^{58} +(5.46059 + 3.15267i) q^{59} +(-1.20379 + 3.68115i) q^{60} +(0.648054 - 0.374154i) q^{61} +1.08867i q^{62} +(-11.5848 + 8.99328i) q^{63} -1.00000 q^{64} +(5.57347 - 2.36355i) q^{65} +(-4.50758 + 3.56115i) q^{66} +(4.34326 + 2.50758i) q^{67} +(4.66684 + 2.69440i) q^{68} +(-4.20106 - 12.2625i) q^{69} +(4.26775 + 10.0637i) q^{70} +1.44418i q^{71} +(2.97209 - 0.408300i) q^{72} -0.851157 q^{73} +(-1.75674 - 3.04276i) q^{74} +(-7.84066 - 3.67751i) q^{75} +(3.18674 + 1.83986i) q^{76} +(-2.98284 + 15.9369i) q^{77} +(-3.53432 - 3.08197i) q^{78} +(-10.1117 + 5.83797i) q^{79} +(0.273267 - 2.21931i) q^{80} +(-8.66658 + 2.42700i) q^{81} -2.02723i q^{82} +(7.93725 - 4.58257i) q^{83} +(5.56497 - 6.38174i) q^{84} +(-7.25499 + 9.62086i) q^{85} +(-2.65199 - 1.53113i) q^{86} +(-13.3575 - 2.61795i) q^{87} +(2.15842 - 2.51818i) q^{88} -5.47167i q^{89} +(0.0939709 + 6.70755i) q^{90} -13.2354 q^{91} +(3.74187 + 6.48110i) q^{92} +(0.611135 + 1.78385i) q^{93} +(1.61908 + 0.934774i) q^{94} +(-4.95405 + 6.56957i) q^{95} +(-1.63856 + 0.561359i) q^{96} +(-7.89969 + 4.56089i) q^{97} -16.8985i q^{98} +(-5.38685 + 8.36552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.13835	+	1.30543i	−0.657229	+	0.753691i
$3$	−1.13835	+	1.30543i	−0.657229	+	0.753691i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.78534	+	1.34631i	0.798430	+	0.602088i
$5$	1.78534	+	1.34631i	0.798430	+	0.602088i
$6$	0.333128	−	1.69971i	0.135999	−	0.693905i
$7$	−2.44430	−	4.23366i	−0.923860	−	1.60017i	−0.793384	−	0.608721i	$-0.791683\pi$
$7$	−2.44430	−	4.23366i	−0.923860	−	1.60017i	−0.130476	−	0.991451i	$-0.541651\pi$
$8$			1.00000i			0.353553i
$9$	−0.408300	−	2.97209i	−0.136100	−	0.990695i
$10$	−2.21931	−	0.273267i	−0.701807	−	0.0864145i
$11$	−2.51818	−	2.15842i	−0.759259	−	0.650789i
$11$	−2.51818	−	2.15842i	−0.759259	−	0.650789i
$12$	0.561359	+	1.63856i	0.162050	+	0.473011i
$13$	1.35370	−	2.34467i	0.375448	−	0.650295i	−0.614946	−	0.788569i	$-0.710822\pi$
$13$	1.35370	−	2.34467i	0.375448	−	0.650295i	0.990394	+	0.138274i	$0.0441555\pi$
$14$	4.23366	+	2.44430i	1.13149	+	0.653268i
$15$	−3.78987	+	0.798065i	−0.978539	+	0.206060i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			5.38880i			1.30698i	0.756937	+	0.653488i	$0.226695\pi$
$17$			5.38880i			1.30698i	−0.756937	+	0.653488i	$0.773305\pi$
$18$	1.83964	+	2.36975i	0.433607	+	0.558556i
$19$			3.67973i			0.844187i	0.906552	+	0.422093i	$0.138705\pi$
$19$			3.67973i			0.844187i	−0.906552	+	0.422093i	$0.861295\pi$
$20$	2.05861	−	0.872998i	0.460319	−	0.195208i
$21$	8.30923	+	1.62853i	1.81322	+	0.355375i
$22$	3.26002	+	0.610161i	0.695038	+	0.130087i
$23$	−3.74187	+	6.48110i	−0.780233	+	1.35140i	0.151573	+	0.988446i	$0.451566\pi$
$23$	−3.74187	+	6.48110i	−0.780233	+	1.35140i	−0.931806	+	0.362957i	$0.881767\pi$
$24$	−1.30543	−	1.13835i	−0.266470	−	0.232366i
$25$	1.37490	+	4.80725i	0.274980	+	0.961450i
$26$			2.70739i			0.530964i
$27$	4.34464	+	2.85028i	0.836127	+	0.548536i
$28$	−4.88861			−0.923860
$29$	3.92934	+	6.80582i	0.729660	+	1.26381i	0.957027	+	0.289999i	$0.0936551\pi$
$29$	3.92934	+	6.80582i	0.729660	+	1.26381i	−0.227367	+	0.973809i	$0.573012\pi$
$30$	2.88309	−	2.58608i	0.526378	−	0.472151i
$31$	0.544335	−	0.942817i	0.0977655	−	0.169335i	−0.812994	−	0.582272i	$-0.802164\pi$
$31$	0.544335	−	0.942817i	0.0977655	−	0.169335i	0.910759	+	0.412937i	$0.135497\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	5.68425	−	0.830254i	0.989501	−	0.144529i
$34$	−2.69440	−	4.66684i	−0.462086	−	0.800356i
$35$	1.33589	−	10.8493i	0.225807	−	1.83387i
$36$	−2.77805	−	1.13244i	−0.463009	−	0.188741i
$37$			3.51348i			0.577612i	0.957388	+	0.288806i	$0.0932583\pi$
$37$			3.51348i			0.577612i	−0.957388	+	0.288806i	$0.906742\pi$
$38$	−1.83986	−	3.18674i	−0.298465	−	0.516957i
$39$	1.51982	+	4.43622i	0.243366	+	0.710364i
$40$	−1.34631	+	1.78534i	−0.212870	+	0.282288i
$41$	−1.01361	+	1.75563i	−0.158300	+	0.274183i	−0.934256	−	0.356604i	$-0.883935\pi$
$41$	−1.01361	+	1.75563i	−0.158300	+	0.274183i	0.775956	+	0.630787i	$0.217268\pi$
$42$	−8.01027	+	2.74427i	−1.23601	+	0.423449i
$43$	1.53113	+	2.65199i	0.233495	+	0.404424i	0.958834	−	0.283967i	$-0.0916506\pi$
$43$	1.53113	+	2.65199i	0.233495	+	0.404424i	−0.725340	+	0.688391i	$0.758317\pi$
$44$	−3.12834	+	1.10159i	−0.471615	+	0.166071i
$45$	3.27239	−	5.85589i	0.487819	−	0.872945i
$46$		−	7.48373i		−	1.10342i
$47$	−0.934774	−	1.61908i	−0.136351	−	0.236166i	0.789762	−	0.613414i	$-0.210204\pi$
$47$	−0.934774	−	1.61908i	−0.136351	−	0.236166i	−0.926113	+	0.377247i	$0.876871\pi$
$48$	1.69971	+	0.333128i	0.245332	+	0.0480829i
$49$	−8.44925	+	14.6345i	−1.20704	+	2.09065i
$50$	−3.59432	−	3.47575i	−0.508314	−	0.491545i
$51$	−7.03471	−	6.13437i	−0.985056	−	0.858983i
$52$	−1.35370	−	2.34467i	−0.187724	−	0.325147i
$53$	13.2351			1.81798			0.908991	−	0.416817i	$-0.136854\pi$
$53$	13.2351			1.81798			0.908991	+	0.416817i	$0.136854\pi$
$54$	−5.18771	−	0.296093i	−0.705958	−	0.0402932i
$55$	−1.58990	−	7.24377i	−0.214382	−	0.976750i
$56$	4.23366	−	2.44430i	0.565747	−	0.326634i
$57$	−4.80363	−	4.18883i	−0.636256	−	0.554824i
$58$	−6.80582	−	3.92934i	−0.893648	−	0.515948i
$59$	5.46059	+	3.15267i	0.710908	+	0.410443i	0.811397	−	0.584495i	$-0.198707\pi$
$59$	5.46059	+	3.15267i	0.710908	+	0.410443i	−0.100489	+	0.994938i	$0.532041\pi$
$60$	−1.20379	+	3.68115i	−0.155408	+	0.475235i
$61$	0.648054	−	0.374154i	0.0829748	−	0.0479055i	−0.457939	−	0.888984i	$-0.651412\pi$
$61$	0.648054	−	0.374154i	0.0829748	−	0.0479055i	0.540913	+	0.841078i	$0.318079\pi$
$62$			1.08867i			0.138261i
$63$	−11.5848	+	8.99328i	−1.45955	+	1.13305i
$64$	−1.00000			−0.125000
$65$	5.57347	−	2.36355i	0.691304	−	0.293162i
$66$	−4.50758	+	3.56115i	−0.554844	+	0.438347i
$67$	4.34326	+	2.50758i	0.530614	+	0.306350i	0.741266	−	0.671211i	$-0.234226\pi$
$67$	4.34326	+	2.50758i	0.530614	+	0.306350i	−0.210653	+	0.977561i	$0.567559\pi$
$68$	4.66684	+	2.69440i	0.565937	+	0.326744i
$69$	−4.20106	−	12.2625i	−0.505748	−	1.47624i
$70$	4.26775	+	10.0637i	0.510093	+	1.20285i
$71$			1.44418i			0.171392i	0.996321	+	0.0856961i	$0.0273114\pi$
$71$			1.44418i			0.171392i	−0.996321	+	0.0856961i	$0.972689\pi$
$72$	2.97209	−	0.408300i	0.350264	−	0.0481186i
$73$	−0.851157			−0.0996204			−0.0498102	−	0.998759i	$-0.515862\pi$
$73$	−0.851157			−0.0996204			−0.0498102	+	0.998759i	$0.515862\pi$
$74$	−1.75674	−	3.04276i	−0.204217	−	0.353714i
$75$	−7.84066	−	3.67751i	−0.905361	−	0.424643i
$76$	3.18674	+	1.83986i	0.365544	+	0.211047i
$77$	−2.98284	+	15.9369i	−0.339926	+	1.81618i
$78$	−3.53432	−	3.08197i	−0.400182	−	0.348965i
$79$	−10.1117	+	5.83797i	−1.13765	+	0.656823i	−0.945848	−	0.324610i	$-0.894767\pi$
$79$	−10.1117	+	5.83797i	−1.13765	+	0.656823i	−0.191803	+	0.981433i	$0.561433\pi$
$80$	0.273267	−	2.21931i	0.0305521	−	0.248126i
$81$	−8.66658	+	2.42700i	−0.962954	+	0.269667i
$82$		−	2.02723i		−	0.223870i
$83$	7.93725	−	4.58257i	0.871227	−	0.503003i	0.00347093	−	0.999994i	$-0.498895\pi$
$83$	7.93725	−	4.58257i	0.871227	−	0.503003i	0.867756	+	0.496991i	$0.165562\pi$
$84$	5.56497	−	6.38174i	0.607188	−	0.696305i
$85$	−7.25499	+	9.62086i	−0.786915	+	1.04353i
$86$	−2.65199	−	1.53113i	−0.285971	−	0.165106i
$87$	−13.3575	−	2.61795i	−1.43208	−	0.280674i
$88$	2.15842	−	2.51818i	0.230089	−	0.268438i
$89$		−	5.47167i		−	0.579996i	−0.957027	−	0.289998i	$-0.906345\pi$
$89$		−	5.47167i		−	0.579996i	0.957027	−	0.289998i	$-0.0936547\pi$
$90$	0.0939709	+	6.70755i	0.00990540	+	0.707037i
$91$	−13.2354			−1.38745
$92$	3.74187	+	6.48110i	0.390116	+	0.675702i
$93$	0.611135	+	1.78385i	0.0633718	+	0.184977i
$94$	1.61908	+	0.934774i	0.166995	+	0.0964146i
$95$	−4.95405	+	6.56957i	−0.508275	+	0.674024i
$96$	−1.63856	+	0.561359i	−0.167235	+	0.0572935i
$97$	−7.89969	+	4.56089i	−0.802092	+	0.463088i	−0.844202	−	0.536025i	$-0.819925\pi$
$97$	−7.89969	+	4.56089i	−0.802092	+	0.463088i	0.0421101	+	0.999113i	$0.486592\pi$
$98$		−	16.8985i		−	1.70701i
$99$	−5.38685	+	8.36552i	−0.541399	+	0.840766i
$100$	4.85065	+	1.21292i	0.485065	+	0.121292i
$101$	−5.04129	−	8.73176i	−0.501627	−	0.868843i	−0.999998	−	0.00187927i	$-0.999402\pi$
$101$	−5.04129	−	8.73176i	−0.501627	−	0.868843i	0.498372	−	0.866964i	$-0.333932\pi$
$102$	9.15942	+	1.79516i	0.906918	+	0.177748i
$103$	14.4031	+	8.31566i	1.41918	+	0.819366i	0.996227	−	0.0867841i	$-0.0276590\pi$
$103$	14.4031	+	8.31566i	1.41918	+	0.819366i	0.422956	+	0.906150i	$0.360992\pi$
$104$	2.34467	+	1.35370i	0.229914	+	0.132741i
$105$	12.6423	+	14.0943i	1.23376	+	1.37546i
$106$	−11.4619	+	6.61755i	−1.11328	+	0.642753i
$107$			7.89082i			0.762835i	0.924403	+	0.381417i	$0.124564\pi$
$107$			7.89082i			0.762835i	−0.924403	+	0.381417i	$0.875436\pi$
$108$	4.64073	−	2.33743i	0.446555	−	0.224919i
$109$		−	2.76998i		−	0.265316i	−0.991162	−	0.132658i	$-0.957649\pi$
$109$		−	2.76998i		−	0.265316i	0.991162	−	0.132658i	$-0.0423512\pi$
$110$	4.99878	+	5.47834i	0.476615	+	0.522339i
$111$	−4.58660	−	3.99958i	−0.435341	−	0.379624i
$112$	−2.44430	+	4.23366i	−0.230965	+	0.400043i
$113$	5.00480	−	8.66857i	0.470812	−	0.815470i	−0.528631	−	0.848852i	$-0.677294\pi$
$113$	5.00480	−	8.66857i	0.470812	−	0.815470i	0.999443	+	0.0333818i	$0.0106277\pi$
$114$	6.25448	+	1.22582i	0.585786	+	0.114809i
$115$	−15.4061	+	6.53328i	−1.43662	+	0.609232i
$116$	7.85868			0.729660
$117$	−7.52128	−	3.06597i	−0.695342	−	0.283449i
$118$	−6.30534			−0.580454
$119$	22.8144	−	13.1719i	2.09139	−	1.20746i
$120$	−0.798065	−	3.78987i	−0.0728531	−	0.345966i
$121$	1.68242	+	10.8706i	0.152947	+	0.988234i
$122$	−0.374154	+	0.648054i	−0.0338743	+	0.0586720i
$123$	−1.13800	−	3.32173i	−0.102610	−	0.299510i
$124$	−0.544335	−	0.942817i	−0.0488828	−	0.0846674i
$125$	−4.01737	+	10.4336i	−0.359325	+	0.933213i
$126$	5.53608	−	13.5808i	0.493193	−	1.20987i
$127$	13.9810			1.24061			0.620306	−	0.784360i	$-0.287008\pi$
$127$	13.9810			1.24061			0.620306	+	0.784360i	$0.287008\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−5.20495	−	1.02012i	−0.458270	−	0.0898168i
$130$	−3.64499	+	4.83363i	−0.319687	+	0.423937i
$131$	−10.5033	+	18.1922i	−0.917677	+	1.58946i	−0.114744	+	0.993395i	$0.536605\pi$
$131$	−10.5033	+	18.1922i	−0.917677	+	1.58946i	−0.802934	+	0.596068i	$0.796729\pi$
$132$	2.12310	−	5.33783i	0.184792	−	0.464599i
$133$	15.5787	−	8.99437i	1.35085	−	0.779911i
$134$	−5.01516			−0.433244
$135$	3.91932	+	10.9380i	0.337321	+	0.941390i
$136$	−5.38880			−0.462086
$137$	−9.48067	−	16.4210i	−0.809988	−	1.40294i	−0.912872	−	0.408247i	$-0.866140\pi$
$137$	−9.48067	−	16.4210i	−0.809988	−	1.40294i	0.102883	−	0.994693i	$-0.467193\pi$
$138$	9.76949	+	8.51914i	0.831635	+	0.725197i
$139$	−10.4498	−	6.03320i	−0.886341	−	0.511729i	−0.0135969	−	0.999908i	$-0.504328\pi$
$139$	−10.4498	−	6.03320i	−0.886341	−	0.511729i	−0.872744	+	0.488179i	$0.837661\pi$
$140$	−8.72784	−	6.58158i	−0.737638	−	0.556245i
$141$	3.17770	+	0.622799i	0.267610	+	0.0524491i
$142$	−0.722088	−	1.25069i	−0.0605963	−	0.104956i
$143$	−8.46964	+	2.98245i	−0.708267	+	0.249405i
$144$	−2.36975	+	1.83964i	−0.197479	+	0.153303i
$145$	−2.14751	+	17.4408i	−0.178341	+	1.44838i
$146$	0.737124	−	0.425579i	0.0610048	−	0.0352211i
$147$	−9.48613	−	27.6892i	−0.782402	−	2.28377i
$148$	3.04276	+	1.75674i	0.250114	+	0.144403i
$149$	−3.57301	+	6.18863i	−0.292712	+	0.506993i	−0.974450	−	0.224604i	$-0.927891\pi$
$149$	−3.57301	+	6.18863i	−0.292712	+	0.506993i	0.681738	+	0.731597i	$0.261225\pi$
$150$	8.62896	−	0.735509i	0.704552	−	0.0600540i
$151$	5.19754	−	3.00080i	0.422969	−	0.244201i	−0.273378	−	0.961907i	$-0.588141\pi$
$151$	5.19754	−	3.00080i	0.422969	−	0.244201i	0.696347	+	0.717705i	$0.254808\pi$
$152$	−3.67973			−0.298465
$153$	16.0160	−	2.20025i	1.29482	−	0.177879i
$154$	−5.38526	−	15.2932i	−0.433956	−	1.23236i
$155$	2.24115	−	0.950407i	0.180013	−	0.0763386i
$156$	4.60179	+	0.901909i	0.368438	+	0.0722105i
$157$	−13.7436	−	7.93486i	−1.09686	−	0.633271i	−0.161464	−	0.986879i	$-0.551622\pi$
$157$	−13.7436	−	7.93486i	−1.09686	−	0.633271i	−0.935394	+	0.353608i	$0.884955\pi$
$158$	5.83797	−	10.1117i	0.464444	−	0.804441i
$159$	−15.0662	+	17.2775i	−1.19483	+	1.37020i
$160$	0.872998	+	2.05861i	0.0690165	+	0.162747i
$161$	36.5850			2.88330
$162$	6.29198	−	6.43514i	0.494345	−	0.505592i
$163$		−	15.7246i		−	1.23165i	−0.787884	−	0.615823i	$-0.788823\pi$
$163$		−	15.7246i		−	1.23165i	0.787884	−	0.615823i	$-0.211177\pi$
$164$	1.01361	+	1.75563i	0.0791498	+	0.137092i
$165$	11.2661	+	6.17047i	0.877066	+	0.480370i
$166$	−4.58257	+	7.93725i	−0.355677	+	0.616050i
$167$	4.76377	+	2.75037i	0.368632	+	0.212830i	0.672861	−	0.739769i	$-0.265065\pi$
$167$	4.76377	+	2.75037i	0.368632	+	0.212830i	−0.304229	+	0.952599i	$0.598399\pi$
$168$	−1.62853	+	8.30923i	−0.125644	+	0.641071i
$169$	2.83501	+	4.91038i	0.218078	+	0.377722i
$170$	1.47258	−	11.9594i	0.112942	−	0.917245i
$171$	10.9365	−	1.50243i	0.836332	−	0.114894i
$172$	3.06225			0.233495
$173$	−12.4182	+	7.16963i	−0.944136	+	0.545097i	−0.891254	−	0.453504i	$-0.850174\pi$
$173$	−12.4182	+	7.16963i	−0.944136	+	0.545097i	−0.0528815	+	0.998601i	$0.516841\pi$
$174$	12.8769	−	4.41154i	0.976196	−	0.334438i
$175$	16.9916	−	17.5712i	1.28444	−	1.32826i
$176$	−0.610161	+	3.26002i	−0.0459926	+	0.245733i
$177$	−10.3317	+	3.53956i	−0.776576	+	0.266050i
$178$	2.73584	+	4.73861i	0.205060	+	0.355174i
$179$		−	21.0073i		−	1.57016i	−0.619393	−	0.785081i	$-0.712621\pi$
$179$		−	21.0073i		−	1.57016i	0.619393	−	0.785081i	$-0.287379\pi$
$180$	−3.43515	−	5.76192i	−0.256041	−	0.429468i
$181$	17.3600			1.29036			0.645179	−	0.764032i	$-0.276783\pi$
$181$	17.3600			1.29036			0.645179	+	0.764032i	$0.276783\pi$
$182$	11.4622	−	6.61769i	0.849633	−	0.490536i
$183$	−0.249283	+	1.27191i	−0.0184275	+	0.0940223i
$184$	−6.48110	−	3.74187i	−0.477793	−	0.275854i
$185$	−4.73023	+	6.27277i	−0.347773	+	0.461183i
$186$	−1.42118	−	1.23929i	−0.104206	−	0.0908694i
$187$	11.6313	−	13.5700i	0.850566	−	0.992333i
$188$	−1.86955			−0.136351
$189$	1.44748	−	25.3607i	0.105289	−	1.84472i
$190$	1.00555	−	8.16644i	0.0729500	−	0.592456i
$191$	14.1344	−	8.16051i	1.02273	−	0.590474i	0.107837	−	0.994169i	$-0.465608\pi$
$191$	14.1344	−	8.16051i	1.02273	−	0.590474i	0.914894	+	0.403695i	$0.132274\pi$
$192$	1.13835	−	1.30543i	0.0821536	−	0.0942114i
$193$	3.62980	−	6.28699i	0.261278	−	0.452547i	−0.705304	−	0.708905i	$-0.749189\pi$
$193$	3.62980	−	6.28699i	0.261278	−	0.452547i	0.966582	+	0.256358i	$0.0825226\pi$
$194$	4.56089	−	7.89969i	0.327453	−	0.567165i
$195$	−3.25913	+	9.96633i	−0.233391	+	0.713704i
$196$	8.44925	+	14.6345i	0.603518	+	1.04532i
$197$			18.8679i			1.34428i	0.740422	+	0.672142i	$0.234625\pi$
$197$			18.8679i			1.34428i	−0.740422	+	0.672142i	$0.765375\pi$
$198$	0.482389	−	9.93817i	0.0342819	−	0.706275i
$199$	−13.0492			−0.925035			−0.462517	−	0.886610i	$-0.653054\pi$
$199$	−13.0492			−0.925035			−0.462517	+	0.886610i	$0.653054\pi$
$200$	−4.80725	+	1.37490i	−0.339924	+	0.0972202i
$201$	−8.21764	+	2.81531i	−0.579628	+	0.198577i
$202$	8.73176	+	5.04129i	0.614365	+	0.354704i
$203$	19.2090	−	33.2710i	1.34821	−	2.33517i
$204$	−8.82987	+	3.02505i	−0.618215	+	0.211796i
$205$	−4.17327	+	1.76976i	−0.291474	+	0.123606i
$206$	−16.6313			−1.15876
$207$	20.7902	+	8.47491i	1.44502	+	0.589047i
$208$	−2.70739			−0.187724
$209$	7.94241	−	9.26620i	0.549388	−	0.640956i
$210$	−17.9957	−	5.88485i	−1.24182	−	0.406093i
$211$	−14.5660	−	8.40971i	−1.00277	−	0.578948i	−0.0937019	−	0.995600i	$-0.529870\pi$
$211$	−14.5660	−	8.40971i	−1.00277	−	0.578948i	−0.909066	+	0.416652i	$0.863203\pi$
$212$	6.61755	−	11.4619i	0.454495	−	0.787209i
$213$	−1.88527	−	1.64398i	−0.129177	−	0.112644i
$214$	−3.94541	−	6.83365i	−0.269703	−	0.467139i
$215$	−0.836811	+	6.79608i	−0.0570700	+	0.463489i
$216$	−2.85028	+	4.34464i	−0.193937	+	0.295615i
$217$	−5.32209			−0.361287
$218$	1.38499	+	2.39887i	0.0938034	+	0.162472i
$219$	0.968919	−	1.11113i	0.0654734	−	0.0750830i
$220$	−7.06824	−	2.24499i	−0.476541	−	0.151357i
$221$	12.6350	+	7.29480i	0.849920	+	0.490702i
$222$	5.97191	+	1.17044i	0.400808	+	0.0785547i
$223$	−7.08759	+	4.09202i	−0.474620	+	0.274022i	−0.718172	−	0.695866i	$-0.755021\pi$
$223$	−7.08759	+	4.09202i	−0.474620	+	0.274022i	0.243551	+	0.969888i	$0.421688\pi$
$224$		−	4.88861i		−	0.326634i
$225$	13.7262	−	6.04912i	0.915079	−	0.403275i
$226$			10.0096i			0.665829i
$227$	−9.86396	+	5.69496i	−0.654694	+	0.377988i	−0.790252	−	0.612782i	$-0.790051\pi$
$227$	−9.86396	+	5.69496i	−0.654694	+	0.377988i	0.135558	+	0.990769i	$0.456717\pi$
$228$	−6.02945	+	2.06565i	−0.399310	+	0.136801i
$229$	0.814485	−	1.41073i	0.0538227	−	0.0932236i	−0.837859	−	0.545887i	$-0.816193\pi$
$229$	0.814485	−	1.41073i	0.0538227	−	0.0932236i	0.891681	+	0.452663i	$0.149526\pi$
$230$	10.0754	−	13.3610i	0.664353	−	0.881000i
$231$	−17.4090	−	22.0358i	−1.14543	−	1.44985i
$232$	−6.80582	+	3.92934i	−0.446824	+	0.257974i
$233$			15.0891i			0.988523i	0.869313	+	0.494261i	$0.164561\pi$
$233$			15.0891i			0.988523i	−0.869313	+	0.494261i	$0.835439\pi$
$234$	8.04661	−	1.10543i	0.526023	−	0.0722641i
$235$	0.510885	−	4.14910i	0.0333264	−	0.270658i
$236$	5.46059	−	3.15267i	0.355454	−	0.205221i
$237$	3.88959	−	19.8458i	0.252656	−	1.28912i
$238$	−13.1719	+	22.8144i	−0.853806	+	1.47883i
$239$	−1.24031	+	2.14828i	−0.0802288	+	0.138960i	−0.903348	−	0.428908i	$-0.858898\pi$
$239$	−1.24031	+	2.14828i	−0.0802288	+	0.138960i	0.823119	+	0.567868i	$0.192232\pi$
$240$	2.58608	+	2.88309i	0.166931	+	0.186103i
$241$	12.0505	−	6.95737i	0.776242	−	0.448163i	−0.0588549	−	0.998267i	$-0.518745\pi$
$241$	12.0505	−	6.95737i	0.776242	−	0.448163i	0.835097	+	0.550103i	$0.185412\pi$
$242$	−6.89231	−	8.57299i	−0.443054	−	0.551092i
$243$	6.69736	−	14.0764i	0.429636	−	0.903002i
$244$		−	0.748308i		−	0.0479055i
$245$	−34.7874	+	14.7524i	−2.22249	+	0.942493i
$246$	2.64640	+	2.30770i	0.168728	+	0.147134i
$247$	8.62775	+	4.98123i	0.548971	+	0.316948i
$248$	0.942817	+	0.544335i	0.0598689	+	0.0345653i
$249$	−3.05317	+	15.5781i	−0.193487	+	0.987224i
$250$	−1.73767	−	11.0445i	−0.109900	−	0.698514i
$251$			30.4390i			1.92129i	0.277776	+	0.960646i	$0.410403\pi$
$251$			30.4390i			1.92129i	−0.277776	+	0.960646i	$0.589597\pi$
$252$	1.99602	+	14.5294i	0.125737	+	0.915264i
$253$	23.4116	−	8.24402i	1.47188	−	0.518297i
$254$	−12.1079	+	6.99049i	−0.759717	+	0.438623i
$255$	−4.30062	−	20.4228i	−0.269315	−	1.27893i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.0976	+	19.2215i	−0.692246	+	1.19901i	0.278854	+	0.960333i	$0.410045\pi$
$257$	−11.0976	+	19.2215i	−0.692246	+	1.19901i	−0.971100	+	0.238672i	$0.923288\pi$
$258$	5.01768	−	1.71902i	0.312387	−	0.107022i
$259$	14.8749	−	8.58801i	0.924280	−	0.533633i
$260$	0.739840	−	6.00854i	0.0458829	−	0.372634i
$261$	18.6231	−	14.4571i	1.15274	−	0.894875i
$262$		−	21.0066i		−	1.29779i
$263$	−18.0550	+	10.4240i	−1.11332	+	0.642774i	−0.939686	−	0.342037i	$-0.888883\pi$
$263$	−18.0550	+	10.4240i	−1.11332	+	0.642774i	−0.173630	+	0.984811i	$0.555550\pi$
$264$	0.830254	+	5.68425i	0.0510986	+	0.349841i
$265$	23.6292	+	17.8185i	1.45153	+	1.09458i
$266$	−8.99437	+	15.5787i	−0.551480	+	0.955192i
$267$	7.14289	+	6.22870i	0.437138	+	0.381190i
$268$	4.34326	−	2.50758i	0.265307	−	0.153175i
$269$			16.4928i			1.00558i	0.864407	+	0.502792i	$0.167694\pi$
$269$			16.4928i			1.00558i	−0.864407	+	0.502792i	$0.832306\pi$
$270$	−8.86321	−	7.51289i	−0.539398	−	0.457220i
$271$		−	6.86296i		−	0.416895i	−0.978034	−	0.208448i	$-0.933159\pi$
$271$		−	6.86296i		−	0.416895i	0.978034	−	0.208448i	$-0.0668411\pi$
$272$	4.66684	−	2.69440i	0.282969	−	0.163372i
$273$	15.0666	−	17.2779i	0.911870	−	1.04571i
$274$	16.4210	+	9.48067i	0.992029	+	0.572748i
$275$	6.91383	−	15.0731i	0.416920	−	0.908943i
$276$	−12.7202	−	2.49304i	−0.765666	−	0.150063i
$277$	−3.00665	−	5.20767i	−0.180652	−	0.312899i	0.761451	−	0.648223i	$-0.224487\pi$
$277$	−3.00665	−	5.20767i	−0.180652	−	0.312899i	−0.942103	+	0.335324i	$0.891154\pi$
$278$	12.0664			0.723694
$279$	−3.02438	−	1.23286i	−0.181065	−	0.0738094i
$280$	10.8493	+	1.33589i	0.648371	+	0.0798349i
$281$	−2.16172	−	3.74421i	−0.128957	−	0.223361i	0.794316	−	0.607505i	$-0.207830\pi$
$281$	−2.16172	−	3.74421i	−0.128957	−	0.223361i	−0.923273	+	0.384145i	$0.874496\pi$
$282$	−3.06336	+	1.04949i	−0.182421	+	0.0624961i
$283$	6.16434	−	10.6770i	0.366432	−	0.634679i	−0.622573	−	0.782562i	$-0.713912\pi$
$283$	6.16434	−	10.6770i	0.366432	−	0.634679i	0.989005	+	0.147883i	$0.0472458\pi$
$284$	1.25069	+	0.722088i	0.0742150	+	0.0428480i
$285$	−2.93666	−	13.9457i	−0.173953	−	0.826070i
$286$	5.84370	−	6.81769i	0.345545	−	0.403139i
$287$	9.91031			0.584987
$288$	1.13244	−	2.77805i	0.0667300	−	0.163698i
$289$	−12.0392			−0.708187
$290$	−6.86061	−	16.1780i	−0.402869	−	0.950003i
$291$	3.03872	−	15.5044i	0.178133	−	0.908884i
$292$	−0.425579	+	0.737124i	−0.0249051	+	0.0431369i
$293$	−3.85305	−	2.22456i	−0.225098	−	0.129960i	0.383211	−	0.923661i	$-0.374818\pi$
$293$	−3.85305	−	2.22456i	−0.225098	−	0.129960i	−0.608308	+	0.793701i	$0.708152\pi$
$294$	22.0598	+	19.2365i	1.28655	+	1.12189i
$295$	5.50455	+	12.9802i	0.320487	+	0.755739i
$296$	−3.51348			−0.204217
$297$	−4.78846	−	16.5551i	−0.277855	−	0.960623i
$298$		−	7.14602i		−	0.413958i
$299$	10.1307	+	17.5469i	0.585874	+	1.01476i
$300$	−7.10515	+	4.95145i	−0.410216	+	0.285872i
$301$	7.48508	−	12.9645i	0.431433	−	0.747263i
$302$	−3.00080	+	5.19754i	−0.172677	+	0.299085i
$303$	17.1375	+	3.35879i	0.984522	+	0.192957i
$304$	3.18674	−	1.83986i	0.182772	−	0.105523i
$305$	1.66073	+	0.204488i	0.0950929	+	0.0117089i
$306$	−12.7701	+	9.91346i	−0.730019	+	0.566715i
$307$	−25.4257			−1.45112			−0.725562	−	0.688157i	$-0.758420\pi$
$307$	−25.4257			−1.45112			−0.725562	+	0.688157i	$0.758420\pi$
$308$	12.3104	+	10.5517i	0.701449	+	0.601238i
$309$	−27.2514	+	9.33614i	−1.55028	+	0.531114i
$310$	−1.46569	+	1.94365i	−0.0832455	+	0.110392i
$311$	10.2161	+	5.89826i	0.579301	+	0.334460i	0.760856	−	0.648921i	$-0.224780\pi$
$311$	10.2161	+	5.89826i	0.579301	+	0.334460i	−0.181554	+	0.983381i	$0.558113\pi$
$312$	−4.43622	+	1.51982i	−0.251152	+	0.0860429i
$313$	−5.99521	+	3.46134i	−0.338869	+	0.195646i	−0.659772	−	0.751466i	$-0.729347\pi$
$313$	−5.99521	+	3.46134i	−0.338869	+	0.195646i	0.320903	+	0.947112i	$0.396014\pi$
$314$	15.8697			0.895581
$315$	−32.7906	+	0.459387i	−1.84754	+	0.0258835i
$316$			11.6759i			0.656823i
$317$	−4.70805	−	8.15457i	−0.264430	−	0.458007i	0.702984	−	0.711206i	$-0.251851\pi$
$317$	−4.70805	−	8.15457i	−0.264430	−	0.458007i	−0.967414	+	0.253199i	$0.918517\pi$
$318$	4.40899	−	22.4959i	0.247244	−	1.26151i
$319$	4.79506	−	25.6194i	0.268472	−	1.43441i
$320$	−1.78534	−	1.34631i	−0.0998037	−	0.0752610i
$321$	−10.3009	−	8.98255i	−0.574942	−	0.501357i
$322$	−31.6836	+	18.2925i	−1.76566	+	1.01940i
$323$	−19.8293			−1.10333
$324$	−2.23145	+	8.71898i	−0.123969	+	0.484388i
$325$	13.1326	+	3.28386i	0.728467	+	0.182156i
$326$	7.86231	+	13.6179i	0.435453	+	0.754227i
$327$	3.61602	+	3.15322i	0.199966	+	0.174373i
$328$	−1.75563	−	1.01361i	−0.0969384	−	0.0559674i
$329$	−4.56974	+	7.91503i	−0.251938	+	0.436370i
$330$	−12.8420	+	0.289275i	−0.706927	+	0.0159241i
$331$	4.35068	+	7.53559i	0.239135	+	0.414194i	0.960466	−	0.278396i	$-0.0898029\pi$
$331$	4.35068	+	7.53559i	0.239135	+	0.414194i	−0.721331	+	0.692590i	$0.756470\pi$
$332$		−	9.16515i		−	0.503003i
$333$	10.4424	−	1.43455i	0.572238	−	0.0786130i
$334$	−5.50073			−0.300987
$335$	4.37823	+	10.3243i	0.239208	+	0.564075i
$336$	−2.74427	−	8.01027i	−0.149712	−	0.436996i
$337$	−10.7222	+	18.5714i	−0.584074	+	1.01165i	0.410916	+	0.911673i	$0.365209\pi$
$337$	−10.7222	+	18.5714i	−0.584074	+	1.01165i	−0.994990	+	0.0999733i	$0.968124\pi$
$338$	−4.91038	−	2.83501i	−0.267090	−	0.154204i
$339$	5.61898	+	16.4013i	0.305181	+	0.890797i
$340$	4.70441	+	11.0934i	0.255133	+	0.601626i
$341$	−3.40573	+	1.19927i	−0.184431	+	0.0649442i
$342$	−8.72004	+	6.76937i	−0.471526	+	0.366046i
$343$	48.3899			2.61281
$344$	−2.65199	+	1.53113i	−0.142986	+	0.0825528i
$345$	9.00883	−	27.5488i	0.485019	−	1.48318i
$346$	7.16963	−	12.4182i	0.385442	−	0.667605i
$347$	20.8938	+	12.0631i	1.12164	+	0.647578i	0.941819	−	0.336121i	$-0.109115\pi$
$347$	20.8938	+	12.0631i	1.12164	+	0.647578i	0.179820	+	0.983700i	$0.442448\pi$
$348$	−8.94596	+	10.2590i	−0.479554	+	0.549938i
$349$	−2.42852	+	1.40211i	−0.129996	+	0.0750530i	−0.563588	−	0.826056i	$-0.690579\pi$
$349$	−2.42852	+	1.40211i	−0.129996	+	0.0750530i	0.433592	+	0.901109i	$0.357246\pi$
$350$	−5.92951	+	23.7129i	−0.316946	+	1.26751i
$351$	12.5643	−	6.32834i	0.670632	−	0.337782i
$352$	−1.10159	−	3.12834i	−0.0587151	−	0.166741i
$353$	−1.37486	−	2.38132i	−0.0731762	−	0.126745i	0.827116	−	0.562032i	$-0.189980\pi$
$353$	−1.37486	−	2.38132i	−0.0731762	−	0.126745i	−0.900292	+	0.435287i	$0.856647\pi$
$354$	7.17771	−	8.23119i	0.381491	−	0.437483i
$355$	−1.94431	+	2.57835i	−0.103193	+	0.136845i
$356$	−4.73861	−	2.73584i	−0.251146	−	0.144999i
$357$	−8.77584	+	44.7768i	−0.464467	+	2.36984i
$358$	10.5037	+	18.1929i	0.555136	+	0.961524i
$359$	−2.32663			−0.122795			−0.0613974	−	0.998113i	$-0.519556\pi$
$359$	−2.32663			−0.122795			−0.0613974	+	0.998113i	$0.519556\pi$
$360$	5.85589	+	3.27239i	0.308633	+	0.172470i
$361$	5.45962			0.287348
$362$	−15.0342	+	8.67999i	−0.790179	+	0.456210i
$363$	−16.1060	−	10.1783i	−0.845345	−	0.534221i
$364$	−6.61769	+	11.4622i	−0.346861	+	0.600782i
$365$	−1.51961	−	1.14592i	−0.0795399	−	0.0599803i
$366$	−0.420070	−	1.22615i	−0.0219574	−	0.0640917i
$367$	−13.5115	+	7.80087i	−0.705295	+	0.407202i	−0.809316	−	0.587373i	$-0.800162\pi$
$367$	−13.5115	+	7.80087i	−0.705295	+	0.407202i	0.104022	+	0.994575i	$0.466829\pi$
$368$	7.48373			0.390116
$369$	5.63174	+	2.29572i	0.293176	+	0.119510i
$370$	0.960116	−	7.79749i	0.0499141	−	0.405372i
$371$	−32.3506	−	56.0329i	−1.67956	−	2.90908i
$372$	1.85043	+	0.362667i	0.0959402	+	0.0188034i
$373$	−2.56630	+	4.44496i	−0.132878	+	0.230151i	−0.924785	−	0.380491i	$-0.875755\pi$
$373$	−2.56630	+	4.44496i	−0.132878	+	0.230151i	0.791907	+	0.610642i	$0.209088\pi$
$374$	−3.28804	+	17.5676i	−0.170020	+	0.908398i
$375$	−9.04719	−	17.1216i	−0.467195	−	0.884154i
$376$	1.61908	−	0.934774i	0.0834975	−	0.0482073i
$377$	21.2765			1.09580
$378$	11.4268	+	22.6867i	0.587730	+	1.16688i
$379$	−22.4000			−1.15061			−0.575305	−	0.817939i	$-0.695117\pi$
$379$	−22.4000			−1.15061			−0.575305	+	0.817939i	$0.695117\pi$
$380$	3.21239	+	7.57512i	0.164792	+	0.388595i
$381$	−15.9153	+	18.2512i	−0.815366	+	0.935038i
$382$	−8.16051	+	14.1344i	−0.417528	+	0.723180i
$383$	−4.39738	+	7.61649i	−0.224696	+	0.389184i	−0.956228	−	0.292622i	$-0.905472\pi$
$383$	−4.39738	+	7.61649i	−0.224696	+	0.389184i	0.731532	+	0.681807i	$0.238805\pi$
$384$	−0.333128	+	1.69971i	−0.0169999	+	0.0867381i
$385$	−26.7814	+	24.4371i	−1.36491	+	1.24543i
$386$			7.25959i			0.369503i
$387$	7.25678	−	5.63344i	0.368883	−	0.286364i
$388$			9.12178i			0.463088i
$389$	18.0840	−	10.4408i	0.916893	−	0.529369i	0.0342507	−	0.999413i	$-0.489096\pi$
$389$	18.0840	−	10.4408i	0.916893	−	0.529369i	0.882643	+	0.470045i	$0.155762\pi$
$390$	−2.16068	−	10.2607i	−0.109410	−	0.519569i
$391$	−34.9254	−	20.1642i	−1.76625	−	1.01975i
$392$	−14.6345	−	8.44925i	−0.739155	−	0.426751i
$393$	−11.7922	−	34.4205i	−0.594840	−	1.73629i
$394$	−9.43396	−	16.3401i	−0.475276	−	0.823202i
$395$	−25.9125	−	3.19064i	−1.30380	−	0.160539i
$396$	4.55133	+	8.84791i	0.228713	+	0.444624i
$397$		−	9.39800i		−	0.471672i	−0.971793	−	0.235836i	$-0.924217\pi$
$397$		−	9.39800i		−	0.471672i	0.971793	−	0.235836i	$-0.0757828\pi$
$398$	11.3010	−	6.52461i	0.566466	−	0.327049i
$399$	−5.99256	+	30.5757i	−0.300003	+	1.53070i
$400$	3.47575	−	3.59432i	0.173787	−	0.179716i
$401$	−21.3273	−	12.3133i	−1.06503	−	0.614898i	−0.138214	−	0.990402i	$-0.544136\pi$
$401$	−21.3273	−	12.3133i	−1.06503	−	0.614898i	−0.926821	+	0.375504i	$0.877469\pi$
$402$	5.70903	−	6.54695i	0.284741	−	0.326532i
$403$	−1.47373	−	2.55258i	−0.0734117	−	0.127153i
$404$	−10.0826			−0.501627
$405$	−18.7403	−	7.33487i	−0.931214	−	0.364473i
$406$			38.4180i			1.90665i
$407$	7.58358	−	8.84756i	0.375904	−	0.438557i
$408$	6.13437	−	7.03471i	0.303696	−	0.348270i
$409$	18.1190	+	10.4610i	0.895925	+	0.517262i	0.875876	−	0.482537i	$-0.160284\pi$
$409$	18.1190	+	10.4610i	0.895925	+	0.517262i	0.0200490	+	0.999799i	$0.493618\pi$
$410$	2.72927	−	3.61929i	0.134789	−	0.178744i
$411$	32.2288	+	6.31655i	1.58973	+	0.311573i
$412$	14.4031	−	8.31566i	0.709592	−	0.409683i
$413$		−	30.8244i		−	1.51677i
$414$	−22.2423	+	3.05560i	−1.09315	+	0.150175i
$415$	20.3403	+	2.50453i	0.998465	+	0.122942i
$416$	2.34467	−	1.35370i	0.114957	−	0.0663704i
$417$	19.7715	−	6.77358i	0.968214	−	0.331704i
$418$	−2.24523	+	11.9960i	−0.109818	+	0.586742i
$419$	−10.8144	−	6.24368i	−0.528317	−	0.305024i	0.212014	−	0.977267i	$-0.431998\pi$
$419$	−10.8144	−	6.24368i	−0.528317	−	0.305024i	−0.740331	+	0.672243i	$0.765331\pi$
$420$	18.5272	−	3.90143i	0.904034	−	0.190370i
$421$	8.65115	+	14.9842i	0.421631	+	0.730286i	0.996099	−	0.0882405i	$-0.0281244\pi$
$421$	8.65115	+	14.9842i	0.421631	+	0.730286i	−0.574468	+	0.818527i	$0.694791\pi$
$422$	16.8194			0.818757
$423$	−4.43036	+	3.43930i	−0.215412	+	0.167224i
$424$			13.2351i			0.642753i
$425$	−25.9053	+	7.40907i	−1.25659	+	0.359393i
$426$	2.45469	+	0.481096i	0.118930	+	0.0233092i
$427$	−3.16808	−	1.82909i	−0.153314	−	0.0885160i
$428$	6.83365	+	3.94541i	0.330317	+	0.190709i
$429$	5.74807	−	14.4516i	0.277520	−	0.697730i
$430$	−2.67334	−	6.30398i	−0.128920	−	0.304005i
$431$	26.3119			1.26740			0.633699	−	0.773580i	$-0.281536\pi$
$431$	26.3119			1.26740			0.633699	+	0.773580i	$0.281536\pi$
$432$	0.296093	−	5.18771i	0.0142458	−	0.249594i
$433$		−	10.9372i		−	0.525607i	−0.964849	−	0.262803i	$-0.915353\pi$
$433$		−	10.9372i		−	0.525607i	0.964849	−	0.262803i	$-0.0846471\pi$
$434$	4.60906	−	2.66104i	0.221242	−	0.127734i
$435$	−20.3232	−	22.6573i	−0.974421	−	1.08633i
$436$	−2.39887	−	1.38499i	−0.114885	−	0.0663290i
$437$	−23.8487	−	13.7690i	−1.14084	−	0.658663i
$438$	−0.283545	+	1.44672i	−0.0135483	+	0.0691271i
$439$	7.09793	−	4.09799i	0.338766	−	0.195587i	−0.320960	−	0.947093i	$-0.604006\pi$
$439$	7.09793	−	4.09799i	0.338766	−	0.195587i	0.659726	+	0.751506i	$0.270672\pi$
$440$	7.24377	−	1.58990i	0.345333	−	0.0757957i
$441$	46.9449	+	19.1366i	2.23547	+	0.911267i
$442$	−14.5896			−0.693957
$443$	6.80456	+	11.7858i	0.323295	+	0.559963i	0.981166	−	0.193168i	$-0.0618762\pi$
$443$	6.80456	+	11.7858i	0.323295	+	0.559963i	−0.657871	+	0.753130i	$0.728543\pi$
$444$	−5.75704	+	1.97232i	−0.273217	+	0.0936024i
$445$	7.36657	−	9.76882i	0.349209	−	0.463086i
$446$	4.09202	−	7.08759i	0.193763	−	0.335607i
$447$	−4.01148	−	11.7092i	−0.189737	−	0.553825i
$448$	2.44430	+	4.23366i	0.115483	+	0.200022i
$449$		−	11.9701i		−	0.564903i	−0.959282	−	0.282452i	$-0.908852\pi$
$449$		−	11.9701i		−	0.564903i	0.959282	−	0.282452i	$-0.0911477\pi$
$450$	−8.86266	+	12.1018i	−0.417790	+	0.570484i
$451$	6.34184	−	2.23318i	0.298626	−	0.105156i
$452$	−5.00480	−	8.66857i	−0.235406	−	0.407735i
$453$	−1.99930	+	10.2010i	−0.0939354	+	0.479285i
$454$	5.69496	−	9.86396i	0.267278	−	0.462939i
$455$	−23.6297	−	17.8189i	−1.10778	−	0.835364i
$456$	4.18883	−	4.80363i	0.196160	−	0.224950i
$457$	0.805987	+	1.39601i	0.0377025	+	0.0653026i	0.884261	−	0.466993i	$-0.154663\pi$
$457$	0.805987	+	1.39601i	0.0377025	+	0.0653026i	−0.846558	+	0.532296i	$0.821329\pi$
$458$			1.62897i			0.0761167i
$459$	−15.3596	+	23.4124i	−0.716924	+	1.09280i
$460$	−2.04505	+	16.6087i	−0.0953511	+	0.774385i
$461$	−1.08847	−	1.88528i	−0.0506950	−	0.0878064i	0.839564	−	0.543260i	$-0.182810\pi$
$461$	−1.08847	−	1.88528i	−0.0506950	−	0.0878064i	−0.890259	+	0.455454i	$0.849477\pi$
$462$	26.0946	+	10.3790i	1.21403	+	0.482876i
$463$	18.9829	+	10.9598i	0.882210	+	0.509344i	0.871386	−	0.490597i	$-0.163221\pi$
$463$	18.9829	+	10.9598i	0.882210	+	0.509344i	0.0108233	+	0.999941i	$0.496555\pi$
$464$	3.92934	−	6.80582i	0.182415	−	0.315952i
$465$	−1.31053	+	4.00756i	−0.0607744	+	0.185846i
$466$	−7.54457	−	13.0676i	−0.349496	−	0.605344i
$467$	−35.4899			−1.64228			−0.821139	−	0.570728i	$-0.806661\pi$
$467$	−35.4899			−1.64228			−0.821139	+	0.570728i	$0.806661\pi$
$468$	−6.41585	+	4.98063i	−0.296573	+	0.230230i
$469$		−	24.5172i		−	1.13210i
$470$	1.63211	+	3.84867i	0.0752837	+	0.177526i
$471$	26.0035	−	8.90862i	1.19818	−	0.410487i
$472$	−3.15267	+	5.46059i	−0.145113	+	0.251344i
$473$	1.86847	−	9.98299i	0.0859122	−	0.459018i
$474$	6.55440	+	19.1317i	0.301053	+	0.878749i
$475$	−17.6894	+	5.05926i	−0.811643	+	0.232135i
$476$		−	26.3437i		−	1.20746i
$477$	−5.40389	−	39.3359i	−0.247427	−	1.80107i
$478$		−	2.48062i		−	0.113461i
$479$	−3.85905	−	6.68407i	−0.176324	−	0.305403i	0.764294	−	0.644868i	$-0.223087\pi$
$479$	−3.85905	−	6.68407i	−0.176324	−	0.305403i	−0.940619	+	0.339465i	$0.889754\pi$
$480$	−3.68115	−	1.20379i	−0.168021	−	0.0549452i
$481$	8.23796	+	4.75619i	0.375618	+	0.216863i
$482$	−6.95737	+	12.0505i	−0.316899	+	0.548886i
$483$	−41.6467	+	47.7592i	−1.89499	+	2.17312i
$484$	10.2554	+	3.97827i	0.466155	+	0.180831i
$485$	−20.2440	−	2.49268i	−0.919234	−	0.113187i
$486$	1.23813	+	15.5392i	0.0561625	+	0.704873i
$487$			15.5946i			0.706658i	0.935499	+	0.353329i	$0.114950\pi$
$487$			15.5946i			0.706658i	−0.935499	+	0.353329i	$0.885050\pi$
$488$	0.374154	+	0.648054i	0.0169372	+	0.0293360i
$489$	20.5274	+	17.9002i	0.928281	+	0.809474i
$490$	22.7506	−	30.1696i	1.02777	−	1.36292i
$491$	−2.96302	+	5.13210i	−0.133719	+	0.231608i	−0.925107	−	0.379705i	$-0.876025\pi$
$491$	−2.96302	+	5.13210i	−0.133719	+	0.231608i	0.791388	+	0.611314i	$0.209359\pi$
$492$	−3.44570	−	0.675326i	−0.155344	−	0.0304460i
$493$	−36.6752	+	21.1744i	−1.65177	+	0.953649i
$494$	−9.96247			−0.448233
$495$	−20.8799	+	7.68296i	−0.938484	+	0.345323i
$496$	−1.08867			−0.0488828
$497$	6.11415	−	3.53001i	0.274257	−	0.158342i
$498$	−5.14494	−	15.0176i	−0.230550	−	0.672956i
$499$	−0.107017	+	0.185359i	−0.00479074	+	0.00829781i	−0.868411	−	0.495845i	$-0.834858\pi$
$499$	−0.107017	+	0.185359i	−0.00479074	+	0.00829781i	0.863620	+	0.504143i	$0.168192\pi$
$500$	7.02711	+	8.69596i	0.314262	+	0.388895i
$501$	−9.01327	+	3.08789i	−0.402683	+	0.137957i
$502$	−15.2195	−	26.3609i	−0.679279	−	1.17655i
$503$			20.3989i			0.909544i	0.890608	+	0.454772i	$0.150279\pi$
$503$			20.3989i			0.909544i	−0.890608	+	0.454772i	$0.849721\pi$
$504$	−8.99328	−	11.5848i	−0.400593	−	0.516027i
$505$	2.75523	−	22.3763i	0.122606	−	0.995733i
$506$	−16.1531	+	18.8454i	−0.718091	+	0.837778i
$507$	−9.63741	−	1.88884i	−0.428012	−	0.0838865i
$508$	6.99049	−	12.1079i	0.310153	−	0.537201i
$509$	18.3910	+	10.6181i	0.815169	+	0.470638i	0.848748	−	0.528798i	$-0.177357\pi$
$509$	18.3910	+	10.6181i	0.815169	+	0.470638i	−0.0335788	+	0.999436i	$0.510690\pi$
$510$	13.9359	+	15.5364i	0.617090	+	0.687963i
$511$	2.08049	+	3.60351i	0.0920354	+	0.159410i
$512$		−	1.00000i		−	0.0441942i
$513$	−10.4882	+	15.9871i	−0.463067	+	0.705847i
$514$		−	22.1951i		−	0.978984i
$515$	14.5191	+	34.2374i	0.639788	+	1.50868i
$516$	−3.48593	+	3.99756i	−0.153459	+	0.175983i
$517$	−1.14073	+	6.09476i	−0.0501691	+	0.268047i
$518$	−8.58801	+	14.8749i	−0.377336	+	0.653564i
$519$	4.77681	−	24.3726i	0.209679	−	1.06984i
$520$	2.36355	+	5.57347i	0.103648	+	0.244413i
$521$		−	6.08438i		−	0.266561i	−0.991078	−	0.133281i	$-0.957449\pi$
$521$		−	6.08438i		−	0.266561i	0.991078	−	0.133281i	$-0.0425512\pi$
$522$	−8.89952	+	21.8318i	−0.389522	+	0.955553i
$523$	9.70416			0.424333			0.212167	−	0.977233i	$-0.431948\pi$
$523$	9.70416			0.424333			0.212167	+	0.977233i	$0.431948\pi$
$524$	10.5033	+	18.1922i	0.458839	+	0.794732i
$525$	3.59561	+	42.1836i	0.156925	+	1.84104i
$526$	10.4240	−	18.0550i	0.454510	−	0.787234i
$527$	5.08065	+	2.93332i	0.221317	+	0.127777i
$528$	−3.56115	−	4.50758i	−0.154979	−	0.196167i
$529$	−16.5031	−	28.5842i	−0.717527	−	1.24279i
$530$	−29.3728	−	3.61671i	−1.27587	−	0.157100i
$531$	7.14045	−	17.5166i	0.309869	−	0.760154i
$532$		−	17.9887i		−	0.779911i
$533$	2.74425	+	4.75318i	0.118867	+	0.205883i
$534$	−9.30028	−	1.82277i	−0.402462	−	0.0788789i
$535$	−10.6235	+	14.0878i	−0.459294	+	0.609070i
$536$	−2.50758	+	4.34326i	−0.108311	+	0.187600i
$537$	27.4236	+	23.9138i	1.18342	+	1.03196i
$538$	−8.24641	−	14.2832i	−0.355528	−	0.615792i
$539$	52.8642	−	18.6153i	2.27702	−	0.801816i
$540$	11.4322	+	2.07475i	0.491964	+	0.0892830i
$541$			39.6188i			1.70334i	0.524076	+	0.851672i	$0.324411\pi$
$541$			39.6188i			1.70334i	−0.524076	+	0.851672i	$0.675589\pi$
$542$	3.43148	+	5.94350i	0.147395	+	0.255295i
$543$	−19.7618	+	22.6623i	−0.848060	+	0.972531i
$544$	−2.69440	+	4.66684i	−0.115521	+	0.200089i
$545$	3.72925	−	4.94537i	0.159744	−	0.211836i
$546$	−4.40908	+	22.4964i	−0.188691	+	0.962756i
$547$	−10.6748	−	18.4893i	−0.456420	−	0.790543i	0.542348	−	0.840154i	$-0.317535\pi$
$547$	−10.6748	−	18.4893i	−0.456420	−	0.790543i	−0.998769	+	0.0496105i	$0.984202\pi$
$548$	−18.9613			−0.809988
$549$	−1.37662	−	1.77330i	−0.0587526	−	0.0756828i
$550$	1.54900	+	16.5106i	0.0660497	+	0.704015i
$551$	−25.0435	+	14.4589i	−1.06689	+	0.615970i
$552$	12.2625	−	4.20106i	0.521928	−	0.178809i
$553$	49.4320	+	28.5396i	2.10206	+	1.21363i
$554$	5.20767	+	3.00665i	0.221253	+	0.127740i
$555$	−2.80399	−	13.3156i	−0.119023	−	0.565217i
$556$	−10.4498	+	6.03320i	−0.443170	+	0.255865i
$557$		−	12.2306i		−	0.518226i	−0.965847	−	0.259113i	$-0.916570\pi$
$557$		−	12.2306i		−	0.518226i	0.965847	−	0.259113i	$-0.0834301\pi$
$558$	3.23562	−	0.444504i	0.136975	−	0.0188173i
$559$	8.29072			0.350660
$560$	−10.0637	+	4.26775i	−0.425271	+	0.180345i
$561$	4.47408	+	30.6313i	0.188896	+	1.29325i
$562$	3.74421	+	2.16172i	0.157940	+	0.0911866i
$563$	21.2058	+	12.2432i	0.893718	+	0.515988i	0.875157	−	0.483839i	$-0.160758\pi$
$563$	21.2058	+	12.2432i	0.893718	+	0.515988i	0.0185613	+	0.999828i	$0.494091\pi$
$564$	2.12821	−	2.44057i	0.0896137	−	0.102766i
$565$	20.6059	−	8.73836i	0.866895	−	0.367626i
$566$			12.3287i			0.518213i
$567$	31.4589	+	30.7590i	1.32115	+	1.29176i
$568$	−1.44418			−0.0605963
$569$	13.5887	+	23.5363i	0.569669	+	0.986695i	0.996598	+	0.0824103i	$0.0262618\pi$
$569$	13.5887	+	23.5363i	0.569669	+	0.986695i	−0.426930	+	0.904285i	$0.640405\pi$
$570$	9.51606	+	10.6090i	0.398584	+	0.444361i
$571$	31.0698	+	17.9382i	1.30023	+	0.750689i	0.980443	−	0.196801i	$-0.0630552\pi$
$571$	31.0698	+	17.9382i	1.30023	+	0.750689i	0.319787	+	0.947489i	$0.396389\pi$
$572$	−1.65195	+	8.82615i	−0.0690714	+	0.369040i
$573$	−5.43699	+	27.7411i	−0.227134	+	1.15890i
$574$	−8.58258	+	4.95515i	−0.358230	+	0.206824i
$575$	−36.3010	−	9.07720i	−1.51386	−	0.378546i
$576$	0.408300	+	2.97209i	0.0170125	+	0.123837i
$577$		−	18.6282i		−	0.775503i	−0.921764	−	0.387751i	$-0.873252\pi$
$577$		−	18.6282i		−	0.775503i	0.921764	−	0.387751i	$-0.126748\pi$
$578$	10.4262	−	6.01959i	0.433674	−	0.250382i
$579$	4.07524	+	11.8953i	0.169361	+	0.494350i
$580$	14.0304	+	10.5802i	0.582583	+	0.439320i
$581$	−38.8021	−	22.4024i	−1.60978	−	0.929409i
$582$	5.12059	+	14.9466i	0.212255	+	0.619555i
$583$	−33.3283	−	28.5670i	−1.38032	−	1.18312i
$584$		−	0.851157i		−	0.0352211i
$585$	−9.30031	−	15.5998i	−0.384521	−	0.644972i
$586$	4.44912			0.183791
$587$	18.0016	+	31.1797i	0.743006	+	1.28692i	0.951121	+	0.308820i	$0.0999339\pi$
$587$	18.0016	+	31.1797i	0.743006	+	1.28692i	−0.208115	+	0.978104i	$0.566733\pi$
$588$	−28.7226	−	5.62936i	−1.18450	−	0.232151i
$589$	3.46931	+	2.00301i	0.142950	+	0.0825324i
$590$	−11.2572	−	8.48894i	−0.463452	−	0.349484i
$591$	−24.6308	−	21.4784i	−1.01317	−	0.883502i
$592$	3.04276	−	1.75674i	0.125057	−	0.0722016i
$593$		−	5.17998i		−	0.212716i	−0.994328	−	0.106358i	$-0.966081\pi$
$593$		−	5.17998i		−	0.212716i	0.994328	−	0.106358i	$-0.0339190\pi$
$594$	12.4245	+	11.9429i	0.509782	+	0.490023i
$595$	58.4649	+	7.19886i	2.39683	+	0.295125i
$596$	3.57301	+	6.18863i	0.146356	+	0.253496i
$597$	14.8546	−	17.0349i	0.607960	−	0.697190i
$598$	−17.5469	−	10.1307i	−0.717546	−	0.414275i
$599$	−7.70958	−	4.45113i	−0.315005	−	0.181868i	0.334159	−	0.942517i	$-0.391548\pi$
$599$	−7.70958	−	4.45113i	−0.315005	−	0.181868i	−0.649164	+	0.760649i	$0.724881\pi$
$600$	3.67751	−	7.84066i	0.150134	−	0.320093i
$601$	6.89247	−	3.97937i	0.281150	−	0.162322i	−0.352794	−	0.935701i	$-0.614768\pi$
$601$	6.89247	−	3.97937i	0.281150	−	0.162322i	0.633944	+	0.773379i	$0.281435\pi$
$602$			14.9702i			0.610138i
$603$	5.67940	−	13.9324i	0.231283	−	0.567370i
$604$		−	6.00160i		−	0.244201i
$605$	−11.6315	+	21.6728i	−0.472886	+	0.881123i
$606$	−16.5209	+	5.65994i	−0.671115	+	0.229919i
$607$	−3.13958	+	5.43790i	−0.127431	+	0.220718i	−0.922681	−	0.385565i	$-0.874007\pi$
$607$	−3.13958	+	5.43790i	−0.127431	+	0.220718i	0.795249	+	0.606283i	$0.207340\pi$
$608$	−1.83986	+	3.18674i	−0.0746163	+	0.129239i
$609$	21.5663	+	62.9502i	0.873911	+	2.55087i
$610$	−1.54047	+	0.653272i	−0.0623720	+	0.0264502i
$611$	−5.06160			−0.204770
$612$	6.10252	−	14.9704i	0.246680	−	0.605141i
$613$	−34.8535			−1.40772			−0.703860	−	0.710338i	$-0.748542\pi$
$613$	−34.8535			−1.40772			−0.703860	+	0.710338i	$0.748542\pi$
$614$	22.0193	−	12.7129i	0.888628	−	0.513050i
$615$	2.44035	−	7.46253i	0.0984044	−	0.300918i
$616$	−15.9369	−	2.98284i	−0.642118	−	0.120182i
$617$	12.3321	−	21.3598i	0.496471	−	0.859914i	−0.503520	−	0.863983i	$-0.667962\pi$
$617$	12.3321	−	21.3598i	0.496471	−	0.859914i	0.999992	+	0.00406963i	$0.00129541\pi$
$618$	18.9323	−	21.7110i	0.761570	−	0.873346i
$619$	−17.3788	−	30.1009i	−0.698513	−	1.20986i	−0.968982	−	0.247131i	$-0.920512\pi$
$619$	−17.3788	−	30.1009i	−0.698513	−	1.20986i	0.270470	−	0.962729i	$-0.412821\pi$
$620$	0.297497	−	2.41610i	0.0119478	−	0.0970327i
$621$	−34.7300	+	17.4927i	−1.39367	+	0.701958i
$622$	−11.7965			−0.472998
$623$	−23.1652	+	13.3744i	−0.928094	+	0.535836i
$624$	3.08197	−	3.53432i	0.123378	−	0.141486i
$625$	−21.2193	+	13.2190i	−0.848772	+	0.528760i
$626$	3.46134	−	5.99521i	0.138343	−	0.239617i
$627$	3.05511	+	20.9165i	0.122009	+	0.835324i
$628$	−13.7436	+	7.93486i	−0.548429	+	0.316636i
$629$	−18.9334			−0.754926
$630$	28.1678	−	16.7931i	1.12223	−	0.669054i
$631$	22.0133			0.876336			0.438168	−	0.898893i	$-0.355627\pi$
$631$	22.0133			0.876336			0.438168	+	0.898893i	$0.355627\pi$
$632$	−5.83797	−	10.1117i	−0.232222	−	0.402220i
$633$	27.5596	−	9.44174i	1.09540	−	0.375275i
$634$	8.15457	+	4.70805i	0.323860	+	0.186980i
$635$	24.9609	+	18.8227i	0.990542	+	0.746957i
$636$	7.42965	+	21.6865i	0.294605	+	0.859926i
$637$	22.8754	+	39.6214i	0.906358	+	1.56986i
$638$	8.65707	+	24.5846i	0.342737	+	0.973314i
$639$	4.29221	−	0.589656i	0.169797	−	0.0233264i
$640$	2.21931	+	0.273267i	0.0877258	+	0.0108018i
$641$	−15.4565	+	8.92380i	−0.610494	+	0.352469i	−0.773159	−	0.634213i	$-0.781324\pi$
$641$	−15.4565	+	8.92380i	−0.610494	+	0.352469i	0.162665	+	0.986681i	$0.447991\pi$
$642$	13.4121	+	2.62866i	0.529335	+	0.103745i
$643$	12.5959	+	7.27226i	0.496735	+	0.286790i	0.727364	−	0.686252i	$-0.240745\pi$
$643$	12.5959	+	7.27226i	0.496735	+	0.286790i	−0.230629	+	0.973042i	$0.574078\pi$
$644$	18.2925	−	31.6836i	0.720826	−	1.24851i
$645$	−7.91922	−	8.82874i	−0.311819	−	0.347631i
$646$	17.1727	−	9.91466i	0.675650	−	0.390087i
$647$	14.1915			0.557924			0.278962	−	0.960302i	$-0.410010\pi$
$647$	14.1915			0.557924			0.278962	+	0.960302i	$0.410010\pi$
$648$	−2.42700	−	8.66658i	−0.0953417	−	0.340456i
$649$	−6.94592	−	19.7252i	−0.272651	−	0.774283i
$650$	−13.0151	+	3.72240i	−0.510495	+	0.146005i
$651$	6.05842	−	6.94762i	0.237448	−	0.272299i
$652$	−13.6179	−	7.86231i	−0.533319	−	0.307912i
$653$	4.78904	−	8.29487i	0.187410	−	0.324603i	−0.756976	−	0.653443i	$-0.773324\pi$
$653$	4.78904	−	8.29487i	0.187410	−	0.324603i	0.944386	+	0.328839i	$0.106657\pi$
$654$	−4.70817	−	0.922759i	−0.184104	−	0.0360827i
$655$	−43.2444	+	18.3387i	−1.68970	+	0.716553i
$656$	2.02723			0.0791498
$657$	0.347527	+	2.52971i	0.0135583	+	0.0986935i
$658$		−	9.13949i		−	0.356294i
$659$	−22.6253	−	39.1882i	−0.881356	−	1.52655i	−0.849834	−	0.527051i	$-0.823298\pi$
$659$	−22.6253	−	39.1882i	−0.881356	−	1.52655i	−0.0315230	−	0.999503i	$-0.510036\pi$
$660$	10.9768	−	6.67151i	0.427273	−	0.259688i
$661$	24.5180	−	42.4664i	0.953640	−	1.65175i	0.216190	−	0.976351i	$-0.430637\pi$
$661$	24.5180	−	42.4664i	0.953640	−	1.65175i	0.737450	−	0.675401i	$-0.236030\pi$
$662$	−7.53559	−	4.35068i	−0.292879	−	0.169094i
$663$	−23.9059	+	8.19001i	−0.928430	+	0.318074i
$664$	4.58257	+	7.93725i	0.177838	+	0.308025i
$665$	39.9225	+	4.91572i	1.54813	+	0.190623i
$666$	−8.32607	+	6.46354i	−0.322629	+	0.250457i
$667$	−58.8123			−2.27722
$668$	4.76377	−	2.75037i	0.184316	−	0.106415i
$669$	2.72634	−	13.9105i	0.105406	−	0.537812i
$670$	−8.95379	−	6.75196i	−0.345915	−	0.260851i
$671$	−2.43950	−	0.456589i	−0.0941757	−	0.0176264i
$672$	6.38174	+	5.56497i	0.246181	+	0.214673i
$673$	2.71968	+	4.71062i	0.104836	+	0.181581i	0.913671	−	0.406454i	$-0.133235\pi$
$673$	2.71968	+	4.71062i	0.104836	+	0.181581i	−0.808835	+	0.588035i	$0.799902\pi$
$674$		−	21.4444i		−	0.826006i
$675$	−7.72855	+	24.8046i	−0.297472	+	0.954731i
$676$	5.67002			0.218078
$677$	3.64781	−	2.10606i	0.140197	−	0.0809426i	−0.428261	−	0.903655i	$-0.640874\pi$
$677$	3.64781	−	2.10606i	0.140197	−	0.0809426i	0.568458	+	0.822712i	$0.307540\pi$
$678$	−13.0668	−	11.3945i	−0.501829	−	0.437602i
$679$	38.6185	+	22.2964i	1.48204	+	0.855657i
$680$	−9.62086	−	7.25499i	−0.368943	−	0.278216i
$681$	3.79430	−	19.3596i	0.145398	−	0.741862i
$682$	2.34981	−	2.74146i	0.0899790	−	0.104976i
$683$	−14.2789			−0.546368			−0.273184	−	0.961962i	$-0.588077\pi$
$683$	−14.2789			−0.546368			−0.273184	+	0.961962i	$0.588077\pi$
$684$	4.16709	−	10.2225i	0.159333	−	0.390866i
$685$	5.18150	−	42.0810i	0.197975	−	1.60783i
$686$	−41.9069	+	24.1949i	−1.60001	+	0.923767i
$687$	0.914437	+	2.66916i	0.0348879	+	0.101835i
$688$	1.53113	−	2.65199i	0.0583736	−	0.101106i
$689$	17.9163	−	31.0320i	0.682557	−	1.18222i
$690$	5.97251	+	28.3623i	0.227369	+	1.07974i
$691$	−0.417533	−	0.723188i	−0.0158837	−	0.0275114i	0.857974	−	0.513693i	$-0.171723\pi$
$691$	−0.417533	−	0.723188i	−0.0158837	−	0.0275114i	−0.873858	+	0.486181i	$0.838389\pi$
$692$			14.3393i			0.545097i
$693$	48.5838	+	2.35821i	1.84555	+	0.0895810i
$694$	−24.1261			−0.915814
$695$	−10.5339	−	24.8400i	−0.399575	−	0.942235i
$696$	2.61795	−	13.3575i	0.0992331	−	0.506315i
$697$	−9.46073	−	5.46216i	−0.358351	−	0.206894i
$698$	1.40211	−	2.42852i	0.0530705	−	0.0919208i
$699$	−19.6978	−	17.1768i	−0.745041	−	0.649686i
$700$	−6.72136	−	23.5008i	−0.254043	−	0.888245i
$701$	−6.63741			−0.250692			−0.125346	−	0.992113i	$-0.540004\pi$
$701$	−6.63741			−0.250692			−0.125346	+	0.992113i	$0.540004\pi$
$702$	−7.71683	+	11.7627i	−0.291253	+	0.443953i
$703$	−12.9286			−0.487613
$704$	2.51818	+	2.15842i	0.0949073	+	0.0813486i
$705$	4.83480	+	5.39007i	0.182089	+	0.203002i
$706$	2.38132	+	1.37486i	0.0896222	+	0.0517434i
$707$	−24.6449	+	42.6862i	−0.926866	+	1.60538i
$708$	−2.10049	+	10.7173i	−0.0789412	+	0.402780i
$709$	−8.03395	−	13.9152i	−0.301721	−	0.522597i	0.674805	−	0.737996i	$-0.264228\pi$
$709$	−8.03395	−	13.9152i	−0.301721	−	0.522597i	−0.976526	+	0.215400i	$0.930895\pi$
$710$	0.394645	−	3.20507i	0.0148108	−	0.120284i
$711$	21.4795	+	27.6691i	0.805546	+	1.03767i
$712$	5.47167			0.205060
$713$	4.07366	+	7.05579i	0.152560	+	0.264241i
$714$	−14.7883	−	43.1658i	−0.553438	−	1.61544i
$715$	−19.1365	−	6.07807i	−0.715665	−	0.227307i
$716$	−18.1929	−	10.5037i	−0.679900	−	0.392541i
$717$	−1.39252	−	4.06464i	−0.0520045	−	0.151797i
$718$	2.01492	−	1.16332i	0.0751962	−	0.0434146i
$719$			50.4585i			1.88178i	0.338707	+	0.940892i	$0.390010\pi$
$719$			50.4585i			1.88178i	−0.338707	+	0.940892i	$0.609990\pi$
$720$	−6.70755	+	0.0939709i	−0.249975	+	0.00350209i
$721$		−	81.3040i		−	3.02792i
$722$	−4.72817	+	2.72981i	−0.175964	+	0.101593i
$723$	−4.63539	+	23.6511i	−0.172392	+	0.879592i
$724$	8.67999	−	15.0342i	0.322589	−	0.558741i
$725$	−27.3148	+	28.2467i	−1.01445	+	1.04905i
$726$	19.0373	+	0.761666i	0.706542	+	0.0282681i
$727$	−6.45324	+	3.72578i	−0.239337	+	0.138182i	−0.614872	−	0.788627i	$-0.710792\pi$
$727$	−6.45324	+	3.72578i	−0.239337	+	0.138182i	0.375535	+	0.926808i	$0.377459\pi$
$728$		−	13.2354i		−	0.490536i
$729$	10.7518	+	24.7669i	0.398216	+	0.917292i
$730$	1.88898	+	0.232593i	0.0699143	+	0.00860865i
$731$	−14.2910	+	8.25094i	−0.528573	+	0.305172i
$732$	0.976865	+	0.851840i	0.0361060	+	0.0314849i
$733$	22.1331	−	38.3357i	0.817505	−	1.41596i	−0.0900102	−	0.995941i	$-0.528690\pi$
$733$	22.1331	−	38.3357i	0.817505	−	1.41596i	0.907515	−	0.420019i	$-0.137977\pi$
$734$	7.80087	−	13.5115i	0.287935	−	0.498719i
$735$	20.3422	−	62.2060i	0.750334	−	2.29450i
$736$	−6.48110	+	3.74187i	−0.238897	+	0.137927i
$737$	−5.52467	−	15.6891i	−0.203504	−	0.577916i
$738$	−6.02509	+	0.827715i	−0.221786	+	0.0304686i
$739$			9.54604i			0.351157i	0.984465	+	0.175578i	$0.0561795\pi$
$739$			9.54604i			0.351157i	−0.984465	+	0.175578i	$0.943820\pi$
$740$	3.06726	+	7.23288i	0.112755	+	0.265886i
$741$	−16.3241	+	5.59252i	−0.599680	+	0.205446i
$742$	56.0329	+	32.3506i	2.05703	+	1.18763i
$743$	4.98773	+	2.87967i	0.182982	+	0.105645i	0.588693	−	0.808357i	$-0.299643\pi$
$743$	4.98773	+	2.87967i	0.182982	+	0.105645i	−0.405711	+	0.914001i	$0.632976\pi$
$744$	−1.78385	+	0.611135i	−0.0653992	+	0.0224053i
$745$	−14.7109	+	6.23846i	−0.538964	+	0.228560i
$746$		−	5.13260i		−	0.187918i
$747$	−16.8606	−	21.7191i	−0.616896	−	0.794661i
$748$	−5.93626	−	16.8580i	−0.217051	−	0.616389i
$749$	33.4071	−	19.2876i	1.22067	−	0.704753i
$750$	16.3959	+	10.3041i	0.598693	+	0.376253i
$751$	2.44686	−	4.23809i	0.0892873	−	0.154650i	−0.817923	−	0.575328i	$-0.804874\pi$
$751$	2.44686	−	4.23809i	0.0892873	−	0.154650i	0.907210	+	0.420678i	$0.138208\pi$
$752$	−0.934774	+	1.61908i	−0.0340877	+	0.0590416i
$753$	−39.7360	−	34.6503i	−1.44806	−	1.26273i
$754$	−18.4260	+	10.6383i	−0.671036	+	0.387423i
$755$	13.3194	+	1.64004i	0.484742	+	0.0596870i
$756$	−21.2393	−	13.9339i	−0.772464	−	0.506771i
$757$			3.31796i			0.120593i	0.998181	+	0.0602966i	$0.0192047\pi$
$757$			3.31796i			0.120593i	−0.998181	+	0.0602966i	$0.980795\pi$
$758$	19.3990	−	11.2000i	0.704602	−	0.406802i
$759$	−15.8887	+	39.9469i	−0.576724	+	1.44998i
$760$	−6.56957	−	4.95405i	−0.238303	−	0.179702i
$761$	21.9954	−	38.0971i	0.797332	−	1.38102i	−0.124016	−	0.992280i	$-0.539577\pi$
$761$	21.9954	−	38.0971i	0.797332	−	1.38102i	0.921348	−	0.388739i	$-0.127089\pi$
$762$	4.65746	−	23.7637i	0.168722	−	0.860867i
$763$	−11.7272	+	6.77068i	−0.424552	+	0.245115i
$764$		−	16.3210i		−	0.590474i
$765$	31.5562	+	17.6343i	1.14092	+	0.637568i
$766$		−	8.79477i		−	0.317768i
$767$	14.7840	−	8.53552i	0.533818	−	0.308200i
$768$	−0.561359	−	1.63856i	−0.0202563	−	0.0591264i
$769$	−0.0158264	−	0.00913739i	−0.000570715	−	0.000329503i	0.499715	−	0.866190i	$-0.333438\pi$
$769$	−0.0158264	−	0.00913739i	−0.000570715	−	0.000329503i	−0.500285	+	0.865861i	$0.666772\pi$
$770$	10.9749	−	34.5539i	0.395507	−	1.24523i
$771$	−12.4594	−	36.3680i	−0.448715	−	1.30976i
$772$	−3.62980	−	6.28699i	−0.130639	−	0.226274i
$773$	−44.1446			−1.58777			−0.793886	−	0.608067i	$-0.791945\pi$
$773$	−44.1446			−1.58777			−0.793886	+	0.608067i	$0.791945\pi$
$774$	−3.46783	+	8.50709i	−0.124649	+	0.305781i
$775$	5.28076	+	1.32048i	0.189691	+	0.0474329i
$776$	−4.56089	−	7.89969i	−0.163726	−	0.283582i
$777$	−5.72182	+	29.1943i	−0.205269	+	1.04734i
$778$	−10.4408	+	18.0840i	−0.374320	+	0.648342i
$779$	−6.46023	−	3.72982i	−0.231462	−	0.133635i
$780$	7.00153	+	7.80566i	0.250695	+	0.279487i
$781$	3.11714	−	3.63669i	0.111540	−	0.130131i
$782$	40.3283			1.44214
$783$	−2.32690	+	40.7686i	−0.0831567	+	1.45695i
$784$	16.8985			0.603518
$785$	−13.8542	−	32.6696i	−0.494479	−	1.16603i
$786$	27.4227	+	23.9129i	0.978134	+	0.852946i
$787$	8.55726	−	14.8216i	0.305033	−	0.528333i	−0.672235	−	0.740337i	$-0.734666\pi$
$787$	8.55726	−	14.8216i	0.305033	−	0.528333i	0.977269	+	0.212004i	$0.0679991\pi$
$788$	16.3401	+	9.43396i	0.582092	+	0.336071i
$789$	6.94508	−	35.4357i	0.247251	−	1.26155i
$790$	24.0362	−	10.1931i	0.855170	−	0.362653i
$791$	−48.9330			−1.73986
$792$	−8.36552	−	5.38685i	−0.297256	−	0.191413i
$793$		−	2.02597i		−	0.0719441i
$794$	4.69900	+	8.13890i	0.166761	+	0.288839i
$795$	−50.1593	+	10.5625i	−1.77897	+	0.374612i
$796$	−6.52461	+	11.3010i	−0.231259	+	0.400552i
$797$	3.47335	−	6.01601i	0.123032	−	0.213098i	−0.797930	−	0.602750i	$-0.794071\pi$
$797$	3.47335	−	6.01601i	0.123032	−	0.213098i	0.920962	+	0.389652i	$0.127405\pi$
$798$	−10.0981	−	29.4756i	−0.357470	−	1.04343i
$799$	8.72488	−	5.03731i	0.308664	−	0.178207i
$800$	−1.21292	+	4.85065i	−0.0428834	+	0.171496i
$801$	−16.2623	+	2.23408i	−0.574600	+	0.0789374i
$802$	24.6266			0.869597
$803$	2.14336	+	1.83716i	0.0756377	+	0.0648319i
$804$	−1.67069	+	8.52434i	−0.0589208	+	0.300630i
$805$	65.3169	+	49.2548i	2.30212	+	1.73600i
$806$	2.55258	+	1.47373i	0.0899106	+	0.0519099i
$807$	−21.5302	−	18.7747i	−0.757900	−	0.660899i
$808$	8.73176	−	5.04129i	0.307182	−	0.177352i
$809$	10.0543			0.353491			0.176745	−	0.984257i	$-0.443443\pi$
$809$	10.0543			0.353491			0.176745	+	0.984257i	$0.443443\pi$
$810$	19.8970	−	3.01798i	0.699110	−	0.106041i
$811$			20.2126i			0.709759i	0.934912	+	0.354879i	$0.115478\pi$
$811$			20.2126i			0.709759i	−0.934912	+	0.354879i	$0.884522\pi$
$812$	−19.2090	−	33.2710i	−0.674104	−	1.16758i
$813$	8.95912	+	7.81248i	0.314210	+	0.273996i
$814$	−2.14379	+	11.4540i	−0.0751398	+	0.401462i
$815$	21.1702	−	28.0738i	0.741560	−	0.983384i
$816$	−1.79516	+	9.15942i	−0.0628432	+	0.320644i
$817$	−9.75859	+	5.63412i	−0.341410	+	0.197113i
$818$	−20.9220			−0.731520
$819$	5.40400	+	39.3367i	0.188831	+	1.37454i
$820$	−0.553973	+	4.49904i	−0.0193456	+	0.157113i
$821$	7.94106	+	13.7543i	0.277145	+	0.480029i	0.970674	−	0.240400i	$-0.0772785\pi$
$821$	7.94106	+	13.7543i	0.277145	+	0.480029i	−0.693529	+	0.720428i	$0.743945\pi$
$822$	−31.0693	+	10.6441i	−1.08367	+	0.371256i
$823$	−22.0913	−	12.7544i	−0.770055	−	0.444592i	0.0628392	−	0.998024i	$-0.479984\pi$
$823$	−22.0913	−	12.7544i	−0.770055	−	0.444592i	−0.832894	+	0.553432i	$0.813318\pi$
$824$	−8.31566	+	14.4031i	−0.289690	+	0.501757i
$825$	11.8065	+	26.1841i	0.411050	+	0.911613i
$826$	15.4122	+	26.6947i	0.536258	+	0.928826i
$827$		−	9.59633i		−	0.333697i	−0.985983	−	0.166848i	$-0.946641\pi$
$827$		−	9.59633i		−	0.333697i	0.985983	−	0.166848i	$-0.0533591\pi$
$828$	17.7346	−	13.7674i	0.616319	−	0.478449i
$829$	−32.1586			−1.11691			−0.558457	−	0.829533i	$-0.688607\pi$
$829$	−32.1586			−1.11691			−0.558457	+	0.829533i	$0.688607\pi$
$830$	−18.8675	+	8.00116i	−0.654899	+	0.277724i
$831$	10.2209	+	2.00320i	0.354559	+	0.0694902i
$832$	−1.35370	+	2.34467i	−0.0469310	+	0.0812869i
$833$	−78.8626	−	45.5313i	−2.73243	−	1.57757i
$834$	−13.7358	+	15.7518i	−0.475633	+	0.545442i
$835$	4.80213	+	11.3239i	0.166184	+	0.391878i
$836$	−4.05356	−	11.5114i	−0.140195	−	0.398131i
$837$	5.05223	−	2.54469i	0.174631	−	0.0879574i
$838$	12.4874			0.431369
$839$	−36.9732	+	21.3465i	−1.27646	+	0.736963i	−0.976195	−	0.216894i	$-0.930407\pi$
$839$	−36.9732	+	21.3465i	−1.27646	+	0.736963i	−0.300262	+	0.953857i	$0.597074\pi$
$840$	−14.0943	+	12.6423i	−0.486299	+	0.436202i
$841$	−16.3794	+	28.3700i	−0.564808	+	0.978277i
$842$	−14.9842	−	8.65115i	−0.516391	−	0.298138i
$843$	7.34861	+	1.44026i	0.253099	+	0.0496052i
$844$	−14.5660	+	8.40971i	−0.501384	+	0.289474i
$845$	−1.54943	+	12.5835i	−0.0533019	+	0.432886i
$846$	2.11716	−	5.19370i	0.0727895	−	0.178563i
$847$	41.9100	−	33.6938i	1.44004	−	1.15773i
$848$	−6.61755	−	11.4619i	−0.227248	−	0.393604i
$849$	6.92082	+	20.2013i	0.237522	+	0.693306i
$850$	18.7301	−	19.3691i	0.642438	−	0.664355i
$851$	−22.7712	−	13.1470i	−0.780587	−	0.450672i
$852$	−2.36637	+	0.810702i	−0.0810704	+	0.0277742i
$853$	−2.10579	−	3.64733i	−0.0721008	−	0.124882i	0.827721	−	0.561140i	$-0.189637\pi$
$853$	−2.10579	−	3.64733i	−0.0721008	−	0.124882i	−0.899822	+	0.436258i	$0.856304\pi$
$854$	3.65819			0.125181
$855$	21.5481	+	12.0415i	0.736928	+	0.411811i
$856$	−7.89082			−0.269703
$857$	46.9041	−	27.0801i	1.60221	−	0.925039i	0.611171	−	0.791498i	$-0.290699\pi$
$857$	46.9041	−	27.0801i	1.60221	−	0.925039i	0.991043	−	0.133541i	$-0.0426347\pi$
$858$	2.24783	+	15.3895i	0.0767395	+	0.525389i
$859$	14.9050	−	25.8161i	0.508550	−	0.880835i	−0.491401	−	0.870934i	$-0.663515\pi$
$859$	14.9050	−	25.8161i	0.508550	−	0.880835i	0.999951	−	0.00990141i	$-0.00315177\pi$
$860$	5.46717	+	4.12274i	0.186429	+	0.140584i
$861$	−11.2814	+	12.9372i	−0.384471	+	0.440899i
$862$	−22.7867	+	13.1559i	−0.776119	+	0.448093i
$863$	22.0884			0.751897			0.375948	−	0.926641i	$-0.377317\pi$
$863$	22.0884			0.751897			0.375948	+	0.926641i	$0.377317\pi$
$864$	2.33743	+	4.64073i	0.0795210	+	0.157881i
$865$	−31.8232	−	3.91844i	−1.08202	−	0.133231i
$866$	5.46858	+	9.47187i	0.185830	+	0.321867i
$867$	13.7049	−	15.7163i	0.465441	−	0.533754i
$868$	−2.66104	+	4.60906i	−0.0903217	+	0.156442i
$869$	38.0638	+	7.12421i	1.29122	+	0.241672i
$870$	28.9290	+	9.46019i	0.980786	+	0.320731i
$871$	11.7589	−	6.78901i	0.398436	−	0.230037i
$872$	2.76998			0.0938034
$873$	16.7808	+	21.6163i	0.567944	+	0.731602i
$874$	27.5381			0.931489
$875$	53.9921	−	8.49479i	1.82527	−	0.287176i
$876$	−0.477805	−	1.39467i	−0.0161435	−	0.0471216i
$877$	−4.55473	+	7.88903i	−0.153802	+	0.266393i	−0.932622	−	0.360854i	$-0.882485\pi$
$877$	−4.55473	+	7.88903i	−0.153802	+	0.266393i	0.778820	+	0.627248i	$0.215819\pi$
$878$	−4.09799	+	7.09793i	−0.138301	+	0.239544i
$879$	7.29014	−	2.49755i	0.245890	−	0.0842404i
$880$	−5.47834	+	4.99878i	−0.184675	+	0.168509i
$881$		−	42.6780i		−	1.43786i	−0.695084	−	0.718929i	$-0.744633\pi$
$881$		−	42.6780i		−	1.43786i	0.695084	−	0.718929i	$-0.255367\pi$
$882$	−50.2238	+	6.89965i	−1.69112	+	0.232323i
$883$		−	55.3727i		−	1.86344i	−0.363178	−	0.931720i	$-0.618308\pi$
$883$		−	55.3727i		−	1.86344i	0.363178	−	0.931720i	$-0.381692\pi$
$884$	12.6350	−	7.29480i	0.424960	−	0.245351i
$885$	−23.2109	−	7.59030i	−0.780227	−	0.255145i
$886$	−11.7858	−	6.80456i	−0.395953	−	0.228604i
$887$	19.7758	+	11.4176i	0.664006	+	0.383364i	0.793802	−	0.608177i	$-0.208099\pi$
$887$	19.7758	+	11.4176i	0.664006	+	0.383364i	−0.129796	+	0.991541i	$0.541432\pi$
$888$	3.99958	−	4.58660i	0.134217	−	0.153916i
$889$	−34.1738	−	59.1907i	−1.14615	−	1.98519i
$890$	−1.49523	+	12.1433i	−0.0501201	+	0.407045i
$891$	27.0625	+	12.5945i	0.906627	+	0.421933i
$892$			8.18405i			0.274022i
$893$	5.95776	−	3.43971i	0.199369	−	0.115106i
$894$	9.32863	+	8.13470i	0.311996	+	0.272065i
$895$	28.2824	−	37.5053i	0.945376	−	1.25366i
$896$	−4.23366	−	2.44430i	−0.141437	−	0.0816585i
$897$	−34.4386	−	6.74965i	−1.14987	−	0.225364i
$898$	5.98504	+	10.3664i	0.199723	+	0.345931i
$899$	8.55552			0.285343
$900$	1.62440	−	14.9118i	0.0541466	−	0.497060i
$901$			71.3213i			2.37606i
$902$	−4.37561	+	5.10491i	−0.145692	+	0.169975i
$903$	8.40363	+	24.5295i	0.279655	+	0.816290i
$904$	8.66857	+	5.00480i	0.288312	+	0.166457i
$905$	30.9935	+	23.3719i	1.03026	+	0.776909i
$906$	−3.36905	−	9.83397i	−0.111929	−	0.326712i
$907$	42.0840	−	24.2972i	1.39738	−	0.806776i	0.403260	−	0.915086i	$-0.367877\pi$
$907$	42.0840	−	24.2972i	1.39738	−	0.806776i	0.994117	+	0.108309i	$0.0345437\pi$
$908$			11.3899i			0.377988i
$909$	−23.8932	+	18.5483i	−0.792487	+	0.615208i
$910$	29.3734	+	3.61679i	0.973719	+	0.119895i
$911$	4.60131	−	2.65657i	0.152448	−	0.0880160i	−0.421835	−	0.906672i	$-0.638614\pi$
$911$	4.60131	−	2.65657i	0.152448	−	0.0880160i	0.574284	+	0.818656i	$0.305281\pi$
$912$	−1.22582	+	6.25448i	−0.0405910	+	0.207106i
$913$	−29.8785	−	5.59222i	−0.988835	−	0.185075i
$914$	−1.39601	−	0.805987i	−0.0461759	−	0.0266597i
$915$	−2.15744	+	1.93518i	−0.0713227	+	0.0639752i
$916$	−0.814485	−	1.41073i	−0.0269113	−	0.0466118i
$917$	102.693			3.39122
$918$	1.59559	−	27.9555i	0.0526622	−	0.922670i
$919$		−	3.10157i		−	0.102312i	−0.998691	−	0.0511558i	$-0.983710\pi$
$919$		−	3.10157i		−	0.102312i	0.998691	−	0.0511558i	$-0.0162905\pi$
$920$	−6.53328	−	15.4061i	−0.215396	−	0.507924i
$921$	28.9435	−	33.1915i	0.953721	−	1.09370i
$922$	1.88528	+	1.08847i	0.0620885	+	0.0358468i
$923$	3.38612	+	1.95498i	0.111455	+	0.0643488i
$924$	−27.7881	+	4.05879i	−0.914160	+	0.133524i
$925$	−16.8902	+	4.83069i	−0.555345	+	0.158832i
$926$	−21.9196			−0.720321
$927$	18.8340	−	46.2026i	0.618591	−	1.51749i
$928$			7.85868i			0.257974i
$929$	11.4141	−	6.58992i	0.374484	−	0.216208i	−0.300932	−	0.953646i	$-0.597298\pi$
$929$	11.4141	−	6.58992i	0.374484	−	0.216208i	0.675415	+	0.737437i	$0.263964\pi$
$930$	−0.868831	−	4.12592i	−0.0284901	−	0.135294i
$931$	−53.8510	−	31.0909i	−1.76490	−	1.01896i
$932$	13.0676	+	7.54457i	0.428043	+	0.247131i
$933$	−19.3293	+	6.62209i	−0.632813	+	0.216797i
$934$	30.7352	−	17.7450i	1.00569	−	0.580633i
$935$	39.0352	−	8.56767i	1.27659	−	0.280193i
$936$	3.06597	−	7.52128i	0.100214	−	0.245841i
$937$	39.3886			1.28677			0.643384	−	0.765544i	$-0.277530\pi$
$937$	39.3886			1.28677			0.643384	+	0.765544i	$0.277530\pi$
$938$	12.2586	+	21.2325i	0.400257	+	0.693266i
$939$	2.30614	−	11.7666i	0.0752580	−	0.383987i
$940$	−3.33778	−	2.51699i	−0.108867	−	0.0820952i
$941$	2.14846	−	3.72124i	0.0700378	−	0.121309i	−0.828880	−	0.559427i	$-0.811021\pi$
$941$	2.14846	−	3.72124i	0.0700378	−	0.121309i	0.898918	+	0.438118i	$0.144355\pi$
$942$	−18.0654	+	20.7168i	−0.588602	+	0.674991i
$943$	−7.58560	−	13.1387i	−0.247021	−	0.427853i
$944$		−	6.30534i		−	0.205221i
$945$	36.7276	−	43.3288i	1.19475	−	1.40948i
$946$	3.37335	+	9.57976i	0.109677	+	0.311465i
$947$	−12.3162	−	21.3324i	−0.400224	−	0.693209i	0.593528	−	0.804813i	$-0.297734\pi$
$947$	−12.3162	−	21.3324i	−0.400224	−	0.693209i	−0.993753	+	0.111604i	$0.964401\pi$
$948$	−15.2421	−	13.2914i	−0.495042	−	0.431683i
$949$	−1.15221	+	1.99568i	−0.0374023	+	0.0647827i
$950$	12.7898	−	13.2261i	0.414956	−	0.429112i
$951$	16.0047	+	3.13677i	0.518987	+	0.101717i
$952$	13.1719	+	22.8144i	0.426903	+	0.739417i
$953$		−	42.5719i		−	1.37904i	−0.724266	−	0.689520i	$-0.757821\pi$
$953$		−	42.5719i		−	1.37904i	0.724266	−	0.689520i	$-0.242179\pi$
$954$	24.3478	+	31.3639i	0.788290	+	1.01544i
$955$	36.2214	+	4.45999i	1.17210	+	0.144322i
$956$	1.24031	+	2.14828i	0.0401144	+	0.0694802i
$957$	27.9859	+	35.4236i	0.904656	+	1.14508i
$958$	6.68407	+	3.85905i	0.215952	+	0.124680i
$959$	−46.3473	+	80.2758i	−1.49663	+	2.59224i
$960$	3.78987	−	0.798065i	0.122317	−	0.0257574i
$961$	14.9074	+	25.8204i	0.480884	+	0.832915i
$962$	−9.51237			−0.306691
$963$	23.4522	−	3.22182i	0.755737	−	0.103822i
$964$		−	13.9147i		−	0.448163i
$965$	14.9447	−	6.33761i	0.481086	−	0.204015i
$966$	12.1875	−	62.1841i	0.392127	−	2.00074i
$967$	24.2595	−	42.0186i	0.780132	−	1.35123i	−0.151733	−	0.988422i	$-0.548485\pi$
$967$	24.2595	−	42.0186i	0.780132	−	1.35123i	0.931864	−	0.362807i	$-0.118181\pi$
$968$	−10.8706	+	1.68242i	−0.349394	+	0.0540750i
$969$	22.5728	−	25.8858i	0.725142	−	0.831572i
$970$	18.7782	−	7.96329i	0.602931	−	0.255686i
$971$			44.3268i			1.42252i	0.702931	+	0.711258i	$0.251874\pi$
$971$			44.3268i			1.42252i	−0.702931	+	0.711258i	$0.748126\pi$
$972$	−8.84185	−	12.8383i	−0.283603	−	0.411788i
$973$			58.9879i			1.89106i
$974$	−7.79729	−	13.5053i	−0.249841	−	0.432738i
$975$	−19.2364	+	13.4055i	−0.616059	+	0.429320i
$976$	−0.648054	−	0.374154i	−0.0207437	−	0.0119764i
$977$	−16.9768	+	29.4048i	−0.543138	+	0.940742i	0.455584	+	0.890193i	$0.349430\pi$
$977$	−16.9768	+	29.4048i	−0.543138	+	0.940742i	−0.998722	+	0.0505490i	$0.983903\pi$
$978$	−26.7273	−	5.23831i	−0.854646	−	0.167503i
$979$	−11.8102	+	13.7786i	−0.377455	+	0.440367i
$980$	−4.61779	+	37.5030i	−0.147510	+	1.19799i
$981$	−8.23262	+	1.13098i	−0.262847	+	0.0361095i
$982$		−	5.92604i		−	0.189108i
$983$	0.412546	+	0.714550i	0.0131582	+	0.0227906i	0.872530	−	0.488561i	$-0.162478\pi$
$983$	0.412546	+	0.714550i	0.0131582	+	0.0227906i	−0.859371	+	0.511352i	$0.829145\pi$
$984$	3.32173	−	1.13800i	0.105893	−	0.0362782i
$985$	−25.4021	+	33.6857i	−0.809377	+	1.07332i
$986$	21.1744	−	36.6752i	0.674332	−	1.16798i
$987$	−5.13054	−	14.9756i	−0.163307	−	0.476678i
$988$	8.62775	−	4.98123i	0.274485	−	0.158474i
$989$	−22.9171			−0.728721
$990$	14.2411	−	17.0936i	0.452611	−	0.543271i
$991$	−20.3115			−0.645217			−0.322609	−	0.946532i	$-0.604560\pi$
$991$	−20.3115			−0.645217			−0.322609	+	0.946532i	$0.604560\pi$
$992$	0.942817	−	0.544335i	0.0299345	−	0.0172827i
$993$	−14.7898	−	2.89867i	−0.469340	−	0.0919864i
$994$	−3.53001	+	6.11415i	−0.111965	+	0.193929i
$995$	−23.2973	−	17.5683i	−0.738575	−	0.556952i
$996$	11.9645	+	10.4332i	0.379109	+	0.330588i
$997$	28.5253	+	49.4073i	0.903406	+	1.56475i	0.823042	+	0.567980i	$0.192275\pi$
$997$	28.5253	+	49.4073i	0.903406	+	1.56475i	0.0803638	+	0.996766i	$0.474392\pi$
$998$		−	0.214034i		−	0.00677513i
$999$	−10.0144	+	15.2648i	−0.316841	+	0.482957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.10	✓	144
5.4	even	2	inner	990.2.o.a.329.63	yes	144
9.2	odd	6	inner	990.2.o.a.659.27	yes	144
11.10	odd	2	inner	990.2.o.a.329.46	yes	144
45.29	odd	6	inner	990.2.o.a.659.46	yes	144
55.54	odd	2	inner	990.2.o.a.329.27	yes	144
99.65	even	6	inner	990.2.o.a.659.63	yes	144
495.164	even	6	inner	990.2.o.a.659.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.10	✓	144	1.1	even	1	trivial
990.2.o.a.329.27	yes	144	55.54	odd	2	inner
990.2.o.a.329.46	yes	144	11.10	odd	2	inner
990.2.o.a.329.63	yes	144	5.4	even	2	inner
990.2.o.a.659.10	yes	144	495.164	even	6	inner
990.2.o.a.659.27	yes	144	9.2	odd	6	inner
990.2.o.a.659.46	yes	144	45.29	odd	6	inner
990.2.o.a.659.63	yes	144	99.65	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.13835 + 1.30543i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.78534 + 1.34631i) q^{5} +(0.333128 - 1.69971i) q^{6} +(-2.44430 - 4.23366i) q^{7} +1.00000i q^{8} +(-0.408300 - 2.97209i) q^{9} +(-2.21931 - 0.273267i) q^{10} +(-2.51818 - 2.15842i) q^{11} +(0.561359 + 1.63856i) q^{12} +(1.35370 - 2.34467i) q^{13} +(4.23366 + 2.44430i) q^{14} +(-3.78987 + 0.798065i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.38880i q^{17} +(1.83964 + 2.36975i) q^{18} +3.67973i q^{19} +(2.05861 - 0.872998i) q^{20} +(8.30923 + 1.62853i) q^{21} +(3.26002 + 0.610161i) q^{22} +(-3.74187 + 6.48110i) q^{23} +(-1.30543 - 1.13835i) q^{24} +(1.37490 + 4.80725i) q^{25} +2.70739i q^{26} +(4.34464 + 2.85028i) q^{27} -4.88861 q^{28} +(3.92934 + 6.80582i) q^{29} +(2.88309 - 2.58608i) q^{30} +(0.544335 - 0.942817i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.68425 - 0.830254i) q^{33} +(-2.69440 - 4.66684i) q^{34} +(1.33589 - 10.8493i) q^{35} +(-2.77805 - 1.13244i) q^{36} +3.51348i q^{37} +(-1.83986 - 3.18674i) q^{38} +(1.51982 + 4.43622i) q^{39} +(-1.34631 + 1.78534i) q^{40} +(-1.01361 + 1.75563i) q^{41} +(-8.01027 + 2.74427i) q^{42} +(1.53113 + 2.65199i) q^{43} +(-3.12834 + 1.10159i) q^{44} +(3.27239 - 5.85589i) q^{45} -7.48373i q^{46} +(-0.934774 - 1.61908i) q^{47} +(1.69971 + 0.333128i) q^{48} +(-8.44925 + 14.6345i) q^{49} +(-3.59432 - 3.47575i) q^{50} +(-7.03471 - 6.13437i) q^{51} +(-1.35370 - 2.34467i) q^{52} +13.2351 q^{53} +(-5.18771 - 0.296093i) q^{54} +(-1.58990 - 7.24377i) q^{55} +(4.23366 - 2.44430i) q^{56} +(-4.80363 - 4.18883i) q^{57} +(-6.80582 - 3.92934i) q^{58} +(5.46059 + 3.15267i) q^{59} +(-1.20379 + 3.68115i) q^{60} +(0.648054 - 0.374154i) q^{61} +1.08867i q^{62} +(-11.5848 + 8.99328i) q^{63} -1.00000 q^{64} +(5.57347 - 2.36355i) q^{65} +(-4.50758 + 3.56115i) q^{66} +(4.34326 + 2.50758i) q^{67} +(4.66684 + 2.69440i) q^{68} +(-4.20106 - 12.2625i) q^{69} +(4.26775 + 10.0637i) q^{70} +1.44418i q^{71} +(2.97209 - 0.408300i) q^{72} -0.851157 q^{73} +(-1.75674 - 3.04276i) q^{74} +(-7.84066 - 3.67751i) q^{75} +(3.18674 + 1.83986i) q^{76} +(-2.98284 + 15.9369i) q^{77} +(-3.53432 - 3.08197i) q^{78} +(-10.1117 + 5.83797i) q^{79} +(0.273267 - 2.21931i) q^{80} +(-8.66658 + 2.42700i) q^{81} -2.02723i q^{82} +(7.93725 - 4.58257i) q^{83} +(5.56497 - 6.38174i) q^{84} +(-7.25499 + 9.62086i) q^{85} +(-2.65199 - 1.53113i) q^{86} +(-13.3575 - 2.61795i) q^{87} +(2.15842 - 2.51818i) q^{88} -5.47167i q^{89} +(0.0939709 + 6.70755i) q^{90} -13.2354 q^{91} +(3.74187 + 6.48110i) q^{92} +(0.611135 + 1.78385i) q^{93} +(1.61908 + 0.934774i) q^{94} +(-4.95405 + 6.56957i) q^{95} +(-1.63856 + 0.561359i) q^{96} +(-7.89969 + 4.56089i) q^{97} -16.8985i q^{98} +(-5.38685 + 8.36552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

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