LMFDB - Embedded newform 810.2.w.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(23,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(108))

chi = DirichletCharacter(H, H._module([22, 81]))

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

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

chi := DirichletCharacter("810.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.w (of order $108$, degree $36$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$1944$
Relative dimension:	$54$ over $\Q(\zeta_{108})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{108}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	810.23
Dual form			810.2.w.a.317.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.989442 + 0.144932i) q^{2} +(-1.72613 - 0.143043i) q^{3} +(0.957990 - 0.286803i) q^{4} +(-0.303554 - 2.21537i) q^{5} +(1.72864 - 0.108639i) q^{6} +(-2.33951 - 0.0680727i) q^{7} +(-0.906308 + 0.422618i) q^{8} +(2.95908 + 0.493822i) q^{9} +(0.621426 + 2.14798i) q^{10} +(1.69597 - 3.37696i) q^{11} +(-1.69464 + 0.358027i) q^{12} +(3.01420 - 1.19747i) q^{13} +(2.32467 - 0.271715i) q^{14} +(0.207082 + 3.86744i) q^{15} +(0.835488 - 0.549509i) q^{16} +(0.0954658 + 1.09118i) q^{17} +(-2.99941 - 0.0597436i) q^{18} +(0.924324 + 1.10157i) q^{19} +(-0.926176 - 2.03524i) q^{20} +(4.02857 + 0.452153i) q^{21} +(-1.18864 + 3.58711i) q^{22} +(-0.155607 - 5.34788i) q^{23} +(1.62486 - 0.599855i) q^{24} +(-4.81571 + 1.34497i) q^{25} +(-2.80883 + 1.62168i) q^{26} +(-5.03713 - 1.27568i) q^{27} +(-2.26075 + 0.605766i) q^{28} +(0.946671 + 0.110650i) q^{29} +(-0.765411 - 3.79660i) q^{30} +(-1.51328 - 0.358653i) q^{31} +(-0.747025 + 0.664796i) q^{32} +(-3.41053 + 5.58649i) q^{33} +(-0.252604 - 1.06582i) q^{34} +(0.559361 + 5.20354i) q^{35} +(2.97640 - 0.375597i) q^{36} +(-1.30498 - 1.86370i) q^{37} +(-1.07422 - 0.955972i) q^{38} +(-5.37421 + 1.63583i) q^{39} +(1.21137 + 1.87952i) q^{40} +(5.45946 - 4.06441i) q^{41} +(-4.05156 + 0.136489i) q^{42} +(-5.45239 + 6.12680i) q^{43} +(0.656202 - 3.72150i) q^{44} +(0.195758 - 6.70535i) q^{45} +(0.929042 + 5.26886i) q^{46} +(-5.88500 - 3.62992i) q^{47} +(-1.52077 + 0.829016i) q^{48} +(-1.51949 - 0.0885003i) q^{49} +(4.56994 - 2.02872i) q^{50} +(-0.00870144 - 1.89718i) q^{51} +(2.54414 - 2.01164i) q^{52} +(0.346109 + 1.29170i) q^{53} +(5.16883 + 0.532169i) q^{54} +(-7.99603 - 2.73212i) q^{55} +(2.14908 - 0.927024i) q^{56} +(-1.43794 - 2.03367i) q^{57} +(-0.952713 + 0.0277211i) q^{58} +(-3.64982 + 1.83301i) q^{59} +(1.30758 + 3.64558i) q^{60} +(-2.08630 + 6.96874i) q^{61} +(1.54928 + 0.135544i) q^{62} +(-6.88917 - 1.35673i) q^{63} +(0.642788 - 0.766044i) q^{64} +(-3.56780 - 6.31407i) q^{65} +(2.56486 - 6.02180i) q^{66} +(-6.35353 + 8.03535i) q^{67} +(0.404409 + 1.01796i) q^{68} +(-0.496376 + 9.25341i) q^{69} +(-1.30761 - 5.06753i) q^{70} +(-4.09602 - 11.2537i) q^{71} +(-2.89053 + 0.803005i) q^{72} +(0.215703 + 0.462576i) q^{73} +(1.56131 + 1.65489i) q^{74} +(8.50495 - 1.63274i) q^{75} +(1.20143 + 0.790190i) q^{76} +(-4.19762 + 7.78498i) q^{77} +(5.08038 - 2.39745i) q^{78} +(-13.2732 - 9.88152i) q^{79} +(-1.47098 - 1.68411i) q^{80} +(8.51228 + 2.92252i) q^{81} +(-4.81275 + 4.81275i) q^{82} +(-2.29986 - 15.7010i) q^{83} +(3.98900 - 0.722249i) q^{84} +(2.38838 - 0.542723i) q^{85} +(4.50686 - 6.85234i) q^{86} +(-1.61825 - 0.326411i) q^{87} +(-0.109909 + 3.77732i) q^{88} +(-4.11788 - 1.49878i) q^{89} +(0.778127 + 6.66292i) q^{90} +(-7.13327 + 2.59630i) q^{91} +(-1.68286 - 5.07858i) q^{92} +(2.56082 + 0.835547i) q^{93} +(6.34896 + 2.73867i) q^{94} +(2.15979 - 2.38210i) q^{95} +(1.38456 - 1.04067i) q^{96} +(1.86519 - 9.03313i) q^{97} +(1.51628 - 0.132657i) q^{98} +(6.68614 - 9.15518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1944 q + 36 q^{20} + 108 q^{30} + 108 q^{35} + 36 q^{41} + 216 q^{51} + 108 q^{67} - 144 q^{72} - 576 q^{77} - 576 q^{87} - 144 q^{92} + 36 q^{93} + 108 q^{97}+O(q^{100}) $ 1944 * q + 36 * q^20 + 108 * q^30 + 108 * q^35 + 36 * q^41 + 216 * q^51 + 108 * q^67 - 144 * q^72 - 576 * q^77 - 576 * q^87 - 144 * q^92 + 36 * q^93 + 108 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{54}\right)$

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 $

$2$	−0.989442	+	0.144932i	−0.699641	+	0.102482i
$2$	−0.989442	+	0.144932i	−0.699641	+	0.102482i
$3$	−1.72613	−	0.143043i	−0.996584	−	0.0825858i
$3$	−1.72613	−	0.143043i	−0.996584	−	0.0825858i
$4$	0.957990	−	0.286803i	0.478995	−	0.143402i
$5$	−0.303554	−	2.21537i	−0.135753	−	0.990743i
$5$	−0.303554	−	2.21537i	−0.135753	−	0.990743i
$6$	1.72864	−	0.108639i	0.705714	−	0.0443518i
$7$	−2.33951	−	0.0680727i	−0.884251	−	0.0257291i	−0.416041	−	0.909346i	$-0.636583\pi$
$7$	−2.33951	−	0.0680727i	−0.884251	−	0.0257291i	−0.468210	+	0.883617i	$0.655101\pi$
$8$	−0.906308	+	0.422618i	−0.320428	+	0.149418i
$9$	2.95908	+	0.493822i	0.986359	+	0.164607i
$10$	0.621426	+	2.14798i	0.196512	+	0.679252i
$11$	1.69597	−	3.37696i	0.511355	−	1.01819i	−0.478761	−	0.877945i	$-0.658914\pi$
$11$	1.69597	−	3.37696i	0.511355	−	1.01819i	0.990117	−	0.140247i	$-0.0447897\pi$
$12$	−1.69464	+	0.358027i	−0.489201	+	0.103354i
$13$	3.01420	−	1.19747i	0.835990	−	0.332117i	0.0882408	−	0.996099i	$-0.471876\pi$
$13$	3.01420	−	1.19747i	0.835990	−	0.332117i	0.747749	+	0.663982i	$0.231135\pi$
$14$	2.32467	−	0.271715i	0.621295	−	0.0726190i
$15$	0.207082	+	3.86744i	0.0534684	+	0.998570i
$16$	0.835488	−	0.549509i	0.208872	−	0.137377i
$17$	0.0954658	+	1.09118i	0.0231539	+	0.264650i	0.998944	+	0.0459415i	$0.0146288\pi$
$17$	0.0954658	+	1.09118i	0.0231539	+	0.264650i	−0.975790	+	0.218708i	$0.929816\pi$
$18$	−2.99941	−	0.0597436i	−0.706967	−	0.0140817i
$19$	0.924324	+	1.10157i	0.212055	+	0.252717i	0.861579	−	0.507624i	$-0.169476\pi$
$19$	0.924324	+	1.10157i	0.212055	+	0.252717i	−0.649524	+	0.760341i	$0.725032\pi$
$20$	−0.926176	−	2.03524i	−0.207099	−	0.455093i
$21$	4.02857	+	0.452153i	0.879106	+	0.0986678i
$22$	−1.18864	+	3.58711i	−0.253418	+	0.764774i
$23$	−0.155607	−	5.34788i	−0.0324464	−	1.11511i	−0.845854	−	0.533415i	$-0.820908\pi$
$23$	−0.155607	−	5.34788i	−0.0324464	−	1.11511i	0.813407	−	0.581694i	$-0.197610\pi$
$24$	1.62486	−	0.599855i	0.331673	−	0.122445i
$25$	−4.81571	+	1.34497i	−0.963142	+	0.268993i
$26$	−2.80883	+	1.62168i	−0.550856	+	0.318037i
$27$	−5.03713	−	1.27568i	−0.969395	−	0.245504i
$28$	−2.26075	+	0.605766i	−0.427241	+	0.114479i
$29$	0.946671	+	0.110650i	0.175792	+	0.0205472i	0.203534	−	0.979068i	$-0.434757\pi$
$29$	0.946671	+	0.110650i	0.175792	+	0.0205472i	−0.0277412	+	0.999615i	$0.508831\pi$
$30$	−0.765411	−	3.79660i	−0.139744	−	0.693161i
$31$	−1.51328	−	0.358653i	−0.271793	−	0.0644160i	0.0924594	−	0.995716i	$-0.470527\pi$
$31$	−1.51328	−	0.358653i	−0.271793	−	0.0644160i	−0.364252	+	0.931300i	$0.618675\pi$
$32$	−0.747025	+	0.664796i	−0.132057	+	0.117520i
$33$	−3.41053	+	5.58649i	−0.593697	+	0.972483i
$34$	−0.252604	−	1.06582i	−0.0433213	−	0.182787i
$35$	0.559361	+	5.20354i	0.0945492	+	0.879558i
$36$	2.97640	−	0.375597i	0.496066	−	0.0625994i
$37$	−1.30498	−	1.86370i	−0.214537	−	0.306391i	0.697431	−	0.716652i	$-0.254326\pi$
$37$	−1.30498	−	1.86370i	−0.214537	−	0.306391i	−0.911968	+	0.410261i	$0.865437\pi$
$38$	−1.07422	−	0.955972i	−0.174261	−	0.155079i
$39$	−5.37421	+	1.63583i	−0.860562	+	0.261942i
$40$	1.21137	+	1.87952i	0.191534	+	0.297178i
$41$	5.45946	−	4.06441i	0.852624	−	0.634755i	−0.0795241	−	0.996833i	$-0.525340\pi$
$41$	5.45946	−	4.06441i	0.852624	−	0.634755i	0.932148	+	0.362078i	$0.117933\pi$
$42$	−4.05156	+	0.136489i	−0.625170	+	0.0210607i
$43$	−5.45239	+	6.12680i	−0.831482	+	0.934329i	−0.998668	−	0.0515966i	$-0.983569\pi$
$43$	−5.45239	+	6.12680i	−0.831482	+	0.934329i	0.167186	+	0.985925i	$0.446532\pi$
$44$	0.656202	−	3.72150i	0.0989261	−	0.561038i
$45$	0.195758	−	6.70535i	0.0291819	−	0.999574i
$46$	0.929042	+	5.26886i	0.136980	+	0.776851i
$47$	−5.88500	−	3.62992i	−0.858416	−	0.529479i	0.0241279	−	0.999709i	$-0.492319\pi$
$47$	−5.88500	−	3.62992i	−0.858416	−	0.529479i	−0.882544	+	0.470230i	$0.844171\pi$
$48$	−1.52077	+	0.829016i	−0.219504	+	0.119658i
$49$	−1.51949	−	0.0885003i	−0.217070	−	0.0126429i
$50$	4.56994	−	2.02872i	0.646286	−	0.286904i
$51$	−0.00870144	−	1.89718i	−0.00121844	−	0.265658i
$52$	2.54414	−	2.01164i	0.352808	−	0.278965i
$53$	0.346109	+	1.29170i	0.0475418	+	0.177428i	0.985614	−	0.169011i	$-0.0540573\pi$
$53$	0.346109	+	1.29170i	0.0475418	+	0.177428i	−0.938072	+	0.346439i	$0.887391\pi$
$54$	5.16883	+	0.532169i	0.703389	+	0.0724190i
$55$	−7.99603	−	2.73212i	−1.07818	−	0.368399i
$56$	2.14908	−	0.927024i	0.287183	−	0.123879i
$57$	−1.43794	−	2.03367i	−0.190459	−	0.269366i
$58$	−0.952713	+	0.0277211i	−0.125097	+	0.00363996i
$59$	−3.64982	+	1.83301i	−0.475166	+	0.238637i	−0.670230	−	0.742153i	$-0.733805\pi$
$59$	−3.64982	+	1.83301i	−0.475166	+	0.238637i	0.195065	+	0.980790i	$0.437508\pi$
$60$	1.30758	+	3.64558i	0.168808	+	0.470642i
$61$	−2.08630	+	6.96874i	−0.267124	+	0.892255i	0.714208	+	0.699933i	$0.246787\pi$
$61$	−2.08630	+	6.96874i	−0.267124	+	0.892255i	−0.981332	+	0.192322i	$0.938398\pi$
$62$	1.54928	+	0.135544i	0.196759	+	0.0172142i
$63$	−6.88917	−	1.35673i	−0.867954	−	0.170932i
$64$	0.642788	−	0.766044i	0.0803485	−	0.0957556i
$65$	−3.56780	−	6.31407i	−0.442531	−	0.783164i
$66$	2.56486	−	6.02180i	0.315712	−	0.741233i
$67$	−6.35353	+	8.03535i	−0.776207	+	0.981674i	0.223768	+	0.974642i	$0.428164\pi$
$67$	−6.35353	+	8.03535i	−0.776207	+	0.981674i	−0.999975	+	0.00703164i	$0.997762\pi$
$68$	0.404409	+	1.01796i	0.0490418	+	0.123446i
$69$	−0.496376	+	9.25341i	−0.0597567	+	1.11398i
$70$	−1.30761	−	5.06753i	−0.156290	−	0.605685i
$71$	−4.09602	−	11.2537i	−0.486108	−	1.33557i	−0.904178	−	0.427156i	$-0.859515\pi$
$71$	−4.09602	−	11.2537i	−0.486108	−	1.33557i	0.418070	−	0.908415i	$-0.362707\pi$
$72$	−2.89053	+	0.803005i	−0.340653	+	0.0946351i
$73$	0.215703	+	0.462576i	0.0252461	+	0.0541404i	0.918526	−	0.395360i	$-0.129380\pi$
$73$	0.215703	+	0.462576i	0.0252461	+	0.0541404i	−0.893280	+	0.449500i	$0.851602\pi$
$74$	1.56131	+	1.65489i	0.181498	+	0.192377i
$75$	8.50495	−	1.63274i	0.982067	−	0.188533i
$76$	1.20143	+	0.790190i	0.137813	+	0.0906411i
$77$	−4.19762	+	7.78498i	−0.478364	+	0.887181i
$78$	5.08038	−	2.39745i	0.575240	−	0.271458i
$79$	−13.2732	−	9.88152i	−1.49335	−	1.11176i	−0.964842	−	0.262830i	$-0.915344\pi$
$79$	−13.2732	−	9.88152i	−1.49335	−	1.11176i	−0.528508	−	0.848928i	$-0.677248\pi$
$80$	−1.47098	−	1.68411i	−0.164461	−	0.188289i
$81$	8.51228	+	2.92252i	0.945809	+	0.324724i
$82$	−4.81275	+	4.81275i	−0.531479	+	0.531479i
$83$	−2.29986	−	15.7010i	−0.252442	−	1.72341i	−0.612493	−	0.790476i	$-0.709833\pi$
$83$	−2.29986	−	15.7010i	−0.252442	−	1.72341i	0.360051	−	0.932933i	$-0.382759\pi$
$84$	3.98900	−	0.722249i	0.435236	−	0.0788038i
$85$	2.38838	−	0.542723i	0.259057	−	0.0588666i
$86$	4.50686	−	6.85234i	0.485987	−	0.738907i
$87$	−1.61825	−	0.326411i	−0.173495	−	0.0349950i
$88$	−0.109909	+	3.77732i	−0.0117163	+	0.402663i
$89$	−4.11788	−	1.49878i	−0.436494	−	0.158871i	0.114421	−	0.993432i	$-0.463499\pi$
$89$	−4.11788	−	1.49878i	−0.436494	−	0.158871i	−0.550915	+	0.834562i	$0.685721\pi$
$90$	0.778127	+	6.66292i	0.0820218	+	0.702334i
$91$	−7.13327	+	2.59630i	−0.747770	+	0.272166i
$92$	−1.68286	−	5.07858i	−0.175450	−	0.529479i
$93$	2.56082	+	0.835547i	0.265544	+	0.0866422i
$94$	6.34896	+	2.73867i	0.654845	+	0.282473i
$95$	2.15979	−	2.38210i	0.221590	−	0.244399i
$96$	1.38456	−	1.04067i	0.141311	−	0.106213i
$97$	1.86519	−	9.03313i	0.189381	−	0.917175i	−0.770645	−	0.637265i	$-0.780066\pi$
$97$	1.86519	−	9.03313i	0.189381	−	0.917175i	0.960026	−	0.279910i	$-0.0903047\pi$
$98$	1.51628	−	0.132657i	0.153167	−	0.0134004i
$99$	6.68614	−	9.15518i	0.671982	−	0.920130i
$100$	−4.22766	+	2.66963i	−0.422766	+	0.266963i
$101$	3.52552	+	1.05547i	0.350803	+	0.105023i	0.457356	−	0.889284i	$-0.348796\pi$
$101$	3.52552	+	1.05547i	0.350803	+	0.105023i	−0.106554	+	0.994307i	$0.533982\pi$
$102$	0.283571	+	1.87588i	0.0280777	+	0.185740i
$103$	−0.671555	−	0.222529i	−0.0661703	−	0.0219264i	0.281269	−	0.959629i	$-0.409245\pi$
$103$	−0.671555	−	0.222529i	−0.0661703	−	0.0219264i	−0.347439	+	0.937703i	$0.612949\pi$
$104$	−2.22572	+	2.35913i	−0.218250	+	0.231332i
$105$	−0.221203	−	9.06201i	−0.0215872	−	0.884362i
$106$	−0.529663	−	1.22790i	−0.0514454	−	0.119264i
$107$	−2.40402	+	8.97191i	−0.232405	+	0.867347i	0.746896	+	0.664940i	$0.231543\pi$
$107$	−2.40402	+	8.97191i	−0.232405	+	0.867347i	−0.979301	+	0.202407i	$0.935124\pi$
$108$	−5.19138	+	0.222578i	−0.499541	+	0.0214176i
$109$	−16.9706	−	9.79798i	−1.62549	−	0.938476i	−0.985416	−	0.170161i	$-0.945571\pi$
$109$	−16.9706	−	9.79798i	−1.62549	−	0.938476i	−0.640072	−	0.768315i	$-0.721095\pi$
$110$	8.30758	+	1.54439i	0.792096	+	0.147252i
$111$	1.98598	+	3.40366i	0.188501	+	0.323062i
$112$	−1.99204	+	1.22871i	−0.188230	+	0.116102i
$113$	−1.30185	−	1.46287i	−0.122467	−	0.137615i	0.682616	−	0.730778i	$-0.260842\pi$
$113$	−1.30185	−	1.46287i	−0.122467	−	0.137615i	−0.805083	+	0.593162i	$0.797879\pi$
$114$	1.71750	+	1.80380i	0.160858	+	0.168941i
$115$	−11.8003	+	1.96810i	−1.10038	+	0.183526i
$116$	0.938636	−	0.165507i	0.0871501	−	0.0153669i
$117$	9.51060	−	2.05492i	0.879255	−	0.189977i
$118$	3.34562	−	2.34263i	0.307989	−	0.215656i
$119$	−0.149063	−	2.55932i	−0.0136646	−	0.234613i
$120$	−1.82213	−	3.41758i	−0.166337	−	0.311981i
$121$	−1.95880	−	2.63112i	−0.178073	−	0.239193i
$122$	1.05428	−	7.19753i	0.0954503	−	0.651634i
$123$	−10.0051	+	6.23479i	−0.902133	+	0.562172i
$124$	−1.55257	+	0.0904267i	−0.139425	+	0.00812056i
$125$	4.44142	+	10.2603i	0.397253	+	0.917709i
$126$	7.01307	+	0.343948i	0.624774	+	0.0306414i
$127$	18.1913	+	12.7377i	1.61422	+	1.13029i	0.905101	+	0.425196i	$0.139795\pi$
$127$	18.1913	+	12.7377i	1.61422	+	1.13029i	0.709117	+	0.705091i	$0.249094\pi$
$128$	−0.524977	+	0.851117i	−0.0464018	+	0.0752288i
$129$	10.2880	−	9.79576i	0.905804	−	0.862468i
$130$	4.44524	+	5.73032i	0.389873	+	0.502582i
$131$	−2.44707	+	10.3250i	−0.213802	+	0.902101i	0.755288	+	0.655393i	$0.227497\pi$
$131$	−2.44707	+	10.3250i	−0.213802	+	0.902101i	−0.969090	+	0.246708i	$0.920651\pi$
$132$	−1.66503	+	6.32995i	−0.144922	+	0.550952i
$133$	−2.08748	−	2.64005i	−0.181007	−	0.228921i
$134$	5.12187	−	8.87134i	0.442462	−	0.766367i
$135$	−1.29706	+	11.5463i	−0.111633	+	0.993750i
$136$	−0.547674	−	0.948599i	−0.0469626	−	0.0813417i
$137$	−2.01472	+	5.07134i	−0.172129	+	0.433274i	−0.989810	−	0.142398i	$-0.954519\pi$
$137$	−2.01472	+	5.07134i	−0.172129	+	0.433274i	0.817681	+	0.575672i	$0.195259\pi$
$138$	−0.849979	−	9.22765i	−0.0723550	−	0.785510i
$139$	15.6775	+	14.7910i	1.32975	+	1.25455i	0.943176	+	0.332293i	$0.107822\pi$
$139$	15.6775	+	14.7910i	1.32975	+	1.25455i	0.386571	+	0.922259i	$0.373659\pi$
$140$	2.02825	+	4.82451i	0.171419	+	0.407745i
$141$	9.63907	+	7.10754i	0.811756	+	0.598563i
$142$	5.68380	+	10.5413i	0.476974	+	0.884603i
$143$	1.06821	−	12.2097i	0.0893284	−	1.02103i
$144$	2.74363	−	1.21346i	0.228636	−	0.101121i
$145$	−0.0422352	−	2.13081i	−0.00350745	−	0.176954i
$146$	−0.280467	−	0.426429i	−0.0232116	−	0.0352916i
$147$	2.61019	+	0.370116i	0.215285	+	0.0305266i
$148$	−1.78467	−	1.41113i	−0.146699	−	0.115995i
$149$	−5.83623	+	13.5299i	−0.478123	+	1.10841i	0.493043	+	0.870005i	$0.335885\pi$
$149$	−5.83623	+	13.5299i	−0.478123	+	1.10841i	−0.971165	+	0.238408i	$0.923375\pi$
$150$	−8.17851	+	2.84814i	−0.667773	+	0.232550i
$151$	14.6835	+	7.37433i	1.19493	+	0.600115i	0.931209	−	0.364485i	$-0.118755\pi$
$151$	14.6835	+	7.37433i	1.19493	+	0.600115i	0.263718	+	0.964600i	$0.415051\pi$
$152$	−1.30326	−	0.607722i	−0.105709	−	0.0492928i
$153$	−0.256358	+	3.27603i	−0.0207253	+	0.264851i
$154$	3.02501	−	8.31115i	0.243762	−	0.669732i
$155$	−0.335188	+	3.46134i	−0.0269229	+	0.278021i
$156$	−4.67927	+	3.10845i	−0.374642	+	0.248875i
$157$	18.0711	−	3.73138i	1.44223	−	0.297796i	0.584289	−	0.811546i	$-0.301374\pi$
$157$	18.0711	−	3.73138i	1.44223	−	0.297796i	0.857940	+	0.513749i	$0.171744\pi$
$158$	14.5652	+	7.85348i	1.15874	+	0.624790i
$159$	−0.412663	−	2.27915i	−0.0327263	−	0.180749i
$160$	1.69953	+	1.45313i	0.134360	+	0.114880i
$161$			12.5220i			0.986871i
$162$	−8.84597	−	1.65796i	−0.695005	−	0.130262i
$163$	−7.96946	−	7.96946i	−0.624216	−	0.624216i	0.322390	−	0.946607i	$-0.395514\pi$
$163$	−7.96946	−	7.96946i	−0.624216	−	0.624216i	−0.946607	+	0.322390i	$0.895514\pi$
$164$	4.06441	−	5.45946i	0.317377	−	0.426312i
$165$	13.4114	+	5.85977i	1.04408	+	0.456183i
$166$	4.55115	+	15.2019i	0.353238	+	1.17990i
$167$	0.696249	+	3.37194i	0.0538774	+	0.260928i	0.997550	−	0.0699510i	$-0.0222843\pi$
$167$	0.696249	+	3.37194i	0.0538774	+	0.260928i	−0.943673	+	0.330879i	$0.892655\pi$
$168$	−3.84221	+	1.29276i	−0.296433	+	0.0997384i
$169$	−1.80436	+	1.70233i	−0.138797	+	0.130948i
$170$	−2.28451	+	0.883146i	−0.175214	+	0.0677342i
$171$	2.19117	+	3.71607i	0.167563	+	0.284175i
$172$	−3.46615	+	7.43318i	−0.264291	+	0.566774i
$173$	2.04075	−	0.676231i	0.155155	−	0.0514129i	−0.235915	−	0.971774i	$-0.575809\pi$
$173$	2.04075	−	0.676231i	0.155155	−	0.0514129i	0.391070	+	0.920361i	$0.372105\pi$
$174$	1.64847	+	0.0884283i	0.124971	+	0.00670374i
$175$	11.3579	−	2.81874i	0.858580	−	0.213077i
$176$	−0.438705	−	3.75336i	−0.0330687	−	0.282920i
$177$	6.56227	−	2.64194i	0.493251	−	0.198580i
$178$	4.29162	+	0.886148i	0.321670	+	0.0664196i
$179$	−9.74656	−	8.17834i	−0.728492	−	0.611278i	0.201228	−	0.979544i	$-0.435507\pi$
$179$	−9.74656	−	8.17834i	−0.728492	−	0.611278i	−0.929720	+	0.368267i	$0.879951\pi$
$180$	−1.73558	−	6.47980i	−0.129363	−	0.482975i
$181$	0.762842	−	0.640100i	0.0567016	−	0.0475783i	−0.613996	−	0.789309i	$-0.710439\pi$
$181$	0.762842	−	0.640100i	0.0567016	−	0.0475783i	0.670698	+	0.741731i	$0.265995\pi$
$182$	6.68167	−	3.60272i	0.495278	−	0.267052i
$183$	4.59807	−	11.7305i	0.339899	−	0.867147i
$184$	2.40114	+	4.78106i	0.177014	+	0.352464i
$185$	−3.73265	+	3.45674i	−0.274430	+	0.254144i
$186$	−2.65488	−	0.455581i	−0.194665	−	0.0334048i
$187$	3.84678	+	1.52823i	0.281304	+	0.111755i
$188$	−6.67885	−	1.78959i	−0.487105	−	0.130519i
$189$	11.6976	+	3.32735i	0.850872	+	0.242029i
$190$	−1.79175	+	2.66998i	−0.129987	+	0.193700i
$191$	−0.522837	+	4.47316i	−0.0378312	+	0.323666i	0.961050	+	0.276375i	$0.0891331\pi$
$191$	−0.522837	+	4.47316i	−0.0378312	+	0.323666i	−0.998881	+	0.0472915i	$0.984941\pi$
$192$	−1.21911	+	1.23035i	−0.0879820	+	0.0887928i
$193$	2.68603	+	4.35471i	0.193345	+	0.313459i	0.933234	−	0.359269i	$-0.116974\pi$
$193$	2.68603	+	4.35471i	0.193345	+	0.313459i	−0.739889	+	0.672729i	$0.765122\pi$
$194$	−0.536310	+	9.20808i	−0.0385048	+	0.661102i
$195$	5.25532	+	11.4093i	0.376341	+	0.817036i
$196$	−1.48104	+	0.351013i	−0.105789	+	0.0250723i
$197$	11.3463	−	16.2042i	0.808391	−	1.15450i	−0.177003	−	0.984210i	$-0.556640\pi$
$197$	11.3463	−	16.2042i	0.808391	−	1.15450i	0.985394	−	0.170291i	$-0.0544709\pi$
$198$	−5.28866	+	10.0276i	−0.375849	+	0.712627i
$199$	0.411189	+	0.0725037i	0.0291484	+	0.00513965i	0.188203	−	0.982130i	$-0.439734\pi$
$199$	0.411189	+	0.0725037i	0.0291484	+	0.00513965i	−0.159055	+	0.987270i	$0.550845\pi$
$200$	3.79611	−	3.25416i	0.268425	−	0.230104i
$201$	12.1164	−	12.9613i	0.854628	−	0.914217i
$202$	−3.64127	−	0.533368i	−0.256199	−	0.0375276i
$203$	−2.20721	−	0.323309i	−0.154916	−	0.0226918i
$204$	−0.552452	−	1.81498i	−0.0386794	−	0.127074i
$205$	−10.6614	−	10.8609i	−0.744625	−	0.758561i
$206$	0.696716	+	0.122850i	0.0485425	+	0.00855935i
$207$	2.18045	−	15.9016i	0.151551	−	1.10524i
$208$	1.86031	−	2.65680i	0.128989	−	0.184216i
$209$	5.28758	−	1.25318i	0.365750	−	0.0866842i
$210$	1.53224	+	8.93427i	0.105735	+	0.616523i
$211$	1.49619	−	25.6886i	0.103002	−	1.76848i	−0.411902	−	0.911228i	$-0.635136\pi$
$211$	1.49619	−	25.6886i	0.103002	−	1.76848i	0.514904	−	0.857248i	$-0.327827\pi$
$212$	0.702032	+	1.13817i	0.0482158	+	0.0781697i
$213$	5.46052	+	20.0113i	0.374148	+	1.37115i
$214$	1.07832	−	9.22560i	0.0737123	−	0.630649i
$215$	15.2282	+	10.2192i	1.03856	+	0.696946i
$216$	5.10431	−	0.972625i	0.347304	−	0.0661787i
$217$	3.51591	+	0.942085i	0.238675	+	0.0639529i
$218$	18.2114	+	7.23495i	1.23344	+	0.490012i
$219$	−0.306163	−	0.829322i	−0.0206886	−	0.0560404i
$220$	−8.44369	−	0.324051i	−0.569274	−	0.0218475i
$221$	1.59440	+	3.17472i	0.107251	+	0.213555i
$222$	−2.45831	−	3.07990i	−0.164991	−	0.206709i
$223$	−7.59187	+	4.09350i	−0.508389	+	0.274121i	−0.708573	−	0.705637i	$-0.750661\pi$
$223$	−7.59187	+	4.09350i	−0.508389	+	0.274121i	0.200184	+	0.979758i	$0.435846\pi$
$224$	1.79293	−	1.50444i	0.119795	−	0.100520i
$225$	−14.9142	+	1.60176i	−0.994282	+	0.106784i
$226$	1.50012	+	1.25875i	0.0997863	+	0.0837307i
$227$	−21.3650	−	4.41153i	−1.41805	−	0.292803i	−0.569530	−	0.821970i	$-0.692875\pi$
$227$	−21.3650	−	4.41153i	−1.41805	−	0.292803i	−0.848518	+	0.529167i	$0.822505\pi$
$228$	−1.96079	−	1.53583i	−0.129857	−	0.101713i
$229$	−2.70194	−	23.1166i	−0.178549	−	1.52759i	−0.724209	−	0.689581i	$-0.757795\pi$
$229$	−2.70194	−	23.1166i	−0.178549	−	1.52759i	0.545659	−	0.838007i	$-0.316279\pi$
$230$	11.3904	−	3.65755i	0.751064	−	0.241172i
$231$	8.35925	−	12.8375i	0.549998	−	0.844644i
$232$	−0.904738	+	0.299798i	−0.0593990	+	0.0196827i
$233$	6.42591	−	13.7804i	0.420975	−	0.902785i	−0.575412	−	0.817864i	$-0.695158\pi$
$233$	6.42591	−	13.7804i	0.420975	−	0.902785i	0.996388	−	0.0849213i	$-0.0270639\pi$
$234$	−9.11236	+	3.41161i	−0.595693	+	0.223024i
$235$	−6.25520	+	14.1393i	−0.408044	+	0.922348i
$236$	−2.97077	+	2.80278i	−0.193381	+	0.182446i
$237$	21.4978	+	18.9555i	1.39643	+	1.23129i
$238$	0.518417	+	2.51069i	0.0336040	+	0.162744i
$239$	4.33456	+	14.4784i	0.280379	+	0.936531i	0.975935	+	0.218060i	$0.0699728\pi$
$239$	4.33456	+	14.4784i	0.280379	+	0.936531i	−0.695556	+	0.718472i	$0.744842\pi$
$240$	2.29821	+	3.11741i	0.148349	+	0.201228i
$241$	0.107682	−	0.144642i	0.00693640	−	0.00931720i	−0.798641	−	0.601807i	$-0.794448\pi$
$241$	0.107682	−	0.144642i	0.00693640	−	0.00931720i	0.805578	+	0.592490i	$0.201855\pi$
$242$	2.31945	+	2.31945i	0.149100	+	0.149100i
$243$	−14.2753	−	6.26227i	−0.915760	−	0.401725i
$244$			7.27433i			0.465692i
$245$	0.265187	+	3.39310i	0.0169422	+	0.216777i
$246$	8.99588	−	7.61902i	0.573556	−	0.485771i
$247$	4.10519	+	2.21350i	0.261207	+	0.140842i
$248$	1.52307	−	0.314488i	0.0967149	−	0.0199700i
$249$	1.72395	+	27.4310i	0.109251	+	1.73837i
$250$	−5.88157	−	9.50826i	−0.371983	−	0.601355i
$251$	−4.42840	+	12.1669i	−0.279518	+	0.767970i	0.717899	+	0.696147i	$0.245104\pi$
$251$	−4.42840	+	12.1669i	−0.279518	+	0.767970i	−0.997417	+	0.0718226i	$0.977118\pi$
$252$	−6.98887	+	0.676100i	−0.440257	+	0.0425903i
$253$	−18.3235	−	8.54438i	−1.15199	−	0.537180i
$254$	−19.8453	−	9.96670i	−1.24521	−	0.625367i
$255$	−4.20030	+	0.595172i	−0.263033	+	0.0372711i
$256$	0.396080	−	0.918216i	0.0247550	−	0.0573885i
$257$	3.89667	+	3.08109i	0.243068	+	0.192193i	0.734280	−	0.678847i	$-0.237520\pi$
$257$	3.89667	+	3.08109i	0.243068	+	0.192193i	−0.491212	+	0.871040i	$0.663446\pi$
$258$	−8.75961	+	11.1834i	−0.545350	+	0.696247i
$259$	2.92614	+	4.44898i	0.181821	+	0.276446i
$260$	−5.22881	−	5.02556i	−0.324277	−	0.311672i
$261$	2.74663	+	0.794909i	0.170012	+	0.0492036i
$262$	0.924813	−	10.5707i	0.0571351	−	0.653058i
$263$	−14.2162	−	26.3657i	−0.876611	−	1.62578i	−0.775895	−	0.630862i	$-0.782701\pi$
$263$	−14.2162	−	26.3657i	−0.876611	−	1.62578i	−0.100716	−	0.994915i	$-0.532113\pi$
$264$	0.730035	−	6.50443i	0.0449306	−	0.400320i
$265$	2.75652	−	1.15886i	0.169332	−	0.0711882i
$266$	2.44806	+	2.30963i	0.150100	+	0.141612i
$267$	6.89362	+	3.17614i	0.421882	+	0.194376i
$268$	−3.78205	+	9.51999i	−0.231026	+	0.581526i
$269$	−13.5029	−	23.3878i	−0.823289	−	1.42598i	−0.903220	−	0.429177i	$-0.858803\pi$
$269$	−13.5029	−	23.3878i	−0.823289	−	1.42598i	0.0799315	−	0.996800i	$-0.474530\pi$
$270$	−0.390068	−	11.6124i	−0.0237388	−	0.706708i
$271$	8.71329	−	15.0919i	0.529294	−	0.916765i	−0.470122	−	0.882602i	$-0.655790\pi$
$271$	8.71329	−	15.0919i	0.529294	−	0.916765i	0.999416	−	0.0341633i	$-0.0108766\pi$
$272$	0.679373	+	0.859208i	0.0411931	+	0.0520971i
$273$	12.6844	−	3.46119i	0.767692	−	0.209481i
$274$	1.25844	−	5.30980i	0.0760254	−	0.320776i
$275$	−3.62542	+	18.5435i	−0.218621	+	1.11821i
$276$	2.17838	+	9.00703i	0.131123	+	0.542160i
$277$	−7.83187	+	12.6974i	−0.470572	+	0.762913i	−0.996134	−	0.0878421i	$-0.972003\pi$
$277$	−7.83187	+	12.6974i	−0.470572	+	0.762913i	0.525563	+	0.850755i	$0.323855\pi$
$278$	−17.6556	−	12.3626i	−1.05892	−	0.741460i
$279$	−4.30079	−	1.80857i	−0.257482	−	0.108276i
$280$	−2.70606	−	4.47961i	−0.161718	−	0.267708i
$281$	−21.8482	+	1.27251i	−1.30335	+	0.0759116i	−0.695723	−	0.718310i	$-0.744916\pi$
$281$	−21.8482	+	1.27251i	−1.30335	+	0.0759116i	−0.607628	+	0.794222i	$0.707879\pi$
$282$	−10.5674	−	5.63549i	−0.629280	−	0.335589i
$283$	−0.546644	+	3.73191i	−0.0324946	+	0.221839i	−0.999452	−	0.0330988i	$-0.989462\pi$
$283$	−0.546644	+	3.73191i	−0.0324946	+	0.221839i	0.966957	+	0.254938i	$0.0820550\pi$
$284$	−7.15155	−	9.60620i	−0.424366	−	0.570023i
$285$	−4.06884	+	3.80289i	−0.241017	+	0.225264i
$286$	0.712644	+	12.2356i	0.0421395	+	0.723508i
$287$	−13.0491	+	9.13709i	−0.770265	+	0.539345i
$288$	−2.53880	+	1.59828i	−0.149600	+	0.0941798i
$289$	15.5602	−	2.74368i	0.915304	−	0.161393i
$290$	0.350612	+	2.10219i	0.0205886	+	0.123445i
$291$	−4.51169	+	15.3256i	−0.264480	+	0.898402i
$292$	0.339309	+	0.381278i	0.0198566	+	0.0223126i
$293$	9.78276	−	6.03410i	0.571515	−	0.352516i	−0.208746	−	0.977970i	$-0.566938\pi$
$293$	9.78276	−	6.03410i	0.571515	−	0.352516i	0.780261	+	0.625454i	$0.215086\pi$
$294$	−2.63627	+	0.0120913i	−0.153750	+	0.000705179i
$295$	5.16870	+	7.52927i	0.300933	+	0.438371i
$296$	1.97035	+	1.13758i	0.114524	+	0.0661205i
$297$	−12.8508	+	14.8467i	−0.745676	+	0.861491i
$298$	3.81370	−	14.2329i	0.220921	−	0.824490i
$299$	−6.87293	−	15.9333i	−0.397472	−	0.921444i
$300$	7.67938	−	4.00340i	0.443369	−	0.231136i
$301$	13.1730	−	13.9625i	0.759278	−	0.804788i
$302$	−15.5972	−	5.16837i	−0.897521	−	0.297406i
$303$	−5.93455	−	2.32619i	−0.340931	−	0.133636i
$304$	1.37758	+	0.412421i	0.0790098	+	0.0236540i
$305$	16.0716	+	2.50654i	0.920258	+	0.143524i
$306$	−0.221150	−	3.27859i	−0.0126423	−	0.187425i
$307$	14.7463	−	1.29013i	0.841615	−	0.0736318i	0.341809	−	0.939769i	$-0.388960\pi$
$307$	14.7463	−	1.29013i	0.841615	−	0.0736318i	0.499806	+	0.866138i	$0.333405\pi$
$308$	−1.78852	+	8.66182i	−0.101911	+	0.493553i
$309$	1.12736	+	0.480176i	0.0641334	+	0.0273163i
$310$	−0.170009	−	3.47337i	−0.00965586	−	0.197274i
$311$	8.30798	+	3.58371i	0.471102	+	0.203214i	0.618376	−	0.785882i	$-0.287791\pi$
$311$	8.30798	+	3.58371i	0.471102	+	0.203214i	−0.147274	+	0.989096i	$0.547050\pi$
$312$	4.17936	−	3.75380i	0.236609	−	0.212517i
$313$	0.985808	+	2.97500i	0.0557211	+	0.168157i	0.973372	−	0.229230i	$-0.0736208\pi$
$313$	0.985808	+	2.97500i	0.0557211	+	0.168157i	−0.917651	+	0.397387i	$0.869917\pi$
$314$	−17.3395	+	6.31106i	−0.978524	+	0.356153i
$315$	−0.914430	+	15.6739i	−0.0515223	+	0.883124i
$316$	−15.5496	−	5.65960i	−0.874735	−	0.318377i
$317$	−0.0144471	+	0.496516i	−0.000811433	+	0.0278871i	−0.999885	−	0.0151383i	$-0.995181\pi$
$317$	−0.0144471	+	0.496516i	−0.000811433	+	0.0278871i	0.999074	+	0.0430255i	$0.0136997\pi$
$318$	0.738628	+	2.19528i	0.0414202	+	0.123105i
$319$	1.97919	−	3.00921i	0.110813	−	0.168484i
$320$	−1.89219	−	1.19148i	−0.105777	−	0.0666055i
$321$	5.43302	−	15.1428i	0.303242	−	0.845191i
$322$	−1.81484	−	12.3898i	−0.101137	−	0.690456i
$323$	−1.11377	+	1.11377i	−0.0619716	+	0.0619716i
$324$	8.99286	+	0.358390i	0.499603	+	0.0199106i
$325$	−12.9050	+	9.82065i	−0.715839	+	0.544752i
$326$	9.04035	+	6.73029i	0.500699	+	0.372756i
$327$	27.8920	+	19.3401i	1.54243	+	1.06951i
$328$	−3.23025	+	5.99088i	−0.178361	+	0.330791i
$329$	13.5209	+	8.89285i	0.745432	+	0.490278i
$330$	−14.1191	−	3.85416i	−0.777230	−	0.212165i
$331$	6.78293	+	7.18948i	0.372824	+	0.395170i	0.886435	−	0.462853i	$-0.153174\pi$
$331$	6.78293	+	7.18948i	0.372824	+	0.395170i	−0.513612	+	0.858023i	$0.671693\pi$
$332$	−6.70634	−	14.3818i	−0.368058	−	0.789303i
$333$	−2.94119	−	6.15926i	−0.161176	−	0.337525i
$334$	−1.17760	−	3.23543i	−0.0644354	−	0.177035i
$335$	19.7299	+	11.6362i	1.07796	+	0.635756i
$336$	3.61428	−	1.83597i	0.197175	−	0.100160i
$337$	−6.75385	−	17.0005i	−0.367906	−	0.926074i	−0.989734	−	0.142920i	$-0.954351\pi$
$337$	−6.75385	−	17.0005i	−0.367906	−	0.926074i	0.621829	−	0.783153i	$-0.286390\pi$
$338$	1.53859	−	1.94586i	0.0836882	−	0.105841i
$339$	2.03791	+	2.71133i	0.110684	+	0.147259i
$340$	2.13239	−	1.20492i	0.115645	−	0.0653459i
$341$	−3.77764	+	4.50201i	−0.204570	+	0.243798i
$342$	−2.70661	−	3.35927i	−0.146357	−	0.181648i
$343$	19.8700	+	1.73840i	1.07288	+	0.0938647i
$344$	2.35225	−	7.85705i	0.126825	−	0.423624i
$345$	20.6504	−	1.70925i	1.11178	−	0.0920230i
$346$	−1.92119	+	0.964860i	−0.103284	+	0.0518712i
$347$	−4.55034	+	0.132401i	−0.244275	+	0.00710768i	−0.151004	−	0.988533i	$-0.548251\pi$
$347$	−4.55034	+	0.132401i	−0.244275	+	0.00710768i	−0.0932708	+	0.995641i	$0.529732\pi$
$348$	−1.64389	+	0.151422i	−0.0881215	+	0.00811706i
$349$	−19.1945	+	8.27969i	−1.02746	+	0.443201i	−0.842015	−	0.539454i	$-0.818631\pi$
$349$	−19.1945	+	8.27969i	−1.02746	+	0.443201i	−0.185441	+	0.982655i	$0.559371\pi$
$350$	−10.8295	+	4.43511i	−0.578861	+	0.237067i
$351$	−16.7105	+	2.18664i	−0.891941	+	0.116714i
$352$	0.978055	+	3.65015i	0.0521305	+	0.194554i
$353$	4.89885	−	3.87350i	0.260739	−	0.206166i	−0.481240	−	0.876589i	$-0.659813\pi$
$353$	4.89885	−	3.87350i	0.260739	−	0.206166i	0.741979	+	0.670423i	$0.233887\pi$
$354$	−6.11009	+	3.56512i	−0.324747	+	0.189484i
$355$	−23.6878	+	12.4903i	−1.25722	+	0.662916i
$356$	−4.37474	−	0.254799i	−0.231861	−	0.0135043i
$357$	−0.108789	+	4.43905i	−0.00575772	+	0.234940i
$358$	10.8290	+	6.67940i	0.572328	+	0.353017i
$359$	−4.49698	−	25.5036i	−0.237342	−	1.34603i	−0.837626	−	0.546244i	$-0.816057\pi$
$359$	−4.49698	−	25.5036i	−0.237342	−	1.34603i	0.600285	−	0.799786i	$-0.295054\pi$
$360$	2.65638	+	6.15984i	0.140004	+	0.324652i
$361$	2.94024	−	16.6749i	0.154750	−	0.877628i
$362$	−0.662016	+	0.743902i	−0.0347948	+	0.0390986i
$363$	3.00478	+	4.82186i	0.157710	+	0.253082i
$364$	−6.08897	+	4.53307i	−0.319149	+	0.237597i
$365$	0.959298	−	0.618277i	0.0502120	−	0.0323621i
$366$	−2.84939	+	12.2731i	−0.148940	+	0.641525i
$367$	−0.191328	−	0.170268i	−0.00998724	−	0.00888789i	0.659787	−	0.751452i	$-0.270646\pi$
$367$	−0.191328	−	0.170268i	−0.00998724	−	0.00888789i	−0.669775	+	0.742564i	$0.733609\pi$
$368$	−3.06871	−	4.38258i	−0.159968	−	0.228458i
$369$	18.1620	−	9.33092i	0.945479	−	0.485748i
$370$	3.19225	−	3.96122i	0.165957	−	0.205934i
$371$	−0.721796	−	3.04550i	−0.0374738	−	0.158114i
$372$	2.69287	+	0.0659949i	0.139619	+	0.00342167i
$373$	7.70131	−	6.85358i	0.398759	−	0.354865i	−0.441301	−	0.897359i	$-0.645483\pi$
$373$	7.70131	−	6.85358i	0.398759	−	0.354865i	0.840060	+	0.542494i	$0.182520\pi$
$374$	−4.02765	−	0.954571i	−0.208265	−	0.0493597i
$375$	−6.19883	−	18.3460i	−0.320106	−	0.947382i
$376$	6.86770	+	0.802719i	0.354174	+	0.0413971i
$377$	2.98596	−	0.800085i	0.153785	−	0.0412065i
$378$	−12.0563	−	1.59687i	−0.620109	−	0.0821341i
$379$	−19.2011	+	11.0858i	−0.986294	+	0.569437i	−0.904164	−	0.427185i	$-0.859505\pi$
$379$	−19.2011	+	11.0858i	−0.986294	+	0.569437i	−0.0821296	+	0.996622i	$0.526172\pi$
$380$	1.38586	−	2.90147i	0.0710934	−	0.148842i
$381$	−29.5786	−	24.5891i	−1.51536	−	1.25974i
$382$	−0.130986	−	4.50170i	−0.00670183	−	0.230327i
$383$	−0.0728914	+	0.219974i	−0.00372458	+	0.0112401i	−0.951088	−	0.308919i	$-0.900033\pi$
$383$	−0.0728914	+	0.219974i	−0.00372458	+	0.0112401i	0.947364	+	0.320159i	$0.103736\pi$
$384$	1.02793	−	1.39405i	0.0524561	−	0.0711397i
$385$	18.5208	+	6.93612i	0.943907	+	0.353497i
$386$	−3.28880	−	3.91944i	−0.167396	−	0.199494i
$387$	−19.1596	+	15.4372i	−0.973937	+	0.784716i
$388$	−0.803897	−	9.18859i	−0.0408117	−	0.466480i
$389$	−19.3854	+	12.7499i	−0.982876	+	0.646448i	−0.935833	−	0.352445i	$-0.885350\pi$
$389$	−19.3854	+	12.7499i	−0.982876	+	0.646448i	−0.0470437	+	0.998893i	$0.514980\pi$
$390$	−6.85340	−	10.5272i	−0.347035	−	0.533063i
$391$	5.82064	−	0.680335i	0.294362	−	0.0344060i
$392$	1.41453	−	0.561957i	0.0714445	−	0.0283831i
$393$	5.70090	−	17.4723i	0.287572	−	0.881362i
$394$	−8.87800	+	17.6776i	−0.447267	+	0.890582i
$395$	−17.8621	+	32.4046i	−0.898739	+	1.63045i
$396$	3.77951	−	10.6882i	0.189928	−	0.537101i
$397$	26.2713	−	12.2505i	1.31852	−	0.614835i	0.369257	−	0.929327i	$-0.379612\pi$
$397$	26.2713	−	12.2505i	1.31852	−	0.614835i	0.949260	+	0.314492i	$0.101834\pi$
$398$	−0.417356	−	0.0121438i	−0.0209202	−	0.000608714i
$399$	3.22563	+	4.85567i	0.161483	+	0.243088i
$400$	−3.28440	+	3.76998i	−0.164220	+	0.188499i
$401$	−20.2514	+	6.06287i	−1.01131	+	0.302765i	−0.749250	−	0.662288i	$-0.769586\pi$
$401$	−20.2514	+	6.06287i	−1.01131	+	0.302765i	−0.262056	+	0.965053i	$0.584401\pi$
$402$	−10.1100	+	14.5805i	−0.504242	+	0.727208i
$403$	−4.99080	+	0.731044i	−0.248609	+	0.0364159i
$404$	3.68013			0.183093
$405$	3.89051	−	19.7450i	0.193321	−	0.981136i
$406$	2.23077			0.110711
$407$	−8.50685	+	1.24607i	−0.421669	+	0.0617654i
$408$	0.809668	+	1.71575i	0.0400845	+	0.0849422i
$409$	12.1408	−	3.63471i	0.600323	−	0.179725i	0.0277998	−	0.999614i	$-0.491150\pi$
$409$	12.1408	−	3.63471i	0.600323	−	0.179725i	0.572523	+	0.819889i	$0.305965\pi$
$410$	12.1229	+	9.20108i	0.598709	+	0.454409i
$411$	4.20309	−	8.46563i	0.207323	−	0.417579i
$412$	−0.707164	−	0.0205764i	−0.0348395	−	0.00101373i
$413$	8.66356	−	4.03988i	0.426306	−	0.198790i
$414$	0.147228	+	16.0497i	0.00723586	+	0.788802i
$415$	−34.0854	+	9.86113i	−1.67318	+	0.484064i
$416$	−1.45561	+	2.89837i	−0.0713674	+	0.142104i
$417$	−24.9457	−	27.7737i	−1.22160	−	1.36008i
$418$	−5.05013	+	2.00629i	−0.247010	+	0.0981307i
$419$	23.9770	−	2.80251i	1.17135	−	0.136911i	0.491914	−	0.870644i	$-0.336298\pi$
$419$	23.9770	−	2.80251i	1.17135	−	0.136911i	0.679438	+	0.733733i	$0.262223\pi$
$420$	−2.81092	−	8.61787i	−0.137159	−	0.420509i
$421$	−21.3610	+	14.0494i	−1.04107	+	0.684724i	−0.950360	−	0.311153i	$-0.899285\pi$
$421$	−21.3610	+	14.0494i	−1.04107	+	0.684724i	−0.0907126	+	0.995877i	$0.528914\pi$
$422$	2.24270	+	25.6342i	0.109173	+	1.24785i
$423$	−15.6216	−	13.6474i	−0.759550	−	0.663558i
$424$	−0.859577	−	1.02440i	−0.0417447	−	0.0497494i
$425$	−1.92734	−	5.12640i	−0.0934895	−	0.248667i
$426$	−8.30314	−	19.0086i	−0.402289	−	0.920972i
$427$	5.35530	−	16.1614i	0.259161	−	0.782105i
$428$	0.270151	+	9.28448i	0.0130582	+	0.448782i
$429$	−3.59039	+	20.9228i	−0.173346	+	1.01016i
$430$	−16.5485	−	7.90429i	−0.798041	−	0.381179i
$431$	−27.7166	+	16.0022i	−1.33506	+	0.770798i	−0.986071	−	0.166328i	$-0.946809\pi$
$431$	−27.7166	+	16.0022i	−1.33506	+	0.770798i	−0.348991	+	0.937126i	$0.613476\pi$
$432$	−4.90945	+	1.70213i	−0.236206	+	0.0818939i
$433$	−2.61466	+	0.700595i	−0.125652	+	0.0336685i	−0.321097	−	0.947046i	$-0.604052\pi$
$433$	−2.61466	+	0.700595i	−0.125652	+	0.0336685i	0.195445	+	0.980715i	$0.437385\pi$
$434$	−3.61532	−	0.422571i	−0.173541	−	0.0202841i
$435$	−0.231894	+	3.68411i	−0.0111185	+	0.176640i
$436$	−19.0677	−	4.51914i	−0.913179	−	0.216427i
$437$	5.74721	−	5.11458i	0.274926	−	0.244664i
$438$	0.423126	+	0.776193i	0.0202177	+	0.0370879i
$439$	−2.74835	−	11.5962i	−0.131172	−	0.553456i	−0.998451	−	0.0556350i	$-0.982282\pi$
$439$	−2.74835	−	11.5962i	−0.131172	−	0.553456i	0.867280	−	0.497821i	$-0.165866\pi$
$440$	8.40151	−	0.903131i	0.400526	−	0.0430551i
$441$	−4.45259	−	1.01224i	−0.212028	−	0.0482018i
$442$	−2.03769	−	2.91012i	−0.0969229	−	0.138420i
$443$	13.8319	+	12.3093i	0.657172	+	0.584833i	0.925617	−	0.378462i	$-0.123547\pi$
$443$	13.8319	+	12.3093i	0.657172	+	0.584833i	−0.268445	+	0.963295i	$0.586510\pi$
$444$	2.87873	+	2.69109i	0.136618	+	0.127714i
$445$	−2.07036	+	9.57757i	−0.0981446	+	0.454020i
$446$	6.91843	−	5.15058i	0.327597	−	0.243887i
$447$	12.0095	−	22.5196i	0.568029	−	1.06514i
$448$	−1.55595	+	1.74841i	−0.0735119	+	0.0826047i
$449$	−3.86727	+	21.9324i	−0.182508	+	1.03505i	0.746609	+	0.665264i	$0.231681\pi$
$449$	−3.86727	+	21.9324i	−0.182508	+	1.03505i	−0.929116	+	0.369788i	$0.879430\pi$
$450$	14.5246	−	3.74639i	0.684697	−	0.176607i
$451$	−4.46628	−	25.3295i	−0.210309	−	1.19272i
$452$	−1.66671	−	1.02804i	−0.0783955	−	0.0483551i
$453$	−24.2909	−	14.8295i	−1.14128	−	0.696749i
$454$	21.7788	+	1.26847i	1.02213	+	0.0595324i
$455$	7.91708	+	15.0147i	0.371159	+	0.703900i
$456$	2.16268	+	1.23543i	0.101277	+	0.0578544i
$457$	−3.28480	+	2.59728i	−0.153656	+	0.121496i	−0.694082	−	0.719896i	$-0.744189\pi$
$457$	−3.28480	+	2.59728i	−0.153656	+	0.121496i	0.540425	+	0.841392i	$0.318263\pi$
$458$	6.02375	+	22.4809i	0.281471	+	1.05046i
$459$	0.911120	−	5.61819i	0.0425274	−	0.262235i
$460$	−10.7401	+	5.26977i	−0.500759	+	0.245704i
$461$	38.5020	−	16.6082i	1.79322	−	0.773519i	0.811190	−	0.584782i	$-0.198820\pi$
$461$	38.5020	−	16.6082i	1.79322	−	0.773519i	0.982028	−	0.188736i	$-0.0604392\pi$
$462$	−6.41043	+	13.9135i	−0.298240	+	0.647313i
$463$	38.0134	−	1.10608i	1.76663	−	0.0514038i	0.869703	−	0.493575i	$-0.164310\pi$
$463$	38.0134	−	1.10608i	1.76663	−	0.0514038i	0.896930	+	0.442172i	$0.145792\pi$
$464$	0.851735	−	0.427758i	0.0395408	−	0.0198581i
$465$	1.07370	−	5.92678i	0.0497916	−	0.274848i
$466$	−4.36084	+	14.5662i	−0.202012	+	0.674768i
$467$	0.677659	+	0.0592875i	0.0313583	+	0.00274350i	0.102824	−	0.994700i	$-0.467212\pi$
$467$	0.677659	+	0.0592875i	0.0313583	+	0.00274350i	−0.0714658	+	0.997443i	$0.522768\pi$
$468$	8.52169	−	4.69626i	0.393915	−	0.217085i
$469$	15.4111	−	18.3663i	0.711620	−	0.848075i
$470$	4.13992	−	14.8966i	0.190960	−	0.687130i
$471$	−31.7269	+	3.85592i	−1.46190	+	0.177671i
$472$	2.53320	−	3.20375i	0.116600	−	0.147464i
$473$	11.4429	+	28.8034i	0.526144	+	1.32438i
$474$	−24.0181	−	15.6396i	−1.10319	−	0.718351i
$475$	−5.93285	−	4.06164i	−0.272218	−	0.186361i
$476$	−0.876823	−	2.40905i	−0.0401891	−	0.110419i
$477$	0.386296	+	3.99315i	0.0176873	+	0.182834i
$478$	−6.38717	−	13.6973i	−0.292143	−	0.626502i
$479$	−12.8114	−	13.5793i	−0.585367	−	0.620453i	0.365216	−	0.930923i	$-0.380995\pi$
$479$	−12.8114	−	13.5793i	−0.585367	−	0.620453i	−0.950583	+	0.310470i	$0.899514\pi$
$480$	−2.72576	−	2.75141i	−0.124413	−	0.125584i
$481$	−6.16519	−	4.05491i	−0.281108	−	0.184888i
$482$	−0.0855817	+	0.158721i	−0.00389814	+	0.00722956i
$483$	1.79118	−	21.6146i	0.0815016	−	0.983500i
$484$	−2.63112	−	1.95880i	−0.119596	−	0.0890363i
$485$	−20.5779	−	1.39004i	−0.934394	−	0.0631186i
$486$	15.0322	+	4.12721i	0.681873	+	0.187214i
$487$	25.1129	−	25.1129i	1.13797	−	1.13797i	0.149162	−	0.988813i	$-0.452342\pi$
$487$	25.1129	−	25.1129i	1.13797	−	1.13797i	0.988813	−	0.149162i	$-0.0476576\pi$
$488$	−1.05428	−	7.19753i	−0.0477251	−	0.325817i
$489$	12.6164	+	14.8963i	0.570533	+	0.673636i
$490$	−0.754155	−	3.31884i	−0.0340692	−	0.149930i
$491$	5.15531	−	7.83827i	0.232656	−	0.353736i	−0.700224	−	0.713923i	$-0.746917\pi$
$491$	5.15531	−	7.83827i	0.232656	−	0.353736i	0.932880	+	0.360187i	$0.117287\pi$
$492$	−7.79666	+	8.84237i	−0.351501	+	0.398645i
$493$	−0.0303642	+	1.04355i	−0.00136754	+	0.0469992i
$494$	−4.38265	−	1.59516i	−0.197185	−	0.0717694i
$495$	−22.3117	−	12.0332i	−1.00284	−	0.540850i
$496$	−1.46141	+	0.531909i	−0.0656191	+	0.0238834i
$497$	8.81660	+	26.6070i	0.395479	+	1.19349i
$498$	−5.68137	−	26.8915i	−0.254588	−	1.20504i
$499$	−18.9525	−	8.17530i	−0.848430	−	0.365977i	−0.0729395	−	0.997336i	$-0.523238\pi$
$499$	−18.9525	−	8.17530i	−0.848430	−	0.365977i	−0.775490	+	0.631360i	$0.782497\pi$
$500$	7.19752	+	8.55544i	0.321883	+	0.382611i
$501$	−0.719488	−	5.92001i	−0.0321443	−	0.264487i
$502$	2.61827	−	12.6803i	0.116859	−	0.565949i
$503$	23.7496	−	2.07782i	1.05894	−	0.0926455i	0.455645	−	0.890161i	$-0.349409\pi$
$503$	23.7496	−	2.07782i	1.05894	−	0.0926455i	0.603298	+	0.797516i	$0.293853\pi$
$504$	6.81709	−	1.68187i	0.303657	−	0.0749165i
$505$	1.26807	−	8.13072i	0.0564285	−	0.361812i
$506$	19.3684	+	5.79851i	0.861029	+	0.257775i
$507$	3.35808	−	2.68035i	0.149137	−	0.119038i
$508$	21.0803	+	6.98525i	0.935287	+	0.309920i
$509$	−14.2223	+	15.0748i	−0.630392	+	0.668177i	−0.961306	−	0.275484i	$-0.911162\pi$
$509$	−14.2223	+	15.0748i	−0.630392	+	0.668177i	0.330913	+	0.943661i	$0.392643\pi$
$510$	4.06970	−	1.19765i	0.180209	−	0.0530327i
$511$	−0.473149	−	1.09688i	−0.0209309	−	0.0485233i
$512$	−0.258819	+	0.965926i	−0.0114383	+	0.0426883i
$513$	−3.25069	−	6.72787i	−0.143522	−	0.297043i
$514$	−4.30207	−	2.48380i	−0.189756	−	0.109556i
$515$	−0.289131	+	1.55529i	−0.0127406	+	0.0685343i
$516$	7.04630	−	12.3349i	0.310196	−	0.543012i
$517$	−22.2389	+	13.7172i	−0.978067	+	0.603281i
$518$	−3.54004	−	3.97791i	−0.155540	−	0.174779i
$519$	−3.61934	+	0.875350i	−0.158871	+	0.0384236i
$520$	5.90197	+	4.21468i	0.258818	+	0.184826i
$521$	37.3987	−	6.59440i	1.63847	−	0.288906i	0.722864	−	0.690990i	$-0.242825\pi$
$521$	37.3987	−	6.59440i	1.63847	−	0.288906i	0.915603	+	0.402084i	$0.131714\pi$
$522$	−2.83284	−	0.388442i	−0.123990	−	0.0170016i
$523$	−4.80828	+	3.36679i	−0.210251	+	0.147220i	−0.673959	−	0.738769i	$-0.735408\pi$
$523$	−4.80828	+	3.36679i	−0.210251	+	0.147220i	0.463708	+	0.885988i	$0.346519\pi$
$524$	0.616977	+	10.5931i	0.0269528	+	0.462761i
$525$	−20.0085	+	3.24085i	−0.873244	+	0.141442i
$526$	17.8874	+	24.0269i	0.779926	+	1.04762i
$527$	0.246889	−	1.68550i	0.0107546	−	0.0734213i
$528$	0.220372	+	6.54156i	0.00959048	+	0.284685i
$529$	−5.61448	+	0.327006i	−0.244108	+	0.0142177i
$530$	−2.55946	+	1.54613i	−0.111176	+	0.0671597i
$531$	−11.7053	+	3.62165i	−0.507966	+	0.157166i
$532$	−2.75696	−	1.93044i	−0.119529	−	0.0836952i
$533$	11.5889	−	18.7885i	0.501971	−	0.813820i
$534$	−7.28115	−	2.14350i	−0.315086	−	0.0927581i
$535$	20.6058	+	2.60232i	0.890868	+	0.112508i
$536$	2.36237	−	9.96762i	0.102039	−	0.430535i
$537$	15.6540	+	15.5111i	0.675521	+	0.669352i
$538$	16.7500	+	21.1838i	0.722144	+	0.913300i
$539$	−2.87588	+	4.98117i	−0.123873	+	0.214554i
$540$	2.06896	+	11.4333i	0.0890337	+	0.492009i
$541$	−4.29103	−	7.43228i	−0.184486	−	0.319539i	0.758917	−	0.651187i	$-0.225729\pi$
$541$	−4.29103	−	7.43228i	−0.184486	−	0.319539i	−0.943403	+	0.331648i	$0.892395\pi$
$542$	−6.43400	+	16.1953i	−0.276364	+	0.695650i
$543$	−1.40833	+	0.995780i	−0.0604372	+	0.0427330i
$544$	−0.796727	−	0.751673i	−0.0341594	−	0.0322277i
$545$	−16.5546	+	40.5703i	−0.709123	+	1.73784i
$546$	−12.0488	+	5.26302i	−0.515641	+	0.225236i
$547$	−9.26028	−	17.1743i	−0.395941	−	0.734319i	0.601997	−	0.798498i	$-0.294372\pi$
$547$	−9.26028	−	17.1743i	−0.395941	−	0.734319i	−0.997938	+	0.0641796i	$0.979557\pi$
$548$	−0.475599	+	5.43612i	−0.0203166	+	0.232220i
$549$	−9.61485	+	19.5908i	−0.410352	+	0.836114i
$550$	0.899595	−	18.8731i	0.0383589	−	0.804754i
$551$	0.753143	+	1.14510i	0.0320850	+	0.0487828i
$552$	−3.46079	−	8.59622i	−0.147301	−	0.365879i
$553$	30.3801	+	24.0214i	1.29189	+	1.02150i
$554$	5.90892	−	13.6984i	0.251046	−	0.581990i
$555$	6.93752	−	5.43286i	0.294481	−	0.230612i
$556$	19.2610	+	9.67322i	0.816847	+	0.410236i
$557$	−25.7402	−	12.0028i	−1.09065	−	0.508577i	−0.207768	−	0.978178i	$-0.566620\pi$
$557$	−25.7402	−	12.0028i	−1.09065	−	0.508577i	−0.882878	+	0.469602i	$0.844398\pi$
$558$	4.51750	+	1.16615i	0.191241	+	0.0493673i
$559$	−9.09798	+	24.9965i	−0.384803	+	1.05724i
$560$	3.32673	+	4.04012i	0.140580	+	0.170726i
$561$	−6.42145	−	3.18818i	−0.271114	−	0.134605i
$562$	21.4330	−	4.42557i	0.904098	−	0.186681i
$563$	6.20202	+	3.34410i	0.261384	+	0.140937i	0.600032	−	0.799976i	$-0.295155\pi$
$563$	6.20202	+	3.34410i	0.261384	+	0.140937i	−0.338648	+	0.940913i	$0.609969\pi$
$564$	11.2726	+	4.04444i	0.474662	+	0.170301i
$565$	−2.84562	+	3.32813i	−0.119716	+	0.140015i
$566$		−	3.77173i		−	0.158538i
$567$	−19.7156	−	7.41670i	−0.827978	−	0.311472i
$568$	8.46828	+	8.46828i	0.355321	+	0.355321i
$569$	12.1943	−	16.3798i	0.511212	−	0.686677i	−0.469322	−	0.883027i	$-0.655502\pi$
$569$	12.1943	−	16.3798i	0.511212	−	0.686677i	0.980534	+	0.196350i	$0.0629090\pi$
$570$	3.47472	−	4.35244i	0.145540	−	0.182304i
$571$	−5.34957	−	17.8688i	−0.223873	−	0.747786i	−0.993950	−	0.109836i	$-0.964968\pi$
$571$	−5.34957	−	17.8688i	−0.223873	−	0.747786i	0.770077	−	0.637951i	$-0.220218\pi$
$572$	−2.47845	−	12.0032i	−0.103629	−	0.501877i
$573$	1.54234	−	7.64648i	0.0644322	−	0.319436i
$574$	11.5871	−	10.9318i	0.483636	−	0.456287i
$575$	7.94208	+	25.5445i	0.331207	+	1.06528i
$576$	2.28035	−	1.94936i	0.0950145	−	0.0812234i
$577$	14.2050	−	30.4626i	0.591360	−	1.26818i	−0.351874	−	0.936047i	$-0.614456\pi$
$577$	14.2050	−	30.4626i	0.591360	−	1.26818i	0.943234	−	0.332128i	$-0.107767\pi$
$578$	−14.9982	+	4.96987i	−0.623844	+	0.206720i
$579$	−4.01353	−	7.90104i	−0.166797	−	0.328356i
$580$	−0.651585	−	2.02918i	−0.0270556	−	0.0842573i
$581$	4.31173	+	36.8892i	0.178881	+	1.53042i
$582$	2.24289	−	15.8177i	0.0929709	−	0.655663i
$583$	4.94901	+	1.02189i	0.204967	+	0.0423223i
$584$	−0.390986	−	0.328076i	−0.0161791	−	0.0135759i
$585$	−7.43937	−	20.4457i	−0.307580	−	0.845325i
$586$	−8.80494	+	7.38822i	−0.363729	+	0.305205i
$587$	36.9660	−	19.9319i	1.52575	−	0.822676i	0.526133	−	0.850402i	$-0.323641\pi$
$587$	36.9660	−	19.9319i	1.52575	−	0.822676i	0.999616	+	0.0277258i	$0.00882653\pi$
$588$	2.60668	−	0.394043i	0.107498	−	0.0162501i
$589$	−1.00368	−	1.99849i	−0.0413558	−	0.0823462i
$590$	−6.20536	−	6.70067i	−0.255471	−	0.275862i
$591$	−21.9031	+	26.3476i	−0.900975	+	1.08380i
$592$	−2.11441	−	0.840003i	−0.0869018	−	0.0345239i
$593$	−12.9566	−	3.47172i	−0.532066	−	0.142567i	−0.0172236	−	0.999852i	$-0.505483\pi$
$593$	−12.9566	−	3.47172i	−0.532066	−	0.142567i	−0.514842	+	0.857285i	$0.672149\pi$
$594$	10.5633	−	16.5524i	0.433418	−	0.679153i
$595$	−5.62459	+	1.10712i	−0.230586	+	0.0453876i
$596$	−1.71063	+	14.6354i	−0.0700700	+	0.599487i
$597$	−0.699396	−	0.183969i	−0.0286244	−	0.00752934i
$598$	9.10960	+	14.7689i	0.372519	+	0.603946i
$599$	0.451500	−	7.75196i	0.0184478	−	0.316736i	−0.976443	−	0.215777i	$-0.930772\pi$
$599$	0.451500	−	7.75196i	0.0184478	−	0.316736i	0.994891	−	0.100960i	$-0.0321913\pi$
$600$	−7.01808	+	5.07411i	−0.286512	+	0.207150i
$601$	−23.8549	+	5.65372i	−0.973063	+	0.230620i	−0.686250	−	0.727366i	$-0.740744\pi$
$601$	−23.8549	+	5.65372i	−0.973063	+	0.230620i	−0.286814	+	0.957986i	$0.592596\pi$
$602$	−11.0103	+	15.7243i	−0.448746	+	0.640875i
$603$	−22.7686	+	20.6397i	−0.927210	+	0.840514i
$604$	16.1816	+	2.85326i	0.658421	+	0.116097i
$605$	−5.23430	+	5.13815i	−0.212805	+	0.208895i
$606$	6.20903	+	1.44152i	0.252224	+	0.0585578i
$607$	−10.1671	−	1.48927i	−0.412672	−	0.0604475i	−0.0645903	−	0.997912i	$-0.520574\pi$
$607$	−10.1671	−	1.48927i	−0.412672	−	0.0604475i	−0.348081	+	0.937464i	$0.613167\pi$
$608$	−1.42281	−	0.208411i	−0.0577026	−	0.00845219i
$609$	3.76370	+	0.873801i	0.152513	+	0.0354082i
$610$	−16.2652	−	0.150787i	−0.658559	−	0.00610517i
$611$	−22.0853	−	3.89424i	−0.893476	−	0.157544i
$612$	0.693987	+	3.21192i	0.0280528	+	0.129834i
$613$	−6.06656	+	8.66395i	−0.245026	+	0.349934i	−0.922761	−	0.385373i	$-0.874073\pi$
$613$	−6.06656	+	8.66395i	−0.245026	+	0.349934i	0.677735	+	0.735306i	$0.262962\pi$
$614$	−14.4036	+	3.41372i	−0.581282	+	0.137766i
$615$	16.8494	+	20.2725i	0.679435	+	0.817465i
$616$	0.514265	−	8.82958i	0.0207203	−	0.355754i
$617$	−16.0625	−	26.0412i	−0.646651	−	1.04838i	−0.993866	−	0.110595i	$-0.964724\pi$
$617$	−16.0625	−	26.0412i	−0.646651	−	1.04838i	0.347215	−	0.937786i	$-0.387128\pi$
$618$	−1.18505	−	0.311715i	−0.0476698	−	0.0125390i
$619$	3.46042	−	29.6058i	0.139086	−	1.18996i	−0.725770	−	0.687938i	$-0.758516\pi$
$619$	3.46042	−	29.6058i	0.139086	−	1.18996i	0.864856	−	0.502020i	$-0.167410\pi$
$620$	0.671616	+	3.41206i	0.0269727	+	0.137031i
$621$	−6.03835	+	27.1364i	−0.242311	+	1.08895i
$622$	−8.73966	−	2.34178i	−0.350428	−	0.0938970i
$623$	9.53178	+	3.78673i	0.381883	+	0.151712i
$624$	−3.59118	+	4.31989i	−0.143762	+	0.172934i
$625$	21.3821	−	12.9539i	0.855285	−	0.518158i
$626$	−1.40657	−	2.80071i	−0.0562179	−	0.111939i
$627$	−9.30633	+	1.40681i	−0.371659	+	0.0561824i
$628$	16.2417	−	8.75746i	0.648116	−	0.349461i
$629$	1.90905	−	1.60188i	0.0761188	−	0.0638713i
$630$	−1.36687	−	15.6409i	−0.0544574	−	0.623150i
$631$	29.5435	+	24.7900i	1.17611	+	0.986873i	0.999997	+	0.00250283i	$0.000796677\pi$
$631$	29.5435	+	24.7900i	1.17611	+	0.986873i	0.176112	+	0.984370i	$0.443648\pi$
$632$	16.2057	+	3.34621i	0.644628	+	0.133105i
$633$	−6.25719	+	44.1279i	−0.248701	+	1.75393i
$634$	−0.0576664	−	0.493368i	−0.00229023	−	0.0195941i
$635$	22.6966	−	44.1670i	0.900688	−	1.75271i
$636$	−1.04900	−	2.06505i	−0.0415954	−	0.0818846i
$637$	−4.68603	+	1.55278i	−0.185667	+	0.0615235i
$638$	−1.52216	+	3.26429i	−0.0602630	+	0.129234i
$639$	−6.56310	−	35.3233i	−0.259632	−	1.39737i
$640$	2.04490	+	0.904657i	0.0808316	+	0.0357597i
$641$	−29.9672	+	28.2726i	−1.18363	+	1.11670i	−0.192854	+	0.981228i	$0.561774\pi$
$641$	−29.9672	+	28.2726i	−1.18363	+	1.11670i	−0.990781	+	0.135474i	$0.956744\pi$
$642$	−3.18098	+	15.7704i	−0.125543	+	0.622407i
$643$	6.22522	+	30.1487i	0.245499	+	1.18895i	0.901021	+	0.433775i	$0.142819\pi$
$643$	6.22522	+	30.1487i	0.245499	+	1.18895i	−0.655523	+	0.755176i	$0.727552\pi$
$644$	3.59135	+	11.9959i	0.141519	+	0.472706i
$645$	−24.8242	−	19.8181i	−0.977450	−	0.780336i
$646$	0.940586	−	1.26343i	0.0370069	−	0.0497088i
$647$	−23.0952	−	23.0952i	−0.907968	−	0.907968i	0.0881402	−	0.996108i	$-0.471908\pi$
$647$	−23.0952	−	23.0952i	−0.907968	−	0.907968i	−0.996108	+	0.0881402i	$0.971908\pi$
$648$	−8.94985	+	0.948746i	−0.351583	+	0.0372702i
$649$			15.4340i			0.605838i
$650$	11.3454	−	11.5873i	0.445003	−	0.454492i
$651$	−5.93417	−	2.12909i	−0.232579	−	0.0834456i
$652$	−9.92033	−	5.34899i	−0.388510	−	0.209483i
$653$	−40.0382	+	8.26723i	−1.56682	+	0.323522i	−0.904756	−	0.425929i	$-0.859947\pi$
$653$	−40.0382	+	8.26723i	−1.56682	+	0.323522i	−0.662060	+	0.749451i	$0.730318\pi$
$654$	−30.4005	−	15.0935i	−1.18875	−	0.590203i
$655$	23.6165	+	2.28697i	0.922774	+	0.0893593i
$656$	2.32788	−	6.39579i	0.0908883	−	0.249714i
$657$	0.409851	+	1.47532i	0.0159898	+	0.0575576i
$658$	−14.6670	−	6.83934i	−0.571780	−	0.266625i
$659$	17.0294	+	8.55248i	0.663371	+	0.333157i	0.748425	−	0.663219i	$-0.230810\pi$
$659$	17.0294	+	8.55248i	0.663371	+	0.333157i	−0.0850546	+	0.996376i	$0.527106\pi$
$660$	14.5286	+	1.76717i	0.565525	+	0.0687868i
$661$	7.07236	−	16.3956i	0.275083	−	0.637713i	−0.723534	−	0.690288i	$-0.757484\pi$
$661$	7.07236	−	16.3956i	0.275083	−	0.637713i	0.998617	+	0.0525750i	$0.0167429\pi$
$662$	−7.75330	−	6.13051i	−0.301340	−	0.238269i
$663$	−2.29803	−	5.70806i	−0.0892482	−	0.221683i
$664$	8.71991	+	13.2580i	0.338398	+	0.514509i
$665$	−5.21501	+	5.42593i	−0.202229	+	0.210408i
$666$	3.80281	+	5.66796i	0.147356	+	0.219629i
$667$	0.444434	−	5.07990i	0.0172085	−	0.196694i
$668$	1.63408	+	3.03059i	0.0632245	+	0.117257i
$669$	13.6901	−	5.97997i	0.529291	−	0.231199i
$670$	−21.2080	−	8.65390i	−0.819338	−	0.334329i
$671$	19.9948	+	18.8642i	0.771892	+	0.728243i
$672$	−3.31003	+	2.34041i	−0.127687	+	0.0902831i
$673$	0.145701	−	0.366751i	0.00561635	−	0.0141372i	−0.926512	−	0.376264i	$-0.877209\pi$
$673$	0.145701	−	0.366751i	0.00561635	−	0.0141372i	0.932129	+	0.362127i	$0.117949\pi$
$674$	9.14645	+	15.8421i	0.352308	+	0.610215i
$675$	25.9731	−	0.631473i	0.999705	−	0.0243054i
$676$	−1.24033	+	2.14831i	−0.0477049	+	0.0826273i
$677$	6.29715	+	7.96405i	0.242019	+	0.306083i	0.890351	−	0.455275i	$-0.150459\pi$
$677$	6.29715	+	7.96405i	0.242019	+	0.306083i	−0.648332	+	0.761358i	$0.724533\pi$
$678$	−2.40935	−	2.38735i	−0.0925305	−	0.0916856i
$679$	−4.97854	+	21.0061i	−0.191059	+	0.806141i
$680$	−1.93525	+	1.50125i	−0.0742133	+	0.0575703i
$681$	36.2479	+	10.6710i	1.38902	+	0.408914i
$682$	3.08527	−	5.00198i	0.118141	−	0.191536i
$683$	17.8640	+	12.5085i	0.683546	+	0.478624i	0.863040	−	0.505135i	$-0.168557\pi$
$683$	17.8640	+	12.5085i	0.683546	+	0.478624i	−0.179495	+	0.983759i	$0.557446\pi$
$684$	3.16490	+	2.93153i	0.121013	+	0.112090i
$685$	11.8465	+	2.92391i	0.452630	+	0.111717i
$686$	−19.9121	+	1.15975i	−0.760249	+	0.0442795i
$687$	1.35725	+	40.2888i	0.0517824	+	1.53711i
$688$	−1.18867	+	8.11501i	−0.0453178	+	0.309382i
$689$	2.59001	+	3.47899i	0.0986715	+	0.132539i
$690$	−20.1846	+	4.68410i	−0.768416	+	0.178321i
$691$	0.422918	+	7.26121i	0.0160885	+	0.276230i	0.996752	+	0.0805291i	$0.0256610\pi$
$691$	0.422918	+	7.26121i	0.0160885	+	0.276230i	−0.980664	+	0.195700i	$0.937302\pi$
$692$	1.76107	−	1.23312i	0.0669459	−	0.0468760i
$693$	−16.2655	+	20.9635i	−0.617875	+	0.796337i
$694$	4.48311	−	0.790493i	0.170176	−	0.0300067i
$695$	28.0084	−	39.2213i	1.06242	−	1.48775i
$696$	1.60458	−	0.388075i	0.0608216	−	0.0147099i
$697$	4.95619	+	5.56923i	0.187729	+	0.210950i
$698$	17.7918	−	10.9742i	0.673430	−	0.415378i
$699$	−13.0632	+	22.8677i	−0.494095	+	0.864934i
$700$	10.0724	−	5.95782i	0.380700	−	0.225185i
$701$	8.94484	+	5.16431i	0.337842	+	0.195053i	0.659317	−	0.751865i	$-0.270845\pi$
$701$	8.94484	+	5.16431i	0.337842	+	0.195053i	−0.321475	+	0.946918i	$0.604179\pi$
$702$	16.2172	−	4.58543i	0.612077	−	0.173066i
$703$	0.846769	−	3.16018i	0.0319365	−	0.119189i
$704$	−1.49675	−	3.46986i	−0.0564110	−	0.130775i
$705$	12.8198	−	23.5116i	0.482823	−	0.885498i
$706$	−4.28573	+	4.54261i	−0.161295	+	0.170963i
$707$	−8.17614	−	2.70928i	−0.307495	−	0.101893i
$708$	5.52887	−	4.41303i	0.207788	−	0.165852i
$709$	24.5527	+	7.35060i	0.922096	+	0.276057i	0.712452	−	0.701720i	$-0.247584\pi$
$709$	24.5527	+	7.35060i	0.922096	+	0.276057i	0.209644	+	0.977778i	$0.432770\pi$
$710$	21.6274	−	15.7915i	0.811663	−	0.592646i
$711$	−34.3967	−	35.7948i	−1.28998	−	1.34241i
$712$	4.36548	−	0.381930i	0.163603	−	0.0143134i
$713$	−1.68256	+	8.14863i	−0.0630122	+	0.305168i
$714$	−0.535720	−	4.40795i	−0.0200488	−	0.164963i
$715$	−27.3733	+	1.33982i	−1.02370	+	0.0501066i
$716$	−11.6827	−	5.03941i	−0.436602	−	0.188332i
$717$	−5.41099	−	25.6117i	−0.202077	−	0.956487i
$718$	8.14579	+	24.5826i	0.303998	+	0.917415i
$719$	4.84600	−	1.76380i	0.180725	−	0.0657787i	−0.250072	−	0.968227i	$-0.580454\pi$
$719$	4.84600	−	1.76380i	0.180725	−	0.0657787i	0.430798	+	0.902448i	$0.358232\pi$
$720$	−3.52109	−	5.70981i	−0.131223	−	0.212792i
$721$	1.55596	+	0.566323i	0.0579470	+	0.0210910i
$722$	−0.492468	+	16.9250i	−0.0183277	+	0.629884i
$723$	−0.206563	+	0.234268i	−0.00768218	+	0.00871253i
$724$	0.547211	−	0.831995i	0.0203370	−	0.0309208i
$725$	−4.70771	+	0.740383i	−0.174840	+	0.0274971i
$726$	−3.67190	−	4.33546i	−0.136277	−	0.160904i
$727$	−3.47482	−	23.7224i	−0.128874	−	0.879815i	−0.950708	−	0.310088i	$-0.899642\pi$
$727$	−3.47482	−	23.7224i	−0.128874	−	0.879815i	0.821834	−	0.569727i	$-0.192951\pi$
$728$	5.36769	−	5.36769i	0.198940	−	0.198940i
$729$	23.7453	+	12.8515i	0.879455	+	0.475982i
$730$	−0.859561	+	0.750782i	−0.0318138	+	0.0277877i
$731$	−7.20596	−	5.36464i	−0.266522	−	0.198418i
$732$	1.04054	−	12.5565i	0.0384595	−	0.464101i
$733$	−16.5700	+	30.7311i	−0.612029	+	1.13508i	0.366781	+	0.930307i	$0.380460\pi$
$733$	−16.5700	+	30.7311i	−0.612029	+	1.13508i	−0.978810	+	0.204771i	$0.934355\pi$
$734$	0.213985	+	0.140740i	0.00789834	+	0.00519482i
$735$	0.0276103	−	5.89488i	0.00101842	−	0.217436i
$736$	3.67149	+	3.89155i	0.135333	+	0.143444i
$737$	16.3596	+	35.0834i	0.602615	+	1.29231i
$738$	−16.6179	+	11.8647i	−0.611715	+	0.436744i
$739$	−2.39531	−	6.58106i	−0.0881129	−	0.242088i	0.887808	−	0.460215i	$-0.152228\pi$
$739$	−2.39531	−	6.58106i	−0.0881129	−	0.242088i	−0.975920	+	0.218127i	$0.930005\pi$
$740$	−2.58444	+	4.38206i	−0.0950058	+	0.161088i
$741$	−6.76948	−	4.40801i	−0.248683	−	0.161932i
$742$	1.15557	+	2.90873i	0.0424221	+	0.106783i
$743$	17.5285	−	22.1684i	0.643059	−	0.813280i	−0.349255	−	0.937028i	$-0.613565\pi$
$743$	17.5285	−	22.1684i	0.643059	−	0.813280i	0.992314	+	0.123747i	$0.0394913\pi$
$744$	−2.67400	+	0.324985i	−0.0980338	+	0.0119145i
$745$	31.7453	+	8.82234i	1.16306	+	0.323226i
$746$	−6.62669	+	7.89738i	−0.242620	+	0.289144i
$747$	0.948044	−	47.5962i	0.0346871	−	1.74145i
$748$	4.12347	+	0.360757i	0.150769	+	0.0131906i
$749$	6.23496	−	20.8262i	0.227820	−	0.760973i
$750$	8.79230	+	17.2539i	0.321049	+	0.630022i
$751$	8.33079	−	4.18388i	0.303995	−	0.152672i	−0.290262	−	0.956947i	$-0.593742\pi$
$751$	8.33079	−	4.18388i	0.303995	−	0.152672i	0.594257	+	0.804275i	$0.297446\pi$
$752$	−6.91152	+	0.201105i	−0.252037	+	0.00733354i
$753$	9.38440	−	20.3683i	0.341987	−	0.742262i
$754$	−2.83847	+	1.22440i	−0.103371	+	0.0445900i
$755$	11.8796	−	34.7679i	0.432344	−	1.26533i
$756$	12.1604	−	0.167332i	0.442271	−	0.00608579i
$757$	0.551450	+	2.05804i	0.0200428	+	0.0748008i	0.975223	−	0.221225i	$-0.0710054\pi$
$757$	0.551450	+	2.05804i	0.0200428	+	0.0748008i	−0.955180	+	0.296025i	$0.904339\pi$
$758$	17.3917	−	13.7516i	0.631694	−	0.499479i
$759$	30.4066	+	17.3698i	1.10369	+	0.630483i
$760$	−0.950718	+	3.07169i	−0.0344862	+	0.111422i
$761$	−14.0837	−	0.820280i	−0.510533	−	0.0297351i	−0.199054	−	0.979988i	$-0.563787\pi$
$761$	−14.0837	−	0.820280i	−0.510533	−	0.0297351i	−0.311478	+	0.950253i	$0.600824\pi$
$762$	32.8300	+	20.0426i	1.18931	+	0.726067i
$763$	39.0359	+	24.0777i	1.41319	+	0.871671i
$764$	0.782043	+	4.43519i	0.0282933	+	0.160459i
$765$	7.33542	−	0.426524i	0.265213	−	0.0154210i
$766$	0.0402406	−	0.228216i	0.00145395	−	0.00824577i
$767$	−8.80633	+	9.89559i	−0.317978	+	0.357309i
$768$	−0.815031	+	1.52831i	−0.0294099	+	0.0551481i
$769$	42.1757	−	31.3986i	1.52089	−	1.13226i	0.570464	−	0.821323i	$-0.306764\pi$
$769$	42.1757	−	31.3986i	1.52089	−	1.13226i	0.950429	−	0.310940i	$-0.100644\pi$
$770$	−19.3305	−	4.17863i	−0.696623	−	0.150587i
$771$	−6.28545	−	5.87576i	−0.226365	−	0.211610i
$772$	3.82213	+	3.40141i	0.137562	+	0.122419i
$773$	20.3757	+	29.0996i	0.732864	+	1.04664i	0.996628	+	0.0820514i	$0.0261472\pi$
$773$	20.3757	+	29.0996i	0.732864	+	1.04664i	−0.263764	+	0.964587i	$0.584964\pi$
$774$	16.7200	−	18.0510i	0.600987	−	0.648831i
$775$	7.76988	−	0.308137i	0.279102	−	0.0110686i
$776$	2.12713	+	8.97506i	0.0763595	+	0.322186i
$777$	−4.41451	−	8.09809i	−0.158370	−	0.290517i
$778$	17.3328	−	15.4249i	0.621411	−	0.553009i
$779$	9.52353	+	2.25712i	0.341216	+	0.0808697i
$780$	8.30676	+	9.42273i	0.297430	+	0.337388i
$781$	−44.9501	−	5.25392i	−1.60844	−	0.188000i
$782$	−5.66058	+	1.51675i	−0.202422	+	0.0542388i
$783$	−4.62735	−	1.76501i	−0.165368	−	0.0630762i
$784$	−1.31815	+	0.761034i	−0.0470767	+	0.0271798i
$785$	−13.7519	−	38.9014i	−0.490827	−	1.38845i
$786$	−3.10841	+	18.1141i	−0.110873	+	0.646108i
$787$	1.22173	+	41.9882i	0.0435500	+	1.49672i	0.684431	+	0.729077i	$0.260050\pi$
$787$	1.22173	+	41.9882i	0.0435500	+	1.49672i	−0.640881	+	0.767640i	$0.721431\pi$
$788$	6.22222	−	18.7776i	0.221658	−	0.668925i
$789$	20.7677	+	47.5442i	0.739351	+	1.69262i
$790$	12.9770	−	34.6512i	0.461702	−	1.23283i
$791$	2.94610	+	3.51102i	0.104751	+	0.124838i
$792$	−2.19055	+	11.1231i	−0.0778378	+	0.395242i
$793$	2.05629	+	23.5035i	0.0730209	+	0.834633i
$794$	−24.2184	+	15.9287i	−0.859479	+	0.565288i
$795$	−4.92390	+	1.60605i	−0.174633	+	0.0569606i
$796$	0.414709	−	0.0484726i	0.0146990	−	0.00171806i
$797$	35.8288	−	14.2339i	1.26912	−	0.504190i	0.364818	−	0.931079i	$-0.381131\pi$
$797$	35.8288	−	14.2339i	1.26912	−	0.504190i	0.904304	+	0.426889i	$0.140391\pi$
$798$	−3.89531	−	4.33691i	−0.137893	−	0.153525i
$799$	3.39908	−	6.76813i	0.120251	−	0.239439i
$800$	2.70333	−	4.20619i	0.0955771	−	0.148711i
$801$	−11.4450	−	6.46852i	−0.404389	−	0.228554i
$802$	19.1589	−	8.93392i	0.676523	−	0.315468i
$803$	1.92793	+	0.0560969i	0.0680350	+	0.00197962i
$804$	7.89009	−	15.8918i	0.278262	−	0.560460i
$805$	27.7408	−	3.80110i	0.977736	−	0.133971i
$806$	4.83215	−	1.44665i	0.170205	−	0.0509561i
$807$	19.9624	+	42.3019i	0.702711	+	1.48910i
$808$	−3.64127	+	0.533368i	−0.128099	+	0.0187638i
$809$	−18.9605			−0.666615			−0.333307	−	0.942818i	$-0.608165\pi$
$809$	−18.9605			−0.666615			−0.333307	+	0.942818i	$0.608165\pi$
$810$	−0.987760	+	20.1004i	−0.0347064	+	0.706255i
$811$	36.1188			1.26830			0.634151	−	0.773209i	$-0.281350\pi$
$811$	36.1188			1.26830			0.634151	+	0.773209i	$0.281350\pi$
$812$	−2.20721	+	0.323309i	−0.0774580	+	0.0113459i
$813$	−17.1991	+	24.8042i	−0.603198	+	0.869921i
$814$	8.23644	−	2.46583i	0.288687	−	0.0864272i
$815$	−15.2361	+	20.0745i	−0.533698	+	0.703177i
$816$	−1.04979	−	1.58029i	−0.0367499	−	0.0553211i
$817$	−11.7889	−	0.343021i	−0.412440	−	0.0120008i
$818$	−11.4858	+	5.35592i	−0.401592	+	0.187265i
$819$	−22.3900	+	4.16008i	−0.782370	+	0.145365i
$820$	−13.3285	−	7.34693i	−0.465450	−	0.256566i
$821$	6.18834	−	12.3220i	0.215975	−	0.430041i	−0.759391	−	0.650634i	$-0.774503\pi$
$821$	6.18834	−	12.3220i	0.215975	−	0.430041i	0.975366	+	0.220593i	$0.0707994\pi$
$822$	−2.93177	+	8.98541i	−0.102257	+	0.313402i
$823$	−16.2817	+	6.46830i	−0.567544	+	0.225471i	−0.635345	−	0.772228i	$-0.719142\pi$
$823$	−16.2817	+	6.46830i	−0.567544	+	0.225471i	0.0678017	+	0.997699i	$0.478401\pi$
$824$	0.702680	−	0.0821315i	0.0244790	−	0.00286119i
$825$	8.91047	−	31.4900i	0.310223	−	1.09634i
$826$	−7.98658	+	5.25285i	−0.277888	+	0.182770i
$827$	0.887366	+	10.1426i	0.0308567	+	0.352694i	0.995890	+	0.0905677i	$0.0288681\pi$
$827$	0.887366	+	10.1426i	0.0308567	+	0.352694i	−0.965034	+	0.262126i	$0.915576\pi$
$828$	−2.47179	−	15.8589i	−0.0859007	−	0.551136i
$829$	16.4925	+	19.6550i	0.572807	+	0.682645i	0.972205	−	0.234133i	$-0.0752250\pi$
$829$	16.4925	+	19.6550i	0.572807	+	0.682645i	−0.399397	+	0.916778i	$0.630781\pi$
$830$	32.2963	−	14.6971i	1.12102	−	0.510143i
$831$	15.3351	−	20.7971i	0.531970	−	0.721444i
$832$	1.02018	−	3.07873i	0.0353684	−	0.106736i
$833$	−0.0484898	−	1.66649i	−0.00168007	−	0.0577403i
$834$	28.7076	+	23.8650i	0.994064	+	0.826379i
$835$	7.25873	−	2.56601i	0.251199	−	0.0888005i
$836$	4.70603	−	2.71703i	0.162761	−	0.0939704i
$837$	7.16504	+	3.73704i	0.247660	+	0.129171i
$838$	−23.3176	+	6.24795i	−0.805495	+	0.215832i
$839$	46.2956	+	5.41118i	1.59830	+	0.186815i	0.868090	−	0.496407i	$-0.165347\pi$
$839$	46.2956	+	5.41118i	1.59830	+	0.186815i	0.730211	+	0.683221i	$0.239422\pi$
$840$	4.03025	+	8.11949i	0.139057	+	0.280149i
$841$	−27.3344	−	6.47836i	−0.942564	−	0.223392i
$842$	19.0993	−	16.9969i	0.658205	−	0.585752i
$843$	37.8949	+	0.928698i	1.30517	+	0.0319861i
$844$	−5.93424	−	25.0385i	−0.204265	−	0.861861i
$845$	4.31900	+	3.48058i	0.148578	+	0.119736i
$846$	17.4346	+	11.2392i	0.599415	+	0.386412i
$847$	4.40352	+	6.28887i	0.151307	+	0.216088i
$848$	0.998970	+	0.889008i	0.0343048	+	0.0305286i
$849$	1.47740	−	6.36358i	0.0507044	−	0.218398i
$850$	2.64997	+	4.79295i	0.0908931	+	0.164397i
$851$	−9.76378	+	7.26886i	−0.334698	+	0.249173i
$852$	10.9704	+	17.6046i	0.375841	+	0.603122i
$853$	8.26644	−	9.28892i	0.283037	−	0.318046i	−0.588384	−	0.808582i	$-0.700236\pi$
$853$	8.26644	−	9.28892i	0.283037	−	0.318046i	0.871421	+	0.490535i	$0.163199\pi$
$854$	−2.95646	+	16.7669i	−0.101168	+	0.573752i
$855$	7.56733	−	5.98228i	0.258797	−	0.204589i
$856$	−1.61291	−	9.14729i	−0.0551283	−	0.312648i
$857$	−18.7948	−	11.5928i	−0.642018	−	0.396003i	0.165197	−	0.986261i	$-0.447174\pi$
$857$	−18.7948	−	11.5928i	−0.642018	−	0.396003i	−0.807215	+	0.590258i	$0.799026\pi$
$858$	0.520099	−	21.2223i	0.0177559	−	0.724516i
$859$	−35.4224	−	2.06312i	−1.20860	−	0.0703928i	−0.558017	−	0.829830i	$-0.688437\pi$
$859$	−35.4224	−	2.06312i	−1.20860	−	0.0703928i	−0.650581	+	0.759437i	$0.725475\pi$
$860$	17.5194	+	5.42242i	0.597406	+	0.184903i
$861$	23.8315	−	13.9053i	0.812176	−	0.473890i
$862$	25.1047	−	19.8503i	0.855071	−	0.676102i
$863$	−6.61825	−	24.6996i	−0.225288	−	0.840786i	−0.982289	−	0.187372i	$-0.940003\pi$
$863$	−6.61825	−	24.6996i	−0.225288	−	0.840786i	0.757001	−	0.653414i	$-0.226664\pi$
$864$	4.61093	−	2.39570i	0.156867	−	0.0815033i
$865$	−2.11758	−	4.31574i	−0.0719998	−	0.146739i
$866$	2.48551	−	1.07215i	0.0844611	−	0.0364330i
$867$	−27.2514	+	2.51019i	−0.925506	+	0.0852504i
$868$	3.63840	−	0.105867i	0.123495	−	0.00359334i
$869$	−55.8805	+	28.0642i	−1.89562	+	0.952014i
$870$	−0.304500	−	3.67882i	−0.0103235	−	0.124724i
$871$	−9.52877	+	31.8283i	−0.322870	+	1.07846i
$872$	19.5214	+	1.70790i	0.661077	+	0.0578368i
$873$	9.98000	−	25.8087i	0.337772	−	0.873491i
$874$	−4.94526	+	5.89354i	−0.167276	+	0.199352i
$875$	−9.69230	−	24.3064i	−0.327660	−	0.821706i
$876$	−0.531154	−	0.706673i	−0.0179460	−	0.0238763i
$877$	−15.0727	+	19.0625i	−0.508968	+	0.643694i	−0.969831	−	0.243776i	$-0.921614\pi$
$877$	−15.0727	+	19.0625i	−0.508968	+	0.643694i	0.460864	+	0.887471i	$0.347540\pi$
$878$	4.39999	+	11.0754i	0.148492	+	0.373778i
$879$	−17.7495	+	9.01630i	−0.598675	+	0.304112i
$880$	−8.18191	+	2.11124i	−0.275812	+	0.0711699i
$881$	9.56043	+	26.2671i	0.322099	+	0.884960i	0.990045	+	0.140750i	$0.0449514\pi$
$881$	9.56043	+	26.2671i	0.322099	+	0.884960i	−0.667946	+	0.744210i	$0.732826\pi$
$882$	4.55228	+	0.356228i	0.153283	+	0.0119948i
$883$	23.0816	+	49.4986i	0.776757	+	1.66576i	0.745737	+	0.666241i	$0.232098\pi$
$883$	23.0816	+	49.4986i	0.776757	+	1.66576i	0.0310199	+	0.999519i	$0.490124\pi$
$884$	2.43794	+	2.58407i	0.0819968	+	0.0869116i
$885$	−7.84486	−	13.7359i	−0.263702	−	0.461727i
$886$	−15.4698	−	10.1747i	−0.519719	−	0.341825i
$887$	25.4880	−	47.2705i	0.855804	−	1.58719i	0.0471611	−	0.998887i	$-0.484983\pi$
$887$	25.4880	−	47.2705i	0.855804	−	1.58719i	0.808643	−	0.588300i	$-0.200203\pi$
$888$	−3.23836	−	2.24546i	−0.108672	−	0.0753526i
$889$	−41.6916	−	31.0383i	−1.39829	−	1.04099i
$890$	0.660407	−	9.77651i	0.0221369	−	0.327709i
$891$	24.3058	−	23.7891i	0.814276	−	0.796966i
$892$	−6.09890	+	6.09890i	−0.204206	+	0.204206i
$893$	−1.44105	−	9.83795i	−0.0482228	−	0.329215i
$894$	−8.61886	+	24.0224i	−0.288258	+	0.803429i
$895$	−15.1594	+	24.0748i	−0.506723	+	0.804731i
$896$	1.28612	−	1.95546i	0.0429664	−	0.0653273i
$897$	9.58447	+	28.4861i	0.320016	+	0.951122i
$898$	0.647737	−	22.2613i	0.0216153	−	0.742868i
$899$	−1.39289	−	0.506971i	−0.0464555	−	0.0169084i
$900$	−13.8283	+	5.81192i	−0.460943	+	0.193731i
$901$	−1.37643	+	0.500980i	−0.0458556	+	0.0166901i
$902$	8.09017	+	24.4148i	0.269373	+	0.812923i
$903$	−24.7356	+	22.2169i	−0.823149	+	0.739333i
$904$	1.79811	+	0.775629i	0.0598043	+	0.0257970i
$905$	−1.64962	−	1.49567i	−0.0548352	−	0.0497177i
$906$	26.1836	+	11.1524i	0.869893	+	0.370513i
$907$	−7.98638	+	38.6781i	−0.265183	+	1.28428i	0.606842	+	0.794823i	$0.292436\pi$
$907$	−7.98638	+	38.6781i	−0.265183	+	1.28428i	−0.872025	+	0.489461i	$0.837193\pi$
$908$	−21.7327	+	1.90137i	−0.721226	+	0.0630991i
$909$	9.91108	+	4.86421i	0.328730	+	0.161336i
$910$	−10.0096	−	13.7087i	−0.331815	−	0.454440i
$911$	30.7388	+	9.20259i	1.01842	+	0.304895i	0.752142	−	0.659001i	$-0.229020\pi$
$911$	30.7388	+	9.20259i	1.01842	+	0.304895i	0.266279	+	0.963896i	$0.414206\pi$
$912$	−2.31890	−	0.908948i	−0.0767864	−	0.0300983i
$913$	−56.9222	−	18.8620i	−1.88385	−	0.624240i
$914$	2.87369	−	3.04593i	0.0950531	−	0.100750i
$915$	−27.3832	−	6.62556i	−0.905262	−	0.219034i
$916$	−9.21835	−	21.3705i	−0.304583	−	0.706102i
$917$	6.42780	−	23.9889i	0.212265	−	0.792183i
$918$	−0.0872450	+	5.69092i	−0.00287952	+	0.187828i
$919$	14.5452	+	8.39766i	0.479801	+	0.277013i	0.720334	−	0.693628i	$-0.243989\pi$
$919$	14.5452	+	8.39766i	0.479801	+	0.277013i	−0.240532	+	0.970641i	$0.577322\pi$
$920$	9.86293	−	6.77071i	0.325171	−	0.223224i
$921$	−25.6386	+	0.117592i	−0.844821	+	0.00387479i
$922$	−35.6885	+	22.0130i	−1.17534	+	0.724958i
$923$	−25.8222	−	29.0162i	−0.849948	−	0.955078i
$924$	4.32624	−	14.6956i	0.142323	−	0.483451i
$925$	8.79101	+	7.21989i	0.289047	+	0.237389i
$926$	−37.4518	+	6.60375i	−1.23074	+	0.217013i
$927$	−1.87729	−	0.990109i	−0.0616584	−	0.0325195i
$928$	−0.780747	+	0.546685i	−0.0256293	+	0.0179458i
$929$	0.349547	+	6.00149i	0.0114683	+	0.196903i	0.999176	+	0.0405899i	$0.0129237\pi$
$929$	0.349547	+	6.00149i	0.0114683	+	0.196903i	−0.987708	+	0.156313i	$0.950039\pi$
$930$	−0.203382	+	6.01982i	−0.00666916	+	0.197398i
$931$	−1.30701	−	1.75563i	−0.0428357	−	0.0575383i
$932$	2.20369	−	15.0445i	0.0721842	−	0.492798i
$933$	−13.8281	−	7.37437i	−0.452710	−	0.241426i
$934$	−0.679097	+	0.0395529i	−0.0222207	+	0.00129421i
$935$	2.21788	−	8.98593i	0.0725325	−	0.293871i
$936$	−7.75108	+	5.88174i	−0.253352	+	0.192251i
$937$	20.1053	+	14.0779i	0.656811	+	0.459904i	0.853869	−	0.520488i	$-0.174250\pi$
$937$	20.1053	+	14.0779i	0.656811	+	0.459904i	−0.197058	+	0.980392i	$0.563139\pi$
$938$	−12.5866	+	20.4059i	−0.410965	+	0.666277i
$939$	−1.27608	−	5.27626i	−0.0416434	−	0.172184i
$940$	−1.93721	+	15.3393i	−0.0631850	+	0.500314i
$941$	10.0277	−	42.3101i	0.326893	−	1.37927i	−0.523009	−	0.852327i	$-0.675191\pi$
$941$	10.0277	−	42.3101i	0.326893	−	1.37927i	0.849902	−	0.526941i	$-0.176661\pi$
$942$	30.8330	−	8.41344i	1.00459	−	0.274125i
$943$	−22.5855	−	28.5640i	−0.735486	−	0.930173i
$944$	−2.04212	+	3.53706i	−0.0664655	+	0.115122i
$945$	3.82047	−	26.9244i	0.124280	−	0.875852i
$946$	−15.4966	−	26.8409i	−0.503837	−	0.872672i
$947$	−16.9034	+	42.5485i	−0.549287	+	1.38264i	0.346455	+	0.938066i	$0.387385\pi$
$947$	−16.9034	+	42.5485i	−0.549287	+	1.38264i	−0.895743	+	0.444573i	$0.853356\pi$
$948$	26.0312	+	11.9935i	0.845453	+	0.389531i
$949$	1.20409	+	1.13600i	0.0390864	+	0.0368761i
$950$	6.45887	+	3.15890i	0.209553	+	0.102488i
$951$	0.0959608	−	0.854987i	0.00311174	−	0.0277249i
$952$	1.21671	+	2.25654i	0.0394339	+	0.0731347i
$953$	−0.812438	+	9.28621i	−0.0263174	+	0.300810i	0.971616	+	0.236562i	$0.0760205\pi$
$953$	−0.812438	+	9.28621i	−0.0263174	+	0.300810i	−0.997934	+	0.0642482i	$0.979535\pi$
$954$	−0.960952	−	3.89500i	−0.0311120	−	0.126105i
$955$	10.0684	−	0.199567i	0.325806	−	0.00645785i
$956$	8.30492	+	12.6270i	0.268600	+	0.408387i
$957$	−3.84679	+	4.91120i	−0.124349	+	0.158756i
$958$	14.6442	+	11.5791i	0.473132	+	0.374105i
$959$	5.05867	−	11.7273i	0.163353	−	0.378694i
$960$	3.09574	+	2.32731i	0.0999147	+	0.0751136i
$961$	−25.5412	−	12.8273i	−0.823911	−	0.413784i
$962$	6.68778	+	3.11856i	0.215623	+	0.100546i
$963$	−11.5442	+	25.3614i	−0.372007	+	0.817260i
$964$	0.0616744	−	0.169449i	0.00198640	−	0.00545758i
$965$	8.83194	−	7.27243i	0.284310	−	0.234108i
$966$	1.36038	+	21.6460i	0.0437695	+	0.696449i
$967$	36.2168	−	7.47816i	1.16465	−	0.240481i	0.419740	−	0.907644i	$-0.362121\pi$
$967$	36.2168	−	7.47816i	1.16465	−	0.240481i	0.744912	+	0.667163i	$0.232491\pi$
$968$	2.88723	+	1.55678i	0.0927992	+	0.0500369i
$969$	2.08182	−	1.76319i	0.0668778	−	0.0566419i
$970$	20.5621	−	1.60703i	0.660209	−	0.0515985i
$971$		−	0.610740i		−	0.0195996i	−0.999952	−	0.00979979i	$-0.996881\pi$
$971$		−	0.610740i		−	0.0195996i	0.999952	−	0.00979979i	$-0.00311942\pi$
$972$	−15.4716	−	1.90499i	−0.496252	−	0.0611027i
$973$	−35.6708	−	35.6708i	−1.14355	−	1.14355i
$974$	−21.2081	+	28.4874i	−0.679551	+	0.912796i
$975$	23.6805	−	15.1058i	0.758383	−	0.483773i
$976$	2.08630	+	6.96874i	0.0667809	+	0.223064i
$977$	−8.08788	−	39.1696i	−0.258754	−	1.25315i	−0.882048	−	0.471160i	$-0.843836\pi$
$977$	−8.08788	−	39.1696i	−0.258754	−	1.25315i	0.623294	−	0.781988i	$-0.285794\pi$
$978$	−14.6421	−	12.9105i	−0.468204	−	0.412833i
$979$	−12.0451	+	11.3640i	−0.384965	+	0.363195i
$980$	1.22720	+	3.17450i	0.0392014	+	0.101406i
$981$	−45.3788	−	37.3734i	−1.44883	−	1.19324i
$982$	−3.96487	+	8.50268i	−0.126524	+	0.271332i
$983$	31.4938	−	10.4359i	1.00450	−	0.332854i	0.235339	−	0.971913i	$-0.424380\pi$
$983$	31.4938	−	10.4359i	1.00450	−	0.332854i	0.769157	+	0.639060i	$0.220676\pi$
$984$	6.43280	−	9.87899i	0.205070	−	0.314931i
$985$	−39.3425	−	20.2174i	−1.25356	−	0.644180i
$986$	−0.121200	−	1.03693i	−0.00385980	−	0.0330227i
$987$	−22.0669	−	17.2843i	−0.702396	−	0.550166i
$988$	4.56757	+	0.943127i	0.145314	+	0.0300049i
$989$	33.6138	+	28.2053i	1.06886	+	0.896878i
$990$	23.8201	+	8.67244i	0.757053	+	0.275628i
$991$	−31.9626	+	26.8198i	−1.01533	+	0.851959i	−0.989033	−	0.147695i	$-0.952815\pi$
$991$	−31.9626	+	26.8198i	−1.01533	+	0.851959i	−0.0262925	+	0.999654i	$0.508370\pi$
$992$	1.36889	−	0.738097i	0.0434622	−	0.0234346i
$993$	−10.6798	−	13.3803i	−0.338915	−	0.424610i
$994$	−12.5797	−	25.0483i	−0.399004	−	0.794483i
$995$	0.0358044	−	0.932944i	0.00113508	−	0.0295763i
$996$	9.51883	+	25.7842i	0.301616	+	0.817003i
$997$	55.0172	+	21.8569i	1.74241	+	0.692216i	0.999746	+	0.0225552i	$0.00718015\pi$
$997$	55.0172	+	21.8569i	1.74241	+	0.692216i	0.742667	+	0.669661i	$0.233561\pi$
$998$	19.9372	+	5.34217i	0.631102	+	0.169103i
$999$	4.19585	+	11.0524i	0.132751	+	0.349683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.w.a.23.2	✓	1944
5.2	odd	4	inner	810.2.w.a.347.13	yes	1944
81.74	odd	54	inner	810.2.w.a.803.13	yes	1944
405.317	even	108	inner	810.2.w.a.317.2	yes	1944

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.2.w.a.23.2	✓	1944	1.1	even	1	trivial
810.2.w.a.317.2	yes	1944	405.317	even	108	inner
810.2.w.a.347.13	yes	1944	5.2	odd	4	inner
810.2.w.a.803.13	yes	1944	81.74	odd	54	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.w (of order \(108\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989442 + 0.144932i) q^{2} +(-1.72613 - 0.143043i) q^{3} +(0.957990 - 0.286803i) q^{4} +(-0.303554 - 2.21537i) q^{5} +(1.72864 - 0.108639i) q^{6} +(-2.33951 - 0.0680727i) q^{7} +(-0.906308 + 0.422618i) q^{8} +(2.95908 + 0.493822i) q^{9} +(0.621426 + 2.14798i) q^{10} +(1.69597 - 3.37696i) q^{11} +(-1.69464 + 0.358027i) q^{12} +(3.01420 - 1.19747i) q^{13} +(2.32467 - 0.271715i) q^{14} +(0.207082 + 3.86744i) q^{15} +(0.835488 - 0.549509i) q^{16} +(0.0954658 + 1.09118i) q^{17} +(-2.99941 - 0.0597436i) q^{18} +(0.924324 + 1.10157i) q^{19} +(-0.926176 - 2.03524i) q^{20} +(4.02857 + 0.452153i) q^{21} +(-1.18864 + 3.58711i) q^{22} +(-0.155607 - 5.34788i) q^{23} +(1.62486 - 0.599855i) q^{24} +(-4.81571 + 1.34497i) q^{25} +(-2.80883 + 1.62168i) q^{26} +(-5.03713 - 1.27568i) q^{27} +(-2.26075 + 0.605766i) q^{28} +(0.946671 + 0.110650i) q^{29} +(-0.765411 - 3.79660i) q^{30} +(-1.51328 - 0.358653i) q^{31} +(-0.747025 + 0.664796i) q^{32} +(-3.41053 + 5.58649i) q^{33} +(-0.252604 - 1.06582i) q^{34} +(0.559361 + 5.20354i) q^{35} +(2.97640 - 0.375597i) q^{36} +(-1.30498 - 1.86370i) q^{37} +(-1.07422 - 0.955972i) q^{38} +(-5.37421 + 1.63583i) q^{39} +(1.21137 + 1.87952i) q^{40} +(5.45946 - 4.06441i) q^{41} +(-4.05156 + 0.136489i) q^{42} +(-5.45239 + 6.12680i) q^{43} +(0.656202 - 3.72150i) q^{44} +(0.195758 - 6.70535i) q^{45} +(0.929042 + 5.26886i) q^{46} +(-5.88500 - 3.62992i) q^{47} +(-1.52077 + 0.829016i) q^{48} +(-1.51949 - 0.0885003i) q^{49} +(4.56994 - 2.02872i) q^{50} +(-0.00870144 - 1.89718i) q^{51} +(2.54414 - 2.01164i) q^{52} +(0.346109 + 1.29170i) q^{53} +(5.16883 + 0.532169i) q^{54} +(-7.99603 - 2.73212i) q^{55} +(2.14908 - 0.927024i) q^{56} +(-1.43794 - 2.03367i) q^{57} +(-0.952713 + 0.0277211i) q^{58} +(-3.64982 + 1.83301i) q^{59} +(1.30758 + 3.64558i) q^{60} +(-2.08630 + 6.96874i) q^{61} +(1.54928 + 0.135544i) q^{62} +(-6.88917 - 1.35673i) q^{63} +(0.642788 - 0.766044i) q^{64} +(-3.56780 - 6.31407i) q^{65} +(2.56486 - 6.02180i) q^{66} +(-6.35353 + 8.03535i) q^{67} +(0.404409 + 1.01796i) q^{68} +(-0.496376 + 9.25341i) q^{69} +(-1.30761 - 5.06753i) q^{70} +(-4.09602 - 11.2537i) q^{71} +(-2.89053 + 0.803005i) q^{72} +(0.215703 + 0.462576i) q^{73} +(1.56131 + 1.65489i) q^{74} +(8.50495 - 1.63274i) q^{75} +(1.20143 + 0.790190i) q^{76} +(-4.19762 + 7.78498i) q^{77} +(5.08038 - 2.39745i) q^{78} +(-13.2732 - 9.88152i) q^{79} +(-1.47098 - 1.68411i) q^{80} +(8.51228 + 2.92252i) q^{81} +(-4.81275 + 4.81275i) q^{82} +(-2.29986 - 15.7010i) q^{83} +(3.98900 - 0.722249i) q^{84} +(2.38838 - 0.542723i) q^{85} +(4.50686 - 6.85234i) q^{86} +(-1.61825 - 0.326411i) q^{87} +(-0.109909 + 3.77732i) q^{88} +(-4.11788 - 1.49878i) q^{89} +(0.778127 + 6.66292i) q^{90} +(-7.13327 + 2.59630i) q^{91} +(-1.68286 - 5.07858i) q^{92} +(2.56082 + 0.835547i) q^{93} +(6.34896 + 2.73867i) q^{94} +(2.15979 - 2.38210i) q^{95} +(1.38456 - 1.04067i) q^{96} +(1.86519 - 9.03313i) q^{97} +(1.51628 - 0.132657i) q^{98} +(6.68614 - 9.15518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1944 q + 36 q^{20} + 108 q^{30} + 108 q^{35} + 36 q^{41} + 216 q^{51} + 108 q^{67} - 144 q^{72} - 576 q^{77} - 576 q^{87} - 144 q^{92} + 36 q^{93} + 108 q^{97}+O(q^{100}) \) 1944 * q + 36 * q^20 + 108 * q^30 + 108 * q^35 + 36 * q^41 + 216 * q^51 + 108 * q^67 - 144 * q^72 - 576 * q^77 - 576 * q^87 - 144 * q^92 + 36 * q^93 + 108 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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