LMFDB - Embedded newform 966.2.k.b.367.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.4
Character	$\chi$	$=$	966.367
Dual form			966.2.k.b.229.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.139134 - 0.240988i) q^{5} -1.00000i q^{6} +(2.42763 - 1.05197i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.139134 - 0.240988i) q^{5} -1.00000i q^{6} +(2.42763 - 1.05197i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.139134 - 0.240988i) q^{10} +(1.25854 + 0.726620i) q^{11} +(0.866025 - 0.500000i) q^{12} -5.02248i q^{13} +(2.12484 + 1.57640i) q^{14} +0.278269i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.48923 + 4.31148i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.02940 - 1.78298i) q^{19} +0.278269 q^{20} +(-2.62837 - 0.302783i) q^{21} +1.45324i q^{22} +(2.68233 - 3.97556i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.46128 - 4.26307i) q^{25} +(4.34959 - 2.51124i) q^{26} -1.00000i q^{27} +(-0.302783 + 2.62837i) q^{28} +5.24874 q^{29} +(-0.240988 + 0.139134i) q^{30} +(0.516456 + 0.298176i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.726620 - 1.25854i) q^{33} -4.97847 q^{34} +(-0.591278 - 0.438664i) q^{35} -1.00000 q^{36} +(2.31382 - 1.33588i) q^{37} +(1.02940 - 1.78298i) q^{38} +(-2.51124 + 4.34959i) q^{39} +(0.139134 + 0.240988i) q^{40} -3.01009i q^{41} +(-1.05197 - 2.42763i) q^{42} +6.84595i q^{43} +(-1.25854 + 0.726620i) q^{44} +(0.139134 - 0.240988i) q^{45} +(4.78410 + 0.335188i) q^{46} +(8.05896 - 4.65284i) q^{47} +1.00000i q^{48} +(4.78673 - 5.10756i) q^{49} +4.92257 q^{50} +(4.31148 - 2.48923i) q^{51} +(4.34959 + 2.51124i) q^{52} +(8.65735 + 4.99832i) q^{53} +(0.866025 - 0.500000i) q^{54} -0.404392i q^{55} +(-2.42763 + 1.05197i) q^{56} +2.05881i q^{57} +(2.62437 + 4.54554i) q^{58} +(2.40462 + 1.38831i) q^{59} +(-0.240988 - 0.139134i) q^{60} +(0.995536 + 1.72432i) q^{61} +0.596352i q^{62} +(2.12484 + 1.57640i) q^{63} +1.00000 q^{64} +(-1.21036 + 0.698800i) q^{65} +(0.726620 - 1.25854i) q^{66} +(5.81351 + 3.35643i) q^{67} +(-2.48923 - 4.31148i) q^{68} +(-4.31075 + 2.10177i) q^{69} +(0.0842550 - 0.731393i) q^{70} -0.995488 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-13.8151 - 7.97614i) q^{73} +(2.31382 + 1.33588i) q^{74} +(-4.26307 + 2.46128i) q^{75} +2.05881 q^{76} +(3.81965 + 0.440016i) q^{77} -5.02248 q^{78} +(2.24875 - 1.29832i) q^{79} +(-0.139134 + 0.240988i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.60682 - 1.50505i) q^{82} -8.53132 q^{83} +(1.57640 - 2.12484i) q^{84} +1.38535 q^{85} +(-5.92877 + 3.42298i) q^{86} +(-4.54554 - 2.62437i) q^{87} +(-1.25854 - 0.726620i) q^{88} +(3.83696 + 6.64582i) q^{89} +0.278269 q^{90} +(-5.28348 - 12.1927i) q^{91} +(2.10177 + 4.31075i) q^{92} +(-0.298176 - 0.516456i) q^{93} +(8.05896 + 4.65284i) q^{94} +(-0.286451 + 0.496147i) q^{95} +(-0.866025 + 0.500000i) q^{96} +4.93232 q^{97} +(6.81665 + 1.59165i) q^{98} +1.45324i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.139134	−	0.240988i	−0.0622228	−	0.107773i	0.833236	−	0.552918i	$-0.186486\pi$
$5$	−0.139134	−	0.240988i	−0.0622228	−	0.107773i	−0.895459	+	0.445145i	$0.853152\pi$
$6$		−	1.00000i		−	0.408248i
$7$	2.42763	−	1.05197i	0.917556	−	0.397606i
$7$	2.42763	−	1.05197i	0.917556	−	0.397606i
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.139134	−	0.240988i	0.0439982	−	0.0762071i
$11$	1.25854	+	0.726620i	0.379465	+	0.219084i	0.677585	−	0.735444i	$-0.263026\pi$
$11$	1.25854	+	0.726620i	0.379465	+	0.219084i	−0.298120	+	0.954528i	$0.596360\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		−	5.02248i		−	1.39298i	−0.717564	−	0.696492i	$-0.754743\pi$
$13$		−	5.02248i		−	1.39298i	0.717564	−	0.696492i	$-0.245257\pi$
$14$	2.12484	+	1.57640i	0.567888	+	0.421311i
$15$			0.278269i			0.0718487i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.48923	+	4.31148i	−0.603728	+	1.04569i	0.388523	+	0.921439i	$0.372985\pi$
$17$	−2.48923	+	4.31148i	−0.603728	+	1.04569i	−0.992251	+	0.124249i	$0.960348\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−1.02940	−	1.78298i	−0.236161	−	0.409043i	0.723448	−	0.690379i	$-0.242556\pi$
$19$	−1.02940	−	1.78298i	−0.236161	−	0.409043i	−0.959610	+	0.281335i	$0.909223\pi$
$20$	0.278269			0.0622228
$21$	−2.62837	−	0.302783i	−0.573557	−	0.0660726i
$22$			1.45324i			0.309832i
$23$	2.68233	−	3.97556i	0.559305	−	0.828962i
$23$	2.68233	−	3.97556i	0.559305	−	0.828962i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	2.46128	−	4.26307i	0.492257	−	0.852614i
$26$	4.34959	−	2.51124i	0.853025	−	0.492494i
$27$		−	1.00000i		−	0.192450i
$28$	−0.302783	+	2.62837i	−0.0572206	+	0.496715i
$29$	5.24874			0.974666			0.487333	−	0.873216i	$-0.337970\pi$
$29$	5.24874			0.974666			0.487333	+	0.873216i	$0.337970\pi$
$30$	−0.240988	+	0.139134i	−0.0439982	+	0.0254024i
$31$	0.516456	+	0.298176i	0.0927582	+	0.0535540i	0.545662	−	0.838006i	$-0.316278\pi$
$31$	0.516456	+	0.298176i	0.0927582	+	0.0535540i	−0.452903	+	0.891560i	$0.649612\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.726620	−	1.25854i	−0.126488	−	0.219084i
$34$	−4.97847			−0.853800
$35$	−0.591278	−	0.438664i	−0.0999442	−	0.0741477i
$36$	−1.00000			−0.166667
$37$	2.31382	−	1.33588i	0.380389	−	0.219618i	−0.297598	−	0.954691i	$-0.596186\pi$
$37$	2.31382	−	1.33588i	0.380389	−	0.219618i	0.677988	+	0.735073i	$0.262852\pi$
$38$	1.02940	−	1.78298i	0.166991	−	0.289237i
$39$	−2.51124	+	4.34959i	−0.402120	+	0.696492i
$40$	0.139134	+	0.240988i	0.0219991	+	0.0381035i
$41$		−	3.01009i		−	0.470098i	−0.971984	−	0.235049i	$-0.924475\pi$
$41$		−	3.01009i		−	0.470098i	0.971984	−	0.235049i	$-0.0755250\pi$
$42$	−1.05197	−	2.42763i	−0.162322	−	0.374591i
$43$			6.84595i			1.04400i	0.852946	+	0.521999i	$0.174814\pi$
$43$			6.84595i			1.04400i	−0.852946	+	0.521999i	$0.825186\pi$
$44$	−1.25854	+	0.726620i	−0.189732	+	0.109542i
$45$	0.139134	−	0.240988i	0.0207409	−	0.0359244i
$46$	4.78410	+	0.335188i	0.705378	+	0.0494207i
$47$	8.05896	−	4.65284i	1.17552	−	0.678687i	0.220546	−	0.975377i	$-0.429216\pi$
$47$	8.05896	−	4.65284i	1.17552	−	0.678687i	0.954974	+	0.296690i	$0.0958827\pi$
$48$			1.00000i			0.144338i
$49$	4.78673	−	5.10756i	0.683819	−	0.729652i
$50$	4.92257			0.696156
$51$	4.31148	−	2.48923i	0.603728	−	0.348563i
$52$	4.34959	+	2.51124i	0.603180	+	0.348246i
$53$	8.65735	+	4.99832i	1.18918	+	0.686573i	0.958120	−	0.286367i	$-0.0924477\pi$
$53$	8.65735	+	4.99832i	1.18918	+	0.686573i	0.231059	+	0.972940i	$0.425781\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		−	0.404392i		−	0.0545281i
$56$	−2.42763	+	1.05197i	−0.324405	+	0.140575i
$57$			2.05881i			0.272695i
$58$	2.62437	+	4.54554i	0.344596	+	0.596858i
$59$	2.40462	+	1.38831i	0.313055	+	0.180742i	0.648293	−	0.761391i	$-0.275483\pi$
$59$	2.40462	+	1.38831i	0.313055	+	0.180742i	−0.335238	+	0.942134i	$0.608817\pi$
$60$	−0.240988	−	0.139134i	−0.0311114	−	0.0179622i
$61$	0.995536	+	1.72432i	0.127465	+	0.220776i	0.922694	−	0.385533i	$-0.125983\pi$
$61$	0.995536	+	1.72432i	0.127465	+	0.220776i	−0.795229	+	0.606310i	$0.792649\pi$
$62$			0.596352i			0.0757367i
$63$	2.12484	+	1.57640i	0.267705	+	0.198608i
$64$	1.00000			0.125000
$65$	−1.21036	+	0.698800i	−0.150126	+	0.0866754i
$66$	0.726620	−	1.25854i	0.0894408	−	0.154916i
$67$	5.81351	+	3.35643i	0.710233	+	0.410053i	0.811147	−	0.584842i	$-0.198843\pi$
$67$	5.81351	+	3.35643i	0.710233	+	0.410053i	−0.100914	+	0.994895i	$0.532177\pi$
$68$	−2.48923	−	4.31148i	−0.301864	−	0.522844i
$69$	−4.31075	+	2.10177i	−0.518953	+	0.253023i
$70$	0.0842550	−	0.731393i	0.0100704	−	0.0874182i
$71$	−0.995488			−0.118143			−0.0590713	−	0.998254i	$-0.518814\pi$
$71$	−0.995488			−0.118143			−0.0590713	+	0.998254i	$0.518814\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−13.8151	−	7.97614i	−1.61693	−	0.933537i	−0.987707	−	0.156315i	$-0.950039\pi$
$73$	−13.8151	−	7.97614i	−1.61693	−	0.933537i	−0.629226	−	0.777222i	$-0.716628\pi$
$74$	2.31382	+	1.33588i	0.268976	+	0.155293i
$75$	−4.26307	+	2.46128i	−0.492257	+	0.284205i
$76$	2.05881			0.236161
$77$	3.81965	+	0.440016i	0.435290	+	0.0501445i
$78$	−5.02248			−0.568684
$79$	2.24875	−	1.29832i	0.253005	−	0.146072i	−0.368135	−	0.929772i	$-0.620003\pi$
$79$	2.24875	−	1.29832i	0.253005	−	0.146072i	0.621139	+	0.783700i	$0.286670\pi$
$80$	−0.139134	+	0.240988i	−0.0155557	+	0.0269433i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.60682	−	1.50505i	0.287875	−	0.166205i
$83$	−8.53132			−0.936434			−0.468217	−	0.883614i	$-0.655103\pi$
$83$	−8.53132			−0.936434			−0.468217	+	0.883614i	$0.655103\pi$
$84$	1.57640	−	2.12484i	0.172000	−	0.231839i
$85$	1.38535			0.150263
$86$	−5.92877	+	3.42298i	−0.639316	+	0.369109i
$87$	−4.54554	−	2.62437i	−0.487333	−	0.281362i
$88$	−1.25854	−	0.726620i	−0.134161	−	0.0774580i
$89$	3.83696	+	6.64582i	0.406717	+	0.704455i	0.994520	−	0.104549i	$-0.0333400\pi$
$89$	3.83696	+	6.64582i	0.406717	+	0.704455i	−0.587802	+	0.809005i	$0.700007\pi$
$90$	0.278269			0.0293321
$91$	−5.28348	−	12.1927i	−0.553859	−	1.27814i
$92$	2.10177	+	4.31075i	0.219125	+	0.449427i
$93$	−0.298176	−	0.516456i	−0.0309194	−	0.0535540i
$94$	8.05896	+	4.65284i	0.831218	+	0.479904i
$95$	−0.286451	+	0.496147i	−0.0293892	+	0.0509036i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	4.93232			0.500802			0.250401	−	0.968142i	$-0.419438\pi$
$97$	4.93232			0.500802			0.250401	+	0.968142i	$0.419438\pi$
$98$	6.81665	+	1.59165i	0.688585	+	0.160781i
$99$			1.45324i			0.146056i
$100$	2.46128	+	4.26307i	0.246128	+	0.426307i
$101$	10.4065	+	6.00820i	1.03549	+	0.597838i	0.918552	−	0.395301i	$-0.129360\pi$
$101$	10.4065	+	6.00820i	1.03549	+	0.597838i	0.116935	+	0.993140i	$0.462693\pi$
$102$	4.31148	+	2.48923i	0.426900	+	0.246471i
$103$	−9.18802	−	15.9141i	−0.905322	−	1.56806i	−0.820484	−	0.571670i	$-0.806296\pi$
$103$	−9.18802	−	15.9141i	−0.905322	−	1.56806i	−0.0848386	−	0.996395i	$-0.527037\pi$
$104$			5.02248i			0.492494i
$105$	0.292730	+	0.675533i	0.0285675	+	0.0659252i
$106$			9.99665i			0.970960i
$107$	−12.9046	+	7.45046i	−1.24753	+	0.720264i	−0.970617	−	0.240631i	$-0.922646\pi$
$107$	−12.9046	+	7.45046i	−1.24753	+	0.720264i	−0.276916	+	0.960894i	$0.589312\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	11.0866	+	6.40085i	1.06190	+	0.613090i	0.925958	−	0.377627i	$-0.123260\pi$
$109$	11.0866	+	6.40085i	1.06190	+	0.613090i	0.135945	+	0.990716i	$0.456593\pi$
$110$	0.350213	−	0.202196i	0.0333915	−	0.0192786i
$111$	−2.67177			−0.253593
$112$	−2.12484	−	1.57640i	−0.200779	−	0.148956i
$113$		−	16.8220i		−	1.58248i	−0.611507	−	0.791239i	$-0.709437\pi$
$113$		−	16.8220i		−	1.58248i	0.611507	−	0.791239i	$-0.290563\pi$
$114$	−1.78298	+	1.02940i	−0.166991	+	0.0964124i
$115$	−1.33127	−	0.0932723i	−0.124141	−	0.00869768i
$116$	−2.62437	+	4.54554i	−0.243666	+	0.422043i
$117$	4.34959	−	2.51124i	0.402120	−	0.232164i
$118$			2.77662i			0.255608i
$119$	−1.50739	+	13.0853i	−0.138183	+	1.19952i
$120$		−	0.278269i		−	0.0254024i
$121$	−4.44405	−	7.69731i	−0.404004	−	0.699756i
$122$	−0.995536	+	1.72432i	−0.0901316	+	0.156113i
$123$	−1.50505	+	2.60682i	−0.135706	+	0.235049i
$124$	−0.516456	+	0.298176i	−0.0463791	+	0.0267770i
$125$	−2.76114			−0.246964
$126$	−0.302783	+	2.62837i	−0.0269740	+	0.234154i
$127$	−16.6311			−1.47577			−0.737886	−	0.674926i	$-0.764176\pi$
$127$	−16.6311			−1.47577			−0.737886	+	0.674926i	$0.764176\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	3.42298	−	5.92877i	0.301376	−	0.521999i
$130$	−1.21036	−	0.698800i	−0.106155	−	0.0612888i
$131$	−7.13164	+	4.11746i	−0.623094	+	0.359744i	−0.778073	−	0.628174i	$-0.783803\pi$
$131$	−7.13164	+	4.11746i	−0.623094	+	0.359744i	0.154978	+	0.987918i	$0.450469\pi$
$132$	1.45324			0.126488
$133$	−4.37464	−	3.24551i	−0.379329	−	0.281421i
$134$			6.71286i			0.579903i
$135$	−0.240988	+	0.139134i	−0.0207409	+	0.0119748i
$136$	2.48923	−	4.31148i	0.213450	−	0.369706i
$137$	2.87537	+	1.66010i	0.245659	+	0.141832i	0.617775	−	0.786355i	$-0.288034\pi$
$137$	2.87537	+	1.66010i	0.245659	+	0.141832i	−0.372116	+	0.928186i	$0.621368\pi$
$138$	−3.97556	−	2.68233i	−0.338422	−	0.228335i
$139$			3.39108i			0.287628i	0.989605	+	0.143814i	$0.0459366\pi$
$139$			3.39108i			0.287628i	−0.989605	+	0.143814i	$0.954063\pi$
$140$	0.675533	−	0.292730i	0.0570929	−	0.0247402i
$141$	−9.30569			−0.783680
$142$	−0.497744	−	0.862118i	−0.0417697	−	0.0723473i
$143$	3.64943	−	6.32100i	0.305181	−	0.528589i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−0.730280	−	1.26488i	−0.0606464	−	0.105043i
$146$		−	15.9523i		−	1.32022i
$147$	−6.69921	+	2.02991i	−0.552542	+	0.167424i
$148$			2.67177i			0.219618i
$149$	−15.5768	+	8.99329i	−1.27610	+	0.736759i	−0.976130	−	0.217188i	$-0.930311\pi$
$149$	−15.5768	+	8.99329i	−1.27610	+	0.736759i	−0.299974	+	0.953947i	$0.596978\pi$
$150$	−4.26307	−	2.46128i	−0.348078	−	0.200963i
$151$	−6.22898	+	10.7889i	−0.506907	+	0.877988i	0.493061	+	0.869995i	$0.335878\pi$
$151$	−6.22898	+	10.7889i	−0.506907	+	0.877988i	−0.999968	+	0.00799384i	$0.997455\pi$
$152$	1.02940	+	1.78298i	0.0834956	+	0.144619i
$153$	−4.97847			−0.402485
$154$	1.52876	+	3.52792i	0.123191	+	0.284288i
$155$		−	0.165946i		−	0.0133291i
$156$	−2.51124	−	4.34959i	−0.201060	−	0.348246i
$157$	1.75657	−	3.04247i	0.140189	−	0.242815i	−0.787378	−	0.616470i	$-0.788562\pi$
$157$	1.75657	−	3.04247i	0.140189	−	0.242815i	0.927568	+	0.373655i	$0.121896\pi$
$158$	2.24875	+	1.29832i	0.178901	+	0.103289i
$159$	−4.99832	−	8.65735i	−0.396393	−	0.686573i
$160$	−0.278269			−0.0219991
$161$	2.32954	−	12.4729i	0.183593	−	0.983002i
$162$	−1.00000			−0.0785674
$163$	−8.13414	−	14.0887i	−0.637115	−	1.10352i	−0.986063	−	0.166373i	$-0.946794\pi$
$163$	−8.13414	−	14.0887i	−0.637115	−	1.10352i	0.348948	−	0.937142i	$-0.386539\pi$
$164$	2.60682	+	1.50505i	0.203558	+	0.117524i
$165$	−0.202196	+	0.350213i	−0.0157409	+	0.0272641i
$166$	−4.26566	−	7.38834i	−0.331079	−	0.573446i
$167$			1.88937i			0.146204i	0.997324	+	0.0731019i	$0.0232898\pi$
$167$			1.88937i			0.146204i	−0.997324	+	0.0731019i	$0.976710\pi$
$168$	2.62837	+	0.302783i	0.202783	+	0.0233602i
$169$	−12.2253			−0.940406
$170$	0.692677	+	1.19975i	0.0531259	+	0.0920167i
$171$	1.02940	−	1.78298i	0.0787204	−	0.136348i
$172$	−5.92877	−	3.42298i	−0.452064	−	0.260999i
$173$	−2.63472	+	1.52116i	−0.200314	+	0.115652i	−0.596802	−	0.802388i	$-0.703562\pi$
$173$	−2.63472	+	1.52116i	−0.200314	+	0.115652i	0.396488	+	0.918040i	$0.370229\pi$
$174$		−	5.24874i		−	0.397906i
$175$	1.49047	−	12.9383i	0.112669	−	0.978045i
$176$		−	1.45324i		−	0.109542i
$177$	−1.38831	−	2.40462i	−0.104352	−	0.180742i
$178$	−3.83696	+	6.64582i	−0.287593	+	0.498125i
$179$	−9.89020	+	17.1303i	−0.739228	+	1.28038i	0.213615	+	0.976918i	$0.431476\pi$
$179$	−9.89020	+	17.1303i	−0.739228	+	1.28038i	−0.952843	+	0.303463i	$0.901857\pi$
$180$	0.139134	+	0.240988i	0.0103705	+	0.0179622i
$181$	12.9611			0.963390			0.481695	−	0.876339i	$-0.340021\pi$
$181$	12.9611			0.963390			0.481695	+	0.876339i	$0.340021\pi$
$182$	7.91744	−	10.6720i	0.586880	−	0.791059i
$183$		−	1.99107i		−	0.147184i
$184$	−2.68233	+	3.97556i	−0.197744	+	0.293082i
$185$	−0.643863	−	0.371735i	−0.0473378	−	0.0273305i
$186$	0.298176	−	0.516456i	0.0218633	−	0.0378684i
$187$	−6.26562	+	3.61746i	−0.458187	+	0.264535i
$188$			9.30569i			0.678687i
$189$	−1.05197	−	2.42763i	−0.0765193	−	0.176584i
$190$	−0.572902			−0.0415626
$191$	6.47964	−	3.74102i	0.468850	−	0.270691i	−0.246908	−	0.969039i	$-0.579415\pi$
$191$	6.47964	−	3.74102i	0.468850	−	0.270691i	0.715758	+	0.698348i	$0.246081\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−6.83388	+	11.8366i	−0.491914	+	0.852019i	−0.999957	−	0.00931234i	$-0.997036\pi$
$193$	−6.83388	+	11.8366i	−0.491914	+	0.852019i	0.508043	+	0.861332i	$0.330369\pi$
$194$	2.46616	+	4.27152i	0.177060	+	0.306677i
$195$	1.39760			0.100084
$196$	2.02991	+	6.69921i	0.144994	+	0.478515i
$197$	22.4667			1.60069			0.800344	−	0.599540i	$-0.204650\pi$
$197$	22.4667			1.60069			0.800344	+	0.599540i	$0.204650\pi$
$198$	−1.25854	+	0.726620i	−0.0894408	+	0.0516386i
$199$	−11.2769	+	19.5322i	−0.799400	+	1.38460i	0.120608	+	0.992700i	$0.461516\pi$
$199$	−11.2769	+	19.5322i	−0.799400	+	1.38460i	−0.920008	+	0.391901i	$0.871818\pi$
$200$	−2.46128	+	4.26307i	−0.174039	+	0.301444i
$201$	−3.35643	−	5.81351i	−0.236744	−	0.410053i
$202$			12.0164i			0.845471i
$203$	12.7420	−	5.52150i	0.894311	−	0.387533i
$204$			4.97847i			0.348563i
$205$	−0.725396	+	0.418808i	−0.0506639	+	0.0292508i
$206$	9.18802	−	15.9141i	0.640160	−	1.10879i
$207$	4.78410	+	0.335188i	0.332518	+	0.0232971i
$208$	−4.34959	+	2.51124i	−0.301590	+	0.174123i
$209$		−	2.99194i		−	0.206957i
$210$	−0.438664	+	0.591278i	−0.0302707	+	0.0408020i
$211$	−9.48946			−0.653281			−0.326641	−	0.945149i	$-0.605917\pi$
$211$	−9.48946			−0.653281			−0.326641	+	0.945149i	$0.605917\pi$
$212$	−8.65735	+	4.99832i	−0.594589	+	0.343286i
$213$	0.862118	+	0.497744i	0.0590713	+	0.0341048i
$214$	−12.9046	−	7.45046i	−0.882139	−	0.509303i
$215$	1.64979	−	0.952508i	0.112515	−	0.0649605i
$216$			1.00000i			0.0680414i
$217$	1.56743	+	0.180565i	0.106404	+	0.0122575i
$218$			12.8017i			0.867040i
$219$	7.97614	+	13.8151i	0.538978	+	0.933537i
$220$	0.350213	+	0.202196i	0.0236114	+	0.0136320i
$221$	21.6543	+	12.5021i	1.45663	+	0.840984i
$222$	−1.33588	−	2.31382i	−0.0896586	−	0.155293i
$223$		−	3.96221i		−	0.265329i	−0.991161	−	0.132664i	$-0.957647\pi$
$223$		−	3.96221i		−	0.265329i	0.991161	−	0.132664i	$-0.0423533\pi$
$224$	0.302783	−	2.62837i	0.0202305	−	0.175615i
$225$	4.92257			0.328171
$226$	14.5683	−	8.41098i	0.969066	−	0.559490i
$227$	−9.70885	+	16.8162i	−0.644399	+	1.11613i	0.340041	+	0.940411i	$0.389559\pi$
$227$	−9.70885	+	16.8162i	−0.644399	+	1.11613i	−0.984440	+	0.175721i	$0.943774\pi$
$228$	−1.78298	−	1.02940i	−0.118081	−	0.0681739i
$229$	−10.7428	−	18.6070i	−0.709902	−	1.22959i	−0.964893	−	0.262642i	$-0.915406\pi$
$229$	−10.7428	−	18.6070i	−0.709902	−	1.22959i	0.254992	−	0.966943i	$-0.417927\pi$
$230$	−0.584858	−	1.19955i	−0.0385644	−	0.0790958i
$231$	−3.08791	−	2.29089i	−0.203169	−	0.150730i
$232$	−5.24874			−0.344596
$233$	2.13431	+	3.69673i	0.139823	+	0.242181i	0.927430	−	0.373998i	$-0.122013\pi$
$233$	2.13431	+	3.69673i	0.139823	+	0.242181i	−0.787606	+	0.616179i	$0.788680\pi$
$234$	4.34959	+	2.51124i	0.284342	+	0.164165i
$235$	−2.24256	−	1.29474i	−0.146288	−	0.0844596i
$236$	−2.40462	+	1.38831i	−0.156528	+	0.0903712i
$237$	−2.59664			−0.168670
$238$	−12.0859	+	5.23718i	−0.783410	+	0.339476i
$239$	−16.3611			−1.05831			−0.529155	−	0.848525i	$-0.677491\pi$
$239$	−16.3611			−1.05831			−0.529155	+	0.848525i	$0.677491\pi$
$240$	0.240988	−	0.139134i	0.0155557	−	0.00898109i
$241$	4.89018	−	8.47005i	0.315004	−	0.545604i	−0.664434	−	0.747347i	$-0.731327\pi$
$241$	4.89018	−	8.47005i	0.315004	−	0.545604i	0.979438	+	0.201743i	$0.0646607\pi$
$242$	4.44405	−	7.69731i	0.285674	−	0.494802i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−1.99107			−0.127465
$245$	−1.89686	−	0.442906i	−0.121186	−	0.0282963i
$246$	−3.01009			−0.191917
$247$	−8.95497	+	5.17015i	−0.569791	+	0.328969i
$248$	−0.516456	−	0.298176i	−0.0327950	−	0.0189342i
$249$	7.38834	+	4.26566i	0.468217	+	0.270325i
$250$	−1.38057	−	2.39122i	−0.0873150	−	0.151234i
$251$	−13.4746			−0.850510			−0.425255	−	0.905074i	$-0.639816\pi$
$251$	−13.4746			−0.850510			−0.425255	+	0.905074i	$0.639816\pi$
$252$	−2.42763	+	1.05197i	−0.152926	+	0.0662677i
$253$	6.26455	−	3.05438i	0.393849	−	0.192027i
$254$	−8.31555	−	14.4030i	−0.521764	−	0.903722i
$255$	−1.19975	−	0.692677i	−0.0751313	−	0.0433771i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.9057	−	10.3379i	1.11693	−	0.644858i	0.176312	−	0.984334i	$-0.443583\pi$
$257$	17.9057	−	10.3379i	1.11693	−	0.644858i	0.940614	+	0.339477i	$0.110250\pi$
$258$	6.84595			0.426210
$259$	4.21178	−	5.67708i	0.261707	−	0.352757i
$260$		−	1.39760i		−	0.0866754i
$261$	2.62437	+	4.54554i	0.162444	+	0.281362i
$262$	−7.13164	−	4.11746i	−0.440594	−	0.254377i
$263$	21.9199	+	12.6554i	1.35164	+	0.780368i	0.988479	−	0.151360i	$-0.0483651\pi$
$263$	21.9199	+	12.6554i	1.35164	+	0.780368i	0.363158	+	0.931728i	$0.381698\pi$
$264$	0.726620	+	1.25854i	0.0447204	+	0.0774580i
$265$		−	2.78176i		−	0.170882i
$266$	0.623371	−	5.41130i	0.0382213	−	0.331788i
$267$		−	7.67393i		−	0.469637i
$268$	−5.81351	+	3.35643i	−0.355117	+	0.205027i
$269$	1.65705	+	0.956701i	0.101032	+	0.0583311i	0.549665	−	0.835385i	$-0.314755\pi$
$269$	1.65705	+	0.956701i	0.101032	+	0.0583311i	−0.448632	+	0.893716i	$0.648089\pi$
$270$	−0.240988	−	0.139134i	−0.0146661	−	0.00846745i
$271$	16.2938	−	9.40723i	0.989778	−	0.571448i	0.0845698	−	0.996418i	$-0.473048\pi$
$271$	16.2938	−	9.40723i	0.989778	−	0.571448i	0.905208	+	0.424969i	$0.139715\pi$
$272$	4.97847			0.301864
$273$	−1.52072	+	13.2009i	−0.0920381	+	0.798956i
$274$			3.32019i			0.200580i
$275$	6.19526	−	3.57684i	0.373588	−	0.215691i
$276$	0.335188	−	4.78410i	0.0201759	−	0.287969i
$277$	−2.82129	+	4.88662i	−0.169515	+	0.293609i	−0.938249	−	0.345959i	$-0.887553\pi$
$277$	−2.82129	+	4.88662i	−0.169515	+	0.293609i	0.768734	+	0.639568i	$0.220887\pi$
$278$	−2.93676	+	1.69554i	−0.176135	+	0.101692i
$279$			0.596352i			0.0357026i
$280$	0.591278	+	0.438664i	0.0353356	+	0.0262152i
$281$			9.86793i			0.588671i	0.955702	+	0.294336i	$0.0950983\pi$
$281$			9.86793i			0.588671i	−0.955702	+	0.294336i	$0.904902\pi$
$282$	−4.65284	−	8.05896i	−0.277073	−	0.479904i
$283$	0.299057	−	0.517982i	0.0177771	−	0.0307908i	−0.857000	−	0.515316i	$-0.827674\pi$
$283$	0.299057	−	0.517982i	0.0177771	−	0.0307908i	0.874777	+	0.484526i	$0.161008\pi$
$284$	0.497744	−	0.862118i	0.0295357	−	0.0511573i
$285$	0.496147	−	0.286451i	0.0293892	−	0.0169679i
$286$	7.29887			0.431591
$287$	−3.16652	−	7.30738i	−0.186914	−	0.431341i
$288$	1.00000			0.0589256
$289$	−3.89258	−	6.74214i	−0.228975	−	0.396596i
$290$	0.730280	−	1.26488i	0.0428835	−	0.0742764i
$291$	−4.27152	−	2.46616i	−0.250401	−	0.144569i
$292$	13.8151	−	7.97614i	0.808467	−	0.466769i
$293$	−23.6190			−1.37984			−0.689918	−	0.723887i	$-0.742354\pi$
$293$	−23.6190			−1.37984			−0.689918	+	0.723887i	$0.742354\pi$
$294$	−5.10756	−	4.78673i	−0.297879	−	0.279168i
$295$		−	0.772647i		−	0.0449852i
$296$	−2.31382	+	1.33588i	−0.134488	+	0.0776466i
$297$	0.726620	−	1.25854i	0.0421628	−	0.0730281i
$298$	−15.5768	−	8.99329i	−0.902342	−	0.520967i
$299$	−19.9672	−	13.4720i	−1.15473	−	0.779103i
$300$		−	4.92257i		−	0.284205i
$301$	7.20171	+	16.6194i	0.415100	+	0.957927i
$302$	−12.4580			−0.716875
$303$	−6.00820	−	10.4065i	−0.345162	−	0.597838i
$304$	−1.02940	+	1.78298i	−0.0590403	+	0.102261i
$305$	0.277027	−	0.479824i	0.0158625	−	0.0274747i
$306$	−2.48923	−	4.31148i	−0.142300	−	0.246471i
$307$		−	13.2254i		−	0.754812i	−0.926048	−	0.377406i	$-0.876816\pi$
$307$		−	13.2254i		−	0.754812i	0.926048	−	0.377406i	$-0.123184\pi$
$308$	−2.29089	+	3.08791i	−0.130536	+	0.175950i
$309$			18.3760i			1.04538i
$310$	0.143714	−	0.0829731i	0.00816238	−	0.00471255i
$311$	−20.3311	−	11.7382i	−1.15287	−	0.665610i	−0.203285	−	0.979120i	$-0.565162\pi$
$311$	−20.3311	−	11.7382i	−1.15287	−	0.665610i	−0.949585	+	0.313510i	$0.898495\pi$
$312$	2.51124	−	4.34959i	0.142171	−	0.246247i
$313$	8.95215	+	15.5056i	0.506006	+	0.876427i	0.999976	+	0.00694863i	$0.00221184\pi$
$313$	8.95215	+	15.5056i	0.506006	+	0.876427i	−0.493970	+	0.869479i	$0.664455\pi$
$314$	3.51314			0.198258
$315$	0.0842550	−	0.731393i	0.00474723	−	0.0412093i
$316$			2.59664i			0.146072i
$317$	4.20294	+	7.27971i	0.236061	+	0.408869i	0.959580	−	0.281435i	$-0.0908103\pi$
$317$	4.20294	+	7.27971i	0.236061	+	0.408869i	−0.723520	+	0.690304i	$0.757477\pi$
$318$	4.99832	−	8.65735i	0.280292	−	0.485480i
$319$	6.60576	+	3.81384i	0.369852	+	0.213534i
$320$	−0.139134	−	0.240988i	−0.00777785	−	0.0134716i
$321$	14.9009			0.831689
$322$	11.9666	−	4.21901i	0.666874	−	0.235116i
$323$	10.2497			0.570309
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−21.4112	−	12.3617i	−1.18768	−	0.685706i
$326$	8.13414	−	14.0887i	0.450508	−	0.780303i
$327$	−6.40085	−	11.0866i	−0.353968	−	0.613090i
$328$			3.01009i			0.166205i
$329$	14.6695	−	19.7731i	0.808756	−	1.09013i
$330$	−0.404392			−0.0222610
$331$	−0.0738206	−	0.127861i	−0.00405755	−	0.00702787i	0.863990	−	0.503510i	$-0.167958\pi$
$331$	−0.0738206	−	0.127861i	−0.00405755	−	0.00702787i	−0.868047	+	0.496482i	$0.834625\pi$
$332$	4.26566	−	7.38834i	0.234108	−	0.405488i
$333$	2.31382	+	1.33588i	0.126796	+	0.0732059i
$334$	−1.63624	+	0.944685i	−0.0895312	+	0.0516909i
$335$		−	1.86798i		−	0.102059i
$336$	1.05197	+	2.42763i	0.0573895	+	0.132438i
$337$			26.5506i			1.44630i	0.690689	+	0.723152i	$0.257307\pi$
$337$			26.5506i			1.44630i	−0.690689	+	0.723152i	$0.742693\pi$
$338$	−6.11264	−	10.5874i	−0.332484	−	0.575879i
$339$	−8.41098	+	14.5683i	−0.456822	+	0.791239i
$340$	−0.692677	+	1.19975i	−0.0375657	+	0.0650656i
$341$	0.433321	+	0.750534i	0.0234657	+	0.0406437i
$342$	2.05881			0.111327
$343$	6.24740	−	17.4347i	0.337328	−	0.941387i
$344$		−	6.84595i		−	0.369109i
$345$	1.10628	+	0.746410i	0.0595599	+	0.0401854i
$346$	−2.63472	−	1.52116i	−0.141644	−	0.0817780i
$347$	−3.99997	+	6.92816i	−0.214730	+	0.371923i	−0.953189	−	0.302375i	$-0.902220\pi$
$347$	−3.99997	+	6.92816i	−0.214730	+	0.371923i	0.738459	+	0.674298i	$0.235554\pi$
$348$	4.54554	−	2.62437i	0.243666	−	0.140681i
$349$			33.9485i			1.81722i	0.417642	+	0.908612i	$0.362857\pi$
$349$			33.9485i			1.81722i	−0.417642	+	0.908612i	$0.637143\pi$
$350$	11.9501	−	5.17838i	0.638762	−	0.276796i
$351$	−5.02248			−0.268080
$352$	1.25854	−	0.726620i	0.0670806	−	0.0387290i
$353$	16.5387	+	9.54860i	0.880264	+	0.508221i	0.870745	−	0.491734i	$-0.163637\pi$
$353$	16.5387	+	9.54860i	0.880264	+	0.508221i	0.00951850	+	0.999955i	$0.496970\pi$
$354$	1.38831	−	2.40462i	0.0737878	−	0.127804i
$355$	0.138507	+	0.239901i	0.00735117	+	0.0127326i
$356$	−7.67393			−0.406717
$357$	7.84807	−	10.5785i	0.415364	−	0.559872i
$358$	−19.7804			−1.04543
$359$	−15.3719	+	8.87498i	−0.811298	+	0.468403i	−0.847407	−	0.530945i	$-0.821837\pi$
$359$	−15.3719	+	8.87498i	−0.811298	+	0.468403i	0.0361083	+	0.999348i	$0.488504\pi$
$360$	−0.139134	+	0.240988i	−0.00733303	+	0.0127012i
$361$	7.38066	−	12.7837i	0.388456	−	0.672825i
$362$	6.48055	+	11.2246i	0.340610	+	0.589954i
$363$			8.88809i			0.466504i
$364$	13.2009	+	1.52072i	0.691916	+	0.0797073i
$365$			4.43903i			0.232349i
$366$	1.72432	−	0.995536i	0.0901316	−	0.0520375i
$367$	−0.753044	+	1.30431i	−0.0393086	+	0.0680845i	−0.885010	−	0.465571i	$-0.845849\pi$
$367$	−0.753044	+	1.30431i	−0.0393086	+	0.0680845i	0.845702	+	0.533656i	$0.179182\pi$
$368$	−4.78410	−	0.335188i	−0.249389	−	0.0174729i
$369$	2.60682	−	1.50505i	0.135706	−	0.0783496i
$370$		−	0.743469i		−	0.0386511i
$371$	26.2749	+	3.02681i	1.36412	+	0.157144i
$372$	0.596352			0.0309194
$373$	−15.6481	+	9.03445i	−0.810230	+	0.467786i	−0.847036	−	0.531536i	$-0.821615\pi$
$373$	−15.6481	+	9.03445i	−0.810230	+	0.467786i	0.0368060	+	0.999322i	$0.488282\pi$
$374$	−6.26562	−	3.61746i	−0.323987	−	0.187054i
$375$	2.39122	+	1.38057i	0.123482	+	0.0712924i
$376$	−8.05896	+	4.65284i	−0.415609	+	0.239952i
$377$		−	26.3617i		−	1.35769i
$378$	1.57640	−	2.12484i	0.0810814	−	0.109290i
$379$			4.50478i			0.231395i	0.993284	+	0.115697i	$0.0369103\pi$
$379$			4.50478i			0.231395i	−0.993284	+	0.115697i	$0.963090\pi$
$380$	−0.286451	−	0.496147i	−0.0146946	−	0.0254518i
$381$	14.4030	+	8.31555i	0.737886	+	0.426019i
$382$	6.47964	+	3.74102i	0.331527	+	0.191407i
$383$	−0.360283	−	0.624029i	−0.0184096	−	0.0318864i	0.856674	−	0.515858i	$-0.172527\pi$
$383$	−0.360283	−	0.624029i	−0.0184096	−	0.0318864i	−0.875083	+	0.483972i	$0.839194\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−0.425407	−	0.981711i	−0.0216807	−	0.0500326i
$386$	−13.6678			−0.695671
$387$	−5.92877	+	3.42298i	−0.301376	+	0.174000i
$388$	−2.46616	+	4.27152i	−0.125200	+	0.216853i
$389$	−13.8804	−	8.01386i	−0.703764	−	0.406319i	0.104984	−	0.994474i	$-0.466521\pi$
$389$	−13.8804	−	8.01386i	−0.703764	−	0.406319i	−0.808748	+	0.588155i	$0.799854\pi$
$390$	0.698800	+	1.21036i	0.0353851	+	0.0612888i
$391$	10.4636	+	21.4609i	0.529167	+	1.08533i
$392$	−4.78673	+	5.10756i	−0.241766	+	0.257971i
$393$	8.23491			0.415396
$394$	11.2334	+	19.4568i	0.565929	+	0.980218i
$395$	−0.625758	−	0.361282i	−0.0314853	−	0.0181781i
$396$	−1.25854	−	0.726620i	−0.0632442	−	0.0365140i
$397$	14.0889	−	8.13423i	0.707101	−	0.408245i	−0.102886	−	0.994693i	$-0.532808\pi$
$397$	14.0889	−	8.13423i	0.707101	−	0.408245i	0.809987	+	0.586448i	$0.199474\pi$
$398$	−22.5538			−1.13052
$399$	2.16580	+	4.99801i	0.108425	+	0.250213i
$400$	−4.92257			−0.246128
$401$	5.37637	−	3.10405i	0.268483	−	0.155009i	−0.359715	−	0.933062i	$-0.617126\pi$
$401$	5.37637	−	3.10405i	0.268483	−	0.155009i	0.628198	+	0.778053i	$0.283793\pi$
$402$	3.35643	−	5.81351i	0.167404	−	0.289951i
$403$	1.49758	−	2.59389i	0.0745998	−	0.129211i
$404$	−10.4065	+	6.00820i	−0.517743	+	0.298919i
$405$	0.278269			0.0138273
$406$	11.1527	+	8.27412i	0.553501	+	0.410638i
$407$	3.88272			0.192459
$408$	−4.31148	+	2.48923i	−0.213450	+	0.123235i
$409$	17.5282	+	10.1199i	0.866712	+	0.500396i	0.866254	−	0.499603i	$-0.166521\pi$
$409$	17.5282	+	10.1199i	0.866712	+	0.500396i	0.000457799		1.00000i	$0.499854\pi$
$410$	−0.725396	−	0.418808i	−0.0358248	−	0.0206834i
$411$	−1.66010	−	2.87537i	−0.0818865	−	0.141832i
$412$	18.3760			0.905322
$413$	7.29798	+	0.840712i	0.359110	+	0.0413687i
$414$	2.10177	+	4.31075i	0.103296	+	0.211862i
$415$	1.18700	+	2.05594i	0.0582675	+	0.100922i
$416$	−4.34959	−	2.51124i	−0.213256	−	0.123124i
$417$	1.69554	−	2.93676i	0.0830309	−	0.143814i
$418$	2.59110	−	1.49597i	0.126735	−	0.0731703i
$419$	−8.90997			−0.435281			−0.217640	−	0.976029i	$-0.569836\pi$
$419$	−8.90997			−0.435281			−0.217640	+	0.976029i	$0.569836\pi$
$420$	−0.731393	−	0.0842550i	−0.0356883	−	0.00411122i
$421$		−	36.2767i		−	1.76802i	−0.467469	−	0.884009i	$-0.654834\pi$
$421$		−	36.2767i		−	1.76802i	0.467469	−	0.884009i	$-0.345166\pi$
$422$	−4.74473	−	8.21811i	−0.230970	−	0.400051i
$423$	8.05896	+	4.65284i	0.391840	+	0.226229i
$424$	−8.65735	−	4.99832i	−0.420438	−	0.242740i
$425$	12.2534	+	21.2235i	0.594378	+	1.02949i
$426$			0.995488i			0.0482315i
$427$	4.23072	+	3.13873i	0.204739	+	0.151894i
$428$		−	14.9009i		−	0.720264i
$429$	−6.32100	+	3.64943i	−0.305181	+	0.176196i
$430$	1.64979	+	0.952508i	0.0795600	+	0.0459340i
$431$	−1.00463	−	0.580021i	−0.0483911	−	0.0279386i	0.475609	−	0.879657i	$-0.342228\pi$
$431$	−1.00463	−	0.580021i	−0.0483911	−	0.0279386i	−0.524000	+	0.851718i	$0.675561\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	17.5484			0.843325			0.421662	−	0.906753i	$-0.361447\pi$
$433$	17.5484			0.843325			0.421662	+	0.906753i	$0.361447\pi$
$434$	0.627342	+	1.44772i	0.0301134	+	0.0694927i
$435$			1.46056i			0.0700285i
$436$	−11.0866	+	6.40085i	−0.530951	+	0.306545i
$437$	−9.84954	−	0.690086i	−0.471167	−	0.0330113i
$438$	−7.97614	+	13.8151i	−0.381115	+	0.660110i
$439$	−16.9006	+	9.75755i	−0.806620	+	0.465702i	−0.845781	−	0.533531i	$-0.820865\pi$
$439$	−16.9006	+	9.75755i	−0.806620	+	0.465702i	0.0391606	+	0.999233i	$0.487532\pi$
$440$			0.404392i			0.0192786i
$441$	6.81665	+	1.59165i	0.324602	+	0.0757928i
$442$			25.0042i			1.18933i
$443$	−0.389410	−	0.674478i	−0.0185014	−	0.0320454i	0.856626	−	0.515937i	$-0.172556\pi$
$443$	−0.389410	−	0.674478i	−0.0185014	−	0.0320454i	−0.875128	+	0.483892i	$0.839223\pi$
$444$	1.33588	−	2.31382i	0.0633982	−	0.109809i
$445$	1.06771	−	1.84932i	0.0506142	−	0.0876664i
$446$	3.43137	−	1.98110i	0.162480	−	0.0938079i
$447$	17.9866			0.850736
$448$	2.42763	−	1.05197i	0.114695	−	0.0497008i
$449$	25.0675			1.18301			0.591504	−	0.806302i	$-0.298534\pi$
$449$	25.0675			1.18301			0.591504	+	0.806302i	$0.298534\pi$
$450$	2.46128	+	4.26307i	0.116026	+	0.200963i
$451$	2.18720	−	3.78833i	0.102991	−	0.178386i
$452$	14.5683	+	8.41098i	0.685233	+	0.395619i
$453$	10.7889	−	6.22898i	0.506907	−	0.292663i
$454$	−19.4177			−0.911318
$455$	−2.20318	+	2.96968i	−0.103287	+	0.139221i
$456$		−	2.05881i		−	0.0964124i
$457$	−13.3581	+	7.71230i	−0.624866	+	0.360766i	−0.778761	−	0.627321i	$-0.784151\pi$
$457$	−13.3581	+	7.71230i	−0.624866	+	0.360766i	0.153895	+	0.988087i	$0.450818\pi$
$458$	10.7428	−	18.6070i	0.501976	−	0.869448i
$459$	4.31148	+	2.48923i	0.201243	+	0.116188i
$460$	0.746410	−	1.10628i	0.0348015	−	0.0515803i
$461$		−	8.17952i		−	0.380958i	−0.981691	−	0.190479i	$-0.938996\pi$
$461$		−	8.17952i		−	0.380958i	0.981691	−	0.190479i	$-0.0610042\pi$
$462$	0.440016	−	3.81965i	0.0204714	−	0.177706i
$463$	23.6105			1.09727			0.548637	−	0.836061i	$-0.315147\pi$
$463$	23.6105			1.09727			0.548637	+	0.836061i	$0.315147\pi$
$464$	−2.62437	−	4.54554i	−0.121833	−	0.211021i
$465$	−0.0829731	+	0.143714i	−0.00384778	+	0.00666456i
$466$	−2.13431	+	3.69673i	−0.0988700	+	0.171248i
$467$	−4.19554	−	7.26688i	−0.194146	−	0.336271i	0.752474	−	0.658622i	$-0.228860\pi$
$467$	−4.19554	−	7.26688i	−0.194146	−	0.336271i	−0.946620	+	0.322351i	$0.895527\pi$
$468$			5.02248i			0.232164i
$469$	17.6439	+	2.03254i	0.814718	+	0.0938539i
$470$		−	2.58948i		−	0.119444i
$471$	−3.04247	+	1.75657i	−0.140189	+	0.0809384i
$472$	−2.40462	−	1.38831i	−0.110682	−	0.0639021i
$473$	−4.97441	+	8.61592i	−0.228723	+	0.396161i
$474$	−1.29832	−	2.24875i	−0.0596338	−	0.103289i
$475$	−10.1346			−0.465008
$476$	−10.5785	−	7.84807i	−0.484863	−	0.359716i
$477$			9.99665i			0.457715i
$478$	−8.18054	−	14.1691i	−0.374169	−	0.648080i
$479$	0.233245	−	0.403992i	0.0106572	−	0.0184589i	−0.860648	−	0.509201i	$-0.829941\pi$
$479$	0.233245	−	0.403992i	0.0106572	−	0.0184589i	0.871305	+	0.490742i	$0.163274\pi$
$480$	0.240988	+	0.139134i	0.0109995	+	0.00635059i
$481$	−6.70944	−	11.6211i	−0.305924	−	0.529876i
$482$	9.78037			0.445483
$483$	−8.25389	+	9.63708i	−0.375565	+	0.438502i
$484$	8.88809			0.404004
$485$	−0.686256	−	1.18863i	−0.0311613	−	0.0539729i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	12.5261	−	21.6958i	0.567610	−	0.983129i	−0.429192	−	0.903213i	$-0.641202\pi$
$487$	12.5261	−	21.6958i	0.567610	−	0.983129i	0.996802	−	0.0799156i	$-0.0254651\pi$
$488$	−0.995536	−	1.72432i	−0.0450658	−	0.0780563i
$489$			16.2683i			0.735677i
$490$	−0.564862	−	1.86418i	−0.0255179	−	0.0842152i
$491$	2.14815			0.0969448			0.0484724	−	0.998825i	$-0.484565\pi$
$491$	2.14815			0.0969448			0.0484724	+	0.998825i	$0.484565\pi$
$492$	−1.50505	−	2.60682i	−0.0678528	−	0.117524i
$493$	−13.0653	+	22.6298i	−0.588433	+	1.01920i
$494$	−8.95497	−	5.17015i	−0.402903	−	0.232616i
$495$	0.350213	−	0.202196i	0.0157409	−	0.00908802i
$496$		−	0.596352i		−	0.0267770i
$497$	−2.41667	+	1.04722i	−0.108403	+	0.0469742i
$498$			8.53132i			0.382297i
$499$	17.7523	+	30.7479i	0.794702	+	1.37646i	0.923029	+	0.384732i	$0.125706\pi$
$499$	17.7523	+	30.7479i	0.794702	+	1.37646i	−0.128327	+	0.991732i	$0.540961\pi$
$500$	1.38057	−	2.39122i	0.0617410	−	0.106939i
$501$	0.944685	−	1.63624i	0.0422054	−	0.0731019i
$502$	−6.73730	−	11.6694i	−0.300701	−	0.520829i
$503$	28.2838			1.26111			0.630556	−	0.776144i	$-0.282827\pi$
$503$	28.2838			1.26111			0.630556	+	0.776144i	$0.282827\pi$
$504$	−2.12484	−	1.57640i	−0.0946480	−	0.0702185i
$505$		−	3.34379i		−	0.148797i
$506$	5.77745	+	3.89807i	0.256839	+	0.173291i
$507$	10.5874	+	6.11264i	0.470203	+	0.271472i
$508$	8.31555	−	14.4030i	0.368943	−	0.639028i
$509$	−21.4524	+	12.3855i	−0.950859	+	0.548979i	−0.893348	−	0.449366i	$-0.851650\pi$
$509$	−21.4524	+	12.3855i	−0.950859	+	0.548979i	−0.0575113	+	0.998345i	$0.518317\pi$
$510$		−	1.38535i		−	0.0613445i
$511$	−41.9285	−	4.83008i	−1.85481	−	0.213670i
$512$	−1.00000			−0.0441942
$513$	−1.78298	+	1.02940i	−0.0787204	+	0.0454492i
$514$	17.9057	+	10.3379i	0.789786	+	0.455983i
$515$	−2.55674	+	4.42840i	−0.112663	+	0.195139i
$516$	3.42298	+	5.92877i	0.150688	+	0.260999i
$517$	13.5234			0.594758
$518$	7.02238	+	0.808964i	0.308546	+	0.0355439i
$519$	3.04232			0.133543
$520$	1.21036	−	0.698800i	0.0530776	−	0.0306444i
$521$	−20.7362	+	35.9161i	−0.908467	+	1.57351i	−0.0922736	+	0.995734i	$0.529413\pi$
$521$	−20.7362	+	35.9161i	−0.908467	+	1.57351i	−0.816194	+	0.577778i	$0.803920\pi$
$522$	−2.62437	+	4.54554i	−0.114865	+	0.198953i
$523$	13.2843	+	23.0090i	0.580880	+	1.00611i	0.995375	+	0.0960622i	$0.0306248\pi$
$523$	13.2843	+	23.0090i	0.580880	+	1.00611i	−0.414495	+	0.910051i	$0.636042\pi$
$524$		−	8.23491i		−	0.359744i
$525$	−7.75994	+	10.4597i	−0.338672	+	0.456498i
$526$			25.3109i			1.10361i
$527$	−2.57116	+	1.48446i	−0.112001	+	0.0646640i
$528$	−0.726620	+	1.25854i	−0.0316221	+	0.0547711i
$529$	−8.61018	−	21.3276i	−0.374356	−	0.927285i
$530$	2.40907	−	1.39088i	0.104643	−	0.0604159i
$531$			2.77662i			0.120495i
$532$	4.99801	−	2.16580i	0.216691	−	0.0938991i
$533$	−15.1181			−0.654839
$534$	6.64582	−	3.83696i	0.287593	−	0.166042i
$535$	3.59094	+	2.07323i	0.155250	+	0.0896337i
$536$	−5.81351	−	3.35643i	−0.251105	−	0.144976i
$537$	17.1303	−	9.89020i	0.739228	−	0.426794i
$538$			1.91340i			0.0824926i
$539$	9.73557	−	2.94995i	0.419340	−	0.127063i
$540$		−	0.278269i		−	0.0119748i
$541$	−3.35014	−	5.80261i	−0.144034	−	0.249474i	0.784978	−	0.619523i	$-0.212674\pi$
$541$	−3.35014	−	5.80261i	−0.144034	−	0.249474i	−0.929012	+	0.370050i	$0.879341\pi$
$542$	16.2938	+	9.40723i	0.699879	+	0.404075i
$543$	−11.2246	−	6.48055i	−0.481695	−	0.278107i
$544$	2.48923	+	4.31148i	0.106725	+	0.184853i
$545$		−	3.56231i		−	0.152593i
$546$	−12.1927	+	5.28348i	−0.521799	+	0.226112i
$547$	13.8116			0.590543			0.295271	−	0.955413i	$-0.404590\pi$
$547$	13.8116			0.590543			0.295271	+	0.955413i	$0.404590\pi$
$548$	−2.87537	+	1.66010i	−0.122830	+	0.0709158i
$549$	−0.995536	+	1.72432i	−0.0424885	+	0.0735922i
$550$	6.19526	+	3.57684i	0.264167	+	0.152517i
$551$	−5.40306	−	9.35838i	−0.230178	−	0.398680i
$552$	4.31075	−	2.10177i	0.183478	−	0.0894573i
$553$	4.09335	−	5.51745i	0.174067	−	0.234626i
$554$	−5.64259			−0.239731
$555$	0.371735	+	0.643863i	0.0157793	+	0.0273305i
$556$	−2.93676	−	1.69554i	−0.124546	−	0.0719069i
$557$	13.0235	+	7.51910i	0.551822	+	0.318595i	0.749857	−	0.661600i	$-0.230122\pi$
$557$	13.0235	+	7.51910i	0.551822	+	0.318595i	−0.198034	+	0.980195i	$0.563456\pi$
$558$	−0.516456	+	0.298176i	−0.0218633	+	0.0126228i
$559$	34.3836			1.45427
$560$	−0.0842550	+	0.731393i	−0.00356042	+	0.0309070i
$561$	7.23491			0.305458
$562$	−8.54587	+	4.93396i	−0.360486	+	0.208127i
$563$	−15.0948	+	26.1449i	−0.636169	+	1.10188i	0.350098	+	0.936713i	$0.386148\pi$
$563$	−15.0948	+	26.1449i	−0.636169	+	1.10188i	−0.986266	+	0.165163i	$0.947185\pi$
$564$	4.65284	−	8.05896i	0.195920	−	0.339343i
$565$	−4.05389	+	2.34052i	−0.170548	+	0.0984662i
$566$	0.598114			0.0251406
$567$	−0.302783	+	2.62837i	−0.0127157	+	0.110381i
$568$	0.995488			0.0417697
$569$	−5.12949	+	2.96151i	−0.215039	+	0.124153i	−0.603651	−	0.797249i	$-0.706288\pi$
$569$	−5.12949	+	2.96151i	−0.215039	+	0.124153i	0.388612	+	0.921402i	$0.372955\pi$
$570$	0.496147	+	0.286451i	0.0207813	+	0.0119981i
$571$	9.92289	+	5.72898i	0.415260	+	0.239750i	0.693047	−	0.720892i	$-0.256268\pi$
$571$	9.92289	+	5.72898i	0.415260	+	0.239750i	−0.277787	+	0.960643i	$0.589601\pi$
$572$	3.64943	+	6.32100i	0.152590	+	0.264294i
$573$	−7.48204			−0.312567
$574$	4.74512	−	6.39598i	0.198057	−	0.266963i
$575$	−10.3461	−	21.2199i	−0.431463	−	0.884933i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−4.01217	−	2.31643i	−0.167029	−	0.0964342i	0.414155	−	0.910206i	$-0.364077\pi$
$577$	−4.01217	−	2.31643i	−0.167029	−	0.0964342i	−0.581184	+	0.813772i	$0.697410\pi$
$578$	3.89258	−	6.74214i	0.161910	−	0.280436i
$579$	11.8366	−	6.83388i	0.491914	−	0.284006i
$580$	1.46056			0.0606464
$581$	−20.7108	+	8.97466i	−0.859231	+	0.372332i
$582$		−	4.93232i		−	0.204451i
$583$	7.26377	+	12.5812i	0.300834	+	0.521061i
$584$	13.8151	+	7.97614i	0.571672	+	0.330055i
$585$	−1.21036	−	0.698800i	−0.0500421	−	0.0288918i
$586$	−11.8095	−	20.4547i	−0.487846	−	0.844974i
$587$			26.8682i			1.10897i	0.832194	+	0.554485i	$0.187085\pi$
$587$			26.8682i			1.10897i	−0.832194	+	0.554485i	$0.812915\pi$
$588$	1.59165	−	6.81665i	0.0656385	−	0.281114i
$589$		−	1.22777i		−	0.0505895i
$590$	0.669132	−	0.386323i	0.0275477	−	0.0159047i
$591$	−19.4568	−	11.2334i	−0.800344	−	0.462079i
$592$	−2.31382	−	1.33588i	−0.0950973	−	0.0549044i
$593$	21.6059	−	12.4742i	0.887250	−	0.512254i	0.0142078	−	0.999899i	$-0.495477\pi$
$593$	21.6059	−	12.4742i	0.887250	−	0.512254i	0.873042	+	0.487645i	$0.162144\pi$
$594$	1.45324			0.0596272
$595$	3.36312	−	1.45735i	0.137874	−	0.0597453i
$596$		−	17.9866i		−	0.736759i
$597$	19.5322	−	11.2769i	0.799400	−	0.461534i
$598$	1.68347	−	24.0281i	0.0688423	−	0.982580i
$599$	−12.9076	+	22.3566i	−0.527390	+	0.913466i	0.472100	+	0.881545i	$0.343496\pi$
$599$	−12.9076	+	22.3566i	−0.527390	+	0.913466i	−0.999490	+	0.0319215i	$0.989837\pi$
$600$	4.26307	−	2.46128i	0.174039	−	0.100481i
$601$		−	8.13523i		−	0.331843i	−0.986139	−	0.165921i	$-0.946940\pi$
$601$		−	8.13523i		−	0.331843i	0.986139	−	0.165921i	$-0.0530598\pi$
$602$	−10.7920	+	14.5466i	−0.439848	+	0.592874i
$603$			6.71286i			0.273369i
$604$	−6.22898	−	10.7889i	−0.253453	−	0.438994i
$605$	−1.23664	+	2.14192i	−0.0502766	+	0.0870816i
$606$	6.00820	−	10.4065i	0.244066	−	0.422736i
$607$	32.7070	−	18.8834i	1.32753	−	0.766452i	0.342617	−	0.939475i	$-0.388687\pi$
$607$	32.7070	−	18.8834i	1.32753	−	0.766452i	0.984918	+	0.173023i	$0.0553534\pi$
$608$	−2.05881			−0.0834956
$609$	−13.7956	−	1.58923i	−0.559026	−	0.0643987i
$610$	0.554054			0.0224330
$611$	−23.3688	−	40.4759i	−0.945400	−	1.63748i
$612$	2.48923	−	4.31148i	0.100621	−	0.174281i
$613$	−18.8185	−	10.8648i	−0.760070	−	0.438827i	0.0692507	−	0.997599i	$-0.477939\pi$
$613$	−18.8185	−	10.8648i	−0.760070	−	0.438827i	−0.829321	+	0.558772i	$0.811273\pi$
$614$	11.4535	−	6.61269i	0.462226	−	0.266866i
$615$	0.837616			0.0337759
$616$	−3.81965	−	0.440016i	−0.153898	−	0.0177288i
$617$		−	31.4466i		−	1.26599i	−0.774155	−	0.632996i	$-0.781825\pi$
$617$		−	31.4466i		−	1.26599i	0.774155	−	0.632996i	$-0.218175\pi$
$618$	−15.9141	+	9.18802i	−0.640160	+	0.369596i
$619$	−7.06979	+	12.2452i	−0.284159	+	0.492177i	−0.972405	−	0.233300i	$-0.925048\pi$
$619$	−7.06979	+	12.2452i	−0.284159	+	0.492177i	0.688246	+	0.725477i	$0.258381\pi$
$620$	0.143714	+	0.0829731i	0.00577168	+	0.00333228i
$621$	−3.97556	−	2.68233i	−0.159534	−	0.107638i
$622$		−	23.4763i		−	0.941314i
$623$	16.3059	+	12.0972i	0.653282	+	0.484664i
$624$	5.02248			0.201060
$625$	−11.9222	−	20.6499i	−0.476890	−	0.825997i
$626$	−8.95215	+	15.5056i	−0.357800	+	0.619728i
$627$	−1.49597	+	2.59110i	−0.0597433	+	0.103478i
$628$	1.75657	+	3.04247i	0.0700947	+	0.121408i
$629$			13.3013i			0.530358i
$630$	0.675533	−	0.292730i	0.0269139	−	0.0116626i
$631$			41.5475i			1.65398i	0.562216	+	0.826991i	$0.309949\pi$
$631$			41.5475i			1.65398i	−0.562216	+	0.826991i	$0.690051\pi$
$632$	−2.24875	+	1.29832i	−0.0894506	+	0.0516444i
$633$	8.21811	+	4.74473i	0.326641	+	0.188586i
$634$	−4.20294	+	7.27971i	−0.166920	+	0.289114i
$635$	2.31396	+	4.00790i	0.0918267	+	0.159048i
$636$	9.99665			0.396393
$637$	−25.6526	−	24.0412i	−1.01639	−	0.952549i
$638$			7.62767i			0.301982i
$639$	−0.497744	−	0.862118i	−0.0196904	−	0.0341048i
$640$	0.139134	−	0.240988i	0.00549977	−	0.00952588i
$641$	21.7291	+	12.5453i	0.858249	+	0.495510i	0.863426	−	0.504476i	$-0.168314\pi$
$641$	21.7291	+	12.5453i	0.858249	+	0.495510i	−0.00517640	+	0.999987i	$0.501648\pi$
$642$	7.45046	+	12.9046i	0.294046	+	0.509303i
$643$	35.3614			1.39452			0.697259	−	0.716819i	$-0.254403\pi$
$643$	35.3614			1.39452			0.697259	+	0.716819i	$0.254403\pi$
$644$	9.63708	+	8.25389i	0.379754	+	0.325249i
$645$	−1.90502			−0.0750099
$646$	5.12485	+	8.87650i	0.201635	+	0.349241i
$647$	−34.5265	−	19.9339i	−1.35738	−	0.783682i	−0.368107	−	0.929783i	$-0.619994\pi$
$647$	−34.5265	−	19.9339i	−1.35738	−	0.783682i	−0.989270	+	0.146101i	$0.953327\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	2.01755	+	3.49449i	0.0791957	+	0.137171i
$650$		−	24.7235i		−	0.969735i
$651$	−1.26715	−	0.940090i	−0.0496637	−	0.0368450i
$652$	16.2683			0.637115
$653$	4.50651	+	7.80550i	0.176353	+	0.305453i	0.940629	−	0.339437i	$-0.110237\pi$
$653$	4.50651	+	7.80550i	0.176353	+	0.305453i	−0.764275	+	0.644890i	$0.776903\pi$
$654$	6.40085	−	11.0866i	0.250293	−	0.433520i
$655$	1.98451	+	1.14576i	0.0775414	+	0.0447685i
$656$	−2.60682	+	1.50505i	−0.101779	+	0.0587622i
$657$		−	15.9523i		−	0.622358i
$658$	24.4588	+	2.81760i	0.953502	+	0.109842i
$659$		−	26.1914i		−	1.02027i	−0.860094	−	0.510136i	$-0.829595\pi$
$659$		−	26.1914i		−	1.02027i	0.860094	−	0.510136i	$-0.170405\pi$
$660$	−0.202196	−	0.350213i	−0.00787046	−	0.0136320i
$661$	−13.8305	+	23.9551i	−0.537944	+	0.931746i	0.461071	+	0.887363i	$0.347465\pi$
$661$	−13.8305	+	23.9551i	−0.537944	+	0.931746i	−0.999015	+	0.0443825i	$0.985868\pi$
$662$	0.0738206	−	0.127861i	0.00286912	−	0.00496946i
$663$	−12.5021	−	21.6543i	−0.485542	−	0.840984i
$664$	8.53132			0.331079
$665$	−0.173465	+	1.50580i	−0.00672667	+	0.0583923i
$666$			2.67177i			0.103529i
$667$	14.0789	−	20.8667i	0.545135	−	0.807961i
$668$	−1.63624	−	0.944685i	−0.0633081	−	0.0365510i
$669$	−1.98110	+	3.43137i	−0.0765939	+	0.132664i
$670$	1.61772	−	0.933990i	0.0624979	−	0.0360832i
$671$			2.89351i			0.111703i
$672$	−1.57640	+	2.12484i	−0.0608110	+	0.0819676i
$673$	26.5244			1.02244			0.511221	−	0.859449i	$-0.329193\pi$
$673$	26.5244			1.02244			0.511221	+	0.859449i	$0.329193\pi$
$674$	−22.9935	+	13.2753i	−0.885677	+	0.511346i
$675$	−4.26307	−	2.46128i	−0.164086	−	0.0947348i
$676$	6.11264	−	10.5874i	0.235101	−	0.407208i
$677$	−7.79131	−	13.4950i	−0.299445	−	0.518653i	0.676564	−	0.736383i	$-0.263468\pi$
$677$	−7.79131	−	13.4950i	−0.299445	−	0.518653i	−0.976009	+	0.217730i	$0.930135\pi$
$678$	−16.8220			−0.646044
$679$	11.9738	−	5.18864i	0.459514	−	0.199122i
$680$	−1.38535			−0.0531259
$681$	16.8162	−	9.70885i	0.644399	−	0.372044i
$682$	−0.433321	+	0.750534i	−0.0165927	+	0.0287394i
$683$	−13.7433	+	23.8040i	−0.525872	+	0.910836i	0.473674	+	0.880700i	$0.342927\pi$
$683$	−13.7433	+	23.8040i	−0.525872	+	0.910836i	−0.999546	+	0.0301361i	$0.990406\pi$
$684$	1.02940	+	1.78298i	0.0393602	+	0.0681739i
$685$		−	0.923906i		−	0.0353006i
$686$	18.2226	−	3.30696i	0.695743	−	0.126260i
$687$			21.4855i			0.819724i
$688$	5.92877	−	3.42298i	0.226032	−	0.130500i
$689$	25.1040	−	43.4814i	0.956385	−	1.65651i
$690$	−0.0932723	+	1.33127i	−0.00355081	+	0.0506805i
$691$	2.01095	−	1.16102i	0.0765002	−	0.0441674i	−0.461262	−	0.887264i	$-0.652603\pi$
$691$	2.01095	−	1.16102i	0.0765002	−	0.0441674i	0.537762	+	0.843097i	$0.319270\pi$
$692$		−	3.04232i		−	0.115652i
$693$	1.52876	+	3.52792i	0.0580728	+	0.134015i
$694$	−7.99995			−0.303674
$695$	0.817209	−	0.471816i	0.0309985	−	0.0178970i
$696$	4.54554	+	2.62437i	0.172298	+	0.0994764i
$697$	12.9780	+	7.49283i	0.491575	+	0.283811i
$698$	−29.4003	+	16.9743i	−1.11282	+	0.642486i
$699$		−	4.26862i		−	0.161454i
$700$	10.4597	+	7.75994i	0.395339	+	0.293298i
$701$			8.60233i			0.324906i	0.986716	+	0.162453i	$0.0519405\pi$
$701$			8.60233i			0.324906i	−0.986716	+	0.162453i	$0.948059\pi$
$702$	−2.51124	−	4.34959i	−0.0947806	−	0.164165i
$703$	−4.76370	−	2.75032i	−0.179666	−	0.103730i
$704$	1.25854	+	0.726620i	0.0474331	+	0.0273855i
$705$	1.29474	+	2.24256i	0.0487628	+	0.0844596i
$706$			19.0972i			0.718732i
$707$	31.5835	+	3.63836i	1.18782	+	0.136835i
$708$	2.77662			0.104352
$709$	39.5163	−	22.8148i	1.48407	−	0.856827i	0.484231	−	0.874940i	$-0.339099\pi$
$709$	39.5163	−	22.8148i	1.48407	−	0.856827i	0.999836	+	0.0181134i	$0.00576598\pi$
$710$	−0.138507	+	0.239901i	−0.00519806	+	0.00900331i
$711$	2.24875	+	1.29832i	0.0843349	+	0.0486908i
$712$	−3.83696	−	6.64582i	−0.143796	−	0.249063i
$713$	2.57072	−	1.25339i	0.0962743	−	0.0469400i
$714$	13.0853	+	1.50739i	0.489703	+	0.0564128i
$715$	−2.03105			−0.0759569
$716$	−9.89020	−	17.1303i	−0.369614	−	0.640190i
$717$	14.1691	+	8.18054i	0.529155	+	0.305508i
$718$	−15.3719	−	8.87498i	−0.573675	−	0.331211i
$719$	−4.58681	+	2.64820i	−0.171059	+	0.0987611i	−0.583085	−	0.812411i	$-0.698155\pi$
$719$	−4.58681	+	2.64820i	−0.171059	+	0.0987611i	0.412026	+	0.911172i	$0.364821\pi$
$720$	−0.278269			−0.0103705
$721$	−39.0462	−	28.9680i	−1.45416	−	1.07883i
$722$	14.7613			0.549359
$723$	−8.47005	+	4.89018i	−0.315004	+	0.181868i
$724$	−6.48055	+	11.2246i	−0.240848	+	0.417160i
$725$	12.9186	−	22.3757i	0.479786	−	0.831013i
$726$	−7.69731	+	4.44405i	−0.285674	+	0.164934i
$727$	42.7188			1.58435			0.792177	−	0.610292i	$-0.208948\pi$
$727$	42.7188			1.58435			0.792177	+	0.610292i	$0.208948\pi$
$728$	5.28348	+	12.1927i	0.195819	+	0.451891i
$729$	−1.00000			−0.0370370
$730$	−3.84431	+	2.21951i	−0.142284	+	0.0821479i
$731$	−29.5162	−	17.0412i	−1.09170	−	0.630291i
$732$	1.72432	+	0.995536i	0.0637327	+	0.0367961i
$733$	5.60709	+	9.71177i	0.207103	+	0.358712i	0.950801	−	0.309803i	$-0.100263\pi$
$733$	5.60709	+	9.71177i	0.207103	+	0.358712i	−0.743698	+	0.668516i	$0.766930\pi$
$734$	−1.50609			−0.0555907
$735$	1.42128	+	1.33200i	0.0524246	+	0.0491315i
$736$	−2.10177	−	4.31075i	−0.0774723	−	0.158896i
$737$	4.87770	+	8.44842i	0.179672	+	0.311202i
$738$	2.60682	+	1.50505i	0.0959583	+	0.0554016i
$739$	16.5349	−	28.6394i	0.608247	−	1.05352i	−0.383282	−	0.923631i	$-0.625206\pi$
$739$	16.5349	−	28.6394i	0.608247	−	1.05352i	0.991529	−	0.129884i	$-0.0414605\pi$
$740$	0.643863	−	0.371735i	0.0236689	−	0.0136652i
$741$	10.3403			0.379861
$742$	10.5161	+	24.2681i	0.386060	+	0.890911i
$743$		−	48.1965i		−	1.76816i	−0.467337	−	0.884079i	$-0.654786\pi$
$743$		−	48.1965i		−	1.76816i	0.467337	−	0.884079i	$-0.345214\pi$
$744$	0.298176	+	0.516456i	0.0109317	+	0.0189342i
$745$	4.33455	+	2.50255i	0.158806	+	0.0916865i
$746$	−15.6481	−	9.03445i	−0.572919	−	0.330775i
$747$	−4.26566	−	7.38834i	−0.156072	−	0.270325i
$748$		−	7.23491i		−	0.264535i
$749$	−23.4899	+	31.6621i	−0.858300	+	1.15691i
$750$			2.76114i			0.100823i
$751$	−42.6259	+	24.6101i	−1.55544	+	0.898034i	−0.557758	+	0.830004i	$0.688338\pi$
$751$	−42.6259	+	24.6101i	−1.55544	+	0.898034i	−0.997683	+	0.0680307i	$0.978328\pi$
$752$	−8.05896	−	4.65284i	−0.293880	−	0.169672i
$753$	11.6694	+	6.73730i	0.425255	+	0.245521i
$754$	22.8299	−	13.1808i	0.831414	−	0.480017i
$755$	3.46666			0.126165
$756$	2.62837	+	0.302783i	0.0955928	+	0.0110121i
$757$		−	50.3061i		−	1.82841i	−0.405255	−	0.914204i	$-0.632817\pi$
$757$		−	50.3061i		−	1.82841i	0.405255	−	0.914204i	$-0.367183\pi$
$758$	−3.90125	+	2.25239i	−0.141700	+	0.0818105i
$759$	−6.95245	−	0.487108i	−0.252358	−	0.0176809i
$760$	0.286451	−	0.496147i	0.0103907	−	0.0179972i
$761$	−1.60034	+	0.923955i	−0.0580122	+	0.0334934i	−0.528726	−	0.848793i	$-0.677330\pi$
$761$	−1.60034	+	0.923955i	−0.0580122	+	0.0334934i	0.470713	+	0.882286i	$0.343997\pi$
$762$			16.6311i			0.602481i
$763$	33.6476	+	3.87613i	1.21812	+	0.140325i
$764$			7.48204i			0.270691i
$765$	0.692677	+	1.19975i	0.0250438	+	0.0433771i
$766$	0.360283	−	0.624029i	0.0130176	−	0.0225471i
$767$	6.97275	−	12.0772i	0.251771	−	0.436081i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−41.7478			−1.50546			−0.752732	−	0.658327i	$-0.771264\pi$
$769$	−41.7478			−1.50546			−0.752732	+	0.658327i	$0.771264\pi$
$770$	0.637484	−	0.859268i	0.0229733	−	0.0309659i
$771$	−20.6757			−0.744617
$772$	−6.83388	−	11.8366i	−0.245957	−	0.426010i
$773$	−12.9260	+	22.3886i	−0.464917	+	0.805260i	−0.999198	−	0.0400470i	$-0.987249\pi$
$773$	−12.9260	+	22.3886i	−0.464917	+	0.805260i	0.534281	+	0.845307i	$0.320583\pi$
$774$	−5.92877	−	3.42298i	−0.213105	−	0.123036i
$775$	2.54229	−	1.46779i	0.0913217	−	0.0527246i
$776$	−4.93232			−0.177060
$777$	−6.48605	+	2.81061i	−0.232686	+	0.100830i
$778$		−	16.0277i		−	0.574621i
$779$	−5.36693	+	3.09860i	−0.192290	+	0.111019i
$780$	−0.698800	+	1.21036i	−0.0250210	+	0.0433377i
$781$	−1.25286	−	0.723341i	−0.0448310	−	0.0258832i
$782$	−13.3539	+	19.7922i	−0.477535	+	0.707768i
$783$		−	5.24874i		−	0.187575i
$784$	−6.81665	−	1.59165i	−0.243452	−	0.0568446i
$785$	−0.977597			−0.0348919
$786$	4.11746	+	7.13164i	0.146865	+	0.254377i
$787$	−13.8316	+	23.9571i	−0.493044	+	0.853977i	−0.999968	−	0.00801348i	$-0.997449\pi$
$787$	−13.8316	+	23.9571i	−0.493044	+	0.853977i	0.506924	+	0.861991i	$0.330783\pi$
$788$	−11.2334	+	19.4568i	−0.400172	+	0.693119i
$789$	−12.6554	−	21.9199i	−0.450546	−	0.780368i
$790$		−	0.722564i		−	0.0257077i
$791$	−17.6962	−	40.8374i	−0.629203	−	1.45201i
$792$		−	1.45324i		−	0.0516386i
$793$	8.66035	−	5.00006i	0.307538	−	0.177557i
$794$	14.0889	+	8.13423i	0.499996	+	0.288673i
$795$	−1.39088	+	2.40907i	−0.0493294	+	0.0854410i
$796$	−11.2769	−	19.5322i	−0.399700	−	0.692300i
$797$	−43.0699			−1.52561			−0.762807	−	0.646626i	$-0.776179\pi$
$797$	−43.0699			−1.52561			−0.762807	+	0.646626i	$0.776179\pi$
$798$	−3.24551	+	4.37464i	−0.114890	+	0.154861i
$799$			46.3281i			1.63897i
$800$	−2.46128	−	4.26307i	−0.0870195	−	0.150722i
$801$	−3.83696	+	6.64582i	−0.135572	+	0.234818i
$802$	5.37637	+	3.10405i	0.189846	+	0.109608i
$803$	−11.5913	−	20.0766i	−0.409046	−	0.708489i
$804$	6.71286			0.236744
$805$	−3.32994	+	1.17402i	−0.117365	+	0.0413787i
$806$	2.99516			0.105500
$807$	−0.956701	−	1.65705i	−0.0336775	−	0.0583311i
$808$	−10.4065	−	6.00820i	−0.366100	−	0.211368i
$809$	−3.62789	+	6.28369i	−0.127550	+	0.220923i	−0.922727	−	0.385455i	$-0.874045\pi$
$809$	−3.62789	+	6.28369i	−0.127550	+	0.220923i	0.795177	+	0.606378i	$0.207378\pi$
$810$	0.139134	+	0.240988i	0.00488869	+	0.00846745i
$811$			19.3552i			0.679652i	0.940488	+	0.339826i	$0.110368\pi$
$811$			19.3552i			0.679652i	−0.940488	+	0.339826i	$0.889632\pi$
$812$	−1.58923	+	13.7956i	−0.0557709	+	0.484131i
$813$	−18.8145			−0.659852
$814$	1.94136	+	3.36253i	0.0680446	+	0.117857i
$815$	−2.26348	+	3.92046i	−0.0792862	+	0.137328i
$816$	−4.31148	−	2.48923i	−0.150932	−	0.0871406i
$817$	12.2062	−	7.04724i	0.427040	−	0.246552i
$818$			20.2398i			0.707667i
$819$	7.91744	−	10.6720i	0.276658	−	0.372909i
$820$		−	0.837616i		−	0.0292508i
$821$	6.20841	+	10.7533i	0.216675	+	0.375292i	0.953789	−	0.300476i	$-0.0971455\pi$
$821$	6.20841	+	10.7533i	0.216675	+	0.375292i	−0.737114	+	0.675768i	$0.763812\pi$
$822$	1.66010	−	2.87537i	0.0579025	−	0.100290i
$823$	−1.89373	+	3.28004i	−0.0660113	+	0.114335i	−0.897142	−	0.441742i	$-0.854361\pi$
$823$	−1.89373	+	3.28004i	−0.0660113	+	0.114335i	0.831131	+	0.556077i	$0.187694\pi$
$824$	9.18802	+	15.9141i	0.320080	+	0.554394i
$825$	−7.15367			−0.249059
$826$	2.92091	+	6.74059i	0.101631	+	0.234535i
$827$		−	54.9015i		−	1.90911i	−0.298034	−	0.954555i	$-0.596331\pi$
$827$		−	54.9015i		−	1.90911i	0.298034	−	0.954555i	$-0.403669\pi$
$828$	−2.68233	+	3.97556i	−0.0932175	+	0.138160i
$829$	−4.52448	−	2.61221i	−0.157142	−	0.0907258i	0.419367	−	0.907817i	$-0.362252\pi$
$829$	−4.52448	−	2.61221i	−0.157142	−	0.0907258i	−0.576509	+	0.817091i	$0.695585\pi$
$830$	−1.18700	+	2.05594i	−0.0412014	+	0.0713629i
$831$	4.88662	−	2.82129i	0.169515	−	0.0978696i
$832$		−	5.02248i		−	0.174123i
$833$	10.1059	+	33.3518i	0.350147	+	1.15557i
$834$	3.39108			0.117423
$835$	0.455315	−	0.262876i	0.0157568	−	0.00909721i
$836$	2.59110	+	1.49597i	0.0896149	+	0.0517392i
$837$	0.298176	−	0.516456i	0.0103065	−	0.0178513i
$838$	−4.45499	−	7.71626i	−0.153895	−	0.266554i
$839$	−43.9656			−1.51786			−0.758930	−	0.651172i	$-0.774278\pi$
$839$	−43.9656			−1.51786			−0.758930	+	0.651172i	$0.774278\pi$
$840$	−0.292730	−	0.675533i	−0.0101001	−	0.0233081i
$841$	−1.45078			−0.0500268
$842$	31.4166	−	18.1384i	1.08269	−	0.625089i
$843$	4.93396	−	8.54587i	0.169935	−	0.294336i
$844$	4.74473	−	8.21811i	0.163320	−	0.282879i
$845$	1.70096	+	2.94614i	0.0585147	+	0.101350i
$846$			9.30569i			0.319936i
$847$	−18.8858	−	14.0112i	−0.648924	−	0.481431i
$848$		−	9.99665i		−	0.343286i
$849$	−0.517982	+	0.299057i	−0.0177771	+	0.0102636i
$850$	−12.2534	+	21.2235i	−0.420289	+	0.727962i
$851$	0.895542	−	12.7820i	0.0306988	−	0.438161i
$852$	−0.862118	+	0.497744i	−0.0295357	+	0.0170524i
$853$		−	4.98034i		−	0.170524i	−0.996359	−	0.0852618i	$-0.972827\pi$
$853$		−	4.98034i		−	0.170524i	0.996359	−	0.0852618i	$-0.0271727\pi$
$854$	−0.602862	+	5.23327i	−0.0206295	+	0.179079i
$855$	−0.572902			−0.0195928
$856$	12.9046	−	7.45046i	0.441070	−	0.254652i
$857$	−37.7406	−	21.7896i	−1.28920	−	0.744318i	−0.310685	−	0.950513i	$-0.600558\pi$
$857$	−37.7406	−	21.7896i	−1.28920	−	0.744318i	−0.978511	+	0.206195i	$0.933892\pi$
$858$	−6.32100	−	3.64943i	−0.215795	−	0.124590i
$859$	−16.9065	+	9.76097i	−0.576842	+	0.333040i	−0.759877	−	0.650066i	$-0.774741\pi$
$859$	−16.9065	+	9.76097i	−0.576842	+	0.333040i	0.183035	+	0.983106i	$0.441408\pi$
$860$			1.90502i			0.0649605i
$861$	−0.911405	+	7.91164i	−0.0310606	+	0.269628i
$862$		−	1.16004i		−	0.0395112i
$863$	−4.74463	−	8.21794i	−0.161509	−	0.279742i	0.773901	−	0.633307i	$-0.218303\pi$
$863$	−4.74463	−	8.21794i	−0.161509	−	0.279742i	−0.935410	+	0.353565i	$0.884969\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	0.733161	+	0.423291i	0.0249282	+	0.0143923i
$866$	8.77422	+	15.1974i	0.298160	+	0.516429i
$867$			7.78515i			0.264398i
$868$	−0.940090	+	1.26715i	−0.0319087	+	0.0430100i
$869$	3.77354			0.128009
$870$	−1.26488	+	0.730280i	−0.0428835	+	0.0247588i
$871$	16.8576	−	29.1982i	0.571198	−	0.989344i
$872$	−11.0866	−	6.40085i	−0.375439	−	0.216760i
$873$	2.46616	+	4.27152i	0.0834669	+	0.144569i
$874$	−4.32714	−	8.87499i	−0.146368	−	0.300201i
$875$	−6.70302	+	2.90463i	−0.226603	+	0.0981944i
$876$	−15.9523			−0.538978
$877$	23.2436	+	40.2592i	0.784882	+	1.35946i	0.929069	+	0.369905i	$0.120610\pi$
$877$	23.2436	+	40.2592i	0.784882	+	1.35946i	−0.144187	+	0.989550i	$0.546057\pi$
$878$	−16.9006	−	9.75755i	−0.570367	−	0.329301i
$879$	20.4547	+	11.8095i	0.689918	+	0.398325i
$880$	−0.350213	+	0.202196i	−0.0118057	+	0.00681602i
$881$	16.8333			0.567127			0.283564	−	0.958953i	$-0.408483\pi$
$881$	16.8333			0.567127			0.283564	+	0.958953i	$0.408483\pi$
$882$	2.02991	+	6.69921i	0.0683508	+	0.225574i
$883$	−18.3341			−0.616993			−0.308497	−	0.951225i	$-0.599826\pi$
$883$	−18.3341			−0.616993			−0.308497	+	0.951225i	$0.599826\pi$
$884$	−21.6543	+	12.5021i	−0.728313	+	0.420492i
$885$	−0.386323	+	0.669132i	−0.0129861	+	0.0224926i
$886$	0.389410	−	0.674478i	0.0130825	−	0.0226595i
$887$	−29.8410	+	17.2287i	−1.00196	+	0.578483i	−0.908828	−	0.417171i	$-0.863022\pi$
$887$	−29.8410	+	17.2287i	−1.00196	+	0.578483i	−0.0931333	+	0.995654i	$0.529688\pi$
$888$	2.67177			0.0896586
$889$	−40.3741	+	17.4954i	−1.35410	+	0.586776i
$890$	2.13542			0.0715793
$891$	−1.25854	+	0.726620i	−0.0421628	+	0.0243427i
$892$	3.43137	+	1.98110i	0.114891	+	0.0663322i
$893$	−16.5918	−	9.57930i	−0.555225	−	0.320559i
$894$	8.99329	+	15.5768i	0.300781	+	0.520967i
$895$	5.50427			0.183987
$896$	2.12484	+	1.57640i	0.0709860	+	0.0526639i
$897$	10.5561	+	21.6506i	0.352458	+	0.722894i
$898$	12.5338	+	21.7091i	0.418257	+	0.724442i
$899$	2.71074	+	1.56505i	0.0904082	+	0.0521972i
$900$	−2.46128	+	4.26307i	−0.0820428	+	0.142102i
$901$	−43.1004	+	24.8840i	−1.43588	+	0.829006i
$902$	4.37439			0.145651
$903$	2.07284	−	17.9937i	0.0689797	−	0.598792i
$904$			16.8220i			0.559490i
$905$	−1.80333	−	3.12347i	−0.0599449	−	0.103828i
$906$	10.7889	+	6.22898i	0.358437	+	0.206944i
$907$	−16.6813	−	9.63096i	−0.553894	−	0.319791i	0.196797	−	0.980444i	$-0.436946\pi$
$907$	−16.6813	−	9.63096i	−0.553894	−	0.319791i	−0.750691	+	0.660653i	$0.770279\pi$
$908$	−9.70885	−	16.8162i	−0.322200	−	0.558066i
$909$			12.0164i			0.398559i
$910$	−3.67341	−	0.423169i	−0.121772	−	0.0140279i
$911$		−	20.0169i		−	0.663191i	−0.943422	−	0.331595i	$-0.892413\pi$
$911$		−	20.0169i		−	0.663191i	0.943422	−	0.331595i	$-0.107587\pi$
$912$	1.78298	−	1.02940i	0.0590403	−	0.0340869i
$913$	−10.7370	−	6.19903i	−0.355344	−	0.205158i
$914$	−13.3581	−	7.71230i	−0.441847	−	0.255100i
$915$	−0.479824	+	0.277027i	−0.0158625	+	0.00915822i
$916$	21.4855			0.709902
$917$	−12.9815	+	17.4979i	−0.428688	+	0.577831i
$918$			4.97847i			0.164314i
$919$	15.7091	−	9.06966i	0.518196	−	0.299181i	−0.218000	−	0.975949i	$-0.569953\pi$
$919$	15.7091	−	9.06966i	0.518196	−	0.299181i	0.736196	+	0.676768i	$0.236620\pi$
$920$	1.33127	+	0.0932723i	0.0438906	+	0.00307510i
$921$	−6.61269	+	11.4535i	−0.217895	+	0.377406i
$922$	7.08367	−	4.08976i	0.233288	−	0.134689i
$923$			4.99981i			0.164571i
$924$	3.52792	−	1.52876i	0.116060	−	0.0502925i
$925$		−	13.1519i		−	0.432433i
$926$	11.8053	+	20.4473i	0.387945	+	0.671940i
$927$	9.18802	−	15.9141i	0.301774	−	0.522688i
$928$	2.62437	−	4.54554i	0.0861491	−	0.149215i
$929$	−29.2612	+	16.8939i	−0.960028	+	0.554272i	−0.896182	−	0.443688i	$-0.853670\pi$
$929$	−29.2612	+	16.8939i	−0.960028	+	0.554272i	−0.0638460	+	0.997960i	$0.520337\pi$
$930$	−0.165946			−0.00544159
$931$	−14.0341	−	3.27690i	−0.459951	−	0.107396i
$932$	−4.26862			−0.139823
$933$	11.7382	+	20.3311i	0.384290	+	0.665610i
$934$	4.19554	−	7.26688i	0.137282	−	0.237780i
$935$	1.74353	+	1.00663i	0.0570194	+	0.0329202i
$936$	−4.34959	+	2.51124i	−0.142171	+	0.0820824i
$937$	37.0047			1.20889			0.604446	−	0.796646i	$-0.293395\pi$
$937$	37.0047			1.20889			0.604446	+	0.796646i	$0.293395\pi$
$938$	7.06171	+	16.2963i	0.230573	+	0.532094i
$939$		−	17.9043i		−	0.584285i
$940$	2.24256	−	1.29474i	0.0731442	−	0.0422298i
$941$	16.5258	−	28.6235i	0.538726	−	0.933101i	−0.460247	−	0.887791i	$-0.652239\pi$
$941$	16.5258	−	28.6235i	0.538726	−	0.933101i	0.998973	−	0.0453099i	$-0.0144275\pi$
$942$	−3.04247	−	1.75657i	−0.0991289	−	0.0572321i
$943$	−11.9668	−	8.07407i	−0.389693	−	0.262928i
$944$		−	2.77662i		−	0.0903712i
$945$	−0.438664	+	0.591278i	−0.0142697	+	0.0192343i
$946$	−9.94881			−0.323464
$947$	−15.7760	−	27.3249i	−0.512652	−	0.887940i	−0.999892	−	0.0146716i	$-0.995330\pi$
$947$	−15.7760	−	27.3249i	−0.512652	−	0.887940i	0.487240	−	0.873268i	$-0.338004\pi$
$948$	1.29832	−	2.24875i	0.0421674	−	0.0730361i
$949$	−40.0600	+	69.3860i	−1.30040	+	2.25236i
$950$	−5.06730	−	8.77683i	−0.164405	−	0.284758i
$951$		−	8.40588i		−	0.272579i
$952$	1.50739	−	13.0853i	0.0488549	−	0.424095i
$953$		−	44.6275i		−	1.44563i	−0.691043	−	0.722813i	$-0.742849\pi$
$953$		−	44.6275i		−	1.44563i	0.691043	−	0.722813i	$-0.257151\pi$
$954$	−8.65735	+	4.99832i	−0.280292	+	0.161827i
$955$	−1.80308	−	1.04101i	−0.0583464	−	0.0336863i
$956$	8.18054	−	14.1691i	0.264578	−	0.458262i
$957$	−3.81384	−	6.60576i	−0.123284	−	0.213534i
$958$	0.466489			0.0150716
$959$	8.72669	+	1.00530i	0.281799	+	0.0324627i
$960$			0.278269i			0.00898109i
$961$	−15.3222	−	26.5388i	−0.494264	−	0.856090i
$962$	6.70944	−	11.6211i	0.216321	−	0.374679i
$963$	−12.9046	−	7.45046i	−0.415844	−	0.240088i
$964$	4.89018	+	8.47005i	0.157502	+	0.272802i
$965$	3.80331			0.122433
$966$	−12.4729	−	2.32954i	−0.401309	−	0.0749517i
$967$	−43.5435			−1.40027			−0.700133	−	0.714013i	$-0.746876\pi$
$967$	−43.5435			−1.40027			−0.700133	+	0.714013i	$0.746876\pi$
$968$	4.44405	+	7.69731i	0.142837	+	0.247401i
$969$	−8.87650	−	5.12485i	−0.285154	−	0.164634i
$970$	0.686256	−	1.18863i	0.0220344	−	0.0381646i
$971$	10.1990	+	17.6651i	0.327300	+	0.566901i	0.981975	−	0.189010i	$-0.0605278\pi$
$971$	10.1990	+	17.6651i	0.327300	+	0.566901i	−0.654675	+	0.755911i	$0.727194\pi$
$972$			1.00000i			0.0320750i
$973$	3.56730	+	8.23227i	0.114363	+	0.263915i
$974$	25.0521			0.802721
$975$	12.3617	+	21.4112i	0.395892	+	0.685706i
$976$	0.995536	−	1.72432i	0.0318663	−	0.0551941i
$977$	12.5614	+	7.25231i	0.401874	+	0.232022i	0.687292	−	0.726381i	$-0.258799\pi$
$977$	12.5614	+	7.25231i	0.401874	+	0.232022i	−0.285418	+	0.958403i	$0.592133\pi$
$978$	−14.0887	+	8.13414i	−0.450508	+	0.260101i
$979$			11.1521i			0.356421i
$980$	1.33200	−	1.42128i	0.0425491	−	0.0454010i
$981$			12.8017i			0.408727i
$982$	1.07408	+	1.86036i	0.0342752	+	0.0593663i
$983$	−12.9159	+	22.3710i	−0.411954	+	0.713524i	−0.995103	−	0.0988402i	$-0.968487\pi$
$983$	−12.9159	+	22.3710i	−0.411954	+	0.713524i	0.583150	+	0.812365i	$0.301820\pi$
$984$	1.50505	−	2.60682i	0.0479792	−	0.0831023i
$985$	−3.12590	−	5.41421i	−0.0995994	−	0.172511i
$986$	−26.1307			−0.832170
$987$	−22.5907	+	9.78927i	−0.719071	+	0.311596i
$988$		−	10.3403i		−	0.328969i
$989$	27.2165	+	18.3631i	0.865434	+	0.583913i
$990$	0.350213	+	0.202196i	0.0111305	+	0.00642620i
$991$	−24.3217	+	42.1264i	−0.772605	+	1.33819i	0.163526	+	0.986539i	$0.447713\pi$
$991$	−24.3217	+	42.1264i	−0.772605	+	1.33819i	−0.936131	+	0.351652i	$0.885620\pi$
$992$	0.516456	−	0.298176i	0.0163975	−	0.00946709i
$993$			0.147641i			0.00468525i
$994$	−2.11525	−	1.56929i	−0.0670918	−	0.0497748i
$995$	6.27603			0.198964
$996$	−7.38834	+	4.26566i	−0.234108	+	0.135163i
$997$	32.1334	+	18.5522i	1.01767	+	0.587554i	0.913429	−	0.406997i	$-0.133424\pi$
$997$	32.1334	+	18.5522i	1.01767	+	0.587554i	0.104245	+	0.994552i	$0.466757\pi$
$998$	−17.7523	+	30.7479i	−0.561939	+	0.973307i
$999$	−1.33588	−	2.31382i	−0.0422655	−	0.0732059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.b.367.4	yes	32
7.5	odd	6	inner	966.2.k.b.229.5	yes	32
23.22	odd	2	inner	966.2.k.b.367.5	yes	32
161.68	even	6	inner	966.2.k.b.229.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.4	✓	32	161.68	even	6	inner
966.2.k.b.229.5	yes	32	7.5	odd	6	inner
966.2.k.b.367.4	yes	32	1.1	even	1	trivial
966.2.k.b.367.5	yes	32	23.22	odd	2	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.139134 - 0.240988i) q^{5} -1.00000i q^{6} +(2.42763 - 1.05197i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.139134 - 0.240988i) q^{5} -1.00000i q^{6} +(2.42763 - 1.05197i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.139134 - 0.240988i) q^{10} +(1.25854 + 0.726620i) q^{11} +(0.866025 - 0.500000i) q^{12} -5.02248i q^{13} +(2.12484 + 1.57640i) q^{14} +0.278269i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.48923 + 4.31148i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.02940 - 1.78298i) q^{19} +0.278269 q^{20} +(-2.62837 - 0.302783i) q^{21} +1.45324i q^{22} +(2.68233 - 3.97556i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.46128 - 4.26307i) q^{25} +(4.34959 - 2.51124i) q^{26} -1.00000i q^{27} +(-0.302783 + 2.62837i) q^{28} +5.24874 q^{29} +(-0.240988 + 0.139134i) q^{30} +(0.516456 + 0.298176i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.726620 - 1.25854i) q^{33} -4.97847 q^{34} +(-0.591278 - 0.438664i) q^{35} -1.00000 q^{36} +(2.31382 - 1.33588i) q^{37} +(1.02940 - 1.78298i) q^{38} +(-2.51124 + 4.34959i) q^{39} +(0.139134 + 0.240988i) q^{40} -3.01009i q^{41} +(-1.05197 - 2.42763i) q^{42} +6.84595i q^{43} +(-1.25854 + 0.726620i) q^{44} +(0.139134 - 0.240988i) q^{45} +(4.78410 + 0.335188i) q^{46} +(8.05896 - 4.65284i) q^{47} +1.00000i q^{48} +(4.78673 - 5.10756i) q^{49} +4.92257 q^{50} +(4.31148 - 2.48923i) q^{51} +(4.34959 + 2.51124i) q^{52} +(8.65735 + 4.99832i) q^{53} +(0.866025 - 0.500000i) q^{54} -0.404392i q^{55} +(-2.42763 + 1.05197i) q^{56} +2.05881i q^{57} +(2.62437 + 4.54554i) q^{58} +(2.40462 + 1.38831i) q^{59} +(-0.240988 - 0.139134i) q^{60} +(0.995536 + 1.72432i) q^{61} +0.596352i q^{62} +(2.12484 + 1.57640i) q^{63} +1.00000 q^{64} +(-1.21036 + 0.698800i) q^{65} +(0.726620 - 1.25854i) q^{66} +(5.81351 + 3.35643i) q^{67} +(-2.48923 - 4.31148i) q^{68} +(-4.31075 + 2.10177i) q^{69} +(0.0842550 - 0.731393i) q^{70} -0.995488 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-13.8151 - 7.97614i) q^{73} +(2.31382 + 1.33588i) q^{74} +(-4.26307 + 2.46128i) q^{75} +2.05881 q^{76} +(3.81965 + 0.440016i) q^{77} -5.02248 q^{78} +(2.24875 - 1.29832i) q^{79} +(-0.139134 + 0.240988i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.60682 - 1.50505i) q^{82} -8.53132 q^{83} +(1.57640 - 2.12484i) q^{84} +1.38535 q^{85} +(-5.92877 + 3.42298i) q^{86} +(-4.54554 - 2.62437i) q^{87} +(-1.25854 - 0.726620i) q^{88} +(3.83696 + 6.64582i) q^{89} +0.278269 q^{90} +(-5.28348 - 12.1927i) q^{91} +(2.10177 + 4.31075i) q^{92} +(-0.298176 - 0.516456i) q^{93} +(8.05896 + 4.65284i) q^{94} +(-0.286451 + 0.496147i) q^{95} +(-0.866025 + 0.500000i) q^{96} +4.93232 q^{97} +(6.81665 + 1.59165i) q^{98} +1.45324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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