LMFDB - Embedded newform 966.2.k.b.229.5

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			229.5
Character	$\chi$	$=$	966.229
Dual form			966.2.k.b.367.5

$q$-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} +(-4.78410 - 0.335188i) 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} +(-2.68233 + 3.97556i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.813514\pi$
$5$	0.139134	−	0.240988i	0.0622228	−	0.107773i	0.895459	+	0.445145i	$0.146848\pi$
$6$			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	$-0.736974\pi$
$11$	−1.25854	+	0.726620i	−0.379465	+	0.219084i	0.298120	+	0.954528i	$0.403640\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$			5.02248i			1.39298i	0.717564	+	0.696492i	$0.245257\pi$
$13$			5.02248i			1.39298i	−0.717564	+	0.696492i	$0.754743\pi$
$14$	−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	0.992251	+	0.124249i	$0.0396520\pi$
$17$	2.48923	+	4.31148i	0.603728	+	1.04569i	−0.388523	+	0.921439i	$0.627015\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.02940	−	1.78298i	0.236161	−	0.409043i	−0.723448	−	0.690379i	$-0.757444\pi$
$19$	1.02940	−	1.78298i	0.236161	−	0.409043i	0.959610	+	0.281335i	$0.0907773\pi$
$20$	−0.278269			−0.0622228
$21$	2.62837	−	0.302783i	0.573557	−	0.0660726i
$22$			1.45324i			0.309832i
$23$	−4.78410	−	0.335188i	−0.997555	−	0.0698914i
$23$	−4.78410	−	0.335188i	−0.997555	−	0.0698914i
$24$	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	−0.452903	−	0.891560i	$-0.649612\pi$
$31$	0.516456	−	0.298176i	0.0927582	−	0.0535540i	0.545662	+	0.838006i	$0.316278\pi$
$32$	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	$-0.403814\pi$
$37$	−2.31382	−	1.33588i	−0.380389	−	0.219618i	−0.677988	+	0.735073i	$0.737148\pi$
$38$	−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	$0.0755250\pi$
$41$			3.01009i			0.470098i	−0.971984	+	0.235049i	$0.924475\pi$
$42$	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
$46$	−2.68233	+	3.97556i	−0.395488	+	0.586165i
$47$	8.05896	+	4.65284i	1.17552	+	0.678687i	0.954974	−	0.296690i	$-0.0958827\pi$
$47$	8.05896	+	4.65284i	1.17552	+	0.678687i	0.220546	+	0.975377i	$0.429216\pi$
$48$		−	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	$-0.907552\pi$
$53$	−8.65735	+	4.99832i	−1.18918	+	0.686573i	−0.231059	+	0.972940i	$0.574219\pi$
$54$	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	−0.335238	−	0.942134i	$-0.608817\pi$
$59$	2.40462	−	1.38831i	0.313055	−	0.180742i	0.648293	+	0.761391i	$0.275483\pi$
$60$	0.240988	−	0.139134i	0.0311114	−	0.0179622i
$61$	−0.995536	+	1.72432i	−0.127465	+	0.220776i	−0.922694	−	0.385533i	$-0.874017\pi$
$61$	−0.995536	+	1.72432i	−0.127465	+	0.220776i	0.795229	+	0.606310i	$0.207351\pi$
$62$		−	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	$-0.801157\pi$
$67$	−5.81351	+	3.35643i	−0.710233	+	0.410053i	0.100914	+	0.994895i	$0.467823\pi$
$68$	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	−0.629226	+	0.777222i	$0.716628\pi$
$73$	−13.8151	+	7.97614i	−1.61693	+	0.933537i	−0.987707	+	0.156315i	$0.950039\pi$
$74$	−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	$-0.379997\pi$
$79$	−2.24875	−	1.29832i	−0.253005	−	0.146072i	−0.621139	+	0.783700i	$0.713330\pi$
$80$	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	$-0.344897\pi$
$83$	8.53132			0.936434			0.468217	+	0.883614i	$0.344897\pi$
$84$	−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	$-0.966660\pi$
$89$	−3.83696	+	6.64582i	−0.406717	+	0.704455i	0.587802	+	0.809005i	$0.299993\pi$
$90$	−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	$-0.580562\pi$
$97$	−4.93232			−0.500802			−0.250401	+	0.968142i	$0.580562\pi$
$98$	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	0.116935	−	0.993140i	$-0.462693\pi$
$101$	10.4065	−	6.00820i	1.03549	−	0.597838i	0.918552	+	0.395301i	$0.129360\pi$
$102$	−4.31148	+	2.48923i	−0.426900	+	0.246471i
$103$	9.18802	−	15.9141i	0.905322	−	1.56806i	0.0848386	−	0.996395i	$-0.472963\pi$
$103$	9.18802	−	15.9141i	0.905322	−	1.56806i	0.820484	−	0.571670i	$-0.193704\pi$
$104$		−	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	$-0.0773542\pi$
$107$	12.9046	+	7.45046i	1.24753	+	0.720264i	0.276916	+	0.960894i	$0.410688\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−11.0866	+	6.40085i	−1.06190	+	0.613090i	−0.925958	−	0.377627i	$-0.876740\pi$
$109$	−11.0866	+	6.40085i	−1.06190	+	0.613090i	−0.135945	+	0.990716i	$0.543407\pi$
$110$	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
$115$	−0.746410	+	1.10628i	−0.0696031	+	0.103161i
$116$	−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	0.154978	−	0.987918i	$-0.450469\pi$
$131$	−7.13164	−	4.11746i	−0.623094	−	0.359744i	−0.778073	+	0.628174i	$0.783803\pi$
$132$	−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	$-0.711966\pi$
$137$	−2.87537	+	1.66010i	−0.245659	+	0.141832i	0.372116	+	0.928186i	$0.378632\pi$
$138$	0.335188	−	4.78410i	0.0285331	−	0.407250i
$139$		−	3.39108i		−	0.287628i	−0.989605	−	0.143814i	$-0.954063\pi$
$139$		−	3.39108i		−	0.287628i	0.989605	−	0.143814i	$-0.0459366\pi$
$140$	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	$-0.0696885\pi$
$149$	15.5768	+	8.99329i	1.27610	+	0.736759i	0.299974	+	0.953947i	$0.403022\pi$
$150$	−4.26307	+	2.46128i	−0.348078	+	0.200963i
$151$	−6.22898	−	10.7889i	−0.506907	−	0.877988i	−0.999968	−	0.00799384i	$-0.997455\pi$
$151$	−6.22898	−	10.7889i	−0.506907	−	0.877988i	0.493061	−	0.869995i	$-0.335878\pi$
$152$	−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	$-0.211438\pi$
$157$	−1.75657	−	3.04247i	−0.140189	−	0.242815i	−0.927568	+	0.373655i	$0.878104\pi$
$158$	−2.24875	+	1.29832i	−0.178901	+	0.103289i
$159$	4.99832	−	8.65735i	0.396393	−	0.686573i
$160$	0.278269			0.0219991
$161$	11.2614	+	5.84643i	0.887523	+	0.460763i
$162$	−1.00000			−0.0785674
$163$	−8.13414	+	14.0887i	−0.637115	+	1.10352i	0.348948	+	0.937142i	$0.386539\pi$
$163$	−8.13414	+	14.0887i	−0.637115	+	1.10352i	−0.986063	+	0.166373i	$0.946794\pi$
$164$	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	$-0.976710\pi$
$167$		−	1.88937i		−	0.146204i	0.997324	−	0.0731019i	$-0.0232898\pi$
$168$	−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	0.396488	−	0.918040i	$-0.370229\pi$
$173$	−2.63472	−	1.52116i	−0.200314	−	0.115652i	−0.596802	+	0.802388i	$0.703562\pi$
$174$			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	−0.952843	−	0.303463i	$-0.901857\pi$
$179$	−9.89020	−	17.1303i	−0.739228	−	1.28038i	0.213615	−	0.976918i	$-0.431476\pi$
$180$	−0.139134	+	0.240988i	−0.0103705	+	0.0179622i
$181$	−12.9611			−0.963390			−0.481695	−	0.876339i	$-0.659979\pi$
$181$	−12.9611			−0.963390			−0.481695	+	0.876339i	$0.659979\pi$
$182$	−7.91744	−	10.6720i	−0.586880	−	0.791059i
$183$		−	1.99107i		−	0.147184i
$184$	4.78410	+	0.335188i	0.352689	+	0.0247104i
$185$	−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	$-0.420585\pi$
$191$	−6.47964	−	3.74102i	−0.468850	−	0.270691i	−0.715758	+	0.698348i	$0.753919\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−6.83388	−	11.8366i	−0.491914	−	0.852019i	0.508043	−	0.861332i	$-0.330369\pi$
$193$	−6.83388	−	11.8366i	−0.491914	−	0.852019i	−0.999957	+	0.00931234i	$0.997036\pi$
$194$	−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	0.920008	+	0.391901i	$0.128182\pi$
$199$	11.2769	+	19.5322i	0.799400	+	1.38460i	−0.120608	+	0.992700i	$0.538484\pi$
$200$	−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
$207$	−2.68233	+	3.97556i	−0.186435	+	0.276321i
$208$	−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	$0.0423533\pi$
$223$			3.96221i			0.265329i	−0.991161	+	0.132664i	$0.957647\pi$
$224$	−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	0.984440	+	0.175721i	$0.0562257\pi$
$227$	9.70885	+	16.8162i	0.644399	+	1.11613i	−0.340041	+	0.940411i	$0.610441\pi$
$228$	1.78298	−	1.02940i	0.118081	−	0.0681739i
$229$	10.7428	−	18.6070i	0.709902	−	1.22959i	−0.254992	−	0.966943i	$-0.582073\pi$
$229$	10.7428	−	18.6070i	0.709902	−	1.22959i	0.964893	−	0.262642i	$-0.0845940\pi$
$230$	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	−0.787606	−	0.616179i	$-0.788680\pi$
$233$	2.13431	−	3.69673i	0.139823	−	0.242181i	0.927430	+	0.373998i	$0.122013\pi$
$234$	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	$-0.268673\pi$
$241$	−4.89018	−	8.47005i	−0.315004	−	0.545604i	−0.979438	+	0.201743i	$0.935339\pi$
$242$	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	$-0.360184\pi$
$251$	13.4746			0.850510			0.425255	+	0.905074i	$0.360184\pi$
$252$	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	0.940614	−	0.339477i	$-0.110250\pi$
$257$	17.9057	+	10.3379i	1.11693	+	0.644858i	0.176312	+	0.984334i	$0.443583\pi$
$258$	−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	$-0.951635\pi$
$263$	−21.9199	+	12.6554i	−1.35164	+	0.780368i	−0.363158	+	0.931728i	$0.618302\pi$
$264$	−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	−0.448632	−	0.893716i	$-0.648089\pi$
$269$	1.65705	−	0.956701i	0.101032	−	0.0583311i	0.549665	+	0.835385i	$0.314755\pi$
$270$	0.240988	−	0.139134i	0.0146661	−	0.00846745i
$271$	16.2938	+	9.40723i	0.989778	+	0.571448i	0.905208	−	0.424969i	$-0.139715\pi$
$271$	16.2938	+	9.40723i	0.989778	+	0.571448i	0.0845698	+	0.996418i	$0.473048\pi$
$272$	−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
$276$	−3.97556	−	2.68233i	−0.239301	−	0.161457i
$277$	−2.82129	−	4.88662i	−0.169515	−	0.293609i	0.768734	−	0.639568i	$-0.220887\pi$
$277$	−2.82129	−	4.88662i	−0.169515	−	0.293609i	−0.938249	+	0.345959i	$0.887553\pi$
$278$	−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	$-0.172326\pi$
$283$	−0.299057	−	0.517982i	−0.0177771	−	0.0307908i	−0.874777	+	0.484526i	$0.838992\pi$
$284$	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	$-0.257646\pi$
$293$	23.6190			1.37984			0.689918	+	0.723887i	$0.257646\pi$
$294$	−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
$299$	1.68347	−	24.0281i	0.0973577	−	1.38958i
$300$			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	$0.123184\pi$
$307$			13.2254i			0.754812i	−0.926048	+	0.377406i	$0.876816\pi$
$308$	−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	−0.949585	−	0.313510i	$-0.898495\pi$
$311$	−20.3311	+	11.7382i	−1.15287	+	0.665610i	−0.203285	+	0.979120i	$0.565162\pi$
$312$	2.51124	+	4.34959i	0.142171	+	0.246247i
$313$	−8.95215	+	15.5056i	−0.506006	+	0.876427i	0.493970	+	0.869479i	$0.335545\pi$
$313$	−8.95215	+	15.5056i	−0.506006	+	0.876427i	−0.999976	+	0.00694863i	$0.997788\pi$
$314$	−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	−0.723520	−	0.690304i	$-0.757477\pi$
$317$	4.20294	−	7.27971i	0.236061	−	0.408869i	0.959580	+	0.281435i	$0.0908103\pi$
$318$	−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
$322$	10.6939	−	6.82945i	0.595945	−	0.380590i
$323$	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	−0.868047	−	0.496482i	$-0.834625\pi$
$331$	−0.0738206	+	0.127861i	−0.00405755	+	0.00702787i	0.863990	+	0.503510i	$0.167958\pi$
$332$	−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
$345$	0.0932723	−	1.33127i	0.00502161	−	0.0716730i
$346$	−2.63472	+	1.52116i	−0.141644	+	0.0817780i
$347$	−3.99997	−	6.92816i	−0.214730	−	0.371923i	0.738459	−	0.674298i	$-0.235554\pi$
$347$	−3.99997	−	6.92816i	−0.214730	−	0.371923i	−0.953189	+	0.302375i	$0.902220\pi$
$348$	4.54554	+	2.62437i	0.243666	+	0.140681i
$349$		−	33.9485i		−	1.81722i	−0.417642	−	0.908612i	$-0.637143\pi$
$349$		−	33.9485i		−	1.81722i	0.417642	−	0.908612i	$-0.362857\pi$
$350$	−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	0.00951850	−	0.999955i	$-0.496970\pi$
$353$	16.5387	−	9.54860i	0.880264	−	0.508221i	0.870745	+	0.491734i	$0.163637\pi$
$354$	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	$-0.178163\pi$
$359$	15.3719	+	8.87498i	0.811298	+	0.468403i	−0.0361083	+	0.999348i	$0.511496\pi$
$360$	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	$-0.154151\pi$
$367$	0.753044	+	1.30431i	0.0393086	+	0.0680845i	−0.845702	+	0.533656i	$0.820818\pi$
$368$	2.68233	−	3.97556i	0.139826	−	0.207240i
$369$	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	$-0.178385\pi$
$373$	15.6481	+	9.03445i	0.810230	+	0.467786i	−0.0368060	+	0.999322i	$0.511718\pi$
$374$	−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	$-0.827473\pi$
$383$	0.360283	−	0.624029i	0.0184096	−	0.0318864i	0.875083	+	0.483972i	$0.160806\pi$
$384$			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	$-0.533479\pi$
$389$	13.8804	−	8.01386i	0.703764	−	0.406319i	0.808748	+	0.588155i	$0.200146\pi$
$390$	−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	0.809987	−	0.586448i	$-0.199474\pi$
$397$	14.0889	+	8.13423i	0.707101	+	0.408245i	−0.102886	+	0.994693i	$0.532808\pi$
$398$	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	$-0.382874\pi$
$401$	−5.37637	−	3.10405i	−0.268483	−	0.155009i	−0.628198	+	0.778053i	$0.716207\pi$
$402$	−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	0.000457799	−	1.00000i	$-0.499854\pi$
$409$	17.5282	−	10.1199i	0.866712	−	0.500396i	0.866254	+	0.499603i	$0.166521\pi$
$410$	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	$-0.430164\pi$
$419$	8.90997			0.435281			0.217640	+	0.976029i	$0.430164\pi$
$420$	−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	$-0.657772\pi$
$431$	1.00463	−	0.580021i	0.0483911	−	0.0279386i	0.524000	+	0.851718i	$0.324439\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−17.5484			−0.843325			−0.421662	−	0.906753i	$-0.638553\pi$
$433$	−17.5484			−0.843325			−0.421662	+	0.906753i	$0.638553\pi$
$434$	−0.627342	+	1.44772i	−0.0301134	+	0.0694927i
$435$			1.46056i			0.0700285i
$436$	11.0866	+	6.40085i	0.530951	+	0.306545i
$437$	−5.52240	+	8.18491i	−0.264172	+	0.391537i
$438$	−7.97614	−	13.8151i	−0.381115	−	0.660110i
$439$	−16.9006	−	9.75755i	−0.806620	−	0.465702i	0.0391606	−	0.999233i	$-0.487532\pi$
$439$	−16.9006	−	9.75755i	−0.806620	−	0.465702i	−0.845781	+	0.533531i	$0.820865\pi$
$440$		−	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	−0.875128	−	0.483892i	$-0.839223\pi$
$443$	−0.389410	+	0.674478i	−0.0185014	+	0.0320454i	0.856626	+	0.515937i	$0.172556\pi$
$444$	−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	$-0.215849\pi$
$457$	13.3581	+	7.71230i	0.624866	+	0.360766i	−0.153895	+	0.988087i	$0.549182\pi$
$458$	−10.7428	−	18.6070i	−0.501976	−	0.869448i
$459$	−4.31148	+	2.48923i	−0.201243	+	0.116188i
$460$	1.33127	+	0.0932723i	0.0620707	+	0.00434884i
$461$			8.17952i			0.380958i	0.981691	+	0.190479i	$0.0610042\pi$
$461$			8.17952i			0.380958i	−0.981691	+	0.190479i	$0.938996\pi$
$462$	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	$-0.771140\pi$
$467$	4.19554	−	7.26688i	0.194146	−	0.336271i	0.946620	+	0.322351i	$0.104473\pi$
$468$		−	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	$-0.170059\pi$
$479$	−0.233245	−	0.403992i	−0.0106572	−	0.0184589i	−0.871305	+	0.490742i	$0.836726\pi$
$480$	−0.240988	+	0.139134i	−0.0109995	+	0.00635059i
$481$	6.70944	−	11.6211i	0.305924	−	0.529876i
$482$	−9.78037			−0.445483
$483$	−12.6759	+	0.567548i	−0.576772	+	0.0258243i
$484$	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	0.996802	+	0.0799156i	$0.0254651\pi$
$487$	12.5261	+	21.6958i	0.567610	+	0.983129i	−0.429192	+	0.903213i	$0.641202\pi$
$488$	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	−0.128327	−	0.991732i	$-0.540961\pi$
$499$	17.7523	−	30.7479i	0.794702	−	1.37646i	0.923029	−	0.384732i	$-0.125706\pi$
$500$	−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	$-0.717173\pi$
$503$	−28.2838			−1.26111			−0.630556	+	0.776144i	$0.717173\pi$
$504$	2.12484	−	1.57640i	0.0946480	−	0.0702185i
$505$		−	3.34379i		−	0.148797i
$506$	0.487108	−	6.95245i	0.0216546	−	0.309074i
$507$	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	−0.0575113	−	0.998345i	$-0.518317\pi$
$509$	−21.4524	−	12.3855i	−0.950859	−	0.548979i	−0.893348	+	0.449366i	$0.851650\pi$
$510$			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	0.816194	+	0.577778i	$0.196080\pi$
$521$	20.7362	+	35.9161i	0.908467	+	1.57351i	0.0922736	+	0.995734i	$0.470587\pi$
$522$	−2.62437	−	4.54554i	−0.114865	−	0.198953i
$523$	−13.2843	+	23.0090i	−0.580880	+	1.00611i	0.414495	+	0.910051i	$0.363958\pi$
$523$	−13.2843	+	23.0090i	−0.580880	+	1.00611i	−0.995375	+	0.0960622i	$0.969375\pi$
$524$			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
$529$	22.7753	+	3.20714i	0.990230	+	0.139441i
$530$	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	−0.929012	−	0.370050i	$-0.879341\pi$
$541$	−3.35014	+	5.80261i	−0.144034	+	0.249474i	0.784978	+	0.619523i	$0.212674\pi$
$542$	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	$-0.769878\pi$
$557$	−13.0235	+	7.51910i	−0.551822	+	0.318595i	0.198034	+	0.980195i	$0.436544\pi$
$558$	−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	0.986266	+	0.165163i	$0.0528151\pi$
$563$	15.0948	+	26.1449i	0.636169	+	1.10188i	−0.350098	+	0.936713i	$0.613852\pi$
$564$	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	$-0.293712\pi$
$569$	5.12949	+	2.96151i	0.215039	+	0.124153i	−0.388612	+	0.921402i	$0.627045\pi$
$570$	0.496147	−	0.286451i	0.0207813	−	0.0119981i
$571$	−9.92289	+	5.72898i	−0.415260	+	0.239750i	−0.693047	−	0.720892i	$-0.743732\pi$
$571$	−9.92289	+	5.72898i	−0.415260	+	0.239750i	0.277787	+	0.960643i	$0.410399\pi$
$572$	−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	−0.581184	−	0.813772i	$-0.697410\pi$
$577$	−4.01217	+	2.31643i	−0.167029	+	0.0964342i	0.414155	+	0.910206i	$0.364077\pi$
$578$	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	$-0.812915\pi$
$587$		−	26.8682i		−	1.10897i	0.832194	−	0.554485i	$-0.187085\pi$
$588$	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	0.873042	−	0.487645i	$-0.162144\pi$
$593$	21.6059	+	12.4742i	0.887250	+	0.512254i	0.0142078	+	0.999899i	$0.495477\pi$
$594$	−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
$598$	−19.9672	−	13.4720i	−0.816518	−	0.550909i
$599$	−12.9076	−	22.3566i	−0.527390	−	0.913466i	−0.999490	−	0.0319215i	$-0.989837\pi$
$599$	−12.9076	−	22.3566i	−0.527390	−	0.913466i	0.472100	−	0.881545i	$-0.343496\pi$
$600$	4.26307	+	2.46128i	0.174039	+	0.100481i
$601$			8.13523i			0.331843i	0.986139	+	0.165921i	$0.0530598\pi$
$601$			8.13523i			0.331843i	−0.986139	+	0.165921i	$0.946940\pi$
$602$	−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	0.984918	−	0.173023i	$-0.0553534\pi$
$607$	32.7070	+	18.8834i	1.32753	+	0.766452i	0.342617	+	0.939475i	$0.388687\pi$
$608$	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	$-0.522061\pi$
$613$	18.8185	−	10.8648i	0.760070	−	0.438827i	0.829321	+	0.558772i	$0.188727\pi$
$614$	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	$-0.0749524\pi$
$619$	7.06979	+	12.2452i	0.284159	+	0.492177i	−0.688246	+	0.725477i	$0.741619\pi$
$620$	−0.143714	+	0.0829731i	−0.00577168	+	0.00333228i
$621$	0.335188	−	4.78410i	0.0134506	−	0.191979i
$622$			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	$-0.831686\pi$
$641$	−21.7291	+	12.5453i	−0.858249	+	0.495510i	0.00517640	+	0.999987i	$0.498352\pi$
$642$	−7.45046	+	12.9046i	−0.294046	+	0.509303i
$643$	−35.3614			−1.39452			−0.697259	−	0.716819i	$-0.745597\pi$
$643$	−35.3614			−1.39452			−0.697259	+	0.716819i	$0.745597\pi$
$644$	−0.567548	−	12.6759i	−0.0223645	−	0.499500i
$645$	−1.90502			−0.0750099
$646$	5.12485	−	8.87650i	0.201635	−	0.349241i
$647$	−34.5265	+	19.9339i	−1.35738	+	0.783682i	−0.989270	−	0.146101i	$-0.953327\pi$
$647$	−34.5265	+	19.9339i	−1.35738	+	0.783682i	−0.368107	+	0.929783i	$0.619994\pi$
$648$	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	−0.764275	−	0.644890i	$-0.776903\pi$
$653$	4.50651	−	7.80550i	0.176353	−	0.305453i	0.940629	+	0.339437i	$0.110237\pi$
$654$	−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	0.999015	+	0.0443825i	$0.0141320\pi$
$661$	13.8305	+	23.9551i	0.537944	+	0.931746i	−0.461071	+	0.887363i	$0.652535\pi$
$662$	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
$667$	−25.1105	−	1.75931i	−0.972282	−	0.0681208i
$668$	−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	$-0.736532\pi$
$677$	7.79131	−	13.4950i	0.299445	−	0.518653i	0.976009	+	0.217730i	$0.0698653\pi$
$678$	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	−0.999546	−	0.0301361i	$-0.990406\pi$
$683$	−13.7433	−	23.8040i	−0.525872	−	0.910836i	0.473674	−	0.880700i	$-0.342927\pi$
$684$	−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
$690$	−1.10628	−	0.746410i	−0.0421152	−	0.0284153i
$691$	2.01095	+	1.16102i	0.0765002	+	0.0441674i	0.537762	−	0.843097i	$-0.319270\pi$
$691$	2.01095	+	1.16102i	0.0765002	+	0.0441674i	−0.461262	+	0.887264i	$0.652603\pi$
$692$			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	$-0.660901\pi$
$709$	−39.5163	−	22.8148i	−1.48407	−	0.856827i	−0.999836	+	0.0181134i	$0.994234\pi$
$710$	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	0.412026	−	0.911172i	$-0.364821\pi$
$719$	−4.58681	−	2.64820i	−0.171059	−	0.0987611i	−0.583085	+	0.812411i	$0.698155\pi$
$720$	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	$-0.791052\pi$
$727$	−42.7188			−1.58435			−0.792177	+	0.610292i	$0.791052\pi$
$728$	−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	$-0.899737\pi$
$733$	−5.60709	+	9.71177i	−0.207103	+	0.358712i	0.743698	+	0.668516i	$0.233070\pi$
$734$	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	0.991529	+	0.129884i	$0.0414605\pi$
$739$	16.5349	+	28.6394i	0.608247	+	1.05352i	−0.383282	+	0.923631i	$0.625206\pi$
$740$	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	0.997683	+	0.0680307i	$0.0216716\pi$
$751$	42.6259	+	24.6101i	1.55544	+	0.898034i	0.557758	+	0.830004i	$0.311662\pi$
$752$	−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
$759$	−3.89807	+	5.77745i	−0.141491	+	0.209708i
$760$	0.286451	+	0.496147i	0.0103907	+	0.0179972i
$761$	−1.60034	−	0.923955i	−0.0580122	−	0.0334934i	0.470713	−	0.882286i	$-0.343997\pi$
$761$	−1.60034	−	0.923955i	−0.0580122	−	0.0334934i	−0.528726	+	0.848793i	$0.677330\pi$
$762$		−	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	$-0.228736\pi$
$769$	41.7478			1.50546			0.752732	+	0.658327i	$0.228736\pi$
$770$	−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	$-0.0127508\pi$
$773$	12.9260	+	22.3886i	0.464917	+	0.805260i	−0.534281	+	0.845307i	$0.679417\pi$
$774$	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
$782$	−23.8175	−	1.66872i	−0.851712	−	0.0596733i
$783$			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	$-0.00255080\pi$
$787$	13.8316	+	23.9571i	0.493044	+	0.853977i	−0.506924	+	0.861991i	$0.669217\pi$
$788$	−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	$-0.223821\pi$
$797$	43.0699			1.52561			0.762807	+	0.646626i	$0.223821\pi$
$798$	−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
$805$	2.97577	−	1.90042i	0.104882	−	0.0669811i
$806$	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	0.795177	−	0.606378i	$-0.207378\pi$
$809$	−3.62789	−	6.28369i	−0.127550	−	0.220923i	−0.922727	+	0.385455i	$0.874045\pi$
$810$	−0.139134	+	0.240988i	−0.00488869	+	0.00846745i
$811$		−	19.3552i		−	0.679652i	−0.940488	−	0.339826i	$-0.889632\pi$
$811$		−	19.3552i		−	0.679652i	0.940488	−	0.339826i	$-0.110368\pi$
$812$	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	−0.737114	−	0.675768i	$-0.763812\pi$
$821$	6.20841	−	10.7533i	0.216675	−	0.375292i	0.953789	+	0.300476i	$0.0971455\pi$
$822$	−1.66010	−	2.87537i	−0.0579025	−	0.100290i
$823$	−1.89373	−	3.28004i	−0.0660113	−	0.114335i	0.831131	−	0.556077i	$-0.187694\pi$
$823$	−1.89373	−	3.28004i	−0.0660113	−	0.114335i	−0.897142	+	0.441742i	$0.854361\pi$
$824$	−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	$-0.403669\pi$
$828$	4.78410	+	0.335188i	0.166259	+	0.0116486i
$829$	−4.52448	+	2.61221i	−0.157142	+	0.0907258i	−0.576509	−	0.817091i	$-0.695585\pi$
$829$	−4.52448	+	2.61221i	−0.157142	+	0.0907258i	0.419367	+	0.907817i	$0.362252\pi$
$830$	−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	$-0.225722\pi$
$839$	43.9656			1.51786			0.758930	+	0.651172i	$0.225722\pi$
$840$	−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
$851$	10.6218	+	7.16656i	0.364110	+	0.245667i
$852$	−0.862118	−	0.497744i	−0.0295357	−	0.0170524i
$853$			4.98034i			0.170524i	0.996359	+	0.0852618i	$0.0271727\pi$
$853$			4.98034i			0.170524i	−0.996359	+	0.0852618i	$0.972827\pi$
$854$	−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	−0.978511	−	0.206195i	$-0.933892\pi$
$857$	−37.7406	+	21.7896i	−1.28920	+	0.744318i	−0.310685	+	0.950513i	$0.600558\pi$
$858$	6.32100	−	3.64943i	0.215795	−	0.124590i
$859$	−16.9065	−	9.76097i	−0.576842	−	0.333040i	0.183035	−	0.983106i	$-0.441408\pi$
$859$	−16.9065	−	9.76097i	−0.576842	−	0.333040i	−0.759877	+	0.650066i	$0.774741\pi$
$860$		−	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	−0.935410	−	0.353565i	$-0.884969\pi$
$863$	−4.74463	+	8.21794i	−0.161509	+	0.279742i	0.773901	+	0.633307i	$0.218303\pi$
$864$	−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	−0.144187	−	0.989550i	$-0.546057\pi$
$877$	23.2436	−	40.2592i	0.784882	−	1.35946i	0.929069	−	0.369905i	$-0.120610\pi$
$878$	−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	$-0.591517\pi$
$881$	−16.8333			−0.567127			−0.283564	+	0.958953i	$0.591517\pi$
$882$	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	−0.0931333	−	0.995654i	$-0.529688\pi$
$887$	−29.8410	−	17.2287i	−1.00196	−	0.578483i	−0.908828	+	0.417171i	$0.863022\pi$
$888$	−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	$-0.563054\pi$
$907$	16.6813	−	9.63096i	0.553894	−	0.319791i	0.750691	+	0.660653i	$0.229721\pi$
$908$	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	$-0.430047\pi$
$919$	−15.7091	−	9.06966i	−0.518196	−	0.299181i	−0.736196	+	0.676768i	$0.763380\pi$
$920$	0.746410	−	1.10628i	0.0246084	−	0.0364728i
$921$	−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	−0.0638460	−	0.997960i	$-0.520337\pi$
$929$	−29.2612	−	16.8939i	−0.960028	−	0.554272i	−0.896182	+	0.443688i	$0.853670\pi$
$930$	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	$-0.706605\pi$
$937$	−37.0047			−1.20889			−0.604446	+	0.796646i	$0.706605\pi$
$938$	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	−0.998973	−	0.0453099i	$-0.985572\pi$
$941$	−16.5258	−	28.6235i	−0.538726	−	0.933101i	0.460247	−	0.887791i	$-0.347761\pi$
$942$	3.04247	−	1.75657i	0.0991289	−	0.0572321i
$943$	1.00895	−	14.4006i	0.0328558	−	0.468948i
$944$			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	0.487240	+	0.873268i	$0.338004\pi$
$947$	−15.7760	+	27.3249i	−0.512652	+	0.887940i	−0.999892	+	0.0146716i	$0.995330\pi$
$948$	−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
$966$	−5.84643	+	11.2614i	−0.188106	+	0.362330i
$967$	−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	$-0.939472\pi$
$971$	−10.1990	+	17.6651i	−0.327300	+	0.566901i	0.654675	+	0.755911i	$0.272806\pi$
$972$		−	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	$-0.741201\pi$
$977$	−12.5614	+	7.25231i	−0.401874	+	0.232022i	0.285418	+	0.958403i	$0.407867\pi$
$978$	−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	$-0.0315133\pi$
$983$	12.9159	+	22.3710i	0.411954	+	0.713524i	−0.583150	+	0.812365i	$0.698180\pi$
$984$	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
$989$	2.29468	−	32.7517i	0.0729665	−	1.04144i
$990$	0.350213	−	0.202196i	0.0111305	−	0.00642620i
$991$	−24.3217	−	42.1264i	−0.772605	−	1.33819i	−0.936131	−	0.351652i	$-0.885620\pi$
$991$	−24.3217	−	42.1264i	−0.772605	−	1.33819i	0.163526	−	0.986539i	$-0.447713\pi$
$992$	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	0.104245	−	0.994552i	$-0.466757\pi$
$997$	32.1334	−	18.5522i	1.01767	−	0.587554i	0.913429	+	0.406997i	$0.133424\pi$
$998$	−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.229.5	yes	32
7.3	odd	6	inner	966.2.k.b.367.4	yes	32
23.22	odd	2	inner	966.2.k.b.229.4	✓	32
161.45	even	6	inner	966.2.k.b.367.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.4	✓	32	23.22	odd	2	inner
966.2.k.b.229.5	yes	32	1.1	even	1	trivial
966.2.k.b.367.4	yes	32	7.3	odd	6	inner
966.2.k.b.367.5	yes	32	161.45	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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} +(-4.78410 - 0.335188i) 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} +(-2.68233 + 3.97556i) 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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