LMFDB - Embedded newform 966.2.h.a.827.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (of order $2$, degree $1$, 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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.10
Character	$\chi$	$=$	966.827
Dual form			966.2.h.a.827.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.55095 - 0.771068i) q^{3} -1.00000 q^{4} +2.18892 q^{5} +(-0.771068 - 1.55095i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(1.81091 - 2.39178i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.55095 - 0.771068i) q^{3} -1.00000 q^{4} +2.18892 q^{5} +(-0.771068 - 1.55095i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(1.81091 - 2.39178i) q^{9} -2.18892i q^{10} +0.121613 q^{11} +(-1.55095 + 0.771068i) q^{12} -5.51136 q^{13} +1.00000 q^{14} +(3.39491 - 1.68781i) q^{15} +1.00000 q^{16} +6.85016 q^{17} +(-2.39178 - 1.81091i) q^{18} -5.61876i q^{19} -2.18892 q^{20} +(0.771068 + 1.55095i) q^{21} -0.121613i q^{22} +(2.15811 - 4.28282i) q^{23} +(0.771068 + 1.55095i) q^{24} -0.208628 q^{25} +5.51136i q^{26} +(0.964405 - 5.10587i) q^{27} -1.00000i q^{28} -4.75300i q^{29} +(-1.68781 - 3.39491i) q^{30} +6.85642 q^{31} -1.00000i q^{32} +(0.188616 - 0.0937719i) q^{33} -6.85016i q^{34} +2.18892i q^{35} +(-1.81091 + 2.39178i) q^{36} +6.93548i q^{37} -5.61876 q^{38} +(-8.54785 + 4.24963i) q^{39} +2.18892i q^{40} +3.19205i q^{41} +(1.55095 - 0.771068i) q^{42} +1.82564i q^{43} -0.121613 q^{44} +(3.96393 - 5.23542i) q^{45} +(-4.28282 - 2.15811i) q^{46} +2.93340i q^{47} +(1.55095 - 0.771068i) q^{48} -1.00000 q^{49} +0.208628i q^{50} +(10.6243 - 5.28194i) q^{51} +5.51136 q^{52} +10.6872 q^{53} +(-5.10587 - 0.964405i) q^{54} +0.266201 q^{55} -1.00000 q^{56} +(-4.33245 - 8.71443i) q^{57} -4.75300 q^{58} +4.63693i q^{59} +(-3.39491 + 1.68781i) q^{60} -3.29609i q^{61} -6.85642i q^{62} +(2.39178 + 1.81091i) q^{63} -1.00000 q^{64} -12.0639 q^{65} +(-0.0937719 - 0.188616i) q^{66} +7.80455i q^{67} -6.85016 q^{68} +(0.0447773 - 8.30650i) q^{69} +2.18892 q^{70} +8.83434i q^{71} +(2.39178 + 1.81091i) q^{72} -14.3724 q^{73} +6.93548 q^{74} +(-0.323572 + 0.160867i) q^{75} +5.61876i q^{76} +0.121613i q^{77} +(4.24963 + 8.54785i) q^{78} -4.84656i q^{79} +2.18892 q^{80} +(-2.44123 - 8.66259i) q^{81} +3.19205 q^{82} -6.52137 q^{83} +(-0.771068 - 1.55095i) q^{84} +14.9945 q^{85} +1.82564 q^{86} +(-3.66489 - 7.37167i) q^{87} +0.121613i q^{88} -13.9682 q^{89} +(-5.23542 - 3.96393i) q^{90} -5.51136i q^{91} +(-2.15811 + 4.28282i) q^{92} +(10.6340 - 5.28677i) q^{93} +2.93340 q^{94} -12.2990i q^{95} +(-0.771068 - 1.55095i) q^{96} +4.32736i q^{97} +1.00000i q^{98} +(0.220230 - 0.290872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.55095	−	0.771068i	0.895443	−	0.445176i
$3$	1.55095	−	0.771068i	0.895443	−	0.445176i
$4$	−1.00000			−0.500000
$5$	2.18892			0.978915			0.489457	−	0.872027i	$-0.337195\pi$
$5$	2.18892			0.978915			0.489457	+	0.872027i	$0.337195\pi$
$6$	−0.771068	−	1.55095i	−0.314787	−	0.633174i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$	1.81091	−	2.39178i	0.603636	−	0.797260i
$10$		−	2.18892i		−	0.692197i
$11$	0.121613			0.0366677			0.0183338	−	0.999832i	$-0.494164\pi$
$11$	0.121613			0.0366677			0.0183338	+	0.999832i	$0.494164\pi$
$12$	−1.55095	+	0.771068i	−0.447721	+	0.222588i
$13$	−5.51136			−1.52858			−0.764288	−	0.644875i	$-0.776909\pi$
$13$	−5.51136			−1.52858			−0.764288	+	0.644875i	$0.776909\pi$
$14$	1.00000			0.267261
$15$	3.39491	−	1.68781i	0.876562	−	0.435790i
$16$	1.00000			0.250000
$17$	6.85016			1.66141			0.830704	−	0.556714i	$-0.187938\pi$
$17$	6.85016			1.66141			0.830704	+	0.556714i	$0.187938\pi$
$18$	−2.39178	−	1.81091i	−0.563748	−	0.426835i
$19$		−	5.61876i		−	1.28903i	−0.764591	−	0.644516i	$-0.777059\pi$
$19$		−	5.61876i		−	1.28903i	0.764591	−	0.644516i	$-0.222941\pi$
$20$	−2.18892			−0.489457
$21$	0.771068	+	1.55095i	0.168261	+	0.338446i
$22$		−	0.121613i		−	0.0259280i
$23$	2.15811	−	4.28282i	0.449997	−	0.893030i
$23$	2.15811	−	4.28282i	0.449997	−	0.893030i
$24$	0.771068	+	1.55095i	0.157394	+	0.316587i
$25$	−0.208628			−0.0417256
$26$			5.51136i			1.08087i
$27$	0.964405	−	5.10587i	0.185600	−	0.982625i
$28$		−	1.00000i		−	0.188982i
$29$		−	4.75300i		−	0.882610i	−0.897357	−	0.441305i	$-0.854516\pi$
$29$		−	4.75300i		−	0.882610i	0.897357	−	0.441305i	$-0.145484\pi$
$30$	−1.68781	−	3.39491i	−0.308150	−	0.619823i
$31$	6.85642			1.23145			0.615725	−	0.787961i	$-0.288863\pi$
$31$	6.85642			1.23145			0.615725	+	0.787961i	$0.288863\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.188616	−	0.0937719i	0.0328338	−	0.0163236i
$34$		−	6.85016i		−	1.17479i
$35$			2.18892i			0.369995i
$36$	−1.81091	+	2.39178i	−0.301818	+	0.398630i
$37$			6.93548i			1.14019i	0.821580	+	0.570093i	$0.193093\pi$
$37$			6.93548i			1.14019i	−0.821580	+	0.570093i	$0.806907\pi$
$38$	−5.61876			−0.911484
$39$	−8.54785	+	4.24963i	−1.36875	+	0.680486i
$40$			2.18892i			0.346099i
$41$			3.19205i			0.498515i	0.968437	+	0.249258i	$0.0801866\pi$
$41$			3.19205i			0.498515i	−0.968437	+	0.249258i	$0.919813\pi$
$42$	1.55095	−	0.771068i	0.239317	−	0.118978i
$43$			1.82564i			0.278408i	0.990264	+	0.139204i	$0.0444544\pi$
$43$			1.82564i			0.278408i	−0.990264	+	0.139204i	$0.955546\pi$
$44$	−0.121613			−0.0183338
$45$	3.96393	−	5.23542i	0.590908	−	0.780450i
$46$	−4.28282	−	2.15811i	−0.631468	−	0.318196i
$47$			2.93340i			0.427880i	0.976847	+	0.213940i	$0.0686297\pi$
$47$			2.93340i			0.427880i	−0.976847	+	0.213940i	$0.931370\pi$
$48$	1.55095	−	0.771068i	0.223861	−	0.111294i
$49$	−1.00000			−0.142857
$50$			0.208628i			0.0295045i
$51$	10.6243	−	5.28194i	1.48770	−	0.739620i
$52$	5.51136			0.764288
$53$	10.6872			1.46800			0.734002	−	0.679147i	$-0.237650\pi$
$53$	10.6872			1.46800			0.734002	+	0.679147i	$0.237650\pi$
$54$	−5.10587	−	0.964405i	−0.694821	−	0.131239i
$55$	0.266201			0.0358946
$56$	−1.00000			−0.133631
$57$	−4.33245	−	8.71443i	−0.573847	−	1.15426i
$58$	−4.75300			−0.624099
$59$			4.63693i			0.603677i	0.953359	+	0.301839i	$0.0976004\pi$
$59$			4.63693i			0.603677i	−0.953359	+	0.301839i	$0.902400\pi$
$60$	−3.39491	+	1.68781i	−0.438281	+	0.217895i
$61$		−	3.29609i		−	0.422021i	−0.977484	−	0.211010i	$-0.932325\pi$
$61$		−	3.29609i		−	0.422021i	0.977484	−	0.211010i	$-0.0676754\pi$
$62$		−	6.85642i		−	0.870766i
$63$	2.39178	+	1.81091i	0.301336	+	0.228153i
$64$	−1.00000			−0.125000
$65$	−12.0639			−1.49635
$66$	−0.0937719	−	0.188616i	−0.0115425	−	0.0232170i
$67$			7.80455i			0.953477i	0.879045	+	0.476739i	$0.158181\pi$
$67$			7.80455i			0.953477i	−0.879045	+	0.476739i	$0.841819\pi$
$68$	−6.85016			−0.830704
$69$	0.0447773	−	8.30650i	0.00539055	−	0.999985i
$70$	2.18892			0.261626
$71$			8.83434i			1.04844i	0.851582	+	0.524222i	$0.175644\pi$
$71$			8.83434i			1.04844i	−0.851582	+	0.524222i	$0.824356\pi$
$72$	2.39178	+	1.81091i	0.281874	+	0.213417i
$73$	−14.3724			−1.68217			−0.841084	−	0.540905i	$-0.818082\pi$
$73$	−14.3724			−1.68217			−0.841084	+	0.540905i	$0.818082\pi$
$74$	6.93548			0.806233
$75$	−0.323572	+	0.160867i	−0.0373629	+	0.0185753i
$76$			5.61876i			0.644516i
$77$			0.121613i			0.0138591i
$78$	4.24963	+	8.54785i	0.481176	+	0.967854i
$79$		−	4.84656i		−	0.545281i	−0.962116	−	0.272640i	$-0.912103\pi$
$79$		−	4.84656i		−	0.545281i	0.962116	−	0.272640i	$-0.0878969\pi$
$80$	2.18892			0.244729
$81$	−2.44123	−	8.66259i	−0.271248	−	0.962510i
$82$	3.19205			0.352503
$83$	−6.52137			−0.715813			−0.357906	−	0.933757i	$-0.616509\pi$
$83$	−6.52137			−0.715813			−0.357906	+	0.933757i	$0.616509\pi$
$84$	−0.771068	−	1.55095i	−0.0841304	−	0.169223i
$85$	14.9945			1.62638
$86$	1.82564			0.196864
$87$	−3.66489	−	7.37167i	−0.392917	−	0.790326i
$88$			0.121613i			0.0129640i
$89$	−13.9682			−1.48063			−0.740315	−	0.672260i	$-0.765324\pi$
$89$	−13.9682			−1.48063			−0.740315	+	0.672260i	$0.765324\pi$
$90$	−5.23542	−	3.96393i	−0.551861	−	0.417835i
$91$		−	5.51136i		−	0.577747i
$92$	−2.15811	+	4.28282i	−0.224998	+	0.446515i
$93$	10.6340	−	5.28677i	1.10269	−	0.548212i
$94$	2.93340			0.302557
$95$		−	12.2990i		−	1.26185i
$96$	−0.771068	−	1.55095i	−0.0786968	−	0.158293i
$97$			4.32736i			0.439377i	0.975570	+	0.219688i	$0.0705041\pi$
$97$			4.32736i			0.439377i	−0.975570	+	0.219688i	$0.929496\pi$
$98$			1.00000i			0.101015i
$99$	0.220230	−	0.290872i	0.0221339	−	0.0292337i
$100$	0.208628			0.0208628
$101$		−	0.838144i		−	0.0833985i	−0.999130	−	0.0416992i	$-0.986723\pi$
$101$		−	0.838144i		−	0.0833985i	0.999130	−	0.0416992i	$-0.0132771\pi$
$102$	−5.28194	−	10.6243i	−0.522990	−	1.05196i
$103$			16.8341i			1.65871i	0.558719	+	0.829357i	$0.311293\pi$
$103$			16.8341i			1.65871i	−0.558719	+	0.829357i	$0.688707\pi$
$104$		−	5.51136i		−	0.540433i
$105$	1.68781	+	3.39491i	0.164713	+	0.331309i
$106$		−	10.6872i		−	1.03804i
$107$	−3.11341			−0.300985			−0.150492	−	0.988611i	$-0.548086\pi$
$107$	−3.11341			−0.300985			−0.150492	+	0.988611i	$0.548086\pi$
$108$	−0.964405	+	5.10587i	−0.0927999	+	0.491313i
$109$			19.0554i			1.82517i	0.408883	+	0.912587i	$0.365919\pi$
$109$			19.0554i			1.82517i	−0.408883	+	0.912587i	$0.634081\pi$
$110$		−	0.266201i		−	0.0253813i
$111$	5.34773	+	10.7566i	0.507584	+	1.02097i
$112$			1.00000i			0.0944911i
$113$	−8.31141			−0.781872			−0.390936	−	0.920418i	$-0.627849\pi$
$113$	−8.31141			−0.781872			−0.390936	+	0.920418i	$0.627849\pi$
$114$	−8.71443	+	4.33245i	−0.816182	+	0.405771i
$115$	4.72393	−	9.37476i	0.440509	−	0.874200i
$116$			4.75300i			0.441305i
$117$	−9.98056	+	13.1820i	−0.922703	+	1.21867i
$118$	4.63693			0.426864
$119$			6.85016i			0.627953i
$120$	1.68781	+	3.39491i	0.154075	+	0.309912i
$121$	−10.9852			−0.998655
$122$	−3.29609			−0.298414
$123$	2.46129	+	4.95072i	0.221927	+	0.446392i
$124$	−6.85642			−0.615725
$125$	−11.4013			−1.01976
$126$	1.81091	−	2.39178i	0.161328	−	0.213077i
$127$	4.59255			0.407523			0.203761	−	0.979021i	$-0.434683\pi$
$127$	4.59255			0.407523			0.203761	+	0.979021i	$0.434683\pi$
$128$			1.00000i			0.0883883i
$129$	1.40770	+	2.83149i	0.123941	+	0.249299i
$130$			12.0639i			1.05808i
$131$		−	12.0371i		−	1.05168i	−0.850583	−	0.525841i	$-0.823751\pi$
$131$		−	12.0371i		−	1.05168i	0.850583	−	0.525841i	$-0.176249\pi$
$132$	−0.188616	+	0.0937719i	−0.0164169	+	0.00816180i
$133$	5.61876			0.487209
$134$	7.80455			0.674210
$135$	2.11101	−	11.1763i	0.181686	−	0.961907i
$136$			6.85016i			0.587396i
$137$	−10.6220			−0.907503			−0.453751	−	0.891128i	$-0.649915\pi$
$137$	−10.6220			−0.907503			−0.453751	+	0.891128i	$0.649915\pi$
$138$	−8.30650	−	0.0447773i	−0.707097	−	0.00381169i
$139$	12.0931			1.02573			0.512864	−	0.858470i	$-0.328585\pi$
$139$	12.0931			1.02573			0.512864	+	0.858470i	$0.328585\pi$
$140$		−	2.18892i		−	0.184998i
$141$	2.26185	+	4.54956i	0.190482	+	0.383142i
$142$	8.83434			0.741361
$143$	−0.670253			−0.0560493
$144$	1.81091	−	2.39178i	0.150909	−	0.199315i
$145$		−	10.4039i		−	0.864000i
$146$			14.3724i			1.18947i
$147$	−1.55095	+	0.771068i	−0.127920	+	0.0635966i
$148$		−	6.93548i		−	0.570093i
$149$	14.3276			1.17376			0.586882	−	0.809673i	$-0.300355\pi$
$149$	14.3276			1.17376			0.586882	+	0.809673i	$0.300355\pi$
$150$	0.160867	+	0.323572i	0.0131347	+	0.0264196i
$151$	−16.0921			−1.30955			−0.654776	−	0.755823i	$-0.727237\pi$
$151$	−16.0921			−1.30955			−0.654776	+	0.755823i	$0.727237\pi$
$152$	5.61876			0.455742
$153$	12.4050	−	16.3841i	1.00289	−	1.32457i
$154$	0.121613			0.00979985
$155$	15.0082			1.20548
$156$	8.54785	−	4.24963i	0.684376	−	0.340243i
$157$			14.9372i			1.19212i	0.802941	+	0.596058i	$0.203267\pi$
$157$			14.9372i			1.19212i	−0.802941	+	0.596058i	$0.796733\pi$
$158$	−4.84656			−0.385572
$159$	16.5754	−	8.24059i	1.31451	−	0.653521i
$160$		−	2.18892i		−	0.173049i
$161$	4.28282	+	2.15811i	0.337534	+	0.170083i
$162$	−8.66259	+	2.44123i	−0.680597	+	0.191801i
$163$	−3.03696			−0.237873			−0.118937	−	0.992902i	$-0.537949\pi$
$163$	−3.03696			−0.237873			−0.118937	+	0.992902i	$0.537949\pi$
$164$		−	3.19205i		−	0.249258i
$165$	0.412865	−	0.205259i	0.0321415	−	0.0159794i
$166$			6.52137i			0.506156i
$167$			4.72583i			0.365696i	0.983141	+	0.182848i	$0.0585316\pi$
$167$			4.72583i			0.365696i	−0.983141	+	0.182848i	$0.941468\pi$
$168$	−1.55095	+	0.771068i	−0.119659	+	0.0594892i
$169$	17.3751			1.33654
$170$		−	14.9945i		−	1.15002i
$171$	−13.4388	−	10.1751i	−1.02769	−	0.778106i
$172$		−	1.82564i		−	0.139204i
$173$		−	10.7105i		−	0.814308i	−0.913360	−	0.407154i	$-0.866521\pi$
$173$		−	10.7105i		−	0.814308i	0.913360	−	0.407154i	$-0.133479\pi$
$174$	−7.37167	+	3.66489i	−0.558845	+	0.277834i
$175$		−	0.208628i		−	0.0157708i
$176$	0.121613			0.00916692
$177$	3.57539	+	7.19166i	0.268743	+	0.540558i
$178$			13.9682i			1.04696i
$179$		−	1.88128i		−	0.140614i	−0.997525	−	0.0703069i	$-0.977602\pi$
$179$		−	1.88128i		−	0.140614i	0.997525	−	0.0703069i	$-0.0223979\pi$
$180$	−3.96393	+	5.23542i	−0.295454	+	0.390225i
$181$			0.681479i			0.0506539i	0.999679	+	0.0253270i	$0.00806269\pi$
$181$			0.681479i			0.0506539i	−0.999679	+	0.0253270i	$0.991937\pi$
$182$	−5.51136			−0.408529
$183$	−2.54151	−	5.11207i	−0.187874	−	0.377895i
$184$	4.28282	+	2.15811i	0.315734	+	0.159098i
$185$			15.1812i			1.11615i
$186$	−5.28677	−	10.6340i	−0.387645	−	0.779722i
$187$	0.833069			0.0609200
$188$		−	2.93340i		−	0.213940i
$189$	5.10587	+	0.964405i	0.371397	+	0.0701502i
$190$	−12.2990			−0.892265
$191$	−3.98250			−0.288164			−0.144082	−	0.989566i	$-0.546023\pi$
$191$	−3.98250			−0.288164			−0.144082	+	0.989566i	$0.546023\pi$
$192$	−1.55095	+	0.771068i	−0.111930	+	0.0556471i
$193$	−10.6251			−0.764811			−0.382405	−	0.923995i	$-0.624904\pi$
$193$	−10.6251			−0.764811			−0.382405	+	0.923995i	$0.624904\pi$
$194$	4.32736			0.310686
$195$	−18.7106	+	9.30211i	−1.33989	+	0.666138i
$196$	1.00000			0.0714286
$197$		−	13.2720i		−	0.945589i	−0.881173	−	0.472794i	$-0.843245\pi$
$197$		−	13.2720i		−	0.945589i	0.881173	−	0.472794i	$-0.156755\pi$
$198$	−0.290872	−	0.220230i	−0.0206713	−	0.0156511i
$199$			4.29365i			0.304369i	0.988352	+	0.152184i	$0.0486307\pi$
$199$			4.29365i			0.304369i	−0.988352	+	0.152184i	$0.951369\pi$
$200$		−	0.208628i		−	0.0147522i
$201$	6.01784	+	12.1045i	0.424466	+	0.853785i
$202$	−0.838144			−0.0589716
$203$	4.75300			0.333595
$204$	−10.6243	+	5.28194i	−0.743848	+	0.369810i
$205$			6.98715i			0.488004i
$206$	16.8341			1.17289
$207$	−6.33543	−	12.9175i	−0.440343	−	0.897830i
$208$	−5.51136			−0.382144
$209$		−	0.683315i		−	0.0472659i
$210$	3.39491	−	1.68781i	0.234271	−	0.116470i
$211$	21.6460			1.49017			0.745086	−	0.666968i	$-0.232408\pi$
$211$	21.6460			1.49017			0.745086	+	0.666968i	$0.232408\pi$
$212$	−10.6872			−0.734002
$213$	6.81188	+	13.7016i	0.466742	+	0.938821i
$214$			3.11341i			0.212828i
$215$			3.99619i			0.272538i
$216$	5.10587	+	0.964405i	0.347411	+	0.0656195i
$217$			6.85642i			0.465444i
$218$	19.0554			1.29059
$219$	−22.2910	+	11.0821i	−1.50629	+	0.748861i
$220$	−0.266201			−0.0179473
$221$	−37.7537			−2.53959
$222$	10.7566	−	5.34773i	0.721936	−	0.358916i
$223$	16.6007			1.11167			0.555834	−	0.831293i	$-0.312399\pi$
$223$	16.6007			1.11167			0.555834	+	0.831293i	$0.312399\pi$
$224$	1.00000			0.0668153
$225$	−0.377806	+	0.498993i	−0.0251871	+	0.0332662i
$226$			8.31141i			0.552867i
$227$	21.9541			1.45715			0.728573	−	0.684968i	$-0.240184\pi$
$227$	21.9541			1.45715			0.728573	+	0.684968i	$0.240184\pi$
$228$	4.33245	+	8.71443i	0.286924	+	0.577128i
$229$			22.8002i			1.50668i	0.657632	+	0.753339i	$0.271558\pi$
$229$			22.8002i			1.50668i	−0.657632	+	0.753339i	$0.728442\pi$
$230$	−9.37476	−	4.72393i	−0.618153	−	0.311487i
$231$	0.0937719	+	0.188616i	0.00616974	+	0.0124100i
$232$	4.75300			0.312050
$233$			19.3033i			1.26460i	0.774723	+	0.632301i	$0.217889\pi$
$233$			19.3033i			1.26460i	−0.774723	+	0.632301i	$0.782111\pi$
$234$	13.1820	+	9.98056i	0.861732	+	0.652450i
$235$			6.42097i			0.418858i
$236$		−	4.63693i		−	0.301839i
$237$	−3.73703	−	7.51679i	−0.242746	−	0.488268i
$238$	6.85016			0.444030
$239$		−	14.6788i		−	0.949491i	−0.880123	−	0.474745i	$-0.842540\pi$
$239$		−	14.6788i		−	0.949491i	0.880123	−	0.474745i	$-0.157460\pi$
$240$	3.39491	−	1.68781i	0.219141	−	0.108947i
$241$		−	5.98480i		−	0.385515i	−0.981246	−	0.192757i	$-0.938257\pi$
$241$		−	5.98480i		−	0.385515i	0.981246	−	0.192757i	$-0.0617431\pi$
$242$			10.9852i			0.706156i
$243$	−10.4657	−	11.5529i	−0.671373	−	0.741119i
$244$			3.29609i			0.211010i
$245$	−2.18892			−0.139845
$246$	4.95072	−	2.46129i	0.315647	−	0.156926i
$247$			30.9670i			1.97038i
$248$			6.85642i			0.435383i
$249$	−10.1143	+	5.02842i	−0.640970	+	0.318663i
$250$			11.4013i			0.721080i
$251$	9.90978			0.625500			0.312750	−	0.949836i	$-0.398750\pi$
$251$	9.90978			0.625500			0.312750	+	0.949836i	$0.398750\pi$
$252$	−2.39178	−	1.81091i	−0.150668	−	0.114076i
$253$	0.262454	−	0.520847i	0.0165004	−	0.0327454i
$254$		−	4.59255i		−	0.288162i
$255$	23.2557	−	11.5617i	1.45633	−	0.724025i
$256$	1.00000			0.0625000
$257$			16.6565i			1.03900i	0.854470	+	0.519500i	$0.173882\pi$
$257$			16.6565i			1.03900i	−0.854470	+	0.519500i	$0.826118\pi$
$258$	2.83149	−	1.40770i	0.176281	−	0.0876393i
$259$	−6.93548			−0.430950
$260$	12.0639			0.748173
$261$	−11.3681	−	8.60724i	−0.703670	−	0.532775i
$262$	−12.0371			−0.743652
$263$	8.58450			0.529343			0.264671	−	0.964339i	$-0.414737\pi$
$263$	8.58450			0.529343			0.264671	+	0.964339i	$0.414737\pi$
$264$	0.0937719	+	0.188616i	0.00577126	+	0.0116085i
$265$	23.3935			1.43705
$266$		−	5.61876i		−	0.344508i
$267$	−21.6641	+	10.7705i	−1.32582	+	0.659141i
$268$		−	7.80455i		−	0.476739i
$269$			17.0512i			1.03963i	0.854278	+	0.519816i	$0.173999\pi$
$269$			17.0512i			1.03963i	−0.854278	+	0.519816i	$0.826001\pi$
$270$	−11.1763	−	2.11101i	−0.680171	−	0.128472i
$271$	18.3394			1.11404			0.557019	−	0.830500i	$-0.311945\pi$
$271$	18.3394			1.11404			0.557019	+	0.830500i	$0.311945\pi$
$272$	6.85016			0.415352
$273$	−4.24963	−	8.54785i	−0.257200	−	0.517340i
$274$			10.6220i			0.641701i
$275$	−0.0253719			−0.00152998
$276$	−0.0447773	+	8.30650i	−0.00269527	+	0.499993i
$277$	−25.3102			−1.52074			−0.760370	−	0.649490i	$-0.774983\pi$
$277$	−25.3102			−1.52074			−0.760370	+	0.649490i	$0.774983\pi$
$278$		−	12.0931i		−	0.725299i
$279$	12.4163	−	16.3991i	0.743347	−	0.981786i
$280$	−2.18892			−0.130813
$281$	−3.98263			−0.237584			−0.118792	−	0.992919i	$-0.537902\pi$
$281$	−3.98263			−0.237584			−0.118792	+	0.992919i	$0.537902\pi$
$282$	4.54956	−	2.26185i	0.270922	−	0.134691i
$283$		−	21.7678i		−	1.29396i	−0.762506	−	0.646981i	$-0.776031\pi$
$283$		−	21.7678i		−	1.29396i	0.762506	−	0.646981i	$-0.223969\pi$
$284$		−	8.83434i		−	0.524222i
$285$	−9.48339	−	19.0752i	−0.561747	−	1.12992i
$286$			0.670253i			0.0396329i
$287$	−3.19205			−0.188421
$288$	−2.39178	−	1.81091i	−0.140937	−	0.106709i
$289$	29.9247			1.76028
$290$	−10.4039			−0.610940
$291$	3.33669	+	6.71153i	0.195600	+	0.393437i
$292$	14.3724			0.841084
$293$	21.7170			1.26872			0.634360	−	0.773037i	$-0.281264\pi$
$293$	21.7170			1.26872			0.634360	+	0.773037i	$0.281264\pi$
$294$	0.771068	+	1.55095i	0.0449696	+	0.0904534i
$295$			10.1499i			0.590948i
$296$	−6.93548			−0.403117
$297$	0.117284	−	0.620940i	0.00680552	−	0.0360306i
$298$		−	14.3276i		−	0.829976i
$299$	−11.8941	+	23.6042i	−0.687854	+	1.36506i
$300$	0.323572	−	0.160867i	0.0186815	−	0.00928764i
$301$	−1.82564			−0.105228
$302$			16.0921i			0.925994i
$303$	−0.646266	−	1.29992i	−0.0371270	−	0.0746786i
$304$		−	5.61876i		−	0.322258i
$305$		−	7.21487i		−	0.413122i
$306$	−16.3841	−	12.4050i	−0.936616	−	0.709147i
$307$	6.58967			0.376092			0.188046	−	0.982160i	$-0.439785\pi$
$307$	6.58967			0.376092			0.188046	+	0.982160i	$0.439785\pi$
$308$		−	0.121613i		−	0.00692954i
$309$	12.9802	+	26.1089i	0.738420	+	1.48528i
$310$		−	15.0082i		−	0.852406i
$311$		−	11.0636i		−	0.627359i	−0.949529	−	0.313680i	$-0.898438\pi$
$311$		−	11.0636i		−	0.627359i	0.949529	−	0.313680i	$-0.101562\pi$
$312$	−4.24963	−	8.54785i	−0.240588	−	0.483927i
$313$		−	33.8845i		−	1.91526i	−0.287997	−	0.957631i	$-0.592989\pi$
$313$		−	33.8845i		−	1.91526i	0.287997	−	0.957631i	$-0.407011\pi$
$314$	14.9372			0.842954
$315$	5.23542	+	3.96393i	0.294982	+	0.223342i
$316$			4.84656i			0.272640i
$317$		−	15.3693i		−	0.863226i	−0.902059	−	0.431613i	$-0.857945\pi$
$317$		−	15.3693i		−	0.863226i	0.902059	−	0.431613i	$-0.142055\pi$
$318$	−8.24059	−	16.5754i	−0.462109	−	0.929502i
$319$		−	0.578026i		−	0.0323633i
$320$	−2.18892			−0.122364
$321$	−4.82875	+	2.40065i	−0.269514	+	0.133991i
$322$	2.15811	−	4.28282i	0.120267	−	0.238672i
$323$		−	38.4894i		−	2.14161i
$324$	2.44123	+	8.66259i	0.135624	+	0.481255i
$325$	1.14982			0.0637808
$326$			3.03696i			0.168202i
$327$	14.6930	+	29.5540i	0.812525	+	1.63434i
$328$	−3.19205			−0.176252
$329$	−2.93340			−0.161723
$330$	−0.205259	−	0.412865i	−0.0112992	−	0.0227275i
$331$	−28.8440			−1.58541			−0.792705	−	0.609605i	$-0.791328\pi$
$331$	−28.8440			−1.58541			−0.792705	+	0.609605i	$0.791328\pi$
$332$	6.52137			0.357906
$333$	16.5882	+	12.5595i	0.909025	+	0.688257i
$334$	4.72583			0.258586
$335$			17.0835i			0.933373i
$336$	0.771068	+	1.55095i	0.0420652	+	0.0846114i
$337$		−	17.2449i		−	0.939392i	−0.882828	−	0.469696i	$-0.844364\pi$
$337$		−	17.2449i		−	0.939392i	0.882828	−	0.469696i	$-0.155636\pi$
$338$		−	17.3751i		−	0.945079i
$339$	−12.8906	+	6.40866i	−0.700121	+	0.348071i
$340$	−14.9945			−0.813189
$341$	0.833830			0.0451544
$342$	−10.1751	+	13.4388i	−0.550204	+	0.726690i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.82564			−0.0984321
$345$	0.0980138	−	18.1823i	0.00527689	−	0.978901i
$346$	−10.7105			−0.575802
$347$			2.69806i			0.144839i	0.997374	+	0.0724197i	$0.0230721\pi$
$347$			2.69806i			0.144839i	−0.997374	+	0.0724197i	$0.976928\pi$
$348$	3.66489	+	7.37167i	0.196459	+	0.395163i
$349$	3.53816			0.189394			0.0946968	−	0.995506i	$-0.469812\pi$
$349$	3.53816			0.189394			0.0946968	+	0.995506i	$0.469812\pi$
$350$	−0.208628			−0.0111516
$351$	−5.31518	+	28.1403i	−0.283703	+	1.50202i
$352$		−	0.121613i		−	0.00648199i
$353$			22.9436i			1.22117i	0.791952	+	0.610583i	$0.209065\pi$
$353$			22.9436i			1.22117i	−0.791952	+	0.610583i	$0.790935\pi$
$354$	7.19166	−	3.57539i	0.382232	−	0.190030i
$355$			19.3377i			1.02634i
$356$	13.9682			0.740315
$357$	5.28194	+	10.6243i	0.279550	+	0.562296i
$358$	−1.88128			−0.0994290
$359$	−21.0773			−1.11242			−0.556209	−	0.831043i	$-0.687744\pi$
$359$	−21.0773			−1.11242			−0.556209	+	0.831043i	$0.687744\pi$
$360$	5.23542	+	3.96393i	0.275931	+	0.208918i
$361$	−12.5705			−0.661605
$362$	0.681479			0.0358177
$363$	−17.0375	+	8.47035i	−0.894239	+	0.444578i
$364$			5.51136i			0.288874i
$365$	−31.4601			−1.64670
$366$	−5.11207	+	2.54151i	−0.267212	+	0.132847i
$367$			24.8298i			1.29611i	0.761595	+	0.648053i	$0.224417\pi$
$367$			24.8298i			1.29611i	−0.761595	+	0.648053i	$0.775583\pi$
$368$	2.15811	−	4.28282i	0.112499	−	0.223258i
$369$	7.63469	+	5.78051i	0.397446	+	0.300922i
$370$	15.1812			0.789234
$371$			10.6872i			0.554854i
$372$	−10.6340	+	5.28677i	−0.551346	+	0.274106i
$373$		−	18.2235i		−	0.943576i	−0.881712	−	0.471788i	$-0.843609\pi$
$373$		−	18.2235i		−	0.943576i	0.881712	−	0.471788i	$-0.156391\pi$
$374$		−	0.833069i		−	0.0430769i
$375$	−17.6828	+	8.79116i	−0.913137	+	0.453974i
$376$	−2.93340			−0.151278
$377$			26.1955i			1.34914i
$378$	0.964405	−	5.10587i	0.0496036	−	0.262618i
$379$		−	6.02327i		−	0.309395i	−0.987962	−	0.154697i	$-0.950560\pi$
$379$		−	6.02327i		−	0.309395i	0.987962	−	0.154697i	$-0.0494402\pi$
$380$			12.2990i			0.630927i
$381$	7.12282	−	3.54117i	0.364913	−	0.181420i
$382$			3.98250i			0.203763i
$383$	23.4051			1.19594			0.597972	−	0.801517i	$-0.295973\pi$
$383$	23.4051			1.19594			0.597972	+	0.801517i	$0.295973\pi$
$384$	0.771068	+	1.55095i	0.0393484	+	0.0791467i
$385$			0.266201i			0.0135669i
$386$			10.6251i			0.540803i
$387$	4.36654	+	3.30607i	0.221964	+	0.168057i
$388$		−	4.32736i		−	0.219688i
$389$	−15.4177			−0.781709			−0.390854	−	0.920453i	$-0.627820\pi$
$389$	−15.4177			−0.781709			−0.390854	+	0.920453i	$0.627820\pi$
$390$	9.30211	+	18.7106i	0.471031	+	0.947447i
$391$	14.7834	−	29.3380i	0.747629	−	1.48369i
$392$		−	1.00000i		−	0.0505076i
$393$	−9.28140	−	18.6689i	−0.468184	−	0.941722i
$394$	−13.2720			−0.668632
$395$		−	10.6087i		−	0.533783i
$396$	−0.220230	+	0.290872i	−0.0110670	+	0.0146168i
$397$	4.89779			0.245813			0.122907	−	0.992418i	$-0.460778\pi$
$397$	4.89779			0.245813			0.122907	+	0.992418i	$0.460778\pi$
$398$	4.29365			0.215221
$399$	8.71443	−	4.33245i	0.436267	−	0.216894i
$400$	−0.208628			−0.0104314
$401$	−32.1932			−1.60765			−0.803825	−	0.594866i	$-0.797205\pi$
$401$	−32.1932			−1.60765			−0.803825	+	0.594866i	$0.797205\pi$
$402$	12.1045	−	6.01784i	0.603717	−	0.300143i
$403$	−37.7882			−1.88236
$404$			0.838144i			0.0416992i
$405$	−5.34366	−	18.9617i	−0.265528	−	0.942215i
$406$		−	4.75300i		−	0.235887i
$407$			0.843445i			0.0418080i
$408$	5.28194	+	10.6243i	0.261495	+	0.525980i
$409$	−12.0398			−0.595331			−0.297665	−	0.954670i	$-0.596208\pi$
$409$	−12.0398			−0.595331			−0.297665	+	0.954670i	$0.596208\pi$
$410$	6.98715			0.345071
$411$	−16.4743	+	8.19032i	−0.812617	+	0.403999i
$412$		−	16.8341i		−	0.829357i
$413$	−4.63693			−0.228168
$414$	−12.9175	+	6.33543i	−0.634861	+	0.311370i
$415$	−14.2747			−0.700720
$416$			5.51136i			0.270217i
$417$	18.7559	−	9.32464i	0.918480	−	0.456630i
$418$	−0.683315			−0.0334220
$419$	13.0095			0.635554			0.317777	−	0.948165i	$-0.397064\pi$
$419$	13.0095			0.635554			0.317777	+	0.948165i	$0.397064\pi$
$420$	−1.68781	−	3.39491i	−0.0823565	−	0.165655i
$421$		−	37.8096i		−	1.84273i	−0.388702	−	0.921364i	$-0.627076\pi$
$421$		−	37.8096i		−	1.84273i	0.388702	−	0.921364i	$-0.372924\pi$
$422$		−	21.6460i		−	1.05371i
$423$	7.01604	+	5.31211i	0.341132	+	0.258284i
$424$			10.6872i			0.519018i
$425$	−1.42914			−0.0693233
$426$	13.7016	−	6.81188i	0.663847	−	0.330037i
$427$	3.29609			0.159509
$428$	3.11341			0.150492
$429$	−1.03953	+	0.516811i	−0.0501890	+	0.0249519i
$430$	3.99619			0.192713
$431$	32.8974			1.58461			0.792305	−	0.610125i	$-0.208881\pi$
$431$	32.8974			1.58461			0.792305	+	0.610125i	$0.208881\pi$
$432$	0.964405	−	5.10587i	0.0464000	−	0.245656i
$433$		−	9.17816i		−	0.441074i	−0.975379	−	0.220537i	$-0.929219\pi$
$433$		−	9.17816i		−	0.441074i	0.975379	−	0.220537i	$-0.0707810\pi$
$434$	6.85642			0.329119
$435$	−8.02214	−	16.1360i	−0.384632	−	0.773662i
$436$		−	19.0554i		−	0.912587i
$437$	−24.0642	−	12.1259i	−1.15114	−	0.580061i
$438$	11.0821	+	22.2910i	0.529525	+	1.06510i
$439$	−39.2976			−1.87557			−0.937787	−	0.347211i	$-0.887129\pi$
$439$	−39.2976			−1.87557			−0.937787	+	0.347211i	$0.887129\pi$
$440$			0.266201i			0.0126906i
$441$	−1.81091	+	2.39178i	−0.0862337	+	0.113894i
$442$			37.7537i			1.79576i
$443$		−	24.1259i		−	1.14626i	−0.819465	−	0.573129i	$-0.805729\pi$
$443$		−	24.1259i		−	1.14626i	0.819465	−	0.573129i	$-0.194271\pi$
$444$	−5.34773	−	10.7566i	−0.253792	−	0.510486i
$445$	−30.5753			−1.44941
$446$		−	16.6007i		−	0.786068i
$447$	22.2214	−	11.0476i	1.05104	−	0.522532i
$448$		−	1.00000i		−	0.0472456i
$449$		−	3.29140i		−	0.155331i	−0.996979	−	0.0776653i	$-0.975253\pi$
$449$		−	3.29140i		−	0.155331i	0.996979	−	0.0776653i	$-0.0247466\pi$
$450$	0.498993	+	0.377806i	0.0235228	+	0.0178100i
$451$			0.388195i			0.0182794i
$452$	8.31141			0.390936
$453$	−24.9580	+	12.4081i	−1.17263	+	0.582982i
$454$		−	21.9541i		−	1.03036i
$455$		−	12.0639i		−	0.565565i
$456$	8.71443	−	4.33245i	0.408091	−	0.202886i
$457$			20.0964i			0.940071i	0.882648	+	0.470036i	$0.155759\pi$
$457$			20.0964i			0.940071i	−0.882648	+	0.470036i	$0.844241\pi$
$458$	22.8002			1.06538
$459$	6.60633	−	34.9760i	0.308357	−	1.63254i
$460$	−4.72393	+	9.37476i	−0.220254	+	0.437100i
$461$			35.2763i			1.64298i	0.570222	+	0.821490i	$0.306857\pi$
$461$			35.2763i			1.64298i	−0.570222	+	0.821490i	$0.693143\pi$
$462$	0.188616	−	0.0937719i	0.00877521	−	0.00436266i
$463$	−17.1026			−0.794824			−0.397412	−	0.917640i	$-0.630092\pi$
$463$	−17.1026			−0.794824			−0.397412	+	0.917640i	$0.630092\pi$
$464$		−	4.75300i		−	0.220652i
$465$	23.2769	−	11.5723i	1.07944	−	0.536653i
$466$	19.3033			0.894209
$467$	9.51490			0.440297			0.220148	−	0.975466i	$-0.429346\pi$
$467$	9.51490			0.440297			0.220148	+	0.975466i	$0.429346\pi$
$468$	9.98056	−	13.1820i	0.461352	−	0.609336i
$469$	−7.80455			−0.360381
$470$	6.42097			0.296177
$471$	11.5176	+	23.1669i	0.530702	+	1.06747i
$472$	−4.63693			−0.213432
$473$			0.222022i			0.0102086i
$474$	−7.51679	+	3.73703i	−0.345257	+	0.171647i
$475$			1.17223i			0.0537857i
$476$		−	6.85016i		−	0.313977i
$477$	19.3536	−	25.5615i	0.886140	−	1.17038i
$478$	−14.6788			−0.671391
$479$	−18.2788			−0.835178			−0.417589	−	0.908636i	$-0.637125\pi$
$479$	−18.2788			−0.835178			−0.417589	+	0.908636i	$0.637125\pi$
$480$	−1.68781	−	3.39491i	−0.0770375	−	0.154956i
$481$		−	38.2239i		−	1.74286i
$482$	−5.98480			−0.272600
$483$	8.30650	+	0.0447773i	0.377959	+	0.00203744i
$484$	10.9852			0.499328
$485$			9.47224i			0.430112i
$486$	−11.5529	+	10.4657i	−0.524050	+	0.474733i
$487$	32.8792			1.48990			0.744949	−	0.667122i	$-0.232474\pi$
$487$	32.8792			1.48990			0.744949	+	0.667122i	$0.232474\pi$
$488$	3.29609			0.149207
$489$	−4.71019	+	2.34171i	−0.213002	+	0.105896i
$490$			2.18892i			0.0988853i
$491$		−	19.6044i		−	0.884734i	−0.896834	−	0.442367i	$-0.854139\pi$
$491$		−	19.6044i		−	0.884734i	0.896834	−	0.442367i	$-0.145861\pi$
$492$	−2.46129	−	4.95072i	−0.110964	−	0.223196i
$493$		−	32.5588i		−	1.46637i
$494$	30.9670			1.39327
$495$	0.482066	−	0.636695i	0.0216672	−	0.0286173i
$496$	6.85642			0.307862
$497$	−8.83434			−0.396274
$498$	5.02842	+	10.1143i	0.225329	+	0.453234i
$499$	−22.1435			−0.991277			−0.495638	−	0.868529i	$-0.665066\pi$
$499$	−22.1435			−0.991277			−0.495638	+	0.868529i	$0.665066\pi$
$500$	11.4013			0.509880
$501$	3.64394	+	7.32954i	0.162799	+	0.327460i
$502$		−	9.90978i		−	0.442295i
$503$	9.48915			0.423100			0.211550	−	0.977367i	$-0.432149\pi$
$503$	9.48915			0.423100			0.211550	+	0.977367i	$0.432149\pi$
$504$	−1.81091	+	2.39178i	−0.0806642	+	0.106538i
$505$		−	1.83463i		−	0.0816400i
$506$	−0.520847	−	0.262454i	−0.0231545	−	0.0116675i
$507$	26.9479	−	13.3974i	1.19680	−	0.594998i
$508$	−4.59255			−0.203761
$509$		−	30.4783i		−	1.35092i	−0.737394	−	0.675462i	$-0.763944\pi$
$509$		−	30.4783i		−	1.35092i	0.737394	−	0.675462i	$-0.236056\pi$
$510$	−11.5617	−	23.2557i	−0.511963	−	1.02978i
$511$		−	14.3724i		−	0.635800i
$512$		−	1.00000i		−	0.0441942i
$513$	−28.6887	−	5.41876i	−1.26664	−	0.239244i
$514$	16.6565			0.734685
$515$			36.8485i			1.62374i
$516$	−1.40770	−	2.83149i	−0.0619704	−	0.124649i
$517$			0.356739i			0.0156894i
$518$			6.93548i			0.304728i
$519$	−8.25856	−	16.6115i	−0.362511	−	0.729166i
$520$		−	12.0639i		−	0.529038i
$521$	−4.38702			−0.192199			−0.0960994	−	0.995372i	$-0.530637\pi$
$521$	−4.38702			−0.192199			−0.0960994	+	0.995372i	$0.530637\pi$
$522$	−8.60724	+	11.3681i	−0.376729	+	0.497570i
$523$		−	26.4004i		−	1.15441i	−0.816600	−	0.577204i	$-0.804144\pi$
$523$		−	26.4004i		−	1.15441i	0.816600	−	0.577204i	$-0.195856\pi$
$524$			12.0371i			0.525841i
$525$	−0.160867	−	0.323572i	−0.00702079	−	0.0141219i
$526$		−	8.58450i		−	0.374302i
$527$	46.9676			2.04594
$528$	0.188616	−	0.0937719i	0.00820846	−	0.00408090i
$529$	−13.6851	−	18.4856i	−0.595005	−	0.803722i
$530$		−	23.3935i		−	1.01615i
$531$	11.0905	+	8.39705i	0.481288	+	0.364401i
$532$	−5.61876			−0.243604
$533$		−	17.5926i		−	0.762018i
$534$	10.7705	+	21.6641i	0.466083	+	0.937496i
$535$	−6.81500			−0.294638
$536$	−7.80455			−0.337105
$537$	−1.45060	−	2.91778i	−0.0625980	−	0.125912i
$538$	17.0512			0.735131
$539$	−0.121613			−0.00523824
$540$	−2.11101	+	11.1763i	−0.0908432	+	0.480953i
$541$	−7.53208			−0.323830			−0.161915	−	0.986805i	$-0.551767\pi$
$541$	−7.53208			−0.323830			−0.161915	+	0.986805i	$0.551767\pi$
$542$		−	18.3394i		−	0.787744i
$543$	0.525467	+	1.05694i	0.0225499	+	0.0453577i
$544$		−	6.85016i		−	0.293698i
$545$			41.7107i			1.78669i
$546$	−8.54785	+	4.24963i	−0.365814	+	0.181868i
$547$	31.3776			1.34161			0.670805	−	0.741634i	$-0.265949\pi$
$547$	31.3776			1.34161			0.670805	+	0.741634i	$0.265949\pi$
$548$	10.6220			0.453751
$549$	−7.88352	−	5.96891i	−0.336460	−	0.254747i
$550$			0.0253719i			0.00108186i
$551$	−26.7060			−1.13771
$552$	8.30650	+	0.0447773i	0.353548	+	0.00190585i
$553$	4.84656			0.206097
$554$			25.3102i			1.07533i
$555$	11.7058	+	23.5453i	0.496882	+	0.999444i
$556$	−12.0931			−0.512864
$557$	−13.9032			−0.589096			−0.294548	−	0.955637i	$-0.595169\pi$
$557$	−13.9032			−0.589096			−0.294548	+	0.955637i	$0.595169\pi$
$558$	−16.3991	−	12.4163i	−0.694227	−	0.525626i
$559$		−	10.0618i		−	0.425568i
$560$			2.18892i			0.0924988i
$561$	1.29205	−	0.642353i	0.0545504	−	0.0271202i
$562$			3.98263i			0.167997i
$563$	43.6945			1.84150			0.920752	−	0.390149i	$-0.127576\pi$
$563$	43.6945			1.84150			0.920752	+	0.390149i	$0.127576\pi$
$564$	−2.26185	−	4.54956i	−0.0952411	−	0.191571i
$565$	−18.1930			−0.765386
$566$	−21.7678			−0.914970
$567$	8.66259	−	2.44123i	0.363794	−	0.102522i
$568$	−8.83434			−0.370681
$569$	−2.70768			−0.113512			−0.0567559	−	0.998388i	$-0.518076\pi$
$569$	−2.70768			−0.113512			−0.0567559	+	0.998388i	$0.518076\pi$
$570$	−19.0752	+	9.48339i	−0.798972	+	0.397215i
$571$			28.8629i			1.20788i	0.797032	+	0.603938i	$0.206402\pi$
$571$			28.8629i			1.20788i	−0.797032	+	0.603938i	$0.793598\pi$
$572$	0.670253			0.0280247
$573$	−6.17667	+	3.07078i	−0.258034	+	0.128284i
$574$			3.19205i			0.133234i
$575$	−0.450243	+	0.893517i	−0.0187764	+	0.0372623i
$576$	−1.81091	+	2.39178i	−0.0754545	+	0.0996575i
$577$	11.4805			0.477940			0.238970	−	0.971027i	$-0.423190\pi$
$577$	11.4805			0.477940			0.238970	+	0.971027i	$0.423190\pi$
$578$		−	29.9247i		−	1.24470i
$579$	−16.4790	+	8.19267i	−0.684844	+	0.340476i
$580$			10.4039i			0.432000i
$581$		−	6.52137i		−	0.270552i
$582$	6.71153	−	3.33669i	0.278202	−	0.138310i
$583$	1.29971			0.0538284
$584$		−	14.3724i		−	0.594736i
$585$	−21.8466	+	28.8543i	−0.903248	+	1.19298i
$586$		−	21.7170i		−	0.897121i
$587$		−	25.5077i		−	1.05282i	−0.850232	−	0.526408i	$-0.823539\pi$
$587$		−	25.5077i		−	1.05282i	0.850232	−	0.526408i	$-0.176461\pi$
$588$	1.55095	−	0.771068i	0.0639602	−	0.0317983i
$589$		−	38.5246i		−	1.58738i
$590$	10.1499			0.417864
$591$	−10.2336	−	20.5842i	−0.420954	−	0.846721i
$592$			6.93548i			0.285047i
$593$		−	23.4839i		−	0.964369i	−0.876070	−	0.482184i	$-0.839843\pi$
$593$		−	23.4839i		−	0.964369i	0.876070	−	0.482184i	$-0.160157\pi$
$594$	−0.620940	−	0.117284i	−0.0254775	−	0.00481223i
$595$			14.9945i			0.614713i
$596$	−14.3276			−0.586882
$597$	3.31070	+	6.65925i	0.135498	+	0.272545i
$598$	23.6042	+	11.8941i	0.965246	+	0.486387i
$599$		−	30.2113i		−	1.23440i	−0.786807	−	0.617199i	$-0.788267\pi$
$599$		−	30.2113i		−	1.23440i	0.786807	−	0.617199i	$-0.211733\pi$
$600$	−0.160867	−	0.323572i	−0.00656735	−	0.0132098i
$601$	−9.49729			−0.387402			−0.193701	−	0.981061i	$-0.562049\pi$
$601$	−9.49729			−0.387402			−0.193701	+	0.981061i	$0.562049\pi$
$602$			1.82564i			0.0744077i
$603$	18.6668	+	14.1333i	0.760170	+	0.575553i
$604$	16.0921			0.654776
$605$	−24.0457			−0.977599
$606$	−1.29992	+	0.646266i	−0.0528057	+	0.0262528i
$607$	45.8380			1.86051			0.930254	−	0.366915i	$-0.119586\pi$
$607$	45.8380			1.86051			0.930254	+	0.366915i	$0.119586\pi$
$608$	−5.61876			−0.227871
$609$	7.37167	−	3.66489i	0.298715	−	0.148509i
$610$	−7.21487			−0.292122
$611$		−	16.1670i		−	0.654047i
$612$	−12.4050	+	16.3841i	−0.501443	+	0.662287i
$613$		−	35.6311i		−	1.43913i	−0.694427	−	0.719564i	$-0.744342\pi$
$613$		−	35.6311i		−	1.43913i	0.694427	−	0.719564i	$-0.255658\pi$
$614$		−	6.58967i		−	0.265937i
$615$	5.38757	+	10.8367i	0.217248	+	0.436980i
$616$	−0.121613			−0.00489993
$617$	−34.9933			−1.40878			−0.704388	−	0.709815i	$-0.748778\pi$
$617$	−34.9933			−1.40878			−0.704388	+	0.709815i	$0.748778\pi$
$618$	26.1089	−	12.9802i	1.05025	−	0.522142i
$619$		−	34.6763i		−	1.39376i	−0.717188	−	0.696879i	$-0.754571\pi$
$619$		−	34.6763i		−	1.39376i	0.717188	−	0.696879i	$-0.245429\pi$
$620$	−15.0082			−0.602742
$621$	−19.7862	−	15.1494i	−0.793995	−	0.607925i
$622$	−11.0636			−0.443610
$623$		−	13.9682i		−	0.559625i
$624$	−8.54785	+	4.24963i	−0.342188	+	0.170121i
$625$	−23.9133			−0.956533
$626$	−33.8845			−1.35430
$627$	−0.526882	−	1.05979i	−0.0210416	−	0.0423239i
$628$		−	14.9372i		−	0.596058i
$629$			47.5092i			1.89431i
$630$	3.96393	−	5.23542i	0.157927	−	0.208584i
$631$			4.90638i			0.195320i	0.995220	+	0.0976600i	$0.0311358\pi$
$631$			4.90638i			0.195320i	−0.995220	+	0.0976600i	$0.968864\pi$
$632$	4.84656			0.192786
$633$	33.5719	−	16.6905i	1.33436	−	0.663390i
$634$	−15.3693			−0.610393
$635$	10.0527			0.398930
$636$	−16.5754	+	8.24059i	−0.657257	+	0.326761i
$637$	5.51136			0.218368
$638$	−0.578026			−0.0228843
$639$	21.1298	+	15.9982i	0.835882	+	0.632878i
$640$			2.18892i			0.0865247i
$641$	17.4923			0.690905			0.345452	−	0.938436i	$-0.387725\pi$
$641$	17.4923			0.690905			0.345452	+	0.938436i	$0.387725\pi$
$642$	2.40065	+	4.82875i	0.0947461	+	0.190575i
$643$			0.426244i			0.0168094i	0.999965	+	0.00840472i	$0.00267534\pi$
$643$			0.426244i			0.0168094i	−0.999965	+	0.00840472i	$0.997325\pi$
$644$	−4.28282	−	2.15811i	−0.168767	−	0.0850414i
$645$	3.08133	+	6.19790i	0.121327	+	0.244042i
$646$	−38.4894			−1.51435
$647$			8.59770i			0.338011i	0.985615	+	0.169005i	$0.0540555\pi$
$647$			8.59770i			0.338011i	−0.985615	+	0.169005i	$0.945945\pi$
$648$	8.66259	−	2.44123i	0.340299	−	0.0959005i
$649$			0.563911i			0.0221354i
$650$		−	1.14982i		−	0.0450998i
$651$	5.28677	+	10.6340i	0.207205	+	0.416779i
$652$	3.03696			0.118937
$653$			42.0146i			1.64416i	0.569373	+	0.822079i	$0.307186\pi$
$653$			42.0146i			1.64416i	−0.569373	+	0.822079i	$0.692814\pi$
$654$	29.5540	−	14.6930i	1.15565	−	0.574542i
$655$		−	26.3482i		−	1.02951i
$656$			3.19205i			0.124629i
$657$	−26.0272	+	34.3757i	−1.01542	+	1.34113i
$658$			2.93340i			0.114356i
$659$	−20.0460			−0.780881			−0.390440	−	0.920628i	$-0.627677\pi$
$659$	−20.0460			−0.780881			−0.390440	+	0.920628i	$0.627677\pi$
$660$	−0.412865	+	0.205259i	−0.0160708	+	0.00798971i
$661$			47.2048i			1.83605i	0.396517	+	0.918027i	$0.370219\pi$
$661$			47.2048i			1.83605i	−0.396517	+	0.918027i	$0.629781\pi$
$662$			28.8440i			1.12105i
$663$	−58.5542	+	29.1107i	−2.27406	+	1.13056i
$664$		−	6.52137i		−	0.253078i
$665$	12.2990			0.476936
$666$	12.5595	−	16.5882i	0.486671	−	0.642778i
$667$	−20.3562	−	10.2575i	−0.788197	−	0.397172i
$668$		−	4.72583i		−	0.182848i
$669$	25.7470	−	12.8003i	0.995435	−	0.494889i
$670$	17.0835			0.659995
$671$		−	0.400847i		−	0.0154745i
$672$	1.55095	−	0.771068i	0.0598293	−	0.0297446i
$673$	−17.7612			−0.684646			−0.342323	−	0.939582i	$-0.611214\pi$
$673$	−17.7612			−0.684646			−0.342323	+	0.939582i	$0.611214\pi$
$674$	−17.2449			−0.664250
$675$	−0.201202	+	1.06523i	−0.00774427	+	0.0410007i
$676$	−17.3751			−0.668272
$677$	−38.4398			−1.47736			−0.738681	−	0.674055i	$-0.764551\pi$
$677$	−38.4398			−1.47736			−0.738681	+	0.674055i	$0.764551\pi$
$678$	6.40866	+	12.8906i	0.246123	+	0.495061i
$679$	−4.32736			−0.166069
$680$			14.9945i			0.575011i
$681$	34.0498	−	16.9281i	1.30479	−	0.648688i
$682$		−	0.833830i		−	0.0319290i
$683$		−	6.95703i		−	0.266203i	−0.991102	−	0.133102i	$-0.957506\pi$
$683$		−	6.95703i		−	0.266203i	0.991102	−	0.133102i	$-0.0424937\pi$
$684$	13.4388	+	10.1751i	0.513847	+	0.389053i
$685$	−23.2508			−0.888368
$686$	−1.00000			−0.0381802
$687$	17.5805	+	35.3620i	0.670738	+	1.34914i
$688$			1.82564i			0.0696020i
$689$	−58.9012			−2.24396
$690$	−18.1823	−	0.0980138i	−0.692187	−	0.00373132i
$691$	23.1238			0.879670			0.439835	−	0.898079i	$-0.355037\pi$
$691$	23.1238			0.879670			0.439835	+	0.898079i	$0.355037\pi$
$692$			10.7105i			0.407154i
$693$	0.290872	+	0.220230i	0.0110493	+	0.00836584i
$694$	2.69806			0.102417
$695$	26.4709			1.00410
$696$	7.37167	−	3.66489i	0.279423	−	0.138917i
$697$			21.8661i			0.828237i
$698$		−	3.53816i		−	0.133922i
$699$	14.8842	+	29.9385i	0.562971	+	1.13238i
$700$			0.208628i			0.00788541i
$701$	27.0000			1.01978			0.509889	−	0.860240i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509889	+	0.860240i	$0.329687\pi$
$702$	28.1403	+	5.31518i	1.06209	+	0.200609i
$703$	38.9688			1.46974
$704$	−0.121613			−0.00458346
$705$	4.95101	+	9.95862i	0.186466	+	0.375063i
$706$	22.9436			0.863495
$707$	0.838144			0.0315217
$708$	−3.57539	−	7.19166i	−0.134371	−	0.270279i
$709$		−	19.9428i		−	0.748966i	−0.927234	−	0.374483i	$-0.877820\pi$
$709$		−	19.9428i		−	0.748966i	0.927234	−	0.374483i	$-0.122180\pi$
$710$	19.3377			0.725730
$711$	−11.5919	−	8.77667i	−0.434731	−	0.329151i
$712$		−	13.9682i		−	0.523482i
$713$	14.7969	−	29.3648i	0.554149	−	1.09972i
$714$	10.6243	−	5.28194i	0.397603	−	0.197672i
$715$	−1.46713			−0.0548675
$716$			1.88128i			0.0703069i
$717$	−11.3183	−	22.7661i	−0.422691	−	0.850215i
$718$			21.0773i			0.786598i
$719$			41.2128i			1.53698i	0.639863	+	0.768489i	$0.278991\pi$
$719$			41.2128i			1.53698i	−0.639863	+	0.768489i	$0.721009\pi$
$720$	3.96393	−	5.23542i	0.147727	−	0.195112i
$721$	−16.8341			−0.626935
$722$			12.5705i			0.467825i
$723$	−4.61469	−	9.28214i	−0.171622	−	0.345207i
$724$		−	0.681479i		−	0.0253270i
$725$			0.991610i			0.0368275i
$726$	8.47035	+	17.0375i	0.314364	+	0.632322i
$727$		−	17.6466i		−	0.654477i	−0.944942	−	0.327239i	$-0.893882\pi$
$727$		−	17.6466i		−	0.654477i	0.944942	−	0.327239i	$-0.106118\pi$
$728$	5.51136			0.204265
$729$	−25.1398	−	9.84826i	−0.931105	−	0.364750i
$730$			31.4601i			1.16439i
$731$			12.5060i			0.462549i
$732$	2.54151	+	5.11207i	0.0939368	+	0.188948i
$733$			27.3682i			1.01087i	0.862865	+	0.505435i	$0.168668\pi$
$733$			27.3682i			1.01087i	−0.862865	+	0.505435i	$0.831332\pi$
$734$	24.8298			0.916486
$735$	−3.39491	+	1.68781i	−0.125223	+	0.0622557i
$736$	−4.28282	−	2.15811i	−0.157867	−	0.0795490i
$737$			0.949135i			0.0349618i
$738$	5.78051	−	7.63469i	0.212784	−	0.281037i
$739$	8.70479			0.320211			0.160106	−	0.987100i	$-0.448817\pi$
$739$	8.70479			0.320211			0.160106	+	0.987100i	$0.448817\pi$
$740$		−	15.1812i		−	0.558073i
$741$	23.8777	+	48.0284i	0.877169	+	1.76437i
$742$	10.6872			0.392341
$743$	7.85698			0.288245			0.144122	−	0.989560i	$-0.453964\pi$
$743$	7.85698			0.288245			0.144122	+	0.989560i	$0.453964\pi$
$744$	5.28677	+	10.6340i	0.193822	+	0.389861i
$745$	31.3620			1.14901
$746$	−18.2235			−0.667209
$747$	−11.8096	+	15.5977i	−0.432090	+	0.570689i
$748$	−0.833069			−0.0304600
$749$		−	3.11341i		−	0.113761i
$750$	8.79116	+	17.6828i	0.321008	+	0.645686i
$751$			38.2123i			1.39439i	0.716884	+	0.697193i	$0.245568\pi$
$751$			38.2123i			1.39439i	−0.716884	+	0.697193i	$0.754432\pi$
$752$			2.93340i			0.106970i
$753$	15.3696	−	7.64111i	0.560099	−	0.278458i
$754$	26.1955			0.953983
$755$	−35.2242			−1.28194
$756$	−5.10587	−	0.964405i	−0.185699	−	0.0350751i
$757$			31.7644i			1.15450i	0.816568	+	0.577249i	$0.195874\pi$
$757$			31.7644i			1.15450i	−0.816568	+	0.577249i	$0.804126\pi$
$758$	−6.02327			−0.218775
$759$	0.00544550	−	1.01018i	0.000197659	−	0.0366672i
$760$	12.2990			0.446132
$761$			4.30186i			0.155942i	0.996956	+	0.0779712i	$0.0248442\pi$
$761$			4.30186i			0.155942i	−0.996956	+	0.0779712i	$0.975156\pi$
$762$	−3.54117	−	7.12282i	−0.128283	−	0.258033i
$763$	−19.0554			−0.689851
$764$	3.98250			0.144082
$765$	27.1536	−	35.8634i	0.981739	−	1.29665i
$766$		−	23.4051i		−	0.845660i
$767$		−	25.5558i		−	0.922766i
$768$	1.55095	−	0.771068i	0.0559652	−	0.0278235i
$769$			49.4634i			1.78370i	0.452335	+	0.891848i	$0.350591\pi$
$769$			49.4634i			1.78370i	−0.452335	+	0.891848i	$0.649409\pi$
$770$	0.266201			0.00959322
$771$	12.8433	+	25.8334i	0.462539	+	0.930366i
$772$	10.6251			0.382405
$773$	35.6885			1.28363			0.641814	−	0.766861i	$-0.278182\pi$
$773$	35.6885			1.28363			0.641814	+	0.766861i	$0.278182\pi$
$774$	3.30607	−	4.36654i	0.118834	−	0.156952i
$775$	−1.43044			−0.0513830
$776$	−4.32736			−0.155343
$777$	−10.7566	+	5.34773i	−0.385891	+	0.191849i
$778$			15.4177i			0.552752i
$779$	17.9354			0.642602
$780$	18.7106	−	9.30211i	0.669946	−	0.333069i
$781$			1.07437i			0.0384440i
$782$	−29.3380	−	14.7834i	−1.04913	−	0.528653i
$783$	−24.2682	−	4.58382i	−0.867275	−	0.163812i
$784$	−1.00000			−0.0357143
$785$			32.6963i			1.16698i
$786$	−18.6689	+	9.28140i	−0.665898	+	0.331056i
$787$			10.9548i			0.390495i	0.980754	+	0.195248i	$0.0625510\pi$
$787$			10.9548i			0.390495i	−0.980754	+	0.195248i	$0.937449\pi$
$788$			13.2720i			0.472794i
$789$	13.3141	−	6.61923i	0.473996	−	0.235651i
$790$	−10.6087			−0.377442
$791$		−	8.31141i		−	0.295520i
$792$	0.290872	+	0.220230i	0.0103357	+	0.00782553i
$793$			18.1659i			0.645090i
$794$		−	4.89779i		−	0.173816i
$795$	36.2822	−	18.0380i	1.28680	−	0.639742i
$796$		−	4.29365i		−	0.152184i
$797$	32.3275			1.14510			0.572550	−	0.819870i	$-0.305954\pi$
$797$	32.3275			1.14510			0.572550	+	0.819870i	$0.305954\pi$
$798$	−4.33245	−	8.71443i	−0.153367	−	0.308488i
$799$			20.0942i			0.710883i
$800$			0.208628i			0.00737612i
$801$	−25.2952	+	33.4089i	−0.893761	+	1.18045i
$802$			32.1932i			1.13678i
$803$	−1.74788			−0.0616812
$804$	−6.01784	−	12.1045i	−0.212233	−	0.426892i
$805$	9.37476	+	4.72393i	0.330417	+	0.166497i
$806$			37.7882i			1.33103i
$807$	13.1477	+	26.4456i	0.462820	+	0.930931i
$808$	0.838144			0.0294858
$809$		−	28.7544i		−	1.01095i	−0.862841	−	0.505476i	$-0.831317\pi$
$809$		−	28.7544i		−	1.01095i	0.862841	−	0.505476i	$-0.168683\pi$
$810$	−18.9617	+	5.34366i	−0.666247	+	0.187757i
$811$	−7.00897			−0.246118			−0.123059	−	0.992399i	$-0.539270\pi$
$811$	−7.00897			−0.246118			−0.123059	+	0.992399i	$0.539270\pi$
$812$	−4.75300			−0.166798
$813$	28.4435	−	14.1409i	0.997558	−	0.495944i
$814$	0.843445			0.0295627
$815$	−6.64767			−0.232858
$816$	10.6243	−	5.28194i	0.371924	−	0.184905i
$817$	10.2579			0.358877
$818$			12.0398i			0.420962i
$819$	−13.1820	−	9.98056i	−0.460615	−	0.348749i
$820$		−	6.98715i		−	0.244002i
$821$		−	21.9293i		−	0.765337i	−0.923886	−	0.382668i	$-0.875005\pi$
$821$		−	21.9293i		−	0.765337i	0.923886	−	0.382668i	$-0.124995\pi$
$822$	8.19032	+	16.4743i	0.285670	+	0.574607i
$823$	−10.1837			−0.354981			−0.177490	−	0.984123i	$-0.556798\pi$
$823$	−10.1837			−0.354981			−0.177490	+	0.984123i	$0.556798\pi$
$824$	−16.8341			−0.586444
$825$	−0.0393506	+	0.0195635i	−0.00137001	+	0.000681113i
$826$			4.63693i			0.161339i
$827$	−18.2005			−0.632895			−0.316447	−	0.948610i	$-0.602490\pi$
$827$	−18.2005			−0.632895			−0.316447	+	0.948610i	$0.602490\pi$
$828$	6.33543	+	12.9175i	0.220172	+	0.448915i
$829$	−17.4425			−0.605802			−0.302901	−	0.953022i	$-0.597955\pi$
$829$	−17.4425			−0.605802			−0.302901	+	0.953022i	$0.597955\pi$
$830$			14.2747i			0.495484i
$831$	−39.2549	+	19.5159i	−1.36174	+	0.676998i
$832$	5.51136			0.191072
$833$	−6.85016			−0.237344
$834$	−9.32464	−	18.7559i	−0.322886	−	0.649464i
$835$			10.3445i			0.357985i
$836$			0.683315i			0.0236329i
$837$	6.61237	−	35.0080i	0.228557	−	1.21005i
$838$		−	13.0095i		−	0.449405i
$839$	10.4894			0.362133			0.181066	−	0.983471i	$-0.442045\pi$
$839$	10.4894			0.362133			0.181066	+	0.983471i	$0.442045\pi$
$840$	−3.39491	+	1.68781i	−0.117136	+	0.0582349i
$841$	6.40901			0.221000
$842$	−37.8096			−1.30300
$843$	−6.17688	+	3.07088i	−0.212743	+	0.105767i
$844$	−21.6460			−0.745086
$845$	38.0326			1.30836
$846$	5.31211	−	7.01604i	0.182634	−	0.241217i
$847$		−	10.9852i		−	0.377456i
$848$	10.6872			0.367001
$849$	−16.7845	−	33.7609i	−0.576042	−	1.15867i
$850$			1.42914i			0.0490190i
$851$	29.7034	+	14.9675i	1.01822	+	0.513080i
$852$	−6.81188	−	13.7016i	−0.233371	−	0.469410i
$853$	−15.3706			−0.526279			−0.263140	−	0.964758i	$-0.584758\pi$
$853$	−15.3706			−0.526279			−0.263140	+	0.964758i	$0.584758\pi$
$854$		−	3.29609i		−	0.112790i
$855$	−29.4166	−	22.2724i	−1.00603	−	0.761700i
$856$		−	3.11341i		−	0.106414i
$857$		−	1.09799i		−	0.0375065i	−0.999824	−	0.0187533i	$-0.994030\pi$
$857$		−	1.09799i		−	0.0375065i	0.999824	−	0.0187533i	$-0.00596970\pi$
$858$	0.516811	+	1.03953i	0.0176436	+	0.0354890i
$859$	−37.8979			−1.29306			−0.646531	−	0.762888i	$-0.723781\pi$
$859$	−37.8979			−1.29306			−0.646531	+	0.762888i	$0.723781\pi$
$860$		−	3.99619i		−	0.136269i
$861$	−4.95072	+	2.46129i	−0.168720	+	0.0838806i
$862$		−	32.8974i		−	1.12049i
$863$			40.1581i			1.36700i	0.729952	+	0.683499i	$0.239543\pi$
$863$			40.1581i			1.36700i	−0.729952	+	0.683499i	$0.760457\pi$
$864$	−5.10587	−	0.964405i	−0.173705	−	0.0328097i
$865$		−	23.4445i		−	0.797138i
$866$	−9.17816			−0.311887
$867$	46.4118	−	23.0740i	1.57623	−	0.783634i
$868$		−	6.85642i		−	0.232722i
$869$		−	0.589405i		−	0.0199942i
$870$	−16.1360	+	8.02214i	−0.547062	+	0.271976i
$871$		−	43.0137i		−	1.45746i
$872$	−19.0554			−0.645296
$873$	10.3501	+	7.83645i	0.350298	+	0.265224i
$874$	−12.1259	+	24.0642i	−0.410165	+	0.813982i
$875$		−	11.4013i		−	0.385433i
$876$	22.2910	−	11.0821i	0.753143	−	0.374431i
$877$	−3.29363			−0.111218			−0.0556090	−	0.998453i	$-0.517710\pi$
$877$	−3.29363			−0.111218			−0.0556090	+	0.998453i	$0.517710\pi$
$878$			39.2976i			1.32623i
$879$	33.6820	−	16.7453i	1.13607	−	0.564805i
$880$	0.266201			0.00897364
$881$	−6.01730			−0.202728			−0.101364	−	0.994849i	$-0.532321\pi$
$881$	−6.01730			−0.202728			−0.101364	+	0.994849i	$0.532321\pi$
$882$	2.39178	+	1.81091i	0.0805354	+	0.0609764i
$883$	1.03677			0.0348899			0.0174450	−	0.999848i	$-0.494447\pi$
$883$	1.03677			0.0348899			0.0174450	+	0.999848i	$0.494447\pi$
$884$	37.7537			1.26979
$885$	7.82625	+	15.7420i	0.263076	+	0.529161i
$886$	−24.1259			−0.810527
$887$			41.7048i			1.40031i	0.713992	+	0.700154i	$0.246885\pi$
$887$			41.7048i			1.40031i	−0.713992	+	0.700154i	$0.753115\pi$
$888$	−10.7566	+	5.34773i	−0.360968	+	0.179458i
$889$			4.59255i			0.154029i
$890$			30.5753i			1.02489i
$891$	−0.296885	−	1.05348i	−0.00994603	−	0.0352930i
$892$	−16.6007			−0.555834
$893$	16.4821			0.551551
$894$	−11.0476	−	22.2214i	−0.369486	−	0.743196i
$895$		−	4.11798i		−	0.137649i
$896$	−1.00000			−0.0334077
$897$	−0.246784	+	45.7801i	−0.00823986	+	1.52855i
$898$	−3.29140			−0.109835
$899$		−	32.5886i		−	1.08689i
$900$	0.377806	−	0.498993i	0.0125935	−	0.0166331i
$901$	73.2093			2.43895
$902$	0.388195			0.0129255
$903$	−2.83149	+	1.40770i	−0.0942260	+	0.0468452i
$904$		−	8.31141i		−	0.276433i
$905$			1.49170i			0.0495859i
$906$	12.4081	+	24.9580i	0.412231	+	0.829174i
$907$			18.0176i			0.598264i	0.954212	+	0.299132i	$0.0966970\pi$
$907$			18.0176i			0.598264i	−0.954212	+	0.299132i	$0.903303\pi$
$908$	−21.9541			−0.728573
$909$	−2.00466	−	1.51780i	−0.0664903	−	0.0503423i
$910$	−12.0639			−0.399915
$911$	−30.1593			−0.999223			−0.499611	−	0.866250i	$-0.666524\pi$
$911$	−30.1593			−0.999223			−0.499611	+	0.866250i	$0.666524\pi$
$912$	−4.33245	−	8.71443i	−0.143462	−	0.288564i
$913$	−0.793083			−0.0262472
$914$	20.0964			0.664731
$915$	−5.56316	−	11.1899i	−0.183912	−	0.369927i
$916$		−	22.8002i		−	0.753339i
$917$	12.0371			0.397499
$918$	−34.9760	−	6.60633i	−1.15438	−	0.218041i
$919$			10.3190i			0.340393i	0.985410	+	0.170196i	$0.0544402\pi$
$919$			10.3190i			0.340393i	−0.985410	+	0.170196i	$0.945560\pi$
$920$	9.37476	+	4.72393i	0.309077	+	0.155743i
$921$	10.2203	−	5.08109i	0.336769	−	0.167427i
$922$	35.2763			1.16176
$923$		−	48.6892i		−	1.60262i
$924$	−0.0937719	−	0.188616i	−0.00308487	−	0.00620501i
$925$		−	1.44694i		−	0.0475750i
$926$			17.1026i			0.562025i
$927$	40.2635	+	30.4850i	1.32243	+	1.00126i
$928$	−4.75300			−0.156025
$929$		−	29.5964i		−	0.971027i	−0.874229	−	0.485514i	$-0.838633\pi$
$929$		−	29.5964i		−	0.971027i	0.874229	−	0.485514i	$-0.161367\pi$
$930$	−11.5723	−	23.2769i	−0.379471	−	0.763281i
$931$			5.61876i			0.184148i
$932$		−	19.3033i		−	0.632301i
$933$	−8.53079	−	17.1591i	−0.279286	−	0.561764i
$934$		−	9.51490i		−	0.311337i
$935$	1.82352			0.0596355
$936$	−13.1820	−	9.98056i	−0.430866	−	0.326225i
$937$			42.3798i			1.38449i	0.721663	+	0.692245i	$0.243378\pi$
$937$			42.3798i			1.38449i	−0.721663	+	0.692245i	$0.756622\pi$
$938$			7.80455i			0.254828i
$939$	−26.1272	−	52.5532i	−0.852630	−	1.71501i
$940$		−	6.42097i		−	0.209429i
$941$	18.4616			0.601832			0.300916	−	0.953651i	$-0.402708\pi$
$941$	18.4616			0.601832			0.300916	+	0.953651i	$0.402708\pi$
$942$	23.1669	−	11.5176i	0.754817	−	0.375263i
$943$	13.6710	+	6.88880i	0.445189	+	0.224330i
$944$			4.63693i			0.150919i
$945$	11.1763	+	2.11101i	0.363567	+	0.0686710i
$946$	0.222022			0.00721856
$947$			43.2716i			1.40614i	0.711121	+	0.703069i	$0.248188\pi$
$947$			43.2716i			1.40614i	−0.711121	+	0.703069i	$0.751812\pi$
$948$	3.73703	+	7.51679i	0.121373	+	0.244134i
$949$	79.2117			2.57132
$950$	1.17223			0.0380322
$951$	−11.8508	−	23.8370i	−0.384288	−	0.772969i
$952$	−6.85016			−0.222015
$953$	−39.4671			−1.27847			−0.639233	−	0.769013i	$-0.720748\pi$
$953$	−39.4671			−1.27847			−0.639233	+	0.769013i	$0.720748\pi$
$954$	−25.5615	−	19.3536i	−0.827585	−	0.626596i
$955$	−8.71738			−0.282088
$956$			14.6788i			0.474745i
$957$	−0.445698	−	0.896491i	−0.0144074	−	0.0289795i
$958$			18.2788i			0.590560i
$959$		−	10.6220i		−	0.343004i
$960$	−3.39491	+	1.68781i	−0.109570	+	0.0544737i
$961$	16.0105			0.516469
$962$	−38.2239			−1.23239
$963$	−5.63809	+	7.44659i	−0.181685	+	0.239963i
$964$			5.98480i			0.192757i
$965$	−23.2575			−0.748684
$966$	0.0447773	−	8.30650i	0.00144068	−	0.267257i
$967$	−0.897512			−0.0288620			−0.0144310	−	0.999896i	$-0.504594\pi$
$967$	−0.897512			−0.0288620			−0.0144310	+	0.999896i	$0.504594\pi$
$968$		−	10.9852i		−	0.353078i
$969$	−29.6780	−	59.6953i	−0.953394	−	1.91769i
$970$	9.47224			0.304135
$971$	42.4174			1.36124			0.680619	−	0.732637i	$-0.261711\pi$
$971$	42.4174			1.36124			0.680619	+	0.732637i	$0.261711\pi$
$972$	10.4657	+	11.5529i	0.335687	+	0.370560i
$973$			12.0931i			0.387688i
$974$		−	32.8792i		−	1.05352i
$975$	1.78332	−	0.886593i	0.0571121	−	0.0283937i
$976$		−	3.29609i		−	0.105505i
$977$	−33.7627			−1.08016			−0.540082	−	0.841612i	$-0.681607\pi$
$977$	−33.7627			−1.08016			−0.540082	+	0.841612i	$0.681607\pi$
$978$	2.34171	+	4.71019i	0.0748795	+	0.150615i
$979$	−1.69872			−0.0542913
$980$	2.18892			0.0699225
$981$	45.5763	+	34.5075i	1.45514	+	1.10174i
$982$	−19.6044			−0.625602
$983$	−7.52595			−0.240040			−0.120020	−	0.992771i	$-0.538296\pi$
$983$	−7.52595			−0.240040			−0.120020	+	0.992771i	$0.538296\pi$
$984$	−4.95072	+	2.46129i	−0.157823	+	0.0784631i
$985$		−	29.0513i		−	0.925651i
$986$	−32.5588			−1.03688
$987$	−4.54956	+	2.26185i	−0.144814	+	0.0719955i
$988$		−	30.9670i		−	0.985192i
$989$	7.81891	+	3.93994i	0.248627	+	0.125283i
$990$	−0.636695	−	0.482066i	−0.0202355	−	0.0153211i
$991$	20.9265			0.664753			0.332377	−	0.943147i	$-0.392149\pi$
$991$	20.9265			0.664753			0.332377	+	0.943147i	$0.392149\pi$
$992$		−	6.85642i		−	0.217692i
$993$	−44.7357	+	22.2407i	−1.41964	+	0.705787i
$994$			8.83434i			0.280208i
$995$			9.39846i			0.297951i
$996$	10.1143	−	5.02842i	0.320485	−	0.159332i
$997$	−28.4560			−0.901211			−0.450606	−	0.892723i	$-0.648792\pi$
$997$	−28.4560			−0.901211			−0.450606	+	0.892723i	$0.648792\pi$
$998$			22.1435i			0.700939i
$999$	35.4117	+	6.68861i	1.12038	+	0.211618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.a.827.10	✓	24
3.2	odd	2		966.2.h.b.827.22	yes	24
23.22	odd	2		966.2.h.b.827.10	yes	24
69.68	even	2	inner	966.2.h.a.827.22	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.10	✓	24	1.1	even	1	trivial
966.2.h.a.827.22	yes	24	69.68	even	2	inner
966.2.h.b.827.10	yes	24	23.22	odd	2
966.2.h.b.827.22	yes	24	3.2	odd	2

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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.55095 - 0.771068i) q^{3} -1.00000 q^{4} +2.18892 q^{5} +(-0.771068 - 1.55095i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(1.81091 - 2.39178i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.55095 - 0.771068i) q^{3} -1.00000 q^{4} +2.18892 q^{5} +(-0.771068 - 1.55095i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(1.81091 - 2.39178i) q^{9} -2.18892i q^{10} +0.121613 q^{11} +(-1.55095 + 0.771068i) q^{12} -5.51136 q^{13} +1.00000 q^{14} +(3.39491 - 1.68781i) q^{15} +1.00000 q^{16} +6.85016 q^{17} +(-2.39178 - 1.81091i) q^{18} -5.61876i q^{19} -2.18892 q^{20} +(0.771068 + 1.55095i) q^{21} -0.121613i q^{22} +(2.15811 - 4.28282i) q^{23} +(0.771068 + 1.55095i) q^{24} -0.208628 q^{25} +5.51136i q^{26} +(0.964405 - 5.10587i) q^{27} -1.00000i q^{28} -4.75300i q^{29} +(-1.68781 - 3.39491i) q^{30} +6.85642 q^{31} -1.00000i q^{32} +(0.188616 - 0.0937719i) q^{33} -6.85016i q^{34} +2.18892i q^{35} +(-1.81091 + 2.39178i) q^{36} +6.93548i q^{37} -5.61876 q^{38} +(-8.54785 + 4.24963i) q^{39} +2.18892i q^{40} +3.19205i q^{41} +(1.55095 - 0.771068i) q^{42} +1.82564i q^{43} -0.121613 q^{44} +(3.96393 - 5.23542i) q^{45} +(-4.28282 - 2.15811i) q^{46} +2.93340i q^{47} +(1.55095 - 0.771068i) q^{48} -1.00000 q^{49} +0.208628i q^{50} +(10.6243 - 5.28194i) q^{51} +5.51136 q^{52} +10.6872 q^{53} +(-5.10587 - 0.964405i) q^{54} +0.266201 q^{55} -1.00000 q^{56} +(-4.33245 - 8.71443i) q^{57} -4.75300 q^{58} +4.63693i q^{59} +(-3.39491 + 1.68781i) q^{60} -3.29609i q^{61} -6.85642i q^{62} +(2.39178 + 1.81091i) q^{63} -1.00000 q^{64} -12.0639 q^{65} +(-0.0937719 - 0.188616i) q^{66} +7.80455i q^{67} -6.85016 q^{68} +(0.0447773 - 8.30650i) q^{69} +2.18892 q^{70} +8.83434i q^{71} +(2.39178 + 1.81091i) q^{72} -14.3724 q^{73} +6.93548 q^{74} +(-0.323572 + 0.160867i) q^{75} +5.61876i q^{76} +0.121613i q^{77} +(4.24963 + 8.54785i) q^{78} -4.84656i q^{79} +2.18892 q^{80} +(-2.44123 - 8.66259i) q^{81} +3.19205 q^{82} -6.52137 q^{83} +(-0.771068 - 1.55095i) q^{84} +14.9945 q^{85} +1.82564 q^{86} +(-3.66489 - 7.37167i) q^{87} +0.121613i q^{88} -13.9682 q^{89} +(-5.23542 - 3.96393i) q^{90} -5.51136i q^{91} +(-2.15811 + 4.28282i) q^{92} +(10.6340 - 5.28677i) q^{93} +2.93340 q^{94} -12.2990i q^{95} +(-0.771068 - 1.55095i) q^{96} +4.32736i q^{97} +1.00000i q^{98} +(0.220230 - 0.290872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

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