LMFDB - Embedded newform 966.2.f.c.461.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (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:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.7
Character	$\chi$	$=$	966.461
Dual form			966.2.f.c.461.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.436762 - 1.67608i) q^{3} -1.00000 q^{4} -3.48442 q^{5} +(-1.67608 + 0.436762i) q^{6} +(-1.82520 + 1.91537i) q^{7} +1.00000i q^{8} +(-2.61848 + 1.46409i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.436762 - 1.67608i) q^{3} -1.00000 q^{4} -3.48442 q^{5} +(-1.67608 + 0.436762i) q^{6} +(-1.82520 + 1.91537i) q^{7} +1.00000i q^{8} +(-2.61848 + 1.46409i) q^{9} +3.48442i q^{10} +4.19412i q^{11} +(0.436762 + 1.67608i) q^{12} -5.14983i q^{13} +(1.91537 + 1.82520i) q^{14} +(1.52186 + 5.84016i) q^{15} +1.00000 q^{16} +3.35216 q^{17} +(1.46409 + 2.61848i) q^{18} -6.99187i q^{19} +3.48442 q^{20} +(4.00749 + 2.22261i) q^{21} +4.19412 q^{22} -1.00000i q^{23} +(1.67608 - 0.436762i) q^{24} +7.14118 q^{25} -5.14983 q^{26} +(3.59759 + 3.74932i) q^{27} +(1.82520 - 1.91537i) q^{28} +1.32229i q^{29} +(5.84016 - 1.52186i) q^{30} +8.35896i q^{31} -1.00000i q^{32} +(7.02967 - 1.83183i) q^{33} -3.35216i q^{34} +(6.35975 - 6.67397i) q^{35} +(2.61848 - 1.46409i) q^{36} +10.1726 q^{37} -6.99187 q^{38} +(-8.63152 + 2.24925i) q^{39} -3.48442i q^{40} -6.46467 q^{41} +(2.22261 - 4.00749i) q^{42} -0.124320 q^{43} -4.19412i q^{44} +(9.12388 - 5.10152i) q^{45} -1.00000 q^{46} -0.718233 q^{47} +(-0.436762 - 1.67608i) q^{48} +(-0.337317 - 6.99187i) q^{49} -7.14118i q^{50} +(-1.46409 - 5.61848i) q^{51} +5.14983i q^{52} +9.13660i q^{53} +(3.74932 - 3.59759i) q^{54} -14.6141i q^{55} +(-1.91537 - 1.82520i) q^{56} +(-11.7189 + 3.05378i) q^{57} +1.32229 q^{58} +1.13971 q^{59} +(-1.52186 - 5.84016i) q^{60} +11.7043i q^{61} +8.35896 q^{62} +(1.97495 - 7.68762i) q^{63} -1.00000 q^{64} +17.9442i q^{65} +(-1.83183 - 7.02967i) q^{66} +0.852497 q^{67} -3.35216 q^{68} +(-1.67608 + 0.436762i) q^{69} +(-6.67397 - 6.35975i) q^{70} +8.48358i q^{71} +(-1.46409 - 2.61848i) q^{72} +4.79667i q^{73} -10.1726i q^{74} +(-3.11900 - 11.9692i) q^{75} +6.99187i q^{76} +(-8.03331 - 7.65509i) q^{77} +(2.24925 + 8.63152i) q^{78} +5.87691 q^{79} -3.48442 q^{80} +(4.71286 - 7.66740i) q^{81} +6.46467i q^{82} +17.0226 q^{83} +(-4.00749 - 2.22261i) q^{84} -11.6803 q^{85} +0.124320i q^{86} +(2.21626 - 0.577525i) q^{87} -4.19412 q^{88} -5.57357 q^{89} +(-5.10152 - 9.12388i) q^{90} +(9.86385 + 9.39945i) q^{91} +1.00000i q^{92} +(14.0103 - 3.65087i) q^{93} +0.718233i q^{94} +24.3626i q^{95} +(-1.67608 + 0.436762i) q^{96} -8.82586i q^{97} +(-6.99187 + 0.337317i) q^{98} +(-6.14058 - 10.9822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * 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
$3$	−0.436762	−	1.67608i	−0.252164	−	0.967684i
$3$	−0.436762	−	1.67608i	−0.252164	−	0.967684i
$4$	−1.00000			−0.500000
$5$	−3.48442			−1.55828			−0.779140	−	0.626850i	$-0.784344\pi$
$5$	−3.48442			−1.55828			−0.779140	+	0.626850i	$0.784344\pi$
$6$	−1.67608	+	0.436762i	−0.684256	+	0.178307i
$7$	−1.82520	+	1.91537i	−0.689859	+	0.723943i
$7$	−1.82520	+	1.91537i	−0.689859	+	0.723943i
$8$			1.00000i			0.353553i
$9$	−2.61848	+	1.46409i	−0.872826	+	0.488031i
$10$			3.48442i			1.10187i
$11$			4.19412i			1.26457i	0.774734	+	0.632287i	$0.217884\pi$
$11$			4.19412i			1.26457i	−0.774734	+	0.632287i	$0.782116\pi$
$12$	0.436762	+	1.67608i	0.126082	+	0.483842i
$13$		−	5.14983i		−	1.42831i	−0.699990	−	0.714153i	$-0.746812\pi$
$13$		−	5.14983i		−	1.42831i	0.699990	−	0.714153i	$-0.253188\pi$
$14$	1.91537	+	1.82520i	0.511905	+	0.487804i
$15$	1.52186	+	5.84016i	0.392943	+	1.50792i
$16$	1.00000			0.250000
$17$	3.35216			0.813018			0.406509	−	0.913647i	$-0.366746\pi$
$17$	3.35216			0.813018			0.406509	+	0.913647i	$0.366746\pi$
$18$	1.46409	+	2.61848i	0.345090	+	0.617181i
$19$		−	6.99187i		−	1.60404i	−0.597294	−	0.802022i	$-0.703758\pi$
$19$		−	6.99187i		−	1.60404i	0.597294	−	0.802022i	$-0.296242\pi$
$20$	3.48442			0.779140
$21$	4.00749	+	2.22261i	0.874507	+	0.485013i
$22$	4.19412			0.894189
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	1.67608	−	0.436762i	0.342128	−	0.0891536i
$25$	7.14118			1.42824
$26$	−5.14983			−1.00996
$27$	3.59759	+	3.74932i	0.692356	+	0.721556i
$28$	1.82520	−	1.91537i	0.344930	−	0.361972i
$29$			1.32229i			0.245543i	0.992435	+	0.122771i	$0.0391782\pi$
$29$			1.32229i			0.245543i	−0.992435	+	0.122771i	$0.960822\pi$
$30$	5.84016	−	1.52186i	1.06626	−	0.277853i
$31$			8.35896i			1.50131i	0.660692	+	0.750657i	$0.270263\pi$
$31$			8.35896i			1.50131i	−0.660692	+	0.750657i	$0.729737\pi$
$32$		−	1.00000i		−	0.176777i
$33$	7.02967	−	1.83183i	1.22371	−	0.318881i
$34$		−	3.35216i		−	0.574890i
$35$	6.35975	−	6.67397i	1.07499	−	1.12811i
$36$	2.61848	−	1.46409i	0.436413	−	0.244016i
$37$	10.1726			1.67237			0.836184	−	0.548449i	$-0.184782\pi$
$37$	10.1726			1.67237			0.836184	+	0.548449i	$0.184782\pi$
$38$	−6.99187			−1.13423
$39$	−8.63152	+	2.24925i	−1.38215	+	0.360168i
$40$		−	3.48442i		−	0.550935i
$41$	−6.46467			−1.00961			−0.504806	−	0.863233i	$-0.668436\pi$
$41$	−6.46467			−1.00961			−0.504806	+	0.863233i	$0.668436\pi$
$42$	2.22261	−	4.00749i	0.342956	−	0.618370i
$43$	−0.124320			−0.0189587			−0.00947933	−	0.999955i	$-0.503017\pi$
$43$	−0.124320			−0.0189587			−0.00947933	+	0.999955i	$0.503017\pi$
$44$		−	4.19412i		−	0.632287i
$45$	9.12388	−	5.10152i	1.36011	−	0.760489i
$46$	−1.00000			−0.147442
$47$	−0.718233			−0.104765			−0.0523825	−	0.998627i	$-0.516682\pi$
$47$	−0.718233			−0.104765			−0.0523825	+	0.998627i	$0.516682\pi$
$48$	−0.436762	−	1.67608i	−0.0630411	−	0.241921i
$49$	−0.337317	−	6.99187i	−0.0481882	−	0.998838i
$50$		−	7.14118i		−	1.00992i
$51$	−1.46409	−	5.61848i	−0.205014	−	0.786744i
$52$			5.14983i			0.714153i
$53$			9.13660i			1.25501i	0.778613	+	0.627504i	$0.215923\pi$
$53$			9.13660i			1.25501i	−0.778613	+	0.627504i	$0.784077\pi$
$54$	3.74932	−	3.59759i	0.510217	−	0.489570i
$55$		−	14.6141i		−	1.97056i
$56$	−1.91537	−	1.82520i	−0.255953	−	0.243902i
$57$	−11.7189	+	3.05378i	−1.55221	+	0.404483i
$58$	1.32229			0.173625
$59$	1.13971			0.148378			0.0741888	−	0.997244i	$-0.476363\pi$
$59$	1.13971			0.148378			0.0741888	+	0.997244i	$0.476363\pi$
$60$	−1.52186	−	5.84016i	−0.196471	−	0.753962i
$61$			11.7043i			1.49858i	0.662242	+	0.749290i	$0.269605\pi$
$61$			11.7043i			1.49858i	−0.662242	+	0.749290i	$0.730395\pi$
$62$	8.35896			1.06159
$63$	1.97495	−	7.68762i	0.248820	−	0.968550i
$64$	−1.00000			−0.125000
$65$			17.9442i			2.22570i
$66$	−1.83183	−	7.02967i	−0.225483	−	0.865293i
$67$	0.852497			0.104149			0.0520745	−	0.998643i	$-0.483417\pi$
$67$	0.852497			0.104149			0.0520745	+	0.998643i	$0.483417\pi$
$68$	−3.35216			−0.406509
$69$	−1.67608	+	0.436762i	−0.201776	+	0.0525799i
$70$	−6.67397	−	6.35975i	−0.797692	−	0.760136i
$71$			8.48358i			1.00682i	0.864049	+	0.503408i	$0.167921\pi$
$71$			8.48358i			1.00682i	−0.864049	+	0.503408i	$0.832079\pi$
$72$	−1.46409	−	2.61848i	−0.172545	−	0.308591i
$73$			4.79667i			0.561408i	0.959794	+	0.280704i	$0.0905679\pi$
$73$			4.79667i			0.561408i	−0.959794	+	0.280704i	$0.909432\pi$
$74$		−	10.1726i		−	1.18254i
$75$	−3.11900	−	11.9692i	−0.360151	−	1.38208i
$76$			6.99187i			0.802022i
$77$	−8.03331	−	7.65509i	−0.915481	−	0.872379i
$78$	2.24925	+	8.63152i	0.254677	+	0.977327i
$79$	5.87691			0.661204			0.330602	−	0.943770i	$-0.392748\pi$
$79$	5.87691			0.661204			0.330602	+	0.943770i	$0.392748\pi$
$80$	−3.48442			−0.389570
$81$	4.71286	−	7.66740i	0.523651	−	0.851933i
$82$			6.46467i			0.713904i
$83$	17.0226			1.86847			0.934237	−	0.356654i	$-0.116082\pi$
$83$	17.0226			1.86847			0.934237	+	0.356654i	$0.116082\pi$
$84$	−4.00749	−	2.22261i	−0.437253	−	0.242507i
$85$	−11.6803			−1.26691
$86$			0.124320i			0.0134058i
$87$	2.21626	−	0.577525i	0.237608	−	0.0619172i
$88$	−4.19412			−0.447095
$89$	−5.57357			−0.590798			−0.295399	−	0.955374i	$-0.595453\pi$
$89$	−5.57357			−0.590798			−0.295399	+	0.955374i	$0.595453\pi$
$90$	−5.10152	−	9.12388i	−0.537747	−	0.961741i
$91$	9.86385	+	9.39945i	1.03401	+	0.985330i
$92$			1.00000i			0.104257i
$93$	14.0103	−	3.65087i	1.45280	−	0.378578i
$94$			0.718233i			0.0740800i
$95$			24.3626i			2.49955i
$96$	−1.67608	+	0.436762i	−0.171064	+	0.0445768i
$97$		−	8.82586i		−	0.896130i	−0.894001	−	0.448065i	$-0.852113\pi$
$97$		−	8.82586i		−	0.896130i	0.894001	−	0.448065i	$-0.147887\pi$
$98$	−6.99187	+	0.337317i	−0.706285	+	0.0340742i
$99$	−6.14058	−	10.9822i	−0.617152	−	1.10375i
$100$	−7.14118			−0.714118
$101$	−3.72950			−0.371099			−0.185550	−	0.982635i	$-0.559407\pi$
$101$	−3.72950			−0.371099			−0.185550	+	0.982635i	$0.559407\pi$
$102$	−5.61848	+	1.46409i	−0.556312	+	0.144967i
$103$			9.25903i			0.912320i	0.889898	+	0.456160i	$0.150775\pi$
$103$			9.25903i			0.912320i	−0.889898	+	0.456160i	$0.849225\pi$
$104$	5.14983			0.504982
$105$	−13.9638	−	7.74451i	−1.36273	−	0.755787i
$106$	9.13660			0.887425
$107$			5.16006i			0.498842i	0.968395	+	0.249421i	$0.0802403\pi$
$107$			5.16006i			0.498842i	−0.968395	+	0.249421i	$0.919760\pi$
$108$	−3.59759	−	3.74932i	−0.346178	−	0.360778i
$109$	11.6021			1.11128			0.555639	−	0.831424i	$-0.312474\pi$
$109$	11.6021			1.11128			0.555639	+	0.831424i	$0.312474\pi$
$110$	−14.6141			−1.39340
$111$	−4.44301	−	17.0501i	−0.421712	−	1.61832i
$112$	−1.82520	+	1.91537i	−0.172465	+	0.180986i
$113$		−	12.6892i		−	1.19370i	−0.802352	−	0.596851i	$-0.796419\pi$
$113$		−	12.6892i		−	1.19370i	0.802352	−	0.596851i	$-0.203581\pi$
$114$	3.05378	+	11.7189i	0.286013	+	1.09758i
$115$			3.48442i			0.324924i
$116$		−	1.32229i		−	0.122771i
$117$	7.53983	+	13.4847i	0.697058	+	1.24666i
$118$		−	1.13971i		−	0.104919i
$119$	−6.11834	+	6.42064i	−0.560868	+	0.588579i
$120$	−5.84016	+	1.52186i	−0.533131	+	0.138926i
$121$	−6.59064			−0.599149
$122$	11.7043			1.05966
$123$	2.82352	+	10.8353i	0.254588	+	0.976986i
$124$		−	8.35896i		−	0.750657i
$125$	−7.46079			−0.667313
$126$	−7.68762	−	1.97495i	−0.684868	−	0.175943i
$127$	−14.6938			−1.30387			−0.651934	−	0.758276i	$-0.726042\pi$
$127$	−14.6938			−1.30387			−0.651934	+	0.758276i	$0.726042\pi$
$128$			1.00000i			0.0883883i
$129$	0.0542983	+	0.208370i	0.00478070	+	0.0183460i
$130$	17.9442			1.57381
$131$	10.7108			0.935806			0.467903	−	0.883780i	$-0.345010\pi$
$131$	10.7108			0.935806			0.467903	+	0.883780i	$0.345010\pi$
$132$	−7.02967	+	1.83183i	−0.611855	+	0.159440i
$133$	13.3920	+	12.7615i	1.16124	+	1.10657i
$134$		−	0.852497i		−	0.0736445i
$135$	−12.5355	−	13.0642i	−1.07888	−	1.12439i
$136$			3.35216i			0.287445i
$137$			3.02608i			0.258535i	0.991610	+	0.129268i	$0.0412626\pi$
$137$			3.02608i			0.258535i	−0.991610	+	0.129268i	$0.958737\pi$
$138$	0.436762	+	1.67608i	0.0371796	+	0.142677i
$139$			10.7158i			0.908903i	0.890771	+	0.454452i	$0.150165\pi$
$139$			10.7158i			0.908903i	−0.890771	+	0.454452i	$0.849835\pi$
$140$	−6.35975	+	6.67397i	−0.537497	+	0.564053i
$141$	0.313697	+	1.20381i	0.0264180	+	0.101379i
$142$	8.48358			0.711926
$143$	21.5990			1.80620
$144$	−2.61848	+	1.46409i	−0.218207	+	0.122008i
$145$		−	4.60741i		−	0.382624i
$146$	4.79667			0.396975
$147$	−11.5716	+	3.61915i	−0.954409	+	0.298502i
$148$	−10.1726			−0.836184
$149$		−	20.3122i		−	1.66404i	−0.554747	−	0.832019i	$-0.687185\pi$
$149$		−	20.3122i		−	1.66404i	0.554747	−	0.832019i	$-0.312815\pi$
$150$	−11.9692	+	3.11900i	−0.977280	+	0.254665i
$151$	18.0327			1.46748			0.733739	−	0.679432i	$-0.237774\pi$
$151$	18.0327			1.46748			0.733739	+	0.679432i	$0.237774\pi$
$152$	6.99187			0.567115
$153$	−8.77755	+	4.90787i	−0.709623	+	0.396778i
$154$	−7.65509	+	8.03331i	−0.616865	+	0.647342i
$155$		−	29.1261i		−	2.33947i
$156$	8.63152	−	2.24925i	0.691074	−	0.180084i
$157$			14.2458i			1.13694i	0.822704	+	0.568470i	$0.192465\pi$
$157$			14.2458i			1.13694i	−0.822704	+	0.568470i	$0.807535\pi$
$158$		−	5.87691i		−	0.467542i
$159$	15.3137	−	3.99052i	1.21445	−	0.316468i
$160$			3.48442i			0.275468i
$161$	1.91537	+	1.82520i	0.150953	+	0.143846i
$162$	−7.66740	−	4.71286i	−0.602408	−	0.370277i
$163$	12.2176			0.956954			0.478477	−	0.878100i	$-0.341189\pi$
$163$	12.2176			0.956954			0.478477	+	0.878100i	$0.341189\pi$
$164$	6.46467			0.504806
$165$	−24.4943	+	6.38287i	−1.90688	+	0.496906i
$166$		−	17.0226i		−	1.32121i
$167$	−3.15509			−0.244148			−0.122074	−	0.992521i	$-0.538955\pi$
$167$	−3.15509			−0.244148			−0.122074	+	0.992521i	$0.538955\pi$
$168$	−2.22261	+	4.00749i	−0.171478	+	0.309185i
$169$	−13.5207			−1.04006
$170$			11.6803i			0.895840i
$171$	10.2368	+	18.3081i	0.782824	+	1.40005i
$172$	0.124320			0.00947933
$173$	−12.7701			−0.970896			−0.485448	−	0.874266i	$-0.661343\pi$
$173$	−12.7701			−0.970896			−0.485448	+	0.874266i	$0.661343\pi$
$174$	−0.577525	−	2.21626i	−0.0437820	−	0.168014i
$175$	−13.0341	+	13.6780i	−0.985283	+	1.03396i
$176$			4.19412i			0.316144i
$177$	−0.497782	−	1.91024i	−0.0374156	−	0.143583i
$178$			5.57357i			0.417757i
$179$		−	3.55077i		−	0.265397i	−0.991156	−	0.132699i	$-0.957636\pi$
$179$		−	3.55077i		−	0.265397i	0.991156	−	0.132699i	$-0.0423642\pi$
$180$	−9.12388	+	5.10152i	−0.680054	+	0.380245i
$181$		−	6.72826i		−	0.500108i	−0.968232	−	0.250054i	$-0.919552\pi$
$181$		−	6.72826i		−	0.500108i	0.968232	−	0.250054i	$-0.0804484\pi$
$182$	9.39945	−	9.86385i	0.696733	−	0.731157i
$183$	19.6173	−	5.11199i	1.45015	−	0.377889i
$184$	1.00000			0.0737210
$185$	−35.4457			−2.60602
$186$	−3.65087	−	14.0103i	−0.267695	−	1.02728i
$187$			14.0593i			1.02812i
$188$	0.718233			0.0523825
$189$	−13.7476	+	0.0474891i	−0.999994	+	0.00345432i
$190$	24.3626			1.76745
$191$		−	3.46178i		−	0.250486i	−0.992126	−	0.125243i	$-0.960029\pi$
$191$		−	3.46178i		−	0.250486i	0.992126	−	0.125243i	$-0.0399710\pi$
$192$	0.436762	+	1.67608i	0.0315206	+	0.120961i
$193$	−10.4060			−0.749037			−0.374519	−	0.927219i	$-0.622192\pi$
$193$	−10.4060			−0.749037			−0.374519	+	0.927219i	$0.622192\pi$
$194$	−8.82586			−0.633660
$195$	30.0758	−	7.83732i	2.15377	−	0.561242i
$196$	0.337317	+	6.99187i	0.0240941	+	0.499419i
$197$			18.4857i			1.31705i	0.752558	+	0.658526i	$0.228820\pi$
$197$			18.4857i			1.31705i	−0.752558	+	0.658526i	$0.771180\pi$
$198$	−10.9822	+	6.14058i	−0.780472	+	0.436392i
$199$			7.26210i			0.514797i	0.966305	+	0.257398i	$0.0828652\pi$
$199$			7.26210i			0.514797i	−0.966305	+	0.257398i	$0.917135\pi$
$200$			7.14118i			0.504958i
$201$	−0.372338	−	1.42885i	−0.0262627	−	0.100783i
$202$			3.72950i			0.262407i
$203$	−2.53268	−	2.41344i	−0.177759	−	0.169390i
$204$	1.46409	+	5.61848i	0.102507	+	0.393372i
$205$	22.5256			1.57326
$206$	9.25903			0.645107
$207$	1.46409	+	2.61848i	0.101762	+	0.181997i
$208$		−	5.14983i		−	0.357076i
$209$	29.3247			2.02843
$210$	−7.74451	+	13.9638i	−0.534422	+	0.963593i
$211$	−4.70667			−0.324021			−0.162010	−	0.986789i	$-0.551798\pi$
$211$	−4.70667			−0.324021			−0.162010	+	0.986789i	$0.551798\pi$
$212$		−	9.13660i		−	0.627504i
$213$	14.2191	−	3.70530i	0.974280	−	0.253883i
$214$	5.16006			0.352735
$215$	0.433184			0.0295429
$216$	−3.74932	+	3.59759i	−0.255109	+	0.244785i
$217$	−16.0105	−	15.2567i	−1.08687	−	1.03570i
$218$		−	11.6021i		−	0.785792i
$219$	8.03960	−	2.09500i	0.543266	−	0.141567i
$220$			14.6141i			0.985281i
$221$		−	17.2630i		−	1.16124i
$222$	−17.0501	+	4.44301i	−1.14433	+	0.298195i
$223$			3.59109i			0.240477i	0.992745	+	0.120239i	$0.0383660\pi$
$223$			3.59109i			0.240477i	−0.992745	+	0.120239i	$0.961634\pi$
$224$	1.91537	+	1.82520i	0.127976	+	0.121951i
$225$	−18.6990	+	10.4554i	−1.24660	+	0.697024i
$226$	−12.6892			−0.844074
$227$	25.7980			1.71227			0.856137	−	0.516749i	$-0.172858\pi$
$227$	25.7980			1.71227			0.856137	+	0.516749i	$0.172858\pi$
$228$	11.7189	−	3.05378i	0.776104	−	0.202242i
$229$			3.16475i			0.209133i	0.994518	+	0.104566i	$0.0333455\pi$
$229$			3.16475i			0.209133i	−0.994518	+	0.104566i	$0.966655\pi$
$230$	3.48442			0.229756
$231$	−9.32189	+	16.8079i	−0.613336	+	1.10588i
$232$	−1.32229			−0.0868125
$233$			19.5350i			1.27978i	0.768466	+	0.639891i	$0.221020\pi$
$233$			19.5350i			1.27978i	−0.768466	+	0.639891i	$0.778980\pi$
$234$	13.4847	−	7.53983i	0.881523	−	0.492894i
$235$	2.50262			0.163253
$236$	−1.13971			−0.0741888
$237$	−2.56681	−	9.85016i	−0.166732	−	0.639837i
$238$	6.42064	+	6.11834i	0.416188	+	0.396593i
$239$			8.56751i			0.554186i	0.960843	+	0.277093i	$0.0893711\pi$
$239$			8.56751i			0.554186i	−0.960843	+	0.277093i	$0.910629\pi$
$240$	1.52186	+	5.84016i	0.0982357	+	0.376981i
$241$			4.78063i			0.307948i	0.988075	+	0.153974i	$0.0492072\pi$
$241$			4.78063i			0.307948i	−0.988075	+	0.153974i	$0.950793\pi$
$242$			6.59064i			0.423662i
$243$	−14.9096	−	4.55030i	−0.956448	−	0.291902i
$244$		−	11.7043i		−	0.749290i
$245$	1.17535	+	24.3626i	0.0750906	+	1.55647i
$246$	10.8353	−	2.82352i	0.690833	−	0.180021i
$247$	−36.0069			−2.29107
$248$	−8.35896			−0.530795
$249$	−7.43482	−	28.5312i	−0.471163	−	1.80809i
$250$			7.46079i			0.471862i
$251$	−27.8363			−1.75701			−0.878505	−	0.477733i	$-0.841459\pi$
$251$	−27.8363			−1.75701			−0.878505	+	0.477733i	$0.841459\pi$
$252$	−1.97495	+	7.68762i	−0.124410	+	0.484275i
$253$	4.19412			0.263682
$254$			14.6938i			0.921974i
$255$	5.10152	+	19.5771i	0.319469	+	1.22597i
$256$	1.00000			0.0625000
$257$	−17.3741			−1.08376			−0.541882	−	0.840455i	$-0.682288\pi$
$257$	−17.3741			−1.08376			−0.541882	+	0.840455i	$0.682288\pi$
$258$	0.208370	−	0.0542983i	0.0129726	−	0.00338046i
$259$	−18.5670	+	19.4844i	−1.15370	+	1.21070i
$260$		−	17.9442i		−	1.11285i
$261$	−1.93595	−	3.46238i	−0.119833	−	0.214316i
$262$		−	10.7108i		−	0.661715i
$263$			3.52547i			0.217390i	0.994075	+	0.108695i	$0.0346671\pi$
$263$			3.52547i			0.217390i	−0.994075	+	0.108695i	$0.965333\pi$
$264$	1.83183	+	7.02967i	0.112741	+	0.432647i
$265$		−	31.8357i		−	1.95565i
$266$	12.7615	−	13.3920i	0.782460	−	0.821119i
$267$	2.43432	+	9.34175i	0.148978	+	0.571706i
$268$	−0.852497			−0.0520745
$269$	−18.0738			−1.10198			−0.550989	−	0.834512i	$-0.685750\pi$
$269$	−18.0738			−1.10198			−0.550989	+	0.834512i	$0.685750\pi$
$270$	−13.0642	+	12.5355i	−0.795061	+	0.762887i
$271$		−	12.4477i		−	0.756147i	−0.925776	−	0.378073i	$-0.876587\pi$
$271$		−	12.4477i		−	0.756147i	0.925776	−	0.378073i	$-0.123413\pi$
$272$	3.35216			0.203254
$273$	11.4461	−	20.6379i	0.692747	−	1.24906i
$274$	3.02608			0.182812
$275$			29.9510i			1.80611i
$276$	1.67608	−	0.436762i	0.100888	−	0.0262900i
$277$	−0.644534			−0.0387263			−0.0193632	−	0.999813i	$-0.506164\pi$
$277$	−0.644534			−0.0387263			−0.0193632	+	0.999813i	$0.506164\pi$
$278$	10.7158			0.642692
$279$	−12.2383	−	21.8878i	−0.732688	−	1.31039i
$280$	6.67397	+	6.35975i	0.398846	+	0.380068i
$281$			18.3917i			1.09715i	0.836100	+	0.548577i	$0.184830\pi$
$281$			18.3917i			1.09715i	−0.836100	+	0.548577i	$0.815170\pi$
$282$	1.20381	−	0.313697i	0.0716861	−	0.0186804i
$283$			7.35879i			0.437435i	0.975788	+	0.218717i	$0.0701873\pi$
$283$			7.35879i			0.437435i	−0.975788	+	0.218717i	$0.929813\pi$
$284$		−	8.48358i		−	0.503408i
$285$	40.8336	−	10.6407i	2.41878	−	0.630298i
$286$		−	21.5990i		−	1.27718i
$287$	11.7993	−	12.3823i	0.696490	−	0.730902i
$288$	1.46409	+	2.61848i	0.0862726	+	0.154295i
$289$	−5.76304			−0.339003
$290$	−4.60741			−0.270556
$291$	−14.7928	+	3.85480i	−0.867171	+	0.225972i
$292$		−	4.79667i		−	0.280704i
$293$	−13.8700			−0.810292			−0.405146	−	0.914252i	$-0.632779\pi$
$293$	−13.8700			−0.810292			−0.405146	+	0.914252i	$0.632779\pi$
$294$	3.61915	+	11.5716i	0.211073	+	0.674869i
$295$	−3.97123			−0.231214
$296$			10.1726i			0.591271i
$297$	−15.7251	+	15.0887i	−0.912462	+	0.875536i
$298$	−20.3122			−1.17665
$299$	−5.14983			−0.297822
$300$	3.11900	+	11.9692i	0.180075	+	0.691041i
$301$	0.226909	−	0.238120i	0.0130788	−	0.0137250i
$302$		−	18.0327i		−	1.03766i
$303$	1.62890	+	6.25094i	0.0935780	+	0.359107i
$304$		−	6.99187i		−	0.401011i
$305$		−	40.7827i		−	2.33521i
$306$	4.90787	+	8.77755i	0.280564	+	0.501779i
$307$			22.8398i			1.30354i	0.758419	+	0.651768i	$0.225972\pi$
$307$			22.8398i			1.30354i	−0.758419	+	0.651768i	$0.774028\pi$
$308$	8.03331	+	7.65509i	0.457740	+	0.436189i
$309$	15.5189	−	4.04399i	0.882837	−	0.230055i
$310$	−29.1261			−1.65425
$311$	3.32900			0.188770			0.0943852	−	0.995536i	$-0.469911\pi$
$311$	3.32900			0.188770			0.0943852	+	0.995536i	$0.469911\pi$
$312$	−2.24925	−	8.63152i	−0.127339	−	0.488663i
$313$			15.3261i			0.866285i	0.901326	+	0.433142i	$0.142595\pi$
$313$			15.3261i			0.866285i	−0.901326	+	0.433142i	$0.857405\pi$
$314$	14.2458			0.803939
$315$	−6.88155	+	26.7869i	−0.387732	+	1.50927i
$316$	−5.87691			−0.330602
$317$		−	27.2559i		−	1.53085i	−0.643528	−	0.765423i	$-0.722530\pi$
$317$		−	27.2559i		−	1.53085i	0.643528	−	0.765423i	$-0.277470\pi$
$318$	−3.99052	−	15.3137i	−0.223777	−	0.858747i
$319$	−5.54584			−0.310507
$320$	3.48442			0.194785
$321$	8.64867	−	2.25372i	0.482722	−	0.125790i
$322$	1.82520	−	1.91537i	0.101714	−	0.106740i
$323$		−	23.4378i		−	1.30412i
$324$	−4.71286	+	7.66740i	−0.261826	+	0.425966i
$325$		−	36.7759i		−	2.03996i
$326$		−	12.2176i		−	0.676669i
$327$	−5.06735	−	19.4460i	−0.280225	−	1.07537i
$328$		−	6.46467i		−	0.356952i
$329$	1.31092	−	1.37568i	0.0722731	−	0.0758439i
$330$	6.38287	+	24.4943i	0.351365	+	1.34837i
$331$	−11.0278			−0.606143			−0.303072	−	0.952968i	$-0.598012\pi$
$331$	−11.0278			−0.606143			−0.303072	+	0.952968i	$0.598012\pi$
$332$	−17.0226			−0.934237
$333$	−26.6368	+	14.8937i	−1.45969	+	0.816168i
$334$			3.15509i			0.172639i
$335$	−2.97046			−0.162293
$336$	4.00749	+	2.22261i	0.218627	+	0.121253i
$337$	30.5839			1.66601			0.833006	−	0.553263i	$-0.186618\pi$
$337$	30.5839			1.66601			0.833006	+	0.553263i	$0.186618\pi$
$338$			13.5207i			0.735430i
$339$	−21.2681	+	5.54216i	−1.15513	+	0.301009i
$340$	11.6803			0.633455
$341$	−35.0585			−1.89852
$342$	18.3081	−	10.2368i	0.989986	−	0.553540i
$343$	14.0077	+	12.1154i	0.756345	+	0.654172i
$344$		−	0.124320i		−	0.00670290i
$345$	5.84016	−	1.52186i	0.314424	−	0.0819343i
$346$			12.7701i			0.686527i
$347$		−	10.8821i		−	0.584180i	−0.956391	−	0.292090i	$-0.905649\pi$
$347$		−	10.8821i		−	0.584180i	0.956391	−	0.292090i	$-0.0943508\pi$
$348$	−2.21626	+	0.577525i	−0.118804	+	0.0309586i
$349$			3.69686i			0.197888i	0.995093	+	0.0989442i	$0.0315465\pi$
$349$			3.69686i			0.197888i	−0.995093	+	0.0989442i	$0.968453\pi$
$350$	13.6780	+	13.0341i	0.731122	+	0.696700i
$351$	19.3083	−	18.5270i	1.03060	−	0.988896i
$352$	4.19412			0.223547
$353$	22.0601			1.17414			0.587071	−	0.809536i	$-0.300281\pi$
$353$	22.0601			1.17414			0.587071	+	0.809536i	$0.300281\pi$
$354$	−1.91024	+	0.497782i	−0.101528	+	0.0264568i
$355$		−	29.5604i		−	1.56890i
$356$	5.57357			0.295399
$357$	13.4337	+	7.45054i	0.710989	+	0.394324i
$358$	−3.55077			−0.187664
$359$			26.5329i			1.40035i	0.713969	+	0.700177i	$0.246896\pi$
$359$			26.5329i			1.40035i	−0.713969	+	0.700177i	$0.753104\pi$
$360$	5.10152	+	9.12388i	0.268874	+	0.480871i
$361$	−29.8862			−1.57296
$362$	−6.72826			−0.353630
$363$	2.87854	+	11.0464i	0.151084	+	0.579787i
$364$	−9.86385	−	9.39945i	−0.517006	−	0.492665i
$365$		−	16.7136i		−	0.874831i
$366$	−5.11199	−	19.6173i	−0.267208	−	1.02541i
$367$			33.9438i			1.77185i	0.463826	+	0.885926i	$0.346476\pi$
$367$			33.9438i			1.77185i	−0.463826	+	0.885926i	$0.653524\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	16.9276	−	9.46489i	0.881216	−	0.492722i
$370$			35.4457i			1.84273i
$371$	−17.5000	−	16.6761i	−0.908555	−	0.865779i
$372$	−14.0103	+	3.65087i	−0.726399	+	0.189289i
$373$	8.74496			0.452797			0.226398	−	0.974035i	$-0.427305\pi$
$373$	8.74496			0.452797			0.226398	+	0.974035i	$0.427305\pi$
$374$	14.0593			0.726992
$375$	3.25859	+	12.5049i	0.168273	+	0.645748i
$376$		−	0.718233i		−	0.0370400i
$377$	6.80956			0.350710
$378$	0.0474891	+	13.7476i	0.00244257	+	0.707103i
$379$	26.4429			1.35828			0.679141	−	0.734008i	$-0.262352\pi$
$379$	26.4429			1.35828			0.679141	+	0.734008i	$0.262352\pi$
$380$		−	24.3626i		−	1.24978i
$381$	6.41771	+	24.6280i	0.328789	+	1.26173i
$382$	−3.46178			−0.177120
$383$	21.8401			1.11598			0.557989	−	0.829848i	$-0.311573\pi$
$383$	21.8401			1.11598			0.557989	+	0.829848i	$0.311573\pi$
$384$	1.67608	−	0.436762i	0.0855320	−	0.0222884i
$385$	27.9914	+	26.6736i	1.42658	+	1.35941i
$386$			10.4060i			0.529649i
$387$	0.325530	−	0.182016i	0.0165476	−	0.00925241i
$388$			8.82586i			0.448065i
$389$		−	16.5459i		−	0.838913i	−0.907776	−	0.419456i	$-0.862221\pi$
$389$		−	16.5459i		−	0.838913i	0.907776	−	0.419456i	$-0.137779\pi$
$390$	−7.83732	−	30.0758i	−0.396858	−	1.52295i
$391$		−	3.35216i		−	0.169526i
$392$	6.99187	−	0.337317i	0.353143	−	0.0170371i
$393$	−4.67806	−	17.9521i	−0.235977	−	0.905565i
$394$	18.4857			0.931296
$395$	−20.4776			−1.03034
$396$	6.14058	+	10.9822i	0.308576	+	0.551877i
$397$			19.0757i			0.957383i	0.877983	+	0.478691i	$0.158889\pi$
$397$			19.0757i			0.957383i	−0.877983	+	0.478691i	$0.841111\pi$
$398$	7.26210			0.364016
$399$	15.5402	−	28.0199i	0.777983	−	1.40275i
$400$	7.14118			0.357059
$401$		−	26.3401i		−	1.31536i	−0.753297	−	0.657680i	$-0.771538\pi$
$401$		−	26.3401i		−	1.31536i	0.753297	−	0.657680i	$-0.228462\pi$
$402$	−1.42885	+	0.372338i	−0.0712646	+	0.0185705i
$403$	43.0472			2.14433
$404$	3.72950			0.185550
$405$	−16.4216	+	26.7164i	−0.815995	+	1.32755i
$406$	−2.41344	+	2.53268i	−0.119777	+	0.125695i
$407$			42.6652i			2.11483i
$408$	5.61848	−	1.46409i	0.278156	−	0.0724834i
$409$		−	27.5945i		−	1.36446i	−0.731137	−	0.682230i	$-0.761010\pi$
$409$		−	27.5945i		−	1.36446i	0.731137	−	0.682230i	$-0.238990\pi$
$410$		−	22.5256i		−	1.11246i
$411$	5.07194	−	1.32167i	0.250180	−	0.0651934i
$412$		−	9.25903i		−	0.456160i
$413$	−2.08020	+	2.18297i	−0.102360	+	0.107417i
$414$	2.61848	−	1.46409i	0.128691	−	0.0719563i
$415$	−59.3139			−2.91160
$416$	−5.14983			−0.252491
$417$	17.9605	−	4.68026i	0.879532	−	0.229193i
$418$		−	29.3247i		−	1.43432i
$419$	10.3735			0.506776			0.253388	−	0.967365i	$-0.418455\pi$
$419$	10.3735			0.506776			0.253388	+	0.967365i	$0.418455\pi$
$420$	13.9638	+	7.74451i	0.681363	+	0.377893i
$421$	−12.5131			−0.609851			−0.304925	−	0.952376i	$-0.598631\pi$
$421$	−12.5131			−0.609851			−0.304925	+	0.952376i	$0.598631\pi$
$422$			4.70667i			0.229117i
$423$	1.88068	−	1.05156i	0.0914416	−	0.0511286i
$424$	−9.13660			−0.443712
$425$	23.9384			1.16118
$426$	−3.70530	−	14.2191i	−0.179522	−	0.688920i
$427$	−22.4181	−	21.3626i	−1.08489	−	1.03381i
$428$		−	5.16006i		−	0.249421i
$429$	−9.43361	−	36.2016i	−0.455459	−	1.74783i
$430$		−	0.433184i		−	0.0208900i
$431$			26.7872i			1.29030i	0.764058	+	0.645148i	$0.223204\pi$
$431$			26.7872i			1.29030i	−0.764058	+	0.645148i	$0.776796\pi$
$432$	3.59759	+	3.74932i	0.173089	+	0.180389i
$433$		−	13.9306i		−	0.669461i	−0.942314	−	0.334731i	$-0.891355\pi$
$433$		−	13.9306i		−	0.669461i	0.942314	−	0.334731i	$-0.108645\pi$
$434$	−15.2567	+	16.0105i	−0.732347	+	0.768531i
$435$	−7.72238	+	2.01234i	−0.370260	+	0.0964843i
$436$	−11.6021			−0.555639
$437$	−6.99187			−0.334466
$438$	−2.09500	−	8.03960i	−0.100103	−	0.384147i
$439$		−	12.0011i		−	0.572781i	−0.958113	−	0.286390i	$-0.907545\pi$
$439$		−	12.0011i		−	0.572781i	0.958113	−	0.286390i	$-0.0924555\pi$
$440$	14.6141			0.696699
$441$	11.1200	+	17.8142i	0.529524	+	0.848295i
$442$	−17.2630			−0.821119
$443$		−	24.9029i		−	1.18317i	−0.806241	−	0.591587i	$-0.798502\pi$
$443$		−	24.9029i		−	1.18317i	0.806241	−	0.591587i	$-0.201498\pi$
$444$	4.44301	+	17.0501i	0.210856	+	0.809162i
$445$	19.4207			0.920628
$446$	3.59109			0.170043
$447$	−34.0448	+	8.87158i	−1.61026	+	0.419611i
$448$	1.82520	−	1.91537i	0.0862324	−	0.0904929i
$449$			12.7284i			0.600692i	0.953830	+	0.300346i	$0.0971021\pi$
$449$			12.7284i			0.600692i	−0.953830	+	0.300346i	$0.902898\pi$
$450$	10.4554	+	18.6990i	0.492871	+	0.881481i
$451$		−	27.1136i		−	1.27673i
$452$			12.6892i			0.596851i
$453$	−7.87598	−	30.2242i	−0.370046	−	1.42005i
$454$		−	25.7980i		−	1.21076i
$455$	−34.3698	−	32.7516i	−1.61128	−	1.53542i
$456$	−3.05378	−	11.7189i	−0.143006	−	0.548789i
$457$	12.6758			0.592947			0.296474	−	0.955041i	$-0.404189\pi$
$457$	12.6758			0.592947			0.296474	+	0.955041i	$0.404189\pi$
$458$	3.16475			0.147879
$459$	12.0597	+	12.5683i	0.562898	+	0.586638i
$460$		−	3.48442i		−	0.162462i
$461$	27.9968			1.30394			0.651970	−	0.758244i	$-0.273943\pi$
$461$	27.9968			1.30394			0.651970	+	0.758244i	$0.273943\pi$
$462$	16.8079	+	9.32189i	0.781975	+	0.433694i
$463$	7.94271			0.369129			0.184564	−	0.982820i	$-0.440913\pi$
$463$	7.94271			0.369129			0.184564	+	0.982820i	$0.440913\pi$
$464$			1.32229i			0.0613857i
$465$	−48.8177	+	12.7212i	−2.26387	+	0.589931i
$466$	19.5350			0.904942
$467$	25.6793			1.18830			0.594148	−	0.804356i	$-0.297489\pi$
$467$	25.6793			1.18830			0.594148	+	0.804356i	$0.297489\pi$
$468$	−7.53983	−	13.4847i	−0.348529	−	0.623331i
$469$	−1.55597	+	1.63285i	−0.0718482	+	0.0753980i
$470$		−	2.50262i		−	0.115437i
$471$	23.8771	−	6.22203i	1.10020	−	0.286696i
$472$			1.13971i			0.0524594i
$473$		−	0.521414i		−	0.0239746i
$474$	−9.85016	+	2.56681i	−0.452433	+	0.117897i
$475$		−	49.9302i		−	2.29096i
$476$	6.11834	−	6.42064i	0.280434	−	0.294289i
$477$	−13.3768	−	23.9240i	−0.612483	−	1.09540i
$478$	8.56751			0.391869
$479$	−3.60791			−0.164849			−0.0824247	−	0.996597i	$-0.526266\pi$
$479$	−3.60791			−0.164849			−0.0824247	+	0.996597i	$0.526266\pi$
$480$	5.84016	−	1.52186i	0.266566	−	0.0694631i
$481$		−	52.3872i		−	2.38865i
$482$	4.78063			0.217752
$483$	2.22261	−	4.00749i	0.101132	−	0.182347i
$484$	6.59064			0.299575
$485$			30.7530i			1.39642i
$486$	−4.55030	+	14.9096i	−0.206406	+	0.676311i
$487$	34.9643			1.58438			0.792191	−	0.610273i	$-0.208940\pi$
$487$	34.9643			1.58438			0.792191	+	0.610273i	$0.208940\pi$
$488$	−11.7043			−0.529828
$489$	−5.33617	−	20.4776i	−0.241310	−	0.926030i
$490$	24.3626	−	1.17535i	1.10059	−	0.0530971i
$491$			12.6102i			0.569090i	0.958663	+	0.284545i	$0.0918426\pi$
$491$			12.6102i			0.569090i	−0.958663	+	0.284545i	$0.908157\pi$
$492$	−2.82352	−	10.8353i	−0.127294	−	0.488493i
$493$			4.43252i			0.199631i
$494$			36.0069i			1.62003i
$495$	21.3964	+	38.2666i	0.961696	+	1.71996i
$496$			8.35896i			0.375329i
$497$	−16.2492	−	15.4842i	−0.728877	−	0.694561i
$498$	−28.5312	+	7.43482i	−1.27851	+	0.333162i
$499$	−11.0243			−0.493513			−0.246757	−	0.969077i	$-0.579365\pi$
$499$	−11.0243			−0.493513			−0.246757	+	0.969077i	$0.579365\pi$
$500$	7.46079			0.333657
$501$	1.37802	+	5.28818i	0.0615655	+	0.236259i
$502$			27.8363i			1.24239i
$503$	−17.3047			−0.771576			−0.385788	−	0.922587i	$-0.626070\pi$
$503$	−17.3047			−0.771576			−0.385788	+	0.922587i	$0.626070\pi$
$504$	7.68762	+	1.97495i	0.342434	+	0.0879713i
$505$	12.9951			0.578277
$506$		−	4.19412i		−	0.186451i
$507$	5.90533	+	22.6618i	0.262265	+	1.00645i
$508$	14.6938			0.651934
$509$	21.4914			0.952591			0.476295	−	0.879285i	$-0.341979\pi$
$509$	21.4914			0.952591			0.476295	+	0.879285i	$0.341979\pi$
$510$	19.5771	−	5.10152i	0.866890	−	0.225899i
$511$	−9.18742	−	8.75486i	−0.406427	−	0.387292i
$512$		−	1.00000i		−	0.0441942i
$513$	26.2147	−	25.1539i	1.15741	−	1.11057i
$514$			17.3741i			0.766337i
$515$		−	32.2624i		−	1.42165i
$516$	−0.0542983	−	0.208370i	−0.00239035	−	0.00917300i
$517$		−	3.01235i		−	0.132483i
$518$	19.4844	+	18.5670i	0.856094	+	0.815788i
$519$	5.57751	+	21.4038i	0.244825	+	0.939521i
$520$	−17.9442			−0.786904
$521$	−39.3393			−1.72348			−0.861742	−	0.507347i	$-0.830626\pi$
$521$	−39.3393			−1.72348			−0.861742	+	0.507347i	$0.830626\pi$
$522$	−3.46238	+	1.93595i	−0.151544	+	0.0847344i
$523$			12.2882i			0.537325i	0.963234	+	0.268663i	$0.0865817\pi$
$523$			12.2882i			0.537325i	−0.963234	+	0.268663i	$0.913418\pi$
$524$	−10.7108			−0.467903
$525$	28.6182	+	15.8721i	1.24900	+	0.692714i
$526$	3.52547			0.153718
$527$			28.0206i			1.22059i
$528$	7.02967	−	1.83183i	0.305927	−	0.0797202i
$529$	−1.00000			−0.0434783
$530$	−31.8357			−1.38286
$531$	−2.98431	+	1.66864i	−0.129508	+	0.0724130i
$532$	−13.3920	−	12.7615i	−0.580619	−	0.553283i
$533$			33.2920i			1.44203i
$534$	9.34175	−	2.43432i	0.404257	−	0.105343i
$535$		−	17.9798i		−	0.777336i
$536$			0.852497i			0.0368222i
$537$	−5.95137	+	1.55084i	−0.256821	+	0.0669237i
$538$			18.0738i			0.779217i
$539$	29.3247	−	1.41475i	1.26311	−	0.0609375i
$540$	12.5355	+	13.0642i	0.539442	+	0.562193i
$541$	−11.4216			−0.491051			−0.245526	−	0.969390i	$-0.578961\pi$
$541$	−11.4216			−0.491051			−0.245526	+	0.969390i	$0.578961\pi$
$542$	−12.4477			−0.534677
$543$	−11.2771	+	2.93865i	−0.483947	+	0.126109i
$544$		−	3.35216i		−	0.143723i
$545$	−40.4265			−1.73168
$546$	−20.6379	−	11.4461i	−0.883221	−	0.489846i
$547$	12.5526			0.536712			0.268356	−	0.963320i	$-0.413520\pi$
$547$	12.5526			0.536712			0.268356	+	0.963320i	$0.413520\pi$
$548$		−	3.02608i		−	0.129268i
$549$	−17.1362	−	30.6474i	−0.731354	−	1.30800i
$550$	29.9510			1.27711
$551$	9.24526			0.393862
$552$	−0.436762	−	1.67608i	−0.0185898	−	0.0713386i
$553$	−10.7265	+	11.2565i	−0.456138	+	0.478674i
$554$			0.644534i			0.0273836i
$555$	15.4813	+	59.4097i	0.657145	+	2.52180i
$556$		−	10.7158i		−	0.454452i
$557$			36.6694i			1.55373i	0.629667	+	0.776865i	$0.283191\pi$
$557$			36.6694i			1.55373i	−0.629667	+	0.776865i	$0.716809\pi$
$558$	−21.8878	+	12.2383i	−0.926583	+	0.518089i
$559$			0.640228i			0.0270787i
$560$	6.35975	−	6.67397i	0.268749	−	0.282027i
$561$	23.5646	−	6.14058i	0.994897	−	0.259256i
$562$	18.3917			0.775806
$563$	8.46600			0.356799			0.178400	−	0.983958i	$-0.442908\pi$
$563$	8.46600			0.356799			0.178400	+	0.983958i	$0.442908\pi$
$564$	−0.313697	−	1.20381i	−0.0132090	−	0.0506897i
$565$			44.2146i			1.86012i
$566$	7.35879			0.309313
$567$	6.08404	+	23.0214i	0.255506	+	0.966808i
$568$	−8.48358			−0.355963
$569$		−	39.5702i		−	1.65887i	−0.558605	−	0.829434i	$-0.688663\pi$
$569$		−	39.5702i		−	1.65887i	0.558605	−	0.829434i	$-0.311337\pi$
$570$	−10.6407	−	40.8336i	−0.445688	−	1.71033i
$571$	33.4510			1.39988			0.699941	−	0.714201i	$-0.253210\pi$
$571$	33.4510			1.39988			0.699941	+	0.714201i	$0.253210\pi$
$572$	−21.5990			−0.903099
$573$	−5.80222	+	1.51197i	−0.242391	+	0.0631636i
$574$	−12.3823	−	11.7993i	−0.516826	−	0.492493i
$575$		−	7.14118i		−	0.297808i
$576$	2.61848	−	1.46409i	0.109103	−	0.0610039i
$577$		−	2.15147i		−	0.0895671i	−0.998997	−	0.0447835i	$-0.985740\pi$
$577$		−	2.15147i		−	0.0895671i	0.998997	−	0.0447835i	$-0.0142598\pi$
$578$			5.76304i			0.239711i
$579$	4.54492	+	17.4412i	0.188881	+	0.724831i
$580$			4.60741i			0.191312i
$581$	−31.0696	+	32.6047i	−1.28898	+	1.35267i
$582$	3.85480	+	14.7928i	0.159787	+	0.613183i
$583$	−38.3200			−1.58705
$584$	−4.79667			−0.198488
$585$	−26.2719	−	46.9864i	−1.08621	−	1.94265i
$586$			13.8700i			0.572963i
$587$	6.15957			0.254233			0.127116	−	0.991888i	$-0.459428\pi$
$587$	6.15957			0.254233			0.127116	+	0.991888i	$0.459428\pi$
$588$	11.5716	−	3.61915i	0.477204	−	0.149251i
$589$	58.4448			2.40817
$590$			3.97123i			0.163493i
$591$	30.9835	−	8.07384i	1.27449	−	0.332113i
$592$	10.1726			0.418092
$593$	20.4096			0.838124			0.419062	−	0.907958i	$-0.362359\pi$
$593$	20.4096			0.838124			0.419062	+	0.907958i	$0.362359\pi$
$594$	15.0887	+	15.7251i	0.619097	+	0.645208i
$595$	21.3189	−	22.3722i	0.873989	−	0.917170i
$596$			20.3122i			0.832019i
$597$	12.1718	−	3.17181i	0.498161	−	0.129813i
$598$			5.14983i			0.210592i
$599$			23.9656i			0.979208i	0.871945	+	0.489604i	$0.162859\pi$
$599$			23.9656i			0.979208i	−0.871945	+	0.489604i	$0.837141\pi$
$600$	11.9692	−	3.11900i	0.488640	−	0.127332i
$601$		−	20.1496i		−	0.821921i	−0.911653	−	0.410961i	$-0.865193\pi$
$601$		−	20.1496i		−	0.821921i	0.911653	−	0.410961i	$-0.134807\pi$
$602$	−0.238120	−	0.226909i	−0.00970503	−	0.00924811i
$603$	−2.23224	+	1.24813i	−0.0909040	+	0.0508280i
$604$	−18.0327			−0.733739
$605$	22.9646			0.933642
$606$	6.25094	−	1.62890i	0.253927	−	0.0661697i
$607$		−	24.6139i		−	0.999049i	−0.866300	−	0.499524i	$-0.833508\pi$
$607$		−	24.6139i		−	0.999049i	0.866300	−	0.499524i	$-0.166492\pi$
$608$	−6.99187			−0.283558
$609$	−2.93893	+	5.29906i	−0.119092	+	0.214729i
$610$	−40.7827			−1.65124
$611$			3.69877i			0.149636i
$612$	8.77755	−	4.90787i	0.354811	−	0.198389i
$613$	−23.5415			−0.950833			−0.475416	−	0.879761i	$-0.657703\pi$
$613$	−23.5415			−0.950833			−0.475416	+	0.879761i	$0.657703\pi$
$614$	22.8398			0.921739
$615$	−9.83833	−	37.7547i	−0.396720	−	1.52242i
$616$	7.65509	−	8.03331i	0.308432	−	0.323671i
$617$		−	33.6426i		−	1.35440i	−0.735799	−	0.677200i	$-0.763193\pi$
$617$		−	33.6426i		−	1.35440i	0.735799	−	0.677200i	$-0.236807\pi$
$618$	−4.04399	−	15.5189i	−0.162673	−	0.624260i
$619$		−	16.4068i		−	0.659443i	−0.944078	−	0.329722i	$-0.893045\pi$
$619$		−	16.4068i		−	0.659443i	0.944078	−	0.329722i	$-0.106955\pi$
$620$			29.1261i			1.16973i
$621$	3.74932	−	3.59759i	0.150455	−	0.144366i
$622$		−	3.32900i		−	0.133481i
$623$	10.1729	−	10.6755i	0.407567	−	0.427704i
$624$	−8.63152	+	2.24925i	−0.345537	+	0.0900420i
$625$	−9.70941			−0.388376
$626$	15.3261			0.612556
$627$	−12.8079	−	49.1506i	−0.511499	−	1.96288i
$628$		−	14.2458i		−	0.568470i
$629$	34.1002			1.35966
$630$	26.7869	+	6.88155i	1.06722	+	0.274168i
$631$	43.8049			1.74384			0.871922	−	0.489645i	$-0.162874\pi$
$631$	43.8049			1.74384			0.871922	+	0.489645i	$0.162874\pi$
$632$			5.87691i			0.233771i
$633$	2.05569	+	7.88875i	0.0817065	+	0.313550i
$634$	−27.2559			−1.08247
$635$	51.1995			2.03179
$636$	−15.3137	+	3.99052i	−0.607226	+	0.158234i
$637$	−36.0069	+	1.73712i	−1.42665	+	0.0688274i
$638$			5.54584i			0.219562i
$639$	−12.4208	−	22.2141i	−0.491357	−	0.878775i
$640$		−	3.48442i		−	0.137734i
$641$			36.8418i			1.45516i	0.686022	+	0.727581i	$0.259355\pi$
$641$			36.8418i			1.45516i	−0.686022	+	0.727581i	$0.740645\pi$
$642$	−2.25372	−	8.64867i	−0.0889471	−	0.341336i
$643$		−	30.8232i		−	1.21555i	−0.794110	−	0.607774i	$-0.792063\pi$
$643$		−	30.8232i		−	1.21555i	0.794110	−	0.607774i	$-0.207937\pi$
$644$	−1.91537	−	1.82520i	−0.0754763	−	0.0719228i
$645$	−0.189198	−	0.726050i	−0.00744967	−	0.0285882i
$646$	−23.4378			−0.922149
$647$	−4.75784			−0.187050			−0.0935251	−	0.995617i	$-0.529814\pi$
$647$	−4.75784			−0.187050			−0.0935251	+	0.995617i	$0.529814\pi$
$648$	7.66740	+	4.71286i	0.301204	+	0.185139i
$649$			4.78008i			0.187635i
$650$	−36.7759			−1.44247
$651$	−18.5787	+	33.4985i	−0.728157	+	1.31291i
$652$	−12.2176			−0.478477
$653$			42.3143i			1.65589i	0.560811	+	0.827944i	$0.310489\pi$
$653$			42.3143i			1.65589i	−0.560811	+	0.827944i	$0.689511\pi$
$654$	−19.4460	+	5.06735i	−0.760399	+	0.198149i
$655$	−37.3209			−1.45825
$656$	−6.46467			−0.252403
$657$	−7.02277	−	12.5600i	−0.273985	−	0.490011i
$658$	−1.37568	−	1.31092i	−0.0536298	−	0.0511048i
$659$		−	2.01233i		−	0.0783892i	−0.999232	−	0.0391946i	$-0.987521\pi$
$659$		−	2.01233i		−	0.0783892i	0.999232	−	0.0391946i	$-0.0124792\pi$
$660$	24.4943	−	6.38287i	0.953441	−	0.248453i
$661$		−	14.3677i		−	0.558838i	−0.960169	−	0.279419i	$-0.909858\pi$
$661$		−	14.3677i		−	0.558838i	0.960169	−	0.279419i	$-0.0901418\pi$
$662$			11.0278i			0.428608i
$663$	−28.9342	+	7.53983i	−1.12371	+	0.292823i
$664$			17.0226i			0.660605i
$665$	−46.6635	−	44.4665i	−1.80953	−	1.72434i
$666$	14.8937	+	26.6368i	0.577118	+	1.03215i
$667$	1.32229			0.0511992
$668$	3.15509			0.122074
$669$	6.01896	−	1.56845i	0.232706	−	0.0606399i
$670$			2.97046i			0.114759i
$671$	−49.0892			−1.89507
$672$	2.22261	−	4.00749i	0.0857391	−	0.154592i
$673$	−37.7330			−1.45450			−0.727249	−	0.686374i	$-0.759202\pi$
$673$	−37.7330			−1.45450			−0.727249	+	0.686374i	$0.759202\pi$
$674$		−	30.5839i		−	1.17805i
$675$	25.6910	+	26.7746i	0.988848	+	1.03055i
$676$	13.5207			0.520028
$677$	−6.32457			−0.243073			−0.121536	−	0.992587i	$-0.538782\pi$
$677$	−6.32457			−0.243073			−0.121536	+	0.992587i	$0.538782\pi$
$678$	5.54216	+	21.2681i	0.212846	+	0.816797i
$679$	16.9048	+	16.1089i	0.648748	+	0.618204i
$680$		−	11.6803i		−	0.447920i
$681$	−11.2676	−	43.2395i	−0.431775	−	1.65694i
$682$			35.0585i			1.34246i
$683$		−	12.7943i		−	0.489559i	−0.969579	−	0.244780i	$-0.921284\pi$
$683$		−	12.7943i		−	0.489559i	0.969579	−	0.244780i	$-0.0787156\pi$
$684$	−10.2368	−	18.3081i	−0.391412	−	0.700026i
$685$		−	10.5441i		−	0.402870i
$686$	12.1154	−	14.0077i	0.462570	−	0.534817i
$687$	5.30437	−	1.38224i	0.202374	−	0.0527358i
$688$	−0.124320			−0.00473966
$689$	47.0519			1.79253
$690$	−1.52186	−	5.84016i	−0.0579363	−	0.222331i
$691$		−	13.9749i		−	0.531632i	−0.964024	−	0.265816i	$-0.914359\pi$
$691$		−	13.9749i		−	0.531632i	0.964024	−	0.265816i	$-0.0856413\pi$
$692$	12.7701			0.485448
$693$	32.2428	+	8.28318i	1.22480	+	0.314652i
$694$	−10.8821			−0.413078
$695$		−	37.3384i		−	1.41633i
$696$	0.577525	+	2.21626i	0.0218910	+	0.0840071i
$697$	−21.6706			−0.820832
$698$	3.69686			0.139928
$699$	32.7422	−	8.53214i	1.23842	−	0.322715i
$700$	13.0341	−	13.6780i	0.492641	−	0.516981i
$701$			1.37382i			0.0518885i	0.999663	+	0.0259443i	$0.00825924\pi$
$701$			1.37382i			0.0518885i	−0.999663	+	0.0259443i	$0.991741\pi$
$702$	−18.5270	−	19.3083i	−0.699255	−	0.728746i
$703$		−	71.1256i		−	2.68255i
$704$		−	4.19412i		−	0.158072i
$705$	−1.09305	−	4.19460i	−0.0411667	−	0.157978i
$706$		−	22.0601i		−	0.830243i
$707$	6.80707	−	7.14339i	0.256006	−	0.268655i
$708$	0.497782	+	1.91024i	0.0187078	+	0.0717914i
$709$	36.1629			1.35812			0.679062	−	0.734081i	$-0.262387\pi$
$709$	36.1629			1.35812			0.679062	+	0.734081i	$0.262387\pi$
$710$	−29.5604			−1.10938
$711$	−15.3886	+	8.60434i	−0.577116	+	0.322688i
$712$		−	5.57357i		−	0.208879i
$713$	8.35896			0.313046
$714$	7.45054	−	13.4337i	0.278829	−	0.502745i
$715$	−75.2600			−2.81456
$716$			3.55077i			0.132699i
$717$	14.3598	−	3.74196i	0.536278	−	0.139746i
$718$	26.5329			0.990200
$719$	13.2412			0.493814			0.246907	−	0.969039i	$-0.420586\pi$
$719$	13.2412			0.493814			0.246907	+	0.969039i	$0.420586\pi$
$720$	9.12388	−	5.10152i	0.340027	−	0.190122i
$721$	−17.7345	−	16.8996i	−0.660468	−	0.629372i
$722$			29.8862i			1.11225i
$723$	8.01272	−	2.08800i	0.297996	−	0.0776535i
$724$			6.72826i			0.250054i
$725$			9.44270i			0.350693i
$726$	11.0464	−	2.87854i	0.409971	−	0.106833i
$727$			35.4031i			1.31303i	0.754314	+	0.656513i	$0.227969\pi$
$727$			35.4031i			1.31303i	−0.754314	+	0.656513i	$0.772031\pi$
$728$	−9.39945	+	9.86385i	−0.348367	+	0.365578i
$729$	−1.11473	+	26.9770i	−0.0412864	+	0.999147i
$730$	−16.7136			−0.618599
$731$	−0.416741			−0.0154137
$732$	−19.6173	+	5.11199i	−0.725077	+	0.188944i
$733$			39.6130i			1.46314i	0.681767	+	0.731569i	$0.261212\pi$
$733$			39.6130i			1.46314i	−0.681767	+	0.731569i	$0.738788\pi$
$734$	33.9438			1.25289
$735$	40.3203	−	12.6106i	1.48724	−	0.465150i
$736$	−1.00000			−0.0368605
$737$			3.57547i			0.131704i
$738$	−9.46489	−	16.9276i	−0.348407	−	0.623114i
$739$	4.18098			0.153800			0.0769000	−	0.997039i	$-0.475498\pi$
$739$	4.18098			0.153800			0.0769000	+	0.997039i	$0.475498\pi$
$740$	35.4457			1.30301
$741$	15.7264	+	60.3504i	0.577725	+	2.21703i
$742$	−16.6761	+	17.5000i	−0.612198	+	0.642445i
$743$			14.3321i			0.525794i	0.964824	+	0.262897i	$0.0846779\pi$
$743$			14.3321i			0.525794i	−0.964824	+	0.262897i	$0.915322\pi$
$744$	3.65087	+	14.0103i	0.133848	+	0.513642i
$745$			70.7762i			2.59304i
$746$		−	8.74496i		−	0.320176i
$747$	−44.5733	+	24.9227i	−1.63085	+	0.911873i
$748$		−	14.0593i		−	0.514061i
$749$	−9.88345	−	9.41813i	−0.361133	−	0.344131i
$750$	12.5049	−	3.25859i	0.456613	−	0.118987i
$751$	−6.95743			−0.253880			−0.126940	−	0.991910i	$-0.540516\pi$
$751$	−6.95743			−0.253880			−0.126940	+	0.991910i	$0.540516\pi$
$752$	−0.718233			−0.0261913
$753$	12.1578	+	46.6558i	0.443056	+	1.70023i
$754$		−	6.80956i		−	0.247989i
$755$	−62.8334			−2.28674
$756$	13.7476	−	0.0474891i	0.499997	−	0.00172716i
$757$	−29.7664			−1.08188			−0.540939	−	0.841062i	$-0.681931\pi$
$757$	−29.7664			−1.08188			−0.540939	+	0.841062i	$0.681931\pi$
$758$		−	26.4429i		−	0.960451i
$759$	−1.83183	−	7.02967i	−0.0664912	−	0.255161i
$760$	−24.3626			−0.883725
$761$	32.1660			1.16602			0.583008	−	0.812466i	$-0.301875\pi$
$761$	32.1660			1.16602			0.583008	+	0.812466i	$0.301875\pi$
$762$	24.6280	−	6.41771i	0.892180	−	0.232489i
$763$	−21.1761	+	22.2223i	−0.766625	+	0.804502i
$764$			3.46178i			0.125243i
$765$	30.5847	−	17.1011i	1.10579	−	0.618291i
$766$		−	21.8401i		−	0.789116i
$767$		−	5.86931i		−	0.211929i
$768$	−0.436762	−	1.67608i	−0.0157603	−	0.0604803i
$769$		−	4.23002i		−	0.152538i	−0.997087	−	0.0762692i	$-0.975699\pi$
$769$		−	4.23002i		−	0.152538i	0.997087	−	0.0762692i	$-0.0243008\pi$
$770$	26.6736	−	27.9914i	0.961248	−	1.00874i
$771$	7.58832	+	29.1203i	0.273287	+	1.04874i
$772$	10.4060			0.374519
$773$	10.3014			0.370517			0.185259	−	0.982690i	$-0.440688\pi$
$773$	10.3014			0.370517			0.185259	+	0.982690i	$0.440688\pi$
$774$	−0.182016	−	0.325530i	−0.00654245	−	0.0117009i
$775$			59.6929i			2.14423i
$776$	8.82586			0.316830
$777$	40.7667	+	22.6098i	1.46250	+	0.811121i
$778$	−16.5459			−0.593201
$779$			45.2001i			1.61946i
$780$	−30.0758	+	7.83732i	−1.07689	+	0.280621i
$781$	−35.5811			−1.27319
$782$	−3.35216			−0.119873
$783$	−4.95768	+	4.75705i	−0.177173	+	0.170003i
$784$	−0.337317	−	6.99187i	−0.0120470	−	0.249710i
$785$		−	49.6385i		−	1.77167i
$786$	−17.9521	+	4.67806i	−0.640331	+	0.166861i
$787$			8.67167i			0.309112i	0.987984	+	0.154556i	$0.0493946\pi$
$787$			8.67167i			0.309112i	−0.987984	+	0.154556i	$0.950605\pi$
$788$		−	18.4857i		−	0.658526i
$789$	5.90896	−	1.53979i	0.210364	−	0.0548179i
$790$			20.4776i			0.728561i
$791$	24.3046	+	23.1603i	0.864172	+	0.823486i
$792$	10.9822	−	6.14058i	0.390236	−	0.218196i
$793$	60.2751			2.14043
$794$	19.0757			0.676972
$795$	−53.3592	+	13.9046i	−1.89246	+	0.493146i
$796$		−	7.26210i		−	0.257398i
$797$	7.70578			0.272953			0.136476	−	0.990643i	$-0.456422\pi$
$797$	7.70578			0.272953			0.136476	+	0.990643i	$0.456422\pi$
$798$	−28.0199	−	15.5402i	−0.991892	−	0.550117i
$799$	−2.40763			−0.0851758
$800$		−	7.14118i		−	0.252479i
$801$	14.5943	−	8.16024i	0.515664	−	0.288328i
$802$	−26.3401			−0.930100
$803$	−20.1178			−0.709942
$804$	0.372338	+	1.42885i	0.0131313	+	0.0503917i
$805$	−6.67397	−	6.35975i	−0.235226	−	0.224152i
$806$		−	43.0472i		−	1.51627i
$807$	7.89394	+	30.2931i	0.277880	+	1.06637i
$808$		−	3.72950i		−	0.131203i
$809$		−	16.5569i		−	0.582108i	−0.956707	−	0.291054i	$-0.905994\pi$
$809$		−	16.5569i		−	0.582108i	0.956707	−	0.291054i	$-0.0940060\pi$
$810$	26.7164	+	16.4216i	0.938720	+	0.576996i
$811$			26.0147i			0.913500i	0.889595	+	0.456750i	$0.150987\pi$
$811$			26.0147i			0.913500i	−0.889595	+	0.456750i	$0.849013\pi$
$812$	2.53268	+	2.41344i	0.0888795	+	0.0846950i
$813$	−20.8634	+	5.43670i	−0.731711	+	0.190673i
$814$	42.6652			1.49541
$815$	−42.5712			−1.49120
$816$	−1.46409	−	5.61848i	−0.0512535	−	0.196686i
$817$			0.869230i			0.0304105i
$818$	−27.5945			−0.964819
$819$	−39.5899	−	10.1707i	−1.38338	−	0.355391i
$820$	−22.5256			−0.786629
$821$		−	21.6799i		−	0.756634i	−0.925676	−	0.378317i	$-0.876503\pi$
$821$		−	21.6799i		−	0.756634i	0.925676	−	0.378317i	$-0.123497\pi$
$822$	−1.32167	−	5.07194i	−0.0460987	−	0.176904i
$823$	−16.5277			−0.576118			−0.288059	−	0.957613i	$-0.593010\pi$
$823$	−16.5277			−0.576118			−0.288059	+	0.957613i	$0.593010\pi$
$824$	−9.25903			−0.322554
$825$	50.2002	−	13.0814i	1.74775	−	0.455437i
$826$	2.18297	+	2.08020i	0.0759553	+	0.0723793i
$827$			54.1329i			1.88239i	0.337868	+	0.941194i	$0.390294\pi$
$827$			54.1329i			1.88239i	−0.337868	+	0.941194i	$0.609706\pi$
$828$	−1.46409	−	2.61848i	−0.0508808	−	0.0909984i
$829$			6.67219i			0.231735i	0.993265	+	0.115867i	$0.0369647\pi$
$829$			6.67219i			0.231735i	−0.993265	+	0.115867i	$0.963035\pi$
$830$			59.3139i			2.05882i
$831$	0.281508	+	1.08029i	0.00976540	+	0.0374749i
$832$			5.14983i			0.178538i
$833$	−1.13074	−	23.4378i	−0.0391778	−	0.812073i
$834$	−4.68026	−	17.9605i	−0.162064	−	0.621923i
$835$	10.9937			0.380452
$836$	−29.3247			−1.01422
$837$	−31.3404	+	30.0721i	−1.08328	+	1.03944i
$838$		−	10.3735i		−	0.358345i
$839$	−28.8123			−0.994713			−0.497356	−	0.867546i	$-0.665696\pi$
$839$	−28.8123			−0.994713			−0.497356	+	0.867546i	$0.665696\pi$
$840$	7.74451	−	13.9638i	0.267211	−	0.481797i
$841$	27.2516			0.939709
$842$			12.5131i			0.431229i
$843$	30.8259	−	8.03277i	1.06170	−	0.276663i
$844$	4.70667			0.162010
$845$	47.1119			1.62070
$846$	−1.05156	−	1.88068i	−0.0361534	−	0.0646590i
$847$	12.0292	−	12.6235i	0.413329	−	0.433750i
$848$			9.13660i			0.313752i
$849$	12.3339	−	3.21404i	0.423299	−	0.110306i
$850$		−	23.9384i		−	0.821079i
$851$		−	10.1726i		−	0.348713i
$852$	−14.2191	+	3.70530i	−0.487140	+	0.126942i
$853$		−	26.6655i		−	0.913011i	−0.889721	−	0.456505i	$-0.849101\pi$
$853$		−	26.6655i		−	0.913011i	0.889721	−	0.456505i	$-0.150899\pi$
$854$	−21.3626	+	22.4181i	−0.731014	+	0.767131i
$855$	−35.6691	−	63.7930i	−1.21986	−	2.18167i
$856$	−5.16006			−0.176367
$857$	−34.0075			−1.16167			−0.580837	−	0.814020i	$-0.697275\pi$
$857$	−34.0075			−1.16167			−0.580837	+	0.814020i	$0.697275\pi$
$858$	−36.2016	+	9.43361i	−1.23590	+	0.322058i
$859$		−	11.2862i		−	0.385082i	−0.981289	−	0.192541i	$-0.938327\pi$
$859$		−	11.2862i		−	0.385082i	0.981289	−	0.192541i	$-0.0616728\pi$
$860$	−0.433184			−0.0147714
$861$	−25.9071	−	14.3684i	−0.882913	−	0.489675i
$862$	26.7872			0.912377
$863$		−	17.7496i		−	0.604203i	−0.953276	−	0.302101i	$-0.902312\pi$
$863$		−	17.7496i		−	0.604203i	0.953276	−	0.302101i	$-0.0976881\pi$
$864$	3.74932	−	3.59759i	0.127554	−	0.122392i
$865$	44.4965			1.51293
$866$	−13.9306			−0.473381
$867$	2.51708	+	9.65931i	0.0854844	+	0.328047i
$868$	16.0105	+	15.2567i	0.543433	+	0.517848i
$869$			24.6485i			0.836142i
$870$	2.01234	+	7.72238i	0.0682247	+	0.261813i
$871$		−	4.39021i		−	0.148757i
$872$			11.6021i			0.392896i
$873$	12.9219	+	23.1103i	0.437340	+	0.782166i
$874$			6.99187i			0.236503i
$875$	13.6174	−	14.2902i	0.460352	−	0.483097i
$876$	−8.03960	+	2.09500i	−0.271633	+	0.0707835i
$877$	−46.0786			−1.55596			−0.777982	−	0.628287i	$-0.783756\pi$
$877$	−46.0786			−1.55596			−0.777982	+	0.628287i	$0.783756\pi$
$878$	−12.0011			−0.405017
$879$	6.05787	+	23.2472i	0.204327	+	0.784107i
$880$		−	14.6141i		−	0.492640i
$881$	−48.5614			−1.63607			−0.818037	−	0.575165i	$-0.804938\pi$
$881$	−48.5614			−1.63607			−0.818037	+	0.575165i	$0.804938\pi$
$882$	17.8142	−	11.1200i	0.599835	−	0.374430i
$883$	45.4121			1.52824			0.764119	−	0.645075i	$-0.223174\pi$
$883$	45.4121			1.52824			0.764119	+	0.645075i	$0.223174\pi$
$884$			17.2630i			0.580619i
$885$	1.73448	+	6.65610i	0.0583040	+	0.223742i
$886$	−24.9029			−0.836631
$887$	−1.03744			−0.0348337			−0.0174169	−	0.999848i	$-0.505544\pi$
$887$	−1.03744			−0.0348337			−0.0174169	+	0.999848i	$0.505544\pi$
$888$	17.0501	−	4.44301i	0.572164	−	0.149098i
$889$	26.8191	−	28.1442i	0.899485	−	0.943926i
$890$		−	19.4207i		−	0.650982i
$891$	32.1580	+	19.7663i	1.07733	+	0.662196i
$892$		−	3.59109i		−	0.120239i
$893$			5.02179i			0.168048i
$894$	8.87158	+	34.0448i	0.296710	+	1.13863i
$895$			12.3724i			0.413563i
$896$	−1.91537	−	1.82520i	−0.0639882	−	0.0609755i
$897$	2.24925	+	8.63152i	0.0751002	+	0.288198i
$898$	12.7284			0.424753
$899$	−11.0530			−0.368637
$900$	18.6990	−	10.4554i	0.623301	−	0.348512i
$901$			30.6273i			1.02034i
$902$	−27.1136			−0.902785
$903$	−0.498212	−	0.276315i	−0.0165795	−	0.00919520i
$904$	12.6892			0.422037
$905$			23.4441i			0.779308i
$906$	−30.2242	+	7.87598i	−1.00413	+	0.261662i
$907$	30.9997			1.02933			0.514665	−	0.857391i	$-0.327916\pi$
$907$	30.9997			1.02933			0.514665	+	0.857391i	$0.327916\pi$
$908$	−25.7980			−0.856137
$909$	9.76562	−	5.46034i	0.323905	−	0.181108i
$910$	−32.7516	+	34.3698i	−1.08571	+	1.13935i
$911$		−	17.5097i		−	0.580123i	−0.957008	−	0.290062i	$-0.906324\pi$
$911$		−	17.5097i		−	0.580123i	0.957008	−	0.290062i	$-0.0936758\pi$
$912$	−11.7189	+	3.05378i	−0.388052	+	0.101121i
$913$			71.3948i			2.36282i
$914$		−	12.6758i		−	0.419277i
$915$	−68.3550	+	17.8123i	−2.25975	+	0.588857i
$916$		−	3.16475i		−	0.104566i
$917$	−19.5493	+	20.5152i	−0.645574	+	0.677470i
$918$	12.5683	−	12.0597i	0.414816	−	0.398029i
$919$	−31.7425			−1.04709			−0.523545	−	0.851998i	$-0.675391\pi$
$919$	−31.7425			−1.04709			−0.523545	+	0.851998i	$0.675391\pi$
$920$	−3.48442			−0.114878
$921$	38.2813	−	9.97554i	1.26141	−	0.328705i
$922$		−	27.9968i		−	0.922025i
$923$	43.6890			1.43804
$924$	9.32189	−	16.8079i	0.306668	−	0.552940i
$925$	72.6445			2.38854
$926$		−	7.94271i		−	0.261014i
$927$	−13.5561	−	24.2446i	−0.445240	−	0.796296i
$928$	1.32229			0.0434062
$929$	−46.4363			−1.52353			−0.761763	−	0.647855i	$-0.775666\pi$
$929$	−46.4363			−1.52353			−0.761763	+	0.647855i	$0.775666\pi$
$930$	12.7212	+	48.8177i	0.417144	+	1.60080i
$931$	−48.8862	+	2.35848i	−1.60218	+	0.0772960i
$932$		−	19.5350i		−	0.639891i
$933$	−1.45398	−	5.57967i	−0.0476012	−	0.182670i
$934$		−	25.6793i		−	0.840252i
$935$		−	48.9887i		−	1.60210i
$936$	−13.4847	+	7.53983i	−0.440762	+	0.246447i
$937$			25.8117i			0.843230i	0.906775	+	0.421615i	$0.138537\pi$
$937$			25.8117i			0.843230i	−0.906775	+	0.421615i	$0.861463\pi$
$938$	1.63285	+	1.55597i	0.0533144	+	0.0508043i
$939$	25.6878	−	6.69387i	0.838290	−	0.218446i
$940$	−2.50262			−0.0816266
$941$	0.988937			0.0322384			0.0161192	−	0.999870i	$-0.494869\pi$
$941$	0.988937			0.0322384			0.0161192	+	0.999870i	$0.494869\pi$
$942$	−6.22203	−	23.8771i	−0.202725	−	0.777959i
$943$			6.46467i			0.210519i
$944$	1.13971			0.0370944
$945$	47.9026	−	0.165472i	1.55827	−	0.00538280i
$946$	−0.521414			−0.0169526
$947$			24.8669i			0.808065i	0.914745	+	0.404032i	$0.132392\pi$
$947$			24.8669i			0.808065i	−0.914745	+	0.404032i	$0.867608\pi$
$948$	2.56681	+	9.85016i	0.0833661	+	0.319918i
$949$	24.7020			0.801862
$950$	−49.9302			−1.61995
$951$	−45.6831	+	11.9043i	−1.48138	+	0.386025i
$952$	−6.42064	−	6.11834i	−0.208094	−	0.198297i
$953$			9.97349i			0.323073i	0.986867	+	0.161537i	$0.0516450\pi$
$953$			9.97349i			0.323073i	−0.986867	+	0.161537i	$0.948355\pi$
$954$	−23.9240	+	13.3768i	−0.774568	+	0.433091i
$955$			12.0623i			0.390327i
$956$		−	8.56751i		−	0.277093i
$957$	2.42221	+	9.29526i	0.0782989	+	0.300473i
$958$			3.60791i			0.116566i
$959$	−5.79607	−	5.52318i	−0.187165	−	0.178353i
$960$	−1.52186	−	5.84016i	−0.0491179	−	0.188490i
$961$	−38.8723			−1.25394
$962$	−52.3872			−1.68903
$963$	−7.55481	−	13.5115i	−0.243450	−	0.435402i
$964$		−	4.78063i		−	0.153974i
$965$	36.2587			1.16721
$966$	−4.00749	−	2.22261i	−0.128939	−	0.0715113i
$967$	−51.9551			−1.67076			−0.835382	−	0.549669i	$-0.814754\pi$
$967$	−51.9551			−1.67076			−0.835382	+	0.549669i	$0.814754\pi$
$968$		−	6.59064i		−	0.211831i
$969$	−39.2837	+	10.2368i	−1.26197	+	0.328852i
$970$	30.7530			0.987420
$971$	42.9079			1.37698			0.688490	−	0.725246i	$-0.258274\pi$
$971$	42.9079			1.37698			0.688490	+	0.725246i	$0.258274\pi$
$972$	14.9096	+	4.55030i	0.478224	+	0.145951i
$973$	−20.5248	−	19.5585i	−0.657995	−	0.627016i
$974$		−	34.9643i		−	1.12033i
$975$	−61.6392	+	16.0623i	−1.97404	+	0.514405i
$976$			11.7043i			0.374645i
$977$		−	3.19518i		−	0.102223i	−0.998693	−	0.0511114i	$-0.983724\pi$
$977$		−	3.19518i		−	0.102223i	0.998693	−	0.0511114i	$-0.0162764\pi$
$978$	−20.4776	+	5.33617i	−0.654802	+	0.170632i
$979$		−	23.3762i		−	0.747108i
$980$	−1.17535	−	24.3626i	−0.0375453	−	0.778235i
$981$	−30.3798	+	16.9865i	−0.969952	+	0.542338i
$982$	12.6102			0.402408
$983$	1.88464			0.0601106			0.0300553	−	0.999548i	$-0.490432\pi$
$983$	1.88464			0.0601106			0.0300553	+	0.999548i	$0.490432\pi$
$984$	−10.8353	+	2.82352i	−0.345417	+	0.0900106i
$985$		−	64.4119i		−	2.05233i
$986$	4.43252			0.141160
$987$	−2.87831	−	1.59635i	−0.0916177	−	0.0508124i
$988$	36.0069			1.14553
$989$			0.124320i			0.00395315i
$990$	38.2666	−	21.3964i	1.21619	−	0.680021i
$991$	−17.9616			−0.570570			−0.285285	−	0.958443i	$-0.592088\pi$
$991$	−17.9616			−0.570570			−0.285285	+	0.958443i	$0.592088\pi$
$992$	8.35896			0.265397
$993$	4.81653	+	18.4835i	0.152848	+	0.586556i
$994$	−15.4842	+	16.2492i	−0.491129	+	0.515394i
$995$		−	25.3042i		−	0.802197i
$996$	7.43482	+	28.5312i	0.235581	+	0.904046i
$997$			16.5742i			0.524909i	0.964944	+	0.262454i	$0.0845320\pi$
$997$			16.5742i			0.524909i	−0.964944	+	0.262454i	$0.915468\pi$
$998$			11.0243i			0.348967i
$999$	36.5969	+	38.1403i	1.15787	+	1.20671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.c.461.7	✓	28
3.2	odd	2	inner	966.2.f.c.461.22	yes	28
7.6	odd	2	inner	966.2.f.c.461.8	yes	28
21.20	even	2	inner	966.2.f.c.461.21	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.c.461.7	✓	28	1.1	even	1	trivial
966.2.f.c.461.8	yes	28	7.6	odd	2	inner
966.2.f.c.461.21	yes	28	21.20	even	2	inner
966.2.f.c.461.22	yes	28	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.436762 - 1.67608i) q^{3} -1.00000 q^{4} -3.48442 q^{5} +(-1.67608 + 0.436762i) q^{6} +(-1.82520 + 1.91537i) q^{7} +1.00000i q^{8} +(-2.61848 + 1.46409i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.436762 - 1.67608i) q^{3} -1.00000 q^{4} -3.48442 q^{5} +(-1.67608 + 0.436762i) q^{6} +(-1.82520 + 1.91537i) q^{7} +1.00000i q^{8} +(-2.61848 + 1.46409i) q^{9} +3.48442i q^{10} +4.19412i q^{11} +(0.436762 + 1.67608i) q^{12} -5.14983i q^{13} +(1.91537 + 1.82520i) q^{14} +(1.52186 + 5.84016i) q^{15} +1.00000 q^{16} +3.35216 q^{17} +(1.46409 + 2.61848i) q^{18} -6.99187i q^{19} +3.48442 q^{20} +(4.00749 + 2.22261i) q^{21} +4.19412 q^{22} -1.00000i q^{23} +(1.67608 - 0.436762i) q^{24} +7.14118 q^{25} -5.14983 q^{26} +(3.59759 + 3.74932i) q^{27} +(1.82520 - 1.91537i) q^{28} +1.32229i q^{29} +(5.84016 - 1.52186i) q^{30} +8.35896i q^{31} -1.00000i q^{32} +(7.02967 - 1.83183i) q^{33} -3.35216i q^{34} +(6.35975 - 6.67397i) q^{35} +(2.61848 - 1.46409i) q^{36} +10.1726 q^{37} -6.99187 q^{38} +(-8.63152 + 2.24925i) q^{39} -3.48442i q^{40} -6.46467 q^{41} +(2.22261 - 4.00749i) q^{42} -0.124320 q^{43} -4.19412i q^{44} +(9.12388 - 5.10152i) q^{45} -1.00000 q^{46} -0.718233 q^{47} +(-0.436762 - 1.67608i) q^{48} +(-0.337317 - 6.99187i) q^{49} -7.14118i q^{50} +(-1.46409 - 5.61848i) q^{51} +5.14983i q^{52} +9.13660i q^{53} +(3.74932 - 3.59759i) q^{54} -14.6141i q^{55} +(-1.91537 - 1.82520i) q^{56} +(-11.7189 + 3.05378i) q^{57} +1.32229 q^{58} +1.13971 q^{59} +(-1.52186 - 5.84016i) q^{60} +11.7043i q^{61} +8.35896 q^{62} +(1.97495 - 7.68762i) q^{63} -1.00000 q^{64} +17.9442i q^{65} +(-1.83183 - 7.02967i) q^{66} +0.852497 q^{67} -3.35216 q^{68} +(-1.67608 + 0.436762i) q^{69} +(-6.67397 - 6.35975i) q^{70} +8.48358i q^{71} +(-1.46409 - 2.61848i) q^{72} +4.79667i q^{73} -10.1726i q^{74} +(-3.11900 - 11.9692i) q^{75} +6.99187i q^{76} +(-8.03331 - 7.65509i) q^{77} +(2.24925 + 8.63152i) q^{78} +5.87691 q^{79} -3.48442 q^{80} +(4.71286 - 7.66740i) q^{81} +6.46467i q^{82} +17.0226 q^{83} +(-4.00749 - 2.22261i) q^{84} -11.6803 q^{85} +0.124320i q^{86} +(2.21626 - 0.577525i) q^{87} -4.19412 q^{88} -5.57357 q^{89} +(-5.10152 - 9.12388i) q^{90} +(9.86385 + 9.39945i) q^{91} +1.00000i q^{92} +(14.0103 - 3.65087i) q^{93} +0.718233i q^{94} +24.3626i q^{95} +(-1.67608 + 0.436762i) q^{96} -8.82586i q^{97} +(-6.99187 + 0.337317i) q^{98} +(-6.14058 - 10.9822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

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