LMFDB - Embedded newform 1026.2.h.g.505.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1026,2,Mod(505,1026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1026, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("1026.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1026 = 2 \cdot 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1026.h (of order $3$, degree $2$, not 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:	$8.19265124738$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 342)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.5
Root			$-1.68875 + 0.384872i$ of defining polynomial
Character	$\chi$	$=$	1026.505
Dual form			1026.2.h.g.577.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.149615 q^{5} +(-0.733568 + 1.27058i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.149615 q^{5} +(-0.733568 + 1.27058i) q^{7} +1.00000 q^{8} +(0.0748074 + 0.129570i) q^{10} +(1.57904 - 2.73498i) q^{11} +(-1.16813 + 2.02325i) q^{13} +1.46714 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.345473 + 0.598376i) q^{17} +(4.31202 + 0.637588i) q^{19} +(0.0748074 - 0.129570i) q^{20} -3.15808 q^{22} +(-1.41813 + 2.45627i) q^{23} -4.97762 q^{25} +2.33625 q^{26} +(-0.733568 - 1.27058i) q^{28} +5.27900 q^{29} +(3.37898 + 5.85257i) q^{31} +(-0.500000 + 0.866025i) q^{32} +0.690946 q^{34} +(0.109753 - 0.190097i) q^{35} +7.86561 q^{37} +(-1.60384 - 4.05311i) q^{38} -0.149615 q^{40} +0.586609 q^{41} +(4.32926 + 7.49850i) q^{43} +(1.57904 + 2.73498i) q^{44} +2.83626 q^{46} +0.377376 q^{47} +(2.42376 + 4.19807i) q^{49} +(2.48881 + 4.31074i) q^{50} +(-1.16813 - 2.02325i) q^{52} +(0.204535 + 0.354265i) q^{53} +(-0.236248 + 0.409193i) q^{55} +(-0.733568 + 1.27058i) q^{56} +(-2.63950 - 4.57175i) q^{58} -4.57304 q^{59} +8.43809 q^{61} +(3.37898 - 5.85257i) q^{62} +1.00000 q^{64} +(0.174769 - 0.302709i) q^{65} +(1.79331 - 3.10610i) q^{67} +(-0.345473 - 0.598376i) q^{68} -0.219505 q^{70} +(0.861623 - 1.49237i) q^{71} +(0.499579 - 0.865295i) q^{73} +(-3.93281 - 6.81182i) q^{74} +(-2.70818 + 3.41552i) q^{76} +(2.31667 + 4.01259i) q^{77} +(7.24959 + 12.5567i) q^{79} +(0.0748074 + 0.129570i) q^{80} +(-0.293304 - 0.508018i) q^{82} +(1.15630 - 2.00276i) q^{83} +(0.0516879 - 0.0895260i) q^{85} +(4.32926 - 7.49850i) q^{86} +(1.57904 - 2.73498i) q^{88} +(1.57359 + 2.72553i) q^{89} +(-1.71380 - 2.96839i) q^{91} +(-1.41813 - 2.45627i) q^{92} +(-0.188688 - 0.326817i) q^{94} +(-0.645142 - 0.0953927i) q^{95} +(-0.970110 - 1.68028i) q^{97} +(2.42376 - 4.19807i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1026\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.149615			−0.0669098			−0.0334549	−	0.999440i	$-0.510651\pi$
$5$	−0.149615			−0.0669098			−0.0334549	+	0.999440i	$0.510651\pi$
$6$		0			0
$7$	−0.733568	+	1.27058i	−0.277263	+	0.480233i	−0.970703	−	0.240281i	$-0.922761\pi$
$7$	−0.733568	+	1.27058i	−0.277263	+	0.480233i	0.693441	+	0.720514i	$0.256094\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.0748074	+	0.129570i	0.0236562	+	0.0409737i
$11$	1.57904	−	2.73498i	0.476099	−	0.824627i	−0.523526	−	0.852009i	$-0.675384\pi$
$11$	1.57904	−	2.73498i	0.476099	−	0.824627i	0.999625	+	0.0273824i	$0.00871717\pi$
$12$		0			0
$13$	−1.16813	+	2.02325i	−0.323980	+	0.561150i	−0.981305	−	0.192457i	$-0.938354\pi$
$13$	−1.16813	+	2.02325i	−0.323980	+	0.561150i	0.657326	+	0.753607i	$0.271688\pi$
$14$	1.46714			0.392109
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.345473	+	0.598376i	−0.0837894	+	0.145128i	−0.904875	−	0.425678i	$-0.860036\pi$
$17$	−0.345473	+	0.598376i	−0.0837894	+	0.145128i	0.821085	+	0.570806i	$0.193369\pi$
$18$		0			0
$19$	4.31202	+	0.637588i	0.989244	+	0.146273i
$19$	4.31202	+	0.637588i	0.989244	+	0.146273i
$20$	0.0748074	−	0.129570i	0.0167275	−	0.0289728i
$21$		0			0
$22$	−3.15808			−0.673305
$23$	−1.41813	+	2.45627i	−0.295700	+	0.512168i	−0.975148	−	0.221557i	$-0.928886\pi$
$23$	−1.41813	+	2.45627i	−0.295700	+	0.512168i	0.679447	+	0.733724i	$0.262220\pi$
$24$		0			0
$25$	−4.97762			−0.995523
$26$	2.33625			0.458177
$27$		0			0
$28$	−0.733568	−	1.27058i	−0.138631	−	0.240116i
$29$	5.27900			0.980286			0.490143	−	0.871642i	$-0.336945\pi$
$29$	5.27900			0.980286			0.490143	+	0.871642i	$0.336945\pi$
$30$		0			0
$31$	3.37898	+	5.85257i	0.606883	+	1.05115i	0.991751	+	0.128180i	$0.0409137\pi$
$31$	3.37898	+	5.85257i	0.606883	+	1.05115i	−0.384868	+	0.922972i	$0.625753\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	0.690946			0.118496
$35$	0.109753	−	0.190097i	0.0185516	−	0.0321323i
$36$		0			0
$37$	7.86561			1.29310			0.646549	−	0.762872i	$-0.276211\pi$
$37$	7.86561			1.29310			0.646549	+	0.762872i	$0.276211\pi$
$38$	−1.60384	−	4.05311i	−0.260177	−	0.657501i
$39$		0			0
$40$	−0.149615			−0.0236562
$41$	0.586609			0.0916129			0.0458064	−	0.998950i	$-0.485414\pi$
$41$	0.586609			0.0916129			0.0458064	+	0.998950i	$0.485414\pi$
$42$		0			0
$43$	4.32926	+	7.49850i	0.660206	+	1.14351i	0.980561	+	0.196213i	$0.0628645\pi$
$43$	4.32926	+	7.49850i	0.660206	+	1.14351i	−0.320355	+	0.947298i	$0.603802\pi$
$44$	1.57904	+	2.73498i	0.238049	+	0.412314i
$45$		0			0
$46$	2.83626			0.418183
$47$	0.377376			0.0550459			0.0275230	−	0.999621i	$-0.491238\pi$
$47$	0.377376			0.0550459			0.0275230	+	0.999621i	$0.491238\pi$
$48$		0			0
$49$	2.42376	+	4.19807i	0.346251	+	0.599724i
$50$	2.48881	+	4.31074i	0.351971	+	0.609631i
$51$		0			0
$52$	−1.16813	−	2.02325i	−0.161990	−	0.280575i
$53$	0.204535	+	0.354265i	0.0280950	+	0.0486620i	0.879731	−	0.475472i	$-0.157723\pi$
$53$	0.204535	+	0.354265i	0.0280950	+	0.0486620i	−0.851636	+	0.524134i	$0.824389\pi$
$54$		0			0
$55$	−0.236248	+	0.409193i	−0.0318557	+	0.0551756i
$56$	−0.733568	+	1.27058i	−0.0980271	+	0.169788i
$57$		0			0
$58$	−2.63950	−	4.57175i	−0.346583	−	0.600300i
$59$	−4.57304			−0.595359			−0.297680	−	0.954666i	$-0.596213\pi$
$59$	−4.57304			−0.595359			−0.297680	+	0.954666i	$0.596213\pi$
$60$		0			0
$61$	8.43809			1.08039			0.540193	−	0.841541i	$-0.318351\pi$
$61$	8.43809			1.08039			0.540193	+	0.841541i	$0.318351\pi$
$62$	3.37898	−	5.85257i	0.429131	−	0.743277i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.174769	−	0.302709i	0.0216774	−	0.0375464i
$66$		0			0
$67$	1.79331	−	3.10610i	0.219088	−	0.379471i	−0.735442	−	0.677588i	$-0.763025\pi$
$67$	1.79331	−	3.10610i	0.219088	−	0.379471i	0.954529	+	0.298117i	$0.0963586\pi$
$68$	−0.345473	−	0.598376i	−0.0418947	−	0.0725638i
$69$		0			0
$70$	−0.219505			−0.0262359
$71$	0.861623	−	1.49237i	0.102256	−	0.177112i	−0.810358	−	0.585935i	$-0.800727\pi$
$71$	0.861623	−	1.49237i	0.102256	−	0.177112i	0.912614	+	0.408823i	$0.134061\pi$
$72$		0			0
$73$	0.499579	−	0.865295i	0.0584712	−	0.101275i	−0.835308	−	0.549782i	$-0.814711\pi$
$73$	0.499579	−	0.865295i	0.0584712	−	0.101275i	0.893779	+	0.448507i	$0.148044\pi$
$74$	−3.93281	−	6.81182i	−0.457179	−	0.791858i
$75$		0			0
$76$	−2.70818	+	3.41552i	−0.310649	+	0.391787i
$77$	2.31667	+	4.01259i	0.264009	+	0.457277i
$78$		0			0
$79$	7.24959	+	12.5567i	0.815642	+	1.41273i	0.908866	+	0.417088i	$0.136949\pi$
$79$	7.24959	+	12.5567i	0.815642	+	1.41273i	−0.0932238	+	0.995645i	$0.529717\pi$
$80$	0.0748074	+	0.129570i	0.00836373	+	0.0144864i
$81$		0			0
$82$	−0.293304	−	0.508018i	−0.0323900	−	0.0561012i
$83$	1.15630	−	2.00276i	0.126920	−	0.219832i	−0.795562	−	0.605872i	$-0.792824\pi$
$83$	1.15630	−	2.00276i	0.126920	−	0.219832i	0.922482	+	0.386041i	$0.126158\pi$
$84$		0			0
$85$	0.0516879	−	0.0895260i	0.00560634	−	0.00971046i
$86$	4.32926	−	7.49850i	0.466836	−	0.808584i
$87$		0			0
$88$	1.57904	−	2.73498i	0.168326	−	0.291550i
$89$	1.57359	+	2.72553i	0.166800	+	0.288906i	0.937293	−	0.348543i	$-0.113323\pi$
$89$	1.57359	+	2.72553i	0.166800	+	0.288906i	−0.770493	+	0.637448i	$0.779990\pi$
$90$		0			0
$91$	−1.71380	−	2.96839i	−0.179655	−	0.311172i
$92$	−1.41813	−	2.45627i	−0.147850	−	0.256084i
$93$		0			0
$94$	−0.188688	−	0.326817i	−0.0194617	−	0.0337086i
$95$	−0.645142	−	0.0953927i	−0.0661901	−	0.00978708i
$96$		0			0
$97$	−0.970110	−	1.68028i	−0.0984998	−	0.170607i	0.812564	−	0.582872i	$-0.198071\pi$
$97$	−0.970110	−	1.68028i	−0.0984998	−	0.170607i	−0.911064	+	0.412265i	$0.864738\pi$
$98$	2.42376	−	4.19807i	0.244836	−	0.424069i
$99$		0			0
$100$	2.48881	−	4.31074i	0.248881	−	0.431074i
$101$	17.2381			1.71526			0.857629	−	0.514270i	$-0.171937\pi$
$101$	17.2381			1.71526			0.857629	+	0.514270i	$0.171937\pi$
$102$		0			0
$103$	−8.37347	−	14.5033i	−0.825063	−	1.42905i	−0.901871	−	0.432005i	$-0.857806\pi$
$103$	−8.37347	−	14.5033i	−0.825063	−	1.42905i	0.0768087	−	0.997046i	$-0.475527\pi$
$104$	−1.16813	+	2.02325i	−0.114544	+	0.198396i
$105$		0			0
$106$	0.204535	−	0.354265i	0.0198662	−	0.0344093i
$107$	−19.2873			−1.86457			−0.932286	−	0.361722i	$-0.882189\pi$
$107$	−19.2873			−1.86457			−0.932286	+	0.361722i	$0.882189\pi$
$108$		0			0
$109$	3.88169	−	6.72328i	0.371798	−	0.643973i	−0.618044	−	0.786143i	$-0.712075\pi$
$109$	3.88169	−	6.72328i	0.371798	−	0.643973i	0.989842	+	0.142170i	$0.0454080\pi$
$110$	0.472496			0.0450507
$111$		0			0
$112$	1.46714			0.138631
$113$	7.56156	+	13.0970i	0.711332	+	1.23206i	0.964357	+	0.264603i	$0.0852409\pi$
$113$	7.56156	+	13.0970i	0.711332	+	1.23206i	−0.253026	+	0.967459i	$0.581426\pi$
$114$		0			0
$115$	0.212173	−	0.367494i	0.0197852	−	0.0342690i
$116$	−2.63950	+	4.57175i	−0.245072	+	0.424476i
$117$		0			0
$118$	2.28652	+	3.96037i	0.210491	+	0.364582i
$119$	−0.506855	−	0.877899i	−0.0464634	−	0.0804769i
$120$		0			0
$121$	0.513261	+	0.888994i	0.0466601	+	0.0808176i
$122$	−4.21905	−	7.30760i	−0.381974	−	0.661599i
$123$		0			0
$124$	−6.75796			−0.606883
$125$	1.49280			0.133520
$126$		0			0
$127$	−7.58853	−	13.1437i	−0.673373	−	1.16632i	−0.976942	−	0.213507i	$-0.931512\pi$
$127$	−7.58853	−	13.1437i	−0.673373	−	1.16632i	0.303569	−	0.952810i	$-0.401822\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.349538			−0.0306565
$131$	3.61280			0.315652			0.157826	−	0.987467i	$-0.449552\pi$
$131$	3.61280			0.315652			0.157826	+	0.987467i	$0.449552\pi$
$132$		0			0
$133$	−3.97326	+	5.01103i	−0.344525	+	0.434512i
$134$	−3.58662			−0.309837
$135$		0			0
$136$	−0.345473	+	0.598376i	−0.0296240	+	0.0513103i
$137$	−8.72696			−0.745595			−0.372797	−	0.927913i	$-0.621601\pi$
$137$	−8.72696			−0.745595			−0.372797	+	0.927913i	$0.621601\pi$
$138$		0			0
$139$	−2.60938	+	4.51958i	−0.221325	+	0.383346i	−0.955210	−	0.295927i	$-0.904371\pi$
$139$	−2.60938	+	4.51958i	−0.221325	+	0.383346i	0.733886	+	0.679273i	$0.237705\pi$
$140$	0.109753	+	0.190097i	0.00927579	+	0.0160661i
$141$		0			0
$142$	−1.72325			−0.144612
$143$	3.68904	+	6.38960i	0.308493	+	0.534325i
$144$		0			0
$145$	−0.789817			−0.0655908
$146$	−0.999157			−0.0826908
$147$		0			0
$148$	−3.93281	+	6.81182i	−0.323275	+	0.559928i
$149$	−4.91597			−0.402732			−0.201366	−	0.979516i	$-0.564538\pi$
$149$	−4.91597			−0.402732			−0.201366	+	0.979516i	$0.564538\pi$
$150$		0			0
$151$	2.14333	−	3.71236i	0.174422	−	0.302108i	−0.765539	−	0.643389i	$-0.777528\pi$
$151$	2.14333	−	3.71236i	0.174422	−	0.302108i	0.939961	+	0.341282i	$0.110861\pi$
$152$	4.31202	+	0.637588i	0.349751	+	0.0517152i
$153$		0			0
$154$	2.31667	−	4.01259i	0.186682	−	0.323343i
$155$	−0.505546	−	0.875631i	−0.0406064	−	0.0703324i
$156$		0			0
$157$	6.64423			0.530268			0.265134	−	0.964212i	$-0.414584\pi$
$157$	6.64423			0.530268			0.265134	+	0.964212i	$0.414584\pi$
$158$	7.24959	−	12.5567i	0.576746	−	0.998954i
$159$		0			0
$160$	0.0748074	−	0.129570i	0.00591405	−	0.0102434i
$161$	−2.08059	−	3.60368i	−0.163973	−	0.284010i
$162$		0			0
$163$	0.631834			0.0494891			0.0247445	−	0.999694i	$-0.492123\pi$
$163$	0.631834			0.0494891			0.0247445	+	0.999694i	$0.492123\pi$
$164$	−0.293304	+	0.508018i	−0.0229032	+	0.0396695i
$165$		0			0
$166$	−2.31259			−0.179492
$167$	3.56500	−	6.17476i	0.275868	−	0.477818i	−0.694486	−	0.719507i	$-0.744368\pi$
$167$	3.56500	−	6.17476i	0.275868	−	0.477818i	0.970354	+	0.241689i	$0.0777014\pi$
$168$		0			0
$169$	3.77096	+	6.53150i	0.290074	+	0.502423i
$170$	−0.103376			−0.00792856
$171$		0			0
$172$	−8.65852			−0.660206
$173$	11.3189	+	19.6049i	0.860560	+	1.49053i	0.871389	+	0.490593i	$0.163220\pi$
$173$	11.3189	+	19.6049i	0.860560	+	1.49053i	−0.0108287	+	0.999941i	$0.503447\pi$
$174$		0			0
$175$	3.65142	−	6.32444i	0.276021	−	0.478083i
$176$	−3.15808			−0.238049
$177$		0			0
$178$	1.57359	−	2.72553i	0.117945	−	0.204287i
$179$	−7.83883			−0.585901			−0.292951	−	0.956128i	$-0.594637\pi$
$179$	−7.83883			−0.585901			−0.292951	+	0.956128i	$0.594637\pi$
$180$		0			0
$181$	−4.45937	−	7.72386i	−0.331463	−	0.574110i	0.651336	−	0.758789i	$-0.274209\pi$
$181$	−4.45937	−	7.72386i	−0.331463	−	0.574110i	−0.982799	+	0.184679i	$0.940875\pi$
$182$	−1.71380	+	2.96839i	−0.127035	+	0.220032i
$183$		0			0
$184$	−1.41813	+	2.45627i	−0.104546	+	0.181079i
$185$	−1.17681			−0.0865210
$186$		0			0
$187$	1.09103	+	1.88972i	0.0797841	+	0.138190i
$188$	−0.188688	+	0.326817i	−0.0137615	+	0.0238356i
$189$		0			0
$190$	0.239958	+	0.606405i	0.0174084	+	0.0439933i
$191$	−2.13214	+	3.69297i	−0.154276	+	0.267214i	−0.932795	−	0.360407i	$-0.882638\pi$
$191$	−2.13214	+	3.69297i	−0.154276	+	0.267214i	0.778519	+	0.627621i	$0.215971\pi$
$192$		0			0
$193$	−20.8559			−1.50124			−0.750619	−	0.660735i	$-0.770245\pi$
$193$	−20.8559			−1.50124			−0.750619	+	0.660735i	$0.770245\pi$
$194$	−0.970110	+	1.68028i	−0.0696498	+	0.120637i
$195$		0			0
$196$	−4.84751			−0.346251
$197$	0.291092			0.0207395			0.0103697	−	0.999946i	$-0.496699\pi$
$197$	0.291092			0.0207395			0.0103697	+	0.999946i	$0.496699\pi$
$198$		0			0
$199$	−3.54111	−	6.13339i	−0.251023	−	0.434785i	0.712785	−	0.701383i	$-0.247434\pi$
$199$	−3.54111	−	6.13339i	−0.251023	−	0.434785i	−0.963808	+	0.266598i	$0.914100\pi$
$200$	−4.97762			−0.351971
$201$		0			0
$202$	−8.61906	−	14.9287i	−0.606435	−	1.05038i
$203$	−3.87251	+	6.70738i	−0.271797	+	0.470766i
$204$		0			0
$205$	−0.0877654			−0.00612980
$206$	−8.37347	+	14.5033i	−0.583407	+	1.01049i
$207$		0			0
$208$	2.33625			0.161990
$209$	8.55264	−	10.7865i	0.591598	−	0.746117i
$210$		0			0
$211$	−26.9650			−1.85634			−0.928172	−	0.372151i	$-0.878621\pi$
$211$	−26.9650			−1.85634			−0.928172	+	0.372151i	$0.878621\pi$
$212$	−0.409070			−0.0280950
$213$		0			0
$214$	9.64364	+	16.7033i	0.659226	+	1.14181i
$215$	−0.647722	−	1.12189i	−0.0441743	−	0.0765121i
$216$		0			0
$217$	−9.91485			−0.673064
$218$	−7.76337			−0.525802
$219$		0			0
$220$	−0.236248	−	0.409193i	−0.0159278	−	0.0275878i
$221$	−0.807111	−	1.39796i	−0.0542922	−	0.0940368i
$222$		0			0
$223$	2.03840	+	3.53061i	0.136501	+	0.236427i	0.926170	−	0.377106i	$-0.123081\pi$
$223$	2.03840	+	3.53061i	0.136501	+	0.236427i	−0.789669	+	0.613534i	$0.789748\pi$
$224$	−0.733568	−	1.27058i	−0.0490136	−	0.0848940i
$225$		0			0
$226$	7.56156	−	13.0970i	0.502987	−	0.871200i
$227$	−13.6961	+	23.7224i	−0.909044	+	1.57451i	−0.0936500	+	0.995605i	$0.529853\pi$
$227$	−13.6961	+	23.7224i	−0.909044	+	1.57451i	−0.815394	+	0.578906i	$0.803480\pi$
$228$		0			0
$229$	−6.03094	−	10.4459i	−0.398536	−	0.690284i	0.595010	−	0.803719i	$-0.297148\pi$
$229$	−6.03094	−	10.4459i	−0.398536	−	0.690284i	−0.993546	+	0.113434i	$0.963815\pi$
$230$	−0.424346			−0.0279806
$231$		0			0
$232$	5.27900			0.346583
$233$	10.7521	−	18.6232i	0.704395	−	1.22005i	−0.262514	−	0.964928i	$-0.584552\pi$
$233$	10.7521	−	18.6232i	0.704395	−	1.22005i	0.966909	−	0.255120i	$-0.0821150\pi$
$234$		0			0
$235$	−0.0564610			−0.00368311
$236$	2.28652	−	3.96037i	0.148840	−	0.257798i
$237$		0			0
$238$	−0.506855	+	0.877899i	−0.0328546	+	0.0569058i
$239$	−12.1710	−	21.0808i	−0.787275	−	1.36360i	−0.927630	−	0.373500i	$-0.878158\pi$
$239$	−12.1710	−	21.0808i	−0.787275	−	1.36360i	0.140355	−	0.990101i	$-0.455176\pi$
$240$		0			0
$241$	5.68592			0.366262			0.183131	−	0.983089i	$-0.441377\pi$
$241$	5.68592			0.366262			0.183131	+	0.983089i	$0.441377\pi$
$242$	0.513261	−	0.888994i	0.0329937	−	0.0571467i
$243$		0			0
$244$	−4.21905	+	7.30760i	−0.270097	+	0.467821i
$245$	−0.362630	−	0.628093i	−0.0231676	−	0.0401274i
$246$		0			0
$247$	−6.32698	+	7.97952i	−0.402576	+	0.507725i
$248$	3.37898	+	5.85257i	0.214566	+	0.371638i
$249$		0			0
$250$	−0.746400	−	1.29280i	−0.0472065	−	0.0817640i
$251$	−11.8819	−	20.5800i	−0.749979	−	1.29900i	−0.947832	−	0.318769i	$-0.896730\pi$
$251$	−11.8819	−	20.5800i	−0.749979	−	1.29900i	0.197854	−	0.980232i	$-0.436603\pi$
$252$		0			0
$253$	4.47856	+	7.75710i	0.281565	+	0.487685i
$254$	−7.58853	+	13.1437i	−0.476147	+	0.824710i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.61365	+	4.52698i	−0.163035	+	0.282385i	−0.935956	−	0.352118i	$-0.885462\pi$
$257$	−2.61365	+	4.52698i	−0.163035	+	0.282385i	0.772921	+	0.634503i	$0.218795\pi$
$258$		0			0
$259$	−5.76996	+	9.99386i	−0.358528	+	0.620989i
$260$	0.174769	+	0.302709i	0.0108387	+	0.0187732i
$261$		0			0
$262$	−1.80640	−	3.12878i	−0.111600	−	0.193296i
$263$	9.66411	+	16.7387i	0.595915	+	1.03215i	0.993417	+	0.114553i	$0.0365437\pi$
$263$	9.66411	+	16.7387i	0.595915	+	1.03215i	−0.397502	+	0.917601i	$0.630123\pi$
$264$		0			0
$265$	−0.0306015	−	0.0530033i	−0.00187983	−	0.00325597i
$266$	6.32631	+	0.935428i	0.387891	+	0.0573548i
$267$		0			0
$268$	1.79331	+	3.10610i	0.109544	+	0.189735i
$269$	−10.1636	+	17.6039i	−0.619687	+	1.07333i	0.369855	+	0.929089i	$0.379407\pi$
$269$	−10.1636	+	17.6039i	−0.619687	+	1.07333i	−0.989543	+	0.144241i	$0.953926\pi$
$270$		0			0
$271$	−0.115369	+	0.199826i	−0.00700819	+	0.0121385i	−0.869508	−	0.493918i	$-0.835564\pi$
$271$	−0.115369	+	0.199826i	−0.00700819	+	0.0121385i	0.862500	+	0.506057i	$0.168897\pi$
$272$	0.690946			0.0418947
$273$		0			0
$274$	4.36348	+	7.55777i	0.263608	+	0.456582i
$275$	−7.85986	+	13.6137i	−0.473967	+	0.820935i
$276$		0			0
$277$	3.91702	−	6.78448i	0.235351	−	0.407640i	−0.724024	−	0.689775i	$-0.757709\pi$
$277$	3.91702	−	6.78448i	0.235351	−	0.407640i	0.959375	+	0.282135i	$0.0910427\pi$
$278$	5.21876			0.313000
$279$		0			0
$280$	0.109753	−	0.190097i	0.00655898	−	0.0113605i
$281$	−25.8532			−1.54227			−0.771137	−	0.636669i	$-0.780312\pi$
$281$	−25.8532			−1.54227			−0.771137	+	0.636669i	$0.780312\pi$
$282$		0			0
$283$	21.1355			1.25638			0.628189	−	0.778061i	$-0.283797\pi$
$283$	21.1355			1.25638			0.628189	+	0.778061i	$0.283797\pi$
$284$	0.861623	+	1.49237i	0.0511279	+	0.0885561i
$285$		0			0
$286$	3.68904	−	6.38960i	0.218137	−	0.377825i
$287$	−0.430317	+	0.745331i	−0.0254008	+	0.0439955i
$288$		0			0
$289$	8.26130	+	14.3090i	0.485959	+	0.841705i
$290$	0.394909	+	0.684002i	0.0231898	+	0.0401660i
$291$		0			0
$292$	0.499579	+	0.865295i	0.0292356	+	0.0506376i
$293$	2.04303	+	3.53864i	0.119355	+	0.206729i	0.919512	−	0.393061i	$-0.128584\pi$
$293$	2.04303	+	3.53864i	0.119355	+	0.206729i	−0.800157	+	0.599791i	$0.795251\pi$
$294$		0			0
$295$	0.684195			0.0398354
$296$	7.86561			0.457179
$297$		0			0
$298$	2.45799	+	4.25736i	0.142387	+	0.246622i
$299$	−3.31310	−	5.73847i	−0.191602	−	0.331864i
$300$		0			0
$301$	−12.7032			−0.732202
$302$	−4.28666			−0.246670
$303$		0			0
$304$	−1.60384	−	4.05311i	−0.0919866	−	0.232462i
$305$	−1.26246			−0.0722885
$306$		0			0
$307$	−13.2827	+	23.0064i	−0.758085	+	1.31304i	0.185741	+	0.982599i	$0.440532\pi$
$307$	−13.2827	+	23.0064i	−0.758085	+	1.31304i	−0.943826	+	0.330443i	$0.892802\pi$
$308$	−4.63333			−0.264009
$309$		0			0
$310$	−0.505546	+	0.875631i	−0.0287131	+	0.0497325i
$311$	1.60809	+	2.78529i	0.0911864	+	0.157939i	0.908011	−	0.418947i	$-0.137601\pi$
$311$	1.60809	+	2.78529i	0.0911864	+	0.157939i	−0.816824	+	0.576887i	$0.804267\pi$
$312$		0			0
$313$	−4.86711			−0.275105			−0.137553	−	0.990494i	$-0.543924\pi$
$313$	−4.86711			−0.275105			−0.137553	+	0.990494i	$0.543924\pi$
$314$	−3.32212	−	5.75408i	−0.187478	−	0.324721i
$315$		0			0
$316$	−14.4992			−0.815642
$317$	−30.6705			−1.72262			−0.861312	−	0.508076i	$-0.830357\pi$
$317$	−30.6705			−1.72262			−0.861312	+	0.508076i	$0.830357\pi$
$318$		0			0
$319$	8.33576	−	14.4380i	0.466713	−	0.808371i
$320$	−0.149615			−0.00836373
$321$		0			0
$322$	−2.08059	+	3.60368i	−0.115947	+	0.200825i
$323$	−1.87120	+	2.35994i	−0.104116	+	0.131311i
$324$		0			0
$325$	5.81448	−	10.0710i	0.322529	−	0.558637i
$326$	−0.315917	−	0.547185i	−0.0174970	−	0.0303058i
$327$		0			0
$328$	0.586609			0.0323900
$329$	−0.276831	+	0.479485i	−0.0152622	+	0.0264349i
$330$		0			0
$331$	−3.98086	+	6.89505i	−0.218808	+	0.378986i	−0.954444	−	0.298391i	$-0.903550\pi$
$331$	−3.98086	+	6.89505i	−0.218808	+	0.378986i	0.735636	+	0.677377i	$0.236883\pi$
$332$	1.15630	+	2.00276i	0.0634600	+	0.109916i
$333$		0			0
$334$	−7.13000			−0.390136
$335$	−0.268306	+	0.464719i	−0.0146591	+	0.0253903i
$336$		0			0
$337$	11.4521			0.623836			0.311918	−	0.950109i	$-0.399029\pi$
$337$	11.4521			0.623836			0.311918	+	0.950109i	$0.399029\pi$
$338$	3.77096	−	6.53150i	0.205113	−	0.355267i
$339$		0			0
$340$	0.0516879	+	0.0895260i	0.00280317	+	0.00485523i
$341$	21.3422			1.15574
$342$		0			0
$343$	−17.3819			−0.938535
$344$	4.32926	+	7.49850i	0.233418	+	0.404292i
$345$		0			0
$346$	11.3189	−	19.6049i	0.608508	−	1.05397i
$347$	−27.0528			−1.45227			−0.726135	−	0.687552i	$-0.758685\pi$
$347$	−27.0528			−1.45227			−0.726135	+	0.687552i	$0.758685\pi$
$348$		0			0
$349$	15.7323	−	27.2491i	0.842131	−	1.45861i	−0.0459595	−	0.998943i	$-0.514635\pi$
$349$	15.7323	−	27.2491i	0.842131	−	1.45861i	0.888090	−	0.459670i	$-0.152032\pi$
$350$	−7.30284			−0.390353
$351$		0			0
$352$	1.57904	+	2.73498i	0.0841632	+	0.145775i
$353$	16.3802	−	28.3714i	0.871831	−	1.51006i	0.0117302	−	0.999931i	$-0.496266\pi$
$353$	16.3802	−	28.3714i	0.871831	−	1.51006i	0.860101	−	0.510124i	$-0.170401\pi$
$354$		0			0
$355$	−0.128912	+	0.223281i	−0.00684191	+	0.0118505i
$356$	−3.14717			−0.166800
$357$		0			0
$358$	3.91941	+	6.78862i	0.207147	+	0.358790i
$359$	9.64663	−	16.7085i	0.509130	−	0.881838i	−0.490814	−	0.871264i	$-0.663301\pi$
$359$	9.64663	−	16.7085i	0.509130	−	0.881838i	0.999944	−	0.0105742i	$-0.00336595\pi$
$360$		0			0
$361$	18.1870	+	5.49858i	0.957209	+	0.289399i
$362$	−4.45937	+	7.72386i	−0.234379	+	0.405957i
$363$		0			0
$364$	3.42760			0.179655
$365$	−0.0747444	+	0.129461i	−0.00391230	+	0.00677630i
$366$		0			0
$367$	−19.4650			−1.01607			−0.508033	−	0.861338i	$-0.669627\pi$
$367$	−19.4650			−1.01607			−0.508033	+	0.861338i	$0.669627\pi$
$368$	2.83626			0.147850
$369$		0			0
$370$	0.588406	+	1.01915i	0.0305898	+	0.0529831i
$371$	−0.600161			−0.0311588
$372$		0			0
$373$	5.67541	+	9.83010i	0.293862	+	0.508983i	0.974719	−	0.223432i	$-0.0717262\pi$
$373$	5.67541	+	9.83010i	0.293862	+	0.508983i	−0.680858	+	0.732416i	$0.738393\pi$
$374$	1.09103	−	1.88972i	0.0564159	−	0.0977152i
$375$		0			0
$376$	0.377376			0.0194617
$377$	−6.16654	+	10.6808i	−0.317593	+	0.550087i
$378$		0			0
$379$	23.9426			1.22985			0.614923	−	0.788587i	$-0.289187\pi$
$379$	23.9426			1.22985			0.614923	+	0.788587i	$0.289187\pi$
$380$	0.405183	−	0.511013i	0.0207855	−	0.0262144i
$381$		0			0
$382$	4.26428			0.218180
$383$	−8.75291			−0.447253			−0.223626	−	0.974675i	$-0.571790\pi$
$383$	−8.75291			−0.447253			−0.223626	+	0.974675i	$0.571790\pi$
$384$		0			0
$385$	−0.346608	−	0.600342i	−0.0176648	−	0.0305963i
$386$	10.4279	+	18.0617i	0.530768	+	0.919317i
$387$		0			0
$388$	1.94022			0.0984998
$389$	−0.594895			−0.0301623			−0.0150812	−	0.999886i	$-0.504801\pi$
$389$	−0.594895			−0.0301623			−0.0150812	+	0.999886i	$0.504801\pi$
$390$		0			0
$391$	−0.979849	−	1.69715i	−0.0495531	−	0.0858285i
$392$	2.42376	+	4.19807i	0.122418	+	0.212034i
$393$		0			0
$394$	−0.145546	−	0.252093i	−0.00733251	−	0.0127003i
$395$	−1.08465	−	1.87866i	−0.0545745	−	0.0945257i
$396$		0			0
$397$	12.5042	−	21.6580i	0.627569	−	1.08698i	−0.360469	−	0.932771i	$-0.617383\pi$
$397$	12.5042	−	21.6580i	0.627569	−	1.08698i	0.988038	−	0.154211i	$-0.0492835\pi$
$398$	−3.54111	+	6.13339i	−0.177500	+	0.307439i
$399$		0			0
$400$	2.48881	+	4.31074i	0.124440	+	0.215537i
$401$	34.9940			1.74752			0.873758	−	0.486362i	$-0.161676\pi$
$401$	34.9940			1.74752			0.873758	+	0.486362i	$0.161676\pi$
$402$		0			0
$403$	−15.7883			−0.786471
$404$	−8.61906	+	14.9287i	−0.428814	+	0.742728i
$405$		0			0
$406$	7.74501			0.384379
$407$	12.4201	−	21.5123i	0.615642	−	1.06632i
$408$		0			0
$409$	9.97404	−	17.2756i	0.493185	−	0.854221i	−0.506784	−	0.862073i	$-0.669166\pi$
$409$	9.97404	−	17.2756i	0.493185	−	0.854221i	0.999969	+	0.00785181i	$0.00249933\pi$
$410$	0.0438827	+	0.0760070i	0.00216721	+	0.00375372i
$411$		0			0
$412$	16.7469			0.825063
$413$	3.35464	−	5.81040i	0.165071	−	0.285911i
$414$		0			0
$415$	−0.172999	+	0.299643i	−0.00849219	+	0.0147089i
$416$	−1.16813	−	2.02325i	−0.0572721	−	0.0991982i
$417$		0			0
$418$	−13.6177	−	2.01356i	−0.666063	−	0.0984862i
$419$	−14.8751	−	25.7644i	−0.726696	−	1.25867i	−0.958272	−	0.285857i	$-0.907722\pi$
$419$	−14.8751	−	25.7644i	−0.726696	−	1.25867i	0.231576	−	0.972817i	$-0.425612\pi$
$420$		0			0
$421$	−9.81305	−	16.9967i	−0.478259	−	0.828369i	0.521431	−	0.853294i	$-0.325399\pi$
$421$	−9.81305	−	16.9967i	−0.478259	−	0.828369i	−0.999689	+	0.0249252i	$0.992065\pi$
$422$	13.4825	+	23.3523i	0.656317	+	1.13677i
$423$		0			0
$424$	0.204535	+	0.354265i	0.00993310	+	0.0172046i
$425$	1.71963	−	2.97849i	0.0834143	−	0.144478i
$426$		0			0
$427$	−6.18991	+	10.7212i	−0.299551	+	0.518837i
$428$	9.64364	−	16.7033i	0.466143	−	0.807383i
$429$		0			0
$430$	−0.647722	+	1.12189i	−0.0312359	+	0.0541022i
$431$	−16.0450	−	27.7907i	−0.772858	−	1.33863i	−0.935990	−	0.352025i	$-0.885493\pi$
$431$	−16.0450	−	27.7907i	−0.772858	−	1.33863i	0.163132	−	0.986604i	$-0.447840\pi$
$432$		0			0
$433$	1.40581	+	2.43494i	0.0675591	+	0.117016i	0.897826	−	0.440350i	$-0.145146\pi$
$433$	1.40581	+	2.43494i	0.0675591	+	0.117016i	−0.830267	+	0.557366i	$0.811812\pi$
$434$	4.95743	+	8.58651i	0.237964	+	0.412166i
$435$		0			0
$436$	3.88169	+	6.72328i	0.185899	+	0.321987i
$437$	−7.68108	+	9.68729i	−0.367436	+	0.463406i
$438$		0			0
$439$	−6.07199	−	10.5170i	−0.289800	−	0.501949i	0.683962	−	0.729518i	$-0.260256\pi$
$439$	−6.07199	−	10.5170i	−0.289800	−	0.501949i	−0.973762	+	0.227569i	$0.926922\pi$
$440$	−0.236248	+	0.409193i	−0.0112627	+	0.0195075i
$441$		0			0
$442$	−0.807111	+	1.39796i	−0.0383904	+	0.0664941i
$443$	21.9463			1.04270			0.521350	−	0.853343i	$-0.325428\pi$
$443$	21.9463			1.04270			0.521350	+	0.853343i	$0.325428\pi$
$444$		0			0
$445$	−0.235432	−	0.407780i	−0.0111605	−	0.0193306i
$446$	2.03840	−	3.53061i	0.0965210	−	0.167179i
$447$		0			0
$448$	−0.733568	+	1.27058i	−0.0346578	+	0.0600291i
$449$	−7.95330			−0.375339			−0.187670	−	0.982232i	$-0.560093\pi$
$449$	−7.95330			−0.375339			−0.187670	+	0.982232i	$0.560093\pi$
$450$		0			0
$451$	0.926279	−	1.60436i	0.0436168	−	0.0755464i
$452$	−15.1231			−0.711332
$453$		0			0
$454$	27.3923			1.28558
$455$	0.256410	+	0.444115i	0.0120207	+	0.0208204i
$456$		0			0
$457$	13.2396	−	22.9317i	0.619323	−	1.07270i	−0.370286	−	0.928918i	$-0.620740\pi$
$457$	13.2396	−	22.9317i	0.619323	−	1.07270i	0.989609	−	0.143782i	$-0.0459264\pi$
$458$	−6.03094	+	10.4459i	−0.281807	+	0.488105i
$459$		0			0
$460$	0.212173	+	0.367494i	0.00989262	+	0.0171345i
$461$	−3.67967	−	6.37338i	−0.171379	−	0.296838i	0.767523	−	0.641021i	$-0.221489\pi$
$461$	−3.67967	−	6.37338i	−0.171379	−	0.296838i	−0.938902	+	0.344184i	$0.888156\pi$
$462$		0			0
$463$	14.7707	+	25.5836i	0.686452	+	1.18897i	0.972978	+	0.230897i	$0.0741662\pi$
$463$	14.7707	+	25.5836i	0.686452	+	1.18897i	−0.286526	+	0.958072i	$0.592501\pi$
$464$	−2.63950	−	4.57175i	−0.122536	−	0.212238i
$465$		0			0
$466$	−21.5042			−0.996165
$467$	39.3966			1.82306			0.911529	−	0.411236i	$-0.134903\pi$
$467$	39.3966			1.82306			0.911529	+	0.411236i	$0.134903\pi$
$468$		0			0
$469$	2.63103	+	4.55707i	0.121490	+	0.210426i
$470$	0.0282305	+	0.0488967i	0.00130218	+	0.00225544i
$471$		0			0
$472$	−4.57304			−0.210491
$473$	27.3443			1.25729
$474$		0			0
$475$	−21.4636	−	3.17367i	−0.984816	−	0.145618i
$476$	1.01371			0.0464634
$477$		0			0
$478$	−12.1710	+	21.0808i	−0.556688	+	0.964212i
$479$	39.7281			1.81522			0.907612	−	0.419809i	$-0.137903\pi$
$479$	39.7281			1.81522			0.907612	+	0.419809i	$0.137903\pi$
$480$		0			0
$481$	−9.18802	+	15.9141i	−0.418938	+	0.725622i
$482$	−2.84296	−	4.92415i	−0.129493	−	0.224289i
$483$		0			0
$484$	−1.02652			−0.0466601
$485$	0.145143	+	0.251395i	0.00659060	+	0.0114153i
$486$		0			0
$487$	−29.7730			−1.34914			−0.674572	−	0.738209i	$-0.735672\pi$
$487$	−29.7730			−1.34914			−0.674572	+	0.738209i	$0.735672\pi$
$488$	8.43809			0.381974
$489$		0			0
$490$	−0.362630	+	0.628093i	−0.0163820	+	0.0283744i
$491$	16.3341			0.737149			0.368575	−	0.929598i	$-0.379846\pi$
$491$	16.3341			0.737149			0.368575	+	0.929598i	$0.379846\pi$
$492$		0			0
$493$	−1.82375	+	3.15883i	−0.0821376	+	0.142267i
$494$	10.0740	+	1.48957i	0.453249	+	0.0670188i
$495$		0			0
$496$	3.37898	−	5.85257i	0.151721	−	0.262788i
$497$	1.26412	+	2.18952i	0.0567034	+	0.0982132i
$498$		0			0
$499$	14.7158			0.658769			0.329385	−	0.944196i	$-0.393159\pi$
$499$	14.7158			0.658769			0.329385	+	0.944196i	$0.393159\pi$
$500$	−0.746400	+	1.29280i	−0.0333800	+	0.0578159i
$501$		0			0
$502$	−11.8819	+	20.5800i	−0.530315	+	0.918532i
$503$	−5.90608	−	10.2296i	−0.263339	−	0.456117i	0.703788	−	0.710410i	$-0.251490\pi$
$503$	−5.90608	−	10.2296i	−0.263339	−	0.456117i	−0.967127	+	0.254293i	$0.918157\pi$
$504$		0			0
$505$	−2.57908			−0.114768
$506$	4.47856	−	7.75710i	0.199096	−	0.344845i
$507$		0			0
$508$	15.1771			0.673373
$509$	0.674813	−	1.16881i	0.0299105	−	0.0518066i	−0.850683	−	0.525680i	$-0.823811\pi$
$509$	0.674813	−	1.16881i	0.0299105	−	0.0518066i	0.880593	+	0.473873i	$0.157144\pi$
$510$		0			0
$511$	0.732950	+	1.26951i	0.0324238	+	0.0561596i
$512$	1.00000			0.0441942
$513$		0			0
$514$	5.22730			0.230566
$515$	1.25280	+	2.16991i	0.0552048	+	0.0956175i
$516$		0			0
$517$	0.595892	−	1.03211i	0.0262073	−	0.0453924i
$518$	11.5399			0.507035
$519$		0			0
$520$	0.174769	−	0.302709i	0.00766413	−	0.0132747i
$521$	30.6763			1.34395			0.671976	−	0.740573i	$-0.265446\pi$
$521$	30.6763			1.34395			0.671976	+	0.740573i	$0.265446\pi$
$522$		0			0
$523$	−0.469579	−	0.813334i	−0.0205332	−	0.0355646i	0.855576	−	0.517677i	$-0.173203\pi$
$523$	−0.469579	−	0.813334i	−0.0205332	−	0.0355646i	−0.876109	+	0.482112i	$0.839870\pi$
$524$	−1.80640	+	3.12878i	−0.0789129	+	0.136681i
$525$		0			0
$526$	9.66411	−	16.7387i	0.421375	−	0.729843i
$527$	−4.66938			−0.203402
$528$		0			0
$529$	7.47783	+	12.9520i	0.325123	+	0.563129i
$530$	−0.0306015	+	0.0530033i	−0.00132924	+	0.00230232i
$531$		0			0
$532$	−2.35305	−	5.94646i	−0.102018	−	0.257812i
$533$	−0.685233	+	1.18686i	−0.0296807	+	0.0514085i
$534$		0			0
$535$	2.88566			0.124758
$536$	1.79331	−	3.10610i	0.0774591	−	0.134163i
$537$		0			0
$538$	20.3273			0.876370
$539$	15.3088			0.659398
$540$		0			0
$541$	19.4907	+	33.7589i	0.837970	+	1.45141i	0.891589	+	0.452846i	$0.149591\pi$
$541$	19.4907	+	33.7589i	0.837970	+	1.45141i	−0.0536184	+	0.998561i	$0.517075\pi$
$542$	0.230739			0.00991107
$543$		0			0
$544$	−0.345473	−	0.598376i	−0.0148120	−	0.0256552i
$545$	−0.580758	+	1.00590i	−0.0248769	+	0.0430881i
$546$		0			0
$547$	−10.0575			−0.430027			−0.215014	−	0.976611i	$-0.568980\pi$
$547$	−10.0575			−0.430027			−0.215014	+	0.976611i	$0.568980\pi$
$548$	4.36348	−	7.55777i	0.186399	−	0.322852i
$549$		0			0
$550$	15.7197			0.670291
$551$	22.7631	+	3.36583i	0.969742	+	0.143389i
$552$		0			0
$553$	−21.2723			−0.904588
$554$	−7.83404			−0.332837
$555$		0			0
$556$	−2.60938	−	4.51958i	−0.110662	−	0.191673i
$557$	12.0197	+	20.8188i	0.509292	+	0.882120i	0.999942	+	0.0107631i	$0.00342606\pi$
$557$	12.0197	+	20.8188i	0.509292	+	0.882120i	−0.490650	+	0.871357i	$0.663241\pi$
$558$		0			0
$559$	−20.2285			−0.855574
$560$	−0.219505			−0.00927579
$561$		0			0
$562$	12.9266	+	22.3896i	0.545277	+	0.944447i
$563$	−12.4023	−	21.4814i	−0.522695	−	0.905335i	−0.999651	−	0.0264077i	$-0.991593\pi$
$563$	−12.4023	−	21.4814i	−0.522695	−	0.905335i	0.476956	−	0.878927i	$-0.341740\pi$
$564$		0			0
$565$	−1.13132	−	1.95951i	−0.0475951	−	0.0824370i
$566$	−10.5678	−	18.3039i	−0.444196	−	0.769371i
$567$		0			0
$568$	0.861623	−	1.49237i	0.0361529	−	0.0626186i
$569$	17.2338	−	29.8499i	0.722480	−	1.25137i	−0.237522	−	0.971382i	$-0.576335\pi$
$569$	17.2338	−	29.8499i	0.722480	−	1.25137i	0.960003	−	0.279991i	$-0.0903313\pi$
$570$		0			0
$571$	2.14626	+	3.71743i	0.0898181	+	0.155570i	0.907434	−	0.420194i	$-0.138038\pi$
$571$	2.14626	+	3.71743i	0.0898181	+	0.155570i	−0.817616	+	0.575764i	$0.804705\pi$
$572$	−7.37807			−0.308493
$573$		0			0
$574$	0.860634			0.0359222
$575$	7.05890	−	12.2264i	0.294376	−	0.509875i
$576$		0			0
$577$	−16.8005			−0.699412			−0.349706	−	0.936859i	$-0.613719\pi$
$577$	−16.8005			−0.699412			−0.349706	+	0.936859i	$0.613719\pi$
$578$	8.26130	−	14.3090i	0.343625	−	0.595175i
$579$		0			0
$580$	0.394909	−	0.684002i	0.0163977	−	0.0284016i
$581$	1.69644	+	2.93833i	0.0703803	+	0.121902i
$582$		0			0
$583$	1.29188			0.0535040
$584$	0.499579	−	0.865295i	0.0206727	−	0.0358062i
$585$		0			0
$586$	2.04303	−	3.53864i	0.0843970	−	0.146180i
$587$	−5.10348	−	8.83948i	−0.210643	−	0.364844i	0.741273	−	0.671204i	$-0.234222\pi$
$587$	−5.10348	−	8.83948i	−0.210643	−	0.364844i	−0.951916	+	0.306359i	$0.900889\pi$
$588$		0			0
$589$	10.8387	+	27.3908i	0.446601	+	1.12862i
$590$	−0.342098	−	0.592530i	−0.0140839	−	0.0243941i
$591$		0			0
$592$	−3.93281	−	6.81182i	−0.161637	−	0.279964i
$593$	−6.75053	−	11.6923i	−0.277211	−	0.480144i	0.693479	−	0.720476i	$-0.256077\pi$
$593$	−6.75053	−	11.6923i	−0.277211	−	0.480144i	−0.970691	+	0.240333i	$0.922743\pi$
$594$		0			0
$595$	0.0758331	+	0.131347i	0.00310885	+	0.00538469i
$596$	2.45799	−	4.25736i	0.100683	−	0.174388i
$597$		0			0
$598$	−3.31310	+	5.73847i	−0.135483	+	0.234663i
$599$	−2.32634	+	4.02934i	−0.0950518	+	0.164634i	−0.909630	−	0.415419i	$-0.863635\pi$
$599$	−2.32634	+	4.02934i	−0.0950518	+	0.164634i	0.814578	+	0.580053i	$0.196968\pi$
$600$		0			0
$601$	2.62873	−	4.55309i	0.107228	−	0.185725i	−0.807418	−	0.589979i	$-0.799136\pi$
$601$	2.62873	−	4.55309i	0.107228	−	0.185725i	0.914646	+	0.404255i	$0.132469\pi$
$602$	6.35162	+	11.0013i	0.258873	+	0.448380i
$603$		0			0
$604$	2.14333	+	3.71236i	0.0872110	+	0.151054i
$605$	−0.0767914	−	0.133007i	−0.00312202	−	0.00540749i
$606$		0			0
$607$	5.65449	+	9.79386i	0.229509	+	0.397521i	0.957663	−	0.287893i	$-0.0929547\pi$
$607$	5.65449	+	9.79386i	0.229509	+	0.397521i	−0.728154	+	0.685414i	$0.759621\pi$
$608$	−2.70818	+	3.41552i	−0.109831	+	0.138518i
$609$		0			0
$610$	0.631232	+	1.09333i	0.0255578	+	0.0442675i
$611$	−0.440823	+	0.763527i	−0.0178338	+	0.0308890i
$612$		0			0
$613$	16.0294	−	27.7637i	0.647421	−	1.12137i	−0.336316	−	0.941749i	$-0.609181\pi$
$613$	16.0294	−	27.7637i	0.647421	−	1.12137i	0.983737	−	0.179617i	$-0.0574858\pi$
$614$	26.5654			1.07209
$615$		0			0
$616$	2.31667	+	4.01259i	0.0933412	+	0.161672i
$617$	−17.1112	+	29.6375i	−0.688873	+	1.19316i	0.283330	+	0.959022i	$0.408561\pi$
$617$	−17.1112	+	29.6375i	−0.688873	+	1.19316i	−0.972203	+	0.234140i	$0.924773\pi$
$618$		0			0
$619$	14.0068	−	24.2605i	0.562980	−	0.975111i	−0.434254	−	0.900790i	$-0.642988\pi$
$619$	14.0068	−	24.2605i	0.562980	−	0.975111i	0.997234	−	0.0743202i	$-0.0236787\pi$
$620$	1.01109			0.0406064
$621$		0			0
$622$	1.60809	−	2.78529i	0.0644785	−	0.111680i
$623$	−4.61733			−0.184989
$624$		0			0
$625$	24.6647			0.986589
$626$	2.43356	+	4.21504i	0.0972645	+	0.168467i
$627$		0			0
$628$	−3.32212	+	5.75408i	−0.132567	+	0.229613i
$629$	−2.71735	+	4.70660i	−0.108348	+	0.187664i
$630$		0			0
$631$	−0.303425	−	0.525547i	−0.0120791	−	0.0209217i	0.859923	−	0.510424i	$-0.170512\pi$
$631$	−0.303425	−	0.525547i	−0.0120791	−	0.0209217i	−0.872002	+	0.489503i	$0.837178\pi$
$632$	7.24959	+	12.5567i	0.288373	+	0.499477i
$633$		0			0
$634$	15.3352	+	26.5614i	0.609040	+	1.05489i
$635$	1.13536	+	1.96650i	0.0450552	+	0.0780380i
$636$		0			0
$637$	−11.3250			−0.448713
$638$	−16.6715			−0.660032
$639$		0			0
$640$	0.0748074	+	0.129570i	0.00295702	+	0.00512171i
$641$	−3.68796	−	6.38773i	−0.145666	−	0.252300i	0.783955	−	0.620817i	$-0.213199\pi$
$641$	−3.68796	−	6.38773i	−0.145666	−	0.252300i	−0.929621	+	0.368517i	$0.879866\pi$
$642$		0			0
$643$	−39.5258			−1.55875			−0.779373	−	0.626561i	$-0.784462\pi$
$643$	−39.5258			−1.55875			−0.779373	+	0.626561i	$0.784462\pi$
$644$	4.16117			0.163973
$645$		0			0
$646$	2.97937	+	0.440539i	0.117222	+	0.0173328i
$647$	−16.2542			−0.639017			−0.319508	−	0.947583i	$-0.603518\pi$
$647$	−16.2542			−0.639017			−0.319508	+	0.947583i	$0.603518\pi$
$648$		0			0
$649$	−7.22102	+	12.5072i	−0.283450	+	0.490949i
$650$	−11.6290			−0.456125
$651$		0			0
$652$	−0.315917	+	0.547185i	−0.0123723	+	0.0214294i
$653$	19.5594	+	33.8779i	0.765418	+	1.32574i	0.940025	+	0.341105i	$0.110801\pi$
$653$	19.5594	+	33.8779i	0.765418	+	1.32574i	−0.174607	+	0.984638i	$0.555866\pi$
$654$		0			0
$655$	−0.540528			−0.0211202
$656$	−0.293304	−	0.508018i	−0.0114516	−	0.0198348i
$657$		0			0
$658$	0.553662			0.0215840
$659$	−37.3525			−1.45505			−0.727524	−	0.686082i	$-0.759329\pi$
$659$	−37.3525			−1.45505			−0.727524	+	0.686082i	$0.759329\pi$
$660$		0			0
$661$	23.2831	−	40.3276i	0.905609	−	1.56856i	0.0855123	−	0.996337i	$-0.472747\pi$
$661$	23.2831	−	40.3276i	0.905609	−	1.56856i	0.820097	−	0.572224i	$-0.193919\pi$
$662$	7.96172			0.309441
$663$		0			0
$664$	1.15630	−	2.00276i	0.0448730	−	0.0777223i
$665$	0.594459	−	0.749725i	0.0230521	−	0.0290731i
$666$		0			0
$667$	−7.48630	+	12.9667i	−0.289871	+	0.502071i
$668$	3.56500	+	6.17476i	0.137934	+	0.238909i
$669$		0			0
$670$	0.536611			0.0207311
$671$	13.3241	−	23.0780i	0.514371	−	0.890916i
$672$		0			0
$673$	2.77918	−	4.81368i	0.107129	−	0.185554i	−0.807477	−	0.589899i	$-0.799167\pi$
$673$	2.77918	−	4.81368i	0.107129	−	0.185554i	0.914606	+	0.404346i	$0.132501\pi$
$674$	−5.72606	−	9.91782i	−0.220559	−	0.382020i
$675$		0			0
$676$	−7.54193			−0.290074
$677$	−20.6787	+	35.8166i	−0.794749	+	1.37655i	0.128250	+	0.991742i	$0.459064\pi$
$677$	−20.6787	+	35.8166i	−0.794749	+	1.37655i	−0.922999	+	0.384803i	$0.874269\pi$
$678$		0			0
$679$	2.84657			0.109241
$680$	0.0516879	−	0.0895260i	0.00198214	−	0.00343317i
$681$		0			0
$682$	−10.6711	−	18.4829i	−0.408617	−	0.707746i
$683$	31.6423			1.21076			0.605380	−	0.795937i	$-0.293021\pi$
$683$	31.6423			1.21076			0.605380	+	0.795937i	$0.293021\pi$
$684$		0			0
$685$	1.30568			0.0498876
$686$	8.69096	+	15.0532i	0.331822	+	0.574733i
$687$		0			0
$688$	4.32926	−	7.49850i	0.165052	−	0.285878i
$689$	−0.955691			−0.0364089
$690$		0			0
$691$	4.00447	−	6.93595i	0.152337	−	0.263856i	−0.779749	−	0.626092i	$-0.784653\pi$
$691$	4.00447	−	6.93595i	0.152337	−	0.263856i	0.932086	+	0.362236i	$0.117987\pi$
$692$	−22.6378			−0.860560
$693$		0			0
$694$	13.5264	+	23.4284i	0.513455	+	0.889330i
$695$	0.390402	−	0.676196i	0.0148088	−	0.0256496i
$696$		0			0
$697$	−0.202657	+	0.351013i	−0.00767619	+	0.0132956i
$698$	−31.4646			−1.19095
$699$		0			0
$700$	3.65142	+	6.32444i	0.138011	+	0.239042i
$701$	−2.08727	+	3.61526i	−0.0788351	+	0.136546i	−0.902748	−	0.430171i	$-0.858453\pi$
$701$	−2.08727	+	3.61526i	−0.0788351	+	0.136546i	0.823912	+	0.566717i	$0.191787\pi$
$702$		0			0
$703$	33.9166	+	5.01502i	1.27919	+	0.189145i
$704$	1.57904	−	2.73498i	0.0595123	−	0.103078i
$705$		0			0
$706$	−32.7604			−1.23296
$707$	−12.6453	+	21.9024i	−0.475577	+	0.823723i
$708$		0			0
$709$	15.2773			0.573752			0.286876	−	0.957968i	$-0.407383\pi$
$709$	15.2773			0.573752			0.286876	+	0.957968i	$0.407383\pi$
$710$	0.257823			0.00967593
$711$		0			0
$712$	1.57359	+	2.72553i	0.0589726	+	0.102144i
$713$	−19.1673			−0.717822
$714$		0			0
$715$	−0.551935	−	0.955979i	−0.0206412	−	0.0357516i
$716$	3.91941	−	6.78862i	0.146475	−	0.253703i
$717$		0			0
$718$	−19.2933			−0.720018
$719$	−23.7224	+	41.0884i	−0.884696	+	1.53234i	−0.0386338	+	0.999253i	$0.512301\pi$
$719$	−23.7224	+	41.0884i	−0.884696	+	1.53234i	−0.846062	+	0.533085i	$0.821033\pi$
$720$		0			0
$721$	24.5700			0.915036
$722$	−4.33157	−	18.4997i	−0.161204	−	0.688486i
$723$		0			0
$724$	8.91875			0.331463
$725$	−26.2768			−0.975897
$726$		0			0
$727$	−14.3502	−	24.8552i	−0.532218	−	0.921829i	−0.999292	−	0.0376111i	$-0.988025\pi$
$727$	−14.3502	−	24.8552i	−0.532218	−	0.921829i	0.467074	−	0.884218i	$-0.345308\pi$
$728$	−1.71380	−	2.96839i	−0.0635176	−	0.110016i
$729$		0			0
$730$	0.149489			0.00553283
$731$	−5.98257			−0.221273
$732$		0			0
$733$	11.3898	+	19.7276i	0.420690	+	0.728657i	0.996007	−	0.0892738i	$-0.0284546\pi$
$733$	11.3898	+	19.7276i	0.420690	+	0.728657i	−0.575317	+	0.817931i	$0.695121\pi$
$734$	9.73251	+	16.8572i	0.359234	+	0.622211i
$735$		0			0
$736$	−1.41813	−	2.45627i	−0.0522729	−	0.0905393i
$737$	−5.66341	−	9.80932i	−0.208615	−	0.361331i
$738$		0			0
$739$	−15.7066	+	27.2046i	−0.577777	+	1.00074i	0.417957	+	0.908467i	$0.362746\pi$
$739$	−15.7066	+	27.2046i	−0.577777	+	1.00074i	−0.995734	+	0.0922717i	$0.970587\pi$
$740$	0.588406	−	1.01915i	0.0216302	−	0.0374647i
$741$		0			0
$742$	0.300081	+	0.519755i	0.0110163	+	0.0190808i
$743$	4.10766			0.150695			0.0753477	−	0.997157i	$-0.475993\pi$
$743$	4.10766			0.150695			0.0753477	+	0.997157i	$0.475993\pi$
$744$		0			0
$745$	0.735503			0.0269467
$746$	5.67541	−	9.83010i	0.207792	−	0.359905i
$747$		0			0
$748$	−2.18206			−0.0797841
$749$	14.1485	−	24.5060i	0.516976	−	0.895429i
$750$		0			0
$751$	19.8141	−	34.3191i	0.723028	−	1.25232i	−0.236753	−	0.971570i	$-0.576083\pi$
$751$	19.8141	−	34.3191i	0.723028	−	1.25232i	0.959781	−	0.280751i	$-0.0905836\pi$
$752$	−0.188688	−	0.326817i	−0.00688074	−	0.0119178i
$753$		0			0
$754$	12.3331			0.449144
$755$	−0.320674	+	0.555424i	−0.0116705	+	0.0202140i
$756$		0			0
$757$	−8.71216	+	15.0899i	−0.316649	+	0.548452i	−0.979787	−	0.200045i	$-0.935891\pi$
$757$	−8.71216	+	15.0899i	−0.316649	+	0.548452i	0.663138	+	0.748497i	$0.269224\pi$
$758$	−11.9713	−	20.7349i	−0.434816	−	0.753124i
$759$		0			0
$760$	−0.645142	−	0.0953927i	−0.0234017	−	0.00346026i
$761$	21.5078	+	37.2526i	0.779658	+	1.35041i	0.932139	+	0.362100i	$0.117940\pi$
$761$	21.5078	+	37.2526i	0.779658	+	1.35041i	−0.152482	+	0.988306i	$0.548726\pi$
$762$		0			0
$763$	5.69496	+	9.86396i	0.206171	+	0.357099i
$764$	−2.13214	−	3.69297i	−0.0771381	−	0.133607i
$765$		0			0
$766$	4.37646	+	7.58024i	0.158128	+	0.273885i
$767$	5.34189	−	9.25242i	0.192884	−	0.334086i
$768$		0			0
$769$	9.01825	−	15.6201i	0.325207	−	0.563274i	−0.656348	−	0.754459i	$-0.727899\pi$
$769$	9.01825	−	15.6201i	0.325207	−	0.563274i	0.981554	+	0.191184i	$0.0612328\pi$
$770$	−0.346608	+	0.600342i	−0.0124909	+	0.0216348i
$771$		0			0
$772$	10.4279	−	18.0617i	0.375310	−	0.650055i
$773$	1.75824	+	3.04536i	0.0632394	+	0.109534i	0.895912	−	0.444232i	$-0.146523\pi$
$773$	1.75824	+	3.04536i	0.0632394	+	0.109534i	−0.832672	+	0.553766i	$0.813190\pi$
$774$		0			0
$775$	−16.8193	−	29.1318i	−0.604166	−	1.04645i
$776$	−0.970110	−	1.68028i	−0.0348249	−	0.0603185i
$777$		0			0
$778$	0.297447	+	0.515194i	0.0106640	+	0.0184706i
$779$	2.52947	+	0.374015i	0.0906275	+	0.0134005i
$780$		0			0
$781$	−2.72107	−	4.71304i	−0.0973677	−	0.168646i
$782$	−0.979849	+	1.69715i	−0.0350393	+	0.0606899i
$783$		0			0
$784$	2.42376	−	4.19807i	0.0865627	−	0.149931i
$785$	−0.994076			−0.0354801
$786$		0			0
$787$	−5.07885	−	8.79682i	−0.181041	−	0.313573i	0.761194	−	0.648524i	$-0.224613\pi$
$787$	−5.07885	−	8.79682i	−0.181041	−	0.313573i	−0.942235	+	0.334951i	$0.891280\pi$
$788$	−0.145546	+	0.252093i	−0.00518487	+	0.00898046i
$789$		0			0
$790$	−1.08465	+	1.87866i	−0.0385900	+	0.0668398i
$791$	−22.1877			−0.788903
$792$		0			0
$793$	−9.85675	+	17.0724i	−0.350024	+	0.606259i
$794$	−25.0085			−0.887517
$795$		0			0
$796$	7.08223			0.251023
$797$	−20.4870	−	35.4846i	−0.725688	−	1.25693i	−0.958690	−	0.284452i	$-0.908188\pi$
$797$	−20.4870	−	35.4846i	−0.725688	−	1.25693i	0.233002	−	0.972476i	$-0.425145\pi$
$798$		0			0
$799$	−0.130373	+	0.225813i	−0.00461227	+	0.00798868i
$800$	2.48881	−	4.31074i	0.0879926	−	0.152408i
$801$		0			0
$802$	−17.4970	−	30.3057i	−0.617840	−	1.07013i
$803$	−1.57771	−	2.73267i	−0.0556762	−	0.0964340i
$804$		0			0
$805$	0.311287	+	0.539164i	0.0109714	+	0.0190030i
$806$	7.89415	+	13.6731i	0.278060	+	0.481613i
$807$		0			0
$808$	17.2381			0.606435
$809$	−10.2240			−0.359455			−0.179728	−	0.983716i	$-0.557522\pi$
$809$	−10.2240			−0.359455			−0.179728	+	0.983716i	$0.557522\pi$
$810$		0			0
$811$	0.791699	+	1.37126i	0.0278003	+	0.0481516i	0.879591	−	0.475731i	$-0.157816\pi$
$811$	0.791699	+	1.37126i	0.0278003	+	0.0481516i	−0.851791	+	0.523883i	$0.824483\pi$
$812$	−3.87251	−	6.70738i	−0.135898	−	0.235383i
$813$		0			0
$814$	−24.8402			−0.870650
$815$	−0.0945318			−0.00331131
$816$		0			0
$817$	13.8869	+	35.0939i	0.485841	+	1.22778i
$818$	−19.9481			−0.697469
$819$		0			0
$820$	0.0438827	−	0.0760070i	0.00153245	−	0.00265428i
$821$	−51.1987			−1.78685			−0.893423	−	0.449216i	$-0.851703\pi$
$821$	−51.1987			−1.78685			−0.893423	+	0.449216i	$0.851703\pi$
$822$		0			0
$823$	0.622724	−	1.07859i	0.0217068	−	0.0375973i	−0.854968	−	0.518681i	$-0.826423\pi$
$823$	0.622724	−	1.07859i	0.0217068	−	0.0375973i	0.876675	+	0.481084i	$0.159757\pi$
$824$	−8.37347	−	14.5033i	−0.291704	−	0.505246i
$825$		0			0
$826$	−6.70927			−0.233446
$827$	−15.7173	−	27.2232i	−0.546546	−	0.946645i	−0.998508	−	0.0546079i	$-0.982609\pi$
$827$	−15.7173	−	27.2232i	−0.546546	−	0.946645i	0.451962	−	0.892037i	$-0.350724\pi$
$828$		0			0
$829$	−40.2857			−1.39918			−0.699590	−	0.714545i	$-0.746634\pi$
$829$	−40.2857			−1.39918			−0.699590	+	0.714545i	$0.746634\pi$
$830$	0.345998			0.0120098
$831$		0			0
$832$	−1.16813	+	2.02325i	−0.0404975	+	0.0701437i
$833$	−3.34937			−0.116049
$834$		0			0
$835$	−0.533377	+	0.923836i	−0.0184583	+	0.0319707i
$836$	5.06506	+	12.8000i	0.175179	+	0.442699i
$837$		0			0
$838$	−14.8751	+	25.7644i	−0.513852	+	0.890017i
$839$	15.5289	+	26.8969i	0.536119	+	0.928585i	0.999108	+	0.0422212i	$0.0134434\pi$
$839$	15.5289	+	26.8969i	0.536119	+	0.928585i	−0.462990	+	0.886364i	$0.653223\pi$
$840$		0			0
$841$	−1.13213			−0.0390391
$842$	−9.81305	+	16.9967i	−0.338180	+	0.585745i
$843$		0			0
$844$	13.4825	−	23.3523i	0.464086	−	0.803821i
$845$	−0.564192	−	0.977210i	−0.0194088	−	0.0336170i
$846$		0			0
$847$	−1.50605			−0.0517484
$848$	0.204535	−	0.354265i	0.00702376	−	0.0121655i
$849$		0			0
$850$	−3.43926			−0.117966
$851$	−11.1544	+	19.3201i	−0.382369	+	0.662283i
$852$		0			0
$853$	−10.8895	−	18.8611i	−0.372848	−	0.645792i	0.617154	−	0.786842i	$-0.288285\pi$
$853$	−10.8895	−	18.8611i	−0.372848	−	0.645792i	−0.990002	+	0.141050i	$0.954952\pi$
$854$	12.3798			0.423629
$855$		0			0
$856$	−19.2873			−0.659226
$857$	−22.2204	−	38.4869i	−0.759034	−	1.31469i	−0.943344	−	0.331818i	$-0.892338\pi$
$857$	−22.2204	−	38.4869i	−0.759034	−	1.31469i	0.184309	−	0.982868i	$-0.440995\pi$
$858$		0			0
$859$	−20.1723	+	34.9395i	−0.688271	+	1.19212i	0.284126	+	0.958787i	$0.408296\pi$
$859$	−20.1723	+	34.9395i	−0.688271	+	1.19212i	−0.972397	+	0.233333i	$0.925037\pi$
$860$	1.29544			0.0441743
$861$		0			0
$862$	−16.0450	+	27.7907i	−0.546493	+	0.946554i
$863$	−25.0766			−0.853617			−0.426809	−	0.904342i	$-0.640362\pi$
$863$	−25.0766			−0.853617			−0.426809	+	0.904342i	$0.640362\pi$
$864$		0			0
$865$	−1.69348	−	2.93319i	−0.0575799	−	0.0997313i
$866$	1.40581	−	2.43494i	0.0477715	−	0.0827426i
$867$		0			0
$868$	4.95743	−	8.58651i	0.168266	−	0.291445i
$869$	45.7896			1.55330
$870$		0			0
$871$	4.18962	+	7.25664i	0.141960	+	0.245882i
$872$	3.88169	−	6.72328i	0.131451	−	0.227679i
$873$		0			0
$874$	12.2300	+	1.80836i	0.413685	+	0.0611688i
$875$	−1.09507	+	1.89672i	−0.0370201	+	0.0641207i
$876$		0			0
$877$	2.81916			0.0951962			0.0475981	−	0.998867i	$-0.484843\pi$
$877$	2.81916			0.0951962			0.0475981	+	0.998867i	$0.484843\pi$
$878$	−6.07199	+	10.5170i	−0.204920	+	0.354931i
$879$		0			0
$880$	0.472496			0.0159278
$881$	−22.7761			−0.767347			−0.383673	−	0.923469i	$-0.625341\pi$
$881$	−22.7761			−0.767347			−0.383673	+	0.923469i	$0.625341\pi$
$882$		0			0
$883$	6.20119	+	10.7408i	0.208687	+	0.361456i	0.951301	−	0.308263i	$-0.0997478\pi$
$883$	6.20119	+	10.7408i	0.208687	+	0.361456i	−0.742614	+	0.669719i	$0.766414\pi$
$884$	1.61422			0.0542922
$885$		0			0
$886$	−10.9732	−	19.0061i	−0.368650	−	0.638521i
$887$	10.7850	−	18.6802i	0.362126	−	0.627221i	−0.626185	−	0.779675i	$-0.715384\pi$
$887$	10.7850	−	18.6802i	0.362126	−	0.627221i	0.988311	+	0.152454i	$0.0487177\pi$
$888$		0			0
$889$	22.2668			0.746805
$890$	−0.235432	+	0.407780i	−0.00789169	+	0.0136688i
$891$		0			0
$892$	−4.07680			−0.136501
$893$	1.62725	+	0.240610i	0.0544539	+	0.00805172i
$894$		0			0
$895$	1.17280			0.0392025
$896$	1.46714			0.0490136
$897$		0			0
$898$	3.97665	+	6.88776i	0.132702	+	0.229847i
$899$	17.8377	+	30.8957i	0.594919	+	1.03043i
$900$		0			0
$901$	−0.282645			−0.00941627
$902$	−1.85256			−0.0616834
$903$		0			0
$904$	7.56156	+	13.0970i	0.251494	+	0.435600i
$905$	0.667189	+	1.15560i	0.0221781	+	0.0384136i
$906$		0			0
$907$	2.51606	+	4.35794i	0.0835443	+	0.144703i	0.904770	−	0.425901i	$-0.140043\pi$
$907$	2.51606	+	4.35794i	0.0835443	+	0.144703i	−0.821226	+	0.570604i	$0.806709\pi$
$908$	−13.6961	−	23.7224i	−0.454522	−	0.787256i
$909$		0			0
$910$	0.256410	−	0.444115i	0.00849991	−	0.0147223i
$911$	2.94574	−	5.10217i	0.0975966	−	0.169042i	−0.813093	−	0.582134i	$-0.802218\pi$
$911$	2.94574	−	5.10217i	0.0975966	−	0.169042i	0.910689	+	0.413092i	$0.135551\pi$
$912$		0			0
$913$	−3.65168	−	6.32489i	−0.120853	−	0.209323i
$914$	−26.4792			−0.875856
$915$		0			0
$916$	12.0619			0.398536
$917$	−2.65023	+	4.59034i	−0.0875184	+	0.151586i
$918$		0			0
$919$	−35.8784			−1.18352			−0.591759	−	0.806115i	$-0.701566\pi$
$919$	−35.8784			−1.18352			−0.591759	+	0.806115i	$0.701566\pi$
$920$	0.212173	−	0.367494i	0.00699514	−	0.0121159i
$921$		0			0
$922$	−3.67967	+	6.37338i	−0.121184	+	0.209896i
$923$	2.01297	+	3.48656i	0.0662576	+	0.114762i
$924$		0			0
$925$	−39.1520			−1.28731
$926$	14.7707	−	25.5836i	0.485395	−	0.840729i
$927$		0			0
$928$	−2.63950	+	4.57175i	−0.0866459	+	0.150075i
$929$	15.7766	+	27.3259i	0.517614	+	0.896534i	0.999791	+	0.0204596i	$0.00651295\pi$
$929$	15.7766	+	27.3259i	0.517614	+	0.896534i	−0.482177	+	0.876074i	$0.660154\pi$
$930$		0			0
$931$	7.77464	+	19.6475i	0.254803	+	0.643921i
$932$	10.7521	+	18.6232i	0.352198	+	0.610024i
$933$		0			0
$934$	−19.6983	−	34.1185i	−0.644548	−	1.11639i
$935$	−0.163234	−	0.282730i	−0.00533834	−	0.00924627i
$936$		0			0
$937$	11.5757	+	20.0497i	0.378161	+	0.654994i	0.990795	−	0.135373i	$-0.0432233\pi$
$937$	11.5757	+	20.0497i	0.378161	+	0.654994i	−0.612634	+	0.790367i	$0.709890\pi$
$938$	2.63103	−	4.55707i	0.0859061	−	0.148794i
$939$		0			0
$940$	0.0282305	−	0.0488967i	0.000920778	−	0.00159483i
$941$	19.3703	−	33.5503i	0.631452	−	1.09371i	−0.355803	−	0.934561i	$-0.615793\pi$
$941$	19.3703	−	33.5503i	0.631452	−	1.09371i	0.987255	−	0.159146i	$-0.0508741\pi$
$942$		0			0
$943$	−0.831886	+	1.44087i	−0.0270899	+	0.0469211i
$944$	2.28652	+	3.96037i	0.0744199	+	0.128899i
$945$		0			0
$946$	−13.6722	−	23.6809i	−0.444520	−	0.769932i
$947$	17.8389	+	30.8978i	0.579685	+	1.00404i	0.995515	+	0.0946013i	$0.0301576\pi$
$947$	17.8389	+	30.8978i	0.579685	+	1.00404i	−0.415830	+	0.909442i	$0.636509\pi$
$948$		0			0
$949$	1.16714	+	2.02155i	0.0378870	+	0.0656222i
$950$	7.98330	+	20.1748i	0.259012	+	0.654558i
$951$		0			0
$952$	−0.506855	−	0.877899i	−0.0164273	−	0.0284529i
$953$	−23.6334	+	40.9343i	−0.765562	+	1.32599i	0.174387	+	0.984677i	$0.444206\pi$
$953$	−23.6334	+	40.9343i	−0.765562	+	1.32599i	−0.939949	+	0.341315i	$0.889128\pi$
$954$		0			0
$955$	0.319000	−	0.552524i	0.0103226	−	0.0178793i
$956$	24.3420			0.787275
$957$		0			0
$958$	−19.8641	−	34.4056i	−0.641779	−	1.11159i
$959$	6.40182	−	11.0883i	0.206726	−	0.358059i
$960$		0			0
$961$	−7.33503	+	12.7046i	−0.236614	+	0.409827i
$962$	18.3760			0.592468
$963$		0			0
$964$	−2.84296	+	4.92415i	−0.0915655	+	0.158596i
$965$	3.12035			0.100448
$966$		0			0
$967$	39.9050			1.28326			0.641629	−	0.767015i	$-0.278259\pi$
$967$	39.9050			1.28326			0.641629	+	0.767015i	$0.278259\pi$
$968$	0.513261	+	0.888994i	0.0164968	+	0.0285733i
$969$		0			0
$970$	0.145143	−	0.251395i	0.00466026	−	0.00807180i
$971$	−1.64493	+	2.84910i	−0.0527883	+	0.0914320i	−0.891212	−	0.453587i	$-0.850144\pi$
$971$	−1.64493	+	2.84910i	−0.0527883	+	0.0914320i	0.838424	+	0.545019i	$0.183478\pi$
$972$		0			0
$973$	−3.82831	−	6.63083i	−0.122730	−	0.212575i
$974$	14.8865	+	25.7842i	0.476994	+	0.826178i
$975$		0			0
$976$	−4.21905	−	7.30760i	−0.135048	−	0.233911i
$977$	0.342132	+	0.592590i	0.0109458	+	0.0189586i	0.871446	−	0.490491i	$-0.163182\pi$
$977$	0.342132	+	0.592590i	0.0109458	+	0.0189586i	−0.860501	+	0.509449i	$0.829849\pi$
$978$		0			0
$979$	9.93903			0.317653
$980$	0.725260			0.0231676
$981$		0			0
$982$	−8.16707	−	14.1458i	−0.260622	−	0.451410i
$983$	27.9574	+	48.4236i	0.891702	+	1.54447i	0.837834	+	0.545925i	$0.183822\pi$
$983$	27.9574	+	48.4236i	0.891702	+	1.54447i	0.0538678	+	0.998548i	$0.482845\pi$
$984$		0			0
$985$	−0.0435518			−0.00138767
$986$	3.64750			0.116160
$987$		0			0
$988$	−3.74698	−	9.46908i	−0.119207	−	0.301252i
$989$	−24.5578			−0.780892
$990$		0			0
$991$	17.1536	−	29.7109i	0.544903	−	0.943799i	−0.453710	−	0.891149i	$-0.649900\pi$
$991$	17.1536	−	29.7109i	0.544903	−	0.943799i	0.998613	−	0.0526499i	$-0.0167667\pi$
$992$	−6.75796			−0.214566
$993$		0			0
$994$	1.26412	−	2.18952i	0.0400954	−	0.0694472i
$995$	0.529803	+	0.917646i	0.0167959	+	0.0290913i
$996$		0			0
$997$	−11.3801			−0.360410			−0.180205	−	0.983629i	$-0.557676\pi$
$997$	−11.3801			−0.360410			−0.180205	+	0.983629i	$0.557676\pi$
$998$	−7.35789	−	12.7442i	−0.232910	−	0.403412i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1026.2.h.g.505.5		18
3.2	odd	2		342.2.h.g.277.4	yes	18
9.4	even	3		1026.2.f.g.847.5		18
9.5	odd	6		342.2.f.g.49.3	yes	18
19.7	even	3		1026.2.f.g.235.5		18
57.26	odd	6		342.2.f.g.7.3	✓	18
171.121	even	3	inner	1026.2.h.g.577.5		18
171.140	odd	6		342.2.h.g.121.4	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.3	✓	18	57.26	odd	6
342.2.f.g.49.3	yes	18	9.5	odd	6
342.2.h.g.121.4	yes	18	171.140	odd	6
342.2.h.g.277.4	yes	18	3.2	odd	2
1026.2.f.g.235.5		18	19.7	even	3
1026.2.f.g.847.5		18	9.4	even	3
1026.2.h.g.505.5		18	1.1	even	1	trivial
1026.2.h.g.577.5		18	171.121	even	3	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:	\( N \)	\(=\)	\( 1026 = 2 \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1026.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.149615 q^{5} +(-0.733568 + 1.27058i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.149615 q^{5} +(-0.733568 + 1.27058i) q^{7} +1.00000 q^{8} +(0.0748074 + 0.129570i) q^{10} +(1.57904 - 2.73498i) q^{11} +(-1.16813 + 2.02325i) q^{13} +1.46714 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.345473 + 0.598376i) q^{17} +(4.31202 + 0.637588i) q^{19} +(0.0748074 - 0.129570i) q^{20} -3.15808 q^{22} +(-1.41813 + 2.45627i) q^{23} -4.97762 q^{25} +2.33625 q^{26} +(-0.733568 - 1.27058i) q^{28} +5.27900 q^{29} +(3.37898 + 5.85257i) q^{31} +(-0.500000 + 0.866025i) q^{32} +0.690946 q^{34} +(0.109753 - 0.190097i) q^{35} +7.86561 q^{37} +(-1.60384 - 4.05311i) q^{38} -0.149615 q^{40} +0.586609 q^{41} +(4.32926 + 7.49850i) q^{43} +(1.57904 + 2.73498i) q^{44} +2.83626 q^{46} +0.377376 q^{47} +(2.42376 + 4.19807i) q^{49} +(2.48881 + 4.31074i) q^{50} +(-1.16813 - 2.02325i) q^{52} +(0.204535 + 0.354265i) q^{53} +(-0.236248 + 0.409193i) q^{55} +(-0.733568 + 1.27058i) q^{56} +(-2.63950 - 4.57175i) q^{58} -4.57304 q^{59} +8.43809 q^{61} +(3.37898 - 5.85257i) q^{62} +1.00000 q^{64} +(0.174769 - 0.302709i) q^{65} +(1.79331 - 3.10610i) q^{67} +(-0.345473 - 0.598376i) q^{68} -0.219505 q^{70} +(0.861623 - 1.49237i) q^{71} +(0.499579 - 0.865295i) q^{73} +(-3.93281 - 6.81182i) q^{74} +(-2.70818 + 3.41552i) q^{76} +(2.31667 + 4.01259i) q^{77} +(7.24959 + 12.5567i) q^{79} +(0.0748074 + 0.129570i) q^{80} +(-0.293304 - 0.508018i) q^{82} +(1.15630 - 2.00276i) q^{83} +(0.0516879 - 0.0895260i) q^{85} +(4.32926 - 7.49850i) q^{86} +(1.57904 - 2.73498i) q^{88} +(1.57359 + 2.72553i) q^{89} +(-1.71380 - 2.96839i) q^{91} +(-1.41813 - 2.45627i) q^{92} +(-0.188688 - 0.326817i) q^{94} +(-0.645142 - 0.0953927i) q^{95} +(-0.970110 - 1.68028i) q^{97} +(2.42376 - 4.19807i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

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