LMFDB - Embedded newform 1026.2.n.d.791.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1026,2,Mod(179,1026)]

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([5, 1]))

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

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

chi := DirichletCharacter("1026.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1026 = 2 \cdot 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1026.n (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.764411904.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 21x^{4} - 54x^{2} + 81 $ x^8 - 6x^6 + 21x^4 - 54*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 342)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			791.3
Root			$-1.27970 - 1.16721i$ of defining polynomial
Character	$\chi$	$=$	1026.791
Dual form			1026.2.n.d.179.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-0.275255 - 0.158919i) q^{5} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.275255 - 0.158919i) q^{5} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +(0.275255 + 0.158919i) q^{10} +(-0.427828 - 0.247006i) q^{11} -3.61953i q^{13} +(1.37098 - 2.37461i) q^{14} +1.00000 q^{16} +(4.85821 - 2.80489i) q^{17} +(2.54077 + 3.54182i) q^{19} +(-0.275255 - 0.158919i) q^{20} +(0.427828 + 0.247006i) q^{22} +4.30391i q^{23} +(-2.44949 - 4.24264i) q^{25} +3.61953i q^{26} +(-1.37098 + 2.37461i) q^{28} +(4.85821 + 8.41466i) q^{29} +(-7.64794 + 4.41554i) q^{31} -1.00000 q^{32} +(-4.85821 + 2.80489i) q^{34} +(0.754740 - 0.435749i) q^{35} +10.1162i q^{37} +(-2.54077 - 3.54182i) q^{38} +(0.275255 + 0.158919i) q^{40} +(1.92594 - 3.33582i) q^{41} +5.30136 q^{43} +(-0.427828 - 0.247006i) q^{44} -4.30391i q^{46} +(-3.38101 + 1.95203i) q^{47} +(-0.259183 - 0.448918i) q^{49} +(2.44949 + 4.24264i) q^{50} -3.61953i q^{52} +(2.35187 - 4.07356i) q^{53} +(0.0785079 + 0.135980i) q^{55} +(1.37098 - 2.37461i) q^{56} +(-4.85821 - 8.41466i) q^{58} +(-2.44760 + 4.23936i) q^{59} +(1.35187 + 2.34151i) q^{61} +(7.64794 - 4.41554i) q^{62} +1.00000 q^{64} +(-0.575211 + 0.996295i) q^{65} +3.30332i q^{67} +(4.85821 - 2.80489i) q^{68} +(-0.754740 + 0.435749i) q^{70} +(6.72919 + 11.6553i) q^{71} +(3.11624 + 5.39749i) q^{73} -10.1162i q^{74} +(2.54077 + 3.54182i) q^{76} +(1.17309 - 0.677283i) q^{77} -0.316216i q^{79} +(-0.275255 - 0.158919i) q^{80} +(-1.92594 + 3.33582i) q^{82} +(1.66346 + 0.960397i) q^{83} -1.78299 q^{85} -5.30136 q^{86} +(0.427828 + 0.247006i) q^{88} +(1.39009 - 2.40771i) q^{89} +(8.59498 + 4.96231i) q^{91} +4.30391i q^{92} +(3.38101 - 1.95203i) q^{94} +(-0.136500 - 1.37868i) q^{95} +4.82426i q^{97} +(0.259183 + 0.448918i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 12 q^{5} - 8 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 12 * q^5 - 8 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 12 q^{5} - 8 q^{7} - 8 q^{8} + 12 q^{10} + 8 q^{14} + 8 q^{16} + 12 q^{17} + 8 q^{19} - 12 q^{20} - 8 q^{28} + 12 q^{29} + 24 q^{31} - 8 q^{32} - 12 q^{34} + 24 q^{35} - 8 q^{38} + 12 q^{40} + 12 q^{41} + 16 q^{43} + 24 q^{47} + 12 q^{53} - 16 q^{55} + 8 q^{56} - 12 q^{58} + 4 q^{61} - 24 q^{62} + 8 q^{64} + 12 q^{68} - 24 q^{70} + 24 q^{71} + 4 q^{73} + 8 q^{76} - 12 q^{77} - 12 q^{80} - 12 q^{82} + 24 q^{83} + 8 q^{85} - 16 q^{86} + 12 q^{89} + 48 q^{91} - 24 q^{94} + 24 q^{95}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 12 * q^5 - 8 * q^7 - 8 * q^8 + 12 * q^10 + 8 * q^14 + 8 * q^16 + 12 * q^17 + 8 * q^19 - 12 * q^20 - 8 * q^28 + 12 * q^29 + 24 * q^31 - 8 * q^32 - 12 * q^34 + 24 * q^35 - 8 * q^38 + 12 * q^40 + 12 * q^41 + 16 * q^43 + 24 * q^47 + 12 * q^53 - 16 * q^55 + 8 * q^56 - 12 * q^58 + 4 * q^61 - 24 * q^62 + 8 * q^64 + 12 * q^68 - 24 * q^70 + 24 * q^71 + 4 * q^73 + 8 * q^76 - 12 * q^77 - 12 * q^80 - 12 * q^82 + 24 * q^83 + 8 * q^85 - 16 * q^86 + 12 * q^89 + 48 * q^91 - 24 * q^94 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.275255	−	0.158919i	−0.123098	−	0.0710706i	0.437187	−	0.899371i	$-0.355975\pi$
$5$	−0.275255	−	0.158919i	−0.123098	−	0.0710706i	−0.560285	+	0.828300i	$0.689308\pi$
$6$		0			0
$7$	−1.37098	+	2.37461i	−0.518182	+	0.897518i	0.481594	+	0.876394i	$0.340058\pi$
$7$	−1.37098	+	2.37461i	−0.518182	+	0.897518i	−0.999777	+	0.0211241i	$0.993275\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.275255	+	0.158919i	0.0870433	+	0.0502545i
$11$	−0.427828	−	0.247006i	−0.128995	−	0.0744752i	0.434114	−	0.900858i	$-0.357062\pi$
$11$	−0.427828	−	0.247006i	−0.128995	−	0.0744752i	−0.563109	+	0.826383i	$0.690395\pi$
$12$		0			0
$13$		−	3.61953i		−	1.00388i	−0.864903	−	0.501939i	$-0.832620\pi$
$13$		−	3.61953i		−	1.00388i	0.864903	−	0.501939i	$-0.167380\pi$
$14$	1.37098	−	2.37461i	0.366410	−	0.634641i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.85821	−	2.80489i	1.17829	−	0.680285i	0.222670	−	0.974894i	$-0.428523\pi$
$17$	4.85821	−	2.80489i	1.17829	−	0.680285i	0.955618	+	0.294609i	$0.0951894\pi$
$18$		0			0
$19$	2.54077	+	3.54182i	0.582893	+	0.812549i
$19$	2.54077	+	3.54182i	0.582893	+	0.812549i
$20$	−0.275255	−	0.158919i	−0.0615489	−	0.0355353i
$21$		0			0
$22$	0.427828	+	0.247006i	0.0912132	+	0.0526620i
$23$			4.30391i			0.897427i	0.893676	+	0.448714i	$0.148118\pi$
$23$			4.30391i			0.897427i	−0.893676	+	0.448714i	$0.851882\pi$
$24$		0			0
$25$	−2.44949	−	4.24264i	−0.489898	−	0.848528i
$26$			3.61953i			0.709849i
$27$		0			0
$28$	−1.37098	+	2.37461i	−0.259091	+	0.448759i
$29$	4.85821	+	8.41466i	0.902146	+	1.56256i	0.824703	+	0.565566i	$0.191342\pi$
$29$	4.85821	+	8.41466i	0.902146	+	1.56256i	0.0774434	+	0.996997i	$0.475324\pi$
$30$		0			0
$31$	−7.64794	+	4.41554i	−1.37361	+	0.793054i	−0.991381	−	0.131013i	$-0.958177\pi$
$31$	−7.64794	+	4.41554i	−1.37361	+	0.793054i	−0.382229	+	0.924067i	$0.624844\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−4.85821	+	2.80489i	−0.833175	+	0.481034i
$35$	0.754740	−	0.435749i	0.127574	−	0.0736550i
$36$		0			0
$37$			10.1162i			1.66309i	0.555456	+	0.831546i	$0.312544\pi$
$37$			10.1162i			1.66309i	−0.555456	+	0.831546i	$0.687456\pi$
$38$	−2.54077	−	3.54182i	−0.412168	−	0.574559i
$39$		0			0
$40$	0.275255	+	0.158919i	0.0435217	+	0.0251272i
$41$	1.92594	−	3.33582i	0.300781	−	0.520967i	−0.675532	−	0.737330i	$-0.736086\pi$
$41$	1.92594	−	3.33582i	0.300781	−	0.520967i	0.976313	+	0.216363i	$0.0694195\pi$
$42$		0			0
$43$	5.30136			0.808450			0.404225	−	0.914660i	$-0.367541\pi$
$43$	5.30136			0.808450			0.404225	+	0.914660i	$0.367541\pi$
$44$	−0.427828	−	0.247006i	−0.0644975	−	0.0372376i
$45$		0			0
$46$		−	4.30391i		−	0.634577i
$47$	−3.38101	+	1.95203i	−0.493172	+	0.284733i	−0.725889	−	0.687812i	$-0.758572\pi$
$47$	−3.38101	+	1.95203i	−0.493172	+	0.284733i	0.232718	+	0.972544i	$0.425238\pi$
$48$		0			0
$49$	−0.259183	−	0.448918i	−0.0370261	−	0.0641311i
$50$	2.44949	+	4.24264i	0.346410	+	0.600000i
$51$		0			0
$52$		−	3.61953i		−	0.501939i
$53$	2.35187	−	4.07356i	0.323054	−	0.559546i	−0.658062	−	0.752963i	$-0.728624\pi$
$53$	2.35187	−	4.07356i	0.323054	−	0.559546i	0.981117	+	0.193417i	$0.0619570\pi$
$54$		0			0
$55$	0.0785079	+	0.135980i	0.0105860	+	0.0183355i
$56$	1.37098	−	2.37461i	0.183205	−	0.317321i
$57$		0			0
$58$	−4.85821	−	8.41466i	−0.637914	−	1.10490i
$59$	−2.44760	+	4.23936i	−0.318650	+	0.551918i	−0.980207	−	0.197977i	$-0.936563\pi$
$59$	−2.44760	+	4.23936i	−0.318650	+	0.551918i	0.661557	+	0.749895i	$0.269896\pi$
$60$		0			0
$61$	1.35187	+	2.34151i	0.173089	+	0.299799i	0.939498	−	0.342553i	$-0.111292\pi$
$61$	1.35187	+	2.34151i	0.173089	+	0.299799i	−0.766409	+	0.642353i	$0.777958\pi$
$62$	7.64794	−	4.41554i	0.971289	−	0.560774i
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.575211	+	0.996295i	−0.0713462	+	0.123575i
$66$		0			0
$67$			3.30332i			0.403564i	0.979430	+	0.201782i	$0.0646733\pi$
$67$			3.30332i			0.403564i	−0.979430	+	0.201782i	$0.935327\pi$
$68$	4.85821	−	2.80489i	0.589144	−	0.340142i
$69$		0			0
$70$	−0.754740	+	0.435749i	−0.0902086	+	0.0520820i
$71$	6.72919	+	11.6553i	0.798608	+	1.38323i	0.920523	+	0.390689i	$0.127763\pi$
$71$	6.72919	+	11.6553i	0.798608	+	1.38323i	−0.121915	+	0.992541i	$0.538904\pi$
$72$		0			0
$73$	3.11624	+	5.39749i	0.364729	+	0.631728i	0.988733	−	0.149693i	$-0.0478284\pi$
$73$	3.11624	+	5.39749i	0.364729	+	0.631728i	−0.624004	+	0.781421i	$0.714495\pi$
$74$		−	10.1162i		−	1.17598i
$75$		0			0
$76$	2.54077	+	3.54182i	0.291447	+	0.406274i
$77$	1.17309	−	0.677283i	0.133686	−	0.0771835i
$78$		0			0
$79$		−	0.316216i		−	0.0355771i	−0.999842	−	0.0177885i	$-0.994337\pi$
$79$		−	0.316216i		−	0.0355771i	0.999842	−	0.0177885i	$-0.00566256\pi$
$80$	−0.275255	−	0.158919i	−0.0307745	−	0.0177676i
$81$		0			0
$82$	−1.92594	+	3.33582i	−0.212684	+	0.368379i
$83$	1.66346	+	0.960397i	0.182588	+	0.105417i	0.588508	−	0.808491i	$-0.299716\pi$
$83$	1.66346	+	0.960397i	0.182588	+	0.105417i	−0.405920	+	0.913909i	$0.633049\pi$
$84$		0			0
$85$	−1.78299			−0.193393
$86$	−5.30136			−0.571660
$87$		0			0
$88$	0.427828	+	0.247006i	0.0456066	+	0.0263310i
$89$	1.39009	−	2.40771i	0.147350	−	0.255217i	−0.782897	−	0.622151i	$-0.786259\pi$
$89$	1.39009	−	2.40771i	0.147350	−	0.255217i	0.930247	+	0.366934i	$0.119592\pi$
$90$		0			0
$91$	8.59498	+	4.96231i	0.900999	+	0.520192i
$92$			4.30391i			0.448714i
$93$		0			0
$94$	3.38101	−	1.95203i	0.348725	−	0.201336i
$95$	−0.136500	−	1.37868i	−0.0140046	−	0.141450i
$96$		0			0
$97$			4.82426i			0.489829i	0.969545	+	0.244915i	$0.0787600\pi$
$97$			4.82426i			0.489829i	−0.969545	+	0.244915i	$0.921240\pi$
$98$	0.259183	+	0.448918i	0.0261814	+	0.0453475i
$99$		0			0
$100$	−2.44949	−	4.24264i	−0.244949	−	0.424264i
$101$	−8.35102	+	4.82146i	−0.830958	+	0.479754i	−0.854180	−	0.519977i	$-0.825941\pi$
$101$	−8.35102	+	4.82146i	−0.830958	+	0.479754i	0.0232229	+	0.999730i	$0.492607\pi$
$102$		0			0
$103$	9.19615	−	5.30940i	0.906124	−	0.523151i	0.0269420	−	0.999637i	$-0.491423\pi$
$103$	9.19615	−	5.30940i	0.906124	−	0.523151i	0.879182	+	0.476486i	$0.158090\pi$
$104$			3.61953i			0.354924i
$105$		0			0
$106$	−2.35187	+	4.07356i	−0.228434	+	0.395659i
$107$	2.11598			0.204560			0.102280	−	0.994756i	$-0.467386\pi$
$107$	2.11598			0.204560			0.102280	+	0.994756i	$0.467386\pi$
$108$		0			0
$109$	−12.6573	+	7.30770i	−1.21235	+	0.699951i	−0.963271	−	0.268532i	$-0.913461\pi$
$109$	−12.6573	+	7.30770i	−1.21235	+	0.699951i	−0.249080	+	0.968483i	$0.580128\pi$
$110$	−0.0785079	−	0.135980i	−0.00748543	−	0.0129651i
$111$		0			0
$112$	−1.37098	+	2.37461i	−0.129546	+	0.224380i
$113$	2.22730	+	3.85779i	0.209526	+	0.362910i	0.951565	−	0.307446i	$-0.0994745\pi$
$113$	2.22730	+	3.85779i	0.209526	+	0.362910i	−0.742039	+	0.670357i	$0.766141\pi$
$114$		0			0
$115$	0.683971	−	1.18467i	0.0637807	−	0.110471i
$116$	4.85821	+	8.41466i	0.451073	+	0.781282i
$117$		0			0
$118$	2.44760	−	4.23936i	0.225320	−	0.390265i
$119$			15.3818i			1.41005i
$120$		0			0
$121$	−5.37798	−	9.31493i	−0.488907	−	0.846812i
$122$	−1.35187	−	2.34151i	−0.122393	−	0.211990i
$123$		0			0
$124$	−7.64794	+	4.41554i	−0.686805	+	0.396527i
$125$			3.14626i			0.281410i
$126$		0			0
$127$	8.32681	+	4.80748i	0.738885	+	0.426595i	0.821664	−	0.569973i	$-0.193046\pi$
$127$	8.32681	+	4.80748i	0.738885	+	0.426595i	−0.0827790	+	0.996568i	$0.526380\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	0.575211	−	0.996295i	0.0504494	−	0.0873809i
$131$	−18.0495	−	10.4209i	−1.57699	−	0.910475i	−0.995276	−	0.0970809i	$-0.969049\pi$
$131$	−18.0495	−	10.4209i	−1.57699	−	0.910475i	−0.581713	−	0.813394i	$-0.697617\pi$
$132$		0			0
$133$	−11.8938	+	1.17758i	−1.03132	+	0.102109i
$134$		−	3.30332i		−	0.285363i
$135$		0			0
$136$	−4.85821	+	2.80489i	−0.416588	+	0.240517i
$137$	1.01343	−	0.585106i	0.0865835	−	0.0499890i	−0.456083	−	0.889937i	$-0.650748\pi$
$137$	1.01343	−	0.585106i	0.0865835	−	0.0499890i	0.542667	+	0.839948i	$0.317415\pi$
$138$		0			0
$139$	15.6177			1.32467			0.662337	−	0.749206i	$-0.269565\pi$
$139$	15.6177			1.32467			0.662337	+	0.749206i	$0.269565\pi$
$140$	0.754740	−	0.435749i	0.0637871	−	0.0368275i
$141$		0			0
$142$	−6.72919	−	11.6553i	−0.564701	−	0.978091i
$143$	−0.894048	+	1.54854i	−0.0747641	+	0.129495i
$144$		0			0
$145$		−	3.08824i		−	0.256464i
$146$	−3.11624	−	5.39749i	−0.257902	−	0.446699i
$147$		0			0
$148$			10.1162i			0.831546i
$149$	16.5375	+	9.54795i	1.35481	+	0.782199i	0.988919	−	0.148459i	$-0.0474314\pi$
$149$	16.5375	+	9.54795i	1.35481	+	0.782199i	0.365890	+	0.930658i	$0.380765\pi$
$150$		0			0
$151$	5.12154	+	2.95692i	0.416785	+	0.240631i	0.693701	−	0.720263i	$-0.255979\pi$
$151$	5.12154	+	2.95692i	0.416785	+	0.240631i	−0.276916	+	0.960894i	$0.589312\pi$
$152$	−2.54077	−	3.54182i	−0.206084	−	0.287279i
$153$		0			0
$154$	−1.17309	+	0.677283i	−0.0945301	+	0.0545770i
$155$	2.80685			0.225451
$156$		0			0
$157$	9.71615	−	16.8289i	0.775434	−	1.34309i	−0.159117	−	0.987260i	$-0.550865\pi$
$157$	9.71615	−	16.8289i	0.775434	−	1.34309i	0.934550	−	0.355831i	$-0.115802\pi$
$158$			0.316216i			0.0251568i
$159$		0			0
$160$	0.275255	+	0.158919i	0.0217608	+	0.0125636i
$161$	−10.2201	−	5.90058i	−0.805457	−	0.465031i
$162$		0			0
$163$	13.0895			1.02525			0.512623	−	0.858614i	$-0.328674\pi$
$163$	13.0895			1.02525			0.512623	+	0.858614i	$0.328674\pi$
$164$	1.92594	−	3.33582i	0.150390	−	0.260484i
$165$		0			0
$166$	−1.66346	−	0.960397i	−0.129109	−	0.0745412i
$167$	−0.767515			−0.0593921			−0.0296961	−	0.999559i	$-0.509454\pi$
$167$	−0.767515			−0.0593921			−0.0296961	+	0.999559i	$0.509454\pi$
$168$		0			0
$169$	−0.101021			−0.00777081
$170$	1.78299			0.136749
$171$		0			0
$172$	5.30136			0.404225
$173$	−1.40519			−0.106835			−0.0534173	−	0.998572i	$-0.517011\pi$
$173$	−1.40519			−0.106835			−0.0534173	+	0.998572i	$0.517011\pi$
$174$		0			0
$175$	13.4328			1.01543
$176$	−0.427828	−	0.247006i	−0.0322487	−	0.0186188i
$177$		0			0
$178$	−1.39009	+	2.40771i	−0.104192	+	0.180466i
$179$	−24.0695			−1.79904			−0.899518	−	0.436883i	$-0.856082\pi$
$179$	−24.0695			−1.79904			−0.899518	+	0.436883i	$0.856082\pi$
$180$		0			0
$181$	−7.90038	−	4.56129i	−0.587231	−	0.339038i	0.176771	−	0.984252i	$-0.443435\pi$
$181$	−7.90038	−	4.56129i	−0.587231	−	0.339038i	−0.764002	+	0.645214i	$0.776768\pi$
$182$	−8.59498	−	4.96231i	−0.637102	−	0.367831i
$183$		0			0
$184$		−	4.30391i		−	0.317288i
$185$	1.60765	−	2.78453i	0.118197	−	0.204723i
$186$		0			0
$187$	−2.77130			−0.202658
$188$	−3.38101	+	1.95203i	−0.246586	+	0.142366i
$189$		0			0
$190$	0.136500	+	1.37868i	0.00990276	+	0.100020i
$191$	10.7981	+	6.23426i	0.781320	+	0.451096i	0.836898	−	0.547359i	$-0.184367\pi$
$191$	10.7981	+	6.23426i	0.781320	+	0.451096i	−0.0555776	+	0.998454i	$0.517700\pi$
$192$		0			0
$193$	18.8559	+	10.8864i	1.35727	+	0.783623i	0.989256	−	0.146195i	$-0.0467028\pi$
$193$	18.8559	+	10.8864i	1.35727	+	0.783623i	0.368019	+	0.929818i	$0.380036\pi$
$194$		−	4.82426i		−	0.346362i
$195$		0			0
$196$	−0.259183	−	0.448918i	−0.0185130	−	0.0320655i
$197$		−	26.2753i		−	1.87204i	−0.351947	−	0.936020i	$-0.614480\pi$
$197$		−	26.2753i		−	1.87204i	0.351947	−	0.936020i	$-0.385520\pi$
$198$		0			0
$199$	−0.352359	+	0.610303i	−0.0249781	+	0.0432633i	−0.878244	−	0.478212i	$-0.841285\pi$
$199$	−0.352359	+	0.610303i	−0.0249781	+	0.0432633i	0.853266	+	0.521476i	$0.174618\pi$
$200$	2.44949	+	4.24264i	0.173205	+	0.300000i
$201$		0			0
$202$	8.35102	−	4.82146i	0.587576	−	0.339237i
$203$	−26.6421			−1.86991
$204$		0			0
$205$	−1.06025	+	0.612134i	−0.0740509	+	0.0427533i
$206$	−9.19615	+	5.30940i	−0.640726	+	0.369924i
$207$		0			0
$208$		−	3.61953i		−	0.250969i
$209$	−0.212162	−	2.14288i	−0.0146755	−	0.148226i
$210$		0			0
$211$	−17.5567	−	10.1363i	−1.20865	−	0.697814i	−0.246186	−	0.969223i	$-0.579177\pi$
$211$	−17.5567	−	10.1363i	−1.20865	−	0.697814i	−0.962464	+	0.271408i	$0.912511\pi$
$212$	2.35187	−	4.07356i	0.161527	−	0.279773i
$213$		0			0
$214$	−2.11598			−0.144646
$215$	−1.45923	−	0.842485i	−0.0995184	−	0.0574570i
$216$		0			0
$217$		−	24.2145i		−	1.64379i
$218$	12.6573	−	7.30770i	0.857261	−	0.494940i
$219$		0			0
$220$	0.0785079	+	0.135980i	0.00529300	+	0.00916774i
$221$	−10.1524	−	17.5844i	−0.682923	−	1.18286i
$222$		0			0
$223$		−	11.0154i		−	0.737647i	−0.929500	−	0.368823i	$-0.879761\pi$
$223$		−	11.0154i		−	0.737647i	0.929500	−	0.368823i	$-0.120239\pi$
$224$	1.37098	−	2.37461i	0.0916026	−	0.158660i
$225$		0			0
$226$	−2.22730	−	3.85779i	−0.148157	−	0.256616i
$227$	0.189561	−	0.328329i	0.0125816	−	0.0217920i	−0.859666	−	0.510856i	$-0.829328\pi$
$227$	0.189561	−	0.328329i	0.0125816	−	0.0217920i	0.872248	+	0.489064i	$0.162662\pi$
$228$		0			0
$229$	−6.17045	−	10.6875i	−0.407755	−	0.706252i	0.586883	−	0.809672i	$-0.300355\pi$
$229$	−6.17045	−	10.6875i	−0.407755	−	0.706252i	−0.994638	+	0.103420i	$0.967022\pi$
$230$	−0.683971	+	1.18467i	−0.0450997	+	0.0781150i
$231$		0			0
$232$	−4.85821	−	8.41466i	−0.318957	−	0.552449i
$233$	−10.4076	+	6.00881i	−0.681823	+	0.393650i	−0.800541	−	0.599277i	$-0.795455\pi$
$233$	−10.4076	+	6.00881i	−0.681823	+	0.393650i	0.118719	+	0.992928i	$0.462121\pi$
$234$		0			0
$235$	1.24086			0.0809445
$236$	−2.44760	+	4.23936i	−0.159325	+	0.275959i
$237$		0			0
$238$		−	15.3818i		−	0.997054i
$239$	4.53510	−	2.61834i	0.293351	−	0.169366i	−0.346101	−	0.938197i	$-0.612495\pi$
$239$	4.53510	−	2.61834i	0.293351	−	0.169366i	0.639452	+	0.768831i	$0.279161\pi$
$240$		0			0
$241$	−14.5433	+	8.39659i	−0.936818	+	0.540872i	−0.888961	−	0.457982i	$-0.848572\pi$
$241$	−14.5433	+	8.39659i	−0.936818	+	0.540872i	−0.0478565	+	0.998854i	$0.515239\pi$
$242$	5.37798	+	9.31493i	0.345709	+	0.598786i
$243$		0			0
$244$	1.35187	+	2.34151i	0.0865446	+	0.149900i
$245$			0.164756i			0.0105259i
$246$		0			0
$247$	12.8197	−	9.19641i	0.815700	−	0.585154i
$248$	7.64794	−	4.41554i	0.485644	−	0.280387i
$249$		0			0
$250$		−	3.14626i		−	0.198987i
$251$	−13.6697	−	7.89221i	−0.862824	−	0.498152i	0.00213293	−	0.999998i	$-0.499321\pi$
$251$	−13.6697	−	7.89221i	−0.862824	−	0.498152i	−0.864957	+	0.501846i	$0.832654\pi$
$252$		0			0
$253$	1.06309	−	1.84133i	0.0668361	−	0.115764i
$254$	−8.32681	−	4.80748i	−0.522470	−	0.301648i
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.25484			0.452545			0.226272	−	0.974064i	$-0.427346\pi$
$257$	7.25484			0.452545			0.226272	+	0.974064i	$0.427346\pi$
$258$		0			0
$259$	−24.0220	−	13.8691i	−1.49266	−	0.861785i
$260$	−0.575211	+	0.996295i	−0.0356731	+	0.0617876i
$261$		0			0
$262$	18.0495	+	10.4209i	1.11510	+	0.643803i
$263$		−	23.6406i		−	1.45774i	−0.684652	−	0.728870i	$-0.740046\pi$
$263$		−	23.6406i		−	1.45774i	0.684652	−	0.728870i	$-0.259954\pi$
$264$		0			0
$265$	−1.29473	+	0.747512i	−0.0795346	+	0.0459193i
$266$	11.8938	−	1.17758i	0.729255	−	0.0722020i
$267$		0			0
$268$			3.30332i			0.201782i
$269$	4.14179	+	7.17380i	0.252530	+	0.437394i	0.964222	−	0.265098i	$-0.0854041\pi$
$269$	4.14179	+	7.17380i	0.252530	+	0.437394i	−0.711692	+	0.702492i	$0.752071\pi$
$270$		0			0
$271$	9.25036	+	16.0221i	0.561919	+	0.973273i	0.997329	+	0.0730405i	$0.0232702\pi$
$271$	9.25036	+	16.0221i	0.561919	+	0.973273i	−0.435410	+	0.900232i	$0.643396\pi$
$272$	4.85821	−	2.80489i	0.294572	−	0.170071i
$273$		0			0
$274$	−1.01343	+	0.585106i	−0.0612238	+	0.0353476i
$275$			2.42016i			0.145941i
$276$		0			0
$277$	6.87912	−	11.9150i	0.413326	−	0.715902i	−0.581925	−	0.813243i	$-0.697700\pi$
$277$	6.87912	−	11.9150i	0.413326	−	0.715902i	0.995251	+	0.0973403i	$0.0310335\pi$
$278$	−15.6177			−0.936686
$279$		0			0
$280$	−0.754740	+	0.435749i	−0.0451043	+	0.0260410i
$281$	−6.11854	−	10.5976i	−0.365001	−	0.632201i	0.623775	−	0.781604i	$-0.285598\pi$
$281$	−6.11854	−	10.5976i	−0.365001	−	0.632201i	−0.988776	+	0.149403i	$0.952265\pi$
$282$		0			0
$283$	−10.8216	+	18.7436i	−0.643278	+	1.11419i	0.341418	+	0.939912i	$0.389093\pi$
$283$	−10.8216	+	18.7436i	−0.643278	+	1.11419i	−0.984696	+	0.174279i	$0.944240\pi$
$284$	6.72919	+	11.6553i	0.399304	+	0.691615i
$285$		0			0
$286$	0.894048	−	1.54854i	0.0528662	−	0.0915669i
$287$	5.28084	+	9.14669i	0.311718	+	0.539912i
$288$		0			0
$289$	7.23478	−	12.5310i	0.425575	−	0.737118i
$290$			3.08824i			0.181348i
$291$		0			0
$292$	3.11624	+	5.39749i	0.182364	+	0.315864i
$293$	−12.0645	−	20.8963i	−0.704815	−	1.22078i	−0.966758	−	0.255693i	$-0.917696\pi$
$293$	−12.0645	−	20.8963i	−0.704815	−	1.22078i	0.261943	−	0.965083i	$-0.415637\pi$
$294$		0			0
$295$	1.34743	−	0.777938i	0.0784503	−	0.0452933i
$296$		−	10.1162i		−	0.587992i
$297$		0			0
$298$	−16.5375	−	9.54795i	−0.957994	−	0.553098i
$299$	15.5781			0.900907
$300$		0			0
$301$	−7.26807	+	12.5887i	−0.418925	+	0.725599i
$302$	−5.12154	−	2.95692i	−0.294711	−	0.170152i
$303$		0			0
$304$	2.54077	+	3.54182i	0.145723	+	0.203137i
$305$		−	0.859350i		−	0.0492062i
$306$		0			0
$307$	1.24755	−	0.720275i	0.0712016	−	0.0411083i	−0.463977	−	0.885847i	$-0.653578\pi$
$307$	1.24755	−	0.720275i	0.0712016	−	0.0411083i	0.535178	+	0.844739i	$0.320244\pi$
$308$	1.17309	−	0.677283i	0.0668429	−	0.0385918i
$309$		0			0
$310$	−2.80685			−0.159418
$311$	−6.78947	+	3.91990i	−0.384996	+	0.222277i	−0.679990	−	0.733222i	$-0.738016\pi$
$311$	−6.78947	+	3.91990i	−0.384996	+	0.222277i	0.294994	+	0.955499i	$0.404682\pi$
$312$		0			0
$313$	−5.76922	−	9.99257i	−0.326095	−	0.564814i	0.655638	−	0.755075i	$-0.272400\pi$
$313$	−5.76922	−	9.99257i	−0.326095	−	0.564814i	−0.981733	+	0.190262i	$0.939066\pi$
$314$	−9.71615	+	16.8289i	−0.548314	+	0.949708i
$315$		0			0
$316$		−	0.316216i		−	0.0177885i
$317$	0.623429	+	1.07981i	0.0350152	+	0.0606482i	0.883002	−	0.469369i	$-0.155519\pi$
$317$	0.623429	+	1.07981i	0.0350152	+	0.0606482i	−0.847987	+	0.530017i	$0.822185\pi$
$318$		0			0
$319$		−	4.80003i		−	0.268750i
$320$	−0.275255	−	0.158919i	−0.0153872	−	0.00888382i
$321$		0			0
$322$	10.2201	+	5.90058i	0.569544	+	0.328827i
$323$	22.2780	+	10.0803i	1.23958	+	0.560883i
$324$		0			0
$325$	−15.3564	+	8.86601i	−0.851819	+	0.491798i
$326$	−13.0895			−0.724958
$327$		0			0
$328$	−1.92594	+	3.33582i	−0.106342	+	0.184190i
$329$		−	10.7048i		−	0.590174i
$330$		0			0
$331$	−11.2469	−	6.49338i	−0.618184	−	0.356909i	0.157978	−	0.987443i	$-0.449503\pi$
$331$	−11.2469	−	6.49338i	−0.618184	−	0.356909i	−0.776162	+	0.630534i	$0.782836\pi$
$332$	1.66346	+	0.960397i	0.0912940	+	0.0527086i
$333$		0			0
$334$	0.767515			0.0419966
$335$	0.524959	−	0.909255i	0.0286816	−	0.0496779i
$336$		0			0
$337$	−21.4194	−	12.3665i	−1.16679	−	0.673646i	−0.213867	−	0.976863i	$-0.568606\pi$
$337$	−21.4194	−	12.3665i	−1.16679	−	0.673646i	−0.952922	+	0.303217i	$0.901939\pi$
$338$	0.101021			0.00549479
$339$		0			0
$340$	−1.78299			−0.0966965
$341$	4.36267			0.236252
$342$		0			0
$343$	−17.7724			−0.959620
$344$	−5.30136			−0.285830
$345$		0			0
$346$	1.40519			0.0755434
$347$	30.8720	+	17.8240i	1.65730	+	0.956840i	0.973955	+	0.226741i	$0.0728069\pi$
$347$	30.8720	+	17.8240i	1.65730	+	0.956840i	0.683341	+	0.730100i	$0.260526\pi$
$348$		0			0
$349$	−3.98014	+	6.89381i	−0.213052	+	0.369017i	−0.952668	−	0.304012i	$-0.901674\pi$
$349$	−3.98014	+	6.89381i	−0.213052	+	0.369017i	0.739616	+	0.673029i	$0.235007\pi$
$350$	−13.4328			−0.718015
$351$		0			0
$352$	0.427828	+	0.247006i	0.0228033	+	0.0131655i
$353$	10.0732	+	5.81577i	0.536143	+	0.309542i	0.743514	−	0.668720i	$-0.233157\pi$
$353$	10.0732	+	5.81577i	0.536143	+	0.309542i	−0.207371	+	0.978262i	$0.566491\pi$
$354$		0			0
$355$		−	4.27757i		−	0.227030i
$356$	1.39009	−	2.40771i	0.0736748	−	0.127608i
$357$		0			0
$358$	24.0695			1.27211
$359$	9.33259	−	5.38817i	0.492555	−	0.284377i	−0.233079	−	0.972458i	$-0.574880\pi$
$359$	9.33259	−	5.38817i	0.492555	−	0.284377i	0.725634	+	0.688081i	$0.241547\pi$
$360$		0			0
$361$	−6.08894	+	17.9979i	−0.320471	+	0.947258i
$362$	7.90038	+	4.56129i	0.415235	+	0.239736i
$363$		0			0
$364$	8.59498	+	4.96231i	0.450499	+	0.260096i
$365$		−	1.98092i		−	0.103686i
$366$		0			0
$367$	3.64794	+	6.31841i	0.190421	+	0.329818i	0.945390	−	0.325942i	$-0.105681\pi$
$367$	3.64794	+	6.31841i	0.190421	+	0.329818i	−0.754969	+	0.655761i	$0.772348\pi$
$368$			4.30391i			0.224357i
$369$		0			0
$370$	−1.60765	+	2.78453i	−0.0835778	+	0.144761i
$371$	6.44874	+	11.1696i	0.334802	+	0.579894i
$372$		0			0
$373$	−27.4833	+	15.8675i	−1.42303	+	0.821589i	−0.996557	−	0.0829103i	$-0.973579\pi$
$373$	−27.4833	+	15.8675i	−1.42303	+	0.821589i	−0.426476	+	0.904499i	$0.640245\pi$
$374$	2.77130			0.143301
$375$		0			0
$376$	3.38101	−	1.95203i	0.174363	−	0.100668i
$377$	30.4571	−	17.5844i	1.56862	−	0.905645i
$378$		0			0
$379$		−	36.3198i		−	1.86562i	−0.360365	−	0.932811i	$-0.617348\pi$
$379$		−	36.3198i		−	1.86562i	0.360365	−	0.932811i	$-0.382652\pi$
$380$	−0.136500	−	1.37868i	−0.00700231	−	0.0707248i
$381$		0			0
$382$	−10.7981	−	6.23426i	−0.552477	−	0.318973i
$383$	−3.61465	+	6.26075i	−0.184700	+	0.319909i	−0.943475	−	0.331443i	$-0.892465\pi$
$383$	−3.61465	+	6.26075i	−0.184700	+	0.319909i	0.758776	+	0.651352i	$0.225798\pi$
$384$		0			0
$385$	−0.430531			−0.0219419
$386$	−18.8559	−	10.8864i	−0.959738	−	0.554105i
$387$		0			0
$388$			4.82426i			0.244915i
$389$	19.4798	−	11.2467i	0.987667	−	0.570230i	0.0830912	−	0.996542i	$-0.473521\pi$
$389$	19.4798	−	11.2467i	0.987667	−	0.570230i	0.904576	+	0.426312i	$0.140187\pi$
$390$		0			0
$391$	12.0720	+	20.9093i	0.610506	+	1.05743i
$392$	0.259183	+	0.448918i	0.0130907	+	0.0226738i
$393$		0			0
$394$			26.2753i			1.32373i
$395$	−0.0502526	+	0.0870400i	−0.00252848	+	0.00437946i
$396$		0			0
$397$	−5.86909	−	10.1656i	−0.294561	−	0.510195i	0.680322	−	0.732914i	$-0.261840\pi$
$397$	−5.86909	−	10.1656i	−0.294561	−	0.510195i	−0.974883	+	0.222719i	$0.928507\pi$
$398$	0.352359	−	0.610303i	0.0176622	−	0.0305917i
$399$		0			0
$400$	−2.44949	−	4.24264i	−0.122474	−	0.212132i
$401$	−16.0823	+	27.8553i	−0.803110	+	1.39103i	0.114449	+	0.993429i	$0.463490\pi$
$401$	−16.0823	+	27.8553i	−0.803110	+	1.39103i	−0.917559	+	0.397599i	$0.869844\pi$
$402$		0			0
$403$	15.9822	+	27.6820i	0.796129	+	1.37894i
$404$	−8.35102	+	4.82146i	−0.415479	+	0.239877i
$405$		0			0
$406$	26.6421			1.32222
$407$	2.49877	−	4.32799i	0.123859	−	0.214530i
$408$		0			0
$409$		−	22.7117i		−	1.12302i	−0.827469	−	0.561511i	$-0.810220\pi$
$409$		−	22.7117i		−	1.12302i	0.827469	−	0.561511i	$-0.189780\pi$
$410$	1.06025	−	0.612134i	0.0523619	−	0.0302311i
$411$		0			0
$412$	9.19615	−	5.30940i	0.453062	−	0.261575i
$413$	−6.71122	−	11.6242i	−0.330238	−	0.571988i
$414$		0			0
$415$	−0.305250	−	0.528708i	−0.0149841	−	0.0259533i
$416$			3.61953i			0.177462i
$417$		0			0
$418$	0.212162	+	2.14288i	0.0103772	+	0.104811i
$419$	−5.78208	+	3.33828i	−0.282473	+	0.163086i	−0.634542	−	0.772888i	$-0.718811\pi$
$419$	−5.78208	+	3.33828i	−0.282473	+	0.163086i	0.352069	+	0.935974i	$0.385478\pi$
$420$		0			0
$421$		−	3.15721i		−	0.153873i	−0.997036	−	0.0769365i	$-0.975486\pi$
$421$		−	3.15721i		−	0.153873i	0.997036	−	0.0769365i	$-0.0245139\pi$
$422$	17.5567	+	10.1363i	0.854645	+	0.493429i
$423$		0			0
$424$	−2.35187	+	4.07356i	−0.114217	+	0.197830i
$425$	−23.8003	−	13.7411i	−1.15448	−	0.666540i
$426$		0			0
$427$	−7.41356			−0.358767
$428$	2.11598			0.102280
$429$		0			0
$430$	1.45923	+	0.842485i	0.0703702	+	0.0406282i
$431$	−6.09250	+	10.5525i	−0.293465	+	0.508297i	−0.974627	−	0.223837i	$-0.928142\pi$
$431$	−6.09250	+	10.5525i	−0.293465	+	0.508297i	0.681162	+	0.732133i	$0.261475\pi$
$432$		0			0
$433$	0.218755	+	0.126298i	0.0105127	+	0.00606950i	0.505247	−	0.862975i	$-0.331401\pi$
$433$	0.218755	+	0.126298i	0.0105127	+	0.00606950i	−0.494734	+	0.869044i	$0.664735\pi$
$434$			24.2145i			1.16233i
$435$		0			0
$436$	−12.6573	+	7.30770i	−0.606175	+	0.349975i
$437$	−15.2437	+	10.9353i	−0.729203	+	0.523104i
$438$		0			0
$439$			32.8142i			1.56614i	0.621936	+	0.783068i	$0.286347\pi$
$439$			32.8142i			1.56614i	−0.621936	+	0.783068i	$0.713653\pi$
$440$	−0.0785079	−	0.135980i	−0.00374271	−	0.00648257i
$441$		0			0
$442$	10.1524	+	17.5844i	0.482899	+	0.836406i
$443$	31.6964	−	18.2999i	1.50594	−	0.869455i	0.505963	−	0.862555i	$-0.331137\pi$
$443$	31.6964	−	18.2999i	1.50594	−	0.869455i	0.999976	−	0.00689971i	$-0.00219626\pi$
$444$		0			0
$445$	−0.765261	+	0.441823i	−0.0362768	+	0.0209444i
$446$			11.0154i			0.521595i
$447$		0			0
$448$	−1.37098	+	2.37461i	−0.0647728	+	0.112190i
$449$	13.3834			0.631603			0.315801	−	0.948825i	$-0.397727\pi$
$449$	13.3834			0.631603			0.315801	+	0.948825i	$0.397727\pi$
$450$		0			0
$451$	−1.64794	+	0.951437i	−0.0775983	+	0.0448014i
$452$	2.22730	+	3.85779i	0.104763	+	0.181455i
$453$		0			0
$454$	−0.189561	+	0.328329i	−0.00889654	+	0.0154093i
$455$	−1.57721	−	2.73181i	−0.0739407	−	0.128069i
$456$		0			0
$457$	13.9859	−	24.2243i	0.654232	−	1.13316i	−0.327854	−	0.944729i	$-0.606325\pi$
$457$	13.9859	−	24.2243i	0.654232	−	1.13316i	0.982086	−	0.188435i	$-0.0603414\pi$
$458$	6.17045	+	10.6875i	0.288326	+	0.499396i
$459$		0			0
$460$	0.683971	−	1.18467i	0.0318903	−	0.0552357i
$461$			2.86456i			0.133416i	0.997773	+	0.0667080i	$0.0212496\pi$
$461$			2.86456i			0.133416i	−0.997773	+	0.0667080i	$0.978750\pi$
$462$		0			0
$463$	15.1652	+	26.2668i	0.704785	+	1.22072i	0.966769	+	0.255651i	$0.0822897\pi$
$463$	15.1652	+	26.2668i	0.704785	+	1.22072i	−0.261985	+	0.965072i	$0.584377\pi$
$464$	4.85821	+	8.41466i	0.225537	+	0.390641i
$465$		0			0
$466$	10.4076	−	6.00881i	0.482121	−	0.278353i
$467$		−	20.9149i		−	0.967826i	−0.875116	−	0.483913i	$-0.839215\pi$
$467$		−	20.9149i		−	0.967826i	0.875116	−	0.483913i	$-0.160785\pi$
$468$		0			0
$469$	−7.84409	−	4.52879i	−0.362206	−	0.209120i
$470$	−1.24086			−0.0572364
$471$		0			0
$472$	2.44760	−	4.23936i	0.112660	−	0.195132i
$473$	−2.26807	−	1.30947i	−0.104286	−	0.0602095i
$474$		0			0
$475$	8.80306	−	19.4552i	0.403912	−	0.892667i
$476$			15.3818i			0.705023i
$477$		0			0
$478$	−4.53510	+	2.61834i	−0.207430	+	0.119760i
$479$	−10.2165	+	5.89851i	−0.466805	+	0.269510i	−0.714901	−	0.699226i	$-0.753528\pi$
$479$	−10.2165	+	5.89851i	−0.466805	+	0.269510i	0.248097	+	0.968735i	$0.420195\pi$
$480$		0			0
$481$	36.6159			1.66954
$482$	14.5433	−	8.39659i	0.662430	−	0.382454i
$483$		0			0
$484$	−5.37798	−	9.31493i	−0.244453	−	0.423406i
$485$	0.766665	−	1.32790i	0.0348125	−	0.0602969i
$486$		0			0
$487$		−	11.7862i		−	0.534083i	−0.963685	−	0.267042i	$-0.913954\pi$
$487$		−	11.7862i		−	0.534083i	0.963685	−	0.267042i	$-0.0860461\pi$
$488$	−1.35187	−	2.34151i	−0.0611963	−	0.105995i
$489$		0			0
$490$		−	0.164756i		−	0.00744291i
$491$	15.8419	+	9.14633i	0.714935	+	0.412768i	0.812886	−	0.582423i	$-0.197895\pi$
$491$	15.8419	+	9.14633i	0.714935	+	0.412768i	−0.0979506	+	0.995191i	$0.531229\pi$
$492$		0			0
$493$	47.2043	+	27.2534i	2.12598	+	1.22743i
$494$	−12.8197	+	9.19641i	−0.576787	+	0.413766i
$495$		0			0
$496$	−7.64794	+	4.41554i	−0.343403	+	0.198264i
$497$	−36.9024			−1.65530
$498$		0			0
$499$	−10.8098	+	18.7231i	−0.483911	+	0.838159i	−0.999829	−	0.0184791i	$-0.994118\pi$
$499$	−10.8098	+	18.7231i	−0.483911	+	0.838159i	0.515918	+	0.856638i	$0.327451\pi$
$500$			3.14626i			0.140705i
$501$		0			0
$502$	13.6697	+	7.89221i	0.610109	+	0.352246i
$503$	−3.33259	−	1.92407i	−0.148593	−	0.0857901i	0.423860	−	0.905728i	$-0.360675\pi$
$503$	−3.33259	−	1.92407i	−0.148593	−	0.0857901i	−0.572453	+	0.819938i	$0.694008\pi$
$504$		0			0
$505$	3.06488			0.136385
$506$	−1.06309	+	1.84133i	−0.0472603	+	0.0818572i
$507$		0			0
$508$	8.32681	+	4.80748i	0.369442	+	0.213298i
$509$	45.0412			1.99642			0.998209	−	0.0598250i	$-0.0190543\pi$
$509$	45.0412			1.99642			0.998209	+	0.0598250i	$0.0190543\pi$
$510$		0			0
$511$	−17.0892			−0.755984
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.25484			−0.319997
$515$	−3.37505			−0.148723
$516$		0			0
$517$	1.92866			0.0848222
$518$	24.0220	+	13.8691i	1.05547	+	0.609374i
$519$		0			0
$520$	0.575211	−	0.996295i	0.0252247	−	0.0436904i
$521$	12.1832			0.533754			0.266877	−	0.963731i	$-0.414008\pi$
$521$	12.1832			0.533754			0.266877	+	0.963731i	$0.414008\pi$
$522$		0			0
$523$	7.37872	+	4.26011i	0.322649	+	0.186281i	0.652573	−	0.757726i	$-0.273690\pi$
$523$	7.37872	+	4.26011i	0.322649	+	0.186281i	−0.329924	+	0.944008i	$0.607023\pi$
$524$	−18.0495	−	10.4209i	−0.788495	−	0.455238i
$525$		0			0
$526$			23.6406i			1.03078i
$527$	−24.7702	+	42.9032i	−1.07901	+	1.86889i
$528$		0			0
$529$	4.47636			0.194624
$530$	1.29473	−	0.747512i	0.0562394	−	0.0324698i
$531$		0			0
$532$	−11.8938	+	1.17758i	−0.515661	+	0.0510545i
$533$	−12.0741	−	6.97099i	−0.522987	−	0.301947i
$534$		0			0
$535$	−0.582436	−	0.336269i	−0.0251809	−	0.0145382i
$536$		−	3.30332i		−	0.142682i
$537$		0			0
$538$	−4.14179	−	7.17380i	−0.178565	−	0.309284i
$539$			0.256079i			0.0110301i
$540$		0			0
$541$	−10.8633	+	18.8158i	−0.467050	+	0.808954i	−0.999291	−	0.0376382i	$-0.988017\pi$
$541$	−10.8633	+	18.8158i	−0.467050	+	0.808954i	0.532241	+	0.846593i	$0.321350\pi$
$542$	−9.25036	−	16.0221i	−0.397337	−	0.688208i
$543$		0			0
$544$	−4.85821	+	2.80489i	−0.208294	+	0.120259i
$545$	4.64532			0.198984
$546$		0			0
$547$	−8.82706	+	5.09631i	−0.377418	+	0.217902i	−0.676694	−	0.736264i	$-0.736588\pi$
$547$	−8.82706	+	5.09631i	−0.377418	+	0.217902i	0.299276	+	0.954167i	$0.403255\pi$
$548$	1.01343	−	0.585106i	0.0432918	−	0.0249945i
$549$		0			0
$550$		−	2.42016i		−	0.103196i
$551$	−17.4596	+	38.5866i	−0.743803	+	1.64385i
$552$		0			0
$553$	0.750889	+	0.433526i	0.0319311	+	0.0184354i
$554$	−6.87912	+	11.9150i	−0.292266	+	0.506219i
$555$		0			0
$556$	15.6177			0.662337
$557$	−2.73682	−	1.58011i	−0.115963	−	0.0669513i	0.440897	−	0.897558i	$-0.354661\pi$
$557$	−2.73682	−	1.58011i	−0.115963	−	0.0669513i	−0.556860	+	0.830607i	$0.687994\pi$
$558$		0			0
$559$		−	19.1884i		−	0.811585i
$560$	0.754740	−	0.435749i	0.0318936	−	0.0184138i
$561$		0			0
$562$	6.11854	+	10.5976i	0.258095	+	0.447033i
$563$	−3.78225	−	6.55105i	−0.159403	−	0.276094i	0.775251	−	0.631654i	$-0.217624\pi$
$563$	−3.78225	−	6.55105i	−0.159403	−	0.276094i	−0.934653	+	0.355560i	$0.884290\pi$
$564$		0			0
$565$		−	1.41583i		−	0.0595646i
$566$	10.8216	−	18.7436i	0.454867	−	0.787852i
$567$		0			0
$568$	−6.72919	−	11.6553i	−0.282350	−	0.489045i
$569$	−20.6624	+	35.7883i	−0.866213	+	1.50033i	−0.000376125		1.00000i	$0.500120\pi$
$569$	−20.6624	+	35.7883i	−0.866213	+	1.50033i	−0.865837	+	0.500326i	$0.833214\pi$
$570$		0			0
$571$	5.60925	+	9.71550i	0.234740	+	0.406581i	0.959197	−	0.282739i	$-0.0912429\pi$
$571$	5.60925	+	9.71550i	0.234740	+	0.406581i	−0.724457	+	0.689320i	$0.757910\pi$
$572$	−0.894048	+	1.54854i	−0.0373820	+	0.0647476i
$573$		0			0
$574$	−5.28084	−	9.14669i	−0.220418	−	0.381776i
$575$	18.2599	−	10.5424i	0.761492	−	0.439648i
$576$		0			0
$577$	7.34788			0.305896			0.152948	−	0.988234i	$-0.451123\pi$
$577$	7.34788			0.305896			0.152948	+	0.988234i	$0.451123\pi$
$578$	−7.23478	+	12.5310i	−0.300927	+	0.521221i
$579$		0			0
$580$		−	3.08824i		−	0.128232i
$581$	−4.56114	+	2.63337i	−0.189228	+	0.109251i
$582$		0			0
$583$	−2.01239	+	1.16185i	−0.0833447	+	0.0481191i
$584$	−3.11624	−	5.39749i	−0.128951	−	0.223350i
$585$		0			0
$586$	12.0645	+	20.8963i	0.498380	+	0.863219i
$587$		−	25.1468i		−	1.03792i	−0.854798	−	0.518961i	$-0.826319\pi$
$587$		−	25.1468i		−	1.03792i	0.854798	−	0.518961i	$-0.173681\pi$
$588$		0			0
$589$	−35.0707	−	15.8687i	−1.44506	−	0.653859i
$590$	−1.34743	+	0.777938i	−0.0554727	+	0.0320272i
$591$		0			0
$592$			10.1162i			0.415773i
$593$	−37.4358	−	21.6136i	−1.53731	−	0.887564i	−0.998995	−	0.0448173i	$-0.985729\pi$
$593$	−37.4358	−	21.6136i	−1.53731	−	0.887564i	−0.538311	−	0.842747i	$-0.680937\pi$
$594$		0			0
$595$	2.44445	−	4.23392i	0.100213	−	0.173574i
$596$	16.5375	+	9.54795i	0.677404	+	0.391099i
$597$		0			0
$598$	−15.5781			−0.637038
$599$	−15.9442			−0.651463			−0.325731	−	0.945462i	$-0.605611\pi$
$599$	−15.9442			−0.651463			−0.325731	+	0.945462i	$0.605611\pi$
$600$		0			0
$601$	29.0452	+	16.7692i	1.18478	+	0.684031i	0.957115	−	0.289709i	$-0.0935586\pi$
$601$	29.0452	+	16.7692i	1.18478	+	0.684031i	0.227662	+	0.973740i	$0.426892\pi$
$602$	7.26807	−	12.5887i	0.296224	−	0.513076i
$603$		0			0
$604$	5.12154	+	2.95692i	0.208392	+	0.120315i
$605$			3.41864i			0.138988i
$606$		0			0
$607$	−23.5567	+	13.6004i	−0.956135	+	0.552025i	−0.894981	−	0.446104i	$-0.852811\pi$
$607$	−23.5567	+	13.6004i	−0.956135	+	0.552025i	−0.0611537	+	0.998128i	$0.519478\pi$
$608$	−2.54077	−	3.54182i	−0.103042	−	0.143640i
$609$		0			0
$610$			0.859350i			0.0347940i
$611$	7.06544	+	12.2377i	0.285837	+	0.495084i
$612$		0			0
$613$	4.81339	+	8.33704i	0.194411	+	0.336730i	0.946707	−	0.322095i	$-0.104387\pi$
$613$	4.81339	+	8.33704i	0.194411	+	0.336730i	−0.752296	+	0.658825i	$0.771054\pi$
$614$	−1.24755	+	0.720275i	−0.0503472	+	0.0290679i
$615$		0			0
$616$	−1.17309	+	0.677283i	−0.0472651	+	0.0272885i
$617$		−	25.4714i		−	1.02544i	−0.858556	−	0.512719i	$-0.828638\pi$
$617$		−	25.4714i		−	1.02544i	0.858556	−	0.512719i	$-0.171362\pi$
$618$		0			0
$619$	−3.25614	+	5.63981i	−0.130875	+	0.226683i	−0.924014	−	0.382358i	$-0.875112\pi$
$619$	−3.25614	+	5.63981i	−0.130875	+	0.226683i	0.793139	+	0.609041i	$0.208445\pi$
$620$	2.80685			0.112726
$621$		0			0
$622$	6.78947	−	3.91990i	0.272233	−	0.157174i
$623$	3.81159	+	6.60186i	0.152708	+	0.264498i
$624$		0			0
$625$	−11.7474	+	20.3472i	−0.469898	+	0.813887i
$626$	5.76922	+	9.99257i	0.230584	+	0.399384i
$627$		0			0
$628$	9.71615	−	16.8289i	0.387717	−	0.671545i
$629$	28.3748	+	49.1466i	1.13138	+	1.95960i
$630$		0			0
$631$	14.0897	−	24.4041i	0.560902	−	0.971510i	−0.436516	−	0.899696i	$-0.643788\pi$
$631$	14.0897	−	24.4041i	0.560902	−	0.971510i	0.997418	−	0.0718138i	$-0.0228787\pi$
$632$			0.316216i			0.0125784i
$633$		0			0
$634$	−0.623429	−	1.07981i	−0.0247595	−	0.0428847i
$635$	−1.52800	−	2.64657i	−0.0606367	−	0.105026i
$636$		0			0
$637$	−1.62487	+	0.938120i	−0.0643798	+	0.0371697i
$638$			4.80003i			0.190035i
$639$		0			0
$640$	0.275255	+	0.158919i	0.0108804	+	0.00628181i
$641$	34.0579			1.34521			0.672603	−	0.740003i	$-0.265176\pi$
$641$	34.0579			1.34521			0.672603	+	0.740003i	$0.265176\pi$
$642$		0			0
$643$	0.332759	−	0.576356i	0.0131227	−	0.0227292i	−0.859389	−	0.511322i	$-0.829156\pi$
$643$	0.332759	−	0.576356i	0.0131227	−	0.0227292i	0.872512	+	0.488592i	$0.162489\pi$
$644$	−10.2201	−	5.90058i	−0.402729	−	0.232516i
$645$		0			0
$646$	−22.2780	−	10.0803i	−0.876516	−	0.396604i
$647$		−	30.6089i		−	1.20336i	−0.798737	−	0.601680i	$-0.794498\pi$
$647$		−	30.6089i		−	1.20336i	0.798737	−	0.601680i	$-0.205502\pi$
$648$		0			0
$649$	2.09430	−	1.20914i	0.0822085	−	0.0474631i
$650$	15.3564	−	8.86601i	0.602327	−	0.347754i
$651$		0			0
$652$	13.0895			0.512623
$653$	−6.97798	+	4.02874i	−0.273069	+	0.157657i	−0.630282	−	0.776367i	$-0.717061\pi$
$653$	−6.97798	+	4.02874i	−0.273069	+	0.157657i	0.357212	+	0.934023i	$0.383727\pi$
$654$		0			0
$655$	3.31214	+	5.73679i	0.129416	+	0.224155i
$656$	1.92594	−	3.33582i	0.0751951	−	0.130242i
$657$		0			0
$658$			10.7048i			0.417316i
$659$	21.1666	+	36.6616i	0.824534	+	1.42813i	0.902275	+	0.431161i	$0.141896\pi$
$659$	21.1666	+	36.6616i	0.824534	+	1.42813i	−0.0777416	+	0.996974i	$0.524771\pi$
$660$		0			0
$661$		−	20.7509i		−	0.807116i	−0.914954	−	0.403558i	$-0.867773\pi$
$661$		−	20.7509i		−	0.807116i	0.914954	−	0.403558i	$-0.132227\pi$
$662$	11.2469	+	6.49338i	0.437122	+	0.252373i
$663$		0			0
$664$	−1.66346	−	0.960397i	−0.0645546	−	0.0372706i
$665$	3.46097	+	1.56601i	0.134211	+	0.0607273i
$666$		0			0
$667$	−36.2159	+	20.9093i	−1.40229	+	0.809611i
$668$	−0.767515			−0.0296961
$669$		0			0
$670$	−0.524959	+	0.909255i	−0.0202809	+	0.0351276i
$671$		−	1.33568i		−	0.0515635i
$672$		0			0
$673$	−15.3082	−	8.83817i	−0.590086	−	0.340686i	0.175045	−	0.984560i	$-0.443993\pi$
$673$	−15.3082	−	8.83817i	−0.590086	−	0.340686i	−0.765132	+	0.643874i	$0.777326\pi$
$674$	21.4194	+	12.3665i	0.825044	+	0.476339i
$675$		0			0
$676$	−0.101021			−0.00388540
$677$	20.6377	−	35.7456i	0.793172	−	1.37381i	−0.130822	−	0.991406i	$-0.541762\pi$
$677$	20.6377	−	35.7456i	0.793172	−	1.37381i	0.923994	−	0.382408i	$-0.124905\pi$
$678$		0			0
$679$	−11.4557	−	6.61397i	−0.439631	−	0.253821i
$680$	1.78299			0.0683747
$681$		0			0
$682$	−4.36267			−0.167055
$683$	24.0477			0.920160			0.460080	−	0.887878i	$-0.347821\pi$
$683$	24.0477			0.920160			0.460080	+	0.887878i	$0.347821\pi$
$684$		0			0
$685$	−0.371937			−0.0142110
$686$	17.7724			0.678554
$687$		0			0
$688$	5.30136			0.202112
$689$	−14.7444	−	8.51267i	−0.561716	−	0.324307i
$690$		0			0
$691$	1.07816	−	1.86743i	0.0410152	−	0.0710405i	−0.844789	−	0.535099i	$-0.820274\pi$
$691$	1.07816	−	1.86743i	0.0410152	−	0.0710405i	0.885804	+	0.464059i	$0.153607\pi$
$692$	−1.40519			−0.0534173
$693$		0			0
$694$	−30.8720	−	17.8240i	−1.17189	−	0.676588i
$695$	−4.29885	−	2.48194i	−0.163065	−	0.0941454i
$696$		0			0
$697$		−	21.6081i		−	0.818466i
$698$	3.98014	−	6.89381i	0.150651	−	0.260935i
$699$		0			0
$700$	13.4328			0.507713
$701$	−12.5290	+	7.23359i	−0.473212	+	0.273209i	−0.717583	−	0.696473i	$-0.754752\pi$
$701$	−12.5290	+	7.23359i	−0.473212	+	0.273209i	0.244371	+	0.969682i	$0.421418\pi$
$702$		0			0
$703$	−35.8297	+	25.7030i	−1.35134	+	0.969406i
$704$	−0.427828	−	0.247006i	−0.0161244	−	0.00930941i
$705$		0			0
$706$	−10.0732	−	5.81577i	−0.379110	−	0.218879i
$707$		−	26.4406i		−	0.994399i
$708$		0			0
$709$	−23.9414	−	41.4677i	−0.899137	−	1.55735i	−0.828600	−	0.559842i	$-0.810862\pi$
$709$	−23.9414	−	41.4677i	−0.899137	−	1.55735i	−0.0705371	−	0.997509i	$-0.522471\pi$
$710$			4.27757i			0.160534i
$711$		0			0
$712$	−1.39009	+	2.40771i	−0.0520959	+	0.0902328i
$713$	−19.0041	−	32.9160i	−0.711708	−	1.23272i
$714$		0			0
$715$	0.492183	−	0.284162i	0.0184066	−	0.0106270i
$716$	−24.0695			−0.899518
$717$		0			0
$718$	−9.33259	+	5.38817i	−0.348289	+	0.201085i
$719$	8.56691	−	4.94611i	0.319492	−	0.184459i	−0.331674	−	0.943394i	$-0.607614\pi$
$719$	8.56691	−	4.94611i	0.319492	−	0.184459i	0.651166	+	0.758935i	$0.274280\pi$
$720$		0			0
$721$			29.1164i			1.08435i
$722$	6.08894	−	17.9979i	0.226607	−	0.669813i
$723$		0			0
$724$	−7.90038	−	4.56129i	−0.293615	−	0.169519i
$725$	23.8003	−	41.2232i	0.883919	−	1.53099i
$726$		0			0
$727$	43.9597			1.63037			0.815187	−	0.579197i	$-0.196634\pi$
$727$	43.9597			1.63037			0.815187	+	0.579197i	$0.196634\pi$
$728$	−8.59498	−	4.96231i	−0.318551	−	0.183916i
$729$		0			0
$730$			1.98092i			0.0733170i
$731$	25.7551	−	14.8697i	0.952587	−	0.549976i
$732$		0			0
$733$	6.59524	+	11.4233i	0.243601	+	0.421929i	0.961737	−	0.273973i	$-0.0883380\pi$
$733$	6.59524	+	11.4233i	0.243601	+	0.421929i	−0.718137	+	0.695902i	$0.755005\pi$
$734$	−3.64794	−	6.31841i	−0.134648	−	0.233217i
$735$		0			0
$736$		−	4.30391i		−	0.158644i
$737$	0.815941	−	1.41325i	0.0300556	−	0.0520578i
$738$		0			0
$739$	3.33374	+	5.77420i	0.122633	+	0.212407i	0.920805	−	0.390022i	$-0.127533\pi$
$739$	3.33374	+	5.77420i	0.122633	+	0.212407i	−0.798172	+	0.602430i	$0.794199\pi$
$740$	1.60765	−	2.78453i	0.0590985	−	0.102362i
$741$		0			0
$742$	−6.44874	−	11.1696i	−0.236741	−	0.410047i
$743$	−19.7679	+	34.2390i	−0.725213	+	1.25611i	0.233673	+	0.972315i	$0.424925\pi$
$743$	−19.7679	+	34.2390i	−0.725213	+	1.25611i	−0.958886	+	0.283791i	$0.908408\pi$
$744$		0			0
$745$	−3.03470	−	5.25625i	−0.111183	−	0.192574i
$746$	27.4833	−	15.8675i	1.00624	−	0.580951i
$747$		0			0
$748$	−2.77130			−0.101329
$749$	−2.90098	+	5.02464i	−0.105999	+	0.183596i
$750$		0			0
$751$			12.9141i			0.471244i	0.971845	+	0.235622i	$0.0757126\pi$
$751$			12.9141i			0.471244i	−0.971845	+	0.235622i	$0.924287\pi$
$752$	−3.38101	+	1.95203i	−0.123293	+	0.0711832i
$753$		0			0
$754$	−30.4571	+	17.5844i	−1.10918	+	0.640387i
$755$	−0.939819	−	1.62781i	−0.0342035	−	0.0592423i
$756$		0			0
$757$	−9.40872	−	16.2964i	−0.341966	−	0.592302i	0.642832	−	0.766007i	$-0.277759\pi$
$757$	−9.40872	−	16.2964i	−0.341966	−	0.592302i	−0.984798	+	0.173705i	$0.944426\pi$
$758$			36.3198i			1.31919i
$759$		0			0
$760$	0.136500	+	1.37868i	0.00495138	+	0.0500100i
$761$	30.1496	−	17.4069i	1.09292	−	0.630999i	0.158569	−	0.987348i	$-0.449312\pi$
$761$	30.1496	−	17.4069i	1.09292	−	0.630999i	0.934353	+	0.356349i	$0.115978\pi$
$762$		0			0
$763$		−	40.0749i		−	1.45081i
$764$	10.7981	+	6.23426i	0.390660	+	0.225548i
$765$		0			0
$766$	3.61465	−	6.26075i	0.130602	−	0.226210i
$767$	15.3445	+	8.85916i	0.554058	+	0.319886i
$768$		0			0
$769$	27.6727			0.997903			0.498952	−	0.866630i	$-0.333719\pi$
$769$	27.6727			0.997903			0.498952	+	0.866630i	$0.333719\pi$
$770$	0.430531			0.0155153
$771$		0			0
$772$	18.8559	+	10.8864i	0.678637	+	0.391811i
$773$	−17.3327	+	30.0211i	−0.623414	+	1.07978i	0.365432	+	0.930838i	$0.380921\pi$
$773$	−17.3327	+	30.0211i	−0.623414	+	1.07978i	−0.988845	+	0.148946i	$0.952412\pi$
$774$		0			0
$775$	37.4671	+	21.6316i	1.34586	+	0.777031i
$776$		−	4.82426i		−	0.173181i
$777$		0			0
$778$	−19.4798	+	11.2467i	−0.698386	+	0.403214i
$779$	16.7082	−	1.65425i	0.598634	−	0.0592695i
$780$		0			0
$781$		−	6.64861i		−	0.237906i
$782$	−12.0720	−	20.9093i	−0.431693	−	0.747714i
$783$		0			0
$784$	−0.259183	−	0.448918i	−0.00925652	−	0.0160328i
$785$	−5.34884	+	3.08816i	−0.190908	+	0.110221i
$786$		0			0
$787$	3.53395	−	2.04033i	0.125972	−	0.0727298i	−0.435690	−	0.900097i	$-0.643496\pi$
$787$	3.53395	−	2.04033i	0.125972	−	0.0727298i	0.561662	+	0.827367i	$0.310162\pi$
$788$		−	26.2753i		−	0.936020i
$789$		0			0
$790$	0.0502526	−	0.0870400i	0.00178791	−	0.00309675i
$791$	−12.2143			−0.434291
$792$		0			0
$793$	8.47517	−	4.89314i	0.300962	−	0.173761i
$794$	5.86909	+	10.1656i	0.208286	+	0.360762i
$795$		0			0
$796$	−0.352359	+	0.610303i	−0.0124890	+	0.0216316i
$797$	−2.24196	−	3.88320i	−0.0794144	−	0.137550i	0.823583	−	0.567196i	$-0.191972\pi$
$797$	−2.24196	−	3.88320i	−0.0794144	−	0.137550i	−0.902997	+	0.429646i	$0.858638\pi$
$798$		0			0
$799$	−10.9504	+	18.9667i	−0.387399	+	0.670994i
$800$	2.44949	+	4.24264i	0.0866025	+	0.150000i
$801$		0			0
$802$	16.0823	−	27.8553i	0.567885	−	0.983605i
$803$		−	3.07893i		−	0.108653i
$804$		0			0
$805$	1.87542	+	3.24833i	0.0661000	+	0.114489i
$806$	−15.9822	−	27.6820i	−0.562949	−	0.975056i
$807$		0			0
$808$	8.35102	−	4.82146i	0.293788	−	0.169618i
$809$			4.38153i			0.154047i	0.997029	+	0.0770233i	$0.0245416\pi$
$809$			4.38153i			0.154047i	−0.997029	+	0.0770233i	$0.975458\pi$
$810$		0			0
$811$	−43.1755	−	24.9274i	−1.51610	−	0.875320i	−0.999821	−	0.0188977i	$-0.993984\pi$
$811$	−43.1755	−	24.9274i	−1.51610	−	0.875320i	−0.516277	−	0.856422i	$-0.672682\pi$
$812$	−26.6421			−0.934953
$813$		0			0
$814$	−2.49877	+	4.32799i	−0.0875817	+	0.151696i
$815$	−3.60294	−	2.08016i	−0.126205	−	0.0728648i
$816$		0			0
$817$	13.4696	+	18.7764i	0.471240	+	0.656905i
$818$			22.7117i			0.794096i
$819$		0			0
$820$	−1.06025	+	0.612134i	−0.0370254	+	0.0213766i
$821$	−16.8440	+	9.72491i	−0.587861	+	0.339402i	−0.764251	−	0.644919i	$-0.776891\pi$
$821$	−16.8440	+	9.72491i	−0.587861	+	0.339402i	0.176390	+	0.984320i	$0.443558\pi$
$822$		0			0
$823$	8.54405			0.297827			0.148913	−	0.988850i	$-0.452422\pi$
$823$	8.54405			0.297827			0.148913	+	0.988850i	$0.452422\pi$
$824$	−9.19615	+	5.30940i	−0.320363	+	0.184962i
$825$		0			0
$826$	6.71122	+	11.6242i	0.233513	+	0.404457i
$827$	−21.7071	+	37.5978i	−0.754829	+	1.30740i	0.190630	+	0.981662i	$0.438947\pi$
$827$	−21.7071	+	37.5978i	−0.754829	+	1.30740i	−0.945459	+	0.325740i	$0.894387\pi$
$828$		0			0
$829$		−	55.5704i		−	1.93004i	−0.262180	−	0.965019i	$-0.584441\pi$
$829$		−	55.5704i		−	1.93004i	0.262180	−	0.965019i	$-0.415559\pi$
$830$	0.305250	+	0.528708i	0.0105954	+	0.0183517i
$831$		0			0
$832$		−	3.61953i		−	0.125485i
$833$	−2.51833	−	1.45396i	−0.0872548	−	0.0503766i
$834$		0			0
$835$	0.211263	+	0.121972i	0.00731104	+	0.00422103i
$836$	−0.212162	−	2.14288i	−0.00733776	−	0.0741129i
$837$		0			0
$838$	5.78208	−	3.33828i	0.199739	−	0.115319i
$839$	22.2266			0.767348			0.383674	−	0.923469i	$-0.374659\pi$
$839$	22.2266			0.767348			0.383674	+	0.923469i	$0.374659\pi$
$840$		0			0
$841$	−32.7043	+	56.6456i	−1.12774	+	1.95330i
$842$			3.15721i			0.108805i
$843$		0			0
$844$	−17.5567	−	10.1363i	−0.604325	−	0.348907i
$845$	0.0278064	+	0.0160540i	0.000956570	+	0.000552276i
$846$		0			0
$847$	29.4924			1.01337
$848$	2.35187	−	4.07356i	0.0807636	−	0.139887i
$849$		0			0
$850$	23.8003	+	13.7411i	0.816342	+	0.471315i
$851$	−43.5392			−1.49250
$852$		0			0
$853$	−18.8943			−0.646928			−0.323464	−	0.946240i	$-0.604848\pi$
$853$	−18.8943			−0.646928			−0.323464	+	0.946240i	$0.604848\pi$
$854$	7.41356			0.253687
$855$		0			0
$856$	−2.11598			−0.0723229
$857$	−44.7737			−1.52944			−0.764721	−	0.644362i	$-0.777123\pi$
$857$	−44.7737			−1.52944			−0.764721	+	0.644362i	$0.777123\pi$
$858$		0			0
$859$	1.21003			0.0412856			0.0206428	−	0.999787i	$-0.493429\pi$
$859$	1.21003			0.0412856			0.0206428	+	0.999787i	$0.493429\pi$
$860$	−1.45923	−	0.842485i	−0.0497592	−	0.0287285i
$861$		0			0
$862$	6.09250	−	10.5525i	0.207511	−	0.359420i
$863$	−5.34378			−0.181905			−0.0909523	−	0.995855i	$-0.528991\pi$
$863$	−5.34378			−0.181905			−0.0909523	+	0.995855i	$0.528991\pi$
$864$		0			0
$865$	0.386785	+	0.223311i	0.0131511	+	0.00759279i
$866$	−0.218755	−	0.126298i	−0.00743359	−	0.00429179i
$867$		0			0
$868$		−	24.2145i		−	0.821893i
$869$	−0.0781074	+	0.135286i	−0.00264961	+	0.00458926i
$870$		0			0
$871$	11.9565			0.405129
$872$	12.6573	−	7.30770i	0.428631	−	0.247470i
$873$		0			0
$874$	15.2437	−	10.9353i	0.515625	−	0.369891i
$875$	−7.47115	−	4.31347i	−0.252571	−	0.145822i
$876$		0			0
$877$	−10.8120	−	6.24233i	−0.365096	−	0.210788i	0.306218	−	0.951961i	$-0.400936\pi$
$877$	−10.8120	−	6.24233i	−0.365096	−	0.210788i	−0.671314	+	0.741173i	$0.734270\pi$
$878$		−	32.8142i		−	1.10743i
$879$		0			0
$880$	0.0785079	+	0.135980i	0.00264650	+	0.00458387i
$881$			18.5298i			0.624283i	0.950036	+	0.312142i	$0.101046\pi$
$881$			18.5298i			0.624283i	−0.950036	+	0.312142i	$0.898954\pi$
$882$		0			0
$883$	15.6893	−	27.1746i	0.527986	−	0.914498i	−0.471482	−	0.881876i	$-0.656281\pi$
$883$	15.6893	−	27.1746i	0.527986	−	0.914498i	0.999468	−	0.0326225i	$-0.0103859\pi$
$884$	−10.1524	−	17.5844i	−0.341461	−	0.591429i
$885$		0			0
$886$	−31.6964	+	18.2999i	−1.06486	+	0.614797i
$887$	2.50646			0.0841587			0.0420794	−	0.999114i	$-0.486602\pi$
$887$	2.50646			0.0841587			0.0420794	+	0.999114i	$0.486602\pi$
$888$		0			0
$889$	−22.8318	+	13.1819i	−0.765754	+	0.442108i
$890$	0.765261	−	0.441823i	0.0256516	−	0.0148100i
$891$		0			0
$892$		−	11.0154i		−	0.368823i
$893$	−15.5041	−	7.01527i	−0.518826	−	0.234757i
$894$		0			0
$895$	6.62524	+	3.82509i	0.221457	+	0.127859i
$896$	1.37098	−	2.37461i	0.0458013	−	0.0793302i
$897$		0			0
$898$	−13.3834			−0.446611
$899$	−74.3105	−	42.9032i	−2.47839	−	1.43090i
$900$		0			0
$901$		−	26.3869i		−	0.879076i
$902$	1.64794	−	0.951437i	0.0548703	−	0.0316794i
$903$		0			0
$904$	−2.22730	−	3.85779i	−0.0740787	−	0.128308i
$905$	1.44975	+	2.51104i	0.0481912	+	0.0834697i
$906$		0			0
$907$		−	6.33985i		−	0.210511i	−0.994445	−	0.105256i	$-0.966434\pi$
$907$		−	6.33985i		−	0.210511i	0.994445	−	0.105256i	$-0.0335661\pi$
$908$	0.189561	−	0.328329i	0.00629080	−	0.0108960i
$909$		0			0
$910$	1.57721	+	2.73181i	0.0522839	+	0.0905585i
$911$	−13.1513	+	22.7788i	−0.435723	+	0.754695i	−0.997354	−	0.0726929i	$-0.976841\pi$
$911$	−13.1513	+	22.7788i	−0.435723	+	0.754695i	0.561631	+	0.827388i	$0.310174\pi$
$912$		0			0
$913$	−0.474448	−	0.821769i	−0.0157019	−	0.0271966i
$914$	−13.9859	+	24.2243i	−0.462612	+	0.801267i
$915$		0			0
$916$	−6.17045	−	10.6875i	−0.203877	−	0.353126i
$917$	49.4910	−	28.5736i	1.63434	−	0.943585i
$918$		0			0
$919$	−39.5968			−1.30618			−0.653090	−	0.757281i	$-0.726528\pi$
$919$	−39.5968			−1.30618			−0.653090	+	0.757281i	$0.726528\pi$
$920$	−0.683971	+	1.18467i	−0.0225499	+	0.0390575i
$921$		0			0
$922$		−	2.86456i		−	0.0943393i
$923$	42.1867	−	24.3565i	1.38859	−	0.801705i
$924$		0			0
$925$	42.9194	−	24.7795i	1.41118	−	0.814746i
$926$	−15.1652	−	26.2668i	−0.498358	−	0.863181i
$927$		0			0
$928$	−4.85821	−	8.41466i	−0.159478	−	0.276225i
$929$			29.4265i			0.965451i	0.875772	+	0.482725i	$0.160353\pi$
$929$			29.4265i			0.965451i	−0.875772	+	0.482725i	$0.839647\pi$
$930$		0			0
$931$	0.931460	−	2.05858i	0.0305274	−	0.0674671i
$932$	−10.4076	+	6.00881i	−0.340911	+	0.196825i
$933$		0			0
$934$			20.9149i			0.684357i
$935$	0.762815	+	0.440411i	0.0249467	+	0.0144030i
$936$		0			0
$937$	15.6328	−	27.0768i	0.510701	−	0.884560i	−0.489222	−	0.872159i	$-0.662719\pi$
$937$	15.6328	−	27.0768i	0.510701	−	0.884560i	0.999923	−	0.0124005i	$-0.00394729\pi$
$938$	7.84409	+	4.52879i	0.256119	+	0.147870i
$939$		0			0
$940$	1.24086			0.0404722
$941$	48.1832			1.57073			0.785363	−	0.619035i	$-0.212476\pi$
$941$	48.1832			1.57073			0.785363	+	0.619035i	$0.212476\pi$
$942$		0			0
$943$	14.3571	+	8.28905i	0.467530	+	0.269929i
$944$	−2.44760	+	4.23936i	−0.0796625	+	0.137980i
$945$		0			0
$946$	2.26807	+	1.30947i	0.0737413	+	0.0425745i
$947$			0.421379i			0.0136930i	0.999977	+	0.00684650i	$0.00217932\pi$
$947$			0.421379i			0.0136930i	−0.999977	+	0.00684650i	$0.997821\pi$
$948$		0			0
$949$	19.5364	−	11.2793i	0.634178	−	0.366143i
$950$	−8.80306	+	19.4552i	−0.285609	+	0.631211i
$951$		0			0
$952$		−	15.3818i		−	0.498527i
$953$	23.9224	+	41.4349i	0.774924	+	1.34221i	0.934837	+	0.355077i	$0.115545\pi$
$953$	23.9224	+	41.4349i	0.774924	+	1.34221i	−0.159913	+	0.987131i	$0.551121\pi$
$954$		0			0
$955$	−1.98148	−	3.43203i	−0.0641192	−	0.111058i
$956$	4.53510	−	2.61834i	0.146675	−	0.0846831i
$957$		0			0
$958$	10.2165	−	5.89851i	0.330081	−	0.190572i
$959$			3.20868i			0.103614i
$960$		0			0
$961$	23.4940	−	40.6927i	0.757870	−	1.31267i
$962$	−36.6159			−1.18054
$963$		0			0
$964$	−14.5433	+	8.39659i	−0.468409	+	0.270436i
$965$	−3.46012	−	5.99310i	−0.111385	−	0.192925i
$966$		0			0
$967$	25.7510	−	44.6021i	0.828098	−	1.43431i	−0.0714310	−	0.997446i	$-0.522757\pi$
$967$	25.7510	−	44.6021i	0.828098	−	1.43431i	0.899529	−	0.436862i	$-0.143910\pi$
$968$	5.37798	+	9.31493i	0.172855	+	0.299393i
$969$		0			0
$970$	−0.766665	+	1.32790i	−0.0246161	+	0.0426364i
$971$	−24.2447	−	41.9931i	−0.778050	−	1.34762i	−0.933064	−	0.359709i	$-0.882876\pi$
$971$	−24.2447	−	41.9931i	−0.778050	−	1.34762i	0.155015	−	0.987912i	$-0.450457\pi$
$972$		0			0
$973$	−21.4116	+	37.0859i	−0.686423	+	1.18892i
$974$			11.7862i			0.377654i
$975$		0			0
$976$	1.35187	+	2.34151i	0.0432723	+	0.0749499i
$977$	−26.0687	−	45.1524i	−0.834013	−	1.44455i	−0.894831	−	0.446404i	$-0.852704\pi$
$977$	−26.0687	−	45.1524i	−0.834013	−	1.44455i	0.0608182	−	0.998149i	$-0.480629\pi$
$978$		0			0
$979$	−1.18944	+	0.686724i	−0.0380147	+	0.0219478i
$980$			0.164756i			0.00526293i
$981$		0			0
$982$	−15.8419	−	9.14633i	−0.505535	−	0.291871i
$983$	−18.7497			−0.598021			−0.299011	−	0.954250i	$-0.596657\pi$
$983$	−18.7497			−0.598021			−0.299011	+	0.954250i	$0.596657\pi$
$984$		0			0
$985$	−4.17564	+	7.23242i	−0.133047	+	0.230444i
$986$	−47.2043	−	27.2534i	−1.50329	−	0.867926i
$987$		0			0
$988$	12.8197	−	9.19641i	0.407850	−	0.292577i
$989$			22.8166i			0.725525i
$990$		0			0
$991$	26.0009	−	15.0116i	0.825945	−	0.476860i	−0.0265172	−	0.999648i	$-0.508442\pi$
$991$	26.0009	−	15.0116i	0.825945	−	0.476860i	0.852462	+	0.522789i	$0.175108\pi$
$992$	7.64794	−	4.41554i	0.242822	−	0.140193i
$993$		0			0
$994$	36.9024			1.17047
$995$	0.193977	−	0.111993i	0.00614949	−	0.00355041i
$996$		0			0
$997$	26.8797	+	46.5570i	0.851289	+	1.47448i	0.880045	+	0.474889i	$0.157512\pi$
$997$	26.8797	+	46.5570i	0.851289	+	1.47448i	−0.0287564	+	0.999586i	$0.509155\pi$
$998$	10.8098	−	18.7231i	0.342177	−	0.592668i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1026.2.n.d.791.3		8
3.2	odd	2		342.2.n.d.335.4	yes	8
9.4	even	3		342.2.j.d.221.3	yes	8
9.5	odd	6		1026.2.j.d.449.3		8
19.8	odd	6		1026.2.j.d.521.1		8
57.8	even	6		342.2.j.d.65.3	✓	8
171.103	odd	6		342.2.n.d.293.4	yes	8
171.122	even	6	inner	1026.2.n.d.179.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.j.d.65.3	✓	8	57.8	even	6
342.2.j.d.221.3	yes	8	9.4	even	3
342.2.n.d.293.4	yes	8	171.103	odd	6
342.2.n.d.335.4	yes	8	3.2	odd	2
1026.2.j.d.449.3		8	9.5	odd	6
1026.2.j.d.521.1		8	19.8	odd	6
1026.2.n.d.179.3		8	171.122	even	6	inner
1026.2.n.d.791.3		8	1.1	even	1	trivial

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.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.275255 - 0.158919i) q^{5} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.275255 - 0.158919i) q^{5} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +(0.275255 + 0.158919i) q^{10} +(-0.427828 - 0.247006i) q^{11} -3.61953i q^{13} +(1.37098 - 2.37461i) q^{14} +1.00000 q^{16} +(4.85821 - 2.80489i) q^{17} +(2.54077 + 3.54182i) q^{19} +(-0.275255 - 0.158919i) q^{20} +(0.427828 + 0.247006i) q^{22} +4.30391i q^{23} +(-2.44949 - 4.24264i) q^{25} +3.61953i q^{26} +(-1.37098 + 2.37461i) q^{28} +(4.85821 + 8.41466i) q^{29} +(-7.64794 + 4.41554i) q^{31} -1.00000 q^{32} +(-4.85821 + 2.80489i) q^{34} +(0.754740 - 0.435749i) q^{35} +10.1162i q^{37} +(-2.54077 - 3.54182i) q^{38} +(0.275255 + 0.158919i) q^{40} +(1.92594 - 3.33582i) q^{41} +5.30136 q^{43} +(-0.427828 - 0.247006i) q^{44} -4.30391i q^{46} +(-3.38101 + 1.95203i) q^{47} +(-0.259183 - 0.448918i) q^{49} +(2.44949 + 4.24264i) q^{50} -3.61953i q^{52} +(2.35187 - 4.07356i) q^{53} +(0.0785079 + 0.135980i) q^{55} +(1.37098 - 2.37461i) q^{56} +(-4.85821 - 8.41466i) q^{58} +(-2.44760 + 4.23936i) q^{59} +(1.35187 + 2.34151i) q^{61} +(7.64794 - 4.41554i) q^{62} +1.00000 q^{64} +(-0.575211 + 0.996295i) q^{65} +3.30332i q^{67} +(4.85821 - 2.80489i) q^{68} +(-0.754740 + 0.435749i) q^{70} +(6.72919 + 11.6553i) q^{71} +(3.11624 + 5.39749i) q^{73} -10.1162i q^{74} +(2.54077 + 3.54182i) q^{76} +(1.17309 - 0.677283i) q^{77} -0.316216i q^{79} +(-0.275255 - 0.158919i) q^{80} +(-1.92594 + 3.33582i) q^{82} +(1.66346 + 0.960397i) q^{83} -1.78299 q^{85} -5.30136 q^{86} +(0.427828 + 0.247006i) q^{88} +(1.39009 - 2.40771i) q^{89} +(8.59498 + 4.96231i) q^{91} +4.30391i q^{92} +(3.38101 - 1.95203i) q^{94} +(-0.136500 - 1.37868i) q^{95} +4.82426i q^{97} +(0.259183 + 0.448918i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 12 q^{5} - 8 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 12 * q^5 - 8 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 12 q^{5} - 8 q^{7} - 8 q^{8} + 12 q^{10} + 8 q^{14} + 8 q^{16} + 12 q^{17} + 8 q^{19} - 12 q^{20} - 8 q^{28} + 12 q^{29} + 24 q^{31} - 8 q^{32} - 12 q^{34} + 24 q^{35} - 8 q^{38} + 12 q^{40} + 12 q^{41} + 16 q^{43} + 24 q^{47} + 12 q^{53} - 16 q^{55} + 8 q^{56} - 12 q^{58} + 4 q^{61} - 24 q^{62} + 8 q^{64} + 12 q^{68} - 24 q^{70} + 24 q^{71} + 4 q^{73} + 8 q^{76} - 12 q^{77} - 12 q^{80} - 12 q^{82} + 24 q^{83} + 8 q^{85} - 16 q^{86} + 12 q^{89} + 48 q^{91} - 24 q^{94} + 24 q^{95}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 12 * q^5 - 8 * q^7 - 8 * q^8 + 12 * q^10 + 8 * q^14 + 8 * q^16 + 12 * q^17 + 8 * q^19 - 12 * q^20 - 8 * q^28 + 12 * q^29 + 24 * q^31 - 8 * q^32 - 12 * q^34 + 24 * q^35 - 8 * q^38 + 12 * q^40 + 12 * q^41 + 16 * q^43 + 24 * q^47 + 12 * q^53 - 16 * q^55 + 8 * q^56 - 12 * q^58 + 4 * q^61 - 24 * q^62 + 8 * q^64 + 12 * q^68 - 24 * q^70 + 24 * q^71 + 4 * q^73 + 8 * q^76 - 12 * q^77 - 12 * q^80 - 12 * q^82 + 24 * q^83 + 8 * q^85 - 16 * q^86 + 12 * q^89 + 48 * q^91 - 24 * q^94 + 24 * q^95

Introduction

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