LMFDB - Embedded newform 1134.2.t.e.593.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(593,1134)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1134.593"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1134, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,0,-8,0,0,12,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1134.593
Dual form			1134.2.t.e.1025.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -4.18154 q^{5} +(-1.00000 - 2.44949i) q^{7} +1.00000i q^{8} +(3.62132 - 2.09077i) q^{10} -3.00000i q^{11} +(2.12132 - 1.22474i) q^{13} +(2.09077 + 1.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.507306 - 0.878680i) q^{17} +(-0.878680 - 0.507306i) q^{19} +(-2.09077 + 3.62132i) q^{20} +(1.50000 + 2.59808i) q^{22} +4.24264i q^{23} +12.4853 q^{25} +(-1.22474 + 2.12132i) q^{26} +(-2.62132 - 0.358719i) q^{28} +(-1.07616 - 0.621320i) q^{29} +(-4.86396 - 2.80821i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.878680 + 0.507306i) q^{34} +(4.18154 + 10.2426i) q^{35} +(-4.12132 + 7.13834i) q^{37} +1.01461 q^{38} -4.18154i q^{40} +(-1.01461 - 1.75736i) q^{41} +(-4.12132 + 7.13834i) q^{43} +(-2.59808 - 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(-0.507306 - 0.878680i) q^{47} +(-5.00000 + 4.89898i) q^{49} +(-10.8126 + 6.24264i) q^{50} -2.44949i q^{52} +(1.07616 - 0.621320i) q^{53} +12.5446i q^{55} +(2.44949 - 1.00000i) q^{56} +1.24264 q^{58} +(-5.76500 + 9.98528i) q^{59} +(-5.12132 + 2.95680i) q^{61} +5.61642 q^{62} -1.00000 q^{64} +(-8.87039 + 5.12132i) q^{65} +(5.00000 - 8.66025i) q^{67} -1.01461 q^{68} +(-8.74264 - 6.77962i) q^{70} +10.2426i q^{71} +(7.24264 - 4.18154i) q^{73} -8.24264i q^{74} +(-0.878680 + 0.507306i) q^{76} +(-7.34847 + 3.00000i) q^{77} +(5.62132 + 9.73641i) q^{79} +(2.09077 + 3.62132i) q^{80} +(1.75736 + 1.01461i) q^{82} +(1.58346 - 2.74264i) q^{83} +(2.12132 + 3.67423i) q^{85} -8.24264i q^{86} +3.00000 q^{88} +(5.19615 - 9.00000i) q^{89} +(-5.12132 - 3.97141i) q^{91} +(3.67423 + 2.12132i) q^{92} +(0.878680 + 0.507306i) q^{94} +(3.67423 + 2.12132i) q^{95} +(-3.25736 - 1.88064i) q^{97} +(1.88064 - 6.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} + 12 q^{22} + 32 q^{25} - 4 q^{28} + 12 q^{31} + 24 q^{34} - 16 q^{37} - 16 q^{43} - 40 q^{49} - 24 q^{58} - 24 q^{61} - 8 q^{64} + 40 q^{67} - 36 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 + 12 * q^22 + 32 * q^25 - 4 * q^28 + 12 * q^31 + 24 * q^34 - 16 * q^37 - 16 * q^43 - 40 * q^49 - 24 * q^58 - 24 * q^61 - 8 * q^64 + 40 * q^67 - 36 * q^70 + 24 * q^73 - 24 * q^76 + 28 * q^79 + 48 * q^82 + 24 * q^88 - 24 * q^91 + 24 * q^94 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−4.18154			−1.87004			−0.935021	−	0.354593i	$-0.884620\pi$
$5$	−4.18154			−1.87004			−0.935021	+	0.354593i	$0.884620\pi$
$6$		0			0
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	3.62132	−	2.09077i	1.14516	−	0.661160i
$11$		−	3.00000i		−	0.904534i	−0.891883	−	0.452267i	$-0.850615\pi$
$11$		−	3.00000i		−	0.904534i	0.891883	−	0.452267i	$-0.149385\pi$
$12$		0			0
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	−0.176096	−	0.984373i	$-0.556347\pi$
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	0.764444	+	0.644690i	$0.223014\pi$
$14$	2.09077	+	1.62132i	0.558782	+	0.433316i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.507306	−	0.878680i	−0.123040	−	0.213111i	0.797925	−	0.602756i	$-0.205931\pi$
$17$	−0.507306	−	0.878680i	−0.123040	−	0.213111i	−0.920965	+	0.389645i	$0.872598\pi$
$18$		0			0
$19$	−0.878680	−	0.507306i	−0.201583	−	0.116384i	0.395811	−	0.918332i	$-0.370464\pi$
$19$	−0.878680	−	0.507306i	−0.201583	−	0.116384i	−0.597394	+	0.801948i	$0.703797\pi$
$20$	−2.09077	+	3.62132i	−0.467510	+	0.809752i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$			4.24264i			0.884652i	0.896854	+	0.442326i	$0.145847\pi$
$23$			4.24264i			0.884652i	−0.896854	+	0.442326i	$0.854153\pi$
$24$		0			0
$25$	12.4853			2.49706
$26$	−1.22474	+	2.12132i	−0.240192	+	0.416025i
$27$		0			0
$28$	−2.62132	−	0.358719i	−0.495383	−	0.0677916i
$29$	−1.07616	−	0.621320i	−0.199838	−	0.115376i	0.396742	−	0.917930i	$-0.370141\pi$
$29$	−1.07616	−	0.621320i	−0.199838	−	0.115376i	−0.596580	+	0.802554i	$0.703474\pi$
$30$		0			0
$31$	−4.86396	−	2.80821i	−0.873593	−	0.504369i	−0.00505256	−	0.999987i	$-0.501608\pi$
$31$	−4.86396	−	2.80821i	−0.873593	−	0.504369i	−0.868541	+	0.495618i	$0.834942\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	0.878680	+	0.507306i	0.150692	+	0.0870023i
$35$	4.18154	+	10.2426i	0.706809	+	1.73132i
$36$		0			0
$37$	−4.12132	+	7.13834i	−0.677541	+	1.17354i	0.298178	+	0.954510i	$0.403621\pi$
$37$	−4.12132	+	7.13834i	−0.677541	+	1.17354i	−0.975719	+	0.219025i	$0.929712\pi$
$38$	1.01461			0.164592
$39$		0			0
$40$		−	4.18154i		−	0.661160i
$41$	−1.01461	−	1.75736i	−0.158456	−	0.274453i	0.775856	−	0.630910i	$-0.217318\pi$
$41$	−1.01461	−	1.75736i	−0.158456	−	0.274453i	−0.934312	+	0.356456i	$0.883985\pi$
$42$		0			0
$43$	−4.12132	+	7.13834i	−0.628495	+	1.08859i	0.359358	+	0.933200i	$0.382996\pi$
$43$	−4.12132	+	7.13834i	−0.628495	+	1.08859i	−0.987854	+	0.155386i	$0.950338\pi$
$44$	−2.59808	−	1.50000i	−0.391675	−	0.226134i
$45$		0			0
$46$	−2.12132	−	3.67423i	−0.312772	−	0.541736i
$47$	−0.507306	−	0.878680i	−0.0739982	−	0.128169i	0.826652	−	0.562713i	$-0.190243\pi$
$47$	−0.507306	−	0.878680i	−0.0739982	−	0.128169i	−0.900650	+	0.434545i	$0.856909\pi$
$48$		0			0
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$	−10.8126	+	6.24264i	−1.52913	+	0.882843i
$51$		0			0
$52$		−	2.44949i		−	0.339683i
$53$	1.07616	−	0.621320i	0.147822	−	0.0853449i	−0.424265	−	0.905538i	$-0.639467\pi$
$53$	1.07616	−	0.621320i	0.147822	−	0.0853449i	0.572087	+	0.820193i	$0.306134\pi$
$54$		0			0
$55$			12.5446i			1.69152i
$56$	2.44949	−	1.00000i	0.327327	−	0.133631i
$57$		0			0
$58$	1.24264			0.163167
$59$	−5.76500	+	9.98528i	−0.750540	+	1.29997i	0.197022	+	0.980399i	$0.436873\pi$
$59$	−5.76500	+	9.98528i	−0.750540	+	1.29997i	−0.947561	+	0.319574i	$0.896460\pi$
$60$		0			0
$61$	−5.12132	+	2.95680i	−0.655718	+	0.378579i	−0.790643	−	0.612277i	$-0.790254\pi$
$61$	−5.12132	+	2.95680i	−0.655718	+	0.378579i	0.134926	+	0.990856i	$0.456920\pi$
$62$	5.61642			0.713286
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.87039	+	5.12132i	−1.10024	+	0.635222i
$66$		0			0
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$	−1.01461			−0.123040
$69$		0			0
$70$	−8.74264	−	6.77962i	−1.04495	−	0.810319i
$71$			10.2426i			1.21558i	0.794099	+	0.607789i	$0.207943\pi$
$71$			10.2426i			1.21558i	−0.794099	+	0.607789i	$0.792057\pi$
$72$		0			0
$73$	7.24264	−	4.18154i	0.847687	−	0.489412i	−0.0121828	−	0.999926i	$-0.503878\pi$
$73$	7.24264	−	4.18154i	0.847687	−	0.489412i	0.859870	+	0.510513i	$0.170545\pi$
$74$		−	8.24264i		−	0.958188i
$75$		0			0
$76$	−0.878680	+	0.507306i	−0.100791	+	0.0581920i
$77$	−7.34847	+	3.00000i	−0.837436	+	0.341882i
$78$		0			0
$79$	5.62132	+	9.73641i	0.632448	+	1.09543i	0.987050	+	0.160415i	$0.0512831\pi$
$79$	5.62132	+	9.73641i	0.632448	+	1.09543i	−0.354602	+	0.935017i	$0.615384\pi$
$80$	2.09077	+	3.62132i	0.233755	+	0.404876i
$81$		0			0
$82$	1.75736	+	1.01461i	0.194068	+	0.112045i
$83$	1.58346	−	2.74264i	0.173808	−	0.301044i	−0.765940	−	0.642912i	$-0.777726\pi$
$83$	1.58346	−	2.74264i	0.173808	−	0.301044i	0.939748	+	0.341868i	$0.111060\pi$
$84$		0			0
$85$	2.12132	+	3.67423i	0.230089	+	0.398527i
$86$		−	8.24264i		−	0.888827i
$87$		0			0
$88$	3.00000			0.319801
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	−0.447427	−	0.894321i	$-0.647659\pi$
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	0.998218	−	0.0596775i	$-0.0190072\pi$
$90$		0			0
$91$	−5.12132	−	3.97141i	−0.536860	−	0.416317i
$92$	3.67423	+	2.12132i	0.383065	+	0.221163i
$93$		0			0
$94$	0.878680	+	0.507306i	0.0906289	+	0.0523246i
$95$	3.67423	+	2.12132i	0.376969	+	0.217643i
$96$		0			0
$97$	−3.25736	−	1.88064i	−0.330735	−	0.190950i	0.325433	−	0.945565i	$-0.394490\pi$
$97$	−3.25736	−	1.88064i	−0.330735	−	0.190950i	−0.656167	+	0.754615i	$0.727823\pi$
$98$	1.88064	−	6.74264i	0.189973	−	0.681110i
$99$		0			0
$100$	6.24264	−	10.8126i	0.624264	−	1.08126i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$			15.2913i			1.50670i	0.657623	+	0.753348i	$0.271562\pi$
$103$			15.2913i			1.50670i	−0.657623	+	0.753348i	$0.728438\pi$
$104$	1.22474	+	2.12132i	0.120096	+	0.208013i
$105$		0			0
$106$	−0.621320	+	1.07616i	−0.0603480	+	0.104526i
$107$	4.75039	+	2.74264i	0.459238	+	0.265141i	0.711724	−	0.702459i	$-0.247915\pi$
$107$	4.75039	+	2.74264i	0.459238	+	0.265141i	−0.252486	+	0.967601i	$0.581248\pi$
$108$		0			0
$109$	−0.757359	−	1.31178i	−0.0725419	−	0.125646i	0.827473	−	0.561506i	$-0.189778\pi$
$109$	−0.757359	−	1.31178i	−0.0725419	−	0.125646i	−0.900015	+	0.435860i	$0.856444\pi$
$110$	−6.27231	−	10.8640i	−0.598041	−	1.03584i
$111$		0			0
$112$	−1.62132	+	2.09077i	−0.153200	+	0.197559i
$113$	7.34847	−	4.24264i	0.691286	−	0.399114i	−0.112808	−	0.993617i	$-0.535984\pi$
$113$	7.34847	−	4.24264i	0.691286	−	0.399114i	0.804094	+	0.594503i	$0.202651\pi$
$114$		0			0
$115$		−	17.7408i		−	1.65434i
$116$	−1.07616	+	0.621320i	−0.0999188	+	0.0576881i
$117$		0			0
$118$		−	11.5300i		−	1.06142i
$119$	−1.64501	+	2.12132i	−0.150798	+	0.194461i
$120$		0			0
$121$	2.00000			0.181818
$122$	2.95680	−	5.12132i	0.267696	−	0.463663i
$123$		0			0
$124$	−4.86396	+	2.80821i	−0.436797	+	0.252185i
$125$	−31.3000			−2.79956
$126$		0			0
$127$	−5.24264			−0.465209			−0.232605	−	0.972571i	$-0.574725\pi$
$127$	−5.24264			−0.465209			−0.232605	+	0.972571i	$0.574725\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	5.12132	−	8.87039i	0.449170	−	0.777984i
$131$	5.19615			0.453990			0.226995	−	0.973896i	$-0.427110\pi$
$131$	5.19615			0.453990			0.226995	+	0.973896i	$0.427110\pi$
$132$		0			0
$133$	−0.363961	+	2.65962i	−0.0315594	+	0.230619i
$134$			10.0000i			0.863868i
$135$		0			0
$136$	0.878680	−	0.507306i	0.0753462	−	0.0435011i
$137$			14.4853i			1.23756i	0.785564	+	0.618781i	$0.212373\pi$
$137$			14.4853i			1.23756i	−0.785564	+	0.618781i	$0.787627\pi$
$138$		0			0
$139$	−17.4853	+	10.0951i	−1.48308	+	0.856258i	−0.999815	−	0.0192152i	$-0.993883\pi$
$139$	−17.4853	+	10.0951i	−1.48308	+	0.856258i	−0.483267	+	0.875473i	$0.660550\pi$
$140$	10.9612	+	1.50000i	0.926387	+	0.126773i
$141$		0			0
$142$	−5.12132	−	8.87039i	−0.429772	−	0.744386i
$143$	−3.67423	−	6.36396i	−0.307255	−	0.532181i
$144$		0			0
$145$	4.50000	+	2.59808i	0.373705	+	0.215758i
$146$	−4.18154	+	7.24264i	−0.346067	+	0.599405i
$147$		0			0
$148$	4.12132	+	7.13834i	0.338770	+	0.586768i
$149$			20.4853i			1.67822i	0.543962	+	0.839110i	$0.316924\pi$
$149$			20.4853i			1.67822i	−0.543962	+	0.839110i	$0.683076\pi$
$150$		0			0
$151$	−3.24264			−0.263882			−0.131941	−	0.991258i	$-0.542121\pi$
$151$	−3.24264			−0.263882			−0.131941	+	0.991258i	$0.542121\pi$
$152$	0.507306	−	0.878680i	0.0411479	−	0.0712703i
$153$		0			0
$154$	4.86396	−	6.27231i	0.391949	−	0.505437i
$155$	20.3389	+	11.7426i	1.63366	+	0.943192i
$156$		0			0
$157$	12.7279	+	7.34847i	1.01580	+	0.586472i	0.912884	−	0.408219i	$-0.133850\pi$
$157$	12.7279	+	7.34847i	1.01580	+	0.586472i	0.102915	+	0.994690i	$0.467183\pi$
$158$	−9.73641	−	5.62132i	−0.774587	−	0.447208i
$159$		0			0
$160$	−3.62132	−	2.09077i	−0.286291	−	0.165290i
$161$	10.3923	−	4.24264i	0.819028	−	0.334367i
$162$		0			0
$163$	−3.12132	+	5.40629i	−0.244481	+	0.423453i	−0.961985	−	0.273101i	$-0.911951\pi$
$163$	−3.12132	+	5.40629i	−0.244481	+	0.423453i	0.717505	+	0.696554i	$0.245284\pi$
$164$	−2.02922			−0.158456
$165$		0			0
$166$			3.16693i			0.245801i
$167$	−11.5300	−	19.9706i	−0.892219	−	1.54537i	−0.837209	−	0.546883i	$-0.815814\pi$
$167$	−11.5300	−	19.9706i	−0.892219	−	1.54537i	−0.0550097	−	0.998486i	$-0.517519\pi$
$168$		0			0
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$	−3.67423	−	2.12132i	−0.281801	−	0.162698i
$171$		0			0
$172$	4.12132	+	7.13834i	0.314248	+	0.544293i
$173$	−10.3923	−	18.0000i	−0.790112	−	1.36851i	−0.925897	−	0.377776i	$-0.876689\pi$
$173$	−10.3923	−	18.0000i	−0.790112	−	1.36851i	0.135785	−	0.990738i	$-0.456644\pi$
$174$		0			0
$175$	−12.4853	−	30.5826i	−0.943799	−	2.31182i
$176$	−2.59808	+	1.50000i	−0.195837	+	0.113067i
$177$		0			0
$178$			10.3923i			0.778936i
$179$	8.23999	−	4.75736i	0.615886	−	0.355582i	−0.159380	−	0.987217i	$-0.550949\pi$
$179$	8.23999	−	4.75736i	0.615886	−	0.355582i	0.775265	+	0.631636i	$0.217616\pi$
$180$		0			0
$181$			2.02922i			0.150831i	0.997152	+	0.0754155i	$0.0240283\pi$
$181$			2.02922i			0.150831i	−0.997152	+	0.0754155i	$0.975972\pi$
$182$	6.42090	+	0.878680i	0.475949	+	0.0651321i
$183$		0			0
$184$	−4.24264			−0.312772
$185$	17.2335	−	29.8492i	1.26703	−	2.19456i
$186$		0			0
$187$	−2.63604	+	1.52192i	−0.192766	+	0.111294i
$188$	−1.01461			−0.0739982
$189$		0			0
$190$	−4.24264			−0.307794
$191$	7.34847	−	4.24264i	0.531717	−	0.306987i	−0.209999	−	0.977702i	$-0.567346\pi$
$191$	7.34847	−	4.24264i	0.531717	−	0.306987i	0.741715	+	0.670715i	$0.234013\pi$
$192$		0			0
$193$	3.74264	−	6.48244i	0.269401	−	0.466617i	−0.699306	−	0.714822i	$-0.746508\pi$
$193$	3.74264	−	6.48244i	0.269401	−	0.466617i	0.968707	+	0.248206i	$0.0798409\pi$
$194$	3.76127			0.270044
$195$		0			0
$196$	1.74264	+	6.77962i	0.124474	+	0.484258i
$197$			9.51472i			0.677896i	0.940805	+	0.338948i	$0.110071\pi$
$197$			9.51472i			0.677896i	−0.940805	+	0.338948i	$0.889929\pi$
$198$		0			0
$199$	−13.9706	+	8.06591i	−0.990347	+	0.571777i	−0.905378	−	0.424607i	$-0.860412\pi$
$199$	−13.9706	+	8.06591i	−0.990347	+	0.571777i	−0.0849690	+	0.996384i	$0.527079\pi$
$200$			12.4853i			0.882843i
$201$		0			0
$202$		0			0
$203$	−0.445759	+	3.25736i	−0.0312862	+	0.228622i
$204$		0			0
$205$	4.24264	+	7.34847i	0.296319	+	0.513239i
$206$	−7.64564	−	13.2426i	−0.532697	−	0.922658i
$207$		0			0
$208$	−2.12132	−	1.22474i	−0.147087	−	0.0849208i
$209$	−1.52192	+	2.63604i	−0.105273	+	0.182339i
$210$		0			0
$211$	−4.12132	−	7.13834i	−0.283723	−	0.491423i	0.688575	−	0.725165i	$-0.258236\pi$
$211$	−4.12132	−	7.13834i	−0.283723	−	0.491423i	−0.972299	+	0.233741i	$0.924903\pi$
$212$		−	1.24264i		−	0.0853449i
$213$		0			0
$214$	−5.48528			−0.374966
$215$	17.2335	−	29.8492i	1.17531	−	2.03570i
$216$		0			0
$217$	−2.01472	+	14.7224i	−0.136768	+	0.999424i
$218$	1.31178	+	0.757359i	0.0888453	+	0.0512948i
$219$		0			0
$220$	10.8640	+	6.27231i	0.732448	+	0.422879i
$221$	−2.15232	−	1.24264i	−0.144780	−	0.0835891i
$222$		0			0
$223$	10.8640	+	6.27231i	0.727505	+	0.420025i	0.817509	−	0.575916i	$-0.195355\pi$
$223$	10.8640	+	6.27231i	0.727505	+	0.420025i	−0.0900039	+	0.995941i	$0.528688\pi$
$224$	0.358719	−	2.62132i	0.0239680	−	0.175144i
$225$		0			0
$226$	−4.24264	+	7.34847i	−0.282216	+	0.488813i
$227$	−15.5885			−1.03464			−0.517321	−	0.855791i	$-0.673071\pi$
$227$	−15.5885			−1.03464			−0.517321	+	0.855791i	$0.673071\pi$
$228$		0			0
$229$			13.8564i			0.915657i	0.889041	+	0.457829i	$0.151373\pi$
$229$			13.8564i			0.915657i	−0.889041	+	0.457829i	$0.848627\pi$
$230$	8.87039	+	15.3640i	0.584896	+	1.01307i
$231$		0			0
$232$	0.621320	−	1.07616i	0.0407917	−	0.0706533i
$233$	−5.82655	−	3.36396i	−0.381710	−	0.220380i	0.296852	−	0.954924i	$-0.404063\pi$
$233$	−5.82655	−	3.36396i	−0.381710	−	0.220380i	−0.678562	+	0.734543i	$0.737397\pi$
$234$		0			0
$235$	2.12132	+	3.67423i	0.138380	+	0.239681i
$236$	5.76500	+	9.98528i	0.375270	+	0.649986i
$237$		0			0
$238$	0.363961	−	2.65962i	0.0235921	−	0.172398i
$239$	11.0227	−	6.36396i	0.712999	−	0.411650i	−0.0991712	−	0.995070i	$-0.531619\pi$
$239$	11.0227	−	6.36396i	0.712999	−	0.411650i	0.812171	+	0.583420i	$0.198286\pi$
$240$		0			0
$241$			17.0233i			1.09657i	0.836292	+	0.548285i	$0.184719\pi$
$241$			17.0233i			1.09657i	−0.836292	+	0.548285i	$0.815281\pi$
$242$	−1.73205	+	1.00000i	−0.111340	+	0.0642824i
$243$		0			0
$244$			5.91359i			0.378579i
$245$	20.9077	−	20.4853i	1.33574	−	1.30876i
$246$		0			0
$247$	−2.48528			−0.158135
$248$	2.80821	−	4.86396i	0.178321	−	0.308862i
$249$		0			0
$250$	27.1066	−	15.6500i	1.71437	−	0.989793i
$251$	−17.6177			−1.11202			−0.556009	−	0.831176i	$-0.687668\pi$
$251$	−17.6177			−1.11202			−0.556009	+	0.831176i	$0.687668\pi$
$252$		0			0
$253$	12.7279			0.800198
$254$	4.54026	−	2.62132i	0.284881	−	0.164476i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	25.0892			1.56502			0.782512	−	0.622636i	$-0.213938\pi$
$257$	25.0892			1.56502			0.782512	+	0.622636i	$0.213938\pi$
$258$		0			0
$259$	21.6066	+	2.95680i	1.34257	+	0.183726i
$260$			10.2426i			0.635222i
$261$		0			0
$262$	−4.50000	+	2.59808i	−0.278011	+	0.160510i
$263$		−	27.2132i		−	1.67804i	−0.544102	−	0.839019i	$-0.683130\pi$
$263$		−	27.2132i		−	1.67804i	0.544102	−	0.839019i	$-0.316870\pi$
$264$		0			0
$265$	−4.50000	+	2.59808i	−0.276433	+	0.159599i
$266$	−1.01461	−	2.48528i	−0.0622098	−	0.152382i
$267$		0			0
$268$	−5.00000	−	8.66025i	−0.305424	−	0.529009i
$269$	5.25770	+	9.10660i	0.320568	+	0.555239i	0.980605	−	0.195993i	$-0.0627930\pi$
$269$	5.25770	+	9.10660i	0.320568	+	0.555239i	−0.660038	+	0.751232i	$0.729460\pi$
$270$		0			0
$271$	−9.62132	−	5.55487i	−0.584454	−	0.337434i	0.178448	−	0.983949i	$-0.442892\pi$
$271$	−9.62132	−	5.55487i	−0.584454	−	0.337434i	−0.762901	+	0.646515i	$0.776226\pi$
$272$	−0.507306	+	0.878680i	−0.0307599	+	0.0532778i
$273$		0			0
$274$	−7.24264	−	12.5446i	−0.437544	−	0.757848i
$275$		−	37.4558i		−	2.25867i
$276$		0			0
$277$	−20.9706			−1.26000			−0.630000	−	0.776596i	$-0.716945\pi$
$277$	−20.9706			−1.26000			−0.630000	+	0.776596i	$0.716945\pi$
$278$	10.0951	−	17.4853i	0.605466	−	1.04870i
$279$		0			0
$280$	−10.2426	+	4.18154i	−0.612115	+	0.249895i
$281$	5.19615	+	3.00000i	0.309976	+	0.178965i	0.646916	−	0.762561i	$-0.276058\pi$
$281$	5.19615	+	3.00000i	0.309976	+	0.178965i	−0.336939	+	0.941526i	$0.609392\pi$
$282$		0			0
$283$	5.63604	+	3.25397i	0.335028	+	0.193428i	0.658071	−	0.752956i	$-0.271373\pi$
$283$	5.63604	+	3.25397i	0.335028	+	0.193428i	−0.323043	+	0.946384i	$0.604706\pi$
$284$	8.87039	+	5.12132i	0.526361	+	0.303894i
$285$		0			0
$286$	6.36396	+	3.67423i	0.376309	+	0.217262i
$287$	−3.29002	+	4.24264i	−0.194204	+	0.250435i
$288$		0			0
$289$	7.98528	−	13.8309i	0.469722	−	0.813583i
$290$	−5.19615			−0.305129
$291$		0			0
$292$		−	8.36308i		−	0.489412i
$293$	−2.09077	−	3.62132i	−0.122144	−	0.211560i	0.798469	−	0.602036i	$-0.205644\pi$
$293$	−2.09077	−	3.62132i	−0.122144	−	0.211560i	−0.920613	+	0.390476i	$0.872310\pi$
$294$		0			0
$295$	24.1066	−	41.7539i	1.40354	−	2.43100i
$296$	−7.13834	−	4.12132i	−0.414907	−	0.239547i
$297$		0			0
$298$	−10.2426	−	17.7408i	−0.593340	−	1.02770i
$299$	5.19615	+	9.00000i	0.300501	+	0.520483i
$300$		0			0
$301$	21.6066	+	2.95680i	1.24538	+	0.170427i
$302$	2.80821	−	1.62132i	0.161594	−	0.0932965i
$303$		0			0
$304$			1.01461i			0.0581920i
$305$	21.4150	−	12.3640i	1.22622	−	0.707958i
$306$		0			0
$307$		−	24.6690i		−	1.40793i	−0.710233	−	0.703966i	$-0.751411\pi$
$307$		−	24.6690i		−	1.40793i	0.710233	−	0.703966i	$-0.248589\pi$
$308$	−1.07616	+	7.86396i	−0.0613198	+	0.448091i
$309$		0			0
$310$	−23.4853			−1.33387
$311$	−9.37769	+	16.2426i	−0.531760	+	0.921036i	0.467552	+	0.883965i	$0.345136\pi$
$311$	−9.37769	+	16.2426i	−0.531760	+	0.921036i	−0.999313	+	0.0370703i	$0.988197\pi$
$312$		0			0
$313$	0.985281	−	0.568852i	0.0556914	−	0.0321534i	−0.471896	−	0.881654i	$-0.656430\pi$
$313$	0.985281	−	0.568852i	0.0556914	−	0.0321534i	0.527587	+	0.849501i	$0.323097\pi$
$314$	−14.6969			−0.829396
$315$		0			0
$316$	11.2426			0.632448
$317$	6.27231	−	3.62132i	0.352288	−	0.203394i	−0.313404	−	0.949620i	$-0.601470\pi$
$317$	6.27231	−	3.62132i	0.352288	−	0.203394i	0.665693	+	0.746226i	$0.268136\pi$
$318$		0			0
$319$	−1.86396	+	3.22848i	−0.104362	+	0.180760i
$320$	4.18154			0.233755
$321$		0			0
$322$	−6.87868	+	8.87039i	−0.383334	+	0.494327i
$323$			1.02944i			0.0572794i
$324$		0			0
$325$	26.4853	−	15.2913i	1.46914	−	0.848208i
$326$		−	6.24264i		−	0.345748i
$327$		0			0
$328$	1.75736	−	1.01461i	0.0970339	−	0.0560226i
$329$	−1.64501	+	2.12132i	−0.0906924	+	0.116952i
$330$		0			0
$331$	−8.72792	−	15.1172i	−0.479730	−	0.830917i	0.520000	−	0.854166i	$-0.325932\pi$
$331$	−8.72792	−	15.1172i	−0.479730	−	0.830917i	−0.999730	+	0.0232497i	$0.992599\pi$
$332$	−1.58346	−	2.74264i	−0.0869039	−	0.150522i
$333$		0			0
$334$	19.9706	+	11.5300i	1.09274	+	0.630894i
$335$	−20.9077	+	36.2132i	−1.14231	+	1.97854i
$336$		0			0
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	0.926049	−	0.377403i	$-0.123183\pi$
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	−0.789865	+	0.613280i	$0.789850\pi$
$338$		−	7.00000i		−	0.380750i
$339$		0			0
$340$	4.24264			0.230089
$341$	−8.42463	+	14.5919i	−0.456219	+	0.790195i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	−7.13834	−	4.12132i	−0.384873	−	0.222207i
$345$		0			0
$346$	18.0000	+	10.3923i	0.967686	+	0.558694i
$347$	12.5446	+	7.24264i	0.673431	+	0.388805i	0.797375	−	0.603484i	$-0.206221\pi$
$347$	12.5446	+	7.24264i	0.673431	+	0.388805i	−0.123945	+	0.992289i	$0.539555\pi$
$348$		0			0
$349$	−31.9706	−	18.4582i	−1.71134	−	0.988045i	−0.932754	−	0.360514i	$-0.882601\pi$
$349$	−31.9706	−	18.4582i	−1.71134	−	0.988045i	−0.778591	−	0.627531i	$-0.784065\pi$
$350$	26.1039	+	20.2426i	1.39531	+	1.08201i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	18.7554			0.998248			0.499124	−	0.866530i	$-0.333655\pi$
$353$	18.7554			0.998248			0.499124	+	0.866530i	$0.333655\pi$
$354$		0			0
$355$		−	42.8300i		−	2.27318i
$356$	−5.19615	−	9.00000i	−0.275396	−	0.476999i
$357$		0			0
$358$	−4.75736	+	8.23999i	−0.251434	+	0.435497i
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	0.0286287	−	0.999590i	$-0.490886\pi$
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	−0.851356	+	0.524588i	$0.824219\pi$
$360$		0			0
$361$	−8.98528	−	15.5630i	−0.472910	−	0.819103i
$362$	−1.01461	−	1.75736i	−0.0533268	−	0.0923648i
$363$		0			0
$364$	−6.00000	+	2.44949i	−0.314485	+	0.128388i
$365$	−30.2854	+	17.4853i	−1.58521	+	0.915221i
$366$		0			0
$367$			18.8785i			0.985449i	0.870185	+	0.492724i	$0.163999\pi$
$367$			18.8785i			0.985449i	−0.870185	+	0.492724i	$0.836001\pi$
$368$	3.67423	−	2.12132i	0.191533	−	0.110581i
$369$		0			0
$370$			34.4669i			1.79185i
$371$	−2.59808	−	2.01472i	−0.134885	−	0.104599i
$372$		0			0
$373$	21.4558			1.11094			0.555471	−	0.831536i	$-0.312538\pi$
$373$	21.4558			1.11094			0.555471	+	0.831536i	$0.312538\pi$
$374$	1.52192	−	2.63604i	0.0786965	−	0.136306i
$375$		0			0
$376$	0.878680	−	0.507306i	0.0453144	−	0.0261623i
$377$	−3.04384			−0.156766
$378$		0			0
$379$	−4.48528			−0.230393			−0.115197	−	0.993343i	$-0.536750\pi$
$379$	−4.48528			−0.230393			−0.115197	+	0.993343i	$0.536750\pi$
$380$	3.67423	−	2.12132i	0.188484	−	0.108821i
$381$		0			0
$382$	−4.24264	+	7.34847i	−0.217072	+	0.375980i
$383$	12.4215			0.634710			0.317355	−	0.948307i	$-0.397205\pi$
$383$	12.4215			0.634710			0.317355	+	0.948307i	$0.397205\pi$
$384$		0			0
$385$	30.7279	−	12.5446i	1.56604	−	0.639333i
$386$			7.48528i			0.380991i
$387$		0			0
$388$	−3.25736	+	1.88064i	−0.165367	+	0.0954749i
$389$			19.4558i			0.986450i	0.869902	+	0.493225i	$0.164182\pi$
$389$			19.4558i			0.986450i	−0.869902	+	0.493225i	$0.835818\pi$
$390$		0			0
$391$	3.72792	−	2.15232i	0.188529	−	0.108847i
$392$	−4.89898	−	5.00000i	−0.247436	−	0.252538i
$393$		0			0
$394$	−4.75736	−	8.23999i	−0.239672	−	0.415125i
$395$	−23.5058	−	40.7132i	−1.18270	−	2.04850i
$396$		0			0
$397$	12.0000	+	6.92820i	0.602263	+	0.347717i	0.769931	−	0.638127i	$-0.220290\pi$
$397$	12.0000	+	6.92820i	0.602263	+	0.347717i	−0.167668	+	0.985843i	$0.553624\pi$
$398$	8.06591	−	13.9706i	0.404307	−	0.700281i
$399$		0			0
$400$	−6.24264	−	10.8126i	−0.312132	−	0.540629i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$	−13.7574			−0.685303
$404$		0			0
$405$		0			0
$406$	−1.24264	−	3.04384i	−0.0616712	−	0.151063i
$407$	21.4150	+	12.3640i	1.06150	+	0.612859i
$408$		0			0
$409$	3.98528	+	2.30090i	0.197059	+	0.113772i	0.595283	−	0.803516i	$-0.297040\pi$
$409$	3.98528	+	2.30090i	0.197059	+	0.113772i	−0.398224	+	0.917288i	$0.630373\pi$
$410$	−7.34847	−	4.24264i	−0.362915	−	0.209529i
$411$		0			0
$412$	13.2426	+	7.64564i	0.652418	+	0.376674i
$413$	30.2238	+	4.13604i	1.48722	+	0.203521i
$414$		0			0
$415$	−6.62132	+	11.4685i	−0.325028	+	0.562965i
$416$	2.44949			0.120096
$417$		0			0
$418$		−	3.04384i		−	0.148879i
$419$	−2.02922	−	3.51472i	−0.0991341	−	0.171705i	0.812192	−	0.583390i	$-0.198274\pi$
$419$	−2.02922	−	3.51472i	−0.0991341	−	0.171705i	−0.911326	+	0.411684i	$0.864941\pi$
$420$		0			0
$421$	2.87868	−	4.98602i	0.140298	−	0.243004i	−0.787311	−	0.616557i	$-0.788527\pi$
$421$	2.87868	−	4.98602i	0.140298	−	0.243004i	0.927609	+	0.373553i	$0.121861\pi$
$422$	7.13834	+	4.12132i	0.347489	+	0.200623i
$423$		0			0
$424$	0.621320	+	1.07616i	0.0301740	+	0.0522629i
$425$	−6.33386	−	10.9706i	−0.307237	−	0.532150i
$426$		0			0
$427$	12.3640	+	9.58783i	0.598334	+	0.463987i
$428$	4.75039	−	2.74264i	0.229619	−	0.132571i
$429$		0			0
$430$			34.4669i			1.66214i
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	−0.862181	−	0.506600i	$-0.830902\pi$
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	0.00763808	+	0.999971i	$0.497569\pi$
$432$		0			0
$433$		−	3.46410i		−	0.166474i	−0.996530	−	0.0832370i	$-0.973474\pi$
$433$		−	3.46410i		−	0.166474i	0.996530	−	0.0832370i	$-0.0265259\pi$
$434$	−5.61642	−	13.7574i	−0.269597	−	0.660374i
$435$		0			0
$436$	−1.51472			−0.0725419
$437$	2.15232	−	3.72792i	0.102959	−	0.178331i
$438$		0			0
$439$	−23.5919	+	13.6208i	−1.12598	+	0.650084i	−0.942921	−	0.333018i	$-0.891933\pi$
$439$	−23.5919	+	13.6208i	−1.12598	+	0.650084i	−0.183059	+	0.983102i	$0.558600\pi$
$440$	−12.5446			−0.598041
$441$		0			0
$442$	2.48528			0.118213
$443$	−29.8396	+	17.2279i	−1.41772	+	0.818523i	−0.996099	−	0.0882469i	$-0.971874\pi$
$443$	−29.8396	+	17.2279i	−1.41772	+	0.818523i	−0.421625	+	0.906770i	$0.638540\pi$
$444$		0			0
$445$	−21.7279	+	37.6339i	−1.03000	+	1.78402i
$446$	−12.5446			−0.594005
$447$		0			0
$448$	1.00000	+	2.44949i	0.0472456	+	0.115728i
$449$			10.2426i			0.483380i	0.970354	+	0.241690i	$0.0777017\pi$
$449$			10.2426i			0.483380i	−0.970354	+	0.241690i	$0.922298\pi$
$450$		0			0
$451$	−5.27208	+	3.04384i	−0.248252	+	0.143329i
$452$		−	8.48528i		−	0.399114i
$453$		0			0
$454$	13.5000	−	7.79423i	0.633586	−	0.365801i
$455$	21.4150	+	16.6066i	1.00395	+	0.778529i
$456$		0			0
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$	−6.92820	−	12.0000i	−0.323734	−	0.560723i
$459$		0			0
$460$	−15.3640	−	8.87039i	−0.716348	−	0.413584i
$461$	−11.4069	+	19.7574i	−0.531273	+	0.920192i	0.468061	+	0.883696i	$0.344953\pi$
$461$	−11.4069	+	19.7574i	−0.531273	+	0.920192i	−0.999334	+	0.0364957i	$0.988380\pi$
$462$		0			0
$463$	−10.7279	−	18.5813i	−0.498569	−	0.863547i	0.501430	−	0.865198i	$-0.332808\pi$
$463$	−10.7279	−	18.5813i	−0.498569	−	0.863547i	−0.999999	+	0.00165180i	$0.999474\pi$
$464$			1.24264i			0.0576881i
$465$		0			0
$466$	6.72792			0.311665
$467$	−9.50079	+	16.4558i	−0.439644	+	0.761486i	−0.997662	−	0.0683432i	$-0.978229\pi$
$467$	−9.50079	+	16.4558i	−0.439644	+	0.761486i	0.558018	+	0.829829i	$0.311562\pi$
$468$		0			0
$469$	−26.2132	−	3.58719i	−1.21041	−	0.165641i
$470$	−3.67423	−	2.12132i	−0.169480	−	0.0978492i
$471$		0			0
$472$	−9.98528	−	5.76500i	−0.459610	−	0.265356i
$473$	21.4150	+	12.3640i	0.984663	+	0.568496i
$474$		0			0
$475$	−10.9706	−	6.33386i	−0.503364	−	0.290617i
$476$	1.01461	+	2.48528i	0.0465047	+	0.113913i
$477$		0			0
$478$	−6.36396	+	11.0227i	−0.291081	+	0.504167i
$479$	−36.4962			−1.66755			−0.833776	−	0.552103i	$-0.813826\pi$
$479$	−36.4962			−1.66755			−0.833776	+	0.552103i	$0.813826\pi$
$480$		0			0
$481$			20.1903i			0.920597i
$482$	−8.51167	−	14.7426i	−0.387696	−	0.671509i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	13.6208	+	7.86396i	0.618488	+	0.357084i
$486$		0			0
$487$	−14.1066	−	24.4334i	−0.639231	−	1.10718i	−0.985602	−	0.169083i	$-0.945919\pi$
$487$	−14.1066	−	24.4334i	−0.639231	−	1.10718i	0.346371	−	0.938098i	$-0.387414\pi$
$488$	−2.95680	−	5.12132i	−0.133848	−	0.231831i
$489$		0			0
$490$	−7.86396	+	28.1946i	−0.355258	+	1.27370i
$491$	−17.2950	+	9.98528i	−0.780513	+	0.450629i	−0.836612	−	0.547796i	$-0.815467\pi$
$491$	−17.2950	+	9.98528i	−0.780513	+	0.450629i	0.0560990	+	0.998425i	$0.482134\pi$
$492$		0			0
$493$			1.26080i			0.0567835i
$494$	2.15232	−	1.24264i	0.0968373	−	0.0559090i
$495$		0			0
$496$			5.61642i			0.252185i
$497$	25.0892	−	10.2426i	1.12541	−	0.459445i
$498$		0			0
$499$	−35.9411			−1.60895			−0.804473	−	0.593989i	$-0.797552\pi$
$499$	−35.9411			−1.60895			−0.804473	+	0.593989i	$0.797552\pi$
$500$	−15.6500	+	27.1066i	−0.699889	+	1.21224i
$501$		0			0
$502$	15.2574	−	8.80884i	0.680969	−	0.393158i
$503$	3.29002			0.146695			0.0733474	−	0.997306i	$-0.476632\pi$
$503$	3.29002			0.146695			0.0733474	+	0.997306i	$0.476632\pi$
$504$		0			0
$505$		0			0
$506$	−11.0227	+	6.36396i	−0.490019	+	0.282913i
$507$		0			0
$508$	−2.62132	+	4.54026i	−0.116302	+	0.201441i
$509$	−41.6923			−1.84798			−0.923990	−	0.382418i	$-0.875092\pi$
$509$	−41.6923			−1.84798			−0.923990	+	0.382418i	$0.875092\pi$
$510$		0			0
$511$	−17.4853	−	13.5592i	−0.773503	−	0.599825i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−21.7279	+	12.5446i	−0.958378	+	0.553320i
$515$		−	63.9411i		−	2.81758i
$516$		0			0
$517$	−2.63604	+	1.52192i	−0.115933	+	0.0669339i
$518$	−20.1903	+	8.24264i	−0.887109	+	0.362161i
$519$		0			0
$520$	−5.12132	−	8.87039i	−0.224585	−	0.388992i
$521$	10.0081	+	17.3345i	0.438462	+	0.759439i	0.997571	−	0.0696551i	$-0.0221899\pi$
$521$	10.0081	+	17.3345i	0.438462	+	0.759439i	−0.559109	+	0.829094i	$0.688857\pi$
$522$		0			0
$523$	−23.8492	−	13.7694i	−1.04285	−	0.602092i	−0.122214	−	0.992504i	$-0.538999\pi$
$523$	−23.8492	−	13.7694i	−1.04285	−	0.602092i	−0.920641	+	0.390411i	$0.872333\pi$
$524$	2.59808	−	4.50000i	0.113497	−	0.196583i
$525$		0			0
$526$	13.6066	+	23.5673i	0.593276	+	1.02758i
$527$			5.69848i			0.248230i
$528$		0			0
$529$	5.00000			0.217391
$530$	2.59808	−	4.50000i	0.112853	−	0.195468i
$531$		0			0
$532$	2.12132	+	1.64501i	0.0919709	+	0.0713203i
$533$	−4.30463	−	2.48528i	−0.186454	−	0.107649i
$534$		0			0
$535$	−19.8640	−	11.4685i	−0.858794	−	0.495825i
$536$	8.66025	+	5.00000i	0.374066	+	0.215967i
$537$		0			0
$538$	−9.10660	−	5.25770i	−0.392613	−	0.226675i
$539$	14.6969	+	15.0000i	0.633042	+	0.646096i
$540$		0			0
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	−0.727374	−	0.686241i	$-0.759260\pi$
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	0.957989	+	0.286804i	$0.0925930\pi$
$542$	11.1097			0.477204
$543$		0			0
$544$		−	1.01461i		−	0.0435011i
$545$	3.16693	+	5.48528i	0.135656	+	0.234964i
$546$		0			0
$547$	−9.84924	+	17.0594i	−0.421123	+	0.729407i	−0.996050	−	0.0887983i	$-0.971697\pi$
$547$	−9.84924	+	17.0594i	−0.421123	+	0.729407i	0.574926	+	0.818205i	$0.305031\pi$
$548$	12.5446	+	7.24264i	0.535880	+	0.309390i
$549$		0			0
$550$	18.7279	+	32.4377i	0.798561	+	1.38315i
$551$	0.630399	+	1.09188i	0.0268559	+	0.0465158i
$552$		0			0
$553$	18.2279	−	23.5058i	0.775130	−	0.999567i
$554$	18.1610	−	10.4853i	0.771589	−	0.445477i
$555$		0			0
$556$			20.1903i			0.856258i
$557$	−13.6208	+	7.86396i	−0.577131	+	0.333207i	−0.759992	−	0.649932i	$-0.774797\pi$
$557$	−13.6208	+	7.86396i	−0.577131	+	0.333207i	0.182861	+	0.983139i	$0.441464\pi$
$558$		0			0
$559$			20.1903i			0.853957i
$560$	6.77962	−	8.74264i	0.286491	−	0.369444i
$561$		0			0
$562$	−6.00000			−0.253095
$563$	−12.0989	+	20.9558i	−0.509906	+	0.883184i	0.490028	+	0.871707i	$0.336987\pi$
$563$	−12.0989	+	20.9558i	−0.509906	+	0.883184i	−0.999934	+	0.0114768i	$0.996347\pi$
$564$		0			0
$565$	−30.7279	+	17.7408i	−1.29273	+	0.746360i
$566$	−6.50794			−0.273549
$567$		0			0
$568$	−10.2426			−0.429772
$569$	1.52192	−	0.878680i	0.0638021	−	0.0368362i	−0.467760	−	0.883856i	$-0.654939\pi$
$569$	1.52192	−	0.878680i	0.0638021	−	0.0368362i	0.531562	+	0.847020i	$0.321605\pi$
$570$		0			0
$571$	8.36396	−	14.4868i	0.350021	−	0.606254i	−0.636232	−	0.771498i	$-0.719508\pi$
$571$	8.36396	−	14.4868i	0.350021	−	0.606254i	0.986253	+	0.165244i	$0.0528412\pi$
$572$	−7.34847			−0.307255
$573$		0			0
$574$	0.727922	−	5.31925i	0.0303829	−	0.222021i
$575$			52.9706i			2.20903i
$576$		0			0
$577$	17.7426	−	10.2437i	0.738636	−	0.426452i	−0.0829373	−	0.996555i	$-0.526430\pi$
$577$	17.7426	−	10.2437i	0.738636	−	0.426452i	0.821573	+	0.570103i	$0.193097\pi$
$578$			15.9706i			0.664288i
$579$		0			0
$580$	4.50000	−	2.59808i	0.186852	−	0.107879i
$581$	−8.30153	−	1.13604i	−0.344406	−	0.0471308i
$582$		0			0
$583$	−1.86396	−	3.22848i	−0.0771974	−	0.133710i
$584$	4.18154	+	7.24264i	0.173033	+	0.299703i
$585$		0			0
$586$	3.62132	+	2.09077i	0.149595	+	0.0863689i
$587$	−2.59808	+	4.50000i	−0.107234	+	0.185735i	−0.914649	−	0.404249i	$-0.867533\pi$
$587$	−2.59808	+	4.50000i	−0.107234	+	0.185735i	0.807415	+	0.589984i	$0.200866\pi$
$588$		0			0
$589$	2.84924	+	4.93503i	0.117401	+	0.203344i
$590$			48.2132i			1.98491i
$591$		0			0
$592$	8.24264			0.338770
$593$	15.2042	−	26.3345i	0.624363	−	1.08143i	−0.364300	−	0.931282i	$-0.618692\pi$
$593$	15.2042	−	26.3345i	0.624363	−	1.08143i	0.988664	−	0.150148i	$-0.0479749\pi$
$594$		0			0
$595$	6.87868	−	8.87039i	0.281998	−	0.363650i
$596$	17.7408	+	10.2426i	0.726690	+	0.419555i
$597$		0			0
$598$	−9.00000	−	5.19615i	−0.368037	−	0.212486i
$599$	−37.6339	−	21.7279i	−1.53768	−	0.887779i	−0.998974	−	0.0452836i	$-0.985581\pi$
$599$	−37.6339	−	21.7279i	−1.53768	−	0.887779i	−0.538704	−	0.842495i	$-0.681086\pi$
$600$		0			0
$601$	5.22792	+	3.01834i	0.213251	+	0.123121i	0.602822	−	0.797876i	$-0.294043\pi$
$601$	5.22792	+	3.01834i	0.213251	+	0.123121i	−0.389570	+	0.920997i	$0.627376\pi$
$602$	−20.1903	+	8.24264i	−0.822894	+	0.335945i
$603$		0			0
$604$	−1.62132	+	2.80821i	−0.0659706	+	0.114264i
$605$	−8.36308			−0.340008
$606$		0			0
$607$			24.9662i			1.01334i	0.862139	+	0.506672i	$0.169125\pi$
$607$			24.9662i			1.01334i	−0.862139	+	0.506672i	$0.830875\pi$
$608$	−0.507306	−	0.878680i	−0.0205740	−	0.0356352i
$609$		0			0
$610$	−12.3640	+	21.4150i	−0.500602	+	0.867068i
$611$	−2.15232	−	1.24264i	−0.0870734	−	0.0502719i
$612$		0			0
$613$	−2.60660	−	4.51477i	−0.105280	−	0.182350i	0.808573	−	0.588396i	$-0.200240\pi$
$613$	−2.60660	−	4.51477i	−0.105280	−	0.182350i	−0.913852	+	0.406046i	$0.866907\pi$
$614$	12.3345	+	21.3640i	0.497779	+	0.862179i
$615$		0			0
$616$	−3.00000	−	7.34847i	−0.120873	−	0.296078i
$617$	−36.1119	+	20.8492i	−1.45381	+	0.839359i	−0.998695	−	0.0510726i	$-0.983736\pi$
$617$	−36.1119	+	20.8492i	−1.45381	+	0.839359i	−0.455117	+	0.890431i	$0.650403\pi$
$618$		0			0
$619$		−	47.7290i		−	1.91839i	−0.282745	−	0.959195i	$-0.591245\pi$
$619$		−	47.7290i		−	1.91839i	0.282745	−	0.959195i	$-0.408755\pi$
$620$	20.3389	−	11.7426i	0.816828	−	0.471596i
$621$		0			0
$622$		−	18.7554i		−	0.752022i
$623$	−27.2416	−	3.72792i	−1.09141	−	0.149356i
$624$		0			0
$625$	68.4558			2.73823
$626$	−0.568852	+	0.985281i	−0.0227359	+	0.0393798i
$627$		0			0
$628$	12.7279	−	7.34847i	0.507899	−	0.293236i
$629$	8.36308			0.333458
$630$		0			0
$631$	33.2426			1.32337			0.661684	−	0.749783i	$-0.269842\pi$
$631$	33.2426			1.32337			0.661684	+	0.749783i	$0.269842\pi$
$632$	−9.73641	+	5.62132i	−0.387294	+	0.223604i
$633$		0			0
$634$	−3.62132	+	6.27231i	−0.143821	+	0.249105i
$635$	21.9223			0.869961
$636$		0			0
$637$	−4.60660	+	16.5160i	−0.182520	+	0.654389i
$638$		−	3.72792i		−	0.147590i
$639$		0			0
$640$	−3.62132	+	2.09077i	−0.143145	+	0.0826450i
$641$			41.6985i			1.64699i	0.567323	+	0.823496i	$0.307979\pi$
$641$			41.6985i			1.64699i	−0.567323	+	0.823496i	$0.692021\pi$
$642$		0			0
$643$	2.27208	−	1.31178i	0.0896020	−	0.0517317i	−0.454530	−	0.890732i	$-0.650193\pi$
$643$	2.27208	−	1.31178i	0.0896020	−	0.0517317i	0.544132	+	0.839000i	$0.316859\pi$
$644$	1.52192	−	11.1213i	0.0599720	−	0.438241i
$645$		0			0
$646$	−0.514719	−	0.891519i	−0.0202513	−	0.0350763i
$647$	5.82655	+	10.0919i	0.229065	+	0.396753i	0.957531	−	0.288329i	$-0.0930997\pi$
$647$	5.82655	+	10.0919i	0.229065	+	0.396753i	−0.728466	+	0.685082i	$0.759766\pi$
$648$		0			0
$649$	29.9558	+	17.2950i	1.17587	+	0.678889i
$650$	−15.2913	+	26.4853i	−0.599774	+	1.03884i
$651$		0			0
$652$	3.12132	+	5.40629i	0.122240	+	0.211726i
$653$		−	10.7574i		−	0.420968i	−0.977597	−	0.210484i	$-0.932496\pi$
$653$		−	10.7574i		−	0.420968i	0.977597	−	0.210484i	$-0.0675040\pi$
$654$		0			0
$655$	−21.7279			−0.848980
$656$	−1.01461	+	1.75736i	−0.0396139	+	0.0686134i
$657$		0			0
$658$	0.363961	−	2.65962i	0.0141887	−	0.103683i
$659$	5.19615	+	3.00000i	0.202413	+	0.116863i	0.597781	−	0.801660i	$-0.296049\pi$
$659$	5.19615	+	3.00000i	0.202413	+	0.116863i	−0.395367	+	0.918523i	$0.629383\pi$
$660$		0			0
$661$	−35.1213	−	20.2773i	−1.36606	−	0.788696i	−0.375639	−	0.926766i	$-0.622577\pi$
$661$	−35.1213	−	20.2773i	−1.36606	−	0.788696i	−0.990422	+	0.138071i	$0.955910\pi$
$662$	15.1172	+	8.72792i	0.587547	+	0.339220i
$663$		0			0
$664$	2.74264	+	1.58346i	0.106435	+	0.0614503i
$665$	1.52192	−	11.1213i	0.0590174	−	0.431266i
$666$		0			0
$667$	2.63604	−	4.56575i	0.102068	−	0.176787i
$668$	−23.0600			−0.892219
$669$		0			0
$670$		−	41.8154i		−	1.61547i
$671$	8.87039	+	15.3640i	0.342437	+	0.593119i
$672$		0			0
$673$	7.98528	−	13.8309i	0.307810	−	0.533143i	−0.670073	−	0.742295i	$-0.733737\pi$
$673$	7.98528	−	13.8309i	0.307810	−	0.533143i	0.977883	+	0.209153i	$0.0670706\pi$
$674$	−4.33013	−	2.50000i	−0.166790	−	0.0962964i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	−6.27231	−	10.8640i	−0.241064	−	0.417536i	0.719953	−	0.694023i	$-0.244163\pi$
$677$	−6.27231	−	10.8640i	−0.241064	−	0.417536i	−0.961018	+	0.276487i	$0.910830\pi$
$678$		0			0
$679$	−1.34924	+	9.85951i	−0.0517792	+	0.378373i
$680$	−3.67423	+	2.12132i	−0.140900	+	0.0813489i
$681$		0			0
$682$		−	16.8493i		−	0.645191i
$683$	22.4912	−	12.9853i	0.860601	−	0.496868i	−0.00361277	−	0.999993i	$-0.501150\pi$
$683$	22.4912	−	12.9853i	0.860601	−	0.496868i	0.864213	+	0.503125i	$0.167817\pi$
$684$		0			0
$685$		−	60.5708i		−	2.31429i
$686$	−18.3967	+	2.13604i	−0.702388	+	0.0815543i
$687$		0			0
$688$	8.24264			0.314248
$689$	1.52192	−	2.63604i	0.0579805	−	0.100425i
$690$		0			0
$691$	0.727922	−	0.420266i	0.0276915	−	0.0159877i	−0.486090	−	0.873909i	$-0.661577\pi$
$691$	0.727922	−	0.420266i	0.0276915	−	0.0159877i	0.513782	+	0.857921i	$0.328244\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	−14.4853			−0.549854
$695$	73.1154	−	42.2132i	2.77343	−	1.60124i
$696$		0			0
$697$	−1.02944	+	1.78304i	−0.0389927	+	0.0675374i
$698$	36.9164			1.39731
$699$		0			0
$700$	−32.7279	−	4.47871i	−1.23700	−	0.169279i
$701$			38.6985i			1.46162i	0.682580	+	0.730811i	$0.260858\pi$
$701$			38.6985i			1.46162i	−0.682580	+	0.730811i	$0.739142\pi$
$702$		0			0
$703$	7.24264	−	4.18154i	0.273161	−	0.157710i
$704$			3.00000i			0.113067i
$705$		0			0
$706$	−16.2426	+	9.37769i	−0.611300	+	0.352934i
$707$		0			0
$708$		0			0
$709$	3.48528	+	6.03668i	0.130892	+	0.226712i	0.924021	−	0.382342i	$-0.124882\pi$
$709$	3.48528	+	6.03668i	0.130892	+	0.226712i	−0.793128	+	0.609055i	$0.791549\pi$
$710$	21.4150	+	37.0919i	0.803691	+	1.39203i
$711$		0			0
$712$	9.00000	+	5.19615i	0.337289	+	0.194734i
$713$	11.9142	−	20.6360i	0.446191	−	0.772826i
$714$		0			0
$715$	15.3640	+	26.6112i	0.574580	+	0.995201i
$716$		−	9.51472i		−	0.355582i
$717$		0			0
$718$	18.0000			0.671754
$719$	11.5300	−	19.9706i	0.429997	−	0.744776i	−0.566876	−	0.823803i	$-0.691848\pi$
$719$	11.5300	−	19.9706i	0.429997	−	0.744776i	0.996872	+	0.0790270i	$0.0251813\pi$
$720$		0			0
$721$	37.4558	−	15.2913i	1.39493	−	0.569477i
$722$	15.5630	+	8.98528i	0.579194	+	0.334398i
$723$		0			0
$724$	1.75736	+	1.01461i	0.0653117	+	0.0377078i
$725$	−13.4361	−	7.75736i	−0.499006	−	0.288101i
$726$		0			0
$727$	22.8640	+	13.2005i	0.847977	+	0.489580i	0.859968	−	0.510348i	$-0.170483\pi$
$727$	22.8640	+	13.2005i	0.847977	+	0.489580i	−0.0119905	+	0.999928i	$0.503817\pi$
$728$	3.97141	−	5.12132i	0.147190	−	0.189809i
$729$		0			0
$730$	17.4853	−	30.2854i	0.647159	−	1.12091i
$731$	8.36308			0.309320
$732$		0			0
$733$			39.3659i			1.45401i	0.686630	+	0.727007i	$0.259089\pi$
$733$			39.3659i			1.45401i	−0.686630	+	0.727007i	$0.740911\pi$
$734$	−9.43924	−	16.3492i	−0.348409	−	0.603462i
$735$		0			0
$736$	−2.12132	+	3.67423i	−0.0781929	+	0.135434i
$737$	−25.9808	−	15.0000i	−0.957014	−	0.552532i
$738$		0			0
$739$	17.7279	+	30.7057i	0.652132	+	1.12953i	0.982605	+	0.185710i	$0.0594586\pi$
$739$	17.7279	+	30.7057i	0.652132	+	1.12953i	−0.330472	+	0.943816i	$0.607208\pi$
$740$	−17.2335	−	29.8492i	−0.633515	−	1.09728i
$741$		0			0
$742$	3.25736	+	0.445759i	0.119581	+	0.0163643i
$743$	−18.6323	+	10.7574i	−0.683553	+	0.394649i	−0.801192	−	0.598407i	$-0.795801\pi$
$743$	−18.6323	+	10.7574i	−0.683553	+	0.394649i	0.117640	+	0.993056i	$0.462467\pi$
$744$		0			0
$745$		−	85.6600i		−	3.13834i
$746$	−18.5813	+	10.7279i	−0.680310	+	0.392777i
$747$		0			0
$748$			3.04384i			0.111294i
$749$	1.96768	−	14.3787i	0.0718974	−	0.525386i
$750$		0			0
$751$	26.7574			0.976390			0.488195	−	0.872735i	$-0.337655\pi$
$751$	26.7574			0.976390			0.488195	+	0.872735i	$0.337655\pi$
$752$	−0.507306	+	0.878680i	−0.0184995	+	0.0320422i
$753$		0			0
$754$	2.63604	−	1.52192i	0.0959989	−	0.0554250i
$755$	13.5592			0.493471
$756$		0			0
$757$	−42.2426			−1.53533			−0.767667	−	0.640848i	$-0.778583\pi$
$757$	−42.2426			−1.53533			−0.767667	+	0.640848i	$0.778583\pi$
$758$	3.88437	−	2.24264i	0.141087	−	0.0814564i
$759$		0			0
$760$	−2.12132	+	3.67423i	−0.0769484	+	0.133278i
$761$	5.07306			0.183898			0.0919491	−	0.995764i	$-0.470690\pi$
$761$	5.07306			0.183898			0.0919491	+	0.995764i	$0.470690\pi$
$762$		0			0
$763$	−2.45584	+	3.16693i	−0.0889075	+	0.114651i
$764$		−	8.48528i		−	0.306987i
$765$		0			0
$766$	−10.7574	+	6.21076i	−0.388679	+	0.224404i
$767$			28.2426i			1.01978i
$768$		0			0
$769$	42.4706	−	24.5204i	1.53153	−	0.884228i	0.532236	−	0.846596i	$-0.321352\pi$
$769$	42.4706	−	24.5204i	1.53153	−	0.884228i	0.999292	−	0.0376319i	$-0.0119814\pi$
$770$	−20.3389	+	26.2279i	−0.732961	+	0.945189i
$771$		0			0
$772$	−3.74264	−	6.48244i	−0.134701	−	0.233308i
$773$	−11.5300	−	19.9706i	−0.414706	−	0.718291i	0.580692	−	0.814123i	$-0.302782\pi$
$773$	−11.5300	−	19.9706i	−0.414706	−	0.718291i	−0.995398	+	0.0958322i	$0.969449\pi$
$774$		0			0
$775$	−60.7279	−	35.0613i	−2.18141	−	1.25944i
$776$	1.88064	−	3.25736i	0.0675109	−	0.116932i
$777$		0			0
$778$	−9.72792	−	16.8493i	−0.348763	−	0.604075i
$779$			2.05887i			0.0737668i
$780$		0			0
$781$	30.7279			1.09953
$782$	−2.15232	+	3.72792i	−0.0769667	+	0.133310i
$783$		0			0
$784$	6.74264	+	1.88064i	0.240809	+	0.0671656i
$785$	−53.2223	−	30.7279i	−1.89959	−	1.09673i
$786$		0			0
$787$	−32.1213	−	18.5453i	−1.14500	−	0.661067i	−0.197337	−	0.980336i	$-0.563229\pi$
$787$	−32.1213	−	18.5453i	−1.14500	−	0.661067i	−0.947664	+	0.319269i	$0.896563\pi$
$788$	8.23999	+	4.75736i	0.293537	+	0.169474i
$789$		0			0
$790$	40.7132	+	23.5058i	1.44851	+	0.836298i
$791$	−17.7408	−	13.7574i	−0.630789	−	0.489155i
$792$		0			0
$793$	−7.24264	+	12.5446i	−0.257194	+	0.445473i
$794$	−13.8564			−0.491745
$795$		0			0
$796$			16.1318i			0.571777i
$797$	18.8169	+	32.5919i	0.666530	+	1.15446i	0.978868	+	0.204493i	$0.0655545\pi$
$797$	18.8169	+	32.5919i	0.666530	+	1.15446i	−0.312338	+	0.949971i	$0.601112\pi$
$798$		0			0
$799$	−0.514719	+	0.891519i	−0.0182094	+	0.0315397i
$800$	10.8126	+	6.24264i	0.382282	+	0.220711i
$801$		0			0
$802$		0			0
$803$	−12.5446	−	21.7279i	−0.442690	−	0.766762i
$804$		0			0
$805$	−43.4558	+	17.7408i	−1.53162	+	0.625280i
$806$	11.9142	−	6.87868i	0.419661	−	0.242291i
$807$		0			0
$808$		0			0
$809$	−35.4815	+	20.4853i	−1.24746	+	0.720224i	−0.970603	−	0.240686i	$-0.922628\pi$
$809$	−35.4815	+	20.4853i	−1.24746	+	0.720224i	−0.276862	+	0.960910i	$0.589294\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	2.59808	+	2.01472i	0.0911746	+	0.0707028i
$813$		0			0
$814$	−24.7279			−0.866713
$815$	13.0519	−	22.6066i	0.457189	−	0.791875i
$816$		0			0
$817$	7.24264	−	4.18154i	0.253388	−	0.146294i
$818$	−4.60181			−0.160898
$819$		0			0
$820$	8.48528			0.296319
$821$	−42.6454	+	24.6213i	−1.48833	+	0.859290i	−0.999911	−	0.0133172i	$-0.995761\pi$
$821$	−42.6454	+	24.6213i	−1.48833	+	0.859290i	−0.488423	+	0.872607i	$0.662428\pi$
$822$		0			0
$823$	18.9706	−	32.8580i	0.661272	−	1.14536i	−0.319009	−	0.947752i	$-0.603350\pi$
$823$	18.9706	−	32.8580i	0.661272	−	1.14536i	0.980282	−	0.197606i	$-0.0633165\pi$
$824$	−15.2913			−0.532697
$825$		0			0
$826$	−28.2426	+	11.5300i	−0.982687	+	0.401180i
$827$		−	4.02944i		−	0.140117i	−0.997543	−	0.0700586i	$-0.977681\pi$
$827$		−	4.02944i		−	0.140117i	0.997543	−	0.0700586i	$-0.0223186\pi$
$828$		0			0
$829$	−35.3345	+	20.4004i	−1.22722	+	0.708535i	−0.966447	−	0.256865i	$-0.917310\pi$
$829$	−35.3345	+	20.4004i	−1.22722	+	0.708535i	−0.260772	+	0.965401i	$0.583977\pi$
$830$		−	13.2426i		−	0.459659i
$831$		0			0
$832$	−2.12132	+	1.22474i	−0.0735436	+	0.0424604i
$833$	6.84116	+	1.90812i	0.237032	+	0.0661123i
$834$		0			0
$835$	48.2132	+	83.5077i	1.66849	+	2.88990i
$836$	1.52192	+	2.63604i	0.0526366	+	0.0911693i
$837$		0			0
$838$	3.51472	+	2.02922i	0.121414	+	0.0700984i
$839$	12.0373	−	20.8492i	0.415574	−	0.719796i	−0.579914	−	0.814678i	$-0.696914\pi$
$839$	12.0373	−	20.8492i	0.415574	−	0.719796i	0.995489	+	0.0948817i	$0.0302473\pi$
$840$		0			0
$841$	−13.7279	−	23.7775i	−0.473377	−	0.819912i
$842$			5.75736i			0.198412i
$843$		0			0
$844$	−8.24264			−0.283723
$845$	14.6354	−	25.3492i	0.503473	−	0.872040i
$846$		0			0
$847$	−2.00000	−	4.89898i	−0.0687208	−	0.168331i
$848$	−1.07616	−	0.621320i	−0.0369554	−	0.0213362i
$849$		0			0
$850$	10.9706	+	6.33386i	0.376287	+	0.217250i
$851$	−30.2854	−	17.4853i	−1.03817	−	0.599388i
$852$		0			0
$853$	1.97056	+	1.13770i	0.0674708	+	0.0389543i	0.533356	−	0.845891i	$-0.320931\pi$
$853$	1.97056	+	1.13770i	0.0674708	+	0.0389543i	−0.465885	+	0.884845i	$0.654264\pi$
$854$	−15.5014	−	2.12132i	−0.530448	−	0.0725901i
$855$		0			0
$856$	−2.74264	+	4.75039i	−0.0937415	+	0.162365i
$857$	20.0162			0.683740			0.341870	−	0.939747i	$-0.388940\pi$
$857$	20.0162			0.683740			0.341870	+	0.939747i	$0.388940\pi$
$858$		0			0
$859$		−	4.47871i		−	0.152812i	−0.997077	−	0.0764059i	$-0.975656\pi$
$859$		−	4.47871i		−	0.152812i	0.997077	−	0.0764059i	$-0.0243445\pi$
$860$	−17.2335	−	29.8492i	−0.587656	−	1.01785i
$861$		0			0
$862$	10.2426	−	17.7408i	0.348866	−	0.604253i
$863$	43.7215	+	25.2426i	1.48830	+	0.859269i	0.999911	−	0.0133573i	$-0.00425189\pi$
$863$	43.7215	+	25.2426i	1.48830	+	0.859269i	0.488388	+	0.872627i	$0.337585\pi$
$864$		0			0
$865$	43.4558	+	75.2677i	1.47754	+	2.55918i
$866$	1.73205	+	3.00000i	0.0588575	+	0.101944i
$867$		0			0
$868$	11.7426	+	9.10601i	0.398571	+	0.309078i
$869$	29.2092	−	16.8640i	0.990856	−	0.572071i
$870$		0			0
$871$		−	24.4949i		−	0.829978i
$872$	1.31178	−	0.757359i	0.0444226	−	0.0256474i
$873$		0			0
$874$			4.30463i			0.145606i
$875$	31.3000	+	76.6690i	1.05813	+	2.59189i
$876$		0			0
$877$	−12.4853			−0.421598			−0.210799	−	0.977529i	$-0.567607\pi$
$877$	−12.4853			−0.421598			−0.210799	+	0.977529i	$0.567607\pi$
$878$	13.6208	−	23.5919i	0.459679	−	0.796187i
$879$		0			0
$880$	10.8640	−	6.27231i	0.366224	−	0.211440i
$881$	−39.7862			−1.34043			−0.670215	−	0.742167i	$-0.733798\pi$
$881$	−39.7862			−1.34043			−0.670215	+	0.742167i	$0.733798\pi$
$882$		0			0
$883$	−9.45584			−0.318214			−0.159107	−	0.987261i	$-0.550862\pi$
$883$	−9.45584			−0.318214			−0.159107	+	0.987261i	$0.550862\pi$
$884$	−2.15232	+	1.24264i	−0.0723902	+	0.0417945i
$885$		0			0
$886$	17.2279	−	29.8396i	0.578783	−	1.00248i
$887$	−44.8592			−1.50623			−0.753113	−	0.657891i	$-0.771449\pi$
$887$	−44.8592			−1.50623			−0.753113	+	0.657891i	$0.771449\pi$
$888$		0			0
$889$	5.24264	+	12.8418i	0.175833	+	0.430700i
$890$		−	43.4558i		−	1.45664i
$891$		0			0
$892$	10.8640	−	6.27231i	0.363752	−	0.210012i
$893$			1.02944i			0.0344488i
$894$		0			0
$895$	−34.4558	+	19.8931i	−1.15173	+	0.664953i
$896$	−2.09077	−	1.62132i	−0.0698477	−	0.0541645i
$897$		0			0
$898$	−5.12132	−	8.87039i	−0.170901	−	0.296009i
$899$	3.48960	+	6.04416i	0.116385	+	0.201584i
$900$		0			0
$901$	−1.09188	−	0.630399i	−0.0363759	−	0.0210016i
$902$	3.04384	−	5.27208i	0.101349	−	0.175541i
$903$		0			0
$904$	4.24264	+	7.34847i	0.141108	+	0.244406i
$905$		−	8.48528i		−	0.282060i
$906$		0			0
$907$	27.6985			0.919713			0.459857	−	0.887993i	$-0.347901\pi$
$907$	27.6985			0.919713			0.459857	+	0.887993i	$0.347901\pi$
$908$	−7.79423	+	13.5000i	−0.258661	+	0.448013i
$909$		0			0
$910$	−26.8492	−	3.67423i	−0.890044	−	0.121800i
$911$	16.2189	+	9.36396i	0.537355	+	0.310242i	0.744006	−	0.668173i	$-0.232923\pi$
$911$	16.2189	+	9.36396i	0.537355	+	0.310242i	−0.206651	+	0.978415i	$0.566257\pi$
$912$		0			0
$913$	−8.22792	−	4.75039i	−0.272304	−	0.157215i
$914$	−19.9186	−	11.5000i	−0.658848	−	0.380386i
$915$		0			0
$916$	12.0000	+	6.92820i	0.396491	+	0.228914i
$917$	−5.19615	−	12.7279i	−0.171592	−	0.420313i
$918$		0			0
$919$	−9.75736	+	16.9002i	−0.321866	+	0.557488i	−0.980873	−	0.194649i	$-0.937643\pi$
$919$	−9.75736	+	16.9002i	−0.321866	+	0.557488i	0.659007	+	0.752136i	$0.270977\pi$
$920$	17.7408			0.584896
$921$		0			0
$922$		−	22.8138i		−	0.751334i
$923$	12.5446	+	21.7279i	0.412911	+	0.715183i
$924$		0			0
$925$	−51.4558	+	89.1241i	−1.69186	+	2.93038i
$926$	18.5813	+	10.7279i	0.610620	+	0.352541i
$927$		0			0
$928$	−0.621320	−	1.07616i	−0.0203958	−	0.0353266i
$929$	1.64501	+	2.84924i	0.0539711	+	0.0934806i	0.891749	−	0.452531i	$-0.149479\pi$
$929$	1.64501	+	2.84924i	0.0539711	+	0.0934806i	−0.837778	+	0.546012i	$0.816145\pi$
$930$		0			0
$931$	6.87868	−	1.76810i	0.225440	−	0.0579473i
$932$	−5.82655	+	3.36396i	−0.190855	+	0.110190i
$933$		0			0
$934$		−	19.0016i		−	0.621750i
$935$	11.0227	−	6.36396i	0.360481	−	0.208124i
$936$		0			0
$937$			4.00746i			0.130918i	0.997855	+	0.0654590i	$0.0208512\pi$
$937$			4.00746i			0.130918i	−0.997855	+	0.0654590i	$0.979149\pi$
$938$	24.4949	−	10.0000i	0.799787	−	0.326512i
$939$		0			0
$940$	4.24264			0.138380
$941$	26.0423	−	45.1066i	0.848955	−	1.47043i	−0.0331867	−	0.999449i	$-0.510566\pi$
$941$	26.0423	−	45.1066i	0.848955	−	1.47043i	0.882142	−	0.470984i	$-0.156101\pi$
$942$		0			0
$943$	7.45584	−	4.30463i	0.242796	−	0.140178i
$944$	11.5300			0.375270
$945$		0			0
$946$	−24.7279			−0.803974
$947$	−19.8931	+	11.4853i	−0.646439	+	0.373221i	−0.787090	−	0.616838i	$-0.788414\pi$
$947$	−19.8931	+	11.4853i	−0.646439	+	0.373221i	0.140652	+	0.990059i	$0.455080\pi$
$948$		0			0
$949$	10.2426	−	17.7408i	0.332490	−	0.575890i
$950$	12.6677			0.410995
$951$		0			0
$952$	−2.12132	−	1.64501i	−0.0687524	−	0.0533151i
$953$		−	41.6985i		−	1.35075i	−0.737476	−	0.675373i	$-0.763983\pi$
$953$		−	41.6985i		−	1.35075i	0.737476	−	0.675373i	$-0.236017\pi$
$954$		0			0
$955$	−30.7279	+	17.7408i	−0.994332	+	0.574078i
$956$		−	12.7279i		−	0.411650i
$957$		0			0
$958$	31.6066	−	18.2481i	1.02116	−	0.589569i
$959$	35.4815	−	14.4853i	1.14576	−	0.467754i
$960$		0			0
$961$	0.272078	+	0.471253i	0.00877671	+	0.0152017i
$962$	−10.0951	−	17.4853i	−0.325480	−	0.563748i
$963$		0			0
$964$	14.7426	+	8.51167i	0.474828	+	0.274142i
$965$	−15.6500	+	27.1066i	−0.503791	+	0.872592i
$966$		0			0
$967$	−11.1360	−	19.2882i	−0.358111	−	0.620266i	0.629534	−	0.776973i	$-0.283246\pi$
$967$	−11.1360	−	19.2882i	−0.358111	−	0.620266i	−0.987645	+	0.156706i	$0.949912\pi$
$968$			2.00000i			0.0642824i
$969$		0			0
$970$	−15.7279			−0.504993
$971$	−25.6581	+	44.4411i	−0.823407	+	1.42618i	0.0797229	+	0.996817i	$0.474596\pi$
$971$	−25.6581	+	44.4411i	−0.823407	+	1.42618i	−0.903130	+	0.429367i	$0.858737\pi$
$972$		0			0
$973$	42.2132	+	32.7349i	1.35329	+	1.04943i
$974$	24.4334	+	14.1066i	0.782895	+	0.452005i
$975$		0			0
$976$	5.12132	+	2.95680i	0.163929	+	0.0946447i
$977$	27.5027	+	15.8787i	0.879889	+	0.508004i	0.870622	−	0.491953i	$-0.163717\pi$
$977$	27.5027	+	15.8787i	0.879889	+	0.508004i	0.00926698	+	0.999957i	$0.497050\pi$
$978$		0			0
$979$	−27.0000	−	15.5885i	−0.862924	−	0.498209i
$980$	−7.28692	−	28.3492i	−0.232772	−	0.905583i
$981$		0			0
$982$	9.98528	−	17.2950i	0.318643	−	0.551906i
$983$	8.11689			0.258889			0.129444	−	0.991587i	$-0.458681\pi$
$983$	8.11689			0.258889			0.129444	+	0.991587i	$0.458681\pi$
$984$		0			0
$985$		−	39.7862i		−	1.26769i
$986$	−0.630399	−	1.09188i	−0.0200760	−	0.0347726i
$987$		0			0
$988$	−1.24264	+	2.15232i	−0.0395337	+	0.0684743i
$989$	−30.2854	−	17.4853i	−0.963020	−	0.556000i
$990$		0			0
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	0.777777	−	0.628541i	$-0.216347\pi$
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	−0.933221	+	0.359304i	$0.883014\pi$
$992$	−2.80821	−	4.86396i	−0.0891607	−	0.154431i
$993$		0			0
$994$	−16.6066	+	21.4150i	−0.526729	+	0.679243i
$995$	58.4185	−	33.7279i	1.85199	−	1.06925i
$996$		0			0
$997$		−	9.55177i		−	0.302508i	−0.988495	−	0.151254i	$-0.951669\pi$
$997$		−	9.55177i		−	0.302508i	0.988495	−	0.151254i	$-0.0483311\pi$
$998$	31.1259	−	17.9706i	0.985274	−	0.568848i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.t.e.593.1		8
3.2	odd	2	inner	1134.2.t.e.593.4		8
7.3	odd	6		1134.2.l.f.269.1		8
9.2	odd	6		126.2.k.a.89.1	yes	8
9.4	even	3		1134.2.l.f.215.2		8
9.5	odd	6		1134.2.l.f.215.3		8
9.7	even	3		126.2.k.a.89.4	yes	8
21.17	even	6		1134.2.l.f.269.4		8
36.7	odd	6		1008.2.bt.c.593.4		8
36.11	even	6		1008.2.bt.c.593.1		8
45.2	even	12		3150.2.bp.e.1349.1		8
45.7	odd	12		3150.2.bp.b.1349.1		8
45.29	odd	6		3150.2.bf.a.1601.4		8
45.34	even	6		3150.2.bf.a.1601.2		8
45.38	even	12		3150.2.bp.b.1349.4		8
45.43	odd	12		3150.2.bp.e.1349.4		8
63.2	odd	6		882.2.d.a.881.8		8
63.11	odd	6		882.2.k.a.521.3		8
63.16	even	3		882.2.d.a.881.1		8
63.20	even	6		882.2.k.a.215.2		8
63.25	even	3		882.2.k.a.521.2		8
63.31	odd	6	inner	1134.2.t.e.1025.4		8
63.34	odd	6		882.2.k.a.215.3		8
63.38	even	6		126.2.k.a.17.4	yes	8
63.47	even	6		882.2.d.a.881.5		8
63.52	odd	6		126.2.k.a.17.1	✓	8
63.59	even	6	inner	1134.2.t.e.1025.1		8
63.61	odd	6		882.2.d.a.881.4		8
252.47	odd	6		7056.2.k.f.881.1		8
252.79	odd	6		7056.2.k.f.881.2		8
252.115	even	6		1008.2.bt.c.17.1		8
252.187	even	6		7056.2.k.f.881.8		8
252.191	even	6		7056.2.k.f.881.7		8
252.227	odd	6		1008.2.bt.c.17.4		8
315.38	odd	12		3150.2.bp.b.899.1		8
315.52	even	12		3150.2.bp.b.899.4		8
315.164	even	6		3150.2.bf.a.1151.2		8
315.178	even	12		3150.2.bp.e.899.1		8
315.227	odd	12		3150.2.bp.e.899.4		8
315.304	odd	6		3150.2.bf.a.1151.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.1	✓	8	63.52	odd	6
126.2.k.a.17.4	yes	8	63.38	even	6
126.2.k.a.89.1	yes	8	9.2	odd	6
126.2.k.a.89.4	yes	8	9.7	even	3
882.2.d.a.881.1		8	63.16	even	3
882.2.d.a.881.4		8	63.61	odd	6
882.2.d.a.881.5		8	63.47	even	6
882.2.d.a.881.8		8	63.2	odd	6
882.2.k.a.215.2		8	63.20	even	6
882.2.k.a.215.3		8	63.34	odd	6
882.2.k.a.521.2		8	63.25	even	3
882.2.k.a.521.3		8	63.11	odd	6
1008.2.bt.c.17.1		8	252.115	even	6
1008.2.bt.c.17.4		8	252.227	odd	6
1008.2.bt.c.593.1		8	36.11	even	6
1008.2.bt.c.593.4		8	36.7	odd	6
1134.2.l.f.215.2		8	9.4	even	3
1134.2.l.f.215.3		8	9.5	odd	6
1134.2.l.f.269.1		8	7.3	odd	6
1134.2.l.f.269.4		8	21.17	even	6
1134.2.t.e.593.1		8	1.1	even	1	trivial
1134.2.t.e.593.4		8	3.2	odd	2	inner
1134.2.t.e.1025.1		8	63.59	even	6	inner
1134.2.t.e.1025.4		8	63.31	odd	6	inner
3150.2.bf.a.1151.2		8	315.164	even	6
3150.2.bf.a.1151.4		8	315.304	odd	6
3150.2.bf.a.1601.2		8	45.34	even	6
3150.2.bf.a.1601.4		8	45.29	odd	6
3150.2.bp.b.899.1		8	315.38	odd	12
3150.2.bp.b.899.4		8	315.52	even	12
3150.2.bp.b.1349.1		8	45.7	odd	12
3150.2.bp.b.1349.4		8	45.38	even	12
3150.2.bp.e.899.1		8	315.178	even	12
3150.2.bp.e.899.4		8	315.227	odd	12
3150.2.bp.e.1349.1		8	45.2	even	12
3150.2.bp.e.1349.4		8	45.43	odd	12
7056.2.k.f.881.1		8	252.47	odd	6
7056.2.k.f.881.2		8	252.79	odd	6
7056.2.k.f.881.7		8	252.191	even	6
7056.2.k.f.881.8		8	252.187	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -4.18154 q^{5} +(-1.00000 - 2.44949i) q^{7} +1.00000i q^{8} +(3.62132 - 2.09077i) q^{10} -3.00000i q^{11} +(2.12132 - 1.22474i) q^{13} +(2.09077 + 1.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.507306 - 0.878680i) q^{17} +(-0.878680 - 0.507306i) q^{19} +(-2.09077 + 3.62132i) q^{20} +(1.50000 + 2.59808i) q^{22} +4.24264i q^{23} +12.4853 q^{25} +(-1.22474 + 2.12132i) q^{26} +(-2.62132 - 0.358719i) q^{28} +(-1.07616 - 0.621320i) q^{29} +(-4.86396 - 2.80821i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.878680 + 0.507306i) q^{34} +(4.18154 + 10.2426i) q^{35} +(-4.12132 + 7.13834i) q^{37} +1.01461 q^{38} -4.18154i q^{40} +(-1.01461 - 1.75736i) q^{41} +(-4.12132 + 7.13834i) q^{43} +(-2.59808 - 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(-0.507306 - 0.878680i) q^{47} +(-5.00000 + 4.89898i) q^{49} +(-10.8126 + 6.24264i) q^{50} -2.44949i q^{52} +(1.07616 - 0.621320i) q^{53} +12.5446i q^{55} +(2.44949 - 1.00000i) q^{56} +1.24264 q^{58} +(-5.76500 + 9.98528i) q^{59} +(-5.12132 + 2.95680i) q^{61} +5.61642 q^{62} -1.00000 q^{64} +(-8.87039 + 5.12132i) q^{65} +(5.00000 - 8.66025i) q^{67} -1.01461 q^{68} +(-8.74264 - 6.77962i) q^{70} +10.2426i q^{71} +(7.24264 - 4.18154i) q^{73} -8.24264i q^{74} +(-0.878680 + 0.507306i) q^{76} +(-7.34847 + 3.00000i) q^{77} +(5.62132 + 9.73641i) q^{79} +(2.09077 + 3.62132i) q^{80} +(1.75736 + 1.01461i) q^{82} +(1.58346 - 2.74264i) q^{83} +(2.12132 + 3.67423i) q^{85} -8.24264i q^{86} +3.00000 q^{88} +(5.19615 - 9.00000i) q^{89} +(-5.12132 - 3.97141i) q^{91} +(3.67423 + 2.12132i) q^{92} +(0.878680 + 0.507306i) q^{94} +(3.67423 + 2.12132i) q^{95} +(-3.25736 - 1.88064i) q^{97} +(1.88064 - 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} + 12 q^{22} + 32 q^{25} - 4 q^{28} + 12 q^{31} + 24 q^{34} - 16 q^{37} - 16 q^{43} - 40 q^{49} - 24 q^{58} - 24 q^{61} - 8 q^{64} + 40 q^{67} - 36 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 + 12 * q^22 + 32 * q^25 - 4 * q^28 + 12 * q^31 + 24 * q^34 - 16 * q^37 - 16 * q^43 - 40 * q^49 - 24 * q^58 - 24 * q^61 - 8 * q^64 + 40 * q^67 - 36 * q^70 + 24 * q^73 - 24 * q^76 + 28 * q^79 + 48 * q^82 + 24 * q^88 - 24 * q^91 + 24 * q^94 - 60 * q^97

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