LMFDB - Embedded newform 1134.2.t.g.593.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(593,1134)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.1
Root			$0.500000 - 1.76390i$ of defining polynomial
Character	$\chi$	$=$	1134.593
Dual form			1134.2.t.g.1025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.50892 q^{5} +(-2.27270 + 1.35456i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.50892 q^{5} +(-2.27270 + 1.35456i) q^{7} +1.00000i q^{8} +(3.03881 - 1.75446i) q^{10} +5.45384i q^{11} +(2.18124 - 1.25934i) q^{13} +(1.29094 - 2.30943i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.852422 - 1.47644i) q^{17} +(-4.19863 - 2.42408i) q^{19} +(-1.75446 + 3.03881i) q^{20} +(-2.72692 - 4.72317i) q^{22} +5.35497i q^{23} +7.31249 q^{25} +(-1.25934 + 2.18124i) q^{26} +(0.0367291 + 2.64550i) q^{28} +(-6.16843 - 3.56135i) q^{29} +(5.25960 + 3.03663i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.47644 + 0.852422i) q^{34} +(7.97472 - 4.75303i) q^{35} +(4.14969 - 7.18748i) q^{37} +4.84816 q^{38} -3.50892i q^{40} +(-2.37578 - 4.11497i) q^{41} +(-3.22845 + 5.59184i) q^{43} +(4.72317 + 2.72692i) q^{44} +(-2.67749 - 4.63754i) q^{46} +(-4.31175 - 7.46818i) q^{47} +(3.33035 - 6.15701i) q^{49} +(-6.33280 + 3.65625i) q^{50} -2.51868i q^{52} +(10.0707 - 5.81430i) q^{53} -19.1371i q^{55} +(-1.35456 - 2.27270i) q^{56} +7.12269 q^{58} +(3.94779 - 6.83778i) q^{59} +(7.26397 - 4.19385i) q^{61} -6.07327 q^{62} -1.00000 q^{64} +(-7.65379 + 4.41892i) q^{65} +(0.895732 - 1.55145i) q^{67} -1.70484 q^{68} +(-4.52980 + 8.10360i) q^{70} +0.791392i q^{71} +(-11.5492 + 6.66795i) q^{73} +8.29939i q^{74} +(-4.19863 + 2.42408i) q^{76} +(-7.38754 - 12.3950i) q^{77} +(-2.40919 - 4.17283i) q^{79} +(1.75446 + 3.03881i) q^{80} +(4.11497 + 2.37578i) q^{82} +(0.232835 - 0.403282i) q^{83} +(2.99108 + 5.18070i) q^{85} -6.45690i q^{86} -5.45384 q^{88} +(1.09184 - 1.89113i) q^{89} +(-3.25146 + 5.81672i) q^{91} +(4.63754 + 2.67749i) q^{92} +(7.46818 + 4.31175i) q^{94} +(14.7326 + 8.50589i) q^{95} +(-4.24103 - 2.44856i) q^{97} +(0.194333 + 6.99730i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 4 * q^7	$ 16 q + 8 q^{4} - 4 q^{7} + 12 q^{13} - 12 q^{14} - 8 q^{16} + 16 q^{25} + 4 q^{28} - 48 q^{29} - 12 q^{31} + 60 q^{35} + 4 q^{37} + 24 q^{38} + 24 q^{41} + 16 q^{43} + 12 q^{44} + 16 q^{49} + 24 q^{50} - 12 q^{56} + 24 q^{58} - 24 q^{59} + 12 q^{61} - 48 q^{62} - 16 q^{64} - 48 q^{65} - 4 q^{67} + 12 q^{70} + 36 q^{73} - 36 q^{77} + 8 q^{79} + 36 q^{83} - 12 q^{85} + 24 q^{89} - 12 q^{91} - 12 q^{92} + 36 q^{94} - 12 q^{95} + 12 q^{97} + 36 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^13 - 12 * q^14 - 8 * q^16 + 16 * q^25 + 4 * q^28 - 48 * q^29 - 12 * q^31 + 60 * q^35 + 4 * q^37 + 24 * q^38 + 24 * q^41 + 16 * q^43 + 12 * q^44 + 16 * q^49 + 24 * q^50 - 12 * q^56 + 24 * q^58 - 24 * q^59 + 12 * q^61 - 48 * q^62 - 16 * q^64 - 48 * q^65 - 4 * q^67 + 12 * q^70 + 36 * q^73 - 36 * q^77 + 8 * q^79 + 36 * q^83 - 12 * q^85 + 24 * q^89 - 12 * q^91 - 12 * q^92 + 36 * q^94 - 12 * q^95 + 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

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
$5$	−3.50892			−1.56924			−0.784618	−	0.619980i	$-0.787141\pi$
$5$	−3.50892			−1.56924			−0.784618	+	0.619980i	$0.787141\pi$
$6$		0			0
$7$	−2.27270	+	1.35456i	−0.859001	+	0.511974i
$7$	−2.27270	+	1.35456i	−0.859001	+	0.511974i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	3.03881	−	1.75446i	0.960956	−	0.554808i
$11$			5.45384i			1.64440i	0.569202	+	0.822198i	$0.307252\pi$
$11$			5.45384i			1.64440i	−0.569202	+	0.822198i	$0.692748\pi$
$12$		0			0
$13$	2.18124	−	1.25934i	0.604967	−	0.349278i	−0.166026	−	0.986121i	$-0.553094\pi$
$13$	2.18124	−	1.25934i	0.604967	−	0.349278i	0.770993	+	0.636843i	$0.219760\pi$
$14$	1.29094	−	2.30943i	0.345018	−	0.617222i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.852422	−	1.47644i	−0.206743	−	0.358089i	0.743944	−	0.668242i	$-0.232953\pi$
$17$	−0.852422	−	1.47644i	−0.206743	−	0.358089i	−0.950687	+	0.310153i	$0.899620\pi$
$18$		0			0
$19$	−4.19863	−	2.42408i	−0.963231	−	0.556122i	−0.0660649	−	0.997815i	$-0.521044\pi$
$19$	−4.19863	−	2.42408i	−0.963231	−	0.556122i	−0.897166	+	0.441694i	$0.854378\pi$
$20$	−1.75446	+	3.03881i	−0.392309	+	0.679499i
$21$		0			0
$22$	−2.72692	−	4.72317i	−0.581382	−	1.00698i
$23$			5.35497i			1.11659i	0.829643	+	0.558294i	$0.188544\pi$
$23$			5.35497i			1.11659i	−0.829643	+	0.558294i	$0.811456\pi$
$24$		0			0
$25$	7.31249			1.46250
$26$	−1.25934	+	2.18124i	−0.246977	+	0.427776i
$27$		0			0
$28$	0.0367291	+	2.64550i	0.00694115	+	0.499952i
$29$	−6.16843	−	3.56135i	−1.14545	−	0.661326i	−0.197675	−	0.980268i	$-0.563339\pi$
$29$	−6.16843	−	3.56135i	−1.14545	−	0.661326i	−0.947774	+	0.318942i	$0.896672\pi$
$30$		0			0
$31$	5.25960	+	3.03663i	0.944653	+	0.545395i	0.891416	−	0.453186i	$-0.149713\pi$
$31$	5.25960	+	3.03663i	0.944653	+	0.545395i	0.0532369	+	0.998582i	$0.483046\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	1.47644	+	0.852422i	0.253207	+	0.146189i
$35$	7.97472	−	4.75303i	1.34797	−	0.803408i
$36$		0			0
$37$	4.14969	−	7.18748i	0.682205	−	1.18161i	−0.292101	−	0.956387i	$-0.594354\pi$
$37$	4.14969	−	7.18748i	0.682205	−	1.18161i	0.974306	−	0.225227i	$-0.0723123\pi$
$38$	4.84816			0.786475
$39$		0			0
$40$		−	3.50892i		−	0.554808i
$41$	−2.37578	−	4.11497i	−0.371034	−	0.642650i	0.618691	−	0.785635i	$-0.287663\pi$
$41$	−2.37578	−	4.11497i	−0.371034	−	0.642650i	−0.989725	+	0.142984i	$0.954330\pi$
$42$		0			0
$43$	−3.22845	+	5.59184i	−0.492334	+	0.852747i	−0.999961	−	0.00882976i	$-0.997189\pi$
$43$	−3.22845	+	5.59184i	−0.492334	+	0.852747i	0.507627	+	0.861577i	$0.330523\pi$
$44$	4.72317	+	2.72692i	0.712044	+	0.411099i
$45$		0			0
$46$	−2.67749	−	4.63754i	−0.394774	−	0.683768i
$47$	−4.31175	−	7.46818i	−0.628934	−	1.08935i	−0.987766	−	0.155943i	$-0.950158\pi$
$47$	−4.31175	−	7.46818i	−0.628934	−	1.08935i	0.358832	−	0.933402i	$-0.383175\pi$
$48$		0			0
$49$	3.33035	−	6.15701i	0.475765	−	0.879573i
$50$	−6.33280	+	3.65625i	−0.895594	+	0.517071i
$51$		0			0
$52$		−	2.51868i		−	0.349278i
$53$	10.0707	−	5.81430i	1.38331	−	0.798655i	0.390761	−	0.920492i	$-0.372212\pi$
$53$	10.0707	−	5.81430i	1.38331	−	0.798655i	0.992550	+	0.121837i	$0.0388786\pi$
$54$		0			0
$55$		−	19.1371i		−	2.58044i
$56$	−1.35456	−	2.27270i	−0.181010	−	0.303703i
$57$		0			0
$58$	7.12269			0.935256
$59$	3.94779	−	6.83778i	0.513959	−	0.890203i	−0.485910	−	0.874009i	$-0.661512\pi$
$59$	3.94779	−	6.83778i	0.513959	−	0.890203i	0.999869	−	0.0161942i	$-0.00515499\pi$
$60$		0			0
$61$	7.26397	−	4.19385i	0.930056	−	0.536968i	0.0432265	−	0.999065i	$-0.486236\pi$
$61$	7.26397	−	4.19385i	0.930056	−	0.536968i	0.886829	+	0.462097i	$0.152903\pi$
$62$	−6.07327			−0.771306
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.65379	+	4.41892i	−0.949336	+	0.548099i
$66$		0			0
$67$	0.895732	−	1.55145i	0.109431	−	0.189540i	−0.806109	−	0.591767i	$-0.798430\pi$
$67$	0.895732	−	1.55145i	0.109431	−	0.189540i	0.915540	+	0.402227i	$0.131764\pi$
$68$	−1.70484			−0.206743
$69$		0			0
$70$	−4.52980	+	8.10360i	−0.541415	+	0.968566i
$71$			0.791392i			0.0939209i	0.998897	+	0.0469605i	$0.0149535\pi$
$71$			0.791392i			0.0939209i	−0.998897	+	0.0469605i	$0.985047\pi$
$72$		0			0
$73$	−11.5492	+	6.66795i	−1.35173	+	0.780424i	−0.988492	−	0.151271i	$-0.951663\pi$
$73$	−11.5492	+	6.66795i	−1.35173	+	0.780424i	−0.363242	+	0.931695i	$0.618330\pi$
$74$			8.29939i			0.964784i
$75$		0			0
$76$	−4.19863	+	2.42408i	−0.481615	+	0.278061i
$77$	−7.38754	−	12.3950i	−0.841888	−	1.41254i
$78$		0			0
$79$	−2.40919	−	4.17283i	−0.271055	−	0.469481i	0.698077	−	0.716022i	$-0.254039\pi$
$79$	−2.40919	−	4.17283i	−0.271055	−	0.469481i	−0.969132	+	0.246542i	$0.920706\pi$
$80$	1.75446	+	3.03881i	0.196154	+	0.339749i
$81$		0			0
$82$	4.11497	+	2.37578i	0.454422	+	0.262361i
$83$	0.232835	−	0.403282i	0.0255569	−	0.0442659i	−0.852964	−	0.521970i	$-0.825197\pi$
$83$	0.232835	−	0.403282i	0.0255569	−	0.0442659i	0.878521	+	0.477704i	$0.158531\pi$
$84$		0			0
$85$	2.99108	+	5.18070i	0.324428	+	0.561926i
$86$		−	6.45690i		−	0.696265i
$87$		0			0
$88$	−5.45384			−0.581382
$89$	1.09184	−	1.89113i	0.115735	−	0.200459i	−0.802338	−	0.596870i	$-0.796411\pi$
$89$	1.09184	−	1.89113i	0.115735	−	0.200459i	0.918073	+	0.396410i	$0.129744\pi$
$90$		0			0
$91$	−3.25146	+	5.81672i	−0.340846	+	0.609758i
$92$	4.63754	+	2.67749i	0.483497	+	0.279147i
$93$		0			0
$94$	7.46818	+	4.31175i	0.770284	+	0.444723i
$95$	14.7326	+	8.50589i	1.51154	+	0.872685i
$96$		0			0
$97$	−4.24103	−	2.44856i	−0.430611	−	0.248613i	0.268996	−	0.963141i	$-0.413308\pi$
$97$	−4.24103	−	2.44856i	−0.430611	−	0.248613i	−0.699607	+	0.714528i	$0.746642\pi$
$98$	0.194333	+	6.99730i	0.0196306	+	0.706834i
$99$		0			0
$100$	3.65625	−	6.33280i	0.365625	−	0.633280i
$101$	14.5576			1.44853			0.724266	−	0.689520i	$-0.242179\pi$
$101$	14.5576			1.44853			0.724266	+	0.689520i	$0.242179\pi$
$102$		0			0
$103$		−	4.45949i		−	0.439406i	−0.975567	−	0.219703i	$-0.929491\pi$
$103$		−	4.45949i		−	0.439406i	0.975567	−	0.219703i	$-0.0705089\pi$
$104$	1.25934	+	2.18124i	0.123488	+	0.213888i
$105$		0			0
$106$	−5.81430	+	10.0707i	−0.564734	+	0.978149i
$107$	−5.99791	−	3.46290i	−0.579840	−	0.334771i	0.181230	−	0.983441i	$-0.441992\pi$
$107$	−5.99791	−	3.46290i	−0.579840	−	0.334771i	−0.761070	+	0.648670i	$0.775326\pi$
$108$		0			0
$109$	1.25470	+	2.17320i	0.120178	+	0.208155i	0.919838	−	0.392299i	$-0.128320\pi$
$109$	1.25470	+	2.17320i	0.120178	+	0.208155i	−0.799660	+	0.600454i	$0.794987\pi$
$110$	9.56854	+	16.5732i	0.912325	+	1.58019i
$111$		0			0
$112$	2.30943	+	1.29094i	0.218221	+	0.121982i
$113$	4.25572	−	2.45704i	0.400345	−	0.231139i	−0.286288	−	0.958144i	$-0.592421\pi$
$113$	4.25572	−	2.45704i	0.400345	−	0.231139i	0.686633	+	0.727004i	$0.259088\pi$
$114$		0			0
$115$		−	18.7901i		−	1.75219i
$116$	−6.16843	+	3.56135i	−0.572725	+	0.330663i
$117$		0			0
$118$			7.89559i			0.726848i
$119$	3.93722	+	2.20085i	0.360925	+	0.201752i
$120$		0			0
$121$	−18.7444			−1.70404
$122$	−4.19385	+	7.26397i	−0.379694	+	0.657649i
$123$		0			0
$124$	5.25960	−	3.03663i	0.472326	−	0.272698i
$125$	−8.11435			−0.725769
$126$		0			0
$127$	−11.0996			−0.984929			−0.492464	−	0.870333i	$-0.663904\pi$
$127$	−11.0996			−0.984929			−0.492464	+	0.870333i	$0.663904\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	4.41892	−	7.65379i	0.387565	−	0.671282i
$131$	−9.84985			−0.860585			−0.430293	−	0.902689i	$-0.641590\pi$
$131$	−9.84985			−0.860585			−0.430293	+	0.902689i	$0.641590\pi$
$132$		0			0
$133$	12.8258	−	0.178068i	1.11214	−	0.0154405i
$134$			1.79146i			0.154759i
$135$		0			0
$136$	1.47644	−	0.852422i	0.126604	−	0.0730946i
$137$		−	1.76449i		−	0.150751i	−0.997155	−	0.0753754i	$-0.975984\pi$
$137$		−	1.76449i		−	0.150751i	0.997155	−	0.0753754i	$-0.0240155\pi$
$138$		0			0
$139$	16.6425	−	9.60855i	1.41160	−	0.814986i	0.416059	−	0.909338i	$-0.363411\pi$
$139$	16.6425	−	9.60855i	1.41160	−	0.814986i	0.995539	+	0.0943514i	$0.0300777\pi$
$140$	−0.128879	−	9.28283i	−0.0108923	−	0.784542i
$141$		0			0
$142$	−0.395696	−	0.685366i	−0.0332061	−	0.0575146i
$143$	6.86824	+	11.8961i	0.574351	+	0.994806i
$144$		0			0
$145$	21.6445	+	12.4965i	1.79748	+	1.03778i
$146$	6.66795	−	11.5492i	0.551843	−	0.955820i
$147$		0			0
$148$	−4.14969	−	7.18748i	−0.341103	−	0.590807i
$149$		−	13.4790i		−	1.10424i	−0.833764	−	0.552120i	$-0.813819\pi$
$149$		−	13.4790i		−	1.10424i	0.833764	−	0.552120i	$-0.186181\pi$
$150$		0			0
$151$	−1.54391			−0.125641			−0.0628207	−	0.998025i	$-0.520010\pi$
$151$	−1.54391			−0.125641			−0.0628207	+	0.998025i	$0.520010\pi$
$152$	2.42408	−	4.19863i	0.196619	−	0.340554i
$153$		0			0
$154$	12.5953	+	7.04058i	1.01496	+	0.567346i
$155$	−18.4555	−	10.6553i	−1.48238	−	0.855854i
$156$		0			0
$157$	14.1141	+	8.14881i	1.12643	+	0.650346i	0.943035	−	0.332693i	$-0.107957\pi$
$157$	14.1141	+	8.14881i	1.12643	+	0.650346i	0.183397	+	0.983039i	$0.441291\pi$
$158$	4.17283	+	2.40919i	0.331973	+	0.191665i
$159$		0			0
$160$	−3.03881	−	1.75446i	−0.240239	−	0.138702i
$161$	−7.25361	−	12.1703i	−0.571665	−	0.959151i
$162$		0			0
$163$	−7.89989	+	13.6830i	−0.618768	+	1.07174i	0.370943	+	0.928655i	$0.379034\pi$
$163$	−7.89989	+	13.6830i	−0.618768	+	1.07174i	−0.989711	+	0.143081i	$0.954299\pi$
$164$	−4.75156			−0.371034
$165$		0			0
$166$			0.465669i			0.0361430i
$167$	4.73769	+	8.20592i	0.366613	+	0.634993i	0.989034	−	0.147690i	$-0.0471838\pi$
$167$	4.73769	+	8.20592i	0.366613	+	0.634993i	−0.622420	+	0.782683i	$0.713851\pi$
$168$		0			0
$169$	−3.32813	+	5.76449i	−0.256010	+	0.443422i
$170$	−5.18070	−	2.99108i	−0.397341	−	0.229405i
$171$		0			0
$172$	3.22845	+	5.59184i	0.246167	+	0.426374i
$173$	−0.267898	−	0.464013i	−0.0203679	−	0.0352782i	0.855662	−	0.517535i	$-0.173150\pi$
$173$	−0.267898	−	0.464013i	−0.0203679	−	0.0352782i	−0.876030	+	0.482257i	$0.839817\pi$
$174$		0			0
$175$	−16.6191	+	9.90519i	−1.25629	+	0.748762i
$176$	4.72317	−	2.72692i	0.356022	−	0.205549i
$177$		0			0
$178$			2.18369i			0.163674i
$179$	8.69412	−	5.01955i	0.649829	−	0.375179i	−0.138562	−	0.990354i	$-0.544248\pi$
$179$	8.69412	−	5.01955i	0.649829	−	0.375179i	0.788391	+	0.615175i	$0.210915\pi$
$180$		0			0
$181$		−	20.7151i		−	1.53974i	−0.638202	−	0.769869i	$-0.720321\pi$
$181$		−	20.7151i		−	1.53974i	0.638202	−	0.769869i	$-0.279679\pi$
$182$	−0.0925088	−	6.66316i	−0.00685721	−	0.493906i
$183$		0			0
$184$	−5.35497			−0.394774
$185$	−14.5609	+	25.2203i	−1.07054	+	1.85423i
$186$		0			0
$187$	8.05227	−	4.64898i	0.588840	−	0.339967i
$188$	−8.62351			−0.628934
$189$		0			0
$190$	−17.0118			−1.23416
$191$	9.73142	−	5.61844i	0.704141	−	0.406536i	−0.104747	−	0.994499i	$-0.533403\pi$
$191$	9.73142	−	5.61844i	0.704141	−	0.406536i	0.808888	+	0.587963i	$0.200070\pi$
$192$		0			0
$193$	−10.4136	+	18.0369i	−0.749586	+	1.29832i	0.198435	+	0.980114i	$0.436414\pi$
$193$	−10.4136	+	18.0369i	−0.749586	+	1.29832i	−0.948021	+	0.318207i	$0.896919\pi$
$194$	4.89711			0.351592
$195$		0			0
$196$	−3.66695	−	5.96267i	−0.261925	−	0.425905i
$197$			20.4964i			1.46031i	0.683284	+	0.730153i	$0.260551\pi$
$197$			20.4964i			1.46031i	−0.683284	+	0.730153i	$0.739449\pi$
$198$		0			0
$199$	2.57476	−	1.48654i	0.182520	−	0.105378i	−0.405956	−	0.913893i	$-0.633061\pi$
$199$	2.57476	−	1.48654i	0.182520	−	0.105378i	0.588476	+	0.808515i	$0.299728\pi$
$200$			7.31249i			0.517071i
$201$		0			0
$202$	−12.6072	+	7.27879i	−0.887041	+	0.512134i
$203$	18.8431	−	0.261610i	1.32252	−	0.0183614i
$204$		0			0
$205$	8.33641	+	14.4391i	0.582240	+	1.00847i
$206$	2.22974	+	3.86203i	0.155354	+	0.269080i
$207$		0			0
$208$	−2.18124	−	1.25934i	−0.151242	−	0.0873195i
$209$	13.2205	−	22.8986i	0.914484	−	1.58393i
$210$		0			0
$211$	8.57258	+	14.8481i	0.590161	+	1.02219i	0.994210	+	0.107451i	$0.0342690\pi$
$211$	8.57258	+	14.8481i	0.590161	+	1.02219i	−0.404050	+	0.914737i	$0.632398\pi$
$212$		−	11.6286i		−	0.798655i
$213$		0			0
$214$	6.92579			0.473437
$215$	11.3284	−	19.6213i	0.772587	−	1.33816i
$216$		0			0
$217$	−16.0668	+	0.223066i	−1.09069	+	0.0151427i
$218$	−2.17320	−	1.25470i	−0.147188	−	0.0849789i
$219$		0			0
$220$	−16.5732	−	9.56854i	−1.11736	−	0.645111i
$221$	−3.71868	−	2.14698i	−0.250145	−	0.144421i
$222$		0			0
$223$	−10.5032	−	6.06403i	−0.703346	−	0.406077i	0.105246	−	0.994446i	$-0.466437\pi$
$223$	−10.5032	−	6.06403i	−0.703346	−	0.406077i	−0.808593	+	0.588369i	$0.799770\pi$
$224$	−2.64550	+	0.0367291i	−0.176760	+	0.00245407i
$225$		0			0
$226$	−2.45704	+	4.25572i	−0.163440	+	0.283087i
$227$	1.41026			0.0936019			0.0468010	−	0.998904i	$-0.485097\pi$
$227$	1.41026			0.0936019			0.0468010	+	0.998904i	$0.485097\pi$
$228$		0			0
$229$			16.3901i			1.08309i	0.840673	+	0.541544i	$0.182160\pi$
$229$			16.3901i			1.08309i	−0.840673	+	0.541544i	$0.817840\pi$
$230$	9.39507	+	16.2727i	0.619493	+	1.07299i
$231$		0			0
$232$	3.56135	−	6.16843i	0.233814	−	0.404978i
$233$	−10.6058	−	6.12326i	−0.694808	−	0.401148i	0.110602	−	0.993865i	$-0.464722\pi$
$233$	−10.6058	−	6.12326i	−0.694808	−	0.401148i	−0.805411	+	0.592717i	$0.798055\pi$
$234$		0			0
$235$	15.1296	+	26.2052i	0.986945	+	1.70944i
$236$	−3.94779	−	6.83778i	−0.256979	−	0.445102i
$237$		0			0
$238$	−4.51016	+	0.0626174i	−0.292350	+	0.00405888i
$239$	10.3774	−	5.99139i	0.671257	−	0.387551i	−0.125296	−	0.992119i	$-0.539988\pi$
$239$	10.3774	−	5.99139i	0.671257	−	0.387551i	0.796553	+	0.604569i	$0.206655\pi$
$240$		0			0
$241$			0.00355814i			0.000229200i	1.00000		0.000114600i	$3.64783e-5\pi$
$241$			0.00355814i			0.000229200i	−1.00000		0.000114600i	$0.999964\pi$
$242$	16.2331	−	9.37221i	1.04351	−	0.602468i
$243$		0			0
$244$		−	8.38771i		−	0.536968i
$245$	−11.6859	+	21.6044i	−0.746587	+	1.38026i
$246$		0			0
$247$	−12.2109			−0.776964
$248$	−3.03663	+	5.25960i	−0.192826	+	0.333985i
$249$		0			0
$250$	7.02723	−	4.05717i	0.444441	−	0.256598i
$251$	−11.1743			−0.705318			−0.352659	−	0.935752i	$-0.614722\pi$
$251$	−11.1743			−0.705318			−0.352659	+	0.935752i	$0.614722\pi$
$252$		0			0
$253$	−29.2052			−1.83611
$254$	9.61252	−	5.54979i	0.603143	−	0.348225i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.50749			−0.343548			−0.171774	−	0.985136i	$-0.554950\pi$
$257$	−5.50749			−0.343548			−0.171774	+	0.985136i	$0.554950\pi$
$258$		0			0
$259$	0.304829	+	21.9560i	0.0189412	+	1.36428i
$260$			8.83783i			0.548099i
$261$		0			0
$262$	8.53022	−	4.92492i	0.526999	−	0.304263i
$263$		−	26.8561i		−	1.65602i	−0.560715	−	0.828009i	$-0.689474\pi$
$263$		−	26.8561i		−	1.65602i	0.560715	−	0.828009i	$-0.310526\pi$
$264$		0			0
$265$	−35.3371	+	20.4019i	−2.17074	+	1.25328i
$266$	−11.0184	+	6.56710i	−0.675582	+	0.402655i
$267$		0			0
$268$	−0.895732	−	1.55145i	−0.0547155	−	0.0947701i
$269$	−13.8309	−	23.9558i	−0.843284	−	1.46061i	−0.887103	−	0.461571i	$-0.847286\pi$
$269$	−13.8309	−	23.9558i	−0.843284	−	1.46061i	0.0438192	−	0.999039i	$-0.486047\pi$
$270$		0			0
$271$	24.3120	+	14.0365i	1.47685	+	0.852658i	0.999658	−	0.0261428i	$-0.00832247\pi$
$271$	24.3120	+	14.0365i	1.47685	+	0.852658i	0.477189	+	0.878801i	$0.341656\pi$
$272$	−0.852422	+	1.47644i	−0.0516857	+	0.0895222i
$273$		0			0
$274$	0.882247	+	1.52810i	0.0532985	+	0.0923157i
$275$			39.8812i			2.40493i
$276$		0			0
$277$	−27.7504			−1.66736			−0.833681	−	0.552247i	$-0.813771\pi$
$277$	−27.7504			−1.66736			−0.833681	+	0.552247i	$0.813771\pi$
$278$	−9.60855	+	16.6425i	−0.576282	+	0.998150i
$279$		0			0
$280$	4.75303	+	7.97472i	0.284048	+	0.476581i
$281$	−0.398066	−	0.229824i	−0.0237466	−	0.0137101i	0.488080	−	0.872799i	$-0.337698\pi$
$281$	−0.398066	−	0.229824i	−0.0237466	−	0.0137101i	−0.511826	+	0.859089i	$0.671031\pi$
$282$		0			0
$283$	−15.6655	−	9.04449i	−0.931219	−	0.537639i	−0.0440218	−	0.999031i	$-0.514017\pi$
$283$	−15.6655	−	9.04449i	−0.931219	−	0.537639i	−0.887197	+	0.461391i	$0.847350\pi$
$284$	0.685366	+	0.395696i	0.0406690	+	0.0234802i
$285$		0			0
$286$	−11.8961	−	6.86824i	−0.703434	−	0.406128i
$287$	10.9734	+	6.13397i	0.647739	+	0.362077i
$288$		0			0
$289$	7.04675	−	12.2053i	0.414515	−	0.717961i
$290$	−24.9929			−1.46764
$291$		0			0
$292$			13.3359i			0.780424i
$293$	−8.23716	−	14.2672i	−0.481220	−	0.833497i	0.518548	−	0.855049i	$-0.326473\pi$
$293$	−8.23716	−	14.2672i	−0.481220	−	0.833497i	−0.999768	+	0.0215512i	$0.993140\pi$
$294$		0			0
$295$	−13.8525	+	23.9932i	−0.806522	+	1.39694i
$296$	7.18748	+	4.14969i	0.417764	+	0.241196i
$297$		0			0
$298$	6.73949	+	11.6731i	0.390408	+	0.676207i
$299$	6.74373	+	11.6805i	0.390000	+	0.675500i
$300$		0			0
$301$	−0.237156	−	17.0817i	−0.0136694	−	0.984573i
$302$	1.33706	−	0.771954i	0.0769394	−	0.0444210i
$303$		0			0
$304$			4.84816i			0.278061i
$305$	−25.4887	+	14.7159i	−1.45948	+	0.842629i
$306$		0			0
$307$			17.8324i			1.01775i	0.860841	+	0.508874i	$0.169938\pi$
$307$			17.8324i			1.01775i	−0.860841	+	0.508874i	$0.830062\pi$
$308$	−14.4281	+	0.200315i	−0.822119	+	0.0114140i
$309$		0			0
$310$	21.3106			1.21036
$311$	−9.05812	+	15.6891i	−0.513639	+	0.889649i	0.486236	+	0.873828i	$0.338370\pi$
$311$	−9.05812	+	15.6891i	−0.513639	+	0.889649i	−0.999875	+	0.0158211i	$0.994964\pi$
$312$		0			0
$313$	8.65414	−	4.99647i	0.489161	−	0.282417i	−0.235065	−	0.971980i	$-0.575530\pi$
$313$	8.65414	−	4.99647i	0.489161	−	0.282417i	0.724226	+	0.689562i	$0.242197\pi$
$314$	−16.2976			−0.919728
$315$		0			0
$316$	−4.81837			−0.271055
$317$	−4.86356	+	2.80797i	−0.273164	+	0.157712i	−0.630325	−	0.776331i	$-0.717078\pi$
$317$	−4.86356	+	2.80797i	−0.273164	+	0.157712i	0.357160	+	0.934043i	$0.383745\pi$
$318$		0			0
$319$	19.4230	−	33.6417i	1.08748	−	1.88357i
$320$	3.50892			0.196154
$321$		0			0
$322$	12.3669	+	6.91295i	0.689183	+	0.385243i
$323$			8.26535i			0.459896i
$324$		0			0
$325$	15.9503	−	9.20891i	0.884764	−	0.510819i
$326$		−	15.7998i		−	0.875069i
$327$		0			0
$328$	4.11497	−	2.37578i	0.227211	−	0.131180i
$329$	19.9154	+	11.1324i	1.09797	+	0.613751i
$330$		0			0
$331$	−4.61238	−	7.98888i	−0.253520	−	0.439109i	0.710973	−	0.703220i	$-0.248255\pi$
$331$	−4.61238	−	7.98888i	−0.253520	−	0.439109i	−0.964492	+	0.264111i	$0.914922\pi$
$332$	−0.232835	−	0.403282i	−0.0127785	−	0.0221330i
$333$		0			0
$334$	−8.20592	−	4.73769i	−0.449008	−	0.259235i
$335$	−3.14305	+	5.44392i	−0.171723	+	0.297433i
$336$		0			0
$337$	−8.03024	−	13.9088i	−0.437435	−	0.757660i	0.560056	−	0.828455i	$-0.310780\pi$
$337$	−8.03024	−	13.9088i	−0.437435	−	0.757660i	−0.997491	+	0.0707950i	$0.977446\pi$
$338$		−	6.65625i		−	0.362053i
$339$		0			0
$340$	5.98216			0.324428
$341$	−16.5613	+	28.6851i	−0.896846	+	1.55338i
$342$		0			0
$343$	0.771113	+	18.5042i	0.0416362	+	0.999133i
$344$	−5.59184	−	3.22845i	−0.301492	−	0.174066i
$345$		0			0
$346$	0.464013	+	0.267898i	0.0249455	+	0.0144023i
$347$	−11.2614	−	6.50175i	−0.604542	−	0.349032i	0.166284	−	0.986078i	$-0.446823\pi$
$347$	−11.2614	−	6.50175i	−0.604542	−	0.349032i	−0.770826	+	0.637045i	$0.780156\pi$
$348$		0			0
$349$	−8.95678	−	5.17120i	−0.479446	−	0.276808i	0.240740	−	0.970590i	$-0.422610\pi$
$349$	−8.95678	−	5.17120i	−0.479446	−	0.276808i	−0.720185	+	0.693782i	$0.755943\pi$
$350$	9.43999	−	16.8877i	0.504589	−	0.902686i
$351$		0			0
$352$	−2.72692	+	4.72317i	−0.145345	+	0.251746i
$353$	−0.311331			−0.0165705			−0.00828524	−	0.999966i	$-0.502637\pi$
$353$	−0.311331			−0.0165705			−0.00828524	+	0.999966i	$0.502637\pi$
$354$		0			0
$355$		−	2.77693i		−	0.147384i
$356$	−1.09184	−	1.89113i	−0.0578676	−	0.100230i
$357$		0			0
$358$	−5.01955	+	8.69412i	−0.265291	+	0.459498i
$359$	3.73192	+	2.15462i	0.196963	+	0.113717i	0.595238	−	0.803549i	$-0.297058\pi$
$359$	3.73192	+	2.15462i	0.196963	+	0.113717i	−0.398275	+	0.917266i	$0.630391\pi$
$360$		0			0
$361$	2.25230	+	3.90111i	0.118542	+	0.205321i
$362$	10.3575	+	17.9398i	0.544380	+	0.942893i
$363$		0			0
$364$	3.41169	+	5.72421i	0.178821	+	0.300030i
$365$	40.5253	−	23.3973i	2.12119	−	1.22467i
$366$		0			0
$367$		−	23.5742i		−	1.23056i	−0.788307	−	0.615282i	$-0.789042\pi$
$367$		−	23.5742i		−	1.23056i	0.788307	−	0.615282i	$-0.210958\pi$
$368$	4.63754	−	2.67749i	0.241749	−	0.139574i
$369$		0			0
$370$		−	29.1219i		−	1.51397i
$371$	−15.0118	+	26.8554i	−0.779374	+	1.39426i
$372$		0			0
$373$	18.1985			0.942281			0.471140	−	0.882058i	$-0.343843\pi$
$373$	18.1985			0.942281			0.471140	+	0.882058i	$0.343843\pi$
$374$	−4.64898	+	8.05227i	−0.240393	+	0.416373i
$375$		0			0
$376$	7.46818	−	4.31175i	0.385142	−	0.222362i
$377$	−17.9398			−0.923946
$378$		0			0
$379$	11.2842			0.579628			0.289814	−	0.957083i	$-0.406406\pi$
$379$	11.2842			0.579628			0.289814	+	0.957083i	$0.406406\pi$
$380$	14.7326	−	8.50589i	0.755768	−	0.436343i
$381$		0			0
$382$	−5.61844	+	9.73142i	−0.287464	+	0.497903i
$383$	−34.8445			−1.78047			−0.890235	−	0.455502i	$-0.849460\pi$
$383$	−34.8445			−1.78047			−0.890235	+	0.455502i	$0.849460\pi$
$384$		0			0
$385$	25.9223	+	43.4929i	1.32112	+	2.21660i
$386$		−	20.8272i		−	1.06007i
$387$		0			0
$388$	−4.24103	+	2.44856i	−0.215305	+	0.124307i
$389$			6.15978i			0.312313i	0.987732	+	0.156157i	$0.0499105\pi$
$389$			6.15978i			0.312313i	−0.987732	+	0.156157i	$0.950090\pi$
$390$		0			0
$391$	7.90629	−	4.56470i	0.399838	−	0.230847i
$392$	6.15701	+	3.33035i	0.310976	+	0.168208i
$393$		0			0
$394$	−10.2482	−	17.7504i	−0.516296	−	0.894251i
$395$	8.45364	+	14.6421i	0.425349	+	0.736725i
$396$		0			0
$397$	0.950888	+	0.548996i	0.0477237	+	0.0275533i	0.523672	−	0.851920i	$-0.324562\pi$
$397$	0.950888	+	0.548996i	0.0477237	+	0.0275533i	−0.475948	+	0.879473i	$0.657895\pi$
$398$	−1.48654	+	2.57476i	−0.0745136	+	0.129061i
$399$		0			0
$400$	−3.65625	−	6.33280i	−0.182812	−	0.316640i
$401$			17.7165i			0.884719i	0.896838	+	0.442359i	$0.145858\pi$
$401$			17.7165i			0.884719i	−0.896838	+	0.442359i	$0.854142\pi$
$402$		0			0
$403$	15.2966			0.761979
$404$	7.27879	−	12.6072i	0.362133	−	0.627233i
$405$		0			0
$406$	−16.1878	+	9.64809i	−0.803385	+	0.478827i
$407$	39.1994	+	22.6318i	1.94304	+	1.12182i
$408$		0			0
$409$	−19.2273	−	11.1009i	−0.950729	−	0.548904i	−0.0574216	−	0.998350i	$-0.518288\pi$
$409$	−19.2273	−	11.1009i	−0.950729	−	0.548904i	−0.893307	+	0.449446i	$0.851621\pi$
$410$	−14.4391	−	8.33641i	−0.713095	−	0.411706i
$411$		0			0
$412$	−3.86203	−	2.22974i	−0.190269	−	0.109852i
$413$	0.289998	+	20.8877i	0.0142699	+	1.02782i
$414$		0			0
$415$	−0.816998	+	1.41508i	−0.0401048	+	0.0694636i
$416$	2.51868			0.123488
$417$		0			0
$418$			26.4411i			1.29328i
$419$	3.30677	+	5.72749i	0.161546	+	0.279806i	0.935423	−	0.353529i	$-0.115019\pi$
$419$	3.30677	+	5.72749i	0.161546	+	0.279806i	−0.773877	+	0.633336i	$0.781685\pi$
$420$		0			0
$421$	20.0090	−	34.6565i	0.975177	−	1.68906i	0.295826	−	0.955242i	$-0.404405\pi$
$421$	20.0090	−	34.6565i	0.975177	−	1.68906i	0.679351	−	0.733814i	$-0.262261\pi$
$422$	−14.8481	−	8.57258i	−0.722796	−	0.417307i
$423$		0			0
$424$	5.81430	+	10.0707i	0.282367	+	0.489074i
$425$	−6.23333	−	10.7964i	−0.302361	−	0.523705i
$426$		0			0
$427$	−10.8280	+	19.3708i	−0.524005	+	0.937420i
$428$	−5.99791	+	3.46290i	−0.289920	+	0.167385i
$429$		0			0
$430$			22.6567i			1.09260i
$431$	20.2750	−	11.7058i	0.976611	−	0.563846i	0.0753654	−	0.997156i	$-0.475988\pi$
$431$	20.2750	−	11.7058i	0.976611	−	0.563846i	0.901245	+	0.433310i	$0.142654\pi$
$432$		0			0
$433$		−	33.2342i		−	1.59713i	−0.601905	−	0.798567i	$-0.705592\pi$
$433$		−	33.2342i		−	1.59713i	0.601905	−	0.798567i	$-0.294408\pi$
$434$	13.8027	−	8.22658i	0.662552	−	0.394889i
$435$		0			0
$436$	2.50940			0.120178
$437$	12.9809	−	22.4835i	0.620959	−	1.07553i
$438$		0			0
$439$	−3.95900	+	2.28573i	−0.188953	+	0.109092i	−0.591492	−	0.806311i	$-0.701461\pi$
$439$	−3.95900	+	2.28573i	−0.188953	+	0.109092i	0.402539	+	0.915403i	$0.368128\pi$
$440$	19.1371			0.912325
$441$		0			0
$442$	4.29396			0.204243
$443$	−2.28815	+	1.32106i	−0.108713	+	0.0627657i	−0.553371	−	0.832935i	$-0.686659\pi$
$443$	−2.28815	+	1.32106i	−0.108713	+	0.0627657i	0.444657	+	0.895701i	$0.353325\pi$
$444$		0			0
$445$	−3.83119	+	6.63582i	−0.181616	+	0.314568i
$446$	12.1281			0.574280
$447$		0			0
$448$	2.27270	−	1.35456i	0.107375	−	0.0639968i
$449$			7.56836i			0.357173i	0.983924	+	0.178587i	$0.0571525\pi$
$449$			7.56836i			0.357173i	−0.983924	+	0.178587i	$0.942848\pi$
$450$		0			0
$451$	22.4424	−	12.9571i	1.05677	−	0.610127i
$452$		−	4.91409i		−	0.231139i
$453$		0			0
$454$	−1.22132	+	0.705128i	−0.0573192	+	0.0330933i
$455$	11.4091	−	20.4104i	0.534867	−	0.956853i
$456$		0			0
$457$	−11.0409	−	19.1234i	−0.516472	−	0.894556i	−0.999817	−	0.0191257i	$-0.993912\pi$
$457$	−11.0409	−	19.1234i	−0.516472	−	0.894556i	0.483345	−	0.875430i	$-0.339422\pi$
$458$	−8.19504	−	14.1942i	−0.382929	−	0.663253i
$459$		0			0
$460$	−16.2727	−	9.39507i	−0.758721	−	0.438048i
$461$	13.3560	−	23.1332i	0.622049	−	1.07742i	−0.367054	−	0.930199i	$-0.619634\pi$
$461$	13.3560	−	23.1332i	0.622049	−	1.07742i	0.989104	−	0.147221i	$-0.0470330\pi$
$462$		0			0
$463$	5.22568	+	9.05114i	0.242858	+	0.420642i	0.961527	−	0.274710i	$-0.0885818\pi$
$463$	5.22568	+	9.05114i	0.242858	+	0.420642i	−0.718669	+	0.695352i	$0.755248\pi$
$464$			7.12269i			0.330663i
$465$		0			0
$466$	12.2465			0.567309
$467$	15.3539	−	26.5937i	0.710492	−	1.23061i	−0.254180	−	0.967157i	$-0.581806\pi$
$467$	15.3539	−	26.5937i	0.710492	−	1.23061i	0.964672	−	0.263452i	$-0.0848611\pi$
$468$		0			0
$469$	0.0657988	+	4.73931i	0.00303831	+	0.218841i
$470$	−26.2052	−	15.1296i	−1.20876	−	0.697876i
$471$		0			0
$472$	6.83778	+	3.94779i	0.314734	+	0.181712i
$473$	−30.4970	−	17.6075i	−1.40225	−	0.809591i
$474$		0			0
$475$	−30.7024	−	17.7261i	−1.40872	−	0.813327i
$476$	3.87460	−	2.30931i	0.177592	−	0.105847i
$477$		0			0
$478$	−5.99139	+	10.3774i	−0.274040	+	0.474651i
$479$	−14.0147			−0.640349			−0.320174	−	0.947359i	$-0.603742\pi$
$479$	−14.0147			−0.640349			−0.320174	+	0.947359i	$0.603742\pi$
$480$		0			0
$481$		−	20.9035i		−	0.953117i
$482$	−0.00177907	−	0.00308144i	−8.10343e−5	−	0.000140356i
$483$		0			0
$484$	−9.37221	+	16.2331i	−0.426009	+	0.737870i
$485$	14.8814	+	8.59178i	0.675730	+	0.390133i
$486$		0			0
$487$	0.643017	+	1.11374i	0.0291379	+	0.0504683i	0.880227	−	0.474554i	$-0.157390\pi$
$487$	0.643017	+	1.11374i	0.0291379	+	0.0504683i	−0.851089	+	0.525022i	$0.824057\pi$
$488$	4.19385	+	7.26397i	0.189847	+	0.328824i
$489$		0			0
$490$	−0.681900	−	24.5529i	−0.0308051	−	1.10919i
$491$	0.458760	−	0.264865i	0.0207036	−	0.0119532i	−0.489613	−	0.871940i	$-0.662862\pi$
$491$	0.458760	−	0.264865i	0.0207036	−	0.0119532i	0.510316	+	0.859987i	$0.329528\pi$
$492$		0			0
$493$			12.1431i			0.546897i
$494$	10.5750	−	6.10547i	0.475791	−	0.274698i
$495$		0			0
$496$		−	6.07327i		−	0.272698i
$497$	−1.07199	−	1.79860i	−0.0480851	−	0.0806782i
$498$		0			0
$499$	22.0187			0.985690			0.492845	−	0.870117i	$-0.335957\pi$
$499$	22.0187			0.985690			0.492845	+	0.870117i	$0.335957\pi$
$500$	−4.05717	+	7.02723i	−0.181442	+	0.314267i
$501$		0			0
$502$	9.67726	−	5.58717i	0.431917	−	0.249368i
$503$	4.10902			0.183212			0.0916060	−	0.995795i	$-0.470800\pi$
$503$	4.10902			0.183212			0.0916060	+	0.995795i	$0.470800\pi$
$504$		0			0
$505$	−51.0813			−2.27309
$506$	25.2924	−	14.6026i	1.12439	−	0.649164i
$507$		0			0
$508$	−5.54979	+	9.61252i	−0.246232	+	0.426487i
$509$	−32.9629			−1.46105			−0.730527	−	0.682884i	$-0.760726\pi$
$509$	−32.9629			−1.46105			−0.730527	+	0.682884i	$0.760726\pi$
$510$		0			0
$511$	17.2158	−	30.7983i	0.761584	−	1.36244i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	4.76963	−	2.75375i	0.210379	−	0.121463i
$515$			15.6480i			0.689532i
$516$		0			0
$517$	40.7303	−	23.5156i	1.79132	−	1.03422i
$518$	−11.2420	−	18.8620i	−0.493945	−	0.828750i
$519$		0			0
$520$	−4.41892	−	7.65379i	−0.193782	−	0.335641i
$521$	−0.803764	−	1.39216i	−0.0352135	−	0.0609917i	0.847882	−	0.530186i	$-0.177878\pi$
$521$	−0.803764	−	1.39216i	−0.0352135	−	0.0609917i	−0.883095	+	0.469194i	$0.844544\pi$
$522$		0			0
$523$	−13.5752	−	7.83764i	−0.593602	−	0.342716i	0.172918	−	0.984936i	$-0.444680\pi$
$523$	−13.5752	−	7.83764i	−0.593602	−	0.342716i	−0.766520	+	0.642220i	$0.778014\pi$
$524$	−4.92492	+	8.53022i	−0.215146	+	0.372644i
$525$		0			0
$526$	13.4280	+	23.2581i	0.585491	+	1.01410i
$527$		−	10.3540i		−	0.451026i
$528$		0			0
$529$	−5.67572			−0.246770
$530$	20.4019	−	35.3371i	0.886201	−	1.53495i
$531$		0			0
$532$	6.25868	−	11.1965i	0.271348	−	0.485429i
$533$	−10.3643	−	5.98382i	−0.448927	−	0.259188i
$534$		0			0
$535$	21.0462	+	12.1510i	0.909905	+	0.525334i
$536$	1.55145	+	0.895732i	0.0670126	+	0.0386897i
$537$		0			0
$538$	23.9558	+	13.8309i	1.03281	+	0.596292i
$539$	33.5794	+	18.1632i	1.44637	+	0.782346i
$540$		0			0
$541$	19.2112	−	33.2747i	0.825953	−	1.43059i	−0.0752366	−	0.997166i	$-0.523971\pi$
$541$	19.2112	−	33.2747i	0.825953	−	1.43059i	0.901189	−	0.433426i	$-0.142695\pi$
$542$	−28.0730			−1.20584
$543$		0			0
$544$		−	1.70484i		−	0.0730946i
$545$	−4.40263	−	7.62558i	−0.188588	−	0.326644i
$546$		0			0
$547$	−21.1201	+	36.5811i	−0.903032	+	1.56410i	−0.0794935	+	0.996835i	$0.525330\pi$
$547$	−21.1201	+	36.5811i	−0.903032	+	1.56410i	−0.823538	+	0.567261i	$0.808003\pi$
$548$	−1.52810	−	0.882247i	−0.0652770	−	0.0376877i
$549$		0			0
$550$	−19.9406	−	34.5381i	−0.850270	−	1.47271i
$551$	17.2660	+	29.9055i	0.735555	+	1.27402i
$552$		0			0
$553$	11.1277	+	6.22023i	0.473198	+	0.264511i
$554$	24.0326	−	13.8752i	1.02105	−	0.589501i
$555$		0			0
$556$		−	19.2171i		−	0.814986i
$557$	11.6088	−	6.70235i	0.491881	−	0.283988i	−0.233473	−	0.972363i	$-0.575009\pi$
$557$	11.6088	−	6.70235i	0.491881	−	0.283988i	0.725355	+	0.688375i	$0.241676\pi$
$558$		0			0
$559$			16.2629i			0.687845i
$560$	−8.10360	−	4.52980i	−0.342440	−	0.191419i
$561$		0			0
$562$	0.459647			0.0193890
$563$	10.8186	−	18.7384i	0.455949	−	0.789728i	−0.542793	−	0.839867i	$-0.682633\pi$
$563$	10.8186	−	18.7384i	0.455949	−	0.789728i	0.998742	+	0.0501391i	$0.0159665\pi$
$564$		0			0
$565$	−14.9330	+	8.62156i	−0.628235	+	0.362712i
$566$	18.0890			0.760337
$567$		0			0
$568$	−0.791392			−0.0332061
$569$	−12.2352	+	7.06398i	−0.512925	+	0.296138i	−0.734035	−	0.679111i	$-0.762365\pi$
$569$	−12.2352	+	7.06398i	−0.512925	+	0.296138i	0.221110	+	0.975249i	$0.429032\pi$
$570$		0			0
$571$	12.2107	−	21.1495i	0.511002	−	0.885081i	−0.488917	−	0.872330i	$-0.662608\pi$
$571$	12.2107	−	21.1495i	0.511002	−	0.885081i	0.999919	−	0.0127507i	$-0.00405880\pi$
$572$	13.7365			0.574351
$573$		0			0
$574$	−12.5702	+	0.174520i	−0.524671	+	0.00728434i
$575$			39.1582i			1.63301i
$576$		0			0
$577$	10.7949	−	6.23246i	0.449399	−	0.259461i	−0.258177	−	0.966098i	$-0.583122\pi$
$577$	10.7949	−	6.23246i	0.449399	−	0.259461i	0.707576	+	0.706637i	$0.249789\pi$
$578$			14.0935i			0.586213i
$579$		0			0
$580$	21.6445	−	12.4965i	0.898740	−	0.518888i
$581$	0.0171036	+	1.23193i	0.000709578	+	0.0511089i
$582$		0			0
$583$	31.7103	+	54.9238i	1.31330	+	2.27471i
$584$	−6.66795	−	11.5492i	−0.275922	−	0.477910i
$585$		0			0
$586$	14.2672	+	8.23716i	0.589372	+	0.340274i
$587$	8.61219	−	14.9167i	0.355463	−	0.615680i	−0.631734	−	0.775185i	$-0.717657\pi$
$587$	8.61219	−	14.9167i	0.355463	−	0.615680i	0.987197	+	0.159505i	$0.0509899\pi$
$588$		0			0
$589$	−14.7221	−	25.4994i	−0.606612	−	1.05068i
$590$		−	27.7050i		−	1.14060i
$591$		0			0
$592$	−8.29939			−0.341103
$593$	−6.92426	+	11.9932i	−0.284345	+	0.492500i	−0.972450	−	0.233111i	$-0.925110\pi$
$593$	−6.92426	+	11.9932i	−0.284345	+	0.492500i	0.688105	+	0.725611i	$0.258443\pi$
$594$		0			0
$595$	−13.8154	−	7.72260i	−0.566375	−	0.316596i
$596$	−11.6731	−	6.73949i	−0.478150	−	0.276060i
$597$		0			0
$598$	−11.6805	−	6.74373i	−0.477650	−	0.275772i
$599$	16.6669	+	9.62266i	0.680992	+	0.393171i	0.800229	−	0.599695i	$-0.204711\pi$
$599$	16.6669	+	9.62266i	0.680992	+	0.393171i	−0.119237	+	0.992866i	$0.538045\pi$
$600$		0			0
$601$	−11.5612	−	6.67486i	−0.471591	−	0.272273i	0.245314	−	0.969444i	$-0.421109\pi$
$601$	−11.5612	−	6.67486i	−0.471591	−	0.272273i	−0.716906	+	0.697170i	$0.754442\pi$
$602$	8.74623	+	14.6746i	0.356470	+	0.598092i
$603$		0			0
$604$	−0.771954	+	1.33706i	−0.0314104	+	0.0544044i
$605$	65.7726			2.67404
$606$		0			0
$607$		−	20.5073i		−	0.832364i	−0.909281	−	0.416182i	$-0.863368\pi$
$607$		−	20.5073i		−	0.832364i	0.909281	−	0.416182i	$-0.136632\pi$
$608$	−2.42408	−	4.19863i	−0.0983093	−	0.170277i
$609$		0			0
$610$	14.7159	−	25.4887i	0.595829	−	1.03201i
$611$	−18.8099	−	10.8599i	−0.760969	−	0.439346i
$612$		0			0
$613$	−9.18064	−	15.9013i	−0.370803	−	0.642249i	0.618887	−	0.785480i	$-0.287584\pi$
$613$	−9.18064	−	15.9013i	−0.370803	−	0.642249i	−0.989689	+	0.143231i	$0.954251\pi$
$614$	−8.91619	−	15.4433i	−0.359828	−	0.623240i
$615$		0			0
$616$	12.3950	−	7.38754i	0.499407	−	0.297652i
$617$	−28.1051	+	16.2265i	−1.13147	+	0.653255i	−0.944304	−	0.329074i	$-0.893264\pi$
$617$	−28.1051	+	16.2265i	−1.13147	+	0.653255i	−0.187166	+	0.982328i	$0.559930\pi$
$618$		0			0
$619$		−	40.4220i		−	1.62470i	−0.583172	−	0.812349i	$-0.698189\pi$
$619$		−	40.4220i		−	1.62470i	0.583172	−	0.812349i	$-0.301811\pi$
$620$	−18.4555	+	10.6553i	−0.741191	+	0.427927i
$621$		0			0
$622$		−	18.1162i		−	0.726395i
$623$	0.0802049	+	5.77694i	0.00321334	+	0.231448i
$624$		0			0
$625$	−8.08991			−0.323596
$626$	−4.99647	+	8.65414i	−0.199699	+	0.345889i
$627$		0			0
$628$	14.1141	−	8.14881i	0.563216	−	0.325173i
$629$	−14.1492			−0.564164
$630$		0			0
$631$	−20.8745			−0.830999			−0.415500	−	0.909593i	$-0.636393\pi$
$631$	−20.8745			−0.830999			−0.415500	+	0.909593i	$0.636393\pi$
$632$	4.17283	−	2.40919i	0.165986	−	0.0958323i
$633$		0			0
$634$	2.80797	−	4.86356i	0.111519	−	0.193156i
$635$	38.9475			1.54559
$636$		0			0
$637$	−0.489464	−	17.6240i	−0.0193933	−	0.698287i
$638$			38.8461i			1.53793i
$639$		0			0
$640$	−3.03881	+	1.75446i	−0.120120	+	0.0693510i
$641$			42.4515i			1.67673i	0.545108	+	0.838366i	$0.316489\pi$
$641$			42.4515i			1.67673i	−0.545108	+	0.838366i	$0.683511\pi$
$642$		0			0
$643$	15.0599	−	8.69484i	0.593904	−	0.342891i	−0.172735	−	0.984968i	$-0.555261\pi$
$643$	15.0599	−	8.69484i	0.593904	−	0.342891i	0.766640	+	0.642077i	$0.221927\pi$
$644$	−14.1666	+	0.196683i	−0.558241	+	0.00775041i
$645$		0			0
$646$	−4.13268	−	7.15800i	−0.162598	−	0.281628i
$647$	−0.164842	−	0.285514i	−0.00648060	−	0.0112247i	0.862767	−	0.505602i	$-0.168730\pi$
$647$	−0.164842	−	0.285514i	−0.00648060	−	0.0112247i	−0.869248	+	0.494377i	$0.835396\pi$
$648$		0			0
$649$	37.2922	+	21.5307i	1.46385	+	0.845152i
$650$	−9.20891	+	15.9503i	−0.361203	+	0.625622i
$651$		0			0
$652$	7.89989	+	13.6830i	0.309384	+	0.535868i
$653$		−	39.2793i		−	1.53712i	−0.639778	−	0.768560i	$-0.720974\pi$
$653$		−	39.2793i		−	1.53712i	0.639778	−	0.768560i	$-0.279026\pi$
$654$		0			0
$655$	34.5623			1.35046
$656$	−2.37578	+	4.11497i	−0.0927586	+	0.160663i
$657$		0			0
$658$	−22.8135	+	0.316734i	−0.889361	+	0.0123476i
$659$	24.4389	+	14.1098i	0.952002	+	0.549639i	0.893702	−	0.448660i	$-0.148099\pi$
$659$	24.4389	+	14.1098i	0.952002	+	0.549639i	0.0583000	+	0.998299i	$0.481432\pi$
$660$		0			0
$661$	27.0293	+	15.6054i	1.05132	+	0.606978i	0.923018	−	0.384758i	$-0.125715\pi$
$661$	27.0293	+	15.6054i	1.05132	+	0.606978i	0.128299	+	0.991736i	$0.459048\pi$
$662$	7.98888	+	4.61238i	0.310497	+	0.179265i
$663$		0			0
$664$	0.403282	+	0.232835i	0.0156504	+	0.00903574i
$665$	−45.0046	+	0.624827i	−1.74520	+	0.0242298i
$666$		0			0
$667$	19.0709	−	33.0318i	0.738429	−	1.27900i
$668$	9.47538			0.366613
$669$		0			0
$670$		−	6.28609i		−	0.242853i
$671$	22.8726	+	39.6165i	0.882988	+	1.52938i
$672$		0			0
$673$	−22.1804	+	38.4176i	−0.854991	+	1.48089i	0.0216619	+	0.999765i	$0.493104\pi$
$673$	−22.1804	+	38.4176i	−0.854991	+	1.48089i	−0.876653	+	0.481123i	$0.840229\pi$
$674$	13.9088	+	8.03024i	0.535747	+	0.309313i
$675$		0			0
$676$	3.32813	+	5.76449i	0.128005	+	0.221711i
$677$	1.47585	+	2.55624i	0.0567214	+	0.0982444i	0.892992	−	0.450073i	$-0.148602\pi$
$677$	1.47585	+	2.55624i	0.0567214	+	0.0982444i	−0.836270	+	0.548317i	$0.815269\pi$
$678$		0			0
$679$	12.9553	−	0.179867i	0.497179	−	0.00690265i
$680$	−5.18070	+	2.99108i	−0.198671	+	0.114703i
$681$		0			0
$682$		−	33.1227i		−	1.26833i
$683$	−17.2361	+	9.95129i	−0.659523	+	0.380776i	−0.792095	−	0.610398i	$-0.791010\pi$
$683$	−17.2361	+	9.95129i	−0.659523	+	0.380776i	0.132572	+	0.991173i	$0.457676\pi$
$684$		0			0
$685$			6.19146i			0.236564i
$686$	−9.91990	−	15.6396i	−0.378744	−	0.597121i
$687$		0			0
$688$	6.45690			0.246167
$689$	14.6443	−	25.3648i	0.557905	−	0.966320i
$690$		0			0
$691$	−30.2954	+	17.4910i	−1.15249	+	0.665390i	−0.949493	−	0.313789i	$-0.898401\pi$
$691$	−30.2954	+	17.4910i	−1.15249	+	0.665390i	−0.202997	+	0.979179i	$0.565068\pi$
$692$	−0.535796			−0.0203679
$693$		0			0
$694$	13.0035			0.493606
$695$	−58.3971	+	33.7156i	−2.21513	+	1.27891i
$696$		0			0
$697$	−4.05033	+	7.01538i	−0.153417	+	0.265727i
$698$	10.3424			0.391466
$699$		0			0
$700$	0.268581	+	19.3452i	0.0101514	+	0.731179i
$701$		−	43.8877i		−	1.65761i	−0.559534	−	0.828807i	$-0.689020\pi$
$701$		−	43.8877i		−	1.65761i	0.559534	−	0.828807i	$-0.310980\pi$
$702$		0			0
$703$	−34.8460	+	20.1184i	−1.31424	+	0.758778i
$704$		−	5.45384i		−	0.205549i
$705$		0			0
$706$	0.269620	−	0.155665i	0.0101473	−	0.00585855i
$707$	−33.0850	+	19.7191i	−1.24429	+	0.741611i
$708$		0			0
$709$	6.73054	+	11.6576i	0.252771	+	0.437812i	0.964288	−	0.264857i	$-0.0853248\pi$
$709$	6.73054	+	11.6576i	0.252771	+	0.437812i	−0.711517	+	0.702669i	$0.751992\pi$
$710$	1.38846	+	2.40489i	0.0521081	+	0.0902539i
$711$		0			0
$712$	1.89113	+	1.09184i	0.0708731	+	0.0409186i
$713$	−16.2611	+	28.1650i	−0.608982	+	1.05479i
$714$		0			0
$715$	−24.1001	−	41.7426i	−0.901292	−	1.56108i
$716$		−	10.0391i		−	0.375179i
$717$		0			0
$718$	−4.30925			−0.160820
$719$	21.7574	−	37.6849i	0.811413	−	1.40541i	−0.100462	−	0.994941i	$-0.532032\pi$
$719$	21.7574	−	37.6849i	0.811413	−	1.40541i	0.911875	−	0.410468i	$-0.134635\pi$
$720$		0			0
$721$	6.04063	+	10.1351i	0.224965	+	0.377450i
$722$	−3.90111	−	2.25230i	−0.145184	−	0.0838221i
$723$		0			0
$724$	−17.9398	−	10.3575i	−0.666726	−	0.384935i
$725$	−45.1066	−	26.0423i	−1.67522	−	0.967188i
$726$		0			0
$727$	−30.6479	−	17.6945i	−1.13667	−	0.656254i	−0.191063	−	0.981578i	$-0.561194\pi$
$727$	−30.6479	−	17.6945i	−1.13667	−	0.656254i	−0.945603	+	0.325323i	$0.894527\pi$
$728$	−5.81672	−	3.25146i	−0.215582	−	0.120507i
$729$		0			0
$730$	−23.3973	+	40.5253i	−0.865972	+	1.49991i
$731$	11.0080			0.407146
$732$		0			0
$733$		−	6.45651i		−	0.238477i	−0.992866	−	0.119238i	$-0.961955\pi$
$733$		−	6.45651i		−	0.238477i	0.992866	−	0.119238i	$-0.0380453\pi$
$734$	11.7871	+	20.4159i	0.435070	+	0.753563i
$735$		0			0
$736$	−2.67749	+	4.63754i	−0.0986934	+	0.170942i
$737$	8.46138	+	4.88518i	0.311679	+	0.179948i
$738$		0			0
$739$	−12.0461	−	20.8645i	−0.443124	−	0.767514i	0.554795	−	0.831987i	$-0.312797\pi$
$739$	−12.0461	−	20.8645i	−0.443124	−	0.767514i	−0.997919	+	0.0644733i	$0.979463\pi$
$740$	14.5609	+	25.2203i	0.535270	+	0.927115i
$741$		0			0
$742$	−0.427108	−	30.7634i	−0.0156796	−	1.12936i
$743$	−19.4191	+	11.2116i	−0.712419	+	0.411316i	−0.811956	−	0.583718i	$-0.801597\pi$
$743$	−19.4191	+	11.2116i	−0.712419	+	0.411316i	0.0995368	+	0.995034i	$0.468264\pi$
$744$		0			0
$745$			47.2966i			1.73281i
$746$	−15.7603	+	9.09923i	−0.577027	+	0.333147i
$747$		0			0
$748$		−	9.29796i		−	0.339967i
$749$	18.3222	−	0.254378i	0.669477	−	0.00929477i
$750$		0			0
$751$	5.09455			0.185903			0.0929514	−	0.995671i	$-0.470370\pi$
$751$	5.09455			0.185903			0.0929514	+	0.995671i	$0.470370\pi$
$752$	−4.31175	+	7.46818i	−0.157233	+	0.272336i
$753$		0			0
$754$	15.5363	−	8.96989i	0.565799	−	0.326664i
$755$	5.41744			0.197161
$756$		0			0
$757$	20.2782			0.737025			0.368513	−	0.929623i	$-0.379867\pi$
$757$	20.2782			0.737025			0.368513	+	0.929623i	$0.379867\pi$
$758$	−9.77237	+	5.64208i	−0.354948	+	0.204930i
$759$		0			0
$760$	−8.50589	+	14.7326i	−0.308541	+	0.534409i
$761$	−38.6753			−1.40198			−0.700989	−	0.713173i	$-0.747258\pi$
$761$	−38.6753			−1.40198			−0.700989	+	0.713173i	$0.747258\pi$
$762$		0			0
$763$	−5.79528	−	3.23948i	−0.209803	−	0.117277i
$764$		−	11.2369i		−	0.406536i
$765$		0			0
$766$	30.1762	−	17.4222i	1.09031	−	0.629491i
$767$		−	19.8865i		−	0.718058i
$768$		0			0
$769$	−29.1535	+	16.8318i	−1.05130	+	0.606969i	−0.923013	−	0.384768i	$-0.874281\pi$
$769$	−29.1535	+	16.8318i	−1.05130	+	0.606969i	−0.128287	+	0.991737i	$0.540948\pi$
$770$	−44.1958	−	24.7048i	−1.59271	−	0.890300i
$771$		0			0
$772$	10.4136	+	18.0369i	0.374793	+	0.649161i
$773$	20.5474	+	35.5892i	0.739040	+	1.28006i	0.952928	+	0.303197i	$0.0980540\pi$
$773$	20.5474	+	35.5892i	0.739040	+	1.28006i	−0.213888	+	0.976858i	$0.568613\pi$
$774$		0			0
$775$	38.4608	+	22.2054i	1.38155	+	0.797640i
$776$	2.44856	−	4.24103i	0.0878981	−	0.152244i
$777$		0			0
$778$	−3.07989	−	5.33453i	−0.110419	−	0.191252i
$779$			23.0363i			0.825361i
$780$		0			0
$781$	−4.31613			−0.154443
$782$	−4.56470	+	7.90629i	−0.163233	+	0.282728i
$783$		0			0
$784$	−6.99730	+	0.194333i	−0.249904	+	0.00694048i
$785$	−49.5254	−	28.5935i	−1.76764	−	1.02055i
$786$		0			0
$787$	13.6515	+	7.88171i	0.486624	+	0.280953i	0.723173	−	0.690667i	$-0.242683\pi$
$787$	13.6515	+	7.88171i	0.486624	+	0.280953i	−0.236549	+	0.971620i	$0.576016\pi$
$788$	17.7504	+	10.2482i	0.632331	+	0.365077i
$789$		0			0
$790$	−14.6421	−	8.45364i	−0.520943	−	0.300767i
$791$	−6.34379	+	11.3487i	−0.225559	+	0.403515i
$792$		0			0
$793$	10.5630	−	18.2956i	0.375102	−	0.649696i
$794$	−1.09799			−0.0389663
$795$		0			0
$796$		−	2.97308i		−	0.105378i
$797$	15.4937	+	26.8359i	0.548816	+	0.950578i	0.998356	+	0.0573173i	$0.0182547\pi$
$797$	15.4937	+	26.8359i	0.548816	+	0.950578i	−0.449540	+	0.893260i	$0.648412\pi$
$798$		0			0
$799$	−7.35087	+	12.7321i	−0.260055	+	0.450429i
$800$	6.33280	+	3.65625i	0.223898	+	0.129268i
$801$		0			0
$802$	−8.85824	−	15.3429i	−0.312795	−	0.541777i
$803$	−36.3659	−	62.9877i	−1.28333	−	2.22279i
$804$		0			0
$805$	25.4523	+	42.7044i	0.897076	+	1.50513i
$806$	−13.2473	+	7.64831i	−0.466615	+	0.269400i
$807$		0			0
$808$			14.5576i			0.512134i
$809$	4.14321	−	2.39209i	0.145668	−	0.0841013i	−0.425395	−	0.905008i	$-0.639865\pi$
$809$	4.14321	−	2.39209i	0.145668	−	0.0841013i	0.571062	+	0.820907i	$0.306531\pi$
$810$		0			0
$811$		−	25.0977i		−	0.881299i	−0.897679	−	0.440650i	$-0.854748\pi$
$811$		−	25.0977i		−	0.881299i	0.897679	−	0.440650i	$-0.145252\pi$
$812$	9.19497	−	16.4494i	0.322680	−	0.577260i
$813$		0			0
$814$	−45.2636			−1.58649
$815$	27.7201	−	48.0126i	0.970992	−	1.68181i
$816$		0			0
$817$	27.1101	−	15.6520i	0.948462	−	0.547595i
$818$	22.2018			0.776267
$819$		0			0
$820$	16.6728			0.582240
$821$	−2.61774	+	1.51135i	−0.0913598	+	0.0527466i	−0.544984	−	0.838447i	$-0.683464\pi$
$821$	−2.61774	+	1.51135i	−0.0913598	+	0.0527466i	0.453624	+	0.891193i	$0.350131\pi$
$822$		0			0
$823$	−5.60074	+	9.70077i	−0.195230	+	0.338147i	−0.946976	−	0.321305i	$-0.895879\pi$
$823$	−5.60074	+	9.70077i	−0.195230	+	0.338147i	0.751746	+	0.659453i	$0.229212\pi$
$824$	4.45949			0.155354
$825$		0			0
$826$	−10.6950	−	17.9443i	−0.372127	−	0.624363i
$827$		−	15.0061i		−	0.521812i	−0.965364	−	0.260906i	$-0.915979\pi$
$827$		−	15.0061i		−	0.521812i	0.965364	−	0.260906i	$-0.0840212\pi$
$828$		0			0
$829$	−17.3276	+	10.0041i	−0.601813	+	0.347457i	−0.769754	−	0.638340i	$-0.779621\pi$
$829$	−17.3276	+	10.0041i	−0.601813	+	0.347457i	0.167942	+	0.985797i	$0.446288\pi$
$830$		−	1.63400i		−	0.0567168i
$831$		0			0
$832$	−2.18124	+	1.25934i	−0.0756209	+	0.0436597i
$833$	−11.9293	+	0.331308i	−0.413326	+	0.0114791i
$834$		0			0
$835$	−16.6242	−	28.7939i	−0.575303	−	0.996453i
$836$	−13.2205	−	22.8986i	−0.457242	−	0.791966i
$837$		0			0
$838$	−5.72749	−	3.30677i	−0.197853	−	0.114230i
$839$	−1.25310	+	2.17043i	−0.0432618	+	0.0749316i	−0.886845	−	0.462066i	$-0.847108\pi$
$839$	−1.25310	+	2.17043i	−0.0432618	+	0.0749316i	0.843584	+	0.536998i	$0.180442\pi$
$840$		0			0
$841$	10.8664	+	18.8211i	0.374703	+	0.649005i
$842$			40.0179i			1.37911i
$843$		0			0
$844$	17.1452			0.590161
$845$	11.6781	−	20.2271i	0.401740	−	0.695833i
$846$		0			0
$847$	42.6005	−	25.3904i	1.46377	−	0.872423i
$848$	−10.0707	−	5.81430i	−0.345828	−	0.199664i
$849$		0			0
$850$	10.7964	+	6.23333i	0.370315	+	0.213802i
$851$	38.4887	+	22.2215i	1.31938	+	0.761743i
$852$		0			0
$853$	25.9938	+	15.0075i	0.890010	+	0.513847i	0.873946	−	0.486024i	$-0.161553\pi$
$853$	25.9938	+	15.0075i	0.890010	+	0.513847i	0.0160640	+	0.999871i	$0.494886\pi$
$854$	−0.308073	−	22.1896i	−0.0105420	−	0.759314i
$855$		0			0
$856$	3.46290	−	5.99791i	0.118359	−	0.205004i
$857$	7.53624			0.257433			0.128716	−	0.991681i	$-0.458914\pi$
$857$	7.53624			0.257433			0.128716	+	0.991681i	$0.458914\pi$
$858$		0			0
$859$		−	9.60427i		−	0.327694i	−0.986486	−	0.163847i	$-0.947610\pi$
$859$		−	9.60427i		−	0.327694i	0.986486	−	0.163847i	$-0.0523903\pi$
$860$	−11.3284	−	19.6213i	−0.386294	−	0.669080i
$861$		0			0
$862$	−11.7058	+	20.2750i	−0.398700	+	0.690568i
$863$	24.9184	+	14.3867i	0.848234	+	0.489728i	0.860055	−	0.510202i	$-0.170429\pi$
$863$	24.9184	+	14.3867i	0.848234	+	0.489728i	−0.0118207	+	0.999930i	$0.503763\pi$
$864$		0			0
$865$	0.940031	+	1.62818i	0.0319620	+	0.0553598i
$866$	16.6171	+	28.7817i	0.564672	+	0.978041i
$867$		0			0
$868$	−7.84022	+	14.0258i	−0.266114	+	0.476067i
$869$	22.7580	−	13.1393i	0.772012	−	0.445721i
$870$		0			0
$871$		−	4.51212i		−	0.152887i
$872$	−2.17320	+	1.25470i	−0.0735939	+	0.0424895i
$873$		0			0
$874$			25.9617i			0.878169i
$875$	18.4415	−	10.9913i	0.623436	−	0.371575i
$876$		0			0
$877$	−36.0765			−1.21822			−0.609109	−	0.793086i	$-0.708473\pi$
$877$	−36.0765			−1.21822			−0.609109	+	0.793086i	$0.708473\pi$
$878$	2.28573	−	3.95900i	0.0771397	−	0.133610i
$879$		0			0
$880$	−16.5732	+	9.56854i	−0.558682	+	0.322555i
$881$	53.7648			1.81138			0.905692	−	0.423937i	$-0.139352\pi$
$881$	53.7648			1.81138			0.905692	+	0.423937i	$0.139352\pi$
$882$		0			0
$883$	−12.1377			−0.408466			−0.204233	−	0.978922i	$-0.565470\pi$
$883$	−12.1377			−0.408466			−0.204233	+	0.978922i	$0.565470\pi$
$884$	−3.71868	+	2.14698i	−0.125073	+	0.0722107i
$885$		0			0
$886$	1.32106	−	2.28815i	0.0443820	−	0.0768719i
$887$	−15.3248			−0.514556			−0.257278	−	0.966337i	$-0.582826\pi$
$887$	−15.3248			−0.514556			−0.257278	+	0.966337i	$0.582826\pi$
$888$		0			0
$889$	25.2261	−	15.0350i	0.846055	−	0.504258i
$890$		−	7.66238i		−	0.256844i
$891$		0			0
$892$	−10.5032	+	6.06403i	−0.351673	+	0.203039i
$893$			41.8081i			1.39905i
$894$		0			0
$895$	−30.5069	+	17.6132i	−1.01973	+	0.588744i
$896$	−1.29094	+	2.30943i	−0.0431273	+	0.0771527i
$897$		0			0
$898$	−3.78418	−	6.55440i	−0.126280	−	0.218723i
$899$	−21.6290	−	37.4625i	−0.721368	−	1.24945i
$900$		0			0
$901$	−17.1689	−	9.91247i	−0.571979	−	0.330232i
$902$	−12.9571	+	22.4424i	−0.431425	+	0.747250i
$903$		0			0
$904$	2.45704	+	4.25572i	0.0817200	+	0.141543i
$905$			72.6874i			2.41621i
$906$		0			0
$907$	36.4270			1.20954			0.604769	−	0.796401i	$-0.293265\pi$
$907$	36.4270			1.20954			0.604769	+	0.796401i	$0.293265\pi$
$908$	0.705128	−	1.22132i	0.0234005	−	0.0405308i
$909$		0			0
$910$	0.324606	+	23.3805i	0.0107606	+	0.775055i
$911$	−14.9598	−	8.63706i	−0.495641	−	0.286159i	0.231271	−	0.972889i	$-0.425712\pi$
$911$	−14.9598	−	8.63706i	−0.495641	−	0.286159i	−0.726912	+	0.686731i	$0.759045\pi$
$912$		0			0
$913$	2.19943	+	1.26984i	0.0727907	+	0.0420257i
$914$	19.1234	+	11.0409i	0.632546	+	0.365201i
$915$		0			0
$916$	14.1942	+	8.19504i	0.468991	+	0.270772i
$917$	22.3858	−	13.3422i	0.739243	−	0.440598i
$918$		0			0
$919$	−5.58467	+	9.67294i	−0.184221	+	0.319081i	−0.943314	−	0.331902i	$-0.892310\pi$
$919$	−5.58467	+	9.67294i	−0.184221	+	0.319081i	0.759093	+	0.650983i	$0.225643\pi$
$920$	18.7901			0.619493
$921$		0			0
$922$			26.7119i			0.879710i
$923$	0.996631	+	1.72622i	0.0328045	+	0.0568191i
$924$		0			0
$925$	30.3446	−	52.5584i	0.997724	−	1.72811i
$926$	−9.05114	−	5.22568i	−0.297439	−	0.171726i
$927$		0			0
$928$	−3.56135	−	6.16843i	−0.116907	−	0.202489i
$929$	−6.45089	−	11.1733i	−0.211647	−	0.366583i	0.740583	−	0.671965i	$-0.234549\pi$
$929$	−6.45089	−	11.1733i	−0.211647	−	0.366583i	−0.952230	+	0.305381i	$0.901216\pi$
$930$		0			0
$931$	−28.9080	+	17.7779i	−0.947421	+	0.582648i
$932$	−10.6058	+	6.12326i	−0.347404	+	0.200574i
$933$		0			0
$934$			30.7077i			1.00479i
$935$	−28.2547	+	16.3129i	−0.924028	+	0.533488i
$936$		0			0
$937$			30.7926i			1.00595i	0.864301	+	0.502975i	$0.167761\pi$
$937$			30.7926i			1.00595i	−0.864301	+	0.502975i	$0.832239\pi$
$938$	−2.42664	−	4.07146i	−0.0792325	−	0.132938i
$939$		0			0
$940$	30.2592			0.986945
$941$	4.47172	−	7.74525i	0.145774	−	0.252488i	−0.783887	−	0.620903i	$-0.786766\pi$
$941$	4.47172	−	7.74525i	0.145774	−	0.252488i	0.929661	+	0.368415i	$0.120099\pi$
$942$		0			0
$943$	22.0355	−	12.7222i	0.717576	−	0.414293i
$944$	−7.89559			−0.256979
$945$		0			0
$946$	35.2149			1.14494
$947$	24.5088	−	14.1501i	0.796428	−	0.459818i	−0.0457926	−	0.998951i	$-0.514581\pi$
$947$	24.5088	−	14.1501i	0.796428	−	0.459818i	0.842221	+	0.539133i	$0.181248\pi$
$948$		0			0
$949$	−16.7944	+	29.0888i	−0.545170	+	0.944262i
$950$	35.4521			1.15022
$951$		0			0
$952$	−2.20085	+	3.93722i	−0.0713300	+	0.127606i
$953$		−	22.6378i		−	0.733311i	−0.930357	−	0.366656i	$-0.880503\pi$
$953$		−	22.6378i		−	0.733311i	0.930357	−	0.366656i	$-0.119497\pi$
$954$		0			0
$955$	−34.1467	+	19.7146i	−1.10496	+	0.637950i
$956$		−	11.9828i		−	0.387551i
$957$		0			0
$958$	12.1371	−	7.00736i	0.392132	−	0.226398i
$959$	2.39011	+	4.01017i	0.0771805	+	0.129495i
$960$		0			0
$961$	2.94229	+	5.09619i	0.0949125	+	0.164393i
$962$	10.4517	+	18.1030i	0.336978	+	0.583663i
$963$		0			0
$964$	0.00308144	+	0.00177907i	9.92464e−5	+	5.72999e-5i
$965$	36.5404	−	63.2898i	1.17628	−	2.03737i
$966$		0			0
$967$	−3.13531	−	5.43051i	−0.100825	−	0.174634i	0.811200	−	0.584769i	$-0.198815\pi$
$967$	−3.13531	−	5.43051i	−0.100825	−	0.174634i	−0.912025	+	0.410135i	$0.865481\pi$
$968$		−	18.7444i		−	0.602468i
$969$		0			0
$970$	−17.1836			−0.551731
$971$	−26.2604	+	45.4843i	−0.842736	+	1.45966i	0.0448374	+	0.998994i	$0.485723\pi$
$971$	−26.2604	+	45.4843i	−0.842736	+	1.45966i	−0.887573	+	0.460667i	$0.847610\pi$
$972$		0			0
$973$	−24.8081	+	44.3806i	−0.795312	+	1.42278i
$974$	−1.11374	−	0.643017i	−0.0356865	−	0.0206036i
$975$		0			0
$976$	−7.26397	−	4.19385i	−0.232514	−	0.134242i
$977$	−5.70488	−	3.29371i	−0.182515	−	0.105375i	0.405959	−	0.913891i	$-0.366938\pi$
$977$	−5.70488	−	3.29371i	−0.182515	−	0.105375i	−0.588474	+	0.808516i	$0.700271\pi$
$978$		0			0
$979$	10.3139	+	5.95475i	0.329635	+	0.190315i
$980$	12.8670	+	20.9225i	0.411022	+	0.668346i
$981$		0			0
$982$	−0.264865	+	0.458760i	−0.00845219	+	0.0146396i
$983$	−25.2775			−0.806227			−0.403114	−	0.915150i	$-0.632072\pi$
$983$	−25.2775			−0.806227			−0.403114	+	0.915150i	$0.632072\pi$
$984$		0			0
$985$		−	71.9201i		−	2.29156i
$986$	−6.07154	−	10.5162i	−0.193357	−	0.334905i
$987$		0			0
$988$	−6.10547	+	10.5750i	−0.194241	+	0.336435i
$989$	−29.9441	−	17.2882i	−0.952168	−	0.549734i
$990$		0			0
$991$	−17.1153	−	29.6445i	−0.543684	−	0.941689i	−0.998688	−	0.0511994i	$-0.983696\pi$
$991$	−17.1153	−	29.6445i	−0.543684	−	0.941689i	0.455004	−	0.890489i	$-0.349638\pi$
$992$	3.03663	+	5.25960i	0.0964132	+	0.166993i
$993$		0			0
$994$	1.82767	+	1.02164i	0.0579700	+	0.0324044i
$995$	−9.03463	+	5.21615i	−0.286417	+	0.165363i
$996$		0			0
$997$		−	12.4543i		−	0.394432i	−0.980360	−	0.197216i	$-0.936810\pi$
$997$		−	12.4543i		−	0.394432i	0.980360	−	0.197216i	$-0.0631901\pi$
$998$	−19.0687	+	11.0093i	−0.603610	+	0.348494i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.t.g.593.1		16
3.2	odd	2		1134.2.t.h.593.8		16
7.3	odd	6		1134.2.l.h.269.1		16
9.2	odd	6		1134.2.k.c.971.1	yes	16
9.4	even	3		1134.2.l.g.215.4		16
9.5	odd	6		1134.2.l.h.215.5		16
9.7	even	3		1134.2.k.d.971.8	yes	16
21.17	even	6		1134.2.l.g.269.8		16
63.31	odd	6		1134.2.t.h.1025.8		16
63.38	even	6		1134.2.k.d.647.8	yes	16
63.52	odd	6		1134.2.k.c.647.1	✓	16
63.59	even	6	inner	1134.2.t.g.1025.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.1	✓	16	63.52	odd	6
1134.2.k.c.971.1	yes	16	9.2	odd	6
1134.2.k.d.647.8	yes	16	63.38	even	6
1134.2.k.d.971.8	yes	16	9.7	even	3
1134.2.l.g.215.4		16	9.4	even	3
1134.2.l.g.269.8		16	21.17	even	6
1134.2.l.h.215.5		16	9.5	odd	6
1134.2.l.h.269.1		16	7.3	odd	6
1134.2.t.g.593.1		16	1.1	even	1	trivial
1134.2.t.g.1025.1		16	63.59	even	6	inner
1134.2.t.h.593.8		16	3.2	odd	2
1134.2.t.h.1025.8		16	63.31	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.50892 q^{5} +(-2.27270 + 1.35456i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.50892 q^{5} +(-2.27270 + 1.35456i) q^{7} +1.00000i q^{8} +(3.03881 - 1.75446i) q^{10} +5.45384i q^{11} +(2.18124 - 1.25934i) q^{13} +(1.29094 - 2.30943i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.852422 - 1.47644i) q^{17} +(-4.19863 - 2.42408i) q^{19} +(-1.75446 + 3.03881i) q^{20} +(-2.72692 - 4.72317i) q^{22} +5.35497i q^{23} +7.31249 q^{25} +(-1.25934 + 2.18124i) q^{26} +(0.0367291 + 2.64550i) q^{28} +(-6.16843 - 3.56135i) q^{29} +(5.25960 + 3.03663i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.47644 + 0.852422i) q^{34} +(7.97472 - 4.75303i) q^{35} +(4.14969 - 7.18748i) q^{37} +4.84816 q^{38} -3.50892i q^{40} +(-2.37578 - 4.11497i) q^{41} +(-3.22845 + 5.59184i) q^{43} +(4.72317 + 2.72692i) q^{44} +(-2.67749 - 4.63754i) q^{46} +(-4.31175 - 7.46818i) q^{47} +(3.33035 - 6.15701i) q^{49} +(-6.33280 + 3.65625i) q^{50} -2.51868i q^{52} +(10.0707 - 5.81430i) q^{53} -19.1371i q^{55} +(-1.35456 - 2.27270i) q^{56} +7.12269 q^{58} +(3.94779 - 6.83778i) q^{59} +(7.26397 - 4.19385i) q^{61} -6.07327 q^{62} -1.00000 q^{64} +(-7.65379 + 4.41892i) q^{65} +(0.895732 - 1.55145i) q^{67} -1.70484 q^{68} +(-4.52980 + 8.10360i) q^{70} +0.791392i q^{71} +(-11.5492 + 6.66795i) q^{73} +8.29939i q^{74} +(-4.19863 + 2.42408i) q^{76} +(-7.38754 - 12.3950i) q^{77} +(-2.40919 - 4.17283i) q^{79} +(1.75446 + 3.03881i) q^{80} +(4.11497 + 2.37578i) q^{82} +(0.232835 - 0.403282i) q^{83} +(2.99108 + 5.18070i) q^{85} -6.45690i q^{86} -5.45384 q^{88} +(1.09184 - 1.89113i) q^{89} +(-3.25146 + 5.81672i) q^{91} +(4.63754 + 2.67749i) q^{92} +(7.46818 + 4.31175i) q^{94} +(14.7326 + 8.50589i) q^{95} +(-4.24103 - 2.44856i) q^{97} +(0.194333 + 6.99730i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 4 * q^7	\( 16 q + 8 q^{4} - 4 q^{7} + 12 q^{13} - 12 q^{14} - 8 q^{16} + 16 q^{25} + 4 q^{28} - 48 q^{29} - 12 q^{31} + 60 q^{35} + 4 q^{37} + 24 q^{38} + 24 q^{41} + 16 q^{43} + 12 q^{44} + 16 q^{49} + 24 q^{50} - 12 q^{56} + 24 q^{58} - 24 q^{59} + 12 q^{61} - 48 q^{62} - 16 q^{64} - 48 q^{65} - 4 q^{67} + 12 q^{70} + 36 q^{73} - 36 q^{77} + 8 q^{79} + 36 q^{83} - 12 q^{85} + 24 q^{89} - 12 q^{91} - 12 q^{92} + 36 q^{94} - 12 q^{95} + 12 q^{97} + 36 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^13 - 12 * q^14 - 8 * q^16 + 16 * q^25 + 4 * q^28 - 48 * q^29 - 12 * q^31 + 60 * q^35 + 4 * q^37 + 24 * q^38 + 24 * q^41 + 16 * q^43 + 12 * q^44 + 16 * q^49 + 24 * q^50 - 12 * q^56 + 24 * q^58 - 24 * q^59 + 12 * q^61 - 48 * q^62 - 16 * q^64 - 48 * q^65 - 4 * q^67 + 12 * q^70 + 36 * q^73 - 36 * q^77 + 8 * q^79 + 36 * q^83 - 12 * q^85 + 24 * q^89 - 12 * q^91 - 12 * q^92 + 36 * q^94 - 12 * q^95 + 12 * q^97 + 36 * q^98

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