LMFDB - Embedded newform 1134.2.l.g.215.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(215,1134)]

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([5, 5]))

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

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

chi := DirichletCharacter("1134.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.l (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			215.4
Root			$0.500000 - 1.76390i$ of defining polynomial
Character	$\chi$	$=$	1134.215
Dual form			1134.2.l.g.269.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(1.75446 + 3.03881i) q^{5} +(-0.0367291 - 2.64550i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.75446 + 3.03881i) q^{5} +(-0.0367291 - 2.64550i) q^{7} +1.00000i q^{8} +(3.03881 - 1.75446i) q^{10} +(-4.72317 - 2.72692i) q^{11} +(-2.18124 - 1.25934i) q^{13} +(-2.64550 + 0.0367291i) q^{14} +1.00000 q^{16} +(-0.852422 - 1.47644i) q^{17} +(-4.19863 - 2.42408i) q^{19} +(-1.75446 - 3.03881i) q^{20} +(-2.72692 + 4.72317i) q^{22} +(4.63754 - 2.67749i) q^{23} +(-3.65625 + 6.33280i) q^{25} +(-1.25934 + 2.18124i) q^{26} +(0.0367291 + 2.64550i) q^{28} +(6.16843 - 3.56135i) q^{29} -6.07327i q^{31} -1.00000i q^{32} +(-1.47644 + 0.852422i) q^{34} +(7.97472 - 4.75303i) q^{35} +(4.14969 - 7.18748i) q^{37} +(-2.42408 + 4.19863i) q^{38} +(-3.03881 + 1.75446i) q^{40} +(-2.37578 + 4.11497i) q^{41} +(-3.22845 - 5.59184i) q^{43} +(4.72317 + 2.72692i) q^{44} +(-2.67749 - 4.63754i) q^{46} +8.62351 q^{47} +(-6.99730 + 0.194333i) q^{49} +(6.33280 + 3.65625i) q^{50} +(2.18124 + 1.25934i) q^{52} +(10.0707 - 5.81430i) q^{53} -19.1371i q^{55} +(2.64550 - 0.0367291i) q^{56} +(-3.56135 - 6.16843i) q^{58} -7.89559 q^{59} +8.38771i q^{61} -6.07327 q^{62} -1.00000 q^{64} -8.83783i q^{65} -1.79146 q^{67} +(0.852422 + 1.47644i) q^{68} +(-4.75303 - 7.97472i) q^{70} +0.791392i q^{71} +(-11.5492 + 6.66795i) q^{73} +(-7.18748 - 4.14969i) q^{74} +(4.19863 + 2.42408i) q^{76} +(-7.04058 + 12.5953i) q^{77} +4.81837 q^{79} +(1.75446 + 3.03881i) q^{80} +(4.11497 + 2.37578i) q^{82} +(0.232835 + 0.403282i) q^{83} +(2.99108 - 5.18070i) q^{85} +(-5.59184 + 3.22845i) q^{86} +(2.72692 - 4.72317i) q^{88} +(1.09184 - 1.89113i) q^{89} +(-3.25146 + 5.81672i) q^{91} +(-4.63754 + 2.67749i) q^{92} -8.62351i q^{94} -17.0118i q^{95} +(4.24103 - 2.44856i) q^{97} +(0.194333 + 6.99730i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 - 4 * q^7	$ 16 q - 16 q^{4} - 4 q^{7} - 12 q^{11} - 12 q^{13} + 16 q^{16} - 12 q^{23} - 8 q^{25} + 4 q^{28} + 48 q^{29} + 60 q^{35} + 4 q^{37} - 12 q^{38} + 24 q^{41} + 16 q^{43} + 12 q^{44} - 20 q^{49} - 24 q^{50} + 12 q^{52} - 12 q^{58} + 48 q^{59} - 48 q^{62} - 16 q^{64} + 8 q^{67} + 12 q^{70} + 36 q^{73} - 36 q^{74} - 48 q^{77} - 16 q^{79} + 36 q^{83} - 12 q^{85} - 24 q^{86} + 24 q^{89} - 12 q^{91} + 12 q^{92} - 12 q^{97} + 36 q^{98}+O(q^{100}) $ 16 * q - 16 * q^4 - 4 * q^7 - 12 * q^11 - 12 * q^13 + 16 * q^16 - 12 * q^23 - 8 * q^25 + 4 * q^28 + 48 * q^29 + 60 * q^35 + 4 * q^37 - 12 * q^38 + 24 * q^41 + 16 * q^43 + 12 * q^44 - 20 * q^49 - 24 * q^50 + 12 * q^52 - 12 * q^58 + 48 * q^59 - 48 * q^62 - 16 * q^64 + 8 * q^67 + 12 * q^70 + 36 * q^73 - 36 * q^74 - 48 * q^77 - 16 * q^79 + 36 * q^83 - 12 * q^85 - 24 * q^86 + 24 * q^89 - 12 * q^91 + 12 * q^92 - 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.75446	+	3.03881i	0.784618	+	1.35900i	0.929227	+	0.369509i	$0.120474\pi$
$5$	1.75446	+	3.03881i	0.784618	+	1.35900i	−0.144610	+	0.989489i	$0.546193\pi$
$6$		0			0
$7$	−0.0367291	−	2.64550i	−0.0138823	−	0.999904i
$7$	−0.0367291	−	2.64550i	−0.0138823	−	0.999904i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	3.03881	−	1.75446i	0.960956	−	0.554808i
$11$	−4.72317	−	2.72692i	−1.42409	−	0.822198i	−0.427443	−	0.904042i	$-0.640586\pi$
$11$	−4.72317	−	2.72692i	−1.42409	−	0.822198i	−0.996645	+	0.0818442i	$0.973919\pi$
$12$		0			0
$13$	−2.18124	−	1.25934i	−0.604967	−	0.349278i	0.166026	−	0.986121i	$-0.446906\pi$
$13$	−2.18124	−	1.25934i	−0.604967	−	0.349278i	−0.770993	+	0.636843i	$0.780240\pi$
$14$	−2.64550	+	0.0367291i	−0.707039	+	0.00981627i
$15$		0			0
$16$	1.00000			0.250000
$17$	−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
$23$	4.63754	−	2.67749i	0.966994	−	0.558294i	0.0686756	−	0.997639i	$-0.478123\pi$
$23$	4.63754	−	2.67749i	0.966994	−	0.558294i	0.898319	+	0.439345i	$0.144789\pi$
$24$		0			0
$25$	−3.65625	+	6.33280i	−0.731249	+	1.26656i
$26$	−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	$-0.436661\pi$
$29$	6.16843	−	3.56135i	1.14545	−	0.661326i	0.947774	+	0.318942i	$0.103328\pi$
$30$		0			0
$31$		−	6.07327i		−	1.09079i	−0.838179	−	0.545395i	$-0.816379\pi$
$31$		−	6.07327i		−	1.09079i	0.838179	−	0.545395i	$-0.183621\pi$
$32$		−	1.00000i		−	0.176777i
$33$		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	$-0.0723123\pi$
$38$	−2.42408	+	4.19863i	−0.393237	+	0.681107i
$39$		0			0
$40$	−3.03881	+	1.75446i	−0.480478	+	0.277404i
$41$	−2.37578	+	4.11497i	−0.371034	+	0.642650i	−0.989725	−	0.142984i	$-0.954330\pi$
$41$	−2.37578	+	4.11497i	−0.371034	+	0.642650i	0.618691	+	0.785635i	$0.287663\pi$
$42$		0			0
$43$	−3.22845	−	5.59184i	−0.492334	−	0.852747i	0.507627	−	0.861577i	$-0.330523\pi$
$43$	−3.22845	−	5.59184i	−0.492334	−	0.852747i	−0.999961	+	0.00882976i	$0.997189\pi$
$44$	4.72317	+	2.72692i	0.712044	+	0.411099i
$45$		0			0
$46$	−2.67749	−	4.63754i	−0.394774	−	0.683768i
$47$	8.62351			1.25787			0.628934	−	0.777459i	$-0.283492\pi$
$47$	8.62351			1.25787			0.628934	+	0.777459i	$0.283492\pi$
$48$		0			0
$49$	−6.99730	+	0.194333i	−0.999615	+	0.0277619i
$50$	6.33280	+	3.65625i	0.895594	+	0.517071i
$51$		0			0
$52$	2.18124	+	1.25934i	0.302484	+	0.174639i
$53$	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
$56$	2.64550	−	0.0367291i	0.353519	−	0.00490813i
$57$		0			0
$58$	−3.56135	−	6.16843i	−0.467628	−	0.809955i
$59$	−7.89559			−1.02792			−0.513959	−	0.857815i	$-0.671822\pi$
$59$	−7.89559			−1.02792			−0.513959	+	0.857815i	$0.671822\pi$
$60$		0			0
$61$			8.38771i			1.07394i	0.843603	+	0.536968i	$0.180430\pi$
$61$			8.38771i			1.07394i	−0.843603	+	0.536968i	$0.819570\pi$
$62$	−6.07327			−0.771306
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	8.83783i		−	1.09620i
$66$		0			0
$67$	−1.79146			−0.218862			−0.109431	−	0.993994i	$-0.534903\pi$
$67$	−1.79146			−0.218862			−0.109431	+	0.993994i	$0.534903\pi$
$68$	0.852422	+	1.47644i	0.103371	+	0.179044i
$69$		0			0
$70$	−4.75303	−	7.97472i	−0.568095	−	0.953162i
$71$			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	$0.618330\pi$
$74$	−7.18748	−	4.14969i	−0.835527	−	0.482392i
$75$		0			0
$76$	4.19863	+	2.42408i	0.481615	+	0.278061i
$77$	−7.04058	+	12.5953i	−0.802349	+	1.43537i
$78$		0			0
$79$	4.81837			0.542109			0.271055	−	0.962564i	$-0.412628\pi$
$79$	4.81837			0.542109			0.271055	+	0.962564i	$0.412628\pi$
$80$	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	0.878521	−	0.477704i	$-0.158531\pi$
$83$	0.232835	+	0.403282i	0.0255569	+	0.0442659i	−0.852964	+	0.521970i	$0.825197\pi$
$84$		0			0
$85$	2.99108	−	5.18070i	0.324428	−	0.561926i
$86$	−5.59184	+	3.22845i	−0.602983	+	0.348133i
$87$		0			0
$88$	2.72692	−	4.72317i	0.290691	−	0.503491i
$89$	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
$94$		−	8.62351i		−	0.889447i
$95$		−	17.0118i		−	1.74537i
$96$		0			0
$97$	4.24103	−	2.44856i	0.430611	−	0.248613i	−0.268996	−	0.963141i	$-0.586692\pi$
$97$	4.24103	−	2.44856i	0.430611	−	0.248613i	0.699607	+	0.714528i	$0.253358\pi$
$98$	0.194333	+	6.99730i	0.0196306	+	0.706834i
$99$		0			0
$100$	3.65625	−	6.33280i	0.365625	−	0.633280i
$101$	−7.27879	+	12.6072i	−0.724266	+	1.25447i	0.235009	+	0.971993i	$0.424488\pi$
$101$	−7.27879	+	12.6072i	−0.724266	+	1.25447i	−0.959275	+	0.282473i	$0.908845\pi$
$102$		0			0
$103$	−3.86203	+	2.22974i	−0.380537	+	0.219703i	−0.678052	−	0.735014i	$-0.737176\pi$
$103$	−3.86203	+	2.22974i	−0.380537	+	0.219703i	0.297515	+	0.954717i	$0.403842\pi$
$104$	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	$0.794987\pi$
$110$	−19.1371			−1.82465
$111$		0			0
$112$	−0.0367291	−	2.64550i	−0.00347057	−	0.249976i
$113$	−4.25572	−	2.45704i	−0.400345	−	0.231139i	0.286288	−	0.958144i	$-0.407579\pi$
$113$	−4.25572	−	2.45704i	−0.400345	−	0.231139i	−0.686633	+	0.727004i	$0.740912\pi$
$114$		0			0
$115$	16.2727	+	9.39507i	1.51744	+	0.876095i
$116$	−6.16843	+	3.56135i	−0.572725	+	0.330663i
$117$		0			0
$118$			7.89559i			0.726848i
$119$	−3.87460	+	2.30931i	−0.355184	+	0.211694i
$120$		0			0
$121$	9.37221	+	16.2331i	0.852019	+	1.47574i
$122$	8.38771			0.759387
$123$		0			0
$124$			6.07327i			0.545395i
$125$	−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	$0.663904\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−8.83783			−0.775129
$131$	4.92492	+	8.53022i	0.430293	+	0.745289i	0.996898	−	0.0787003i	$-0.0250770\pi$
$131$	4.92492	+	8.53022i	0.430293	+	0.745289i	−0.566606	+	0.823989i	$0.691744\pi$
$132$		0			0
$133$	−6.25868	+	11.1965i	−0.542696	+	0.970858i
$134$			1.79146i			0.154759i
$135$		0			0
$136$	1.47644	−	0.852422i	0.126604	−	0.0730946i
$137$	1.52810	+	0.882247i	0.130554	+	0.0753754i	0.563855	−	0.825874i	$-0.309318\pi$
$137$	1.52810	+	0.882247i	0.130554	+	0.0753754i	−0.433301	+	0.901249i	$0.642651\pi$
$138$		0			0
$139$	−16.6425	−	9.60855i	−1.41160	−	0.814986i	−0.416059	−	0.909338i	$-0.636589\pi$
$139$	−16.6425	−	9.60855i	−1.41160	−	0.814986i	−0.995539	+	0.0943514i	$0.969922\pi$
$140$	−7.97472	+	4.75303i	−0.673987	+	0.401704i
$141$		0			0
$142$	0.791392			0.0664121
$143$	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
$149$	−11.6731	+	6.73949i	−0.956300	+	0.552120i	−0.895032	−	0.446001i	$-0.852848\pi$
$149$	−11.6731	+	6.73949i	−0.956300	+	0.552120i	−0.0612680	+	0.998121i	$0.519514\pi$
$150$		0			0
$151$	0.771954	−	1.33706i	0.0628207	−	0.108809i	−0.832904	−	0.553417i	$-0.813324\pi$
$151$	0.771954	−	1.33706i	0.0628207	−	0.108809i	0.895725	+	0.444608i	$0.146657\pi$
$152$	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
$157$		−	16.2976i		−	1.30069i	−0.759638	−	0.650346i	$-0.774624\pi$
$157$		−	16.2976i		−	1.30069i	0.759638	−	0.650346i	$-0.225376\pi$
$158$		−	4.81837i		−	0.383329i
$159$		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	$0.954299\pi$
$164$	2.37578	−	4.11497i	0.185517	−	0.321325i
$165$		0			0
$166$	0.403282	−	0.232835i	0.0313007	−	0.0180715i
$167$	4.73769	−	8.20592i	0.366613	−	0.634993i	−0.622420	−	0.782683i	$-0.713851\pi$
$167$	4.73769	−	8.20592i	0.366613	−	0.634993i	0.989034	+	0.147690i	$0.0471838\pi$
$168$		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
$173$	0.535796			0.0407358			0.0203679	−	0.999793i	$-0.493516\pi$
$173$	0.535796			0.0407358			0.0203679	+	0.999793i	$0.493516\pi$
$174$		0			0
$175$	16.8877	+	9.43999i	1.27659	+	0.713596i
$176$	−4.72317	−	2.72692i	−0.356022	−	0.205549i
$177$		0			0
$178$	−1.89113	−	1.09184i	−0.141746	−	0.0818372i
$179$	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	$-0.279679\pi$
$182$	5.81672	+	3.25146i	0.431164	+	0.241015i
$183$		0			0
$184$	2.67749	+	4.63754i	0.197387	+	0.341884i
$185$	29.1219			2.14108
$186$		0			0
$187$			9.29796i			0.679934i
$188$	−8.62351			−0.628934
$189$		0			0
$190$	−17.0118			−1.23416
$191$			11.2369i			0.813072i	0.913635	+	0.406536i	$0.133263\pi$
$191$			11.2369i			0.813072i	−0.913635	+	0.406536i	$0.866737\pi$
$192$		0			0
$193$	20.8272			1.49917			0.749586	−	0.661907i	$-0.230253\pi$
$193$	20.8272			1.49917			0.749586	+	0.661907i	$0.230253\pi$
$194$	−2.44856	−	4.24103i	−0.175796	−	0.304488i
$195$		0			0
$196$	6.99730	−	0.194333i	0.499807	−	0.0138810i
$197$			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	$0.299728\pi$
$200$	−6.33280	−	3.65625i	−0.447797	−	0.258536i
$201$		0			0
$202$	12.6072	+	7.27879i	0.887041	+	0.512134i
$203$	−9.64809	−	16.1878i	−0.677163	−	1.13616i
$204$		0			0
$205$	−16.6728			−1.16448
$206$	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	−0.404050	−	0.914737i	$-0.632398\pi$
$211$	8.57258	−	14.8481i	0.590161	−	1.02219i	0.994210	−	0.107451i	$-0.0342690\pi$
$212$	−10.0707	+	5.81430i	−0.691656	+	0.399327i
$213$		0			0
$214$	−3.46290	+	5.99791i	−0.236719	+	0.410009i
$215$	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
$220$			19.1371i			1.29022i
$221$			4.29396i			0.288843i
$222$		0			0
$223$	10.5032	−	6.06403i	0.703346	−	0.406077i	−0.105246	−	0.994446i	$-0.533563\pi$
$223$	10.5032	−	6.06403i	0.703346	−	0.406077i	0.808593	+	0.588369i	$0.200230\pi$
$224$	−2.64550	+	0.0367291i	−0.176760	+	0.00245407i
$225$		0			0
$226$	−2.45704	+	4.25572i	−0.163440	+	0.283087i
$227$	−0.705128	+	1.22132i	−0.0468010	+	0.0810616i	−0.888477	−	0.458921i	$-0.848236\pi$
$227$	−0.705128	+	1.22132i	−0.0468010	+	0.0810616i	0.841676	+	0.539983i	$0.181569\pi$
$228$		0			0
$229$	14.1942	−	8.19504i	0.937981	−	0.541544i	0.0486542	−	0.998816i	$-0.484507\pi$
$229$	14.1942	−	8.19504i	0.937981	−	0.541544i	0.889327	+	0.457272i	$0.151173\pi$
$230$	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
$236$	7.89559			0.513959
$237$		0			0
$238$	2.30931	+	3.87460i	0.149690	+	0.251153i
$239$	−10.3774	−	5.99139i	−0.671257	−	0.387551i	0.125296	−	0.992119i	$-0.460012\pi$
$239$	−10.3774	−	5.99139i	−0.671257	−	0.387551i	−0.796553	+	0.604569i	$0.793345\pi$
$240$		0			0
$241$	−0.00308144	−	0.00177907i	−0.000198493	−	0.000114600i	0.499901	−	0.866083i	$-0.333370\pi$
$241$	−0.00308144	−	0.00177907i	−0.000198493	−	0.000114600i	−0.500099	+	0.865968i	$0.666703\pi$
$242$	16.2331	−	9.37221i	1.04351	−	0.602468i
$243$		0			0
$244$		−	8.38771i		−	0.536968i
$245$	−12.8670	−	20.9225i	−0.822043	−	1.33669i
$246$		0			0
$247$	6.10547	+	10.5750i	0.388482	+	0.672871i
$248$	6.07327			0.385653
$249$		0			0
$250$			8.11435i			0.513196i
$251$	−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
$254$			11.0996i			0.696450i
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.75375	+	4.76963i	0.171774	+	0.297521i	0.939040	−	0.343808i	$-0.111717\pi$
$257$	2.75375	+	4.76963i	0.171774	+	0.297521i	−0.767266	+	0.641329i	$0.778383\pi$
$258$		0			0
$259$	−19.1669	−	10.7140i	−1.19097	−	0.665736i
$260$			8.83783i			0.548099i
$261$		0			0
$262$	8.53022	−	4.92492i	0.526999	−	0.304263i
$263$	23.2581	+	13.4280i	1.43415	+	0.828009i	0.997434	−	0.0715888i	$-0.0228069\pi$
$263$	23.2581	+	13.4280i	1.43415	+	0.828009i	0.436719	+	0.899598i	$0.356140\pi$
$264$		0			0
$265$	35.3371	+	20.4019i	2.17074	+	1.25328i
$266$	11.1965	+	6.25868i	0.686500	+	0.383744i
$267$		0			0
$268$	1.79146			0.109431
$269$	−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
$275$	34.5381	−	19.9406i	2.08273	−	1.20246i
$276$		0			0
$277$	13.8752	−	24.0326i	0.833681	−	1.44398i	−0.0614191	−	0.998112i	$-0.519563\pi$
$277$	13.8752	−	24.0326i	0.833681	−	1.44398i	0.895100	−	0.445865i	$-0.147104\pi$
$278$	−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	$-0.662302\pi$
$281$	0.398066	−	0.229824i	0.0237466	−	0.0137101i	0.511826	+	0.859089i	$0.328969\pi$
$282$		0			0
$283$			18.0890i			1.07528i	0.843175	+	0.537639i	$0.180684\pi$
$283$			18.0890i			1.07528i	−0.843175	+	0.537639i	$0.819316\pi$
$284$		−	0.791392i		−	0.0469605i
$285$		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
$290$	12.4965	−	21.6445i	0.733818	−	1.27101i
$291$		0			0
$292$	11.5492	−	6.66795i	0.675867	−	0.390212i
$293$	−8.23716	+	14.2672i	−0.481220	+	0.833497i	−0.999768	−	0.0215512i	$-0.993140\pi$
$293$	−8.23716	+	14.2672i	−0.481220	+	0.833497i	0.518548	+	0.855049i	$0.326473\pi$
$294$		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
$299$	−13.4875			−0.780000
$300$		0			0
$301$	−14.6746	+	8.74623i	−0.845830	+	0.504124i
$302$	−1.33706	−	0.771954i	−0.0769394	−	0.0444210i
$303$		0			0
$304$	−4.19863	−	2.42408i	−0.240808	−	0.139030i
$305$	−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	$0.830062\pi$
$308$	7.04058	−	12.5953i	0.401175	−	0.717683i
$309$		0			0
$310$	−10.6553	−	18.4555i	−0.605180	−	1.04820i
$311$	18.1162			1.02728			0.513639	−	0.858006i	$-0.328297\pi$
$311$	18.1162			1.02728			0.513639	+	0.858006i	$0.328297\pi$
$312$		0			0
$313$			9.99294i			0.564834i	0.959292	+	0.282417i	$0.0911362\pi$
$313$			9.99294i			0.564834i	−0.959292	+	0.282417i	$0.908864\pi$
$314$	−16.2976			−0.919728
$315$		0			0
$316$	−4.81837			−0.271055
$317$		−	5.61595i		−	0.315423i	−0.987485	−	0.157712i	$-0.949588\pi$
$317$		−	5.61595i		−	0.315423i	0.987485	−	0.157712i	$-0.0504116\pi$
$318$		0			0
$319$	−38.8461			−2.17496
$320$	−1.75446	−	3.03881i	−0.0980772	−	0.169875i
$321$		0			0
$322$	−12.1703	+	7.25361i	−0.678222	+	0.404228i
$323$			8.26535i			0.459896i
$324$		0			0
$325$	15.9503	−	9.20891i	0.884764	−	0.510819i
$326$	13.6830	+	7.89989i	0.757832	+	0.437535i
$327$		0			0
$328$	−4.11497	−	2.37578i	−0.227211	−	0.131180i
$329$	−0.316734	−	22.8135i	−0.0174621	−	1.25775i
$330$		0			0
$331$	9.22477			0.507039			0.253520	−	0.967330i	$-0.418412\pi$
$331$	9.22477			0.507039			0.253520	+	0.967330i	$0.418412\pi$
$332$	−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	−0.997491	−	0.0707950i	$-0.977446\pi$
$337$	−8.03024	+	13.9088i	−0.437435	+	0.757660i	0.560056	+	0.828455i	$0.310780\pi$
$338$	−5.76449	+	3.32813i	−0.313547	+	0.181026i
$339$		0			0
$340$	−2.99108	+	5.18070i	−0.162214	+	0.280963i
$341$	−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
$346$		−	0.535796i		−	0.0288045i
$347$			13.0035i			0.698065i	0.937111	+	0.349032i	$0.113490\pi$
$347$			13.0035i			0.698065i	−0.937111	+	0.349032i	$0.886510\pi$
$348$		0			0
$349$	8.95678	−	5.17120i	0.479446	−	0.276808i	−0.240740	−	0.970590i	$-0.577390\pi$
$349$	8.95678	−	5.17120i	0.479446	−	0.276808i	0.720185	+	0.693782i	$0.244057\pi$
$350$	9.43999	−	16.8877i	0.504589	−	0.902686i
$351$		0			0
$352$	−2.72692	+	4.72317i	−0.145345	+	0.251746i
$353$	0.155665	−	0.269620i	0.00828524	−	0.0143505i	−0.861853	−	0.507158i	$-0.830696\pi$
$353$	0.155665	−	0.269620i	0.00828524	−	0.0143505i	0.870138	+	0.492808i	$0.164029\pi$
$354$		0			0
$355$	−2.40489	+	1.38846i	−0.127638	+	0.0736920i
$356$	−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
$362$	−20.7151			−1.08876
$363$		0			0
$364$	3.25146	−	5.81672i	0.170423	−	0.304879i
$365$	−40.5253	−	23.3973i	−2.12119	−	1.22467i
$366$		0			0
$367$	20.4159	+	11.7871i	1.06570	+	0.615282i	0.927003	−	0.375053i	$-0.122376\pi$
$367$	20.4159	+	11.7871i	1.06570	+	0.615282i	0.138696	+	0.990335i	$0.455709\pi$
$368$	4.63754	−	2.67749i	0.241749	−	0.139574i
$369$		0			0
$370$		−	29.1219i		−	1.51397i
$371$	−15.7516	−	26.4283i	−0.817782	−	1.37209i
$372$		0			0
$373$	−9.09923	−	15.7603i	−0.471140	−	0.816039i	0.528315	−	0.849049i	$-0.322824\pi$
$373$	−9.09923	−	15.7603i	−0.471140	−	0.816039i	−0.999455	+	0.0330095i	$0.989491\pi$
$374$	9.29796			0.480786
$375$		0			0
$376$			8.62351i			0.444723i
$377$	−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	$0.406406\pi$
$380$			17.0118i			0.872685i
$381$		0			0
$382$	11.2369			0.574929
$383$	17.4222	+	30.1762i	0.890235	+	1.54193i	0.839594	+	0.543215i	$0.182793\pi$
$383$	17.4222	+	30.1762i	0.890235	+	1.54193i	0.0506413	+	0.998717i	$0.483873\pi$
$384$		0			0
$385$	−50.6271	+	0.702888i	−2.58019	+	0.0358225i
$386$		−	20.8272i		−	1.06007i
$387$		0			0
$388$	−4.24103	+	2.44856i	−0.215305	+	0.124307i
$389$	−5.33453	−	3.07989i	−0.270471	−	0.156157i	0.358631	−	0.933480i	$-0.383244\pi$
$389$	−5.33453	−	3.07989i	−0.270471	−	0.156157i	−0.629102	+	0.777323i	$0.716577\pi$
$390$		0			0
$391$	−7.90629	−	4.56470i	−0.399838	−	0.230847i
$392$	−0.194333	−	6.99730i	−0.00981532	−	0.353417i
$393$		0			0
$394$	20.4964			1.03259
$395$	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
$401$	15.3429	−	8.85824i	0.766189	−	0.442359i	−0.0653244	−	0.997864i	$-0.520808\pi$
$401$	15.3429	−	8.85824i	0.766189	−	0.442359i	0.831513	+	0.555505i	$0.187475\pi$
$402$		0			0
$403$	−7.64831	+	13.2473i	−0.380989	+	0.659893i
$404$	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
$409$			22.2018i			1.09781i	0.835886	+	0.548904i	$0.184955\pi$
$409$			22.2018i			1.09781i	−0.835886	+	0.548904i	$0.815045\pi$
$410$			16.6728i			0.823412i
$411$		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
$416$	−1.25934	+	2.18124i	−0.0617442	+	0.106944i
$417$		0			0
$418$	22.8986	−	13.2205i	1.12001	−	0.646638i
$419$	3.30677	−	5.72749i	0.161546	−	0.279806i	−0.773877	−	0.633336i	$-0.781685\pi$
$419$	3.30677	−	5.72749i	0.161546	−	0.279806i	0.935423	+	0.353529i	$0.115019\pi$
$420$		0			0
$421$	20.0090	+	34.6565i	0.975177	+	1.68906i	0.679351	+	0.733814i	$0.262261\pi$
$421$	20.0090	+	34.6565i	0.975177	+	1.68906i	0.295826	+	0.955242i	$0.404405\pi$
$422$	−14.8481	−	8.57258i	−0.722796	−	0.417307i
$423$		0			0
$424$	5.81430	+	10.0707i	0.282367	+	0.489074i
$425$	12.4667			0.604722
$426$		0			0
$427$	22.1896	−	0.308073i	1.07383	−	0.0149087i
$428$	5.99791	+	3.46290i	0.289920	+	0.167385i
$429$		0			0
$430$	−19.6213	−	11.3284i	−0.946222	−	0.546302i
$431$	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	$-0.294408\pi$
$434$	0.223066	+	16.0668i	0.0107075	+	0.771231i
$435$		0			0
$436$	−1.25470	−	2.17320i	−0.0600892	−	0.104077i
$437$	−25.9617			−1.24192
$438$		0			0
$439$		−	4.57146i		−	0.218184i	−0.994032	−	0.109092i	$-0.965206\pi$
$439$		−	4.57146i		−	0.218184i	0.994032	−	0.109092i	$-0.0347943\pi$
$440$	19.1371			0.912325
$441$		0			0
$442$	4.29396			0.204243
$443$		−	2.64213i		−	0.125531i	−0.998028	−	0.0627657i	$-0.980008\pi$
$443$		−	2.64213i		−	0.125531i	0.998028	−	0.0627657i	$-0.0199921\pi$
$444$		0			0
$445$	7.66238			0.363232
$446$	−6.06403	−	10.5032i	−0.287140	−	0.497341i
$447$		0			0
$448$	0.0367291	+	2.64550i	0.00173529	+	0.124988i
$449$			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
$452$	4.25572	+	2.45704i	0.200172	+	0.115570i
$453$		0			0
$454$	1.22132	+	0.705128i	0.0573192	+	0.0330933i
$455$	−23.3805	+	0.324606i	−1.09609	+	0.0152178i
$456$		0			0
$457$	22.0818			1.03294			0.516472	−	0.856304i	$-0.327245\pi$
$457$	22.0818			1.03294			0.516472	+	0.856304i	$0.327245\pi$
$458$	−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	0.989104	+	0.147221i	$0.0470330\pi$
$461$	13.3560	+	23.1332i	0.622049	+	1.07742i	−0.367054	+	0.930199i	$0.619634\pi$
$462$		0			0
$463$	5.22568	−	9.05114i	0.242858	−	0.420642i	−0.718669	−	0.695352i	$-0.755248\pi$
$463$	5.22568	−	9.05114i	0.242858	−	0.420642i	0.961527	+	0.274710i	$0.0885818\pi$
$464$	6.16843	−	3.56135i	0.286362	−	0.165331i
$465$		0			0
$466$	−6.12326	+	10.6058i	−0.283654	+	0.491304i
$467$	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
$472$		−	7.89559i		−	0.363424i
$473$			35.2149i			1.61918i
$474$		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
$479$	7.00736	−	12.1371i	0.320174	−	0.554558i	−0.660349	−	0.750958i	$-0.729592\pi$
$479$	7.00736	−	12.1371i	0.320174	−	0.554558i	0.980524	+	0.196400i	$0.0629251\pi$
$480$		0			0
$481$	−18.1030	+	10.4517i	−0.825424	+	0.476559i
$482$	−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	$0.824057\pi$
$488$	−8.38771			−0.379694
$489$		0			0
$490$	−20.9225	+	12.8670i	−0.945183	+	0.581273i
$491$	−0.458760	−	0.264865i	−0.0207036	−	0.0119532i	0.489613	−	0.871940i	$-0.337138\pi$
$491$	−0.458760	−	0.264865i	−0.0207036	−	0.0119532i	−0.510316	+	0.859987i	$0.670472\pi$
$492$		0			0
$493$	−10.5162	−	6.07154i	−0.473627	−	0.273449i
$494$	10.5750	−	6.10547i	0.475791	−	0.274698i
$495$		0			0
$496$		−	6.07327i		−	0.272698i
$497$	2.09362	−	0.0290671i	0.0939119	−	0.00130384i
$498$		0			0
$499$	−11.0093	−	19.0687i	−0.492845	−	0.853633i	0.507121	−	0.861875i	$-0.330710\pi$
$499$	−11.0093	−	19.0687i	−0.492845	−	0.853633i	−0.999966	+	0.00824199i	$0.997376\pi$
$500$	8.11435			0.362885
$501$		0			0
$502$			11.1743i			0.498735i
$503$	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
$506$			29.2052i			1.29833i
$507$		0			0
$508$	11.0996			0.492464
$509$	16.4814	+	28.5467i	0.730527	+	1.26531i	0.956658	+	0.291213i	$0.0940589\pi$
$509$	16.4814	+	28.5467i	0.730527	+	1.26531i	−0.226131	+	0.974097i	$0.572608\pi$
$510$		0			0
$511$	18.0642	+	30.3085i	0.799114	+	1.34077i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	4.76963	−	2.75375i	0.210379	−	0.121463i
$515$	−13.5515	−	7.82399i	−0.597152	−	0.344766i
$516$		0			0
$517$	−40.7303	−	23.5156i	−1.79132	−	1.03422i
$518$	−10.7140	+	19.1669i	−0.470746	+	0.842144i
$519$		0			0
$520$	8.83783			0.387565
$521$	−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
$527$	−8.96681	+	5.17699i	−0.390600	+	0.225513i
$528$		0			0
$529$	2.83786	−	4.91532i	0.123385	−	0.213709i
$530$	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
$535$		−	24.3020i		−	1.05067i
$536$		−	1.79146i		−	0.0773794i
$537$		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	$-0.142695\pi$
$542$	14.0365	−	24.3120i	0.602920	−	1.04429i
$543$		0			0
$544$	−1.47644	+	0.852422i	−0.0633018	+	0.0365473i
$545$	−4.40263	+	7.62558i	−0.188588	+	0.326644i
$546$		0			0
$547$	−21.1201	−	36.5811i	−0.903032	−	1.56410i	−0.823538	−	0.567261i	$-0.808003\pi$
$547$	−21.1201	−	36.5811i	−0.903032	−	1.56410i	−0.0794935	−	0.996835i	$-0.525330\pi$
$548$	−1.52810	−	0.882247i	−0.0652770	−	0.0376877i
$549$		0			0
$550$	−19.9406	−	34.5381i	−0.850270	−	1.47271i
$551$	−34.5319			−1.47111
$552$		0			0
$553$	−0.176975	−	12.7470i	−0.00752572	−	0.542057i
$554$	−24.0326	−	13.8752i	−1.02105	−	0.589501i
$555$		0			0
$556$	16.6425	+	9.60855i	0.705799	+	0.407493i
$557$	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
$560$	7.97472	−	4.75303i	0.336994	−	0.200852i
$561$		0			0
$562$	−0.229824	−	0.398066i	−0.00969452	−	0.0167914i
$563$	−21.6372			−0.911899			−0.455949	−	0.890006i	$-0.650700\pi$
$563$	−21.6372			−0.911899			−0.455949	+	0.890006i	$0.650700\pi$
$564$		0			0
$565$		−	17.2431i		−	0.725423i
$566$	18.0890			0.760337
$567$		0			0
$568$	−0.791392			−0.0332061
$569$		−	14.1280i		−	0.592275i	−0.955145	−	0.296138i	$-0.904301\pi$
$569$		−	14.1280i		−	0.592275i	0.955145	−	0.296138i	$-0.0956987\pi$
$570$		0			0
$571$	−24.4214			−1.02200			−0.511002	−	0.859580i	$-0.670725\pi$
$571$	−24.4214			−1.02200			−0.511002	+	0.859580i	$0.670725\pi$
$572$	−6.86824	−	11.8961i	−0.287176	−	0.497403i
$573$		0			0
$574$	6.13397	−	10.9734i	0.256027	−	0.458021i
$575$			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	$0.249789\pi$
$578$	−12.2053	−	7.04675i	−0.507675	−	0.293106i
$579$		0			0
$580$	−21.6445	−	12.4965i	−0.898740	−	0.518888i
$581$	1.05833	−	0.630776i	0.0439069	−	0.0261690i
$582$		0			0
$583$	−63.4205			−2.62661
$584$	−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	0.987197	−	0.159505i	$-0.0509899\pi$
$587$	8.61219	+	14.9167i	0.355463	+	0.615680i	−0.631734	+	0.775185i	$0.717657\pi$
$588$		0			0
$589$	−14.7221	+	25.4994i	−0.606612	+	1.05068i
$590$	−23.9932	+	13.8525i	−0.987784	+	0.570298i
$591$		0			0
$592$	4.14969	−	7.18748i	0.170551	−	0.295404i
$593$	−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
$598$			13.4875i			0.551543i
$599$		−	19.2453i		−	0.786342i	−0.919465	−	0.393171i	$-0.871378\pi$
$599$		−	19.2453i		−	0.786342i	0.919465	−	0.393171i	$-0.128622\pi$
$600$		0			0
$601$	11.5612	−	6.67486i	0.471591	−	0.272273i	−0.245314	−	0.969444i	$-0.578891\pi$
$601$	11.5612	−	6.67486i	0.471591	−	0.272273i	0.716906	+	0.697170i	$0.245558\pi$
$602$	8.74623	+	14.6746i	0.356470	+	0.598092i
$603$		0			0
$604$	−0.771954	+	1.33706i	−0.0314104	+	0.0544044i
$605$	−32.8863	+	56.9607i	−1.33702	+	2.31578i
$606$		0			0
$607$	−17.7598	+	10.2536i	−0.720849	+	0.416182i	−0.815065	−	0.579370i	$-0.803299\pi$
$607$	−17.7598	+	10.2536i	−0.720849	+	0.416182i	0.0942162	+	0.995552i	$0.469965\pi$
$608$	−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	$0.954251\pi$
$614$	17.8324			0.719656
$615$		0			0
$616$	−12.5953	−	7.04058i	−0.507478	−	0.283673i
$617$	28.1051	+	16.2265i	1.13147	+	0.653255i	0.944304	−	0.329074i	$-0.106736\pi$
$617$	28.1051	+	16.2265i	1.13147	+	0.653255i	0.187166	+	0.982328i	$0.440070\pi$
$618$		0			0
$619$	35.0065	+	20.2110i	1.40703	+	0.812349i	0.995101	−	0.0988677i	$-0.0315221\pi$
$619$	35.0065	+	20.2110i	1.40703	+	0.812349i	0.411928	+	0.911216i	$0.364855\pi$
$620$	−18.4555	+	10.6553i	−0.741191	+	0.427927i
$621$		0			0
$622$		−	18.1162i		−	0.726395i
$623$	−5.04308	−	2.81901i	−0.202047	−	0.112941i
$624$		0			0
$625$	4.04495	+	7.00607i	0.161798	+	0.280243i
$626$	9.99294			0.399398
$627$		0			0
$628$			16.2976i			0.650346i
$629$	−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	$0.636393\pi$
$632$			4.81837i			0.191665i
$633$		0			0
$634$	−5.61595			−0.223038
$635$	−19.4738	−	33.7295i	−0.772793	−	1.33852i
$636$		0			0
$637$	15.5075	+	8.38809i	0.614431	+	0.332348i
$638$			38.8461i			1.53793i
$639$		0			0
$640$	−3.03881	+	1.75446i	−0.120120	+	0.0693510i
$641$	−36.7640	−	21.2257i	−1.45209	−	0.838366i	−0.453492	−	0.891260i	$-0.649822\pi$
$641$	−36.7640	−	21.2257i	−1.45209	−	0.838366i	−0.998600	+	0.0528940i	$0.983155\pi$
$642$		0			0
$643$	−15.0599	−	8.69484i	−0.593904	−	0.342891i	0.172735	−	0.984968i	$-0.444739\pi$
$643$	−15.0599	−	8.69484i	−0.593904	−	0.342891i	−0.766640	+	0.642077i	$0.778073\pi$
$644$	7.25361	+	12.1703i	0.285832	+	0.479575i
$645$		0			0
$646$	8.26535			0.325196
$647$	−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
$653$	−34.0169	+	19.6397i	−1.33118	+	0.768560i	−0.985481	−	0.169784i	$-0.945693\pi$
$653$	−34.0169	+	19.6397i	−1.33118	+	0.768560i	−0.345703	+	0.938344i	$0.612360\pi$
$654$		0			0
$655$	−17.2811	+	29.9318i	−0.675230	+	1.16953i
$656$	−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	$-0.851901\pi$
$659$	−24.4389	+	14.1098i	−0.952002	+	0.549639i	−0.0583000	+	0.998299i	$0.518568\pi$
$660$		0			0
$661$		−	31.2107i		−	1.21396i	−0.794719	−	0.606978i	$-0.792382\pi$
$661$		−	31.2107i		−	1.21396i	0.794719	−	0.606978i	$-0.207618\pi$
$662$		−	9.22477i		−	0.358531i
$663$		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
$668$	−4.73769	+	8.20592i	−0.183307	+	0.317497i
$669$		0			0
$670$	−5.44392	+	3.14305i	−0.210317	+	0.121427i
$671$	22.8726	−	39.6165i	0.882988	−	1.52938i
$672$		0			0
$673$	−22.1804	−	38.4176i	−0.854991	−	1.48089i	−0.876653	−	0.481123i	$-0.840229\pi$
$673$	−22.1804	−	38.4176i	−0.854991	−	1.48089i	0.0216619	−	0.999765i	$-0.493104\pi$
$674$	13.9088	+	8.03024i	0.535747	+	0.309313i
$675$		0			0
$676$	3.32813	+	5.76449i	0.128005	+	0.221711i
$677$	−2.95169			−0.113443			−0.0567214	−	0.998390i	$-0.518065\pi$
$677$	−2.95169			−0.113443			−0.0567214	+	0.998390i	$0.518065\pi$
$678$		0			0
$679$	−6.63342	−	11.1297i	−0.254567	−	0.427118i
$680$	5.18070	+	2.99108i	0.198671	+	0.114703i
$681$		0			0
$682$	28.6851	+	16.5613i	1.09841	+	0.634166i
$683$	−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
$686$	18.5042	−	0.771113i	0.706494	−	0.0294412i
$687$		0			0
$688$	−3.22845	−	5.59184i	−0.123083	−	0.213187i
$689$	−29.2887			−1.11581
$690$		0			0
$691$		−	34.9821i		−	1.33078i	−0.746496	−	0.665390i	$-0.768265\pi$
$691$		−	34.9821i		−	1.33078i	0.746496	−	0.665390i	$-0.231735\pi$
$692$	−0.535796			−0.0203679
$693$		0			0
$694$	13.0035			0.493606
$695$		−	67.4312i		−	2.55781i
$696$		0			0
$697$	8.10067			0.306835
$698$	−5.17120	−	8.95678i	−0.195733	−	0.339019i
$699$		0			0
$700$	−16.8877	−	9.43999i	−0.638295	−	0.356798i
$701$		−	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
$704$	4.72317	+	2.72692i	0.178011	+	0.102775i
$705$		0			0
$706$	−0.269620	−	0.155665i	−0.0101473	−	0.00585855i
$707$	33.6197	+	18.7929i	1.26440	+	0.706782i
$708$		0			0
$709$	−13.4611			−0.505541			−0.252771	−	0.967526i	$-0.581342\pi$
$709$	−13.4611			−0.505541			−0.252771	+	0.967526i	$0.581342\pi$
$710$	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
$716$	−8.69412	+	5.01955i	−0.324914	+	0.187589i
$717$		0			0
$718$	2.15462	−	3.73192i	0.0804098	−	0.139274i
$719$	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
$724$			20.7151i			0.769869i
$725$			52.0847i			1.93438i
$726$		0			0
$727$	30.6479	−	17.6945i	1.13667	−	0.656254i	0.191063	−	0.981578i	$-0.438806\pi$
$727$	30.6479	−	17.6945i	1.13667	−	0.656254i	0.945603	+	0.325323i	$0.105473\pi$
$728$	−5.81672	−	3.25146i	−0.215582	−	0.120507i
$729$		0			0
$730$	−23.3973	+	40.5253i	−0.865972	+	1.49991i
$731$	−5.50400	+	9.53321i	−0.203573	+	0.352599i
$732$		0			0
$733$	−5.59150	+	3.22826i	−0.206527	+	0.119238i	−0.599696	−	0.800228i	$-0.704712\pi$
$733$	−5.59150	+	3.22826i	−0.206527	+	0.119238i	0.393169	+	0.919466i	$0.371379\pi$
$734$	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	$0.979463\pi$
$740$	−29.1219			−1.07054
$741$		0			0
$742$	−26.4283	+	15.7516i	−0.970215	+	0.578259i
$743$	19.4191	+	11.2116i	0.712419	+	0.411316i	0.811956	−	0.583718i	$-0.198403\pi$
$743$	19.4191	+	11.2116i	0.712419	+	0.411316i	−0.0995368	+	0.995034i	$0.531736\pi$
$744$		0			0
$745$	−40.9601	−	23.6483i	−1.50066	−	0.866407i
$746$	−15.7603	+	9.09923i	−0.577027	+	0.333147i
$747$		0			0
$748$		−	9.29796i		−	0.339967i
$749$	−8.94078	+	15.9946i	−0.326689	+	0.584431i
$750$		0			0
$751$	−2.54728	−	4.41201i	−0.0929514	−	0.160997i	0.815800	−	0.578334i	$-0.196297\pi$
$751$	−2.54728	−	4.41201i	−0.0929514	−	0.160997i	−0.908752	+	0.417337i	$0.862963\pi$
$752$	8.62351			0.314467
$753$		0			0
$754$			17.9398i			0.653328i
$755$	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	$0.379867\pi$
$758$		−	11.2842i		−	0.409859i
$759$		0			0
$760$	17.0118			0.617082
$761$	19.3376	+	33.4938i	0.700989	+	1.21415i	0.968120	+	0.250488i	$0.0805910\pi$
$761$	19.3376	+	33.4938i	0.700989	+	1.21415i	−0.267131	+	0.963660i	$0.586076\pi$
$762$		0			0
$763$	5.70311	−	3.39912i	0.206467	−	0.123056i
$764$		−	11.2369i		−	0.406536i
$765$		0			0
$766$	30.1762	−	17.4222i	1.09031	−	0.629491i
$767$	17.2222	+	9.94323i	0.621857	+	0.359029i
$768$		0			0
$769$	29.1535	+	16.8318i	1.05130	+	0.606969i	0.923013	−	0.384768i	$-0.125719\pi$
$769$	29.1535	+	16.8318i	1.05130	+	0.606969i	0.128287	+	0.991737i	$0.459052\pi$
$770$	0.702888	+	50.6271i	0.0253303	+	1.82447i
$771$		0			0
$772$	−20.8272			−0.749586
$773$	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
$779$	19.9500	−	11.5181i	0.714783	−	0.412680i
$780$		0			0
$781$	2.15806	−	3.73788i	0.0772216	−	0.133752i
$782$	−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
$787$		−	15.7634i		−	0.561905i	−0.959722	−	0.280953i	$-0.909350\pi$
$787$		−	15.7634i		−	0.561905i	0.959722	−	0.280953i	$-0.0906503\pi$
$788$		−	20.4964i		−	0.730153i
$789$		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
$794$	0.548996	−	0.950888i	0.0194831	−	0.0337458i
$795$		0			0
$796$	−2.57476	+	1.48654i	−0.0912601	+	0.0526890i
$797$	15.4937	−	26.8359i	0.548816	−	0.950578i	−0.449540	−	0.893260i	$-0.648412\pi$
$797$	15.4937	−	26.8359i	0.548816	−	0.950578i	0.998356	−	0.0573173i	$-0.0182547\pi$
$798$		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
$803$	72.7319			2.56665
$804$		0			0
$805$	24.2569	−	43.3946i	0.854945	−	1.52946i
$806$	13.2473	+	7.64831i	0.466615	+	0.269400i
$807$		0			0
$808$	−12.6072	−	7.27879i	−0.443521	−	0.256067i
$809$	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	$-0.145252\pi$
$812$	9.64809	+	16.1878i	0.338582	+	0.568079i
$813$		0			0
$814$	22.6318	+	39.1994i	0.793243	+	1.37394i
$815$	−55.4401			−1.94198
$816$		0			0
$817$			31.3040i			1.09519i
$818$	22.2018			0.776267
$819$		0			0
$820$	16.6728			0.582240
$821$		−	3.02271i		−	0.105493i	−0.998608	−	0.0527466i	$-0.983202\pi$
$821$		−	3.02271i		−	0.105493i	0.998608	−	0.0527466i	$-0.0167976\pi$
$822$		0			0
$823$	11.2015			0.390459			0.195230	−	0.980758i	$-0.437455\pi$
$823$	11.2015			0.390459			0.195230	+	0.980758i	$0.437455\pi$
$824$	−2.22974	−	3.86203i	−0.0776768	−	0.134540i
$825$		0			0
$826$	20.8877	−	0.289998i	0.726778	−	0.0100903i
$827$		−	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	$0.446288\pi$
$830$	1.41508	+	0.816998i	0.0491182	+	0.0283584i
$831$		0			0
$832$	2.18124	+	1.25934i	0.0756209	+	0.0436597i
$833$	6.25158	+	10.1654i	0.216604	+	0.352211i
$834$		0			0
$835$	33.2483			1.15061
$836$	−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	0.843584	−	0.536998i	$-0.180442\pi$
$839$	−1.25310	−	2.17043i	−0.0432618	−	0.0749316i	−0.886845	+	0.462066i	$0.847108\pi$
$840$		0			0
$841$	10.8664	−	18.8211i	0.374703	−	0.649005i
$842$	34.6565	−	20.0090i	1.19434	−	0.689554i
$843$		0			0
$844$	−8.57258	+	14.8481i	−0.295080	+	0.511094i
$845$	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
$850$		−	12.4667i		−	0.427603i
$851$		−	44.4430i		−	1.52349i
$852$		0			0
$853$	−25.9938	+	15.0075i	−0.890010	+	0.513847i	−0.873946	−	0.486024i	$-0.838447\pi$
$853$	−25.9938	+	15.0075i	−0.890010	+	0.513847i	−0.0160640	+	0.999871i	$0.505114\pi$
$854$	−0.308073	−	22.1896i	−0.0105420	−	0.759314i
$855$		0			0
$856$	3.46290	−	5.99791i	0.118359	−	0.205004i
$857$	−3.76812	+	6.52657i	−0.128716	+	0.222944i	−0.923180	−	0.384369i	$-0.874419\pi$
$857$	−3.76812	+	6.52657i	−0.128716	+	0.222944i	0.794463	+	0.607312i	$0.207752\pi$
$858$		0			0
$859$	−8.31754	+	4.80214i	−0.283791	+	0.163847i	−0.635138	−	0.772398i	$-0.719057\pi$
$859$	−8.31754	+	4.80214i	−0.283791	+	0.163847i	0.351347	+	0.936245i	$0.385724\pi$
$860$	−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
$866$	−33.2342			−1.12934
$867$		0			0
$868$	16.0668	−	0.223066i	0.545343	−	0.00757134i
$869$	−22.7580	−	13.1393i	−0.772012	−	0.445721i
$870$		0			0
$871$	3.90761	+	2.25606i	0.132404	+	0.0764437i
$872$	−2.17320	+	1.25470i	−0.0735939	+	0.0424895i
$873$		0			0
$874$			25.9617i			0.878169i
$875$	0.298033	+	21.4665i	0.0100753	+	0.725699i
$876$		0			0
$877$	18.0383	+	31.2432i	0.609109	+	1.05501i	0.991388	+	0.130961i	$0.0418062\pi$
$877$	18.0383	+	31.2432i	0.609109	+	1.05501i	−0.382279	+	0.924047i	$0.624861\pi$
$878$	−4.57146			−0.154279
$879$		0			0
$880$		−	19.1371i		−	0.645111i
$881$	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	$0.565470\pi$
$884$		−	4.29396i		−	0.144421i
$885$		0			0
$886$	−2.64213			−0.0887641
$887$	7.66240	+	13.2717i	0.257278	+	0.445619i	0.965512	−	0.260359i	$-0.0838410\pi$
$887$	7.66240	+	13.2717i	0.257278	+	0.445619i	−0.708234	+	0.705978i	$0.750508\pi$
$888$		0			0
$889$	0.407678	+	29.3639i	0.0136731	+	0.984834i
$890$		−	7.66238i		−	0.256844i
$891$		0			0
$892$	−10.5032	+	6.06403i	−0.351673	+	0.203039i
$893$	−36.2069	−	20.9041i	−1.21162	−	0.699527i
$894$		0			0
$895$	30.5069	+	17.6132i	1.01973	+	0.588744i
$896$	2.64550	−	0.0367291i	0.0883798	−	0.00122703i
$897$		0			0
$898$	7.56836			0.252560
$899$	−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
$905$	62.9491	−	36.3437i	2.09250	−	1.20811i
$906$		0			0
$907$	−18.2135	+	31.5467i	−0.604769	+	1.04749i	0.387319	+	0.921946i	$0.373401\pi$
$907$	−18.2135	+	31.5467i	−0.604769	+	1.04749i	−0.992088	+	0.125545i	$0.959932\pi$
$908$	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	$-0.574288\pi$
$911$	14.9598	−	8.63706i	0.495641	−	0.286159i	0.726912	+	0.686731i	$0.240955\pi$
$912$		0			0
$913$		−	2.53969i		−	0.0840514i
$914$		−	22.0818i		−	0.730402i
$915$		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	$0.225643\pi$
$920$	−9.39507	+	16.2727i	−0.309746	+	0.536496i
$921$		0			0
$922$	23.1332	−	13.3560i	0.761852	−	0.439855i
$923$	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
$929$	12.9018			0.423294			0.211647	−	0.977346i	$-0.432117\pi$
$929$	12.9018			0.423294			0.211647	+	0.977346i	$0.432117\pi$
$930$		0			0
$931$	29.8501	+	16.1461i	0.978299	+	0.529166i
$932$	10.6058	+	6.12326i	0.347404	+	0.200574i
$933$		0			0
$934$	−26.5937	−	15.3539i	−0.870172	−	0.502394i
$935$	−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	$0.832239\pi$
$938$	4.73931	−	0.0657988i	0.154744	−	0.00214841i
$939$		0			0
$940$	−15.1296	−	26.2052i	−0.493473	−	0.854720i
$941$	−8.94345			−0.291548			−0.145774	−	0.989318i	$-0.546567\pi$
$941$	−8.94345			−0.291548			−0.145774	+	0.989318i	$0.546567\pi$
$942$		0			0
$943$			25.4445i			0.828585i
$944$	−7.89559			−0.256979
$945$		0			0
$946$	35.2149			1.14494
$947$			28.3003i			0.919636i	0.888013	+	0.459818i	$0.152085\pi$
$947$			28.3003i			0.919636i	−0.888013	+	0.459818i	$0.847915\pi$
$948$		0			0
$949$	33.5888			1.09034
$950$	−17.7261	−	30.7024i	−0.575109	−	0.996118i
$951$		0			0
$952$	−2.30931	−	3.87460i	−0.0748451	−	0.125577i
$953$		−	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
$956$	10.3774	+	5.99139i	0.335629	+	0.193775i
$957$		0			0
$958$	−12.1371	−	7.00736i	−0.392132	−	0.226398i
$959$	2.27785	−	4.07498i	0.0735558	−	0.131588i
$960$		0			0
$961$	−5.88457			−0.189825
$962$	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	−0.912025	−	0.410135i	$-0.865481\pi$
$967$	−3.13531	+	5.43051i	−0.100825	+	0.174634i	0.811200	+	0.584769i	$0.198815\pi$
$968$	−16.2331	+	9.37221i	−0.521753	+	0.301234i
$969$		0			0
$970$	8.59178	−	14.8814i	0.275866	−	0.477813i
$971$	−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
$976$			8.38771i			0.268484i
$977$			6.58743i			0.210751i	0.994433	+	0.105375i	$0.0336044\pi$
$977$			6.58743i			0.210751i	−0.994433	+	0.105375i	$0.966396\pi$
$978$		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
$983$	12.6388	−	21.8910i	0.403114	−	0.698213i	−0.590986	−	0.806682i	$-0.701261\pi$
$983$	12.6388	−	21.8910i	0.403114	−	0.698213i	0.994100	+	0.108468i	$0.0345946\pi$
$984$		0			0
$985$	−62.2846	+	35.9600i	−1.98455	+	1.14578i
$986$	−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	$-0.349638\pi$
$992$	−6.07327			−0.192826
$993$		0			0
$994$	−0.0290671	−	2.09362i	−0.000921953	−	0.0664057i
$995$	9.03463	+	5.21615i	0.286417	+	0.165363i
$996$		0			0
$997$	10.7858	+	6.22716i	0.341588	+	0.197216i	0.660974	−	0.750409i	$-0.270143\pi$
$997$	10.7858	+	6.22716i	0.341588	+	0.197216i	−0.319386	+	0.947625i	$0.603477\pi$
$998$	−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.l.g.215.4		16
3.2	odd	2		1134.2.l.h.215.5		16
7.3	odd	6		1134.2.t.h.1025.8		16
9.2	odd	6		1134.2.t.h.593.8		16
9.4	even	3		1134.2.k.d.971.8	yes	16
9.5	odd	6		1134.2.k.c.971.1	yes	16
9.7	even	3		1134.2.t.g.593.1		16
21.17	even	6		1134.2.t.g.1025.1		16
63.31	odd	6		1134.2.k.c.647.1	✓	16
63.38	even	6	inner	1134.2.l.g.269.8		16
63.52	odd	6		1134.2.l.h.269.1		16
63.59	even	6		1134.2.k.d.647.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.1	✓	16	63.31	odd	6
1134.2.k.c.971.1	yes	16	9.5	odd	6
1134.2.k.d.647.8	yes	16	63.59	even	6
1134.2.k.d.971.8	yes	16	9.4	even	3
1134.2.l.g.215.4		16	1.1	even	1	trivial
1134.2.l.g.269.8		16	63.38	even	6	inner
1134.2.l.h.215.5		16	3.2	odd	2
1134.2.l.h.269.1		16	63.52	odd	6
1134.2.t.g.593.1		16	9.7	even	3
1134.2.t.g.1025.1		16	21.17	even	6
1134.2.t.h.593.8		16	9.2	odd	6
1134.2.t.h.1025.8		16	7.3	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.75446 + 3.03881i) q^{5} +(-0.0367291 - 2.64550i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.75446 + 3.03881i) q^{5} +(-0.0367291 - 2.64550i) q^{7} +1.00000i q^{8} +(3.03881 - 1.75446i) q^{10} +(-4.72317 - 2.72692i) q^{11} +(-2.18124 - 1.25934i) q^{13} +(-2.64550 + 0.0367291i) q^{14} +1.00000 q^{16} +(-0.852422 - 1.47644i) q^{17} +(-4.19863 - 2.42408i) q^{19} +(-1.75446 - 3.03881i) q^{20} +(-2.72692 + 4.72317i) q^{22} +(4.63754 - 2.67749i) q^{23} +(-3.65625 + 6.33280i) q^{25} +(-1.25934 + 2.18124i) q^{26} +(0.0367291 + 2.64550i) q^{28} +(6.16843 - 3.56135i) q^{29} -6.07327i q^{31} -1.00000i q^{32} +(-1.47644 + 0.852422i) q^{34} +(7.97472 - 4.75303i) q^{35} +(4.14969 - 7.18748i) q^{37} +(-2.42408 + 4.19863i) q^{38} +(-3.03881 + 1.75446i) q^{40} +(-2.37578 + 4.11497i) q^{41} +(-3.22845 - 5.59184i) q^{43} +(4.72317 + 2.72692i) q^{44} +(-2.67749 - 4.63754i) q^{46} +8.62351 q^{47} +(-6.99730 + 0.194333i) q^{49} +(6.33280 + 3.65625i) q^{50} +(2.18124 + 1.25934i) q^{52} +(10.0707 - 5.81430i) q^{53} -19.1371i q^{55} +(2.64550 - 0.0367291i) q^{56} +(-3.56135 - 6.16843i) q^{58} -7.89559 q^{59} +8.38771i q^{61} -6.07327 q^{62} -1.00000 q^{64} -8.83783i q^{65} -1.79146 q^{67} +(0.852422 + 1.47644i) q^{68} +(-4.75303 - 7.97472i) q^{70} +0.791392i q^{71} +(-11.5492 + 6.66795i) q^{73} +(-7.18748 - 4.14969i) q^{74} +(4.19863 + 2.42408i) q^{76} +(-7.04058 + 12.5953i) q^{77} +4.81837 q^{79} +(1.75446 + 3.03881i) q^{80} +(4.11497 + 2.37578i) q^{82} +(0.232835 + 0.403282i) q^{83} +(2.99108 - 5.18070i) q^{85} +(-5.59184 + 3.22845i) q^{86} +(2.72692 - 4.72317i) q^{88} +(1.09184 - 1.89113i) q^{89} +(-3.25146 + 5.81672i) q^{91} +(-4.63754 + 2.67749i) q^{92} -8.62351i q^{94} -17.0118i q^{95} +(4.24103 - 2.44856i) q^{97} +(0.194333 + 6.99730i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 - 4 * q^7	\( 16 q - 16 q^{4} - 4 q^{7} - 12 q^{11} - 12 q^{13} + 16 q^{16} - 12 q^{23} - 8 q^{25} + 4 q^{28} + 48 q^{29} + 60 q^{35} + 4 q^{37} - 12 q^{38} + 24 q^{41} + 16 q^{43} + 12 q^{44} - 20 q^{49} - 24 q^{50} + 12 q^{52} - 12 q^{58} + 48 q^{59} - 48 q^{62} - 16 q^{64} + 8 q^{67} + 12 q^{70} + 36 q^{73} - 36 q^{74} - 48 q^{77} - 16 q^{79} + 36 q^{83} - 12 q^{85} - 24 q^{86} + 24 q^{89} - 12 q^{91} + 12 q^{92} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) 16 * q - 16 * q^4 - 4 * q^7 - 12 * q^11 - 12 * q^13 + 16 * q^16 - 12 * q^23 - 8 * q^25 + 4 * q^28 + 48 * q^29 + 60 * q^35 + 4 * q^37 - 12 * q^38 + 24 * q^41 + 16 * q^43 + 12 * q^44 - 20 * q^49 - 24 * q^50 + 12 * q^52 - 12 * q^58 + 48 * q^59 - 48 * q^62 - 16 * q^64 + 8 * q^67 + 12 * q^70 + 36 * q^73 - 36 * q^74 - 48 * q^77 - 16 * q^79 + 36 * q^83 - 12 * q^85 - 24 * q^86 + 24 * q^89 - 12 * q^91 + 12 * q^92 - 12 * q^97 + 36 * q^98

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