LMFDB - Embedded newform 48.2.k.a.35.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,2,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, 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:	$0.383281929702$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			35.6
Root			$-0.204810 - 1.39930i$ of defining polynomial
Character	$\chi$	$=$	48.35
Dual form			48.2.k.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39930 + 0.204810i) q^{2} +(-1.52878 + 0.814141i) q^{3} +(1.91611 + 0.573183i) q^{4} +(-2.08397 - 2.08397i) q^{5} +(-2.30598 + 0.826122i) q^{6} -1.14637 q^{7} +(2.56382 + 1.19449i) q^{8} +(1.67435 - 2.48929i) q^{9} +O(q^{10})$	\(q+(1.39930 + 0.204810i) q^{2} +(-1.52878 + 0.814141i) q^{3} +(1.91611 + 0.573183i) q^{4} +(-2.08397 - 2.08397i) q^{5} +(-2.30598 + 0.826122i) q^{6} -1.14637 q^{7} +(2.56382 + 1.19449i) q^{8} +(1.67435 - 2.48929i) q^{9} +(-2.48929 - 3.34292i) q^{10} +(-1.67435 + 1.67435i) q^{11} +(-3.39596 + 0.683709i) q^{12} +(0.146365 + 0.146365i) q^{13} +(-1.60411 - 0.234787i) q^{14} +(4.88258 + 1.48929i) q^{15} +(3.34292 + 2.19656i) q^{16} +5.59722i q^{17} +(2.85275 - 3.14035i) q^{18} +(1.48929 - 1.48929i) q^{19} +(-2.79861 - 5.18760i) q^{20} +(1.75254 - 0.933303i) q^{21} +(-2.68585 + 2.00000i) q^{22} -3.34870i q^{23} +(-4.89201 + 0.261191i) q^{24} +3.68585i q^{25} +(0.174833 + 0.234787i) q^{26} +(-0.533081 + 5.16874i) q^{27} +(-2.19656 - 0.657077i) q^{28} +(3.51325 - 3.51325i) q^{29} +(6.52719 + 3.08397i) q^{30} -5.83221i q^{31} +(4.22789 + 3.75832i) q^{32} +(1.19656 - 3.92287i) q^{33} +(-1.14637 + 7.83221i) q^{34} +(2.38899 + 2.38899i) q^{35} +(4.63505 - 3.81003i) q^{36} +(-4.83221 + 4.83221i) q^{37} +(2.38899 - 1.77895i) q^{38} +(-0.342923 - 0.104599i) q^{39} +(-2.85363 - 7.83221i) q^{40} -0.610042 q^{41} +(2.64349 - 0.947037i) q^{42} +(-1.48929 - 1.48929i) q^{43} +(-4.16794 + 2.24852i) q^{44} +(-8.67689 + 1.69831i) q^{45} +(0.685846 - 4.68585i) q^{46} -6.41646 q^{47} +(-6.89891 - 0.636446i) q^{48} -5.68585 q^{49} +(-0.754898 + 5.15762i) q^{50} +(-4.55693 - 8.55693i) q^{51} +(0.196558 + 0.364346i) q^{52} +(-0.164553 - 0.164553i) q^{53} +(-1.80455 + 7.12345i) q^{54} +6.97858 q^{55} +(-2.93908 - 1.36933i) q^{56} +(-1.06431 + 3.48929i) q^{57} +(5.63565 - 4.19656i) q^{58} +(9.05051 - 9.05051i) q^{59} +(8.50190 + 5.65224i) q^{60} +(4.53948 + 4.53948i) q^{61} +(1.19449 - 8.16104i) q^{62} +(-1.91942 + 2.85363i) q^{63} +(5.14637 + 6.12494i) q^{64} -0.610042i q^{65} +(2.47779 - 5.24422i) q^{66} +(-0.635654 + 0.635654i) q^{67} +(-3.20823 + 10.7249i) q^{68} +(2.72631 + 5.11943i) q^{69} +(2.85363 + 3.83221i) q^{70} +6.90659i q^{71} +(7.26617 - 4.38209i) q^{72} -7.07896i q^{73} +(-7.75142 + 5.77205i) q^{74} +(-3.00080 - 5.63485i) q^{75} +(3.70727 - 2.00000i) q^{76} +(1.91942 - 1.91942i) q^{77} +(-0.458431 - 0.216600i) q^{78} +9.83221i q^{79} +(-2.38899 - 11.5441i) q^{80} +(-3.39312 - 8.33587i) q^{81} +(-0.853635 - 0.124943i) q^{82} +(8.09081 + 8.09081i) q^{83} +(3.89301 - 0.783781i) q^{84} +(11.6644 - 11.6644i) q^{85} +(-1.77895 - 2.38899i) q^{86} +(-2.51071 + 8.23127i) q^{87} +(-6.29273 + 2.29273i) q^{88} -0.490134 q^{89} +(-12.4894 + 0.599340i) q^{90} +(-0.167788 - 0.167788i) q^{91} +(1.91942 - 6.41646i) q^{92} +(4.74824 + 8.91618i) q^{93} +(-8.97858 - 1.31415i) q^{94} -6.20726 q^{95} +(-9.52332 - 2.30355i) q^{96} +12.3503 q^{97} +(-7.95623 - 1.16452i) q^{98} +(1.36449 + 6.97138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.39930	+	0.204810i	0.989458	+	0.144822i
$2$	1.39930	+	0.204810i	0.989458	+	0.144822i
$3$	−1.52878	+	0.814141i	−0.882643	+	0.470045i
$3$	−1.52878	+	0.814141i	−0.882643	+	0.470045i
$4$	1.91611	+	0.573183i	0.958053	+	0.286591i
$5$	−2.08397	−	2.08397i	−0.931979	−	0.931979i	0.0658506	−	0.997829i	$-0.479024\pi$
$5$	−2.08397	−	2.08397i	−0.931979	−	0.931979i	−0.997829	+	0.0658506i	$0.979024\pi$
$6$	−2.30598	+	0.826122i	−0.941411	+	0.337263i
$7$	−1.14637			−0.433285			−0.216643	−	0.976251i	$-0.569511\pi$
$7$	−1.14637			−0.433285			−0.216643	+	0.976251i	$0.569511\pi$
$8$	2.56382	+	1.19449i	0.906448	+	0.422318i
$9$	1.67435	−	2.48929i	0.558116	−	0.829763i
$10$	−2.48929	−	3.34292i	−0.787182	−	1.05713i
$11$	−1.67435	+	1.67435i	−0.504835	+	0.504835i	−0.912937	−	0.408102i	$-0.866191\pi$
$11$	−1.67435	+	1.67435i	−0.504835	+	0.504835i	0.408102	+	0.912937i	$0.366191\pi$
$12$	−3.39596	+	0.683709i	−0.980329	+	0.197370i
$13$	0.146365	+	0.146365i	0.0405945	+	0.0405945i	0.727113	−	0.686518i	$-0.240862\pi$
$13$	0.146365	+	0.146365i	0.0405945	+	0.0405945i	−0.686518	+	0.727113i	$0.740862\pi$
$14$	−1.60411	−	0.234787i	−0.428718	−	0.0627495i
$15$	4.88258	+	1.48929i	1.26068	+	0.384533i
$16$	3.34292	+	2.19656i	0.835731	+	0.549139i
$17$			5.59722i			1.35752i	0.734358	+	0.678762i	$0.237483\pi$
$17$			5.59722i			1.35752i	−0.734358	+	0.678762i	$0.762517\pi$
$18$	2.85275	−	3.14035i	0.672401	−	0.740187i
$19$	1.48929	−	1.48929i	0.341666	−	0.341666i	−0.515327	−	0.856993i	$-0.672330\pi$
$19$	1.48929	−	1.48929i	0.341666	−	0.341666i	0.856993	+	0.515327i	$0.172330\pi$
$20$	−2.79861	−	5.18760i	−0.625788	−	1.15998i
$21$	1.75254	−	0.933303i	0.382436	−	0.203663i
$22$	−2.68585	+	2.00000i	−0.572624	+	0.426401i
$23$		−	3.34870i		−	0.698252i	−0.937076	−	0.349126i	$-0.886479\pi$
$23$		−	3.34870i		−	0.698252i	0.937076	−	0.349126i	$-0.113521\pi$
$24$	−4.89201	+	0.261191i	−0.998578	+	0.0533154i
$25$			3.68585i			0.737169i
$26$	0.174833	+	0.234787i	0.0342875	+	0.0460455i
$27$	−0.533081	+	5.16874i	−0.102592	+	0.994724i
$28$	−2.19656	−	0.657077i	−0.415110	−	0.124176i
$29$	3.51325	−	3.51325i	0.652394	−	0.652394i	−0.301175	−	0.953569i	$-0.597379\pi$
$29$	3.51325	−	3.51325i	0.652394	−	0.652394i	0.953569	+	0.301175i	$0.0973788\pi$
$30$	6.52719	+	3.08397i	1.19170	+	0.563053i
$31$		−	5.83221i		−	1.04750i	−0.851873	−	0.523748i	$-0.824533\pi$
$31$		−	5.83221i		−	1.04750i	0.851873	−	0.523748i	$-0.175467\pi$
$32$	4.22789	+	3.75832i	0.747392	+	0.664383i
$33$	1.19656	−	3.92287i	0.208294	−	0.682884i
$34$	−1.14637	+	7.83221i	−0.196600	+	1.34321i
$35$	2.38899	+	2.38899i	0.403813	+	0.403813i
$36$	4.63505	−	3.81003i	0.772508	−	0.635005i
$37$	−4.83221	+	4.83221i	−0.794411	+	0.794411i	−0.982208	−	0.187797i	$-0.939865\pi$
$37$	−4.83221	+	4.83221i	−0.794411	+	0.794411i	0.187797	+	0.982208i	$0.439865\pi$
$38$	2.38899	−	1.77895i	0.387545	−	0.288583i
$39$	−0.342923	−	0.104599i	−0.0549116	−	0.0167492i
$40$	−2.85363	−	7.83221i	−0.451199	−	1.23838i
$41$	−0.610042			−0.0952726			−0.0476363	−	0.998865i	$-0.515169\pi$
$41$	−0.610042			−0.0952726			−0.0476363	+	0.998865i	$0.515169\pi$
$42$	2.64349	−	0.947037i	0.407899	−	0.146131i
$43$	−1.48929	−	1.48929i	−0.227114	−	0.227114i	0.584372	−	0.811486i	$-0.301341\pi$
$43$	−1.48929	−	1.48929i	−0.227114	−	0.227114i	−0.811486	+	0.584372i	$0.801341\pi$
$44$	−4.16794	+	2.24852i	−0.628340	+	0.338977i
$45$	−8.67689	+	1.69831i	−1.29347	+	0.253169i
$46$	0.685846	−	4.68585i	0.101123	−	0.690890i
$47$	−6.41646			−0.935936			−0.467968	−	0.883745i	$-0.655014\pi$
$47$	−6.41646			−0.935936			−0.467968	+	0.883745i	$0.655014\pi$
$48$	−6.89891	−	0.636446i	−0.995772	−	0.0918631i
$49$	−5.68585			−0.812264
$50$	−0.754898	+	5.15762i	−0.106759	+	0.729398i
$51$	−4.55693	−	8.55693i	−0.638097	−	1.19821i
$52$	0.196558	+	0.364346i	0.0272576	+	0.0505257i
$53$	−0.164553	−	0.164553i	−0.0226031	−	0.0226031i	0.695715	−	0.718318i	$-0.255088\pi$
$53$	−0.164553	−	0.164553i	−0.0226031	−	0.0226031i	−0.718318	+	0.695715i	$0.755088\pi$
$54$	−1.80455	+	7.12345i	−0.245568	+	0.969379i
$55$	6.97858			0.940991
$56$	−2.93908	−	1.36933i	−0.392751	−	0.182984i
$57$	−1.06431	+	3.48929i	−0.140971	+	0.462168i
$58$	5.63565	−	4.19656i	0.739998	−	0.551035i
$59$	9.05051	−	9.05051i	1.17828	−	1.17828i	0.198093	−	0.980183i	$-0.436525\pi$
$59$	9.05051	−	9.05051i	1.17828	−	1.17828i	0.980183	−	0.198093i	$-0.0634749\pi$
$60$	8.50190	+	5.65224i	1.09759	+	0.729701i
$61$	4.53948	+	4.53948i	0.581221	+	0.581221i	0.935239	−	0.354018i	$-0.115185\pi$
$61$	4.53948	+	4.53948i	0.581221	+	0.581221i	−0.354018	+	0.935239i	$0.615185\pi$
$62$	1.19449	−	8.16104i	0.151701	−	1.03645i
$63$	−1.91942	+	2.85363i	−0.241824	+	0.359524i
$64$	5.14637	+	6.12494i	0.643296	+	0.765618i
$65$		−	0.610042i		−	0.0756664i
$66$	2.47779	−	5.24422i	0.304995	−	0.645519i
$67$	−0.635654	+	0.635654i	−0.0776575	+	0.0776575i	−0.744869	−	0.667211i	$-0.767488\pi$
$67$	−0.635654	+	0.635654i	−0.0776575	+	0.0776575i	0.667211	+	0.744869i	$0.267488\pi$
$68$	−3.20823	+	10.7249i	−0.389055	+	1.30058i
$69$	2.72631	+	5.11943i	0.328209	+	0.616307i
$70$	2.85363	+	3.83221i	0.341075	+	0.458037i
$71$			6.90659i			0.819662i	0.912162	+	0.409831i	$0.134412\pi$
$71$			6.90659i			0.819662i	−0.912162	+	0.409831i	$0.865588\pi$
$72$	7.26617	−	4.38209i	0.856327	−	0.516435i
$73$		−	7.07896i		−	0.828530i	−0.910156	−	0.414265i	$-0.864039\pi$
$73$		−	7.07896i		−	0.828530i	0.910156	−	0.414265i	$-0.135961\pi$
$74$	−7.75142	+	5.77205i	−0.901084	+	0.670987i
$75$	−3.00080	−	5.63485i	−0.346502	−	0.650657i
$76$	3.70727	−	2.00000i	0.425253	−	0.229416i
$77$	1.91942	−	1.91942i	0.218738	−	0.218738i
$78$	−0.458431	−	0.216600i	−0.0519071	−	0.0245251i
$79$			9.83221i			1.10621i	0.833111	+	0.553105i	$0.186557\pi$
$79$			9.83221i			1.10621i	−0.833111	+	0.553105i	$0.813443\pi$
$80$	−2.38899	−	11.5441i	−0.267097	−	1.29067i
$81$	−3.39312	−	8.33587i	−0.377013	−	0.926208i
$82$	−0.853635	−	0.124943i	−0.0942682	−	0.0137976i
$83$	8.09081	+	8.09081i	0.888081	+	0.888081i	0.994339	−	0.106257i	$-0.0338867\pi$
$83$	8.09081	+	8.09081i	0.888081	+	0.888081i	−0.106257	+	0.994339i	$0.533887\pi$
$84$	3.89301	−	0.783781i	0.424762	−	0.0855175i
$85$	11.6644	−	11.6644i	1.26518	−	1.26518i
$86$	−1.77895	−	2.38899i	−0.191829	−	0.257611i
$87$	−2.51071	+	8.23127i	−0.269177	+	0.882485i
$88$	−6.29273	+	2.29273i	−0.670807	+	0.244406i
$89$	−0.490134			−0.0519541			−0.0259770	−	0.999663i	$-0.508270\pi$
$89$	−0.490134			−0.0519541			−0.0259770	+	0.999663i	$0.508270\pi$
$90$	−12.4894	+	0.599340i	−1.31650	+	0.0631760i
$91$	−0.167788	−	0.167788i	−0.0175890	−	0.0175890i
$92$	1.91942	−	6.41646i	0.200113	−	0.668962i
$93$	4.74824	+	8.91618i	0.492370	+	0.924565i
$94$	−8.97858	−	1.31415i	−0.926070	−	0.135545i
$95$	−6.20726			−0.636851
$96$	−9.52332	−	2.30355i	−0.971970	−	0.235105i
$97$	12.3503			1.25398			0.626990	−	0.779027i	$-0.284287\pi$
$97$	12.3503			1.25398			0.626990	+	0.779027i	$0.284287\pi$
$98$	−7.95623	−	1.16452i	−0.803701	−	0.117634i
$99$	1.36449	+	6.97138i	0.137137	+	0.700650i
$100$	−2.11266	+	7.06247i	−0.211266	+	0.706247i
$101$	8.29123	+	8.29123i	0.825008	+	0.825008i	0.986821	−	0.161813i	$-0.0517343\pi$
$101$	8.29123	+	8.29123i	0.825008	+	0.825008i	−0.161813	+	0.986821i	$0.551734\pi$
$102$	−4.62398	−	12.9070i	−0.457843	−	1.27799i
$103$	−12.2253			−1.20460			−0.602299	−	0.798271i	$-0.705748\pi$
$103$	−12.2253			−1.20460			−0.602299	+	0.798271i	$0.705748\pi$
$104$	0.200422	+	0.550088i	0.0196530	+	0.0539405i
$105$	−5.59722	−	1.70727i	−0.546233	−	0.166612i
$106$	−0.196558	−	0.263962i	−0.0190914	−	0.0256382i
$107$	0.714641	−	0.714641i	0.0690869	−	0.0690869i	−0.671719	−	0.740806i	$-0.734444\pi$
$107$	0.714641	−	0.714641i	0.0690869	−	0.0690869i	0.740806	+	0.671719i	$0.234444\pi$
$108$	−3.98407	+	9.59829i	−0.383367	+	0.923596i
$109$	−12.4966	−	12.4966i	−1.19696	−	1.19696i	−0.975072	−	0.221888i	$-0.928778\pi$
$109$	−12.4966	−	12.4966i	−1.19696	−	1.19696i	−0.221888	−	0.975072i	$-0.571222\pi$
$110$	9.76515	+	1.42928i	0.931071	+	0.136277i
$111$	3.45330	−	11.3215i	0.327772	−	1.07459i
$112$	−3.83221	−	2.51806i	−0.362110	−	0.237934i
$113$		−	5.47731i		−	0.515262i	−0.966243	−	0.257631i	$-0.917058\pi$
$113$		−	5.47731i		−	0.515262i	0.966243	−	0.257631i	$-0.0829419\pi$
$114$	−2.20393	+	4.66460i	−0.206417	+	0.436879i
$115$	−6.97858	+	6.97858i	−0.650756	+	0.650756i
$116$	8.74549	−	4.71802i	0.811999	−	0.438058i
$117$	0.609413	−	0.119279i	0.0563402	−	0.0110274i
$118$	14.5181	−	10.8108i	1.33650	−	0.995214i
$119$		−	6.41646i		−	0.588196i
$120$	10.7391	+	9.65048i	0.980342	+	0.880964i
$121$			5.39312i			0.490283i
$122$	5.42238	+	7.28185i	0.490920	+	0.659267i
$123$	0.932621	−	0.496660i	0.0840916	−	0.0447824i
$124$	3.34292	−	11.1751i	0.300203	−	1.00356i
$125$	−2.73865	+	2.73865i	−0.244953	+	0.244953i
$126$	−3.27030	+	3.59999i	−0.291341	+	0.320712i
$127$			7.20390i			0.639243i	0.947545	+	0.319622i	$0.103556\pi$
$127$			7.20390i			0.639243i	−0.947545	+	0.319622i	$0.896444\pi$
$128$	5.94688	+	9.62469i	0.525635	+	0.850710i
$129$	3.48929	+	1.06431i	0.307215	+	0.0937069i
$130$	0.124943	−	0.853635i	0.0109582	−	0.0748687i
$131$	−9.05051	−	9.05051i	−0.790747	−	0.790747i	0.190869	−	0.981616i	$-0.438870\pi$
$131$	−9.05051	−	9.05051i	−0.790747	−	0.790747i	−0.981616	+	0.190869i	$0.938870\pi$
$132$	4.54125	−	6.83079i	0.395265	−	0.594544i
$133$	−1.70727	+	1.70727i	−0.148039	+	0.148039i
$134$	−1.01966	+	0.759285i	−0.0880854	+	0.0655923i
$135$	11.8824	−	9.66056i	1.02267	−	0.831448i
$136$	−6.68585	+	14.3503i	−0.573307	+	1.23053i
$137$	−13.4430			−1.14851			−0.574255	−	0.818677i	$-0.694708\pi$
$137$	−13.4430			−1.14851			−0.574255	+	0.818677i	$0.694708\pi$
$138$	2.76643	+	7.72201i	0.235494	+	0.657341i
$139$	8.63565	+	8.63565i	0.732467	+	0.732467i	0.971108	−	0.238641i	$-0.0767020\pi$
$139$	8.63565	+	8.63565i	0.732467	+	0.732467i	−0.238641	+	0.971108i	$0.576702\pi$
$140$	3.20823	+	5.94688i	0.271145	+	0.502603i
$141$	9.80936	−	5.22390i	0.826097	−	0.439932i
$142$	−1.41454	+	9.66442i	−0.118705	+	0.811020i
$143$	−0.490134			−0.0409870
$144$	11.0651	−	4.64370i	0.922090	−	0.386975i
$145$	−14.6430			−1.21603
$146$	1.44984	−	9.90562i	0.119990	−	0.819795i
$147$	8.69242	−	4.62908i	0.716939	−	0.381800i
$148$	−12.0288	+	6.48929i	−0.988759	+	0.533416i
$149$	−11.6399	−	11.6399i	−0.953580	−	0.953580i	0.0453896	−	0.998969i	$-0.485547\pi$
$149$	−11.6399	−	11.6399i	−0.953580	−	0.953580i	−0.998969	+	0.0453896i	$0.985547\pi$
$150$	−3.04496	−	8.49947i	−0.248620	−	0.693979i
$151$	−0.810789			−0.0659811			−0.0329905	−	0.999456i	$-0.510503\pi$
$151$	−0.810789			−0.0659811			−0.0329905	+	0.999456i	$0.510503\pi$
$152$	5.59722	−	2.03932i	0.453994	−	0.165411i
$153$	13.9331	+	9.37169i	1.12642	+	0.757656i
$154$	3.07896	−	2.29273i	0.248110	−	0.184754i
$155$	−12.1541	+	12.1541i	−0.976244	+	0.976244i
$156$	−0.597123	−	0.396980i	−0.0478081	−	0.0317838i
$157$	5.51806	+	5.51806i	0.440389	+	0.440389i	0.892143	−	0.451754i	$-0.149201\pi$
$157$	5.51806	+	5.51806i	0.440389	+	0.440389i	−0.451754	+	0.892143i	$0.649201\pi$
$158$	−2.01373	+	13.7583i	−0.160204	+	1.09455i
$159$	0.385535	+	0.117596i	0.0305749	+	0.00932599i
$160$	−0.978577	−	16.6430i	−0.0773633	−	1.31574i
$161$			3.83883i			0.302542i
$162$	−3.04073	−	12.3594i	−0.238902	−	0.971044i
$163$	10.0748	−	10.0748i	0.789115	−	0.789115i	−0.192234	−	0.981349i	$-0.561573\pi$
$163$	10.0748	−	10.0748i	0.789115	−	0.789115i	0.981349	+	0.192234i	$0.0615732\pi$
$164$	−1.16891	−	0.349666i	−0.0912762	−	0.0273043i
$165$	−10.6687	+	5.68155i	−0.830559	+	0.442308i
$166$	9.66442	+	12.9786i	0.750105	+	1.00733i
$167$			2.36843i			0.183275i	0.995792	+	0.0916373i	$0.0292100\pi$
$167$			2.36843i			0.183275i	−0.995792	+	0.0916373i	$0.970790\pi$
$168$	5.60803	−	0.299421i	0.432669	−	0.0231008i
$169$		−	12.9572i		−	0.996704i
$170$	18.7111	−	13.9331i	1.43507	−	1.06862i
$171$	−1.21368	−	6.20086i	−0.0928125	−	0.474191i
$172$	−2.00000	−	3.70727i	−0.152499	−	0.282677i
$173$	−5.22347	+	5.22347i	−0.397133	+	0.397133i	−0.877221	−	0.480088i	$-0.840605\pi$
$173$	−5.22347	+	5.22347i	−0.397133	+	0.397133i	0.480088	+	0.877221i	$0.340605\pi$
$174$	−5.19910	+	11.0038i	−0.394142	+	0.834199i
$175$		−	4.22533i		−	0.319405i
$176$	−9.27502	+	1.91942i	−0.699131	+	0.144681i
$177$	−6.46787	+	21.2047i	−0.486155	+	1.59384i
$178$	−0.685846	−	0.100384i	−0.0514063	−	0.00752411i
$179$	−7.13110	−	7.13110i	−0.533003	−	0.533003i	0.388462	−	0.921465i	$-0.373007\pi$
$179$	−7.13110	−	7.13110i	−0.533003	−	0.533003i	−0.921465	+	0.388462i	$0.873007\pi$
$180$	−17.5993	−	1.71930i	−1.31177	−	0.128149i
$181$	−6.73183	+	6.73183i	−0.500373	+	0.500373i	−0.911554	−	0.411181i	$-0.865116\pi$
$181$	−6.73183	+	6.73183i	−0.500373	+	0.500373i	0.411181	+	0.911554i	$0.365116\pi$
$182$	−0.200422	−	0.269152i	−0.0148563	−	0.0199509i
$183$	−10.6357	−	3.24410i	−0.786210	−	0.239811i
$184$	4.00000	−	8.58546i	0.294884	−	0.632929i
$185$	20.1403			1.48075
$186$	4.81812	+	13.4489i	0.353281	+	0.986124i
$187$	−9.37169	−	9.37169i	−0.685326	−	0.685326i
$188$	−12.2946	−	3.67780i	−0.896677	−	0.268231i
$189$	0.611106	−	5.92526i	0.0444514	−	0.430999i
$190$	−8.68585	−	1.27131i	−0.630138	−	0.0922304i
$191$	25.5284			1.84717			0.923584	−	0.383396i	$-0.125246\pi$
$191$	25.5284			1.84717			0.923584	+	0.383396i	$0.125246\pi$
$192$	−12.8542	−	5.17383i	−0.927675	−	0.373389i
$193$	9.07896			0.653518			0.326759	−	0.945108i	$-0.394043\pi$
$193$	9.07896			0.653518			0.326759	+	0.945108i	$0.394043\pi$
$194$	17.2818	+	2.52946i	1.24076	+	0.181604i
$195$	0.496660	+	0.932621i	0.0355666	+	0.0667864i
$196$	−10.8947	−	3.25903i	−0.778192	−	0.232788i
$197$	−3.18414	−	3.18414i	−0.226861	−	0.226861i	0.584519	−	0.811380i	$-0.301283\pi$
$197$	−3.18414	−	3.18414i	−0.226861	−	0.226861i	−0.811380	+	0.584519i	$0.801283\pi$
$198$	0.481535	+	10.0345i	0.0342212	+	0.713124i
$199$	19.5542			1.38616			0.693079	−	0.720861i	$-0.256254\pi$
$199$	19.5542			1.38616			0.693079	+	0.720861i	$0.256254\pi$
$200$	−4.40272	+	9.44985i	−0.311320	+	0.668206i
$201$	0.454264	−	1.48929i	0.0320413	−	0.105046i
$202$	9.90383	+	13.3001i	0.696831	+	0.935790i
$203$	−4.02747	+	4.02747i	−0.282673	+	0.282673i
$204$	−3.82687	−	19.0079i	−0.267934	−	1.33082i
$205$	1.27131	+	1.27131i	0.0887920	+	0.0887920i
$206$	−17.1070	−	2.50387i	−1.19190	−	0.174453i
$207$	−8.33587	−	5.60688i	−0.579383	−	0.389705i
$208$	0.167788	+	0.810789i	0.0116340	+	0.0562181i
$209$			4.98718i			0.344970i
$210$	−7.48255	−	3.53535i	−0.516345	−	0.243963i
$211$	−10.3429	+	10.3429i	−0.712036	+	0.712036i	−0.966961	−	0.254925i	$-0.917949\pi$
$211$	−10.3429	+	10.3429i	−0.712036	+	0.712036i	0.254925	+	0.966961i	$0.417949\pi$
$212$	−0.220982	−	0.409620i	−0.0151771	−	0.0281328i
$213$	−5.62294	−	10.5587i	−0.385277	−	0.723468i
$214$	1.14637	−	0.853635i	0.0783639	−	0.0583533i
$215$			6.20726i			0.423332i
$216$	−7.54075	+	12.6150i	−0.513083	+	0.858339i
$217$			6.68585i			0.453865i
$218$	−14.9272	−	20.0460i	−1.01100	−	1.35769i
$219$	5.76327	+	10.8222i	0.389446	+	0.731296i
$220$	13.3717	+	4.00000i	0.901519	+	0.269680i
$221$	−0.819240	+	0.819240i	−0.0551080	+	0.0551080i
$222$	7.15097	−	15.1350i	0.479941	−	1.01579i
$223$		−	22.6184i		−	1.51464i	−0.653042	−	0.757321i	$-0.726508\pi$
$223$		−	22.6184i		−	1.51464i	0.653042	−	0.757321i	$-0.273492\pi$
$224$	−4.84671	−	4.30840i	−0.323834	−	0.287867i
$225$	9.17513	+	6.17139i	0.611676	+	0.411426i
$226$	1.12181	−	7.66442i	0.0746215	−	0.509830i
$227$	−1.46515	−	1.46515i	−0.0972455	−	0.0972455i	0.656810	−	0.754056i	$-0.271905\pi$
$227$	−1.46515	−	1.46515i	−0.0972455	−	0.0972455i	−0.754056	+	0.656810i	$0.771905\pi$
$228$	−4.03932	+	6.07580i	−0.267511	+	0.402380i
$229$	−7.51806	+	7.51806i	−0.496807	+	0.496807i	−0.910443	−	0.413635i	$-0.864259\pi$
$229$	−7.51806	+	7.51806i	−0.496807	+	0.496807i	0.413635	+	0.910443i	$0.364259\pi$
$230$	−11.1944	+	8.33587i	−0.738139	+	0.549651i
$231$	−1.37169	+	4.49704i	−0.0902507	+	0.295884i
$232$	13.2039	−	4.81079i	0.866879	−	0.315844i
$233$	18.3820			1.20424			0.602121	−	0.798405i	$-0.294322\pi$
$233$	18.3820			1.20424			0.602121	+	0.798405i	$0.294322\pi$
$234$	0.877184	−	0.0420941i	0.0573433	−	0.00275177i
$235$	13.3717	+	13.3717i	0.872273	+	0.872273i
$236$	22.5293	−	12.1541i	1.46654	−	0.791167i
$237$	−8.00481	−	15.0313i	−0.519968	−	0.976388i
$238$	1.31415	−	8.97858i	0.0851839	−	0.581995i
$239$	13.5322			0.875328			0.437664	−	0.899139i	$-0.355806\pi$
$239$	13.5322			0.875328			0.437664	+	0.899139i	$0.355806\pi$
$240$	13.0508	+	15.7034i	0.842424	+	1.01365i
$241$	4.87819			0.314232			0.157116	−	0.987580i	$-0.449780\pi$
$241$	4.87819			0.314232			0.157116	+	0.987580i	$0.449780\pi$
$242$	−1.10456	+	7.54661i	−0.0710040	+	0.485114i
$243$	11.9739	+	9.98126i	0.768127	+	0.640298i
$244$	6.09617	+	11.3001i	0.390268	+	0.723413i
$245$	11.8491	+	11.8491i	0.757013	+	0.757013i
$246$	1.40674	−	0.503969i	0.0896906	−	0.0321319i
$247$	0.435961			0.0277395
$248$	6.96655	−	14.9528i	0.442376	−	0.949501i
$249$	−18.9561	−	5.78202i	−1.20130	−	0.366421i
$250$	−4.39312	+	3.27131i	−0.277845	+	0.206896i
$251$	−5.23224	+	5.23224i	−0.330256	+	0.330256i	−0.852684	−	0.522427i	$-0.825027\pi$
$251$	−5.23224	+	5.23224i	−0.330256	+	0.330256i	0.522427	+	0.852684i	$0.325027\pi$
$252$	−5.31346	+	4.36769i	−0.334716	+	0.275139i
$253$	5.60688	+	5.60688i	0.352502	+	0.352502i
$254$	−1.47543	+	10.0805i	−0.0925768	+	0.632504i
$255$	−8.33587	+	27.3288i	−0.522013	+	1.71140i
$256$	6.35027	+	14.6858i	0.396892	+	0.917865i
$257$		−	12.8329i		−	0.800495i	−0.916407	−	0.400248i	$-0.868924\pi$
$257$		−	12.8329i		−	0.800495i	0.916407	−	0.400248i	$-0.131076\pi$
$258$	4.66460	+	2.20393i	0.290405	+	0.137211i
$259$	5.53948	−	5.53948i	0.344207	−	0.344207i
$260$	0.349666	−	1.16891i	0.0216853	−	0.0724924i
$261$	−2.86309	−	14.6279i	−0.177221	−	0.905444i
$262$	−10.8108	−	14.5181i	−0.667893	−	0.896929i
$263$		−	28.3152i		−	1.74599i	−0.487729	−	0.872995i	$-0.662175\pi$
$263$		−	28.3152i		−	1.74599i	0.487729	−	0.872995i	$-0.337825\pi$
$264$	7.75361	−	8.62826i	0.477202	−	0.531033i
$265$			0.685846i			0.0421312i
$266$	−2.73865	+	2.03932i	−0.167918	+	0.125039i
$267$	0.749307	−	0.399038i	0.0458569	−	0.0244207i
$268$	−1.58233	+	0.853635i	−0.0966560	+	0.0521440i
$269$	−6.58101	+	6.58101i	−0.401251	+	0.401251i	−0.878674	−	0.477423i	$-0.841571\pi$
$269$	−6.58101	+	6.58101i	−0.401251	+	0.401251i	0.477423	+	0.878674i	$0.341571\pi$
$270$	18.6057	−	11.0844i	1.13231	−	0.674577i
$271$			8.66129i			0.526136i	0.964777	+	0.263068i	$0.0847343\pi$
$271$			8.66129i			0.526136i	−0.964777	+	0.263068i	$0.915266\pi$
$272$	−12.2946	+	18.7111i	−0.745470	+	1.13453i
$273$	0.393115	+	0.119908i	0.0237924	+	0.00725719i
$274$	−18.8108	−	2.75325i	−1.13640	−	0.166330i
$275$	−6.17139	−	6.17139i	−0.372149	−	0.372149i
$276$	2.28953	+	11.3720i	0.137814	+	0.684516i
$277$	13.1249	−	13.1249i	0.788601	−	0.788601i	−0.192664	−	0.981265i	$-0.561713\pi$
$277$	13.1249	−	13.1249i	0.788601	−	0.788601i	0.981265	+	0.192664i	$0.0617126\pi$
$278$	10.3152	+	13.8526i	0.618667	+	0.830822i
$279$	−14.5181	−	9.76515i	−0.869173	−	0.584624i
$280$	3.27131	+	8.97858i	0.195498	+	0.536573i
$281$	−26.1560			−1.56033			−0.780167	−	0.625571i	$-0.784866\pi$
$281$	−26.1560			−1.56033			−0.780167	+	0.625571i	$0.784866\pi$
$282$	14.7962	−	5.30077i	0.881100	−	0.315657i
$283$	−17.9070	−	17.9070i	−1.06446	−	1.06446i	−0.997774	−	0.0666843i	$-0.978758\pi$
$283$	−17.9070	−	17.9070i	−1.06446	−	1.06446i	−0.0666843	−	0.997774i	$-0.521242\pi$
$284$	−3.95874	+	13.2338i	−0.234908	+	0.785279i
$285$	9.48955	−	5.05359i	0.562112	−	0.299349i
$286$	−0.685846	−	0.100384i	−0.0405549	−	0.00593584i
$287$	0.699331			0.0412802
$288$	16.4345	−	4.23171i	0.968412	−	0.249356i
$289$	−14.3288			−0.842873
$290$	−20.4900	−	2.99903i	−1.20322	−	0.176109i
$291$	−18.8809	+	10.0549i	−1.10682	+	0.589426i
$292$	4.05754	−	13.5640i	0.237449	−	0.793775i
$293$	0.654687	+	0.654687i	0.0382472	+	0.0382472i	0.725972	−	0.687725i	$-0.241390\pi$
$293$	0.654687	+	0.654687i	0.0382472	+	0.0382472i	−0.687725	+	0.725972i	$0.741390\pi$
$294$	13.1114	−	4.69720i	0.764674	−	0.273946i
$295$	−37.7220			−2.19626
$296$	−18.1610	+	6.61688i	−1.05559	+	0.384598i
$297$	−7.76170	−	9.54683i	−0.450379	−	0.553963i
$298$	−13.9038	−	18.6718i	−0.805427	−	1.08163i
$299$	0.490134	−	0.490134i	0.0283452	−	0.0283452i
$300$	−2.52005	−	12.5170i	−0.145495	−	0.722668i
$301$	1.70727	+	1.70727i	0.0984054	+	0.0984054i
$302$	−1.13454	−	0.166058i	−0.0652855	−	0.00955554i
$303$	−19.4257	−	5.92525i	−1.11598	−	0.340397i
$304$	8.24989	−	1.70727i	0.473163	−	0.0979186i
$305$		−	18.9203i		−	1.08337i
$306$	17.5772	+	15.9675i	1.00482	+	0.912800i
$307$	−0.971231	+	0.971231i	−0.0554311	+	0.0554311i	−0.734279	−	0.678848i	$-0.762480\pi$
$307$	−0.971231	+	0.971231i	−0.0554311	+	0.0554311i	0.678848	+	0.734279i	$0.262480\pi$
$308$	4.77798	−	2.57763i	0.272251	−	0.146874i
$309$	18.6899	−	9.95314i	1.06323	−	0.566214i
$310$	−19.4966	+	14.5181i	−1.10733	+	0.824570i
$311$			33.1343i			1.87887i	0.342723	+	0.939437i	$0.388651\pi$
$311$			33.1343i			1.87887i	−0.342723	+	0.939437i	$0.611349\pi$
$312$	−0.754251	−	0.677792i	−0.0427011	−	0.0383724i
$313$			13.2285i			0.747717i	0.927486	+	0.373858i	$0.121965\pi$
$313$			13.2285i			0.747717i	−0.927486	+	0.373858i	$0.878035\pi$
$314$	6.59129	+	8.85160i	0.371968	+	0.499524i
$315$	9.94688	−	1.94688i	0.560443	−	0.109694i
$316$	−5.63565	+	18.8396i	−0.317030	+	1.05981i
$317$	7.89038	−	7.89038i	0.443168	−	0.443168i	−0.449907	−	0.893075i	$-0.648543\pi$
$317$	7.89038	−	7.89038i	0.443168	−	0.443168i	0.893075	+	0.449907i	$0.148543\pi$
$318$	0.515396	+	0.243514i	0.0289020	+	0.0136556i
$319$			11.7648i			0.658703i
$320$	2.03932	−	23.4890i	0.114002	−	1.31308i
$321$	−0.510711	+	1.67435i	−0.0285051	+	0.0934530i
$322$	−0.786230	+	5.37169i	−0.0438149	+	0.299353i
$323$	8.33587	+	8.33587i	0.463820	+	0.463820i
$324$	−1.72359	−	17.9173i	−0.0957550	−	0.995405i
$325$	−0.539481	+	0.539481i	−0.0299250	+	0.0299250i
$326$	16.1611	−	12.0342i	0.895078	−	0.666515i
$327$	29.2787	+	8.93060i	1.61911	+	0.493864i
$328$	−1.56404	−	0.728692i	−0.0863596	−	0.0402353i
$329$	7.35561			0.405528
$330$	−16.0924	+	5.76515i	−0.885859	+	0.317361i
$331$	−3.02877	−	3.02877i	−0.166476	−	0.166476i	0.618952	−	0.785429i	$-0.287557\pi$
$331$	−3.02877	−	3.02877i	−0.166476	−	0.166476i	−0.785429	+	0.618952i	$0.787557\pi$
$332$	10.8653	+	20.1403i	0.596312	+	1.10535i
$333$	3.93796	+	20.1196i	0.215799	+	1.10255i
$334$	−0.485078	+	3.31415i	−0.0265423	+	0.181342i
$335$	2.64937			0.144750
$336$	7.90867	+	0.729600i	0.431453	+	0.0398029i
$337$	15.2285			0.829547			0.414774	−	0.909925i	$-0.363861\pi$
$337$	15.2285			0.829547			0.414774	+	0.909925i	$0.363861\pi$
$338$	2.65375	−	18.1310i	0.144345	−	0.986197i
$339$	4.45930	+	8.37361i	0.242196	+	0.454792i
$340$	29.0361	−	15.6644i	1.57470	−	0.849523i
$341$	9.76515	+	9.76515i	0.528813	+	0.528813i
$342$	−0.428313	−	8.92546i	−0.0231605	−	0.482634i
$343$	14.5426			0.785227
$344$	−2.03932	−	5.59722i	−0.109953	−	0.301782i
$345$	4.98718	−	16.3503i	0.268501	−	0.880269i
$346$	−8.37904	+	6.23940i	−0.450460	+	0.335432i
$347$	16.2175	−	16.2175i	0.870600	−	0.870600i	−0.121938	−	0.992538i	$-0.538911\pi$
$347$	16.2175	−	16.2175i	0.870600	−	0.870600i	0.992538	+	0.121938i	$0.0389108\pi$
$348$	−9.52881	+	14.3329i	−0.510798	+	0.768324i
$349$	−6.14637	−	6.14637i	−0.329007	−	0.329007i	0.523202	−	0.852209i	$-0.324737\pi$
$349$	−6.14637	−	6.14637i	−0.329007	−	0.329007i	−0.852209	+	0.523202i	$0.824737\pi$
$350$	0.865389	−	5.91252i	0.0462570	−	0.316037i
$351$	−0.834549	+	0.678500i	−0.0445449	+	0.0362156i
$352$	−13.3717	+	0.786230i	−0.712714	+	0.0419062i
$353$		−	22.9507i		−	1.22154i	−0.791806	−	0.610772i	$-0.790859\pi$
$353$		−	22.9507i		−	1.22154i	0.791806	−	0.610772i	$-0.209141\pi$
$354$	−13.3934	+	28.3471i	−0.711853	+	1.50663i
$355$	14.3931	−	14.3931i	0.763907	−	0.763907i
$356$	−0.939148	−	0.280936i	−0.0497747	−	0.0148896i
$357$	5.22390	+	9.80936i	0.276478	+	0.519167i
$358$	−8.51806	−	11.4391i	−0.450193	−	0.604575i
$359$			18.3408i			0.967993i	0.875070	+	0.483996i	$0.160815\pi$
$359$			18.3408i			0.967993i	−0.875070	+	0.483996i	$0.839185\pi$
$360$	−24.2746	−	6.01033i	−1.27938	−	0.316772i
$361$			14.5640i			0.766528i
$362$	−10.7986	+	8.04113i	−0.567563	+	0.422632i
$363$	−4.39076	−	8.24490i	−0.230455	−	0.432745i
$364$	−0.225327	−	0.417674i	−0.0118103	−	0.0218920i
$365$	−14.7523	+	14.7523i	−0.772172	+	0.772172i
$366$	−14.2181	−	6.71777i	−0.743192	−	0.351143i
$367$		−	2.86833i		−	0.149725i	−0.997194	−	0.0748627i	$-0.976148\pi$
$367$		−	2.86833i		−	0.149725i	0.997194	−	0.0748627i	$-0.0238519\pi$
$368$	7.35561	−	11.1944i	0.383437	−	0.583550i
$369$	−1.02142	+	1.51857i	−0.0531731	+	0.0790536i
$370$	28.1825	+	4.12494i	1.46514	+	0.214446i
$371$	0.188638	+	0.188638i	0.00979359	+	0.00979359i
$372$	3.98754	+	19.8060i	0.206744	+	1.02689i
$373$	−17.2253	+	17.2253i	−0.891894	+	0.891894i	−0.994701	−	0.102808i	$-0.967217\pi$
$373$	−17.2253	+	17.2253i	−0.891894	+	0.891894i	0.102808	+	0.994701i	$0.467217\pi$
$374$	−11.1944	−	15.0333i	−0.578850	−	0.777352i
$375$	1.95715	−	6.41646i	0.101067	−	0.331344i
$376$	−16.4507	−	7.66442i	−0.848378	−	0.395262i
$377$	1.02844			0.0529672
$378$	2.06867	−	8.16608i	0.106401	−	0.420018i
$379$	5.83956	+	5.83956i	0.299958	+	0.299958i	0.840997	−	0.541039i	$-0.181969\pi$
$379$	5.83956	+	5.83956i	0.299958	+	0.299958i	−0.541039	+	0.840997i	$0.681969\pi$
$380$	−11.8938	−	3.55789i	−0.610137	−	0.182516i
$381$	−5.86499	−	11.0132i	−0.300473	−	0.564223i
$382$	35.7220	+	5.22846i	1.82769	+	0.267511i
$383$	−30.7659			−1.57206			−0.786031	−	0.618187i	$-0.787867\pi$
$383$	−30.7659			−1.57206			−0.786031	+	0.618187i	$0.787867\pi$
$384$	−16.9273	−	9.87244i	−0.863820	−	0.503801i
$385$	−8.00000			−0.407718
$386$	12.7042	+	1.85946i	0.646628	+	0.0946441i
$387$	−6.20086	+	1.21368i	−0.315207	+	0.0616949i
$388$	23.6644	+	7.07896i	1.20138	+	0.359380i
$389$	11.0299	+	11.0299i	0.559237	+	0.559237i	0.929090	−	0.369853i	$-0.120592\pi$
$389$	11.0299	+	11.0299i	0.559237	+	0.559237i	−0.369853	+	0.929090i	$0.620592\pi$
$390$	0.503969	+	1.40674i	0.0255195	+	0.0712331i
$391$	18.7434			0.947894
$392$	−14.5775	−	6.79171i	−0.736275	−	0.343033i
$393$	21.2047	+	6.46787i	1.06963	+	0.326261i
$394$	−3.80344	−	5.10773i	−0.191615	−	0.257324i
$395$	20.4900	−	20.4900i	1.03096	−	1.03096i
$396$	−1.38136	+	14.1400i	−0.0694159	+	0.710562i
$397$	−1.75325	−	1.75325i	−0.0879931	−	0.0879931i	0.661740	−	0.749733i	$-0.269818\pi$
$397$	−1.75325	−	1.75325i	−0.0879931	−	0.0879931i	−0.749733	+	0.661740i	$0.769818\pi$
$398$	27.3622	+	4.00489i	1.37155	+	0.200747i
$399$	1.22008	−	4.00000i	0.0610806	−	0.200250i
$400$	−8.09617	+	12.3215i	−0.404809	+	0.616075i
$401$			24.4693i			1.22194i	0.791654	+	0.610970i	$0.209220\pi$
$401$			24.4693i			1.22194i	−0.791654	+	0.610970i	$0.790780\pi$
$402$	0.940675	−	1.99093i	0.0469166	−	0.0992986i
$403$	0.853635	−	0.853635i	0.0425226	−	0.0425226i
$404$	11.1345	+	20.6393i	0.553961	+	1.02684i
$405$	−10.3005	+	24.4428i	−0.511838	+	1.21457i
$406$	−6.46052	+	4.81079i	−0.320630	+	0.238755i
$407$		−	16.1816i		−	0.802093i
$408$	−1.46194	−	27.3817i	−0.0723770	−	1.35559i
$409$		−	8.78623i		−	0.434451i	−0.976121	−	0.217226i	$-0.930299\pi$
$409$		−	8.78623i		−	0.434451i	0.976121	−	0.217226i	$-0.0697007\pi$
$410$	1.51857	+	2.03932i	0.0749969	+	0.100715i
$411$	20.5513	−	10.9445i	1.01372	−	0.539851i
$412$	−23.4250	−	7.00735i	−1.15407	−	0.345227i
$413$	−10.3752	+	10.3752i	−0.510530	+	0.510530i
$414$	−10.5161	−	9.55301i	−0.516837	−	0.469505i
$415$		−	33.7220i		−	1.65535i
$416$	0.0687294	+	1.16891i	0.00336974	+	0.0573103i
$417$	−20.2327	−	6.17139i	−0.990798	−	0.302214i
$418$	−1.02142	+	6.97858i	−0.0499594	+	0.341333i
$419$	−3.52202	−	3.52202i	−0.172062	−	0.172062i	0.615823	−	0.787885i	$-0.288824\pi$
$419$	−3.52202	−	3.52202i	−0.172062	−	0.172062i	−0.787885	+	0.615823i	$0.788824\pi$
$420$	−9.74628	−	6.47954i	−0.475570	−	0.316169i
$421$	11.2253	−	11.2253i	0.547089	−	0.547089i	−0.378509	−	0.925598i	$-0.623563\pi$
$421$	11.2253	−	11.2253i	0.547089	−	0.547089i	0.925598	+	0.378509i	$0.123563\pi$
$422$	−16.5912	+	12.3546i	−0.807648	+	0.601411i
$423$	−10.7434	+	15.9724i	−0.522361	+	0.776605i
$424$	−0.225327	−	0.618442i	−0.0109428	−	0.0300342i
$425$	−20.6305			−1.00073
$426$	−5.70568	−	15.9264i	−0.276441	−	0.771638i
$427$	−5.20390	−	5.20390i	−0.251835	−	0.251835i
$428$	1.77895	−	0.959708i	0.0859887	−	0.0463892i
$429$	0.749307	−	0.399038i	0.0361769	−	0.0192657i
$430$	−1.27131	+	8.68585i	−0.0613079	+	0.418869i
$431$	−12.1336			−0.584454			−0.292227	−	0.956349i	$-0.594396\pi$
$431$	−12.1336			−0.584454			−0.292227	+	0.956349i	$0.594396\pi$
$432$	−13.1355	+	16.1077i	−0.631981	+	0.774984i
$433$	−12.1495			−0.583868			−0.291934	−	0.956439i	$-0.594299\pi$
$433$	−12.1495			−0.583868			−0.291934	+	0.956439i	$0.594299\pi$
$434$	−1.36933	+	9.35553i	−0.0657298	+	0.449080i
$435$	22.3860	−	11.9215i	1.07332	−	0.571591i
$436$	−16.7820	−	31.1077i	−0.803713	−	1.48979i
$437$	−4.98718	−	4.98718i	−0.238569	−	0.238569i
$438$	5.84808	+	16.3239i	0.279432	+	0.779987i
$439$	27.1035			1.29358			0.646790	−	0.762668i	$-0.276111\pi$
$439$	27.1035			1.29358			0.646790	+	0.762668i	$0.276111\pi$
$440$	17.8918	+	8.33587i	0.852959	+	0.397397i
$441$	−9.52009	+	14.1537i	−0.453337	+	0.673986i
$442$	−1.31415	+	0.978577i	−0.0625079	+	0.0465462i
$443$	−28.8412	+	28.8412i	−1.37029	+	1.37029i	−0.510276	+	0.860011i	$0.670457\pi$
$443$	−28.8412	+	28.8412i	−1.37029	+	1.37029i	−0.860011	+	0.510276i	$0.829543\pi$
$444$	13.1062	−	19.7138i	0.621991	−	0.935577i
$445$	1.02142	+	1.02142i	0.0484201	+	0.0484201i
$446$	4.63248	−	31.6501i	0.219354	−	1.49868i
$447$	27.2714	+	8.31836i	1.28990	+	0.393445i
$448$	−5.89962	−	7.02142i	−0.278731	−	0.331731i
$449$			9.67586i			0.456632i	0.973587	+	0.228316i	$0.0733220\pi$
$449$			9.67586i			0.456632i	−0.973587	+	0.228316i	$0.926678\pi$
$450$	11.5748	+	10.5148i	0.545643	+	0.495673i
$451$	1.02142	−	1.02142i	0.0480969	−	0.0480969i
$452$	3.13950	−	10.4951i	0.147670	−	0.493648i
$453$	1.23952	−	0.660097i	0.0582377	−	0.0310140i
$454$	−1.75011	−	2.35027i	−0.0821370	−	0.110304i
$455$			0.699331i			0.0327851i
$456$	−6.89663	+	7.67461i	−0.322964	+	0.359396i
$457$			4.20077i			0.196504i	0.995162	+	0.0982518i	$0.0313251\pi$
$457$			4.20077i			0.196504i	−0.995162	+	0.0982518i	$0.968675\pi$
$458$	−12.0598	+	8.98028i	−0.563519	+	0.419621i
$459$	−28.9305	−	2.98377i	−1.35036	−	0.139271i
$460$	−17.3717	+	9.37169i	−0.809959	+	0.436957i
$461$	27.5406	−	27.5406i	1.28269	−	1.28269i	0.343565	−	0.939129i	$-0.388366\pi$
$461$	27.5406	−	27.5406i	1.28269	−	1.28269i	0.939129	−	0.343565i	$-0.111634\pi$
$462$	−2.84045	+	6.01179i	−0.132150	+	0.279694i
$463$			37.4109i			1.73863i	0.494255	+	0.869317i	$0.335441\pi$
$463$			37.4109i			1.73863i	−0.494255	+	0.869317i	$0.664559\pi$
$464$	19.4616	−	4.02747i	0.903481	−	0.186971i
$465$	8.68585	−	28.4762i	0.402796	−	1.32055i
$466$	25.7220	+	3.76481i	1.19155	+	0.174401i
$467$	−16.9168	−	16.9168i	−0.782817	−	0.782817i	0.197489	−	0.980305i	$-0.436721\pi$
$467$	−16.9168	−	16.9168i	−0.782817	−	0.782817i	−0.980305	+	0.197489i	$0.936721\pi$
$468$	1.23607	+	0.120753i	0.0571373	+	0.00558183i
$469$	0.728692	−	0.728692i	0.0336479	−	0.0336479i
$470$	15.9724	+	21.4497i	0.736753	+	0.989402i
$471$	−12.9284	−	3.94343i	−0.595709	−	0.181704i
$472$	34.0147	−	12.3931i	1.56565	−	0.570439i
$473$	4.98718			0.229311
$474$	−8.12260	−	22.6728i	−0.373084	−	1.04140i
$475$	5.48929	+	5.48929i	0.251866	+	0.251866i
$476$	3.67780	−	12.2946i	0.168572	−	0.563523i
$477$	−0.685139	+	0.134101i	−0.0313703	+	0.00614005i
$478$	18.9357	+	2.77154i	0.866100	+	0.126767i
$479$	−18.5500			−0.847573			−0.423786	−	0.905762i	$-0.639299\pi$
$479$	−18.5500			−0.847573			−0.423786	+	0.905762i	$0.639299\pi$
$480$	15.0458	+	24.6468i	0.686743	+	1.12497i
$481$	−1.41454			−0.0644974
$482$	6.82608	+	0.999102i	0.310919	+	0.0455079i
$483$	−3.12535	−	5.86873i	−0.142208	−	0.267037i
$484$	−3.09124	+	10.3338i	−0.140511	+	0.469717i
$485$	−25.7376	−	25.7376i	−1.16868	−	1.16868i
$486$	14.7109	+	16.4192i	0.667299	+	0.744790i
$487$	−40.9259			−1.85453			−0.927264	−	0.374408i	$-0.877846\pi$
$487$	−40.9259			−1.85453			−0.927264	+	0.374408i	$0.877846\pi$
$488$	6.21604	+	17.0608i	0.281387	+	0.772306i
$489$	−7.19983	+	23.6044i	−0.325587	+	1.06743i
$490$	14.1537	+	19.0073i	0.639400	+	0.858664i
$491$	−5.04360	+	5.04360i	−0.227615	+	0.227615i	−0.811696	−	0.584081i	$-0.801455\pi$
$491$	−5.04360	+	5.04360i	−0.227615	+	0.227615i	0.584081	+	0.811696i	$0.301455\pi$
$492$	2.07168	−	0.417091i	0.0933985	−	0.0188039i
$493$	19.6644	+	19.6644i	0.885641	+	0.885641i
$494$	0.610042	+	0.0892891i	0.0274471	+	0.00401731i
$495$	11.6846	−	17.3717i	0.525182	−	0.780800i
$496$	12.8108	−	19.4966i	0.575221	−	0.875425i
$497$		−	7.91748i		−	0.355147i
$498$	−25.3412	−	11.9732i	−1.13557	−	0.536532i
$499$	−11.4647	+	11.4647i	−0.513232	+	0.513232i	−0.915515	−	0.402283i	$-0.868217\pi$
$499$	−11.4647	+	11.4647i	−0.513232	+	0.513232i	0.402283	+	0.915515i	$0.368217\pi$
$500$	−6.81730	+	3.67780i	−0.304879	+	0.164476i
$501$	−1.92824	−	3.62081i	−0.0861472	−	0.161766i
$502$	−8.39312	+	6.24989i	−0.374603	+	0.278946i
$503$		−	32.7159i		−	1.45873i	−0.684125	−	0.729365i	$-0.739816\pi$
$503$		−	32.7159i		−	1.45873i	0.684125	−	0.729365i	$-0.260184\pi$
$504$	−8.32969	+	5.02348i	−0.371034	+	0.223764i
$505$		−	34.5573i		−	1.53778i
$506$	6.69739	+	8.99408i	0.297735	+	0.399836i
$507$	10.5490	+	19.8087i	0.468495	+	0.879734i
$508$	−4.12915	+	13.8034i	−0.183202	+	0.612429i
$509$	−10.1389	+	10.1389i	−0.449399	+	0.449399i	−0.895155	−	0.445756i	$-0.852935\pi$
$509$	−10.1389	+	10.1389i	−0.449399	+	0.449399i	0.445756	+	0.895155i	$0.352935\pi$
$510$	−17.2616	+	36.5341i	−0.764358	+	1.61776i
$511$			8.11508i			0.358990i
$512$	5.87815	+	21.8506i	0.259780	+	0.965668i
$513$	6.90383	+	8.49165i	0.304811	+	0.374916i
$514$	2.62831	−	17.9572i	0.115930	−	0.792056i
$515$	25.4772	+	25.4772i	1.12266	+	1.12266i
$516$	6.07580	+	4.03932i	0.267472	+	0.177821i
$517$	10.7434	−	10.7434i	0.472494	−	0.472494i
$518$	8.88596	−	6.61688i	0.390427	−	0.290729i
$519$	3.73290	−	12.2382i	0.163856	−	0.537197i
$520$	0.728692	−	1.56404i	0.0319553	−	0.0685877i
$521$	−6.08735			−0.266692			−0.133346	−	0.991070i	$-0.542572\pi$
$521$	−6.08735			−0.266692			−0.133346	+	0.991070i	$0.542572\pi$
$522$	−1.01039	−	21.0553i	−0.0442238	−	0.921564i
$523$	15.8824	+	15.8824i	0.694489	+	0.694489i	0.963216	−	0.268727i	$-0.0866030\pi$
$523$	15.8824	+	15.8824i	0.694489	+	0.694489i	−0.268727	+	0.963216i	$0.586603\pi$
$524$	−12.1541	−	22.5293i	−0.530956	−	0.984199i
$525$	3.44001	+	6.45960i	0.150134	+	0.281920i
$526$	5.79923	−	39.6216i	0.252859	−	1.72758i
$527$	32.6442			1.42200
$528$	12.6168	−	10.4855i	0.549076	−	0.456325i
$529$	11.7862			0.512445
$530$	−0.140468	+	0.959708i	−0.00610154	+	0.0416870i
$531$	−7.37563	−	37.6831i	−0.320075	−	1.63531i
$532$	−4.24989	+	2.29273i	−0.184256	+	0.0994025i
$533$	−0.0892891	−	0.0892891i	−0.00386754	−	0.00386754i
$534$	1.13024	−	0.404910i	0.0489101	−	0.0175222i
$535$	−2.97858			−0.128775
$536$	−2.38899	+	0.870418i	−0.103189	+	0.0375964i
$537$	16.7076	+	5.09617i	0.720987	+	0.219916i
$538$	−10.5567	+	7.86098i	−0.455131	+	0.338911i
$539$	9.52009	−	9.52009i	0.410059	−	0.410059i
$540$	28.3052	−	11.6999i	1.21806	−	0.503482i
$541$	−25.6184	−	25.6184i	−1.10142	−	1.10142i	−0.994239	−	0.107184i	$-0.965817\pi$
$541$	−25.6184	−	25.6184i	−1.10142	−	1.10142i	−0.107184	−	0.994239i	$-0.534183\pi$
$542$	−1.77392	+	12.1198i	−0.0761963	+	0.520589i
$543$	4.81084	−	15.7722i	0.206453	−	0.676848i
$544$	−21.0361	+	23.6644i	−0.901916	+	1.01460i
$545$			52.0852i			2.23108i
$546$	0.525529	+	0.248302i	0.0224906	+	0.0106264i
$547$	−27.2113	+	27.2113i	−1.16347	+	1.16347i	−0.179758	+	0.983711i	$0.557532\pi$
$547$	−27.2113	+	27.2113i	−1.16347	+	1.16347i	−0.983711	+	0.179758i	$0.942468\pi$
$548$	−25.7581	−	7.70527i	−1.10033	−	0.329153i
$549$	18.9007	−	3.69941i	0.806664	−	0.157887i
$550$	−7.37169	−	9.89962i	−0.314330	−	0.422121i
$551$		−	10.4645i		−	0.445802i
$552$	0.874650	+	16.3819i	0.0372276	+	0.697258i
$553$		−	11.2713i		−	0.479305i
$554$	21.0539	−	15.6777i	0.894495	−	0.666080i
$555$	−30.7902	+	16.3971i	−1.30697	+	0.696018i
$556$	11.5970	+	21.4966i	0.491823	+	0.911660i
$557$	26.1831	−	26.1831i	1.10941	−	1.10941i	0.116184	−	0.993228i	$-0.462934\pi$
$557$	26.1831	−	26.1831i	1.10941	−	1.10941i	0.993228	−	0.116184i	$-0.0370662\pi$
$558$	−18.3152	−	16.6379i	−0.775344	−	0.704337i
$559$		−	0.435961i		−	0.0184392i
$560$	2.73865	+	13.2338i	0.115729	+	0.559228i
$561$	21.9572	+	6.69739i	0.927032	+	0.282764i
$562$	−36.6002	−	5.35700i	−1.54388	−	0.225971i
$563$	25.0435	+	25.0435i	1.05546	+	1.05546i	0.998369	+	0.0570880i	$0.0181816\pi$
$563$	25.0435	+	25.0435i	1.05546	+	1.05546i	0.0570880	+	0.998369i	$0.481818\pi$
$564$	21.7900	−	4.38699i	0.917526	−	0.184726i
$565$	−11.4145	+	11.4145i	−0.480213	+	0.480213i
$566$	−21.3898	−	28.7248i	−0.899079	−	1.20739i
$567$	3.88975	+	9.55596i	0.163354	+	0.401312i
$568$	−8.24989	+	17.7073i	−0.346157	+	0.742981i
$569$	12.5449			0.525911			0.262955	−	0.964808i	$-0.415303\pi$
$569$	12.5449			0.525911			0.262955	+	0.964808i	$0.415303\pi$
$570$	14.3138	−	5.12795i	0.599539	−	0.214786i
$571$	−4.48615	−	4.48615i	−0.187740	−	0.187740i	0.606979	−	0.794718i	$-0.292381\pi$
$571$	−4.48615	−	4.48615i	−0.187740	−	0.187740i	−0.794718	+	0.606979i	$0.792381\pi$
$572$	−0.939148	−	0.280936i	−0.0392677	−	0.0117465i
$573$	−39.0273	+	20.7837i	−1.63039	+	0.868251i
$574$	0.978577	+	0.143230i	0.0408450	+	0.00597830i
$575$	12.3428			0.514730
$576$	23.8636	−	2.55550i	0.994315	−	0.106479i
$577$	4.48508			0.186716			0.0933581	−	0.995633i	$-0.470240\pi$
$577$	4.48508			0.186716			0.0933581	+	0.995633i	$0.470240\pi$
$578$	−20.0504	−	2.93469i	−0.833987	−	0.122067i
$579$	−13.8798	+	7.39156i	−0.576823	+	0.307183i
$580$	−28.0575	−	8.39312i	−1.16503	−	0.348505i
$581$	−9.27502	−	9.27502i	−0.384793	−	0.384793i
$582$	−28.4794	+	10.2028i	−1.18051	+	0.422921i
$583$	0.551038			0.0228217
$584$	8.45578	−	18.1492i	0.349903	−	0.751019i
$585$	−1.51857	−	1.02142i	−0.0627852	−	0.0422306i
$586$	0.782020	+	1.05019i	0.0323049	+	0.0433830i
$587$	−11.9808	+	11.9808i	−0.494501	+	0.494501i	−0.909721	−	0.415220i	$-0.863705\pi$
$587$	−11.9808	+	11.9808i	−0.494501	+	0.494501i	0.415220	+	0.909721i	$0.363705\pi$
$588$	19.3089	−	3.88747i	0.796286	−	0.160316i
$589$	−8.68585	−	8.68585i	−0.357894	−	0.357894i
$590$	−52.7845	−	7.72583i	−2.17310	−	0.318067i
$591$	7.46020	+	2.27552i	0.306872	+	0.0936023i
$592$	−26.7679	+	5.53948i	−1.10016	+	0.227671i
$593$			3.27696i			0.134569i	0.997734	+	0.0672843i	$0.0214334\pi$
$593$			3.27696i			0.134569i	−0.997734	+	0.0672843i	$0.978567\pi$
$594$	−8.90570	−	14.9486i	−0.365405	−	0.613348i
$595$	−13.3717	+	13.3717i	−0.548186	+	0.548186i
$596$	−15.6315	−	28.9751i	−0.640292	−	1.18687i
$597$	−29.8941	+	15.9199i	−1.22348	+	0.651556i
$598$	0.786230	−	0.585462i	0.0321514	−	0.0239413i
$599$			38.9889i			1.59304i	0.604611	+	0.796521i	$0.293329\pi$
$599$			38.9889i			1.59304i	−0.604611	+	0.796521i	$0.706671\pi$
$600$	−0.962711	−	18.0312i	−0.0393025	−	0.736121i
$601$		−	23.5787i		−	0.961797i	−0.876776	−	0.480898i	$-0.840311\pi$
$601$		−	23.5787i		−	0.961797i	0.876776	−	0.480898i	$-0.159689\pi$
$602$	2.03932	+	2.73865i	0.0831166	+	0.111619i
$603$	0.518020	+	2.64663i	0.0210954	+	0.107779i
$604$	−1.55356	−	0.464730i	−0.0632133	−	0.0189096i
$605$	11.2391	−	11.2391i	0.456934	−	0.456934i
$606$	−25.9689	−	12.2698i	−1.05492	−	0.498427i
$607$		−	22.2829i		−	0.904434i	−0.891908	−	0.452217i	$-0.850633\pi$
$607$		−	22.2829i		−	0.904434i	0.891908	−	0.452217i	$-0.149367\pi$
$608$	11.8938	−	0.699331i	0.482356	−	0.0283616i
$609$	2.87819	−	9.43605i	0.116630	−	0.382368i
$610$	3.87506	−	26.4752i	0.156896	−	1.07195i
$611$	−0.939148	−	0.939148i	−0.0379939	−	0.0379939i
$612$	21.3256	+	25.9434i	0.862036	+	1.04870i
$613$	22.1611	−	22.1611i	0.895077	−	0.895077i	−0.0999189	−	0.994996i	$-0.531858\pi$
$613$	22.1611	−	22.1611i	0.895077	−	0.895077i	0.994996	+	0.0999189i	$0.0318583\pi$
$614$	−1.55797	+	1.16013i	−0.0628744	+	0.0468190i
$615$	−2.97858	−	0.908529i	−0.120108	−	0.0366354i
$616$	7.21377	−	2.62831i	0.290651	−	0.105898i
$617$	25.7376			1.03616			0.518078	−	0.855334i	$-0.326648\pi$
$617$	25.7376			1.03616			0.518078	+	0.855334i	$0.326648\pi$
$618$	28.1913	−	10.0996i	1.13402	−	0.406266i
$619$	7.71462	+	7.71462i	0.310077	+	0.310077i	0.844939	−	0.534863i	$-0.179637\pi$
$619$	7.71462	+	7.71462i	0.310077	+	0.310077i	−0.534863	+	0.844939i	$0.679637\pi$
$620$	−30.2552	+	16.3221i	−1.21508	+	0.655510i
$621$	17.3085	+	1.78513i	0.694567	+	0.0716347i
$622$	−6.78623	+	46.3650i	−0.272103	+	1.85907i
$623$	0.561872			0.0225109
$624$	−0.916608	−	1.10292i	−0.0366937	−	0.0441520i
$625$	29.8438			1.19375
$626$	−2.70932	+	18.5106i	−0.108286	+	0.739834i
$627$	−4.06027	−	7.62430i	−0.162151	−	0.304485i
$628$	7.41033	+	13.7360i	0.295704	+	0.548128i
$629$	−27.0469	−	27.0469i	−1.07843	−	1.07843i
$630$	14.3175	−	0.687063i	0.570421	−	0.0273732i
$631$	2.26817			0.0902945			0.0451473	−	0.998980i	$-0.485624\pi$
$631$	2.26817			0.0902945			0.0451473	+	0.998980i	$0.485624\pi$
$632$	−11.7445	+	25.2080i	−0.467172	+	1.00272i
$633$	7.39147	−	24.2327i	0.293785	−	0.963162i
$634$	12.6571	−	9.42502i	0.502677	−	0.374315i
$635$	15.0127	−	15.0127i	0.595761	−	0.595761i
$636$	0.671322	+	0.446309i	0.0266196	+	0.0176973i
$637$	−0.832212	−	0.832212i	−0.0329734	−	0.0329734i
$638$	−2.40955	+	16.4625i	−0.0953950	+	0.651758i
$639$	17.1925	+	11.5640i	0.680125	+	0.457466i
$640$	7.66442	−	32.4507i	0.302963	−	1.28272i
$641$			20.0686i			0.792662i	0.918108	+	0.396331i	$0.129717\pi$
$641$			20.0686i			0.792662i	−0.918108	+	0.396331i	$0.870283\pi$
$642$	−1.05756	+	2.23832i	−0.0417387	+	0.0883396i
$643$	14.0748	−	14.0748i	0.555054	−	0.555054i	−0.372841	−	0.927895i	$-0.621616\pi$
$643$	14.0748	−	14.0748i	0.555054	−	0.555054i	0.927895	+	0.372841i	$0.121616\pi$
$644$	−2.20035	+	7.35561i	−0.0867060	+	0.289851i
$645$	−5.05359	−	9.48955i	−0.198985	−	0.373651i
$646$	9.95715	+	13.3717i	0.391759	+	0.526102i
$647$		−	1.95003i		−	0.0766638i	−0.999265	−	0.0383319i	$-0.987796\pi$
$647$		−	1.95003i		−	0.0766638i	0.999265	−	0.0383319i	$-0.0122044\pi$
$648$	1.25781	−	25.4247i	0.0494115	−	0.998779i
$649$			30.3074i			1.18967i
$650$	−0.865389	+	0.644407i	−0.0339433	+	0.0252757i
$651$	−5.44322	−	10.2212i	−0.213337	−	0.400600i
$652$	25.0790	−	13.5296i	0.982168	−	0.529861i
$653$	−5.80289	+	5.80289i	−0.227085	+	0.227085i	−0.811474	−	0.584389i	$-0.801334\pi$
$653$	−5.80289	+	5.80289i	−0.227085	+	0.227085i	0.584389	+	0.811474i	$0.301334\pi$
$654$	39.1407	+	18.4932i	1.53052	+	0.723141i
$655$			37.7220i			1.47392i
$656$	−2.03932	−	1.33999i	−0.0796222	−	0.0523179i
$657$	−17.6216	−	11.8526i	−0.687483	−	0.462416i
$658$	10.2927	+	1.50650i	0.401252	+	0.0587295i
$659$	−5.49262	−	5.49262i	−0.213962	−	0.213962i	0.591986	−	0.805948i	$-0.298344\pi$
$659$	−5.49262	−	5.49262i	−0.213962	−	0.213962i	−0.805948	+	0.591986i	$0.798344\pi$
$660$	−23.6990	+	4.77132i	−0.922481	+	0.185723i
$661$	−5.86833	+	5.86833i	−0.228251	+	0.228251i	−0.811962	−	0.583710i	$-0.801600\pi$
$661$	−5.86833	+	5.86833i	−0.228251	+	0.228251i	0.583710	+	0.811962i	$0.301600\pi$
$662$	−3.61785	−	4.85849i	−0.140612	−	0.188831i
$663$	0.585462	−	1.91942i	0.0227375	−	0.0745439i
$664$	11.0790	+	30.4078i	0.429947	+	1.18005i
$665$	7.11579			0.275938
$666$	1.38972	+	28.9599i	0.0538506	+	1.12218i
$667$	−11.7648	−	11.7648i	−0.455535	−	0.455535i
$668$	−1.35754	+	4.53816i	−0.0525249	+	0.175587i
$669$	18.4146	+	34.5787i	0.711950	+	1.33689i
$670$	3.70727	+	0.542616i	0.143224	+	0.0209631i
$671$	−15.2013			−0.586841
$672$	10.9172	+	2.64071i	0.421140	+	0.101867i
$673$	−22.8929			−0.882456			−0.441228	−	0.897395i	$-0.645457\pi$
$673$	−22.8929			−0.882456			−0.441228	+	0.897395i	$0.645457\pi$
$674$	21.3093	+	3.11894i	0.820802	+	0.120137i
$675$	−19.0512	−	1.96486i	−0.733280	−	0.0756273i
$676$	7.42682	−	24.8273i	0.285647	−	0.954895i
$677$	13.7685	+	13.7685i	0.529168	+	0.529168i	0.920324	−	0.391156i	$-0.127925\pi$
$677$	13.7685	+	13.7685i	0.529168	+	0.529168i	−0.391156	+	0.920324i	$0.627925\pi$
$678$	4.52492	+	12.6305i	0.173779	+	0.485073i
$679$	−14.1579			−0.543331
$680$	43.8386	−	15.9724i	1.68113	−	0.612514i
$681$	3.43274	+	1.04706i	0.131543	+	0.0401233i
$682$	11.6644	+	15.6644i	0.446654	+	0.599822i
$683$	5.72238	−	5.72238i	0.218961	−	0.218961i	−0.589100	−	0.808060i	$-0.700517\pi$
$683$	5.72238	−	5.72238i	0.218961	−	0.218961i	0.808060	+	0.589100i	$0.200517\pi$
$684$	1.22868	−	12.5772i	0.0469799	−	0.480900i
$685$	28.0147	+	28.0147i	1.07039	+	1.07039i
$686$	20.3495	+	2.97847i	0.776949	+	0.113719i
$687$	5.37271	−	17.6142i	0.204982	−	0.672025i
$688$	−1.70727	−	8.24989i	−0.0650890	−	0.314524i
$689$		−	0.0481697i		−	0.00183512i
$690$	10.3273	−	21.8576i	0.393153	−	0.832104i
$691$	24.2327	−	24.2327i	0.921854	−	0.921854i	−0.0753061	−	0.997160i	$-0.523993\pi$
$691$	24.2327	−	24.2327i	0.921854	−	0.921854i	0.997160	+	0.0753061i	$0.0239934\pi$
$692$	−13.0027	+	7.01471i	−0.494289	+	0.266659i
$693$	−1.56421	−	7.99175i	−0.0594194	−	0.303581i
$694$	26.0147	−	19.3717i	0.987504	−	0.735339i
$695$		−	35.9929i		−	1.36529i
$696$	−16.2692	+	18.1045i	−0.616684	+	0.686249i
$697$		−	3.41454i		−	0.129335i
$698$	−7.34180	−	9.85947i	−0.277891	−	0.373187i
$699$	−28.1020	+	14.9655i	−1.06292	+	0.566048i
$700$	2.42188	−	8.09617i	0.0915386	−	0.306007i
$701$	10.9100	−	10.9100i	0.412064	−	0.412064i	−0.470393	−	0.882457i	$-0.655888\pi$
$701$	10.9100	−	10.9100i	0.412064	−	0.412064i	0.882457	+	0.470393i	$0.155888\pi$
$702$	−1.30675	+	0.778504i	−0.0493202	+	0.0293827i
$703$			14.3931i			0.542847i
$704$	−18.8721	−	1.63848i	−0.711269	−	0.0617525i
$705$	−31.3288	−	9.55596i	−1.17991	−	0.359898i
$706$	4.70054	−	32.1151i	0.176907	−	1.20867i
$707$	−9.50478	−	9.50478i	−0.357464	−	0.357464i
$708$	−24.5473	+	36.9231i	−0.922542	+	1.38765i
$709$	−14.0031	+	14.0031i	−0.525899	+	0.525899i	−0.919347	−	0.393448i	$-0.871282\pi$
$709$	−14.0031	+	14.0031i	−0.525899	+	0.525899i	0.393448	+	0.919347i	$0.371282\pi$
$710$	23.0882	−	17.1925i	0.866485	−	0.645223i
$711$	24.4752	+	16.4625i	0.917892	+	0.617394i
$712$	−1.25662	−	0.585462i	−0.0470937	−	0.0219411i
$713$	−19.5303			−0.731416
$714$	5.30077	+	14.7962i	0.198377	+	0.553734i
$715$	1.02142	+	1.02142i	0.0381990	+	0.0381990i
$716$	−9.57652	−	17.7514i	−0.357891	−	0.663400i
$717$	−20.6879	+	11.0172i	−0.772602	+	0.411443i
$718$	−3.75639	+	25.6644i	−0.140187	+	0.957788i
$719$	−30.0665			−1.12129			−0.560646	−	0.828055i	$-0.689447\pi$
$719$	−30.0665			−1.12129			−0.560646	+	0.828055i	$0.689447\pi$
$720$	−32.7366	−	13.3820i	−1.22002	−	0.498716i
$721$	14.0147			0.521934
$722$	−2.98286	+	20.3795i	−0.111011	+	0.758447i
$723$	−7.45769	+	3.97154i	−0.277355	+	0.147703i
$724$	−16.7575	+	9.04033i	−0.622786	+	0.335981i
$725$	12.9493	+	12.9493i	0.480925	+	0.480925i
$726$	−4.45537	−	12.4364i	−0.165354	−	0.461558i
$727$	9.48194			0.351666			0.175833	−	0.984420i	$-0.443738\pi$
$727$	9.48194			0.351666			0.175833	+	0.984420i	$0.443738\pi$
$728$	−0.229757	−	0.630602i	−0.00851537	−	0.0233717i
$729$	−26.4316	−	5.51071i	−0.978950	−	0.204100i
$730$	−23.6644	+	17.6216i	−0.875860	+	0.652204i
$731$	8.33587	−	8.33587i	0.308313	−	0.308313i
$732$	−18.5196	−	12.3122i	−0.684503	−	0.455072i
$733$	−29.4752	−	29.4752i	−1.08869	−	1.08869i	−0.995663	−	0.0930283i	$-0.970345\pi$
$733$	−29.4752	−	29.4752i	−1.08869	−	1.08869i	−0.0930283	−	0.995663i	$-0.529655\pi$
$734$	0.587462	−	4.01366i	0.0216836	−	0.148147i
$735$	−27.7616	−	8.46787i	−1.02400	−	0.312342i
$736$	12.5855	−	14.1579i	0.463906	−	0.521868i
$737$		−	2.12861i		−	0.0784085i
$738$	−1.74030	+	1.91575i	−0.0640613	+	0.0705196i
$739$	22.1077	−	22.1077i	0.813246	−	0.813246i	−0.171873	−	0.985119i	$-0.554982\pi$
$739$	22.1077	−	22.1077i	0.813246	−	0.813246i	0.985119	+	0.171873i	$0.0549819\pi$
$740$	38.5910	+	11.5441i	1.41863	+	0.424370i
$741$	−0.666489	+	0.354934i	−0.0244841	+	0.0130388i
$742$	0.225327	+	0.302597i	0.00827201	+	0.0111087i
$743$		−	0.908529i		−	0.0333307i	−0.999861	−	0.0166653i	$-0.994695\pi$
$743$		−	0.908529i		−	0.0333307i	0.999861	−	0.0166653i	$-0.00530499\pi$
$744$	1.52332	+	28.5312i	0.0558477	+	1.04601i
$745$			48.5145i			1.77743i
$746$	−27.6314	+	20.5756i	−1.01166	+	0.753325i
$747$	33.6872	−	6.59352i	1.23255	−	0.241244i
$748$	−12.5855	−	23.3288i	−0.460170	−	0.852987i
$749$	−0.819240	+	0.819240i	−0.0299344	+	0.0299344i
$750$	4.05281	−	8.57773i	0.147988	−	0.313215i
$751$		−	39.1182i		−	1.42744i	−0.700429	−	0.713722i	$-0.747008\pi$
$751$		−	39.1182i		−	1.42744i	0.700429	−	0.713722i	$-0.252992\pi$
$752$	−21.4497	−	14.0941i	−0.782191	−	0.513960i
$753$	3.73917	−	12.2587i	0.136263	−	0.446733i
$754$	1.43910	+	0.210634i	0.0524088	+	0.00767084i
$755$	1.68966	+	1.68966i	0.0614930	+	0.0614930i
$756$	4.56720	−	11.0031i	0.166107	−	0.400181i
$757$	−8.97544	+	8.97544i	−0.326218	+	0.326218i	−0.851146	−	0.524928i	$-0.824092\pi$
$757$	−8.97544	+	8.97544i	−0.326218	+	0.326218i	0.524928	+	0.851146i	$0.324092\pi$
$758$	6.97532	+	9.36732i	0.253355	+	0.340236i
$759$	−13.1365	−	4.00691i	−0.476825	−	0.145442i
$760$	−15.9143	−	7.41454i	−0.577273	−	0.268954i
$761$	−30.6766			−1.11202			−0.556012	−	0.831174i	$-0.687669\pi$
$761$	−30.6766			−1.11202			−0.556012	+	0.831174i	$0.687669\pi$
$762$	−5.95130	−	16.6120i	−0.215593	−	0.601790i
$763$	14.3257	+	14.3257i	0.518626	+	0.518626i
$764$	48.9151	+	14.6324i	1.76968	+	0.529382i
$765$	−9.50581	−	48.5664i	−0.343683	−	1.75592i
$766$	−43.0508	−	6.30115i	−1.55549	−	0.227670i
$767$	2.64937			0.0956630
$768$	−21.6645	−	17.2814i	−0.781751	−	0.623590i
$769$	−41.7795			−1.50661			−0.753304	−	0.657673i	$-0.771541\pi$
$769$	−41.7795			−1.50661			−0.753304	+	0.657673i	$0.771541\pi$
$770$	−11.1944	−	1.63848i	−0.403419	−	0.0590467i
$771$	10.4478	+	19.6187i	0.376268	+	0.706551i
$772$	17.3963	+	5.20390i	0.626105	+	0.187293i
$773$	17.6074	+	17.6074i	0.633293	+	0.633293i	0.948892	−	0.315599i	$-0.102206\pi$
$773$	17.6074	+	17.6074i	0.633293	+	0.633293i	−0.315599	+	0.948892i	$0.602206\pi$
$774$	−8.92546	+	0.428313i	−0.320819	+	0.0153954i
$775$	21.4966			0.772182
$776$	31.6639	+	14.7523i	1.13667	+	0.529578i
$777$	−3.95874	+	12.9786i	−0.142019	+	0.465604i
$778$	13.1751	+	17.6932i	0.472351	+	0.634332i
$779$	−0.908529	+	0.908529i	−0.0325514	+	0.0325514i
$780$	0.417091	+	2.07168i	0.0149343	+	0.0741780i
$781$	−11.5640	−	11.5640i	−0.413794	−	0.413794i
$782$	26.2277	+	3.83883i	0.937901	+	0.137276i
$783$	16.2862	+	20.0319i	0.582022	+	0.715882i
$784$	−19.0073	−	12.4893i	−0.678834	−	0.446046i
$785$		−	22.9989i		−	0.820866i
$786$	28.3471	+	13.3934i	1.01111	+	0.477728i
$787$	1.69006	−	1.69006i	0.0602440	−	0.0602440i	−0.676343	−	0.736587i	$-0.736436\pi$
$787$	1.69006	−	1.69006i	0.0602440	−	0.0602440i	0.736587	+	0.676343i	$0.236436\pi$
$788$	−4.27606	−	7.92625i	−0.152328	−	0.282361i
$789$	23.0526	+	43.2878i	0.820693	+	1.54108i
$790$	32.8683	−	24.4752i	1.16940	−	0.870789i
$791$			6.27900i			0.223255i
$792$	−4.82895	+	19.5033i	−0.171589	+	0.693018i
$793$			1.32885i			0.0471887i
$794$	−2.09425	−	2.81241i	−0.0743221	−	0.0998088i
$795$	−0.558376	−	1.04851i	−0.0198035	−	0.0371868i
$796$	37.4679	+	11.2081i	1.32801	+	0.397261i
$797$	−5.76177	+	5.76177i	−0.204092	+	0.204092i	−0.801751	−	0.597658i	$-0.796098\pi$
$797$	−5.76177	+	5.76177i	−0.204092	+	0.204092i	0.597658	+	0.801751i	$0.296098\pi$
$798$	2.52651	−	5.34733i	0.0894374	−	0.189294i
$799$		−	35.9143i		−	1.27056i
$800$	−13.8526	+	15.5834i	−0.489763	+	0.550955i
$801$	−0.820654	+	1.22008i	−0.0289964	+	0.0431096i
$802$	−5.01156	+	34.2400i	−0.176964	+	1.20906i
$803$	11.8526	+	11.8526i	0.418271	+	0.418271i
$804$	1.72405	−	2.59326i	0.0608027	−	0.0914572i
$805$	8.00000	−	8.00000i	0.281963	−	0.281963i
$806$	1.36933	−	1.01966i	0.0482325	−	0.0359161i
$807$	4.70306	−	15.4188i	0.165555	−	0.542767i
$808$	11.3534	+	31.1611i	0.399411	+	1.09624i
$809$	14.1012			0.495771			0.247885	−	0.968789i	$-0.420264\pi$
$809$	14.1012			0.495771			0.247885	+	0.968789i	$0.420264\pi$
$810$	−19.4197	+	32.0933i	−0.682340	+	1.12764i
$811$	−16.2327	−	16.2327i	−0.570006	−	0.570006i	0.362124	−	0.932130i	$-0.382052\pi$
$811$	−16.2327	−	16.2327i	−0.570006	−	0.570006i	−0.932130	+	0.362124i	$0.882052\pi$
$812$	−10.0255	+	5.40858i	−0.351827	+	0.189804i
$813$	−7.05151	−	13.2412i	−0.247307	−	0.464390i
$814$	3.31415	−	22.6430i	0.116161	−	0.793637i
$815$	−41.9909			−1.47088
$816$	3.56233	−	38.6147i	0.124706	−	1.35178i
$817$	−4.43596			−0.155195
$818$	1.79951	−	12.2946i	0.0629183	−	0.429871i
$819$	−0.698610	+	0.136737i	−0.0244114	+	0.00477799i
$820$	1.70727	+	3.16465i	0.0596204	+	0.110514i
$821$	17.2853	+	17.2853i	0.603262	+	0.603262i	0.941177	−	0.337915i	$-0.109722\pi$
$821$	17.2853	+	17.2853i	0.603262	+	0.603262i	−0.337915	+	0.941177i	$0.609722\pi$
$822$	30.9991	−	11.1055i	1.08122	−	0.387349i
$823$	7.35341			0.256324			0.128162	−	0.991753i	$-0.459092\pi$
$823$	7.35341			0.256324			0.128162	+	0.991753i	$0.459092\pi$
$824$	−31.3436	−	14.6031i	−1.09190	−	0.508723i
$825$	14.4591	+	4.41033i	0.503401	+	0.153548i
$826$	−16.6430	+	12.3931i	−0.579084	+	0.431212i
$827$	−0.224507	+	0.224507i	−0.00780688	+	0.00780688i	−0.710999	−	0.703193i	$-0.751757\pi$
$827$	−0.224507	+	0.224507i	−0.00780688	+	0.00780688i	0.703193	+	0.710999i	$0.251757\pi$
$828$	−12.7586	−	15.5214i	−0.443394	−	0.539405i
$829$	29.5181	+	29.5181i	1.02520	+	1.02520i	0.999674	+	0.0255305i	$0.00812749\pi$
$829$	29.5181	+	29.5181i	1.02520	+	1.02520i	0.0255305	+	0.999674i	$0.491873\pi$
$830$	6.90659	−	47.1873i	0.239731	−	1.63789i
$831$	−9.37962	+	30.7507i	−0.325375	+	1.06673i
$832$	−0.143230	+	1.64973i	−0.00496560	+	0.0571941i
$833$		−	31.8249i		−	1.10267i
$834$	−27.0477	−	12.7795i	−0.936586	−	0.442518i
$835$	4.93573	−	4.93573i	0.170808	−	0.170808i
$836$	−2.85856	+	9.55596i	−0.0988655	+	0.330500i
$837$	30.1452	+	3.10904i	1.04197	+	0.107464i
$838$	−4.20704	−	5.64973i	−0.145330	−	0.195167i
$839$			14.0224i			0.484106i	0.970263	+	0.242053i	$0.0778208\pi$
$839$			14.0224i			0.484106i	−0.970263	+	0.242053i	$0.922179\pi$
$840$	−12.3109	−	11.0630i	−0.424768	−	0.381709i
$841$			4.31415i			0.148764i
$842$	18.0067	−	13.4086i	0.620552	−	0.462091i
$843$	39.9868	−	21.2946i	1.37722	−	0.733427i
$844$	−25.7465	+	13.8898i	−0.886232	+	0.478105i
$845$	−27.0023	+	27.0023i	−0.928907	+	0.928907i
$846$	−18.3046	+	20.1499i	−0.629324	+	0.692768i
$847$		−	6.18248i		−	0.212433i
$848$	−0.188638	−	0.911538i	−0.00647785	−	0.0313023i
$849$	41.9546	+	12.7970i	1.43988	+	0.439193i
$850$	−28.8683	−	4.22533i	−0.990175	−	0.144928i
$851$	16.1816	+	16.1816i	0.554698	+	0.554698i
$852$	−4.72210	−	23.4545i	−0.161776	−	0.803538i
$853$	−8.55417	+	8.55417i	−0.292889	+	0.292889i	−0.838221	−	0.545331i	$-0.816404\pi$
$853$	−8.55417	+	8.55417i	−0.292889	+	0.292889i	0.545331	+	0.838221i	$0.316404\pi$
$854$	−6.21604	−	8.34766i	−0.212708	−	0.285651i
$855$	−10.3931	+	15.4517i	−0.355437	+	0.528436i
$856$	2.68585	−	0.978577i	0.0918003	−	0.0334471i
$857$	−43.5095			−1.48626			−0.743128	−	0.669149i	$-0.766659\pi$
$857$	−43.5095			−1.48626			−0.743128	+	0.669149i	$0.766659\pi$
$858$	1.13024	−	0.404910i	0.0385856	−	0.0138234i
$859$	−8.70306	−	8.70306i	−0.296945	−	0.296945i	0.542871	−	0.839816i	$-0.317337\pi$
$859$	−8.70306	−	8.70306i	−0.296945	−	0.296945i	−0.839816	+	0.542871i	$0.817337\pi$
$860$	−3.55789	+	11.8938i	−0.121323	+	0.405574i
$861$	−1.06912	+	0.569354i	−0.0364357	+	0.0194035i
$862$	−16.9786	−	2.48508i	−0.578293	−	0.0846421i
$863$	26.9270			0.916607			0.458303	−	0.888796i	$-0.348457\pi$
$863$	26.9270			0.916607			0.458303	+	0.888796i	$0.348457\pi$
$864$	−21.6796	+	19.8494i	−0.737553	+	0.675289i
$865$	21.7711			0.740239
$866$	−17.0009	−	2.48834i	−0.577712	−	0.0845572i
$867$	21.9057	−	11.6657i	0.743956	−	0.396188i
$868$	−3.83221	+	12.8108i	−0.130074	+	0.434827i
$869$	−16.4625	−	16.4625i	−0.558454	−	0.558454i
$870$	33.7664	−	12.0969i	1.14479	−	0.410123i
$871$	−0.186076			−0.00630493
$872$	−17.1120	−	46.9663i	−0.579485	−	1.59048i
$873$	20.6787	−	30.7434i	0.699866	−	1.04051i
$874$	−5.95715	−	8.00000i	−0.201504	−	0.270604i
$875$	3.13950	−	3.13950i	0.106134	−	0.106134i
$876$	4.83995	+	24.0399i	0.163527	+	0.812232i
$877$	39.7251	+	39.7251i	1.34142	+	1.34142i	0.894646	+	0.446775i	$0.147427\pi$
$877$	39.7251	+	39.7251i	1.34142	+	1.34142i	0.446775	+	0.894646i	$0.352573\pi$
$878$	37.9261	+	5.55107i	1.27994	+	0.187339i
$879$	−1.53388	−	0.467866i	−0.0517365	−	0.0157807i
$880$	23.3288	+	15.3288i	0.786415	+	0.516735i
$881$			1.63848i			0.0552018i	0.999619	+	0.0276009i	$0.00878675\pi$
$881$			1.63848i			0.0552018i	−0.999619	+	0.0276009i	$0.991213\pi$
$882$	−16.2203	+	17.8555i	−0.546167	+	0.601227i
$883$	−31.7967	+	31.7967i	−1.07004	+	1.07004i	−0.0726900	+	0.997355i	$0.523158\pi$
$883$	−31.7967	+	31.7967i	−1.07004	+	1.07004i	−0.997355	+	0.0726900i	$0.976842\pi$
$884$	−2.03932	+	1.10018i	−0.0685899	+	0.0370029i
$885$	57.6687	−	30.7110i	1.93851	−	1.03234i
$886$	−46.2646	+	34.4507i	−1.55429	+	1.15739i
$887$			29.8573i			1.00251i	0.865299	+	0.501256i	$0.167128\pi$
$887$			29.8573i			1.00251i	−0.865299	+	0.501256i	$0.832872\pi$
$888$	22.3771	−	24.9014i	0.750926	−	0.835635i
$889$		−	8.25831i		−	0.276975i
$890$	1.22008	+	1.63848i	0.0408973	+	0.0549219i
$891$	19.6384	+	8.27590i	0.657912	+	0.277253i
$892$	12.9645	−	43.3393i	0.434084	−	1.45111i
$893$	−9.55596	+	9.55596i	−0.319778	+	0.319778i
$894$	36.4574	+	17.2254i	1.21932	+	0.576103i
$895$			29.7220i			0.993496i
$896$	−6.81730	−	11.0334i	−0.227750	−	0.368600i
$897$	−0.350269	+	1.14835i	−0.0116952	+	0.0383421i
$898$	−1.98171	+	13.5395i	−0.0661306	+	0.451818i
$899$	−20.4900	−	20.4900i	−0.683380	−	0.683380i
$900$	14.0432	+	17.0841i	0.468106	+	0.569469i
$901$	0.921039	−	0.921039i	0.0306842	−	0.0306842i
$902$	1.63848	−	1.22008i	0.0545554	−	0.0406244i
$903$	−4.00000	−	1.22008i	−0.133112	−	0.0406019i
$904$	6.54262	−	14.0428i	0.217604	−	0.467058i
$905$	28.0578			0.932674
$906$	1.86966	−	0.669810i	0.0621153	−	0.0222530i
$907$	−12.1176	−	12.1176i	−0.402358	−	0.402358i	0.476705	−	0.879063i	$-0.341831\pi$
$907$	−12.1176	−	12.1176i	−0.402358	−	0.402358i	−0.879063	+	0.476705i	$0.841831\pi$
$908$	−1.96758	−	3.64718i	−0.0652966	−	0.121036i
$909$	34.5217	−	6.75686i	1.14501	−	0.224111i
$910$	−0.143230	+	0.978577i	−0.00474803	+	0.0324395i
$911$	−4.53816			−0.150356			−0.0751780	−	0.997170i	$-0.523952\pi$
$911$	−4.53816			−0.150356			−0.0751780	+	0.997170i	$0.523952\pi$
$912$	−11.2223	+	9.32661i	−0.371608	+	0.308835i
$913$	−27.0937			−0.896669
$914$	−0.860359	+	5.87815i	−0.0284581	+	0.194432i
$915$	15.4038	+	28.9250i	0.509233	+	0.956230i
$916$	−18.7146	+	10.0962i	−0.618348	+	0.333587i
$917$	10.3752	+	10.3752i	0.342619	+	0.342619i
$918$	−39.8715	−	10.1005i	−1.31596	−	0.333365i
$919$	−33.6461			−1.10988			−0.554942	−	0.831889i	$-0.687259\pi$
$919$	−33.6461			−1.10988			−0.554942	+	0.831889i	$0.687259\pi$
$920$	−26.2277	+	9.55596i	−0.864702	+	0.315051i
$921$	0.694081	−	2.27552i	0.0228707	−	0.0749809i
$922$	44.1783	−	32.8971i	1.45493	−	1.08341i
$923$	−1.01089	+	1.01089i	−0.0332737	+	0.0332737i
$924$	−5.20593	+	7.83058i	−0.171263	+	0.257607i
$925$	−17.8108	−	17.8108i	−0.585615	−	0.585615i
$926$	−7.66213	+	52.3493i	−0.251793	+	1.72030i
$927$	−20.4695	+	30.4324i	−0.672305	+	0.999530i
$928$	28.0575	−	1.64973i	0.921034	−	0.0541551i
$929$		−	27.1844i		−	0.891891i	−0.895060	−	0.445946i	$-0.852867\pi$
$929$		−	27.1844i		−	0.891891i	0.895060	−	0.445946i	$-0.147133\pi$
$930$	17.9864	−	38.0680i	0.589796	−	1.24830i
$931$	−8.46787	+	8.46787i	−0.277523	+	0.277523i
$932$	35.2218	+	10.5362i	1.15373	+	0.345125i
$933$	−26.9760	−	50.6551i	−0.883154	−	1.65837i
$934$	−20.2070	−	27.1365i	−0.661195	−	0.887933i
$935$			39.0606i			1.27742i
$936$	1.70490	+	0.422130i	0.0557265	+	0.0137977i
$937$		−	22.1495i		−	0.723593i	−0.932257	−	0.361796i	$-0.882164\pi$
$937$		−	22.1495i		−	0.723593i	0.932257	−	0.361796i	$-0.117836\pi$
$938$	1.16891	−	0.870418i	0.0381661	−	0.0284202i
$939$	−10.7698	−	20.2234i	−0.351460	−	0.659967i
$940$	17.9572	+	33.2860i	0.585698	+	1.08567i
$941$	7.35208	−	7.35208i	0.239671	−	0.239671i	−0.577043	−	0.816714i	$-0.695793\pi$
$941$	7.35208	−	7.35208i	0.239671	−	0.239671i	0.816714	+	0.577043i	$0.195793\pi$
$942$	−17.2831	−	8.16592i	−0.563114	−	0.266060i
$943$			2.04285i			0.0665242i
$944$	50.1351	−	10.3752i	1.63176	−	0.337684i
$945$	−13.6216	+	11.0745i	−0.443110	+	0.360254i
$946$	6.97858	+	1.02142i	0.226893	+	0.0332093i
$947$	−9.29033	−	9.29033i	−0.301895	−	0.301895i	0.539860	−	0.841755i	$-0.318477\pi$
$947$	−9.29033	−	9.29033i	−0.301895	−	0.301895i	−0.841755	+	0.539860i	$0.818477\pi$
$948$	−6.72237	−	33.3898i	−0.218333	−	1.08445i
$949$	1.03612	−	1.03612i	0.0336337	−	0.0336337i
$950$	6.55693	+	8.80545i	0.212735	+	0.285686i
$951$	−5.63879	+	18.4866i	−0.182850	+	0.599468i
$952$	7.66442	−	16.4507i	0.248405	−	0.533169i
$953$	−12.6413			−0.409491			−0.204745	−	0.978815i	$-0.565637\pi$
$953$	−12.6413			−0.409491			−0.204745	+	0.978815i	$0.565637\pi$
$954$	−0.986183	+	0.0473247i	−0.0319288	+	0.00153219i
$955$	−53.2003	−	53.2003i	−1.72152	−	1.72152i
$956$	25.9292	+	7.75645i	0.838611	+	0.250862i
$957$	−9.57821	−	17.9858i	−0.309620	−	0.581399i
$958$	−25.9572	−	3.79923i	−0.838638	−	0.122748i
$959$	15.4105			0.497632
$960$	16.0057	+	37.5699i	0.516582	+	1.21256i
$961$	−3.01469			−0.0972482
$962$	−1.97937	−	0.289711i	−0.0638174	−	0.00934067i
$963$	−0.582390	−	2.97550i	−0.0187672	−	0.0958843i
$964$	9.34713	+	2.79610i	0.301051	+	0.0900562i
$965$	−18.9203	−	18.9203i	−0.609065	−	0.609065i
$966$	−3.17134	−	8.85225i	−0.102036	−	0.284816i
$967$	23.3043			0.749415			0.374708	−	0.927143i	$-0.377743\pi$
$967$	23.3043			0.749415			0.374708	+	0.927143i	$0.377743\pi$
$968$	−6.44205	+	13.8270i	−0.207055	+	0.444416i
$969$	−19.5303	−	5.95715i	−0.627404	−	0.191371i
$970$	−30.7434	−	41.2860i	−0.987111	−	1.32561i
$971$	−6.17139	+	6.17139i	−0.198049	+	0.198049i	−0.799163	−	0.601114i	$-0.794724\pi$
$971$	−6.17139	+	6.17139i	−0.198049	+	0.198049i	0.601114	+	0.799163i	$0.294724\pi$
$972$	17.2222	+	25.9884i	0.552402	+	0.833578i
$973$	−9.89962	−	9.89962i	−0.317367	−	0.317367i
$974$	−57.2677	−	8.38202i	−1.83498	−	0.268577i
$975$	0.385535	−	1.26396i	0.0123470	−	0.0404792i
$976$	5.20390	+	25.1464i	0.166573	+	0.804916i
$977$		−	9.43605i		−	0.301886i	−0.988542	−	0.150943i	$-0.951769\pi$
$977$		−	9.43605i		−	0.301886i	0.988542	−	0.150943i	$-0.0482310\pi$
$978$	−14.9092	+	31.5551i	−0.476742	+	1.00902i
$979$	0.820654	−	0.820654i	0.0262282	−	0.0262282i
$980$	15.9125	+	29.4959i	0.508305	+	0.942211i
$981$	−52.0315	+	10.1840i	−1.66124	+	0.325150i
$982$	−8.09052	+	6.02456i	−0.258179	+	0.192251i
$983$		−	25.8750i		−	0.825285i	−0.910893	−	0.412643i	$-0.864606\pi$
$983$		−	25.8750i		−	0.825285i	0.910893	−	0.412643i	$-0.135394\pi$
$984$	2.98433	−	0.159338i	0.0951371	−	0.00507950i
$985$			13.2713i			0.422859i
$986$	23.4890	+	31.5440i	0.748044	+	1.00457i
$987$	−11.2451	+	5.98850i	−0.357936	+	0.190616i
$988$	0.835347	+	0.249885i	0.0265759	+	0.00794991i
$989$	−4.98718	+	4.98718i	−0.158583	+	0.158583i
$990$	19.9082	−	21.9152i	0.632723	−	0.696510i
$991$			23.5886i			0.749316i	0.927163	+	0.374658i	$0.122240\pi$
$991$			23.5886i			0.749316i	−0.927163	+	0.374658i	$0.877760\pi$
$992$	21.9193	−	24.6580i	0.695938	−	0.782891i
$993$	7.09617	+	2.16448i	0.225190	+	0.0686878i
$994$	1.62158	−	11.0790i	0.0514333	−	0.351403i
$995$	−40.7503	−	40.7503i	−1.29187	−	1.29187i
$996$	−33.0078	−	21.9443i	−1.04589	−	0.695331i
$997$	3.16779	−	3.16779i	0.100325	−	0.100325i	−0.655163	−	0.755488i	$-0.727400\pi$
$997$	3.16779	−	3.16779i	0.100325	−	0.100325i	0.755488	+	0.655163i	$0.227400\pi$
$998$	−18.3907	+	13.6946i	−0.582149	+	0.433494i
$999$	−22.4005	−	27.5524i	−0.708719	−	0.871719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.2.k.a.35.6	yes	12
3.2	odd	2	inner	48.2.k.a.35.1	yes	12
4.3	odd	2		192.2.k.a.47.6		12
8.3	odd	2		384.2.k.a.95.1		12
8.5	even	2		384.2.k.b.95.6		12
12.11	even	2		192.2.k.a.47.4		12
16.3	odd	4		384.2.k.b.287.4		12
16.5	even	4		192.2.k.a.143.4		12
16.11	odd	4	inner	48.2.k.a.11.1	✓	12
16.13	even	4		384.2.k.a.287.3		12
24.5	odd	2		384.2.k.b.95.4		12
24.11	even	2		384.2.k.a.95.3		12
48.5	odd	4		192.2.k.a.143.6		12
48.11	even	4	inner	48.2.k.a.11.6	yes	12
48.29	odd	4		384.2.k.a.287.1		12
48.35	even	4		384.2.k.b.287.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.k.a.11.1	✓	12	16.11	odd	4	inner
48.2.k.a.11.6	yes	12	48.11	even	4	inner
48.2.k.a.35.1	yes	12	3.2	odd	2	inner
48.2.k.a.35.6	yes	12	1.1	even	1	trivial
192.2.k.a.47.4		12	12.11	even	2
192.2.k.a.47.6		12	4.3	odd	2
192.2.k.a.143.4		12	16.5	even	4
192.2.k.a.143.6		12	48.5	odd	4
384.2.k.a.95.1		12	8.3	odd	2
384.2.k.a.95.3		12	24.11	even	2
384.2.k.a.287.1		12	48.29	odd	4
384.2.k.a.287.3		12	16.13	even	4
384.2.k.b.95.4		12	24.5	odd	2
384.2.k.b.95.6		12	8.5	even	2
384.2.k.b.287.4		12	16.3	odd	4
384.2.k.b.287.6		12	48.35	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39930 + 0.204810i) q^{2} +(-1.52878 + 0.814141i) q^{3} +(1.91611 + 0.573183i) q^{4} +(-2.08397 - 2.08397i) q^{5} +(-2.30598 + 0.826122i) q^{6} -1.14637 q^{7} +(2.56382 + 1.19449i) q^{8} +(1.67435 - 2.48929i) q^{9} +O(q^{10})\)	\(q+(1.39930 + 0.204810i) q^{2} +(-1.52878 + 0.814141i) q^{3} +(1.91611 + 0.573183i) q^{4} +(-2.08397 - 2.08397i) q^{5} +(-2.30598 + 0.826122i) q^{6} -1.14637 q^{7} +(2.56382 + 1.19449i) q^{8} +(1.67435 - 2.48929i) q^{9} +(-2.48929 - 3.34292i) q^{10} +(-1.67435 + 1.67435i) q^{11} +(-3.39596 + 0.683709i) q^{12} +(0.146365 + 0.146365i) q^{13} +(-1.60411 - 0.234787i) q^{14} +(4.88258 + 1.48929i) q^{15} +(3.34292 + 2.19656i) q^{16} +5.59722i q^{17} +(2.85275 - 3.14035i) q^{18} +(1.48929 - 1.48929i) q^{19} +(-2.79861 - 5.18760i) q^{20} +(1.75254 - 0.933303i) q^{21} +(-2.68585 + 2.00000i) q^{22} -3.34870i q^{23} +(-4.89201 + 0.261191i) q^{24} +3.68585i q^{25} +(0.174833 + 0.234787i) q^{26} +(-0.533081 + 5.16874i) q^{27} +(-2.19656 - 0.657077i) q^{28} +(3.51325 - 3.51325i) q^{29} +(6.52719 + 3.08397i) q^{30} -5.83221i q^{31} +(4.22789 + 3.75832i) q^{32} +(1.19656 - 3.92287i) q^{33} +(-1.14637 + 7.83221i) q^{34} +(2.38899 + 2.38899i) q^{35} +(4.63505 - 3.81003i) q^{36} +(-4.83221 + 4.83221i) q^{37} +(2.38899 - 1.77895i) q^{38} +(-0.342923 - 0.104599i) q^{39} +(-2.85363 - 7.83221i) q^{40} -0.610042 q^{41} +(2.64349 - 0.947037i) q^{42} +(-1.48929 - 1.48929i) q^{43} +(-4.16794 + 2.24852i) q^{44} +(-8.67689 + 1.69831i) q^{45} +(0.685846 - 4.68585i) q^{46} -6.41646 q^{47} +(-6.89891 - 0.636446i) q^{48} -5.68585 q^{49} +(-0.754898 + 5.15762i) q^{50} +(-4.55693 - 8.55693i) q^{51} +(0.196558 + 0.364346i) q^{52} +(-0.164553 - 0.164553i) q^{53} +(-1.80455 + 7.12345i) q^{54} +6.97858 q^{55} +(-2.93908 - 1.36933i) q^{56} +(-1.06431 + 3.48929i) q^{57} +(5.63565 - 4.19656i) q^{58} +(9.05051 - 9.05051i) q^{59} +(8.50190 + 5.65224i) q^{60} +(4.53948 + 4.53948i) q^{61} +(1.19449 - 8.16104i) q^{62} +(-1.91942 + 2.85363i) q^{63} +(5.14637 + 6.12494i) q^{64} -0.610042i q^{65} +(2.47779 - 5.24422i) q^{66} +(-0.635654 + 0.635654i) q^{67} +(-3.20823 + 10.7249i) q^{68} +(2.72631 + 5.11943i) q^{69} +(2.85363 + 3.83221i) q^{70} +6.90659i q^{71} +(7.26617 - 4.38209i) q^{72} -7.07896i q^{73} +(-7.75142 + 5.77205i) q^{74} +(-3.00080 - 5.63485i) q^{75} +(3.70727 - 2.00000i) q^{76} +(1.91942 - 1.91942i) q^{77} +(-0.458431 - 0.216600i) q^{78} +9.83221i q^{79} +(-2.38899 - 11.5441i) q^{80} +(-3.39312 - 8.33587i) q^{81} +(-0.853635 - 0.124943i) q^{82} +(8.09081 + 8.09081i) q^{83} +(3.89301 - 0.783781i) q^{84} +(11.6644 - 11.6644i) q^{85} +(-1.77895 - 2.38899i) q^{86} +(-2.51071 + 8.23127i) q^{87} +(-6.29273 + 2.29273i) q^{88} -0.490134 q^{89} +(-12.4894 + 0.599340i) q^{90} +(-0.167788 - 0.167788i) q^{91} +(1.91942 - 6.41646i) q^{92} +(4.74824 + 8.91618i) q^{93} +(-8.97858 - 1.31415i) q^{94} -6.20726 q^{95} +(-9.52332 - 2.30355i) q^{96} +12.3503 q^{97} +(-7.95623 - 1.16452i) q^{98} +(1.36449 + 6.97138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

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