LMFDB - Embedded newform 48.2.k.a.11.1

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			11.1
Root			$0.204810 - 1.39930i$ of defining polynomial
Character	$\chi$	$=$	48.11
Dual form			48.2.k.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39930 + 0.204810i) q^{2} +(-0.814141 - 1.52878i) q^{3} +(1.91611 - 0.573183i) q^{4} +(2.08397 - 2.08397i) q^{5} +(1.45234 + 1.97249i) q^{6} -1.14637 q^{7} +(-2.56382 + 1.19449i) q^{8} +(-1.67435 + 2.48929i) q^{9} +O(q^{10})$	\(q+(-1.39930 + 0.204810i) q^{2} +(-0.814141 - 1.52878i) q^{3} +(1.91611 - 0.573183i) q^{4} +(2.08397 - 2.08397i) q^{5} +(1.45234 + 1.97249i) 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} +(-2.43625 - 2.46266i) 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} +(1.83309 - 3.82620i) q^{18} +(1.48929 + 1.48929i) q^{19} +(2.79861 - 5.18760i) q^{20} +(0.933303 + 1.75254i) q^{21} +(-2.68585 - 2.00000i) q^{22} -3.34870i q^{23} +(3.91343 + 2.94704i) q^{24} -3.68585i q^{25} +(-0.174833 + 0.234787i) q^{26} +(5.16874 + 0.533081i) q^{27} +(-2.19656 + 0.657077i) q^{28} +(-3.51325 - 3.51325i) q^{29} +(7.13723 + 1.08397i) 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} +(-1.78141 + 5.72945i) 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} +(-1.66491 - 2.26119i) q^{42} +(-1.48929 + 1.48929i) q^{43} +(4.16794 + 2.24852i) q^{44} +(1.69831 + 8.67689i) q^{45} +(0.685846 + 4.68585i) q^{46} +6.41646 q^{47} +(-6.07967 - 3.32229i) q^{48} -5.68585 q^{49} +(0.754898 + 5.15762i) q^{50} +(8.55693 - 4.55693i) q^{51} +(0.196558 - 0.364346i) q^{52} +(0.164553 - 0.164553i) q^{53} +(-7.34181 + 0.312665i) 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} +(-10.2092 - 0.0550256i) 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} +(-0.870906 + 5.73436i) q^{66} +(-0.635654 - 0.635654i) q^{67} +(3.20823 + 10.7249i) q^{68} +(-5.11943 + 2.72631i) q^{69} +(2.85363 - 3.83221i) q^{70} +6.90659i q^{71} +(1.31929 - 8.38209i) q^{72} +7.07896i q^{73} +(7.75142 + 5.77205i) q^{74} +(-5.63485 + 3.00080i) q^{75} +(3.70727 + 2.00000i) q^{76} +(-1.91942 - 1.91942i) q^{77} +(0.501277 + 0.0761315i) 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} +(2.79284 + 2.82310i) 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} +(-4.15356 - 11.7938i) q^{90} +(-0.167788 + 0.167788i) q^{91} +(-1.91942 - 6.41646i) q^{92} +(8.91618 - 4.74824i) q^{93} +(-8.97858 + 1.31415i) q^{94} +6.20726 q^{95} +(9.18775 + 3.40372i) q^{96} +12.3503 q^{97} +(7.95623 - 1.16452i) q^{98} +(-6.97138 + 1.36449i) 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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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
$3$	−0.814141	−	1.52878i	−0.470045	−	0.882643i
$3$	−0.814141	−	1.52878i	−0.470045	−	0.882643i
$4$	1.91611	−	0.573183i	0.958053	−	0.286591i
$5$	2.08397	−	2.08397i	0.931979	−	0.931979i	−0.0658506	−	0.997829i	$-0.520976\pi$
$5$	2.08397	−	2.08397i	0.931979	−	0.931979i	0.997829	+	0.0658506i	$0.0209761\pi$
$6$	1.45234	+	1.97249i	0.592916	+	0.805265i
$7$	−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	$-0.133809\pi$
$11$	1.67435	+	1.67435i	0.504835	+	0.504835i	−0.408102	+	0.912937i	$0.633809\pi$
$12$	−2.43625	−	2.46266i	−0.703285	−	0.710908i
$13$	0.146365	−	0.146365i	0.0405945	−	0.0405945i	−0.686518	−	0.727113i	$-0.740862\pi$
$13$	0.146365	−	0.146365i	0.0405945	−	0.0405945i	0.727113	+	0.686518i	$0.240862\pi$
$14$	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	$0.762517\pi$
$18$	1.83309	−	3.82620i	0.432064	−	0.901843i
$19$	1.48929	+	1.48929i	0.341666	+	0.341666i	0.856993	−	0.515327i	$-0.172330\pi$
$19$	1.48929	+	1.48929i	0.341666	+	0.341666i	−0.515327	+	0.856993i	$0.672330\pi$
$20$	2.79861	−	5.18760i	0.625788	−	1.15998i
$21$	0.933303	+	1.75254i	0.203663	+	0.382436i
$22$	−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	$-0.113521\pi$
$24$	3.91343	+	2.94704i	0.798826	+	0.601561i
$25$		−	3.68585i		−	0.737169i
$26$	−0.174833	+	0.234787i	−0.0342875	+	0.0460455i
$27$	5.16874	+	0.533081i	0.994724	+	0.102592i
$28$	−2.19656	+	0.657077i	−0.415110	+	0.124176i
$29$	−3.51325	−	3.51325i	−0.652394	−	0.652394i	0.301175	−	0.953569i	$-0.402621\pi$
$29$	−3.51325	−	3.51325i	−0.652394	−	0.652394i	−0.953569	+	0.301175i	$0.902621\pi$
$30$	7.13723	+	1.08397i	1.30307	+	0.197905i
$31$			5.83221i			1.04750i	0.851873	+	0.523748i	$0.175467\pi$
$31$			5.83221i			1.04750i	−0.851873	+	0.523748i	$0.824533\pi$
$32$	−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
$36$	−1.78141	+	5.72945i	−0.296902	+	0.954908i
$37$	−4.83221	−	4.83221i	−0.794411	−	0.794411i	0.187797	−	0.982208i	$-0.439865\pi$
$37$	−4.83221	−	4.83221i	−0.794411	−	0.794411i	−0.982208	+	0.187797i	$0.939865\pi$
$38$	−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	$-0.484831\pi$
$41$	0.610042			0.0952726			0.0476363	+	0.998865i	$0.484831\pi$
$42$	−1.66491	−	2.26119i	−0.256902	−	0.348909i
$43$	−1.48929	+	1.48929i	−0.227114	+	0.227114i	−0.811486	−	0.584372i	$-0.801341\pi$
$43$	−1.48929	+	1.48929i	−0.227114	+	0.227114i	0.584372	+	0.811486i	$0.301341\pi$
$44$	4.16794	+	2.24852i	0.628340	+	0.338977i
$45$	1.69831	+	8.67689i	0.253169	+	1.29347i
$46$	0.685846	+	4.68585i	0.101123	+	0.690890i
$47$	6.41646			0.935936			0.467968	−	0.883745i	$-0.344986\pi$
$47$	6.41646			0.935936			0.467968	+	0.883745i	$0.344986\pi$
$48$	−6.07967	−	3.32229i	−0.877525	−	0.479532i
$49$	−5.68585			−0.812264
$50$	0.754898	+	5.15762i	0.106759	+	0.729398i
$51$	8.55693	−	4.55693i	1.19821	−	0.638097i
$52$	0.196558	−	0.364346i	0.0272576	−	0.0505257i
$53$	0.164553	−	0.164553i	0.0226031	−	0.0226031i	−0.695715	−	0.718318i	$-0.744912\pi$
$53$	0.164553	−	0.164553i	0.0226031	−	0.0226031i	0.718318	+	0.695715i	$0.244912\pi$
$54$	−7.34181	+	0.312665i	−0.999094	+	0.0425483i
$55$	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	−0.980183	−	0.198093i	$-0.936525\pi$
$59$	−9.05051	−	9.05051i	−1.17828	−	1.17828i	−0.198093	−	0.980183i	$-0.563475\pi$
$60$	−10.2092	−	0.0550256i	−1.31800	−	0.00710378i
$61$	4.53948	−	4.53948i	0.581221	−	0.581221i	−0.354018	−	0.935239i	$-0.615185\pi$
$61$	4.53948	−	4.53948i	0.581221	−	0.581221i	0.935239	+	0.354018i	$0.115185\pi$
$62$	−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
$66$	−0.870906	+	5.73436i	−0.107201	+	0.705850i
$67$	−0.635654	−	0.635654i	−0.0776575	−	0.0776575i	0.667211	−	0.744869i	$-0.267488\pi$
$67$	−0.635654	−	0.635654i	−0.0776575	−	0.0776575i	−0.744869	+	0.667211i	$0.767488\pi$
$68$	3.20823	+	10.7249i	0.389055	+	1.30058i
$69$	−5.11943	+	2.72631i	−0.616307	+	0.328209i
$70$	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	$0.865588\pi$
$72$	1.31929	−	8.38209i	0.155480	−	0.987839i
$73$			7.07896i			0.828530i	0.910156	+	0.414265i	$0.135961\pi$
$73$			7.07896i			0.828530i	−0.910156	+	0.414265i	$0.864039\pi$
$74$	7.75142	+	5.77205i	0.901084	+	0.670987i
$75$	−5.63485	+	3.00080i	−0.650657	+	0.346502i
$76$	3.70727	+	2.00000i	0.425253	+	0.229416i
$77$	−1.91942	−	1.91942i	−0.218738	−	0.218738i
$78$	0.501277	+	0.0761315i	0.0567584	+	0.00862019i
$79$		−	9.83221i		−	1.10621i	−0.833111	−	0.553105i	$-0.813443\pi$
$79$		−	9.83221i		−	1.10621i	0.833111	−	0.553105i	$-0.186557\pi$
$80$	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	$-0.966113\pi$
$83$	−8.09081	+	8.09081i	−0.888081	+	0.888081i	0.106257	+	0.994339i	$0.466113\pi$
$84$	2.79284	+	2.82310i	0.304723	+	0.308026i
$85$	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	$-0.491730\pi$
$89$	0.490134			0.0519541			0.0259770	+	0.999663i	$0.491730\pi$
$90$	−4.15356	−	11.7938i	−0.437824	−	1.24317i
$91$	−0.167788	+	0.167788i	−0.0175890	+	0.0175890i
$92$	−1.91942	−	6.41646i	−0.200113	−	0.668962i
$93$	8.91618	−	4.74824i	0.924565	−	0.492370i
$94$	−8.97858	+	1.31415i	−0.926070	+	0.135545i
$95$	6.20726			0.636851
$96$	9.18775	+	3.40372i	0.937720	+	0.347391i
$97$	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
$99$	−6.97138	+	1.36449i	−0.700650	+	0.137137i
$100$	−2.11266	−	7.06247i	−0.211266	−	0.706247i
$101$	−8.29123	+	8.29123i	−0.825008	+	0.825008i	−0.986821	−	0.161813i	$-0.948266\pi$
$101$	−8.29123	+	8.29123i	−0.825008	+	0.825008i	0.161813	+	0.986821i	$0.448266\pi$
$102$	−11.0404	+	8.12907i	−1.09317	+	0.804898i
$103$	−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	$-0.265556\pi$
$107$	−0.714641	−	0.714641i	−0.0690869	−	0.0690869i	−0.740806	+	0.671719i	$0.765556\pi$
$108$	10.2094	−	1.94119i	0.982400	−	0.186791i
$109$	−12.4966	+	12.4966i	−1.19696	+	1.19696i	−0.221888	+	0.975072i	$0.571222\pi$
$109$	−12.4966	+	12.4966i	−1.19696	+	1.19696i	−0.975072	+	0.221888i	$0.928778\pi$
$110$	−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	$-0.0829419\pi$
$114$	−0.774648	+	5.10056i	−0.0725524	+	0.477711i
$115$	−6.97858	−	6.97858i	−0.650756	−	0.650756i
$116$	−8.74549	−	4.71802i	−0.811999	−	0.438058i
$117$	0.119279	+	0.609413i	0.0110274	+	0.0563402i
$118$	14.5181	+	10.8108i	1.33650	+	0.995214i
$119$		−	6.41646i		−	0.588196i
$120$	14.2970	−	2.01394i	1.30513	−	0.183847i
$121$		−	5.39312i		−	0.490283i
$122$	−5.42238	+	7.28185i	−0.490920	+	0.659267i
$123$	−0.496660	−	0.932621i	−0.0447824	−	0.0840916i
$124$	3.34292	+	11.1751i	0.300203	+	1.00356i
$125$	2.73865	+	2.73865i	0.244953	+	0.244953i
$126$	−2.10139	+	4.38622i	−0.187207	+	0.390755i
$127$		−	7.20390i		−	0.639243i	−0.947545	−	0.319622i	$-0.896444\pi$
$127$		−	7.20390i		−	0.639243i	0.947545	−	0.319622i	$-0.103556\pi$
$128$	−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	$-0.561130\pi$
$131$	9.05051	−	9.05051i	0.790747	−	0.790747i	0.981616	+	0.190869i	$0.0611304\pi$
$132$	0.0442099	−	8.20248i	0.00384798	−	0.713934i
$133$	−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	$-0.305292\pi$
$137$	13.4430			1.14851			0.574255	+	0.818677i	$0.305292\pi$
$138$	6.60526	−	4.86345i	0.562277	−	0.414004i
$139$	8.63565	−	8.63565i	0.732467	−	0.732467i	−0.238641	−	0.971108i	$-0.576702\pi$
$139$	8.63565	−	8.63565i	0.732467	−	0.732467i	0.971108	+	0.238641i	$0.0767020\pi$
$140$	−3.20823	+	5.94688i	−0.271145	+	0.502603i
$141$	−5.22390	−	9.80936i	−0.439932	−	0.826097i
$142$	−1.41454	−	9.66442i	−0.118705	−	0.811020i
$143$	0.490134			0.0409870
$144$	−0.129352	+	11.9993i	−0.0107793	+	0.999942i
$145$	−14.6430			−1.21603
$146$	−1.44984	−	9.90562i	−0.119990	−	0.819795i
$147$	4.62908	+	8.69242i	0.381800	+	0.716939i
$148$	−12.0288	−	6.48929i	−0.988759	−	0.533416i
$149$	11.6399	−	11.6399i	0.953580	−	0.953580i	−0.0453896	−	0.998969i	$-0.514453\pi$
$149$	11.6399	−	11.6399i	0.953580	−	0.953580i	0.998969	+	0.0453896i	$0.0144529\pi$
$150$	7.27028	−	5.35311i	0.593616	−	0.437079i
$151$	−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
$156$	−0.717031	−	0.00386467i	−0.0574084	−	0.000309421i
$157$	5.51806	−	5.51806i	0.440389	−	0.440389i	−0.451754	−	0.892143i	$-0.649201\pi$
$157$	5.51806	−	5.51806i	0.440389	−	0.440389i	0.892143	+	0.451754i	$0.149201\pi$
$158$	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
$162$	6.45527	+	10.9695i	0.507174	+	0.861844i
$163$	10.0748	+	10.0748i	0.789115	+	0.789115i	0.981349	−	0.192234i	$-0.0615732\pi$
$163$	10.0748	+	10.0748i	0.789115	+	0.789115i	−0.192234	+	0.981349i	$0.561573\pi$
$164$	1.16891	−	0.349666i	0.0912762	−	0.0273043i
$165$	−5.68155	−	10.6687i	−0.442308	−	0.830559i
$166$	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	$0.970790\pi$
$168$	−4.48623	−	3.37838i	−0.346120	−	0.260648i
$169$			12.9572i			0.996704i
$170$	−18.7111	−	13.9331i	−1.43507	−	1.06862i
$171$	−6.20086	+	1.21368i	−0.474191	+	0.0928125i
$172$	−2.00000	+	3.70727i	−0.152499	+	0.282677i
$173$	5.22347	+	5.22347i	0.397133	+	0.397133i	0.877221	−	0.480088i	$-0.159395\pi$
$173$	5.22347	+	5.22347i	0.397133	+	0.397133i	−0.480088	+	0.877221i	$0.659395\pi$
$174$	1.82740	−	12.0323i	0.138535	−	0.912165i
$175$			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	$-0.626993\pi$
$179$	7.13110	−	7.13110i	0.533003	−	0.533003i	0.921465	+	0.388462i	$0.126993\pi$
$180$	8.22758	+	15.6524i	0.613248	+	1.16666i
$181$	−6.73183	−	6.73183i	−0.500373	−	0.500373i	0.411181	−	0.911554i	$-0.365116\pi$
$181$	−6.73183	−	6.73183i	−0.500373	−	0.500373i	−0.911554	+	0.411181i	$0.865116\pi$
$182$	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
$186$	−11.5040	+	8.47036i	−0.843511	+	0.621077i
$187$	−9.37169	+	9.37169i	−0.685326	+	0.685326i
$188$	12.2946	−	3.67780i	0.896677	−	0.268231i
$189$	−5.92526	−	0.611106i	−0.430999	−	0.0444514i
$190$	−8.68585	+	1.27131i	−0.630138	+	0.0922304i
$191$	−25.5284			−1.84717			−0.923584	−	0.383396i	$-0.874754\pi$
$191$	−25.5284			−1.84717			−0.923584	+	0.383396i	$0.874754\pi$
$192$	−13.5536	−	2.88110i	−0.978145	−	0.207926i
$193$	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
$195$	−0.932621	+	0.496660i	−0.0667864	+	0.0355666i
$196$	−10.8947	+	3.25903i	−0.778192	+	0.232788i
$197$	3.18414	−	3.18414i	0.226861	−	0.226861i	−0.584519	−	0.811380i	$-0.698717\pi$
$197$	3.18414	−	3.18414i	0.226861	−	0.226861i	0.811380	+	0.584519i	$0.198717\pi$
$198$	9.47562	−	3.33715i	0.673403	−	0.237161i
$199$	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
$204$	13.7840	−	13.6362i	0.965075	−	0.954727i
$205$	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
$210$	−8.18188	−	1.24262i	−0.564603	−	0.0857492i
$211$	−10.3429	−	10.3429i	−0.712036	−	0.712036i	0.254925	−	0.966961i	$-0.417949\pi$
$211$	−10.3429	−	10.3429i	−0.712036	−	0.712036i	−0.966961	+	0.254925i	$0.917949\pi$
$212$	0.220982	−	0.409620i	0.0151771	−	0.0281328i
$213$	10.5587	−	5.62294i	0.723468	−	0.385277i
$214$	1.14637	+	0.853635i	0.0783639	+	0.0583533i
$215$			6.20726i			0.423332i
$216$	−13.8885	+	4.80730i	−0.944991	+	0.327095i
$217$		−	6.68585i		−	0.453865i
$218$	14.9272	−	20.0460i	1.01100	−	1.35769i
$219$	10.8222	−	5.76327i	0.731296	−	0.389446i
$220$	13.3717	−	4.00000i	0.901519	−	0.269680i
$221$	0.819240	+	0.819240i	0.0551080	+	0.0551080i
$222$	2.51346	−	16.5495i	0.168692	−	1.11073i
$223$			22.6184i			1.51464i	0.653042	+	0.757321i	$0.273492\pi$
$223$			22.6184i			1.51464i	−0.653042	+	0.757321i	$0.726508\pi$
$224$	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	$-0.728095\pi$
$227$	1.46515	−	1.46515i	0.0972455	−	0.0972455i	0.754056	+	0.656810i	$0.228095\pi$
$228$	0.0393236	−	7.29589i	0.00260427	−	0.483182i
$229$	−7.51806	−	7.51806i	−0.496807	−	0.496807i	0.413635	−	0.910443i	$-0.364259\pi$
$229$	−7.51806	−	7.51806i	−0.496807	−	0.496807i	−0.910443	+	0.413635i	$0.864259\pi$
$230$	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	$-0.705678\pi$
$233$	−18.3820			−1.20424			−0.602121	+	0.798405i	$0.705678\pi$
$234$	−0.291722	−	0.828324i	−0.0190704	−	0.0541493i
$235$	13.3717	−	13.3717i	0.872273	−	0.872273i
$236$	−22.5293	−	12.1541i	−1.46654	−	0.791167i
$237$	−15.0313	+	8.00481i	−0.976388	+	0.519968i
$238$	1.31415	+	8.97858i	0.0851839	+	0.581995i
$239$	−13.5322			−0.875328			−0.437664	−	0.899139i	$-0.644194\pi$
$239$	−13.5322			−0.875328			−0.437664	+	0.899139i	$0.644194\pi$
$240$	−19.5934	+	5.74628i	−1.26475	+	0.370921i
$241$	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
$243$	−9.98126	+	11.9739i	−0.640298	+	0.768127i
$244$	6.09617	−	11.3001i	0.390268	−	0.723413i
$245$	−11.8491	+	11.8491i	−0.757013	+	0.757013i
$246$	0.885989	+	1.20330i	0.0564886	+	0.0767196i
$247$	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	$-0.174973\pi$
$251$	5.23224	+	5.23224i	0.330256	+	0.330256i	−0.522427	+	0.852684i	$0.674973\pi$
$252$	2.04215	−	6.56804i	0.128643	−	0.413748i
$253$	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	$-0.131076\pi$
$258$	−5.10056	−	0.774648i	−0.317547	−	0.0482275i
$259$	5.53948	+	5.53948i	0.344207	+	0.344207i
$260$	−0.349666	−	1.16891i	−0.0216853	−	0.0724924i
$261$	14.6279	−	2.86309i	0.905444	−	0.177221i
$262$	−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	$-0.337825\pi$
$264$	1.61809	+	11.4868i	0.0995863	+	0.706965i
$265$		−	0.685846i		−	0.0421312i
$266$	2.73865	+	2.03932i	0.167918	+	0.125039i
$267$	−0.399038	−	0.749307i	−0.0244207	−	0.0458569i
$268$	−1.58233	−	0.853635i	−0.0966560	−	0.0521440i
$269$	6.58101	+	6.58101i	0.401251	+	0.401251i	0.878674	−	0.477423i	$-0.158429\pi$
$269$	6.58101	+	6.58101i	0.401251	+	0.401251i	−0.477423	+	0.878674i	$0.658429\pi$
$270$	−14.6485	+	15.9517i	−0.891481	+	0.970789i
$271$		−	8.66129i		−	0.526136i	−0.964777	−	0.263068i	$-0.915266\pi$
$271$		−	8.66129i		−	0.526136i	0.964777	−	0.263068i	$-0.0847343\pi$
$272$	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
$276$	−8.24669	+	8.15827i	−0.496392	+	0.491070i
$277$	13.1249	+	13.1249i	0.788601	+	0.788601i	0.981265	−	0.192664i	$-0.0617126\pi$
$277$	13.1249	+	13.1249i	0.788601	+	0.788601i	−0.192664	+	0.981265i	$0.561713\pi$
$278$	−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	$-0.215134\pi$
$281$	26.1560			1.56033			0.780167	+	0.625571i	$0.215134\pi$
$282$	9.31888	+	12.6564i	0.554931	+	0.753676i
$283$	−17.9070	+	17.9070i	−1.06446	+	1.06446i	−0.0666843	+	0.997774i	$0.521242\pi$
$283$	−17.9070	+	17.9070i	−1.06446	+	1.06446i	−0.997774	+	0.0666843i	$0.978758\pi$
$284$	3.95874	+	13.2338i	0.234908	+	0.785279i
$285$	−5.05359	−	9.48955i	−0.299349	−	0.562112i
$286$	−0.685846	+	0.100384i	−0.0405549	+	0.00593584i
$287$	−0.699331			−0.0412802
$288$	−2.27657	−	16.8172i	−0.134148	−	0.990961i
$289$	−14.3288			−0.842873
$290$	20.4900	−	2.99903i	1.20322	−	0.176109i
$291$	−10.0549	−	18.8809i	−0.589426	−	1.10682i
$292$	4.05754	+	13.5640i	0.237449	+	0.793775i
$293$	−0.654687	+	0.654687i	−0.0382472	+	0.0382472i	−0.725972	−	0.687725i	$-0.758610\pi$
$293$	−0.654687	+	0.654687i	−0.0382472	+	0.0382472i	0.687725	+	0.725972i	$0.258610\pi$
$294$	−8.25779	−	11.2153i	−0.481604	−	0.654087i
$295$	−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
$300$	−9.07697	+	8.97965i	−0.524059	+	0.518440i
$301$	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
$306$	21.4161	+	10.2602i	1.22427	+	0.586538i
$307$	−0.971231	−	0.971231i	−0.0554311	−	0.0554311i	0.678848	−	0.734279i	$-0.262480\pi$
$307$	−0.971231	−	0.971231i	−0.0554311	−	0.0554311i	−0.734279	+	0.678848i	$0.762480\pi$
$308$	−4.77798	−	2.57763i	−0.272251	−	0.146874i
$309$	9.95314	+	18.6899i	0.566214	+	1.06323i
$310$	−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	$0.611349\pi$
$312$	1.00414	−	0.141447i	0.0568480	−	0.00800787i
$313$		−	13.2285i		−	0.747717i	−0.927486	−	0.373858i	$-0.878035\pi$
$313$		−	13.2285i		−	0.747717i	0.927486	−	0.373858i	$-0.121965\pi$
$314$	−6.59129	+	8.85160i	−0.371968	+	0.499524i
$315$	−1.94688	−	9.94688i	−0.109694	−	0.560443i
$316$	−5.63565	−	18.8396i	−0.317030	−	1.05981i
$317$	−7.89038	−	7.89038i	−0.443168	−	0.443168i	0.449907	−	0.893075i	$-0.351457\pi$
$317$	−7.89038	−	7.89038i	−0.443168	−	0.443168i	−0.893075	+	0.449907i	$0.851457\pi$
$318$	0.563566	+	0.0855916i	0.0316032	+	0.00479974i
$319$		−	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
$324$	−11.2795	−	14.0275i	−0.626641	−	0.779308i
$325$	−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
$330$	10.1353	+	13.7652i	0.557928	+	0.757747i
$331$	−3.02877	+	3.02877i	−0.166476	+	0.166476i	−0.785429	−	0.618952i	$-0.787557\pi$
$331$	−3.02877	+	3.02877i	−0.166476	+	0.166476i	0.618952	+	0.785429i	$0.287557\pi$
$332$	−10.8653	+	20.1403i	−0.596312	+	1.10535i
$333$	20.1196	−	3.93796i	1.10255	−	0.215799i
$334$	−0.485078	−	3.31415i	−0.0265423	−	0.181342i
$335$	−2.64937			−0.144750
$336$	6.96952	+	3.80856i	0.380219	+	0.207774i
$337$	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
$339$	−8.37361	+	4.45930i	−0.454792	+	0.242196i
$340$	29.0361	+	15.6644i	1.57470	+	0.849523i
$341$	−9.76515	+	9.76515i	−0.528813	+	0.528813i
$342$	8.42831	−	2.96831i	0.455751	−	0.160508i
$343$	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	$-0.461089\pi$
$347$	−16.2175	−	16.2175i	−0.870600	−	0.870600i	−0.992538	+	0.121938i	$0.961089\pi$
$348$	−0.0927648	+	17.2111i	−0.00497271	+	0.922611i
$349$	−6.14637	+	6.14637i	−0.329007	+	0.329007i	−0.852209	−	0.523202i	$-0.824737\pi$
$349$	−6.14637	+	6.14637i	−0.329007	+	0.329007i	0.523202	+	0.852209i	$0.324737\pi$
$350$	−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	$-0.209141\pi$
$354$	4.70759	−	30.9965i	0.250206	−	1.64744i
$355$	14.3931	+	14.3931i	0.763907	+	0.763907i
$356$	0.939148	−	0.280936i	0.0497747	−	0.0148896i
$357$	−9.80936	+	5.22390i	−0.519167	+	0.276478i
$358$	−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	$0.839185\pi$
$360$	−14.7187	−	20.2174i	−0.775741	−	1.06555i
$361$		−	14.5640i		−	0.766528i
$362$	10.7986	+	8.04113i	0.567563	+	0.422632i
$363$	−8.24490	+	4.39076i	−0.432745	+	0.230455i
$364$	−0.225327	+	0.417674i	−0.0118103	+	0.0218920i
$365$	14.7523	+	14.7523i	0.772172	+	0.772172i
$366$	15.5469	+	2.36119i	0.812652	+	0.123422i
$367$			2.86833i			0.149725i	0.997194	+	0.0748627i	$0.0238519\pi$
$367$			2.86833i			0.149725i	−0.997194	+	0.0748627i	$0.976148\pi$
$368$	−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
$372$	14.3627	−	14.2087i	0.744673	−	0.736689i
$373$	−17.2253	−	17.2253i	−0.891894	−	0.891894i	0.102808	−	0.994701i	$-0.467217\pi$
$373$	−17.2253	−	17.2253i	−0.891894	−	0.891894i	−0.994701	+	0.102808i	$0.967217\pi$
$374$	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
$378$	8.41640	−	0.358429i	0.432893	−	0.0184356i
$379$	5.83956	−	5.83956i	0.299958	−	0.299958i	−0.541039	−	0.840997i	$-0.681969\pi$
$379$	5.83956	−	5.83956i	0.299958	−	0.299958i	0.840997	+	0.541039i	$0.181969\pi$
$380$	11.8938	−	3.55789i	0.610137	−	0.182516i
$381$	−11.0132	+	5.86499i	−0.564223	+	0.300473i
$382$	35.7220	−	5.22846i	1.82769	−	0.267511i
$383$	30.7659			1.57206			0.786031	−	0.618187i	$-0.212133\pi$
$383$	30.7659			1.57206			0.786031	+	0.618187i	$0.212133\pi$
$384$	19.5556	+	1.25563i	0.997945	+	0.0640763i
$385$	−8.00000			−0.407718
$386$	−12.7042	+	1.85946i	−0.646628	+	0.0946441i
$387$	−1.21368	−	6.20086i	−0.0616949	−	0.315207i
$388$	23.6644	−	7.07896i	1.20138	−	0.359380i
$389$	−11.0299	+	11.0299i	−0.559237	+	0.559237i	−0.929090	−	0.369853i	$-0.879408\pi$
$389$	−11.0299	+	11.0299i	−0.559237	+	0.559237i	0.369853	+	0.929090i	$0.379408\pi$
$390$	1.20330	−	0.885989i	0.0609315	−	0.0448638i
$391$	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
$396$	−12.5758	+	6.61039i	−0.631957	+	0.332185i
$397$	−1.75325	+	1.75325i	−0.0879931	+	0.0879931i	−0.749733	−	0.661740i	$-0.769818\pi$
$397$	−1.75325	+	1.75325i	−0.0879931	+	0.0879931i	0.661740	+	0.749733i	$0.269818\pi$
$398$	−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	$0.790780\pi$
$402$	0.330633	−	2.17701i	0.0164905	−	0.108579i
$403$	0.853635	+	0.853635i	0.0425226	+	0.0425226i
$404$	−11.1345	+	20.6393i	−0.553961	+	1.02684i
$405$	−24.4428	−	10.3005i	−1.21457	−	0.511838i
$406$	−6.46052	−	4.81079i	−0.320630	−	0.238755i
$407$		−	16.1816i		−	0.802093i
$408$	−16.4952	+	21.9043i	−0.816635	+	1.08443i
$409$			8.78623i			0.434451i	0.976121	+	0.217226i	$0.0697007\pi$
$409$			8.78623i			0.434451i	−0.976121	+	0.217226i	$0.930299\pi$
$410$	−1.51857	+	2.03932i	−0.0749969	+	0.100715i
$411$	−10.9445	−	20.5513i	−0.539851	−	1.01372i
$412$	−23.4250	+	7.00735i	−1.15407	+	0.345227i
$413$	10.3752	+	10.3752i	0.510530	+	0.510530i
$414$	−12.8128	−	6.13847i	−0.629713	−	0.301689i
$415$			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	$-0.711176\pi$
$419$	3.52202	−	3.52202i	0.172062	−	0.172062i	0.787885	+	0.615823i	$0.211176\pi$
$420$	11.7034	+	0.0630795i	0.571069	+	0.00307796i
$421$	11.2253	+	11.2253i	0.547089	+	0.547089i	0.925598	−	0.378509i	$-0.123563\pi$
$421$	11.2253	+	11.2253i	0.547089	+	0.547089i	−0.378509	+	0.925598i	$0.623563\pi$
$422$	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
$426$	−13.6232	+	10.0307i	−0.660044	+	0.485990i
$427$	−5.20390	+	5.20390i	−0.251835	+	0.251835i
$428$	−1.77895	−	0.959708i	−0.0859887	−	0.0463892i
$429$	−0.399038	−	0.749307i	−0.0192657	−	0.0361769i
$430$	−1.27131	−	8.68585i	−0.0613079	−	0.418869i
$431$	12.1336			0.584454			0.292227	−	0.956349i	$-0.405604\pi$
$431$	12.1336			0.584454			0.292227	+	0.956349i	$0.405604\pi$
$432$	18.4496	−	9.57138i	0.887658	−	0.460503i
$433$	−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
$435$	11.9215	+	22.3860i	0.571591	+	1.07332i
$436$	−16.7820	+	31.1077i	−0.803713	+	1.48979i
$437$	4.98718	−	4.98718i	0.238569	−	0.238569i
$438$	−13.9632	+	10.2811i	−0.667186	+	0.491248i
$439$	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	0.860011	+	0.510276i	$0.170457\pi$
$443$	28.8412	+	28.8412i	1.37029	+	1.37029i	0.510276	+	0.860011i	$0.329543\pi$
$444$	−0.127591	+	23.6726i	−0.00605520	+	1.12345i
$445$	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	$0.926678\pi$
$450$	−14.1028	−	6.75650i	−0.664811	−	0.318504i
$451$	1.02142	+	1.02142i	0.0480969	+	0.0480969i
$452$	−3.13950	−	10.4951i	−0.147670	−	0.493648i
$453$	0.660097	+	1.23952i	0.0310140	+	0.0582377i
$454$	−1.75011	+	2.35027i	−0.0821370	+	0.110304i
$455$			0.699331i			0.0327851i
$456$	1.43924	+	10.2172i	0.0673988	+	0.478465i
$457$		−	4.20077i		−	0.196504i	−0.995162	−	0.0982518i	$-0.968675\pi$
$457$		−	4.20077i		−	0.196504i	0.995162	−	0.0982518i	$-0.0313251\pi$
$458$	12.0598	+	8.98028i	0.563519	+	0.419621i
$459$	−2.98377	+	28.9305i	−0.139271	+	1.35036i
$460$	−17.3717	−	9.37169i	−0.809959	−	0.436957i
$461$	−27.5406	−	27.5406i	−1.28269	−	1.28269i	−0.939129	−	0.343565i	$-0.888366\pi$
$461$	−27.5406	−	27.5406i	−1.28269	−	1.28269i	−0.343565	−	0.939129i	$-0.611634\pi$
$462$	0.998377	−	6.57367i	0.0464487	−	0.305835i
$463$		−	37.4109i		−	1.73863i	−0.494255	−	0.869317i	$-0.664559\pi$
$463$		−	37.4109i		−	1.73863i	0.494255	−	0.869317i	$-0.335441\pi$
$464$	−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	$-0.563279\pi$
$467$	16.9168	−	16.9168i	0.782817	−	0.782817i	0.980305	+	0.197489i	$0.0632785\pi$
$468$	0.577856	+	1.09933i	0.0267114	+	0.0508166i
$469$	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
$474$	19.3939	−	14.2797i	0.890792	−	0.655889i
$475$	5.48929	−	5.48929i	0.251866	−	0.251866i
$476$	−3.67780	−	12.2946i	−0.168572	−	0.563523i
$477$	0.134101	+	0.685139i	0.00614005	+	0.0313703i
$478$	18.9357	−	2.77154i	0.866100	−	0.126767i
$479$	18.5500			0.847573			0.423786	−	0.905762i	$-0.360701\pi$
$479$	18.5500			0.847573			0.423786	+	0.905762i	$0.360701\pi$
$480$	26.2402	−	12.0537i	1.19770	−	0.550175i
$481$	−1.41454			−0.0644974
$482$	−6.82608	+	0.999102i	−0.310919	+	0.0455079i
$483$	5.86873	−	3.12535i	0.267037	−	0.142208i
$484$	−3.09124	−	10.3338i	−0.140511	−	0.469717i
$485$	25.7376	−	25.7376i	1.16868	−	1.16868i
$486$	11.5144	−	18.7994i	0.522306	−	0.852758i
$487$	−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	$-0.198545\pi$
$491$	5.04360	+	5.04360i	0.227615	+	0.227615i	−0.584081	+	0.811696i	$0.698545\pi$
$492$	−1.48622	−	1.50232i	−0.0670038	−	0.0677300i
$493$	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
$498$	−27.7096	−	4.20840i	−1.24170	−	0.188583i
$499$	−11.4647	−	11.4647i	−0.513232	−	0.513232i	0.402283	−	0.915515i	$-0.368217\pi$
$499$	−11.4647	−	11.4647i	−0.513232	−	0.513232i	−0.915515	+	0.402283i	$0.868217\pi$
$500$	6.81730	+	3.67780i	0.304879	+	0.164476i
$501$	3.62081	−	1.92824i	0.161766	−	0.0861472i
$502$	−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	$-0.260184\pi$
$504$	−1.51239	+	9.60894i	−0.0673671	+	0.428016i
$505$			34.5573i			1.53778i
$506$	−6.69739	+	8.99408i	−0.297735	+	0.399836i
$507$	19.8087	−	10.5490i	0.879734	−	0.468495i
$508$	−4.12915	−	13.8034i	−0.183202	−	0.612429i
$509$	10.1389	+	10.1389i	0.449399	+	0.449399i	0.895155	−	0.445756i	$-0.147065\pi$
$509$	10.1389	+	10.1389i	0.449399	+	0.449399i	−0.445756	+	0.895155i	$0.647065\pi$
$510$	−6.06721	+	39.9486i	−0.268660	+	1.76896i
$511$		−	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
$516$	7.29589	+	0.0393236i	0.321184	+	0.00173112i
$517$	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	$-0.457428\pi$
$521$	6.08735			0.266692			0.133346	+	0.991070i	$0.457428\pi$
$522$	−19.8825	+	7.00227i	−0.870233	+	0.306481i
$523$	15.8824	−	15.8824i	0.694489	−	0.694489i	−0.268727	−	0.963216i	$-0.586603\pi$
$523$	15.8824	−	15.8824i	0.694489	−	0.694489i	0.963216	+	0.268727i	$0.0866030\pi$
$524$	12.1541	−	22.5293i	0.530956	−	0.984199i
$525$	6.45960	−	3.44001i	0.281920	−	0.150134i
$526$	5.79923	+	39.6216i	0.252859	+	1.72758i
$527$	−32.6442			−1.42200
$528$	−4.61681	−	15.7422i	−0.200921	−	0.685090i
$529$	11.7862			0.512445
$530$	0.140468	+	0.959708i	0.00610154	+	0.0416870i
$531$	37.6831	−	7.37563i	1.63531	−	0.320075i
$532$	−4.24989	−	2.29273i	−0.184256	−	0.0994025i
$533$	0.0892891	−	0.0892891i	0.00386754	−	0.00386754i
$534$	0.711841	+	0.966782i	0.0308044	+	0.0418368i
$535$	−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
$540$	17.2307	−	25.3214i	0.741490	−	1.08966i
$541$	−25.6184	+	25.6184i	−1.10142	+	1.10142i	−0.107184	+	0.994239i	$0.534183\pi$
$541$	−25.6184	+	25.6184i	−1.10142	+	1.10142i	−0.994239	+	0.107184i	$0.965817\pi$
$542$	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
$546$	−0.574646	−	0.0872745i	−0.0245926	−	0.00373500i
$547$	−27.2113	−	27.2113i	−1.16347	−	1.16347i	−0.983711	−	0.179758i	$-0.942468\pi$
$547$	−27.2113	−	27.2113i	−1.16347	−	1.16347i	−0.179758	−	0.983711i	$-0.557532\pi$
$548$	25.7581	−	7.70527i	1.10033	−	0.329153i
$549$	3.69941	+	18.9007i	0.157887	+	0.806664i
$550$	−7.37169	+	9.89962i	−0.314330	+	0.422121i
$551$		−	10.4645i		−	0.445802i
$552$	9.86873	−	13.1049i	0.420041	−	0.557782i
$553$			11.2713i			0.479305i
$554$	−21.0539	−	15.6777i	−0.894495	−	0.666080i
$555$	16.3971	+	30.7902i	0.696018	+	1.30697i
$556$	11.5970	−	21.4966i	0.491823	−	0.911660i
$557$	−26.1831	−	26.1831i	−1.10941	−	1.10941i	−0.993228	−	0.116184i	$-0.962934\pi$
$557$	−26.1831	−	26.1831i	−1.10941	−	1.10941i	−0.116184	−	0.993228i	$-0.537066\pi$
$558$	22.3152	+	10.6910i	0.944677	+	0.452585i
$559$			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	−0.0570880	+	0.998369i	$0.518182\pi$
$563$	−25.0435	+	25.0435i	−1.05546	+	1.05546i	−0.998369	+	0.0570880i	$0.981818\pi$
$564$	−15.6321	−	15.8015i	−0.658230	−	0.665364i
$565$	−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	$-0.584697\pi$
$569$	−12.5449			−0.525911			−0.262955	+	0.964808i	$0.584697\pi$
$570$	9.01506	+	12.2437i	0.377599	+	0.512834i
$571$	−4.48615	+	4.48615i	−0.187740	+	0.187740i	−0.794718	−	0.606979i	$-0.792381\pi$
$571$	−4.48615	+	4.48615i	−0.187740	+	0.187740i	0.606979	+	0.794718i	$0.292381\pi$
$572$	0.939148	−	0.280936i	0.0392677	−	0.0117465i
$573$	20.7837	+	39.0273i	0.868251	+	1.63039i
$574$	0.978577	−	0.143230i	0.0408450	−	0.00597830i
$575$	−12.3428			−0.514730
$576$	6.62994	+	23.0661i	0.276248	+	0.961087i
$577$	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
$579$	−7.39156	−	13.8798i	−0.307183	−	0.576823i
$580$	−28.0575	+	8.39312i	−1.16503	+	0.348505i
$581$	9.27502	−	9.27502i	0.384793	−	0.384793i
$582$	17.9368	+	24.3607i	0.743504	+	1.00979i
$583$	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	$-0.136295\pi$
$587$	11.9808	+	11.9808i	0.494501	+	0.494501i	−0.415220	+	0.909721i	$0.636295\pi$
$588$	13.8522	+	14.0023i	0.571253	+	0.577444i
$589$	−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	$0.978567\pi$
$594$	−12.8163	−	11.7692i	−0.525858	−	0.482898i
$595$	−13.3717	−	13.3717i	−0.548186	−	0.548186i
$596$	15.6315	−	28.9751i	0.640292	−	1.18687i
$597$	−15.9199	−	29.8941i	−0.651556	−	1.22348i
$598$	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	$0.706671\pi$
$600$	10.8623	−	14.4243i	0.443453	−	0.588870i
$601$			23.5787i			0.961797i	0.876776	+	0.480898i	$0.159689\pi$
$601$			23.5787i			0.961797i	−0.876776	+	0.480898i	$0.840311\pi$
$602$	−2.03932	+	2.73865i	−0.0831166	+	0.111619i
$603$	2.64663	−	0.518020i	0.107779	−	0.0210954i
$604$	−1.55356	+	0.464730i	−0.0632133	+	0.0189096i
$605$	−11.2391	−	11.2391i	−0.456934	−	0.456934i
$606$	−28.3960	−	4.31265i	−1.15351	−	0.175189i
$607$			22.2829i			0.904434i	0.891908	+	0.452217i	$0.149367\pi$
$607$			22.2829i			0.904434i	−0.891908	+	0.452217i	$0.850633\pi$
$608$	−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
$612$	−32.0690	−	9.97095i	−1.29631	−	0.403052i
$613$	22.1611	+	22.1611i	0.895077	+	0.895077i	0.994996	−	0.0999189i	$-0.0318583\pi$
$613$	22.1611	+	22.1611i	0.895077	+	0.895077i	−0.0999189	+	0.994996i	$0.531858\pi$
$614$	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	$-0.673352\pi$
$617$	−25.7376			−1.03616			−0.518078	+	0.855334i	$0.673352\pi$
$618$	−17.7553	−	24.1143i	−0.714225	−	0.970019i
$619$	7.71462	−	7.71462i	0.310077	−	0.310077i	−0.534863	−	0.844939i	$-0.679637\pi$
$619$	7.71462	−	7.71462i	0.310077	−	0.310077i	0.844939	+	0.534863i	$0.179637\pi$
$620$	30.2552	+	16.3221i	1.21508	+	0.655510i
$621$	1.78513	−	17.3085i	0.0716347	−	0.694567i
$622$	−6.78623	−	46.3650i	−0.272103	−	1.85907i
$623$	−0.561872			−0.0225109
$624$	−1.37612	+	0.403585i	−0.0550890	+	0.0161563i
$625$	29.8438			1.19375
$626$	2.70932	+	18.5106i	0.108286	+	0.739834i
$627$	7.62430	−	4.06027i	0.304485	−	0.162151i
$628$	7.41033	−	13.7360i	0.295704	−	0.548128i
$629$	27.0469	−	27.0469i	1.07843	−	1.07843i
$630$	4.76150	+	13.5200i	0.189703	+	0.538649i
$631$	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
$636$	−0.806130	−	0.00434490i	−0.0319651	−	0.000172286i
$637$	−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	$0.870283\pi$
$642$	0.371718	−	2.44752i	0.0146705	−	0.0965960i
$643$	14.0748	+	14.0748i	0.555054	+	0.555054i	0.927895	−	0.372841i	$-0.121616\pi$
$643$	14.0748	+	14.0748i	0.555054	+	0.555054i	−0.372841	+	0.927895i	$0.621616\pi$
$644$	2.20035	+	7.35561i	0.0867060	+	0.289851i
$645$	9.48955	−	5.05359i	0.373651	−	0.198985i
$646$	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	$-0.0122044\pi$
$648$	18.6565	+	17.3186i	0.732896	+	0.680340i
$649$		−	30.3074i		−	1.18967i
$650$	0.865389	+	0.644407i	0.0339433	+	0.0252757i
$651$	−10.2212	+	5.44322i	−0.400600	+	0.213337i
$652$	25.0790	+	13.5296i	0.982168	+	0.529861i
$653$	5.80289	+	5.80289i	0.227085	+	0.227085i	0.811474	−	0.584389i	$-0.198666\pi$
$653$	5.80289	+	5.80289i	0.227085	+	0.227085i	−0.584389	+	0.811474i	$0.698666\pi$
$654$	−42.7988	−	6.50008i	−1.67357	−	0.254173i
$655$		−	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	$-0.701656\pi$
$659$	5.49262	−	5.49262i	0.213962	−	0.213962i	0.805948	+	0.591986i	$0.201656\pi$
$660$	−17.0016	−	17.1858i	−0.661785	−	0.668958i
$661$	−5.86833	−	5.86833i	−0.228251	−	0.228251i	0.583710	−	0.811962i	$-0.301600\pi$
$661$	−5.86833	−	5.86833i	−0.228251	−	0.228251i	−0.811962	+	0.583710i	$0.801600\pi$
$662$	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
$666$	−27.3469	+	9.63110i	−1.05967	+	0.373197i
$667$	−11.7648	+	11.7648i	−0.455535	+	0.455535i
$668$	1.35754	+	4.53816i	0.0525249	+	0.175587i
$669$	34.5787	−	18.4146i	1.33689	−	0.711950i
$670$	3.70727	−	0.542616i	0.143224	−	0.0209631i
$671$	15.2013			0.586841
$672$	−10.5325	−	3.90191i	−0.406301	−	0.150519i
$673$	−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
$675$	1.96486	−	19.0512i	0.0756273	−	0.733280i
$676$	7.42682	+	24.8273i	0.285647	+	0.954895i
$677$	−13.7685	+	13.7685i	−0.529168	+	0.529168i	−0.920324	−	0.391156i	$-0.872075\pi$
$677$	−13.7685	+	13.7685i	−0.529168	+	0.529168i	0.391156	+	0.920324i	$0.372075\pi$
$678$	10.8039	−	7.95492i	0.414922	−	0.305507i
$679$	−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	$-0.299483\pi$
$683$	−5.72238	−	5.72238i	−0.218961	−	0.218961i	−0.808060	+	0.589100i	$0.799483\pi$
$684$	−11.1858	+	5.87977i	−0.427701	+	0.224818i
$685$	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
$690$	3.62988	−	23.9004i	0.138187	−	0.909874i
$691$	24.2327	+	24.2327i	0.921854	+	0.921854i	0.997160	−	0.0753061i	$-0.0239934\pi$
$691$	24.2327	+	24.2327i	0.921854	+	0.921854i	−0.0753061	+	0.997160i	$0.523993\pi$
$692$	13.0027	+	7.01471i	0.494289	+	0.266659i
$693$	7.99175	−	1.56421i	0.303581	−	0.0594194i
$694$	26.0147	+	19.3717i	0.987504	+	0.735339i
$695$		−	35.9929i		−	1.36529i
$696$	−3.39519	−	24.1026i	−0.128695	−	0.913605i
$697$			3.41454i			0.129335i
$698$	7.34180	−	9.85947i	0.277891	−	0.373187i
$699$	14.9655	+	28.1020i	0.566048	+	1.06292i
$700$	2.42188	+	8.09617i	0.0915386	+	0.306007i
$701$	−10.9100	−	10.9100i	−0.412064	−	0.412064i	0.470393	−	0.882457i	$-0.344112\pi$
$701$	−10.9100	−	10.9100i	−0.412064	−	0.412064i	−0.882457	+	0.470393i	$0.844112\pi$
$702$	−1.02882	+	1.12035i	−0.0388305	+	0.0422849i
$703$		−	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
$708$	−0.238972	+	44.3376i	−0.00898112	+	1.66631i
$709$	−14.0031	−	14.0031i	−0.525899	−	0.525899i	0.393448	−	0.919347i	$-0.371282\pi$
$709$	−14.0031	−	14.0031i	−0.525899	−	0.525899i	−0.919347	+	0.393448i	$0.871282\pi$
$710$	−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
$714$	12.6564	−	9.31888i	0.473653	−	0.348750i
$715$	1.02142	−	1.02142i	0.0381990	−	0.0381990i
$716$	9.57652	−	17.7514i	0.357891	−	0.663400i
$717$	11.0172	+	20.6879i	0.411443	+	0.772602i
$718$	−3.75639	−	25.6644i	−0.140187	−	0.957788i
$719$	30.0665			1.12129			0.560646	−	0.828055i	$-0.310553\pi$
$719$	30.0665			1.12129			0.560646	+	0.828055i	$0.310553\pi$
$720$	24.7366	+	25.2757i	0.921879	+	0.941971i
$721$	14.0147			0.521934
$722$	2.98286	+	20.3795i	0.111011	+	0.758447i
$723$	−3.97154	−	7.45769i	−0.147703	−	0.277355i
$724$	−16.7575	−	9.04033i	−0.622786	−	0.335981i
$725$	−12.9493	+	12.9493i	−0.480925	+	0.480925i
$726$	10.6379	−	7.83264i	0.394808	−	0.290697i
$727$	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
$732$	−22.2385	−	0.119862i	−0.821959	−	0.00443021i
$733$	−29.4752	+	29.4752i	−1.08869	+	1.08869i	−0.0930283	+	0.995663i	$0.529655\pi$
$733$	−29.4752	+	29.4752i	−1.08869	+	1.08869i	−0.995663	+	0.0930283i	$0.970345\pi$
$734$	−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
$738$	1.11826	−	2.33414i	0.0411638	−	0.0859209i
$739$	22.1077	+	22.1077i	0.813246	+	0.813246i	0.985119	−	0.171873i	$-0.0549819\pi$
$739$	22.1077	+	22.1077i	0.813246	+	0.813246i	−0.171873	+	0.985119i	$0.554982\pi$
$740$	−38.5910	+	11.5441i	−1.41863	+	0.424370i
$741$	−0.354934	−	0.666489i	−0.0130388	−	0.0244841i
$742$	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	$-0.00530499\pi$
$744$	−17.1877	+	22.8240i	−0.630133	+	0.836768i
$745$		−	48.5145i		−	1.77743i
$746$	27.6314	+	20.5756i	1.01166	+	0.753325i
$747$	−6.59352	−	33.6872i	−0.241244	−	1.23255i
$748$	−12.5855	+	23.3288i	−0.460170	+	0.852987i
$749$	0.819240	+	0.819240i	0.0299344	+	0.0299344i
$750$	−1.42450	+	9.37942i	−0.0520154	+	0.342488i
$751$			39.1182i			1.42744i	0.700429	+	0.713722i	$0.252992\pi$
$751$			39.1182i			1.42744i	−0.700429	+	0.713722i	$0.747008\pi$
$752$	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
$756$	−11.7037	+	2.22531i	−0.425659	+	0.0809339i
$757$	−8.97544	−	8.97544i	−0.326218	−	0.326218i	0.524928	−	0.851146i	$-0.324092\pi$
$757$	−8.97544	−	8.97544i	−0.326218	−	0.326218i	−0.851146	+	0.524928i	$0.824092\pi$
$758$	−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	$-0.312331\pi$
$761$	30.6766			1.11202			0.556012	+	0.831174i	$0.312331\pi$
$762$	14.2096	−	10.4625i	0.514760	−	0.379017i
$763$	14.3257	−	14.3257i	0.518626	−	0.518626i
$764$	−48.9151	+	14.6324i	−1.76968	+	0.529382i
$765$	−48.5664	+	9.50581i	−1.75592	+	0.343683i
$766$	−43.0508	+	6.30115i	−1.55549	+	0.227670i
$767$	−2.64937			−0.0956630
$768$	−27.6215	+	2.24817i	−0.996704	+	0.0811240i
$769$	−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
$771$	−19.6187	+	10.4478i	−0.706551	+	0.376268i
$772$	17.3963	−	5.20390i	0.626105	−	0.187293i
$773$	−17.6074	+	17.6074i	−0.633293	+	0.633293i	−0.948892	−	0.315599i	$-0.897794\pi$
$773$	−17.6074	+	17.6074i	−0.633293	+	0.633293i	0.315599	+	0.948892i	$0.397794\pi$
$774$	2.96831	+	8.42831i	0.106694	+	0.302949i
$775$	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
$780$	−1.50232	+	1.48622i	−0.0537918	+	0.0532151i
$781$	−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
$786$	30.9965	+	4.70759i	1.10561	+	0.167914i
$787$	1.69006	+	1.69006i	0.0602440	+	0.0602440i	0.736587	−	0.676343i	$-0.236436\pi$
$787$	1.69006	+	1.69006i	0.0602440	+	0.0602440i	−0.676343	+	0.736587i	$0.736436\pi$
$788$	4.27606	−	7.92625i	0.152328	−	0.282361i
$789$	−43.2878	+	23.0526i	−1.54108	+	0.820693i
$790$	32.8683	+	24.4752i	1.16940	+	0.870789i
$791$			6.27900i			0.223255i
$792$	16.2435	−	11.8256i	0.577187	−	0.420204i
$793$		−	1.32885i		−	0.0471887i
$794$	2.09425	−	2.81241i	0.0743221	−	0.0998088i
$795$	−1.04851	+	0.558376i	−0.0371868	+	0.0198035i
$796$	37.4679	−	11.2081i	1.32801	−	0.397261i
$797$	5.76177	+	5.76177i	0.204092	+	0.204092i	0.801751	−	0.597658i	$-0.203902\pi$
$797$	5.76177	+	5.76177i	0.204092	+	0.204092i	−0.597658	+	0.801751i	$0.703902\pi$
$798$	0.888030	−	5.84710i	0.0314359	−	0.206985i
$799$			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
$804$	−0.0167840	+	3.11401i	−0.000591925	+	0.109823i
$805$	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	$-0.579736\pi$
$809$	−14.1012			−0.495771			−0.247885	+	0.968789i	$0.579736\pi$
$810$	36.3126	+	9.40747i	1.27590	+	0.330545i
$811$	−16.2327	+	16.2327i	−0.570006	+	0.570006i	−0.932130	−	0.362124i	$-0.882052\pi$
$811$	−16.2327	+	16.2327i	−0.570006	+	0.570006i	0.362124	+	0.932130i	$0.382052\pi$
$812$	10.0255	+	5.40858i	0.351827	+	0.189804i
$813$	−13.2412	+	7.05151i	−0.464390	+	0.247307i
$814$	3.31415	+	22.6430i	0.116161	+	0.793637i
$815$	41.9909			1.47088
$816$	18.5956	−	34.0292i	0.650976	−	1.19126i
$817$	−4.43596			−0.155195
$818$	−1.79951	−	12.2946i	−0.0629183	−	0.429871i
$819$	−0.136737	−	0.698610i	−0.00477799	−	0.0244114i
$820$	1.70727	−	3.16465i	0.0596204	−	0.110514i
$821$	−17.2853	+	17.2853i	−0.603262	+	0.603262i	−0.941177	−	0.337915i	$-0.890278\pi$
$821$	−17.2853	+	17.2853i	−0.603262	+	0.603262i	0.337915	+	0.941177i	$0.390278\pi$
$822$	19.5238	+	26.5161i	0.680969	+	0.924854i
$823$	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	$-0.248243\pi$
$827$	0.224507	+	0.224507i	0.00780688	+	0.00780688i	−0.703193	+	0.710999i	$0.748243\pi$
$828$	19.1862	+	5.96541i	0.666766	+	0.207312i
$829$	29.5181	−	29.5181i	1.02520	−	1.02520i	0.0255305	−	0.999674i	$-0.491873\pi$
$829$	29.5181	−	29.5181i	1.02520	−	1.02520i	0.999674	−	0.0255305i	$-0.00812749\pi$
$830$	−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
$834$	29.5756	+	4.49180i	1.02412	+	0.155538i
$835$	4.93573	+	4.93573i	0.170808	+	0.170808i
$836$	2.85856	+	9.55596i	0.0988655	+	0.330500i
$837$	−3.10904	+	30.1452i	−0.107464	+	1.04197i
$838$	−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	$0.922179\pi$
$840$	−16.3896	+	2.30871i	−0.565495	+	0.0796581i
$841$		−	4.31415i		−	0.148764i
$842$	−18.0067	−	13.4086i	−0.620552	−	0.462091i
$843$	−21.2946	−	39.9868i	−0.733427	−	1.37722i
$844$	−25.7465	−	13.8898i	−0.886232	−	0.478105i
$845$	27.0023	+	27.0023i	0.928907	+	0.928907i
$846$	11.7620	−	24.5506i	0.404384	−	0.844068i
$847$			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
$852$	17.0086	−	16.8262i	0.582704	−	0.576456i
$853$	−8.55417	−	8.55417i	−0.292889	−	0.292889i	0.545331	−	0.838221i	$-0.316404\pi$
$853$	−8.55417	−	8.55417i	−0.292889	−	0.292889i	−0.838221	+	0.545331i	$0.816404\pi$
$854$	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	$-0.233341\pi$
$857$	43.5095			1.48626			0.743128	+	0.669149i	$0.233341\pi$
$858$	0.711841	+	0.966782i	0.0243019	+	0.0330054i
$859$	−8.70306	+	8.70306i	−0.296945	+	0.296945i	−0.839816	−	0.542871i	$-0.817337\pi$
$859$	−8.70306	+	8.70306i	−0.296945	+	0.296945i	0.542871	+	0.839816i	$0.317337\pi$
$860$	3.55789	+	11.8938i	0.121323	+	0.405574i
$861$	0.569354	+	1.06912i	0.0194035	+	0.0364357i
$862$	−16.9786	+	2.48508i	−0.578293	+	0.0846421i
$863$	−26.9270			−0.916607			−0.458303	−	0.888796i	$-0.651543\pi$
$863$	−26.9270			−0.916607			−0.458303	+	0.888796i	$0.651543\pi$
$864$	−23.8563	+	17.1719i	−0.811609	+	0.584201i
$865$	21.7711			0.740239
$866$	17.0009	−	2.48834i	0.577712	−	0.0845572i
$867$	11.6657	+	21.9057i	0.396188	+	0.743956i
$868$	−3.83221	−	12.8108i	−0.130074	−	0.434827i
$869$	16.4625	−	16.4625i	0.558454	−	0.558454i
$870$	−21.2666	−	28.8831i	−0.721006	−	0.979230i
$871$	−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
$876$	17.4330	−	17.2461i	0.589008	−	0.582693i
$877$	39.7251	−	39.7251i	1.34142	−	1.34142i	0.446775	−	0.894646i	$-0.352573\pi$
$877$	39.7251	−	39.7251i	1.34142	−	1.34142i	0.894646	−	0.446775i	$-0.147427\pi$
$878$	−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	$0.991213\pi$
$882$	−10.4227	+	21.7552i	−0.350950	+	0.732534i
$883$	−31.7967	−	31.7967i	−1.07004	−	1.07004i	−0.997355	−	0.0726900i	$-0.976842\pi$
$883$	−31.7967	−	31.7967i	−1.07004	−	1.07004i	−0.0726900	−	0.997355i	$-0.523158\pi$
$884$	2.03932	+	1.10018i	0.0685899	+	0.0370029i
$885$	30.7110	+	57.6687i	1.03234	+	1.93851i
$886$	−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	$0.832872\pi$
$888$	−4.66984	−	33.1513i	−0.156709	−	1.11248i
$889$			8.25831i			0.276975i
$890$	−1.22008	+	1.63848i	−0.0408973	+	0.0549219i
$891$	8.27590	−	19.6384i	0.277253	−	0.657912i
$892$	12.9645	+	43.3393i	0.434084	+	1.45111i
$893$	9.55596	+	9.55596i	0.319778	+	0.319778i
$894$	39.8647	+	6.05446i	1.33328	+	0.202492i
$895$		−	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
$900$	21.1179	+	6.56601i	0.703929	+	0.218867i
$901$	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
$906$	−1.17754	−	1.59927i	−0.0391212	−	0.0531322i
$907$	−12.1176	+	12.1176i	−0.402358	+	0.402358i	−0.879063	−	0.476705i	$-0.841831\pi$
$907$	−12.1176	+	12.1176i	−0.402358	+	0.402358i	0.476705	+	0.879063i	$0.341831\pi$
$908$	1.96758	−	3.64718i	0.0652966	−	0.121036i
$909$	−6.75686	−	34.5217i	−0.224111	−	1.14501i
$910$	−0.143230	−	0.978577i	−0.00474803	−	0.0324395i
$911$	4.53816			0.150356			0.0751780	−	0.997170i	$-0.476048\pi$
$911$	4.53816			0.150356			0.0751780	+	0.997170i	$0.476048\pi$
$912$	−4.10653	−	14.0022i	−0.135981	−	0.463660i
$913$	−27.0937			−0.896669
$914$	0.860359	+	5.87815i	0.0284581	+	0.194432i
$915$	−28.9250	+	15.4038i	−0.956230	+	0.509233i
$916$	−18.7146	−	10.0962i	−0.618348	−	0.333587i
$917$	−10.3752	+	10.3752i	−0.342619	+	0.342619i
$918$	−1.75005	−	41.0937i	−0.0577604	−	1.35630i
$919$	−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
$924$	−0.0506807	+	9.40304i	−0.00166727	+	0.309337i
$925$	−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	$-0.147133\pi$
$930$	−6.32193	+	41.6259i	−0.207304	+	1.36497i
$931$	−8.46787	−	8.46787i	−0.277523	−	0.277523i
$932$	−35.2218	+	10.5362i	−1.15373	+	0.345125i
$933$	50.6551	−	26.9760i	1.65837	−	0.883154i
$934$	−20.2070	+	27.1365i	−0.661195	+	0.887933i
$935$			39.0606i			1.27742i
$936$	−1.03375	−	1.41995i	−0.0337892	−	0.0464124i
$937$			22.1495i			0.723593i	0.932257	+	0.361796i	$0.117836\pi$
$937$			22.1495i			0.723593i	−0.932257	+	0.361796i	$0.882164\pi$
$938$	−1.16891	−	0.870418i	−0.0381661	−	0.0284202i
$939$	−20.2234	+	10.7698i	−0.659967	+	0.351460i
$940$	17.9572	−	33.2860i	0.585698	−	1.08567i
$941$	−7.35208	−	7.35208i	−0.239671	−	0.239671i	0.577043	−	0.816714i	$-0.304207\pi$
$941$	−7.35208	−	7.35208i	−0.239671	−	0.239671i	−0.816714	+	0.577043i	$0.804207\pi$
$942$	18.8984	+	2.87020i	0.615743	+	0.0935161i
$943$		−	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	$-0.681523\pi$
$947$	9.29033	−	9.29033i	0.301895	−	0.301895i	0.841755	+	0.539860i	$0.181523\pi$
$948$	−24.2134	+	23.9537i	−0.786413	+	0.777981i
$949$	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	$-0.434363\pi$
$953$	12.6413			0.409491			0.204745	+	0.978815i	$0.434363\pi$
$954$	−0.327971	−	0.931252i	−0.0106185	−	0.0301504i
$955$	−53.2003	+	53.2003i	−1.72152	+	1.72152i
$956$	−25.9292	+	7.75645i	−0.838611	+	0.250862i
$957$	−17.9858	+	9.57821i	−0.581399	+	0.309620i
$958$	−25.9572	+	3.79923i	−0.838638	+	0.122748i
$959$	−15.4105			−0.497632
$960$	−34.2493	+	22.2411i	−1.10539	+	0.717828i
$961$	−3.01469			−0.0972482
$962$	1.97937	−	0.289711i	0.0638174	−	0.00934067i
$963$	2.97550	−	0.582390i	0.0958843	−	0.0187672i
$964$	9.34713	−	2.79610i	0.301051	−	0.0900562i
$965$	18.9203	−	18.9203i	0.609065	−	0.609065i
$966$	−7.57204	+	5.57529i	−0.243627	+	0.179382i
$967$	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	$-0.205276\pi$
$971$	6.17139	+	6.17139i	0.198049	+	0.198049i	−0.601114	+	0.799163i	$0.705276\pi$
$972$	−12.2619	+	28.6644i	−0.393301	+	0.919410i
$973$	−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	$-0.0482310\pi$
$978$	−5.24034	+	34.5043i	−0.167568	+	1.10333i
$979$	0.820654	+	0.820654i	0.0262282	+	0.0262282i
$980$	−15.9125	+	29.4959i	−0.508305	+	0.942211i
$981$	−10.1840	−	52.0315i	−0.325150	−	1.66124i
$982$	−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	$-0.135394\pi$
$984$	2.38736	+	1.79782i	0.0761062	+	0.0573123i
$985$		−	13.2713i		−	0.422859i
$986$	−23.4890	+	31.5440i	−0.748044	+	1.00457i
$987$	5.98850	+	11.2451i	0.190616	+	0.357936i
$988$	0.835347	−	0.249885i	0.0265759	−	0.00794991i
$989$	4.98718	+	4.98718i	0.158583	+	0.158583i
$990$	12.7924	−	26.7014i	0.406568	−	0.848626i
$991$		−	23.5886i		−	0.749316i	−0.927163	−	0.374658i	$-0.877760\pi$
$991$		−	23.5886i		−	0.749316i	0.927163	−	0.374658i	$-0.122240\pi$
$992$	−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
$996$	39.6361	+	0.213632i	1.25592	+	0.00676918i
$997$	3.16779	+	3.16779i	0.100325	+	0.100325i	0.755488	−	0.655163i	$-0.227400\pi$
$997$	3.16779	+	3.16779i	0.100325	+	0.100325i	−0.655163	+	0.755488i	$0.727400\pi$
$998$	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.11.1	✓	12
3.2	odd	2	inner	48.2.k.a.11.6	yes	12
4.3	odd	2		192.2.k.a.143.4		12
8.3	odd	2		384.2.k.a.287.3		12
8.5	even	2		384.2.k.b.287.4		12
12.11	even	2		192.2.k.a.143.6		12
16.3	odd	4	inner	48.2.k.a.35.6	yes	12
16.5	even	4		384.2.k.a.95.1		12
16.11	odd	4		384.2.k.b.95.6		12
16.13	even	4		192.2.k.a.47.6		12
24.5	odd	2		384.2.k.b.287.6		12
24.11	even	2		384.2.k.a.287.1		12
48.5	odd	4		384.2.k.a.95.3		12
48.11	even	4		384.2.k.b.95.4		12
48.29	odd	4		192.2.k.a.47.4		12
48.35	even	4	inner	48.2.k.a.35.1	yes	12

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

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)

\(f(q)\)	\(=\)	\(q+(-1.39930 + 0.204810i) q^{2} +(-0.814141 - 1.52878i) q^{3} +(1.91611 - 0.573183i) q^{4} +(2.08397 - 2.08397i) q^{5} +(1.45234 + 1.97249i) q^{6} -1.14637 q^{7} +(-2.56382 + 1.19449i) q^{8} +(-1.67435 + 2.48929i) q^{9} +O(q^{10})\)	\(q+(-1.39930 + 0.204810i) q^{2} +(-0.814141 - 1.52878i) q^{3} +(1.91611 - 0.573183i) q^{4} +(2.08397 - 2.08397i) q^{5} +(1.45234 + 1.97249i) 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} +(-2.43625 - 2.46266i) 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} +(1.83309 - 3.82620i) q^{18} +(1.48929 + 1.48929i) q^{19} +(2.79861 - 5.18760i) q^{20} +(0.933303 + 1.75254i) q^{21} +(-2.68585 - 2.00000i) q^{22} -3.34870i q^{23} +(3.91343 + 2.94704i) q^{24} -3.68585i q^{25} +(-0.174833 + 0.234787i) q^{26} +(5.16874 + 0.533081i) q^{27} +(-2.19656 + 0.657077i) q^{28} +(-3.51325 - 3.51325i) q^{29} +(7.13723 + 1.08397i) 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} +(-1.78141 + 5.72945i) 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} +(-1.66491 - 2.26119i) q^{42} +(-1.48929 + 1.48929i) q^{43} +(4.16794 + 2.24852i) q^{44} +(1.69831 + 8.67689i) q^{45} +(0.685846 + 4.68585i) q^{46} +6.41646 q^{47} +(-6.07967 - 3.32229i) q^{48} -5.68585 q^{49} +(0.754898 + 5.15762i) q^{50} +(8.55693 - 4.55693i) q^{51} +(0.196558 - 0.364346i) q^{52} +(0.164553 - 0.164553i) q^{53} +(-7.34181 + 0.312665i) 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} +(-10.2092 - 0.0550256i) 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} +(-0.870906 + 5.73436i) q^{66} +(-0.635654 - 0.635654i) q^{67} +(3.20823 + 10.7249i) q^{68} +(-5.11943 + 2.72631i) q^{69} +(2.85363 - 3.83221i) q^{70} +6.90659i q^{71} +(1.31929 - 8.38209i) q^{72} +7.07896i q^{73} +(7.75142 + 5.77205i) q^{74} +(-5.63485 + 3.00080i) q^{75} +(3.70727 + 2.00000i) q^{76} +(-1.91942 - 1.91942i) q^{77} +(0.501277 + 0.0761315i) 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} +(2.79284 + 2.82310i) 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} +(-4.15356 - 11.7938i) q^{90} +(-0.167788 + 0.167788i) q^{91} +(-1.91942 - 6.41646i) q^{92} +(8.91618 - 4.74824i) q^{93} +(-8.97858 + 1.31415i) q^{94} +6.20726 q^{95} +(9.18775 + 3.40372i) q^{96} +12.3503 q^{97} +(7.95623 - 1.16452i) q^{98} +(-6.97138 + 1.36449i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more