LMFDB - Embedded newform 966.2.l.d.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.67384 + 0.445275i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04467 + 1.80941i) q^{5} +(1.67222 + 0.451299i) q^{6} +(-2.62205 - 0.353363i) q^{7} -1.00000i q^{8} +(2.60346 - 1.49064i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67384 + 0.445275i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04467 + 1.80941i) q^{5} +(1.67222 + 0.451299i) q^{6} +(-2.62205 - 0.353363i) q^{7} -1.00000i q^{8} +(2.60346 - 1.49064i) q^{9} +(1.80941 - 1.04467i) q^{10} +(-4.35244 + 2.51288i) q^{11} +(-1.22254 - 1.22695i) q^{12} -0.776166i q^{13} +(2.09408 + 1.61705i) q^{14} +(0.942912 - 3.49383i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.09997 + 1.90520i) q^{17} +(-2.99998 - 0.0108008i) q^{18} +(-7.09187 - 4.09449i) q^{19} -2.08933 q^{20} +(4.54622 - 0.576061i) q^{21} +5.02576 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.445275 + 1.67384i) q^{24} +(0.317348 + 0.549662i) q^{25} +(-0.388083 + 0.672180i) q^{26} +(-3.69402 + 3.65434i) q^{27} +(-1.00500 - 2.44744i) q^{28} +9.23666i q^{29} +(-2.56350 + 2.55429i) q^{30} +(5.63719 - 3.25463i) q^{31} +(0.866025 - 0.500000i) q^{32} +(6.16635 - 6.14418i) q^{33} -2.19994i q^{34} +(3.37854 - 4.37522i) q^{35} +(2.59266 + 1.50934i) q^{36} +(3.77210 - 6.53347i) q^{37} +(4.09449 + 7.09187i) q^{38} +(0.345608 + 1.29918i) q^{39} +(1.80941 + 1.04467i) q^{40} -6.65401 q^{41} +(-4.22518 - 1.77423i) q^{42} +2.58203 q^{43} +(-4.35244 - 2.51288i) q^{44} +(-0.0225665 + 6.26795i) q^{45} +(0.500000 + 0.866025i) q^{46} +(3.82245 - 6.62068i) q^{47} +(0.451299 - 1.67222i) q^{48} +(6.75027 + 1.85307i) q^{49} -0.634695i q^{50} +(-2.68951 - 2.69921i) q^{51} +(0.672180 - 0.388083i) q^{52} +(5.68919 - 3.28466i) q^{53} +(5.02629 - 1.31774i) q^{54} -10.5005i q^{55} +(-0.353363 + 2.62205i) q^{56} +(13.6938 + 3.69568i) q^{57} +(4.61833 - 7.99919i) q^{58} +(-1.82936 - 3.16855i) q^{59} +(3.49720 - 0.930328i) q^{60} +(-2.91159 - 1.68101i) q^{61} -6.50927 q^{62} +(-7.35313 + 2.98855i) q^{63} -1.00000 q^{64} +(1.40441 + 0.810834i) q^{65} +(-8.41230 + 2.23785i) q^{66} +(6.59763 + 11.4274i) q^{67} +(-1.09997 + 1.90520i) q^{68} +(1.67222 + 0.451299i) q^{69} +(-5.11352 + 2.09978i) q^{70} -3.55436i q^{71} +(-1.49064 - 2.60346i) q^{72} +(2.57128 - 1.48453i) q^{73} +(-6.53347 + 3.77210i) q^{74} +(-0.775939 - 0.778738i) q^{75} -8.18899i q^{76} +(12.3003 - 5.05090i) q^{77} +(0.350283 - 1.29792i) q^{78} +(1.96986 - 3.41189i) q^{79} +(-1.04467 - 1.80941i) q^{80} +(4.55601 - 7.76162i) q^{81} +(5.76254 + 3.32700i) q^{82} +16.9290 q^{83} +(2.77200 + 3.64912i) q^{84} -4.59640 q^{85} +(-2.23611 - 1.29102i) q^{86} +(-4.11286 - 15.4607i) q^{87} +(2.51288 + 4.35244i) q^{88} +(-1.57290 + 2.72434i) q^{89} +(3.15352 - 5.41692i) q^{90} +(-0.274269 + 2.03515i) q^{91} -1.00000i q^{92} +(-7.98653 + 7.95783i) q^{93} +(-6.62068 + 3.82245i) q^{94} +(14.8173 - 8.55476i) q^{95} +(-1.22695 + 1.22254i) q^{96} -15.6628i q^{97} +(-4.91937 - 4.97994i) q^{98} +(-7.58560 + 13.0301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.67384	+	0.445275i	−0.966390	+	0.257080i
$3$	−1.67384	+	0.445275i	−0.966390	+	0.257080i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.04467	+	1.80941i	−0.467189	+	0.809194i	−0.999297	−	0.0374816i	$-0.988066\pi$
$5$	−1.04467	+	1.80941i	−0.467189	+	0.809194i	0.532109	+	0.846676i	$0.321400\pi$
$6$	1.67222	+	0.451299i	0.682682	+	0.184242i
$7$	−2.62205	−	0.353363i	−0.991041	−	0.133559i
$7$	−2.62205	−	0.353363i	−0.991041	−	0.133559i
$8$		−	1.00000i		−	0.353553i
$9$	2.60346	−	1.49064i	0.867820	−	0.496879i
$10$	1.80941	−	1.04467i	0.572187	−	0.330352i
$11$	−4.35244	+	2.51288i	−1.31231	+	0.757662i	−0.982478	−	0.186378i	$-0.940325\pi$
$11$	−4.35244	+	2.51288i	−1.31231	+	0.757662i	−0.329831	+	0.944040i	$0.606992\pi$
$12$	−1.22254	−	1.22695i	−0.352916	−	0.354189i
$13$		−	0.776166i		−	0.215270i	−0.994190	−	0.107635i	$-0.965672\pi$
$13$		−	0.776166i		−	0.215270i	0.994190	−	0.107635i	$-0.0343278\pi$
$14$	2.09408	+	1.61705i	0.559666	+	0.432174i
$15$	0.942912	−	3.49383i	0.243459	−	0.902102i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.09997	+	1.90520i	0.266782	+	0.462080i	0.968029	−	0.250838i	$-0.0807063\pi$
$17$	1.09997	+	1.90520i	0.266782	+	0.462080i	−0.701247	+	0.712918i	$0.747373\pi$
$18$	−2.99998	−	0.0108008i	−0.707102	−	0.00254578i
$19$	−7.09187	−	4.09449i	−1.62699	−	0.939341i	−0.984985	−	0.172638i	$-0.944771\pi$
$19$	−7.09187	−	4.09449i	−1.62699	−	0.939341i	−0.642002	−	0.766703i	$-0.721896\pi$
$20$	−2.08933			−0.467189
$21$	4.54622	−	0.576061i	0.992067	−	0.125707i
$22$	5.02576			1.07150
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	0.445275	+	1.67384i	0.0908914	+	0.341671i
$25$	0.317348	+	0.549662i	0.0634695	+	0.109932i
$26$	−0.388083	+	0.672180i	−0.0761094	+	0.131825i
$27$	−3.69402	+	3.65434i	−0.710915	+	0.703278i
$28$	−1.00500	−	2.44744i	−0.189928	−	0.462523i
$29$			9.23666i			1.71521i	0.514313	+	0.857603i	$0.328047\pi$
$29$			9.23666i			1.71521i	−0.514313	+	0.857603i	$0.671953\pi$
$30$	−2.56350	+	2.55429i	−0.468029	+	0.466347i
$31$	5.63719	−	3.25463i	1.01247	−	0.584550i	0.100556	−	0.994931i	$-0.467938\pi$
$31$	5.63719	−	3.25463i	1.01247	−	0.584550i	0.911914	+	0.410382i	$0.134605\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	6.16635	−	6.14418i	1.07342	−	1.06957i
$34$		−	2.19994i		−	0.377287i
$35$	3.37854	−	4.37522i	0.571078	−	0.739548i
$36$	2.59266	+	1.50934i	0.432110	+	0.251557i
$37$	3.77210	−	6.53347i	0.620129	−	1.07410i	−0.369332	−	0.929298i	$-0.620413\pi$
$37$	3.77210	−	6.53347i	0.620129	−	1.07410i	0.989461	−	0.144798i	$-0.0462533\pi$
$38$	4.09449	+	7.09187i	0.664215	+	1.15045i
$39$	0.345608	+	1.29918i	0.0553415	+	0.208035i
$40$	1.80941	+	1.04467i	0.286093	+	0.165176i
$41$	−6.65401			−1.03918			−0.519591	−	0.854415i	$-0.673916\pi$
$41$	−6.65401			−1.03918			−0.519591	+	0.854415i	$0.673916\pi$
$42$	−4.22518	−	1.77423i	−0.651959	−	0.273769i
$43$	2.58203			0.393756			0.196878	−	0.980428i	$-0.436920\pi$
$43$	2.58203			0.393756			0.196878	+	0.980428i	$0.436920\pi$
$44$	−4.35244	−	2.51288i	−0.656155	−	0.378831i
$45$	−0.0225665	+	6.26795i	−0.00336402	+	0.934371i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	3.82245	−	6.62068i	0.557562	−	0.965725i	−0.440138	−	0.897930i	$-0.645070\pi$
$47$	3.82245	−	6.62068i	0.557562	−	0.965725i	0.997699	−	0.0677948i	$-0.0215963\pi$
$48$	0.451299	−	1.67222i	0.0651394	−	0.241365i
$49$	6.75027	+	1.85307i	0.964324	+	0.264724i
$50$		−	0.634695i		−	0.0897594i
$51$	−2.68951	−	2.69921i	−0.376607	−	0.377965i
$52$	0.672180	−	0.388083i	0.0932146	−	0.0538174i
$53$	5.68919	−	3.28466i	0.781470	−	0.451182i	−0.0554808	−	0.998460i	$-0.517669\pi$
$53$	5.68919	−	3.28466i	0.781470	−	0.451182i	0.836951	+	0.547278i	$0.184336\pi$
$54$	5.02629	−	1.31774i	0.683991	−	0.179321i
$55$		−	10.5005i		−	1.41588i
$56$	−0.353363	+	2.62205i	−0.0472201	+	0.350386i
$57$	13.6938	+	3.69568i	1.81379	+	0.489505i
$58$	4.61833	−	7.99919i	0.606417	−	1.05034i
$59$	−1.82936	−	3.16855i	−0.238163	−	0.412510i	0.722024	−	0.691868i	$-0.243212\pi$
$59$	−1.82936	−	3.16855i	−0.238163	−	0.412510i	−0.960187	+	0.279358i	$0.909878\pi$
$60$	3.49720	−	0.930328i	0.451487	−	0.120105i
$61$	−2.91159	−	1.68101i	−0.372791	−	0.215231i	0.301886	−	0.953344i	$-0.402384\pi$
$61$	−2.91159	−	1.68101i	−0.372791	−	0.215231i	−0.674677	+	0.738113i	$0.735717\pi$
$62$	−6.50927			−0.826678
$63$	−7.35313	+	2.98855i	−0.926408	+	0.376522i
$64$	−1.00000			−0.125000
$65$	1.40441	+	0.810834i	0.174195	+	0.100572i
$66$	−8.41230	+	2.23785i	−1.03548	+	0.275460i
$67$	6.59763	+	11.4274i	0.806028	+	1.39608i	0.915595	+	0.402102i	$0.131720\pi$
$67$	6.59763	+	11.4274i	0.806028	+	1.39608i	−0.109567	+	0.993979i	$0.534946\pi$
$68$	−1.09997	+	1.90520i	−0.133391	+	0.231040i
$69$	1.67222	+	0.451299i	0.201312	+	0.0543300i
$70$	−5.11352	+	2.09978i	−0.611182	+	0.250972i
$71$		−	3.55436i		−	0.421825i	−0.977505	−	0.210912i	$-0.932357\pi$
$71$		−	3.55436i		−	0.421825i	0.977505	−	0.210912i	$-0.0676435\pi$
$72$	−1.49064	−	2.60346i	−0.175673	−	0.306821i
$73$	2.57128	−	1.48453i	0.300945	−	0.173751i	−0.341922	−	0.939728i	$-0.611078\pi$
$73$	2.57128	−	1.48453i	0.300945	−	0.173751i	0.642867	+	0.765978i	$0.277745\pi$
$74$	−6.53347	+	3.77210i	−0.759500	+	0.438498i
$75$	−0.775939	−	0.778738i	−0.0895977	−	0.0899209i
$76$		−	8.18899i		−	0.939341i
$77$	12.3003	−	5.05090i	1.40174	−	0.575604i
$78$	0.350283	−	1.29792i	0.0396617	−	0.146961i
$79$	1.96986	−	3.41189i	0.221626	−	0.383868i	−0.733676	−	0.679500i	$-0.762197\pi$
$79$	1.96986	−	3.41189i	0.221626	−	0.383868i	0.955302	+	0.295632i	$0.0955301\pi$
$80$	−1.04467	−	1.80941i	−0.116797	−	0.202299i
$81$	4.55601	−	7.76162i	0.506223	−	0.862403i
$82$	5.76254	+	3.32700i	0.636366	+	0.367406i
$83$	16.9290			1.85820			0.929098	−	0.369833i	$-0.120585\pi$
$83$	16.9290			1.85820			0.929098	+	0.369833i	$0.120585\pi$
$84$	2.77200	+	3.64912i	0.302449	+	0.398151i
$85$	−4.59640			−0.498550
$86$	−2.23611	−	1.29102i	−0.241126	−	0.139214i
$87$	−4.11286	−	15.4607i	−0.440945	−	1.65756i
$88$	2.51288	+	4.35244i	0.267874	+	0.463971i
$89$	−1.57290	+	2.72434i	−0.166727	+	0.288780i	−0.937267	−	0.348612i	$-0.886653\pi$
$89$	−1.57290	+	2.72434i	−0.166727	+	0.288780i	0.770540	+	0.637391i	$0.219987\pi$
$90$	3.15352	−	5.41692i	0.332410	−	0.570994i
$91$	−0.274269	+	2.03515i	−0.0287512	+	0.213341i
$92$		−	1.00000i		−	0.104257i
$93$	−7.98653	+	7.95783i	−0.828165	+	0.825188i
$94$	−6.62068	+	3.82245i	−0.682871	+	0.394256i
$95$	14.8173	−	8.55476i	1.52022	−	0.877699i
$96$	−1.22695	+	1.22254i	−0.125225	+	0.124775i
$97$		−	15.6628i		−	1.59032i	−0.606400	−	0.795160i	$-0.707387\pi$
$97$		−	15.6628i		−	1.59032i	0.606400	−	0.795160i	$-0.292613\pi$
$98$	−4.91937	−	4.97994i	−0.496931	−	0.503050i
$99$	−7.58560	+	13.0301i	−0.762382	+	1.30957i
$100$	−0.317348	+	0.549662i	−0.0317348	+	0.0549662i
$101$	−1.93610	−	3.35342i	−0.192649	−	0.333678i	0.753478	−	0.657473i	$-0.228375\pi$
$101$	−1.93610	−	3.35342i	−0.192649	−	0.333678i	−0.946127	+	0.323795i	$0.895041\pi$
$102$	0.979579	+	3.68234i	0.0969928	+	0.364606i
$103$	−12.1295	−	7.00299i	−1.19516	−	0.690025i	−0.235686	−	0.971829i	$-0.575734\pi$
$103$	−12.1295	−	7.00299i	−1.19516	−	0.690025i	−0.959472	+	0.281805i	$0.909067\pi$
$104$	−0.776166			−0.0761094
$105$	−3.70695	+	8.82779i	−0.361761	+	0.861504i
$106$	−6.56931			−0.638068
$107$	−9.48218	−	5.47454i	−0.916677	−	0.529244i	−0.0341038	−	0.999418i	$-0.510858\pi$
$107$	−9.48218	−	5.47454i	−0.916677	−	0.529244i	−0.882574	+	0.470174i	$0.844191\pi$
$108$	−5.01176	−	1.37195i	−0.482257	−	0.132016i
$109$	−7.83623	−	13.5727i	−0.750575	−	1.30003i	−0.947544	−	0.319624i	$-0.896443\pi$
$109$	−7.83623	−	13.5727i	−0.750575	−	1.30003i	0.196970	−	0.980410i	$-0.436890\pi$
$110$	−5.25024	+	9.09368i	−0.500591	+	0.867049i
$111$	−3.40469	+	12.6156i	−0.323159	+	1.19742i
$112$	1.61705	−	2.09408i	0.152796	−	0.197872i
$113$			5.01441i			0.471716i	0.971787	+	0.235858i	$0.0757901\pi$
$113$			5.01441i			0.471716i	−0.971787	+	0.235858i	$0.924210\pi$
$114$	−10.0114	−	10.0475i	−0.937649	−	0.941031i
$115$	1.80941	−	1.04467i	0.168729	−	0.0974156i
$116$	−7.99919	+	4.61833i	−0.742706	+	0.428801i
$117$	−1.15698	−	2.02072i	−0.106963	−	0.186815i
$118$			3.65872i			0.336813i
$119$	−2.21095	−	5.38423i	−0.202677	−	0.493571i
$120$	−3.49383	−	0.942912i	−0.318941	−	0.0860757i
$121$	7.12914	−	12.3480i	0.648103	−	1.12255i
$122$	1.68101	+	2.91159i	0.152191	+	0.263603i
$123$	11.1377	−	2.96287i	1.00425	−	0.267153i
$124$	5.63719	+	3.25463i	0.506235	+	0.292275i
$125$	−11.7727			−1.05299
$126$	7.86228	+	1.08840i	0.700427	+	0.0969626i
$127$	13.1325			1.16532			0.582661	−	0.812715i	$-0.302011\pi$
$127$	13.1325			1.16532			0.582661	+	0.812715i	$0.302011\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−4.32190	+	1.14972i	−0.380522	+	0.101227i
$130$	−0.810834	−	1.40441i	−0.0711149	−	0.123175i
$131$	−3.33134	+	5.77005i	−0.291060	+	0.504132i	−0.974061	−	0.226287i	$-0.927341\pi$
$131$	−3.33134	+	5.77005i	−0.291060	+	0.504132i	0.683000	+	0.730418i	$0.260675\pi$
$132$	8.40419	+	2.26812i	0.731491	+	0.197414i
$133$	17.1484	+	13.2420i	1.48695	+	1.14822i
$134$		−	13.1953i		−	1.13990i
$135$	−2.75319	−	10.5016i	−0.236957	−	0.903832i
$136$	1.90520	−	1.09997i	0.163370	−	0.0943217i
$137$	7.97240	−	4.60287i	0.681128	−	0.393250i	−0.119152	−	0.992876i	$-0.538018\pi$
$137$	7.97240	−	4.60287i	0.681128	−	0.393250i	0.800280	+	0.599626i	$0.204684\pi$
$138$	−1.22254	−	1.22695i	−0.104069	−	0.104445i
$139$		−	1.40797i		−	0.119422i	−0.998216	−	0.0597112i	$-0.980982\pi$
$139$		−	1.40797i		−	0.119422i	0.998216	−	0.0597112i	$-0.0190180\pi$
$140$	5.47833	+	0.738293i	0.463003	+	0.0623971i
$141$	−3.45013	+	12.7840i	−0.290554	+	1.07661i
$142$	−1.77718	+	3.07816i	−0.149138	+	0.258314i
$143$	1.95041	+	3.37821i	0.163102	+	0.282500i
$144$	−0.0108008	+	2.99998i	−0.000900069	+	0.249998i
$145$	−16.7129	−	9.64922i	−1.38793	−	0.801324i
$146$	−2.96905			−0.245721
$147$	−12.1240	−	0.0960092i	−0.999969	−	0.00791870i
$148$	7.54420			0.620129
$149$	6.71786	+	3.87856i	0.550349	+	0.317744i	0.749263	−	0.662273i	$-0.230408\pi$
$149$	6.71786	+	3.87856i	0.550349	+	0.317744i	−0.198914	+	0.980017i	$0.563741\pi$
$150$	0.282614	+	1.06238i	0.0230753	+	0.0867426i
$151$	7.37630	+	12.7761i	0.600275	+	1.03971i	0.992779	+	0.119957i	$0.0382755\pi$
$151$	7.37630	+	12.7761i	0.600275	+	1.03971i	−0.392504	+	0.919750i	$0.628391\pi$
$152$	−4.09449	+	7.09187i	−0.332107	+	0.575227i
$153$	5.70370	+	3.32047i	0.461117	+	0.268444i
$154$	−13.1778	−	1.77592i	−1.06190	−	0.143108i
$155$			13.6000i			1.09238i
$156$	−0.952315	+	0.948893i	−0.0762462	+	0.0759722i
$157$	−9.35198	+	5.39937i	−0.746369	+	0.430916i	−0.824381	−	0.566036i	$-0.808476\pi$
$157$	−9.35198	+	5.39937i	−0.746369	+	0.430916i	0.0780113	+	0.996952i	$0.475143\pi$
$158$	−3.41189	+	1.96986i	−0.271436	+	0.156713i
$159$	−8.06020	+	8.03123i	−0.639215	+	0.636918i
$160$			2.08933i			0.165176i
$161$	2.09408	+	1.61705i	0.165036	+	0.127441i
$162$	−7.82643	+	4.44376i	−0.614902	+	0.349135i
$163$	−0.378425	+	0.655451i	−0.0296405	+	0.0513389i	−0.880465	−	0.474111i	$-0.842770\pi$
$163$	−0.378425	+	0.655451i	−0.0296405	+	0.0513389i	0.850825	+	0.525450i	$0.176103\pi$
$164$	−3.32700	−	5.76254i	−0.259795	−	0.449979i
$165$	4.67560	+	17.5761i	0.363995	+	1.36830i
$166$	−14.6609	−	8.46449i	−1.13791	−	0.656972i
$167$	13.3108			1.03002			0.515009	−	0.857185i	$-0.327789\pi$
$167$	13.3108			1.03002			0.515009	+	0.857185i	$0.327789\pi$
$168$	−0.576061	−	4.54622i	−0.0444441	−	0.350749i
$169$	12.3976			0.953659
$170$	3.98060	+	2.29820i	0.305298	+	0.176264i
$171$	−24.5668	−	0.0884479i	−1.87867	−	0.00676378i
$172$	1.29102	+	2.23611i	0.0984391	+	0.170501i
$173$	0.750518	−	1.29994i	0.0570608	−	0.0988323i	−0.836084	−	0.548601i	$-0.815160\pi$
$173$	0.750518	−	1.29994i	0.0570608	−	0.0988323i	0.893145	+	0.449769i	$0.148494\pi$
$174$	−4.16849	+	15.4458i	−0.316013	+	1.17094i
$175$	−0.637870	−	1.55338i	−0.0482184	−	0.117424i
$176$		−	5.02576i		−	0.378831i
$177$	4.47293	+	4.48906i	0.336206	+	0.337419i
$178$	2.72434	−	1.57290i	0.204198	−	0.117894i
$179$	1.70253	−	0.982958i	0.127253	−	0.0734697i	−0.435022	−	0.900420i	$-0.643259\pi$
$179$	1.70253	−	0.982958i	0.127253	−	0.0734697i	0.562275	+	0.826950i	$0.309926\pi$
$180$	−5.43949	+	3.11443i	−0.405436	+	0.232136i
$181$			7.15346i			0.531713i	0.964013	+	0.265856i	$0.0856547\pi$
$181$			7.15346i			0.531713i	−0.964013	+	0.265856i	$0.914345\pi$
$182$	1.25510	−	1.62535i	0.0930339	−	0.120479i
$183$	5.62204	+	1.51727i	0.415593	+	0.112160i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	7.88117	+	13.6506i	0.579435	+	1.00361i
$186$	10.8955	−	2.89842i	0.798893	−	0.212522i
$187$	−9.57510	−	5.52819i	−0.700201	−	0.404261i
$188$	7.64490			0.557562
$189$	10.9772	−	8.27652i	0.798475	−	0.602028i
$190$	−17.1095			−1.24125
$191$	3.40589	+	1.96639i	0.246442	+	0.142283i	0.618134	−	0.786073i	$-0.287889\pi$
$191$	3.40589	+	1.96639i	0.246442	+	0.142283i	−0.371692	+	0.928356i	$0.621222\pi$
$192$	1.67384	−	0.445275i	0.120799	−	0.0321350i
$193$	−0.159806	−	0.276792i	−0.0115031	−	0.0199239i	0.860217	−	0.509929i	$-0.170328\pi$
$193$	−0.159806	−	0.276792i	−0.0115031	−	0.0199239i	−0.871720	+	0.490005i	$0.836995\pi$
$194$	−7.83141	+	13.5644i	−0.562263	+	0.973868i
$195$	−2.71179	−	0.731857i	−0.194195	−	0.0524094i
$196$	1.77033	+	6.77244i	0.126452	+	0.483746i
$197$			11.2889i			0.804302i	0.915573	+	0.402151i	$0.131737\pi$
$197$			11.2889i			0.804302i	−0.915573	+	0.402151i	$0.868263\pi$
$198$	13.0844	−	7.49158i	0.929865	−	0.532404i
$199$	−19.1608	+	11.0625i	−1.35827	+	0.784198i	−0.989391	−	0.145279i	$-0.953592\pi$
$199$	−19.1608	+	11.0625i	−1.35827	+	0.784198i	−0.368880	+	0.929477i	$0.620259\pi$
$200$	0.549662	−	0.317348i	0.0388670	−	0.0224399i
$201$	−16.1317	−	16.1899i	−1.13784	−	1.14195i
$202$			3.87220i			0.272447i
$203$	3.26390	−	24.2190i	0.229081	−	1.69984i
$204$	0.992830	−	3.67879i	0.0695120	−	0.257567i
$205$	6.95121	−	12.0399i	0.485494	−	0.840900i
$206$	7.00299	+	12.1295i	0.487921	+	0.845104i
$207$	−2.99998	−	0.0108008i	−0.208513	−	0.000750709i
$208$	0.672180	+	0.388083i	0.0466073	+	0.0269087i
$209$	41.1559			2.84681
$210$	7.62421	−	5.79162i	0.526120	−	0.399660i
$211$	−15.3139			−1.05425			−0.527127	−	0.849786i	$-0.676731\pi$
$211$	−15.3139			−1.05425			−0.527127	+	0.849786i	$0.676731\pi$
$212$	5.68919	+	3.28466i	0.390735	+	0.225591i
$213$	1.58267	+	5.94942i	0.108443	+	0.407647i
$214$	5.47454	+	9.48218i	0.374232	+	0.648189i
$215$	−2.69736	+	4.67197i	−0.183958	+	0.318625i
$216$	3.65434	+	3.69402i	0.248646	+	0.251346i
$217$	−15.9311	+	6.54183i	−1.08147	+	0.444088i
$218$			15.6725i			1.06147i
$219$	−3.64287	+	3.62978i	−0.246163	+	0.245278i
$220$	9.09368	−	5.25024i	0.613096	−	0.353971i
$221$	1.47876	−	0.853760i	0.0994719	−	0.0574301i
$222$	9.25634	−	9.22307i	0.621245	−	0.619012i
$223$			14.7813i			0.989832i	0.868941	+	0.494916i	$0.164801\pi$
$223$			14.7813i			0.989832i	−0.868941	+	0.494916i	$0.835199\pi$
$224$	−2.44744	+	1.00500i	−0.163527	+	0.0671495i
$225$	1.64555	+	0.957973i	0.109703	+	0.0638649i
$226$	2.50721	−	4.34261i	0.166777	−	0.288866i
$227$	−1.54930	−	2.68347i	−0.102831	−	0.178108i	0.810019	−	0.586403i	$-0.199457\pi$
$227$	−1.54930	−	2.68347i	−0.102831	−	0.178108i	−0.912850	+	0.408296i	$0.866123\pi$
$228$	3.64635	+	13.7070i	0.241486	+	0.907770i
$229$	4.05805	+	2.34292i	0.268163	+	0.154824i	0.628053	−	0.778171i	$-0.283852\pi$
$229$	4.05805	+	2.34292i	0.268163	+	0.154824i	−0.359889	+	0.932995i	$0.617186\pi$
$230$	−2.08933			−0.137766
$231$	−18.3396	+	13.9314i	−1.20666	+	0.916618i
$232$	9.23666			0.606417
$233$	−13.7534	−	7.94052i	−0.901015	−	0.520201i	−0.0234854	−	0.999724i	$-0.507476\pi$
$233$	−13.7534	−	7.94052i	−0.901015	−	0.520201i	−0.877529	+	0.479523i	$0.840810\pi$
$234$	−0.00838324	+	2.32848i	−0.000548029	+	0.152218i
$235$	7.98636	+	13.8328i	0.520973	+	0.902352i
$236$	1.82936	−	3.16855i	0.119081	−	0.206255i
$237$	−1.77799	+	6.58808i	−0.115493	+	0.427942i
$238$	−0.777378	+	5.76835i	−0.0503899	+	0.373907i
$239$		−	15.2972i		−	0.989495i	−0.869037	−	0.494748i	$-0.835260\pi$
$239$		−	15.2972i		−	0.989495i	0.869037	−	0.494748i	$-0.164740\pi$
$240$	2.55429	+	2.56350i	0.164879	+	0.165473i
$241$	−18.0665	+	10.4307i	−1.16376	+	0.671899i	−0.952203	−	0.305465i	$-0.901188\pi$
$241$	−18.0665	+	10.4307i	−1.16376	+	0.671899i	−0.211561	+	0.977365i	$0.567855\pi$
$242$	−12.3480	+	7.12914i	−0.793761	+	0.458278i
$243$	−4.16995	+	15.0204i	−0.267502	+	0.963557i
$244$		−	3.36201i		−	0.215231i
$245$	−10.4047	+	10.2782i	−0.664735	+	0.656650i
$246$	−11.1270	−	3.00295i	−0.709431	−	0.191461i
$247$	−3.17801	+	5.50447i	−0.202212	+	0.350241i
$248$	−3.25463	−	5.63719i	−0.206669	−	0.357962i
$249$	−28.3363	+	7.53805i	−1.79574	+	0.477705i
$250$	10.1955	+	5.88637i	0.644820	+	0.372287i
$251$	−19.2730			−1.21650			−0.608249	−	0.793746i	$-0.708128\pi$
$251$	−19.2730			−1.21650			−0.608249	+	0.793746i	$0.708128\pi$
$252$	−6.26473	−	4.87372i	−0.394641	−	0.307016i
$253$	5.02576			0.315967
$254$	−11.3731	−	6.56626i	−0.713611	−	0.412004i
$255$	7.69363	−	2.04667i	0.481794	−	0.128167i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.85541	−	17.0701i	0.614763	−	1.06480i	−0.375662	−	0.926757i	$-0.622585\pi$
$257$	9.85541	−	17.0701i	0.614763	−	1.06480i	0.990426	−	0.138045i	$-0.0440819\pi$
$258$	4.31773	+	1.16527i	0.268810	+	0.0725464i
$259$	−12.1993	+	15.7981i	−0.758029	+	0.981649i
$260$			1.62167i			0.100572i
$261$	13.7685	+	24.0473i	0.852249	+	1.48849i
$262$	5.77005	−	3.33134i	0.356475	−	0.205811i
$263$	−19.1716	+	11.0687i	−1.18217	+	0.682528i	−0.956516	−	0.291679i	$-0.905786\pi$
$263$	−19.1716	+	11.0687i	−1.18217	+	0.682528i	−0.225657	+	0.974207i	$0.572453\pi$
$264$	−6.14418	−	6.16635i	−0.378148	−	0.379512i
$265$			13.7255i			0.843149i
$266$	−8.22995	−	20.0421i	−0.504611	−	1.22886i
$267$	1.41970	−	5.26048i	0.0868840	−	0.321936i
$268$	−6.59763	+	11.4274i	−0.403014	+	0.698041i
$269$	−2.93315	−	5.08036i	−0.178837	−	0.309755i	0.762645	−	0.646817i	$-0.223900\pi$
$269$	−2.93315	−	5.08036i	−0.178837	−	0.309755i	−0.941483	+	0.337062i	$0.890567\pi$
$270$	−2.86646	+	10.4712i	−0.174447	+	0.637259i
$271$	0.820851	+	0.473918i	0.0498631	+	0.0287885i	0.524724	−	0.851272i	$-0.324168\pi$
$271$	0.820851	+	0.473918i	0.0498631	+	0.0287885i	−0.474861	+	0.880061i	$0.657502\pi$
$272$	−2.19994			−0.133391
$273$	−0.447119	−	3.52863i	−0.0270609	−	0.213562i
$274$	−9.20574			−0.556139
$275$	−2.76247	−	1.59491i	−0.166583	−	0.0961769i
$276$	0.445275	+	1.67384i	0.0268024	+	0.100753i
$277$	5.83452	+	10.1057i	0.350562	+	0.607192i	0.986348	−	0.164674i	$-0.0526571\pi$
$277$	5.83452	+	10.1057i	0.350562	+	0.607192i	−0.635786	+	0.771866i	$0.719324\pi$
$278$	−0.703984	+	1.21934i	−0.0422222	+	0.0731310i
$279$	9.82473	−	16.8763i	0.588191	−	1.01036i
$280$	−4.37522	−	3.37854i	−0.261470	−	0.201907i
$281$		−	23.1479i		−	1.38089i	−0.723385	−	0.690445i	$-0.757415\pi$
$281$		−	23.1479i		−	1.38089i	0.723385	−	0.690445i	$-0.242585\pi$
$282$	9.37989	−	9.34618i	0.558564	−	0.556557i
$283$	27.4995	−	15.8768i	1.63467	−	0.943780i	0.652050	−	0.758176i	$-0.273909\pi$
$283$	27.4995	−	15.8768i	1.63467	−	0.943780i	0.982625	−	0.185604i	$-0.0594240\pi$
$284$	3.07816	−	1.77718i	0.182655	−	0.105456i
$285$	−20.9925	+	20.9170i	−1.24349	+	1.23902i
$286$		−	3.90083i		−	0.230661i
$287$	17.4471	+	2.35128i	1.02987	+	0.138792i
$288$	1.50934	−	2.59266i	0.0889390	−	0.152774i
$289$	6.08013	−	10.5311i	0.357655	−	0.619476i
$290$	9.64922	+	16.7129i	0.566622	+	0.981418i
$291$	6.97427	+	26.2170i	0.408839	+	1.53687i
$292$	2.57128	+	1.48453i	0.150473	+	0.0868753i
$293$	−24.6678			−1.44111			−0.720554	−	0.693399i	$-0.756112\pi$
$293$	−24.6678			−1.44111			−0.720554	+	0.693399i	$0.756112\pi$
$294$	10.4517	+	6.14513i	0.609554	+	0.358392i
$295$	7.64429			0.445068
$296$	−6.53347	−	3.77210i	−0.379750	−	0.219249i
$297$	6.89509	−	25.1879i	0.400094	−	1.46155i
$298$	−3.87856	−	6.71786i	−0.224679	−	0.389155i
$299$	−0.388083	+	0.672180i	−0.0224434	+	0.0388732i
$300$	0.286437	−	1.06135i	0.0165375	−	0.0612772i
$301$	−6.77021	−	0.912395i	−0.390229	−	0.0525896i
$302$		−	14.7526i		−	0.848917i
$303$	4.73391	+	4.75098i	0.271956	+	0.272937i
$304$	7.09187	−	4.09449i	0.406747	−	0.234835i
$305$	6.08327	−	3.51218i	0.348327	−	0.201107i
$306$	−3.27931	−	5.72746i	−0.187466	−	0.327417i
$307$		−	27.3757i		−	1.56241i	−0.624272	−	0.781207i	$-0.714604\pi$
$307$		−	27.3757i		−	1.56241i	0.624272	−	0.781207i	$-0.285396\pi$
$308$	10.5243	+	8.12688i	0.599680	+	0.463072i
$309$	23.4211	+	6.32088i	1.33238	+	0.359582i
$310$	6.80001	−	11.7780i	0.386215	−	0.668943i
$311$	1.66052	+	2.87611i	0.0941595	+	0.163089i	0.909258	−	0.416234i	$-0.136650\pi$
$311$	1.66052	+	2.87611i	0.0941595	+	0.163089i	−0.815098	+	0.579323i	$0.803317\pi$
$312$	1.29918	−	0.345608i	0.0735513	−	0.0195662i
$313$	17.4739	+	10.0886i	0.987682	+	0.570239i	0.904581	−	0.426302i	$-0.140184\pi$
$313$	17.4739	+	10.0886i	0.987682	+	0.570239i	0.0831016	+	0.996541i	$0.473517\pi$
$314$	10.7987			0.609408
$315$	2.27403	−	16.4269i	0.128127	−	0.925551i
$316$	3.93972			0.221626
$317$	−21.4200	−	12.3669i	−1.20307	−	0.694592i	−0.241833	−	0.970318i	$-0.577749\pi$
$317$	−21.4200	−	12.3669i	−1.20307	−	0.694592i	−0.961236	+	0.275726i	$0.911082\pi$
$318$	10.9960	−	2.92515i	0.616623	−	0.164034i
$319$	−23.2106	−	40.2020i	−1.29955	−	2.25088i
$320$	1.04467	−	1.80941i	0.0583986	−	0.101149i
$321$	18.3093	+	4.94131i	1.02193	+	0.275797i
$322$	−1.00500	−	2.44744i	−0.0560066	−	0.136391i
$323$		−	18.0153i		−	1.00240i
$324$	8.99977	+	0.0648045i	0.499987	+	0.00360025i
$325$	0.426629	−	0.246314i	0.0236651	−	0.0136631i
$326$	0.655451	−	0.378425i	0.0363021	−	0.0209590i
$327$	19.1602	+	19.2293i	1.05956	+	1.06338i
$328$			6.65401i			0.367406i
$329$	−12.3622	+	16.0090i	−0.681547	+	0.882606i
$330$	4.73885	−	17.5591i	0.260865	−	0.966599i
$331$	10.4974	−	18.1821i	0.576992	−	0.999379i	−0.418830	−	0.908065i	$-0.637560\pi$
$331$	10.4974	−	18.1821i	0.576992	−	0.999379i	0.995822	−	0.0913148i	$-0.0291070\pi$
$332$	8.46449	+	14.6609i	0.464549	+	0.804623i
$333$	0.0814836	−	22.6325i	0.00446527	−	1.24025i
$334$	−11.5275	−	6.65538i	−0.630755	−	0.364166i
$335$	−27.5692			−1.50627
$336$	−1.77423	+	4.22518i	−0.0967921	+	0.230502i
$337$	3.40543			0.185506			0.0927528	−	0.995689i	$-0.470433\pi$
$337$	3.40543			0.185506			0.0927528	+	0.995689i	$0.470433\pi$
$338$	−10.7366	−	6.19878i	−0.583994	−	0.337169i
$339$	−2.23279	−	8.39331i	−0.121269	−	0.455862i
$340$	−2.29820	−	3.98060i	−0.124638	−	0.215879i
$341$	−16.3570	+	28.3312i	−0.885782	+	1.53422i
$342$	21.2313	+	12.3600i	1.14805	+	0.668352i
$343$	−17.0447	−	7.24414i	−0.920328	−	0.391147i
$344$		−	2.58203i		−	0.139214i
$345$	−2.56350	+	2.55429i	−0.138014	+	0.137518i
$346$	−1.29994	+	0.750518i	−0.0698850	+	0.0403481i
$347$	22.9738	−	13.2639i	1.23330	−	0.712045i	0.265582	−	0.964088i	$-0.414436\pi$
$347$	22.9738	−	13.2639i	1.23330	−	0.712045i	0.967716	+	0.252043i	$0.0811025\pi$
$348$	11.3329	−	11.2922i	0.607507	−	0.605324i
$349$			6.36902i			0.340926i	0.985364	+	0.170463i	$0.0545263\pi$
$349$			6.36902i			0.340926i	−0.985364	+	0.170463i	$0.945474\pi$
$350$	−0.224278	+	1.66420i	−0.0119882	+	0.0889553i
$351$	2.83637	+	2.86718i	0.151394	+	0.153039i
$352$	−2.51288	+	4.35244i	−0.133937	+	0.231986i
$353$	−14.7160	−	25.4888i	−0.783253	−	1.35663i	−0.930037	−	0.367466i	$-0.880225\pi$
$353$	−14.7160	−	25.4888i	−0.783253	−	1.35663i	0.146784	−	0.989169i	$-0.453108\pi$
$354$	−1.62914	−	6.12411i	−0.0865878	−	0.325493i
$355$	6.43131	+	3.71312i	0.341338	+	0.197072i
$356$	−3.14580			−0.166727
$357$	6.09823	+	8.02784i	0.322752	+	0.424878i
$358$	−1.96592			−0.103902
$359$	−1.80170	−	1.04021i	−0.0950903	−	0.0549004i	0.451701	−	0.892170i	$-0.350817\pi$
$359$	−1.80170	−	1.04021i	−0.0950903	−	0.0549004i	−0.546791	+	0.837269i	$0.684151\pi$
$360$	6.26795	+	0.0225665i	0.330350	+	0.00118936i
$361$	24.0298	+	41.6208i	1.26472	+	2.19057i
$362$	3.57673	−	6.19508i	0.187989	−	0.325606i
$363$	−6.43474	+	23.8430i	−0.337736	+	1.25143i
$364$	−1.89962	+	0.780049i	−0.0995672	+	0.0408857i
$365$			6.20333i			0.324697i
$366$	−4.11019	−	4.12501i	−0.214843	−	0.215618i
$367$	30.5338	−	17.6287i	1.59385	−	0.920212i	0.601216	−	0.799086i	$-0.294683\pi$
$367$	30.5338	−	17.6287i	1.59385	−	0.920212i	0.992637	−	0.121126i	$-0.0386504\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	−17.3234	+	9.91871i	−0.901822	+	0.516347i
$370$		−	15.7623i		−	0.819445i
$371$	−16.0780	+	6.60217i	−0.834728	+	0.342768i
$372$	−10.8849	−	2.93762i	−0.564358	−	0.152309i
$373$	−2.37163	+	4.10778i	−0.122798	+	0.212693i	−0.920870	−	0.389870i	$-0.872520\pi$
$373$	−2.37163	+	4.10778i	−0.122798	+	0.212693i	0.798072	+	0.602562i	$0.205853\pi$
$374$	5.52819	+	9.57510i	0.285856	+	0.495117i
$375$	19.7057	−	5.24211i	1.01760	−	0.270702i
$376$	−6.62068	−	3.82245i	−0.341435	−	0.197128i
$377$	7.16919			0.369232
$378$	−13.6448	+	1.67907i	−0.701813	+	0.0863620i
$379$	−33.7870			−1.73552			−0.867761	−	0.496982i	$-0.834441\pi$
$379$	−33.7870			−1.73552			−0.867761	+	0.496982i	$0.834441\pi$
$380$	14.8173	+	8.55476i	0.760110	+	0.438850i
$381$	−21.9817	+	5.84759i	−1.12616	+	0.299581i
$382$	−1.96639	−	3.40589i	−0.100609	−	0.174261i
$383$	8.10467	−	14.0377i	0.414129	−	0.717293i	−0.581207	−	0.813755i	$-0.697419\pi$
$383$	8.10467	−	14.0377i	0.414129	−	0.717293i	0.995337	+	0.0964626i	$0.0307528\pi$
$384$	−1.67222	−	0.451299i	−0.0853353	−	0.0230302i
$385$	−3.71048	+	27.5328i	−0.189104	+	1.40320i
$386$			0.319612i			0.0162678i
$387$	6.72222	−	3.84887i	0.341710	−	0.195649i
$388$	13.5644	−	7.83141i	0.688628	−	0.397580i
$389$	12.1498	−	7.01470i	0.616020	−	0.355659i	−0.159298	−	0.987231i	$-0.550923\pi$
$389$	12.1498	−	7.01470i	0.616020	−	0.355659i	0.775318	+	0.631571i	$0.217590\pi$
$390$	1.98255	+	1.98970i	0.100390	+	0.100752i
$391$		−	2.19994i		−	0.111256i
$392$	1.85307	−	6.75027i	0.0935942	−	0.340940i
$393$	3.00686	−	11.1415i	0.151676	−	0.562014i
$394$	5.64446	−	9.77648i	0.284364	−	0.492532i
$395$	4.11569	+	7.12858i	0.207083	+	0.358678i
$396$	−15.0772	−	0.0542824i	−0.757657	−	0.00272779i
$397$	14.9426	+	8.62712i	0.749948	+	0.432983i	0.825675	−	0.564146i	$-0.190794\pi$
$397$	14.9426	+	8.62712i	0.749948	+	0.432983i	−0.0757269	+	0.997129i	$0.524128\pi$
$398$	22.1250			1.10902
$399$	−34.5999	−	14.5291i	−1.73216	−	0.727367i
$400$	−0.634695			−0.0317348
$401$	3.47413	+	2.00579i	0.173490	+	0.100164i	0.584230	−	0.811588i	$-0.301397\pi$
$401$	3.47413	+	2.00579i	0.173490	+	0.100164i	−0.410741	+	0.911752i	$0.634730\pi$
$402$	5.87552	+	22.0867i	0.293044	+	1.10158i
$403$	−2.52614	−	4.37540i	−0.125836	−	0.217954i
$404$	1.93610	−	3.35342i	0.0963245	−	0.166839i
$405$	9.28449	+	16.3520i	0.461350	+	0.812538i
$406$	−14.9361	+	19.3423i	−0.741266	+	0.959942i
$407$			37.9154i			1.87939i
$408$	−2.69921	+	2.68951i	−0.133631	+	0.133151i
$409$	7.69418	−	4.44224i	0.380453	−	0.219655i	−0.297562	−	0.954702i	$-0.596174\pi$
$409$	7.69418	−	4.44224i	0.380453	−	0.219655i	0.678015	+	0.735048i	$0.262840\pi$
$410$	−12.0399	+	6.95121i	−0.594606	+	0.343296i
$411$	−11.2950	+	11.2544i	−0.557139	+	0.555137i
$412$		−	14.0060i		−	0.690025i
$413$	3.67703	+	8.95452i	0.180935	+	0.440623i
$414$	2.59266	+	1.50934i	0.127422	+	0.0741802i
$415$	−17.6851	+	30.6315i	−0.868128	+	1.50364i
$416$	−0.388083	−	0.672180i	−0.0190273	−	0.0329563i
$417$	0.626934	+	2.35671i	0.0307011	+	0.115409i
$418$	−35.6421	−	20.5780i	−1.74331	−	1.00650i
$419$	−26.1705			−1.27851			−0.639257	−	0.768994i	$-0.720758\pi$
$419$	−26.1705			−1.27851			−0.639257	+	0.768994i	$0.720758\pi$
$420$	−9.49857	+	1.20358i	−0.463483	+	0.0587288i
$421$	8.31175			0.405090			0.202545	−	0.979273i	$-0.435079\pi$
$421$	8.31175			0.405090			0.202545	+	0.979273i	$0.435079\pi$
$422$	13.2623	+	7.65697i	0.645597	+	0.372735i
$423$	0.0825713	−	22.9346i	0.00401475	−	1.11512i
$424$	−3.28466	−	5.68919i	−0.159517	−	0.276291i
$425$	−0.698146	+	1.20922i	−0.0338650	+	0.0586560i
$426$	1.60408	−	5.94368i	0.0777178	−	0.287972i
$427$	7.04032	+	5.43653i	0.340705	+	0.263092i
$428$		−	10.9491i		−	0.529244i
$429$	−4.76891	−	4.78611i	−0.230245	−	0.231076i
$430$	4.67197	−	2.69736i	0.225302	−	0.130078i
$431$	−7.96036	+	4.59592i	−0.383437	+	0.221377i	−0.679313	−	0.733849i	$-0.737722\pi$
$431$	−7.96036	+	4.59592i	−0.383437	+	0.221377i	0.295876	+	0.955226i	$0.404389\pi$
$432$	−1.31774	−	5.02629i	−0.0633997	−	0.241827i
$433$		−	14.6047i		−	0.701859i	−0.936402	−	0.350929i	$-0.885866\pi$
$433$		−	14.6047i		−	0.701859i	0.936402	−	0.350929i	$-0.114134\pi$
$434$	17.0676	+	2.30014i	0.819272	+	0.110410i
$435$	32.2713	+	8.70937i	1.54729	+	0.417582i
$436$	7.83623	−	13.5727i	0.375287	−	0.650017i
$437$	4.09449	+	7.09187i	0.195866	+	0.339250i
$438$	4.96971	−	1.32205i	0.237462	−	0.0631698i
$439$	−5.12978	−	2.96168i	−0.244831	−	0.141353i	0.372564	−	0.928006i	$-0.378479\pi$
$439$	−5.12978	−	2.96168i	−0.244831	−	0.141353i	−0.617395	+	0.786653i	$0.711812\pi$
$440$	−10.5005			−0.500591
$441$	20.3363	−	5.23780i	0.968396	−	0.249419i
$442$	−1.70752			−0.0812184
$443$	−23.9847	−	13.8476i	−1.13955	−	0.657917i	−0.193228	−	0.981154i	$-0.561896\pi$
$443$	−23.9847	−	13.8476i	−1.13955	−	0.657917i	−0.946318	+	0.323236i	$0.895229\pi$
$444$	−12.6278	+	3.35925i	−0.599287	+	0.159423i
$445$	−3.28631	−	5.69206i	−0.155786	−	0.269829i
$446$	7.39067	−	12.8010i	0.349958	−	0.606146i
$447$	−12.9716	−	3.50078i	−0.613537	−	0.165581i
$448$	2.62205	+	0.353363i	0.123880	+	0.0166948i
$449$		−	28.7884i		−	1.35861i	−0.733857	−	0.679304i	$-0.762282\pi$
$449$		−	28.7884i		−	1.35861i	0.733857	−	0.679304i	$-0.237718\pi$
$450$	−0.946100	−	1.65240i	−0.0445996	−	0.0778950i
$451$	28.9611	−	16.7207i	1.36373	−	0.787348i
$452$	−4.34261	+	2.50721i	−0.204259	+	0.117929i
$453$	−18.0356	−	18.1007i	−0.847387	−	0.850444i
$454$			3.09860i			0.145424i
$455$	−3.39590	−	2.62231i	−0.159202	−	0.122936i
$456$	3.69568	−	13.6938i	0.173066	−	0.641272i
$457$	−3.36144	+	5.82218i	−0.157241	+	0.272350i	−0.933873	−	0.357605i	$-0.883593\pi$
$457$	−3.36144	+	5.82218i	−0.157241	+	0.272350i	0.776632	+	0.629955i	$0.216927\pi$
$458$	−2.34292	−	4.05805i	−0.109477	−	0.189620i
$459$	−11.0256	−	3.01821i	−0.514630	−	0.140878i
$460$	1.80941	+	1.04467i	0.0843644	+	0.0487078i
$461$	15.7725			0.734600			0.367300	−	0.930103i	$-0.380282\pi$
$461$	15.7725			0.734600			0.367300	+	0.930103i	$0.380282\pi$
$462$	22.8482	−	2.89514i	1.06300	−	0.134694i
$463$	−23.1541			−1.07606			−0.538031	−	0.842925i	$-0.680832\pi$
$463$	−23.1541			−1.07606			−0.538031	+	0.842925i	$0.680832\pi$
$464$	−7.99919	−	4.61833i	−0.371353	−	0.214401i
$465$	−6.05575	−	22.7642i	−0.280829	−	1.05567i
$466$	7.94052	+	13.7534i	0.367838	+	0.637114i
$467$	16.1736	−	28.0136i	0.748427	−	1.29631i	−0.200149	−	0.979765i	$-0.564143\pi$
$467$	16.1736	−	28.0136i	0.748427	−	1.29631i	0.948576	−	0.316548i	$-0.102524\pi$
$468$	1.17150	−	2.01233i	0.0541527	−	0.0930202i
$469$	−13.2613	−	32.2946i	−0.612348	−	1.49123i
$470$		−	15.9727i		−	0.736767i
$471$	13.2495	−	13.2019i	0.610504	−	0.608310i
$472$	−3.16855	+	1.82936i	−0.145844	+	0.0842032i
$473$	−11.2381	+	6.48834i	−0.516730	+	0.298334i
$474$	4.83383	−	4.81645i	0.222025	−	0.221227i
$475$		−	5.19751i		−	0.238478i
$476$	3.55740	−	4.60685i	0.163053	−	0.211155i
$477$	9.91535	−	17.0320i	0.453993	−	0.779841i
$478$	−7.64861	+	13.2478i	−0.349839	+	0.605940i
$479$	−0.542497	−	0.939632i	−0.0247873	−	0.0429329i	0.853366	−	0.521313i	$-0.174558\pi$
$479$	−0.542497	−	0.939632i	−0.0247873	−	0.0429329i	−0.878153	+	0.478380i	$0.841224\pi$
$480$	−0.930328	−	3.49720i	−0.0424635	−	0.159625i
$481$	−5.07106	−	2.92778i	−0.231220	−	0.133495i
$482$	20.8614			0.950209
$483$	−4.22518	−	1.77423i	−0.192252	−	0.0807302i
$484$	14.2583			0.648103
$485$	28.3405	+	16.3624i	1.28688	+	0.742979i
$486$	11.1215	−	10.9230i	0.504480	−	0.495479i
$487$	5.56954	+	9.64673i	0.252380	+	0.437135i	0.964181	−	0.265246i	$-0.0854533\pi$
$487$	5.56954	+	9.64673i	0.252380	+	0.437135i	−0.711801	+	0.702382i	$0.752120\pi$
$488$	−1.68101	+	2.91159i	−0.0760956	+	0.131801i
$489$	0.341565	−	1.26562i	0.0154461	−	0.0572334i
$490$	14.1499	−	3.69880i	0.639226	−	0.167095i
$491$			25.9875i			1.17280i	0.810021	+	0.586400i	$0.199455\pi$
$491$			25.9875i			1.17280i	−0.810021	+	0.586400i	$0.800545\pi$
$492$	8.13478	+	8.16412i	0.366744	+	0.368067i
$493$	−17.5977	+	10.1601i	−0.792562	+	0.457586i
$494$	5.50447	−	3.17801i	0.247658	−	0.142985i
$495$	−15.6524	−	27.3376i	−0.703523	−	1.22873i
$496$			6.50927i			0.292275i
$497$	−1.25598	+	9.31970i	−0.0563384	+	0.418046i
$498$	28.3090	+	7.64002i	1.26856	+	0.342358i
$499$	10.2914	−	17.8253i	0.460707	−	0.797968i	−0.538289	−	0.842760i	$-0.680929\pi$
$499$	10.2914	−	17.8253i	0.460707	−	0.797968i	0.998996	+	0.0447920i	$0.0142625\pi$
$500$	−5.88637	−	10.1955i	−0.263247	−	0.455956i
$501$	−22.2801	+	5.92696i	−0.995399	+	0.264797i
$502$	16.6909	+	9.63648i	0.744950	+	0.430097i
$503$	−22.9013			−1.02112			−0.510560	−	0.859842i	$-0.670562\pi$
$503$	−22.9013			−1.02112			−0.510560	+	0.859842i	$0.670562\pi$
$504$	2.98855	+	7.35313i	0.133121	+	0.327535i
$505$	8.09030			0.360014
$506$	−4.35244	−	2.51288i	−0.193489	−	0.111711i
$507$	−20.7515	+	5.52033i	−0.921607	+	0.245166i
$508$	6.56626	+	11.3731i	0.291331	+	0.504600i
$509$	−19.0516	+	32.9984i	−0.844449	+	1.46263i	0.0416498	+	0.999132i	$0.486739\pi$
$509$	−19.0516	+	32.9984i	−0.844449	+	1.46263i	−0.886099	+	0.463496i	$0.846595\pi$
$510$	−7.68621	−	2.07435i	−0.340351	−	0.0918538i
$511$	−7.26658	+	2.98391i	−0.321455	+	0.132000i
$512$			1.00000i			0.0441942i
$513$	41.1602	−	10.7909i	1.81727	−	0.476432i
$514$	−17.0701	+	9.85541i	−0.752928	+	0.434703i
$515$	25.3426	−	14.6316i	1.11673	−	0.644743i
$516$	−3.15663	−	3.16802i	−0.138963	−	0.139464i
$517$			38.4214i			1.68977i
$518$	18.4640	−	7.58194i	0.811261	−	0.333131i
$519$	−0.677416	+	2.51007i	−0.0297352	+	0.110180i
$520$	0.810834	−	1.40441i	0.0355574	−	0.0615873i
$521$	−9.58707	−	16.6053i	−0.420017	−	0.727491i	0.575923	−	0.817504i	$-0.304643\pi$
$521$	−9.58707	−	16.6053i	−0.420017	−	0.727491i	−0.995941	+	0.0900126i	$0.971309\pi$
$522$	0.0997636	−	27.7098i	0.00436653	−	1.21283i
$523$	−1.51628	−	0.875422i	−0.0663021	−	0.0382795i	0.466482	−	0.884530i	$-0.345521\pi$
$523$	−1.51628	−	0.875422i	−0.0663021	−	0.0382795i	−0.532785	+	0.846251i	$0.678854\pi$
$524$	−6.66268			−0.291060
$525$	1.75937	+	2.31608i	0.0767853	+	0.101082i
$526$	22.1375			0.965240
$527$	12.4015	+	7.16000i	0.540217	+	0.311895i
$528$	2.23785	+	8.41230i	0.0973898	+	0.366099i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	6.86273	−	11.8866i	0.298098	−	0.516321i
$531$	−9.48583	−	5.52227i	−0.411650	−	0.239646i
$532$	−2.89369	+	21.4719i	−0.125457	+	0.930926i
$533$			5.16462i			0.223704i
$534$	−3.85973	+	3.84586i	−0.167027	+	0.166427i
$535$	19.8114	−	11.4381i	0.856523	−	0.494514i
$536$	11.4274	−	6.59763i	0.493589	−	0.284974i
$537$	−2.41208	+	2.40341i	−0.104089	+	0.103715i
$538$			5.86630i			0.252914i
$539$	−34.0367	+	8.89725i	−1.46606	+	0.383232i
$540$	7.71804	−	7.63512i	0.332131	−	0.328563i
$541$	18.6580	−	32.3166i	0.802170	−	1.38940i	−0.116015	−	0.993248i	$-0.537012\pi$
$541$	18.6580	−	32.3166i	0.802170	−	1.38940i	0.918185	−	0.396152i	$-0.129655\pi$
$542$	−0.473918	−	0.820851i	−0.0203565	−	0.0352586i
$543$	−3.18526	−	11.9737i	−0.136693	−	0.513842i
$544$	1.90520	+	1.09997i	0.0816850	+	0.0471608i
$545$	32.7450			1.40264
$546$	−1.37710	+	3.27944i	−0.0589343	+	0.140347i
$547$	−11.2862			−0.482562			−0.241281	−	0.970455i	$-0.577568\pi$
$547$	−11.2862			−0.482562			−0.241281	+	0.970455i	$0.577568\pi$
$548$	7.97240	+	4.60287i	0.340564	+	0.196625i
$549$	−10.0860	−	0.0363125i	−0.430459	−	0.00154978i
$550$	1.59491	+	2.76247i	0.0680073	+	0.117792i
$551$	37.8195	−	65.5052i	1.61116	−	2.79062i
$552$	0.451299	−	1.67222i	0.0192085	−	0.0711745i
$553$	−6.37070	+	8.25007i	−0.270910	+	0.350829i
$554$		−	11.6690i		−	0.495770i
$555$	−19.2701	−	19.3396i	−0.817968	−	0.820919i
$556$	1.21934	−	0.703984i	0.0517114	−	0.0298556i
$557$	21.6225	−	12.4838i	0.916176	−	0.528955i	0.0337632	−	0.999430i	$-0.489251\pi$
$557$	21.6225	−	12.4838i	0.916176	−	0.528955i	0.882413	+	0.470475i	$0.155917\pi$
$558$	−16.9466	+	9.70295i	−0.717408	+	0.410759i
$559$		−	2.00409i		−	0.0847638i
$560$	2.09978	+	5.11352i	0.0887320	+	0.216085i
$561$	18.4887	+	4.98973i	0.780595	+	0.210667i
$562$	−11.5740	+	20.0467i	−0.488218	+	0.845619i
$563$	−3.78677	−	6.55887i	−0.159593	−	0.276424i	0.775129	−	0.631803i	$-0.217685\pi$
$563$	−3.78677	−	6.55887i	−0.159593	−	0.276424i	−0.934722	+	0.355380i	$0.884352\pi$
$564$	−12.7963	+	3.40409i	−0.538822	+	0.143338i
$565$	−9.07315	−	5.23839i	−0.381710	−	0.220381i
$566$	−31.7537			−1.33471
$567$	−14.6887	+	18.7414i	−0.616869	+	0.787066i
$568$	−3.55436			−0.149138
$569$	−23.5803	−	13.6141i	−0.988539	−	0.570733i	−0.0837016	−	0.996491i	$-0.526674\pi$
$569$	−23.5803	−	13.6141i	−0.988539	−	0.570733i	−0.904837	+	0.425758i	$0.860008\pi$
$570$	28.6385	−	7.61844i	1.19954	−	0.319101i
$571$	22.6047	+	39.1525i	0.945978	+	1.63848i	0.753780	+	0.657127i	$0.228228\pi$
$571$	22.6047	+	39.1525i	0.945978	+	1.63848i	0.192198	+	0.981356i	$0.438438\pi$
$572$	−1.95041	+	3.37821i	−0.0815509	+	0.141250i
$573$	−6.57650	−	1.77486i	−0.274737	−	0.0741459i
$574$	−13.9340	−	10.7598i	−0.581594	−	0.449107i
$575$		−	0.634695i		−	0.0264686i
$576$	−2.60346	+	1.49064i	−0.108477	+	0.0621099i
$577$	8.26393	−	4.77118i	0.344032	−	0.198627i	−0.318022	−	0.948083i	$-0.603019\pi$
$577$	8.26393	−	4.77118i	0.344032	−	0.198627i	0.662053	+	0.749457i	$0.269685\pi$
$578$	−10.5311	+	6.08013i	−0.438036	+	0.252900i
$579$	0.390738	+	0.392147i	0.0162385	+	0.0162971i
$580$		−	19.2984i		−	0.801324i
$581$	−44.3886	−	5.98208i	−1.84155	−	0.248178i
$582$	7.06861	−	26.1917i	0.293003	−	1.08568i
$583$	−16.5079	+	28.5925i	−0.683687	+	1.18418i
$584$	−1.48453	−	2.57128i	−0.0614301	−	0.106400i
$585$	4.86497	+	0.0175154i	0.201142	+	0.000724171i
$586$	21.3629	+	12.3339i	0.882495	+	0.509509i
$587$	10.2166			0.421686			0.210843	−	0.977520i	$-0.432379\pi$
$587$	10.2166			0.421686			0.210843	+	0.977520i	$0.432379\pi$
$588$	−5.97884	−	10.5477i	−0.246563	−	0.434979i
$589$	−53.3043			−2.19637
$590$	−6.62015	−	3.82214i	−0.272547	−	0.157355i
$591$	−5.02667	−	18.8958i	−0.206770	−	0.777269i
$592$	3.77210	+	6.53347i	0.155032	+	0.268524i
$593$	2.18233	−	3.77991i	0.0896177	−	0.155222i	−0.817732	−	0.575599i	$-0.804769\pi$
$593$	2.18233	−	3.77991i	0.0896177	−	0.155222i	0.907350	+	0.420377i	$0.138102\pi$
$594$	−18.5653	+	18.3658i	−0.761743	+	0.753559i
$595$	12.0520	+	1.62420i	0.494084	+	0.0665857i
$596$			7.75712i			0.317744i
$597$	27.1462	−	27.0486i	1.11102	−	1.10703i
$598$	0.672180	−	0.388083i	0.0274875	−	0.0158699i
$599$	33.5531	−	19.3719i	1.37094	−	0.791515i	0.379897	−	0.925029i	$-0.375959\pi$
$599$	33.5531	−	19.3719i	1.37094	−	0.791515i	0.991047	+	0.133514i	$0.0426260\pi$
$600$	−0.778738	+	0.775939i	−0.0317918	+	0.0316776i
$601$		−	0.397727i		−	0.0162236i	−0.999967	−	0.00811182i	$-0.997418\pi$
$601$		−	0.397727i		−	0.0162236i	0.999967	−	0.00811182i	$-0.00258210\pi$
$602$	5.40698	+	4.17526i	0.220372	+	0.170171i
$603$	34.2108	+	19.9162i	1.39317	+	0.811049i
$604$	−7.37630	+	12.7761i	−0.300137	+	0.519853i
$605$	14.8951	+	25.7991i	0.605573	+	1.04888i
$606$	−1.72419	−	6.48142i	−0.0700406	−	0.263290i
$607$	14.7326	+	8.50585i	0.597977	+	0.345242i	0.768245	−	0.640156i	$-0.221130\pi$
$607$	14.7326	+	8.50585i	0.597977	+	0.345242i	−0.170269	+	0.985398i	$0.554464\pi$
$608$	−8.18899			−0.332107
$609$	5.32088	+	41.9919i	0.215613	+	1.70160i
$610$	−7.02436			−0.284408
$611$	−5.13875	−	2.96686i	−0.207891	−	0.120026i
$612$	−0.0237612	+	6.59978i	−0.000960489	+	0.266780i
$613$	−21.6516	−	37.5016i	−0.874499	−	1.51468i	−0.857295	−	0.514825i	$-0.827857\pi$
$613$	−21.6516	−	37.5016i	−0.874499	−	1.51468i	−0.0172037	−	0.999852i	$-0.505476\pi$
$614$	−13.6879	+	23.7081i	−0.552397	+	0.956779i
$615$	−6.27415	+	23.2480i	−0.252998	+	0.937448i
$616$	−5.05090	−	12.3003i	−0.203507	−	0.495591i
$617$			14.1911i			0.571311i	0.958332	+	0.285656i	$0.0922114\pi$
$617$			14.1911i			0.571311i	−0.958332	+	0.285656i	$0.907789\pi$
$618$	−17.1228	−	17.1846i	−0.688781	−	0.691266i
$619$	8.35524	−	4.82390i	0.335826	−	0.193889i	−0.322599	−	0.946536i	$-0.604557\pi$
$619$	8.35524	−	4.82390i	0.335826	−	0.193889i	0.658425	+	0.752647i	$0.271223\pi$
$620$	−11.7780	+	6.80001i	−0.473014	+	0.273095i
$621$	5.02629	−	1.31774i	0.201698	−	0.0528790i
$622$		−	3.32104i		−	0.133162i
$623$	5.08690	−	6.58755i	0.203802	−	0.263925i
$624$	−1.29792	−	0.350283i	−0.0519585	−	0.0140225i
$625$	10.7118	−	18.5535i	0.428474	−	0.742138i
$626$	−10.0886	−	17.4739i	−0.403220	−	0.698397i
$627$	−68.8883	+	18.3257i	−2.75113	+	0.731858i
$628$	−9.35198	−	5.39937i	−0.373185	−	0.215458i
$629$	16.5968			0.661758
$630$	−10.1828	+	13.0891i	−0.405693	+	0.521482i
$631$	9.28189			0.369506			0.184753	−	0.982785i	$-0.440851\pi$
$631$	9.28189			0.369506			0.184753	+	0.982785i	$0.440851\pi$
$632$	−3.41189	−	1.96986i	−0.135718	−	0.0783567i
$633$	25.6330	−	6.81892i	1.01882	−	0.271028i
$634$	12.3669	+	21.4200i	0.491151	+	0.850698i
$635$	−13.7191	+	23.7622i	−0.544426	+	0.942973i
$636$	−10.9854	−	2.96472i	−0.435598	−	0.117559i
$637$	1.43829	−	5.23933i	0.0569871	−	0.207590i
$638$			46.4213i			1.83784i
$639$	−5.29826	−	9.25363i	−0.209596	−	0.366068i
$640$	−1.80941	+	1.04467i	−0.0715234	+	0.0412940i
$641$	31.7176	−	18.3122i	1.25277	−	0.723288i	0.281112	−	0.959675i	$-0.409297\pi$
$641$	31.7176	−	18.3122i	1.25277	−	0.723288i	0.971659	+	0.236387i	$0.0759634\pi$
$642$	−13.3857	−	13.4340i	−0.528290	−	0.530196i
$643$			13.1673i			0.519266i	0.965707	+	0.259633i	$0.0836017\pi$
$643$			13.1673i			0.519266i	−0.965707	+	0.259633i	$0.916398\pi$
$644$	−0.353363	+	2.62205i	−0.0139245	+	0.103323i
$645$	2.43463	−	9.02118i	0.0958635	−	0.355208i
$646$	−9.00765	+	15.6017i	−0.354401	+	0.613841i
$647$	13.5788	+	23.5192i	0.533838	+	0.924635i	0.999219	+	0.0395239i	$0.0125841\pi$
$647$	13.5788	+	23.5192i	0.533838	+	0.924635i	−0.465381	+	0.885111i	$0.654083\pi$
$648$	−7.76162	−	4.55601i	−0.304905	−	0.178977i
$649$	15.9244	+	9.19394i	0.625086	+	0.360894i
$650$	−0.492629			−0.0193225
$651$	23.7531	−	18.0437i	0.930956	−	0.707187i
$652$	−0.756850			−0.0296405
$653$	27.1871	+	15.6965i	1.06391	+	0.614251i	0.926512	−	0.376265i	$-0.122792\pi$
$653$	27.1871	+	15.6965i	1.06391	+	0.614251i	0.137401	+	0.990515i	$0.456125\pi$
$654$	−6.97856	−	26.2331i	−0.272883	−	1.02580i
$655$	−6.96027	−	12.0555i	−0.271960	−	0.471049i
$656$	3.32700	−	5.76254i	0.129898	−	0.224989i
$657$	4.48132	−	7.69774i	0.174833	−	0.300318i
$658$	18.7104	−	7.68314i	0.729409	−	0.299520i
$659$			6.29151i			0.245083i	0.992463	+	0.122541i	$0.0391044\pi$
$659$			6.29151i			0.245083i	−0.992463	+	0.122541i	$0.960896\pi$
$660$	−12.8835	+	12.8372i	−0.501491	+	0.499689i
$661$	27.4766	−	15.8636i	1.06872	−	0.617024i	0.140887	−	0.990026i	$-0.455005\pi$
$661$	27.4766	−	15.8636i	1.06872	−	0.617024i	0.927831	+	0.373001i	$0.121671\pi$
$662$	−18.1821	+	10.4974i	−0.706668	+	0.407995i
$663$	−2.09504	+	2.08751i	−0.0813645	+	0.0810721i
$664$		−	16.9290i		−	0.656972i
$665$	−41.8745	+	17.1951i	−1.62382	+	0.666797i
$666$	−11.3868	+	19.5595i	−0.441229	+	0.757917i
$667$	4.61833	−	7.99919i	0.178823	−	0.309730i
$668$	6.65538	+	11.5275i	0.257504	+	0.446011i
$669$	−6.58176	−	24.7415i	−0.254466	−	0.956564i
$670$	23.8757	+	13.7846i	0.922398	+	0.532546i
$671$	16.8967			0.652289
$672$	3.64912	−	2.77200i	0.140768	−	0.106932i
$673$	−22.2560			−0.857905			−0.428952	−	0.903327i	$-0.641117\pi$
$673$	−22.2560			−0.857905			−0.428952	+	0.903327i	$0.641117\pi$
$674$	−2.94919	−	1.70272i	−0.113599	−	0.0655862i
$675$	−3.18094	−	0.870769i	−0.122434	−	0.0335159i
$676$	6.19878	+	10.7366i	0.238415	+	0.412946i
$677$	2.65203	−	4.59346i	0.101926	−	0.176541i	−0.810552	−	0.585666i	$-0.800833\pi$
$677$	2.65203	−	4.59346i	0.101926	−	0.176541i	0.912478	+	0.409126i	$0.134166\pi$
$678$	−2.26300	+	8.38522i	−0.0869099	+	0.322032i
$679$	−5.53467	+	41.0687i	−0.212401	+	1.57607i
$680$			4.59640i			0.176264i
$681$	3.78816	+	3.80182i	0.145162	+	0.145686i
$682$	28.3312	−	16.3570i	1.08486	−	0.626342i
$683$	−1.11229	+	0.642181i	−0.0425606	+	0.0245724i	−0.521129	−	0.853478i	$-0.674489\pi$
$683$	−1.11229	+	0.642181i	−0.0425606	+	0.0245724i	0.478569	+	0.878050i	$0.341156\pi$
$684$	−12.2068	−	21.3197i	−0.466739	−	0.815179i
$685$			19.2338i			0.734887i
$686$	11.1391	+	14.7960i	0.425293	+	0.564913i
$687$	−7.83576	−	2.11471i	−0.298953	−	0.0806812i
$688$	−1.29102	+	2.23611i	−0.0492195	+	0.0852507i
$689$	−2.54944	−	4.41576i	−0.0971259	−	0.168227i
$690$	3.49720	−	0.930328i	0.133136	−	0.0354170i
$691$	27.0402	+	15.6117i	1.02866	+	0.593896i	0.916600	−	0.399805i	$-0.130922\pi$
$691$	27.0402	+	15.6117i	1.02866	+	0.593896i	0.112058	+	0.993702i	$0.464256\pi$
$692$	1.50104			0.0570608
$693$	24.4942	−	31.4850i	0.930456	−	1.19602i
$694$	−26.5279			−1.00698
$695$	2.54760	+	1.47086i	0.0966359	+	0.0557928i
$696$	−15.4607	+	4.11286i	−0.586035	+	0.155897i
$697$	−7.31921	−	12.6772i	−0.277235	−	0.480185i
$698$	3.18451	−	5.51573i	0.120535	−	0.208774i
$699$	26.5567	+	7.16710i	1.00446	+	0.271084i
$700$	1.02633	−	1.32910i	0.0387917	−	0.0502353i
$701$			14.2250i			0.537271i	0.963242	+	0.268636i	$0.0865728\pi$
$701$			14.2250i			0.537271i	−0.963242	+	0.268636i	$0.913427\pi$
$702$	−1.02278	−	3.90123i	−0.0386025	−	0.147243i
$703$	−53.5025	+	30.8897i	−2.01789	+	1.16503i
$704$	4.35244	−	2.51288i	0.164039	−	0.0947077i
$705$	−19.5273	−	19.5977i	−0.735440	−	0.738092i
$706$			29.4320i			1.10769i
$707$	3.89157	+	9.47697i	0.146357	+	0.356418i
$708$	−1.65118	+	6.11820i	−0.0620551	+	0.229936i
$709$	−9.82265	+	17.0133i	−0.368897	+	0.638949i	−0.989393	−	0.145261i	$-0.953598\pi$
$709$	−9.82265	+	17.0133i	−0.368897	+	0.638949i	0.620496	+	0.784210i	$0.286931\pi$
$710$	−3.71312	−	6.43131i	−0.139351	−	0.241363i
$711$	0.0425522	−	11.8191i	0.00159583	−	0.443250i
$712$	2.72434	+	1.57290i	0.102099	+	0.0589469i
$713$	−6.50927			−0.243774
$714$	−1.26730	−	10.0014i	−0.0474275	−	0.374294i
$715$	−8.15012			−0.304797
$716$	1.70253	+	0.982958i	0.0636266	+	0.0367349i
$717$	6.81148	+	25.6051i	0.254379	+	0.956239i
$718$	1.04021	+	1.80170i	0.0388205	+	0.0672390i
$719$	−21.5857	+	37.3875i	−0.805010	+	1.39432i	0.111274	+	0.993790i	$0.464507\pi$
$719$	−21.5857	+	37.3875i	−0.805010	+	1.39432i	−0.916284	+	0.400529i	$0.868826\pi$
$720$	−5.41692	−	3.15352i	−0.201877	−	0.117525i
$721$	29.3296	+	22.6483i	1.09229	+	0.843466i
$722$		−	48.0595i		−	1.78859i
$723$	25.5958	−	25.5038i	0.951918	−	0.948497i
$724$	−6.19508	+	3.57673i	−0.230238	+	0.132928i
$725$	−5.07704	+	2.93123i	−0.188557	+	0.108863i
$726$	17.4942	−	17.4313i	0.649269	−	0.646936i
$727$			14.9544i			0.554628i	0.960779	+	0.277314i	$0.0894442\pi$
$727$			14.9544i			0.554628i	−0.960779	+	0.277314i	$0.910556\pi$
$728$	2.03515	+	0.274269i	0.0754275	+	0.0101651i
$729$	0.291617	−	26.9984i	0.0108006	−	0.999942i
$730$	3.10167	−	5.37225i	0.114798	−	0.198836i
$731$	2.84016	+	4.91930i	0.105047	+	0.181947i
$732$	1.49702	+	5.62746i	0.0553315	+	0.207997i
$733$	4.04871	+	2.33752i	0.149542	+	0.0863384i	0.572904	−	0.819622i	$-0.305817\pi$
$733$	4.04871	+	2.33752i	0.149542	+	0.0863384i	−0.423362	+	0.905961i	$0.639150\pi$
$734$	−35.2574			−1.30138
$735$	12.8392	−	21.8370i	0.473582	−	0.805470i
$736$	−1.00000			−0.0368605
$737$	−57.4315	−	33.1581i	−2.11552	−	1.22139i
$738$	19.9619	+	0.0718688i	0.734807	+	0.00264553i
$739$	−5.61685	−	9.72867i	−0.206619	−	0.357875i	0.744028	−	0.668148i	$-0.232913\pi$
$739$	−5.61685	−	9.72867i	−0.206619	−	0.357875i	−0.950647	+	0.310273i	$0.899579\pi$
$740$	−7.88117	+	13.6506i	−0.289717	+	0.501805i
$741$	2.86846	−	10.6287i	0.105376	−	0.390454i
$742$	17.2250	+	2.32135i	0.632351	+	0.0852195i
$743$			38.9738i			1.42981i	0.699222	+	0.714904i	$0.253530\pi$
$743$			38.9738i			1.42981i	−0.699222	+	0.714904i	$0.746470\pi$
$744$	7.95783	+	7.98653i	0.291748	+	0.292800i
$745$	−14.0358	+	8.10360i	−0.514233	+	0.296893i
$746$	4.10778	−	2.37163i	0.150396	−	0.0868314i
$747$	44.0739	−	25.2349i	1.61258	−	0.923298i
$748$		−	11.0564i		−	0.404261i
$749$	22.9282	+	17.7052i	0.837780	+	0.646933i
$750$	−19.6867	−	5.31302i	−0.718855	−	0.194004i
$751$	13.5751	−	23.5127i	0.495362	−	0.857991i	−0.504624	−	0.863339i	$-0.668369\pi$
$751$	13.5751	−	23.5127i	0.495362	−	0.857991i	0.999986	+	0.00534780i	$0.00170227\pi$
$752$	3.82245	+	6.62068i	0.139390	+	0.241431i
$753$	32.2598	−	8.58177i	1.17561	−	0.312737i
$754$	−6.20870	−	3.58459i	−0.226107	−	0.130543i
$755$	−30.8231			−1.12177
$756$	12.6563	+	5.36829i	0.460305	+	0.195243i
$757$	44.1850			1.60593			0.802966	−	0.596025i	$-0.203254\pi$
$757$	44.1850			1.60593			0.802966	+	0.596025i	$0.203254\pi$
$758$	29.2604	+	16.8935i	1.06279	+	0.613600i
$759$	−8.41230	+	2.23785i	−0.305347	+	0.0812287i
$760$	−8.55476	−	14.8173i	−0.310314	−	0.537479i
$761$	0.198087	−	0.343097i	0.00718065	−	0.0124373i	−0.862413	−	0.506206i	$-0.831048\pi$
$761$	0.198087	−	0.343097i	0.00718065	−	0.0124373i	0.869593	+	0.493768i	$0.164381\pi$
$762$	21.9605	+	5.92669i	0.795545	+	0.214701i
$763$	15.7509	+	38.3574i	0.570219	+	1.38863i
$764$			3.93279i			0.142283i
$765$	−11.9666	+	6.85157i	−0.432652	+	0.247719i
$766$	−14.0377	+	8.10467i	−0.507203	+	0.292834i
$767$	−2.45932	+	1.41989i	−0.0888009	+	0.0512692i
$768$	1.22254	+	1.22695i	0.0441145	+	0.0442737i
$769$		−	30.5347i		−	1.10111i	−0.834799	−	0.550554i	$-0.814416\pi$
$769$		−	30.5347i		−	1.10111i	0.834799	−	0.550554i	$-0.185584\pi$
$770$	16.9798	−	21.9888i	0.611908	−	0.792422i
$771$	−8.89547	+	32.9609i	−0.320362	+	1.18706i
$772$	0.159806	−	0.276792i	0.00575154	−	0.00996196i
$773$	−20.3012	−	35.1628i	−0.730185	−	1.26472i	−0.956804	−	0.290734i	$-0.906101\pi$
$773$	−20.3012	−	35.1628i	−0.730185	−	1.26472i	0.226619	−	0.973984i	$-0.427233\pi$
$774$	−7.74605	−	0.0278881i	−0.278426	−	0.00100242i
$775$	3.57790	+	2.06570i	0.128522	+	0.0742021i
$776$	−15.6628			−0.562263
$777$	13.3851	−	31.8756i	0.480189	−	1.14353i
$778$	−14.0294			−0.502978
$779$	47.1894	+	27.2448i	1.69073	+	0.976146i
$780$	−0.722089	−	2.71441i	−0.0258549	−	0.0971914i
$781$	8.93168	+	15.4701i	0.319601	+	0.553564i
$782$	−1.09997	+	1.90520i	−0.0393349	+	0.0681300i
$783$	−33.7539	−	34.1205i	−1.20627	−	1.21937i
$784$	−4.97994	+	4.91937i	−0.177855	+	0.175692i
$785$		−	22.5621i		−	0.805277i
$786$	−8.17476	+	8.14538i	−0.291584	+	0.290536i
$787$	−27.1068	+	15.6501i	−0.966252	+	0.557866i	−0.898092	−	0.439809i	$-0.855046\pi$
$787$	−27.1068	+	15.6501i	−0.966252	+	0.557866i	−0.0681604	+	0.997674i	$0.521713\pi$
$788$	−9.77648	+	5.64446i	−0.348273	+	0.201075i
$789$	27.1615	−	27.0639i	0.966976	−	0.963501i
$790$		−	8.23137i		−	0.292859i
$791$	1.77191	−	13.1480i	0.0630018	−	0.467490i
$792$	13.0301	+	7.58560i	0.463004	+	0.269543i
$793$	−1.30474	+	2.25988i	−0.0463327	+	0.0802506i
$794$	−8.62712	−	14.9426i	−0.306165	−	0.530294i
$795$	−6.11161	−	22.9742i	−0.216757	−	0.814811i
$796$	−19.1608	−	11.0625i	−0.679136	−	0.392099i
$797$	2.06186			0.0730348			0.0365174	−	0.999333i	$-0.488374\pi$
$797$	2.06186			0.0730348			0.0365174	+	0.999333i	$0.488374\pi$
$798$	22.6998	+	29.8826i	0.803566	+	1.05783i
$799$	16.8183			0.594990
$800$	0.549662	+	0.317348i	0.0194335	+	0.0112199i
$801$	−0.0339773	+	9.43734i	−0.00120053	+	0.333452i
$802$	−2.00579	−	3.47413i	−0.0708268	−	0.122676i
$803$	−7.46088	+	12.9226i	−0.263289	+	0.456029i
$804$	5.95500	−	22.0654i	0.210017	−	0.778187i
$805$	−5.11352	+	2.09978i	−0.180228	+	0.0740076i
$806$			5.05227i			0.177959i
$807$	7.17177	+	7.19764i	0.252458	+	0.253369i
$808$	−3.35342	+	1.93610i	−0.117973	+	0.0681117i
$809$	15.6561	−	9.03907i	0.550440	−	0.317797i	−0.198859	−	0.980028i	$-0.563724\pi$
$809$	15.6561	−	9.03907i	0.550440	−	0.317797i	0.749300	+	0.662231i	$0.230390\pi$
$810$	0.135398	−	18.8035i	0.00475741	−	0.660687i
$811$			25.0697i			0.880315i	0.897921	+	0.440158i	$0.145077\pi$
$811$			25.0697i			0.880315i	−0.897921	+	0.440158i	$0.854923\pi$
$812$	22.6062	−	9.28287i	0.793322	−	0.325765i
$813$	−1.58499	−	0.427757i	−0.0555882	−	0.0150021i
$814$	18.9577	−	32.8357i	0.664466	−	1.15089i
$815$	−0.790655	−	1.36945i	−0.0276954	−	0.0479699i
$816$	3.68234	−	0.979579i	0.128908	−	0.0342921i
$817$	−18.3114	−	10.5721i	−0.640636	−	0.369872i
$818$	−8.88447			−0.310638
$819$	2.31961	+	5.70725i	0.0810539	+	0.199428i
$820$	13.9024			0.485494
$821$	1.49122	+	0.860957i	0.0520440	+	0.0300476i	0.525796	−	0.850611i	$-0.323767\pi$
$821$	1.49122	+	0.860957i	0.0520440	+	0.0300476i	−0.473752	+	0.880658i	$0.657101\pi$
$822$	15.4089	−	4.09909i	0.537447	−	0.142972i
$823$	−4.25702	−	7.37337i	−0.148390	−	0.257020i	0.782242	−	0.622974i	$-0.214076\pi$
$823$	−4.25702	−	7.37337i	−0.148390	−	0.257020i	−0.930633	+	0.365955i	$0.880743\pi$
$824$	−7.00299	+	12.1295i	−0.243961	+	0.422552i
$825$	5.33410	+	1.43956i	0.185710	+	0.0501192i
$826$	1.29286	−	9.59335i	0.0449843	−	0.333795i
$827$		−	10.0225i		−	0.348515i	−0.984700	−	0.174258i	$-0.944247\pi$
$827$		−	10.0225i		−	0.348515i	0.984700	−	0.174258i	$-0.0557525\pi$
$828$	−1.49064	−	2.60346i	−0.0518032	−	0.0904765i
$829$	27.5762	−	15.9211i	0.957761	−	0.552963i	0.0622777	−	0.998059i	$-0.480164\pi$
$829$	27.5762	−	15.9211i	0.957761	−	0.552963i	0.895483	+	0.445095i	$0.146830\pi$
$830$	30.6315	−	17.6851i	1.06324	−	0.613859i
$831$	−14.2659	−	14.3173i	−0.494877	−	0.496662i
$832$			0.776166i			0.0269087i
$833$	3.89462	+	14.8990i	0.134941	+	0.516219i
$834$	0.635415	−	2.35444i	0.0220026	−	0.0815275i
$835$	−13.9053	+	24.0847i	−0.481213	+	0.833485i
$836$	20.5780	+	35.6421i	0.711703	+	1.23271i
$837$	−8.93038	+	32.6229i	−0.308679	+	1.12761i
$838$	22.6643	+	13.0853i	0.782926	+	0.452023i
$839$	30.6566			1.05838			0.529191	−	0.848503i	$-0.322495\pi$
$839$	30.6566			1.05838			0.529191	+	0.848503i	$0.322495\pi$
$840$	8.82779	+	3.70695i	0.304588	+	0.127902i
$841$	−56.3160			−1.94193
$842$	−7.19819	−	4.15587i	−0.248066	−	0.143221i
$843$	10.3072	+	38.7459i	0.354999	+	1.33448i
$844$	−7.65697	−	13.2623i	−0.263564	−	0.456506i
$845$	−12.9513	+	22.4323i	−0.445539	+	0.771696i
$846$	−11.5388	+	19.8206i	−0.396712	+	0.681447i
$847$	−23.0563	+	29.8579i	−0.792223	+	1.02593i
$848$			6.56931i			0.225591i
$849$	−38.9601	+	38.8201i	−1.33711	+	1.33230i
$850$	1.20922	−	0.698146i	0.0414760	−	0.0239462i
$851$	−6.53347	+	3.77210i	−0.223964	+	0.129306i
$852$	−4.36101	+	4.34534i	−0.149406	+	0.148869i
$853$		−	15.6530i		−	0.535949i	−0.963426	−	0.267975i	$-0.913646\pi$
$853$		−	15.6530i		−	0.535949i	0.963426	−	0.267975i	$-0.0863543\pi$
$854$	−3.37883	−	8.22833i	−0.115621	−	0.281568i
$855$	25.8241	−	44.3591i	0.883167	−	1.51705i
$856$	−5.47454	+	9.48218i	−0.187116	+	0.324094i
$857$	−24.0327	−	41.6258i	−0.820940	−	1.42191i	−0.904983	−	0.425448i	$-0.860116\pi$
$857$	−24.0327	−	41.6258i	−0.820940	−	1.42191i	0.0840423	−	0.996462i	$-0.473217\pi$
$858$	1.73694	+	6.52935i	0.0592982	+	0.222908i
$859$	4.77971	+	2.75957i	0.163082	+	0.0941552i	0.579320	−	0.815101i	$-0.303318\pi$
$859$	4.77971	+	2.75957i	0.163082	+	0.0941552i	−0.416238	+	0.909256i	$0.636652\pi$
$860$	−5.39472			−0.183958
$861$	−30.2506	+	3.83311i	−1.03094	+	0.130632i
$862$	9.19183			0.313075
$863$	27.9415	+	16.1320i	0.951139	+	0.549140i	0.893434	−	0.449194i	$-0.148289\pi$
$863$	27.9415	+	16.1320i	0.951139	+	0.549140i	0.0577042	+	0.998334i	$0.481622\pi$
$864$	−1.37195	+	5.01176i	−0.0466746	+	0.170504i
$865$	1.56808	+	2.71600i	0.0533163	+	0.0923466i
$866$	−7.30237	+	12.6481i	−0.248144	+	0.429799i
$867$	−5.48791	+	20.3347i	−0.186379	+	0.690601i
$868$	−13.6309	−	10.5258i	−0.462664	−	0.357268i
$869$			19.8001i			0.671671i
$870$	−23.5931	−	23.6782i	−0.799881	−	0.802766i
$871$	8.86958	−	5.12085i	0.300534	−	0.173514i
$872$	−13.5727	+	7.83623i	−0.459631	+	0.265368i
$873$	−23.3476	−	40.7775i	−0.790196	−	1.38011i
$874$		−	8.18899i		−	0.276997i
$875$	30.8687	+	4.16005i	1.04355	+	0.140636i
$876$	−4.96492	−	1.33993i	−0.167749	−	0.0452720i
$877$	14.3002	−	24.7687i	0.482883	−	0.836378i	−0.516924	−	0.856031i	$-0.672923\pi$
$877$	14.3002	−	24.7687i	0.482883	−	0.836378i	0.999807	+	0.0196533i	$0.00625624\pi$
$878$	2.96168	+	5.12978i	0.0999519	+	0.173122i
$879$	41.2899	−	10.9840i	1.39267	−	0.370480i
$880$	9.09368	+	5.25024i	0.306548	+	0.176986i
$881$	−44.4067			−1.49610			−0.748050	−	0.663643i	$-0.769010\pi$
$881$	−44.4067			−1.49610			−0.748050	+	0.663643i	$0.769010\pi$
$882$	−20.2307	−	5.63208i	−0.681202	−	0.189642i
$883$	−18.1933			−0.612253			−0.306126	−	0.951991i	$-0.599033\pi$
$883$	−18.1933			−0.612253			−0.306126	+	0.951991i	$0.599033\pi$
$884$	1.47876	+	0.853760i	0.0497359	+	0.0287151i
$885$	−12.7953	+	3.40381i	−0.430109	+	0.114418i
$886$	13.8476	+	23.9847i	0.465218	+	0.805781i
$887$	−1.69817	+	2.94132i	−0.0570191	+	0.0987599i	−0.893126	−	0.449807i	$-0.851493\pi$
$887$	−1.69817	+	2.94132i	−0.0570191	+	0.0987599i	0.836107	+	0.548567i	$0.184826\pi$
$888$	12.6156	+	3.40469i	0.423351	+	0.114254i
$889$	−34.4341	−	4.64055i	−1.15488	−	0.155639i
$890$			6.57262i			0.220315i
$891$	−0.325692	+	45.2307i	−0.0109111	+	1.51528i
$892$	−12.8010	+	7.39067i	−0.428610	+	0.247458i
$893$	−54.2167	+	31.3020i	−1.81429	+	1.04748i
$894$	9.48337	+	9.51758i	0.317171	+	0.318315i
$895$			4.10745i			0.137297i
$896$	−2.09408	−	1.61705i	−0.0699582	−	0.0540217i
$897$	0.350283	−	1.29792i	0.0116956	−	0.0433364i
$898$	−14.3942	+	24.9315i	−0.480340	+	0.831974i
$899$	30.0620	+	52.0688i	1.00262	+	1.73659i
$900$	−0.00685523	+	1.90407i	−0.000228508	+	0.0634691i
$901$	12.5159	+	7.22605i	0.416964	+	0.240735i
$902$	−33.4415			−1.11348
$903$	11.7385	−	1.48741i	0.390633	−	0.0494978i
$904$	5.01441			0.166777
$905$	−12.9436	−	7.47298i	−0.430259	−	0.248410i
$906$	6.56897	+	24.6935i	0.218239	+	0.820385i
$907$	14.1695	+	24.5423i	0.470490	+	0.814913i	0.999430	−	0.0337460i	$-0.0107437\pi$
$907$	14.1695	+	24.5423i	0.470490	+	0.814913i	−0.528940	+	0.848659i	$0.677410\pi$
$908$	1.54930	−	2.68347i	0.0514153	−	0.0890539i
$909$	−10.0393	−	5.84447i	−0.332982	−	0.193849i
$910$	1.62978	+	3.96894i	0.0540267	+	0.131569i
$911$			19.1613i			0.634842i	0.948285	+	0.317421i	$0.102817\pi$
$911$			19.1613i			0.634842i	−0.948285	+	0.317421i	$0.897183\pi$
$912$	−10.0475	+	10.0114i	−0.332705	+	0.331509i
$913$	−73.6823	+	42.5405i	−2.43853	+	1.40788i
$914$	5.82218	−	3.36144i	0.192581	−	0.111186i
$915$	−8.61852	+	8.58755i	−0.284920	+	0.283896i
$916$			4.68583i			0.154824i
$917$	10.7739	−	13.9522i	0.355784	−	0.460741i
$918$	8.03933	+	8.12663i	0.265337	+	0.268219i
$919$	1.48378	−	2.56998i	0.0489453	−	0.0847758i	−0.840515	−	0.541789i	$-0.817747\pi$
$919$	1.48378	−	2.56998i	0.0489453	−	0.0847758i	0.889460	+	0.457013i	$0.151081\pi$
$920$	−1.04467	−	1.80941i	−0.0344416	−	0.0596546i
$921$	12.1897	+	45.8225i	0.401665	+	1.50990i
$922$	−13.6594	−	7.88626i	−0.449849	−	0.259720i
$923$	−2.75877			−0.0908061
$924$	−21.2347	−	8.91685i	−0.698571	−	0.293343i
$925$	4.78827			0.157437
$926$	20.0520	+	11.5770i	0.658951	+	0.380445i
$927$	−42.0176	−	0.151276i	−1.38004	−	0.00496856i
$928$	4.61833	+	7.99919i	0.151604	+	0.262586i
$929$	9.62660	−	16.6738i	0.315838	−	0.547048i	−0.663777	−	0.747931i	$-0.731048\pi$
$929$	9.62660	−	16.6738i	0.315838	−	0.547048i	0.979615	+	0.200882i	$0.0643809\pi$
$930$	−6.13767	+	22.7423i	−0.201262	+	0.745748i
$931$	−40.2847	−	40.7807i	−1.32028	−	1.33653i
$932$		−	15.8810i		−	0.520201i
$933$	−4.06010	−	4.07474i	−0.132922	−	0.133401i
$934$	−28.0136	+	16.1736i	−0.916632	+	0.529218i
$935$	20.0056	−	11.5502i	0.654252	−	0.377732i
$936$	−2.02072	+	1.15698i	−0.0660492	+	0.0378171i
$937$			5.88351i			0.192206i	0.995371	+	0.0961030i	$0.0306378\pi$
$937$			5.88351i			0.192206i	−0.995371	+	0.0961030i	$0.969362\pi$
$938$	−4.66272	+	34.5986i	−0.152243	+	1.12968i
$939$	−33.7406	−	9.10590i	−1.10108	−	0.297160i
$940$	−7.98636	+	13.8328i	−0.260487	+	0.451176i
$941$	5.09212	+	8.81981i	0.165998	+	0.287517i	0.937009	−	0.349304i	$-0.113582\pi$
$941$	5.09212	+	8.81981i	0.165998	+	0.287517i	−0.771011	+	0.636822i	$0.780249\pi$
$942$	−18.0753	+	4.80841i	−0.588926	+	0.156666i
$943$	5.76254	+	3.32700i	0.187654	+	0.108342i
$944$	3.65872			0.119081
$945$	3.50813	+	28.5085i	0.114119	+	0.927382i
$946$	12.9767			0.421908
$947$	32.2873	+	18.6411i	1.04920	+	0.605753i	0.922424	−	0.386178i	$-0.126205\pi$
$947$	32.2873	+	18.6411i	1.04920	+	0.605753i	0.126772	+	0.991932i	$0.459538\pi$
$948$	−6.59444	+	1.75426i	−0.214178	+	0.0569757i
$949$	−1.15224	−	1.99574i	−0.0374033	−	0.0647844i
$950$	−2.59876	+	4.50118i	−0.0843148	+	0.146037i
$951$	41.3603	+	11.1623i	1.34120	+	0.361962i
$952$	−5.38423	+	2.21095i	−0.174504	+	0.0716572i
$953$		−	23.8043i		−	0.771096i	−0.922688	−	0.385548i	$-0.874012\pi$
$953$		−	23.8043i		−	0.771096i	0.922688	−	0.385548i	$-0.125988\pi$
$954$	−17.1029	+	9.79245i	−0.553728	+	0.317042i
$955$	−7.11604	+	4.10845i	−0.230270	+	0.132946i
$956$	13.2478	−	7.64861i	0.428464	−	0.247374i
$957$	56.7518	+	56.9565i	1.83452	+	1.84114i
$958$			1.08499i			0.0350546i
$959$	−22.5305	+	9.25179i	−0.727548	+	0.298756i
$960$	−0.942912	+	3.49383i	−0.0304324	+	0.112763i
$961$	5.68529	−	9.84721i	0.183396	−	0.317652i
$962$	2.92778	+	5.07106i	0.0943953	+	0.163497i
$963$	−32.8470	−	0.118259i	−1.05848	−	0.00381085i
$964$	−18.0665	−	10.4307i	−0.581882	−	0.335950i
$965$	0.667775			0.0214964
$966$	2.77200	+	3.64912i	0.0891875	+	0.117408i
$967$	−19.3334			−0.621721			−0.310861	−	0.950456i	$-0.600617\pi$
$967$	−19.3334			−0.621721			−0.310861	+	0.950456i	$0.600617\pi$
$968$	−12.3480	−	7.12914i	−0.396881	−	0.229139i
$969$	8.02176	+	30.1547i	0.257696	+	0.968707i
$970$	−16.3624	−	28.3405i	−0.525366	−	0.909960i
$971$	7.41456	−	12.8424i	0.237944	−	0.412132i	−0.722180	−	0.691705i	$-0.756860\pi$
$971$	7.41456	−	12.8424i	0.237944	−	0.412132i	0.960124	+	0.279573i	$0.0901931\pi$
$972$	−15.0930	+	3.89890i	−0.484108	+	0.125057i
$973$	−0.497524	+	3.69176i	−0.0159499	+	0.118352i
$974$		−	11.1391i		−	0.356919i
$975$	−0.604430	+	0.602258i	−0.0193572	+	0.0192877i
$976$	2.91159	−	1.68101i	0.0931977	−	0.0538077i
$977$	4.45561	−	2.57245i	0.142548	−	0.0822999i	−0.427030	−	0.904237i	$-0.640440\pi$
$977$	4.45561	−	2.57245i	0.142548	−	0.0822999i	0.569578	+	0.821938i	$0.307107\pi$
$978$	−0.928615	+	0.925278i	−0.0296938	+	0.0295871i
$979$		−	15.8100i		−	0.505291i
$980$	−14.1035	−	3.87168i	−0.450521	−	0.123676i
$981$	−40.6333	−	23.6551i	−1.29732	−	0.755250i
$982$	12.9938	−	22.5059i	0.414648	−	0.718191i
$983$	−19.5126	−	33.7968i	−0.622355	−	1.07795i	−0.989046	−	0.147608i	$-0.952843\pi$
$983$	−19.5126	−	33.7968i	−0.622355	−	1.07795i	0.366691	−	0.930343i	$-0.380491\pi$
$984$	−2.96287	−	11.1377i	−0.0944527	−	0.355058i
$985$	−20.4263	−	11.7931i	−0.650836	−	0.375761i
$986$	20.3201			0.647124
$987$	13.5638	−	32.3011i	0.431741	−	1.02815i
$988$	−6.35602			−0.202212
$989$	−2.23611	−	1.29102i	−0.0711040	−	0.0410519i
$990$	−0.113414	+	31.5012i	−0.00360453	+	1.00117i
$991$	−29.3756	−	50.8800i	−0.933145	−	1.61626i	−0.777908	−	0.628378i	$-0.783719\pi$
$991$	−29.3756	−	50.8800i	−0.933145	−	1.61626i	−0.155237	−	0.987877i	$-0.549614\pi$
$992$	3.25463	−	5.63719i	0.103335	−	0.178981i
$993$	−9.47497	+	35.1082i	−0.300679	+	1.11412i
$994$	5.74756	−	7.44311i	0.182302	−	0.236081i
$995$		−	46.2264i		−	1.46547i
$996$	−20.6963	−	20.7710i	−0.655788	−	0.658153i
$997$	−0.876697	+	0.506161i	−0.0277653	+	0.0160303i	−0.513818	−	0.857899i	$-0.671769\pi$
$997$	−0.876697	+	0.506161i	−0.0277653	+	0.0160303i	0.486053	+	0.873929i	$0.338436\pi$
$998$	−17.8253	+	10.2914i	−0.564249	+	0.325769i
$999$	9.94128	+	37.9193i	0.314528	+	1.19971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.3	✓	56
3.2	odd	2	inner	966.2.l.d.47.18	yes	56
7.3	odd	6	inner	966.2.l.d.185.18	yes	56
21.17	even	6	inner	966.2.l.d.185.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.3	✓	56	1.1	even	1	trivial
966.2.l.d.47.18	yes	56	3.2	odd	2	inner
966.2.l.d.185.3	yes	56	21.17	even	6	inner
966.2.l.d.185.18	yes	56	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67384 + 0.445275i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04467 + 1.80941i) q^{5} +(1.67222 + 0.451299i) q^{6} +(-2.62205 - 0.353363i) q^{7} -1.00000i q^{8} +(2.60346 - 1.49064i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67384 + 0.445275i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04467 + 1.80941i) q^{5} +(1.67222 + 0.451299i) q^{6} +(-2.62205 - 0.353363i) q^{7} -1.00000i q^{8} +(2.60346 - 1.49064i) q^{9} +(1.80941 - 1.04467i) q^{10} +(-4.35244 + 2.51288i) q^{11} +(-1.22254 - 1.22695i) q^{12} -0.776166i q^{13} +(2.09408 + 1.61705i) q^{14} +(0.942912 - 3.49383i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.09997 + 1.90520i) q^{17} +(-2.99998 - 0.0108008i) q^{18} +(-7.09187 - 4.09449i) q^{19} -2.08933 q^{20} +(4.54622 - 0.576061i) q^{21} +5.02576 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.445275 + 1.67384i) q^{24} +(0.317348 + 0.549662i) q^{25} +(-0.388083 + 0.672180i) q^{26} +(-3.69402 + 3.65434i) q^{27} +(-1.00500 - 2.44744i) q^{28} +9.23666i q^{29} +(-2.56350 + 2.55429i) q^{30} +(5.63719 - 3.25463i) q^{31} +(0.866025 - 0.500000i) q^{32} +(6.16635 - 6.14418i) q^{33} -2.19994i q^{34} +(3.37854 - 4.37522i) q^{35} +(2.59266 + 1.50934i) q^{36} +(3.77210 - 6.53347i) q^{37} +(4.09449 + 7.09187i) q^{38} +(0.345608 + 1.29918i) q^{39} +(1.80941 + 1.04467i) q^{40} -6.65401 q^{41} +(-4.22518 - 1.77423i) q^{42} +2.58203 q^{43} +(-4.35244 - 2.51288i) q^{44} +(-0.0225665 + 6.26795i) q^{45} +(0.500000 + 0.866025i) q^{46} +(3.82245 - 6.62068i) q^{47} +(0.451299 - 1.67222i) q^{48} +(6.75027 + 1.85307i) q^{49} -0.634695i q^{50} +(-2.68951 - 2.69921i) q^{51} +(0.672180 - 0.388083i) q^{52} +(5.68919 - 3.28466i) q^{53} +(5.02629 - 1.31774i) q^{54} -10.5005i q^{55} +(-0.353363 + 2.62205i) q^{56} +(13.6938 + 3.69568i) q^{57} +(4.61833 - 7.99919i) q^{58} +(-1.82936 - 3.16855i) q^{59} +(3.49720 - 0.930328i) q^{60} +(-2.91159 - 1.68101i) q^{61} -6.50927 q^{62} +(-7.35313 + 2.98855i) q^{63} -1.00000 q^{64} +(1.40441 + 0.810834i) q^{65} +(-8.41230 + 2.23785i) q^{66} +(6.59763 + 11.4274i) q^{67} +(-1.09997 + 1.90520i) q^{68} +(1.67222 + 0.451299i) q^{69} +(-5.11352 + 2.09978i) q^{70} -3.55436i q^{71} +(-1.49064 - 2.60346i) q^{72} +(2.57128 - 1.48453i) q^{73} +(-6.53347 + 3.77210i) q^{74} +(-0.775939 - 0.778738i) q^{75} -8.18899i q^{76} +(12.3003 - 5.05090i) q^{77} +(0.350283 - 1.29792i) q^{78} +(1.96986 - 3.41189i) q^{79} +(-1.04467 - 1.80941i) q^{80} +(4.55601 - 7.76162i) q^{81} +(5.76254 + 3.32700i) q^{82} +16.9290 q^{83} +(2.77200 + 3.64912i) q^{84} -4.59640 q^{85} +(-2.23611 - 1.29102i) q^{86} +(-4.11286 - 15.4607i) q^{87} +(2.51288 + 4.35244i) q^{88} +(-1.57290 + 2.72434i) q^{89} +(3.15352 - 5.41692i) q^{90} +(-0.274269 + 2.03515i) q^{91} -1.00000i q^{92} +(-7.98653 + 7.95783i) q^{93} +(-6.62068 + 3.82245i) q^{94} +(14.8173 - 8.55476i) q^{95} +(-1.22695 + 1.22254i) q^{96} -15.6628i q^{97} +(-4.91937 - 4.97994i) q^{98} +(-7.58560 + 13.0301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Introduction

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