LMFDB - Embedded newform 546.2.bg.a.311.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.15
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.a.467.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19770 - 1.26884i) q^{5} +(0.170404 - 1.72365i) q^{6} +(-2.61925 - 0.373536i) q^{7} +1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19770 - 1.26884i) q^{5} +(0.170404 - 1.72365i) q^{6} +(-2.61925 - 0.373536i) q^{7} +1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +(-2.19770 - 1.26884i) q^{10} +(1.32440 - 2.29393i) q^{11} +(-1.57792 + 0.714250i) q^{12} +(3.59958 - 0.207354i) q^{13} +(0.986133 + 2.45511i) q^{14} +(4.37407 + 0.432430i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.84623 - 3.19777i) q^{17} +(1.97969 - 2.25407i) q^{18} +(-0.241819 - 0.418842i) q^{19} +2.53768i q^{20} +(-3.30960 - 3.16963i) q^{21} -2.64880 q^{22} +(4.09436 - 2.36388i) q^{23} +(1.40752 + 1.00940i) q^{24} +(0.719909 - 1.24692i) q^{25} +(-1.97937 - 3.01365i) q^{26} +(-1.51384 + 4.97074i) q^{27} +(1.63312 - 2.08157i) q^{28} +6.93400i q^{29} +(-1.81254 - 4.00427i) q^{30} +(-2.71148 + 4.69643i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.17960 - 1.89190i) q^{33} -3.69246 q^{34} +(-6.23027 + 2.50249i) q^{35} +(-2.94193 - 0.587433i) q^{36} +(5.90071 - 3.40678i) q^{37} +(-0.241819 + 0.418842i) q^{38} +(5.27579 + 3.34156i) q^{39} +(2.19770 - 1.26884i) q^{40} -3.03693i q^{41} +(-1.09018 + 4.45101i) q^{42} +5.11062 q^{43} +(1.32440 + 2.29393i) q^{44} +(5.72010 + 5.02383i) q^{45} +(-4.09436 - 2.36388i) q^{46} +(-6.66192 + 3.84626i) q^{47} +(0.170404 - 1.72365i) q^{48} +(6.72094 + 1.95677i) q^{49} -1.43982 q^{50} +(5.82643 - 2.63734i) q^{51} +(-1.62022 + 3.22101i) q^{52} +(-8.13530 - 4.69692i) q^{53} +(5.06171 - 1.17435i) q^{54} -6.72180i q^{55} +(-2.61925 - 0.373536i) q^{56} +(0.0824136 - 0.833620i) q^{57} +(6.00502 - 3.46700i) q^{58} +(-4.98510 - 2.87815i) q^{59} +(-2.56153 + 3.57184i) q^{60} +(4.25236 - 2.45510i) q^{61} +5.42297 q^{62} +(-1.45892 - 7.80202i) q^{63} +1.00000 q^{64} +(7.64769 - 5.02300i) q^{65} +(-3.72824 - 2.67369i) q^{66} +(-1.38217 - 0.797996i) q^{67} +(1.84623 + 3.19777i) q^{68} +(8.14900 + 0.805629i) q^{69} +(5.28236 + 4.14433i) q^{70} -12.9028 q^{71} +(0.962231 + 2.84150i) q^{72} +(-6.57447 + 11.3873i) q^{73} +(-5.90071 - 3.40678i) q^{74} +(2.27193 - 1.02839i) q^{75} +0.483637 q^{76} +(-4.32580 + 5.51365i) q^{77} +(0.255978 - 6.23975i) q^{78} +(-3.75864 - 6.51016i) q^{79} +(-2.19770 - 1.26884i) q^{80} +(-7.14822 + 5.46836i) q^{81} +(-2.63006 + 1.51847i) q^{82} -3.10022i q^{83} +(4.39978 - 1.28139i) q^{84} -9.37029i q^{85} +(-2.55531 - 4.42592i) q^{86} +(-6.99916 + 9.75974i) q^{87} +(1.32440 - 2.29393i) q^{88} +(-2.37997 + 1.37408i) q^{89} +(1.49072 - 7.46566i) q^{90} +(-9.50566 - 0.801464i) q^{91} +4.72776i q^{92} +(-8.55703 + 3.87335i) q^{93} +(6.66192 + 3.84626i) q^{94} +(-1.06289 - 0.613658i) q^{95} +(-1.57792 + 0.714250i) q^{96} +5.91584 q^{97} +(-1.66586 - 6.79889i) q^{98} +(7.79256 + 1.55599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.40752	+	1.00940i	0.812633	+	0.582776i
$3$	1.40752	+	1.00940i	0.812633	+	0.582776i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.19770	−	1.26884i	0.982839	−	0.567442i	0.0797131	−	0.996818i	$-0.474600\pi$
$5$	2.19770	−	1.26884i	0.982839	−	0.567442i	0.903126	+	0.429375i	$0.141266\pi$
$6$	0.170404	−	1.72365i	0.0695671	−	0.703676i
$7$	−2.61925	−	0.373536i	−0.989983	−	0.141183i
$7$	−2.61925	−	0.373536i	−0.989983	−	0.141183i
$8$	1.00000			0.353553
$9$	0.962231	+	2.84150i	0.320744	+	0.947166i
$10$	−2.19770	−	1.26884i	−0.694972	−	0.401242i
$11$	1.32440	−	2.29393i	0.399321	−	0.691645i	−0.594321	−	0.804228i	$-0.702579\pi$
$11$	1.32440	−	2.29393i	0.399321	−	0.691645i	0.993642	+	0.112583i	$0.0359125\pi$
$12$	−1.57792	+	0.714250i	−0.455508	+	0.206186i
$13$	3.59958	−	0.207354i	0.998345	−	0.0575096i
$13$	3.59958	−	0.207354i	0.998345	−	0.0575096i
$14$	0.986133	+	2.45511i	0.263555	+	0.656154i
$15$	4.37407	+	0.432430i	1.12938	+	0.111653i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.84623	−	3.19777i	0.447777	−	0.775572i	−0.550464	−	0.834859i	$-0.685549\pi$
$17$	1.84623	−	3.19777i	0.447777	−	0.775572i	0.998241	+	0.0592866i	$0.0188826\pi$
$18$	1.97969	−	2.25407i	0.466618	−	0.531288i
$19$	−0.241819	−	0.418842i	−0.0554770	−	0.0960890i	0.836953	−	0.547274i	$-0.184335\pi$
$19$	−0.241819	−	0.418842i	−0.0554770	−	0.0960890i	−0.892430	+	0.451185i	$0.851001\pi$
$20$			2.53768i			0.567442i
$21$	−3.30960	−	3.16963i	−0.722214	−	0.691669i
$22$	−2.64880			−0.564725
$23$	4.09436	−	2.36388i	0.853734	−	0.492903i	−0.00817520	−	0.999967i	$-0.502602\pi$
$23$	4.09436	−	2.36388i	0.853734	−	0.492903i	0.861909	+	0.507063i	$0.169269\pi$
$24$	1.40752	+	1.00940i	0.287309	+	0.206043i
$25$	0.719909	−	1.24692i	0.143982	−	0.249384i
$26$	−1.97937	−	3.01365i	−0.388186	−	0.591026i
$27$	−1.51384	+	4.97074i	−0.291339	+	0.956620i
$28$	1.63312	−	2.08157i	0.308630	−	0.393380i
$29$			6.93400i			1.28761i	0.765189	+	0.643805i	$0.222645\pi$
$29$			6.93400i			1.28761i	−0.765189	+	0.643805i	$0.777355\pi$
$30$	−1.81254	−	4.00427i	−0.330923	−	0.731076i
$31$	−2.71148	+	4.69643i	−0.486997	+	0.843503i	−0.999888	−	0.0149503i	$-0.995241\pi$
$31$	−2.71148	+	4.69643i	−0.486997	+	0.843503i	0.512891	+	0.858453i	$0.328574\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	4.17960	−	1.89190i	0.727575	−	0.329338i
$34$	−3.69246			−0.633252
$35$	−6.23027	+	2.50249i	−1.05311	+	0.422998i
$36$	−2.94193	−	0.587433i	−0.490321	−	0.0979054i
$37$	5.90071	−	3.40678i	0.970071	−	0.560071i	0.0708132	−	0.997490i	$-0.477441\pi$
$37$	5.90071	−	3.40678i	0.970071	−	0.560071i	0.899258	+	0.437419i	$0.144107\pi$
$38$	−0.241819	+	0.418842i	−0.0392282	+	0.0679452i
$39$	5.27579	+	3.34156i	0.844803	+	0.535078i
$40$	2.19770	−	1.26884i	0.347486	−	0.200621i
$41$		−	3.03693i		−	0.474289i	−0.971474	−	0.237145i	$-0.923788\pi$
$41$		−	3.03693i		−	0.474289i	0.971474	−	0.237145i	$-0.0762115\pi$
$42$	−1.09018	+	4.45101i	−0.168218	+	0.686806i
$43$	5.11062			0.779362			0.389681	−	0.920950i	$-0.372585\pi$
$43$	5.11062			0.779362			0.389681	+	0.920950i	$0.372585\pi$
$44$	1.32440	+	2.29393i	0.199661	+	0.345822i
$45$	5.72010	+	5.02383i	0.852702	+	0.748908i
$46$	−4.09436	−	2.36388i	−0.603681	−	0.348535i
$47$	−6.66192	+	3.84626i	−0.971741	+	0.561035i	−0.899767	−	0.436371i	$-0.856263\pi$
$47$	−6.66192	+	3.84626i	−0.971741	+	0.561035i	−0.0719745	+	0.997406i	$0.522930\pi$
$48$	0.170404	−	1.72365i	0.0245957	−	0.248787i
$49$	6.72094	+	1.95677i	0.960134	+	0.279539i
$50$	−1.43982			−0.203621
$51$	5.82643	−	2.63734i	0.815863	−	0.369302i
$52$	−1.62022	+	3.22101i	−0.224684	+	0.446673i
$53$	−8.13530	−	4.69692i	−1.11747	−	0.645171i	−0.176716	−	0.984262i	$-0.556547\pi$
$53$	−8.13530	−	4.69692i	−1.11747	−	0.645171i	−0.940754	+	0.339091i	$0.889881\pi$
$54$	5.06171	−	1.17435i	0.688812	−	0.159808i
$55$		−	6.72180i		−	0.906367i
$56$	−2.61925	−	0.373536i	−0.350012	−	0.0499159i
$57$	0.0824136	−	0.833620i	0.0109160	−	0.110416i
$58$	6.00502	−	3.46700i	0.788497	−	0.455239i
$59$	−4.98510	−	2.87815i	−0.649005	−	0.374703i	0.139070	−	0.990283i	$-0.455589\pi$
$59$	−4.98510	−	2.87815i	−0.649005	−	0.374703i	−0.788075	+	0.615579i	$0.788922\pi$
$60$	−2.56153	+	3.57184i	−0.330692	+	0.461122i
$61$	4.25236	−	2.45510i	0.544459	−	0.314343i	−0.202425	−	0.979298i	$-0.564882\pi$
$61$	4.25236	−	2.45510i	0.544459	−	0.314343i	0.746884	+	0.664954i	$0.231549\pi$
$62$	5.42297			0.688717
$63$	−1.45892	−	7.80202i	−0.183807	−	0.982962i
$64$	1.00000			0.125000
$65$	7.64769	−	5.02300i	0.948579	−	0.623026i
$66$	−3.72824	−	2.67369i	−0.458914	−	0.329109i
$67$	−1.38217	−	0.797996i	−0.168859	−	0.0974908i	0.413189	−	0.910645i	$-0.364415\pi$
$67$	−1.38217	−	0.797996i	−0.168859	−	0.0974908i	−0.582048	+	0.813155i	$0.697748\pi$
$68$	1.84623	+	3.19777i	0.223888	+	0.387786i
$69$	8.14900	+	0.805629i	0.981024	+	0.0969863i
$70$	5.28236	+	4.14433i	0.631362	+	0.495342i
$71$	−12.9028			−1.53128			−0.765638	−	0.643272i	$-0.777577\pi$
$71$	−12.9028			−1.53128			−0.765638	+	0.643272i	$0.777577\pi$
$72$	0.962231	+	2.84150i	0.113400	+	0.334874i
$73$	−6.57447	+	11.3873i	−0.769484	+	1.33279i	0.168359	+	0.985726i	$0.446153\pi$
$73$	−6.57447	+	11.3873i	−0.769484	+	1.33279i	−0.937843	+	0.347060i	$0.887180\pi$
$74$	−5.90071	−	3.40678i	−0.685944	−	0.396030i
$75$	2.27193	−	1.02839i	0.262339	−	0.118748i
$76$	0.483637			0.0554770
$77$	−4.32580	+	5.51365i	−0.492970	+	0.628339i
$78$	0.255978	−	6.23975i	0.0289838	−	0.706513i
$79$	−3.75864	−	6.51016i	−0.422880	−	0.732450i	0.573339	−	0.819318i	$-0.305648\pi$
$79$	−3.75864	−	6.51016i	−0.422880	−	0.732450i	−0.996220	+	0.0868676i	$0.972314\pi$
$80$	−2.19770	−	1.26884i	−0.245710	−	0.141861i
$81$	−7.14822	+	5.46836i	−0.794247	+	0.607595i
$82$	−2.63006	+	1.51847i	−0.290442	+	0.167687i
$83$		−	3.10022i		−	0.340293i	−0.985419	−	0.170146i	$-0.945576\pi$
$83$		−	3.10022i		−	0.340293i	0.985419	−	0.170146i	$-0.0544241\pi$
$84$	4.39978	−	1.28139i	0.480055	−	0.139811i
$85$		−	9.37029i		−	1.01635i
$86$	−2.55531	−	4.42592i	−0.275546	−	0.477260i
$87$	−6.99916	+	9.75974i	−0.750389	+	1.04635i
$88$	1.32440	−	2.29393i	0.141181	−	0.244533i
$89$	−2.37997	+	1.37408i	−0.252276	+	0.145652i	−0.620806	−	0.783964i	$-0.713195\pi$
$89$	−2.37997	+	1.37408i	−0.252276	+	0.145652i	0.368530	+	0.929616i	$0.379861\pi$
$90$	1.49072	−	7.46566i	0.157135	−	0.786950i
$91$	−9.50566	−	0.801464i	−0.996464	−	0.0840162i
$92$			4.72776i			0.492903i
$93$	−8.55703	+	3.87335i	−0.887323	+	0.401648i
$94$	6.66192	+	3.84626i	0.687125	+	0.396712i
$95$	−1.06289	−	0.613658i	−0.109050	−	0.0629600i
$96$	−1.57792	+	0.714250i	−0.161046	+	0.0728978i
$97$	5.91584			0.600663			0.300331	−	0.953835i	$-0.402903\pi$
$97$	5.91584			0.600663			0.300331	+	0.953835i	$0.402903\pi$
$98$	−1.66586	−	6.79889i	−0.168277	−	0.686792i
$99$	7.79256	+	1.55599i	0.783182	+	0.156383i
$100$	0.719909	+	1.24692i	0.0719909	+	0.124692i
$101$	6.93191	−	12.0064i	0.689751	−	1.19468i	−0.282167	−	0.959365i	$-0.591053\pi$
$101$	6.93191	−	12.0064i	0.689751	−	1.19468i	0.971918	−	0.235318i	$-0.0756133\pi$
$102$	−5.19722	−	3.72716i	−0.514601	−	0.369044i
$103$	−7.90784	+	4.56559i	−0.779183	+	0.449861i	−0.836141	−	0.548515i	$-0.815193\pi$
$103$	−7.90784	+	4.56559i	−0.779183	+	0.449861i	0.0569579	+	0.998377i	$0.481860\pi$
$104$	3.59958	−	0.207354i	0.352968	−	0.0203327i
$105$	−11.2952	−	2.76652i	−1.10230	−	0.269984i
$106$			9.39383i			0.912410i
$107$	6.73065	−	3.88594i	0.650677	−	0.375668i	−0.138039	−	0.990427i	$-0.544080\pi$
$107$	6.73065	−	3.88594i	0.650677	−	0.375668i	0.788716	+	0.614758i	$0.210746\pi$
$108$	−3.54787	−	3.79640i	−0.341394	−	0.365308i
$109$	−11.8250	−	6.82718i	−1.13263	−	0.653925i	−0.188037	−	0.982162i	$-0.560212\pi$
$109$	−11.8250	−	6.82718i	−1.13263	−	0.653925i	−0.944596	+	0.328237i	$0.893546\pi$
$110$	−5.82125	+	3.36090i	−0.555034	+	0.320449i
$111$	11.7442	+	1.16106i	1.11471	+	0.110203i
$112$	0.986133	+	2.45511i	0.0931808	+	0.231986i
$113$			20.5235i			1.93068i	0.260987	+	0.965342i	$0.415952\pi$
$113$			20.5235i			1.93068i	−0.260987	+	0.965342i	$0.584048\pi$
$114$	−0.763143	+	0.345438i	−0.0714749	+	0.0323532i
$115$	5.99877	−	10.3902i	0.559389	−	0.968889i
$116$	−6.00502	−	3.46700i	−0.557552	−	0.321903i
$117$	4.05283	+	10.0287i	0.374684	+	0.927153i
$118$			5.75630i			0.529910i
$119$	−6.03022	+	7.68611i	−0.552790	+	0.704585i
$120$	4.37407	+	0.432430i	0.399296	+	0.0394753i
$121$	1.99194	+	3.45014i	0.181085	+	0.313649i
$122$	−4.25236	−	2.45510i	−0.384990	−	0.222274i
$123$	3.06547	−	4.27455i	0.276405	−	0.385423i
$124$	−2.71148	−	4.69643i	−0.243498	−	0.421752i
$125$			9.03460i			0.808079i
$126$	−6.02729	+	5.16447i	−0.536954	+	0.460088i
$127$	−10.7047			−0.949889			−0.474945	−	0.880016i	$-0.657532\pi$
$127$	−10.7047			−0.949889			−0.474945	+	0.880016i	$0.657532\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	7.19330	+	5.15865i	0.633335	+	0.454193i
$130$	−8.17389	−	4.11159i	−0.716897	−	0.360611i
$131$	−3.16842	−	5.48787i	−0.276826	−	0.479478i	0.693768	−	0.720199i	$-0.255949\pi$
$131$	−3.16842	−	5.48787i	−0.276826	−	0.479478i	−0.970594	+	0.240721i	$0.922616\pi$
$132$	−0.451365	+	4.56559i	−0.0392863	+	0.397384i
$133$	0.476931	+	1.18738i	0.0413551	+	0.102959i
$134$			1.59599i			0.137873i
$135$	2.98011	+	12.8450i	0.256487	+	1.10552i
$136$	1.84623	−	3.19777i	0.158313	−	0.274206i
$137$	−8.84134	+	15.3136i	−0.755367	+	1.30833i	0.189825	+	0.981818i	$0.439208\pi$
$137$	−8.84134	+	15.3136i	−0.755367	+	1.30833i	−0.945192	+	0.326515i	$0.894126\pi$
$138$	−3.37680	−	7.46005i	−0.287453	−	0.635042i
$139$			16.0938i			1.36506i	0.730858	+	0.682530i	$0.239120\pi$
$139$			16.0938i			1.36506i	−0.730858	+	0.682530i	$0.760880\pi$
$140$	0.947916	−	6.64682i	0.0801135	−	0.561759i
$141$	−13.2592	−	1.31084i	−1.11663	−	0.110392i
$142$	6.45138	+	11.1741i	0.541388	+	0.937711i
$143$	4.29163	−	8.53180i	0.358884	−	0.713465i
$144$	1.97969	−	2.25407i	0.164975	−	0.187839i
$145$	8.79813	+	15.2388i	0.730645	+	1.26551i
$146$	13.1489			1.08821
$147$	7.48471	+	9.53830i	0.617328	+	0.786706i
$148$			6.81356i			0.560071i
$149$	−1.28692	−	2.22901i	−0.105429	−	0.182608i	0.808485	−	0.588517i	$-0.200288\pi$
$149$	−1.28692	−	2.22901i	−0.105429	−	0.182608i	−0.913913	+	0.405910i	$0.866955\pi$
$150$	−2.02658	−	1.45335i	−0.165469	−	0.118666i
$151$	3.68114	+	2.12531i	0.299567	+	0.172955i	0.642248	−	0.766497i	$-0.278002\pi$
$151$	3.68114	+	2.12531i	0.299567	+	0.172955i	−0.342681	+	0.939452i	$0.611335\pi$
$152$	−0.241819	−	0.418842i	−0.0196141	−	0.0339726i
$153$	10.8629	+	2.16907i	0.878217	+	0.175359i
$154$	6.93786	+	0.989422i	0.559069	+	0.0797299i
$155$			13.7618i			1.10537i
$156$	−5.53177	+	2.89819i	−0.442896	+	0.232041i
$157$	−0.823957	−	0.475712i	−0.0657589	−	0.0379659i	0.466760	−	0.884384i	$-0.345421\pi$
$157$	−0.823957	−	0.475712i	−0.0657589	−	0.0379659i	−0.532519	+	0.846418i	$0.678755\pi$
$158$	−3.75864	+	6.51016i	−0.299022	+	0.517921i
$159$	−6.70955	−	14.8228i	−0.532102	−	1.17552i
$160$			2.53768i			0.200621i
$161$	−11.6072	+	4.66220i	−0.914772	+	0.367433i
$162$	8.30985	+	3.45636i	0.652883	+	0.271558i
$163$	−4.74897	+	2.74182i	−0.371968	+	0.214756i	−0.674318	−	0.738441i	$-0.735562\pi$
$163$	−4.74897	+	2.74182i	−0.371968	+	0.214756i	0.302350	+	0.953197i	$0.402229\pi$
$164$	2.63006	+	1.51847i	0.205373	+	0.118572i
$165$	6.78497	−	9.46107i	0.528209	−	0.736544i
$166$	−2.68487	+	1.55011i	−0.208386	+	0.120312i
$167$			6.15740i			0.476474i	0.971207	+	0.238237i	$0.0765694\pi$
$167$			6.15740i			0.476474i	−0.971207	+	0.238237i	$0.923431\pi$
$168$	−3.30960	−	3.16963i	−0.255341	−	0.244542i
$169$	12.9140	−	1.49278i	0.993385	−	0.114829i
$170$	−8.11491	+	4.68514i	−0.622385	+	0.359334i
$171$	0.957454	−	1.09015i	0.0732183	−	0.0833658i
$172$	−2.55531	+	4.42592i	−0.194840	+	0.337473i
$173$	−3.45361	−	5.98183i	−0.262573	−	0.454790i	0.704352	−	0.709851i	$-0.251238\pi$
$173$	−3.45361	−	5.98183i	−0.262573	−	0.454790i	−0.966925	+	0.255061i	$0.917905\pi$
$174$	11.9518	+	1.18158i	0.906061	+	0.0895753i
$175$	−2.35139	+	2.99708i	−0.177749	+	0.226558i
$176$	−2.64880			−0.199661
$177$	−4.11144	−	9.08301i	−0.309035	−	0.682721i
$178$	2.37997	+	1.37408i	0.178386	+	0.102991i
$179$	−1.49413	−	0.862637i	−0.111677	−	0.0644765i	0.443121	−	0.896462i	$-0.353871\pi$
$179$	−1.49413	−	0.862637i	−0.111677	−	0.0644765i	−0.554798	+	0.831985i	$0.687204\pi$
$180$	−7.21081	+	2.44183i	−0.537462	+	0.182004i
$181$		−	22.0637i		−	1.63998i	−0.572376	−	0.819991i	$-0.693978\pi$
$181$		−	22.0637i		−	1.63998i	0.572376	−	0.819991i	$-0.306022\pi$
$182$	4.05874	+	8.63288i	0.300854	+	0.639912i
$183$	8.46346	+	0.836717i	0.625637	+	0.0618519i
$184$	4.09436	−	2.36388i	0.301840	−	0.174268i
$185$	8.64531	−	14.9741i	0.635616	−	1.10092i
$186$	7.63294	+	5.47393i	0.559674	+	0.401368i
$187$	−4.89029	−	8.47023i	−0.357614	−	0.619405i
$188$		−	7.69252i		−	0.561035i
$189$	5.82188	−	12.4541i	0.423480	−	0.905906i
$190$			1.22732i			0.0890389i
$191$	−22.6677	+	13.0872i	−1.64018	+	0.946957i	−0.659409	+	0.751785i	$0.729193\pi$
$191$	−22.6677	+	13.0872i	−1.64018	+	0.946957i	−0.980769	+	0.195172i	$0.937473\pi$
$192$	1.40752	+	1.00940i	0.101579	+	0.0728470i
$193$	−1.84511	−	1.06527i	−0.132814	−	0.0766801i	0.432121	−	0.901816i	$-0.357765\pi$
$193$	−1.84511	−	1.06527i	−0.132814	−	0.0766801i	−0.564935	+	0.825136i	$0.691099\pi$
$194$	−2.95792	−	5.12327i	−0.212366	−	0.367829i
$195$	15.8345	+	0.649589i	1.13393	+	0.0465181i
$196$	−5.05508	+	4.84212i	−0.361077	+	0.345866i
$197$	−4.36762			−0.311180			−0.155590	−	0.987822i	$-0.549728\pi$
$197$	−4.36762			−0.311180			−0.155590	+	0.987822i	$0.549728\pi$
$198$	−2.54875	−	7.52655i	−0.181132	−	0.534889i
$199$	−23.1724	−	13.3786i	−1.64265	−	0.948383i	−0.979887	−	0.199551i	$-0.936052\pi$
$199$	−23.1724	−	13.3786i	−1.64265	−	0.948383i	−0.662760	−	0.748832i	$-0.730615\pi$
$200$	0.719909	−	1.24692i	0.0509053	−	0.0881705i
$201$	−1.13994	−	2.51836i	−0.0804050	−	0.177631i
$202$	−13.8638			−0.975455
$203$	2.59010	−	18.1619i	0.181789	−	1.27471i
$204$	−0.629210	+	6.36451i	−0.0440535	+	0.445604i
$205$	−3.85338	−	6.67425i	−0.269132	−	0.466150i
$206$	7.90784	+	4.56559i	0.550965	+	0.318100i
$207$	10.6567	+	9.35952i	0.740691	+	0.650532i
$208$	−1.97937	−	3.01365i	−0.137244	−	0.208959i
$209$	−1.28106			−0.0886125
$210$	3.25175	+	11.1652i	0.224392	+	0.770474i
$211$	−17.3315			−1.19315			−0.596575	−	0.802557i	$-0.703472\pi$
$211$	−17.3315			−1.19315			−0.596575	+	0.802557i	$0.703472\pi$
$212$	8.13530	−	4.69692i	0.558735	−	0.322586i
$213$	−18.1609	−	13.0240i	−1.24437	−	0.892391i
$214$	−6.73065	−	3.88594i	−0.460098	−	0.265638i
$215$	11.2316	−	6.48455i	0.765987	−	0.442243i
$216$	−1.51384	+	4.97074i	−0.103004	+	0.338216i
$217$	8.85634	−	11.2883i	0.601207	−	0.766298i
$218$			13.6544i			0.924790i
$219$	−20.7481	+	9.39164i	−1.40202	+	0.634628i
$220$	5.82125	+	3.36090i	0.392468	+	0.226592i
$221$	5.98259	−	11.8935i	0.402433	−	0.800040i
$222$	−4.86658	−	10.7513i	−0.326624	−	0.721579i
$223$	4.35497			0.291630			0.145815	−	0.989312i	$-0.453420\pi$
$223$	4.35497			0.291630			0.145815	+	0.989312i	$0.453420\pi$
$224$	1.63312	−	2.08157i	0.109117	−	0.139081i
$225$	4.23584	+	0.845796i	0.282389	+	0.0563864i
$226$	17.7738	−	10.2617i	1.18230	−	0.682600i
$227$	17.3580	+	10.0217i	1.15209	+	0.665160i	0.949396	−	0.314081i	$-0.101696\pi$
$227$	17.3580	+	10.0217i	1.15209	+	0.665160i	0.202696	+	0.979242i	$0.435030\pi$
$228$	0.680730	+	0.488182i	0.0450824	+	0.0323307i
$229$	13.3120	+	23.0571i	0.879683	+	1.52365i	0.851689	+	0.524047i	$0.175578\pi$
$229$	13.3120	+	23.0571i	0.879683	+	1.52365i	0.0279931	+	0.999608i	$0.491088\pi$
$230$	−11.9975			−0.791095
$231$	−11.6541	+	3.39413i	−0.766785	+	0.223318i
$232$			6.93400i			0.455239i
$233$	−20.2573	+	11.6956i	−1.32710	+	0.766203i	−0.984850	−	0.173406i	$-0.944523\pi$
$233$	−20.2573	+	11.6956i	−1.32710	+	0.766203i	−0.342252	+	0.939608i	$0.611190\pi$
$234$	6.65869	−	8.52420i	0.435292	−	0.557244i
$235$	−9.76058	+	16.9058i	−0.636710	+	1.10281i
$236$	4.98510	−	2.87815i	0.324503	−	0.187352i
$237$	1.28097	−	12.9572i	0.0832082	−	0.841658i
$238$	9.67148	+	1.37927i	0.626909	+	0.0894047i
$239$	10.6771			0.690642			0.345321	−	0.938485i	$-0.387770\pi$
$239$	10.6771			0.690642			0.345321	+	0.938485i	$0.387770\pi$
$240$	−1.81254	−	4.00427i	−0.116999	−	0.258474i
$241$	6.08041	−	10.5316i	0.391673	−	0.678398i	−0.600997	−	0.799251i	$-0.705230\pi$
$241$	6.08041	−	10.5316i	0.391673	−	0.678398i	0.992670	+	0.120853i	$0.0385630\pi$
$242$	1.99194	−	3.45014i	0.128047	−	0.221783i
$243$	−15.5810	+	0.481423i	−0.999523	+	0.0308833i
$244$			4.91020i			0.314343i
$245$	17.2534	−	4.22741i	1.10228	−	0.270080i
$246$	−5.23460	−	0.517505i	−0.333746	−	0.0329949i
$247$	−0.957295	−	1.45752i	−0.0609112	−	0.0927395i
$248$	−2.71148	+	4.69643i	−0.172179	+	0.298223i
$249$	3.12935	−	4.36362i	0.198315	−	0.276533i
$250$	7.82419	−	4.51730i	0.494845	−	0.285699i
$251$	25.7551			1.62565			0.812825	−	0.582508i	$-0.197928\pi$
$251$	25.7551			1.62565			0.812825	+	0.582508i	$0.197928\pi$
$252$	7.48621	+	2.63755i	0.471587	+	0.166150i
$253$		−	12.5229i		−	0.787307i
$254$	5.35236	+	9.27055i	0.335837	+	0.581686i
$255$	9.45835	−	13.1889i	0.592305	−	0.825919i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.74076	−	15.1394i	−0.545233	−	0.944372i	−0.998592	−	0.0530439i	$-0.983108\pi$
$257$	−8.74076	−	15.1394i	−0.545233	−	0.944372i	0.453359	−	0.891328i	$-0.350226\pi$
$258$	0.870869	−	8.80890i	0.0542179	−	0.548418i
$259$	−16.7280	+	6.71907i	−1.03943	+	0.417503i
$260$	0.526198	+	9.13459i	0.0326334	+	0.566503i
$261$	−19.7029	+	6.67211i	−1.21958	+	0.412993i
$262$	−3.16842	+	5.48787i	−0.195746	+	0.339042i
$263$	17.8986	+	10.3338i	1.10368	+	0.637208i	0.937184	−	0.348834i	$-0.113422\pi$
$263$	17.8986	+	10.3338i	1.10368	+	0.637208i	0.166493	+	0.986043i	$0.446756\pi$
$264$	4.17960	−	1.89190i	0.257237	−	0.116439i
$265$	−23.8385			−1.46439
$266$	0.789836	−	1.00672i	0.0484280	−	0.0617262i
$267$	−4.73684	−	0.468295i	−0.289890	−	0.0286592i
$268$	1.38217	−	0.797996i	0.0844295	−	0.0487454i
$269$	0.237662	−	0.411643i	0.0144905	−	0.0250983i	−0.858689	−	0.512497i	$-0.828721\pi$
$269$	0.237662	−	0.411643i	0.0144905	−	0.0250983i	0.873180	+	0.487398i	$0.162054\pi$
$270$	9.63404	−	9.00335i	0.586309	−	0.547927i
$271$	−0.772450	−	1.33792i	−0.0469230	−	0.0812730i	0.841610	−	0.540086i	$-0.181608\pi$
$271$	−0.772450	−	1.33792i	−0.0469230	−	0.0812730i	−0.888533	+	0.458813i	$0.848275\pi$
$272$	−3.69246			−0.223888
$273$	−12.5704	−	10.7231i	−0.760797	−	0.648990i
$274$	17.6827			1.06825
$275$	−1.90689	−	3.30284i	−0.114990	−	0.199169i
$276$	−4.77219	+	6.65443i	−0.287252	+	0.400549i
$277$	14.0171	−	24.2784i	0.842209	−	1.45875i	−0.0458149	−	0.998950i	$-0.514588\pi$
$277$	14.0171	−	24.2784i	0.842209	−	1.45875i	0.888023	−	0.459798i	$-0.152078\pi$
$278$	13.9377	−	8.04691i	0.835925	−	0.482622i
$279$	−15.9540	−	3.18563i	−0.955139	−	0.190718i
$280$	−6.23027	+	2.50249i	−0.372330	+	0.149552i
$281$	30.3889			1.81285			0.906426	−	0.422365i	$-0.138800\pi$
$281$	30.3889			1.81285			0.906426	+	0.422365i	$0.138800\pi$
$282$	5.49439	+	12.1382i	0.327186	+	0.722821i
$283$	6.07652	+	3.50828i	0.361212	+	0.208546i	0.669612	−	0.742711i	$-0.266460\pi$
$283$	6.07652	+	3.50828i	0.361212	+	0.208546i	−0.308400	+	0.951257i	$0.599794\pi$
$284$	6.45138	−	11.1741i	0.382819	−	0.663062i
$285$	−0.876611	−	1.93661i	−0.0519259	−	0.114715i
$286$	−9.53457	+	0.549239i	−0.563791	+	0.0324772i
$287$	−1.13441	+	7.95449i	−0.0669618	+	0.469539i
$288$	−2.94193	−	0.587433i	−0.173355	−	0.0346148i
$289$	1.68286	+	2.91480i	0.0989918	+	0.171459i
$290$	8.79813	−	15.2388i	0.516644	−	0.894854i
$291$	8.32667	+	5.97144i	0.488118	+	0.350052i
$292$	−6.57447	−	11.3873i	−0.384742	−	0.666393i
$293$		−	32.4228i		−	1.89416i	−0.321000	−	0.947079i	$-0.604019\pi$
$293$		−	32.4228i		−	1.89416i	0.321000	−	0.947079i	$-0.395981\pi$
$294$	4.51806	−	11.2511i	0.263498	−	0.656177i
$295$	−14.6076			−0.850490
$296$	5.90071	−	3.40678i	0.342972	−	0.198015i
$297$	9.39758	+	10.0559i	0.545303	+	0.583502i
$298$	−1.28692	+	2.22901i	−0.0745493	+	0.129123i
$299$	14.2478	−	9.35797i	0.823974	−	0.541186i
$300$	−0.245351	+	2.48174i	−0.0141653	+	0.143283i
$301$	−13.3860	−	1.90900i	−0.771555	−	0.110033i
$302$		−	4.25062i		−	0.244595i
$303$	21.8761	−	9.90223i	1.25675	−	0.568868i
$304$	−0.241819	+	0.418842i	−0.0138692	+	0.0240222i
$305$	6.23026	−	10.7911i	0.356743	−	0.617898i
$306$	−3.55300	−	10.4921i	−0.203112	−	0.599795i
$307$	30.0357			1.71423			0.857113	−	0.515128i	$-0.172256\pi$
$307$	30.0357			1.71423			0.857113	+	0.515128i	$0.172256\pi$
$308$	−2.61207	−	6.50308i	−0.148836	−	0.370547i
$309$	−15.7390	−	1.55599i	−0.895358	−	0.0885172i
$310$	11.9180	−	6.88088i	0.676898	−	0.390808i
$311$	3.19493	−	5.53379i	0.181168	−	0.313792i	−0.761111	−	0.648622i	$-0.775346\pi$
$311$	3.19493	−	5.53379i	0.181168	−	0.313792i	0.942279	+	0.334830i	$0.108679\pi$
$312$	5.27579	+	3.34156i	0.298683	+	0.189178i
$313$	8.58761	−	4.95806i	0.485400	−	0.280246i	−0.237264	−	0.971445i	$-0.576251\pi$
$313$	8.58761	−	4.95806i	0.485400	−	0.280246i	0.722664	+	0.691199i	$0.242917\pi$
$314$			0.951424i			0.0536920i
$315$	−13.1058	−	15.2953i	−0.738427	−	0.861794i
$316$	7.51729			0.422880
$317$	15.9691	+	27.6594i	0.896916	+	1.55350i	0.831415	+	0.555652i	$0.187531\pi$
$317$	15.9691	+	27.6594i	0.896916	+	1.55350i	0.0655007	+	0.997853i	$0.479136\pi$
$318$	−9.48212	+	13.2220i	−0.531731	+	0.741454i
$319$	15.9061	+	9.18337i	0.890569	+	0.514170i
$320$	2.19770	−	1.26884i	0.122855	−	0.0709303i
$321$	13.3960	+	1.32436i	0.747692	+	0.0739186i
$322$	9.84116	+	7.72099i	0.548427	+	0.430274i
$323$	−1.78581			−0.0993652
$324$	−1.16162	−	8.92472i	−0.0645346	−	0.495818i
$325$	2.33282	−	4.63767i	0.129402	−	0.257252i
$326$	4.74897	+	2.74182i	0.263021	+	0.151855i
$327$	−9.75263	−	21.5456i	−0.539322	−	1.19147i
$328$		−	3.03693i		−	0.167687i
$329$	18.8860	−	7.58585i	1.04122	−	0.418222i
$330$	−11.5860	−	1.14542i	−0.637789	−	0.0630533i
$331$	−13.1995	+	7.62074i	−0.725511	+	0.418874i	−0.816778	−	0.576953i	$-0.804242\pi$
$331$	−13.1995	+	7.62074i	−0.725511	+	0.418874i	0.0912670	+	0.995826i	$0.470908\pi$
$332$	2.68487	+	1.55011i	0.147351	+	0.0850732i
$333$	15.3582	+	13.4888i	0.841624	+	0.739179i
$334$	5.33246	−	3.07870i	0.291779	−	0.168459i
$335$	−4.05012			−0.221282
$336$	−1.09018	+	4.45101i	−0.0594740	+	0.242823i
$337$	23.2445			1.26621			0.633103	−	0.774067i	$-0.281781\pi$
$337$	23.2445			1.26621			0.633103	+	0.774067i	$0.281781\pi$
$338$	−7.74979	−	10.4375i	−0.421533	−	0.567724i
$339$	−20.7163	+	28.8872i	−1.12516	+	1.56894i
$340$	8.11491	+	4.68514i	0.440093	+	0.254088i
$341$	7.18217	+	12.4399i	0.388936	+	0.673657i
$342$	−1.42282	−	0.284104i	−0.0769375	−	0.0153626i
$343$	−16.8729	−	7.63579i	−0.911051	−	0.412294i
$344$	5.11062			0.275546
$345$	18.9312	−	8.56925i	1.01922	−	0.461353i
$346$	−3.45361	+	5.98183i	−0.185667	+	0.321585i
$347$	−21.2374	−	12.2614i	−1.14008	−	0.658226i	−0.193631	−	0.981074i	$-0.562026\pi$
$347$	−21.2374	−	12.2614i	−1.14008	−	0.658226i	−0.946451	+	0.322848i	$0.895360\pi$
$348$	−4.95261	−	10.9413i	−0.265488	−	0.586517i
$349$	−1.10347			−0.0590671			−0.0295336	−	0.999564i	$-0.509402\pi$
$349$	−1.10347			−0.0590671			−0.0295336	+	0.999564i	$0.509402\pi$
$350$	3.77125	+	0.537825i	0.201582	+	0.0287479i
$351$	−4.41850	+	18.2065i	−0.235842	+	0.971791i
$352$	1.32440	+	2.29393i	0.0705907	+	0.122267i
$353$	5.34237	+	3.08442i	0.284346	+	0.164167i	0.635389	−	0.772192i	$-0.280840\pi$
$353$	5.34237	+	3.08442i	0.284346	+	0.164167i	−0.351043	+	0.936359i	$0.614173\pi$
$354$	−5.81040	+	8.10211i	−0.308819	+	0.430622i
$355$	−28.3563	+	16.3715i	−1.50500	+	0.868911i
$356$		−	2.74815i		−	0.145652i
$357$	−16.2460	+	4.73147i	−0.859830	+	0.250416i
$358$			1.72527i			0.0911836i
$359$	−6.24235	−	10.8121i	−0.329459	−	0.570639i	0.652946	−	0.757405i	$-0.273533\pi$
$359$	−6.24235	−	10.8121i	−0.329459	−	0.570639i	−0.982405	+	0.186765i	$0.940200\pi$
$360$	5.72010	+	5.02383i	0.301476	+	0.264779i
$361$	9.38305	−	16.2519i	0.493845	−	0.855364i
$362$	−19.1077	+	11.0319i	−1.00428	+	0.579821i
$363$	−0.678868	+	6.86680i	−0.0356313	+	0.360413i
$364$	5.44692	−	7.83141i	0.285496	−	0.410478i
$365$			33.3678i			1.74655i
$366$	−3.50711	−	7.74793i	−0.183320	−	0.404991i
$367$	20.5085	+	11.8406i	1.07053	+	0.618073i	0.928327	−	0.371764i	$-0.121247\pi$
$367$	20.5085	+	11.8406i	1.07053	+	0.618073i	0.142207	+	0.989837i	$0.454580\pi$
$368$	−4.09436	−	2.36388i	−0.213433	−	0.123226i
$369$	8.62944	−	2.92223i	0.449231	−	0.152125i
$370$	−17.2906			−0.898897
$371$	19.5539	+	15.3412i	1.01519	+	0.796477i
$372$	0.924094	−	9.34729i	0.0479121	−	0.484634i
$373$	1.11557	+	1.93222i	0.0577619	+	0.100046i	0.893460	−	0.449142i	$-0.148270\pi$
$373$	1.11557	+	1.93222i	0.0577619	+	0.100046i	−0.835699	+	0.549188i	$0.814937\pi$
$374$	−4.89029	+	8.47023i	−0.252871	+	0.437985i
$375$	−9.11951	+	12.7164i	−0.470929	+	0.656672i
$376$	−6.66192	+	3.84626i	−0.343562	+	0.198356i
$377$	1.43779	+	24.9595i	0.0740500	+	1.28548i
$378$	−13.6965	+	1.18517i	−0.704474	+	0.0609586i
$379$		−	7.75732i		−	0.398467i	−0.979952	−	0.199233i	$-0.936155\pi$
$379$		−	7.75732i		−	0.398467i	0.979952	−	0.199233i	$-0.0638452\pi$
$380$	1.06289	−	0.613658i	0.0545250	−	0.0314800i
$381$	−15.0671	−	10.8053i	−0.771911	−	0.553573i
$382$	22.6677	+	13.0872i	1.15978	+	0.669600i
$383$	−7.94443	+	4.58672i	−0.405941	+	0.234370i	−0.689044	−	0.724719i	$-0.741970\pi$
$383$	−7.94443	+	4.58672i	−0.405941	+	0.234370i	0.283103	+	0.959090i	$0.408636\pi$
$384$	0.170404	−	1.72365i	0.00869589	−	0.0879595i
$385$	−2.51084	+	17.6061i	−0.127964	+	0.897288i
$386$			2.13055i			0.108442i
$387$	4.91759	+	14.5218i	0.249975	+	0.738185i
$388$	−2.95792	+	5.12327i	−0.150166	+	0.260095i
$389$	−29.7827	−	17.1950i	−1.51004	−	0.871823i	−0.999931	−	0.0117132i	$-0.996271\pi$
$389$	−29.7827	−	17.1950i	−1.51004	−	0.871823i	−0.510110	−	0.860109i	$-0.670395\pi$
$390$	−7.35468	−	14.0379i	−0.372419	−	0.710835i
$391$		−	17.4571i		−	0.882843i
$392$	6.72094	+	1.95677i	0.339459	+	0.0988318i
$393$	1.07982	−	10.9225i	0.0544699	−	0.550967i
$394$	2.18381	+	3.78247i	0.110019	+	0.190558i
$395$	−16.5207	−	9.53823i	−0.831247	−	0.479921i
$396$	−5.24381	+	5.97056i	−0.263511	+	0.300032i
$397$	6.32491	+	10.9551i	0.317438	+	0.549819i	0.979953	−	0.199230i	$-0.0638442\pi$
$397$	6.32491	+	10.9551i	0.317438	+	0.549819i	−0.662515	+	0.749049i	$0.730511\pi$
$398$			26.7572i			1.34122i
$399$	−0.527249	+	2.15268i	−0.0263955	+	0.107769i
$400$	−1.43982			−0.0719909
$401$	−11.1563	−	19.3233i	−0.557121	−	0.964962i	−0.997735	−	0.0672652i	$-0.978573\pi$
$401$	−11.1563	−	19.3233i	−0.557121	−	0.964962i	0.440614	−	0.897697i	$-0.354761\pi$
$402$	−1.61099	+	2.24639i	−0.0803490	+	0.112040i
$403$	−8.78639	+	17.4674i	−0.437681	+	0.870114i
$404$	6.93191	+	12.0064i	0.344875	+	0.597342i
$405$	−8.77115	+	21.0877i	−0.435842	+	1.04786i
$406$	−17.0237	+	6.83784i	−0.844872	+	0.339356i
$407$		−	18.0477i		−	0.894593i
$408$	5.82643	−	2.63734i	0.288451	−	0.130568i
$409$	15.2106	−	26.3456i	0.752118	−	1.30271i	−0.194677	−	0.980867i	$-0.562366\pi$
$409$	15.2106	−	26.3456i	0.752118	−	1.30271i	0.946794	−	0.321839i	$-0.104301\pi$
$410$	−3.85338	+	6.67425i	−0.190305	+	0.329618i
$411$	−27.9019	+	12.6299i	−1.37630	+	0.622985i
$412$		−	9.13119i		−	0.449861i
$413$	11.9821	+	9.40071i	0.589602	+	0.462579i
$414$	2.77724	−	13.9087i	0.136494	−	0.683577i
$415$	−3.93368	−	6.81333i	−0.193097	−	0.334453i
$416$	−1.62022	+	3.22101i	−0.0794377	+	0.157923i
$417$	−16.2451	+	22.6524i	−0.795525	+	1.10929i
$418$	0.640528	+	1.10943i	0.0313293	+	0.0542639i
$419$	22.9563			1.12149			0.560744	−	0.827989i	$-0.310515\pi$
$419$	22.9563			1.12149			0.560744	+	0.827989i	$0.310515\pi$
$420$	8.04350	−	8.39871i	0.392482	−	0.409815i
$421$		−	11.7102i		−	0.570721i	−0.958420	−	0.285360i	$-0.907887\pi$
$421$		−	11.7102i		−	0.570721i	0.958420	−	0.285360i	$-0.0921133\pi$
$422$	8.66575	+	15.0095i	0.421842	+	0.730652i
$423$	−17.3395	−	15.2288i	−0.843073	−	0.740452i
$424$	−8.13530	−	4.69692i	−0.395085	−	0.228102i
$425$	−2.65824	−	4.60420i	−0.128944	−	0.223337i
$426$	−2.19868	+	22.2398i	−0.106526	+	1.07752i
$427$	−12.0551	+	4.84211i	−0.583385	+	0.234326i
$428$			7.77189i			0.375668i
$429$	14.6525	−	7.67672i	0.707431	−	0.370636i
$430$	−11.2316	−	6.48455i	−0.541635	−	0.312713i
$431$	9.15519	−	15.8573i	0.440990	−	0.763817i	−0.556773	−	0.830664i	$-0.687961\pi$
$431$	9.15519	−	15.8573i	0.440990	−	0.763817i	0.997763	+	0.0668476i	$0.0212941\pi$
$432$	5.06171	−	1.17435i	0.243532	−	0.0565007i
$433$			21.1787i			1.01778i	0.860831	+	0.508891i	$0.169944\pi$
$433$			21.1787i			1.01778i	−0.860831	+	0.508891i	$0.830056\pi$
$434$	−14.2041	−	2.02568i	−0.681819	−	0.0972355i
$435$	−2.99847	+	30.3298i	−0.143766	+	1.45420i
$436$	11.8250	−	6.82718i	0.566316	−	0.326963i
$437$	−1.98019	−	1.14326i	−0.0947251	−	0.0546896i
$438$	18.5074	+	13.2725i	0.884319	+	0.634186i
$439$	−7.13298	+	4.11823i	−0.340439	+	0.196552i	−0.660466	−	0.750856i	$-0.729641\pi$
$439$	−7.13298	+	4.11823i	−0.340439	+	0.196552i	0.320027	+	0.947408i	$0.396308\pi$
$440$		−	6.72180i		−	0.320449i
$441$	0.906938	+	20.9804i	0.0431875	+	0.999067i
$442$	−13.2913	+	0.765647i	−0.632204	+	0.0364181i
$443$	−7.54716	+	4.35736i	−0.358577	+	0.207024i	−0.668456	−	0.743752i	$-0.733045\pi$
$443$	−7.54716	+	4.35736i	−0.358577	+	0.207024i	0.309880	+	0.950776i	$0.399711\pi$
$444$	−6.87759	+	9.59022i	−0.326396	+	0.455132i
$445$	−3.48696	+	6.03960i	−0.165298	+	0.286304i
$446$	−2.17749	−	3.77151i	−0.103107	−	0.178586i
$447$	0.438593	−	4.43640i	0.0207447	−	0.209834i
$448$	−2.61925	−	0.373536i	−0.123748	−	0.0176479i
$449$	−22.6845			−1.07055			−0.535274	−	0.844679i	$-0.679792\pi$
$449$	−22.6845			−1.07055			−0.535274	+	0.844679i	$0.679792\pi$
$450$	−1.38544	−	4.09124i	−0.0653102	−	0.192863i
$451$	−6.96650	−	4.02211i	−0.328040	−	0.189394i
$452$	−17.7738	−	10.2617i	−0.836011	−	0.482671i
$453$	3.03600	+	6.70715i	0.142644	+	0.315130i
$454$		−	20.0433i		−	0.940679i
$455$	−21.9075	+	10.2998i	−1.02704	+	0.482862i
$456$	0.0824136	−	0.833620i	0.00385937	−	0.0390378i
$457$	−11.5835	+	6.68771i	−0.541851	+	0.312838i	−0.745829	−	0.666138i	$-0.767946\pi$
$457$	−11.5835	+	6.68771i	−0.541851	+	0.312838i	0.203978	+	0.978976i	$0.434613\pi$
$458$	13.3120	−	23.0571i	0.622029	−	1.07739i
$459$	13.1004	+	14.0181i	0.611473	+	0.654307i
$460$	5.99877	+	10.3902i	0.279694	+	0.484445i
$461$			0.777510i			0.0362123i	0.999836	+	0.0181061i	$0.00576367\pi$
$461$			0.777510i			0.0362123i	−0.999836	+	0.0181061i	$0.994236\pi$
$462$	8.76647	+	8.39570i	0.407853	+	0.390603i
$463$		−	3.19686i		−	0.148571i	−0.997237	−	0.0742854i	$-0.976332\pi$
$463$		−	3.19686i		−	0.148571i	0.997237	−	0.0742854i	$-0.0236676\pi$
$464$	6.00502	−	3.46700i	0.278776	−	0.160951i
$465$	−13.8911	+	19.3700i	−0.644184	+	0.898260i
$466$	20.2573	+	11.6956i	0.938403	+	0.541787i
$467$	−0.719079	−	1.24548i	−0.0332750	−	0.0576340i	0.848908	−	0.528540i	$-0.177260\pi$
$467$	−0.719079	−	1.24548i	−0.0332750	−	0.0576340i	−0.882183	+	0.470906i	$0.843927\pi$
$468$	−10.7115	−	1.50449i	−0.495140	−	0.0695452i
$469$	3.32217	+	2.60644i	0.153404	+	0.120354i
$470$	19.5212			0.900444
$471$	−0.679554	−	1.50128i	−0.0313122	−	0.0691751i
$472$	−4.98510	−	2.87815i	−0.229458	−	0.132478i
$473$	6.76849	−	11.7234i	0.311216	−	0.539041i
$474$	−11.8617	+	5.36922i	−0.544826	+	0.246616i
$475$	−0.696350			−0.0319507
$476$	−3.64126	−	9.06538i	−0.166897	−	0.415511i
$477$	5.51824	−	27.6360i	0.252663	−	1.26536i
$478$	−5.33853	−	9.24661i	−0.244179	−	0.422930i
$479$	9.04541	+	5.22237i	0.413295	+	0.238616i	0.692205	−	0.721701i	$-0.256640\pi$
$479$	9.04541	+	5.22237i	0.413295	+	0.238616i	−0.278909	+	0.960317i	$0.589973\pi$
$480$	−2.56153	+	3.57184i	−0.116917	+	0.163031i
$481$	20.5337	−	13.4865i	0.936256	−	0.614932i
$482$	−12.1608			−0.553910
$483$	−21.0433	−	5.15409i	−0.957505	−	0.234519i
$484$	−3.98387			−0.181085
$485$	13.0012	−	7.50626i	0.590355	−	0.340842i
$486$	8.20744	+	13.2528i	0.372297	+	0.601161i
$487$	2.08097	+	1.20145i	0.0942979	+	0.0544429i	0.546407	−	0.837520i	$-0.315995\pi$
$487$	2.08097	+	1.20145i	0.0942979	+	0.0544429i	−0.452109	+	0.891962i	$0.649328\pi$
$488$	4.25236	−	2.45510i	0.192495	−	0.111137i
$489$	−9.45187	−	0.934434i	−0.427428	−	0.0422565i
$490$	−12.2878	−	12.8282i	−0.555104	−	0.579518i
$491$			12.3575i			0.557686i	0.960337	+	0.278843i	$0.0899509\pi$
$491$			12.3575i			0.557686i	−0.960337	+	0.278843i	$0.910049\pi$
$492$	2.16913	+	4.79205i	0.0977919	+	0.216042i
$493$	22.1733	+	12.8018i	0.998635	+	0.576562i
$494$	−0.783598	+	1.55780i	−0.0352557	+	0.0700887i
$495$	19.1000	−	6.46792i	0.858480	−	0.290712i
$496$	5.42297			0.243498
$497$	33.7956	+	4.81965i	1.51594	+	0.216191i
$498$	−5.34368	−	0.528289i	−0.239456	−	0.0236732i
$499$	−14.9074	+	8.60680i	−0.667348	+	0.385293i	−0.795071	−	0.606516i	$-0.792566\pi$
$499$	−14.9074	+	8.60680i	−0.667348	+	0.385293i	0.127723	+	0.991810i	$0.459233\pi$
$500$	−7.82419	−	4.51730i	−0.349909	−	0.202020i
$501$	−6.21526	+	8.66666i	−0.277678	+	0.387198i
$502$	−12.8776	−	22.3046i	−0.574754	−	0.995503i
$503$	−31.1852			−1.39048			−0.695240	−	0.718778i	$-0.744702\pi$
$503$	−31.1852			−1.39048			−0.695240	+	0.718778i	$0.744702\pi$
$504$	−1.45892	−	7.80202i	−0.0649855	−	0.347530i
$505$		−	35.1819i		−	1.56558i
$506$	−10.8451	+	6.26144i	−0.482125	+	0.278355i
$507$	19.6835	+	10.9343i	0.874177	+	0.485608i
$508$	5.35236	−	9.27055i	0.237472	−	0.411314i
$509$	4.87130	−	2.81245i	0.215917	−	0.124660i	−0.388141	−	0.921600i	$-0.626883\pi$
$509$	4.87130	−	2.81245i	0.215917	−	0.124660i	0.604058	+	0.796940i	$0.293549\pi$
$510$	−16.1511	−	1.59673i	−0.715182	−	0.0707045i
$511$	21.4738	−	27.3704i	0.949944	−	1.21080i
$512$	1.00000			0.0441942
$513$	2.44803	−	0.567957i	0.108083	−	0.0250759i
$514$	−8.74076	+	15.1394i	−0.385538	+	0.667772i
$515$	−11.5860	+	20.0676i	−0.510541	+	0.884283i
$516$	−8.06417	+	3.65026i	−0.355005	+	0.160694i
$517$			20.3759i			0.896133i
$518$	14.1829	+	11.1273i	0.623160	+	0.488907i
$519$	1.17702	−	11.9056i	0.0516654	−	0.522599i
$520$	7.64769	−	5.02300i	0.335373	−	0.220273i
$521$	1.86664	−	3.23312i	0.0817791	−	0.141646i	−0.822235	−	0.569148i	$-0.807273\pi$
$521$	1.86664	−	3.23312i	0.0817791	−	0.141646i	0.904014	+	0.427502i	$0.140606\pi$
$522$	15.6297	+	13.7272i	0.684093	+	0.600823i
$523$	20.8918	−	12.0619i	0.913533	−	0.527428i	0.0319666	−	0.999489i	$-0.489823\pi$
$523$	20.8918	−	12.0619i	0.913533	−	0.527428i	0.881566	+	0.472061i	$0.156490\pi$
$524$	6.33685			0.276826
$525$	−6.33488	+	1.84496i	−0.276477	+	0.0805209i
$526$		−	20.6676i		−	0.901149i
$527$	10.0120	+	17.3414i	0.436132	+	0.755402i
$528$	−3.72824	−	2.67369i	−0.162251	−	0.116357i
$529$	−0.324129	+	0.561408i	−0.0140926	+	0.0244090i
$530$	11.9193	+	20.6448i	0.517740	+	0.896752i
$531$	3.38144	−	16.9346i	0.146742	−	0.734899i
$532$	−1.26677	−	0.180656i	−0.0549213	−	0.00783244i
$533$	−0.629720	−	10.9317i	−0.0272762	−	0.473504i
$534$	1.96287	+	4.33638i	0.0849415	+	0.187653i
$535$	9.86128	−	17.0802i	0.426340	−	0.738443i
$536$	−1.38217	−	0.797996i	−0.0597007	−	0.0344682i
$537$	−1.23228	−	2.72235i	−0.0531767	−	0.117478i
$538$	−0.475324			−0.0204927
$539$	13.3899	−	12.8258i	0.576743	−	0.552446i
$540$	−12.6142	−	3.84165i	−0.542827	−	0.165318i
$541$	−29.5203	+	17.0435i	−1.26917	+	0.732759i	−0.974832	−	0.222941i	$-0.928434\pi$
$541$	−29.5203	+	17.0435i	−1.26917	+	0.732759i	−0.294343	+	0.955700i	$0.595101\pi$
$542$	−0.772450	+	1.33792i	−0.0331796	+	0.0574687i
$543$	22.2711	−	31.0551i	0.955743	−	1.33270i
$544$	1.84623	+	3.19777i	0.0791565	+	0.137103i
$545$	−34.6504			−1.48426
$546$	−3.00124	+	16.2478i	−0.128441	+	0.695344i
$547$	16.3522			0.699170			0.349585	−	0.936905i	$-0.386323\pi$
$547$	16.3522			0.699170			0.349585	+	0.936905i	$0.386323\pi$
$548$	−8.84134	−	15.3136i	−0.377683	−	0.654167i
$549$	11.0679	+	9.72069i	0.472367	+	0.414869i
$550$	−1.90689	+	3.30284i	−0.0813102	+	0.140833i
$551$	2.90425	−	1.67677i	0.123725	−	0.0714328i
$552$	8.14900	+	0.805629i	0.346844	+	0.0342898i
$553$	7.41304	+	18.4557i	0.315235	+	0.784817i
$554$	−28.0343			−1.19106
$555$	27.2833	−	12.3498i	1.15811	−	0.524221i
$556$	−13.9377	−	8.04691i	−0.591088	−	0.341265i
$557$	−9.83768	+	17.0394i	−0.416836	+	0.721981i	−0.995619	−	0.0935006i	$-0.970194\pi$
$557$	−9.83768	+	17.0394i	−0.416836	+	0.721981i	0.578784	+	0.815481i	$0.303528\pi$
$558$	5.21815	+	15.4093i	0.220902	+	0.652330i
$559$	18.3961	−	1.05971i	0.778072	−	0.0448208i
$560$	5.28236	+	4.14433i	0.223220	+	0.175130i
$561$	1.66665	−	16.8583i	0.0703660	−	0.711757i
$562$	−15.1945	−	26.3176i	−0.640940	−	1.11014i
$563$	7.14030	−	12.3674i	0.300928	−	0.521222i	−0.675419	−	0.737435i	$-0.736037\pi$
$563$	7.14030	−	12.3674i	0.300928	−	0.521222i	0.976346	+	0.216212i	$0.0693704\pi$
$564$	7.76482	−	10.8274i	0.326958	−	0.455915i
$565$	26.0410	+	45.1043i	1.09555	+	1.89755i
$566$		−	7.01656i		−	0.294928i
$567$	20.7656	−	11.6529i	0.872074	−	0.489374i
$568$	−12.9028			−0.541388
$569$	−14.4405	+	8.33720i	−0.605376	+	0.349514i	−0.771153	−	0.636649i	$-0.780320\pi$
$569$	−14.4405	+	8.33720i	−0.605376	+	0.349514i	0.165778	+	0.986163i	$0.446987\pi$
$570$	−1.23885	+	1.72747i	−0.0518897	+	0.0723559i
$571$	−0.208287	+	0.360764i	−0.00871655	+	0.0150975i	−0.870351	−	0.492432i	$-0.836108\pi$
$571$	−0.208287	+	0.360764i	−0.00871655	+	0.0150975i	0.861634	+	0.507530i	$0.169441\pi$
$572$	5.24294	+	7.98256i	0.219218	+	0.333768i
$573$	−45.1155	−	4.46022i	−1.88473	−	0.186328i
$574$	7.45599	−	2.99482i	0.311207	−	0.125001i
$575$		−	6.80712i		−	0.283877i
$576$	0.962231	+	2.84150i	0.0400930	+	0.118396i
$577$	−1.18972	+	2.06066i	−0.0495287	+	0.0857863i	−0.889727	−	0.456493i	$-0.849105\pi$
$577$	−1.18972	+	2.06066i	−0.0495287	+	0.0857863i	0.840198	+	0.542279i	$0.182439\pi$
$578$	1.68286	−	2.91480i	0.0699978	−	0.121240i
$579$	−1.52174	−	3.36184i	−0.0632415	−	0.139713i
$580$	−17.5963			−0.730645
$581$	−1.15804	+	8.12024i	−0.0480437	+	0.336884i
$582$	1.00808	−	10.1968i	0.0417864	−	0.422672i
$583$	−21.5488	+	12.4412i	−0.892458	+	0.515261i
$584$	−6.57447	+	11.3873i	−0.272054	+	0.471211i
$585$	21.6317	+	16.8976i	0.894360	+	0.698630i
$586$	−28.0789	+	16.2114i	−1.15993	+	0.669686i
$587$			28.1076i			1.16013i	0.814572	+	0.580063i	$0.196972\pi$
$587$			28.1076i			1.16013i	−0.814572	+	0.580063i	$0.803028\pi$
$588$	−12.0028	+	1.71279i	−0.494986	+	0.0706345i
$589$	2.62275			0.108068
$590$	7.30382	+	12.6506i	0.300694	+	0.520817i
$591$	−6.14751	−	4.40866i	−0.252875	−	0.181348i
$592$	−5.90071	−	3.40678i	−0.242518	−	0.140018i
$593$	−16.2280	+	9.36924i	−0.666404	+	0.384749i	−0.794713	−	0.606986i	$-0.792379\pi$
$593$	−16.2280	+	9.36924i	−0.666404	+	0.384749i	0.128309	+	0.991734i	$0.459045\pi$
$594$	4.00986	−	13.1665i	0.164527	−	0.540228i
$595$	−3.50014	+	24.5431i	−0.143492	+	1.00617i
$596$	2.57384			0.105429
$597$	−19.1113	−	42.2208i	−0.782174	−	1.72798i
$598$	−15.2282	−	7.66001i	−0.622726	−	0.313241i
$599$	−0.243067	−	0.140335i	−0.00993147	−	0.00573394i	0.495026	−	0.868878i	$-0.335159\pi$
$599$	−0.243067	−	0.140335i	−0.00993147	−	0.00573394i	−0.504958	+	0.863144i	$0.668492\pi$
$600$	2.27193	−	1.02839i	0.0927510	−	0.0419839i
$601$		−	7.38730i		−	0.301334i	−0.988585	−	0.150667i	$-0.951858\pi$
$601$		−	7.38730i		−	0.301334i	0.988585	−	0.150667i	$-0.0481421\pi$
$602$	5.03975	+	12.5471i	0.205405	+	0.511382i
$603$	0.937538	−	4.69529i	0.0381795	−	0.191207i
$604$	−3.68114	+	2.12531i	−0.149784	+	0.0864776i
$605$	8.75534	+	5.05490i	0.355955	+	0.205511i
$606$	−19.5136	−	13.9941i	−0.792687	−	0.568472i
$607$	22.6313	−	13.0662i	0.918577	−	0.530341i	0.0353963	−	0.999373i	$-0.488731\pi$
$607$	22.6313	−	13.0662i	0.918577	−	0.530341i	0.883181	+	0.469033i	$0.155397\pi$
$608$	0.483637			0.0196141
$609$	21.9782	−	22.9488i	0.890601	−	0.929931i
$610$	−12.4605			−0.504511
$611$	−23.1826	+	15.2263i	−0.937868	+	0.615991i
$612$	−7.30995	+	8.32305i	−0.295487	+	0.336439i
$613$	−15.4716	−	8.93253i	−0.624892	−	0.360781i	0.153879	−	0.988090i	$-0.450823\pi$
$613$	−15.4716	−	8.93253i	−0.624892	−	0.360781i	−0.778771	+	0.627308i	$0.784157\pi$
$614$	−15.0178	−	26.0117i	−0.606071	−	1.04974i
$615$	1.31326	−	13.2837i	0.0529558	−	0.535652i
$616$	−4.32580	+	5.51365i	−0.174291	+	0.222151i
$617$	−29.5144			−1.18821			−0.594103	−	0.804389i	$-0.702493\pi$
$617$	−29.5144			−1.18821			−0.594103	+	0.804389i	$0.702493\pi$
$618$	6.52195	+	14.4083i	0.262351	+	0.579588i
$619$	16.8277	−	29.1465i	0.676363	−	1.17149i	−0.299706	−	0.954032i	$-0.596888\pi$
$619$	16.8277	−	29.1465i	0.676363	−	1.17149i	0.976069	−	0.217463i	$-0.0697782\pi$
$620$	−11.9180	−	6.88088i	−0.478640	−	0.276343i
$621$	5.55203	+	23.9306i	0.222795	+	0.960301i
$622$	−6.38987			−0.256210
$623$	6.74700	−	2.71004i	0.270313	−	0.108576i
$624$	0.255978	−	6.23975i	0.0102473	−	0.249790i
$625$	15.0630	+	26.0899i	0.602520	+	1.04360i
$626$	−8.58761	−	4.95806i	−0.343230	−	0.198164i
$627$	−1.80311	−	1.29310i	−0.0720094	−	0.0516413i
$628$	0.823957	−	0.475712i	0.0328795	−	0.0189830i
$629$		−	25.1588i		−	1.00315i
$630$	−6.69325	+	18.9976i	−0.266666	+	0.756883i
$631$			41.0344i			1.63356i	0.576953	+	0.816778i	$0.304242\pi$
$631$			41.0344i			1.63356i	−0.576953	+	0.816778i	$0.695758\pi$
$632$	−3.75864	−	6.51016i	−0.149511	−	0.258960i
$633$	−24.3945	−	17.4944i	−0.969593	−	0.695340i
$634$	15.9691	−	27.6594i	0.634215	−	1.09849i
$635$	−23.5257	+	13.5826i	−0.933589	+	0.539008i
$636$	16.1917	+	1.60075i	0.642041	+	0.0634737i
$637$	24.5983	+	5.64995i	0.974622	+	0.223859i
$638$		−	18.3667i		−	0.727146i
$639$	−12.4154	−	36.6632i	−0.491147	−	1.45037i
$640$	−2.19770	−	1.26884i	−0.0868715	−	0.0501553i
$641$	−10.8867	−	6.28542i	−0.429998	−	0.248259i	0.269348	−	0.963043i	$-0.413192\pi$
$641$	−10.8867	−	6.28542i	−0.429998	−	0.248259i	−0.699346	+	0.714784i	$0.746525\pi$
$642$	−5.55107	−	12.2635i	−0.219083	−	0.484000i
$643$	44.1388			1.74067			0.870333	−	0.492464i	$-0.163904\pi$
$643$	44.1388			1.74067			0.870333	+	0.492464i	$0.163904\pi$
$644$	1.76599	−	12.3832i	0.0695898	−	0.487966i
$645$	22.3542	+	2.20999i	0.880195	+	0.0870181i
$646$	0.892906	+	1.54656i	0.0351309	+	0.0608485i
$647$	6.42771	−	11.1331i	0.252699	−	0.437688i	−0.711569	−	0.702616i	$-0.752015\pi$
$647$	6.42771	−	11.1331i	0.252699	−	0.437688i	0.964268	+	0.264928i	$0.0853483\pi$
$648$	−7.14822	+	5.46836i	−0.280809	+	0.214817i
$649$	−13.2045	+	7.62364i	−0.518323	+	0.299254i
$650$	−5.18275	+	0.298552i	−0.203284	+	0.0117102i
$651$	23.8598	−	6.94892i	0.935141	−	0.272350i
$652$		−	5.48364i		−	0.214756i
$653$	38.8978	−	22.4576i	1.52219	−	0.878835i	0.522531	−	0.852620i	$-0.324988\pi$
$653$	38.8978	−	22.4576i	1.52219	−	0.878835i	0.999656	−	0.0262147i	$-0.00834536\pi$
$654$	−13.7827	+	19.2188i	−0.538946	+	0.751515i
$655$	−13.9265	−	8.04045i	−0.544152	−	0.314166i
$656$	−2.63006	+	1.51847i	−0.102687	+	0.0592862i
$657$	−38.6832	−	7.72412i	−1.50918	−	0.301347i
$658$	−16.0125	−	12.5628i	−0.624233	−	0.489749i
$659$		−	4.26760i		−	0.166242i	−0.996539	−	0.0831210i	$-0.973511\pi$
$659$		−	4.26760i		−	0.166242i	0.996539	−	0.0831210i	$-0.0264888\pi$
$660$	4.80104	+	10.6065i	0.186880	+	0.412857i
$661$	6.63233	−	11.4875i	0.257968	−	0.446814i	−0.707729	−	0.706484i	$-0.750280\pi$
$661$	6.63233	−	11.4875i	0.257968	−	0.446814i	0.965697	+	0.259670i	$0.0836138\pi$
$662$	13.1995	+	7.62074i	0.513013	+	0.296188i
$663$	20.4259	−	10.7015i	0.793274	−	0.415610i
$664$		−	3.10022i		−	0.120312i
$665$	2.55474	+	2.00435i	0.0990687	+	0.0777254i
$666$	4.00250	−	20.0450i	0.155094	−	0.776727i
$667$	16.3911	+	28.3903i	0.634668	+	1.09928i
$668$	−5.33246	−	3.07870i	−0.206319	−	0.119118i
$669$	6.12971	+	4.39590i	0.236988	+	0.169955i
$670$	2.02506	+	3.50751i	0.0782349	+	0.135507i
$671$		−	13.0061i		−	0.502096i
$672$	4.39978	−	1.28139i	0.169725	−	0.0494306i
$673$	5.86953			0.226254			0.113127	−	0.993581i	$-0.463913\pi$
$673$	5.86953			0.226254			0.113127	+	0.993581i	$0.463913\pi$
$674$	−11.6222	−	20.1303i	−0.447672	−	0.775390i
$675$	5.10829	+	5.46612i	0.196618	+	0.210391i
$676$	−5.16422	+	11.9302i	−0.198624	+	0.458856i
$677$	18.4065	+	31.8810i	0.707419	+	1.22529i	0.965811	+	0.259245i	$0.0834739\pi$
$677$	18.4065	+	31.8810i	0.707419	+	1.22529i	−0.258393	+	0.966040i	$0.583193\pi$
$678$	35.3752	+	3.49728i	1.35858	+	0.134312i
$679$	−15.4951	−	2.20978i	−0.594646	−	0.0848037i
$680$		−	9.37029i		−	0.359334i
$681$	14.3159	+	31.6268i	0.548588	+	1.21194i
$682$	7.18217	−	12.4399i	0.275019	−	0.476348i
$683$	−5.49782	+	9.52250i	−0.210368	+	0.364368i	−0.951830	−	0.306627i	$-0.900800\pi$
$683$	−5.49782	+	9.52250i	−0.210368	+	0.364368i	0.741462	+	0.670995i	$0.234133\pi$
$684$	0.465371	+	1.37425i	0.0177939	+	0.0525459i
$685$			44.8730i			1.71451i
$686$	1.82366	+	18.4303i	0.0696278	+	0.703670i
$687$	−4.53684	+	45.8904i	−0.173091	+	1.75083i
$688$	−2.55531	−	4.42592i	−0.0974202	−	0.168737i
$689$	−30.2576	−	15.2201i	−1.15272	−	0.579838i
$690$	−16.8868	−	12.1103i	−0.642870	−	0.461031i
$691$	−17.4124	−	30.1592i	−0.662400	−	1.14731i	−0.979983	−	0.199081i	$-0.936204\pi$
$691$	−17.4124	−	30.1592i	−0.662400	−	1.14731i	0.317583	−	0.948231i	$-0.397129\pi$
$692$	6.90723			0.262573
$693$	−19.8294	−	6.98633i	−0.753259	−	0.265389i
$694$			24.5228i			0.930873i
$695$	20.4205	+	35.3693i	0.774593	+	1.34163i
$696$	−6.99916	+	9.75974i	−0.265303	+	0.369942i
$697$	−9.71140	−	5.60688i	−0.367846	−	0.212376i
$698$	0.551733	+	0.955629i	0.0208834	+	0.0361711i
$699$	−40.3181	−	3.98594i	−1.52497	−	0.150762i
$700$	−1.41985	−	3.53491i	−0.0536654	−	0.133607i
$701$		−	32.7821i		−	1.23816i	−0.785327	−	0.619081i	$-0.787505\pi$
$701$		−	32.7821i		−	1.23816i	0.785327	−	0.619081i	$-0.212495\pi$
$702$	17.9765	−	5.27672i	0.678481	−	0.199157i
$703$	−2.85380	−	1.64764i	−0.107633	−	0.0621421i
$704$	1.32440	−	2.29393i	0.0499151	−	0.0864556i
$705$	−30.8029	+	13.9430i	−1.16011	+	0.525123i
$706$		−	6.16884i		−	0.232167i
$707$	−22.6412	+	28.8585i	−0.851512	+	1.08534i
$708$	9.92184	+	0.980896i	0.372885	+	0.0368643i
$709$	−30.7026	+	17.7261i	−1.15306	+	0.665719i	−0.949631	−	0.313371i	$-0.898542\pi$
$709$	−30.7026	+	17.7261i	−1.15306	+	0.665719i	−0.203428	+	0.979090i	$0.565208\pi$
$710$	28.3563	+	16.3715i	1.06419	+	0.614413i
$711$	14.8819	−	16.9445i	0.558116	−	0.635467i
$712$	−2.37997	+	1.37408i	−0.0891931	+	0.0514956i
$713$			25.6385i			0.960169i
$714$	12.2206	+	11.7037i	0.457344	+	0.438001i
$715$	−1.39379	−	24.1957i	−0.0521249	−	0.904867i
$716$	1.49413	−	0.862637i	0.0558383	−	0.0322383i
$717$	15.0282	+	10.7774i	0.561238	+	0.402490i
$718$	−6.24235	+	10.8121i	−0.232962	+	0.403503i
$719$	22.2486	+	38.5357i	0.829733	+	1.43714i	0.898248	+	0.439489i	$0.144841\pi$
$719$	22.2486	+	38.5357i	0.829733	+	1.43714i	−0.0685151	+	0.997650i	$0.521826\pi$
$720$	1.49072	−	7.46566i	0.0555557	−	0.278229i
$721$	22.4180	−	9.00456i	0.834891	−	0.335348i
$722$	−18.7661			−0.698402
$723$	19.1888	−	8.68586i	0.713641	−	0.323031i
$724$	19.1077	+	11.0319i	0.710133	+	0.409996i
$725$	8.64614	+	4.99185i	0.321109	+	0.185393i
$726$	6.28625	−	2.84548i	0.233305	−	0.105606i
$727$			4.60691i			0.170861i	0.996344	+	0.0854305i	$0.0272265\pi$
$727$			4.60691i			0.170861i	−0.996344	+	0.0854305i	$0.972773\pi$
$728$	−9.50566	−	0.801464i	−0.352303	−	0.0297042i
$729$	−22.4166	−	15.0498i	−0.830243	−	0.557402i
$730$	28.8974	−	16.6839i	1.06954	−	0.617499i
$731$	9.43538	−	16.3426i	0.348980	−	0.604451i
$732$	−4.95635	+	6.91121i	−0.183192	+	0.255446i
$733$	0.675297	+	1.16965i	0.0249427	+	0.0432020i	0.878227	−	0.478243i	$-0.158726\pi$
$733$	0.675297	+	1.16965i	0.0249427	+	0.0432020i	−0.853285	+	0.521445i	$0.825393\pi$
$734$		−	23.6812i		−	0.874088i
$735$	28.5517	+	11.4654i	1.05314	+	0.422907i
$736$			4.72776i			0.174268i
$737$	−3.66109	+	2.11373i	−0.134858	+	0.0778603i
$738$	−6.84545	−	6.01220i	−0.251984	−	0.221312i
$739$	−21.6402	−	12.4940i	−0.796049	−	0.459599i	0.0460384	−	0.998940i	$-0.485340\pi$
$739$	−21.6402	−	12.4940i	−0.796049	−	0.459599i	−0.842088	+	0.539340i	$0.818674\pi$
$740$	8.64531	+	14.9741i	0.317808	+	0.550460i
$741$	0.123800	−	3.01777i	0.00454792	−	0.110861i
$742$	3.50894	−	24.6048i	0.128817	−	0.903271i
$743$	45.1839			1.65764			0.828818	−	0.559519i	$-0.189014\pi$
$743$	45.1839			1.65764			0.828818	+	0.559519i	$0.189014\pi$
$744$	−8.55703	+	3.87335i	−0.313716	+	0.142004i
$745$	−5.65652	−	3.26579i	−0.207239	−	0.119649i
$746$	1.11557	−	1.93222i	0.0408438	−	0.0707435i
$747$	8.80926	−	2.98312i	0.322314	−	0.109147i
$748$	9.78058			0.357614
$749$	−19.0808	+	7.66412i	−0.697198	+	0.280041i
$750$	15.5725	+	1.53953i	0.568626	+	0.0562157i
$751$	−13.1428	−	22.7639i	−0.479586	−	0.830667i	0.520140	−	0.854081i	$-0.325880\pi$
$751$	−13.1428	−	22.7639i	−0.479586	−	0.830667i	−0.999726	+	0.0234139i	$0.992546\pi$
$752$	6.66192	+	3.84626i	0.242935	+	0.140259i
$753$	36.2509	+	25.9972i	1.32106	+	0.947390i
$754$	20.8967	−	13.7249i	0.761012	−	0.499832i
$755$	10.7867			0.392568
$756$	7.87466	+	11.2690i	0.286399	+	0.409849i
$757$	−15.5743			−0.566056			−0.283028	−	0.959112i	$-0.591339\pi$
$757$	−15.5743			−0.566056			−0.283028	+	0.959112i	$0.591339\pi$
$758$	−6.71804	+	3.87866i	−0.244010	+	0.140879i
$759$	12.6406	−	17.6262i	0.458824	−	0.639791i
$760$	−1.06289	−	0.613658i	−0.0385550	−	0.0222597i
$761$	12.9920	−	7.50093i	0.470959	−	0.271909i	−0.245682	−	0.969351i	$-0.579012\pi$
$761$	12.9920	−	7.50093i	0.470959	−	0.271909i	0.716641	+	0.697442i	$0.245679\pi$
$762$	−1.82412	+	18.4512i	−0.0660810	+	0.668415i
$763$	28.4225	+	22.2992i	1.02896	+	0.807284i
$764$		−	26.1744i		−	0.946957i
$765$	26.6257	−	9.01638i	0.962652	−	0.325988i
$766$	7.94443	+	4.58672i	0.287044	+	0.165725i
$767$	−18.5411	−	9.32646i	−0.669480	−	0.336759i
$768$	−1.57792	+	0.714250i	−0.0569385	+	0.0257733i
$769$	−34.6475			−1.24942			−0.624710	−	0.780857i	$-0.714783\pi$
$769$	−34.6475			−1.24942			−0.624710	+	0.780857i	$0.714783\pi$
$770$	16.5027	−	6.62859i	0.594717	−	0.238878i
$771$	2.97892	−	30.1320i	0.107283	−	1.08518i
$772$	1.84511	−	1.06527i	0.0664069	−	0.0383400i
$773$	0.0831890	+	0.0480292i	0.00299210	+	0.00172749i	0.501495	−	0.865160i	$-0.332783\pi$
$773$	0.0831890	+	0.0480292i	0.00299210	+	0.00172749i	−0.498503	+	0.866888i	$0.666117\pi$
$774$	10.1175	−	11.5197i	0.363664	−	0.414066i
$775$	3.90404	+	6.76200i	0.140237	+	0.242898i
$776$	5.91584			0.212366
$777$	−30.3272	−	7.42797i	−1.08798	−	0.266477i
$778$			34.3901i			1.23294i
$779$	−1.27200	+	0.734387i	−0.0455740	+	0.0263121i
$780$	−8.47980	+	13.3883i	−0.303626	+	0.479377i
$781$	−17.0884	+	29.5980i	−0.611471	+	1.05910i
$782$	−15.1183	+	8.72854i	−0.540629	+	0.312132i
$783$	−34.4671	−	10.4970i	−1.23175	−	0.375131i
$784$	−1.66586	−	6.79889i	−0.0594949	−	0.242818i
$785$	−2.41441			−0.0861740
$786$	−9.99907	+	4.52609i	−0.356655	+	0.161440i
$787$	−22.1104	+	38.2963i	−0.788150	+	1.36512i	0.138949	+	0.990300i	$0.455628\pi$
$787$	−22.1104	+	38.2963i	−0.788150	+	1.36512i	−0.927099	+	0.374817i	$0.877706\pi$
$788$	2.18381	−	3.78247i	0.0777949	−	0.134745i
$789$	14.7618	+	32.6119i	0.525534	+	1.16101i
$790$			19.0765i			0.678710i
$791$	7.66626	−	53.7561i	0.272581	−	1.91135i
$792$	7.79256	+	1.55599i	0.276897	+	0.0552897i
$793$	14.7976	−	9.71908i	0.525480	−	0.345135i
$794$	6.32491	−	10.9551i	0.224462	−	0.388780i
$795$	−33.5533	−	24.0626i	−1.19001	−	0.853412i
$796$	23.1724	−	13.3786i	0.821324	−	0.474191i
$797$	−50.7960			−1.79929			−0.899644	−	0.436624i	$-0.856174\pi$
$797$	−50.7960			−1.79929			−0.899644	+	0.436624i	$0.856174\pi$
$798$	2.12790	−	0.619726i	0.0753267	−	0.0219381i
$799$			28.4044i			1.00487i
$800$	0.719909	+	1.24692i	0.0254526	+	0.0440853i
$801$	−6.19451	−	5.44050i	−0.218872	−	0.192231i
$802$	−11.1563	+	19.3233i	−0.393944	+	0.682331i
$803$	17.4144	+	30.1627i	0.614543	+	1.06442i
$804$	2.75093	+	0.271963i	0.0970178	+	0.00959141i
$805$	−19.5934	+	24.9737i	−0.690577	+	0.880208i
$806$	19.5204	−	1.12447i	0.687578	−	0.0396079i
$807$	0.750026	−	0.339500i	0.0264022	−	0.0119510i
$808$	6.93191	−	12.0064i	0.243864	−	0.422384i
$809$	−17.7051	−	10.2220i	−0.622477	−	0.359387i	0.155356	−	0.987859i	$-0.450348\pi$
$809$	−17.7051	−	10.2220i	−0.622477	−	0.359387i	−0.777833	+	0.628471i	$0.783681\pi$
$810$	22.6481	−	2.94783i	0.795773	−	0.103576i
$811$	41.1944			1.44653			0.723266	−	0.690570i	$-0.242640\pi$
$811$	41.1944			1.44653			0.723266	+	0.690570i	$0.242640\pi$
$812$	14.4336	+	11.3240i	0.506520	+	0.397395i
$813$	0.263257	−	2.66286i	0.00923282	−	0.0933907i
$814$	−15.6298	+	9.02386i	−0.547824	+	0.316286i
$815$	−6.95786	+	12.0514i	−0.243723	+	0.422141i
$816$	−5.19722	−	3.72716i	−0.181939	−	0.130477i
$817$	−1.23584	−	2.14054i	−0.0432366	−	0.0748881i
$818$	−30.4213			−1.06366
$819$	−6.86929	−	27.7815i	−0.240032	−	0.970765i
$820$	7.70676			0.269132
$821$	−17.3162	−	29.9925i	−0.604338	−	1.04674i	−0.992156	−	0.125008i	$-0.960104\pi$
$821$	−17.3162	−	29.9925i	−0.604338	−	1.04674i	0.387818	−	0.921736i	$-0.373229\pi$
$822$	24.8887	+	17.8489i	0.868094	+	0.622550i
$823$	5.62828	−	9.74847i	0.196190	−	0.339810i	−0.751100	−	0.660188i	$-0.770477\pi$
$823$	5.62828	−	9.74847i	0.196190	−	0.339810i	0.947290	+	0.320378i	$0.103810\pi$
$824$	−7.90784	+	4.56559i	−0.275483	+	0.159050i
$825$	0.649884	−	6.57363i	0.0226261	−	0.228864i
$826$	2.15019	−	15.0772i	0.0748146	−	0.524602i
$827$	35.0834			1.21997			0.609985	−	0.792413i	$-0.291176\pi$
$827$	35.0834			1.21997			0.609985	+	0.792413i	$0.291176\pi$
$828$	−13.4339	+	4.54920i	−0.466861	+	0.158096i
$829$	39.8985	+	23.0354i	1.38573	+	0.800054i	0.992831	−	0.119526i	$-0.0381376\pi$
$829$	39.8985	+	23.0354i	1.38573	+	0.800054i	0.392903	+	0.919580i	$0.371471\pi$
$830$	−3.93368	+	6.81333i	−0.136540	+	0.236494i
$831$	44.2360	−	20.0235i	1.53453	−	0.694607i
$832$	3.59958	−	0.207354i	0.124793	−	0.00718871i
$833$	18.6657	−	17.8793i	0.646728	−	0.619483i
$834$	27.7401	+	2.74245i	0.960560	+	0.0949632i
$835$	7.81275	+	13.5321i	0.270371	+	0.468297i
$836$	0.640528	−	1.10943i	0.0221531	−	0.0383704i
$837$	−19.2400	−	20.5877i	−0.665031	−	0.711616i
$838$	−11.4781	−	19.8807i	−0.396506	−	0.686768i
$839$		−	53.0141i		−	1.83025i	−0.403171	−	0.915125i	$-0.632092\pi$
$839$		−	53.0141i		−	1.83025i	0.403171	−	0.915125i	$-0.367908\pi$
$840$	−11.2952	−	2.76652i	−0.389723	−	0.0954539i
$841$	−19.0803			−0.657941
$842$	−10.1413	+	5.85510i	−0.349494	+	0.201780i
$843$	42.7731	+	30.6745i	1.47318	+	1.05649i
$844$	8.66575	−	15.0095i	0.298288	−	0.516649i
$845$	26.4870	−	19.6665i	0.911179	−	0.676547i
$846$	−4.51884	+	22.6308i	−0.155361	+	0.778064i
$847$	−3.92863	−	9.78083i	−0.134989	−	0.336073i
$848$			9.39383i			0.322586i
$849$	5.01158	+	11.0716i	0.171997	+	0.379977i
$850$	−2.65824	+	4.60420i	−0.0911768	+	0.157923i
$851$	16.1064	−	27.8972i	0.552122	−	0.956303i
$852$	20.3596	−	9.21580i	0.697508	−	0.315728i
$853$	−22.2010			−0.760147			−0.380074	−	0.924956i	$-0.624101\pi$
$853$	−22.2010			−0.760147			−0.380074	+	0.924956i	$0.624101\pi$
$854$	10.2209	+	8.01893i	0.349753	+	0.274402i
$855$	0.720966	−	3.61067i	0.0246565	−	0.123482i
$856$	6.73065	−	3.88594i	0.230049	−	0.132819i
$857$	−18.4059	+	31.8799i	−0.628732	+	1.08900i	0.359074	+	0.933309i	$0.383093\pi$
$857$	−18.4059	+	31.8799i	−0.628732	+	1.08900i	−0.987806	+	0.155687i	$0.950241\pi$
$858$	−13.9745	−	8.85111i	−0.477082	−	0.302172i
$859$	−6.38470	+	3.68621i	−0.217843	+	0.125772i	−0.604951	−	0.796263i	$-0.706807\pi$
$859$	−6.38470	+	3.68621i	−0.217843	+	0.125772i	0.387108	+	0.922034i	$0.373474\pi$
$860$			12.9691i			0.442243i
$861$	−9.62594	+	10.0510i	−0.328051	+	0.342539i
$862$	−18.3104			−0.623654
$863$	−17.7758	−	30.7886i	−0.605096	−	1.04806i	−0.992036	−	0.125952i	$-0.959801\pi$
$863$	−17.7758	−	30.7886i	−0.605096	−	1.04806i	0.386940	−	0.922105i	$-0.373532\pi$
$864$	−3.54787	−	3.79640i	−0.120701	−	0.129156i
$865$	−15.1800	−	8.76417i	−0.516135	−	0.297991i
$866$	18.3413	−	10.5893i	0.623261	−	0.359840i
$867$	−0.573532	+	5.80132i	−0.0194782	+	0.197023i
$868$	5.34777	+	13.3140i	0.181515	+	0.451905i
$869$	−19.9118			−0.675460
$870$	27.7656	−	12.5681i	0.941341	−	0.426099i
$871$	−5.14071	−	2.58586i	−0.174186	−	0.0876184i
$872$	−11.8250	−	6.82718i	−0.400446	−	0.231198i
$873$	5.69241	+	16.8099i	0.192659	+	0.568928i
$874$			2.28652i			0.0773428i
$875$	3.37475	−	23.6639i	0.114087	−	0.799985i
$876$	2.24063	−	22.6642i	0.0757039	−	0.765751i
$877$	33.3702	−	19.2663i	1.12683	−	0.650576i	0.183695	−	0.982983i	$-0.441194\pi$
$877$	33.3702	−	19.2663i	1.12683	−	0.650576i	0.943136	+	0.332407i	$0.107861\pi$
$878$	7.13298	+	4.11823i	0.240727	+	0.138984i
$879$	32.7275	−	45.6357i	1.10387	−	1.53925i
$880$	−5.82125	+	3.36090i	−0.196234	+	0.113296i
$881$	19.2791			0.649530			0.324765	−	0.945795i	$-0.394715\pi$
$881$	19.2791			0.649530			0.324765	+	0.945795i	$0.394715\pi$
$882$	17.7161	−	11.2756i	0.596532	−	0.379670i
$883$	5.53806			0.186371			0.0931853	−	0.995649i	$-0.470295\pi$
$883$	5.53806			0.186371			0.0931853	+	0.995649i	$0.470295\pi$
$884$	7.30873	+	11.1278i	0.245819	+	0.374269i
$885$	−20.5606	−	14.7449i	−0.691136	−	0.495645i
$886$	7.54716	+	4.35736i	0.253552	+	0.146388i
$887$	25.0298	+	43.3529i	0.840418	+	1.45565i	0.889541	+	0.456855i	$0.151024\pi$
$887$	25.0298	+	43.3529i	0.840418	+	1.45565i	−0.0491228	+	0.998793i	$0.515643\pi$
$888$	11.7442	+	1.16106i	0.394109	+	0.0389625i
$889$	28.0383	+	3.99860i	0.940375	+	0.134109i
$890$	6.97393			0.233767
$891$	3.07690	+	23.6398i	0.103080	+	0.791962i
$892$	−2.17749	+	3.77151i	−0.0729076	+	0.126280i
$893$	3.22195	+	1.86020i	0.107819	+	0.0622491i
$894$	−4.06133	+	1.83837i	−0.135831	+	0.0614842i
$895$	−4.37819			−0.146347
$896$	0.986133	+	2.45511i	0.0329444	+	0.0820193i
$897$	29.5001	+	1.21020i	0.984978	+	0.0404075i
$898$	11.3423	+	19.6454i	0.378496	+	0.655574i
$899$	−32.5650	−	18.8014i	−1.08610	−	0.627062i
$900$	−2.85040	+	3.24545i	−0.0950134	+	0.108182i
$901$	−30.0393	+	17.3432i	−1.00075	+	0.577785i
$902$			8.04422i			0.267843i
$903$	−16.9141	−	16.1987i	−0.562866	−	0.539060i
$904$			20.5235i			0.682600i
$905$	−27.9953	−	48.4893i	−0.930596	−	1.61184i
$906$	4.29056	−	5.98283i	0.142544	−	0.198766i
$907$	2.26274	−	3.91918i	0.0751330	−	0.130134i	−0.826011	−	0.563654i	$-0.809395\pi$
$907$	2.26274	−	3.91918i	0.0751330	−	0.130134i	0.901144	+	0.433520i	$0.142729\pi$
$908$	−17.3580	+	10.0217i	−0.576046	+	0.332580i
$909$	40.7863	+	8.14406i	1.35280	+	0.270121i
$910$	19.8736	+	13.8225i	0.658804	+	0.458213i
$911$		−	35.0796i		−	1.16224i	−0.813818	−	0.581120i	$-0.802615\pi$
$911$		−	35.0796i		−	1.16224i	0.813818	−	0.581120i	$-0.197385\pi$
$912$	−0.763143	+	0.345438i	−0.0252702	+	0.0114386i
$913$	−7.11166	−	4.10592i	−0.235362	−	0.135886i
$914$	11.5835	+	6.68771i	0.383147	+	0.221210i
$915$	19.6618	−	8.89992i	0.649998	−	0.294222i
$916$	−26.6240			−0.879683
$917$	6.24897	+	15.5576i	0.206359	+	0.513758i
$918$	5.58981	−	18.3543i	0.184491	−	0.605781i
$919$	−20.4670	−	35.4499i	−0.675144	−	1.16938i	−0.976427	−	0.215848i	$-0.930748\pi$
$919$	−20.4670	−	35.4499i	−0.675144	−	1.16938i	0.301283	−	0.953535i	$-0.402585\pi$
$920$	5.99877	−	10.3902i	0.197774	−	0.342554i
$921$	42.2758	+	30.3179i	1.39304	+	0.999010i
$922$	0.673343	−	0.388755i	0.0221754	−	0.0128030i
$923$	−46.4446	+	2.67544i	−1.52874	+	0.0880632i
$924$	2.88765	−	11.7898i	0.0949968	−	0.387857i
$925$		−	9.81029i		−	0.322560i
$926$	−2.76857	+	1.59843i	−0.0909807	+	0.0525277i
$927$	−20.5823	−	18.0770i	−0.676011	−	0.593725i
$928$	−6.00502	−	3.46700i	−0.197124	−	0.113810i
$929$	15.4303	−	8.90866i	0.506250	−	0.292284i	−0.225041	−	0.974349i	$-0.572251\pi$
$929$	15.4303	−	8.90866i	0.506250	−	0.292284i	0.731291	+	0.682066i	$0.238918\pi$
$930$	23.7204	+	2.34506i	0.777823	+	0.0768974i
$931$	−0.805671	−	3.28820i	−0.0264048	−	0.107766i
$932$		−	23.3912i		−	0.766203i
$933$	10.0827	−	4.56396i	0.330094	−	0.149417i
$934$	−0.719079	+	1.24548i	−0.0235290	+	0.0407534i
$935$	−21.4947	−	12.4100i	−0.702953	−	0.405850i
$936$	4.05283	+	10.0287i	0.132471	+	0.327798i
$937$		−	30.8788i		−	1.00877i	−0.863480	−	0.504383i	$-0.831720\pi$
$937$		−	30.8788i		−	1.00877i	0.863480	−	0.504383i	$-0.168280\pi$
$938$	0.596161	−	4.18030i	0.0194654	−	0.136492i
$939$	17.0919	+	1.68974i	0.557773	+	0.0551427i
$940$	−9.76058	−	16.9058i	−0.318355	−	0.551407i
$941$	12.9864	+	7.49770i	0.423344	+	0.244418i	0.696507	−	0.717550i	$-0.254736\pi$
$941$	12.9864	+	7.49770i	0.423344	+	0.244418i	−0.273163	+	0.961968i	$0.588070\pi$
$942$	−0.960365	+	1.33915i	−0.0312904	+	0.0436318i
$943$	−7.17895	−	12.4343i	−0.233779	−	0.404917i
$944$			5.75630i			0.187352i
$945$	−3.00758	−	34.7574i	−0.0978367	−	1.13066i
$946$	−13.5370			−0.440125
$947$	8.13729	+	14.0942i	0.264426	+	0.458000i	0.967413	−	0.253203i	$-0.0814841\pi$
$947$	8.13729	+	14.0942i	0.264426	+	0.458000i	−0.702987	+	0.711203i	$0.748151\pi$
$948$	10.5807	+	7.58793i	0.343646	+	0.246445i
$949$	−21.3042	+	42.3529i	−0.691563	+	1.37483i
$950$	0.348175	+	0.603057i	0.0112963	+	0.0195657i
$951$	−5.44240	+	55.0503i	−0.176482	+	1.78513i
$952$	−6.03022	+	7.68611i	−0.195441	+	0.249108i
$953$			35.3790i			1.14604i	0.819542	+	0.573019i	$0.194228\pi$
$953$			35.3790i			1.14604i	−0.819542	+	0.573019i	$0.805772\pi$
$954$	−26.6926	+	9.03904i	−0.864204	+	0.292650i
$955$	−33.2111	+	57.5234i	−1.07469	+	1.86141i
$956$	−5.33853	+	9.24661i	−0.172660	+	0.299057i
$957$	13.1184	+	28.9813i	0.424059	+	0.936834i
$958$		−	10.4447i		−	0.337454i
$959$	28.8779	−	36.8077i	0.932515	−	1.18858i
$960$	4.37407	+	0.432430i	0.141172	+	0.0139566i
$961$	0.795717	+	1.37822i	0.0256683	+	0.0444588i
$962$	−21.9465	−	11.0394i	−0.707584	−	0.355926i
$963$	17.5183	+	15.3860i	0.564521	+	0.495806i
$964$	6.08041	+	10.5316i	0.195837	+	0.339199i
$965$	−5.40665			−0.174046
$966$	6.05809	+	20.8011i	0.194916	+	0.669265i
$967$		−	8.97650i		−	0.288665i	−0.989529	−	0.144332i	$-0.953897\pi$
$967$		−	8.97650i		−	0.288665i	0.989529	−	0.144332i	$-0.0461035\pi$
$968$	1.99194	+	3.45014i	0.0640233	+	0.110892i
$969$	−2.51357	−	1.80260i	−0.0807474	−	0.0579077i
$970$	−13.0012	−	7.50626i	−0.417444	−	0.241011i
$971$	−1.17336	−	2.03232i	−0.0376550	−	0.0652203i	0.846584	−	0.532256i	$-0.178655\pi$
$971$	−1.17336	−	2.03232i	−0.0376550	−	0.0652203i	−0.884239	+	0.467035i	$0.845322\pi$
$972$	7.37359	−	13.7343i	0.236508	−	0.440527i
$973$	6.01163	−	42.1537i	0.192724	−	1.35139i
$974$		−	2.40290i		−	0.0769939i
$975$	7.96475	−	4.17287i	0.255076	−	0.133639i
$976$	−4.25236	−	2.45510i	−0.136115	−	0.0785858i
$977$	−17.3396	+	30.0330i	−0.554742	+	0.960841i	0.443182	+	0.896432i	$0.353850\pi$
$977$	−17.3396	+	30.0330i	−0.554742	+	0.960841i	−0.997924	+	0.0644089i	$0.979484\pi$
$978$	3.91669	+	8.65277i	0.125242	+	0.276685i
$979$			7.27929i			0.232647i
$980$	−4.96566	+	17.0556i	−0.158622	+	0.544821i
$981$	8.02102	−	40.1701i	0.256091	−	1.28253i
$982$	10.7019	−	6.17874i	0.341511	−	0.197172i
$983$	22.3427	+	12.8996i	0.712621	+	0.411432i	0.812031	−	0.583615i	$-0.198362\pi$
$983$	22.3427	+	12.8996i	0.712621	+	0.411432i	−0.0994096	+	0.995047i	$0.531695\pi$
$984$	3.06547	−	4.27455i	0.0977238	−	0.136268i
$985$	−9.59869	+	5.54180i	−0.305840	+	0.176577i
$986$		−	25.6035i		−	0.815382i
$987$	34.2395	+	8.38620i	1.08986	+	0.266936i
$988$	1.74089	−	0.100284i	0.0553852	−	0.00319046i
$989$	20.9247	−	12.0809i	0.665367	−	0.384150i
$990$	−15.1514	−	13.3071i	−0.481542	−	0.422928i
$991$	25.4169	−	44.0233i	0.807394	−	1.39845i	−0.107270	−	0.994230i	$-0.534211\pi$
$991$	25.4169	−	44.0233i	0.807394	−	1.39845i	0.914663	−	0.404217i	$-0.132456\pi$
$992$	−2.71148	−	4.69643i	−0.0860897	−	0.149112i
$993$	−26.2709	−	2.59721i	−0.833683	−	0.0824199i
$994$	−12.7238	−	31.6776i	−0.403576	−	1.00475i
$995$	−67.9011			−2.15261
$996$	2.21433	+	4.89191i	0.0701637	+	0.155006i
$997$	−31.3253	−	18.0857i	−0.992082	−	0.572779i	−0.0861859	−	0.996279i	$-0.527468\pi$
$997$	−31.3253	−	18.0857i	−0.992082	−	0.572779i	−0.905896	+	0.423500i	$0.860801\pi$
$998$	14.9074	+	8.60680i	0.471886	+	0.272444i
$999$	8.00147	+	34.4882i	0.253155	+	1.09116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.a.311.15	✓	36
3.2	odd	2		546.2.bg.b.311.16	yes	36
7.5	odd	6	inner	546.2.bg.a.467.16	yes	36
13.12	even	2		546.2.bg.b.311.15	yes	36
21.5	even	6		546.2.bg.b.467.15	yes	36
39.38	odd	2	inner	546.2.bg.a.311.16	yes	36
91.12	odd	6		546.2.bg.b.467.16	yes	36
273.194	even	6	inner	546.2.bg.a.467.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.15	✓	36	1.1	even	1	trivial
546.2.bg.a.311.16	yes	36	39.38	odd	2	inner
546.2.bg.a.467.15	yes	36	273.194	even	6	inner
546.2.bg.a.467.16	yes	36	7.5	odd	6	inner
546.2.bg.b.311.15	yes	36	13.12	even	2
546.2.bg.b.311.16	yes	36	3.2	odd	2
546.2.bg.b.467.15	yes	36	21.5	even	6
546.2.bg.b.467.16	yes	36	91.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19770 - 1.26884i) q^{5} +(0.170404 - 1.72365i) q^{6} +(-2.61925 - 0.373536i) q^{7} +1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19770 - 1.26884i) q^{5} +(0.170404 - 1.72365i) q^{6} +(-2.61925 - 0.373536i) q^{7} +1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +(-2.19770 - 1.26884i) q^{10} +(1.32440 - 2.29393i) q^{11} +(-1.57792 + 0.714250i) q^{12} +(3.59958 - 0.207354i) q^{13} +(0.986133 + 2.45511i) q^{14} +(4.37407 + 0.432430i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.84623 - 3.19777i) q^{17} +(1.97969 - 2.25407i) q^{18} +(-0.241819 - 0.418842i) q^{19} +2.53768i q^{20} +(-3.30960 - 3.16963i) q^{21} -2.64880 q^{22} +(4.09436 - 2.36388i) q^{23} +(1.40752 + 1.00940i) q^{24} +(0.719909 - 1.24692i) q^{25} +(-1.97937 - 3.01365i) q^{26} +(-1.51384 + 4.97074i) q^{27} +(1.63312 - 2.08157i) q^{28} +6.93400i q^{29} +(-1.81254 - 4.00427i) q^{30} +(-2.71148 + 4.69643i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.17960 - 1.89190i) q^{33} -3.69246 q^{34} +(-6.23027 + 2.50249i) q^{35} +(-2.94193 - 0.587433i) q^{36} +(5.90071 - 3.40678i) q^{37} +(-0.241819 + 0.418842i) q^{38} +(5.27579 + 3.34156i) q^{39} +(2.19770 - 1.26884i) q^{40} -3.03693i q^{41} +(-1.09018 + 4.45101i) q^{42} +5.11062 q^{43} +(1.32440 + 2.29393i) q^{44} +(5.72010 + 5.02383i) q^{45} +(-4.09436 - 2.36388i) q^{46} +(-6.66192 + 3.84626i) q^{47} +(0.170404 - 1.72365i) q^{48} +(6.72094 + 1.95677i) q^{49} -1.43982 q^{50} +(5.82643 - 2.63734i) q^{51} +(-1.62022 + 3.22101i) q^{52} +(-8.13530 - 4.69692i) q^{53} +(5.06171 - 1.17435i) q^{54} -6.72180i q^{55} +(-2.61925 - 0.373536i) q^{56} +(0.0824136 - 0.833620i) q^{57} +(6.00502 - 3.46700i) q^{58} +(-4.98510 - 2.87815i) q^{59} +(-2.56153 + 3.57184i) q^{60} +(4.25236 - 2.45510i) q^{61} +5.42297 q^{62} +(-1.45892 - 7.80202i) q^{63} +1.00000 q^{64} +(7.64769 - 5.02300i) q^{65} +(-3.72824 - 2.67369i) q^{66} +(-1.38217 - 0.797996i) q^{67} +(1.84623 + 3.19777i) q^{68} +(8.14900 + 0.805629i) q^{69} +(5.28236 + 4.14433i) q^{70} -12.9028 q^{71} +(0.962231 + 2.84150i) q^{72} +(-6.57447 + 11.3873i) q^{73} +(-5.90071 - 3.40678i) q^{74} +(2.27193 - 1.02839i) q^{75} +0.483637 q^{76} +(-4.32580 + 5.51365i) q^{77} +(0.255978 - 6.23975i) q^{78} +(-3.75864 - 6.51016i) q^{79} +(-2.19770 - 1.26884i) q^{80} +(-7.14822 + 5.46836i) q^{81} +(-2.63006 + 1.51847i) q^{82} -3.10022i q^{83} +(4.39978 - 1.28139i) q^{84} -9.37029i q^{85} +(-2.55531 - 4.42592i) q^{86} +(-6.99916 + 9.75974i) q^{87} +(1.32440 - 2.29393i) q^{88} +(-2.37997 + 1.37408i) q^{89} +(1.49072 - 7.46566i) q^{90} +(-9.50566 - 0.801464i) q^{91} +4.72776i q^{92} +(-8.55703 + 3.87335i) q^{93} +(6.66192 + 3.84626i) q^{94} +(-1.06289 - 0.613658i) q^{95} +(-1.57792 + 0.714250i) q^{96} +5.91584 q^{97} +(-1.66586 - 6.79889i) q^{98} +(7.79256 + 1.55599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

Introduction

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