LMFDB - Embedded newform 471.2.e.b.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.2
Character	$\chi$	$=$	471.301
Dual form			471.2.e.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44281 q^{2} +(0.500000 - 0.866025i) q^{3} +3.96732 q^{4} +(0.189821 - 0.328779i) q^{5} +(-1.22140 + 2.11553i) q^{6} -0.758173 q^{7} -4.80578 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-2.44281 q^{2} +(0.500000 - 0.866025i) q^{3} +3.96732 q^{4} +(0.189821 - 0.328779i) q^{5} +(-1.22140 + 2.11553i) q^{6} -0.758173 q^{7} -4.80578 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.463696 + 0.803145i) q^{10} +(-2.13942 + 3.70558i) q^{11} +(1.98366 - 3.43580i) q^{12} +(3.17100 + 5.49234i) q^{13} +1.85207 q^{14} +(-0.189821 - 0.328779i) q^{15} +3.80497 q^{16} +(-1.15161 + 1.99464i) q^{17} +(1.22140 + 2.11553i) q^{18} +(0.788598 - 1.36589i) q^{19} +(0.753079 - 1.30437i) q^{20} +(-0.379087 + 0.656597i) q^{21} +(5.22619 - 9.05202i) q^{22} -8.72135 q^{23} +(-2.40289 + 4.16193i) q^{24} +(2.42794 + 4.20531i) q^{25} +(-7.74615 - 13.4167i) q^{26} -1.00000 q^{27} -3.00791 q^{28} +6.04904 q^{29} +(0.463696 + 0.803145i) q^{30} +(-3.76271 - 6.51720i) q^{31} +0.316752 q^{32} +(2.13942 + 3.70558i) q^{33} +(2.81315 - 4.87252i) q^{34} +(-0.143917 + 0.249272i) q^{35} +(-1.98366 - 3.43580i) q^{36} +(3.15999 + 5.47326i) q^{37} +(-1.92640 + 3.33661i) q^{38} +6.34200 q^{39} +(-0.912237 + 1.58004i) q^{40} -1.29065 q^{41} +(0.926036 - 1.60394i) q^{42} +(4.06221 + 7.03596i) q^{43} +(-8.48775 + 14.7012i) q^{44} -0.379642 q^{45} +21.3046 q^{46} +(5.06570 + 8.77405i) q^{47} +(1.90248 - 3.29520i) q^{48} -6.42517 q^{49} +(-5.93098 - 10.2728i) q^{50} +(1.15161 + 1.99464i) q^{51} +(12.5804 + 21.7898i) q^{52} +(-0.364008 - 0.630481i) q^{53} +2.44281 q^{54} +(0.812212 + 1.40679i) q^{55} +3.64361 q^{56} +(-0.788598 - 1.36589i) q^{57} -14.7767 q^{58} +11.1846 q^{59} +(-0.753079 - 1.30437i) q^{60} +(-1.09299 + 1.89312i) q^{61} +(9.19158 + 15.9203i) q^{62} +(0.379087 + 0.656597i) q^{63} -8.38369 q^{64} +2.40769 q^{65} +(-5.22619 - 9.05202i) q^{66} +1.85241 q^{67} +(-4.56878 + 7.91337i) q^{68} +(-4.36068 + 7.55291i) q^{69} +(0.351562 - 0.608923i) q^{70} +(4.02190 + 6.96613i) q^{71} +(2.40289 + 4.16193i) q^{72} +(0.744416 - 1.28937i) q^{73} +(-7.71925 - 13.3701i) q^{74} +4.85587 q^{75} +(3.12862 - 5.41893i) q^{76} +(1.62205 - 2.80947i) q^{77} -15.4923 q^{78} -6.94426 q^{79} +(0.722262 - 1.25099i) q^{80} +(-0.500000 + 0.866025i) q^{81} +3.15281 q^{82} +(4.04016 + 6.99776i) q^{83} +(-1.50396 + 2.60493i) q^{84} +(0.437197 + 0.757248i) q^{85} +(-9.92321 - 17.1875i) q^{86} +(3.02452 - 5.23863i) q^{87} +(10.2816 - 17.8082i) q^{88} +(1.54760 - 2.68052i) q^{89} +0.927392 q^{90} +(-2.40417 - 4.16414i) q^{91} -34.6004 q^{92} -7.52542 q^{93} +(-12.3745 - 21.4333i) q^{94} +(-0.299385 - 0.518550i) q^{95} +(0.158376 - 0.274315i) q^{96} +(-0.0305212 - 0.0528643i) q^{97} +15.6955 q^{98} +4.27883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.44281			−1.72733			−0.863663	−	0.504069i	$-0.831836\pi$
$2$	−2.44281			−1.72733			−0.863663	+	0.504069i	$0.831836\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	3.96732			1.98366
$5$	0.189821	−	0.328779i	0.0848905	−	0.147035i	−0.820454	−	0.571712i	$-0.806279\pi$
$5$	0.189821	−	0.328779i	0.0848905	−	0.147035i	0.905345	+	0.424678i	$0.139613\pi$
$6$	−1.22140	+	2.11553i	−0.498636	+	0.863663i
$7$	−0.758173			−0.286562			−0.143281	−	0.989682i	$-0.545765\pi$
$7$	−0.758173			−0.286562			−0.143281	+	0.989682i	$0.545765\pi$
$8$	−4.80578			−1.69910
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.463696	+	0.803145i	−0.146634	+	0.253977i
$11$	−2.13942	+	3.70558i	−0.645059	+	1.11727i	0.339229	+	0.940704i	$0.389834\pi$
$11$	−2.13942	+	3.70558i	−0.645059	+	1.11727i	−0.984288	+	0.176571i	$0.943500\pi$
$12$	1.98366	−	3.43580i	0.572633	−	0.991829i
$13$	3.17100	+	5.49234i	0.879477	+	1.52330i	0.851915	+	0.523680i	$0.175441\pi$
$13$	3.17100	+	5.49234i	0.879477	+	1.52330i	0.0275622	+	0.999620i	$0.491226\pi$
$14$	1.85207			0.494987
$15$	−0.189821	−	0.328779i	−0.0490115	−	0.0848905i
$16$	3.80497			0.951241
$17$	−1.15161	+	1.99464i	−0.279305	+	0.483771i	−0.971212	−	0.238216i	$-0.923438\pi$
$17$	−1.15161	+	1.99464i	−0.279305	+	0.483771i	0.691907	+	0.721987i	$0.256771\pi$
$18$	1.22140	+	2.11553i	0.287888	+	0.498636i
$19$	0.788598	−	1.36589i	0.180917	−	0.313357i	−0.761276	−	0.648428i	$-0.775427\pi$
$19$	0.788598	−	1.36589i	0.180917	−	0.313357i	0.942193	+	0.335071i	$0.108760\pi$
$20$	0.753079	−	1.30437i	0.168394	−	0.291666i
$21$	−0.379087	+	0.656597i	−0.0827235	+	0.143281i
$22$	5.22619	−	9.05202i	1.11423	−	1.92990i
$23$	−8.72135			−1.81853			−0.909264	−	0.416220i	$-0.863355\pi$
$23$	−8.72135			−1.81853			−0.909264	+	0.416220i	$0.863355\pi$
$24$	−2.40289	+	4.16193i	−0.490488	+	0.849550i
$25$	2.42794	+	4.20531i	0.485587	+	0.841062i
$26$	−7.74615	−	13.4167i	−1.51915	−	2.63124i
$27$	−1.00000			−0.192450
$28$	−3.00791			−0.568442
$29$	6.04904			1.12328			0.561640	−	0.827382i	$-0.310171\pi$
$29$	6.04904			1.12328			0.561640	+	0.827382i	$0.310171\pi$
$30$	0.463696	+	0.803145i	0.0846589	+	0.146634i
$31$	−3.76271	−	6.51720i	−0.675803	−	1.17052i	−0.976234	−	0.216721i	$-0.930464\pi$
$31$	−3.76271	−	6.51720i	−0.675803	−	1.17052i	0.300431	−	0.953804i	$-0.402870\pi$
$32$	0.316752			0.0559944
$33$	2.13942	+	3.70558i	0.372425	+	0.645059i
$34$	2.81315	−	4.87252i	0.482452	−	0.835631i
$35$	−0.143917	+	0.249272i	−0.0243264	+	0.0421346i
$36$	−1.98366	−	3.43580i	−0.330610	−	0.572633i
$37$	3.15999	+	5.47326i	0.519499	+	0.899798i	0.999743	+	0.0226637i	$0.00721469\pi$
$37$	3.15999	+	5.47326i	0.519499	+	0.899798i	−0.480244	+	0.877135i	$0.659452\pi$
$38$	−1.92640	+	3.33661i	−0.312503	+	0.541270i
$39$	6.34200			1.01553
$40$	−0.912237	+	1.58004i	−0.144237	+	0.249826i
$41$	−1.29065			−0.201566			−0.100783	−	0.994908i	$-0.532135\pi$
$41$	−1.29065			−0.201566			−0.100783	+	0.994908i	$0.532135\pi$
$42$	0.926036	−	1.60394i	0.142890	−	0.247494i
$43$	4.06221	+	7.03596i	0.619481	+	1.07297i	0.989580	+	0.143981i	$0.0459904\pi$
$43$	4.06221	+	7.03596i	0.619481	+	1.07297i	−0.370099	+	0.928992i	$0.620676\pi$
$44$	−8.48775	+	14.7012i	−1.27958	+	2.21629i
$45$	−0.379642			−0.0565936
$46$	21.3046			3.14119
$47$	5.06570	+	8.77405i	0.738909	+	1.27983i	0.952987	+	0.303011i	$0.0979918\pi$
$47$	5.06570	+	8.77405i	0.738909	+	1.27983i	−0.214078	+	0.976816i	$0.568675\pi$
$48$	1.90248	−	3.29520i	0.274600	−	0.475621i
$49$	−6.42517			−0.917882
$50$	−5.93098	−	10.2728i	−0.838768	−	1.45279i
$51$	1.15161	+	1.99464i	0.161257	+	0.279305i
$52$	12.5804	+	21.7898i	1.74458	+	3.02171i
$53$	−0.364008	−	0.630481i	−0.0500004	−	0.0866032i	0.839942	−	0.542676i	$-0.182589\pi$
$53$	−0.364008	−	0.630481i	−0.0500004	−	0.0866032i	−0.889942	+	0.456073i	$0.849256\pi$
$54$	2.44281			0.332424
$55$	0.812212	+	1.40679i	0.109519	+	0.189692i
$56$	3.64361			0.486898
$57$	−0.788598	−	1.36589i	−0.104452	−	0.180917i
$58$	−14.7767			−1.94027
$59$	11.1846			1.45611			0.728056	−	0.685518i	$-0.240424\pi$
$59$	11.1846			1.45611			0.728056	+	0.685518i	$0.240424\pi$
$60$	−0.753079	−	1.30437i	−0.0972221	−	0.168394i
$61$	−1.09299	+	1.89312i	−0.139943	+	0.242389i	−0.927475	−	0.373885i	$-0.878025\pi$
$61$	−1.09299	+	1.89312i	−0.139943	+	0.242389i	0.787532	+	0.616274i	$0.211359\pi$
$62$	9.19158	+	15.9203i	1.16733	+	2.02188i
$63$	0.379087	+	0.656597i	0.0477604	+	0.0827235i
$64$	−8.38369			−1.04796
$65$	2.40769			0.298637
$66$	−5.22619	−	9.05202i	−0.643299	−	1.11423i
$67$	1.85241			0.226308			0.113154	−	0.993577i	$-0.463905\pi$
$67$	1.85241			0.226308			0.113154	+	0.993577i	$0.463905\pi$
$68$	−4.56878	+	7.91337i	−0.554046	+	0.959637i
$69$	−4.36068	+	7.55291i	−0.524964	+	0.909264i
$70$	0.351562	−	0.608923i	0.0420197	−	0.0727802i
$71$	4.02190	+	6.96613i	0.477312	+	0.826728i	0.999662	−	0.0260030i	$-0.00827794\pi$
$71$	4.02190	+	6.96613i	0.477312	+	0.826728i	−0.522350	+	0.852731i	$0.674945\pi$
$72$	2.40289	+	4.16193i	0.283183	+	0.490488i
$73$	0.744416	−	1.28937i	0.0871273	−	0.150909i	−0.819168	−	0.573553i	$-0.805565\pi$
$73$	0.744416	−	1.28937i	0.0871273	−	0.150909i	0.906296	+	0.422644i	$0.138898\pi$
$74$	−7.71925	−	13.3701i	−0.897344	−	1.55425i
$75$	4.85587			0.560708
$76$	3.12862	−	5.41893i	0.358877	−	0.621594i
$77$	1.62205	−	2.80947i	0.184850	−	0.320169i
$78$	−15.4923			−1.75416
$79$	−6.94426			−0.781290			−0.390645	−	0.920541i	$-0.627748\pi$
$79$	−6.94426			−0.781290			−0.390645	+	0.920541i	$0.627748\pi$
$80$	0.722262	−	1.25099i	0.0807513	−	0.139865i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.15281			0.348170
$83$	4.04016	+	6.99776i	0.443465	+	0.768104i	0.997944	−	0.0640939i	$-0.0204157\pi$
$83$	4.04016	+	6.99776i	0.443465	+	0.768104i	−0.554479	+	0.832198i	$0.687082\pi$
$84$	−1.50396	+	2.60493i	−0.164095	+	0.284221i
$85$	0.437197	+	0.757248i	0.0474207	+	0.0821351i
$86$	−9.92321	−	17.1875i	−1.07005	−	1.85338i
$87$	3.02452	−	5.23863i	0.324263	−	0.561640i
$88$	10.2816	−	17.8082i	1.09602	−	1.89836i
$89$	1.54760	−	2.68052i	0.164045	−	0.284134i	−0.772271	−	0.635294i	$-0.780879\pi$
$89$	1.54760	−	2.68052i	0.164045	−	0.284134i	0.936316	+	0.351159i	$0.114212\pi$
$90$	0.927392			0.0977557
$91$	−2.40417	−	4.16414i	−0.252025	−	0.436521i
$92$	−34.6004			−3.60734
$93$	−7.52542			−0.780350
$94$	−12.3745	−	21.4333i	−1.27634	−	2.21068i
$95$	−0.299385	−	0.518550i	−0.0307162	−	0.0532021i
$96$	0.158376	−	0.274315i	0.0161642	−	0.0279972i
$97$	−0.0305212	−	0.0528643i	−0.00309896	−	0.00536756i	0.864472	−	0.502681i	$-0.167653\pi$
$97$	−0.0305212	−	0.0528643i	−0.00309896	−	0.00536756i	−0.867571	+	0.497314i	$0.834320\pi$
$98$	15.6955			1.58548
$99$	4.27883			0.430039
$100$	9.63239	+	16.6838i	0.963239	+	1.66838i
$101$	8.31099			0.826975			0.413487	−	0.910510i	$-0.364311\pi$
$101$	8.31099			0.826975			0.413487	+	0.910510i	$0.364311\pi$
$102$	−2.81315	−	4.87252i	−0.278544	−	0.482452i
$103$	−6.74109			−0.664219			−0.332110	−	0.943241i	$-0.607760\pi$
$103$	−6.74109			−0.664219			−0.332110	+	0.943241i	$0.607760\pi$
$104$	−15.2391	−	26.3949i	−1.49432	−	2.58824i
$105$	0.143917	+	0.249272i	0.0140449	+	0.0243264i
$106$	0.889203	+	1.54014i	0.0863670	+	0.149592i
$107$	−8.56696	−	14.8384i	−0.828199	−	1.43448i	−0.899450	−	0.437024i	$-0.856032\pi$
$107$	−8.56696	−	14.8384i	−0.828199	−	1.43448i	0.0712505	−	0.997458i	$-0.477301\pi$
$108$	−3.96732			−0.381755
$109$	−0.218999	+	0.379318i	−0.0209763	+	0.0363321i	−0.876323	−	0.481724i	$-0.840011\pi$
$109$	−0.218999	+	0.379318i	−0.0209763	+	0.0363321i	0.855347	+	0.518056i	$0.173344\pi$
$110$	−1.98408	−	3.43653i	−0.189174	−	0.327660i
$111$	6.31998			0.599866
$112$	−2.88482			−0.272590
$113$	3.29484	−	5.70683i	0.309952	−	0.536853i	−0.668399	−	0.743803i	$-0.733020\pi$
$113$	3.29484	−	5.70683i	0.309952	−	0.536853i	0.978352	+	0.206949i	$0.0663536\pi$
$114$	1.92640	+	3.33661i	0.180423	+	0.312503i
$115$	−1.65549	+	2.86740i	−0.154376	+	0.267386i
$116$	23.9985			2.22820
$117$	3.17100	−	5.49234i	0.293159	−	0.507767i
$118$	−27.3219			−2.51518
$119$	0.873116	−	1.51228i	0.0800385	−	0.138631i
$120$	0.912237	+	1.58004i	0.0832754	+	0.144237i
$121$	−3.65421	−	6.32928i	−0.332201	−	0.575389i
$122$	2.66997	−	4.62453i	0.241728	−	0.418685i
$123$	−0.645325	+	1.11774i	−0.0581870	+	0.100783i
$124$	−14.9279	−	25.8558i	−1.34056	−	2.32192i
$125$	3.74170			0.334668
$126$	−0.926036	−	1.60394i	−0.0824978	−	0.142890i
$127$	−2.88497	−	4.99692i	−0.256000	−	0.443405i	0.709167	−	0.705041i	$-0.249071\pi$
$127$	−2.88497	−	4.99692i	−0.256000	−	0.443405i	−0.965167	+	0.261636i	$0.915738\pi$
$128$	19.8463			1.75418
$129$	8.12442			0.715315
$130$	−5.88152			−0.515844
$131$	−6.72426	−	11.6468i	−0.587501	−	1.01758i	−0.994559	−	0.104179i	$-0.966778\pi$
$131$	−6.72426	−	11.6468i	−0.587501	−	1.01758i	0.407057	−	0.913403i	$-0.366555\pi$
$132$	8.48775	+	14.7012i	0.738763	+	1.27958i
$133$	−0.597894	+	1.03558i	−0.0518440	+	0.0897964i
$134$	−4.52508			−0.390908
$135$	−0.189821	+	0.328779i	−0.0163372	+	0.0282968i
$136$	5.53436	−	9.58579i	0.474568	−	0.821975i
$137$	−10.5243	+	18.2286i	−0.899149	+	1.55737i	−0.0705656	+	0.997507i	$0.522480\pi$
$137$	−10.5243	+	18.2286i	−0.899149	+	1.55737i	−0.828584	+	0.559865i	$0.810853\pi$
$138$	10.6523	−	18.4503i	0.906784	−	1.57060i
$139$	−4.94573	−	8.56625i	−0.419491	−	0.726580i	0.576397	−	0.817170i	$-0.304458\pi$
$139$	−4.94573	−	8.56625i	−0.419491	−	0.726580i	−0.995888	+	0.0905897i	$0.971125\pi$
$140$	−0.570964	+	0.988939i	−0.0482553	+	0.0835806i
$141$	10.1314			0.853218
$142$	−9.82473	−	17.0169i	−0.824473	−	1.42803i
$143$	−27.1364			−2.26926
$144$	−1.90248	−	3.29520i	−0.158540	−	0.274600i
$145$	1.14823	−	1.98880i	0.0953557	−	0.165161i
$146$	−1.81847	+	3.14968i	−0.150497	+	0.260669i
$147$	−3.21259	+	5.56436i	−0.264970	+	0.458941i
$148$	12.5367	+	21.7142i	1.03051	+	1.78489i
$149$	15.3481			1.25737			0.628683	−	0.777662i	$-0.283594\pi$
$149$	15.3481			1.25737			0.628683	+	0.777662i	$0.283594\pi$
$150$	−11.8620			−0.968526
$151$	6.20335	−	10.7445i	0.504821	−	0.874376i	−0.495163	−	0.868800i	$-0.664892\pi$
$151$	6.20335	−	10.7445i	0.504821	−	0.874376i	0.999984	−	0.00557621i	$-0.00177497\pi$
$152$	−3.78983	+	6.56418i	−0.307396	+	0.532425i
$153$	2.30321			0.186204
$154$	−3.96236	+	6.86300i	−0.319296	+	0.553036i
$155$	−2.85696			−0.229477
$156$	25.1607			2.01447
$157$	−11.6617	+	4.58322i	−0.930701	+	0.365780i
$157$	−11.6617	+	4.58322i	−0.930701	+	0.365780i
$158$	16.9635			1.34954
$159$	−0.728017			−0.0577355
$160$	0.0601261	−	0.104141i	0.00475339	−	0.00823311i
$161$	6.61230			0.521122
$162$	1.22140	−	2.11553i	0.0959626	−	0.166212i
$163$	−6.58729	+	11.4095i	−0.515957	+	0.893663i	0.483872	+	0.875139i	$0.339230\pi$
$163$	−6.58729	+	11.4095i	−0.515957	+	0.893663i	−0.999828	+	0.0185243i	$0.994103\pi$
$164$	−5.12042			−0.399838
$165$	1.62442			0.126461
$166$	−9.86934	−	17.0942i	−0.766009	−	1.32677i
$167$	−4.54989	+	7.88064i	−0.352081	+	0.609822i	−0.986614	−	0.163074i	$-0.947859\pi$
$167$	−4.54989	+	7.88064i	−0.352081	+	0.609822i	0.634533	+	0.772896i	$0.281193\pi$
$168$	1.82181	−	3.15546i	0.140555	−	0.243449i
$169$	−13.6105	+	23.5741i	−1.04696	+	1.81339i
$170$	−1.06799	−	1.84981i	−0.0819111	−	0.141874i
$171$	−1.57720			−0.120611
$172$	16.1161	+	27.9139i	1.22884	+	2.12841i
$173$	−8.16123			−0.620487			−0.310243	−	0.950657i	$-0.600411\pi$
$173$	−8.16123			−0.620487			−0.310243	+	0.950657i	$0.600411\pi$
$174$	−7.38833	+	12.7970i	−0.560108	+	0.970135i
$175$	−1.84080	−	3.18835i	−0.139151	−	0.241017i
$176$	−8.14041	+	14.0996i	−0.613606	+	1.06280i
$177$	5.59230	−	9.68615i	0.420343	−	0.728056i
$178$	−3.78049	+	6.54800i	−0.283359	+	0.490793i
$179$	−12.1625	+	21.0660i	−0.909064	+	1.57455i	−0.0936979	+	0.995601i	$0.529869\pi$
$179$	−12.1625	+	21.0660i	−0.909064	+	1.57455i	−0.815367	+	0.578945i	$0.803465\pi$
$180$	−1.50616			−0.112262
$181$	7.64640	−	13.2440i	0.568352	−	0.984415i	−0.428377	−	0.903600i	$-0.640914\pi$
$181$	7.64640	−	13.2440i	0.568352	−	0.984415i	0.996729	−	0.0808151i	$-0.0257523\pi$
$182$	5.87292	+	10.1722i	0.435330	+	0.754014i
$183$	1.09299	+	1.89312i	0.0807963	+	0.139943i
$184$	41.9129			3.08986
$185$	2.39933			0.176402
$186$	18.3832			1.34792
$187$	−4.92753	−	8.53473i	−0.360337	−	0.624122i
$188$	20.0972	+	34.8094i	1.46574	+	2.53874i
$189$	0.758173			0.0551490
$190$	0.731340	+	1.26672i	0.0530570	+	0.0918974i
$191$	11.8085	−	20.4529i	0.854434	−	1.47992i	−0.0227352	−	0.999742i	$-0.507237\pi$
$191$	11.8085	−	20.4529i	0.854434	−	1.47992i	0.877169	−	0.480181i	$-0.159429\pi$
$192$	−4.19185	+	7.26049i	−0.302521	+	0.523981i
$193$	1.94649	+	3.37143i	0.140112	+	0.242681i	0.927539	−	0.373727i	$-0.121920\pi$
$193$	1.94649	+	3.37143i	0.140112	+	0.242681i	−0.787427	+	0.616408i	$0.788587\pi$
$194$	0.0745575	+	0.129137i	0.00535292	+	0.00927152i
$195$	1.20384	−	2.08512i	0.0862091	−	0.149318i
$196$	−25.4907			−1.82076
$197$	4.03261	−	6.98468i	0.287311	−	0.497638i	−0.685856	−	0.727737i	$-0.740572\pi$
$197$	4.03261	−	6.98468i	0.287311	−	0.497638i	0.973167	+	0.230100i	$0.0739053\pi$
$198$	−10.4524			−0.742818
$199$	1.86983	−	3.23864i	0.132549	−	0.229581i	−0.792110	−	0.610379i	$-0.791017\pi$
$199$	1.86983	−	3.23864i	0.132549	−	0.229581i	0.924658	+	0.380798i	$0.124351\pi$
$200$	−11.6681	−	20.2098i	−0.825061	−	1.42905i
$201$	0.926205	−	1.60423i	0.0653295	−	0.113154i
$202$	−20.3022			−1.42846
$203$	−4.58622			−0.321890
$204$	4.56878	+	7.91337i	0.319879	+	0.554046i
$205$	−0.244992	+	0.424339i	−0.0171110	+	0.0296371i
$206$	16.4672			1.14732
$207$	4.36068	+	7.55291i	0.303088	+	0.524964i
$208$	12.0655	+	20.8981i	0.836595	+	1.44903i
$209$	3.37428	+	5.84443i	0.233404	+	0.404268i
$210$	−0.351562	−	0.608923i	−0.0242601	−	0.0420197i
$211$	16.8744			1.16168			0.580842	−	0.814016i	$-0.302723\pi$
$211$	16.8744			1.16168			0.580842	+	0.814016i	$0.302723\pi$
$212$	−1.44414	−	2.50132i	−0.0991837	−	0.171791i
$213$	8.04380			0.551152
$214$	20.9274	+	36.2474i	1.43057	+	2.47782i
$215$	3.08437			0.210352
$216$	4.80578			0.326992
$217$	2.85279	+	4.94117i	0.193660	+	0.335428i
$218$	0.534974	−	0.926602i	0.0362330	−	0.0627574i
$219$	−0.744416	−	1.28937i	−0.0503030	−	0.0871273i
$220$	3.22230	+	5.58119i	0.217248	+	0.376284i
$221$	−14.6070			−0.982571
$222$	−15.4385			−1.03616
$223$	9.14596	+	15.8413i	0.612459	+	1.06081i	0.990825	+	0.135154i	$0.0431528\pi$
$223$	9.14596	+	15.8413i	0.612459	+	1.06081i	−0.378366	+	0.925656i	$0.623514\pi$
$224$	−0.240153			−0.0160459
$225$	2.42794	−	4.20531i	0.161862	−	0.280354i
$226$	−8.04866	+	13.9407i	−0.535389	+	0.927321i
$227$	9.80250	−	16.9784i	0.650615	−	1.12690i	−0.332359	−	0.943153i	$-0.607845\pi$
$227$	9.80250	−	16.9784i	0.650615	−	1.12690i	0.982974	−	0.183745i	$-0.0588221\pi$
$228$	−3.12862	−	5.41893i	−0.207198	−	0.358877i
$229$	−5.20801	−	9.02054i	−0.344155	−	0.596094i	0.641045	−	0.767503i	$-0.278501\pi$
$229$	−5.20801	−	9.02054i	−0.344155	−	0.596094i	−0.985200	+	0.171410i	$0.945168\pi$
$230$	4.04406	−	7.00451i	0.266657	−	0.461864i
$231$	−1.62205	−	2.80947i	−0.106723	−	0.184850i
$232$	−29.0704			−1.90856
$233$	−4.88956	+	8.46896i	−0.320325	+	0.554820i	−0.980555	−	0.196244i	$-0.937126\pi$
$233$	−4.88956	+	8.46896i	−0.320325	+	0.554820i	0.660230	+	0.751064i	$0.270459\pi$
$234$	−7.74615	+	13.4167i	−0.506382	+	0.877079i
$235$	3.84630			0.250905
$236$	44.3729			2.88843
$237$	−3.47213	+	6.01390i	−0.225539	+	0.390645i
$238$	−2.13286	+	3.69422i	−0.138253	+	0.239460i
$239$	−11.5607			−0.747800			−0.373900	−	0.927469i	$-0.621980\pi$
$239$	−11.5607			−0.747800			−0.373900	+	0.927469i	$0.621980\pi$
$240$	−0.722262	−	1.25099i	−0.0466218	−	0.0807513i
$241$	−0.538514	+	0.932733i	−0.0346887	+	0.0600826i	−0.882849	−	0.469658i	$-0.844377\pi$
$241$	−0.538514	+	0.932733i	−0.0346887	+	0.0600826i	0.848160	+	0.529740i	$0.177711\pi$
$242$	8.92655	+	15.4612i	0.573820	+	0.993886i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.33625	+	7.51060i	−0.277600	+	0.480817i
$245$	−1.21963	+	2.11246i	−0.0779194	+	0.134960i
$246$	1.57641	−	2.73042i	0.100508	−	0.174085i
$247$	10.0026			0.636449
$248$	18.0827	+	31.3202i	1.14826	+	1.98884i
$249$	8.08032			0.512069
$250$	−9.14026			−0.578081
$251$	1.97151	+	3.41475i	0.124440	+	0.215537i	0.921514	−	0.388345i	$-0.126953\pi$
$251$	1.97151	+	3.41475i	0.124440	+	0.215537i	−0.797074	+	0.603882i	$0.793620\pi$
$252$	1.50396	+	2.60493i	0.0947403	+	0.164095i
$253$	18.6586	−	32.3177i	1.17306	−	2.03179i
$254$	7.04743	+	12.2065i	0.442195	+	0.765905i
$255$	0.874395			0.0547567
$256$	−31.7132			−1.98208
$257$	−14.1340	−	24.4808i	−0.881656	−	1.52707i	−0.849499	−	0.527590i	$-0.823096\pi$
$257$	−14.1340	−	24.4808i	−0.881656	−	1.52707i	−0.0321565	−	0.999483i	$-0.510238\pi$
$258$	−19.8464			−1.23558
$259$	−2.39582	−	4.14968i	−0.148869	−	0.257848i
$260$	9.55206			0.592394
$261$	−3.02452	−	5.23863i	−0.187213	−	0.324263i
$262$	16.4261	+	28.4508i	1.01481	+	1.75770i
$263$	−3.65254	−	6.32639i	−0.225225	−	0.390102i	0.731162	−	0.682204i	$-0.238979\pi$
$263$	−3.65254	−	6.32639i	−0.225225	−	0.390102i	−0.956387	+	0.292102i	$0.905645\pi$
$264$	−10.2816	−	17.8082i	−0.632787	−	1.09602i
$265$	−0.276386			−0.0169782
$266$	1.46054	−	2.52973i	0.0895515	−	0.155108i
$267$	−1.54760	−	2.68052i	−0.0947115	−	0.164045i
$268$	7.34910			0.448918
$269$	0.747858			0.0455977			0.0227989	−	0.999740i	$-0.492742\pi$
$269$	0.747858			0.0455977			0.0227989	+	0.999740i	$0.492742\pi$
$270$	0.463696	−	0.803145i	0.0282196	−	0.0488779i
$271$	−13.9872	−	24.2265i	−0.849660	−	1.47165i	−0.881512	−	0.472162i	$-0.843474\pi$
$271$	−13.9872	−	24.2265i	−0.849660	−	1.47165i	0.0318515	−	0.999493i	$-0.489860\pi$
$272$	−4.38182	+	7.58953i	−0.265687	+	0.460183i
$273$	−4.80834			−0.291014
$274$	25.7088	−	44.5289i	1.55312	−	2.69009i
$275$	−20.7775			−1.25293
$276$	−17.3002	+	29.9648i	−1.04135	+	1.80367i
$277$	−3.28023	−	5.68152i	−0.197090	−	0.341370i	0.750494	−	0.660878i	$-0.229816\pi$
$277$	−3.28023	−	5.68152i	−0.197090	−	0.341370i	−0.947584	+	0.319508i	$0.896482\pi$
$278$	12.0815	+	20.9257i	0.724598	+	1.25504i
$279$	−3.76271	+	6.51720i	−0.225268	+	0.390175i
$280$	0.691633	−	1.19794i	0.0413330	−	0.0715908i
$281$	6.19470	+	10.7295i	0.369545	+	0.640071i	0.989494	−	0.144571i	$-0.0461802\pi$
$281$	6.19470	+	10.7295i	0.369545	+	0.640071i	−0.619949	+	0.784642i	$0.712847\pi$
$282$	−24.7491			−1.47379
$283$	3.75142	+	6.49765i	0.222999	+	0.386245i	0.955717	−	0.294287i	$-0.0950821\pi$
$283$	3.75142	+	6.49765i	0.222999	+	0.386245i	−0.732718	+	0.680532i	$0.761749\pi$
$284$	15.9561	+	27.6369i	0.946823	+	1.63995i
$285$	−0.598770			−0.0354681
$286$	66.2890			3.91975
$287$	0.978537			0.0577612
$288$	−0.158376	−	0.274315i	−0.00933239	−	0.0161642i
$289$	5.84761	+	10.1284i	0.343977	+	0.595786i
$290$	−2.80492	+	4.85826i	−0.164710	+	0.285287i
$291$	−0.0610424			−0.00357837
$292$	2.95333	−	5.11533i	0.172831	−	0.299352i
$293$	−4.22658	+	7.32064i	−0.246919	+	0.427677i	−0.962669	−	0.270680i	$-0.912752\pi$
$293$	−4.22658	+	7.32064i	−0.246919	+	0.427677i	0.715750	+	0.698356i	$0.246085\pi$
$294$	7.84774	−	13.5927i	0.457689	−	0.792741i
$295$	2.12307	−	3.67727i	0.123610	−	0.214099i
$296$	−15.1862	−	26.3033i	−0.882680	−	1.52885i
$297$	2.13942	−	3.70558i	0.124142	−	0.215020i
$298$	−37.4925			−2.17188
$299$	−27.6554	−	47.9006i	−1.59935	−	2.77016i
$300$	19.2648			1.11225
$301$	−3.07986	−	5.33447i	−0.177520	−	0.307474i
$302$	−15.1536	+	26.2468i	−0.871992	+	1.51033i
$303$	4.15550	−	7.19753i	0.238727	−	0.413487i
$304$	3.00059	−	5.19717i	0.172096	−	0.298078i
$305$	0.414945	+	0.718706i	0.0237597	+	0.0411530i
$306$	−5.62631			−0.321634
$307$	6.49749			0.370832			0.185416	−	0.982660i	$-0.440637\pi$
$307$	6.49749			0.370832			0.185416	+	0.982660i	$0.440637\pi$
$308$	6.43518	−	11.1461i	0.366678	−	0.635106i
$309$	−3.37054	+	5.83795i	−0.191744	+	0.332110i
$310$	6.97901			0.396381
$311$	−0.168530	+	0.291903i	−0.00955647	+	0.0165523i	−0.870764	−	0.491701i	$-0.836375\pi$
$311$	−0.168530	+	0.291903i	−0.00955647	+	0.0165523i	0.861208	+	0.508253i	$0.169709\pi$
$312$	−30.4783			−1.72549
$313$	−21.5858			−1.22010			−0.610052	−	0.792361i	$-0.708851\pi$
$313$	−21.5858			−1.22010			−0.610052	+	0.792361i	$0.708851\pi$
$314$	28.4872	−	11.1959i	1.60763	−	0.631822i
$315$	0.287834			0.0162176
$316$	−27.5501			−1.54981
$317$	−6.80847	+	11.7926i	−0.382402	+	0.662339i	−0.991405	−	0.130829i	$-0.958236\pi$
$317$	−6.80847	+	11.7926i	−0.382402	+	0.662339i	0.609003	+	0.793168i	$0.291570\pi$
$318$	1.77841			0.0997281
$319$	−12.9414	+	22.4152i	−0.724581	+	1.25501i
$320$	−1.59140	+	2.75639i	−0.0889620	+	0.154087i
$321$	−17.1339			−0.956322
$322$	−16.1526			−0.900148
$323$	1.81631	+	3.14594i	0.101062	+	0.175045i
$324$	−1.98366	+	3.43580i	−0.110203	+	0.190878i
$325$	−15.3980	+	26.6701i	−0.854126	+	1.47939i
$326$	16.0915	−	27.8713i	0.891226	−	1.54365i
$327$	0.218999	+	0.379318i	0.0121107	+	0.0209763i
$328$	6.20258			0.342480
$329$	−3.84068	−	6.65225i	−0.211743	−	0.366750i
$330$	−3.96816			−0.218440
$331$	−15.4283	+	26.7226i	−0.848017	+	1.46881i	0.0349574	+	0.999389i	$0.488870\pi$
$331$	−15.4283	+	26.7226i	−0.848017	+	1.46881i	−0.882975	+	0.469420i	$0.844463\pi$
$332$	16.0286	+	27.7623i	0.879683	+	1.52366i
$333$	3.15999	−	5.47326i	0.173166	−	0.299933i
$334$	11.1145	−	19.2509i	0.608159	−	1.05336i
$335$	0.351626	−	0.609034i	0.0192114	−	0.0332751i
$336$	−1.44241	+	2.49833i	−0.0786900	+	0.136295i
$337$	17.7814			0.968614			0.484307	−	0.874898i	$-0.339072\pi$
$337$	17.7814			0.968614			0.484307	+	0.874898i	$0.339072\pi$
$338$	33.2478	−	57.5870i	1.80844	−	3.13232i
$339$	−3.29484	−	5.70683i	−0.178951	−	0.309952i
$340$	1.73450	+	3.00424i	0.0940665	+	0.162928i
$341$	32.2000			1.74373
$342$	3.85279			0.208335
$343$	10.1786			0.549593
$344$	−19.5221	−	33.8132i	−1.05256	−	1.82309i
$345$	1.65549	+	2.86740i	0.0891288	+	0.154376i
$346$	19.9363			1.07178
$347$	1.91617	+	3.31890i	0.102865	+	0.178168i	0.912864	−	0.408264i	$-0.133866\pi$
$347$	1.91617	+	3.31890i	0.102865	+	0.178168i	−0.809999	+	0.586432i	$0.800532\pi$
$348$	11.9992	−	20.7833i	0.643227	−	1.11410i
$349$	−5.56779	+	9.64369i	−0.298037	+	0.516215i	−0.975687	−	0.219170i	$-0.929665\pi$
$349$	−5.56779	+	9.64369i	−0.298037	+	0.516215i	0.677650	+	0.735385i	$0.262998\pi$
$350$	4.49671	+	7.78853i	0.240359	+	0.416315i
$351$	−3.17100	−	5.49234i	−0.169256	−	0.293159i
$352$	−0.677665	+	1.17375i	−0.0361196	+	0.0625611i
$353$	31.5340			1.67838			0.839192	−	0.543836i	$-0.183029\pi$
$353$	31.5340			1.67838			0.839192	+	0.543836i	$0.183029\pi$
$354$	−13.6609	+	23.6614i	−0.726070	+	1.25759i
$355$	3.05376			0.162077
$356$	6.13981	−	10.6345i	0.325409	−	0.563626i
$357$	−0.873116	−	1.51228i	−0.0462102	−	0.0800385i
$358$	29.7106	−	51.4602i	1.57025	−	2.71976i
$359$	20.6009			1.08727			0.543636	−	0.839321i	$-0.317047\pi$
$359$	20.6009			1.08727			0.543636	+	0.839321i	$0.317047\pi$
$360$	1.82447			0.0961582
$361$	8.25622	+	14.3002i	0.434538	+	0.752642i
$362$	−18.6787	+	32.3525i	−0.981731	+	1.70041i
$363$	−7.30843			−0.383593
$364$	−9.53809	−	16.5205i	−0.499932	−	0.865908i
$365$	−0.282611	−	0.489497i	−0.0147926	−	0.0256215i
$366$	−2.66997	−	4.62453i	−0.139562	−	0.241728i
$367$	−17.0595	−	29.5479i	−0.890498	−	1.54239i	−0.839280	−	0.543700i	$-0.817023\pi$
$367$	−17.0595	−	29.5479i	−0.890498	−	1.54239i	−0.0512184	−	0.998687i	$-0.516310\pi$
$368$	−33.1844			−1.72986
$369$	0.645325	+	1.11774i	0.0335943	+	0.0581870i
$370$	−5.86110			−0.304704
$371$	0.275981	+	0.478014i	0.0143282	+	0.0248172i
$372$	−29.8557			−1.54795
$373$	33.2822			1.72329			0.861644	−	0.507513i	$-0.169435\pi$
$373$	33.2822			1.72329			0.861644	+	0.507513i	$0.169435\pi$
$374$	12.0370	+	20.8487i	0.622419	+	1.07806i
$375$	1.87085	−	3.24041i	0.0966103	−	0.167334i
$376$	−24.3446	−	42.1662i	−1.25548	−	2.17455i
$377$	19.1815	+	33.2234i	0.987899	+	1.71109i
$378$	−1.85207			−0.0952603
$379$	−33.7978			−1.73607			−0.868037	−	0.496499i	$-0.834619\pi$
$379$	−33.7978			−1.73607			−0.868037	+	0.496499i	$0.834619\pi$
$380$	−1.18775	−	2.05725i	−0.0609305	−	0.105535i
$381$	−5.76994			−0.295603
$382$	−28.8459	+	49.9626i	−1.47589	+	2.55631i
$383$	−1.27819	+	2.21389i	−0.0653125	+	0.113125i	−0.896833	−	0.442370i	$-0.854138\pi$
$383$	−1.27819	+	2.21389i	−0.0653125	+	0.113125i	0.831520	+	0.555495i	$0.187471\pi$
$384$	9.92313	−	17.1874i	0.506388	−	0.877089i
$385$	−0.615797	−	1.06659i	−0.0313839	−	0.0543586i
$386$	−4.75492	−	8.23576i	−0.242019	−	0.419189i
$387$	4.06221	−	7.03596i	0.206494	−	0.357658i
$388$	−0.121087	−	0.209729i	−0.00614728	−	0.0106474i
$389$	−17.6773			−0.896277			−0.448138	−	0.893964i	$-0.647913\pi$
$389$	−17.6773			−0.896277			−0.448138	+	0.893964i	$0.647913\pi$
$390$	−2.94076	+	5.09355i	−0.148911	+	0.257922i
$391$	10.0436	−	17.3960i	0.507925	−	0.879751i
$392$	30.8780			1.55957
$393$	−13.4485			−0.678388
$394$	−9.85088	+	17.0622i	−0.496280	+	0.859583i
$395$	−1.31816	+	2.28313i	−0.0663240	+	0.114877i
$396$	16.9755			0.853051
$397$	5.69214	+	9.85908i	0.285680	+	0.494813i	0.972774	−	0.231756i	$-0.0744471\pi$
$397$	5.69214	+	9.85908i	0.285680	+	0.494813i	−0.687094	+	0.726569i	$0.741114\pi$
$398$	−4.56764	+	7.91139i	−0.228955	+	0.396562i
$399$	0.597894	+	1.03558i	0.0299321	+	0.0518440i
$400$	9.23821	+	16.0011i	0.461911	+	0.800053i
$401$	11.0983	−	19.2227i	0.554220	−	0.959938i	−0.443744	−	0.896154i	$-0.646350\pi$
$401$	11.0983	−	19.2227i	0.554220	−	0.959938i	0.997964	−	0.0637837i	$-0.0203168\pi$
$402$	−2.26254	+	3.91884i	−0.112845	+	0.195454i
$403$	23.8631	−	41.3321i	1.18871	−	2.05890i
$404$	32.9723			1.64043
$405$	0.189821	+	0.328779i	0.00943227	+	0.0163372i
$406$	11.2033			0.556009
$407$	−27.0421			−1.34043
$408$	−5.53436	−	9.58579i	−0.273992	−	0.474568i
$409$	12.6328	+	21.8807i	0.624653	+	1.08193i	0.988608	+	0.150514i	$0.0480927\pi$
$409$	12.6328	+	21.8807i	0.624653	+	1.08193i	−0.363955	+	0.931416i	$0.618574\pi$
$410$	0.598470	−	1.03658i	0.0295563	−	0.0511930i
$411$	10.5243	+	18.2286i	0.519124	+	0.899149i
$412$	−26.7440			−1.31758
$413$	−8.47987			−0.417267
$414$	−10.6523	−	18.4503i	−0.523532	−	0.906784i
$415$	3.06762			0.150584
$416$	1.00442	+	1.73971i	0.0492458	+	0.0852962i
$417$	−9.89146			−0.484387
$418$	−8.24273	−	14.2768i	−0.403165	−	0.698302i
$419$	−17.4110	−	30.1567i	−0.850582	−	1.47325i	−0.880684	−	0.473704i	$-0.842917\pi$
$419$	−17.4110	−	30.1567i	−0.850582	−	1.47325i	0.0301025	−	0.999547i	$-0.490417\pi$
$420$	0.570964	+	0.988939i	0.0278602	+	0.0482553i
$421$	−19.4201	−	33.6366i	−0.946478	−	1.63935i	−0.752764	−	0.658290i	$-0.771280\pi$
$421$	−19.4201	−	33.6366i	−0.946478	−	1.63935i	−0.193714	−	0.981058i	$-0.562053\pi$
$422$	−41.2210			−2.00661
$423$	5.06570	−	8.77405i	0.246303	−	0.426609i
$424$	1.74934	+	3.02995i	0.0849556	+	0.147147i
$425$	−11.1841			−0.542509
$426$	−19.6495			−0.952020
$427$	0.828677	−	1.43531i	0.0401025	−	0.0694596i
$428$	−33.9878	−	58.8687i	−1.64286	−	2.84552i
$429$	−13.5682	+	23.5008i	−0.655078	+	1.13463i
$430$	−7.53452			−0.363347
$431$	−0.371039	+	0.642658i	−0.0178723	+	0.0309557i	−0.874823	−	0.484442i	$-0.839023\pi$
$431$	−0.371039	+	0.642658i	−0.0178723	+	0.0309557i	0.856951	+	0.515398i	$0.172356\pi$
$432$	−3.80497			−0.183066
$433$	9.47759	−	16.4157i	0.455464	−	0.788887i	−0.543251	−	0.839570i	$-0.682807\pi$
$433$	9.47759	−	16.4157i	0.455464	−	0.788887i	0.998715	+	0.0506838i	$0.0161401\pi$
$434$	−6.96881	−	12.0703i	−0.334514	−	0.579395i
$435$	−1.14823	−	1.98880i	−0.0550536	−	0.0953557i
$436$	−0.868840	+	1.50488i	−0.0416099	+	0.0720704i
$437$	−6.87765	+	11.9124i	−0.329002	+	0.569849i
$438$	1.81847	+	3.14968i	0.0868897	+	0.150497i
$439$	26.1943			1.25019			0.625093	−	0.780550i	$-0.285061\pi$
$439$	26.1943			1.25019			0.625093	+	0.780550i	$0.285061\pi$
$440$	−3.90331	−	6.76073i	−0.186083	−	0.322305i
$441$	3.21259	+	5.56436i	0.152980	+	0.264970i
$442$	35.6820			1.69722
$443$	−9.89053			−0.469913			−0.234957	−	0.972006i	$-0.575495\pi$
$443$	−9.89053			−0.469913			−0.234957	+	0.972006i	$0.575495\pi$
$444$	25.0733			1.18993
$445$	−0.587533	−	1.01764i	−0.0278517	−	0.0482406i
$446$	−22.3418	−	38.6972i	−1.05792	−	1.83237i
$447$	7.67405	−	13.2918i	0.362970	−	0.628683i
$448$	6.35629			0.300307
$449$	−8.95640	+	15.5129i	−0.422679	+	0.732101i	−0.996201	−	0.0870892i	$-0.972244\pi$
$449$	−8.95640	+	15.5129i	−0.422679	+	0.732101i	0.573522	+	0.819190i	$0.305577\pi$
$450$	−5.93098	+	10.2728i	−0.279589	+	0.484263i
$451$	2.76124	−	4.78261i	0.130022	−	0.225204i
$452$	13.0717	−	22.6408i	0.614839	−	1.06493i
$453$	−6.20335	−	10.7445i	−0.291459	−	0.504821i
$454$	−23.9456	+	41.4751i	−1.12382	+	1.94652i
$455$	−1.82544			−0.0855781
$456$	3.78983	+	6.56418i	0.177475	+	0.307396i
$457$	26.8315			1.25513			0.627563	−	0.778566i	$-0.284053\pi$
$457$	26.8315			1.25513			0.627563	+	0.778566i	$0.284053\pi$
$458$	12.7222	+	22.0354i	0.594468	+	1.02965i
$459$	1.15161	−	1.99464i	0.0537524	−	0.0931018i
$460$	−6.56787	+	11.3759i	−0.306229	+	0.530403i
$461$	−4.08181	+	7.06991i	−0.190109	+	0.329278i	−0.945286	−	0.326242i	$-0.894217\pi$
$461$	−4.08181	+	7.06991i	−0.190109	+	0.329278i	0.755177	+	0.655521i	$0.227551\pi$
$462$	3.96236	+	6.86300i	0.184345	+	0.319296i
$463$	−2.38863			−0.111009			−0.0555045	−	0.998458i	$-0.517677\pi$
$463$	−2.38863			−0.111009			−0.0555045	+	0.998458i	$0.517677\pi$
$464$	23.0164			1.06851
$465$	−1.42848	+	2.47420i	−0.0662442	+	0.114738i
$466$	11.9443	−	20.6881i	0.553307	−	0.958355i
$467$	3.78564			0.175178			0.0875892	−	0.996157i	$-0.472084\pi$
$467$	3.78564			0.175178			0.0875892	+	0.996157i	$0.472084\pi$
$468$	12.5804	−	21.7898i	0.581528	−	1.00724i
$469$	−1.40445			−0.0648514
$470$	−9.39578			−0.433395
$471$	−1.86164	+	12.3909i	−0.0857800	+	0.570942i
$472$	−53.7507			−2.47408
$473$	−34.7631			−1.59841
$474$	8.48175	−	14.6908i	0.389579	−	0.674771i
$475$	7.65867			0.351404
$476$	3.46393	−	5.99970i	0.158769	−	0.274996i
$477$	−0.364008	+	0.630481i	−0.0166668	+	0.0288677i
$478$	28.2406			1.29170
$479$	−2.83529			−0.129548			−0.0647739	−	0.997900i	$-0.520633\pi$
$479$	−2.83529			−0.129548			−0.0647739	+	0.997900i	$0.520633\pi$
$480$	−0.0601261	−	0.104141i	−0.00274437	−	0.00475339i
$481$	−20.0407	+	34.7114i	−0.913775	+	1.58270i
$482$	1.31549	−	2.27849i	0.0599188	−	0.103782i
$483$	3.30615	−	5.72642i	0.150435	−	0.260561i
$484$	−14.4974	−	25.1103i	−0.658974	−	1.14138i
$485$	−0.0231742			−0.00105229
$486$	−1.22140	−	2.11553i	−0.0554040	−	0.0959626i
$487$	12.7665			0.578507			0.289254	−	0.957252i	$-0.406593\pi$
$487$	12.7665			0.578507			0.289254	+	0.957252i	$0.406593\pi$
$488$	5.25268	−	9.09790i	0.237778	−	0.411843i
$489$	6.58729	+	11.4095i	0.297888	+	0.515957i
$490$	2.97933	−	5.16035i	0.134592	−	0.233121i
$491$	−7.19355	+	12.4596i	−0.324640	+	0.562294i	−0.981440	−	0.191772i	$-0.938577\pi$
$491$	−7.19355	+	12.4596i	−0.324640	+	0.562294i	0.656799	+	0.754066i	$0.271910\pi$
$492$	−2.56021	+	4.43441i	−0.115423	+	0.199919i
$493$	−6.96611	+	12.0657i	−0.313738	+	0.543410i
$494$	−24.4344			−1.09936
$495$	0.812212	−	1.40679i	0.0365062	−	0.0632306i
$496$	−14.3170	−	24.7977i	−0.642851	−	1.11345i
$497$	−3.04930	−	5.28154i	−0.136780	−	0.236909i
$498$	−19.7387			−0.884511
$499$	39.3025			1.75942			0.879711	−	0.475509i	$-0.157736\pi$
$499$	39.3025			1.75942			0.879711	+	0.475509i	$0.157736\pi$
$500$	14.8445			0.663866
$501$	4.54989	+	7.88064i	0.203274	+	0.352081i
$502$	−4.81602	−	8.34159i	−0.214949	−	0.372303i
$503$	18.1000			0.807041			0.403521	−	0.914971i	$-0.367786\pi$
$503$	18.1000			0.807041			0.403521	+	0.914971i	$0.367786\pi$
$504$	−1.82181	−	3.15546i	−0.0811497	−	0.140555i
$505$	1.57760	−	2.73248i	0.0702023	−	0.121594i
$506$	−45.5794	+	78.9459i	−2.02625	+	3.50957i
$507$	13.6105	+	23.5741i	0.604463	+	1.04696i
$508$	−11.4456	−	19.8243i	−0.507816	−	0.879563i
$509$	−8.26530	+	14.3159i	−0.366353	+	0.634542i	−0.988992	−	0.147967i	$-0.952727\pi$
$509$	−8.26530	+	14.3159i	−0.366353	+	0.634542i	0.622639	+	0.782509i	$0.286060\pi$
$510$	−2.13598			−0.0945828
$511$	−0.564396	+	0.977563i	−0.0249674	+	0.0432449i
$512$	37.7769			1.66952
$513$	−0.788598	+	1.36589i	−0.0348175	+	0.0603056i
$514$	34.5267	+	59.8020i	1.52291	+	2.63775i
$515$	−1.27960	+	2.21633i	−0.0563859	+	0.0976632i
$516$	32.2321			1.41894
$517$	−43.3506			−1.90656
$518$	5.85253	+	10.1369i	0.257145	+	0.445389i
$519$	−4.08061	+	7.06783i	−0.179119	+	0.310243i
$520$	−11.5708			−0.507414
$521$	16.3578	+	28.3326i	0.716650	+	1.24127i	0.962320	+	0.271921i	$0.0876589\pi$
$521$	16.3578	+	28.3326i	0.716650	+	1.24127i	−0.245670	+	0.969354i	$0.579008\pi$
$522$	7.38833	+	12.7970i	0.323378	+	0.560108i
$523$	9.50765	+	16.4677i	0.415741	+	0.720084i	0.995506	−	0.0946998i	$-0.0301891\pi$
$523$	9.50765	+	16.4677i	0.415741	+	0.720084i	−0.579765	+	0.814783i	$0.696856\pi$
$524$	−26.6773	−	46.2064i	−1.16540	−	2.01853i
$525$	−3.68159			−0.160678
$526$	8.92246	+	15.4542i	0.389038	+	0.673833i
$527$	17.3326			0.755021
$528$	8.14041	+	14.0996i	0.354266	+	0.613606i
$529$	53.0620			2.30704
$530$	0.675157			0.0293269
$531$	−5.59230	−	9.68615i	−0.242685	−	0.420343i
$532$	−2.37204	+	4.10849i	−0.102841	+	0.178125i
$533$	−4.09265	−	7.08869i	−0.177273	−	0.307045i
$534$	3.78049	+	6.54800i	0.163598	+	0.283359i
$535$	−6.50475			−0.281225
$536$	−8.90227			−0.384520
$537$	12.1625	+	21.0660i	0.524849	+	0.909064i
$538$	−1.82687			−0.0787622
$539$	13.7461	−	23.8090i	0.592088	−	1.02553i
$540$	−0.753079	+	1.30437i	−0.0324074	+	0.0561312i
$541$	12.9349	−	22.4040i	0.556116	−	0.963222i	−0.441699	−	0.897163i	$-0.645624\pi$
$541$	12.9349	−	22.4040i	0.556116	−	0.963222i	0.997816	−	0.0660586i	$-0.0210424\pi$
$542$	34.1680	+	59.1807i	1.46764	+	2.54203i
$543$	−7.64640	−	13.2440i	−0.328138	−	0.568352i
$544$	−0.364773	+	0.631806i	−0.0156395	+	0.0270885i
$545$	0.0831413	+	0.144005i	0.00356138	+	0.00616850i
$546$	11.7458			0.502676
$547$	−15.0739	+	26.1087i	−0.644512	+	1.11633i	0.339903	+	0.940461i	$0.389606\pi$
$547$	−15.0739	+	26.1087i	−0.644512	+	1.11633i	−0.984414	+	0.175866i	$0.943727\pi$
$548$	−41.7531	+	72.3185i	−1.78360	+	3.08929i
$549$	2.18598			0.0932955
$550$	50.7554			2.16422
$551$	4.77027	−	8.26234i	0.203220	−	0.351988i
$552$	20.9564	−	36.2976i	0.891966	−	1.54493i
$553$	5.26495			0.223888
$554$	8.01297	+	13.8789i	0.340439	+	0.589657i
$555$	1.19966	−	2.07788i	0.0509229	−	0.0882010i
$556$	−19.6213	−	33.9850i	−0.832127	−	1.44129i
$557$	14.9004	+	25.8082i	0.631350	+	1.09353i	0.987276	+	0.159016i	$0.0508323\pi$
$557$	14.9004	+	25.8082i	0.631350	+	1.09353i	−0.355926	+	0.934514i	$0.615834\pi$
$558$	9.19158	−	15.9203i	0.389111	−	0.673959i
$559$	−25.7626	+	44.6220i	−1.08964	+	1.88731i
$560$	−0.547599	+	0.948470i	−0.0231403	+	0.0400802i
$561$	−9.85506			−0.416081
$562$	−15.1325	−	26.2102i	−0.638325	−	1.10561i
$563$	−6.36432			−0.268224			−0.134112	−	0.990966i	$-0.542818\pi$
$563$	−6.36432			−0.268224			−0.134112	+	0.990966i	$0.542818\pi$
$564$	40.1945			1.69249
$565$	−1.25086	−	2.16655i	−0.0526240	−	0.0911474i
$566$	−9.16400	−	15.8725i	−0.385192	−	0.667171i
$567$	0.379087	−	0.656597i	0.0159201	−	0.0275745i
$568$	−19.3284	−	33.4777i	−0.811000	−	1.40469i
$569$	9.20726			0.385988			0.192994	−	0.981200i	$-0.438180\pi$
$569$	9.20726			0.385988			0.192994	+	0.981200i	$0.438180\pi$
$570$	1.46268			0.0612649
$571$	14.7089	+	25.4766i	0.615549	+	1.06616i	0.990288	+	0.139032i	$0.0443991\pi$
$571$	14.7089	+	25.4766i	0.615549	+	1.06616i	−0.374739	+	0.927130i	$0.622268\pi$
$572$	−107.659			−4.50143
$573$	−11.8085	−	20.4529i	−0.493308	−	0.854434i
$574$	−2.39038			−0.0997724
$575$	−21.1749	−	36.6760i	−0.883054	−	1.52949i
$576$	4.19185	+	7.26049i	0.174660	+	0.302521i
$577$	−6.83205	−	11.8335i	−0.284422	−	0.492633i	0.688047	−	0.725666i	$-0.258468\pi$
$577$	−6.83205	−	11.8335i	−0.284422	−	0.492633i	−0.972469	+	0.233033i	$0.925135\pi$
$578$	−14.2846	−	24.7416i	−0.594161	−	1.02912i
$579$	3.89299			0.161787
$580$	4.55541	−	7.89020i	0.189153	−	0.327623i
$581$	−3.06314	−	5.30551i	−0.127080	−	0.220110i
$582$	0.149115			0.00618102
$583$	3.11506			0.129013
$584$	−3.57750	+	6.19641i	−0.148038	+	0.256409i
$585$	−1.20384	−	2.08512i	−0.0497728	−	0.0862091i
$586$	10.3247	−	17.8829i	0.426510	−	0.738737i
$587$	25.0897			1.03556			0.517782	−	0.855512i	$-0.326758\pi$
$587$	25.0897			1.03556			0.517782	+	0.855512i	$0.326758\pi$
$588$	−12.7453	+	22.0756i	−0.525609	+	0.910382i
$589$	−11.8691			−0.489056
$590$	−5.18626	+	8.98286i	−0.213515	+	0.369818i
$591$	−4.03261	−	6.98468i	−0.165879	−	0.287311i
$592$	12.0236	+	20.8256i	0.494169	+	0.855925i
$593$	14.2238	−	24.6364i	0.584103	−	1.01170i	−0.410883	−	0.911688i	$-0.634780\pi$
$593$	14.2238	−	24.6364i	0.584103	−	1.01170i	0.994987	−	0.100008i	$-0.0318870\pi$
$594$	−5.22619	+	9.05202i	−0.214433	+	0.371409i
$595$	−0.331471	−	0.574125i	−0.0135890	−	0.0235368i
$596$	60.8908			2.49418
$597$	−1.86983	−	3.23864i	−0.0765271	−	0.132549i
$598$	67.5569	+	117.012i	2.76261	+	4.78498i
$599$	−24.8312			−1.01457			−0.507287	−	0.861777i	$-0.669352\pi$
$599$	−24.8312			−1.01457			−0.507287	+	0.861777i	$0.669352\pi$
$600$	−23.3362			−0.952698
$601$	22.2477			0.907501			0.453751	−	0.891129i	$-0.350086\pi$
$601$	22.2477			0.907501			0.453751	+	0.891129i	$0.350086\pi$
$602$	7.52351	+	13.0311i	0.306635	+	0.531108i
$603$	−0.926205	−	1.60423i	−0.0377180	−	0.0653295i
$604$	24.6106	−	42.6269i	1.00139	−	1.73446i
$605$	−2.77458			−0.112803
$606$	−10.1511	+	17.5822i	−0.412360	+	0.714228i
$607$	18.3934	−	31.8583i	0.746564	−	1.29309i	−0.202896	−	0.979200i	$-0.565035\pi$
$607$	18.3934	−	31.8583i	0.746564	−	1.29309i	0.949460	−	0.313887i	$-0.101631\pi$
$608$	0.249790	−	0.432649i	0.0101303	−	0.0175462i
$609$	−2.29311	+	3.97178i	−0.0929216	+	0.160945i
$610$	−1.01363	−	1.75566i	−0.0410408	−	0.0710847i
$611$	−32.1267	+	55.6451i	−1.29971	+	2.25116i
$612$	9.13757			0.369364
$613$	−13.3562	−	23.1335i	−0.539450	−	0.934355i	−0.998934	−	0.0461689i	$-0.985299\pi$
$613$	−13.3562	−	23.1335i	−0.539450	−	0.934355i	0.459483	−	0.888186i	$-0.348035\pi$
$614$	−15.8721			−0.640547
$615$	0.244992	+	0.424339i	0.00987905	+	0.0171110i
$616$	−7.79521	+	13.5017i	−0.314078	+	0.543999i
$617$	19.5443	−	33.8517i	0.786824	−	1.36282i	−0.141080	−	0.989998i	$-0.545057\pi$
$617$	19.5443	−	33.8517i	0.786824	−	1.36282i	0.927903	−	0.372821i	$-0.121609\pi$
$618$	8.23359	−	14.2610i	0.331204	−	0.573662i
$619$	−4.31148	−	7.46769i	−0.173293	−	0.300152i	0.766276	−	0.642511i	$-0.222107\pi$
$619$	−4.31148	−	7.46769i	−0.173293	−	0.300152i	−0.939569	+	0.342359i	$0.888774\pi$
$620$	−11.3345			−0.455203
$621$	8.72135			0.349976
$622$	0.411687	−	0.713063i	0.0165071	−	0.0285912i
$623$	−1.17335	+	2.03230i	−0.0470092	+	0.0814223i
$624$	24.1311			0.966017
$625$	−11.4294	+	19.7964i	−0.457177	+	0.791854i
$626$	52.7301			2.10752
$627$	6.74857			0.269512
$628$	−46.2655	+	18.1831i	−1.84619	+	0.725583i
$629$	−14.5562			−0.580395
$630$	−0.703124			−0.0280131
$631$	22.5207	−	39.0070i	0.896536	−	1.55285i	0.0646442	−	0.997908i	$-0.479409\pi$
$631$	22.5207	−	39.0070i	0.896536	−	1.55285i	0.831892	−	0.554938i	$-0.187258\pi$
$632$	33.3726			1.32749
$633$	8.43722	−	14.6137i	0.335349	−	0.580842i
$634$	16.6318	−	28.8071i	0.660532	−	1.14408i
$635$	−2.19051			−0.0869277
$636$	−2.88827			−0.114527
$637$	−20.3742	−	35.2892i	−0.807257	−	1.39821i
$638$	31.6134	−	54.7561i	1.25159	−	2.16781i
$639$	4.02190	−	6.96613i	0.159104	−	0.275576i
$640$	3.76723	−	6.52504i	0.148913	−	0.257925i
$641$	−0.567735	−	0.983346i	−0.0224242	−	0.0388398i	0.854596	−	0.519294i	$-0.173805\pi$
$641$	−0.567735	−	0.983346i	−0.0224242	−	0.0388398i	−0.877020	+	0.480454i	$0.840472\pi$
$642$	41.8549			1.65188
$643$	7.53993	+	13.0595i	0.297346	+	0.515018i	0.975528	−	0.219876i	$-0.0705653\pi$
$643$	7.53993	+	13.0595i	0.297346	+	0.515018i	−0.678182	+	0.734894i	$0.737232\pi$
$644$	26.2331			1.03373
$645$	1.54218	−	2.67114i	0.0607235	−	0.105176i
$646$	−4.43690	−	7.68493i	−0.174567	−	0.302360i
$647$	−0.588985	+	1.02015i	−0.0231554	+	0.0401063i	−0.877371	−	0.479813i	$-0.840705\pi$
$647$	−0.588985	+	1.02015i	−0.0231554	+	0.0401063i	0.854216	+	0.519919i	$0.174038\pi$
$648$	2.40289	−	4.16193i	0.0943944	−	0.163496i
$649$	−23.9285	+	41.4454i	−0.939277	+	1.62688i
$650$	37.6143	−	65.1499i	1.47535	−	2.55539i
$651$	5.70557			0.223619
$652$	−26.1339	+	45.2652i	−1.02348	+	1.77272i
$653$	−7.78327	−	13.4810i	−0.304583	−	0.527553i	0.672585	−	0.740019i	$-0.265184\pi$
$653$	−7.78327	−	13.4810i	−0.304583	−	0.527553i	−0.977168	+	0.212466i	$0.931850\pi$
$654$	−0.534974	−	0.926602i	−0.0209191	−	0.0362330i
$655$	−5.10562			−0.199493
$656$	−4.91088			−0.191738
$657$	−1.48883			−0.0580849
$658$	9.38205	+	16.2502i	0.365750	+	0.633498i
$659$	14.2351	+	24.6560i	0.554522	+	0.960461i	0.997941	+	0.0641462i	$0.0204324\pi$
$659$	14.2351	+	24.6560i	0.554522	+	0.960461i	−0.443418	+	0.896315i	$0.646234\pi$
$660$	6.44460			0.250856
$661$	8.23217	+	14.2585i	0.320194	+	0.554593i	0.980528	−	0.196380i	$-0.0629185\pi$
$661$	8.23217	+	14.2585i	0.320194	+	0.554593i	−0.660334	+	0.750972i	$0.729585\pi$
$662$	37.6885	−	65.2783i	1.46480	−	2.53711i
$663$	−7.30349	+	12.6500i	−0.283644	+	0.491286i
$664$	−19.4161	−	33.6297i	−0.753491	−	1.30508i
$665$	0.226986	+	0.393150i	0.00880212	+	0.0152457i
$666$	−7.71925	+	13.3701i	−0.299115	+	0.518082i
$667$	−52.7559			−2.04271
$668$	−18.0509	+	31.2650i	−0.698408	+	1.20968i
$669$	18.2919			0.707207
$670$	−0.858955	+	1.48775i	−0.0331843	+	0.0574770i
$671$	−4.67673	−	8.10034i	−0.180543	−	0.312710i
$672$	−0.120076	+	0.207978i	−0.00463205	+	0.00802294i
$673$	14.3825			0.554403			0.277201	−	0.960812i	$-0.410593\pi$
$673$	14.3825			0.554403			0.277201	+	0.960812i	$0.410593\pi$
$674$	−43.4365			−1.67311
$675$	−2.42794	−	4.20531i	−0.0934513	−	0.161862i
$676$	−53.9971	+	93.5258i	−2.07681	+	3.59715i
$677$	−14.8046			−0.568989			−0.284494	−	0.958678i	$-0.591826\pi$
$677$	−14.8046			−0.568989			−0.284494	+	0.958678i	$0.591826\pi$
$678$	8.04866	+	13.9407i	0.309107	+	0.535389i
$679$	0.0231404	+	0.0400803i	0.000888046	+	0.00153814i
$680$	−2.10107	−	3.63917i	−0.0805725	−	0.139556i
$681$	−9.80250	−	16.9784i	−0.375633	−	0.650615i
$682$	−78.6585			−3.01199
$683$	−1.10587	−	1.91542i	−0.0423148	−	0.0732913i	0.844092	−	0.536198i	$-0.180140\pi$
$683$	−1.10587	−	1.91542i	−0.0423148	−	0.0732913i	−0.886407	+	0.462907i	$0.846807\pi$
$684$	−6.25724			−0.239252
$685$	3.99545	+	6.92033i	0.152658	+	0.264412i
$686$	−24.8644			−0.949327
$687$	−10.4160			−0.397396
$688$	15.4566	+	26.7716i	0.589276	+	1.02066i
$689$	2.30854	−	3.99851i	0.0879485	−	0.152331i
$690$	−4.04406	−	7.00451i	−0.153955	−	0.266657i
$691$	3.47774	+	6.02363i	0.132300	+	0.229150i	0.924563	−	0.381030i	$-0.124431\pi$
$691$	3.47774	+	6.02363i	0.132300	+	0.229150i	−0.792263	+	0.610180i	$0.791097\pi$
$692$	−32.3782			−1.23083
$693$	−3.24410			−0.123233
$694$	−4.68083	−	8.10744i	−0.177682	−	0.307754i
$695$	−3.75521			−0.142443
$696$	−14.5352	+	25.1757i	−0.550955	+	0.954281i
$697$	1.48632	−	2.57438i	0.0562984	−	0.0975117i
$698$	13.6010	−	23.5577i	0.514807	−	0.891672i
$699$	4.88956	+	8.46896i	0.184940	+	0.320325i
$700$	−7.30302	−	12.6492i	−0.276028	−	0.478095i
$701$	−5.33624	+	9.24264i	−0.201547	+	0.349090i	−0.949027	−	0.315195i	$-0.897930\pi$
$701$	−5.33624	+	9.24264i	−0.201547	+	0.349090i	0.747480	+	0.664284i	$0.231264\pi$
$702$	7.74615	+	13.4167i	0.292360	+	0.506382i
$703$	9.96785			0.375945
$704$	17.9362	−	31.0665i	0.675997	−	1.17086i
$705$	1.92315	−	3.33100i	0.0724301	−	0.125453i
$706$	−77.0314			−2.89912
$707$	−6.30117			−0.236980
$708$	22.1864	−	38.4280i	0.833817	−	1.44421i
$709$	23.1724	−	40.1357i	0.870256	−	1.50733i	0.00852390	−	0.999964i	$-0.497287\pi$
$709$	23.1724	−	40.1357i	0.870256	−	1.50733i	0.861732	−	0.507364i	$-0.169380\pi$
$710$	−7.45976			−0.279960
$711$	3.47213	+	6.01390i	0.130215	+	0.225539i
$712$	−7.43741	+	12.8820i	−0.278729	+	0.482773i
$713$	32.8159	+	56.8389i	1.22897	+	2.12863i
$714$	2.13286	+	3.69422i	0.0798202	+	0.138253i
$715$	−5.15105	+	8.92188i	−0.192638	+	0.333659i
$716$	−48.2523	+	83.5754i	−1.80327	+	3.12336i
$717$	−5.78036	+	10.0119i	−0.215871	+	0.373900i
$718$	−50.3239			−1.87807
$719$	−23.2215	−	40.2208i	−0.866016	−	1.49998i	−0.866035	−	0.499984i	$-0.833339\pi$
$719$	−23.2215	−	40.2208i	−0.866016	−	1.49998i	1.89920e−5	−	1.00000i	$-0.499994\pi$
$720$	−1.44452			−0.0538342
$721$	5.11091			0.190340
$722$	−20.1684	−	34.9327i	−0.750589	−	1.30006i
$723$	0.538514	+	0.932733i	0.0200275	+	0.0346887i
$724$	30.3357	−	52.5430i	1.12742	−	1.95274i
$725$	14.6867	+	25.4381i	0.545450	+	0.944747i
$726$	17.8531			0.662590
$727$	41.2086			1.52834			0.764172	−	0.645013i	$-0.223148\pi$
$727$	41.2086			1.52834			0.764172	+	0.645013i	$0.223148\pi$
$728$	11.5539	+	20.0119i	0.428216	+	0.741692i
$729$	1.00000			0.0370370
$730$	0.690366	+	1.19575i	0.0255516	+	0.0442566i
$731$	−18.7123			−0.692098
$732$	4.33625	+	7.51060i	0.160272	+	0.277600i
$733$	−12.2146	−	21.1563i	−0.451156	−	0.781425i	0.547302	−	0.836935i	$-0.315655\pi$
$733$	−12.2146	−	21.1563i	−0.451156	−	0.781425i	−0.998458	+	0.0555103i	$0.982321\pi$
$734$	41.6731	+	72.1799i	1.53818	+	2.66421i
$735$	1.21963	+	2.11246i	0.0449868	+	0.0779194i
$736$	−2.76251			−0.101827
$737$	−3.96308	+	6.86425i	−0.145982	+	0.252848i
$738$	−1.57641	−	2.73042i	−0.0580283	−	0.100508i
$739$	−31.8116			−1.17021			−0.585104	−	0.810958i	$-0.698946\pi$
$739$	−31.8116			−1.17021			−0.585104	+	0.810958i	$0.698946\pi$
$740$	9.51889			0.349921
$741$	5.00129	−	8.66249i	0.183727	−	0.318225i
$742$	−0.674170	−	1.16770i	−0.0247496	−	0.0428675i
$743$	19.5515	−	33.8643i	0.717277	−	1.24236i	−0.244798	−	0.969574i	$-0.578722\pi$
$743$	19.5515	−	33.8643i	0.717277	−	1.24236i	0.962075	−	0.272786i	$-0.0879450\pi$
$744$	36.1655			1.32589
$745$	2.91339	−	5.04614i	0.106738	−	0.184876i
$746$	−81.3021			−2.97668
$747$	4.04016	−	6.99776i	0.147822	−	0.256035i
$748$	−19.5491	−	33.8600i	−0.714785	−	1.23804i
$749$	6.49524	+	11.2501i	0.237331	+	0.411069i
$750$	−4.57013	+	7.91570i	−0.166878	+	0.289040i
$751$	12.5854	−	21.7986i	0.459248	−	0.795441i	−0.539673	−	0.841875i	$-0.681452\pi$
$751$	12.5854	−	21.7986i	0.459248	−	0.795441i	0.998921	+	0.0464335i	$0.0147856\pi$
$752$	19.2748	+	33.3850i	0.702880	+	1.21742i
$753$	3.94302			0.143691
$754$	−46.8568	−	81.1584i	−1.70642	−	2.95561i
$755$	−2.35505	−	4.07907i	−0.0857090	−	0.148452i
$756$	3.00791			0.109397
$757$	10.5888			0.384857			0.192429	−	0.981311i	$-0.438364\pi$
$757$	10.5888			0.384857			0.192429	+	0.981311i	$0.438364\pi$
$758$	82.5615			2.99877
$759$	−18.6586	−	32.3177i	−0.677265	−	1.17306i
$760$	1.43878	+	2.49203i	0.0521899	+	0.0903956i
$761$	7.39634	−	12.8108i	0.268117	−	0.464392i	−0.700259	−	0.713889i	$-0.746932\pi$
$761$	7.39634	−	12.8108i	0.268117	−	0.464392i	0.968376	+	0.249497i	$0.0802653\pi$
$762$	14.0949			0.510603
$763$	0.166039	−	0.287589i	0.00601103	−	0.0104114i
$764$	46.8481	−	81.1433i	1.69490	−	2.93566i
$765$	0.437197	−	0.757248i	0.0158069	−	0.0273784i
$766$	3.12238	−	5.40812i	0.112816	−	0.195403i
$767$	35.4664	+	61.4296i	1.28062	+	2.21809i
$768$	−15.8566	+	27.4645i	−0.572176	+	0.991039i
$769$	24.1888			0.872271			0.436135	−	0.899881i	$-0.356347\pi$
$769$	24.1888			0.872271			0.436135	+	0.899881i	$0.356347\pi$
$770$	1.50428	+	2.60548i	0.0542103	+	0.0938950i
$771$	−28.2680			−1.01805
$772$	7.72236	+	13.3755i	0.277934	+	0.481396i
$773$	22.4525	−	38.8889i	0.807560	−	1.39874i	−0.106989	−	0.994260i	$-0.534121\pi$
$773$	22.4525	−	38.8889i	0.807560	−	1.39874i	0.914549	−	0.404475i	$-0.132546\pi$
$774$	−9.92321	+	17.1875i	−0.356682	+	0.617792i
$775$	18.2712	−	31.6467i	0.656322	−	1.13678i
$776$	0.146678	+	0.254054i	0.00526544	+	0.00912001i
$777$	−4.79164			−0.171899
$778$	43.1824			1.54816
$779$	−1.01781	+	1.76289i	−0.0364667	+	0.0631621i
$780$	4.77603	−	8.27233i	0.171009	−	0.296197i
$781$	−34.4181			−1.23158
$782$	−24.5345	+	42.4950i	−0.877352	+	1.51962i
$783$	−6.04904			−0.216175
$784$	−24.4476			−0.873127
$785$	−0.706758	+	4.70410i	−0.0252253	+	0.167897i
$786$	32.8522			1.17180
$787$	31.4349			1.12053			0.560266	−	0.828313i	$-0.310699\pi$
$787$	31.4349			1.12053			0.560266	+	0.828313i	$0.310699\pi$
$788$	15.9986	−	27.7104i	0.569927	−	0.987143i
$789$	−7.30508			−0.260068
$790$	3.22002	−	5.57724i	0.114563	−	0.198429i
$791$	−2.49806	+	4.32676i	−0.0888207	+	0.153842i
$792$	−20.5631			−0.730679
$793$	−13.8635			−0.492308
$794$	−13.9048	−	24.0838i	−0.493463	−	0.854703i
$795$	−0.138193	+	0.239357i	−0.00490119	+	0.00848911i
$796$	7.41821	−	12.8487i	0.262932	−	0.455411i
$797$	14.2272	−	24.6423i	0.503955	−	0.872875i	−0.496035	−	0.868303i	$-0.665211\pi$
$797$	14.2272	−	24.6423i	0.503955	−	0.872875i	0.999990	−	0.00457258i	$-0.00145550\pi$
$798$	−1.46054	−	2.52973i	−0.0517026	−	0.0895515i
$799$	−23.3348			−0.825525
$800$	0.769053	+	1.33204i	0.0271901	+	0.0470947i
$801$	−3.09520			−0.109363
$802$	−27.1109	+	46.9575i	−0.957319	+	1.65813i
$803$	3.18523	+	5.51699i	0.112404	+	0.194690i
$804$	3.67455	−	6.36451i	0.129591	−	0.224459i
$805$	1.25515	−	2.17399i	0.0442383	−	0.0766229i
$806$	−58.2930	+	100.966i	−2.05328	+	3.55639i
$807$	0.373929	−	0.647664i	0.0131629	−	0.0227989i
$808$	−39.9408			−1.40511
$809$	−0.690876	+	1.19663i	−0.0242899	+	0.0420714i	−0.877915	−	0.478817i	$-0.841066\pi$
$809$	−0.690876	+	1.19663i	−0.0242899	+	0.0420714i	0.853625	+	0.520888i	$0.174399\pi$
$810$	−0.463696	−	0.803145i	−0.0162926	−	0.0282196i
$811$	−16.4264	−	28.4513i	−0.576809	−	0.999062i	−0.995843	−	0.0910912i	$-0.970965\pi$
$811$	−16.4264	−	28.4513i	−0.576809	−	0.999062i	0.419034	−	0.907971i	$-0.362369\pi$
$812$	−18.1950			−0.638519
$813$	−27.9743			−0.981103
$814$	66.0588			2.31536
$815$	2.50081	+	4.33153i	0.0875996	+	0.151727i
$816$	4.38182	+	7.58953i	0.153394	+	0.265687i
$817$	12.8138			0.448299
$818$	−30.8596	−	53.4503i	−1.07898	−	1.86885i
$819$	−2.40417	+	4.16414i	−0.0840084	+	0.145507i
$820$	−0.971962	+	1.68349i	−0.0339424	+	0.0587899i
$821$	−14.1225	−	24.4609i	−0.492879	−	0.853692i	0.507087	−	0.861895i	$-0.330722\pi$
$821$	−14.1225	−	24.4609i	−0.492879	−	0.853692i	−0.999966	+	0.00820317i	$0.997389\pi$
$822$	−25.7088	−	44.5289i	−0.896697	−	1.55312i
$823$	−11.4673	+	19.8620i	−0.399727	+	0.692347i	−0.993692	−	0.112144i	$-0.964228\pi$
$823$	−11.4673	+	19.8620i	−0.399727	+	0.692347i	0.593965	+	0.804491i	$0.297562\pi$
$824$	32.3962			1.12857
$825$	−10.3887	+	17.9938i	−0.361689	+	0.626464i
$826$	20.7147			0.720756
$827$	−6.38989	+	11.0676i	−0.222198	+	0.384859i	−0.955475	−	0.295071i	$-0.904657\pi$
$827$	−6.38989	+	11.0676i	−0.222198	+	0.384859i	0.733277	+	0.679930i	$0.237990\pi$
$828$	17.3002	+	29.9648i	0.601223	+	1.04135i
$829$	−11.7589	+	20.3669i	−0.408402	+	0.707373i	−0.994711	−	0.102715i	$-0.967247\pi$
$829$	−11.7589	+	20.3669i	−0.408402	+	0.707373i	0.586309	+	0.810088i	$0.300580\pi$
$830$	−7.49362			−0.260107
$831$	−6.56046			−0.227580
$832$	−26.5847	−	46.0461i	−0.921659	−	1.59636i
$833$	7.39927	−	12.8159i	0.256369	−	0.444045i
$834$	24.1629			0.836694
$835$	1.72733	+	2.99182i	0.0597766	+	0.103536i
$836$	13.3868	+	23.1867i	0.462994	+	0.801929i
$837$	3.76271	+	6.51720i	0.130058	+	0.225268i
$838$	42.5317	+	73.6670i	1.46923	+	2.54479i
$839$	2.63324			0.0909095			0.0454547	−	0.998966i	$-0.485526\pi$
$839$	2.63324			0.0909095			0.0454547	+	0.998966i	$0.485526\pi$
$840$	−0.691633	−	1.19794i	−0.0238636	−	0.0413330i
$841$	7.59093			0.261756
$842$	47.4396	+	82.1678i	1.63488	+	2.83169i
$843$	12.3894			0.426714
$844$	66.9462			2.30438
$845$	5.16711	+	8.94970i	0.177754	+	0.307879i
$846$	−12.3745	+	21.4333i	−0.425446	+	0.736893i
$847$	2.77053	+	4.79869i	0.0951964	+	0.164885i
$848$	−1.38504	−	2.39896i	−0.0475624	−	0.0823806i
$849$	7.50284			0.257497
$850$	27.3206			0.937090
$851$	−27.5594	−	47.7342i	−0.944723	−	1.63631i
$852$	31.9123			1.09330
$853$	−24.5661	+	42.5498i	−0.841128	+	1.45688i	0.0478137	+	0.998856i	$0.484775\pi$
$853$	−24.5661	+	42.5498i	−0.841128	+	1.45688i	−0.888942	+	0.458020i	$0.848559\pi$
$854$	−2.02430	+	3.50619i	−0.0692701	+	0.119979i
$855$	−0.299385	+	0.518550i	−0.0102387	+	0.0177340i
$856$	41.1709	+	71.3101i	1.40719	+	2.43733i
$857$	14.6915	+	25.4464i	0.501851	+	0.869231i	0.999998	+	0.00213847i	$0.000680698\pi$
$857$	14.6915	+	25.4464i	0.501851	+	0.869231i	−0.498147	+	0.867093i	$0.665986\pi$
$858$	33.1445	−	57.4080i	1.13153	−	1.95988i
$859$	23.6069	+	40.8884i	0.805458	+	1.39509i	0.915982	+	0.401220i	$0.131414\pi$
$859$	23.6069	+	40.8884i	0.805458	+	1.39509i	−0.110524	+	0.993873i	$0.535253\pi$
$860$	12.2367			0.417267
$861$	0.489268	−	0.847437i	0.0166742	−	0.0288806i
$862$	0.906376	−	1.56989i	0.0308713	−	0.0534707i
$863$	−37.2828			−1.26912			−0.634561	−	0.772873i	$-0.718819\pi$
$863$	−37.2828			−1.26912			−0.634561	+	0.772873i	$0.718819\pi$
$864$	−0.316752			−0.0107761
$865$	−1.54917	+	2.68324i	−0.0526734	+	0.0912330i
$866$	−23.1519	+	40.1003i	−0.786735	+	1.36267i
$867$	11.6952			0.397190
$868$	11.3179	+	19.6032i	0.384155	+	0.665375i
$869$	14.8567	−	25.7325i	0.503978	−	0.872915i
$870$	2.80492	+	4.85826i	0.0950956	+	0.164710i
$871$	5.87400	+	10.1741i	0.199033	+	0.344735i
$872$	1.05246	−	1.82292i	0.0356409	−	0.0617318i
$873$	−0.0305212	+	0.0528643i	−0.00103299	+	0.00178919i
$874$	16.8008	−	29.0998i	0.568295	−	0.984315i
$875$	−2.83686			−0.0959032
$876$	−2.95333	−	5.11533i	−0.0997839	−	0.172831i
$877$	−14.9059			−0.503335			−0.251668	−	0.967814i	$-0.580979\pi$
$877$	−14.9059			−0.503335			−0.251668	+	0.967814i	$0.580979\pi$
$878$	−63.9877			−2.15948
$879$	4.22658	+	7.32064i	0.142559	+	0.246919i
$880$	3.09044	+	5.35280i	0.104179	+	0.180443i
$881$	15.4322	−	26.7293i	0.519924	−	0.900534i	−0.479808	−	0.877373i	$-0.659294\pi$
$881$	15.4322	−	26.7293i	0.519924	−	0.900534i	0.999732	−	0.0231608i	$-0.00737297\pi$
$882$	−7.84774	−	13.5927i	−0.264247	−	0.457689i
$883$	26.6517			0.896902			0.448451	−	0.893808i	$-0.351976\pi$
$883$	26.6517			0.896902			0.448451	+	0.893808i	$0.351976\pi$
$884$	−57.9505			−1.94909
$885$	−2.12307	−	3.67727i	−0.0713662	−	0.123610i
$886$	24.1607			0.811694
$887$	15.7704	+	27.3151i	0.529519	+	0.917153i	0.999407	+	0.0344273i	$0.0109607\pi$
$887$	15.7704	+	27.3151i	0.529519	+	0.917153i	−0.469889	+	0.882726i	$0.655706\pi$
$888$	−30.3724			−1.01923
$889$	2.18731	+	3.78853i	0.0733599	+	0.127063i
$890$	1.43523	+	2.48589i	0.0481090	+	0.0833273i
$891$	−2.13942	−	3.70558i	−0.0716732	−	0.124142i
$892$	36.2849	+	62.8473i	1.21491	+	2.10428i
$893$	15.9792			0.534724
$894$	−18.7462	+	32.4694i	−0.626968	+	1.08594i
$895$	4.61737	+	7.99753i	0.154342	+	0.267328i
$896$	−15.0469			−0.502682
$897$	−55.3108			−1.84678
$898$	21.8788	−	37.8952i	0.730105	−	1.26458i
$899$	−22.7608	−	39.4229i	−0.759115	−	1.31483i
$900$	9.63239	−	16.6838i	0.321080	−	0.556126i
$901$	1.67678			0.0558615
$902$	−6.74518	+	11.6830i	−0.224590	+	0.389001i
$903$	−6.15972			−0.204983
$904$	−15.8343	+	27.4257i	−0.526640	+	0.912167i
$905$	−2.90289	−	5.02796i	−0.0964954	−	0.167135i
$906$	15.1536	+	26.2468i	0.503445	+	0.871992i
$907$	19.2229	−	33.2951i	0.638287	−	1.10555i	−0.347521	−	0.937672i	$-0.612977\pi$
$907$	19.2229	−	33.2951i	0.638287	−	1.10555i	0.985808	−	0.167874i	$-0.0536901\pi$
$908$	38.8896	−	67.3588i	1.29060	−	2.23538i
$909$	−4.15550	−	7.19753i	−0.137829	−	0.238727i
$910$	4.45921			0.147821
$911$	−2.54614	−	4.41005i	−0.0843575	−	0.146112i	0.820760	−	0.571274i	$-0.193550\pi$
$911$	−2.54614	−	4.41005i	−0.0843575	−	0.146112i	−0.905117	+	0.425162i	$0.860217\pi$
$912$	−3.00059	−	5.19717i	−0.0993595	−	0.172096i
$913$	−34.5743			−1.14424
$914$	−65.5443			−2.16801
$915$	0.829891			0.0274353
$916$	−20.6618	−	35.7873i	−0.682686	−	1.18245i
$917$	5.09815	+	8.83026i	0.168356	+	0.291601i
$918$	−2.81315	+	4.87252i	−0.0928479	+	0.160817i
$919$	−0.567029			−0.0187046			−0.00935228	−	0.999956i	$-0.502977\pi$
$919$	−0.567029			−0.0187046			−0.00935228	+	0.999956i	$0.502977\pi$
$920$	7.95594	−	13.7801i	0.262300	−	0.454316i
$921$	3.24875	−	5.62699i	0.107050	−	0.185416i
$922$	9.97109	−	17.2704i	0.328380	−	0.568772i
$923$	−25.5069	+	44.1792i	−0.839570	+	1.45418i
$924$	−6.43518	−	11.1461i	−0.211702	−	0.366678i
$925$	−15.3445	+	26.5775i	−0.504524	+	0.873861i
$926$	5.83496			0.191749
$927$	3.37054	+	5.83795i	0.110703	+	0.191744i
$928$	1.91605			0.0628973
$929$	20.7613	+	35.9597i	0.681158	+	1.17980i	0.974628	+	0.223831i	$0.0718565\pi$
$929$	20.7613	+	35.9597i	0.681158	+	1.17980i	−0.293470	+	0.955968i	$0.594810\pi$
$930$	3.48951	−	6.04400i	0.114425	−	0.198191i
$931$	−5.06688	+	8.77610i	−0.166060	+	0.287625i
$932$	−19.3984	+	33.5990i	−0.635416	+	1.10057i
$933$	0.168530	+	0.291903i	0.00551743	+	0.00955647i
$934$	−9.24759			−0.302590
$935$	−3.74139			−0.122357
$936$	−15.2391	+	26.3949i	−0.498106	+	0.862746i
$937$	−7.38369	+	12.7889i	−0.241215	+	0.417796i	−0.961061	−	0.276338i	$-0.910879\pi$
$937$	−7.38369	+	12.7889i	−0.241215	+	0.417796i	0.719846	+	0.694134i	$0.244212\pi$
$938$	3.43080			0.112020
$939$	−10.7929	+	18.6939i	−0.352214	+	0.610052i
$940$	15.2595			0.497710
$941$	52.7689			1.72022			0.860109	−	0.510110i	$-0.170395\pi$
$941$	52.7689			1.72022			0.860109	+	0.510110i	$0.170395\pi$
$942$	4.54764	−	30.2686i	0.148170	−	0.986204i
$943$	11.2562			0.366553
$944$	42.5570			1.38511
$945$	0.143917	−	0.249272i	0.00468162	−	0.00810881i
$946$	84.9195			2.76097
$947$	−2.77160	+	4.80055i	−0.0900649	+	0.155997i	−0.907538	−	0.419969i	$-0.862041\pi$
$947$	−2.77160	+	4.80055i	−0.0900649	+	0.155997i	0.817473	+	0.575966i	$0.195374\pi$
$948$	−13.7750	+	23.8591i	−0.447392	+	0.774906i
$949$	9.44218			0.306506
$950$	−18.7087			−0.606989
$951$	6.80847	+	11.7926i	0.220780	+	0.382402i
$952$	−4.19600	+	7.26769i	−0.135993	+	0.235547i
$953$	−20.5118	+	35.5275i	−0.664442	+	1.15085i	0.314994	+	0.949094i	$0.397997\pi$
$953$	−20.5118	+	35.5275i	−0.664442	+	1.15085i	−0.979436	+	0.201754i	$0.935336\pi$
$954$	0.889203	−	1.54014i	0.0287890	−	0.0498640i
$955$	−4.48300	−	7.76479i	−0.145067	−	0.251263i
$956$	−45.8650			−1.48338
$957$	12.9414	+	22.4152i	0.418337	+	0.724581i
$958$	6.92608			0.223771
$959$	7.97922	−	13.8204i	0.257662	−	0.446284i
$960$	1.59140	+	2.75639i	0.0513622	+	0.0889620i
$961$	−12.8160	+	22.1979i	−0.413418	+	0.716062i
$962$	48.9555	−	84.7934i	1.57839	−	2.73385i
$963$	−8.56696	+	14.8384i	−0.276066	+	0.478161i
$964$	−2.13645	+	3.70045i	−0.0688106	+	0.119183i
$965$	1.47794			0.0475766
$966$	−8.07629	+	13.9885i	−0.259850	+	0.450074i
$967$	−16.4354	−	28.4670i	−0.528528	−	0.915437i	−0.999447	−	0.0332606i	$-0.989411\pi$
$967$	−16.4354	−	28.4670i	−0.528528	−	0.915437i	0.470919	−	0.882177i	$-0.343922\pi$
$968$	17.5613	+	30.4171i	0.564443	+	0.977644i
$969$	3.63262			0.116697
$970$	0.0566103			0.00181765
$971$	25.8985			0.831121			0.415560	−	0.909566i	$-0.363585\pi$
$971$	25.8985			0.831121			0.415560	+	0.909566i	$0.363585\pi$
$972$	1.98366	+	3.43580i	0.0636259	+	0.110203i
$973$	3.74972	+	6.49470i	0.120210	+	0.208211i
$974$	−31.1862			−0.999271
$975$	15.3980	+	26.6701i	0.493130	+	0.854126i
$976$	−4.15880	+	7.20325i	−0.133120	+	0.230570i
$977$	0.693752	−	1.20161i	0.0221951	−	0.0384430i	−0.854715	−	0.519098i	$-0.826268\pi$
$977$	0.693752	−	1.20161i	0.0221951	−	0.0384430i	0.876910	+	0.480655i	$0.159601\pi$
$978$	−16.0915	−	27.8713i	−0.514550	−	0.891226i
$979$	6.62192	+	11.4695i	0.211637	+	0.366567i
$980$	−4.83866	+	8.38081i	−0.154565	+	0.267715i
$981$	0.437999			0.0139842
$982$	17.5725	−	30.4364i	0.560760	−	0.971265i
$983$	1.94734			0.0621104			0.0310552	−	0.999518i	$-0.490113\pi$
$983$	1.94734			0.0621104			0.0310552	+	0.999518i	$0.490113\pi$
$984$	3.10129	−	5.37159i	0.0988655	−	0.171240i
$985$	−1.53094	−	2.65167i	−0.0487800	−	0.0844894i
$986$	17.0169	−	29.4741i	0.541928	−	0.938647i
$987$	−7.68136			−0.244500
$988$	39.6834			1.26250
$989$	−35.4280	−	61.3631i	−1.12654	−	1.95123i
$990$	−1.98408	+	3.43653i	−0.0630582	+	0.109220i
$991$	−2.78544			−0.0884823			−0.0442411	−	0.999021i	$-0.514087\pi$
$991$	−2.78544			−0.0884823			−0.0442411	+	0.999021i	$0.514087\pi$
$992$	−1.19185	−	2.06434i	−0.0378411	−	0.0655428i
$993$	15.4283	+	26.7226i	0.489603	+	0.848017i
$994$	7.44885	+	12.9018i	0.236263	+	0.409220i
$995$	−0.709866	−	1.22952i	−0.0225043	−	0.0389785i
$996$	32.0572			1.01577
$997$	1.48362	+	2.56970i	0.0469867	+	0.0813833i	0.888562	−	0.458756i	$-0.151705\pi$
$997$	1.48362	+	2.56970i	0.0469867	+	0.0813833i	−0.841576	+	0.540139i	$0.818371\pi$
$998$	−96.0085			−3.03910
$999$	−3.15999	−	5.47326i	−0.0999776	−	0.173166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.b.301.2	yes	22
157.12	even	3	inner	471.2.e.b.169.2	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.b.169.2	✓	22	157.12	even	3	inner
471.2.e.b.301.2	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.44281 q^{2} +(0.500000 - 0.866025i) q^{3} +3.96732 q^{4} +(0.189821 - 0.328779i) q^{5} +(-1.22140 + 2.11553i) q^{6} -0.758173 q^{7} -4.80578 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-2.44281 q^{2} +(0.500000 - 0.866025i) q^{3} +3.96732 q^{4} +(0.189821 - 0.328779i) q^{5} +(-1.22140 + 2.11553i) q^{6} -0.758173 q^{7} -4.80578 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.463696 + 0.803145i) q^{10} +(-2.13942 + 3.70558i) q^{11} +(1.98366 - 3.43580i) q^{12} +(3.17100 + 5.49234i) q^{13} +1.85207 q^{14} +(-0.189821 - 0.328779i) q^{15} +3.80497 q^{16} +(-1.15161 + 1.99464i) q^{17} +(1.22140 + 2.11553i) q^{18} +(0.788598 - 1.36589i) q^{19} +(0.753079 - 1.30437i) q^{20} +(-0.379087 + 0.656597i) q^{21} +(5.22619 - 9.05202i) q^{22} -8.72135 q^{23} +(-2.40289 + 4.16193i) q^{24} +(2.42794 + 4.20531i) q^{25} +(-7.74615 - 13.4167i) q^{26} -1.00000 q^{27} -3.00791 q^{28} +6.04904 q^{29} +(0.463696 + 0.803145i) q^{30} +(-3.76271 - 6.51720i) q^{31} +0.316752 q^{32} +(2.13942 + 3.70558i) q^{33} +(2.81315 - 4.87252i) q^{34} +(-0.143917 + 0.249272i) q^{35} +(-1.98366 - 3.43580i) q^{36} +(3.15999 + 5.47326i) q^{37} +(-1.92640 + 3.33661i) q^{38} +6.34200 q^{39} +(-0.912237 + 1.58004i) q^{40} -1.29065 q^{41} +(0.926036 - 1.60394i) q^{42} +(4.06221 + 7.03596i) q^{43} +(-8.48775 + 14.7012i) q^{44} -0.379642 q^{45} +21.3046 q^{46} +(5.06570 + 8.77405i) q^{47} +(1.90248 - 3.29520i) q^{48} -6.42517 q^{49} +(-5.93098 - 10.2728i) q^{50} +(1.15161 + 1.99464i) q^{51} +(12.5804 + 21.7898i) q^{52} +(-0.364008 - 0.630481i) q^{53} +2.44281 q^{54} +(0.812212 + 1.40679i) q^{55} +3.64361 q^{56} +(-0.788598 - 1.36589i) q^{57} -14.7767 q^{58} +11.1846 q^{59} +(-0.753079 - 1.30437i) q^{60} +(-1.09299 + 1.89312i) q^{61} +(9.19158 + 15.9203i) q^{62} +(0.379087 + 0.656597i) q^{63} -8.38369 q^{64} +2.40769 q^{65} +(-5.22619 - 9.05202i) q^{66} +1.85241 q^{67} +(-4.56878 + 7.91337i) q^{68} +(-4.36068 + 7.55291i) q^{69} +(0.351562 - 0.608923i) q^{70} +(4.02190 + 6.96613i) q^{71} +(2.40289 + 4.16193i) q^{72} +(0.744416 - 1.28937i) q^{73} +(-7.71925 - 13.3701i) q^{74} +4.85587 q^{75} +(3.12862 - 5.41893i) q^{76} +(1.62205 - 2.80947i) q^{77} -15.4923 q^{78} -6.94426 q^{79} +(0.722262 - 1.25099i) q^{80} +(-0.500000 + 0.866025i) q^{81} +3.15281 q^{82} +(4.04016 + 6.99776i) q^{83} +(-1.50396 + 2.60493i) q^{84} +(0.437197 + 0.757248i) q^{85} +(-9.92321 - 17.1875i) q^{86} +(3.02452 - 5.23863i) q^{87} +(10.2816 - 17.8082i) q^{88} +(1.54760 - 2.68052i) q^{89} +0.927392 q^{90} +(-2.40417 - 4.16414i) q^{91} -34.6004 q^{92} -7.52542 q^{93} +(-12.3745 - 21.4333i) q^{94} +(-0.299385 - 0.518550i) q^{95} +(0.158376 - 0.274315i) q^{96} +(-0.0305212 - 0.0528643i) q^{97} +15.6955 q^{98} +4.27883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Introduction

L-functions

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