LMFDB - Embedded newform 471.2.e.b.169.3

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			169.3
Character	$\chi$	$=$	471.169
Dual form			471.2.e.b.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18058 q^{2} +(0.500000 + 0.866025i) q^{3} +2.75495 q^{4} +(1.44529 + 2.50331i) q^{5} +(-1.09029 - 1.88844i) q^{6} -2.39860 q^{7} -1.64623 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-2.18058 q^{2} +(0.500000 + 0.866025i) q^{3} +2.75495 q^{4} +(1.44529 + 2.50331i) q^{5} +(-1.09029 - 1.88844i) q^{6} -2.39860 q^{7} -1.64623 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.15157 - 5.45869i) q^{10} +(1.50356 + 2.60424i) q^{11} +(1.37748 + 2.38586i) q^{12} +(-1.85855 + 3.21911i) q^{13} +5.23035 q^{14} +(-1.44529 + 2.50331i) q^{15} -1.92015 q^{16} +(0.282388 + 0.489110i) q^{17} +(1.09029 - 1.88844i) q^{18} +(-1.70237 - 2.94859i) q^{19} +(3.98170 + 6.89650i) q^{20} +(-1.19930 - 2.07725i) q^{21} +(-3.27864 - 5.67877i) q^{22} +3.26184 q^{23} +(-0.823117 - 1.42568i) q^{24} +(-1.67772 + 2.90589i) q^{25} +(4.05274 - 7.01954i) q^{26} -1.00000 q^{27} -6.60802 q^{28} -1.17911 q^{29} +(3.15157 - 5.45869i) q^{30} +(2.06996 - 3.58528i) q^{31} +7.47951 q^{32} +(-1.50356 + 2.60424i) q^{33} +(-0.615770 - 1.06655i) q^{34} +(-3.46667 - 6.00444i) q^{35} +(-1.37748 + 2.38586i) q^{36} +(-0.400693 + 0.694021i) q^{37} +(3.71216 + 6.42964i) q^{38} -3.71711 q^{39} +(-2.37928 - 4.12104i) q^{40} -8.20410 q^{41} +(2.61517 + 4.52962i) q^{42} +(-2.18395 + 3.78271i) q^{43} +(4.14223 + 7.17455i) q^{44} -2.89058 q^{45} -7.11272 q^{46} +(-3.83982 + 6.65076i) q^{47} +(-0.960074 - 1.66290i) q^{48} -1.24672 q^{49} +(3.65840 - 6.33654i) q^{50} +(-0.282388 + 0.489110i) q^{51} +(-5.12023 + 8.86849i) q^{52} +(-6.24445 + 10.8157i) q^{53} +2.18058 q^{54} +(-4.34615 + 7.52776i) q^{55} +3.94866 q^{56} +(1.70237 - 2.94859i) q^{57} +2.57114 q^{58} +4.41510 q^{59} +(-3.98170 + 6.89650i) q^{60} +(-0.833969 - 1.44448i) q^{61} +(-4.51373 + 7.81801i) q^{62} +(1.19930 - 2.07725i) q^{63} -12.4694 q^{64} -10.7446 q^{65} +(3.27864 - 5.67877i) q^{66} -4.61609 q^{67} +(0.777964 + 1.34747i) q^{68} +(1.63092 + 2.82483i) q^{69} +(7.55936 + 13.0932i) q^{70} +(6.39668 - 11.0794i) q^{71} +(0.823117 - 1.42568i) q^{72} +(-2.04217 - 3.53714i) q^{73} +(0.873745 - 1.51337i) q^{74} -3.35543 q^{75} +(-4.68994 - 8.12321i) q^{76} +(-3.60644 - 6.24653i) q^{77} +8.10547 q^{78} +8.08956 q^{79} +(-2.77517 - 4.80673i) q^{80} +(-0.500000 - 0.866025i) q^{81} +17.8897 q^{82} +(-2.73010 + 4.72867i) q^{83} +(-3.30401 - 5.72272i) q^{84} +(-0.816263 + 1.41381i) q^{85} +(4.76228 - 8.24851i) q^{86} +(-0.589554 - 1.02114i) q^{87} +(-2.47521 - 4.28719i) q^{88} +(5.21901 + 9.03959i) q^{89} +6.30315 q^{90} +(4.45793 - 7.72136i) q^{91} +8.98620 q^{92} +4.13992 q^{93} +(8.37304 - 14.5025i) q^{94} +(4.92082 - 8.52312i) q^{95} +(3.73976 + 6.47745i) q^{96} +(-1.79721 + 3.11285i) q^{97} +2.71858 q^{98} -3.00712 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 $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.18058			−1.54191			−0.770953	−	0.636892i	$-0.780220\pi$
$2$	−2.18058			−1.54191			−0.770953	+	0.636892i	$0.780220\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.75495			1.37748
$5$	1.44529	+	2.50331i	0.646353	+	1.11952i	0.983987	+	0.178238i	$0.0570398\pi$
$5$	1.44529	+	2.50331i	0.646353	+	1.11952i	−0.337635	+	0.941277i	$0.609627\pi$
$6$	−1.09029	−	1.88844i	−0.445110	−	0.770953i
$7$	−2.39860			−0.906585			−0.453293	−	0.891362i	$-0.649751\pi$
$7$	−2.39860			−0.906585			−0.453293	+	0.891362i	$0.649751\pi$
$8$	−1.64623			−0.582032
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−3.15157	−	5.45869i	−0.996615	−	1.72619i
$11$	1.50356	+	2.60424i	0.453340	+	0.785208i	0.998591	−	0.0530649i	$-0.0168990\pi$
$11$	1.50356	+	2.60424i	0.453340	+	0.785208i	−0.545251	+	0.838273i	$0.683566\pi$
$12$	1.37748	+	2.38586i	0.397643	+	0.688738i
$13$	−1.85855	+	3.21911i	−0.515470	+	0.892821i	0.484368	+	0.874864i	$0.339049\pi$
$13$	−1.85855	+	3.21911i	−0.515470	+	0.892821i	−0.999839	+	0.0179566i	$0.994284\pi$
$14$	5.23035			1.39787
$15$	−1.44529	+	2.50331i	−0.373172	+	0.646353i
$16$	−1.92015			−0.480037
$17$	0.282388	+	0.489110i	0.0684891	+	0.118627i	0.898236	−	0.439513i	$-0.144849\pi$
$17$	0.282388	+	0.489110i	0.0684891	+	0.118627i	−0.829747	+	0.558139i	$0.811516\pi$
$18$	1.09029	−	1.88844i	0.256984	−	0.445110i
$19$	−1.70237	−	2.94859i	−0.390550	−	0.676452i	0.601972	−	0.798517i	$-0.294382\pi$
$19$	−1.70237	−	2.94859i	−0.390550	−	0.676452i	−0.992522	+	0.122065i	$0.961048\pi$
$20$	3.98170	+	6.89650i	0.890335	+	1.54210i
$21$	−1.19930	−	2.07725i	−0.261709	−	0.453293i
$22$	−3.27864	−	5.67877i	−0.699008	−	1.21072i
$23$	3.26184			0.680140			0.340070	−	0.940400i	$-0.389549\pi$
$23$	3.26184			0.680140			0.340070	+	0.940400i	$0.389549\pi$
$24$	−0.823117	−	1.42568i	−0.168018	−	0.291016i
$25$	−1.67772	+	2.90589i	−0.335543	+	0.581178i
$26$	4.05274	−	7.01954i	0.794807	−	1.37665i
$27$	−1.00000			−0.192450
$28$	−6.60802			−1.24880
$29$	−1.17911			−0.218955			−0.109477	−	0.993989i	$-0.534918\pi$
$29$	−1.17911			−0.218955			−0.109477	+	0.993989i	$0.534918\pi$
$30$	3.15157	−	5.45869i	0.575396	−	0.996615i
$31$	2.06996	−	3.58528i	0.371776	−	0.643935i	−0.618063	−	0.786129i	$-0.712082\pi$
$31$	2.06996	−	3.58528i	0.371776	−	0.643935i	0.989839	+	0.142194i	$0.0454156\pi$
$32$	7.47951			1.32220
$33$	−1.50356	+	2.60424i	−0.261736	+	0.453340i
$34$	−0.615770	−	1.06655i	−0.105604	−	0.182911i
$35$	−3.46667	−	6.00444i	−0.585974	−	1.01494i
$36$	−1.37748	+	2.38586i	−0.229579	+	0.397643i
$37$	−0.400693	+	0.694021i	−0.0658735	+	0.114096i	−0.897081	−	0.441866i	$-0.854317\pi$
$37$	−0.400693	+	0.694021i	−0.0658735	+	0.114096i	0.831208	+	0.555962i	$0.187650\pi$
$38$	3.71216	+	6.42964i	0.602191	+	1.04303i
$39$	−3.71711			−0.595214
$40$	−2.37928	−	4.12104i	−0.376198	−	0.651593i
$41$	−8.20410			−1.28127			−0.640633	−	0.767847i	$-0.721328\pi$
$41$	−8.20410			−1.28127			−0.640633	+	0.767847i	$0.721328\pi$
$42$	2.61517	+	4.52962i	0.403530	+	0.698935i
$43$	−2.18395	+	3.78271i	−0.333049	+	0.576857i	−0.983108	−	0.183026i	$-0.941411\pi$
$43$	−2.18395	+	3.78271i	−0.333049	+	0.576857i	0.650059	+	0.759883i	$0.274744\pi$
$44$	4.14223	+	7.17455i	0.624465	+	1.08160i
$45$	−2.89058			−0.430902
$46$	−7.11272			−1.04871
$47$	−3.83982	+	6.65076i	−0.560095	+	0.970112i	0.437393	+	0.899271i	$0.355902\pi$
$47$	−3.83982	+	6.65076i	−0.560095	+	0.970112i	−0.997488	+	0.0708419i	$0.977431\pi$
$48$	−0.960074	−	1.66290i	−0.138575	−	0.240019i
$49$	−1.24672			−0.178103
$50$	3.65840	−	6.33654i	0.517376	−	0.896122i
$51$	−0.282388	+	0.489110i	−0.0395422	+	0.0684891i
$52$	−5.12023	+	8.86849i	−0.710048	+	1.22984i
$53$	−6.24445	+	10.8157i	−0.857741	+	1.48565i	0.0163367	+	0.999867i	$0.494800\pi$
$53$	−6.24445	+	10.8157i	−0.857741	+	1.48565i	−0.874078	+	0.485785i	$0.838534\pi$
$54$	2.18058			0.296740
$55$	−4.34615	+	7.52776i	−0.586035	+	1.01504i
$56$	3.94866			0.527661
$57$	1.70237	−	2.94859i	0.225484	−	0.390550i
$58$	2.57114			0.337608
$59$	4.41510			0.574796			0.287398	−	0.957811i	$-0.407210\pi$
$59$	4.41510			0.574796			0.287398	+	0.957811i	$0.407210\pi$
$60$	−3.98170	+	6.89650i	−0.514035	+	0.890335i
$61$	−0.833969	−	1.44448i	−0.106779	−	0.184946i	0.807685	−	0.589615i	$-0.200720\pi$
$61$	−0.833969	−	1.44448i	−0.106779	−	0.184946i	−0.914464	+	0.404668i	$0.867387\pi$
$62$	−4.51373	+	7.81801i	−0.573244	+	0.992888i
$63$	1.19930	−	2.07725i	0.151098	−	0.261709i
$64$	−12.4694			−1.55868
$65$	−10.7446			−1.33270
$66$	3.27864	−	5.67877i	0.403572	−	0.699008i
$67$	−4.61609			−0.563946			−0.281973	−	0.959422i	$-0.590989\pi$
$67$	−4.61609			−0.563946			−0.281973	+	0.959422i	$0.590989\pi$
$68$	0.777964	+	1.34747i	0.0943420	+	0.163405i
$69$	1.63092	+	2.82483i	0.196340	+	0.340070i
$70$	7.55936	+	13.0932i	0.903517	+	1.56494i
$71$	6.39668	−	11.0794i	0.759147	−	1.31488i	−0.184140	−	0.982900i	$-0.558950\pi$
$71$	6.39668	−	11.0794i	0.759147	−	1.31488i	0.943286	−	0.331980i	$-0.107717\pi$
$72$	0.823117	−	1.42568i	0.0970053	−	0.168018i
$73$	−2.04217	−	3.53714i	−0.239018	−	0.413990i	0.721415	−	0.692503i	$-0.243492\pi$
$73$	−2.04217	−	3.53714i	−0.239018	−	0.413990i	−0.960433	+	0.278512i	$0.910159\pi$
$74$	0.873745	−	1.51337i	0.101571	−	0.175926i
$75$	−3.35543			−0.387452
$76$	−4.68994	−	8.12321i	−0.537973	−	0.931796i
$77$	−3.60644	−	6.24653i	−0.410991	−	0.711858i
$78$	8.10547			0.917764
$79$	8.08956			0.910147			0.455073	−	0.890454i	$-0.349613\pi$
$79$	8.08956			0.910147			0.455073	+	0.890454i	$0.349613\pi$
$80$	−2.77517	−	4.80673i	−0.310273	−	0.537409i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	17.8897			1.97559
$83$	−2.73010	+	4.72867i	−0.299667	+	0.519039i	−0.976060	−	0.217502i	$-0.930209\pi$
$83$	−2.73010	+	4.72867i	−0.299667	+	0.519039i	0.676392	+	0.736541i	$0.263542\pi$
$84$	−3.30401	−	5.72272i	−0.360497	−	0.624399i
$85$	−0.816263	+	1.41381i	−0.0885362	+	0.153349i
$86$	4.76228	−	8.24851i	0.513530	−	0.889460i
$87$	−0.589554	−	1.02114i	−0.0632068	−	0.109477i
$88$	−2.47521	−	4.28719i	−0.263858	−	0.457016i
$89$	5.21901	+	9.03959i	0.553214	+	0.958195i	0.998040	+	0.0625777i	$0.0199321\pi$
$89$	5.21901	+	9.03959i	0.553214	+	0.958195i	−0.444826	+	0.895617i	$0.646735\pi$
$90$	6.30315			0.664410
$91$	4.45793	−	7.72136i	0.467318	−	0.809418i
$92$	8.98620			0.936876
$93$	4.13992			0.429290
$94$	8.37304	−	14.5025i	0.863614	−	1.49582i
$95$	4.92082	−	8.52312i	0.504866	−	0.874453i
$96$	3.73976	+	6.47745i	0.381687	+	0.661102i
$97$	−1.79721	+	3.11285i	−0.182479	+	0.316062i	−0.942724	−	0.333574i	$-0.891745\pi$
$97$	−1.79721	+	3.11285i	−0.182479	+	0.316062i	0.760245	+	0.649636i	$0.225079\pi$
$98$	2.71858			0.274618
$99$	−3.00712			−0.302227
$100$	−4.62203	+	8.00558i	−0.462203	+	0.800558i
$101$	−6.04962			−0.601959			−0.300980	−	0.953631i	$-0.597314\pi$
$101$	−6.04962			−0.601959			−0.300980	+	0.953631i	$0.597314\pi$
$102$	0.615770	−	1.06655i	0.0609703	−	0.105604i
$103$	18.1264			1.78604			0.893022	−	0.450013i	$-0.148581\pi$
$103$	18.1264			1.78604			0.893022	+	0.450013i	$0.148581\pi$
$104$	3.05962	−	5.29941i	0.300020	−	0.519650i
$105$	3.46667	−	6.00444i	0.338312	−	0.585974i
$106$	13.6166	−	23.5846i	1.32256	−	2.29074i
$107$	−7.67691	+	13.2968i	−0.742155	+	1.28545i	0.209357	+	0.977839i	$0.432863\pi$
$107$	−7.67691	+	13.2968i	−0.742155	+	1.28545i	−0.951512	+	0.307611i	$0.900470\pi$
$108$	−2.75495			−0.265095
$109$	2.44843	+	4.24080i	0.234517	+	0.406195i	0.959132	−	0.282958i	$-0.0913158\pi$
$109$	2.44843	+	4.24080i	0.234517	+	0.406195i	−0.724615	+	0.689154i	$0.757982\pi$
$110$	9.47715	−	16.4149i	0.903611	−	1.56510i
$111$	−0.801386			−0.0760642
$112$	4.60567			0.435195
$113$	7.55047	+	13.0778i	0.710289	+	1.23026i	0.964749	+	0.263173i	$0.0847690\pi$
$113$	7.55047	+	13.0778i	0.710289	+	1.23026i	−0.254460	+	0.967083i	$0.581898\pi$
$114$	−3.71216	+	6.42964i	−0.347675	+	0.602191i
$115$	4.71430	+	8.16540i	0.439610	+	0.761428i
$116$	−3.24838			−0.301605
$117$	−1.85855	−	3.21911i	−0.171823	−	0.297607i
$118$	−9.62749			−0.886282
$119$	−0.677335	−	1.17318i	−0.0620912	−	0.107545i
$120$	2.37928	−	4.12104i	0.217198	−	0.376198i
$121$	0.978622	−	1.69502i	0.0889656	−	0.154093i
$122$	1.81854	+	3.14980i	0.164643	+	0.285170i
$123$	−4.10205	−	7.10496i	−0.369870	−	0.640633i
$124$	5.70264	−	9.87727i	0.512113	−	0.887005i
$125$	4.75375			0.425188
$126$	−2.61517	+	4.52962i	−0.232978	+	0.403530i
$127$	5.88874	−	10.1996i	0.522542	−	0.905069i	−0.477114	−	0.878841i	$-0.658317\pi$
$127$	5.88874	−	10.1996i	0.522542	−	0.905069i	0.999656	−	0.0262274i	$-0.00834939\pi$
$128$	12.2316			1.08113
$129$	−4.36789			−0.384571
$130$	23.4295			2.05490
$131$	11.3915	−	19.7307i	0.995282	−	1.72388i	0.413612	−	0.910453i	$-0.364267\pi$
$131$	11.3915	−	19.7307i	0.995282	−	1.72388i	0.581670	−	0.813425i	$-0.302399\pi$
$132$	−4.14223	+	7.17455i	−0.360535	+	0.624465i
$133$	4.08330	+	7.07248i	0.354067	+	0.613262i
$134$	10.0658			0.869551
$135$	−1.44529	−	2.50331i	−0.124391	−	0.215451i
$136$	−0.464876	−	0.805189i	−0.0398628	−	0.0690444i
$137$	−10.2334	−	17.7248i	−0.874300	−	1.51433i	−0.857506	−	0.514474i	$-0.827987\pi$
$137$	−10.2334	−	17.7248i	−0.874300	−	1.51433i	−0.0167945	−	0.999859i	$-0.505346\pi$
$138$	−3.55636	−	6.15979i	−0.302737	−	0.524356i
$139$	−3.60114	+	6.23735i	−0.305445	+	0.529045i	−0.977360	−	0.211582i	$-0.932138\pi$
$139$	−3.60114	+	6.23735i	−0.305445	+	0.529045i	0.671916	+	0.740628i	$0.265472\pi$
$140$	−9.55050	−	16.5419i	−0.807164	−	1.39805i
$141$	−7.67963			−0.646742
$142$	−13.9485	+	24.1595i	−1.17053	+	2.02742i
$143$	−11.1778			−0.934733
$144$	0.960074	−	1.66290i	0.0800062	−	0.138575i
$145$	−1.70415	−	2.95168i	−0.141522	−	0.245123i
$146$	4.45312	+	7.71303i	0.368543	+	0.638335i
$147$	−0.623361	−	1.07969i	−0.0514139	−	0.0890515i
$148$	−1.10389	+	1.91199i	−0.0907391	+	0.157165i
$149$	12.6968			1.04017			0.520083	−	0.854116i	$-0.325901\pi$
$149$	12.6968			1.04017			0.520083	+	0.854116i	$0.325901\pi$
$150$	7.31681			0.597415
$151$	−8.25649	−	14.3007i	−0.671904	−	1.16377i	−0.977364	−	0.211566i	$-0.932144\pi$
$151$	−8.25649	−	14.3007i	−0.671904	−	1.16377i	0.305460	−	0.952205i	$-0.401190\pi$
$152$	2.80249	+	4.85406i	0.227312	+	0.393717i
$153$	−0.564775			−0.0456594
$154$	7.86414	+	13.6211i	0.633710	+	1.09762i
$155$	11.9668			0.961194
$156$	−10.2405			−0.819892
$157$	12.3353	−	2.19991i	0.984467	−	0.175572i
$157$	12.3353	−	2.19991i	0.984467	−	0.175572i
$158$	−17.6400			−1.40336
$159$	−12.4889			−0.990435
$160$	10.8101	+	18.7236i	0.854610	+	1.48023i
$161$	−7.82384			−0.616605
$162$	1.09029	+	1.88844i	0.0856615	+	0.148370i
$163$	3.30868	+	5.73081i	0.259156	+	0.448872i	0.966016	−	0.258482i	$-0.0832222\pi$
$163$	3.30868	+	5.73081i	0.259156	+	0.448872i	−0.706860	+	0.707354i	$0.749889\pi$
$164$	−22.6019			−1.76491
$165$	−8.69230			−0.676695
$166$	5.95321	−	10.3113i	0.462059	−	0.800310i
$167$	−0.442834	−	0.767010i	−0.0342675	−	0.0593530i	0.848383	−	0.529383i	$-0.177576\pi$
$167$	−0.442834	−	0.767010i	−0.0342675	−	0.0593530i	−0.882651	+	0.470030i	$0.844243\pi$
$168$	1.97433	+	3.41964i	0.152323	+	0.263831i
$169$	−0.408450	−	0.707457i	−0.0314192	−	0.0544197i
$170$	1.77993	−	3.08293i	0.136514	−	0.236450i
$171$	3.40473			0.260367
$172$	−6.01666	+	10.4212i	−0.458766	+	0.794607i
$173$	1.28295			0.0975412			0.0487706	−	0.998810i	$-0.484470\pi$
$173$	1.28295			0.0975412			0.0487706	+	0.998810i	$0.484470\pi$
$174$	1.28557	+	2.22668i	0.0974590	+	0.168804i
$175$	4.02417	−	6.97007i	0.304199	−	0.526887i
$176$	−2.88706	−	5.00053i	−0.217620	−	0.376929i
$177$	2.20755	+	3.82358i	0.165929	+	0.287398i
$178$	−11.3805	−	19.7116i	−0.853004	−	1.47745i
$179$	12.2152	+	21.1573i	0.913004	+	1.58137i	0.809798	+	0.586709i	$0.199577\pi$
$179$	12.2152	+	21.1573i	0.913004	+	1.58137i	0.103206	+	0.994660i	$0.467090\pi$
$180$	−7.96340			−0.593556
$181$	9.69951	+	16.8000i	0.720959	+	1.24874i	0.960616	+	0.277880i	$0.0896318\pi$
$181$	9.69951	+	16.8000i	0.720959	+	1.24874i	−0.239657	+	0.970858i	$0.577035\pi$
$182$	−9.72089	+	16.8371i	−0.720560	+	1.24805i
$183$	0.833969	−	1.44448i	0.0616488	−	0.106779i
$184$	−5.36975			−0.395863
$185$	−2.31647			−0.170310
$186$	−9.02746			−0.661925
$187$	−0.849173	+	1.47081i	−0.0620977	+	0.107556i
$188$	−10.5785	+	18.3225i	−0.771517	+	1.33631i
$189$	2.39860			0.174472
$190$	−10.7303	+	18.5854i	−0.778456	+	1.34832i
$191$	12.7857	+	22.1454i	0.925137	+	1.60239i	0.791340	+	0.611376i	$0.209384\pi$
$191$	12.7857	+	22.1454i	0.925137	+	1.60239i	0.133797	+	0.991009i	$0.457283\pi$
$192$	−6.23471	−	10.7988i	−0.449951	−	0.779339i
$193$	−4.68897	+	8.12153i	−0.337519	+	0.584600i	−0.983965	−	0.178359i	$-0.942921\pi$
$193$	−4.68897	+	8.12153i	−0.337519	+	0.584600i	0.646446	+	0.762960i	$0.276254\pi$
$194$	3.91896	−	6.78784i	0.281365	−	0.487338i
$195$	−5.37229	−	9.30509i	−0.384718	−	0.666351i
$196$	−3.43466			−0.245333
$197$	−6.79545	−	11.7701i	−0.484156	−	0.838582i	0.515679	−	0.856782i	$-0.327540\pi$
$197$	−6.79545	−	11.7701i	−0.484156	−	0.838582i	−0.999834	+	0.0181998i	$0.994207\pi$
$198$	6.55728			0.466005
$199$	1.51130	+	2.61765i	0.107133	+	0.185560i	0.914608	−	0.404342i	$-0.132499\pi$
$199$	1.51130	+	2.61765i	0.107133	+	0.185560i	−0.807474	+	0.589903i	$0.799166\pi$
$200$	2.76191	−	4.78378i	0.195297	−	0.338264i
$201$	−2.30805	−	3.99766i	−0.162797	−	0.281973i
$202$	13.1917			0.928165
$203$	2.82821			0.198501
$204$	−0.777964	+	1.34747i	−0.0544684	+	0.0943420i
$205$	−11.8573	−	20.5374i	−0.828149	−	1.43440i
$206$	−39.5261			−2.75391
$207$	−1.63092	+	2.82483i	−0.113357	+	0.196340i
$208$	3.56870	−	6.18117i	0.247445	−	0.428587i
$209$	5.11922	−	8.86675i	0.354104	−	0.613326i
$210$	−7.55936	+	13.0932i	−0.521646	+	0.903517i
$211$	1.86517			0.128403			0.0642017	−	0.997937i	$-0.479550\pi$
$211$	1.86517			0.128403			0.0642017	+	0.997937i	$0.479550\pi$
$212$	−17.2032	+	29.7967i	−1.18152	+	2.04645i
$213$	12.7934			0.876587
$214$	16.7402	−	28.9948i	1.14433	−	1.98204i
$215$	−12.6257			−0.861067
$216$	1.64623			0.112012
$217$	−4.96501	+	8.59965i	−0.337047	+	0.583782i
$218$	−5.33901	−	9.24743i	−0.361603	−	0.626315i
$219$	2.04217	−	3.53714i	0.137997	−	0.239018i
$220$	−11.9734	+	20.7386i	−0.807249	+	1.39820i
$221$	−2.09933			−0.141216
$222$	1.74749			0.117284
$223$	2.66439	−	4.61485i	0.178420	−	0.309033i	−0.762919	−	0.646494i	$-0.776235\pi$
$223$	2.66439	−	4.61485i	0.178420	−	0.309033i	0.941340	+	0.337461i	$0.109568\pi$
$224$	−17.9404			−1.19869
$225$	−1.67772	−	2.90589i	−0.111848	−	0.193726i
$226$	−16.4645	−	28.5173i	−1.09520	−	1.89694i
$227$	11.6827	+	20.2351i	0.775409	+	1.34305i	0.934564	+	0.355794i	$0.115790\pi$
$227$	11.6827	+	20.2351i	0.775409	+	1.34305i	−0.159155	+	0.987254i	$0.550877\pi$
$228$	4.68994	−	8.12321i	0.310599	−	0.537973i
$229$	−6.44976	+	11.1713i	−0.426212	+	0.738221i	−0.996533	−	0.0832009i	$-0.973486\pi$
$229$	−6.44976	+	11.1713i	−0.426212	+	0.738221i	0.570321	+	0.821422i	$0.306819\pi$
$230$	−10.2799	−	17.8054i	−0.677838	−	1.17405i
$231$	3.60644	−	6.24653i	0.237286	−	0.410991i
$232$	1.94109			0.127439
$233$	−1.34784	−	2.33453i	−0.0883002	−	0.152940i	0.818493	−	0.574517i	$-0.194810\pi$
$233$	−1.34784	−	2.33453i	−0.0883002	−	0.152940i	−0.906793	+	0.421577i	$0.861477\pi$
$234$	4.05274	+	7.01954i	0.264936	+	0.458882i
$235$	−22.1986			−1.44807
$236$	12.1634			0.791768
$237$	4.04478	+	7.00577i	0.262737	+	0.455073i
$238$	1.47699	+	2.55822i	0.0957388	+	0.165824i
$239$	27.3199			1.76718			0.883589	−	0.468263i	$-0.155120\pi$
$239$	27.3199			1.76718			0.883589	+	0.468263i	$0.155120\pi$
$240$	2.77517	−	4.80673i	0.179136	−	0.310273i
$241$	−1.36538	−	2.36491i	−0.0879519	−	0.152337i	0.818693	−	0.574231i	$-0.194699\pi$
$241$	−1.36538	−	2.36491i	−0.0879519	−	0.152337i	−0.906645	+	0.421894i	$0.861366\pi$
$242$	−2.13397	+	3.69614i	−0.137177	+	0.237597i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.29754	−	3.97946i	−0.147085	−	0.254759i
$245$	−1.80187	−	3.12093i	−0.115117	−	0.199389i
$246$	8.94487	+	15.4930i	0.570304	+	0.987796i
$247$	12.6558			0.805267
$248$	−3.40764	+	5.90221i	−0.216385	+	0.374791i
$249$	−5.46020			−0.346026
$250$	−10.3659			−0.655600
$251$	−7.26484	+	12.5831i	−0.458553	+	0.794236i	−0.998885	−	0.0472155i	$-0.984965\pi$
$251$	−7.26484	+	12.5831i	−0.458553	+	0.794236i	0.540332	+	0.841452i	$0.318299\pi$
$252$	3.30401	−	5.72272i	0.208133	−	0.360497i
$253$	4.90437	+	8.49461i	0.308335	+	0.534052i
$254$	−12.8409	+	22.2411i	−0.805710	+	1.39553i
$255$	−1.63253			−0.102233
$256$	−1.73320			−0.108325
$257$	7.50558	−	13.0000i	0.468185	−	0.810920i	−0.531154	−	0.847275i	$-0.678241\pi$
$257$	7.50558	−	13.0000i	0.468185	−	0.810920i	0.999339	+	0.0363551i	$0.0115748\pi$
$258$	9.52456			0.592973
$259$	0.961102	−	1.66468i	0.0597200	−	0.103438i
$260$	−29.6008			−1.83576
$261$	0.589554	−	1.02114i	0.0364925	−	0.0632068i
$262$	−24.8402	+	43.0244i	−1.53463	+	2.65806i
$263$	8.62334	−	14.9361i	0.531738	−	0.920997i	−0.467576	−	0.883953i	$-0.654872\pi$
$263$	8.62334	−	14.9361i	0.531738	−	0.920997i	0.999314	−	0.0370442i	$-0.0117942\pi$
$264$	2.47521	−	4.28719i	0.152339	−	0.263858i
$265$	−36.1001			−2.21761
$266$	−8.90398	−	15.4221i	−0.545938	−	0.945592i
$267$	−5.21901	+	9.03959i	−0.319398	+	0.553214i
$268$	−12.7171			−0.776821
$269$	−10.4418			−0.636650			−0.318325	−	0.947982i	$-0.603120\pi$
$269$	−10.4418			−0.636650			−0.318325	+	0.947982i	$0.603120\pi$
$270$	3.15157	+	5.45869i	0.191799	+	0.332205i
$271$	6.71385	−	11.6287i	0.407838	−	0.706395i	−0.586810	−	0.809725i	$-0.699616\pi$
$271$	6.71385	−	11.6287i	0.407838	−	0.706395i	0.994647	+	0.103330i	$0.0329497\pi$
$272$	−0.542226	−	0.939163i	−0.0328773	−	0.0569451i
$273$	8.91586			0.539612
$274$	22.3149	+	38.6505i	1.34809	+	2.33496i
$275$	−10.0902			−0.608461
$276$	4.49310	+	7.78228i	0.270453	+	0.468438i
$277$	−15.8474	+	27.4486i	−0.952181	+	1.64923i	−0.211489	+	0.977380i	$0.567831\pi$
$277$	−15.8474	+	27.4486i	−0.952181	+	1.64923i	−0.740692	+	0.671845i	$0.765502\pi$
$278$	7.85259	−	13.6011i	0.470967	−	0.815738i
$279$	2.06996	+	3.58528i	0.123925	+	0.214645i
$280$	5.70695	+	9.88472i	0.341055	+	0.590725i
$281$	10.3959	−	18.0062i	0.620168	−	1.07416i	−0.369287	−	0.929316i	$-0.620398\pi$
$281$	10.3959	−	18.0062i	0.620168	−	1.07416i	0.989454	−	0.144846i	$-0.0462687\pi$
$282$	16.7461			0.997215
$283$	−10.2951	+	17.8317i	−0.611983	+	1.05999i	0.378923	+	0.925428i	$0.376295\pi$
$283$	−10.2951	+	17.8317i	−0.611983	+	1.05999i	−0.990906	+	0.134557i	$0.957039\pi$
$284$	17.6225	−	30.5231i	1.04571	−	1.81122i
$285$	9.84165			0.582969
$286$	24.3741			1.44127
$287$	19.6784			1.16158
$288$	−3.73976	+	6.47745i	−0.220367	+	0.381687i
$289$	8.34051	−	14.4462i	0.490618	−	0.849776i
$290$	3.71604	+	6.43638i	0.218214	+	0.377957i
$291$	−3.59441			−0.210708
$292$	−5.62607	−	9.74464i	−0.329241	−	0.570262i
$293$	4.09515	+	7.09301i	0.239241	+	0.414378i	0.960497	−	0.278291i	$-0.0897680\pi$
$293$	4.09515	+	7.09301i	0.239241	+	0.414378i	−0.721256	+	0.692669i	$0.756435\pi$
$294$	1.35929	+	2.35436i	0.0792754	+	0.137309i
$295$	6.38109	+	11.0524i	0.371521	+	0.643494i
$296$	0.659634	−	1.14252i	0.0383405	−	0.0664076i
$297$	−1.50356	−	2.60424i	−0.0872453	−	0.151113i
$298$	−27.6865			−1.60384
$299$	−6.06230	+	10.5002i	−0.350592	+	0.607243i
$300$	−9.24405			−0.533706
$301$	5.23841	−	9.07320i	0.301937	−	0.522970i
$302$	18.0040	+	31.1838i	1.03601	+	1.79443i
$303$	−3.02481	−	5.23912i	−0.173771	−	0.300980i
$304$	3.26880	+	5.66172i	0.187478	+	0.324722i
$305$	2.41065	−	4.17537i	0.138033	−	0.239081i
$306$	1.23154			0.0704025
$307$	14.0190			0.800108			0.400054	−	0.916491i	$-0.368991\pi$
$307$	14.0190			0.800108			0.400054	+	0.916491i	$0.368991\pi$
$308$	−9.93555	−	17.2089i	−0.566131	−	0.980567i
$309$	9.06318	+	15.6979i	0.515587	+	0.893022i
$310$	−26.0946			−1.48207
$311$	−8.08413	−	14.0021i	−0.458409	−	0.793987i	0.540468	−	0.841364i	$-0.318247\pi$
$311$	−8.08413	−	14.0021i	−0.458409	−	0.793987i	−0.998877	+	0.0473772i	$0.984914\pi$
$312$	6.11923			0.346433
$313$	13.6923			0.773936			0.386968	−	0.922093i	$-0.373522\pi$
$313$	13.6923			0.773936			0.386968	+	0.922093i	$0.373522\pi$
$314$	−26.8982	+	4.79710i	−1.51796	+	0.270716i
$315$	6.93334			0.390649
$316$	22.2863			1.25370
$317$	10.4643	+	18.1247i	0.587733	+	1.01798i	0.994529	+	0.104464i	$0.0333126\pi$
$317$	10.4643	+	18.1247i	0.587733	+	1.01798i	−0.406796	+	0.913519i	$0.633354\pi$
$318$	27.2331			1.52716
$319$	−1.77286	−	3.07068i	−0.0992610	−	0.171925i
$320$	−18.0219	−	31.2149i	−1.00746	−	1.74496i
$321$	−15.3538			−0.856967
$322$	17.0606			0.950748
$323$	0.961455	−	1.66529i	0.0534968	−	0.0926592i
$324$	−1.37748	−	2.38586i	−0.0765264	−	0.132548i
$325$	−6.23626	−	10.8015i	−0.345925	−	0.599160i
$326$	−7.21487	−	12.4965i	−0.399595	−	0.692118i
$327$	−2.44843	+	4.24080i	−0.135398	+	0.234517i
$328$	13.5059			0.745737
$329$	9.21018	−	15.9525i	0.507774	−	0.879490i
$330$	18.9543			1.04340
$331$	−17.6839	−	30.6293i	−0.971993	−	1.68354i	−0.689522	−	0.724265i	$-0.742179\pi$
$331$	−17.6839	−	30.6293i	−0.971993	−	1.68354i	−0.282471	−	0.959276i	$-0.591154\pi$
$332$	−7.52129	+	13.0273i	−0.412784	+	0.714964i
$333$	−0.400693	−	0.694021i	−0.0219578	−	0.0380321i
$334$	0.965636	+	1.67253i	0.0528373	+	0.0915168i
$335$	−6.67159	−	11.5555i	−0.364508	−	0.631346i
$336$	2.30283	+	3.98862i	0.125630	+	0.217597i
$337$	−8.50176			−0.463120			−0.231560	−	0.972821i	$-0.574383\pi$
$337$	−8.50176			−0.463120			−0.231560	+	0.972821i	$0.574383\pi$
$338$	0.890660	+	1.54267i	0.0484455	+	0.0839101i
$339$	−7.55047	+	13.0778i	−0.410085	+	0.710289i
$340$	−2.24876	+	3.89497i	−0.121956	+	0.211235i
$341$	12.4492			0.674164
$342$	−7.42431			−0.401461
$343$	19.7806			1.06805
$344$	3.59529	−	6.22722i	0.193845	−	0.335749i
$345$	−4.71430	+	8.16540i	−0.253809	+	0.439610i
$346$	−2.79759			−0.150399
$347$	0.233378	−	0.404222i	0.0125284	−	0.0216998i	−0.859693	−	0.510811i	$-0.829345\pi$
$347$	0.233378	−	0.404222i	0.0125284	−	0.0216998i	0.872222	+	0.489111i	$0.162679\pi$
$348$	−1.62419	−	2.81318i	−0.0870658	−	0.150802i
$349$	−8.61616	−	14.9236i	−0.461212	−	0.798843i	0.537809	−	0.843067i	$-0.319252\pi$
$349$	−8.61616	−	14.9236i	−0.461212	−	0.798843i	−0.999022	+	0.0442232i	$0.985919\pi$
$350$	−8.77504	+	15.1988i	−0.469046	+	0.812411i
$351$	1.85855	−	3.21911i	0.0992023	−	0.171823i
$352$	11.2459	+	19.4785i	0.599408	+	1.03820i
$353$	−35.4621			−1.88746			−0.943728	−	0.330721i	$-0.892708\pi$
$353$	−35.4621			−1.88746			−0.943728	+	0.330721i	$0.892708\pi$
$354$	−4.81375	−	8.33765i	−0.255848	−	0.443141i
$355$	36.9802			1.96271
$356$	14.3781	+	24.9036i	0.762039	+	1.31989i
$357$	0.677335	−	1.17318i	0.0358484	−	0.0620912i
$358$	−26.6362	−	46.1352i	−1.40777	−	2.43832i
$359$	−7.09936			−0.374690			−0.187345	−	0.982294i	$-0.559988\pi$
$359$	−7.09936			−0.374690			−0.187345	+	0.982294i	$0.559988\pi$
$360$	4.75857			0.250798
$361$	3.70389	−	6.41533i	0.194942	−	0.337649i
$362$	−21.1506	−	36.6339i	−1.11165	−	1.92544i
$363$	1.95724			0.102729
$364$	12.2814	−	21.2720i	0.643719	−	1.11495i
$365$	5.90304	−	10.2244i	0.308979	−	0.535168i
$366$	−1.81854	+	3.14980i	−0.0950566	+	0.164643i
$367$	14.3570	−	24.8671i	0.749429	−	1.29805i	−0.198667	−	0.980067i	$-0.563661\pi$
$367$	14.3570	−	24.8671i	0.749429	−	1.29805i	0.948097	−	0.317983i	$-0.103005\pi$
$368$	−6.26321			−0.326493
$369$	4.10205	−	7.10496i	0.213544	−	0.369870i
$370$	5.05125			0.262602
$371$	14.9779	−	25.9426i	0.777616	−	1.34687i
$372$	11.4053			0.591337
$373$	10.9589			0.567429			0.283714	−	0.958909i	$-0.408433\pi$
$373$	10.9589			0.567429			0.283714	+	0.958909i	$0.408433\pi$
$374$	1.85169	−	3.20723i	0.0957488	−	0.165842i
$375$	2.37687	+	4.11687i	0.122741	+	0.212594i
$376$	6.32123	−	10.9487i	0.325993	−	0.564636i
$377$	2.19144	−	3.79568i	0.112865	−	0.195487i
$378$	−5.23035			−0.269020
$379$	−34.5978			−1.77717			−0.888586	−	0.458711i	$-0.848311\pi$
$379$	−34.5978			−1.77717			−0.888586	+	0.458711i	$0.848311\pi$
$380$	13.5566	−	23.4808i	0.695440	−	1.20454i
$381$	11.7775			0.603379
$382$	−27.8802	−	48.2899i	−1.42648	−	2.47073i
$383$	1.34013	+	2.32117i	0.0684772	+	0.118606i	0.898231	−	0.439523i	$-0.144853\pi$
$383$	1.34013	+	2.32117i	0.0684772	+	0.118606i	−0.829754	+	0.558129i	$0.811519\pi$
$384$	6.11580	+	10.5929i	0.312096	+	0.540565i
$385$	10.4247	−	18.0561i	0.531291	−	0.920223i
$386$	10.2247	−	17.7097i	0.520423	−	0.901399i
$387$	−2.18395	−	3.78271i	−0.111016	−	0.192286i
$388$	−4.95121	+	8.57575i	−0.251360	+	0.435368i
$389$	5.06152			0.256629			0.128315	−	0.991734i	$-0.459043\pi$
$389$	5.06152			0.256629			0.128315	+	0.991734i	$0.459043\pi$
$390$	11.7147	+	20.2905i	0.593199	+	1.02745i
$391$	0.921103	+	1.59540i	0.0465822	+	0.0806827i
$392$	2.05239			0.103662
$393$	22.7830			1.14925
$394$	14.8181	+	25.6656i	0.746523	+	1.29302i
$395$	11.6917	+	20.2507i	0.588276	+	1.01892i
$396$	−8.28446			−0.416310
$397$	−0.121026	+	0.209624i	−0.00607414	+	0.0105207i	−0.869046	−	0.494730i	$-0.835267\pi$
$397$	−0.121026	+	0.209624i	−0.00607414	+	0.0105207i	0.862972	+	0.505251i	$0.168600\pi$
$398$	−3.29552	−	5.70801i	−0.165190	−	0.286117i
$399$	−4.08330	+	7.07248i	−0.204421	+	0.354067i
$400$	3.22146	−	5.57974i	0.161073	−	0.278987i
$401$	12.1568	+	21.0562i	0.607082	+	1.05150i	0.991719	+	0.128429i	$0.0409933\pi$
$401$	12.1568	+	21.0562i	0.607082	+	1.05150i	−0.384637	+	0.923068i	$0.625673\pi$
$402$	5.03289	+	8.71723i	0.251018	+	0.434776i
$403$	7.69428	+	13.3269i	0.383279	+	0.663859i
$404$	−16.6664			−0.829184
$405$	1.44529	−	2.50331i	0.0718170	−	0.124391i
$406$	−6.16715			−0.306070
$407$	−2.40986			−0.119452
$408$	0.464876	−	0.805189i	0.0230148	−	0.0398628i
$409$	−13.7900	+	23.8851i	−0.681874	+	1.18104i	0.292535	+	0.956255i	$0.405501\pi$
$409$	−13.7900	+	23.8851i	−0.681874	+	1.18104i	−0.974408	+	0.224785i	$0.927832\pi$
$410$	25.8558	+	44.7836i	1.27693	+	2.21171i
$411$	10.2334	−	17.7248i	0.504778	−	0.874300i
$412$	49.9373			2.46023
$413$	−10.5900			−0.521102
$414$	3.55636	−	6.15979i	0.174785	−	0.302737i
$415$	−15.7831			−0.774763
$416$	−13.9011	+	24.0774i	−0.681557	+	1.18049i
$417$	−7.20228			−0.352697
$418$	−11.1629	+	19.3347i	−0.545995	+	0.945691i
$419$	4.37782	−	7.58261i	0.213871	−	0.370435i	−0.739052	−	0.673648i	$-0.764726\pi$
$419$	4.37782	−	7.58261i	0.213871	−	0.370435i	0.952923	+	0.303214i	$0.0980596\pi$
$420$	9.55050	−	16.5419i	0.466017	−	0.807164i
$421$	−1.11174	+	1.92559i	−0.0541829	+	0.0938475i	−0.891845	−	0.452342i	$-0.850589\pi$
$421$	−1.11174	+	1.92559i	−0.0541829	+	0.0938475i	0.837662	+	0.546189i	$0.183922\pi$
$422$	−4.06716			−0.197986
$423$	−3.83982	−	6.65076i	−0.186698	−	0.323371i
$424$	10.2798	−	17.8052i	0.499233	−	0.864696i
$425$	−1.89507			−0.0919242
$426$	−27.8970			−1.35162
$427$	2.00036	+	3.46472i	0.0968041	+	0.167670i
$428$	−21.1495	+	36.6320i	−1.02230	+	1.77068i
$429$	−5.58889	−	9.68024i	−0.269834	−	0.467367i
$430$	27.5315			1.32769
$431$	1.80690	+	3.12964i	0.0870353	+	0.150750i	0.906257	−	0.422728i	$-0.138927\pi$
$431$	1.80690	+	3.12964i	0.0870353	+	0.150750i	−0.819221	+	0.573477i	$0.805594\pi$
$432$	1.92015			0.0923832
$433$	−3.88475	−	6.72859i	−0.186689	−	0.323356i	0.757455	−	0.652887i	$-0.226442\pi$
$433$	−3.88475	−	6.72859i	−0.186689	−	0.323356i	−0.944145	+	0.329532i	$0.893109\pi$
$434$	10.8266	−	18.7523i	0.519695	−	0.900138i
$435$	1.70415	−	2.95168i	0.0817078	−	0.141522i
$436$	6.74530	+	11.6832i	0.323041	+	0.559524i
$437$	−5.55285	−	9.61781i	−0.265629	−	0.460082i
$438$	−4.45312	+	7.71303i	−0.212778	+	0.368543i
$439$	−1.53954			−0.0734784			−0.0367392	−	0.999325i	$-0.511697\pi$
$439$	−1.53954			−0.0734784			−0.0367392	+	0.999325i	$0.511697\pi$
$440$	7.15478	−	12.3924i	0.341091	−	0.590787i
$441$	0.623361	−	1.07969i	0.0296838	−	0.0514139i
$442$	4.57777			0.217742
$443$	10.3253			0.490572			0.245286	−	0.969451i	$-0.421118\pi$
$443$	10.3253			0.490572			0.245286	+	0.969451i	$0.421118\pi$
$444$	−2.20778			−0.104777
$445$	−15.0859	+	26.1296i	−0.715143	+	1.23866i
$446$	−5.80992	+	10.0631i	−0.275108	+	0.476500i
$447$	6.34842	+	10.9958i	0.300270	+	0.520083i
$448$	29.9091			1.41307
$449$	14.6703	+	25.4097i	0.692335	+	1.19916i	0.971071	+	0.238792i	$0.0767513\pi$
$449$	14.6703	+	25.4097i	0.692335	+	1.19916i	−0.278736	+	0.960368i	$0.589915\pi$
$450$	3.65840	+	6.33654i	0.172459	+	0.298707i
$451$	−12.3354	−	21.3655i	−0.580849	−	1.00606i
$452$	20.8012	+	36.0287i	0.978405	+	1.69465i
$453$	8.25649	−	14.3007i	0.387924	−	0.671904i
$454$	−25.4752	−	44.1243i	−1.19561	−	2.07085i
$455$	25.7720			1.20821
$456$	−2.80249	+	4.85406i	−0.131239	+	0.227312i
$457$	8.45622			0.395565			0.197783	−	0.980246i	$-0.436626\pi$
$457$	8.45622			0.395565			0.197783	+	0.980246i	$0.436626\pi$
$458$	14.0643	−	24.3600i	0.657179	−	1.13827i
$459$	−0.282388	−	0.489110i	−0.0131807	−	0.0228297i
$460$	12.9877	+	22.4953i	0.605553	+	1.04885i
$461$	−15.9202	−	27.5746i	−0.741477	−	1.28428i	−0.951823	−	0.306649i	$-0.900792\pi$
$461$	−15.9202	−	27.5746i	−0.741477	−	1.28428i	0.210345	−	0.977627i	$-0.432541\pi$
$462$	−7.86414	+	13.6211i	−0.365873	+	0.633710i
$463$	−18.2329			−0.847353			−0.423677	−	0.905814i	$-0.639261\pi$
$463$	−18.2329			−0.847353			−0.423677	+	0.905814i	$0.639261\pi$
$464$	2.26406			0.105106
$465$	5.98338	+	10.3635i	0.277473	+	0.480597i
$466$	2.93909	+	5.09065i	0.136151	+	0.235820i
$467$	−1.02992			−0.0476591			−0.0238295	−	0.999716i	$-0.507586\pi$
$467$	−1.02992			−0.0476591			−0.0238295	+	0.999716i	$0.507586\pi$
$468$	−5.12023	−	8.86849i	−0.236683	−	0.409946i
$469$	11.0722			0.511265
$470$	48.4058			2.23280
$471$	8.07285	+	9.58275i	0.371977	+	0.441550i
$472$	−7.26828			−0.334550
$473$	−13.1348			−0.603937
$474$	−8.81999	−	15.2767i	−0.405116	−	0.701681i
$475$	11.4244			0.524186
$476$	−1.86602	−	3.23205i	−0.0855291	−	0.148141i
$477$	−6.24445	−	10.8157i	−0.285914	−	0.495217i
$478$	−59.5734			−2.72482
$479$	−28.3759			−1.29653			−0.648265	−	0.761415i	$-0.724505\pi$
$479$	−28.3759			−1.29653			−0.648265	+	0.761415i	$0.724505\pi$
$480$	−10.8101	+	18.7236i	−0.493409	+	0.854610i
$481$	−1.48942	−	2.57975i	−0.0679117	−	0.117626i
$482$	2.97733	+	5.15689i	0.135614	+	0.234890i
$483$	−3.91192	−	6.77565i	−0.177999	−	0.308303i
$484$	2.69606	−	4.66971i	0.122548	−	0.212259i
$485$	−10.3899			−0.471782
$486$	−1.09029	+	1.88844i	−0.0494567	+	0.0856615i
$487$	12.7806			0.579145			0.289573	−	0.957156i	$-0.406487\pi$
$487$	12.7806			0.579145			0.289573	+	0.957156i	$0.406487\pi$
$488$	1.37291	+	2.37795i	0.0621486	+	0.107645i
$489$	−3.30868	+	5.73081i	−0.149624	+	0.259156i
$490$	3.92913	+	6.80546i	0.177500	+	0.307439i
$491$	15.7145	+	27.2184i	0.709187	+	1.22835i	0.965159	+	0.261664i	$0.0842713\pi$
$491$	15.7145	+	27.2184i	0.709187	+	1.22835i	−0.255972	+	0.966684i	$0.582395\pi$
$492$	−11.3009	−	19.5738i	−0.509486	−	0.882456i
$493$	−0.332965	−	0.576713i	−0.0149960	−	0.0259739i
$494$	−27.5970			−1.24165
$495$	−4.34615	−	7.52776i	−0.195345	−	0.338347i
$496$	−3.97463	+	6.88427i	−0.178466	+	0.309113i
$497$	−15.3431	+	26.5750i	−0.688231	+	1.19205i
$498$	11.9064			0.533540
$499$	3.49781			0.156583			0.0782917	−	0.996930i	$-0.475053\pi$
$499$	3.49781			0.156583			0.0782917	+	0.996930i	$0.475053\pi$
$500$	13.0963			0.585686
$501$	0.442834	−	0.767010i	0.0197843	−	0.0342675i
$502$	15.8416	−	27.4385i	0.707045	−	1.22464i
$503$	−1.52586			−0.0680349			−0.0340175	−	0.999421i	$-0.510830\pi$
$503$	−1.52586			−0.0680349			−0.0340175	+	0.999421i	$0.510830\pi$
$504$	−1.97433	+	3.41964i	−0.0879436	+	0.152323i
$505$	−8.74344	−	15.1441i	−0.389078	−	0.673903i
$506$	−10.6944	−	18.5232i	−0.475423	−	0.823458i
$507$	0.408450	−	0.707457i	0.0181399	−	0.0314192i
$508$	16.2232	−	28.0994i	0.719788	−	1.24671i
$509$	−3.30822	−	5.73001i	−0.146634	−	0.253978i	0.783347	−	0.621584i	$-0.213511\pi$
$509$	−3.30822	−	5.73001i	−0.146634	−	0.253978i	−0.929981	+	0.367606i	$0.880177\pi$
$510$	3.55986			0.157633
$511$	4.89834	+	8.48417i	0.216690	+	0.375318i
$512$	−20.6838			−0.914104
$513$	1.70237	+	2.94859i	0.0751614	+	0.130183i
$514$	−16.3665	+	28.3477i	−0.721897	+	1.25036i
$515$	26.1978	+	45.3760i	1.15441	+	1.99950i
$516$	−12.0333			−0.529738
$517$	−23.0936			−1.01565
$518$	−2.09576	+	3.62997i	−0.0920826	+	0.159492i
$519$	0.641477	+	1.11107i	0.0281577	+	0.0487706i
$520$	17.6881			0.775675
$521$	−19.5346	+	33.8349i	−0.855827	+	1.48234i	0.0200496	+	0.999799i	$0.493618\pi$
$521$	−19.5346	+	33.8349i	−0.855827	+	1.48234i	−0.875876	+	0.482536i	$0.839716\pi$
$522$	−1.28557	+	2.22668i	−0.0562680	+	0.0974590i
$523$	20.0455	−	34.7199i	0.876529	−	1.51819i	0.0214047	−	0.999771i	$-0.493186\pi$
$523$	20.0455	−	34.7199i	0.876529	−	1.51819i	0.855125	−	0.518422i	$-0.173481\pi$
$524$	31.3831	−	54.3571i	1.37098	−	2.37460i
$525$	8.04834			0.351258
$526$	−18.8039	+	32.5694i	−0.819890	+	1.42009i
$527$	2.33813			0.101850
$528$	2.88706	−	5.00053i	0.125643	−	0.217620i
$529$	−12.3604			−0.537409
$530$	78.7194			3.41935
$531$	−2.20755	+	3.82358i	−0.0957994	+	0.165929i
$532$	11.2493	+	19.4843i	0.487718	+	0.844753i
$533$	15.2478	−	26.4099i	0.660454	−	1.14394i
$534$	11.3805	−	19.7116i	0.492482	−	0.853004i
$535$	−44.3814			−1.91878
$536$	7.59917			0.328234
$537$	−12.2152	+	21.1573i	−0.527123	+	0.913004i
$538$	22.7693			0.981654
$539$	−1.87452	−	3.24676i	−0.0807412	−	0.139848i
$540$	−3.98170	−	6.89650i	−0.171345	−	0.296778i
$541$	15.5756	+	26.9777i	0.669647	+	1.15986i	0.978003	+	0.208591i	$0.0668878\pi$
$541$	15.5756	+	26.9777i	0.669647	+	1.15986i	−0.308356	+	0.951271i	$0.599779\pi$
$542$	−14.6401	+	25.3574i	−0.628847	+	1.08920i
$543$	−9.69951	+	16.8000i	−0.416246	+	0.720959i
$544$	2.11212	+	3.65830i	0.0905565	+	0.156848i
$545$	−7.07737	+	12.2584i	−0.303161	+	0.525091i
$546$	−19.4418			−0.832031
$547$	7.00889	+	12.1398i	0.299679	+	0.519059i	0.976062	−	0.217491i	$-0.0697872\pi$
$547$	7.00889	+	12.1398i	0.299679	+	0.519059i	−0.676384	+	0.736549i	$0.736454\pi$
$548$	−28.1926	−	48.8310i	−1.20433	−	2.08596i
$549$	1.66794			0.0711859
$550$	22.0025			0.938190
$551$	2.00727	+	3.47670i	0.0855128	+	0.148112i
$552$	−2.68487	−	4.65034i	−0.114276	−	0.197932i
$553$	−19.4036			−0.825126
$554$	34.5567	−	59.8540i	1.46817	−	2.54295i
$555$	−1.15823	−	2.00612i	−0.0491643	−	0.0851550i
$556$	−9.92096	+	17.1836i	−0.420742	+	0.728747i
$557$	−17.3291	+	30.0148i	−0.734257	+	1.27177i	0.220792	+	0.975321i	$0.429136\pi$
$557$	−17.3291	+	30.0148i	−0.734257	+	1.27177i	−0.955049	+	0.296449i	$0.904198\pi$
$558$	−4.51373	−	7.81801i	−0.191081	−	0.330963i
$559$	−8.11797	−	14.0607i	−0.343353	−	0.594706i
$560$	6.65652	+	11.5294i	0.281289	+	0.487207i
$561$	−1.69835			−0.0717042
$562$	−22.6691	+	39.2641i	−0.956240	+	1.65626i
$563$	3.82352			0.161142			0.0805711	−	0.996749i	$-0.474326\pi$
$563$	3.82352			0.161142			0.0805711	+	0.996749i	$0.474326\pi$
$564$	−21.1570			−0.890871
$565$	−21.8252	+	37.8024i	−0.918194	+	1.59036i
$566$	22.4494	−	38.8836i	0.943621	−	1.63440i
$567$	1.19930	+	2.07725i	0.0503659	+	0.0872362i
$568$	−10.5304	+	18.2393i	−0.441847	+	0.765302i
$569$	−7.87957			−0.330329			−0.165164	−	0.986266i	$-0.552815\pi$
$569$	−7.87957			−0.330329			−0.165164	+	0.986266i	$0.552815\pi$
$570$	−21.4605			−0.898883
$571$	−7.23986	+	12.5398i	−0.302979	+	0.524774i	−0.976809	−	0.214112i	$-0.931314\pi$
$571$	−7.23986	+	12.5398i	−0.302979	+	0.524774i	0.673831	+	0.738886i	$0.264648\pi$
$572$	−30.7942			−1.28757
$573$	−12.7857	+	22.1454i	−0.534128	+	0.925137i
$574$	−42.9103			−1.79104
$575$	−5.47244	+	9.47854i	−0.228217	+	0.395283i
$576$	6.23471	−	10.7988i	0.259780	−	0.449951i
$577$	19.3947	−	33.5926i	0.807412	−	1.39848i	−0.107239	−	0.994233i	$-0.534201\pi$
$577$	19.3947	−	33.5926i	0.807412	−	1.39848i	0.914651	−	0.404245i	$-0.132466\pi$
$578$	−18.1872	+	31.5012i	−0.756488	+	1.31028i
$579$	−9.37793			−0.389734
$580$	−4.69485	−	8.13172i	−0.194943	−	0.337651i
$581$	6.54842	−	11.3422i	0.271674	−	0.470553i
$582$	7.83792			0.324892
$583$	−37.5556			−1.55539
$584$	3.36188	+	5.82295i	0.139116	+	0.240956i
$585$	5.37229	−	9.30509i	0.222117	−	0.384718i
$586$	−8.92982	−	15.4669i	−0.368888	−	0.638932i
$587$	−13.2378			−0.546382			−0.273191	−	0.961960i	$-0.588079\pi$
$587$	−13.2378			−0.546382			−0.273191	+	0.961960i	$0.588079\pi$
$588$	−1.71733	−	2.97450i	−0.0708214	−	0.122666i
$589$	−14.0953			−0.580789
$590$	−13.9145	−	24.1006i	−0.572851	−	0.992207i
$591$	6.79545	−	11.7701i	0.279527	−	0.484156i
$592$	0.769390	−	1.33262i	0.0316217	−	0.0547704i
$593$	10.0071	+	17.3328i	0.410943	+	0.711775i	0.994993	−	0.0999431i	$-0.0318661\pi$
$593$	10.0071	+	17.3328i	0.410943	+	0.711775i	−0.584050	+	0.811718i	$0.698533\pi$
$594$	3.27864	+	5.67877i	0.134524	+	0.233003i
$595$	1.95789	−	3.39116i	0.0802656	−	0.139024i
$596$	34.9792			1.43280
$597$	−1.51130	+	2.61765i	−0.0618535	+	0.107133i
$598$	13.2194	−	22.8966i	0.540580	−	0.936312i
$599$	13.1003			0.535262			0.267631	−	0.963521i	$-0.413759\pi$
$599$	13.1003			0.535262			0.267631	+	0.963521i	$0.413759\pi$
$600$	5.52383			0.225509
$601$	11.3890			0.464567			0.232284	−	0.972648i	$-0.425380\pi$
$601$	11.3890			0.464567			0.232284	+	0.972648i	$0.425380\pi$
$602$	−11.4228	+	19.7849i	−0.465559	+	0.806371i
$603$	2.30805	−	3.99766i	0.0939910	−	0.162797i
$604$	−22.7462	−	39.3976i	−0.925531	−	1.60307i
$605$	5.65756			0.230013
$606$	6.59585	+	11.4243i	0.267938	+	0.464082i
$607$	−13.1627	−	22.7985i	−0.534259	−	0.925363i	−0.999199	−	0.0400211i	$-0.987257\pi$
$607$	−13.1627	−	22.7985i	−0.534259	−	0.925363i	0.464940	−	0.885342i	$-0.346076\pi$
$608$	−12.7329	−	22.0540i	−0.516386	−	0.894408i
$609$	1.41410	+	2.44930i	0.0573024	+	0.0992506i
$610$	−5.25663	+	9.10475i	−0.212835	+	0.368641i
$611$	−14.2730	−	24.7216i	−0.577424	−	1.00013i
$612$	−1.55593			−0.0628947
$613$	−17.1279	+	29.6664i	−0.691790	+	1.19822i	0.279460	+	0.960157i	$0.409844\pi$
$613$	−17.1279	+	29.6664i	−0.691790	+	1.19822i	−0.971251	+	0.238059i	$0.923489\pi$
$614$	−30.5697			−1.23369
$615$	11.8573	−	20.5374i	0.478132	−	0.828149i
$616$	5.93704	+	10.2832i	0.239210	+	0.414324i
$617$	3.23611	+	5.60511i	0.130281	+	0.225653i	0.923785	−	0.382912i	$-0.125079\pi$
$617$	3.23611	+	5.60511i	0.130281	+	0.225653i	−0.793504	+	0.608565i	$0.791745\pi$
$618$	−19.7630	−	34.2306i	−0.794986	−	1.37696i
$619$	2.30064	−	3.98482i	0.0924704	−	0.160163i	−0.816080	−	0.577939i	$-0.803857\pi$
$619$	2.30064	−	3.98482i	0.0924704	−	0.160163i	0.908550	+	0.417776i	$0.137190\pi$
$620$	32.9679			1.32402
$621$	−3.26184			−0.130893
$622$	17.6281	+	30.5328i	0.706823	+	1.22425i
$623$	−12.5183	−	21.6824i	−0.501536	−	0.868685i
$624$	7.13740			0.285725
$625$	15.2591	+	26.4296i	0.610365	+	1.05718i
$626$	−29.8573			−1.19334
$627$	10.2384			0.408884
$628$	33.9832	−	6.06065i	1.35608	−	0.241846i
$629$	−0.452603			−0.0180465
$630$	−15.1187			−0.602344
$631$	−9.02557	−	15.6327i	−0.359302	−	0.622330i	0.628542	−	0.777776i	$-0.283652\pi$
$631$	−9.02557	−	15.6327i	−0.359302	−	0.622330i	−0.987844	+	0.155446i	$0.950319\pi$
$632$	−13.3173			−0.529734
$633$	0.932584	+	1.61528i	0.0370669	+	0.0642017i
$634$	−22.8183	−	39.5224i	−0.906229	−	1.56963i
$635$	34.0437			1.35098
$636$	−34.4063			−1.36430
$637$	2.31710	−	4.01333i	0.0918068	−	0.159014i
$638$	3.86587	+	6.69588i	0.153051	+	0.265092i
$639$	6.39668	+	11.0794i	0.253049	+	0.438294i
$640$	17.6782	+	30.6195i	0.698792	+	1.21034i
$641$	−18.2299	+	31.5752i	−0.720039	+	1.24714i	0.240944	+	0.970539i	$0.422543\pi$
$641$	−18.2299	+	31.5752i	−0.720039	+	1.24714i	−0.960984	+	0.276606i	$0.910790\pi$
$642$	33.4803			1.32136
$643$	16.8798	−	29.2366i	0.665672	−	1.15298i	−0.313430	−	0.949611i	$-0.601478\pi$
$643$	16.8798	−	29.2366i	0.665672	−	1.15298i	0.979103	−	0.203367i	$-0.0651885\pi$
$644$	−21.5543			−0.849358
$645$	−6.31286	−	10.9342i	−0.248569	−	0.430534i
$646$	−2.09653	+	3.63130i	−0.0824870	+	0.142872i
$647$	4.57693	+	7.92748i	0.179938	+	0.311661i	0.941859	−	0.336008i	$-0.109077\pi$
$647$	4.57693	+	7.92748i	0.179938	+	0.311661i	−0.761921	+	0.647670i	$0.775744\pi$
$648$	0.823117	+	1.42568i	0.0323351	+	0.0560060i
$649$	6.63836	+	11.4980i	0.260578	+	0.451335i
$650$	13.5987	+	23.5536i	0.533384	+	0.923849i
$651$	−9.93002			−0.389188
$652$	9.11526	+	15.7881i	0.356981	+	0.618310i
$653$	0.223091	−	0.386405i	0.00873024	−	0.0151212i	−0.861627	−	0.507542i	$-0.830554\pi$
$653$	0.223091	−	0.386405i	0.00873024	−	0.0151212i	0.870358	+	0.492420i	$0.163888\pi$
$654$	5.33901	−	9.24743i	0.208772	−	0.361603i
$655$	65.8561			2.57321
$656$	15.7531			0.615055
$657$	4.08433			0.159345
$658$	−20.0836	+	34.7858i	−0.782939	+	1.35609i
$659$	23.4682	−	40.6480i	0.914189	−	1.58342i	0.106105	−	0.994355i	$-0.466162\pi$
$659$	23.4682	−	40.6480i	0.914189	−	1.58342i	0.808084	−	0.589067i	$-0.200505\pi$
$660$	−23.9469			−0.932131
$661$	13.3309	−	23.0899i	0.518513	−	0.898091i	−0.481255	−	0.876580i	$-0.659819\pi$
$661$	13.3309	−	23.0899i	0.518513	−	0.898091i	0.999769	−	0.0215109i	$-0.00684767\pi$
$662$	38.5612	+	66.7899i	1.49872	+	2.59586i
$663$	−1.04967	−	1.81807i	−0.0407656	−	0.0706082i
$664$	4.49438	−	7.78450i	0.174416	−	0.302097i
$665$	−11.8031	+	20.4435i	−0.457704	+	0.792766i
$666$	0.873745	+	1.51337i	0.0338569	+	0.0586419i
$667$	−3.84606			−0.148920
$668$	−1.21998	−	2.11308i	−0.0472026	−	0.0817574i
$669$	5.32877			0.206022
$670$	14.5480	+	25.1978i	0.562037	+	0.973476i
$671$	2.50784	−	4.34371i	0.0968142	−	0.167687i
$672$	−8.97018	−	15.5368i	−0.346032	−	0.599345i
$673$	20.3728			0.785314			0.392657	−	0.919685i	$-0.371556\pi$
$673$	20.3728			0.785314			0.392657	+	0.919685i	$0.371556\pi$
$674$	18.5388			0.714088
$675$	1.67772	−	2.90589i	0.0645753	−	0.111848i
$676$	−1.12526	−	1.94901i	−0.0432792	−	0.0749618i
$677$	−24.1806			−0.929336			−0.464668	−	0.885485i	$-0.653826\pi$
$677$	−24.1806			−0.929336			−0.464668	+	0.885485i	$0.653826\pi$
$678$	16.4645	−	28.5173i	0.632313	−	1.09520i
$679$	4.31078	−	7.46648i	0.165432	−	0.286537i
$680$	1.34376	−	2.32746i	0.0515309	−	0.0892541i
$681$	−11.6827	+	20.2351i	−0.447683	+	0.775409i
$682$	−27.1466			−1.03950
$683$	13.6394	−	23.6241i	0.521896	−	0.903951i	−0.477779	−	0.878480i	$-0.658558\pi$
$683$	13.6394	−	23.6241i	0.521896	−	0.903951i	0.999676	−	0.0254710i	$-0.00810855\pi$
$684$	9.37988			0.358649
$685$	29.5805	−	51.2349i	1.13021	−	1.95759i
$686$	−43.1332			−1.64683
$687$	−12.8995			−0.492148
$688$	4.19350	−	7.26336i	0.159876	−	0.276913i
$689$	−23.2113	−	40.2032i	−0.884281	−	1.53162i
$690$	10.2799	−	17.8054i	0.391350	−	0.677838i
$691$	−7.85020	+	13.5969i	−0.298636	+	0.517252i	−0.975824	−	0.218558i	$-0.929865\pi$
$691$	−7.85020	+	13.5969i	−0.298636	+	0.517252i	0.677188	+	0.735810i	$0.263198\pi$
$692$	3.53448			0.134361
$693$	7.21287			0.273994
$694$	−0.508900	+	0.881441i	−0.0193176	+	0.0334591i
$695$	−20.8187			−0.789699
$696$	0.970544	+	1.68103i	0.0367884	+	0.0637193i
$697$	−2.31674	−	4.01271i	−0.0877527	−	0.151992i
$698$	18.7883	+	32.5422i	0.711146	+	1.23174i
$699$	1.34784	−	2.33453i	0.0509801	−	0.0883002i
$700$	11.0864	−	19.2022i	0.419026	−	0.725775i
$701$	6.93606	+	12.0136i	0.261971	+	0.453747i	0.966766	−	0.255664i	$-0.0822941\pi$
$701$	6.93606	+	12.0136i	0.261971	+	0.453747i	−0.704794	+	0.709412i	$0.748961\pi$
$702$	−4.05274	+	7.01954i	−0.152961	+	0.264936i
$703$	2.72851			0.102908
$704$	−18.7485	−	32.4734i	−0.706611	−	1.22389i
$705$	−11.0993	−	19.2245i	−0.418023	−	0.724037i
$706$	77.3281			2.91028
$707$	14.5106			0.545727
$708$	6.08169	+	10.5338i	0.228564	+	0.395884i
$709$	−4.34341	−	7.52300i	−0.163120	−	0.282532i	0.772866	−	0.634569i	$-0.218822\pi$
$709$	−4.34341	−	7.52300i	−0.163120	−	0.282532i	−0.935986	+	0.352037i	$0.885489\pi$
$710$	−80.6385			−3.02631
$711$	−4.04478	+	7.00577i	−0.151691	+	0.262737i
$712$	−8.59171	−	14.8813i	−0.321988	−	0.557700i
$713$	6.75188	−	11.6946i	0.252860	−	0.437966i
$714$	−1.47699	+	2.55822i	−0.0552748	+	0.0957388i
$715$	−16.1551	−	27.9815i	−0.604167	−	1.04645i
$716$	33.6522	+	58.2873i	1.25764	+	2.17830i
$717$	13.6600	+	23.6597i	0.510141	+	0.883589i
$718$	15.4808			0.577737
$719$	12.7511	−	22.0856i	0.475537	−	0.823654i	−0.524071	−	0.851675i	$-0.675587\pi$
$719$	12.7511	−	22.0856i	0.475537	−	0.823654i	0.999607	+	0.0280210i	$0.00892053\pi$
$720$	5.55034			0.206849
$721$	−43.4779			−1.61920
$722$	−8.07665	+	13.9892i	−0.300582	+	0.520623i
$723$	1.36538	−	2.36491i	0.0507791	−	0.0879519i
$724$	26.7217	+	46.2833i	0.993103	+	1.72011i
$725$	1.97821	−	3.42636i	0.0734688	−	0.127252i
$726$	−4.26794			−0.158398
$727$	42.2730			1.56782			0.783910	−	0.620875i	$-0.213223\pi$
$727$	42.2730			1.56782			0.783910	+	0.620875i	$0.213223\pi$
$728$	−7.33879	+	12.7112i	−0.271994	+	0.471107i
$729$	1.00000			0.0370370
$730$	−12.8721	+	22.2951i	−0.476417	+	0.825178i
$731$	−2.46688			−0.0912408
$732$	2.29754	−	3.97946i	0.0849196	−	0.147085i
$733$	−12.9886	+	22.4969i	−0.479744	+	0.830940i	−0.999730	−	0.0232343i	$-0.992604\pi$
$733$	−12.9886	+	22.4969i	−0.479744	+	0.830940i	0.519986	+	0.854174i	$0.325937\pi$
$734$	−31.3067	+	54.2247i	−1.15555	+	2.00147i
$735$	1.80187	−	3.12093i	0.0664630	−	0.115117i
$736$	24.3970			0.899284
$737$	−6.94057	−	12.0214i	−0.255659	−	0.442815i
$738$	−8.94487	+	15.4930i	−0.329265	+	0.570304i
$739$	−7.64182			−0.281109			−0.140554	−	0.990073i	$-0.544888\pi$
$739$	−7.64182			−0.281109			−0.140554	+	0.990073i	$0.544888\pi$
$740$	−6.38175			−0.234598
$741$	6.32789	+	10.9602i	0.232461	+	0.402634i
$742$	−32.6607	+	56.5699i	−1.19901	+	2.07675i
$743$	−3.05607	−	5.29326i	−0.112116	−	0.194191i	0.804507	−	0.593943i	$-0.202430\pi$
$743$	−3.05607	−	5.29326i	−0.112116	−	0.194191i	−0.916623	+	0.399752i	$0.869096\pi$
$744$	−6.81528			−0.249860
$745$	18.3506	+	31.7842i	0.672314	+	1.16448i
$746$	−23.8968			−0.874922
$747$	−2.73010	−	4.72867i	−0.0998891	−	0.173013i
$748$	−2.33943	+	4.05201i	−0.0855380	+	0.148156i
$749$	18.4138	−	31.8937i	0.672827	−	1.16537i
$750$	−5.18297	−	8.97718i	−0.189255	−	0.327800i
$751$	21.7732	+	37.7123i	0.794516	+	1.37614i	0.923146	+	0.384449i	$0.125609\pi$
$751$	21.7732	+	37.7123i	0.794516	+	1.37614i	−0.128630	+	0.991693i	$0.541058\pi$
$752$	7.37302	−	12.7704i	0.268866	−	0.465690i
$753$	−14.5297			−0.529491
$754$	−4.77861	+	8.27680i	−0.174027	+	0.301423i
$755$	23.8660	−	41.3371i	0.868573	−	1.50441i
$756$	6.60802			0.240331
$757$	46.9641			1.70694			0.853470	−	0.521142i	$-0.174494\pi$
$757$	46.9641			1.70694			0.853470	+	0.521142i	$0.174494\pi$
$758$	75.4435			2.74023
$759$	−4.90437	+	8.49461i	−0.178017	+	0.308335i
$760$	−8.10083	+	14.0310i	−0.293848	+	0.508959i
$761$	−6.96325	−	12.0607i	−0.252418	−	0.437200i	0.711773	−	0.702409i	$-0.247892\pi$
$761$	−6.96325	−	12.0607i	−0.252418	−	0.437200i	−0.964191	+	0.265209i	$0.914559\pi$
$762$	−25.6818			−0.930354
$763$	−5.87280	−	10.1720i	−0.212610	−	0.368251i
$764$	35.2238	+	61.0095i	1.27435	+	2.20725i
$765$	−0.816263	−	1.41381i	−0.0295121	−	0.0511164i
$766$	−2.92226	−	5.06150i	−0.105585	−	0.182879i
$767$	−8.20570	+	14.2127i	−0.296291	+	0.513190i
$768$	−0.866602	−	1.50100i	−0.0312708	−	0.0541626i
$769$	−8.83829			−0.318717			−0.159359	−	0.987221i	$-0.550943\pi$
$769$	−8.83829			−0.318717			−0.159359	+	0.987221i	$0.550943\pi$
$770$	−22.7319	+	39.3728i	−0.819201	+	1.41890i
$771$	15.0112			0.540613
$772$	−12.9179	+	22.3744i	−0.464924	+	0.805273i
$773$	2.83995	+	4.91893i	0.102146	+	0.176922i	0.912568	−	0.408924i	$-0.134096\pi$
$773$	2.83995	+	4.91893i	0.102146	+	0.176922i	−0.810423	+	0.585846i	$0.800763\pi$
$774$	4.76228	+	8.24851i	0.171177	+	0.296487i
$775$	6.94562	+	12.0302i	0.249494	+	0.432136i
$776$	2.95862	−	5.12448i	0.106208	−	0.183958i
$777$	1.92220			0.0689587
$778$	−11.0371			−0.395698
$779$	13.9664	+	24.1905i	0.500398	+	0.866715i
$780$	−14.8004	−	25.6351i	−0.529940	−	0.917882i
$781$	38.4712			1.37661
$782$	−2.00854	−	3.47890i	−0.0718254	−	0.124405i
$783$	1.17911			0.0421379
$784$	2.39389			0.0854961
$785$	23.3352	+	27.6997i	0.832868	+	0.988644i
$786$	−49.6803			−1.77204
$787$	−38.1385			−1.35949			−0.679746	−	0.733448i	$-0.737910\pi$
$787$	−38.1385			−1.35949			−0.679746	+	0.733448i	$0.737910\pi$
$788$	−18.7211	−	32.4259i	−0.666913	−	1.15513i
$789$	17.2467			0.613998
$790$	−25.4949	−	44.1584i	−0.907066	−	1.57108i
$791$	−18.1106	−	31.3684i	−0.643937	−	1.11533i
$792$	4.95042			0.175905
$793$	6.19991			0.220165
$794$	0.263908	−	0.457103i	0.00936576	−	0.0162220i
$795$	−18.0501	−	31.2636i	−0.640170	−	1.10881i
$796$	4.16356	+	7.21150i	0.147574	+	0.255605i
$797$	−19.9802	−	34.6066i	−0.707733	−	1.22583i	−0.965696	−	0.259675i	$-0.916384\pi$
$797$	−19.9802	−	34.6066i	−0.707733	−	1.22583i	0.257963	−	0.966155i	$-0.416949\pi$
$798$	8.90398	−	15.4221i	0.315197	−	0.545938i
$799$	−4.33727			−0.153441
$800$	−12.5485	+	21.7346i	−0.443657	+	0.768436i
$801$	−10.4380			−0.368809
$802$	−26.5089	−	45.9148i	−0.936063	−	1.62131i
$803$	6.14103	−	10.6366i	0.216712	−	0.375357i
$804$	−6.35856	−	11.0133i	−0.224249	−	0.388411i
$805$	−11.3077	−	19.5855i	−0.398544	−	0.690299i
$806$	−16.7780	−	29.0604i	−0.590981	−	1.02361i
$807$	−5.22092	−	9.04289i	−0.183785	−	0.318325i
$808$	9.95908			0.350359
$809$	14.1040	+	24.4289i	0.495871	+	0.858873i	0.999989	−	0.00476140i	$-0.00151561\pi$
$809$	14.1040	+	24.4289i	0.495871	+	0.858873i	−0.504118	+	0.863635i	$0.668182\pi$
$810$	−3.15157	+	5.45869i	−0.110735	+	0.191799i
$811$	−15.1658	+	26.2680i	−0.532544	+	0.922394i	0.466734	+	0.884398i	$0.345431\pi$
$811$	−15.1658	+	26.2680i	−0.532544	+	0.922394i	−0.999278	+	0.0379957i	$0.987903\pi$
$812$	7.79157			0.273431
$813$	13.4277			0.470930
$814$	5.25491			0.184184
$815$	−9.56401	+	16.5653i	−0.335013	+	0.580259i
$816$	0.542226	−	0.939163i	0.0189817	−	0.0328773i
$817$	14.8715			0.520288
$818$	30.0704	−	52.0834i	1.05139	−	1.82105i
$819$	4.45793	+	7.72136i	0.155773	+	0.269806i
$820$	−32.6663	−	56.5796i	−1.14076	−	1.97585i
$821$	4.34483	−	7.52547i	0.151636	−	0.262641i	−0.780193	−	0.625539i	$-0.784879\pi$
$821$	4.34483	−	7.52547i	0.151636	−	0.262641i	0.931829	+	0.362898i	$0.118213\pi$
$822$	−22.3149	+	38.6505i	−0.778320	+	1.34809i
$823$	−15.3219	−	26.5383i	−0.534087	−	0.925066i	−0.999207	−	0.0398182i	$-0.987322\pi$
$823$	−15.3219	−	26.5383i	−0.534087	−	0.925066i	0.465120	−	0.885248i	$-0.346011\pi$
$824$	−29.8402			−1.03953
$825$	−5.04509	−	8.73835i	−0.175648	−	0.304230i
$826$	23.0925			0.803491
$827$	−0.945954	−	1.63844i	−0.0328940	−	0.0569741i	0.849110	−	0.528216i	$-0.177139\pi$
$827$	−0.945954	−	1.63844i	−0.0328940	−	0.0569741i	−0.882004	+	0.471242i	$0.843806\pi$
$828$	−4.49310	+	7.78228i	−0.156146	+	0.270453i
$829$	−1.30121	−	2.25376i	−0.0451929	−	0.0782764i	0.842544	−	0.538627i	$-0.181057\pi$
$829$	−1.30121	−	2.25376i	−0.0451929	−	0.0782764i	−0.887737	+	0.460351i	$0.847724\pi$
$830$	34.4164			1.19461
$831$	−31.6949			−1.09948
$832$	23.1751	−	40.1404i	0.803452	−	1.39162i
$833$	−0.352059	−	0.609784i	−0.0121981	−	0.0211277i
$834$	15.7052			0.543826
$835$	1.28004	−	2.21710i	0.0442978	−	0.0767260i
$836$	14.1032	−	24.4274i	0.487769	−	0.844841i
$837$	−2.06996	+	3.58528i	−0.0715484	+	0.123925i
$838$	−9.54622	+	16.5345i	−0.329769	+	0.571176i
$839$	−31.3741			−1.08315			−0.541577	−	0.840651i	$-0.682173\pi$
$839$	−31.3741			−1.08315			−0.541577	+	0.840651i	$0.682173\pi$
$840$	−5.70695	+	9.88472i	−0.196908	+	0.341055i
$841$	−27.6097			−0.952059
$842$	2.42424	−	4.19891i	0.0835449	−	0.144704i
$843$	20.7918			0.716108
$844$	5.13845			0.176873
$845$	1.18066	−	2.04496i	0.0406158	−	0.0703487i
$846$	8.37304	+	14.5025i	0.287871	+	0.498608i
$847$	−2.34732	+	4.06568i	−0.0806550	+	0.139698i
$848$	11.9903	−	20.7678i	0.411748	−	0.713168i
$849$	−20.5903			−0.706657
$850$	4.13235			0.141738
$851$	−1.30700	+	2.26378i	−0.0448032	+	0.0776015i
$852$	35.2451			1.20748
$853$	−26.3690	−	45.6725i	−0.902858	−	1.56380i	−0.823767	−	0.566929i	$-0.808131\pi$
$853$	−26.3690	−	45.6725i	−0.902858	−	1.56380i	−0.0790914	−	0.996867i	$-0.525202\pi$
$854$	−4.36195	−	7.55512i	−0.149263	−	0.258531i
$855$	4.92082	+	8.52312i	0.168289	+	0.291484i
$856$	12.6380	−	21.8896i	0.431958	−	0.748173i
$857$	−15.5117	+	26.8671i	−0.529870	+	0.917761i	0.469523	+	0.882920i	$0.344426\pi$
$857$	−15.5117	+	26.8671i	−0.529870	+	0.917761i	−0.999393	+	0.0348411i	$0.988907\pi$
$858$	12.1871	+	21.1086i	0.416059	+	0.720636i
$859$	−15.1534	+	26.2465i	−0.517028	+	0.895519i	0.482776	+	0.875744i	$0.339628\pi$
$859$	−15.1534	+	26.2465i	−0.517028	+	0.895519i	−0.999804	+	0.0197753i	$0.993705\pi$
$860$	−34.7833			−1.18610
$861$	9.83918	+	17.0420i	0.335318	+	0.580788i
$862$	−3.94010	−	6.82445i	−0.134200	−	0.232442i
$863$	27.3293			0.930300			0.465150	−	0.885232i	$-0.346000\pi$
$863$	27.3293			0.930300			0.465150	+	0.885232i	$0.346000\pi$
$864$	−7.47951			−0.254458
$865$	1.85424	+	3.21164i	0.0630460	+	0.109199i
$866$	8.47104	+	14.6723i	0.287858	+	0.498584i
$867$	16.6810			0.566517
$868$	−13.6784	+	23.6916i	−0.464274	+	0.804146i
$869$	12.1631	+	21.0672i	0.412606	+	0.714655i
$870$	−3.71604	+	6.43638i	−0.125986	+	0.218214i
$871$	8.57926	−	14.8597i	0.290697	−	0.503502i
$872$	−4.03069	−	6.98136i	−0.136496	−	0.236419i
$873$	−1.79721	−	3.11285i	−0.0608262	−	0.105354i
$874$	12.1085	+	20.9725i	0.409575	+	0.709404i
$875$	−11.4023			−0.385469
$876$	5.62607	−	9.74464i	0.190087	−	0.329241i
$877$	32.0856			1.08345			0.541726	−	0.840555i	$-0.317771\pi$
$877$	32.0856			1.08345			0.541726	+	0.840555i	$0.317771\pi$
$878$	3.35711			0.113297
$879$	−4.09515	+	7.09301i	−0.138126	+	0.239241i
$880$	8.34526	−	14.4544i	0.281319	−	0.487258i
$881$	−15.1950	−	26.3185i	−0.511933	−	0.886694i	−0.999904	−	0.0138340i	$-0.995596\pi$
$881$	−15.1950	−	26.3185i	−0.511933	−	0.886694i	0.487972	−	0.872860i	$-0.337737\pi$
$882$	−1.35929	+	2.35436i	−0.0457697	+	0.0792754i
$883$	−51.1513			−1.72138			−0.860689	−	0.509130i	$-0.829967\pi$
$883$	−51.1513			−1.72138			−0.860689	+	0.509130i	$0.829967\pi$
$884$	−5.78355			−0.194522
$885$	−6.38109	+	11.0524i	−0.214498	+	0.371521i
$886$	−22.5153			−0.756415
$887$	−1.81921	+	3.15097i	−0.0610831	+	0.105799i	−0.894950	−	0.446167i	$-0.852789\pi$
$887$	−1.81921	+	3.15097i	−0.0610831	+	0.105799i	0.833867	+	0.551966i	$0.186122\pi$
$888$	1.31927			0.0442718
$889$	−14.1247	+	24.4648i	−0.473729	+	0.820522i
$890$	32.8962	−	56.9779i	1.10268	−	1.90990i
$891$	1.50356	−	2.60424i	0.0503711	−	0.0872453i
$892$	7.34025	−	12.7137i	0.245770	−	0.425686i
$893$	26.1471			0.874980
$894$	−13.8433	−	23.9772i	−0.462988	−	0.801919i
$895$	−35.3089	+	61.1567i	−1.18024	+	2.04424i
$896$	−29.3387			−0.980137
$897$	−12.1246			−0.404829
$898$	−31.9899	−	55.4081i	−1.06752	−	1.84899i
$899$	−2.44071	+	4.22743i	−0.0814022	+	0.140993i
$900$	−4.62203	−	8.00558i	−0.154068	−	0.266853i
$901$	−7.05343			−0.234984
$902$	26.8983	+	46.5892i	0.895615	+	1.55125i
$903$	10.4768			0.348647
$904$	−12.4298	−	21.5291i	−0.413411	−	0.716048i
$905$	−28.0372	+	48.5618i	−0.931988	+	1.61425i
$906$	−18.0040	+	31.1838i	−0.598142	+	1.03601i
$907$	−15.6609	−	27.1256i	−0.520013	−	0.900689i	−0.999729	−	0.0232656i	$-0.992594\pi$
$907$	−15.6609	−	27.1256i	−0.520013	−	0.900689i	0.479716	−	0.877424i	$-0.340740\pi$
$908$	32.1853	+	55.7466i	1.06811	+	1.85002i
$909$	3.02481	−	5.23912i	0.100327	−	0.173771i
$910$	−56.1980			−1.86294
$911$	−12.0226	+	20.8238i	−0.398327	+	0.689923i	−0.993520	−	0.113660i	$-0.963743\pi$
$911$	−12.0226	+	20.8238i	−0.398327	+	0.689923i	0.595192	+	0.803583i	$0.297076\pi$
$912$	−3.26880	+	5.66172i	−0.108241	+	0.187478i
$913$	−16.4195			−0.543405
$914$	−18.4395			−0.609924
$915$	4.82130			0.159387
$916$	−17.7688	+	30.7764i	−0.587097	+	1.01688i
$917$	−27.3237	+	47.3260i	−0.902308	+	1.56284i
$918$	0.615770	+	1.06655i	0.0203234	+	0.0352012i
$919$	21.6145			0.712998			0.356499	−	0.934296i	$-0.383970\pi$
$919$	21.6145			0.712998			0.356499	+	0.934296i	$0.383970\pi$
$920$	−7.76084	−	13.4422i	−0.255867	−	0.443175i
$921$	7.00952	+	12.1408i	0.230971	+	0.400054i
$922$	34.7153	+	60.1287i	1.14329	+	1.98023i
$923$	23.7772	+	41.1833i	0.782635	+	1.35556i
$924$	9.93555	−	17.2089i	0.326856	−	0.566131i
$925$	−1.34450	−	2.32874i	−0.0442068	−	0.0765685i
$926$	39.7583			1.30654
$927$	−9.06318	+	15.6979i	−0.297674	+	0.515587i
$928$	−8.81915			−0.289503
$929$	9.05550	−	15.6846i	0.297101	−	0.514595i	−0.678370	−	0.734720i	$-0.737313\pi$
$929$	9.05550	−	15.6846i	0.297101	−	0.514595i	0.975472	+	0.220126i	$0.0706467\pi$
$930$	−13.0473	−	22.5985i	−0.427837	−	0.741036i
$931$	2.12238	+	3.67607i	0.0695581	+	0.120478i
$932$	−3.71324	−	6.43153i	−0.121631	−	0.210672i
$933$	8.08413	−	14.0021i	0.264662	−	0.458409i
$934$	2.24583			0.0734858
$935$	−4.90920			−0.160548
$936$	3.05962	+	5.29941i	0.100007	+	0.173217i
$937$	7.00410	+	12.1315i	0.228814	+	0.396318i	0.957457	−	0.288576i	$-0.0931819\pi$
$937$	7.00410	+	12.1315i	0.228814	+	0.396318i	−0.728643	+	0.684894i	$0.759849\pi$
$938$	−24.1438			−0.788323
$939$	6.84616	+	11.8579i	0.223416	+	0.386968i
$940$	−61.1559			−1.99469
$941$	31.2794			1.01968			0.509840	−	0.860270i	$-0.329705\pi$
$941$	31.2794			1.01968			0.509840	+	0.860270i	$0.329705\pi$
$942$	−17.6035	−	20.8960i	−0.573554	−	0.680829i
$943$	−26.7605			−0.871440
$944$	−8.47764			−0.275924
$945$	3.46667	+	6.00444i	0.112771	+	0.195325i
$946$	28.6415			0.931215
$947$	−9.17538	−	15.8922i	−0.298160	−	0.516428i	0.677555	−	0.735472i	$-0.263040\pi$
$947$	−9.17538	−	15.8922i	−0.298160	−	0.516428i	−0.975715	+	0.219044i	$0.929706\pi$
$948$	11.1432	+	19.3005i	0.361913	+	0.626852i
$949$	15.1819			0.492826
$950$	−24.9118			−0.808245
$951$	−10.4643	+	18.1247i	−0.339328	+	0.587733i
$952$	1.11505	+	1.93133i	0.0361390	+	0.0625946i
$953$	−13.8609	−	24.0077i	−0.448997	−	0.777686i	0.549324	−	0.835610i	$-0.314885\pi$
$953$	−13.8609	−	24.0077i	−0.448997	−	0.777686i	−0.998321	+	0.0579236i	$0.981552\pi$
$954$	13.6166	+	23.5846i	0.440852	+	0.763579i
$955$	−36.9579	+	64.0130i	−1.19593	+	2.07141i
$956$	75.2650			2.43424
$957$	1.77286	−	3.07068i	0.0573083	−	0.0992610i
$958$	61.8761			1.99913
$959$	24.5459	+	42.5147i	0.792628	+	1.37287i
$960$	18.0219	−	31.2149i	0.581655	−	1.00746i
$961$	6.93051	+	12.0040i	0.223565	+	0.387226i
$962$	3.24781	+	5.62536i	0.104713	+	0.181369i
$963$	−7.67691	−	13.2968i	−0.247385	−	0.428483i
$964$	−3.76156	−	6.51521i	−0.121152	−	0.209841i
$965$	−27.1076			−0.872626
$966$	8.53028	+	14.7749i	0.274457	+	0.475374i
$967$	20.5407	−	35.5775i	0.660544	−	1.14410i	−0.319929	−	0.947442i	$-0.603659\pi$
$967$	20.5407	−	35.5775i	0.660544	−	1.14410i	0.980473	−	0.196654i	$-0.0630076\pi$
$968$	−1.61104	+	2.79040i	−0.0517808	+	0.0896870i
$969$	1.92291			0.0617728
$970$	22.6561			0.727444
$971$	5.40205			0.173360			0.0866799	−	0.996236i	$-0.472374\pi$
$971$	5.40205			0.173360			0.0866799	+	0.996236i	$0.472374\pi$
$972$	1.37748	−	2.38586i	0.0441825	−	0.0765264i
$973$	8.63769	−	14.9609i	0.276912	−	0.479625i
$974$	−27.8692			−0.892988
$975$	6.23626	−	10.8015i	0.199720	−	0.345925i
$976$	1.60134	+	2.77361i	0.0512578	+	0.0887811i
$977$	−5.95699	−	10.3178i	−0.190581	−	0.330096i	0.754862	−	0.655884i	$-0.227704\pi$
$977$	−5.95699	−	10.3178i	−0.190581	−	0.330096i	−0.945443	+	0.325788i	$0.894371\pi$
$978$	7.21487	−	12.4965i	0.230706	−	0.399595i
$979$	−15.6942	+	27.1831i	−0.501588	+	0.868776i
$980$	−4.96407	−	8.59802i	−0.158571	−	0.274654i
$981$	−4.89686			−0.156345
$982$	−34.2669	−	59.3520i	−1.09350	−	1.89400i
$983$	−20.0903			−0.640782			−0.320391	−	0.947285i	$-0.603814\pi$
$983$	−20.0903			−0.640782			−0.320391	+	0.947285i	$0.603814\pi$
$984$	6.75294	+	11.6964i	0.215276	+	0.372869i
$985$	19.6428	−	34.0223i	0.625871	−	1.08404i
$986$	0.726059	+	1.25757i	0.0231224	+	0.0400492i
$987$	18.4204			0.586326
$988$	34.8660			1.10924
$989$	−7.12368	+	12.3386i	−0.226520	+	0.392344i
$990$	9.47715	+	16.4149i	0.301204	+	0.521700i
$991$	37.9524			1.20560			0.602800	−	0.797893i	$-0.294052\pi$
$991$	37.9524			1.20560			0.602800	+	0.797893i	$0.294052\pi$
$992$	15.4823	−	26.8161i	0.491564	−	0.851414i
$993$	17.6839	−	30.6293i	0.561180	−	0.971993i
$994$	33.4569	−	57.9490i	1.06119	−	1.83803i
$995$	−4.36854	+	7.56653i	−0.138492	+	0.239875i
$996$	−15.0426			−0.476642
$997$	30.3407	−	52.5516i	0.960900	−	1.66433i	0.240650	−	0.970612i	$-0.422639\pi$
$997$	30.3407	−	52.5516i	0.960900	−	1.66433i	0.720249	−	0.693715i	$-0.244027\pi$
$998$	−7.62727			−0.241437
$999$	0.400693	−	0.694021i	0.0126774	−	0.0219578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.b.169.3	✓	22
157.144	even	3	inner	471.2.e.b.301.3	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.b.169.3	✓	22	1.1	even	1	trivial
471.2.e.b.301.3	yes	22	157.144	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.18058 q^{2} +(0.500000 + 0.866025i) q^{3} +2.75495 q^{4} +(1.44529 + 2.50331i) q^{5} +(-1.09029 - 1.88844i) q^{6} -2.39860 q^{7} -1.64623 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-2.18058 q^{2} +(0.500000 + 0.866025i) q^{3} +2.75495 q^{4} +(1.44529 + 2.50331i) q^{5} +(-1.09029 - 1.88844i) q^{6} -2.39860 q^{7} -1.64623 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.15157 - 5.45869i) q^{10} +(1.50356 + 2.60424i) q^{11} +(1.37748 + 2.38586i) q^{12} +(-1.85855 + 3.21911i) q^{13} +5.23035 q^{14} +(-1.44529 + 2.50331i) q^{15} -1.92015 q^{16} +(0.282388 + 0.489110i) q^{17} +(1.09029 - 1.88844i) q^{18} +(-1.70237 - 2.94859i) q^{19} +(3.98170 + 6.89650i) q^{20} +(-1.19930 - 2.07725i) q^{21} +(-3.27864 - 5.67877i) q^{22} +3.26184 q^{23} +(-0.823117 - 1.42568i) q^{24} +(-1.67772 + 2.90589i) q^{25} +(4.05274 - 7.01954i) q^{26} -1.00000 q^{27} -6.60802 q^{28} -1.17911 q^{29} +(3.15157 - 5.45869i) q^{30} +(2.06996 - 3.58528i) q^{31} +7.47951 q^{32} +(-1.50356 + 2.60424i) q^{33} +(-0.615770 - 1.06655i) q^{34} +(-3.46667 - 6.00444i) q^{35} +(-1.37748 + 2.38586i) q^{36} +(-0.400693 + 0.694021i) q^{37} +(3.71216 + 6.42964i) q^{38} -3.71711 q^{39} +(-2.37928 - 4.12104i) q^{40} -8.20410 q^{41} +(2.61517 + 4.52962i) q^{42} +(-2.18395 + 3.78271i) q^{43} +(4.14223 + 7.17455i) q^{44} -2.89058 q^{45} -7.11272 q^{46} +(-3.83982 + 6.65076i) q^{47} +(-0.960074 - 1.66290i) q^{48} -1.24672 q^{49} +(3.65840 - 6.33654i) q^{50} +(-0.282388 + 0.489110i) q^{51} +(-5.12023 + 8.86849i) q^{52} +(-6.24445 + 10.8157i) q^{53} +2.18058 q^{54} +(-4.34615 + 7.52776i) q^{55} +3.94866 q^{56} +(1.70237 - 2.94859i) q^{57} +2.57114 q^{58} +4.41510 q^{59} +(-3.98170 + 6.89650i) q^{60} +(-0.833969 - 1.44448i) q^{61} +(-4.51373 + 7.81801i) q^{62} +(1.19930 - 2.07725i) q^{63} -12.4694 q^{64} -10.7446 q^{65} +(3.27864 - 5.67877i) q^{66} -4.61609 q^{67} +(0.777964 + 1.34747i) q^{68} +(1.63092 + 2.82483i) q^{69} +(7.55936 + 13.0932i) q^{70} +(6.39668 - 11.0794i) q^{71} +(0.823117 - 1.42568i) q^{72} +(-2.04217 - 3.53714i) q^{73} +(0.873745 - 1.51337i) q^{74} -3.35543 q^{75} +(-4.68994 - 8.12321i) q^{76} +(-3.60644 - 6.24653i) q^{77} +8.10547 q^{78} +8.08956 q^{79} +(-2.77517 - 4.80673i) q^{80} +(-0.500000 - 0.866025i) q^{81} +17.8897 q^{82} +(-2.73010 + 4.72867i) q^{83} +(-3.30401 - 5.72272i) q^{84} +(-0.816263 + 1.41381i) q^{85} +(4.76228 - 8.24851i) q^{86} +(-0.589554 - 1.02114i) q^{87} +(-2.47521 - 4.28719i) q^{88} +(5.21901 + 9.03959i) q^{89} +6.30315 q^{90} +(4.45793 - 7.72136i) q^{91} +8.98620 q^{92} +4.13992 q^{93} +(8.37304 - 14.5025i) q^{94} +(4.92082 - 8.52312i) q^{95} +(3.73976 + 6.47745i) q^{96} +(-1.79721 + 3.11285i) q^{97} +2.71858 q^{98} -3.00712 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

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