LMFDB - Embedded newform 1001.2.i.d.144.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.10
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.d.716.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.702891 - 1.21744i) q^{2} +(1.64875 - 2.85573i) q^{3} +(0.0118876 - 0.0205898i) q^{4} +(1.08426 + 1.87799i) q^{5} -4.63558 q^{6} +(2.39918 - 1.11532i) q^{7} -2.84499 q^{8} +(-3.93679 - 6.81871i) q^{9} +O(q^{10})$	\(q+(-0.702891 - 1.21744i) q^{2} +(1.64875 - 2.85573i) q^{3} +(0.0118876 - 0.0205898i) q^{4} +(1.08426 + 1.87799i) q^{5} -4.63558 q^{6} +(2.39918 - 1.11532i) q^{7} -2.84499 q^{8} +(-3.93679 - 6.81871i) q^{9} +(1.52423 - 2.64005i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.0391993 - 0.0678952i) q^{12} -1.00000 q^{13} +(-3.04420 - 2.13691i) q^{14} +7.15071 q^{15} +(1.97594 + 3.42243i) q^{16} +(1.92020 - 3.32588i) q^{17} +(-5.53426 + 9.58563i) q^{18} +(1.02845 + 1.78133i) q^{19} +0.0515568 q^{20} +(0.770604 - 8.69029i) q^{21} +1.40578 q^{22} +(-2.62162 - 4.54078i) q^{23} +(-4.69069 + 8.12451i) q^{24} +(0.148763 - 0.257665i) q^{25} +(0.702891 + 1.21744i) q^{26} -16.0706 q^{27} +(0.00555607 - 0.0626572i) q^{28} -1.87563 q^{29} +(-5.02617 - 8.70559i) q^{30} +(-1.46934 + 2.54497i) q^{31} +(-0.0672426 + 0.116468i) q^{32} +(1.64875 + 2.85573i) q^{33} -5.39876 q^{34} +(4.69590 + 3.29634i) q^{35} -0.187195 q^{36} +(5.16913 + 8.95320i) q^{37} +(1.44578 - 2.50416i) q^{38} +(-1.64875 + 2.85573i) q^{39} +(-3.08471 - 5.34287i) q^{40} -5.46796 q^{41} +(-11.1216 + 5.17016i) q^{42} -1.35470 q^{43} +(0.0118876 + 0.0205898i) q^{44} +(8.53699 - 14.7865i) q^{45} +(-3.68542 + 6.38334i) q^{46} +(-3.74473 - 6.48606i) q^{47} +13.0314 q^{48} +(4.51212 - 5.35171i) q^{49} -0.418257 q^{50} +(-6.33187 - 10.9671i) q^{51} +(-0.0118876 + 0.0205898i) q^{52} +(6.06393 - 10.5030i) q^{53} +(11.2959 + 19.5651i) q^{54} -2.16852 q^{55} +(-6.82563 + 3.17308i) q^{56} +6.78265 q^{57} +(1.31837 + 2.28348i) q^{58} +(4.29437 - 7.43806i) q^{59} +(0.0850045 - 0.147232i) q^{60} +(7.22557 + 12.5151i) q^{61} +4.13114 q^{62} +(-17.0501 - 11.9685i) q^{63} +8.09283 q^{64} +(-1.08426 - 1.87799i) q^{65} +(2.31779 - 4.01453i) q^{66} +(4.45797 - 7.72144i) q^{67} +(-0.0456529 - 0.0790731i) q^{68} -17.2896 q^{69} +(0.712404 - 8.03396i) q^{70} +6.06950 q^{71} +(11.2001 + 19.3992i) q^{72} +(-4.52963 + 7.84555i) q^{73} +(7.26667 - 12.5862i) q^{74} +(-0.490547 - 0.849653i) q^{75} +0.0489030 q^{76} +(-0.233693 + 2.63541i) q^{77} +4.63558 q^{78} +(7.56626 + 13.1051i) q^{79} +(-4.28487 + 7.42161i) q^{80} +(-14.6862 + 25.4372i) q^{81} +(3.84338 + 6.65693i) q^{82} -6.95845 q^{83} +(-0.169771 - 0.119173i) q^{84} +8.32797 q^{85} +(0.952207 + 1.64927i) q^{86} +(-3.09246 + 5.35630i) q^{87} +(1.42249 - 2.46383i) q^{88} +(7.64816 + 13.2470i) q^{89} -24.0023 q^{90} +(-2.39918 + 1.11532i) q^{91} -0.124658 q^{92} +(4.84516 + 8.39206i) q^{93} +(-5.26428 + 9.11799i) q^{94} +(-2.23021 + 3.86284i) q^{95} +(0.221733 + 0.384053i) q^{96} +4.81765 q^{97} +(-9.68693 - 1.73158i) q^{98} +7.87357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) $ 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.702891	−	1.21744i	−0.497019	−	0.860863i	0.502975	−	0.864301i	$-0.332239\pi$
$2$	−0.702891	−	1.21744i	−0.497019	−	0.860863i	−0.999994	+	0.00343849i	$0.998905\pi$
$3$	1.64875	−	2.85573i	0.951909	−	1.64875i	0.210621	−	0.977568i	$-0.432451\pi$
$3$	1.64875	−	2.85573i	0.951909	−	1.64875i	0.741288	−	0.671187i	$-0.234215\pi$
$4$	0.0118876	−	0.0205898i	0.00594378	−	0.0102949i
$5$	1.08426	+	1.87799i	0.484896	+	0.839864i	0.999849	−	0.0173542i	$-0.00552428\pi$
$5$	1.08426	+	1.87799i	0.484896	+	0.839864i	−0.514954	+	0.857218i	$0.672191\pi$
$6$	−4.63558			−1.89247
$7$	2.39918	−	1.11532i	0.906804	−	0.421552i
$7$	2.39918	−	1.11532i	0.906804	−	0.421552i
$8$	−2.84499			−1.00586
$9$	−3.93679	−	6.81871i	−1.31226	−	2.27290i
$10$	1.52423	−	2.64005i	0.482005	−	0.834857i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.0391993	−	0.0678952i	−0.0113159	−	0.0195997i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−3.04420	−	2.13691i	−0.813597	−	0.571114i
$15$	7.15071			1.84631
$16$	1.97594	+	3.42243i	0.493986	+	0.855608i
$17$	1.92020	−	3.32588i	0.465716	−	0.806644i	−0.533517	−	0.845789i	$-0.679130\pi$
$17$	1.92020	−	3.32588i	0.465716	−	0.806644i	0.999234	+	0.0391451i	$0.0124635\pi$
$18$	−5.53426	+	9.58563i	−1.30444	+	2.25935i
$19$	1.02845	+	1.78133i	0.235943	+	0.408665i	0.959546	−	0.281551i	$-0.0908489\pi$
$19$	1.02845	+	1.78133i	0.235943	+	0.408665i	−0.723604	+	0.690216i	$0.757516\pi$
$20$	0.0515568			0.0115284
$21$	0.770604	−	8.69029i	0.168160	−	1.89638i
$22$	1.40578			0.299714
$23$	−2.62162	−	4.54078i	−0.546645	−	0.946817i	−0.998501	−	0.0547263i	$-0.982571\pi$
$23$	−2.62162	−	4.54078i	−0.546645	−	0.946817i	0.451856	−	0.892091i	$-0.350762\pi$
$24$	−4.69069	+	8.12451i	−0.957483	+	1.65841i
$25$	0.148763	−	0.257665i	0.0297526	−	0.0515330i
$26$	0.702891	+	1.21744i	0.137848	+	0.238760i
$27$	−16.0706			−3.09280
$28$	0.00555607	−	0.0626572i	0.00105000	−	0.0118411i
$29$	−1.87563			−0.348297			−0.174148	−	0.984719i	$-0.555717\pi$
$29$	−1.87563			−0.348297			−0.174148	+	0.984719i	$0.555717\pi$
$30$	−5.02617	−	8.70559i	−0.917650	−	1.58942i
$31$	−1.46934	+	2.54497i	−0.263901	+	0.457090i	−0.967275	−	0.253730i	$-0.918343\pi$
$31$	−1.46934	+	2.54497i	−0.263901	+	0.457090i	0.703374	+	0.710820i	$0.251676\pi$
$32$	−0.0672426	+	0.116468i	−0.0118869	+	0.0205888i
$33$	1.64875	+	2.85573i	0.287011	+	0.497118i
$34$	−5.39876			−0.925879
$35$	4.69590	+	3.29634i	0.793751	+	0.557183i
$36$	−0.187195			−0.0311992
$37$	5.16913	+	8.95320i	0.849800	+	1.47190i	0.881387	+	0.472396i	$0.156611\pi$
$37$	5.16913	+	8.95320i	0.849800	+	1.47190i	−0.0315868	+	0.999501i	$0.510056\pi$
$38$	1.44578	−	2.50416i	0.234536	−	0.406228i
$39$	−1.64875	+	2.85573i	−0.264012	+	0.457282i
$40$	−3.08471	−	5.34287i	−0.487735	−	0.844781i
$41$	−5.46796			−0.853951			−0.426976	−	0.904263i	$-0.640421\pi$
$41$	−5.46796			−0.853951			−0.426976	+	0.904263i	$0.640421\pi$
$42$	−11.1216	+	5.17016i	−1.71610	+	0.797774i
$43$	−1.35470			−0.206590			−0.103295	−	0.994651i	$-0.532939\pi$
$43$	−1.35470			−0.206590			−0.103295	+	0.994651i	$0.532939\pi$
$44$	0.0118876	+	0.0205898i	0.00179212	+	0.00310404i
$45$	8.53699	−	14.7865i	1.27262	−	2.20424i
$46$	−3.68542	+	6.38334i	−0.543386	+	0.941173i
$47$	−3.74473	−	6.48606i	−0.546225	−	0.946089i	−0.998529	−	0.0542254i	$-0.982731\pi$
$47$	−3.74473	−	6.48606i	−0.546225	−	0.946089i	0.452304	−	0.891864i	$-0.350602\pi$
$48$	13.0314			1.88092
$49$	4.51212	−	5.35171i	0.644588	−	0.764530i
$50$	−0.418257			−0.0591504
$51$	−6.33187	−	10.9671i	−0.886639	−	1.53570i
$52$	−0.0118876	+	0.0205898i	−0.00164851	+	0.00285530i
$53$	6.06393	−	10.5030i	0.832945	−	1.44270i	−0.0627469	−	0.998029i	$-0.519986\pi$
$53$	6.06393	−	10.5030i	0.832945	−	1.44270i	0.895692	−	0.444674i	$-0.146681\pi$
$54$	11.2959	+	19.5651i	1.53718	+	2.66247i
$55$	−2.16852			−0.292403
$56$	−6.82563	+	3.17308i	−0.912114	+	0.424020i
$57$	6.78265			0.898384
$58$	1.31837	+	2.28348i	0.173110	+	0.299835i
$59$	4.29437	−	7.43806i	0.559079	−	0.968354i	−0.438494	−	0.898734i	$-0.644488\pi$
$59$	4.29437	−	7.43806i	0.559079	−	0.968354i	0.997574	−	0.0696197i	$-0.0221786\pi$
$60$	0.0850045	−	0.147232i	0.0109740	−	0.0190076i
$61$	7.22557	+	12.5151i	0.925139	+	1.60239i	0.791337	+	0.611380i	$0.209385\pi$
$61$	7.22557	+	12.5151i	0.925139	+	1.60239i	0.133802	+	0.991008i	$0.457281\pi$
$62$	4.13114			0.524656
$63$	−17.0501	−	11.9685i	−2.14811	−	1.50789i
$64$	8.09283			1.01160
$65$	−1.08426	−	1.87799i	−0.134486	−	0.232936i
$66$	2.31779	−	4.01453i	0.285300	−	0.494155i
$67$	4.45797	−	7.72144i	0.544628	−	0.943324i	−0.454002	−	0.891001i	$-0.650004\pi$
$67$	4.45797	−	7.72144i	0.544628	−	0.943324i	0.998630	−	0.0523230i	$-0.0166625\pi$
$68$	−0.0456529	−	0.0790731i	−0.00553623	−	0.00958902i
$69$	−17.2896			−2.08143
$70$	0.712404	−	8.03396i	0.0851486	−	0.960242i
$71$	6.06950			0.720317			0.360159	−	0.932891i	$-0.382723\pi$
$71$	6.06950			0.720317			0.360159	+	0.932891i	$0.382723\pi$
$72$	11.2001	+	19.3992i	1.31995	+	2.28621i
$73$	−4.52963	+	7.84555i	−0.530153	+	0.918253i	0.469228	+	0.883077i	$0.344532\pi$
$73$	−4.52963	+	7.84555i	−0.530153	+	0.918253i	−0.999381	+	0.0351754i	$0.988801\pi$
$74$	7.26667	−	12.5862i	0.844734	−	1.46312i
$75$	−0.490547	−	0.849653i	−0.0566435	−	0.0981095i
$76$	0.0489030			0.00560956
$77$	−0.233693	+	2.63541i	−0.0266318	+	0.300333i
$78$	4.63558			0.524876
$79$	7.56626	+	13.1051i	0.851270	+	1.47444i	0.880062	+	0.474858i	$0.157501\pi$
$79$	7.56626	+	13.1051i	0.851270	+	1.47444i	−0.0287918	+	0.999585i	$0.509166\pi$
$80$	−4.28487	+	7.42161i	−0.479063	+	0.829761i
$81$	−14.6862	+	25.4372i	−1.63180	+	2.82636i
$82$	3.84338	+	6.65693i	0.424430	+	0.735135i
$83$	−6.95845			−0.763789			−0.381895	−	0.924206i	$-0.624728\pi$
$83$	−6.95845			−0.763789			−0.381895	+	0.924206i	$0.624728\pi$
$84$	−0.169771	−	0.119173i	−0.0185236	−	0.0130028i
$85$	8.32797			0.903295
$86$	0.952207	+	1.64927i	0.102679	+	0.177845i
$87$	−3.09246	+	5.35630i	−0.331547	+	0.574256i
$88$	1.42249	−	2.46383i	0.151638	−	0.262645i
$89$	7.64816	+	13.2470i	0.810703	+	1.40418i	0.912372	+	0.409361i	$0.134248\pi$
$89$	7.64816	+	13.2470i	0.810703	+	1.40418i	−0.101669	+	0.994818i	$0.532418\pi$
$90$	−24.0023			−2.53007
$91$	−2.39918	+	1.11532i	−0.251502	+	0.116917i
$92$	−0.124658			−0.0129965
$93$	4.84516	+	8.39206i	0.502420	+	0.870216i
$94$	−5.26428	+	9.11799i	−0.542969	+	0.940449i
$95$	−2.23021	+	3.86284i	−0.228815	+	0.396319i
$96$	0.221733	+	0.384053i	0.0226305	+	0.0391972i
$97$	4.81765			0.489158			0.244579	−	0.969629i	$-0.421350\pi$
$97$	4.81765			0.489158			0.244579	+	0.969629i	$0.421350\pi$
$98$	−9.68693	−	1.73158i	−0.978528	−	0.174916i
$99$	7.87357			0.791324
$100$	−0.00353686	−	0.00612601i	−0.000353686	−	0.000612601i
$101$	−1.87314	+	3.24437i	−0.186384	+	0.322827i	−0.944042	−	0.329825i	$-0.893010\pi$
$101$	−1.87314	+	3.24437i	−0.186384	+	0.322827i	0.757658	+	0.652652i	$0.226344\pi$
$102$	−8.90123	+	15.4174i	−0.881353	+	1.52655i
$103$	−6.47062	−	11.2074i	−0.637569	−	1.10430i	−0.985965	−	0.166955i	$-0.946607\pi$
$103$	−6.47062	−	11.2074i	−0.637569	−	1.10430i	0.348395	−	0.937348i	$-0.386727\pi$
$104$	2.84499			0.278974
$105$	17.1558	−	7.97534i	1.67424	−	0.778314i
$106$	−17.0491			−1.65596
$107$	2.66689	+	4.61919i	0.257818	+	0.446554i	0.965657	−	0.259820i	$-0.0836632\pi$
$107$	2.66689	+	4.61919i	0.257818	+	0.446554i	−0.707839	+	0.706374i	$0.750330\pi$
$108$	−0.191041	+	0.330892i	−0.0183829	+	0.0318401i
$109$	0.601763	−	1.04228i	0.0576384	−	0.0998326i	−0.835766	−	0.549085i	$-0.814976\pi$
$109$	0.601763	−	1.04228i	0.0576384	−	0.0998326i	0.893405	+	0.449252i	$0.148310\pi$
$110$	1.52423	+	2.64005i	0.145330	+	0.251719i
$111$	34.0905			3.23573
$112$	8.55775	+	6.00722i	0.808631	+	0.567629i
$113$	−0.112536			−0.0105865			−0.00529327	−	0.999986i	$-0.501685\pi$
$113$	−0.112536			−0.0105865			−0.00529327	+	0.999986i	$0.501685\pi$
$114$	−4.76747	−	8.25749i	−0.446514	−	0.773385i
$115$	5.68503	−	9.84676i	0.530132	−	0.918215i
$116$	−0.0222967	+	0.0386190i	−0.00207020	+	0.00358569i
$117$	3.93679	+	6.81871i	0.363956	+	0.630390i
$118$	−12.0739			−1.11149
$119$	0.897472	−	10.1210i	0.0822711	−	0.927792i
$120$	−20.3437			−1.85712
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	10.1576	−	17.5934i	0.919624	−	1.59284i
$123$	−9.01532	+	15.6150i	−0.812884	+	1.40796i
$124$	0.0349337	+	0.0605069i	0.00313714	+	0.00543368i
$125$	11.4878			1.02750
$126$	−2.58663	+	29.1701i	−0.230436	+	2.59868i
$127$	4.74878			0.421386			0.210693	−	0.977552i	$-0.432428\pi$
$127$	4.74878			0.421386			0.210693	+	0.977552i	$0.432428\pi$
$128$	−5.55389	−	9.61962i	−0.490899	−	0.850263i
$129$	−2.23357	+	3.86865i	−0.196655	+	0.340616i
$130$	−1.52423	+	2.64005i	−0.133684	+	0.231548i
$131$	9.26754	+	16.0519i	0.809709	+	1.40246i	0.913066	+	0.407812i	$0.133708\pi$
$131$	9.26754	+	16.0519i	0.809709	+	1.40246i	−0.103357	+	0.994644i	$0.532958\pi$
$132$	0.0783986			0.00682373
$133$	4.45419	+	3.12667i	0.386227	+	0.271117i
$134$	−12.5339			−1.08276
$135$	−17.4247	−	30.1806i	−1.49968	−	2.59753i
$136$	−5.46294	+	9.46208i	−0.468443	+	0.811367i
$137$	−4.24731	+	7.35656i	−0.362872	+	0.628513i	−0.988432	−	0.151663i	$-0.951537\pi$
$137$	−4.24731	+	7.35656i	−0.362872	+	0.628513i	0.625560	+	0.780176i	$0.284871\pi$
$138$	12.1527	+	21.0491i	1.03451	+	1.79182i
$139$	−1.87185			−0.158768			−0.0793840	−	0.996844i	$-0.525295\pi$
$139$	−1.87185			−0.158768			−0.0793840	+	0.996844i	$0.525295\pi$
$140$	0.123694	−	0.0575024i	0.0104540	−	0.00485984i
$141$	−24.6966			−2.07983
$142$	−4.26620	−	7.38927i	−0.358011	−	0.620094i
$143$	0.500000	−	0.866025i	0.0418121	−	0.0724207i
$144$	15.5577	−	26.9468i	1.29648	−	2.24556i
$145$	−2.03367	−	3.52243i	−0.168887	−	0.292522i
$146$	12.7354			1.05399
$147$	−7.84365	−	21.7090i	−0.646933	−	1.79053i
$148$	0.245793			0.0202041
$149$	−0.500901	−	0.867586i	−0.0410354	−	0.0710754i	0.844778	−	0.535117i	$-0.179732\pi$
$149$	−0.500901	−	0.867586i	−0.0410354	−	0.0710754i	−0.885814	+	0.464041i	$0.846399\pi$
$150$	−0.689603	+	1.19443i	−0.0563058	+	0.0975246i
$151$	5.17161	−	8.95749i	0.420860	−	0.728950i	−0.575164	−	0.818038i	$-0.695062\pi$
$151$	5.17161	−	8.95749i	0.420860	−	0.728950i	0.996024	+	0.0890879i	$0.0283952\pi$
$152$	−2.92593	−	5.06786i	−0.237324	−	0.411058i
$153$	−30.2376			−2.44457
$154$	3.37272	−	1.56790i	0.271782	−	0.126345i
$155$	−6.37258			−0.511858
$156$	0.0391993	+	0.0678952i	0.00313846	+	0.00543597i
$157$	2.92919	−	5.07351i	0.233775	−	0.404910i	−0.725141	−	0.688600i	$-0.758225\pi$
$157$	2.92919	−	5.07351i	0.233775	−	0.404910i	0.958916	+	0.283690i	$0.0915587\pi$
$158$	10.6365	−	18.4230i	0.846196	−	1.46565i
$159$	−19.9959	−	34.6339i	−1.58578	−	2.74665i
$160$	−0.291634			−0.0230557
$161$	−11.3542	−	7.97018i	−0.894833	−	0.628139i
$162$	41.2912			3.24414
$163$	2.33714	+	4.04804i	0.183059	+	0.317067i	0.942921	−	0.333018i	$-0.108067\pi$
$163$	2.33714	+	4.04804i	0.183059	+	0.317067i	−0.759862	+	0.650084i	$0.774734\pi$
$164$	−0.0650006	+	0.112584i	−0.00507570	+	0.00879136i
$165$	−3.57536	+	6.19270i	−0.278341	+	0.482101i
$166$	4.89104	+	8.47152i	0.379618	+	0.657518i
$167$	12.7285			0.984965			0.492482	−	0.870322i	$-0.336090\pi$
$167$	12.7285			0.984965			0.492482	+	0.870322i	$0.336090\pi$
$168$	−2.19236	+	24.7238i	−0.169144	+	1.90748i
$169$	1.00000			0.0769231
$170$	−5.85365	−	10.1388i	−0.448955	−	0.777613i
$171$	8.09758	−	14.0254i	0.619237	−	1.07255i
$172$	−0.0161041	+	0.0278931i	−0.00122792	+	0.00212683i
$173$	−1.33833	−	2.31806i	−0.101752	−	0.176239i	0.810655	−	0.585524i	$-0.199111\pi$
$173$	−1.33833	−	2.31806i	−0.101752	−	0.176239i	−0.912406	+	0.409285i	$0.865778\pi$
$174$	8.69466			0.659140
$175$	0.0695296	−	0.784103i	0.00525595	−	0.0592726i
$176$	−3.95188			−0.297885
$177$	−14.1607	−	24.5271i	−1.06439	−	1.84357i
$178$	10.7517	−	18.6224i	0.805870	−	1.39581i
$179$	−10.6671	+	18.4760i	−0.797300	+	1.38096i	0.124068	+	0.992274i	$0.460406\pi$
$179$	−10.6671	+	18.4760i	−0.797300	+	1.38096i	−0.921368	+	0.388690i	$0.872928\pi$
$180$	−0.202968	−	0.351551i	−0.0151283	−	0.0262030i
$181$	5.72589			0.425602			0.212801	−	0.977096i	$-0.431741\pi$
$181$	5.72589			0.425602			0.212801	+	0.977096i	$0.431741\pi$
$182$	3.04420	+	2.13691i	0.225651	+	0.158399i
$183$	47.6528			3.52259
$184$	7.45847	+	12.9185i	0.549846	+	0.952361i
$185$	−11.2094	+	19.4152i	−0.824128	+	1.42743i
$186$	6.81124	−	11.7974i	0.499424	−	0.865028i
$187$	1.92020	+	3.32588i	0.140419	+	0.243212i
$188$	−0.178063			−0.0129866
$189$	−38.5564	+	17.9239i	−2.80456	+	1.30377i
$190$	6.27039			0.454902
$191$	1.78025	+	3.08349i	0.128815	+	0.223114i	0.923218	−	0.384278i	$-0.125549\pi$
$191$	1.78025	+	3.08349i	0.128815	+	0.223114i	−0.794403	+	0.607391i	$0.792216\pi$
$192$	13.3431	−	23.1109i	0.962954	−	1.66789i
$193$	3.28731	−	5.69379i	0.236626	−	0.409848i	−0.723118	−	0.690724i	$-0.757292\pi$
$193$	3.28731	−	5.69379i	0.236626	−	0.409848i	0.959744	+	0.280877i	$0.0906251\pi$
$194$	−3.38628	−	5.86521i	−0.243121	−	0.421098i
$195$	−7.15071			−0.512073
$196$	−0.0565529	−	0.156523i	−0.00403949	−	0.0111802i
$197$	20.7038			1.47509			0.737544	−	0.675299i	$-0.235986\pi$
$197$	20.7038			1.47509			0.737544	+	0.675299i	$0.235986\pi$
$198$	−5.53426	−	9.58563i	−0.393303	−	0.681221i
$199$	5.15929	−	8.93615i	0.365732	−	0.633467i	−0.623161	−	0.782094i	$-0.714152\pi$
$199$	5.15929	−	8.93615i	0.365732	−	0.633467i	0.988893	+	0.148627i	$0.0474852\pi$
$200$	−0.423229	+	0.733054i	−0.0299268	+	0.0518347i
$201$	−14.7002	−	25.4615i	−1.03687	−	1.79592i
$202$	5.26646			0.370547
$203$	−4.49998	+	2.09194i	−0.315837	+	0.146825i
$204$	−0.301082			−0.0210799
$205$	−5.92868	−	10.2688i	−0.414077	−	0.717203i
$206$	−9.09629	+	15.7552i	−0.633769	+	1.09772i
$207$	−20.6415	+	35.7521i	−1.43468	+	2.48494i
$208$	−1.97594	−	3.42243i	−0.137007	−	0.237303i
$209$	−2.05690			−0.142279
$210$	−21.7682	−	15.2805i	−1.50215	−	1.05445i
$211$	9.32466			0.641936			0.320968	−	0.947090i	$-0.395992\pi$
$211$	9.32466			0.641936			0.320968	+	0.947090i	$0.395992\pi$
$212$	−0.144171	−	0.249711i	−0.00990168	−	0.0171502i
$213$	10.0071	−	17.3328i	0.685676	−	1.18763i
$214$	3.74907	−	6.49357i	0.256281	−	0.443891i
$215$	−1.46885	−	2.54412i	−0.100174	−	0.173507i
$216$	45.7208			3.11091
$217$	−0.686747	+	7.74462i	−0.0466195	+	0.525739i
$218$	−1.69189			−0.114590
$219$	14.9365	+	25.8708i	1.00932	+	1.74819i
$220$	−0.0257784	+	0.0446495i	−0.00173798	+	0.00301027i
$221$	−1.92020	+	3.32588i	−0.129166	+	0.223723i
$222$	−23.9619	−	41.5033i	−1.60822	−	2.78552i
$223$	0.855848			0.0573118			0.0286559	−	0.999589i	$-0.490877\pi$
$223$	0.855848			0.0573118			0.0286559	+	0.999589i	$0.490877\pi$
$224$	−0.0314282	+	0.354424i	−0.00209988	+	0.0236809i
$225$	−2.34259			−0.156173
$226$	0.0791009	+	0.137007i	0.00526171	+	0.00911355i
$227$	3.71840	−	6.44046i	0.246799	−	0.427469i	−0.715837	−	0.698268i	$-0.753955\pi$
$227$	3.71840	−	6.44046i	0.246799	−	0.427469i	0.962636	+	0.270799i	$0.0872879\pi$
$228$	0.0806291	−	0.139654i	0.00533979	−	0.00924879i
$229$	−5.84723	−	10.1277i	−0.386396	−	0.669257i	0.605566	−	0.795795i	$-0.292947\pi$
$229$	−5.84723	−	10.1277i	−0.386396	−	0.669257i	−0.991962	+	0.126538i	$0.959613\pi$
$230$	−15.9838			−1.05394
$231$	7.14071	+	5.01251i	0.469824	+	0.329799i
$232$	5.33616			0.350336
$233$	−11.6108	−	20.1105i	−0.760648	−	1.31748i	−0.942517	−	0.334158i	$-0.891548\pi$
$233$	−11.6108	−	20.1105i	−0.760648	−	1.31748i	0.181869	−	0.983323i	$-0.441785\pi$
$234$	5.53426	−	9.58563i	0.361786	−	0.626632i
$235$	8.12052	−	14.0651i	0.529724	−	0.917509i
$236$	−0.102099	−	0.176841i	−0.00664608	−	0.0115114i
$237$	49.8996			3.24133
$238$	−12.9526	+	6.02135i	−0.839591	+	0.390306i
$239$	−28.7369			−1.85884			−0.929418	−	0.369030i	$-0.879690\pi$
$239$	−28.7369			−1.85884			−0.929418	+	0.369030i	$0.879690\pi$
$240$	14.1294	+	24.4728i	0.912048	+	1.57971i
$241$	−4.53834	+	7.86064i	−0.292340	+	0.506349i	−0.974363	−	0.224983i	$-0.927767\pi$
$241$	−4.53834	+	7.86064i	−0.292340	+	0.506349i	0.682022	+	0.731331i	$0.261101\pi$
$242$	−0.702891	+	1.21744i	−0.0451836	+	0.0782602i
$243$	24.3219	+	42.1268i	1.56025	+	2.70244i
$244$	0.343577			0.0219953
$245$	14.9428	+	2.67108i	0.954659	+	0.170649i
$246$	25.3472			1.61608
$247$	−1.02845	−	1.78133i	−0.0654387	−	0.113343i
$248$	4.18025	−	7.24041i	0.265446	−	0.459766i
$249$	−11.4728	+	19.8714i	−0.727058	+	1.25930i
$250$	−8.07466	−	13.9857i	−0.510687	−	0.884535i
$251$	−13.2530			−0.836520			−0.418260	−	0.908327i	$-0.637360\pi$
$251$	−13.2530			−0.836520			−0.418260	+	0.908327i	$0.637360\pi$
$252$	−0.449114	+	0.208783i	−0.0282915	+	0.0131521i
$253$	5.24324			0.329639
$254$	−3.33787	−	5.78137i	−0.209437	−	0.362755i
$255$	13.7308	−	23.7824i	0.859854	−	1.48931i
$256$	0.285261	−	0.494086i	0.0178288	−	0.0308804i
$257$	−0.166490	−	0.288369i	−0.0103854	−	0.0179880i	0.860786	−	0.508967i	$-0.169972\pi$
$257$	−0.166490	−	0.288369i	−0.0103854	−	0.0179880i	−0.871171	+	0.490979i	$0.836639\pi$
$258$	6.27982			0.390965
$259$	22.3874	+	15.7151i	1.39108	+	0.976487i
$260$	−0.0515568			−0.00319742
$261$	7.38397	+	12.7894i	0.457056	+	0.791645i
$262$	13.0281	−	22.5654i	0.804882	−	1.39410i
$263$	6.78708	−	11.7556i	0.418510	−	0.724880i	−0.577280	−	0.816546i	$-0.695886\pi$
$263$	6.78708	−	11.7556i	0.418510	−	0.724880i	0.995790	+	0.0916663i	$0.0292193\pi$
$264$	−4.69069	−	8.12451i	−0.288692	−	0.500029i
$265$	26.2995			1.61557
$266$	0.675735	−	7.62044i	0.0414320	−	0.467239i
$267$	50.4398			3.08686
$268$	−0.105989	−	0.183578i	−0.00647430	−	0.0112138i
$269$	−15.3365	+	26.5635i	−0.935080	+	1.61961i	−0.160589	+	0.987021i	$0.551339\pi$
$269$	−15.3365	+	26.5635i	−0.935080	+	1.61961i	−0.774491	+	0.632585i	$0.781994\pi$
$270$	−24.4954	+	42.4273i	−1.49074	+	2.58204i
$271$	−9.16417	−	15.8728i	−0.556684	−	0.964205i	−0.997770	−	0.0667401i	$-0.978740\pi$
$271$	−9.16417	−	15.8728i	−0.556684	−	0.964205i	0.441087	−	0.897465i	$-0.354593\pi$
$272$	15.1768			0.920228
$273$	−0.770604	+	8.69029i	−0.0466391	+	0.525960i
$274$	11.9416			0.721418
$275$	0.148763	+	0.257665i	0.00897075	+	0.0155378i
$276$	−0.205531	+	0.355991i	−0.0123715	+	0.0214281i
$277$	−8.77255	+	15.1945i	−0.527092	+	0.912949i	0.472410	+	0.881379i	$0.343384\pi$
$277$	−8.77255	+	15.1945i	−0.527092	+	0.912949i	−0.999502	+	0.0315705i	$0.989949\pi$
$278$	1.31570	+	2.27887i	0.0789107	+	0.136677i
$279$	23.1379			1.38523
$280$	−13.3598	−	9.37805i	−0.798399	−	0.560446i
$281$	−21.8576			−1.30391			−0.651957	−	0.758256i	$-0.726052\pi$
$281$	−21.8576			−1.30391			−0.651957	+	0.758256i	$0.726052\pi$
$282$	17.3590	+	30.0667i	1.03371	+	1.79044i
$283$	−2.24402	+	3.88675i	−0.133393	+	0.231043i	−0.924982	−	0.380010i	$-0.875921\pi$
$283$	−2.24402	+	3.88675i	−0.133393	+	0.231043i	0.791589	+	0.611053i	$0.209254\pi$
$284$	0.0721515	−	0.124970i	0.00428140	−	0.00741561i
$285$	7.35415	+	12.7378i	0.435622	+	0.754520i
$286$	−1.40578			−0.0831257
$287$	−13.1186	+	6.09853i	−0.774367	+	0.359985i
$288$	1.05888			0.0623950
$289$	1.12569	+	1.94975i	0.0662170	+	0.114691i
$290$	−2.85890	+	4.95177i	−0.167881	+	0.290778i
$291$	7.94312	−	13.7579i	0.465634	−	0.806501i
$292$	0.107692	+	0.186529i	0.00630223	+	0.0109158i
$293$	−0.460172			−0.0268835			−0.0134418	−	0.999910i	$-0.504279\pi$
$293$	−0.460172			−0.0268835			−0.0134418	+	0.999910i	$0.504279\pi$
$294$	−20.9163	+	24.8083i	−1.21986	+	1.44685i
$295$	18.6248			1.08438
$296$	−14.7061	−	25.4717i	−0.854776	−	1.48051i
$297$	8.03532	−	13.9176i	0.466257	−	0.807580i
$298$	−0.704158	+	1.21964i	−0.0407908	+	0.0706517i
$299$	2.62162	+	4.54078i	0.151612	+	0.262600i
$300$	−0.0233256			−0.00134671
$301$	−3.25017	+	1.51093i	−0.187337	+	0.0870883i
$302$	−14.5403			−0.836701
$303$	6.17670	+	10.6984i	0.354842	+	0.614604i
$304$	−4.06432	+	7.03960i	−0.233105	+	0.403749i
$305$	−15.6688	+	27.1391i	−0.897192	+	1.55398i
$306$	21.2538	+	36.8126i	1.21500	+	2.10444i
$307$	3.69550			0.210914			0.105457	−	0.994424i	$-0.466370\pi$
$307$	3.69550			0.210914			0.105457	+	0.994424i	$0.466370\pi$
$308$	0.0514847	+	0.0361403i	0.00293361	+	0.00205928i
$309$	−42.6739			−2.42763
$310$	4.47923	+	7.75825i	0.254403	+	0.440639i
$311$	15.2755	−	26.4579i	0.866193	−	1.50029i	0.000335541	−	1.00000i	$-0.499893\pi$
$311$	15.2755	−	26.4579i	0.866193	−	1.50029i	0.865858	−	0.500291i	$-0.166773\pi$
$312$	4.69069	−	8.12451i	0.265558	−	0.459960i
$313$	−10.3631	−	17.9495i	−0.585759	−	1.01456i	−0.994780	−	0.102040i	$-0.967463\pi$
$313$	−10.3631	−	17.9495i	−0.585759	−	1.01456i	0.409021	−	0.912525i	$-0.365870\pi$
$314$	−8.23562			−0.464763
$315$	3.99007	−	44.9970i	0.224815	−	2.53529i
$316$	0.359777			0.0202390
$317$	−1.00509	−	1.74087i	−0.0564517	−	0.0977772i	0.836419	−	0.548091i	$-0.184645\pi$
$317$	−1.00509	−	1.74087i	−0.0564517	−	0.0977772i	−0.892870	+	0.450314i	$0.851312\pi$
$318$	−28.1099	+	48.6877i	−1.57632	+	2.73027i
$319$	0.937817	−	1.62435i	0.0525077	−	0.0909460i
$320$	8.77472	+	15.1983i	0.490522	+	0.849609i
$321$	17.5882			0.981676
$322$	−1.72251	+	19.4252i	−0.0959919	+	1.08252i
$323$	7.89931			0.439529
$324$	0.349166	+	0.604773i	0.0193981	+	0.0335985i
$325$	−0.148763	+	0.257665i	−0.00825189	+	0.0142927i
$326$	3.28550	−	5.69066i	0.181967	−	0.315177i
$327$	−1.98432	−	3.43694i	−0.109733	−	0.190063i
$328$	15.5563			0.858951
$329$	−16.2183	−	11.3846i	−0.894145	−	0.627656i
$330$	10.0523			0.553363
$331$	2.57336	+	4.45718i	0.141444	+	0.244989i	0.928041	−	0.372479i	$-0.121492\pi$
$331$	2.57336	+	4.45718i	0.141444	+	0.244989i	−0.786596	+	0.617468i	$0.788159\pi$
$332$	−0.0827190	+	0.143273i	−0.00453979	+	0.00786315i
$333$	40.6995	−	70.4936i	2.23032	−	3.86303i
$334$	−8.94679	−	15.4963i	−0.489546	−	0.847919i
$335$	19.3344			1.05635
$336$	31.2646	−	14.5342i	1.70562	−	0.792904i
$337$	−20.5188			−1.11773			−0.558864	−	0.829259i	$-0.688763\pi$
$337$	−20.5188			−1.11773			−0.558864	+	0.829259i	$0.688763\pi$
$338$	−0.702891	−	1.21744i	−0.0382322	−	0.0662202i
$339$	−0.185545	+	0.321373i	−0.0100774	+	0.0174546i
$340$	0.0989991	−	0.171472i	0.00536898	−	0.00929935i
$341$	−1.46934	−	2.54497i	−0.0795692	−	0.137818i
$342$	−22.7669			−1.23109
$343$	4.85650	−	17.8722i	0.262226	−	0.965006i
$344$	3.85411			0.207799
$345$	−18.7464	−	32.4698i	−1.00927	−	1.74811i
$346$	−1.88141	+	3.25869i	−0.101145	+	0.175188i
$347$	−9.85849	+	17.0754i	−0.529231	+	0.916656i	0.470187	+	0.882567i	$0.344186\pi$
$347$	−9.85849	+	17.0754i	−0.529231	+	0.916656i	−0.999419	+	0.0340891i	$0.989147\pi$
$348$	0.0735236	+	0.127347i	0.00394128	+	0.00682650i
$349$	−1.76193			−0.0943138			−0.0471569	−	0.998887i	$-0.515016\pi$
$349$	−1.76193			−0.0943138			−0.0471569	+	0.998887i	$0.515016\pi$
$350$	−1.00347	+	0.466491i	−0.0536379	+	0.0249350i
$351$	16.0706			0.857788
$352$	−0.0672426	−	0.116468i	−0.00358404	−	0.00620774i
$353$	−8.14472	+	14.1071i	−0.433500	+	0.750843i	−0.997172	−	0.0751552i	$-0.976055\pi$
$353$	−8.14472	+	14.1071i	−0.433500	+	0.750843i	0.563672	+	0.825999i	$0.309388\pi$
$354$	−19.9069	+	34.4798i	−1.05804	+	1.83258i
$355$	6.58091	+	11.3985i	0.349279	+	0.604968i
$356$	0.363672			0.0192746
$357$	−27.4231	−	19.2500i	−1.45139	−	1.01882i
$358$	29.9914			1.58509
$359$	−15.5734	−	26.9739i	−0.821931	−	1.42363i	−0.904242	−	0.427020i	$-0.859563\pi$
$359$	−15.5734	−	26.9739i	−0.821931	−	1.42363i	0.0823110	−	0.996607i	$-0.473770\pi$
$360$	−24.2876	+	42.0674i	−1.28007	+	2.21715i
$361$	7.38458	−	12.7905i	0.388662	−	0.673182i
$362$	−4.02468	−	6.97095i	−0.211532	−	0.366385i
$363$	−3.29751			−0.173074
$364$	−0.00555607	+	0.0626572i	−0.000291217	+	0.00328413i
$365$	−19.6452			−1.02828
$366$	−33.4947	−	58.0146i	−1.75080	−	3.03247i
$367$	−18.2992	+	31.6952i	−0.955212	+	1.65448i	−0.221329	+	0.975199i	$0.571040\pi$
$367$	−18.2992	+	31.6952i	−0.955212	+	1.65448i	−0.733883	+	0.679276i	$0.762294\pi$
$368$	10.3603	−	17.9446i	0.540070	−	0.935428i
$369$	21.5262	+	37.2844i	1.12061	+	1.94095i
$370$	31.5158			1.63843
$371$	2.83419	−	31.9619i	0.147144	−	1.65938i
$372$	0.230388			0.0119451
$373$	−14.8537	−	25.7274i	−0.769098	−	1.33212i	−0.938053	−	0.346492i	$-0.887373\pi$
$373$	−14.8537	−	25.7274i	−0.769098	−	1.33212i	0.168955	−	0.985624i	$-0.445961\pi$
$374$	2.69938	−	4.67546i	0.139582	−	0.241762i
$375$	18.9405	−	32.8060i	0.978085	−	1.69409i
$376$	10.6537	+	18.4528i	0.549423	+	0.951629i
$377$	1.87563			0.0966001
$378$	48.9223	+	34.3416i	2.51629	+	1.76634i
$379$	−34.8737			−1.79134			−0.895671	−	0.444717i	$-0.853304\pi$
$379$	−34.8737			−1.79134			−0.895671	+	0.444717i	$0.853304\pi$
$380$	0.0530236	+	0.0918395i	0.00272005	+	0.00471127i
$381$	7.82957	−	13.5612i	0.401121	−	0.694762i
$382$	2.50265	−	4.33472i	0.128047	−	0.221783i
$383$	16.7952	+	29.0902i	0.858196	+	1.48644i	0.873648	+	0.486558i	$0.161748\pi$
$383$	16.7952	+	29.0902i	0.858196	+	1.48644i	−0.0154524	+	0.999881i	$0.504919\pi$
$384$	−36.6280			−1.86917
$385$	−5.20266	+	2.41860i	−0.265152	+	0.123263i
$386$	−9.24249			−0.470430
$387$	5.33316	+	9.23731i	0.271100	+	0.469559i
$388$	0.0572700	−	0.0991946i	0.00290745	−	0.00503584i
$389$	−10.5667	+	18.3020i	−0.535752	+	0.927950i	0.463374	+	0.886163i	$0.346639\pi$
$389$	−10.5667	+	18.3020i	−0.535752	+	0.927950i	−0.999127	+	0.0417876i	$0.986695\pi$
$390$	5.02617	+	8.70559i	0.254510	+	0.440825i
$391$	−20.1361			−1.01833
$392$	−12.8369	+	15.2256i	−0.648362	+	0.769007i
$393$	61.1196			3.08308
$394$	−14.5525	−	25.2058i	−0.733147	−	1.26985i
$395$	−16.4076	+	28.4187i	−0.825555	+	1.42990i
$396$	0.0935975	−	0.162116i	0.00470345	−	0.00814662i
$397$	13.3636	+	23.1465i	0.670701	+	1.16169i	0.977706	+	0.209980i	$0.0673399\pi$
$397$	13.3636	+	23.1465i	0.670701	+	1.16169i	−0.307005	+	0.951708i	$0.599327\pi$
$398$	−14.5057			−0.727104
$399$	16.2728	−	7.56484i	0.814658	−	0.378715i
$400$	1.17579			0.0587894
$401$	11.4148	+	19.7710i	0.570027	+	0.987316i	0.996562	+	0.0828454i	$0.0264008\pi$
$401$	11.4148	+	19.7710i	0.570027	+	0.987316i	−0.426535	+	0.904471i	$0.640266\pi$
$402$	−20.6653	+	35.7934i	−1.03069	+	1.78521i
$403$	1.46934	−	2.54497i	0.0731930	−	0.126774i
$404$	0.0445341	+	0.0771353i	0.00221565	+	0.00383763i
$405$	−63.6946			−3.16501
$406$	5.70981	+	4.00807i	0.283373	+	0.198917i
$407$	−10.3383			−0.512449
$408$	18.0141	+	31.2013i	0.891830	+	1.54470i
$409$	−8.36853	+	14.4947i	−0.413797	+	0.716718i	−0.995301	−	0.0968256i	$-0.969131\pi$
$409$	−8.36853	+	14.4947i	−0.413797	+	0.716718i	0.581504	+	0.813543i	$0.302464\pi$
$410$	−8.33444	+	14.4357i	−0.411609	+	0.712927i
$411$	14.0055	+	24.2583i	0.690843	+	1.19657i
$412$	−0.307680			−0.0151583
$413$	2.00712	−	22.6348i	0.0987642	−	1.11379i
$414$	58.0349			2.85226
$415$	−7.54477	−	13.0679i	−0.370358	−	0.641479i
$416$	0.0672426	−	0.116468i	0.00329684	−	0.00571029i
$417$	−3.08622	+	5.34548i	−0.151133	+	0.261769i
$418$	1.44578	+	2.50416i	0.0707153	+	0.122482i
$419$	35.6805			1.74311			0.871554	−	0.490299i	$-0.163112\pi$
$419$	35.6805			1.74311			0.871554	+	0.490299i	$0.163112\pi$
$420$	0.0397298	−	0.448043i	0.00193862	−	0.0218623i
$421$	−6.84814			−0.333758			−0.166879	−	0.985977i	$-0.553369\pi$
$421$	−6.84814			−0.333758			−0.166879	+	0.985977i	$0.553369\pi$
$422$	−6.55422	−	11.3522i	−0.319054	−	0.552618i
$423$	−29.4844	+	51.0685i	−1.43358	+	2.48303i
$424$	−17.2518	+	29.8810i	−0.837822	+	1.45115i
$425$	−0.571308	−	0.989535i	−0.0277125	−	0.0479995i
$426$	−28.1357			−1.36318
$427$	31.2937	+	21.9670i	1.51441	+	1.06306i
$428$	0.126811			0.00612965
$429$	−1.64875	−	2.85573i	−0.0796026	−	0.137876i
$430$	−2.06488	+	3.57647i	−0.0995773	+	0.172473i
$431$	10.2388	−	17.7341i	0.493185	−	0.854222i	−0.506784	−	0.862073i	$-0.669166\pi$
$431$	10.2388	−	17.7341i	0.493185	−	0.854222i	0.999969	+	0.00785094i	$0.00249906\pi$
$432$	−31.7547	−	55.0007i	−1.52780	−	2.64622i
$433$	28.5733			1.37314			0.686572	−	0.727062i	$-0.259115\pi$
$433$	28.5733			1.37314			0.686572	+	0.727062i	$0.259115\pi$
$434$	9.91135	−	4.60755i	0.475760	−	0.221170i
$435$	−13.4121			−0.643062
$436$	−0.0143070	−	0.0247804i	−0.000685180	−	0.00118677i
$437$	5.39241	−	9.33992i	0.257954	−	0.446789i
$438$	20.9975	−	36.3687i	1.00330	−	1.73776i
$439$	2.28851	+	3.96382i	0.109225	+	0.189183i	0.915456	−	0.402417i	$-0.131830\pi$
$439$	2.28851	+	3.96382i	0.109225	+	0.189183i	−0.806232	+	0.591600i	$0.798497\pi$
$440$	6.16941			0.294115
$441$	−54.2550	−	9.69829i	−2.58357	−	0.461823i
$442$	5.39876			0.256793
$443$	−3.74765	−	6.49111i	−0.178056	−	0.308402i	0.763159	−	0.646211i	$-0.223647\pi$
$443$	−3.74765	−	6.49111i	−0.178056	−	0.308402i	−0.941215	+	0.337809i	$0.890314\pi$
$444$	0.405253	−	0.701919i	0.0192324	−	0.0333116i
$445$	−16.5852	+	28.7264i	−0.786213	+	1.36176i
$446$	−0.601568	−	1.04195i	−0.0284851	−	0.0493376i
$447$	−3.30345			−0.156248
$448$	19.4161	−	9.02610i	0.917326	−	0.426443i
$449$	−19.4295			−0.916937			−0.458468	−	0.888711i	$-0.651602\pi$
$449$	−19.4295			−0.916937			−0.458468	+	0.888711i	$0.651602\pi$
$450$	1.64659	+	2.85197i	0.0776209	+	0.134443i
$451$	2.73398	−	4.73539i	0.128738	−	0.222981i
$452$	−0.00133778	+	0.00231711i	−6.29240e−5	+	0.000108988i
$453$	−17.0534	−	29.5374i	−0.801240	−	1.38779i
$454$	−10.4545			−0.490656
$455$	−4.69590	−	3.29634i	−0.220147	−	0.154535i
$456$	−19.2966			−0.903644
$457$	−4.99384	−	8.64958i	−0.233602	−	0.404610i	0.725264	−	0.688471i	$-0.241718\pi$
$457$	−4.99384	−	8.64958i	−0.233602	−	0.404610i	−0.958865	+	0.283861i	$0.908385\pi$
$458$	−8.21994	+	14.2373i	−0.384092	+	0.665268i
$459$	−30.8588	+	53.4490i	−1.44037	+	2.49479i
$460$	−0.135162	−	0.234108i	−0.00630197	−	0.0109153i
$461$	35.4990			1.65335			0.826677	−	0.562677i	$-0.190229\pi$
$461$	35.4990			1.65335			0.826677	+	0.562677i	$0.190229\pi$
$462$	1.08330	−	12.2167i	0.0503997	−	0.568371i
$463$	−31.8344			−1.47947			−0.739735	−	0.672898i	$-0.765049\pi$
$463$	−31.8344			−1.47947			−0.739735	+	0.672898i	$0.765049\pi$
$464$	−3.70615	−	6.41923i	−0.172053	−	0.298005i
$465$	−10.5068	+	18.1983i	−0.487242	+	0.843928i
$466$	−16.3222	+	28.2709i	−0.756113	+	1.30963i
$467$	−6.32236	−	10.9506i	−0.292564	−	0.506736i	0.681851	−	0.731491i	$-0.261175\pi$
$467$	−6.32236	−	10.9506i	−0.292564	−	0.506736i	−0.974415	+	0.224755i	$0.927842\pi$
$468$	0.187195			0.00865309
$469$	2.08359	−	23.4972i	0.0962113	−	1.08500i
$470$	−22.8314			−1.05313
$471$	−9.65904	−	16.7300i	−0.445065	−	0.770876i
$472$	−12.2174	+	21.1612i	−0.562353	+	0.974023i
$473$	0.677350	−	1.17320i	0.0311446	−	0.0539440i
$474$	−35.0740	−	60.7500i	−1.61100	−	2.79034i
$475$	0.611981			0.0280796
$476$	−0.197721	−	0.138793i	−0.00906254	−	0.00636156i
$477$	−95.4896			−4.37217
$478$	20.1989	+	34.9855i	0.923877	+	1.60020i
$479$	1.80256	−	3.12213i	0.0823611	−	0.142654i	−0.821903	−	0.569628i	$-0.807087\pi$
$479$	1.80256	−	3.12213i	0.0823611	−	0.142654i	0.904264	+	0.426974i	$0.140421\pi$
$480$	−0.480832	+	0.832826i	−0.0219469	+	0.0380131i
$481$	−5.16913	−	8.95320i	−0.235692	−	0.408231i
$482$	12.7599			0.581195
$483$	−41.4809	+	19.2835i	−1.88745	+	0.877429i
$484$	−0.0237751			−0.00108069
$485$	5.22358	+	9.04750i	0.237190	+	0.410826i
$486$	34.1913	−	59.2211i	1.55095	−	2.68632i
$487$	8.62917	−	14.9462i	0.391025	−	0.677275i	−0.601560	−	0.798828i	$-0.705454\pi$
$487$	8.62917	−	14.9462i	0.391025	−	0.677275i	0.992585	+	0.121553i	$0.0387873\pi$
$488$	−20.5567	−	35.6052i	−0.930556	−	1.61177i
$489$	15.4135			0.697020
$490$	−7.25126	−	20.0695i	−0.327579	−	0.906646i
$491$	−3.97042			−0.179183			−0.0895913	−	0.995979i	$-0.528556\pi$
$491$	−3.97042			−0.179183			−0.0895913	+	0.995979i	$0.528556\pi$
$492$	0.214340	+	0.371248i	0.00966320	+	0.0167372i
$493$	−3.60159	+	6.23813i	−0.162207	+	0.280951i
$494$	−1.44578	+	2.50416i	−0.0650486	+	0.112668i
$495$	8.53699	+	14.7865i	0.383709	+	0.664604i
$496$	−11.6133			−0.521453
$497$	14.5618	−	6.76944i	0.653187	−	0.303651i
$498$	32.2565			1.44545
$499$	−4.11507	−	7.12751i	−0.184216	−	0.319071i	0.759096	−	0.650978i	$-0.225641\pi$
$499$	−4.11507	−	7.12751i	−0.184216	−	0.319071i	−0.943312	+	0.331907i	$0.892308\pi$
$500$	0.136562	−	0.236532i	0.00610722	−	0.0105780i
$501$	20.9863	−	36.3493i	0.937597	−	1.62397i
$502$	9.31540	+	16.1347i	0.415767	+	0.720129i
$503$	−2.07009			−0.0923008			−0.0461504	−	0.998935i	$-0.514695\pi$
$503$	−2.07009			−0.0923008			−0.0461504	+	0.998935i	$0.514695\pi$
$504$	48.5073	+	34.0503i	2.16069	+	1.51672i
$505$	−8.12388			−0.361508
$506$	−3.68542	−	6.38334i	−0.163837	−	0.283774i
$507$	1.64875	−	2.85573i	0.0732238	−	0.126827i
$508$	0.0564513	−	0.0977766i	0.00250462	−	0.00433813i
$509$	−5.88016	−	10.1847i	−0.260633	−	0.451430i	0.705777	−	0.708434i	$-0.250598\pi$
$509$	−5.88016	−	10.1847i	−0.260633	−	0.451430i	−0.966410	+	0.257004i	$0.917265\pi$
$510$	−38.6050			−1.70946
$511$	−2.11708	+	23.8749i	−0.0936543	+	1.05616i
$512$	−23.0176			−1.01724
$513$	−16.5279	−	28.6271i	−0.729723	−	1.26392i
$514$	−0.234049	+	0.405385i	−0.0103235	+	0.0178808i
$515$	14.0317	−	24.3036i	0.618309	−	1.07094i
$516$	0.0531033	+	0.0919777i	0.00233774	+	0.00404909i
$517$	7.48946			0.329386
$518$	3.39634	−	38.3013i	0.149226	−	1.68286i
$519$	−8.82634			−0.387434
$520$	3.08471	+	5.34287i	0.135273	+	0.234300i
$521$	−2.45386	+	4.25021i	−0.107506	+	0.186205i	−0.914759	−	0.404000i	$-0.867620\pi$
$521$	−2.45386	+	4.25021i	−0.107506	+	0.186205i	0.807254	+	0.590205i	$0.200953\pi$
$522$	10.3803	−	17.9791i	0.454332	−	0.786925i
$523$	10.5043	+	18.1941i	0.459323	+	0.795570i	0.998925	−	0.0463495i	$-0.0147588\pi$
$523$	10.5043	+	18.1941i	0.459323	+	0.795570i	−0.539603	+	0.841920i	$0.681425\pi$
$524$	0.440674			0.0192509
$525$	−2.12455	−	1.49135i	−0.0927228	−	0.0650879i
$526$	−19.0823			−0.832029
$527$	5.64284	+	9.77368i	0.245806	+	0.425748i
$528$	−6.51569	+	11.2855i	−0.283559	+	0.491139i
$529$	−2.24576	+	3.88977i	−0.0976417	+	0.169120i
$530$	−18.4857	−	32.0182i	−0.802967	−	1.39078i
$531$	−67.6240			−2.93463
$532$	0.117327	−	0.0545426i	0.00508678	−	0.00236472i
$533$	5.46796			0.236844
$534$	−35.4537	−	61.4076i	−1.53423	−	2.65737i
$535$	−5.78320	+	10.0168i	−0.250029	+	0.433064i
$536$	−12.6829	+	21.9674i	−0.547817	+	0.948847i
$537$	35.1750	+	60.9249i	1.51791	+	2.62910i
$538$	43.1194			1.85901
$539$	2.37866	+	6.58346i	0.102456	+	0.283570i
$540$	−0.828551			−0.0356551
$541$	−7.94427	−	13.7599i	−0.341551	−	0.591583i	0.643170	−	0.765723i	$-0.277619\pi$
$541$	−7.94427	−	13.7599i	−0.341551	−	0.591583i	−0.984721	+	0.174140i	$0.944285\pi$
$542$	−12.8828	+	22.3137i	−0.553365	+	0.958457i
$543$	9.44059	−	16.3516i	0.405134	−	0.701713i
$544$	0.258238	+	0.447281i	0.0110719	+	0.0191770i
$545$	2.60987			0.111794
$546$	11.1216	−	5.17016i	0.475960	−	0.221263i
$547$	26.4260			1.12989			0.564947	−	0.825127i	$-0.308897\pi$
$547$	26.4260			1.12989			0.564947	+	0.825127i	$0.308897\pi$
$548$	0.100980	+	0.174903i	0.00431366	+	0.00747148i
$549$	56.8910	−	98.5382i	2.42805	−	4.20551i
$550$	0.209128	−	0.362221i	0.00891727	−	0.0154452i
$551$	−1.92900	−	3.34112i	−0.0821780	−	0.142337i
$552$	49.1888			2.09361
$553$	32.7692	+	23.0028i	1.39349	+	0.978177i
$554$	24.6646			1.04790
$555$	36.9630	+	64.0217i	1.56899	+	2.71757i
$556$	−0.0222517	+	0.0385410i	−0.000943681	+	0.00163450i
$557$	−21.6295	+	37.4634i	−0.916471	+	1.58737i	−0.111738	+	0.993738i	$0.535642\pi$
$557$	−21.6295	+	37.4634i	−0.916471	+	1.58737i	−0.804733	+	0.593637i	$0.797692\pi$
$558$	−16.2634	−	28.1691i	−0.688485	−	1.19249i
$559$	1.35470			0.0572977
$560$	−2.00268	+	22.5848i	−0.0846289	+	0.954381i
$561$	12.6637			0.534663
$562$	15.3635	+	26.6104i	0.648070	+	1.12249i
$563$	−4.09500	+	7.09275i	−0.172584	+	0.298924i	−0.939322	−	0.343036i	$-0.888545\pi$
$563$	−4.09500	+	7.09275i	−0.172584	+	0.298924i	0.766739	+	0.641959i	$0.221878\pi$
$564$	−0.293582	+	0.508498i	−0.0123620	+	0.0214116i
$565$	−0.122019	−	0.211343i	−0.00513337	−	0.00889125i
$566$	6.30920			0.265195
$567$	−6.86411	+	77.4083i	−0.288266	+	3.25084i
$568$	−17.2677			−0.724535
$569$	1.11414	+	1.92975i	0.0467072	+	0.0808992i	0.888434	−	0.459005i	$-0.151794\pi$
$569$	1.11414	+	1.92975i	0.0467072	+	0.0808992i	−0.841727	+	0.539904i	$0.818461\pi$
$570$	10.3383	−	17.9065i	0.433025	−	0.750022i
$571$	7.78741	−	13.4882i	0.325893	−	0.564463i	−0.655800	−	0.754935i	$-0.727668\pi$
$571$	7.78741	−	13.4882i	0.325893	−	0.564463i	0.981693	+	0.190472i	$0.0610018\pi$
$572$	−0.0118876	−	0.0205898i	−0.000497044	−	0.000860905i
$573$	11.7408			0.490479
$574$	16.6456	+	11.6846i	0.694773	+	0.487704i
$575$	−1.56000			−0.0650564
$576$	−31.8597	−	55.1827i	−1.32749	−	2.29928i
$577$	−18.3286	+	31.7462i	−0.763032	+	1.32161i	0.178249	+	0.983985i	$0.442957\pi$
$577$	−18.3286	+	31.7462i	−0.763032	+	1.32161i	−0.941281	+	0.337624i	$0.890377\pi$
$578$	1.58247	−	2.74093i	0.0658222	−	0.114007i
$579$	−10.8399	−	18.7753i	−0.450492	−	0.780276i
$580$	−0.0967017			−0.00401532
$581$	−16.6946	+	7.76091i	−0.692607	+	0.321977i
$582$	−22.3326			−0.925716
$583$	6.06393	+	10.5030i	0.251143	+	0.434992i
$584$	12.8867	−	22.3205i	0.533257	−	0.923629i
$585$	−8.53699	+	14.7865i	−0.352961	+	0.611347i
$586$	0.323451	+	0.560233i	0.0133616	+	0.0231430i
$587$	−3.80315			−0.156973			−0.0784863	−	0.996915i	$-0.525009\pi$
$587$	−3.80315			−0.156973			−0.0784863	+	0.996915i	$0.525009\pi$
$588$	−0.540227	−	0.0965677i	−0.0222786	−	0.00398238i
$589$	−6.04457			−0.249062
$590$	−13.0912	−	22.6747i	−0.538958	−	0.933502i
$591$	34.1356	−	59.1245i	1.40415	−	2.43206i
$592$	−20.4278	+	35.3820i	−0.839578	+	1.45419i
$593$	21.5636	+	37.3493i	0.885512	+	1.53375i	0.845125	+	0.534568i	$0.179526\pi$
$593$	21.5636	+	37.3493i	0.885512	+	1.53375i	0.0403867	+	0.999184i	$0.487141\pi$
$594$	−22.5918			−0.926954
$595$	19.9803	−	9.28836i	0.819112	−	0.380786i
$596$	−0.0238179			−0.000975621
$597$	−17.0128	−	29.4670i	−0.696288	−	1.20601i
$598$	3.68542	−	6.38334i	0.150708	−	0.261034i
$599$	6.99812	−	12.1211i	0.285935	−	0.495255i	−0.686900	−	0.726752i	$-0.741029\pi$
$599$	6.99812	−	12.1211i	0.285935	−	0.495255i	0.972836	+	0.231497i	$0.0743624\pi$
$600$	1.39560	+	2.41725i	0.0569752	+	0.0986839i
$601$	−14.5293			−0.592664			−0.296332	−	0.955085i	$-0.595763\pi$
$601$	−14.5293			−0.592664			−0.296332	+	0.955085i	$0.595763\pi$
$602$	4.12398	+	2.89488i	0.168081	+	0.117986i
$603$	−70.2003			−2.85878
$604$	−0.122956	−	0.212965i	−0.00500299	−	0.00866543i
$605$	1.08426	−	1.87799i	0.0440814	−	0.0763512i
$606$	8.68309	−	15.0396i	0.352727	−	0.610940i
$607$	−7.51636	−	13.0187i	−0.305080	−	0.528414i	0.672199	−	0.740370i	$-0.265350\pi$
$607$	−7.51636	−	13.0187i	−0.305080	−	0.528414i	−0.977279	+	0.211957i	$0.932016\pi$
$608$	−0.276623			−0.0112185
$609$	−1.44537	+	16.2998i	−0.0585694	+	0.660502i
$610$	44.0538			1.78369
$611$	3.74473	+	6.48606i	0.151496	+	0.262398i
$612$	−0.359451	+	0.622588i	−0.0145300	+	0.0251666i
$613$	−17.7771	+	30.7908i	−0.718009	+	1.24363i	0.243778	+	0.969831i	$0.421613\pi$
$613$	−17.7771	+	30.7908i	−0.718009	+	1.24363i	−0.961787	+	0.273797i	$0.911720\pi$
$614$	−2.59754	−	4.49907i	−0.104828	−	0.181568i
$615$	−39.0998			−1.57666
$616$	0.664853	−	7.49771i	0.0267877	−	0.302091i
$617$	4.47445			0.180134			0.0900672	−	0.995936i	$-0.471292\pi$
$617$	4.47445			0.180134			0.0900672	+	0.995936i	$0.471292\pi$
$618$	29.9951	+	51.9530i	1.20658	+	2.08986i
$619$	−10.4608	+	18.1186i	−0.420454	+	0.728248i	−0.995984	−	0.0895330i	$-0.971463\pi$
$619$	−10.4608	+	18.1186i	−0.420454	+	0.728248i	0.575530	+	0.817781i	$0.304796\pi$
$620$	−0.0757544	+	0.131210i	−0.00304237	+	0.00526954i
$621$	42.1311	+	72.9732i	1.69066	+	2.92831i
$622$	−42.9480			−1.72206
$623$	33.1240	+	23.2518i	1.32708	+	0.931562i
$624$	−13.0314			−0.521673
$625$	11.7119	+	20.2856i	0.468477	+	0.811426i
$626$	−14.5683	+	25.2331i	−0.582267	+	1.00852i
$627$	−3.39133	+	5.87395i	−0.135436	+	0.234583i
$628$	−0.0696419	−	0.120623i	−0.00277901	−	0.00481339i
$629$	39.7030			1.58306
$630$	−57.5858	+	26.7703i	−2.29427	+	1.06655i
$631$	−18.5687			−0.739208			−0.369604	−	0.929189i	$-0.620507\pi$
$631$	−18.5687			−0.739208			−0.369604	+	0.929189i	$0.620507\pi$
$632$	−21.5259	−	37.2840i	−0.856255	−	1.48308i
$633$	15.3741	−	26.6287i	0.611064	−	1.05839i
$634$	−1.41294	+	2.44729i	−0.0561151	+	0.0971943i
$635$	5.14891	+	8.91817i	0.204328	+	0.353907i
$636$	−0.950809			−0.0377020
$637$	−4.51212	+	5.35171i	−0.178777	+	0.212042i
$638$	−2.63673			−0.104389
$639$	−23.8943	−	41.3862i	−0.945244	−	1.63721i
$640$	12.0437	−	20.8603i	0.476070	−	0.824577i
$641$	11.9956	−	20.7769i	0.473797	−	0.820640i	−0.525753	−	0.850637i	$-0.676217\pi$
$641$	11.9956	−	20.7769i	0.473797	−	0.820640i	0.999550	+	0.0299972i	$0.00954984\pi$
$642$	−12.3626	−	21.4126i	−0.487912	−	0.845088i
$643$	−15.9506			−0.629031			−0.314516	−	0.949252i	$-0.601842\pi$
$643$	−15.9506			−0.629031			−0.314516	+	0.949252i	$0.601842\pi$
$644$	−0.299078	+	0.139034i	−0.0117853	+	0.00547872i
$645$	−9.68707			−0.381428
$646$	−5.55236	−	9.61696i	−0.218454	−	0.378374i
$647$	5.76001	−	9.97663i	0.226449	−	0.392222i	−0.730304	−	0.683122i	$-0.760622\pi$
$647$	5.76001	−	9.97663i	0.226449	−	0.392222i	0.956753	+	0.290900i	$0.0939549\pi$
$648$	41.7821	−	72.3687i	1.64135	−	2.84291i
$649$	4.29437	+	7.43806i	0.168569	+	0.291970i
$650$	0.418257			0.0164054
$651$	20.9842	+	14.7301i	0.822438	+	0.577320i
$652$	0.111131			0.00435224
$653$	17.4201	+	30.1725i	0.681701	+	1.18074i	0.974461	+	0.224555i	$0.0720930\pi$
$653$	17.4201	+	30.1725i	0.681701	+	1.18074i	−0.292760	+	0.956186i	$0.594574\pi$
$654$	−2.78952	+	4.83159i	−0.109079	+	0.188930i
$655$	−20.0968	+	34.8087i	−0.785248	+	1.36009i
$656$	−10.8044	−	18.7137i	−0.421840	−	0.730648i
$657$	71.3288			2.78280
$658$	−2.46045	+	27.7471i	−0.0959181	+	1.08169i
$659$	−1.48810			−0.0579681			−0.0289841	−	0.999580i	$-0.509227\pi$
$659$	−1.48810			−0.0579681			−0.0289841	+	0.999580i	$0.509227\pi$
$660$	0.0850045	+	0.147232i	0.00330879	+	0.00573100i
$661$	−8.95835	+	15.5163i	−0.348440	+	0.603515i	−0.985972	−	0.166908i	$-0.946622\pi$
$661$	−8.95835	+	15.5163i	−0.348440	+	0.603515i	0.637533	+	0.770423i	$0.279955\pi$
$662$	3.61758	−	6.26583i	0.140601	−	0.243528i
$663$	6.33187	+	10.9671i	0.245909	+	0.425927i
$664$	19.7967			0.768261
$665$	−1.04237	+	11.7551i	−0.0404213	+	0.455842i
$666$	−114.429			−4.43405
$667$	4.91720	+	8.51683i	0.190395	+	0.329773i
$668$	0.151311	−	0.262079i	0.00585441	−	0.0101401i
$669$	1.41108	−	2.44407i	0.0545556	−	0.0944931i
$670$	−13.5900	−	23.5385i	−0.525027	−	0.909373i
$671$	−14.4511			−0.557880
$672$	0.960320	+	0.674108i	0.0370451	+	0.0260043i
$673$	44.5476			1.71718			0.858591	−	0.512661i	$-0.171340\pi$
$673$	44.5476			1.71718			0.858591	+	0.512661i	$0.171340\pi$
$674$	14.4225	+	24.9805i	0.555533	+	0.962211i
$675$	−2.39072	+	4.14084i	−0.0920187	+	0.159381i
$676$	0.0118876	−	0.0205898i	0.000457214	−	0.000791917i
$677$	4.15367	+	7.19436i	0.159638	+	0.276502i	0.934738	−	0.355337i	$-0.115634\pi$
$677$	4.15367	+	7.19436i	0.159638	+	0.276502i	−0.775100	+	0.631839i	$0.782301\pi$
$678$	0.521672			0.0200347
$679$	11.5584	−	5.37322i	0.443570	−	0.206205i
$680$	−23.6930			−0.908584
$681$	−12.2615	−	21.2375i	−0.469861	−	0.813822i
$682$	−2.06557	+	3.57767i	−0.0790948	+	0.136996i
$683$	7.65131	−	13.2525i	0.292769	−	0.507091i	−0.681694	−	0.731637i	$-0.738757\pi$
$683$	7.65131	−	13.2525i	0.292769	−	0.507091i	0.974463	+	0.224546i	$0.0720899\pi$
$684$	−0.192521	−	0.333456i	−0.00736121	−	0.0127500i
$685$	−18.4207			−0.703821
$686$	−25.1719	+	6.64968i	−0.961069	+	0.253886i
$687$	−38.5626			−1.47126
$688$	−2.67681	−	4.63637i	−0.102052	−	0.176760i
$689$	−6.06393	+	10.5030i	−0.231018	+	0.400134i
$690$	−26.3534	+	45.6454i	−1.00326	+	1.73769i
$691$	23.8847	+	41.3695i	0.908616	+	1.57377i	0.815989	+	0.578068i	$0.196193\pi$
$691$	23.8847	+	41.3695i	0.908616	+	1.57377i	0.0926270	+	0.995701i	$0.470474\pi$
$692$	−0.0636381			−0.00241916
$693$	18.8901	−	8.78156i	0.717576	−	0.333584i
$694$	27.7178			1.05215
$695$	−2.02957	−	3.51531i	−0.0769859	−	0.133343i
$696$	8.79802	−	15.2386i	0.333488	−	0.577618i
$697$	−10.4996	+	18.1858i	−0.397699	+	0.688835i
$698$	1.23844	+	2.14505i	0.0468758	+	0.0811912i
$699$	−76.5733			−2.89627
$700$	−0.0153180	−	0.0107527i	−0.000578967	−	0.000406413i
$701$	−45.7603			−1.72834			−0.864171	−	0.503199i	$-0.832156\pi$
$701$	−45.7603			−1.72834			−0.864171	+	0.503199i	$0.832156\pi$
$702$	−11.2959	−	19.5651i	−0.426337	−	0.738437i
$703$	−10.6324	+	18.4158i	−0.401008	+	0.694566i
$704$	−4.04641	+	7.00859i	−0.152505	+	0.264146i
$705$	−26.7775	−	46.3800i	−1.00850	−	1.74677i
$706$	22.8994			0.861831
$707$	−0.875478	+	9.87299i	−0.0329257	+	0.371312i
$708$	−0.673345			−0.0253059
$709$	−1.35860	−	2.35317i	−0.0510233	−	0.0883750i	0.839386	−	0.543536i	$-0.182915\pi$
$709$	−1.35860	−	2.35317i	−0.0510233	−	0.0883750i	−0.890409	+	0.455161i	$0.849582\pi$
$710$	9.25133	−	16.0238i	0.347196	−	0.601362i
$711$	59.5735	−	103.184i	2.23418	−	3.86971i
$712$	−21.7589	−	37.6876i	−0.815450	−	1.41240i
$713$	15.4082			0.577041
$714$	−4.16030	+	46.9168i	−0.155695	+	1.75582i
$715$	2.16852			0.0810980
$716$	0.253613	+	0.439270i	0.00947795	+	0.0164163i
$717$	−47.3801	+	82.0647i	−1.76944	+	3.06476i
$718$	−21.8928	+	37.9194i	−0.817031	+	1.41514i
$719$	7.46856	+	12.9359i	0.278530	+	0.482428i	0.971020	−	0.239000i	$-0.0768195\pi$
$719$	7.46856	+	12.9359i	0.278530	+	0.482428i	−0.692490	+	0.721428i	$0.743486\pi$
$720$	67.4744			2.51462
$721$	−28.0241	−	19.6718i	−1.04367	−	0.732618i
$722$	−20.7622			−0.772690
$723$	14.9652	+	25.9205i	0.556563	+	0.963995i
$724$	0.0680668	−	0.117895i	0.00252968	−	0.00438154i
$725$	−0.279025	+	0.483285i	−0.0103627	+	0.0179488i
$726$	2.31779	+	4.01453i	0.0860213	+	0.148993i
$727$	−2.18770			−0.0811374			−0.0405687	−	0.999177i	$-0.512917\pi$
$727$	−2.18770			−0.0811374			−0.0405687	+	0.999177i	$0.512917\pi$
$728$	6.82563	−	3.17308i	0.252975	−	0.117602i
$729$	72.2863			2.67727
$730$	13.8084	+	23.9169i	0.511073	+	0.885204i
$731$	−2.60129	+	4.50557i	−0.0962122	+	0.166644i
$732$	0.566475	−	0.981163i	0.0209375	−	0.0362648i
$733$	1.45002	+	2.51151i	0.0535578	+	0.0927649i	0.891561	−	0.452900i	$-0.149611\pi$
$733$	1.45002	+	2.51151i	0.0535578	+	0.0927649i	−0.838004	+	0.545665i	$0.816277\pi$
$734$	51.4495			1.89903
$735$	32.2648	−	38.2685i	1.19011	−	1.41156i
$736$	0.705137			0.0259917
$737$	4.45797	+	7.72144i	0.164212	+	0.284423i
$738$	30.2611	−	52.4138i	1.11393	−	1.92938i
$739$	−1.07975	+	1.87017i	−0.0397191	+	0.0687954i	−0.885202	−	0.465208i	$-0.845980\pi$
$739$	−1.07975	+	1.87017i	−0.0397191	+	0.0687954i	0.845482	+	0.534003i	$0.179313\pi$
$740$	0.266504	+	0.461598i	0.00979687	+	0.0169687i
$741$	−6.78265			−0.249167
$742$	−40.9040	+	19.0153i	−1.50163	+	0.698073i
$743$	−6.43330			−0.236015			−0.118007	−	0.993013i	$-0.537651\pi$
$743$	−6.43330			−0.236015			−0.118007	+	0.993013i	$0.537651\pi$
$744$	−13.7844	−	23.8753i	−0.505361	−	0.875312i
$745$	1.08621	−	1.88138i	0.0397958	−	0.0689283i
$746$	−20.8811	+	36.1672i	−0.764513	+	1.32417i
$747$	27.3939	+	47.4477i	1.00229	+	1.73602i
$748$	0.0913058			0.00333847
$749$	11.5502	+	8.10781i	0.422036	+	0.296253i
$750$	−53.2526			−1.94451
$751$	13.8197	+	23.9365i	0.504290	+	0.873455i	0.999988	+	0.00496022i	$0.00157889\pi$
$751$	13.8197	+	23.9365i	0.504290	+	0.873455i	−0.495698	+	0.868495i	$0.665088\pi$
$752$	14.7987	−	25.6322i	0.539654	−	0.934709i
$753$	−21.8509	+	37.8469i	−0.796291	+	1.37922i
$754$	−1.31837	−	2.28348i	−0.0480121	−	0.0831594i
$755$	22.4295			0.816292
$756$	−0.0892896	+	1.00694i	−0.00324743	+	0.0366221i
$757$	33.1028			1.20314			0.601572	−	0.798819i	$-0.294541\pi$
$757$	33.1028			1.20314			0.601572	+	0.798819i	$0.294541\pi$
$758$	24.5124	+	42.4568i	0.890332	+	1.54210i
$759$	8.64481	−	14.9733i	0.313787	−	0.543495i
$760$	6.34493	−	10.9897i	0.230155	−	0.398640i
$761$	12.0178	+	20.8155i	0.435647	+	0.754562i	0.997348	−	0.0727778i	$-0.0231864\pi$
$761$	12.0178	+	20.8155i	0.435647	+	0.754562i	−0.561701	+	0.827340i	$0.689853\pi$
$762$	−22.0133			−0.797459
$763$	0.281255	−	3.17178i	0.0101821	−	0.114826i
$764$	0.0846515			0.00306258
$765$	−32.7854	−	56.7860i	−1.18536	−	2.05310i
$766$	23.6104	−	40.8945i	0.853080	−	1.47758i
$767$	−4.29437	+	7.43806i	−0.155061	+	0.268573i
$768$	−0.940650	−	1.62925i	−0.0339428	−	0.0587906i
$769$	42.3170			1.52599			0.762995	−	0.646405i	$-0.223728\pi$
$769$	42.3170			1.52599			0.762995	+	0.646405i	$0.223728\pi$
$770$	6.60141	+	4.63394i	0.237898	+	0.166996i
$771$	−1.09801			−0.0395437
$772$	−0.0781561	−	0.135370i	−0.00281290	−	0.00487209i
$773$	18.4797	−	32.0078i	0.664669	−	1.15124i	−0.314705	−	0.949189i	$-0.601906\pi$
$773$	18.4797	−	32.0078i	0.664669	−	1.15124i	0.979375	−	0.202052i	$-0.0647609\pi$
$774$	7.49727	−	12.9857i	0.269484	−	0.466760i
$775$	0.437166	+	0.757195i	0.0157035	+	0.0271992i
$776$	−13.7061			−0.492022
$777$	81.7892	−	38.0219i	2.93417	−	1.36403i
$778$	29.7089			1.06512
$779$	−5.62352	−	9.74023i	−0.201484	−	0.348980i
$780$	−0.0850045	+	0.147232i	−0.00304365	+	0.00527175i
$781$	−3.03475	+	5.25634i	−0.108592	+	0.188087i
$782$	14.1535	+	24.5145i	0.506127	+	0.876638i
$783$	30.1427			1.07721
$784$	27.2315	+	4.86774i	0.972555	+	0.173848i
$785$	12.7040			0.453426
$786$	−42.9604	−	74.4097i	−1.53235	−	2.65410i
$787$	0.149760	−	0.259392i	0.00533836	−	0.00924631i	−0.863344	−	0.504616i	$-0.831634\pi$
$787$	0.149760	−	0.259392i	0.00533836	−	0.00924631i	0.868682	+	0.495370i	$0.164967\pi$
$788$	0.246118	−	0.426289i	0.00876759	−	0.0151859i
$789$	−22.3805	−	38.7641i	−0.796766	−	1.38004i
$790$	46.1310			1.64127
$791$	−0.269995	+	0.125514i	−0.00959992	+	0.00446277i
$792$	−22.4002			−0.795957
$793$	−7.22557	−	12.5151i	−0.256587	−	0.444423i
$794$	18.7863	−	32.5389i	0.666702	−	1.15476i
$795$	43.3614	−	75.1042i	1.53787	−	2.66367i
$796$	−0.122663	−	0.212458i	−0.00434766	−	0.00753037i
$797$	−8.60817			−0.304917			−0.152459	−	0.988310i	$-0.548719\pi$
$797$	−8.60817			−0.304917			−0.152459	+	0.988310i	$0.548719\pi$
$798$	−20.6478	−	14.4939i	−0.730923	−	0.513080i
$799$	−28.7625			−1.01754
$800$	0.0200064	+	0.0346521i	0.000707334	+	0.00122514i
$801$	60.2183	−	104.301i	2.12771	−	3.68530i
$802$	16.0467	−	27.7937i	0.566629	−	0.981431i
$803$	−4.52963	−	7.84555i	−0.159847	−	0.276864i
$804$	−0.698998			−0.0246518
$805$	2.65710	−	29.9648i	0.0936504	−	1.05612i
$806$	−4.13114			−0.145513
$807$	50.5721	+	87.5934i	1.78022	+	3.08344i
$808$	5.32906	−	9.23020i	0.187476	−	0.324717i
$809$	−24.9915	+	43.2865i	−0.878653	+	1.52187i	−0.0258342	+	0.999666i	$0.508224\pi$
$809$	−24.9915	+	43.2865i	−0.878653	+	1.52187i	−0.852819	+	0.522206i	$0.825109\pi$
$810$	44.7704	+	77.5446i	1.57307	+	2.72464i
$811$	48.0379			1.68684			0.843419	−	0.537257i	$-0.180539\pi$
$811$	48.0379			1.68684			0.843419	+	0.537257i	$0.180539\pi$
$812$	−0.0104212	+	0.117522i	−0.000365711	+	0.00412421i
$813$	−60.4379			−2.11965
$814$	7.26667	+	12.5862i	0.254697	+	0.441148i
$815$	−5.06812	+	8.77824i	−0.177529	+	0.307488i
$816$	25.0228	−	43.3408i	0.875974	−	1.51723i
$817$	−1.39324	−	2.41317i	−0.0487434	−	0.0844260i
$818$	23.5287			0.822661
$819$	17.0501	+	11.9685i	0.595779	+	0.418214i
$820$	−0.281910			−0.00984473
$821$	7.64266	+	13.2375i	0.266731	+	0.461991i	0.968016	−	0.250890i	$-0.0807233\pi$
$821$	7.64266	+	13.2375i	0.266731	+	0.461991i	−0.701285	+	0.712881i	$0.747390\pi$
$822$	19.6888	−	34.1019i	0.686724	−	1.18944i
$823$	9.30866	−	16.1231i	0.324480	−	0.562015i	−0.656927	−	0.753954i	$-0.728144\pi$
$823$	9.30866	−	16.1231i	0.324480	−	0.562015i	0.981407	+	0.191939i	$0.0614775\pi$
$824$	18.4088	+	31.8851i	0.641303	+	1.11077i
$825$	0.981095			0.0341573
$826$	−28.9674	+	13.4663i	−1.00791	+	0.468552i
$827$	9.11263			0.316877			0.158439	−	0.987369i	$-0.449354\pi$
$827$	9.11263			0.316877			0.158439	+	0.987369i	$0.449354\pi$
$828$	0.490754	+	0.850010i	0.0170549	+	0.0295399i
$829$	13.6390	−	23.6234i	0.473701	−	0.820474i	−0.525846	−	0.850580i	$-0.676251\pi$
$829$	13.6390	−	23.6234i	0.473701	−	0.820474i	0.999547	+	0.0301057i	$0.00958440\pi$
$830$	−10.6063	+	18.3707i	−0.368150	+	0.637655i
$831$	28.9276	+	50.1040i	1.00349	+	1.73809i
$832$	−8.09283			−0.280568
$833$	−9.13499	−	25.2831i	−0.316509	−	0.876007i
$834$	8.67710			0.300463
$835$	13.8010	+	23.9041i	0.477605	+	0.827236i
$836$	−0.0244515	+	0.0423513i	−0.000845673	+	0.00146475i
$837$	23.6132	−	40.8993i	0.816192	−	1.41369i
$838$	−25.0795	−	43.4390i	−0.866359	−	1.50058i
$839$	−13.7212			−0.473708			−0.236854	−	0.971545i	$-0.576116\pi$
$839$	−13.7212			−0.473708			−0.236854	+	0.971545i	$0.576116\pi$
$840$	−48.8081	+	22.6898i	−1.68404	+	0.782871i
$841$	−25.4820			−0.878689
$842$	4.81350	+	8.33722i	0.165884	+	0.287320i
$843$	−36.0378	+	62.4193i	−1.24121	+	2.14983i
$844$	0.110847	−	0.191993i	0.00381552	−	0.00660868i
$845$	1.08426	+	1.87799i	0.0372997	+	0.0646049i
$846$	82.8973			2.85007
$847$	−2.16549	−	1.52009i	−0.0744070	−	0.0522309i
$848$	47.9279			1.64585
$849$	7.39967	+	12.8166i	0.253956	+	0.439865i
$850$	−0.803135	+	1.39107i	−0.0275473	+	0.0477134i
$851$	27.1030	−	46.9437i	0.929078	−	1.60921i
$852$	−0.237920	−	0.412090i	−0.00815101	−	0.0141180i
$853$	6.13407			0.210026			0.105013	−	0.994471i	$-0.466512\pi$
$853$	6.13407			0.210026			0.105013	+	0.994471i	$0.466512\pi$
$854$	4.74750	−	53.5388i	0.162456	−	1.83206i
$855$	35.1195			1.20106
$856$	−7.58726	−	13.1415i	−0.259327	−	0.449168i
$857$	5.96489	−	10.3315i	0.203757	−	0.352917i	−0.745979	−	0.665969i	$-0.768018\pi$
$857$	5.96489	−	10.3315i	0.203757	−	0.352917i	0.949736	+	0.313052i	$0.101352\pi$
$858$	−2.31779	+	4.01453i	−0.0791281	+	0.137054i
$859$	−22.7848	−	39.4644i	−0.777407	−	1.34651i	−0.933432	−	0.358755i	$-0.883201\pi$
$859$	−22.7848	−	39.4644i	−0.777407	−	1.34651i	0.156025	−	0.987753i	$-0.450132\pi$
$860$	−0.0698440			−0.00238166
$861$	−4.21363	+	47.5181i	−0.143600	+	1.61941i
$862$	−28.7870			−0.980491
$863$	−14.0920	−	24.4080i	−0.479697	−	0.830860i	0.520032	−	0.854147i	$-0.325920\pi$
$863$	−14.0920	−	24.4080i	−0.479697	−	0.830860i	−0.999729	+	0.0232873i	$0.992587\pi$
$864$	1.08063	−	1.87171i	0.0367638	−	0.0636768i
$865$	2.90220	−	5.02677i	0.0986779	−	0.170915i
$866$	−20.0839	−	34.7864i	−0.682479	−	1.18209i
$867$	7.42394			0.252130
$868$	0.151297	+	0.106205i	0.00513535	+	0.00360482i
$869$	−15.1325			−0.513335
$870$	9.42726	+	16.3285i	0.319614	+	0.553588i
$871$	−4.45797	+	7.72144i	−0.151053	+	0.261631i
$872$	−1.71201	+	2.96528i	−0.0579759	+	0.100417i
$873$	−18.9660	−	32.8501i	−0.641903	−	1.11181i
$874$	−15.1611			−0.512832
$875$	27.5612	−	12.8126i	0.931740	−	0.433144i
$876$	0.710234			0.0239966
$877$	−18.8686	−	32.6814i	−0.637147	−	1.10357i	−0.986056	−	0.166414i	$-0.946781\pi$
$877$	−18.8686	−	32.6814i	−0.637147	−	1.10357i	0.348909	−	0.937157i	$-0.386552\pi$
$878$	3.21715	−	5.57227i	0.108574	−	0.188055i
$879$	−0.758711	+	1.31413i	−0.0255907	+	0.0443244i
$880$	−4.28487	−	7.42161i	−0.144443	−	0.250182i
$881$	−39.5870			−1.33372			−0.666860	−	0.745183i	$-0.732362\pi$
$881$	−39.5870			−1.33372			−0.666860	+	0.745183i	$0.732362\pi$
$882$	26.3283	+	72.8692i	0.886519	+	2.45364i
$883$	−25.0977			−0.844605			−0.422302	−	0.906455i	$-0.638778\pi$
$883$	−25.0977			−0.844605			−0.422302	+	0.906455i	$0.638778\pi$
$884$	0.0456529	+	0.0790731i	0.00153547	+	0.00265952i
$885$	30.7078	−	53.1875i	1.03223	−	1.78788i
$886$	−5.26838	+	9.12509i	−0.176995	+	0.306564i
$887$	−8.38340	−	14.5205i	−0.281487	−	0.487550i	0.690264	−	0.723557i	$-0.257494\pi$
$887$	−8.38340	−	14.5205i	−0.281487	−	0.487550i	−0.971751	+	0.236008i	$0.924161\pi$
$888$	−96.9871			−3.25467
$889$	11.3932	−	5.29641i	0.382114	−	0.177636i
$890$	46.6303			1.56305
$891$	−14.6862	−	25.4372i	−0.492006	−	0.852180i
$892$	0.0101739	−	0.0176218i	0.000340648	−	0.000590020i
$893$	7.70254	−	13.3412i	0.257756	−	0.446446i
$894$	2.32197	+	4.02176i	0.0776582	+	0.134508i
$895$	−46.2638			−1.54643
$896$	−24.0538	−	16.8848i	−0.803579	−	0.564082i
$897$	17.2896			0.577284
$898$	13.6569	+	23.6544i	0.455735	+	0.789357i
$899$	2.75594	−	4.77343i	0.0919158	−	0.159203i
$900$	−0.0278477	+	0.0482336i	−0.000928256	+	0.00160779i
$901$	−23.2879	−	40.3358i	−0.775832	−	1.34378i
$902$	−7.68676			−0.255941
$903$	−1.04394	+	11.7727i	−0.0347401	+	0.391772i
$904$	0.320165			0.0106485
$905$	6.20835	+	10.7532i	0.206372	+	0.357448i
$906$	−23.9734	+	41.5232i	−0.796463	+	1.37952i
$907$	8.21423	−	14.2275i	0.272749	−	0.472415i	−0.696816	−	0.717250i	$-0.745400\pi$
$907$	8.21423	−	14.2275i	0.272749	−	0.472415i	0.969565	+	0.244835i	$0.0787338\pi$
$908$	−0.0884054	−	0.153123i	−0.00293384	−	0.00508156i
$909$	29.4966			0.978340
$910$	−0.712404	+	8.03396i	−0.0236160	+	0.266323i
$911$	31.9170			1.05746			0.528729	−	0.848791i	$-0.322669\pi$
$911$	31.9170			1.05746			0.528729	+	0.848791i	$0.322669\pi$
$912$	13.4021	+	23.2132i	0.443789	+	0.768665i
$913$	3.47923	−	6.02620i	0.115146	−	0.199438i
$914$	−7.02025	+	12.1594i	−0.232209	+	0.402198i
$915$	51.6680	+	89.4915i	1.70809	+	2.95850i
$916$	−0.278037			−0.00918660
$917$	40.1375	+	28.1750i	1.32546	+	0.930420i
$918$	86.7615			2.86356
$919$	12.6050	+	21.8326i	0.415802	+	0.720190i	0.995512	−	0.0946328i	$-0.0301677\pi$
$919$	12.6050	+	21.8326i	0.415802	+	0.720190i	−0.579711	+	0.814822i	$0.696834\pi$
$920$	−16.1738	+	28.0139i	−0.533236	+	0.923591i
$921$	6.09298	−	10.5534i	0.200771	−	0.347745i
$922$	−24.9519	−	43.2180i	−0.821748	−	1.42331i
$923$	−6.06950			−0.199780
$924$	0.188092	−	0.0874397i	0.00618778	−	0.00287655i
$925$	3.07590			0.101135
$926$	22.3761	+	38.7566i	0.735325	+	1.27362i
$927$	−50.9469	+	88.2426i	−1.67332	+	2.89827i
$928$	0.126123	−	0.218451i	0.00414017	−	0.00717099i
$929$	6.06854	+	10.5110i	0.199102	+	0.344855i	0.948238	−	0.317562i	$-0.102864\pi$
$929$	6.06854	+	10.5110i	0.199102	+	0.344855i	−0.749135	+	0.662417i	$0.769531\pi$
$930$	29.5406			0.968675
$931$	14.1736	+	2.53359i	0.464522	+	0.0830351i
$932$	−0.552095			−0.0180845
$933$	−50.3711	−	87.2452i	−1.64907	−	2.85628i
$934$	−8.88786	+	15.3942i	−0.290820	+	0.503715i
$935$	−4.16398	+	7.21223i	−0.136177	+	0.235865i
$936$	−11.2001	−	19.3992i	−0.366087	−	0.634081i
$937$	−36.5598			−1.19436			−0.597178	−	0.802108i	$-0.703712\pi$
$937$	−36.5598			−1.19436			−0.597178	+	0.802108i	$0.703712\pi$
$938$	−30.0710	+	13.9793i	−0.981854	+	0.456441i
$939$	−68.3451			−2.23036
$940$	−0.193066	−	0.334400i	−0.00629712	−	0.0109069i
$941$	20.1722	−	34.9392i	0.657593	−	1.13899i	−0.323644	−	0.946179i	$-0.604908\pi$
$941$	20.1722	−	34.9392i	0.657593	−	1.13899i	0.981237	−	0.192806i	$-0.0617588\pi$
$942$	−13.5785	+	23.5187i	−0.442412	+	0.766280i
$943$	14.3349	+	24.8288i	0.466808	+	0.808536i
$944$	33.9417			1.10471
$945$	−75.4661	−	52.9743i	−2.45491	−	1.72326i
$946$	−1.90441			−0.0619178
$947$	0.836239	+	1.44841i	0.0271741	+	0.0470670i	0.879293	−	0.476282i	$-0.158016\pi$
$947$	0.836239	+	1.44841i	0.0271741	+	0.0470670i	−0.852119	+	0.523349i	$0.824682\pi$
$948$	0.593184	−	1.02743i	0.0192657	−	0.0333692i
$949$	4.52963	−	7.84555i	0.147038	−	0.254677i
$950$	−0.430156	−	0.745053i	−0.0139561	−	0.0241727i
$951$	−6.62861			−0.214947
$952$	−2.55330	+	28.7942i	−0.0827528	+	0.933224i
$953$	−44.7721			−1.45031			−0.725155	−	0.688585i	$-0.758232\pi$
$953$	−44.7721			−1.45031			−0.725155	+	0.688585i	$0.758232\pi$
$954$	67.1188	+	116.253i	2.17305	+	3.76384i
$955$	−3.86052	+	6.68661i	−0.124923	+	0.216374i
$956$	−0.341611	+	0.591688i	−0.0110485	+	0.0191366i
$957$	−3.09246	−	5.35630i	−0.0999651	−	0.173145i
$958$	−5.06802			−0.163740
$959$	−1.98513	+	22.3868i	−0.0641032	+	0.722908i
$960$	57.8695			1.86773
$961$	11.1821	+	19.3679i	0.360712	+	0.624772i
$962$	−7.26667	+	12.5862i	−0.234287	+	0.405797i
$963$	20.9979	−	36.3695i	0.676649	−	1.17199i
$964$	0.107900	+	0.186888i	0.00347521	+	0.00601925i
$965$	14.2572			0.458955
$966$	52.6331	+	36.9464i	1.69344	+	1.18873i
$967$	44.9844			1.44660			0.723300	−	0.690534i	$-0.242625\pi$
$967$	44.9844			1.44660			0.723300	+	0.690534i	$0.242625\pi$
$968$	1.42249	+	2.46383i	0.0457207	+	0.0791906i
$969$	13.0240	−	22.5583i	0.418392	−	0.724676i
$970$	7.34322	−	12.7188i	0.235776	−	0.408377i
$971$	18.8287	+	32.6122i	0.604240	+	1.04658i	0.992171	+	0.124886i	$0.0398567\pi$
$971$	18.8287	+	32.6122i	0.604240	+	1.04658i	−0.387931	+	0.921689i	$0.626810\pi$
$972$	1.15651			0.0370952
$973$	−4.49089	+	2.08771i	−0.143971	+	0.0669289i
$974$	−24.2615			−0.777387
$975$	0.490547	+	0.849653i	0.0157101	+	0.0272107i
$976$	−28.5546	+	49.4580i	−0.914011	+	1.58311i
$977$	−17.5341	+	30.3700i	−0.560966	+	0.971622i	0.436446	+	0.899730i	$0.356237\pi$
$977$	−17.5341	+	30.3700i	−0.560966	+	0.971622i	−0.997412	+	0.0718919i	$0.977096\pi$
$978$	−10.8340	−	18.7650i	−0.346433	−	0.600039i
$979$	−15.2963			−0.488873
$980$	0.232630	−	0.275917i	0.00743110	−	0.00881384i
$981$	−9.47604			−0.302547
$982$	2.79077	+	4.83376i	0.0890572	+	0.154252i
$983$	−13.0603	+	22.6212i	−0.416560	+	0.721504i	−0.995591	−	0.0938023i	$-0.970098\pi$
$983$	−13.0603	+	22.6212i	−0.416560	+	0.721504i	0.579031	+	0.815306i	$0.303431\pi$
$984$	25.6485	−	44.4245i	0.817644	−	1.41620i
$985$	22.4483	+	38.8817i	0.715263	+	1.23887i
$986$	10.1261			0.322481
$987$	−59.2515	+	27.5446i	−1.88599	+	0.876754i
$988$	−0.0489030			−0.00155581
$989$	3.55151	+	6.15139i	0.112931	+	0.195603i
$990$	12.0012	−	20.7866i	0.381422	−	0.660642i
$991$	−15.7050	+	27.2018i	−0.498884	+	0.864093i	−0.999999	−	0.00128774i	$-0.999590\pi$
$991$	−15.7050	+	27.2018i	−0.498884	+	0.864093i	0.501115	+	0.865381i	$0.332923\pi$
$992$	−0.197604	−	0.342261i	−0.00627394	−	0.0108668i
$993$	16.9713			0.538569
$994$	−18.4768	−	12.9700i	−0.586048	−	0.411383i
$995$	22.3760			0.709368
$996$	0.272767	+	0.472446i	0.00864294	+	0.0149700i
$997$	11.1119	−	19.2464i	0.351917	−	0.609539i	−0.634668	−	0.772785i	$-0.718863\pi$
$997$	11.1119	−	19.2464i	0.351917	−	0.609539i	0.986585	+	0.163246i	$0.0521965\pi$
$998$	−5.78489	+	10.0197i	−0.183118	+	0.317169i
$999$	−83.0713	−	143.884i	−2.62826	−	4.55228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.d.144.10	✓	50
7.2	even	3	inner	1001.2.i.d.716.10	yes	50
7.3	odd	6		7007.2.a.bi.1.16		25
7.4	even	3		7007.2.a.bh.1.16		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.10	✓	50	1.1	even	1	trivial
1001.2.i.d.716.10	yes	50	7.2	even	3	inner
7007.2.a.bh.1.16		25	7.4	even	3
7007.2.a.bi.1.16		25	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.702891 - 1.21744i) q^{2} +(1.64875 - 2.85573i) q^{3} +(0.0118876 - 0.0205898i) q^{4} +(1.08426 + 1.87799i) q^{5} -4.63558 q^{6} +(2.39918 - 1.11532i) q^{7} -2.84499 q^{8} +(-3.93679 - 6.81871i) q^{9} +O(q^{10})\)	\(q+(-0.702891 - 1.21744i) q^{2} +(1.64875 - 2.85573i) q^{3} +(0.0118876 - 0.0205898i) q^{4} +(1.08426 + 1.87799i) q^{5} -4.63558 q^{6} +(2.39918 - 1.11532i) q^{7} -2.84499 q^{8} +(-3.93679 - 6.81871i) q^{9} +(1.52423 - 2.64005i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.0391993 - 0.0678952i) q^{12} -1.00000 q^{13} +(-3.04420 - 2.13691i) q^{14} +7.15071 q^{15} +(1.97594 + 3.42243i) q^{16} +(1.92020 - 3.32588i) q^{17} +(-5.53426 + 9.58563i) q^{18} +(1.02845 + 1.78133i) q^{19} +0.0515568 q^{20} +(0.770604 - 8.69029i) q^{21} +1.40578 q^{22} +(-2.62162 - 4.54078i) q^{23} +(-4.69069 + 8.12451i) q^{24} +(0.148763 - 0.257665i) q^{25} +(0.702891 + 1.21744i) q^{26} -16.0706 q^{27} +(0.00555607 - 0.0626572i) q^{28} -1.87563 q^{29} +(-5.02617 - 8.70559i) q^{30} +(-1.46934 + 2.54497i) q^{31} +(-0.0672426 + 0.116468i) q^{32} +(1.64875 + 2.85573i) q^{33} -5.39876 q^{34} +(4.69590 + 3.29634i) q^{35} -0.187195 q^{36} +(5.16913 + 8.95320i) q^{37} +(1.44578 - 2.50416i) q^{38} +(-1.64875 + 2.85573i) q^{39} +(-3.08471 - 5.34287i) q^{40} -5.46796 q^{41} +(-11.1216 + 5.17016i) q^{42} -1.35470 q^{43} +(0.0118876 + 0.0205898i) q^{44} +(8.53699 - 14.7865i) q^{45} +(-3.68542 + 6.38334i) q^{46} +(-3.74473 - 6.48606i) q^{47} +13.0314 q^{48} +(4.51212 - 5.35171i) q^{49} -0.418257 q^{50} +(-6.33187 - 10.9671i) q^{51} +(-0.0118876 + 0.0205898i) q^{52} +(6.06393 - 10.5030i) q^{53} +(11.2959 + 19.5651i) q^{54} -2.16852 q^{55} +(-6.82563 + 3.17308i) q^{56} +6.78265 q^{57} +(1.31837 + 2.28348i) q^{58} +(4.29437 - 7.43806i) q^{59} +(0.0850045 - 0.147232i) q^{60} +(7.22557 + 12.5151i) q^{61} +4.13114 q^{62} +(-17.0501 - 11.9685i) q^{63} +8.09283 q^{64} +(-1.08426 - 1.87799i) q^{65} +(2.31779 - 4.01453i) q^{66} +(4.45797 - 7.72144i) q^{67} +(-0.0456529 - 0.0790731i) q^{68} -17.2896 q^{69} +(0.712404 - 8.03396i) q^{70} +6.06950 q^{71} +(11.2001 + 19.3992i) q^{72} +(-4.52963 + 7.84555i) q^{73} +(7.26667 - 12.5862i) q^{74} +(-0.490547 - 0.849653i) q^{75} +0.0489030 q^{76} +(-0.233693 + 2.63541i) q^{77} +4.63558 q^{78} +(7.56626 + 13.1051i) q^{79} +(-4.28487 + 7.42161i) q^{80} +(-14.6862 + 25.4372i) q^{81} +(3.84338 + 6.65693i) q^{82} -6.95845 q^{83} +(-0.169771 - 0.119173i) q^{84} +8.32797 q^{85} +(0.952207 + 1.64927i) q^{86} +(-3.09246 + 5.35630i) q^{87} +(1.42249 - 2.46383i) q^{88} +(7.64816 + 13.2470i) q^{89} -24.0023 q^{90} +(-2.39918 + 1.11532i) q^{91} -0.124658 q^{92} +(4.84516 + 8.39206i) q^{93} +(-5.26428 + 9.11799i) q^{94} +(-2.23021 + 3.86284i) q^{95} +(0.221733 + 0.384053i) q^{96} +4.81765 q^{97} +(-9.68693 - 1.73158i) q^{98} +7.87357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Introduction

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