LMFDB - Embedded newform 273.2.k.b.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6040683.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} - 2x^{3} + 25x^{2} - 5x + 1 $ x^6 + 5x^4 - 2x^3 + 25x^2 - 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$0.100820 + 0.174625i$ of defining polynomial
Character	$\chi$	$=$	273.22
Dual form			273.2.k.b.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.100820 + 0.174625i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.979671 + 1.69684i) q^{4} +3.75770 q^{5} +(0.100820 + 0.174625i) q^{6} +(-0.500000 - 0.866025i) q^{7} -0.798360 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.100820 + 0.174625i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.979671 + 1.69684i) q^{4} +3.75770 q^{5} +(0.100820 + 0.174625i) q^{6} +(-0.500000 - 0.866025i) q^{7} -0.798360 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.378851 + 0.656189i) q^{10} +(-2.87885 + 4.98632i) q^{11} +1.95934 q^{12} +(0.121149 - 3.60352i) q^{13} +0.201640 q^{14} +(1.87885 - 3.25427i) q^{15} +(-1.87885 + 3.25427i) q^{16} +(-2.10082 - 3.63873i) q^{17} +0.201640 q^{18} +(-0.701640 - 1.21528i) q^{19} +(3.68131 + 6.37622i) q^{20} -1.00000 q^{21} +(-0.580491 - 1.00544i) q^{22} +(-0.479671 + 0.830814i) q^{23} +(-0.399180 + 0.691400i) q^{24} +9.12032 q^{25} +(0.617050 + 0.384462i) q^{26} -1.00000 q^{27} +(0.979671 - 1.69684i) q^{28} +(-1.39918 + 2.42345i) q^{29} +(0.378851 + 0.656189i) q^{30} +4.35442 q^{31} +(-1.17721 - 2.03899i) q^{32} +(2.87885 + 4.98632i) q^{33} +0.847217 q^{34} +(-1.87885 - 3.25427i) q^{35} +(0.979671 - 1.69684i) q^{36} +(5.03983 - 8.72925i) q^{37} +0.282957 q^{38} +(-3.06016 - 1.90668i) q^{39} -3.00000 q^{40} +(-1.40328 + 2.43055i) q^{41} +(0.100820 - 0.174625i) q^{42} +(-0.479671 - 0.830814i) q^{43} -11.2813 q^{44} +(-1.87885 - 3.25427i) q^{45} +(-0.0967206 - 0.167525i) q^{46} -6.67638 q^{47} +(1.87885 + 3.25427i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.919509 + 1.59264i) q^{50} -4.20164 q^{51} +(6.23327 - 3.32469i) q^{52} -10.9187 q^{53} +(0.100820 - 0.174625i) q^{54} +(-10.8179 + 18.7371i) q^{55} +(0.399180 + 0.691400i) q^{56} -1.40328 q^{57} +(-0.282130 - 0.488664i) q^{58} +(6.19671 + 10.7330i) q^{59} +7.36262 q^{60} +(-6.66098 - 11.5372i) q^{61} +(-0.439012 + 0.760391i) q^{62} +(-0.500000 + 0.866025i) q^{63} -7.04066 q^{64} +(0.455242 - 13.5409i) q^{65} -1.16098 q^{66} +(-3.80246 + 6.58605i) q^{67} +(4.11622 - 7.12951i) q^{68} +(0.479671 + 0.830814i) q^{69} +0.757702 q^{70} +(-1.81869 - 3.15006i) q^{71} +(0.399180 + 0.691400i) q^{72} -7.95934 q^{73} +(1.01623 + 1.76016i) q^{74} +(4.56016 - 7.89843i) q^{75} +(1.37475 - 2.38114i) q^{76} +5.75770 q^{77} +(0.641478 - 0.342150i) q^{78} +3.56426 q^{79} +(-7.06016 + 12.2286i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.282957 - 0.490096i) q^{82} +14.5643 q^{83} +(-0.979671 - 1.69684i) q^{84} +(-7.89425 - 13.6732i) q^{85} +0.193441 q^{86} +(1.39918 + 2.42345i) q^{87} +(2.29836 - 3.98088i) q^{88} +(0.903279 - 1.56453i) q^{89} +0.757702 q^{90} +(-3.18131 + 1.69684i) q^{91} -1.87968 q^{92} +(2.17721 - 3.77104i) q^{93} +(0.673112 - 1.16586i) q^{94} +(-2.63655 - 4.56664i) q^{95} -2.35442 q^{96} +(8.13655 + 14.0929i) q^{97} +(-0.100820 - 0.174625i) q^{98} +5.75770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} - 8 q^{11} - 8 q^{12} + 10 q^{13} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 3 q^{19} + 11 q^{20} - 6 q^{21} + 7 q^{22} + 7 q^{23} - 3 q^{24} + 14 q^{25} + 16 q^{26} - 6 q^{27} - 4 q^{28} - 9 q^{29} - 7 q^{30} + 10 q^{31} + q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{35} - 4 q^{36} + 40 q^{38} + 2 q^{39} - 18 q^{40} - 6 q^{41} + 7 q^{43} - 6 q^{44} - 2 q^{45} - 3 q^{46} + 18 q^{47} + 2 q^{48} - 3 q^{49} - 16 q^{50} - 24 q^{51} + 12 q^{52} - 26 q^{53} - 26 q^{55} + 3 q^{56} - 6 q^{57} + 10 q^{58} - 11 q^{59} + 22 q^{60} - 19 q^{61} + 27 q^{62} - 3 q^{63} - 62 q^{64} - 14 q^{65} + 14 q^{66} - 21 q^{67} - 13 q^{68} - 7 q^{69} - 14 q^{70} - 22 q^{71} + 3 q^{72} - 28 q^{73} + 19 q^{74} + 7 q^{75} + 2 q^{76} + 16 q^{77} + 23 q^{78} - 2 q^{79} - 22 q^{80} - 3 q^{81} - 40 q^{82} + 64 q^{83} + 4 q^{84} - q^{85} + 6 q^{86} + 9 q^{87} + 15 q^{88} + 3 q^{89} - 14 q^{90} - 8 q^{91} - 52 q^{92} + 5 q^{93} - q^{94} + 12 q^{95} + 2 q^{96} + 21 q^{97} + 16 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 - 8 * q^11 - 8 * q^12 + 10 * q^13 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 3 * q^19 + 11 * q^20 - 6 * q^21 + 7 * q^22 + 7 * q^23 - 3 * q^24 + 14 * q^25 + 16 * q^26 - 6 * q^27 - 4 * q^28 - 9 * q^29 - 7 * q^30 + 10 * q^31 + q^32 + 8 * q^33 + 20 * q^34 - 2 * q^35 - 4 * q^36 + 40 * q^38 + 2 * q^39 - 18 * q^40 - 6 * q^41 + 7 * q^43 - 6 * q^44 - 2 * q^45 - 3 * q^46 + 18 * q^47 + 2 * q^48 - 3 * q^49 - 16 * q^50 - 24 * q^51 + 12 * q^52 - 26 * q^53 - 26 * q^55 + 3 * q^56 - 6 * q^57 + 10 * q^58 - 11 * q^59 + 22 * q^60 - 19 * q^61 + 27 * q^62 - 3 * q^63 - 62 * q^64 - 14 * q^65 + 14 * q^66 - 21 * q^67 - 13 * q^68 - 7 * q^69 - 14 * q^70 - 22 * q^71 + 3 * q^72 - 28 * q^73 + 19 * q^74 + 7 * q^75 + 2 * q^76 + 16 * q^77 + 23 * q^78 - 2 * q^79 - 22 * q^80 - 3 * q^81 - 40 * q^82 + 64 * q^83 + 4 * q^84 - q^85 + 6 * q^86 + 9 * q^87 + 15 * q^88 + 3 * q^89 - 14 * q^90 - 8 * q^91 - 52 * q^92 + 5 * q^93 - q^94 + 12 * q^95 + 2 * q^96 + 21 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.100820	+	0.174625i	−0.0712904	+	0.123479i	−0.899467	−	0.436989i	$-0.856045\pi$
$2$	−0.100820	+	0.174625i	−0.0712904	+	0.123479i	0.828177	+	0.560467i	$0.189378\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.979671	+	1.69684i	0.489835	+	0.848420i
$5$	3.75770			1.68050			0.840248	−	0.542203i	$-0.182410\pi$
$5$	3.75770			1.68050			0.840248	+	0.542203i	$0.182410\pi$
$6$	0.100820	+	0.174625i	0.0411595	+	0.0712904i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−0.798360			−0.282263
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.378851	+	0.656189i	−0.119803	+	0.207505i
$11$	−2.87885	+	4.98632i	−0.868006	+	1.50343i	−0.00397528	+	0.999992i	$0.501265\pi$
$11$	−2.87885	+	4.98632i	−0.868006	+	1.50343i	−0.864031	+	0.503439i	$0.832068\pi$
$12$	1.95934			0.565613
$13$	0.121149	−	3.60352i	0.0336007	−	0.999435i
$13$	0.121149	−	3.60352i	0.0336007	−	0.999435i
$14$	0.201640			0.0538905
$15$	1.87885	−	3.25427i	0.485117	−	0.840248i
$16$	−1.87885	+	3.25427i	−0.469713	+	0.813566i
$17$	−2.10082	−	3.63873i	−0.509524	−	0.882521i	−0.999939	−	0.0110321i	$-0.996488\pi$
$17$	−2.10082	−	3.63873i	−0.509524	−	0.882521i	0.490415	−	0.871489i	$-0.336845\pi$
$18$	0.201640			0.0475269
$19$	−0.701640	−	1.21528i	−0.160967	−	0.278803i	0.774249	−	0.632882i	$-0.218128\pi$
$19$	−0.701640	−	1.21528i	−0.160967	−	0.278803i	−0.935216	+	0.354078i	$0.884795\pi$
$20$	3.68131	+	6.37622i	0.823166	+	1.42577i
$21$	−1.00000			−0.218218
$22$	−0.580491	−	1.00544i	−0.123761	−	0.214360i
$23$	−0.479671	+	0.830814i	−0.100018	+	0.173237i	−0.911692	−	0.410874i	$-0.865223\pi$
$23$	−0.479671	+	0.830814i	−0.100018	+	0.173237i	0.811674	+	0.584111i	$0.198557\pi$
$24$	−0.399180	+	0.691400i	−0.0814823	+	0.141131i
$25$	9.12032			1.82406
$26$	0.617050	+	0.384462i	0.121013	+	0.0753991i
$27$	−1.00000			−0.192450
$28$	0.979671	−	1.69684i	0.185140	−	0.320673i
$29$	−1.39918	+	2.42345i	−0.259821	+	0.450024i	−0.966194	−	0.257817i	$-0.916997\pi$
$29$	−1.39918	+	2.42345i	−0.259821	+	0.450024i	0.706373	+	0.707840i	$0.250330\pi$
$30$	0.378851	+	0.656189i	0.0691684	+	0.119803i
$31$	4.35442			0.782077			0.391039	−	0.920374i	$-0.372116\pi$
$31$	4.35442			0.782077			0.391039	+	0.920374i	$0.372116\pi$
$32$	−1.17721	−	2.03899i	−0.208104	−	0.360446i
$33$	2.87885	+	4.98632i	0.501144	+	0.868006i
$34$	0.847217			0.145297
$35$	−1.87885	−	3.25427i	−0.317584	−	0.550071i
$36$	0.979671	−	1.69684i	0.163278	−	0.282807i
$37$	5.03983	−	8.72925i	0.828543	−	1.43508i	−0.0706377	−	0.997502i	$-0.522503\pi$
$37$	5.03983	−	8.72925i	0.828543	−	1.43508i	0.899181	−	0.437577i	$-0.144163\pi$
$38$	0.282957			0.0459017
$39$	−3.06016	−	1.90668i	−0.490018	−	0.305312i
$40$	−3.00000			−0.474342
$41$	−1.40328	+	2.43055i	−0.219155	+	0.379588i	−0.954550	−	0.298051i	$-0.903664\pi$
$41$	−1.40328	+	2.43055i	−0.219155	+	0.379588i	0.735395	+	0.677639i	$0.236997\pi$
$42$	0.100820	−	0.174625i	0.0155568	−	0.0269452i
$43$	−0.479671	−	0.830814i	−0.0731491	−	0.126698i	0.827131	−	0.562009i	$-0.189972\pi$
$43$	−0.479671	−	0.830814i	−0.0731491	−	0.126698i	−0.900280	+	0.435312i	$0.856638\pi$
$44$	−11.2813			−1.70072
$45$	−1.87885	−	3.25427i	−0.280083	−	0.485117i
$46$	−0.0967206	−	0.167525i	−0.0142607	−	0.0247002i
$47$	−6.67638			−0.973851			−0.486925	−	0.873444i	$-0.661882\pi$
$47$	−6.67638			−0.973851			−0.486925	+	0.873444i	$0.661882\pi$
$48$	1.87885	+	3.25427i	0.271189	+	0.469713i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.919509	+	1.59264i	−0.130038	+	0.225233i
$51$	−4.20164			−0.588347
$52$	6.23327	−	3.32469i	0.864399	−	0.461051i
$53$	−10.9187			−1.49980			−0.749898	−	0.661553i	$-0.769898\pi$
$53$	−10.9187			−1.49980			−0.749898	+	0.661553i	$0.769898\pi$
$54$	0.100820	−	0.174625i	0.0137198	−	0.0237635i
$55$	−10.8179	+	18.7371i	−1.45868	+	2.52651i
$56$	0.399180	+	0.691400i	0.0533427	+	0.0923923i
$57$	−1.40328			−0.185869
$58$	−0.282130	−	0.488664i	−0.0370455	−	0.0641647i
$59$	6.19671	+	10.7330i	0.806743	+	1.39732i	0.915108	+	0.403209i	$0.132105\pi$
$59$	6.19671	+	10.7330i	0.806743	+	1.39732i	−0.108364	+	0.994111i	$0.534561\pi$
$60$	7.36262			0.950510
$61$	−6.66098	−	11.5372i	−0.852851	−	1.47718i	−0.878624	−	0.477514i	$-0.841538\pi$
$61$	−6.66098	−	11.5372i	−0.852851	−	1.47718i	0.0257730	−	0.999668i	$-0.491795\pi$
$62$	−0.439012	+	0.760391i	−0.0557546	+	0.0965698i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	−7.04066			−0.880082
$65$	0.455242	−	13.5409i	0.0564659	−	1.67955i
$66$	−1.16098			−0.142907
$67$	−3.80246	+	6.58605i	−0.464544	+	0.804614i	−0.999181	−	0.0404677i	$-0.987115\pi$
$67$	−3.80246	+	6.58605i	−0.464544	+	0.804614i	0.534636	+	0.845082i	$0.320449\pi$
$68$	4.11622	−	7.12951i	0.499165	−	0.864580i
$69$	0.479671	+	0.830814i	0.0577456	+	0.100018i
$70$	0.757702			0.0905627
$71$	−1.81869	−	3.15006i	−0.215839	−	0.373844i	0.737693	−	0.675136i	$-0.235915\pi$
$71$	−1.81869	−	3.15006i	−0.215839	−	0.373844i	−0.953532	+	0.301293i	$0.902582\pi$
$72$	0.399180	+	0.691400i	0.0470438	+	0.0814823i
$73$	−7.95934			−0.931570			−0.465785	−	0.884898i	$-0.654228\pi$
$73$	−7.95934			−0.931570			−0.465785	+	0.884898i	$0.654228\pi$
$74$	1.01623	+	1.76016i	0.118134	+	0.204615i
$75$	4.56016	−	7.89843i	0.526562	−	0.912032i
$76$	1.37475	−	2.38114i	0.157695	−	0.273135i
$77$	5.75770			0.656151
$78$	0.641478	−	0.342150i	0.0726331	−	0.0387409i
$79$	3.56426			0.401011			0.200505	−	0.979693i	$-0.435742\pi$
$79$	3.56426			0.401011			0.200505	+	0.979693i	$0.435742\pi$
$80$	−7.06016	+	12.2286i	−0.789350	+	1.36719i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.282957	−	0.490096i	−0.0312474	−	0.0541220i
$83$	14.5643			1.59864			0.799318	−	0.600909i	$-0.205194\pi$
$83$	14.5643			1.59864			0.799318	+	0.600909i	$0.205194\pi$
$84$	−0.979671	−	1.69684i	−0.106891	−	0.185140i
$85$	−7.89425	−	13.6732i	−0.856252	−	1.48307i
$86$	0.193441			0.0208593
$87$	1.39918	+	2.42345i	0.150008	+	0.259821i
$88$	2.29836	−	3.98088i	0.245006	−	0.424363i
$89$	0.903279	−	1.56453i	0.0957474	−	0.165839i	−0.814173	−	0.580623i	$-0.802809\pi$
$89$	0.903279	−	1.56453i	0.0957474	−	0.165839i	0.909920	+	0.414783i	$0.136143\pi$
$90$	0.757702			0.0798688
$91$	−3.18131	+	1.69684i	−0.333492	+	0.177877i
$92$	−1.87968			−0.195970
$93$	2.17721	−	3.77104i	0.225766	−	0.391039i
$94$	0.673112	−	1.16586i	0.0694262	−	0.120250i
$95$	−2.63655	−	4.56664i	−0.270505	−	0.468528i
$96$	−2.35442			−0.240297
$97$	8.13655	+	14.0929i	0.826142	+	1.43092i	0.901044	+	0.433729i	$0.142802\pi$
$97$	8.13655	+	14.0929i	0.826142	+	1.43092i	−0.0749018	+	0.997191i	$0.523864\pi$
$98$	−0.100820	−	0.174625i	−0.0101843	−	0.0176398i
$99$	5.75770			0.578671
$100$	8.93491	+	15.4757i	0.893491	+	1.54757i
$101$	1.08459	−	1.87856i	0.107921	−	0.186924i	−0.807007	−	0.590542i	$-0.798914\pi$
$101$	1.08459	−	1.87856i	0.107921	−	0.186924i	0.914928	+	0.403618i	$0.132247\pi$
$102$	0.423609	−	0.733712i	0.0419435	−	0.0726483i
$103$	−8.43409			−0.831035			−0.415518	−	0.909585i	$-0.636400\pi$
$103$	−8.43409			−0.831035			−0.415518	+	0.909585i	$0.636400\pi$
$104$	−0.0967206	+	2.87690i	−0.00948424	+	0.282104i
$105$	−3.75770			−0.366714
$106$	1.10082	−	1.90668i	0.106921	−	0.185193i
$107$	3.73737	−	6.47332i	0.361305	−	0.625799i	−0.626871	−	0.779123i	$-0.715665\pi$
$107$	3.73737	−	6.47332i	0.361305	−	0.625799i	0.988176	+	0.153324i	$0.0489978\pi$
$108$	−0.979671	−	1.69684i	−0.0942689	−	0.163278i
$109$	9.52360			0.912196			0.456098	−	0.889930i	$-0.349247\pi$
$109$	9.52360			0.912196			0.456098	+	0.889930i	$0.349247\pi$
$110$	−2.18131	−	3.77814i	−0.207980	−	0.360232i
$111$	−5.03983	−	8.72925i	−0.478360	−	0.828543i
$112$	3.75770			0.355069
$113$	4.93491	+	8.54752i	0.464238	+	0.804083i	0.999167	−	0.0408138i	$-0.0129951\pi$
$113$	4.93491	+	8.54752i	0.464238	+	0.804083i	−0.534929	+	0.844897i	$0.679662\pi$
$114$	0.141478	−	0.245048i	0.0132507	−	0.0229508i
$115$	−1.80246	+	3.12195i	−0.168080	+	0.291123i
$116$	−5.48294			−0.509079
$117$	−3.18131	+	1.69684i	−0.294112	+	0.156873i
$118$	−2.49901			−0.230052
$119$	−2.10082	+	3.63873i	−0.192582	+	0.333562i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−11.0756	−	19.1834i	−1.00687	−	1.74395i
$122$	2.68624			0.243200
$123$	1.40328	+	2.43055i	0.126529	+	0.219155i
$124$	4.26590	+	7.38876i	0.383089	+	0.663530i
$125$	15.4829			1.38484
$126$	−0.100820	−	0.174625i	−0.00898175	−	0.0155568i
$127$	3.48377	−	6.03407i	0.309135	−	0.535437i	−0.669039	−	0.743228i	$-0.733294\pi$
$127$	3.48377	−	6.03407i	0.309135	−	0.535437i	0.978173	+	0.207791i	$0.0666273\pi$
$128$	3.06426	−	5.30745i	0.270845	−	0.469117i
$129$	−0.959341			−0.0844653
$130$	2.31869	+	1.44469i	0.203363	+	0.126708i
$131$	−9.75770			−0.852534			−0.426267	−	0.904597i	$-0.640172\pi$
$131$	−9.75770			−0.852534			−0.426267	+	0.904597i	$0.640172\pi$
$132$	−5.64065	+	9.76990i	−0.490956	+	0.850360i
$133$	−0.701640	+	1.21528i	−0.0608399	+	0.105378i
$134$	−0.766727	−	1.32801i	−0.0662351	−	0.114723i
$135$	−3.75770			−0.323411
$136$	1.67721	+	2.90502i	0.143820	+	0.249103i
$137$	1.66098	+	2.87690i	0.141907	+	0.245790i	0.928215	−	0.372045i	$-0.121343\pi$
$137$	1.66098	+	2.87690i	0.141907	+	0.245790i	−0.786308	+	0.617835i	$0.788010\pi$
$138$	−0.193441			−0.0164668
$139$	−0.399180	−	0.691400i	−0.0338580	−	0.0586438i	0.848600	−	0.529035i	$-0.177446\pi$
$139$	−0.399180	−	0.691400i	−0.0338580	−	0.0586438i	−0.882458	+	0.470391i	$0.844113\pi$
$140$	3.68131	−	6.37622i	0.311128	−	0.538889i
$141$	−3.33819	+	5.78192i	−0.281127	+	0.486925i
$142$	0.733440			0.0615489
$143$	17.6195	+	10.9781i	1.47342	+	0.918032i
$144$	3.75770			0.313142
$145$	−5.25770	+	9.10661i	−0.436628	+	0.756263i
$146$	0.802460	−	1.38990i	0.0664120	−	0.115029i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$	19.7495			1.62340
$149$	9.75688	+	16.8994i	0.799314	+	1.38445i	0.920063	+	0.391770i	$0.128137\pi$
$149$	9.75688	+	16.8994i	0.799314	+	1.38445i	−0.120749	+	0.992683i	$0.538530\pi$
$150$	0.919509	+	1.59264i	0.0750776	+	0.130038i
$151$	9.11212			0.741534			0.370767	−	0.928726i	$-0.379095\pi$
$151$	9.11212			0.741534			0.370767	+	0.928726i	$0.379095\pi$
$152$	0.560161	+	0.970228i	0.0454351	+	0.0786959i
$153$	−2.10082	+	3.63873i	−0.169841	+	0.294174i
$154$	−0.580491	+	1.00544i	−0.0467773	+	0.0810206i
$155$	16.3626			1.31428
$156$	0.237372	−	7.06052i	0.0190050	−	0.565294i
$157$	−1.62918			−0.130023			−0.0650114	−	0.997885i	$-0.520708\pi$
$157$	−1.62918			−0.130023			−0.0650114	+	0.997885i	$0.520708\pi$
$158$	−0.359348	+	0.622409i	−0.0285882	+	0.0495162i
$159$	−5.45934	+	9.45586i	−0.432954	+	0.749898i
$160$	−4.42361	−	7.66191i	−0.349717	−	0.605728i
$161$	0.959341			0.0756067
$162$	−0.100820	−	0.174625i	−0.00792115	−	0.0137198i
$163$	1.58132	+	2.73892i	0.123858	+	0.214529i	0.921286	−	0.388886i	$-0.127140\pi$
$163$	1.58132	+	2.73892i	0.123858	+	0.214529i	−0.797428	+	0.603414i	$0.793807\pi$
$164$	−5.49901			−0.429400
$165$	10.8179	+	18.7371i	0.842169	+	1.45868i
$166$	−1.46837	+	2.54329i	−0.113967	+	0.197397i
$167$	−5.41868	+	9.38543i	−0.419310	+	0.726267i	−0.995870	−	0.0907881i	$-0.971061\pi$
$167$	−5.41868	+	9.38543i	−0.419310	+	0.726267i	0.576560	+	0.817055i	$0.304395\pi$
$168$	0.798360			0.0615948
$169$	−12.9706	−	0.873125i	−0.997742	−	0.0671635i
$170$	3.18359			0.244170
$171$	−0.701640	+	1.21528i	−0.0536557	+	0.0929344i
$172$	0.939839	−	1.62785i	0.0716620	−	0.124122i
$173$	−4.43901	−	7.68859i	−0.337492	−	0.584553i	0.646468	−	0.762941i	$-0.276245\pi$
$173$	−4.43901	−	7.68859i	−0.337492	−	0.584553i	−0.983960	+	0.178388i	$0.942912\pi$
$174$	−0.564260			−0.0427765
$175$	−4.56016	−	7.89843i	−0.344716	−	0.597065i
$176$	−10.8179	−	18.7371i	−0.815427	−	1.41236i
$177$	12.3934			0.931547
$178$	0.182137	+	0.315470i	0.0136517	+	0.0236455i
$179$	2.55196	−	4.42013i	0.190743	−	0.330376i	−0.754754	−	0.656008i	$-0.772244\pi$
$179$	2.55196	−	4.42013i	0.190743	−	0.330376i	0.945497	+	0.325632i	$0.105577\pi$
$180$	3.68131	−	6.37622i	0.274389	−	0.475255i
$181$	11.2649			0.837314			0.418657	−	0.908144i	$-0.362501\pi$
$181$	11.2649			0.837314			0.418657	+	0.908144i	$0.362501\pi$
$182$	0.0244285	−	0.726612i	0.00181076	−	0.0538600i
$183$	−13.3220			−0.984788
$184$	0.382950	−	0.663289i	0.0282315	−	0.0488983i
$185$	18.9382	−	32.8019i	1.39236	−	2.41164i
$186$	0.439012	+	0.760391i	0.0321899	+	0.0557546i
$187$	24.1918			1.76908
$188$	−6.54066	−	11.3288i	−0.477027	−	0.826234i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	1.06327			0.0771375
$191$	−6.87475	−	11.9074i	−0.497440	−	0.861591i	0.502556	−	0.864545i	$-0.332393\pi$
$191$	−6.87475	−	11.9074i	−0.497440	−	0.861591i	−0.999996	+	0.00295401i	$0.999060\pi$
$192$	−3.52033	+	6.09739i	−0.254058	+	0.440041i
$193$	−7.95442	+	13.7775i	−0.572571	+	0.991723i	0.423729	+	0.905789i	$0.360721\pi$
$193$	−7.95442	+	13.7775i	−0.572571	+	0.991723i	−0.996301	+	0.0859339i	$0.972613\pi$
$194$	−3.28130			−0.235584
$195$	−11.4992	−	7.16472i	−0.823473	−	0.513076i
$196$	−1.95934			−0.139953
$197$	0.859348	−	1.48843i	0.0612260	−	0.106047i	−0.833788	−	0.552085i	$-0.813832\pi$
$197$	0.859348	−	1.48843i	0.0612260	−	0.106047i	0.895014	+	0.446039i	$0.147166\pi$
$198$	−0.580491	+	1.00544i	−0.0412537	+	0.0714534i
$199$	−3.97147	−	6.87879i	−0.281530	−	0.487625i	0.690232	−	0.723588i	$-0.257509\pi$
$199$	−3.97147	−	6.87879i	−0.281530	−	0.487625i	−0.971762	+	0.235964i	$0.924175\pi$
$200$	−7.28130			−0.514866
$201$	3.80246	+	6.58605i	0.268205	+	0.464544i
$202$	0.218696	+	0.378793i	0.0153874	+	0.0266518i
$203$	2.79836			0.196406
$204$	−4.11622	−	7.12951i	−0.288193	−	0.499165i
$205$	−5.27311	+	9.13329i	−0.368290	+	0.637896i
$206$	0.850323	−	1.47280i	0.0592448	−	0.102615i
$207$	0.959341			0.0666788
$208$	11.4992	+	7.16472i	0.797324	+	0.496784i
$209$	8.07966			0.558882
$210$	0.378851	−	0.656189i	0.0261432	−	0.0452813i
$211$	−12.6000	+	21.8238i	−0.867419	+	1.50241i	−0.00279458	+	0.999996i	$0.500890\pi$
$211$	−12.6000	+	21.8238i	−0.867419	+	1.50241i	−0.864625	+	0.502418i	$0.832444\pi$
$212$	−10.6967	−	18.5273i	−0.734653	−	1.27246i
$213$	−3.63738			−0.249229
$214$	0.753603	+	1.30528i	0.0515152	+	0.0892270i
$215$	−1.80246	−	3.12195i	−0.122927	−	0.212915i
$216$	0.798360			0.0543215
$217$	−2.17721	−	3.77104i	−0.147799	−	0.255995i
$218$	−0.960168	+	1.66306i	−0.0650308	+	0.112637i
$219$	−3.97967	+	6.89299i	−0.268921	+	0.465785i
$220$	−42.3918			−2.85805
$221$	−13.3667	+	7.12951i	−0.899143	+	0.479583i
$222$	2.03246			0.136410
$223$	2.33902	−	4.05130i	0.156632	−	0.271295i	−0.777020	−	0.629476i	$-0.783270\pi$
$223$	2.33902	−	4.05130i	0.156632	−	0.271295i	0.933652	+	0.358181i	$0.116603\pi$
$224$	−1.17721	+	2.03899i	−0.0786557	+	0.136236i
$225$	−4.56016	−	7.89843i	−0.304011	−	0.526562i
$226$	−1.99015			−0.132383
$227$	−7.89425	−	13.6732i	−0.523960	−	0.907525i	−0.999611	−	0.0278913i	$-0.991121\pi$
$227$	−7.89425	−	13.6732i	−0.523960	−	0.907525i	0.475651	−	0.879634i	$-0.342213\pi$
$228$	−1.37475	−	2.38114i	−0.0910452	−	0.157695i
$229$	22.3770			1.47872			0.739358	−	0.673313i	$-0.235129\pi$
$229$	22.3770			1.47872			0.739358	+	0.673313i	$0.235129\pi$
$230$	−0.363447	−	0.629509i	−0.0239650	−	0.0415086i
$231$	2.87885	−	4.98632i	0.189414	−	0.328076i
$232$	1.11705	−	1.93479i	0.0733379	−	0.127025i
$233$	7.64392			0.500770			0.250385	−	0.968146i	$-0.419443\pi$
$233$	7.64392			0.500770			0.250385	+	0.968146i	$0.419443\pi$
$234$	0.0244285	−	0.726612i	0.00159694	−	0.0475001i
$235$	−25.0879			−1.63655
$236$	−12.1415	+	21.0297i	−0.790343	+	1.36891i
$237$	1.78213	−	3.08674i	0.115762	−	0.200505i
$238$	−0.423609	−	0.733712i	−0.0274585	−	0.0475595i
$239$	19.5967			1.26761			0.633803	−	0.773494i	$-0.281493\pi$
$239$	19.5967			1.26761			0.633803	+	0.773494i	$0.281493\pi$
$240$	7.06016	+	12.2286i	0.455731	+	0.789350i
$241$	9.45032	+	16.3684i	0.608748	+	1.05438i	0.991447	+	0.130510i	$0.0416614\pi$
$241$	9.45032	+	16.3684i	0.608748	+	1.05438i	−0.382699	+	0.923873i	$0.625005\pi$
$242$	4.46655			0.287120
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	13.0511	−	22.6052i	0.835513	−	1.44715i
$245$	−1.87885	+	3.25427i	−0.120035	+	0.207907i
$246$	−0.565914			−0.0360813
$247$	−4.46427	+	2.38114i	−0.284055	+	0.151508i
$248$	−3.47640			−0.220751
$249$	7.28213	−	12.6130i	0.461486	−	0.799318i
$250$	−1.56099	+	2.70371i	−0.0987255	+	0.170998i
$251$	2.66181	+	4.61039i	0.168012	+	0.291005i	0.937721	−	0.347390i	$-0.112932\pi$
$251$	2.66181	+	4.61039i	0.168012	+	0.291005i	−0.769709	+	0.638395i	$0.779599\pi$
$252$	−1.95934			−0.123427
$253$	−2.76180	−	4.78358i	−0.173633	−	0.300741i
$254$	0.702466	+	1.21671i	0.0440767	+	0.0763430i
$255$	−15.7885			−0.988715
$256$	−6.42278	−	11.1246i	−0.401424	−	0.695287i
$257$	5.89835	−	10.2162i	0.367929	−	0.637272i	−0.621312	−	0.783563i	$-0.713400\pi$
$257$	5.89835	−	10.2162i	0.367929	−	0.637272i	0.989242	+	0.146291i	$0.0467335\pi$
$258$	0.0967206	−	0.167525i	0.00602156	−	0.0104297i
$259$	−10.0797			−0.626320
$260$	23.4228	−	12.4932i	1.45262	−	0.774794i
$261$	2.79836			0.173214
$262$	0.983770	−	1.70394i	0.0607775	−	0.105270i
$263$	−7.09179	+	12.2833i	−0.437299	+	0.757424i	−0.997480	−	0.0709463i	$-0.977398\pi$
$263$	−7.09179	+	12.2833i	−0.437299	+	0.757424i	0.560181	+	0.828370i	$0.310731\pi$
$264$	−2.29836	−	3.98088i	−0.141454	−	0.245006i
$265$	−41.0292			−2.52040
$266$	−0.141478	−	0.245048i	−0.00867460	−	0.0150248i
$267$	−0.903279	−	1.56453i	−0.0552798	−	0.0957474i
$268$	−14.9006			−0.910201
$269$	10.4992	+	18.1851i	0.640146	+	1.10877i	0.985400	+	0.170256i	$0.0544594\pi$
$269$	10.4992	+	18.1851i	0.640146	+	1.10877i	−0.345254	+	0.938509i	$0.612207\pi$
$270$	0.378851	−	0.656189i	0.0230561	−	0.0399344i
$271$	5.50410	−	9.53338i	0.334350	−	0.579112i	−0.649010	−	0.760780i	$-0.724817\pi$
$271$	5.50410	−	9.53338i	0.334350	−	0.579112i	0.983360	+	0.181669i	$0.0581498\pi$
$272$	15.7885			0.957319
$273$	−0.121149	+	3.60352i	−0.00733228	+	0.218095i
$274$	−0.669839			−0.0404665
$275$	−26.2560	+	45.4768i	−1.58330	+	2.74235i
$276$	−0.939839	+	1.62785i	−0.0565716	+	0.0979850i
$277$	15.0879	+	26.1329i	0.906542	+	1.57018i	0.818834	+	0.574030i	$0.194621\pi$
$277$	15.0879	+	26.1329i	0.906542	+	1.57018i	0.0877077	+	0.996146i	$0.472046\pi$
$278$	0.160981			0.00965501
$279$	−2.17721	−	3.77104i	−0.130346	−	0.225766i
$280$	1.50000	+	2.59808i	0.0896421	+	0.155265i
$281$	−7.48294			−0.446395			−0.223197	−	0.974773i	$-0.571649\pi$
$281$	−7.48294			−0.446395			−0.223197	+	0.974773i	$0.571649\pi$
$282$	−0.673112	−	1.16586i	−0.0400832	−	0.0694262i
$283$	−1.03656	+	1.79537i	−0.0616171	+	0.106724i	−0.895188	−	0.445688i	$-0.852959\pi$
$283$	−1.03656	+	1.79537i	−0.0616171	+	0.106724i	0.833571	+	0.552412i	$0.186292\pi$
$284$	3.56343	−	6.17205i	0.211451	−	0.366244i
$285$	−5.27311			−0.312352
$286$	−3.69344	+	1.97000i	−0.218398	+	0.116488i
$287$	2.80656			0.165666
$288$	−1.17721	+	2.03899i	−0.0693678	+	0.120149i
$289$	−0.326888	+	0.566187i	−0.0192287	+	0.0333051i
$290$	−1.06016	−	1.83625i	−0.0622548	−	0.107829i
$291$	16.2731			0.953946
$292$	−7.79753	−	13.5057i	−0.456316	−	0.790363i
$293$	−8.88705	−	15.3928i	−0.519187	−	0.899258i	−0.999751	−	0.0222988i	$-0.992901\pi$
$293$	−8.88705	−	15.3928i	−0.519187	−	0.899258i	0.480564	−	0.876959i	$-0.340432\pi$
$294$	−0.201640			−0.0117599
$295$	23.2854	+	40.3315i	1.35573	+	2.34819i
$296$	−4.02360	+	6.96908i	−0.233867	+	0.405070i
$297$	2.87885	−	4.98632i	0.167048	−	0.289335i
$298$	−3.93475			−0.227934
$299$	2.93574	+	1.82915i	0.169778	+	0.105783i
$300$	17.8698			1.03171
$301$	−0.479671	+	0.830814i	−0.0276478	+	0.0478873i
$302$	−0.918683	+	1.59121i	−0.0528643	+	0.0915636i
$303$	−1.08459	−	1.87856i	−0.0623081	−	0.107921i
$304$	5.27311			0.302433
$305$	−25.0300	−	43.3532i	−1.43321	−	2.48240i
$306$	−0.423609	−	0.733712i	−0.0242161	−	0.0419435i
$307$	−3.84556			−0.219478			−0.109739	−	0.993960i	$-0.535001\pi$
$307$	−3.84556			−0.219478			−0.109739	+	0.993960i	$0.535001\pi$
$308$	5.64065	+	9.76990i	0.321406	+	0.556691i
$309$	−4.21704	+	7.30413i	−0.239899	+	0.415518i
$310$	−1.64968	+	2.85732i	−0.0936953	+	0.162285i
$311$	−2.52360			−0.143100			−0.0715502	−	0.997437i	$-0.522795\pi$
$311$	−2.52360			−0.143100			−0.0715502	+	0.997437i	$0.522795\pi$
$312$	2.44311	+	1.52221i	0.138314	+	0.0861784i
$313$	29.2731			1.65461			0.827307	−	0.561750i	$-0.189872\pi$
$313$	29.2731			1.65461			0.827307	+	0.561750i	$0.189872\pi$
$314$	0.164254	−	0.284496i	0.00926938	−	0.0160550i
$315$	−1.87885	+	3.25427i	−0.105861	+	0.183357i
$316$	3.49180	+	6.04798i	0.196429	+	0.340225i
$317$	9.81476			0.551252			0.275626	−	0.961265i	$-0.411115\pi$
$317$	9.81476			0.551252			0.275626	+	0.961265i	$0.411115\pi$
$318$	−1.10082	−	1.90668i	−0.0617309	−	0.106921i
$319$	−8.05606	−	13.9535i	−0.451053	−	0.781247i
$320$	−26.4567			−1.47897
$321$	−3.73737	−	6.47332i	−0.208600	−	0.361305i
$322$	−0.0967206	+	0.167525i	−0.00539003	+	0.00933581i
$323$	−2.94804	+	5.10615i	−0.164033	+	0.284114i
$324$	−1.95934			−0.108852
$325$	1.10492	−	32.8652i	0.0612899	−	1.82303i
$326$	−0.637713			−0.0353196
$327$	4.76180	−	8.24768i	0.263328	−	0.456098i
$328$	1.12032	−	1.94046i	0.0618595	−	0.107144i
$329$	3.33819	+	5.78192i	0.184041	+	0.318767i
$330$	−4.36262			−0.240154
$331$	−17.3585	−	30.0658i	−0.954111	−	1.65257i	−0.736390	−	0.676557i	$-0.763471\pi$
$331$	−17.3585	−	30.0658i	−0.954111	−	1.65257i	−0.217720	−	0.976011i	$-0.569862\pi$
$332$	14.2682	+	24.7132i	0.783068	+	1.35631i
$333$	−10.0797			−0.552362
$334$	−1.09262	−	1.89248i	−0.0597856	−	0.103552i
$335$	−14.2885	+	24.7484i	−0.780665	+	1.35215i
$336$	1.87885	−	3.25427i	0.102500	−	0.177535i
$337$	5.46655			0.297782			0.148891	−	0.988854i	$-0.452430\pi$
$337$	5.46655			0.297782			0.148891	+	0.988854i	$0.452430\pi$
$338$	1.46017	−	2.17697i	0.0794227	−	0.118412i
$339$	9.86983			0.536055
$340$	15.4675	−	26.7906i	0.838845	−	1.45292i
$341$	−12.5357	+	21.7125i	−0.678848	+	1.17580i
$342$	−0.141478	−	0.245048i	−0.00765028	−	0.0132507i
$343$	1.00000			0.0539949
$344$	0.382950	+	0.663289i	0.0206473	+	0.0357621i
$345$	1.80246	+	3.12195i	0.0970412	+	0.168080i
$346$	1.79016			0.0962397
$347$	−11.0349	−	19.1130i	−0.592385	−	1.02604i	−0.993910	−	0.110193i	$-0.964853\pi$
$347$	−11.0349	−	19.1130i	−0.592385	−	1.02604i	0.401525	−	0.915848i	$-0.368480\pi$
$348$	−2.74147	+	4.74837i	−0.146958	+	0.254539i
$349$	6.67229	−	11.5567i	0.357159	−	0.618618i	−0.630326	−	0.776331i	$-0.717079\pi$
$349$	6.67229	−	11.5567i	0.357159	−	0.618618i	0.987485	+	0.157713i	$0.0504120\pi$
$350$	1.83902			0.0982997
$351$	−0.121149	+	3.60352i	−0.00646646	+	0.192341i
$352$	13.5561			0.722541
$353$	13.6602	−	23.6601i	0.727057	−	1.25930i	−0.231065	−	0.972938i	$-0.574221\pi$
$353$	13.6602	−	23.6601i	0.727057	−	1.25930i	0.958122	−	0.286361i	$-0.0924456\pi$
$354$	−1.24950	+	2.16420i	−0.0664104	+	0.115026i
$355$	−6.83409	−	11.8370i	−0.362716	−	0.628243i
$356$	3.53967			0.187602
$357$	2.10082	+	3.63873i	0.111187	+	0.192582i
$358$	0.514577	+	0.891273i	0.0271962	+	0.0471053i
$359$	2.16263			0.114139			0.0570697	−	0.998370i	$-0.481824\pi$
$359$	2.16263			0.114139			0.0570697	+	0.998370i	$0.481824\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	8.51540	−	14.7491i	0.448179	−	0.776269i
$362$	−1.13573	+	1.96714i	−0.0596924	+	0.103390i
$363$	−22.1511			−1.16263
$364$	−5.99590	−	3.73583i	−0.314271	−	0.195811i
$365$	−29.9088			−1.56550
$366$	1.34312	−	2.32635i	0.0702059	−	0.121600i
$367$	7.35770	−	12.7439i	0.384069	−	0.665226i	−0.607571	−	0.794265i	$-0.707856\pi$
$367$	7.35770	−	12.7439i	0.384069	−	0.665226i	0.991639	+	0.129039i	$0.0411893\pi$
$368$	−1.80246	−	3.12195i	−0.0939597	−	0.162743i
$369$	2.80656			0.146104
$370$	3.81869	+	6.61416i	0.198524	+	0.343854i
$371$	5.45934	+	9.45586i	0.283435	+	0.490924i
$372$	8.53180			0.442353
$373$	15.9138	+	27.5634i	0.823983	+	1.42718i	0.902694	+	0.430283i	$0.141586\pi$
$373$	15.9138	+	27.5634i	0.823983	+	1.42718i	−0.0787109	+	0.996897i	$0.525080\pi$
$374$	−2.43901	+	4.22449i	−0.126118	+	0.218443i
$375$	7.74147	−	13.4086i	0.399768	−	0.692418i
$376$	5.33016			0.274882
$377$	8.56343	+	5.33557i	0.441039	+	0.274796i
$378$	−0.201640			−0.0103712
$379$	13.8292	−	23.9528i	0.710357	−	1.23037i	−0.254367	−	0.967108i	$-0.581867\pi$
$379$	13.8292	−	23.9528i	0.710357	−	1.23037i	0.964723	−	0.263266i	$-0.0847997\pi$
$380$	5.16591	−	8.94761i	0.265005	−	0.459003i
$381$	−3.48377	−	6.03407i	−0.178479	−	0.309135i
$382$	2.77245			0.141851
$383$	11.8374	+	20.5029i	0.604861	+	1.04765i	0.992073	+	0.125660i	$0.0401047\pi$
$383$	11.8374	+	20.5029i	0.604861	+	1.04765i	−0.387212	+	0.921991i	$0.626562\pi$
$384$	−3.06426	−	5.30745i	−0.156372	−	0.270845i
$385$	21.6357			1.10266
$386$	−1.60393	−	2.77808i	−0.0816377	−	0.141401i
$387$	−0.479671	+	0.830814i	−0.0243830	+	0.0422327i
$388$	−15.9423	+	27.6128i	−0.809347	+	1.40183i
$389$	8.79016			0.445679			0.222839	−	0.974855i	$-0.428467\pi$
$389$	8.79016			0.445679			0.222839	+	0.974855i	$0.428467\pi$
$390$	2.41048	−	1.28570i	0.122060	−	0.0651039i
$391$	4.03081			0.203847
$392$	0.399180	−	0.691400i	0.0201616	−	0.0349210i
$393$	−4.87885	+	8.45042i	−0.246105	+	0.426267i
$394$	0.173279	+	0.300127i	0.00872965	+	0.0151202i
$395$	13.3934			0.673896
$396$	5.64065	+	9.76990i	0.283453	+	0.490956i
$397$	8.56343	+	14.8323i	0.429786	+	0.744412i	0.996854	−	0.0792593i	$-0.0252555\pi$
$397$	8.56343	+	14.8323i	0.429786	+	0.744412i	−0.567068	+	0.823671i	$0.691922\pi$
$398$	1.60161			0.0802816
$399$	0.701640	+	1.21528i	0.0351259	+	0.0608399i
$400$	−17.1357	+	29.6799i	−0.856786	+	1.48400i
$401$	−8.91458	+	15.4405i	−0.445173	+	0.771062i	−0.998064	−	0.0621911i	$-0.980191\pi$
$401$	−8.91458	+	15.4405i	−0.445173	+	0.771062i	0.552891	+	0.833253i	$0.313525\pi$
$402$	−1.53345			−0.0764817
$403$	0.527534	−	15.6912i	0.0262784	−	0.781636i
$404$	4.25016			0.211454
$405$	−1.87885	+	3.25427i	−0.0933609	+	0.161706i
$406$	−0.282130	+	0.488664i	−0.0140019	+	0.0242520i
$407$	29.0178	+	50.2604i	1.43836	+	2.49132i
$408$	3.35442			0.166069
$409$	8.87393	+	15.3701i	0.438787	+	0.760002i	0.997596	−	0.0692945i	$-0.0220748\pi$
$409$	8.87393	+	15.3701i	0.438787	+	0.760002i	−0.558809	+	0.829296i	$0.688741\pi$
$410$	−1.06327	−	1.84163i	−0.0525110	−	0.0909518i
$411$	3.32196			0.163860
$412$	−8.26263	−	14.3113i	−0.407070	−	0.705067i
$413$	6.19671	−	10.7330i	0.304920	−	0.528138i
$414$	−0.0967206	+	0.167525i	−0.00475356	+	0.00823341i
$415$	54.7281			2.68650
$416$	−7.49015	+	3.99508i	−0.367235	+	0.195875i
$417$	−0.798360			−0.0390959
$418$	−0.814590	+	1.41091i	−0.0398429	+	0.0690100i
$419$	−3.99917	+	6.92677i	−0.195372	+	0.338395i	−0.947023	−	0.321167i	$-0.895925\pi$
$419$	−3.99917	+	6.92677i	−0.195372	+	0.338395i	0.751650	+	0.659562i	$0.229258\pi$
$420$	−3.68131	−	6.37622i	−0.179630	−	0.311128i
$421$	−23.7721			−1.15858			−0.579291	−	0.815121i	$-0.696670\pi$
$421$	−23.7721			−1.15858			−0.579291	+	0.815121i	$0.696670\pi$
$422$	−2.54066	−	4.40055i	−0.123677	−	0.214215i
$423$	3.33819	+	5.78192i	0.162308	+	0.281127i
$424$	8.71704			0.423337
$425$	−19.1602	−	33.1864i	−0.929404	−	1.60977i
$426$	0.366720	−	0.635178i	0.0177676	−	0.0307745i
$427$	−6.66098	+	11.5372i	−0.322347	+	0.558322i
$428$	14.6456			0.707921
$429$	18.3170	−	9.76990i	0.884355	−	0.471695i
$430$	0.726895			0.0350540
$431$	−3.01623	+	5.22426i	−0.145287	+	0.251644i	−0.929480	−	0.368873i	$-0.879744\pi$
$431$	−3.01623	+	5.22426i	−0.145287	+	0.251644i	0.784193	+	0.620517i	$0.213077\pi$
$432$	1.87885	−	3.25427i	0.0903963	−	0.156571i
$433$	−3.14558	−	5.44830i	−0.151167	−	0.261829i	0.780490	−	0.625168i	$-0.214970\pi$
$433$	−3.14558	−	5.44830i	−0.151167	−	0.261829i	−0.931657	+	0.363340i	$0.881636\pi$
$434$	0.878024			0.0421465
$435$	5.25770	+	9.10661i	0.252088	+	0.436628i
$436$	9.32999	+	16.1600i	0.446826	+	0.773925i
$437$	1.34622			0.0643986
$438$	−0.802460	−	1.38990i	−0.0383430	−	0.0664120i
$439$	−14.7519	+	25.5511i	−0.704072	+	1.21949i	0.262953	+	0.964809i	$0.415304\pi$
$439$	−14.7519	+	25.5511i	−0.704072	+	1.21949i	−0.967025	+	0.254680i	$0.918030\pi$
$440$	8.63655	−	14.9589i	0.411731	−	0.713140i
$441$	1.00000			0.0476190
$442$	0.102640	−	3.05296i	0.00488207	−	0.145215i
$443$	−14.5318			−0.690427			−0.345213	−	0.938524i	$-0.612193\pi$
$443$	−14.5318			−0.690427			−0.345213	+	0.938524i	$0.612193\pi$
$444$	9.87475	−	17.1036i	0.468635	−	0.811700i
$445$	3.39425	−	5.87902i	0.160903	−	0.278692i
$446$	0.471639	+	0.816903i	0.0223328	+	0.0386815i
$447$	19.5138			0.922969
$448$	3.52033	+	6.09739i	0.166320	+	0.288075i
$449$	−5.04803	−	8.74345i	−0.238231	−	0.412629i	0.721976	−	0.691919i	$-0.243234\pi$
$449$	−5.04803	−	8.74345i	−0.238231	−	0.412629i	−0.960207	+	0.279290i	$0.909901\pi$
$450$	1.83902			0.0866922
$451$	−8.07966	−	13.9944i	−0.380457	−	0.658970i
$452$	−9.66918	+	16.7475i	−0.454800	+	0.787737i
$453$	4.55606	−	7.89133i	0.214062	−	0.370767i
$454$	3.18359			0.149413
$455$	−11.9544	+	6.37622i	−0.560432	+	0.298922i
$456$	1.12032			0.0524639
$457$	−9.30884	+	16.1234i	−0.435449	+	0.754220i	−0.997332	−	0.0729967i	$-0.976744\pi$
$457$	−9.30884	+	16.1234i	−0.435449	+	0.754220i	0.561883	+	0.827217i	$0.310077\pi$
$458$	−2.25605	+	3.90759i	−0.105418	+	0.182590i
$459$	2.10082	+	3.63873i	0.0980579	+	0.169841i
$460$	−7.06327			−0.329327
$461$	−15.3690	−	26.6199i	−0.715806	−	1.23981i	−0.962648	−	0.270756i	$-0.912726\pi$
$461$	−15.3690	−	26.6199i	−0.715806	−	1.23981i	0.246842	−	0.969056i	$-0.420607\pi$
$462$	0.580491	+	1.00544i	0.0270069	+	0.0467773i
$463$	−30.4747			−1.41628			−0.708141	−	0.706071i	$-0.750466\pi$
$463$	−30.4747			−1.41628			−0.708141	+	0.706071i	$0.750466\pi$
$464$	−5.25770	−	9.10661i	−0.244083	−	0.422764i
$465$	8.18131	−	14.1704i	0.379399	−	0.657139i
$466$	−0.770659	+	1.33482i	−0.0357001	+	0.0618344i
$467$	−10.7006			−0.495167			−0.247583	−	0.968867i	$-0.579636\pi$
$467$	−10.7006			−0.495167			−0.247583	+	0.968867i	$0.579636\pi$
$468$	−5.99590	−	3.73583i	−0.277161	−	0.172689i
$469$	7.60492			0.351163
$470$	2.52935	−	4.38097i	0.116670	−	0.202079i
$471$	−0.814590	+	1.41091i	−0.0375343	+	0.0650114i
$472$	−4.94721	−	8.56882i	−0.227714	−	0.394412i
$473$	5.52360			0.253975
$474$	0.359348	+	0.622409i	0.0165054	+	0.0285882i
$475$	−6.39918	−	11.0837i	−0.293615	−	0.508555i
$476$	−8.23245			−0.377334
$477$	5.45934	+	9.45586i	0.249966	+	0.432954i
$478$	−1.97574	+	3.42208i	−0.0903682	+	0.156522i
$479$	3.57639	−	6.19449i	0.163409	−	0.283034i	−0.772680	−	0.634796i	$-0.781084\pi$
$479$	3.57639	−	6.19449i	0.163409	−	0.283034i	0.936089	+	0.351762i	$0.114417\pi$
$480$	−8.84722			−0.403818
$481$	−30.8454	−	19.2187i	−1.40643	−	0.876295i
$482$	−3.81112			−0.173592
$483$	0.479671	−	0.830814i	0.0218258	−	0.0378033i
$484$	21.7008	−	37.5869i	0.986401	−	1.70850i
$485$	30.5747	+	52.9570i	1.38833	+	2.40465i
$486$	−0.201640			−0.00914656
$487$	18.1162	+	31.3782i	0.820924	+	1.42188i	0.904995	+	0.425423i	$0.139875\pi$
$487$	18.1162	+	31.3782i	0.820924	+	1.42188i	−0.0840702	+	0.996460i	$0.526792\pi$
$488$	5.31786	+	9.21081i	0.240728	+	0.416954i
$489$	3.16263			0.143019
$490$	−0.378851	−	0.656189i	−0.0171147	−	0.0296436i
$491$	3.56016	−	6.16638i	0.160668	−	0.278285i	−0.774441	−	0.632647i	$-0.781969\pi$
$491$	3.56016	−	6.16638i	0.160668	−	0.278285i	0.935108	+	0.354362i	$0.115302\pi$
$492$	−2.74950	+	4.76228i	−0.123957	+	0.214700i
$493$	11.7577			0.529540
$494$	0.0342800	−	1.01964i	0.00154233	−	0.0458757i
$495$	21.6357			0.972454
$496$	−8.18131	+	14.1704i	−0.367352	+	0.636272i
$497$	−1.81869	+	3.15006i	−0.0815794	+	0.141300i
$498$	1.46837	+	2.54329i	0.0657991	+	0.113967i
$499$	−32.2797			−1.44504			−0.722518	−	0.691352i	$-0.757015\pi$
$499$	−32.2797			−1.44504			−0.722518	+	0.691352i	$0.757015\pi$
$500$	15.1682	+	26.2721i	0.678342	+	1.17492i
$501$	5.41868	+	9.38543i	0.242089	+	0.419310i
$502$	−1.07345			−0.0479105
$503$	−18.1275	−	31.3978i	−0.808267	−	1.39996i	−0.914064	−	0.405571i	$-0.867073\pi$
$503$	−18.1275	−	31.3978i	−0.808267	−	1.39996i	0.105797	−	0.994388i	$-0.466261\pi$
$504$	0.399180	−	0.691400i	0.0177809	−	0.0307974i
$505$	4.07556	−	7.05909i	0.181360	−	0.314125i
$506$	1.11378			0.0495134
$507$	−7.24147	+	10.7963i	−0.321605	+	0.479483i
$508$	13.6518			0.605700
$509$	6.27311	−	10.8653i	0.278051	−	0.481598i	−0.692850	−	0.721082i	$-0.743645\pi$
$509$	6.27311	−	10.8653i	0.278051	−	0.481598i	0.970900	+	0.239484i	$0.0769784\pi$
$510$	1.59179	−	2.75707i	0.0704859	−	0.122085i
$511$	3.97967	+	6.89299i	0.176050	+	0.304928i
$512$	14.8472			0.656161
$513$	0.701640	+	1.21528i	0.0309781	+	0.0536557i
$514$	1.18934	+	2.06000i	0.0524596	+	0.0908627i
$515$	−31.6928			−1.39655
$516$	−0.939839	−	1.62785i	−0.0413741	−	0.0716620i
$517$	19.2203	−	33.2906i	0.845309	−	1.46412i
$518$	1.01623	−	1.76016i	0.0446506	−	0.0773371i
$519$	−8.87802			−0.389702
$520$	−0.363447	+	10.8105i	−0.0159382	+	0.474074i
$521$	−27.0390			−1.18460			−0.592300	−	0.805717i	$-0.701780\pi$
$521$	−27.0390			−1.18460			−0.592300	+	0.805717i	$0.701780\pi$
$522$	−0.282130	+	0.488664i	−0.0123485	+	0.0213882i
$523$	−5.32999	+	9.23182i	−0.233064	+	0.403679i	−0.958708	−	0.284391i	$-0.908209\pi$
$523$	−5.32999	+	9.23182i	−0.233064	+	0.403679i	0.725644	+	0.688070i	$0.241542\pi$
$524$	−9.55933	−	16.5573i	−0.417601	−	0.723307i
$525$	−9.12032			−0.398044
$526$	−1.42999	−	2.47681i	−0.0623504	−	0.107994i
$527$	−9.14786	−	15.8446i	−0.398487	−	0.690200i
$528$	−21.6357			−0.941574
$529$	11.0398	+	19.1215i	0.479993	+	0.831372i
$530$	4.13655	−	7.16472i	0.179680	−	0.311216i
$531$	6.19671	−	10.7330i	0.268914	−	0.465774i
$532$	−2.74950			−0.119206
$533$	8.58852	+	5.35120i	0.372010	+	0.231786i
$534$	0.364274			0.0157637
$535$	14.0439	−	24.3248i	0.607172	−	1.05165i
$536$	3.03573	−	5.25804i	0.131124	−	0.227113i
$537$	−2.55196	−	4.42013i	−0.110125	−	0.190743i
$538$	−4.23410			−0.182545
$539$	−2.87885	−	4.98632i	−0.124001	−	0.214776i
$540$	−3.68131	−	6.37622i	−0.158418	−	0.274389i
$541$	−5.20164			−0.223636			−0.111818	−	0.993729i	$-0.535667\pi$
$541$	−5.20164			−0.223636			−0.111818	+	0.993729i	$0.535667\pi$
$542$	1.10984	+	1.92231i	0.0476719	+	0.0825702i
$543$	5.63245	−	9.75570i	0.241712	−	0.418657i
$544$	−4.94622	+	8.56710i	−0.212067	+	0.367311i
$545$	35.7869			1.53294
$546$	−0.617050	−	0.384462i	−0.0264073	−	0.0164534i
$547$	−27.4567			−1.17396			−0.586982	−	0.809600i	$-0.699684\pi$
$547$	−27.4567			−1.17396			−0.586982	+	0.809600i	$0.699684\pi$
$548$	−3.25443	+	5.63684i	−0.139022	+	0.240794i
$549$	−6.66098	+	11.5372i	−0.284284	+	0.492394i
$550$	−5.29426	−	9.16993i	−0.225748	−	0.391007i
$551$	3.92688			0.167291
$552$	−0.382950	−	0.663289i	−0.0162994	−	0.0282315i
$553$	−1.78213	−	3.08674i	−0.0757839	−	0.131262i
$554$	−6.08462			−0.258511
$555$	−18.9382	−	32.8019i	−0.803881	−	1.39236i
$556$	0.782130	−	1.35469i	0.0331697	−	0.0574516i
$557$	−7.19754	+	12.4665i	−0.304970	+	0.528223i	−0.977255	−	0.212070i	$-0.931980\pi$
$557$	−7.19754	+	12.4665i	−0.304970	+	0.528223i	0.672285	+	0.740292i	$0.265313\pi$
$558$	0.878024			0.0371697
$559$	−3.05196	+	1.62785i	−0.129084	+	0.0688507i
$560$	14.1203			0.596693
$561$	12.0959	−	20.9507i	0.510689	−	0.884539i
$562$	0.754429	−	1.30671i	0.0318237	−	0.0551202i
$563$	−5.31066	−	9.19833i	−0.223818	−	0.387663i	0.732146	−	0.681147i	$-0.238519\pi$
$563$	−5.31066	−	9.19833i	−0.223818	−	0.387663i	−0.955964	+	0.293484i	$0.905185\pi$
$564$	−13.0813			−0.550823
$565$	18.5439	+	32.1190i	0.780149	+	1.35126i
$566$	−0.209011	−	0.362019i	−0.00878541	−	0.0152168i
$567$	1.00000			0.0419961
$568$	1.45197	+	2.51489i	0.0609233	+	0.105522i
$569$	9.20491	−	15.9434i	0.385890	−	0.668381i	−0.606002	−	0.795463i	$-0.707228\pi$
$569$	9.20491	−	15.9434i	0.385890	−	0.668381i	0.991892	+	0.127082i	$0.0405611\pi$
$570$	0.531634	−	0.920816i	0.0222677	−	0.0385688i
$571$	−17.0698			−0.714349			−0.357175	−	0.934038i	$-0.616260\pi$
$571$	−17.0698			−0.714349			−0.357175	+	0.934038i	$0.616260\pi$
$572$	−1.36672	+	40.6524i	−0.0571454	+	1.69976i
$573$	−13.7495			−0.574394
$574$	−0.282957	+	0.490096i	−0.0118104	+	0.0204562i
$575$	−4.37475	+	7.57729i	−0.182440	+	0.315995i
$576$	3.52033	+	6.09739i	0.146680	+	0.254058i
$577$	−5.84722			−0.243423			−0.121711	−	0.992566i	$-0.538838\pi$
$577$	−5.84722			−0.243423			−0.121711	+	0.992566i	$0.538838\pi$
$578$	−0.0659136	−	0.114166i	−0.00274164	−	0.00474867i
$579$	7.95442	+	13.7775i	0.330574	+	0.572571i
$580$	−20.6033			−0.855504
$581$	−7.28213	−	12.6130i	−0.302114	−	0.523276i
$582$	−1.64065	+	2.84169i	−0.0680072	+	0.117792i
$583$	31.4333	−	54.4440i	1.30183	−	2.25484i
$584$	6.35442			0.262948
$585$	−11.9544	+	6.37622i	−0.494254	+	0.263624i
$586$	3.58396			0.148052
$587$	−16.0244	+	27.7551i	−0.661399	+	1.14558i	0.318849	+	0.947805i	$0.396704\pi$
$587$	−16.0244	+	27.7551i	−0.661399	+	1.14558i	−0.980248	+	0.197771i	$0.936630\pi$
$588$	−0.979671	+	1.69684i	−0.0404009	+	0.0699765i
$589$	−3.05524	−	5.29182i	−0.125889	−	0.218046i
$590$	−9.39052			−0.386602
$591$	−0.859348	−	1.48843i	−0.0353489	−	0.0612260i
$592$	18.9382	+	32.8019i	0.778355	+	1.34815i
$593$	14.1347			0.580444			0.290222	−	0.956959i	$-0.406271\pi$
$593$	14.1347			0.580444			0.290222	+	0.956959i	$0.406271\pi$
$594$	0.580491	+	1.00544i	0.0238178	+	0.0412537i
$595$	−7.89425	+	13.6732i	−0.323633	+	0.560549i
$596$	−19.1170	+	33.1117i	−0.783065	+	1.35631i
$597$	−7.94294			−0.325083
$598$	−0.615397	+	0.328239i	−0.0251654	+	0.0134227i
$599$	−16.5154			−0.674801			−0.337401	−	0.941361i	$-0.609548\pi$
$599$	−16.5154			−0.674801			−0.337401	+	0.941361i	$0.609548\pi$
$600$	−3.64065	+	6.30579i	−0.148629	+	0.257433i
$601$	1.87885	−	3.25427i	0.0766399	−	0.132744i	−0.825158	−	0.564902i	$-0.808914\pi$
$601$	1.87885	−	3.25427i	0.0766399	−	0.132744i	0.901798	+	0.432157i	$0.142247\pi$
$602$	−0.0967206	−	0.167525i	−0.00394204	−	0.00682781i
$603$	7.60492			0.309696
$604$	8.92688	+	15.4618i	0.363230	+	0.629132i
$605$	−41.6187	−	72.0857i	−1.69204	−	2.93070i
$606$	0.437393			0.0177679
$607$	−5.35132	−	9.26875i	−0.217203	−	0.376207i	0.736749	−	0.676167i	$-0.236360\pi$
$607$	−5.35132	−	9.26875i	−0.217203	−	0.376207i	−0.953952	+	0.299960i	$0.903027\pi$
$608$	−1.65196	+	2.86127i	−0.0669957	+	0.116040i
$609$	1.39918	−	2.42345i	0.0566976	−	0.0982032i
$610$	10.0941			0.408697
$611$	−0.808838	+	24.0585i	−0.0327221	+	0.973301i
$612$	−8.23245			−0.332777
$613$	4.17001	−	7.22266i	0.168425	−	0.291721i	−0.769441	−	0.638718i	$-0.779465\pi$
$613$	4.17001	−	7.22266i	0.168425	−	0.291721i	0.937866	+	0.346997i	$0.112799\pi$
$614$	0.387709	−	0.671532i	0.0156467	−	0.0271008i
$615$	5.27311	+	9.13329i	0.212632	+	0.368290i
$616$	−4.59672			−0.185207
$617$	0.475572	+	0.823714i	0.0191458	+	0.0331615i	0.875440	−	0.483328i	$-0.160572\pi$
$617$	0.475572	+	0.823714i	0.0191458	+	0.0331615i	−0.856294	+	0.516489i	$0.827239\pi$
$618$	−0.850323	−	1.47280i	−0.0342050	−	0.0592448i
$619$	13.2098			0.530948			0.265474	−	0.964118i	$-0.414472\pi$
$619$	13.2098			0.530948			0.265474	+	0.964118i	$0.414472\pi$
$620$	16.0300	+	27.7647i	0.643780	+	1.11506i
$621$	0.479671	−	0.830814i	0.0192485	−	0.0333394i
$622$	0.254429	−	0.440684i	0.0102017	−	0.0176698i
$623$	−1.80656			−0.0723782
$624$	11.9544	−	6.37622i	0.478560	−	0.255253i
$625$	12.5787			0.503147
$626$	−2.95131	+	5.11182i	−0.117958	+	0.204309i
$627$	4.03983	−	6.99719i	0.161335	−	0.279441i
$628$	−1.59606	−	2.76446i	−0.0636898	−	0.110314i
$629$	−42.3511			−1.68865
$630$	−0.378851	−	0.656189i	−0.0150938	−	0.0261432i
$631$	−18.5756	−	32.1738i	−0.739482	−	1.28082i	−0.952729	−	0.303821i	$-0.901737\pi$
$631$	−18.5756	−	32.1738i	−0.739482	−	1.28082i	0.213247	−	0.976998i	$-0.431596\pi$
$632$	−2.84556			−0.113190
$633$	12.6000	+	21.8238i	0.500805	+	0.867419i
$634$	−0.989522	+	1.71390i	−0.0392989	+	0.0680678i
$635$	13.0910	−	22.6742i	0.519499	−	0.899799i
$636$	−21.3934			−0.848305
$637$	3.06016	+	1.90668i	0.121248	+	0.0755452i
$638$	3.24884			0.128623
$639$	−1.81869	+	3.15006i	−0.0719462	+	0.124615i
$640$	11.5146	−	19.9438i	0.455154	−	0.788349i
$641$	8.47967	+	14.6872i	0.334927	+	0.580110i	0.983471	−	0.181067i	$-0.0579551\pi$
$641$	8.47967	+	14.6872i	0.334927	+	0.580110i	−0.648544	+	0.761177i	$0.724622\pi$
$642$	1.50721			0.0594846
$643$	−11.3066	−	19.5835i	−0.445887	−	0.772299i	0.552226	−	0.833694i	$-0.313778\pi$
$643$	−11.3066	−	19.5835i	−0.445887	−	0.772299i	−0.998114	+	0.0613950i	$0.980445\pi$
$644$	0.939839	+	1.62785i	0.0370348	+	0.0641462i
$645$	−3.60492			−0.141944
$646$	−0.594441	−	1.02960i	−0.0233880	−	0.0405092i
$647$	−0.641478	+	1.11107i	−0.0252191	+	0.0436808i	−0.878360	−	0.478001i	$-0.841362\pi$
$647$	−0.641478	+	1.11107i	−0.0252191	+	0.0436808i	0.853140	+	0.521681i	$0.174695\pi$
$648$	0.399180	−	0.691400i	0.0156813	−	0.0271608i
$649$	−71.3577			−2.80103
$650$	5.62769	+	3.50641i	0.220736	+	0.137533i
$651$	−4.35442			−0.170663
$652$	−3.09834	+	5.36648i	−0.121340	+	0.210168i
$653$	24.4901	−	42.4182i	0.958374	−	1.65995i	0.231922	−	0.972734i	$-0.425499\pi$
$653$	24.4901	−	42.4182i	0.958374	−	1.65995i	0.726452	−	0.687217i	$-0.241168\pi$
$654$	0.960168	+	1.66306i	0.0375455	+	0.0650308i
$655$	−36.6665			−1.43268
$656$	−5.27311	−	9.13329i	−0.205880	−	0.356595i
$657$	3.97967	+	6.89299i	0.155262	+	0.268921i
$658$	−1.34622			−0.0524813
$659$	−5.10575	−	8.84341i	−0.198892	−	0.344490i	0.749278	−	0.662256i	$-0.230401\pi$
$659$	−5.10575	−	8.84341i	−0.198892	−	0.344490i	−0.948169	+	0.317766i	$0.897068\pi$
$660$	−21.1959	+	36.7124i	−0.825049	+	1.42903i
$661$	−12.8536	+	22.2631i	−0.499947	+	0.865933i	−1.00000		6.12722e-5i	$-0.999980\pi$
$661$	−12.8536	+	22.2631i	−0.499947	+	0.865933i	0.500053	+	0.865995i	$0.333314\pi$
$662$	7.00033			0.272076
$663$	−0.509025	+	15.1407i	−0.0197689	+	0.588015i
$664$	−11.6275			−0.451236
$665$	−2.63655	+	4.56664i	−0.102241	+	0.177087i
$666$	1.01623	−	1.76016i	0.0393781	−	0.0682049i
$667$	−1.34229	−	2.32492i	−0.0519737	−	0.0900211i
$668$	−21.2341			−0.821572
$669$	−2.33902	−	4.05130i	−0.0904317	−	0.156632i
$670$	−2.88113	−	4.99026i	−0.111308	−	0.192791i
$671$	76.7039			2.96112
$672$	1.17721	+	2.03899i	0.0454119	+	0.0786557i
$673$	−4.29443	+	7.43817i	−0.165538	+	0.286720i	−0.936846	−	0.349742i	$-0.886269\pi$
$673$	−4.29443	+	7.43817i	−0.165538	+	0.286720i	0.771308	+	0.636462i	$0.219603\pi$
$674$	−0.551136	+	0.954596i	−0.0212290	+	0.0367697i
$675$	−9.12032			−0.351041
$676$	−11.2254	−	22.8645i	−0.431746	−	0.879403i
$677$	8.70065			0.334393			0.167197	−	0.985924i	$-0.446529\pi$
$677$	8.70065			0.334393			0.167197	+	0.985924i	$0.446529\pi$
$678$	−0.995074	+	1.72352i	−0.0382156	+	0.0661914i
$679$	8.13655	−	14.0929i	0.312252	−	0.540837i
$680$	6.30246	+	10.9162i	0.241688	+	0.418616i
$681$	−15.7885			−0.605017
$682$	−2.52770	−	4.37811i	−0.0967907	−	0.167646i
$683$	−11.2374	−	19.4637i	−0.429986	−	0.744758i	0.566885	−	0.823797i	$-0.308148\pi$
$683$	−11.2374	−	19.4637i	−0.429986	−	0.744758i	−0.996872	+	0.0790389i	$0.974815\pi$
$684$	−2.74950			−0.105130
$685$	6.24147	+	10.8105i	0.238474	+	0.413050i
$686$	−0.100820	+	0.174625i	−0.00384932	+	0.00666722i
$687$	11.1885	−	19.3791i	0.426868	−	0.739358i
$688$	3.60492			0.137436
$689$	−1.32279	+	39.3456i	−0.0503942	+	1.49895i
$690$	−0.726895			−0.0276724
$691$	11.9138	−	20.6352i	0.453221	−	0.785001i	−0.545363	−	0.838200i	$-0.683608\pi$
$691$	11.9138	−	20.6352i	0.453221	−	0.785001i	0.998584	+	0.0531986i	$0.0169416\pi$
$692$	8.69754	−	15.0646i	0.330631	−	0.572669i
$693$	−2.87885	−	4.98632i	−0.109359	−	0.189414i
$694$	4.45015			0.168925
$695$	−1.50000	−	2.59808i	−0.0568982	−	0.0985506i
$696$	−1.11705	−	1.93479i	−0.0423417	−	0.0733379i
$697$	11.7921			0.446659
$698$	1.34540	+	2.33030i	0.0509240	+	0.0882030i
$699$	3.82196	−	6.61983i	0.144560	−	0.250385i
$700$	8.93491	−	15.4757i	0.337708	−	0.584927i
$701$	−51.9885			−1.96358			−0.981789	−	0.189974i	$-0.939160\pi$
$701$	−51.9885			−1.96358			−0.981789	+	0.189974i	$0.939160\pi$
$702$	−0.617050	−	0.384462i	−0.0232890	−	0.0145106i
$703$	−14.1446			−0.533473
$704$	20.2690	−	35.1069i	0.763917	−	1.32314i
$705$	−12.5439	+	21.7267i	−0.472432	+	0.818276i
$706$	2.75443	+	4.77081i	0.103664	+	0.179552i
$707$	−2.16918			−0.0815804
$708$	12.1415	+	21.0297i	0.456305	+	0.790343i
$709$	3.81704	+	6.61130i	0.143352	+	0.248293i	0.928757	−	0.370690i	$-0.120879\pi$
$709$	3.81704	+	6.61130i	0.143352	+	0.248293i	−0.785405	+	0.618982i	$0.787545\pi$
$710$	2.75605			0.103433
$711$	−1.78213	−	3.08674i	−0.0668351	−	0.115762i
$712$	−0.721142	+	1.24906i	−0.0270260	+	0.0468103i
$713$	−2.08869	+	3.61772i	−0.0782220	+	0.135485i
$714$	−0.847217			−0.0317063
$715$	66.2088	+	41.2523i	2.47607	+	1.54275i
$716$	10.0003			0.373730
$717$	9.79836	−	16.9713i	0.365926	−	0.633803i
$718$	−0.218036	+	0.377650i	−0.00813705	+	0.0140938i
$719$	14.5521	+	25.2050i	0.542703	+	0.939989i	0.998748	+	0.0500321i	$0.0159324\pi$
$719$	14.5521	+	25.2050i	0.542703	+	0.939989i	−0.456045	+	0.889957i	$0.650734\pi$
$720$	14.1203			0.526233
$721$	4.21704	+	7.30413i	0.157051	+	0.272020i
$722$	1.71704	+	2.97401i	0.0639017	+	0.110681i
$723$	18.9006			0.702922
$724$	11.0359	+	19.1147i	0.410146	+	0.710394i
$725$	−12.7610	+	22.1027i	−0.473931	+	0.820872i
$726$	2.23327	−	3.86814i	0.0828845	−	0.143560i
$727$	−4.23245			−0.156973			−0.0784864	−	0.996915i	$-0.525009\pi$
$727$	−4.23245			−0.156973			−0.0784864	+	0.996915i	$0.525009\pi$
$728$	2.53983	−	1.35469i	0.0941324	−	0.0502081i
$729$	1.00000			0.0370370
$730$	3.01540	−	5.22283i	0.111605	−	0.193306i
$731$	−2.01540	+	3.49078i	−0.0745424	+	0.129111i
$732$	−13.0511	−	22.6052i	−0.482384	−	0.835513i
$733$	−28.6993			−1.06003			−0.530017	−	0.847987i	$-0.677814\pi$
$733$	−28.6993			−1.06003			−0.530017	+	0.847987i	$0.677814\pi$
$734$	1.48360	+	2.56968i	0.0547608	+	0.0948485i
$735$	1.87885	+	3.25427i	0.0693025	+	0.120035i
$736$	2.25869			0.0832566
$737$	−21.8934	−	37.9205i	−0.806455	−	1.39682i
$738$	−0.282957	+	0.490096i	−0.0104158	+	0.0180407i
$739$	−1.26163	+	2.18521i	−0.0464100	+	0.0803844i	−0.888297	−	0.459269i	$-0.848111\pi$
$739$	−1.26163	+	2.18521i	−0.0464100	+	0.0803844i	0.841887	+	0.539653i	$0.181445\pi$
$740$	74.2127			2.72811
$741$	−0.170006	+	5.05674i	−0.00624533	+	0.185764i
$742$	−2.20164			−0.0808247
$743$	13.3585	−	23.1376i	0.490077	−	0.848838i	−0.509858	−	0.860258i	$-0.670302\pi$
$743$	13.3585	−	23.1376i	0.490077	−	0.848838i	0.999935	+	0.0114209i	$0.00363545\pi$
$744$	−1.73820	+	3.01065i	−0.0637255	+	0.110376i
$745$	36.6634	+	63.5029i	1.34324	+	2.32657i
$746$	−6.41769			−0.234968
$747$	−7.28213	−	12.6130i	−0.266439	−	0.461486i
$748$	23.7000	+	41.0496i	0.866557	+	1.50092i
$749$	−7.47474			−0.273121
$750$	1.56099	+	2.70371i	0.0569992	+	0.0987255i
$751$	18.8415	−	32.6344i	0.687535	−	1.19085i	−0.285098	−	0.958498i	$-0.592026\pi$
$751$	18.8415	−	32.6344i	0.687535	−	1.19085i	0.972633	−	0.232347i	$-0.0746405\pi$
$752$	12.5439	−	21.7267i	0.457430	−	0.792292i
$753$	5.32362			0.194003
$754$	−1.79509	+	0.957459i	−0.0653732	+	0.0348686i
$755$	34.2406			1.24614
$756$	−0.979671	+	1.69684i	−0.0356303	+	0.0617135i
$757$	3.20491	−	5.55107i	0.116485	−	0.201757i	−0.801888	−	0.597475i	$-0.796171\pi$
$757$	3.20491	−	5.55107i	0.116485	−	0.201757i	0.918372	+	0.395718i	$0.129504\pi$
$758$	2.78851	+	4.82984i	0.101283	+	0.175428i
$759$	−5.52360			−0.200494
$760$	2.10492	+	3.64583i	0.0763534	+	0.132248i
$761$	2.10575	+	3.64726i	0.0763332	+	0.132213i	0.901665	−	0.432435i	$-0.142345\pi$
$761$	2.10575	+	3.64726i	0.0763332	+	0.132213i	−0.825332	+	0.564648i	$0.809012\pi$
$762$	1.40493			0.0508953
$763$	−4.76180	−	8.24768i	−0.172389	−	0.298586i
$764$	13.4700	−	23.3307i	0.487327	−	0.844075i
$765$	−7.89425	+	13.6732i	−0.285417	+	0.494357i
$766$	−4.77377			−0.172483
$767$	39.4273	−	21.0297i	1.42364	−	0.759337i
$768$	−12.8456			−0.463524
$769$	−13.6928	+	23.7166i	−0.493774	+	0.855242i	−0.999974	−	0.00717393i	$-0.997716\pi$
$769$	−13.6928	+	23.7166i	−0.493774	+	0.855242i	0.506200	+	0.862416i	$0.331050\pi$
$770$	−2.18131	+	3.77814i	−0.0786090	+	0.136155i
$771$	−5.89835	−	10.2162i	−0.212424	−	0.367929i
$772$	−31.1708			−1.12186
$773$	4.39198	+	7.60712i	0.157968	+	0.273609i	0.934136	−	0.356917i	$-0.116172\pi$
$773$	4.39198	+	7.60712i	0.157968	+	0.273609i	−0.776168	+	0.630527i	$0.782839\pi$
$774$	−0.0967206	−	0.167525i	−0.00347655	−	0.00602156i
$775$	39.7137			1.42656
$776$	−6.49590	−	11.2512i	−0.233189	−	0.403896i
$777$	−5.03983	+	8.72925i	−0.180803	+	0.313160i
$778$	−0.886223	+	1.53498i	−0.0317726	+	0.0550318i
$779$	3.93839			0.141107
$780$	0.891975	−	26.5313i	0.0319378	−	0.949974i
$781$	20.9429			0.749397
$782$	−0.406385	+	0.703880i	−0.0145323	+	0.0251707i
$783$	1.39918	−	2.42345i	0.0500026	−	0.0866071i
$784$	−1.87885	−	3.25427i	−0.0671018	−	0.116224i
$785$	−6.12198			−0.218503
$786$	−0.983770	−	1.70394i	−0.0350899	−	0.0607775i
$787$	−15.7519	−	27.2832i	−0.561496	−	0.972540i	−0.997366	−	0.0725305i	$-0.976893\pi$
$787$	−15.7519	−	27.2832i	−0.561496	−	0.972540i	0.435870	−	0.900010i	$-0.356441\pi$
$788$	3.36751			0.119963
$789$	7.09179	+	12.2833i	0.252475	+	0.437299i
$790$	−1.35032	+	2.33883i	−0.0480423	+	0.0832118i
$791$	4.93491	−	8.54752i	0.175465	−	0.303915i
$792$	−4.59672			−0.163337
$793$	−42.3813	+	22.6052i	−1.50500	+	0.802735i
$794$	−3.45346			−0.122559
$795$	−20.5146	+	35.5323i	−0.727577	+	1.26020i
$796$	7.78147	−	13.4779i	0.275807	−	0.477712i
$797$	−14.2285	−	24.6445i	−0.504000	−	0.872953i	−0.999989	−	0.00462478i	$-0.998528\pi$
$797$	−14.2285	−	24.6445i	−0.504000	−	0.872953i	0.495989	−	0.868329i	$-0.334805\pi$
$798$	−0.282957			−0.0100166
$799$	14.0259	+	24.2935i	0.496200	+	0.859444i
$800$	−10.7365	−	18.5962i	−0.379594	−	0.657476i
$801$	−1.80656			−0.0638316
$802$	−1.79753	−	3.11342i	−0.0634731	−	0.109939i
$803$	22.9138	−	39.6878i	0.808609	−	1.40055i
$804$	−7.45032	+	12.9043i	−0.262752	+	0.455101i
$805$	3.60492			0.127057
$806$	2.68690	+	1.67411i	0.0946419	+	0.0589679i
$807$	20.9983			0.739177
$808$	−0.865893	+	1.49977i	−0.0304620	+	0.0527618i
$809$	11.1497	−	19.3118i	0.392002	−	0.678967i	−0.600712	−	0.799466i	$-0.705116\pi$
$809$	11.1497	−	19.3118i	0.392002	−	0.678967i	0.992713	+	0.120499i	$0.0384494\pi$
$810$	−0.378851	−	0.656189i	−0.0133115	−	0.0230561i
$811$	40.2616			1.41378			0.706888	−	0.707325i	$-0.250098\pi$
$811$	40.2616			1.41378			0.706888	+	0.707325i	$0.250098\pi$
$812$	2.74147	+	4.74837i	0.0962068	+	0.166635i
$813$	−5.50410	−	9.53338i	−0.193037	−	0.334350i
$814$	−11.7023			−0.410165
$815$	5.94212	+	10.2921i	0.208143	+	0.360515i
$816$	7.89425	−	13.6732i	0.276354	−	0.478659i
$817$	−0.673112	+	1.16586i	−0.0235492	+	0.0407884i
$818$	−3.57867			−0.125125
$819$	3.06016	+	1.90668i	0.106931	+	0.0666246i
$820$	−20.6636			−0.721605
$821$	8.03246	−	13.9126i	0.280335	−	0.485554i	−0.691132	−	0.722728i	$-0.742888\pi$
$821$	8.03246	−	13.9126i	0.280335	−	0.485554i	0.971467	+	0.237174i	$0.0762212\pi$
$822$	−0.334920	+	0.580098i	−0.0116817	+	0.0202332i
$823$	3.70164	+	6.41143i	0.129031	+	0.223488i	0.923301	−	0.384076i	$-0.125480\pi$
$823$	3.70164	+	6.41143i	0.129031	+	0.223488i	−0.794270	+	0.607564i	$0.792147\pi$
$824$	6.73344			0.234570
$825$	26.2560	+	45.4768i	0.914118	+	1.58330i
$826$	1.24950	+	2.16420i	0.0434758	+	0.0753023i
$827$	−52.4226			−1.82291			−0.911456	−	0.411398i	$-0.865041\pi$
$827$	−52.4226			−1.82291			−0.911456	+	0.411398i	$0.865041\pi$
$828$	0.939839	+	1.62785i	0.0326617	+	0.0565716i
$829$	−4.70884	+	8.15596i	−0.163545	+	0.283268i	−0.936138	−	0.351634i	$-0.885626\pi$
$829$	−4.70884	+	8.15596i	−0.163545	+	0.283268i	0.772593	+	0.634902i	$0.218960\pi$
$830$	−5.51768	+	9.55691i	−0.191522	+	0.331725i
$831$	30.1757			1.04678
$832$	−0.852970	+	25.3711i	−0.0295714	+	0.879585i
$833$	4.20164			0.145578
$834$	0.0804906	−	0.139414i	0.00278716	−	0.00482750i
$835$	−20.3618	+	35.2677i	−0.704649	+	1.22049i
$836$	7.91541	+	13.7099i	0.273760	+	0.474167i
$837$	−4.35442			−0.150511
$838$	−0.806392	−	1.39671i	−0.0278564	−	0.0482486i
$839$	22.3651	+	38.7374i	0.772128	+	1.33736i	0.936395	+	0.350949i	$0.114141\pi$
$839$	22.3651	+	38.7374i	0.772128	+	1.33736i	−0.164267	+	0.986416i	$0.552526\pi$
$840$	3.00000			0.103510
$841$	10.5846	+	18.3330i	0.364986	+	0.632174i
$842$	2.39670	−	4.15121i	0.0825958	−	0.143060i
$843$	−3.74147	+	6.48042i	−0.128863	+	0.223197i
$844$	−49.3754			−1.69957
$845$	−48.7398	−	3.28094i	−1.67670	−	0.112868i
$846$	−1.34622			−0.0462841
$847$	−11.0756	+	19.1834i	−0.380561	+	0.659151i
$848$	20.5146	−	35.5323i	0.704473	−	1.22018i
$849$	1.03656	+	1.79537i	0.0355746	+	0.0616171i
$850$	7.72689			0.265030
$851$	4.83492	+	8.37433i	0.165739	+	0.287068i
$852$	−3.56343	−	6.17205i	−0.122081	−	0.211451i
$853$	−41.4550			−1.41939			−0.709697	−	0.704507i	$-0.751168\pi$
$853$	−41.4550			−1.41939			−0.709697	+	0.704507i	$0.751168\pi$
$854$	−1.34312	−	2.32635i	−0.0459606	−	0.0796060i
$855$	−2.63655	+	4.56664i	−0.0901682	+	0.156176i
$856$	−2.98377	+	5.16804i	−0.101983	+	0.176640i
$857$	19.9885			0.682794			0.341397	−	0.939919i	$-0.389100\pi$
$857$	19.9885			0.682794			0.341397	+	0.939919i	$0.389100\pi$
$858$	−0.140652	+	4.18361i	−0.00480177	+	0.142826i
$859$	29.9642			1.02237			0.511183	−	0.859472i	$-0.329207\pi$
$859$	29.9642			1.02237			0.511183	+	0.859472i	$0.329207\pi$
$860$	3.53163	−	6.11697i	0.120428	−	0.208587i
$861$	1.40328	−	2.43055i	0.0478236	−	0.0828330i
$862$	−0.608192	−	1.05342i	−0.0207151	−	0.0358796i
$863$	25.1351			0.855608			0.427804	−	0.903872i	$-0.359287\pi$
$863$	25.1351			0.855608			0.427804	+	0.903872i	$0.359287\pi$
$864$	1.17721	+	2.03899i	0.0400495	+	0.0693678i
$865$	−16.6805	−	28.8914i	−0.567153	−	0.982339i
$866$	1.26855			0.0431070
$867$	0.326888	+	0.566187i	0.0111017	+	0.0192287i
$868$	4.26590	−	7.38876i	0.144794	−	0.250791i
$869$	−10.2610	+	17.7725i	−0.348080	+	0.602892i
$870$	−2.12032			−0.0718857
$871$	23.2723	+	14.5001i	0.788551	+	0.491318i
$872$	−7.60327			−0.257479
$873$	8.13655	−	14.0929i	0.275381	−	0.476973i
$874$	−0.135726	+	0.235084i	−0.00459100	+	0.00795185i
$875$	−7.74147	−	13.4086i	−0.261710	−	0.453294i
$876$	−15.5951			−0.526909
$877$	−12.8723	−	22.2954i	−0.434666	−	0.752863i	0.562603	−	0.826728i	$-0.309800\pi$
$877$	−12.8723	−	22.2954i	−0.434666	−	0.752863i	−0.997268	+	0.0738644i	$0.976467\pi$
$878$	−2.97458	−	5.15212i	−0.100387	−	0.173876i
$879$	−17.7741			−0.599505
$880$	−40.6503	−	70.4084i	−1.37032	−	2.37347i
$881$	−25.5503	+	44.2544i	−0.860812	+	1.49097i	0.0103347	+	0.999947i	$0.496710\pi$
$881$	−25.5503	+	44.2544i	−0.860812	+	1.49097i	−0.871147	+	0.491023i	$0.836623\pi$
$882$	−0.100820	+	0.174625i	−0.00339478	+	0.00587993i
$883$	−26.6115			−0.895547			−0.447774	−	0.894147i	$-0.647783\pi$
$883$	−26.6115			−0.895547			−0.447774	+	0.894147i	$0.647783\pi$
$884$	−25.1926	−	15.6966i	−0.847319	−	0.527934i
$885$	46.5708			1.56546
$886$	1.46509	−	2.53762i	0.0492208	−	0.0852529i
$887$	12.5154	−	21.6773i	0.420226	−	0.727853i	−0.575735	−	0.817636i	$-0.695284\pi$
$887$	12.5154	−	21.6773i	0.420226	−	0.727853i	0.995961	+	0.0897832i	$0.0286174\pi$
$888$	4.02360	+	6.96908i	0.135023	+	0.233867i
$889$	−6.96754			−0.233684
$890$	0.684416	+	1.18544i	0.0229417	+	0.0397362i
$891$	−2.87885	−	4.98632i	−0.0964451	−	0.167048i
$892$	9.16587			0.306896
$893$	4.68442	+	8.11365i	0.156758	+	0.271513i
$894$	−1.96737	+	3.40759i	−0.0657988	+	0.113967i
$895$	9.58952	−	16.6095i	0.320542	−	0.555195i
$896$	−6.12852			−0.204740
$897$	3.05196	−	1.62785i	0.101902	−	0.0543523i
$898$	2.03577			0.0679344
$899$	−6.09262	+	10.5527i	−0.203200	+	0.351953i
$900$	8.93491	−	15.4757i	0.297830	−	0.515857i
$901$	22.9382	+	39.7301i	0.764182	+	1.32360i
$902$	3.25836			0.108492
$903$	0.479671	+	0.830814i	0.0159624	+	0.0276478i
$904$	−3.93984	−	6.82400i	−0.131037	−	0.226963i
$905$	42.3302			1.40710
$906$	0.918683	+	1.59121i	0.0305212	+	0.0528643i
$907$	−8.35360	+	14.4689i	−0.277377	+	0.480430i	−0.970732	−	0.240165i	$-0.922798\pi$
$907$	−8.35360	+	14.4689i	−0.277377	+	0.480430i	0.693355	+	0.720596i	$0.256132\pi$
$908$	15.4675	−	26.7906i	0.513308	−	0.889076i
$909$	−2.16918			−0.0719471
$910$	0.0917949	−	2.73039i	0.00304297	−	0.0905115i
$911$	57.5593			1.90702			0.953512	−	0.301354i	$-0.0974386\pi$
$911$	57.5593			1.90702			0.953512	+	0.301354i	$0.0974386\pi$
$912$	2.63655	−	4.56664i	0.0873050	−	0.151217i
$913$	−41.9283	+	72.6220i	−1.38763	+	2.40344i
$914$	−1.87703	−	3.25111i	−0.0620867	−	0.107537i
$915$	−50.0600			−1.65493
$916$	21.9221	+	37.9702i	0.724327	+	1.25457i
$917$	4.87885	+	8.45042i	0.161114	+	0.279057i
$918$	−0.847217			−0.0279623
$919$	7.13655	+	12.3609i	0.235413	+	0.407748i	0.959393	−	0.282074i	$-0.0910223\pi$
$919$	7.13655	+	12.3609i	0.235413	+	0.407748i	−0.723980	+	0.689821i	$0.757689\pi$
$920$	1.43901	−	2.49244i	0.0474428	−	0.0821734i
$921$	−1.92278	+	3.33036i	−0.0633578	+	0.109739i
$922$	6.19800			0.204120
$923$	−11.5716	+	6.17205i	−0.380885	+	0.203155i
$924$	11.2813			0.371128
$925$	45.9649	−	79.6135i	1.51132	−	2.61768i
$926$	3.07246	−	5.32165i	0.100967	−	0.174880i
$927$	4.21704	+	7.30413i	0.138506	+	0.239899i
$928$	6.58852			0.216279
$929$	−26.9066	−	46.6035i	−0.882775	−	1.52901i	−0.848242	−	0.529608i	$-0.822339\pi$
$929$	−26.9066	−	46.6035i	−0.882775	−	1.52901i	−0.0345329	−	0.999404i	$-0.510994\pi$
$930$	1.64968	+	2.85732i	0.0540950	+	0.0936953i
$931$	1.40328			0.0459906
$932$	7.48853	+	12.9705i	0.245295	+	0.424863i
$933$	−1.26180	+	2.18550i	−0.0413095	+	0.0715502i
$934$	1.07884	−	1.86860i	0.0353006	−	0.0611425i
$935$	90.9055			2.97293
$936$	2.53983	−	1.35469i	0.0830170	−	0.0442794i
$937$	59.2715			1.93631			0.968157	−	0.250344i	$-0.0805437\pi$
$937$	59.2715			1.93631			0.968157	+	0.250344i	$0.0805437\pi$
$938$	−0.766727	+	1.32801i	−0.0250345	+	0.0433611i
$939$	14.6366	−	25.3513i	0.477646	−	0.827307i
$940$	−24.5778	−	42.5701i	−0.801641	−	1.38848i
$941$	−16.3367			−0.532561			−0.266281	−	0.963896i	$-0.585795\pi$
$941$	−16.3367			−0.532561			−0.266281	+	0.963896i	$0.585795\pi$
$942$	−0.164254	−	0.284496i	−0.00535168	−	0.00926938i
$943$	−1.34622	−	2.33173i	−0.0438391	−	0.0759315i
$944$	−46.5708			−1.51575
$945$	1.87885	+	3.25427i	0.0611190	+	0.105861i
$946$	−0.556889	+	0.964559i	−0.0181060	+	0.0313605i
$947$	−28.7090	+	49.7255i	−0.932918	+	1.61586i	−0.154612	+	0.987975i	$0.549413\pi$
$947$	−28.7090	+	49.7255i	−0.932918	+	1.61586i	−0.778306	+	0.627885i	$0.783921\pi$
$948$	6.98360			0.226817
$949$	−0.964267	+	28.6816i	−0.0313014	+	0.931044i
$950$	2.58066			0.0837276
$951$	4.90738	−	8.49983i	0.159133	−	0.275626i
$952$	1.67721	−	2.90502i	0.0543587	−	0.0941521i
$953$	−12.3415	−	21.3760i	−0.399779	−	0.692438i	0.593919	−	0.804525i	$-0.297580\pi$
$953$	−12.3415	−	21.3760i	−0.399779	−	0.692438i	−0.993698	+	0.112087i	$0.964247\pi$
$954$	−2.20164			−0.0712807
$955$	−25.8333	−	44.7445i	−0.835945	−	1.44790i
$956$	19.1983	+	33.2525i	0.620918	+	1.07546i
$957$	−16.1121			−0.520831
$958$	0.721142	+	1.24906i	0.0232991	+	0.0403551i
$959$	1.66098	−	2.87690i	0.0536359	−	0.0929001i
$960$	−13.2283	+	22.9122i	−0.426943	+	0.739487i
$961$	−12.0390			−0.388355
$962$	6.46589	−	3.44876i	0.208469	−	0.111192i
$963$	−7.47474			−0.240870
$964$	−18.5164	+	32.0713i	−0.596373	+	1.03295i
$965$	−29.8903	+	51.7716i	−0.962204	+	1.66659i
$966$	0.0967206	+	0.167525i	0.00311194	+	0.00539003i
$967$	18.2098			0.585589			0.292794	−	0.956175i	$-0.405415\pi$
$967$	18.2098			0.585589			0.292794	+	0.956175i	$0.405415\pi$
$968$	8.84229	+	15.3153i	0.284202	+	0.492252i
$969$	2.94804	+	5.10615i	0.0947046	+	0.164033i
$970$	−12.3302			−0.395898
$971$	−4.62198	−	8.00550i	−0.148326	−	0.256909i	0.782283	−	0.622924i	$-0.214055\pi$
$971$	−4.62198	−	8.00550i	−0.148326	−	0.256909i	−0.930609	+	0.366015i	$0.880722\pi$
$972$	−0.979671	+	1.69684i	−0.0314230	+	0.0544262i
$973$	−0.399180	+	0.691400i	−0.0127971	+	0.0221653i
$974$	−7.30590			−0.234096
$975$	−27.9097	−	17.3895i	−0.893824	−	0.556910i
$976$	50.0600			1.60238
$977$	−5.87475	+	10.1754i	−0.187950	+	0.325539i	−0.944567	−	0.328320i	$-0.893518\pi$
$977$	−5.87475	+	10.1754i	−0.187950	+	0.325539i	0.756617	+	0.653859i	$0.226851\pi$
$978$	−0.318856	+	0.552275i	−0.0101959	+	0.0176598i
$979$	5.20081	+	9.00807i	0.166219	+	0.287899i
$980$	−7.36262			−0.235190
$981$	−4.76180	−	8.24768i	−0.152033	−	0.263328i
$982$	0.717870	+	1.24339i	0.0229081	+	0.0396781i
$983$	24.1121			0.769057			0.384529	−	0.923113i	$-0.374364\pi$
$983$	24.1121			0.769057			0.384529	+	0.923113i	$0.374364\pi$
$984$	−1.12032	−	1.94046i	−0.0357146	−	0.0618595i
$985$	3.22917	−	5.59309i	0.102890	−	0.178211i
$986$	−1.18541	+	2.05319i	−0.0377511	+	0.0653869i
$987$	6.67638			0.212512
$988$	−8.41392	−	5.24241i	−0.267683	−	0.166783i
$989$	0.920336			0.0292650
$990$	−2.18131	+	3.77814i	−0.0693266	+	0.120077i
$991$	12.5113	−	21.6702i	0.397435	−	0.688377i	−0.595974	−	0.803004i	$-0.703234\pi$
$991$	12.5113	−	21.6702i	0.397435	−	0.688377i	0.993409	+	0.114627i	$0.0365672\pi$
$992$	−5.12607	−	8.87862i	−0.162753	−	0.281897i
$993$	−34.7170			−1.10171
$994$	−0.366720	−	0.635178i	−0.0116317	−	0.0201466i
$995$	−14.9236	−	25.8484i	−0.473110	−	0.819451i
$996$	28.5364			0.904209
$997$	−22.9495	−	39.7497i	−0.726818	−	1.25889i	−0.958221	−	0.286027i	$-0.907665\pi$
$997$	−22.9495	−	39.7497i	−0.726818	−	1.25889i	0.231404	−	0.972858i	$-0.425668\pi$
$998$	3.25443	−	5.63684i	0.103017	−	0.178431i
$999$	−5.03983	+	8.72925i	−0.159453	+	0.276181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.b.22.2	✓	6
3.2	odd	2		819.2.o.f.568.2		6
13.3	even	3	inner	273.2.k.b.211.2	yes	6
13.4	even	6		3549.2.a.l.1.2		3
13.9	even	3		3549.2.a.m.1.2		3
39.29	odd	6		819.2.o.f.757.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.b.22.2	✓	6	1.1	even	1	trivial
273.2.k.b.211.2	yes	6	13.3	even	3	inner
819.2.o.f.568.2		6	3.2	odd	2
819.2.o.f.757.2		6	39.29	odd	6
3549.2.a.l.1.2		3	13.4	even	6
3549.2.a.m.1.2		3	13.9	even	3

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.100820 + 0.174625i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.979671 + 1.69684i) q^{4} +3.75770 q^{5} +(0.100820 + 0.174625i) q^{6} +(-0.500000 - 0.866025i) q^{7} -0.798360 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.100820 + 0.174625i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.979671 + 1.69684i) q^{4} +3.75770 q^{5} +(0.100820 + 0.174625i) q^{6} +(-0.500000 - 0.866025i) q^{7} -0.798360 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.378851 + 0.656189i) q^{10} +(-2.87885 + 4.98632i) q^{11} +1.95934 q^{12} +(0.121149 - 3.60352i) q^{13} +0.201640 q^{14} +(1.87885 - 3.25427i) q^{15} +(-1.87885 + 3.25427i) q^{16} +(-2.10082 - 3.63873i) q^{17} +0.201640 q^{18} +(-0.701640 - 1.21528i) q^{19} +(3.68131 + 6.37622i) q^{20} -1.00000 q^{21} +(-0.580491 - 1.00544i) q^{22} +(-0.479671 + 0.830814i) q^{23} +(-0.399180 + 0.691400i) q^{24} +9.12032 q^{25} +(0.617050 + 0.384462i) q^{26} -1.00000 q^{27} +(0.979671 - 1.69684i) q^{28} +(-1.39918 + 2.42345i) q^{29} +(0.378851 + 0.656189i) q^{30} +4.35442 q^{31} +(-1.17721 - 2.03899i) q^{32} +(2.87885 + 4.98632i) q^{33} +0.847217 q^{34} +(-1.87885 - 3.25427i) q^{35} +(0.979671 - 1.69684i) q^{36} +(5.03983 - 8.72925i) q^{37} +0.282957 q^{38} +(-3.06016 - 1.90668i) q^{39} -3.00000 q^{40} +(-1.40328 + 2.43055i) q^{41} +(0.100820 - 0.174625i) q^{42} +(-0.479671 - 0.830814i) q^{43} -11.2813 q^{44} +(-1.87885 - 3.25427i) q^{45} +(-0.0967206 - 0.167525i) q^{46} -6.67638 q^{47} +(1.87885 + 3.25427i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.919509 + 1.59264i) q^{50} -4.20164 q^{51} +(6.23327 - 3.32469i) q^{52} -10.9187 q^{53} +(0.100820 - 0.174625i) q^{54} +(-10.8179 + 18.7371i) q^{55} +(0.399180 + 0.691400i) q^{56} -1.40328 q^{57} +(-0.282130 - 0.488664i) q^{58} +(6.19671 + 10.7330i) q^{59} +7.36262 q^{60} +(-6.66098 - 11.5372i) q^{61} +(-0.439012 + 0.760391i) q^{62} +(-0.500000 + 0.866025i) q^{63} -7.04066 q^{64} +(0.455242 - 13.5409i) q^{65} -1.16098 q^{66} +(-3.80246 + 6.58605i) q^{67} +(4.11622 - 7.12951i) q^{68} +(0.479671 + 0.830814i) q^{69} +0.757702 q^{70} +(-1.81869 - 3.15006i) q^{71} +(0.399180 + 0.691400i) q^{72} -7.95934 q^{73} +(1.01623 + 1.76016i) q^{74} +(4.56016 - 7.89843i) q^{75} +(1.37475 - 2.38114i) q^{76} +5.75770 q^{77} +(0.641478 - 0.342150i) q^{78} +3.56426 q^{79} +(-7.06016 + 12.2286i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.282957 - 0.490096i) q^{82} +14.5643 q^{83} +(-0.979671 - 1.69684i) q^{84} +(-7.89425 - 13.6732i) q^{85} +0.193441 q^{86} +(1.39918 + 2.42345i) q^{87} +(2.29836 - 3.98088i) q^{88} +(0.903279 - 1.56453i) q^{89} +0.757702 q^{90} +(-3.18131 + 1.69684i) q^{91} -1.87968 q^{92} +(2.17721 - 3.77104i) q^{93} +(0.673112 - 1.16586i) q^{94} +(-2.63655 - 4.56664i) q^{95} -2.35442 q^{96} +(8.13655 + 14.0929i) q^{97} +(-0.100820 - 0.174625i) q^{98} +5.75770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 4 q^{4} + 4 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} - 8 q^{11} - 8 q^{12} + 10 q^{13} + 2 q^{15} - 2 q^{16} - 12 q^{17} - 3 q^{19} + 11 q^{20} - 6 q^{21} + 7 q^{22} + 7 q^{23} - 3 q^{24} + 14 q^{25} + 16 q^{26} - 6 q^{27} - 4 q^{28} - 9 q^{29} - 7 q^{30} + 10 q^{31} + q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{35} - 4 q^{36} + 40 q^{38} + 2 q^{39} - 18 q^{40} - 6 q^{41} + 7 q^{43} - 6 q^{44} - 2 q^{45} - 3 q^{46} + 18 q^{47} + 2 q^{48} - 3 q^{49} - 16 q^{50} - 24 q^{51} + 12 q^{52} - 26 q^{53} - 26 q^{55} + 3 q^{56} - 6 q^{57} + 10 q^{58} - 11 q^{59} + 22 q^{60} - 19 q^{61} + 27 q^{62} - 3 q^{63} - 62 q^{64} - 14 q^{65} + 14 q^{66} - 21 q^{67} - 13 q^{68} - 7 q^{69} - 14 q^{70} - 22 q^{71} + 3 q^{72} - 28 q^{73} + 19 q^{74} + 7 q^{75} + 2 q^{76} + 16 q^{77} + 23 q^{78} - 2 q^{79} - 22 q^{80} - 3 q^{81} - 40 q^{82} + 64 q^{83} + 4 q^{84} - q^{85} + 6 q^{86} + 9 q^{87} + 15 q^{88} + 3 q^{89} - 14 q^{90} - 8 q^{91} - 52 q^{92} + 5 q^{93} - q^{94} + 12 q^{95} + 2 q^{96} + 21 q^{97} + 16 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 4 * q^4 + 4 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 - 8 * q^11 - 8 * q^12 + 10 * q^13 + 2 * q^15 - 2 * q^16 - 12 * q^17 - 3 * q^19 + 11 * q^20 - 6 * q^21 + 7 * q^22 + 7 * q^23 - 3 * q^24 + 14 * q^25 + 16 * q^26 - 6 * q^27 - 4 * q^28 - 9 * q^29 - 7 * q^30 + 10 * q^31 + q^32 + 8 * q^33 + 20 * q^34 - 2 * q^35 - 4 * q^36 + 40 * q^38 + 2 * q^39 - 18 * q^40 - 6 * q^41 + 7 * q^43 - 6 * q^44 - 2 * q^45 - 3 * q^46 + 18 * q^47 + 2 * q^48 - 3 * q^49 - 16 * q^50 - 24 * q^51 + 12 * q^52 - 26 * q^53 - 26 * q^55 + 3 * q^56 - 6 * q^57 + 10 * q^58 - 11 * q^59 + 22 * q^60 - 19 * q^61 + 27 * q^62 - 3 * q^63 - 62 * q^64 - 14 * q^65 + 14 * q^66 - 21 * q^67 - 13 * q^68 - 7 * q^69 - 14 * q^70 - 22 * q^71 + 3 * q^72 - 28 * q^73 + 19 * q^74 + 7 * q^75 + 2 * q^76 + 16 * q^77 + 23 * q^78 - 2 * q^79 - 22 * q^80 - 3 * q^81 - 40 * q^82 + 64 * q^83 + 4 * q^84 - q^85 + 6 * q^86 + 9 * q^87 + 15 * q^88 + 3 * q^89 - 14 * q^90 - 8 * q^91 - 52 * q^92 + 5 * q^93 - q^94 + 12 * q^95 + 2 * q^96 + 21 * q^97 + 16 * q^99

Introduction

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