LMFDB - Embedded newform 287.2.e.c.247.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 $ x^10 - x^9 + 7x^8 + 4x^7 + 32x^6 + 3x^5 + 30x^4 - 7x^3 + 26x^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			247.3
Root			$-0.863288 + 1.49526i$ of defining polynomial
Character	$\chi$	$=$	287.247
Dual form			287.2.e.c.165.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.564230 - 0.977276i) q^{2} +(-1.46472 - 2.53697i) q^{3} +(0.363288 + 0.629233i) q^{4} +(1.46472 - 2.53697i) q^{5} -3.30576 q^{6} +(1.22536 - 2.34489i) q^{7} +3.07683 q^{8} +(-2.79081 + 4.83382i) q^{9} +O(q^{10})$	\(q+(0.564230 - 0.977276i) q^{2} +(-1.46472 - 2.53697i) q^{3} +(0.363288 + 0.629233i) q^{4} +(1.46472 - 2.53697i) q^{5} -3.30576 q^{6} +(1.22536 - 2.34489i) q^{7} +3.07683 q^{8} +(-2.79081 + 4.83382i) q^{9} +(-1.65288 - 2.86287i) q^{10} +(1.90049 + 3.29174i) q^{11} +(1.06423 - 1.84330i) q^{12} -2.92944 q^{13} +(-1.60022 - 2.52057i) q^{14} -8.58161 q^{15} +(1.00947 - 1.74845i) q^{16} +(-1.11568 - 1.93241i) q^{17} +(3.14932 + 5.45478i) q^{18} +(-3.06615 + 5.31073i) q^{19} +2.12846 q^{20} +(-7.74371 + 0.325901i) q^{21} +4.28925 q^{22} +(-0.527734 + 0.914062i) q^{23} +(-4.50670 - 7.80583i) q^{24} +(-1.79081 - 3.10177i) q^{25} +(-1.65288 + 2.86287i) q^{26} +7.56268 q^{27} +(1.92064 - 0.0808318i) q^{28} +3.63708 q^{29} +(-4.84201 + 8.38660i) q^{30} +(3.27187 + 5.66705i) q^{31} +(1.93769 + 3.35618i) q^{32} +(5.56737 - 9.64296i) q^{33} -2.51800 q^{34} +(-4.15409 - 6.54330i) q^{35} -4.05547 q^{36} +(4.67705 - 8.10089i) q^{37} +(3.46003 + 5.99295i) q^{38} +(4.29081 + 7.43190i) q^{39} +(4.50670 - 7.80583i) q^{40} -1.00000 q^{41} +(-4.05074 + 7.75163i) q^{42} -5.51434 q^{43} +(-1.38085 + 2.39170i) q^{44} +(8.17550 + 14.1604i) q^{45} +(0.595527 + 1.03148i) q^{46} +(-0.886243 + 1.53502i) q^{47} -5.91435 q^{48} +(-3.99699 - 5.74666i) q^{49} -4.04171 q^{50} +(-3.26831 + 5.66088i) q^{51} +(-1.06423 - 1.84330i) q^{52} +(0.467066 + 0.808982i) q^{53} +(4.26709 - 7.39082i) q^{54} +11.1347 q^{55} +(3.77023 - 7.21483i) q^{56} +17.9642 q^{57} +(2.05215 - 3.55443i) q^{58} +(6.65531 + 11.5273i) q^{59} +(-3.11760 - 5.39984i) q^{60} +(7.17897 - 12.4343i) q^{61} +7.38436 q^{62} +(7.91501 + 12.4673i) q^{63} +8.41108 q^{64} +(-4.29081 + 7.43190i) q^{65} +(-6.28256 - 10.8817i) q^{66} +(-5.23851 - 9.07337i) q^{67} +(0.810625 - 1.40404i) q^{68} +3.09193 q^{69} +(-8.73848 + 0.367767i) q^{70} -9.53905 q^{71} +(-8.58685 + 14.8729i) q^{72} +(5.88259 + 10.1889i) q^{73} +(-5.27787 - 9.14153i) q^{74} +(-5.24606 + 9.08644i) q^{75} -4.45558 q^{76} +(10.0475 - 0.422860i) q^{77} +9.68401 q^{78} +(7.53443 - 13.0500i) q^{79} +(-2.95717 - 5.12197i) q^{80} +(-2.70478 - 4.68482i) q^{81} +(-0.564230 + 0.977276i) q^{82} -1.86216 q^{83} +(-3.01827 - 4.75421i) q^{84} -6.53662 q^{85} +(-3.11136 + 5.38903i) q^{86} +(-5.32730 - 9.22716i) q^{87} +(5.84749 + 10.1282i) q^{88} +(-8.11032 + 14.0475i) q^{89} +18.4515 q^{90} +(-3.58962 + 6.86920i) q^{91} -0.766878 q^{92} +(9.58475 - 16.6013i) q^{93} +(1.00009 + 1.73221i) q^{94} +(8.98210 + 15.5575i) q^{95} +(5.67635 - 9.83172i) q^{96} -7.70326 q^{97} +(-7.87129 + 0.663716i) q^{98} -21.2156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9} + q^{10} + 6 q^{11} + 7 q^{12} + 4 q^{13} - 24 q^{14} - 40 q^{15} + 12 q^{16} + 3 q^{17} + 8 q^{18} - 7 q^{19} + 14 q^{20} - 15 q^{21} - 26 q^{22} - 16 q^{24} + 5 q^{25} + q^{26} + 26 q^{27} - 5 q^{28} - 20 q^{29} - 14 q^{30} + 6 q^{31} + 3 q^{32} + 17 q^{33} + 2 q^{34} - 9 q^{35} - 30 q^{36} + 18 q^{37} + 7 q^{38} + 20 q^{39} + 16 q^{40} - 10 q^{41} - 35 q^{42} - 28 q^{43} - 2 q^{44} + 7 q^{45} + 3 q^{46} - 3 q^{47} + 18 q^{48} - 8 q^{49} - 8 q^{50} - 7 q^{52} + 9 q^{53} + 25 q^{54} + 34 q^{55} - 15 q^{56} + 62 q^{57} + 5 q^{58} + 19 q^{59} + 3 q^{60} + 23 q^{61} + 72 q^{62} + 13 q^{63} - 2 q^{64} - 20 q^{65} - 23 q^{66} + 11 q^{67} + 24 q^{68} + 38 q^{69} - 40 q^{70} - 25 q^{72} - 13 q^{73} - 2 q^{74} - 11 q^{75} + 24 q^{76} + 23 q^{77} + 28 q^{78} + 41 q^{79} + 9 q^{80} + 7 q^{81} - 2 q^{82} - 4 q^{83} - 23 q^{84} - 20 q^{86} - 32 q^{87} + 10 q^{88} - 14 q^{89} + 44 q^{90} - 6 q^{91} + 34 q^{92} + 15 q^{93} - 10 q^{94} + 31 q^{95} + 33 q^{96} - 54 q^{97} - 85 q^{98} - 18 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9 + q^10 + 6 * q^11 + 7 * q^12 + 4 * q^13 - 24 * q^14 - 40 * q^15 + 12 * q^16 + 3 * q^17 + 8 * q^18 - 7 * q^19 + 14 * q^20 - 15 * q^21 - 26 * q^22 - 16 * q^24 + 5 * q^25 + q^26 + 26 * q^27 - 5 * q^28 - 20 * q^29 - 14 * q^30 + 6 * q^31 + 3 * q^32 + 17 * q^33 + 2 * q^34 - 9 * q^35 - 30 * q^36 + 18 * q^37 + 7 * q^38 + 20 * q^39 + 16 * q^40 - 10 * q^41 - 35 * q^42 - 28 * q^43 - 2 * q^44 + 7 * q^45 + 3 * q^46 - 3 * q^47 + 18 * q^48 - 8 * q^49 - 8 * q^50 - 7 * q^52 + 9 * q^53 + 25 * q^54 + 34 * q^55 - 15 * q^56 + 62 * q^57 + 5 * q^58 + 19 * q^59 + 3 * q^60 + 23 * q^61 + 72 * q^62 + 13 * q^63 - 2 * q^64 - 20 * q^65 - 23 * q^66 + 11 * q^67 + 24 * q^68 + 38 * q^69 - 40 * q^70 - 25 * q^72 - 13 * q^73 - 2 * q^74 - 11 * q^75 + 24 * q^76 + 23 * q^77 + 28 * q^78 + 41 * q^79 + 9 * q^80 + 7 * q^81 - 2 * q^82 - 4 * q^83 - 23 * q^84 - 20 * q^86 - 32 * q^87 + 10 * q^88 - 14 * q^89 + 44 * q^90 - 6 * q^91 + 34 * q^92 + 15 * q^93 - 10 * q^94 + 31 * q^95 + 33 * q^96 - 54 * q^97 - 85 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.564230	−	0.977276i	0.398971	−	0.691038i	−0.594628	−	0.804001i	$-0.702701\pi$
$2$	0.564230	−	0.977276i	0.398971	−	0.691038i	0.993599	+	0.112963i	$0.0360340\pi$
$3$	−1.46472	−	2.53697i	−0.845656	−	1.46472i	−0.885050	−	0.465496i	$-0.845876\pi$
$3$	−1.46472	−	2.53697i	−0.845656	−	1.46472i	0.0393939	−	0.999224i	$-0.487457\pi$
$4$	0.363288	+	0.629233i	0.181644	+	0.314617i
$5$	1.46472	−	2.53697i	0.655042	−	1.13457i	−0.326841	−	0.945079i	$-0.605984\pi$
$5$	1.46472	−	2.53697i	0.655042	−	1.13457i	0.981883	−	0.189487i	$-0.0606826\pi$
$6$	−3.30576			−1.34957
$7$	1.22536	−	2.34489i	0.463143	−	0.886284i
$7$	1.22536	−	2.34489i	0.463143	−	0.886284i
$8$	3.07683			1.08783
$9$	−2.79081	+	4.83382i	−0.930269	+	1.61127i
$10$	−1.65288	−	2.86287i	−0.522686	−	0.905319i
$11$	1.90049	+	3.29174i	0.573019	+	0.992498i	0.996254	+	0.0864780i	$0.0275612\pi$
$11$	1.90049	+	3.29174i	0.573019	+	0.992498i	−0.423235	+	0.906020i	$0.639105\pi$
$12$	1.06423	−	1.84330i	0.307217	−	0.532115i
$13$	−2.92944			−0.812480			−0.406240	−	0.913766i	$-0.633160\pi$
$13$	−2.92944			−0.812480			−0.406240	+	0.913766i	$0.633160\pi$
$14$	−1.60022	−	2.52057i	−0.427676	−	0.673651i
$15$	−8.58161			−2.21576
$16$	1.00947	−	1.74845i	0.252367	−	0.437112i
$17$	−1.11568	−	1.93241i	−0.270592	−	0.468678i	0.698422	−	0.715686i	$-0.253886\pi$
$17$	−1.11568	−	1.93241i	−0.270592	−	0.468678i	−0.969013	+	0.247008i	$0.920553\pi$
$18$	3.14932	+	5.45478i	0.742301	+	1.28570i
$19$	−3.06615	+	5.31073i	−0.703423	+	1.21836i	0.263834	+	0.964568i	$0.415013\pi$
$19$	−3.06615	+	5.31073i	−0.703423	+	1.21836i	−0.967258	+	0.253797i	$0.918321\pi$
$20$	2.12846			0.475938
$21$	−7.74371	+	0.325901i	−1.68982	+	0.0711174i
$22$	4.28925			0.914472
$23$	−0.527734	+	0.914062i	−0.110040	+	0.190595i	−0.915786	−	0.401666i	$-0.868431\pi$
$23$	−0.527734	+	0.914062i	−0.110040	+	0.190595i	0.805746	+	0.592261i	$0.201765\pi$
$24$	−4.50670	−	7.80583i	−0.919926	−	1.59336i
$25$	−1.79081	−	3.10177i	−0.358161	−	0.620354i
$26$	−1.65288	+	2.86287i	−0.324156	+	0.561455i
$27$	7.56268			1.45544
$28$	1.92064	−	0.0808318i	0.362967	−	0.0152758i
$29$	3.63708			0.675389			0.337694	−	0.941256i	$-0.390353\pi$
$29$	3.63708			0.675389			0.337694	+	0.941256i	$0.390353\pi$
$30$	−4.84201	+	8.38660i	−0.884025	+	1.53118i
$31$	3.27187	+	5.66705i	0.587646	+	1.01783i	0.994540	+	0.104357i	$0.0332784\pi$
$31$	3.27187	+	5.66705i	0.587646	+	1.01783i	−0.406894	+	0.913475i	$0.633388\pi$
$32$	1.93769	+	3.35618i	0.342538	+	0.593294i
$33$	5.56737	−	9.64296i	0.969154	−	1.67862i
$34$	−2.51800			−0.431833
$35$	−4.15409	−	6.54330i	−0.702170	−	1.10602i
$36$	−4.05547			−0.675911
$37$	4.67705	−	8.10089i	0.768902	−	1.33178i	−0.169256	−	0.985572i	$-0.554137\pi$
$37$	4.67705	−	8.10089i	0.768902	−	1.33178i	0.938159	−	0.346206i	$-0.112530\pi$
$38$	3.46003	+	5.99295i	0.561291	+	0.972185i
$39$	4.29081	+	7.43190i	0.687079	+	1.19006i
$40$	4.50670	−	7.80583i	0.712572	−	1.23421i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	−4.05074	+	7.75163i	−0.625043	+	1.19610i
$43$	−5.51434			−0.840928			−0.420464	−	0.907309i	$-0.638133\pi$
$43$	−5.51434			−0.840928			−0.420464	+	0.907309i	$0.638133\pi$
$44$	−1.38085	+	2.39170i	−0.208171	+	0.360563i
$45$	8.17550	+	14.1604i	1.21873	+	2.11090i
$46$	0.595527	+	1.03148i	0.0878056	+	0.152084i
$47$	−0.886243	+	1.53502i	−0.129272	+	0.223905i	−0.923395	−	0.383852i	$-0.874597\pi$
$47$	−0.886243	+	1.53502i	−0.129272	+	0.223905i	0.794123	+	0.607757i	$0.207931\pi$
$48$	−5.91435			−0.853662
$49$	−3.99699	−	5.74666i	−0.570998	−	0.820952i
$50$	−4.04171			−0.571584
$51$	−3.26831	+	5.66088i	−0.457655	+	0.792681i
$52$	−1.06423	−	1.84330i	−0.147582	−	0.255620i
$53$	0.467066	+	0.808982i	0.0641565	+	0.111122i	0.896319	−	0.443409i	$-0.146231\pi$
$53$	0.467066	+	0.808982i	0.0641565	+	0.111122i	−0.832163	+	0.554531i	$0.812898\pi$
$54$	4.26709	−	7.39082i	0.580678	−	1.00576i
$55$	11.1347			1.50141
$56$	3.77023	−	7.21483i	0.503818	−	0.964122i
$57$	17.9642			2.37942
$58$	2.05215	−	3.55443i	0.269461	−	0.466720i
$59$	6.65531	+	11.5273i	0.866448	+	1.50073i	0.865603	+	0.500732i	$0.166936\pi$
$59$	6.65531	+	11.5273i	0.866448	+	1.50073i	0.000845172		1.00000i	$0.499731\pi$
$60$	−3.11760	−	5.39984i	−0.402480	−	0.697116i
$61$	7.17897	−	12.4343i	0.919173	−	1.59205i	0.118499	−	0.992954i	$-0.462192\pi$
$61$	7.17897	−	12.4343i	0.919173	−	1.59205i	0.800674	−	0.599100i	$-0.204475\pi$
$62$	7.38436			0.937815
$63$	7.91501	+	12.4673i	0.997198	+	1.57073i
$64$	8.41108			1.05139
$65$	−4.29081	+	7.43190i	−0.532209	+	0.921813i
$66$	−6.28256	−	10.8817i	−0.773329	−	1.33945i
$67$	−5.23851	−	9.07337i	−0.639986	−	1.10849i	−0.985435	−	0.170051i	$-0.945607\pi$
$67$	−5.23851	−	9.07337i	−0.639986	−	1.10849i	0.345449	−	0.938437i	$-0.387727\pi$
$68$	0.810625	−	1.40404i	0.0983027	−	0.170265i
$69$	3.09193			0.372224
$70$	−8.73848	+	0.367767i	−1.04445	+	0.0439565i
$71$	−9.53905			−1.13208			−0.566039	−	0.824379i	$-0.691525\pi$
$71$	−9.53905			−1.13208			−0.566039	+	0.824379i	$0.691525\pi$
$72$	−8.58685	+	14.8729i	−1.01197	+	1.75278i
$73$	5.88259	+	10.1889i	0.688505	+	1.19253i	0.972321	+	0.233647i	$0.0750661\pi$
$73$	5.88259	+	10.1889i	0.688505	+	1.19253i	−0.283816	+	0.958879i	$0.591601\pi$
$74$	−5.27787	−	9.14153i	−0.613540	−	1.06268i
$75$	−5.24606	+	9.08644i	−0.605763	+	1.04921i
$76$	−4.45558			−0.511091
$77$	10.0475	−	0.422860i	1.14502	−	0.0481894i
$78$	9.68401			1.09650
$79$	7.53443	−	13.0500i	0.847690	−	1.46824i	−0.0355745	−	0.999367i	$-0.511326\pi$
$79$	7.53443	−	13.0500i	0.847690	−	1.46824i	0.883265	−	0.468875i	$-0.155341\pi$
$80$	−2.95717	−	5.12197i	−0.330622	−	0.572654i
$81$	−2.70478	−	4.68482i	−0.300531	−	0.520536i
$82$	−0.564230	+	0.977276i	−0.0623088	+	0.107922i
$83$	−1.86216			−0.204399			−0.102199	−	0.994764i	$-0.532588\pi$
$83$	−1.86216			−0.204399			−0.102199	+	0.994764i	$0.532588\pi$
$84$	−3.01827	−	4.75421i	−0.329320	−	0.518727i
$85$	−6.53662			−0.708996
$86$	−3.11136	+	5.38903i	−0.335506	+	0.581114i
$87$	−5.32730	−	9.22716i	−0.571147	−	0.989255i
$88$	5.84749	+	10.1282i	0.623345	+	1.07966i
$89$	−8.11032	+	14.0475i	−0.859692	+	1.48903i	0.0125312	+	0.999921i	$0.496011\pi$
$89$	−8.11032	+	14.0475i	−0.859692	+	1.48903i	−0.872223	+	0.489108i	$0.837322\pi$
$90$	18.4515			1.94495
$91$	−3.58962	+	6.86920i	−0.376294	+	0.720088i
$92$	−0.766878			−0.0799525
$93$	9.58475	−	16.6013i	0.993892	−	1.72147i
$94$	1.00009	+	1.73221i	0.103151	+	0.178664i
$95$	8.98210	+	15.5575i	0.921544	+	1.59616i
$96$	5.67635	−	9.83172i	0.579340	−	1.00345i
$97$	−7.70326			−0.782148			−0.391074	−	0.920359i	$-0.627896\pi$
$97$	−7.70326			−0.782148			−0.391074	+	0.920359i	$0.627896\pi$
$98$	−7.87129	+	0.663716i	−0.795121	+	0.0670455i
$99$	−21.2156			−2.13225
$100$	1.30116	−	2.25367i	0.130116	−	0.225367i
$101$	−5.24073	−	9.07721i	−0.521472	−	0.903217i	−0.999688	−	0.0249742i	$-0.992050\pi$
$101$	−5.24073	−	9.07721i	−0.521472	−	0.903217i	0.478216	−	0.878242i	$-0.341284\pi$
$102$	3.68816	+	6.38808i	0.365182	+	0.632514i
$103$	−3.02468	+	5.23890i	−0.298031	+	0.516205i	−0.975685	−	0.219176i	$-0.929663\pi$
$103$	−3.02468	+	5.23890i	−0.298031	+	0.516205i	0.677655	+	0.735380i	$0.262997\pi$
$104$	−9.01340			−0.883836
$105$	−10.5156	+	20.1229i	−1.02621	+	1.96379i
$106$	1.05413			0.102386
$107$	0.420393	−	0.728142i	0.0406409	−	0.0703922i	−0.844989	−	0.534783i	$-0.820393\pi$
$107$	0.420393	−	0.728142i	0.0406409	−	0.0703922i	0.885630	+	0.464391i	$0.153727\pi$
$108$	2.74743	+	4.75869i	0.264372	+	0.457905i
$109$	0.713021	+	1.23499i	0.0682950	+	0.118290i	0.898151	−	0.439687i	$-0.144911\pi$
$109$	0.713021	+	1.23499i	0.0682950	+	0.118290i	−0.829856	+	0.557978i	$0.811577\pi$
$110$	6.28256	−	10.8817i	0.599018	−	1.03753i
$111$	−27.4023			−2.60091
$112$	−2.86295	−	4.50957i	−0.270524	−	0.426114i
$113$	−5.76585			−0.542406			−0.271203	−	0.962522i	$-0.587421\pi$
$113$	−5.76585			−0.542406			−0.271203	+	0.962522i	$0.587421\pi$
$114$	10.1360	−	17.5560i	0.949319	−	1.64427i
$115$	1.54596	+	2.67769i	0.144162	+	0.249696i
$116$	1.32131	+	2.28857i	0.122680	+	0.212489i
$117$	8.17550	−	14.1604i	0.755825	−	1.30913i
$118$	15.0205			1.38275
$119$	−5.89839	+	0.248239i	−0.540704	+	0.0227560i
$120$	−26.4042			−2.41036
$121$	−1.72372	+	2.98557i	−0.156702	+	0.271415i
$122$	−8.10119	−	14.0317i	−0.733447	−	1.27037i
$123$	1.46472	+	2.53697i	0.132069	+	0.228751i
$124$	−2.37726	+	4.11754i	−0.213485	+	0.369766i
$125$	4.15508			0.371641
$126$	16.6499	−	0.700725i	1.48329	−	0.0624255i
$127$	−13.7471			−1.21986			−0.609929	−	0.792456i	$-0.708802\pi$
$127$	−13.7471			−1.21986			−0.609929	+	0.792456i	$0.708802\pi$
$128$	0.870409	−	1.50759i	0.0769340	−	0.133254i
$129$	8.07696	+	13.9897i	0.711136	+	1.23172i
$130$	4.84201	+	8.38660i	0.424672	+	0.735554i
$131$	0.987638	−	1.71064i	0.0862903	−	0.149459i	−0.819650	−	0.572865i	$-0.805832\pi$
$131$	0.987638	−	1.71064i	0.0862903	−	0.149459i	0.905940	+	0.423405i	$0.139165\pi$
$132$	8.09023			0.704164
$133$	8.69592	+	13.6973i	0.754032	+	1.18771i
$134$	−11.8229			−1.02134
$135$	11.0772	−	19.1863i	0.953374	−	1.65129i
$136$	−3.43276	−	5.94571i	−0.294356	−	0.509840i
$137$	−0.103953	−	0.180051i	−0.00888126	−	0.0153828i	0.861551	−	0.507672i	$-0.169494\pi$
$137$	−0.103953	−	0.180051i	−0.00888126	−	0.0153828i	−0.870432	+	0.492289i	$0.836160\pi$
$138$	1.74456	−	3.02167i	0.148507	−	0.257221i
$139$	6.86618			0.582381			0.291191	−	0.956665i	$-0.405949\pi$
$139$	6.86618			0.582381			0.291191	+	0.956665i	$0.405949\pi$
$140$	2.60813	−	4.99100i	0.220427	−	0.421816i
$141$	5.19239			0.437278
$142$	−5.38222	+	9.32228i	−0.451666	+	0.782309i
$143$	−5.56737	−	9.64296i	−0.465567	−	0.806385i
$144$	5.63446	+	9.75916i	0.469538	+	0.813264i
$145$	5.32730	−	9.22716i	0.442408	−	0.766274i
$146$	13.2765			1.09877
$147$	−8.72463	+	18.5575i	−0.719596	+	1.53059i
$148$	6.79647			0.558666
$149$	1.99461	−	3.45476i	0.163405	−	0.283025i	−0.772683	−	0.634792i	$-0.781086\pi$
$149$	1.99461	−	3.45476i	0.163405	−	0.283025i	0.936088	+	0.351767i	$0.114419\pi$
$150$	5.91997	+	10.2537i	0.483364	+	0.837210i
$151$	7.55927	+	13.0930i	0.615165	+	1.06550i	0.990356	+	0.138549i	$0.0442439\pi$
$151$	7.55927	+	13.0930i	0.615165	+	1.06550i	−0.375191	+	0.926948i	$0.622423\pi$
$152$	−9.43404	+	16.3402i	−0.765202	+	1.32537i
$153$	12.4546			1.00689
$154$	5.25588	−	10.0578i	0.423531	−	0.810482i
$155$	19.1695			1.53973
$156$	−3.11760	+	5.39984i	−0.249608	+	0.432333i
$157$	−3.52371	−	6.10325i	−0.281223	−	0.487092i	0.690463	−	0.723367i	$-0.257407\pi$
$157$	−3.52371	−	6.10325i	−0.281223	−	0.487092i	−0.971686	+	0.236275i	$0.924073\pi$
$158$	−8.50231	−	14.7264i	−0.676408	−	1.17157i
$159$	1.36824	−	2.36986i	0.108509	−	0.187942i
$160$	11.3527			0.897509
$161$	1.49671	+	2.35753i	0.117957	+	0.185799i
$162$	−6.10448			−0.479614
$163$	−8.08692	+	14.0070i	−0.633416	+	1.09711i	0.353432	+	0.935460i	$0.385015\pi$
$163$	−8.08692	+	14.0070i	−0.633416	+	1.09711i	−0.986848	+	0.161649i	$0.948319\pi$
$164$	−0.363288	−	0.629233i	−0.0283680	−	0.0491349i
$165$	−16.3093	−	28.2485i	−1.26967	−	2.19914i
$166$	−1.05069	+	1.81985i	−0.0815493	+	0.141247i
$167$	−5.14849			−0.398402			−0.199201	−	0.979959i	$-0.563835\pi$
$167$	−5.14849			−0.398402			−0.199201	+	0.979959i	$0.563835\pi$
$168$	−23.8261	+	1.00274i	−1.83823	+	0.0773633i
$169$	−4.41839			−0.339876
$170$	−3.68816	+	6.38808i	−0.282869	+	0.489943i
$171$	−17.1141	−	29.6424i	−1.30875	−	2.26681i
$172$	−2.00329	−	3.46981i	−0.152750	−	0.264570i
$173$	−4.37427	+	7.57646i	−0.332570	+	0.576028i	−0.983015	−	0.183525i	$-0.941249\pi$
$173$	−4.37427	+	7.57646i	−0.332570	+	0.576028i	0.650445	+	0.759553i	$0.274582\pi$
$174$	−12.0233			−0.911484
$175$	−9.46768	+	0.398456i	−0.715689	+	0.0301204i
$176$	7.67393			0.578444
$177$	19.4963	−	33.7686i	1.46543	−	2.53821i
$178$	9.15217	+	15.8520i	0.685984	+	1.18816i
$179$	3.69184	+	6.39446i	0.275941	+	0.477944i	0.970372	−	0.241615i	$-0.0776771\pi$
$179$	3.69184	+	6.39446i	0.275941	+	0.477944i	−0.694431	+	0.719559i	$0.744344\pi$
$180$	−5.94012	+	10.2886i	−0.442751	+	0.766867i
$181$	9.92440			0.737675			0.368837	−	0.929494i	$-0.379756\pi$
$181$	9.92440			0.737675			0.368837	+	0.929494i	$0.379756\pi$
$182$	4.68773	+	7.38386i	0.347478	+	0.547328i
$183$	−42.0607			−3.10922
$184$	−1.62375	+	2.81242i	−0.119704	+	0.207334i
$185$	−13.7011	−	23.7311i	−1.00733	−	1.74474i
$186$	−10.8160	−	18.7339i	−0.793069	−	1.37364i
$187$	4.24067	−	7.34505i	0.310108	−	0.537123i
$188$	−1.28785			−0.0939258
$189$	9.26700	−	17.7336i	0.674075	−	1.28993i
$190$	20.2719			1.47068
$191$	0.810378	−	1.40362i	0.0586369	−	0.101562i	−0.835217	−	0.549921i	$-0.814658\pi$
$191$	0.810378	−	1.40362i	0.0586369	−	0.101562i	0.893854	+	0.448359i	$0.147991\pi$
$192$	−12.3199	−	21.3387i	−0.889111	−	1.53998i
$193$	−1.77550	−	3.07526i	−0.127803	−	0.221362i	0.795022	−	0.606581i	$-0.207459\pi$
$193$	−1.77550	−	3.07526i	−0.127803	−	0.221362i	−0.922825	+	0.385219i	$0.874126\pi$
$194$	−4.34641	+	7.52821i	−0.312054	+	0.540494i
$195$	25.1393			1.80026
$196$	2.16393	−	4.60273i	0.154567	−	0.328766i
$197$	6.37250			0.454022			0.227011	−	0.973892i	$-0.427105\pi$
$197$	6.37250			0.454022			0.227011	+	0.973892i	$0.427105\pi$
$198$	−11.9705	+	20.7335i	−0.850705	+	1.47346i
$199$	−4.88658	−	8.46381i	−0.346400	−	0.599983i	0.639207	−	0.769035i	$-0.279263\pi$
$199$	−4.88658	−	8.46381i	−0.346400	−	0.599983i	−0.985607	+	0.169052i	$0.945930\pi$
$200$	−5.51002	−	9.54363i	−0.389617	−	0.674836i
$201$	−15.3459	+	26.5799i	−1.08242	+	1.87480i
$202$	−11.8279			−0.832210
$203$	4.45673	−	8.52854i	0.312801	−	0.598586i
$204$	−4.74935			−0.332521
$205$	−1.46472	+	2.53697i	−0.102300	+	0.177190i
$206$	3.41324	+	5.91190i	0.237811	+	0.411901i
$207$	−2.94561	−	5.10194i	−0.204734	−	0.354609i
$208$	−2.95717	+	5.12197i	−0.205043	+	0.355145i
$209$	−23.3087			−1.61230
$210$	13.7324	+	21.6306i	0.947628	+	1.49265i
$211$	−4.31500			−0.297057			−0.148528	−	0.988908i	$-0.547454\pi$
$211$	−4.31500			−0.297057			−0.148528	+	0.988908i	$0.547454\pi$
$212$	−0.339359	+	0.587787i	−0.0233073	+	0.0403694i
$213$	13.9720	+	24.2003i	0.957348	+	1.65818i
$214$	−0.474397	−	0.821680i	−0.0324291	−	0.0561689i
$215$	−8.07696	+	13.9897i	−0.550844	+	0.954090i
$216$	23.2691			1.58326
$217$	17.2978	−	0.727994i	1.17425	−	0.0494194i
$218$	1.60923			0.108991
$219$	17.2327	−	29.8479i	1.16448	−	2.01693i
$220$	4.04512	+	7.00635i	0.272722	+	0.472368i
$221$	3.26831	+	5.66088i	0.219850	+	0.380792i
$222$	−15.4612	+	26.7796i	−1.03769	+	1.79733i
$223$	−11.7245			−0.785130			−0.392565	−	0.919724i	$-0.628412\pi$
$223$	−11.7245			−0.785130			−0.392565	+	0.919724i	$0.628412\pi$
$224$	10.2442	−	0.431137i	0.684471	−	0.0288066i
$225$	19.9912			1.33275
$226$	−3.25327	+	5.63483i	−0.216404	+	0.374823i
$227$	10.0735	+	17.4479i	0.668604	+	1.15806i	0.978295	+	0.207219i	$0.0664414\pi$
$227$	10.0735	+	17.4479i	0.668604	+	1.15806i	−0.309690	+	0.950838i	$0.600225\pi$
$228$	6.52618	+	11.3037i	0.432207	+	0.748604i
$229$	11.3705	−	19.6943i	0.751385	−	1.30144i	−0.195767	−	0.980650i	$-0.562720\pi$
$229$	11.3705	−	19.6943i	0.751385	−	1.30144i	0.947152	−	0.320786i	$-0.103947\pi$
$230$	3.48912			0.230066
$231$	−15.7896	−	24.8709i	−1.03888	−	1.63639i
$232$	11.1907			0.734705
$233$	−6.31695	+	10.9413i	−0.413837	+	0.716787i	−0.995306	−	0.0967818i	$-0.969145\pi$
$233$	−6.31695	+	10.9413i	−0.413837	+	0.716787i	0.581468	+	0.813569i	$0.302478\pi$
$234$	−9.22573	−	15.9794i	−0.603105	−	1.04461i
$235$	2.59619	+	4.49674i	0.169357	+	0.293335i
$236$	−4.83559	+	8.37549i	−0.314770	+	0.545198i
$237$	−44.1433			−2.86742
$238$	−3.08545	+	5.90442i	−0.200000	+	0.382726i
$239$	20.8294			1.34734			0.673670	−	0.739033i	$-0.264717\pi$
$239$	20.8294			1.34734			0.673670	+	0.739033i	$0.264717\pi$
$240$	−8.66286	+	15.0045i	−0.559185	+	0.968537i
$241$	−3.80246	−	6.58606i	−0.244938	−	0.424245i	0.717176	−	0.696892i	$-0.245434\pi$
$241$	−3.80246	−	6.58606i	−0.244938	−	0.424245i	−0.962114	+	0.272647i	$0.912101\pi$
$242$	1.94515	+	3.36910i	0.125039	+	0.216574i
$243$	3.42052	−	5.92451i	0.219426	−	0.380058i
$244$	10.4321			0.667849
$245$	−20.4336	+	1.72298i	−1.30545	+	0.110077i
$246$	3.30576			0.210767
$247$	8.98210	−	15.5575i	0.571517	−	0.989897i
$248$	10.0670	+	17.4366i	0.639256	+	1.10722i
$249$	2.72755	+	4.72425i	0.172851	+	0.299387i
$250$	2.34442	−	4.06066i	0.148274	−	0.256818i
$251$	30.2279			1.90797			0.953984	−	0.299858i	$-0.0969393\pi$
$251$	30.2279			1.90797			0.953984	+	0.299858i	$0.0969393\pi$
$252$	−4.96941	+	9.50961i	−0.313043	+	0.599049i
$253$	−4.01181			−0.252220
$254$	−7.75653	+	13.4347i	−0.486688	+	0.842969i
$255$	9.57431	+	16.5832i	0.599567	+	1.03848i
$256$	7.42886	+	12.8672i	0.464304	+	0.804198i
$257$	−4.93699	+	8.55111i	−0.307961	+	0.533404i	−0.977916	−	0.208998i	$-0.932980\pi$
$257$	−4.93699	+	8.55111i	−0.307961	+	0.533404i	0.669955	+	0.742401i	$0.266313\pi$
$258$	18.2291			1.13489
$259$	−13.2646	−	20.8937i	−0.824222	−	1.29827i
$260$	−6.23520			−0.386690
$261$	−10.1504	+	17.5810i	−0.628293	+	1.08824i
$262$	−1.11451	−	1.93039i	−0.0688547	−	0.119260i
$263$	14.1132	+	24.4448i	0.870256	+	1.50733i	0.861731	+	0.507365i	$0.169380\pi$
$263$	14.1132	+	24.4448i	0.870256	+	1.50733i	0.00852506	+	0.999964i	$0.497286\pi$
$264$	17.1299	−	29.6698i	1.05427	−	1.82605i
$265$	2.73648			0.168101
$266$	18.2926	−	0.769859i	1.12159	−	0.0472031i
$267$	47.5174			2.90801
$268$	3.80618	−	6.59249i	0.232499	−	0.402701i
$269$	−9.88421	−	17.1200i	−0.602651	−	1.04382i	−0.992418	−	0.122909i	$-0.960778\pi$
$269$	−9.88421	−	17.1200i	−0.602651	−	1.04382i	0.389767	−	0.920913i	$-0.372556\pi$
$270$	−12.5002	−	21.6510i	−0.760737	−	1.31764i
$271$	−10.7419	+	18.6055i	−0.652524	+	1.13020i	0.329985	+	0.943986i	$0.392956\pi$
$271$	−10.7419	+	18.6055i	−0.652524	+	1.13020i	−0.982508	+	0.186218i	$0.940377\pi$
$272$	−4.50496			−0.273153
$273$	22.6847	−	0.954707i	1.37294	−	0.0577815i
$274$	−0.234613			−0.0141735
$275$	6.80682	−	11.7898i	0.410467	−	0.710949i
$276$	1.12326	+	1.94554i	0.0676123	+	0.117108i
$277$	7.08902	+	12.2785i	0.425938	+	0.737746i	0.996507	−	0.0835033i	$-0.0266109\pi$
$277$	7.08902	+	12.2785i	0.425938	+	0.737746i	−0.570570	+	0.821249i	$0.693278\pi$
$278$	3.87410	−	6.71015i	0.232353	−	0.402448i
$279$	−36.5246			−2.18667
$280$	−12.7815	−	20.1327i	−0.763838	−	1.20316i
$281$	−8.15392			−0.486422			−0.243211	−	0.969973i	$-0.578201\pi$
$281$	−8.15392			−0.486422			−0.243211	+	0.969973i	$0.578201\pi$
$282$	2.92970	−	5.07440i	0.174461	−	0.302176i
$283$	−9.66083	−	16.7330i	−0.574276	−	0.994676i	−0.996120	−	0.0880073i	$-0.971950\pi$
$283$	−9.66083	−	16.7330i	−0.574276	−	0.994676i	0.421843	−	0.906669i	$-0.361383\pi$
$284$	−3.46542	−	6.00229i	−0.205635	−	0.356170i
$285$	26.3125	−	45.5746i	1.55862	−	2.69961i
$286$	−12.5651			−0.742991
$287$	−1.22536	+	2.34489i	−0.0723307	+	0.138414i
$288$	−21.6309			−1.27461
$289$	6.01053	−	10.4105i	0.353560	−	0.612385i
$290$	−6.01165	−	10.4125i	−0.353016	−	0.611442i
$291$	11.2831	+	19.5429i	0.661428	+	1.14563i
$292$	−4.27415	+	7.40305i	−0.250126	+	0.433231i
$293$	−27.5658			−1.61041			−0.805206	−	0.592996i	$-0.797945\pi$
$293$	−27.5658			−1.61041			−0.805206	+	0.592996i	$0.797945\pi$
$294$	13.2131	+	18.9971i	0.770601	+	1.10793i
$295$	38.9927			2.27024
$296$	14.3905	−	24.9251i	0.836431	−	1.44874i
$297$	14.3728	+	24.8944i	0.833994	+	1.44452i
$298$	−2.25084	−	3.89856i	−0.130387	−	0.225838i
$299$	1.54596	−	2.67769i	0.0894054	−	0.154855i
$300$	−7.62332			−0.440133
$301$	−6.75705	+	12.9305i	−0.389470	+	0.745301i
$302$	17.0607			0.981732
$303$	−15.3524	+	26.5911i	−0.881973	+	1.52762i
$304$	6.19036	+	10.7220i	0.355041	+	0.614950i
$305$	−21.0304	−	36.4256i	−1.20419	−	2.08573i
$306$	7.02724	−	12.1715i	0.401721	−	0.695801i
$307$	4.66137			0.266039			0.133019	−	0.991113i	$-0.457533\pi$
$307$	4.66137			0.266039			0.133019	+	0.991113i	$0.457533\pi$
$308$	3.91623	+	6.16863i	0.223148	+	0.351491i
$309$	17.7212			1.00813
$310$	10.8160	−	18.7339i	0.614308	−	1.06401i
$311$	−0.990569	−	1.71572i	−0.0561700	−	0.0972893i	0.836573	−	0.547855i	$-0.184556\pi$
$311$	−0.990569	−	1.71572i	−0.0561700	−	0.0972893i	−0.892743	+	0.450566i	$0.851222\pi$
$312$	13.2021	+	22.8667i	0.747422	+	1.29457i
$313$	−9.02161	+	15.6259i	−0.509932	+	0.883228i	0.490002	+	0.871721i	$0.336996\pi$
$313$	−9.02161	+	15.6259i	−0.509932	+	0.883228i	−0.999934	+	0.0115064i	$0.996337\pi$
$314$	−7.95274			−0.448799
$315$	43.2224	−	1.81905i	2.43531	−	0.102492i
$316$	10.9487			0.615911
$317$	−0.931077	+	1.61267i	−0.0522945	+	0.0905767i	−0.890988	−	0.454028i	$-0.849987\pi$
$317$	−0.931077	+	1.61267i	−0.0522945	+	0.0905767i	0.838693	+	0.544604i	$0.183320\pi$
$318$	−1.54401	−	2.67430i	−0.0865836	−	0.149967i
$319$	6.91223	+	11.9723i	0.387011	+	0.670322i
$320$	12.3199	−	21.3387i	0.688702	−	1.19287i
$321$	−2.46303			−0.137473
$322$	3.14844	−	0.132505i	0.175456	−	0.00738422i
$323$	13.6833			0.761362
$324$	1.96523	−	3.40388i	0.109180	−	0.189104i
$325$	5.24606	+	9.08644i	0.290999	+	0.504025i
$326$	9.12577	+	15.8063i	0.505430	+	0.875430i
$327$	2.08875	−	3.61782i	0.115508	−	0.200066i
$328$	−3.07683			−0.169890
$329$	2.51348	+	3.95909i	0.138572	+	0.218272i
$330$	−36.8087			−2.02625
$331$	−4.03824	+	6.99443i	−0.221962	+	0.384449i	−0.955404	−	0.295303i	$-0.904579\pi$
$331$	−4.03824	+	6.99443i	−0.221962	+	0.384449i	0.733442	+	0.679752i	$0.237913\pi$
$332$	−0.676501	−	1.17173i	−0.0371278	−	0.0643073i
$333$	26.1055	+	45.2160i	1.43057	+	2.47782i
$334$	−2.90494	+	5.03150i	−0.158951	+	0.275311i
$335$	−30.6918			−1.67687
$336$	−7.24720	+	13.8685i	−0.395367	+	0.756587i
$337$	−28.8996			−1.57426			−0.787130	−	0.616788i	$-0.788434\pi$
$337$	−28.8996			−1.57426			−0.787130	+	0.616788i	$0.788434\pi$
$338$	−2.49299	+	4.31798i	−0.135601	+	0.234867i
$339$	8.44536	+	14.6278i	0.458689	+	0.794473i
$340$	−2.37468	−	4.11306i	−0.128785	−	0.223062i
$341$	−12.4363	+	21.5403i	−0.673464	+	1.16647i
$342$	−38.6251			−2.08861
$343$	−18.3730	+	2.33075i	−0.992049	+	0.125849i
$344$	−16.9667			−0.914783
$345$	4.52881	−	7.84412i	0.243823	−	0.422313i
$346$	4.93620	+	8.54974i	0.265372	+	0.459637i
$347$	−5.28106	−	9.14707i	−0.283502	−	0.491040i	0.688743	−	0.725006i	$-0.258163\pi$
$347$	−5.28106	−	9.14707i	−0.283502	−	0.491040i	−0.972245	+	0.233966i	$0.924830\pi$
$348$	3.87069	−	6.70424i	0.207491	−	0.359385i
$349$	10.3215			0.552498			0.276249	−	0.961086i	$-0.410908\pi$
$349$	10.3215			0.552498			0.276249	+	0.961086i	$0.410908\pi$
$350$	−4.95255	+	9.47735i	−0.264725	+	0.506586i
$351$	−22.1544			−1.18251
$352$	−7.36512	+	12.7568i	−0.392562	+	0.679938i
$353$	10.0473	+	17.4025i	0.534765	+	0.926240i	0.999175	+	0.0406192i	$0.0129331\pi$
$353$	10.0473	+	17.4025i	0.534765	+	0.926240i	−0.464410	+	0.885620i	$0.653734\pi$
$354$	−22.0008	−	38.1066i	−1.16933	−	2.02534i
$355$	−13.9720	+	24.2003i	−0.741559	+	1.28442i
$356$	−11.7855			−0.624632
$357$	9.26926	+	14.6004i	0.490581	+	0.772737i
$358$	8.33220			0.440371
$359$	−1.34095	+	2.32259i	−0.0707725	+	0.122582i	−0.899240	−	0.437455i	$-0.855880\pi$
$359$	−1.34095	+	2.32259i	−0.0707725	+	0.122582i	0.828468	+	0.560037i	$0.189213\pi$
$360$	25.1547	+	43.5691i	1.32577	+	2.29630i
$361$	−9.30256	−	16.1125i	−0.489609	−	0.848027i
$362$	5.59965	−	9.69887i	0.294311	−	0.509761i
$363$	10.0991			0.530063
$364$	−5.62640	+	0.236792i	−0.294903	+	0.0124113i
$365$	34.4654			1.80400
$366$	−23.7319	+	41.1049i	−1.24049	+	2.14859i
$367$	−13.7432	−	23.8039i	−0.717389	−	1.24255i	−0.962031	−	0.272941i	$-0.912004\pi$
$367$	−13.7432	−	23.8039i	−0.717389	−	1.24255i	0.244642	−	0.969614i	$-0.421330\pi$
$368$	1.06546	+	1.84543i	0.0555409	+	0.0961997i
$369$	2.79081	−	4.83382i	0.145284	−	0.251639i
$370$	−30.9224			−1.60758
$371$	2.46930	−	0.103922i	0.128199	−	0.00539539i
$372$	13.9281			0.722139
$373$	3.36972	−	5.83652i	0.174477	−	0.302204i	−0.765503	−	0.643432i	$-0.777510\pi$
$373$	3.36972	−	5.83652i	0.174477	−	0.302204i	0.939980	+	0.341229i	$0.110843\pi$
$374$	−4.78543	−	8.28860i	−0.247448	−	0.428593i
$375$	−6.08602	−	10.5413i	−0.314281	−	0.544350i
$376$	−2.72682	+	4.72300i	−0.140625	+	0.243570i
$377$	−10.6546			−0.548740
$378$	−12.1019	−	19.0623i	−0.622455	−	0.980457i
$379$	−34.3338			−1.76361			−0.881803	−	0.471617i	$-0.843670\pi$
$379$	−34.3338			−1.76361			−0.881803	+	0.471617i	$0.843670\pi$
$380$	−6.52618	+	11.3037i	−0.334786	+	0.579866i
$381$	20.1356	+	34.8760i	1.03158	+	1.78675i
$382$	−0.914480	−	1.58393i	−0.0467889	−	0.0810407i
$383$	0.657725	−	1.13921i	0.0336082	−	0.0582111i	−0.848732	−	0.528823i	$-0.822634\pi$
$383$	0.657725	−	1.13921i	0.0336082	−	0.0582111i	0.882340	+	0.470612i	$0.155967\pi$
$384$	−5.09962			−0.260239
$385$	13.6441	−	26.1097i	0.695366	−	1.33067i
$386$	−4.00717			−0.203960
$387$	15.3894	−	26.6553i	0.782290	−	1.35497i
$388$	−2.79850	−	4.84715i	−0.142072	−	0.246077i
$389$	−7.68881	−	13.3174i	−0.389838	−	0.675219i	0.602590	−	0.798051i	$-0.294136\pi$
$389$	−7.68881	−	13.3174i	−0.389838	−	0.675219i	−0.992427	+	0.122832i	$0.960802\pi$
$390$	14.1844	−	24.5680i	0.718253	−	1.24405i
$391$	2.35512			0.119104
$392$	−12.2981	−	17.6815i	−0.621146	−	0.893052i
$393$	−5.78645			−0.291888
$394$	3.59556	−	6.22769i	0.181142	−	0.313747i
$395$	−22.0717	−	38.2292i	−1.11055	−	1.92352i
$396$	−7.70737	−	13.3496i	−0.387310	−	0.670841i
$397$	8.76209	−	15.1764i	0.439757	−	0.761681i	−0.557914	−	0.829899i	$-0.688398\pi$
$397$	8.76209	−	15.1764i	0.439757	−	0.761681i	0.997670	+	0.0682181i	$0.0217314\pi$
$398$	−11.0286			−0.552815
$399$	22.0126	−	42.1240i	1.10201	−	2.10884i
$400$	−7.23104			−0.361552
$401$	7.56171	−	13.0973i	0.377614	−	0.654046i	−0.613101	−	0.790005i	$-0.710078\pi$
$401$	7.56171	−	13.0973i	0.377614	−	0.654046i	0.990715	+	0.135959i	$0.0434114\pi$
$402$	17.3172	+	29.9944i	0.863706	+	1.49598i
$403$	−9.58475	−	16.6013i	−0.477450	−	0.826968i
$404$	3.80779	−	6.59529i	0.189445	−	0.328128i
$405$	−15.8470			−0.787444
$406$	−5.82011	−	9.16752i	−0.288847	−	0.454976i
$407$	35.5547			1.76238
$408$	−10.0560	+	17.4176i	−0.497848	+	0.862299i
$409$	3.71473	+	6.43409i	0.183681	+	0.318145i	0.943131	−	0.332420i	$-0.107865\pi$
$409$	3.71473	+	6.43409i	0.183681	+	0.318145i	−0.759450	+	0.650566i	$0.774532\pi$
$410$	1.65288	+	2.86287i	0.0816299	+	0.141387i
$411$	−0.304523	+	0.527449i	−0.0150210	+	0.0260171i
$412$	−4.39533			−0.216542
$413$	35.1854	−	1.48081i	1.73136	−	0.0728659i
$414$	−6.64800			−0.326731
$415$	−2.72755	+	4.72425i	−0.133890	+	0.231904i
$416$	−5.67635	−	9.83172i	−0.278306	−	0.482040i
$417$	−10.0570	−	17.4193i	−0.492494	−	0.853025i
$418$	−13.1515	+	22.7791i	−0.643261	+	1.11416i
$419$	−11.2835			−0.551234			−0.275617	−	0.961268i	$-0.588882\pi$
$419$	−11.2835			−0.551234			−0.275617	+	0.961268i	$0.588882\pi$
$420$	−16.4822	+	0.693668i	−0.804248	+	0.0338475i
$421$	−21.1179			−1.02922			−0.514611	−	0.857424i	$-0.672064\pi$
$421$	−21.1179			−1.02922			−0.514611	+	0.857424i	$0.672064\pi$
$422$	−2.43465	+	4.21694i	−0.118517	+	0.205278i
$423$	−4.94667	−	8.56788i	−0.240515	−	0.416584i
$424$	1.43708	+	2.48910i	0.0697910	+	0.120882i
$425$	−3.99593	+	6.92115i	−0.193831	+	0.335725i
$426$	31.5338			1.52782
$427$	−20.3603	−	32.0704i	−0.985304	−	1.55200i
$428$	0.610895			0.0295287
$429$	−16.3093	+	28.2485i	−0.787419	+	1.36385i
$430$	9.11453	+	15.7868i	0.439542	+	0.761308i
$431$	−8.79677	−	15.2364i	−0.423725	−	0.733914i	0.572575	−	0.819852i	$-0.305944\pi$
$431$	−8.79677	−	15.2364i	−0.423725	−	0.733914i	−0.996300	+	0.0859385i	$0.972611\pi$
$432$	7.63428	−	13.2230i	0.367304	−	0.636190i
$433$	9.24372			0.444225			0.222113	−	0.975021i	$-0.428705\pi$
$433$	9.24372			0.444225			0.222113	+	0.975021i	$0.428705\pi$
$434$	9.04850	−	17.3155i	0.434342	−	0.831170i
$435$	−31.2120			−1.49650
$436$	−0.518064	+	0.897314i	−0.0248108	+	0.0429735i
$437$	−3.23622	−	5.60530i	−0.154810	−	0.268138i
$438$	−19.4464	−	33.6822i	−0.929186	−	1.60940i
$439$	−12.4682	+	21.5955i	−0.595073	+	1.03070i	0.398463	+	0.917184i	$0.369544\pi$
$439$	−12.4682	+	21.5955i	−0.595073	+	1.03070i	−0.993537	+	0.113513i	$0.963790\pi$
$440$	34.2597			1.63327
$441$	38.9331	−	3.28289i	1.85396	−	0.156328i
$442$	7.37632			0.350856
$443$	−15.4922	+	26.8333i	−0.736057	+	1.27489i	0.218201	+	0.975904i	$0.429981\pi$
$443$	−15.4922	+	26.8333i	−0.736057	+	1.27489i	−0.954258	+	0.298984i	$0.903352\pi$
$444$	−9.95492	−	17.2424i	−0.472439	−	0.818289i
$445$	23.7587	+	41.1512i	1.12627	+	1.95076i
$446$	−6.61532	+	11.4581i	−0.313244	+	0.542555i
$447$	−11.6862			−0.552736
$448$	10.3066	−	19.7230i	0.486941	−	0.931826i
$449$	−9.24437			−0.436269			−0.218134	−	0.975919i	$-0.569997\pi$
$449$	−9.24437			−0.436269			−0.218134	+	0.975919i	$0.569997\pi$
$450$	11.2796	−	19.5369i	0.531727	−	0.920978i
$451$	−1.90049	−	3.29174i	−0.0894905	−	0.155002i
$452$	−2.09467	−	3.62807i	−0.0985248	−	0.170650i
$453$	22.1444	−	38.3553i	1.04044	−	1.80209i
$454$	22.7352			1.06702
$455$	12.1692	+	19.1682i	0.570499	+	0.898619i
$456$	55.2729			2.58839
$457$	11.0368	−	19.1162i	0.516278	−	0.894220i	−0.483543	−	0.875321i	$-0.660650\pi$
$457$	11.0368	−	19.1162i	0.516278	−	0.894220i	0.999821	−	0.0188997i	$-0.00601633\pi$
$458$	−12.8312	−	22.2243i	−0.599562	−	1.03847i
$459$	−8.43751	−	14.6142i	−0.393829	−	0.682132i
$460$	−1.12326	+	1.94554i	−0.0523723	+	0.0907115i
$461$	42.2569			1.96810			0.984051	−	0.177886i	$-0.0569259\pi$
$461$	42.2569			1.96810			0.984051	+	0.177886i	$0.0569259\pi$
$462$	−33.2148	+	1.39787i	−1.54529	+	0.0650349i
$463$	−36.1774			−1.68131			−0.840654	−	0.541573i	$-0.817829\pi$
$463$	−36.1774			−1.68131			−0.840654	+	0.541573i	$0.817829\pi$
$464$	3.67151	−	6.35925i	0.170446	−	0.295221i
$465$	−28.0779	−	48.6324i	−1.30208	−	2.25527i
$466$	7.12843	+	12.3468i	0.330218	+	0.571955i
$467$	−6.45596	+	11.1820i	−0.298746	+	0.517443i	−0.975849	−	0.218445i	$-0.929902\pi$
$467$	−6.45596	+	11.1820i	−0.298746	+	0.517443i	0.677103	+	0.735888i	$0.263235\pi$
$468$	11.8802			0.549165
$469$	−27.6951	+	1.16557i	−1.27884	+	0.0538211i
$470$	5.85941			0.270274
$471$	−10.3225	+	17.8791i	−0.475636	+	0.823825i
$472$	20.4773	+	35.4677i	0.942544	+	1.63253i
$473$	−10.4799	−	18.1518i	−0.481868	−	0.834620i
$474$	−24.9070	+	43.1402i	−1.14402	+	1.98150i
$475$	21.9635			1.00776
$476$	−2.29901	−	3.62128i	−0.105375	−	0.165981i
$477$	−5.21396			−0.238731
$478$	11.7526	−	20.3560i	0.537549	−	0.931063i
$479$	4.28187	+	7.41642i	0.195644	+	0.338865i	0.947111	−	0.320905i	$-0.103987\pi$
$479$	4.28187	+	7.41642i	0.195644	+	0.338865i	−0.751468	+	0.659770i	$0.770654\pi$
$480$	−16.6285	−	28.8014i	−0.758984	−	1.31460i
$481$	−13.7011	+	23.7311i	−0.624718	+	1.08204i
$482$	−8.58186			−0.390893
$483$	3.78872	−	7.25022i	0.172393	−	0.329896i
$484$	−2.50482			−0.113856
$485$	−11.2831	+	19.5429i	−0.512340	+	0.887399i
$486$	−3.85992	−	6.68558i	−0.175090	−	0.303264i
$487$	−2.55326	−	4.42237i	−0.115699	−	0.200397i	0.802360	−	0.596841i	$-0.203578\pi$
$487$	−2.55326	−	4.42237i	−0.115699	−	0.200397i	−0.918059	+	0.396444i	$0.870244\pi$
$488$	22.0885	−	38.2584i	0.999900	−	1.73188i
$489$	47.3803			2.14261
$490$	−9.84541	+	20.9414i	−0.444770	+	0.946035i
$491$	1.80345			0.0813884			0.0406942	−	0.999172i	$-0.487043\pi$
$491$	1.80345			0.0813884			0.0406942	+	0.999172i	$0.487043\pi$
$492$	−1.06423	+	1.84330i	−0.0479792	+	0.0831024i
$493$	−4.05781	−	7.02833i	−0.182755	−	0.316540i
$494$	−10.1360	−	17.5560i	−0.456038	−	0.789881i
$495$	−31.0749	+	53.8233i	−1.39671	+	2.41918i
$496$	13.2114			0.593209
$497$	−11.6888	+	22.3680i	−0.524313	+	1.00334i
$498$	6.15586			0.275851
$499$	9.84134	−	17.0457i	0.440559	−	0.763070i	−0.557172	−	0.830397i	$-0.688114\pi$
$499$	9.84134	−	17.0457i	0.440559	−	0.763070i	0.997731	+	0.0673267i	$0.0214470\pi$
$500$	1.50949	+	2.61451i	0.0675065	+	0.116925i
$501$	7.54110	+	13.0616i	0.336911	+	0.583548i
$502$	17.0555	−	29.5410i	0.761224	−	1.31848i
$503$	3.71758			0.165759			0.0828795	−	0.996560i	$-0.473588\pi$
$503$	3.71758			0.165759			0.0828795	+	0.996560i	$0.473588\pi$
$504$	24.3532	+	38.3598i	1.08478	+	1.70868i
$505$	−30.7048			−1.36635
$506$	−2.26358	+	3.92064i	−0.100629	+	0.174294i
$507$	6.47170	+	11.2093i	0.287418	+	0.497823i
$508$	−4.99416	−	8.65014i	−0.221580	−	0.383788i
$509$	−0.216423	+	0.374856i	−0.00959278	+	0.0166152i	−0.870782	−	0.491669i	$-0.836387\pi$
$509$	−0.216423	+	0.374856i	−0.00959278	+	0.0166152i	0.861189	+	0.508285i	$0.169720\pi$
$510$	21.6085			0.956839
$511$	31.1002	−	1.30888i	1.37579	−	0.0579015i
$512$	20.2480			0.894843
$513$	−23.1883	+	40.1633i	−1.02379	+	1.77325i
$514$	5.57119	+	9.64959i	0.245735	+	0.425625i
$515$	8.86062	+	15.3471i	0.390446	+	0.676272i
$516$	−5.86852	+	10.1646i	−0.258347	+	0.447471i
$517$	−6.73718			−0.296301
$518$	−27.9031	+	1.17433i	−1.22599	+	0.0515970i
$519$	25.6283			1.12496
$520$	−13.2021	+	22.8667i	−0.578950	+	1.00277i
$521$	−11.7860	−	20.4139i	−0.516353	−	0.894350i	−0.999820	−	0.0189868i	$-0.993956\pi$
$521$	−11.7860	−	20.4139i	−0.516353	−	0.894350i	0.483467	−	0.875363i	$-0.339377\pi$
$522$	11.4543	+	19.8395i	0.501342	+	0.868349i
$523$	11.8331	−	20.4956i	0.517427	−	0.896210i	−0.482368	−	0.875969i	$-0.660223\pi$
$523$	11.8331	−	20.4956i	0.517427	−	0.896210i	0.999795	−	0.0202415i	$-0.00644350\pi$
$524$	1.43519			0.0626965
$525$	14.8784	+	23.4356i	0.649345	+	1.02281i
$526$	31.8524			1.38883
$527$	7.30071	−	12.6452i	0.318024	−	0.550833i
$528$	−11.2401	−	19.4685i	−0.489165	−	0.847258i
$529$	10.9430	+	18.9538i	0.475782	+	0.824079i
$530$	1.54401	−	2.67430i	0.0670674	−	0.116164i
$531$	−74.2947			−3.22412
$532$	−5.45970	+	10.4478i	−0.236708	+	0.452971i
$533$	2.92944			0.126888
$534$	26.8107	−	46.4376i	1.16021	−	2.00955i
$535$	−1.23152	−	2.13305i	−0.0532431	−	0.0922197i
$536$	−16.1180	−	27.9173i	−0.696193	−	1.20584i
$537$	10.8150	−	18.7322i	0.466703	−	0.808353i
$538$	−22.3079			−0.961761
$539$	11.3203	−	24.0785i	0.487600	−	1.03714i
$540$	16.0969			0.692699
$541$	−8.44557	+	14.6282i	−0.363103	+	0.628914i	−0.988470	−	0.151418i	$-0.951616\pi$
$541$	−8.44557	+	14.6282i	−0.363103	+	0.628914i	0.625366	+	0.780331i	$0.284950\pi$
$542$	12.1218	+	20.9956i	0.520676	+	0.901838i
$543$	−14.5365	−	25.1779i	−0.623819	−	1.08049i
$544$	4.32367	−	7.48882i	0.185376	−	0.321081i
$545$	4.17750			0.178945
$546$	11.8664	−	22.7079i	0.507835	−	0.971809i
$547$	33.0460			1.41295			0.706473	−	0.707740i	$-0.250285\pi$
$547$	33.0460			1.41295			0.706473	+	0.707740i	$0.250285\pi$
$548$	0.0755294	−	0.130821i	0.00322646	−	0.00558839i
$549$	40.0702	+	69.4037i	1.71016	+	2.96208i
$550$	−7.68123	−	13.3043i	−0.327529	−	0.567296i
$551$	−11.1518	+	19.3156i	−0.475084	+	0.822870i
$552$	9.51335			0.404915
$553$	−21.3684	−	33.6584i	−0.908678	−	1.43130i
$554$	15.9994			0.679747
$555$	−40.1366	+	69.5187i	−1.70371	+	2.95090i
$556$	2.49440	+	4.32043i	0.105786	+	0.183227i
$557$	19.4619	+	33.7091i	0.824629	+	1.42830i	0.902202	+	0.431313i	$0.141950\pi$
$557$	19.4619	+	33.7091i	0.824629	+	1.42830i	−0.0775731	+	0.996987i	$0.524717\pi$
$558$	−20.6083	+	35.6947i	−0.872420	+	1.51108i
$559$	16.1539			0.683238
$560$	−15.6340	+	0.657973i	−0.660659	+	0.0278044i
$561$	−24.8455			−1.04898
$562$	−4.60069	+	7.96863i	−0.194068	+	0.336136i
$563$	−10.1683	−	17.6121i	−0.428544	−	0.742260i	0.568200	−	0.822891i	$-0.307640\pi$
$563$	−10.1683	−	17.6121i	−0.428544	−	0.742260i	−0.996744	+	0.0806302i	$0.974307\pi$
$564$	1.88633	+	3.26723i	0.0794290	+	0.137575i
$565$	−8.44536	+	14.6278i	−0.355299	+	0.615396i
$566$	−21.8037			−0.916479
$567$	−14.2997	+	0.601816i	−0.600531	+	0.0252739i
$568$	−29.3501			−1.23150
$569$	−9.70797	+	16.8147i	−0.406979	+	0.704909i	−0.994550	−	0.104264i	$-0.966751\pi$
$569$	−9.70797	+	16.8147i	−0.406979	+	0.704909i	0.587570	+	0.809173i	$0.300085\pi$
$570$	−29.6926	−	51.4292i	−1.24369	−	2.15413i
$571$	−1.82279	−	3.15717i	−0.0762816	−	0.132124i	0.825361	−	0.564605i	$-0.190971\pi$
$571$	−1.82279	−	3.15717i	−0.0762816	−	0.132124i	−0.901643	+	0.432481i	$0.857638\pi$
$572$	4.04512	−	7.00635i	0.169135	−	0.292950i
$573$	−4.74791			−0.198347
$574$	1.60022	+	2.52057i	0.0667917	+	0.105207i
$575$	3.78028			0.157648
$576$	−23.4737	+	40.6577i	−0.978071	+	1.69407i
$577$	4.31906	+	7.48083i	0.179805	+	0.311431i	0.941814	−	0.336136i	$-0.109120\pi$
$577$	4.31906	+	7.48083i	0.179805	+	0.311431i	−0.762009	+	0.647567i	$0.775787\pi$
$578$	−6.78264	−	11.7479i	−0.282121	−	0.488648i
$579$	−5.20123	+	9.00879i	−0.216156	+	0.374392i
$580$	7.74138			0.321443
$581$	−2.28182	+	4.36656i	−0.0946658	+	0.181155i
$582$	25.4651			1.05556
$583$	−1.77531	+	3.07492i	−0.0735257	+	0.127350i
$584$	18.0998	+	31.3497i	0.748973	+	1.29726i
$585$	−23.9496	−	41.4820i	−0.990195	−	1.71507i
$586$	−15.5535	+	26.9394i	−0.642508	+	1.11286i
$587$	29.1822			1.20448			0.602238	−	0.798316i	$-0.294276\pi$
$587$	29.1822			1.20448			0.602238	+	0.798316i	$0.294276\pi$
$588$	−14.8465	+	1.25188i	−0.612261	+	0.0516265i
$589$	−40.1282			−1.65345
$590$	22.0008	−	38.1066i	0.905760	−	1.56882i
$591$	−9.33393	−	16.1668i	−0.383947	−	0.665015i
$592$	−9.44266	−	16.3552i	−0.388091	−	0.672193i
$593$	6.09454	−	10.5560i	0.250273	−	0.433485i	−0.713328	−	0.700830i	$-0.752813\pi$
$593$	6.09454	−	10.5560i	0.250273	−	0.433485i	0.963601	+	0.267345i	$0.0861464\pi$
$594$	32.4383			1.33096
$595$	−8.00971	+	15.3276i	−0.328366	+	0.628372i
$596$	2.89847			0.118726
$597$	−14.3149	+	24.7942i	−0.585871	+	1.01476i
$598$	−1.74456	−	3.02167i	−0.0713403	−	0.123565i
$599$	−18.7216	−	32.4267i	−0.764942	−	1.32492i	−0.940277	−	0.340410i	$-0.889434\pi$
$599$	−18.7216	−	32.4267i	−0.764942	−	1.32492i	0.175335	−	0.984509i	$-0.443899\pi$
$600$	−16.1413	+	27.9575i	−0.658964	+	1.14136i
$601$	32.4249			1.32264			0.661320	−	0.750104i	$-0.269997\pi$
$601$	32.4249			1.32264			0.661320	+	0.750104i	$0.269997\pi$
$602$	8.82413	+	13.8993i	0.359645	+	0.566492i
$603$	58.4787			2.38144
$604$	−5.49239	+	9.51309i	−0.223482	+	0.387082i
$605$	5.04953	+	8.74604i	0.205292	+	0.355577i
$606$	17.3246	+	30.0071i	0.703763	+	1.21895i
$607$	9.89025	−	17.1304i	0.401433	−	0.695302i	−0.592466	−	0.805595i	$-0.701846\pi$
$607$	9.89025	−	17.1304i	0.401433	−	0.695302i	0.993899	+	0.110293i	$0.0351790\pi$
$608$	−23.7650			−0.963798
$609$	−28.1645	+	1.18533i	−1.14128	+	0.0480319i
$610$	−47.4639			−1.92176
$611$	2.59619	−	4.49674i	0.105031	−	0.181919i
$612$	4.52459	+	7.83683i	0.182896	+	0.316785i
$613$	−20.5654	−	35.6203i	−0.830628	−	1.43869i	−0.897541	−	0.440931i	$-0.854648\pi$
$613$	−20.5654	−	35.6203i	−0.830628	−	1.43869i	0.0669127	−	0.997759i	$-0.478685\pi$
$614$	2.63009	−	4.55545i	0.106142	−	0.183843i
$615$	8.58161			0.346044
$616$	30.9146	−	1.30107i	1.24559	−	0.0524216i
$617$	2.77289			0.111633			0.0558163	−	0.998441i	$-0.482224\pi$
$617$	2.77289			0.111633			0.0558163	+	0.998441i	$0.482224\pi$
$618$	9.99887	−	17.3185i	0.402213	−	0.696654i
$619$	−4.73675	−	8.20429i	−0.190386	−	0.329758i	0.754992	−	0.655734i	$-0.227641\pi$
$619$	−4.73675	−	8.20429i	−0.190386	−	0.329758i	−0.945378	+	0.325975i	$0.894307\pi$
$620$	6.96405	+	12.0621i	0.279683	+	0.484425i
$621$	−3.99108	+	6.91275i	−0.160157	+	0.277399i
$622$	−2.23564			−0.0896409
$623$	23.0017	+	36.2310i	0.921543	+	1.45156i
$624$	17.3257			0.693584
$625$	15.0401	−	26.0501i	0.601602	−	1.04201i
$626$	10.1805	+	17.6332i	0.406896	+	0.704765i
$627$	34.1408	+	59.1336i	1.36345	+	2.36157i
$628$	2.56025	−	4.43448i	0.102165	−	0.176955i
$629$	−20.8723			−0.832234
$630$	22.6097	−	43.2666i	0.900791	−	1.72378i
$631$	−18.4744			−0.735455			−0.367727	−	0.929934i	$-0.619864\pi$
$631$	−18.4744			−0.735455			−0.367727	+	0.929934i	$0.619864\pi$
$632$	23.1822	−	40.1528i	0.922139	−	1.59719i
$633$	6.32026	+	10.9470i	0.251208	+	0.435105i
$634$	1.05068	+	1.81984i	0.0417280	+	0.0722750i
$635$	−20.1356	+	34.8760i	−0.799059	+	1.38401i
$636$	1.98826			0.0788398
$637$	11.7089	+	16.8345i	0.463925	+	0.667007i
$638$	15.6004			0.617624
$639$	26.6216	−	46.1100i	1.05314	−	1.82409i
$640$	−2.54981	−	4.41640i	−0.100790	−	0.174574i
$641$	11.7424	+	20.3384i	0.463797	+	0.803320i	0.999146	−	0.0413105i	$-0.0131533\pi$
$641$	11.7424	+	20.3384i	0.463797	+	0.803320i	−0.535349	+	0.844631i	$0.679820\pi$
$642$	−1.38972	+	2.40706i	−0.0548478	+	0.0949991i
$643$	−5.24905			−0.207002			−0.103501	−	0.994629i	$-0.533005\pi$
$643$	−5.24905			−0.207002			−0.103501	+	0.994629i	$0.533005\pi$
$644$	−0.939701	+	1.79824i	−0.0370294	+	0.0708606i
$645$	47.3219			1.86330
$646$	7.72056	−	13.3724i	0.303761	−	0.526130i
$647$	5.45257	+	9.44413i	0.214363	+	0.371287i	0.953075	−	0.302734i	$-0.0978992\pi$
$647$	5.45257	+	9.44413i	0.214363	+	0.371287i	−0.738713	+	0.674021i	$0.764566\pi$
$648$	−8.32217	−	14.4144i	−0.326926	−	0.566252i
$649$	−25.2967	+	43.8152i	−0.992982	+	1.71990i
$650$	11.8399			0.464401
$651$	−27.1833	−	42.8177i	−1.06540	−	1.67816i
$652$	−11.7515			−0.460225
$653$	6.52702	−	11.3051i	0.255422	−	0.442404i	−0.709588	−	0.704617i	$-0.751119\pi$
$653$	6.52702	−	11.3051i	0.255422	−	0.442404i	0.965010	+	0.262213i	$0.0844522\pi$
$654$	−2.35707	−	4.08257i	−0.0921689	−	0.159641i
$655$	−2.89323	−	5.01121i	−0.113048	−	0.195804i
$656$	−1.00947	+	1.74845i	−0.0394131	+	0.0682654i
$657$	−65.6687			−2.56198
$658$	5.28730	−	0.222521i	0.206120	−	0.00867476i
$659$	10.2628			0.399784			0.199892	−	0.979818i	$-0.435941\pi$
$659$	10.2628			0.399784			0.199892	+	0.979818i	$0.435941\pi$
$660$	11.8499	−	20.5247i	0.461258	−	0.798922i
$661$	−13.2790	−	22.9998i	−0.516492	−	0.894590i	−0.999817	−	0.0191488i	$-0.993904\pi$
$661$	−13.2790	−	22.9998i	−0.516492	−	0.894590i	0.483325	−	0.875441i	$-0.339429\pi$
$662$	4.55699	+	7.89294i	0.177113	+	0.306768i
$663$	9.57431	−	16.5832i	0.371836	−	0.644038i
$664$	−5.72957			−0.222350
$665$	47.4868	−	1.99852i	1.84146	−	0.0774994i
$666$	58.9180			2.28303
$667$	−1.91941	+	3.32452i	−0.0743199	+	0.128726i
$668$	−1.87039	−	3.23960i	−0.0723674	−	0.125344i
$669$	17.1731	+	29.7447i	0.663950	+	1.15000i
$670$	−17.3172	+	29.9944i	−0.669024	+	1.15878i
$671$	54.5742			2.10681
$672$	−16.0987	−	25.3578i	−0.621021	−	0.978198i
$673$	35.7468			1.37794			0.688969	−	0.724790i	$-0.258063\pi$
$673$	35.7468			1.37794			0.688969	+	0.724790i	$0.258063\pi$
$674$	−16.3060	+	28.2428i	−0.628084	+	1.08787i
$675$	−13.5433	−	23.4577i	−0.521282	−	0.902886i
$676$	−1.60515	−	2.78020i	−0.0617364	−	0.106931i
$677$	−3.51193	+	6.08284i	−0.134974	+	0.233782i	−0.925588	−	0.378533i	$-0.876429\pi$
$677$	−3.51193	+	6.08284i	−0.134974	+	0.233782i	0.790613	+	0.612316i	$0.209762\pi$
$678$	19.0605			0.732015
$679$	−9.43927	+	18.0633i	−0.362246	+	0.693205i
$680$	−20.1121			−0.771264
$681$	29.5098	−	51.1125i	1.13082	−	1.95864i
$682$	14.0339	+	24.3074i	0.537386	+	0.930779i
$683$	−14.7859	−	25.6100i	−0.565768	−	0.979939i	−0.996978	−	0.0776876i	$-0.975246\pi$
$683$	−14.7859	−	25.6100i	−0.565768	−	0.979939i	0.431209	−	0.902252i	$-0.358087\pi$
$684$	12.4347	−	21.5375i	0.475452	−	0.823507i
$685$	−0.609045			−0.0232704
$686$	−8.08883	+	19.2706i	−0.308833	+	0.735754i
$687$	−66.6184			−2.54165
$688$	−5.56654	+	9.64153i	−0.212222	+	0.367580i
$689$	−1.36824	−	2.36986i	−0.0521259	−	0.0902846i
$690$	−5.11058	−	8.85179i	−0.194557	−	0.336982i
$691$	4.69722	−	8.13582i	0.178691	−	0.309501i	−0.762742	−	0.646703i	$-0.776147\pi$
$691$	4.69722	−	8.13582i	0.178691	−	0.309501i	0.941432	+	0.337202i	$0.109481\pi$
$692$	−6.35649			−0.241637
$693$	−25.9967	+	49.7482i	−0.987534	+	1.88978i
$694$	−11.9189			−0.452437
$695$	10.0570	−	17.4193i	0.381485	−	0.660751i
$696$	−16.3912	−	28.3904i	−0.621308	−	1.07614i
$697$	1.11568	+	1.93241i	0.0422593	+	0.0731953i
$698$	5.82372	−	10.0870i	0.220431	−	0.381798i
$699$	37.0103			1.39986
$700$	−3.69022	−	5.81263i	−0.139477	−	0.219697i
$701$	20.0205			0.756162			0.378081	−	0.925773i	$-0.376584\pi$
$701$	20.0205			0.756162			0.378081	+	0.925773i	$0.376584\pi$
$702$	−12.5002	+	21.6510i	−0.471789	+	0.817163i
$703$	28.6811	+	49.6771i	1.08173	+	1.87361i
$704$	15.9852	+	27.6871i	0.602464	+	1.04350i
$705$	7.60539	−	13.1729i	0.286436	−	0.496121i
$706$	22.6760			0.853423
$707$	−27.7068	+	1.16607i	−1.04202	+	0.0438544i
$708$	28.3311			1.06475
$709$	4.67070	−	8.08989i	0.175412	−	0.303822i	−0.764892	−	0.644159i	$-0.777208\pi$
$709$	4.67070	−	8.08989i	0.175412	−	0.303822i	0.940304	+	0.340336i	$0.110541\pi$
$710$	15.7669	+	27.3091i	0.591721	+	1.02489i
$711$	42.0543	+	72.8402i	1.57716	+	2.73172i
$712$	−24.9541	+	43.2218i	−0.935194	+	1.61980i
$713$	−6.90671			−0.258658
$714$	19.4986	−	0.820618i	0.729718	−	0.0307108i
$715$	−32.6185			−1.21986
$716$	−2.68241	+	4.64606i	−0.100246	+	0.173632i
$717$	−30.5092	−	52.8434i	−1.13939	−	1.97347i
$718$	1.51321	+	2.62095i	0.0564724	+	0.0978130i
$719$	8.05115	−	13.9450i	0.300257	−	0.520061i	−0.675937	−	0.736959i	$-0.736261\pi$
$719$	8.05115	−	13.9450i	0.300257	−	0.520061i	0.976194	+	0.216899i	$0.0695942\pi$
$720$	33.0116			1.23027
$721$	8.57831	+	13.5121i	0.319473	+	0.503216i
$722$	−20.9952			−0.781359
$723$	−11.1391	+	19.2935i	−0.414267	+	0.717532i
$724$	3.60542	+	6.24476i	0.133994	+	0.232085i
$725$	−6.51331	−	11.2814i	−0.241898	−	0.418980i
$726$	5.69819	−	9.86956i	0.211480	−	0.366294i
$727$	2.78212			0.103183			0.0515915	−	0.998668i	$-0.483571\pi$
$727$	2.78212			0.103183			0.0515915	+	0.998668i	$0.483571\pi$
$728$	−11.0447	+	21.1354i	−0.409342	+	0.783330i
$729$	−36.2691			−1.34330
$730$	19.4464	−	33.6822i	0.719744	−	1.24663i
$731$	6.15222	+	10.6560i	0.227548	+	0.394125i
$732$	−15.2802	−	26.4660i	−0.564771	−	0.978212i
$733$	−8.68886	+	15.0495i	−0.320930	+	0.555868i	−0.980680	−	0.195618i	$-0.937329\pi$
$733$	−8.68886	+	15.0495i	−0.320930	+	0.555868i	0.659750	+	0.751485i	$0.270662\pi$
$734$	−31.0173			−1.14487
$735$	34.3006	+	49.3156i	1.26520	+	1.81903i
$736$	−4.09034			−0.150772
$737$	19.9115	−	34.4877i	0.733448	−	1.27037i
$738$	−3.14932	−	5.45478i	−0.115928	−	0.200793i
$739$	−14.4269	−	24.9880i	−0.530700	−	0.919200i	−0.999358	−	0.0358202i	$-0.988596\pi$
$739$	−14.4269	−	24.9880i	−0.530700	−	0.919200i	0.468658	−	0.883380i	$-0.344738\pi$
$740$	9.95492	−	17.2424i	0.365950	−	0.633844i
$741$	−52.6250			−1.93323
$742$	1.29169	−	2.47182i	0.0474195	−	0.0907433i
$743$	−2.11198			−0.0774811			−0.0387405	−	0.999249i	$-0.512335\pi$
$743$	−2.11198			−0.0774811			−0.0387405	+	0.999249i	$0.512335\pi$
$744$	29.4907	−	51.0794i	1.08118	−	1.87266i
$745$	−5.84308	−	10.1205i	−0.214074	−	0.370787i
$746$	−3.80259	−	6.58629i	−0.139223	−	0.241141i
$747$	5.19694	−	9.00136i	0.190146	−	0.329342i
$748$	6.16233			0.225317
$749$	−1.19228	−	1.87801i	−0.0435649	−	0.0686210i
$750$	−13.7357			−0.501556
$751$	8.52822	−	14.7713i	0.311199	−	0.539013i	−0.667423	−	0.744679i	$-0.732603\pi$
$751$	8.52822	−	14.7713i	0.311199	−	0.539013i	0.978622	+	0.205666i	$0.0659360\pi$
$752$	1.78927	+	3.09910i	0.0652478	+	0.113013i
$753$	−44.2754	−	76.6872i	−1.61348	−	2.79464i
$754$	−6.01165	+	10.4125i	−0.218931	+	0.379200i
$755$	44.2889			1.61184
$756$	14.5252	−	0.611305i	0.528276	−	0.0222330i
$757$	−49.7155			−1.80694			−0.903470	−	0.428652i	$-0.858989\pi$
$757$	−49.7155			−1.80694			−0.903470	+	0.428652i	$0.858989\pi$
$758$	−19.3722	+	33.5535i	−0.703628	+	1.21872i
$759$	5.87618	+	10.1778i	0.213292	+	0.369432i
$760$	27.6364	+	47.8677i	1.00248	+	1.73634i
$761$	24.3569	−	42.1874i	0.882937	−	1.52929i	0.0348772	−	0.999392i	$-0.488896\pi$
$761$	24.3569	−	42.1874i	0.882937	−	1.52929i	0.848060	−	0.529900i	$-0.177771\pi$
$762$	45.4446			1.64628
$763$	3.76962	−	0.158648i	0.136469	−	0.00574343i
$764$	1.17760			0.0426042
$765$	18.2424	−	31.5968i	0.659557	−	1.14239i
$766$	−0.742217	−	1.28556i	−0.0268174	−	0.0464491i
$767$	−19.4963	−	33.7686i	−0.703972	−	1.21931i
$768$	21.7624	−	37.6936i	0.785283	−	1.36015i
$769$	−1.23591			−0.0445680			−0.0222840	−	0.999752i	$-0.507094\pi$
$769$	−1.23591			−0.0445680			−0.0222840	+	0.999752i	$0.507094\pi$
$770$	−17.8180	−	28.0659i	−0.642115	−	1.01142i
$771$	28.9252			1.04172
$772$	1.29004	−	2.23441i	0.0464295	−	0.0804182i
$773$	17.8417	+	30.9026i	0.641720	+	1.11149i	0.985049	+	0.172276i	$0.0551120\pi$
$773$	17.8417	+	30.9026i	0.641720	+	1.11149i	−0.343329	+	0.939215i	$0.611555\pi$
$774$	−17.3664	−	30.0795i	−0.624222	−	1.08118i
$775$	11.7186	−	20.2972i	0.420944	−	0.729096i
$776$	−23.7017			−0.850840
$777$	−33.5776	+	64.2552i	−1.20459	+	2.30514i
$778$	−17.3530			−0.622136
$779$	3.06615	−	5.31073i	0.109856	−	0.190277i
$780$	9.13281	+	15.8185i	0.327007	+	0.566393i
$781$	−18.1289	−	31.4001i	−0.648702	−	1.12358i
$782$	1.32883	−	2.30160i	0.0475189	−	0.0823052i
$783$	27.5061			0.982987
$784$	−14.0826	+	1.18746i	−0.502949	+	0.0424092i
$785$	−20.6450			−0.736852
$786$	−3.26489	+	5.65496i	−0.116455	+	0.201706i
$787$	−9.67197	−	16.7523i	−0.344769	−	0.597157i	0.640543	−	0.767922i	$-0.278709\pi$
$787$	−9.67197	−	16.7523i	−0.344769	−	0.597157i	−0.985312	+	0.170766i	$0.945376\pi$
$788$	2.31505	+	4.00979i	0.0824704	+	0.142843i
$789$	41.3437	−	71.6094i	1.47188	−	2.54936i
$790$	−49.8140			−1.77230
$791$	−7.06525	+	13.5203i	−0.251211	+	0.480726i
$792$	−65.2769			−2.31951
$793$	−21.0304	+	36.4256i	−0.746810	+	1.29351i
$794$	−9.88767	−	17.1260i	−0.350900	−	0.607777i
$795$	−4.00818	−	6.94237i	−0.142156	−	0.246221i
$796$	3.55047	−	6.14960i	0.125843	−	0.217967i
$797$	38.0350			1.34727			0.673635	−	0.739065i	$-0.264732\pi$
$797$	38.0350			1.34727			0.673635	+	0.739065i	$0.264732\pi$
$798$	−28.7466	−	45.2801i	−1.01762	−	1.60290i
$799$	3.95505			0.139919
$800$	6.94006	−	12.0205i	0.245368	−	0.424990i
$801$	−45.2686	−	78.4076i	−1.59949	−	2.77040i
$802$	−8.53309	−	14.7797i	−0.301314	−	0.521891i
$803$	−22.3596	+	38.7280i	−0.789053	+	1.36668i
$804$	−22.2999			−0.786458
$805$	8.17324	−	0.343978i	0.288069	−	0.0121236i
$806$	−21.6320			−0.761956
$807$	−28.9552	+	50.1519i	−1.01927	+	1.76543i
$808$	−16.1249	−	27.9291i	−0.567271	−	0.982542i
$809$	19.3300	+	33.4806i	0.679607	+	1.17711i	0.975099	+	0.221769i	$0.0711830\pi$
$809$	19.3300	+	33.4806i	0.679607	+	1.17711i	−0.295492	+	0.955345i	$0.595484\pi$
$810$	−8.94136	+	15.4869i	−0.314167	+	0.544154i
$811$	25.3938			0.891696			0.445848	−	0.895109i	$-0.352902\pi$
$811$	25.3938			0.891696			0.445848	+	0.895109i	$0.352902\pi$
$812$	6.98552	−	0.293992i	0.245144	−	0.0103171i
$813$	62.9355			2.20724
$814$	20.0611	−	34.7468i	0.703140	−	1.21787i
$815$	23.6901	+	41.0325i	0.829829	+	1.43731i
$816$	6.59850	+	11.4289i	0.230994	+	0.400093i
$817$	16.9078	−	29.2851i	0.591529	−	1.02456i
$818$	8.38385			0.293134
$819$	−23.1866	−	36.5222i	−0.810204	−	1.27619i
$820$	−2.12846			−0.0743291
$821$	−11.9400	+	20.6807i	−0.416708	+	0.721760i	−0.995606	−	0.0936403i	$-0.970150\pi$
$821$	−11.9400	+	20.6807i	−0.416708	+	0.721760i	0.578898	+	0.815400i	$0.303483\pi$
$822$	0.343642	+	0.595205i	0.0119859	+	0.0207602i
$823$	13.9346	+	24.1355i	0.485731	+	0.841311i	0.999866	−	0.0163987i	$-0.00522010\pi$
$823$	13.9346	+	24.1355i	0.485731	+	0.841311i	−0.514134	+	0.857710i	$0.671887\pi$
$824$	−9.30645	+	16.1192i	−0.324205	+	0.561540i
$825$	−39.8803			−1.38845
$826$	18.4055	−	35.2214i	0.640411	−	1.22551i
$827$	29.0555			1.01036			0.505179	−	0.863014i	$-0.331426\pi$
$827$	29.0555			1.01036			0.505179	+	0.863014i	$0.331426\pi$
$828$	2.14021	−	3.70695i	0.0743773	−	0.128825i
$829$	−0.986164	−	1.70809i	−0.0342509	−	0.0593243i	0.848392	−	0.529369i	$-0.177571\pi$
$829$	−0.986164	−	1.70809i	−0.0342509	−	0.0593243i	−0.882643	+	0.470045i	$0.844238\pi$
$830$	3.07793	+	5.33113i	0.106836	+	0.185046i
$831$	20.7668	−	35.9692i	0.720394	−	1.24776i
$832$	−24.6398			−0.854230
$833$	−6.64556	+	14.1352i	−0.230255	+	0.489757i
$834$	−22.6979			−0.785964
$835$	−7.54110	+	13.0616i	−0.260970	+	0.452014i
$836$	−8.46779	−	14.6666i	−0.292865	−	0.507256i
$837$	24.7441	+	42.8581i	0.855282	+	1.48139i
$838$	−6.36648	+	11.0271i	−0.219926	+	0.380924i
$839$	−22.2354			−0.767653			−0.383826	−	0.923405i	$-0.625394\pi$
$839$	−22.2354			−0.767653			−0.383826	+	0.923405i	$0.625394\pi$
$840$	−32.3547	+	61.9149i	−1.11634	+	2.13627i
$841$	−15.7716			−0.543850
$842$	−11.9153	+	20.6380i	−0.410630	+	0.711232i
$843$	11.9432	+	20.6862i	0.411346	+	0.712472i
$844$	−1.56759	−	2.71514i	−0.0539586	−	0.0934590i
$845$	−6.47170	+	11.2093i	−0.222633	+	0.385612i
$846$	−11.1642			−0.383834
$847$	4.88864	+	7.70032i	0.167976	+	0.264586i
$848$	1.88595			0.0647638
$849$	−28.3008	+	49.0184i	−0.971281	+	1.68231i
$850$	4.50925	+	7.81024i	0.154666	+	0.267889i
$851$	4.93647	+	8.55022i	0.169220	+	0.293098i
$852$	−10.1517	+	17.5833i	−0.347793	+	0.602395i
$853$	−7.48352			−0.256231			−0.128115	−	0.991759i	$-0.540893\pi$
$853$	−7.48352			−0.256231			−0.128115	+	0.991759i	$0.540893\pi$
$854$	−42.8295	+	1.80252i	−1.46560	+	0.0616809i
$855$	−100.269			−3.42914
$856$	1.29348	−	2.24037i	0.0442102	−	0.0765744i
$857$	5.67207	+	9.82431i	0.193754	+	0.335592i	0.946491	−	0.322729i	$-0.104600\pi$
$857$	5.67207	+	9.82431i	0.193754	+	0.335592i	−0.752737	+	0.658321i	$0.771267\pi$
$858$	18.4044	+	31.8773i	0.628315	+	1.08827i
$859$	−2.37668	+	4.11653i	−0.0810913	+	0.140454i	−0.903719	−	0.428126i	$-0.859174\pi$
$859$	−2.37668	+	4.11653i	−0.0810913	+	0.140454i	0.822628	+	0.568580i	$0.192507\pi$
$860$	−11.7370			−0.400230
$861$	7.74371	−	0.325901i	0.263905	−	0.0111067i
$862$	−19.8536			−0.676217
$863$	−20.8252	+	36.0703i	−0.708897	+	1.22785i	0.256369	+	0.966579i	$0.417474\pi$
$863$	−20.8252	+	36.0703i	−0.708897	+	1.22785i	−0.965266	+	0.261267i	$0.915860\pi$
$864$	14.6541	+	25.3817i	0.498544	+	0.863503i
$865$	12.8142	+	22.1948i	0.435695	+	0.754645i
$866$	5.21559	−	9.03367i	0.177233	−	0.306977i
$867$	−35.2149			−1.19596
$868$	6.74217	+	10.6199i	0.228844	+	0.360462i
$869$	57.2764			1.94297
$870$	−17.6108	+	30.5027i	−0.597061	+	1.03414i
$871$	15.3459	+	26.5799i	0.519976	+	0.900625i
$872$	2.19385	+	3.79986i	0.0742931	+	0.128679i
$873$	21.4983	−	37.2362i	0.727608	−	1.26025i
$874$	−7.30390			−0.247058
$875$	5.09147	−	9.74319i	0.172123	−	0.329380i
$876$	25.0417			0.846082
$877$	−13.6739	+	23.6839i	−0.461735	+	0.799749i	−0.999048	−	0.0436346i	$-0.986106\pi$
$877$	−13.6739	+	23.6839i	−0.461735	+	0.799749i	0.537312	+	0.843383i	$0.319440\pi$
$878$	14.0698	+	24.3697i	0.474834	+	0.822437i
$879$	40.3762	+	69.9336i	1.36185	+	2.35880i
$880$	11.2401	−	19.4685i	0.378905	−	0.656283i
$881$	−32.2910			−1.08791			−0.543956	−	0.839114i	$-0.683074\pi$
$881$	−32.2910			−1.08791			−0.543956	+	0.839114i	$0.683074\pi$
$882$	18.7590	−	39.9007i	0.631647	−	1.34353i
$883$	29.5079			0.993020			0.496510	−	0.868031i	$-0.334615\pi$
$883$	29.5079			0.993020			0.496510	+	0.868031i	$0.334615\pi$
$884$	−2.37468	+	4.11306i	−0.0798690	+	0.138337i
$885$	−57.1133	−	98.9231i	−1.91984	−	3.32527i
$886$	17.4823	+	30.2803i	0.587331	+	1.01729i
$887$	18.0100	−	31.1943i	0.604717	−	1.04740i	−0.387379	−	0.921921i	$-0.626619\pi$
$887$	18.0100	−	31.1943i	0.604717	−	1.04740i	0.992096	−	0.125481i	$-0.0400473\pi$
$888$	−84.3122			−2.82933
$889$	−16.8451	+	32.2354i	−0.564968	+	1.08114i
$890$	53.6215			1.79740
$891$	10.2808	−	17.8069i	0.344421	−	0.596554i
$892$	−4.25937	−	7.37745i	−0.142614	−	0.247015i
$893$	−5.43471	−	9.41319i	−0.181866	−	0.315001i
$894$	−6.59369	+	11.4206i	−0.220526	+	0.381962i
$895$	21.6301			0.723013
$896$	−2.46857	−	3.88835i	−0.0824691	−	0.129901i
$897$	−9.05761			−0.302425
$898$	−5.21595	+	9.03430i	−0.174059	+	0.301478i
$899$	11.9001	+	20.6115i	0.396889	+	0.687432i
$900$	7.26256	+	12.5791i	0.242085	+	0.419304i
$901$	1.04219	−	1.80513i	0.0347204	−	0.0601375i
$902$	−4.28925			−0.142817
$903$	42.7014	−	1.79713i	1.42101	−	0.0598047i
$904$	−17.7406			−0.590043
$905$	14.5365	−	25.1779i	0.483208	−	0.836941i
$906$	−24.9891	−	43.2824i	−0.830208	−	1.43796i
$907$	−14.6680	−	25.4057i	−0.487042	−	0.843582i	0.512847	−	0.858480i	$-0.328591\pi$
$907$	−14.6680	−	25.4057i	−0.487042	−	0.843582i	−0.999889	+	0.0148982i	$0.995258\pi$
$908$	−7.31920	+	12.6772i	−0.242896	+	0.420708i
$909$	58.5035			1.94044
$910$	25.5988	−	1.07735i	0.848593	−	0.0357138i
$911$	27.7708			0.920086			0.460043	−	0.887897i	$-0.347834\pi$
$911$	27.7708			0.920086			0.460043	+	0.887897i	$0.347834\pi$
$912$	18.1343	−	31.4095i	0.600486	−	1.04007i
$913$	−3.53902	−	6.12976i	−0.117124	−	0.202865i
$914$	−12.4546	−	21.5719i	−0.411960	−	0.713536i
$915$	−61.6071	+	106.707i	−2.03667	+	3.52761i
$916$	16.5231			0.545938
$917$	−2.80104	−	4.41205i	−0.0924986	−	0.145699i
$918$	−19.0428			−0.628506
$919$	5.55496	−	9.62147i	0.183241	−	0.317383i	−0.759741	−	0.650225i	$-0.774674\pi$
$919$	5.55496	−	9.62147i	0.183241	−	0.317383i	0.942982	+	0.332843i	$0.108008\pi$
$920$	4.75667	+	8.23880i	0.156823	+	0.271625i
$921$	−6.82760	−	11.8258i	−0.224977	−	0.389672i
$922$	23.8427	−	41.2967i	0.785216	−	1.36003i
$923$	27.9441			0.919790
$924$	9.91345	−	18.9707i	0.326129	−	0.624090i
$925$	−33.5028			−1.10156
$926$	−20.4124	+	35.3553i	−0.670793	+	1.16185i
$927$	−16.8826	−	29.2415i	−0.554498	−	0.960418i
$928$	7.04754	+	12.2067i	0.231347	+	0.400704i
$929$	−12.9830	+	22.4872i	−0.425959	+	0.737782i	−0.996509	−	0.0834801i	$-0.973396\pi$
$929$	−12.9830	+	22.4872i	−0.425959	+	0.737782i	0.570551	+	0.821262i	$0.306730\pi$
$930$	−63.3697			−2.07797
$931$	42.7743	−	3.60678i	1.40187	−	0.118207i
$932$	−9.17949			−0.300684
$933$	−2.90181	+	5.02609i	−0.0950011	+	0.164547i
$934$	7.28530	+	12.6185i	0.238382	+	0.412890i
$935$	−12.4228	−	21.5169i	−0.406268	−	0.703677i
$936$	25.1547	−	43.5691i	0.822206	−	1.42410i
$937$	30.0886			0.982953			0.491476	−	0.870891i	$-0.336457\pi$
$937$	30.0886			0.982953			0.491476	+	0.870891i	$0.336457\pi$
$938$	−14.4873	+	27.7234i	−0.473028	+	0.905201i
$939$	52.8565			1.72491
$940$	−1.88633	+	3.26723i	−0.0615254	+	0.106565i
$941$	−18.5838	−	32.1881i	−0.605814	−	1.04930i	−0.991922	−	0.126847i	$-0.959514\pi$
$941$	−18.5838	−	32.1881i	−0.605814	−	1.04930i	0.386108	−	0.922453i	$-0.373819\pi$
$942$	11.6485	+	20.1759i	0.379530	+	0.657365i
$943$	0.527734	−	0.914062i	0.0171854	−	0.0297659i
$944$	26.8733			0.874651
$945$	−31.4161	−	49.4849i	−1.02197	−	1.60974i
$946$	−23.6524			−0.769006
$947$	8.65662	−	14.9937i	0.281302	−	0.487230i	−0.690403	−	0.723425i	$-0.742567\pi$
$947$	8.65662	−	14.9937i	0.281302	−	0.487230i	0.971706	+	0.236195i	$0.0759003\pi$
$948$	−16.0367	−	27.7765i	−0.520849	−	0.902137i
$949$	−17.2327	−	29.8479i	−0.559397	−	0.968904i
$950$	12.3925	−	21.4644i	0.402066	−	0.696398i
$951$	5.45506			0.176893
$952$	−18.1484	+	0.763790i	−0.588192	+	0.0247546i
$953$	18.4287			0.596965			0.298482	−	0.954415i	$-0.403520\pi$
$953$	18.4287			0.596965			0.298482	+	0.954415i	$0.403520\pi$
$954$	−2.94188	+	5.09548i	−0.0952468	+	0.164972i
$955$	−2.37395	−	4.11181i	−0.0768193	−	0.133055i
$956$	7.56706	+	13.1065i	0.244736	+	0.423895i
$957$	20.2490	−	35.0722i	0.654556	−	1.13372i
$958$	9.66385			0.312225
$959$	−0.549579	+	0.0231295i	−0.0177468	+	0.000746891i
$960$	−72.1807			−2.32962
$961$	−5.91029	+	10.2369i	−0.190655	+	0.330224i
$962$	15.4612	+	26.7796i	0.498489	+	0.863408i
$963$	2.34647	+	4.06421i	0.0756140	+	0.130967i
$964$	2.76278	−	4.78528i	0.0889832	−	0.154123i
$965$	−10.4025			−0.334867
$966$	−4.94775	−	7.79342i	−0.159191	−	0.250749i
$967$	−0.639722			−0.0205721			−0.0102860	−	0.999947i	$-0.503274\pi$
$967$	−0.639722			−0.0205721			−0.0102860	+	0.999947i	$0.503274\pi$
$968$	−5.30359	+	9.18610i	−0.170464	+	0.295252i
$969$	−20.0423	−	34.7142i	−0.643850	−	1.11518i
$970$	12.7326	+	22.0534i	0.408818	+	0.708093i
$971$	3.19595	−	5.53556i	0.102563	−	0.177644i	−0.810177	−	0.586185i	$-0.800629\pi$
$971$	3.19595	−	5.53556i	0.102563	−	0.177644i	0.912740	+	0.408541i	$0.133962\pi$
$972$	4.97054			0.159430
$973$	8.41354	−	16.1004i	0.269726	−	0.516155i
$974$	−5.76251			−0.184643
$975$	15.3680	−	26.6182i	0.492170	−	0.852464i
$976$	−14.4939	−	25.1041i	−0.463937	−	0.803563i
$977$	−16.2218	−	28.0969i	−0.518980	−	0.898900i	−0.999757	−	0.0220565i	$-0.992979\pi$
$977$	−16.2218	−	28.0969i	−0.518980	−	0.898900i	0.480777	−	0.876843i	$-0.340355\pi$
$978$	26.7334	−	46.3036i	0.854839	−	1.48063i
$979$	−61.6543			−1.97048
$980$	−8.50743	−	12.2315i	−0.271760	−	0.390722i
$981$	−7.95962			−0.254131
$982$	1.01756	−	1.76247i	0.0324716	−	0.0562425i
$983$	23.3925	+	40.5170i	0.746104	+	1.29229i	0.949677	+	0.313230i	$0.101411\pi$
$983$	23.3925	+	40.5170i	0.746104	+	1.29229i	−0.203573	+	0.979060i	$0.565255\pi$
$984$	4.50670	+	7.80583i	0.143668	+	0.248841i
$985$	9.33393	−	16.1668i	0.297404	−	0.515118i
$986$	−9.15816			−0.291655
$987$	6.36255	−	12.1756i	0.202522	−	0.387552i
$988$	13.0524			0.415251
$989$	2.91010	−	5.04044i	0.0925358	−	0.160277i
$990$	35.0668	+	60.7375i	1.11450	+	1.93036i
$991$	−2.61989	−	4.53778i	−0.0832234	−	0.144147i	0.821409	−	0.570339i	$-0.193188\pi$
$991$	−2.61989	−	4.53778i	−0.0832234	−	0.144147i	−0.904633	+	0.426192i	$0.859855\pi$
$992$	−12.6797	+	21.9620i	−0.402582	+	0.697293i
$993$	23.6595			0.750813
$994$	15.2645	+	24.0439i	0.484162	+	0.762625i
$995$	−28.6299			−0.907628
$996$	−1.98177	+	3.43253i	−0.0627948	+	0.108764i
$997$	−4.59151	−	7.95272i	−0.145414	−	0.251865i	0.784113	−	0.620618i	$-0.213118\pi$
$997$	−4.59151	−	7.95272i	−0.145414	−	0.251865i	−0.929528	+	0.368753i	$0.879785\pi$
$998$	−11.1056	−	19.2354i	−0.351541	−	0.608886i
$999$	35.3710	−	61.2644i	1.11909	−	1.93832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.c.247.3	yes	10
7.2	even	3		2009.2.a.l.1.3		5
7.4	even	3	inner	287.2.e.c.165.3	✓	10
7.5	odd	6		2009.2.a.m.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.c.165.3	✓	10	7.4	even	3	inner
287.2.e.c.247.3	yes	10	1.1	even	1	trivial
2009.2.a.l.1.3		5	7.2	even	3
2009.2.a.m.1.3		5	7.5	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.564230 - 0.977276i) q^{2} +(-1.46472 - 2.53697i) q^{3} +(0.363288 + 0.629233i) q^{4} +(1.46472 - 2.53697i) q^{5} -3.30576 q^{6} +(1.22536 - 2.34489i) q^{7} +3.07683 q^{8} +(-2.79081 + 4.83382i) q^{9} +O(q^{10})\)	\(q+(0.564230 - 0.977276i) q^{2} +(-1.46472 - 2.53697i) q^{3} +(0.363288 + 0.629233i) q^{4} +(1.46472 - 2.53697i) q^{5} -3.30576 q^{6} +(1.22536 - 2.34489i) q^{7} +3.07683 q^{8} +(-2.79081 + 4.83382i) q^{9} +(-1.65288 - 2.86287i) q^{10} +(1.90049 + 3.29174i) q^{11} +(1.06423 - 1.84330i) q^{12} -2.92944 q^{13} +(-1.60022 - 2.52057i) q^{14} -8.58161 q^{15} +(1.00947 - 1.74845i) q^{16} +(-1.11568 - 1.93241i) q^{17} +(3.14932 + 5.45478i) q^{18} +(-3.06615 + 5.31073i) q^{19} +2.12846 q^{20} +(-7.74371 + 0.325901i) q^{21} +4.28925 q^{22} +(-0.527734 + 0.914062i) q^{23} +(-4.50670 - 7.80583i) q^{24} +(-1.79081 - 3.10177i) q^{25} +(-1.65288 + 2.86287i) q^{26} +7.56268 q^{27} +(1.92064 - 0.0808318i) q^{28} +3.63708 q^{29} +(-4.84201 + 8.38660i) q^{30} +(3.27187 + 5.66705i) q^{31} +(1.93769 + 3.35618i) q^{32} +(5.56737 - 9.64296i) q^{33} -2.51800 q^{34} +(-4.15409 - 6.54330i) q^{35} -4.05547 q^{36} +(4.67705 - 8.10089i) q^{37} +(3.46003 + 5.99295i) q^{38} +(4.29081 + 7.43190i) q^{39} +(4.50670 - 7.80583i) q^{40} -1.00000 q^{41} +(-4.05074 + 7.75163i) q^{42} -5.51434 q^{43} +(-1.38085 + 2.39170i) q^{44} +(8.17550 + 14.1604i) q^{45} +(0.595527 + 1.03148i) q^{46} +(-0.886243 + 1.53502i) q^{47} -5.91435 q^{48} +(-3.99699 - 5.74666i) q^{49} -4.04171 q^{50} +(-3.26831 + 5.66088i) q^{51} +(-1.06423 - 1.84330i) q^{52} +(0.467066 + 0.808982i) q^{53} +(4.26709 - 7.39082i) q^{54} +11.1347 q^{55} +(3.77023 - 7.21483i) q^{56} +17.9642 q^{57} +(2.05215 - 3.55443i) q^{58} +(6.65531 + 11.5273i) q^{59} +(-3.11760 - 5.39984i) q^{60} +(7.17897 - 12.4343i) q^{61} +7.38436 q^{62} +(7.91501 + 12.4673i) q^{63} +8.41108 q^{64} +(-4.29081 + 7.43190i) q^{65} +(-6.28256 - 10.8817i) q^{66} +(-5.23851 - 9.07337i) q^{67} +(0.810625 - 1.40404i) q^{68} +3.09193 q^{69} +(-8.73848 + 0.367767i) q^{70} -9.53905 q^{71} +(-8.58685 + 14.8729i) q^{72} +(5.88259 + 10.1889i) q^{73} +(-5.27787 - 9.14153i) q^{74} +(-5.24606 + 9.08644i) q^{75} -4.45558 q^{76} +(10.0475 - 0.422860i) q^{77} +9.68401 q^{78} +(7.53443 - 13.0500i) q^{79} +(-2.95717 - 5.12197i) q^{80} +(-2.70478 - 4.68482i) q^{81} +(-0.564230 + 0.977276i) q^{82} -1.86216 q^{83} +(-3.01827 - 4.75421i) q^{84} -6.53662 q^{85} +(-3.11136 + 5.38903i) q^{86} +(-5.32730 - 9.22716i) q^{87} +(5.84749 + 10.1282i) q^{88} +(-8.11032 + 14.0475i) q^{89} +18.4515 q^{90} +(-3.58962 + 6.86920i) q^{91} -0.766878 q^{92} +(9.58475 - 16.6013i) q^{93} +(1.00009 + 1.73221i) q^{94} +(8.98210 + 15.5575i) q^{95} +(5.67635 - 9.83172i) q^{96} -7.70326 q^{97} +(-7.87129 + 0.663716i) q^{98} -21.2156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9} + q^{10} + 6 q^{11} + 7 q^{12} + 4 q^{13} - 24 q^{14} - 40 q^{15} + 12 q^{16} + 3 q^{17} + 8 q^{18} - 7 q^{19} + 14 q^{20} - 15 q^{21} - 26 q^{22} - 16 q^{24} + 5 q^{25} + q^{26} + 26 q^{27} - 5 q^{28} - 20 q^{29} - 14 q^{30} + 6 q^{31} + 3 q^{32} + 17 q^{33} + 2 q^{34} - 9 q^{35} - 30 q^{36} + 18 q^{37} + 7 q^{38} + 20 q^{39} + 16 q^{40} - 10 q^{41} - 35 q^{42} - 28 q^{43} - 2 q^{44} + 7 q^{45} + 3 q^{46} - 3 q^{47} + 18 q^{48} - 8 q^{49} - 8 q^{50} - 7 q^{52} + 9 q^{53} + 25 q^{54} + 34 q^{55} - 15 q^{56} + 62 q^{57} + 5 q^{58} + 19 q^{59} + 3 q^{60} + 23 q^{61} + 72 q^{62} + 13 q^{63} - 2 q^{64} - 20 q^{65} - 23 q^{66} + 11 q^{67} + 24 q^{68} + 38 q^{69} - 40 q^{70} - 25 q^{72} - 13 q^{73} - 2 q^{74} - 11 q^{75} + 24 q^{76} + 23 q^{77} + 28 q^{78} + 41 q^{79} + 9 q^{80} + 7 q^{81} - 2 q^{82} - 4 q^{83} - 23 q^{84} - 20 q^{86} - 32 q^{87} + 10 q^{88} - 14 q^{89} + 44 q^{90} - 6 q^{91} + 34 q^{92} + 15 q^{93} - 10 q^{94} + 31 q^{95} + 33 q^{96} - 54 q^{97} - 85 q^{98} - 18 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9 + q^10 + 6 * q^11 + 7 * q^12 + 4 * q^13 - 24 * q^14 - 40 * q^15 + 12 * q^16 + 3 * q^17 + 8 * q^18 - 7 * q^19 + 14 * q^20 - 15 * q^21 - 26 * q^22 - 16 * q^24 + 5 * q^25 + q^26 + 26 * q^27 - 5 * q^28 - 20 * q^29 - 14 * q^30 + 6 * q^31 + 3 * q^32 + 17 * q^33 + 2 * q^34 - 9 * q^35 - 30 * q^36 + 18 * q^37 + 7 * q^38 + 20 * q^39 + 16 * q^40 - 10 * q^41 - 35 * q^42 - 28 * q^43 - 2 * q^44 + 7 * q^45 + 3 * q^46 - 3 * q^47 + 18 * q^48 - 8 * q^49 - 8 * q^50 - 7 * q^52 + 9 * q^53 + 25 * q^54 + 34 * q^55 - 15 * q^56 + 62 * q^57 + 5 * q^58 + 19 * q^59 + 3 * q^60 + 23 * q^61 + 72 * q^62 + 13 * q^63 - 2 * q^64 - 20 * q^65 - 23 * q^66 + 11 * q^67 + 24 * q^68 + 38 * q^69 - 40 * q^70 - 25 * q^72 - 13 * q^73 - 2 * q^74 - 11 * q^75 + 24 * q^76 + 23 * q^77 + 28 * q^78 + 41 * q^79 + 9 * q^80 + 7 * q^81 - 2 * q^82 - 4 * q^83 - 23 * q^84 - 20 * q^86 - 32 * q^87 + 10 * q^88 - 14 * q^89 + 44 * q^90 - 6 * q^91 + 34 * q^92 + 15 * q^93 - 10 * q^94 + 31 * q^95 + 33 * q^96 - 54 * q^97 - 85 * q^98 - 18 * q^99

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