LMFDB - Embedded newform 117.2.h.a.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(16,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("117.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.h (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	117.16
Dual form			117.2.h.a.22.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.13584 q^{2} +(1.69295 + 0.365956i) q^{3} -0.709859 q^{4} +(-0.0587384 - 0.101738i) q^{5} +(1.92293 + 0.415669i) q^{6} +(-0.424723 - 0.735641i) q^{7} -3.07798 q^{8} +(2.73215 + 1.23909i) q^{9} +O(q^{10})$	\(q+1.13584 q^{2} +(1.69295 + 0.365956i) q^{3} -0.709859 q^{4} +(-0.0587384 - 0.101738i) q^{5} +(1.92293 + 0.415669i) q^{6} +(-0.424723 - 0.735641i) q^{7} -3.07798 q^{8} +(2.73215 + 1.23909i) q^{9} +(-0.0667177 - 0.115558i) q^{10} -0.463942 q^{11} +(-1.20175 - 0.259777i) q^{12} +(-3.59350 - 0.294508i) q^{13} +(-0.482419 - 0.835574i) q^{14} +(-0.0622095 - 0.193733i) q^{15} -2.07638 q^{16} +(-1.26296 + 2.18751i) q^{17} +(3.10330 + 1.40741i) q^{18} +(3.09113 - 5.35399i) q^{19} +(0.0416960 + 0.0722196i) q^{20} +(-0.449821 - 1.40083i) q^{21} -0.526966 q^{22} +(-3.32887 + 5.76577i) q^{23} +(-5.21086 - 1.12640i) q^{24} +(2.49310 - 4.31818i) q^{25} +(-4.08166 - 0.334515i) q^{26} +(4.17194 + 3.09756i) q^{27} +(0.301493 + 0.522201i) q^{28} +1.90453 q^{29} +(-0.0706603 - 0.220050i) q^{30} +(0.657577 + 1.13896i) q^{31} +3.79751 q^{32} +(-0.785431 - 0.169783i) q^{33} +(-1.43452 + 2.48467i) q^{34} +(-0.0498951 + 0.0864208i) q^{35} +(-1.93944 - 0.879579i) q^{36} +(-2.01347 - 3.48743i) q^{37} +(3.51104 - 6.08129i) q^{38} +(-5.97584 - 1.81365i) q^{39} +(0.180795 + 0.313147i) q^{40} +(-4.84331 + 8.38887i) q^{41} +(-0.510927 - 1.59113i) q^{42} +(2.10477 + 3.64556i) q^{43} +0.329333 q^{44} +(-0.0344198 - 0.350746i) q^{45} +(-3.78107 + 6.54901i) q^{46} +(1.34586 - 2.33109i) q^{47} +(-3.51521 - 0.759865i) q^{48} +(3.13922 - 5.43729i) q^{49} +(2.83177 - 4.90477i) q^{50} +(-2.93865 + 3.24115i) q^{51} +(2.55088 + 0.209059i) q^{52} -0.389682 q^{53} +(4.73867 + 3.51835i) q^{54} +(0.0272512 + 0.0472005i) q^{55} +(1.30729 + 2.26429i) q^{56} +(7.19244 - 7.93281i) q^{57} +2.16325 q^{58} +11.0732 q^{59} +(0.0441600 + 0.137523i) q^{60} +(3.88380 + 6.72693i) q^{61} +(0.746905 + 1.29368i) q^{62} +(-0.248881 - 2.53615i) q^{63} +8.46614 q^{64} +(0.181114 + 0.382895i) q^{65} +(-0.892126 - 0.192846i) q^{66} +(0.511351 - 0.885686i) q^{67} +(0.896521 - 1.55282i) q^{68} +(-7.74562 + 8.54293i) q^{69} +(-0.0566730 + 0.0981605i) q^{70} +(3.61012 - 6.25291i) q^{71} +(-8.40950 - 3.81389i) q^{72} -3.31321 q^{73} +(-2.28699 - 3.96117i) q^{74} +(5.80095 - 6.39808i) q^{75} +(-2.19426 + 3.80057i) q^{76} +(0.197047 + 0.341295i) q^{77} +(-6.78762 - 2.06002i) q^{78} +(-4.41302 + 7.64357i) q^{79} +(0.121963 + 0.211247i) q^{80} +(5.92931 + 6.77077i) q^{81} +(-5.50125 + 9.52844i) q^{82} +(1.75800 - 3.04495i) q^{83} +(0.319310 + 0.994393i) q^{84} +0.296736 q^{85} +(2.39069 + 4.14079i) q^{86} +(3.22427 + 0.696975i) q^{87} +1.42800 q^{88} +(-6.62760 - 11.4793i) q^{89} +(-0.0390955 - 0.398392i) q^{90} +(1.30959 + 2.76861i) q^{91} +(2.36303 - 4.09288i) q^{92} +(0.696436 + 2.16884i) q^{93} +(1.52868 - 2.64776i) q^{94} -0.726272 q^{95} +(6.42898 + 1.38972i) q^{96} +(-7.87273 - 13.6360i) q^{97} +(3.56567 - 6.17591i) q^{98} +(-1.26756 - 0.574866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22} + 17 q^{23} - 12 q^{24} - 6 q^{25} - 12 q^{26} + 2 q^{27} - 24 q^{29} - 8 q^{30} - 6 q^{31} - 38 q^{32} + 11 q^{33} + 18 q^{35} - 28 q^{36} - 3 q^{37} + 8 q^{38} + 3 q^{39} - 12 q^{40} + 5 q^{41} + 15 q^{42} - 3 q^{43} + 44 q^{44} + 19 q^{45} - 6 q^{46} + 21 q^{47} + 23 q^{48} + 3 q^{49} - 20 q^{50} + 7 q^{51} - 24 q^{52} - 20 q^{53} + 39 q^{54} + 3 q^{55} + 40 q^{56} + 9 q^{57} + 18 q^{58} + 38 q^{59} + 51 q^{60} - 6 q^{61} + 19 q^{62} + 13 q^{63} - 42 q^{64} - 2 q^{65} - 18 q^{66} - 6 q^{67} - 31 q^{69} + 27 q^{70} + 14 q^{71} - 18 q^{72} + 6 q^{73} + 29 q^{74} + 74 q^{75} - 15 q^{76} + 4 q^{77} + 80 q^{78} + 3 q^{79} - 16 q^{80} - 27 q^{81} - 9 q^{82} - 33 q^{83} + 5 q^{84} + 72 q^{86} - 32 q^{87} - 78 q^{88} - q^{89} + 21 q^{90} - 6 q^{91} - 10 q^{92} - 84 q^{93} - 9 q^{94} - 100 q^{95} - 79 q^{96} + 24 q^{97} - 61 q^{98} + 18 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.13584			0.803163			0.401581	−	0.915823i	$-0.368461\pi$
$2$	1.13584			0.803163			0.401581	+	0.915823i	$0.368461\pi$
$3$	1.69295	+	0.365956i	0.977425	+	0.211285i
$3$	1.69295	+	0.365956i	0.977425	+	0.211285i
$4$	−0.709859			−0.354929
$5$	−0.0587384	−	0.101738i	−0.0262686	−	0.0454986i	0.852592	−	0.522577i	$-0.175029\pi$
$5$	−0.0587384	−	0.101738i	−0.0262686	−	0.0454986i	−0.878861	+	0.477078i	$0.841696\pi$
$6$	1.92293	+	0.415669i	0.785031	+	0.169696i
$7$	−0.424723	−	0.735641i	−0.160530	−	0.278046i	0.774529	−	0.632539i	$-0.217987\pi$
$7$	−0.424723	−	0.735641i	−0.160530	−	0.278046i	−0.935059	+	0.354492i	$0.884654\pi$
$8$	−3.07798			−1.08823
$9$	2.73215	+	1.23909i	0.910717	+	0.413030i
$10$	−0.0667177	−	0.115558i	−0.0210980	−	0.0365428i
$11$	−0.463942			−0.139884			−0.0699419	−	0.997551i	$-0.522281\pi$
$11$	−0.463942			−0.139884			−0.0699419	+	0.997551i	$0.522281\pi$
$12$	−1.20175	−	0.259777i	−0.346917	−	0.0749912i
$13$	−3.59350	−	0.294508i	−0.996658	−	0.0816817i
$13$	−3.59350	−	0.294508i	−0.996658	−	0.0816817i
$14$	−0.482419	−	0.835574i	−0.128932	−	0.223316i
$15$	−0.0622095	−	0.193733i	−0.0160624	−	0.0500216i
$16$	−2.07638			−0.519096
$17$	−1.26296	+	2.18751i	−0.306312	+	0.530548i	−0.977553	−	0.210692i	$-0.932428\pi$
$17$	−1.26296	+	2.18751i	−0.306312	+	0.530548i	0.671240	+	0.741240i	$0.265762\pi$
$18$	3.10330	+	1.40741i	0.731454	+	0.331730i
$19$	3.09113	−	5.35399i	0.709153	−	1.22829i	−0.256019	−	0.966672i	$-0.582411\pi$
$19$	3.09113	−	5.35399i	0.709153	−	1.22829i	0.965172	−	0.261617i	$-0.0842558\pi$
$20$	0.0416960	+	0.0722196i	0.00932350	+	0.0161488i
$21$	−0.449821	−	1.40083i	−0.0981590	−	0.305687i
$22$	−0.526966			−0.112350
$23$	−3.32887	+	5.76577i	−0.694117	+	1.20225i	0.276361	+	0.961054i	$0.410872\pi$
$23$	−3.32887	+	5.76577i	−0.694117	+	1.20225i	−0.970478	+	0.241192i	$0.922462\pi$
$24$	−5.21086	−	1.12640i	−1.06366	−	0.229926i
$25$	2.49310	−	4.31818i	0.498620	−	0.863635i
$26$	−4.08166	−	0.334515i	−0.800479	−	0.0656037i
$27$	4.17194	+	3.09756i	0.802890	+	0.596127i
$28$	0.301493	+	0.522201i	0.0569768	+	0.0986868i
$29$	1.90453			0.353662			0.176831	−	0.984241i	$-0.443415\pi$
$29$	1.90453			0.353662			0.176831	+	0.984241i	$0.443415\pi$
$30$	−0.0706603	−	0.220050i	−0.0129007	−	0.0401755i
$31$	0.657577	+	1.13896i	0.118104	+	0.204563i	0.919016	−	0.394219i	$-0.128985\pi$
$31$	0.657577	+	1.13896i	0.118104	+	0.204563i	−0.800912	+	0.598782i	$0.795652\pi$
$32$	3.79751			0.671310
$33$	−0.785431	−	0.169783i	−0.136726	−	0.0295553i
$34$	−1.43452	+	2.48467i	−0.246019	+	0.426117i
$35$	−0.0498951	+	0.0864208i	−0.00843381	+	0.0146078i
$36$	−1.93944	−	0.879579i	−0.323240	−	0.146597i
$37$	−2.01347	−	3.48743i	−0.331012	−	0.573330i	0.651698	−	0.758478i	$-0.274057\pi$
$37$	−2.01347	−	3.48743i	−0.331012	−	0.573330i	−0.982711	+	0.185148i	$0.940723\pi$
$38$	3.51104	−	6.08129i	0.569565	−	0.986516i
$39$	−5.97584	−	1.81365i	−0.956900	−	0.290417i
$40$	0.180795	+	0.313147i	0.0285863	+	0.0495129i
$41$	−4.84331	+	8.38887i	−0.756399	+	1.31012i	0.188277	+	0.982116i	$0.439710\pi$
$41$	−4.84331	+	8.38887i	−0.756399	+	1.31012i	−0.944676	+	0.328005i	$0.893624\pi$
$42$	−0.510927	−	1.59113i	−0.0788377	−	0.245516i
$43$	2.10477	+	3.64556i	0.320974	+	0.555943i	0.980689	−	0.195573i	$-0.0626565\pi$
$43$	2.10477	+	3.64556i	0.320974	+	0.555943i	−0.659715	+	0.751516i	$0.729323\pi$
$44$	0.329333			0.0496489
$45$	−0.0344198	−	0.350746i	−0.00513100	−	0.0522861i
$46$	−3.78107	+	6.54901i	−0.557489	+	0.965599i
$47$	1.34586	−	2.33109i	0.196313	−	0.340025i	−0.751017	−	0.660283i	$-0.770436\pi$
$47$	1.34586	−	2.33109i	0.196313	−	0.340025i	0.947330	+	0.320258i	$0.103770\pi$
$48$	−3.51521	−	0.759865i	−0.507377	−	0.109677i
$49$	3.13922	−	5.43729i	0.448460	−	0.776756i
$50$	2.83177	−	4.90477i	0.400473	−	0.693640i
$51$	−2.93865	+	3.24115i	−0.411494	+	0.453852i
$52$	2.55088	+	0.209059i	0.353743	+	0.0289912i
$53$	−0.389682			−0.0535269			−0.0267634	−	0.999642i	$-0.508520\pi$
$53$	−0.389682			−0.0535269			−0.0267634	+	0.999642i	$0.508520\pi$
$54$	4.73867	+	3.51835i	0.644852	+	0.478787i
$55$	0.0272512	+	0.0472005i	0.00367456	+	0.00636452i
$56$	1.30729	+	2.26429i	0.174693	+	0.302578i
$57$	7.19244	−	7.93281i	0.952662	−	1.05073i
$58$	2.16325			0.284049
$59$	11.0732			1.44161			0.720805	−	0.693137i	$-0.243772\pi$
$59$	11.0732			1.44161			0.720805	+	0.693137i	$0.243772\pi$
$60$	0.0441600	+	0.137523i	0.00570103	+	0.0177541i
$61$	3.88380	+	6.72693i	0.497269	+	0.861295i	0.999995	−	0.00315044i	$-0.00100282\pi$
$61$	3.88380	+	6.72693i	0.497269	+	0.861295i	−0.502726	+	0.864446i	$0.667669\pi$
$62$	0.746905	+	1.29368i	0.0948570	+	0.164297i
$63$	−0.248881	−	2.53615i	−0.0313560	−	0.319525i
$64$	8.46614			1.05827
$65$	0.181114	+	0.382895i	0.0224644	+	0.0474922i
$66$	−0.892126	−	0.192846i	−0.109813	−	0.0237378i
$67$	0.511351	−	0.885686i	0.0624715	−	0.108204i	−0.833098	−	0.553125i	$-0.813435\pi$
$67$	0.511351	−	0.885686i	0.0624715	−	0.108204i	0.895570	+	0.444922i	$0.146768\pi$
$68$	0.896521	−	1.55282i	0.108719	−	0.188307i
$69$	−7.74562	+	8.54293i	−0.932463	+	1.02845i
$70$	−0.0566730	+	0.0981605i	−0.00677372	+	0.0117324i
$71$	3.61012	−	6.25291i	0.428442	−	0.742083i	−0.568293	−	0.822826i	$-0.692396\pi$
$71$	3.61012	−	6.25291i	0.428442	−	0.742083i	0.996735	+	0.0807430i	$0.0257293\pi$
$72$	−8.40950	−	3.81389i	−0.991069	−	0.449471i
$73$	−3.31321			−0.387782			−0.193891	−	0.981023i	$-0.562111\pi$
$73$	−3.31321			−0.387782			−0.193891	+	0.981023i	$0.562111\pi$
$74$	−2.28699	−	3.96117i	−0.265857	−	0.460477i
$75$	5.80095	−	6.39808i	0.669836	−	0.738787i
$76$	−2.19426	+	3.80057i	−0.251699	+	0.435956i
$77$	0.197047	+	0.341295i	0.0224556	+	0.0388942i
$78$	−6.78762	−	2.06002i	−0.768547	−	0.233252i
$79$	−4.41302	+	7.64357i	−0.496503	+	0.859969i	−0.999992	−	0.00403289i	$-0.998716\pi$
$79$	−4.41302	+	7.64357i	−0.496503	+	0.859969i	0.503489	+	0.864002i	$0.332050\pi$
$80$	0.121963	+	0.211247i	0.0136359	+	0.0236181i
$81$	5.92931	+	6.77077i	0.658812	+	0.752307i
$82$	−5.50125	+	9.52844i	−0.607511	+	1.05224i
$83$	1.75800	−	3.04495i	0.192966	−	0.334227i	−0.753266	−	0.657716i	$-0.771523\pi$
$83$	1.75800	−	3.04495i	0.192966	−	0.334227i	0.946232	+	0.323489i	$0.104856\pi$
$84$	0.319310	+	0.994393i	0.0348395	+	0.108497i
$85$	0.296736			0.0321856
$86$	2.39069	+	4.14079i	0.257794	+	0.446513i
$87$	3.22427	+	0.696975i	0.345678	+	0.0747236i
$88$	1.42800			0.152226
$89$	−6.62760	−	11.4793i	−0.702525	−	1.21681i	−0.967577	−	0.252574i	$-0.918723\pi$
$89$	−6.62760	−	11.4793i	−0.702525	−	1.21681i	0.265053	−	0.964234i	$-0.414611\pi$
$90$	−0.0390955	−	0.398392i	−0.00412103	−	0.0419942i
$91$	1.30959	+	2.76861i	0.137282	+	0.290230i
$92$	2.36303	−	4.09288i	0.246362	−	0.426712i
$93$	0.696436	+	2.16884i	0.0722170	+	0.224898i
$94$	1.52868	−	2.64776i	0.157672	−	0.273095i
$95$	−0.726272			−0.0745139
$96$	6.42898	+	1.38972i	0.656155	+	0.141838i
$97$	−7.87273	−	13.6360i	−0.799354	−	1.38452i	−0.920037	−	0.391831i	$-0.871842\pi$
$97$	−7.87273	−	13.6360i	−0.799354	−	1.38452i	0.120683	−	0.992691i	$-0.461492\pi$
$98$	3.56567	−	6.17591i	0.360187	−	0.623861i
$99$	−1.26756	−	0.574866i	−0.127395	−	0.0577762i
$100$	−1.76975	+	3.06529i	−0.176975	+	0.306529i
$101$	−15.6382			−1.55606			−0.778028	−	0.628229i	$-0.783780\pi$
$101$	−15.6382			−1.55606			−0.778028	+	0.628229i	$0.783780\pi$
$102$	−3.33785	+	3.68144i	−0.330497	+	0.364517i
$103$	7.23270	+	12.5274i	0.712659	+	1.23436i	0.963855	+	0.266426i	$0.0858428\pi$
$103$	7.23270	+	12.5274i	0.712659	+	1.23436i	−0.251196	+	0.967936i	$0.580824\pi$
$104$	11.0607	+	0.906488i	1.08459	+	0.0888884i
$105$	−0.116096	+	0.128047i	−0.0113298	+	0.0124961i
$106$	−0.442617			−0.0429908
$107$	3.13817	+	5.43546i	0.303378	+	0.525466i	0.976899	−	0.213702i	$-0.0685522\pi$
$107$	3.13817	+	5.43546i	0.303378	+	0.525466i	−0.673521	+	0.739168i	$0.735219\pi$
$108$	−2.96149	−	2.19883i	−0.284969	−	0.211583i
$109$	−17.5426			−1.68028			−0.840138	−	0.542373i	$-0.817526\pi$
$109$	−17.5426			−1.68028			−0.840138	+	0.542373i	$0.817526\pi$
$110$	0.0309532	+	0.0536124i	0.00295127	+	0.00511174i
$111$	−2.13245	−	6.64088i	−0.202403	−	0.630324i
$112$	0.881887	+	1.52747i	0.0833305	+	0.144333i
$113$	−13.1498			−1.23703			−0.618516	−	0.785772i	$-0.712266\pi$
$113$	−13.1498			−1.23703			−0.618516	+	0.785772i	$0.712266\pi$
$114$	8.16949	−	9.01043i	0.765143	−	0.843904i
$115$	0.782130			0.0729340
$116$	−1.35195			−0.125525
$117$	−9.45308	−	5.25731i	−0.873937	−	0.486039i
$118$	12.5775			1.15785
$119$	2.14563			0.196689
$120$	0.191479	+	0.596305i	0.0174796	+	0.0544350i
$121$	−10.7848			−0.980433
$122$	4.41139	+	7.64075i	0.399388	+	0.691761i
$123$	−11.2694	+	12.4295i	−1.01613	+	1.12073i
$124$	−0.466787	−	0.808498i	−0.0419187	−	0.0726053i
$125$	−1.17315			−0.104929
$126$	−0.282690	−	2.88067i	−0.0251840	−	0.256631i
$127$	−4.75121	−	8.22934i	−0.421602	−	0.730236i	0.574494	−	0.818509i	$-0.305199\pi$
$127$	−4.75121	−	8.22934i	−0.421602	−	0.730236i	−0.996096	+	0.0882724i	$0.971865\pi$
$128$	2.02120			0.178651
$129$	2.22915	+	6.94200i	0.196265	+	0.611209i
$130$	0.205717	+	0.434908i	0.0180426	+	0.0381440i
$131$	−8.21488	−	14.2286i	−0.717738	−	1.24316i	−0.961894	−	0.273422i	$-0.911844\pi$
$131$	−8.21488	−	14.2286i	−0.717738	−	1.24316i	0.244157	−	0.969736i	$-0.421489\pi$
$132$	0.557545	+	0.120522i	0.0485280	+	0.0104901i
$133$	−5.25149			−0.455362
$134$	0.580815	−	1.00600i	0.0501748	−	0.0869052i
$135$	0.0700866	−	0.606391i	0.00603209	−	0.0521898i
$136$	3.88735	−	6.73309i	0.333338	−	0.577358i
$137$	9.71549	+	16.8277i	0.830050	+	1.43769i	0.897998	+	0.440000i	$0.145022\pi$
$137$	9.71549	+	16.8277i	0.830050	+	1.43769i	−0.0679473	+	0.997689i	$0.521645\pi$
$138$	−8.79782	+	9.70343i	−0.748920	+	0.826011i
$139$	15.0728			1.27846			0.639229	−	0.769016i	$-0.279253\pi$
$139$	15.0728			1.27846			0.639229	+	0.769016i	$0.279253\pi$
$140$	0.0354185	−	0.0613466i	0.00299341	−	0.00518473i
$141$	3.13154	−	3.45389i	0.263723	−	0.290870i
$142$	4.10053	−	7.10232i	0.344109	−	0.596014i
$143$	1.66718	+	0.136635i	0.139416	+	0.0114260i
$144$	−5.67299	−	2.57283i	−0.472750	−	0.214402i
$145$	−0.111869	−	0.193763i	−0.00929023	−	0.0160911i
$146$	−3.76329			−0.311452
$147$	7.30435	−	8.05624i	0.602453	−	0.664467i
$148$	1.42928	+	2.47558i	0.117486	+	0.203492i
$149$	−14.1014			−1.15523			−0.577616	−	0.816308i	$-0.696017\pi$
$149$	−14.1014			−1.15523			−0.577616	+	0.816308i	$0.696017\pi$
$150$	6.58898	−	7.26723i	0.537988	−	0.593366i
$151$	3.33115	−	5.76972i	0.271085	−	0.469534i	−0.698055	−	0.716044i	$-0.745951\pi$
$151$	3.33115	−	5.76972i	0.271085	−	0.469534i	0.969140	+	0.246511i	$0.0792841\pi$
$152$	−9.51441	+	16.4794i	−0.771721	+	1.33666i
$153$	−6.16111	+	4.41168i	−0.498096	+	0.356663i
$154$	0.223814	+	0.387658i	0.0180355	+	0.0312384i
$155$	0.0772501	−	0.133801i	0.00620487	−	0.0107472i
$156$	4.24200	+	1.28744i	0.339632	+	0.103077i
$157$	−5.87578	−	10.1771i	−0.468938	−	0.812224i	0.530432	−	0.847728i	$-0.322030\pi$
$157$	−5.87578	−	10.1771i	−0.468938	−	0.812224i	−0.999370	+	0.0355033i	$0.988697\pi$
$158$	−5.01250	+	8.68190i	−0.398773	+	0.690695i
$159$	−0.659711	−	0.142606i	−0.0523185	−	0.0113094i
$160$	−0.223059	−	0.386350i	−0.0176344	−	0.0305437i
$161$	5.65538			0.445706
$162$	6.73477	+	7.69053i	0.529134	+	0.604225i
$163$	−7.13612	+	12.3601i	−0.558944	+	0.968119i	0.438641	+	0.898662i	$0.355460\pi$
$163$	−7.13612	+	12.3601i	−0.558944	+	0.968119i	−0.997585	+	0.0694568i	$0.977873\pi$
$164$	3.43807	−	5.95491i	0.268468	−	0.465000i
$165$	0.0288616	+	0.0898808i	0.00224687	+	0.00699721i
$166$	1.99682	−	3.45859i	0.154983	−	0.268438i
$167$	5.58538	−	9.67416i	0.432210	−	0.748609i	−0.564854	−	0.825191i	$-0.691067\pi$
$167$	5.58538	−	9.67416i	0.432210	−	0.748609i	0.997063	+	0.0765820i	$0.0244007\pi$
$168$	1.38454	+	4.31173i	0.106820	+	0.332657i
$169$	12.8265	+	2.11663i	0.986656	+	0.162818i
$170$	0.337046			0.0258503
$171$	15.0795	−	10.7977i	1.15316	−	0.825723i
$172$	−1.49409	−	2.58783i	−0.113923	−	0.197320i
$173$	6.19153	+	10.7241i	0.470734	+	0.815335i	0.999440	−	0.0334704i	$-0.0106559\pi$
$173$	6.19153	+	10.7241i	0.470734	+	0.815335i	−0.528706	+	0.848805i	$0.677323\pi$
$174$	3.66227	+	0.791655i	0.277636	+	0.0600152i
$175$	−4.23550			−0.320174
$176$	0.963322			0.0726131
$177$	18.7464	+	4.05232i	1.40907	+	0.304591i
$178$	−7.52792	−	13.0387i	−0.564242	−	0.977295i
$179$	12.0175	+	20.8149i	0.898230	+	1.55578i	0.829755	+	0.558128i	$0.188480\pi$
$179$	12.0175	+	20.8149i	0.898230	+	1.55578i	0.0684753	+	0.997653i	$0.478187\pi$
$180$	0.0244332	+	0.248980i	0.00182114	+	0.0185579i
$181$	21.6433			1.60873			0.804366	−	0.594135i	$-0.202505\pi$
$181$	21.6433			1.60873			0.804366	+	0.594135i	$0.202505\pi$
$182$	1.48749	+	3.14471i	0.110260	+	0.233102i
$183$	4.11331	+	12.8097i	0.304064	+	0.946917i
$184$	10.2462	−	17.7469i	0.755358	−	1.30832i
$185$	−0.236536	+	0.409692i	−0.0173905	+	0.0301212i
$186$	0.791042	+	2.46346i	0.0580020	+	0.180630i
$187$	0.585939	−	1.01488i	0.0428481	−	0.0742151i
$188$	−0.955368	+	1.65475i	−0.0696773	+	0.120685i
$189$	0.506778	−	4.38466i	0.0368627	−	0.318937i
$190$	−0.824931			−0.0598468
$191$	−2.74747	−	4.75876i	−0.198800	−	0.344331i	0.749340	−	0.662186i	$-0.230371\pi$
$191$	−2.74747	−	4.75876i	−0.198800	−	0.344331i	−0.948140	+	0.317854i	$0.897038\pi$
$192$	14.3327	+	3.09824i	1.03438	+	0.223596i
$193$	−0.0643594	+	0.111474i	−0.00463269	+	0.00802405i	−0.868332	−	0.495983i	$-0.834808\pi$
$193$	−0.0643594	+	0.111474i	−0.00463269	+	0.00802405i	0.863700	+	0.504007i	$0.168141\pi$
$194$	−8.94219	−	15.4883i	−0.642012	−	1.11200i
$195$	0.166494	+	0.714501i	0.0119229	+	0.0511665i
$196$	−2.22840	+	3.85971i	−0.159172	+	0.275693i
$197$	−1.80122	−	3.11981i	−0.128332	−	0.222277i	0.794699	−	0.607004i	$-0.207629\pi$
$197$	−1.80122	−	3.11981i	−0.128332	−	0.222277i	−0.923030	+	0.384727i	$0.874296\pi$
$198$	−1.43975	−	0.652958i	−0.102319	−	0.0464037i
$199$	10.2188	−	17.6995i	0.724394	−	1.25469i	−0.234829	−	0.972037i	$-0.575453\pi$
$199$	10.2188	−	17.6995i	0.724394	−	1.25469i	0.959223	−	0.282650i	$-0.0912135\pi$
$200$	−7.67370	+	13.2912i	−0.542613	+	0.939833i
$201$	1.18981	−	1.31229i	0.0839230	−	0.0925617i
$202$	−17.7625			−1.24977
$203$	−0.808897	−	1.40105i	−0.0567735	−	0.0983345i
$204$	2.08603	−	2.30076i	0.146051	−	0.161085i
$205$	1.13795			0.0794782
$206$	8.21522	+	14.2292i	0.572382	+	0.991394i
$207$	−16.2393	+	11.6282i	−1.12871	+	0.808215i
$208$	7.46149	+	0.611511i	0.517361	+	0.0424006i
$209$	−1.43410	+	2.48394i	−0.0991990	+	0.171818i
$210$	−0.131867	+	0.145441i	−0.00909969	+	0.0100364i
$211$	−3.55102	+	6.15055i	−0.244462	+	0.423421i	−0.961980	−	0.273119i	$-0.911945\pi$
$211$	−3.55102	+	6.15055i	−0.244462	+	0.423421i	0.717518	+	0.696540i	$0.245278\pi$
$212$	0.276619			0.0189983
$213$	8.40003	−	9.26470i	0.575561	−	0.634807i
$214$	3.56447	+	6.17384i	0.243662	+	0.422035i
$215$	0.247261	−	0.428269i	0.0168631	−	0.0292077i
$216$	−12.8411	−	9.53423i	−0.873729	−	0.648722i
$217$	0.558576	−	0.967481i	0.0379186	−	0.0656769i
$218$	−19.9256			−1.34954
$219$	−5.60909	−	1.21249i	−0.379027	−	0.0819324i
$220$	−0.0193445	−	0.0335057i	−0.00130421	−	0.00225895i
$221$	5.18268	−	7.48886i	0.348625	−	0.503755i
$222$	−2.42213	−	7.54300i	−0.162563	−	0.506253i
$223$	−14.0263			−0.939273			−0.469636	−	0.882860i	$-0.655615\pi$
$223$	−14.0263			−0.939273			−0.469636	+	0.882860i	$0.655615\pi$
$224$	−1.61289	−	2.79360i	−0.107766	−	0.186655i
$225$	12.1621	−	8.70874i	0.810809	−	0.580582i
$226$	−14.9362			−0.993539
$227$	6.96867	+	12.0701i	0.462527	+	0.801120i	0.999086	−	0.0427425i	$-0.0136095\pi$
$227$	6.96867	+	12.0701i	0.462527	+	0.801120i	−0.536559	+	0.843863i	$0.680276\pi$
$228$	−5.10562	+	5.63117i	−0.338128	+	0.372934i
$229$	−1.62150	−	2.80852i	−0.107152	−	0.185593i	0.807463	−	0.589918i	$-0.200840\pi$
$229$	−1.62150	−	2.80852i	−0.107152	−	0.185593i	−0.914615	+	0.404325i	$0.867506\pi$
$230$	0.888377			0.0585779
$231$	0.208691	+	0.649906i	0.0137309	+	0.0427606i
$232$	−5.86210			−0.384866
$233$	−9.70153			−0.635568			−0.317784	−	0.948163i	$-0.602939\pi$
$233$	−9.70153			−0.635568			−0.317784	+	0.948163i	$0.602939\pi$
$234$	−10.7372	−	5.97149i	−0.701914	−	0.390368i
$235$	−0.316214			−0.0206275
$236$	−7.86042			−0.511670
$237$	−10.2682	+	11.3252i	−0.666993	+	0.735651i
$238$	2.43710			0.157973
$239$	−4.81288	−	8.33616i	−0.311319	−	0.539221i	0.667329	−	0.744763i	$-0.267438\pi$
$239$	−4.81288	−	8.33616i	−0.311319	−	0.539221i	−0.978648	+	0.205542i	$0.934104\pi$
$240$	0.129171	+	0.402264i	0.00833794	+	0.0259660i
$241$	0.143150	+	0.247943i	0.00922111	+	0.0159714i	0.870599	−	0.491993i	$-0.163731\pi$
$241$	0.143150	+	0.247943i	0.00922111	+	0.0159714i	−0.861378	+	0.507964i	$0.830398\pi$
$242$	−12.2498			−0.787447
$243$	7.56021	+	13.6324i	0.484988	+	0.874521i
$244$	−2.75695	−	4.77517i	−0.176495	−	0.305699i
$245$	−0.737572			−0.0471217
$246$	−12.8003	+	14.1180i	−0.816119	+	0.900128i
$247$	−12.6848	+	18.3292i	−0.807112	+	1.16626i
$248$	−2.02401	−	3.50568i	−0.128525	−	0.222611i
$249$	4.09053	−	4.51159i	0.259226	−	0.285910i
$250$	−1.33251			−0.0842755
$251$	12.2860	−	21.2800i	0.775488	−	1.34318i	−0.159032	−	0.987273i	$-0.550837\pi$
$251$	12.2860	−	21.2800i	0.775488	−	1.34318i	0.934520	−	0.355911i	$-0.115829\pi$
$252$	0.176670	+	1.80031i	0.0111292	+	0.113409i
$253$	1.54440	−	2.67498i	0.0970957	−	0.168175i
$254$	−5.39664	−	9.34725i	−0.338615	−	0.586499i
$255$	0.502360	+	0.108593i	0.0314590	+	0.00680033i
$256$	−14.6365			−0.914782
$257$	−0.647550	+	1.12159i	−0.0403930	+	0.0699628i	−0.885515	−	0.464611i	$-0.846194\pi$
$257$	−0.647550	+	1.12159i	−0.0403930	+	0.0699628i	0.845122	+	0.534573i	$0.179528\pi$
$258$	2.53196	+	7.88503i	0.157633	+	0.490901i
$259$	−1.71033	+	2.96238i	−0.106275	+	0.184073i
$260$	−0.128565	−	0.271801i	−0.00797329	−	0.0168564i
$261$	5.20347	+	2.35989i	0.322087	+	0.146073i
$262$	−9.33082	−	16.1615i	−0.576460	−	0.998458i
$263$	−11.7285			−0.723208			−0.361604	−	0.932332i	$-0.617771\pi$
$263$	−11.7285			−0.723208			−0.361604	+	0.932332i	$0.617771\pi$
$264$	2.41754	+	0.522587i	0.148789	+	0.0321630i
$265$	0.0228893	+	0.0396454i	0.00140608	+	0.00243540i
$266$	−5.96487			−0.365729
$267$	−7.01926	−	21.8594i	−0.429572	−	1.33777i
$268$	−0.362987	+	0.628712i	−0.0221730	+	0.0384047i
$269$	13.4278	−	23.2576i	0.818705	−	1.41804i	−0.0879319	−	0.996126i	$-0.528026\pi$
$269$	13.4278	−	23.2576i	0.818705	−	1.41804i	0.906637	−	0.421912i	$-0.138641\pi$
$270$	0.0796074	−	0.688765i	0.00484475	−	0.0419169i
$271$	14.1476	+	24.5044i	0.859408	+	1.48854i	0.872494	+	0.488625i	$0.162501\pi$
$271$	14.1476	+	24.5044i	0.859408	+	1.48854i	−0.0130858	+	0.999914i	$0.504165\pi$
$272$	2.62238	−	4.54210i	0.159005	−	0.275405i
$273$	1.20388	+	5.16637i	0.0728620	+	0.312683i
$274$	11.0353	+	19.1137i	0.666666	+	1.15470i
$275$	−1.15665	+	2.00338i	−0.0697489	+	0.120809i
$276$	5.49830	−	6.06427i	0.330959	−	0.365026i
$277$	8.30879	+	14.3912i	0.499227	+	0.864686i	1.00000		0.000892577i	$-0.000284116\pi$
$277$	8.30879	+	14.3912i	0.499227	+	0.864686i	−0.500773	+	0.865579i	$0.666951\pi$
$278$	17.1204			1.02681
$279$	0.385330	+	3.92660i	0.0230691	+	0.235079i
$280$	0.153576	−	0.266001i	0.00917791	−	0.0158966i
$281$	−0.612801	+	1.06140i	−0.0365567	+	0.0633180i	−0.883725	−	0.468007i	$-0.844972\pi$
$281$	−0.612801	+	1.06140i	−0.0365567	+	0.0633180i	0.847168	+	0.531325i	$0.178306\pi$
$282$	3.55694	−	3.92308i	0.211813	−	0.233616i
$283$	−1.52039	+	2.63339i	−0.0903776	+	0.156539i	−0.907670	−	0.419684i	$-0.862141\pi$
$283$	−1.52039	+	2.63339i	−0.0903776	+	0.156539i	0.817292	+	0.576223i	$0.195474\pi$
$284$	−2.56267	+	4.43868i	−0.152067	+	0.263387i
$285$	−1.22954	−	0.265784i	−0.0728317	−	0.0157437i
$286$	1.89365	+	0.155195i	0.111974	+	0.00917690i
$287$	8.22826			0.485699
$288$	10.3754	+	4.70545i	0.611374	+	0.277271i
$289$	5.30988	+	9.19698i	0.312346	+	0.540999i
$290$	−0.127066	−	0.220085i	−0.00746156	−	0.0129238i
$291$	−8.33796	−	25.9661i	−0.488780	−	1.52216i
$292$	2.35191			0.137635
$293$	27.6041			1.61265			0.806325	−	0.591473i	$-0.201453\pi$
$293$	27.6041			1.61265			0.806325	+	0.591473i	$0.201453\pi$
$294$	8.29660	−	9.15063i	0.483868	−	0.533676i
$295$	−0.650424	−	1.12657i	−0.0378691	−	0.0655913i
$296$	6.19741	+	10.7342i	0.360217	+	0.623914i
$297$	−1.93554	−	1.43709i	−0.112311	−	0.0833885i
$298$	−16.0170			−0.927840
$299$	13.6604	−	19.7389i	0.789999	−	1.14153i
$300$	−4.11786	+	4.54174i	−0.237745	+	0.262217i
$301$	1.78788	−	3.09671i	0.103052	−	0.178491i
$302$	3.78367	−	6.55351i	0.217726	−	0.377112i
$303$	−26.4746	−	5.72289i	−1.52093	−	0.328771i
$304$	−6.41836	+	11.1169i	−0.368118	+	0.637600i
$305$	0.456256	−	0.790259i	0.0261252	−	0.0452501i
$306$	−6.99806	+	5.01098i	−0.400052	+	0.286459i
$307$	7.74191			0.441854			0.220927	−	0.975290i	$-0.429092\pi$
$307$	7.74191			0.441854			0.220927	+	0.975290i	$0.429092\pi$
$308$	−0.139875	−	0.242271i	−0.00797014	−	0.0138047i
$309$	7.66011	+	23.8551i	0.435769	+	1.35707i
$310$	0.0877440	−	0.151977i	0.00498352	−	0.00863172i
$311$	−4.70886	−	8.15598i	−0.267015	−	0.462483i	0.701075	−	0.713088i	$-0.252704\pi$
$311$	−4.70886	−	8.15598i	−0.267015	−	0.462483i	−0.968090	+	0.250605i	$0.919371\pi$
$312$	18.3935	+	5.58238i	1.04133	+	0.316040i
$313$	6.58566	−	11.4067i	0.372243	−	0.644744i	−0.617667	−	0.786440i	$-0.711922\pi$
$313$	6.58566	−	11.4067i	0.372243	−	0.644744i	0.989910	+	0.141695i	$0.0452554\pi$
$314$	−6.67396	−	11.5596i	−0.376634	−	0.652349i
$315$	−0.243404	+	0.174290i	−0.0137143	+	0.00982014i
$316$	3.13262	−	5.42586i	0.176224	−	0.305228i
$317$	−12.5673	+	21.7671i	−0.705848	+	1.22256i	0.260537	+	0.965464i	$0.416100\pi$
$317$	−12.5673	+	21.7671i	−0.705848	+	1.22256i	−0.966385	+	0.257100i	$0.917233\pi$
$318$	−0.749329	−	0.161979i	−0.0420203	−	0.00908331i
$319$	−0.883592			−0.0494717
$320$	−0.497288	−	0.861328i	−0.0277992	−	0.0481497i
$321$	3.32361	+	10.3504i	0.185506	+	0.577702i
$322$	6.42363			0.357975
$323$	7.80792	+	13.5237i	0.434444	+	0.752480i
$324$	−4.20897	−	4.80629i	−0.233832	−	0.267016i
$325$	−10.2307	+	14.7831i	−0.567497	+	0.820021i
$326$	−8.10551	+	14.0392i	−0.448923	+	0.777557i
$327$	−29.6987	−	6.41982i	−1.64234	−	0.355017i
$328$	14.9076	−	25.8207i	0.823135	−	1.42571i
$329$	−2.28646			−0.126057
$330$	0.0327823	+	0.102091i	0.00180461	+	0.00561990i
$331$	14.5554	+	25.2107i	0.800036	+	1.38570i	0.919592	+	0.392876i	$0.128520\pi$
$331$	14.5554	+	25.2107i	0.800036	+	1.38570i	−0.119555	+	0.992828i	$0.538147\pi$
$332$	−1.24793	+	2.16148i	−0.0684892	+	0.118627i
$333$	−1.17986	−	12.0231i	−0.0646560	−	0.658859i
$334$	6.34412	−	10.9883i	0.347135	−	0.601255i
$335$	−0.120144			−0.00656416
$336$	0.934001	+	2.90867i	0.0509540	+	0.158681i
$337$	−7.69878	−	13.3347i	−0.419379	−	0.726386i	0.576498	−	0.817099i	$-0.304419\pi$
$337$	−7.69878	−	13.3347i	−0.419379	−	0.726386i	−0.995877	+	0.0907124i	$0.971086\pi$
$338$	14.5689	+	2.40416i	0.792446	+	0.130769i
$339$	−22.2620	−	4.81227i	−1.20911	−	0.261366i
$340$	−0.210641			−0.0114236
$341$	−0.305078	−	0.528410i	−0.0165209	−	0.0286150i
$342$	17.1280	−	12.2645i	0.926174	−	0.663190i
$343$	−11.2793			−0.609026
$344$	−6.47842	−	11.2210i	−0.349293	−	0.604993i
$345$	1.32411	+	0.286225i	0.0712874	+	0.0154098i
$346$	7.03262	+	12.1808i	0.378076	+	0.654847i
$347$	10.4286			0.559834			0.279917	−	0.960024i	$-0.409693\pi$
$347$	10.4286			0.559834			0.279917	+	0.960024i	$0.409693\pi$
$348$	−2.28878	−	0.494754i	−0.122691	−	0.0265216i
$349$	14.1381			0.756794			0.378397	−	0.925643i	$-0.376475\pi$
$349$	14.1381			0.756794			0.378397	+	0.925643i	$0.376475\pi$
$350$	−4.81087			−0.257152
$351$	−14.0796	−	12.3598i	−0.751515	−	0.659716i
$352$	−1.76182			−0.0939055
$353$	14.7547			0.785314			0.392657	−	0.919685i	$-0.371556\pi$
$353$	14.7547			0.785314			0.392657	+	0.919685i	$0.371556\pi$
$354$	21.2930	+	4.60280i	1.13171	+	0.244636i
$355$	−0.848210			−0.0450183
$356$	4.70466	+	8.14871i	0.249347	+	0.431881i
$357$	3.63244	+	0.785205i	0.192249	+	0.0415575i
$358$	13.6500	+	23.6425i	0.721425	+	1.24955i
$359$	−0.0643609			−0.00339684			−0.00169842	−	0.999999i	$-0.500541\pi$
$359$	−0.0643609			−0.00339684			−0.00169842	+	0.999999i	$0.500541\pi$
$360$	0.105943	+	1.07959i	0.00558371	+	0.0568992i
$361$	−9.61012	−	16.6452i	−0.505796	−	0.876064i
$362$	24.5834			1.29207
$363$	−18.2580	−	3.94675i	−0.958299	−	0.207151i
$364$	−0.929624	−	1.96532i	−0.0487255	−	0.103011i
$365$	0.194613	+	0.337079i	0.0101865	+	0.0176435i
$366$	4.67207	+	14.5498i	0.244213	+	0.760528i
$367$	−7.14756			−0.373100			−0.186550	−	0.982446i	$-0.559731\pi$
$367$	−7.14756			−0.373100			−0.186550	+	0.982446i	$0.559731\pi$
$368$	6.91200	−	11.9719i	0.360313	−	0.624081i
$369$	−23.6272	+	16.9184i	−1.22998	+	0.880734i
$370$	−0.268668	+	0.465346i	−0.0139674	+	0.0241922i
$371$	0.165507	+	0.286666i	0.00859267	+	0.0148829i
$372$	−0.494371	−	1.53957i	−0.0256319	−	0.0798230i
$373$	19.7982			1.02511			0.512557	−	0.858653i	$-0.328698\pi$
$373$	19.7982			1.02511			0.512557	+	0.858653i	$0.328698\pi$
$374$	0.665535	−	1.15274i	0.0344140	−	0.0596068i
$375$	−1.98608	−	0.429321i	−0.102561	−	0.0221700i
$376$	−4.14251	+	7.17504i	−0.213634	+	0.370025i
$377$	−6.84394	−	0.560899i	−0.352481	−	0.0288878i
$378$	0.575621	−	4.98029i	0.0296068	−	0.256158i
$379$	10.8356	+	18.7679i	0.556589	+	0.964041i	0.997778	+	0.0666264i	$0.0212236\pi$
$379$	10.8356	+	18.7679i	0.556589	+	0.964041i	−0.441189	+	0.897414i	$0.645443\pi$
$380$	0.515550			0.0264472
$381$	−5.03198	−	15.6706i	−0.257796	−	0.802829i
$382$	−3.12070	−	5.40520i	−0.159669	−	0.276554i
$383$	−22.7358			−1.16175			−0.580874	−	0.813994i	$-0.697289\pi$
$383$	−22.7358			−1.16175			−0.580874	+	0.813994i	$0.697289\pi$
$384$	3.42179	+	0.739672i	0.174618	+	0.0377462i
$385$	0.0231484	−	0.0400943i	0.00117975	−	0.00204339i
$386$	−0.0731022	+	0.126617i	−0.00372080	+	0.00644462i
$387$	1.23336	+	12.5682i	0.0626952	+	0.638879i
$388$	5.58852	+	9.67961i	0.283714	+	0.491408i
$389$	6.49522	−	11.2501i	0.329321	−	0.570400i	−0.653057	−	0.757309i	$-0.726514\pi$
$389$	6.49522	−	11.2501i	0.329321	−	0.570400i	0.982377	+	0.186909i	$0.0598469\pi$
$390$	0.189112	+	0.811561i	0.00957604	+	0.0410950i
$391$	−8.40843	−	14.5638i	−0.425233	−	0.736525i
$392$	−9.66245	+	16.7359i	−0.488027	+	0.845288i
$393$	−8.70033	−	27.0946i	−0.438874	−	1.36674i
$394$	−2.04591	−	3.54362i	−0.103071	−	0.178525i
$395$	1.03685			0.0521698
$396$	0.899789	+	0.408074i	0.0452161	+	0.0205065i
$397$	−6.19600	+	10.7318i	−0.310968	+	0.538613i	−0.978572	−	0.205904i	$-0.933987\pi$
$397$	−6.19600	+	10.7318i	−0.310968	+	0.538613i	0.667604	+	0.744517i	$0.267320\pi$
$398$	11.6070	−	20.1039i	0.581806	−	1.00772i
$399$	−8.89050	−	1.92181i	−0.445081	−	0.0962110i
$400$	−5.17663	+	8.96619i	−0.258832	+	0.448309i
$401$	−4.12399	+	7.14296i	−0.205942	+	0.356702i	−0.950433	−	0.310931i	$-0.899359\pi$
$401$	−4.12399	+	7.14296i	−0.205942	+	0.356702i	0.744490	+	0.667633i	$0.232693\pi$
$402$	1.35144	−	1.49056i	0.0674038	−	0.0743421i
$403$	−2.02757	−	4.28651i	−0.101001	−	0.213526i
$404$	11.1009			0.552290
$405$	0.340566	−	1.00094i	0.0169228	−	0.0497371i
$406$	−0.918781	−	1.59138i	−0.0455983	−	0.0789786i
$407$	0.934133	+	1.61797i	0.0463032	+	0.0801996i
$408$	9.04511	−	9.97618i	0.447799	−	0.493894i
$409$	9.28608			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$409$	9.28608			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$410$	1.29254			0.0638339
$411$	10.2896	+	32.0439i	0.507549	+	1.58061i
$412$	−5.13420	−	8.89269i	−0.252944	−	0.438111i
$413$	−4.70305	−	8.14592i	−0.231422	−	0.400834i
$414$	−18.4453	+	13.2078i	−0.906536	+	0.649128i
$415$	−0.413049			−0.0202758
$416$	−13.6463	−	1.11839i	−0.669067	−	0.0548338i
$417$	25.5175	+	5.51599i	1.24960	+	0.270119i
$418$	−1.62892	+	2.82137i	−0.0796730	+	0.137998i
$419$	0.152855	−	0.264753i	0.00746747	−	0.0129340i	−0.862268	−	0.506453i	$-0.830956\pi$
$419$	0.152855	−	0.264753i	0.00746747	−	0.0129340i	0.869735	+	0.493519i	$0.164290\pi$
$420$	0.0824118	−	0.0908950i	0.00402128	−	0.00443522i
$421$	10.2975	−	17.8358i	0.501869	−	0.869262i	−0.498129	−	0.867103i	$-0.665979\pi$
$421$	10.2975	−	17.8358i	0.501869	−	0.869262i	0.999998	−	0.00215912i	$-0.000687270\pi$
$422$	−4.03341	+	6.98607i	−0.196343	+	0.340076i
$423$	6.56552	−	4.70126i	0.319226	−	0.228583i
$424$	1.19943			0.0582495
$425$	6.29736	+	10.9073i	0.305467	+	0.529084i
$426$	9.54113	−	10.5233i	0.462269	−	0.509854i
$427$	3.29907	−	5.71416i	0.159653	−	0.276528i
$428$	−2.22765	−	3.85841i	−0.107678	−	0.186503i
$429$	2.77244	+	0.841429i	0.133855	+	0.0406246i
$430$	0.280850	−	0.486447i	0.0135438	−	0.0234586i
$431$	−1.90600	−	3.30129i	−0.0918088	−	0.159017i	0.816463	−	0.577397i	$-0.195932\pi$
$431$	−1.90600	−	3.30129i	−0.0918088	−	0.159017i	−0.908272	+	0.418380i	$0.862598\pi$
$432$	−8.66255	−	6.43173i	−0.416777	−	0.309447i
$433$	7.23683	−	12.5346i	0.347780	−	0.602373i	−0.638075	−	0.769974i	$-0.720269\pi$
$433$	7.23683	−	12.5346i	0.347780	−	0.602373i	0.985855	+	0.167602i	$0.0536023\pi$
$434$	0.634455	−	1.09891i	0.0304548	−	0.0527493i
$435$	−0.118480	−	0.368970i	−0.00568068	−	0.0176908i
$436$	12.4528			0.596379
$437$	20.5799	+	35.6454i	0.984470	+	1.70515i
$438$	−6.37105	−	1.37720i	−0.304421	−	0.0658051i
$439$	−8.99472			−0.429295			−0.214647	−	0.976692i	$-0.568860\pi$
$439$	−8.99472			−0.429295			−0.214647	+	0.976692i	$0.568860\pi$
$440$	−0.0838787	−	0.145282i	−0.00399876	−	0.00692605i
$441$	15.3141	−	10.9657i	0.729244	−	0.522177i
$442$	5.88671	−	8.50617i	0.280002	−	0.404597i
$443$	−0.560007	+	0.969961i	−0.0266068	+	0.0460842i	−0.879022	−	0.476781i	$-0.841804\pi$
$443$	−0.560007	+	0.969961i	−0.0266068	+	0.0460842i	0.852415	+	0.522865i	$0.175137\pi$
$444$	1.51374	+	4.71409i	0.0718389	+	0.223721i
$445$	−0.778590	+	1.34856i	−0.0369087	+	0.0639278i
$446$	−15.9317			−0.754389
$447$	−23.8730	−	5.16050i	−1.12915	−	0.244083i
$448$	−3.59576	−	6.22804i	−0.169884	−	0.294247i
$449$	−7.92893	+	13.7333i	−0.374189	+	0.648115i	−0.990205	−	0.139619i	$-0.955412\pi$
$449$	−7.92893	+	13.7333i	−0.374189	+	0.648115i	0.616016	+	0.787734i	$0.288746\pi$
$450$	13.8143	−	9.89176i	0.651212	−	0.466302i
$451$	2.24702	−	3.89195i	0.105808	−	0.183265i
$452$	9.33453			0.439059
$453$	7.75094	−	8.54879i	0.364171	−	0.401657i
$454$	7.91532	+	13.7097i	0.371484	+	0.643430i
$455$	0.204750	−	0.295859i	0.00959881	−	0.0138701i
$456$	−22.1382	+	24.4170i	−1.03671	+	1.14343i
$457$	−34.0842			−1.59439			−0.797196	−	0.603721i	$-0.793684\pi$
$457$	−34.0842			−1.59439			−0.797196	+	0.603721i	$0.793684\pi$
$458$	−1.84177	−	3.19005i	−0.0860604	−	0.149061i
$459$	−12.0449	+	5.21405i	−0.562209	+	0.243371i
$460$	−0.555202			−0.0258864
$461$	2.56128	+	4.43627i	0.119291	+	0.206618i	0.919487	−	0.393121i	$-0.128605\pi$
$461$	2.56128	+	4.43627i	0.119291	+	0.206618i	−0.800196	+	0.599739i	$0.795271\pi$
$462$	0.237040	+	0.738191i	0.0110281	+	0.0343438i
$463$	3.59883	+	6.23335i	0.167252	+	0.289688i	0.937453	−	0.348113i	$-0.113177\pi$
$463$	3.59883	+	6.23335i	0.167252	+	0.289688i	−0.770201	+	0.637801i	$0.779844\pi$
$464$	−3.95454			−0.183585
$465$	0.179746	−	0.198248i	0.00833551	−	0.00919354i
$466$	−11.0194			−0.510465
$467$	−31.2424			−1.44573			−0.722863	−	0.690992i	$-0.757174\pi$
$467$	−31.2424			−1.44573			−0.722863	+	0.690992i	$0.757174\pi$
$468$	6.71035	+	3.73195i	0.310186	+	0.172509i
$469$	−0.868729			−0.0401142
$470$	−0.359170			−0.0165673
$471$	−6.22300	−	19.3797i	−0.286741	−	0.892968i
$472$	−34.0831			−1.56880
$473$	−0.976490	−	1.69133i	−0.0448991	−	0.0777675i
$474$	−11.6631	+	12.8637i	−0.535704	+	0.590848i
$475$	−15.4130	−	26.6960i	−0.707196	−	1.22490i
$476$	−1.52309			−0.0698108
$477$	−1.06467	−	0.482851i	−0.0487479	−	0.0221082i
$478$	−5.46668	−	9.46857i	−0.250040	−	0.433082i
$479$	−30.4658			−1.39202			−0.696008	−	0.718034i	$-0.745042\pi$
$479$	−30.4658			−1.39202			−0.696008	+	0.718034i	$0.745042\pi$
$480$	−0.236241	−	0.735701i	−0.0107829	−	0.0335800i
$481$	6.20833	+	13.1251i	0.283075	+	0.598452i
$482$	0.162596	+	0.281625i	0.00740606	+	0.0128277i
$483$	9.57427	+	2.06962i	0.435644	+	0.0941711i
$484$	7.65565			0.347984
$485$	−0.924863	+	1.60191i	−0.0419959	+	0.0727390i
$486$	8.58722	+	15.4843i	0.389524	+	0.702383i
$487$	−10.3039	+	17.8469i	−0.466914	+	0.808719i	−0.999286	−	0.0377916i	$-0.987968\pi$
$487$	−10.3039	+	17.8469i	−0.466914	+	0.808719i	0.532371	+	0.846511i	$0.321301\pi$
$488$	−11.9542	−	20.7053i	−0.541143	−	0.937287i
$489$	−16.6043	+	18.3135i	−0.750874	+	0.828167i
$490$	−0.837766			−0.0378464
$491$	21.4867	−	37.2161i	0.969682	−	1.67954i	0.273212	−	0.961954i	$-0.411914\pi$
$491$	21.4867	−	37.2161i	0.969682	−	1.67954i	0.696471	−	0.717585i	$-0.254753\pi$
$492$	7.99971	−	8.82318i	0.360655	−	0.397779i
$493$	−2.40534	+	4.16617i	−0.108331	+	0.187635i
$494$	−14.4079	+	20.8191i	−0.648242	+	0.936697i
$495$	0.0159688	+	0.162726i	0.000717744	+	0.00731398i
$496$	−1.36538	−	2.36491i	−0.0613074	−	0.106188i
$497$	−6.13319			−0.275111
$498$	4.64620	−	5.12446i	0.208201	−	0.229633i
$499$	−2.11925	−	3.67064i	−0.0948705	−	0.164321i	0.814684	−	0.579905i	$-0.196910\pi$
$499$	−2.11925	−	3.67064i	−0.0948705	−	0.164321i	−0.909555	+	0.415585i	$0.863577\pi$
$500$	0.832769			0.0372425
$501$	12.9961	−	14.3339i	0.580622	−	0.640390i
$502$	13.9550	−	24.1708i	0.622843	−	1.07880i
$503$	1.12652	−	1.95120i	0.0502292	−	0.0869995i	−0.839818	−	0.542869i	$-0.817338\pi$
$503$	1.12652	−	1.95120i	0.0502292	−	0.0869995i	0.890047	+	0.455869i	$0.150671\pi$
$504$	0.766050	+	7.80622i	0.0341226	+	0.347717i
$505$	0.918562	+	1.59100i	0.0408755	+	0.0707984i
$506$	1.75420	−	3.03836i	0.0779837	−	0.135072i
$507$	20.9401	+	8.27729i	0.929981	+	0.367607i
$508$	3.37269	+	5.84167i	0.149639	+	0.259182i
$509$	−7.05621	+	12.2217i	−0.312761	+	0.541718i	−0.978959	−	0.204057i	$-0.934587\pi$
$509$	−7.05621	+	12.2217i	−0.312761	+	0.541718i	0.666198	+	0.745775i	$0.267921\pi$
$510$	0.570602	+	0.123344i	0.0252667	+	0.00546177i
$511$	1.40719	+	2.43733i	0.0622506	+	0.107821i
$512$	−20.6672			−0.913370
$513$	29.4803	−	12.7616i	1.30159	−	0.563437i
$514$	−0.735515	+	1.27395i	−0.0324422	+	0.0561915i
$515$	0.849675	−	1.47168i	0.0374412	−	0.0648500i
$516$	−1.58238	−	4.92784i	−0.0696603	−	0.216936i
$517$	−0.624399	+	1.08149i	−0.0274611	+	0.0475639i
$518$	−1.94267	+	3.36480i	−0.0853560	+	0.147841i
$519$	6.55742	+	20.4211i	0.287839	+	0.896387i
$520$	−0.557465	−	1.17854i	−0.0244465	−	0.0516824i
$521$	−17.6305			−0.772405			−0.386202	−	0.922414i	$-0.626213\pi$
$521$	−17.6305			−0.772405			−0.386202	+	0.922414i	$0.626213\pi$
$522$	5.91033	+	2.68046i	0.258688	+	0.117321i
$523$	0.106583	+	0.184608i	0.00466057	+	0.00807234i	0.868346	−	0.495958i	$-0.165183\pi$
$523$	0.106583	+	0.184608i	0.00466057	+	0.00807234i	−0.863686	+	0.504031i	$0.831850\pi$
$524$	5.83141	+	10.1003i	0.254746	+	0.441233i
$525$	−7.17049	−	1.55001i	−0.312946	−	0.0676479i
$526$	−13.3217			−0.580854
$527$	−3.32197			−0.144707
$528$	1.63085	+	0.352534i	0.0709738	+	0.0153421i
$529$	−10.6627	−	18.4684i	−0.463596	−	0.802972i
$530$	0.0259987	+	0.0450310i	0.00112931	+	0.00195602i
$531$	30.2537	+	13.7207i	1.31290	+	0.595429i
$532$	3.72781			0.161621
$533$	19.8751	−	28.7190i	0.860884	−	1.24396i
$534$	−7.97278	−	24.8288i	−0.345016	−	1.07445i
$535$	0.368662	−	0.638541i	0.0159386	−	0.0276065i
$536$	−1.57393	+	2.72612i	−0.0679833	+	0.117750i
$537$	12.7277	+	39.6365i	0.549239	+	1.71044i
$538$	15.2518	−	26.4170i	0.657553	−	1.13892i
$539$	−1.45642	+	2.52259i	−0.0627323	+	0.108656i
$540$	−0.0497516	+	0.430452i	−0.00214097	+	0.0185237i
$541$	−20.0920			−0.863821			−0.431910	−	0.901917i	$-0.642160\pi$
$541$	−20.0920			−0.863821			−0.431910	+	0.901917i	$0.642160\pi$
$542$	16.0695	+	27.8332i	0.690245	+	1.19554i
$543$	36.6409	+	7.92049i	1.57241	+	0.339901i
$544$	−4.79609	+	8.30707i	−0.205631	+	0.356163i
$545$	1.03042	+	1.78475i	0.0441385	+	0.0764502i
$546$	1.36742	+	5.86819i	0.0585201	+	0.251135i
$547$	3.84585	−	6.66121i	0.164437	−	0.284813i	−0.772018	−	0.635600i	$-0.780753\pi$
$547$	3.84585	−	6.66121i	0.164437	−	0.284813i	0.936455	+	0.350787i	$0.114086\pi$
$548$	−6.89662	−	11.9453i	−0.294609	−	0.510278i
$549$	2.27584	+	23.1914i	0.0971307	+	0.989784i
$550$	−1.31378	+	2.27553i	−0.0560197	+	0.0970290i
$551$	5.88714	−	10.1968i	0.250801	−	0.434400i
$552$	23.8408	−	26.2949i	1.01473	−	1.11919i
$553$	7.49724			0.318815
$554$	9.43749	+	16.3462i	0.400960	+	0.694484i
$555$	−0.550373	+	0.607026i	−0.0233620	+	0.0257668i
$556$	−10.6996			−0.453763
$557$	−13.4015	−	23.2121i	−0.567841	−	0.983529i	−0.996779	−	0.0801952i	$-0.974446\pi$
$557$	−13.4015	−	23.2121i	−0.567841	−	0.983529i	0.428938	−	0.903334i	$-0.358888\pi$
$558$	0.437675	+	4.46000i	0.0185282	+	0.188807i
$559$	−6.48984	−	13.7202i	−0.274491	−	0.580303i
$560$	0.103601	−	0.179443i	0.00437795	−	0.00758284i
$561$	1.36337	−	1.50371i	0.0575613	−	0.0634865i
$562$	−0.696047	+	1.20559i	−0.0293610	+	0.0508547i
$563$	−17.6265			−0.742870			−0.371435	−	0.928459i	$-0.621134\pi$
$563$	−17.6265			−0.742870			−0.371435	+	0.928459i	$0.621134\pi$
$564$	−2.22295	+	2.45178i	−0.0936032	+	0.103238i
$565$	0.772401	+	1.33784i	0.0324951	+	0.0562832i
$566$	−1.72692	+	2.99112i	−0.0725879	+	0.125726i
$567$	2.46254	−	7.23754i	0.103417	−	0.303948i
$568$	−11.1119	+	19.2463i	−0.466243	+	0.807557i
$569$	−9.02265			−0.378249			−0.189125	−	0.981953i	$-0.560565\pi$
$569$	−9.02265			−0.378249			−0.189125	+	0.981953i	$0.560565\pi$
$570$	−1.39657	−	0.301889i	−0.0584957	−	0.0126447i
$571$	−0.221208	−	0.383144i	−0.00925727	−	0.0160341i	0.861360	−	0.507996i	$-0.169613\pi$
$571$	−0.221208	−	0.383144i	−0.00925727	−	0.0160341i	−0.870617	+	0.491962i	$0.836280\pi$
$572$	−1.18346	−	0.0969912i	−0.0494830	−	0.00405541i
$573$	−2.90983	−	9.06178i	−0.121560	−	0.378561i
$574$	9.34602			0.390095
$575$	16.5984	+	28.7493i	0.692201	+	1.19893i
$576$	23.1308	+	10.4903i	0.963783	+	0.437096i
$577$	26.2964			1.09474			0.547368	−	0.836892i	$-0.315630\pi$
$577$	26.2964			1.09474			0.547368	+	0.836892i	$0.315630\pi$
$578$	6.03119	+	10.4463i	0.250865	+	0.434510i
$579$	−0.149752	+	0.165167i	−0.00622347	+	0.00686409i
$580$	0.0794113	+	0.137544i	0.00329737	+	0.00571122i
$581$	−2.98665			−0.123907
$582$	−9.47062	−	29.4934i	−0.392570	−	1.22254i
$583$	0.180790			0.00748755
$584$	10.1980			0.421995
$585$	0.0203904	+	1.27054i	0.000843039	+	0.0525305i
$586$	31.3540			1.29522
$587$	30.4116			1.25522			0.627610	−	0.778528i	$-0.284033\pi$
$587$	30.4116			1.25522			0.627610	+	0.778528i	$0.284033\pi$
$588$	−5.18506	+	5.71879i	−0.213828	+	0.235839i
$589$	8.13061			0.335016
$590$	−0.738780	−	1.27960i	−0.0304151	−	0.0526805i
$591$	−1.90767	−	5.94085i	−0.0784709	−	0.244374i
$592$	4.18073	+	7.24124i	0.171827	+	0.297613i
$593$	−29.4682			−1.21011			−0.605056	−	0.796183i	$-0.706849\pi$
$593$	−29.4682			−1.21011			−0.605056	+	0.796183i	$0.706849\pi$
$594$	−2.19847	−	1.63231i	−0.0902044	−	0.0669745i
$595$	−0.126031	−	0.218292i	−0.00516675	−	0.00894908i
$596$	10.0100			0.410026
$597$	23.7772	−	26.2248i	0.973137	−	1.07331i
$598$	15.5160	−	22.4203i	0.634498	−	0.916836i
$599$	17.9709	+	31.1266i	0.734273	+	1.27180i	0.955042	+	0.296472i	$0.0958102\pi$
$599$	17.9709	+	31.1266i	0.734273	+	1.27180i	−0.220768	+	0.975326i	$0.570857\pi$
$600$	−17.8552	+	19.6932i	−0.728935	+	0.803970i
$601$	3.07908			0.125598			0.0627992	−	0.998026i	$-0.479997\pi$
$601$	3.07908			0.125598			0.0627992	+	0.998026i	$0.479997\pi$
$602$	2.03076	−	3.51737i	0.0827675	−	0.143357i
$603$	2.49453	−	1.78622i	0.101585	−	0.0727404i
$604$	−2.36465	+	4.09569i	−0.0962161	+	0.166651i
$605$	0.633480	+	1.09722i	0.0257546	+	0.0446083i
$606$	−30.0710	−	6.50031i	−1.22155	−	0.264057i
$607$	6.90552			0.280286			0.140143	−	0.990131i	$-0.455244\pi$
$607$	6.90552			0.280286			0.140143	+	0.990131i	$0.455244\pi$
$608$	11.7386	−	20.3318i	0.476062	−	0.824563i
$609$	−0.856698	−	2.66793i	−0.0347152	−	0.108110i
$610$	0.518236	−	0.897611i	0.0209828	−	0.0363432i
$611$	−5.52286	+	7.98042i	−0.223431	+	0.322853i
$612$	4.37352	−	3.13167i	0.176789	−	0.126590i
$613$	4.37980	+	7.58604i	0.176899	+	0.306397i	0.940817	−	0.338916i	$-0.110060\pi$
$613$	4.37980	+	7.58604i	0.176899	+	0.306397i	−0.763918	+	0.645313i	$0.776727\pi$
$614$	8.79360			0.354881
$615$	1.92650	+	0.416442i	0.0776839	+	0.0167925i
$616$	−0.606505	−	1.05050i	−0.0244368	−	0.0423258i
$617$	−19.8862			−0.800588			−0.400294	−	0.916387i	$-0.631092\pi$
$617$	−19.8862			−0.800588			−0.400294	+	0.916387i	$0.631092\pi$
$618$	8.70069	+	27.0957i	0.349993	+	1.08995i
$619$	−1.74906	+	3.02947i	−0.0703008	+	0.121765i	−0.899033	−	0.437881i	$-0.855729\pi$
$619$	−1.74906	+	3.02947i	−0.0703008	+	0.121765i	0.828732	+	0.559645i	$0.189063\pi$
$620$	−0.0548366	+	0.0949798i	−0.00220229	+	0.00381448i
$621$	−31.7477	+	13.7431i	−1.27399	+	0.551490i
$622$	−5.34852	−	9.26392i	−0.214456	−	0.371449i
$623$	−5.62979	+	9.75108i	−0.225553	+	0.390669i
$624$	12.4081	+	3.76584i	0.496723	+	0.150754i
$625$	−12.3966	−	21.4715i	−0.495864	−	0.858861i
$626$	7.48028	−	12.9562i	0.298972	−	0.517835i
$627$	−3.33688	+	3.68037i	−0.133262	+	0.146980i
$628$	4.17097	+	7.22433i	0.166440	+	0.288282i
$629$	10.1717			0.405572
$630$	−0.276469	+	0.197967i	−0.0110148	+	0.00788718i
$631$	14.5446	−	25.1919i	0.579010	−	1.00287i	−0.416584	−	0.909097i	$-0.636773\pi$
$631$	14.5446	−	25.1919i	0.579010	−	1.00287i	0.995593	−	0.0937767i	$-0.0298940\pi$
$632$	13.5832	−	23.5267i	0.540309	−	0.935843i
$633$	−8.26253	+	9.11305i	−0.328406	+	0.362211i
$634$	−14.2744	+	24.7241i	−0.566911	+	0.981918i
$635$	−0.558158	+	0.966757i	−0.0221498	+	0.0383646i
$636$	0.468302	+	0.101230i	0.0185694	+	0.00401405i
$637$	−12.8821	+	18.6144i	−0.510408	+	0.737529i
$638$	−1.00362			−0.0397338
$639$	17.6113	−	12.6106i	0.696692	−	0.498869i
$640$	−0.118722	−	0.205633i	−0.00469291	−	0.00812836i
$641$	5.64684	+	9.78062i	0.223037	+	0.386311i	0.955729	−	0.294249i	$-0.0950696\pi$
$641$	5.64684	+	9.78062i	0.223037	+	0.386311i	−0.732692	+	0.680561i	$0.761736\pi$
$642$	3.77510	+	11.7564i	0.148992	+	0.463989i
$643$	7.68555			0.303088			0.151544	−	0.988450i	$-0.451575\pi$
$643$	7.68555			0.303088			0.151544	+	0.988450i	$0.451575\pi$
$644$	−4.01452			−0.158194
$645$	0.575329	−	0.634551i	0.0226535	−	0.0249854i
$646$	8.86858	+	15.3608i	0.348930	+	0.604364i
$647$	10.5548	+	18.2815i	0.414952	+	0.718718i	0.995423	−	0.0955626i	$-0.0304650\pi$
$647$	10.5548	+	18.2815i	0.414952	+	0.718718i	−0.580471	+	0.814281i	$0.697132\pi$
$648$	−18.2503	−	20.8403i	−0.716939	−	0.818683i
$649$	−5.13734			−0.201658
$650$	−11.6205	+	16.7913i	−0.455793	+	0.658610i
$651$	1.29970	−	1.43348i	0.0509391	−	0.0561826i
$652$	5.06563	−	8.77394i	0.198386	−	0.343614i
$653$	−11.2120	+	19.4198i	−0.438760	+	0.759955i	−0.997594	−	0.0693244i	$-0.977916\pi$
$653$	−11.2120	+	19.4198i	−0.438760	+	0.759955i	0.558834	+	0.829280i	$0.311249\pi$
$654$	−33.7331	−	7.29191i	−1.31907	−	0.285136i
$655$	−0.965058	+	1.67153i	−0.0377080	+	0.0653121i
$656$	10.0566	−	17.4185i	0.392643	−	0.680078i
$657$	−9.05219	−	4.10536i	−0.353159	−	0.160166i
$658$	−2.59706			−0.101244
$659$	−24.6209	−	42.6447i	−0.959095	−	1.66120i	−0.724707	−	0.689057i	$-0.758025\pi$
$659$	−24.6209	−	42.6447i	−0.959095	−	1.66120i	−0.234388	−	0.972143i	$-0.575308\pi$
$660$	−0.0204877	−	0.0638027i	−0.000797482	−	0.00248352i
$661$	6.69816	−	11.6016i	0.260528	−	0.451248i	−0.705854	−	0.708357i	$-0.749437\pi$
$661$	6.69816	−	11.6016i	0.260528	−	0.451248i	0.966382	+	0.257109i	$0.0827699\pi$
$662$	16.5326	+	28.6354i	0.642559	+	1.11295i
$663$	11.5146	−	10.7816i	0.447190	−	0.418724i
$664$	−5.41109	+	9.37228i	−0.209991	+	0.363715i
$665$	0.308464	+	0.534275i	0.0119617	+	0.0207183i
$666$	−1.34014	−	13.6563i	−0.0519293	−	0.529171i
$667$	−6.33993	+	10.9811i	−0.245483	+	0.425189i
$668$	−3.96483	+	6.86729i	−0.153404	+	0.265703i
$669$	−23.7459	−	5.13302i	−0.918068	−	0.198454i
$670$	−0.136465			−0.00527209
$671$	−1.80186	−	3.12091i	−0.0695599	−	0.120481i
$672$	−1.70820	−	5.31967i	−0.0658952	−	0.205211i
$673$	−10.8567			−0.418496			−0.209248	−	0.977863i	$-0.567102\pi$
$673$	−10.8567			−0.418496			−0.209248	+	0.977863i	$0.567102\pi$
$674$	−8.74461	−	15.1461i	−0.336830	−	0.583407i
$675$	23.7769	−	10.2926i	0.915173	−	0.396164i
$676$	−9.10502	−	1.50251i	−0.350193	−	0.0577887i
$677$	13.6699	−	23.6769i	0.525377	−	0.909979i	−0.474186	−	0.880424i	$-0.657258\pi$
$677$	13.6699	−	23.6769i	0.525377	−	0.909979i	0.999563	−	0.0295547i	$-0.00940891\pi$
$678$	−25.2862	−	5.46598i	−0.971109	−	0.209920i
$679$	−6.68745	+	11.5830i	−0.256641	+	0.444515i
$680$	−0.913348			−0.0350253
$681$	7.38048	+	22.9843i	0.282821	+	0.880759i
$682$	−0.346521	−	0.600191i	−0.0132690	−	0.0229825i
$683$	−14.9448	+	25.8851i	−0.571846	+	0.990466i	0.424531	+	0.905414i	$0.360439\pi$
$683$	−14.9448	+	25.8851i	−0.571846	+	0.990466i	−0.996376	+	0.0850523i	$0.972894\pi$
$684$	−10.7043	+	7.66486i	−0.409290	+	0.293073i
$685$	1.14135	−	1.97687i	0.0436086	−	0.0755322i
$686$	−12.8115			−0.489147
$687$	−1.71732	−	5.34809i	−0.0655200	−	0.204042i
$688$	−4.37030	−	7.56958i	−0.166616	−	0.288588i
$689$	1.40032	+	0.114764i	0.0533480	+	0.00437217i
$690$	1.50398	+	0.325107i	0.0572554	+	0.0123766i
$691$	22.7913			0.867020			0.433510	−	0.901149i	$-0.357275\pi$
$691$	22.7913			0.867020			0.433510	+	0.901149i	$0.357275\pi$
$692$	−4.39511	−	7.61256i	−0.167077	−	0.289386i
$693$	0.115466	+	1.17663i	0.00438620	+	0.0446964i
$694$	11.8452			0.449638
$695$	−0.885353	−	1.53348i	−0.0335834	−	0.0581681i
$696$	−9.92424	−	2.14527i	−0.376177	−	0.0813163i
$697$	−12.2338	−	21.1896i	−0.463388	−	0.802612i
$698$	16.0587			0.607829
$699$	−16.4242	−	3.55033i	−0.621220	−	0.134286i
$700$	3.00661			0.113639
$701$	36.2555			1.36935			0.684675	−	0.728848i	$-0.259944\pi$
$701$	36.2555			1.36935			0.684675	+	0.728848i	$0.259944\pi$
$702$	−15.9923	−	14.0388i	−0.603589	−	0.529860i
$703$	−24.8955			−0.938953
$704$	−3.92780			−0.148035
$705$	−0.535334	−	0.115720i	−0.0201618	−	0.00435828i
$706$	16.7590			0.630735
$707$	6.64189	+	11.5041i	0.249794	+	0.432656i
$708$	−13.3073	−	2.87657i	−0.500119	−	0.108108i
$709$	9.93974	+	17.2161i	0.373295	+	0.646566i	0.990070	−	0.140573i	$-0.0448946\pi$
$709$	9.93974	+	17.2161i	0.373295	+	0.646566i	−0.616775	+	0.787139i	$0.711561\pi$
$710$	−0.963434			−0.0361570
$711$	−21.5281	+	15.4153i	−0.807367	+	0.578118i
$712$	20.3996	+	35.3332i	0.764508	+	1.32417i
$713$	−8.75594			−0.327913
$714$	4.12588	+	0.891871i	0.154407	+	0.0333774i
$715$	−0.0840265	−	0.177641i	−0.00314241	−	0.00664339i
$716$	−8.53073	−	14.7757i	−0.318808	−	0.552192i
$717$	−5.09730	−	15.8740i	−0.190362	−	0.592825i
$718$	−0.0731039			−0.00272821
$719$	4.26020	−	7.37888i	0.158879	−	0.275186i	−0.775586	−	0.631242i	$-0.782545\pi$
$719$	4.26020	−	7.37888i	0.158879	−	0.275186i	0.934465	+	0.356056i	$0.115879\pi$
$720$	0.0714687	+	0.728283i	0.00266348	+	0.0271415i
$721$	6.14378	−	10.6413i	0.228806	−	0.396304i
$722$	−10.9156	−	18.9064i	−0.406236	−	0.703622i
$723$	0.151610	+	0.472142i	0.00563842	+	0.0175592i
$724$	−15.3637			−0.570986
$725$	4.74818	−	8.22410i	0.176343	−	0.305435i
$726$	−20.7383	−	4.48289i	−0.769670	−	0.166376i
$727$	−7.74562	+	13.4158i	−0.287269	+	0.497565i	−0.973157	−	0.230143i	$-0.926081\pi$
$727$	−7.74562	+	13.4158i	−0.287269	+	0.497565i	0.685888	+	0.727707i	$0.259414\pi$
$728$	−4.03089	−	8.52173i	−0.149395	−	0.315836i
$729$	7.81018	+	25.8457i	0.289266	+	0.957249i
$730$	0.221050	+	0.382869i	0.00818141	+	0.0141706i
$731$	−10.6329			−0.393273
$732$	−2.91987	−	9.09304i	−0.107921	−	0.336089i
$733$	16.9965	+	29.4388i	0.627779	+	1.08735i	0.987996	+	0.154477i	$0.0493694\pi$
$733$	16.9965	+	29.4388i	0.627779	+	1.08735i	−0.360217	+	0.932869i	$0.617297\pi$
$734$	−8.11851			−0.299660
$735$	−1.24867	−	0.269919i	−0.0460579	−	0.00995611i
$736$	−12.6414	+	21.8955i	−0.465968	+	0.807080i
$737$	−0.237237	+	0.410907i	−0.00873875	+	0.0151360i
$738$	−26.8369	+	19.2166i	−0.987878	+	0.707373i
$739$	−24.2722	−	42.0407i	−0.892867	−	1.54649i	−0.836423	−	0.548085i	$-0.815357\pi$
$739$	−24.2722	−	42.0407i	−0.892867	−	1.54649i	−0.0564440	−	0.998406i	$-0.517976\pi$
$740$	0.167907	−	0.290824i	0.00617239	−	0.0106909i
$741$	−28.1823	+	26.3884i	−1.03530	+	0.969400i
$742$	0.187990	+	0.325608i	0.00690132	+	0.0119534i
$743$	17.0493	−	29.5303i	0.625478	−	1.08336i	−0.362970	−	0.931801i	$-0.618237\pi$
$743$	17.0493	−	29.5303i	0.625478	−	1.08336i	0.988448	−	0.151560i	$-0.0484295\pi$
$744$	−2.14361	−	6.67564i	−0.0785887	−	0.244741i
$745$	0.828295	+	1.43465i	0.0303464	+	0.0525615i
$746$	22.4877			0.823333
$747$	8.57609	−	6.14094i	0.313783	−	0.224685i
$748$	−0.415934	+	0.720419i	−0.0152081	+	0.0263411i
$749$	2.66570	−	4.61713i	0.0974025	−	0.168706i
$750$	−2.25587	−	0.487641i	−0.0823729	−	0.0178061i
$751$	11.4844	−	19.8916i	0.419072	−	0.725854i	−0.576775	−	0.816903i	$-0.695689\pi$
$751$	11.4844	−	19.8916i	0.419072	−	0.725854i	0.995846	+	0.0910498i	$0.0290223\pi$
$752$	−2.79451	+	4.84024i	−0.101905	+	0.176505i
$753$	28.5872	−	31.5299i	1.04178	−	1.14901i
$754$	−7.77364	−	0.637094i	−0.283099	−	0.0232016i
$755$	−0.782666			−0.0284841
$756$	−0.359741	+	3.11249i	−0.0130837	+	0.113200i
$757$	4.65491	+	8.06254i	0.169186	+	0.293038i	0.938134	−	0.346273i	$-0.112553\pi$
$757$	4.65491	+	8.06254i	0.169186	+	0.293038i	−0.768948	+	0.639311i	$0.779220\pi$
$758$	12.3076	+	21.3174i	0.447032	+	0.774282i
$759$	3.59352	−	3.96343i	0.130437	−	0.143863i
$760$	2.23545			0.0810882
$761$	−24.2721			−0.879862			−0.439931	−	0.898032i	$-0.644997\pi$
$761$	−24.2721			−0.879862			−0.439931	+	0.898032i	$0.644997\pi$
$762$	−5.71555	−	17.7993i	−0.207052	−	0.644802i
$763$	7.45074	+	12.9051i	0.269735	+	0.467194i
$764$	1.95031	+	3.37804i	0.0705599	+	0.122213i
$765$	0.810729	+	0.367683i	0.0293120	+	0.0132936i
$766$	−25.8244			−0.933072
$767$	−39.7917	−	3.26115i	−1.43679	−	0.117753i
$768$	−24.7789	−	5.35632i	−0.894130	−	0.193280i
$769$	−15.9182	+	27.5712i	−0.574026	+	0.994241i	0.422121	+	0.906539i	$0.361286\pi$
$769$	−15.9182	+	27.5712i	−0.574026	+	0.994241i	−0.996147	+	0.0877020i	$0.972048\pi$
$770$	0.0262930	−	0.0455408i	0.000947534	−	0.00164118i
$771$	−1.50672	+	1.66182i	−0.0542632	+	0.0598489i
$772$	0.0456861	−	0.0791306i	0.00164428	−	0.00284797i
$773$	25.7735	−	44.6410i	0.927007	−	1.60562i	0.138707	−	0.990334i	$-0.455705\pi$
$773$	25.7735	−	44.6410i	0.927007	−	1.60562i	0.788301	−	0.615290i	$-0.210961\pi$
$774$	1.40091	+	14.2755i	0.0503545	+	0.513124i
$775$	6.55762			0.235557
$776$	24.2321	+	41.9712i	0.869881	+	1.50668i
$777$	−3.97960	+	4.38925i	−0.142768	+	0.157464i
$778$	7.37756	−	12.7783i	0.264498	−	0.458124i
$779$	29.9426	+	51.8621i	1.07280	+	1.85815i
$780$	−0.118187	−	0.507195i	−0.00423179	−	0.0181605i
$781$	−1.67489	+	2.90099i	−0.0599321	+	0.103805i
$782$	−9.55067	−	16.5422i	−0.341531	−	0.591549i
$783$	7.94559	+	5.89941i	0.283952	+	0.210828i
$784$	−6.51823	+	11.2899i	−0.232794	+	0.403211i
$785$	−0.690268	+	1.19558i	−0.0246367	+	0.0426720i
$786$	−9.88222	−	30.7752i	−0.352487	−	1.09772i
$787$	−8.07530			−0.287853			−0.143927	−	0.989588i	$-0.545973\pi$
$787$	−8.07530			−0.287853			−0.143927	+	0.989588i	$0.545973\pi$
$788$	1.27861	+	2.21463i	0.0455488	+	0.0788928i
$789$	−19.8557	−	4.29210i	−0.706881	−	0.152803i
$790$	1.17771			0.0419009
$791$	5.58503	+	9.67356i	0.198581	+	0.343952i
$792$	3.90152	+	1.76943i	0.138635	+	0.0628738i
$793$	−11.9753	−	25.3171i	−0.425255	−	0.899035i
$794$	−7.03769	+	12.1896i	−0.249758	+	0.432594i
$795$	0.0242419	+	0.0754941i	0.000859772	+	0.00267750i
$796$	−7.25393	+	12.5642i	−0.257109	+	0.445325i
$797$	−5.79598			−0.205304			−0.102652	−	0.994717i	$-0.532733\pi$
$797$	−5.79598			−0.205304			−0.102652	+	0.994717i	$0.532733\pi$
$798$	−10.0982	−	2.18288i	−0.357473	−	0.0772731i
$799$	3.39952	+	5.88814i	0.120266	+	0.208307i
$800$	9.46756	−	16.3983i	0.334729	−	0.579767i
$801$	−3.88367	−	39.5755i	−0.137223	−	1.39833i
$802$	−4.68421	+	8.11329i	−0.165405	+	0.286490i
$803$	1.53714			0.0542444
$804$	−0.844599	+	0.931540i	−0.0297867	+	0.0328529i
$805$	−0.332188	−	0.575367i	−0.0117081	−	0.0202790i
$806$	−2.30301	−	4.86880i	−0.0811200	−	0.171496i
$807$	31.2438	−	34.4599i	1.09983	−	1.21305i
$808$	48.1339			1.69335
$809$	0.705053	+	1.22119i	0.0247884	+	0.0429347i	0.878153	−	0.478379i	$-0.158775\pi$
$809$	0.705053	+	1.22119i	0.0247884	+	0.0429347i	−0.853365	+	0.521314i	$0.825442\pi$
$810$	0.386829	−	1.13691i	0.0135918	−	0.0399470i
$811$	30.4340			1.06868			0.534341	−	0.845269i	$-0.320560\pi$
$811$	30.4340			1.06868			0.534341	+	0.845269i	$0.320560\pi$
$812$	0.574203	+	0.994548i	0.0201506	+	0.0349018i
$813$	14.9837	+	46.6622i	0.525501	+	1.63651i
$814$	1.06103	+	1.83776i	0.0371891	+	0.0644133i
$815$	1.67666			0.0587307
$816$	6.10177	−	6.72987i	0.213605	−	0.235592i
$817$	26.0244			0.910478
$818$	10.5475			0.368786
$819$	0.147438	+	9.18697i	0.00515189	+	0.321019i
$820$	−0.807787			−0.0282091
$821$	29.1732			1.01815			0.509076	−	0.860722i	$-0.329987\pi$
$821$	29.1732			1.01815			0.509076	+	0.860722i	$0.329987\pi$
$822$	11.6874	+	36.3969i	0.407645	+	1.26949i
$823$	22.0750			0.769486			0.384743	−	0.923024i	$-0.374290\pi$
$823$	22.0750			0.769486			0.384743	+	0.923024i	$0.374290\pi$
$824$	−22.2621	−	38.5591i	−0.775537	−	1.34327i
$825$	−2.69131	+	2.96834i	−0.0936993	+	0.103344i
$826$	−5.34193	−	9.25249i	−0.185869	−	0.321935i
$827$	−46.3762			−1.61266			−0.806329	−	0.591467i	$-0.798549\pi$
$827$	−46.3762			−1.61266			−0.806329	+	0.591467i	$0.798549\pi$
$828$	11.5276	−	8.25437i	0.400612	−	0.286859i
$829$	7.67652	+	13.2961i	0.266616	+	0.461793i	0.967986	−	0.251005i	$-0.0807610\pi$
$829$	7.67652	+	13.2961i	0.266616	+	0.461793i	−0.701369	+	0.712798i	$0.747428\pi$
$830$	−0.469159			−0.0162848
$831$	8.79979	+	27.4043i	0.305261	+	0.950645i
$832$	−30.4231	−	2.49334i	−1.05473	−	0.0864411i
$833$	7.92940	+	13.7341i	0.274738	+	0.475859i
$834$	28.9839	+	6.26530i	1.00363	+	0.216950i
$835$	−1.31231			−0.0454142
$836$	1.01801	−	1.76325i	0.0352087	−	0.0609832i
$837$	−0.784620	+	6.78855i	−0.0271204	+	0.234647i
$838$	0.173620	−	0.300718i	0.00599759	−	0.0103881i
$839$	−10.5188	−	18.2191i	−0.363149	−	0.628993i	0.625328	−	0.780362i	$-0.284965\pi$
$839$	−10.5188	−	18.2191i	−0.363149	−	0.628993i	−0.988477	+	0.151369i	$0.951632\pi$
$840$	0.357341	−	0.394124i	0.0123294	−	0.0135986i
$841$	−25.3728			−0.874923
$842$	11.6963	−	20.2586i	0.403082	−	0.698159i
$843$	−1.42587	+	1.57264i	−0.0491095	+	0.0541647i
$844$	2.52072	−	4.36602i	0.0867669	−	0.150285i
$845$	−0.538069	−	1.42927i	−0.0185101	−	0.0491685i
$846$	7.45740	−	5.33990i	0.256391	−	0.183589i
$847$	4.58053	+	7.93371i	0.157389	+	0.272606i
$848$	0.809128			0.0277856
$849$	−3.53764	+	3.90179i	−0.121412	+	0.133909i
$850$	7.15281	+	12.3890i	0.245339	+	0.424940i
$851$	26.8103			0.919044
$852$	−5.96284	+	6.57663i	−0.204283	+	0.225312i
$853$	−16.5578	+	28.6789i	−0.566928	+	0.981947i	0.429940	+	0.902858i	$0.358535\pi$
$853$	−16.5578	+	28.6789i	−0.566928	+	0.981947i	−0.996867	+	0.0790899i	$0.974799\pi$
$854$	3.74723	−	6.49039i	0.128228	−	0.222097i
$855$	−1.98428	−	0.899916i	−0.0678611	−	0.0307765i
$856$	−9.65920	−	16.7302i	−0.330145	−	0.571827i
$857$	10.2603	−	17.7714i	0.350486	−	0.607060i	−0.635848	−	0.771814i	$-0.719350\pi$
$857$	10.2603	−	17.7714i	0.350486	−	0.607060i	0.986335	+	0.164754i	$0.0526830\pi$
$858$	3.14906	+	0.955732i	0.107507	+	0.0326282i
$859$	3.24826	+	5.62615i	0.110829	+	0.191962i	0.916105	−	0.400939i	$-0.131316\pi$
$859$	3.24826	+	5.62615i	0.110829	+	0.191962i	−0.805276	+	0.592901i	$0.797983\pi$
$860$	−0.175521	+	0.304011i	−0.00598520	+	0.0103667i
$861$	13.9300	+	3.01118i	0.474734	+	0.102621i
$862$	−2.16492	−	3.74975i	−0.0737374	−	0.127717i
$863$	23.8577			0.812124			0.406062	−	0.913845i	$-0.366902\pi$
$863$	23.8577			0.812124			0.406062	+	0.913845i	$0.366902\pi$
$864$	15.8430	+	11.7630i	0.538989	+	0.400186i
$865$	0.727362	−	1.25983i	0.0247310	−	0.0428354i
$866$	8.21991	−	14.2373i	0.279324	−	0.483803i
$867$	5.62366	+	17.5132i	0.190990	+	0.594779i
$868$	−0.396510	+	0.686775i	−0.0134584	+	0.0233107i
$869$	2.04739	−	3.54618i	0.0694528	−	0.120296i
$870$	−0.134575	−	0.419092i	−0.00456251	−	0.0142086i
$871$	−2.09838	+	3.03212i	−0.0711010	+	0.102739i
$872$	53.9957			1.82852
$873$	−4.61330	−	47.0105i	−0.156136	−	1.59107i
$874$	23.3755	+	40.4876i	0.790690	+	1.36951i
$875$	0.498262	+	0.863015i	0.0168443	+	0.0291752i
$876$	3.98166	+	0.860696i	0.134528	+	0.0290802i
$877$	−14.2897			−0.482530			−0.241265	−	0.970459i	$-0.577562\pi$
$877$	−14.2897			−0.482530			−0.241265	+	0.970459i	$0.577562\pi$
$878$	−10.2166			−0.344794
$879$	46.7324	+	10.1019i	1.57624	+	0.340729i
$880$	−0.0565840	−	0.0980064i	−0.00190745	−	0.00330379i
$881$	2.05178	+	3.55379i	0.0691263	+	0.119730i	0.898517	−	0.438939i	$-0.144646\pi$
$881$	2.05178	+	3.55379i	0.0691263	+	0.119730i	−0.829391	+	0.558669i	$0.811312\pi$
$882$	17.3945	−	12.4554i	0.585702	−	0.419394i
$883$	−4.59858			−0.154755			−0.0773773	−	0.997002i	$-0.524655\pi$
$883$	−4.59858			−0.154755			−0.0773773	+	0.997002i	$0.524655\pi$
$884$	−3.67897	+	5.31603i	−0.123737	+	0.178797i
$885$	−0.688860	−	2.14525i	−0.0231558	−	0.0721117i
$886$	−0.636081	+	1.10172i	−0.0213696	+	0.0370132i
$887$	29.0641	−	50.3405i	0.975877	−	1.69027i	0.298865	−	0.954295i	$-0.403392\pi$
$887$	29.0641	−	50.3405i	0.975877	−	1.69027i	0.677012	−	0.735972i	$-0.263275\pi$
$888$	6.56364	+	20.4405i	0.220261	+	0.685937i
$889$	−4.03590	+	6.99038i	−0.135360	+	0.234450i
$890$	−0.884357	+	1.53175i	−0.0296437	+	0.0513444i
$891$	−2.75086	−	3.14124i	−0.0921572	−	0.105236i
$892$	9.95671			0.333375
$893$	−8.32042	−	14.4114i	−0.278432	−	0.482259i
$894$	−27.1160	−	5.86152i	−0.906894	−	0.196039i
$895$	1.41178	−	2.44527i	0.0471905	−	0.0817364i
$896$	−0.858450	−	1.48688i	−0.0286788	−	0.0496732i
$897$	30.3499	−	28.4179i	1.01335	−	0.948846i
$898$	−9.00603	+	15.5989i	−0.300535	+	0.520542i
$899$	1.25238	+	2.16918i	0.0417691	+	0.0723461i
$900$	−8.63340	+	6.18197i	−0.287780	+	0.206066i
$901$	0.492151	−	0.852431i	0.0163959	−	0.0283986i
$902$	2.55226	−	4.42065i	0.0849810	−	0.147191i
$903$	4.16005	−	4.58828i	0.138438	−	0.152688i
$904$	40.4749			1.34617
$905$	−1.27129	−	2.20194i	−0.0422592	−	0.0731950i
$906$	8.80385	−	9.71009i	0.292488	−	0.322596i
$907$	30.8331			1.02380			0.511898	−	0.859046i	$-0.328943\pi$
$907$	30.8331			1.02380			0.511898	+	0.859046i	$0.328943\pi$
$908$	−4.94677	−	8.56806i	−0.164164	−	0.284341i
$909$	−42.7259	−	19.3771i	−1.41713	−	0.642698i
$910$	0.232564	−	0.336050i	0.00770941	−	0.0111399i
$911$	−25.0010	+	43.3031i	−0.828322	+	1.43470i	0.0710324	+	0.997474i	$0.477371\pi$
$911$	−25.0010	+	43.3031i	−0.828322	+	1.43470i	−0.899354	+	0.437221i	$0.855963\pi$
$912$	−14.9343	+	16.4716i	−0.494523	+	0.545428i
$913$	−0.815611	+	1.41268i	−0.0269928	+	0.0467529i
$914$	−38.7143			−1.28056
$915$	1.06162	−	1.17090i	0.0350960	−	0.0387087i
$916$	1.15104	+	1.99366i	0.0380314	+	0.0658722i
$917$	−6.97809	+	12.0864i	−0.230437	+	0.399128i
$918$	−13.6812	+	5.92235i	−0.451545	+	0.195467i
$919$	−8.08276	+	13.9998i	−0.266626	+	0.461809i	−0.967988	−	0.250995i	$-0.919242\pi$
$919$	−8.08276	+	13.9998i	−0.266626	+	0.461809i	0.701363	+	0.712805i	$0.252575\pi$
$920$	−2.40738			−0.0793689
$921$	13.1067	+	2.83320i	0.431879	+	0.0933571i
$922$	2.90922	+	5.03891i	0.0958099	+	0.165948i
$923$	−14.8145	+	21.4066i	−0.487625	+	0.704608i
$924$	−0.148141	−	0.461341i	−0.00487349	−	0.0151770i
$925$	−20.0791			−0.660197
$926$	4.08770	+	7.08011i	0.134330	+	0.232667i
$927$	4.23825	+	43.1888i	0.139202	+	1.41850i
$928$	7.23247			0.237417
$929$	19.1446	+	33.1594i	0.628114	+	1.08792i	0.987930	+	0.154902i	$0.0495060\pi$
$929$	19.1446	+	33.1594i	0.628114	+	1.08792i	−0.359816	+	0.933023i	$0.617161\pi$
$930$	0.204163	−	0.225179i	0.00669477	−	0.00738391i
$931$	−19.4075	−	33.6147i	−0.636054	−	1.10168i
$932$	6.88671			0.225582
$933$	−4.98712	−	15.5309i	−0.163271	−	0.508458i
$934$	−35.4865			−1.16115
$935$	−0.137669			−0.00450224
$936$	29.0963	+	16.1819i	0.951044	+	0.528922i
$937$	−3.73973			−0.122172			−0.0610858	−	0.998133i	$-0.519456\pi$
$937$	−3.73973			−0.122172			−0.0610858	+	0.998133i	$0.519456\pi$
$938$	−0.986741			−0.0322182
$939$	15.3235	−	16.9009i	0.500064	−	0.551539i
$940$	0.224467			0.00732131
$941$	−27.4352	−	47.5192i	−0.894363	−	1.54908i	−0.834591	−	0.550871i	$-0.814296\pi$
$941$	−27.4352	−	47.5192i	−0.894363	−	1.54908i	−0.0597725	−	0.998212i	$-0.519038\pi$
$942$	−7.06836	−	22.0123i	−0.230300	−	0.717198i
$943$	−32.2455	−	55.8508i	−1.05006	−	1.81875i
$944$	−22.9923			−0.748334
$945$	−0.475853	+	0.205989i	−0.0154795	+	0.00670083i
$946$	−1.10914	−	1.92109i	−0.0360613	−	0.0624599i
$947$	−37.7014			−1.22513			−0.612565	−	0.790420i	$-0.709862\pi$
$947$	−37.7014			−1.22513			−0.612565	+	0.790420i	$0.709862\pi$
$948$	7.28899	−	8.03930i	0.236735	−	0.261104i
$949$	11.9060	+	0.975765i	0.386486	+	0.0316747i
$950$	−17.5067	−	30.3225i	−0.567993	−	0.983793i
$951$	−29.2416	+	32.2516i	−0.948222	+	1.04583i
$952$	−6.60419			−0.214043
$953$	−19.3375	+	33.4935i	−0.626402	+	1.08496i	0.361866	+	0.932230i	$0.382140\pi$
$953$	−19.3375	+	33.4935i	−0.626402	+	1.08496i	−0.988268	+	0.152730i	$0.951194\pi$
$954$	−1.20930	−	0.548443i	−0.0391525	−	0.0177565i
$955$	−0.322764	+	0.559044i	−0.0104444	+	0.0180902i
$956$	3.41647	+	5.91749i	0.110496	+	0.191385i
$957$	−1.49588	−	0.323356i	−0.0483548	−	0.0104526i
$958$	−34.6043			−1.11802
$959$	8.25278	−	14.2942i	0.266496	−	0.461585i
$960$	−0.526675	−	1.64017i	−0.0169983	−	0.0529362i
$961$	14.6352	−	25.3489i	0.472103	−	0.817706i
$962$	7.05169	+	14.9080i	0.227356	+	0.480654i
$963$	1.83892	+	18.7390i	0.0592583	+	0.603855i
$964$	−0.101616	−	0.176005i	−0.00327284	−	0.00566873i
$965$	0.0151215			0.000486777
$966$	10.8749	+	2.35077i	0.349893	+	0.0756347i
$967$	3.01037	+	5.21412i	0.0968070	+	0.167675i	0.910361	−	0.413814i	$-0.135804\pi$
$967$	3.01037	+	5.21412i	0.0968070	+	0.167675i	−0.813554	+	0.581489i	$0.802470\pi$
$968$	33.1952			1.06694
$969$	8.26932	+	25.7523i	0.265649	+	0.827284i
$970$	−1.05050	+	1.81952i	−0.0337295	+	0.0584213i
$971$	9.27919	−	16.0720i	0.297783	−	0.515776i	−0.677845	−	0.735205i	$-0.737086\pi$
$971$	9.27919	−	16.0720i	0.297783	−	0.515776i	0.975629	+	0.219429i	$0.0704194\pi$
$972$	−5.36668	−	9.67710i	−0.172136	−	0.310393i
$973$	−6.40176	−	11.0882i	−0.205231	−	0.355471i
$974$	−11.7036	+	20.2713i	−0.375008	+	0.649533i
$975$	−22.7300	+	21.2831i	−0.727944	+	0.681605i
$976$	−8.06425	−	13.9677i	−0.258130	−	0.447095i
$977$	−15.4804	+	26.8129i	−0.495262	+	0.857819i	−0.999985	−	0.00546221i	$-0.998261\pi$
$977$	−15.4804	+	26.8129i	−0.495262	+	0.857819i	0.504723	+	0.863281i	$0.331595\pi$
$978$	−18.8599	+	20.8013i	−0.603074	+	0.665153i
$979$	3.07483	+	5.32575i	0.0982718	+	0.170212i
$980$	0.523572			0.0167249
$981$	−47.9290	−	21.7369i	−1.53026	−	0.694004i
$982$	24.4056	−	42.2717i	0.778813	−	1.34894i
$983$	−20.2634	+	35.0972i	−0.646301	+	1.11943i	0.337699	+	0.941254i	$0.390351\pi$
$983$	−20.2634	+	35.0972i	−0.646301	+	1.11943i	−0.983999	+	0.178171i	$0.942982\pi$
$984$	34.6871	−	38.2577i	1.10578	−	1.21961i
$985$	−0.211602	+	0.366506i	−0.00674220	+	0.0116778i
$986$	−2.73209	+	4.73212i	−0.0870075	+	0.150701i
$987$	−3.87086	−	0.836745i	−0.123211	−	0.0266339i
$988$	9.00439	−	13.0111i	0.286468	−	0.413940i
$989$	−28.0260			−0.891173
$990$	0.0181381	+	0.184831i	0.000576466	+	0.00587432i
$991$	−21.8458	−	37.8381i	−0.693955	−	1.20197i	−0.970532	−	0.240973i	$-0.922533\pi$
$991$	−21.8458	−	37.8381i	−0.693955	−	1.20197i	0.276577	−	0.960992i	$-0.410800\pi$
$992$	2.49715	+	4.32519i	0.0792847	+	0.137325i
$993$	15.4155	+	48.0070i	0.489197	+	1.52346i
$994$	−6.96635			−0.220959
$995$	−2.40095			−0.0761153
$996$	−2.90369	+	3.20259i	−0.0920071	+	0.101478i
$997$	13.4456	+	23.2885i	0.425827	+	0.737554i	0.996497	−	0.0836255i	$-0.0266499\pi$
$997$	13.4456	+	23.2885i	0.425827	+	0.737554i	−0.570670	+	0.821179i	$0.693317\pi$
$998$	−2.40713	−	4.16928i	−0.0761965	−	0.131976i
$999$	2.40247	−	20.7862i	0.0760107	−	0.657646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.h.a.16.9	yes	24
3.2	odd	2		351.2.h.a.289.4		24
9.4	even	3		117.2.f.a.94.4	yes	24
9.5	odd	6		351.2.f.a.172.9		24
13.9	even	3		117.2.f.a.61.4	✓	24
39.35	odd	6		351.2.f.a.100.9		24
117.22	even	3	inner	117.2.h.a.22.9	yes	24
117.113	odd	6		351.2.h.a.334.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.4	✓	24	13.9	even	3
117.2.f.a.94.4	yes	24	9.4	even	3
117.2.h.a.16.9	yes	24	1.1	even	1	trivial
117.2.h.a.22.9	yes	24	117.22	even	3	inner
351.2.f.a.100.9		24	39.35	odd	6
351.2.f.a.172.9		24	9.5	odd	6
351.2.h.a.289.4		24	3.2	odd	2
351.2.h.a.334.4		24	117.113	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.13584 q^{2} +(1.69295 + 0.365956i) q^{3} -0.709859 q^{4} +(-0.0587384 - 0.101738i) q^{5} +(1.92293 + 0.415669i) q^{6} +(-0.424723 - 0.735641i) q^{7} -3.07798 q^{8} +(2.73215 + 1.23909i) q^{9} +O(q^{10})\)	\(q+1.13584 q^{2} +(1.69295 + 0.365956i) q^{3} -0.709859 q^{4} +(-0.0587384 - 0.101738i) q^{5} +(1.92293 + 0.415669i) q^{6} +(-0.424723 - 0.735641i) q^{7} -3.07798 q^{8} +(2.73215 + 1.23909i) q^{9} +(-0.0667177 - 0.115558i) q^{10} -0.463942 q^{11} +(-1.20175 - 0.259777i) q^{12} +(-3.59350 - 0.294508i) q^{13} +(-0.482419 - 0.835574i) q^{14} +(-0.0622095 - 0.193733i) q^{15} -2.07638 q^{16} +(-1.26296 + 2.18751i) q^{17} +(3.10330 + 1.40741i) q^{18} +(3.09113 - 5.35399i) q^{19} +(0.0416960 + 0.0722196i) q^{20} +(-0.449821 - 1.40083i) q^{21} -0.526966 q^{22} +(-3.32887 + 5.76577i) q^{23} +(-5.21086 - 1.12640i) q^{24} +(2.49310 - 4.31818i) q^{25} +(-4.08166 - 0.334515i) q^{26} +(4.17194 + 3.09756i) q^{27} +(0.301493 + 0.522201i) q^{28} +1.90453 q^{29} +(-0.0706603 - 0.220050i) q^{30} +(0.657577 + 1.13896i) q^{31} +3.79751 q^{32} +(-0.785431 - 0.169783i) q^{33} +(-1.43452 + 2.48467i) q^{34} +(-0.0498951 + 0.0864208i) q^{35} +(-1.93944 - 0.879579i) q^{36} +(-2.01347 - 3.48743i) q^{37} +(3.51104 - 6.08129i) q^{38} +(-5.97584 - 1.81365i) q^{39} +(0.180795 + 0.313147i) q^{40} +(-4.84331 + 8.38887i) q^{41} +(-0.510927 - 1.59113i) q^{42} +(2.10477 + 3.64556i) q^{43} +0.329333 q^{44} +(-0.0344198 - 0.350746i) q^{45} +(-3.78107 + 6.54901i) q^{46} +(1.34586 - 2.33109i) q^{47} +(-3.51521 - 0.759865i) q^{48} +(3.13922 - 5.43729i) q^{49} +(2.83177 - 4.90477i) q^{50} +(-2.93865 + 3.24115i) q^{51} +(2.55088 + 0.209059i) q^{52} -0.389682 q^{53} +(4.73867 + 3.51835i) q^{54} +(0.0272512 + 0.0472005i) q^{55} +(1.30729 + 2.26429i) q^{56} +(7.19244 - 7.93281i) q^{57} +2.16325 q^{58} +11.0732 q^{59} +(0.0441600 + 0.137523i) q^{60} +(3.88380 + 6.72693i) q^{61} +(0.746905 + 1.29368i) q^{62} +(-0.248881 - 2.53615i) q^{63} +8.46614 q^{64} +(0.181114 + 0.382895i) q^{65} +(-0.892126 - 0.192846i) q^{66} +(0.511351 - 0.885686i) q^{67} +(0.896521 - 1.55282i) q^{68} +(-7.74562 + 8.54293i) q^{69} +(-0.0566730 + 0.0981605i) q^{70} +(3.61012 - 6.25291i) q^{71} +(-8.40950 - 3.81389i) q^{72} -3.31321 q^{73} +(-2.28699 - 3.96117i) q^{74} +(5.80095 - 6.39808i) q^{75} +(-2.19426 + 3.80057i) q^{76} +(0.197047 + 0.341295i) q^{77} +(-6.78762 - 2.06002i) q^{78} +(-4.41302 + 7.64357i) q^{79} +(0.121963 + 0.211247i) q^{80} +(5.92931 + 6.77077i) q^{81} +(-5.50125 + 9.52844i) q^{82} +(1.75800 - 3.04495i) q^{83} +(0.319310 + 0.994393i) q^{84} +0.296736 q^{85} +(2.39069 + 4.14079i) q^{86} +(3.22427 + 0.696975i) q^{87} +1.42800 q^{88} +(-6.62760 - 11.4793i) q^{89} +(-0.0390955 - 0.398392i) q^{90} +(1.30959 + 2.76861i) q^{91} +(2.36303 - 4.09288i) q^{92} +(0.696436 + 2.16884i) q^{93} +(1.52868 - 2.64776i) q^{94} -0.726272 q^{95} +(6.42898 + 1.38972i) q^{96} +(-7.87273 - 13.6360i) q^{97} +(3.56567 - 6.17591i) q^{98} +(-1.26756 - 0.574866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22} + 17 q^{23} - 12 q^{24} - 6 q^{25} - 12 q^{26} + 2 q^{27} - 24 q^{29} - 8 q^{30} - 6 q^{31} - 38 q^{32} + 11 q^{33} + 18 q^{35} - 28 q^{36} - 3 q^{37} + 8 q^{38} + 3 q^{39} - 12 q^{40} + 5 q^{41} + 15 q^{42} - 3 q^{43} + 44 q^{44} + 19 q^{45} - 6 q^{46} + 21 q^{47} + 23 q^{48} + 3 q^{49} - 20 q^{50} + 7 q^{51} - 24 q^{52} - 20 q^{53} + 39 q^{54} + 3 q^{55} + 40 q^{56} + 9 q^{57} + 18 q^{58} + 38 q^{59} + 51 q^{60} - 6 q^{61} + 19 q^{62} + 13 q^{63} - 42 q^{64} - 2 q^{65} - 18 q^{66} - 6 q^{67} - 31 q^{69} + 27 q^{70} + 14 q^{71} - 18 q^{72} + 6 q^{73} + 29 q^{74} + 74 q^{75} - 15 q^{76} + 4 q^{77} + 80 q^{78} + 3 q^{79} - 16 q^{80} - 27 q^{81} - 9 q^{82} - 33 q^{83} + 5 q^{84} + 72 q^{86} - 32 q^{87} - 78 q^{88} - q^{89} + 21 q^{90} - 6 q^{91} - 10 q^{92} - 84 q^{93} - 9 q^{94} - 100 q^{95} - 79 q^{96} + 24 q^{97} - 61 q^{98} + 18 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

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