LMFDB - Embedded newform 117.2.f.a.94.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(61,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.61"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			94.5
Character	$\chi$	$=$	117.94
Dual form			117.2.f.a.61.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.348782 + 0.604108i) q^{2} +(1.58866 - 0.690034i) q^{3} +(0.756702 + 1.31065i) q^{4} +(1.44568 - 2.50399i) q^{5} +(-0.137242 + 1.20040i) q^{6} -3.17282 q^{7} -2.45082 q^{8} +(2.04771 - 2.19246i) q^{9} +(1.00846 + 1.74670i) q^{10} +(-1.15647 + 2.00306i) q^{11} +(2.10654 + 1.56003i) q^{12} +(0.0625290 + 3.60501i) q^{13} +(1.10662 - 1.91673i) q^{14} +(0.568861 - 4.97558i) q^{15} +(-0.658602 + 1.14073i) q^{16} +(2.69365 - 4.66554i) q^{17} +(0.610282 + 2.00173i) q^{18} +(-2.58760 + 4.48186i) q^{19} +4.37581 q^{20} +(-5.04055 + 2.18936i) q^{21} +(-0.806710 - 1.39726i) q^{22} -6.54158 q^{23} +(-3.89353 + 1.69115i) q^{24} +(-1.67999 - 2.90983i) q^{25} +(-2.19962 - 1.21959i) q^{26} +(1.74024 - 4.89608i) q^{27} +(-2.40088 - 4.15845i) q^{28} +(-2.01034 + 3.48201i) q^{29} +(2.80738 + 2.07904i) q^{30} +(4.23854 - 7.34137i) q^{31} +(-2.91024 - 5.04068i) q^{32} +(-0.455059 + 3.98019i) q^{33} +(1.87899 + 3.25451i) q^{34} +(-4.58689 + 7.94473i) q^{35} +(4.42305 + 1.02478i) q^{36} +(-2.42323 - 4.19715i) q^{37} +(-1.80502 - 3.12638i) q^{38} +(2.58692 + 5.68400i) q^{39} +(-3.54311 + 6.13685i) q^{40} +2.51431 q^{41} +(0.435445 - 3.80864i) q^{42} +5.98639 q^{43} -3.50041 q^{44} +(-2.52959 - 8.29705i) q^{45} +(2.28159 - 3.95182i) q^{46} +(0.521283 + 0.902888i) q^{47} +(-0.259153 + 2.26670i) q^{48} +3.06680 q^{49} +2.34381 q^{50} +(1.05992 - 9.27068i) q^{51} +(-4.67758 + 2.80987i) q^{52} -1.29495 q^{53} +(2.35079 + 2.75896i) q^{54} +(3.34377 + 5.79158i) q^{55} +7.77603 q^{56} +(-1.01820 + 8.90570i) q^{57} +(-1.40234 - 2.42892i) q^{58} +(2.35226 + 4.07423i) q^{59} +(6.95168 - 3.01945i) q^{60} +7.43682 q^{61} +(2.95665 + 5.12107i) q^{62} +(-6.49701 + 6.95630i) q^{63} +1.42575 q^{64} +(9.11732 + 5.05513i) q^{65} +(-2.24575 - 1.66312i) q^{66} +8.36736 q^{67} +8.15316 q^{68} +(-10.3924 + 4.51392i) q^{69} +(-3.19965 - 5.54196i) q^{70} +(-0.680710 + 1.17903i) q^{71} +(-5.01857 + 5.37334i) q^{72} +1.41722 q^{73} +3.38071 q^{74} +(-4.67683 - 3.46350i) q^{75} -7.83218 q^{76} +(3.66927 - 6.35536i) q^{77} +(-4.33602 - 0.419700i) q^{78} +(-0.0365793 - 0.0633573i) q^{79} +(1.90426 + 3.29827i) q^{80} +(-0.613800 - 8.97905i) q^{81} +(-0.876947 + 1.51892i) q^{82} +(-1.08808 - 1.88462i) q^{83} +(-6.68367 - 4.94969i) q^{84} +(-7.78832 - 13.4898i) q^{85} +(-2.08795 + 3.61643i) q^{86} +(-0.791048 + 6.91895i) q^{87} +(2.83430 - 4.90915i) q^{88} +(-0.0891486 - 0.154410i) q^{89} +(5.89459 + 1.36572i) q^{90} +(-0.198393 - 11.4381i) q^{91} +(-4.95003 - 8.57371i) q^{92} +(1.66782 - 14.5877i) q^{93} -0.727256 q^{94} +(7.48170 + 12.9587i) q^{95} +(-8.10164 - 5.99979i) q^{96} +0.130900 q^{97} +(-1.06965 + 1.85268i) q^{98} +(2.02353 + 6.63720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.348782	+	0.604108i	−0.246626	+	0.427169i	−0.962588	−	0.270971i	$-0.912655\pi$
$2$	−0.348782	+	0.604108i	−0.246626	+	0.427169i	0.715962	+	0.698140i	$0.245989\pi$
$3$	1.58866	−	0.690034i	0.917216	−	0.398391i
$3$	1.58866	−	0.690034i	0.917216	−	0.398391i
$4$	0.756702	+	1.31065i	0.378351	+	0.655324i
$5$	1.44568	−	2.50399i	0.646529	−	1.11982i	−0.337417	−	0.941355i	$-0.609553\pi$
$5$	1.44568	−	2.50399i	0.646529	−	1.11982i	0.983946	−	0.178465i	$-0.0571133\pi$
$6$	−0.137242	+	1.20040i	−0.0560289	+	0.490059i
$7$	−3.17282			−1.19921			−0.599607	−	0.800295i	$-0.704676\pi$
$7$	−3.17282			−1.19921			−0.599607	+	0.800295i	$0.704676\pi$
$8$	−2.45082			−0.866497
$9$	2.04771	−	2.19246i	0.682569	−	0.730821i
$10$	1.00846	+	1.74670i	0.318902	+	0.552354i
$11$	−1.15647	+	2.00306i	−0.348688	+	0.603946i	−0.986017	−	0.166646i	$-0.946706\pi$
$11$	−1.15647	+	2.00306i	−0.348688	+	0.603946i	0.637328	+	0.770592i	$0.280039\pi$
$12$	2.10654	+	1.56003i	0.608105	+	0.450341i
$13$	0.0625290	+	3.60501i	0.0173424	+	0.999850i
$13$	0.0625290	+	3.60501i	0.0173424	+	0.999850i
$14$	1.10662	−	1.91673i	0.295757	−	0.512267i
$15$	0.568861	−	4.97558i	0.146879	−	1.28469i
$16$	−0.658602	+	1.14073i	−0.164651	+	0.285183i
$17$	2.69365	−	4.66554i	0.653306	−	1.13156i	−0.329010	−	0.944326i	$-0.606715\pi$
$17$	2.69365	−	4.66554i	0.653306	−	1.13156i	0.982316	−	0.187232i	$-0.0599517\pi$
$18$	0.610282	+	2.00173i	0.143845	+	0.471812i
$19$	−2.58760	+	4.48186i	−0.593636	+	1.02821i	0.400101	+	0.916471i	$0.368975\pi$
$19$	−2.58760	+	4.48186i	−0.593636	+	1.02821i	−0.993738	+	0.111738i	$0.964358\pi$
$20$	4.37581			0.978460
$21$	−5.04055	+	2.18936i	−1.09994	+	0.477757i
$22$	−0.806710	−	1.39726i	−0.171991	−	0.297898i
$23$	−6.54158			−1.36401			−0.682007	−	0.731345i	$-0.738893\pi$
$23$	−6.54158			−1.36401			−0.682007	+	0.731345i	$0.738893\pi$
$24$	−3.89353	+	1.69115i	−0.794764	+	0.345205i
$25$	−1.67999	−	2.90983i	−0.335999	−	0.581967i
$26$	−2.19962	−	1.21959i	−0.431382	−	0.239181i
$27$	1.74024	−	4.89608i	0.334910	−	0.942250i
$28$	−2.40088	−	4.15845i	−0.453724	−	0.785873i
$29$	−2.01034	+	3.48201i	−0.373311	+	0.646593i	−0.990073	−	0.140557i	$-0.955111\pi$
$29$	−2.01034	+	3.48201i	−0.373311	+	0.646593i	0.616762	+	0.787150i	$0.288444\pi$
$30$	2.80738	+	2.07904i	0.512554	+	0.379580i
$31$	4.23854	−	7.34137i	0.761264	−	1.31855i	−0.180935	−	0.983495i	$-0.557912\pi$
$31$	4.23854	−	7.34137i	0.761264	−	1.31855i	0.942199	−	0.335053i	$-0.108754\pi$
$32$	−2.91024	−	5.04068i	−0.514463	−	0.891076i
$33$	−0.455059	+	3.98019i	−0.0792155	+	0.692863i
$34$	1.87899	+	3.25451i	0.322244	+	0.558144i
$35$	−4.58689	+	7.94473i	−0.775326	+	1.34290i
$36$	4.42305	+	1.02478i	0.737175	+	0.170796i
$37$	−2.42323	−	4.19715i	−0.398376	−	0.690008i	0.595150	−	0.803615i	$-0.297093\pi$
$37$	−2.42323	−	4.19715i	−0.398376	−	0.690008i	−0.993526	+	0.113607i	$0.963759\pi$
$38$	−1.80502	−	3.12638i	−0.292812	−	0.507166i
$39$	2.58692	+	5.68400i	0.414238	+	0.910169i
$40$	−3.54311	+	6.13685i	−0.560215	+	0.970321i
$41$	2.51431			0.392670			0.196335	−	0.980537i	$-0.437096\pi$
$41$	2.51431			0.392670			0.196335	+	0.980537i	$0.437096\pi$
$42$	0.435445	−	3.80864i	0.0671906	−	0.587686i
$43$	5.98639			0.912917			0.456458	−	0.889745i	$-0.349118\pi$
$43$	5.98639			0.912917			0.456458	+	0.889745i	$0.349118\pi$
$44$	−3.50041			−0.527707
$45$	−2.52959	−	8.29705i	−0.377089	−	1.23685i
$46$	2.28159	−	3.95182i	0.336401	−	0.582664i
$47$	0.521283	+	0.902888i	0.0760369	+	0.131700i	0.901537	−	0.432703i	$-0.142440\pi$
$47$	0.521283	+	0.902888i	0.0760369	+	0.131700i	−0.825500	+	0.564402i	$0.809107\pi$
$48$	−0.259153	+	2.26670i	−0.0374056	+	0.327170i
$49$	3.06680			0.438115
$50$	2.34381			0.331464
$51$	1.05992	−	9.27068i	0.148419	−	1.29815i
$52$	−4.67758	+	2.80987i	−0.648664	+	0.389659i
$53$	−1.29495			−0.177875			−0.0889376	−	0.996037i	$-0.528347\pi$
$53$	−1.29495			−0.177875			−0.0889376	+	0.996037i	$0.528347\pi$
$54$	2.35079	+	2.75896i	0.319902	+	0.375446i
$55$	3.34377	+	5.79158i	0.450874	+	0.780937i
$56$	7.77603			1.03912
$57$	−1.01820	+	8.90570i	−0.134863	+	1.17959i
$58$	−1.40234	−	2.42892i	−0.184136	−	0.318933i
$59$	2.35226	+	4.07423i	0.306238	+	0.530419i	0.977536	−	0.210768i	$-0.0675964\pi$
$59$	2.35226	+	4.07423i	0.306238	+	0.530419i	−0.671298	+	0.741187i	$0.734263\pi$
$60$	6.95168	−	3.01945i	0.897459	−	0.389810i
$61$	7.43682			0.952187			0.476094	−	0.879395i	$-0.342052\pi$
$61$	7.43682			0.952187			0.476094	+	0.879395i	$0.342052\pi$
$62$	2.95665	+	5.12107i	0.375495	+	0.650377i
$63$	−6.49701	+	6.95630i	−0.818546	+	0.876411i
$64$	1.42575			0.178218
$65$	9.11732	+	5.05513i	1.13086	+	0.627011i
$66$	−2.24575	−	1.66312i	−0.276433	−	0.204716i
$67$	8.36736			1.02224			0.511118	−	0.859510i	$-0.329231\pi$
$67$	8.36736			1.02224			0.511118	+	0.859510i	$0.329231\pi$
$68$	8.15316			0.988716
$69$	−10.3924	+	4.51392i	−1.25110	+	0.543412i
$70$	−3.19965	−	5.54196i	−0.382431	−	0.662390i
$71$	−0.680710	+	1.17903i	−0.0807855	+	0.139925i	−0.903588	−	0.428403i	$-0.859076\pi$
$71$	−0.680710	+	1.17903i	−0.0807855	+	0.139925i	0.822802	+	0.568328i	$0.192410\pi$
$72$	−5.01857	+	5.37334i	−0.591444	+	0.633255i
$73$	1.41722			0.165873			0.0829365	−	0.996555i	$-0.473570\pi$
$73$	1.41722			0.165873			0.0829365	+	0.996555i	$0.473570\pi$
$74$	3.38071			0.393000
$75$	−4.67683	−	3.46350i	−0.540034	−	0.399930i
$76$	−7.83218			−0.898412
$77$	3.66927	−	6.35536i	0.418152	−	0.724261i
$78$	−4.33602	−	0.419700i	−0.490957	−	0.0475216i
$79$	−0.0365793	−	0.0633573i	−0.00411550	−	0.00712825i	0.863960	−	0.503560i	$-0.167977\pi$
$79$	−0.0365793	−	0.0633573i	−0.00411550	−	0.00712825i	−0.868076	+	0.496432i	$0.834643\pi$
$80$	1.90426	+	3.29827i	0.212903	+	0.368758i
$81$	−0.613800	−	8.97905i	−0.0682000	−	0.997672i
$82$	−0.876947	+	1.51892i	−0.0968426	+	0.167736i
$83$	−1.08808	−	1.88462i	−0.119433	−	0.206863i	0.800110	−	0.599853i	$-0.204774\pi$
$83$	−1.08808	−	1.88462i	−0.119433	−	0.206863i	−0.919543	+	0.392989i	$0.871441\pi$
$84$	−6.68367	−	4.94969i	−0.729248	−	0.540055i
$85$	−7.78832	−	13.4898i	−0.844762	−	1.46317i
$86$	−2.08795	+	3.61643i	−0.225149	+	0.389969i
$87$	−0.791048	+	6.91895i	−0.0848093	+	0.741789i
$88$	2.83430	−	4.90915i	0.302137	−	0.523317i
$89$	−0.0891486	−	0.154410i	−0.00944973	−	0.0163674i	0.861262	−	0.508161i	$-0.169675\pi$
$89$	−0.0891486	−	0.154410i	−0.00944973	−	0.0163674i	−0.870712	+	0.491794i	$0.836341\pi$
$90$	5.89459	+	1.36572i	0.621344	+	0.143959i
$91$	−0.198393	−	11.4381i	−0.0207973	−	1.19903i
$92$	−4.95003	−	8.57371i	−0.516077	−	0.893871i
$93$	1.66782	−	14.5877i	0.172945	−	1.51267i
$94$	−0.727256			−0.0750107
$95$	7.48170	+	12.9587i	0.767606	+	1.32953i
$96$	−8.10164	−	5.99979i	−0.826870	−	0.612351i
$97$	0.130900			0.0132909			0.00664545	−	0.999978i	$-0.497885\pi$
$97$	0.130900			0.0132909			0.00664545	+	0.999978i	$0.497885\pi$
$98$	−1.06965	+	1.85268i	−0.108050	+	0.187149i
$99$	2.02353	+	6.63720i	0.203373	+	0.667063i
$100$	2.54251	−	4.40376i	0.254251	−	0.440376i
$101$	−4.36995	+	7.56897i	−0.434826	+	0.753141i	−0.997281	−	0.0736867i	$-0.976524\pi$
$101$	−4.36995	+	7.56897i	−0.434826	+	0.753141i	0.562455	+	0.826828i	$0.309857\pi$
$102$	5.23081	+	3.87375i	0.517927	+	0.383559i
$103$	−8.78259	+	15.2119i	−0.865375	+	1.49887i	0.00130026	+	0.999999i	$0.499586\pi$
$103$	−8.78259	+	15.2119i	−0.865375	+	1.49887i	−0.866675	+	0.498874i	$0.833747\pi$
$104$	−0.153247	−	8.83524i	−0.0150272	−	0.866367i
$105$	−1.80490	+	15.7866i	−0.176140	+	1.54062i
$106$	0.451655	−	0.782290i	0.0438686	−	0.0759827i
$107$	−6.23288	−	10.7957i	−0.602555	−	1.04366i	−0.992433	−	0.122790i	$-0.960816\pi$
$107$	−6.23288	−	10.7957i	−0.602555	−	1.04366i	0.389877	−	0.920867i	$-0.372517\pi$
$108$	7.73387	−	1.42403i	0.744192	−	0.137027i
$109$	4.84430			0.463999			0.232000	−	0.972716i	$-0.425473\pi$
$109$	4.84430			0.463999			0.232000	+	0.972716i	$0.425473\pi$
$110$	−4.66499			−0.444789
$111$	−6.74587	−	4.99576i	−0.640290	−	0.474176i
$112$	2.08963	−	3.61934i	0.197451	−	0.341996i
$113$	−3.07358	−	5.32360i	−0.289138	−	0.500802i	0.684466	−	0.729045i	$-0.260035\pi$
$113$	−3.07358	−	5.32360i	−0.289138	−	0.500802i	−0.973604	+	0.228243i	$0.926702\pi$
$114$	−5.02487	−	3.72125i	−0.470623	−	0.348527i
$115$	−9.45705	+	16.3801i	−0.881874	+	1.52745i
$116$	−6.08491			−0.564970
$117$	8.03189	+	7.24491i	0.742549	+	0.669792i
$118$	−3.28170			−0.302105
$119$	−8.54647	+	14.8029i	−0.783454	+	1.35698i
$120$	−1.39418	+	12.1943i	−0.127271	+	1.11318i
$121$	2.82516	+	4.89332i	0.256833	+	0.444848i
$122$	−2.59383	+	4.49264i	−0.234834	+	0.406745i
$123$	3.99440	−	1.73496i	0.360163	−	0.156436i
$124$	12.8293			1.15210
$125$	4.74187			0.424126
$126$	−1.93632	−	6.35112i	−0.172501	−	0.565803i
$127$	−2.10206	−	3.64088i	−0.186528	−	0.323076i	0.757562	−	0.652763i	$-0.226390\pi$
$127$	−2.10206	−	3.64088i	−0.186528	−	0.323076i	−0.944090	+	0.329687i	$0.893057\pi$
$128$	5.32321	−	9.22006i	0.470509	−	0.814946i
$129$	9.51037	−	4.13082i	0.837341	−	0.363698i
$130$	−6.23380	+	3.74471i	−0.546740	+	0.328433i
$131$	0.309051	−	0.535292i	0.0270019	−	0.0467687i	−0.852209	−	0.523202i	$-0.824737\pi$
$131$	0.309051	−	0.535292i	0.0270019	−	0.0467687i	0.879211	+	0.476433i	$0.158071\pi$
$132$	−5.56098	+	2.41540i	−0.484021	+	0.210234i
$133$	8.21000	−	14.2201i	0.711897	−	1.23304i
$134$	−2.91838	+	5.05479i	−0.252110	+	0.436667i
$135$	−9.74391	−	11.4357i	−0.838622	−	0.984231i
$136$	−6.60166	+	11.4344i	−0.566087	+	0.980492i
$137$	18.9555			1.61948			0.809739	−	0.586791i	$-0.199609\pi$
$137$	18.9555			1.61948			0.809739	+	0.586791i	$0.199609\pi$
$138$	0.897781	−	7.85249i	0.0764242	−	0.668448i
$139$	1.51122	+	2.61752i	0.128180	+	0.222015i	0.922972	−	0.384868i	$-0.125753\pi$
$139$	1.51122	+	2.61752i	0.128180	+	0.222015i	−0.794791	+	0.606883i	$0.792420\pi$
$140$	−13.8837			−1.17338
$141$	1.45117	+	1.07468i	0.122210	+	0.0905046i
$142$	−0.474839	−	0.822445i	−0.0398476	−	0.0690181i
$143$	−7.29337	−	4.04383i	−0.609902	−	0.338162i
$144$	1.15239	+	3.77985i	0.0960326	+	0.314987i
$145$	5.81262	+	10.0678i	0.482712	+	0.836082i
$146$	−0.494301	+	0.856154i	−0.0409086	+	0.0708558i
$147$	4.87212	−	2.11620i	0.401846	−	0.174541i
$148$	3.66732	−	6.35199i	0.301452	−	0.522131i
$149$	2.86713	+	4.96601i	0.234884	+	0.406832i	0.959239	−	0.282596i	$-0.0911955\pi$
$149$	2.86713	+	4.96601i	0.234884	+	0.406832i	−0.724355	+	0.689428i	$0.757862\pi$
$150$	3.72352	−	1.61731i	0.304024	−	0.132052i
$151$	−1.05976	−	1.83556i	−0.0862420	−	0.149376i	0.819678	−	0.572825i	$-0.194153\pi$
$151$	−1.05976	−	1.83556i	−0.0862420	−	0.149376i	−0.905920	+	0.423449i	$0.860819\pi$
$152$	6.34175	−	10.9842i	0.514384	−	0.890940i
$153$	−4.71322	−	15.4594i	−0.381041	−	1.24982i
$154$	2.55955	+	4.43327i	0.206254	+	0.357243i
$155$	−12.2552	−	21.2266i	−0.984358	−	1.70496i
$156$	−5.49219	+	7.69163i	−0.439727	+	0.615823i
$157$	7.70204	−	13.3403i	0.614690	−	1.06467i	−0.375749	−	0.926721i	$-0.622615\pi$
$157$	7.70204	−	13.3403i	0.614690	−	1.06467i	0.990439	−	0.137952i	$-0.0440520\pi$
$158$	0.0510328			0.00405995
$159$	−2.05724	+	0.893560i	−0.163150	+	0.0708639i
$160$	−16.8291			−1.33046
$161$	20.7553			1.63575
$162$	5.63839	+	2.76093i	0.442994	+	0.216919i
$163$	−6.56126	+	11.3644i	−0.513918	+	0.890131i	0.485952	+	0.873985i	$0.338473\pi$
$163$	−6.56126	+	11.3644i	−0.513918	+	0.890131i	−0.999870	+	0.0161459i	$0.994860\pi$
$164$	1.90259	+	3.29538i	0.148567	+	0.257326i
$165$	9.30852	+	6.89356i	0.724667	+	0.536663i
$166$	1.51801			0.117821
$167$	−5.81744			−0.450167			−0.225084	−	0.974339i	$-0.572266\pi$
$167$	−5.81744			−0.450167			−0.225084	+	0.974339i	$0.572266\pi$
$168$	12.3535	−	5.36572i	0.953093	−	0.413975i
$169$	−12.9922	+	0.450835i	−0.999398	+	0.0346796i
$170$	10.8657			0.833361
$171$	4.52766	+	14.8508i	0.346239	+	1.13567i
$172$	4.52992	+	7.84605i	0.345403	+	0.598256i
$173$	−18.0837			−1.37488			−0.687441	−	0.726240i	$-0.741266\pi$
$173$	−18.0837			−1.37488			−0.687441	+	0.726240i	$0.741266\pi$
$174$	−3.90389	−	2.89108i	−0.295953	−	0.219172i
$175$	5.33032	+	9.23239i	0.402934	+	0.697903i
$176$	−1.52331	−	2.63844i	−0.114823	−	0.198880i
$177$	6.54830	+	4.84944i	0.492200	+	0.364506i
$178$	0.124374			0.00932220
$179$	10.9345	+	18.9391i	0.817283	+	1.41558i	0.907677	+	0.419670i	$0.137854\pi$
$179$	10.9345	+	18.9391i	0.817283	+	1.41558i	−0.0903935	+	0.995906i	$0.528812\pi$
$180$	8.96036	−	9.59380i	0.667866	−	0.715079i
$181$	−10.9883			−0.816754			−0.408377	−	0.912813i	$-0.633905\pi$
$181$	−10.9883			−0.816754			−0.408377	+	0.912813i	$0.633905\pi$
$182$	6.97901	+	3.86953i	0.517319	+	0.286829i
$183$	11.8146	−	5.13166i	0.873361	−	0.379343i
$184$	16.0323			1.18191
$185$	−14.0129			−1.03025
$186$	8.23084	+	6.09547i	0.603514	+	0.446942i
$187$	6.23024	+	10.7911i	0.455600	+	0.789123i
$188$	−0.788912	+	1.36644i	−0.0575373	+	0.0996575i
$189$	−5.52148	+	15.5344i	−0.401628	+	1.12996i
$190$	−10.4379			−0.757246
$191$	−17.9834			−1.30124			−0.650618	−	0.759405i	$-0.725490\pi$
$191$	−17.9834			−1.30124			−0.650618	+	0.759405i	$0.725490\pi$
$192$	2.26503	−	0.983814i	0.163465	−	0.0710006i
$193$	3.80167			0.273650			0.136825	−	0.990595i	$-0.456310\pi$
$193$	3.80167			0.273650			0.136825	+	0.990595i	$0.456310\pi$
$194$	−0.0456556	+	0.0790778i	−0.00327788	+	0.00567745i
$195$	17.9726	+	1.73963i	1.28704	+	0.124578i
$196$	2.32066	+	4.01950i	0.165761	+	0.287107i
$197$	−12.3633	−	21.4139i	−0.880848	−	1.52567i	−0.850399	−	0.526138i	$-0.823640\pi$
$197$	−12.3633	−	21.4139i	−0.880848	−	1.52567i	−0.0304487	−	0.999536i	$-0.509694\pi$
$198$	−4.71536	−	1.09250i	−0.335106	−	0.0776406i
$199$	13.8440	−	23.9785i	0.981376	−	1.69979i	0.324329	−	0.945944i	$-0.394862\pi$
$199$	13.8440	−	23.9785i	0.981376	−	1.69979i	0.657047	−	0.753849i	$-0.271805\pi$
$200$	4.11737	+	7.13149i	0.291142	+	0.504273i
$201$	13.2929	−	5.77377i	0.937611	−	0.407250i
$202$	−3.04832	−	5.27984i	−0.214479	−	0.371488i
$203$	6.37845	−	11.0478i	0.447679	−	0.775403i
$204$	12.9526	−	5.62596i	0.906866	−	0.393896i
$205$	3.63490	−	6.29583i	0.253872	−	0.439720i
$206$	−6.12642	−	10.6113i	−0.426848	−	0.739322i
$207$	−13.3952	+	14.3422i	−0.931034	+	0.996851i
$208$	−4.15353	−	2.30294i	−0.287996	−	0.159680i
$209$	−5.98496	−	10.3663i	−0.413988	−	0.717049i
$210$	−8.90731	−	6.59644i	−0.614663	−	0.455197i
$211$	−3.79212			−0.261060			−0.130530	−	0.991444i	$-0.541668\pi$
$211$	−3.79212			−0.261060			−0.130530	+	0.991444i	$0.541668\pi$
$212$	−0.979892	−	1.69722i	−0.0672993	−	0.116566i
$213$	−0.267853	+	2.34279i	−0.0183530	+	0.160525i
$214$	8.69566			0.594423
$215$	8.65442	−	14.9899i	0.590227	−	1.02230i
$216$	−4.26503	+	11.9994i	−0.290198	+	0.816457i
$217$	−13.4481	+	23.2929i	−0.912919	+	1.58122i
$218$	−1.68960	+	2.92648i	−0.114434	+	0.198206i
$219$	2.25149	−	0.977930i	0.152141	−	0.0660824i
$220$	−5.06048	+	8.76501i	−0.341178	+	0.590937i
$221$	16.9877	+	9.41890i	1.14272	+	0.633584i
$222$	5.37081	−	2.33281i	0.360465	−	0.156568i
$223$	−0.555329	+	0.961858i	−0.0371876	+	0.0644108i	−0.884020	−	0.467449i	$-0.845173\pi$
$223$	−0.555329	+	0.961858i	−0.0371876	+	0.0644108i	0.846833	+	0.531860i	$0.178507\pi$
$224$	9.23368	+	15.9932i	0.616951	+	1.06859i
$225$	−9.81984	−	2.27516i	−0.654656	−	0.151677i
$226$	4.28803			0.285236
$227$	−8.34446			−0.553841			−0.276921	−	0.960893i	$-0.589314\pi$
$227$	−8.34446			−0.553841			−0.276921	+	0.960893i	$0.589314\pi$
$228$	−12.4427	+	5.40447i	−0.824038	+	0.357920i
$229$	−3.79878	+	6.57968i	−0.251030	+	0.434797i	−0.963810	−	0.266591i	$-0.914103\pi$
$229$	−3.79878	+	6.57968i	−0.251030	+	0.434797i	0.712779	+	0.701388i	$0.247436\pi$
$230$	−6.59689	−	11.4262i	−0.434986	−	0.753418i
$231$	1.44382	−	12.6285i	0.0949964	−	0.830891i
$232$	4.92699	−	8.53379i	0.323473	−	0.560271i
$233$	0.767797			0.0503001			0.0251500	−	0.999684i	$-0.491994\pi$
$233$	0.767797			0.0503001			0.0251500	+	0.999684i	$0.491994\pi$
$234$	−7.17808	+	2.32524i	−0.469246	+	0.152006i
$235$	3.01444			0.196640
$236$	−3.55992	+	6.16596i	−0.231731	+	0.401370i
$237$	−0.101831	−	0.0754124i	−0.00661463	−	0.00489856i
$238$	−5.96171	−	10.3260i	−0.386440	−	0.669334i
$239$	−10.6216	+	18.3972i	−0.687055	+	1.19001i	0.285732	+	0.958310i	$0.407763\pi$
$239$	−10.6216	+	18.3972i	−0.687055	+	1.19001i	−0.972786	+	0.231704i	$0.925570\pi$
$240$	5.30115	+	3.92584i	0.342188	+	0.253412i
$241$	−22.8611			−1.47261			−0.736306	−	0.676649i	$-0.763431\pi$
$241$	−22.8611			−1.47261			−0.736306	+	0.676649i	$0.763431\pi$
$242$	−3.94146			−0.253367
$243$	−7.17097	−	13.8411i	−0.460018	−	0.887910i
$244$	5.62746	+	9.74704i	0.360261	+	0.623991i
$245$	4.43362	−	7.67926i	0.283254	−	0.490610i
$246$	−0.345070	+	3.01817i	−0.0220008	+	0.192432i
$247$	−16.3189	−	9.04808i	−1.03835	−	0.575716i
$248$	−10.3879	+	17.9924i	−0.659633	+	1.14252i
$249$	−3.02905	−	2.24321i	−0.191958	−	0.142157i
$250$	−1.65388	+	2.86460i	−0.104601	+	0.181173i
$251$	8.21662	−	14.2316i	0.518629	−	0.898291i	−0.481137	−	0.876645i	$-0.659776\pi$
$251$	8.21662	−	14.2316i	0.518629	−	0.898291i	0.999766	−	0.0216457i	$-0.00689057\pi$
$252$	−14.0336	−	3.25144i	−0.884031	−	0.204821i
$253$	7.56513	−	13.1032i	0.475616	−	0.823791i
$254$	2.93265			0.184011
$255$	−21.6814	−	16.0565i	−1.35774	−	1.00550i
$256$	5.13902	+	8.90105i	0.321189	+	0.556315i
$257$	−3.65314			−0.227877			−0.113938	−	0.993488i	$-0.536347\pi$
$257$	−3.65314			−0.227877			−0.113938	+	0.993488i	$0.536347\pi$
$258$	−0.821586	+	7.18604i	−0.0511497	+	0.447383i
$259$	7.68847	+	13.3168i	0.477738	+	0.827467i
$260$	0.273615	+	15.7748i	0.0169689	+	0.978313i
$261$	3.51760	+	11.5377i	0.217734	+	0.714167i
$262$	0.215583	+	0.373400i	0.0133187	+	0.0230688i
$263$	12.4449	−	21.5552i	0.767384	−	1.32915i	−0.171593	−	0.985168i	$-0.554891\pi$
$263$	12.4449	−	21.5552i	0.767384	−	1.32915i	0.938977	−	0.343980i	$-0.111775\pi$
$264$	1.11527	−	9.75476i	0.0686400	−	0.600364i
$265$	−1.87209	+	3.24255i	−0.115001	+	0.199188i
$266$	5.72700	+	9.91945i	0.351145	+	0.608201i
$267$	−0.248175	−	0.183790i	−0.0151881	−	0.0112478i
$268$	6.33161	+	10.9667i	0.386764	+	0.669896i
$269$	−4.43529	+	7.68215i	−0.270424	+	0.468389i	−0.968971	−	0.247176i	$-0.920497\pi$
$269$	−4.43529	+	7.68215i	−0.270424	+	0.468389i	0.698546	+	0.715565i	$0.253831\pi$
$270$	10.3069	−	1.89780i	0.627259	−	0.115496i
$271$	−5.20415	−	9.01385i	−0.316129	−	0.547552i	0.663548	−	0.748134i	$-0.269050\pi$
$271$	−5.20415	−	9.01385i	−0.316129	−	0.547552i	−0.979677	+	0.200582i	$0.935717\pi$
$272$	3.54809	+	6.14547i	0.215134	+	0.372624i
$273$	−8.20783	−	18.0343i	−0.496760	−	1.09149i
$274$	−6.61133	+	11.4512i	−0.399405	+	0.691790i
$275$	7.77144			0.468635
$276$	−13.7801	−	10.2050i	−0.829464	−	0.614272i
$277$	−24.8624			−1.49384			−0.746918	−	0.664916i	$-0.768467\pi$
$277$	−24.8624			−1.49384			−0.746918	+	0.664916i	$0.768467\pi$
$278$	−2.10835			−0.126450
$279$	−7.41640	−	24.3258i	−0.444008	−	1.45635i
$280$	11.2417	−	19.4711i	0.671818	−	1.16362i
$281$	−5.46747	−	9.46994i	−0.326162	−	0.564929i	0.655585	−	0.755122i	$-0.272422\pi$
$281$	−5.46747	−	9.46994i	−0.326162	−	0.564929i	−0.981747	+	0.190192i	$0.939089\pi$
$282$	−1.15536	+	0.501831i	−0.0688010	+	0.0298836i
$283$	29.6384			1.76182			0.880909	−	0.473285i	$-0.156932\pi$
$283$	29.6384			1.76182			0.880909	+	0.473285i	$0.156932\pi$
$284$	−2.06038			−0.122261
$285$	20.8278	+	15.4244i	1.23373	+	0.913660i
$286$	4.98670	−	2.99557i	0.294870	−	0.177132i
$287$	−7.97747			−0.470895
$288$	−17.0108	−	3.94124i	−1.00237	−	0.232240i
$289$	−6.01149	−	10.4122i	−0.353617	−	0.612482i
$290$	−8.10935			−0.476197
$291$	0.207956	−	0.0903255i	0.0121906	−	0.00529498i
$292$	1.07241	+	1.85748i	0.0627583	+	0.108701i
$293$	7.63814	+	13.2296i	0.446225	+	0.772884i	0.998137	−	0.0610186i	$-0.0194349\pi$
$293$	7.63814	+	13.2296i	0.446225	+	0.772884i	−0.551912	+	0.833902i	$0.686102\pi$
$294$	−0.420895	+	3.68138i	−0.0245471	+	0.214702i
$295$	13.6025			0.791966
$296$	5.93890	+	10.2865i	0.345192	+	0.597890i
$297$	7.79461	+	9.14797i	0.452289	+	0.530819i
$298$	−4.00001			−0.231714
$299$	−0.409038	−	23.5825i	−0.0236553	−	1.36381i
$300$	1.00045	−	8.75051i	0.0577611	−	0.505211i
$301$	−18.9938			−1.09478
$302$	1.47850			0.0850781
$303$	−1.71953	+	15.0400i	−0.0987845	+	0.864024i
$304$	−3.40840	−	5.90352i	−0.195485	−	0.338590i
$305$	10.7513	−	18.6218i	0.615616	−	1.06628i
$306$	10.9830	+	2.54466i	0.627857	+	0.145468i
$307$	−2.96530			−0.169238			−0.0846192	−	0.996413i	$-0.526967\pi$
$307$	−2.96530			−0.169238			−0.0846192	+	0.996413i	$0.526967\pi$
$308$	11.1062			0.632833
$309$	−3.45586	+	30.2269i	−0.196597	+	1.71955i
$310$	17.0975			0.971074
$311$	0.483334	−	0.837159i	0.0274073	−	0.0474709i	−0.851996	−	0.523548i	$-0.824608\pi$
$311$	0.483334	−	0.837159i	0.0274073	−	0.0474709i	0.879404	+	0.476077i	$0.157942\pi$
$312$	−6.34008	−	13.9305i	−0.358936	−	0.788658i
$313$	−1.56622	−	2.71277i	−0.0885279	−	0.153335i	0.818361	−	0.574704i	$-0.194883\pi$
$313$	−1.56622	−	2.71277i	−0.0885279	−	0.153335i	−0.906889	+	0.421369i	$0.861550\pi$
$314$	5.37266	+	9.30572i	0.303197	+	0.525152i
$315$	8.02593	+	26.3251i	0.452210	+	1.48325i
$316$	0.0553594	−	0.0958852i	0.00311421	−	0.00539397i
$317$	14.5827	+	25.2580i	0.819046	+	1.41863i	0.906386	+	0.422451i	$0.138830\pi$
$317$	14.5827	+	25.2580i	0.819046	+	1.41863i	−0.0873393	+	0.996179i	$0.527836\pi$
$318$	0.177722	−	1.55445i	0.00996614	−	0.0871694i
$319$	−4.64979	−	8.05367i	−0.260338	−	0.450919i
$320$	2.06118	−	3.57006i	0.115223	−	0.199573i
$321$	−17.3513	−	12.8498i	−0.968457	−	0.717205i
$322$	−7.23907	+	12.5384i	−0.403417	+	0.698739i
$323$	13.9402	+	24.1451i	0.775652	+	1.34347i
$324$	11.3039	−	7.59894i	0.627994	−	0.422163i
$325$	10.3849	−	6.23834i	0.576052	−	0.346041i
$326$	−4.57690	−	7.92742i	−0.253491	−	0.439059i
$327$	7.69596	−	3.34273i	0.425588	−	0.184853i
$328$	−6.16214			−0.340247
$329$	−1.65394	−	2.86470i	−0.0911845	−	0.157936i
$330$	−7.41110	+	3.21900i	−0.407967	+	0.177200i
$331$	7.15450			0.393247			0.196624	−	0.980479i	$-0.437002\pi$
$331$	7.15450			0.393247			0.196624	+	0.980479i	$0.437002\pi$
$332$	1.64671	−	2.85219i	0.0903750	−	0.156534i
$333$	−14.1642	−	3.28170i	−0.776192	−	0.179836i
$334$	2.02902	−	3.51436i	0.111023	−	0.192297i
$335$	12.0966	−	20.9518i	0.660905	−	1.14472i
$336$	0.822248	−	7.19183i	0.0448573	−	0.392347i
$337$	−7.36818	+	12.7621i	−0.401370	+	0.695194i	−0.993892	−	0.110361i	$-0.964799\pi$
$337$	−7.36818	+	12.7621i	−0.401370	+	0.695194i	0.592521	+	0.805555i	$0.298133\pi$
$338$	4.25908	−	8.00592i	0.231664	−	0.435465i
$339$	−8.55635	−	6.33653i	−0.464717	−	0.344153i
$340$	11.7869	−	20.4155i	0.639233	−	1.10718i
$341$	9.80348	+	16.9801i	0.530888	+	0.919525i
$342$	−10.5506	−	2.44447i	−0.570512	−	0.132182i
$343$	12.4793			0.673821
$344$	−14.6716			−0.791039
$345$	−3.72125	+	32.5481i	−0.200346	+	1.75233i
$346$	6.30728	−	10.9245i	0.339081	−	0.587306i
$347$	9.95655	+	17.2453i	0.534496	+	0.925774i	0.999188	+	0.0403011i	$0.0128317\pi$
$347$	9.95655	+	17.2453i	0.534496	+	0.925774i	−0.464692	+	0.885472i	$0.653835\pi$
$348$	−9.66688	+	4.19880i	−0.518199	+	0.225079i
$349$	13.8845	−	24.0487i	0.743221	−	1.28730i	−0.207801	−	0.978171i	$-0.566630\pi$
$349$	13.8845	−	24.0487i	0.743221	−	1.28730i	0.951021	−	0.309125i	$-0.100036\pi$
$350$	−7.43648			−0.397496
$351$	17.7592	+	5.96744i	0.947917	+	0.318518i
$352$	13.4624			0.717549
$353$	−14.2852	+	24.7427i	−0.760326	+	1.31692i	0.182357	+	0.983232i	$0.441627\pi$
$353$	−14.2852	+	24.7427i	−0.760326	+	1.31692i	−0.942683	+	0.333691i	$0.891706\pi$
$354$	−5.21351	+	2.26448i	−0.277095	+	0.120356i
$355$	1.96818	+	3.40899i	0.104460	+	0.180930i
$356$	0.134918	−	0.233685i	0.00715064	−	0.0123853i
$357$	−3.36295	+	29.4142i	−0.177986	+	1.55677i
$358$	−15.2550			−0.806253
$359$	−15.4518			−0.815515			−0.407757	−	0.913090i	$-0.633689\pi$
$359$	−15.4518			−0.815515			−0.407757	+	0.913090i	$0.633689\pi$
$360$	6.19957	+	20.3346i	0.326746	+	1.07173i
$361$	−3.89136	−	6.74004i	−0.204809	−	0.354739i
$362$	3.83252	−	6.63812i	0.201433	−	0.348892i
$363$	7.86479	+	5.82439i	0.412795	+	0.305701i
$364$	14.8411	−	8.91523i	0.777886	−	0.467285i
$365$	2.04885	−	3.54871i	0.107242	−	0.185748i
$366$	−1.02064	+	8.92712i	−0.0533500	+	0.466628i
$367$	−0.235591	+	0.408055i	−0.0122977	+	0.0213003i	−0.872109	−	0.489312i	$-0.837248\pi$
$367$	−0.235591	+	0.408055i	−0.0122977	+	0.0213003i	0.859811	+	0.510612i	$0.170581\pi$
$368$	4.30830	−	7.46220i	0.224586	−	0.388994i
$369$	5.14858	−	5.51254i	0.268024	−	0.286972i
$370$	4.88743	−	8.46528i	0.254086	−	0.440089i
$371$	4.10865			0.213310
$372$	20.3814	−	8.85262i	1.05673	−	0.458987i
$373$	−16.1744	−	28.0148i	−0.837478	−	1.45055i	−0.891997	−	0.452041i	$-0.850696\pi$
$373$	−16.1744	−	28.0148i	−0.837478	−	1.45055i	0.0545197	−	0.998513i	$-0.482637\pi$
$374$	−8.69198			−0.449451
$375$	7.53324	−	3.27205i	0.389015	−	0.168968i
$376$	−1.27757	−	2.21282i	−0.0658857	−	0.114117i
$377$	−12.6784	−	7.02956i	−0.652970	−	0.362041i
$378$	−7.45865	−	8.75368i	−0.383632	−	0.450241i
$379$	0.713364	+	1.23558i	0.0366430	+	0.0634676i	0.883765	−	0.467930i	$-0.155000\pi$
$379$	0.713364	+	1.23558i	0.0366430	+	0.0634676i	−0.847122	+	0.531398i	$0.821667\pi$
$380$	−11.3228	+	19.6117i	−0.580849	+	1.00606i
$381$	−5.85181	−	4.33364i	−0.299797	−	0.222019i
$382$	6.27229	−	10.8639i	0.320919	−	0.555847i
$383$	7.97219	+	13.8082i	0.407360	+	0.705568i	0.994593	−	0.103850i	$-0.0331162\pi$
$383$	7.97219	+	13.8082i	0.407360	+	0.705568i	−0.587233	+	0.809418i	$0.699783\pi$
$384$	2.09463	−	18.3208i	0.106891	−	0.934928i
$385$	−10.6092	−	18.3757i	−0.540695	−	0.936510i
$386$	−1.32595	+	2.29662i	−0.0674892	+	0.116895i
$387$	12.2584	−	13.1250i	0.623128	−	0.667179i
$388$	0.0990524	+	0.171564i	0.00502863	+	0.00870984i
$389$	10.0545	+	17.4150i	0.509785	+	0.882973i	0.999936	+	0.0113357i	$0.00360835\pi$
$389$	10.0545	+	17.4150i	0.509785	+	0.882973i	−0.490151	+	0.871638i	$0.663058\pi$
$390$	−7.31943	+	10.2506i	−0.370634	+	0.519060i
$391$	−17.6207	+	30.5200i	−0.891119	+	1.54346i
$392$	−7.51619			−0.379625
$393$	0.121608	−	1.06366i	0.00613434	−	0.0536543i
$394$	17.2484			0.868960
$395$	−0.211528			−0.0106431
$396$	−7.16781	+	7.67452i	−0.360196	+	0.385659i
$397$	1.77422	−	3.07304i	0.0890454	−	0.154231i	−0.818062	−	0.575129i	$-0.804952\pi$
$397$	1.77422	−	3.07304i	0.0890454	−	0.154231i	0.907108	+	0.420898i	$0.138285\pi$
$398$	9.65708	+	16.7266i	0.484066	+	0.838427i
$399$	3.23055	−	28.2562i	0.161730	−	1.41458i
$400$	4.42579			0.221290
$401$	26.6424			1.33046			0.665229	−	0.746640i	$-0.268334\pi$
$401$	26.6424			1.33046			0.665229	+	0.746640i	$0.268334\pi$
$402$	−1.14835	+	10.0441i	−0.0572747	+	0.500957i
$403$	26.7307	+	14.8209i	1.33155	+	0.738283i
$404$	−13.2270			−0.658068
$405$	−23.3708	−	11.4439i	−1.16131	−	0.568652i
$406$	4.44937	+	7.70654i	0.220819	+	0.382469i
$407$	11.2095			0.555636
$408$	−2.59769	+	22.7208i	−0.128605	+	1.12485i
$409$	6.76077	+	11.7100i	0.334299	+	0.579022i	0.983350	−	0.181723i	$-0.0581673\pi$
$409$	6.76077	+	11.7100i	0.334299	+	0.579022i	−0.649051	+	0.760745i	$0.724834\pi$
$410$	2.53557	+	4.39174i	0.125223	+	0.216893i
$411$	30.1139	−	13.0799i	1.48541	−	0.645186i
$412$	−26.5832			−1.30966
$413$	−7.46329	−	12.9268i	−0.367245	−	0.636086i
$414$	−3.99221	−	13.0945i	−0.196207	−	0.643558i
$415$	−6.29209			−0.308866
$416$	17.9897	−	10.8066i	0.882020	−	0.529839i
$417$	4.20700	+	3.11556i	0.206018	+	0.152570i
$418$	8.34978			0.408401
$419$	−12.6059			−0.615837			−0.307918	−	0.951413i	$-0.599632\pi$
$419$	−12.6059			−0.615837			−0.307918	+	0.951413i	$0.599632\pi$
$420$	−22.0565	+	9.58019i	−1.07625	+	0.467466i
$421$	4.49703	+	7.78908i	0.219172	+	0.379617i	0.954555	−	0.298035i	$-0.0963312\pi$
$421$	4.49703	+	7.78908i	0.219172	+	0.379617i	−0.735383	+	0.677651i	$0.762998\pi$
$422$	1.32262	−	2.29085i	0.0643842	−	0.111517i
$423$	3.04698	+	0.705956i	0.148149	+	0.0343247i
$424$	3.17370			0.154128
$425$	−18.1013			−0.878040
$426$	−1.32187	−	0.978934i	−0.0640450	−	0.0474295i
$427$	−23.5957			−1.14188
$428$	9.43287	−	16.3382i	0.455955	−	0.789737i
$429$	−14.3771	−	1.39161i	−0.694133	−	0.0671877i
$430$	6.03701	+	10.4564i	0.291131	+	0.504253i
$431$	−8.05558	−	13.9527i	−0.388024	−	0.672077i	0.604160	−	0.796863i	$-0.293509\pi$
$431$	−8.05558	−	13.9527i	−0.388024	−	0.672077i	−0.992184	+	0.124786i	$0.960175\pi$
$432$	4.43899	+	5.20972i	0.213571	+	0.250653i
$433$	−13.5252	+	23.4264i	−0.649981	+	1.12580i	0.333146	+	0.942875i	$0.391890\pi$
$433$	−13.5252	+	23.4264i	−0.649981	+	1.12580i	−0.983127	+	0.182924i	$0.941444\pi$
$434$	−9.38093	−	16.2482i	−0.450299	−	0.779941i
$435$	16.1814	+	11.9834i	0.775839	+	0.574559i
$436$	3.66569	+	6.34916i	0.175555	+	0.304070i
$437$	16.9270	−	29.3184i	0.809729	−	1.40249i
$438$	−0.194502	+	1.70122i	−0.00929368	+	0.0812877i
$439$	−1.15165	+	1.99471i	−0.0549651	+	0.0952024i	−0.892199	−	0.451643i	$-0.850838\pi$
$439$	−1.15165	+	1.99471i	−0.0549651	+	0.0952024i	0.837234	+	0.546845i	$0.184171\pi$
$440$	−8.19499	−	14.1941i	−0.390681	−	0.676679i
$441$	6.27991	−	6.72386i	0.299043	−	0.320184i
$442$	−11.6150	+	6.97728i	−0.552471	+	0.331875i
$443$	13.1481	+	22.7731i	0.624683	+	1.08198i	0.988602	+	0.150552i	$0.0481053\pi$
$443$	13.1481	+	22.7731i	0.624683	+	1.08198i	−0.363919	+	0.931431i	$0.618561\pi$
$444$	1.44306	−	12.6218i	0.0684844	−	0.599002i
$445$	−0.515522			−0.0244381
$446$	−0.387377	−	0.670957i	−0.0183428	−	0.0317707i
$447$	7.98162	+	5.91091i	0.377518	+	0.279576i
$448$	−4.52364			−0.213722
$449$	−4.46646	+	7.73613i	−0.210785	+	0.365091i	−0.951960	−	0.306221i	$-0.900935\pi$
$449$	−4.46646	+	7.73613i	−0.210785	+	0.365091i	0.741175	+	0.671311i	$0.234269\pi$
$450$	4.79942	−	5.13871i	0.226247	−	0.242241i
$451$	−2.90772	+	5.03633i	−0.136919	+	0.237151i
$452$	4.65157	−	8.05676i	0.218791	−	0.378958i
$453$	−2.95020	−	2.18481i	−0.138612	−	0.102652i
$454$	2.91040	−	5.04095i	0.136592	−	0.236584i
$455$	−28.9276	−	16.0390i	−1.35615	−	0.751921i
$456$	2.49542	−	21.8263i	0.116859	−	1.02211i
$457$	−9.44075	+	16.3519i	−0.441620	+	0.764907i	−0.997810	−	0.0661475i	$-0.978929\pi$
$457$	−9.44075	+	16.3519i	−0.441620	+	0.764907i	0.556190	+	0.831055i	$0.312263\pi$
$458$	−2.64989	−	4.58974i	−0.123821	−	0.214465i
$459$	−18.1552	−	21.3075i	−0.847413	−	0.994548i
$460$	−28.6247			−1.33463
$461$	−23.2255			−1.08172			−0.540860	−	0.841113i	$-0.681901\pi$
$461$	−23.2255			−1.08172			−0.540860	+	0.841113i	$0.681901\pi$
$462$	7.12537	+	5.27680i	0.331502	+	0.245499i
$463$	1.15005	−	1.99194i	0.0534473	−	0.0925735i	−0.838064	−	0.545572i	$-0.816312\pi$
$463$	1.15005	−	1.99194i	0.0534473	−	0.0925735i	0.891511	+	0.452999i	$0.149646\pi$
$464$	−2.64803	−	4.58652i	−0.122932	−	0.212924i
$465$	−34.1164	−	25.2654i	−1.58211	−	1.17165i
$466$	−0.267794	+	0.463832i	−0.0124053	+	0.0214866i
$467$	−22.4713			−1.03985			−0.519925	−	0.854212i	$-0.674040\pi$
$467$	−22.4713			−1.03985			−0.519925	+	0.854212i	$0.674040\pi$
$468$	−3.41776	+	16.0092i	−0.157986	+	0.740026i
$469$	−26.5482			−1.22588
$470$	−1.05138	+	1.82104i	−0.0484966	+	0.0839985i
$471$	3.03067	−	26.5080i	0.139646	−	1.22142i
$472$	−5.76497	−	9.98521i	−0.265354	−	0.459607i
$473$	−6.92308	+	11.9911i	−0.318323	+	0.551352i
$474$	0.0810740	−	0.0352144i	0.00372385	−	0.00161745i
$475$	17.3886			0.797845
$476$	−25.8685			−1.18568
$477$	−2.65168	+	2.83913i	−0.121412	+	0.129995i
$478$	−7.40925	−	12.8332i	−0.338891	−	0.586976i
$479$	2.43604	−	4.21935i	0.111306	−	0.192787i	−0.804991	−	0.593287i	$-0.797830\pi$
$479$	2.43604	−	4.21935i	0.111306	−	0.192787i	0.916297	+	0.400500i	$0.131163\pi$
$480$	−26.7358	+	11.6127i	−1.22032	+	0.530044i
$481$	14.9793	−	8.99820i	0.682995	−	0.410283i
$482$	7.97353	−	13.8106i	0.363184	−	0.629054i
$483$	32.9732	−	14.3219i	1.50033	−	0.651667i
$484$	−4.27561	+	7.40558i	−0.194346	+	0.336617i
$485$	0.189240	−	0.327773i	0.00859294	−	0.0148834i
$486$	10.8626	+	0.495501i	0.492740	+	0.0224764i
$487$	−6.17126	+	10.6889i	−0.279647	+	0.484362i	−0.971297	−	0.237870i	$-0.923551\pi$
$487$	−6.17126	+	10.6889i	−0.279647	+	0.484362i	0.691650	+	0.722233i	$0.256884\pi$
$488$	−18.2263			−0.825067
$489$	−2.58179	+	22.5818i	−0.116753	+	1.02118i
$490$	3.09273	+	5.35677i	0.139715	+	0.241994i
$491$	−28.1584			−1.27077			−0.635386	−	0.772194i	$-0.719159\pi$
$491$	−28.1584			−1.27077			−0.635386	+	0.772194i	$0.719159\pi$
$492$	5.29649	+	3.92240i	0.238784	+	0.176835i
$493$	10.8303	+	18.7586i	0.487772	+	0.844846i
$494$	11.1578	−	6.70259i	0.502012	−	0.301564i
$495$	19.5449	+	4.52836i	0.878478	+	0.203535i
$496$	5.58303	+	9.67008i	0.250685	+	0.434200i
$497$	2.15977	−	3.74084i	0.0968791	−	0.167799i
$498$	2.41161	−	1.04748i	0.108067	−	0.0469388i
$499$	12.0417	−	20.8568i	0.539061	−	0.933681i	−0.459894	−	0.887974i	$-0.652113\pi$
$499$	12.0417	−	20.8568i	0.539061	−	0.933681i	0.998955	−	0.0457069i	$-0.0145540\pi$
$500$	3.58819	+	6.21492i	0.160469	+	0.277940i
$501$	−9.24196	+	4.01423i	−0.412900	+	0.179343i
$502$	5.73162	+	9.92745i	0.255815	+	0.443084i
$503$	−1.66703	+	2.88738i	−0.0743291	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$503$	−1.66703	+	2.88738i	−0.0743291	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$504$	15.9230	−	17.0487i	0.709268	−	0.759408i
$505$	12.6351	+	21.8847i	0.562255	+	0.973855i
$506$	5.27716	+	9.14031i	0.234598	+	0.406336i
$507$	−20.3291	+	9.68127i	−0.902848	+	0.429960i
$508$	3.18127	−	5.51013i	0.141146	−	0.244472i
$509$	34.1316			1.51286			0.756429	−	0.654076i	$-0.226942\pi$
$509$	34.1316			1.51286			0.756429	+	0.654076i	$0.226942\pi$
$510$	17.2619	−	7.49770i	0.764372	−	0.332004i
$511$	−4.49659			−0.198917
$512$	14.1232			0.624165
$513$	17.4405	+	20.4686i	0.770015	+	0.903711i
$514$	1.27415	−	2.20689i	0.0562004	−	0.0973419i
$515$	25.3937	+	43.9831i	1.11898	+	1.93813i
$516$	12.6106	+	9.33894i	0.555149	+	0.411124i
$517$	−2.41139			−0.106053
$518$	−10.7264			−0.471291
$519$	−28.7290	+	12.4784i	−1.26106	+	0.547741i
$520$	−22.3449	−	12.3892i	−0.979891	−	0.543303i
$521$	42.5774			1.86535			0.932675	−	0.360719i	$-0.117469\pi$
$521$	42.5774			1.86535			0.932675	+	0.360719i	$0.117469\pi$
$522$	−8.19691	−	1.89914i	−0.358769	−	0.0831232i
$523$	−1.45092	−	2.51307i	−0.0634443	−	0.109889i	0.832559	−	0.553937i	$-0.186875\pi$
$523$	−1.45092	−	2.51307i	−0.0634443	−	0.109889i	−0.896003	+	0.444048i	$0.853542\pi$
$524$	0.935439			0.0408648
$525$	14.8388	+	10.9891i	0.647616	+	0.479602i
$526$	8.68109	+	15.0361i	0.378514	+	0.655605i
$527$	−22.8343	−	39.5501i	−0.994677	−	1.72283i
$528$	−4.24064	−	3.14047i	−0.184550	−	0.136671i
$529$	19.7923			0.860535
$530$	−1.30590	−	2.26188i	−0.0567247	−	0.0982500i
$531$	13.7493	+	3.18558i	0.596670	+	0.138243i
$532$	24.8501			1.07739
$533$	0.157217	+	9.06412i	0.00680984	+	0.392611i
$534$	0.197588	−	0.0858220i	0.00855046	−	0.00371388i
$535$	−36.0431			−1.55828
$536$	−20.5069			−0.885765
$537$	30.4399	+	22.5427i	1.31358	+	0.972790i
$538$	−3.09390	−	5.35879i	−0.133387	−	0.231034i
$539$	−3.54666	+	6.14300i	−0.152765	+	0.264598i
$540$	7.61496	−	21.4243i	0.327696	−	0.921954i
$541$	22.6048			0.971857			0.485929	−	0.873999i	$-0.338482\pi$
$541$	22.6048			0.971857			0.485929	+	0.873999i	$0.338482\pi$
$542$	7.26045			0.311863
$543$	−17.4567	+	7.58230i	−0.749140	+	0.325388i
$544$	−31.3567			−1.34441
$545$	7.00331	−	12.1301i	0.299989	−	0.519596i
$546$	13.7574	+	1.33163i	0.588763	+	0.0569886i
$547$	−18.1136	−	31.3737i	−0.774481	−	1.34144i	−0.935085	−	0.354422i	$-0.884678\pi$
$547$	−18.1136	−	31.3737i	−0.774481	−	1.34144i	0.160604	−	0.987019i	$-0.448656\pi$
$548$	14.3437	+	24.8440i	0.612731	+	1.06128i
$549$	15.2284	−	16.3050i	0.649933	−	0.695879i
$550$	−2.71054	+	4.69479i	−0.115578	+	0.200186i
$551$	−10.4039	−	18.0201i	−0.443222	−	0.767682i
$552$	25.4699	−	11.0628i	1.08407	−	0.470864i
$553$	0.116060	+	0.201021i	0.00493536	+	0.00854830i
$554$	8.67155	−	15.0196i	0.368419	−	0.638120i
$555$	−22.2617	+	9.66936i	−0.944958	+	0.410441i
$556$	−2.28709	+	3.96136i	−0.0969944	+	0.167999i
$557$	1.08919	+	1.88653i	0.0461503	+	0.0799347i	0.888178	−	0.459500i	$-0.151971\pi$
$557$	1.08919	+	1.88653i	0.0461503	+	0.0799347i	−0.842027	+	0.539435i	$0.818638\pi$
$558$	17.2821	+	4.00409i	0.731610	+	0.169507i
$559$	0.374323	+	21.5810i	0.0158322	+	0.912779i
$560$	−6.04188	−	10.4648i	−0.255316	−	0.442220i
$561$	17.3440	+	12.8443i	0.732263	+	0.542288i
$562$	7.62782			0.321760
$563$	−3.82852	−	6.63120i	−0.161353	−	0.279472i	0.774001	−	0.633184i	$-0.218252\pi$
$563$	−3.82852	−	6.63120i	−0.161353	−	0.279472i	−0.935354	+	0.353713i	$0.884919\pi$
$564$	−0.310429	+	2.71518i	−0.0130714	+	0.114330i
$565$	−17.7737			−0.747744
$566$	−10.3373	+	17.9048i	−0.434510	+	0.752594i
$567$	1.94748	+	28.4889i	0.0817864	+	1.19642i
$568$	1.66830	−	2.88958i	0.0700004	−	0.121244i
$569$	13.2970	−	23.0311i	0.557440	−	0.965514i	−0.440269	−	0.897866i	$-0.645117\pi$
$569$	13.2970	−	23.0311i	0.557440	−	0.965514i	0.997709	−	0.0676486i	$-0.0215497\pi$
$570$	−16.5823	+	7.20252i	−0.694558	+	0.301680i
$571$	21.6621	−	37.5199i	0.906531	−	1.57016i	0.0876825	−	0.996148i	$-0.472054\pi$
$571$	21.6621	−	37.5199i	0.906531	−	1.57016i	0.818849	−	0.574010i	$-0.194613\pi$
$572$	−0.218877	−	12.6190i	−0.00915171	−	0.527627i
$573$	−28.5696	+	12.4092i	−1.19351	+	0.518401i
$574$	2.78240	−	4.81925i	0.116135	−	0.201152i
$575$	10.9898	+	19.0349i	0.458307	+	0.793811i
$576$	2.91951	−	3.12590i	0.121646	−	0.130246i
$577$	−24.5681			−1.02278			−0.511392	−	0.859348i	$-0.670870\pi$
$577$	−24.5681			−1.02278			−0.511392	+	0.859348i	$0.670870\pi$
$578$	8.38679			0.348844
$579$	6.03957	−	2.62328i	0.250996	−	0.109020i
$580$	−8.79685	+	15.2366i	−0.365269	+	0.632665i
$581$	3.45229	+	5.97955i	0.143225	+	0.248073i
$582$	−0.0179650	+	0.157132i	−0.000744674	+	0.00651333i
$583$	1.49757	−	2.59387i	0.0620230	−	0.107427i
$584$	−3.47336			−0.143729
$585$	29.7528	−	9.63799i	1.23013	−	0.398482i
$586$	−10.6562			−0.440202
$587$	6.97935	−	12.0886i	0.288069	−	0.498950i	−0.685280	−	0.728280i	$-0.740320\pi$
$587$	6.97935	−	12.0886i	0.288069	−	0.498950i	0.973349	+	0.229330i	$0.0736535\pi$
$588$	6.46033	+	4.78430i	0.266420	+	0.197301i
$589$	21.9353	+	37.9931i	0.903829	+	1.56548i
$590$	−4.74429	+	8.21735i	−0.195319	+	0.338303i
$591$	−34.4174	−	25.4883i	−1.41574	−	1.04845i
$592$	6.38377			0.262371
$593$	−42.3659			−1.73976			−0.869880	−	0.493263i	$-0.835804\pi$
$593$	−42.3659			−1.73976			−0.869880	+	0.493263i	$0.835804\pi$
$594$	−8.24498	+	1.51814i	−0.338296	+	0.0622900i
$595$	24.7110	+	42.8006i	1.01305	+	1.75465i
$596$	−4.33913	+	7.51559i	−0.177738	+	0.307851i
$597$	5.44748	−	47.6467i	0.222951	−	1.95005i
$598$	14.3890	+	7.97803i	0.588411	+	0.326246i
$599$	−0.140194	+	0.242822i	−0.00572815	+	0.00992145i	−0.868875	−	0.495031i	$-0.835157\pi$
$599$	−0.140194	+	0.242822i	−0.00572815	+	0.00992145i	0.863147	+	0.504953i	$0.168490\pi$
$600$	11.4621	+	8.48842i	0.467938	+	0.346538i
$601$	−8.78997	+	15.2247i	−0.358550	+	0.621028i	−0.987719	−	0.156241i	$-0.950062\pi$
$601$	−8.78997	+	15.2247i	−0.358550	+	0.621028i	0.629168	+	0.777269i	$0.283396\pi$
$602$	6.62468	−	11.4743i	0.270002	−	0.467657i
$603$	17.1339	−	18.3451i	0.697746	−	0.747072i
$604$	1.60385	−	2.77794i	0.0652596	−	0.113033i
$605$	16.3371			0.664199
$606$	−8.48602	−	6.28445i	−0.344721	−	0.255288i
$607$	20.0915	+	34.7995i	0.815489	+	1.41247i	0.908976	+	0.416848i	$0.136865\pi$
$607$	20.0915	+	34.7995i	0.815489	+	1.41247i	−0.0934872	+	0.995620i	$0.529801\pi$
$608$	30.1222			1.22162
$609$	2.50986	−	21.9526i	0.101704	−	0.889564i
$610$	7.49970	+	12.9899i	0.303654	+	0.525944i
$611$	−3.22232	+	1.93569i	−0.130361	+	0.0783095i
$612$	16.6953	−	17.8755i	0.674867	−	0.722575i
$613$	12.3197	+	21.3384i	0.497589	+	0.861849i	0.999996	−	0.00278192i	$-0.000885515\pi$
$613$	12.3197	+	21.3384i	0.497589	+	0.861849i	−0.502407	+	0.864631i	$0.667552\pi$
$614$	1.03424	−	1.79136i	0.0417386	−	0.0722934i
$615$	1.43030	−	12.5102i	0.0576751	−	0.504458i
$616$	−8.99273	+	15.5759i	−0.362327	+	0.627570i
$617$	−18.0518	−	31.2667i	−0.726739	−	1.25875i	−0.958254	−	0.285918i	$-0.907701\pi$
$617$	−18.0518	−	31.2667i	−0.726739	−	1.25875i	0.231515	−	0.972831i	$-0.425632\pi$
$618$	−17.0550	−	12.6303i	−0.686051	−	0.508065i
$619$	−19.1602	−	33.1865i	−0.770114	−	1.33388i	−0.937500	−	0.347986i	$-0.886866\pi$
$619$	−19.1602	−	33.1865i	−0.770114	−	1.33388i	0.167386	−	0.985892i	$-0.446468\pi$
$620$	18.5470	−	32.1244i	0.744867	−	1.29015i
$621$	−11.3839	+	32.0281i	−0.456822	+	1.28524i
$622$	0.337156	+	0.583971i	0.0135187	+	0.0234151i
$623$	0.282853	+	0.489915i	0.0113323	+	0.0196280i
$624$	−8.18767	−	0.792516i	−0.327769	−	0.0317260i
$625$	15.2552	−	26.4228i	0.610208	−	1.05691i
$626$	2.18507			0.0873331
$627$	−16.6612	−	12.3387i	−0.665382	−	0.492759i
$628$	23.3126			0.930274
$629$	−26.1093			−1.04105
$630$	−18.7025	−	4.33318i	−0.745125	−	0.172638i
$631$	4.85653	−	8.41176i	0.193335	−	0.334867i	−0.753018	−	0.658000i	$-0.771403\pi$
$631$	4.85653	−	8.41176i	0.193335	−	0.334867i	0.946354	+	0.323133i	$0.104736\pi$
$632$	0.0896495	+	0.155278i	0.00356607	+	0.00617661i
$633$	−6.02440	+	2.61669i	−0.239448	+	0.104004i
$634$	−20.3447			−0.807992
$635$	−12.1557			−0.482383
$636$	−2.72786	−	2.02016i	−0.108167	−	0.0801045i
$637$	0.191764	+	11.0559i	0.00759797	+	0.438049i
$638$	6.48704			0.256825
$639$	1.19108	+	3.90673i	0.0471182	+	0.154548i
$640$	−15.3913	−	26.6586i	−0.608396	−	1.05377i
$641$	−29.9584			−1.18329			−0.591643	−	0.806200i	$-0.701521\pi$
$641$	−29.9584			−1.18329			−0.591643	+	0.806200i	$0.701521\pi$
$642$	13.8145	−	6.00030i	0.545214	−	0.236813i
$643$	−9.27872	−	16.0712i	−0.365917	−	0.633787i	0.623006	−	0.782217i	$-0.285911\pi$
$643$	−9.27872	−	16.0712i	−0.365917	−	0.633787i	−0.988923	+	0.148430i	$0.952578\pi$
$644$	15.7056	+	27.2029i	0.618886	+	1.07194i
$645$	3.40543	−	29.7858i	0.134089	−	1.17281i
$646$	−19.4483			−0.765184
$647$	17.4909	+	30.2951i	0.687637	+	1.19102i	0.972600	+	0.232484i	$0.0746852\pi$
$647$	17.4909	+	30.2951i	0.687637	+	1.19102i	−0.284963	+	0.958538i	$0.591981\pi$
$648$	1.50432	+	22.0061i	0.0590951	+	0.864479i
$649$	−10.8812			−0.427126
$650$	0.146556	+	8.44944i	0.00574839	+	0.331414i
$651$	−5.29171	+	46.2842i	−0.207398	+	1.81402i
$652$	−19.8597			−0.777765
$653$	−15.6864			−0.613858			−0.306929	−	0.951732i	$-0.599301\pi$
$653$	−15.6864			−0.613858			−0.306929	+	0.951732i	$0.599301\pi$
$654$	−0.664842	+	5.81507i	−0.0259974	+	0.227387i
$655$	−0.893579	−	1.54772i	−0.0349150	−	0.0604746i
$656$	−1.65593	+	2.86816i	−0.0646533	+	0.111983i
$657$	2.90205	−	3.10720i	0.113220	−	0.121224i
$658$	2.30745			0.0899539
$659$	22.3025			0.868783			0.434391	−	0.900724i	$-0.356963\pi$
$659$	22.3025			0.868783			0.434391	+	0.900724i	$0.356963\pi$
$660$	−1.99125	+	17.4166i	−0.0775092	+	0.677939i
$661$	16.6050			0.645859			0.322930	−	0.946423i	$-0.395332\pi$
$661$	16.6050			0.645859			0.322930	+	0.946423i	$0.395332\pi$
$662$	−2.49536	+	4.32209i	−0.0969849	+	0.167983i
$663$	33.4872	+	3.24135i	1.30053	+	0.125884i
$664$	2.66670	+	4.61886i	0.103488	+	0.179246i
$665$	−23.7381	−	41.1156i	−0.920524	−	1.59439i
$666$	6.92270	−	7.41209i	0.268249	−	0.287213i
$667$	13.1508	−	22.7779i	0.509201	−	0.881962i
$668$	−4.40207	−	7.62462i	−0.170321	−	0.295005i
$669$	−0.218516	+	1.91126i	−0.00844833	+	0.0738938i
$670$	8.43811	+	14.6152i	0.325993	+	0.564636i
$671$	−8.60045	+	14.8964i	−0.332017	+	0.575069i
$672$	25.7051	+	19.0363i	0.991594	+	0.734340i
$673$	4.31242	−	7.46933i	0.166232	−	0.287922i	−0.770860	−	0.637004i	$-0.780173\pi$
$673$	4.31242	−	7.46933i	0.166232	−	0.287922i	0.937092	+	0.349083i	$0.113507\pi$
$674$	−5.13978	−	8.90235i	−0.197977	−	0.342906i
$675$	−17.1704	+	3.16156i	−0.660888	+	0.121689i
$676$	−10.4221	−	16.6870i	−0.400850	−	0.641808i
$677$	11.5236	+	19.9595i	0.442888	+	0.767105i	0.997902	−	0.0647358i	$-0.0206205\pi$
$677$	11.5236	+	19.9595i	0.442888	+	0.767105i	−0.555014	+	0.831841i	$0.687287\pi$
$678$	6.81225	−	2.95889i	0.261623	−	0.113635i
$679$	−0.415323			−0.0159386
$680$	19.0878	+	33.0610i	0.731984	+	1.26783i
$681$	−13.2565	+	5.75796i	−0.507992	+	0.220646i
$682$	−13.6771			−0.523723
$683$	−13.6294	+	23.6068i	−0.521514	+	0.903289i	0.478172	+	0.878266i	$0.341299\pi$
$683$	−13.6294	+	23.6068i	−0.521514	+	0.903289i	−0.999687	+	0.0250235i	$0.992034\pi$
$684$	−16.0380	+	17.1718i	−0.613228	+	0.656579i
$685$	27.4036	−	47.4645i	1.04704	−	1.81352i
$686$	−4.35257	+	7.53886i	−0.166182	+	0.287835i
$687$	−1.49478	+	13.0742i	−0.0570295	+	0.498811i
$688$	−3.94265	+	6.82888i	−0.150312	+	0.260348i
$689$	−0.0809719	−	4.66831i	−0.00308478	−	0.177848i
$690$	−18.3647	−	13.6002i	−0.699132	−	0.517752i
$691$	10.6237	−	18.4008i	0.404144	−	0.699998i	−0.590077	−	0.807347i	$-0.700903\pi$
$691$	10.6237	−	18.4008i	0.404144	−	0.699998i	0.994221	+	0.107349i	$0.0342361\pi$
$692$	−13.6840	−	23.7014i	−0.520188	−	0.900992i
$693$	−6.42032	−	21.0587i	−0.243888	−	0.799952i
$694$	−13.8907			−0.527282
$695$	8.73900			0.331489
$696$	1.93872	−	16.9571i	0.0734870	−	0.642758i
$697$	6.77268	−	11.7306i	0.256533	−	0.444329i
$698$	9.68533	+	16.7755i	0.366595	+	0.634961i
$699$	1.21977	−	0.529806i	0.0461360	−	0.0200391i
$700$	−8.06694	+	13.9723i	−0.304902	+	0.528105i
$701$	10.1915			0.384928			0.192464	−	0.981304i	$-0.438352\pi$
$701$	10.1915			0.384928			0.192464	+	0.981304i	$0.438352\pi$
$702$	−9.79907	+	8.64714i	−0.369842	+	0.326365i
$703$	25.0814			0.945962
$704$	−1.64883	+	2.85586i	−0.0621427	+	0.107634i
$705$	4.78893	−	2.08006i	0.180361	−	0.0783397i
$706$	−9.96486	−	17.2596i	−0.375032	−	0.649575i
$707$	13.8651	−	24.0150i	0.521450	−	0.903177i
$708$	−1.40079	+	12.2521i	−0.0526450	+	0.460462i
$709$	25.7338			0.966454			0.483227	−	0.875495i	$-0.339465\pi$
$709$	25.7338			0.966454			0.483227	+	0.875495i	$0.339465\pi$
$710$	−2.74586			−0.103050
$711$	−0.213812	−	0.0495382i	−0.00801859	−	0.00185783i
$712$	0.218487	+	0.378431i	0.00818816	+	0.0141823i
$713$	−27.7268	+	48.0242i	−1.03838	+	1.79852i
$714$	−16.5964	−	12.2907i	−0.621106	−	0.459969i
$715$	−20.6696	+	12.4165i	−0.773000	+	0.464350i
$716$	−16.5483	+	28.6626i	−0.618440	+	1.07117i
$717$	−4.17949	+	36.5562i	−0.156086	+	1.36522i
$718$	5.38931	−	9.33455i	0.201127	−	0.348362i
$719$	−8.35595	+	14.4729i	−0.311624	+	0.539749i	−0.978714	−	0.205228i	$-0.934206\pi$
$719$	−8.35595	+	14.4729i	−0.311624	+	0.539749i	0.667090	+	0.744977i	$0.267540\pi$
$720$	11.1307	+	2.57887i	0.414817	+	0.0961090i
$721$	27.8656	−	48.2646i	1.03777	−	1.79747i
$722$	5.42895			0.202044
$723$	−36.3186	+	15.7749i	−1.35070	+	0.586676i
$724$	−8.31488	−	14.4018i	−0.309020	−	0.535238i
$725$	13.5094			0.501728
$726$	−6.26166	+	2.71974i	−0.232392	+	0.100939i
$727$	−20.7535	−	35.9461i	−0.769705	−	1.33317i	−0.937723	−	0.347384i	$-0.887070\pi$
$727$	−20.7535	−	35.9461i	−0.769705	−	1.33317i	0.168018	−	0.985784i	$-0.446263\pi$
$728$	0.486227	+	28.0327i	0.0180208	+	1.03896i
$729$	−20.9431	−	17.0407i	−0.775671	−	0.631137i
$730$	1.42920	+	2.47545i	0.0528972	+	0.0916206i
$731$	16.1252	−	27.9297i	0.596414	−	1.03302i
$732$	15.6659	+	11.6016i	0.579030	+	0.428809i
$733$	−18.6541	+	32.3098i	−0.689003	+	1.19339i	0.283157	+	0.959073i	$0.408618\pi$
$733$	−18.6541	+	32.3098i	−0.689003	+	1.19339i	−0.972161	+	0.234315i	$0.924715\pi$
$734$	−0.164340	−	0.284644i	−0.00606588	−	0.0105064i
$735$	1.74459	−	15.2591i	0.0643500	−	0.562841i
$736$	19.0376	+	32.9741i	0.701735	+	1.21544i
$737$	−9.67659	+	16.7604i	−0.356442	+	0.617375i
$738$	1.53444	+	5.03297i	0.0564836	+	0.185266i
$739$	−17.9464	−	31.0841i	−0.660169	−	1.14345i	−0.980571	−	0.196165i	$-0.937151\pi$
$739$	−17.9464	−	31.0841i	−0.660169	−	1.14345i	0.320401	−	0.947282i	$-0.396182\pi$
$740$	−10.6036	−	18.3659i	−0.389795	−	0.675145i
$741$	−32.1688	−	3.11374i	−1.18175	−	0.114386i
$742$	−1.43302	+	2.48207i	−0.0526079	+	0.0911195i
$743$	−1.50358			−0.0551609			−0.0275804	−	0.999620i	$-0.508780\pi$
$743$	−1.50358			−0.0551609			−0.0275804	+	0.999620i	$0.508780\pi$
$744$	−4.08754	+	35.7519i	−0.149856	+	1.31073i
$745$	16.5798			0.607438
$746$	22.5653			0.826175
$747$	−6.36003	−	1.47355i	−0.232701	−	0.0539145i
$748$	−9.42888	+	16.3313i	−0.344754	+	0.597131i
$749$	19.7758	+	34.2527i	0.722593	+	1.25157i
$750$	−0.650785	+	5.69212i	−0.0237633	+	0.207847i
$751$	4.21831			0.153928			0.0769642	−	0.997034i	$-0.475477\pi$
$751$	4.21831			0.153928			0.0769642	+	0.997034i	$0.475477\pi$
$752$	−1.37327			−0.0500781
$753$	3.23316	−	28.2790i	0.117823	−	1.03054i
$754$	8.66860	−	5.20732i	0.315692	−	0.189640i
$755$	−6.12830			−0.223032
$756$	−24.5382	+	4.51819i	−0.892446	+	0.164325i
$757$	−3.70611	−	6.41918i	−0.134701	−	0.233309i	0.790782	−	0.612098i	$-0.209674\pi$
$757$	−3.70611	−	6.41918i	−0.134701	−	0.233309i	−0.925483	+	0.378789i	$0.876341\pi$
$758$	−0.995234			−0.0361485
$759$	2.97680	−	26.0368i	0.108051	−	0.945075i
$760$	−18.3363	−	31.7594i	−0.665128	−	1.15204i
$761$	−18.2564	−	31.6210i	−0.661795	−	1.14626i	−0.980144	−	0.198288i	$-0.936462\pi$
$761$	−18.2564	−	31.6210i	−0.661795	−	1.14626i	0.318349	−	0.947974i	$-0.396872\pi$
$762$	4.65899	−	2.02363i	0.168777	−	0.0733082i
$763$	−15.3701			−0.556435
$764$	−13.6081	−	23.5699i	−0.492324	−	0.852730i
$765$	−45.5240	−	10.5475i	−1.64592	−	0.381344i
$766$	−11.1222			−0.401862
$767$	−14.5405	+	8.73466i	−0.525029	+	0.315390i
$768$	14.3062	+	10.5947i	0.516231	+	0.382302i
$769$	16.0012			0.577018			0.288509	−	0.957477i	$-0.406840\pi$
$769$	16.0012			0.577018			0.288509	+	0.957477i	$0.406840\pi$
$770$	14.8012			0.533397
$771$	−5.80362	+	2.52079i	−0.209012	+	0.0907842i
$772$	2.87673	+	4.98264i	0.103536	+	0.179329i
$773$	14.3128	−	24.7905i	0.514796	−	0.891652i	−0.485057	−	0.874483i	$-0.661201\pi$
$773$	14.3128	−	24.7905i	0.514796	−	0.891652i	0.999853	−	0.0171698i	$-0.00546559\pi$
$774$	3.65339	+	11.9831i	0.131318	+	0.430725i
$775$	−28.4829			−1.02314
$776$	−0.320813			−0.0115165
$777$	21.4035	+	15.8506i	0.767845	+	0.568639i
$778$	−14.0273			−0.502905
$779$	−6.50604	+	11.2688i	−0.233103	+	0.403746i
$780$	11.3198	+	24.8721i	0.405315	+	0.890563i
$781$	−1.57444	−	2.72701i	−0.0563379	−	0.0975801i
$782$	−12.2916	−	21.2896i	−0.439546	−	0.761316i
$783$	13.5497	+	15.9023i	0.484227	+	0.568302i
$784$	−2.01980	+	3.49840i	−0.0721358	+	0.124943i
$785$	−22.2694	−	38.5717i	−0.794829	−	1.37668i
$786$	0.600148	+	0.444448i	0.0214066	+	0.0158529i
$787$	2.87553	+	4.98057i	0.102502	+	0.177538i	0.912715	−	0.408597i	$-0.133982\pi$
$787$	2.87553	+	4.98057i	0.102502	+	0.177538i	−0.810213	+	0.586135i	$0.800649\pi$
$788$	18.7107	−	32.4078i	0.666540	−	1.15448i
$789$	4.89693	−	42.8313i	0.174335	−	1.52483i
$790$	0.0737773	−	0.127786i	0.00262488	−	0.00454642i
$791$	9.75192	+	16.8908i	0.346738	+	0.600569i
$792$	−4.95933	−	16.2666i	−0.176222	−	0.578008i
$793$	0.465017	+	26.8098i	0.0165132	+	0.952044i
$794$	1.23763	+	2.14364i	0.0439218	+	0.0760748i
$795$	−0.736647	+	6.44313i	−0.0261262	+	0.228514i
$796$	41.9032			1.48522
$797$	26.9581	+	46.6928i	0.954905	+	1.65394i	0.734585	+	0.678517i	$0.237377\pi$
$797$	26.9581	+	46.6928i	0.954905	+	1.65394i	0.220320	+	0.975428i	$0.429290\pi$
$798$	15.9430	+	11.8069i	0.564377	+	0.417958i
$799$	5.61661			0.198701
$800$	−9.77837	+	16.9366i	−0.345718	+	0.598801i
$801$	−0.521088	−	0.120731i	−0.0184117	−	0.00426582i
$802$	−9.29238	+	16.0949i	−0.328125	+	0.568330i
$803$	−1.63897	+	2.83878i	−0.0578380	+	0.100178i
$804$	17.6262	+	13.0533i	0.621627	+	0.460355i
$805$	30.0055	−	51.9711i	1.05756	−	1.83174i
$806$	−18.2766	+	10.9790i	−0.643767	+	0.386718i
$807$	−1.74524	+	15.2649i	−0.0614354	+	0.537348i
$808$	10.7100	−	18.5502i	0.376776	−	0.652594i
$809$	2.00874	+	3.47924i	0.0706235	+	0.122324i	0.899175	−	0.437590i	$-0.144168\pi$
$809$	2.00874	+	3.47924i	0.0706235	+	0.122324i	−0.828551	+	0.559913i	$0.810834\pi$
$810$	15.0647	−	10.1271i	0.529319	−	0.355830i
$811$	14.2338			0.499815			0.249908	−	0.968270i	$-0.419600\pi$
$811$	14.2338			0.499815			0.249908	+	0.968270i	$0.419600\pi$
$812$	19.3064			0.677520
$813$	−14.4875	−	10.7289i	−0.508099	−	0.376280i
$814$	−3.90969	+	6.77177i	−0.137034	+	0.237351i
$815$	18.9710	+	32.8587i	0.664525	+	1.15099i
$816$	9.87730	+	7.31478i	0.345775	+	0.256069i
$817$	−15.4904	+	26.8302i	−0.541941	+	0.938669i
$818$	−9.43213			−0.329787
$819$	−25.4838	−	22.9868i	−0.890475	−	0.803224i
$820$	11.0021			0.384212
$821$	24.8337	−	43.0132i	0.866701	−	1.50117i	0.00135317	−	0.999999i	$-0.499569\pi$
$821$	24.8337	−	43.0132i	0.866701	−	1.50117i	0.865348	−	0.501171i	$-0.167097\pi$
$822$	−2.60149	+	22.7541i	−0.0907375	+	0.793640i
$823$	−5.98593	−	10.3679i	−0.208656	−	0.361403i	0.742635	−	0.669696i	$-0.233576\pi$
$823$	−5.98593	−	10.3679i	−0.208656	−	0.361403i	−0.951292	+	0.308293i	$0.900242\pi$
$824$	21.5246	−	37.2817i	0.749844	−	1.29877i
$825$	12.3462	−	5.36256i	0.429840	−	0.186700i
$826$	10.4122			0.362288
$827$	35.1205			1.22126			0.610630	−	0.791916i	$-0.290916\pi$
$827$	35.1205			1.22126			0.610630	+	0.791916i	$0.290916\pi$
$828$	−28.9338	−	6.70366i	−1.00552	−	0.232968i
$829$	−25.4527	−	44.0853i	−0.884008	−	1.53115i	−0.846847	−	0.531837i	$-0.821502\pi$
$829$	−25.4527	−	44.0853i	−0.884008	−	1.53115i	−0.0371606	−	0.999309i	$-0.511831\pi$
$830$	2.19457	−	3.80110i	0.0761745	−	0.131938i
$831$	−39.4980	+	17.1559i	−1.37017	+	0.595132i
$832$	0.0891505	+	5.13983i	0.00309074	+	0.178192i
$833$	8.26089	−	14.3083i	0.286223	−	0.495753i
$834$	−3.34946	+	1.45483i	−0.115982	+	0.0503768i
$835$	−8.41018	+	14.5669i	−0.291046	+	0.504107i
$836$	9.05767	−	15.6883i	0.313266	−	0.542593i
$837$	−28.5678	−	33.5280i	−0.987448	−	1.15890i
$838$	4.39670	−	7.61530i	0.151881	−	0.263066i
$839$	−8.42689			−0.290929			−0.145464	−	0.989364i	$-0.546468\pi$
$839$	−8.42689			−0.290929			−0.145464	+	0.989364i	$0.546468\pi$
$840$	4.42348	−	38.6902i	0.152625	−	1.33494i
$841$	6.41707	+	11.1147i	0.221278	+	0.383265i
$842$	−6.27393			−0.216214
$843$	−15.2206	−	11.2718i	−0.524224	−	0.388222i
$844$	−2.86950	−	4.97013i	−0.0987724	−	0.171079i
$845$	−17.6537	+	33.1841i	−0.607305	+	1.14157i
$846$	−1.48921	+	1.59448i	−0.0512000	+	0.0548194i
$847$	−8.96374	−	15.5256i	−0.307998	−	0.533468i
$848$	0.852857	−	1.47719i	0.0292872	−	0.0507270i
$849$	47.0854	−	20.4515i	1.61597	−	0.701893i
$850$	6.31339	−	10.9351i	0.216547	−	0.375071i
$851$	15.8517	+	27.4560i	0.543391	+	0.941180i
$852$	−3.27325	+	1.42173i	−0.112140	+	0.0487078i
$853$	16.9960	+	29.4380i	0.581932	+	1.00794i	0.995250	+	0.0973495i	$0.0310365\pi$
$853$	16.9960	+	29.4380i	0.581932	+	1.00794i	−0.413318	+	0.910587i	$0.635630\pi$
$854$	8.22975	−	14.2543i	0.281616	−	0.487774i
$855$	43.7318	+	10.1322i	1.49559	+	0.346514i
$856$	15.2757	+	26.4583i	0.522112	+	0.904325i
$857$	26.4677	+	45.8435i	0.904121	+	1.56598i	0.822093	+	0.569353i	$0.192806\pi$
$857$	26.4677	+	45.8435i	0.904121	+	1.56598i	0.0820272	+	0.996630i	$0.473861\pi$
$858$	5.85515	−	8.19994i	0.199892	−	0.279941i
$859$	2.49176	−	4.31585i	0.0850177	−	0.147255i	−0.820381	−	0.571817i	$-0.806239\pi$
$859$	2.49176	−	4.31585i	0.0850177	−	0.147255i	0.905399	+	0.424562i	$0.139572\pi$
$860$	26.1953			0.893252
$861$	−12.6735	+	5.50473i	−0.431912	+	0.187601i
$862$	11.2386			0.382787
$863$	40.1602			1.36707			0.683535	−	0.729918i	$-0.260442\pi$
$863$	40.1602			1.36707			0.683535	+	0.729918i	$0.260442\pi$
$864$	−29.7441	+	5.47675i	−1.01191	+	0.186323i
$865$	−26.1433	+	45.2816i	−0.888900	+	1.53962i
$866$	−9.43470	−	16.3414i	−0.320604	−	0.555303i
$867$	−16.7350	−	12.3934i	−0.568351	−	0.420900i
$868$	−40.7050			−1.38162
$869$	0.169211			0.00574010
$870$	−12.8830	+	5.59573i	−0.436776	+	0.189713i
$871$	0.523203	+	30.1644i	0.0177280	+	1.02208i
$872$	−11.8725			−0.402054
$873$	0.268045	−	0.286994i	0.00907195	−	0.00971327i
$874$	11.8077	+	20.4515i	0.399400	+	0.691782i
$875$	−15.0451			−0.508618
$876$	2.98543	+	2.21090i	0.100868	+	0.0746995i
$877$	−4.05215	−	7.01854i	−0.136832	−	0.236999i	0.789464	−	0.613797i	$-0.210359\pi$
$877$	−4.05215	−	7.01854i	−0.136832	−	0.236999i	−0.926296	+	0.376798i	$0.877025\pi$
$878$	−0.803347	−	1.39144i	−0.0271117	−	0.0469588i
$879$	21.2633	+	15.7469i	0.717194	+	0.531129i
$880$	−8.80886			−0.296947
$881$	8.71424	+	15.0935i	0.293590	+	0.508513i	0.974656	−	0.223709i	$-0.0718165\pi$
$881$	8.71424	+	15.0935i	0.293590	+	0.508513i	−0.681066	+	0.732222i	$0.738483\pi$
$882$	1.87162	+	6.13890i	0.0630206	+	0.206708i
$883$	7.78098			0.261851			0.130925	−	0.991392i	$-0.458205\pi$
$883$	7.78098			0.261851			0.130925	+	0.991392i	$0.458205\pi$
$884$	0.509809	+	29.3922i	0.0171467	+	0.988568i
$885$	21.6097	−	9.38616i	0.726403	−	0.315512i
$886$	−18.3432			−0.616253
$887$	31.9515			1.07283			0.536413	−	0.843956i	$-0.319779\pi$
$887$	31.9515			1.07283			0.536413	+	0.843956i	$0.319779\pi$
$888$	16.5329	+	12.2437i	0.554809	+	0.410872i
$889$	6.66948	+	11.5519i	0.223687	+	0.387437i
$890$	0.179805	−	0.311431i	0.00602707	−	0.0104392i
$891$	18.6954	+	9.15450i	0.626320	+	0.306687i
$892$	−1.68087			−0.0562799
$893$	−5.39549			−0.180553
$894$	−6.35467	+	2.76014i	−0.212532	+	0.0923130i
$895$	63.2313			2.11359
$896$	−16.8896	+	29.2536i	−0.564242	+	0.977295i
$897$	−16.9225	−	37.1824i	−0.565027	−	1.24148i
$898$	−3.11564	−	5.39644i	−0.103970	−	0.180082i
$899$	17.0418	+	29.5173i	0.568376	+	0.984456i
$900$	−4.44877	−	14.5920i	−0.148292	−	0.486399i
$901$	−3.48814	+	6.04164i	−0.116207	+	0.201276i
$902$	−2.02832	−	3.51316i	−0.0675358	−	0.116975i
$903$	−30.1747	+	13.1063i	−1.00415	+	0.436152i
$904$	7.53280	+	13.0472i	0.250537	+	0.433943i
$905$	−15.8856	+	27.5147i	−0.528055	+	0.914618i
$906$	2.34884	−	1.02022i	0.0780350	−	0.0338944i
$907$	−10.2843	+	17.8129i	−0.341484	+	0.591468i	−0.984709	−	0.174210i	$-0.944263\pi$
$907$	−10.2843	+	17.8129i	−0.341484	+	0.591468i	0.643224	+	0.765678i	$0.277596\pi$
$908$	−6.31427	−	10.9366i	−0.209547	−	0.362945i
$909$	7.64633	+	25.0800i	0.253613	+	0.831851i
$910$	19.7787	−	11.8813i	0.655659	−	0.393861i
$911$	−18.5114	−	32.0627i	−0.613311	−	1.06229i	−0.990678	−	0.136222i	$-0.956504\pi$
$911$	−18.5114	−	32.0627i	−0.613311	−	1.06229i	0.377368	−	0.926064i	$-0.376829\pi$
$912$	−9.48844	−	7.02680i	−0.314193	−	0.232681i
$913$	5.03333			0.166579
$914$	−6.58552	−	11.4065i	−0.217830	−	0.377292i
$915$	4.23052	−	37.0025i	0.139857	−	1.22326i
$916$	−11.4982			−0.379911
$917$	−0.980564	+	1.69839i	−0.0323811	+	0.0560857i
$918$	19.2042	−	3.53605i	0.633834	−	0.116707i
$919$	9.27825	−	16.0704i	0.306061	−	0.530114i	−0.671436	−	0.741063i	$-0.734322\pi$
$919$	9.27825	−	16.0704i	0.306061	−	0.530114i	0.977497	+	0.210949i	$0.0676554\pi$
$920$	23.1776	−	40.1447i	0.764142	−	1.32353i
$921$	−4.71086	+	2.04616i	−0.155228	+	0.0674231i
$922$	8.10063	−	14.0307i	0.266780	−	0.462077i
$923$	−4.29296	−	2.38024i	−0.141305	−	0.0783467i
$924$	17.6440	−	7.66364i	0.580445	−	0.252115i
$925$	−8.14201	+	14.1024i	−0.267708	+	0.463683i
$926$	0.802232	+	1.38951i	0.0263630	+	0.0456620i
$927$	15.3674	+	50.4050i	0.504731	+	1.65552i
$928$	23.4023			0.768218
$929$	−48.2623			−1.58344			−0.791718	−	0.610887i	$-0.790813\pi$
$929$	−48.2623			−1.58344			−0.791718	+	0.610887i	$0.790813\pi$
$930$	27.1622	−	11.7979i	0.890684	−	0.386867i
$931$	−7.93566	+	13.7450i	−0.260081	+	0.450473i
$932$	0.580994	+	1.00631i	0.0190311	+	0.0329628i
$933$	0.190187	−	1.66348i	0.00622644	−	0.0544599i
$934$	7.83760	−	13.5751i	0.256454	−	0.444191i
$935$	36.0278			1.17823
$936$	−19.6848	−	17.7560i	−0.643416	−	0.580373i
$937$	37.7556			1.23342			0.616711	−	0.787190i	$-0.288465\pi$
$937$	37.7556			1.23342			0.616711	+	0.787190i	$0.288465\pi$
$938$	9.25952	−	16.0380i	0.302334	−	0.523658i
$939$	−4.36010	−	3.22893i	−0.142286	−	0.105372i
$940$	2.28103	+	3.95086i	0.0743990	+	0.128863i
$941$	−20.6525	+	35.7713i	−0.673254	+	1.16611i	0.303722	+	0.952761i	$0.401770\pi$
$941$	−20.6525	+	35.7713i	−0.673254	+	1.16611i	−0.976976	+	0.213349i	$0.931563\pi$
$942$	14.9566	+	11.0763i	0.487313	+	0.360887i
$943$	−16.4476			−0.535607
$944$	−6.19681			−0.201689
$945$	30.9157	+	36.2835i	1.00569	+	1.18030i
$946$	−4.82929	−	8.36457i	−0.157014	−	0.271956i
$947$	0.883784	−	1.53076i	0.0287191	−	0.0497430i	−0.851309	−	0.524665i	$-0.824190\pi$
$947$	0.883784	−	1.53076i	0.0287191	−	0.0497430i	0.880028	+	0.474922i	$0.157524\pi$
$948$	0.0217833	−	0.190529i	0.000707490	−	0.00618810i
$949$	0.0886173	+	5.10909i	0.00287664	+	0.165848i
$950$	−6.06483	+	10.5046i	−0.196769	+	0.340814i
$951$	40.5959	+	30.0639i	1.31641	+	0.974888i
$952$	20.9459	−	36.2793i	0.678860	−	1.17582i
$953$	17.6033	−	30.4898i	0.570228	−	0.987663i	−0.426315	−	0.904575i	$-0.640188\pi$
$953$	17.6033	−	30.4898i	0.570228	−	0.987663i	0.996542	−	0.0830881i	$-0.0264783\pi$
$954$	−0.790285	−	2.59214i	−0.0255864	−	0.0839235i
$955$	−25.9983	+	45.0304i	−0.841286	+	1.45715i
$956$	−32.1496			−1.03979
$957$	−12.9443	−	9.58606i	−0.418428	−	0.309873i
$958$	1.69930	+	2.94327i	0.0549018	+	0.0950926i
$959$	−60.1424			−1.94210
$960$	0.811052	−	7.09391i	0.0261766	−	0.228955i
$961$	−20.4304	−	35.3866i	−0.659047	−	1.14150i
$962$	0.211392	+	12.1875i	0.00681556	+	0.392941i
$963$	−36.4322	−	8.44098i	−1.17401	−	0.272007i
$964$	−17.2990	−	29.9628i	−0.557164	−	0.965037i
$965$	5.49600	−	9.51935i	0.176923	−	0.306439i
$966$	−2.84850	+	24.9146i	−0.0916490	+	0.801613i
$967$	−26.6427	+	46.1466i	−0.856773	+	1.48397i	0.0182182	+	0.999834i	$0.494201\pi$
$967$	−26.6427	+	46.1466i	−0.856773	+	1.48397i	−0.874991	+	0.484140i	$0.839133\pi$
$968$	−6.92397	−	11.9927i	−0.222545	−	0.385459i
$969$	38.8072	+	28.7392i	1.24667	+	0.923238i
$970$	0.132007	+	0.228643i	0.00423849	+	0.00734127i
$971$	24.0513	−	41.6582i	0.771844	−	1.33687i	−0.164707	−	0.986343i	$-0.552668\pi$
$971$	24.0513	−	41.6582i	0.771844	−	1.33687i	0.936551	−	0.350531i	$-0.113999\pi$
$972$	12.7146	−	19.8722i	0.407820	−	0.637402i
$973$	−4.79485	−	8.30492i	−0.153716	−	0.266243i
$974$	−4.30485	−	7.45622i	−0.137936	−	0.238913i
$975$	12.1935	−	17.0766i	0.390504	−	0.546888i
$976$	−4.89791	+	8.48342i	−0.156778	+	0.271548i
$977$	−55.7438			−1.78340			−0.891700	−	0.452626i	$-0.850487\pi$
$977$	−55.7438			−1.78340			−0.891700	+	0.452626i	$0.850487\pi$
$978$	−12.7413	−	9.43579i	−0.407423	−	0.301723i
$979$	0.412390			0.0131800
$980$	13.4197			0.428678
$981$	9.91970	−	10.6209i	0.316712	−	0.339101i
$982$	9.82115	−	17.0107i	0.313406	−	0.542834i
$983$	−11.9465	−	20.6920i	−0.381035	−	0.659973i	0.610175	−	0.792267i	$-0.291099\pi$
$983$	−11.9465	−	20.6920i	−0.381035	−	0.659973i	−0.991211	+	0.132294i	$0.957766\pi$
$984$	−9.78957	+	4.25209i	−0.312080	+	0.135552i
$985$	−71.4936			−2.27797
$986$	−15.1096			−0.481189
$987$	−4.60429	−	3.40978i	−0.146556	−	0.108534i
$988$	−0.489738	−	28.2351i	−0.0155806	−	0.898277i
$989$	−39.1605			−1.24523
$990$	−9.55252	+	10.2278i	−0.303599	+	0.325061i
$991$	15.5487	+	26.9312i	0.493922	+	0.855498i	0.999975	−	0.00700424i	$-0.00222954\pi$
$991$	15.5487	+	26.9312i	0.493922	+	0.855498i	−0.506054	+	0.862502i	$0.668896\pi$
$992$	−49.3407			−1.56657
$993$	11.3661	−	4.93685i	0.360692	−	0.156666i
$994$	1.50658	+	2.60947i	0.0477858	+	0.0827674i
$995$	−40.0281	−	69.3307i	−1.26898	−	2.19793i
$996$	0.647964	−	5.66745i	0.0205315	−	0.179580i
$997$	21.0784			0.667561			0.333781	−	0.942651i	$-0.391676\pi$
$997$	21.0784			0.667561			0.333781	+	0.942651i	$0.391676\pi$
$998$	8.39986	+	14.5490i	0.265893	+	0.460540i
$999$	−24.7666	+	4.56024i	−0.783580	+	0.144280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.f.a.94.5	yes	24
3.2	odd	2		351.2.f.a.172.8		24
9.2	odd	6		351.2.h.a.289.5		24
9.7	even	3		117.2.h.a.16.8	yes	24
13.9	even	3		117.2.h.a.22.8	yes	24
39.35	odd	6		351.2.h.a.334.5		24
117.61	even	3	inner	117.2.f.a.61.5	✓	24
117.74	odd	6		351.2.f.a.100.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.5	✓	24	117.61	even	3	inner
117.2.f.a.94.5	yes	24	1.1	even	1	trivial
117.2.h.a.16.8	yes	24	9.7	even	3
117.2.h.a.22.8	yes	24	13.9	even	3
351.2.f.a.100.8		24	117.74	odd	6
351.2.f.a.172.8		24	3.2	odd	2
351.2.h.a.289.5		24	9.2	odd	6
351.2.h.a.334.5		24	39.35	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.348782 + 0.604108i) q^{2} +(1.58866 - 0.690034i) q^{3} +(0.756702 + 1.31065i) q^{4} +(1.44568 - 2.50399i) q^{5} +(-0.137242 + 1.20040i) q^{6} -3.17282 q^{7} -2.45082 q^{8} +(2.04771 - 2.19246i) q^{9} +(1.00846 + 1.74670i) q^{10} +(-1.15647 + 2.00306i) q^{11} +(2.10654 + 1.56003i) q^{12} +(0.0625290 + 3.60501i) q^{13} +(1.10662 - 1.91673i) q^{14} +(0.568861 - 4.97558i) q^{15} +(-0.658602 + 1.14073i) q^{16} +(2.69365 - 4.66554i) q^{17} +(0.610282 + 2.00173i) q^{18} +(-2.58760 + 4.48186i) q^{19} +4.37581 q^{20} +(-5.04055 + 2.18936i) q^{21} +(-0.806710 - 1.39726i) q^{22} -6.54158 q^{23} +(-3.89353 + 1.69115i) q^{24} +(-1.67999 - 2.90983i) q^{25} +(-2.19962 - 1.21959i) q^{26} +(1.74024 - 4.89608i) q^{27} +(-2.40088 - 4.15845i) q^{28} +(-2.01034 + 3.48201i) q^{29} +(2.80738 + 2.07904i) q^{30} +(4.23854 - 7.34137i) q^{31} +(-2.91024 - 5.04068i) q^{32} +(-0.455059 + 3.98019i) q^{33} +(1.87899 + 3.25451i) q^{34} +(-4.58689 + 7.94473i) q^{35} +(4.42305 + 1.02478i) q^{36} +(-2.42323 - 4.19715i) q^{37} +(-1.80502 - 3.12638i) q^{38} +(2.58692 + 5.68400i) q^{39} +(-3.54311 + 6.13685i) q^{40} +2.51431 q^{41} +(0.435445 - 3.80864i) q^{42} +5.98639 q^{43} -3.50041 q^{44} +(-2.52959 - 8.29705i) q^{45} +(2.28159 - 3.95182i) q^{46} +(0.521283 + 0.902888i) q^{47} +(-0.259153 + 2.26670i) q^{48} +3.06680 q^{49} +2.34381 q^{50} +(1.05992 - 9.27068i) q^{51} +(-4.67758 + 2.80987i) q^{52} -1.29495 q^{53} +(2.35079 + 2.75896i) q^{54} +(3.34377 + 5.79158i) q^{55} +7.77603 q^{56} +(-1.01820 + 8.90570i) q^{57} +(-1.40234 - 2.42892i) q^{58} +(2.35226 + 4.07423i) q^{59} +(6.95168 - 3.01945i) q^{60} +7.43682 q^{61} +(2.95665 + 5.12107i) q^{62} +(-6.49701 + 6.95630i) q^{63} +1.42575 q^{64} +(9.11732 + 5.05513i) q^{65} +(-2.24575 - 1.66312i) q^{66} +8.36736 q^{67} +8.15316 q^{68} +(-10.3924 + 4.51392i) q^{69} +(-3.19965 - 5.54196i) q^{70} +(-0.680710 + 1.17903i) q^{71} +(-5.01857 + 5.37334i) q^{72} +1.41722 q^{73} +3.38071 q^{74} +(-4.67683 - 3.46350i) q^{75} -7.83218 q^{76} +(3.66927 - 6.35536i) q^{77} +(-4.33602 - 0.419700i) q^{78} +(-0.0365793 - 0.0633573i) q^{79} +(1.90426 + 3.29827i) q^{80} +(-0.613800 - 8.97905i) q^{81} +(-0.876947 + 1.51892i) q^{82} +(-1.08808 - 1.88462i) q^{83} +(-6.68367 - 4.94969i) q^{84} +(-7.78832 - 13.4898i) q^{85} +(-2.08795 + 3.61643i) q^{86} +(-0.791048 + 6.91895i) q^{87} +(2.83430 - 4.90915i) q^{88} +(-0.0891486 - 0.154410i) q^{89} +(5.89459 + 1.36572i) q^{90} +(-0.198393 - 11.4381i) q^{91} +(-4.95003 - 8.57371i) q^{92} +(1.66782 - 14.5877i) q^{93} -0.727256 q^{94} +(7.48170 + 12.9587i) q^{95} +(-8.10164 - 5.99979i) q^{96} +0.130900 q^{97} +(-1.06965 + 1.85268i) q^{98} +(2.02353 + 6.63720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

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