LMFDB - Embedded newform 429.2.y.b.116.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(116,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 5]))

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

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

chi := DirichletCharacter("429.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.y (of order $10$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			116.12
Character	$\chi$	$=$	429.116
Dual form			429.2.y.b.233.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39675 + 0.453832i) q^{2} +(1.60306 - 0.655892i) q^{3} +(0.126919 - 0.0922120i) q^{4} +(-0.121706 + 0.374573i) q^{5} +(-1.94141 + 1.64364i) q^{6} +(-2.86530 + 2.08177i) q^{7} +(1.59106 - 2.18990i) q^{8} +(2.13961 - 2.10287i) q^{9} +O(q^{10})$	\(q+(-1.39675 + 0.453832i) q^{2} +(1.60306 - 0.655892i) q^{3} +(0.126919 - 0.0922120i) q^{4} +(-0.121706 + 0.374573i) q^{5} +(-1.94141 + 1.64364i) q^{6} +(-2.86530 + 2.08177i) q^{7} +(1.59106 - 2.18990i) q^{8} +(2.13961 - 2.10287i) q^{9} -0.578420i q^{10} +(2.76923 - 1.82520i) q^{11} +(0.142978 - 0.231067i) q^{12} +(3.26022 + 1.53979i) q^{13} +(3.05735 - 4.20808i) q^{14} +(0.0505770 + 0.680289i) q^{15} +(-1.32542 + 4.07922i) q^{16} +(-2.09225 + 6.43927i) q^{17} +(-2.03416 + 3.90821i) q^{18} +(3.21619 + 2.33670i) q^{19} +(0.0190933 + 0.0587632i) q^{20} +(-3.22785 + 5.21653i) q^{21} +(-3.03960 + 3.80612i) q^{22} -1.80906i q^{23} +(1.11422 - 4.55410i) q^{24} +(3.91959 + 2.84775i) q^{25} +(-5.25253 - 0.671118i) q^{26} +(2.05067 - 4.77438i) q^{27} +(-0.171698 + 0.528431i) q^{28} +(0.612550 - 0.445044i) q^{29} +(-0.379381 - 0.927242i) q^{30} +(1.96211 - 0.637528i) q^{31} -0.885454i q^{32} +(3.24212 - 4.74222i) q^{33} -9.94359i q^{34} +(-0.431048 - 1.32663i) q^{35} +(0.0776474 - 0.464192i) q^{36} +(1.82078 + 2.50608i) q^{37} +(-5.55269 - 1.80418i) q^{38} +(6.23627 + 0.330033i) q^{39} +(0.626636 + 0.862490i) q^{40} +(0.653340 - 0.899245i) q^{41} +(2.14107 - 8.75110i) q^{42} +8.52229i q^{43} +(0.183163 - 0.487009i) q^{44} +(0.527274 + 1.05737i) q^{45} +(0.821009 + 2.52681i) q^{46} +(-1.16921 - 0.849479i) q^{47} +(0.550800 + 7.40858i) q^{48} +(1.71310 - 5.27239i) q^{49} +(-6.76710 - 2.19876i) q^{50} +(0.869467 + 11.6948i) q^{51} +(0.555771 - 0.105202i) q^{52} +(-5.50674 + 1.78925i) q^{53} +(-0.697512 + 7.59929i) q^{54} +(0.346638 + 1.25942i) q^{55} +9.58693i q^{56} +(6.68838 + 1.63640i) q^{57} +(-0.653606 + 0.899611i) q^{58} +(10.5490 - 7.66433i) q^{59} +(0.0691500 + 0.0816778i) q^{60} +(-6.80221 - 2.21017i) q^{61} +(-2.45125 + 1.78094i) q^{62} +(-1.75296 + 10.4795i) q^{63} +(-2.24899 - 6.92169i) q^{64} +(-0.973554 + 1.03379i) q^{65} +(-2.37626 + 8.09509i) q^{66} -5.08933i q^{67} +(0.328232 + 1.01020i) q^{68} +(-1.18655 - 2.90003i) q^{69} +(1.20413 + 1.65735i) q^{70} +(-1.56757 + 4.82447i) q^{71} +(-1.20083 - 8.03132i) q^{72} +(5.53489 - 4.02133i) q^{73} +(-3.68052 - 2.67405i) q^{74} +(8.15116 + 1.99429i) q^{75} +0.623668 q^{76} +(-4.13506 + 10.9946i) q^{77} +(-8.86030 + 2.36925i) q^{78} +(8.53305 - 2.77256i) q^{79} +(-1.36665 - 0.992933i) q^{80} +(0.155875 - 8.99865i) q^{81} +(-0.504448 + 1.55253i) q^{82} +(-0.334226 - 0.108597i) q^{83} +(0.0713518 + 0.959722i) q^{84} +(-2.15734 - 1.56740i) q^{85} +(-3.86769 - 11.9035i) q^{86} +(0.690055 - 1.11520i) q^{87} +(0.408998 - 8.96833i) q^{88} -14.1914 q^{89} +(-1.21634 - 1.23759i) q^{90} +(-12.5470 + 2.37503i) q^{91} +(-0.166817 - 0.229604i) q^{92} +(2.72723 - 2.30893i) q^{93} +(2.01861 + 0.655887i) q^{94} +(-1.26669 + 0.920308i) q^{95} +(-0.580762 - 1.41944i) q^{96} +(-1.18674 + 0.385594i) q^{97} +8.14168i q^{98} +(2.08692 - 9.72855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 6 q^{3} + 20 q^{4} + 6 q^{9}+O(q^{10}) $ 176 * q - 6 * q^3 + 20 * q^4 + 6 * q^9	$ 176 q - 6 q^{3} + 20 q^{4} + 6 q^{9} + 12 q^{12} - 10 q^{13} + 36 q^{16} - 96 q^{22} - 20 q^{25} + 6 q^{27} - 100 q^{30} - 116 q^{36} + 50 q^{39} + 60 q^{40} + 52 q^{42} + 32 q^{48} - 88 q^{49} - 90 q^{51} + 210 q^{52} - 20 q^{55} - 92 q^{64} - 62 q^{66} + 96 q^{69} + 166 q^{75} - 112 q^{78} - 60 q^{79} + 70 q^{81} - 144 q^{82} - 148 q^{88} + 100 q^{90} + 62 q^{91} - 180 q^{94}+O(q^{100}) $ 176 * q - 6 * q^3 + 20 * q^4 + 6 * q^9 + 12 * q^12 - 10 * q^13 + 36 * q^16 - 96 * q^22 - 20 * q^25 + 6 * q^27 - 100 * q^30 - 116 * q^36 + 50 * q^39 + 60 * q^40 + 52 * q^42 + 32 * q^48 - 88 * q^49 - 90 * q^51 + 210 * q^52 - 20 * q^55 - 92 * q^64 - 62 * q^66 + 96 * q^69 + 166 * q^75 - 112 * q^78 - 60 * q^79 + 70 * q^81 - 144 * q^82 - 148 * q^88 + 100 * q^90 + 62 * q^91 - 180 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.39675	+	0.453832i	−0.987653	+	0.320908i	−0.757921	−	0.652346i	$-0.773785\pi$
$2$	−1.39675	+	0.453832i	−0.987653	+	0.320908i	−0.229732	+	0.973254i	$0.573785\pi$
$3$	1.60306	−	0.655892i	0.925528	−	0.378679i
$3$	1.60306	−	0.655892i	0.925528	−	0.378679i
$4$	0.126919	−	0.0922120i	0.0634595	−	0.0461060i
$5$	−0.121706	+	0.374573i	−0.0544286	+	0.167514i	−0.974576	−	0.224059i	$-0.928069\pi$
$5$	−0.121706	+	0.374573i	−0.0544286	+	0.167514i	0.920147	+	0.391573i	$0.128069\pi$
$6$	−1.94141	+	1.64364i	−0.792579	+	0.671013i
$7$	−2.86530	+	2.08177i	−1.08298	+	0.786833i	−0.978201	−	0.207662i	$-0.933415\pi$
$7$	−2.86530	+	2.08177i	−1.08298	+	0.786833i	−0.104783	+	0.994495i	$0.533415\pi$
$8$	1.59106	−	2.18990i	0.562523	−	0.774246i
$9$	2.13961	−	2.10287i	0.713204	−	0.700957i
$10$		−	0.578420i		−	0.182912i
$11$	2.76923	−	1.82520i	0.834955	−	0.550318i
$11$	2.76923	−	1.82520i	0.834955	−	0.550318i
$12$	0.142978	−	0.231067i	0.0412741	−	0.0667032i
$13$	3.26022	+	1.53979i	0.904222	+	0.427062i
$13$	3.26022	+	1.53979i	0.904222	+	0.427062i
$14$	3.05735	−	4.20808i	0.817111	−	1.12466i
$15$	0.0505770	+	0.680289i	0.0130589	+	0.175650i
$16$	−1.32542	+	4.07922i	−0.331355	+	1.01981i
$17$	−2.09225	+	6.43927i	−0.507444	+	1.56175i	0.289179	+	0.957275i	$0.406618\pi$
$17$	−2.09225	+	6.43927i	−0.507444	+	1.56175i	−0.796623	+	0.604477i	$0.793382\pi$
$18$	−2.03416	+	3.90821i	−0.479455	+	0.921175i
$19$	3.21619	+	2.33670i	0.737845	+	0.536076i	0.892036	−	0.451965i	$-0.149277\pi$
$19$	3.21619	+	2.33670i	0.737845	+	0.536076i	−0.154190	+	0.988041i	$0.549277\pi$
$20$	0.0190933	+	0.0587632i	0.00426939	+	0.0131398i
$21$	−3.22785	+	5.21653i	−0.704374	+	1.13834i
$22$	−3.03960	+	3.80612i	−0.648044	+	0.811467i
$23$		−	1.80906i		−	0.377215i	−0.982053	−	0.188607i	$-0.939603\pi$
$23$		−	1.80906i		−	0.377215i	0.982053	−	0.188607i	$-0.0603974\pi$
$24$	1.11422	−	4.55410i	0.227440	−	0.929602i
$25$	3.91959	+	2.84775i	0.783919	+	0.569550i
$26$	−5.25253	−	0.671118i	−1.03011	−	0.131617i
$27$	2.05067	−	4.77438i	0.394652	−	0.918831i
$28$	−0.171698	+	0.528431i	−0.0324478	+	0.0998641i
$29$	0.612550	−	0.445044i	0.113748	−	0.0826426i	−0.529457	−	0.848337i	$-0.677604\pi$
$29$	0.612550	−	0.445044i	0.113748	−	0.0826426i	0.643205	+	0.765694i	$0.277604\pi$
$30$	−0.379381	−	0.927242i	−0.0692651	−	0.169290i
$31$	1.96211	−	0.637528i	0.352405	−	0.114503i	−0.127465	−	0.991843i	$-0.540684\pi$
$31$	1.96211	−	0.637528i	0.352405	−	0.114503i	0.479870	+	0.877340i	$0.340684\pi$
$32$		−	0.885454i		−	0.156528i
$33$	3.24212	−	4.74222i	0.564380	−	0.825515i
$34$		−	9.94359i		−	1.70531i
$35$	−0.431048	−	1.32663i	−0.0728604	−	0.224241i
$36$	0.0776474	−	0.464192i	0.0129412	−	0.0773653i
$37$	1.82078	+	2.50608i	0.299334	+	0.411998i	0.932018	−	0.362412i	$-0.118047\pi$
$37$	1.82078	+	2.50608i	0.299334	+	0.411998i	−0.632684	+	0.774410i	$0.718047\pi$
$38$	−5.55269	−	1.80418i	−0.900766	−	0.292677i
$39$	6.23627	+	0.330033i	0.998603	+	0.0528475i
$40$	0.626636	+	0.862490i	0.0990798	+	0.136372i
$41$	0.653340	−	0.899245i	0.102035	−	0.140439i	−0.754947	−	0.655786i	$-0.772337\pi$
$41$	0.653340	−	0.899245i	0.102035	−	0.140439i	0.856981	+	0.515348i	$0.172337\pi$
$42$	2.14107	−	8.75110i	0.330374	−	1.35032i
$43$			8.52229i			1.29964i	0.760089	+	0.649819i	$0.225155\pi$
$43$			8.52229i			1.29964i	−0.760089	+	0.649819i	$0.774845\pi$
$44$	0.183163	−	0.487009i	0.0276128	−	0.0734194i
$45$	0.527274	+	1.05737i	0.0786014	+	0.157624i
$46$	0.821009	+	2.52681i	0.121051	+	0.372557i
$47$	−1.16921	−	0.849479i	−0.170546	−	0.123909i	0.499238	−	0.866465i	$-0.333613\pi$
$47$	−1.16921	−	0.849479i	−0.170546	−	0.123909i	−0.669784	+	0.742556i	$0.733613\pi$
$48$	0.550800	+	7.40858i	0.0795012	+	1.06934i
$49$	1.71310	−	5.27239i	0.244729	−	0.753198i
$50$	−6.76710	−	2.19876i	−0.957013	−	0.310952i
$51$	0.869467	+	11.6948i	0.121750	+	1.63760i
$52$	0.555771	−	0.105202i	0.0770716	−	0.0145889i
$53$	−5.50674	+	1.78925i	−0.756409	+	0.245772i	−0.661737	−	0.749736i	$-0.730180\pi$
$53$	−5.50674	+	1.78925i	−0.756409	+	0.245772i	−0.0946723	+	0.995508i	$0.530180\pi$
$54$	−0.697512	+	7.59929i	−0.0949194	+	1.03413i
$55$	0.346638	+	1.25942i	0.0467406	+	0.169820i
$56$			9.58693i			1.28111i
$57$	6.68838	+	1.63640i	0.885897	+	0.216746i
$58$	−0.653606	+	0.899611i	−0.0858226	+	0.118125i
$59$	10.5490	−	7.66433i	1.37337	−	0.997811i	0.375904	−	0.926659i	$-0.377332\pi$
$59$	10.5490	−	7.66433i	1.37337	−	0.997811i	0.997465	−	0.0711526i	$-0.0226677\pi$
$60$	0.0691500	+	0.0816778i	0.00892723	+	0.0105446i
$61$	−6.80221	−	2.21017i	−0.870934	−	0.282984i	−0.160746	−	0.986996i	$-0.551390\pi$
$61$	−6.80221	−	2.21017i	−0.870934	−	0.282984i	−0.710188	+	0.704012i	$0.751390\pi$
$62$	−2.45125	+	1.78094i	−0.311309	+	0.226179i
$63$	−1.75296	+	10.4795i	−0.220852	+	1.32030i
$64$	−2.24899	−	6.92169i	−0.281124	−	0.865211i
$65$	−0.973554	+	1.03379i	−0.120754	+	0.128226i
$66$	−2.37626	+	8.09509i	−0.292497	+	0.996436i
$67$		−	5.08933i		−	0.621760i	−0.950449	−	0.310880i	$-0.899376\pi$
$67$		−	5.08933i		−	0.621760i	0.950449	−	0.310880i	$-0.100624\pi$
$68$	0.328232	+	1.01020i	0.0398040	+	0.122504i
$69$	−1.18655	−	2.90003i	−0.142843	−	0.349123i
$70$	1.20413	+	1.65735i	0.143922	+	0.198091i
$71$	−1.56757	+	4.82447i	−0.186036	+	0.572560i	−0.999965	−	0.00840493i	$-0.997325\pi$
$71$	−1.56757	+	4.82447i	−0.186036	+	0.572560i	0.813929	+	0.580965i	$0.197325\pi$
$72$	−1.20083	−	8.03132i	−0.141520	−	0.946500i
$73$	5.53489	−	4.02133i	0.647810	−	0.470661i	−0.214715	−	0.976677i	$-0.568882\pi$
$73$	5.53489	−	4.02133i	0.647810	−	0.470661i	0.862524	+	0.506015i	$0.168882\pi$
$74$	−3.68052	−	2.67405i	−0.427851	−	0.310852i
$75$	8.15116	+	1.99429i	0.941215	+	0.230281i
$76$	0.623668			0.0715396
$77$	−4.13506	+	10.9946i	−0.471233	+	1.25296i
$78$	−8.86030	+	2.36925i	−1.00323	+	0.268264i
$79$	8.53305	−	2.77256i	0.960043	−	0.311937i	0.213253	−	0.976997i	$-0.431594\pi$
$79$	8.53305	−	2.77256i	0.960043	−	0.311937i	0.746790	+	0.665060i	$0.231594\pi$
$80$	−1.36665	−	0.992933i	−0.152797	−	0.111013i
$81$	0.155875	−	8.99865i	0.0173194	−	0.999850i
$82$	−0.504448	+	1.55253i	−0.0557069	+	0.171448i
$83$	−0.334226	−	0.108597i	−0.0366861	−	0.0119200i	0.290616	−	0.956840i	$-0.406140\pi$
$83$	−0.334226	−	0.108597i	−0.0366861	−	0.0119200i	−0.327303	+	0.944920i	$0.606140\pi$
$84$	0.0713518	+	0.959722i	0.00778512	+	0.104714i
$85$	−2.15734	−	1.56740i	−0.233996	−	0.170008i
$86$	−3.86769	−	11.9035i	−0.417064	−	1.28359i
$87$	0.690055	−	1.11520i	0.0739817	−	0.119562i
$88$	0.408998	−	8.96833i	0.0435994	−	0.956028i
$89$	−14.1914			−1.50428			−0.752141	−	0.659002i	$-0.770979\pi$
$89$	−14.1914			−1.50428			−0.752141	+	0.659002i	$0.770979\pi$
$90$	−1.21634	−	1.23759i	−0.128214	−	0.130454i
$91$	−12.5470	+	2.37503i	−1.31528	+	0.248971i
$92$	−0.166817	−	0.229604i	−0.0173919	−	0.0239379i
$93$	2.72723	−	2.30893i	0.282801	−	0.239425i
$94$	2.01861	+	0.655887i	0.208204	+	0.0676496i
$95$	−1.26669	+	0.920308i	−0.129960	+	0.0944216i
$96$	−0.580762	−	1.41944i	−0.0592738	−	0.144871i
$97$	−1.18674	+	0.385594i	−0.120495	+	0.0391512i	−0.368644	−	0.929571i	$-0.620178\pi$
$97$	−1.18674	+	0.385594i	−0.120495	+	0.0391512i	0.248149	+	0.968722i	$0.420178\pi$
$98$			8.14168i			0.822434i
$99$	2.08692	−	9.72855i	0.209744	−	0.977756i
$100$	0.760067			0.0760067
$101$	−0.168901	−	0.519824i	−0.0168063	−	0.0517245i	0.942302	−	0.334765i	$-0.108657\pi$
$101$	−0.168901	−	0.519824i	−0.0168063	−	0.0517245i	−0.959108	+	0.283040i	$0.908657\pi$
$102$	−6.52192	−	15.9402i	−0.645766	−	1.57831i
$103$	3.98291	−	2.89376i	0.392448	−	0.285130i	−0.374010	−	0.927425i	$-0.622017\pi$
$103$	3.98291	−	2.89376i	0.392448	−	0.285130i	0.766458	+	0.642294i	$0.222017\pi$
$104$	8.55918	−	4.68966i	0.839297	−	0.459859i
$105$	−1.56112	−	1.84395i	−0.152350	−	0.179951i
$106$	6.87953	−	4.99827i	0.668199	−	0.485475i
$107$	−0.390516	−	0.283727i	−0.0377526	−	0.0274289i	0.568749	−	0.822511i	$-0.307428\pi$
$107$	−0.390516	−	0.283727i	−0.0377526	−	0.0274289i	−0.606502	+	0.795082i	$0.707428\pi$
$108$	−0.179986	−	0.795057i	−0.0173192	−	0.0765043i
$109$	−14.2583			−1.36569			−0.682847	−	0.730561i	$-0.739259\pi$
$109$	−14.2583			−1.36569			−0.682847	+	0.730561i	$0.739259\pi$
$110$	−1.05573	−	1.60178i	−0.100660	−	0.152724i
$111$	4.56254	+	2.82317i	0.433057	+	0.267964i
$112$	−4.69425	−	14.4474i	−0.443565	−	1.36515i
$113$	12.2201	−	16.8195i	1.14957	−	1.58225i	0.405575	−	0.914062i	$-0.367071\pi$
$113$	12.2201	−	16.8195i	1.14957	−	1.58225i	0.743995	−	0.668186i	$-0.232929\pi$
$114$	−10.0847	+	0.749757i	−0.944515	+	0.0702212i
$115$	0.677624	+	0.220173i	0.0631888	+	0.0205313i
$116$	0.0367059	−	0.112969i	0.00340805	−	0.0104889i
$117$	10.2136	−	3.56126i	0.944247	−	0.329238i
$118$	−11.2561	+	15.4927i	−1.03621	+	1.42622i
$119$	−7.41013	−	22.8060i	−0.679285	−	2.09063i
$120$	1.57024	+	0.971619i	0.143342	+	0.0886963i
$121$	4.33730	−	10.1088i	0.394300	−	0.918982i
$122$	10.5041			0.950992
$123$	0.457536	−	1.87007i	0.0412547	−	0.168618i
$124$	0.190241	−	0.261844i	0.0170841	−	0.0235143i
$125$	−3.13688	+	2.27908i	−0.280571	+	0.203847i
$126$	−2.30751	−	15.4329i	−0.205569	−	1.37487i
$127$	−17.4139	−	5.65812i	−1.54523	−	0.502077i	−0.592420	−	0.805629i	$-0.701827\pi$
$127$	−17.4139	−	5.65812i	−1.54523	−	0.502077i	−0.952815	+	0.303552i	$0.901827\pi$
$128$	7.32348	+	10.0799i	0.647311	+	0.890947i
$129$	5.58970	+	13.6618i	0.492146	+	1.20285i
$130$	0.890647	−	1.88578i	0.0781149	−	0.165393i
$131$	−16.0405			−1.40147			−0.700734	−	0.713422i	$-0.747144\pi$
$131$	−16.0405			−1.40147			−0.700734	+	0.713422i	$0.747144\pi$
$132$	−0.0258041	−	0.900840i	−0.00224595	−	0.0784081i
$133$	−14.0798			−1.22088
$134$	2.30970	+	7.10853i	0.199528	+	0.614083i
$135$	1.53878	+	1.34920i	0.132437	+	0.116120i
$136$	10.7725	+	14.8270i	0.923732	+	1.27141i
$137$	−2.34213	+	7.20832i	−0.200101	+	0.615849i	0.799778	+	0.600296i	$0.204951\pi$
$137$	−2.34213	+	7.20832i	−0.200101	+	0.615849i	−0.999879	+	0.0155523i	$0.995049\pi$
$138$	2.97344	+	3.51213i	0.253116	+	0.298973i
$139$	−5.05941	−	6.96369i	−0.429134	−	0.590652i	0.538620	−	0.842549i	$-0.318946\pi$
$139$	−5.05941	−	6.96369i	−0.429134	−	0.590652i	−0.967754	+	0.251896i	$0.918946\pi$
$140$	−0.177039	−	0.128627i	−0.0149625	−	0.0108709i
$141$	−2.43148	−	0.594893i	−0.204767	−	0.0500990i
$142$		−	7.45001i		−	0.625191i
$143$	11.8387	−	1.68650i	0.990005	−	0.141032i
$144$	5.74219	+	11.5151i	0.478516	+	0.959595i
$145$	0.0921502	+	0.283609i	0.00765266	+	0.0235525i
$146$	−5.90586	+	8.12872i	−0.488772	+	0.672737i
$147$	−0.711908	−	9.57557i	−0.0587172	−	0.789780i
$148$	0.462182	+	0.150172i	0.0379911	+	0.0123441i
$149$	−7.41600	−	2.40960i	−0.607542	−	0.197402i	−0.0109408	−	0.999940i	$-0.503483\pi$
$149$	−7.41600	−	2.40960i	−0.607542	−	0.197402i	−0.596601	+	0.802538i	$0.703483\pi$
$150$	−12.2902	+	0.913733i	−1.00349	+	0.0746060i
$151$	−0.691011	−	0.502049i	−0.0562337	−	0.0408562i	0.559313	−	0.828956i	$-0.311065\pi$
$151$	−0.691011	−	0.502049i	−0.0562337	−	0.0408562i	−0.615547	+	0.788100i	$0.711065\pi$
$152$	10.2343	−	3.32532i	0.830110	−	0.269719i
$153$	9.06435	+	18.1773i	0.732810	+	1.46954i
$154$	0.785925	−	17.2334i	0.0633317	−	1.38871i
$155$			0.812543i			0.0652651i
$156$	0.821934	−	0.533172i	0.0658074	−	0.0426879i
$157$	11.9343	+	8.67081i	0.952464	+	0.692006i	0.951388	−	0.307994i	$-0.0996576\pi$
$157$	11.9343	+	8.67081i	0.952464	+	0.692006i	0.00107582	+	0.999999i	$0.499658\pi$
$158$	−10.6603	+	7.74515i	−0.848087	+	0.616171i
$159$	−7.65409	+	6.48010i	−0.607009	+	0.513905i
$160$	0.331667	+	0.107765i	0.0262206	+	0.00851958i
$161$	3.76604	+	5.18350i	0.296805	+	0.408517i
$162$	3.86616	+	12.6396i	0.303754	+	0.993063i
$163$	−13.0536	+	4.24138i	−1.02244	+	0.332210i	−0.771797	−	0.635869i	$-0.780642\pi$
$163$	−13.0536	+	4.24138i	−1.02244	+	0.332210i	−0.250642	+	0.968080i	$0.580642\pi$
$164$		−	0.174377i		−	0.0136166i
$165$	1.38172	+	1.79157i	0.107567	+	0.139473i
$166$	0.516115			0.0400583
$167$	7.15934	−	2.32621i	0.554006	−	0.180008i	−0.0186162	−	0.999827i	$-0.505926\pi$
$167$	7.15934	−	2.32621i	0.554006	−	0.180008i	0.572623	+	0.819819i	$0.305926\pi$
$168$	6.28799	+	15.3684i	0.485129	+	1.18570i
$169$	8.25807	+	10.0401i	0.635236	+	0.772318i
$170$	3.72460	+	1.21020i	0.285664	+	0.0928178i
$171$	11.7952	−	1.76360i	0.902000	−	0.134866i
$172$	0.785858	+	1.08164i	0.0599211	+	0.0824743i
$173$	−15.9689	−	11.6021i	−1.21409	−	0.882089i	−0.218495	−	0.975838i	$-0.570115\pi$
$173$	−15.9689	−	11.6021i	−1.21409	−	0.882089i	−0.995596	+	0.0937495i	$0.970115\pi$
$174$	−0.457722	+	1.87083i	−0.0346999	+	0.141827i
$175$	−17.1592			−1.29711
$176$	3.77500	+	13.7155i	0.284551	+	1.03384i
$177$	11.8838	−	19.2054i	0.893241	−	1.44357i
$178$	19.8218	−	6.44051i	1.48571	−	0.482736i
$179$	5.07242	−	6.98158i	0.379130	−	0.521828i	−0.576224	−	0.817292i	$-0.695474\pi$
$179$	5.07242	−	6.98158i	0.379130	−	0.521828i	0.955354	+	0.295464i	$0.0954743\pi$
$180$	0.164424	+	0.0855796i	0.0122554	+	0.00637873i
$181$	−2.73239	+	8.40942i	−0.203097	+	0.625068i	0.796689	+	0.604389i	$0.206583\pi$
$181$	−2.73239	+	8.40942i	−0.203097	+	0.625068i	−0.999786	+	0.0206786i	$0.993417\pi$
$182$	16.4472	−	9.01157i	1.21915	−	0.667982i
$183$	−12.3540	+	0.918474i	−0.913234	+	0.0678955i
$184$	−3.96166	−	2.87831i	−0.292057	−	0.212192i
$185$	−1.16031	+	0.377008i	−0.0853077	+	0.0277182i
$186$	−2.76140	+	4.46270i	−0.202476	+	0.327221i
$187$	5.95903	+	21.6506i	0.435768	+	1.58325i
$188$	−0.226727			−0.0165357
$189$	4.06335	+	17.9491i	0.295565	+	1.30560i
$190$	1.35159	−	1.86031i	0.0980549	−	0.134961i
$191$	−9.75261	−	13.4233i	−0.705674	−	0.971277i	−0.999879	−	0.0155346i	$-0.995055\pi$
$191$	−9.75261	−	13.4233i	−0.705674	−	0.971277i	0.294205	−	0.955742i	$-0.404945\pi$
$192$	−8.14515	−	9.62079i	−0.587826	−	0.694321i
$193$	6.36534	−	19.5905i	0.458187	−	1.41015i	−0.409165	−	0.912460i	$-0.634180\pi$
$193$	6.36534	−	19.5905i	0.458187	−	1.41015i	0.867352	−	0.497694i	$-0.165820\pi$
$194$	1.48258	−	1.07716i	0.106443	−	0.0773355i
$195$	−0.882613	+	2.29577i	−0.0632053	+	0.164404i
$196$	−0.268752	−	0.827135i	−0.0191966	−	0.0590810i
$197$			7.66173i			0.545875i	0.962032	+	0.272938i	$0.0879953\pi$
$197$			7.66173i			0.545875i	−0.962032	+	0.272938i	$0.912005\pi$
$198$	1.50022	+	14.5355i	0.106616	+	1.03299i
$199$	21.5907			1.53052			0.765261	−	0.643720i	$-0.222610\pi$
$199$	21.5907			1.53052			0.765261	+	0.643720i	$0.222610\pi$
$200$	12.4726	−	4.05259i	0.881944	−	0.286561i
$201$	−3.33805	−	8.15850i	−0.235448	−	0.575457i
$202$	0.471826	+	0.649413i	0.0331976	+	0.0456925i
$203$	−0.828666	+	2.55037i	−0.0581610	+	0.179001i
$204$	1.18876	+	1.40412i	0.0832295	+	0.0983081i
$205$	0.257317	+	0.354167i	0.0179718	+	0.0247361i
$206$	−4.24986	+	5.84944i	−0.296102	+	0.407549i
$207$	−3.80421	−	3.87068i	−0.264411	−	0.269031i
$208$	−10.6023	+	11.2583i	−0.735139	+	0.780622i
$209$	13.1713	+	0.600675i	0.911080	+	0.0415495i
$210$	3.01734	+	1.86705i	0.208216	+	0.128839i
$211$	20.9775	−	6.81602i	1.44415	−	0.469234i	0.520964	−	0.853579i	$-0.325573\pi$
$211$	20.9775	−	6.81602i	1.44415	−	0.469234i	0.923190	+	0.384345i	$0.125573\pi$
$212$	−0.533920	+	0.734877i	−0.0366697	+	0.0504716i
$213$	0.651428	+	8.76208i	0.0446351	+	0.600368i
$214$	0.674219	+	0.219067i	0.0460886	+	0.0149751i
$215$	−3.19222	−	1.03721i	−0.217708	−	0.0707375i
$216$	−7.19269	−	12.0871i	−0.489400	−	0.822421i
$217$	−4.29485	+	5.91136i	−0.291554	+	0.401289i
$218$	19.9153	−	6.47087i	1.34883	−	0.438262i
$219$	6.23521	−	10.0767i	0.421336	−	0.680923i
$220$	0.160128	+	0.127880i	0.0107958	+	0.00862165i
$221$	−16.7363	+	17.7718i	−1.12581	+	1.19546i
$222$	−7.65398	−	1.87265i	−0.513702	−	0.125684i
$223$	−11.6790	+	16.0747i	−0.782082	+	1.07644i	0.212967	+	0.977059i	$0.431687\pi$
$223$	−11.6790	+	16.0747i	−0.782082	+	1.07644i	−0.995049	+	0.0993844i	$0.968313\pi$
$224$	1.84331	+	2.53709i	0.123161	+	0.169517i
$225$	14.3749	−	2.14931i	0.958324	−	0.143288i
$226$	−9.43520	+	29.0386i	−0.627620	+	1.93162i
$227$	8.37859	+	11.5321i	0.556107	+	0.765415i	0.990825	−	0.135151i	$-0.0431521\pi$
$227$	8.37859	+	11.5321i	0.556107	+	0.765415i	−0.434718	+	0.900566i	$0.643152\pi$
$228$	0.999778	−	0.409059i	0.0662119	−	0.0270906i
$229$	−18.4615	+	5.99850i	−1.21997	+	0.396392i	−0.847071	−	0.531481i	$-0.821636\pi$
$229$	−18.4615	+	5.99850i	−1.21997	+	0.396392i	−0.372898	+	0.927872i	$0.621636\pi$
$230$	−1.04639			−0.0689972
$231$	0.582549	+	20.3372i	0.0383289	+	1.33809i
$232$		−	2.04951i		−	0.134557i
$233$	7.41262	+	22.8137i	0.485617	+	1.49457i	0.831086	+	0.556144i	$0.187720\pi$
$233$	7.41262	+	22.8137i	0.485617	+	1.49457i	−0.345469	+	0.938430i	$0.612280\pi$
$234$	−12.6496	+	9.60945i	−0.826933	+	0.628190i
$235$	0.460491	−	0.334567i	0.0300391	−	0.0218247i
$236$	0.632131	−	1.94550i	0.0411482	−	0.126641i
$237$	11.8605	−	10.0413i	0.770423	−	0.652255i
$238$	20.7002	+	28.4914i	1.34180	+	1.84682i
$239$	−6.21102	+	8.54873i	−0.401757	+	0.552971i	−0.961184	−	0.275908i	$-0.911021\pi$
$239$	−6.21102	+	8.54873i	−0.401757	+	0.552971i	0.559427	+	0.828880i	$0.311021\pi$
$240$	−2.84209	−	0.695354i	−0.183456	−	0.0448849i
$241$	23.4924			1.51328			0.756641	−	0.653831i	$-0.226839\pi$
$241$	23.4924			1.51328			0.756641	+	0.653831i	$0.226839\pi$
$242$	−1.47043	+	16.0879i	−0.0945226	+	1.03417i
$243$	−5.65227	−	14.5276i	−0.362593	−	0.931948i
$244$	−1.06713	+	0.346733i	−0.0683163	+	0.0221973i
$245$	1.76640	+	1.28336i	0.112851	+	0.0819911i
$246$	0.209632	+	2.81966i	0.0133656	+	0.179775i
$247$	6.88746	+	12.5704i	0.438238	+	0.799838i
$248$	1.72570	−	5.31116i	0.109582	−	0.337259i
$249$	−0.607012	+	0.0451291i	−0.0384678	+	0.00285994i
$250$	3.34713	−	4.60693i	0.211691	−	0.291368i
$251$	3.00427	−	0.976146i	0.189628	−	0.0616138i	−0.212664	−	0.977125i	$-0.568214\pi$
$251$	3.00427	−	0.976146i	0.189628	−	0.0616138i	0.402291	+	0.915512i	$0.368214\pi$
$252$	0.743856	+	1.49169i	0.0468585	+	0.0939679i
$253$	−3.30189	−	5.00970i	−0.207588	−	0.314957i
$254$	26.8908			1.68728
$255$	−4.48638	−	1.09765i	−0.280948	−	0.0687377i
$256$	−3.02780	−	2.19983i	−0.189238	−	0.137489i
$257$	−0.970895	−	1.33632i	−0.0605627	−	0.0833575i	0.777661	−	0.628683i	$-0.216406\pi$
$257$	−0.970895	−	1.33632i	−0.0605627	−	0.0833575i	−0.838224	+	0.545326i	$0.816406\pi$
$258$	−14.0076	−	16.5453i	−0.872074	−	1.03007i
$259$	−10.4342	−	3.39026i	−0.648347	−	0.210661i
$260$	−0.0282348	+	0.220981i	−0.00175105	+	0.0137046i
$261$	0.374750	−	2.24034i	0.0231965	−	0.138673i
$262$	22.4047	−	7.27972i	1.38416	−	0.449742i
$263$	7.89447			0.486794			0.243397	−	0.969927i	$-0.421738\pi$
$263$	7.89447			0.486794			0.243397	+	0.969927i	$0.421738\pi$
$264$	−5.22661	−	14.6450i	−0.321675	−	0.901340i
$265$		−	2.28044i		−	0.140086i
$266$	19.6660	−	6.38988i	1.20580	−	0.391789i
$267$	−22.7496	+	9.30801i	−1.39226	+	0.569641i
$268$	−0.469297	−	0.645932i	−0.0286669	−	0.0394566i
$269$	11.3776	+	3.69680i	0.693703	+	0.225398i	0.634585	−	0.772853i	$-0.281171\pi$
$269$	11.3776	+	3.69680i	0.693703	+	0.225398i	0.0591184	+	0.998251i	$0.481171\pi$
$270$	−2.76160	−	1.18615i	−0.168065	−	0.0721868i
$271$	15.6444	−	11.3663i	0.950328	−	0.690454i	−0.000556267	−	1.00000i	$-0.500177\pi$
$271$	15.6444	−	11.3663i	0.950328	−	0.690454i	0.950884	+	0.309546i	$0.100177\pi$
$272$	−23.4941	−	17.0695i	−1.42454	−	1.03499i
$273$	−18.5559	+	12.0368i	−1.12305	+	0.728501i
$274$		−	11.1312i		−	0.672459i
$275$	16.0520	+	0.732046i	0.967970	+	0.0441440i
$276$	−0.418013	−	0.258655i	−0.0251614	−	0.0155692i
$277$	−30.5466	+	9.92519i	−1.83537	+	0.596347i	−0.836541	+	0.547905i	$0.815426\pi$
$277$	−30.5466	+	9.92519i	−1.83537	+	0.596347i	−0.998826	+	0.0484421i	$0.984574\pi$
$278$	10.2271	+	7.43042i	0.613380	+	0.445647i
$279$	2.85751	−	5.49012i	0.171075	−	0.328685i
$280$	−3.59100	−	1.16679i	−0.214604	−	0.0697289i
$281$	−26.4457	−	8.59272i	−1.57762	−	0.512599i	−0.616175	−	0.787609i	$-0.711319\pi$
$281$	−26.4457	−	8.59272i	−1.57762	−	0.512599i	−0.961441	+	0.275011i	$0.911319\pi$
$282$	3.66615	−	0.272565i	0.218316	−	0.0162310i
$283$	16.9076	−	23.2714i	1.00505	−	1.38334i	0.0828818	−	0.996559i	$-0.473588\pi$
$283$	16.9076	−	23.2714i	1.00505	−	1.38334i	0.922172	−	0.386779i	$-0.126412\pi$
$284$	0.245921	+	0.756866i	0.0145927	+	0.0449117i
$285$	−1.42697	+	2.30612i	−0.0845262	+	0.136603i
$286$	−15.7704	+	7.72843i	−0.932523	+	0.456992i
$287$			3.93671i			0.232377i
$288$	−1.86199	−	1.89453i	−0.109719	−	0.111636i
$289$	−23.3334	−	16.9527i	−1.37255	−	0.997218i
$290$	−0.257422	−	0.354311i	−0.0151163	−	0.0208059i
$291$	−1.64950	+	1.39650i	−0.0966956	+	0.0818644i
$292$	0.331667	−	1.02077i	0.0194094	−	0.0597359i
$293$	11.9056	+	16.3867i	0.695534	+	0.957321i	0.999989	+	0.00479373i	$0.00152590\pi$
$293$	11.9056	+	16.3867i	0.695534	+	0.957321i	−0.304454	+	0.952527i	$0.598474\pi$
$294$	5.34006	+	13.0516i	0.311439	+	0.761186i
$295$	1.58697	+	4.88418i	0.0923968	+	0.284368i
$296$	8.38503			0.487370
$297$	−3.03541	−	16.9643i	−0.176132	−	0.984366i
$298$	11.4519			0.663389
$299$	2.78558	−	5.89793i	0.161094	−	0.341086i
$300$	1.21843	−	0.498522i	0.0703464	−	0.0287822i
$301$	−17.7414	−	24.4190i	−1.02260	−	1.40749i
$302$	1.19302	+	0.387635i	0.0686504	+	0.0223059i
$303$	−0.611708	−	0.722530i	−0.0351417	−	0.0415082i
$304$	−13.7947	+	10.0225i	−0.791182	+	0.574827i
$305$	1.65574	−	2.27893i	0.0948075	−	0.130491i
$306$	−20.9101	−	21.2754i	−1.19535	−	1.21623i
$307$	29.5910			1.68885			0.844424	−	0.535675i	$-0.179943\pi$
$307$	29.5910			1.68885			0.844424	+	0.535675i	$0.179943\pi$
$308$	0.489021	+	1.77673i	0.0278646	+	0.101239i
$309$	4.48686	−	7.25123i	0.255249	−	0.412508i
$310$	−0.368758	−	1.13492i	−0.0209441	−	0.0644592i
$311$	4.36494	−	6.00783i	0.247513	−	0.340673i	−0.667125	−	0.744946i	$-0.732475\pi$
$311$	4.36494	−	6.00783i	0.247513	−	0.340673i	0.914638	+	0.404273i	$0.132475\pi$
$312$	10.6450	−	13.1317i	0.602654	−	0.743437i
$313$	−7.87252	+	24.2291i	−0.444981	+	1.36951i	0.437523	+	0.899207i	$0.355856\pi$
$313$	−7.87252	+	24.2291i	−0.444981	+	1.36951i	−0.882504	+	0.470304i	$0.844144\pi$
$314$	−20.6044	−	6.69478i	−1.16277	−	0.377808i
$315$	−3.71200	−	1.93203i	−0.209148	−	0.108858i
$316$	0.827343	−	1.13874i	0.0465417	−	0.0640591i
$317$	−5.39908	−	16.6167i	−0.303242	−	0.933284i	−0.980327	−	0.197379i	$-0.936757\pi$
$317$	−5.39908	−	16.6167i	−0.303242	−	0.933284i	0.677085	−	0.735905i	$-0.263243\pi$
$318$	7.74999	−	12.5248i	0.434598	−	0.702354i
$319$	0.884001	−	2.35046i	0.0494945	−	0.131600i
$320$	2.86639			0.160236
$321$	−0.812115	−	0.198695i	−0.0453279	−	0.0110901i
$322$	−7.61266	−	5.53092i	−0.424237	−	0.308226i
$323$	−21.7757	+	15.8210i	−1.21163	+	0.880303i
$324$	−0.810000	−	1.15647i	−0.0450000	−	0.0642485i
$325$	8.39378	+	15.3197i	0.465603	+	0.849782i
$326$	16.3078	−	11.8483i	0.903206	−	0.656217i
$327$	−22.8569	+	9.35189i	−1.26399	+	0.517161i
$328$	−0.929757	−	2.86150i	−0.0513373	−	0.158000i
$329$	5.11855			0.282195
$330$	−2.74300	−	1.87530i	−0.150997	−	0.103232i
$331$		−	11.7261i		−	0.644524i	−0.946650	−	0.322262i	$-0.895557\pi$
$331$		−	11.7261i		−	0.644524i	0.946650	−	0.322262i	$-0.104443\pi$
$332$	−0.0524335	+	0.0170367i	−0.00287766	+	0.000935010i
$333$	9.16572	+	1.53319i	0.502279	+	0.0840183i
$334$	−8.94411	+	6.49828i	−0.489400	+	0.355570i
$335$	1.90632	+	0.619402i	0.104154	+	0.0338416i
$336$	−17.0011	−	20.0812i	−0.927488	−	1.09552i
$337$	−3.92544	−	5.40291i	−0.213833	−	0.294315i	0.688604	−	0.725137i	$-0.258224\pi$
$337$	−3.92544	−	5.40291i	−0.213833	−	0.294315i	−0.902437	+	0.430822i	$0.858224\pi$
$338$	−16.0910	−	10.2758i	−0.875236	−	0.558930i
$339$	8.55778	−	34.9778i	0.464795	−	1.89973i
$340$	−0.418340			−0.0226877
$341$	4.26992	−	5.34670i	0.231229	−	0.289540i
$342$	−15.6746	+	7.81635i	−0.847583	+	0.422660i
$343$	−1.59383	−	4.90530i	−0.0860586	−	0.264861i
$344$	18.6630	+	13.5594i	1.00624	+	0.731076i
$345$	1.23068	−	0.0914967i	0.0662577	−	0.00492602i
$346$	27.5699	+	8.95802i	1.48217	+	0.481586i
$347$	−1.34199	+	4.13022i	−0.0720417	+	0.221722i	−0.980594	−	0.196050i	$-0.937189\pi$
$347$	−1.34199	+	4.13022i	−0.0720417	+	0.221722i	0.908552	+	0.417771i	$0.137189\pi$
$348$	−0.0152537	−	0.205171i	−0.000817686	−	0.0109983i
$349$	−16.9746	−	12.3328i	−0.908630	−	0.660158i	0.0320382	−	0.999487i	$-0.489800\pi$
$349$	−16.9746	−	12.3328i	−0.908630	−	0.660158i	−0.940668	+	0.339329i	$0.889800\pi$
$350$	23.9671	−	7.78739i	1.28110	−	0.416253i
$351$	14.0372	−	12.4079i	0.749251	−	0.662286i
$352$	−1.61613	−	2.45203i	−0.0861400	−	0.130693i
$353$	−12.1435			−0.646332			−0.323166	−	0.946342i	$-0.604747\pi$
$353$	−12.1435			−0.646332			−0.323166	+	0.946342i	$0.604747\pi$
$354$	−7.88268	+	32.2185i	−0.418960	+	1.71239i
$355$	−1.61633	−	1.17434i	−0.0857861	−	0.0623273i
$356$	−1.80115	+	1.30862i	−0.0954610	+	0.0693565i
$357$	−26.8372	−	31.6992i	−1.42037	−	1.67770i
$358$	−3.91644	+	12.0536i	−0.206990	+	0.637051i
$359$	−17.4256	−	23.9842i	−0.919685	−	1.26584i	−0.963749	−	0.266810i	$-0.914030\pi$
$359$	−17.4256	−	23.9842i	−0.919685	−	1.26584i	0.0440638	−	0.999029i	$-0.485970\pi$
$360$	3.15446	+	0.527660i	0.166255	+	0.0278101i
$361$	−0.987598	−	3.03951i	−0.0519788	−	0.159974i
$362$		−	12.9859i		−	0.682525i
$363$	0.322669	−	19.0498i	0.0169357	−	0.999857i
$364$	−1.37345	+	1.45842i	−0.0719882	+	0.0764421i
$365$	0.832652	+	2.56264i	0.0435830	+	0.134135i
$366$	16.8386	−	6.88952i	0.880170	−	0.360121i
$367$	−5.11442	+	3.71584i	−0.266971	+	0.193966i	−0.713214	−	0.700946i	$-0.752761\pi$
$367$	−5.11442	+	3.71584i	−0.266971	+	0.193966i	0.446244	+	0.894911i	$0.352761\pi$
$368$	7.37955	+	2.39776i	0.384686	+	0.124992i
$369$	−0.493103	−	3.29793i	−0.0256699	−	0.171683i
$370$	1.44957	−	1.05317i	0.0753595	−	0.0547518i
$371$	12.0537	−	16.5905i	0.625796	−	0.861335i
$372$	0.133226	−	0.544530i	0.00690747	−	0.0282326i
$373$			14.6270i			0.757359i	0.925528	+	0.378680i	$0.123622\pi$
$373$			14.6270i			0.757359i	−0.925528	+	0.378680i	$0.876378\pi$
$374$	−18.1490	−	27.5361i	−0.938464	−	1.42386i
$375$	−3.53379	+	5.71096i	−0.182484	+	0.294913i
$376$	−3.72055	+	1.20888i	−0.191873	+	0.0623432i
$377$	2.68233	−	0.507739i	0.138147	−	0.0261499i
$378$	−13.8214	−	23.2263i	−0.710894	−	1.19463i
$379$	31.4667	+	10.2242i	1.61634	+	0.525180i	0.971074	−	0.238781i	$-0.0767477\pi$
$379$	31.4667	+	10.2242i	1.61634	+	0.525180i	0.645263	+	0.763960i	$0.276748\pi$
$380$	−0.0759042	+	0.233609i	−0.00389380	+	0.0119839i
$381$	−31.6267	+	2.35133i	−1.62028	+	0.120462i
$382$	19.7139	+	14.3230i	1.00865	+	0.732828i
$383$	6.76074	+	20.8074i	0.345458	+	1.06321i	0.961338	+	0.275370i	$0.0888004\pi$
$383$	6.76074	+	20.8074i	0.345458	+	1.06321i	−0.615881	+	0.787840i	$0.711200\pi$
$384$	18.3513	+	11.3553i	0.936487	+	0.579473i
$385$	−3.61503	−	2.88700i	−0.184239	−	0.147135i
$386$			30.2519i			1.53978i
$387$	17.9213	+	18.2344i	0.910990	+	0.926906i
$388$	−0.115063	+	0.158371i	−0.00584144	+	0.00804005i
$389$	4.72238	+	6.49980i	0.239434	+	0.329553i	0.911776	−	0.410688i	$-0.134711\pi$
$389$	4.72238	+	6.49980i	0.239434	+	0.329553i	−0.672342	+	0.740241i	$0.734711\pi$
$390$	0.190897	−	3.60718i	0.00966646	−	0.182657i
$391$	11.6490	+	3.78499i	0.589116	+	0.191415i
$392$	−8.82036	−	12.1402i	−0.445495	−	0.613172i
$393$	−25.7140	+	10.5209i	−1.29710	+	0.530707i
$394$	−3.47714	−	10.7015i	−0.175176	−	0.539135i
$395$			3.53369i			0.177799i
$396$	−0.632219	−	1.42718i	−0.0317702	−	0.0717184i
$397$			19.6242i			0.984908i	0.870338	+	0.492454i	$0.163900\pi$
$397$			19.6242i			0.984908i	−0.870338	+	0.492454i	$0.836100\pi$
$398$	−30.1568	+	9.79855i	−1.51162	+	0.491157i
$399$	−22.5708	+	9.23485i	−1.12996	+	0.462321i
$400$	−16.8117	+	12.2144i	−0.840586	+	0.610721i
$401$	−1.61756	+	4.97832i	−0.0807769	+	0.248606i	−0.983287	−	0.182063i	$-0.941722\pi$
$401$	−1.61756	+	4.97832i	−0.0807769	+	0.248606i	0.902510	+	0.430669i	$0.141722\pi$
$402$	8.36502	+	9.88049i	0.417209	+	0.492794i
$403$	7.37856	+	0.942763i	0.367552	+	0.0469624i
$404$	−0.0693708	−	0.0504009i	−0.00345133	−	0.00250754i
$405$	3.35168	+	1.15358i	0.166546	+	0.0573217i
$406$		−	3.93831i		−	0.195455i
$407$	9.61626	+	3.61665i	0.476660	+	0.179271i
$408$	26.9939	+	16.7031i	1.33640	+	0.826925i
$409$	−10.5690	−	32.5279i	−0.522602	−	1.60840i	−0.769010	−	0.639236i	$-0.779251\pi$
$409$	−10.5690	−	32.5279i	−0.522602	−	1.60840i	0.246409	−	0.969166i	$-0.420749\pi$
$410$	−0.520141	−	0.377905i	−0.0256879	−	0.0186634i
$411$	0.973309	+	13.0916i	0.0480098	+	0.645759i
$412$	0.238668	−	0.734545i	0.0117583	−	0.0361884i
$413$	−14.2709	+	43.9213i	−0.702225	+	2.16123i
$414$	7.07019	+	3.67991i	0.347481	+	0.180858i
$415$	0.0813547	−	0.111975i	0.00399354	−	0.00549664i
$416$	1.36342	−	2.88677i	0.0668470	−	0.141536i
$417$	−12.6780	−	7.84479i	−0.620843	−	0.384161i
$418$	−18.6697	+	5.13858i	−0.913164	+	0.251336i
$419$		−	4.46014i		−	0.217892i	−0.994048	−	0.108946i	$-0.965252\pi$
$419$		−	4.46014i		−	0.217892i	0.994048	−	0.108946i	$-0.0347476\pi$
$420$	−0.368170	−	0.0900776i	−0.0179649	−	0.00439534i
$421$	16.6002	−	22.8483i	0.809046	−	1.11356i	−0.182424	−	0.983220i	$-0.558394\pi$
$421$	16.6002	−	22.8483i	0.809046	−	1.11356i	0.991470	−	0.130336i	$-0.0416056\pi$
$422$	−26.2071	+	19.0406i	−1.27574	+	0.926880i
$423$	−4.28799	+	0.641136i	−0.208489	+	0.0311731i
$424$	−4.84325	+	14.9060i	−0.235209	+	0.723899i
$425$	−26.5382	+	19.2811i	−1.28729	+	0.935271i
$426$	−4.88640	−	11.9428i	−0.236747	−	0.578632i
$427$	24.0915	−	7.82779i	1.16587	−	0.378813i
$428$	−0.0757269			−0.00366040
$429$	17.8721	−	10.4685i	0.862871	−	0.505424i
$430$	4.92946			0.237720
$431$	12.4609	−	4.04878i	0.600219	−	0.195023i	0.00688082	−	0.999976i	$-0.497810\pi$
$431$	12.4609	−	4.04878i	0.600219	−	0.195023i	0.593338	+	0.804953i	$0.297810\pi$
$432$	16.7578	+	14.6932i	0.806259	+	0.706928i
$433$	−7.04895	+	5.12136i	−0.338751	+	0.246117i	−0.744135	−	0.668030i	$-0.767138\pi$
$433$	−7.04895	+	5.12136i	−0.338751	+	0.246117i	0.405384	+	0.914147i	$0.367138\pi$
$434$	3.31608	−	10.2058i	0.159177	−	0.489896i
$435$	0.333740	+	0.394203i	0.0160016	+	0.0189006i
$436$	−1.80965	+	1.31478i	−0.0866663	+	0.0629667i
$437$	4.22723	−	5.81828i	0.202216	−	0.278326i
$438$	−4.13589	+	16.9044i	−0.197621	+	0.807725i
$439$		−	4.92060i		−	0.234848i	−0.993082	−	0.117424i	$-0.962536\pi$
$439$		−	4.92060i		−	0.234848i	0.993082	−	0.117424i	$-0.0374636\pi$
$440$	3.30952	+	1.24470i	0.157775	+	0.0593388i
$441$	−7.42177	−	14.8833i	−0.353418	−	0.708728i
$442$	15.3111	−	32.4183i	0.728274	−	1.54198i
$443$	−10.2700	+	14.1354i	−0.487942	+	0.671594i	−0.980007	−	0.198964i	$-0.936242\pi$
$443$	−10.2700	+	14.1354i	−0.487942	+	0.671594i	0.492065	+	0.870559i	$0.336242\pi$
$444$	0.839403	−	0.0624065i	0.0398363	−	0.00296168i
$445$	1.72718	−	5.31570i	0.0818760	−	0.251989i
$446$	9.01740	−	27.7527i	0.426986	−	1.31413i
$447$	−13.4687	+	1.00135i	−0.637049	+	0.0473623i
$448$	20.8534	+	15.1509i	0.985230	+	0.715811i
$449$	5.38963	+	16.5876i	0.254352	+	0.782816i	0.993957	+	0.109774i	$0.0350126\pi$
$449$	5.38963	+	16.5876i	0.254352	+	0.782816i	−0.739604	+	0.673042i	$0.764987\pi$
$450$	−19.1027	+	9.52583i	−0.900509	+	0.449052i
$451$	0.167948	−	3.68270i	0.00790838	−	0.173411i
$452$		−	3.26156i		−	0.153411i
$453$	−1.43702	−	0.351587i	−0.0675172	−	0.0165190i
$454$	−16.9365	−	12.3051i	−0.794868	−	0.577505i
$455$	0.637425	−	4.98883i	0.0298829	−	0.233880i
$456$	14.2251	−	12.0433i	0.666153	−	0.563978i
$457$	−0.623641	+	1.91937i	−0.0291727	+	0.0897843i	−0.964583	−	0.263780i	$-0.915031\pi$
$457$	−0.623641	+	1.91937i	−0.0291727	+	0.0897843i	0.935410	+	0.353565i	$0.115031\pi$
$458$	23.0638	−	16.7568i	1.07770	−	0.782995i
$459$	26.4530	+	23.1940i	1.23472	+	1.08260i
$460$	0.106306	−	0.0345409i	0.00495654	−	0.00161048i
$461$		−	32.8562i		−	1.53026i	−0.643873	−	0.765132i	$-0.722674\pi$
$461$		−	32.8562i		−	1.53026i	0.643873	−	0.765132i	$-0.277326\pi$
$462$	−10.0434	−	28.1417i	−0.467260	−	1.30927i
$463$		−	24.1120i		−	1.12058i	−0.828296	−	0.560290i	$-0.810690\pi$
$463$		−	24.1120i		−	1.12058i	0.828296	−	0.560290i	$-0.189310\pi$
$464$	1.00355	+	3.08860i	0.0465885	+	0.143385i
$465$	0.532941	+	1.30256i	0.0247145	+	0.0604046i
$466$	−20.7072	−	28.5010i	−0.959241	−	1.32028i
$467$	−14.2535	−	4.63125i	−0.659574	−	0.214309i	−0.0399433	−	0.999202i	$-0.512718\pi$
$467$	−14.2535	−	4.63125i	−0.659574	−	0.214309i	−0.619631	+	0.784893i	$0.712718\pi$
$468$	0.967908	−	1.39381i	0.0447415	−	0.0644288i
$469$	10.5948	+	14.5825i	0.489222	+	0.673356i
$470$	−0.491355	+	0.676292i	−0.0226645	+	0.0311950i
$471$	24.8186	+	6.07220i	1.14358	+	0.279792i
$472$		−	35.2957i		−	1.62462i
$473$	15.5549	+	23.6002i	0.715214	+	1.08514i
$474$	−12.0091	+	19.4079i	−0.551597	+	0.891436i
$475$	5.95182	+	18.3178i	0.273088	+	0.840480i
$476$	−3.04348	−	2.21121i	−0.139497	−	0.101351i
$477$	−8.01973	+	15.4083i	−0.367198	+	0.705496i
$478$	4.79556	−	14.7592i	0.219344	−	0.675071i
$479$	35.9151	+	11.6695i	1.64100	+	0.533194i	0.976762	−	0.214325i	$-0.0687551\pi$
$479$	35.9151	+	11.6695i	1.64100	+	0.533194i	0.664240	+	0.747519i	$0.268755\pi$
$480$	0.602365	−	0.0447836i	0.0274941	−	0.00204408i
$481$	2.07728	+	10.9740i	0.0947157	+	0.500372i
$482$	−32.8131	+	10.6616i	−1.49460	+	0.485624i
$483$	9.43700	+	5.83936i	0.429399	+	0.265700i
$484$	−0.381668	−	1.68295i	−0.0173485	−	0.0764977i
$485$		−	0.491449i		−	0.0223155i
$486$	14.4879	+	17.7263i	0.657185	+	0.804082i
$487$	8.46701	−	11.6538i	0.383677	−	0.528086i	−0.572877	−	0.819641i	$-0.694173\pi$
$487$	8.46701	−	11.6538i	0.383677	−	0.528086i	0.956554	+	0.291555i	$0.0941727\pi$
$488$	−15.6627	+	11.3797i	−0.709019	+	0.515133i
$489$	−18.1439	+	15.3610i	−0.820494	+	0.694646i
$490$	−3.04965	−	0.990892i	−0.137769	−	0.0447639i
$491$	−28.8890	+	20.9891i	−1.30374	+	0.947223i	−0.999985	−	0.00552650i	$-0.998241\pi$
$491$	−28.8890	+	20.9891i	−1.30374	+	0.947223i	−0.303756	+	0.952750i	$0.598241\pi$
$492$	−0.114373	−	0.279537i	−0.00515631	−	0.0126025i
$493$	1.58415	+	4.87552i	0.0713466	+	0.219582i
$494$	−15.3249	−	14.4320i	−0.689502	−	0.649328i
$495$	3.39006	+	1.96573i	0.152372	+	0.0883530i
$496$			8.84887i			0.397326i
$497$	−5.55187	−	17.0869i	−0.249035	−	0.766452i
$498$	0.827365	−	0.338516i	0.0370751	−	0.0151693i
$499$	−2.39437	−	3.29556i	−0.107187	−	0.147530i	0.752054	−	0.659102i	$-0.229063\pi$
$499$	−2.39437	−	3.29556i	−0.107187	−	0.147530i	−0.859240	+	0.511572i	$0.829063\pi$
$500$	−0.187971	+	0.578516i	−0.00840634	+	0.0258720i
$501$	9.95112	−	8.42481i	0.444583	−	0.376393i
$502$	−3.75321	+	2.72687i	−0.167514	+	0.121706i
$503$	9.01581	+	6.55037i	0.401995	+	0.292066i	0.770353	−	0.637618i	$-0.220080\pi$
$503$	9.01581	+	6.55037i	0.401995	+	0.292066i	−0.368358	+	0.929684i	$0.620080\pi$
$504$	20.1601	+	20.5123i	0.898001	+	0.913691i
$505$	0.215268			0.00957932
$506$	6.88549	+	5.49881i	0.306097	+	0.244452i
$507$	19.8234	+	10.6786i	0.880390	+	0.474251i
$508$	−2.73190	+	0.887649i	−0.121209	+	0.0393830i
$509$	−28.1949	−	20.4848i	−1.24972	−	0.907971i	−0.251510	−	0.967855i	$-0.580927\pi$
$509$	−28.1949	−	20.4848i	−1.24972	−	0.907971i	−0.998205	+	0.0598833i	$0.980927\pi$
$510$	6.76452	−	0.502917i	0.299538	−	0.0222695i
$511$	−7.48767	+	23.0447i	−0.331235	+	1.01944i
$512$	−18.4718	−	6.00187i	−0.816348	−	0.265248i
$513$	17.7517	−	10.5635i	0.783755	−	0.466391i
$514$	1.96257	+	1.42589i	0.0865650	+	0.0628932i
$515$	0.599178	+	1.84408i	0.0264029	+	0.0812598i
$516$	1.96922	+	1.21850i	0.0866900	+	0.0536414i
$517$	−4.78827	−	0.218368i	−0.210588	−	0.00960381i
$518$	16.1125			0.707945
$519$	−33.2088	−	8.12497i	−1.45770	−	0.356646i
$520$	0.714913	+	3.77680i	0.0313510	+	0.165624i
$521$	11.7331	+	16.1492i	0.514037	+	0.707511i	0.984594	−	0.174859i	$-0.0559469\pi$
$521$	11.7331	+	16.1492i	0.514037	+	0.707511i	−0.470557	+	0.882370i	$0.655947\pi$
$522$	0.493303	+	3.29927i	0.0215913	+	0.144405i
$523$	−10.2604	−	3.33382i	−0.448657	−	0.145778i	0.0759691	−	0.997110i	$-0.475795\pi$
$523$	−10.2604	−	3.33382i	−0.448657	−	0.145778i	−0.524626	+	0.851333i	$0.675795\pi$
$524$	−2.03585	+	1.47913i	−0.0889365	+	0.0646161i
$525$	−27.5072	+	11.2546i	−1.20051	+	0.491189i
$526$	−11.0266	+	3.58277i	−0.480783	+	0.156216i
$527$			13.9684i			0.608473i
$528$	15.0474	+	19.5108i	0.654855	+	0.849097i
$529$	19.7273			0.857709
$530$	1.03494	+	3.18521i	0.0449548	+	0.138357i
$531$	6.45377	−	38.5820i	0.280070	−	1.67432i
$532$	−1.78700	+	1.29833i	−0.0774762	+	0.0562897i
$533$	3.51469	−	1.92573i	0.152238	−	0.0834126i
$534$	27.5513	−	23.3255i	1.19226	−	1.00939i
$535$	0.153804	−	0.111745i	0.00664955	−	0.00483118i
$536$	−11.1451	−	8.09740i	−0.481396	−	0.349754i
$537$	3.55223	−	14.5189i	0.153290	−	0.626535i
$538$	−17.5694			−0.757470
$539$	−4.87918	−	17.7272i	−0.210161	−	0.763565i
$540$	0.319712	+	0.0293452i	0.0137582	+	0.00126282i
$541$	−5.53282	−	17.0283i	−0.237875	−	0.732103i	−0.996727	−	0.0808403i	$-0.974240\pi$
$541$	−5.53282	−	17.0283i	−0.237875	−	0.732103i	0.758852	−	0.651263i	$-0.225760\pi$
$542$	−16.6929	+	22.9758i	−0.717022	+	0.986897i
$543$	1.13549	+	15.2730i	0.0487285	+	0.655426i
$544$	5.70167	+	1.85259i	0.244457	+	0.0794290i
$545$	1.73532	−	5.34076i	0.0743329	−	0.228773i
$546$	20.4553	−	25.2337i	0.875404	−	1.07990i
$547$	6.67569	−	9.18830i	0.285432	−	0.392863i	−0.642092	−	0.766628i	$-0.721933\pi$
$547$	6.67569	−	9.18830i	0.285432	−	0.392863i	0.927524	+	0.373764i	$0.121933\pi$
$548$	0.367434	+	1.13084i	0.0156960	+	0.0483073i
$549$	−19.2018	+	9.57526i	−0.819513	+	0.408662i
$550$	−22.7529	+	6.26242i	−0.970185	+	0.267030i
$551$	3.01001			0.128231
$552$	−8.23864	−	2.01569i	−0.350660	−	0.0857935i
$553$	−18.6780	+	25.7080i	−0.794268	+	1.09322i
$554$	38.1616	−	27.7261i	1.62133	−	1.17797i
$555$	−1.61277	+	1.36540i	−0.0684584	+	0.0579582i
$556$	−1.28427	−	0.417285i	−0.0544652	−	0.0176968i
$557$	−2.11037	−	2.90467i	−0.0894192	−	0.123075i	0.761964	−	0.647620i	$-0.224235\pi$
$557$	−2.11037	−	2.90467i	−0.0894192	−	0.123075i	−0.851383	+	0.524545i	$0.824235\pi$
$558$	−1.49964	+	8.96517i	−0.0634849	+	0.379526i
$559$	−13.1226	+	27.7845i	−0.555026	+	1.17516i
$560$	5.98293			0.252825
$561$	23.7531	+	30.7987i	1.00286	+	1.30032i
$562$	40.8377			1.72263
$563$	−11.5703	−	35.6096i	−0.487628	−	1.50077i	−0.828138	−	0.560525i	$-0.810599\pi$
$563$	−11.5703	−	35.6096i	−0.487628	−	1.50077i	0.340509	−	0.940241i	$-0.389401\pi$
$564$	−0.363457	+	0.148708i	−0.0153043	+	0.00626175i
$565$	4.81287	+	6.62435i	0.202479	+	0.278689i
$566$	−13.0545	+	40.1775i	−0.548721	+	1.68879i
$567$	18.2865	+	26.1084i	0.767959	+	1.09645i
$568$	8.07103	+	11.1088i	0.338653	+	0.466116i
$569$	0.256343	+	0.186244i	0.0107465	+	0.00780777i	0.593146	−	0.805095i	$-0.297886\pi$
$569$	0.256343	+	0.186244i	0.0107465	+	0.00780777i	−0.582399	+	0.812903i	$0.697886\pi$
$570$	0.946526	−	3.86869i	0.0396456	−	0.162042i
$571$		−	20.4932i		−	0.857614i	−0.903396	−	0.428807i	$-0.858934\pi$
$571$		−	20.4932i		−	0.857614i	0.903396	−	0.428807i	$-0.141066\pi$
$572$	1.34704	−	1.30572i	0.0563228	−	0.0545950i
$573$	−24.4383	−	15.1217i	−1.02092	−	0.631720i
$574$	−1.78661	−	5.49861i	−0.0745716	−	0.229508i
$575$	5.15175	−	7.09077i	0.214843	−	0.295706i
$576$	−19.3674	−	10.0804i	−0.806974	−	0.420016i
$577$	−13.7734	−	4.47526i	−0.573396	−	0.186308i	0.00794418	−	0.999968i	$-0.497471\pi$
$577$	−13.7734	−	4.47526i	−0.573396	−	0.186308i	−0.581340	+	0.813661i	$0.697471\pi$
$578$	40.2847	+	13.0893i	1.67562	+	0.544442i
$579$	−2.64522	−	35.5797i	−0.109932	−	1.47864i
$580$	0.0378478	+	0.0274980i	0.00157154	+	0.00114179i
$581$	1.18373	−	0.384618i	0.0491095	−	0.0159566i
$582$	1.67017	−	2.69917i	0.0692308	−	0.111884i
$583$	−11.9837	+	15.0057i	−0.496314	+	0.621474i
$584$		−	18.5190i		−	0.766322i
$585$	0.0908941	+	4.25916i	0.00375801	+	0.176095i
$586$	−24.0660	−	17.4850i	−0.994158	−	0.722298i
$587$	15.6614	−	11.3787i	0.646415	−	0.469648i	−0.215633	−	0.976475i	$-0.569181\pi$
$587$	15.6614	−	11.3787i	0.646415	−	0.469648i	0.862048	+	0.506826i	$0.169181\pi$
$588$	−0.973337	−	1.14968i	−0.0401398	−	0.0474118i
$589$	7.80023	+	2.53445i	0.321403	+	0.104430i
$590$	−4.43320	−	6.10178i	−0.182512	−	0.251206i
$591$	5.02526	+	12.2822i	0.206712	+	0.505223i
$592$	−12.6362	+	4.10574i	−0.519343	+	0.168745i
$593$		−	6.63012i		−	0.272267i	−0.990691	−	0.136133i	$-0.956532\pi$
$593$		−	6.63012i		−	0.272267i	0.990691	−	0.136133i	$-0.0434675\pi$
$594$	11.9386	+	22.3173i	0.489849	+	0.915690i
$595$	9.44438			0.387182
$596$	−1.16342	+	0.378020i	−0.0476557	+	0.0154843i
$597$	34.6112	−	14.1612i	1.41654	−	0.579577i
$598$	−1.21409	+	9.50213i	−0.0496479	+	0.388571i
$599$	14.1044	+	4.58279i	0.576289	+	0.187248i	0.582637	−	0.812732i	$-0.302021\pi$
$599$	14.1044	+	4.58279i	0.576289	+	0.187248i	−0.00634847	+	0.999980i	$0.502021\pi$
$600$	17.3362	−	14.6772i	0.707749	−	0.599194i
$601$	−19.9247	−	27.4240i	−0.812744	−	1.11865i	−0.990894	−	0.134643i	$-0.957011\pi$
$601$	−19.9247	−	27.4240i	−0.812744	−	1.11865i	0.178150	−	0.984003i	$-0.442989\pi$
$602$	35.8625	+	26.0556i	1.46165	+	1.06195i
$603$	−10.7022	−	10.8892i	−0.435827	−	0.443442i
$604$	−0.133997			−0.00545227
$605$	3.25861	+	2.85494i	0.132481	+	0.116070i
$606$	1.18231	+	0.731582i	0.0480281	+	0.0297185i
$607$	−13.6013	+	4.41933i	−0.552060	+	0.179375i	−0.571745	−	0.820431i	$-0.693733\pi$
$607$	−13.6013	+	4.41933i	−0.552060	+	0.179375i	0.0196856	+	0.999806i	$0.493733\pi$
$608$	2.06904	−	2.84779i	0.0839107	−	0.115493i
$609$	0.344366	+	4.63192i	0.0139544	+	0.187695i
$610$	−1.27841	+	3.93453i	−0.0517612	+	0.159305i
$611$	−2.50385	−	4.56983i	−0.101295	−	0.184875i
$612$	2.82660	+	1.47120i	0.114259	+	0.0594696i
$613$	−35.2224	−	25.5906i	−1.42262	−	1.03359i	−0.991332	−	0.131380i	$-0.958059\pi$
$613$	−35.2224	−	25.5906i	−1.42262	−	1.03359i	−0.431288	−	0.902214i	$-0.641941\pi$
$614$	−41.3313	+	13.4294i	−1.66800	+	0.541965i
$615$	0.644791	+	0.398979i	0.0260005	+	0.0160884i
$616$	17.4981	+	26.5484i	0.705017	+	1.06967i
$617$	−34.7020			−1.39705			−0.698524	−	0.715586i	$-0.746160\pi$
$617$	−34.7020			−1.39705			−0.698524	+	0.715586i	$0.746160\pi$
$618$	−2.97619	+	12.1645i	−0.119720	+	0.489326i
$619$	−11.6834	+	16.0808i	−0.469594	+	0.646340i	−0.976464	−	0.215682i	$-0.930802\pi$
$619$	−11.6834	+	16.0808i	−0.469594	+	0.646340i	0.506870	+	0.862023i	$0.330802\pi$
$620$	0.0749263	+	0.103127i	0.00300911	+	0.00414169i
$621$	−8.63714	−	3.70979i	−0.346596	−	0.148869i
$622$	−3.37020	+	10.3724i	−0.135133	+	0.415895i
$623$	40.6626	−	29.5431i	1.62911	−	1.18362i
$624$	−9.61196	+	25.0017i	−0.384786	+	1.00087i
$625$	7.01385	+	21.5864i	0.280554	+	0.863457i
$626$		−	37.4149i		−	1.49540i
$627$	21.5084	−	7.67605i	0.858964	−	0.306552i
$628$	2.31425			0.0923485
$629$	−19.9469	+	6.48113i	−0.795333	+	0.258419i
$630$	6.06157	+	1.01394i	0.241499	+	0.0403965i
$631$	−6.75890	−	9.30283i	−0.269068	−	0.370340i	0.653007	−	0.757352i	$-0.273507\pi$
$631$	−6.75890	−	9.30283i	−0.269068	−	0.370340i	−0.922075	+	0.387012i	$0.873507\pi$
$632$	7.50494	−	23.0978i	0.298530	−	0.918782i
$633$	29.1577	−	24.6855i	1.15892	−	0.981160i
$634$	15.0824	+	20.7591i	0.598997	+	0.824448i
$635$	4.23876	−	5.83415i	0.168210	−	0.231521i
$636$	−0.373906	+	1.52825i	−0.0148263	+	0.0605989i
$637$	13.7035	−	14.5513i	0.542952	−	0.576544i
$638$	−0.168017	+	3.68419i	−0.00665184	+	0.145859i
$639$	6.79126	+	13.6189i	0.268658	+	0.538755i
$640$	−4.66697	+	1.51639i	−0.184478	+	0.0599406i
$641$	12.0552	−	16.5925i	0.476151	−	0.655366i	−0.501608	−	0.865095i	$-0.667258\pi$
$641$	12.0552	−	16.5925i	0.476151	−	0.655366i	0.977760	+	0.209729i	$0.0672581\pi$
$642$	1.22450	−	0.0910369i	0.0483271	−	0.00359294i
$643$	−27.2192	−	8.84406i	−1.07342	−	0.348776i	−0.281602	−	0.959531i	$-0.590866\pi$
$643$	−27.2192	−	8.84406i	−1.07342	−	0.348776i	−0.791819	+	0.610756i	$0.790866\pi$
$644$	0.955963	+	0.310611i	0.0376702	+	0.0122398i
$645$	−5.79762	+	0.431032i	−0.228281	+	0.0169719i
$646$	23.2352	−	31.9805i	0.914177	−	1.25826i
$647$	2.78490	−	0.904867i	0.109486	−	0.0355740i	−0.253762	−	0.967267i	$-0.581668\pi$
$647$	2.78490	−	0.904867i	0.109486	−	0.0355740i	0.363247	+	0.931693i	$0.381668\pi$
$648$	−19.4581	−	14.6587i	−0.764388	−	0.575848i
$649$	15.2238	−	40.4784i	0.597588	−	1.58892i
$650$	−18.6766	−	17.5884i	−0.732556	−	0.689874i
$651$	−3.00770	+	12.2932i	−0.117881	+	0.481810i
$652$	−1.26565	+	1.74201i	−0.0495665	+	0.0682225i
$653$	20.7048	+	28.4977i	0.810242	+	1.11520i	0.991286	+	0.131728i	$0.0420525\pi$
$653$	20.7048	+	28.4977i	0.810242	+	1.11520i	−0.181044	+	0.983475i	$0.557948\pi$
$654$	27.6812	−	23.4355i	1.08242	−	0.916399i
$655$	1.95223	−	6.00835i	0.0762800	−	0.234766i
$656$	2.80227	+	3.85700i	0.109410	+	0.150590i
$657$	3.38617	−	20.2432i	0.132107	−	0.789764i
$658$	−7.14935	+	2.32296i	−0.278711	+	0.0905586i
$659$	−31.3023			−1.21936			−0.609682	−	0.792646i	$-0.708703\pi$
$659$	−31.3023			−1.21936			−0.609682	+	0.792646i	$0.708703\pi$
$660$	0.340571	+	0.0999722i	0.0132567	+	0.00389141i
$661$			40.8819i			1.59012i	0.606529	+	0.795062i	$0.292561\pi$
$661$			40.8819i			1.59012i	−0.606529	+	0.795062i	$0.707439\pi$
$662$	5.32168	+	16.3784i	0.206833	+	0.636566i
$663$	−15.1730	+	39.4665i	−0.589270	+	1.53275i
$664$	−0.769588	+	0.559138i	−0.0298658	+	0.0216988i
$665$	1.71360	−	5.27392i	0.0664506	−	0.204514i
$666$	−13.4981	+	2.01822i	−0.523039	+	0.0782043i
$667$	−0.805110	−	1.10814i	−0.0311740	−	0.0429073i
$668$	0.694151	−	0.955417i	0.0268575	−	0.0369662i
$669$	−8.17883	+	33.4289i	−0.316212	+	1.29244i
$670$	−2.94377			−0.113728
$671$	−22.8709	+	6.29491i	−0.882922	+	0.243012i
$672$	4.61899	+	2.85811i	0.178182	+	0.110254i
$673$	−0.107711	+	0.0349973i	−0.00415194	+	0.00134905i	−0.311092	−	0.950380i	$-0.600695\pi$
$673$	−0.107711	+	0.0349973i	−0.00415194	+	0.00134905i	0.306940	+	0.951729i	$0.400695\pi$
$674$	7.93489	+	5.76503i	0.305640	+	0.222061i
$675$	21.6341	−	12.8738i	0.832695	−	0.495514i
$676$	1.97393	+	0.512790i	0.0759203	+	0.0197227i
$677$	9.02792	−	27.7851i	0.346971	−	1.06787i	−0.613549	−	0.789657i	$-0.710259\pi$
$677$	9.02792	−	27.7851i	0.346971	−	1.06787i	0.960520	−	0.278211i	$-0.0897413\pi$
$678$	3.92096	+	52.7391i	0.150583	+	2.02543i
$679$	2.59765	−	3.57535i	0.0996885	−	0.137209i
$680$	−6.86488	+	2.23054i	−0.263256	+	0.0855371i
$681$	20.9952	+	12.9913i	0.804539	+	0.497827i
$682$	−3.53751	+	9.40584i	−0.135458	+	0.360168i
$683$	5.15742			0.197343			0.0986716	−	0.995120i	$-0.468541\pi$
$683$	5.15742			0.197343			0.0986716	+	0.995120i	$0.468541\pi$
$684$	1.33441	−	1.31149i	0.0510223	−	0.0501462i
$685$	−2.41499	−	1.75459i	−0.0922721	−	0.0670396i
$686$	4.45236	+	6.12815i	0.169992	+	0.233974i
$687$	−25.6605	+	21.7247i	−0.979010	+	0.828849i
$688$	−34.7643	−	11.2956i	−1.32538	−	0.430641i
$689$	−20.7083	−	2.64590i	−0.788922	−	0.100801i
$690$	−1.67744	+	0.686322i	−0.0638589	+	0.0261278i
$691$	42.4493	−	13.7926i	1.61485	−	0.524696i	0.644129	−	0.764917i	$-0.277220\pi$
$691$	42.4493	−	13.7926i	1.61485	−	0.524696i	0.970718	+	0.240221i	$0.0772199\pi$
$692$	−3.09660			−0.117715
$693$	14.2729	+	32.2198i	0.542182	+	1.22393i
$694$		−	6.37793i		−	0.242103i
$695$	3.22417	−	1.04760i	0.122300	−	0.0397376i
$696$	−1.34426	−	3.28550i	−0.0509540	−	0.124536i
$697$	4.42354	+	6.08847i	0.167553	+	0.230617i
$698$	29.3063	+	9.52220i	1.10926	+	0.360421i
$699$	26.8462	+	31.7099i	1.01542	+	1.19938i
$700$	−2.17782	+	1.58228i	−0.0823140	+	0.0598046i
$701$	−33.1866	−	24.1115i	−1.25344	−	0.910679i	−0.255026	−	0.966934i	$-0.582084\pi$
$701$	−33.1866	−	24.1115i	−1.25344	−	0.910679i	−0.998416	+	0.0562549i	$0.982084\pi$
$702$	−13.9754	+	23.7013i	−0.527467	+	0.894549i
$703$			12.3147i			0.464456i
$704$	−18.8614	−	15.0629i	−0.710867	−	0.567704i
$705$	0.518756	−	0.838363i	0.0195375	−	0.0315746i
$706$	16.9614	−	5.51111i	0.638352	−	0.207413i
$707$	1.56611	+	1.13784i	0.0588995	+	0.0427930i
$708$	−0.262692	−	3.53336i	−0.00987258	−	0.132792i
$709$	20.3010	+	6.59620i	0.762421	+	0.247726i	0.664317	−	0.747451i	$-0.268722\pi$
$709$	20.3010	+	6.59620i	0.762421	+	0.247726i	0.0981036	+	0.995176i	$0.468722\pi$
$710$	2.79057	+	0.906711i	0.104728	+	0.0340283i
$711$	12.4271	−	23.8761i	0.466052	−	0.895424i
$712$	−22.5793	+	31.0777i	−0.846194	+	1.16469i
$713$	−1.15332	−	3.54957i	−0.0431923	−	0.132932i
$714$	51.8710	+	32.0964i	1.94122	+	1.20118i
$715$	−0.809128	+	4.63973i	−0.0302597	+	0.173516i
$716$		−	1.35383i		−	0.0505951i
$717$	−4.34960	+	17.7779i	−0.162439	+	0.663928i
$718$	35.2240	+	25.5917i	1.31455	+	0.955075i
$719$	−23.6740	−	32.5845i	−0.882891	−	1.21520i	−0.975612	−	0.219504i	$-0.929556\pi$
$719$	−23.6740	−	32.5845i	−0.882891	−	1.21520i	0.0927202	−	0.995692i	$-0.470444\pi$
$720$	−5.01212	+	0.749407i	−0.186791	+	0.0279287i
$721$	−5.38814	+	16.5830i	−0.200665	+	0.617583i
$722$	2.75886	+	3.79724i	0.102674	+	0.141319i
$723$	37.6598	−	15.4085i	1.40058	−	0.573048i
$724$	0.428658	+	1.31927i	0.0159310	+	0.0490304i
$725$	3.66832			0.136238
$726$	8.19474	+	26.7543i	0.304135	+	0.992946i
$727$	2.88236			0.106901			0.0534503	−	0.998571i	$-0.482978\pi$
$727$	2.88236			0.106901			0.0534503	+	0.998571i	$0.482978\pi$
$728$	−14.7619	+	31.2555i	−0.547113	+	1.15841i
$729$	−18.5895	−	19.5814i	−0.688499	−	0.725237i
$730$	−2.32602	−	3.20149i	−0.0860898	−	0.118492i
$731$	−54.8773	−	17.8307i	−2.02971	−	0.659493i
$732$	−1.48326	+	1.25576i	−0.0548229	+	0.0464142i
$733$	−1.77460	+	1.28932i	−0.0655463	+	0.0476222i	−0.620076	−	0.784542i	$-0.712898\pi$
$733$	−1.77460	+	1.28932i	−0.0655463	+	0.0476222i	0.554530	+	0.832164i	$0.312898\pi$
$734$	5.45721	−	7.51120i	0.201429	−	0.277244i
$735$	3.67339	+	0.898744i	0.135495	+	0.0331507i
$736$	−1.60184			−0.0590445
$737$	−9.28904	−	14.0935i	−0.342166	−	0.519142i
$738$	2.18545	+	4.38260i	0.0804474	+	0.161326i
$739$	7.42246	+	22.8440i	0.273039	+	0.840329i	0.989731	+	0.142939i	$0.0456554\pi$
$739$	7.42246	+	22.8440i	0.273039	+	0.840329i	−0.716692	+	0.697390i	$0.754345\pi$
$740$	−0.112501	+	0.154844i	−0.00413561	+	0.00569218i
$741$	19.2859	+	15.6337i	0.708484	+	0.574320i
$742$	−9.30672	+	28.6431i	−0.341661	+	1.05152i
$743$	−9.87928	−	3.20997i	−0.362436	−	0.117762i	0.122138	−	0.992513i	$-0.461025\pi$
$743$	−9.87928	−	3.20997i	−0.362436	−	0.117762i	−0.484573	+	0.874751i	$0.661025\pi$
$744$	−0.717143	−	9.64599i	−0.0262918	−	0.353639i
$745$	1.80514	−	2.48457i	0.0661354	−	0.0910275i
$746$	−6.63822	−	20.4303i	−0.243043	−	0.748008i
$747$	−0.943478	+	0.470479i	−0.0345201	+	0.0172139i
$748$	2.75276	+	2.19838i	0.100651	+	0.0803806i
$749$	1.70960			0.0624674
$750$	2.34401	−	9.58054i	0.0855910	−	0.349832i
$751$	−0.947543	−	0.688430i	−0.0345763	−	0.0251212i	0.570363	−	0.821393i	$-0.306803\pi$
$751$	−0.947543	−	0.688430i	−0.0345763	−	0.0251212i	−0.604939	+	0.796272i	$0.706803\pi$
$752$	5.01491	−	3.64354i	0.182875	−	0.132866i
$753$	4.17578	−	3.53530i	0.152174	−	0.128833i
$754$	−3.51611	+	1.92651i	−0.128049	+	0.0701594i
$755$	0.272154	−	0.197732i	0.00990470	−	0.00719619i
$756$	2.17084	+	1.90339i	0.0789526	+	0.0692256i
$757$	11.9163	+	36.6746i	0.433105	+	1.33296i	0.895016	+	0.446034i	$0.147164\pi$
$757$	11.9163	+	36.6746i	0.433105	+	1.33296i	−0.461911	+	0.886926i	$0.652836\pi$
$758$	−48.5913			−1.76491
$759$	−8.57896	−	5.86518i	−0.311397	−	0.212892i
$760$			4.23819i			0.153735i
$761$	21.0783	−	6.84874i	0.764086	−	0.248267i	0.0990547	−	0.995082i	$-0.468418\pi$
$761$	21.0783	−	6.84874i	0.764086	−	0.248267i	0.665031	+	0.746815i	$0.268418\pi$
$762$	43.1075	−	17.6374i	1.56162	−	0.638937i
$763$	40.8543	−	29.6824i	1.47902	−	1.07457i
$764$	−2.47558	−	0.804365i	−0.0895634	−	0.0291009i
$765$	−7.91189	+	1.18298i	−0.286055	+	0.0427707i
$766$	−18.8862	−	25.9946i	−0.682385	−	0.939222i
$767$	46.1937	−	8.74405i	1.66796	−	0.315729i
$768$	−6.29660	−	1.54055i	−0.227209	−	0.0555897i
$769$	−9.89891			−0.356964			−0.178482	−	0.983943i	$-0.557119\pi$
$769$	−9.89891			−0.356964			−0.178482	+	0.983943i	$0.557119\pi$
$770$	6.35952	+	2.39180i	0.229181	+	0.0861944i
$771$	−2.43289	−	1.50540i	−0.0876183	−	0.0542158i
$772$	−0.998597	−	3.07337i	−0.0359403	−	0.110613i
$773$	1.27629	+	0.927278i	0.0459049	+	0.0333519i	0.610501	−	0.792015i	$-0.290968\pi$
$773$	1.27629	+	0.927278i	0.0459049	+	0.0333519i	−0.564596	+	0.825367i	$0.690968\pi$
$774$	−33.3069	−	17.3357i	−1.19719	−	0.623118i
$775$	9.50618	+	3.08875i	0.341472	+	0.110951i
$776$	−1.04375	+	3.21234i	−0.0374685	+	0.115316i
$777$	−18.9502	+	1.40888i	−0.679836	+	0.0505433i
$778$	−9.54581	−	6.93544i	−0.342234	−	0.248648i
$779$	4.20254	−	1.36549i	0.150571	−	0.0489236i
$780$	0.0996773	+	0.372764i	0.00356902	+	0.0133471i
$781$	4.46467	+	16.2212i	0.159758	+	0.580441i
$782$	−17.9885			−0.643269
$783$	−0.868670	−	3.83719i	−0.0310437	−	0.137130i
$784$	19.2367	+	13.9763i	0.687024	+	0.499152i
$785$	−4.70033	+	3.41499i	−0.167762	+	0.121886i
$786$	31.1413	−	26.3649i	1.11077	−	0.940404i
$787$	0.342955	−	1.05551i	0.0122250	−	0.0376248i	−0.944758	−	0.327769i	$-0.893703\pi$
$787$	0.342955	−	1.05551i	0.0122250	−	0.0376248i	0.956983	+	0.290144i	$0.0937033\pi$
$788$	0.706503	+	0.972418i	0.0251681	+	0.0346410i
$789$	12.6553	−	5.17792i	0.450541	−	0.184339i
$790$	−1.60370	−	4.93568i	−0.0570571	−	0.175604i
$791$			73.6324i			2.61807i
$792$	−17.9841	−	20.0488i	−0.639039	−	0.712404i
$793$	−18.7735	−	17.6797i	−0.666666	−	0.627823i
$794$	−8.90608	−	27.4101i	−0.316065	−	0.972748i
$795$	−1.49572	−	3.65568i	−0.0530477	−	0.129654i
$796$	2.74027	−	1.99092i	0.0971262	−	0.0705663i
$797$	18.2563	+	5.93182i	0.646671	+	0.210116i	0.613946	−	0.789348i	$-0.289581\pi$
$797$	18.2563	+	5.93182i	0.646671	+	0.210116i	0.0327250	+	0.999464i	$0.489581\pi$
$798$	27.3348	−	23.1422i	0.967641	−	0.819224i
$799$	7.91629	−	5.75152i	0.280058	−	0.203474i
$800$	2.52155	−	3.47062i	0.0891503	−	0.122705i
$801$	−30.3640	+	29.8426i	−1.07286	+	1.05444i
$802$		−	7.68758i		−	0.271458i
$803$	7.98766	−	21.2383i	0.281878	−	0.749483i
$804$	−1.17597	−	0.727661i	−0.0414734	−	0.0256626i
$805$	−2.39995	+	0.779791i	−0.0845871	+	0.0274840i
$806$	−10.7339	+	2.03183i	−0.378085	+	0.0715680i
$807$	20.6637	−	1.53627i	0.727395	−	0.0540791i
$808$	−1.40709	−	0.457193i	−0.0495014	−	0.0160840i
$809$	−16.2635	+	50.0539i	−0.571794	+	1.75980i	0.0750501	+	0.997180i	$0.476088\pi$
$809$	−16.2635	+	50.0539i	−0.571794	+	1.75980i	−0.646844	+	0.762622i	$0.723912\pi$
$810$	−5.20500	−	0.0901609i	−0.182885	−	0.00316793i
$811$	−28.3445	−	20.5935i	−0.995310	−	0.723135i	−0.0342326	−	0.999414i	$-0.510899\pi$
$811$	−28.3445	−	20.5935i	−0.995310	−	0.723135i	−0.961078	+	0.276279i	$0.910899\pi$
$812$	0.130002	+	0.400104i	0.00456216	+	0.0140409i
$813$	17.6238	−	28.4819i	0.618095	−	0.998904i
$814$	−15.0729	−	0.687394i	−0.528304	−	0.0240932i
$815$		−	5.40573i		−	0.189355i
$816$	−48.8582	−	11.9538i	−1.71038	−	0.418467i
$817$	−19.9140	+	27.4093i	−0.696704	+	0.958931i
$818$	29.5244	+	40.6369i	1.03230	+	1.42084i
$819$	−21.8513	+	31.4664i	−0.763548	+	1.09952i
$820$	0.0653169	+	0.0212228i	0.00228097	+	0.000741131i
$821$	24.6184	+	33.8843i	0.859187	+	1.18257i	0.981763	+	0.190110i	$0.0608845\pi$
$821$	24.6184	+	33.8843i	0.859187	+	1.18257i	−0.122576	+	0.992459i	$0.539115\pi$
$822$	−7.30085	−	17.8440i	−0.254646	−	0.622379i
$823$	−4.98501	−	15.3423i	−0.173767	−	0.534799i	0.825808	−	0.563951i	$-0.190719\pi$
$823$	−4.98501	−	15.3423i	−0.173767	−	0.534799i	−0.999575	+	0.0291521i	$0.990719\pi$
$824$		−	13.3263i		−	0.464244i
$825$	26.2124	−	9.35485i	0.912600	−	0.325694i
$826$		−	67.8238i		−	2.35989i
$827$	−35.5486	+	11.5504i	−1.23615	+	0.401648i	−0.852937	−	0.522014i	$-0.825181\pi$
$827$	−35.5486	+	11.5504i	−1.23615	+	0.401648i	−0.383208	+	0.923662i	$0.625181\pi$
$828$	−0.839750	−	0.140469i	−0.0291833	−	0.00488162i
$829$	15.2834	−	11.1040i	0.530815	−	0.385660i	−0.289848	−	0.957073i	$-0.593605\pi$
$829$	15.2834	−	11.1040i	0.530815	−	0.385660i	0.820662	+	0.571413i	$0.193605\pi$
$830$	−0.0628144	+	0.193323i	−0.00218032	+	0.00671033i
$831$	−42.4582	+	35.9460i	−1.47286	+	1.24695i
$832$	3.32576	−	26.0292i	0.115300	−	0.902401i
$833$	30.3661	+	22.0623i	1.05212	+	0.764412i
$834$	21.2682	+	5.20355i	0.736458	+	0.180184i
$835$			2.96481i			0.102601i
$836$	1.72708	−	1.13832i	0.0597323	−	0.0393695i
$837$	0.979841	−	10.6752i	0.0338682	−	0.368989i
$838$	2.02415	+	6.22971i	0.0699233	+	0.215202i
$839$	4.30806	+	3.12999i	0.148731	+	0.108059i	0.659662	−	0.751562i	$-0.270699\pi$
$839$	4.30806	+	3.12999i	0.148731	+	0.108059i	−0.510931	+	0.859622i	$0.670699\pi$
$840$	−6.52189	+	0.484878i	−0.225026	+	0.0167299i
$841$	−8.78434	+	27.0354i	−0.302908	+	0.932256i
$842$	−12.8171	+	39.4471i	−0.441708	+	1.35944i
$843$	−48.0299	+	3.57085i	−1.65424	+	0.122986i
$844$	2.03393	−	2.79946i	0.0700107	−	0.0963615i
$845$	−4.76582	+	1.87130i	−0.163949	+	0.0643747i
$846$	5.69830	−	2.84154i	0.195911	−	0.0976941i
$847$	8.61648	+	37.9940i	0.296066	+	1.30549i
$848$		−	24.8347i		−	0.852828i
$849$	11.8405	−	48.3950i	0.406364	−	1.66091i
$850$	28.3169	−	38.9748i	0.971260	−	1.33683i
$851$	4.53365	−	3.29389i	0.155412	−	0.112913i
$852$	0.890648	+	1.05201i	0.0305131	+	0.0360411i
$853$	2.29816	−	7.07300i	0.0786874	−	0.242175i	−0.903973	−	0.427590i	$-0.859363\pi$
$853$	2.29816	−	7.07300i	0.0786874	−	0.242175i	0.982660	+	0.185415i	$0.0593629\pi$
$854$	−30.0973	+	21.8670i	−1.02991	+	0.748272i
$855$	−0.774947	+	4.63280i	−0.0265026	+	0.158438i
$856$	−1.24267	+	0.403766i	−0.0424734	+	0.0138005i
$857$	7.38976			0.252430			0.126215	−	0.992003i	$-0.459717\pi$
$857$	7.38976			0.252430			0.126215	+	0.992003i	$0.459717\pi$
$858$	−20.2119	+	22.7328i	−0.690023	+	0.776086i
$859$	−25.9243			−0.884526			−0.442263	−	0.896885i	$-0.645824\pi$
$859$	−25.9243			−0.884526			−0.442263	+	0.896885i	$0.645824\pi$
$860$	−0.500797	+	0.162719i	−0.0170770	+	0.00554866i
$861$	2.58206	+	6.31079i	0.0879963	+	0.215071i
$862$	−15.5673	+	11.3103i	−0.530224	+	0.385230i
$863$	6.89188	−	21.2110i	0.234602	−	0.722032i	−0.762571	−	0.646904i	$-0.776063\pi$
$863$	6.89188	−	21.2110i	0.234602	−	0.722032i	0.997174	−	0.0751280i	$-0.0239365\pi$
$864$	−4.22750	−	1.81578i	−0.143822	−	0.0617739i
$865$	6.28933	−	4.56946i	0.213844	−	0.155366i
$866$	7.52140	−	10.3523i	0.255587	−	0.351786i
$867$	−48.5240	−	11.8720i	−1.64796	−	0.403196i
$868$			1.14630i			0.0389080i
$869$	18.5695	−	23.2524i	0.629928	−	0.788783i
$870$	−0.645053	−	0.399141i	−0.0218694	−	0.0135322i
$871$	7.83652	−	16.5923i	0.265530	−	0.562210i
$872$	−22.6857	+	31.2242i	−0.768235	+	1.05738i
$873$	−1.72830	+	3.32058i	−0.0584941	+	0.112384i
$874$	−3.26387	+	10.0451i	−0.110402	+	0.339782i
$875$	4.24362	−	13.0605i	0.143460	−	0.441526i
$876$	−0.137830	−	1.85389i	−0.00465684	−	0.0626371i
$877$	28.5447	+	20.7390i	0.963887	+	0.700305i	0.954050	−	0.299647i	$-0.0968688\pi$
$877$	28.5447	+	20.7390i	0.963887	+	0.700305i	0.00983672	+	0.999952i	$0.496869\pi$
$878$	2.23313	+	6.87286i	0.0753644	+	0.231948i
$879$	29.8333	+	18.4601i	1.00625	+	0.622643i
$880$	−5.59688	−	0.255244i	−0.188671	−	0.00860429i
$881$			12.2404i			0.412390i	0.978511	+	0.206195i	$0.0661081\pi$
$881$			12.2404i			0.412390i	−0.978511	+	0.206195i	$0.933892\pi$
$882$	17.1209	+	17.4200i	0.576491	+	0.586563i
$883$	−0.573281	−	0.416513i	−0.0192924	−	0.0140168i	0.578097	−	0.815968i	$-0.303795\pi$
$883$	−0.573281	−	0.416513i	−0.0192924	−	0.0140168i	−0.597390	+	0.801951i	$0.703795\pi$
$884$	−0.485383	+	3.79887i	−0.0163252	+	0.127770i
$885$	5.74750	+	6.78877i	0.193200	+	0.228202i
$886$	7.92952	−	24.4045i	0.266397	−	0.819887i
$887$	33.2392	−	24.1497i	1.11606	−	0.810866i	0.132454	−	0.991189i	$-0.457714\pi$
$887$	33.2392	−	24.1497i	1.11606	−	0.810866i	0.983607	+	0.180323i	$0.0577143\pi$
$888$	13.4417	−	5.49967i	0.451074	−	0.184557i
$889$	61.6750	−	20.0394i	2.06851	−	0.672101i
$890$			8.20857i			0.275152i
$891$	−15.9927	−	25.2039i	−0.535775	−	0.844361i
$892$			3.11713i			0.104369i
$893$	−1.77542	−	5.46418i	−0.0594121	−	0.182852i
$894$	18.3580	−	7.51119i	0.613985	−	0.251212i
$895$	1.99777	+	2.74969i	0.0667780	+	0.0919120i
$896$	−41.9680	−	13.6362i	−1.40205	−	0.455555i
$897$	0.597048	−	11.2818i	0.0199349	−	0.376688i
$898$	−15.0559	−	20.7227i	−0.502423	−	0.691527i
$899$	0.918162	−	1.26374i	0.0306224	−	0.0421482i
$900$	1.62625	−	1.59832i	0.0542083	−	0.0532774i
$901$		−	39.2029i		−	1.30604i
$902$	1.43674	+	5.22003i	0.0478383	+	0.173808i
$903$	−44.4568	−	27.5086i	−1.47943	−	0.915430i
$904$	−17.3902	−	53.5216i	−0.578390	−	1.78010i
$905$	−2.81739	−	2.04696i	−0.0936533	−	0.0680431i
$906$	2.16673	−	0.161088i	0.0719847	−	0.00535179i
$907$	−3.12647	+	9.62230i	−0.103813	+	0.319503i	−0.989450	−	0.144875i	$-0.953722\pi$
$907$	−3.12647	+	9.62230i	−0.103813	+	0.319503i	0.885637	+	0.464378i	$0.153722\pi$
$908$	2.12680	+	0.691041i	0.0705805	+	0.0229330i
$909$	−1.45451	−	0.757045i	−0.0482429	−	0.0251096i
$910$	1.37377	+	7.25744i	0.0455399	+	0.240582i
$911$	−17.5114	+	5.68981i	−0.580180	+	0.188512i	−0.584381	−	0.811479i	$-0.698663\pi$
$911$	−17.5114	+	5.68981i	−0.580180	+	0.188512i	0.00420118	+	0.999991i	$0.498663\pi$
$912$	−15.5402	+	25.1145i	−0.514586	+	0.831623i
$913$	−1.12376	+	0.309300i	−0.0371910	+	0.0102363i
$914$		−	2.96391i		−	0.0980375i
$915$	1.15952	−	4.73926i	0.0383326	−	0.156675i
$916$	−1.78998	+	2.46369i	−0.0591425	+	0.0814027i
$917$	45.9610	−	33.3927i	1.51777	−	1.10272i
$918$	−47.4745	−	20.3911i	−1.56689	−	0.673005i
$919$	9.96672	+	3.23838i	0.328772	+	0.106824i	0.468752	−	0.883330i	$-0.344704\pi$
$919$	9.96672	+	3.23838i	0.328772	+	0.106824i	−0.139980	+	0.990154i	$0.544704\pi$
$920$	1.56030	−	1.13362i	0.0514414	−	0.0373744i
$921$	47.4362	−	19.4085i	1.56308	−	0.639532i
$922$	14.9112	+	45.8919i	0.491074	+	1.51137i
$923$	−12.5393	+	13.3151i	−0.412736	+	0.438272i
$924$	1.94927	+	2.52746i	0.0641264	+	0.0831474i
$925$			15.0079i			0.493458i
$926$	10.9428	+	33.6785i	0.359603	+	1.10674i
$927$	2.43669	−	14.5671i	0.0800316	−	0.478445i
$928$	−0.394066	−	0.542385i	−0.0129358	−	0.0178047i
$929$	−12.1387	+	37.3591i	−0.398258	+	1.22571i	0.528136	+	0.849160i	$0.322891\pi$
$929$	−12.1387	+	37.3591i	−0.398258	+	1.22571i	−0.926395	+	0.376554i	$0.877109\pi$
$930$	−1.33553	−	1.57748i	−0.0437937	−	0.0517277i
$931$	17.8297	−	12.9540i	0.584344	−	0.424550i
$932$	3.04450	+	2.21196i	0.0997258	+	0.0724551i
$933$	3.05678	−	12.4938i	0.100075	−	0.409030i
$934$	22.0104			0.720204
$935$	−8.83498	−	0.402917i	−0.288935	−	0.0131768i
$936$	8.45159	−	28.0329i	0.276249	−	0.916284i
$937$	13.8147	−	4.48867i	0.451307	−	0.146639i	−0.0745394	−	0.997218i	$-0.523749\pi$
$937$	13.8147	−	4.48867i	0.451307	−	0.146639i	0.525846	+	0.850580i	$0.323749\pi$
$938$	−21.4163	−	15.5598i	−0.699267	−	0.508047i
$939$	3.27156	+	44.0043i	0.106763	+	1.43603i
$940$	0.0275940	−	0.0849257i	0.000900018	−	0.00276997i
$941$	2.47214	+	0.803247i	0.0805895	+	0.0261851i	0.349034	−	0.937110i	$-0.386510\pi$
$941$	2.47214	+	0.803247i	0.0805895	+	0.0261851i	−0.268445	+	0.963295i	$0.586510\pi$
$942$	−37.4212	+	2.78213i	−1.21925	+	0.0906466i
$943$	−1.62679	−	1.18193i	−0.0529755	−	0.0384889i
$944$	17.2826	+	53.1904i	0.562501	+	1.73120i
$945$	−7.21777	−	0.662494i	−0.234794	−	0.0215509i
$946$	−32.4369	−	25.9043i	−1.05461	−	0.842223i
$947$	3.13139			0.101757			0.0508783	−	0.998705i	$-0.483798\pi$
$947$	3.13139			0.101757			0.0508783	+	0.998705i	$0.483798\pi$
$948$	0.579391	−	2.36812i	0.0188178	−	0.0769129i
$949$	24.2370	−	4.58784i	0.786766	−	0.148928i
$950$	−16.6264	−	22.8843i	−0.539433	−	0.742466i
$951$	−19.5538	−	23.0963i	−0.634075	−	0.748949i
$952$	−61.7328	−	20.0582i	−2.00077	−	0.650090i
$953$	−7.22769	+	5.25122i	−0.234128	+	0.170104i	−0.698663	−	0.715451i	$-0.746221\pi$
$953$	−7.22769	+	5.25122i	−0.234128	+	0.170104i	0.464535	+	0.885555i	$0.346221\pi$
$954$	4.20881	−	25.1611i	0.136265	−	0.814622i
$955$	6.21496	−	2.01936i	0.201111	−	0.0653450i
$956$			1.65773i			0.0536147i
$957$	−0.124538	−	4.34773i	−0.00402575	−	0.140542i
$958$	−55.4605			−1.79185
$959$	−8.29513	−	25.5298i	−0.267864	−	0.824400i
$960$	4.59500	−	1.88004i	0.148303	−	0.0606781i
$961$	−21.6361	+	15.7195i	−0.697939	+	0.507082i
$962$	−7.88180	−	14.3852i	−0.254119	−	0.463798i
$963$	−1.43219	+	0.214140i	−0.0461518	+	0.00690057i
$964$	2.98164	−	2.16629i	0.0960320	−	0.0697714i
$965$	6.56337	+	4.76857i	0.211282	+	0.153506i
$966$	−15.8312	−	3.87332i	−0.509362	−	0.124622i
$967$	−54.6451			−1.75727			−0.878634	−	0.477496i	$-0.841544\pi$
$967$	−54.6451			−1.75727			−0.878634	+	0.477496i	$0.841544\pi$
$968$	−15.2364	−	25.5819i	−0.489716	−	0.822233i
$969$	−24.5309	+	39.6445i	−0.788047	+	1.27357i
$970$	0.223035	+	0.686432i	0.00716123	+	0.0220400i
$971$	25.8092	−	35.5234i	0.828258	−	1.14000i	−0.159987	−	0.987119i	$-0.551145\pi$
$971$	25.8092	−	35.5234i	0.828258	−	1.14000i	0.988245	−	0.152880i	$-0.0488549\pi$
$972$	−2.05700	−	1.32262i	−0.0659784	−	0.0424232i
$973$	28.9935	+	9.42057i	0.929490	+	0.302010i
$974$	−6.53743	+	20.1201i	−0.209473	+	0.644691i
$975$	23.5038	+	19.0529i	0.752724	+	0.610182i
$976$	18.0316	−	24.8183i	0.577177	−	0.794415i
$977$	−4.42514	−	13.6192i	−0.141573	−	0.435717i	0.854981	−	0.518659i	$-0.173568\pi$
$977$	−4.42514	−	13.6192i	−0.141573	−	0.435717i	−0.996554	+	0.0829419i	$0.973568\pi$
$978$	18.3712	−	29.6897i	0.587446	−	0.949373i
$979$	−39.2992	+	25.9021i	−1.25601	+	0.827834i
$980$	0.342531			0.0109418
$981$	−30.5072	+	29.9833i	−0.974019	+	0.957293i
$982$	30.8252	−	42.4273i	0.983672	−	1.35391i
$983$	30.3878	−	22.0780i	0.969220	−	0.704180i	0.0139465	−	0.999903i	$-0.495561\pi$
$983$	30.3878	−	22.0780i	0.969220	−	0.704180i	0.955274	+	0.295723i	$0.0955606\pi$
$984$	−3.36729	−	3.97734i	−0.107345	−	0.126793i
$985$	−2.86987	−	0.932479i	−0.0914418	−	0.0297112i
$986$	−4.42533	−	6.09095i	−0.140931	−	0.193975i
$987$	8.20535	−	3.35722i	0.261179	−	0.106861i
$988$	2.03329	+	0.960320i	0.0646877	+	0.0305518i
$989$	15.4173			0.490242
$990$	−5.62719	−	1.20712i	−0.178844	−	0.0383647i
$991$	−27.4007			−0.870412			−0.435206	−	0.900331i	$-0.643325\pi$
$991$	−27.4007			−0.870412			−0.435206	+	0.900331i	$0.643325\pi$
$992$	−0.564501	−	1.73736i	−0.0179229	−	0.0551611i
$993$	−7.69105	−	18.7976i	−0.244068	−	0.596525i
$994$	15.5092	+	21.3465i	0.491921	+	0.677071i
$995$	−2.62772	+	8.08728i	−0.0833042	+	0.256384i
$996$	−0.0728799	+	0.0617016i	−0.00230929	+	0.00195509i
$997$	27.7227	+	38.1570i	0.877986	+	1.20844i	0.976975	+	0.213355i	$0.0684392\pi$
$997$	27.7227	+	38.1570i	0.877986	+	1.20844i	−0.0989887	+	0.995089i	$0.531561\pi$
$998$	4.83997	+	3.51644i	0.153207	+	0.111311i
$999$	15.6988	−	3.55393i	0.496689	−	0.112441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.y.b.116.12	yes	176
3.2	odd	2	inner	429.2.y.b.116.33	yes	176
11.2	odd	10	inner	429.2.y.b.233.11	yes	176
13.12	even	2	inner	429.2.y.b.116.34	yes	176
33.2	even	10	inner	429.2.y.b.233.34	yes	176
39.38	odd	2	inner	429.2.y.b.116.11	✓	176
143.90	odd	10	inner	429.2.y.b.233.33	yes	176
429.233	even	10	inner	429.2.y.b.233.12	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.b.116.11	✓	176	39.38	odd	2	inner
429.2.y.b.116.12	yes	176	1.1	even	1	trivial
429.2.y.b.116.33	yes	176	3.2	odd	2	inner
429.2.y.b.116.34	yes	176	13.12	even	2	inner
429.2.y.b.233.11	yes	176	11.2	odd	10	inner
429.2.y.b.233.12	yes	176	429.233	even	10	inner
429.2.y.b.233.33	yes	176	143.90	odd	10	inner
429.2.y.b.233.34	yes	176	33.2	even	10	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39675 + 0.453832i) q^{2} +(1.60306 - 0.655892i) q^{3} +(0.126919 - 0.0922120i) q^{4} +(-0.121706 + 0.374573i) q^{5} +(-1.94141 + 1.64364i) q^{6} +(-2.86530 + 2.08177i) q^{7} +(1.59106 - 2.18990i) q^{8} +(2.13961 - 2.10287i) q^{9} +O(q^{10})\)	\(q+(-1.39675 + 0.453832i) q^{2} +(1.60306 - 0.655892i) q^{3} +(0.126919 - 0.0922120i) q^{4} +(-0.121706 + 0.374573i) q^{5} +(-1.94141 + 1.64364i) q^{6} +(-2.86530 + 2.08177i) q^{7} +(1.59106 - 2.18990i) q^{8} +(2.13961 - 2.10287i) q^{9} -0.578420i q^{10} +(2.76923 - 1.82520i) q^{11} +(0.142978 - 0.231067i) q^{12} +(3.26022 + 1.53979i) q^{13} +(3.05735 - 4.20808i) q^{14} +(0.0505770 + 0.680289i) q^{15} +(-1.32542 + 4.07922i) q^{16} +(-2.09225 + 6.43927i) q^{17} +(-2.03416 + 3.90821i) q^{18} +(3.21619 + 2.33670i) q^{19} +(0.0190933 + 0.0587632i) q^{20} +(-3.22785 + 5.21653i) q^{21} +(-3.03960 + 3.80612i) q^{22} -1.80906i q^{23} +(1.11422 - 4.55410i) q^{24} +(3.91959 + 2.84775i) q^{25} +(-5.25253 - 0.671118i) q^{26} +(2.05067 - 4.77438i) q^{27} +(-0.171698 + 0.528431i) q^{28} +(0.612550 - 0.445044i) q^{29} +(-0.379381 - 0.927242i) q^{30} +(1.96211 - 0.637528i) q^{31} -0.885454i q^{32} +(3.24212 - 4.74222i) q^{33} -9.94359i q^{34} +(-0.431048 - 1.32663i) q^{35} +(0.0776474 - 0.464192i) q^{36} +(1.82078 + 2.50608i) q^{37} +(-5.55269 - 1.80418i) q^{38} +(6.23627 + 0.330033i) q^{39} +(0.626636 + 0.862490i) q^{40} +(0.653340 - 0.899245i) q^{41} +(2.14107 - 8.75110i) q^{42} +8.52229i q^{43} +(0.183163 - 0.487009i) q^{44} +(0.527274 + 1.05737i) q^{45} +(0.821009 + 2.52681i) q^{46} +(-1.16921 - 0.849479i) q^{47} +(0.550800 + 7.40858i) q^{48} +(1.71310 - 5.27239i) q^{49} +(-6.76710 - 2.19876i) q^{50} +(0.869467 + 11.6948i) q^{51} +(0.555771 - 0.105202i) q^{52} +(-5.50674 + 1.78925i) q^{53} +(-0.697512 + 7.59929i) q^{54} +(0.346638 + 1.25942i) q^{55} +9.58693i q^{56} +(6.68838 + 1.63640i) q^{57} +(-0.653606 + 0.899611i) q^{58} +(10.5490 - 7.66433i) q^{59} +(0.0691500 + 0.0816778i) q^{60} +(-6.80221 - 2.21017i) q^{61} +(-2.45125 + 1.78094i) q^{62} +(-1.75296 + 10.4795i) q^{63} +(-2.24899 - 6.92169i) q^{64} +(-0.973554 + 1.03379i) q^{65} +(-2.37626 + 8.09509i) q^{66} -5.08933i q^{67} +(0.328232 + 1.01020i) q^{68} +(-1.18655 - 2.90003i) q^{69} +(1.20413 + 1.65735i) q^{70} +(-1.56757 + 4.82447i) q^{71} +(-1.20083 - 8.03132i) q^{72} +(5.53489 - 4.02133i) q^{73} +(-3.68052 - 2.67405i) q^{74} +(8.15116 + 1.99429i) q^{75} +0.623668 q^{76} +(-4.13506 + 10.9946i) q^{77} +(-8.86030 + 2.36925i) q^{78} +(8.53305 - 2.77256i) q^{79} +(-1.36665 - 0.992933i) q^{80} +(0.155875 - 8.99865i) q^{81} +(-0.504448 + 1.55253i) q^{82} +(-0.334226 - 0.108597i) q^{83} +(0.0713518 + 0.959722i) q^{84} +(-2.15734 - 1.56740i) q^{85} +(-3.86769 - 11.9035i) q^{86} +(0.690055 - 1.11520i) q^{87} +(0.408998 - 8.96833i) q^{88} -14.1914 q^{89} +(-1.21634 - 1.23759i) q^{90} +(-12.5470 + 2.37503i) q^{91} +(-0.166817 - 0.229604i) q^{92} +(2.72723 - 2.30893i) q^{93} +(2.01861 + 0.655887i) q^{94} +(-1.26669 + 0.920308i) q^{95} +(-0.580762 - 1.41944i) q^{96} +(-1.18674 + 0.385594i) q^{97} +8.14168i q^{98} +(2.08692 - 9.72855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 6 q^{3} + 20 q^{4} + 6 q^{9}+O(q^{10}) \) 176 * q - 6 * q^3 + 20 * q^4 + 6 * q^9	\( 176 q - 6 q^{3} + 20 q^{4} + 6 q^{9} + 12 q^{12} - 10 q^{13} + 36 q^{16} - 96 q^{22} - 20 q^{25} + 6 q^{27} - 100 q^{30} - 116 q^{36} + 50 q^{39} + 60 q^{40} + 52 q^{42} + 32 q^{48} - 88 q^{49} - 90 q^{51} + 210 q^{52} - 20 q^{55} - 92 q^{64} - 62 q^{66} + 96 q^{69} + 166 q^{75} - 112 q^{78} - 60 q^{79} + 70 q^{81} - 144 q^{82} - 148 q^{88} + 100 q^{90} + 62 q^{91} - 180 q^{94}+O(q^{100}) \) 176 * q - 6 * q^3 + 20 * q^4 + 6 * q^9 + 12 * q^12 - 10 * q^13 + 36 * q^16 - 96 * q^22 - 20 * q^25 + 6 * q^27 - 100 * q^30 - 116 * q^36 + 50 * q^39 + 60 * q^40 + 52 * q^42 + 32 * q^48 - 88 * q^49 - 90 * q^51 + 210 * q^52 - 20 * q^55 - 92 * q^64 - 62 * q^66 + 96 * q^69 + 166 * q^75 - 112 * q^78 - 60 * q^79 + 70 * q^81 - 144 * q^82 - 148 * q^88 + 100 * q^90 + 62 * q^91 - 180 * q^94

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