LMFDB - Embedded newform 154.2.f.a.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(15,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("154.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.f (of order $5$, 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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	154.113
Dual form			154.2.f.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.61803 - 1.17557i) q^{9} -0.381966 q^{10} +(-1.23607 - 3.07768i) q^{11} -1.00000 q^{12} +(4.42705 - 3.21644i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.118034 - 0.363271i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.19098 + 0.865300i) q^{17} +(-0.618034 + 1.90211i) q^{18} +(2.07295 + 6.37988i) q^{19} +(0.309017 - 0.224514i) q^{20} -1.00000 q^{21} +(2.80902 + 1.76336i) q^{22} -3.76393 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.50000 - 4.61653i) q^{25} +(-1.69098 + 5.20431i) q^{26} +(-4.04508 - 2.93893i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-2.92705 + 9.00854i) q^{29} +(0.118034 + 0.363271i) q^{30} +(2.42705 - 1.76336i) q^{31} +1.00000 q^{32} +(-2.54508 + 2.12663i) q^{33} -1.47214 q^{34} +(0.309017 - 0.224514i) q^{35} +(-0.618034 - 1.90211i) q^{36} +(-0.354102 + 1.08981i) q^{37} +(-5.42705 - 3.94298i) q^{38} +(-4.42705 - 3.21644i) q^{39} +(-0.118034 + 0.363271i) q^{40} +(2.00000 + 6.15537i) q^{41} +(0.809017 - 0.587785i) q^{42} -9.61803 q^{43} +(-3.30902 + 0.224514i) q^{44} +0.763932 q^{45} +(3.04508 - 2.21238i) q^{46} +(0.500000 + 1.53884i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(3.92705 + 2.85317i) q^{50} +(0.454915 - 1.40008i) q^{51} +(-1.69098 - 5.20431i) q^{52} +(-0.572949 + 0.416272i) q^{53} +5.00000 q^{54} +(0.309017 - 1.22857i) q^{55} +1.00000 q^{56} +(5.42705 - 3.94298i) q^{57} +(-2.92705 - 9.00854i) q^{58} +(-1.64590 + 5.06555i) q^{59} +(-0.309017 - 0.224514i) q^{60} +(11.2082 + 8.14324i) q^{61} +(-0.927051 + 2.85317i) q^{62} +(-0.618034 - 1.90211i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.09017 q^{65} +(0.809017 - 3.21644i) q^{66} +4.70820 q^{67} +(1.19098 - 0.865300i) q^{68} +(1.16312 + 3.57971i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(2.42705 + 1.76336i) q^{71} +(1.61803 + 1.17557i) q^{72} +(-0.0450850 + 0.138757i) q^{73} +(-0.354102 - 1.08981i) q^{74} +(-3.92705 + 2.85317i) q^{75} +6.70820 q^{76} +(-3.30902 + 0.224514i) q^{77} +5.47214 q^{78} +(11.2812 - 8.19624i) q^{79} +(-0.118034 - 0.363271i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.23607 - 3.80423i) q^{82} +(-7.54508 - 5.48183i) q^{83} +(-0.309017 + 0.951057i) q^{84} +(0.173762 + 0.534785i) q^{85} +(7.78115 - 5.65334i) q^{86} +9.47214 q^{87} +(2.54508 - 2.12663i) q^{88} +8.09017 q^{89} +(-0.618034 + 0.449028i) q^{90} +(-1.69098 - 5.20431i) q^{91} +(-1.16312 + 3.57971i) q^{92} +(-2.42705 - 1.76336i) q^{93} +(-1.30902 - 0.951057i) q^{94} +(-0.791796 + 2.43690i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-10.0902 + 7.33094i) q^{97} +1.00000 q^{98} +(-5.61803 - 3.52671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9} - 6 q^{10} + 4 q^{11} - 4 q^{12} + 11 q^{13} - q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + 15 q^{19} - q^{20} - 4 q^{21} + 9 q^{22} - 24 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} - q^{28} - 5 q^{29} - 4 q^{30} + 3 q^{31} + 4 q^{32} + q^{33} + 12 q^{34} - q^{35} + 2 q^{36} + 12 q^{37} - 15 q^{38} - 11 q^{39} + 4 q^{40} + 8 q^{41} + q^{42} - 34 q^{43} - 11 q^{44} + 12 q^{45} + q^{46} + 2 q^{47} + q^{48} - q^{49} + 9 q^{50} + 13 q^{51} - 9 q^{52} - 9 q^{53} + 20 q^{54} - q^{55} + 4 q^{56} + 15 q^{57} - 5 q^{58} - 20 q^{59} + q^{60} + 18 q^{61} + 3 q^{62} + 2 q^{63} - q^{64} - 14 q^{65} + q^{66} - 8 q^{67} + 7 q^{68} - 11 q^{69} + 4 q^{70} + 3 q^{71} + 2 q^{72} + 11 q^{73} + 12 q^{74} - 9 q^{75} - 11 q^{77} + 4 q^{78} + 25 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} - 19 q^{83} + q^{84} + 32 q^{85} + 11 q^{86} + 20 q^{87} - q^{88} + 10 q^{89} + 2 q^{90} - 9 q^{91} + 11 q^{92} - 3 q^{93} - 3 q^{94} - 30 q^{95} + q^{96} - 18 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9 - 6 * q^10 + 4 * q^11 - 4 * q^12 + 11 * q^13 - q^14 - 4 * q^15 - q^16 + 7 * q^17 + 2 * q^18 + 15 * q^19 - q^20 - 4 * q^21 + 9 * q^22 - 24 * q^23 + q^24 - 6 * q^25 - 9 * q^26 - 5 * q^27 - q^28 - 5 * q^29 - 4 * q^30 + 3 * q^31 + 4 * q^32 + q^33 + 12 * q^34 - q^35 + 2 * q^36 + 12 * q^37 - 15 * q^38 - 11 * q^39 + 4 * q^40 + 8 * q^41 + q^42 - 34 * q^43 - 11 * q^44 + 12 * q^45 + q^46 + 2 * q^47 + q^48 - q^49 + 9 * q^50 + 13 * q^51 - 9 * q^52 - 9 * q^53 + 20 * q^54 - q^55 + 4 * q^56 + 15 * q^57 - 5 * q^58 - 20 * q^59 + q^60 + 18 * q^61 + 3 * q^62 + 2 * q^63 - q^64 - 14 * q^65 + q^66 - 8 * q^67 + 7 * q^68 - 11 * q^69 + 4 * q^70 + 3 * q^71 + 2 * q^72 + 11 * q^73 + 12 * q^74 - 9 * q^75 - 11 * q^77 + 4 * q^78 + 25 * q^79 + 4 * q^80 - q^81 - 12 * q^82 - 19 * q^83 + q^84 + 32 * q^85 + 11 * q^86 + 20 * q^87 - q^88 + 10 * q^89 + 2 * q^90 - 9 * q^91 + 11 * q^92 - 3 * q^93 - 3 * q^94 - 30 * q^95 + q^96 - 18 * q^97 + 4 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i	0.821362	−	0.570408i	$-0.193215\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i	−0.999773	+	0.0213149i	$0.993215\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.309017	+	0.224514i	0.138197	+	0.100406i	0.654736	−	0.755858i	$-0.272780\pi$
$5$	0.309017	+	0.224514i	0.138197	+	0.100406i	−0.516539	+	0.856264i	$0.672780\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.61803	−	1.17557i	0.539345	−	0.391857i
$10$	−0.381966			−0.120788
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$12$	−1.00000			−0.288675
$13$	4.42705	−	3.21644i	1.22784	−	0.892080i	0.231116	−	0.972926i	$-0.425762\pi$
$13$	4.42705	−	3.21644i	1.22784	−	0.892080i	0.996727	+	0.0808459i	$0.0257622\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.118034	−	0.363271i	0.0304762	−	0.0937962i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.19098	+	0.865300i	0.288856	+	0.209866i	0.722771	−	0.691088i	$-0.242868\pi$
$17$	1.19098	+	0.865300i	0.288856	+	0.209866i	−0.433915	+	0.900954i	$0.642868\pi$
$18$	−0.618034	+	1.90211i	−0.145672	+	0.448332i
$19$	2.07295	+	6.37988i	0.475567	+	1.46365i	0.845191	+	0.534464i	$0.179486\pi$
$19$	2.07295	+	6.37988i	0.475567	+	1.46365i	−0.369624	+	0.929181i	$0.620514\pi$
$20$	0.309017	−	0.224514i	0.0690983	−	0.0502029i
$21$	−1.00000			−0.218218
$22$	2.80902	+	1.76336i	0.598884	+	0.375949i
$23$	−3.76393			−0.784834			−0.392417	−	0.919787i	$-0.628361\pi$
$23$	−3.76393			−0.784834			−0.392417	+	0.919787i	$0.628361\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−1.50000	−	4.61653i	−0.300000	−	0.923305i
$26$	−1.69098	+	5.20431i	−0.331629	+	1.02065i
$27$	−4.04508	−	2.93893i	−0.778477	−	0.565597i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−2.92705	+	9.00854i	−0.543540	+	1.67284i	0.180897	+	0.983502i	$0.442100\pi$
$29$	−2.92705	+	9.00854i	−0.543540	+	1.67284i	−0.724437	+	0.689341i	$0.757900\pi$
$30$	0.118034	+	0.363271i	0.0215500	+	0.0663240i
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	−0.348097	−	0.937459i	$-0.613172\pi$
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	0.784008	+	0.620750i	$0.213172\pi$
$32$	1.00000			0.176777
$33$	−2.54508	+	2.12663i	−0.443042	+	0.370198i
$34$	−1.47214			−0.252469
$35$	0.309017	−	0.224514i	0.0522334	−	0.0379498i
$36$	−0.618034	−	1.90211i	−0.103006	−	0.317019i
$37$	−0.354102	+	1.08981i	−0.0582140	+	0.179164i	−0.975935	−	0.218061i	$-0.930027\pi$
$37$	−0.354102	+	1.08981i	−0.0582140	+	0.179164i	0.917721	+	0.397225i	$0.130027\pi$
$38$	−5.42705	−	3.94298i	−0.880384	−	0.639636i
$39$	−4.42705	−	3.21644i	−0.708896	−	0.515043i
$40$	−0.118034	+	0.363271i	−0.0186628	+	0.0574382i
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	0.976833	+	0.214005i	$0.0686510\pi$
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	−0.664485	+	0.747302i	$0.731349\pi$
$42$	0.809017	−	0.587785i	0.124834	−	0.0906972i
$43$	−9.61803			−1.46674			−0.733368	−	0.679832i	$-0.762053\pi$
$43$	−9.61803			−1.46674			−0.733368	+	0.679832i	$0.762053\pi$
$44$	−3.30902	+	0.224514i	−0.498853	+	0.0338468i
$45$	0.763932			0.113880
$46$	3.04508	−	2.21238i	0.448973	−	0.326198i
$47$	0.500000	+	1.53884i	0.0729325	+	0.224463i	0.980877	−	0.194626i	$-0.0623494\pi$
$47$	0.500000	+	1.53884i	0.0729325	+	0.224463i	−0.907945	+	0.419089i	$0.862349\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	3.92705	+	2.85317i	0.555369	+	0.403499i
$51$	0.454915	−	1.40008i	0.0637008	−	0.196051i
$52$	−1.69098	−	5.20431i	−0.234497	−	0.721708i
$53$	−0.572949	+	0.416272i	−0.0787006	+	0.0571793i	−0.626440	−	0.779470i	$-0.715489\pi$
$53$	−0.572949	+	0.416272i	−0.0787006	+	0.0571793i	0.547739	+	0.836649i	$0.315489\pi$
$54$	5.00000			0.680414
$55$	0.309017	−	1.22857i	0.0416678	−	0.165660i
$56$	1.00000			0.133631
$57$	5.42705	−	3.94298i	0.718830	−	0.522261i
$58$	−2.92705	−	9.00854i	−0.384341	−	1.18288i
$59$	−1.64590	+	5.06555i	−0.214278	+	0.659479i	0.784926	+	0.619589i	$0.212701\pi$
$59$	−1.64590	+	5.06555i	−0.214278	+	0.659479i	−0.999204	+	0.0398899i	$0.987299\pi$
$60$	−0.309017	−	0.224514i	−0.0398939	−	0.0289846i
$61$	11.2082	+	8.14324i	1.43506	+	1.04263i	0.989046	+	0.147611i	$0.0471582\pi$
$61$	11.2082	+	8.14324i	1.43506	+	1.04263i	0.446018	+	0.895024i	$0.352842\pi$
$62$	−0.927051	+	2.85317i	−0.117736	+	0.362353i
$63$	−0.618034	−	1.90211i	−0.0778650	−	0.239644i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.09017			0.259254
$66$	0.809017	−	3.21644i	0.0995831	−	0.395916i
$67$	4.70820			0.575199			0.287599	−	0.957751i	$-0.407143\pi$
$67$	4.70820			0.575199			0.287599	+	0.957751i	$0.407143\pi$
$68$	1.19098	−	0.865300i	0.144428	−	0.104933i
$69$	1.16312	+	3.57971i	0.140023	+	0.430947i
$70$	−0.118034	+	0.363271i	−0.0141078	+	0.0434192i
$71$	2.42705	+	1.76336i	0.288038	+	0.209272i	0.722416	−	0.691459i	$-0.243032\pi$
$71$	2.42705	+	1.76336i	0.288038	+	0.209272i	−0.434378	+	0.900731i	$0.643032\pi$
$72$	1.61803	+	1.17557i	0.190687	+	0.138542i
$73$	−0.0450850	+	0.138757i	−0.00527680	+	0.0162403i	−0.953660	−	0.300886i	$-0.902718\pi$
$73$	−0.0450850	+	0.138757i	−0.00527680	+	0.0162403i	0.948383	+	0.317126i	$0.102718\pi$
$74$	−0.354102	−	1.08981i	−0.0411635	−	0.126688i
$75$	−3.92705	+	2.85317i	−0.453457	+	0.329456i
$76$	6.70820			0.769484
$77$	−3.30902	+	0.224514i	−0.377097	+	0.0255857i
$78$	5.47214			0.619597
$79$	11.2812	−	8.19624i	1.26923	−	0.922149i	0.270057	−	0.962844i	$-0.412957\pi$
$79$	11.2812	−	8.19624i	1.26923	−	0.922149i	0.999172	+	0.0406955i	$0.0129574\pi$
$80$	−0.118034	−	0.363271i	−0.0131966	−	0.0406150i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.23607	−	3.80423i	−0.578227	−	0.420106i
$83$	−7.54508	−	5.48183i	−0.828181	−	0.601708i	0.0908634	−	0.995863i	$-0.471037\pi$
$83$	−7.54508	−	5.48183i	−0.828181	−	0.601708i	−0.919044	+	0.394155i	$0.871037\pi$
$84$	−0.309017	+	0.951057i	−0.0337165	+	0.103769i
$85$	0.173762	+	0.534785i	0.0188471	+	0.0580055i
$86$	7.78115	−	5.65334i	0.839063	−	0.609615i
$87$	9.47214			1.01552
$88$	2.54508	−	2.12663i	0.271307	−	0.226699i
$89$	8.09017			0.857556			0.428778	−	0.903410i	$-0.358944\pi$
$89$	8.09017			0.857556			0.428778	+	0.903410i	$0.358944\pi$
$90$	−0.618034	+	0.449028i	−0.0651465	+	0.0473317i
$91$	−1.69098	−	5.20431i	−0.177263	−	0.545560i
$92$	−1.16312	+	3.57971i	−0.121264	+	0.373211i
$93$	−2.42705	−	1.76336i	−0.251673	−	0.182851i
$94$	−1.30902	−	0.951057i	−0.135015	−	0.0980940i
$95$	−0.791796	+	2.43690i	−0.0812366	+	0.250020i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−10.0902	+	7.33094i	−1.02450	+	0.744344i	−0.967201	−	0.254013i	$-0.918249\pi$
$97$	−10.0902	+	7.33094i	−1.02450	+	0.744344i	−0.0573007	+	0.998357i	$0.518249\pi$
$98$	1.00000			0.101015
$99$	−5.61803	−	3.52671i	−0.564634	−	0.354448i
$100$	−4.85410			−0.485410
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	−0.460451	−	0.887685i	$-0.652312\pi$
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	0.701952	+	0.712225i	$0.252312\pi$
$102$	0.454915	+	1.40008i	0.0450433	+	0.138629i
$103$	−0.572949	+	1.76336i	−0.0564543	+	0.173749i	−0.975308	−	0.220851i	$-0.929117\pi$
$103$	−0.572949	+	1.76336i	−0.0564543	+	0.173749i	0.918853	+	0.394599i	$0.129117\pi$
$104$	4.42705	+	3.21644i	0.434108	+	0.315398i
$105$	−0.309017	−	0.224514i	−0.0301570	−	0.0219103i
$106$	0.218847	−	0.673542i	0.0212563	−	0.0654202i
$107$	1.88197	+	5.79210i	0.181937	+	0.559943i	0.999882	−	0.0153525i	$-0.00488705\pi$
$107$	1.88197	+	5.79210i	0.181937	+	0.559943i	−0.817946	+	0.575296i	$0.804887\pi$
$108$	−4.04508	+	2.93893i	−0.389238	+	0.282798i
$109$	−10.3262			−0.989074			−0.494537	−	0.869157i	$-0.664662\pi$
$109$	−10.3262			−0.989074			−0.494537	+	0.869157i	$0.664662\pi$
$110$	0.472136	+	1.17557i	0.0450164	+	0.112086i
$111$	1.14590			0.108764
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	−3.76393	−	11.5842i	−0.354081	−	1.08975i	−0.956540	−	0.291600i	$-0.905813\pi$
$113$	−3.76393	−	11.5842i	−0.354081	−	1.08975i	0.602460	−	0.798149i	$-0.294187\pi$
$114$	−2.07295	+	6.37988i	−0.194149	+	0.597531i
$115$	−1.16312	−	0.845055i	−0.108461	−	0.0788018i
$116$	7.66312	+	5.56758i	0.711503	+	0.516937i
$117$	3.38197	−	10.4086i	0.312663	−	0.962277i
$118$	−1.64590	−	5.06555i	−0.151517	−	0.466322i
$119$	1.19098	−	0.865300i	0.109177	−	0.0793219i
$120$	0.381966			0.0348686
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$	−13.8541			−1.25429
$123$	5.23607	−	3.80423i	0.472120	−	0.343016i
$124$	−0.927051	−	2.85317i	−0.0832516	−	0.256222i
$125$	1.16312	−	3.57971i	0.104033	−	0.320179i
$126$	1.61803	+	1.17557i	0.144146	+	0.104728i
$127$	6.35410	+	4.61653i	0.563835	+	0.409650i	0.832861	−	0.553483i	$-0.186702\pi$
$127$	6.35410	+	4.61653i	0.563835	+	0.409650i	−0.269025	+	0.963133i	$0.586702\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	2.97214	+	9.14729i	0.261682	+	0.805374i
$130$	−1.69098	+	1.22857i	−0.148309	+	0.107753i
$131$	−14.1803			−1.23894			−0.619471	−	0.785020i	$-0.712653\pi$
$131$	−14.1803			−1.23894			−0.619471	+	0.785020i	$0.712653\pi$
$132$	1.23607	+	3.07768i	0.107586	+	0.267878i
$133$	6.70820			0.581675
$134$	−3.80902	+	2.76741i	−0.329049	+	0.239068i
$135$	−0.590170	−	1.81636i	−0.0507937	−	0.156327i
$136$	−0.454915	+	1.40008i	−0.0390086	+	0.120056i
$137$	0.763932	+	0.555029i	0.0652671	+	0.0474193i	0.619940	−	0.784649i	$-0.287157\pi$
$137$	0.763932	+	0.555029i	0.0652671	+	0.0474193i	−0.554673	+	0.832068i	$0.687157\pi$
$138$	−3.04508	−	2.21238i	−0.259215	−	0.188331i
$139$	−5.85410	+	18.0171i	−0.496538	+	1.52819i	0.318007	+	0.948088i	$0.396986\pi$
$139$	−5.85410	+	18.0171i	−0.496538	+	1.52819i	−0.814545	+	0.580100i	$0.803014\pi$
$140$	−0.118034	−	0.363271i	−0.00997569	−	0.0307020i
$141$	1.30902	−	0.951057i	0.110239	−	0.0800934i
$142$	−3.00000			−0.251754
$143$	−15.3713	−	9.64932i	−1.28541	−	0.806917i
$144$	−2.00000			−0.166667
$145$	−2.92705	+	2.12663i	−0.243078	+	0.176607i
$146$	−0.0450850	−	0.138757i	−0.00373126	−	0.0114836i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	0.927051	+	0.673542i	0.0762031	+	0.0553648i
$149$	−1.54508	−	1.12257i	−0.126578	−	0.0919645i	0.522695	−	0.852520i	$-0.324927\pi$
$149$	−1.54508	−	1.12257i	−0.126578	−	0.0919645i	−0.649273	+	0.760555i	$0.724927\pi$
$150$	1.50000	−	4.61653i	0.122474	−	0.376938i
$151$	−2.47214	−	7.60845i	−0.201180	−	0.619167i	−0.999849	−	0.0173966i	$-0.994462\pi$
$151$	−2.47214	−	7.60845i	−0.201180	−	0.619167i	0.798669	−	0.601770i	$-0.205538\pi$
$152$	−5.42705	+	3.94298i	−0.440192	+	0.319818i
$153$	2.94427			0.238030
$154$	2.54508	−	2.12663i	0.205089	−	0.171368i
$155$	1.14590			0.0920407
$156$	−4.42705	+	3.21644i	−0.354448	+	0.257521i
$157$	7.30902	+	22.4948i	0.583323	+	1.79528i	0.605903	+	0.795539i	$0.292812\pi$
$157$	7.30902	+	22.4948i	0.583323	+	1.79528i	−0.0225797	+	0.999745i	$0.507188\pi$
$158$	−4.30902	+	13.2618i	−0.342807	+	1.05505i
$159$	0.572949	+	0.416272i	0.0454378	+	0.0330125i
$160$	0.309017	+	0.224514i	0.0244299	+	0.0177494i
$161$	−1.16312	+	3.57971i	−0.0916666	+	0.282121i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	3.73607	−	2.71441i	0.292631	−	0.212609i	−0.431777	−	0.901981i	$-0.642113\pi$
$163$	3.73607	−	2.71441i	0.292631	−	0.212609i	0.724408	+	0.689371i	$0.242113\pi$
$164$	6.47214			0.505389
$165$	−1.26393	+	0.0857567i	−0.0983970	+	0.00667615i
$166$	9.32624			0.723856
$167$	13.0623	−	9.49032i	1.01079	−	0.734383i	0.0464166	−	0.998922i	$-0.485220\pi$
$167$	13.0623	−	9.49032i	1.01079	−	0.734383i	0.964375	+	0.264539i	$0.0852198\pi$
$168$	−0.309017	−	0.951057i	−0.0238412	−	0.0733756i
$169$	5.23607	−	16.1150i	0.402774	−	1.23961i
$170$	−0.454915	−	0.330515i	−0.0348904	−	0.0253494i
$171$	10.8541	+	7.88597i	0.830034	+	0.603055i
$172$	−2.97214	+	9.14729i	−0.226623	+	0.697475i
$173$	−5.30902	−	16.3395i	−0.403637	−	1.24227i	−0.922028	−	0.387123i	$-0.873469\pi$
$173$	−5.30902	−	16.3395i	−0.403637	−	1.24227i	0.518391	−	0.855144i	$-0.326531\pi$
$174$	−7.66312	+	5.56758i	−0.580940	+	0.422077i
$175$	−4.85410			−0.366936
$176$	−0.809017	+	3.21644i	−0.0609820	+	0.242448i
$177$	5.32624			0.400345
$178$	−6.54508	+	4.75528i	−0.490575	+	0.356423i
$179$	7.50000	+	23.0826i	0.560576	+	1.72528i	0.680743	+	0.732523i	$0.261657\pi$
$179$	7.50000	+	23.0826i	0.560576	+	1.72528i	−0.120166	+	0.992754i	$0.538343\pi$
$180$	0.236068	−	0.726543i	0.0175955	−	0.0541533i
$181$	−11.0902	−	8.05748i	−0.824326	−	0.598908i	0.0936225	−	0.995608i	$-0.470155\pi$
$181$	−11.0902	−	8.05748i	−0.824326	−	0.598908i	−0.917948	+	0.396700i	$0.870155\pi$
$182$	4.42705	+	3.21644i	0.328155	+	0.238418i
$183$	4.28115	−	13.1760i	0.316472	−	0.974000i
$184$	−1.16312	−	3.57971i	−0.0857463	−	0.263900i
$185$	−0.354102	+	0.257270i	−0.0260341	+	0.0189149i
$186$	3.00000			0.219971
$187$	1.19098	−	4.73504i	0.0870933	−	0.346260i
$188$	1.61803			0.118007
$189$	−4.04508	+	2.93893i	−0.294237	+	0.213775i
$190$	−0.791796	−	2.43690i	−0.0574429	−	0.176791i
$191$	0.190983	−	0.587785i	0.0138190	−	0.0425306i	−0.943909	−	0.330205i	$-0.892882\pi$
$191$	0.190983	−	0.587785i	0.0138190	−	0.0425306i	0.957728	+	0.287674i	$0.0928821\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	−11.4271	−	8.30224i	−0.822537	−	0.597608i	0.0949010	−	0.995487i	$-0.469747\pi$
$193$	−11.4271	−	8.30224i	−0.822537	−	0.597608i	−0.917438	+	0.397879i	$0.869747\pi$
$194$	3.85410	−	11.8617i	0.276708	−	0.851621i
$195$	−0.645898	−	1.98787i	−0.0462537	−	0.142354i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	3.32624			0.236985			0.118492	−	0.992955i	$-0.462194\pi$
$197$	3.32624			0.236985			0.118492	+	0.992955i	$0.462194\pi$
$198$	6.61803	−	0.449028i	0.470323	−	0.0319110i
$199$	11.7082			0.829973			0.414986	−	0.909828i	$-0.363786\pi$
$199$	11.7082			0.829973			0.414986	+	0.909828i	$0.363786\pi$
$200$	3.92705	−	2.85317i	0.277684	−	0.201750i
$201$	−1.45492	−	4.47777i	−0.102622	−	0.315837i
$202$	−0.927051	+	2.85317i	−0.0652271	+	0.200748i
$203$	7.66312	+	5.56758i	0.537846	+	0.390768i
$204$	−1.19098	−	0.865300i	−0.0833855	−	0.0605831i
$205$	−0.763932	+	2.35114i	−0.0533553	+	0.164211i
$206$	−0.572949	−	1.76336i	−0.0399192	−	0.122859i
$207$	−6.09017	+	4.42477i	−0.423296	+	0.307543i
$208$	−5.47214			−0.379424
$209$	17.0729	−	14.2658i	1.18096	−	0.986789i
$210$	0.381966			0.0263582
$211$	−16.5172	+	12.0005i	−1.13709	+	0.826146i	−0.986711	−	0.162482i	$-0.948050\pi$
$211$	−16.5172	+	12.0005i	−1.13709	+	0.826146i	−0.150381	+	0.988628i	$0.548050\pi$
$212$	0.218847	+	0.673542i	0.0150305	+	0.0462591i
$213$	0.927051	−	2.85317i	0.0635205	−	0.195496i
$214$	−4.92705	−	3.57971i	−0.336806	−	0.244704i
$215$	−2.97214	−	2.15938i	−0.202698	−	0.147269i
$216$	1.54508	−	4.75528i	0.105130	−	0.323556i
$217$	−0.927051	−	2.85317i	−0.0629323	−	0.193686i
$218$	8.35410	−	6.06961i	0.565811	−	0.411086i
$219$	0.145898			0.00985888
$220$	−1.07295	−	0.673542i	−0.0723382	−	0.0454102i
$221$	8.05573			0.541887
$222$	−0.927051	+	0.673542i	−0.0622196	+	0.0452052i
$223$	1.66312	+	5.11855i	0.111371	+	0.342764i	0.991173	−	0.132576i	$-0.0423250\pi$
$223$	1.66312	+	5.11855i	0.111371	+	0.342764i	−0.879802	+	0.475340i	$0.842325\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−7.85410	−	5.70634i	−0.523607	−	0.380423i
$226$	9.85410	+	7.15942i	0.655485	+	0.476238i
$227$	6.68034	−	20.5600i	0.443390	−	1.36461i	−0.440850	−	0.897581i	$-0.645323\pi$
$227$	6.68034	−	20.5600i	0.443390	−	1.36461i	0.884240	−	0.467033i	$-0.154677\pi$
$228$	−2.07295	−	6.37988i	−0.137284	−	0.422518i
$229$	9.73607	−	7.07367i	0.643377	−	0.467441i	−0.217631	−	0.976031i	$-0.569833\pi$
$229$	9.73607	−	7.07367i	0.643377	−	0.467441i	0.861009	+	0.508590i	$0.169833\pi$
$230$	1.43769			0.0947987
$231$	1.23607	+	3.07768i	0.0813273	+	0.202497i
$232$	−9.47214			−0.621876
$233$	−19.4164	+	14.1068i	−1.27201	+	0.924170i	−0.999281	−	0.0379203i	$-0.987927\pi$
$233$	−19.4164	+	14.1068i	−1.27201	+	0.924170i	−0.272730	+	0.962090i	$0.587927\pi$
$234$	3.38197	+	10.4086i	0.221086	+	0.680433i
$235$	−0.190983	+	0.587785i	−0.0124584	+	0.0383429i
$236$	4.30902	+	3.13068i	0.280493	+	0.203790i
$237$	−11.2812	−	8.19624i	−0.732790	−	0.532403i
$238$	−0.454915	+	1.40008i	−0.0294878	+	0.0907540i
$239$	−1.11803	−	3.44095i	−0.0723196	−	0.222577i	0.908363	−	0.418183i	$-0.137333\pi$
$239$	−1.11803	−	3.44095i	−0.0723196	−	0.222577i	−0.980683	+	0.195606i	$0.937333\pi$
$240$	−0.309017	+	0.224514i	−0.0199470	+	0.0144923i
$241$	0.618034			0.0398111			0.0199055	−	0.999802i	$-0.493663\pi$
$241$	0.618034			0.0398111			0.0199055	+	0.999802i	$0.493663\pi$
$242$	1.95492	−	10.8249i	0.125667	−	0.695850i
$243$	−16.0000			−1.02640
$244$	11.2082	−	8.14324i	0.717532	−	0.521317i
$245$	−0.118034	−	0.363271i	−0.00754091	−	0.0232085i
$246$	−2.00000	+	6.15537i	−0.127515	+	0.392452i
$247$	29.6976	+	21.5765i	1.88961	+	1.37288i
$248$	2.42705	+	1.76336i	0.154118	+	0.111973i
$249$	−2.88197	+	8.86978i	−0.182637	+	0.562099i
$250$	1.16312	+	3.57971i	0.0735621	+	0.226401i
$251$	2.85410	−	2.07363i	0.180149	−	0.130886i	−0.494056	−	0.869430i	$-0.664486\pi$
$251$	2.85410	−	2.07363i	0.180149	−	0.130886i	0.674205	+	0.738544i	$0.264486\pi$
$252$	−2.00000			−0.125988
$253$	4.65248	+	11.5842i	0.292499	+	0.728292i
$254$	−7.85410			−0.492810
$255$	0.454915	−	0.330515i	0.0284879	−	0.0206977i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.87132	−	30.3808i	0.615756	−	1.89510i	0.226300	−	0.974058i	$-0.427337\pi$
$257$	9.87132	−	30.3808i	0.615756	−	1.89510i	0.389456	−	0.921045i	$-0.372663\pi$
$258$	−7.78115	−	5.65334i	−0.484433	−	0.351961i
$259$	0.927051	+	0.673542i	0.0576041	+	0.0418519i
$260$	0.645898	−	1.98787i	0.0400569	−	0.123282i
$261$	5.85410	+	18.0171i	0.362360	+	1.11523i
$262$	11.4721	−	8.33499i	0.708751	−	0.514938i
$263$	20.3820			1.25681			0.628403	−	0.777888i	$-0.283709\pi$
$263$	20.3820			1.25681			0.628403	+	0.777888i	$0.283709\pi$
$264$	−2.80902	−	1.76336i	−0.172883	−	0.108527i
$265$	−0.270510			−0.0166173
$266$	−5.42705	+	3.94298i	−0.332754	+	0.241760i
$267$	−2.50000	−	7.69421i	−0.152998	−	0.470878i
$268$	1.45492	−	4.47777i	0.0888731	−	0.273523i
$269$	−16.0172	−	11.6372i	−0.976587	−	0.709532i	−0.0196439	−	0.999807i	$-0.506253\pi$
$269$	−16.0172	−	11.6372i	−0.976587	−	0.709532i	−0.956943	+	0.290275i	$0.906253\pi$
$270$	1.54508	+	1.12257i	0.0940309	+	0.0683174i
$271$	−2.04508	+	6.29412i	−0.124230	+	0.382341i	−0.993760	−	0.111539i	$-0.964422\pi$
$271$	−2.04508	+	6.29412i	−0.124230	+	0.382341i	0.869530	+	0.493880i	$0.164422\pi$
$272$	−0.454915	−	1.40008i	−0.0275833	−	0.0848926i
$273$	−4.42705	+	3.21644i	−0.267937	+	0.194668i
$274$	−0.944272			−0.0570456
$275$	−12.3541	+	10.3229i	−0.744980	+	0.622492i
$276$	3.76393			0.226562
$277$	−14.2361	+	10.3431i	−0.855362	+	0.621457i	−0.926619	−	0.376001i	$-0.877299\pi$
$277$	−14.2361	+	10.3431i	−0.855362	+	0.621457i	0.0712569	+	0.997458i	$0.477299\pi$
$278$	−5.85410	−	18.0171i	−0.351106	−	1.08059i
$279$	1.85410	−	5.70634i	0.111002	−	0.341630i
$280$	0.309017	+	0.224514i	0.0184673	+	0.0134173i
$281$	8.11803	+	5.89810i	0.484281	+	0.351851i	0.802981	−	0.596005i	$-0.203246\pi$
$281$	8.11803	+	5.89810i	0.484281	+	0.351851i	−0.318700	+	0.947856i	$0.603246\pi$
$282$	−0.500000	+	1.53884i	−0.0297746	+	0.0916367i
$283$	3.83688	+	11.8087i	0.228079	+	0.701955i	0.997964	+	0.0637727i	$0.0203133\pi$
$283$	3.83688	+	11.8087i	0.228079	+	0.701955i	−0.769886	+	0.638182i	$0.779687\pi$
$284$	2.42705	−	1.76336i	0.144019	−	0.104636i
$285$	2.56231			0.151778
$286$	18.1074	−	1.22857i	1.07071	−	0.0726469i
$287$	6.47214			0.382038
$288$	1.61803	−	1.17557i	0.0953436	−	0.0692712i
$289$	−4.58359	−	14.1068i	−0.269623	−	0.829814i
$290$	1.11803	−	3.44095i	0.0656532	−	0.202060i
$291$	10.0902	+	7.33094i	0.591496	+	0.429747i
$292$	0.118034	+	0.0857567i	0.00690742	+	0.00501853i
$293$	−1.95492	+	6.01661i	−0.114207	+	0.351494i	−0.991781	−	0.127948i	$-0.959161\pi$
$293$	−1.95492	+	6.01661i	−0.114207	+	0.351494i	0.877574	+	0.479442i	$0.159161\pi$
$294$	−0.309017	−	0.951057i	−0.0180222	−	0.0554667i
$295$	−1.64590	+	1.19581i	−0.0958279	+	0.0696230i
$296$	−1.14590			−0.0666040
$297$	−4.04508	+	16.0822i	−0.234720	+	0.933184i
$298$	1.90983			0.110633
$299$	−16.6631	+	12.1065i	−0.963653	+	0.700135i
$300$	1.50000	+	4.61653i	0.0866025	+	0.266535i
$301$	−2.97214	+	9.14729i	−0.171311	+	0.527241i
$302$	6.47214	+	4.70228i	0.372430	+	0.270586i
$303$	−2.42705	−	1.76336i	−0.139430	−	0.101302i
$304$	2.07295	−	6.37988i	0.118892	−	0.365911i
$305$	1.63525	+	5.03280i	0.0936344	+	0.288177i
$306$	−2.38197	+	1.73060i	−0.136168	+	0.0989318i
$307$	−10.4164			−0.594496			−0.297248	−	0.954800i	$-0.596069\pi$
$307$	−10.4164			−0.594496			−0.297248	+	0.954800i	$0.596069\pi$
$308$	−0.809017	+	3.21644i	−0.0460980	+	0.183274i
$309$	1.85410			0.105476
$310$	−0.927051	+	0.673542i	−0.0526530	+	0.0382546i
$311$	4.07295	+	12.5352i	0.230956	+	0.710809i	0.997632	+	0.0687750i	$0.0219091\pi$
$311$	4.07295	+	12.5352i	0.230956	+	0.710809i	−0.766676	+	0.642034i	$0.778091\pi$
$312$	1.69098	−	5.20431i	0.0957331	−	0.294636i
$313$	−2.64590	−	1.92236i	−0.149555	−	0.108658i	0.510492	−	0.859883i	$-0.329463\pi$
$313$	−2.64590	−	1.92236i	−0.149555	−	0.108658i	−0.660047	+	0.751225i	$0.729463\pi$
$314$	−19.1353	−	13.9026i	−1.07986	−	0.784568i
$315$	0.236068	−	0.726543i	0.0133009	−	0.0409360i
$316$	−4.30902	−	13.2618i	−0.242401	−	0.746034i
$317$	15.6631	−	11.3799i	0.879728	−	0.639160i	−0.0534512	−	0.998570i	$-0.517022\pi$
$317$	15.6631	−	11.3799i	0.879728	−	0.639160i	0.933180	+	0.359410i	$0.117022\pi$
$318$	−0.708204			−0.0397141
$319$	31.3435	−	2.12663i	1.75490	−	0.119068i
$320$	−0.381966			−0.0213525
$321$	4.92705	−	3.57971i	0.275001	−	0.199800i
$322$	−1.16312	−	3.57971i	−0.0648181	−	0.199490i
$323$	−3.05166	+	9.39205i	−0.169799	+	0.522588i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−21.4894	−	15.6129i	−1.19202	−	0.866050i
$326$	−1.42705	+	4.39201i	−0.0790370	+	0.243251i
$327$	3.19098	+	9.82084i	0.176462	+	0.543093i
$328$	−5.23607	+	3.80423i	−0.289113	+	0.210053i
$329$	1.61803			0.0892051
$330$	0.972136	−	0.812299i	0.0535143	−	0.0447156i
$331$	−6.29180			−0.345828			−0.172914	−	0.984937i	$-0.555318\pi$
$331$	−6.29180			−0.345828			−0.172914	+	0.984937i	$0.555318\pi$
$332$	−7.54508	+	5.48183i	−0.414090	+	0.300854i
$333$	0.708204	+	2.17963i	0.0388093	+	0.119443i
$334$	−4.98936	+	15.3557i	−0.273005	+	0.840224i
$335$	1.45492	+	1.05706i	0.0794905	+	0.0577532i
$336$	0.809017	+	0.587785i	0.0441355	+	0.0320663i
$337$	−3.64590	+	11.2209i	−0.198605	+	0.611242i	0.801311	+	0.598248i	$0.204136\pi$
$337$	−3.64590	+	11.2209i	−0.198605	+	0.611242i	−0.999916	+	0.0129943i	$0.995864\pi$
$338$	5.23607	+	16.1150i	0.284805	+	0.876538i
$339$	−9.85410	+	7.15942i	−0.535201	+	0.388847i
$340$	0.562306			0.0304953
$341$	−8.42705	−	5.29007i	−0.456350	−	0.286473i
$342$	−13.4164			−0.725476
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−2.97214	−	9.14729i	−0.160247	−	0.493189i
$345$	−0.444272	+	1.36733i	−0.0239188	+	0.0736145i
$346$	13.8992	+	10.0984i	0.747225	+	0.542891i
$347$	−17.7533	−	12.8985i	−0.953046	−	0.692429i	−0.00152104	−	0.999999i	$-0.500484\pi$
$347$	−17.7533	−	12.8985i	−0.953046	−	0.692429i	−0.951525	+	0.307570i	$0.900484\pi$
$348$	2.92705	−	9.00854i	0.156906	−	0.482908i
$349$	−8.29180	−	25.5195i	−0.443850	−	1.36603i	−0.883740	−	0.467978i	$-0.844983\pi$
$349$	−8.29180	−	25.5195i	−0.443850	−	1.36603i	0.439891	−	0.898051i	$-0.355017\pi$
$350$	3.92705	−	2.85317i	0.209910	−	0.152508i
$351$	−27.3607			−1.46041
$352$	−1.23607	−	3.07768i	−0.0658826	−	0.164041i
$353$	−24.0902			−1.28219			−0.641095	−	0.767461i	$-0.721520\pi$
$353$	−24.0902			−1.28219			−0.641095	+	0.767461i	$0.721520\pi$
$354$	−4.30902	+	3.13068i	−0.229022	+	0.166394i
$355$	0.354102	+	1.08981i	0.0187938	+	0.0578413i
$356$	2.50000	−	7.69421i	0.132500	−	0.407792i
$357$	−1.19098	−	0.865300i	−0.0630335	−	0.0457965i
$358$	−19.6353	−	14.2658i	−1.03776	−	0.753973i
$359$	7.13525	−	21.9601i	0.376584	−	1.15901i	−0.565819	−	0.824529i	$-0.691440\pi$
$359$	7.13525	−	21.9601i	0.376584	−	1.15901i	0.942404	−	0.334478i	$-0.108560\pi$
$360$	0.236068	+	0.726543i	0.0124419	+	0.0382922i
$361$	−21.0344	+	15.2824i	−1.10708	+	0.804338i
$362$	13.7082			0.720487
$363$	9.69098	+	5.20431i	0.508645	+	0.273155i
$364$	−5.47214			−0.286818
$365$	−0.0450850	+	0.0327561i	−0.00235986	+	0.00171454i
$366$	4.28115	+	13.1760i	0.223779	+	0.688722i
$367$	0.927051	−	2.85317i	0.0483917	−	0.148934i	−0.923941	−	0.382535i	$-0.875051\pi$
$367$	0.927051	−	2.85317i	0.0483917	−	0.148934i	0.972333	+	0.233601i	$0.0750510\pi$
$368$	3.04508	+	2.21238i	0.158736	+	0.115328i
$369$	10.4721	+	7.60845i	0.545158	+	0.396080i
$370$	0.135255	−	0.416272i	0.00703157	−	0.0216409i
$371$	0.218847	+	0.673542i	0.0113620	+	0.0349686i
$372$	−2.42705	+	1.76336i	−0.125837	+	0.0914257i
$373$	−11.6525			−0.603342			−0.301671	−	0.953412i	$-0.597544\pi$
$373$	−11.6525			−0.603342			−0.301671	+	0.953412i	$0.597544\pi$
$374$	1.81966	+	4.53077i	0.0940924	+	0.234280i
$375$	−3.76393			−0.194369
$376$	−1.30902	+	0.951057i	−0.0675074	+	0.0490470i
$377$	16.0172	+	49.2959i	0.824929	+	2.53887i
$378$	1.54508	−	4.75528i	0.0794706	−	0.244585i
$379$	27.4615	+	19.9519i	1.41060	+	1.02486i	0.993235	+	0.116125i	$0.0370472\pi$
$379$	27.4615	+	19.9519i	1.41060	+	1.02486i	0.417367	+	0.908738i	$0.362953\pi$
$380$	2.07295	+	1.50609i	0.106340	+	0.0772606i
$381$	2.42705	−	7.46969i	0.124342	−	0.382684i
$382$	0.190983	+	0.587785i	0.00977154	+	0.0300737i
$383$	10.5451	−	7.66145i	0.538829	−	0.391482i	−0.284821	−	0.958581i	$-0.591934\pi$
$383$	10.5451	−	7.66145i	0.538829	−	0.391482i	0.823650	+	0.567099i	$0.191934\pi$
$384$	−1.00000			−0.0510310
$385$	−1.07295	−	0.673542i	−0.0546825	−	0.0343269i
$386$	14.1246			0.718924
$387$	−15.5623	+	11.3067i	−0.791076	+	0.574751i
$388$	3.85410	+	11.8617i	0.195662	+	0.602187i
$389$	3.55573	−	10.9434i	0.180283	−	0.554853i	−0.819553	−	0.573004i	$-0.805778\pi$
$389$	3.55573	−	10.9434i	0.180283	−	0.554853i	0.999835	+	0.0181511i	$0.00577800\pi$
$390$	1.69098	+	1.22857i	0.0856263	+	0.0622111i
$391$	−4.48278	−	3.25693i	−0.226704	−	0.164710i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	4.38197	+	13.4863i	0.221041	+	0.680294i
$394$	−2.69098	+	1.95511i	−0.135570	+	0.0984972i
$395$	5.32624			0.267992
$396$	−5.09017	+	4.25325i	−0.255791	+	0.213734i
$397$	11.2918			0.566719			0.283359	−	0.959014i	$-0.408551\pi$
$397$	11.2918			0.566719			0.283359	+	0.959014i	$0.408551\pi$
$398$	−9.47214	+	6.88191i	−0.474795	+	0.344959i
$399$	−2.07295	−	6.37988i	−0.103777	−	0.319394i
$400$	−1.50000	+	4.61653i	−0.0750000	+	0.230826i
$401$	−17.3713	−	12.6210i	−0.867482	−	0.630263i	0.0624278	−	0.998049i	$-0.480116\pi$
$401$	−17.3713	−	12.6210i	−0.867482	−	0.630263i	−0.929910	+	0.367787i	$0.880116\pi$
$402$	3.80902	+	2.76741i	0.189977	+	0.138026i
$403$	5.07295	−	15.6129i	0.252702	−	0.777736i
$404$	−0.927051	−	2.85317i	−0.0461225	−	0.141950i
$405$	0.309017	−	0.224514i	0.0153552	−	0.0111562i
$406$	−9.47214			−0.470094
$407$	3.79180	−	0.257270i	0.187952	−	0.0127524i
$408$	1.47214			0.0728816
$409$	5.42705	−	3.94298i	0.268350	−	0.194968i	−0.445470	−	0.895297i	$-0.646963\pi$
$409$	5.42705	−	3.94298i	0.268350	−	0.194968i	0.713820	+	0.700329i	$0.246963\pi$
$410$	−0.763932	−	2.35114i	−0.0377279	−	0.116115i
$411$	0.291796	−	0.898056i	0.0143932	−	0.0442978i
$412$	1.50000	+	1.08981i	0.0738997	+	0.0536913i
$413$	4.30902	+	3.13068i	0.212033	+	0.154051i
$414$	2.32624	−	7.15942i	0.114328	−	0.351867i
$415$	−1.10081	−	3.38795i	−0.0540368	−	0.166308i
$416$	4.42705	−	3.21644i	0.217054	−	0.157699i
$417$	18.9443			0.927705
$418$	−5.42705	+	21.5765i	−0.265446	+	1.05534i
$419$	−26.5066			−1.29493			−0.647466	−	0.762095i	$-0.724171\pi$
$419$	−26.5066			−1.29493			−0.647466	+	0.762095i	$0.724171\pi$
$420$	−0.309017	+	0.224514i	−0.0150785	+	0.0109552i
$421$	−12.1074	−	37.2627i	−0.590078	−	1.81607i	−0.577842	−	0.816149i	$-0.696105\pi$
$421$	−12.1074	−	37.2627i	−0.590078	−	1.81607i	−0.0122360	−	0.999925i	$-0.503895\pi$
$422$	6.30902	−	19.4172i	0.307118	−	0.945212i
$423$	2.61803	+	1.90211i	0.127293	+	0.0924839i
$424$	−0.572949	−	0.416272i	−0.0278249	−	0.0202159i
$425$	2.20820	−	6.79615i	0.107114	−	0.329662i
$426$	0.927051	+	2.85317i	0.0449158	+	0.138237i
$427$	11.2082	−	8.14324i	0.542403	−	0.394079i
$428$	6.09017			0.294379
$429$	−4.42705	+	17.6008i	−0.213740	+	0.849775i
$430$	3.67376			0.177165
$431$	18.2812	−	13.2820i	0.880572	−	0.639773i	−0.0528306	−	0.998603i	$-0.516824\pi$
$431$	18.2812	−	13.2820i	0.880572	−	0.639773i	0.933403	+	0.358830i	$0.116824\pi$
$432$	1.54508	+	4.75528i	0.0743379	+	0.228789i
$433$	3.30902	−	10.1841i	0.159021	−	0.489417i	−0.839525	−	0.543321i	$-0.817167\pi$
$433$	3.30902	−	10.1841i	0.159021	−	0.489417i	0.998546	+	0.0539043i	$0.0171666\pi$
$434$	2.42705	+	1.76336i	0.116502	+	0.0846438i
$435$	2.92705	+	2.12663i	0.140341	+	0.101964i
$436$	−3.19098	+	9.82084i	−0.152820	+	0.470333i
$437$	−7.80244	−	24.0134i	−0.373241	−	1.14872i
$438$	−0.118034	+	0.0857567i	−0.00563988	+	0.00409761i
$439$	−8.29180			−0.395746			−0.197873	−	0.980228i	$-0.563403\pi$
$439$	−8.29180			−0.395746			−0.197873	+	0.980228i	$0.563403\pi$
$440$	1.26393	−	0.0857567i	0.0602556	−	0.00408829i
$441$	−2.00000			−0.0952381
$442$	−6.51722	+	4.73504i	−0.309993	+	0.225223i
$443$	−9.84346	−	30.2951i	−0.467677	−	1.43936i	−0.855585	−	0.517663i	$-0.826802\pi$
$443$	−9.84346	−	30.2951i	−0.467677	−	1.43936i	0.387908	−	0.921698i	$-0.373198\pi$
$444$	0.354102	−	1.08981i	0.0168049	−	0.0517203i
$445$	2.50000	+	1.81636i	0.118511	+	0.0861035i
$446$	−4.35410	−	3.16344i	−0.206173	−	0.149793i
$447$	−0.590170	+	1.81636i	−0.0279141	+	0.0859107i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	16.0172	−	11.6372i	0.755899	−	0.549193i	−0.141750	−	0.989902i	$-0.545273\pi$
$449$	16.0172	−	11.6372i	0.755899	−	0.549193i	0.897650	+	0.440709i	$0.145273\pi$
$450$	9.70820			0.457649
$451$	16.4721	−	13.7638i	0.775643	−	0.648113i
$452$	−12.1803			−0.572915
$453$	−6.47214	+	4.70228i	−0.304087	+	0.220932i
$454$	6.68034	+	20.5600i	0.313524	+	0.964927i
$455$	0.645898	−	1.98787i	0.0302802	−	0.0931928i
$456$	5.42705	+	3.94298i	0.254145	+	0.184647i
$457$	12.4721	+	9.06154i	0.583422	+	0.423881i	0.839956	−	0.542654i	$-0.182581\pi$
$457$	12.4721	+	9.06154i	0.583422	+	0.423881i	−0.256534	+	0.966535i	$0.582581\pi$
$458$	−3.71885	+	11.4454i	−0.173770	+	0.534810i
$459$	−2.27458	−	7.00042i	−0.106168	−	0.326752i
$460$	−1.16312	+	0.845055i	−0.0542307	+	0.0394009i
$461$	36.2705			1.68929			0.844643	−	0.535330i	$-0.179813\pi$
$461$	36.2705			1.68929			0.844643	+	0.535330i	$0.179813\pi$
$462$	−2.80902	−	1.76336i	−0.130687	−	0.0820387i
$463$	24.9787			1.16086			0.580430	−	0.814310i	$-0.302885\pi$
$463$	24.9787			1.16086			0.580430	+	0.814310i	$0.302885\pi$
$464$	7.66312	−	5.56758i	0.355751	−	0.258468i
$465$	−0.354102	−	1.08981i	−0.0164211	−	0.0505389i
$466$	7.41641	−	22.8254i	0.343558	−	1.05736i
$467$	14.6074	+	10.6129i	0.675949	+	0.491106i	0.872011	−	0.489485i	$-0.162815\pi$
$467$	14.6074	+	10.6129i	0.675949	+	0.491106i	−0.196062	+	0.980591i	$0.562815\pi$
$468$	−8.85410	−	6.43288i	−0.409281	−	0.297360i
$469$	1.45492	−	4.47777i	0.0671817	−	0.206764i
$470$	−0.190983	−	0.587785i	−0.00880939	−	0.0271125i
$471$	19.1353	−	13.9026i	0.881706	−	0.640597i
$472$	−5.32624			−0.245160
$473$	11.8885	+	29.6013i	0.546636	+	1.36107i
$474$	13.9443			0.640482
$475$	26.3435	−	19.1396i	1.20872	−	0.878187i
$476$	−0.454915	−	1.40008i	−0.0208510	−	0.0641728i
$477$	−0.437694	+	1.34708i	−0.0200406	+	0.0616787i
$478$	2.92705	+	2.12663i	0.133880	+	0.0972697i
$479$	−32.5623	−	23.6579i	−1.48781	−	1.08096i	−0.974934	−	0.222494i	$-0.928580\pi$
$479$	−32.5623	−	23.6579i	−1.48781	−	1.08096i	−0.512876	−	0.858463i	$-0.671420\pi$
$480$	0.118034	−	0.363271i	0.00538749	−	0.0165810i
$481$	1.93769	+	5.96361i	0.0883512	+	0.271917i
$482$	−0.500000	+	0.363271i	−0.0227744	+	0.0165466i
$483$	3.76393			0.171265
$484$	4.78115	+	9.90659i	0.217325	+	0.450300i
$485$	−4.76393			−0.216319
$486$	12.9443	−	9.40456i	0.587164	−	0.426600i
$487$	−3.21885	−	9.90659i	−0.145860	−	0.448911i	0.851261	−	0.524743i	$-0.175839\pi$
$487$	−3.21885	−	9.90659i	−0.145860	−	0.448911i	−0.997121	+	0.0758325i	$0.975839\pi$
$488$	−4.28115	+	13.1760i	−0.193799	+	0.596451i
$489$	−3.73607	−	2.71441i	−0.168951	−	0.122750i
$490$	0.309017	+	0.224514i	0.0139600	+	0.0101425i
$491$	−5.13525	+	15.8047i	−0.231751	+	0.713256i	0.765785	+	0.643097i	$0.222351\pi$
$491$	−5.13525	+	15.8047i	−0.231751	+	0.713256i	−0.997536	+	0.0701590i	$0.977649\pi$
$492$	−2.00000	−	6.15537i	−0.0901670	−	0.277505i
$493$	−11.2812	+	8.19624i	−0.508078	+	0.369140i
$494$	−36.7082			−1.65158
$495$	−0.944272	−	2.35114i	−0.0424419	−	0.105676i
$496$	−3.00000			−0.134704
$497$	2.42705	−	1.76336i	0.108868	−	0.0790973i
$498$	−2.88197	−	8.86978i	−0.129144	−	0.397464i
$499$	5.69098	−	17.5150i	0.254763	−	0.784081i	−0.739113	−	0.673582i	$-0.764755\pi$
$499$	5.69098	−	17.5150i	0.254763	−	0.784081i	0.993876	−	0.110499i	$-0.0352450\pi$
$500$	−3.04508	−	2.21238i	−0.136180	−	0.0989408i
$501$	−13.0623	−	9.49032i	−0.583581	−	0.423996i
$502$	−1.09017	+	3.35520i	−0.0486567	+	0.149750i
$503$	8.63525	+	26.5766i	0.385027	+	1.18499i	0.936461	+	0.350773i	$0.114081\pi$
$503$	8.63525	+	26.5766i	0.385027	+	1.18499i	−0.551434	+	0.834219i	$0.685919\pi$
$504$	1.61803	−	1.17557i	0.0720730	−	0.0523641i
$505$	1.14590			0.0509918
$506$	−10.5729	−	6.63715i	−0.470025	−	0.295057i
$507$	−16.9443			−0.752522
$508$	6.35410	−	4.61653i	0.281918	−	0.204825i
$509$	10.2016	+	31.3974i	0.452179	+	1.39166i	0.874415	+	0.485178i	$0.161245\pi$
$509$	10.2016	+	31.3974i	0.452179	+	1.39166i	−0.422236	+	0.906486i	$0.638755\pi$
$510$	−0.173762	+	0.534785i	−0.00769431	+	0.0236807i
$511$	0.118034	+	0.0857567i	0.00522152	+	0.00379365i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	10.3647	−	31.8994i	0.457615	−	1.40839i
$514$	9.87132	+	30.3808i	0.435405	+	1.34004i
$515$	−0.572949	+	0.416272i	−0.0252472	+	0.0183431i
$516$	9.61803			0.423410
$517$	4.11803	−	3.44095i	0.181111	−	0.151333i
$518$	−1.14590			−0.0503479
$519$	−13.8992	+	10.0984i	−0.610107	+	0.443268i
$520$	0.645898	+	1.98787i	0.0283245	+	0.0871739i
$521$	−0.0106431	+	0.0327561i	−0.000466283	+	0.00143507i	−0.951289	−	0.308299i	$-0.900240\pi$
$521$	−0.0106431	+	0.0327561i	−0.000466283	+	0.00143507i	0.950823	+	0.309734i	$0.100240\pi$
$522$	−15.3262	−	11.1352i	−0.670811	−	0.487373i
$523$	13.0451	+	9.47781i	0.570422	+	0.414436i	0.835258	−	0.549858i	$-0.185318\pi$
$523$	13.0451	+	9.47781i	0.570422	+	0.414436i	−0.264837	+	0.964293i	$0.585318\pi$
$524$	−4.38197	+	13.4863i	−0.191427	+	0.589152i
$525$	1.50000	+	4.61653i	0.0654654	+	0.201482i
$526$	−16.4894	+	11.9802i	−0.718970	+	0.522362i
$527$	4.41641			0.192382
$528$	3.30902	−	0.224514i	0.144006	−	0.00977072i
$529$	−8.83282			−0.384035
$530$	0.218847	−	0.159002i	0.00950611	−	0.00690659i
$531$	3.29180	+	10.1311i	0.142852	+	0.439653i
$532$	2.07295	−	6.37988i	0.0898737	−	0.276603i
$533$	28.6525	+	20.8172i	1.24108	+	0.901695i
$534$	6.54508	+	4.75528i	0.283234	+	0.205781i
$535$	−0.718847	+	2.21238i	−0.0310785	+	0.0956497i
$536$	1.45492	+	4.47777i	0.0628428	+	0.193410i
$537$	19.6353	−	14.2658i	0.847324	−	0.615617i
$538$	19.7984			0.853569
$539$	−0.809017	+	3.21644i	−0.0348468	+	0.138542i
$540$	−1.90983			−0.0821860
$541$	−13.8541	+	10.0656i	−0.595634	+	0.432754i	−0.844327	−	0.535829i	$-0.819999\pi$
$541$	−13.8541	+	10.0656i	−0.595634	+	0.432754i	0.248692	+	0.968583i	$0.419999\pi$
$542$	−2.04508	−	6.29412i	−0.0878439	−	0.270356i
$543$	−4.23607	+	13.0373i	−0.181787	+	0.559483i
$544$	1.19098	+	0.865300i	0.0510630	+	0.0370994i
$545$	−3.19098	−	2.31838i	−0.136687	−	0.0993087i
$546$	1.69098	−	5.20431i	0.0723674	−	0.222724i
$547$	−7.48936	−	23.0499i	−0.320222	−	0.985541i	−0.973551	−	0.228468i	$-0.926628\pi$
$547$	−7.48936	−	23.0499i	−0.320222	−	0.985541i	0.653330	−	0.757074i	$-0.273372\pi$
$548$	0.763932	−	0.555029i	0.0326336	−	0.0237097i
$549$	27.7082			1.18256
$550$	3.92705	−	15.6129i	0.167450	−	0.665738i
$551$	−63.5410			−2.70694
$552$	−3.04508	+	2.21238i	−0.129607	+	0.0941653i
$553$	−4.30902	−	13.2618i	−0.183238	−	0.563949i
$554$	5.43769	−	16.7355i	0.231025	−	0.711023i
$555$	0.354102	+	0.257270i	0.0150308	+	0.0109205i
$556$	15.3262	+	11.1352i	0.649977	+	0.472236i
$557$	−5.78115	+	17.7926i	−0.244955	+	0.753895i	0.750688	+	0.660656i	$0.229722\pi$
$557$	−5.78115	+	17.7926i	−0.244955	+	0.753895i	−0.995644	+	0.0932386i	$0.970278\pi$
$558$	1.85410	+	5.70634i	0.0784904	+	0.241569i
$559$	−42.5795	+	30.9358i	−1.80092	+	1.30845i
$560$	−0.381966			−0.0161410
$561$	−4.87132	+	0.330515i	−0.205667	+	0.0139544i
$562$	−10.0344			−0.423277
$563$	9.85410	−	7.15942i	0.415301	−	0.301734i	−0.360443	−	0.932781i	$-0.617375\pi$
$563$	9.85410	−	7.15942i	0.415301	−	0.301734i	0.775744	+	0.631047i	$0.217375\pi$
$564$	−0.500000	−	1.53884i	−0.0210538	−	0.0647969i
$565$	1.43769	−	4.42477i	0.0604842	−	0.186151i
$566$	−10.0451	−	7.29818i	−0.422226	−	0.306765i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	−0.927051	+	2.85317i	−0.0388982	+	0.119716i
$569$	−10.0623	−	30.9686i	−0.421834	−	1.29827i	−0.905994	−	0.423291i	$-0.860875\pi$
$569$	−10.0623	−	30.9686i	−0.421834	−	1.29827i	0.484160	−	0.874980i	$-0.339125\pi$
$570$	−2.07295	+	1.50609i	−0.0868263	+	0.0630830i
$571$	−24.7082			−1.03401			−0.517003	−	0.855984i	$-0.672952\pi$
$571$	−24.7082			−1.03401			−0.517003	+	0.855984i	$0.672952\pi$
$572$	−13.9271	+	11.6372i	−0.582319	+	0.486575i
$573$	−0.618034			−0.0258187
$574$	−5.23607	+	3.80423i	−0.218549	+	0.158785i
$575$	5.64590	+	17.3763i	0.235450	+	0.724641i
$576$	−0.618034	+	1.90211i	−0.0257514	+	0.0792547i
$577$	−10.2533	−	7.44945i	−0.426850	−	0.310125i	0.353538	−	0.935420i	$-0.384978\pi$
$577$	−10.2533	−	7.44945i	−0.426850	−	0.310125i	−0.780388	+	0.625295i	$0.784978\pi$
$578$	12.0000	+	8.71851i	0.499134	+	0.362642i
$579$	−4.36475	+	13.4333i	−0.181393	+	0.558269i
$580$	1.11803	+	3.44095i	0.0464238	+	0.142878i
$581$	−7.54508	+	5.48183i	−0.313023	+	0.227424i
$582$	−12.4721			−0.516987
$583$	1.98936	+	1.24882i	0.0823907	+	0.0517207i
$584$	−0.145898			−0.00603730
$585$	3.38197	−	2.45714i	0.139827	−	0.101590i
$586$	−1.95492	−	6.01661i	−0.0807568	−	0.248544i
$587$	−11.8369	+	36.4302i	−0.488560	+	1.50363i	0.338197	+	0.941075i	$0.390183\pi$
$587$	−11.8369	+	36.4302i	−0.488560	+	1.50363i	−0.826757	+	0.562559i	$0.809817\pi$
$588$	0.809017	+	0.587785i	0.0333633	+	0.0242399i
$589$	16.2812	+	11.8290i	0.670853	+	0.487403i
$590$	0.628677	−	1.93487i	0.0258822	−	0.0796573i
$591$	−1.02786	−	3.16344i	−0.0422807	−	0.130127i
$592$	0.927051	−	0.673542i	0.0381016	−	0.0276824i
$593$	−3.23607			−0.132889			−0.0664447	−	0.997790i	$-0.521166\pi$
$593$	−3.23607			−0.132889			−0.0664447	+	0.997790i	$0.521166\pi$
$594$	−6.18034	−	15.3884i	−0.253582	−	0.631394i
$595$	0.562306			0.0230523
$596$	−1.54508	+	1.12257i	−0.0632891	+	0.0459823i
$597$	−3.61803	−	11.1352i	−0.148076	−	0.455732i
$598$	6.36475	−	19.5887i	0.260274	−	0.801040i
$599$	−22.4615	−	16.3192i	−0.917752	−	0.666786i	0.0252117	−	0.999682i	$-0.491974\pi$
$599$	−22.4615	−	16.3192i	−0.917752	−	0.666786i	−0.942963	+	0.332896i	$0.891974\pi$
$600$	−3.92705	−	2.85317i	−0.160321	−	0.116480i
$601$	−9.21885	+	28.3727i	−0.376045	+	1.15735i	0.566727	+	0.823906i	$0.308210\pi$
$601$	−9.21885	+	28.3727i	−0.376045	+	1.15735i	−0.942771	+	0.333440i	$0.891790\pi$
$602$	−2.97214	−	9.14729i	−0.121135	−	0.372816i
$603$	7.61803	−	5.53483i	0.310230	−	0.225396i
$604$	−8.00000			−0.325515
$605$	−4.16312	+	0.567541i	−0.169255	+	0.0230738i
$606$	3.00000			0.121867
$607$	−24.2984	+	17.6538i	−0.986241	+	0.716546i	−0.959095	−	0.283086i	$-0.908642\pi$
$607$	−24.2984	+	17.6538i	−0.986241	+	0.716546i	−0.0271460	+	0.999631i	$0.508642\pi$
$608$	2.07295	+	6.37988i	0.0840692	+	0.258738i
$609$	2.92705	−	9.00854i	0.118610	−	0.365044i
$610$	−4.28115	−	3.11044i	−0.173339	−	0.125938i
$611$	7.16312	+	5.20431i	0.289789	+	0.210544i
$612$	0.909830	−	2.80017i	0.0367777	−	0.113190i
$613$	−8.50000	−	26.1603i	−0.343312	−	1.05660i	−0.962481	−	0.271348i	$-0.912531\pi$
$613$	−8.50000	−	26.1603i	−0.343312	−	1.05660i	0.619170	−	0.785257i	$-0.287469\pi$
$614$	8.42705	−	6.12261i	0.340088	−	0.247088i
$615$	2.47214			0.0996861
$616$	−1.23607	−	3.07768i	−0.0498026	−	0.124003i
$617$	−1.47214			−0.0592660			−0.0296330	−	0.999561i	$-0.509434\pi$
$617$	−1.47214			−0.0592660			−0.0296330	+	0.999561i	$0.509434\pi$
$618$	−1.50000	+	1.08981i	−0.0603388	+	0.0438387i
$619$	−9.57295	−	29.4625i	−0.384769	−	1.18420i	−0.936647	−	0.350273i	$-0.886089\pi$
$619$	−9.57295	−	29.4625i	−0.384769	−	1.18420i	0.551878	−	0.833925i	$-0.313911\pi$
$620$	0.354102	−	1.08981i	0.0142211	−	0.0437680i
$621$	15.2254	+	11.0619i	0.610975	+	0.443900i
$622$	−10.6631	−	7.74721i	−0.427552	−	0.310635i
$623$	2.50000	−	7.69421i	0.100160	−	0.308262i
$624$	1.69098	+	5.20431i	0.0676935	+	0.208339i
$625$	−18.4721	+	13.4208i	−0.738885	+	0.536832i
$626$	3.27051			0.130716
$627$	−18.8435	−	11.8290i	−0.752535	−	0.472403i
$628$	23.6525			0.943837
$629$	−1.36475	+	0.991545i	−0.0544160	+	0.0395355i
$630$	0.236068	+	0.726543i	0.00940517	+	0.0289461i
$631$	−3.42705	+	10.5474i	−0.136429	+	0.419885i	−0.995810	−	0.0914517i	$-0.970849\pi$
$631$	−3.42705	+	10.5474i	−0.136429	+	0.419885i	0.859381	+	0.511336i	$0.170849\pi$
$632$	11.2812	+	8.19624i	0.448740	+	0.326029i
$633$	16.5172	+	12.0005i	0.656501	+	0.476976i
$634$	−5.98278	+	18.4131i	−0.237607	+	0.731278i
$635$	0.927051	+	2.85317i	0.0367889	+	0.113225i
$636$	0.572949	−	0.416272i	0.0227189	−	0.0165063i
$637$	−5.47214			−0.216814
$638$	−24.1074	+	20.1437i	−0.954421	+	0.797497i
$639$	6.00000			0.237356
$640$	0.309017	−	0.224514i	0.0122150	−	0.00887469i
$641$	6.96149	+	21.4253i	0.274962	+	0.846247i	0.989229	+	0.146374i	$0.0467603\pi$
$641$	6.96149	+	21.4253i	0.274962	+	0.846247i	−0.714267	+	0.699873i	$0.753240\pi$
$642$	−1.88197	+	5.79210i	−0.0742753	+	0.228596i
$643$	−3.13525	−	2.27790i	−0.123642	−	0.0898315i	0.524245	−	0.851567i	$-0.324347\pi$
$643$	−3.13525	−	2.27790i	−0.123642	−	0.0898315i	−0.647888	+	0.761736i	$0.724347\pi$
$644$	3.04508	+	2.21238i	0.119993	+	0.0871801i
$645$	−1.13525	+	3.49396i	−0.0447006	+	0.137574i
$646$	−3.05166	−	9.39205i	−0.120066	−	0.369525i
$647$	−4.33688	+	3.15093i	−0.170500	+	0.123876i	−0.669763	−	0.742575i	$-0.733604\pi$
$647$	−4.33688	+	3.15093i	−0.170500	+	0.123876i	0.499263	+	0.866451i	$0.333604\pi$
$648$	1.00000			0.0392837
$649$	17.6246	−	1.19581i	0.691827	−	0.0469398i
$650$	26.5623			1.04186
$651$	−2.42705	+	1.76336i	−0.0951236	+	0.0691114i
$652$	−1.42705	−	4.39201i	−0.0558876	−	0.172004i
$653$	−14.2918	+	43.9856i	−0.559281	+	1.72129i	0.125079	+	0.992147i	$0.460081\pi$
$653$	−14.2918	+	43.9856i	−0.559281	+	1.72129i	−0.684361	+	0.729144i	$0.739919\pi$
$654$	−8.35410	−	6.06961i	−0.326671	−	0.237341i
$655$	−4.38197	−	3.18368i	−0.171218	−	0.124397i
$656$	2.00000	−	6.15537i	0.0780869	−	0.240327i
$657$	0.0901699	+	0.277515i	0.00351786	+	0.0108269i
$658$	−1.30902	+	0.951057i	−0.0510308	+	0.0370760i
$659$	2.56231			0.0998133			0.0499066	−	0.998754i	$-0.484108\pi$
$659$	2.56231			0.0998133			0.0499066	+	0.998754i	$0.484108\pi$
$660$	−0.309017	+	1.22857i	−0.0120285	+	0.0478221i
$661$	6.27051			0.243895			0.121947	−	0.992537i	$-0.461086\pi$
$661$	6.27051			0.243895			0.121947	+	0.992537i	$0.461086\pi$
$662$	5.09017	−	3.69822i	0.197835	−	0.143736i
$663$	−2.48936	−	7.66145i	−0.0966786	−	0.297546i
$664$	2.88197	−	8.86978i	0.111842	−	0.344214i
$665$	2.07295	+	1.50609i	0.0803855	+	0.0584035i
$666$	−1.85410	−	1.34708i	−0.0718450	−	0.0521984i
$667$	11.0172	−	33.9075i	0.426588	−	1.31290i
$668$	−4.98936	−	15.3557i	−0.193044	−	0.594128i
$669$	4.35410	−	3.16344i	0.168339	−	0.122306i
$670$	−1.79837			−0.0694772
$671$	11.2082	−	44.5609i	0.432688	−	1.72025i
$672$	−1.00000			−0.0385758
$673$	−9.19098	+	6.67764i	−0.354286	+	0.257404i	−0.750665	−	0.660683i	$-0.770267\pi$
$673$	−9.19098	+	6.67764i	−0.354286	+	0.257404i	0.396379	+	0.918087i	$0.370267\pi$
$674$	−3.64590	−	11.2209i	−0.140435	−	0.432214i
$675$	−7.50000	+	23.0826i	−0.288675	+	0.888451i
$676$	−13.7082	−	9.95959i	−0.527239	−	0.383061i
$677$	33.1246	+	24.0664i	1.27308	+	0.924948i	0.999321	−	0.0368492i	$-0.0117321\pi$
$677$	33.1246	+	24.0664i	1.27308	+	0.924948i	0.273761	+	0.961798i	$0.411732\pi$
$678$	3.76393	−	11.5842i	0.144553	−	0.444888i
$679$	3.85410	+	11.8617i	0.147907	+	0.455211i
$680$	−0.454915	+	0.330515i	−0.0174452	+	0.0126747i
$681$	−21.6180			−0.828405
$682$	9.92705	−	0.673542i	0.380126	−	0.0257913i
$683$	31.0344			1.18750			0.593750	−	0.804650i	$-0.297647\pi$
$683$	31.0344			1.18750			0.593750	+	0.804650i	$0.297647\pi$
$684$	10.8541	−	7.88597i	0.415017	−	0.301527i
$685$	0.111456	+	0.343027i	0.00425852	+	0.0131064i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−9.73607	−	7.07367i	−0.371454	−	0.269877i
$688$	7.78115	+	5.65334i	0.296654	+	0.215532i
$689$	−1.19756	+	3.68571i	−0.0456234	+	0.140414i
$690$	−0.444272	−	1.36733i	−0.0169131	−	0.0520533i
$691$	16.5344	−	12.0130i	0.629000	−	0.456995i	−0.227054	−	0.973882i	$-0.572909\pi$
$691$	16.5344	−	12.0130i	0.629000	−	0.456995i	0.856054	+	0.516887i	$0.172909\pi$
$692$	−17.1803			−0.653099
$693$	−5.09017	+	4.25325i	−0.193360	+	0.161568i
$694$	21.9443			0.832993
$695$	−5.85410	+	4.25325i	−0.222059	+	0.161335i
$696$	2.92705	+	9.00854i	0.110950	+	0.341468i
$697$	−2.94427	+	9.06154i	−0.111522	+	0.343230i
$698$	21.7082	+	15.7719i	0.821668	+	0.596976i
$699$	19.4164	+	14.1068i	0.734396	+	0.533570i
$700$	−1.50000	+	4.61653i	−0.0566947	+	0.174488i
$701$	6.14590	+	18.9151i	0.232127	+	0.714415i	0.997489	+	0.0708147i	$0.0225599\pi$
$701$	6.14590	+	18.9151i	0.232127	+	0.714415i	−0.765362	+	0.643600i	$0.777440\pi$
$702$	22.1353	−	16.0822i	0.835441	−	0.606984i
$703$	−7.68692			−0.289918
$704$	2.80902	+	1.76336i	0.105869	+	0.0664590i
$705$	0.618034			0.0232765
$706$	19.4894	−	14.1598i	0.733492	−	0.532913i
$707$	−0.927051	−	2.85317i	−0.0348653	−	0.107304i
$708$	1.64590	−	5.06555i	0.0618566	−	0.190375i
$709$	4.20820	+	3.05744i	0.158042	+	0.114825i	0.663996	−	0.747736i	$-0.268859\pi$
$709$	4.20820	+	3.05744i	0.158042	+	0.114825i	−0.505953	+	0.862561i	$0.668859\pi$
$710$	−0.927051	−	0.673542i	−0.0347916	−	0.0252776i
$711$	8.61803	−	26.5236i	0.323202	−	0.994712i
$712$	2.50000	+	7.69421i	0.0936915	+	0.288353i
$713$	−9.13525	+	6.63715i	−0.342118	+	0.248563i
$714$	1.47214			0.0550933
$715$	−2.58359	−	6.43288i	−0.0966209	−	0.240576i
$716$	24.2705			0.907032
$717$	−2.92705	+	2.12663i	−0.109313	+	0.0794203i
$718$	7.13525	+	21.9601i	0.266285	+	0.819542i
$719$	−7.33688	+	22.5806i	−0.273619	+	0.842114i	0.715962	+	0.698139i	$0.245988\pi$
$719$	−7.33688	+	22.5806i	−0.273619	+	0.842114i	−0.989581	+	0.143975i	$0.954012\pi$
$720$	−0.618034	−	0.449028i	−0.0230328	−	0.0167343i
$721$	1.50000	+	1.08981i	0.0558629	+	0.0405868i
$722$	8.03444	−	24.7275i	0.299011	−	0.920261i
$723$	−0.190983	−	0.587785i	−0.00710273	−	0.0218600i
$724$	−11.0902	+	8.05748i	−0.412163	+	0.299454i
$725$	45.9787			1.70761
$726$	−10.8992	+	1.48584i	−0.404507	+	0.0551447i
$727$	−12.1246			−0.449677			−0.224838	−	0.974396i	$-0.572185\pi$
$727$	−12.1246			−0.449677			−0.224838	+	0.974396i	$0.572185\pi$
$728$	4.42705	−	3.21644i	0.164077	−	0.119209i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	0.0172209	−	0.0530006i	0.000637375	−	0.00196164i
$731$	−11.4549	−	8.32248i	−0.423675	−	0.307818i
$732$	−11.2082	−	8.14324i	−0.414267	−	0.300983i
$733$	−16.3885	+	50.4388i	−0.605325	+	1.86300i	−0.110781	+	0.993845i	$0.535335\pi$
$733$	−16.3885	+	50.4388i	−0.605325	+	1.86300i	−0.494543	+	0.869153i	$0.664665\pi$
$734$	0.927051	+	2.85317i	0.0342181	+	0.105312i
$735$	−0.309017	+	0.224514i	−0.0113983	+	0.00828132i
$736$	−3.76393			−0.138740
$737$	−5.81966	−	14.4904i	−0.214370	−	0.533759i
$738$	−12.9443			−0.476485
$739$	29.7984	−	21.6498i	1.09615	−	0.796400i	0.115724	−	0.993281i	$-0.463081\pi$
$739$	29.7984	−	21.6498i	1.09615	−	0.796400i	0.980427	+	0.196881i	$0.0630813\pi$
$740$	0.135255	+	0.416272i	0.00497207	+	0.0153025i
$741$	11.3435	−	34.9116i	0.416712	−	1.28251i
$742$	−0.572949	−	0.416272i	−0.0210336	−	0.0152818i
$743$	11.9894	+	8.71078i	0.439847	+	0.319567i	0.785574	−	0.618768i	$-0.212368\pi$
$743$	11.9894	+	8.71078i	0.439847	+	0.319567i	−0.345727	+	0.938335i	$0.612368\pi$
$744$	0.927051	−	2.85317i	0.0339873	−	0.104602i
$745$	−0.225425	−	0.693786i	−0.00825893	−	0.0254184i
$746$	9.42705	−	6.84915i	0.345149	−	0.250765i
$747$	−18.6525			−0.682458
$748$	−4.13525	−	2.59590i	−0.151200	−	0.0949155i
$749$	6.09017			0.222530
$750$	3.04508	−	2.21238i	0.111191	−	0.0807848i
$751$	−3.00000	−	9.23305i	−0.109472	−	0.336919i	0.881282	−	0.472590i	$-0.156681\pi$
$751$	−3.00000	−	9.23305i	−0.109472	−	0.336919i	−0.990754	+	0.135671i	$0.956681\pi$
$752$	0.500000	−	1.53884i	0.0182331	−	0.0561158i
$753$	−2.85410	−	2.07363i	−0.104009	−	0.0755671i
$754$	−41.9336	−	30.4666i	−1.52713	−	1.10953i
$755$	0.944272	−	2.90617i	0.0343656	−	0.105766i
$756$	1.54508	+	4.75528i	0.0561942	+	0.172948i
$757$	37.5344	−	27.2704i	1.36421	−	0.991158i	0.366048	−	0.930596i	$-0.380711\pi$
$757$	37.5344	−	27.2704i	1.36421	−	0.991158i	0.998164	−	0.0605625i	$-0.0192894\pi$
$758$	−33.9443			−1.23291
$759$	9.57953	−	8.00448i	0.347715	−	0.290544i
$760$	−2.56231			−0.0929446
$761$	7.32624	−	5.32282i	0.265576	−	0.192952i	−0.447026	−	0.894521i	$-0.647517\pi$
$761$	7.32624	−	5.32282i	0.265576	−	0.192952i	0.712602	+	0.701569i	$0.247517\pi$
$762$	2.42705	+	7.46969i	0.0879228	+	0.270598i
$763$	−3.19098	+	9.82084i	−0.115521	+	0.355538i
$764$	−0.500000	−	0.363271i	−0.0180894	−	0.0131427i
$765$	0.909830	+	0.661030i	0.0328950	+	0.0238996i
$766$	−4.02786	+	12.3965i	−0.145533	+	0.447903i
$767$	9.00658	+	27.7194i	0.325209	+	1.00089i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	18.6180			0.671383			0.335692	−	0.941972i	$-0.391030\pi$
$769$	18.6180			0.671383			0.335692	+	0.941972i	$0.391030\pi$
$770$	1.26393	−	0.0857567i	0.0455489	−	0.00309046i
$771$	−31.9443			−1.15044
$772$	−11.4271	+	8.30224i	−0.411269	+	0.298804i
$773$	−4.61803	−	14.2128i	−0.166099	−	0.511201i	0.833016	−	0.553248i	$-0.186612\pi$
$773$	−4.61803	−	14.2128i	−0.166099	−	0.511201i	−0.999116	+	0.0420476i	$0.986612\pi$
$774$	5.94427	−	18.2946i	0.213662	−	0.657585i
$775$	−11.7812	−	8.55951i	−0.423192	−	0.307467i
$776$	−10.0902	−	7.33094i	−0.362216	−	0.263165i
$777$	0.354102	−	1.08981i	0.0127033	−	0.0390969i
$778$	3.55573	+	10.9434i	0.127479	+	0.392340i
$779$	−35.1246	+	25.5195i	−1.25847	+	0.914332i
$780$	−2.09017			−0.0748401
$781$	2.42705	−	9.64932i	0.0868467	−	0.345280i
$782$	5.54102			0.198146
$783$	38.3156	−	27.8379i	1.36929	−	0.994846i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−2.79180	+	8.59226i	−0.0996435	+	0.306671i
$786$	−11.4721	−	8.33499i	−0.409198	−	0.297299i
$787$	13.0623	+	9.49032i	0.465621	+	0.338293i	0.795732	−	0.605649i	$-0.207086\pi$
$787$	13.0623	+	9.49032i	0.465621	+	0.338293i	−0.330111	+	0.943942i	$0.607086\pi$
$788$	1.02786	−	3.16344i	0.0366161	−	0.112693i
$789$	−6.29837	−	19.3844i	−0.224228	−	0.690103i
$790$	−4.30902	+	3.13068i	−0.153308	+	0.111385i
$791$	−12.1803			−0.433083
$792$	1.61803	−	6.43288i	0.0574943	−	0.228582i
$793$	75.8115			2.69215
$794$	−9.13525	+	6.63715i	−0.324198	+	0.235544i
$795$	0.0835921	+	0.257270i	0.00296471	+	0.00912443i
$796$	3.61803	−	11.1352i	0.128238	−	0.394675i
$797$	−27.1246	−	19.7072i	−0.960803	−	0.698064i	−0.00746593	−	0.999972i	$-0.502377\pi$
$797$	−27.1246	−	19.7072i	−0.960803	−	0.698064i	−0.953337	+	0.301908i	$0.902377\pi$
$798$	5.42705	+	3.94298i	0.192116	+	0.139580i
$799$	−0.736068	+	2.26538i	−0.0260402	+	0.0801435i
$800$	−1.50000	−	4.61653i	−0.0530330	−	0.163219i
$801$	13.0902	−	9.51057i	0.462518	−	0.336039i
$802$	21.4721			0.758207
$803$	0.482779	−	0.0327561i	0.0170369	−	0.00115594i
$804$	−4.70820			−0.166046
$805$	−1.16312	+	0.845055i	−0.0409946	+	0.0297843i
$806$	5.07295	+	15.6129i	0.178687	+	0.549942i
$807$	−6.11803	+	18.8294i	−0.215365	+	0.662825i
$808$	2.42705	+	1.76336i	0.0853834	+	0.0620346i
$809$	−4.57295	−	3.32244i	−0.160776	−	0.116811i	0.504488	−	0.863419i	$-0.331681\pi$
$809$	−4.57295	−	3.32244i	−0.160776	−	0.116811i	−0.665264	+	0.746608i	$0.731681\pi$
$810$	−0.118034	+	0.363271i	−0.00414729	+	0.0127641i
$811$	−14.5689	−	44.8384i	−0.511583	−	1.57449i	−0.789415	−	0.613860i	$-0.789616\pi$
$811$	−14.5689	−	44.8384i	−0.511583	−	1.57449i	0.277832	−	0.960630i	$-0.410384\pi$
$812$	7.66312	−	5.56758i	0.268923	−	0.195384i
$813$	6.61803			0.232105
$814$	−2.91641	+	2.43690i	−0.102220	+	0.0854132i
$815$	1.76393			0.0617878
$816$	−1.19098	+	0.865300i	−0.0416927	+	0.0302916i
$817$	−19.9377	−	61.3619i	−0.697532	−	2.14678i
$818$	−2.07295	+	6.37988i	−0.0724790	+	0.223067i
$819$	−8.85410	−	6.43288i	−0.309387	−	0.224783i
$820$	2.00000	+	1.45309i	0.0698430	+	0.0507439i
$821$	−12.2705	+	37.7647i	−0.428244	+	1.31800i	0.471610	+	0.881807i	$0.343673\pi$
$821$	−12.2705	+	37.7647i	−0.428244	+	1.31800i	−0.899854	+	0.436192i	$0.856327\pi$
$822$	0.291796	+	0.898056i	0.0101776	+	0.0313233i
$823$	−20.8992	+	15.1841i	−0.728500	+	0.529286i	−0.889089	−	0.457735i	$-0.848661\pi$
$823$	−20.8992	+	15.1841i	−0.728500	+	0.529286i	0.160589	+	0.987021i	$0.448661\pi$
$824$	−1.85410			−0.0645907
$825$	13.6353	+	8.55951i	0.474719	+	0.298004i
$826$	−5.32624			−0.185324
$827$	7.47214	−	5.42882i	0.259832	−	0.188779i	−0.450241	−	0.892907i	$-0.648662\pi$
$827$	7.47214	−	5.42882i	0.259832	−	0.188779i	0.710073	+	0.704128i	$0.248662\pi$
$828$	2.32624	+	7.15942i	0.0808424	+	0.248807i
$829$	−7.72542	+	23.7764i	−0.268315	+	0.825789i	0.722596	+	0.691271i	$0.242949\pi$
$829$	−7.72542	+	23.7764i	−0.268315	+	0.825789i	−0.990911	+	0.134518i	$0.957051\pi$
$830$	2.88197	+	2.09387i	0.100035	+	0.0726793i
$831$	14.2361	+	10.3431i	0.493844	+	0.358798i
$832$	−1.69098	+	5.20431i	−0.0586243	+	0.180427i
$833$	−0.454915	−	1.40008i	−0.0157619	−	0.0485101i
$834$	−15.3262	+	11.1352i	−0.530704	+	0.385579i
$835$	6.16718			0.213424
$836$	−8.29180	−	20.6457i	−0.286778	−	0.714047i
$837$	−15.0000			−0.518476
$838$	21.4443	−	15.5802i	0.740780	−	0.538208i
$839$	9.57295	+	29.4625i	0.330495	+	1.01716i	0.968899	+	0.247457i	$0.0795950\pi$
$839$	9.57295	+	29.4625i	0.330495	+	1.01716i	−0.638404	+	0.769702i	$0.720405\pi$
$840$	0.118034	−	0.363271i	0.00407256	−	0.0125340i
$841$	−49.1246	−	35.6911i	−1.69395	−	1.23073i
$842$	31.6976	+	23.0296i	1.09237	+	0.793653i
$843$	3.10081	−	9.54332i	0.106798	−	0.328689i
$844$	6.30902	+	19.4172i	0.217165	+	0.668366i
$845$	5.23607	−	3.80423i	0.180126	−	0.130869i
$846$	−3.23607			−0.111258
$847$	4.78115	+	9.90659i	0.164282	+	0.340395i
$848$	0.708204			0.0243198
$849$	10.0451	−	7.29818i	0.344746	−	0.250473i
$850$	2.20820	+	6.79615i	0.0757408	+	0.233106i
$851$	1.33282	−	4.10199i	0.0456883	−	0.140614i
$852$	−2.42705	−	1.76336i	−0.0831494	−	0.0604116i
$853$	−41.0238	−	29.8055i	−1.40463	−	1.02052i	−0.994076	−	0.108685i	$-0.965336\pi$
$853$	−41.0238	−	29.8055i	−1.40463	−	1.02052i	−0.410552	−	0.911837i	$-0.634664\pi$
$854$	−4.28115	+	13.1760i	−0.146498	+	0.450875i
$855$	1.58359	+	4.87380i	0.0541577	+	0.166680i
$856$	−4.92705	+	3.57971i	−0.168403	+	0.122352i
$857$	−12.5279			−0.427944			−0.213972	−	0.976840i	$-0.568640\pi$
$857$	−12.5279			−0.427944			−0.213972	+	0.976840i	$0.568640\pi$
$858$	−6.76393	−	16.8415i	−0.230917	−	0.574959i
$859$	36.7082			1.25247			0.626234	−	0.779635i	$-0.284596\pi$
$859$	36.7082			1.25247			0.626234	+	0.779635i	$0.284596\pi$
$860$	−2.97214	+	2.15938i	−0.101349	+	0.0736344i
$861$	−2.00000	−	6.15537i	−0.0681598	−	0.209774i
$862$	−6.98278	+	21.4908i	−0.237834	+	0.731979i
$863$	−0.635255	−	0.461540i	−0.0216243	−	0.0157110i	0.576921	−	0.816800i	$-0.304254\pi$
$863$	−0.635255	−	0.461540i	−0.0216243	−	0.0157110i	−0.598545	+	0.801089i	$0.704254\pi$
$864$	−4.04508	−	2.93893i	−0.137617	−	0.0999843i
$865$	2.02786	−	6.24112i	0.0689494	−	0.212205i
$866$	3.30902	+	10.1841i	0.112445	+	0.346070i
$867$	−12.0000	+	8.71851i	−0.407541	+	0.296096i
$868$	−3.00000			−0.101827
$869$	−39.1697	−	24.5887i	−1.32874	−	0.834115i
$870$	−3.61803			−0.122663
$871$	20.8435	−	15.1437i	0.706254	−	0.513123i
$872$	−3.19098	−	9.82084i	−0.108060	−	0.332575i
$873$	−7.70820	+	23.7234i	−0.260883	+	0.802916i
$874$	20.4271	+	14.8411i	0.690955	+	0.502008i
$875$	−3.04508	−	2.21238i	−0.102943	−	0.0747922i
$876$	0.0450850	−	0.138757i	0.00152328	−	0.00468817i
$877$	10.2746	+	31.6219i	0.346948	+	1.06780i	0.960533	+	0.278167i	$0.0897268\pi$
$877$	10.2746	+	31.6219i	0.346948	+	1.06780i	−0.613585	+	0.789629i	$0.710273\pi$
$878$	6.70820	−	4.87380i	0.226391	−	0.164483i
$879$	6.32624			0.213379
$880$	−0.972136	+	0.812299i	−0.0327707	+	0.0273826i
$881$	26.3475			0.887671			0.443835	−	0.896108i	$-0.353618\pi$
$881$	26.3475			0.887671			0.443835	+	0.896108i	$0.353618\pi$
$882$	1.61803	−	1.17557i	0.0544820	−	0.0395835i
$883$	−5.34752	−	16.4580i	−0.179959	−	0.553855i	0.819867	−	0.572555i	$-0.194048\pi$
$883$	−5.34752	−	16.4580i	−0.179959	−	0.553855i	−0.999825	+	0.0186992i	$0.994048\pi$
$884$	2.48936	−	7.66145i	0.0837261	−	0.257683i
$885$	1.64590	+	1.19581i	0.0553263	+	0.0401969i
$886$	25.7705	+	18.7234i	0.865777	+	0.629024i
$887$	6.19098	−	19.0539i	0.207873	−	0.639767i	−0.791710	−	0.610897i	$-0.790809\pi$
$887$	6.19098	−	19.0539i	0.207873	−	0.639767i	0.999583	−	0.0288702i	$-0.00919094\pi$
$888$	0.354102	+	1.08981i	0.0118829	+	0.0365718i
$889$	6.35410	−	4.61653i	0.213110	−	0.154833i
$890$	−3.09017			−0.103583
$891$	−3.30902	+	0.224514i	−0.110856	+	0.00752150i
$892$	5.38197			0.180202
$893$	−8.78115	+	6.37988i	−0.293850	+	0.213495i
$894$	−0.590170	−	1.81636i	−0.0197382	−	0.0607480i
$895$	−2.86475	+	8.81678i	−0.0957579	+	0.294712i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	16.6631	+	12.1065i	0.556365	+	0.404223i
$898$	−6.11803	+	18.8294i	−0.204161	+	0.628344i
$899$	8.78115	+	27.0256i	0.292868	+	0.901355i
$900$	−7.85410	+	5.70634i	−0.261803	+	0.190211i
$901$	−1.04257			−0.0347331
$902$	−5.23607	+	20.8172i	−0.174342	+	0.693138i
$903$	9.61803			0.320068
$904$	9.85410	−	7.15942i	0.327743	−	0.238119i
$905$	−1.61803	−	4.97980i	−0.0537853	−	0.165534i
$906$	2.47214	−	7.60845i	0.0821312	−	0.252774i
$907$	10.8262	+	7.86572i	0.359479	+	0.261177i	0.752835	−	0.658209i	$-0.228686\pi$
$907$	10.8262	+	7.86572i	0.359479	+	0.261177i	−0.393356	+	0.919386i	$0.628686\pi$
$908$	−17.4894	−	12.7068i	−0.580405	−	0.421689i
$909$	1.85410	−	5.70634i	0.0614967	−	0.189267i
$910$	0.645898	+	1.98787i	0.0214113	+	0.0658972i
$911$	−6.02786	+	4.37950i	−0.199712	+	0.145099i	−0.683147	−	0.730281i	$-0.739389\pi$
$911$	−6.02786	+	4.37950i	−0.199712	+	0.145099i	0.483435	+	0.875380i	$0.339389\pi$
$912$	−6.70820			−0.222131
$913$	−7.54508	+	29.9973i	−0.249706	+	0.992765i
$914$	−15.4164			−0.509929
$915$	4.28115	−	3.11044i	0.141531	−	0.102828i
$916$	−3.71885	−	11.4454i	−0.122874	−	0.378168i
$917$	−4.38197	+	13.4863i	−0.144705	+	0.445357i
$918$	5.95492	+	4.32650i	0.196541	+	0.142796i
$919$	4.04508	+	2.93893i	0.133435	+	0.0969462i	0.652501	−	0.757788i	$-0.273720\pi$
$919$	4.04508	+	2.93893i	0.133435	+	0.0969462i	−0.519066	+	0.854734i	$0.673720\pi$
$920$	0.444272	−	1.36733i	0.0146472	−	0.0450795i
$921$	3.21885	+	9.90659i	0.106065	+	0.326433i
$922$	−29.3435	+	21.3193i	−0.966375	+	0.702113i
$923$	16.4164			0.540353
$924$	3.30902	−	0.224514i	0.108859	−	0.00738597i
$925$	5.56231			0.182887
$926$	−20.2082	+	14.6821i	−0.664083	+	0.482484i
$927$	1.14590	+	3.52671i	0.0376362	+	0.115832i
$928$	−2.92705	+	9.00854i	−0.0960852	+	0.295720i
$929$	−30.1246	−	21.8868i	−0.988356	−	0.718083i	−0.0287959	−	0.999585i	$-0.509167\pi$
$929$	−30.1246	−	21.8868i	−0.988356	−	0.718083i	−0.959561	+	0.281502i	$0.909167\pi$
$930$	0.927051	+	0.673542i	0.0303992	+	0.0220863i
$931$	2.07295	−	6.37988i	0.0679382	−	0.209092i
$932$	7.41641	+	22.8254i	0.242933	+	0.747669i
$933$	10.6631	−	7.74721i	0.349095	−	0.253632i
$934$	−18.0557			−0.590801
$935$	1.43112	−	1.19581i	0.0468025	−	0.0391073i
$936$	10.9443			0.357725
$937$	−44.2599	+	32.1567i	−1.44591	+	1.05051i	−0.459141	+	0.888364i	$0.651843\pi$
$937$	−44.2599	+	32.1567i	−1.44591	+	1.05051i	−0.986766	+	0.162149i	$0.948157\pi$
$938$	1.45492	+	4.47777i	0.0475047	+	0.146204i
$939$	−1.01064	+	3.11044i	−0.0329811	+	0.101505i
$940$	0.500000	+	0.363271i	0.0163082	+	0.0118486i
$941$	4.92705	+	3.57971i	0.160617	+	0.116695i	0.665191	−	0.746673i	$-0.268350\pi$
$941$	4.92705	+	3.57971i	0.160617	+	0.116695i	−0.504573	+	0.863369i	$0.668350\pi$
$942$	−7.30902	+	22.4948i	−0.238141	+	0.732922i
$943$	−7.52786	−	23.1684i	−0.245141	−	0.754466i
$944$	4.30902	−	3.13068i	0.140247	−	0.101895i
$945$	−1.90983			−0.0621268
$946$	−27.0172	−	16.9600i	−0.878406	−	0.551418i
$947$	15.1591			0.492603			0.246302	−	0.969193i	$-0.420785\pi$
$947$	15.1591			0.492603			0.246302	+	0.969193i	$0.420785\pi$
$948$	−11.2812	+	8.19624i	−0.366395	+	0.266201i
$949$	0.246711	+	0.759299i	0.00800858	+	0.0246479i
$950$	−10.0623	+	30.9686i	−0.326464	+	1.00475i
$951$	−15.6631	−	11.3799i	−0.507911	−	0.369019i
$952$	1.19098	+	0.865300i	0.0386000	+	0.0280445i
$953$	16.3369	−	50.2797i	0.529203	−	1.62872i	−0.226647	−	0.973977i	$-0.572776\pi$
$953$	16.3369	−	50.2797i	0.529203	−	1.62872i	0.755851	−	0.654744i	$-0.227224\pi$
$954$	−0.437694	−	1.34708i	−0.0141709	−	0.0436135i
$955$	0.190983	−	0.138757i	0.00618006	−	0.00449008i
$956$	−3.61803			−0.117016
$957$	−11.7082	−	29.1522i	−0.378472	−	0.942358i
$958$	40.2492			1.30039
$959$	0.763932	−	0.555029i	0.0246687	−	0.0179228i
$960$	0.118034	+	0.363271i	0.00380953	+	0.0117245i
$961$	−6.79837	+	20.9232i	−0.219302	+	0.674943i
$962$	−5.07295	−	3.68571i	−0.163558	−	0.118832i
$963$	9.85410	+	7.15942i	0.317544	+	0.230709i
$964$	0.190983	−	0.587785i	0.00615115	−	0.0189313i
$965$	−1.66718	−	5.13107i	−0.0536686	−	0.165175i
$966$	−3.04508	+	2.21238i	−0.0979740	+	0.0711823i
$967$	−7.32624			−0.235596			−0.117798	−	0.993038i	$-0.537584\pi$
$967$	−7.32624			−0.235596			−0.117798	+	0.993038i	$0.537584\pi$
$968$	−9.69098	−	5.20431i	−0.311480	−	0.167273i
$969$	9.87539			0.317243
$970$	3.85410	−	2.80017i	0.123748	−	0.0899080i
$971$	−7.53444	−	23.1886i	−0.241792	−	0.744158i	−0.996148	−	0.0876927i	$-0.972051\pi$
$971$	−7.53444	−	23.1886i	−0.241792	−	0.744158i	0.754356	−	0.656466i	$-0.227949\pi$
$972$	−4.94427	+	15.2169i	−0.158588	+	0.488082i
$973$	15.3262	+	11.1352i	0.491337	+	0.356977i
$974$	8.42705	+	6.12261i	0.270020	+	0.196181i
$975$	−8.20820	+	25.2623i	−0.262873	+	0.809040i
$976$	−4.28115	−	13.1760i	−0.137036	−	0.421755i
$977$	−35.7426	+	25.9686i	−1.14351	+	0.830808i	−0.987604	−	0.156965i	$-0.949829\pi$
$977$	−35.7426	+	25.9686i	−1.14351	+	0.830808i	−0.155904	+	0.987772i	$0.549829\pi$
$978$	4.61803			0.147668
$979$	−10.0000	−	24.8990i	−0.319601	−	0.795775i
$980$	−0.381966			−0.0122015
$981$	−16.7082	+	12.1392i	−0.533452	+	0.387575i
$982$	−5.13525	−	15.8047i	−0.163873	−	0.504348i
$983$	−6.12461	+	18.8496i	−0.195345	+	0.601209i	0.804628	+	0.593780i	$0.202365\pi$
$983$	−6.12461	+	18.8496i	−0.195345	+	0.601209i	−0.999972	+	0.00742966i	$0.997635\pi$
$984$	5.23607	+	3.80423i	0.166920	+	0.121274i
$985$	1.02786	+	0.746787i	0.0327505	+	0.0237946i
$986$	4.30902	−	13.2618i	0.137227	−	0.422341i
$987$	−0.500000	−	1.53884i	−0.0159152	−	0.0489819i
$988$	29.6976	−	21.5765i	0.944805	−	0.686441i
$989$	36.2016			1.15114
$990$	2.14590	+	1.34708i	0.0682011	+	0.0428131i
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$	2.42705	−	1.76336i	0.0770589	−	0.0559866i
$993$	1.94427	+	5.98385i	0.0616996	+	0.189892i
$994$	−0.927051	+	2.85317i	−0.0294043	+	0.0904970i
$995$	3.61803	+	2.62866i	0.114699	+	0.0833340i
$996$	7.54508	+	5.48183i	0.239075	+	0.173698i
$997$	−11.7361	+	36.1199i	−0.371685	+	1.14393i	0.574003	+	0.818853i	$0.305390\pi$
$997$	−11.7361	+	36.1199i	−0.371685	+	1.14393i	−0.945688	+	0.325076i	$0.894610\pi$
$998$	5.69098	+	17.5150i	0.180145	+	0.554429i
$999$	4.63525	−	3.36771i	0.146653	−	0.106550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.f.a.113.1	yes	4
11.2	odd	10		1694.2.a.k.1.2		2
11.4	even	5	inner	154.2.f.a.15.1	✓	4
11.9	even	5		1694.2.a.q.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.f.a.15.1	✓	4	11.4	even	5	inner
154.2.f.a.113.1	yes	4	1.1	even	1	trivial
1694.2.a.k.1.2		2	11.2	odd	10
1694.2.a.q.1.2		2	11.9	even	5

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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.61803 - 1.17557i) q^{9} -0.381966 q^{10} +(-1.23607 - 3.07768i) q^{11} -1.00000 q^{12} +(4.42705 - 3.21644i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.118034 - 0.363271i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.19098 + 0.865300i) q^{17} +(-0.618034 + 1.90211i) q^{18} +(2.07295 + 6.37988i) q^{19} +(0.309017 - 0.224514i) q^{20} -1.00000 q^{21} +(2.80902 + 1.76336i) q^{22} -3.76393 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.50000 - 4.61653i) q^{25} +(-1.69098 + 5.20431i) q^{26} +(-4.04508 - 2.93893i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-2.92705 + 9.00854i) q^{29} +(0.118034 + 0.363271i) q^{30} +(2.42705 - 1.76336i) q^{31} +1.00000 q^{32} +(-2.54508 + 2.12663i) q^{33} -1.47214 q^{34} +(0.309017 - 0.224514i) q^{35} +(-0.618034 - 1.90211i) q^{36} +(-0.354102 + 1.08981i) q^{37} +(-5.42705 - 3.94298i) q^{38} +(-4.42705 - 3.21644i) q^{39} +(-0.118034 + 0.363271i) q^{40} +(2.00000 + 6.15537i) q^{41} +(0.809017 - 0.587785i) q^{42} -9.61803 q^{43} +(-3.30902 + 0.224514i) q^{44} +0.763932 q^{45} +(3.04508 - 2.21238i) q^{46} +(0.500000 + 1.53884i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(3.92705 + 2.85317i) q^{50} +(0.454915 - 1.40008i) q^{51} +(-1.69098 - 5.20431i) q^{52} +(-0.572949 + 0.416272i) q^{53} +5.00000 q^{54} +(0.309017 - 1.22857i) q^{55} +1.00000 q^{56} +(5.42705 - 3.94298i) q^{57} +(-2.92705 - 9.00854i) q^{58} +(-1.64590 + 5.06555i) q^{59} +(-0.309017 - 0.224514i) q^{60} +(11.2082 + 8.14324i) q^{61} +(-0.927051 + 2.85317i) q^{62} +(-0.618034 - 1.90211i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.09017 q^{65} +(0.809017 - 3.21644i) q^{66} +4.70820 q^{67} +(1.19098 - 0.865300i) q^{68} +(1.16312 + 3.57971i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(2.42705 + 1.76336i) q^{71} +(1.61803 + 1.17557i) q^{72} +(-0.0450850 + 0.138757i) q^{73} +(-0.354102 - 1.08981i) q^{74} +(-3.92705 + 2.85317i) q^{75} +6.70820 q^{76} +(-3.30902 + 0.224514i) q^{77} +5.47214 q^{78} +(11.2812 - 8.19624i) q^{79} +(-0.118034 - 0.363271i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.23607 - 3.80423i) q^{82} +(-7.54508 - 5.48183i) q^{83} +(-0.309017 + 0.951057i) q^{84} +(0.173762 + 0.534785i) q^{85} +(7.78115 - 5.65334i) q^{86} +9.47214 q^{87} +(2.54508 - 2.12663i) q^{88} +8.09017 q^{89} +(-0.618034 + 0.449028i) q^{90} +(-1.69098 - 5.20431i) q^{91} +(-1.16312 + 3.57971i) q^{92} +(-2.42705 - 1.76336i) q^{93} +(-1.30902 - 0.951057i) q^{94} +(-0.791796 + 2.43690i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-10.0902 + 7.33094i) q^{97} +1.00000 q^{98} +(-5.61803 - 3.52671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9} - 6 q^{10} + 4 q^{11} - 4 q^{12} + 11 q^{13} - q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + 15 q^{19} - q^{20} - 4 q^{21} + 9 q^{22} - 24 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} - q^{28} - 5 q^{29} - 4 q^{30} + 3 q^{31} + 4 q^{32} + q^{33} + 12 q^{34} - q^{35} + 2 q^{36} + 12 q^{37} - 15 q^{38} - 11 q^{39} + 4 q^{40} + 8 q^{41} + q^{42} - 34 q^{43} - 11 q^{44} + 12 q^{45} + q^{46} + 2 q^{47} + q^{48} - q^{49} + 9 q^{50} + 13 q^{51} - 9 q^{52} - 9 q^{53} + 20 q^{54} - q^{55} + 4 q^{56} + 15 q^{57} - 5 q^{58} - 20 q^{59} + q^{60} + 18 q^{61} + 3 q^{62} + 2 q^{63} - q^{64} - 14 q^{65} + q^{66} - 8 q^{67} + 7 q^{68} - 11 q^{69} + 4 q^{70} + 3 q^{71} + 2 q^{72} + 11 q^{73} + 12 q^{74} - 9 q^{75} - 11 q^{77} + 4 q^{78} + 25 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} - 19 q^{83} + q^{84} + 32 q^{85} + 11 q^{86} + 20 q^{87} - q^{88} + 10 q^{89} + 2 q^{90} - 9 q^{91} + 11 q^{92} - 3 q^{93} - 3 q^{94} - 30 q^{95} + q^{96} - 18 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9 - 6 * q^10 + 4 * q^11 - 4 * q^12 + 11 * q^13 - q^14 - 4 * q^15 - q^16 + 7 * q^17 + 2 * q^18 + 15 * q^19 - q^20 - 4 * q^21 + 9 * q^22 - 24 * q^23 + q^24 - 6 * q^25 - 9 * q^26 - 5 * q^27 - q^28 - 5 * q^29 - 4 * q^30 + 3 * q^31 + 4 * q^32 + q^33 + 12 * q^34 - q^35 + 2 * q^36 + 12 * q^37 - 15 * q^38 - 11 * q^39 + 4 * q^40 + 8 * q^41 + q^42 - 34 * q^43 - 11 * q^44 + 12 * q^45 + q^46 + 2 * q^47 + q^48 - q^49 + 9 * q^50 + 13 * q^51 - 9 * q^52 - 9 * q^53 + 20 * q^54 - q^55 + 4 * q^56 + 15 * q^57 - 5 * q^58 - 20 * q^59 + q^60 + 18 * q^61 + 3 * q^62 + 2 * q^63 - q^64 - 14 * q^65 + q^66 - 8 * q^67 + 7 * q^68 - 11 * q^69 + 4 * q^70 + 3 * q^71 + 2 * q^72 + 11 * q^73 + 12 * q^74 - 9 * q^75 - 11 * q^77 + 4 * q^78 + 25 * q^79 + 4 * q^80 - q^81 - 12 * q^82 - 19 * q^83 + q^84 + 32 * q^85 + 11 * q^86 + 20 * q^87 - q^88 + 10 * q^89 + 2 * q^90 - 9 * q^91 + 11 * q^92 - 3 * q^93 - 3 * q^94 - 30 * q^95 + q^96 - 18 * q^97 + 4 * q^98 - 18 * q^99

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