LMFDB - Embedded newform 154.2.f.c.15.1

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			15.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	154.15
Dual form			154.2.f.c.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.17557i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.17557i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} -2.00000 q^{10} +(2.54508 + 2.12663i) q^{11} -1.61803 q^{12} +(-2.61803 - 1.90211i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.00000 - 3.07768i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.73607 - 3.44095i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.0450850 + 0.138757i) q^{19} +(-1.61803 - 1.17557i) q^{20} +1.61803 q^{21} +(0.809017 + 3.21644i) q^{22} +8.47214 q^{23} +(-1.30902 - 0.951057i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-1.00000 - 3.07768i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-2.47214 - 7.60845i) q^{29} +(1.00000 - 3.07768i) q^{30} +(3.61803 + 2.62866i) q^{31} -1.00000 q^{32} +(-4.54508 + 2.85317i) q^{33} +5.85410 q^{34} +(1.61803 + 1.17557i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(-2.38197 - 7.33094i) q^{37} +(-0.118034 + 0.0857567i) q^{38} +(4.23607 - 3.07768i) q^{39} +(-0.618034 - 1.90211i) q^{40} +(0.263932 - 0.812299i) q^{41} +(1.30902 + 0.951057i) q^{42} -4.85410 q^{43} +(-1.23607 + 3.07768i) q^{44} -0.763932 q^{45} +(6.85410 + 4.97980i) q^{46} +(0.527864 - 1.62460i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(2.92705 + 9.00854i) q^{51} +(1.00000 - 3.07768i) q^{52} +(-4.00000 - 2.90617i) q^{53} -5.47214 q^{54} +(-6.61803 - 0.449028i) q^{55} +1.00000 q^{56} +(-0.190983 - 0.138757i) q^{57} +(2.47214 - 7.60845i) q^{58} +(1.28115 + 3.94298i) q^{59} +(2.61803 - 1.90211i) q^{60} +(-5.23607 + 3.80423i) q^{61} +(1.38197 + 4.25325i) q^{62} +(0.118034 - 0.363271i) q^{63} +(-0.809017 - 0.587785i) q^{64} +6.47214 q^{65} +(-5.35410 - 0.363271i) q^{66} +1.09017 q^{67} +(4.73607 + 3.44095i) q^{68} +(-4.23607 + 13.0373i) q^{69} +(0.618034 + 1.90211i) q^{70} +(-8.47214 + 6.15537i) q^{71} +(-0.309017 + 0.224514i) q^{72} +(-0.736068 - 2.26538i) q^{73} +(2.38197 - 7.33094i) q^{74} +(-1.30902 - 0.951057i) q^{75} -0.145898 q^{76} +(1.23607 - 3.07768i) q^{77} +5.23607 q^{78} +(1.00000 + 0.726543i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(0.690983 - 0.502029i) q^{82} +(10.5451 - 7.66145i) q^{83} +(0.500000 + 1.53884i) q^{84} +(-3.61803 + 11.1352i) q^{85} +(-3.92705 - 2.85317i) q^{86} +12.9443 q^{87} +(-2.80902 + 1.76336i) q^{88} -15.3262 q^{89} +(-0.618034 - 0.449028i) q^{90} +(-1.00000 + 3.07768i) q^{91} +(2.61803 + 8.05748i) q^{92} +(-5.85410 + 4.25325i) q^{93} +(1.38197 - 1.00406i) q^{94} +(-0.0901699 - 0.277515i) q^{95} +(0.500000 - 1.53884i) q^{96} +(2.54508 + 1.84911i) q^{97} -1.00000 q^{98} +(0.309017 + 1.22857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} - 6 q^{13} - q^{14} - 4 q^{15} - q^{16} + 10 q^{17} - 4 q^{18} + 11 q^{19} - 2 q^{20} + 2 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + q^{25} - 4 q^{26} - 11 q^{27} + q^{28} + 8 q^{29} + 4 q^{30} + 10 q^{31} - 4 q^{32} - 7 q^{33} + 10 q^{34} + 2 q^{35} + 4 q^{36} - 14 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 10 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 12 q^{45} + 14 q^{46} + 20 q^{47} - 2 q^{48} - q^{49} - q^{50} + 5 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 22 q^{55} + 4 q^{56} - 3 q^{57} - 8 q^{58} - 15 q^{59} + 6 q^{60} - 12 q^{61} + 10 q^{62} - 4 q^{63} - q^{64} + 8 q^{65} - 8 q^{66} - 18 q^{67} + 10 q^{68} - 8 q^{69} - 2 q^{70} - 16 q^{71} + q^{72} + 6 q^{73} + 14 q^{74} - 3 q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 4 q^{79} - 2 q^{80} - 14 q^{81} + 5 q^{82} + 31 q^{83} + 2 q^{84} - 10 q^{85} - 9 q^{86} + 16 q^{87} - 9 q^{88} - 30 q^{89} + 2 q^{90} - 4 q^{91} + 6 q^{92} - 10 q^{93} + 10 q^{94} + 22 q^{95} + 2 q^{96} - q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 - 6 * q^13 - q^14 - 4 * q^15 - q^16 + 10 * q^17 - 4 * q^18 + 11 * q^19 - 2 * q^20 + 2 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + q^25 - 4 * q^26 - 11 * q^27 + q^28 + 8 * q^29 + 4 * q^30 + 10 * q^31 - 4 * q^32 - 7 * q^33 + 10 * q^34 + 2 * q^35 + 4 * q^36 - 14 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 10 * q^41 + 3 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 + 14 * q^46 + 20 * q^47 - 2 * q^48 - q^49 - q^50 + 5 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 22 * q^55 + 4 * q^56 - 3 * q^57 - 8 * q^58 - 15 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 - 4 * q^63 - q^64 + 8 * q^65 - 8 * q^66 - 18 * q^67 + 10 * q^68 - 8 * q^69 - 2 * q^70 - 16 * q^71 + q^72 + 6 * q^73 + 14 * q^74 - 3 * q^75 - 14 * q^76 - 4 * q^77 + 12 * q^78 + 4 * q^79 - 2 * q^80 - 14 * q^81 + 5 * q^82 + 31 * q^83 + 2 * q^84 - 10 * q^85 - 9 * q^86 + 16 * q^87 - 9 * q^88 - 30 * q^89 + 2 * q^90 - 4 * q^91 + 6 * q^92 - 10 * q^93 + 10 * q^94 + 22 * q^95 + 2 * q^96 - q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	0.696598	+	0.717462i	$0.254696\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	−0.985273	+	0.170989i	$0.945304\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.61803	+	1.17557i	−0.723607	+	0.525731i	−0.887535	−	0.460741i	$-0.847584\pi$
$5$	−1.61803	+	1.17557i	−0.723607	+	0.525731i	0.163928	+	0.986472i	$0.447584\pi$
$6$	−1.30902	+	0.951057i	−0.534404	+	0.388267i
$7$	−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
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$	−2.00000			−0.632456
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$12$	−1.61803			−0.467086
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	0.162219	−	0.986755i	$-0.448135\pi$
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	−0.888331	+	0.459204i	$0.848135\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	−1.00000	−	3.07768i	−0.258199	−	0.794654i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.73607	−	3.44095i	1.14867	−	0.834554i	0.160362	−	0.987058i	$-0.448734\pi$
$17$	4.73607	−	3.44095i	1.14867	−	0.834554i	0.988303	+	0.152504i	$0.0487337\pi$
$18$	0.118034	+	0.363271i	0.0278209	+	0.0856239i
$19$	−0.0450850	+	0.138757i	−0.0103432	+	0.0318331i	−0.956095	−	0.293057i	$-0.905327\pi$
$19$	−0.0450850	+	0.138757i	−0.0103432	+	0.0318331i	0.945752	+	0.324890i	$0.105327\pi$
$20$	−1.61803	−	1.17557i	−0.361803	−	0.262866i
$21$	1.61803			0.353084
$22$	0.809017	+	3.21644i	0.172483	+	0.685747i
$23$	8.47214			1.76656			0.883281	−	0.468844i	$-0.155329\pi$
$23$	8.47214			1.76656			0.883281	+	0.468844i	$0.155329\pi$
$24$	−1.30902	−	0.951057i	−0.267202	−	0.194134i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	−1.00000	−	3.07768i	−0.196116	−	0.603583i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	−2.47214	−	7.60845i	−0.459064	−	1.41285i	−0.866297	−	0.499530i	$-0.833506\pi$
$29$	−2.47214	−	7.60845i	−0.459064	−	1.41285i	0.407233	−	0.913324i	$-0.366494\pi$
$30$	1.00000	−	3.07768i	0.182574	−	0.561906i
$31$	3.61803	+	2.62866i	0.649818	+	0.472120i	0.863209	−	0.504846i	$-0.168451\pi$
$31$	3.61803	+	2.62866i	0.649818	+	0.472120i	−0.213391	+	0.976967i	$0.568451\pi$
$32$	−1.00000			−0.176777
$33$	−4.54508	+	2.85317i	−0.791198	+	0.496673i
$34$	5.85410			1.00397
$35$	1.61803	+	1.17557i	0.273498	+	0.198708i
$36$	−0.118034	+	0.363271i	−0.0196723	+	0.0605452i
$37$	−2.38197	−	7.33094i	−0.391593	−	1.20520i	−0.931583	−	0.363528i	$-0.881572\pi$
$37$	−2.38197	−	7.33094i	−0.391593	−	1.20520i	0.539991	−	0.841671i	$-0.318428\pi$
$38$	−0.118034	+	0.0857567i	−0.0191476	+	0.0139116i
$39$	4.23607	−	3.07768i	0.678314	−	0.492824i
$40$	−0.618034	−	1.90211i	−0.0977198	−	0.300750i
$41$	0.263932	−	0.812299i	0.0412193	−	0.126860i	−0.928329	−	0.371759i	$-0.878755\pi$
$41$	0.263932	−	0.812299i	0.0412193	−	0.126860i	0.969549	+	0.244899i	$0.0787548\pi$
$42$	1.30902	+	0.951057i	0.201986	+	0.146751i
$43$	−4.85410			−0.740244			−0.370122	−	0.928983i	$-0.620684\pi$
$43$	−4.85410			−0.740244			−0.370122	+	0.928983i	$0.620684\pi$
$44$	−1.23607	+	3.07768i	−0.186344	+	0.463978i
$45$	−0.763932			−0.113880
$46$	6.85410	+	4.97980i	1.01058	+	0.734231i
$47$	0.527864	−	1.62460i	0.0769969	−	0.236972i	−0.905149	−	0.425096i	$-0.860241\pi$
$47$	0.527864	−	1.62460i	0.0769969	−	0.236972i	0.982145	+	0.188123i	$0.0602405\pi$
$48$	−0.500000	−	1.53884i	−0.0721688	−	0.222113i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	2.92705	+	9.00854i	0.409869	+	1.26145i
$52$	1.00000	−	3.07768i	0.138675	−	0.426798i
$53$	−4.00000	−	2.90617i	−0.549442	−	0.399193i	0.278138	−	0.960541i	$-0.410283\pi$
$53$	−4.00000	−	2.90617i	−0.549442	−	0.399193i	−0.827580	+	0.561348i	$0.810283\pi$
$54$	−5.47214			−0.744663
$55$	−6.61803	−	0.449028i	−0.892376	−	0.0605469i
$56$	1.00000			0.133631
$57$	−0.190983	−	0.138757i	−0.0252963	−	0.0183789i
$58$	2.47214	−	7.60845i	0.324607	−	0.999039i
$59$	1.28115	+	3.94298i	0.166792	+	0.513333i	0.999164	−	0.0408847i	$-0.0130176\pi$
$59$	1.28115	+	3.94298i	0.166792	+	0.513333i	−0.832372	+	0.554217i	$0.813018\pi$
$60$	2.61803	−	1.90211i	0.337987	−	0.245562i
$61$	−5.23607	+	3.80423i	−0.670410	+	0.487081i	−0.870162	−	0.492765i	$-0.835986\pi$
$61$	−5.23607	+	3.80423i	−0.670410	+	0.487081i	0.199753	+	0.979846i	$0.435986\pi$
$62$	1.38197	+	4.25325i	0.175510	+	0.540164i
$63$	0.118034	−	0.363271i	0.0148709	−	0.0457679i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	6.47214			0.802770
$66$	−5.35410	−	0.363271i	−0.659044	−	0.0447156i
$67$	1.09017			0.133185			0.0665927	−	0.997780i	$-0.478787\pi$
$67$	1.09017			0.133185			0.0665927	+	0.997780i	$0.478787\pi$
$68$	4.73607	+	3.44095i	0.574333	+	0.417277i
$69$	−4.23607	+	13.0373i	−0.509963	+	1.56950i
$70$	0.618034	+	1.90211i	0.0738692	+	0.227346i
$71$	−8.47214	+	6.15537i	−1.00546	+	0.730508i	−0.963251	−	0.268601i	$-0.913439\pi$
$71$	−8.47214	+	6.15537i	−1.00546	+	0.730508i	−0.0422061	+	0.999109i	$0.513439\pi$
$72$	−0.309017	+	0.224514i	−0.0364180	+	0.0264592i
$73$	−0.736068	−	2.26538i	−0.0861502	−	0.265143i	0.898696	−	0.438572i	$-0.144515\pi$
$73$	−0.736068	−	2.26538i	−0.0861502	−	0.265143i	−0.984846	+	0.173428i	$0.944515\pi$
$74$	2.38197	−	7.33094i	0.276898	−	0.852204i
$75$	−1.30902	−	0.951057i	−0.151152	−	0.109819i
$76$	−0.145898			−0.0167357
$77$	1.23607	−	3.07768i	0.140863	−	0.350735i
$78$	5.23607			0.592868
$79$	1.00000	+	0.726543i	0.112509	+	0.0817424i	0.642617	−	0.766188i	$-0.277849\pi$
$79$	1.00000	+	0.726543i	0.112509	+	0.0817424i	−0.530108	+	0.847930i	$0.677849\pi$
$80$	0.618034	−	1.90211i	0.0690983	−	0.212663i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	0.690983	−	0.502029i	0.0763063	−	0.0554398i
$83$	10.5451	−	7.66145i	1.15747	−	0.840954i	0.168017	−	0.985784i	$-0.446264\pi$
$83$	10.5451	−	7.66145i	1.15747	−	0.840954i	0.989456	+	0.144830i	$0.0462637\pi$
$84$	0.500000	+	1.53884i	0.0545545	+	0.167901i
$85$	−3.61803	+	11.1352i	−0.392431	+	1.20778i
$86$	−3.92705	−	2.85317i	−0.423465	−	0.307665i
$87$	12.9443			1.38777
$88$	−2.80902	+	1.76336i	−0.299442	+	0.187974i
$89$	−15.3262			−1.62458			−0.812289	−	0.583255i	$-0.801779\pi$
$89$	−15.3262			−1.62458			−0.812289	+	0.583255i	$0.801779\pi$
$90$	−0.618034	−	0.449028i	−0.0651465	−	0.0473317i
$91$	−1.00000	+	3.07768i	−0.104828	+	0.322629i
$92$	2.61803	+	8.05748i	0.272949	+	0.840050i
$93$	−5.85410	+	4.25325i	−0.607042	+	0.441042i
$94$	1.38197	−	1.00406i	0.142539	−	0.103561i
$95$	−0.0901699	−	0.277515i	−0.00925124	−	0.0284724i
$96$	0.500000	−	1.53884i	0.0510310	−	0.157057i
$97$	2.54508	+	1.84911i	0.258414	+	0.187749i	0.709448	−	0.704758i	$-0.248944\pi$
$97$	2.54508	+	1.84911i	0.258414	+	0.187749i	−0.451033	+	0.892507i	$0.648944\pi$
$98$	−1.00000			−0.101015
$99$	0.309017	+	1.22857i	0.0310574	+	0.123476i
$100$	−1.00000			−0.100000
$101$	15.0902	+	10.9637i	1.50153	+	1.09092i	0.969768	+	0.244029i	$0.0784692\pi$
$101$	15.0902	+	10.9637i	1.50153	+	1.09092i	0.531760	+	0.846895i	$0.321531\pi$
$102$	−2.92705	+	9.00854i	−0.289821	+	0.891978i
$103$	−3.00000	−	9.23305i	−0.295599	−	0.909760i	−0.983020	−	0.183500i	$-0.941257\pi$
$103$	−3.00000	−	9.23305i	−0.295599	−	0.909760i	0.687421	−	0.726259i	$-0.258743\pi$
$104$	2.61803	−	1.90211i	0.256719	−	0.186518i
$105$	−2.61803	+	1.90211i	−0.255494	+	0.185627i
$106$	−1.52786	−	4.70228i	−0.148399	−	0.456726i
$107$	−2.26393	+	6.96767i	−0.218863	+	0.673590i	0.779994	+	0.625787i	$0.215222\pi$
$107$	−2.26393	+	6.96767i	−0.218863	+	0.673590i	−0.998857	+	0.0478030i	$0.984778\pi$
$108$	−4.42705	−	3.21644i	−0.425993	−	0.309502i
$109$	−10.1803			−0.975100			−0.487550	−	0.873095i	$-0.662109\pi$
$109$	−10.1803			−0.975100			−0.487550	+	0.873095i	$0.662109\pi$
$110$	−5.09017	−	4.25325i	−0.485329	−	0.405532i
$111$	12.4721			1.18380
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	1.42705	−	4.39201i	0.134246	−	0.413166i	−0.861226	−	0.508222i	$-0.830303\pi$
$113$	1.42705	−	4.39201i	0.134246	−	0.413166i	0.995472	+	0.0950561i	$0.0303030\pi$
$114$	−0.0729490	−	0.224514i	−0.00683230	−	0.0210277i
$115$	−13.7082	+	9.95959i	−1.27830	+	0.928737i
$116$	6.47214	−	4.70228i	0.600923	−	0.436596i
$117$	−0.381966	−	1.17557i	−0.0353128	−	0.108682i
$118$	−1.28115	+	3.94298i	−0.117940	+	0.362981i
$119$	−4.73607	−	3.44095i	−0.434155	−	0.315432i
$120$	3.23607			0.295411
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$	−6.47214			−0.585960
$123$	1.11803	+	0.812299i	0.100810	+	0.0732426i
$124$	−1.38197	+	4.25325i	−0.124104	+	0.381953i
$125$	−3.70820	−	11.4127i	−0.331672	−	1.02078i
$126$	0.309017	−	0.224514i	0.0275294	−	0.0200013i
$127$	7.09017	−	5.15131i	0.629151	−	0.457105i	−0.226955	−	0.973905i	$-0.572877\pi$
$127$	7.09017	−	5.15131i	0.629151	−	0.457105i	0.856106	+	0.516800i	$0.172877\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.42705	−	7.46969i	0.213690	−	0.657670i
$130$	5.23607	+	3.80423i	0.459234	+	0.333653i
$131$	15.5623			1.35968			0.679842	−	0.733358i	$-0.262048\pi$
$131$	15.5623			1.35968			0.679842	+	0.733358i	$0.262048\pi$
$132$	−4.11803	−	3.44095i	−0.358429	−	0.299497i
$133$	0.145898			0.0126510
$134$	0.881966	+	0.640786i	0.0761903	+	0.0553555i
$135$	3.38197	−	10.4086i	0.291073	−	0.895831i
$136$	1.80902	+	5.56758i	0.155122	+	0.477416i
$137$	15.6353	−	11.3597i	1.33581	−	0.970523i	0.336223	−	0.941782i	$-0.390850\pi$
$137$	15.6353	−	11.3597i	1.33581	−	0.970523i	0.999587	−	0.0287404i	$-0.00914961\pi$
$138$	−11.0902	+	8.05748i	−0.944058	+	0.685898i
$139$	−4.47214	−	13.7638i	−0.379322	−	1.16743i	−0.940516	−	0.339748i	$-0.889658\pi$
$139$	−4.47214	−	13.7638i	−0.379322	−	1.16743i	0.561195	−	0.827684i	$-0.310342\pi$
$140$	−0.618034	+	1.90211i	−0.0522334	+	0.160758i
$141$	2.23607	+	1.62460i	0.188311	+	0.136816i
$142$	−10.4721			−0.878802
$143$	−2.61803	−	10.4086i	−0.218931	−	0.870413i
$144$	−0.381966			−0.0318305
$145$	12.9443	+	9.40456i	1.07496	+	0.781007i
$146$	0.736068	−	2.26538i	0.0609174	−	0.187485i
$147$	−0.500000	−	1.53884i	−0.0412393	−	0.126922i
$148$	6.23607	−	4.53077i	0.512602	−	0.372427i
$149$	8.70820	−	6.32688i	0.713404	−	0.518318i	−0.170866	−	0.985294i	$-0.554657\pi$
$149$	8.70820	−	6.32688i	0.713404	−	0.518318i	0.884270	+	0.466976i	$0.154657\pi$
$150$	−0.500000	−	1.53884i	−0.0408248	−	0.125646i
$151$	−0.708204	+	2.17963i	−0.0576328	+	0.177376i	−0.975729	−	0.218983i	$-0.929726\pi$
$151$	−0.708204	+	2.17963i	−0.0576328	+	0.177376i	0.918096	+	0.396358i	$0.129726\pi$
$152$	−0.118034	−	0.0857567i	−0.00957382	−	0.00695579i
$153$	2.23607			0.180775
$154$	2.80902	−	1.76336i	0.226357	−	0.142095i
$155$	−8.94427			−0.718421
$156$	4.23607	+	3.07768i	0.339157	+	0.246412i
$157$	−0.854102	+	2.62866i	−0.0681648	+	0.209790i	−0.979337	−	0.202237i	$-0.935179\pi$
$157$	−0.854102	+	2.62866i	−0.0681648	+	0.209790i	0.911172	+	0.412026i	$0.135179\pi$
$158$	0.381966	+	1.17557i	0.0303876	+	0.0935234i
$159$	6.47214	−	4.70228i	0.513274	−	0.372915i
$160$	1.61803	−	1.17557i	0.127917	−	0.0929370i
$161$	−2.61803	−	8.05748i	−0.206330	−	0.635018i
$162$	2.38197	−	7.33094i	0.187145	−	0.575973i
$163$	−18.8262	−	13.6781i	−1.47458	−	1.07135i	−0.979252	−	0.202645i	$-0.935046\pi$
$163$	−18.8262	−	13.6781i	−1.47458	−	1.07135i	−0.495333	−	0.868703i	$-0.664954\pi$
$164$	0.854102			0.0666942
$165$	4.00000	−	9.95959i	0.311400	−	0.775353i
$166$	13.0344			1.01167
$167$	−13.3262	−	9.68208i	−1.03122	−	0.749222i	−0.0626637	−	0.998035i	$-0.519960\pi$
$167$	−13.3262	−	9.68208i	−1.03122	−	0.749222i	−0.968552	+	0.248813i	$0.919960\pi$
$168$	−0.500000	+	1.53884i	−0.0385758	+	0.118724i
$169$	−0.781153	−	2.40414i	−0.0600887	−	0.184934i
$170$	−9.47214	+	6.88191i	−0.726480	+	0.527818i
$171$	−0.0450850	+	0.0327561i	−0.00344773	+	0.00250493i
$172$	−1.50000	−	4.61653i	−0.114374	−	0.352007i
$173$	0.708204	−	2.17963i	0.0538437	−	0.165714i	−0.920518	−	0.390699i	$-0.872233\pi$
$173$	0.708204	−	2.17963i	0.0538437	−	0.165714i	0.974362	+	0.224985i	$0.0722333\pi$
$174$	10.4721	+	7.60845i	0.793891	+	0.576795i
$175$	1.00000			0.0755929
$176$	−3.30902	−	0.224514i	−0.249427	−	0.0169234i
$177$	−6.70820			−0.504219
$178$	−12.3992	−	9.00854i	−0.929358	−	0.675218i
$179$	−7.57295	+	23.3071i	−0.566029	+	1.74206i	0.0988461	+	0.995103i	$0.468485\pi$
$179$	−7.57295	+	23.3071i	−0.566029	+	1.74206i	−0.664875	+	0.746955i	$0.731515\pi$
$180$	−0.236068	−	0.726543i	−0.0175955	−	0.0541533i
$181$	15.1803	−	11.0292i	1.12835	−	0.819791i	0.142893	−	0.989738i	$-0.454360\pi$
$181$	15.1803	−	11.0292i	1.12835	−	0.819791i	0.985453	+	0.169947i	$0.0543597\pi$
$182$	−2.61803	+	1.90211i	−0.194062	+	0.140994i
$183$	−3.23607	−	9.95959i	−0.239217	−	0.736234i
$184$	−2.61803	+	8.05748i	−0.193004	+	0.594005i
$185$	12.4721	+	9.06154i	0.916970	+	0.666217i
$186$	−7.23607			−0.530574
$187$	19.3713	+	1.31433i	1.41657	+	0.0961132i
$188$	1.70820			0.124584
$189$	4.42705	+	3.21644i	0.322021	+	0.233962i
$190$	0.0901699	−	0.277515i	0.00654162	−	0.0201330i
$191$	3.85410	+	11.8617i	0.278873	+	0.858283i	0.988169	+	0.153372i	$0.0490132\pi$
$191$	3.85410	+	11.8617i	0.278873	+	0.858283i	−0.709296	+	0.704911i	$0.750987\pi$
$192$	1.30902	−	0.951057i	0.0944702	−	0.0686366i
$193$	−14.0902	+	10.2371i	−1.01423	+	0.736883i	−0.965093	−	0.261909i	$-0.915648\pi$
$193$	−14.0902	+	10.2371i	−1.01423	+	0.736883i	−0.0491400	+	0.998792i	$0.515648\pi$
$194$	0.972136	+	2.99193i	0.0697953	+	0.214808i
$195$	−3.23607	+	9.95959i	−0.231740	+	0.713221i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−3.52786			−0.251350			−0.125675	−	0.992071i	$-0.540110\pi$
$197$	−3.52786			−0.251350			−0.125675	+	0.992071i	$0.540110\pi$
$198$	−0.472136	+	1.17557i	−0.0335532	+	0.0835442i
$199$	−20.1803			−1.43055			−0.715273	−	0.698845i	$-0.753698\pi$
$199$	−20.1803			−1.43055			−0.715273	+	0.698845i	$0.753698\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	−0.545085	+	1.67760i	−0.0384473	+	0.118329i
$202$	5.76393	+	17.7396i	0.405549	+	1.24815i
$203$	−6.47214	+	4.70228i	−0.454255	+	0.330035i
$204$	−7.66312	+	5.56758i	−0.536526	+	0.389809i
$205$	0.527864	+	1.62460i	0.0368676	+	0.113467i
$206$	3.00000	−	9.23305i	0.209020	−	0.643297i
$207$	2.61803	+	1.90211i	0.181966	+	0.132206i
$208$	3.23607			0.224381
$209$	−0.409830	+	0.257270i	−0.0283485	+	0.0177957i
$210$	−3.23607			−0.223310
$211$	12.8713	+	9.35156i	0.886098	+	0.643788i	0.934858	−	0.355022i	$-0.115527\pi$
$211$	12.8713	+	9.35156i	0.886098	+	0.643788i	−0.0487594	+	0.998811i	$0.515527\pi$
$212$	1.52786	−	4.70228i	0.104934	−	0.322954i
$213$	−5.23607	−	16.1150i	−0.358769	−	1.10418i
$214$	−5.92705	+	4.30625i	−0.405165	+	0.294370i
$215$	7.85410	−	5.70634i	0.535645	−	0.389169i
$216$	−1.69098	−	5.20431i	−0.115057	−	0.354108i
$217$	1.38197	−	4.25325i	0.0938140	−	0.288730i
$218$	−8.23607	−	5.98385i	−0.557817	−	0.405278i
$219$	3.85410			0.260436
$220$	−1.61803	−	6.43288i	−0.109088	−	0.433705i
$221$	−18.9443			−1.27433
$222$	10.0902	+	7.33094i	0.677208	+	0.492020i
$223$	−5.38197	+	16.5640i	−0.360403	+	1.10921i	0.592407	+	0.805639i	$0.298178\pi$
$223$	−5.38197	+	16.5640i	−0.360403	+	1.10921i	−0.952810	+	0.303568i	$0.901822\pi$
$224$	0.309017	+	0.951057i	0.0206471	+	0.0635451i
$225$	−0.309017	+	0.224514i	−0.0206011	+	0.0149676i
$226$	3.73607	−	2.71441i	0.248520	−	0.180560i
$227$	8.42705	+	25.9358i	0.559323	+	1.72142i	0.684245	+	0.729253i	$0.260132\pi$
$227$	8.42705	+	25.9358i	0.559323	+	1.72142i	−0.124922	+	0.992167i	$0.539868\pi$
$228$	0.0729490	−	0.224514i	0.00483117	−	0.0148688i
$229$	18.4164	+	13.3803i	1.21699	+	0.884195i	0.995847	−	0.0910459i	$-0.0290210\pi$
$229$	18.4164	+	13.3803i	1.21699	+	0.884195i	0.221144	+	0.975241i	$0.429021\pi$
$230$	−16.9443			−1.11727
$231$	4.11803	+	3.44095i	0.270947	+	0.226398i
$232$	8.00000			0.525226
$233$	−6.39919	−	4.64928i	−0.419225	−	0.304585i	0.358101	−	0.933683i	$-0.383424\pi$
$233$	−6.39919	−	4.64928i	−0.419225	−	0.304585i	−0.777326	+	0.629098i	$0.783424\pi$
$234$	0.381966	−	1.17557i	0.0249699	−	0.0768494i
$235$	1.05573	+	3.24920i	0.0688681	+	0.211954i
$236$	−3.35410	+	2.43690i	−0.218333	+	0.158629i
$237$	−1.61803	+	1.17557i	−0.105103	+	0.0763615i
$238$	−1.80902	−	5.56758i	−0.117261	−	0.360893i
$239$	0.0901699	−	0.277515i	0.00583261	−	0.0179509i	−0.948098	−	0.317979i	$-0.896996\pi$
$239$	0.0901699	−	0.277515i	0.00583261	−	0.0179509i	0.953930	+	0.300028i	$0.0969960\pi$
$240$	2.61803	+	1.90211i	0.168993	+	0.122781i
$241$	−6.79837			−0.437922			−0.218961	−	0.975734i	$-0.570267\pi$
$241$	−6.79837			−0.437922			−0.218961	+	0.975734i	$0.570267\pi$
$242$	−4.78115	+	9.90659i	−0.307344	+	0.636820i
$243$	−3.94427			−0.253025
$244$	−5.23607	−	3.80423i	−0.335205	−	0.243541i
$245$	0.618034	−	1.90211i	0.0394847	−	0.121522i
$246$	0.427051	+	1.31433i	0.0272278	+	0.0837985i
$247$	0.381966	−	0.277515i	0.0243039	−	0.0176578i
$248$	−3.61803	+	2.62866i	−0.229745	+	0.166920i
$249$	6.51722	+	20.0579i	0.413012	+	1.27112i
$250$	3.70820	−	11.4127i	0.234527	−	0.721801i
$251$	4.00000	+	2.90617i	0.252478	+	0.183436i	0.706824	−	0.707389i	$-0.250127\pi$
$251$	4.00000	+	2.90617i	0.252478	+	0.183436i	−0.454346	+	0.890825i	$0.650127\pi$
$252$	0.381966			0.0240616
$253$	21.5623	+	18.0171i	1.35561	+	1.13272i
$254$	8.76393			0.549898
$255$	−15.3262	−	11.1352i	−0.959766	−	0.697311i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	7.91641	+	24.3642i	0.493812	+	1.51980i	0.818800	+	0.574079i	$0.194640\pi$
$257$	7.91641	+	24.3642i	0.493812	+	1.51980i	−0.324988	+	0.945718i	$0.605360\pi$
$258$	6.35410	−	4.61653i	0.395589	−	0.287412i
$259$	−6.23607	+	4.53077i	−0.387490	+	0.281528i
$260$	2.00000	+	6.15537i	0.124035	+	0.381740i
$261$	0.944272	−	2.90617i	0.0584490	−	0.179887i
$262$	12.5902	+	9.14729i	0.777823	+	0.565122i
$263$	−12.9443			−0.798178			−0.399089	−	0.916912i	$-0.630674\pi$
$263$	−12.9443			−0.798178			−0.399089	+	0.916912i	$0.630674\pi$
$264$	−1.30902	−	5.20431i	−0.0805644	−	0.320303i
$265$	9.88854			0.607448
$266$	0.118034	+	0.0857567i	0.00723713	+	0.00525808i
$267$	7.66312	−	23.5847i	0.468975	−	1.44336i
$268$	0.336881	+	1.03681i	0.0205783	+	0.0633334i
$269$	2.09017	−	1.51860i	0.127440	−	0.0925905i	−0.522239	−	0.852799i	$-0.674903\pi$
$269$	2.09017	−	1.51860i	0.127440	−	0.0925905i	0.649679	+	0.760208i	$0.274903\pi$
$270$	8.85410	−	6.43288i	0.538843	−	0.391493i
$271$	−5.76393	−	17.7396i	−0.350134	−	1.07760i	−0.958778	−	0.284158i	$-0.908286\pi$
$271$	−5.76393	−	17.7396i	−0.350134	−	1.07760i	0.608644	−	0.793444i	$-0.291714\pi$
$272$	−1.80902	+	5.56758i	−0.109688	+	0.337584i
$273$	−4.23607	−	3.07768i	−0.256378	−	0.186270i
$274$	19.3262			1.16754
$275$	−2.80902	+	1.76336i	−0.169390	+	0.106334i
$276$	−13.7082			−0.825137
$277$	−18.7984	−	13.6578i	−1.12948	−	0.820619i	−0.143865	−	0.989597i	$-0.545953\pi$
$277$	−18.7984	−	13.6578i	−1.12948	−	0.820619i	−0.985620	+	0.168979i	$0.945953\pi$
$278$	4.47214	−	13.7638i	0.268221	−	0.825499i
$279$	0.527864	+	1.62460i	0.0316024	+	0.0972622i
$280$	−1.61803	+	1.17557i	−0.0966960	+	0.0702538i
$281$	−7.92705	+	5.75934i	−0.472888	+	0.343573i	−0.798566	−	0.601907i	$-0.794408\pi$
$281$	−7.92705	+	5.75934i	−0.472888	+	0.343573i	0.325678	+	0.945481i	$0.394408\pi$
$282$	0.854102	+	2.62866i	0.0508610	+	0.156534i
$283$	3.41641	−	10.5146i	0.203084	−	0.625029i	−0.796702	−	0.604372i	$-0.793424\pi$
$283$	3.41641	−	10.5146i	0.203084	−	0.625029i	0.999787	−	0.0206574i	$-0.00657592\pi$
$284$	−8.47214	−	6.15537i	−0.502729	−	0.365254i
$285$	0.472136			0.0279669
$286$	4.00000	−	9.95959i	0.236525	−	0.588923i
$287$	−0.854102			−0.0504160
$288$	−0.309017	−	0.224514i	−0.0182090	−	0.0132296i
$289$	5.33688	−	16.4252i	0.313934	−	0.966190i
$290$	4.94427	+	15.2169i	0.290338	+	0.893567i
$291$	−4.11803	+	2.99193i	−0.241403	+	0.175390i
$292$	1.92705	−	1.40008i	0.112772	−	0.0819337i
$293$	8.09017	+	24.8990i	0.472633	+	1.45461i	0.849124	+	0.528194i	$0.177131\pi$
$293$	8.09017	+	24.8990i	0.472633	+	1.45461i	−0.376491	+	0.926420i	$0.622869\pi$
$294$	0.500000	−	1.53884i	0.0291606	−	0.0897471i
$295$	−6.70820	−	4.87380i	−0.390567	−	0.283763i
$296$	7.70820			0.448030
$297$	−18.1074	−	1.22857i	−1.05070	−	0.0712889i
$298$	10.7639			0.623538
$299$	−22.1803	−	16.1150i	−1.28272	−	0.931952i
$300$	0.500000	−	1.53884i	0.0288675	−	0.0888451i
$301$	1.50000	+	4.61653i	0.0864586	+	0.266092i
$302$	−1.85410	+	1.34708i	−0.106692	+	0.0775160i
$303$	−24.4164	+	17.7396i	−1.40269	+	1.01911i
$304$	−0.0450850	−	0.138757i	−0.00258580	−	0.00795828i
$305$	4.00000	−	12.3107i	0.229039	−	0.704911i
$306$	1.80902	+	1.31433i	0.103415	+	0.0751351i
$307$	−17.6180			−1.00551			−0.502757	−	0.864428i	$-0.667681\pi$
$307$	−17.6180			−1.00551			−0.502757	+	0.864428i	$0.667681\pi$
$308$	3.30902	+	0.224514i	0.188549	+	0.0127929i
$309$	15.7082			0.893609
$310$	−7.23607	−	5.25731i	−0.410981	−	0.298595i
$311$	−1.32624	+	4.08174i	−0.0752041	+	0.231454i	−0.981591	−	0.190994i	$-0.938829\pi$
$311$	−1.32624	+	4.08174i	−0.0752041	+	0.231454i	0.906387	+	0.422448i	$0.138829\pi$
$312$	1.61803	+	4.97980i	0.0916031	+	0.281925i
$313$	8.73607	−	6.34712i	0.493792	−	0.358761i	−0.312849	−	0.949803i	$-0.601283\pi$
$313$	8.73607	−	6.34712i	0.493792	−	0.358761i	0.806641	+	0.591042i	$0.201283\pi$
$314$	−2.23607	+	1.62460i	−0.126189	+	0.0916814i
$315$	0.236068	+	0.726543i	0.0133009	+	0.0409360i
$316$	−0.381966	+	1.17557i	−0.0214873	+	0.0661310i
$317$	−9.70820	−	7.05342i	−0.545267	−	0.396160i	0.280770	−	0.959775i	$-0.409410\pi$
$317$	−9.70820	−	7.05342i	−0.545267	−	0.396160i	−0.826037	+	0.563615i	$0.809410\pi$
$318$	8.00000			0.448618
$319$	9.88854	−	24.6215i	0.553652	−	1.37854i
$320$	2.00000			0.111803
$321$	−9.59017	−	6.96767i	−0.535271	−	0.388897i
$322$	2.61803	−	8.05748i	0.145897	−	0.449026i
$323$	0.263932	+	0.812299i	0.0146856	+	0.0451975i
$324$	6.23607	−	4.53077i	0.346448	−	0.251709i
$325$	2.61803	−	1.90211i	0.145222	−	0.105510i
$326$	−7.19098	−	22.1316i	−0.398272	−	1.22575i
$327$	5.09017	−	15.6659i	0.281487	−	0.866328i
$328$	0.690983	+	0.502029i	0.0381532	+	0.0277199i
$329$	−1.70820			−0.0941763
$330$	9.09017	−	5.70634i	0.500397	−	0.314124i
$331$	−4.27051			−0.234728			−0.117364	−	0.993089i	$-0.537444\pi$
$331$	−4.27051			−0.234728			−0.117364	+	0.993089i	$0.537444\pi$
$332$	10.5451	+	7.66145i	0.578737	+	0.420477i
$333$	0.909830	−	2.80017i	0.0498584	−	0.153448i
$334$	−5.09017	−	15.6659i	−0.278522	−	0.857202i
$335$	−1.76393	+	1.28157i	−0.0963739	+	0.0700197i
$336$	−1.30902	+	0.951057i	−0.0714127	+	0.0518844i
$337$	0.371323	+	1.14281i	0.0202272	+	0.0622531i	0.960661	−	0.277725i	$-0.0895804\pi$
$337$	0.371323	+	1.14281i	0.0202272	+	0.0622531i	−0.940433	+	0.339978i	$0.889580\pi$
$338$	0.781153	−	2.40414i	0.0424891	−	0.130768i
$339$	6.04508	+	4.39201i	0.328324	+	0.238541i
$340$	−11.7082			−0.634967
$341$	3.61803	+	14.3844i	0.195928	+	0.778957i
$342$	−0.0557281			−0.00301343
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	1.50000	−	4.61653i	0.0808746	−	0.248906i
$345$	−8.47214	−	26.0746i	−0.456124	−	1.40381i
$346$	1.85410	−	1.34708i	0.0996771	−	0.0724197i
$347$	−9.82624	+	7.13918i	−0.527500	+	0.383251i	−0.819422	−	0.573191i	$-0.805705\pi$
$347$	−9.82624	+	7.13918i	−0.527500	+	0.383251i	0.291922	+	0.956442i	$0.405705\pi$
$348$	4.00000	+	12.3107i	0.214423	+	0.659925i
$349$	−1.41641	+	4.35926i	−0.0758186	+	0.233346i	−0.981782	−	0.190010i	$-0.939148\pi$
$349$	−1.41641	+	4.35926i	−0.0758186	+	0.233346i	0.905964	+	0.423356i	$0.139148\pi$
$350$	0.809017	+	0.587785i	0.0432438	+	0.0314184i
$351$	17.7082			0.945194
$352$	−2.54508	−	2.12663i	−0.135653	−	0.113350i
$353$	1.27051			0.0676224			0.0338112	−	0.999428i	$-0.489236\pi$
$353$	1.27051			0.0676224			0.0338112	+	0.999428i	$0.489236\pi$
$354$	−5.42705	−	3.94298i	−0.288445	−	0.209567i
$355$	6.47214	−	19.9192i	0.343505	−	1.05720i
$356$	−4.73607	−	14.5761i	−0.251011	−	0.772533i
$357$	7.66312	−	5.56758i	0.405575	−	0.294668i
$358$	−19.8262	+	14.4046i	−1.04785	+	0.761307i
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	0.987538	+	0.157379i	$0.0503044\pi$
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	−0.706430	+	0.707783i	$0.749696\pi$
$360$	0.236068	−	0.726543i	0.0124419	−	0.0382922i
$361$	15.3541	+	11.1554i	0.808111	+	0.587127i
$362$	18.7639			0.986210
$363$	−17.6353	−	2.40414i	−0.925611	−	0.126185i
$364$	−3.23607			−0.169616
$365$	3.85410	+	2.80017i	0.201733	+	0.146568i
$366$	3.23607	−	9.95959i	0.169152	−	0.520596i
$367$	−3.70820	−	11.4127i	−0.193567	−	0.595737i	−0.999990	−	0.00439874i	$-0.998600\pi$
$367$	−3.70820	−	11.4127i	−0.193567	−	0.595737i	0.806424	−	0.591338i	$-0.201400\pi$
$368$	−6.85410	+	4.97980i	−0.357295	+	0.259590i
$369$	0.263932	−	0.191758i	0.0137398	−	0.00998251i
$370$	4.76393	+	14.6619i	0.247665	+	0.762235i
$371$	−1.52786	+	4.70228i	−0.0793227	+	0.244130i
$372$	−5.85410	−	4.25325i	−0.303521	−	0.220521i
$373$	30.4721			1.57779			0.788894	−	0.614530i	$-0.210654\pi$
$373$	30.4721			1.57779			0.788894	+	0.614530i	$0.210654\pi$
$374$	14.8992	+	12.4495i	0.770419	+	0.643748i
$375$	19.4164			1.00266
$376$	1.38197	+	1.00406i	0.0712695	+	0.0517803i
$377$	−8.00000	+	24.6215i	−0.412021	+	1.26807i
$378$	1.69098	+	5.20431i	0.0869748	+	0.267681i
$379$	10.3992	−	7.55545i	0.534170	−	0.388097i	−0.287745	−	0.957707i	$-0.592906\pi$
$379$	10.3992	−	7.55545i	0.534170	−	0.388097i	0.821915	+	0.569610i	$0.192906\pi$
$380$	0.236068	−	0.171513i	0.0121100	−	0.00879845i
$381$	4.38197	+	13.4863i	0.224495	+	0.690924i
$382$	−3.85410	+	11.8617i	−0.197193	+	0.606898i
$383$	−2.70820	−	1.96763i	−0.138383	−	0.100541i	0.516440	−	0.856323i	$-0.327257\pi$
$383$	−2.70820	−	1.96763i	−0.138383	−	0.100541i	−0.654823	+	0.755782i	$0.727257\pi$
$384$	1.61803			0.0825700
$385$	1.61803	+	6.43288i	0.0824626	+	0.327850i
$386$	−17.4164			−0.886472
$387$	−1.50000	−	1.08981i	−0.0762493	−	0.0553983i
$388$	−0.972136	+	2.99193i	−0.0493527	+	0.151892i
$389$	2.00000	+	6.15537i	0.101404	+	0.312089i	0.988870	−	0.148784i	$-0.0475360\pi$
$389$	2.00000	+	6.15537i	0.101404	+	0.312089i	−0.887466	+	0.460874i	$0.847536\pi$
$390$	−8.47214	+	6.15537i	−0.429003	+	0.311689i
$391$	40.1246	−	29.1522i	2.02919	−	1.47429i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	−7.78115	+	23.9479i	−0.392507	+	1.20801i
$394$	−2.85410	−	2.07363i	−0.143788	−	0.104468i
$395$	−2.47214			−0.124387
$396$	−1.07295	+	0.673542i	−0.0539177	+	0.0338468i
$397$	−31.5967			−1.58580			−0.792898	−	0.609355i	$-0.791429\pi$
$397$	−31.5967			−1.58580			−0.792898	+	0.609355i	$0.791429\pi$
$398$	−16.3262	−	11.8617i	−0.818360	−	0.594574i
$399$	−0.0729490	+	0.224514i	−0.00365202	+	0.0112398i
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	−3.78115	+	2.74717i	−0.188822	+	0.137187i	−0.678180	−	0.734896i	$-0.737231\pi$
$401$	−3.78115	+	2.74717i	−0.188822	+	0.137187i	0.489358	+	0.872083i	$0.337231\pi$
$402$	−1.42705	+	1.03681i	−0.0711748	+	0.0517115i
$403$	−4.47214	−	13.7638i	−0.222773	−	0.685625i
$404$	−5.76393	+	17.7396i	−0.286766	+	0.882576i
$405$	12.4721	+	9.06154i	0.619745	+	0.450271i
$406$	−8.00000			−0.397033
$407$	9.52786	−	23.7234i	0.472279	−	1.17593i
$408$	−9.47214			−0.468941
$409$	−14.8541	−	10.7921i	−0.734488	−	0.533637i	0.156492	−	0.987679i	$-0.449981\pi$
$409$	−14.8541	−	10.7921i	−0.734488	−	0.533637i	−0.890980	+	0.454042i	$0.849981\pi$
$410$	−0.527864	+	1.62460i	−0.0260693	+	0.0802332i
$411$	9.66312	+	29.7400i	0.476647	+	1.46697i
$412$	7.85410	−	5.70634i	0.386944	−	0.281131i
$413$	3.35410	−	2.43690i	0.165045	−	0.119912i
$414$	1.00000	+	3.07768i	0.0491473	+	0.151260i
$415$	−8.05573	+	24.7930i	−0.395440	+	1.21704i
$416$	2.61803	+	1.90211i	0.128360	+	0.0932588i
$417$	23.4164			1.14671
$418$	−0.482779	−	0.0327561i	−0.0236135	−	0.00160216i
$419$	11.5066			0.562133			0.281067	−	0.959688i	$-0.409312\pi$
$419$	11.5066			0.562133			0.281067	+	0.959688i	$0.409312\pi$
$420$	−2.61803	−	1.90211i	−0.127747	−	0.0928136i
$421$	−1.38197	+	4.25325i	−0.0673529	+	0.207291i	−0.979068	−	0.203531i	$-0.934758\pi$
$421$	−1.38197	+	4.25325i	−0.0673529	+	0.207291i	0.911716	+	0.410822i	$0.134758\pi$
$422$	4.91641	+	15.1311i	0.239327	+	0.736573i
$423$	0.527864	−	0.383516i	0.0256656	−	0.0186472i
$424$	4.00000	−	2.90617i	0.194257	−	0.141136i
$425$	1.80902	+	5.56758i	0.0877502	+	0.270067i
$426$	5.23607	−	16.1150i	0.253688	−	0.780772i
$427$	5.23607	+	3.80423i	0.253391	+	0.184099i
$428$	−7.32624			−0.354127
$429$	17.3262	+	1.17557i	0.836519	+	0.0567571i
$430$	9.70820			0.468171
$431$	−19.9443	−	14.4904i	−0.960682	−	0.697976i	−0.00737279	−	0.999973i	$-0.502347\pi$
$431$	−19.9443	−	14.4904i	−0.960682	−	0.697976i	−0.953309	+	0.301997i	$0.902347\pi$
$432$	1.69098	−	5.20431i	0.0813575	−	0.250393i
$433$	2.01064	+	6.18812i	0.0966253	+	0.297382i	0.987674	−	0.156526i	$-0.0500294\pi$
$433$	2.01064	+	6.18812i	0.0966253	+	0.297382i	−0.891049	+	0.453908i	$0.850029\pi$
$434$	3.61803	−	2.62866i	0.173671	−	0.126180i
$435$	−20.9443	+	15.2169i	−1.00420	+	0.729595i
$436$	−3.14590	−	9.68208i	−0.150661	−	0.463687i
$437$	−0.381966	+	1.17557i	−0.0182719	+	0.0562352i
$438$	3.11803	+	2.26538i	0.148985	+	0.108244i
$439$	−16.9443			−0.808706			−0.404353	−	0.914603i	$-0.632503\pi$
$439$	−16.9443			−0.808706			−0.404353	+	0.914603i	$0.632503\pi$
$440$	2.47214	−	6.15537i	0.117854	−	0.293446i
$441$	−0.381966			−0.0181889
$442$	−15.3262	−	11.1352i	−0.728995	−	0.529646i
$443$	9.91641	−	30.5196i	0.471143	−	1.45003i	−0.379947	−	0.925008i	$-0.624058\pi$
$443$	9.91641	−	30.5196i	0.471143	−	1.45003i	0.851090	−	0.525020i	$-0.175942\pi$
$444$	3.85410	+	11.8617i	0.182908	+	0.562932i
$445$	24.7984	−	18.0171i	1.17556	−	0.854091i
$446$	−14.0902	+	10.2371i	−0.667189	+	0.484741i
$447$	5.38197	+	16.5640i	0.254558	+	0.783450i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	−15.9721	−	11.6044i	−0.753772	−	0.547647i	0.143222	−	0.989691i	$-0.454254\pi$
$449$	−15.9721	−	11.6044i	−0.753772	−	0.547647i	−0.896994	+	0.442043i	$0.854254\pi$
$450$	−0.381966			−0.0180061
$451$	2.39919	−	1.50609i	0.112973	−	0.0709188i
$452$	4.61803			0.217214
$453$	−3.00000	−	2.17963i	−0.140952	−	0.102408i
$454$	−8.42705	+	25.9358i	−0.395501	+	1.21723i
$455$	−2.00000	−	6.15537i	−0.0937614	−	0.288568i
$456$	0.190983	−	0.138757i	0.00894360	−	0.00649790i
$457$	−30.7254	+	22.3233i	−1.43727	+	1.04424i	−0.448672	+	0.893697i	$0.648103\pi$
$457$	−30.7254	+	22.3233i	−1.43727	+	1.04424i	−0.988603	+	0.150544i	$0.951897\pi$
$458$	7.03444	+	21.6498i	0.328698	+	1.01163i
$459$	−9.89919	+	30.4666i	−0.462054	+	1.42206i
$460$	−13.7082	−	9.95959i	−0.639148	−	0.464368i
$461$	−41.0132			−1.91017			−0.955087	−	0.296327i	$-0.904238\pi$
$461$	−41.0132			−1.91017			−0.955087	+	0.296327i	$0.904238\pi$
$462$	1.30902	+	5.20431i	0.0609010	+	0.242126i
$463$	24.7639			1.15088			0.575439	−	0.817845i	$-0.304831\pi$
$463$	24.7639			1.15088			0.575439	+	0.817845i	$0.304831\pi$
$464$	6.47214	+	4.70228i	0.300461	+	0.218298i
$465$	4.47214	−	13.7638i	0.207390	−	0.638282i
$466$	−2.44427	−	7.52270i	−0.113229	−	0.348482i
$467$	−17.7082	+	12.8658i	−0.819438	+	0.595357i	−0.916551	−	0.399917i	$-0.869039\pi$
$467$	−17.7082	+	12.8658i	−0.819438	+	0.595357i	0.0971135	+	0.995273i	$0.469039\pi$
$468$	1.00000	−	0.726543i	0.0462250	−	0.0335844i
$469$	−0.336881	−	1.03681i	−0.0155557	−	0.0478756i
$470$	−1.05573	+	3.24920i	−0.0486971	+	0.149874i
$471$	−3.61803	−	2.62866i	−0.166710	−	0.121122i
$472$	−4.14590			−0.190830
$473$	−12.3541	−	10.3229i	−0.568042	−	0.474646i
$474$	−2.00000			−0.0918630
$475$	−0.118034	−	0.0857567i	−0.00541577	−	0.00393479i
$476$	1.80902	−	5.56758i	0.0829162	−	0.255190i
$477$	−0.583592	−	1.79611i	−0.0267208	−	0.0822383i
$478$	0.236068	−	0.171513i	0.0107975	−	0.00784484i
$479$	7.00000	−	5.08580i	0.319838	−	0.232376i	−0.416268	−	0.909242i	$-0.636662\pi$
$479$	7.00000	−	5.08580i	0.319838	−	0.232376i	0.736106	+	0.676866i	$0.236662\pi$
$480$	1.00000	+	3.07768i	0.0456435	+	0.140476i
$481$	−7.70820	+	23.7234i	−0.351464	+	1.08169i
$482$	−5.50000	−	3.99598i	−0.250518	−	0.182012i
$483$	13.7082			0.623745
$484$	−9.69098	+	5.20431i	−0.440499	+	0.236560i
$485$	−6.29180			−0.285696
$486$	−3.19098	−	2.31838i	−0.144746	−	0.105164i
$487$	−5.96556	+	18.3601i	−0.270325	+	0.831976i	0.720093	+	0.693877i	$0.244099\pi$
$487$	−5.96556	+	18.3601i	−0.270325	+	0.831976i	−0.990419	+	0.138098i	$0.955901\pi$
$488$	−2.00000	−	6.15537i	−0.0905357	−	0.278640i
$489$	30.4615	−	22.1316i	1.37752	−	1.00082i
$490$	1.61803	−	1.17557i	0.0730953	−	0.0531069i
$491$	−5.50000	−	16.9273i	−0.248212	−	0.763917i	−0.995092	−	0.0989578i	$-0.968449\pi$
$491$	−5.50000	−	16.9273i	−0.248212	−	0.763917i	0.746880	−	0.664959i	$-0.231551\pi$
$492$	−0.427051	+	1.31433i	−0.0192529	+	0.0592545i
$493$	−37.8885	−	27.5276i	−1.70641	−	1.23978i
$494$	0.472136			0.0212424
$495$	−1.94427	−	1.62460i	−0.0873885	−	0.0730203i
$496$	−4.47214			−0.200805
$497$	8.47214	+	6.15537i	0.380027	+	0.276106i
$498$	−6.51722	+	20.0579i	−0.292044	+	0.898818i
$499$	8.73607	+	26.8869i	0.391080	+	1.20362i	0.931972	+	0.362529i	$0.118087\pi$
$499$	8.73607	+	26.8869i	0.391080	+	1.20362i	−0.540892	+	0.841092i	$0.681913\pi$
$500$	9.70820	−	7.05342i	0.434164	−	0.315439i
$501$	21.5623	−	15.6659i	0.963333	−	0.699902i
$502$	1.52786	+	4.70228i	0.0681919	+	0.209873i
$503$	6.67376	−	20.5397i	0.297568	−	0.915821i	−0.684778	−	0.728751i	$-0.740101\pi$
$503$	6.67376	−	20.5397i	0.297568	−	0.915821i	0.982347	−	0.187070i	$-0.0598990\pi$
$504$	0.309017	+	0.224514i	0.0137647	+	0.0100006i
$505$	−37.3050			−1.66005
$506$	6.85410	+	27.2501i	0.304702	+	1.21142i
$507$	4.09017			0.181651
$508$	7.09017	+	5.15131i	0.314575	+	0.228552i
$509$	6.09017	−	18.7436i	0.269942	−	0.830796i	−0.720571	−	0.693381i	$-0.756120\pi$
$509$	6.09017	−	18.7436i	0.269942	−	0.830796i	0.990513	−	0.137415i	$-0.0438795\pi$
$510$	−5.85410	−	18.0171i	−0.259224	−	0.797809i
$511$	−1.92705	+	1.40008i	−0.0852477	+	0.0619361i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−0.246711	−	0.759299i	−0.0108926	−	0.0335239i
$514$	−7.91641	+	24.3642i	−0.349178	+	1.07466i
$515$	15.7082	+	11.4127i	0.692186	+	0.502903i
$516$	7.85410			0.345758
$517$	4.79837	−	3.01217i	0.211032	−	0.132475i
$518$	−7.70820			−0.338679
$519$	3.00000	+	2.17963i	0.131685	+	0.0956750i
$520$	−2.00000	+	6.15537i	−0.0877058	+	0.269931i
$521$	−1.04508	−	3.21644i	−0.0457860	−	0.140915i	0.925550	−	0.378625i	$-0.123603\pi$
$521$	−1.04508	−	3.21644i	−0.0457860	−	0.140915i	−0.971336	+	0.237710i	$0.923603\pi$
$522$	2.47214	−	1.79611i	0.108202	−	0.0786137i
$523$	−7.88197	+	5.72658i	−0.344654	+	0.250406i	−0.746623	−	0.665247i	$-0.768326\pi$
$523$	−7.88197	+	5.72658i	−0.344654	+	0.250406i	0.401969	+	0.915653i	$0.368326\pi$
$524$	4.80902	+	14.8006i	0.210083	+	0.646569i
$525$	−0.500000	+	1.53884i	−0.0218218	+	0.0671606i
$526$	−10.4721	−	7.60845i	−0.456607	−	0.331744i
$527$	26.1803			1.14043
$528$	2.00000	−	4.97980i	0.0870388	−	0.216718i
$529$	48.7771			2.12074
$530$	8.00000	+	5.81234i	0.347498	+	0.252472i
$531$	−0.489357	+	1.50609i	−0.0212363	+	0.0653585i
$532$	0.0450850	+	0.138757i	0.00195468	+	0.00601589i
$533$	−2.23607	+	1.62460i	−0.0968549	+	0.0703692i
$534$	20.0623	−	14.5761i	0.868181	−	0.630770i
$535$	−4.52786	−	13.9353i	−0.195757	−	0.602477i
$536$	−0.336881	+	1.03681i	−0.0145510	+	0.0447835i
$537$	−32.0795	−	23.3071i	−1.38433	−	1.00578i
$538$	2.58359			0.111387
$539$	−3.30902	−	0.224514i	−0.142529	−	0.00967050i
$540$	10.9443			0.470966
$541$	23.6525	+	17.1845i	1.01690	+	0.738821i	0.965645	−	0.259865i	$-0.0836781\pi$
$541$	23.6525	+	17.1845i	1.01690	+	0.738821i	0.0512544	+	0.998686i	$0.483678\pi$
$542$	5.76393	−	17.7396i	0.247582	−	0.761979i
$543$	9.38197	+	28.8747i	0.402619	+	1.23913i
$544$	−4.73607	+	3.44095i	−0.203057	+	0.147530i
$545$	16.4721	−	11.9677i	0.705589	−	0.512640i
$546$	−1.61803	−	4.97980i	−0.0692455	−	0.213116i
$547$	2.71885	−	8.36775i	0.116250	−	0.357779i	−0.875956	−	0.482391i	$-0.839769\pi$
$547$	2.71885	−	8.36775i	0.116250	−	0.357779i	0.992206	+	0.124612i	$0.0397685\pi$
$548$	15.6353	+	11.3597i	0.667905	+	0.485261i
$549$	−2.47214			−0.105508
$550$	−3.30902	−	0.224514i	−0.141097	−	0.00957331i
$551$	1.16718			0.0497237
$552$	−11.0902	−	8.05748i	−0.472029	−	0.342949i
$553$	0.381966	−	1.17557i	0.0162428	−	0.0499903i
$554$	−7.18034	−	22.0988i	−0.305063	−	0.938889i
$555$	−20.1803	+	14.6619i	−0.856608	+	0.622362i
$556$	11.7082	−	8.50651i	0.496538	−	0.360756i
$557$	5.52786	+	17.0130i	0.234223	+	0.720865i	0.997224	+	0.0744666i	$0.0237254\pi$
$557$	5.52786	+	17.0130i	0.234223	+	0.720865i	−0.763000	+	0.646398i	$0.776275\pi$
$558$	−0.527864	+	1.62460i	−0.0223463	+	0.0687747i
$559$	12.7082	+	9.23305i	0.537500	+	0.390516i
$560$	−2.00000			−0.0845154
$561$	−11.7082	+	29.1522i	−0.494321	+	1.23081i
$562$	−9.79837			−0.413319
$563$	18.5451	+	13.4738i	0.781582	+	0.567853i	0.905453	−	0.424446i	$-0.139531\pi$
$563$	18.5451	+	13.4738i	0.781582	+	0.567853i	−0.123871	+	0.992298i	$0.539531\pi$
$564$	−0.854102	+	2.62866i	−0.0359642	+	0.110686i
$565$	2.85410	+	8.78402i	0.120073	+	0.369547i
$566$	8.94427	−	6.49839i	0.375956	−	0.273148i
$567$	−6.23607	+	4.53077i	−0.261890	+	0.190274i
$568$	−3.23607	−	9.95959i	−0.135782	−	0.417895i
$569$	13.0451	−	40.1486i	0.546878	−	1.68312i	−0.169603	−	0.985512i	$-0.554249\pi$
$569$	13.0451	−	40.1486i	0.546878	−	1.68312i	0.716481	−	0.697606i	$-0.245751\pi$
$570$	0.381966	+	0.277515i	0.0159988	+	0.0116238i
$571$	18.8328			0.788129			0.394064	−	0.919083i	$-0.371069\pi$
$571$	18.8328			0.788129			0.394064	+	0.919083i	$0.371069\pi$
$572$	9.09017	−	5.70634i	0.380079	−	0.238594i
$573$	−20.1803			−0.843046
$574$	−0.690983	−	0.502029i	−0.0288411	−	0.0209543i
$575$	−2.61803	+	8.05748i	−0.109180	+	0.336020i
$576$	−0.118034	−	0.363271i	−0.00491808	−	0.0151363i
$577$	33.9164	−	24.6417i	1.41196	−	1.02585i	0.418924	−	0.908021i	$-0.362407\pi$
$577$	33.9164	−	24.6417i	1.41196	−	1.02585i	0.993034	−	0.117827i	$-0.0375928\pi$
$578$	13.9721	−	10.1514i	0.581164	−	0.422241i
$579$	−8.70820	−	26.8011i	−0.361901	−	1.11382i
$580$	−4.94427	+	15.2169i	−0.205300	+	0.631848i
$581$	−10.5451	−	7.66145i	−0.437484	−	0.317851i
$582$	−5.09017			−0.210994
$583$	−4.00000	−	15.9030i	−0.165663	−	0.658633i
$584$	2.38197			0.0985665
$585$	2.00000	+	1.45309i	0.0826898	+	0.0600777i
$586$	−8.09017	+	24.8990i	−0.334202	+	1.02857i
$587$	5.66312	+	17.4293i	0.233742	+	0.719384i	0.997286	+	0.0736277i	$0.0234577\pi$
$587$	5.66312	+	17.4293i	0.233742	+	0.719384i	−0.763544	+	0.645756i	$0.776542\pi$
$588$	1.30902	−	0.951057i	0.0539830	−	0.0392209i
$589$	−0.527864	+	0.383516i	−0.0217503	+	0.0158025i
$590$	−2.56231	−	7.88597i	−0.105488	−	0.324660i
$591$	1.76393	−	5.42882i	0.0725585	−	0.223312i
$592$	6.23607	+	4.53077i	0.256301	+	0.186213i
$593$	−11.0902			−0.455419			−0.227709	−	0.973729i	$-0.573124\pi$
$593$	−11.0902			−0.455419			−0.227709	+	0.973729i	$0.573124\pi$
$594$	−13.9271	−	11.6372i	−0.571434	−	0.477480i
$595$	11.7082			0.479990
$596$	8.70820	+	6.32688i	0.356702	+	0.259159i
$597$	10.0902	−	31.0543i	0.412963	−	1.27097i
$598$	−8.47214	−	26.0746i	−0.346451	−	1.06627i
$599$	−2.00000	+	1.45309i	−0.0817178	+	0.0593714i	−0.627894	−	0.778299i	$-0.716083\pi$
$599$	−2.00000	+	1.45309i	−0.0817178	+	0.0593714i	0.546176	+	0.837670i	$0.316083\pi$
$600$	1.30902	−	0.951057i	0.0534404	−	0.0388267i
$601$	−9.79180	−	30.1360i	−0.399416	−	1.22928i	−0.925469	−	0.378823i	$-0.876329\pi$
$601$	−9.79180	−	30.1360i	−0.399416	−	1.22928i	0.526053	−	0.850452i	$-0.323671\pi$
$602$	−1.50000	+	4.61653i	−0.0611354	+	0.188156i
$603$	0.336881	+	0.244758i	0.0137189	+	0.00996733i
$604$	−2.29180			−0.0932519
$605$	−15.8885	−	15.2169i	−0.645961	−	0.618655i
$606$	−30.1803			−1.22599
$607$	−12.0902	−	8.78402i	−0.490725	−	0.356532i	0.314738	−	0.949179i	$-0.398083\pi$
$607$	−12.0902	−	8.78402i	−0.490725	−	0.356532i	−0.805463	+	0.592646i	$0.798083\pi$
$608$	0.0450850	−	0.138757i	0.00182844	−	0.00562735i
$609$	−4.00000	−	12.3107i	−0.162088	−	0.498856i
$610$	10.4721	−	7.60845i	0.424004	−	0.308057i
$611$	−4.47214	+	3.24920i	−0.180923	+	0.131448i
$612$	0.690983	+	2.12663i	0.0279313	+	0.0859638i
$613$	−4.38197	+	13.4863i	−0.176986	+	0.544707i	−0.999719	−	0.0237218i	$-0.992448\pi$
$613$	−4.38197	+	13.4863i	−0.176986	+	0.544707i	0.822733	+	0.568429i	$0.192448\pi$
$614$	−14.2533	−	10.3556i	−0.575216	−	0.417919i
$615$	−2.76393			−0.111452
$616$	2.54508	+	2.12663i	0.102544	+	0.0856842i
$617$	−39.1591			−1.57648			−0.788242	−	0.615365i	$-0.789009\pi$
$617$	−39.1591			−1.57648			−0.788242	+	0.615365i	$0.789009\pi$
$618$	12.7082	+	9.23305i	0.511199	+	0.371408i
$619$	−4.33688	+	13.3475i	−0.174314	+	0.536483i	−0.999601	−	0.0282296i	$-0.991013\pi$
$619$	−4.33688	+	13.3475i	−0.174314	+	0.536483i	0.825287	+	0.564713i	$0.191013\pi$
$620$	−2.76393	−	8.50651i	−0.111002	−	0.341630i
$621$	−37.5066	+	27.2501i	−1.50509	+	1.09351i
$622$	−3.47214	+	2.52265i	−0.139220	+	0.101149i
$623$	4.73607	+	14.5761i	0.189747	+	0.583980i
$624$	−1.61803	+	4.97980i	−0.0647732	+	0.199351i
$625$	15.3713	+	11.1679i	0.614853	+	0.446717i
$626$	10.7984			0.431590
$627$	−0.190983	−	0.759299i	−0.00762713	−	0.0303235i
$628$	−2.76393			−0.110293
$629$	−36.5066	−	26.5236i	−1.45561	−	1.05756i
$630$	−0.236068	+	0.726543i	−0.00940517	+	0.0289461i
$631$	10.8885	+	33.5115i	0.433466	+	1.33407i	0.894650	+	0.446767i	$0.147425\pi$
$631$	10.8885	+	33.5115i	0.433466	+	1.33407i	−0.461184	+	0.887304i	$0.652575\pi$
$632$	−1.00000	+	0.726543i	−0.0397779	+	0.0289003i
$633$	−20.8262	+	15.1311i	−0.827769	+	0.601409i
$634$	−3.70820	−	11.4127i	−0.147272	−	0.453255i
$635$	−5.41641	+	16.6700i	−0.214944	+	0.661528i
$636$	6.47214	+	4.70228i	0.256637	+	0.186458i
$637$	3.23607			0.128218
$638$	22.4721	−	14.1068i	0.889680	−	0.558495i
$639$	−4.00000			−0.158238
$640$	1.61803	+	1.17557i	0.0639584	+	0.0464685i
$641$	7.26393	−	22.3561i	0.286908	−	0.883012i	−0.698912	−	0.715207i	$-0.746332\pi$
$641$	7.26393	−	22.3561i	0.286908	−	0.883012i	0.985820	−	0.167805i	$-0.0536678\pi$
$642$	−3.66312	−	11.2739i	−0.144572	−	0.444946i
$643$	11.6353	−	8.45351i	0.458850	−	0.333374i	−0.334230	−	0.942491i	$-0.608476\pi$
$643$	11.6353	−	8.45351i	0.458850	−	0.333374i	0.793080	+	0.609118i	$0.208476\pi$
$644$	6.85410	−	4.97980i	0.270089	−	0.196231i
$645$	4.85410	+	14.9394i	0.191130	+	0.588238i
$646$	−0.263932	+	0.812299i	−0.0103843	+	0.0319595i
$647$	30.2705	+	21.9928i	1.19006	+	0.864627i	0.993270	−	0.115820i	$-0.0369495\pi$
$647$	30.2705	+	21.9928i	1.19006	+	0.864627i	0.196786	+	0.980446i	$0.436949\pi$
$648$	7.70820			0.302807
$649$	−5.12461	+	12.7598i	−0.201159	+	0.500864i
$650$	3.23607			0.126929
$651$	5.85410	+	4.25325i	0.229440	+	0.166698i
$652$	7.19098	−	22.1316i	0.281621	−	0.866739i
$653$	−1.96556	−	6.04937i	−0.0769182	−	0.236730i	0.905203	−	0.424979i	$-0.139719\pi$
$653$	−1.96556	−	6.04937i	−0.0769182	−	0.236730i	−0.982121	+	0.188249i	$0.939719\pi$
$654$	13.3262	−	9.68208i	0.521097	−	0.378599i
$655$	−25.1803	+	18.2946i	−0.983877	+	0.714829i
$656$	0.263932	+	0.812299i	0.0103048	+	0.0317150i
$657$	0.281153	−	0.865300i	0.0109688	−	0.0337586i
$658$	−1.38197	−	1.00406i	−0.0538746	−	0.0391422i
$659$	16.5066			0.643005			0.321502	−	0.946909i	$-0.395812\pi$
$659$	16.5066			0.643005			0.321502	+	0.946909i	$0.395812\pi$
$660$	10.7082	+	0.726543i	0.416816	+	0.0282806i
$661$	16.4721			0.640692			0.320346	−	0.947301i	$-0.396201\pi$
$661$	16.4721			0.640692			0.320346	+	0.947301i	$0.396201\pi$
$662$	−3.45492	−	2.51014i	−0.134279	−	0.0975595i
$663$	9.47214	−	29.1522i	0.367867	−	1.13218i
$664$	4.02786	+	12.3965i	0.156311	+	0.481077i
$665$	−0.236068	+	0.171513i	−0.00915432	+	0.00665101i
$666$	2.38197	−	1.73060i	0.0922993	−	0.0670594i
$667$	−20.9443	−	64.4598i	−0.810965	−	2.49590i
$668$	5.09017	−	15.6659i	0.196945	−	0.606133i
$669$	−22.7984	−	16.5640i	−0.881436	−	0.640401i
$670$	−2.18034			−0.0842339
$671$	−21.4164	−	1.45309i	−0.826771	−	0.0560957i
$672$	−1.61803			−0.0624170
$673$	37.6246	+	27.3359i	1.45032	+	1.05372i	0.985756	+	0.168182i	$0.0537898\pi$
$673$	37.6246	+	27.3359i	1.45032	+	1.05372i	0.464566	+	0.885538i	$0.346210\pi$
$674$	−0.371323	+	1.14281i	−0.0143028	+	0.0440196i
$675$	−1.69098	−	5.20431i	−0.0650860	−	0.200314i
$676$	2.04508	−	1.48584i	0.0786571	−	0.0571477i
$677$	29.0344	−	21.0948i	1.11588	−	0.810737i	0.132304	−	0.991209i	$-0.457762\pi$
$677$	29.0344	−	21.0948i	1.11588	−	0.810737i	0.983580	+	0.180472i	$0.0577625\pi$
$678$	2.30902	+	7.10642i	0.0886773	+	0.272921i
$679$	0.972136	−	2.99193i	0.0373072	−	0.114820i
$680$	−9.47214	−	6.88191i	−0.363240	−	0.263909i
$681$	−44.1246			−1.69086
$682$	−5.52786	+	13.7638i	−0.211673	+	0.527044i
$683$	24.3607			0.932136			0.466068	−	0.884749i	$-0.345670\pi$
$683$	24.3607			0.932136			0.466068	+	0.884749i	$0.345670\pi$
$684$	−0.0450850	−	0.0327561i	−0.00172387	−	0.00125246i
$685$	−11.9443	+	36.7607i	−0.456367	+	1.40455i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	−29.7984	+	21.6498i	−1.13688	+	0.825991i
$688$	3.92705	−	2.85317i	0.149717	−	0.108776i
$689$	4.94427	+	15.2169i	0.188362	+	0.579718i
$690$	8.47214	−	26.0746i	0.322529	−	0.992641i
$691$	−1.88197	−	1.36733i	−0.0715934	−	0.0520156i	0.551413	−	0.834232i	$-0.314089\pi$
$691$	−1.88197	−	1.36733i	−0.0715934	−	0.0520156i	−0.623006	+	0.782217i	$0.714089\pi$
$692$	2.29180			0.0871210
$693$	1.07295	−	0.673542i	0.0407580	−	0.0255857i
$694$	−12.1459			−0.461052
$695$	23.4164	+	17.0130i	0.888235	+	0.645340i
$696$	−4.00000	+	12.3107i	−0.151620	+	0.466637i
$697$	−1.54508	−	4.75528i	−0.0585243	−	0.180119i
$698$	−3.70820	+	2.69417i	−0.140358	+	0.101976i
$699$	10.3541	−	7.52270i	0.391628	−	0.284534i
$700$	0.309017	+	0.951057i	0.0116797	+	0.0359466i
$701$	15.1803	−	46.7203i	0.573354	−	1.76460i	−0.0683649	−	0.997660i	$-0.521778\pi$
$701$	15.1803	−	46.7203i	0.573354	−	1.76460i	0.641718	−	0.766940i	$-0.278222\pi$
$702$	14.3262	+	10.4086i	0.540709	+	0.392848i
$703$	1.12461			0.0424155
$704$	−0.809017	−	3.21644i	−0.0304910	−	0.121224i
$705$	−5.52786			−0.208191
$706$	1.02786	+	0.746787i	0.0386842	+	0.0281057i
$707$	5.76393	−	17.7396i	0.216775	−	0.667165i
$708$	−2.07295	−	6.37988i	−0.0779062	−	0.239771i
$709$	−7.56231	+	5.49434i	−0.284008	+	0.206344i	−0.720664	−	0.693285i	$-0.756163\pi$
$709$	−7.56231	+	5.49434i	−0.284008	+	0.206344i	0.436656	+	0.899629i	$0.356163\pi$
$710$	16.9443	−	12.3107i	0.635907	−	0.462014i
$711$	0.145898	+	0.449028i	0.00547160	+	0.0168399i
$712$	4.73607	−	14.5761i	0.177492	−	0.546263i
$713$	30.6525	+	22.2703i	1.14794	+	0.834030i
$714$	9.47214			0.354486
$715$	16.4721	+	13.7638i	0.616023	+	0.514738i
$716$	−24.5066			−0.915854
$717$	0.381966	+	0.277515i	0.0142648	+	0.0103640i
$718$	−5.32624	+	16.3925i	−0.198773	+	0.611762i
$719$	1.85410	+	5.70634i	0.0691463	+	0.212811i	0.979659	−	0.200672i	$-0.0643124\pi$
$719$	1.85410	+	5.70634i	0.0691463	+	0.212811i	−0.910512	+	0.413482i	$0.864312\pi$
$720$	0.618034	−	0.449028i	0.0230328	−	0.0167343i
$721$	−7.85410	+	5.70634i	−0.292502	+	0.212515i
$722$	5.86475	+	18.0498i	0.218263	+	0.671745i
$723$	3.39919	−	10.4616i	0.126417	−	0.389072i
$724$	15.1803	+	11.0292i	0.564173	+	0.409896i
$725$	8.00000			0.297113
$726$	−12.8541	−	12.3107i	−0.477060	−	0.456894i
$727$	−29.5279			−1.09513			−0.547564	−	0.836764i	$-0.684445\pi$
$727$	−29.5279			−1.09513			−0.547564	+	0.836764i	$0.684445\pi$
$728$	−2.61803	−	1.90211i	−0.0970308	−	0.0704970i
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$	1.47214	+	4.53077i	0.0544862	+	0.167691i
$731$	−22.9894	+	16.7027i	−0.850292	+	0.617773i
$732$	8.47214	−	6.15537i	0.313139	−	0.227509i
$733$	7.00000	+	21.5438i	0.258551	+	0.795738i	0.993109	+	0.117192i	$0.0373894\pi$
$733$	7.00000	+	21.5438i	0.258551	+	0.795738i	−0.734558	+	0.678546i	$0.762611\pi$
$734$	3.70820	−	11.4127i	0.136872	−	0.421250i
$735$	2.61803	+	1.90211i	0.0965676	+	0.0701605i
$736$	−8.47214			−0.312287
$737$	2.77458	+	2.31838i	0.102203	+	0.0853988i
$738$	0.326238			0.0120090
$739$	−0.354102	−	0.257270i	−0.0130259	−	0.00946383i	0.581253	−	0.813723i	$-0.302563\pi$
$739$	−0.354102	−	0.257270i	−0.0130259	−	0.00946383i	−0.594279	+	0.804259i	$0.702563\pi$
$740$	−4.76393	+	14.6619i	−0.175126	+	0.538981i
$741$	0.236068	+	0.726543i	0.00867217	+	0.0266902i
$742$	−4.00000	+	2.90617i	−0.146845	+	0.106689i
$743$	2.38197	−	1.73060i	0.0873859	−	0.0634895i	−0.543234	−	0.839581i	$-0.682801\pi$
$743$	2.38197	−	1.73060i	0.0873859	−	0.0634895i	0.630620	+	0.776091i	$0.282801\pi$
$744$	−2.23607	−	6.88191i	−0.0819782	−	0.252303i
$745$	−6.65248	+	20.4742i	−0.243728	+	0.750117i
$746$	24.6525	+	17.9111i	0.902591	+	0.655771i
$747$	4.97871			0.182162
$748$	4.73607	+	18.8294i	0.173168	+	0.688470i
$749$	7.32624			0.267695
$750$	15.7082	+	11.4127i	0.573583	+	0.416732i
$751$	−15.2016	+	46.7858i	−0.554715	+	1.70724i	0.141979	+	0.989870i	$0.454653\pi$
$751$	−15.2016	+	46.7858i	−0.554715	+	1.70724i	−0.696694	+	0.717368i	$0.745347\pi$
$752$	0.527864	+	1.62460i	0.0192492	+	0.0592430i
$753$	−6.47214	+	4.70228i	−0.235858	+	0.171361i
$754$	−20.9443	+	15.2169i	−0.762745	+	0.554167i
$755$	−1.41641	−	4.35926i	−0.0515484	−	0.158650i
$756$	−1.69098	+	5.20431i	−0.0615005	+	0.189279i
$757$	−11.3820	−	8.26948i	−0.413685	−	0.300559i	0.361407	−	0.932408i	$-0.382296\pi$
$757$	−11.3820	−	8.26948i	−0.413685	−	0.300559i	−0.775092	+	0.631849i	$0.782296\pi$
$758$	12.8541			0.466882
$759$	−38.5066	+	24.1724i	−1.39770	+	0.877404i
$760$	0.291796			0.0105846
$761$	11.6803	+	8.48626i	0.423412	+	0.307627i	0.779009	−	0.627012i	$-0.215723\pi$
$761$	11.6803	+	8.48626i	0.423412	+	0.307627i	−0.355597	+	0.934639i	$0.615723\pi$
$762$	−4.38197	+	13.4863i	−0.158742	+	0.488557i
$763$	3.14590	+	9.68208i	0.113889	+	0.350515i
$764$	−10.0902	+	7.33094i	−0.365050	+	0.265224i
$765$	−3.61803	+	2.62866i	−0.130810	+	0.0950392i
$766$	−1.03444	−	3.18368i	−0.0373759	−	0.115031i
$767$	4.14590	−	12.7598i	0.149700	−	0.460728i
$768$	1.30902	+	0.951057i	0.0472351	+	0.0343183i
$769$	−22.5836			−0.814385			−0.407193	−	0.913342i	$-0.633492\pi$
$769$	−22.5836			−0.814385			−0.407193	+	0.913342i	$0.633492\pi$
$770$	−2.47214	+	6.15537i	−0.0890896	+	0.221824i
$771$	−41.4508			−1.49282
$772$	−14.0902	−	10.2371i	−0.507116	−	0.368442i
$773$	−9.52786	+	29.3238i	−0.342693	+	1.05470i	0.620114	+	0.784512i	$0.287087\pi$
$773$	−9.52786	+	29.3238i	−0.342693	+	1.05470i	−0.962807	+	0.270190i	$0.912913\pi$
$774$	−0.572949	−	1.76336i	−0.0205942	−	0.0633825i
$775$	−3.61803	+	2.62866i	−0.129964	+	0.0944241i
$776$	−2.54508	+	1.84911i	−0.0913632	+	0.0663793i
$777$	−3.85410	−	11.8617i	−0.138265	−	0.425536i
$778$	−2.00000	+	6.15537i	−0.0717035	+	0.220681i
$779$	0.100813	+	0.0732450i	0.00361200	+	0.00262427i
$780$	−10.4721			−0.374963
$781$	−34.6525	−	2.35114i	−1.23996	−	0.0841304i
$782$	49.5967			1.77358
$783$	35.4164	+	25.7315i	1.26568	+	0.919570i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	−1.70820	−	5.25731i	−0.0609684	−	0.187641i
$786$	−20.3713	+	14.8006i	−0.726621	+	0.527921i
$787$	−3.35410	+	2.43690i	−0.119561	+	0.0868660i	−0.645959	−	0.763372i	$-0.723542\pi$
$787$	−3.35410	+	2.43690i	−0.119561	+	0.0868660i	0.526398	+	0.850238i	$0.323542\pi$
$788$	−1.09017	−	3.35520i	−0.0388357	−	0.119524i
$789$	6.47214	−	19.9192i	0.230414	−	0.709142i
$790$	−2.00000	−	1.45309i	−0.0711568	−	0.0516984i
$791$	−4.61803			−0.164198
$792$	−1.26393	−	0.0857567i	−0.0449119	−	0.00304723i
$793$	20.9443			0.743753
$794$	−25.5623	−	18.5721i	−0.907172	−	0.659099i
$795$	−4.94427	+	15.2169i	−0.175355	+	0.539688i
$796$	−6.23607	−	19.1926i	−0.221032	−	0.680265i
$797$	−34.6525	+	25.1765i	−1.22745	+	0.891797i	−0.996697	−	0.0812141i	$-0.974120\pi$
$797$	−34.6525	+	25.1765i	−1.22745	+	0.891797i	−0.230757	+	0.973011i	$0.574120\pi$
$798$	−0.190983	+	0.138757i	−0.00676073	+	0.00491195i
$799$	−3.09017	−	9.51057i	−0.109322	−	0.336460i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	−4.73607	−	3.44095i	−0.167341	−	0.121580i
$802$	−4.67376			−0.165036
$803$	2.94427	−	7.33094i	0.103901	−	0.258703i
$804$	−1.76393			−0.0622091
$805$	13.7082	+	9.95959i	0.483151	+	0.351030i
$806$	4.47214	−	13.7638i	0.157524	−	0.484810i
$807$	1.29180	+	3.97574i	0.0454734	+	0.139953i
$808$	−15.0902	+	10.9637i	−0.530870	+	0.385700i
$809$	−0.444272	+	0.322782i	−0.0156198	+	0.0113484i	−0.595568	−	0.803305i	$-0.703073\pi$
$809$	−0.444272	+	0.322782i	−0.0156198	+	0.0113484i	0.579948	+	0.814654i	$0.303073\pi$
$810$	4.76393	+	14.6619i	0.167388	+	0.515166i
$811$	9.61146	−	29.5810i	0.337504	−	1.03873i	−0.627972	−	0.778236i	$-0.716115\pi$
$811$	9.61146	−	29.5810i	0.337504	−	1.03873i	0.965475	−	0.260494i	$-0.0838854\pi$
$812$	−6.47214	−	4.70228i	−0.227127	−	0.165018i
$813$	30.1803			1.05847
$814$	21.6525	−	13.5923i	0.758919	−	0.476410i
$815$	46.5410			1.63026
$816$	−7.66312	−	5.56758i	−0.268263	−	0.194904i
$817$	0.218847	−	0.673542i	0.00765649	−	0.0235643i
$818$	−5.67376	−	17.4620i	−0.198378	−	0.610546i
$819$	−1.00000	+	0.726543i	−0.0349428	+	0.0253875i
$820$	−1.38197	+	1.00406i	−0.0482603	+	0.0350632i
$821$	5.00000	+	15.3884i	0.174501	+	0.537059i	0.999610	−	0.0279139i	$-0.00888643\pi$
$821$	5.00000	+	15.3884i	0.174501	+	0.537059i	−0.825109	+	0.564973i	$0.808886\pi$
$822$	−9.66312	+	29.7400i	−0.337040	+	1.03730i
$823$	−7.00000	−	5.08580i	−0.244005	−	0.177280i	0.459061	−	0.888405i	$-0.348186\pi$
$823$	−7.00000	−	5.08580i	−0.244005	−	0.177280i	−0.703066	+	0.711125i	$0.748186\pi$
$824$	9.70820			0.338201
$825$	−1.30902	−	5.20431i	−0.0455741	−	0.181191i
$826$	4.14590			0.144254
$827$	−5.59017	−	4.06150i	−0.194389	−	0.141232i	0.486333	−	0.873773i	$-0.338334\pi$
$827$	−5.59017	−	4.06150i	−0.194389	−	0.141232i	−0.680723	+	0.732541i	$0.738334\pi$
$828$	−1.00000	+	3.07768i	−0.0347524	+	0.106957i
$829$	1.20163	+	3.69822i	0.0417342	+	0.128445i	0.969753	−	0.244089i	$-0.0784890\pi$
$829$	1.20163	+	3.69822i	0.0417342	+	0.128445i	−0.928019	+	0.372534i	$0.878489\pi$
$830$	−21.0902	+	15.3229i	−0.732050	+	0.531866i
$831$	30.4164	−	22.0988i	1.05513	−	0.766599i
$832$	1.00000	+	3.07768i	0.0346688	+	0.106699i
$833$	−1.80902	+	5.56758i	−0.0626787	+	0.192905i
$834$	18.9443	+	13.7638i	0.655986	+	0.476602i
$835$	32.9443			1.14008
$836$	−0.371323	−	0.310271i	−0.0128425	−	0.0107309i
$837$	−24.4721			−0.845881
$838$	9.30902	+	6.76340i	0.321575	+	0.233638i
$839$	−15.0000	+	46.1653i	−0.517858	+	1.59380i	0.260164	+	0.965564i	$0.416223\pi$
$839$	−15.0000	+	46.1653i	−0.517858	+	1.59380i	−0.778022	+	0.628237i	$0.783777\pi$
$840$	−1.00000	−	3.07768i	−0.0345033	−	0.106190i
$841$	−28.3156	+	20.5725i	−0.976400	+	0.709396i
$842$	−3.61803	+	2.62866i	−0.124686	+	0.0905895i
$843$	−4.89919	−	15.0781i	−0.168737	−	0.519319i
$844$	−4.91641	+	15.1311i	−0.169230	+	0.520836i
$845$	4.09017	+	2.97168i	0.140706	+	0.102229i
$846$	0.652476			0.0224326
$847$	9.69098	−	5.20431i	0.332986	−	0.178822i
$848$	4.94427			0.169787
$849$	14.4721	+	10.5146i	0.496682	+	0.360861i
$850$	−1.80902	+	5.56758i	−0.0620488	+	0.190966i
$851$	−20.1803	−	62.1087i	−0.691773	−	2.12906i
$852$	13.7082	−	9.95959i	0.469635	−	0.341210i
$853$	−22.7082	+	16.4985i	−0.777514	+	0.564897i	−0.904232	−	0.427042i	$-0.859556\pi$
$853$	−22.7082	+	16.4985i	−0.777514	+	0.564897i	0.126718	+	0.991939i	$0.459556\pi$
$854$	2.00000	+	6.15537i	0.0684386	+	0.210632i
$855$	0.0344419	−	0.106001i	0.00117789	−	0.00362516i
$856$	−5.92705	−	4.30625i	−0.202582	−	0.147185i
$857$	−16.0902			−0.549630			−0.274815	−	0.961497i	$-0.588617\pi$
$857$	−16.0902			−0.549630			−0.274815	+	0.961497i	$0.588617\pi$
$858$	13.3262	+	11.1352i	0.454950	+	0.380148i
$859$	25.3820			0.866022			0.433011	−	0.901389i	$-0.357451\pi$
$859$	25.3820			0.866022			0.433011	+	0.901389i	$0.357451\pi$
$860$	7.85410	+	5.70634i	0.267823	+	0.194585i
$861$	0.427051	−	1.31433i	0.0145539	−	0.0447922i
$862$	−7.61803	−	23.4459i	−0.259471	−	0.798570i
$863$	32.5623	−	23.6579i	1.10843	−	0.805324i	0.126018	−	0.992028i	$-0.459780\pi$
$863$	32.5623	−	23.6579i	1.10843	−	0.805324i	0.982416	+	0.186704i	$0.0597804\pi$
$864$	4.42705	−	3.21644i	0.150611	−	0.109426i
$865$	1.41641	+	4.35926i	0.0481593	+	0.148219i
$866$	−2.01064	+	6.18812i	−0.0683244	+	0.210281i
$867$	22.6074	+	16.4252i	0.767787	+	0.557830i
$868$	4.47214			0.151794
$869$	1.00000	+	3.97574i	0.0339227	+	0.134868i
$870$	−25.8885			−0.877704
$871$	−2.85410	−	2.07363i	−0.0967076	−	0.0702622i
$872$	3.14590	−	9.68208i	0.106534	−	0.327877i
$873$	0.371323	+	1.14281i	0.0125674	+	0.0386784i
$874$	−1.00000	+	0.726543i	−0.0338255	+	0.0245757i
$875$	−9.70820	+	7.05342i	−0.328197	+	0.238449i
$876$	1.19098	+	3.66547i	0.0402396	+	0.123845i
$877$	11.2918	−	34.7526i	0.381297	−	1.17351i	−0.557834	−	0.829952i	$-0.688368\pi$
$877$	11.2918	−	34.7526i	0.381297	−	1.17351i	0.939131	−	0.343559i	$-0.111632\pi$
$878$	−13.7082	−	9.95959i	−0.462629	−	0.336120i
$879$	−42.3607			−1.42879
$880$	5.61803	−	3.52671i	0.189384	−	0.118885i
$881$	42.9230			1.44611			0.723056	−	0.690789i	$-0.242737\pi$
$881$	42.9230			1.44611			0.723056	+	0.690789i	$0.242737\pi$
$882$	−0.309017	−	0.224514i	−0.0104051	−	0.00755978i
$883$	7.97214	−	24.5357i	0.268284	−	0.825692i	−0.722635	−	0.691230i	$-0.757069\pi$
$883$	7.97214	−	24.5357i	0.268284	−	0.825692i	0.990919	−	0.134463i	$-0.0429308\pi$
$884$	−5.85410	−	18.0171i	−0.196895	−	0.605980i
$885$	10.8541	−	7.88597i	0.364857	−	0.265084i
$886$	25.9615	−	18.8621i	0.872193	−	0.633686i
$887$	−3.85410	−	11.8617i	−0.129408	−	0.398277i	0.865270	−	0.501306i	$-0.167147\pi$
$887$	−3.85410	−	11.8617i	−0.129408	−	0.398277i	−0.994678	+	0.103028i	$0.967147\pi$
$888$	−3.85410	+	11.8617i	−0.129335	+	0.398053i
$889$	−7.09017	−	5.15131i	−0.237797	−	0.172769i
$890$	30.6525			1.02747
$891$	9.52786	−	23.7234i	0.319195	−	0.794764i
$892$	−17.4164			−0.583144
$893$	0.201626	+	0.146490i	0.00674716	+	0.00490210i
$894$	−5.38197	+	16.5640i	−0.180000	+	0.553983i
$895$	−15.1459	−	46.6143i	−0.506272	−	1.55814i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	35.8885	−	26.0746i	1.19828	−	0.870604i
$898$	−6.10081	−	18.7764i	−0.203587	−	0.626576i
$899$	11.0557	−	34.0260i	0.368729	−	1.13483i
$900$	−0.309017	−	0.224514i	−0.0103006	−	0.00748380i
$901$	−28.9443			−0.964274
$902$	2.82624	+	0.191758i	0.0941034	+	0.00638484i
$903$	−7.85410			−0.261368
$904$	3.73607	+	2.71441i	0.124260	+	0.0902800i
$905$	−11.5967	+	35.6911i	−0.385489	+	1.18641i
$906$	−1.14590	−	3.52671i	−0.0380699	−	0.117167i
$907$	2.40983	−	1.75084i	0.0800171	−	0.0581358i	−0.547058	−	0.837095i	$-0.684252\pi$
$907$	2.40983	−	1.75084i	0.0800171	−	0.0581358i	0.627075	+	0.778959i	$0.284252\pi$
$908$	−22.0623	+	16.0292i	−0.732163	+	0.531948i
$909$	2.20163	+	6.77591i	0.0730233	+	0.224743i
$910$	2.00000	−	6.15537i	0.0662994	−	0.204048i
$911$	20.7984	+	15.1109i	0.689081	+	0.500647i	0.876358	−	0.481661i	$-0.159966\pi$
$911$	20.7984	+	15.1109i	0.689081	+	0.500647i	−0.187277	+	0.982307i	$0.559966\pi$
$912$	0.236068			0.00781699
$913$	43.1312	+	2.92641i	1.42743	+	0.0968502i
$914$	−37.9787			−1.25622
$915$	16.9443	+	12.3107i	0.560160	+	0.406980i
$916$	−7.03444	+	21.6498i	−0.232425	+	0.715329i
$917$	−4.80902	−	14.8006i	−0.158808	−	0.488760i
$918$	−25.9164	+	18.8294i	−0.855369	+	0.621462i
$919$	−22.7082	+	16.4985i	−0.749075	+	0.544235i	−0.895540	−	0.444981i	$-0.853210\pi$
$919$	−22.7082	+	16.4985i	−0.749075	+	0.544235i	0.146465	+	0.989216i	$0.453210\pi$
$920$	−5.23607	−	16.1150i	−0.172628	−	0.531295i
$921$	8.80902	−	27.1114i	0.290267	−	0.893350i
$922$	−33.1803	−	24.1069i	−1.09274	−	0.793919i
$923$	33.8885			1.11546
$924$	−2.00000	+	4.97980i	−0.0657952	+	0.163823i
$925$	7.70820			0.253444
$926$	20.0344	+	14.5559i	0.658373	+	0.478336i
$927$	1.14590	−	3.52671i	0.0376362	−	0.115832i
$928$	2.47214	+	7.60845i	0.0811518	+	0.249760i
$929$	32.6246	−	23.7032i	1.07038	−	0.777676i	0.0943985	−	0.995534i	$-0.469907\pi$
$929$	32.6246	−	23.7032i	1.07038	−	0.777676i	0.975980	+	0.217859i	$0.0699072\pi$
$930$	11.7082	−	8.50651i	0.383927	−	0.278939i
$931$	−0.0450850	−	0.138757i	−0.00147760	−	0.00454759i
$932$	2.44427	−	7.52270i	0.0800648	−	0.246414i
$933$	−5.61803	−	4.08174i	−0.183926	−	0.133630i
$934$	−21.8885			−0.716215
$935$	−32.8885	+	20.6457i	−1.07557	+	0.675188i
$936$	1.23607			0.0404021
$937$	21.1525	+	15.3682i	0.691021	+	0.502056i	0.876996	−	0.480498i	$-0.159544\pi$
$937$	21.1525	+	15.3682i	0.691021	+	0.502056i	−0.185974	+	0.982555i	$0.559544\pi$
$938$	0.336881	−	1.03681i	0.0109996	−	0.0338532i
$939$	5.39919	+	16.6170i	0.176196	+	0.542275i
$940$	−2.76393	+	2.00811i	−0.0901495	+	0.0654975i
$941$	17.0344	−	12.3762i	0.555307	−	0.403454i	−0.274431	−	0.961607i	$-0.588490\pi$
$941$	17.0344	−	12.3762i	0.555307	−	0.403454i	0.829738	+	0.558153i	$0.188490\pi$
$942$	−1.38197	−	4.25325i	−0.0450269	−	0.138579i
$943$	2.23607	−	6.88191i	0.0728164	−	0.224106i
$944$	−3.35410	−	2.43690i	−0.109167	−	0.0793143i
$945$	−10.9443			−0.356017
$946$	−3.92705	−	15.6129i	−0.127679	−	0.507620i
$947$	−27.2705			−0.886172			−0.443086	−	0.896479i	$-0.646116\pi$
$947$	−27.2705			−0.886172			−0.443086	+	0.896479i	$0.646116\pi$
$948$	−1.61803	−	1.17557i	−0.0525513	−	0.0381808i
$949$	−2.38197	+	7.33094i	−0.0773219	+	0.237972i
$950$	−0.0450850	−	0.138757i	−0.00146275	−	0.00450188i
$951$	15.7082	−	11.4127i	0.509373	−	0.370081i
$952$	4.73607	−	3.44095i	0.153497	−	0.111522i
$953$	−12.4443	−	38.2995i	−0.403110	−	1.24064i	−0.922464	−	0.386084i	$-0.873827\pi$
$953$	−12.4443	−	38.2995i	−0.403110	−	1.24064i	0.519354	−	0.854559i	$-0.326173\pi$
$954$	0.583592	−	1.79611i	0.0188945	−	0.0581513i
$955$	−20.1803	−	14.6619i	−0.653020	−	0.474447i
$956$	0.291796			0.00943736
$957$	32.9443	+	27.5276i	1.06494	+	0.889842i
$958$	8.65248			0.279549
$959$	−15.6353	−	11.3597i	−0.504889	−	0.366823i
$960$	−1.00000	+	3.07768i	−0.0322749	+	0.0993318i
$961$	−3.39919	−	10.4616i	−0.109651	−	0.337472i
$962$	−20.1803	+	14.6619i	−0.650640	+	0.472718i
$963$	−2.26393	+	1.64484i	−0.0729542	+	0.0530043i
$964$	−2.10081	−	6.46564i	−0.0676626	−	0.208244i
$965$	10.7639	−	33.1280i	0.346503	−	1.06643i
$966$	11.0902	+	8.05748i	0.356820	+	0.259245i
$967$	0.472136			0.0151829			0.00759143	−	0.999971i	$-0.497584\pi$
$967$	0.472136			0.0151829			0.00759143	+	0.999971i	$0.497584\pi$
$968$	−10.8992	−	1.48584i	−0.350313	−	0.0477567i
$969$	−1.38197			−0.0443951
$970$	−5.09017	−	3.69822i	−0.163436	−	0.118743i
$971$	7.88854	−	24.2784i	0.253155	−	0.779132i	−0.741032	−	0.671470i	$-0.765663\pi$
$971$	7.88854	−	24.2784i	0.253155	−	0.779132i	0.994187	−	0.107663i	$-0.0343366\pi$
$972$	−1.21885	−	3.75123i	−0.0390945	−	0.120321i
$973$	−11.7082	+	8.50651i	−0.375348	+	0.272706i
$974$	−15.6180	+	11.3472i	−0.500434	+	0.363587i
$975$	1.61803	+	4.97980i	0.0518186	+	0.159481i
$976$	2.00000	−	6.15537i	0.0640184	−	0.197028i
$977$	22.2705	+	16.1805i	0.712497	+	0.517659i	0.883978	−	0.467528i	$-0.154855\pi$
$977$	22.2705	+	16.1805i	0.712497	+	0.517659i	−0.171481	+	0.985187i	$0.554855\pi$
$978$	37.6525			1.20399
$979$	−39.0066	−	32.5932i	−1.24666	−	1.04168i
$980$	2.00000			0.0638877
$981$	−3.14590	−	2.28563i	−0.100441	−	0.0729745i
$982$	5.50000	−	16.9273i	0.175512	−	0.540171i
$983$	−0.708204	−	2.17963i	−0.0225882	−	0.0695193i	0.939127	−	0.343570i	$-0.111636\pi$
$983$	−0.708204	−	2.17963i	−0.0225882	−	0.0695193i	−0.961715	+	0.274051i	$0.911636\pi$
$984$	−1.11803	+	0.812299i	−0.0356416	+	0.0258952i
$985$	5.70820	−	4.14725i	0.181879	−	0.132142i
$986$	−14.4721	−	44.5407i	−0.460887	−	1.41846i
$987$	0.854102	−	2.62866i	0.0271864	−	0.0836710i
$988$	0.381966	+	0.277515i	0.0121520	+	0.00882891i
$989$	−41.1246			−1.30769
$990$	−0.618034	−	2.45714i	−0.0196424	−	0.0780931i
$991$	33.2361			1.05578			0.527889	−	0.849313i	$-0.322984\pi$
$991$	33.2361			1.05578			0.527889	+	0.849313i	$0.322984\pi$
$992$	−3.61803	−	2.62866i	−0.114873	−	0.0834599i
$993$	2.13525	−	6.57164i	0.0677603	−	0.208545i
$994$	3.23607	+	9.95959i	0.102642	+	0.315899i
$995$	32.6525	−	23.7234i	1.03515	−	0.752083i
$996$	−17.0623	+	12.3965i	−0.540640	+	0.392798i
$997$	−4.85410	−	14.9394i	−0.153731	−	0.473135i	0.844299	−	0.535872i	$-0.180017\pi$
$997$	−4.85410	−	14.9394i	−0.153731	−	0.473135i	−0.998030	+	0.0627369i	$0.980017\pi$
$998$	−8.73607	+	26.8869i	−0.276535	+	0.851088i
$999$	34.1246	+	24.7930i	1.07965	+	0.784415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.f.c.15.1	✓	4
11.3	even	5	inner	154.2.f.c.113.1	yes	4
11.5	even	5		1694.2.a.m.1.1		2
11.6	odd	10		1694.2.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.f.c.15.1	✓	4	1.1	even	1	trivial
154.2.f.c.113.1	yes	4	11.3	even	5	inner
1694.2.a.m.1.1		2	11.5	even	5
1694.2.a.r.1.1		2	11.6	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.17557i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.17557i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} -2.00000 q^{10} +(2.54508 + 2.12663i) q^{11} -1.61803 q^{12} +(-2.61803 - 1.90211i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.00000 - 3.07768i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.73607 - 3.44095i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.0450850 + 0.138757i) q^{19} +(-1.61803 - 1.17557i) q^{20} +1.61803 q^{21} +(0.809017 + 3.21644i) q^{22} +8.47214 q^{23} +(-1.30902 - 0.951057i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-1.00000 - 3.07768i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-2.47214 - 7.60845i) q^{29} +(1.00000 - 3.07768i) q^{30} +(3.61803 + 2.62866i) q^{31} -1.00000 q^{32} +(-4.54508 + 2.85317i) q^{33} +5.85410 q^{34} +(1.61803 + 1.17557i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(-2.38197 - 7.33094i) q^{37} +(-0.118034 + 0.0857567i) q^{38} +(4.23607 - 3.07768i) q^{39} +(-0.618034 - 1.90211i) q^{40} +(0.263932 - 0.812299i) q^{41} +(1.30902 + 0.951057i) q^{42} -4.85410 q^{43} +(-1.23607 + 3.07768i) q^{44} -0.763932 q^{45} +(6.85410 + 4.97980i) q^{46} +(0.527864 - 1.62460i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(2.92705 + 9.00854i) q^{51} +(1.00000 - 3.07768i) q^{52} +(-4.00000 - 2.90617i) q^{53} -5.47214 q^{54} +(-6.61803 - 0.449028i) q^{55} +1.00000 q^{56} +(-0.190983 - 0.138757i) q^{57} +(2.47214 - 7.60845i) q^{58} +(1.28115 + 3.94298i) q^{59} +(2.61803 - 1.90211i) q^{60} +(-5.23607 + 3.80423i) q^{61} +(1.38197 + 4.25325i) q^{62} +(0.118034 - 0.363271i) q^{63} +(-0.809017 - 0.587785i) q^{64} +6.47214 q^{65} +(-5.35410 - 0.363271i) q^{66} +1.09017 q^{67} +(4.73607 + 3.44095i) q^{68} +(-4.23607 + 13.0373i) q^{69} +(0.618034 + 1.90211i) q^{70} +(-8.47214 + 6.15537i) q^{71} +(-0.309017 + 0.224514i) q^{72} +(-0.736068 - 2.26538i) q^{73} +(2.38197 - 7.33094i) q^{74} +(-1.30902 - 0.951057i) q^{75} -0.145898 q^{76} +(1.23607 - 3.07768i) q^{77} +5.23607 q^{78} +(1.00000 + 0.726543i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(0.690983 - 0.502029i) q^{82} +(10.5451 - 7.66145i) q^{83} +(0.500000 + 1.53884i) q^{84} +(-3.61803 + 11.1352i) q^{85} +(-3.92705 - 2.85317i) q^{86} +12.9443 q^{87} +(-2.80902 + 1.76336i) q^{88} -15.3262 q^{89} +(-0.618034 - 0.449028i) q^{90} +(-1.00000 + 3.07768i) q^{91} +(2.61803 + 8.05748i) q^{92} +(-5.85410 + 4.25325i) q^{93} +(1.38197 - 1.00406i) q^{94} +(-0.0901699 - 0.277515i) q^{95} +(0.500000 - 1.53884i) q^{96} +(2.54508 + 1.84911i) q^{97} -1.00000 q^{98} +(0.309017 + 1.22857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} + q^{7} + q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} - 6 q^{13} - q^{14} - 4 q^{15} - q^{16} + 10 q^{17} - 4 q^{18} + 11 q^{19} - 2 q^{20} + 2 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + q^{25} - 4 q^{26} - 11 q^{27} + q^{28} + 8 q^{29} + 4 q^{30} + 10 q^{31} - 4 q^{32} - 7 q^{33} + 10 q^{34} + 2 q^{35} + 4 q^{36} - 14 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 10 q^{41} + 3 q^{42} - 6 q^{43} + 4 q^{44} - 12 q^{45} + 14 q^{46} + 20 q^{47} - 2 q^{48} - q^{49} - q^{50} + 5 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 22 q^{55} + 4 q^{56} - 3 q^{57} - 8 q^{58} - 15 q^{59} + 6 q^{60} - 12 q^{61} + 10 q^{62} - 4 q^{63} - q^{64} + 8 q^{65} - 8 q^{66} - 18 q^{67} + 10 q^{68} - 8 q^{69} - 2 q^{70} - 16 q^{71} + q^{72} + 6 q^{73} + 14 q^{74} - 3 q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 4 q^{79} - 2 q^{80} - 14 q^{81} + 5 q^{82} + 31 q^{83} + 2 q^{84} - 10 q^{85} - 9 q^{86} + 16 q^{87} - 9 q^{88} - 30 q^{89} + 2 q^{90} - 4 q^{91} + 6 q^{92} - 10 q^{93} + 10 q^{94} + 22 q^{95} + 2 q^{96} - q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 3 * q^6 + q^7 + q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 - 6 * q^13 - q^14 - 4 * q^15 - q^16 + 10 * q^17 - 4 * q^18 + 11 * q^19 - 2 * q^20 + 2 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + q^25 - 4 * q^26 - 11 * q^27 + q^28 + 8 * q^29 + 4 * q^30 + 10 * q^31 - 4 * q^32 - 7 * q^33 + 10 * q^34 + 2 * q^35 + 4 * q^36 - 14 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 10 * q^41 + 3 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 + 14 * q^46 + 20 * q^47 - 2 * q^48 - q^49 - q^50 + 5 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 22 * q^55 + 4 * q^56 - 3 * q^57 - 8 * q^58 - 15 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 - 4 * q^63 - q^64 + 8 * q^65 - 8 * q^66 - 18 * q^67 + 10 * q^68 - 8 * q^69 - 2 * q^70 - 16 * q^71 + q^72 + 6 * q^73 + 14 * q^74 - 3 * q^75 - 14 * q^76 - 4 * q^77 + 12 * q^78 + 4 * q^79 - 2 * q^80 - 14 * q^81 + 5 * q^82 + 31 * q^83 + 2 * q^84 - 10 * q^85 - 9 * q^86 + 16 * q^87 - 9 * q^88 - 30 * q^89 + 2 * q^90 - 4 * q^91 + 6 * q^92 - 10 * q^93 + 10 * q^94 + 22 * q^95 + 2 * q^96 - q^97 - 4 * q^98 - q^99

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