LMFDB - Embedded newform 462.2.u.a.139.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.6
Character	$\chi$	$=$	462.139
Dual form			462.2.u.a.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.531600 - 0.731684i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.261116 - 2.63283i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.531600 - 0.731684i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.261116 - 2.63283i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} -0.904411 q^{10} +(2.92034 - 1.57214i) q^{11} -1.00000i q^{12} +(-1.17868 - 0.856359i) q^{13} +(-1.97653 - 1.75879i) q^{14} +(-0.279478 - 0.860146i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.41070 + 1.75148i) q^{17} +(0.951057 - 0.309017i) q^{18} +(0.0587872 - 0.180928i) q^{19} +(-0.531600 + 0.731684i) q^{20} +(1.06193 - 2.42329i) q^{21} +(0.444645 - 3.28668i) q^{22} +1.71378 q^{23} +(-0.809017 - 0.587785i) q^{24} +(1.29232 - 3.97736i) q^{25} +(-1.38562 + 0.450215i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-2.58466 + 0.565255i) q^{28} +(1.14604 - 0.372372i) q^{29} +(-0.860146 - 0.279478i) q^{30} +(1.65420 - 2.27681i) q^{31} +1.00000i q^{32} +(3.26322 - 0.592759i) q^{33} +2.97979i q^{34} +(-2.06521 + 1.20856i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.615389 - 1.89397i) q^{37} +(-0.111820 - 0.153907i) q^{38} +(-0.856359 - 1.17868i) q^{39} +(0.279478 + 0.860146i) q^{40} +(-2.71184 + 8.34619i) q^{41} +(-1.33629 - 2.28349i) q^{42} +7.16039i q^{43} +(-2.39763 - 2.29159i) q^{44} -0.904411i q^{45} +(1.00733 - 1.38647i) q^{46} +(11.9560 + 3.88476i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-6.86364 - 1.37495i) q^{49} +(-2.45814 - 3.38334i) q^{50} +(-2.83395 + 0.920806i) q^{51} +(-0.450215 + 1.38562i) q^{52} +(11.6507 + 8.46470i) q^{53} +1.00000 q^{54} +(-2.70276 - 1.30102i) q^{55} +(-1.06193 + 2.42329i) q^{56} +(0.111820 - 0.153907i) q^{57} +(0.372372 - 1.14604i) q^{58} +(-7.25006 + 2.35569i) q^{59} +(-0.731684 + 0.531600i) q^{60} +(4.85215 - 3.52529i) q^{61} +(-0.869665 - 2.67655i) q^{62} +(1.75879 - 1.97653i) q^{63} +(0.809017 + 0.587785i) q^{64} +1.31766i q^{65} +(1.43852 - 2.98842i) q^{66} -5.99527 q^{67} +(2.41070 + 1.75148i) q^{68} +(1.62990 + 0.529586i) q^{69} +(-0.236156 + 2.38117i) q^{70} +(-7.86234 + 5.71232i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-1.43864 - 4.42767i) q^{73} +(-1.89397 - 0.615389i) q^{74} +(2.45814 - 3.38334i) q^{75} -0.190239 q^{76} +(-3.37664 - 8.09928i) q^{77} -1.45693 q^{78} +(-8.69346 + 11.9655i) q^{79} +(0.860146 + 0.279478i) q^{80} +(0.309017 + 0.951057i) q^{81} +(5.15823 + 7.09969i) q^{82} +(-6.97412 + 5.06699i) q^{83} +(-2.63283 - 0.261116i) q^{84} +(2.56306 + 0.832788i) q^{85} +(5.79288 + 4.20877i) q^{86} +1.20502 q^{87} +(-3.26322 + 0.592759i) q^{88} +7.06273i q^{89} +(-0.731684 - 0.531600i) q^{90} +(-2.56242 + 2.87965i) q^{91} +(-0.529586 - 1.62990i) q^{92} +(2.27681 - 1.65420i) q^{93} +(10.1704 - 7.38925i) q^{94} +(-0.163634 + 0.0531678i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(2.47013 - 3.39985i) q^{97} +(-5.14670 + 4.74462i) q^{98} +(3.28668 + 0.444645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−0.531600	−	0.731684i	−0.237739	−	0.327219i	0.673431	−	0.739250i	$-0.264820\pi$
$5$	−0.531600	−	0.731684i	−0.237739	−	0.327219i	−0.911170	+	0.412031i	$0.864820\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	0.261116	−	2.63283i	0.0986925	−	0.995118i
$7$	0.261116	−	2.63283i	0.0986925	−	0.995118i
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.904411			−0.286000
$11$	2.92034	−	1.57214i	0.880515	−	0.474018i
$11$	2.92034	−	1.57214i	0.880515	−	0.474018i
$12$		−	1.00000i		−	0.288675i
$13$	−1.17868	−	0.856359i	−0.326906	−	0.237511i	0.412210	−	0.911089i	$-0.364757\pi$
$13$	−1.17868	−	0.856359i	−0.326906	−	0.237511i	−0.739117	+	0.673577i	$0.764757\pi$
$14$	−1.97653	−	1.75879i	−0.528249	−	0.470056i
$15$	−0.279478	−	0.860146i	−0.0721610	−	0.222089i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.41070	+	1.75148i	−0.584681	+	0.424796i	−0.840409	−	0.541953i	$-0.817685\pi$
$17$	−2.41070	+	1.75148i	−0.584681	+	0.424796i	0.255728	+	0.966749i	$0.417685\pi$
$18$	0.951057	−	0.309017i	0.224166	−	0.0728360i
$19$	0.0587872	−	0.180928i	0.0134867	−	0.0415078i	−0.944087	−	0.329697i	$-0.893053\pi$
$19$	0.0587872	−	0.180928i	0.0134867	−	0.0415078i	0.957573	+	0.288190i	$0.0930533\pi$
$20$	−0.531600	+	0.731684i	−0.118869	+	0.163610i
$21$	1.06193	−	2.42329i	0.231731	−	0.528804i
$22$	0.444645	−	3.28668i	0.0947986	−	0.700723i
$23$	1.71378			0.357347			0.178673	−	0.983908i	$-0.442819\pi$
$23$	1.71378			0.357347			0.178673	+	0.983908i	$0.442819\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	1.29232	−	3.97736i	0.258464	−	0.795471i
$26$	−1.38562	+	0.450215i	−0.271742	+	0.0882944i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−2.58466	+	0.565255i	−0.488456	+	0.106823i
$29$	1.14604	−	0.372372i	0.212815	−	0.0691477i	−0.200669	−	0.979659i	$-0.564312\pi$
$29$	1.14604	−	0.372372i	0.212815	−	0.0691477i	0.413484	+	0.910511i	$0.364312\pi$
$30$	−0.860146	−	0.279478i	−0.157040	−	0.0510255i
$31$	1.65420	−	2.27681i	0.297103	−	0.408928i	−0.634202	−	0.773168i	$-0.718671\pi$
$31$	1.65420	−	2.27681i	0.297103	−	0.408928i	0.931305	+	0.364240i	$0.118671\pi$
$32$			1.00000i			0.176777i
$33$	3.26322	−	0.592759i	0.568055	−	0.103186i
$34$			2.97979i			0.511030i
$35$	−2.06521	+	1.20856i	−0.349085	+	0.204284i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−0.615389	−	1.89397i	−0.101169	−	0.311367i	0.887643	−	0.460532i	$-0.152341\pi$
$37$	−0.615389	−	1.89397i	−0.101169	−	0.311367i	−0.988812	+	0.149165i	$0.952341\pi$
$38$	−0.111820	−	0.153907i	−0.0181396	−	0.0249670i
$39$	−0.856359	−	1.17868i	−0.137127	−	0.188739i
$40$	0.279478	+	0.860146i	0.0441894	+	0.136001i
$41$	−2.71184	+	8.34619i	−0.423518	+	1.30346i	0.480887	+	0.876782i	$0.340315\pi$
$41$	−2.71184	+	8.34619i	−0.423518	+	1.30346i	−0.904406	+	0.426673i	$0.859685\pi$
$42$	−1.33629	−	2.28349i	−0.206195	−	0.352350i
$43$			7.16039i			1.09195i	0.837802	+	0.545975i	$0.183841\pi$
$43$			7.16039i			1.09195i	−0.837802	+	0.545975i	$0.816159\pi$
$44$	−2.39763	−	2.29159i	−0.361456	−	0.345470i
$45$		−	0.904411i		−	0.134822i
$46$	1.00733	−	1.38647i	0.148523	−	0.204424i
$47$	11.9560	+	3.88476i	1.74397	+	0.566650i	0.995348	−	0.0963479i	$-0.0307161\pi$
$47$	11.9560	+	3.88476i	1.74397	+	0.566650i	0.748621	+	0.662998i	$0.230716\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	−6.86364	−	1.37495i	−0.980520	−	0.196421i
$50$	−2.45814	−	3.38334i	−0.347634	−	0.478477i
$51$	−2.83395	+	0.920806i	−0.396832	+	0.128939i
$52$	−0.450215	+	1.38562i	−0.0624336	+	0.192151i
$53$	11.6507	+	8.46470i	1.60034	+	1.16272i	0.886856	+	0.462045i	$0.152884\pi$
$53$	11.6507	+	8.46470i	1.60034	+	1.16272i	0.713485	+	0.700671i	$0.247116\pi$
$54$	1.00000			0.136083
$55$	−2.70276	−	1.30102i	−0.364440	−	0.175429i
$56$	−1.06193	+	2.42329i	−0.141906	+	0.323825i
$57$	0.111820	−	0.153907i	0.0148109	−	0.0203855i
$58$	0.372372	−	1.14604i	0.0488948	−	0.150483i
$59$	−7.25006	+	2.35569i	−0.943878	+	0.306684i	−0.740225	−	0.672359i	$-0.765281\pi$
$59$	−7.25006	+	2.35569i	−0.943878	+	0.306684i	−0.203652	+	0.979043i	$0.565281\pi$
$60$	−0.731684	+	0.531600i	−0.0944600	+	0.0686292i
$61$	4.85215	−	3.52529i	0.621254	−	0.451367i	−0.232105	−	0.972691i	$-0.574561\pi$
$61$	4.85215	−	3.52529i	0.621254	−	0.451367i	0.853359	+	0.521323i	$0.174561\pi$
$62$	−0.869665	−	2.67655i	−0.110448	−	0.339923i
$63$	1.75879	−	1.97653i	0.221587	−	0.249019i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$			1.31766i			0.163436i
$66$	1.43852	−	2.98842i	0.177070	−	0.367849i
$67$	−5.99527			−0.732438			−0.366219	−	0.930529i	$-0.619348\pi$
$67$	−5.99527			−0.732438			−0.366219	+	0.930529i	$0.619348\pi$
$68$	2.41070	+	1.75148i	0.292341	+	0.212398i
$69$	1.62990	+	0.529586i	0.196217	+	0.0637546i
$70$	−0.236156	+	2.38117i	−0.0282261	+	0.284604i
$71$	−7.86234	+	5.71232i	−0.933088	+	0.677928i	−0.946747	−	0.321979i	$-0.895652\pi$
$71$	−7.86234	+	5.71232i	−0.933088	+	0.677928i	0.0136593	+	0.999907i	$0.495652\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	−1.43864	−	4.42767i	−0.168380	−	0.518219i	0.830890	−	0.556437i	$-0.187832\pi$
$73$	−1.43864	−	4.42767i	−0.168380	−	0.518219i	−0.999269	+	0.0382178i	$0.987832\pi$
$74$	−1.89397	−	0.615389i	−0.220170	−	0.0715375i
$75$	2.45814	−	3.38334i	0.283842	−	0.390675i
$76$	−0.190239			−0.0218220
$77$	−3.37664	−	8.09928i	−0.384803	−	0.922999i
$78$	−1.45693			−0.164964
$79$	−8.69346	+	11.9655i	−0.978091	+	1.34623i	−0.0402390	+	0.999190i	$0.512812\pi$
$79$	−8.69346	+	11.9655i	−0.978091	+	1.34623i	−0.937852	+	0.347036i	$0.887188\pi$
$80$	0.860146	+	0.279478i	0.0961673	+	0.0312466i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	5.15823	+	7.09969i	0.569631	+	0.784030i
$83$	−6.97412	+	5.06699i	−0.765509	+	0.556175i	−0.900595	−	0.434659i	$-0.856869\pi$
$83$	−6.97412	+	5.06699i	−0.765509	+	0.556175i	0.135086	+	0.990834i	$0.456869\pi$
$84$	−2.63283	−	0.261116i	−0.287266	−	0.0284901i
$85$	2.56306	+	0.832788i	0.278003	+	0.0903285i
$86$	5.79288	+	4.20877i	0.624662	+	0.453844i
$87$	1.20502			0.129192
$88$	−3.26322	+	0.592759i	−0.347861	+	0.0631883i
$89$			7.06273i			0.748648i	0.927298	+	0.374324i	$0.122125\pi$
$89$			7.06273i			0.748648i	−0.927298	+	0.374324i	$0.877875\pi$
$90$	−0.731684	−	0.531600i	−0.0771263	−	0.0560355i
$91$	−2.56242	+	2.87965i	−0.268615	+	0.301870i
$92$	−0.529586	−	1.62990i	−0.0552131	−	0.169929i
$93$	2.27681	−	1.65420i	0.236094	−	0.171533i
$94$	10.1704	−	7.38925i	1.04900	−	0.762142i
$95$	−0.163634	+	0.0531678i	−0.0167885	+	0.00545490i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	2.47013	−	3.39985i	0.250804	−	0.345202i	−0.664989	−	0.746854i	$-0.731564\pi$
$97$	2.47013	−	3.39985i	0.250804	−	0.345202i	0.915793	+	0.401651i	$0.131564\pi$
$98$	−5.14670	+	4.74462i	−0.519895	+	0.479279i
$99$	3.28668	+	0.444645i	0.330324	+	0.0446885i
$100$	−4.18204			−0.418204
$101$	7.12300	+	5.17516i	0.708765	+	0.514948i	0.882775	−	0.469796i	$-0.155672\pi$
$101$	7.12300	+	5.17516i	0.708765	+	0.514948i	−0.174010	+	0.984744i	$0.555672\pi$
$102$	−0.920806	+	2.83395i	−0.0911734	+	0.280603i
$103$	17.5846	−	5.71357i	1.73266	−	0.562975i	0.738830	−	0.673892i	$-0.235379\pi$
$103$	17.5846	−	5.71357i	1.73266	−	0.562975i	0.993830	+	0.110917i	$0.0353787\pi$
$104$	0.856359	+	1.17868i	0.0839729	+	0.115579i
$105$	−2.33760	+	0.511223i	−0.228126	+	0.0498902i
$106$	13.6962	−	4.45016i	1.33029	−	0.432237i
$107$	−5.84249	−	1.89834i	−0.564815	−	0.183519i	0.0126718	−	0.999920i	$-0.495966\pi$
$107$	−5.84249	−	1.89834i	−0.564815	−	0.183519i	−0.577486	+	0.816400i	$0.695966\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$		−	4.84923i		−	0.464472i	−0.972659	−	0.232236i	$-0.925396\pi$
$109$		−	4.84923i		−	0.464472i	0.972659	−	0.232236i	$-0.0746042\pi$
$110$	−2.64119	+	1.42186i	−0.251827	+	0.135569i
$111$		−	1.99144i		−	0.189019i
$112$	1.33629	+	2.28349i	0.126268	+	0.215769i
$113$	−1.76215	+	5.42333i	−0.165769	+	0.510184i	−0.999092	−	0.0426017i	$-0.986435\pi$
$113$	−1.76215	+	5.42333i	−0.165769	+	0.510184i	0.833323	+	0.552786i	$0.186435\pi$
$114$	−0.0587872	−	0.180928i	−0.00550593	−	0.0169455i
$115$	−0.911042	−	1.25394i	−0.0849551	−	0.116931i
$116$	−0.708293	−	0.974881i	−0.0657633	−	0.0905155i
$117$	−0.450215	−	1.38562i	−0.0416224	−	0.128100i
$118$	−2.35569	+	7.25006i	−0.216859	+	0.667422i
$119$	3.98188	+	6.80432i	0.365018	+	0.623751i
$120$			0.904411i			0.0825611i
$121$	6.05676	−	9.18236i	0.550614	−	0.834760i
$122$		−	5.99759i		−	0.542996i
$123$	−5.15823	+	7.09969i	−0.465102	+	0.640158i
$124$	−2.67655	−	0.869665i	−0.240362	−	0.0780982i
$125$	−7.89790	+	2.56618i	−0.706409	+	0.229526i
$126$	−0.565255	−	2.58466i	−0.0503569	−	0.230260i
$127$	−2.96640	−	4.08290i	−0.263225	−	0.362298i	0.656863	−	0.754010i	$-0.271883\pi$
$127$	−2.96640	−	4.08290i	−0.263225	−	0.362298i	−0.920088	+	0.391712i	$0.871883\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−2.21268	+	6.80994i	−0.194816	+	0.599582i
$130$	1.06601	+	0.774501i	0.0934952	+	0.0679282i
$131$	10.0350			0.876764			0.438382	−	0.898789i	$-0.355552\pi$
$131$	10.0350			0.876764			0.438382	+	0.898789i	$0.355552\pi$
$132$	−1.57214	−	2.92034i	−0.136837	−	0.254183i
$133$	−0.461004	−	0.202020i	−0.0399741	−	0.0175174i
$134$	−3.52393	+	4.85027i	−0.304421	+	0.419000i
$135$	0.279478	−	0.860146i	0.0240537	−	0.0740296i
$136$	2.83395	−	0.920806i	0.243009	−	0.0789585i
$137$	5.24424	−	3.81016i	0.448046	−	0.325524i	−0.340778	−	0.940144i	$-0.610690\pi$
$137$	5.24424	−	3.81016i	0.448046	−	0.325524i	0.788824	+	0.614619i	$0.210690\pi$
$138$	1.38647	−	1.00733i	0.118024	−	0.0857498i
$139$	1.58198	+	4.86884i	0.134182	+	0.412969i	0.995462	−	0.0951614i	$-0.0303367\pi$
$139$	1.58198	+	4.86884i	0.134182	+	0.412969i	−0.861280	+	0.508131i	$0.830337\pi$
$140$	1.78759	+	1.59067i	0.151079	+	0.134436i
$141$	10.1704	+	7.38925i	0.856504	+	0.622287i
$142$			9.71838i			0.815548i
$143$	−4.78845	−	0.647814i	−0.400431	−	0.0541729i
$144$	−1.00000			−0.0833333
$145$	−0.881694	−	0.640588i	−0.0732207	−	0.0531979i
$146$	−4.42767	−	1.43864i	−0.366436	−	0.119062i
$147$	−6.10282	−	3.42864i	−0.503352	−	0.282789i
$148$	−1.61111	+	1.17054i	−0.132432	+	0.0962178i
$149$	−4.66959	−	6.42713i	−0.382547	−	0.526531i	0.573710	−	0.819059i	$-0.305504\pi$
$149$	−4.66959	−	6.42713i	−0.382547	−	0.526531i	−0.956257	+	0.292527i	$0.905504\pi$
$150$	−1.29232	−	3.97736i	−0.105518	−	0.324750i
$151$	−8.00474	−	2.60090i	−0.651416	−	0.211658i	−0.0353777	−	0.999374i	$-0.511263\pi$
$151$	−8.00474	−	2.60090i	−0.651416	−	0.211658i	−0.616038	+	0.787716i	$0.711263\pi$
$152$	−0.111820	+	0.153907i	−0.00906979	+	0.0124835i
$153$	−2.97979			−0.240902
$154$	−8.53719	−	2.02888i	−0.687947	−	0.163492i
$155$	−2.54528			−0.204442
$156$	−0.856359	+	1.17868i	−0.0685636	+	0.0943697i
$157$	6.09556	+	1.98057i	0.486479	+	0.158066i	0.541979	−	0.840392i	$-0.317675\pi$
$157$	6.09556	+	1.98057i	0.486479	+	0.158066i	−0.0555002	+	0.998459i	$0.517675\pi$
$158$	4.57042	+	14.0663i	0.363603	+	1.11906i
$159$	8.46470	+	11.6507i	0.671294	+	0.923957i
$160$	0.731684	−	0.531600i	0.0578447	−	0.0420266i
$161$	0.447494	−	4.51209i	0.0352675	−	0.355602i
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	16.9484	+	12.3137i	1.32750	+	0.964484i	0.999806	+	0.0196995i	$0.00627095\pi$
$163$	16.9484	+	12.3137i	1.32750	+	0.964484i	0.327692	+	0.944784i	$0.393729\pi$
$164$	8.77570			0.685267
$165$	−2.16844	−	2.07254i	−0.168813	−	0.161347i
$166$			8.62048i			0.669079i
$167$	0.374709	+	0.272242i	0.0289959	+	0.0210667i	0.602189	−	0.798354i	$-0.294295\pi$
$167$	0.374709	+	0.272242i	0.0289959	+	0.0210667i	−0.573193	+	0.819420i	$0.694295\pi$
$168$	−1.75879	+	1.97653i	−0.135693	+	0.152492i
$169$	−3.36129	−	10.3450i	−0.258561	−	0.795769i
$170$	2.18027	−	1.58406i	0.167219	−	0.121492i
$171$	0.153907	−	0.111820i	0.0117696	−	0.00855108i
$172$	6.80994	−	2.21268i	0.519253	−	0.168716i
$173$	3.24343	−	9.98225i	0.246593	−	0.758936i	−0.748777	−	0.662822i	$-0.769359\pi$
$173$	3.24343	−	9.98225i	0.246593	−	0.758936i	0.995370	−	0.0961143i	$-0.0306414\pi$
$174$	0.708293	−	0.974881i	0.0536955	−	0.0739056i
$175$	−10.1343	−	4.44102i	−0.766079	−	0.335710i
$176$	−1.43852	+	2.98842i	−0.108433	+	0.225261i
$177$	−7.62317			−0.572992
$178$	5.71387	+	4.15137i	0.428273	+	0.311158i
$179$	−3.31695	+	10.2085i	−0.247921	+	0.763021i	0.747222	+	0.664575i	$0.231387\pi$
$179$	−3.31695	+	10.2085i	−0.247921	+	0.763021i	−0.995142	+	0.0984464i	$0.968613\pi$
$180$	−0.860146	+	0.279478i	−0.0641115	+	0.0208311i
$181$	−1.03495	−	1.42448i	−0.0769269	−	0.105881i	0.768820	−	0.639466i	$-0.220844\pi$
$181$	−1.03495	−	1.42448i	−0.0769269	−	0.105881i	−0.845746	+	0.533585i	$0.820844\pi$
$182$	0.823534	+	3.76566i	0.0610444	+	0.279130i
$183$	5.70404	−	1.85336i	0.421655	−	0.137004i
$184$	−1.62990	−	0.529586i	−0.120158	−	0.0390416i
$185$	−1.05865	+	1.45711i	−0.0778334	+	0.107129i
$186$		−	2.81430i		−	0.206354i
$187$	−4.28650	+	8.90487i	−0.313460	+	0.651188i
$188$		−	12.5713i		−	0.916859i
$189$	2.28349	−	1.33629i	0.166099	−	0.0972011i
$190$	−0.0531678	+	0.163634i	−0.00385720	+	0.0118712i
$191$	−3.30849	−	10.1825i	−0.239394	−	0.736780i	−0.996508	−	0.0834968i	$-0.973391\pi$
$191$	−3.30849	−	10.1825i	−0.239394	−	0.736780i	0.757114	−	0.653283i	$-0.226609\pi$
$192$	0.587785	+	0.809017i	0.0424197	+	0.0583858i
$193$	−10.7151	−	14.7481i	−0.771290	−	1.06159i	−0.996190	−	0.0872075i	$-0.972206\pi$
$193$	−10.7151	−	14.7481i	−0.771290	−	1.06159i	0.224900	−	0.974382i	$-0.427794\pi$
$194$	−1.29863	−	3.99676i	−0.0932359	−	0.286951i
$195$	−0.407179	+	1.25317i	−0.0291587	+	0.0897413i
$196$	0.813325	+	6.95259i	0.0580947	+	0.496614i
$197$		−	18.9221i		−	1.34814i	−0.738667	−	0.674070i	$-0.764544\pi$
$197$		−	18.9221i		−	1.34814i	0.738667	−	0.674070i	$-0.235456\pi$
$198$	2.29159	−	2.39763i	0.162856	−	0.170392i
$199$			7.85083i			0.556530i	0.960504	+	0.278265i	$0.0897594\pi$
$199$			7.85083i			0.556530i	−0.960504	+	0.278265i	$0.910241\pi$
$200$	−2.45814	+	3.38334i	−0.173817	+	0.239238i
$201$	−5.70184	−	1.85264i	−0.402177	−	0.130675i
$202$	8.37359	−	2.72075i	0.589164	−	0.191431i
$203$	−0.681143	−	3.11457i	−0.0478069	−	0.218600i
$204$	1.75148	+	2.41070i	0.122628	+	0.168783i
$205$	7.54839	−	2.45262i	0.527202	−	0.171298i
$206$	5.71357	−	17.5846i	0.398084	−	1.22518i
$207$	1.38647	+	1.00733i	0.0963665	+	0.0700144i
$208$	1.45693			0.101020
$209$	−0.112766	−	0.620794i	−0.00780019	−	0.0429412i
$210$	−0.960418	+	2.19165i	−0.0662752	+	0.151238i
$211$	−3.96294	+	5.45452i	−0.272820	+	0.375505i	−0.923339	−	0.383985i	$-0.874551\pi$
$211$	−3.96294	+	5.45452i	−0.272820	+	0.375505i	0.650519	+	0.759490i	$0.274551\pi$
$212$	4.45016	−	13.6962i	0.305638	−	0.940657i
$213$	−9.24273	+	3.00314i	−0.633301	+	0.205772i
$214$	−4.96992	+	3.61086i	−0.339736	+	0.246833i
$215$	5.23915	−	3.80646i	0.357307	−	0.259599i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−5.56253	−	4.94975i	−0.377609	−	0.336011i
$218$	−3.92311	−	2.85031i	−0.265707	−	0.193047i
$219$		−	4.65552i		−	0.314591i
$220$	−0.402142	+	2.97251i	−0.0271124	+	0.200407i
$221$	4.34133			0.292030
$222$	−1.61111	−	1.17054i	−0.108131	−	0.0785615i
$223$	−19.3040	−	6.27226i	−1.29269	−	0.420022i	−0.419660	−	0.907681i	$-0.637851\pi$
$223$	−19.3040	−	6.27226i	−1.29269	−	0.420022i	−0.873034	+	0.487660i	$0.837851\pi$
$224$	2.63283	+	0.261116i	0.175914	+	0.0174465i
$225$	3.38334	−	2.45814i	0.225556	−	0.163876i
$226$	3.35181	+	4.61336i	0.222959	+	0.306876i
$227$	0.698313	+	2.14919i	0.0463487	+	0.142647i	0.971553	−	0.236823i	$-0.0761063\pi$
$227$	0.698313	+	2.14919i	0.0463487	+	0.142647i	−0.925204	+	0.379470i	$0.876106\pi$
$228$	−0.180928	−	0.0587872i	−0.0119823	−	0.00389328i
$229$	14.6111	−	20.1105i	0.965530	−	1.32894i	0.0212570	−	0.999774i	$-0.493233\pi$
$229$	14.6111	−	20.1105i	0.965530	−	1.32894i	0.944273	−	0.329164i	$-0.106767\pi$
$230$	−1.54996			−0.102201
$231$	−0.708557	−	8.74631i	−0.0466196	−	0.575465i
$232$	−1.20502			−0.0791134
$233$	1.98318	−	2.72962i	0.129923	−	0.178823i	−0.739100	−	0.673596i	$-0.764749\pi$
$233$	1.98318	−	2.72962i	0.129923	−	0.178823i	0.869022	+	0.494773i	$0.164749\pi$
$234$	−1.38562	−	0.450215i	−0.0905807	−	0.0294315i
$235$	−3.51342	−	10.8132i	−0.229190	−	0.705374i
$236$	4.48078	+	6.16727i	0.291674	+	0.401455i
$237$	−11.9655	+	8.69346i	−0.777244	+	0.564701i
$238$	7.84530	+	0.778071i	0.508535	+	0.0504349i
$239$	−22.7592	−	7.39491i	−1.47217	−	0.478337i	−0.540406	−	0.841404i	$-0.681729\pi$
$239$	−22.7592	−	7.39491i	−1.47217	−	0.478337i	−0.931763	+	0.363067i	$0.881729\pi$
$240$	0.731684	+	0.531600i	0.0472300	+	0.0343146i
$241$	−16.0211			−1.03201			−0.516004	−	0.856586i	$-0.672581\pi$
$241$	−16.0211			−1.03201			−0.516004	+	0.856586i	$0.672581\pi$
$242$	−3.86861	−	10.2973i	−0.248684	−	0.661934i
$243$			1.00000i			0.0641500i
$244$	−4.85215	−	3.52529i	−0.310627	−	0.225684i
$245$	2.64268	+	5.75294i	0.168834	+	0.367542i
$246$	2.71184	+	8.34619i	0.172901	+	0.532134i
$247$	−0.224231	+	0.162913i	−0.0142675	+	0.0103659i
$248$	−2.27681	+	1.65420i	−0.144578	+	0.105042i
$249$	−8.19856	+	2.66388i	−0.519563	+	0.168816i
$250$	−2.56618	+	7.89790i	−0.162300	+	0.499507i
$251$	2.95208	−	4.06319i	0.186334	−	0.256466i	−0.705623	−	0.708588i	$-0.749333\pi$
$251$	2.95208	−	4.06319i	0.186334	−	0.256466i	0.891956	+	0.452121i	$0.149333\pi$
$252$	−2.42329	−	1.06193i	−0.152653	−	0.0668951i
$253$	5.00480	−	2.69429i	0.314649	−	0.169389i
$254$	−5.04674			−0.316660
$255$	2.18027	+	1.58406i	0.136534	+	0.0991974i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.16257	+	0.702662i	−0.134898	+	0.0438309i	−0.375688	−	0.926746i	$-0.622593\pi$
$257$	−2.16257	+	0.702662i	−0.134898	+	0.0438309i	0.240790	+	0.970577i	$0.422593\pi$
$258$	4.20877	+	5.79288i	0.262027	+	0.360649i
$259$	−5.14721	+	1.12567i	−0.319832	+	0.0699458i
$260$	1.25317	−	0.407179i	0.0777182	−	0.0252522i
$261$	1.14604	+	0.372372i	0.0709382	+	0.0230492i
$262$	5.89844	−	8.11851i	0.364407	−	0.501563i
$263$		−	3.23287i		−	0.199348i	−0.995020	−	0.0996738i	$-0.968220\pi$
$263$		−	3.23287i		−	0.199348i	0.995020	−	0.0996738i	$-0.0317799\pi$
$264$	−3.28668	−	0.444645i	−0.202281	−	0.0273660i
$265$		−	13.0244i		−	0.800085i
$266$	−0.434409	+	0.254216i	−0.0266353	+	0.0155870i
$267$	−2.18250	+	6.71706i	−0.133567	+	0.411077i
$268$	1.85264	+	5.70184i	0.113168	+	0.348295i
$269$	−7.39632	−	10.1802i	−0.450962	−	0.620696i	0.521642	−	0.853164i	$-0.325320\pi$
$269$	−7.39632	−	10.1802i	−0.450962	−	0.620696i	−0.972604	+	0.232469i	$0.925320\pi$
$270$	−0.531600	−	0.731684i	−0.0323521	−	0.0445289i
$271$	5.58683	+	17.1945i	0.339376	+	1.04449i	0.964526	+	0.263987i	$0.0850376\pi$
$271$	5.58683	+	17.1945i	0.339376	+	1.04449i	−0.625151	+	0.780504i	$0.714962\pi$
$272$	0.920806	−	2.83395i	0.0558321	−	0.171833i
$273$	−3.32687	+	1.94688i	−0.201351	+	0.117831i
$274$		−	6.48224i		−	0.391606i
$275$	−2.47894	−	13.6469i	−0.149486	−	0.822941i
$276$		−	1.71378i		−	0.103157i
$277$	3.36582	−	4.63266i	0.202233	−	0.278349i	−0.695840	−	0.718197i	$-0.744968\pi$
$277$	3.36582	−	4.63266i	0.202233	−	0.278349i	0.898072	+	0.439848i	$0.144968\pi$
$278$	4.86884	+	1.58198i	0.292013	+	0.0948809i
$279$	2.67655	−	0.869665i	0.160241	−	0.0520655i
$280$	2.33760	−	0.511223i	0.139698	−	0.0305514i
$281$	−11.9851	−	16.4960i	−0.714969	−	0.984071i	−0.999676	−	0.0254559i	$-0.991896\pi$
$281$	−11.9851	−	16.4960i	−0.714969	−	0.984071i	0.284707	−	0.958615i	$-0.408104\pi$
$282$	11.9560	−	3.88476i	0.711972	−	0.231334i
$283$	−2.47618	+	7.62090i	−0.147194	+	0.453015i	−0.997287	−	0.0736174i	$-0.976546\pi$
$283$	−2.47618	+	7.62090i	−0.147194	+	0.453015i	0.850093	+	0.526633i	$0.176546\pi$
$284$	7.86234	+	5.71232i	0.466544	+	0.338964i
$285$	−0.172055			−0.0101916
$286$	−3.33868	+	3.49317i	−0.197420	+	0.206555i
$287$	21.2660	+	9.31915i	1.25529	+	0.550092i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	−2.50948	+	7.72338i	−0.147616	+	0.454316i
$290$	−1.03649	+	0.336777i	−0.0608650	+	0.0197762i
$291$	3.39985	−	2.47013i	0.199303	−	0.144802i
$292$	−3.76640	+	2.73645i	−0.220412	+	0.160139i
$293$	−6.28922	−	19.3562i	−0.367420	−	1.13080i	−0.948452	−	0.316922i	$-0.897351\pi$
$293$	−6.28922	−	19.3562i	−0.367420	−	1.13080i	0.581032	−	0.813881i	$-0.302649\pi$
$294$	−6.36097	+	2.92199i	−0.370980	+	0.170414i
$295$	5.57775	+	4.05247i	0.324749	+	0.235944i
$296$			1.99144i			0.115750i
$297$	2.98842	+	1.43852i	0.173406	+	0.0834716i
$298$	−7.94437			−0.460205
$299$	−2.01999	−	1.46761i	−0.116819	−	0.0848739i
$300$	−3.97736	−	1.29232i	−0.229633	−	0.0746122i
$301$	18.8521	+	1.86969i	1.08662	+	0.107767i
$302$	−6.80923	+	4.94720i	−0.391827	+	0.284679i
$303$	5.17516	+	7.12300i	0.297305	+	0.409206i
$304$	0.0587872	+	0.180928i	0.00337168	+	0.0103770i
$305$	−5.15880	−	1.67620i	−0.295392	−	0.0959787i
$306$	−1.75148	+	2.41070i	−0.100125	+	0.137811i
$307$	−29.3590			−1.67561			−0.837805	−	0.545970i	$-0.816161\pi$
$307$	−29.3590			−1.67561			−0.837805	+	0.545970i	$0.816161\pi$
$308$	−6.65943	+	5.71419i	−0.379457	+	0.325596i
$309$	18.4895			1.05183
$310$	−1.49608	+	2.05917i	−0.0849715	+	0.116953i
$311$	21.8056	+	7.08507i	1.23648	+	0.401758i	0.853059	−	0.521815i	$-0.174745\pi$
$311$	21.8056	+	7.08507i	1.23648	+	0.401758i	0.383424	+	0.923572i	$0.374745\pi$
$312$	0.450215	+	1.38562i	0.0254884	+	0.0784452i
$313$	−6.06358	−	8.34580i	−0.342734	−	0.471733i	0.602504	−	0.798116i	$-0.294170\pi$
$313$	−6.06358	−	8.34580i	−0.342734	−	0.471733i	−0.945237	+	0.326384i	$0.894170\pi$
$314$	5.18519	−	3.76726i	0.292617	−	0.212599i
$315$	−2.38117	−	0.236156i	−0.134163	−	0.0133059i
$316$	14.0663	+	4.57042i	0.791292	+	0.257106i
$317$	14.0810	+	10.2304i	0.790868	+	0.574599i	0.908221	−	0.418491i	$-0.137441\pi$
$317$	14.0810	+	10.2304i	0.790868	+	0.574599i	−0.117353	+	0.993090i	$0.537441\pi$
$318$	14.4010			0.807568
$319$	2.76141	−	2.88919i	0.154609	−	0.161764i
$320$		−	0.904411i		−	0.0505581i
$321$	−4.96992	−	3.61086i	−0.277394	−	0.201538i
$322$	−3.38732	−	3.01417i	−0.188768	−	0.167973i
$323$	0.175174	+	0.539129i	0.00974692	+	0.0299979i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−4.92928	+	3.58133i	−0.273427	+	0.198656i
$326$	19.9240	−	6.47370i	1.10349	−	0.358545i
$327$	1.49850	−	4.61189i	0.0828670	−	0.255038i
$328$	5.15823	−	7.09969i	0.284816	−	0.392015i
$329$	13.3498	−	30.4639i	0.736000	−	1.67953i
$330$	−2.95130	+	0.536098i	−0.162464	+	0.0295112i
$331$	18.6751			1.02648			0.513238	−	0.858246i	$-0.328446\pi$
$331$	18.6751			1.02648			0.513238	+	0.858246i	$0.328446\pi$
$332$	6.97412	+	5.06699i	0.382754	+	0.278087i
$333$	0.615389	−	1.89397i	0.0337231	−	0.103789i
$334$	0.440497	−	0.143126i	0.0241029	−	0.00783152i
$335$	3.18708	+	4.38664i	0.174129	+	0.239668i
$336$	0.565255	+	2.58466i	0.0308372	+	0.141005i
$337$	4.88738	−	1.58801i	0.266233	−	0.0865043i	−0.172859	−	0.984947i	$-0.555300\pi$
$337$	4.88738	−	1.58801i	0.266233	−	0.0865043i	0.439091	+	0.898442i	$0.355300\pi$
$338$	−10.3450	−	3.36129i	−0.562693	−	0.182830i
$339$	−3.35181	+	4.61336i	−0.182045	+	0.250564i
$340$		−	2.69496i		−	0.146155i
$341$	1.25136	−	9.24970i	0.0677650	−	0.500899i
$342$		−	0.190239i		−	0.0102870i
$343$	−5.41222	+	17.7118i	−0.292232	+	0.956347i
$344$	2.21268	−	6.80994i	0.119300	−	0.367167i
$345$	−0.478963	−	1.47410i	−0.0257865	−	0.0793627i
$346$	−6.16937	−	8.49141i	−0.331667	−	0.456501i
$347$	11.6645	+	16.0549i	0.626186	+	0.861871i	0.997785	−	0.0665225i	$-0.0211904\pi$
$347$	11.6645	+	16.0549i	0.626186	+	0.861871i	−0.371599	+	0.928393i	$0.621190\pi$
$348$	−0.372372	−	1.14604i	−0.0199612	−	0.0614343i
$349$	−8.77354	+	27.0022i	−0.469637	+	1.44539i	0.383419	+	0.923575i	$0.374747\pi$
$349$	−8.77354	+	27.0022i	−0.469637	+	1.44539i	−0.853056	+	0.521820i	$0.825253\pi$
$350$	−9.54964	+	5.58844i	−0.510450	+	0.298714i
$351$		−	1.45693i		−	0.0777649i
$352$	1.57214	+	2.92034i	0.0837953	+	0.155655i
$353$			10.9725i			0.584007i	0.956417	+	0.292003i	$0.0943219\pi$
$353$			10.9725i			0.584007i	−0.956417	+	0.292003i	$0.905678\pi$
$354$	−4.48078	+	6.16727i	−0.238151	+	0.327787i
$355$	8.35923	+	2.71608i	0.443662	+	0.144154i
$356$	6.71706	−	2.18250i	0.356003	−	0.115673i
$357$	1.68434	+	7.70176i	0.0891448	+	0.407620i
$358$	6.30922	+	8.68389i	0.333453	+	0.458958i
$359$	−13.0799	+	4.24993i	−0.690332	+	0.224302i	−0.633113	−	0.774059i	$-0.718223\pi$
$359$	−13.0799	+	4.24993i	−0.690332	+	0.224302i	−0.0572188	+	0.998362i	$0.518223\pi$
$360$	−0.279478	+	0.860146i	−0.0147298	+	0.0453337i
$361$	15.3420	+	11.1466i	0.807476	+	0.586666i
$362$	−1.76075			−0.0925432
$363$	8.59782	−	6.86130i	0.451269	−	0.360125i
$364$	3.53055	+	1.54715i	0.185051	+	0.0810926i
$365$	−2.47488	+	3.40637i	−0.129541	+	0.178298i
$366$	1.85336	−	5.70404i	0.0968765	−	0.298155i
$367$	−30.1413	+	9.79351i	−1.57336	+	0.511217i	−0.960336	−	0.278844i	$-0.910049\pi$
$367$	−30.1413	+	9.79351i	−1.57336	+	0.511217i	−0.613028	+	0.790061i	$0.710049\pi$
$368$	−1.38647	+	1.00733i	−0.0722749	+	0.0525108i
$369$	−7.09969	+	5.15823i	−0.369595	+	0.268527i
$370$	0.556565	+	1.71293i	0.0289344	+	0.0890510i
$371$	25.3283	−	28.4640i	1.31498	−	1.47778i
$372$	−2.27681	−	1.65420i	−0.118047	−	0.0857663i
$373$			1.84176i			0.0953627i	0.998863	+	0.0476813i	$0.0151832\pi$
$373$			1.84176i			0.0953627i	−0.998863	+	0.0476813i	$0.984817\pi$
$374$	4.68465	+	8.70200i	0.242237	+	0.449970i
$375$	−8.30434			−0.428834
$376$	−10.1704	−	7.38925i	−0.524500	−	0.381071i
$377$	−1.66970	−	0.542518i	−0.0859938	−	0.0279411i
$378$	0.261116	−	2.63283i	0.0134304	−	0.135418i
$379$	−17.2925	+	12.5637i	−0.888256	+	0.645356i	−0.935423	−	0.353531i	$-0.884981\pi$
$379$	−17.2925	+	12.5637i	−0.888256	+	0.645356i	0.0471664	+	0.998887i	$0.484981\pi$
$380$	0.101131	+	0.139195i	0.00518792	+	0.00714056i
$381$	−1.55953	−	4.79973i	−0.0798970	−	0.245898i
$382$	−10.1825	−	3.30849i	−0.520982	−	0.169277i
$383$	20.7852	−	28.6084i	1.06207	−	1.46182i	0.184223	−	0.982884i	$-0.441023\pi$
$383$	20.7852	−	28.6084i	1.06207	−	1.46182i	0.877850	−	0.478935i	$-0.158977\pi$
$384$	1.00000			0.0510310
$385$	−4.13110	+	6.77620i	−0.210540	+	0.345347i
$386$	−18.2296			−0.927863
$387$	−4.20877	+	5.79288i	−0.213944	+	0.294469i
$388$	−3.99676	−	1.29863i	−0.202905	−	0.0659278i
$389$	3.87006	+	11.9108i	0.196220	+	0.603903i	0.999960	+	0.00892254i	$0.00284017\pi$
$389$	3.87006	+	11.9108i	0.196220	+	0.603903i	−0.803740	+	0.594980i	$0.797160\pi$
$390$	0.774501	+	1.06601i	0.0392184	+	0.0539795i
$391$	−4.13140	+	3.00164i	−0.208934	+	0.151799i
$392$	6.10282	+	3.42864i	0.308239	+	0.173172i
$393$	9.54388	+	3.10099i	0.481425	+	0.156424i
$394$	−15.3083	−	11.1221i	−0.771219	−	0.560324i
$395$	13.3764			0.673041
$396$	−0.592759	−	3.26322i	−0.0297873	−	0.163983i
$397$		−	8.94134i		−	0.448753i	−0.974503	−	0.224377i	$-0.927965\pi$
$397$		−	8.94134i		−	0.448753i	0.974503	−	0.224377i	$-0.0720346\pi$
$398$	6.35145	+	4.61460i	0.318370	+	0.231309i
$399$	−0.376013	−	0.334591i	−0.0188242	−	0.0167505i
$400$	1.29232	+	3.97736i	0.0646161	+	0.198868i
$401$	−21.7442	+	15.7981i	−1.08586	+	0.788920i	−0.978695	−	0.205321i	$-0.934176\pi$
$401$	−21.7442	+	15.7981i	−1.08586	+	0.788920i	−0.107161	+	0.994242i	$0.534176\pi$
$402$	−4.85027	+	3.52393i	−0.241910	+	0.175758i
$403$	−3.89954	+	1.26704i	−0.194250	+	0.0631156i
$404$	2.72075	−	8.37359i	0.135362	−	0.416602i
$405$	0.531600	−	0.731684i	0.0264154	−	0.0363577i
$406$	−2.92011	−	1.27964i	−0.144922	−	0.0635076i
$407$	−4.77473	−	4.56357i	−0.236675	−	0.226208i
$408$	2.97979			0.147522
$409$	29.2257	+	21.2337i	1.44512	+	1.04994i	0.986942	+	0.161078i	$0.0514971\pi$
$409$	29.2257	+	21.2337i	1.44512	+	1.04994i	0.458176	+	0.888861i	$0.348503\pi$
$410$	2.45262	−	7.54839i	0.121126	−	0.372788i
$411$	6.16498	−	2.00312i	0.304096	−	0.0988067i
$412$	−10.8679	−	14.9583i	−0.535421	−	0.736944i
$413$	4.30903	+	19.7033i	0.212034	+	0.969537i
$414$	1.62990	−	0.529586i	0.0801051	−	0.0260277i
$415$	7.41487	+	2.40924i	0.363982	+	0.118265i
$416$	0.856359	−	1.17868i	0.0419865	−	0.0577894i
$417$			5.11940i			0.250698i
$418$	−0.568515	−	0.273664i	−0.0278070	−	0.0133853i
$419$		−	15.4686i		−	0.755688i	−0.925869	−	0.377844i	$-0.876666\pi$
$419$		−	15.4686i		−	0.755688i	0.925869	−	0.377844i	$-0.123334\pi$
$420$	1.20856	+	2.06521i	0.0589717	+	0.100772i
$421$	−10.6212	+	32.6886i	−0.517643	+	1.59314i	0.260777	+	0.965399i	$0.416021\pi$
$421$	−10.6212	+	32.6886i	−0.517643	+	1.59314i	−0.778420	+	0.627743i	$0.783979\pi$
$422$	2.08344	+	6.41217i	0.101420	+	0.312140i
$423$	7.38925	+	10.1704i	0.359277	+	0.494503i
$424$	−8.46470	−	11.6507i	−0.411082	−	0.565806i
$425$	3.85085	+	11.8517i	0.186794	+	0.574892i
$426$	−3.00314	+	9.24273i	−0.145503	+	0.447812i
$427$	−8.01454	−	13.6954i	−0.387851	−	0.662768i
$428$			6.14315i			0.296941i
$429$	−4.35390	−	2.09582i	−0.210209	−	0.101187i
$430$		−	6.47594i		−	0.312298i
$431$	−5.34736	+	7.36000i	−0.257573	+	0.354519i	−0.918146	−	0.396243i	$-0.870314\pi$
$431$	−5.34736	+	7.36000i	−0.257573	+	0.354519i	0.660572	+	0.750762i	$0.270314\pi$
$432$	−0.951057	−	0.309017i	−0.0457577	−	0.0148676i
$433$	27.7690	−	9.02269i	1.33449	−	0.433603i	0.447045	−	0.894512i	$-0.352476\pi$
$433$	27.7690	−	9.02269i	1.33449	−	0.433603i	0.887448	+	0.460909i	$0.152476\pi$
$434$	−7.27401	+	1.59079i	−0.349164	+	0.0763605i
$435$	−0.640588	−	0.881694i	−0.0307138	−	0.0422740i
$436$	−4.61189	+	1.49850i	−0.220870	+	0.0717649i
$437$	0.100748	−	0.310071i	0.00481943	−	0.0148327i
$438$	−3.76640	−	2.73645i	−0.179965	−	0.130753i
$439$	−38.1915			−1.82278			−0.911392	−	0.411540i	$-0.864991\pi$
$439$	−38.1915			−1.82278			−0.911392	+	0.411540i	$0.864991\pi$
$440$	2.16844	+	2.07254i	0.103376	+	0.0988044i
$441$	−4.74462	−	5.14670i	−0.225934	−	0.245081i
$442$	2.55177	−	3.51221i	0.121375	−	0.167059i
$443$	−4.96447	+	15.2791i	−0.235869	+	0.725930i	0.761136	+	0.648592i	$0.224642\pi$
$443$	−4.96447	+	15.2791i	−0.235869	+	0.725930i	−0.997005	+	0.0773379i	$0.975358\pi$
$444$	−1.89397	+	0.615389i	−0.0898840	+	0.0292051i
$445$	5.16769	−	3.75455i	0.244972	−	0.177983i
$446$	−16.4210	+	11.9305i	−0.777556	+	0.564928i
$447$	−2.45495	−	7.55555i	−0.116115	−	0.357365i
$448$	1.75879	−	1.97653i	0.0830950	−	0.0933822i
$449$	−9.82408	−	7.13761i	−0.463627	−	0.336845i	0.331325	−	0.943517i	$-0.392504\pi$
$449$	−9.82408	−	7.13761i	−0.463627	−	0.336845i	−0.794952	+	0.606672i	$0.792504\pi$
$450$		−	4.18204i		−	0.197143i
$451$	5.20188	+	28.6371i	0.244947	+	1.34847i
$452$	5.70243			0.268220
$453$	−6.80923	−	4.94720i	−0.319926	−	0.232440i
$454$	2.14919	+	0.698313i	0.100866	+	0.0327735i
$455$	3.46918	+	0.344062i	0.162638	+	0.0161299i
$456$	−0.153907	+	0.111820i	−0.00720735	+	0.00523645i
$457$	−8.92609	−	12.2857i	−0.417545	−	0.574701i	0.547493	−	0.836810i	$-0.315582\pi$
$457$	−8.92609	−	12.2857i	−0.417545	−	0.574701i	−0.965038	+	0.262109i	$0.915582\pi$
$458$	−7.68152	−	23.6413i	−0.358934	−	1.10468i
$459$	−2.83395	−	0.920806i	−0.132277	−	0.0429796i
$460$	−0.911042	+	1.25394i	−0.0424776	+	0.0584653i
$461$	28.5735			1.33080			0.665400	−	0.746487i	$-0.268261\pi$
$461$	28.5735			1.33080			0.665400	+	0.746487i	$0.268261\pi$
$462$	−7.49239	−	4.56772i	−0.348578	−	0.212509i
$463$	37.0722			1.72289			0.861445	−	0.507851i	$-0.169560\pi$
$463$	37.0722			1.72289			0.861445	+	0.507851i	$0.169560\pi$
$464$	−0.708293	+	0.974881i	−0.0328817	+	0.0452577i
$465$	−2.42071	−	0.786535i	−0.112258	−	0.0364747i
$466$	−1.04262	−	3.20886i	−0.0482985	−	0.148647i
$467$	8.01189	+	11.0274i	0.370746	+	0.510288i	0.953103	−	0.302645i	$-0.0978696\pi$
$467$	8.01189	+	11.0274i	0.370746	+	0.510288i	−0.582357	+	0.812933i	$0.697870\pi$
$468$	−1.17868	+	0.856359i	−0.0544844	+	0.0395852i
$469$	−1.56546	+	15.7845i	−0.0722862	+	0.728863i
$470$	−10.8132	−	3.51342i	−0.498775	−	0.162062i
$471$	5.18519	+	3.76726i	0.238921	+	0.173586i
$472$	7.62317			0.350885
$473$	11.2571	+	20.9108i	0.517604	+	0.961478i
$474$			14.7902i			0.679336i
$475$	−0.643645	−	0.467635i	−0.0295324	−	0.0214566i
$476$	5.24082	−	5.88964i	0.240213	−	0.269951i
$477$	4.45016	+	13.6962i	0.203759	+	0.627105i
$478$	−19.3601	+	14.0660i	−0.885511	+	0.643362i
$479$	−0.588390	+	0.427491i	−0.0268842	+	0.0195325i	−0.601146	−	0.799139i	$-0.705289\pi$
$479$	−0.588390	+	0.427491i	−0.0268842	+	0.0195325i	0.574262	+	0.818672i	$0.305289\pi$
$480$	0.860146	−	0.279478i	0.0392601	−	0.0127564i
$481$	−0.896576	+	2.75938i	−0.0408804	+	0.125817i
$482$	−9.41695	+	12.9613i	−0.428930	+	0.590372i
$483$	1.81990	−	4.15297i	0.0828085	−	0.188966i
$484$	−10.6046	−	2.92281i	−0.482026	−	0.132855i
$485$	−3.80074			−0.172583
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−5.23699	+	16.1178i	−0.237311	+	0.730367i	0.759496	+	0.650512i	$0.225446\pi$
$487$	−5.23699	+	16.1178i	−0.237311	+	0.730367i	−0.996807	+	0.0798547i	$0.974554\pi$
$488$	−5.70404	+	1.85336i	−0.258210	+	0.0838975i
$489$	12.3137	+	16.9484i	0.556845	+	0.766432i
$490$	6.20755	+	1.24352i	0.280429	+	0.0561765i
$491$	−10.7296	+	3.48625i	−0.484219	+	0.157332i	−0.540946	−	0.841058i	$-0.681934\pi$
$491$	−10.7296	+	3.48625i	−0.484219	+	0.157332i	0.0567269	+	0.998390i	$0.481934\pi$
$492$	8.34619	+	2.71184i	0.376275	+	0.122259i
$493$	−2.11057	+	2.90494i	−0.0950551	+	0.130832i
$494$			0.277165i			0.0124702i
$495$	−1.42186	−	2.64119i	−0.0639079	−	0.118713i
$496$			2.81430i			0.126366i
$497$	12.9866	+	22.1918i	0.582529	+	0.995439i
$498$	−2.66388	+	8.19856i	−0.119371	+	0.367386i
$499$	−7.62248	−	23.4596i	−0.341229	−	1.05020i	−0.963572	−	0.267450i	$-0.913819\pi$
$499$	−7.62248	−	23.4596i	−0.341229	−	1.05020i	0.622342	−	0.782745i	$-0.286181\pi$
$500$	4.88117	+	6.71835i	0.218292	+	0.300454i
$501$	0.272242	+	0.374709i	0.0121629	+	0.0167408i
$502$	−1.55200	−	4.77657i	−0.0692692	−	0.213189i
$503$	−2.20784	+	6.79503i	−0.0984427	+	0.302976i	−0.988136	−	0.153584i	$-0.950918\pi$
$503$	−2.20784	+	6.79503i	−0.0984427	+	0.302976i	0.889693	+	0.456559i	$0.150918\pi$
$504$	−2.28349	+	1.33629i	−0.101715	+	0.0595233i
$505$		−	7.96290i		−	0.354345i
$506$	0.762021	−	5.63264i	0.0338760	−	0.250401i
$507$		−	10.8774i		−	0.483081i
$508$	−2.96640	+	4.08290i	−0.131613	+	0.181149i
$509$	−27.5590	−	8.95445i	−1.22153	−	0.396899i	−0.373891	−	0.927473i	$-0.621977\pi$
$509$	−27.5590	−	8.95445i	−1.22153	−	0.396899i	−0.847639	+	0.530574i	$0.821977\pi$
$510$	2.56306	−	0.832788i	0.113494	−	0.0368765i
$511$	−12.0330	+	2.63156i	−0.532307	+	0.116413i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	0.180928	−	0.0587872i	0.00798818	−	0.00259552i
$514$	−0.702662	+	2.16257i	−0.0309931	+	0.0953870i
$515$	−13.5285	−	9.82902i	−0.596136	−	0.433118i
$516$	7.16039			0.315219
$517$	41.0231	−	7.45177i	1.80419	−	0.327729i
$518$	−2.11476	+	4.82583i	−0.0929174	+	0.212035i
$519$	6.16937	−	8.49141i	0.270805	−	0.372732i
$520$	0.407179	−	1.25317i	0.0178560	−	0.0549551i
$521$	−36.1808	+	11.7559i	−1.58511	+	0.515033i	−0.963367	−	0.268188i	$-0.913575\pi$
$521$	−36.1808	+	11.7559i	−1.58511	+	0.515033i	−0.621743	+	0.783221i	$0.713575\pi$
$522$	0.974881	−	0.708293i	0.0426694	−	0.0310011i
$523$	24.4456	−	17.7607i	1.06893	−	0.776623i	0.0932103	−	0.995646i	$-0.470287\pi$
$523$	24.4456	−	17.7607i	1.06893	−	0.776623i	0.975720	+	0.219023i	$0.0702871\pi$
$524$	−3.10099	−	9.54388i	−0.135468	−	0.416926i
$525$	−8.26592	−	7.35532i	−0.360754	−	0.321013i
$526$	−2.61545	−	1.90024i	−0.114039	−	0.0828542i
$527$			8.38601i			0.365301i
$528$	−2.29159	+	2.39763i	−0.0997286	+	0.104343i
$529$	−20.0630			−0.872303
$530$	−10.5370	−	7.65557i	−0.457697	−	0.332537i
$531$	−7.25006	−	2.35569i	−0.314626	−	0.102228i
$532$	−0.0496745	+	0.500869i	−0.00215366	+	0.0217154i
$533$	10.3437	−	7.51516i	0.448036	−	0.325518i
$534$	4.15137	+	5.71387i	0.179647	+	0.247263i
$535$	1.71688	+	5.28401i	0.0742272	+	0.228448i
$536$	5.70184	+	1.85264i	0.246282	+	0.0800218i
$537$	−6.30922	+	8.68389i	−0.272263	+	0.374738i
$538$	−12.5834			−0.542508
$539$	−22.2058	+	6.77527i	−0.956470	+	0.291832i
$540$	−0.904411			−0.0389197
$541$	2.38525	−	3.28302i	0.102550	−	0.141148i	−0.754658	−	0.656119i	$-0.772197\pi$
$541$	2.38525	−	3.28302i	0.102550	−	0.141148i	0.857208	+	0.514970i	$0.172197\pi$
$542$	17.1945	+	5.58683i	0.738567	+	0.239975i
$543$	−0.544103	−	1.67458i	−0.0233497	−	0.0718630i
$544$	−1.75148	−	2.41070i	−0.0750940	−	0.103358i
$545$	−3.54811	+	2.57785i	−0.151984	+	0.110423i
$546$	−0.380426	+	3.83584i	−0.0162807	+	0.164159i
$547$	24.5834	+	7.98764i	1.05111	+	0.341527i	0.783104	−	0.621890i	$-0.213635\pi$
$547$	24.5834	+	7.98764i	1.05111	+	0.341527i	0.268007	+	0.963417i	$0.413635\pi$
$548$	−5.24424	−	3.81016i	−0.224023	−	0.162762i
$549$	5.99759			0.255971
$550$	−12.4977	−	6.01596i	−0.532903	−	0.256522i
$551$		−	0.229242i		−	0.00976605i
$552$	−1.38647	−	1.00733i	−0.0590122	−	0.0428749i
$553$	29.2332	+	26.0128i	1.24312	+	1.10618i
$554$	−1.76952	−	5.44602i	−0.0751796	−	0.231379i
$555$	−1.45711	+	1.05865i	−0.0618507	+	0.0449372i
$556$	4.14168	−	3.00911i	0.175646	−	0.127615i
$557$	15.3763	−	4.99607i	0.651516	−	0.211690i	0.0354334	−	0.999372i	$-0.488719\pi$
$557$	15.3763	−	4.99607i	0.651516	−	0.211690i	0.616082	+	0.787682i	$0.288719\pi$
$558$	0.869665	−	2.67655i	0.0368159	−	0.113308i
$559$	6.13187	−	8.43980i	0.259350	−	0.356965i
$560$	0.960418	−	2.19165i	0.0405851	−	0.0926140i
$561$	−6.82846	+	7.14443i	−0.288298	+	0.301638i
$562$	−20.3902			−0.860109
$563$	−7.59456	−	5.51777i	−0.320073	−	0.232546i	0.416134	−	0.909303i	$-0.363385\pi$
$563$	−7.59456	−	5.51777i	−0.320073	−	0.232546i	−0.736206	+	0.676757i	$0.763385\pi$
$564$	3.88476	−	11.9560i	0.163578	−	0.503441i
$565$	4.90492	−	1.59371i	0.206352	−	0.0670477i
$566$	4.70997	+	6.48272i	0.197975	+	0.272489i
$567$	2.58466	−	0.565255i	0.108546	−	0.0237385i
$568$	9.24273	−	3.00314i	0.387816	−	0.126009i
$569$	−11.0461	−	3.58910i	−0.463077	−	0.150463i	0.0681807	−	0.997673i	$-0.478281\pi$
$569$	−11.0461	−	3.58910i	−0.463077	−	0.150463i	−0.531258	+	0.847210i	$0.678281\pi$
$570$	−0.101131	+	0.139195i	−0.00423592	+	0.00583024i
$571$		−	10.5980i		−	0.443514i	−0.975102	−	0.221757i	$-0.928821\pi$
$571$		−	10.5980i		−	0.443514i	0.975102	−	0.221757i	$-0.0711791\pi$
$572$	0.863606	+	4.75428i	0.0361092	+	0.198786i
$573$		−	10.7065i		−	0.447271i
$574$	20.0392	−	11.7269i	0.836421	−	0.489472i
$575$	2.21475	−	6.81629i	0.0923614	−	0.284259i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−27.2255	−	37.4727i	−1.13341	−	1.56001i	−0.781416	−	0.624010i	$-0.785502\pi$
$577$	−27.2255	−	37.4727i	−1.13341	−	1.56001i	−0.351998	−	0.936001i	$-0.614498\pi$
$578$	4.77331	+	6.56990i	0.198544	+	0.273272i
$579$	−5.63326	−	17.3374i	−0.234110	−	0.720518i
$580$	−0.336777	+	1.03649i	−0.0139839	+	0.0430380i
$581$	11.5195	+	19.6848i	0.477909	+	0.816662i
$582$		−	4.20244i		−	0.174197i
$583$	47.3316	+	6.40333i	1.96027	+	0.265199i
$584$			4.65552i			0.192647i
$585$	−0.774501	+	1.06601i	−0.0320217	+	0.0440741i
$586$	−19.3562	−	6.28922i	−0.799598	−	0.259805i
$587$	−12.6474	+	4.10938i	−0.522013	+	0.169612i	−0.558159	−	0.829734i	$-0.688492\pi$
$587$	−12.6474	+	4.10938i	−0.522013	+	0.169612i	0.0361454	+	0.999347i	$0.488492\pi$
$588$	−1.37495	+	6.86364i	−0.0567020	+	0.283052i
$589$	−0.314694	−	0.433139i	−0.0129667	−	0.0178472i
$590$	6.55704	−	2.13051i	0.269949	−	0.0877117i
$591$	5.84724	−	17.9959i	0.240523	−	0.740254i
$592$	1.61111	+	1.17054i	0.0662162	+	0.0481089i
$593$	−32.7654			−1.34551			−0.672757	−	0.739864i	$-0.734890\pi$
$593$	−32.7654			−1.34551			−0.672757	+	0.739864i	$0.734890\pi$
$594$	2.92034	−	1.57214i	0.119823	−	0.0645057i
$595$	2.86185	−	6.53065i	0.117324	−	0.267731i
$596$	−4.66959	+	6.42713i	−0.191274	+	0.263266i
$597$	−2.42604	+	7.46658i	−0.0992912	+	0.305587i
$598$	−2.37464	+	0.771567i	−0.0971062	+	0.0315517i
$599$	8.25609	−	5.99840i	0.337335	−	0.245088i	−0.406202	−	0.913783i	$-0.633147\pi$
$599$	8.25609	−	5.99840i	0.337335	−	0.245088i	0.743536	+	0.668695i	$0.233147\pi$
$600$	−3.38334	+	2.45814i	−0.138124	+	0.100353i
$601$	11.4909	+	35.3654i	0.468725	+	1.44259i	0.854237	+	0.519884i	$0.174025\pi$
$601$	11.4909	+	35.3654i	0.468725	+	1.44259i	−0.385512	+	0.922703i	$0.625975\pi$
$602$	12.5936	−	14.1527i	0.513278	−	0.576822i
$603$	−4.85027	−	3.52393i	−0.197518	−	0.143506i
$604$			8.41668i			0.342470i
$605$	−9.93835	+	0.449706i	−0.404052	+	0.0182831i
$606$	8.80452			0.357659
$607$	−8.37172	−	6.08241i	−0.339798	−	0.246877i	0.404779	−	0.914415i	$-0.367349\pi$
$607$	−8.37172	−	6.08241i	−0.339798	−	0.246877i	−0.744576	+	0.667537i	$0.767349\pi$
$608$	0.180928	+	0.0587872i	0.00733761	+	0.00238414i
$609$	0.314650	−	3.17262i	0.0127503	−	0.128561i
$610$	−4.38834	+	3.18831i	−0.177679	+	0.129091i
$611$	−10.7656	−	14.8175i	−0.435529	−	0.599454i
$612$	0.920806	+	2.83395i	0.0372214	+	0.114556i
$613$	34.6410	+	11.2555i	1.39913	+	0.454606i	0.908911	−	0.416990i	$-0.136915\pi$
$613$	34.6410	+	11.2555i	1.39913	+	0.454606i	0.490224	+	0.871597i	$0.336915\pi$
$614$	−17.2568	+	23.7520i	−0.696428	+	0.958552i
$615$	7.93684			0.320044
$616$	0.708557	+	8.74631i	0.0285486	+	0.352399i
$617$	−19.4959			−0.784875			−0.392437	−	0.919779i	$-0.628368\pi$
$617$	−19.4959			−0.784875			−0.392437	+	0.919779i	$0.628368\pi$
$618$	10.8679	−	14.9583i	0.437170	−	0.601712i
$619$	−1.79566	−	0.583444i	−0.0721736	−	0.0234506i	0.272708	−	0.962097i	$-0.412081\pi$
$619$	−1.79566	−	0.583444i	−0.0721736	−	0.0234506i	−0.344881	+	0.938646i	$0.612081\pi$
$620$	0.786535	+	2.42071i	0.0315880	+	0.0972179i
$621$	1.00733	+	1.38647i	0.0404228	+	0.0556373i
$622$	18.5490	−	13.4766i	0.743746	−	0.540363i
$623$	18.5950	+	1.84419i	0.744993	+	0.0738860i
$624$	1.38562	+	0.450215i	0.0554691	+	0.0180230i
$625$	−10.8406	−	7.87612i	−0.433622	−	0.315045i
$626$	−10.3160			−0.412309
$627$	0.0845889	−	0.625257i	0.00337816	−	0.0249703i
$628$		−	6.40925i		−	0.255757i
$629$	4.80077	+	3.48796i	0.191419	+	0.139074i
$630$	−1.59067	+	1.78759i	−0.0633737	+	0.0712194i
$631$	1.56149	+	4.80578i	0.0621621	+	0.191315i	0.977315	−	0.211792i	$-0.0679301\pi$
$631$	1.56149	+	4.80578i	0.0621621	+	0.191315i	−0.915153	+	0.403108i	$0.867930\pi$
$632$	11.9655	−	8.69346i	0.475963	−	0.345807i
$633$	−5.45452	+	3.96294i	−0.216798	+	0.157513i
$634$	16.5532	−	5.37846i	0.657412	−	0.213606i
$635$	−1.41045	+	4.34093i	−0.0559722	+	0.172265i
$636$	8.46470	−	11.6507i	0.335647	−	0.461979i
$637$	6.91256	+	7.49836i	0.273886	+	0.297096i
$638$	−0.714286	−	3.93225i	−0.0282789	−	0.155679i
$639$	−9.71838			−0.384453
$640$	−0.731684	−	0.531600i	−0.0289224	−	0.0210133i
$641$	−4.92646	+	15.1621i	−0.194584	+	0.598866i	0.805398	+	0.592735i	$0.201952\pi$
$641$	−4.92646	+	15.1621i	−0.194584	+	0.598866i	−0.999981	+	0.00613164i	$0.998048\pi$
$642$	−5.84249	+	1.89834i	−0.230585	+	0.0749215i
$643$	17.6998	+	24.3617i	0.698012	+	0.960732i	0.999973	+	0.00741102i	$0.00235902\pi$
$643$	17.6998	+	24.3617i	0.698012	+	0.960732i	−0.301960	+	0.953321i	$0.597641\pi$
$644$	−4.42953	+	0.968719i	−0.174548	+	0.0381729i
$645$	6.15898	−	2.00118i	0.242510	−	0.0787962i
$646$	0.539129	+	0.175174i	0.0212117	+	0.00689211i
$647$	−18.2124	+	25.0672i	−0.716002	+	0.985492i	0.283645	+	0.958929i	$0.408456\pi$
$647$	−18.2124	+	25.0672i	−0.716002	+	0.985492i	−0.999647	+	0.0265626i	$0.991544\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−17.4692	+	18.2775i	−0.685725	+	0.717455i
$650$			6.09292i			0.238984i
$651$	−3.76073	−	6.42641i	−0.147394	−	0.251871i
$652$	6.47370	−	19.9240i	0.253530	−	0.780284i
$653$	2.64376	+	8.13664i	0.103458	+	0.318411i	0.989365	−	0.145451i	$-0.0464632\pi$
$653$	2.64376	+	8.13664i	0.103458	+	0.318411i	−0.885907	+	0.463862i	$0.846463\pi$
$654$	−2.85031	−	3.92311i	−0.111456	−	0.153406i
$655$	−5.33461	−	7.34247i	−0.208441	−	0.286894i
$656$	−2.71184	−	8.34619i	−0.105880	−	0.325864i
$657$	1.43864	−	4.42767i	0.0561265	−	0.172740i
$658$	−16.7990	−	28.7065i	−0.654893	−	1.11910i
$659$		−	45.3817i		−	1.76782i	−0.467656	−	0.883910i	$-0.654901\pi$
$659$		−	45.3817i		−	1.76782i	0.467656	−	0.883910i	$-0.345099\pi$
$660$	−1.30102	+	2.70276i	−0.0506420	+	0.105205i
$661$		−	21.0847i		−	0.820102i	−0.912063	−	0.410051i	$-0.865511\pi$
$661$		−	21.0847i		−	0.820102i	0.912063	−	0.410051i	$-0.134489\pi$
$662$	10.9770	−	15.1085i	0.426631	−	0.587208i
$663$	4.12885	+	1.34155i	0.160351	+	0.0521013i
$664$	8.19856	−	2.66388i	0.318166	−	0.103378i
$665$	0.0972547	+	0.444703i	0.00377137	+	0.0172449i
$666$	−1.17054	−	1.61111i	−0.0453575	−	0.0624292i
$667$	1.96406	−	0.638161i	0.0760486	−	0.0247097i
$668$	0.143126	−	0.440497i	0.00553772	−	0.0170433i
$669$	−16.4210	−	11.9305i	−0.634872	−	0.461262i
$670$	5.42219			0.209477
$671$	8.62767	−	17.9233i	0.333067	−	0.691921i
$672$	2.42329	+	1.06193i	0.0934803	+	0.0409647i
$673$	11.4975	−	15.8249i	0.443195	−	0.610006i	−0.527723	−	0.849416i	$-0.676954\pi$
$673$	11.4975	−	15.8249i	0.443195	−	0.610006i	0.970918	+	0.239410i	$0.0769541\pi$
$674$	1.58801	−	4.88738i	0.0611678	−	0.188255i
$675$	3.97736	−	1.29232i	0.153089	−	0.0497415i
$676$	−8.79998	+	6.39356i	−0.338461	+	0.245906i
$677$	−20.9185	+	15.1982i	−0.803963	+	0.584113i	−0.912074	−	0.410026i	$-0.865520\pi$
$677$	−20.9185	+	15.1982i	−0.803963	+	0.584113i	0.108111	+	0.994139i	$0.465520\pi$
$678$	1.76215	+	5.42333i	0.0676749	+	0.208282i
$679$	−8.30625	−	7.39121i	−0.318764	−	0.283649i
$680$	−2.18027	−	1.58406i	−0.0836094	−	0.0607458i
$681$			2.25979i			0.0865953i
$682$	−6.74763	−	6.44921i	−0.258380	−	0.246953i
$683$	40.1808			1.53748			0.768738	−	0.639564i	$-0.220885\pi$
$683$	40.1808			1.53748			0.768738	+	0.639564i	$0.220885\pi$
$684$	−0.153907	−	0.111820i	−0.00588478	−	0.00427554i
$685$	−5.57567	−	1.81165i	−0.213036	−	0.0692194i
$686$	11.1479	+	14.7893i	0.425630	+	0.564659i
$687$	20.1105	−	14.6111i	0.767263	−	0.557449i
$688$	−4.20877	−	5.79288i	−0.160458	−	0.220851i
$689$	−6.48355	−	19.9543i	−0.247003	−	0.760198i
$690$	−1.47410	−	0.478963i	−0.0561179	−	0.0182338i
$691$	−16.3788	+	22.5435i	−0.623080	+	0.857596i	−0.997573	−	0.0696342i	$-0.977817\pi$
$691$	−16.3788	+	22.5435i	−0.623080	+	0.857596i	0.374493	+	0.927230i	$0.377817\pi$
$692$	−10.4960			−0.398997
$693$	2.02888	−	8.53719i	0.0770708	−	0.324301i
$694$	19.8449			0.753303
$695$	2.72147	−	3.74578i	0.103231	−	0.142086i
$696$	−1.14604	−	0.372372i	−0.0434406	−	0.0141147i
$697$	−8.08072	−	24.8699i	−0.306079	−	0.942015i
$698$	16.6883	+	22.9694i	0.631660	+	0.869406i
$699$	2.72962	−	1.98318i	0.103244	−	0.0750109i
$700$	−1.09200	+	11.0106i	−0.0412736	+	0.416162i
$701$	32.7619	+	10.6450i	1.23740	+	0.402056i	0.853390	−	0.521272i	$-0.174542\pi$
$701$	32.7619	+	10.6450i	1.23740	+	0.402056i	0.384011	+	0.923329i	$0.374542\pi$
$702$	−1.17868	−	0.856359i	−0.0444863	−	0.0323212i
$703$	−0.378850			−0.0142886
$704$	3.28668	+	0.444645i	0.123872	+	0.0167582i
$705$		−	11.3697i		−	0.428206i
$706$	8.87693	+	6.44947i	0.334088	+	0.242729i
$707$	15.4853	−	17.4024i	0.582384	−	0.654484i
$708$	2.35569	+	7.25006i	0.0885322	+	0.272474i
$709$	34.1107	−	24.7829i	1.28105	−	0.930740i	0.281469	−	0.959570i	$-0.409178\pi$
$709$	34.1107	−	24.7829i	1.28105	−	0.930740i	0.999584	+	0.0288304i	$0.00917827\pi$
$710$	7.11078	−	5.16629i	0.266863	−	0.193887i
$711$	−14.0663	+	4.57042i	−0.527528	+	0.171404i
$712$	2.18250	−	6.71706i	0.0817928	−	0.251732i
$713$	2.83493	−	3.90194i	0.106169	−	0.146129i
$714$	7.22089	+	3.16432i	0.270235	+	0.118422i
$715$	2.07154	+	3.84801i	0.0774714	+	0.143908i
$716$	10.7339			0.401144
$717$	−19.3601	−	14.0660i	−0.723017	−	0.525303i
$718$	−4.24993	+	13.0799i	−0.158606	+	0.488138i
$719$	−16.9182	+	5.49704i	−0.630941	+	0.205005i	−0.606992	−	0.794708i	$-0.707624\pi$
$719$	−16.9182	+	5.49704i	−0.630941	+	0.205005i	−0.0239490	+	0.999713i	$0.507624\pi$
$720$	0.531600	+	0.731684i	0.0198115	+	0.0272683i
$721$	−10.4513	−	47.7892i	−0.389226	−	1.77976i
$722$	18.0357	−	5.86014i	0.671218	−	0.218092i
$723$	−15.2369	−	4.95078i	−0.566668	−	0.184122i
$724$	−1.03495	+	1.42448i	−0.0384634	+	0.0529404i
$725$		−	5.03944i		−	0.187160i
$726$	−0.497236	−	10.9888i	−0.0184542	−	0.407831i
$727$		−	32.0191i		−	1.18752i	−0.804642	−	0.593761i	$-0.797643\pi$
$727$		−	32.0191i		−	1.18752i	0.804642	−	0.593761i	$-0.202357\pi$
$728$	3.32687	−	1.94688i	0.123302	−	0.0721562i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	1.30112	+	4.00443i	0.0481566	+	0.148211i
$731$	−12.5413	−	17.2616i	−0.463856	−	0.638442i
$732$	−3.52529	−	4.85215i	−0.130299	−	0.179341i
$733$	−0.103709	−	0.319185i	−0.00383059	−	0.0117894i	0.949123	−	0.314906i	$-0.101973\pi$
$733$	−0.103709	−	0.319185i	−0.00383059	−	0.0117894i	−0.952954	+	0.303116i	$0.901973\pi$
$734$	−9.79351	+	30.1413i	−0.361485	+	1.11254i
$735$	0.735581	+	6.28800i	0.0271323	+	0.231936i
$736$			1.71378i			0.0631706i
$737$	−17.5082	+	9.42540i	−0.644923	+	0.347189i
$738$			8.77570i			0.323038i
$739$	20.4246	−	28.1121i	0.751332	−	1.03412i	−0.246554	−	0.969129i	$-0.579298\pi$
$739$	20.4246	−	28.1121i	0.751332	−	1.03412i	0.997886	−	0.0649905i	$-0.0207017\pi$
$740$	1.71293	+	0.556565i	0.0629686	+	0.0204597i
$741$	−0.263599	+	0.0856486i	−0.00968356	+	0.00314638i
$742$	−8.14024	−	37.2218i	−0.298838	−	1.36645i
$743$	−1.31979	−	1.81653i	−0.0484183	−	0.0666421i	0.784121	−	0.620608i	$-0.213114\pi$
$743$	−1.31979	−	1.81653i	−0.0484183	−	0.0666421i	−0.832540	+	0.553965i	$0.813114\pi$
$744$	−2.67655	+	0.869665i	−0.0981272	+	0.0318835i
$745$	−2.22028	+	6.83332i	−0.0813448	+	0.250354i
$746$	1.49001	+	1.08256i	0.0545533	+	0.0396353i
$747$	−8.62048			−0.315407
$748$	9.79363	+	1.32495i	0.358091	+	0.0484449i
$749$	−6.52358	+	14.8866i	−0.238366	+	0.543945i
$750$	−4.88117	+	6.71835i	−0.178235	+	0.245320i
$751$	11.4091	−	35.1135i	0.416323	−	1.28131i	−0.494739	−	0.869042i	$-0.664736\pi$
$751$	11.4091	−	35.1135i	0.416323	−	1.28131i	0.911062	−	0.412270i	$-0.135264\pi$
$752$	−11.9560	+	3.88476i	−0.435992	+	0.141662i
$753$	4.06319	−	2.95208i	0.148071	−	0.107580i
$754$	−1.42033	+	1.03193i	−0.0517254	+	0.0375807i
$755$	2.35228	+	7.23957i	0.0856082	+	0.263475i
$756$	−1.97653	−	1.75879i	−0.0718856	−	0.0639665i
$757$	−20.4728	−	14.8744i	−0.744096	−	0.540618i	0.149895	−	0.988702i	$-0.452106\pi$
$757$	−20.4728	−	14.8744i	−0.744096	−	0.540618i	−0.893991	+	0.448084i	$0.852106\pi$
$758$			21.3747i			0.776365i
$759$	5.59243	−	1.01586i	0.202992	−	0.0368732i
$760$	0.172055			0.00624108
$761$	−31.8629	−	23.1498i	−1.15503	−	0.839178i	−0.165888	−	0.986145i	$-0.553049\pi$
$761$	−31.8629	−	23.1498i	−1.15503	−	0.839178i	−0.989142	+	0.146966i	$0.953049\pi$
$762$	−4.79973	−	1.55953i	−0.173876	−	0.0564957i
$763$	−12.7672	−	1.26621i	−0.462205	−	0.0458399i
$764$	−8.66175	+	6.29313i	−0.313371	+	0.227677i
$765$	1.58406	+	2.18027i	0.0572717	+	0.0788277i
$766$	−10.9274	−	33.6312i	−0.394824	−	1.21514i
$767$	10.5628	+	3.43206i	0.381401	+	0.123925i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	8.73031			0.314823			0.157411	−	0.987533i	$-0.449685\pi$
$769$	8.73031			0.314823			0.157411	+	0.987533i	$0.449685\pi$
$770$	3.05387	+	7.32508i	0.110054	+	0.263978i
$771$	−2.27386			−0.0818912
$772$	−10.7151	+	14.7481i	−0.385645	+	0.530795i
$773$	−1.17313	−	0.381173i	−0.0421945	−	0.0137098i	0.287844	−	0.957677i	$-0.407062\pi$
$773$	−1.17313	−	0.381173i	−0.0421945	−	0.0137098i	−0.330038	+	0.943968i	$0.607062\pi$
$774$	2.21268	+	6.80994i	0.0795333	+	0.244778i
$775$	−6.91794	−	9.52172i	−0.248500	−	0.342030i
$776$	−3.39985	+	2.47013i	−0.122047	+	0.0886726i
$777$	−5.24314	−	0.519997i	−0.188096	−	0.0186548i
$778$	11.9108	+	3.87006i	0.427024	+	0.138748i
$779$	1.35064	+	0.981298i	0.0483917	+	0.0351587i
$780$	1.31766			0.0471798
$781$	−13.9801	+	29.0426i	−0.500248	+	1.03923i
$782$			5.10669i			0.182615i
$783$	0.974881	+	0.708293i	0.0348394	+	0.0253123i
$784$	6.36097	−	2.92199i	0.227178	−	0.104357i
$785$	−1.79125	−	5.51289i	−0.0639323	−	0.196764i
$786$	8.11851	−	5.89844i	0.289578	−	0.210390i
$787$	42.2821	−	30.7197i	1.50719	−	1.09504i	0.539789	−	0.841800i	$-0.318504\pi$
$787$	42.2821	−	30.7197i	1.50719	−	1.09504i	0.967404	−	0.253240i	$-0.0814961\pi$
$788$	−17.9959	+	5.84724i	−0.641079	+	0.208299i
$789$	0.999013	−	3.07465i	0.0355658	−	0.109460i
$790$	7.86246	−	10.8218i	0.279734	−	0.385021i
$791$	13.8186	+	6.05556i	0.491334	+	0.215311i
$792$	−2.98842	−	1.43852i	−0.106189	−	0.0511157i
$793$	−8.73804			−0.310297
$794$	−7.23370	−	5.25559i	−0.256714	−	0.186514i
$795$	4.02477	−	12.3870i	0.142744	−	0.439321i
$796$	7.46658	−	2.42604i	0.264646	−	0.0859887i
$797$	30.4175	+	41.8661i	1.07744	+	1.48297i	0.862304	+	0.506392i	$0.169021\pi$
$797$	30.4175	+	41.8661i	1.07744	+	1.48297i	0.215141	+	0.976583i	$0.430979\pi$
$798$	−0.491705	+	0.107534i	−0.0174062	+	0.00380665i
$799$	−35.6265	+	11.5758i	−1.26038	+	0.409521i
$800$	3.97736	+	1.29232i	0.140621	+	0.0456905i
$801$	−4.15137	+	5.71387i	−0.146681	+	0.201890i
$802$			26.8774i			0.949073i
$803$	−11.1622	−	10.6686i	−0.393906	−	0.376485i
$804$			5.99527i			0.211437i
$805$	−3.53931	+	2.07120i	−0.124744	+	0.0730002i
$806$	−1.26704	+	3.89954i	−0.0446295	+	0.137355i
$807$	−3.88848	−	11.9675i	−0.136881	−	0.421276i
$808$	−5.17516	−	7.12300i	−0.182062	−	0.250586i
$809$	−4.54325	−	6.25325i	−0.159732	−	0.219853i	0.721648	−	0.692260i	$-0.243385\pi$
$809$	−4.54325	−	6.25325i	−0.159732	−	0.219853i	−0.881380	+	0.472408i	$0.843385\pi$
$810$	−0.279478	−	0.860146i	−0.00981987	−	0.0302225i
$811$	−15.1128	+	46.5125i	−0.530683	+	1.63328i	0.222112	+	0.975021i	$0.428705\pi$
$811$	−15.1128	+	46.5125i	−0.530683	+	1.63328i	−0.752796	+	0.658254i	$0.771295\pi$
$812$	−2.75165	+	1.61026i	−0.0965639	+	0.0565091i
$813$			18.0794i			0.634071i
$814$	−6.49852	+	1.18044i	−0.227773	+	0.0413746i
$815$		−	18.9468i		−	0.663678i
$816$	1.75148	−	2.41070i	0.0613140	−	0.0843915i
$817$	1.29552	+	0.420939i	0.0453245	+	0.0147268i
$818$	34.3569	−	11.1632i	1.20126	−	0.390313i
$819$	−3.76566	+	0.823534i	−0.131583	+	0.0287766i
$820$	−4.66516	−	6.42104i	−0.162914	−	0.224233i
$821$	−27.2662	+	8.85933i	−0.951597	+	0.309193i	−0.743364	−	0.668887i	$-0.766771\pi$
$821$	−27.2662	+	8.85933i	−0.951597	+	0.309193i	−0.208233	+	0.978079i	$0.566771\pi$
$822$	2.00312	−	6.16498i	0.0698669	−	0.215028i
$823$	−7.60809	−	5.52760i	−0.265201	−	0.192680i	0.447236	−	0.894416i	$-0.352409\pi$
$823$	−7.60809	−	5.52760i	−0.265201	−	0.192680i	−0.712437	+	0.701736i	$0.752409\pi$
$824$	−18.4895			−0.644113
$825$	1.85952	−	13.7450i	0.0647402	−	0.478541i
$826$	18.4731	+	8.09524i	0.642762	+	0.281670i
$827$	2.20260	−	3.03161i	0.0765917	−	0.105419i	−0.769002	−	0.639246i	$-0.779247\pi$
$827$	2.20260	−	3.03161i	0.0765917	−	0.105419i	0.845594	+	0.533827i	$0.179247\pi$
$828$	0.529586	−	1.62990i	0.0184044	−	0.0566428i
$829$	11.6203	−	3.77567i	0.403590	−	0.131134i	−0.100186	−	0.994969i	$-0.531944\pi$
$829$	11.6203	−	3.77567i	0.403590	−	0.131134i	0.503776	+	0.863834i	$0.331944\pi$
$830$	6.30747	−	4.58264i	0.218935	−	0.159066i
$831$	4.63266	−	3.36582i	0.160705	−	0.116759i
$832$	−0.450215	−	1.38562i	−0.0156084	−	0.0480377i
$833$	18.9544	−	8.70691i	0.656730	−	0.301677i
$834$	4.14168	+	3.00911i	0.143415	+	0.104197i
$835$		−	0.418893i		−	0.0144964i
$836$	−0.555563	+	0.299083i	−0.0192146	+	0.0103440i
$837$	2.81430			0.0972763
$838$	−12.5143	−	9.09219i	−0.432300	−	0.314084i
$839$	−37.2707	−	12.1100i	−1.28673	−	0.418083i	−0.415782	−	0.909464i	$-0.636492\pi$
$839$	−37.2707	−	12.1100i	−1.28673	−	0.418083i	−0.870944	+	0.491382i	$0.836492\pi$
$840$	2.38117	+	0.236156i	0.0821580	+	0.00814816i
$841$	−22.2867	+	16.1923i	−0.768508	+	0.558354i
$842$	20.2026	+	27.8065i	0.696229	+	0.958277i
$843$	−6.30092	−	19.3922i	−0.217015	−	0.667904i
$844$	6.41217	+	2.08344i	0.220716	+	0.0717150i
$845$	−5.78240	+	7.95880i	−0.198921	+	0.273791i
$846$	12.5713			0.432211
$847$	−22.5941	−	18.3441i	−0.776343	−	0.630311i
$848$	−14.4010			−0.494533
$849$	−4.70997	+	6.48272i	−0.161646	+	0.222486i
$850$	11.8517	+	3.85085i	0.406510	+	0.132083i
$851$	−1.05464	−	3.24584i	−0.0361525	−	0.111266i
$852$	5.71232	+	7.86234i	0.195701	+	0.269359i
$853$	27.2884	−	19.8262i	0.934336	−	0.678835i	−0.0127149	−	0.999919i	$-0.504047\pi$
$853$	27.2884	−	19.8262i	0.934336	−	0.678835i	0.947051	+	0.321085i	$0.104047\pi$
$854$	−15.7907	−	1.56607i	−0.540345	−	0.0535896i
$855$	−0.163634	−	0.0531678i	−0.00559615	−	0.00181830i
$856$	4.96992	+	3.61086i	0.169868	+	0.123417i
$857$	41.9374			1.43255			0.716276	−	0.697817i	$-0.245845\pi$
$857$	41.9374			1.43255			0.716276	+	0.697817i	$0.245845\pi$
$858$	−4.25472	+	2.29049i	−0.145254	+	0.0781960i
$859$			31.0514i			1.05946i	0.848166	+	0.529731i	$0.177707\pi$
$859$			31.0514i			1.05946i	−0.848166	+	0.529731i	$0.822293\pi$
$860$	−5.23915	−	3.80646i	−0.178653	−	0.129799i
$861$	17.3454	+	15.4346i	0.591130	+	0.526010i
$862$	2.81127	+	8.65220i	0.0957523	+	0.294695i
$863$	8.57477	−	6.22993i	0.291888	−	0.212069i	−0.432198	−	0.901779i	$-0.642262\pi$
$863$	8.57477	−	6.22993i	0.291888	−	0.212069i	0.724086	+	0.689709i	$0.242262\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−9.02806	+	2.93339i	−0.306963	+	0.0997384i
$866$	9.02269	−	27.7690i	0.306604	−	0.943629i
$867$	−4.77331	+	6.56990i	−0.162110	+	0.223125i
$868$	−2.98858	+	6.81984i	−0.101439	+	0.231480i
$869$	−6.57638	+	48.6107i	−0.223088	+	1.64901i
$870$	−1.08983			−0.0369488
$871$	7.06649	+	5.13410i	0.239439	+	0.173962i
$872$	−1.49850	+	4.61189i	−0.0507455	+	0.156178i
$873$	3.99676	−	1.29863i	0.135270	−	0.0439518i
$874$	−0.191634	−	0.263762i	−0.00648212	−	0.00892187i
$875$	4.69407	+	21.4639i	0.158688	+	0.725613i
$876$	−4.42767	+	1.43864i	−0.149597	+	0.0486070i
$877$	−6.78260	−	2.20380i	−0.229032	−	0.0744170i	0.192253	−	0.981345i	$-0.438421\pi$
$877$	−6.78260	−	2.20380i	−0.229032	−	0.0744170i	−0.421285	+	0.906928i	$0.638421\pi$
$878$	−22.4484	+	30.8976i	−0.757598	+	1.04274i
$879$		−	20.3523i		−	0.686467i
$880$	2.95130	−	0.536098i	0.0994882	−	0.0180719i
$881$			52.8762i			1.78145i	0.454547	+	0.890723i	$0.349801\pi$
$881$			52.8762i			1.78145i	−0.454547	+	0.890723i	$0.650199\pi$
$882$	−6.95259	+	0.813325i	−0.234106	+	0.0273861i
$883$	10.1192	−	31.1436i	0.340537	−	1.04806i	−0.623393	−	0.781908i	$-0.714246\pi$
$883$	10.1192	−	31.1436i	0.340537	−	1.04806i	0.963930	−	0.266156i	$-0.0857536\pi$
$884$	−1.34155	−	4.12885i	−0.0451211	−	0.138868i
$885$	4.05247	+	5.57775i	0.136222	+	0.187494i
$886$	9.44298	+	12.9971i	0.317243	+	0.436648i
$887$	17.6013	+	54.1712i	0.590994	+	1.81889i	0.573734	+	0.819041i	$0.305494\pi$
$887$	17.6013	+	54.1712i	0.590994	+	1.81889i	0.0172595	+	0.999851i	$0.494506\pi$
$888$	−0.615389	+	1.89397i	−0.0206511	+	0.0635576i
$889$	−11.5242	+	6.74393i	−0.386508	+	0.226184i
$890$		−	6.38762i		−	0.214113i
$891$	2.39763	+	2.29159i	0.0803235	+	0.0767711i
$892$			20.2975i			0.679609i
$893$	1.40573	−	1.93481i	0.0470408	−	0.0647461i
$894$	−7.55555	−	2.45495i	−0.252695	−	0.0821057i
$895$	9.23271	−	2.99989i	0.308615	−	0.100275i
$896$	−0.565255	−	2.58466i	−0.0188838	−	0.0863476i
$897$	−1.46761	−	2.01999i	−0.0490020	−	0.0674454i
$898$	−11.5489	+	3.75247i	−0.385392	+	0.125221i
$899$	1.04796	−	3.22530i	0.0349515	−	0.107570i
$900$	−3.38334	−	2.45814i	−0.112778	−	0.0819381i
$901$	−42.9120			−1.42961
$902$	26.2255	+	12.6241i	0.873213	+	0.420335i
$903$	17.3517	+	7.60381i	0.577428	+	0.253039i
$904$	3.35181	−	4.61336i	0.111479	−	0.153438i
$905$	−0.492093	+	1.51451i	−0.0163577	+	0.0503439i
$906$	−8.00474	+	2.60090i	−0.265940	+	0.0864090i
$907$	−16.9499	+	12.3148i	−0.562812	+	0.408907i	−0.832487	−	0.554045i	$-0.813084\pi$
$907$	−16.9499	+	12.3148i	−0.562812	+	0.408907i	0.269675	+	0.962951i	$0.413084\pi$
$908$	1.82821	−	1.32827i	0.0606712	−	0.0440802i
$909$	2.72075	+	8.37359i	0.0902414	+	0.277735i
$910$	2.31749	−	2.60439i	0.0768239	−	0.0863347i
$911$	−27.2126	−	19.7711i	−0.901593	−	0.655046i	0.0372817	−	0.999305i	$-0.488130\pi$
$911$	−27.2126	−	19.7711i	−0.901593	−	0.655046i	−0.938875	+	0.344259i	$0.888130\pi$
$912$			0.190239i			0.00629945i
$913$	−12.4008	+	25.7616i	−0.410405	+	0.852585i
$914$	−15.1860			−0.502307
$915$	−4.38834	−	3.18831i	−0.145074	−	0.105402i
$916$	−23.6413	−	7.68152i	−0.781130	−	0.253805i
$917$	2.62030	−	26.4206i	0.0865301	−	0.872484i
$918$	−2.41070	+	1.75148i	−0.0795650	+	0.0578074i
$919$	20.9699	+	28.8626i	0.691733	+	0.952089i	1.00000		0.000788634i	$0.000251030\pi$
$919$	20.9699	+	28.8626i	0.691733	+	0.952089i	−0.308267	+	0.951300i	$0.599749\pi$
$920$	0.478963	+	1.47410i	0.0157909	+	0.0485995i
$921$	−27.9221	−	9.07245i	−0.920065	−	0.298947i
$922$	16.7951	−	23.1165i	0.553117	−	0.761300i
$923$	14.1590			0.466048
$924$	−8.09928	+	3.37664i	−0.266447	+	0.111083i
$925$	−8.32829			−0.273832
$926$	21.7905	−	29.9920i	0.716079	−	0.985599i
$927$	17.5846	+	5.71357i	0.577553	+	0.187658i
$928$	0.372372	+	1.14604i	0.0122237	+	0.0376207i
$929$	−21.5945	−	29.7223i	−0.708492	−	0.975155i	−0.999828	−	0.0185348i	$-0.994100\pi$
$929$	−21.5945	−	29.7223i	−0.708492	−	0.975155i	0.291336	−	0.956621i	$-0.405900\pi$
$930$	−2.05917	+	1.49608i	−0.0675230	+	0.0490583i
$931$	−0.652261	+	1.16100i	−0.0213770	+	0.0380501i
$932$	−3.20886	−	1.04262i	−0.105110	−	0.0341522i
$933$	18.5490	+	13.4766i	0.607266	+	0.441204i
$934$	13.6306			0.446008
$935$	8.79425	−	1.59746i	0.287603	−	0.0522425i
$936$			1.45693i			0.0476211i
$937$	0.608184	+	0.441872i	0.0198685	+	0.0144353i	0.597675	−	0.801738i	$-0.296091\pi$
$937$	0.608184	+	0.441872i	0.0198685	+	0.0144353i	−0.577807	+	0.816174i	$0.696091\pi$
$938$	11.8498	+	10.5444i	0.386910	+	0.344287i
$939$	−3.18781	−	9.81108i	−0.104030	−	0.320172i
$940$	−9.19824	+	6.68292i	−0.300014	+	0.217973i
$941$	3.40201	−	2.47171i	0.110902	−	0.0805753i	−0.530952	−	0.847402i	$-0.678165\pi$
$941$	3.40201	−	2.47171i	0.110902	−	0.0805753i	0.641854	+	0.766827i	$0.278165\pi$
$942$	6.09556	−	1.98057i	0.198604	−	0.0645304i
$943$	−4.64749	+	14.3035i	−0.151343	+	0.465786i
$944$	4.48078	−	6.16727i	0.145837	−	0.200728i
$945$	−2.19165	−	0.960418i	−0.0712943	−	0.0312424i
$946$	23.5339	+	3.18383i	0.765155	+	0.103515i
$947$	16.0362			0.521105			0.260553	−	0.965460i	$-0.416095\pi$
$947$	16.0362			0.521105			0.260553	+	0.965460i	$0.416095\pi$
$948$	11.9655	+	8.69346i	0.388622	+	0.282350i
$949$	−2.09599	+	6.45078i	−0.0680386	+	0.209401i
$950$	−0.756650	+	0.245850i	−0.0245490	+	0.00797644i
$951$	10.2304	+	14.0810i	0.331745	+	0.456608i
$952$	−1.68434	−	7.70176i	−0.0545898	−	0.249615i
$953$	−22.2349	+	7.22457i	−0.720260	+	0.234027i	−0.646136	−	0.763222i	$-0.723616\pi$
$953$	−22.2349	+	7.22457i	−0.720260	+	0.234027i	−0.0741243	+	0.997249i	$0.523616\pi$
$954$	13.6962	+	4.45016i	0.443430	+	0.144079i
$955$	−5.69158	+	7.83378i	−0.184175	+	0.253495i
$956$			23.9304i			0.773965i
$957$	3.51907	−	1.89446i	0.113755	−	0.0612392i
$958$			0.727290i			0.0234977i
$959$	−8.66218	−	14.8021i	−0.279716	−	0.477985i
$960$	0.279478	−	0.860146i	0.00902013	−	0.0277611i
$961$	7.13203	+	21.9501i	0.230066	+	0.708069i
$962$	1.70539	+	2.34727i	0.0549840	+	0.0756789i
$963$	−3.61086	−	4.96992i	−0.116358	−	0.160153i
$964$	4.95078	+	15.2369i	0.159454	+	0.490749i
$965$	−5.09478	+	15.6801i	−0.164007	+	0.504761i
$966$	−2.29011	−	3.91338i	−0.0736830	−	0.125911i
$967$			52.0738i			1.67458i	0.546759	+	0.837290i	$0.315861\pi$
$967$			52.0738i			1.67458i	−0.546759	+	0.837290i	$0.684139\pi$
$968$	−8.59782	+	6.86130i	−0.276344	+	0.220531i
$969$			0.566874i			0.0182106i
$970$	−2.23402	+	3.07486i	−0.0717300	+	0.0987278i
$971$	10.9554	+	3.55963i	0.351576	+	0.114234i	0.479480	−	0.877553i	$-0.340825\pi$
$971$	10.9554	+	3.55963i	0.351576	+	0.114234i	−0.127905	+	0.991786i	$0.540825\pi$
$972$	0.951057	−	0.309017i	0.0305052	−	0.00991172i
$973$	13.2319	−	2.89376i	0.424196	−	0.0927698i
$974$	9.96134	+	13.7106i	0.319182	+	0.439316i
$975$	−5.79471	+	1.88282i	−0.185579	+	0.0602984i
$976$	−1.85336	+	5.70404i	−0.0593245	+	0.182582i
$977$	−26.4192	−	19.1946i	−0.845224	−	0.614091i	0.0786013	−	0.996906i	$-0.474955\pi$
$977$	−26.4192	−	19.1946i	−0.845224	−	0.614091i	−0.923825	+	0.382815i	$0.874955\pi$
$978$	20.9493			0.669886
$979$	11.1036	+	20.6256i	0.354873	+	0.659196i
$980$	4.65474	−	4.29109i	0.148690	−	0.137074i
$981$	2.85031	−	3.92311i	0.0910033	−	0.125255i
$982$	−3.48625	+	10.7296i	−0.111251	+	0.342394i
$983$	−33.8976	+	11.0140i	−1.08116	+	0.351292i	−0.794826	−	0.606837i	$-0.792438\pi$
$983$	−33.8976	+	11.0140i	−1.08116	+	0.351292i	−0.286338	+	0.958129i	$0.592438\pi$
$984$	7.09969	−	5.15823i	0.226330	−	0.164438i
$985$	−13.8450	+	10.0590i	−0.441137	+	0.320505i
$986$	1.10959	+	3.41497i	0.0353365	+	0.108755i
$987$	22.1103	−	24.8476i	0.703779	−	0.790908i
$988$	0.224231	+	0.162913i	0.00713373	+	0.00518296i
$989$			12.2713i			0.390205i
$990$	−2.97251	−	0.402142i	−0.0944727	−	0.0127809i
$991$	−22.1232			−0.702768			−0.351384	−	0.936231i	$-0.614289\pi$
$991$	−22.1232			−0.702768			−0.351384	+	0.936231i	$0.614289\pi$
$992$	2.27681	+	1.65420i	0.0722889	+	0.0525209i
$993$	17.7611	+	5.77093i	0.563631	+	0.183135i
$994$	25.5869	+	2.53762i	0.811567	+	0.0804885i
$995$	5.74432	−	4.17350i	0.182107	−	0.132309i
$996$	5.06699	+	6.97412i	0.160554	+	0.220983i
$997$	−3.15624	−	9.71391i	−0.0999592	−	0.307643i	0.888555	−	0.458770i	$-0.151710\pi$
$997$	−3.15624	−	9.71391i	−0.0999592	−	0.307643i	−0.988514	+	0.151127i	$0.951710\pi$
$998$	−23.4596	−	7.62248i	−0.742600	−	0.241285i
$999$	1.17054	−	1.61111i	0.0370342	−	0.0509733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.a.139.6	✓	32
7.6	odd	2		462.2.u.b.139.7	yes	32
11.8	odd	10		462.2.u.b.349.7	yes	32
77.41	even	10	inner	462.2.u.a.349.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.6	✓	32	1.1	even	1	trivial
462.2.u.a.349.6	yes	32	77.41	even	10	inner
462.2.u.b.139.7	yes	32	7.6	odd	2
462.2.u.b.349.7	yes	32	11.8	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.531600 - 0.731684i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.261116 - 2.63283i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.531600 - 0.731684i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.261116 - 2.63283i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} -0.904411 q^{10} +(2.92034 - 1.57214i) q^{11} -1.00000i q^{12} +(-1.17868 - 0.856359i) q^{13} +(-1.97653 - 1.75879i) q^{14} +(-0.279478 - 0.860146i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.41070 + 1.75148i) q^{17} +(0.951057 - 0.309017i) q^{18} +(0.0587872 - 0.180928i) q^{19} +(-0.531600 + 0.731684i) q^{20} +(1.06193 - 2.42329i) q^{21} +(0.444645 - 3.28668i) q^{22} +1.71378 q^{23} +(-0.809017 - 0.587785i) q^{24} +(1.29232 - 3.97736i) q^{25} +(-1.38562 + 0.450215i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-2.58466 + 0.565255i) q^{28} +(1.14604 - 0.372372i) q^{29} +(-0.860146 - 0.279478i) q^{30} +(1.65420 - 2.27681i) q^{31} +1.00000i q^{32} +(3.26322 - 0.592759i) q^{33} +2.97979i q^{34} +(-2.06521 + 1.20856i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.615389 - 1.89397i) q^{37} +(-0.111820 - 0.153907i) q^{38} +(-0.856359 - 1.17868i) q^{39} +(0.279478 + 0.860146i) q^{40} +(-2.71184 + 8.34619i) q^{41} +(-1.33629 - 2.28349i) q^{42} +7.16039i q^{43} +(-2.39763 - 2.29159i) q^{44} -0.904411i q^{45} +(1.00733 - 1.38647i) q^{46} +(11.9560 + 3.88476i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-6.86364 - 1.37495i) q^{49} +(-2.45814 - 3.38334i) q^{50} +(-2.83395 + 0.920806i) q^{51} +(-0.450215 + 1.38562i) q^{52} +(11.6507 + 8.46470i) q^{53} +1.00000 q^{54} +(-2.70276 - 1.30102i) q^{55} +(-1.06193 + 2.42329i) q^{56} +(0.111820 - 0.153907i) q^{57} +(0.372372 - 1.14604i) q^{58} +(-7.25006 + 2.35569i) q^{59} +(-0.731684 + 0.531600i) q^{60} +(4.85215 - 3.52529i) q^{61} +(-0.869665 - 2.67655i) q^{62} +(1.75879 - 1.97653i) q^{63} +(0.809017 + 0.587785i) q^{64} +1.31766i q^{65} +(1.43852 - 2.98842i) q^{66} -5.99527 q^{67} +(2.41070 + 1.75148i) q^{68} +(1.62990 + 0.529586i) q^{69} +(-0.236156 + 2.38117i) q^{70} +(-7.86234 + 5.71232i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-1.43864 - 4.42767i) q^{73} +(-1.89397 - 0.615389i) q^{74} +(2.45814 - 3.38334i) q^{75} -0.190239 q^{76} +(-3.37664 - 8.09928i) q^{77} -1.45693 q^{78} +(-8.69346 + 11.9655i) q^{79} +(0.860146 + 0.279478i) q^{80} +(0.309017 + 0.951057i) q^{81} +(5.15823 + 7.09969i) q^{82} +(-6.97412 + 5.06699i) q^{83} +(-2.63283 - 0.261116i) q^{84} +(2.56306 + 0.832788i) q^{85} +(5.79288 + 4.20877i) q^{86} +1.20502 q^{87} +(-3.26322 + 0.592759i) q^{88} +7.06273i q^{89} +(-0.731684 - 0.531600i) q^{90} +(-2.56242 + 2.87965i) q^{91} +(-0.529586 - 1.62990i) q^{92} +(2.27681 - 1.65420i) q^{93} +(10.1704 - 7.38925i) q^{94} +(-0.163634 + 0.0531678i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(2.47013 - 3.39985i) q^{97} +(-5.14670 + 4.74462i) q^{98} +(3.28668 + 0.444645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more