LMFDB - Embedded newform 546.2.cg.b.145.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.9
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.b.241.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.589284 - 0.157898i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.91156 - 1.82919i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.589284 - 0.157898i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.91156 - 1.82919i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.305036 - 0.528338i) q^{10} +(-3.40302 + 0.911835i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.11704 - 3.42815i) q^{13} +(-2.64511 + 0.0582404i) q^{14} +(-0.589284 - 0.157898i) q^{15} -1.00000 q^{16} -0.661787 q^{17} +(0.965926 + 0.258819i) q^{18} +(0.476735 - 1.77920i) q^{19} +(-0.157898 - 0.589284i) q^{20} +(0.740861 + 2.53991i) q^{21} +(-1.76153 + 3.05106i) q^{22} -6.64347i q^{23} +(0.258819 + 0.965926i) q^{24} +(-4.00780 + 2.31391i) q^{25} +(-3.21394 - 1.63420i) q^{26} -1.00000i q^{27} +(-1.82919 + 1.91156i) q^{28} +(2.81107 + 4.86891i) q^{29} +(-0.528338 + 0.305036i) q^{30} +(-0.583910 + 2.17918i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.40302 + 0.911835i) q^{33} +(-0.467954 + 0.467954i) q^{34} +(-1.41528 - 0.776083i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.59669 - 1.59669i) q^{37} +(-0.920982 - 1.59519i) q^{38} +(-0.746686 + 3.52739i) q^{39} +(-0.528338 - 0.305036i) q^{40} +(1.83508 - 6.84860i) q^{41} +(2.31985 + 1.27212i) q^{42} +(-6.91494 - 3.99234i) q^{43} +(0.911835 + 3.40302i) q^{44} +(0.431386 + 0.431386i) q^{45} +(-4.69764 - 4.69764i) q^{46} +(-1.18439 - 4.42021i) q^{47} +(0.866025 + 0.500000i) q^{48} +(0.308105 + 6.99322i) q^{49} +(-1.19777 + 4.47012i) q^{50} +(0.573124 + 0.330893i) q^{51} +(-3.42815 + 1.11704i) q^{52} +(5.24890 + 9.09137i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-1.86137 + 1.07466i) q^{55} +(0.0582404 + 2.64511i) q^{56} +(-1.30246 + 1.30246i) q^{57} +(5.43056 + 1.45511i) q^{58} +(6.82671 - 6.82671i) q^{59} +(-0.157898 + 0.589284i) q^{60} +(11.3835 - 6.57224i) q^{61} +(1.12803 + 1.95380i) q^{62} +(0.628349 - 2.57005i) q^{63} +1.00000i q^{64} +(-1.19956 - 1.84377i) q^{65} +(3.05106 - 1.76153i) q^{66} +(-3.70462 - 13.8258i) q^{67} +0.661787i q^{68} +(-3.32174 + 5.75342i) q^{69} +(-1.54953 + 0.451978i) q^{70} +(3.44163 + 12.8443i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-4.06451 - 1.08908i) q^{73} -2.25805 q^{74} +4.62781 q^{75} +(-1.77920 - 0.476735i) q^{76} +(8.17298 + 4.48175i) q^{77} +(1.96625 + 3.02223i) q^{78} +(-3.20797 + 5.55637i) q^{79} +(-0.589284 + 0.157898i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.54509 - 6.14028i) q^{82} +(5.17053 + 5.17053i) q^{83} +(2.53991 - 0.740861i) q^{84} +(-0.389981 + 0.104495i) q^{85} +(-7.71261 + 2.06659i) q^{86} -5.62213i q^{87} +(3.05106 + 1.76153i) q^{88} +(10.6780 - 10.6780i) q^{89} +0.610072 q^{90} +(-4.13545 + 8.59640i) q^{91} -6.64347 q^{92} +(1.59527 - 1.59527i) q^{93} +(-3.96305 - 2.28807i) q^{94} -1.12373i q^{95} +(0.965926 - 0.258819i) q^{96} +(3.44843 - 0.924004i) q^{97} +(5.16281 + 4.72709i) q^{98} +(-2.49118 - 2.49118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	0.589284	−	0.157898i	0.263536	−	0.0706142i	−0.124632	−	0.992203i	$-0.539775\pi$
$5$	0.589284	−	0.157898i	0.263536	−	0.0706142i	0.388167	+	0.921589i	$0.373108\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	−1.91156	−	1.82919i	−0.722501	−	0.691370i
$7$	−1.91156	−	1.82919i	−0.722501	−	0.691370i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.305036	−	0.528338i	0.0964608	−	0.167075i
$11$	−3.40302	+	0.911835i	−1.02605	+	0.274929i	−0.732320	−	0.680960i	$-0.761563\pi$
$11$	−3.40302	+	0.911835i	−1.02605	+	0.274929i	−0.293728	+	0.955889i	$0.594896\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.11704	−	3.42815i	−0.309812	−	0.950798i
$13$	−1.11704	−	3.42815i	−0.309812	−	0.950798i
$14$	−2.64511	+	0.0582404i	−0.706935	+	0.0155654i
$15$	−0.589284	−	0.157898i	−0.152153	−	0.0407691i
$16$	−1.00000			−0.250000
$17$	−0.661787			−0.160507			−0.0802535	−	0.996774i	$-0.525573\pi$
$17$	−0.661787			−0.160507			−0.0802535	+	0.996774i	$0.525573\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	0.476735	−	1.77920i	0.109371	−	0.408176i	−0.889434	−	0.457064i	$-0.848901\pi$
$19$	0.476735	−	1.77920i	0.109371	−	0.408176i	0.998804	+	0.0488877i	$0.0155676\pi$
$20$	−0.157898	−	0.589284i	−0.0353071	−	0.131768i
$21$	0.740861	+	2.53991i	0.161669	+	0.554253i
$22$	−1.76153	+	3.05106i	−0.375560	+	0.650488i
$23$		−	6.64347i		−	1.38526i	−0.721293	−	0.692630i	$-0.756452\pi$
$23$		−	6.64347i		−	1.38526i	0.721293	−	0.692630i	$-0.243548\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	−4.00780	+	2.31391i	−0.801561	+	0.462781i
$26$	−3.21394	−	1.63420i	−0.630305	−	0.320493i
$27$		−	1.00000i		−	0.192450i
$28$	−1.82919	+	1.91156i	−0.345685	+	0.361250i
$29$	2.81107	+	4.86891i	0.522002	+	0.904134i	0.999672	+	0.0255946i	$0.00814789\pi$
$29$	2.81107	+	4.86891i	0.522002	+	0.904134i	−0.477671	+	0.878539i	$0.658519\pi$
$30$	−0.528338	+	0.305036i	−0.0964608	+	0.0556917i
$31$	−0.583910	+	2.17918i	−0.104873	+	0.391393i	−0.998331	−	0.0577552i	$-0.981606\pi$
$31$	−0.583910	+	2.17918i	−0.104873	+	0.391393i	0.893457	+	0.449148i	$0.148272\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.40302	+	0.911835i	0.592389	+	0.158730i
$34$	−0.467954	+	0.467954i	−0.0802535	+	0.0802535i
$35$	−1.41528	−	0.776083i	−0.239225	−	0.131182i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−1.59669	−	1.59669i	−0.262494	−	0.262494i	0.563573	−	0.826066i	$-0.309426\pi$
$37$	−1.59669	−	1.59669i	−0.262494	−	0.262494i	−0.826066	+	0.563573i	$0.809426\pi$
$38$	−0.920982	−	1.59519i	−0.149403	−	0.258774i
$39$	−0.746686	+	3.52739i	−0.119565	+	0.564834i
$40$	−0.528338	−	0.305036i	−0.0835375	−	0.0482304i
$41$	1.83508	−	6.84860i	0.286591	−	1.06957i	−0.661078	−	0.750317i	$-0.729901\pi$
$41$	1.83508	−	6.84860i	0.286591	−	1.06957i	0.947669	−	0.319254i	$-0.103432\pi$
$42$	2.31985	+	1.27212i	0.357961	+	0.196292i
$43$	−6.91494	−	3.99234i	−1.05452	−	0.608826i	−0.130607	−	0.991434i	$-0.541693\pi$
$43$	−6.91494	−	3.99234i	−1.05452	−	0.608826i	−0.923911	+	0.382608i	$0.875026\pi$
$44$	0.911835	+	3.40302i	0.137464	+	0.513024i
$45$	0.431386	+	0.431386i	0.0643072	+	0.0643072i
$46$	−4.69764	−	4.69764i	−0.692630	−	0.692630i
$47$	−1.18439	−	4.42021i	−0.172761	−	0.644753i	−0.996922	−	0.0783978i	$-0.975020\pi$
$47$	−1.18439	−	4.42021i	−0.172761	−	0.644753i	0.824161	−	0.566356i	$-0.191647\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	0.308105	+	6.99322i	0.0440150	+	0.999031i
$50$	−1.19777	+	4.47012i	−0.169390	+	0.632171i
$51$	0.573124	+	0.330893i	0.0802535	+	0.0463344i
$52$	−3.42815	+	1.11704i	−0.475399	+	0.154906i
$53$	5.24890	+	9.09137i	0.720992	+	1.24880i	0.960602	+	0.277926i	$0.0896471\pi$
$53$	5.24890	+	9.09137i	0.720992	+	1.24880i	−0.239610	+	0.970869i	$0.577020\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−1.86137	+	1.07466i	−0.250987	+	0.144907i
$56$	0.0582404	+	2.64511i	0.00778271	+	0.353468i
$57$	−1.30246	+	1.30246i	−0.172516	+	0.172516i
$58$	5.43056	+	1.45511i	0.713068	+	0.191066i
$59$	6.82671	−	6.82671i	0.888763	−	0.888763i	−0.105642	−	0.994404i	$-0.533690\pi$
$59$	6.82671	−	6.82671i	0.888763	−	0.888763i	0.994404	+	0.105642i	$0.0336897\pi$
$60$	−0.157898	+	0.589284i	−0.0203846	+	0.0760763i
$61$	11.3835	−	6.57224i	1.45750	−	0.841489i	0.458614	−	0.888635i	$-0.348346\pi$
$61$	11.3835	−	6.57224i	1.45750	−	0.841489i	0.998888	+	0.0471460i	$0.0150126\pi$
$62$	1.12803	+	1.95380i	0.143260	+	0.248133i
$63$	0.628349	−	2.57005i	0.0791645	−	0.323796i
$64$			1.00000i			0.125000i
$65$	−1.19956	−	1.84377i	−0.148787	−	0.228692i
$66$	3.05106	−	1.76153i	0.375560	−	0.216829i
$67$	−3.70462	−	13.8258i	−0.452591	−	1.68909i	−0.695074	−	0.718939i	$-0.744628\pi$
$67$	−3.70462	−	13.8258i	−0.452591	−	1.68909i	0.242482	−	0.970156i	$-0.422038\pi$
$68$			0.661787i			0.0802535i
$69$	−3.32174	+	5.75342i	−0.399890	+	0.692630i
$70$	−1.54953	+	0.451978i	−0.185204	+	0.0540217i
$71$	3.44163	+	12.8443i	0.408446	+	1.52434i	0.797610	+	0.603173i	$0.206097\pi$
$71$	3.44163	+	12.8443i	0.408446	+	1.52434i	−0.389164	+	0.921168i	$0.627236\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−4.06451	−	1.08908i	−0.475715	−	0.127467i	0.0129916	−	0.999916i	$-0.495865\pi$
$73$	−4.06451	−	1.08908i	−0.475715	−	0.127467i	−0.488707	+	0.872448i	$0.662531\pi$
$74$	−2.25805			−0.262494
$75$	4.62781			0.534374
$76$	−1.77920	−	0.476735i	−0.204088	−	0.0546853i
$77$	8.17298	+	4.48175i	0.931398	+	0.510742i
$78$	1.96625	+	3.02223i	0.222634	+	0.342200i
$79$	−3.20797	+	5.55637i	−0.360925	+	0.625141i	−0.988113	−	0.153727i	$-0.950872\pi$
$79$	−3.20797	+	5.55637i	−0.360925	+	0.625141i	0.627188	+	0.778868i	$0.284206\pi$
$80$	−0.589284	+	0.157898i	−0.0658840	+	0.0176536i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.54509	−	6.14028i	−0.391490	−	0.678081i
$83$	5.17053	+	5.17053i	0.567540	+	0.567540i	0.931438	−	0.363899i	$-0.118555\pi$
$83$	5.17053	+	5.17053i	0.567540	+	0.567540i	−0.363899	+	0.931438i	$0.618555\pi$
$84$	2.53991	−	0.740861i	0.277127	−	0.0808345i
$85$	−0.389981	+	0.104495i	−0.0422993	+	0.0113341i
$86$	−7.71261	+	2.06659i	−0.831672	+	0.222846i
$87$		−	5.62213i		−	0.602756i
$88$	3.05106	+	1.76153i	0.325244	+	0.187780i
$89$	10.6780	−	10.6780i	1.13186	−	1.13186i	0.141994	−	0.989867i	$-0.454649\pi$
$89$	10.6780	−	10.6780i	1.13186	−	1.13186i	0.989867	−	0.141994i	$-0.0453514\pi$
$90$	0.610072			0.0643072
$91$	−4.13545	+	8.59640i	−0.433513	+	0.901147i
$92$	−6.64347			−0.692630
$93$	1.59527	−	1.59527i	0.165422	−	0.165422i
$94$	−3.96305	−	2.28807i	−0.408757	−	0.235996i
$95$		−	1.12373i		−	0.115292i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	3.44843	−	0.924004i	0.350135	−	0.0938184i	−0.0794650	−	0.996838i	$-0.525321\pi$
$97$	3.44843	−	0.924004i	0.350135	−	0.0938184i	0.429600	+	0.903019i	$0.358655\pi$
$98$	5.16281	+	4.72709i	0.521523	+	0.477508i
$99$	−2.49118	−	2.49118i	−0.250373	−	0.250373i
$100$	2.31391	+	4.00780i	0.231391	+	0.400780i
$101$	5.56394	−	9.63704i	0.553633	−	0.958921i	−0.444375	−	0.895841i	$-0.646574\pi$
$101$	5.56394	−	9.63704i	0.553633	−	0.958921i	0.998008	−	0.0630801i	$-0.0200924\pi$
$102$	0.639237	−	0.171283i	0.0632939	−	0.0169596i
$103$	1.71734	−	2.97452i	0.169214	−	0.293088i	−0.768929	−	0.639334i	$-0.779210\pi$
$103$	1.71734	−	2.97452i	0.169214	−	0.293088i	0.938144	+	0.346246i	$0.112544\pi$
$104$	−1.63420	+	3.21394i	−0.160246	+	0.315153i
$105$	0.837624	+	1.37975i	0.0817438	+	0.134649i
$106$	10.1401	+	2.71703i	0.984894	+	0.263902i
$107$	11.0684			1.07002			0.535012	−	0.844844i	$-0.320307\pi$
$107$	11.0684			1.07002			0.535012	+	0.844844i	$0.320307\pi$
$108$	−1.00000			−0.0962250
$109$	8.51517	+	2.28163i	0.815605	+	0.218541i	0.642424	−	0.766349i	$-0.277929\pi$
$109$	8.51517	+	2.28163i	0.815605	+	0.218541i	0.173181	+	0.984890i	$0.444595\pi$
$110$	−0.556285	+	2.07608i	−0.0530397	+	0.197947i
$111$	0.584428	+	2.18111i	0.0554714	+	0.207022i
$112$	1.91156	+	1.82919i	0.180625	+	0.172843i
$113$	3.05025	−	5.28319i	0.286943	−	0.497000i	−0.686135	−	0.727474i	$-0.740694\pi$
$113$	3.05025	−	5.28319i	0.286943	−	0.497000i	0.973079	+	0.230474i	$0.0740276\pi$
$114$			1.84196i			0.172516i
$115$	−1.04899	−	3.91489i	−0.0978190	−	0.365066i
$116$	4.86891	−	2.81107i	0.452067	−	0.261001i
$117$	2.41034	−	2.68146i	0.222836	−	0.247901i
$118$		−	9.65443i		−	0.888763i
$119$	1.26504	+	1.21054i	0.115966	+	0.110970i
$120$	0.305036	+	0.528338i	0.0278458	+	0.0482304i
$121$	1.22279	−	0.705979i	0.111163	−	0.0641799i
$122$	3.40204	−	12.6966i	0.308007	−	1.14950i
$123$	−5.01352	+	5.01352i	−0.452054	+	0.452054i
$124$	2.17918	+	0.583910i	0.195696	+	0.0524367i
$125$	−4.15330	+	4.15330i	−0.371483	+	0.371483i
$126$	−1.37299	−	2.26161i	−0.122316	−	0.201480i
$127$	3.92526	−	2.26625i	0.348311	−	0.201097i	−0.315630	−	0.948882i	$-0.602216\pi$
$127$	3.92526	−	2.26625i	0.348311	−	0.201097i	0.663941	+	0.747785i	$0.268883\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	3.99234	+	6.91494i	0.351506	+	0.608826i
$130$	−2.15196	−	0.455532i	−0.188739	−	0.0399528i
$131$	7.91260	+	4.56834i	0.691327	+	0.399138i	0.804109	−	0.594482i	$-0.202643\pi$
$131$	7.91260	+	4.56834i	0.691327	+	0.399138i	−0.112782	+	0.993620i	$0.535976\pi$
$132$	0.911835	−	3.40302i	0.0793651	−	0.296194i
$133$	−4.16581	+	2.52900i	−0.361221	+	0.219292i
$134$	−12.3959	−	7.15678i	−1.07084	−	0.618251i
$135$	−0.157898	−	0.589284i	−0.0135897	−	0.0507175i
$136$	0.467954	+	0.467954i	0.0401267	+	0.0401267i
$137$	8.59301	+	8.59301i	0.734151	+	0.734151i	0.971439	−	0.237289i	$-0.0762587\pi$
$137$	8.59301	+	8.59301i	0.734151	+	0.734151i	−0.237289	+	0.971439i	$0.576259\pi$
$138$	1.71946	+	6.41710i	0.146370	+	0.546260i
$139$	−17.3447	−	10.0140i	−1.47116	−	0.849373i	−0.471682	−	0.881769i	$-0.656353\pi$
$139$	−17.3447	−	10.0140i	−1.47116	−	0.849373i	−0.999475	+	0.0323955i	$0.989686\pi$
$140$	−0.776083	+	1.41528i	−0.0655910	+	0.119613i
$141$	−1.18439	+	4.42021i	−0.0997437	+	0.372249i
$142$	11.5159	+	6.64872i	0.966394	+	0.557948i
$143$	6.92723	+	10.6475i	0.579284	+	0.890388i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.42531	+	2.42531i	0.201411	+	0.201411i
$146$	−3.64414	+	2.10395i	−0.301591	+	0.174124i
$147$	3.22978	−	6.21036i	0.266388	−	0.512221i
$148$	−1.59669	+	1.59669i	−0.131247	+	0.131247i
$149$	−16.4771	−	4.41502i	−1.34986	−	0.361693i	−0.489775	−	0.871849i	$-0.662921\pi$
$149$	−16.4771	−	4.41502i	−1.34986	−	0.361693i	−0.860082	+	0.510156i	$0.829588\pi$
$150$	3.27236	−	3.27236i	0.267187	−	0.267187i
$151$	1.12704	−	4.20616i	0.0917170	−	0.342293i	−0.904784	−	0.425870i	$-0.859968\pi$
$151$	1.12704	−	4.20616i	0.0917170	−	0.342293i	0.996501	+	0.0835776i	$0.0266347\pi$
$152$	−1.59519	+	0.920982i	−0.129387	+	0.0747015i
$153$	−0.330893	−	0.573124i	−0.0267512	−	0.0463344i
$154$	8.94825	−	2.61010i	0.721070	−	0.210328i
$155$			1.37636i			0.110552i
$156$	3.52739	+	0.746686i	0.282417	+	0.0597827i
$157$	−11.3079	+	6.52860i	−0.902466	+	0.521039i	−0.877999	−	0.478662i	$-0.841122\pi$
$157$	−11.3079	+	6.52860i	−0.902466	+	0.521039i	−0.0244663	+	0.999701i	$0.507789\pi$
$158$	1.66057	+	6.19733i	0.132108	+	0.493033i
$159$		−	10.4978i		−	0.832530i
$160$	−0.305036	+	0.528338i	−0.0241152	+	0.0417688i
$161$	−12.1522	+	12.6994i	−0.957727	+	1.00085i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	4.71448	−	17.5947i	0.369267	−	1.37812i	−0.492277	−	0.870438i	$-0.663835\pi$
$163$	4.71448	−	17.5947i	0.369267	−	1.37812i	0.861544	−	0.507683i	$-0.169498\pi$
$164$	−6.84860	−	1.83508i	−0.534786	−	0.143295i
$165$	2.14932			0.167324
$166$	7.31224			0.567540
$167$	−12.1764	−	3.26266i	−0.942239	−	0.252472i	−0.245173	−	0.969479i	$-0.578845\pi$
$167$	−12.1764	−	3.26266i	−0.942239	−	0.252472i	−0.697066	+	0.717007i	$0.745511\pi$
$168$	1.27212	−	2.31985i	0.0981460	−	0.178981i
$169$	−10.5044	+	7.65879i	−0.808033	+	0.589138i
$170$	−0.201869	+	0.349647i	−0.0154826	+	0.0268167i
$171$	1.77920	−	0.476735i	0.136059	−	0.0364569i
$172$	−3.99234	+	6.91494i	−0.304413	+	0.527259i
$173$	−0.178580	−	0.309310i	−0.0135772	−	0.0235164i	0.859157	−	0.511712i	$-0.170989\pi$
$173$	−0.178580	−	0.309310i	−0.0135772	−	0.0235164i	−0.872734	+	0.488196i	$0.837655\pi$
$174$	−3.97545	−	3.97545i	−0.301378	−	0.301378i
$175$	11.8937	+	2.90788i	0.899081	+	0.219815i
$176$	3.40302	−	0.911835i	0.256512	−	0.0687322i
$177$	−9.32547	+	2.49875i	−0.700945	+	0.187818i
$178$		−	15.1009i		−	1.13186i
$179$	2.54652	+	1.47023i	0.190336	+	0.109890i	0.592140	−	0.805835i	$-0.298283\pi$
$179$	2.54652	+	1.47023i	0.190336	+	0.109890i	−0.401804	+	0.915726i	$0.631617\pi$
$180$	0.431386	−	0.431386i	0.0321536	−	0.0321536i
$181$	3.08018			0.228948			0.114474	−	0.993426i	$-0.463482\pi$
$181$	3.08018			0.228948			0.114474	+	0.993426i	$0.463482\pi$
$182$	3.15436	+	9.00278i	0.233817	+	0.667330i
$183$	−13.1445			−0.971668
$184$	−4.69764	+	4.69764i	−0.346315	+	0.346315i
$185$	−1.19302	−	0.688788i	−0.0877122	−	0.0506407i
$186$		−	2.25606i		−	0.165422i
$187$	2.25207	−	0.603441i	0.164688	−	0.0441280i
$188$	−4.42021	+	1.18439i	−0.322377	+	0.0863806i
$189$	−1.82919	+	1.91156i	−0.133054	+	0.139045i
$190$	−0.794597	−	0.794597i	−0.0576461	−	0.0576461i
$191$	−0.647368	−	1.12127i	−0.0468419	−	0.0811326i	0.841654	−	0.540017i	$-0.181582\pi$
$191$	−0.647368	−	1.12127i	−0.0468419	−	0.0811326i	−0.888496	+	0.458885i	$0.848249\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−8.36542	+	2.24151i	−0.602156	+	0.161347i	−0.547003	−	0.837131i	$-0.684231\pi$
$193$	−8.36542	+	2.24151i	−0.602156	+	0.161347i	−0.0551531	+	0.998478i	$0.517565\pi$
$194$	1.78504	−	3.09178i	0.128158	−	0.221977i
$195$	0.116958	+	2.19653i	0.00837552	+	0.157297i
$196$	6.99322	−	0.308105i	0.499515	−	0.0220075i
$197$	−2.64884	−	0.709754i	−0.188722	−	0.0505679i	0.163220	−	0.986590i	$-0.447812\pi$
$197$	−2.64884	−	0.709754i	−0.188722	−	0.0505679i	−0.351942	+	0.936022i	$0.614479\pi$
$198$	−3.52306			−0.250373
$199$	−21.1257			−1.49756			−0.748780	−	0.662818i	$-0.769360\pi$
$199$	−21.1257			−1.49756			−0.748780	+	0.662818i	$0.769360\pi$
$200$	4.47012	+	1.19777i	0.316085	+	0.0846948i
$201$	−3.70462	+	13.8258i	−0.261304	+	0.975199i
$202$	−2.88011	−	10.7487i	−0.202644	−	0.756277i
$203$	3.53266	−	14.4492i	0.247944	−	1.01413i
$204$	0.330893	−	0.573124i	0.0231672	−	0.0401267i
$205$		−	4.32552i		−	0.302108i
$206$	−0.888960	−	3.31764i	−0.0619368	−	0.231151i
$207$	5.75342	−	3.32174i	0.399890	−	0.230877i
$208$	1.11704	+	3.42815i	0.0774531	+	0.237699i
$209$			6.48935i			0.448878i
$210$	1.56792	+	0.383338i	0.108197	+	0.0264528i
$211$	1.43098	+	2.47853i	0.0985129	+	0.170629i	0.911069	−	0.412253i	$-0.135258\pi$
$211$	1.43098	+	2.47853i	0.0985129	+	0.170629i	−0.812556	+	0.582883i	$0.801925\pi$
$212$	9.09137	−	5.24890i	0.624398	−	0.360496i
$213$	3.44163	−	12.8443i	0.235816	−	0.880079i
$214$	7.82656	−	7.82656i	0.535012	−	0.535012i
$215$	−4.70525	−	1.26077i	−0.320895	−	0.0859836i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	5.10232	−	3.09755i	0.346368	−	0.210275i
$218$	7.63449	−	4.40778i	0.517073	−	0.298532i
$219$	2.97543	+	2.97543i	0.201061	+	0.201061i
$220$	1.07466	+	1.86137i	0.0724536	+	0.125493i
$221$	0.739245	+	2.26870i	0.0497270	+	0.152610i
$222$	1.95553	+	1.12903i	0.131247	+	0.0757754i
$223$	−1.55649	+	5.80890i	−0.104230	+	0.388993i	−0.998257	−	0.0590214i	$-0.981202\pi$
$223$	−1.55649	+	5.80890i	−0.104230	+	0.388993i	0.894026	+	0.448014i	$0.147869\pi$
$224$	2.64511	−	0.0582404i	0.176734	−	0.00389135i
$225$	−4.00780	−	2.31391i	−0.267187	−	0.154260i
$226$	−1.57892	−	5.89263i	−0.105029	−	0.391972i
$227$	2.34743	+	2.34743i	0.155804	+	0.155804i	0.780705	−	0.624900i	$-0.214860\pi$
$227$	2.34743	+	2.34743i	0.155804	+	0.155804i	−0.624900	+	0.780705i	$0.714860\pi$
$228$	1.30246	+	1.30246i	0.0862578	+	0.0862578i
$229$	5.01006	+	18.6978i	0.331074	+	1.23559i	0.908063	+	0.418833i	$0.137561\pi$
$229$	5.01006	+	18.6978i	0.331074	+	1.23559i	−0.576989	+	0.816752i	$0.695772\pi$
$230$	−3.51000	−	2.02650i	−0.231442	−	0.133623i
$231$	−4.83714	−	7.96780i	−0.318260	−	0.524243i
$232$	1.45511	−	5.43056i	0.0955330	−	0.356534i
$233$	16.0321	+	9.25613i	1.05030	+	0.606389i	0.922732	−	0.385441i	$-0.125951\pi$
$233$	16.0321	+	9.25613i	1.05030	+	0.606389i	0.127564	+	0.991830i	$0.459284\pi$
$234$	−0.191712	−	3.60045i	−0.0125326	−	0.235369i
$235$	−1.39589	−	2.41774i	−0.0910575	−	0.157716i
$236$	−6.82671	−	6.82671i	−0.444381	−	0.444381i
$237$	5.55637	−	3.20797i	0.360925	−	0.208380i
$238$	1.75050	−	0.0385428i	0.113468	−	0.00249836i
$239$	−18.2410	+	18.2410i	−1.17991	+	1.17991i	−0.200144	+	0.979767i	$0.564141\pi$
$239$	−18.2410	+	18.2410i	−1.17991	+	1.17991i	−0.979767	+	0.200144i	$0.935859\pi$
$240$	0.589284	+	0.157898i	0.0380381	+	0.0101923i
$241$	4.29063	−	4.29063i	0.276384	−	0.276384i	−0.555280	−	0.831664i	$-0.687389\pi$
$241$	4.29063	−	4.29063i	0.276384	−	0.276384i	0.831664	+	0.555280i	$0.187389\pi$
$242$	0.365442	−	1.36385i	0.0234915	−	0.0876714i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−6.57224	−	11.3835i	−0.420745	−	0.728751i
$245$	1.28578	+	4.07234i	0.0821453	+	0.260172i
$246$			7.09019i			0.452054i
$247$	−6.63190	+	0.353126i	−0.421978	+	0.0224688i
$248$	1.95380	−	1.12803i	0.124067	−	0.0716298i
$249$	−1.89255	−	7.06308i	−0.119935	−	0.447604i
$250$			5.87366i			0.371483i
$251$	−1.57998	+	2.73660i	−0.0997272	+	0.172733i	−0.911572	−	0.411141i	$-0.865130\pi$
$251$	−1.57998	+	2.73660i	−0.0997272	+	0.172733i	0.811845	+	0.583874i	$0.198464\pi$
$252$	−2.57005	−	0.628349i	−0.161898	−	0.0395823i
$253$	6.05775	+	22.6078i	0.380848	+	1.42134i
$254$	1.17310	−	4.37806i	0.0736067	−	0.274704i
$255$	0.389981	+	0.104495i	0.0244215	+	0.00654373i
$256$	1.00000			0.0625000
$257$	3.59919			0.224511			0.112256	−	0.993679i	$-0.464192\pi$
$257$	3.59919			0.224511			0.112256	+	0.993679i	$0.464192\pi$
$258$	7.71261	+	2.06659i	0.480166	+	0.128660i
$259$	0.131510	+	5.97280i	0.00817164	+	0.371132i
$260$	−1.84377	+	1.19956i	−0.114346	+	0.0743933i
$261$	−2.81107	+	4.86891i	−0.174001	+	0.301378i
$262$	8.82536	−	2.36475i	0.545233	−	0.146095i
$263$	−7.00937	+	12.1406i	−0.432216	+	0.748620i	−0.997064	−	0.0765750i	$-0.975602\pi$
$263$	−7.00937	+	12.1406i	−0.432216	+	0.748620i	0.564848	+	0.825195i	$0.308935\pi$
$264$	−1.76153	−	3.05106i	−0.108415	−	0.187780i
$265$	4.52861	+	4.52861i	0.278190	+	0.278190i
$266$	−1.15740	+	4.73395i	−0.0709645	+	0.290257i
$267$	−14.5864	+	3.90841i	−0.892671	+	0.239191i
$268$	−13.8258	+	3.70462i	−0.844547	+	0.226296i
$269$			10.2215i			0.623214i	0.950211	+	0.311607i	$0.100867\pi$
$269$			10.2215i			0.623214i	−0.950211	+	0.311607i	$0.899133\pi$
$270$	−0.528338	−	0.305036i	−0.0321536	−	0.0185639i
$271$	8.53395	−	8.53395i	0.518401	−	0.518401i	−0.398687	−	0.917087i	$-0.630534\pi$
$271$	8.53395	−	8.53395i	0.518401	−	0.518401i	0.917087	+	0.398687i	$0.130534\pi$
$272$	0.661787			0.0401267
$273$	7.87961	−	5.37697i	0.476895	−	0.325429i
$274$	12.1524			0.734151
$275$	11.5287	−	11.5287i	0.695208	−	0.695208i
$276$	5.75342	+	3.32174i	0.346315	+	0.199945i
$277$		−	22.7747i		−	1.36840i	−0.729294	−	0.684200i	$-0.760152\pi$
$277$		−	22.7747i		−	1.36840i	0.729294	−	0.684200i	$-0.239848\pi$
$278$	−19.3455	+	5.18361i	−1.16027	+	0.310892i
$279$	−2.17918	+	0.583910i	−0.130464	+	0.0349578i
$280$	0.451978	+	1.54953i	0.0270109	+	0.0926019i
$281$	−11.4925	−	11.4925i	−0.685584	−	0.685584i	0.275669	−	0.961253i	$-0.411101\pi$
$281$	−11.4925	−	11.4925i	−0.685584	−	0.685584i	−0.961253	+	0.275669i	$0.911101\pi$
$282$	2.28807	+	3.96305i	0.136252	+	0.235996i
$283$	−15.5043	+	26.8542i	−0.921635	+	1.59632i	−0.124750	+	0.992188i	$0.539813\pi$
$283$	−15.5043	+	26.8542i	−0.921635	+	1.59632i	−0.796885	+	0.604131i	$0.793521\pi$
$284$	12.8443	−	3.44163i	0.762171	−	0.204223i
$285$	−0.561865	+	0.973179i	−0.0332820	+	0.0576461i
$286$	12.4272	+	2.63062i	0.734836	+	0.155552i
$287$	−16.0353	+	9.73478i	−0.946531	+	0.574626i
$288$	−0.965926	−	0.258819i	−0.0569177	−	0.0152511i
$289$	−16.5620			−0.974238
$290$	3.42990			0.201411
$291$	−3.44843	−	0.924004i	−0.202151	−	0.0541661i
$292$	−1.08908	+	4.06451i	−0.0637337	+	0.237858i
$293$	−5.39854	−	20.1476i	−0.315386	−	1.17704i	−0.923630	−	0.383286i	$-0.874792\pi$
$293$	−5.39854	−	20.1476i	−0.315386	−	1.17704i	0.608244	−	0.793750i	$-0.291874\pi$
$294$	−2.10758	−	6.67518i	−0.122917	−	0.389305i
$295$	2.94495	−	5.10080i	0.171462	−	0.296980i
$296$			2.25805i			0.131247i
$297$	0.911835	+	3.40302i	0.0529100	+	0.197463i
$298$	−14.7730	+	8.52917i	−0.855775	+	0.494082i
$299$	−22.7748	+	7.42105i	−1.31710	+	0.429171i
$300$		−	4.62781i		−	0.267187i
$301$	5.91554	+	20.2803i	0.340966	+	1.16894i
$302$	−2.17727	−	3.77114i	−0.125288	−	0.217005i
$303$	−9.63704	+	5.56394i	−0.553633	+	0.319640i
$304$	−0.476735	+	1.77920i	−0.0273426	+	0.102044i
$305$	5.67035	−	5.67035i	0.324683	−	0.324683i
$306$	−0.639237	−	0.171283i	−0.0365428	−	0.00979160i
$307$	15.6514	−	15.6514i	0.893271	−	0.893271i	−0.101559	−	0.994830i	$-0.532383\pi$
$307$	15.6514	−	15.6514i	0.893271	−	0.893271i	0.994830	+	0.101559i	$0.0323830\pi$
$308$	4.48175	−	8.17298i	0.255371	−	0.465699i
$309$	−2.97452	+	1.71734i	−0.169214	+	0.0976960i
$310$	0.973231	+	0.973231i	0.0552758	+	0.0552758i
$311$	−3.13129	−	5.42356i	−0.177559	−	0.307542i	0.763485	−	0.645826i	$-0.223487\pi$
$311$	−3.13129	−	5.42356i	−0.177559	−	0.307542i	−0.941044	+	0.338284i	$0.890154\pi$
$312$	3.02223	−	1.96625i	0.171100	−	0.111317i
$313$	2.02929	+	1.17161i	0.114702	+	0.0662235i	0.556254	−	0.831013i	$-0.312238\pi$
$313$	2.02929	+	1.17161i	0.114702	+	0.0662235i	−0.441551	+	0.897236i	$0.645572\pi$
$314$	−3.37945	+	12.6123i	−0.190713	+	0.711752i
$315$	−0.0355308	−	1.61371i	−0.00200194	−	0.0909221i
$316$	5.55637	+	3.20797i	0.312570	+	0.180463i
$317$	−6.82959	−	25.4884i	−0.383588	−	1.43157i	−0.840381	−	0.541996i	$-0.817669\pi$
$317$	−6.82959	−	25.4884i	−0.383588	−	1.43157i	0.456793	−	0.889573i	$-0.348998\pi$
$318$	−7.42307	−	7.42307i	−0.416265	−	0.416265i
$319$	−14.0057	−	14.0057i	−0.784171	−	0.784171i
$320$	0.157898	+	0.589284i	0.00882678	+	0.0329420i
$321$	−9.58554	−	5.53421i	−0.535012	−	0.308890i
$322$	0.386919	+	17.5727i	0.0215621	+	0.979289i
$323$	−0.315497	+	1.17745i	−0.0175547	+	0.0655151i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	12.4093	+	11.1546i	0.688345	+	0.618747i
$326$	−9.10768	−	15.7750i	−0.504428	−	0.873694i
$327$	−6.23354	−	6.23354i	−0.344715	−	0.344715i
$328$	−6.14028	+	3.54509i	−0.339040	+	0.195745i
$329$	−5.82138	+	10.6160i	−0.320943	+	0.585277i
$330$	1.51980	−	1.51980i	0.0836622	−	0.0836622i
$331$	10.8013	+	2.89420i	0.593692	+	0.159079i	0.543140	−	0.839642i	$-0.317235\pi$
$331$	10.8013	+	2.89420i	0.593692	+	0.159079i	0.0505521	+	0.998721i	$0.483902\pi$
$332$	5.17053	−	5.17053i	0.283770	−	0.283770i
$333$	0.584428	−	2.18111i	0.0320264	−	0.119524i
$334$	−10.9171	+	6.30297i	−0.597355	+	0.344883i
$335$	−4.36615	−	7.56239i	−0.238548	−	0.413178i
$336$	−0.740861	−	2.53991i	−0.0404173	−	0.138563i
$337$			20.8601i			1.13632i	0.822918	+	0.568160i	$0.192344\pi$
$337$			20.8601i			1.13632i	−0.822918	+	0.568160i	$0.807656\pi$
$338$	−2.01217	+	12.8433i	−0.109447	+	0.698585i
$339$	−5.28319	+	3.05025i	−0.286943	+	0.165667i
$340$	0.104495	+	0.389981i	0.00566704	+	0.0211497i
$341$		−	7.94822i		−	0.430420i
$342$	0.920982	−	1.59519i	0.0498010	−	0.0862578i
$343$	12.2030	−	13.9315i	0.658899	−	0.752231i
$344$	2.06659	+	7.71261i	0.111423	+	0.415836i
$345$	−1.04899	+	3.91489i	−0.0564759	+	0.210771i
$346$	−0.344991	−	0.0924401i	−0.0185468	−	0.00496961i
$347$	11.8972			0.638674			0.319337	−	0.947641i	$-0.396540\pi$
$347$	11.8972			0.638674			0.319337	+	0.947641i	$0.396540\pi$
$348$	−5.62213			−0.301378
$349$	−32.7335	−	8.77090i	−1.75218	−	0.469496i	−0.767092	−	0.641537i	$-0.778297\pi$
$349$	−32.7335	−	8.77090i	−1.75218	−	0.469496i	−0.985090	+	0.172041i	$0.944964\pi$
$350$	10.4663	−	6.35395i	0.559448	−	0.339633i
$351$	−3.42815	+	1.11704i	−0.182981	+	0.0596234i
$352$	1.76153	−	3.05106i	0.0938899	−	0.162622i
$353$	7.60446	−	2.03761i	0.404745	−	0.108451i	−0.0507026	−	0.998714i	$-0.516146\pi$
$353$	7.60446	−	2.03761i	0.404745	−	0.108451i	0.455447	+	0.890263i	$0.349479\pi$
$354$	−4.82722	+	8.36098i	−0.256564	+	0.444381i
$355$	4.05619	+	7.02553i	0.215280	+	0.372877i
$356$	−10.6780	−	10.6780i	−0.565931	−	0.565931i
$357$	−0.490292	−	1.68088i	−0.0259490	−	0.0889614i
$358$	2.84027	−	0.761049i	0.150113	−	0.0402227i
$359$	−26.6667	+	7.14533i	−1.40742	+	0.377116i	−0.881002	−	0.473112i	$-0.843131\pi$
$359$	−26.6667	+	7.14533i	−1.40742	+	0.377116i	−0.526414	+	0.850228i	$0.676464\pi$
$360$		−	0.610072i		−	0.0321536i
$361$	13.5162	+	7.80359i	0.711379	+	0.410715i
$362$	2.17801	−	2.17801i	0.114474	−	0.114474i
$363$	−1.41196			−0.0741086
$364$	8.59640	+	4.13545i	0.450574	+	0.216757i
$365$	−2.56712			−0.134369
$366$	−9.29455	+	9.29455i	−0.485834	+	0.485834i
$367$	2.97444	+	1.71730i	0.155265	+	0.0896421i	0.575619	−	0.817718i	$-0.304761\pi$
$367$	2.97444	+	1.71730i	0.155265	+	0.0896421i	−0.420355	+	0.907360i	$0.638094\pi$
$368$			6.64347i			0.346315i
$369$	6.84860	−	1.83508i	0.356524	−	0.0955302i
$370$	−1.33064	+	0.356543i	−0.0691765	+	0.0185358i
$371$	6.59629	−	26.9799i	0.342462	−	1.40073i
$372$	−1.59527	−	1.59527i	−0.0827110	−	0.0827110i
$373$	−5.92593	−	10.2640i	−0.306833	−	0.531450i	0.670835	−	0.741607i	$-0.265936\pi$
$373$	−5.92593	−	10.2640i	−0.306833	−	0.531450i	−0.977668	+	0.210157i	$0.932603\pi$
$374$	1.16576	−	2.01915i	0.0602799	−	0.104408i
$375$	5.67352	−	1.52021i	0.292979	−	0.0785035i
$376$	−2.28807	+	3.96305i	−0.117998	+	0.204379i
$377$	13.5513	−	15.0755i	0.697926	−	0.776430i
$378$	0.0582404	+	2.64511i	0.00299556	+	0.136050i
$379$	19.1079	+	5.11994i	0.981506	+	0.262994i	0.713679	−	0.700473i	$-0.247028\pi$
$379$	19.1079	+	5.11994i	0.981506	+	0.262994i	0.267828	+	0.963467i	$0.413694\pi$
$380$	−1.12373			−0.0576461
$381$	−4.53250			−0.232207
$382$	−1.25062	−	0.335102i	−0.0639873	−	0.0171453i
$383$	4.46650	−	16.6692i	0.228228	−	0.851757i	−0.752858	−	0.658183i	$-0.771325\pi$
$383$	4.46650	−	16.6692i	0.228228	−	0.851757i	0.981086	−	0.193574i	$-0.0620080\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	5.52387	+	1.35052i	0.281522	+	0.0688290i
$386$	−4.33026	+	7.50023i	−0.220404	+	0.381752i
$387$		−	7.98468i		−	0.405884i
$388$	−0.924004	−	3.44843i	−0.0469092	−	0.175068i
$389$	2.98149	−	1.72136i	0.151167	−	0.0872765i	−0.422508	−	0.906359i	$-0.638850\pi$
$389$	2.98149	−	1.72136i	0.151167	−	0.0872765i	0.573676	+	0.819083i	$0.305517\pi$
$390$	1.63589	+	1.47048i	0.0828363	+	0.0744608i
$391$			4.39656i			0.222344i
$392$	4.72709	−	5.16281i	0.238754	−	0.260761i
$393$	−4.56834	−	7.91260i	−0.230442	−	0.399138i
$394$	−2.37488	+	1.37114i	−0.119645	+	0.0690770i
$395$	−1.01307	+	3.78082i	−0.0509729	+	0.190233i
$396$	−2.49118	+	2.49118i	−0.125187	+	0.125187i
$397$	32.5144	+	8.71220i	1.63185	+	0.437253i	0.954452	−	0.298365i	$-0.0964412\pi$
$397$	32.5144	+	8.71220i	1.63185	+	0.437253i	0.677397	+	0.735617i	$0.263108\pi$
$398$	−14.9381	+	14.9381i	−0.748780	+	0.748780i
$399$	4.87220	−	0.107277i	0.243915	−	0.00537055i
$400$	4.00780	−	2.31391i	0.200390	−	0.115695i
$401$	−15.0727	−	15.0727i	−0.752693	−	0.752693i	0.222288	−	0.974981i	$-0.428647\pi$
$401$	−15.0727	−	15.0727i	−0.752693	−	0.752693i	−0.974981	+	0.222288i	$0.928647\pi$
$402$	7.15678	+	12.3959i	0.356948	+	0.618251i
$403$	8.12282	−	0.432512i	0.404626	−	0.0215450i
$404$	−9.63704	−	5.56394i	−0.479460	−	0.276817i
$405$	−0.157898	+	0.589284i	−0.00784602	+	0.0292818i
$406$	−7.71915	−	12.7151i	−0.383095	−	0.631039i
$407$	6.88946	+	3.97763i	0.341498	+	0.197164i
$408$	−0.171283	−	0.639237i	−0.00847978	−	0.0316470i
$409$	−5.32363	−	5.32363i	−0.263237	−	0.263237i	0.563131	−	0.826368i	$-0.309597\pi$
$409$	−5.32363	−	5.32363i	−0.263237	−	0.263237i	−0.826368	+	0.563131i	$0.809597\pi$
$410$	−3.05861	−	3.05861i	−0.151054	−	0.151054i
$411$	−3.14526	−	11.7383i	−0.155144	−	0.579006i
$412$	−2.97452	−	1.71734i	−0.146544	−	0.0846072i
$413$	−25.5370	+	0.562278i	−1.25660	+	0.0276679i
$414$	1.71946	−	6.41710i	0.0845067	−	0.315383i
$415$	3.86333	+	2.23049i	0.189643	+	0.109491i
$416$	3.21394	+	1.63420i	0.157576	+	0.0801232i
$417$	10.0140	+	17.3447i	0.490386	+	0.849373i
$418$	4.58866	+	4.58866i	0.224439	+	0.224439i
$419$	6.59649	−	3.80849i	0.322260	−	0.186057i	−0.330140	−	0.943932i	$-0.607096\pi$
$419$	6.59649	−	3.80849i	0.322260	−	0.186057i	0.652399	+	0.757875i	$0.273763\pi$
$420$	1.37975	−	0.837624i	0.0673247	−	0.0408719i
$421$	13.3231	−	13.3231i	0.649327	−	0.649327i	−0.303503	−	0.952830i	$-0.598156\pi$
$421$	13.3231	−	13.3231i	0.649327	−	0.649327i	0.952830	+	0.303503i	$0.0981562\pi$
$422$	2.76445	+	0.740731i	0.134571	+	0.0360582i
$423$	3.23582	−	3.23582i	0.157331	−	0.157331i
$424$	2.71703	−	10.1401i	0.131951	−	0.492447i
$425$	2.65231	−	1.53131i	0.128656	−	0.0742796i
$426$	−6.64872	−	11.5159i	−0.322131	−	0.557948i
$427$	−33.7820	−	8.25932i	−1.63483	−	0.399697i
$428$		−	11.0684i		−	0.535012i
$429$	−0.675411	−	12.6846i	−0.0326092	−	0.612419i
$430$	−4.21861	+	2.43561i	−0.203439	+	0.117456i
$431$	−0.399053	−	1.48929i	−0.0192217	−	0.0717364i	0.955649	−	0.294509i	$-0.0951560\pi$
$431$	−0.399053	−	1.48929i	−0.0192217	−	0.0717364i	−0.974870	+	0.222772i	$0.928489\pi$
$432$			1.00000i			0.0481125i
$433$	−17.7509	+	30.7454i	−0.853053	+	1.47753i	0.0253870	+	0.999678i	$0.491918\pi$
$433$	−17.7509	+	30.7454i	−0.853053	+	1.47753i	−0.878440	+	0.477853i	$0.841415\pi$
$434$	1.41759	−	5.79819i	0.0680465	−	0.278322i
$435$	−0.887724	−	3.31303i	−0.0425631	−	0.158848i
$436$	2.28163	−	8.51517i	0.109270	−	0.407803i
$437$	−11.8201	−	3.16718i	−0.565431	−	0.151507i
$438$	4.20789			0.201061
$439$	28.5671			1.36343			0.681717	−	0.731616i	$-0.261234\pi$
$439$	28.5671			1.36343			0.681717	+	0.731616i	$0.261234\pi$
$440$	2.07608	+	0.556285i	0.0989734	+	0.0265198i
$441$	−5.90225	+	3.76343i	−0.281060	+	0.179211i
$442$	2.12694	+	1.08149i	0.101168	+	0.0514413i
$443$	−5.73331	+	9.93038i	−0.272398	+	0.471807i	−0.969475	−	0.245189i	$-0.921150\pi$
$443$	−5.73331	+	9.93038i	−0.272398	+	0.471807i	0.697078	+	0.716996i	$0.254483\pi$
$444$	2.18111	−	0.584428i	0.103511	−	0.0277357i
$445$	4.60632	−	7.97838i	0.218361	−	0.378212i
$446$	3.00691	+	5.20812i	0.142381	+	0.246612i
$447$	12.0621	+	12.0621i	0.570516	+	0.570516i
$448$	1.82919	−	1.91156i	0.0864213	−	0.0903126i
$449$	−0.958153	+	0.256736i	−0.0452180	+	0.0121161i	−0.281357	−	0.959603i	$-0.590785\pi$
$449$	−0.958153	+	0.256736i	−0.0452180	+	0.0121161i	0.236139	+	0.971719i	$0.424118\pi$
$450$	−4.47012	+	1.19777i	−0.210724	+	0.0564632i
$451$			24.9792i			1.17622i
$452$	−5.28319	−	3.05025i	−0.248500	−	0.143472i
$453$	−3.07912	+	3.07912i	−0.144670	+	0.144670i
$454$	3.31977			0.155804
$455$	−1.07960	+	5.71870i	−0.0506125	+	0.268097i
$456$	1.84196			0.0862578
$457$	18.4027	−	18.4027i	0.860843	−	0.860843i	−0.130593	−	0.991436i	$-0.541688\pi$
$457$	18.4027	−	18.4027i	0.860843	−	0.860843i	0.991436	+	0.130593i	$0.0416880\pi$
$458$	16.7640	+	9.67869i	0.783330	+	0.452256i
$459$			0.661787i			0.0308896i
$460$	−3.91489	+	1.04899i	−0.182533	+	0.0489095i
$461$	19.4765	−	5.21871i	0.907111	−	0.243060i	0.225044	−	0.974349i	$-0.427748\pi$
$461$	19.4765	−	5.21871i	0.907111	−	0.243060i	0.682068	+	0.731289i	$0.261081\pi$
$462$	−9.05446	−	2.21371i	−0.421251	−	0.102991i
$463$	−14.5403	−	14.5403i	−0.675743	−	0.675743i	0.283291	−	0.959034i	$-0.408574\pi$
$463$	−14.5403	−	14.5403i	−0.675743	−	0.675743i	−0.959034	+	0.283291i	$0.908574\pi$
$464$	−2.81107	−	4.86891i	−0.130500	−	0.226033i
$465$	0.688178	−	1.19196i	0.0319135	−	0.0552758i
$466$	17.8815	−	4.79132i	0.828343	−	0.221954i
$467$	−14.1818	+	24.5637i	−0.656257	+	1.13667i	0.325320	+	0.945604i	$0.394528\pi$
$467$	−14.1818	+	24.5637i	−0.656257	+	1.13667i	−0.981577	+	0.191067i	$0.938805\pi$
$468$	−2.68146	−	2.41034i	−0.123951	−	0.111418i
$469$	−18.2085	+	33.2053i	−0.840792	+	1.53328i
$470$	−2.69664	−	0.722563i	−0.124387	−	0.0333294i
$471$	13.0572			0.601644
$472$	−9.65443			−0.444381
$473$	27.1720	+	7.28071i	1.24937	+	0.334768i
$474$	1.66057	−	6.19733i	0.0762725	−	0.284653i
$475$	2.20624	+	8.23380i	0.101229	+	0.377793i
$476$	1.21054	−	1.26504i	0.0554848	−	0.0579832i
$477$	−5.24890	+	9.09137i	−0.240331	+	0.416265i
$478$			25.7966i			1.17991i
$479$	−0.781041	−	2.91488i	−0.0356867	−	0.133184i	0.945784	−	0.324795i	$-0.105295\pi$
$479$	−0.781041	−	2.91488i	−0.0356867	−	0.133184i	−0.981471	+	0.191611i	$0.938629\pi$
$480$	0.528338	−	0.305036i	0.0241152	−	0.0139229i
$481$	−3.69011	+	7.25725i	−0.168255	+	0.330902i
$482$		−	6.06787i		−	0.276384i
$483$	16.8738	−	4.92189i	0.767785	−	0.223954i
$484$	−0.705979	−	1.22279i	−0.0320900	−	0.0555814i
$485$	1.88621	−	1.08900i	0.0856482	−	0.0494490i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	−9.40414	+	9.40414i	−0.426142	+	0.426142i	−0.887312	−	0.461170i	$-0.847430\pi$
$487$	−9.40414	+	9.40414i	−0.426142	+	0.426142i	0.461170	+	0.887312i	$0.347430\pi$
$488$	−12.6966	−	3.40204i	−0.574748	−	0.154003i
$489$	−12.8802	+	12.8802i	−0.582463	+	0.582463i
$490$	3.78876	+	1.97040i	0.171159	+	0.0890135i
$491$	38.1948	−	22.0518i	1.72371	−	0.995182i	0.812828	−	0.582503i	$-0.197927\pi$
$491$	38.1948	−	22.0518i	1.72371	−	0.995182i	0.910877	−	0.412678i	$-0.135407\pi$
$492$	5.01352	+	5.01352i	0.226027	+	0.226027i
$493$	−1.86033	−	3.22218i	−0.0837849	−	0.145120i
$494$	−4.43976	+	4.93916i	−0.199754	+	0.222223i
$495$	−1.86137	−	1.07466i	−0.0836622	−	0.0483024i
$496$	0.583910	−	2.17918i	0.0262183	−	0.0978482i
$497$	16.9159	−	30.8481i	0.758781	−	1.38373i
$498$	−6.33258	−	3.65612i	−0.283770	−	0.163835i
$499$	3.84420	+	14.3468i	0.172090	+	0.642249i	0.997029	+	0.0770271i	$0.0245428\pi$
$499$	3.84420	+	14.3468i	0.172090	+	0.642249i	−0.824939	+	0.565222i	$0.808791\pi$
$500$	4.15330	+	4.15330i	0.185741	+	0.185741i
$501$	8.91375	+	8.91375i	0.398237	+	0.398237i
$502$	0.817856	+	3.05228i	0.0365027	+	0.136230i
$503$	13.0702	+	7.54607i	0.582770	+	0.336462i	0.762233	−	0.647302i	$-0.224103\pi$
$503$	13.0702	+	7.54607i	0.582770	+	0.336462i	−0.179463	+	0.983765i	$0.557436\pi$
$504$	−2.26161	+	1.37299i	−0.100740	+	0.0611580i
$505$	1.75707	−	6.55749i	0.0781888	−	0.291804i
$506$	20.2696	+	11.7027i	0.901095	+	0.520248i
$507$	12.9265	−	1.38050i	0.574086	−	0.0613100i
$508$	−2.26625	−	3.92526i	−0.100549	−	0.174155i
$509$	8.65298	+	8.65298i	0.383537	+	0.383537i	0.872375	−	0.488838i	$-0.162579\pi$
$509$	8.65298	+	8.65298i	0.383537	+	0.383537i	−0.488838	+	0.872375i	$0.662579\pi$
$510$	0.349647	−	0.201869i	0.0154826	−	0.00893890i
$511$	5.77741	+	9.51662i	0.255577	+	0.420991i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.77920	−	0.476735i	−0.0785536	−	0.0210484i
$514$	2.54501	−	2.54501i	0.112256	−	0.112256i
$515$	0.542329	−	2.02400i	0.0238979	−	0.0891881i
$516$	6.91494	−	3.99234i	0.304413	−	0.175753i
$517$	8.06100	+	13.9621i	0.354522	+	0.614051i
$518$	4.31640	+	4.13042i	0.189652	+	0.181480i
$519$			0.357161i			0.0156776i
$520$	−0.455532	+	2.15196i	−0.0199764	+	0.0943697i
$521$	−22.6198	+	13.0595i	−0.990991	+	0.572149i	−0.905570	−	0.424196i	$-0.860557\pi$
$521$	−22.6198	+	13.0595i	−0.990991	+	0.572149i	−0.0854203	+	0.996345i	$0.527223\pi$
$522$	1.45511	+	5.43056i	0.0636886	+	0.237689i
$523$		−	32.6776i		−	1.42889i	−0.699690	−	0.714447i	$-0.746679\pi$
$523$		−	32.6776i		−	1.42889i	0.699690	−	0.714447i	$-0.253321\pi$
$524$	4.56834	−	7.91260i	0.199569	−	0.345664i
$525$	−8.84633	−	8.46516i	−0.386085	−	0.369450i
$526$	3.62832	+	13.5411i	0.158202	+	0.590418i
$527$	0.386424	−	1.44215i	0.0168329	−	0.0628212i
$528$	−3.40302	−	0.911835i	−0.148097	−	0.0396825i
$529$	−21.1357			−0.918945
$530$	6.40442			0.278190
$531$	9.32547	+	2.49875i	0.404691	+	0.108437i
$532$	2.52900	+	4.16581i	0.109646	+	0.180611i
$533$	−25.5279	+	1.35927i	−1.10574	+	0.0588766i
$534$	−7.55046	+	13.0778i	−0.326740	+	0.565931i
$535$	6.52245	−	1.74768i	0.281990	−	0.0755590i
$536$	−7.15678	+	12.3959i	−0.309126	+	0.535421i
$537$	−1.47023	−	2.54652i	−0.0634453	−	0.109890i
$538$	7.22767	+	7.22767i	0.311607	+	0.311607i
$539$	−7.42515	−	23.5171i	−0.319824	−	1.01295i
$540$	−0.589284	+	0.157898i	−0.0253588	+	0.00679486i
$541$	37.0514	−	9.92791i	1.59297	−	0.426834i	0.650057	−	0.759885i	$-0.274745\pi$
$541$	37.0514	−	9.92791i	1.59297	−	0.426834i	0.942909	+	0.333051i	$0.108078\pi$
$542$		−	12.0688i		−	0.518401i
$543$	−2.66751	−	1.54009i	−0.114474	−	0.0660915i
$544$	0.467954	−	0.467954i	0.0200634	−	0.0200634i
$545$	5.37812			0.230373
$546$	1.76963	−	9.37381i	0.0757332	−	0.401162i
$547$	38.1476			1.63107			0.815536	−	0.578706i	$-0.196442\pi$
$547$	38.1476			1.63107			0.815536	+	0.578706i	$0.196442\pi$
$548$	8.59301	−	8.59301i	0.367075	−	0.367075i
$549$	11.3835	+	6.57224i	0.485834	+	0.280496i
$550$		−	16.3041i		−	0.695208i
$551$	10.0029	−	2.68027i	0.426138	−	0.114183i
$552$	6.41710	−	1.71946i	0.273130	−	0.0731850i
$553$	16.2959	−	4.75332i	0.692972	−	0.202132i
$554$	−16.1042	−	16.1042i	−0.684200	−	0.684200i
$555$	0.688788	+	1.19302i	0.0292374	+	0.0506407i
$556$	−10.0140	+	17.3447i	−0.424687	+	0.735579i
$557$	17.9536	−	4.81066i	0.760720	−	0.203834i	0.142452	−	0.989802i	$-0.454501\pi$
$557$	17.9536	−	4.81066i	0.760720	−	0.203834i	0.618268	+	0.785967i	$0.287835\pi$
$558$	−1.12803	+	1.95380i	−0.0477532	+	0.0827110i
$559$	−5.96205	+	28.1651i	−0.252168	+	1.19126i
$560$	1.41528	+	0.776083i	0.0598064	+	0.0327955i
$561$	−2.25207	−	0.603441i	−0.0950825	−	0.0254773i
$562$	−16.2528			−0.685584
$563$	16.0774			0.677581			0.338791	−	0.940862i	$-0.389982\pi$
$563$	16.0774			0.677581			0.338791	+	0.940862i	$0.389982\pi$
$564$	4.42021	+	1.18439i	0.186124	+	0.0498718i
$565$	0.963257	−	3.59493i	0.0405245	−	0.151240i
$566$	8.02562	+	29.9520i	0.337342	+	1.25898i
$567$	2.53991	−	0.740861i	0.106666	−	0.0311132i
$568$	6.64872	−	11.5159i	0.278974	−	0.483197i
$569$			0.671507i			0.0281511i	0.999901	+	0.0140755i	$0.00448053\pi$
$569$			0.671507i			0.0281511i	−0.999901	+	0.0140755i	$0.995519\pi$
$570$	0.290843	+	1.08544i	0.0121821	+	0.0454641i
$571$	22.2930	−	12.8709i	0.932933	−	0.538629i	0.0451952	−	0.998978i	$-0.485609\pi$
$571$	22.2930	−	12.8709i	0.932933	−	0.538629i	0.887738	+	0.460349i	$0.152276\pi$
$572$	10.6475	−	6.92723i	0.445194	−	0.289642i
$573$			1.29474i			0.0540884i
$574$	−4.45511	+	18.2222i	−0.185953	+	0.760579i
$575$	15.3724	+	26.6257i	0.641072	+	1.11037i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−3.91154	+	14.5981i	−0.162840	+	0.607726i	0.835466	+	0.549542i	$0.185198\pi$
$577$	−3.91154	+	14.5981i	−0.162840	+	0.607726i	−0.998306	+	0.0581840i	$0.981469\pi$
$578$	−11.7111	+	11.7111i	−0.487119	+	0.487119i
$579$	8.36542	+	2.24151i	0.347655	+	0.0931539i
$580$	2.42531	−	2.42531i	0.100705	−	0.100705i
$581$	−0.425868	−	19.3417i	−0.0176680	−	0.802428i
$582$	−3.09178	+	1.78504i	−0.128158	+	0.0739923i
$583$	−26.1519	−	26.1519i	−1.08310	−	1.08310i
$584$	2.10395	+	3.64414i	0.0870619	+	0.150796i
$585$	0.996978	−	1.96073i	0.0412200	−	0.0810663i
$586$	−18.0639	−	10.4292i	−0.746211	−	0.430825i
$587$	1.31954	−	4.92459i	0.0544632	−	0.203259i	−0.933333	−	0.359012i	$-0.883114\pi$
$587$	1.31954	−	4.92459i	0.0544632	−	0.203259i	0.987796	+	0.155753i	$0.0497803\pi$
$588$	−6.21036	−	3.22978i	−0.256111	−	0.133194i
$589$	3.59883	+	2.07779i	0.148287	+	0.0856137i
$590$	−1.52442	−	5.68920i	−0.0627593	−	0.234221i
$591$	1.93908	+	1.93908i	0.0797632	+	0.0797632i
$592$	1.59669	+	1.59669i	0.0656234	+	0.0656234i
$593$	−1.83462	−	6.84690i	−0.0753389	−	0.281169i	0.917971	−	0.396647i	$-0.129826\pi$
$593$	−1.83462	−	6.84690i	−0.0753389	−	0.281169i	−0.993310	+	0.115479i	$0.963160\pi$
$594$	3.05106	+	1.76153i	0.125187	+	0.0722765i
$595$	0.936612	+	0.513602i	0.0383973	+	0.0210556i
$596$	−4.41502	+	16.4771i	−0.180846	+	0.674928i
$597$	18.2954	+	10.5628i	0.748780	+	0.432309i
$598$	−10.8568	+	21.3517i	−0.443966	+	0.873136i
$599$	12.6914	+	21.9821i	0.518555	+	0.898164i	0.999768	+	0.0215601i	$0.00686331\pi$
$599$	12.6914	+	21.9821i	0.518555	+	0.898164i	−0.481212	+	0.876604i	$0.659803\pi$
$600$	−3.27236	−	3.27236i	−0.133593	−	0.133593i
$601$	19.7808	−	11.4204i	0.806875	−	0.465849i	−0.0389947	−	0.999239i	$-0.512416\pi$
$601$	19.7808	−	11.4204i	0.806875	−	0.465849i	0.845869	+	0.533390i	$0.179082\pi$
$602$	18.5233	+	10.1575i	0.754953	+	0.413987i
$603$	10.1212	−	10.1212i	0.412168	−	0.412168i
$604$	−4.20616	−	1.12704i	−0.171146	−	0.0458585i
$605$	0.609099	−	0.609099i	0.0247634	−	0.0247634i
$606$	−2.88011	+	10.7487i	−0.116996	+	0.436637i
$607$	−3.46230	+	1.99896i	−0.140530	+	0.0811352i	−0.568617	−	0.822603i	$-0.692521\pi$
$607$	−3.46230	+	1.99896i	−0.140530	+	0.0811352i	0.428086	+	0.903738i	$0.359188\pi$
$608$	0.920982	+	1.59519i	0.0373507	+	0.0646934i
$609$	−10.2840	+	10.7470i	−0.416727	+	0.435492i
$610$		−	8.01908i		−	0.324683i
$611$	−13.8301	+	8.99784i	−0.559506	+	0.364013i
$612$	−0.573124	+	0.330893i	−0.0231672	+	0.0133756i
$613$	−10.0533	−	37.5193i	−0.406047	−	1.51539i	−0.802116	−	0.597168i	$-0.796292\pi$
$613$	−10.0533	−	37.5193i	−0.406047	−	1.51539i	0.396069	−	0.918221i	$-0.370374\pi$
$614$		−	22.1344i		−	0.893271i
$615$	−2.16276	+	3.74601i	−0.0872110	+	0.151054i
$616$	−2.61010	−	8.94825i	−0.105164	−	0.360535i
$617$	−2.49513	−	9.31195i	−0.100450	−	0.374885i	0.897339	−	0.441342i	$-0.145497\pi$
$617$	−2.49513	−	9.31195i	−0.100450	−	0.374885i	−0.997789	+	0.0664565i	$0.978831\pi$
$618$	−0.888960	+	3.31764i	−0.0357592	+	0.133455i
$619$	5.44832	+	1.45987i	0.218986	+	0.0586772i	0.366644	−	0.930361i	$-0.380507\pi$
$619$	5.44832	+	1.45987i	0.218986	+	0.0586772i	−0.147658	+	0.989039i	$0.547173\pi$
$620$	1.37636			0.0552758
$621$	−6.64347			−0.266593
$622$	−6.04920	−	1.62088i	−0.242551	−	0.0649913i
$623$	−39.9436	+	0.879484i	−1.60031	+	0.0352358i
$624$	0.746686	−	3.52739i	0.0298914	−	0.141208i
$625$	9.77785	−	16.9357i	0.391114	−	0.677430i
$626$	2.26338	−	0.606472i	0.0904630	−	0.0242395i
$627$	3.24467	−	5.61994i	0.129580	−	0.224439i
$628$	6.52860	+	11.3079i	0.260519	+	0.451233i
$629$	1.05667	+	1.05667i	0.0421320	+	0.0421320i
$630$	−1.16619	−	1.11594i	−0.0464620	−	0.0444601i
$631$	1.52391	−	0.408330i	0.0606659	−	0.0162554i	−0.228358	−	0.973577i	$-0.573336\pi$
$631$	1.52391	−	0.408330i	0.0606659	−	0.0162554i	0.289024	+	0.957322i	$0.406669\pi$
$632$	6.19733	−	1.66057i	0.246517	−	0.0660539i
$633$		−	2.86197i		−	0.113753i
$634$	−22.8522	−	13.1937i	−0.907578	−	0.523991i
$635$	1.95526	−	1.95526i	0.0775920	−	0.0775920i
$636$	−10.4978			−0.416265
$637$	23.6296	−	8.86796i	0.936240	−	0.351361i
$638$	−19.8071			−0.784171
$639$	−9.40270	+	9.40270i	−0.371965	+	0.371965i
$640$	0.528338	+	0.305036i	0.0208844	+	0.0120576i
$641$			41.1399i			1.62493i	0.583010	+	0.812465i	$0.301875\pi$
$641$			41.1399i			1.62493i	−0.583010	+	0.812465i	$0.698125\pi$
$642$	−10.6913	+	2.86472i	−0.421951	+	0.113061i
$643$	46.0170	−	12.3302i	1.81473	−	0.486256i	0.818619	−	0.574337i	$-0.194740\pi$
$643$	46.0170	−	12.3302i	1.81473	−	0.486256i	0.996113	+	0.0880805i	$0.0280733\pi$
$644$	12.6994	+	12.1522i	0.500426	+	0.478864i
$645$	3.44448	+	3.44448i	0.135626	+	0.135626i
$646$	0.609494	+	1.05567i	0.0239802	+	0.0415349i
$647$	−19.1270	+	33.1290i	−0.751962	+	1.30244i	0.194909	+	0.980821i	$0.437559\pi$
$647$	−19.1270	+	33.1290i	−0.751962	+	1.30244i	−0.946871	+	0.321615i	$0.895774\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	−17.0066	+	29.4563i	−0.667567	+	1.15626i
$650$	16.6622	−	0.887205i	0.653546	−	0.0347990i
$651$	−5.96752	+	0.131394i	−0.233885	+	0.00514972i
$652$	−17.5947	−	4.71448i	−0.689061	−	0.184633i
$653$	−0.133906			−0.00524013			−0.00262007	−	0.999997i	$-0.500834\pi$
$653$	−0.133906			−0.00524013			−0.00262007	+	0.999997i	$0.500834\pi$
$654$	−8.81555			−0.344715
$655$	5.38410	+	1.44267i	0.210374	+	0.0563696i
$656$	−1.83508	+	6.84860i	−0.0716477	+	0.267393i
$657$	−1.08908	−	4.06451i	−0.0424892	−	0.158572i
$658$	3.39028	+	11.6230i	0.132167	+	0.453110i
$659$	4.72225	−	8.17917i	0.183953	−	0.318615i	−0.759271	−	0.650775i	$-0.774444\pi$
$659$	4.72225	−	8.17917i	0.183953	−	0.318615i	0.943223	+	0.332160i	$0.107777\pi$
$660$		−	2.14932i		−	0.0836622i
$661$	−3.91995	−	14.6294i	−0.152468	−	0.569019i	−0.999309	−	0.0371726i	$-0.988165\pi$
$661$	−3.91995	−	14.6294i	−0.152468	−	0.569019i	0.846841	−	0.531847i	$-0.178502\pi$
$662$	9.68417	−	5.59116i	0.376386	−	0.217306i
$663$	0.494147	−	2.33438i	0.0191911	−	0.0906598i
$664$		−	7.31224i		−	0.283770i
$665$	−2.05552	+	2.14807i	−0.0797096	+	0.0832988i
$666$	−1.12903	−	1.95553i	−0.0437489	−	0.0757754i
$667$	32.3465	−	18.6752i	1.25246	−	0.723108i
$668$	−3.26266	+	12.1764i	−0.126236	+	0.471119i
$669$	4.25241	−	4.25241i	0.164408	−	0.164408i
$670$	−8.43475	−	2.26008i	−0.325863	−	0.0873147i
$671$	−32.7453	+	32.7453i	−1.26412	+	1.26412i
$672$	−2.31985	−	1.27212i	−0.0894903	−	0.0490730i
$673$	−15.0362	+	8.68115i	−0.579602	+	0.334634i	−0.760975	−	0.648781i	$-0.775279\pi$
$673$	−15.0362	+	8.68115i	−0.579602	+	0.334634i	0.181373	+	0.983414i	$0.441946\pi$
$674$	14.7503	+	14.7503i	0.568160	+	0.568160i
$675$	2.31391	+	4.00780i	0.0890623	+	0.154260i
$676$	7.65879	+	10.5044i	0.294569	+	0.404016i
$677$	0.855137	+	0.493714i	0.0328656	+	0.0189750i	0.516343	−	0.856382i	$-0.327293\pi$
$677$	0.855137	+	0.493714i	0.0328656	+	0.0189750i	−0.483477	+	0.875357i	$0.660626\pi$
$678$	−1.57892	+	5.89263i	−0.0606382	+	0.226305i
$679$	−8.28206	−	4.54156i	−0.317836	−	0.174289i
$680$	0.349647	+	0.201869i	0.0134084	+	0.00774131i
$681$	−0.859219	−	3.20665i	−0.0329253	−	0.122879i
$682$	−5.62024	−	5.62024i	−0.215210	−	0.215210i
$683$	13.5640	+	13.5640i	0.519013	+	0.519013i	0.917273	−	0.398260i	$-0.130386\pi$
$683$	13.5640	+	13.5640i	0.519013	+	0.519013i	−0.398260	+	0.917273i	$0.630386\pi$
$684$	−0.476735	−	1.77920i	−0.0182284	−	0.0680294i
$685$	6.42055	+	3.70690i	0.245316	+	0.141634i
$686$	−1.22226	−	18.4799i	−0.0466661	−	0.705565i
$687$	5.01006	−	18.6978i	0.191146	−	0.713366i
$688$	6.91494	+	3.99234i	0.263629	+	0.152207i
$689$	25.3033	−	28.1495i	0.963979	−	1.07241i
$690$	2.02650	+	3.51000i	0.0771475	+	0.133623i
$691$	−16.3727	−	16.3727i	−0.622845	−	0.622845i	0.323413	−	0.946258i	$-0.395170\pi$
$691$	−16.3727	−	16.3727i	−0.622845	−	0.622845i	−0.946258	+	0.323413i	$0.895170\pi$
$692$	−0.309310	+	0.178580i	−0.0117582	+	0.00678861i
$693$	0.205185	+	9.31888i	0.00779432	+	0.353995i
$694$	8.41258	−	8.41258i	0.319337	−	0.319337i
$695$	−11.8021	−	3.16237i	−0.447681	−	0.119956i
$696$	−3.97545	+	3.97545i	−0.150689	+	0.150689i
$697$	−1.21443	+	4.53231i	−0.0459998	+	0.171674i
$698$	−29.3480	+	16.9441i	−1.11084	+	0.641343i
$699$	−9.25613	−	16.0321i	−0.350099	−	0.606389i
$700$	2.90788	−	11.8937i	0.109908	−	0.449541i
$701$		−	17.2532i		−	0.651646i	−0.945431	−	0.325823i	$-0.894359\pi$
$701$		−	17.2532i		−	0.651646i	0.945431	−	0.325823i	$-0.105641\pi$
$702$	−1.63420	+	3.21394i	−0.0616788	+	0.121302i
$703$	−3.60202	+	2.07963i	−0.135853	+	0.0784346i
$704$	−0.911835	−	3.40302i	−0.0343661	−	0.128256i
$705$			2.79177i			0.105144i
$706$	3.93636	−	6.81797i	0.148147	−	0.256598i
$707$	−28.2638	+	8.24422i	−1.06297	+	0.310056i
$708$	2.49875	+	9.32547i	0.0939088	+	0.350472i
$709$	0.212442	−	0.792846i	0.00797844	−	0.0297759i	−0.961822	−	0.273676i	$-0.911760\pi$
$709$	0.212442	−	0.792846i	0.00797844	−	0.0297759i	0.969800	+	0.243900i	$0.0784270\pi$
$710$	7.83596	+	2.09964i	0.294079	+	0.0787981i
$711$	−6.41595			−0.240617
$712$	−15.1009			−0.565931
$713$	14.4773	+	3.87919i	0.542181	+	0.145277i
$714$	−1.53525	−	0.841871i	−0.0574552	−	0.0315062i
$715$	5.76332	+	5.18060i	0.215536	+	0.193743i
$716$	1.47023	−	2.54652i	0.0549452	−	0.0951679i
$717$	24.9176	−	6.67666i	0.930566	−	0.249344i
$718$	−13.8037	+	23.9087i	−0.515150	+	0.892266i
$719$	6.10088	+	10.5670i	0.227524	+	0.394084i	0.957074	−	0.289844i	$-0.0936036\pi$
$719$	6.10088	+	10.5670i	0.227524	+	0.394084i	−0.729549	+	0.683928i	$0.760270\pi$
$720$	−0.431386	−	0.431386i	−0.0160768	−	0.0160768i
$721$	−8.72376	+	2.54462i	−0.324890	+	0.0947665i
$722$	15.0754	−	4.03943i	0.561047	−	0.150332i
$723$	−5.86111	+	1.57048i	−0.217977	+	0.0584067i
$724$		−	3.08018i		−	0.114474i
$725$	−22.5324	−	13.0091i	−0.836832	−	0.483145i
$726$	−0.998405	+	0.998405i	−0.0370543	+	0.0370543i
$727$	−26.9918			−1.00107			−0.500535	−	0.865716i	$-0.666863\pi$
$727$	−26.9918			−1.00107			−0.500535	+	0.865716i	$0.666863\pi$
$728$	9.00278	−	3.15436i	0.333665	−	0.116908i
$729$	−1.00000			−0.0370370
$730$	−1.81523	+	1.81523i	−0.0671845	+	0.0671845i
$731$	4.57622	+	2.64208i	0.169257	+	0.0977208i
$732$			13.1445i			0.485834i
$733$	−23.9381	+	6.41419i	−0.884173	+	0.236914i	−0.672207	−	0.740363i	$-0.734653\pi$
$733$	−23.9381	+	6.41419i	−0.884173	+	0.236914i	−0.211967	+	0.977277i	$0.567987\pi$
$734$	3.31756	−	0.888938i	0.122453	−	0.0328113i
$735$	0.922655	−	4.16964i	0.0340326	−	0.153799i
$736$	4.69764	+	4.69764i	0.173157	+	0.173157i
$737$	25.2138	+	43.6715i	0.928761	+	1.60866i
$738$	3.54509	−	6.14028i	0.130497	−	0.226027i
$739$	−44.6315	+	11.9590i	−1.64179	+	0.439918i	−0.957299	−	0.289100i	$-0.906644\pi$
$739$	−44.6315	+	11.9590i	−1.64179	+	0.439918i	−0.684495	+	0.729017i	$0.739977\pi$
$740$	−0.688788	+	1.19302i	−0.0253203	+	0.0438561i
$741$	5.91996	+	3.01013i	0.217475	+	0.110580i
$742$	−14.4134	−	23.7420i	−0.529133	−	0.871595i
$743$	21.9692	+	5.88663i	0.805972	+	0.215959i	0.638204	−	0.769867i	$-0.279678\pi$
$743$	21.9692	+	5.88663i	0.805972	+	0.215959i	0.167767	+	0.985827i	$0.446344\pi$
$744$	−2.25606			−0.0827110
$745$	−10.4068			−0.381276
$746$	−11.4480	−	3.06749i	−0.419142	−	0.112309i
$747$	−1.89255	+	7.06308i	−0.0692446	+	0.258425i
$748$	−0.603441	−	2.25207i	−0.0220640	−	0.0823439i
$749$	−21.1579	−	20.2463i	−0.773094	−	0.739783i
$750$	2.93683	−	5.08674i	0.107238	−	0.185741i
$751$			31.9064i			1.16428i	0.813088	+	0.582141i	$0.197785\pi$
$751$			31.9064i			1.16428i	−0.813088	+	0.582141i	$0.802215\pi$
$752$	1.18439	+	4.42021i	0.0431903	+	0.161188i
$753$	2.73660	−	1.57998i	0.0997272	−	0.0575775i
$754$	−1.07783	−	20.2422i	−0.0392522	−	0.737178i
$755$		−	2.65658i		−	0.0966829i
$756$	1.91156	+	1.82919i	0.0695227	+	0.0665271i
$757$	−23.5249	−	40.7463i	−0.855028	−	1.48095i	−0.876619	−	0.481184i	$-0.840207\pi$
$757$	−23.5249	−	40.7463i	−0.855028	−	1.48095i	0.0215919	−	0.999767i	$-0.493127\pi$
$758$	17.1317	−	9.89097i	0.622250	−	0.359256i
$759$	6.05775	−	22.6078i	0.219883	−	0.820613i
$760$	−0.794597	+	0.794597i	−0.0288231	+	0.0288231i
$761$	−31.6416	−	8.47833i	−1.14701	−	0.307339i	−0.365241	−	0.930913i	$-0.619013\pi$
$761$	−31.6416	−	8.47833i	−1.14701	−	0.307339i	−0.781765	+	0.623574i	$0.785680\pi$
$762$	−3.20496	+	3.20496i	−0.116104	+	0.116104i
$763$	−12.1037	−	19.9374i	−0.438183	−	0.721781i
$764$	−1.12127	+	0.647368i	−0.0405663	+	0.0234210i
$765$	−0.285486	−	0.285486i	−0.0103218	−	0.0103218i
$766$	−8.62862	−	14.9452i	−0.311765	−	0.539992i
$767$	−31.0287	−	15.7773i	−1.12038	−	0.569684i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	7.72927	−	28.8460i	0.278725	−	1.04021i	−0.674580	−	0.738202i	$-0.735675\pi$
$769$	7.72927	−	28.8460i	0.278725	−	1.04021i	0.953304	−	0.302012i	$-0.0976583\pi$
$770$	4.86093	−	2.95100i	0.175176	−	0.106347i
$771$	−3.11699	−	1.79960i	−0.112256	−	0.0648109i
$772$	2.24151	+	8.36542i	0.0806736	+	0.301078i
$773$	−19.8642	−	19.8642i	−0.714466	−	0.714466i	0.253000	−	0.967466i	$-0.418583\pi$
$773$	−19.8642	−	19.8642i	−0.714466	−	0.714466i	−0.967466	+	0.253000i	$0.918583\pi$
$774$	−5.64602	−	5.64602i	−0.202942	−	0.202942i
$775$	−2.70223	−	10.0848i	−0.0970669	−	0.362258i
$776$	−3.09178	−	1.78504i	−0.110988	−	0.0640792i
$777$	2.87251	−	5.23835i	0.103051	−	0.187925i
$778$	0.891042	−	3.32542i	0.0319454	−	0.119222i
$779$	−11.3102	−	6.52993i	−0.405229	−	0.233959i
$780$	2.19653	−	0.116958i	0.0786485	−	0.00418776i
$781$	−23.4238	−	40.5713i	−0.838170	−	1.45175i
$782$	3.10884	+	3.10884i	0.111172	+	0.111172i
$783$	4.86891	−	2.81107i	0.174001	−	0.100459i
$784$	−0.308105	−	6.99322i	−0.0110037	−	0.249758i
$785$	−5.63269	+	5.63269i	−0.201039	+	0.201039i
$786$	−8.82536	−	2.36475i	−0.314790	−	0.0843478i
$787$	19.7673	−	19.7673i	0.704630	−	0.704630i	−0.260771	−	0.965401i	$-0.583977\pi$
$787$	19.7673	−	19.7673i	0.704630	−	0.704630i	0.965401	+	0.260771i	$0.0839768\pi$
$788$	−0.709754	+	2.64884i	−0.0252839	+	0.0943609i
$789$	12.1406	−	7.00937i	0.432216	−	0.249540i
$790$	1.95709	+	3.38979i	0.0696303	+	0.120603i
$791$	−15.4947	+	4.51962i	−0.550928	+	0.160699i
$792$			3.52306i			0.125187i
$793$	−35.2465	−	31.6827i	−1.25164	−	1.12509i
$794$	29.1516	−	16.8307i	1.03455	−	0.597298i
$795$	−1.65758	−	6.18619i	−0.0587885	−	0.219402i
$796$			21.1257i			0.748780i
$797$	−7.24475	+	12.5483i	−0.256622	+	0.444483i	−0.965335	−	0.261015i	$-0.915943\pi$
$797$	−7.24475	+	12.5483i	−0.256622	+	0.444483i	0.708713	+	0.705497i	$0.249276\pi$
$798$	3.36931	−	3.52102i	0.119272	−	0.124643i
$799$	0.783814	+	2.92523i	0.0277294	+	0.103487i
$800$	1.19777	−	4.47012i	0.0423474	−	0.158043i
$801$	14.5864	+	3.90841i	0.515384	+	0.138097i
$802$	−21.3160			−0.752693
$803$	14.8247			0.523151
$804$	13.8258	+	3.70462i	0.487600	+	0.130652i
$805$	−5.15589	+	9.40235i	−0.181721	+	0.331389i
$806$	5.43787	−	6.04953i	0.191541	−	0.213086i
$807$	5.11073	−	8.85205i	0.179906	−	0.311607i
$808$	−10.7487	+	2.88011i	−0.378139	+	0.101322i
$809$	−11.9398	+	20.6803i	−0.419780	+	0.727081i	−0.995917	−	0.0902724i	$-0.971226\pi$
$809$	−11.9398	+	20.6803i	−0.419780	+	0.727081i	0.576137	+	0.817353i	$0.304560\pi$
$810$	0.305036	+	0.528338i	0.0107179	+	0.0185639i
$811$	21.0744	+	21.0744i	0.740023	+	0.740023i	0.972582	−	0.232559i	$-0.0747099\pi$
$811$	21.0744	+	21.0744i	0.740023	+	0.740023i	−0.232559	+	0.972582i	$0.574710\pi$
$812$	−14.4492	−	3.53266i	−0.507067	−	0.123972i
$813$	−11.6576	+	3.12364i	−0.408850	+	0.109551i
$814$	7.68420	−	2.05897i	0.269331	−	0.0721670i
$815$		−	11.1127i		−	0.389260i
$816$	−0.573124	−	0.330893i	−0.0200634	−	0.0115836i
$817$	−10.3998	+	10.3998i	−0.363842	+	0.363842i
$818$	−7.52875			−0.263237
$819$	−9.51242	+	0.716790i	−0.332391	+	0.0250467i
$820$	−4.32552			−0.151054
$821$	−26.5369	+	26.5369i	−0.926144	+	0.926144i	−0.997454	−	0.0713099i	$-0.977282\pi$
$821$	−26.5369	+	26.5369i	−0.926144	+	0.926144i	0.0713099	+	0.997454i	$0.477282\pi$
$822$	−10.5242	−	6.07618i	−0.367075	−	0.211931i
$823$		−	6.56963i		−	0.229003i	−0.993423	−	0.114502i	$-0.963473\pi$
$823$		−	6.56963i		−	0.229003i	0.993423	−	0.114502i	$-0.0365271\pi$
$824$	−3.31764	+	0.888960i	−0.115576	+	0.0309684i
$825$	−15.7485	+	4.21980i	−0.548293	+	0.146915i
$826$	−17.6598	+	18.4550i	−0.614464	+	0.642132i
$827$	11.7624	+	11.7624i	0.409019	+	0.409019i	0.881396	−	0.472377i	$-0.156604\pi$
$827$	11.7624	+	11.7624i	0.409019	+	0.409019i	−0.472377	+	0.881396i	$0.656604\pi$
$828$	−3.32174	−	5.75342i	−0.115438	−	0.199945i
$829$	−21.8605	+	37.8636i	−0.759248	+	1.31506i	0.183987	+	0.982929i	$0.441100\pi$
$829$	−21.8605	+	37.8636i	−0.759248	+	1.31506i	−0.943235	+	0.332127i	$0.892234\pi$
$830$	4.30899	−	1.15459i	0.149567	−	0.0400764i
$831$	−11.3874	+	19.7235i	−0.395023	+	0.684200i
$832$	3.42815	−	1.11704i	0.118850	−	0.0387265i
$833$	−0.203900	−	4.62802i	−0.00706471	−	0.160351i
$834$	19.3455	+	5.18361i	0.669879	+	0.179494i
$835$	−7.69053			−0.266142
$836$	6.48935			0.224439
$837$	2.17918	+	0.583910i	0.0753236	+	0.0201829i
$838$	1.97142	−	7.35743i	0.0681015	−	0.254158i
$839$	13.9925	+	52.2207i	0.483075	+	1.80286i	0.588577	+	0.808441i	$0.299688\pi$
$839$	13.9925	+	52.2207i	0.483075	+	1.80286i	−0.105502	+	0.994419i	$0.533645\pi$
$840$	0.383338	−	1.56792i	0.0132264	−	0.0540983i
$841$	−1.30418	+	2.25890i	−0.0449717	+	0.0778932i
$842$		−	18.8417i		−	0.649327i
$843$	4.20654	+	15.6990i	0.144881	+	0.540703i
$844$	2.47853	−	1.43098i	0.0853147	−	0.0492565i
$845$	−4.98078	+	6.17183i	−0.171344	+	0.212318i
$846$		−	4.57613i		−	0.157331i
$847$	−3.62881	−	0.887203i	−0.124687	−	0.0304846i
$848$	−5.24890	−	9.09137i	−0.180248	−	0.312199i
$849$	26.8542	−	15.5043i	0.921635	−	0.532106i
$850$	0.792666	−	2.95827i	0.0271882	−	0.101468i
$851$	−10.6075	+	10.6075i	−0.363622	+	0.363622i
$852$	−12.8443	−	3.44163i	−0.440040	−	0.117908i
$853$	36.5229	−	36.5229i	1.25052	−	1.25052i	0.295034	−	0.955487i	$-0.404669\pi$
$853$	36.5229	−	36.5229i	1.25052	−	1.25052i	0.955487	−	0.295034i	$-0.0953309\pi$
$854$	−29.7277	+	18.0473i	−1.01726	+	0.617565i
$855$	0.973179	−	0.561865i	0.0332820	−	0.0192154i
$856$	−7.82656	−	7.82656i	−0.267506	−	0.267506i
$857$	9.54044	+	16.5245i	0.325895	+	0.564467i	0.981693	−	0.190469i	$-0.0610010\pi$
$857$	9.54044	+	16.5245i	0.325895	+	0.564467i	−0.655798	+	0.754936i	$0.727668\pi$
$858$	−9.44696	−	8.49178i	−0.322514	−	0.289905i
$859$	−29.7637	−	17.1841i	−1.01552	−	0.586312i	−0.102719	−	0.994710i	$-0.532754\pi$
$859$	−29.7637	−	17.1841i	−1.01552	−	0.586312i	−0.912804	+	0.408398i	$0.866088\pi$
$860$	−1.26077	+	4.70525i	−0.0429918	+	0.160448i
$861$	18.7543	−	0.412936i	0.639146	−	0.0140728i
$862$	−1.33526	−	0.770911i	−0.0454791	−	0.0262573i
$863$	9.50484	+	35.4725i	0.323548	+	1.20750i	0.915763	+	0.401719i	$0.131587\pi$
$863$	9.50484	+	35.4725i	0.323548	+	1.20750i	−0.592214	+	0.805780i	$0.701746\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−0.154074	−	0.154074i	−0.00523868	−	0.00523868i
$866$	9.18853	+	34.2921i	0.312239	+	1.16529i
$867$	14.3431	+	8.28102i	0.487119	+	0.281238i
$868$	−3.09755	−	5.10232i	−0.105138	−	0.173184i
$869$	5.85029	−	21.8336i	0.198457	−	0.740653i
$870$	−2.97038	−	1.71495i	−0.100705	−	0.0581423i
$871$	−43.2588	+	28.1441i	−1.46577	+	0.953625i
$872$	−4.40778	−	7.63449i	−0.149266	−	0.258537i
$873$	2.52443	+	2.52443i	0.0854389	+	0.0854389i
$874$	−10.5976	+	6.11852i	−0.358469	+	0.206962i
$875$	15.5365	−	0.342084i	0.525229	−	0.0115646i
$876$	2.97543	−	2.97543i	0.100530	−	0.100530i
$877$	15.8446	+	4.24556i	0.535036	+	0.143362i	0.516213	−	0.856460i	$-0.327341\pi$
$877$	15.8446	+	4.24556i	0.535036	+	0.143362i	0.0188230	+	0.999823i	$0.494008\pi$
$878$	20.2000	−	20.2000i	0.681717	−	0.681717i
$879$	−5.39854	+	20.1476i	−0.182088	+	0.679562i
$880$	1.86137	−	1.07466i	0.0627466	−	0.0362268i
$881$	−29.0728	−	50.3556i	−0.979489	−	1.69652i	−0.664248	−	0.747512i	$-0.731248\pi$
$881$	−29.0728	−	50.3556i	−0.979489	−	1.69652i	−0.315240	−	0.949012i	$-0.602085\pi$
$882$	−1.51237	+	6.83467i	−0.0509242	+	0.230135i
$883$		−	44.4751i		−	1.49671i	−0.663300	−	0.748354i	$-0.730845\pi$
$883$		−	44.4751i		−	1.49671i	0.663300	−	0.748354i	$-0.269155\pi$
$884$	2.26870	−	0.739245i	0.0763048	−	0.0248635i
$885$	−5.10080	+	2.94495i	−0.171462	+	0.0989934i
$886$	2.96778	+	11.0759i	0.0997045	+	0.372102i
$887$			34.0507i			1.14331i	0.820493	+	0.571656i	$0.193699\pi$
$887$			34.0507i			1.14331i	−0.820493	+	0.571656i	$0.806301\pi$
$888$	1.12903	−	1.95553i	0.0378877	−	0.0656234i
$889$	−11.6488	−	2.84799i	−0.390687	−	0.0955186i
$890$	−2.38441	−	8.89873i	−0.0799255	−	0.298286i
$891$	0.911835	−	3.40302i	0.0305476	−	0.114005i
$892$	5.80890	+	1.55649i	0.194496	+	0.0521152i
$893$	−8.42907			−0.282068
$894$	17.0583			0.570516
$895$	1.73277	+	0.464295i	0.0579202	+	0.0155197i
$896$	−0.0582404	−	2.64511i	−0.00194568	−	0.0883669i
$897$	23.4341	+	4.96059i	0.782442	+	0.165629i
$898$	−0.495976	+	0.859056i	−0.0165509	+	0.0286671i
$899$	−12.2516	+	3.28282i	−0.408615	+	0.109488i
$900$	−2.31391	+	4.00780i	−0.0771302	+	0.133593i
$901$	−3.47366	−	6.01655i	−0.115724	−	0.200440i
$902$	17.6629	+	17.6629i	0.588112	+	0.588112i
$903$	5.01717	−	20.5211i	0.166961	−	0.682898i
$904$	−5.89263	+	1.57892i	−0.195986	+	0.0525143i
$905$	1.81510	−	0.486354i	0.0603360	−	0.0161670i
$906$			4.35454i			0.144670i
$907$	−37.8976	−	21.8802i	−1.25837	−	0.726520i	−0.285612	−	0.958345i	$-0.592197\pi$
$907$	−37.8976	−	21.8802i	−1.25837	−	0.726520i	−0.972757	+	0.231825i	$0.925530\pi$
$908$	2.34743	−	2.34743i	0.0779022	−	0.0779022i
$909$	11.1279			0.369089
$910$	3.28034	+	4.80713i	0.108742	+	0.159355i
$911$	55.9543			1.85385			0.926925	−	0.375247i	$-0.122442\pi$
$911$	55.9543			1.85385			0.926925	+	0.375247i	$0.122442\pi$
$912$	1.30246	−	1.30246i	0.0431289	−	0.0431289i
$913$	−22.3101	−	12.8807i	−0.738356	−	0.426290i
$914$		−	26.0254i		−	0.860843i
$915$	−7.74584	+	2.07549i	−0.256069	+	0.0686136i
$916$	18.6978	−	5.01006i	0.617793	−	0.165537i
$917$	−6.76901	−	23.2063i	−0.223533	−	0.766341i
$918$	0.467954	+	0.467954i	0.0154448	+	0.0154448i
$919$	6.03794	+	10.4580i	0.199173	+	0.344978i	0.948261	−	0.317493i	$-0.102841\pi$
$919$	6.03794	+	10.4580i	0.199173	+	0.344978i	−0.749087	+	0.662471i	$0.769508\pi$
$920$	−2.02650	+	3.51000i	−0.0668117	+	0.115721i
$921$	−21.3802	+	5.72880i	−0.704501	+	0.188770i
$922$	10.0818	−	17.4622i	0.332026	−	0.575086i
$923$	40.1878	−	26.1461i	1.32280	−	0.860610i
$924$	−7.96780	+	4.83714i	−0.262121	+	0.159130i
$925$	10.0938	+	2.70462i	0.331882	+	0.0889274i
$926$	−20.5630			−0.675743
$927$	3.43468			0.112810
$928$	−5.43056	−	1.45511i	−0.178267	−	0.0477665i
$929$	10.4587	−	39.0323i	0.343138	−	1.28061i	−0.551635	−	0.834085i	$-0.685996\pi$
$929$	10.4587	−	39.0323i	0.343138	−	1.28061i	0.894773	−	0.446522i	$-0.147337\pi$
$930$	−0.356227	−	1.32946i	−0.0116811	−	0.0435946i
$931$	12.5892	+	2.78573i	0.412595	+	0.0912987i
$932$	9.25613	−	16.0321i	0.303195	−	0.525148i
$933$			6.26259i			0.205028i
$934$	7.34106	+	27.3972i	0.240207	+	0.896464i
$935$	1.23183	−	0.711196i	0.0402851	−	0.0232586i
$936$	−3.60045	+	0.191712i	−0.117684	+	0.00626629i
$937$		−	34.9997i		−	1.14339i	−0.820466	−	0.571696i	$-0.806286\pi$
$937$		−	34.9997i		−	1.14339i	0.820466	−	0.571696i	$-0.193714\pi$
$938$	10.6044	+	36.3551i	0.346244	+	1.18704i
$939$	−1.17161	−	2.02929i	−0.0382342	−	0.0662235i
$940$	−2.41774	+	1.39589i	−0.0788581	+	0.0455288i
$941$	11.7772	−	43.9533i	0.383927	−	1.43284i	−0.455924	−	0.890019i	$-0.650691\pi$
$941$	11.7772	−	43.9533i	0.383927	−	1.43284i	0.839851	−	0.542817i	$-0.182642\pi$
$942$	9.23283	−	9.23283i	0.300822	−	0.300822i
$943$	−45.4985	−	12.1913i	−1.48163	−	0.397003i
$944$	−6.82671	+	6.82671i	−0.222191	+	0.222191i
$945$	−0.776083	+	1.41528i	−0.0252460	+	0.0460390i
$946$	24.3617	−	14.0653i	0.792069	−	0.457301i
$947$	39.4656	+	39.4656i	1.28246	+	1.28246i	0.939264	+	0.343197i	$0.111510\pi$
$947$	39.4656	+	39.4656i	1.28246	+	1.28246i	0.343197	+	0.939264i	$0.388490\pi$
$948$	−3.20797	−	5.55637i	−0.104190	−	0.180463i
$949$	0.806702	+	15.1503i	0.0261866	+	0.491800i
$950$	7.38223	+	4.26213i	0.239511	+	0.138282i
$951$	−6.82959	+	25.4884i	−0.221464	+	0.826517i
$952$	−0.0385428	−	1.75050i	−0.00124918	−	0.0567340i
$953$	−42.5001	−	24.5375i	−1.37671	−	0.794846i	−0.384951	−	0.922937i	$-0.625782\pi$
$953$	−42.5001	−	24.5375i	−1.37671	−	0.794846i	−0.991762	+	0.128091i	$0.959115\pi$
$954$	2.71703	+	10.1401i	0.0879672	+	0.328298i
$955$	−0.558531	−	0.558531i	−0.0180736	−	0.0180736i
$956$	18.2410	+	18.2410i	0.589955	+	0.589955i
$957$	5.12646	+	19.1322i	0.165715	+	0.618456i
$958$	−2.61341	−	1.50885i	−0.0844355	−	0.0487489i
$959$	−0.707758	−	32.1443i	−0.0228547	−	1.03799i
$960$	0.157898	−	0.589284i	0.00509614	−	0.0190191i
$961$	22.4389	+	12.9551i	0.723836	+	0.417907i
$962$	2.52235	+	7.74095i	0.0813237	+	0.249578i
$963$	5.53421	+	9.58554i	0.178337	+	0.308890i
$964$	−4.29063	−	4.29063i	−0.138192	−	0.138192i
$965$	−4.57568	+	2.64177i	−0.147296	+	0.0850416i
$966$	8.45128	−	15.4119i	0.271915	−	0.495869i
$967$	−17.4774	+	17.4774i	−0.562035	+	0.562035i	−0.929885	−	0.367850i	$-0.880094\pi$
$967$	−17.4774	+	17.4774i	−0.562035	+	0.562035i	0.367850	+	0.929885i	$0.380094\pi$
$968$	−1.36385	−	0.365442i	−0.0438357	−	0.0117457i
$969$	0.861954	−	0.861954i	0.0276900	−	0.0276900i
$970$	0.563709	−	2.10379i	0.0180996	−	0.0675486i
$971$	−20.9630	+	12.1030i	−0.672734	+	0.388403i	−0.797112	−	0.603832i	$-0.793640\pi$
$971$	−20.9630	+	12.1030i	−0.672734	+	0.388403i	0.124378	+	0.992235i	$0.460307\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	14.8379	+	50.8691i	0.475681	+	1.63079i
$974$			13.2995i			0.426142i
$975$	−5.16947	−	15.8648i	−0.165556	−	0.508081i
$976$	−11.3835	+	6.57224i	−0.364376	+	0.210372i
$977$	−5.17315	−	19.3065i	−0.165504	−	0.617668i	−0.997975	−	0.0636008i	$-0.979742\pi$
$977$	−5.17315	−	19.3065i	−0.165504	−	0.617668i	0.832472	−	0.554068i	$-0.186925\pi$
$978$			18.2154i			0.582463i
$979$	−26.6007	+	46.0738i	−0.850163	+	1.47253i
$980$	4.07234	−	1.28578i	0.130086	−	0.0410727i
$981$	2.28163	+	8.51517i	0.0728469	+	0.271868i
$982$	11.4148	−	42.6007i	0.364262	−	1.35944i
$983$	−28.4504	−	7.62325i	−0.907426	−	0.243144i	−0.225223	−	0.974307i	$-0.572311\pi$
$983$	−28.4504	−	7.62325i	−0.907426	−	0.243144i	−0.682203	+	0.731163i	$0.738978\pi$
$984$	7.09019			0.226027
$985$	−1.67299			−0.0533058
$986$	−3.59387	−	0.962976i	−0.114452	−	0.0306674i
$987$	10.3494	−	6.28300i	0.329426	−	0.199990i
$988$	0.353126	+	6.63190i	0.0112344	+	0.210989i
$989$	−26.5230	+	45.9392i	−0.843383	+	1.46078i
$990$	−2.07608	+	0.556285i	−0.0659823	+	0.0176799i
$991$	−3.60178	+	6.23847i	−0.114414	+	0.198172i	−0.917545	−	0.397631i	$-0.869832\pi$
$991$	−3.60178	+	6.23847i	−0.114414	+	0.198172i	0.803131	+	0.595802i	$0.203166\pi$
$992$	−1.12803	−	1.95380i	−0.0358149	−	0.0620333i
$993$	−7.90709	−	7.90709i	−0.250924	−	0.250924i
$994$	−9.85155	−	33.7742i	−0.312472	−	1.07125i
$995$	−12.4490	+	3.33571i	−0.394661	+	0.105749i
$996$	−7.06308	+	1.89255i	−0.223802	+	0.0599676i
$997$			5.08637i			0.161087i	0.996751	+	0.0805434i	$0.0256656\pi$
$997$			5.08637i			0.161087i	−0.996751	+	0.0805434i	$0.974334\pi$
$998$	12.8630	+	7.42643i	0.407170	+	0.235079i
$999$	−1.59669	+	1.59669i	−0.0505169	+	0.0505169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.145.9	yes	40
7.3	odd	6		546.2.by.b.535.9	yes	40
13.7	odd	12		546.2.by.b.397.9	✓	40
91.59	even	12	inner	546.2.cg.b.241.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.9	✓	40	13.7	odd	12
546.2.by.b.535.9	yes	40	7.3	odd	6
546.2.cg.b.145.9	yes	40	1.1	even	1	trivial
546.2.cg.b.241.9	yes	40	91.59	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.589284 - 0.157898i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.91156 - 1.82919i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.589284 - 0.157898i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.91156 - 1.82919i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.305036 - 0.528338i) q^{10} +(-3.40302 + 0.911835i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.11704 - 3.42815i) q^{13} +(-2.64511 + 0.0582404i) q^{14} +(-0.589284 - 0.157898i) q^{15} -1.00000 q^{16} -0.661787 q^{17} +(0.965926 + 0.258819i) q^{18} +(0.476735 - 1.77920i) q^{19} +(-0.157898 - 0.589284i) q^{20} +(0.740861 + 2.53991i) q^{21} +(-1.76153 + 3.05106i) q^{22} -6.64347i q^{23} +(0.258819 + 0.965926i) q^{24} +(-4.00780 + 2.31391i) q^{25} +(-3.21394 - 1.63420i) q^{26} -1.00000i q^{27} +(-1.82919 + 1.91156i) q^{28} +(2.81107 + 4.86891i) q^{29} +(-0.528338 + 0.305036i) q^{30} +(-0.583910 + 2.17918i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.40302 + 0.911835i) q^{33} +(-0.467954 + 0.467954i) q^{34} +(-1.41528 - 0.776083i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.59669 - 1.59669i) q^{37} +(-0.920982 - 1.59519i) q^{38} +(-0.746686 + 3.52739i) q^{39} +(-0.528338 - 0.305036i) q^{40} +(1.83508 - 6.84860i) q^{41} +(2.31985 + 1.27212i) q^{42} +(-6.91494 - 3.99234i) q^{43} +(0.911835 + 3.40302i) q^{44} +(0.431386 + 0.431386i) q^{45} +(-4.69764 - 4.69764i) q^{46} +(-1.18439 - 4.42021i) q^{47} +(0.866025 + 0.500000i) q^{48} +(0.308105 + 6.99322i) q^{49} +(-1.19777 + 4.47012i) q^{50} +(0.573124 + 0.330893i) q^{51} +(-3.42815 + 1.11704i) q^{52} +(5.24890 + 9.09137i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-1.86137 + 1.07466i) q^{55} +(0.0582404 + 2.64511i) q^{56} +(-1.30246 + 1.30246i) q^{57} +(5.43056 + 1.45511i) q^{58} +(6.82671 - 6.82671i) q^{59} +(-0.157898 + 0.589284i) q^{60} +(11.3835 - 6.57224i) q^{61} +(1.12803 + 1.95380i) q^{62} +(0.628349 - 2.57005i) q^{63} +1.00000i q^{64} +(-1.19956 - 1.84377i) q^{65} +(3.05106 - 1.76153i) q^{66} +(-3.70462 - 13.8258i) q^{67} +0.661787i q^{68} +(-3.32174 + 5.75342i) q^{69} +(-1.54953 + 0.451978i) q^{70} +(3.44163 + 12.8443i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-4.06451 - 1.08908i) q^{73} -2.25805 q^{74} +4.62781 q^{75} +(-1.77920 - 0.476735i) q^{76} +(8.17298 + 4.48175i) q^{77} +(1.96625 + 3.02223i) q^{78} +(-3.20797 + 5.55637i) q^{79} +(-0.589284 + 0.157898i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.54509 - 6.14028i) q^{82} +(5.17053 + 5.17053i) q^{83} +(2.53991 - 0.740861i) q^{84} +(-0.389981 + 0.104495i) q^{85} +(-7.71261 + 2.06659i) q^{86} -5.62213i q^{87} +(3.05106 + 1.76153i) q^{88} +(10.6780 - 10.6780i) q^{89} +0.610072 q^{90} +(-4.13545 + 8.59640i) q^{91} -6.64347 q^{92} +(1.59527 - 1.59527i) q^{93} +(-3.96305 - 2.28807i) q^{94} -1.12373i q^{95} +(0.965926 - 0.258819i) q^{96} +(3.44843 - 0.924004i) q^{97} +(5.16281 + 4.72709i) q^{98} +(-2.49118 - 2.49118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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