LMFDB - Embedded newform 546.2.cg.b.241.9

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			241.9
Character	$\chi$	$=$	546.241
Dual form			546.2.cg.b.145.9

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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	0.388167	−	0.921589i	$-0.373108\pi$
$5$	0.589284	+	0.157898i	0.263536	+	0.0706142i	−0.124632	+	0.992203i	$0.539775\pi$
$6$	−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	−0.293728	−	0.955889i	$-0.594896\pi$
$11$	−3.40302	−	0.911835i	−1.02605	−	0.274929i	−0.732320	+	0.680960i	$0.761563\pi$
$12$	−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	0.998804	−	0.0488877i	$-0.0155676\pi$
$19$	0.476735	+	1.77920i	0.109371	+	0.408176i	−0.889434	+	0.457064i	$0.848901\pi$
$20$	−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	$0.243548\pi$
$23$			6.64347i			1.38526i	−0.721293	+	0.692630i	$0.756452\pi$
$24$	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	−0.477671	−	0.878539i	$-0.658519\pi$
$29$	2.81107	−	4.86891i	0.522002	−	0.904134i	0.999672	−	0.0255946i	$-0.00814789\pi$
$30$	−0.528338	−	0.305036i	−0.0964608	−	0.0556917i
$31$	−0.583910	−	2.17918i	−0.104873	−	0.391393i	0.893457	−	0.449148i	$-0.148272\pi$
$31$	−0.583910	−	2.17918i	−0.104873	−	0.391393i	−0.998331	+	0.0577552i	$0.981606\pi$
$32$	−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	−0.826066	−	0.563573i	$-0.809426\pi$
$37$	−1.59669	+	1.59669i	−0.262494	+	0.262494i	0.563573	+	0.826066i	$0.309426\pi$
$38$	−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	0.947669	+	0.319254i	$0.103432\pi$
$41$	1.83508	+	6.84860i	0.286591	+	1.06957i	−0.661078	+	0.750317i	$0.729901\pi$
$42$	2.31985	−	1.27212i	0.357961	−	0.196292i
$43$	−6.91494	+	3.99234i	−1.05452	+	0.608826i	−0.923911	−	0.382608i	$-0.875026\pi$
$43$	−6.91494	+	3.99234i	−1.05452	+	0.608826i	−0.130607	+	0.991434i	$0.541693\pi$
$44$	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	0.824161	+	0.566356i	$0.191647\pi$
$47$	−1.18439	+	4.42021i	−0.172761	+	0.644753i	−0.996922	+	0.0783978i	$0.975020\pi$
$48$	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	−0.239610	−	0.970869i	$-0.577020\pi$
$53$	5.24890	−	9.09137i	0.720992	−	1.24880i	0.960602	−	0.277926i	$-0.0896471\pi$
$54$	−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	0.994404	−	0.105642i	$-0.0336897\pi$
$59$	6.82671	+	6.82671i	0.888763	+	0.888763i	−0.105642	+	0.994404i	$0.533690\pi$
$60$	−0.157898	−	0.589284i	−0.0203846	−	0.0760763i
$61$	11.3835	+	6.57224i	1.45750	+	0.841489i	0.998888	−	0.0471460i	$-0.0150126\pi$
$61$	11.3835	+	6.57224i	1.45750	+	0.841489i	0.458614	+	0.888635i	$0.348346\pi$
$62$	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	0.242482	+	0.970156i	$0.422038\pi$
$67$	−3.70462	+	13.8258i	−0.452591	+	1.68909i	−0.695074	+	0.718939i	$0.744628\pi$
$68$		−	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	−0.389164	−	0.921168i	$-0.627236\pi$
$71$	3.44163	−	12.8443i	0.408446	−	1.52434i	0.797610	−	0.603173i	$-0.206097\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−4.06451	+	1.08908i	−0.475715	+	0.127467i	−0.488707	−	0.872448i	$-0.662531\pi$
$73$	−4.06451	+	1.08908i	−0.475715	+	0.127467i	0.0129916	+	0.999916i	$0.495865\pi$
$74$	−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	0.627188	−	0.778868i	$-0.284206\pi$
$79$	−3.20797	−	5.55637i	−0.360925	−	0.625141i	−0.988113	+	0.153727i	$0.950872\pi$
$80$	−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	−0.363899	−	0.931438i	$-0.618555\pi$
$83$	5.17053	−	5.17053i	0.567540	−	0.567540i	0.931438	+	0.363899i	$0.118555\pi$
$84$	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	0.989867	+	0.141994i	$0.0453514\pi$
$89$	10.6780	+	10.6780i	1.13186	+	1.13186i	0.141994	+	0.989867i	$0.454649\pi$
$90$	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	0.429600	−	0.903019i	$-0.358655\pi$
$97$	3.44843	+	0.924004i	0.350135	+	0.0938184i	−0.0794650	+	0.996838i	$0.525321\pi$
$98$	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	0.998008	+	0.0630801i	$0.0200924\pi$
$101$	5.56394	+	9.63704i	0.553633	+	0.958921i	−0.444375	+	0.895841i	$0.646574\pi$
$102$	0.639237	+	0.171283i	0.0632939	+	0.0169596i
$103$	1.71734	+	2.97452i	0.169214	+	0.293088i	0.938144	−	0.346246i	$-0.112544\pi$
$103$	1.71734	+	2.97452i	0.169214	+	0.293088i	−0.768929	+	0.639334i	$0.779210\pi$
$104$	−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	0.173181	−	0.984890i	$-0.444595\pi$
$109$	8.51517	−	2.28163i	0.815605	−	0.218541i	0.642424	+	0.766349i	$0.277929\pi$
$110$	−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	0.973079	−	0.230474i	$-0.0740276\pi$
$113$	3.05025	+	5.28319i	0.286943	+	0.497000i	−0.686135	+	0.727474i	$0.740694\pi$
$114$		−	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	0.663941	−	0.747785i	$-0.268883\pi$
$127$	3.92526	+	2.26625i	0.348311	+	0.201097i	−0.315630	+	0.948882i	$0.602216\pi$
$128$	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	−0.112782	−	0.993620i	$-0.535976\pi$
$131$	7.91260	−	4.56834i	0.691327	−	0.399138i	0.804109	+	0.594482i	$0.202643\pi$
$132$	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	−0.237289	−	0.971439i	$-0.576259\pi$
$137$	8.59301	−	8.59301i	0.734151	−	0.734151i	0.971439	+	0.237289i	$0.0762587\pi$
$138$	1.71946	−	6.41710i	0.146370	−	0.546260i
$139$	−17.3447	+	10.0140i	−1.47116	+	0.849373i	−0.999475	−	0.0323955i	$-0.989686\pi$
$139$	−17.3447	+	10.0140i	−1.47116	+	0.849373i	−0.471682	+	0.881769i	$0.656353\pi$
$140$	−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	−0.860082	−	0.510156i	$-0.829588\pi$
$149$	−16.4771	+	4.41502i	−1.34986	+	0.361693i	−0.489775	+	0.871849i	$0.662921\pi$
$150$	3.27236	+	3.27236i	0.267187	+	0.267187i
$151$	1.12704	+	4.20616i	0.0917170	+	0.342293i	0.996501	−	0.0835776i	$-0.0266347\pi$
$151$	1.12704	+	4.20616i	0.0917170	+	0.342293i	−0.904784	+	0.425870i	$0.859968\pi$
$152$	−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	−0.0244663	−	0.999701i	$-0.507789\pi$
$157$	−11.3079	−	6.52860i	−0.902466	−	0.521039i	−0.877999	+	0.478662i	$0.841122\pi$
$158$	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	0.861544	+	0.507683i	$0.169498\pi$
$163$	4.71448	+	17.5947i	0.369267	+	1.37812i	−0.492277	+	0.870438i	$0.663835\pi$
$164$	−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	−0.697066	−	0.717007i	$-0.745511\pi$
$167$	−12.1764	+	3.26266i	−0.942239	+	0.252472i	−0.245173	+	0.969479i	$0.578845\pi$
$168$	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	−0.872734	−	0.488196i	$-0.837655\pi$
$173$	−0.178580	+	0.309310i	−0.0135772	+	0.0235164i	0.859157	+	0.511712i	$0.170989\pi$
$174$	−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	−0.401804	−	0.915726i	$-0.631617\pi$
$179$	2.54652	−	1.47023i	0.190336	−	0.109890i	0.592140	+	0.805835i	$0.298283\pi$
$180$	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	−0.888496	−	0.458885i	$-0.848249\pi$
$191$	−0.647368	+	1.12127i	−0.0468419	+	0.0811326i	0.841654	+	0.540017i	$0.181582\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−8.36542	−	2.24151i	−0.602156	−	0.161347i	−0.0551531	−	0.998478i	$-0.517565\pi$
$193$	−8.36542	−	2.24151i	−0.602156	−	0.161347i	−0.547003	+	0.837131i	$0.684231\pi$
$194$	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	−0.351942	−	0.936022i	$-0.614479\pi$
$197$	−2.64884	+	0.709754i	−0.188722	+	0.0505679i	0.163220	+	0.986590i	$0.447812\pi$
$198$	−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	−0.812556	−	0.582883i	$-0.801925\pi$
$211$	1.43098	−	2.47853i	0.0985129	−	0.170629i	0.911069	+	0.412253i	$0.135258\pi$
$212$	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	0.894026	−	0.448014i	$-0.147869\pi$
$223$	−1.55649	−	5.80890i	−0.104230	−	0.388993i	−0.998257	+	0.0590214i	$0.981202\pi$
$224$	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	−0.624900	−	0.780705i	$-0.714860\pi$
$227$	2.34743	−	2.34743i	0.155804	−	0.155804i	0.780705	+	0.624900i	$0.214860\pi$
$228$	1.30246	−	1.30246i	0.0862578	−	0.0862578i
$229$	5.01006	−	18.6978i	0.331074	−	1.23559i	−0.576989	−	0.816752i	$-0.695772\pi$
$229$	5.01006	−	18.6978i	0.331074	−	1.23559i	0.908063	−	0.418833i	$-0.137561\pi$
$230$	−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	0.127564	−	0.991830i	$-0.459284\pi$
$233$	16.0321	−	9.25613i	1.05030	−	0.606389i	0.922732	+	0.385441i	$0.125951\pi$
$234$	−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	−0.979767	−	0.200144i	$-0.935859\pi$
$239$	−18.2410	−	18.2410i	−1.17991	−	1.17991i	−0.200144	−	0.979767i	$-0.564141\pi$
$240$	0.589284	−	0.157898i	0.0380381	−	0.0101923i
$241$	4.29063	+	4.29063i	0.276384	+	0.276384i	0.831664	−	0.555280i	$-0.187389\pi$
$241$	4.29063	+	4.29063i	0.276384	+	0.276384i	−0.555280	+	0.831664i	$0.687389\pi$
$242$	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	0.811845	−	0.583874i	$-0.198464\pi$
$251$	−1.57998	−	2.73660i	−0.0997272	−	0.172733i	−0.911572	+	0.411141i	$0.865130\pi$
$252$	−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	0.564848	−	0.825195i	$-0.308935\pi$
$263$	−7.00937	−	12.1406i	−0.432216	−	0.748620i	−0.997064	+	0.0765750i	$0.975602\pi$
$264$	−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	$-0.899133\pi$
$269$		−	10.2215i		−	0.623214i	0.950211	−	0.311607i	$-0.100867\pi$
$270$	−0.528338	+	0.305036i	−0.0321536	+	0.0185639i
$271$	8.53395	+	8.53395i	0.518401	+	0.518401i	0.917087	−	0.398687i	$-0.130534\pi$
$271$	8.53395	+	8.53395i	0.518401	+	0.518401i	−0.398687	+	0.917087i	$0.630534\pi$
$272$	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	$0.239848\pi$
$277$			22.7747i			1.36840i	−0.729294	+	0.684200i	$0.760152\pi$
$278$	−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	−0.961253	−	0.275669i	$-0.911101\pi$
$281$	−11.4925	+	11.4925i	−0.685584	+	0.685584i	0.275669	+	0.961253i	$0.411101\pi$
$282$	2.28807	−	3.96305i	0.136252	−	0.235996i
$283$	−15.5043	−	26.8542i	−0.921635	−	1.59632i	−0.796885	−	0.604131i	$-0.793521\pi$
$283$	−15.5043	−	26.8542i	−0.921635	−	1.59632i	−0.124750	−	0.992188i	$-0.539813\pi$
$284$	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	0.608244	+	0.793750i	$0.291874\pi$
$293$	−5.39854	+	20.1476i	−0.315386	+	1.17704i	−0.923630	+	0.383286i	$0.874792\pi$
$294$	−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	0.994830	−	0.101559i	$-0.0323830\pi$
$307$	15.6514	+	15.6514i	0.893271	+	0.893271i	−0.101559	+	0.994830i	$0.532383\pi$
$308$	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	−0.941044	−	0.338284i	$-0.890154\pi$
$311$	−3.13129	+	5.42356i	−0.177559	+	0.307542i	0.763485	+	0.645826i	$0.223487\pi$
$312$	3.02223	+	1.96625i	0.171100	+	0.111317i
$313$	2.02929	−	1.17161i	0.114702	−	0.0662235i	−0.441551	−	0.897236i	$-0.645572\pi$
$313$	2.02929	−	1.17161i	0.114702	−	0.0662235i	0.556254	+	0.831013i	$0.312238\pi$
$314$	−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	0.456793	+	0.889573i	$0.348998\pi$
$317$	−6.82959	+	25.4884i	−0.383588	+	1.43157i	−0.840381	+	0.541996i	$0.817669\pi$
$318$	−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	0.0505521	−	0.998721i	$-0.483902\pi$
$331$	10.8013	−	2.89420i	0.593692	−	0.159079i	0.543140	+	0.839642i	$0.317235\pi$
$332$	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	$-0.807656\pi$
$337$		−	20.8601i		−	1.13632i	0.822918	−	0.568160i	$-0.192344\pi$
$338$	−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	−0.985090	−	0.172041i	$-0.944964\pi$
$349$	−32.7335	+	8.77090i	−1.75218	+	0.469496i	−0.767092	+	0.641537i	$0.778297\pi$
$350$	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	0.455447	−	0.890263i	$-0.349479\pi$
$353$	7.60446	+	2.03761i	0.404745	+	0.108451i	−0.0507026	+	0.998714i	$0.516146\pi$
$354$	−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	−0.526414	−	0.850228i	$-0.676464\pi$
$359$	−26.6667	−	7.14533i	−1.40742	−	0.377116i	−0.881002	+	0.473112i	$0.843131\pi$
$360$			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	−0.420355	−	0.907360i	$-0.638094\pi$
$367$	2.97444	−	1.71730i	0.155265	−	0.0896421i	0.575619	+	0.817718i	$0.304761\pi$
$368$		−	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	−0.977668	−	0.210157i	$-0.932603\pi$
$373$	−5.92593	+	10.2640i	−0.306833	+	0.531450i	0.670835	+	0.741607i	$0.265936\pi$
$374$	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	0.267828	−	0.963467i	$-0.413694\pi$
$379$	19.1079	−	5.11994i	0.981506	−	0.262994i	0.713679	+	0.700473i	$0.247028\pi$
$380$	−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	0.981086	+	0.193574i	$0.0620080\pi$
$383$	4.46650	+	16.6692i	0.228228	+	0.851757i	−0.752858	+	0.658183i	$0.771325\pi$
$384$	−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	0.573676	−	0.819083i	$-0.305517\pi$
$389$	2.98149	+	1.72136i	0.151167	+	0.0872765i	−0.422508	+	0.906359i	$0.638850\pi$
$390$	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	0.677397	−	0.735617i	$-0.263108\pi$
$397$	32.5144	−	8.71220i	1.63185	−	0.437253i	0.954452	+	0.298365i	$0.0964412\pi$
$398$	−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	−0.974981	−	0.222288i	$-0.928647\pi$
$401$	−15.0727	+	15.0727i	−0.752693	+	0.752693i	0.222288	+	0.974981i	$0.428647\pi$
$402$	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	−0.826368	−	0.563131i	$-0.809597\pi$
$409$	−5.32363	+	5.32363i	−0.263237	+	0.263237i	0.563131	+	0.826368i	$0.309597\pi$
$410$	−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	0.652399	−	0.757875i	$-0.273763\pi$
$419$	6.59649	+	3.80849i	0.322260	+	0.186057i	−0.330140	+	0.943932i	$0.607096\pi$
$420$	1.37975	+	0.837624i	0.0673247	+	0.0408719i
$421$	13.3231	+	13.3231i	0.649327	+	0.649327i	0.952830	−	0.303503i	$-0.0981562\pi$
$421$	13.3231	+	13.3231i	0.649327	+	0.649327i	−0.303503	+	0.952830i	$0.598156\pi$
$422$	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	−0.974870	−	0.222772i	$-0.928489\pi$
$431$	−0.399053	+	1.48929i	−0.0192217	+	0.0717364i	0.955649	+	0.294509i	$0.0951560\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−17.7509	−	30.7454i	−0.853053	−	1.47753i	−0.878440	−	0.477853i	$-0.841415\pi$
$433$	−17.7509	−	30.7454i	−0.853053	−	1.47753i	0.0253870	−	0.999678i	$-0.491918\pi$
$434$	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	0.697078	−	0.716996i	$-0.254483\pi$
$443$	−5.73331	−	9.93038i	−0.272398	−	0.471807i	−0.969475	+	0.245189i	$0.921150\pi$
$444$	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	0.236139	−	0.971719i	$-0.424118\pi$
$449$	−0.958153	−	0.256736i	−0.0452180	−	0.0121161i	−0.281357	+	0.959603i	$0.590785\pi$
$450$	−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	0.991436	−	0.130593i	$-0.0416880\pi$
$457$	18.4027	+	18.4027i	0.860843	+	0.860843i	−0.130593	+	0.991436i	$0.541688\pi$
$458$	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	0.682068	−	0.731289i	$-0.261081\pi$
$461$	19.4765	+	5.21871i	0.907111	+	0.243060i	0.225044	+	0.974349i	$0.427748\pi$
$462$	−9.05446	+	2.21371i	−0.421251	+	0.102991i
$463$	−14.5403	+	14.5403i	−0.675743	+	0.675743i	−0.959034	−	0.283291i	$-0.908574\pi$
$463$	−14.5403	+	14.5403i	−0.675743	+	0.675743i	0.283291	+	0.959034i	$0.408574\pi$
$464$	−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	−0.981577	−	0.191067i	$-0.938805\pi$
$467$	−14.1818	−	24.5637i	−0.656257	−	1.13667i	0.325320	−	0.945604i	$-0.394528\pi$
$468$	−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	−0.981471	−	0.191611i	$-0.938629\pi$
$479$	−0.781041	+	2.91488i	−0.0356867	+	0.133184i	0.945784	+	0.324795i	$0.105295\pi$
$480$	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	0.461170	−	0.887312i	$-0.347430\pi$
$487$	−9.40414	−	9.40414i	−0.426142	−	0.426142i	−0.887312	+	0.461170i	$0.847430\pi$
$488$	−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	0.910877	+	0.412678i	$0.135407\pi$
$491$	38.1948	+	22.0518i	1.72371	+	0.995182i	0.812828	+	0.582503i	$0.197927\pi$
$492$	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	−0.824939	−	0.565222i	$-0.808791\pi$
$499$	3.84420	−	14.3468i	0.172090	−	0.642249i	0.997029	−	0.0770271i	$-0.0245428\pi$
$500$	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	−0.179463	−	0.983765i	$-0.557436\pi$
$503$	13.0702	−	7.54607i	0.582770	−	0.336462i	0.762233	+	0.647302i	$0.224103\pi$
$504$	−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	−0.488838	−	0.872375i	$-0.662579\pi$
$509$	8.65298	−	8.65298i	0.383537	−	0.383537i	0.872375	+	0.488838i	$0.162579\pi$
$510$	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	−0.0854203	−	0.996345i	$-0.527223\pi$
$521$	−22.6198	−	13.0595i	−0.990991	−	0.572149i	−0.905570	+	0.424196i	$0.860557\pi$
$522$	1.45511	−	5.43056i	0.0636886	−	0.237689i
$523$			32.6776i			1.42889i	0.699690	+	0.714447i	$0.253321\pi$
$523$			32.6776i			1.42889i	−0.699690	+	0.714447i	$0.746679\pi$
$524$	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	0.942909	−	0.333051i	$-0.108078\pi$
$541$	37.0514	+	9.92791i	1.59297	+	0.426834i	0.650057	+	0.759885i	$0.274745\pi$
$542$			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	0.618268	−	0.785967i	$-0.287835\pi$
$557$	17.9536	+	4.81066i	0.760720	+	0.203834i	0.142452	+	0.989802i	$0.454501\pi$
$558$	−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	$-0.995519\pi$
$569$		−	0.671507i		−	0.0281511i	0.999901	−	0.0140755i	$-0.00448053\pi$
$570$	0.290843	−	1.08544i	0.0121821	−	0.0454641i
$571$	22.2930	+	12.8709i	0.932933	+	0.538629i	0.887738	−	0.460349i	$-0.152276\pi$
$571$	22.2930	+	12.8709i	0.932933	+	0.538629i	0.0451952	+	0.998978i	$0.485609\pi$
$572$	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	−0.998306	−	0.0581840i	$-0.981469\pi$
$577$	−3.91154	−	14.5981i	−0.162840	−	0.607726i	0.835466	−	0.549542i	$-0.185198\pi$
$578$	−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	0.987796	−	0.155753i	$-0.0497803\pi$
$587$	1.31954	+	4.92459i	0.0544632	+	0.203259i	−0.933333	+	0.359012i	$0.883114\pi$
$588$	−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	−0.993310	−	0.115479i	$-0.963160\pi$
$593$	−1.83462	+	6.84690i	−0.0753389	+	0.281169i	0.917971	+	0.396647i	$0.129826\pi$
$594$	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	−0.481212	−	0.876604i	$-0.659803\pi$
$599$	12.6914	−	21.9821i	0.518555	−	0.898164i	0.999768	−	0.0215601i	$-0.00686331\pi$
$600$	−3.27236	+	3.27236i	−0.133593	+	0.133593i
$601$	19.7808	+	11.4204i	0.806875	+	0.465849i	0.845869	−	0.533390i	$-0.179082\pi$
$601$	19.7808	+	11.4204i	0.806875	+	0.465849i	−0.0389947	+	0.999239i	$0.512416\pi$
$602$	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	0.428086	−	0.903738i	$-0.359188\pi$
$607$	−3.46230	−	1.99896i	−0.140530	−	0.0811352i	−0.568617	+	0.822603i	$0.692521\pi$
$608$	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	0.396069	+	0.918221i	$0.370374\pi$
$613$	−10.0533	+	37.5193i	−0.406047	+	1.51539i	−0.802116	+	0.597168i	$0.796292\pi$
$614$			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	−0.997789	−	0.0664565i	$-0.978831\pi$
$617$	−2.49513	+	9.31195i	−0.100450	+	0.374885i	0.897339	+	0.441342i	$0.145497\pi$
$618$	−0.888960	−	3.31764i	−0.0357592	−	0.133455i
$619$	5.44832	−	1.45987i	0.218986	−	0.0586772i	−0.147658	−	0.989039i	$-0.547173\pi$
$619$	5.44832	−	1.45987i	0.218986	−	0.0586772i	0.366644	+	0.930361i	$0.380507\pi$
$620$	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	0.289024	−	0.957322i	$-0.406669\pi$
$631$	1.52391	+	0.408330i	0.0606659	+	0.0162554i	−0.228358	+	0.973577i	$0.573336\pi$
$632$	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	$-0.698125\pi$
$641$		−	41.1399i		−	1.62493i	0.583010	−	0.812465i	$-0.301875\pi$
$642$	−10.6913	−	2.86472i	−0.421951	−	0.113061i
$643$	46.0170	+	12.3302i	1.81473	+	0.486256i	0.996113	−	0.0880805i	$-0.0280733\pi$
$643$	46.0170	+	12.3302i	1.81473	+	0.486256i	0.818619	+	0.574337i	$0.194740\pi$
$644$	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	−0.946871	−	0.321615i	$-0.895774\pi$
$647$	−19.1270	−	33.1290i	−0.751962	−	1.30244i	0.194909	−	0.980821i	$-0.437559\pi$
$648$	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	0.943223	−	0.332160i	$-0.107777\pi$
$659$	4.72225	+	8.17917i	0.183953	+	0.318615i	−0.759271	+	0.650775i	$0.774444\pi$
$660$			2.14932i			0.0836622i
$661$	−3.91995	+	14.6294i	−0.152468	+	0.569019i	0.846841	+	0.531847i	$0.178502\pi$
$661$	−3.91995	+	14.6294i	−0.152468	+	0.569019i	−0.999309	+	0.0371726i	$0.988165\pi$
$662$	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	0.181373	−	0.983414i	$-0.441946\pi$
$673$	−15.0362	−	8.68115i	−0.579602	−	0.334634i	−0.760975	+	0.648781i	$0.775279\pi$
$674$	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	−0.483477	−	0.875357i	$-0.660626\pi$
$677$	0.855137	−	0.493714i	0.0328656	−	0.0189750i	0.516343	+	0.856382i	$0.327293\pi$
$678$	−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	−0.398260	−	0.917273i	$-0.630386\pi$
$683$	13.5640	−	13.5640i	0.519013	−	0.519013i	0.917273	+	0.398260i	$0.130386\pi$
$684$	−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	−0.946258	−	0.323413i	$-0.895170\pi$
$691$	−16.3727	+	16.3727i	−0.622845	+	0.622845i	0.323413	+	0.946258i	$0.395170\pi$
$692$	−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	$0.105641\pi$
$701$			17.2532i			0.651646i	−0.945431	+	0.325823i	$0.894359\pi$
$702$	−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	0.969800	−	0.243900i	$-0.0784270\pi$
$709$	0.212442	+	0.792846i	0.00797844	+	0.0297759i	−0.961822	+	0.273676i	$0.911760\pi$
$710$	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	−0.729549	−	0.683928i	$-0.760270\pi$
$719$	6.10088	−	10.5670i	0.227524	−	0.394084i	0.957074	+	0.289844i	$0.0936036\pi$
$720$	−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	−0.211967	−	0.977277i	$-0.567987\pi$
$733$	−23.9381	−	6.41419i	−0.884173	−	0.236914i	−0.672207	+	0.740363i	$0.734653\pi$
$734$	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	−0.684495	−	0.729017i	$-0.739977\pi$
$739$	−44.6315	−	11.9590i	−1.64179	−	0.439918i	−0.957299	+	0.289100i	$0.906644\pi$
$740$	−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	0.167767	−	0.985827i	$-0.446344\pi$
$743$	21.9692	−	5.88663i	0.805972	−	0.215959i	0.638204	+	0.769867i	$0.279678\pi$
$744$	−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	$-0.802215\pi$
$751$		−	31.9064i		−	1.16428i	0.813088	−	0.582141i	$-0.197785\pi$
$752$	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	0.0215919	+	0.999767i	$0.493127\pi$
$757$	−23.5249	+	40.7463i	−0.855028	+	1.48095i	−0.876619	+	0.481184i	$0.840207\pi$
$758$	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	−0.781765	−	0.623574i	$-0.785680\pi$
$761$	−31.6416	+	8.47833i	−1.14701	+	0.307339i	−0.365241	+	0.930913i	$0.619013\pi$
$762$	−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	0.953304	+	0.302012i	$0.0976583\pi$
$769$	7.72927	+	28.8460i	0.278725	+	1.04021i	−0.674580	+	0.738202i	$0.735675\pi$
$770$	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	−0.967466	−	0.253000i	$-0.918583\pi$
$773$	−19.8642	+	19.8642i	−0.714466	+	0.714466i	0.253000	+	0.967466i	$0.418583\pi$
$774$	−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	0.965401	−	0.260771i	$-0.0839768\pi$
$787$	19.7673	+	19.7673i	0.704630	+	0.704630i	−0.260771	+	0.965401i	$0.583977\pi$
$788$	−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	0.708713	−	0.705497i	$-0.249276\pi$
$797$	−7.24475	−	12.5483i	−0.256622	−	0.444483i	−0.965335	+	0.261015i	$0.915943\pi$
$798$	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	0.576137	−	0.817353i	$-0.304560\pi$
$809$	−11.9398	−	20.6803i	−0.419780	−	0.727081i	−0.995917	+	0.0902724i	$0.971226\pi$
$810$	0.305036	−	0.528338i	0.0107179	−	0.0185639i
$811$	21.0744	−	21.0744i	0.740023	−	0.740023i	−0.232559	−	0.972582i	$-0.574710\pi$
$811$	21.0744	−	21.0744i	0.740023	−	0.740023i	0.972582	+	0.232559i	$0.0747099\pi$
$812$	−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	0.0713099	−	0.997454i	$-0.477282\pi$
$821$	−26.5369	−	26.5369i	−0.926144	−	0.926144i	−0.997454	+	0.0713099i	$0.977282\pi$
$822$	−10.5242	+	6.07618i	−0.367075	+	0.211931i
$823$			6.56963i			0.229003i	0.993423	+	0.114502i	$0.0365271\pi$
$823$			6.56963i			0.229003i	−0.993423	+	0.114502i	$0.963473\pi$
$824$	−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	−0.472377	−	0.881396i	$-0.656604\pi$
$827$	11.7624	−	11.7624i	0.409019	−	0.409019i	0.881396	+	0.472377i	$0.156604\pi$
$828$	−3.32174	+	5.75342i	−0.115438	+	0.199945i
$829$	−21.8605	−	37.8636i	−0.759248	−	1.31506i	−0.943235	−	0.332127i	$-0.892234\pi$
$829$	−21.8605	−	37.8636i	−0.759248	−	1.31506i	0.183987	−	0.982929i	$-0.441100\pi$
$830$	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	−0.105502	−	0.994419i	$-0.533645\pi$
$839$	13.9925	−	52.2207i	0.483075	−	1.80286i	0.588577	−	0.808441i	$-0.299688\pi$
$840$	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	0.955487	+	0.295034i	$0.0953309\pi$
$853$	36.5229	+	36.5229i	1.25052	+	1.25052i	0.295034	+	0.955487i	$0.404669\pi$
$854$	−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	−0.655798	−	0.754936i	$-0.727668\pi$
$857$	9.54044	−	16.5245i	0.325895	−	0.564467i	0.981693	+	0.190469i	$0.0610010\pi$
$858$	−9.44696	+	8.49178i	−0.322514	+	0.289905i
$859$	−29.7637	+	17.1841i	−1.01552	+	0.586312i	−0.912804	−	0.408398i	$-0.866088\pi$
$859$	−29.7637	+	17.1841i	−1.01552	+	0.586312i	−0.102719	+	0.994710i	$0.532754\pi$
$860$	−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	−0.592214	−	0.805780i	$-0.701746\pi$
$863$	9.50484	−	35.4725i	0.323548	−	1.20750i	0.915763	−	0.401719i	$-0.131587\pi$
$864$	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	0.0188230	−	0.999823i	$-0.494008\pi$
$877$	15.8446	−	4.24556i	0.535036	−	0.143362i	0.516213	+	0.856460i	$0.327341\pi$
$878$	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	−0.315240	+	0.949012i	$0.602085\pi$
$881$	−29.0728	+	50.3556i	−0.979489	+	1.69652i	−0.664248	+	0.747512i	$0.731248\pi$
$882$	−1.51237	−	6.83467i	−0.0509242	−	0.230135i
$883$			44.4751i			1.49671i	0.663300	+	0.748354i	$0.269155\pi$
$883$			44.4751i			1.49671i	−0.663300	+	0.748354i	$0.730845\pi$
$884$	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	$-0.806301\pi$
$887$		−	34.0507i		−	1.14331i	0.820493	−	0.571656i	$-0.193699\pi$
$888$	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	−0.972757	−	0.231825i	$-0.925530\pi$
$907$	−37.8976	+	21.8802i	−1.25837	+	0.726520i	−0.285612	+	0.958345i	$0.592197\pi$
$908$	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	−0.749087	−	0.662471i	$-0.769508\pi$
$919$	6.03794	−	10.4580i	0.199173	−	0.344978i	0.948261	+	0.317493i	$0.102841\pi$
$920$	−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	0.894773	+	0.446522i	$0.147337\pi$
$929$	10.4587	+	39.0323i	0.343138	+	1.28061i	−0.551635	+	0.834085i	$0.685996\pi$
$930$	−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	$0.193714\pi$
$937$			34.9997i			1.14339i	−0.820466	+	0.571696i	$0.806286\pi$
$938$	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	0.839851	+	0.542817i	$0.182642\pi$
$941$	11.7772	+	43.9533i	0.383927	+	1.43284i	−0.455924	+	0.890019i	$0.650691\pi$
$942$	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	0.343197	−	0.939264i	$-0.388490\pi$
$947$	39.4656	−	39.4656i	1.28246	−	1.28246i	0.939264	−	0.343197i	$-0.111510\pi$
$948$	−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	−0.991762	−	0.128091i	$-0.959115\pi$
$953$	−42.5001	+	24.5375i	−1.37671	+	0.794846i	−0.384951	+	0.922937i	$0.625782\pi$
$954$	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	0.367850	−	0.929885i	$-0.380094\pi$
$967$	−17.4774	−	17.4774i	−0.562035	−	0.562035i	−0.929885	+	0.367850i	$0.880094\pi$
$968$	−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	0.124378	−	0.992235i	$-0.460307\pi$
$971$	−20.9630	−	12.1030i	−0.672734	−	0.388403i	−0.797112	+	0.603832i	$0.793640\pi$
$972$	−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	0.832472	+	0.554068i	$0.186925\pi$
$977$	−5.17315	+	19.3065i	−0.165504	+	0.617668i	−0.997975	+	0.0636008i	$0.979742\pi$
$978$		−	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	−0.682203	−	0.731163i	$-0.738978\pi$
$983$	−28.4504	+	7.62325i	−0.907426	+	0.243144i	−0.225223	+	0.974307i	$0.572311\pi$
$984$	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	0.803131	−	0.595802i	$-0.203166\pi$
$991$	−3.60178	−	6.23847i	−0.114414	−	0.198172i	−0.917545	+	0.397631i	$0.869832\pi$
$992$	−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	$-0.974334\pi$
$997$		−	5.08637i		−	0.161087i	0.996751	−	0.0805434i	$-0.0256656\pi$
$998$	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.241.9	yes	40
7.5	odd	6		546.2.by.b.397.9	✓	40
13.2	odd	12		546.2.by.b.535.9	yes	40
91.54	even	12	inner	546.2.cg.b.145.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.9	✓	40	7.5	odd	6
546.2.by.b.535.9	yes	40	13.2	odd	12
546.2.cg.b.145.9	yes	40	91.54	even	12	inner
546.2.cg.b.241.9	yes	40	1.1	even	1	trivial

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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