LMFDB - Embedded newform 546.2.bu.a.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.2
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.a.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.60917 - 0.640767i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11813 - 2.11813i) q^{5} +(1.03542 - 1.38849i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.17884 + 2.06220i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.60917 - 0.640767i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11813 - 2.11813i) q^{5} +(1.03542 - 1.38849i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.17884 + 2.06220i) q^{9} +(2.59417 - 1.49774i) q^{10} +(-0.775667 - 0.207839i) q^{11} +(1.07320 + 1.35950i) q^{12} +(0.382979 - 3.58515i) q^{13} +1.00000i q^{14} +(2.05120 + 4.76565i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.86391 + 6.69249i) q^{17} +(-2.55586 + 1.57086i) q^{18} +(-0.311240 - 1.16156i) q^{19} +(0.775289 + 2.89342i) q^{20} +(-1.72018 - 0.202450i) q^{21} +(0.401515 - 0.695444i) q^{22} +(0.763097 + 1.32172i) q^{23} +(-1.59094 + 0.684763i) q^{24} +3.97293i q^{25} +(3.36387 + 1.29784i) q^{26} +(-2.18472 - 4.71455i) q^{27} +(-0.965926 - 0.258819i) q^{28} +(-6.26395 + 3.61650i) q^{29} +(-5.13415 + 0.747863i) q^{30} +(-6.29751 + 6.29751i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.11500 + 0.831469i) q^{33} +(-5.46439 - 5.46439i) q^{34} +(-2.59417 - 1.49774i) q^{35} +(-0.855827 - 2.87534i) q^{36} +(-2.24532 + 8.37964i) q^{37} +1.20254 q^{38} +(-2.91352 + 5.52371i) q^{39} -2.99549 q^{40} +(0.512930 - 1.91428i) q^{41} +(0.640767 - 1.60917i) q^{42} +(6.83180 + 3.94434i) q^{43} +(0.567828 + 0.567828i) q^{44} +(-0.247050 - 8.98306i) q^{45} +(-1.47419 + 0.395008i) q^{46} +(0.633171 - 0.633171i) q^{47} +(-0.249663 - 1.71396i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-3.83756 - 1.02827i) q^{50} +(10.5060 - 8.29347i) q^{51} +(-2.12425 + 2.91334i) q^{52} +6.60837i q^{53} +(5.11935 - 0.890064i) q^{54} +(1.20273 + 2.08319i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-0.243454 + 2.06858i) q^{57} +(-1.87204 - 6.98653i) q^{58} +(-2.31846 - 8.65262i) q^{59} +(0.606436 - 5.15277i) q^{60} +(0.00670528 - 0.0116139i) q^{61} +(-4.45301 - 7.71284i) q^{62} +(2.63833 + 1.42801i) q^{63} -1.00000i q^{64} +(-8.40501 + 6.78262i) q^{65} +(-1.09172 + 0.861808i) q^{66} +(-10.3878 - 2.78339i) q^{67} +(6.69249 - 3.86391i) q^{68} +(-0.381035 - 2.61584i) q^{69} +(2.11813 - 2.11813i) q^{70} +(13.8552 - 3.71249i) q^{71} +(2.99887 - 0.0824740i) q^{72} +(5.65127 + 5.65127i) q^{73} +(-7.51298 - 4.33762i) q^{74} +(2.54572 - 6.39311i) q^{75} +(-0.311240 + 1.16156i) q^{76} -0.803029 q^{77} +(-4.58142 - 4.24389i) q^{78} -5.16613 q^{79} +(0.775289 - 2.89342i) q^{80} +(0.494657 + 8.98640i) q^{81} +(1.71630 + 0.990904i) q^{82} +(-3.82533 - 3.82533i) q^{83} +(1.38849 + 1.03542i) q^{84} +(22.3598 - 5.99129i) q^{85} +(-5.57814 + 5.57814i) q^{86} +(12.3971 - 1.80581i) q^{87} +(-0.695444 + 0.401515i) q^{88} +(-6.45205 - 1.72882i) q^{89} +(8.74091 + 2.08636i) q^{90} +(-0.557977 - 3.56211i) q^{91} -1.52619i q^{92} +(14.1690 - 6.09851i) q^{93} +(0.447720 + 0.775473i) q^{94} +(-1.80109 + 3.11958i) q^{95} +(1.72018 + 0.202450i) q^{96} +(3.08877 + 11.5275i) q^{97} +(0.258819 + 0.965926i) q^{98} +(-1.26144 - 2.05243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.60917	−	0.640767i	−0.929053	−	0.369947i
$3$	−1.60917	−	0.640767i	−0.929053	−	0.369947i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.11813	−	2.11813i	−0.947256	−	0.947256i	0.0514215	−	0.998677i	$-0.483625\pi$
$5$	−2.11813	−	2.11813i	−0.947256	−	0.947256i	−0.998677	+	0.0514215i	$0.983625\pi$
$6$	1.03542	−	1.38849i	0.422707	−	0.566850i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.17884	+	2.06220i	0.726279	+	0.687400i
$10$	2.59417	−	1.49774i	0.820347	−	0.473628i
$11$	−0.775667	−	0.207839i	−0.233872	−	0.0626659i	0.139979	−	0.990154i	$-0.455296\pi$
$11$	−0.775667	−	0.207839i	−0.233872	−	0.0626659i	−0.373852	+	0.927489i	$0.621963\pi$
$12$	1.07320	+	1.35950i	0.309805	+	0.392455i
$13$	0.382979	−	3.58515i	0.106219	−	0.994343i
$13$	0.382979	−	3.58515i	0.106219	−	0.994343i
$14$			1.00000i			0.267261i
$15$	2.05120	+	4.76565i	0.529617	+	1.23048i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.86391	+	6.69249i	−0.937136	+	1.62317i	−0.166356	+	0.986066i	$0.553200\pi$
$17$	−3.86391	+	6.69249i	−0.937136	+	1.62317i	−0.770780	+	0.637101i	$0.780133\pi$
$18$	−2.55586	+	1.57086i	−0.602421	+	0.370255i
$19$	−0.311240	−	1.16156i	−0.0714033	−	0.266481i	0.920990	−	0.389585i	$-0.127382\pi$
$19$	−0.311240	−	1.16156i	−0.0714033	−	0.266481i	−0.992394	+	0.123104i	$0.960715\pi$
$20$	0.775289	+	2.89342i	0.173360	+	0.646988i
$21$	−1.72018	−	0.202450i	−0.375374	−	0.0441782i
$22$	0.401515	−	0.695444i	0.0856032	−	0.148269i
$23$	0.763097	+	1.32172i	0.159117	+	0.275598i	0.934550	−	0.355831i	$-0.115802\pi$
$23$	0.763097	+	1.32172i	0.159117	+	0.275598i	−0.775434	+	0.631429i	$0.782469\pi$
$24$	−1.59094	+	0.684763i	−0.324750	+	0.139777i
$25$			3.97293i			0.794586i
$26$	3.36387	+	1.29784i	0.659709	+	0.254526i
$27$	−2.18472	−	4.71455i	−0.420450	−	0.907316i
$28$	−0.965926	−	0.258819i	−0.182543	−	0.0489122i
$29$	−6.26395	+	3.61650i	−1.16319	+	0.671566i	−0.952066	−	0.305894i	$-0.901045\pi$
$29$	−6.26395	+	3.61650i	−1.16319	+	0.671566i	−0.211121	+	0.977460i	$0.567711\pi$
$30$	−5.13415	+	0.747863i	−0.937363	+	0.136540i
$31$	−6.29751	+	6.29751i	−1.13107	+	1.13107i	−0.141065	+	0.990000i	$0.545053\pi$
$31$	−6.29751	+	6.29751i	−1.13107	+	1.13107i	−0.990000	+	0.141065i	$0.954947\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.11500	+	0.831469i	0.194097	+	0.144740i
$34$	−5.46439	−	5.46439i	−0.937136	−	0.937136i
$35$	−2.59417	−	1.49774i	−0.438494	−	0.253165i
$36$	−0.855827	−	2.87534i	−0.142638	−	0.479223i
$37$	−2.24532	+	8.37964i	−0.369128	+	1.37760i	0.492610	+	0.870250i	$0.336043\pi$
$37$	−2.24532	+	8.37964i	−0.369128	+	1.37760i	−0.861738	+	0.507354i	$0.830624\pi$
$38$	1.20254			0.195077
$39$	−2.91352	+	5.52371i	−0.466537	+	0.884502i
$40$	−2.99549			−0.473628
$41$	0.512930	−	1.91428i	0.0801062	−	0.298960i	−0.914236	−	0.405181i	$-0.867208\pi$
$41$	0.512930	−	1.91428i	0.0801062	−	0.298960i	0.994343	+	0.106221i	$0.0338751\pi$
$42$	0.640767	−	1.60917i	0.0988724	−	0.248300i
$43$	6.83180	+	3.94434i	1.04184	+	0.601506i	0.920354	−	0.391087i	$-0.127901\pi$
$43$	6.83180	+	3.94434i	1.04184	+	0.601506i	0.121486	+	0.992593i	$0.461234\pi$
$44$	0.567828	+	0.567828i	0.0856032	+	0.0856032i
$45$	−0.247050	−	8.98306i	−0.0368280	−	1.33912i
$46$	−1.47419	+	0.395008i	−0.217357	+	0.0582407i
$47$	0.633171	−	0.633171i	0.0923575	−	0.0923575i	−0.659419	−	0.751776i	$-0.729197\pi$
$47$	0.633171	−	0.633171i	0.0923575	−	0.0923575i	0.751776	+	0.659419i	$0.229197\pi$
$48$	−0.249663	−	1.71396i	−0.0360358	−	0.247389i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	−3.83756	−	1.02827i	−0.542713	−	0.145419i
$51$	10.5060	−	8.29347i	1.47113	−	1.16132i
$52$	−2.12425	+	2.91334i	−0.294580	+	0.404008i
$53$			6.60837i			0.907729i	0.891071	+	0.453865i	$0.149955\pi$
$53$			6.60837i			0.907729i	−0.891071	+	0.453865i	$0.850045\pi$
$54$	5.11935	−	0.890064i	0.696656	−	0.121122i
$55$	1.20273	+	2.08319i	0.162176	+	0.280898i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−0.243454	+	2.06858i	−0.0322462	+	0.273990i
$58$	−1.87204	−	6.98653i	−0.245810	−	0.917377i
$59$	−2.31846	−	8.65262i	−0.301838	−	1.12648i	−0.935633	−	0.352974i	$-0.885170\pi$
$59$	−2.31846	−	8.65262i	−0.301838	−	1.12648i	0.633795	−	0.773501i	$-0.281496\pi$
$60$	0.606436	−	5.15277i	0.0782905	−	0.665220i
$61$	0.00670528	−	0.0116139i	0.000858524	−	0.00148701i	−0.865596	−	0.500743i	$-0.833060\pi$
$61$	0.00670528	−	0.0116139i	0.000858524	−	0.00148701i	0.866454	+	0.499256i	$0.166393\pi$
$62$	−4.45301	−	7.71284i	−0.565533	−	0.979532i
$63$	2.63833	+	1.42801i	0.332398	+	0.179912i
$64$		−	1.00000i		−	0.125000i
$65$	−8.40501	+	6.78262i	−1.04251	+	0.841280i
$66$	−1.09172	+	0.861808i	−0.134382	+	0.106081i
$67$	−10.3878	−	2.78339i	−1.26907	−	0.340045i	−0.439393	−	0.898295i	$-0.644806\pi$
$67$	−10.3878	−	2.78339i	−1.26907	−	0.340045i	−0.829673	+	0.558250i	$0.811473\pi$
$68$	6.69249	−	3.86391i	0.811584	−	0.468568i
$69$	−0.381035	−	2.61584i	−0.0458712	−	0.314910i
$70$	2.11813	−	2.11813i	0.253165	−	0.253165i
$71$	13.8552	−	3.71249i	1.64431	−	0.440592i	0.686300	−	0.727319i	$-0.259234\pi$
$71$	13.8552	−	3.71249i	1.64431	−	0.440592i	0.958012	+	0.286727i	$0.0925672\pi$
$72$	2.99887	−	0.0824740i	0.353420	−	0.00971966i
$73$	5.65127	+	5.65127i	0.661432	+	0.661432i	0.955717	−	0.294286i	$-0.0950818\pi$
$73$	5.65127	+	5.65127i	0.661432	+	0.661432i	−0.294286	+	0.955717i	$0.595082\pi$
$74$	−7.51298	−	4.33762i	−0.873366	−	0.504238i
$75$	2.54572	−	6.39311i	0.293955	−	0.738213i
$76$	−0.311240	+	1.16156i	−0.0357017	+	0.133240i
$77$	−0.803029			−0.0915137
$78$	−4.58142	−	4.24389i	−0.518744	−	0.480526i
$79$	−5.16613			−0.581235			−0.290617	−	0.956839i	$-0.593861\pi$
$79$	−5.16613			−0.581235			−0.290617	+	0.956839i	$0.593861\pi$
$80$	0.775289	−	2.89342i	0.0866799	−	0.323494i
$81$	0.494657	+	8.98640i	0.0549619	+	0.998488i
$82$	1.71630	+	0.990904i	0.189533	+	0.109427i
$83$	−3.82533	−	3.82533i	−0.419885	−	0.419885i	0.465279	−	0.885164i	$-0.345954\pi$
$83$	−3.82533	−	3.82533i	−0.419885	−	0.419885i	−0.885164	+	0.465279i	$0.845954\pi$
$84$	1.38849	+	1.03542i	0.151497	+	0.112973i
$85$	22.3598	−	5.99129i	2.42526	−	0.649847i
$86$	−5.57814	+	5.57814i	−0.601506	+	0.601506i
$87$	12.3971	−	1.80581i	1.32911	−	0.193603i
$88$	−0.695444	+	0.401515i	−0.0741346	+	0.0428016i
$89$	−6.45205	−	1.72882i	−0.683916	−	0.183255i	−0.0999008	−	0.994997i	$-0.531853\pi$
$89$	−6.45205	−	1.72882i	−0.683916	−	0.183255i	−0.584015	+	0.811743i	$0.698519\pi$
$90$	8.74091	+	2.08636i	0.921373	+	0.219921i
$91$	−0.557977	−	3.56211i	−0.0584919	−	0.373411i
$92$		−	1.52619i		−	0.159117i
$93$	14.1690	−	6.09851i	1.46925	−	0.632386i
$94$	0.447720	+	0.775473i	0.0461788	+	0.0799840i
$95$	−1.80109	+	3.11958i	−0.184788	+	0.320063i
$96$	1.72018	+	0.202450i	0.175565	+	0.0206625i
$97$	3.08877	+	11.5275i	0.313618	+	1.17044i	0.925270	+	0.379310i	$0.123839\pi$
$97$	3.08877	+	11.5275i	0.313618	+	1.17044i	−0.611652	+	0.791127i	$0.709495\pi$
$98$	0.258819	+	0.965926i	0.0261447	+	0.0975732i
$99$	−1.26144	−	2.05243i	−0.126780	−	0.206277i
$100$	1.98647	−	3.44066i	0.198647	−	0.344066i
$101$	3.32341	+	5.75632i	0.330692	+	0.572775i	0.982648	−	0.185482i	$-0.0593846\pi$
$101$	3.32341	+	5.75632i	0.330692	+	0.572775i	−0.651956	+	0.758257i	$0.726051\pi$
$102$	5.29172	+	12.2945i	0.523959	+	1.21734i
$103$			9.52991i			0.939010i	0.882930	+	0.469505i	$0.155568\pi$
$103$			9.52991i			0.939010i	−0.882930	+	0.469505i	$0.844432\pi$
$104$	−2.26428	−	2.80589i	−0.222031	−	0.275140i
$105$	3.21474	+	4.07237i	0.313727	+	0.397423i
$106$	−6.38319	−	1.71037i	−0.619991	−	0.166126i
$107$	−10.8185	+	6.24605i	−1.04586	+	0.603828i	−0.921488	−	0.388407i	$-0.873025\pi$
$107$	−10.8185	+	6.24605i	−1.04586	+	0.603828i	−0.124373	+	0.992236i	$0.539692\pi$
$108$	−0.465250	+	5.17528i	−0.0447687	+	0.497992i
$109$	−4.01576	+	4.01576i	−0.384640	+	0.384640i	−0.872771	−	0.488131i	$-0.837679\pi$
$109$	−4.01576	+	4.01576i	−0.384640	+	0.384640i	0.488131	+	0.872771i	$0.337679\pi$
$110$	−2.32350	+	0.622580i	−0.221537	+	0.0593606i
$111$	8.98248	−	12.0455i	0.852579	−	1.14331i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−9.09539	−	5.25123i	−0.855623	−	0.493994i	0.00692137	−	0.999976i	$-0.497797\pi$
$113$	−9.09539	−	5.25123i	−0.855623	−	0.493994i	−0.862544	+	0.505982i	$0.831130\pi$
$114$	−1.93508	−	0.770546i	−0.181237	−	0.0721683i
$115$	1.18324	−	4.41591i	0.110338	−	0.411786i
$116$	7.23299			0.671566
$117$	8.22775	−	7.02169i	0.760656	−	0.649155i
$118$	8.95785			0.824637
$119$	−2.00011	+	7.46450i	−0.183350	+	0.684270i
$120$	4.82024	+	1.91941i	0.440025	+	0.175217i
$121$	−8.96782	−	5.17757i	−0.815256	−	0.470688i
$122$	0.00948270	+	0.00948270i	0.000858524	+	0.000858524i
$123$	−2.05200	+	2.75173i	−0.185022	+	0.248115i
$124$	8.60255	−	2.30505i	0.772532	−	0.206999i
$125$	−2.17546	+	2.17546i	−0.194579	+	0.194579i
$126$	−2.06220	+	2.17884i	−0.183715	+	0.194106i
$127$	2.77175	−	1.60027i	0.245953	−	0.142001i	−0.371957	−	0.928250i	$-0.621313\pi$
$127$	2.77175	−	1.60027i	0.245953	−	0.142001i	0.617910	+	0.786249i	$0.287980\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−8.46610	−	10.7247i	−0.745399	−	0.944257i
$130$	−4.37613	−	9.87409i	−0.383812	−	0.866015i
$131$		−	22.0056i		−	1.92264i	−0.275432	−	0.961320i	$-0.588821\pi$
$131$		−	22.0056i		−	1.92264i	0.275432	−	0.961320i	$-0.411179\pi$
$132$	−0.549884	−	1.27757i	−0.0478613	−	0.111199i
$133$	−0.601269	−	1.04143i	−0.0521366	−	0.0903033i
$134$	5.37710	−	9.31340i	0.464510	−	0.804556i
$135$	−5.35850	+	14.6135i	−0.461186	+	1.25773i
$136$	2.00011	+	7.46450i	0.171508	+	0.640076i
$137$	1.52102	+	5.67651i	0.129949	+	0.484977i	0.999968	−	0.00804199i	$-0.00255987\pi$
$137$	1.52102	+	5.67651i	0.129949	+	0.484977i	−0.870018	+	0.493019i	$0.835893\pi$
$138$	2.62532	+	0.308978i	0.223482	+	0.0263019i
$139$	7.08655	−	12.2743i	0.601074	−	1.04109i	−0.391585	−	0.920142i	$-0.628073\pi$
$139$	7.08655	−	12.2743i	0.601074	−	1.04109i	0.992659	−	0.120948i	$-0.0385935\pi$
$140$	1.49774	+	2.59417i	0.126582	+	0.219247i
$141$	−1.42459	+	0.613163i	−0.119972	+	0.0516377i
$142$			14.3440i			1.20372i
$143$	−1.04220	+	2.70129i	−0.0871531	+	0.225893i
$144$	−0.696500	+	2.91803i	−0.0580417	+	0.243169i
$145$	20.9281	+	5.60765i	1.73798	+	0.465690i
$146$	−6.92137	+	3.99605i	−0.572817	+	0.330716i
$147$	−1.71396	+	0.249663i	−0.141365	+	0.0205919i
$148$	6.13432	−	6.13432i	0.504238	−	0.504238i
$149$	15.2232	−	4.07904i	1.24713	−	0.334168i	0.425905	−	0.904768i	$-0.359956\pi$
$149$	15.2232	−	4.07904i	1.24713	−	0.334168i	0.821228	+	0.570600i	$0.193289\pi$
$150$	5.51639	+	4.11364i	0.450411	+	0.335877i
$151$	−5.36253	−	5.36253i	−0.436397	−	0.436397i	0.454401	−	0.890797i	$-0.349853\pi$
$151$	−5.36253	−	5.36253i	−0.436397	−	0.436397i	−0.890797	+	0.454401i	$0.849853\pi$
$152$	−1.04143	−	0.601269i	−0.0844710	−	0.0487694i
$153$	−22.2201	+	6.61368i	−1.79639	+	0.534684i
$154$	0.207839	−	0.775667i	0.0167482	−	0.0625050i
$155$	26.6778			2.14282
$156$	5.28504	−	3.32691i	0.423142	−	0.266366i
$157$	−20.8298			−1.66240			−0.831199	−	0.555975i	$-0.812345\pi$
$157$	−20.8298			−1.66240			−0.831199	+	0.555975i	$0.812345\pi$
$158$	1.33709	−	4.99010i	0.106373	−	0.396991i
$159$	4.23442	−	10.6340i	0.335811	−	0.843329i
$160$	2.59417	+	1.49774i	0.205087	+	0.118407i
$161$	1.07918	+	1.07918i	0.0850514	+	0.0850514i
$162$	−8.80822	−	1.84805i	−0.692039	−	0.145196i
$163$	8.74036	−	2.34197i	0.684597	−	0.183437i	0.100276	−	0.994960i	$-0.468027\pi$
$163$	8.74036	−	2.34197i	0.684597	−	0.183437i	0.584321	+	0.811522i	$0.301361\pi$
$164$	−1.40135	+	1.40135i	−0.109427	+	0.109427i
$165$	−0.600556	−	4.12287i	−0.0467532	−	0.320965i
$166$	4.68506	−	2.70492i	0.363631	−	0.209942i
$167$	−5.43009	−	1.45499i	−0.420193	−	0.112590i	0.0425261	−	0.999095i	$-0.486459\pi$
$167$	−5.43009	−	1.45499i	−0.420193	−	0.112590i	−0.462719	+	0.886505i	$0.653126\pi$
$168$	−1.35950	+	1.07320i	−0.104888	+	0.0827989i
$169$	−12.7067	−	2.74607i	−0.977435	−	0.211237i
$170$			23.1486i			1.77541i
$171$	1.71723	−	3.17269i	0.131320	−	0.242622i
$172$	−3.94434	−	6.83180i	−0.300753	−	0.520920i
$173$	−4.96913	+	8.60679i	−0.377796	+	0.654362i	−0.990741	−	0.135763i	$-0.956651\pi$
$173$	−4.96913	+	8.60679i	−0.377796	+	0.654362i	0.612945	+	0.790125i	$0.289985\pi$
$174$	−1.46432	+	12.4420i	−0.111010	+	0.943228i
$175$	1.02827	+	3.83756i	0.0777299	+	0.290092i
$176$	−0.207839	−	0.775667i	−0.0156665	−	0.0584681i
$177$	−1.81352	+	15.4091i	−0.136312	+	1.15822i
$178$	3.33983	−	5.78475i	0.250331	−	0.433585i
$179$	−2.41334	−	4.18002i	−0.180381	−	0.312429i	0.761629	−	0.648013i	$-0.224400\pi$
$179$	−2.41334	−	4.18002i	−0.180381	−	0.312429i	−0.942010	+	0.335584i	$0.891066\pi$
$180$	−4.27758	+	7.90308i	−0.318832	+	0.589061i
$181$			23.6267i			1.75616i	0.478512	+	0.878081i	$0.341176\pi$
$181$			23.6267i			1.75616i	−0.478512	+	0.878081i	$0.658824\pi$
$182$	3.58515	+	0.382979i	0.265749	+	0.0283883i
$183$	−0.0182317	+	0.0143922i	−0.00134773	+	0.00106390i
$184$	1.47419	+	0.395008i	0.108679	+	0.0291204i
$185$	22.5050	−	12.9933i	1.65460	−	0.955285i
$186$	2.22351	+	15.2646i	0.163035	+	1.11925i
$187$	4.38807	−	4.38807i	0.320887	−	0.320887i
$188$	−0.864928	+	0.231757i	−0.0630814	+	0.0169026i
$189$	−3.33050	−	3.98846i	−0.242258	−	0.290118i
$190$	−2.54713	−	2.54713i	−0.184788	−	0.184788i
$191$	−9.55622	−	5.51729i	−0.691464	−	0.399217i	0.112696	−	0.993629i	$-0.464051\pi$
$191$	−9.55622	−	5.51729i	−0.691464	−	0.399217i	−0.804160	+	0.594413i	$0.797385\pi$
$192$	−0.640767	+	1.60917i	−0.0462433	+	0.116132i
$193$	5.43966	−	20.3011i	0.391555	−	1.46130i	−0.436014	−	0.899940i	$-0.643610\pi$
$193$	5.43966	−	20.3011i	0.391555	−	1.46130i	0.827569	−	0.561364i	$-0.189723\pi$
$194$	−11.9341			−0.856819
$195$	17.8711	−	5.52871i	1.27978	−	0.395919i
$196$	−1.00000			−0.0714286
$197$	1.49755	−	5.58895i	0.106696	−	0.398196i	−0.891836	−	0.452359i	$-0.850583\pi$
$197$	1.49755	−	5.58895i	0.106696	−	0.398196i	0.998532	+	0.0541634i	$0.0172492\pi$
$198$	2.30898	−	0.687255i	0.164092	−	0.0488411i
$199$	−8.18349	−	4.72474i	−0.580113	−	0.334928i	0.181066	−	0.983471i	$-0.442045\pi$
$199$	−8.18349	−	4.72474i	−0.580113	−	0.334928i	−0.761178	+	0.648543i	$0.775379\pi$
$200$	2.80929	+	2.80929i	0.198647	+	0.198647i
$201$	14.9321	+	11.1351i	1.05323	+	0.785407i
$202$	−6.42034	+	1.72032i	−0.451733	+	0.121042i
$203$	−5.11450	+	5.11450i	−0.358967	+	0.358967i
$204$	−13.2452	+	1.92935i	−0.927349	+	0.135082i
$205$	−5.14114	+	2.96824i	−0.359073	+	0.207311i
$206$	−9.20519	−	2.46652i	−0.641356	−	0.171851i
$207$	−1.06299	+	4.45347i	−0.0738832	+	0.309538i
$208$	3.29632	−	1.46091i	0.228559	−	0.101296i
$209$			0.965673i			0.0667970i
$210$	−4.76565	+	2.05120i	−0.328861	+	0.141546i
$211$	−0.571022	−	0.989040i	−0.0393108	−	0.0680883i	0.845701	−	0.533658i	$-0.179183\pi$
$211$	−0.571022	−	0.989040i	−0.0393108	−	0.0680883i	−0.885011	+	0.465569i	$0.845850\pi$
$212$	3.30418	−	5.72301i	0.226932	−	0.393058i
$213$	−24.6742	−	2.90394i	−1.69065	−	0.198974i
$214$	−3.23319	−	12.0664i	−0.221016	−	0.824845i
$215$	−6.11601	−	22.8252i	−0.417108	−	1.55667i
$216$	−4.87852	−	1.78886i	−0.331941	−	0.121716i
$217$	−4.45301	+	7.71284i	−0.302290	+	0.523582i
$218$	−2.83957	−	4.91828i	−0.192320	−	0.333108i
$219$	−5.47270	−	12.7150i	−0.369811	−	0.859199i
$220$		−	2.40546i		−	0.162176i
$221$	22.5138	+	16.4158i	1.51444	+	1.10425i
$222$	9.31023	+	11.7940i	0.624862	+	0.791563i
$223$	−18.9668	−	5.08213i	−1.27011	−	0.340325i	−0.440037	−	0.897980i	$-0.645035\pi$
$223$	−18.9668	−	5.08213i	−1.27011	−	0.340325i	−0.830073	+	0.557655i	$0.811701\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	−8.19298	+	8.65637i	−0.546199	+	0.577091i
$226$	7.42636	−	7.42636i	0.493994	−	0.493994i
$227$	18.5147	−	4.96100i	1.22886	−	0.329273i	0.414727	−	0.909946i	$-0.363877\pi$
$227$	18.5147	−	4.96100i	1.22886	−	0.329273i	0.814137	+	0.580672i	$0.197210\pi$
$228$	1.24513	−	1.66972i	0.0824606	−	0.110580i
$229$	9.36553	+	9.36553i	0.618892	+	0.618892i	0.945247	−	0.326355i	$-0.105821\pi$
$229$	9.36553	+	9.36553i	0.618892	+	0.618892i	−0.326355	+	0.945247i	$0.605821\pi$
$230$	3.95920	+	2.28584i	0.261062	+	0.150724i
$231$	1.29221	+	0.514554i	0.0850211	+	0.0338552i
$232$	−1.87204	+	6.98653i	−0.122905	+	0.458688i
$233$	−18.4253			−1.20708			−0.603542	−	0.797331i	$-0.706244\pi$
$233$	−18.4253			−1.20708			−0.603542	+	0.797331i	$0.706244\pi$
$234$	4.65293	+	9.76475i	0.304171	+	0.638341i
$235$	−2.68228			−0.174972
$236$	−2.31846	+	8.65262i	−0.150919	+	0.563238i
$237$	8.31316	+	3.31028i	0.539998	+	0.215026i
$238$	−6.69249	−	3.86391i	−0.433810	−	0.250460i
$239$	4.47115	+	4.47115i	0.289215	+	0.289215i	0.836770	−	0.547555i	$-0.184441\pi$
$239$	4.47115	+	4.47115i	0.289215	+	0.289215i	−0.547555	+	0.836770i	$0.684441\pi$
$240$	−3.10157	+	4.15921i	−0.200206	+	0.268476i
$241$	−5.88560	+	1.57704i	−0.379125	+	0.101586i	−0.443349	−	0.896349i	$-0.646210\pi$
$241$	−5.88560	+	1.57704i	−0.379125	+	0.101586i	0.0642235	+	0.997936i	$0.479543\pi$
$242$	7.32219	−	7.32219i	0.470688	−	0.470688i
$243$	4.96220	−	14.7776i	0.318325	−	0.947982i
$244$	−0.0116139	+	0.00670528i	−0.000743503	+	0.000429262i
$245$	−2.89342	−	0.775289i	−0.184854	−	0.0495314i
$246$	−2.12687	−	2.69428i	−0.135604	−	0.171781i
$247$	−4.28358	+	0.670989i	−0.272558	+	0.0426940i
$248$			8.90602i			0.565533i
$249$	3.70446	+	8.60675i	0.234760	+	0.545430i
$250$	−1.53828	−	2.66439i	−0.0972897	−	0.168511i
$251$	−4.16999	+	7.22264i	−0.263208	+	0.455889i	−0.967092	−	0.254425i	$-0.918114\pi$
$251$	−4.16999	+	7.22264i	−0.263208	+	0.455889i	0.703885	+	0.710314i	$0.251447\pi$
$252$	−1.57086	−	2.55586i	−0.0989547	−	0.161004i
$253$	−0.317203	−	1.18382i	−0.0199424	−	0.0744260i
$254$	0.828360	+	3.09148i	0.0519760	+	0.193977i
$255$	−39.8197	−	4.68643i	−2.49361	−	0.293475i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.573552	+	0.993421i	0.0357772	+	0.0619679i	0.883360	−	0.468696i	$-0.155276\pi$
$257$	0.573552	+	0.993421i	0.0357772	+	0.0619679i	−0.847582	+	0.530664i	$0.821943\pi$
$258$	12.5504	−	5.40187i	0.781357	−	0.336306i
$259$			8.67524i			0.539053i
$260$	10.6703	−	1.67141i	0.661742	−	0.103657i
$261$	−21.1061	−	5.03778i	−1.30643	−	0.311831i
$262$	21.2558	+	5.69548i	1.31319	+	0.351868i
$263$	−5.51609	+	3.18471i	−0.340137	+	0.196378i	−0.660332	−	0.750973i	$-0.729585\pi$
$263$	−5.51609	+	3.18471i	−0.340137	+	0.196378i	0.320196	+	0.947351i	$0.396251\pi$
$264$	1.37636	−	0.200487i	0.0847093	−	0.0123391i
$265$	13.9974	−	13.9974i	0.859852	−	0.859852i
$266$	1.16156	−	0.311240i	0.0712200	−	0.0190833i
$267$	9.27466	+	6.91622i	0.567600	+	0.423266i
$268$	7.60436	+	7.60436i	0.464510	+	0.464510i
$269$	−7.34111	−	4.23839i	−0.447595	−	0.258419i	0.259219	−	0.965819i	$-0.416535\pi$
$269$	−7.34111	−	4.23839i	−0.447595	−	0.258419i	−0.706814	+	0.707399i	$0.749868\pi$
$270$	−12.7287	−	8.95818i	−0.774645	−	0.545177i
$271$	3.14615	−	11.7416i	0.191115	−	0.713250i	−0.802124	−	0.597158i	$-0.796297\pi$
$271$	3.14615	−	11.7416i	0.191115	−	0.713250i	0.993238	−	0.116092i	$-0.0370368\pi$
$272$	−7.72782			−0.468568
$273$	−1.38461	+	6.08957i	−0.0838001	+	0.368558i
$274$	−5.87676			−0.355028
$275$	0.825731	−	3.08167i	0.0497935	−	0.185832i
$276$	−0.977934	+	2.45590i	−0.0588647	+	0.147828i
$277$	−9.04489	−	5.22207i	−0.543455	−	0.313764i	0.203023	−	0.979174i	$-0.434923\pi$
$277$	−9.04489	−	5.22207i	−0.543455	−	0.313764i	−0.746478	+	0.665410i	$0.768257\pi$
$278$	10.0219	+	10.0219i	0.601074	+	0.601074i
$279$	−26.7080	+	0.734515i	−1.59896	+	0.0439743i
$280$	−2.89342	+	0.775289i	−0.172915	+	0.0463324i
$281$	−11.2938	+	11.2938i	−0.673733	+	0.673733i	−0.958575	−	0.284842i	$-0.908059\pi$
$281$	−11.2938	+	11.2938i	−0.673733	+	0.673733i	0.284842	+	0.958575i	$0.408059\pi$
$282$	−0.223558	−	1.53475i	−0.0133127	−	0.0913930i
$283$	−22.6706	+	13.0889i	−1.34763	+	0.778055i	−0.987913	−	0.155007i	$-0.950460\pi$
$283$	−22.6706	+	13.0889i	−1.34763	+	0.778055i	−0.359717	+	0.933062i	$0.617127\pi$
$284$	−13.8552	−	3.71249i	−0.822156	−	0.220296i
$285$	4.89718	−	3.86585i	0.290084	−	0.228993i
$286$	−2.33950	−	1.70583i	−0.138338	−	0.100868i
$287$		−	1.98181i		−	0.116982i
$288$	−2.63833	−	1.42801i	−0.155465	−	0.0841462i
$289$	−21.3596	−	36.9959i	−1.25645	−	2.17623i
$290$	−10.8332	+	18.7636i	−0.636145	+	1.10184i
$291$	2.41606	−	20.5288i	0.141632	−	1.20342i
$292$	−2.06851	−	7.71978i	−0.121050	−	0.451766i
$293$	−3.61206	−	13.4804i	−0.211019	−	0.787533i	−0.987530	−	0.157430i	$-0.949679\pi$
$293$	−3.61206	−	13.4804i	−0.211019	−	0.787533i	0.776511	−	0.630103i	$-0.216988\pi$
$294$	0.202450	−	1.72018i	0.0118071	−	0.100323i
$295$	−13.4166	+	23.2382i	−0.781142	+	1.35298i
$296$	4.33762	+	7.51298i	0.252119	+	0.436683i
$297$	0.714748	+	4.11099i	0.0414739	+	0.238544i
$298$			15.7602i			0.912965i
$299$	5.03083	−	2.22963i	0.290940	−	0.128943i
$300$	−5.40121	+	4.26373i	−0.311839	+	0.246167i
$301$	7.61988	+	2.04174i	0.439203	+	0.117684i
$302$	6.56774	−	3.79188i	0.377931	−	0.218198i
$303$	−1.65947	−	11.3924i	−0.0953340	−	0.654477i
$304$	0.850323	−	0.850323i	0.0487694	−	0.0487694i
$305$	−0.0388024	+	0.0103971i	−0.00222182	+	0.000595334i
$306$	−0.637345	−	23.1747i	−0.0364346	−	1.32481i
$307$	9.05977	+	9.05977i	0.517068	+	0.517068i	0.916683	−	0.399615i	$-0.130856\pi$
$307$	9.05977	+	9.05977i	0.517068	+	0.517068i	−0.399615	+	0.916683i	$0.630856\pi$
$308$	0.695444	+	0.401515i	0.0396266	+	0.0228784i
$309$	6.10645	−	15.3352i	0.347384	−	0.872390i
$310$	−6.90474	+	25.7688i	−0.392163	+	1.46357i
$311$	12.2345			0.693756			0.346878	−	0.937910i	$-0.387242\pi$
$311$	12.2345			0.693756			0.346878	+	0.937910i	$0.387242\pi$
$312$	1.84568	+	5.96603i	0.104491	+	0.337760i
$313$	−14.4095			−0.814473			−0.407236	−	0.913323i	$-0.633508\pi$
$313$	−14.4095			−0.814473			−0.407236	+	0.913323i	$0.633508\pi$
$314$	5.39115	−	20.1200i	0.304240	−	1.13544i
$315$	−2.56362	−	8.61303i	−0.144444	−	0.485289i
$316$	4.47400	+	2.58306i	0.251682	+	0.145309i
$317$	12.7428	+	12.7428i	0.715710	+	0.715710i	0.967724	−	0.252014i	$-0.0810929\pi$
$317$	12.7428	+	12.7428i	0.715710	+	0.715710i	−0.252014	+	0.967724i	$0.581093\pi$
$318$	9.17568	+	6.84241i	0.514546	+	0.383703i
$319$	5.61039	−	1.50330i	0.314122	−	0.0841686i
$320$	−2.11813	+	2.11813i	−0.118407	+	0.118407i
$321$	21.4110	−	3.11882i	1.19504	−	0.174075i
$322$	−1.32172	+	0.763097i	−0.0736567	+	0.0425257i
$323$	8.97635	+	2.40521i	0.499457	+	0.133829i
$324$	4.06481	−	8.02978i	0.225823	−	0.446099i
$325$	14.2436	+	1.52155i	0.790091	+	0.0844003i
$326$			9.04868i			0.501160i
$327$	9.03519	−	3.88886i	0.499647	−	0.215055i
$328$	−0.990904	−	1.71630i	−0.0547135	−	0.0947666i
$329$	0.447720	−	0.775473i	0.0246836	−	0.0427532i
$330$	4.13783	+	0.486986i	0.227780	+	0.0268077i
$331$	−7.36239	−	27.4768i	−0.404674	−	1.51026i	−0.804657	−	0.593740i	$-0.797651\pi$
$331$	−7.36239	−	27.4768i	−0.404674	−	1.51026i	0.399983	−	0.916523i	$-0.369016\pi$
$332$	1.40017	+	5.22550i	0.0768443	+	0.286787i
$333$	−22.1727	+	13.6276i	−1.21506	+	0.746786i
$334$	2.81082	−	4.86848i	0.153801	−	0.266392i
$335$	16.1070	+	27.8982i	0.880020	+	1.52424i
$336$	−0.684763	−	1.59094i	−0.0373569	−	0.0867931i
$337$			23.3433i			1.27159i	0.771858	+	0.635795i	$0.219328\pi$
$337$			23.3433i			1.27159i	−0.771858	+	0.635795i	$0.780672\pi$
$338$	5.94123	−	11.5629i	0.323160	−	0.628942i
$339$	11.2712	+	14.2781i	0.612167	+	0.775481i
$340$	−22.3598	−	5.99129i	−1.21263	−	0.324923i
$341$	6.19364	−	3.57590i	0.335404	−	0.193646i
$342$	2.62013	+	2.47987i	0.141681	+	0.134096i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	7.61988	−	2.04174i	0.410837	−	0.110083i
$345$	−4.73360	+	6.34776i	−0.254848	+	0.341752i
$346$	−7.02741	−	7.02741i	−0.377796	−	0.377796i
$347$	10.1912	+	5.88391i	0.547094	+	0.315865i	0.747949	−	0.663756i	$-0.231039\pi$
$347$	10.1912	+	5.88391i	0.547094	+	0.315865i	−0.200855	+	0.979621i	$0.564372\pi$
$348$	−11.6391	−	4.63466i	−0.623921	−	0.248444i
$349$	1.29958	−	4.85008i	0.0695647	−	0.259619i	−0.922381	−	0.386281i	$-0.873760\pi$
$349$	1.29958	−	4.85008i	0.0695647	−	0.259619i	0.991946	+	0.126662i	$0.0404263\pi$
$350$	−3.97293			−0.212362
$351$	−17.7391	+	6.02699i	−0.946843	+	0.321697i
$352$	0.803029			0.0428016
$353$	4.30376	−	16.0618i	0.229066	−	0.854885i	−0.751669	−	0.659541i	$-0.770751\pi$
$353$	4.30376	−	16.0618i	0.229066	−	0.854885i	0.980735	−	0.195345i	$-0.0625825\pi$
$354$	−14.4147	−	5.73989i	−0.766132	−	0.305072i
$355$	−37.2107	−	21.4836i	−1.97494	−	1.14023i
$356$	4.72323	+	4.72323i	0.250331	+	0.250331i
$357$	8.00151	−	10.7300i	0.423485	−	0.567893i
$358$	4.66221	−	1.24923i	0.246405	−	0.0660241i
$359$	−0.848325	+	0.848325i	−0.0447729	+	0.0447729i	−0.729139	−	0.684366i	$-0.760079\pi$
$359$	−0.848325	+	0.848325i	−0.0447729	+	0.0447729i	0.684366	+	0.729139i	$0.260079\pi$
$360$	−6.52667	−	6.17729i	−0.343986	−	0.325572i
$361$	15.2021	−	8.77695i	0.800112	−	0.461945i
$362$	−22.8217	−	6.11505i	−1.19948	−	0.321400i
$363$	11.1131	+	14.0779i	0.583287	+	0.738896i
$364$	−1.29784	+	3.36387i	−0.0680250	+	0.176315i
$365$		−	23.9402i		−	1.25309i
$366$	−0.00918305	−	0.0213355i	−0.000480006	−	0.00111522i
$367$	16.9129	+	29.2940i	0.882847	+	1.52914i	0.848161	+	0.529738i	$0.177710\pi$
$367$	16.9129	+	29.2940i	0.882847	+	1.52914i	0.0346860	+	0.999398i	$0.488957\pi$
$368$	−0.763097	+	1.32172i	−0.0397792	+	0.0688995i
$369$	5.06522	−	3.11314i	0.263685	−	0.162064i
$370$	6.72581	+	25.1011i	0.349658	+	1.30494i
$371$	1.71037	+	6.38319i	0.0887981	+	0.331399i
$372$	−15.3199	−	1.80302i	−0.794302	−	0.0934824i
$373$	0.325208	−	0.563277i	0.0168386	−	0.0291654i	−0.857483	−	0.514512i	$-0.827973\pi$
$373$	0.325208	−	0.563277i	0.0168386	−	0.0291654i	0.874322	+	0.485346i	$0.161307\pi$
$374$	3.10283	+	5.37427i	0.160444	+	0.277897i
$375$	4.89465	−	2.10672i	0.252758	−	0.108791i
$376$		−	0.895440i		−	0.0461788i
$377$	10.5667	+	23.8423i	0.544214	+	1.22794i
$378$	4.71455	−	2.18472i	0.242490	−	0.112370i
$379$	0.830428	+	0.222512i	0.0426562	+	0.0114297i	0.280084	−	0.959975i	$-0.409638\pi$
$379$	0.830428	+	0.222512i	0.0426562	+	0.0114297i	−0.237428	+	0.971405i	$0.576304\pi$
$380$	3.11958	−	1.80109i	0.160031	−	0.0923941i
$381$	−5.48560	+	0.799057i	−0.281036	+	0.0409369i
$382$	7.80262	−	7.80262i	0.399217	−	0.399217i
$383$	−11.8921	+	3.18647i	−0.607657	+	0.162821i	−0.549510	−	0.835487i	$-0.685186\pi$
$383$	−11.8921	+	3.18647i	−0.607657	+	0.162821i	−0.0581463	+	0.998308i	$0.518519\pi$
$384$	−1.38849	−	1.03542i	−0.0708563	−	0.0528384i
$385$	1.70092	+	1.70092i	0.0866869	+	0.0866869i
$386$	18.2015	+	10.5086i	0.926430	+	0.534874i
$387$	6.75135	+	22.6826i	0.343191	+	1.15302i
$388$	3.08877	−	11.5275i	0.156809	−	0.585218i
$389$	−13.6987			−0.694553			−0.347277	−	0.937763i	$-0.612893\pi$
$389$	−13.6987			−0.694553			−0.347277	+	0.937763i	$0.612893\pi$
$390$	0.714934	+	18.6931i	0.0362021	+	0.946564i
$391$	−11.7941			−0.596456
$392$	0.258819	−	0.965926i	0.0130723	−	0.0487866i
$393$	−14.1005	+	35.4107i	−0.711275	+	1.78624i
$394$	5.01091	+	2.89305i	0.252446	+	0.145750i
$395$	10.9425	+	10.9425i	0.550578	+	0.550578i
$396$	0.0662291	+	2.40818i	0.00332814	+	0.121015i
$397$	−21.8099	+	5.84393i	−1.09461	+	0.293299i	−0.760566	−	0.649261i	$-0.775078\pi$
$397$	−21.8099	+	5.84393i	−1.09461	+	0.293299i	−0.334039	+	0.942559i	$0.608412\pi$
$398$	6.68180	−	6.68180i	0.334928	−	0.334928i
$399$	0.300230	+	2.06111i	0.0150303	+	0.103184i
$400$	−3.44066	+	1.98647i	−0.172033	+	0.0993233i
$401$	−0.673815	−	0.180548i	−0.0336487	−	0.00901614i	0.241955	−	0.970287i	$-0.422211\pi$
$401$	−0.673815	−	0.180548i	−0.0336487	−	0.00901614i	−0.275604	+	0.961271i	$0.588878\pi$
$402$	−14.6204	+	11.5414i	−0.729197	+	0.575631i
$403$	20.1657	+	24.9893i	1.00453	+	1.24481i
$404$		−	6.64682i		−	0.330692i
$405$	17.9866	−	20.0821i	0.893761	−	0.997887i
$406$	−3.61650	−	6.26395i	−0.179484	−	0.310875i
$407$	3.48324	−	6.03314i	0.172658	−	0.299052i
$408$	1.56450	−	13.2932i	0.0774541	−	0.658113i
$409$	2.01720	+	7.52831i	0.0997443	+	0.372251i	0.997696	−	0.0678431i	$-0.0216117\pi$
$409$	2.01720	+	7.52831i	0.0997443	+	0.372251i	−0.897952	+	0.440094i	$0.854945\pi$
$410$	−1.53647	−	5.73420i	−0.0758810	−	0.283192i
$411$	1.18975	−	10.1091i	0.0586860	−	0.498644i
$412$	4.76495	−	8.25314i	0.234752	−	0.406603i
$413$	−4.47893	−	7.75773i	−0.220394	−	0.381733i
$414$	−4.02660	−	2.17942i	−0.197897	−	0.107112i
$415$			16.2051i			0.795477i
$416$	0.557977	+	3.56211i	0.0273571	+	0.174647i
$417$	−19.2684	+	15.2105i	−0.943577	+	0.744863i
$418$	−0.932769	−	0.249935i	−0.0456232	−	0.0122247i
$419$	−22.0212	+	12.7139i	−1.07581	+	0.621117i	−0.929762	−	0.368161i	$-0.879987\pi$
$419$	−22.0212	+	12.7139i	−1.07581	+	0.621117i	−0.146044	+	0.989278i	$0.546654\pi$
$420$	−0.747863	−	5.13415i	−0.0364920	−	0.250521i
$421$	22.1063	−	22.1063i	1.07740	−	1.07740i	0.0806540	−	0.996742i	$-0.474299\pi$
$421$	22.1063	−	22.1063i	1.07740	−	1.07740i	0.996742	−	0.0806540i	$-0.0257009\pi$
$422$	1.10313	−	0.295583i	0.0536996	−	0.0143888i
$423$	2.68530	−	0.0738505i	0.130564	−	0.00359073i
$424$	4.67282	+	4.67282i	0.226932	+	0.226932i
$425$	−26.5888	−	15.3511i	−1.28975	−	0.744635i
$426$	9.19114	−	23.0819i	0.445312	−	1.11832i
$427$	0.00347091	−	0.0129536i	0.000167969	−	0.000626869i
$428$	12.4921			0.603828
$429$	3.40797	−	3.67901i	0.164538	−	0.177625i
$430$	23.6304			1.13956
$431$	−0.276568	+	1.03217i	−0.0133218	+	0.0497177i	−0.972267	−	0.233874i	$-0.924860\pi$
$431$	−0.276568	+	1.03217i	−0.0133218	+	0.0497177i	0.958945	+	0.283592i	$0.0915262\pi$
$432$	2.99056	−	4.24930i	0.143883	−	0.204445i
$433$	29.1431	+	16.8258i	1.40053	+	0.808594i	0.994446	−	0.105244i	$-0.0335623\pi$
$433$	29.1431	+	16.8258i	1.40053	+	0.808594i	0.406080	+	0.913838i	$0.366896\pi$
$434$	−6.29751	−	6.29751i	−0.302290	−	0.302290i
$435$	−30.0835	−	22.4336i	−1.44240	−	1.07561i
$436$	5.48563	−	1.46987i	0.262714	−	0.0703940i
$437$	1.29776	−	1.29776i	0.0620801	−	0.0620801i
$438$	13.6982	−	1.99534i	0.654524	−	0.0953409i
$439$	11.8832	−	6.86077i	0.567154	−	0.327447i	−0.188858	−	0.982004i	$-0.560479\pi$
$439$	11.8832	−	6.86077i	0.567154	−	0.327447i	0.756012	+	0.654558i	$0.227145\pi$
$440$	2.32350	+	0.622580i	0.110768	+	0.0296803i
$441$	2.91803	+	0.696500i	0.138954	+	0.0331667i
$442$	−21.6834	+	17.4979i	−1.03138	+	0.832293i
$443$			24.4158i			1.16003i	0.814605	+	0.580016i	$0.196954\pi$
$443$			24.4158i			1.16003i	−0.814605	+	0.580016i	$0.803046\pi$
$444$	−13.8018	+	5.94048i	−0.655005	+	0.281923i
$445$	10.0044	+	17.3281i	0.474254	+	0.821433i
$446$	9.81793	−	17.0052i	0.464892	−	0.805217i
$447$	−27.1104	−	3.19065i	−1.28228	−	0.150913i
$448$	−0.258819	−	0.965926i	−0.0122281	−	0.0456357i
$449$	−10.6685	−	39.8154i	−0.503478	−	1.87901i	−0.476121	−	0.879380i	$-0.657958\pi$
$449$	−10.6685	−	39.8154i	−0.503478	−	1.87901i	−0.0273566	−	0.999626i	$-0.508709\pi$
$450$	−6.24091	−	10.1542i	−0.294199	−	0.478676i
$451$	−0.795725	+	1.37824i	−0.0374692	+	0.0648986i
$452$	5.25123	+	9.09539i	0.246997	+	0.427811i
$453$	5.19308	+	12.0653i	0.243992	+	0.566879i
$454$			19.1678i			0.899592i
$455$	−6.36315	+	8.72688i	−0.298309	+	0.409123i
$456$	1.29056	+	1.63485i	0.0604360	+	0.0765591i
$457$	22.5211	+	6.03451i	1.05349	+	0.282282i	0.743694	−	0.668520i	$-0.233072\pi$
$457$	22.5211	+	6.03451i	1.05349	+	0.282282i	0.309798	+	0.950802i	$0.399738\pi$
$458$	−11.4704	+	6.62243i	−0.535976	+	0.309446i
$459$	39.9937	+	3.59537i	1.86674	+	0.167817i
$460$	−3.23267	+	3.23267i	−0.150724	+	0.150724i
$461$	−10.7449	+	2.87910i	−0.500442	+	0.134093i	−0.500205	−	0.865907i	$-0.666742\pi$
$461$	−10.7449	+	2.87910i	−0.500442	+	0.134093i	−0.000236808		1.00000i	$0.500075\pi$
$462$	−0.831469	+	1.11500i	−0.0386835	+	0.0518745i
$463$	19.1983	+	19.1983i	0.892220	+	0.892220i	0.994732	−	0.102511i	$-0.0326878\pi$
$463$	19.1983	+	19.1983i	0.892220	+	0.892220i	−0.102511	+	0.994732i	$0.532688\pi$
$464$	−6.26395	−	3.61650i	−0.290797	−	0.167892i
$465$	−42.9291	−	17.0943i	−1.99079	−	0.792728i
$466$	4.76883	−	17.7975i	0.220912	−	0.824454i
$467$	39.0640			1.80767			0.903834	−	0.427884i	$-0.140741\pi$
$467$	39.0640			1.80767			0.903834	+	0.427884i	$0.140741\pi$
$468$	−10.6363	+	1.96708i	−0.491663	+	0.0909283i
$469$	−10.7542			−0.496582
$470$	0.694224	−	2.59088i	0.0320222	−	0.119508i
$471$	33.5186	+	13.3470i	1.54446	+	0.614999i
$472$	−7.75773	−	4.47893i	−0.357078	−	0.206159i
$473$	−4.47941	−	4.47941i	−0.205964	−	0.205964i
$474$	−5.34909	+	7.17314i	−0.245692	+	0.329473i
$475$	4.61481	−	1.23653i	0.211742	−	0.0567361i
$476$	5.46439	−	5.46439i	0.250460	−	0.250460i
$477$	−13.6278	+	14.3986i	−0.623973	+	0.659265i
$478$	−5.47602	+	3.16158i	−0.250467	+	0.144607i
$479$	−3.08029	−	0.825360i	−0.140742	−	0.0377117i	0.187760	−	0.982215i	$-0.439877\pi$
$479$	−3.08029	−	0.825360i	−0.140742	−	0.0377117i	−0.328502	+	0.944503i	$0.606544\pi$
$480$	−3.21474	−	4.07237i	−0.146732	−	0.185878i
$481$	29.1824	+	11.2590i	1.33060	+	0.513368i
$482$		−	6.09322i		−	0.277539i
$483$	−1.04508	−	2.42809i	−0.0475528	−	0.110482i
$484$	5.17757	+	8.96782i	0.235344	+	0.407628i
$485$	17.8742	−	30.9591i	0.811627	−	1.40578i
$486$	12.9897	+	8.61783i	0.589226	+	0.390913i
$487$	5.27083	+	19.6710i	0.238844	+	0.891379i	0.976378	+	0.216069i	$0.0693235\pi$
$487$	5.27083	+	19.6710i	0.238844	+	0.891379i	−0.737534	+	0.675310i	$0.764010\pi$
$488$	−0.00347091	−	0.0129536i	−0.000157121	−	0.000586383i
$489$	−15.5653	−	1.83190i	−0.703889	−	0.0828416i
$490$	1.49774	−	2.59417i	0.0676611	−	0.117192i
$491$	12.8308	+	22.2237i	0.579048	+	1.00294i	0.995589	+	0.0938234i	$0.0299089\pi$
$491$	12.8308	+	22.2237i	0.579048	+	1.00294i	−0.416541	+	0.909117i	$0.636758\pi$
$492$	3.15294	−	1.35707i	0.142146	−	0.0611814i
$493$		−	55.8953i		−	2.51740i
$494$	0.460546	−	4.31128i	0.0207210	−	0.193974i
$495$	−1.67540	+	7.01921i	−0.0753038	+	0.315490i
$496$	−8.60255	−	2.30505i	−0.386266	−	0.103500i
$497$	12.4222	−	7.17199i	0.557214	−	0.321708i
$498$	−9.27226	+	1.35064i	−0.415500	+	0.0605236i
$499$	−1.14406	+	1.14406i	−0.0512154	+	0.0512154i	−0.732251	−	0.681035i	$-0.761530\pi$
$499$	−1.14406	+	1.14406i	−0.0512154	+	0.0512154i	0.681035	+	0.732251i	$0.261530\pi$
$500$	2.97174	−	0.796275i	0.132900	−	0.0356105i
$501$	7.80561	+	5.82074i	0.348729	+	0.260051i
$502$	−5.89726	−	5.89726i	−0.263208	−	0.263208i
$503$	21.3294	+	12.3145i	0.951029	+	0.549077i	0.893401	−	0.449261i	$-0.148313\pi$
$503$	21.3294	+	12.3145i	0.951029	+	0.549077i	0.0576288	+	0.998338i	$0.481646\pi$
$504$	2.87534	−	0.855827i	0.128078	−	0.0381216i
$505$	5.15321	−	19.2320i	0.229315	−	0.855814i
$506$	1.22558			0.0544836
$507$	18.6875	+	12.5609i	0.829943	+	0.557849i
$508$	−3.20054			−0.142001
$509$	−10.2628	+	38.3011i	−0.454889	+	1.69767i	0.233527	+	0.972350i	$0.424973\pi$
$509$	−10.2628	+	38.3011i	−0.454889	+	1.69767i	−0.688415	+	0.725317i	$0.741693\pi$
$510$	14.8328	−	37.2499i	0.656809	−	1.64945i
$511$	6.92137	+	3.99605i	0.306183	+	0.176775i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.79627	+	4.00505i	−0.211761	+	0.176827i
$514$	−1.10802	+	0.296892i	−0.0488725	+	0.0130954i
$515$	20.1856	−	20.1856i	0.889482	−	0.889482i
$516$	1.96952	+	13.5209i	0.0867031	+	0.595225i
$517$	−0.622728	+	0.359532i	−0.0273875	+	0.0158122i
$518$	−8.37964	−	2.24532i	−0.368180	−	0.0986536i
$519$	13.5111	−	10.6657i	0.593072	−	0.468173i
$520$	−1.14721	+	10.7393i	−0.0503084	+	0.470948i
$521$		−	25.7694i		−	1.12898i	−0.825441	−	0.564489i	$-0.809073\pi$
$521$		−	25.7694i		−	1.12898i	0.825441	−	0.564489i	$-0.190927\pi$
$522$	10.3288	−	19.0830i	0.452078	−	0.835241i
$523$	−13.2941	−	23.0260i	−0.581309	−	1.00686i	−0.995325	−	0.0965865i	$-0.969208\pi$
$523$	−13.2941	−	23.0260i	−0.581309	−	1.00686i	0.414016	−	0.910270i	$-0.364126\pi$
$524$	−11.0028	+	19.0574i	−0.480660	+	0.832528i
$525$	0.804319	−	6.83415i	0.0351034	−	0.298267i
$526$	−1.64853	−	6.15240i	−0.0718793	−	0.268257i
$527$	−17.8130	−	66.4790i	−0.775946	−	2.89587i
$528$	−0.162573	+	1.38135i	−0.00707509	+	0.0601157i
$529$	10.3354	−	17.9014i	0.449364	−	0.778321i
$530$	9.89763	+	17.1432i	0.429926	+	0.744653i
$531$	12.7919	−	23.6338i	0.555121	−	1.02562i
$532$			1.20254i			0.0521366i
$533$	−6.66655	−	2.57206i	−0.288760	−	0.111408i
$534$	−9.08102	+	7.16858i	−0.392974	+	0.310215i
$535$	36.1448	+	9.68498i	1.56268	+	0.418718i
$536$	−9.31340	+	5.37710i	−0.402278	+	0.232255i
$537$	1.20504	+	8.27274i	0.0520015	+	0.356995i
$538$	5.99399	−	5.99399i	0.258419	−	0.258419i
$539$	−0.775667	+	0.207839i	−0.0334103	+	0.00895227i
$540$	11.9474	−	9.97645i	0.514133	−	0.429318i
$541$	−26.1615	−	26.1615i	−1.12477	−	1.12477i	−0.991015	−	0.133754i	$-0.957297\pi$
$541$	−26.1615	−	26.1615i	−1.12477	−	1.12477i	−0.133754	−	0.991015i	$-0.542703\pi$
$542$	10.5272	+	6.07789i	0.452183	+	0.261068i
$543$	15.1392	−	38.0194i	0.649686	−	1.63157i
$544$	2.00011	−	7.46450i	0.0857539	−	0.320038i
$545$	17.0118			0.728705
$546$	−5.52371	−	2.91352i	−0.236393	−	0.124687i
$547$	−33.7268			−1.44205			−0.721027	−	0.692907i	$-0.756330\pi$
$547$	−33.7268			−1.44205			−0.721027	+	0.692907i	$0.756330\pi$
$548$	1.52102	−	5.67651i	0.0649746	−	0.242489i
$549$	0.0385599	−	0.0114771i	0.00164570	−	0.000489832i
$550$	2.76295	+	1.59519i	0.117813	+	0.0680191i
$551$	6.15038	+	6.15038i	0.262015	+	0.262015i
$552$	−2.11911	−	1.58024i	−0.0901953	−	0.0672597i
$553$	−4.99010	+	1.33709i	−0.212201	+	0.0568590i
$554$	7.38512	−	7.38512i	0.313764	−	0.313764i
$555$	−44.5400	+	6.48789i	−1.89062	+	0.275396i
$556$	−12.2743	+	7.08655i	−0.520545	+	0.300537i
$557$	7.52615	+	2.01663i	0.318893	+	0.0854472i	0.414715	−	0.909951i	$-0.363881\pi$
$557$	7.52615	+	2.01663i	0.318893	+	0.0854472i	−0.0958218	+	0.995399i	$0.530548\pi$
$558$	6.20304	−	25.9880i	0.262596	−	1.10016i
$559$	16.7575	−	22.9825i	0.708767	−	0.972054i
$560$		−	2.99549i		−	0.126582i
$561$	−9.87287	+	4.24941i	−0.416833	+	0.179410i
$562$	−7.98594	−	13.8321i	−0.336867	−	0.583470i
$563$	6.11056	−	10.5838i	0.257530	−	0.446054i	−0.708050	−	0.706162i	$-0.750425\pi$
$563$	6.11056	−	10.5838i	0.257530	−	0.446054i	0.965579	+	0.260108i	$0.0837582\pi$
$564$	1.54032	+	0.181282i	0.0648590	+	0.00763333i
$565$	8.14243	+	30.3880i	0.342555	+	1.27843i
$566$	−6.77531	−	25.2858i	−0.284788	−	1.06284i
$567$	2.80365	+	8.55217i	0.117742	+	0.359157i
$568$	7.17199	−	12.4222i	0.300930	−	0.521226i
$569$	12.3234	+	21.3448i	0.516625	+	0.894820i	0.999814	+	0.0193040i	$0.00614505\pi$
$569$	12.3234	+	21.3448i	0.516625	+	0.894820i	−0.483189	+	0.875516i	$0.660522\pi$
$570$	2.46664	+	5.73087i	0.103316	+	0.240040i
$571$			11.0541i			0.462599i	0.972883	+	0.231299i	$0.0742977\pi$
$571$			11.0541i			0.462599i	−0.972883	+	0.231299i	$0.925702\pi$
$572$	2.25321	−	1.81828i	0.0942116	−	0.0760262i
$573$	11.8423	+	15.0015i	0.494718	+	0.626698i
$574$	1.91428	+	0.512930i	0.0799005	+	0.0214093i
$575$	−5.25111	+	3.03173i	−0.218986	+	0.126432i
$576$	2.06220	−	2.17884i	0.0859250	−	0.0907849i
$577$	18.1401	−	18.1401i	0.755182	−	0.755182i	−0.220260	−	0.975441i	$-0.570690\pi$
$577$	18.1401	−	18.1401i	0.755182	−	0.755182i	0.975441	+	0.220260i	$0.0706905\pi$
$578$	41.2636	−	11.0565i	1.71634	−	0.459892i
$579$	−21.7616	+	29.1823i	−0.904380	+	1.21277i
$580$	−15.3204	−	15.3204i	−0.636145	−	0.636145i
$581$	−4.68506	−	2.70492i	−0.194369	−	0.112219i
$582$	19.2040	+	7.64698i	0.796030	+	0.316977i
$583$	1.37348	−	5.12589i	0.0568837	−	0.212293i
$584$	7.99211			0.330716
$585$	−32.3003	−	2.55461i	−1.33545	−	0.105620i
$586$	13.9559			0.576514
$587$	−4.46096	+	16.6485i	−0.184123	+	0.687158i	0.810693	+	0.585471i	$0.199091\pi$
$587$	−4.46096	+	16.6485i	−0.184123	+	0.687158i	−0.994816	+	0.101686i	$0.967576\pi$
$588$	1.60917	+	0.640767i	0.0663609	+	0.0264248i
$589$	9.27498	+	5.35491i	0.382169	+	0.220645i
$590$	−18.9739	−	18.9739i	−0.781142	−	0.781142i
$591$	−5.99102	+	8.03396i	−0.246438	+	0.330473i
$592$	−8.37964	+	2.24532i	−0.344401	+	0.0922820i
$593$	−15.8317	+	15.8317i	−0.650131	+	0.650131i	−0.953025	−	0.302893i	$-0.902047\pi$
$593$	−15.8317	+	15.8317i	−0.650131	+	0.650131i	0.302893	+	0.953025i	$0.402047\pi$
$594$	−4.15590	−	0.373609i	−0.170519	−	0.0153294i
$595$	20.0473	−	11.5743i	0.821857	−	0.474500i
$596$	−15.2232	−	4.07904i	−0.623567	−	0.167084i
$597$	10.1412	+	12.8466i	0.415050	+	0.525777i
$598$	0.851581	+	5.43648i	0.0348237	+	0.222314i
$599$		−	13.0890i		−	0.534803i	−0.963585	−	0.267401i	$-0.913835\pi$
$599$		−	13.0890i		−	0.534803i	0.963585	−	0.267401i	$-0.0861650\pi$
$600$	−2.72051	−	6.32071i	−0.111065	−	0.258042i
$601$	−3.74799	−	6.49171i	−0.152884	−	0.264802i	0.779403	−	0.626523i	$-0.215523\pi$
$601$	−3.74799	−	6.49171i	−0.152884	−	0.264802i	−0.932286	+	0.361721i	$0.882189\pi$
$602$	−3.94434	+	6.83180i	−0.160759	+	0.278443i
$603$	−16.8933	−	27.4862i	−0.687949	−	1.11932i
$604$	1.96282	+	7.32536i	0.0798662	+	0.298065i
$605$	8.02822	+	29.9617i	0.326394	+	1.21812i
$606$	11.4337	+	1.34565i	0.464463	+	0.0546632i
$607$	−15.9295	+	27.5906i	−0.646557	+	1.11987i	0.337383	+	0.941368i	$0.390458\pi$
$607$	−15.9295	+	27.5906i	−0.646557	+	1.11987i	−0.983940	+	0.178502i	$0.942875\pi$
$608$	0.601269	+	1.04143i	0.0243847	+	0.0422355i
$609$	11.5073	−	4.95288i	0.466298	−	0.200701i
$610$		−	0.0401712i		−	0.00162648i
$611$	−2.02753	−	2.51251i	−0.0820249	−	0.101645i
$612$	22.5500	+	5.38243i	0.911530	+	0.217572i
$613$	−23.9059	−	6.40558i	−0.965552	−	0.258719i	−0.258603	−	0.965984i	$-0.583262\pi$
$613$	−23.9059	−	6.40558i	−0.965552	−	0.258719i	−0.706949	+	0.707265i	$0.749929\pi$
$614$	−11.0959	+	6.40622i	−0.447794	+	0.258534i
$615$	10.1749	−	1.48212i	0.410292	−	0.0597649i
$616$	−0.567828	+	0.567828i	−0.0228784	+	0.0228784i
$617$	39.9911	−	10.7156i	1.60998	−	0.431393i	0.661945	−	0.749553i	$-0.269731\pi$
$617$	39.9911	−	10.7156i	1.60998	−	0.431393i	0.948037	+	0.318159i	$0.103065\pi$
$618$	13.2322	+	9.86742i	0.532278	+	0.396926i
$619$	−31.0193	−	31.0193i	−1.24677	−	1.24677i	−0.957138	−	0.289633i	$-0.906467\pi$
$619$	−31.0193	−	31.0193i	−1.24677	−	1.24677i	−0.289633	−	0.957138i	$-0.593533\pi$
$620$	−23.1037	−	13.3389i	−0.927867	−	0.535704i
$621$	4.56417	−	6.48525i	0.183154	−	0.260244i
$622$	−3.16653	+	11.8176i	−0.126966	+	0.473844i
$623$	−6.67966			−0.267615
$624$	−6.24044	+	0.238670i	−0.249817	+	0.00955446i
$625$	29.0805			1.16322
$626$	3.72945	−	13.9185i	0.149059	−	0.556295i
$627$	0.618771	−	1.55393i	0.0247113	−	0.0620580i
$628$	18.0391	+	10.4149i	0.719840	+	0.415600i
$629$	−47.4049	−	47.4049i	−1.89016	−	1.89016i
$630$	8.98306	−	0.247050i	0.357894	−	0.00984270i
$631$	−17.1988	+	4.60841i	−0.684675	+	0.183458i	−0.584356	−	0.811497i	$-0.698653\pi$
$631$	−17.1988	+	4.60841i	−0.684675	+	0.183458i	−0.100319	+	0.994955i	$0.531986\pi$
$632$	−3.65301	+	3.65301i	−0.145309	+	0.145309i
$633$	0.285127	+	1.95742i	0.0113328	+	0.0778006i
$634$	−15.6067	+	9.01055i	−0.619823	+	0.357855i
$635$	−9.26049	−	2.48134i	−0.367491	−	0.0984690i
$636$	−8.98410	+	7.09208i	−0.356243	+	0.281219i
$637$	−1.46091	−	3.29632i	−0.0578833	−	0.130605i
$638$			5.80830i			0.229953i
$639$	37.8442	+	20.4833i	1.49709	+	0.810308i
$640$	−1.49774	−	2.59417i	−0.0592035	−	0.102543i
$641$	−1.92765	+	3.33879i	−0.0761376	+	0.131874i	−0.901580	−	0.432612i	$-0.857592\pi$
$641$	−1.92765	+	3.33879i	−0.0761376	+	0.131874i	0.825443	+	0.564486i	$0.190925\pi$
$642$	−2.52902	+	21.4886i	−0.0998126	+	0.848089i
$643$	5.47355	+	20.4276i	0.215856	+	0.805584i	0.985864	+	0.167550i	$0.0535855\pi$
$643$	5.47355	+	20.4276i	0.215856	+	0.805584i	−0.770008	+	0.638034i	$0.779748\pi$
$644$	−0.395008	−	1.47419i	−0.0155655	−	0.0580912i
$645$	−4.78398	+	40.6486i	−0.188369	+	1.60054i
$646$	−4.64650	+	8.04797i	−0.182814	+	0.316643i
$647$	−12.9944	−	22.5069i	−0.510862	−	0.884839i	−0.999921	−	0.0125879i	$-0.995993\pi$
$647$	−12.9944	−	22.5069i	−0.510862	−	0.884839i	0.489059	−	0.872251i	$-0.337340\pi$
$648$	6.70412	+	6.00457i	0.263363	+	0.235882i
$649$			7.19342i			0.282366i
$650$	−5.15621	+	13.3644i	−0.202243	+	0.524196i
$651$	12.1078	−	9.55791i	0.474541	−	0.374604i
$652$	−8.74036	−	2.34197i	−0.342299	−	0.0917187i
$653$	−3.53174	+	2.03905i	−0.138208	+	0.0797942i	−0.567509	−	0.823367i	$-0.692093\pi$
$653$	−3.53174	+	2.03905i	−0.138208	+	0.0797942i	0.429302	+	0.903161i	$0.358760\pi$
$654$	1.41787	+	9.73384i	0.0554433	+	0.380623i
$655$	−46.6107	+	46.6107i	−1.82123	+	1.82123i
$656$	1.91428	−	0.512930i	0.0747401	−	0.0200265i
$657$	0.659141	+	23.9673i	0.0257156	+	0.935052i
$658$	0.633171	+	0.633171i	0.0246836	+	0.0246836i
$659$	−2.64777	−	1.52869i	−0.103143	−	0.0595494i	0.447541	−	0.894263i	$-0.352300\pi$
$659$	−2.64777	−	1.52869i	−0.103143	−	0.0595494i	−0.550684	+	0.834714i	$0.685633\pi$
$660$	−1.54134	+	3.87079i	−0.0599966	+	0.150670i
$661$	−2.84066	+	10.6015i	−0.110489	+	0.412350i	−0.998910	−	0.0466796i	$-0.985136\pi$
$661$	−2.84066	+	10.6015i	−0.110489	+	0.412350i	0.888421	+	0.459029i	$0.151803\pi$
$662$	28.4461			1.10559
$663$	−25.7098	−	40.8418i	−0.998485	−	1.58617i
$664$	−5.40984			−0.209942
$665$	−0.932314	+	3.47944i	−0.0361536	+	0.134927i
$666$	−7.42451	−	24.9442i	−0.287694	−	0.966569i
$667$	−9.56000	−	5.51947i	−0.370165	−	0.213715i
$668$	3.97510	+	3.97510i	0.153801	+	0.153801i
$669$	27.2643	+	20.3313i	1.05410	+	0.786053i
$670$	−31.1164	+	8.33760i	−1.20213	+	0.322110i
$671$	−0.00761489	+	0.00761489i	−0.000293970	+	0.000293970i
$672$	1.71396	−	0.249663i	0.0661175	−	0.00963097i
$673$	−15.2367	+	8.79689i	−0.587330	+	0.339095i	−0.764041	−	0.645168i	$-0.776788\pi$
$673$	−15.2367	+	8.79689i	−0.587330	+	0.339095i	0.176711	+	0.984263i	$0.443454\pi$
$674$	−22.5479	−	6.04169i	−0.868512	−	0.232717i
$675$	18.7306	−	8.67975i	0.720941	−	0.334084i
$676$	9.63125	+	8.73150i	0.370433	+	0.335827i
$677$			26.2049i			1.00713i	0.863956	+	0.503567i	$0.167979\pi$
$677$			26.2049i			1.00713i	−0.863956	+	0.503567i	$0.832021\pi$
$678$	−16.7088	+	7.19169i	−0.641698	+	0.276195i
$679$	5.96705	+	10.3352i	0.228995	+	0.396630i
$680$	11.5743	−	20.0473i	0.443854	−	0.768777i
$681$	−32.9721	−	3.88053i	−1.26349	−	0.148702i
$682$	1.85102	+	6.90810i	0.0708792	+	0.264525i
$683$	3.57608	+	13.3461i	0.136835	+	0.510675i	0.999984	+	0.00572533i	$0.00182244\pi$
$683$	3.57608	+	13.3461i	0.136835	+	0.510675i	−0.863149	+	0.504950i	$0.831511\pi$
$684$	−3.07352	+	1.88902i	−0.117519	+	0.0722283i
$685$	8.80187	−	15.2453i	0.336302	−	0.582493i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−9.06958	−	21.0718i	−0.346026	−	0.803940i
$688$			7.88868i			0.300753i
$689$	23.6920	+	2.53086i	0.902594	+	0.0964182i
$690$	−4.90632	−	6.21523i	−0.186780	−	0.236610i
$691$	7.89358	+	2.11508i	0.300286	+	0.0804613i	0.405816	−	0.913955i	$-0.366987\pi$
$691$	7.89358	+	2.11508i	0.300286	+	0.0804613i	−0.105530	+	0.994416i	$0.533654\pi$
$692$	8.60679	−	4.96913i	0.327181	−	0.188898i
$693$	−1.74967	−	1.65601i	−0.0664645	−	0.0629065i
$694$	−8.32111	+	8.32111i	−0.315865	+	0.315865i
$695$	−41.0087	+	10.9882i	−1.55555	+	0.416808i
$696$	7.48915	−	10.0430i	0.283876	−	0.380677i
$697$	10.8294	+	10.8294i	0.410192	+	0.410192i
$698$	4.34847	+	2.51059i	0.164592	+	0.0950272i
$699$	29.6494	+	11.8063i	1.12144	+	0.446557i
$700$	1.02827	−	3.83756i	0.0388650	−	0.145046i
$701$	7.59000			0.286670			0.143335	−	0.989674i	$-0.454217\pi$
$701$	7.59000			0.286670			0.143335	+	0.989674i	$0.454217\pi$
$702$	−1.23041	−	18.6945i	−0.0464390	−	0.705580i
$703$	10.4323			0.393462
$704$	−0.207839	+	0.775667i	−0.00783324	+	0.0292340i
$705$	4.31623	+	1.71871i	0.162559	+	0.0647305i
$706$	14.4006	+	8.31422i	0.541975	+	0.312910i
$707$	4.70001	+	4.70001i	0.176762	+	0.176762i
$708$	9.27510	−	12.4379i	0.348580	−	0.467446i
$709$	21.6690	−	5.80620i	0.813797	−	0.218056i	0.172164	−	0.985068i	$-0.444924\pi$
$709$	21.6690	−	5.80620i	0.813797	−	0.218056i	0.641633	+	0.767012i	$0.278257\pi$
$710$	30.3824	−	30.3824i	1.14023	−	1.14023i
$711$	−11.2562	−	10.6536i	−0.422139	−	0.399541i
$712$	−5.78475	+	3.33983i	−0.216793	+	0.125165i
$713$	−13.1292	−	3.51795i	−0.491691	−	0.131748i
$714$	8.29347	+	10.5060i	0.310375	+	0.393177i
$715$	7.92918	−	3.51416i	0.296535	−	0.131422i
$716$			4.82667i			0.180381i
$717$	−4.32986	−	10.0598i	−0.161702	−	0.375690i
$718$	−0.599857	−	1.03898i	−0.0223864	−	0.0387745i
$719$	−24.2716	+	42.0397i	−0.905179	+	1.56782i	−0.0845019	+	0.996423i	$0.526930\pi$
$719$	−24.2716	+	42.0397i	−0.905179	+	1.56782i	−0.820677	+	0.571392i	$0.806403\pi$
$720$	7.65603	−	4.70548i	0.285323	−	0.175363i
$721$	2.46652	+	9.20519i	0.0918581	+	0.342819i
$722$	4.54328	+	16.9558i	0.169084	+	0.631028i
$723$	10.4814	+	1.23357i	0.389809	+	0.0458771i
$724$	11.8134	−	20.4614i	0.439040	−	0.760440i
$725$	−14.3681	−	24.8863i	−0.533617	−	0.924252i
$726$	−16.4744	+	7.09081i	−0.611424	+	0.263165i
$727$		−	45.6074i		−	1.69149i	−0.533590	−	0.845743i	$-0.679157\pi$
$727$		−	45.6074i		−	1.69149i	0.533590	−	0.845743i	$-0.320843\pi$
$728$	−2.91334	−	2.12425i	−0.107976	−	0.0787298i
$729$	−17.4540	+	20.6000i	−0.646444	+	0.762962i
$730$	23.1245	+	6.19619i	0.855876	+	0.229331i
$731$	−52.7949	+	30.4812i	−1.95269	+	1.12739i
$732$	0.0229852	−	0.00334813i	0.000849558	−	0.000123750i
$733$	−5.86475	+	5.86475i	−0.216619	+	0.216619i	−0.807072	−	0.590453i	$-0.798949\pi$
$733$	−5.86475	+	5.86475i	−0.216619	+	0.216619i	0.590453	+	0.807072i	$0.298949\pi$
$734$	−32.6733	+	8.75477i	−1.20599	+	0.323145i
$735$	4.15921	+	3.10157i	0.153415	+	0.114403i
$736$	−1.07918	−	1.07918i	−0.0397792	−	0.0397792i
$737$	7.47894	+	4.31797i	0.275490	+	0.159054i
$738$	1.69609	+	5.69837i	0.0624338	+	0.209760i
$739$	7.90634	−	29.5069i	0.290840	−	1.08543i	−0.653626	−	0.756818i	$-0.726753\pi$
$739$	7.90634	−	29.5069i	0.290840	−	1.08543i	0.944466	−	0.328610i	$-0.106580\pi$
$740$	−25.9866			−0.955285
$741$	7.32294	+	1.66504i	0.269015	+	0.0611668i
$742$	−6.60837			−0.242601
$743$	−0.457078	+	1.70584i	−0.0167686	+	0.0625812i	−0.973803	−	0.227393i	$-0.926980\pi$
$743$	−0.457078	+	1.70584i	−0.0167686	+	0.0625812i	0.957035	+	0.289974i	$0.0936466\pi$
$744$	5.70668	−	14.3313i	0.209217	−	0.525410i
$745$	−40.8846	−	23.6047i	−1.49790	−	0.864811i
$746$	0.459913	+	0.459913i	0.0168386	+	0.0168386i
$747$	−0.446171	−	16.2234i	−0.0163246	−	0.593583i
$748$	−5.99421	+	1.60615i	−0.219170	+	0.0587265i
$749$	−8.83324	+	8.83324i	−0.322760	+	0.322760i
$750$	0.768107	+	5.27312i	0.0280473	+	0.192547i
$751$	−16.0288	+	9.25422i	−0.584898	+	0.337691i	−0.763078	−	0.646307i	$-0.776313\pi$
$751$	−16.0288	+	9.25422i	−0.584898	+	0.337691i	0.178179	+	0.983998i	$0.442979\pi$
$752$	0.864928	+	0.231757i	0.0315407	+	0.00845130i
$753$	11.3382	−	8.95044i	0.413189	−	0.326172i
$754$	−25.7647	+	4.03584i	−0.938297	+	0.146977i
$755$			22.7171i			0.826759i
$756$	0.890064	+	5.11935i	0.0323713	+	0.186189i
$757$	−9.11979	−	15.7959i	−0.331464	−	0.574113i	0.651335	−	0.758790i	$-0.274209\pi$
$757$	−9.11979	−	15.7959i	−0.331464	−	0.574113i	−0.982799	+	0.184677i	$0.940876\pi$
$758$	−0.429861	+	0.744541i	−0.0156133	+	0.0270429i
$759$	−0.248118	+	2.10821i	−0.00900612	+	0.0765233i
$760$	0.932314	+	3.47944i	0.0338186	+	0.126213i
$761$	12.6341	+	47.1509i	0.457984	+	1.70922i	0.679164	+	0.733987i	$0.262343\pi$
$761$	12.6341	+	47.1509i	0.457984	+	1.70922i	−0.221180	+	0.975233i	$0.570991\pi$
$762$	0.647949	−	5.50550i	0.0234727	−	0.199443i
$763$	−2.83957	+	4.91828i	−0.102799	+	0.178054i
$764$	5.51729	+	9.55622i	0.199608	+	0.345732i
$765$	61.0736	+	33.0564i	2.20812	+	1.19516i
$766$		−	12.3116i		−	0.444835i
$767$	−31.9089	+	4.99828i	−1.15216	+	0.180477i
$768$	1.35950	−	1.07320i	0.0490569	−	0.0387256i
$769$	−12.1557	−	3.25710i	−0.438344	−	0.117454i	0.0328962	−	0.999459i	$-0.489527\pi$
$769$	−12.1557	−	3.25710i	−0.438344	−	0.117454i	−0.471240	+	0.882005i	$0.656194\pi$
$770$	−2.08319	+	1.20273i	−0.0750730	+	0.0433434i
$771$	−0.286390	−	1.96609i	−0.0103141	−	0.0708071i
$772$	−14.8614	+	14.8614i	−0.534874	+	0.534874i
$773$	4.68124	−	1.25433i	0.168372	−	0.0451152i	−0.173648	−	0.984808i	$-0.555555\pi$
$773$	4.68124	−	1.25433i	0.168372	−	0.0451152i	0.342020	+	0.939693i	$0.388889\pi$
$774$	−23.6571	+	0.650612i	−0.850337	+	0.0233857i
$775$	−25.0196	−	25.0196i	−0.898729	−	0.898729i
$776$	10.3352	+	5.96705i	0.371014	+	0.214205i
$777$	5.55880	−	13.9599i	0.199421	−	0.500809i
$778$	3.54549	−	13.2320i	0.127112	−	0.474389i
$779$	−2.38320			−0.0853870
$780$	−18.2412	−	4.14757i	−0.653140	−	0.148507i
$781$	−11.5186			−0.412169
$782$	3.05255	−	11.3923i	0.109159	−	0.407387i
$783$	30.7351	+	21.6307i	1.09838	+	0.773018i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	44.1202	+	44.1202i	1.57472	+	1.57472i
$786$	−30.5547	−	22.7850i	−1.08985	−	0.812713i
$787$	17.5995	−	4.71577i	0.627354	−	0.168099i	0.0688854	−	0.997625i	$-0.478056\pi$
$787$	17.5995	−	4.71577i	0.627354	−	0.168099i	0.558469	+	0.829526i	$0.311389\pi$
$788$	−4.09139	+	4.09139i	−0.145750	+	0.145750i
$789$	10.9170	−	1.59021i	0.388654	−	0.0566131i
$790$	−13.4018	+	7.73753i	−0.476815	+	0.275289i
$791$	−10.1446	−	2.71824i	−0.360700	−	0.0966493i
$792$	−2.34326	−	0.559310i	−0.0832642	−	0.0198742i
$793$	−0.0390696	−	0.0284873i	−0.00138740	−	0.00101162i
$794$		−	22.5792i		−	0.801307i
$795$	−31.4931	+	13.5551i	−1.11695	+	0.480748i
$796$	4.72474	+	8.18349i	0.167464	+	0.290056i
$797$	2.85683	−	4.94817i	0.101194	−	0.175273i	−0.810983	−	0.585070i	$-0.801067\pi$
$797$	2.85683	−	4.94817i	0.101194	−	0.175273i	0.912177	+	0.409797i	$0.134400\pi$
$798$	−2.06858	−	0.243454i	−0.0732269	−	0.00861817i
$799$	1.79098	+	6.68401i	0.0633601	+	0.236463i
$800$	−1.02827	−	3.83756i	−0.0363548	−	0.135678i
$801$	−10.4928	−	17.0722i	−0.370744	−	0.603218i
$802$	0.348792	−	0.604126i	0.0123163	−	0.0213324i
$803$	−3.20895	−	5.55806i	−0.113241	−	0.196140i
$804$	−7.36407	−	17.1093i	−0.259711	−	0.603399i
$805$		−	4.57169i		−	0.161131i
$806$	−29.3571	+	13.0109i	−1.03406	+	0.458288i
$807$	9.09725	+	11.5242i	0.320238	+	0.405672i
$808$	6.42034	+	1.72032i	0.225867	+	0.0605208i
$809$	5.57642	−	3.21955i	0.196056	−	0.113193i	−0.398758	−	0.917056i	$-0.630559\pi$
$809$	5.57642	−	3.21955i	0.196056	−	0.113193i	0.594815	+	0.803863i	$0.297225\pi$
$810$	14.7425	+	22.5713i	0.518000	+	0.793076i
$811$	−28.9735	+	28.9735i	−1.01740	+	1.01740i	−0.0175506	+	0.999846i	$0.505587\pi$
$811$	−28.9735	+	28.9735i	−1.01740	+	1.01740i	−0.999846	+	0.0175506i	$0.994413\pi$
$812$	6.98653	−	1.87204i	0.245179	−	0.0656956i
$813$	−12.5863	+	16.8782i	−0.441420	+	0.591945i
$814$	4.92604	+	4.92604i	0.172658	+	0.172658i
$815$	−23.4738	−	13.5526i	−0.822251	−	0.474727i
$816$	12.4354	+	4.95173i	0.435324	+	0.173345i
$817$	2.45527	−	9.16320i	0.0858991	−	0.320580i
$818$	−7.79388			−0.272507
$819$	6.13005	−	8.91193i	0.214201	−	0.311408i
$820$	5.93648			0.207311
$821$	−10.0158	+	37.3795i	−0.349555	+	1.30456i	0.537646	+	0.843171i	$0.319314\pi$
$821$	−10.0158	+	37.3795i	−0.349555	+	1.30456i	−0.887200	+	0.461384i	$0.847353\pi$
$822$	9.45669	+	3.76563i	0.329840	+	0.131341i
$823$	4.95765	+	2.86230i	0.172813	+	0.0997735i	0.583911	−	0.811817i	$-0.301522\pi$
$823$	4.95765	+	2.86230i	0.172813	+	0.0997735i	−0.411099	+	0.911591i	$0.634855\pi$
$824$	6.73866	+	6.73866i	0.234752	+	0.234752i
$825$	−3.30337	+	4.42982i	−0.115009	+	0.154227i
$826$	8.65262	−	2.31846i	0.301063	−	0.0806696i
$827$	14.2761	−	14.2761i	0.496428	−	0.496428i	−0.413896	−	0.910324i	$-0.635832\pi$
$827$	14.2761	−	14.2761i	0.496428	−	0.496428i	0.910324	+	0.413896i	$0.135832\pi$
$828$	3.14732	−	3.32533i	0.109377	−	0.115563i
$829$	15.7537	−	9.09540i	0.547148	−	0.315896i	−0.200823	−	0.979628i	$-0.564362\pi$
$829$	15.7537	−	9.09540i	0.547148	−	0.315896i	0.747971	+	0.663731i	$0.231028\pi$
$830$	−15.6529	−	4.19419i	−0.543321	−	0.145582i
$831$	11.2086	+	14.1988i	0.388822	+	0.492552i
$832$	−3.58515	−	0.382979i	−0.124293	−	0.0132774i
$833$			7.72782i			0.267753i
$834$	−9.70521	−	22.5486i	−0.336064	−	0.780794i
$835$	8.41977	+	14.5835i	0.291378	+	0.504682i
$836$	0.482837	−	0.836298i	0.0166993	−	0.0289240i
$837$	43.4482	+	15.9316i	1.50179	+	0.550677i
$838$	−6.58122	−	24.5615i	−0.227345	−	0.848461i
$839$	−5.72662	−	21.3720i	−0.197705	−	0.737844i	−0.991550	−	0.129725i	$-0.958591\pi$
$839$	−5.72662	−	21.3720i	−0.197705	−	0.737844i	0.793845	−	0.608120i	$-0.208076\pi$
$840$	5.15277	+	0.606436i	0.177787	+	0.0209240i
$841$	11.6581	−	20.1924i	0.402003	−	0.696289i
$842$	15.6315	+	27.0746i	0.538698	+	0.933052i
$843$	25.4104	−	10.9369i	0.875179	−	0.376688i
$844$			1.14204i			0.0393108i
$845$	21.0978	+	32.7309i	0.725786	+	1.12598i
$846$	−0.623674	+	2.61292i	−0.0214423	+	0.0898340i
$847$	−10.0023	−	2.68011i	−0.343683	−	0.0920896i
$848$	−5.72301	+	3.30418i	−0.196529	+	0.113466i
$849$	44.8678	−	6.53564i	1.53986	−	0.224303i
$850$	21.7097	−	21.7097i	0.744635	−	0.744635i
$851$	−12.7889	+	3.42679i	−0.438399	+	0.117469i
$852$	19.9165	+	14.8520i	0.682329	+	0.508821i
$853$	−16.3571	−	16.3571i	−0.560057	−	0.560057i	0.369266	−	0.929324i	$-0.379609\pi$
$853$	−16.3571	−	16.3571i	−0.560057	−	0.560057i	−0.929324	+	0.369266i	$0.879609\pi$
$854$	0.0116139	+	0.00670528i	0.000397419	+	0.000229450i
$855$	−10.3575	+	3.08285i	−0.354219	+	0.105431i
$856$	−3.23319	+	12.0664i	−0.110508	+	0.412422i
$857$	−35.7554			−1.22138			−0.610690	−	0.791870i	$-0.709108\pi$
$857$	−35.7554			−1.22138			−0.610690	+	0.791870i	$0.709108\pi$
$858$	2.67161	+	4.24404i	0.0912072	+	0.144889i
$859$	23.0417			0.786174			0.393087	−	0.919501i	$-0.371407\pi$
$859$	23.0417			0.786174			0.393087	+	0.919501i	$0.371407\pi$
$860$	−6.11601	+	22.8252i	−0.208554	+	0.778334i
$861$	−1.26988	+	3.18906i	−0.0432773	+	0.108683i
$862$	−0.925415	−	0.534289i	−0.0315198	−	0.0181979i
$863$	11.9413	+	11.9413i	0.406486	+	0.406486i	0.880511	−	0.474025i	$-0.157200\pi$
$863$	11.9413	+	11.9413i	0.406486	+	0.406486i	−0.474025	+	0.880511i	$0.657200\pi$
$864$	3.33050	+	3.98846i	0.113306	+	0.135690i
$865$	28.7555	−	7.70502i	0.977718	−	0.261979i
$866$	−23.7952	+	23.7952i	−0.808594	+	0.808594i
$867$	10.6654	+	73.2192i	0.362217	+	2.48665i
$868$	7.71284	−	4.45301i	0.261791	−	0.151145i
$869$	4.00720	+	1.07372i	0.135935	+	0.0364236i
$870$	29.4554	−	23.2522i	0.998633	−	0.788324i
$871$	−13.9572	+	36.1757i	−0.472921	+	1.22577i
$872$			5.67914i			0.192320i
$873$	−17.0420	+	31.4861i	−0.576785	+	1.06564i
$874$	0.917653	+	1.58942i	0.0310401	+	0.0537630i
$875$	−1.53828	+	2.66439i	−0.0520035	+	0.0900727i
$876$	−1.61800	+	13.7479i	−0.0546672	+	0.464497i
$877$	−6.69032	−	24.9686i	−0.225916	−	0.843131i	−0.982035	−	0.188697i	$-0.939574\pi$
$877$	−6.69032	−	24.9686i	−0.225916	−	0.843131i	0.756119	−	0.654434i	$-0.227093\pi$
$878$	3.55139	+	13.2540i	0.119854	+	0.447300i
$879$	−2.82538	+	24.0067i	−0.0952976	+	0.809726i
$880$	−1.20273	+	2.08319i	−0.0405441	+	0.0702244i
$881$	6.34841	+	10.9958i	0.213883	+	0.370457i	0.952927	−	0.303201i	$-0.0980555\pi$
$881$	6.34841	+	10.9958i	0.213883	+	0.370457i	−0.739043	+	0.673658i	$0.764722\pi$
$882$	−1.42801	+	2.63833i	−0.0480835	+	0.0888372i
$883$		−	37.2031i		−	1.25199i	−0.779829	−	0.625993i	$-0.784694\pi$
$883$		−	37.2031i		−	1.25199i	0.779829	−	0.625993i	$-0.215306\pi$
$884$	−11.2896	−	25.4734i	−0.379711	−	0.856763i
$885$	36.4797	−	28.7972i	1.22625	−	0.968007i
$886$	−23.5839	−	6.31928i	−0.792316	−	0.212300i
$887$	−44.3364	+	25.5976i	−1.48867	+	0.859485i	−0.999916	−	0.0129361i	$-0.995882\pi$
$887$	−44.3364	+	25.5976i	−1.48867	+	0.859485i	−0.488755	+	0.872421i	$0.662549\pi$
$888$	−2.16589	−	14.8690i	−0.0726825	−	0.498972i
$889$	2.26312	−	2.26312i	0.0759027	−	0.0759027i
$890$	−19.3270	+	5.17866i	−0.647843	+	0.173589i
$891$	1.48404	−	7.07326i	0.0497171	−	0.236963i
$892$	13.8846	+	13.8846i	0.464892	+	0.464892i
$893$	−0.932536	−	0.538400i	−0.0312061	−	0.0180169i
$894$	10.0986	−	25.3608i	0.337748	−	0.848193i
$895$	−3.74206	+	13.9656i	−0.125083	+	0.466818i
$896$	1.00000			0.0334077
$897$	−9.52411	+	0.364257i	−0.318001	+	0.0121622i
$898$	41.2199			1.37553
$899$	16.6724	−	62.2222i	0.556055	−	2.07523i
$900$	11.4235	−	3.40014i	0.380784	−	0.113338i
$901$	−44.2264	−	25.5341i	−1.47340	−	0.850666i
$902$	−1.12533	−	1.12533i	−0.0374692	−	0.0374692i
$903$	−10.9534	−	8.16807i	−0.364506	−	0.271816i
$904$	−10.1446	+	2.71824i	−0.337404	+	0.0904072i
$905$	50.0445	−	50.0445i	1.66353	−	1.66353i
$906$	−12.9983	+	1.89339i	−0.431840	+	0.0629037i
$907$	20.8162	−	12.0183i	0.691192	−	0.399060i	−0.112867	−	0.993610i	$-0.536003\pi$
$907$	20.8162	−	12.0183i	0.691192	−	0.399060i	0.804058	+	0.594550i	$0.202670\pi$
$908$	−18.5147	−	4.96100i	−0.614432	−	0.164637i
$909$	−4.62951	+	19.3956i	−0.153551	+	0.643312i
$910$	−6.78262	−	8.40501i	−0.224842	−	0.278623i
$911$		−	11.9041i		−	0.394402i	−0.980363	−	0.197201i	$-0.936815\pi$
$911$		−	11.9041i		−	0.394402i	0.980363	−	0.197201i	$-0.0631851\pi$
$912$	−1.91317	+	0.823453i	−0.0633514	+	0.0272673i
$913$	2.17213	+	3.76224i	0.0718870	+	0.124512i
$914$	−11.6578	+	20.1919i	−0.385605	+	0.667887i
$915$	0.0691016	+	0.00813265i	0.00228443	+	0.000268857i
$916$	−3.42802	−	12.7936i	−0.113265	−	0.422711i
$917$	−5.69548	−	21.2558i	−0.188081	−	0.701929i
$918$	−13.8240	+	37.7004i	−0.456259	+	1.24430i
$919$	8.55221	−	14.8129i	0.282111	−	0.488631i	−0.689793	−	0.724006i	$-0.742299\pi$
$919$	8.55221	−	14.8129i	0.282111	−	0.488631i	0.971905	+	0.235375i	$0.0756319\pi$
$920$	−2.28584	−	3.95920i	−0.0753621	−	0.130531i
$921$	−8.77348	−	20.3839i	−0.289096	−	0.671671i
$922$		−	11.1240i		−	0.366349i
$923$	−8.00361	−	51.0949i	−0.263442	−	1.68181i
$924$	−0.861808	−	1.09172i	−0.0283514	−	0.0359150i
$925$	−33.2917	−	8.92049i	−1.09463	−	0.293304i
$926$	−23.5130	+	13.5752i	−0.772686	+	0.446110i
$927$	−19.6526	+	20.7641i	−0.645476	+	0.681983i
$928$	5.11450	−	5.11450i	0.167892	−	0.167892i
$929$	11.8323	−	3.17046i	0.388205	−	0.104019i	−0.0594369	−	0.998232i	$-0.518931\pi$
$929$	11.8323	−	3.17046i	0.388205	−	0.104019i	0.447642	+	0.894213i	$0.352264\pi$
$930$	27.6227	−	37.0420i	0.905783	−	1.21466i
$931$	−0.850323	−	0.850323i	−0.0278682	−	0.0278682i
$932$	15.9568	+	9.21267i	0.522683	+	0.301771i
$933$	−19.6874	−	7.83947i	−0.644536	−	0.256653i
$934$	−10.1105	+	37.7330i	−0.330826	+	1.23466i
$935$	−18.5890			−0.607925
$936$	0.852820	−	10.7830i	0.0278753	−	0.352453i
$937$	−27.0139			−0.882505			−0.441253	−	0.897383i	$-0.645466\pi$
$937$	−27.0139			−0.882505			−0.441253	+	0.897383i	$0.645466\pi$
$938$	2.78339	−	10.3878i	0.0908809	−	0.339172i
$939$	23.1873	+	9.23312i	0.756689	+	0.301312i
$940$	2.32292	+	1.34114i	0.0757653	+	0.0437431i
$941$	−0.434761	−	0.434761i	−0.0141728	−	0.0141728i	0.699985	−	0.714158i	$-0.253190\pi$
$941$	−0.434761	−	0.434761i	−0.0141728	−	0.0141728i	−0.714158	+	0.699985i	$0.753190\pi$
$942$	−21.5675	+	28.9220i	−0.702707	+	0.942331i
$943$	2.92156	−	0.782830i	0.0951391	−	0.0254924i
$944$	6.33416	−	6.33416i	0.206159	−	0.206159i
$945$	−1.39365	+	15.5025i	−0.0453354	+	0.504296i
$946$	5.48614	−	3.16742i	0.178370	−	0.102982i
$947$	18.5748	+	4.97711i	0.603601	+	0.161734i	0.547662	−	0.836700i	$-0.315518\pi$
$947$	18.5748	+	4.97711i	0.603601	+	0.161734i	0.0559393	+	0.998434i	$0.482185\pi$
$948$	−5.54427	−	7.02337i	−0.180070	−	0.228108i
$949$	22.4250	−	18.0964i	0.727946	−	0.587433i
$950$			4.77760i			0.155006i
$951$	−12.3402	−	28.6706i	−0.400158	−	0.929707i
$952$	3.86391	+	6.69249i	0.125230	+	0.216905i
$953$	−7.16693	+	12.4135i	−0.232160	+	0.402112i	−0.958443	−	0.285283i	$-0.907913\pi$
$953$	−7.16693	+	12.4135i	−0.232160	+	0.402112i	0.726284	+	0.687395i	$0.241246\pi$
$954$	−10.3808	−	16.8900i	−0.336091	−	0.546835i
$955$	8.55498	+	31.9276i	0.276833	+	1.03315i
$956$	−1.63655	−	6.10770i	−0.0529299	−	0.197537i
$957$	−9.99132	−	1.17589i	−0.322973	−	0.0380111i
$958$	1.59447	−	2.76171i	0.0515151	−	0.0892268i
$959$	2.93838	+	5.08942i	0.0948852	+	0.164346i
$960$	4.76565	−	2.05120i	0.153811	−	0.0662021i
$961$		−	48.3172i		−	1.55862i
$962$	−18.4283	+	25.2740i	−0.594154	+	0.814865i
$963$	−36.4523	−	8.70074i	−1.17466	−	0.280377i
$964$	5.88560	+	1.57704i	0.189563	+	0.0507931i
$965$	−54.5222	+	31.4784i	−1.75513	+	1.01333i
$966$	2.61584	−	0.381035i	0.0841632	−	0.0122596i
$967$	34.4912	−	34.4912i	1.10916	−	1.10916i	0.115900	−	0.993261i	$-0.463025\pi$
$967$	34.4912	−	34.4912i	1.10916	−	1.10916i	0.993261	−	0.115900i	$-0.0369751\pi$
$968$	−10.0023	+	2.68011i	−0.321486	+	0.0861419i
$969$	−12.9033	−	9.62212i	−0.414513	−	0.309107i
$970$	25.2780	+	25.2780i	0.811627	+	0.811627i
$971$	−14.4179	−	8.32420i	−0.462694	−	0.267136i	0.250483	−	0.968121i	$-0.419411\pi$
$971$	−14.4179	−	8.32420i	−0.462694	−	0.267136i	−0.713176	+	0.700985i	$0.752744\pi$
$972$	−11.6862	+	10.3167i	−0.374834	+	0.330907i
$973$	3.66827	−	13.6902i	0.117599	−	0.438887i
$974$	−20.3649			−0.652535
$975$	−21.9453	−	11.5752i	−0.702813	−	0.370704i
$976$	0.0134106			0.000429262
$977$	15.7189	−	58.6637i	0.502892	−	1.87682i	0.0225301	−	0.999746i	$-0.492828\pi$
$977$	15.7189	−	58.6637i	0.502892	−	1.87682i	0.480361	−	0.877071i	$-0.340505\pi$
$978$	5.79809	−	14.5608i	0.185403	−	0.465604i
$979$	4.64533	+	2.68198i	0.148465	+	0.0857165i
$980$	2.11813	+	2.11813i	0.0676611	+	0.0676611i
$981$	−17.0310	+	0.468382i	−0.543758	+	0.0149543i
$982$	−24.7873	+	6.64173i	−0.790994	+	0.211946i
$983$	−21.1126	+	21.1126i	−0.673389	+	0.673389i	−0.958496	−	0.285107i	$-0.907971\pi$
$983$	−21.1126	+	21.1126i	−0.673389	+	0.673389i	0.285107	+	0.958496i	$0.407971\pi$
$984$	0.494785	+	3.39675i	0.0157732	+	0.108284i
$985$	−15.0101	+	8.66609i	−0.478262	+	0.276125i
$986$	53.9907	+	14.4668i	1.71941	+	0.460715i
$987$	−1.21735	+	0.960982i	−0.0387488	+	0.0305884i
$988$	4.04518	+	1.56070i	0.128694	+	0.0496524i
$989$			12.0397i			0.382839i
$990$	−6.34641	−	3.43502i	−0.201702	−	0.109172i
$991$	16.2502	+	28.1461i	0.516203	+	0.894091i	0.999823	+	0.0188122i	$0.00598848\pi$
$991$	16.2502	+	28.1461i	0.516203	+	0.894091i	−0.483620	+	0.875278i	$0.660678\pi$
$992$	4.45301	−	7.71284i	0.141383	−	0.244883i
$993$	−5.75891	+	48.9324i	−0.182753	+	1.55282i
$994$	3.71249	+	13.8552i	0.117753	+	0.439461i
$995$	7.32608	+	27.3413i	0.232252	+	0.866777i
$996$	1.09522	−	9.30589i	0.0347034	−	0.294868i
$997$	−16.0101	+	27.7303i	−0.507044	+	0.878226i	0.492923	+	0.870073i	$0.335929\pi$
$997$	−16.0101	+	27.7303i	−0.507044	+	0.878226i	−0.999967	+	0.00815320i	$0.997405\pi$
$998$	−0.808976	−	1.40119i	−0.0256077	−	0.0443538i
$999$	44.4116	−	7.72152i	1.40512	−	0.244298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.197.2	✓	56
3.2	odd	2		546.2.bu.b.197.11	yes	56
13.7	odd	12		546.2.bu.b.449.11	yes	56
39.20	even	12	inner	546.2.bu.a.449.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.2	✓	56	1.1	even	1	trivial
546.2.bu.a.449.2	yes	56	39.20	even	12	inner
546.2.bu.b.197.11	yes	56	3.2	odd	2
546.2.bu.b.449.11	yes	56	13.7	odd	12

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.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.60917 - 0.640767i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11813 - 2.11813i) q^{5} +(1.03542 - 1.38849i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.17884 + 2.06220i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.60917 - 0.640767i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11813 - 2.11813i) q^{5} +(1.03542 - 1.38849i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.17884 + 2.06220i) q^{9} +(2.59417 - 1.49774i) q^{10} +(-0.775667 - 0.207839i) q^{11} +(1.07320 + 1.35950i) q^{12} +(0.382979 - 3.58515i) q^{13} +1.00000i q^{14} +(2.05120 + 4.76565i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.86391 + 6.69249i) q^{17} +(-2.55586 + 1.57086i) q^{18} +(-0.311240 - 1.16156i) q^{19} +(0.775289 + 2.89342i) q^{20} +(-1.72018 - 0.202450i) q^{21} +(0.401515 - 0.695444i) q^{22} +(0.763097 + 1.32172i) q^{23} +(-1.59094 + 0.684763i) q^{24} +3.97293i q^{25} +(3.36387 + 1.29784i) q^{26} +(-2.18472 - 4.71455i) q^{27} +(-0.965926 - 0.258819i) q^{28} +(-6.26395 + 3.61650i) q^{29} +(-5.13415 + 0.747863i) q^{30} +(-6.29751 + 6.29751i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.11500 + 0.831469i) q^{33} +(-5.46439 - 5.46439i) q^{34} +(-2.59417 - 1.49774i) q^{35} +(-0.855827 - 2.87534i) q^{36} +(-2.24532 + 8.37964i) q^{37} +1.20254 q^{38} +(-2.91352 + 5.52371i) q^{39} -2.99549 q^{40} +(0.512930 - 1.91428i) q^{41} +(0.640767 - 1.60917i) q^{42} +(6.83180 + 3.94434i) q^{43} +(0.567828 + 0.567828i) q^{44} +(-0.247050 - 8.98306i) q^{45} +(-1.47419 + 0.395008i) q^{46} +(0.633171 - 0.633171i) q^{47} +(-0.249663 - 1.71396i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-3.83756 - 1.02827i) q^{50} +(10.5060 - 8.29347i) q^{51} +(-2.12425 + 2.91334i) q^{52} +6.60837i q^{53} +(5.11935 - 0.890064i) q^{54} +(1.20273 + 2.08319i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-0.243454 + 2.06858i) q^{57} +(-1.87204 - 6.98653i) q^{58} +(-2.31846 - 8.65262i) q^{59} +(0.606436 - 5.15277i) q^{60} +(0.00670528 - 0.0116139i) q^{61} +(-4.45301 - 7.71284i) q^{62} +(2.63833 + 1.42801i) q^{63} -1.00000i q^{64} +(-8.40501 + 6.78262i) q^{65} +(-1.09172 + 0.861808i) q^{66} +(-10.3878 - 2.78339i) q^{67} +(6.69249 - 3.86391i) q^{68} +(-0.381035 - 2.61584i) q^{69} +(2.11813 - 2.11813i) q^{70} +(13.8552 - 3.71249i) q^{71} +(2.99887 - 0.0824740i) q^{72} +(5.65127 + 5.65127i) q^{73} +(-7.51298 - 4.33762i) q^{74} +(2.54572 - 6.39311i) q^{75} +(-0.311240 + 1.16156i) q^{76} -0.803029 q^{77} +(-4.58142 - 4.24389i) q^{78} -5.16613 q^{79} +(0.775289 - 2.89342i) q^{80} +(0.494657 + 8.98640i) q^{81} +(1.71630 + 0.990904i) q^{82} +(-3.82533 - 3.82533i) q^{83} +(1.38849 + 1.03542i) q^{84} +(22.3598 - 5.99129i) q^{85} +(-5.57814 + 5.57814i) q^{86} +(12.3971 - 1.80581i) q^{87} +(-0.695444 + 0.401515i) q^{88} +(-6.45205 - 1.72882i) q^{89} +(8.74091 + 2.08636i) q^{90} +(-0.557977 - 3.56211i) q^{91} -1.52619i q^{92} +(14.1690 - 6.09851i) q^{93} +(0.447720 + 0.775473i) q^{94} +(-1.80109 + 3.11958i) q^{95} +(1.72018 + 0.202450i) q^{96} +(3.08877 + 11.5275i) q^{97} +(0.258819 + 0.965926i) q^{98} +(-1.26144 - 2.05243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

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