LMFDB - Embedded newform 546.2.cg.b.409.9

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			409.9
Character	$\chi$	$=$	546.409
Dual form			546.2.cg.b.271.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.349971 - 1.30611i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.23506 - 1.41580i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.349971 - 1.30611i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.23506 - 1.41580i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.676092 - 1.17103i) q^{10} +(0.147349 - 0.549915i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.33605 - 1.36776i) q^{13} +(-2.58155 + 0.579303i) q^{14} +(-0.349971 - 1.30611i) q^{15} -1.00000 q^{16} +0.975087 q^{17} +(-0.258819 - 0.965926i) q^{18} +(3.14068 - 0.841543i) q^{19} +(-1.30611 - 0.349971i) q^{20} +(-2.64352 - 0.108591i) q^{21} +(-0.284657 - 0.493040i) q^{22} -0.0810273i q^{23} +(-0.965926 - 0.258819i) q^{24} +(2.74668 + 1.58580i) q^{25} +(-3.32610 + 1.39179i) q^{26} -1.00000i q^{27} +(-1.41580 + 2.23506i) q^{28} +(-0.139785 + 0.242115i) q^{29} +(-1.17103 - 0.676092i) q^{30} +(2.48511 - 0.665884i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.147349 - 0.549915i) q^{33} +(0.689491 - 0.689491i) q^{34} +(-2.63140 + 2.42375i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(1.14587 + 1.14587i) q^{37} +(1.62574 - 2.81586i) q^{38} +(-3.57298 + 0.483507i) q^{39} +(-1.17103 + 0.676092i) q^{40} +(2.23576 - 0.599071i) q^{41} +(-1.94604 + 1.79247i) q^{42} +(9.48543 - 5.47642i) q^{43} +(-0.549915 - 0.147349i) q^{44} +(-0.956138 - 0.956138i) q^{45} +(-0.0572950 - 0.0572950i) q^{46} +(-5.55221 - 1.48771i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.99100 + 6.32882i) q^{49} +(3.06353 - 0.820870i) q^{50} +(0.844450 - 0.487543i) q^{51} +(-1.36776 + 3.33605i) q^{52} +(-4.54058 + 7.86452i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.666681 - 0.384909i) q^{55} +(0.579303 + 2.58155i) q^{56} +(2.29914 - 2.29914i) q^{57} +(0.0723580 + 0.270044i) q^{58} +(5.05249 - 5.05249i) q^{59} +(-1.30611 + 0.349971i) q^{60} +(4.95521 + 2.86089i) q^{61} +(1.28639 - 2.22809i) q^{62} +(-2.34365 + 1.22772i) q^{63} +1.00000i q^{64} +(-2.95397 + 3.87857i) q^{65} +(-0.493040 - 0.284657i) q^{66} +(2.09610 + 0.561649i) q^{67} -0.975087i q^{68} +(-0.0405137 - 0.0701717i) q^{69} +(-0.146835 + 3.57453i) q^{70} +(0.466117 + 0.124896i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-0.753163 - 2.81084i) q^{73} +1.62051 q^{74} +3.17160 q^{75} +(-0.841543 - 3.14068i) q^{76} +(-1.10791 + 1.02048i) q^{77} +(-2.18459 + 2.86837i) q^{78} +(1.45438 + 2.51907i) q^{79} +(-0.349971 + 1.30611i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.15732 - 2.00453i) q^{82} +(-2.22649 - 2.22649i) q^{83} +(-0.108591 + 2.64352i) q^{84} +(0.341252 - 1.27357i) q^{85} +(2.83480 - 10.5796i) q^{86} +0.279570i q^{87} +(-0.493040 + 0.284657i) q^{88} +(-7.48471 + 7.48471i) q^{89} -1.35218 q^{90} +(5.51979 + 7.78022i) q^{91} -0.0810273 q^{92} +(1.81923 - 1.81923i) q^{93} +(-4.97797 + 2.87403i) q^{94} -4.39659i q^{95} +(-0.258819 + 0.965926i) q^{96} +(4.34344 - 16.2099i) q^{97} +(6.59011 + 2.36019i) q^{98} +(-0.402566 - 0.402566i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$5$	0.349971	−	1.30611i	0.156512	−	0.584110i	−0.842459	−	0.538760i	$-0.818893\pi$
$5$	0.349971	−	1.30611i	0.156512	−	0.584110i	0.998971	−	0.0453500i	$-0.0144403\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	−2.23506	−	1.41580i	−0.844774	−	0.535123i
$7$	−2.23506	−	1.41580i	−0.844774	−	0.535123i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.676092	−	1.17103i	−0.213799	−	0.370311i
$11$	0.147349	−	0.549915i	0.0444275	−	0.165806i	−0.940148	−	0.340767i	$-0.889313\pi$
$11$	0.147349	−	0.549915i	0.0444275	−	0.165806i	0.984575	+	0.174961i	$0.0559800\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−3.33605	−	1.36776i	−0.925254	−	0.379349i
$13$	−3.33605	−	1.36776i	−0.925254	−	0.379349i
$14$	−2.58155	+	0.579303i	−0.689949	+	0.154825i
$15$	−0.349971	−	1.30611i	−0.0903621	−	0.337236i
$16$	−1.00000			−0.250000
$17$	0.975087			0.236493			0.118247	−	0.992984i	$-0.462273\pi$
$17$	0.975087			0.236493			0.118247	+	0.992984i	$0.462273\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	3.14068	−	0.841543i	0.720522	−	0.193063i	0.120117	−	0.992760i	$-0.461673\pi$
$19$	3.14068	−	0.841543i	0.720522	−	0.193063i	0.600405	+	0.799696i	$0.295006\pi$
$20$	−1.30611	−	0.349971i	−0.292055	−	0.0782559i
$21$	−2.64352	−	0.108591i	−0.576864	−	0.0236964i
$22$	−0.284657	−	0.493040i	−0.0606891	−	0.105117i
$23$		−	0.0810273i		−	0.0168954i	−0.999964	−	0.00844768i	$-0.997311\pi$
$23$		−	0.0810273i		−	0.0168954i	0.999964	−	0.00844768i	$-0.00268901\pi$
$24$	−0.965926	−	0.258819i	−0.197169	−	0.0528312i
$25$	2.74668	+	1.58580i	0.549337	+	0.317160i
$26$	−3.32610	+	1.39179i	−0.652301	+	0.272952i
$27$		−	1.00000i		−	0.192450i
$28$	−1.41580	+	2.23506i	−0.267562	+	0.422387i
$29$	−0.139785	+	0.242115i	−0.0259574	+	0.0449596i	−0.878712	−	0.477352i	$-0.841597\pi$
$29$	−0.139785	+	0.242115i	−0.0259574	+	0.0449596i	0.852755	+	0.522311i	$0.174930\pi$
$30$	−1.17103	−	0.676092i	−0.213799	−	0.123437i
$31$	2.48511	−	0.665884i	0.446339	−	0.119596i	−0.0286467	−	0.999590i	$-0.509120\pi$
$31$	2.48511	−	0.665884i	0.446339	−	0.119596i	0.474986	+	0.879993i	$0.342453\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.147349	−	0.549915i	−0.0256502	−	0.0957280i
$34$	0.689491	−	0.689491i	0.118247	−	0.118247i
$35$	−2.63140	+	2.42375i	−0.444788	+	0.409688i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	1.14587	+	1.14587i	0.188380	+	0.188380i	0.794996	−	0.606615i	$-0.207473\pi$
$37$	1.14587	+	1.14587i	0.188380	+	0.188380i	−0.606615	+	0.794996i	$0.707473\pi$
$38$	1.62574	−	2.81586i	0.263729	−	0.456793i
$39$	−3.57298	+	0.483507i	−0.572135	+	0.0774232i
$40$	−1.17103	+	0.676092i	−0.185155	+	0.106900i
$41$	2.23576	−	0.599071i	0.349168	−	0.0935592i	−0.0799726	−	0.996797i	$-0.525483\pi$
$41$	2.23576	−	0.599071i	0.349168	−	0.0935592i	0.429140	+	0.903238i	$0.358817\pi$
$42$	−1.94604	+	1.79247i	−0.300280	+	0.276584i
$43$	9.48543	−	5.47642i	1.44651	−	0.835146i	0.448243	−	0.893912i	$-0.352050\pi$
$43$	9.48543	−	5.47642i	1.44651	−	0.835146i	0.998272	+	0.0587660i	$0.0187166\pi$
$44$	−0.549915	−	0.147349i	−0.0829028	−	0.0222137i
$45$	−0.956138	−	0.956138i	−0.142533	−	0.142533i
$46$	−0.0572950	−	0.0572950i	−0.00844768	−	0.00844768i
$47$	−5.55221	−	1.48771i	−0.809873	−	0.217005i	−0.169959	−	0.985451i	$-0.554363\pi$
$47$	−5.55221	−	1.48771i	−0.809873	−	0.217005i	−0.639914	+	0.768446i	$0.721030\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	2.99100	+	6.32882i	0.427286	+	0.904117i
$50$	3.06353	−	0.820870i	0.433248	−	0.116089i
$51$	0.844450	−	0.487543i	0.118247	−	0.0682697i
$52$	−1.36776	+	3.33605i	−0.189675	+	0.462627i
$53$	−4.54058	+	7.86452i	−0.623697	+	1.08027i	0.365095	+	0.930970i	$0.381037\pi$
$53$	−4.54058	+	7.86452i	−0.623697	+	1.08027i	−0.988791	+	0.149304i	$0.952297\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−0.666681	−	0.384909i	−0.0898953	−	0.0519011i
$56$	0.579303	+	2.58155i	0.0774127	+	0.344974i
$57$	2.29914	−	2.29914i	0.304528	−	0.304528i
$58$	0.0723580	+	0.270044i	0.00950108	+	0.0354585i
$59$	5.05249	−	5.05249i	0.657778	−	0.657778i	−0.297076	−	0.954854i	$-0.596011\pi$
$59$	5.05249	−	5.05249i	0.657778	−	0.657778i	0.954854	+	0.297076i	$0.0960115\pi$
$60$	−1.30611	+	0.349971i	−0.168618	+	0.0451811i
$61$	4.95521	+	2.86089i	0.634449	+	0.366299i	0.782473	−	0.622684i	$-0.213958\pi$
$61$	4.95521	+	2.86089i	0.634449	+	0.366299i	−0.148024	+	0.988984i	$0.547291\pi$
$62$	1.28639	−	2.22809i	0.163372	−	0.282968i
$63$	−2.34365	+	1.22772i	−0.295272	+	0.154678i
$64$			1.00000i			0.125000i
$65$	−2.95397	+	3.87857i	−0.366395	+	0.481077i
$66$	−0.493040	−	0.284657i	−0.0606891	−	0.0350389i
$67$	2.09610	+	0.561649i	0.256080	+	0.0686163i	0.384575	−	0.923094i	$-0.374348\pi$
$67$	2.09610	+	0.561649i	0.256080	+	0.0686163i	−0.128495	+	0.991710i	$0.541015\pi$
$68$		−	0.975087i		−	0.118247i
$69$	−0.0405137	−	0.0701717i	−0.00487727	−	0.00844768i
$70$	−0.146835	+	3.57453i	−0.0175501	+	0.427238i
$71$	0.466117	+	0.124896i	0.0553179	+	0.0148224i	0.286372	−	0.958119i	$-0.407551\pi$
$71$	0.466117	+	0.124896i	0.0553179	+	0.0148224i	−0.231054	+	0.972941i	$0.574217\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−0.753163	−	2.81084i	−0.0881510	−	0.328984i	0.907741	−	0.419531i	$-0.137805\pi$
$73$	−0.753163	−	2.81084i	−0.0881510	−	0.328984i	−0.995892	+	0.0905465i	$0.971139\pi$
$74$	1.62051			0.188380
$75$	3.17160			0.366225
$76$	−0.841543	−	3.14068i	−0.0965316	−	0.360261i
$77$	−1.10791	+	1.02048i	−0.126258	+	0.116294i
$78$	−2.18459	+	2.86837i	−0.247356	+	0.324779i
$79$	1.45438	+	2.51907i	0.163631	+	0.283417i	0.936168	−	0.351552i	$-0.114346\pi$
$79$	1.45438	+	2.51907i	0.163631	+	0.283417i	−0.772537	+	0.634969i	$0.781013\pi$
$80$	−0.349971	+	1.30611i	−0.0391279	+	0.146027i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.15732	−	2.00453i	0.127804	−	0.221363i
$83$	−2.22649	−	2.22649i	−0.244389	−	0.244389i	0.574274	−	0.818663i	$-0.305284\pi$
$83$	−2.22649	−	2.22649i	−0.244389	−	0.244389i	−0.818663	+	0.574274i	$0.805284\pi$
$84$	−0.108591	+	2.64352i	−0.0118482	+	0.288432i
$85$	0.341252	−	1.27357i	0.0370140	−	0.138138i
$86$	2.83480	−	10.5796i	0.305685	−	1.14083i
$87$			0.279570i			0.0299730i
$88$	−0.493040	+	0.284657i	−0.0525583	+	0.0303445i
$89$	−7.48471	+	7.48471i	−0.793378	+	0.793378i	−0.982042	−	0.188664i	$-0.939584\pi$
$89$	−7.48471	+	7.48471i	−0.793378	+	0.793378i	0.188664	+	0.982042i	$0.439584\pi$
$90$	−1.35218			−0.142533
$91$	5.51979	+	7.78022i	0.578632	+	0.815589i
$92$	−0.0810273			−0.00844768
$93$	1.81923	−	1.81923i	0.188645	−	0.188645i
$94$	−4.97797	+	2.87403i	−0.513439	+	0.296434i
$95$		−	4.39659i		−	0.451081i
$96$	−0.258819	+	0.965926i	−0.0264156	+	0.0985844i
$97$	4.34344	−	16.2099i	0.441009	−	1.64587i	−0.285254	−	0.958452i	$-0.592078\pi$
$97$	4.34344	−	16.2099i	0.441009	−	1.64587i	0.726263	−	0.687417i	$-0.241255\pi$
$98$	6.59011	+	2.36019i	0.665701	+	0.238415i
$99$	−0.402566	−	0.402566i	−0.0404594	−	0.0404594i
$100$	1.58580	−	2.74668i	0.158580	−	0.274668i
$101$	−0.782628	−	1.35555i	−0.0778744	−	0.134882i	0.824458	−	0.565923i	$-0.191480\pi$
$101$	−0.782628	−	1.35555i	−0.0778744	−	0.134882i	−0.902333	+	0.431040i	$0.858147\pi$
$102$	0.252371	−	0.941862i	0.0249885	−	0.0932582i
$103$	3.08156	+	5.33742i	0.303635	+	0.525911i	0.976957	−	0.213439i	$-0.0684663\pi$
$103$	3.08156	+	5.33742i	0.303635	+	0.525911i	−0.673321	+	0.739350i	$0.735133\pi$
$104$	1.39179	+	3.32610i	0.136476	+	0.326151i
$105$	−1.06699	+	3.41473i	−0.104127	+	0.333243i
$106$	2.35038	+	8.77173i	0.228289	+	0.851986i
$107$	−14.0690			−1.36010			−0.680050	−	0.733166i	$-0.738042\pi$
$107$	−14.0690			−1.36010			−0.680050	+	0.733166i	$0.738042\pi$
$108$	−1.00000			−0.0962250
$109$	4.92259	+	18.3713i	0.471498	+	1.75966i	0.634392	+	0.773012i	$0.281251\pi$
$109$	4.92259	+	18.3713i	0.471498	+	1.75966i	−0.162893	+	0.986644i	$0.552083\pi$
$110$	−0.743587	+	0.199243i	−0.0708982	+	0.0189971i
$111$	1.56529	+	0.419419i	0.148571	+	0.0398095i
$112$	2.23506	+	1.41580i	0.211193	+	0.133781i
$113$	9.09354	+	15.7505i	0.855448	+	1.48168i	0.876229	+	0.481896i	$0.160052\pi$
$113$	9.09354	+	15.7505i	0.855448	+	1.48168i	−0.0207805	+	0.999784i	$0.506615\pi$
$114$		−	3.25147i		−	0.304528i
$115$	−0.105831	−	0.0283572i	−0.00986875	−	0.00264432i
$116$	0.242115	+	0.139785i	0.0224798	+	0.0129787i
$117$	−2.85254	+	2.20522i	−0.263718	+	0.203873i
$118$		−	7.14530i		−	0.657778i
$119$	−2.17938	−	1.38053i	−0.199783	−	0.126553i
$120$	−0.676092	+	1.17103i	−0.0617185	+	0.106900i
$121$	9.24558	+	5.33794i	0.840508	+	0.485267i
$122$	5.52681	−	1.48091i	0.500374	−	0.134075i
$123$	1.63669	−	1.63669i	0.147576	−	0.147576i
$124$	−0.665884	−	2.48511i	−0.0597981	−	0.223170i
$125$	7.81318	−	7.81318i	0.698832	−	0.698832i
$126$	−0.789084	+	2.52534i	−0.0702972	+	0.224975i
$127$	7.52749	+	4.34600i	0.667957	+	0.385645i	0.795302	−	0.606213i	$-0.207312\pi$
$127$	7.52749	+	4.34600i	0.667957	+	0.385645i	−0.127345	+	0.991858i	$0.540646\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	5.47642	−	9.48543i	0.482172	−	0.835146i
$130$	0.653791	+	4.83133i	0.0573413	+	0.423736i
$131$	−5.23185	+	3.02061i	−0.457109	+	0.263912i	−0.710828	−	0.703366i	$-0.751679\pi$
$131$	−5.23185	+	3.02061i	−0.457109	+	0.263912i	0.253719	+	0.967278i	$0.418346\pi$
$132$	−0.549915	+	0.147349i	−0.0478640	+	0.0128251i
$133$	−8.21108	−	2.56569i	−0.711991	−	0.222473i
$134$	1.87931	−	1.08502i	0.162348	−	0.0937316i
$135$	−1.30611	−	0.349971i	−0.112412	−	0.0301207i
$136$	−0.689491	−	0.689491i	−0.0591233	−	0.0591233i
$137$	3.11795	+	3.11795i	0.266384	+	0.266384i	0.827641	−	0.561257i	$-0.189682\pi$
$137$	3.11795	+	3.11795i	0.266384	+	0.266384i	−0.561257	+	0.827641i	$0.689682\pi$
$138$	−0.0782664	−	0.0209714i	−0.00666248	−	0.00178521i
$139$	3.93291	−	2.27067i	0.333585	−	0.192596i	−0.323846	−	0.946110i	$-0.604976\pi$
$139$	3.93291	−	2.27067i	0.333585	−	0.192596i	0.657432	+	0.753514i	$0.271643\pi$
$140$	2.42375	+	2.63140i	0.204844	+	0.222394i
$141$	−5.55221	+	1.48771i	−0.467580	+	0.125288i
$142$	0.417909	−	0.241280i	0.0350702	−	0.0202478i
$143$	−1.24372	+	1.63301i	−0.104005	+	0.136559i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.267308	+	0.267308i	0.0221987	+	0.0221987i
$146$	−2.52013	−	1.45500i	−0.208568	−	0.120417i
$147$	5.75469	+	3.98541i	0.474639	+	0.328711i
$148$	1.14587	−	1.14587i	0.0941902	−	0.0941902i
$149$	−2.95481	−	11.0275i	−0.242068	−	0.903409i	−0.974835	−	0.222929i	$-0.928438\pi$
$149$	−2.95481	−	11.0275i	−0.242068	−	0.903409i	0.732767	−	0.680480i	$-0.238229\pi$
$150$	2.24266	−	2.24266i	0.183112	−	0.183112i
$151$	−2.29225	+	0.614206i	−0.186541	+	0.0499834i	−0.350880	−	0.936420i	$-0.614117\pi$
$151$	−2.29225	+	0.614206i	−0.186541	+	0.0499834i	0.164339	+	0.986404i	$0.447451\pi$
$152$	−2.81586	−	1.62574i	−0.228396	−	0.131865i
$153$	0.487543	−	0.844450i	0.0394156	−	0.0682697i
$154$	−0.0618222	+	1.50499i	−0.00498178	+	0.121276i
$155$		−	3.47887i		−	0.279429i
$156$	0.483507	+	3.57298i	0.0387116	+	0.286068i
$157$	−15.0264	−	8.67548i	−1.19924	−	0.692379i	−0.238851	−	0.971056i	$-0.576771\pi$
$157$	−15.0264	−	8.67548i	−1.19924	−	0.692379i	−0.960385	+	0.278677i	$0.910104\pi$
$158$	2.80965	+	0.752844i	0.223524	+	0.0598931i
$159$			9.08116i			0.720183i
$160$	0.676092	+	1.17103i	0.0534498	+	0.0925777i
$161$	−0.114719	+	0.181101i	−0.00904111	+	0.0142728i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	8.19581	−	2.19606i	0.641946	−	0.172009i	0.0768612	−	0.997042i	$-0.475510\pi$
$163$	8.19581	−	2.19606i	0.641946	−	0.172009i	0.565085	+	0.825033i	$0.308844\pi$
$164$	−0.599071	−	2.23576i	−0.0467796	−	0.174584i
$165$	−0.769817			−0.0599302
$166$	−3.14874			−0.244389
$167$	−4.82117	−	17.9928i	−0.373073	−	1.39233i	−0.856140	−	0.516744i	$-0.827144\pi$
$167$	−4.82117	−	17.9928i	−0.373073	−	1.39233i	0.483067	−	0.875583i	$-0.339523\pi$
$168$	1.79247	+	1.94604i	0.138292	+	0.150140i
$169$	9.25845	+	9.12585i	0.712189	+	0.701988i
$170$	−0.659248	−	1.14185i	−0.0505620	−	0.0875760i
$171$	0.841543	−	3.14068i	0.0643544	−	0.240174i
$172$	−5.47642	−	9.48543i	−0.417573	−	0.723257i
$173$	−5.12325	+	8.87374i	−0.389514	+	0.674658i	−0.992384	−	0.123182i	$-0.960690\pi$
$173$	−5.12325	+	8.87374i	−0.389514	+	0.674658i	0.602870	+	0.797839i	$0.294024\pi$
$174$	0.197686	+	0.197686i	0.0149865	+	0.0149865i
$175$	−3.89383	−	7.43313i	−0.294346	−	0.561891i
$176$	−0.147349	+	0.549915i	−0.0111069	+	0.0414514i
$177$	1.84934	−	6.90183i	0.139005	−	0.518773i
$178$			10.5850i			0.793378i
$179$	4.46938	−	2.58040i	0.334057	−	0.192868i	−0.323584	−	0.946199i	$-0.604888\pi$
$179$	4.46938	−	2.58040i	0.334057	−	0.192868i	0.657641	+	0.753332i	$0.271554\pi$
$180$	−0.956138	+	0.956138i	−0.0712664	+	0.0712664i
$181$	4.50812			0.335086			0.167543	−	0.985865i	$-0.446417\pi$
$181$	4.50812			0.335086			0.167543	+	0.985865i	$0.446417\pi$
$182$	9.40453	+	1.59837i	0.697110	+	0.118479i
$183$	5.72178			0.422966
$184$	−0.0572950	+	0.0572950i	−0.00422384	+	0.00422384i
$185$	1.89766	−	1.09561i	0.139519	−	0.0805511i
$186$		−	2.57278i		−	0.188645i
$187$	0.143678	−	0.536215i	0.0105068	−	0.0392119i
$188$	−1.48771	+	5.55221i	−0.108502	+	0.404936i
$189$	−1.41580	+	2.23506i	−0.102985	+	0.162577i
$190$	−3.10886	−	3.10886i	−0.225540	−	0.225540i
$191$	−7.27654	+	12.6033i	−0.526512	+	0.911945i	0.473011	+	0.881056i	$0.343167\pi$
$191$	−7.27654	+	12.6033i	−0.526512	+	0.911945i	−0.999523	+	0.0308887i	$0.990166\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−5.56289	+	20.7610i	−0.400425	+	1.49441i	0.411914	+	0.911223i	$0.364860\pi$
$193$	−5.56289	+	20.7610i	−0.400425	+	1.49441i	−0.812339	+	0.583185i	$0.801806\pi$
$194$	−8.39088	−	14.5334i	−0.602430	−	1.04344i
$195$	−0.618927	+	4.83592i	−0.0443223	+	0.346308i
$196$	6.32882	−	2.99100i	0.452058	−	0.213643i
$197$	3.63389	+	13.5619i	0.258904	+	0.966243i	0.965877	+	0.259002i	$0.0833937\pi$
$197$	3.63389	+	13.5619i	0.258904	+	0.966243i	−0.706973	+	0.707241i	$0.749940\pi$
$198$	−0.569314			−0.0404594
$199$	5.11700			0.362735			0.181367	−	0.983415i	$-0.441948\pi$
$199$	5.11700			0.362735			0.181367	+	0.983415i	$0.441948\pi$
$200$	−0.820870	−	3.06353i	−0.0580443	−	0.216624i
$201$	2.09610	−	0.561649i	0.147848	−	0.0396156i
$202$	−1.51192	−	0.405118i	−0.106378	−	0.0285040i
$203$	0.655215	−	0.343233i	0.0459871	−	0.0240903i
$204$	−0.487543	−	0.844450i	−0.0341349	−	0.0591233i
$205$		−	3.12981i		−	0.218595i
$206$	5.95312	+	1.59513i	0.414773	+	0.111138i
$207$	−0.0701717	−	0.0405137i	−0.00487727	−	0.00281589i
$208$	3.33605	+	1.36776i	0.231313	+	0.0948373i
$209$		−	1.85111i		−	0.128044i
$210$	1.66010	+	3.16905i	0.114558	+	0.218685i
$211$	5.94537	−	10.2977i	0.409296	−	0.708922i	−0.585515	−	0.810662i	$-0.699108\pi$
$211$	5.94537	−	10.2977i	0.409296	−	0.708922i	0.994811	+	0.101740i	$0.0324408\pi$
$212$	7.86452	+	4.54058i	0.540137	+	0.311848i
$213$	0.466117	−	0.124896i	0.0319378	−	0.00855771i
$214$	−9.94827	+	9.94827i	−0.680050	+	0.680050i
$215$	−3.83317	−	14.3056i	−0.261420	−	0.975634i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−6.49714	−	2.03014i	−0.441055	−	0.137815i
$218$	16.4713	+	9.50971i	1.11558	+	0.644079i
$219$	−2.05768	−	2.05768i	−0.139045	−	0.139045i
$220$	−0.384909	+	0.666681i	−0.0259505	+	0.0449477i
$221$	−3.25294	−	1.33369i	−0.218816	−	0.0897135i
$222$	1.40340	−	0.810255i	0.0941902	−	0.0543807i
$223$	−7.79102	+	2.08760i	−0.521725	+	0.139796i	−0.510065	−	0.860136i	$-0.670378\pi$
$223$	−7.79102	+	2.08760i	−0.521725	+	0.139796i	−0.0116608	+	0.999932i	$0.503712\pi$
$224$	2.58155	−	0.579303i	0.172487	−	0.0387063i
$225$	2.74668	−	1.58580i	0.183112	−	0.105720i
$226$	17.5674	+	4.70716i	1.16856	+	0.313116i
$227$	−11.4528	−	11.4528i	−0.760147	−	0.760147i	0.216202	−	0.976349i	$-0.430633\pi$
$227$	−11.4528	−	11.4528i	−0.760147	−	0.760147i	−0.976349	+	0.216202i	$0.930633\pi$
$228$	−2.29914	−	2.29914i	−0.152264	−	0.152264i
$229$	−25.9148	−	6.94386i	−1.71250	−	0.458863i	−0.736465	−	0.676475i	$-0.763507\pi$
$229$	−25.9148	−	6.94386i	−1.71250	−	0.458863i	−0.976035	+	0.217612i	$0.930173\pi$
$230$	−0.0948851	+	0.0547819i	−0.00625654	+	0.00361221i
$231$	−0.449237	+	1.43771i	−0.0295576	+	0.0945945i
$232$	0.270044	−	0.0723580i	0.0177292	−	0.00475054i
$233$	−22.8801	+	13.2098i	−1.49893	+	0.865406i	−0.999999	−	0.00123761i	$-0.999606\pi$
$233$	−22.8801	+	13.2098i	−1.49893	+	0.865406i	−0.498928	+	0.866644i	$0.666273\pi$
$234$	−0.457724	+	3.57638i	−0.0299224	+	0.233795i
$235$	−3.88622	+	6.73113i	−0.253509	+	0.439091i
$236$	−5.05249	−	5.05249i	−0.328889	−	0.328889i
$237$	2.51907	+	1.45438i	0.163631	+	0.0944723i
$238$	−2.51724	+	0.564871i	−0.163168	+	0.0366152i
$239$	7.85321	−	7.85321i	0.507982	−	0.507982i	−0.405925	−	0.913907i	$-0.633050\pi$
$239$	7.85321	−	7.85321i	0.507982	−	0.507982i	0.913907	+	0.405925i	$0.133050\pi$
$240$	0.349971	+	1.30611i	0.0225905	+	0.0843090i
$241$	3.21958	−	3.21958i	0.207392	−	0.207392i	−0.595766	−	0.803158i	$-0.703152\pi$
$241$	3.21958	−	3.21958i	0.207392	−	0.207392i	0.803158	+	0.595766i	$0.203152\pi$
$242$	10.3121	−	2.76312i	0.662888	−	0.177620i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	2.86089	−	4.95521i	0.183150	−	0.317225i
$245$	9.31289	−	1.69167i	0.594979	−	0.108077i
$246$		−	2.31463i		−	0.147576i
$247$	−11.6285	−	1.48828i	−0.739904	−	0.0946969i
$248$	−2.22809	−	1.28639i	−0.141484	−	0.0816858i
$249$	−3.04145	−	0.814953i	−0.192744	−	0.0516455i
$250$		−	11.0495i		−	0.698832i
$251$	−4.91255	−	8.50878i	−0.310077	−	0.537069i	0.668302	−	0.743890i	$-0.267022\pi$
$251$	−4.91255	−	8.50878i	−0.310077	−	0.537069i	−0.978379	+	0.206821i	$0.933688\pi$
$252$	1.22772	+	2.34365i	0.0773390	+	0.147636i
$253$	−0.0445582	−	0.0119393i	−0.00280135	−	0.000750619i
$254$	8.39582	−	2.24965i	0.526801	−	0.141156i
$255$	−0.341252	−	1.27357i	−0.0213700	−	0.0797541i
$256$	1.00000			0.0625000
$257$	−12.9950			−0.810603			−0.405302	−	0.914183i	$-0.632834\pi$
$257$	−12.9950			−0.810603			−0.405302	+	0.914183i	$0.632834\pi$
$258$	−2.83480	−	10.5796i	−0.176487	−	0.658659i
$259$	−0.938766	−	4.18343i	−0.0583321	−	0.259946i
$260$	3.87857	+	2.95397i	0.240539	+	0.183197i
$261$	0.139785	+	0.242115i	0.00865247	+	0.0149865i
$262$	−1.56358	+	5.83537i	−0.0965984	+	0.360510i
$263$	−9.75096	−	16.8892i	−0.601270	−	1.04143i	−0.992629	−	0.121192i	$-0.961328\pi$
$263$	−9.75096	−	16.8892i	−0.601270	−	1.04143i	0.391359	−	0.920238i	$-0.372005\pi$
$264$	−0.284657	+	0.493040i	−0.0175194	+	0.0303445i
$265$	8.68285	+	8.68285i	0.533383	+	0.533383i
$266$	−7.62032	+	3.99189i	−0.467232	+	0.244759i
$267$	−2.73959	+	10.2243i	−0.167660	+	0.625717i
$268$	0.561649	−	2.09610i	0.0343082	−	0.128040i
$269$			29.5050i			1.79895i	0.436973	+	0.899475i	$0.356050\pi$
$269$			29.5050i			1.79895i	−0.436973	+	0.899475i	$0.643950\pi$
$270$	−1.17103	+	0.676092i	−0.0712664	+	0.0411456i
$271$	−5.32799	+	5.32799i	−0.323652	+	0.323652i	−0.850166	−	0.526514i	$-0.823499\pi$
$271$	−5.32799	+	5.32799i	−0.323652	+	0.323652i	0.526514	+	0.850166i	$0.323499\pi$
$272$	−0.975087			−0.0591233
$273$	8.67039	+	3.97797i	0.524756	+	0.240758i
$274$	4.40944			0.266384
$275$	1.27678	−	1.27678i	0.0769926	−	0.0769926i
$276$	−0.0701717	+	0.0405137i	−0.00422384	+	0.00243864i
$277$		−	7.86162i		−	0.472359i	−0.971709	−	0.236179i	$-0.924105\pi$
$277$		−	7.86162i		−	0.472359i	0.971709	−	0.236179i	$-0.0758953\pi$
$278$	1.17538	−	4.38659i	0.0704949	−	0.263090i
$279$	0.665884	−	2.48511i	0.0398654	−	0.148780i
$280$	3.57453	+	0.146835i	0.213619	+	0.00877505i
$281$	−14.1756	−	14.1756i	−0.845648	−	0.845648i	0.143939	−	0.989587i	$-0.454023\pi$
$281$	−14.1756	−	14.1756i	−0.845648	−	0.845648i	−0.989587	+	0.143939i	$0.954023\pi$
$282$	−2.87403	+	4.97797i	−0.171146	+	0.296434i
$283$	−9.90772	−	17.1607i	−0.588953	−	1.02010i	−0.994370	−	0.105965i	$-0.966207\pi$
$283$	−9.90772	−	17.1607i	−0.588953	−	1.02010i	0.405417	−	0.914132i	$-0.367126\pi$
$284$	0.124896	−	0.466117i	0.00741120	−	0.0276590i
$285$	−2.19829	−	3.80756i	−0.130216	−	0.225540i
$286$	0.275268	+	2.03415i	0.0162769	+	0.120282i
$287$	−5.84524	−	1.82644i	−0.345033	−	0.107811i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−16.0492			−0.944071
$290$	0.378030			0.0221987
$291$	−4.34344	−	16.2099i	−0.254617	−	0.950243i
$292$	−2.81084	+	0.753163i	−0.164492	+	0.0440755i
$293$	28.8649	+	7.73434i	1.68631	+	0.451845i	0.969433	−	0.245357i	$-0.0789053\pi$
$293$	28.8649	+	7.73434i	1.68631	+	0.451845i	0.716875	+	0.697202i	$0.245572\pi$
$294$	6.88729	−	1.25107i	0.401675	−	0.0729638i
$295$	−4.83088	−	8.36733i	−0.281265	−	0.487165i
$296$		−	1.62051i		−	0.0941902i
$297$	−0.549915	−	0.147349i	−0.0319093	−	0.00855008i
$298$	−9.88700	−	5.70826i	−0.572738	−	0.330671i
$299$	−0.110826	+	0.270311i	−0.00640924	+	0.0156325i
$300$		−	3.17160i		−	0.183112i
$301$	−28.9541	−	1.18938i	−1.66888	−	0.0685545i
$302$	−1.18656	+	2.05517i	−0.0682786	+	0.118262i
$303$	−1.35555	−	0.782628i	−0.0778744	−	0.0449608i
$304$	−3.14068	+	0.841543i	−0.180130	+	0.0482658i
$305$	5.47081	−	5.47081i	0.313258	−	0.313258i
$306$	−0.252371	−	0.941862i	−0.0144271	−	0.0538426i
$307$	1.31631	−	1.31631i	0.0751256	−	0.0751256i	−0.668546	−	0.743671i	$-0.733083\pi$
$307$	1.31631	−	1.31631i	0.0751256	−	0.0751256i	0.743671	+	0.668546i	$0.233083\pi$
$308$	1.02048	+	1.10791i	0.0581471	+	0.0631288i
$309$	5.33742	+	3.08156i	0.303635	+	0.175304i
$310$	−2.45993	−	2.45993i	−0.139715	−	0.139715i
$311$	11.9503	−	20.6986i	0.677641	−	1.17371i	−0.298049	−	0.954551i	$-0.596336\pi$
$311$	11.9503	−	20.6986i	0.677641	−	1.17371i	0.975689	−	0.219158i	$-0.0703309\pi$
$312$	2.86837	+	2.18459i	0.162390	+	0.123678i
$313$	3.83190	−	2.21235i	0.216592	−	0.125049i	−0.387779	−	0.921752i	$-0.626758\pi$
$313$	3.83190	−	2.21235i	0.216592	−	0.125049i	0.604371	+	0.796703i	$0.293424\pi$
$314$	−16.7597	+	4.49076i	−0.945807	+	0.253428i
$315$	0.783325	+	3.49073i	0.0441353	+	0.196680i
$316$	2.51907	−	1.45438i	0.141709	−	0.0818154i
$317$	−13.0878	−	3.50687i	−0.735086	−	0.196966i	−0.128193	−	0.991749i	$-0.540918\pi$
$317$	−13.0878	−	3.50687i	−0.735086	−	0.196966i	−0.606893	+	0.794784i	$0.707584\pi$
$318$	6.42135	+	6.42135i	0.360091	+	0.360091i
$319$	0.112545	+	0.112545i	0.00630133	+	0.00630133i
$320$	1.30611	+	0.349971i	0.0730137	+	0.0195640i
$321$	−12.1841	+	7.03449i	−0.680050	+	0.392627i
$322$	0.0469394	+	0.209176i	0.00261583	+	0.0116569i
$323$	3.06244	−	0.820578i	0.170399	−	0.0456582i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−6.99408	−	9.04712i	−0.387962	−	0.501844i
$326$	4.24247	−	7.34817i	0.234968	−	0.406977i
$327$	13.4488	+	13.4488i	0.743718	+	0.743718i
$328$	−2.00453	−	1.15732i	−0.110682	−	0.0639021i
$329$	10.3032	+	11.1860i	0.568035	+	0.616702i
$330$	−0.544343	+	0.544343i	−0.0299651	+	0.0299651i
$331$	−4.49089	−	16.7602i	−0.246842	−	0.921226i	−0.972449	−	0.233117i	$-0.925108\pi$
$331$	−4.49089	−	16.7602i	−0.246842	−	0.921226i	0.725607	−	0.688109i	$-0.241559\pi$
$332$	−2.22649	+	2.22649i	−0.122195	+	0.122195i
$333$	1.56529	−	0.419419i	0.0857775	−	0.0229840i
$334$	−16.1319	−	9.31378i	−0.882700	−	0.509627i
$335$	1.46715	−	2.54118i	0.0801589	−	0.138839i
$336$	2.64352	+	0.108591i	0.144216	+	0.00592411i
$337$		−	11.6579i		−	0.635046i	−0.948251	−	0.317523i	$-0.897149\pi$
$337$		−	11.6579i		−	0.635046i	0.948251	−	0.317523i	$-0.102851\pi$
$338$	12.9997	−	0.0937644i	0.707088	−	0.00510011i
$339$	15.7505	+	9.09354i	0.855448	+	0.493893i
$340$	−1.27357	−	0.341252i	−0.0690690	−	0.0185070i
$341$		−	1.46472i		−	0.0793190i
$342$	−1.62574	−	2.81586i	−0.0879098	−	0.152264i
$343$	2.27528	−	18.3800i	0.122854	−	0.992425i
$344$	−10.5796	−	2.83480i	−0.570415	−	0.152842i
$345$	−0.105831	+	0.0283572i	−0.00569773	+	0.00152670i
$346$	2.65199	+	9.89737i	0.142572	+	0.532086i
$347$	−1.26554			−0.0679380			−0.0339690	−	0.999423i	$-0.510815\pi$
$347$	−1.26554			−0.0679380			−0.0339690	+	0.999423i	$0.510815\pi$
$348$	0.279570			0.0149865
$349$	1.87703	+	7.00518i	0.100475	+	0.374979i	0.997793	−	0.0664071i	$-0.0211536\pi$
$349$	1.87703	+	7.00518i	0.100475	+	0.374979i	−0.897317	+	0.441386i	$0.854487\pi$
$350$	−8.00937	−	2.50266i	−0.428119	−	0.133773i
$351$	−1.36776	+	3.33605i	−0.0730058	+	0.178065i
$352$	0.284657	+	0.493040i	0.0151723	+	0.0262791i
$353$	−5.70254	+	21.2822i	−0.303515	+	1.13274i	0.630700	+	0.776027i	$0.282768\pi$
$353$	−5.70254	+	21.2822i	−0.303515	+	1.13274i	−0.934216	+	0.356709i	$0.883899\pi$
$354$	−3.57265	−	6.18801i	−0.189884	−	0.328889i
$355$	0.326255	−	0.565090i	0.0173158	−	0.0299919i
$356$	7.48471	+	7.48471i	0.396689	+	0.396689i
$357$	−2.57766	−	0.105885i	−0.136424	−	0.00560405i
$358$	1.33571	−	4.98494i	0.0705945	−	0.263462i
$359$	−2.11011	+	7.87503i	−0.111367	+	0.415628i	−0.998990	−	0.0449440i	$-0.985689\pi$
$359$	−2.11011	+	7.87503i	−0.111367	+	0.415628i	0.887622	+	0.460572i	$0.152356\pi$
$360$			1.35218i			0.0712664i
$361$	−7.29879	+	4.21396i	−0.384147	+	0.221787i
$362$	3.18772	−	3.18772i	0.167543	−	0.167543i
$363$	10.6759			0.560338
$364$	7.78022	−	5.51979i	0.407795	−	0.289316i
$365$	−3.93485			−0.205960
$366$	4.04591	−	4.04591i	0.211483	−	0.211483i
$367$	−25.9553	+	14.9853i	−1.35485	+	0.782225i	−0.988925	−	0.148417i	$-0.952582\pi$
$367$	−25.9553	+	14.9853i	−1.35485	+	0.782225i	−0.365929	+	0.930643i	$0.619249\pi$
$368$			0.0810273i			0.00422384i
$369$	0.599071	−	2.23576i	0.0311864	−	0.116389i
$370$	0.567131	−	2.11656i	0.0294837	−	0.110035i
$371$	21.2831	−	11.1491i	1.10496	−	0.578833i
$372$	−1.81923	−	1.81923i	−0.0943226	−	0.0943226i
$373$	4.61192	−	7.98809i	0.238796	−	0.413607i	−0.721573	−	0.692339i	$-0.756580\pi$
$373$	4.61192	−	7.98809i	0.238796	−	0.413607i	0.960369	+	0.278731i	$0.0899138\pi$
$374$	−0.277565	−	0.480757i	−0.0143526	−	0.0248594i
$375$	2.85982	−	10.6730i	0.147681	−	0.551151i
$376$	2.87403	+	4.97797i	0.148217	+	0.256719i
$377$	0.797485	−	0.616514i	0.0410726	−	0.0317521i
$378$	0.579303	+	2.58155i	0.0297961	+	0.132781i
$379$	0.121145	+	0.452118i	0.00622278	+	0.0232237i	0.968967	−	0.247188i	$-0.0795067\pi$
$379$	0.121145	+	0.452118i	0.00622278	+	0.0232237i	−0.962745	+	0.270412i	$0.912840\pi$
$380$	−4.39659			−0.225540
$381$	8.69200			0.445304
$382$	3.76661	+	14.0572i	0.192717	+	0.719228i
$383$	3.42760	−	0.918423i	0.175142	−	0.0469292i	−0.170182	−	0.985413i	$-0.554436\pi$
$383$	3.42760	−	0.918423i	0.175142	−	0.0469292i	0.345324	+	0.938483i	$0.387769\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	0.945119	+	1.80418i	0.0481677	+	0.0919498i
$386$	10.7467	+	18.6138i	0.546991	+	0.947416i
$387$		−	10.9528i		−	0.556764i
$388$	−16.2099	−	4.34344i	−0.822934	−	0.220505i
$389$	23.1285	+	13.3533i	1.17266	+	0.677037i	0.954306	−	0.298832i	$-0.0965969\pi$
$389$	23.1285	+	13.3533i	1.17266	+	0.677037i	0.218357	+	0.975869i	$0.429930\pi$
$390$	2.98187	+	3.85716i	0.150993	+	0.195315i
$391$		−	0.0790087i		−	0.00399564i
$392$	2.36019	−	6.59011i	0.119208	−	0.332851i
$393$	−3.02061	+	5.23185i	−0.152370	+	0.263912i
$394$	12.1592	+	7.02014i	0.612574	+	0.353670i
$395$	3.79917	−	1.01798i	0.191157	−	0.0512203i
$396$	−0.402566	+	0.402566i	−0.0202297	+	0.0202297i
$397$	0.873743	+	3.26085i	0.0438519	+	0.163658i	0.984379	−	0.176060i	$-0.0563352\pi$
$397$	0.873743	+	3.26085i	0.0438519	+	0.163658i	−0.940528	+	0.339717i	$0.889669\pi$
$398$	3.61827	−	3.61827i	0.181367	−	0.181367i
$399$	−8.39385	+	1.88359i	−0.420218	+	0.0942974i
$400$	−2.74668	−	1.58580i	−0.137334	−	0.0792900i
$401$	9.52478	+	9.52478i	0.475645	+	0.475645i	0.903736	−	0.428091i	$-0.140814\pi$
$401$	9.52478	+	9.52478i	0.475645	+	0.475645i	−0.428091	+	0.903736i	$0.640814\pi$
$402$	1.08502	−	1.87931i	0.0541160	−	0.0937316i
$403$	−9.20123	−	1.17762i	−0.458346	−	0.0586616i
$404$	−1.35555	+	0.782628i	−0.0674412	+	0.0389372i
$405$	−1.30611	+	0.349971i	−0.0649011	+	0.0173902i
$406$	0.220604	−	0.706009i	0.0109484	−	0.0350387i
$407$	0.798977	−	0.461289i	0.0396038	−	0.0228653i
$408$	−0.941862	−	0.252371i	−0.0466291	−	0.0124942i
$409$	−24.9996	−	24.9996i	−1.23615	−	1.23615i	−0.961561	−	0.274591i	$-0.911458\pi$
$409$	−24.9996	−	24.9996i	−1.23615	−	1.23615i	−0.274591	−	0.961561i	$-0.588542\pi$
$410$	−2.21311	−	2.21311i	−0.109298	−	0.109298i
$411$	4.25919	+	1.14125i	0.210091	+	0.0562936i
$412$	5.33742	−	3.08156i	0.262956	−	0.151818i
$413$	−18.4460	+	4.13929i	−0.907666	+	0.203681i
$414$	−0.0782664	+	0.0209714i	−0.00384658	+	0.00103069i
$415$	−3.68725	+	2.12883i	−0.181000	+	0.104500i
$416$	3.32610	−	1.39179i	0.163075	−	0.0682381i
$417$	2.27067	−	3.93291i	0.111195	−	0.192596i
$418$	−1.30893	−	1.30893i	−0.0640220	−	0.0640220i
$419$	20.6288	+	11.9100i	1.00778	+	0.581843i	0.910542	−	0.413418i	$-0.135665\pi$
$419$	20.6288	+	11.9100i	1.00778	+	0.581843i	0.0972406	+	0.995261i	$0.468998\pi$
$420$	3.41473	+	1.06699i	0.166622	+	0.0520636i
$421$	18.6380	−	18.6380i	0.908362	−	0.908362i	−0.0877779	−	0.996140i	$-0.527977\pi$
$421$	18.6380	−	18.6380i	0.908362	−	0.908362i	0.996140	+	0.0877779i	$0.0279766\pi$
$422$	−3.07755	−	11.4856i	−0.149813	−	0.559109i
$423$	−4.06450	+	4.06450i	−0.197623	+	0.197623i
$424$	8.77173	−	2.35038i	0.425993	−	0.114144i
$425$	2.67826	+	1.54629i	0.129915	+	0.0750062i
$426$	0.241280	−	0.417909i	0.0116901	−	0.0202478i
$427$	−7.02474	−	13.4099i	−0.339951	−	0.648949i
$428$			14.0690i			0.680050i
$429$	−0.260589	+	2.03608i	−0.0125813	+	0.0983030i
$430$	−12.8260	−	7.40512i	−0.618527	−	0.357107i
$431$	−4.38450	−	1.17482i	−0.211194	−	0.0565893i	0.151671	−	0.988431i	$-0.451535\pi$
$431$	−4.38450	−	1.17482i	−0.211194	−	0.0565893i	−0.362865	+	0.931842i	$0.618201\pi$
$432$			1.00000i			0.0481125i
$433$	14.8827	+	25.7776i	0.715218	+	1.23879i	0.962875	+	0.269947i	$0.0870061\pi$
$433$	14.8827	+	25.7776i	0.715218	+	1.23879i	−0.247657	+	0.968848i	$0.579661\pi$
$434$	−6.02970	+	3.15865i	−0.289435	+	0.151620i
$435$	0.365149	+	0.0978414i	0.0175076	+	0.00469113i
$436$	18.3713	−	4.92259i	0.879828	−	0.235749i
$437$	−0.0681880	−	0.254481i	−0.00326187	−	0.0121735i
$438$	−2.91000			−0.139045
$439$	7.86602			0.375425			0.187712	−	0.982224i	$-0.439893\pi$
$439$	7.86602			0.375425			0.187712	+	0.982224i	$0.439893\pi$
$440$	0.199243	+	0.743587i	0.00949856	+	0.0354491i
$441$	6.97642	+	0.574124i	0.332210	+	0.0273392i
$442$	−3.24323	+	1.35712i	−0.154265	+	0.0645514i
$443$	19.0667	+	33.0246i	0.905888	+	1.56904i	0.819720	+	0.572764i	$0.194129\pi$
$443$	19.0667	+	33.0246i	0.905888	+	1.56904i	0.0861680	+	0.996281i	$0.472538\pi$
$444$	0.419419	−	1.56529i	0.0199047	−	0.0742855i
$445$	7.15642	+	12.3953i	0.339247	+	0.587593i
$446$	−4.03293	+	6.98524i	−0.190965	+	0.330761i
$447$	−8.07270	−	8.07270i	−0.381826	−	0.381826i
$448$	1.41580	−	2.23506i	0.0668904	−	0.105597i
$449$	−6.92757	+	25.8540i	−0.326932	+	1.22013i	0.585423	+	0.810728i	$0.300928\pi$
$449$	−6.92757	+	25.8540i	−0.326932	+	1.22013i	−0.912355	+	0.409399i	$0.865738\pi$
$450$	0.820870	−	3.06353i	0.0386962	−	0.144416i
$451$		−	1.31775i		−	0.0620506i
$452$	15.7505	−	9.09354i	0.740840	−	0.427724i
$453$	−1.67804	+	1.67804i	−0.0788413	+	0.0788413i
$454$	−16.1967			−0.760147
$455$	12.0936	−	4.48660i	0.566956	−	0.210335i
$456$	−3.25147			−0.152264
$457$	3.77958	−	3.77958i	0.176801	−	0.176801i	−0.613159	−	0.789960i	$-0.710101\pi$
$457$	3.77958	−	3.77958i	0.176801	−	0.176801i	0.789960	+	0.613159i	$0.210101\pi$
$458$	−23.2346	+	13.4145i	−1.08568	+	0.626819i
$459$		−	0.975087i		−	0.0455132i
$460$	−0.0283572	+	0.105831i	−0.00132216	+	0.00493438i
$461$	9.44607	−	35.2532i	0.439947	−	1.64191i	−0.288995	−	0.957330i	$-0.593321\pi$
$461$	9.44607	−	35.2532i	0.439947	−	1.64191i	0.728943	−	0.684575i	$-0.240012\pi$
$462$	0.698958	+	1.33427i	0.0325184	+	0.0620761i
$463$	−8.27330	−	8.27330i	−0.384493	−	0.384493i	0.488225	−	0.872718i	$-0.337645\pi$
$463$	−8.27330	−	8.27330i	−0.384493	−	0.384493i	−0.872718	+	0.488225i	$0.837645\pi$
$464$	0.139785	−	0.242115i	0.00648936	−	0.0112399i
$465$	−1.73943	−	3.01279i	−0.0806643	−	0.139715i
$466$	−6.83792	+	25.5195i	−0.316761	+	1.18217i
$467$	19.1690	+	33.2016i	0.887035	+	1.53639i	0.843364	+	0.537343i	$0.180572\pi$
$467$	19.1690	+	33.2016i	0.887035	+	1.53639i	0.0436707	+	0.999046i	$0.486095\pi$
$468$	2.20522	+	2.85254i	0.101936	+	0.131859i
$469$	−3.88973	−	4.22299i	−0.179611	−	0.194999i
$470$	2.01166	+	7.50760i	0.0927908	+	0.346300i
$471$	−17.3510			−0.799490
$472$	−7.14530			−0.328889
$473$	−1.61389	−	6.02313i	−0.0742069	−	0.276944i
$474$	2.80965	−	0.752844i	0.129052	−	0.0345793i
$475$	9.96098	+	2.66904i	0.457041	+	0.122464i
$476$	−1.38053	+	2.17938i	−0.0632765	+	0.0998917i
$477$	4.54058	+	7.86452i	0.207899	+	0.360091i
$478$		−	11.1061i		−	0.507982i
$479$	21.2267	+	5.68767i	0.969872	+	0.259876i	0.708774	−	0.705436i	$-0.249249\pi$
$479$	21.2267	+	5.68767i	0.969872	+	0.259876i	0.261098	+	0.965312i	$0.415915\pi$
$480$	1.17103	+	0.676092i	0.0534498	+	0.0308592i
$481$	−2.25541	−	5.38997i	−0.102838	−	0.245762i
$482$		−	4.55318i		−	0.207392i
$483$	−0.00879882	+	0.214198i	−0.000400360	+	0.00974633i
$484$	5.33794	−	9.24558i	0.242634	−	0.420254i
$485$	−19.6519	−	11.3460i	−0.892345	−	0.515196i
$486$	−0.965926	+	0.258819i	−0.0438153	+	0.0117403i
$487$	21.3177	−	21.3177i	0.965996	−	0.965996i	−0.0334450	−	0.999441i	$-0.510648\pi$
$487$	21.3177	−	21.3177i	0.965996	−	0.965996i	0.999441	+	0.0334450i	$0.0106478\pi$
$488$	−1.48091	−	5.52681i	−0.0670374	−	0.250187i
$489$	5.99975	−	5.99975i	0.271318	−	0.271318i
$490$	5.38901	−	7.78140i	0.243451	−	0.351528i
$491$	−23.9198	−	13.8101i	−1.07949	−	0.623242i	−0.148729	−	0.988878i	$-0.547518\pi$
$491$	−23.9198	−	13.8101i	−1.07949	−	0.623242i	−0.930758	+	0.365636i	$0.880852\pi$
$492$	−1.63669	−	1.63669i	−0.0737878	−	0.0737878i
$493$	−0.136303	+	0.236083i	−0.00613876	+	0.0106326i
$494$	−9.27496	+	7.17022i	−0.417300	+	0.322603i
$495$	−0.666681	+	0.384909i	−0.0299651	+	0.0173004i
$496$	−2.48511	+	0.665884i	−0.111585	+	0.0298991i
$497$	−0.864973	−	0.939080i	−0.0387993	−	0.0421235i
$498$	−2.72689	+	1.57437i	−0.122195	+	0.0705491i
$499$	24.5835	+	6.58713i	1.10051	+	0.294881i	0.762972	−	0.646431i	$-0.223739\pi$
$499$	24.5835	+	6.58713i	1.10051	+	0.294881i	0.337537	+	0.941312i	$0.390406\pi$
$500$	−7.81318	−	7.81318i	−0.349416	−	0.349416i
$501$	−13.1717	−	13.1717i	−0.588467	−	0.588467i
$502$	−9.49031	−	2.54292i	−0.423573	−	0.113496i
$503$	−36.0023	+	20.7860i	−1.60527	+	0.926800i	−0.614855	+	0.788640i	$0.710786\pi$
$503$	−36.0023	+	20.7860i	−1.60527	+	0.926800i	−0.990410	+	0.138161i	$0.955881\pi$
$504$	2.52534	+	0.789084i	0.112488	+	0.0351486i
$505$	−2.04439	+	0.547794i	−0.0909744	+	0.0243765i
$506$	−0.0399498	+	0.0230650i	−0.00177598	+	0.00102536i
$507$	12.5810	+	3.27399i	0.558741	+	0.145403i
$508$	4.34600	−	7.52749i	0.192822	−	0.333978i
$509$	25.7173	+	25.7173i	1.13990	+	1.13990i	0.988468	+	0.151430i	$0.0483879\pi$
$509$	25.7173	+	25.7173i	1.13990	+	1.13990i	0.151430	+	0.988468i	$0.451612\pi$
$510$	−1.14185	−	0.659248i	−0.0505620	−	0.0291920i
$511$	−2.29623	+	7.34873i	−0.101579	+	0.325089i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.841543	−	3.14068i	−0.0371550	−	0.138665i
$514$	−9.18882	+	9.18882i	−0.405302	+	0.405302i
$515$	8.04971	−	2.15691i	0.354713	−	0.0950449i
$516$	−9.48543	−	5.47642i	−0.417573	−	0.241086i
$517$	−1.63623	+	2.83403i	−0.0719612	+	0.124640i
$518$	−3.62194	−	2.29432i	−0.159139	−	0.100807i
$519$			10.2465i			0.449772i
$520$	4.83133	−	0.653791i	0.211868	−	0.0286706i
$521$	6.43659	+	3.71616i	0.281992	+	0.162808i	0.634325	−	0.773067i	$-0.281278\pi$
$521$	6.43659	+	3.71616i	0.281992	+	0.162808i	−0.352333	+	0.935875i	$0.614612\pi$
$522$	0.270044	+	0.0723580i	0.0118195	+	0.00316703i
$523$			29.7255i			1.29981i	0.760017	+	0.649903i	$0.225190\pi$
$523$			29.7255i			1.29981i	−0.760017	+	0.649903i	$0.774810\pi$
$524$	3.02061	+	5.23185i	0.131956	+	0.228554i
$525$	−7.08872	−	4.49036i	−0.309377	−	0.195975i
$526$	−18.8374	−	5.04747i	−0.821350	−	0.220080i
$527$	2.42320	−	0.649295i	0.105556	−	0.0282837i
$528$	0.147349	+	0.549915i	0.00641256	+	0.0239320i
$529$	22.9934			0.999715
$530$	12.2794			0.533383
$531$	−1.84934	−	6.90183i	−0.0802545	−	0.299514i
$532$	−2.56569	+	8.21108i	−0.111237	+	0.355995i
$533$	−8.27801	−	1.05946i	−0.358560	−	0.0458905i
$534$	5.29249	+	9.16686i	0.229028	+	0.396689i
$535$	−4.92374	+	18.3756i	−0.212872	+	0.794448i
$536$	−1.08502	−	1.87931i	−0.0468658	−	0.0811740i
$537$	2.58040	−	4.46938i	0.111352	−	0.192868i
$538$	20.8632	+	20.8632i	0.899475	+	0.899475i
$539$	3.92103	−	0.712251i	0.168891	−	0.0306788i
$540$	−0.349971	+	1.30611i	−0.0150604	+	0.0562060i
$541$	−6.59240	+	24.6032i	−0.283429	+	1.05777i	0.666550	+	0.745460i	$0.267770\pi$
$541$	−6.59240	+	24.6032i	−0.283429	+	1.05777i	−0.949979	+	0.312313i	$0.898896\pi$
$542$			7.53491i			0.323652i
$543$	3.90415	−	2.25406i	0.167543	−	0.0967310i
$544$	−0.689491	+	0.689491i	−0.0295617	+	0.0295617i
$545$	25.7177			1.10163
$546$	8.94375	−	3.31804i	0.382757	−	0.141999i
$547$	14.1002			0.602880			0.301440	−	0.953485i	$-0.402533\pi$
$547$	14.1002			0.602880			0.301440	+	0.953485i	$0.402533\pi$
$548$	3.11795	−	3.11795i	0.133192	−	0.133192i
$549$	4.95521	−	2.86089i	0.211483	−	0.122100i
$550$		−	1.80564i		−	0.0769926i
$551$	−0.235270	+	0.878040i	−0.0100228	+	0.0374058i
$552$	−0.0209714	+	0.0782664i	−0.000892603	+	0.00333124i
$553$	0.315865	−	7.68939i	0.0134319	−	0.326986i
$554$	−5.55901	−	5.55901i	−0.236179	−	0.236179i
$555$	1.09561	−	1.89766i	0.0465062	−	0.0805511i
$556$	−2.27067	−	3.93291i	−0.0962978	−	0.166793i
$557$	3.86951	−	14.4412i	0.163957	−	0.611894i	−0.834214	−	0.551440i	$-0.814078\pi$
$557$	3.86951	−	14.4412i	0.163957	−	0.611894i	0.998171	−	0.0604541i	$-0.0192549\pi$
$558$	−1.28639	−	2.22809i	−0.0544572	−	0.0943226i
$559$	−39.1343	+	5.29578i	−1.65520	+	0.223987i
$560$	2.63140	−	2.42375i	0.111197	−	0.102422i
$561$	−0.143678	−	0.536215i	−0.00606611	−	0.0226390i
$562$	−20.0474			−0.845648
$563$	24.1697			1.01863			0.509316	−	0.860580i	$-0.329899\pi$
$563$	24.1697			1.01863			0.509316	+	0.860580i	$0.329899\pi$
$564$	1.48771	+	5.55221i	0.0626439	+	0.233790i
$565$	23.7543	−	6.36495i	0.999351	−	0.267775i
$566$	−19.1402	−	5.12861i	−0.804525	−	0.215572i
$567$	−0.108591	+	2.64352i	−0.00456038	+	0.111017i
$568$	−0.241280	−	0.417909i	−0.0101239	−	0.0175351i
$569$			29.4575i			1.23492i	0.786602	+	0.617461i	$0.211839\pi$
$569$			29.4575i			1.23492i	−0.786602	+	0.617461i	$0.788161\pi$
$570$	−4.24678	−	1.13792i	−0.177878	−	0.0476623i
$571$	19.6643	+	11.3532i	0.822924	+	0.475116i	0.851424	−	0.524478i	$-0.175740\pi$
$571$	19.6643	+	11.3532i	0.822924	+	0.475116i	−0.0284996	+	0.999594i	$0.509073\pi$
$572$	1.63301	+	1.24372i	0.0682794	+	0.0520025i
$573$			14.5531i			0.607963i
$574$	−5.42470	+	2.84172i	−0.226422	+	0.118611i
$575$	0.128493	−	0.222557i	0.00535853	−	0.00928125i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	4.74423	−	1.27121i	0.197505	−	0.0529212i	−0.158711	−	0.987325i	$-0.550734\pi$
$577$	4.74423	−	1.27121i	0.197505	−	0.0529212i	0.356215	+	0.934404i	$0.384067\pi$
$578$	−11.3485	+	11.3485i	−0.472035	+	0.472035i
$579$	5.56289	+	20.7610i	0.231186	+	0.862797i
$580$	0.267308	−	0.267308i	0.0110993	−	0.0110993i
$581$	1.82407	+	8.12862i	0.0756753	+	0.337232i
$582$	−14.5334	−	8.39088i	−0.602430	−	0.347813i
$583$	3.65577	+	3.65577i	0.151406	+	0.151406i
$584$	−1.45500	+	2.52013i	−0.0602083	+	0.104284i
$585$	1.88195	+	4.49750i	0.0778092	+	0.185949i
$586$	25.8796	−	14.9416i	1.06908	−	0.617231i
$587$	12.4252	−	3.32932i	0.512842	−	0.137416i	0.00688845	−	0.999976i	$-0.497807\pi$
$587$	12.4252	−	3.32932i	0.512842	−	0.137416i	0.505954	+	0.862561i	$0.331141\pi$
$588$	3.98541	−	5.75469i	0.164356	−	0.237319i
$589$	7.24458	−	4.18266i	0.298508	−	0.172343i
$590$	−9.33254	−	2.50065i	−0.384215	−	0.102950i
$591$	9.92798	+	9.92798i	0.408382	+	0.408382i
$592$	−1.14587	−	1.14587i	−0.0470951	−	0.0470951i
$593$	−11.6534	−	3.12251i	−0.478547	−	0.128226i	0.0114792	−	0.999934i	$-0.496346\pi$
$593$	−11.6534	−	3.12251i	−0.478547	−	0.128226i	−0.490026	+	0.871708i	$0.663013\pi$
$594$	−0.493040	+	0.284657i	−0.0202297	+	0.0116796i
$595$	−2.56584	+	2.36336i	−0.105189	+	0.0968884i
$596$	−11.0275	+	2.95481i	−0.451705	+	0.121034i
$597$	4.43145	−	2.55850i	0.181367	−	0.104712i
$598$	0.112773	+	0.269505i	0.00461163	+	0.0110209i
$599$	−10.2865	+	17.8168i	−0.420296	+	0.727975i	−0.995968	−	0.0897062i	$-0.971407\pi$
$599$	−10.2865	+	17.8168i	−0.420296	+	0.727975i	0.575672	+	0.817681i	$0.304741\pi$
$600$	−2.24266	−	2.24266i	−0.0915562	−	0.0915562i
$601$	20.0939	+	11.6012i	0.819648	+	0.473224i	0.850295	−	0.526306i	$-0.176423\pi$
$601$	20.0939	+	11.6012i	0.819648	+	0.473224i	−0.0306468	+	0.999530i	$0.509757\pi$
$602$	−21.3146	+	19.6326i	−0.868719	+	0.800165i
$603$	1.53445	−	1.53445i	0.0624877	−	0.0624877i
$604$	0.614206	+	2.29225i	0.0249917	+	0.0932703i
$605$	10.2076	−	10.2076i	0.414999	−	0.414999i
$606$	−1.51192	+	0.405118i	−0.0614176	+	0.0164568i
$607$	18.7551	+	10.8283i	0.761246	+	0.439505i	0.829743	−	0.558146i	$-0.188487\pi$
$607$	18.7551	+	10.8283i	0.761246	+	0.439505i	−0.0684970	+	0.997651i	$0.521820\pi$
$608$	−1.62574	+	2.81586i	−0.0659323	+	0.114198i
$609$	0.395816	−	0.624856i	0.0160393	−	0.0253205i
$610$		−	7.73690i		−	0.313258i
$611$	16.4876	+	12.5572i	0.667017	+	0.508009i
$612$	−0.844450	−	0.487543i	−0.0341349	−	0.0197078i
$613$	−38.4884	−	10.3129i	−1.55453	−	0.416536i	−0.623606	−	0.781739i	$-0.714333\pi$
$613$	−38.4884	−	10.3129i	−1.55453	−	0.416536i	−0.930928	+	0.365203i	$0.881000\pi$
$614$		−	1.86154i		−	0.0751256i
$615$	−1.56490	−	2.71049i	−0.0631030	−	0.109298i
$616$	1.50499	+	0.0618222i	0.0606380	+	0.00249089i
$617$	−18.2128	−	4.88010i	−0.733218	−	0.196465i	−0.127156	−	0.991883i	$-0.540585\pi$
$617$	−18.2128	−	4.88010i	−0.733218	−	0.196465i	−0.606062	+	0.795417i	$0.707252\pi$
$618$	5.95312	−	1.59513i	0.239469	−	0.0641656i
$619$	11.4146	+	42.5998i	0.458790	+	1.71223i	0.676699	+	0.736260i	$0.263410\pi$
$619$	11.4146	+	42.5998i	0.458790	+	1.71223i	−0.217909	+	0.975969i	$0.569924\pi$
$620$	−3.47887			−0.139715
$621$	−0.0810273			−0.00325152
$622$	−6.18594	−	23.0863i	−0.248034	−	0.925674i
$623$	27.3257	−	6.13191i	1.09478	−	0.245670i
$624$	3.57298	−	0.483507i	0.143034	−	0.0193558i
$625$	0.458516	+	0.794172i	0.0183406	+	0.0317669i
$626$	1.14520	−	4.27393i	0.0457712	−	0.170821i
$627$	−0.925555	−	1.60311i	−0.0369631	−	0.0640220i
$628$	−8.67548	+	15.0264i	−0.346189	+	0.599618i
$629$	1.11733	+	1.11733i	0.0445507	+	0.0445507i
$630$	3.02221	+	1.91443i	0.120408	+	0.0762726i
$631$	−4.22390	+	15.7638i	−0.168151	+	0.627547i	0.829467	+	0.558556i	$0.188645\pi$
$631$	−4.22390	+	15.7638i	−0.168151	+	0.627547i	−0.997617	+	0.0689908i	$0.978022\pi$
$632$	0.752844	−	2.80965i	0.0299465	−	0.111762i
$633$		−	11.8907i		−	0.472615i
$634$	−11.7342	+	6.77476i	−0.466026	+	0.269060i
$635$	8.31075	−	8.31075i	0.329802	−	0.329802i
$636$	9.08116			0.360091
$637$	−1.32181	−	25.2042i	−0.0523721	−	0.998628i
$638$	0.159163			0.00630133
$639$	0.341221	−	0.341221i	0.0134985	−	0.0134985i
$640$	1.17103	−	0.676092i	0.0462889	−	0.0267249i
$641$		−	30.6439i		−	1.21036i	−0.796089	−	0.605180i	$-0.793101\pi$
$641$		−	30.6439i		−	1.21036i	0.796089	−	0.605180i	$-0.206899\pi$
$642$	−3.64132	+	13.5896i	−0.143711	+	0.536339i
$643$	−6.79028	+	25.3417i	−0.267783	+	0.999379i	0.692742	+	0.721185i	$0.256402\pi$
$643$	−6.79028	+	25.3417i	−0.267783	+	0.999379i	−0.960525	+	0.278193i	$0.910264\pi$
$644$	0.181101	+	0.114719i	0.00713638	+	0.00452055i
$645$	−10.4724	−	10.4724i	−0.412351	−	0.412351i
$646$	1.58523	−	2.74571i	0.0623702	−	0.108028i
$647$	−17.0291	−	29.4953i	−0.669484	−	1.15958i	−0.978049	−	0.208376i	$-0.933182\pi$
$647$	−17.0291	−	29.4953i	−0.669484	−	1.15958i	0.308565	−	0.951203i	$-0.400151\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−2.03396	−	3.52292i	−0.0798399	−	0.138287i
$650$	−11.3428	−	1.45172i	−0.444903	−	0.0569410i
$651$	−6.64176	+	1.49042i	−0.260311	+	0.0584141i
$652$	−2.19606	−	8.19581i	−0.0860044	−	0.320973i
$653$	13.6892			0.535701			0.267850	−	0.963461i	$-0.413687\pi$
$653$	13.6892			0.535701			0.267850	+	0.963461i	$0.413687\pi$
$654$	19.0194			0.743718
$655$	2.11425	+	7.89049i	0.0826106	+	0.308307i
$656$	−2.23576	+	0.599071i	−0.0872919	+	0.0233898i
$657$	−2.81084	−	0.753163i	−0.109661	−	0.0293837i
$658$	15.1951	+	0.624187i	0.592368	+	0.0243333i
$659$	−20.2242	−	35.0293i	−0.787822	−	1.36455i	−0.927299	−	0.374322i	$-0.877875\pi$
$659$	−20.2242	−	35.0293i	−0.787822	−	1.36455i	0.139477	−	0.990225i	$-0.455458\pi$
$660$			0.769817i			0.0299651i
$661$	4.76881	+	1.27780i	0.185485	+	0.0497006i	0.350366	−	0.936613i	$-0.386057\pi$
$661$	4.76881	+	1.27780i	0.185485	+	0.0497006i	−0.164881	+	0.986314i	$0.552724\pi$
$662$	−15.0268	−	8.67574i	−0.584034	−	0.337192i
$663$	−3.48397	+	0.471462i	−0.135306	+	0.0183101i
$664$			3.14874i			0.122195i
$665$	−6.22471	+	9.82665i	−0.241384	+	0.381061i
$666$	0.810255	−	1.40340i	0.0313967	−	0.0543807i
$667$	0.0196179	+	0.0113264i	0.000759609	+	0.000438560i
$668$	−17.9928	+	4.82117i	−0.696164	+	0.186537i
$669$	−5.70342	+	5.70342i	−0.220507	+	0.220507i
$670$	−0.759452	−	2.83431i	−0.0293402	−	0.109499i
$671$	2.30339	−	2.30339i	0.0889215	−	0.0889215i
$672$	1.94604	−	1.79247i	0.0750700	−	0.0691459i
$673$	13.7664	+	7.94802i	0.530655	+	0.306374i	0.741283	−	0.671193i	$-0.234218\pi$
$673$	13.7664	+	7.94802i	0.530655	+	0.306374i	−0.210628	+	0.977566i	$0.567551\pi$
$674$	−8.24338	−	8.24338i	−0.317523	−	0.317523i
$675$	1.58580	−	2.74668i	0.0610374	−	0.105720i
$676$	9.12585	−	9.25845i	0.350994	−	0.356094i
$677$	16.1179	−	9.30568i	0.619462	−	0.357646i	−0.157198	−	0.987567i	$-0.550246\pi$
$677$	16.1179	−	9.30568i	0.619462	−	0.357646i	0.776659	+	0.629921i	$0.216913\pi$
$678$	17.5674	−	4.70716i	0.674671	−	0.180777i
$679$	−32.6579	+	30.0807i	−1.25330	+	1.15439i
$680$	−1.14185	+	0.659248i	−0.0437880	+	0.0252810i
$681$	−15.6448	−	4.19201i	−0.599509	−	0.160638i
$682$	−1.03571	−	1.03571i	−0.0396595	−	0.0396595i
$683$	−14.4087	−	14.4087i	−0.551334	−	0.551334i	0.375491	−	0.926826i	$-0.377474\pi$
$683$	−14.4087	−	14.4087i	−0.551334	−	0.551334i	−0.926826	+	0.375491i	$0.877474\pi$
$684$	−3.14068	−	0.841543i	−0.120087	−	0.0321772i
$685$	5.16357	−	2.98119i	0.197290	−	0.113905i
$686$	−11.3877	−	14.6055i	−0.434786	−	0.557639i
$687$	−25.9148	+	6.94386i	−0.988713	+	0.264925i
$688$	−9.48543	+	5.47642i	−0.361629	+	0.208786i
$689$	25.9044	−	20.0260i	0.986879	−	0.762929i
$690$	−0.0547819	+	0.0948851i	−0.00208551	+	0.00361221i
$691$	10.0558	+	10.0558i	0.382542	+	0.382542i	0.872017	−	0.489475i	$-0.162812\pi$
$691$	10.0558	+	10.0558i	0.382542	+	0.382542i	−0.489475	+	0.872017i	$0.662812\pi$
$692$	8.87374	+	5.12325i	0.337329	+	0.194757i
$693$	0.329806	+	1.46971i	0.0125283	+	0.0558298i
$694$	−0.894875	+	0.894875i	−0.0339690	+	0.0339690i
$695$	−1.58934	−	5.93148i	−0.0602869	−	0.224994i
$696$	0.197686	−	0.197686i	0.00749326	−	0.00749326i
$697$	2.18006	−	0.584146i	0.0825758	−	0.0221261i
$698$	6.28068	+	3.62615i	0.237727	+	0.137252i
$699$	−13.2098	+	22.8801i	−0.499642	+	0.865406i
$700$	−7.43313	+	3.89383i	−0.280946	+	0.147173i
$701$			22.7395i			0.858858i	0.903101	+	0.429429i	$0.141285\pi$
$701$			22.7395i			0.858858i	−0.903101	+	0.429429i	$0.858715\pi$
$702$	1.39179	+	3.32610i	0.0525297	+	0.125535i
$703$	4.56312	+	2.63452i	0.172102	+	0.0993629i
$704$	0.549915	+	0.147349i	0.0207257	+	0.00555344i
$705$			7.77244i			0.292727i
$706$	11.0165	+	19.0811i	0.414610	+	0.718125i
$707$	−0.169972	+	4.13779i	−0.00639246	+	0.155618i
$708$	−6.90183	−	1.84934i	−0.259387	−	0.0695024i
$709$	10.7060	−	2.86866i	0.402072	−	0.107735i	−0.0521154	−	0.998641i	$-0.516596\pi$
$709$	10.7060	−	2.86866i	0.402072	−	0.107735i	0.454187	+	0.890906i	$0.349930\pi$
$710$	−0.168882	−	0.630276i	−0.00633803	−	0.0236538i
$711$	2.90877			0.109087
$712$	10.5850			0.396689
$713$	−0.0539548	−	0.201362i	−0.00202062	−	0.00754107i
$714$	−1.89756	+	1.74781i	−0.0710142	+	0.0654102i
$715$	1.69762	+	2.19594i	0.0634873	+	0.0821234i
$716$	−2.58040	−	4.46938i	−0.0964339	−	0.167028i
$717$	2.87447	−	10.7277i	0.107349	−	0.400633i
$718$	4.07641	+	7.06056i	0.152130	+	0.263498i
$719$	−0.271876	+	0.470903i	−0.0101393	+	0.0175617i	−0.871051	−	0.491193i	$-0.836561\pi$
$719$	−0.271876	+	0.470903i	−0.0101393	+	0.0175617i	0.860911	+	0.508755i	$0.169894\pi$
$720$	0.956138	+	0.956138i	0.0356332	+	0.0356332i
$721$	0.669258	−	16.2923i	0.0249245	−	0.606758i
$722$	−2.18131	+	8.14075i	−0.0811798	+	0.302967i
$723$	1.17845	−	4.39803i	0.0438270	−	0.163565i
$724$		−	4.50812i		−	0.167543i
$725$	−0.767891	+	0.443342i	−0.0285187	+	0.0164653i
$726$	7.54899	−	7.54899i	0.280169	−	0.280169i
$727$	−34.4524			−1.27777			−0.638884	−	0.769303i	$-0.720604\pi$
$727$	−34.4524			−1.27777			−0.638884	+	0.769303i	$0.720604\pi$
$728$	1.59837	−	9.40453i	0.0592394	−	0.348555i
$729$	−1.00000			−0.0370370
$730$	−2.78236	+	2.78236i	−0.102980	+	0.102980i
$731$	9.24912	−	5.33998i	0.342091	−	0.197506i
$732$		−	5.72178i		−	0.211483i
$733$	6.73516	−	25.1359i	0.248769	−	0.928417i	−0.722683	−	0.691180i	$-0.757091\pi$
$733$	6.73516	−	25.1359i	0.248769	−	0.928417i	0.971452	−	0.237238i	$-0.0762420\pi$
$734$	−7.75695	+	28.9493i	−0.286314	+	1.06854i
$735$	7.21936	−	6.12148i	0.266290	−	0.225794i
$736$	0.0572950	+	0.0572950i	0.00211192	+	0.00211192i
$737$	0.617718	−	1.06992i	0.0227539	−	0.0394110i
$738$	−1.15732	−	2.00453i	−0.0426014	−	0.0737878i
$739$	−10.9038	+	40.6936i	−0.401103	+	1.49694i	0.410028	+	0.912073i	$0.365519\pi$
$739$	−10.9038	+	40.6936i	−0.401103	+	1.49694i	−0.811131	+	0.584864i	$0.801148\pi$
$740$	−1.09561	−	1.89766i	−0.0402755	−	0.0697593i
$741$	−10.8147	+	4.52536i	−0.397289	+	0.166243i
$742$	7.16580	−	22.9330i	0.263065	−	0.841898i
$743$	−9.68987	−	36.1631i	−0.355487	−	1.32670i	−0.879871	−	0.475213i	$-0.842371\pi$
$743$	−9.68987	−	36.1631i	−0.355487	−	1.32670i	0.524384	−	0.851482i	$-0.324296\pi$
$744$	−2.57278			−0.0943226
$745$	−15.4372			−0.565577
$746$	−2.38731	−	8.90955i	−0.0874055	−	0.326202i
$747$	−3.04145	+	0.814953i	−0.111281	+	0.0298176i
$748$	−0.536215	−	0.143678i	−0.0196060	−	0.00525340i
$749$	31.4450	+	19.9189i	1.14898	+	0.727821i
$750$	−5.52475	−	9.56915i	−0.201735	−	0.349416i
$751$			2.14295i			0.0781973i	0.999235	+	0.0390986i	$0.0124487\pi$
$751$			2.14295i			0.0781973i	−0.999235	+	0.0390986i	$0.987551\pi$
$752$	5.55221	+	1.48771i	0.202468	+	0.0542512i
$753$	−8.50878	−	4.91255i	−0.310077	−	0.179023i
$754$	0.127966	−	0.999848i	0.00466024	−	0.0364123i
$755$			3.20888i			0.116783i
$756$	2.23506	+	1.41580i	0.0812884	+	0.0514923i
$757$	13.5526	−	23.4737i	0.492577	−	0.853168i	−0.507387	−	0.861718i	$-0.669388\pi$
$757$	13.5526	−	23.4737i	0.492577	−	0.853168i	0.999963	+	0.00855073i	$0.00272181\pi$
$758$	0.405358	+	0.234034i	0.0147233	+	0.00850048i
$759$	−0.0445582	+	0.0119393i	−0.00161736	+	0.000433370i
$760$	−3.10886	+	3.10886i	−0.112770	+	0.112770i
$761$	−13.2083	−	49.2941i	−0.478801	−	1.78691i	−0.606484	−	0.795096i	$-0.707421\pi$
$761$	−13.2083	−	49.2941i	−0.478801	−	1.78691i	0.127683	−	0.991815i	$-0.459246\pi$
$762$	6.14617	−	6.14617i	0.222652	−	0.222652i
$763$	15.0079	−	48.0305i	0.543323	−	1.73882i
$764$	12.6033	+	7.27654i	0.455973	+	0.263256i
$765$	−0.932318	−	0.932318i	−0.0337080	−	0.0337080i
$766$	1.77426	−	3.07310i	0.0641065	−	0.111036i
$767$	−23.7660	+	9.94474i	−0.858139	+	0.359084i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−30.8477	+	8.26561i	−1.11240	+	0.298066i	−0.767803	−	0.640686i	$-0.778650\pi$
$769$	−30.8477	+	8.26561i	−1.11240	+	0.298066i	−0.344594	+	0.938752i	$0.611983\pi$
$770$	1.94405	+	0.607451i	0.0700587	+	0.0218910i
$771$	−11.2540	+	6.49748i	−0.405302	+	0.234001i
$772$	20.7610	+	5.56289i	0.747204	+	0.200213i
$773$	18.2405	+	18.2405i	0.656064	+	0.656064i	0.954446	−	0.298382i	$-0.0964470\pi$
$773$	18.2405	+	18.2405i	0.656064	+	0.656064i	−0.298382	+	0.954446i	$0.596447\pi$
$774$	−7.74482	−	7.74482i	−0.278382	−	0.278382i
$775$	7.88178	+	2.11192i	0.283122	+	0.0758623i
$776$	−14.5334	+	8.39088i	−0.521719	+	0.301215i
$777$	−2.90471	−	3.15357i	−0.104206	−	0.113134i
$778$	25.7965	−	6.91216i	0.924850	−	0.247813i
$779$	6.51768	−	3.76298i	0.233520	−	0.134823i
$780$	4.83592	+	0.618927i	0.173154	+	0.0221612i
$781$	0.137364	−	0.237922i	0.00491527	−	0.00851350i
$782$	−0.0558676	−	0.0558676i	−0.00199782	−	0.00199782i
$783$	0.242115	+	0.139785i	0.00865247	+	0.00499551i
$784$	−2.99100	−	6.32882i	−0.106822	−	0.226029i
$785$	−16.5899	+	16.5899i	−0.592120	+	0.592120i
$786$	1.56358	+	5.83537i	0.0557711	+	0.208141i
$787$	−5.25432	+	5.25432i	−0.187296	+	0.187296i	−0.794526	−	0.607230i	$-0.792281\pi$
$787$	−5.25432	+	5.25432i	−0.187296	+	0.187296i	0.607230	+	0.794526i	$0.292281\pi$
$788$	13.5619	−	3.63389i	0.483122	−	0.129452i
$789$	−16.8892	−	9.75096i	−0.601270	−	0.347143i
$790$	1.96659	−	3.40624i	0.0699683	−	0.121189i
$791$	1.97495	−	48.0779i	0.0702211	−	1.70945i
$792$			0.569314i			0.0202297i
$793$	−12.6178	−	16.3216i	−0.448071	−	0.579598i
$794$	2.92360	+	1.68794i	0.103755	+	0.0599028i
$795$	11.8610	+	3.17814i	0.420666	+	0.112717i
$796$		−	5.11700i		−	0.181367i
$797$	−16.4874	−	28.5569i	−0.584012	−	1.01154i	−0.994998	−	0.0998967i	$-0.968149\pi$
$797$	−16.4874	−	28.5569i	−0.584012	−	1.01154i	0.410986	−	0.911642i	$-0.365185\pi$
$798$	−4.60345	+	7.26724i	−0.162960	+	0.257258i
$799$	−5.41388	−	1.45065i	−0.191529	−	0.0513202i
$800$	−3.06353	+	0.820870i	−0.108312	+	0.0290221i
$801$	2.73959	+	10.2243i	0.0967988	+	0.361258i
$802$	13.4701			0.475645
$803$	−1.65670			−0.0584638
$804$	−0.561649	−	2.09610i	−0.0198078	−	0.0739238i
$805$	0.196390	+	0.213215i	0.00692182	+	0.00751485i
$806$	−7.33896	+	5.67355i	−0.258504	+	0.199842i
$807$	14.7525	+	25.5520i	0.519312	+	0.899475i
$808$	−0.405118	+	1.51192i	−0.0142520	+	0.0531892i
$809$	−15.9070	−	27.5517i	−0.559259	−	0.968665i	−0.997558	−	0.0698363i	$-0.977752\pi$
$809$	−15.9070	−	27.5517i	−0.559259	−	0.968665i	0.438299	−	0.898829i	$-0.355581\pi$
$810$	−0.676092	+	1.17103i	−0.0237555	+	0.0411456i
$811$	31.9059	+	31.9059i	1.12037	+	1.12037i	0.991686	+	0.128680i	$0.0410740\pi$
$811$	31.9059	+	31.9059i	1.12037	+	1.12037i	0.128680	+	0.991686i	$0.458926\pi$
$812$	−0.343233	−	0.655215i	−0.0120451	−	0.0229935i
$813$	−1.95018	+	7.27817i	−0.0683957	+	0.255256i
$814$	0.238781	−	0.891143i	0.00836927	−	0.0312345i
$815$		−	11.4732i		−	0.401888i
$816$	−0.844450	+	0.487543i	−0.0295617	+	0.0170674i
$817$	25.1821	−	25.1821i	0.881010	−	0.881010i
$818$	−35.3548			−1.23615
$819$	9.49777	−	0.890170i	0.331879	−	0.0311050i
$820$	−3.12981			−0.109298
$821$	22.2584	−	22.2584i	0.776822	−	0.776822i	−0.202467	−	0.979289i	$-0.564896\pi$
$821$	22.2584	−	22.2584i	0.776822	−	0.776822i	0.979289	+	0.202467i	$0.0648959\pi$
$822$	3.81869	−	2.20472i	0.133192	−	0.0768985i
$823$		−	11.5793i		−	0.403629i	−0.979424	−	0.201815i	$-0.935316\pi$
$823$		−	11.5793i		−	0.403629i	0.979424	−	0.201815i	$-0.0646839\pi$
$824$	1.59513	−	5.95312i	0.0555691	−	0.207387i
$825$	0.467333	−	1.74411i	0.0162704	−	0.0607221i
$826$	−10.1163	+	15.9702i	−0.351992	+	0.555674i
$827$	−37.5272	−	37.5272i	−1.30495	−	1.30495i	−0.925014	−	0.379933i	$-0.875947\pi$
$827$	−37.5272	−	37.5272i	−1.30495	−	1.30495i	−0.379933	−	0.925014i	$-0.624053\pi$
$828$	−0.0405137	+	0.0701717i	−0.00140795	+	0.00243864i
$829$	8.79365	+	15.2311i	0.305416	+	0.528996i	0.977354	−	0.211611i	$-0.0678711\pi$
$829$	8.79365	+	15.2311i	0.305416	+	0.528996i	−0.671938	+	0.740608i	$0.734538\pi$
$830$	−1.10197	+	4.11259i	−0.0382498	+	0.142750i
$831$	−3.93081	−	6.80836i	−0.136358	−	0.236179i
$832$	1.36776	−	3.33605i	0.0474186	−	0.115657i
$833$	2.91649	+	6.17115i	0.101050	+	0.213818i
$834$	−1.17538	−	4.38659i	−0.0407002	−	0.151895i
$835$	−25.1879			−0.871663
$836$	−1.85111			−0.0640220
$837$	−0.665884	−	2.48511i	−0.0230163	−	0.0858980i
$838$	23.0084	−	6.16509i	0.794813	−	0.212969i
$839$	−29.4347	−	7.88700i	−1.01620	−	0.272290i	−0.287981	−	0.957636i	$-0.592984\pi$
$839$	−29.4347	−	7.88700i	−1.01620	−	0.272290i	−0.728217	+	0.685346i	$0.759651\pi$
$840$	3.16905	−	1.66010i	0.109343	−	0.0572789i
$841$	14.4609	+	25.0470i	0.498652	+	0.863691i
$842$		−	26.3582i		−	0.908362i
$843$	−19.3643	−	5.18864i	−0.666941	−	0.178706i
$844$	−10.2977	−	5.94537i	−0.354461	−	0.204648i
$845$	15.1595	−	8.89877i	0.521504	−	0.306127i
$846$			5.74807i			0.197623i
$847$	−13.1070	−	25.0206i	−0.450361	−	0.859716i
$848$	4.54058	−	7.86452i	0.155924	−	0.270069i
$849$	−17.1607	−	9.90772i	−0.588953	−	0.340032i
$850$	2.98721	−	0.800420i	0.102460	−	0.0274542i
$851$	0.0928470	−	0.0928470i	0.00318276	−	0.00318276i
$852$	−0.124896	−	0.466117i	−0.00427886	−	0.0159689i
$853$	3.62993	−	3.62993i	0.124287	−	0.124287i	−0.642228	−	0.766514i	$-0.721990\pi$
$853$	3.62993	−	3.62993i	0.124287	−	0.124287i	0.766514	+	0.642228i	$0.221990\pi$
$854$	−14.4494	−	4.51497i	−0.494450	−	0.154499i
$855$	−3.80756	−	2.19829i	−0.130216	−	0.0751801i
$856$	9.94827	+	9.94827i	0.340025	+	0.340025i
$857$	15.3895	−	26.6554i	0.525696	−	0.910532i	−0.473856	−	0.880602i	$-0.657138\pi$
$857$	15.3895	−	26.6554i	0.525696	−	0.910532i	0.999552	−	0.0299299i	$-0.00952839\pi$
$858$	1.25546	+	1.62399i	0.0428608	+	0.0554422i
$859$	7.66671	−	4.42637i	0.261585	−	0.151026i	−0.363473	−	0.931605i	$-0.618409\pi$
$859$	7.66671	−	4.42637i	0.261585	−	0.151026i	0.625057	+	0.780579i	$0.285076\pi$
$860$	−14.3056	+	3.83317i	−0.487817	+	0.130710i
$861$	−5.97534	+	1.34087i	−0.203639	+	0.0456969i
$862$	−3.93104	+	2.26958i	−0.133892	+	0.0773024i
$863$	−41.6620	−	11.1633i	−1.41819	−	0.380003i	−0.533350	−	0.845895i	$-0.679067\pi$
$863$	−41.6620	−	11.1633i	−1.41819	−	0.380003i	−0.884842	+	0.465891i	$0.845734\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	9.79708	+	9.79708i	0.333111	+	0.333111i
$866$	28.7512	+	7.70387i	0.977006	+	0.261788i
$867$	−13.8990	+	8.02460i	−0.472035	+	0.272530i
$868$	−2.03014	+	6.49714i	−0.0689074	+	0.220527i
$869$	1.59957	−	0.428605i	0.0542619	−	0.0145394i
$870$	0.327384	−	0.189015i	0.0110993	−	0.00640821i
$871$	−6.22450	−	4.74066i	−0.210909	−	0.160631i
$872$	9.50971	−	16.4713i	0.322039	−	0.557788i
$873$	−11.8665	−	11.8665i	−0.401620	−	0.401620i
$874$	−0.228162	−	0.131729i	−0.00771768	−	0.00445580i
$875$	−28.5249	+	6.40101i	−0.964316	+	0.216394i
$876$	−2.05768	+	2.05768i	−0.0695225	+	0.0695225i
$877$	0.300512	+	1.12153i	0.0101476	+	0.0378713i	0.970814	−	0.239834i	$-0.0770929\pi$
$877$	0.300512	+	1.12153i	0.0101476	+	0.0378713i	−0.960666	+	0.277705i	$0.910426\pi$
$878$	5.56211	−	5.56211i	0.187712	−	0.187712i
$879$	28.8649	−	7.73434i	0.973590	−	0.260873i
$880$	0.666681	+	0.384909i	0.0224738	+	0.0129753i
$881$	−16.0134	+	27.7360i	−0.539505	+	0.934451i	0.459425	+	0.888216i	$0.348055\pi$
$881$	−16.0134	+	27.7360i	−0.539505	+	0.934451i	−0.998931	+	0.0462344i	$0.985278\pi$
$882$	5.33904	−	4.52710i	0.179775	−	0.152436i
$883$		−	10.0658i		−	0.338742i	−0.985552	−	0.169371i	$-0.945826\pi$
$883$		−	10.0658i		−	0.338742i	0.985552	−	0.169371i	$-0.0541736\pi$
$884$	−1.33369	+	3.25294i	−0.0448568	+	0.109408i
$885$	−8.36733	−	4.83088i	−0.281265	−	0.162388i
$886$	36.8341	+	9.86967i	1.23747	+	0.331578i
$887$			17.3532i			0.582663i	0.956622	+	0.291331i	$0.0940982\pi$
$887$			17.3532i			0.582663i	−0.956622	+	0.291331i	$0.905902\pi$
$888$	−0.810255	−	1.40340i	−0.0271904	−	0.0470951i
$889$	−10.6713	−	20.3710i	−0.357905	−	0.683222i
$890$	13.8251	+	3.70443i	0.463420	+	0.124173i
$891$	−0.549915	+	0.147349i	−0.0184229	+	0.00493639i
$892$	2.08760	+	7.79102i	0.0698979	+	0.260863i
$893$	−18.6897			−0.625427
$894$	−11.4165			−0.381826
$895$	−1.80613	−	6.74056i	−0.0603722	−	0.225312i
$896$	−0.579303	−	2.58155i	−0.0193532	−	0.0862436i
$897$	0.0391773	+	0.289509i	0.00130809	+	0.00966644i
$898$	13.3830	+	23.1801i	0.446598	+	0.773530i
$899$	−0.186161	+	0.694763i	−0.00620882	+	0.0231716i
$900$	−1.58580	−	2.74668i	−0.0528600	−	0.0915562i
$901$	−4.42746	+	7.66859i	−0.147500	+	0.255478i
$902$	−0.931792	−	0.931792i	−0.0310253	−	0.0310253i
$903$	−25.6696	+	13.4470i	−0.854232	+	0.447488i
$904$	4.70716	−	17.5674i	0.156558	−	0.584282i
$905$	1.57771	−	5.88810i	0.0524449	−	0.195727i
$906$			2.37311i			0.0788413i
$907$	6.29197	−	3.63267i	0.208921	−	0.120621i	−0.391889	−	0.920013i	$-0.628178\pi$
$907$	6.29197	−	3.63267i	0.208921	−	0.120621i	0.600810	+	0.799392i	$0.294845\pi$
$908$	−11.4528	+	11.4528i	−0.380074	+	0.380074i
$909$	−1.56526			−0.0519162
$910$	5.37895	−	11.7240i	0.178311	−	0.388646i
$911$	−40.1352			−1.32974			−0.664869	−	0.746960i	$-0.731513\pi$
$911$	−40.1352			−1.32974			−0.664869	+	0.746960i	$0.731513\pi$
$912$	−2.29914	+	2.29914i	−0.0761321	+	0.0761321i
$913$	−1.55245	+	0.896310i	−0.0513787	+	0.0296635i
$914$		−	5.34513i		−	0.176801i
$915$	2.00246	−	7.47327i	0.0661992	−	0.247059i
$916$	−6.94386	+	25.9148i	−0.229432	+	0.856250i
$917$	15.9701	+	0.656020i	0.527379	+	0.0216637i
$918$	−0.689491	−	0.689491i	−0.0227566	−	0.0227566i
$919$	29.2993	−	50.7478i	0.966493	−	1.67402i	0.260945	−	0.965354i	$-0.415966\pi$
$919$	29.2993	−	50.7478i	0.966493	−	1.67402i	0.705548	−	0.708662i	$-0.250701\pi$
$920$	0.0547819	+	0.0948851i	0.00180611	+	0.00312827i
$921$	0.481801	−	1.79811i	0.0158759	−	0.0592497i
$922$	−18.2484	−	31.6072i	−0.600979	−	1.04093i
$923$	−1.38416	−	1.05420i	−0.0455603	−	0.0346993i
$924$	1.43771	+	0.449237i	0.0472973	+	0.0147788i
$925$	1.33023	+	4.96448i	0.0437376	+	0.163231i
$926$	−11.7002			−0.384493
$927$	6.16312			0.202423
$928$	−0.0723580	−	0.270044i	−0.00237527	−	0.00886462i
$929$	−24.3923	+	6.53591i	−0.800287	+	0.214436i	−0.635710	−	0.771928i	$-0.719293\pi$
$929$	−24.3923	+	6.53591i	−0.800287	+	0.214436i	−0.164577	+	0.986364i	$0.552626\pi$
$930$	−3.36033	−	0.900397i	−0.110190	−	0.0295252i
$931$	14.7198	+	17.3597i	0.482421	+	0.568942i
$932$	13.2098	+	22.8801i	0.432703	+	0.749464i
$933$		−	23.9006i		−	0.782472i
$934$	37.0316	+	9.92259i	1.21171	+	0.324677i
$935$	−0.650072	−	0.375319i	−0.0212596	−	0.0122743i
$936$	3.57638	+	0.457724i	0.116898	+	0.0149612i
$937$		−	57.5907i		−	1.88141i	−0.339232	−	0.940703i	$-0.610167\pi$
$937$		−	57.5907i		−	1.88141i	0.339232	−	0.940703i	$-0.389833\pi$
$938$	−5.73656	−	0.235647i	−0.187305	−	0.00769413i
$939$	2.21235	−	3.83190i	0.0721973	−	0.125049i
$940$	6.73113	+	3.88622i	0.219545	+	0.126755i
$941$	−6.11763	+	1.63921i	−0.199429	+	0.0534368i	−0.357151	−	0.934047i	$-0.616252\pi$
$941$	−6.11763	+	1.63921i	−0.199429	+	0.0534368i	0.157722	+	0.987484i	$0.449585\pi$
$942$	−12.2690	+	12.2690i	−0.399745	+	0.399745i
$943$	−0.0485411	−	0.181158i	−0.00158072	−	0.00589932i
$944$	−5.05249	+	5.05249i	−0.164444	+	0.164444i
$945$	2.42375	+	2.63140i	0.0788444	+	0.0855995i
$946$	−5.40019	−	3.11780i	−0.175575	−	0.101368i
$947$	11.9774	+	11.9774i	0.389213	+	0.389213i	0.874407	−	0.485193i	$-0.161251\pi$
$947$	11.9774	+	11.9774i	0.389213	+	0.389213i	−0.485193	+	0.874407i	$0.661251\pi$
$948$	1.45438	−	2.51907i	0.0472362	−	0.0818154i
$949$	−1.33198	+	10.4073i	−0.0432378	+	0.337834i
$950$	8.93077	−	5.15618i	0.289753	−	0.167289i
$951$	−13.0878	+	3.50687i	−0.424402	+	0.113718i
$952$	0.564871	+	2.51724i	0.0183076	+	0.0815841i
$953$	−11.1246	+	6.42281i	−0.360362	+	0.208055i	−0.669240	−	0.743047i	$-0.733380\pi$
$953$	−11.1246	+	6.42281i	−0.360362	+	0.208055i	0.308878	+	0.951102i	$0.400047\pi$
$954$	8.77173	+	2.35038i	0.283995	+	0.0760963i
$955$	13.9148	+	13.9148i	0.450271	+	0.450271i
$956$	−7.85321	−	7.85321i	−0.253991	−	0.253991i
$957$	0.153740	+	0.0411945i	0.00496970	+	0.00133163i
$958$	19.0313	−	10.9877i	0.614874	−	0.354998i
$959$	−2.55440	−	11.3832i	−0.0824860	−	0.367583i
$960$	1.30611	−	0.349971i	0.0421545	−	0.0112953i
$961$	−21.1144	+	12.1904i	−0.681110	+	0.393239i
$962$	−5.40610	−	2.21647i	−0.174300	−	0.0714619i
$963$	−7.03449	+	12.1841i	−0.226683	+	0.392627i
$964$	−3.21958	−	3.21958i	−0.103696	−	0.103696i
$965$	25.1693	+	14.5315i	0.810227	+	0.467785i
$966$	0.145239	+	0.157682i	0.00467298	+	0.00507334i
$967$	2.56512	−	2.56512i	0.0824888	−	0.0824888i	−0.664659	−	0.747147i	$-0.731423\pi$
$967$	2.56512	−	2.56512i	0.0824888	−	0.0824888i	0.747147	+	0.664659i	$0.231423\pi$
$968$	−2.76312	−	10.3121i	−0.0888101	−	0.331444i
$969$	2.24186	−	2.24186i	0.0720189	−	0.0720189i
$970$	−21.9188	+	5.87313i	−0.703770	+	0.188575i
$971$	0.0612354	+	0.0353543i	0.00196514	+	0.00113457i	0.500982	−	0.865458i	$-0.332972\pi$
$971$	0.0612354	+	0.0353543i	0.00196514	+	0.00113457i	−0.499017	+	0.866592i	$0.666306\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−12.0051	−	0.493147i	−0.384867	−	0.0158096i
$974$		−	30.1477i		−	0.965996i
$975$	−10.5806	−	4.33799i	−0.338851	−	0.138927i
$976$	−4.95521	−	2.86089i	−0.158612	−	0.0915749i
$977$	24.9073	+	6.67389i	0.796855	+	0.213517i	0.634203	−	0.773167i	$-0.281328\pi$
$977$	24.9073	+	6.67389i	0.796855	+	0.213517i	0.162653	+	0.986683i	$0.447995\pi$
$978$		−	8.48493i		−	0.271318i
$979$	3.01309	+	5.21882i	0.0962987	+	0.166794i
$980$	−1.69167	−	9.31289i	−0.0540386	−	0.297489i
$981$	18.3713	+	4.92259i	0.586552	+	0.157166i
$982$	−26.6791	+	7.14865i	−0.851365	+	0.228122i
$983$	9.96615	+	37.1942i	0.317871	+	1.18631i	0.921287	+	0.388884i	$0.127139\pi$
$983$	9.96615	+	37.1942i	0.317871	+	1.18631i	−0.603416	+	0.797427i	$0.706194\pi$
$984$	−2.31463			−0.0737878
$985$	18.9850			0.604914
$986$	0.0705554	+	0.263316i	0.00224694	+	0.00838570i
$987$	14.5158	+	4.53571i	0.462044	+	0.144373i
$988$	−1.48828	+	11.6285i	−0.0473484	+	0.369952i
$989$	−0.443739	−	0.768579i	−0.0141101	−	0.0244394i
$990$	−0.199243	+	0.743587i	−0.00633237	+	0.0236327i
$991$	12.8175	+	22.2006i	0.407162	+	0.705226i	0.994570	−	0.104065i	$-0.0331850\pi$
$991$	12.8175	+	22.2006i	0.407162	+	0.705226i	−0.587408	+	0.809291i	$0.699852\pi$
$992$	−1.28639	+	2.22809i	−0.0408429	+	0.0707420i
$993$	−12.2693	−	12.2693i	−0.389356	−	0.389356i
$994$	−1.27566	−	0.0524015i	−0.0404614	−	0.00166208i
$995$	1.79080	−	6.68336i	0.0567722	−	0.211877i
$996$	−0.814953	+	3.04145i	−0.0258228	+	0.0963719i
$997$		−	11.7801i		−	0.373081i	−0.982447	−	0.186540i	$-0.940273\pi$
$997$		−	11.7801i		−	0.373081i	0.982447	−	0.186540i	$-0.0597275\pi$
$998$	22.0410	−	12.7254i	0.697695	−	0.402814i
$999$	1.14587	−	1.14587i	0.0362538	−	0.0362538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.409.9	yes	40
7.5	odd	6		546.2.by.b.19.4	✓	40
13.11	odd	12		546.2.by.b.115.4	yes	40
91.89	even	12	inner	546.2.cg.b.271.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.4	✓	40	7.5	odd	6
546.2.by.b.115.4	yes	40	13.11	odd	12
546.2.cg.b.271.9	yes	40	91.89	even	12	inner
546.2.cg.b.409.9	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.349971 - 1.30611i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.23506 - 1.41580i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.349971 - 1.30611i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.23506 - 1.41580i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.676092 - 1.17103i) q^{10} +(0.147349 - 0.549915i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.33605 - 1.36776i) q^{13} +(-2.58155 + 0.579303i) q^{14} +(-0.349971 - 1.30611i) q^{15} -1.00000 q^{16} +0.975087 q^{17} +(-0.258819 - 0.965926i) q^{18} +(3.14068 - 0.841543i) q^{19} +(-1.30611 - 0.349971i) q^{20} +(-2.64352 - 0.108591i) q^{21} +(-0.284657 - 0.493040i) q^{22} -0.0810273i q^{23} +(-0.965926 - 0.258819i) q^{24} +(2.74668 + 1.58580i) q^{25} +(-3.32610 + 1.39179i) q^{26} -1.00000i q^{27} +(-1.41580 + 2.23506i) q^{28} +(-0.139785 + 0.242115i) q^{29} +(-1.17103 - 0.676092i) q^{30} +(2.48511 - 0.665884i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.147349 - 0.549915i) q^{33} +(0.689491 - 0.689491i) q^{34} +(-2.63140 + 2.42375i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(1.14587 + 1.14587i) q^{37} +(1.62574 - 2.81586i) q^{38} +(-3.57298 + 0.483507i) q^{39} +(-1.17103 + 0.676092i) q^{40} +(2.23576 - 0.599071i) q^{41} +(-1.94604 + 1.79247i) q^{42} +(9.48543 - 5.47642i) q^{43} +(-0.549915 - 0.147349i) q^{44} +(-0.956138 - 0.956138i) q^{45} +(-0.0572950 - 0.0572950i) q^{46} +(-5.55221 - 1.48771i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.99100 + 6.32882i) q^{49} +(3.06353 - 0.820870i) q^{50} +(0.844450 - 0.487543i) q^{51} +(-1.36776 + 3.33605i) q^{52} +(-4.54058 + 7.86452i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.666681 - 0.384909i) q^{55} +(0.579303 + 2.58155i) q^{56} +(2.29914 - 2.29914i) q^{57} +(0.0723580 + 0.270044i) q^{58} +(5.05249 - 5.05249i) q^{59} +(-1.30611 + 0.349971i) q^{60} +(4.95521 + 2.86089i) q^{61} +(1.28639 - 2.22809i) q^{62} +(-2.34365 + 1.22772i) q^{63} +1.00000i q^{64} +(-2.95397 + 3.87857i) q^{65} +(-0.493040 - 0.284657i) q^{66} +(2.09610 + 0.561649i) q^{67} -0.975087i q^{68} +(-0.0405137 - 0.0701717i) q^{69} +(-0.146835 + 3.57453i) q^{70} +(0.466117 + 0.124896i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-0.753163 - 2.81084i) q^{73} +1.62051 q^{74} +3.17160 q^{75} +(-0.841543 - 3.14068i) q^{76} +(-1.10791 + 1.02048i) q^{77} +(-2.18459 + 2.86837i) q^{78} +(1.45438 + 2.51907i) q^{79} +(-0.349971 + 1.30611i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.15732 - 2.00453i) q^{82} +(-2.22649 - 2.22649i) q^{83} +(-0.108591 + 2.64352i) q^{84} +(0.341252 - 1.27357i) q^{85} +(2.83480 - 10.5796i) q^{86} +0.279570i q^{87} +(-0.493040 + 0.284657i) q^{88} +(-7.48471 + 7.48471i) q^{89} -1.35218 q^{90} +(5.51979 + 7.78022i) q^{91} -0.0810273 q^{92} +(1.81923 - 1.81923i) q^{93} +(-4.97797 + 2.87403i) q^{94} -4.39659i q^{95} +(-0.258819 + 0.965926i) q^{96} +(4.34344 - 16.2099i) q^{97} +(6.59011 + 2.36019i) q^{98} +(-0.402566 - 0.402566i) 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

Introduction

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