LMFDB - Embedded newform 547.2.c.a.40.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.c (of order $3$, degree $2$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.19
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.364678 - 0.631642i) q^{2} +1.05712 q^{3} +(0.734019 - 1.27136i) q^{4} +(0.718385 - 1.24428i) q^{5} +(-0.385510 - 0.667723i) q^{6} +(-0.0543155 - 0.0940772i) q^{7} -2.52944 q^{8} -1.88249 q^{9} +O(q^{10})$	\(q+(-0.364678 - 0.631642i) q^{2} +1.05712 q^{3} +(0.734019 - 1.27136i) q^{4} +(0.718385 - 1.24428i) q^{5} +(-0.385510 - 0.667723i) q^{6} +(-0.0543155 - 0.0940772i) q^{7} -2.52944 q^{8} -1.88249 q^{9} -1.04792 q^{10} +(-1.85980 - 3.22126i) q^{11} +(0.775949 - 1.34398i) q^{12} +(-0.0635033 - 0.109991i) q^{13} +(-0.0396154 + 0.0686159i) q^{14} +(0.759422 - 1.31536i) q^{15} +(-0.545607 - 0.945019i) q^{16} +(-0.880604 - 1.52525i) q^{17} +(0.686503 + 1.18906i) q^{18} +(1.63731 - 2.83590i) q^{19} +(-1.05462 - 1.82665i) q^{20} +(-0.0574182 - 0.0994513i) q^{21} +(-1.35645 + 2.34945i) q^{22} +(-1.21892 + 2.11124i) q^{23} -2.67393 q^{24} +(1.46785 + 2.54238i) q^{25} +(-0.0463166 + 0.0802226i) q^{26} -5.16140 q^{27} -0.159475 q^{28} +7.42253 q^{29} -1.10778 q^{30} +6.91707 q^{31} +(-2.92738 + 5.07037i) q^{32} +(-1.96603 - 3.40527i) q^{33} +(-0.642274 + 1.11245i) q^{34} -0.156078 q^{35} +(-1.38178 + 2.39332i) q^{36} +(1.96654 + 3.40616i) q^{37} -2.38836 q^{38} +(-0.0671308 - 0.116274i) q^{39} +(-1.81711 + 3.14733i) q^{40} +(0.619926 + 1.07374i) q^{41} +(-0.0418784 + 0.0725355i) q^{42} +(-0.0720351 - 0.124768i) q^{43} -5.46050 q^{44} +(-1.35235 + 2.34234i) q^{45} +1.77806 q^{46} +(3.55782 - 6.16233i) q^{47} +(-0.576774 - 0.999002i) q^{48} +(3.49410 - 6.05196i) q^{49} +(1.07058 - 1.85431i) q^{50} +(-0.930907 - 1.61238i) q^{51} -0.186451 q^{52} +(-4.87051 - 8.43596i) q^{53} +(1.88225 + 3.26015i) q^{54} -5.34419 q^{55} +(0.137388 + 0.237963i) q^{56} +(1.73084 - 2.99790i) q^{57} +(-2.70683 - 4.68838i) q^{58} +(1.17166 + 2.02937i) q^{59} +(-1.11486 - 1.93099i) q^{60} +(0.329762 + 0.571164i) q^{61} +(-2.52251 - 4.36911i) q^{62} +(0.102248 + 0.177099i) q^{63} +2.08778 q^{64} -0.182479 q^{65} +(-1.43394 + 2.48366i) q^{66} +(2.54734 + 4.41213i) q^{67} -2.58552 q^{68} +(-1.28855 + 2.23184i) q^{69} +(0.0569182 + 0.0985852i) q^{70} +(2.93297 + 5.08005i) q^{71} +4.76164 q^{72} +(0.610163 + 1.05683i) q^{73} +(1.43431 - 2.48430i) q^{74} +(1.55170 + 2.68761i) q^{75} +(-2.40363 - 4.16321i) q^{76} +(-0.202031 + 0.349929i) q^{77} +(-0.0489623 + 0.0848052i) q^{78} +4.16779 q^{79} -1.56782 q^{80} +0.191236 q^{81} +(0.452147 - 0.783141i) q^{82} +(-3.84197 - 6.65448i) q^{83} -0.168584 q^{84} -2.53045 q^{85} +(-0.0525393 + 0.0910007i) q^{86} +7.84653 q^{87} +(4.70424 + 8.14798i) q^{88} -4.50893 q^{89} +1.97269 q^{90} +(-0.00689843 + 0.0119484i) q^{91} +(1.78943 + 3.09938i) q^{92} +7.31220 q^{93} -5.18984 q^{94} +(-2.35243 - 4.07453i) q^{95} +(-3.09460 + 5.36001i) q^{96} +(-2.24614 + 3.89043i) q^{97} -5.09689 q^{98} +(3.50105 + 6.06399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.364678	−	0.631642i	−0.257867	−	0.446638i	0.707804	−	0.706409i	$-0.249686\pi$
$2$	−0.364678	−	0.631642i	−0.257867	−	0.446638i	−0.965670	+	0.259771i	$0.916353\pi$
$3$	1.05712			0.610331			0.305165	−	0.952299i	$-0.401288\pi$
$3$	1.05712			0.610331			0.305165	+	0.952299i	$0.401288\pi$
$4$	0.734019	−	1.27136i	0.367010	−	0.635679i
$5$	0.718385	−	1.24428i	0.321271	−	0.556458i	−0.659479	−	0.751723i	$-0.729223\pi$
$5$	0.718385	−	1.24428i	0.321271	−	0.556458i	0.980751	+	0.195264i	$0.0625565\pi$
$6$	−0.385510	−	0.667723i	−0.157384	−	0.272597i
$7$	−0.0543155	−	0.0940772i	−0.0205293	−	0.0355579i	0.855578	−	0.517674i	$-0.173202\pi$
$7$	−0.0543155	−	0.0940772i	−0.0205293	−	0.0355579i	−0.876108	+	0.482116i	$0.839868\pi$
$8$	−2.52944			−0.894291
$9$	−1.88249			−0.627497
$10$	−1.04792			−0.331381
$11$	−1.85980	−	3.22126i	−0.560749	−	0.971246i	−0.997431	−	0.0716304i	$-0.977180\pi$
$11$	−1.85980	−	3.22126i	−0.560749	−	0.971246i	0.436682	−	0.899616i	$-0.356154\pi$
$12$	0.775949	−	1.34398i	0.223997	−	0.387975i
$13$	−0.0635033	−	0.109991i	−0.0176126	−	0.0305060i	0.857085	−	0.515175i	$-0.172273\pi$
$13$	−0.0635033	−	0.109991i	−0.0176126	−	0.0305060i	−0.874697	+	0.484669i	$0.838940\pi$
$14$	−0.0396154	+	0.0686159i	−0.0105877	+	0.0183384i
$15$	0.759422	−	1.31536i	0.196082	−	0.339624i
$16$	−0.545607	−	0.945019i	−0.136402	−	0.236255i
$17$	−0.880604	−	1.52525i	−0.213578	−	0.369927i	0.739254	−	0.673427i	$-0.235178\pi$
$17$	−0.880604	−	1.52525i	−0.213578	−	0.369927i	−0.952832	+	0.303499i	$0.901845\pi$
$18$	0.686503	+	1.18906i	0.161810	+	0.280264i
$19$	1.63731	−	2.83590i	0.375624	−	0.650600i	−0.614796	−	0.788686i	$-0.710762\pi$
$19$	1.63731	−	2.83590i	0.375624	−	0.650600i	0.990420	+	0.138086i	$0.0440951\pi$
$20$	−1.05462	−	1.82665i	−0.235819	−	0.408451i
$21$	−0.0574182	−	0.0994513i	−0.0125297	−	0.0217020i
$22$	−1.35645	+	2.34945i	−0.289197	+	0.500904i
$23$	−1.21892	+	2.11124i	−0.254163	+	0.440224i	−0.964668	−	0.263469i	$-0.915133\pi$
$23$	−1.21892	+	2.11124i	−0.254163	+	0.440224i	0.710505	+	0.703692i	$0.248467\pi$
$24$	−2.67393			−0.545813
$25$	1.46785	+	2.54238i	0.293569	+	0.508477i
$26$	−0.0463166	+	0.0802226i	−0.00908342	+	0.0157330i
$27$	−5.16140			−0.993311
$28$	−0.159475			−0.0301379
$29$	7.42253			1.37833			0.689164	−	0.724605i	$-0.257978\pi$
$29$	7.42253			1.37833			0.689164	+	0.724605i	$0.257978\pi$
$30$	−1.10778			−0.202252
$31$	6.91707			1.24234			0.621172	−	0.783675i	$-0.286657\pi$
$31$	6.91707			1.24234			0.621172	+	0.783675i	$0.286657\pi$
$32$	−2.92738	+	5.07037i	−0.517493	+	0.896323i
$33$	−1.96603	−	3.40527i	−0.342242	−	0.592781i
$34$	−0.642274	+	1.11245i	−0.110149	+	0.190784i
$35$	−0.156078			−0.0263820
$36$	−1.38178	+	2.39332i	−0.230297	+	0.398887i
$37$	1.96654	+	3.40616i	0.323298	+	0.559968i	0.981166	−	0.193164i	$-0.0618751\pi$
$37$	1.96654	+	3.40616i	0.323298	+	0.559968i	−0.657868	+	0.753133i	$0.728542\pi$
$38$	−2.38836			−0.387444
$39$	−0.0671308	−	0.116274i	−0.0107495	−	0.0186187i
$40$	−1.81711	+	3.14733i	−0.287310	+	0.497636i
$41$	0.619926	+	1.07374i	0.0968161	+	0.167690i	0.910365	−	0.413806i	$-0.135801\pi$
$41$	0.619926	+	1.07374i	0.0968161	+	0.167690i	−0.813549	+	0.581496i	$0.802467\pi$
$42$	−0.0418784	+	0.0725355i	−0.00646197	+	0.0111925i
$43$	−0.0720351	−	0.124768i	−0.0109852	−	0.0190270i	0.860481	−	0.509483i	$-0.170163\pi$
$43$	−0.0720351	−	0.124768i	−0.0109852	−	0.0190270i	−0.871466	+	0.490456i	$0.836830\pi$
$44$	−5.46050			−0.823202
$45$	−1.35235	+	2.34234i	−0.201597	+	0.349176i
$46$	1.77806			0.262161
$47$	3.55782	−	6.16233i	0.518961	−	0.898868i	−0.480796	−	0.876833i	$-0.659652\pi$
$47$	3.55782	−	6.16233i	0.518961	−	0.898868i	0.999757	−	0.0220349i	$-0.00701450\pi$
$48$	−0.576774	−	0.999002i	−0.0832502	−	0.144194i
$49$	3.49410	−	6.05196i	0.499157	−	0.864565i
$50$	1.07058	−	1.85431i	0.151403	−	0.262238i
$51$	−0.930907	−	1.61238i	−0.130353	−	0.225778i
$52$	−0.186451			−0.0258560
$53$	−4.87051	−	8.43596i	−0.669015	−	1.15877i	−0.978180	−	0.207760i	$-0.933383\pi$
$53$	−4.87051	−	8.43596i	−0.669015	−	1.15877i	0.309165	−	0.951009i	$-0.399951\pi$
$54$	1.88225	+	3.26015i	0.256142	+	0.443650i
$55$	−5.34419			−0.720611
$56$	0.137388	+	0.237963i	0.0183592	+	0.0317991i
$57$	1.73084	−	2.99790i	0.229255	−	0.397081i
$58$	−2.70683	−	4.68838i	−0.355425	−	0.615614i
$59$	1.17166	+	2.02937i	0.152537	+	0.264201i	0.932159	−	0.362048i	$-0.117922\pi$
$59$	1.17166	+	2.02937i	0.152537	+	0.264201i	−0.779623	+	0.626250i	$0.784589\pi$
$60$	−1.11486	−	1.93099i	−0.143928	−	0.249290i
$61$	0.329762	+	0.571164i	0.0422217	+	0.0731301i	0.886364	−	0.462989i	$-0.153223\pi$
$61$	0.329762	+	0.571164i	0.0422217	+	0.0731301i	−0.844142	+	0.536119i	$0.819890\pi$
$62$	−2.52251	−	4.36911i	−0.320359	−	0.554878i
$63$	0.102248	+	0.177099i	0.0128821	+	0.0223124i
$64$	2.08778			0.260973
$65$	−0.182479			−0.0226338
$66$	−1.43394	+	2.48366i	−0.176506	+	0.305717i
$67$	2.54734	+	4.41213i	0.311207	+	0.539027i	0.978624	−	0.205658i	$-0.0659333\pi$
$67$	2.54734	+	4.41213i	0.311207	+	0.539027i	−0.667417	+	0.744684i	$0.732600\pi$
$68$	−2.58552			−0.313540
$69$	−1.28855	+	2.23184i	−0.155124	+	0.268682i
$70$	0.0569182	+	0.0985852i	0.00680303	+	0.0117832i
$71$	2.93297	+	5.08005i	0.348079	+	0.602891i	0.985908	−	0.167287i	$-0.0535007\pi$
$71$	2.93297	+	5.08005i	0.348079	+	0.602891i	−0.637829	+	0.770178i	$0.720167\pi$
$72$	4.76164			0.561165
$73$	0.610163	+	1.05683i	0.0714142	+	0.123693i	0.899521	−	0.436877i	$-0.143915\pi$
$73$	0.610163	+	1.05683i	0.0714142	+	0.123693i	−0.828107	+	0.560570i	$0.810582\pi$
$74$	1.43431	−	2.48430i	0.166735	−	0.288794i
$75$	1.55170	+	2.68761i	0.179174	+	0.310339i
$76$	−2.40363	−	4.16321i	−0.275715	−	0.477553i
$77$	−0.202031	+	0.349929i	−0.0230236	+	0.0398781i
$78$	−0.0489623	+	0.0848052i	−0.00554389	+	0.00960230i
$79$	4.16779			0.468913			0.234457	−	0.972127i	$-0.424669\pi$
$79$	4.16779			0.468913			0.234457	+	0.972127i	$0.424669\pi$
$80$	−1.56782			−0.175288
$81$	0.191236			0.0212484
$82$	0.452147	−	0.783141i	0.0499313	−	0.0864835i
$83$	−3.84197	−	6.65448i	−0.421711	−	0.730424i	0.574396	−	0.818577i	$-0.305237\pi$
$83$	−3.84197	−	6.65448i	−0.421711	−	0.730424i	−0.996107	+	0.0881532i	$0.971903\pi$
$84$	−0.168584			−0.0183941
$85$	−2.53045			−0.274466
$86$	−0.0525393	+	0.0910007i	−0.00566546	+	0.00981286i
$87$	7.84653			0.841236
$88$	4.70424	+	8.14798i	0.501473	+	0.868577i
$89$	−4.50893			−0.477946			−0.238973	−	0.971026i	$-0.576811\pi$
$89$	−4.50893			−0.477946			−0.238973	+	0.971026i	$0.576811\pi$
$90$	1.97269			0.207940
$91$	−0.00689843	+	0.0119484i	−0.000723152	+	0.00125254i
$92$	1.78943	+	3.09938i	0.186561	+	0.323133i
$93$	7.31220			0.758240
$94$	−5.18984			−0.535291
$95$	−2.35243	−	4.07453i	−0.241355	−	0.418038i
$96$	−3.09460	+	5.36001i	−0.315842	+	0.547054i
$97$	−2.24614	+	3.89043i	−0.228061	+	0.395013i	−0.957233	−	0.289317i	$-0.906572\pi$
$97$	−2.24614	+	3.89043i	−0.228061	+	0.395013i	0.729172	+	0.684330i	$0.239905\pi$
$98$	−5.09689			−0.514864
$99$	3.50105	+	6.06399i	0.351868	+	0.609454i
$100$	4.30971			0.430971
$101$	5.36161			0.533500			0.266750	−	0.963766i	$-0.414050\pi$
$101$	5.36161			0.533500			0.266750	+	0.963766i	$0.414050\pi$
$102$	−0.678963	+	1.17600i	−0.0672274	+	0.116441i
$103$	5.80877			0.572355			0.286177	−	0.958177i	$-0.407615\pi$
$103$	5.80877			0.572355			0.286177	+	0.958177i	$0.407615\pi$
$104$	0.160628	+	0.278215i	0.0157508	+	0.0272812i
$105$	−0.164994			−0.0161017
$106$	−3.55234	+	6.15283i	−0.345033	+	0.597615i
$107$	2.37733			0.229825			0.114913	−	0.993376i	$-0.463341\pi$
$107$	2.37733			0.229825			0.114913	+	0.993376i	$0.463341\pi$
$108$	−3.78856	+	6.56198i	−0.364555	+	0.631427i
$109$	−7.83943	+	13.5783i	−0.750881	+	1.30056i	0.196515	+	0.980501i	$0.437038\pi$
$109$	−7.83943	+	13.5783i	−0.750881	+	1.30056i	−0.947396	+	0.320064i	$0.896296\pi$
$110$	1.94891	+	3.37562i	0.185822	+	0.321852i
$111$	2.07888	+	3.60073i	0.197319	+	0.341766i
$112$	−0.0592699	+	0.102658i	−0.00560048	+	0.00970031i
$113$	−2.93452	+	5.08273i	−0.276056	+	0.478143i	−0.970401	−	0.241499i	$-0.922361\pi$
$113$	−2.93452	+	5.08273i	−0.276056	+	0.478143i	0.694345	+	0.719642i	$0.255694\pi$
$114$	−2.52479			−0.236469
$115$	1.75131	+	3.03336i	0.163311	+	0.282863i
$116$	5.44828	−	9.43669i	0.505860	−	0.876175i
$117$	0.119544	+	0.207057i	0.0110519	+	0.0191424i
$118$	0.854556	−	1.48013i	0.0786682	−	0.136257i
$119$	−0.0956609	+	0.165689i	−0.00876922	+	0.0151887i
$120$	−1.92091	+	3.32711i	−0.175354	+	0.303722i
$121$	−1.41768	+	2.45549i	−0.128880	+	0.223226i
$122$	0.240514	−	0.416583i	0.0217751	−	0.0377156i
$123$	0.655338	+	1.13508i	0.0590898	+	0.102347i
$124$	5.07727	−	8.79408i	0.455952	−	0.789732i
$125$	11.4018			1.01980
$126$	0.0745756	−	0.129169i	0.00664372	−	0.0115073i
$127$	4.20136	−	7.27697i	0.372811	−	0.645727i	−0.617186	−	0.786817i	$-0.711727\pi$
$127$	4.20136	−	7.27697i	0.372811	−	0.645727i	0.989997	+	0.141090i	$0.0450608\pi$
$128$	5.09339	+	8.82201i	0.450196	+	0.779763i
$129$	−0.0761500	−	0.131896i	−0.00670463	−	0.0116128i
$130$	0.0665462	+	0.115261i	0.00583649	+	0.0101091i
$131$	−9.45839			−0.826384			−0.413192	−	0.910644i	$-0.635586\pi$
$131$	−9.45839			−0.826384			−0.413192	+	0.910644i	$0.635586\pi$
$132$	−5.77243			−0.502425
$133$	−0.355725			−0.0308453
$134$	1.85792	−	3.21801i	0.160500	−	0.277994i
$135$	−3.70787	+	6.42222i	−0.319122	+	0.552736i
$136$	2.22743	+	3.85803i	0.191001	+	0.330823i
$137$	1.67368	+	2.89890i	0.142992	+	0.247670i	0.928622	−	0.371027i	$-0.120994\pi$
$137$	1.67368	+	2.89890i	0.142992	+	0.247670i	−0.785630	+	0.618697i	$0.787661\pi$
$138$	1.87963			0.160005
$139$	0.474815	+	0.822404i	0.0402733	+	0.0697554i	0.885459	−	0.464717i	$-0.153844\pi$
$139$	0.474815	+	0.822404i	0.0402733	+	0.0697554i	−0.845186	+	0.534472i	$0.820510\pi$
$140$	−0.114564	+	0.198431i	−0.00968243	+	0.0167705i
$141$	3.76106	−	6.51434i	0.316738	−	0.548606i
$142$	2.13918	−	3.70517i	0.179516	−	0.310931i
$143$	−0.236206	+	0.409121i	−0.0197526	+	0.0342124i
$144$	1.02710	+	1.77899i	0.0855917	+	0.148249i
$145$	5.33223	−	9.23569i	0.442818	−	0.766983i
$146$	0.445027	−	0.770809i	0.0368307	−	0.0637926i
$147$	3.69370	−	6.39767i	0.304651	−	0.527671i
$148$	5.77393			0.474614
$149$	−5.08844			−0.416861			−0.208430	−	0.978037i	$-0.566835\pi$
$149$	−5.08844			−0.416861			−0.208430	+	0.978037i	$0.566835\pi$
$150$	1.13174	−	1.96023i	0.0924061	−	0.160052i
$151$	15.6068			1.27006			0.635031	−	0.772487i	$-0.280987\pi$
$151$	15.6068			1.27006			0.635031	+	0.772487i	$0.280987\pi$
$152$	−4.14147	+	7.17323i	−0.335917	+	0.581826i
$153$	1.65773	+	2.87127i	0.134019	+	0.232128i
$154$	0.294706			0.0237481
$155$	4.96912	−	8.60677i	0.399129	−	0.691312i
$156$	−0.197101			−0.0157807
$157$	8.79184	+	15.2279i	0.701666	+	1.21532i	0.967881	+	0.251407i	$0.0808933\pi$
$157$	8.79184	+	15.2279i	0.701666	+	1.21532i	−0.266216	+	0.963913i	$0.585773\pi$
$158$	−1.51990	−	2.63255i	−0.120917	−	0.209434i
$159$	−5.14873	−	8.91786i	−0.408321	−	0.707232i
$160$	4.20597	+	7.28496i	0.332511	+	0.575926i
$161$	0.264826			0.0208712
$162$	−0.0697396	−	0.120793i	−0.00547926	−	0.00949036i
$163$	6.82159	+	11.8153i	0.534308	+	0.925449i	0.999196	+	0.0400794i	$0.0127611\pi$
$163$	6.82159	+	11.8153i	0.534308	+	0.925449i	−0.464888	+	0.885369i	$0.653906\pi$
$164$	1.82015			0.142130
$165$	−5.64947			−0.439811
$166$	−2.80216	+	4.85349i	−0.217490	+	0.376704i
$167$	5.53953			0.428662			0.214331	−	0.976761i	$-0.431243\pi$
$167$	5.53953			0.428662			0.214331	+	0.976761i	$0.431243\pi$
$168$	0.145236	+	0.251556i	0.0112052	+	0.0194080i
$169$	6.49193	−	11.2444i	0.499380	−	0.864951i
$170$	0.922800	+	1.59834i	0.0707755	+	0.122587i
$171$	−3.08221	+	5.33855i	−0.235703	+	0.408249i
$172$	−0.211501			−0.0161268
$173$	−9.66925			−0.735140			−0.367570	−	0.929996i	$-0.619810\pi$
$173$	−9.66925			−0.735140			−0.367570	+	0.929996i	$0.619810\pi$
$174$	−2.86146	−	4.95619i	−0.216927	−	0.375728i
$175$	0.159454	−	0.276182i	0.0120536	−	0.0208774i
$176$	−2.02944	+	3.51509i	−0.152974	+	0.264960i
$177$	1.23859	+	2.14529i	0.0930978	+	0.161250i
$178$	1.64431	+	2.84803i	0.123246	+	0.213469i
$179$	11.3047			0.844952			0.422476	−	0.906374i	$-0.361161\pi$
$179$	11.3047			0.844952			0.422476	+	0.906374i	$0.361161\pi$
$180$	1.98530	+	3.43865i	0.147976	+	0.256302i
$181$	−13.0703	+	22.6384i	−0.971506	+	1.68270i	−0.280491	+	0.959857i	$0.590497\pi$
$181$	−13.0703	+	22.6384i	−0.971506	+	1.68270i	−0.691014	+	0.722841i	$0.742836\pi$
$182$	0.0100628			0.000745907
$183$	0.348599	+	0.603791i	0.0257692	+	0.0446335i
$184$	3.08319	−	5.34024i	0.227296	−	0.393688i
$185$	5.65094			0.415466
$186$	−2.66660	−	4.61869i	−0.195525	−	0.338659i
$187$	−3.27548	+	5.67331i	−0.239527	+	0.414873i
$188$	−5.22302	−	9.04653i	−0.380928	−	0.659786i
$189$	0.280344	+	0.485570i	0.0203920	+	0.0353200i
$190$	−1.71576	+	2.97179i	−0.124475	+	0.215596i
$191$	2.18531	−	3.78506i	0.158123	−	0.273878i	−0.776069	−	0.630649i	$-0.782789\pi$
$191$	2.18531	−	3.78506i	0.158123	−	0.273878i	0.934192	+	0.356771i	$0.116122\pi$
$192$	2.20704			0.159280
$193$	0.0596903	−	0.103387i	0.00429660	−	0.00744194i	−0.863869	−	0.503716i	$-0.831966\pi$
$193$	0.0596903	−	0.103387i	0.00429660	−	0.00744194i	0.868166	+	0.496274i	$0.165299\pi$
$194$	3.27648			0.235237
$195$	−0.192903			−0.0138141
$196$	−5.12947	−	8.88451i	−0.366391	−	0.634608i
$197$	−16.7888			−1.19615			−0.598076	−	0.801440i	$-0.704068\pi$
$197$	−16.7888			−1.19615			−0.598076	+	0.801440i	$0.704068\pi$
$198$	2.55351	−	4.42281i	0.181470	−	0.314315i
$199$	7.84745	−	13.5922i	0.556291	−	0.963524i	−0.441511	−	0.897256i	$-0.645557\pi$
$199$	7.84745	−	13.5922i	0.556291	−	0.963524i	0.997802	−	0.0662684i	$-0.0211094\pi$
$200$	−3.71283	−	6.43080i	−0.262536	−	0.454726i
$201$	2.69286	+	4.66416i	0.189939	+	0.328985i
$202$	−1.95526	−	3.38662i	−0.137572	−	0.238282i
$203$	−0.403158	−	0.698291i	−0.0282962	−	0.0490104i
$204$	−2.73321			−0.191363
$205$	1.78138			0.124417
$206$	−2.11833	−	3.66906i	−0.147591	−	0.255635i
$207$	2.29461	−	3.97438i	0.159487	−	0.276239i
$208$	−0.0692957	+	0.120024i	−0.00480479	+	0.00832215i
$209$	−12.1802			−0.842524
$210$	0.0601696	+	0.104217i	0.00415209	+	0.00719164i
$211$	3.72045	−	6.44400i	0.256126	−	0.443623i	−0.709075	−	0.705133i	$-0.750887\pi$
$211$	3.72045	−	6.44400i	0.256126	−	0.443623i	0.965201	+	0.261510i	$0.0842204\pi$
$212$	−14.3002			−0.982140
$213$	3.10051	+	5.37024i	0.212443	+	0.367963i
$214$	−0.866961	−	1.50162i	−0.0592642	−	0.102649i
$215$	−0.206996			−0.0141170
$216$	13.0554			0.888309
$217$	−0.375704	−	0.650739i	−0.0255045	−	0.0441751i
$218$	11.4355			0.774509
$219$	0.645018	+	1.11720i	0.0435863	+	0.0754937i
$220$	−3.92274	+	6.79439i	−0.264471	+	0.458078i
$221$	−0.111842	+	0.193717i	−0.00752334	+	0.0130308i
$222$	1.51625	−	2.62622i	0.101764	−	0.176260i
$223$	−5.58644	+	9.67600i	−0.374096	+	0.647953i	−0.990191	−	0.139719i	$-0.955380\pi$
$223$	−5.58644	+	9.67600i	−0.374096	+	0.647953i	0.616095	+	0.787671i	$0.288714\pi$
$224$	0.636009			0.0424951
$225$	−2.76321	−	4.78601i	−0.184214	−	0.319068i
$226$	4.28062			0.284743
$227$	−10.8211	+	18.7427i	−0.718221	+	1.24399i	0.243483	+	0.969905i	$0.421710\pi$
$227$	−10.8211	+	18.7427i	−0.718221	+	1.24399i	−0.961704	+	0.274090i	$0.911623\pi$
$228$	−2.54093	−	4.40103i	−0.168278	−	0.291465i
$229$	4.69978	−	8.14026i	0.310570	−	0.537924i	−0.667916	−	0.744237i	$-0.732813\pi$
$229$	4.69978	−	8.14026i	0.310570	−	0.537924i	0.978486	+	0.206313i	$0.0661467\pi$
$230$	1.27733	−	2.21240i	0.0842248	−	0.145882i
$231$	−0.213572	+	0.369918i	−0.0140520	+	0.0243388i
$232$	−18.7748			−1.23263
$233$	1.76737	−	3.06118i	0.115784	−	0.200544i	−0.802309	−	0.596909i	$-0.796395\pi$
$233$	1.76737	−	3.06118i	0.115784	−	0.200544i	0.918093	+	0.396365i	$0.129729\pi$
$234$	0.0871904	−	0.151018i	0.00569982	−	0.00987237i
$235$	−5.11177	−	8.85384i	−0.333455	−	0.577561i
$236$	3.44007			0.223930
$237$	4.40587			0.286192
$238$	0.139542			0.00904515
$239$	−13.6440	−	23.6321i	−0.882556	−	1.52863i	−0.848489	−	0.529213i	$-0.822487\pi$
$239$	−13.6440	−	23.6321i	−0.882556	−	1.52863i	−0.0340675	−	0.999420i	$-0.510846\pi$
$240$	−1.65738			−0.106984
$241$	−6.45869	+	11.1868i	−0.416040	+	0.720603i	−0.995537	−	0.0943714i	$-0.969916\pi$
$241$	−6.45869	+	11.1868i	−0.416040	+	0.720603i	0.579497	+	0.814975i	$0.303249\pi$
$242$	2.06798			0.132935
$243$	15.6863			1.00628
$244$	0.968206			0.0619831
$245$	−5.02022	−	8.69527i	−0.320730	−	0.555520i
$246$	0.477975	−	0.827877i	0.0304746	−	0.0527835i
$247$	−0.415898			−0.0264629
$248$	−17.4963			−1.11102
$249$	−4.06143	−	7.03461i	−0.257383	−	0.445800i
$250$	−4.15798	−	7.20183i	−0.262974	−	0.455484i
$251$	−5.22054	−	9.04224i	−0.329518	−	0.570741i	0.652899	−	0.757445i	$-0.273553\pi$
$251$	−5.22054	−	9.04224i	−0.329518	−	0.570741i	−0.982416	+	0.186704i	$0.940219\pi$
$252$	0.300209			0.0189114
$253$	9.06779			0.570087
$254$	−6.12858			−0.384542
$255$	−2.67500			−0.167515
$256$	5.80268	−	10.0505i	0.362668	−	0.628159i
$257$	−0.888732			−0.0554376			−0.0277188	−	0.999616i	$-0.508824\pi$
$257$	−0.888732			−0.0554376			−0.0277188	+	0.999616i	$0.508824\pi$
$258$	−0.0555405	+	0.0961990i	−0.00345780	+	0.00598909i
$259$	0.213628	−	0.370014i	0.0132742	−	0.0229916i
$260$	−0.133943	+	0.231997i	−0.00830681	+	0.0143878i
$261$	−13.9728			−0.864896
$262$	3.44927	+	5.97431i	0.213097	+	0.369094i
$263$	−22.4924			−1.38694			−0.693471	−	0.720485i	$-0.743919\pi$
$263$	−22.4924			−1.38694			−0.693471	+	0.720485i	$0.743919\pi$
$264$	4.97296	+	8.61342i	0.306064	+	0.530119i
$265$	−13.9956			−0.859742
$266$	0.129725	+	0.224691i	0.00795396	+	0.0137767i
$267$	−4.76650			−0.291705
$268$	7.47919			0.456864
$269$	8.89487	−	15.4064i	0.542330	−	0.939343i	−0.456440	−	0.889754i	$-0.650876\pi$
$269$	8.89487	−	15.4064i	0.542330	−	0.939343i	0.998770	−	0.0495887i	$-0.0157910\pi$
$270$	5.40872			0.329164
$271$	3.06256	+	5.30451i	0.186037	+	0.322226i	0.943926	−	0.330158i	$-0.107102\pi$
$271$	3.06256	+	5.30451i	0.186037	+	0.322226i	−0.757888	+	0.652384i	$0.773769\pi$
$272$	−0.960927	+	1.66438i	−0.0582648	+	0.100918i
$273$	−0.00729249	+	0.0126310i	−0.000441362	+	0.000764461i
$274$	1.22071	−	2.11433i	0.0737459	−	0.127732i
$275$	5.45979	−	9.45663i	0.329238	−	0.570256i
$276$	1.89165	+	3.27643i	0.113864	+	0.197218i
$277$	−22.4595			−1.34946			−0.674731	−	0.738063i	$-0.735741\pi$
$277$	−22.4595			−1.34946			−0.674731	+	0.738063i	$0.735741\pi$
$278$	0.346310	−	0.599826i	0.0207703	−	0.0359752i
$279$	−13.0213			−0.779566
$280$	0.394789			0.0235932
$281$	13.9540	+	24.1690i	0.832426	+	1.44180i	0.896109	+	0.443834i	$0.146382\pi$
$281$	13.9540	+	24.1690i	0.832426	+	1.44180i	−0.0636826	+	0.997970i	$0.520285\pi$
$282$	−5.48630			−0.326705
$283$	−5.77088	−	9.99546i	−0.343043	−	0.594168i	0.641953	−	0.766744i	$-0.278124\pi$
$283$	−5.77088	−	9.99546i	−0.343043	−	0.594168i	−0.984996	+	0.172576i	$0.944791\pi$
$284$	8.61142			0.510994
$285$	−2.48681	−	4.30729i	−0.147306	−	0.255142i
$286$	0.344557			0.0203741
$287$	0.0673432	−	0.116642i	0.00397514	−	0.00688515i
$288$	5.51076	−	9.54492i	0.324725	−	0.562440i
$289$	6.94907	−	12.0362i	0.408769	−	0.708009i
$290$	−7.77820			−0.456751
$291$	−2.37445	+	4.11266i	−0.139193	+	0.241089i
$292$	1.79149			0.104839
$293$	−18.4178			−1.07598			−0.537990	−	0.842951i	$-0.680816\pi$
$293$	−18.4178			−1.07598			−0.537990	+	0.842951i	$0.680816\pi$
$294$	−5.38804			−0.314237
$295$	3.36680			0.196023
$296$	−4.97425	−	8.61566i	−0.289123	−	0.500775i
$297$	9.59914	+	16.6262i	0.556998	+	0.964750i
$298$	1.85564	+	3.21407i	0.107494	+	0.186186i
$299$	0.309623			0.0179059
$300$	4.55590			0.263035
$301$	−0.00782525	+	0.0135537i	−0.000451040	+	0.000781224i
$302$	−5.69146	−	9.85789i	−0.327507	−	0.567258i
$303$	5.66789			0.325612
$304$	−3.57331			−0.204943
$305$	0.947584			0.0542585
$306$	1.20907	−	2.09418i	0.0691182	−	0.119716i
$307$	−10.9256			−0.623558			−0.311779	−	0.950155i	$-0.600925\pi$
$307$	−10.9256			−0.623558			−0.311779	+	0.950155i	$0.600925\pi$
$308$	0.296590	+	0.513709i	0.0168998	+	0.0292713i
$309$	6.14058			0.349326
$310$	−7.24852			−0.411689
$311$	−24.0925			−1.36616			−0.683080	−	0.730344i	$-0.739360\pi$
$311$	−24.0925			−1.36616			−0.683080	+	0.730344i	$0.739360\pi$
$312$	0.169803	+	0.294108i	0.00961322	+	0.0166506i
$313$	−2.64610	+	4.58317i	−0.149566	+	0.259056i	−0.931067	−	0.364848i	$-0.881121\pi$
$313$	−2.64610	+	4.58317i	−0.149566	+	0.259056i	0.781501	+	0.623904i	$0.214454\pi$
$314$	6.41239	−	11.1066i	0.361872	−	0.626781i
$315$	0.293815			0.0165546
$316$	3.05924	−	5.29876i	0.172096	−	0.298078i
$317$	−4.01155	+	6.94821i	−0.225311	+	0.390251i	−0.956413	−	0.292018i	$-0.905673\pi$
$317$	−4.01155	+	6.94821i	−0.225311	+	0.390251i	0.731102	+	0.682269i	$0.239007\pi$
$318$	−3.75526	+	6.50430i	−0.210584	+	0.364743i
$319$	−13.8044	−	23.9099i	−0.772897	−	1.33870i
$320$	1.49983	−	2.59778i	0.0838430	−	0.145220i
$321$	2.51313			0.140269
$322$	−0.0965763	−	0.167275i	−0.00538199	−	0.00932187i
$323$	−5.76727			−0.320900
$324$	0.140371	−	0.243129i	0.00779838	−	0.0135072i
$325$	0.186426	−	0.322900i	0.0103411	−	0.0179112i
$326$	4.97537	−	8.61760i	0.275560	−	0.477285i
$327$	−8.28725	+	14.3539i	−0.458286	+	0.793774i
$328$	−1.56806	−	2.71596i	−0.0865818	−	0.149964i
$329$	−0.772979			−0.0426157
$330$	2.06024	+	3.56844i	0.113413	+	0.196436i
$331$	19.3016			1.06091			0.530455	−	0.847713i	$-0.322021\pi$
$331$	19.3016			1.06091			0.530455	+	0.847713i	$0.322021\pi$
$332$	−11.2803			−0.619087
$333$	−3.70200	−	6.41205i	−0.202868	−	0.351378i
$334$	−2.02015	−	3.49900i	−0.110538	−	0.191457i
$335$	7.31989			0.399928
$336$	−0.0626556	+	0.108523i	−0.00341814	+	0.00592040i
$337$	15.7650	+	27.3057i	0.858773	+	1.48744i	0.873100	+	0.487542i	$0.162106\pi$
$337$	15.7650	+	27.3057i	0.858773	+	1.48744i	−0.0143266	+	0.999897i	$0.504560\pi$
$338$	−9.46987			−0.515093
$339$	−3.10215	+	5.37308i	−0.168486	+	0.291825i
$340$	−1.85740	+	3.21711i	−0.100732	+	0.174472i
$341$	−12.8643	−	22.2817i	−0.696643	−	1.20662i
$342$	4.49607			0.243120
$343$	−1.51955			−0.0820481
$344$	0.182208	+	0.315594i	0.00982401	+	0.0170157i
$345$	1.85135	+	3.20664i	0.0996736	+	0.172640i
$346$	3.52617	+	6.10750i	0.189568	+	0.328341i
$347$	10.4093	+	18.0294i	0.558798	+	0.967866i	0.997597	+	0.0692812i	$0.0220706\pi$
$347$	10.4093	+	18.0294i	0.558798	+	0.967866i	−0.438799	+	0.898585i	$0.644596\pi$
$348$	5.75950	−	9.97575i	0.308742	−	0.534756i
$349$	−0.225710	+	0.390941i	−0.0120820	+	0.0209266i	−0.872003	−	0.489500i	$-0.837179\pi$
$349$	−0.225710	+	0.390941i	−0.0120820	+	0.0209266i	0.859921	+	0.510427i	$0.170513\pi$
$350$	−0.232597			−0.0124328
$351$	0.327766	+	0.567707i	0.0174948	+	0.0303019i
$352$	21.7773			1.16073
$353$	22.7586			1.21132			0.605658	−	0.795725i	$-0.292910\pi$
$353$	22.7586			1.21132			0.605658	+	0.795725i	$0.292910\pi$
$354$	0.903371	−	1.56468i	0.0480136	−	0.0831621i
$355$	8.42800			0.447312
$356$	−3.30964	+	5.73247i	−0.175411	+	0.303820i
$357$	−0.101125	+	0.175154i	−0.00535212	+	0.00927015i
$358$	−4.12258	−	7.14051i	−0.217885	−	0.377388i
$359$	−12.9653	−	22.4565i	−0.684280	−	1.18521i	−0.973662	−	0.227994i	$-0.926783\pi$
$359$	−12.9653	−	22.4565i	−0.684280	−	1.18521i	0.289382	−	0.957214i	$-0.406550\pi$
$360$	3.42069	−	5.92481i	0.180286	−	0.312265i
$361$	4.13845	+	7.16800i	0.217813	+	0.377263i
$362$	19.0658			1.00208
$363$	−1.49866	+	2.59575i	−0.0786592	+	0.136242i
$364$	0.0101272	+	0.0175408i	0.000530807	+	0.000919385i
$365$	1.75333			0.0917734
$366$	0.254253	−	0.440379i	0.0132900	−	0.0230190i
$367$	−4.07935	−	7.06563i	−0.212940	−	0.368823i	0.739693	−	0.672944i	$-0.234971\pi$
$367$	−4.07935	−	7.06563i	−0.212940	−	0.368823i	−0.952633	+	0.304121i	$0.901637\pi$
$368$	2.66021			0.138673
$369$	−1.16700	−	2.02131i	−0.0607518	−	0.105225i
$370$	−2.06078	−	3.56937i	−0.107135	−	0.185563i
$371$	−0.529088	+	0.916407i	−0.0274689	+	0.0475775i
$372$	5.36730	−	9.29643i	0.278281	−	0.481998i
$373$	4.09472	+	7.09226i	0.212016	+	0.367223i	0.952345	−	0.305021i	$-0.0986636\pi$
$373$	4.09472	+	7.09226i	0.212016	+	0.367223i	−0.740329	+	0.672245i	$0.765330\pi$
$374$	4.77799			0.247064
$375$	12.0531			0.622418
$376$	−8.99928	+	15.5872i	−0.464103	+	0.803849i
$377$	−0.471355	−	0.816410i	−0.0242760	−	0.0420473i
$378$	0.204471	−	0.354154i	0.0105168	−	0.0182157i
$379$	−10.3106	−	17.8585i	−0.529620	−	0.917329i	−0.999403	−	0.0345469i	$-0.989001\pi$
$379$	−10.3106	−	17.8585i	−0.529620	−	0.917329i	0.469783	−	0.882782i	$-0.344332\pi$
$380$	−6.90693			−0.354318
$381$	4.44136	−	7.69266i	0.227538	−	0.394107i
$382$	−3.18774			−0.163099
$383$	15.2117			0.777283			0.388641	−	0.921389i	$-0.372945\pi$
$383$	15.2117			0.777283			0.388641	+	0.921389i	$0.372945\pi$
$384$	5.38434	+	9.32596i	0.274769	+	0.475913i
$385$	0.290273	+	0.502767i	0.0147937	+	0.0256234i
$386$	−0.0870711			−0.00443180
$387$	0.135605	+	0.234875i	0.00689320	+	0.0119394i
$388$	3.29742	+	5.71130i	0.167401	+	0.289947i
$389$	9.42318	+	16.3214i	0.477774	+	0.827529i	0.999675	−	0.0254769i	$-0.00811044\pi$
$389$	9.42318	+	16.3214i	0.477774	+	0.827529i	−0.521901	+	0.853006i	$0.674777\pi$
$390$	0.0703476	+	0.121846i	0.00356219	+	0.00616989i
$391$	4.29355			0.217134
$392$	−8.83811	+	15.3081i	−0.446392	+	0.773173i
$393$	−9.99869			−0.504367
$394$	6.12251	+	10.6045i	0.308448	+	0.534247i
$395$	2.99408	−	5.18589i	0.150648	−	0.260931i
$396$	10.2793			0.516556
$397$	9.79101	−	16.9585i	0.491397	−	0.851124i	−0.508554	−	0.861030i	$-0.669820\pi$
$397$	9.79101	−	16.9585i	0.491397	−	0.851124i	0.999951	+	0.00990589i	$0.00315319\pi$
$398$	−11.4472			−0.573795
$399$	−0.376045			−0.0188258
$400$	1.60174	−	2.77429i	0.0800868	−	0.138714i
$401$	5.66553	−	9.81299i	0.282923	−	0.490037i	−0.689180	−	0.724590i	$-0.742029\pi$
$401$	5.66553	−	9.81299i	0.282923	−	0.490037i	0.972103	+	0.234553i	$0.0753625\pi$
$402$	1.96405	−	3.40184i	0.0979580	−	0.169668i
$403$	−0.439257	−	0.760815i	−0.0218809	−	0.0378989i
$404$	3.93553	−	6.81653i	0.195800	−	0.339135i
$405$	0.137381	−	0.237951i	0.00682652	−	0.0118239i
$406$	−0.294046	+	0.509303i	−0.0145933	+	0.0252763i
$407$	7.31474	−	12.6695i	0.362578	−	0.628004i
$408$	2.35467	+	4.07841i	0.116574	+	0.201911i
$409$	−35.9274			−1.77650			−0.888248	−	0.459364i	$-0.848077\pi$
$409$	−35.9274			−1.77650			−0.888248	+	0.459364i	$0.848077\pi$
$410$	−0.649631	−	1.12519i	−0.0320830	−	0.0555694i
$411$	1.76929	+	3.06450i	0.0872726	+	0.151161i
$412$	4.26375	−	7.38503i	0.210060	−	0.363834i
$413$	0.127278	−	0.220452i	0.00626296	−	0.0108478i
$414$	−3.34718			−0.164505
$415$	−11.0400			−0.541934
$416$	0.743593			0.0364576
$417$	0.501938	+	0.869383i	0.0245800	+	0.0425739i
$418$	4.44187	+	7.69354i	0.217259	+	0.376303i
$419$	−1.39282	−	2.41243i	−0.0680435	−	0.117855i	0.829997	−	0.557769i	$-0.188342\pi$
$419$	−1.39282	−	2.41243i	−0.0680435	−	0.117855i	−0.898040	+	0.439914i	$0.855009\pi$
$420$	−0.121108	+	0.209766i	−0.00590949	+	0.0102355i
$421$	−16.6952	+	28.9169i	−0.813673	+	1.40932i	0.0966039	+	0.995323i	$0.469202\pi$
$421$	−16.6952	+	28.9169i	−0.813673	+	1.40932i	−0.910277	+	0.414000i	$0.864131\pi$
$422$	−5.42707			−0.264185
$423$	−6.69756	+	11.6005i	−0.325646	+	0.564036i
$424$	12.3196	+	21.3382i	0.598295	+	1.03628i
$425$	2.58518	−	4.47767i	0.125400	−	0.217199i
$426$	2.26138	−	3.91682i	0.109564	−	0.189771i
$427$	0.0358224	−	0.0620462i	0.00173357	−	0.00300263i
$428$	1.74501	−	3.02244i	0.0843481	−	0.146095i
$429$	−0.249699	+	0.432492i	−0.0120556	+	0.0208809i
$430$	0.0754868	+	0.130747i	0.00364030	+	0.00630518i
$431$	−7.50266	+	12.9950i	−0.361390	+	0.625947i	−0.988190	−	0.153234i	$-0.951031\pi$
$431$	−7.50266	+	12.9950i	−0.361390	+	0.625947i	0.626800	+	0.779181i	$0.284365\pi$
$432$	2.81609	+	4.87762i	0.135489	+	0.234675i
$433$	14.4465			0.694252			0.347126	−	0.937818i	$-0.387158\pi$
$433$	14.4465			0.694252			0.347126	+	0.937818i	$0.387158\pi$
$434$	−0.274023	+	0.474621i	−0.0131535	+	0.0227825i
$435$	5.63683	−	9.76327i	0.270265	−	0.468113i
$436$	11.5086	+	19.9335i	0.551161	+	0.954639i
$437$	3.99151	+	6.91349i	0.190940	+	0.330717i
$438$	0.470448	−	0.814840i	0.0224789	−	0.0389346i
$439$	14.2095	−	24.6116i	0.678183	−	1.17465i	−0.297345	−	0.954770i	$-0.596101\pi$
$439$	14.2095	−	24.6116i	0.678183	−	1.17465i	0.975528	−	0.219877i	$-0.0705655\pi$
$440$	13.5178			0.644436
$441$	−6.57761	+	11.3927i	−0.313219	+	0.542512i
$442$	0.163146			0.00776007
$443$	−5.26680	−	9.12236i	−0.250233	−	0.433417i	0.713357	−	0.700801i	$-0.247174\pi$
$443$	−5.26680	−	9.12236i	−0.250233	−	0.433417i	−0.963590	+	0.267384i	$0.913841\pi$
$444$	6.10375			0.289671
$445$	−3.23915	+	5.61037i	−0.153550	+	0.265957i
$446$	8.14902			0.385867
$447$	−5.37911			−0.254423
$448$	−0.113399	−	0.196413i	−0.00535759	−	0.00927962i
$449$	2.00320			0.0945367			0.0472684	−	0.998882i	$-0.484948\pi$
$449$	2.00320			0.0945367			0.0472684	+	0.998882i	$0.484948\pi$
$450$	−2.01536	+	3.49071i	−0.0950051	+	0.164554i
$451$	2.30587	−	3.99388i	0.108579	−	0.188065i
$452$	4.30798	+	7.46165i	0.202631	+	0.350966i
$453$	16.4983			0.775158
$454$	15.7849			0.740821
$455$	0.00991145	+	0.0171671i	0.000464656	+	0.000804808i
$456$	−4.37804	+	7.58299i	−0.205021	+	0.355106i
$457$	−13.5280			−0.632815			−0.316407	−	0.948623i	$-0.602477\pi$
$457$	−13.5280			−0.632815			−0.316407	+	0.948623i	$0.602477\pi$
$458$	−6.85564			−0.320343
$459$	4.54514	+	7.87242i	0.212149	+	0.367453i
$460$	5.14199			0.239746
$461$	−19.0485	+	32.9929i	−0.887176	+	1.53663i	−0.0439779	+	0.999033i	$0.514003\pi$
$461$	−19.0485	+	32.9929i	−0.887176	+	1.53663i	−0.843199	+	0.537602i	$0.819330\pi$
$462$	0.311541			0.0144942
$463$	−27.9748			−1.30010			−0.650049	−	0.759893i	$-0.725252\pi$
$463$	−27.9748			−1.30010			−0.650049	+	0.759893i	$0.725252\pi$
$464$	−4.04978	−	7.01443i	−0.188006	−	0.325637i
$465$	5.25298	−	9.09842i	0.243601	−	0.421929i
$466$	−2.57809			−0.119428
$467$	42.5174			1.96747			0.983735	−	0.179624i	$-0.0574880\pi$
$467$	42.5174			1.96747			0.983735	+	0.179624i	$0.0574880\pi$
$468$	0.350991			0.0162246
$469$	0.276720	−	0.479294i	0.0127778	−	0.0221317i
$470$	−3.72830	+	6.45761i	−0.171974	+	0.297867i
$471$	9.29407	+	16.0978i	0.428248	+	0.741747i
$472$	−2.96363	−	5.13316i	−0.136412	−	0.236273i
$473$	−0.267941	+	0.464087i	−0.0123199	+	0.0213388i
$474$	−1.60673	−	2.78293i	−0.0737994	−	0.127824i
$475$	9.61326			0.441087
$476$	0.140434	+	0.243239i	0.00643678	+	0.0111488i
$477$	9.16868	+	15.8806i	0.419805	+	0.727123i
$478$	−9.95134	+	17.2362i	−0.455164	+	0.788367i
$479$	13.8420			0.632459			0.316229	−	0.948683i	$-0.397583\pi$
$479$	13.8420			0.632459			0.316229	+	0.948683i	$0.397583\pi$
$480$	4.44623	+	7.70110i	0.202942	+	0.351505i
$481$	0.249764	−	0.432604i	0.0113883	−	0.0197251i
$482$	9.42137			0.429132
$483$	0.279954			0.0127383
$484$	2.08120	+	3.60475i	0.0946001	+	0.163852i
$485$	3.22719	+	5.58965i	0.146539	+	0.253813i
$486$	−5.72047	−	9.90815i	−0.259486	−	0.449443i
$487$	−2.50302	−	4.33537i	−0.113423	−	0.196454i	0.803725	−	0.595000i	$-0.202848\pi$
$487$	−2.50302	−	4.33537i	−0.113423	−	0.196454i	−0.917148	+	0.398546i	$0.869515\pi$
$488$	−0.834112	−	1.44472i	−0.0377585	−	0.0653996i
$489$	7.21126	+	12.4903i	0.326105	+	0.564830i
$490$	−3.66153	+	6.34195i	−0.165411	+	0.286500i
$491$	−6.44511	−	11.1633i	−0.290864	−	0.503791i	0.683150	−	0.730278i	$-0.260609\pi$
$491$	−6.44511	−	11.1633i	−0.290864	−	0.503791i	−0.974014	+	0.226487i	$0.927276\pi$
$492$	1.92412			0.0867462
$493$	−6.53630	−	11.3212i	−0.294380	−	0.509882i
$494$	0.151669	+	0.262698i	0.00682391	+	0.0118194i
$495$	10.0604			0.452181
$496$	−3.77401	−	6.53677i	−0.169458	−	0.293510i
$497$	0.318611	−	0.551851i	0.0142917	−	0.0247539i
$498$	−2.96223	+	5.13074i	−0.132741	+	0.229914i
$499$	−19.8490	−	34.3794i	−0.888562	−	1.53903i	−0.841576	−	0.540139i	$-0.818372\pi$
$499$	−19.8490	−	34.3794i	−0.888562	−	1.53903i	−0.0469861	−	0.998896i	$-0.514962\pi$
$500$	8.36911	−	14.4957i	0.374278	−	0.648269i
$501$	5.85597			0.261625
$502$	−3.80764	+	6.59502i	−0.169943	+	0.294350i
$503$	18.9075			0.843043			0.421522	−	0.906818i	$-0.361496\pi$
$503$	18.9075			0.843043			0.421522	+	0.906818i	$0.361496\pi$
$504$	−0.258631	−	0.447962i	−0.0115203	−	0.0199538i
$505$	3.85170	−	6.67134i	0.171398	−	0.296871i
$506$	−3.30683	−	5.72760i	−0.147006	−	0.254623i
$507$	6.86278	−	11.8867i	0.304787	−	0.527906i
$508$	−6.16776	−	10.6829i	−0.273650	−	0.473976i
$509$	1.53140			0.0678783			0.0339392	−	0.999424i	$-0.489195\pi$
$509$	1.53140			0.0678783			0.0339392	+	0.999424i	$0.489195\pi$
$510$	0.975514	+	1.68964i	0.0431965	+	0.0748185i
$511$	0.0662827	−	0.114805i	0.00293217	−	0.00507867i
$512$	11.9091			0.526314
$513$	−8.45079	+	14.6372i	−0.373112	+	0.646248i
$514$	0.324101	+	0.561360i	0.0142955	+	0.0247605i
$515$	4.17293	−	7.22773i	0.183881	−	0.318492i
$516$	−0.223582			−0.00984266
$517$	−26.4673			−1.16403
$518$	−0.311622			−0.0136919
$519$	−10.2216			−0.448678
$520$	0.461570			0.0202412
$521$	−6.89283	+	11.9387i	−0.301980	+	0.523045i	−0.976584	−	0.215135i	$-0.930981\pi$
$521$	−6.89283	+	11.9387i	−0.301980	+	0.523045i	0.674604	+	0.738180i	$0.264314\pi$
$522$	5.09559	+	8.82582i	0.223028	+	0.386296i
$523$	26.1140			1.14189			0.570944	−	0.820989i	$-0.306577\pi$
$523$	26.1140			1.14189			0.570944	+	0.820989i	$0.306577\pi$
$524$	−6.94264	+	12.0250i	−0.303291	+	0.525315i
$525$	0.168562	−	0.291958i	0.00735666	−	0.0127421i
$526$	8.20249	+	14.2071i	0.357646	+	0.619461i
$527$	−6.09120	−	10.5503i	−0.265337	−	0.459577i
$528$	−2.14536	+	3.71588i	−0.0933650	+	0.161713i
$529$	8.52845	+	14.7717i	0.370802	+	0.642248i
$530$	5.10389	+	8.84019i	0.221699	+	0.383994i
$531$	−2.20563	−	3.82027i	−0.0957163	−	0.165785i
$532$	−0.261109	+	0.452254i	−0.0113205	+	0.0196077i
$533$	0.0787346	−	0.136372i	0.00341038	−	0.00590694i
$534$	1.73824	+	3.01072i	0.0752210	+	0.130287i
$535$	1.70784	−	2.95806i	0.0738363	−	0.127888i
$536$	−6.44334	−	11.1602i	−0.278310	−	0.482047i
$537$	11.9505			0.515700
$538$	−12.9751			−0.559395
$539$	−25.9932			−1.11961
$540$	5.44329	+	9.42806i	0.234242	+	0.405719i
$541$	−0.630251	−	1.09163i	−0.0270966	−	0.0469327i	0.852159	−	0.523283i	$-0.175293\pi$
$541$	−0.630251	−	1.09163i	−0.0270966	−	0.0469327i	−0.879256	+	0.476350i	$0.841960\pi$
$542$	2.23370	−	3.86888i	0.0959456	−	0.166183i
$543$	−13.8169	+	23.9316i	−0.592940	+	1.02700i
$544$	10.3114			0.442100
$545$	11.2635	+	19.5089i	0.482473	+	0.835669i
$546$	0.0106377			0.000455250
$547$	−2.73792	+	23.2272i	−0.117065	+	0.993124i
$547$	−2.73792	+	23.2272i	−0.117065	+	0.993124i
$548$	4.91406			0.209918
$549$	−0.620773	−	1.07521i	−0.0264940	−	0.0458889i
$550$	−7.96427			−0.339597
$551$	12.1530	−	21.0495i	0.517733	−	0.896740i
$552$	3.25932	−	5.64530i	0.138726	−	0.240280i
$553$	−0.226376	−	0.392094i	−0.00962647	−	0.0166735i
$554$	8.19051	+	14.1864i	0.347981	+	0.602721i
$555$	5.97375			0.253571
$556$	1.39409			0.0591228
$557$	−20.2229			−0.856873			−0.428436	−	0.903572i	$-0.640935\pi$
$557$	−20.2229			−0.856873			−0.428436	+	0.903572i	$0.640935\pi$
$558$	4.74859	+	8.22481i	0.201024	+	0.348184i
$559$	−0.00914893	+	0.0158464i	−0.000386958	+	0.000670232i
$560$	0.0851572	+	0.147497i	0.00359855	+	0.00623287i
$561$	−3.46259	+	5.99739i	−0.146191	+	0.253210i
$562$	10.1775	−	17.6279i	0.429310	−	0.743586i
$563$	6.91916	+	11.9843i	0.291608	+	0.505079i	0.974190	−	0.225729i	$-0.0724765\pi$
$563$	6.91916	+	11.9843i	0.291608	+	0.505079i	−0.682582	+	0.730809i	$0.739143\pi$
$564$	−5.52138	−	9.56330i	−0.232492	−	0.402688i
$565$	4.21623	+	7.30272i	0.177378	+	0.307228i
$566$	−4.20903	+	7.29026i	−0.176919	+	0.306432i
$567$	−0.0103871	−	0.0179909i	−0.000436216	−	0.000755549i
$568$	−7.41876	−	12.8497i	−0.311284	−	0.539160i
$569$	−10.7022	+	18.5367i	−0.448658	+	0.777099i	−0.998299	−	0.0583025i	$-0.981431\pi$
$569$	−10.7022	+	18.5367i	−0.448658	+	0.777099i	0.549641	+	0.835401i	$0.314765\pi$
$570$	−1.81377	+	3.14155i	−0.0759706	+	0.131585i
$571$	−18.5752			−0.777348			−0.388674	−	0.921375i	$-0.627067\pi$
$571$	−18.5752			−0.777348			−0.388674	+	0.921375i	$0.627067\pi$
$572$	0.346760	+	0.600606i	0.0144988	+	0.0251126i
$573$	2.31014	−	4.00128i	0.0965075	−	0.167156i
$574$	−0.0982344			−0.00410022
$575$	−7.15677			−0.298458
$576$	−3.93022			−0.163759
$577$	−20.1938			−0.840679			−0.420340	−	0.907367i	$-0.638089\pi$
$577$	−20.1938			−0.840679			−0.420340	+	0.907367i	$0.638089\pi$
$578$	−10.1367			−0.421632
$579$	0.0631001	−	0.109293i	0.00262235	−	0.00454204i
$580$	−7.82792	−	13.5584i	−0.325037	−	0.562980i
$581$	−0.417357	+	0.722883i	−0.0173149	+	0.0299902i
$582$	3.46364			0.143572
$583$	−18.1163	+	31.3783i	−0.750300	+	1.29956i
$584$	−1.54337	−	2.67320i	−0.0638651	−	0.110618i
$585$	0.343515			0.0142026
$586$	6.71658	+	11.6335i	0.277460	+	0.480574i
$587$	−3.88695	+	6.73239i	−0.160431	+	0.277875i	−0.935023	−	0.354586i	$-0.884622\pi$
$587$	−3.88695	+	6.73239i	−0.160431	+	0.277875i	0.774592	+	0.632461i	$0.217955\pi$
$588$	−5.42249	−	9.39202i	−0.223620	−	0.387321i
$589$	11.3254	−	19.6161i	0.466654	−	0.808268i
$590$	−1.22780	−	2.12661i	−0.0505477	−	0.0875512i
$591$	−17.7478			−0.730048
$592$	2.14592	−	3.71685i	0.0881969	−	0.152761i
$593$	−10.6567			−0.437620			−0.218810	−	0.975767i	$-0.570217\pi$
$593$	−10.6567			−0.437620			−0.218810	+	0.975767i	$0.570217\pi$
$594$	7.00120	−	12.1264i	0.287263	−	0.497553i
$595$	0.137443	+	0.238058i	0.00563460	+	0.00975941i
$596$	−3.73501	+	6.46923i	−0.152992	+	0.264990i
$597$	8.29573	−	14.3686i	0.339521	−	0.588068i
$598$	−0.112913	−	0.195571i	−0.00461734	−	0.00799747i
$599$	17.4763			0.714063			0.357032	−	0.934092i	$-0.383789\pi$
$599$	17.4763			0.714063			0.357032	+	0.934092i	$0.383789\pi$
$600$	−3.92492	−	6.79815i	−0.160234	−	0.277533i
$601$	−9.25061	−	16.0225i	−0.377340	−	0.653572i	0.613334	−	0.789823i	$-0.289828\pi$
$601$	−9.25061	−	16.0225i	−0.377340	−	0.653572i	−0.990674	+	0.136251i	$0.956495\pi$
$602$	0.0114148			0.000465232
$603$	−4.79534	−	8.30578i	−0.195282	−	0.338238i
$604$	11.4557	−	19.8418i	0.466125	−	0.807352i
$605$	2.03687	+	3.52797i	0.0828107	+	0.143432i
$606$	−2.06696	−	3.58007i	−0.0839644	−	0.145431i
$607$	−12.5993	−	21.8227i	−0.511391	−	0.885756i	−0.999913	−	0.0132037i	$-0.995797\pi$
$607$	−12.5993	−	21.8227i	−0.511391	−	0.885756i	0.488522	−	0.872552i	$-0.337536\pi$
$608$	9.58604	+	16.6035i	0.388765	+	0.673361i
$609$	−0.426188	−	0.738180i	−0.0172700	−	0.0299125i
$610$	−0.345563	−	0.598533i	−0.0139915	−	0.0242339i
$611$	−0.903733			−0.0365611
$612$	4.86721			0.196745
$613$	−5.75856	+	9.97412i	−0.232586	+	0.402851i	−0.958568	−	0.284862i	$-0.908052\pi$
$613$	−5.75856	+	9.97412i	−0.232586	+	0.402851i	0.725982	+	0.687713i	$0.241385\pi$
$614$	3.98434	+	6.90107i	0.160795	+	0.278505i
$615$	1.88314			0.0759355
$616$	0.511026	−	0.885123i	0.0205898	−	0.0356626i
$617$	13.7921	+	23.8886i	0.555248	+	0.961718i	0.997884	+	0.0650169i	$0.0207101\pi$
$617$	13.7921	+	23.8886i	0.555248	+	0.961718i	−0.442636	+	0.896701i	$0.645957\pi$
$618$	−2.23934	−	3.87865i	−0.0900794	−	0.156022i
$619$	−11.0064			−0.442384			−0.221192	−	0.975230i	$-0.570995\pi$
$619$	−11.0064			−0.442384			−0.221192	+	0.975230i	$0.570995\pi$
$620$	−7.29486	−	12.6351i	−0.292969	−	0.507437i
$621$	6.29135	−	10.8969i	0.252463	−	0.437279i
$622$	8.78601	+	15.2178i	0.352287	+	0.610179i
$623$	0.244905	+	0.424188i	0.00981191	+	0.0169947i
$624$	−0.0732541	+	0.126880i	−0.00293251	+	0.00507926i
$625$	0.851621	−	1.47505i	0.0340648	−	0.0590020i
$626$	3.85990			0.154272
$627$	−12.8760			−0.514218
$628$	25.8135			1.03007
$629$	3.46349	−	5.99894i	0.138098	−	0.239194i
$630$	−0.107148	−	0.185586i	−0.00426888	−	0.00739391i
$631$	3.03804			0.120942			0.0604712	−	0.998170i	$-0.480740\pi$
$631$	3.03804			0.120942			0.0604712	+	0.998170i	$0.480740\pi$
$632$	−10.5422			−0.419345
$633$	3.93297	−	6.81211i	0.156322	−	0.270757i
$634$	5.85171			0.232401
$635$	−6.03639	−	10.4553i	−0.239547	−	0.414907i
$636$	−15.1171			−0.599430
$637$	−0.887547			−0.0351659
$638$	−10.0683	+	17.4388i	−0.398608	+	0.690410i
$639$	−5.52128	−	9.56314i	−0.218419	−	0.378312i
$640$	14.6361			0.578541
$641$	−2.52535			−0.0997455			−0.0498727	−	0.998756i	$-0.515882\pi$
$641$	−2.52535			−0.0997455			−0.0498727	+	0.998756i	$0.515882\pi$
$642$	−0.916485	−	1.58740i	−0.0361708	−	0.0626496i
$643$	−8.74314	+	15.1436i	−0.344796	+	0.597204i	−0.985317	−	0.170737i	$-0.945385\pi$
$643$	−8.74314	+	15.1436i	−0.344796	+	0.597204i	0.640521	+	0.767941i	$0.278719\pi$
$644$	0.194387	−	0.336689i	0.00765993	−	0.0132674i
$645$	−0.218820			−0.00861603
$646$	2.10320	+	3.64285i	0.0827493	+	0.143326i
$647$	32.5026			1.27781			0.638905	−	0.769286i	$-0.279388\pi$
$647$	32.5026			1.27781			0.638905	+	0.769286i	$0.279388\pi$
$648$	−0.483719			−0.0190023
$649$	4.35808	−	7.54842i	0.171070	−	0.296301i
$650$	−0.271942			−0.0106665
$651$	−0.397166	−	0.687912i	−0.0155662	−	0.0269614i
$652$	20.0287			0.784385
$653$	−18.5405	+	32.1130i	−0.725544	+	1.25668i	0.233205	+	0.972428i	$0.425079\pi$
$653$	−18.5405	+	32.1130i	−0.725544	+	1.25668i	−0.958750	+	0.284252i	$0.908255\pi$
$654$	12.0887			0.472706
$655$	−6.79477	+	11.7689i	−0.265493	+	0.459848i
$656$	0.676472	−	1.17168i	0.0264118	−	0.0457466i
$657$	−1.14863	−	1.98948i	−0.0448122	−	0.0776170i
$658$	0.281889	+	0.488246i	0.0109892	+	0.0190338i
$659$	22.4266	−	38.8440i	0.873617	−	1.51315i	0.0153881	−	0.999882i	$-0.495102\pi$
$659$	22.4266	−	38.8440i	0.873617	−	1.51315i	0.858229	−	0.513267i	$-0.171565\pi$
$660$	−4.14682	+	7.18251i	−0.161415	+	0.279579i
$661$	−21.7521			−0.846058			−0.423029	−	0.906116i	$-0.639033\pi$
$661$	−21.7521			−0.846058			−0.423029	+	0.906116i	$0.639033\pi$
$662$	−7.03886	−	12.1917i	−0.273573	−	0.473843i
$663$	−0.118231	+	0.204783i	−0.00459172	+	0.00795310i
$664$	9.71801	+	16.8321i	0.377132	+	0.653212i
$665$	−0.255547	+	0.442621i	−0.00990970	+	0.0171641i
$666$	−2.70008	+	4.67667i	−0.104626	+	0.181217i
$667$	−9.04749	+	15.6707i	−0.350320	+	0.606773i
$668$	4.06612	−	7.04273i	0.157323	−	0.272491i
$669$	−5.90556	+	10.2287i	−0.228322	+	0.395465i
$670$	−2.66940	−	4.62354i	−0.103128	−	0.178623i
$671$	1.22658	−	2.12450i	0.0473516	−	0.0820153i
$672$	0.672340			0.0259361
$673$	12.2608	−	21.2364i	0.472620	−	0.818602i	−0.526889	−	0.849934i	$-0.676642\pi$
$673$	12.2608	−	21.2364i	0.472620	−	0.818602i	0.999509	+	0.0313323i	$0.00997501\pi$
$674$	11.4983	−	19.9156i	0.442898	−	0.767122i
$675$	−7.57614	−	13.1223i	−0.291606	−	0.505076i
$676$	−9.53041	−	16.5072i	−0.366554	−	0.634891i
$677$	6.50132	+	11.2606i	0.249866	+	0.432781i	0.963488	−	0.267750i	$-0.0862801\pi$
$677$	6.50132	+	11.2606i	0.249866	+	0.432781i	−0.713622	+	0.700531i	$0.752947\pi$
$678$	4.52514			0.173787
$679$	0.488001			0.0187278
$680$	6.40061			0.245452
$681$	−11.4392	+	19.8133i	−0.438352	+	0.759248i
$682$	−9.38269	+	16.2513i	−0.359282	+	0.622295i
$683$	23.7243	+	41.0917i	0.907786	+	1.57233i	0.817133	+	0.576449i	$0.195562\pi$
$683$	23.7243	+	41.0917i	0.907786	+	1.57233i	0.0906532	+	0.995883i	$0.471105\pi$
$684$	4.52481	+	7.83720i	0.173010	+	0.299663i
$685$	4.80939			0.183757
$686$	0.554148	+	0.959813i	0.0211575	+	0.0366458i
$687$	4.96825	−	8.60526i	0.189551	−	0.328311i
$688$	−0.0786057	+	0.136149i	−0.00299682	+	0.00519064i
$689$	−0.618586	+	1.07142i	−0.0235663	+	0.0408180i
$690$	1.35030	−	2.33878i	0.0514050	−	0.0890360i
$691$	0.918535	+	1.59095i	0.0349427	+	0.0605226i	0.882968	−	0.469433i	$-0.155542\pi$
$691$	0.918535	+	1.59095i	0.0349427	+	0.0605226i	−0.848025	+	0.529956i	$0.822208\pi$
$692$	−7.09742	+	12.2931i	−0.269803	+	0.467313i
$693$	0.380322	−	0.658737i	0.0144472	−	0.0250234i
$694$	7.59206	−	13.1498i	0.288191	−	0.499161i
$695$	1.36440			0.0517547
$696$	−19.8473			−0.752310
$697$	1.09182	−	1.89108i	0.0413555	−	0.0716299i
$698$	0.329246			0.0124622
$699$	1.86833	−	3.23604i	0.0706667	−	0.122398i
$700$	−0.234084	−	0.405446i	−0.00884755	−	0.0153244i
$701$	−17.8903			−0.675708			−0.337854	−	0.941199i	$-0.609701\pi$
$701$	−17.8903			−0.675708			−0.337854	+	0.941199i	$0.609701\pi$
$702$	0.239058	−	0.414061i	0.00902267	−	0.0156277i
$703$	12.8794			0.485754
$704$	−3.88284	−	6.72528i	−0.146340	−	0.253469i
$705$	−5.40377	−	9.35961i	−0.203518	−	0.352503i
$706$	−8.29956	−	14.3753i	−0.312358	−	0.541020i
$707$	−0.291219	−	0.504406i	−0.0109524	−	0.0189701i
$708$	3.63658			0.136671
$709$	−23.3338	−	40.4154i	−0.876320	−	1.51783i	−0.855350	−	0.518050i	$-0.826658\pi$
$709$	−23.3338	−	40.4154i	−0.876320	−	1.51783i	−0.0209699	−	0.999780i	$-0.506675\pi$
$710$	−3.07351	−	5.32347i	−0.115347	−	0.199786i
$711$	−7.84582			−0.294241
$712$	11.4051			0.427423
$713$	−8.43139	+	14.6036i	−0.315758	+	0.546909i
$714$	0.147513			0.00552053
$715$	0.339374	+	0.587813i	0.0126919	+	0.0219830i
$716$	8.29786	−	14.3723i	0.310106	−	0.537119i
$717$	−14.4234	−	24.9820i	−0.538651	−	0.932971i
$718$	−9.45630	+	16.3788i	−0.352906	+	0.611251i
$719$	32.1196			1.19786			0.598930	−	0.800801i	$-0.295593\pi$
$719$	32.1196			1.19786			0.598930	+	0.800801i	$0.295593\pi$
$720$	2.95141			0.109993
$721$	−0.315506	−	0.546473i	−0.0117501	−	0.0203517i
$722$	3.01841	−	5.22803i	0.112333	−	0.194567i
$723$	−6.82763	+	11.8258i	−0.253922	+	0.439806i
$724$	19.1877	+	33.2340i	0.713104	+	1.23513i
$725$	10.8951	+	18.8709i	0.404635	+	0.700848i
$726$	2.18611			0.0811343
$727$	7.38238	+	12.7867i	0.273797	+	0.474231i	0.969831	−	0.243778i	$-0.0783869\pi$
$727$	7.38238	+	12.7867i	0.273797	+	0.474231i	−0.696034	+	0.718009i	$0.745054\pi$
$728$	0.0174491	−	0.0302228i	0.000646708	−	0.00112013i
$729$	16.0087			0.592915
$730$	−0.639401	−	1.10747i	−0.0236653	−	0.0409895i
$731$	−0.126869	+	0.219743i	−0.00469241	+	0.00812749i
$732$	1.02351			0.0378302
$733$	0.182751	+	0.316533i	0.00675004	+	0.0116914i	0.869381	−	0.494143i	$-0.164518\pi$
$733$	0.182751	+	0.316533i	0.00675004	+	0.0116914i	−0.862631	+	0.505834i	$0.831185\pi$
$734$	−2.97530	+	5.15337i	−0.109820	+	0.190214i
$735$	−5.30699	−	9.19198i	−0.195751	−	0.339051i
$736$	−7.13651	−	12.3608i	−0.263055	−	0.455625i
$737$	9.47507	−	16.4113i	0.349019	−	0.604518i
$738$	−0.851162	+	1.47426i	−0.0313317	+	0.0542681i
$739$	18.1126			0.666282			0.333141	−	0.942877i	$-0.391891\pi$
$739$	18.1126			0.666282			0.333141	+	0.942877i	$0.391891\pi$
$740$	4.14790	−	7.18438i	0.152480	−	0.264103i
$741$	−0.439655			−0.0161511
$742$	0.771788			0.0283332
$743$	−18.8757	−	32.6936i	−0.692482	−	1.19941i	−0.971022	−	0.238989i	$-0.923184\pi$
$743$	−18.8757	−	32.6936i	−0.692482	−	1.19941i	0.278540	−	0.960424i	$-0.410149\pi$
$744$	−18.4958			−0.678087
$745$	−3.65545	+	6.33143i	−0.133925	+	0.231966i
$746$	2.98651	−	5.17279i	0.109344	−	0.189389i
$747$	7.23246	+	12.5270i	0.264622	+	0.458339i
$748$	4.80854	+	8.32863i	0.175818	+	0.304525i
$749$	−0.129126	−	0.223653i	−0.00471816	−	0.00817209i
$750$	−4.39550	−	7.61322i	−0.160501	−	0.277996i
$751$	−4.22035			−0.154003			−0.0770013	−	0.997031i	$-0.524535\pi$
$751$	−4.22035			−0.154003			−0.0770013	+	0.997031i	$0.524535\pi$
$752$	−7.76469			−0.283149
$753$	−5.51876	−	9.55877i	−0.201115	−	0.348341i
$754$	−0.343786	+	0.595455i	−0.0125199	+	0.0216852i
$755$	11.2117	−	19.4192i	0.408035	−	0.706737i
$756$	0.823111			0.0299363
$757$	10.7922	+	18.6926i	0.392248	+	0.679394i	0.992746	−	0.120233i	$-0.0383641\pi$
$757$	10.7922	+	18.6926i	0.392248	+	0.679394i	−0.600497	+	0.799627i	$0.705031\pi$
$758$	−7.52011	+	13.0252i	−0.273143	+	0.473097i
$759$	9.58578			0.347942
$760$	5.95033	+	10.3063i	0.215841	+	0.373848i
$761$	4.37748	+	7.58202i	0.158684	+	0.274848i	0.934394	−	0.356241i	$-0.115942\pi$
$761$	4.37748	+	7.58202i	0.158684	+	0.274848i	−0.775711	+	0.631089i	$0.782608\pi$
$762$	−6.47867			−0.234697
$763$	1.70321			0.0616604
$764$	−3.20812	−	5.55662i	−0.116066	−	0.201031i
$765$	4.76354			0.172226
$766$	−5.54739	−	9.60835i	−0.200435	−	0.347164i
$767$	0.148808	−	0.257743i	0.00537315	−	0.00930657i
$768$	6.13415	−	10.6247i	0.221347	−	0.383384i
$769$	0.862017	−	1.49306i	0.0310851	−	0.0538410i	−0.850064	−	0.526679i	$-0.823437\pi$
$769$	0.862017	−	1.49306i	0.0310851	−	0.0538410i	0.881149	+	0.472838i	$0.156770\pi$
$770$	0.211712	−	0.366697i	0.00762958	−	0.0132148i
$771$	−0.939499			−0.0338352
$772$	−0.0876277	−	0.151776i	−0.00315379	−	0.00546253i
$773$	1.88615			0.0678400			0.0339200	−	0.999425i	$-0.489201\pi$
$773$	1.88615			0.0678400			0.0339200	+	0.999425i	$0.489201\pi$
$774$	0.0989046	−	0.171308i	0.00355505	−	0.00615753i
$775$	10.1532	+	17.5859i	0.364714	+	0.631703i
$776$	5.68147	−	9.84060i	0.203953	−	0.353257i
$777$	0.225831	−	0.391151i	0.00810164	−	0.0140325i
$778$	6.87286	−	11.9041i	0.246404	−	0.426784i
$779$	4.06003			0.145466
$780$	−0.141595	+	0.245249i	−0.00506990	+	0.00878132i
$781$	10.9094	−	18.8957i	0.390370	−	0.676141i
$782$	−1.56577	−	2.71199i	−0.0559917	−	0.0969805i
$783$	−38.3106			−1.36911
$784$	−7.62562			−0.272344
$785$	25.2637			0.901701
$786$	3.64631	+	6.31559i	0.130059	+	0.225270i
$787$	−13.3466			−0.475754			−0.237877	−	0.971295i	$-0.576452\pi$
$787$	−13.3466			−0.475754			−0.237877	+	0.971295i	$0.576452\pi$
$788$	−12.3233	+	21.3446i	−0.438999	+	0.760369i
$789$	−23.7773			−0.846493
$790$	−4.36750			−0.155389
$791$	0.637559			0.0226690
$792$	−8.85568	−	15.3385i	−0.314673	−	0.545029i
$793$	0.0418819	−	0.0725416i	0.00148727	−	0.00257603i
$794$	−14.2823			−0.506859
$795$	−14.7951			−0.524727
$796$	−11.5204	−	19.9539i	−0.408328	−	0.707245i
$797$	−15.5967	−	27.0142i	−0.552462	−	0.956893i	−0.998096	−	0.0616773i	$-0.980355\pi$
$797$	−15.5967	−	27.0142i	−0.552462	−	0.956893i	0.445634	−	0.895215i	$-0.352978\pi$
$798$	0.137136	+	0.237526i	0.00485455	+	0.00840832i
$799$	−12.5321			−0.443354
$800$	−17.1878			−0.607680
$801$	8.48802			0.299909
$802$	−8.26439			−0.291826
$803$	2.26956	−	3.93099i	0.0800909	−	0.138722i
$804$	7.90643			0.278838
$805$	0.190247	−	0.329517i	0.00670532	−	0.0116140i
$806$	−0.320375	+	0.554906i	−0.0112847	+	0.0195457i
$807$	9.40298	−	16.2864i	0.331001	−	0.573310i
$808$	−13.5619			−0.477105
$809$	−14.1266	−	24.4680i	−0.496665	−	0.860249i	0.503327	−	0.864096i	$-0.332109\pi$
$809$	−14.1266	−	24.4680i	−0.496665	−	0.860249i	−0.999993	+	0.00384639i	$0.998776\pi$
$810$	−0.200400			−0.00704132
$811$	1.64467	+	2.84865i	0.0577521	+	0.100030i	0.893456	−	0.449151i	$-0.148273\pi$
$811$	1.64467	+	2.84865i	0.0577521	+	0.100030i	−0.835704	+	0.549180i	$0.814940\pi$
$812$	−1.18370			−0.0415399
$813$	3.23750	+	5.60752i	0.113544	+	0.196664i
$814$	−10.6701			−0.373987
$815$	19.6021			0.686632
$816$	−1.01582	+	1.75945i	−0.0355608	+	0.0615931i
$817$	−0.471774			−0.0165053
$818$	13.1019	+	22.6932i	0.458099	+	0.793451i
$819$	0.0129862	−	0.0224928i	0.000453775	−	0.000785962i
$820$	1.30757	−	2.26477i	0.0456622	−	0.0790893i
$821$	13.5058	−	23.3928i	0.471357	−	0.816414i	−0.528106	−	0.849178i	$-0.677098\pi$
$821$	13.5058	−	23.3928i	0.471357	−	0.816414i	0.999463	+	0.0327642i	$0.0104310\pi$
$822$	1.29044	−	2.23511i	0.0450094	−	0.0779585i
$823$	−23.8675	−	41.3397i	−0.831968	−	1.44101i	−0.896476	−	0.443093i	$-0.853881\pi$
$823$	−23.8675	−	41.3397i	−0.831968	−	1.44101i	0.0645077	−	0.997917i	$-0.479452\pi$
$824$	−14.6929			−0.511852
$825$	5.77167	−	9.99683i	0.200944	−	0.348045i
$826$	−0.185663			−0.00646003
$827$	16.3398			0.568190			0.284095	−	0.958796i	$-0.408307\pi$
$827$	16.3398			0.568190			0.284095	+	0.958796i	$0.408307\pi$
$828$	−3.36858	−	5.83455i	−0.117066	−	0.202765i
$829$	−19.4623			−0.675953			−0.337977	−	0.941155i	$-0.609742\pi$
$829$	−19.4623			−0.675953			−0.337977	+	0.941155i	$0.609742\pi$
$830$	4.02606	+	6.97335i	0.139747	+	0.242048i
$831$	−23.7425			−0.823618
$832$	−0.132581	−	0.229637i	−0.00459642	−	0.00796123i
$833$	−12.3077			−0.426435
$834$	0.366092	−	0.634090i	0.0126767	−	0.0219568i
$835$	3.97952	−	6.89272i	0.137717	−	0.238533i
$836$	−8.94052	+	15.4854i	−0.309214	+	0.535575i
$837$	−35.7018			−1.23403
$838$	−1.01586	+	1.75952i	−0.0350923	+	0.0607816i
$839$	36.9895			1.27702			0.638509	−	0.769614i	$-0.279551\pi$
$839$	36.9895			1.27702			0.638509	+	0.769614i	$0.279551\pi$
$840$	0.417341			0.0143996
$841$	26.0939			0.899789
$842$	24.3535			0.839276
$843$	14.7511	+	25.5497i	0.508055	+	0.879977i
$844$	−5.46176	−	9.46004i	−0.188001	−	0.325628i
$845$	−9.32741	−	16.1556i	−0.320873	−	0.555768i
$846$	9.76982			0.335893
$847$	0.308007			0.0105833
$848$	−5.31477	+	9.20544i	−0.182510	+	0.316116i
$849$	−6.10053	−	10.5664i	−0.209370	−	0.362639i
$850$	−3.77104			−0.129346
$851$	−9.58827			−0.328682
$852$	9.10334			0.311875
$853$	0.365162	−	0.632479i	0.0125029	−	0.0216557i	−0.859706	−	0.510789i	$-0.829353\pi$
$853$	0.365162	−	0.632479i	0.0125029	−	0.0216557i	0.872209	+	0.489133i	$0.162687\pi$
$854$	−0.0522546			−0.00178812
$855$	4.42843	+	7.67027i	0.151449	+	0.262318i
$856$	−6.01331			−0.205531
$857$	−46.1633			−1.57691			−0.788454	−	0.615094i	$-0.789118\pi$
$857$	−46.1633			−1.57691			−0.788454	+	0.615094i	$0.789118\pi$
$858$	0.364240			0.0124349
$859$	3.38704	+	5.86653i	0.115564	+	0.200163i	0.918005	−	0.396568i	$-0.129799\pi$
$859$	3.38704	+	5.86653i	0.115564	+	0.200163i	−0.802441	+	0.596732i	$0.796466\pi$
$860$	−0.151939	+	0.263166i	−0.00518107	+	0.00897388i
$861$	0.0711900	−	0.123305i	0.00242615	−	0.00420222i
$862$	10.9442			0.372762
$863$	1.21585	−	2.10591i	0.0413880	−	0.0716861i	−0.844589	−	0.535415i	$-0.820155\pi$
$863$	1.21585	−	2.10591i	0.0413880	−	0.0716861i	0.885977	+	0.463729i	$0.153489\pi$
$864$	15.1094	−	26.1702i	0.514031	−	0.890328i
$865$	−6.94624	+	12.0312i	−0.236179	+	0.409075i
$866$	−5.26831	−	9.12498i	−0.179024	−	0.310079i
$867$	7.34603	−	12.7237i	0.249484	−	0.432119i
$868$	−1.10310			−0.0374416
$869$	−7.75124	−	13.4255i	−0.262943	−	0.455430i
$870$	−8.22252			−0.278769
$871$	0.323529	−	0.560369i	0.0109624	−	0.0189874i
$872$	19.8294	−	34.3454i	0.671507	−	1.16308i
$873$	4.22834	−	7.32369i	0.143107	−	0.247869i
$874$	2.91123	−	5.04240i	0.0984739	−	0.170562i
$875$	−0.619293	−	1.07265i	−0.0209359	−	0.0362621i
$876$	1.89382			0.0639863
$877$	−15.4442	−	26.7501i	−0.521513	−	0.903287i	−0.999687	−	0.0250217i	$-0.992034\pi$
$877$	−15.4442	−	26.7501i	−0.521513	−	0.903287i	0.478174	−	0.878265i	$-0.341299\pi$
$878$	−20.7276			−0.699523
$879$	−19.4699			−0.656704
$880$	2.91583	+	5.05037i	0.0982927	+	0.170248i
$881$	29.0761	+	50.3612i	0.979598	+	1.69671i	0.663842	+	0.747873i	$0.268925\pi$
$881$	29.0761	+	50.3612i	0.979598	+	1.69671i	0.315756	+	0.948841i	$0.397742\pi$
$882$	9.59484			0.323075
$883$	−8.17117	+	14.1529i	−0.274982	+	0.476282i	−0.970131	−	0.242583i	$-0.922005\pi$
$883$	−8.17117	+	14.1529i	−0.274982	+	0.476282i	0.695149	+	0.718866i	$0.255338\pi$
$884$	0.164189	+	0.284384i	0.00552227	+	0.00956486i
$885$	3.55913			0.119639
$886$	−3.84138	+	6.65346i	−0.129054	+	0.223527i
$887$	3.16057	−	5.47427i	0.106122	−	0.183808i	−0.808074	−	0.589081i	$-0.799490\pi$
$887$	3.16057	−	5.47427i	0.106122	−	0.183808i	0.914196	+	0.405273i	$0.132823\pi$
$888$	−5.25840	−	9.10782i	−0.176460	−	0.305638i
$889$	−0.912797			−0.0306142
$890$	4.72499			0.158382
$891$	−0.355660	−	0.616021i	−0.0119150	−	0.0206375i
$892$	8.20111	+	14.2047i	0.274594	+	0.475610i
$893$	−11.6505	−	20.1792i	−0.389869	−	0.675273i
$894$	1.96164	+	3.39767i	0.0656072	+	0.113635i
$895$	8.12112	−	14.0662i	0.271459	−	0.470181i
$896$	0.553300	−	0.958344i	0.0184845	−	0.0320160i
$897$	0.327309			0.0109285
$898$	−0.730523	−	1.26530i	−0.0243779	−	0.0422237i
$899$	51.3422			1.71236
$900$	−8.11299			−0.270433
$901$	−8.57797	+	14.8575i	−0.285774	+	0.494974i
$902$	−3.36360			−0.111996
$903$	−0.00827225	+	0.0143280i	−0.000275283	+	0.000476805i
$904$	7.42268	−	12.8565i	0.246875	−	0.427599i
$905$	18.7790	+	32.5261i	0.624234	+	1.08121i
$906$	−6.01657	−	10.4210i	−0.199887	−	0.346215i
$907$	4.98726	−	8.63818i	0.165599	−	0.286826i	−0.771269	−	0.636510i	$-0.780378\pi$
$907$	4.98726	−	8.63818i	0.165599	−	0.286826i	0.936868	+	0.349684i	$0.113711\pi$
$908$	15.8858	+	27.5150i	0.527188	+	0.913116i
$909$	−10.0932			−0.334770
$910$	0.00722899	−	0.0125210i	0.000239639	−	0.000415066i
$911$	4.51283	+	7.81645i	0.149517	+	0.258971i	0.931049	−	0.364894i	$-0.118895\pi$
$911$	4.51283	+	7.81645i	0.149517	+	0.258971i	−0.781532	+	0.623865i	$0.785562\pi$
$912$	−3.77743			−0.125083
$913$	−14.2905	+	24.7519i	−0.472948	+	0.819170i
$914$	4.93338	+	8.54487i	0.163182	+	0.282639i
$915$	1.00171			0.0331156
$916$	−6.89946	−	11.9502i	−0.227965	−	0.394846i
$917$	0.513738	+	0.889819i	0.0169651	+	0.0293844i
$918$	3.31503	−	5.74180i	0.109412	−	0.189508i
$919$	2.03366	−	3.52241i	0.0670844	−	0.116194i	−0.830532	−	0.556970i	$-0.811964\pi$
$919$	2.03366	−	3.52241i	0.0670844	−	0.116194i	0.897617	+	0.440777i	$0.145297\pi$
$920$	−4.42984	−	7.67270i	−0.146047	−	0.252961i
$921$	−11.5497			−0.380576
$922$	27.7863			0.915093
$923$	0.372506	−	0.645200i	0.0122612	−	0.0212370i
$924$	0.313532	+	0.543054i	0.0103145	+	0.0178652i
$925$	−5.77317	+	9.99943i	−0.189821	+	0.328779i
$926$	10.2018	+	17.6700i	0.335252	+	0.580673i
$927$	−10.9349			−0.359151
$928$	−21.7286	+	37.6350i	−0.713275	+	1.23543i
$929$	51.2519			1.68152			0.840760	−	0.541407i	$-0.182108\pi$
$929$	51.2519			1.68152			0.840760	+	0.541407i	$0.182108\pi$
$930$	−7.66259			−0.251266
$931$	−11.4418	−	19.8178i	−0.374991	−	0.649503i
$932$	−2.59457	−	4.49393i	−0.0849880	−	0.147203i
$933$	−25.4687			−0.833809
$934$	−15.5052	−	26.8558i	−0.507345	−	0.878747i
$935$	4.70612	+	8.15123i	0.153906	+	0.266574i
$936$	−0.302380	−	0.523737i	−0.00988359	−	0.0171189i
$937$	1.91237	+	3.31232i	0.0624743	+	0.108209i	0.895571	−	0.444919i	$-0.146768\pi$
$937$	1.91237	+	3.31232i	0.0624743	+	0.108209i	−0.833097	+	0.553128i	$0.813434\pi$
$938$	−0.403656			−0.0131798
$939$	−2.79725	+	4.84498i	−0.0912848	+	0.158110i
$940$	−15.0085			−0.489525
$941$	2.45496	+	4.25212i	0.0800295	+	0.138615i	0.903262	−	0.429089i	$-0.141165\pi$
$941$	2.45496	+	4.25212i	0.0800295	+	0.138615i	−0.823233	+	0.567704i	$0.807832\pi$
$942$	6.77869	−	11.7410i	0.220862	−	0.382544i
$943$	−3.02257			−0.0984284
$944$	1.27853	−	2.21448i	0.0416126	−	0.0720751i
$945$	0.805579			0.0262055
$946$	0.390849			0.0127076
$947$	4.21693	−	7.30394i	0.137032	−	0.237346i	−0.789340	−	0.613956i	$-0.789577\pi$
$947$	4.21693	−	7.30394i	0.137032	−	0.237346i	0.926372	+	0.376610i	$0.122910\pi$
$948$	3.23399	−	5.60144i	0.105035	−	0.181926i
$949$	0.0774948	−	0.134225i	0.00251559	−	0.00435712i
$950$	−3.50575	−	6.07214i	−0.113742	−	0.197006i
$951$	−4.24071	+	7.34512i	−0.137514	+	0.238182i
$952$	0.241968	−	0.419101i	0.00784224	−	0.0135831i
$953$	−16.5706	+	28.7011i	−0.536774	+	0.929721i	0.462301	+	0.886723i	$0.347024\pi$
$953$	−16.5706	+	28.7011i	−0.536774	+	0.929721i	−0.999075	+	0.0429974i	$0.986309\pi$
$954$	6.68724	−	11.5826i	0.216507	−	0.375002i
$955$	−3.13978	−	5.43827i	−0.101601	−	0.175978i
$956$	−40.0598			−1.29563
$957$	−14.5929	−	25.2757i	−0.471723	−	0.817047i
$958$	−5.04789	−	8.74321i	−0.163090	−	0.282480i
$959$	0.181814	−	0.314911i	0.00587108	−	0.0101690i
$960$	1.58551	−	2.74618i	0.0511720	−	0.0886324i
$961$	16.8459			0.543416
$962$	−0.364334			−0.0117466
$963$	−4.47530			−0.144215
$964$	9.48160	+	16.4226i	0.305382	+	0.528937i
$965$	−0.0857613	−	0.148543i	−0.00276075	−	0.00478176i
$966$	−0.102093	−	0.176830i	−0.00328479	−	0.00568943i
$967$	12.3441	−	21.3807i	0.396960	−	0.687556i	−0.596389	−	0.802696i	$-0.703398\pi$
$967$	12.3441	−	21.3807i	0.396960	−	0.687556i	0.993349	+	0.115140i	$0.0367317\pi$
$968$	3.58592	−	6.21100i	0.115256	−	0.199629i
$969$	−6.09672			−0.195855
$970$	2.35377	−	4.07685i	0.0755750	−	0.130900i
$971$	2.83341	+	4.90762i	0.0909286	+	0.157493i	0.907902	−	0.419182i	$-0.137683\pi$
$971$	2.83341	+	4.90762i	0.0909286	+	0.157493i	−0.816974	+	0.576675i	$0.804350\pi$
$972$	11.5141	−	19.9430i	0.369314	−	0.639671i
$973$	0.0515797	−	0.0893386i	0.00165357	−	0.00286406i
$974$	−1.82560	+	3.16203i	−0.0584959	+	0.101318i
$975$	0.197076	−	0.341345i	0.00631147	−	0.0109318i
$976$	0.359841	−	0.623263i	0.0115182	−	0.0199502i
$977$	15.5943	+	27.0101i	0.498906	+	0.864131i	0.999999	−	0.00126250i	$-0.000401867\pi$
$977$	15.5943	+	27.0101i	0.498906	+	0.864131i	−0.501093	+	0.865393i	$0.667069\pi$
$978$	5.25958	−	9.10987i	0.168183	−	0.291301i
$979$	8.38569	+	14.5244i	0.268008	+	0.464203i
$980$	−14.7397			−0.470844
$981$	14.7576	−	25.5610i	0.471175	−	0.816100i
$982$	−4.70079	+	8.14200i	−0.150008	+	0.259822i
$983$	−13.4355	−	23.2709i	−0.428525	−	0.742227i	0.568217	−	0.822879i	$-0.307633\pi$
$983$	−13.4355	−	23.2709i	−0.428525	−	0.742227i	−0.996742	+	0.0806512i	$0.974300\pi$
$984$	−1.65764	−	2.87111i	−0.0528435	−	0.0915277i
$985$	−12.0608	+	20.8899i	−0.384289	+	0.665609i
$986$	−4.76730	+	8.25720i	−0.151822	+	0.262963i
$987$	−0.817135			−0.0260097
$988$	−0.305277	+	0.528755i	−0.00971215	+	0.0168219i
$989$	0.351221			0.0111682
$990$	−3.66881	−	6.35456i	−0.116602	−	0.201961i
$991$	26.3242			0.836217			0.418109	−	0.908397i	$-0.362693\pi$
$991$	26.3242			0.836217			0.418109	+	0.908397i	$0.362693\pi$
$992$	−20.2489	+	35.0721i	−0.642903	+	1.11354i
$993$	20.4041			0.647506
$994$	−0.464763			−0.0147414
$995$	−11.2750	−	19.5288i	−0.357441	−	0.619106i
$996$	−11.9247			−0.377848
$997$	11.1148	−	19.2514i	0.352009	−	0.609698i	−0.634592	−	0.772847i	$-0.718832\pi$
$997$	11.1148	−	19.2514i	0.352009	−	0.609698i	0.986601	+	0.163149i	$0.0521652\pi$
$998$	−14.4770	+	25.0749i	−0.458261	+	0.793731i
$999$	−10.1501	−	17.5805i	−0.321135	−	0.556223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.19	✓	90
547.506	even	3	inner	547.2.c.a.506.19	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.19	✓	90	1.1	even	1	trivial
547.2.c.a.506.19	yes	90	547.506	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.364678 - 0.631642i) q^{2} +1.05712 q^{3} +(0.734019 - 1.27136i) q^{4} +(0.718385 - 1.24428i) q^{5} +(-0.385510 - 0.667723i) q^{6} +(-0.0543155 - 0.0940772i) q^{7} -2.52944 q^{8} -1.88249 q^{9} +O(q^{10})\)	\(q+(-0.364678 - 0.631642i) q^{2} +1.05712 q^{3} +(0.734019 - 1.27136i) q^{4} +(0.718385 - 1.24428i) q^{5} +(-0.385510 - 0.667723i) q^{6} +(-0.0543155 - 0.0940772i) q^{7} -2.52944 q^{8} -1.88249 q^{9} -1.04792 q^{10} +(-1.85980 - 3.22126i) q^{11} +(0.775949 - 1.34398i) q^{12} +(-0.0635033 - 0.109991i) q^{13} +(-0.0396154 + 0.0686159i) q^{14} +(0.759422 - 1.31536i) q^{15} +(-0.545607 - 0.945019i) q^{16} +(-0.880604 - 1.52525i) q^{17} +(0.686503 + 1.18906i) q^{18} +(1.63731 - 2.83590i) q^{19} +(-1.05462 - 1.82665i) q^{20} +(-0.0574182 - 0.0994513i) q^{21} +(-1.35645 + 2.34945i) q^{22} +(-1.21892 + 2.11124i) q^{23} -2.67393 q^{24} +(1.46785 + 2.54238i) q^{25} +(-0.0463166 + 0.0802226i) q^{26} -5.16140 q^{27} -0.159475 q^{28} +7.42253 q^{29} -1.10778 q^{30} +6.91707 q^{31} +(-2.92738 + 5.07037i) q^{32} +(-1.96603 - 3.40527i) q^{33} +(-0.642274 + 1.11245i) q^{34} -0.156078 q^{35} +(-1.38178 + 2.39332i) q^{36} +(1.96654 + 3.40616i) q^{37} -2.38836 q^{38} +(-0.0671308 - 0.116274i) q^{39} +(-1.81711 + 3.14733i) q^{40} +(0.619926 + 1.07374i) q^{41} +(-0.0418784 + 0.0725355i) q^{42} +(-0.0720351 - 0.124768i) q^{43} -5.46050 q^{44} +(-1.35235 + 2.34234i) q^{45} +1.77806 q^{46} +(3.55782 - 6.16233i) q^{47} +(-0.576774 - 0.999002i) q^{48} +(3.49410 - 6.05196i) q^{49} +(1.07058 - 1.85431i) q^{50} +(-0.930907 - 1.61238i) q^{51} -0.186451 q^{52} +(-4.87051 - 8.43596i) q^{53} +(1.88225 + 3.26015i) q^{54} -5.34419 q^{55} +(0.137388 + 0.237963i) q^{56} +(1.73084 - 2.99790i) q^{57} +(-2.70683 - 4.68838i) q^{58} +(1.17166 + 2.02937i) q^{59} +(-1.11486 - 1.93099i) q^{60} +(0.329762 + 0.571164i) q^{61} +(-2.52251 - 4.36911i) q^{62} +(0.102248 + 0.177099i) q^{63} +2.08778 q^{64} -0.182479 q^{65} +(-1.43394 + 2.48366i) q^{66} +(2.54734 + 4.41213i) q^{67} -2.58552 q^{68} +(-1.28855 + 2.23184i) q^{69} +(0.0569182 + 0.0985852i) q^{70} +(2.93297 + 5.08005i) q^{71} +4.76164 q^{72} +(0.610163 + 1.05683i) q^{73} +(1.43431 - 2.48430i) q^{74} +(1.55170 + 2.68761i) q^{75} +(-2.40363 - 4.16321i) q^{76} +(-0.202031 + 0.349929i) q^{77} +(-0.0489623 + 0.0848052i) q^{78} +4.16779 q^{79} -1.56782 q^{80} +0.191236 q^{81} +(0.452147 - 0.783141i) q^{82} +(-3.84197 - 6.65448i) q^{83} -0.168584 q^{84} -2.53045 q^{85} +(-0.0525393 + 0.0910007i) q^{86} +7.84653 q^{87} +(4.70424 + 8.14798i) q^{88} -4.50893 q^{89} +1.97269 q^{90} +(-0.00689843 + 0.0119484i) q^{91} +(1.78943 + 3.09938i) q^{92} +7.31220 q^{93} -5.18984 q^{94} +(-2.35243 - 4.07453i) q^{95} +(-3.09460 + 5.36001i) q^{96} +(-2.24614 + 3.89043i) q^{97} -5.09689 q^{98} +(3.50105 + 6.06399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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