LMFDB - Embedded newform 770.2.bv.a.157.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			157.33
Character	$\chi$	$=$	770.157
Dual form			770.2.bv.a.103.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.358368 + 0.933580i) q^{2} +(-0.837605 - 1.28980i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.48465 - 1.67207i) q^{5} +(0.903960 - 1.24419i) q^{6} +(2.63859 + 0.194548i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(0.258211 - 0.579952i) q^{9} +O(q^{10})$	\(q+(0.358368 + 0.933580i) q^{2} +(-0.837605 - 1.28980i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.48465 - 1.67207i) q^{5} +(0.903960 - 1.24419i) q^{6} +(2.63859 + 0.194548i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(0.258211 - 0.579952i) q^{9} +(2.09306 + 0.786822i) q^{10} +(-0.852145 - 3.20528i) q^{11} +(1.48551 + 0.398040i) q^{12} +(-2.56353 - 0.406023i) q^{13} +(0.763960 + 2.53305i) q^{14} +(-3.40018 - 0.514363i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-0.247607 + 0.645039i) q^{17} +(0.633967 + 0.0332248i) q^{18} +(-1.35537 + 1.50529i) q^{19} +(0.0155247 + 2.23601i) q^{20} +(-1.95917 - 3.56620i) q^{21} +(2.68701 - 1.94422i) q^{22} +(1.91793 + 0.513907i) q^{23} +(0.160755 + 1.52948i) q^{24} +(-0.591638 - 4.96487i) q^{25} +(-0.539631 - 2.53877i) q^{26} +(-5.52122 + 0.874476i) q^{27} +(-2.09103 + 1.62098i) q^{28} +(-4.99572 - 1.62321i) q^{29} +(-0.738317 - 3.35868i) q^{30} +(6.69489 - 0.703662i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.42041 + 3.78386i) q^{33} -0.690930 q^{34} +(4.24267 - 4.12307i) q^{35} +(0.196175 + 0.603766i) q^{36} +(-0.790201 - 0.513163i) q^{37} +(-1.89102 - 0.725896i) q^{38} +(1.62354 + 3.64652i) q^{39} +(-2.08194 + 0.815809i) q^{40} +(-3.48874 + 1.13356i) q^{41} +(2.62723 - 3.10705i) q^{42} +(7.61122 - 7.61122i) q^{43} +(2.77802 + 1.81179i) q^{44} +(-0.586368 - 1.29277i) q^{45} +(0.207550 + 1.97471i) q^{46} +(-0.623773 - 11.9023i) q^{47} +(-1.37029 + 0.698196i) q^{48} +(6.92430 + 1.02666i) q^{49} +(4.42308 - 2.33159i) q^{50} +(1.03937 - 0.220924i) q^{51} +(2.17676 - 1.41360i) q^{52} +(9.76349 + 7.90632i) q^{53} +(-2.79502 - 4.84112i) q^{54} +(-6.62460 - 3.33387i) q^{55} +(-2.26268 - 1.37124i) q^{56} +(3.07678 + 0.487314i) q^{57} +(-0.274911 - 5.24561i) q^{58} +(-5.73484 - 6.36919i) q^{59} +(2.87100 - 1.89292i) q^{60} +(-3.98951 - 0.419314i) q^{61} +(3.05616 + 5.99805i) q^{62} +(0.794142 - 1.48002i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-4.48484 + 3.68360i) q^{65} +(-4.75830 - 1.83722i) q^{66} +(14.1612 - 3.79447i) q^{67} +(-0.247607 - 0.645039i) q^{68} +(-0.943630 - 2.90419i) q^{69} +(5.36966 + 2.48330i) q^{70} +(-1.72082 - 1.25025i) q^{71} +(-0.493361 + 0.399516i) q^{72} +(-0.498810 + 9.51787i) q^{73} +(0.195896 - 0.921617i) q^{74} +(-5.90813 + 4.92170i) q^{75} -2.02556i q^{76} +(-1.62488 - 8.62321i) q^{77} +(-2.82250 + 2.82250i) q^{78} +(-0.170998 + 0.384067i) q^{79} +(-1.50772 - 1.65129i) q^{80} +(4.47814 + 4.97348i) q^{81} +(-2.30852 - 2.85079i) q^{82} +(1.16214 + 7.33745i) q^{83} +(3.84220 + 1.33927i) q^{84} +(0.710941 + 1.37167i) q^{85} +(9.83330 + 4.37807i) q^{86} +(2.09083 + 7.80308i) q^{87} +(-0.695902 + 3.24280i) q^{88} +(2.28526 + 3.95818i) q^{89} +(0.996772 - 1.01071i) q^{90} +(-6.68511 - 1.57006i) q^{91} +(-1.76917 + 0.901437i) q^{92} +(-6.51526 - 8.04568i) q^{93} +(10.8882 - 4.84774i) q^{94} +(0.504703 + 4.50109i) q^{95} +(-1.14289 - 1.02906i) q^{96} +(-1.12547 + 7.10596i) q^{97} +(1.52298 + 6.83232i) q^{98} +(-2.07895 - 0.333438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.358368	+	0.933580i	0.253404	+	0.660141i
$2$	0.358368	+	0.933580i	0.253404	+	0.660141i
$3$	−0.837605	−	1.28980i	−0.483592	−	0.744666i	0.509694	−	0.860356i	$-0.329759\pi$
$3$	−0.837605	−	1.28980i	−0.483592	−	0.744666i	−0.993285	+	0.115690i	$0.963092\pi$
$4$	−0.743145	+	0.669131i	−0.371572	+	0.334565i
$5$	1.48465	−	1.67207i	0.663955	−	0.747773i
$5$	1.48465	−	1.67207i	0.663955	−	0.747773i
$6$	0.903960	−	1.24419i	0.369040	−	0.507940i
$7$	2.63859	+	0.194548i	0.997293	+	0.0735322i
$7$	2.63859	+	0.194548i	0.997293	+	0.0735322i
$8$	−0.891007	−	0.453990i	−0.315018	−	0.160510i
$9$	0.258211	−	0.579952i	0.0860705	−	0.193317i
$10$	2.09306	+	0.786822i	0.661884	+	0.248815i
$11$	−0.852145	−	3.20528i	−0.256931	−	0.966430i
$11$	−0.852145	−	3.20528i	−0.256931	−	0.966430i
$12$	1.48551	+	0.398040i	0.428829	+	0.114904i
$13$	−2.56353	−	0.406023i	−0.710995	−	0.112611i	−0.209547	−	0.977798i	$-0.567199\pi$
$13$	−2.56353	−	0.406023i	−0.710995	−	0.112611i	−0.501448	+	0.865188i	$0.667199\pi$
$14$	0.763960	+	2.53305i	0.204177	+	0.676987i
$15$	−3.40018	−	0.514363i	−0.877924	−	0.132808i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−0.247607	+	0.645039i	−0.0600536	+	0.156445i	−0.960324	−	0.278885i	$-0.910035\pi$
$17$	−0.247607	+	0.645039i	−0.0600536	+	0.156445i	0.900271	+	0.435330i	$0.143368\pi$
$18$	0.633967	+	0.0332248i	0.149427	+	0.00783116i
$19$	−1.35537	+	1.50529i	−0.310942	+	0.345336i	−0.878278	−	0.478150i	$-0.841307\pi$
$19$	−1.35537	+	1.50529i	−0.310942	+	0.345336i	0.567336	+	0.823486i	$0.307974\pi$
$20$	0.0155247	+	2.23601i	0.00347142	+	0.499988i
$21$	−1.95917	−	3.56620i	−0.427525	−	0.778209i
$22$	2.68701	−	1.94422i	0.572872	−	0.414508i
$23$	1.91793	+	0.513907i	0.399916	+	0.107157i	0.453171	−	0.891424i	$-0.350293\pi$
$23$	1.91793	+	0.513907i	0.399916	+	0.107157i	−0.0532547	+	0.998581i	$0.516960\pi$
$24$	0.160755	+	1.52948i	0.0328140	+	0.312205i
$25$	−0.591638	−	4.96487i	−0.118328	−	0.992975i
$26$	−0.539631	−	2.53877i	−0.105830	−	0.497893i
$27$	−5.52122	+	0.874476i	−1.06256	+	0.168293i
$28$	−2.09103	+	1.62098i	−0.395168	+	0.306337i
$29$	−4.99572	−	1.62321i	−0.927682	−	0.301422i	−0.194068	−	0.980988i	$-0.562168\pi$
$29$	−4.99572	−	1.62321i	−0.927682	−	0.301422i	−0.733614	+	0.679566i	$0.762168\pi$
$30$	−0.738317	−	3.35868i	−0.134798	−	0.613207i
$31$	6.69489	−	0.703662i	1.20244	−	0.126381i	0.517954	−	0.855409i	$-0.326694\pi$
$31$	6.69489	−	0.703662i	1.20244	−	0.126381i	0.684485	+	0.729027i	$0.260027\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−3.42041	+	3.78386i	−0.595417	+	0.658685i
$34$	−0.690930			−0.118494
$35$	4.24267	−	4.12307i	0.717143	−	0.696926i
$36$	0.196175	+	0.603766i	0.0326959	+	0.100628i
$37$	−0.790201	−	0.513163i	−0.129908	−	0.0843634i	0.478049	−	0.878333i	$-0.341344\pi$
$37$	−0.790201	−	0.513163i	−0.129908	−	0.0843634i	−0.607957	+	0.793970i	$0.708011\pi$
$38$	−1.89102	−	0.725896i	−0.306765	−	0.117756i
$39$	1.62354	+	3.64652i	0.259974	+	0.583911i
$40$	−2.08194	+	0.815809i	−0.329183	+	0.128991i
$41$	−3.48874	+	1.13356i	−0.544850	+	0.177033i	−0.568493	−	0.822688i	$-0.692473\pi$
$41$	−3.48874	+	1.13356i	−0.544850	+	0.177033i	0.0236432	+	0.999720i	$0.492473\pi$
$42$	2.62723	−	3.10705i	0.405391	−	0.479429i
$43$	7.61122	−	7.61122i	1.16070	−	1.16070i	0.176377	−	0.984323i	$-0.443562\pi$
$43$	7.61122	−	7.61122i	1.16070	−	1.16070i	0.984323	−	0.176377i	$-0.0564379\pi$
$44$	2.77802	+	1.81179i	0.418802	+	0.273138i
$45$	−0.586368	−	1.29277i	−0.0874106	−	0.192715i
$46$	0.207550	+	1.97471i	0.0306016	+	0.291155i
$47$	−0.623773	−	11.9023i	−0.0909866	−	1.73613i	−0.539179	−	0.842191i	$-0.681265\pi$
$47$	−0.623773	−	11.9023i	−0.0909866	−	1.73613i	0.448192	−	0.893937i	$-0.352068\pi$
$48$	−1.37029	+	0.698196i	−0.197784	+	0.100776i
$49$	6.92430	+	1.02666i	0.989186	+	0.146666i
$50$	4.42308	−	2.33159i	0.625519	−	0.329737i
$51$	1.03937	−	0.220924i	0.145541	−	0.0309356i
$52$	2.17676	−	1.41360i	0.301862	−	0.196031i
$53$	9.76349	+	7.90632i	1.34112	+	1.08602i	0.988657	+	0.150189i	$0.0479884\pi$
$53$	9.76349	+	7.90632i	1.34112	+	1.08602i	0.352461	+	0.935827i	$0.385345\pi$
$54$	−2.79502	−	4.84112i	−0.380355	−	0.658793i
$55$	−6.62460	−	3.33387i	−0.893260	−	0.449540i
$56$	−2.26268	−	1.37124i	−0.302363	−	0.183239i
$57$	3.07678	+	0.487314i	0.407529	+	0.0645463i
$58$	−0.274911	−	5.24561i	−0.0360976	−	0.688783i
$59$	−5.73484	−	6.36919i	−0.746613	−	0.829198i	0.243437	−	0.969917i	$-0.421725\pi$
$59$	−5.73484	−	6.36919i	−0.746613	−	0.829198i	−0.990050	+	0.140719i	$0.955059\pi$
$60$	2.87100	−	1.89292i	0.370645	−	0.244375i
$61$	−3.98951	−	0.419314i	−0.510804	−	0.0536876i	−0.154379	−	0.988012i	$-0.549338\pi$
$61$	−3.98951	−	0.419314i	−0.510804	−	0.0536876i	−0.356425	+	0.934324i	$0.616004\pi$
$62$	3.05616	+	5.99805i	0.388133	+	0.761753i
$63$	0.794142	−	1.48002i	0.100053	−	0.186465i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−4.48484	+	3.68360i	−0.556276	+	0.456894i
$66$	−4.75830	−	1.83722i	−0.585706	−	0.226146i
$67$	14.1612	−	3.79447i	1.73006	−	0.463568i	0.749864	−	0.661592i	$-0.230119\pi$
$67$	14.1612	−	3.79447i	1.73006	−	0.463568i	0.980197	+	0.198024i	$0.0634524\pi$
$68$	−0.247607	−	0.645039i	−0.0300268	−	0.0782224i
$69$	−0.943630	−	2.90419i	−0.113600	−	0.349624i
$70$	5.36966	+	2.48330i	0.641797	+	0.296811i
$71$	−1.72082	−	1.25025i	−0.204223	−	0.148377i	0.480973	−	0.876735i	$-0.340284\pi$
$71$	−1.72082	−	1.25025i	−0.204223	−	0.148377i	−0.685196	+	0.728359i	$0.740284\pi$
$72$	−0.493361	+	0.399516i	−0.0581432	+	0.0470834i
$73$	−0.498810	+	9.51787i	−0.0583813	+	1.11398i	0.799677	+	0.600430i	$0.205004\pi$
$73$	−0.498810	+	9.51787i	−0.0583813	+	1.11398i	−0.858059	+	0.513552i	$0.828329\pi$
$74$	0.195896	−	0.921617i	0.0227724	−	0.107136i
$75$	−5.90813	+	4.92170i	−0.682212	+	0.568309i
$76$		−	2.02556i		−	0.232348i
$77$	−1.62488	−	8.62321i	−0.185172	−	0.982706i
$78$	−2.82250	+	2.82250i	−0.319585	+	0.319585i
$79$	−0.170998	+	0.384067i	−0.0192387	+	0.0432109i	−0.922909	−	0.385017i	$-0.874195\pi$
$79$	−0.170998	+	0.384067i	−0.0192387	+	0.0432109i	0.903671	+	0.428228i	$0.140862\pi$
$80$	−1.50772	−	1.65129i	−0.168569	−	0.184620i
$81$	4.47814	+	4.97348i	0.497571	+	0.552608i
$82$	−2.30852	−	2.85079i	−0.254934	−	0.314817i
$83$	1.16214	+	7.33745i	0.127561	+	0.805390i	0.965648	+	0.259853i	$0.0836741\pi$
$83$	1.16214	+	7.33745i	0.127561	+	0.805390i	−0.838087	+	0.545537i	$0.816326\pi$
$84$	3.84220	+	1.33927i	0.419218	+	0.146126i
$85$	0.710941	+	1.37167i	0.0771123	+	0.148779i
$86$	9.83330	+	4.37807i	1.06035	+	0.472099i
$87$	2.09083	+	7.80308i	0.224160	+	0.836578i
$88$	−0.695902	+	3.24280i	−0.0741834	+	0.345683i
$89$	2.28526	+	3.95818i	0.242237	+	0.419566i	0.961351	−	0.275326i	$-0.0887857\pi$
$89$	2.28526	+	3.95818i	0.242237	+	0.419566i	−0.719114	+	0.694892i	$0.755452\pi$
$90$	0.996772	−	1.01071i	0.105069	−	0.106538i
$91$	−6.68511	−	1.57006i	−0.700790	−	0.164587i
$92$	−1.76917	+	0.901437i	−0.184449	+	0.0939813i
$93$	−6.51526	−	8.04568i	−0.675601	−	0.834298i
$94$	10.8882	−	4.84774i	1.12303	−	0.500007i
$95$	0.504703	+	4.50109i	0.0517814	+	0.461802i
$96$	−1.14289	−	1.02906i	−0.116646	−	0.105028i
$97$	−1.12547	+	7.10596i	−0.114275	+	0.721501i	0.862312	+	0.506377i	$0.169016\pi$
$97$	−1.12547	+	7.10596i	−0.114275	+	0.721501i	−0.976587	+	0.215124i	$0.930984\pi$
$98$	1.52298	+	6.83232i	0.153844	+	0.690168i
$99$	−2.07895	−	0.333438i	−0.208942	−	0.0335118i
$100$	3.76182	+	3.29374i	0.376182	+	0.329374i
$101$	−7.50242	+	0.788536i	−0.746518	+	0.0784622i	−0.470146	−	0.882588i	$-0.655799\pi$
$101$	−7.50242	+	0.788536i	−0.746518	+	0.0784622i	−0.276372	+	0.961051i	$0.589132\pi$
$102$	0.578727	+	0.891161i	0.0573025	+	0.0882381i
$103$	3.38675	+	2.19938i	0.333707	+	0.216712i	0.700605	−	0.713549i	$-0.252914\pi$
$103$	3.38675	+	2.19938i	0.333707	+	0.216712i	−0.366898	+	0.930261i	$0.619580\pi$
$104$	2.09979	+	1.52559i	0.205901	+	0.149596i
$105$	−8.87162	−	2.01869i	−0.865781	−	0.197004i
$106$	−3.88226	+	11.9484i	−0.377079	+	1.16053i
$107$	−8.65895	+	0.453796i	−0.837092	+	0.0438702i	−0.466064	−	0.884751i	$-0.654328\pi$
$107$	−8.65895	+	0.453796i	−0.837092	+	0.0438702i	−0.371029	+	0.928621i	$0.620995\pi$
$108$	3.51793	−	4.34428i	0.338513	−	0.418029i
$109$	3.41695	+	1.97277i	0.327284	+	0.188958i	0.654635	−	0.755945i	$-0.272822\pi$
$109$	3.41695	+	1.97277i	0.327284	+	0.188958i	−0.327351	+	0.944903i	$0.606156\pi$
$110$	0.738397	−	7.37935i	0.0704034	−	0.703593i
$111$			1.44903i			0.137536i
$112$	0.469290	−	2.60380i	0.0443437	−	0.246036i
$113$	5.61742	+	2.86222i	0.528443	+	0.269255i	0.697791	−	0.716301i	$-0.254166\pi$
$113$	5.61742	+	2.86222i	0.528443	+	0.269255i	−0.169349	+	0.985556i	$0.554166\pi$
$114$	0.647672	+	3.04706i	0.0606600	+	0.285383i
$115$	3.70674	−	2.44394i	0.345655	−	0.227899i
$116$	4.79868	−	2.13651i	0.445547	−	0.198370i
$117$	−0.897407	+	1.38189i	−0.0829653	+	0.127755i
$118$	3.89096	−	7.63645i	0.358192	−	0.702992i
$119$	−0.778824	+	1.65382i	−0.0713947	+	0.151605i
$120$	2.79607	+	2.00195i	0.255245	+	0.182752i
$121$	−9.54770	+	5.46273i	−0.867973	+	0.496612i
$122$	−1.03825	−	3.87479i	−0.0939985	−	0.350807i
$123$	4.38425	+	3.55030i	0.395315	+	0.320120i
$124$	−4.50443	+	5.00268i	−0.404510	+	0.449254i
$125$	−9.17999	−	6.38183i	−0.821083	−	0.570808i
$126$	1.66631	+	0.211003i	0.148447	+	0.0187977i
$127$	2.21034	+	13.9555i	0.196136	+	1.23835i	0.867579	+	0.497299i	$0.165675\pi$
$127$	2.21034	+	13.9555i	0.196136	+	1.23835i	−0.671443	+	0.741056i	$0.734325\pi$
$128$	−0.544639	+	0.838671i	−0.0481397	+	0.0741287i
$129$	−16.1921	−	3.44174i	−1.42564	−	0.303029i
$130$	−5.04616	−	2.86687i	−0.442577	−	0.251441i
$131$	−1.74873	+	1.00963i	−0.152787	+	0.0882117i	−0.574444	−	0.818544i	$-0.694782\pi$
$131$	−1.74873	+	1.00963i	−0.152787	+	0.0882117i	0.421657	+	0.906755i	$0.361449\pi$
$132$	0.00996589	−	5.10066i	0.000867420	−	0.443955i
$133$	−3.86910	+	3.70815i	−0.335494	+	0.321537i
$134$	8.61735	+	11.8608i	0.744426	+	1.02461i
$135$	−6.73489	+	10.5302i	−0.579647	+	0.906292i
$136$	0.513461	−	0.462322i	0.0440289	−	0.0396438i
$137$	18.9524	+	7.27515i	1.61921	+	0.621558i	0.988056	−	0.154096i	$-0.0492467\pi$
$137$	18.9524	+	7.27515i	1.61921	+	0.621558i	0.631158	+	0.775654i	$0.282580\pi$
$138$	2.37313	−	1.92172i	0.202014	−	0.163588i
$139$	−3.83701	+	11.8091i	−0.325451	+	1.00163i	0.645786	+	0.763519i	$0.276530\pi$
$139$	−3.83701	+	11.8091i	−0.325451	+	1.00163i	−0.971237	+	0.238116i	$0.923470\pi$
$140$	−0.394048	+	5.90294i	−0.0333032	+	0.498890i
$141$	−14.8291	+	10.7740i	−1.24883	+	0.907332i
$142$	0.550520	−	2.05457i	0.0461986	−	0.172416i
$143$	0.883078	+	8.56283i	0.0738467	+	0.716060i
$144$	−0.549785	−	0.317418i	−0.0458154	−	0.0264515i
$145$	−10.1310	+	5.94330i	−0.841335	+	0.493565i
$146$	−9.06445	+	2.94522i	−0.750179	+	0.243748i
$147$	−4.47564	−	9.79089i	−0.369145	−	0.807539i
$148$	0.930607	−	0.147394i	0.0764954	−	0.0121157i
$149$	−16.0586	−	1.68783i	−1.31557	−	0.138272i	−0.579386	−	0.815053i	$-0.696708\pi$
$149$	−16.0586	−	1.68783i	−1.31557	−	0.138272i	−0.736185	+	0.676781i	$0.763374\pi$
$150$	−6.71208	−	3.75193i	−0.548039	−	0.306344i
$151$	15.3470	+	3.26210i	1.24892	+	0.265466i	0.784488	−	0.620144i	$-0.212926\pi$
$151$	15.3470	+	3.26210i	1.24892	+	0.265466i	0.464430	+	0.885610i	$0.346259\pi$
$152$	1.89102	−	0.725896i	0.153382	−	0.0588780i
$153$	0.310157	+	0.310157i	0.0250747	+	0.0250747i
$154$	7.46816	−	4.60724i	0.601801	−	0.371262i
$155$	8.76299	−	12.2390i	0.703861	−	0.983062i
$156$	−3.64652	−	1.62354i	−0.291956	−	0.129987i
$157$	−7.21661	+	4.68652i	−0.575948	+	0.374025i	−0.799499	−	0.600667i	$-0.794902\pi$
$157$	−7.21661	+	4.68652i	−0.575948	+	0.374025i	0.223551	+	0.974692i	$0.428235\pi$
$158$	−0.419838	−	0.0220028i	−0.0334005	−	0.00175045i
$159$	2.01961	−	19.2153i	0.160165	−	1.52387i
$160$	1.00130	−	1.99935i	0.0791594	−	0.158063i
$161$	4.96065	+	1.72912i	0.390954	+	0.136274i
$162$	−3.03832	+	5.96304i	−0.238713	+	0.468500i
$163$	−3.81253	+	1.46349i	−0.298621	+	0.114630i	−0.503065	−	0.864248i	$-0.667794\pi$
$163$	−3.81253	+	1.46349i	−0.298621	+	0.114630i	0.204445	+	0.978878i	$0.434461\pi$
$164$	1.83414	−	3.17682i	0.143222	−	0.248068i
$165$	1.24877	+	11.3369i	0.0972165	+	0.882574i
$166$	−6.43363	+	3.71446i	−0.499346	+	0.288298i
$167$	2.34312	−	14.7939i	0.181316	−	1.14478i	−0.714262	−	0.699878i	$-0.753238\pi$
$167$	2.34312	−	14.7939i	0.181316	−	1.14478i	0.895578	−	0.444905i	$-0.146762\pi$
$168$	0.126609	+	4.06695i	0.00976811	+	0.313772i
$169$	−5.95691	−	1.93552i	−0.458224	−	0.148886i
$170$	−1.02579	+	1.15528i	−0.0786744	+	0.0886062i
$171$	0.523023	+	1.17473i	0.0399966	+	0.0898338i
$172$	−0.563338	+	10.7491i	−0.0429542	+	0.819614i
$173$	21.1493	−	1.10839i	1.60795	−	0.0842692i	0.772932	−	0.634489i	$-0.218789\pi$
$173$	21.1493	−	1.10839i	1.60795	−	0.0842692i	0.835020	+	0.550220i	$0.185456\pi$
$174$	−6.53552	+	4.74833i	−0.495456	+	0.359970i
$175$	−0.595185	−	13.2154i	−0.0449918	−	0.998987i
$176$	−3.27680	+	0.512433i	−0.246998	+	0.0386261i
$177$	−3.41144	+	12.7317i	−0.256419	+	0.956970i
$178$	−2.87632	+	3.55195i	−0.215589	+	0.266230i
$179$	2.50026	−	11.7628i	0.186878	−	0.879193i	−0.780361	−	0.625329i	$-0.784965\pi$
$179$	2.50026	−	11.7628i	0.186878	−	0.879193i	0.967240	−	0.253865i	$-0.0817017\pi$
$180$	1.30079	+	0.568361i	0.0969552	+	0.0423631i
$181$	6.58139	−	9.05850i	0.489191	−	0.673313i	−0.491048	−	0.871133i	$-0.663386\pi$
$181$	6.58139	−	9.05850i	0.489191	−	0.673313i	0.980238	+	0.197819i	$0.0633860\pi$
$182$	−0.929954	−	6.80375i	−0.0689328	−	0.504327i
$183$	2.80080	+	5.49688i	0.207041	+	0.406341i
$184$	−1.47558	−	1.32862i	−0.108781	−	0.0979469i
$185$	−2.03121	+	0.559406i	−0.149338	+	0.0411283i
$186$	5.17643	−	8.96583i	0.379554	−	0.657407i
$187$	2.27853	+	0.243985i	0.166623	+	0.0178420i
$188$	8.42775	+	8.42775i	0.614657	+	0.614657i
$189$	−14.7384	+	1.23324i	−1.07206	+	0.0897051i
$190$	−4.02126	+	2.08423i	−0.291733	+	0.151206i
$191$	18.6278	−	3.95946i	1.34786	−	0.286497i	0.523242	−	0.852184i	$-0.324722\pi$
$191$	18.6278	−	3.95946i	1.34786	−	0.286497i	0.824620	+	0.565687i	$0.191389\pi$
$192$	0.551137	−	1.43576i	0.0397749	−	0.103617i
$193$	−4.64356	+	12.0969i	−0.334251	+	0.870753i	0.658719	+	0.752389i	$0.271098\pi$
$193$	−4.64356	+	12.0969i	−0.334251	+	0.870753i	−0.992970	+	0.118364i	$0.962235\pi$
$194$	−7.03732	+	1.49583i	−0.505250	+	0.107394i
$195$	8.50763	+	2.69914i	0.609244	+	0.193289i
$196$	−5.83273	+	3.87030i	−0.416624	+	0.276450i
$197$	7.62041	+	7.62041i	0.542931	+	0.542931i	0.924387	−	0.381456i	$-0.124577\pi$
$197$	7.62041	+	7.62041i	0.542931	+	0.542931i	−0.381456	+	0.924387i	$0.624577\pi$
$198$	−0.433737	−	2.06036i	−0.0308243	−	0.146423i
$199$	8.53451	−	14.7822i	0.604995	−	1.04788i	−0.387057	−	0.922056i	$-0.626508\pi$
$199$	8.53451	−	14.7822i	0.604995	−	1.04788i	0.992052	−	0.125827i	$-0.0401584\pi$
$200$	−1.72685	+	4.69233i	−0.122107	+	0.331798i
$201$	−16.7556	−	15.0868i	−1.18185	−	1.06414i
$202$	−3.42479	−	6.72152i	−0.240967	−	0.472925i
$203$	−12.8659	−	5.25489i	−0.903007	−	0.368821i
$204$	−0.624573	+	0.859651i	−0.0437289	+	0.0601876i
$205$	−3.28416	+	7.51636i	−0.229376	+	0.524966i
$206$	−0.839598	+	3.95000i	−0.0584975	+	0.275209i
$207$	0.793273	−	0.979611i	0.0551363	−	0.0680876i
$208$	−0.671761	+	2.50705i	−0.0465782	+	0.173832i
$209$	5.97984	+	3.06161i	0.413634	+	0.211776i
$210$	−1.29469	−	9.00580i	−0.0893423	−	0.621459i
$211$	−9.02439	+	6.55660i	−0.621265	+	0.451375i	−0.853363	−	0.521317i	$-0.825441\pi$
$211$	−9.02439	+	6.55660i	−0.621265	+	0.451375i	0.232098	+	0.972692i	$0.425441\pi$
$212$	−12.5460	+	0.657510i	−0.861666	+	0.0451580i
$213$	−0.171201	+	3.26672i	−0.0117305	+	0.223832i
$214$	−3.52675	−	7.92120i	−0.241083	−	0.541482i
$215$	−1.42651	−	24.0265i	−0.0972871	−	1.63859i
$216$	5.31645	+	1.72742i	0.361739	+	0.117536i
$217$	17.8020	−	0.554197i	1.20848	−	0.0376213i
$218$	−0.617220	+	3.89697i	−0.0418034	+	0.263936i
$219$	12.6939	−	7.32885i	0.857777	−	0.495238i
$220$	7.15383	−	1.95517i	0.482311	−	0.131817i
$221$	0.896649	−	1.55304i	0.0603151	−	0.104469i
$222$	−1.35278	+	0.519285i	−0.0907929	+	0.0348521i
$223$	−11.9839	+	23.5197i	−0.802502	+	1.57500i	0.0155675	+	0.999879i	$0.495045\pi$
$223$	−11.9839	+	23.5197i	−0.802502	+	1.57500i	−0.818069	+	0.575120i	$0.804955\pi$
$224$	2.59903	−	0.494998i	0.173655	−	0.0330735i
$225$	−3.03216	−	0.938865i	−0.202144	−	0.0625910i
$226$	−0.659008	+	6.27004i	−0.0438366	+	0.417077i
$227$	26.0307	+	1.36421i	1.72772	+	0.0905458i	0.890116	−	0.455735i	$-0.150623\pi$
$227$	26.0307	+	1.36421i	1.72772	+	0.0905458i	0.837602	+	0.546281i	$0.183957\pi$
$228$	−2.61257	+	1.69662i	−0.173021	+	0.112361i
$229$	3.32541	+	1.48057i	0.219750	+	0.0978388i	0.513659	−	0.857995i	$-0.328290\pi$
$229$	3.32541	+	1.48057i	0.219750	+	0.0978388i	−0.293909	+	0.955833i	$0.594956\pi$
$230$	3.60999	+	2.58471i	0.238036	+	0.170431i
$231$	−9.76120	+	9.31861i	−0.642240	+	0.613120i
$232$	3.71430	+	3.71430i	0.243856	+	0.243856i
$233$	10.8763	−	4.17501i	0.712528	−	0.273514i	0.0250162	−	0.999687i	$-0.492036\pi$
$233$	10.8763	−	4.17501i	0.712528	−	0.273514i	0.687512	+	0.726173i	$0.258703\pi$
$234$	−1.61170	−	0.342578i	−0.105360	−	0.0223950i
$235$	−20.8276	−	16.6277i	−1.35864	−	1.08467i
$236$	8.52364	+	0.895870i	0.554841	+	0.0583162i
$237$	0.638598	−	0.101144i	0.0414814	−	0.00657000i
$238$	−1.82308	−	0.134419i	−0.118173	−	0.00871309i
$239$	−5.66665	+	1.84121i	−0.366545	+	0.119098i	−0.486498	−	0.873682i	$-0.661726\pi$
$239$	−5.66665	+	1.84121i	−0.366545	+	0.119098i	0.119952	+	0.992780i	$0.461726\pi$
$240$	−0.866961	+	3.32779i	−0.0559621	+	0.214808i
$241$	−10.2302	−	5.90639i	−0.658983	−	0.380464i	0.132906	−	0.991129i	$-0.457569\pi$
$241$	−10.2302	−	5.90639i	−0.658983	−	0.380464i	−0.791889	+	0.610665i	$0.790902\pi$
$242$	−8.52149	−	6.95588i	−0.547782	−	0.447141i
$243$	−1.67656	+	6.25701i	−0.107551	+	0.401387i
$244$	3.24536	−	2.35789i	0.207763	−	0.150948i
$245$	11.9968	−	10.0537i	0.766448	−	0.642306i
$246$	−1.74331	+	5.36537i	−0.111150	+	0.342083i
$247$	4.08570	−	3.30853i	0.259967	−	0.210517i
$248$	−6.28465	−	2.41245i	−0.399076	−	0.153191i
$249$	8.49042	−	7.64481i	0.538059	−	0.484470i
$250$	2.66814	−	10.8573i	0.168748	−	0.686676i
$251$	4.74926	+	6.53680i	0.299771	+	0.412599i	0.932157	−	0.362054i	$-0.117924\pi$
$251$	4.74926	+	6.53680i	0.299771	+	0.412599i	−0.632386	+	0.774653i	$0.717924\pi$
$252$	0.400165	+	1.63126i	0.0252080	+	0.102759i
$253$	0.0128669	−	6.58543i	0.000808936	−	0.414023i
$254$	−12.2365	+	7.06475i	−0.767787	+	0.443282i
$255$	1.17369	−	2.06589i	0.0734996	−	0.129371i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−0.216457	+	0.333315i	−0.0135022	+	0.0207916i	−0.845357	−	0.534201i	$-0.820612\pi$
$257$	−0.216457	+	0.333315i	−0.0135022	+	0.0207916i	0.831855	+	0.554993i	$0.187279\pi$
$258$	−2.58960	−	16.3501i	−0.161221	−	1.01791i
$259$	−1.98518	−	1.50776i	−0.123353	−	0.0936875i
$260$	0.868076	−	5.73839i	0.0538358	−	0.355880i
$261$	−2.23134	+	2.47815i	−0.138116	+	0.153394i
$262$	−1.56926	−	1.27076i	−0.0969491	−	0.0785078i
$263$	−5.89658	−	22.0063i	−0.363599	−	1.35697i	−0.869311	−	0.494266i	$-0.835437\pi$
$263$	−5.89658	−	22.0063i	−0.363599	−	1.35697i	0.505712	−	0.862702i	$-0.331230\pi$
$264$	4.76544	−	1.81861i	0.293293	−	0.111928i
$265$	27.7153	−	4.58714i	1.70253	−	0.281786i
$266$	−4.84842	−	2.28324i	−0.297275	−	0.139994i
$267$	3.19111	−	6.26291i	0.195293	−	0.383284i
$268$	−7.98480	+	12.2955i	−0.487749	+	0.751068i
$269$	−17.8333	+	7.93990i	−1.08732	+	0.484105i	−0.870530	−	0.492115i	$-0.836224\pi$
$269$	−17.8333	+	7.93990i	−1.08732	+	0.484105i	−0.216786	+	0.976219i	$0.569557\pi$
$270$	−12.2443	−	2.51389i	−0.745166	−	0.152990i
$271$	3.57115	+	16.8010i	0.216932	+	1.02059i	0.942956	+	0.332916i	$0.108033\pi$
$271$	3.57115	+	16.8010i	0.216932	+	1.02059i	−0.726024	+	0.687669i	$0.758634\pi$
$272$	0.615623	+	0.313676i	0.0373276	+	0.0190194i
$273$	3.57442	+	9.93753i	0.216334	+	0.601447i
$274$			20.3008i			1.22641i
$275$	−15.4097	+	6.12716i	−0.929238	+	0.369482i
$276$	2.64454	+	1.52682i	0.159183	+	0.0919041i
$277$	−15.9834	+	19.7379i	−0.960352	+	1.18594i	0.0221629	+	0.999754i	$0.492945\pi$
$277$	−15.9834	+	19.7379i	−0.960352	+	1.18594i	−0.982515	+	0.186182i	$0.940389\pi$
$278$	−12.3998	+	0.649846i	−0.743691	+	0.0389752i
$279$	1.32061	−	4.06441i	0.0790627	−	0.243330i
$280$	−5.65209	+	1.74755i	−0.337777	+	0.104436i
$281$	2.55805	+	1.85853i	0.152600	+	0.110871i	0.661465	−	0.749976i	$-0.269935\pi$
$281$	2.55805	+	1.85853i	0.152600	+	0.110871i	−0.508865	+	0.860846i	$0.669935\pi$
$282$	−15.3726	−	9.98311i	−0.915427	−	0.594485i
$283$	0.810682	+	1.24834i	0.0481900	+	0.0742061i	0.861944	−	0.507003i	$-0.169247\pi$
$283$	0.810682	+	1.24834i	0.0481900	+	0.0742061i	−0.813754	+	0.581209i	$0.802580\pi$
$284$	2.11539	−	0.222337i	0.125526	−	0.0131933i
$285$	5.38275	−	4.42110i	0.318847	−	0.261883i
$286$	−7.67763	+	3.89307i	−0.453987	+	0.230202i
$287$	−9.42589	+	2.31227i	−0.556393	+	0.136489i
$288$	0.0993104	−	0.627021i	0.00585192	−	0.0369476i
$289$	12.2787	+	11.0558i	0.722276	+	0.650340i
$290$	−9.17918	−	7.32822i	−0.539020	−	0.430328i
$291$	10.1080	−	4.50036i	0.592539	−	0.263816i
$292$	−5.99801	−	7.40692i	−0.351007	−	0.433457i
$293$	−11.7900	+	6.00733i	−0.688782	+	0.350952i	−0.763098	−	0.646283i	$-0.776323\pi$
$293$	−11.7900	+	6.00733i	−0.688782	+	0.350952i	0.0743161	+	0.997235i	$0.476323\pi$
$294$	7.53666	−	7.68711i	0.439547	−	0.448322i
$295$	−19.1640	+	0.133055i	−1.11577	+	0.00774678i
$296$	0.471103	+	0.815975i	0.0273823	+	0.0474276i
$297$	7.50783	+	16.9519i	0.435648	+	0.983650i
$298$	−4.17916	−	15.5968i	−0.242092	−	0.903501i
$299$	−4.70801	−	2.09614i	−0.272271	−	0.121223i
$300$	1.09734	−	7.61084i	0.0633547	−	0.439412i
$301$	21.5636	−	18.6021i	1.24291	−	1.07221i
$302$	2.45443	+	15.4967i	0.141236	+	0.891732i
$303$	7.30112	+	9.01613i	0.419438	+	0.517963i
$304$	1.35537	+	1.50529i	0.0777355	+	0.0863341i
$305$	−6.62414	+	6.04820i	−0.379297	+	0.346319i
$306$	−0.178406	+	0.400707i	−0.0101988	+	0.0229069i
$307$	6.68874	−	6.68874i	0.381747	−	0.381747i	−0.489984	−	0.871731i	$-0.662998\pi$
$307$	6.68874	−	6.68874i	0.381747	−	0.381747i	0.871731	+	0.489984i	$0.162998\pi$
$308$	6.97757	+	5.32104i	0.397584	+	0.303194i
$309$		−	6.21045i		−	0.353300i
$310$	14.5665	+	3.79488i	0.827321	+	0.215535i
$311$	−0.531955	+	2.50265i	−0.0301644	+	0.141912i	−0.990653	−	0.136408i	$-0.956444\pi$
$311$	−0.531955	+	2.50265i	−0.0301644	+	0.141912i	0.960488	+	0.278320i	$0.0897776\pi$
$312$	0.208905	−	3.98615i	0.0118269	−	0.225671i
$313$	−6.33410	+	5.12925i	−0.358024	+	0.289922i	−0.791409	−	0.611286i	$-0.790652\pi$
$313$	−6.33410	+	5.12925i	−0.358024	+	0.289922i	0.433385	+	0.901209i	$0.357319\pi$
$314$	−6.96144	−	5.05778i	−0.392857	−	0.285427i
$315$	−1.29568	−	3.52517i	−0.0730032	−	0.198621i
$316$	−0.129915	−	0.399837i	−0.00730829	−	0.0224926i
$317$	−2.57339	−	6.70390i	−0.144536	−	0.376529i	0.842133	−	0.539270i	$-0.181300\pi$
$317$	−2.57339	−	6.70390i	−0.144536	−	0.376529i	−0.986669	+	0.162741i	$0.947966\pi$
$318$	18.6628	−	5.00068i	1.04656	−	0.280424i
$319$	−0.945767	+	17.3959i	−0.0529528	+	0.973984i
$320$	2.22539	+	0.218288i	0.124403	+	0.0122026i
$321$	7.83809	+	10.7882i	0.437479	+	0.602139i
$322$	0.163465	+	5.25082i	0.00910952	+	0.292617i
$323$	−0.635369	−	1.24698i	−0.0353529	−	0.0693840i
$324$	−6.65581	−	0.699554i	−0.369767	−	0.0388641i
$325$	−0.499171	+	12.9678i	−0.0276890	+	0.719325i
$326$	−2.73258	−	3.03484i	−0.151344	−	0.168084i
$327$	−0.317569	−	6.05958i	−0.0175616	−	0.335095i
$328$	3.62312	+	0.573846i	0.200053	+	0.0316853i
$329$	0.669686	−	31.5266i	0.0369210	−	1.73812i
$330$	−10.1364	+	5.22860i	−0.557988	+	0.287825i
$331$	3.15630	+	5.46686i	0.173486	+	0.300486i	0.939636	−	0.342175i	$-0.111164\pi$
$331$	3.15630	+	5.46686i	0.173486	+	0.300486i	−0.766150	+	0.642661i	$0.777830\pi$
$332$	−5.77335	−	4.67517i	−0.316854	−	0.256583i
$333$	−0.501649	+	0.325775i	−0.0274902	+	0.0178523i
$334$	14.6510	−	3.11416i	0.801664	−	0.170399i
$335$	14.6797	−	29.3119i	0.802039	−	1.60148i
$336$	−3.75146	+	1.57567i	−0.204659	+	0.0859596i
$337$	21.2052	−	10.8046i	1.15512	−	0.588563i	0.231864	−	0.972748i	$-0.425518\pi$
$337$	21.2052	−	10.8046i	1.15512	−	0.588563i	0.923256	+	0.384185i	$0.125518\pi$
$338$	−0.327804	−	6.25488i	−0.0178302	−	0.340221i
$339$	−1.01349	−	9.64275i	−0.0550455	−	0.523723i
$340$	−1.44616	−	0.543639i	−0.0784290	−	0.0294830i
$341$	−7.96046	−	20.8594i	−0.431083	−	1.12960i
$342$	−0.909270	+	0.909270i	−0.0491677	+	0.0491677i
$343$	18.0707	+	4.05605i	0.975723	+	0.219006i
$344$	−10.2371	+	3.32622i	−0.551946	+	0.179338i
$345$	−6.25697	−	2.73389i	−0.336864	−	0.147188i
$346$	8.61400	+	19.3474i	0.463092	+	1.04012i
$347$	31.5873	+	12.1252i	1.69569	+	0.650916i	0.997863	−	0.0653460i	$-0.0208151\pi$
$347$	31.5873	+	12.1252i	1.69569	+	0.650916i	0.697831	+	0.716262i	$0.254148\pi$
$348$	−6.77507	−	4.39978i	−0.363182	−	0.235853i
$349$	−2.15403	−	6.62944i	−0.115303	−	0.354866i	0.876707	−	0.481024i	$-0.159735\pi$
$349$	−2.15403	−	6.62944i	−0.115303	−	0.354866i	−0.992010	+	0.126159i	$0.959735\pi$
$350$	12.1243	−	5.29161i	0.648071	−	0.282849i
$351$	14.5089			0.774427
$352$	−1.65270	−	2.87552i	−0.0880891	−	0.153266i
$353$	−29.3344	+	7.86013i	−1.56131	+	0.418352i	−0.933079	−	0.359672i	$-0.882889\pi$
$353$	−29.3344	+	7.86013i	−1.56131	+	0.418352i	−0.628234	+	0.778025i	$0.716222\pi$
$354$	−13.1086	+	1.37777i	−0.696713	+	0.0732275i
$355$	−4.64531	+	1.02115i	−0.246547	+	0.0541970i
$356$	−4.34681	−	1.41237i	−0.230381	−	0.0748552i
$357$	2.78544	−	0.380722i	0.147421	−	0.0201499i
$358$	11.8775	−	1.88122i	0.627747	−	0.0994254i
$359$	−6.41453	−	30.1780i	−0.338546	−	1.59273i	−0.737228	−	0.675645i	$-0.763865\pi$
$359$	−6.41453	−	30.1780i	−0.338546	−	1.59273i	0.398682	−	0.917089i	$-0.369468\pi$
$360$	−0.0644490	+	1.41807i	−0.00339676	+	0.0747391i
$361$	1.55717	+	14.8155i	0.0819564	+	0.779763i
$362$	10.8154	+	2.89798i	0.568445	+	0.152314i
$363$	15.0430	+	7.73900i	0.789554	+	0.406192i
$364$	6.01858	−	3.30643i	0.315459	−	0.173304i
$365$	15.1740	+	14.9647i	0.794243	+	0.783290i
$366$	−4.12806	+	4.58468i	−0.215777	+	0.239645i
$367$	34.6893	+	1.81799i	1.81077	+	0.0948982i	0.927466	−	0.373909i	$-0.121983\pi$
$367$	34.6893	+	1.81799i	1.81077	+	0.0948982i	0.883301	+	0.468807i	$0.155316\pi$
$368$	0.711570	−	1.85370i	0.0370932	−	0.0966310i
$369$	−0.243422	+	2.31600i	−0.0126720	+	0.120566i
$370$	−1.25017	−	1.69583i	−0.0649934	−	0.0881620i
$371$	24.2237	+	22.7610i	1.25763	+	1.18169i
$372$	10.2254	+	1.61954i	0.530162	+	0.0839694i
$373$	−11.5327	−	3.09017i	−0.597139	−	0.160003i	−0.0524248	−	0.998625i	$-0.516695\pi$
$373$	−11.5327	−	3.09017i	−0.597139	−	0.160003i	−0.544714	+	0.838622i	$0.683362\pi$
$374$	0.588772	+	2.21463i	0.0304447	+	0.114516i
$375$	−0.542068	+	17.1858i	−0.0279923	+	0.887471i
$376$	−4.84774	+	10.8882i	−0.250003	+	0.561517i
$377$	12.1476	+	6.18952i	0.625634	+	0.318777i
$378$	−6.43309	−	13.3175i	−0.330882	−	0.684978i
$379$	−4.21141	+	5.79650i	−0.216325	+	0.297746i	−0.903364	−	0.428874i	$-0.858910\pi$
$379$	−4.21141	+	5.79650i	−0.216325	+	0.297746i	0.687039	+	0.726621i	$0.258910\pi$
$380$	−3.38688	−	3.00725i	−0.173743	−	0.154269i
$381$	16.1485	−	14.5401i	0.827310	−	0.744914i
$382$	10.3721	+	15.9716i	0.530682	+	0.817179i
$383$	−0.695107	−	1.81082i	−0.0355183	−	0.0925284i	0.914674	−	0.404192i	$-0.132447\pi$
$383$	−0.695107	−	1.81082i	−0.0355183	−	0.0925284i	−0.950193	+	0.311663i	$0.899114\pi$
$384$	1.53791			0.0784811
$385$	−16.8310	−	10.0855i	−0.857787	−	0.514006i
$386$	−12.9575			−0.659521
$387$	−2.44884	−	6.37945i	−0.124482	−	0.324286i
$388$	−3.91843	−	6.03385i	−0.198928	−	0.306322i
$389$	6.40493	−	5.76702i	0.324743	−	0.292400i	−0.490592	−	0.871389i	$-0.663219\pi$
$389$	6.40493	−	5.76702i	0.324743	−	0.292400i	0.815335	+	0.578990i	$0.196553\pi$
$390$	0.528998	+	8.90984i	0.0267869	+	0.451167i
$391$	−0.806383	+	1.10989i	−0.0407805	+	0.0561296i
$392$	−5.70350	−	4.05833i	−0.288070	−	0.204977i
$393$	2.76696	+	1.40984i	0.139575	+	0.0711169i
$394$	−4.38335	+	9.84517i	−0.220830	+	0.495993i
$395$	0.388316	+	0.856125i	0.0195383	+	0.0430763i
$396$	1.76807	−	1.14329i	0.0888489	−	0.0574527i
$397$	−2.92465	−	0.783657i	−0.146784	−	0.0393306i	0.184679	−	0.982799i	$-0.440875\pi$
$397$	−2.92465	−	0.783657i	−0.146784	−	0.0393306i	−0.331463	+	0.943468i	$0.607542\pi$
$398$	16.8589	+	2.67018i	0.845059	+	0.133844i
$399$	8.02354	+	1.88440i	0.401680	+	0.0943380i
$400$	−4.99952	+	0.0694267i	−0.249976	+	0.00347133i
$401$	−2.31036	+	21.9816i	−0.115374	+	1.09771i	0.771670	+	0.636023i	$0.219422\pi$
$401$	−2.31036	+	21.9816i	−0.115374	+	1.09771i	−0.887044	+	0.461685i	$0.847245\pi$
$402$	8.08006	−	21.0493i	0.402997	−	1.04984i
$403$	−17.4483	−	0.914425i	−0.869160	−	0.0455507i
$404$	5.04775	−	5.60609i	0.251135	−	0.278914i
$405$	14.9645	−	0.103898i	0.743590	−	0.00516275i
$406$	0.295146	−	13.8945i	0.0146478	−	0.689573i
$407$	−0.971467	+	2.97011i	−0.0481538	+	0.147223i
$408$	−1.02638	−	0.275018i	−0.0508134	−	0.0136154i
$409$	3.35610	+	31.9312i	0.165948	+	1.57889i	0.687827	+	0.725874i	$0.258565\pi$
$409$	3.35610	+	31.9312i	0.165948	+	1.57889i	−0.521879	+	0.853020i	$0.674769\pi$
$410$	−8.19407	−	0.372406i	−0.404676	−	0.0183918i
$411$	−6.49116	−	30.5385i	−0.320185	−	1.50635i
$412$	−3.98852	+	0.631720i	−0.196501	+	0.0311226i
$413$	−13.8928	−	17.9214i	−0.683619	−	0.881853i
$414$	1.19883	+	0.389523i	0.0589192	+	0.0191440i
$415$	13.9941	+	8.95036i	0.686943	+	0.439356i
$416$	−2.58127	+	0.271302i	−0.126557	+	0.0133017i
$417$	18.4453	−	4.94239i	0.903268	−	0.242030i
$418$	−0.715278	+	6.67984i	−0.0349854	+	0.326722i
$419$	−19.3763			−0.946594			−0.473297	−	0.880903i	$-0.656936\pi$
$419$	−19.3763			−0.946594			−0.473297	+	0.880903i	$0.656936\pi$
$420$	7.94366	−	4.43609i	0.387611	−	0.216459i
$421$	−10.3903	−	31.9779i	−0.506390	−	1.55851i	−0.798421	−	0.602100i	$-0.794331\pi$
$421$	−10.3903	−	31.9779i	−0.506390	−	1.55851i	0.292030	−	0.956409i	$-0.405669\pi$
$422$	−9.35517	−	6.07532i	−0.455402	−	0.295742i
$423$	−7.06383	−	2.71155i	−0.343455	−	0.131840i
$424$	−5.10994	−	11.4771i	−0.248161	−	0.557378i
$425$	3.34903	+	0.847709i	0.162452	+	0.0411199i
$426$	−3.11110	+	1.01086i	−0.150733	+	0.0489762i
$427$	−10.4451	−	1.88255i	−0.505473	−	0.0911028i
$428$	6.13121	−	6.13121i	0.296363	−	0.296363i
$429$	10.3047	−	8.31126i	0.497514	−	0.401272i
$430$	21.9194	−	9.94208i	1.05705	−	0.479450i
$431$	2.40490	+	22.8811i	0.115840	+	1.10214i	0.885805	+	0.464057i	$0.153607\pi$
$431$	2.40490	+	22.8811i	0.115840	+	1.10214i	−0.769965	+	0.638086i	$0.779726\pi$
$432$	0.292560	+	5.58239i	0.0140758	+	0.268583i
$433$	17.8891	−	9.11497i	0.859697	−	0.438037i	0.0321825	−	0.999482i	$-0.489754\pi$
$433$	17.8891	−	9.11497i	0.859697	−	0.438037i	0.827514	+	0.561445i	$0.189754\pi$
$434$	6.89704	+	16.4210i	0.331069	+	0.788232i
$435$	16.1515	+	8.08882i	0.774403	+	0.387829i
$436$	−3.85933	+	0.820326i	−0.184828	+	0.0392865i
$437$	−3.37307	+	2.19050i	−0.161356	+	0.104786i
$438$	11.3912	+	9.22439i	0.544291	+	0.440758i
$439$	9.79684	+	16.9686i	0.467578	+	0.809868i	0.999314	−	0.0370420i	$-0.0117935\pi$
$439$	9.79684	+	16.9686i	0.467578	+	0.809868i	−0.531736	+	0.846910i	$0.678460\pi$
$440$	4.38901	+	5.97801i	0.209238	+	0.284990i
$441$	2.38335	−	3.75067i	0.113493	−	0.178603i
$442$	1.77122	+	0.280534i	0.0842483	+	0.0133436i
$443$	−0.567605	−	10.8306i	−0.0269677	−	0.514575i	−0.978400	−	0.206718i	$-0.933722\pi$
$443$	−0.567605	−	10.8306i	−0.0269677	−	0.514575i	0.951433	−	0.307857i	$-0.0996117\pi$
$444$	−0.969589	−	1.07684i	−0.0460147	−	0.0511045i
$445$	10.0112	+	2.05540i	0.474574	+	0.0974351i
$446$	−26.2522	−	2.75922i	−1.24308	−	0.130653i
$447$	11.2738	+	22.1261i	0.533232	+	1.04653i
$448$	1.39353	+	2.24902i	0.0658382	+	0.106256i
$449$	−7.51222	−	10.3397i	−0.354524	−	0.487960i	0.594089	−	0.804399i	$-0.297513\pi$
$449$	−7.51222	−	10.3397i	−0.354524	−	0.487960i	−0.948613	+	0.316439i	$0.897513\pi$
$450$	−0.210122	−	3.16722i	−0.00990526	−	0.149304i
$451$	6.60630	+	10.2165i	0.311078	+	0.481074i
$452$	−6.08976	+	1.63175i	−0.286438	+	0.0767509i
$453$	−8.64724	−	22.5268i	−0.406283	−	1.05840i
$454$	8.05497	+	24.7906i	0.378038	+	1.16348i
$455$	−12.5503	+	8.84699i	−0.588366	+	0.414753i
$456$	−2.52019	−	1.83103i	−0.118019	−	0.0857457i
$457$	18.0740	−	14.6361i	0.845467	−	0.684646i	−0.105337	−	0.994437i	$-0.533592\pi$
$457$	18.0740	−	14.6361i	0.845467	−	0.684646i	0.950805	+	0.309791i	$0.100259\pi$
$458$	−0.190509	+	3.63513i	−0.00890191	+	0.169858i
$459$	0.803024	−	3.77793i	0.0374819	−	0.176339i
$460$	−1.11933	+	4.29649i	−0.0521890	+	0.200325i
$461$		−	20.5337i		−	0.956348i	−0.878265	−	0.478174i	$-0.841299\pi$
$461$		−	20.5337i		−	0.956348i	0.878265	−	0.478174i	$-0.158701\pi$
$462$	−12.1978	−	5.77337i	−0.567492	−	0.268602i
$463$	5.21922	−	5.21922i	0.242558	−	0.242558i	−0.575350	−	0.817908i	$-0.695134\pi$
$463$	5.21922	−	5.21922i	0.242558	−	0.242558i	0.817908	+	0.575350i	$0.195134\pi$
$464$	−2.13651	+	4.79868i	−0.0991851	+	0.222773i
$465$	−23.1258	−	1.05103i	−1.07243	−	0.0487402i
$466$	7.79541	+	8.65768i	0.361116	+	0.401059i
$467$	−19.8603	−	24.5255i	−0.919027	−	1.13490i	−0.990507	−	0.137462i	$-0.956106\pi$
$467$	−19.8603	−	24.5255i	−0.919027	−	1.13490i	0.0714803	−	0.997442i	$-0.477228\pi$
$468$	−0.257759	−	1.62742i	−0.0119149	−	0.0752277i
$469$	38.1037	−	7.25703i	1.75946	−	0.335098i
$470$	8.05940	−	25.4031i	0.371752	−	1.17176i
$471$	12.0893	+	5.38252i	0.557047	+	0.248013i
$472$	2.21823	+	8.27855i	0.102102	+	0.381051i
$473$	−30.8820	−	17.9103i	−1.41996	−	0.823515i
$474$	0.323279	+	0.559936i	0.0148487	+	0.0257187i
$475$	8.27544	+	5.83863i	0.379703	+	0.267895i
$476$	−0.527843	−	1.75016i	−0.0241936	−	0.0802186i
$477$	7.10633	−	3.62086i	0.325377	−	0.165788i
$478$	−3.74966	−	4.63045i	−0.171506	−	0.211792i
$479$	−16.4019	+	7.30261i	−0.749424	+	0.333665i	−0.745659	−	0.666328i	$-0.767865\pi$
$479$	−16.4019	+	7.30261i	−0.749424	+	0.333665i	−0.00376496	+	0.999993i	$0.501198\pi$
$480$	−3.41745	+	0.383196i	−0.155985	+	0.0174904i
$481$	1.81735	+	1.63635i	0.0828639	+	0.0746110i
$482$	1.84793	−	11.6673i	0.0841707	−	0.531433i
$483$	−1.92485	−	7.84655i	−0.0875835	−	0.357031i
$484$	3.44004	−	10.4483i	0.156366	−	0.474921i
$485$	10.2107	+	12.4317i	0.463646	+	0.564496i
$486$	−6.44225	+	0.677107i	−0.292226	+	0.0307142i
$487$	4.67128	+	7.19314i	0.211676	+	0.325952i	0.928521	−	0.371280i	$-0.121081\pi$
$487$	4.67128	+	7.19314i	0.211676	+	0.325952i	−0.716845	+	0.697233i	$0.754414\pi$
$488$	3.36431	+	2.18481i	0.152295	+	0.0989017i
$489$	5.08101	+	3.69157i	0.229771	+	0.166939i
$490$	13.6852	+	7.59707i	0.618234	+	0.343200i
$491$	5.82642	−	17.9319i	0.262942	−	0.809254i	−0.729218	−	0.684282i	$-0.760116\pi$
$491$	5.82642	−	17.9319i	0.262942	−	0.809254i	0.992160	−	0.124972i	$-0.0398841\pi$
$492$	−5.63375	+	0.295252i	−0.253989	+	0.0133110i
$493$	2.28401	−	2.82052i	0.102867	−	0.127030i
$494$	4.55297	+	2.62866i	0.204848	+	0.118269i
$495$	−3.64404	+	2.98111i	−0.163787	+	0.133991i
$496$		−	6.73177i		−	0.302265i
$497$	−4.29729	−	3.63367i	−0.192760	−	0.162992i
$498$	10.1797	+	5.18684i	0.456165	+	0.232428i
$499$	5.11447	+	24.0617i	0.228955	+	1.07715i	0.931001	+	0.365017i	$0.118937\pi$
$499$	5.11447	+	24.0617i	0.228955	+	1.07715i	−0.702046	+	0.712132i	$0.747730\pi$
$500$	11.0923	−	1.39999i	0.496065	−	0.0626094i
$501$	−21.0437	+	9.36926i	−0.940163	+	0.418588i
$502$	−4.40064	+	6.77640i	−0.196410	+	0.302445i
$503$	8.66732	−	17.0106i	0.386457	−	0.758464i	−0.613044	−	0.790049i	$-0.710055\pi$
$503$	8.66732	−	17.0106i	0.386457	−	0.758464i	0.999501	+	0.0315843i	$0.0100553\pi$
$504$	−1.37950	+	0.958176i	−0.0614479	+	0.0426805i
$505$	−9.81996	+	13.7153i	−0.436983	+	0.610321i
$506$	6.15264	−	2.34800i	0.273518	−	0.104381i
$507$	2.49311	+	9.30441i	0.110723	+	0.413223i
$508$	−10.9807	−	8.89198i	−0.487189	−	0.394518i
$509$	5.57953	−	6.19669i	0.247308	−	0.274664i	−0.606691	−	0.794938i	$-0.707504\pi$
$509$	5.57953	−	6.19669i	0.247308	−	0.274664i	0.853999	+	0.520274i	$0.174170\pi$
$510$	2.34929	+	0.355389i	0.104028	+	0.0157369i
$511$	−3.16784	+	25.0167i	−0.140137	+	1.10667i
$512$	−0.156434	−	0.987688i	−0.00691349	−	0.0436501i
$513$	6.16694	−	9.49626i	0.272277	−	0.419270i
$514$	−0.388748	−	0.0826309i	−0.0171469	−	0.00364469i
$515$	8.70567	−	2.39758i	0.383617	−	0.105650i
$516$	14.3361	−	8.27694i	0.631111	−	0.364372i
$517$	−37.6187	+	12.1418i	−1.65447	+	0.533998i
$518$	0.696187	−	2.39366i	0.0305887	−	0.105171i
$519$	−19.1444	−	26.3500i	−0.840344	−	1.15663i
$520$	5.66834	−	1.24604i	0.248573	−	0.0546423i
$521$	3.55791	−	3.20355i	0.155875	−	0.140350i	−0.587503	−	0.809222i	$-0.699889\pi$
$521$	3.55791	−	3.20355i	0.155875	−	0.140350i	0.743378	+	0.668872i	$0.233222\pi$
$522$	−3.11319	−	1.19504i	−0.136261	−	0.0523056i
$523$	−4.69805	+	3.80440i	−0.205431	+	0.166355i	−0.726515	−	0.687151i	$-0.758861\pi$
$523$	−4.69805	+	3.80440i	−0.205431	+	0.166355i	0.521084	+	0.853506i	$0.325528\pi$
$524$	0.623985	−	1.92043i	0.0272589	−	0.0838943i
$525$	−16.5466	+	11.8369i	−0.722154	+	0.516606i
$526$	18.4315	−	13.3913i	0.803653	−	0.583888i
$527$	−1.20381	+	4.49270i	−0.0524390	+	0.195705i
$528$	3.40560	+	3.79719i	0.148210	+	0.165252i
$529$	−16.5042	−	9.52872i	−0.717575	−	0.414292i
$530$	14.2147	+	24.2305i	0.617448	+	1.05251i
$531$	−5.17463	+	1.68134i	−0.224560	+	0.0729639i
$532$	0.394069	−	5.34462i	0.0170850	−	0.231719i
$533$	9.40375	−	1.48941i	0.407321	−	0.0645134i
$534$	6.99052	+	0.734733i	0.302509	+	0.0317950i
$535$	−12.0967	+	15.1521i	−0.522987	+	0.655083i
$536$	−14.3403	−	3.04813i	−0.619408	−	0.131659i
$537$	−17.2659	+	6.62775i	−0.745078	+	0.286009i
$538$	−13.8034	−	13.8034i	−0.595108	−	0.595108i
$539$	−2.60976	−	23.0692i	−0.112410	−	0.993662i
$540$	−2.04106	−	12.3320i	−0.0878331	−	0.530683i
$541$	−7.19594	−	3.20384i	−0.309378	−	0.137744i	0.246174	−	0.969226i	$-0.420826\pi$
$541$	−7.19594	−	3.20384i	−0.309378	−	0.137744i	−0.555552	+	0.831482i	$0.687493\pi$
$542$	−14.4053	+	9.35488i	−0.618759	+	0.401827i
$543$	−17.1962	−	0.901217i	−0.737962	−	0.0386749i
$544$	−0.0722219	+	0.687145i	−0.00309649	+	0.0294611i
$545$	8.37158	−	2.78450i	0.358599	−	0.119275i
$546$	−7.99653	+	6.89831i	−0.342220	+	0.295220i
$547$	13.6698	−	26.8285i	0.584480	−	1.14711i	−0.389618	−	0.920977i	$-0.627393\pi$
$547$	13.6698	−	26.8285i	0.584480	−	1.14711i	0.974097	−	0.226129i	$-0.0726072\pi$
$548$	−18.9524	+	7.27515i	−0.809607	+	0.310779i
$549$	−1.27332	+	2.20545i	−0.0543439	+	0.0941264i
$550$	−11.2425	−	12.1904i	−0.479383	−	0.519800i
$551$	9.21442	−	5.31995i	0.392548	−	0.226637i
$552$	−0.477696	+	3.01605i	−0.0203321	+	0.128372i
$553$	−0.525912	+	0.980128i	−0.0223640	+	0.0416793i
$554$	−24.1549	−	7.84840i	−1.02624	−	0.333447i
$555$	2.42288	+	2.15130i	0.102845	+	0.0913175i
$556$	−5.05038	−	11.3433i	−0.214184	−	0.481065i
$557$	0.538068	−	10.2670i	0.0227987	−	0.435025i	−0.963254	−	0.268592i	$-0.913442\pi$
$557$	0.538068	−	10.2670i	0.0227987	−	0.435025i	0.986053	−	0.166433i	$-0.0532250\pi$
$558$	4.26772	−	0.223662i	0.180667	−	0.00946836i
$559$	−22.6019	+	16.4213i	−0.955959	+	0.694545i
$560$	−3.65700	−	4.65041i	−0.154537	−	0.196516i
$561$	−1.59382	−	3.14321i	−0.0672910	−	0.132706i
$562$	−0.818365	+	3.05418i	−0.0345207	+	0.128833i
$563$	−22.1955	+	27.4091i	−0.935427	+	1.15516i	0.0522473	+	0.998634i	$0.483362\pi$
$563$	−22.1955	+	27.4091i	−0.935427	+	1.15516i	−0.987674	+	0.156522i	$0.949972\pi$
$564$	3.81097	−	17.9292i	0.160471	−	0.754956i
$565$	13.1257	−	5.14334i	0.552204	−	0.216382i
$566$	−0.874904	+	1.20420i	−0.0367750	+	0.0506164i
$567$	10.8484	+	13.9942i	0.455589	+	0.587700i
$568$	0.965659	+	1.89521i	0.0405181	+	0.0795213i
$569$	−1.51102	−	1.36053i	−0.0633452	−	0.0570362i	0.636850	−	0.770988i	$-0.280237\pi$
$569$	−1.51102	−	1.36053i	−0.0633452	−	0.0570362i	−0.700195	+	0.713951i	$0.746904\pi$
$570$	6.05646	+	3.44085i	0.253677	+	0.144122i
$571$	14.9684	−	25.9260i	0.626408	−	1.08497i	−0.361859	−	0.932233i	$-0.617858\pi$
$571$	14.9684	−	25.9260i	0.626408	−	1.08497i	0.988267	−	0.152737i	$-0.0488089\pi$
$572$	−6.38591	−	5.77253i	−0.267008	−	0.241362i
$573$	−20.7097	−	20.7097i	−0.865159	−	0.865159i
$574$	−5.53663	−	7.97118i	−0.231095	−	0.332711i
$575$	1.41677	−	9.82632i	0.0590832	−	0.409786i
$576$	0.620964	−	0.131990i	0.0258735	−	0.00549958i
$577$	0.631224	−	1.64440i	0.0262782	−	0.0684571i	−0.919814	−	0.392356i	$-0.871660\pi$
$577$	0.631224	−	1.64440i	0.0262782	−	0.0684571i	0.946092	+	0.323898i	$0.104994\pi$
$578$	−5.92118	+	15.4252i	−0.246288	+	0.641603i
$579$	19.4920	−	4.14316i	0.810061	−	0.172184i
$580$	3.55196	−	11.1957i	0.147487	−	0.464876i
$581$	1.63892	+	19.5866i	0.0679938	+	0.812589i
$582$	7.82381	+	7.82381i	0.324308	+	0.324308i
$583$	17.0221	−	38.0321i	0.704983	−	1.57513i
$584$	4.76546	−	8.25403i	0.197196	−	0.341554i
$585$	0.978276	+	3.55214i	0.0404467	+	0.146863i
$586$	−9.83350	−	8.85412i	−0.406218	−	0.365760i
$587$	−18.8548	−	37.0047i	−0.778222	−	1.52735i	−0.848127	−	0.529793i	$-0.822270\pi$
$587$	−18.8548	−	37.0047i	−0.778222	−	1.52735i	0.0699053	−	0.997554i	$-0.477730\pi$
$588$	9.87744	+	4.28126i	0.407339	+	0.176556i
$589$	−8.01482	+	11.0314i	−0.330245	+	0.454543i
$590$	−6.99196	−	17.8434i	−0.287855	−	0.734601i
$591$	3.44590	−	16.2117i	0.141745	−	0.666859i
$592$	−0.592950	+	0.732232i	−0.0243701	+	0.0300946i
$593$	3.52585	−	13.1586i	0.144789	−	0.540361i	−0.854976	−	0.518668i	$-0.826428\pi$
$593$	3.52585	−	13.1586i	0.144789	−	0.540361i	0.999765	−	0.0216922i	$-0.00690540\pi$
$594$	−13.1354	+	13.0842i	−0.538952	+	0.536851i
$595$	1.60902	+	3.75759i	0.0659636	+	0.154046i
$596$	13.0632	−	9.49100i	0.535091	−	0.388766i
$597$	−26.2146	+	1.37385i	−1.07289	+	0.0562279i
$598$	0.269716	−	5.14649i	0.0110295	−	0.210456i
$599$	2.74640	+	6.16851i	0.112215	+	0.252038i	0.960919	−	0.276829i	$-0.0892835\pi$
$599$	2.74640	+	6.16851i	0.112215	+	0.252038i	−0.848704	+	0.528867i	$0.822617\pi$
$600$	7.49858	−	1.70303i	0.306128	−	0.0695259i
$601$	−23.9333	−	7.77641i	−0.976260	−	0.317206i	−0.222920	−	0.974837i	$-0.571559\pi$
$601$	−23.9333	−	7.77641i	−0.976260	−	0.317206i	−0.753341	+	0.657631i	$0.771559\pi$
$602$	25.0943	+	13.4650i	1.02277	+	0.548791i
$603$	1.45596	−	9.19257i	0.0592913	−	0.374351i
$604$	−13.5878	+	7.84491i	−0.552879	+	0.319205i
$605$	−5.04090	+	24.0747i	−0.204942	+	0.978774i
$606$	−5.80079	+	10.0473i	−0.235641	+	0.408142i
$607$	−31.6453	+	12.1475i	−1.28444	+	0.493052i	−0.902323	−	0.431061i	$-0.858139\pi$
$607$	−31.6453	+	12.1475i	−1.28444	+	0.493052i	−0.382121	+	0.924112i	$0.624806\pi$
$608$	−0.919586	+	1.80479i	−0.0372941	+	0.0731938i
$609$	3.99877	+	20.9959i	0.162038	+	0.850797i
$610$	−8.02036	−	4.01668i	−0.324735	−	0.162631i
$611$	−3.23355	+	30.7652i	−0.130815	+	1.24462i
$612$	−0.438027	−	0.0229560i	−0.0177062	−	0.000927942i
$613$	9.74674	−	6.32961i	0.393667	−	0.255650i	−0.332593	−	0.943070i	$-0.607924\pi$
$613$	9.74674	−	6.32961i	0.393667	−	0.255650i	0.726260	+	0.687420i	$0.241257\pi$
$614$	8.64151	+	3.84745i	0.348743	+	0.155270i
$615$	12.4454	−	2.05984i	0.501848	−	0.0830606i
$616$	−2.46708	+	8.42102i	−0.0994014	+	0.339292i
$617$	−27.3925	−	27.3925i	−1.10278	−	1.10278i	−0.994074	−	0.108707i	$-0.965329\pi$
$617$	−27.3925	−	27.3925i	−1.10278	−	1.10278i	−0.108707	−	0.994074i	$-0.534671\pi$
$618$	5.79795	−	2.22563i	0.233228	−	0.0895278i
$619$	−18.2648	−	3.88231i	−0.734126	−	0.156043i	−0.174346	−	0.984685i	$-0.555781\pi$
$619$	−18.2648	−	3.88231i	−0.734126	−	0.156043i	−0.559780	+	0.828641i	$0.689114\pi$
$620$	1.67733	+	14.9590i	0.0673633	+	0.600766i
$621$	−11.0387	−	1.16022i	−0.442968	−	0.0465579i
$622$	−2.52706	+	0.400247i	−0.101326	+	0.0160485i
$623$	5.25979	+	10.8886i	0.210729	+	0.436242i
$624$	3.79625	−	1.23348i	0.151972	−	0.0493786i
$625$	−24.2999	+	5.87482i	−0.971997	+	0.234993i
$626$	−7.05851	−	4.07523i	−0.282115	−	0.162879i
$627$	−1.05988	−	10.2772i	−0.0423275	−	0.410432i
$628$	2.22709	−	8.31161i	0.0888706	−	0.331669i
$629$	0.526669	−	0.382648i	0.0209997	−	0.0152572i
$630$	2.82670	−	2.47293i	0.112619	−	0.0985238i
$631$	−10.7103	+	32.9631i	−0.426372	+	1.31224i	0.475302	+	0.879823i	$0.342339\pi$
$631$	−10.7103	+	32.9631i	−0.426372	+	1.31224i	−0.901674	+	0.432416i	$0.857661\pi$
$632$	0.326723	−	0.264575i	0.0129963	−	0.0105242i
$633$	16.0156	+	6.14780i	0.636562	+	0.244353i
$634$	5.33641	−	4.80493i	0.211936	−	0.190828i
$635$	26.6162	+	17.0232i	1.05623	+	0.675546i
$636$	11.3567	+	15.6311i	0.450322	+	0.619815i
$637$	−17.3338	−	5.44331i	−0.686790	−	0.215672i
$638$	−16.5794	+	5.35119i	−0.656386	+	0.211856i
$639$	−1.16942	+	0.675164i	−0.0462615	+	0.0267091i
$640$	0.593719	+	2.15581i	0.0234688	+	0.0852157i
$641$	12.7531	+	2.71075i	0.503716	+	0.107068i	0.452759	−	0.891633i	$-0.350440\pi$
$641$	12.7531	+	2.71075i	0.503716	+	0.107068i	0.0509565	+	0.998701i	$0.483773\pi$
$642$	−7.26273	+	11.1836i	−0.286637	+	0.441383i
$643$	0.959485	+	6.05795i	0.0378384	+	0.238902i	0.999358	−	0.0358351i	$-0.0114091\pi$
$643$	0.959485	+	6.05795i	0.0378384	+	0.238902i	−0.961519	+	0.274737i	$0.911409\pi$
$644$	−4.84348	+	2.03433i	−0.190860	+	0.0801640i
$645$	−29.7945	+	21.9646i	−1.17316	+	0.864856i
$646$	0.936463	−	1.04005i	0.0368446	−	0.0409201i
$647$	−26.7777	−	21.6842i	−1.05274	−	0.852492i	−0.0633812	−	0.997989i	$-0.520188\pi$
$647$	−26.7777	−	21.6842i	−1.05274	−	0.852492i	−0.989359	+	0.145497i	$0.953522\pi$
$648$	−1.73214	−	6.46443i	−0.0680448	−	0.253947i
$649$	−15.5281	+	23.8093i	−0.609533	+	0.934596i
$650$	−12.2854	+	4.18123i	−0.481873	+	0.164001i
$651$	−15.6258	−	22.4968i	−0.612424	−	0.881718i
$652$	1.85399	−	3.63867i	0.0726080	−	0.142501i
$653$	−15.3078	+	23.5720i	−0.599042	+	0.922444i	0.400938	+	0.916105i	$0.368684\pi$
$653$	−15.3078	+	23.5720i	−0.599042	+	0.922444i	−0.999980	+	0.00633886i	$0.997982\pi$
$654$	5.54330	−	2.46803i	0.216760	−	0.0965078i
$655$	−0.908076	+	4.42294i	−0.0354815	+	0.172819i
$656$	0.762679	+	3.58812i	0.0297776	+	0.140093i
$657$	5.39111	+	2.74691i	0.210327	+	0.107167i
$658$	29.6726	−	10.6729i	1.15676	−	0.416074i
$659$		−	3.28935i		−	0.128135i	−0.997946	−	0.0640675i	$-0.979593\pi$
$659$		−	3.28935i		−	0.128135i	0.997946	−	0.0640675i	$-0.0204073\pi$
$660$	−8.51386	−	7.58934i	−0.331402	−	0.295415i
$661$	13.2691	+	7.66090i	0.516107	+	0.297974i	0.735340	−	0.677698i	$-0.237022\pi$
$661$	13.2691	+	7.66090i	0.516107	+	0.297974i	−0.219233	+	0.975672i	$0.570356\pi$
$662$	−3.97264	+	4.90580i	−0.154401	+	0.190670i
$663$	−2.75415	+	0.144339i	−0.106962	+	0.00560566i
$664$	2.29566	−	7.06532i	0.0890889	−	0.274187i
$665$	0.456026	+	11.9747i	0.0176839	+	0.464359i
$666$	−0.483912	−	0.351582i	−0.0187512	−	0.0136235i
$667$	−8.74726	−	5.68054i	−0.338695	−	0.219951i
$668$	8.15775	+	12.5618i	0.315633	+	0.486032i
$669$	40.3735	−	4.24343i	1.56093	−	0.164060i
$670$	32.6258	+	3.20025i	1.26044	+	0.123636i
$671$	2.05562	+	13.1448i	0.0793562	+	0.507450i
$672$	−2.81541	−	2.93762i	−0.108607	−	0.113321i
$673$	0.0367746	−	0.232186i	0.00141756	−	0.00895011i	−0.986969	−	0.160908i	$-0.948558\pi$
$673$	0.0367746	−	0.232186i	0.00141756	−	0.00895011i	0.988387	+	0.151958i	$0.0485578\pi$
$674$	17.6862	+	15.9247i	0.681247	+	0.613397i
$675$	7.60823	+	26.8948i	0.292841	+	1.03518i
$676$	5.72196	−	2.54758i	0.220075	−	0.0979838i
$677$	18.7629	+	23.1702i	0.721116	+	0.890504i	0.997509	−	0.0705408i	$-0.0224725\pi$
$677$	18.7629	+	23.1702i	0.721116	+	0.890504i	−0.276393	+	0.961045i	$0.589139\pi$
$678$	8.63908	−	4.40183i	0.331782	−	0.169051i
$679$	−4.35211	+	18.5308i	−0.167019	+	0.711145i
$680$	−0.0107264	−	1.54493i	−0.000411341	−	0.0592453i
$681$	−20.0439	−	34.7170i	−0.768083	−	1.33036i
$682$	16.6212	−	14.9071i	0.636458	−	0.570821i
$683$	12.2893	+	45.8642i	0.470237	+	1.75495i	0.638917	+	0.769276i	$0.279383\pi$
$683$	12.2893	+	45.8642i	0.470237	+	1.75495i	−0.168680	+	0.985671i	$0.553951\pi$
$684$	−1.17473	−	0.523023i	−0.0449169	−	0.0199983i
$685$	40.3022	−	20.8887i	1.53987	−	0.798117i
$686$	2.68929	+	18.3240i	0.102678	+	0.699612i
$687$	−0.875747	−	5.52925i	−0.0334118	−	0.210954i
$688$	−6.77393	−	8.36511i	−0.258254	−	0.318917i
$689$	−21.8188	−	24.2323i	−0.831232	−	0.923176i
$690$	0.310008	−	6.82113i	0.0118018	−	0.259676i
$691$	2.75521	−	6.18831i	0.104813	−	0.235414i	−0.853524	−	0.521053i	$-0.825539\pi$
$691$	2.75521	−	6.18831i	0.104813	−	0.235414i	0.958337	+	0.285639i	$0.0922059\pi$
$692$	−14.9753	+	14.9753i	−0.569277	+	0.569277i
$693$	−5.42061	−	1.28426i	−0.205912	−	0.0487850i
$694$			33.8346i			1.28434i
$695$	14.0490	+	23.9481i	0.532910	+	0.908404i
$696$	1.67958	−	7.90182i	0.0636644	−	0.299518i
$697$	0.132647	−	2.53105i	0.00502436	−	0.0958704i
$698$	5.41717	−	4.38674i	0.205043	−	0.166041i
$699$	−14.4949	−	10.5312i	−0.548249	−	0.398326i
$700$	9.28511	+	9.42267i	0.350944	+	0.356143i
$701$	2.63482	+	8.10914i	0.0995158	+	0.306278i	0.988404	−	0.151846i	$-0.0485217\pi$
$701$	2.63482	+	8.10914i	0.0995158	+	0.306278i	−0.888888	+	0.458124i	$0.848522\pi$
$702$	5.19952	+	13.5452i	0.196243	+	0.511231i
$703$	1.84347	−	0.493956i	0.0695277	−	0.0186299i
$704$	2.09225	−	2.57342i	0.0788547	−	0.0969894i
$705$	−4.00116	+	40.7908i	−0.150692	+	1.53627i
$706$	−17.8506	−	24.5692i	−0.671815	−	0.924674i
$707$	−19.9492	+	0.621043i	−0.750267	+	0.0233567i
$708$	−5.98395	−	11.7442i	−0.224891	−	0.441373i
$709$	47.4839	+	4.99076i	1.78330	+	0.187432i	0.937946	−	0.346781i	$-0.112725\pi$
$709$	47.4839	+	4.99076i	1.78330	+	0.187432i	0.845350	+	0.534213i	$0.179392\pi$
$710$	−2.61805	−	3.97082i	−0.0982538	−	0.149022i
$711$	0.178587	+	0.198341i	0.00669754	+	0.00743837i
$712$	−0.239202	−	4.56425i	−0.00896448	−	0.171052i
$713$	13.2019	+	2.09098i	0.494417	+	0.0783079i
$714$	1.35365	+	2.46400i	0.0506590	+	0.0922128i
$715$	15.6287	+	11.2362i	0.584481	+	0.420211i
$716$	6.01280	+	10.4145i	0.224709	+	0.389207i
$717$	7.12120	+	5.76664i	0.265946	+	0.215359i
$718$	25.8748	−	16.8033i	0.965640	−	0.627094i
$719$	−26.2224	+	5.57375i	−0.977932	+	0.207866i	−0.669036	−	0.743230i	$-0.733293\pi$
$719$	−26.2224	+	5.57375i	−0.977932	+	0.207866i	−0.308896	+	0.951096i	$0.599960\pi$
$720$	−1.34698	+	0.448024i	−0.0501991	+	0.0166969i
$721$	8.50837	+	6.46216i	0.316868	+	0.240663i
$722$	−13.2734	+	6.76314i	−0.493985	+	0.251698i
$723$	0.950786	+	18.1421i	0.0353601	+	0.674711i
$724$	1.17040	+	11.1356i	0.0434975	+	0.413851i
$725$	−5.10336	+	25.7635i	−0.189534	+	0.956832i
$726$	−1.83404	+	16.8173i	−0.0680675	+	0.624148i
$727$	−16.8467	+	16.8467i	−0.624810	+	0.624810i	−0.946758	−	0.321948i	$-0.895663\pi$
$727$	−16.8467	+	16.8467i	−0.624810	+	0.624810i	0.321948	+	0.946758i	$0.395663\pi$
$728$	5.24368	+	4.43391i	0.194344	+	0.164332i
$729$	28.5693	−	9.28274i	1.05812	−	0.343805i
$730$	−8.53291	+	19.5290i	−0.315817	+	0.722801i
$731$	3.02494	+	6.79412i	0.111881	+	0.251290i
$732$	−5.75953	−	2.21088i	−0.212878	−	0.0817163i
$733$	−18.3840	−	11.9387i	−0.679028	−	0.440966i	0.158501	−	0.987359i	$-0.449334\pi$
$733$	−18.3840	−	11.9387i	−0.679028	−	0.440966i	−0.837529	+	0.546393i	$0.816001\pi$
$734$	10.7343	+	33.0368i	0.396210	+	1.21941i
$735$	−23.0158	−	7.05245i	−0.848951	−	0.260133i
$736$	1.98559			0.0731897
$737$	−24.2297	−	42.1571i	−0.892513	−	1.55288i
$738$	−2.24941	+	0.602728i	−0.0828019	+	0.0221867i
$739$	30.5977	−	3.21595i	1.12555	−	0.118301i	0.476595	−	0.879123i	$-0.341871\pi$
$739$	30.5977	−	3.21595i	1.12555	−	0.118301i	0.648960	+	0.760823i	$0.275204\pi$
$740$	1.13517	−	1.77487i	0.0417297	−	0.0652454i
$741$	−7.68955	−	2.49849i	−0.282483	−	0.0917841i
$742$	−12.5682	+	30.7716i	−0.461394	+	1.12966i
$743$	−3.78982	+	0.600248i	−0.139035	+	0.0220210i	−0.225564	−	0.974228i	$-0.572422\pi$
$743$	−3.78982	+	0.600248i	−0.139035	+	0.0220210i	0.0865291	+	0.996249i	$0.472422\pi$
$744$	2.15248	+	10.1266i	0.0789137	+	0.371260i
$745$	−26.6635	+	24.3453i	−0.976876	+	0.891941i
$746$	−1.24802	−	11.8741i	−0.0456931	−	0.434741i
$747$	4.55545	+	1.22063i	0.166675	+	0.0446605i
$748$	−1.85654	+	1.34332i	−0.0678817	+	0.0491166i
$749$	−22.9357	−	0.487198i	−0.838052	−	0.0178018i
$750$	−16.2386	+	5.65277i	−0.592949	+	0.206410i
$751$	−10.7064	+	11.8906i	−0.390681	+	0.433895i	−0.906113	−	0.423035i	$-0.860965\pi$
$751$	−10.7064	+	11.8906i	−0.390681	+	0.433895i	0.515433	+	0.856930i	$0.327631\pi$
$752$	−11.9023	−	0.623773i	−0.434032	−	0.0227467i
$753$	4.45315	−	11.6008i	0.162282	−	0.422758i
$754$	−1.42510	+	13.5589i	−0.0518990	+	0.493786i
$755$	28.2393	−	20.8181i	1.02773	−	0.757649i
$756$	10.1275	−	10.7784i	0.368335	−	0.392006i
$757$	−31.2067	−	4.94266i	−1.13423	−	0.179644i	−0.439036	−	0.898469i	$-0.644680\pi$
$757$	−31.2067	−	4.94266i	−1.13423	−	0.179644i	−0.695191	+	0.718826i	$0.744680\pi$
$758$	−6.92073	−	1.85440i	−0.251372	−	0.0673550i
$759$	−8.50466	+	5.49939i	−0.308700	+	0.199615i
$760$	1.59376	−	4.23963i	0.0578116	−	0.153787i
$761$	18.7634	−	42.1434i	0.680174	−	1.52770i	−0.161013	−	0.986952i	$-0.551476\pi$
$761$	18.7634	−	42.1434i	0.680174	−	1.52770i	0.841187	−	0.540744i	$-0.181857\pi$
$762$	19.3615	+	9.86516i	0.701392	+	0.357377i
$763$	8.63212	+	5.87010i	0.312504	+	0.212512i
$764$	−11.1938	+	15.4069i	−0.404976	+	0.557402i
$765$	0.979078	−	0.0581302i	0.0353986	−	0.00210170i
$766$	1.44144	−	1.29788i	0.0520813	−	0.0468942i
$767$	12.1154	+	18.6561i	0.437462	+	0.673632i
$768$	0.551137	+	1.43576i	0.0198874	+	0.0518086i
$769$	7.59178			0.273766			0.136883	−	0.990587i	$-0.456291\pi$
$769$	7.59178			0.273766			0.136883	+	0.990587i	$0.456291\pi$
$770$	3.38396	−	19.3274i	0.121950	−	0.696512i
$771$	0.611215			0.0220124
$772$	−4.64356	−	12.0969i	−0.167125	−	0.435377i
$773$	28.0461	+	43.1871i	1.00875	+	1.55333i	0.820850	+	0.571144i	$0.193500\pi$
$773$	28.0461	+	43.1871i	1.00875	+	1.55333i	0.187897	+	0.982189i	$0.439833\pi$
$774$	5.07814	−	4.57238i	0.182530	−	0.164351i
$775$	−7.45455	−	32.8230i	−0.267775	−	1.17904i
$776$	4.22884	−	5.82051i	0.151807	−	0.208944i
$777$	−0.281905	+	3.82339i	−0.0101133	+	0.137163i
$778$	7.67930	+	3.91280i	0.275316	+	0.140281i
$779$	3.02219	−	6.78794i	0.108281	−	0.243203i
$780$	−8.12847	+	3.68686i	−0.291046	+	0.132011i
$781$	−2.54101	+	6.58110i	−0.0909245	+	0.235490i
$782$	−1.32515	−	0.355074i	−0.0473874	−	0.0126974i
$783$	29.0020	+	4.59346i	1.03645	+	0.164157i
$784$	1.74483	−	6.77905i	0.0623152	−	0.242109i
$785$	−2.87793	+	19.0245i	−0.102718	+	0.679014i
$786$	−0.324606	+	3.08842i	−0.0115783	+	0.110160i
$787$	19.6853	−	51.2820i	0.701705	−	1.82801i	0.160664	−	0.987009i	$-0.448636\pi$
$787$	19.6853	−	51.2820i	0.701705	−	1.82801i	0.541041	−	0.840996i	$-0.318030\pi$
$788$	−10.7621	−	0.564018i	−0.383384	−	0.0200923i
$789$	−23.4447	+	26.0380i	−0.834655	+	0.926978i
$790$	−0.660101	+	0.669332i	−0.0234853	+	0.0238137i
$791$	14.2652	+	8.64508i	0.507213	+	0.307384i
$792$	1.70098	+	1.24092i	0.0604416	+	0.0440941i
$793$	10.0570	+	2.69476i	0.357133	+	0.0956936i
$794$	−0.316493	−	3.01123i	−0.0112319	−	0.106865i
$795$	−29.1309	−	31.9049i	−1.03317	−	1.13155i
$796$	3.54885	+	16.6960i	0.125786	+	0.591775i
$797$	−17.0170	+	2.69522i	−0.602772	+	0.0954697i	−0.450360	−	0.892847i	$-0.648704\pi$
$797$	−17.0170	+	2.69522i	−0.602772	+	0.0954697i	−0.152413	+	0.988317i	$0.548704\pi$
$798$	1.11614	+	8.16593i	0.0395110	+	0.289071i
$799$	7.83189	+	2.54474i	0.277072	+	0.0900263i
$800$	−1.85648	−	4.64257i	−0.0656366	−	0.164140i
$801$	2.88563	−	0.303292i	0.101959	−	0.0107163i
$802$	−21.3495	+	5.72059i	−0.753878	+	0.202001i
$803$	30.9325	−	6.51177i	1.09159	−	0.229795i
$804$	22.5468			0.795166
$805$	10.2560	−	5.72741i	0.361477	−	0.201865i
$806$	−5.39921	−	16.6171i	−0.190179	−	0.585311i
$807$	25.1782	+	16.3509i	0.886313	+	0.575578i
$808$	7.04269	+	2.70344i	0.247761	+	0.0951065i
$809$	−1.67023	−	3.75140i	−0.0587222	−	0.131892i	0.881801	−	0.471622i	$-0.156331\pi$
$809$	−1.67023	−	3.75140i	−0.0587222	−	0.131892i	−0.940523	+	0.339729i	$0.889665\pi$
$810$	5.45978	+	13.9333i	0.191837	+	0.489566i
$811$	2.44461	−	0.794301i	0.0858418	−	0.0278917i	−0.265781	−	0.964033i	$-0.585630\pi$
$811$	2.44461	−	0.794301i	0.0858418	−	0.0278917i	0.351623	+	0.936142i	$0.385630\pi$
$812$	13.0774	−	4.70380i	0.458927	−	0.165071i
$813$	18.6786	−	18.6786i	0.655088	−	0.655088i
$814$	−3.12098	+	0.157449i	−0.109390	+	0.00551860i
$815$	−3.21320	+	8.54759i	−0.112554	+	0.299409i
$816$	−0.111071	−	1.05677i	−0.00388825	−	0.0369942i
$817$	1.14108	+	21.7730i	0.0399212	+	0.761742i
$818$	−28.6076	+	14.5763i	−1.00024	+	0.509648i
$819$	−2.63673	+	3.47164i	−0.0921348	+	0.121309i
$820$	−2.58882	−	7.78328i	−0.0904055	−	0.271804i
$821$	−0.907969	+	0.192995i	−0.0316884	+	0.00673557i	−0.223729	−	0.974651i	$-0.571823\pi$
$821$	−0.907969	+	0.192995i	−0.0316884	+	0.00673557i	0.192040	+	0.981387i	$0.438490\pi$
$822$	26.1839	−	17.0040i	0.913269	−	0.593084i
$823$	−8.32271	−	6.73960i	−0.290111	−	0.234928i	0.473205	−	0.880952i	$-0.343097\pi$
$823$	−8.32271	−	6.73960i	−0.290111	−	0.234928i	−0.763317	+	0.646025i	$0.776430\pi$
$824$	−2.01912	−	3.49722i	−0.0703394	−	0.121831i
$825$	20.8100	+	14.7432i	0.724512	+	0.513293i
$826$	11.7523	−	19.3925i	0.408915	−	0.674750i
$827$	24.5006	+	3.88051i	0.851969	+	0.134939i	0.567122	−	0.823634i	$-0.308057\pi$
$827$	24.5006	+	3.88051i	0.851969	+	0.134939i	0.284848	+	0.958573i	$0.408057\pi$
$828$	0.0659707	+	1.25880i	0.00229264	+	0.0437462i
$829$	−16.8035	−	18.6622i	−0.583610	−	0.648164i	0.376951	−	0.926233i	$-0.376972\pi$
$829$	−16.8035	−	18.6622i	−0.583610	−	0.648164i	−0.960561	+	0.278069i	$0.910306\pi$
$830$	−3.34084	+	16.2721i	−0.115962	+	0.564814i
$831$	38.8458	+	4.08285i	1.34754	+	0.141633i
$832$	−1.17833	−	2.31259i	−0.0408511	−	0.0801747i
$833$	−2.37674	+	4.21223i	−0.0823493	+	0.145945i
$834$	11.2243	+	15.4489i	0.388666	+	0.534953i
$835$	−21.2577	−	25.8815i	−0.735652	−	0.895667i
$836$	−6.49250	+	1.72607i	−0.224548	+	0.0596974i
$837$	−36.3487	+	9.73960i	−1.25639	+	0.336650i
$838$	−6.94385	−	18.0893i	−0.239871	−	0.624886i
$839$	11.3757	+	35.0107i	0.392732	+	1.20870i	0.930714	+	0.365748i	$0.119187\pi$
$839$	11.3757	+	35.0107i	0.392732	+	1.20870i	−0.537982	+	0.842956i	$0.680813\pi$
$840$	6.98820	+	5.82630i	0.241116	+	0.201026i
$841$	−1.13906	−	0.827576i	−0.0392779	−	0.0285371i
$842$	26.1304	−	21.1600i	0.900514	−	0.729222i
$843$	0.254496	−	4.85608i	0.00876532	−	0.167252i
$844$	2.31920	−	10.9110i	0.0798303	−	0.375572i
$845$	−12.0802	+	7.08681i	−0.415573	+	0.243794i
$846$		−	7.56639i		−	0.260138i
$847$	−26.2552	+	12.5564i	−0.902140	+	0.431444i
$848$	8.88357	−	8.88357i	0.305063	−	0.305063i
$849$	0.931077	−	2.09123i	0.0319545	−	0.0717709i
$850$	0.408781	+	3.43038i	0.0140211	+	0.117661i
$851$	−1.25183	−	1.39030i	−0.0429122	−	0.0476589i
$852$	−2.05863	−	2.54220i	−0.0705276	−	0.0870944i
$853$	4.07890	+	25.7531i	0.139659	+	0.881771i	0.953655	+	0.300901i	$0.0972875\pi$
$853$	4.07890	+	25.7531i	0.139659	+	0.881771i	−0.813997	+	0.580870i	$0.802713\pi$
$854$	−1.98568	−	10.4260i	−0.0679484	−	0.356769i
$855$	2.74074	+	0.869529i	0.0937312	+	0.0297372i
$856$	7.92120	+	3.52675i	0.270741	+	0.120542i
$857$	−4.06957	−	15.1878i	−0.139014	−	0.518807i	−0.999949	−	0.0100922i	$-0.996788\pi$
$857$	−4.06957	−	15.1878i	−0.139014	−	0.518807i	0.860935	−	0.508715i	$-0.169879\pi$
$858$	11.4521	+	6.64174i	0.390968	+	0.226745i
$859$	16.7177	+	28.9559i	0.570401	+	0.987964i	0.996525	+	0.0832989i	$0.0265456\pi$
$859$	16.7177	+	28.9559i	0.570401	+	0.987964i	−0.426123	+	0.904665i	$0.640121\pi$
$860$	17.1370	+	16.9006i	0.584365	+	0.576307i
$861$	10.8775	+	10.2207i	0.370706	+	0.348321i
$862$	−20.4995	+	10.4450i	−0.698216	+	0.355759i
$863$	6.02335	+	7.43821i	0.205037	+	0.253200i	0.869283	−	0.494314i	$-0.164581\pi$
$863$	6.02335	+	7.43821i	0.205037	+	0.253200i	−0.664246	+	0.747514i	$0.731247\pi$
$864$	−5.10676	+	2.27368i	−0.173736	+	0.0773521i
$865$	29.5460	−	37.0087i	1.00459	−	1.25833i
$866$	14.9204	+	13.4344i	0.507017	+	0.456521i
$867$	3.97504	−	25.0974i	0.135000	−	0.852353i
$868$	−12.8586	+	12.3237i	−0.436450	+	0.418293i
$869$	1.37676	+	0.220815i	0.0467033	+	0.00749065i
$870$	−1.76340	+	17.9775i	−0.0597849	+	0.609493i
$871$	−37.8432	+	3.97748i	−1.28227	+	0.134772i
$872$	−2.14890	−	3.30902i	−0.0727709	−	0.112057i
$873$	3.83051	+	2.48756i	0.129643	+	0.0841912i
$874$	−3.25381	−	2.36403i	−0.110062	−	0.0799645i
$875$	−22.9807	−	18.6250i	−0.776888	−	0.629639i
$876$	−4.52948	+	13.9403i	−0.153037	+	0.470999i
$877$	−29.9813	+	1.57126i	−1.01240	+	0.0530575i	−0.551313	−	0.834298i	$-0.685873\pi$
$877$	−29.9813	+	1.57126i	−1.01240	+	0.0530575i	−0.461085	+	0.887356i	$0.652540\pi$
$878$	−12.3307	+	15.2271i	−0.416141	+	0.513891i
$879$	17.6236	+	10.1750i	0.594431	+	0.343195i
$880$	−4.00807	+	6.23982i	−0.135112	+	0.210344i
$881$		−	41.0286i		−	1.38229i	−0.722717	−	0.691144i	$-0.757107\pi$
$881$		−	41.0286i		−	1.38229i	0.722717	−	0.691144i	$-0.242893\pi$
$882$	4.35567	+	0.880929i	0.146663	+	0.0296624i
$883$	−52.0283	−	26.5097i	−1.75089	−	0.892123i	−0.959922	−	0.280266i	$-0.909577\pi$
$883$	−52.0283	−	26.5097i	−1.75089	−	0.892123i	−0.790968	−	0.611857i	$-0.790423\pi$
$884$	0.372848	+	1.75411i	0.0125402	+	0.0589971i
$885$	16.2234	+	24.6062i	0.545345	+	0.827128i
$886$	9.90778	−	4.41123i	0.332858	−	0.148198i
$887$	−29.5850	+	45.5570i	−0.993368	+	1.52965i	−0.152579	+	0.988291i	$0.548758\pi$
$887$	−29.5850	+	45.5570i	−0.993368	+	1.52965i	−0.840790	+	0.541362i	$0.817909\pi$
$888$	0.657845	−	1.29109i	0.0220758	−	0.0433263i
$889$	3.11716	+	37.2530i	0.104546	+	1.24942i
$890$	1.66880	+	10.0828i	0.0559383	+	0.337976i
$891$	12.1254	−	18.5918i	0.406216	−	0.622850i
$892$	−6.83200	−	25.4974i	−0.228752	−	0.853715i
$893$	18.7618	+	15.1930i	0.627840	+	0.508415i
$894$	−16.6163	+	18.4543i	−0.555732	+	0.617203i
$895$	−15.9562	−	21.6442i	−0.533358	−	0.723487i
$896$	−1.60024	+	2.10695i	−0.0534603	+	0.0703882i
$897$	1.23985	+	7.82812i	0.0413975	+	0.261373i
$898$	6.96079	−	10.7187i	0.232285	−	0.357687i
$899$	−34.5880	−	7.35191i	−1.15358	−	0.245200i
$900$	2.88156	−	1.33120i	0.0960519	−	0.0443732i
$901$	−7.51739	+	4.34017i	−0.250441	+	0.144592i
$902$	−7.17040	+	9.82876i	−0.238748	+	0.327262i
$903$	−42.0548	−	12.2315i	−1.39950	−	0.407039i
$904$	−3.70574	−	5.10051i	−0.123251	−	0.169641i
$905$	−5.37541	−	24.4532i	−0.178685	−	0.812853i
$906$	17.9317	−	16.1458i	0.595741	−	0.536408i
$907$	−33.4236	−	12.8301i	−1.10981	−	0.426017i	−0.266713	−	0.963776i	$-0.585938\pi$
$907$	−33.4236	−	12.8301i	−1.10981	−	0.426017i	−0.843098	+	0.537760i	$0.819271\pi$
$908$	−20.2574	+	16.4041i	−0.672266	+	0.544390i
$909$	−1.47990	+	4.55465i	−0.0490851	+	0.151068i
$910$	−12.7570	−	8.54622i	−0.422890	−	0.283304i
$911$	−3.74580	+	2.72149i	−0.124104	+	0.0901668i	−0.648106	−	0.761550i	$-0.724439\pi$
$911$	−3.74580	+	2.72149i	−0.124104	+	0.0901668i	0.524002	+	0.851717i	$0.324439\pi$
$912$	0.806255	−	3.00898i	0.0266978	−	0.0996374i
$913$	22.5283	−	9.97755i	0.745578	−	0.330209i
$914$	20.1411	+	11.6285i	0.666208	+	0.384635i
$915$	13.3494	+	3.47780i	0.441317	+	0.114972i
$916$	−3.46196	+	1.12486i	−0.114386	+	0.0371664i
$917$	−4.81060	+	2.32378i	−0.158860	+	0.0767381i
$918$	3.81478	−	0.604202i	0.125906	−	0.0199416i
$919$	−45.6972	−	4.80297i	−1.50741	−	0.158435i	−0.685509	−	0.728064i	$-0.740420\pi$
$919$	−45.6972	−	4.80297i	−1.50741	−	0.158435i	−0.821902	+	0.569628i	$0.807087\pi$
$920$	−4.41225	+	0.494742i	−0.145468	+	0.0163112i
$921$	−14.2297	−	3.02461i	−0.468883	−	0.0996642i
$922$	19.1698	−	7.35861i	0.631325	−	0.242343i
$923$	3.90373	+	3.90373i	0.128493	+	0.128493i
$924$	1.01862	−	13.4566i	0.0335101	−	0.442690i
$925$	−2.08027	+	4.22685i	−0.0683990	+	0.138978i
$926$	6.74297	+	3.00216i	0.221588	+	0.0986572i
$927$	2.15004	−	1.39625i	0.0706165	−	0.0458589i
$928$	−5.24561	−	0.274911i	−0.172196	−	0.00902440i
$929$	4.52108	−	43.0152i	0.148332	−	1.41128i	−0.626651	−	0.779300i	$-0.715575\pi$
$929$	4.52108	−	43.0152i	0.148332	−	1.41128i	0.774983	−	0.631982i	$-0.217758\pi$
$930$	−7.30633	−	21.9665i	−0.239584	−	0.720308i
$931$	−10.9304	+	9.03155i	−0.358229	+	0.295997i
$932$	−5.28902	+	10.3803i	−0.173248	+	0.340017i
$933$	3.67349	−	1.41012i	0.120265	−	0.0461652i
$934$	15.7792	−	27.3304i	0.516311	−	0.894277i
$935$	3.79078	−	3.44763i	0.123972	−	0.112750i
$936$	1.42696	−	0.823855i	0.0466416	−	0.0269285i
$937$	−1.67005	+	10.5443i	−0.0545580	+	0.344466i	0.945276	+	0.326271i	$0.105792\pi$
$937$	−1.67005	+	10.5443i	−0.0545580	+	0.344466i	−0.999834	+	0.0181953i	$0.994208\pi$
$938$	20.4302	+	32.9722i	0.667068	+	1.07658i
$939$	11.9212	+	3.87342i	0.389033	+	0.126404i
$940$	26.6040	−	1.57954i	0.867728	−	0.0515191i
$941$	0.226136	+	0.507910i	0.00737182	+	0.0165574i	0.917194	−	0.398441i	$-0.130449\pi$
$941$	0.226136	+	0.507910i	0.00737182	+	0.0165574i	−0.909822	+	0.414999i	$0.863782\pi$
$942$	−0.692584	+	13.2153i	−0.0225656	+	0.430577i
$943$	−7.27371	+	0.381199i	−0.236864	+	0.0124135i
$944$	−6.93375	+	5.03766i	−0.225674	+	0.163962i
$945$	−19.8192	+	26.4745i	−0.644720	+	0.861216i
$946$	5.65356	−	35.2493i	0.183813	−	1.14605i
$947$	−9.14862	+	34.1431i	−0.297290	+	1.10950i	0.642091	+	0.766628i	$0.278067\pi$
$947$	−9.14862	+	34.1431i	−0.297290	+	1.10950i	−0.939382	+	0.342874i	$0.888600\pi$
$948$	−0.406892	+	0.502470i	−0.0132152	+	0.0163195i
$949$	5.14319	−	24.1968i	0.166955	−	0.785461i
$950$	−2.48518	+	9.81817i	−0.0806299	+	0.318543i
$951$	−6.49120	+	8.93437i	−0.210492	+	0.289717i
$952$	1.44476	−	1.11999i	0.0468248	−	0.0362990i
$953$	3.82271	+	7.50249i	0.123830	+	0.243030i	0.944596	−	0.328234i	$-0.106453\pi$
$953$	3.82271	+	7.50249i	0.123830	+	0.243030i	−0.820767	+	0.571263i	$0.806453\pi$
$954$	5.92704	+	5.33673i	0.191895	+	0.172783i
$955$	21.0353	−	37.0254i	0.680685	−	1.19811i
$956$	2.97914	−	5.16001i	0.0963521	−	0.166887i
$957$	23.2294	−	13.3511i	0.750900	−	0.431579i
$958$	−12.6955	−	12.6955i	−0.410173	−	0.410173i
$959$	48.5923	+	22.8833i	1.56913	+	0.738940i
$960$	−1.58245	−	3.05314i	−0.0510733	−	0.0985397i
$961$	14.0039	−	2.97662i	0.451739	−	0.0960200i
$962$	−0.876383	+	2.28305i	−0.0282557	+	0.0736086i
$963$	−1.97266	+	5.13896i	−0.0635681	+	0.165601i
$964$	11.5546	−	2.45602i	0.372150	−	0.0791029i
$965$	13.3328	+	25.7240i	0.429198	+	0.828084i
$966$	6.63559	−	4.60895i	0.213496	−	0.148291i
$967$	−7.10398	−	7.10398i	−0.228448	−	0.228448i	0.583596	−	0.812044i	$-0.301645\pi$
$967$	−7.10398	−	7.10398i	−0.228448	−	0.228448i	−0.812044	+	0.583596i	$0.801645\pi$
$968$	10.9871	−	0.532766i	0.353138	−	0.0171237i
$969$	−1.07617	+	1.86398i	−0.0345715	+	0.0598796i
$970$	−7.94682	+	13.9877i	−0.255157	+	0.449117i
$971$	−12.5210	−	11.2740i	−0.401819	−	0.361799i	0.443304	−	0.896371i	$-0.353806\pi$
$971$	−12.5210	−	11.2740i	−0.401819	−	0.361799i	−0.845123	+	0.534572i	$0.820473\pi$
$972$	−2.94083	−	5.77170i	−0.0943271	−	0.185127i
$973$	−12.4217	+	30.4129i	−0.398222	+	0.974992i
$974$	−5.04134	+	6.93881i	−0.161535	+	0.222334i
$975$	17.1440	−	10.2181i	0.549047	−	0.327240i
$976$	−0.834034	+	3.92382i	−0.0266968	+	0.125598i
$977$	−28.7757	+	35.5351i	−0.920617	+	1.13687i	0.0696334	+	0.997573i	$0.477817\pi$
$977$	−28.7757	+	35.5351i	−0.920617	+	1.13687i	−0.990251	+	0.139295i	$0.955516\pi$
$978$	−1.62551	+	6.06647i	−0.0519779	+	0.193984i
$979$	10.7397	−	10.6978i	0.343243	−	0.341904i
$980$	−2.18814	+	15.4988i	−0.0698975	+	0.495090i
$981$	2.02641	−	1.47227i	0.0646983	−	0.0470061i
$982$	18.8288	−	0.986778i	0.600852	−	0.0314893i
$983$	1.90927	−	36.4311i	0.0608963	−	1.16197i	−0.781782	−	0.623552i	$-0.785689\pi$
$983$	1.90927	−	36.4311i	0.0608963	−	1.16197i	0.842678	−	0.538418i	$-0.180978\pi$
$984$	−2.29460	−	5.15375i	−0.0731491	−	0.164296i
$985$	24.0555	−	1.42823i	0.766471	−	0.0455072i
$986$	3.45169	+	1.12152i	0.109924	+	0.0357166i
$987$	−41.2239	+	25.5431i	−1.31217	+	0.813046i
$988$	−0.822425	+	5.19259i	−0.0261648	+	0.165198i
$989$	18.5092	−	10.6863i	0.588560	−	0.339805i
$990$	−4.08901	−	2.33367i	−0.129957	−	0.0741688i
$991$	23.0873	−	39.9883i	0.733392	−	1.27027i	−0.222034	−	0.975039i	$-0.571269\pi$
$991$	23.0873	−	39.9883i	0.733392	−	1.27027i	0.955425	−	0.295233i	$-0.0953972\pi$
$992$	6.28465	−	2.41245i	0.199538	−	0.0765954i
$993$	4.40743	−	8.65006i	0.139865	−	0.274501i
$994$	1.85231	−	5.31406i	0.0587516	−	0.168552i
$995$	−12.0461	−	36.2167i	−0.381888	−	1.14815i
$996$	−1.19424	+	11.3624i	−0.0378408	+	0.360031i
$997$	16.3908	+	0.859003i	0.519101	+	0.0272049i	0.310088	−	0.950708i	$-0.399642\pi$
$997$	16.3908	+	0.859003i	0.519101	+	0.0272049i	0.209013	+	0.977913i	$0.432975\pi$
$998$	−20.6307	+	13.3977i	−0.653052	+	0.424097i
$999$	4.81163	+	2.14227i	0.152233	+	0.0677785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.157.33	yes	768
5.3	odd	4	inner	770.2.bv.a.3.40	✓	768
7.5	odd	6	inner	770.2.bv.a.47.33	yes	768
11.4	even	5	inner	770.2.bv.a.367.9	yes	768
35.33	even	12	inner	770.2.bv.a.663.9	yes	768
55.48	odd	20	inner	770.2.bv.a.213.33	yes	768
77.26	odd	30	inner	770.2.bv.a.257.40	yes	768
385.103	even	60	inner	770.2.bv.a.103.33	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.40	✓	768	5.3	odd	4	inner
770.2.bv.a.47.33	yes	768	7.5	odd	6	inner
770.2.bv.a.103.33	yes	768	385.103	even	60	inner
770.2.bv.a.157.33	yes	768	1.1	even	1	trivial
770.2.bv.a.213.33	yes	768	55.48	odd	20	inner
770.2.bv.a.257.40	yes	768	77.26	odd	30	inner
770.2.bv.a.367.9	yes	768	11.4	even	5	inner
770.2.bv.a.663.9	yes	768	35.33	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.358368 + 0.933580i) q^{2} +(-0.837605 - 1.28980i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.48465 - 1.67207i) q^{5} +(0.903960 - 1.24419i) q^{6} +(2.63859 + 0.194548i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(0.258211 - 0.579952i) q^{9} +O(q^{10})\)	\(q+(0.358368 + 0.933580i) q^{2} +(-0.837605 - 1.28980i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.48465 - 1.67207i) q^{5} +(0.903960 - 1.24419i) q^{6} +(2.63859 + 0.194548i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(0.258211 - 0.579952i) q^{9} +(2.09306 + 0.786822i) q^{10} +(-0.852145 - 3.20528i) q^{11} +(1.48551 + 0.398040i) q^{12} +(-2.56353 - 0.406023i) q^{13} +(0.763960 + 2.53305i) q^{14} +(-3.40018 - 0.514363i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-0.247607 + 0.645039i) q^{17} +(0.633967 + 0.0332248i) q^{18} +(-1.35537 + 1.50529i) q^{19} +(0.0155247 + 2.23601i) q^{20} +(-1.95917 - 3.56620i) q^{21} +(2.68701 - 1.94422i) q^{22} +(1.91793 + 0.513907i) q^{23} +(0.160755 + 1.52948i) q^{24} +(-0.591638 - 4.96487i) q^{25} +(-0.539631 - 2.53877i) q^{26} +(-5.52122 + 0.874476i) q^{27} +(-2.09103 + 1.62098i) q^{28} +(-4.99572 - 1.62321i) q^{29} +(-0.738317 - 3.35868i) q^{30} +(6.69489 - 0.703662i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.42041 + 3.78386i) q^{33} -0.690930 q^{34} +(4.24267 - 4.12307i) q^{35} +(0.196175 + 0.603766i) q^{36} +(-0.790201 - 0.513163i) q^{37} +(-1.89102 - 0.725896i) q^{38} +(1.62354 + 3.64652i) q^{39} +(-2.08194 + 0.815809i) q^{40} +(-3.48874 + 1.13356i) q^{41} +(2.62723 - 3.10705i) q^{42} +(7.61122 - 7.61122i) q^{43} +(2.77802 + 1.81179i) q^{44} +(-0.586368 - 1.29277i) q^{45} +(0.207550 + 1.97471i) q^{46} +(-0.623773 - 11.9023i) q^{47} +(-1.37029 + 0.698196i) q^{48} +(6.92430 + 1.02666i) q^{49} +(4.42308 - 2.33159i) q^{50} +(1.03937 - 0.220924i) q^{51} +(2.17676 - 1.41360i) q^{52} +(9.76349 + 7.90632i) q^{53} +(-2.79502 - 4.84112i) q^{54} +(-6.62460 - 3.33387i) q^{55} +(-2.26268 - 1.37124i) q^{56} +(3.07678 + 0.487314i) q^{57} +(-0.274911 - 5.24561i) q^{58} +(-5.73484 - 6.36919i) q^{59} +(2.87100 - 1.89292i) q^{60} +(-3.98951 - 0.419314i) q^{61} +(3.05616 + 5.99805i) q^{62} +(0.794142 - 1.48002i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-4.48484 + 3.68360i) q^{65} +(-4.75830 - 1.83722i) q^{66} +(14.1612 - 3.79447i) q^{67} +(-0.247607 - 0.645039i) q^{68} +(-0.943630 - 2.90419i) q^{69} +(5.36966 + 2.48330i) q^{70} +(-1.72082 - 1.25025i) q^{71} +(-0.493361 + 0.399516i) q^{72} +(-0.498810 + 9.51787i) q^{73} +(0.195896 - 0.921617i) q^{74} +(-5.90813 + 4.92170i) q^{75} -2.02556i q^{76} +(-1.62488 - 8.62321i) q^{77} +(-2.82250 + 2.82250i) q^{78} +(-0.170998 + 0.384067i) q^{79} +(-1.50772 - 1.65129i) q^{80} +(4.47814 + 4.97348i) q^{81} +(-2.30852 - 2.85079i) q^{82} +(1.16214 + 7.33745i) q^{83} +(3.84220 + 1.33927i) q^{84} +(0.710941 + 1.37167i) q^{85} +(9.83330 + 4.37807i) q^{86} +(2.09083 + 7.80308i) q^{87} +(-0.695902 + 3.24280i) q^{88} +(2.28526 + 3.95818i) q^{89} +(0.996772 - 1.01071i) q^{90} +(-6.68511 - 1.57006i) q^{91} +(-1.76917 + 0.901437i) q^{92} +(-6.51526 - 8.04568i) q^{93} +(10.8882 - 4.84774i) q^{94} +(0.504703 + 4.50109i) q^{95} +(-1.14289 - 1.02906i) q^{96} +(-1.12547 + 7.10596i) q^{97} +(1.52298 + 6.83232i) q^{98} +(-2.07895 - 0.333438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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