LMFDB - Embedded newform 770.2.bv.a.3.17

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			3.17
Character	$\chi$	$=$	770.3
Dual form			770.2.bv.a.257.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 + 0.358368i) q^{2} +(1.03126 - 0.669709i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.319857 + 2.21307i) q^{5} +(-0.722763 + 0.994798i) q^{6} +(-2.37940 - 1.15692i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.605220 + 1.35935i) q^{9} +O(q^{10})$	\(q+(-0.933580 + 0.358368i) q^{2} +(1.03126 - 0.669709i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.319857 + 2.21307i) q^{5} +(-0.722763 + 0.994798i) q^{6} +(-2.37940 - 1.15692i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.605220 + 1.35935i) q^{9} +(-0.494482 - 2.18071i) q^{10} +(1.16436 - 3.10552i) q^{11} +(0.318254 - 1.18774i) q^{12} +(-0.501310 + 3.16515i) q^{13} +(2.63596 + 0.227380i) q^{14} +(1.15226 + 2.49647i) q^{15} +(0.104528 - 0.994522i) q^{16} +(2.44228 + 0.937504i) q^{17} +(0.0778754 - 1.48595i) q^{18} +(-2.34659 + 2.60616i) q^{19} +(1.24313 + 1.85866i) q^{20} +(-3.22858 + 0.400415i) q^{21} +(0.0258983 + 3.31652i) q^{22} +(-1.76370 + 6.58223i) q^{23} +(0.128532 + 1.22290i) q^{24} +(-4.79538 - 1.41574i) q^{25} +(-0.666275 - 3.13458i) q^{26} +(0.863300 + 5.45066i) q^{27} +(-2.54237 + 0.732367i) q^{28} +(-4.23771 - 1.37692i) q^{29} +(-1.97038 - 1.91772i) q^{30} +(3.98581 - 0.418926i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.879039 - 3.98239i) q^{33} -2.61604 q^{34} +(3.32142 - 4.89573i) q^{35} +(0.459814 + 1.41516i) q^{36} +(-6.21460 + 9.56964i) q^{37} +(1.25677 - 3.27400i) q^{38} +(1.60275 + 3.59983i) q^{39} +(-1.82665 - 1.28971i) q^{40} +(-6.29067 + 2.04396i) q^{41} +(2.87064 - 1.53084i) q^{42} +(-2.45310 - 2.45310i) q^{43} +(-1.21271 - 3.08696i) q^{44} +(-2.81475 - 1.77419i) q^{45} +(-0.712301 - 6.77709i) q^{46} +(9.68318 - 0.507474i) q^{47} +(-0.558244 - 1.09562i) q^{48} +(4.32306 + 5.50555i) q^{49} +(4.98423 - 0.396808i) q^{50} +(3.14648 - 0.668806i) q^{51} +(1.74535 + 2.68761i) q^{52} +(0.356291 - 0.439983i) q^{53} +(-2.75930 - 4.77925i) q^{54} +(6.50032 + 3.57013i) q^{55} +(2.11105 - 1.59483i) q^{56} +(-0.674585 + 4.25916i) q^{57} +(4.44969 - 0.233198i) q^{58} +(-6.77339 - 7.52261i) q^{59} +(2.52676 + 1.08423i) q^{60} +(6.73117 + 0.707475i) q^{61} +(-3.57095 + 1.81949i) q^{62} +(3.01272 - 2.53423i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-6.84436 - 2.12183i) q^{65} +(2.24781 + 3.40286i) q^{66} +(3.21747 + 12.0078i) q^{67} +(2.44228 - 0.937504i) q^{68} +(2.58934 + 7.96917i) q^{69} +(-1.34634 + 5.76085i) q^{70} +(2.64170 + 1.91931i) q^{71} +(-0.936422 - 1.15639i) q^{72} +(-11.3434 - 0.594481i) q^{73} +(2.37237 - 11.1611i) q^{74} +(-5.89342 + 1.75152i) q^{75} +3.50693i q^{76} +(-6.36332 + 6.04220i) q^{77} +(-2.78636 - 2.78636i) q^{78} +(-0.395208 + 0.887651i) q^{79} +(2.16752 + 0.549434i) q^{80} +(1.55367 + 1.72552i) q^{81} +(5.14035 - 4.16258i) q^{82} +(1.04404 - 0.165360i) q^{83} +(-2.13137 + 2.45791i) q^{84} +(-2.85595 + 5.10508i) q^{85} +(3.16928 + 1.41105i) q^{86} +(-5.29232 + 1.41807i) q^{87} +(2.23843 + 2.44733i) q^{88} +(-1.35473 - 2.34645i) q^{89} +(3.26361 + 0.647636i) q^{90} +(4.85465 - 6.95117i) q^{91} +(3.09368 + 6.07170i) q^{92} +(3.82985 - 3.10136i) q^{93} +(-8.85817 + 3.94391i) q^{94} +(-5.01704 - 6.02678i) q^{95} +(0.913799 + 0.822789i) q^{96} +(0.117005 + 0.0185318i) q^{97} +(-6.00894 - 3.59063i) q^{98} +(3.51679 + 3.46229i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$3$	1.03126	−	0.669709i	0.595399	−	0.386657i	−0.211472	−	0.977384i	$-0.567826\pi$
$3$	1.03126	−	0.669709i	0.595399	−	0.386657i	0.806871	+	0.590727i	$0.201159\pi$
$4$	0.743145	−	0.669131i	0.371572	−	0.334565i
$5$	−0.319857	+	2.21307i	−0.143045	+	0.989716i
$5$	−0.319857	+	2.21307i	−0.143045	+	0.989716i
$6$	−0.722763	+	0.994798i	−0.295067	+	0.406125i
$7$	−2.37940	−	1.15692i	−0.899328	−	0.437275i
$7$	−2.37940	−	1.15692i	−0.899328	−	0.437275i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−0.605220	+	1.35935i	−0.201740	+	0.453115i
$10$	−0.494482	−	2.18071i	−0.156369	−	0.689600i
$11$	1.16436	−	3.10552i	0.351067	−	0.936350i
$11$	1.16436	−	3.10552i	0.351067	−	0.936350i
$12$	0.318254	−	1.18774i	0.0918720	−	0.342871i
$13$	−0.501310	+	3.16515i	−0.139039	+	0.877855i	0.815281	+	0.579066i	$0.196583\pi$
$13$	−0.501310	+	3.16515i	−0.139039	+	0.877855i	−0.954319	+	0.298789i	$0.903417\pi$
$14$	2.63596	+	0.227380i	0.704491	+	0.0607698i
$15$	1.15226	+	2.49647i	0.297512	+	0.644585i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	2.44228	+	0.937504i	0.592340	+	0.227378i	0.636026	−	0.771667i	$-0.280577\pi$
$17$	2.44228	+	0.937504i	0.592340	+	0.227378i	−0.0436864	+	0.999045i	$0.513910\pi$
$18$	0.0778754	−	1.48595i	0.0183554	−	0.350242i
$19$	−2.34659	+	2.60616i	−0.538346	+	0.597893i	−0.949537	−	0.313656i	$-0.898446\pi$
$19$	−2.34659	+	2.60616i	−0.538346	+	0.597893i	0.411191	+	0.911549i	$0.365113\pi$
$20$	1.24313	+	1.85866i	0.277973	+	0.415609i
$21$	−3.22858	+	0.400415i	−0.704534	+	0.0873777i
$22$	0.0258983	+	3.31652i	0.00552153	+	0.707085i
$23$	−1.76370	+	6.58223i	−0.367757	+	1.37249i	0.495887	+	0.868387i	$0.334843\pi$
$23$	−1.76370	+	6.58223i	−0.367757	+	1.37249i	−0.863644	+	0.504102i	$0.831824\pi$
$24$	0.128532	+	1.22290i	0.0262365	+	0.249624i
$25$	−4.79538	−	1.41574i	−0.959076	−	0.283147i
$26$	−0.666275	−	3.13458i	−0.130667	−	0.614741i
$27$	0.863300	+	5.45066i	0.166142	+	1.04898i
$28$	−2.54237	+	0.732367i	−0.480463	+	0.138404i
$29$	−4.23771	−	1.37692i	−0.786923	−	0.255687i	−0.112130	−	0.993694i	$-0.535767\pi$
$29$	−4.23771	−	1.37692i	−0.786923	−	0.255687i	−0.674793	+	0.738007i	$0.735767\pi$
$30$	−1.97038	−	1.91772i	−0.359740	−	0.350126i
$31$	3.98581	−	0.418926i	0.715873	−	0.0752413i	0.260413	−	0.965497i	$-0.416141\pi$
$31$	3.98581	−	0.418926i	0.715873	−	0.0752413i	0.455460	+	0.890256i	$0.349475\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−0.879039	−	3.98239i	−0.153021	−	0.693244i
$34$	−2.61604			−0.448647
$35$	3.32142	−	4.89573i	0.561422	−	0.827529i
$36$	0.459814	+	1.41516i	0.0766357	+	0.235860i
$37$	−6.21460	+	9.56964i	−1.02167	+	1.57324i	−0.219980	+	0.975504i	$0.570599\pi$
$37$	−6.21460	+	9.56964i	−1.02167	+	1.57324i	−0.801694	+	0.597735i	$0.796067\pi$
$38$	1.25677	−	3.27400i	0.203875	−	0.531113i
$39$	1.60275	+	3.59983i	0.256645	+	0.576434i
$40$	−1.82665	−	1.28971i	−0.288819	−	0.203921i
$41$	−6.29067	+	2.04396i	−0.982437	+	0.319213i	−0.755826	−	0.654772i	$-0.772765\pi$
$41$	−6.29067	+	2.04396i	−0.982437	+	0.319213i	−0.226611	+	0.973985i	$0.572765\pi$
$42$	2.87064	−	1.53084i	0.442950	−	0.236214i
$43$	−2.45310	−	2.45310i	−0.374095	−	0.374095i	0.494872	−	0.868966i	$-0.335215\pi$
$43$	−2.45310	−	2.45310i	−0.374095	−	0.374095i	−0.868966	+	0.494872i	$0.835215\pi$
$44$	−1.21271	−	3.08696i	−0.182823	−	0.465377i
$45$	−2.81475	−	1.77419i	−0.419598	−	0.264481i
$46$	−0.712301	−	6.77709i	−0.105023	−	0.999228i
$47$	9.68318	−	0.507474i	1.41244	−	0.0740227i	0.669216	−	0.743068i	$-0.266630\pi$
$47$	9.68318	−	0.507474i	1.41244	−	0.0740227i	0.743222	+	0.669045i	$0.233297\pi$
$48$	−0.558244	−	1.09562i	−0.0805756	−	0.158139i
$49$	4.32306	+	5.50555i	0.617581	+	0.786508i
$50$	4.98423	−	0.396808i	0.704876	−	0.0561171i
$51$	3.14648	−	0.668806i	0.440596	−	0.0936516i
$52$	1.74535	+	2.68761i	0.242037	+	0.372704i
$53$	0.356291	−	0.439983i	0.0489404	−	0.0604363i	−0.752088	−	0.659063i	$-0.770953\pi$
$53$	0.356291	−	0.439983i	0.0489404	−	0.0604363i	0.801028	+	0.598626i	$0.204287\pi$
$54$	−2.75930	−	4.77925i	−0.375493	−	0.650374i
$55$	6.50032	+	3.57013i	0.876503	+	0.481397i
$56$	2.11105	−	1.59483i	0.282101	−	0.213118i
$57$	−0.674585	+	4.25916i	−0.0893510	+	0.564140i
$58$	4.44969	−	0.233198i	0.584272	−	0.0306204i
$59$	−6.77339	−	7.52261i	−0.881820	−	0.979360i	0.118087	−	0.993003i	$-0.462324\pi$
$59$	−6.77339	−	7.52261i	−0.881820	−	0.979360i	−0.999907	+	0.0136432i	$0.995657\pi$
$60$	2.52676	+	1.08423i	0.326203	+	0.139973i
$61$	6.73117	+	0.707475i	0.861838	+	0.0905829i	0.525126	−	0.851025i	$-0.324018\pi$
$61$	6.73117	+	0.707475i	0.861838	+	0.0905829i	0.336713	+	0.941607i	$0.390685\pi$
$62$	−3.57095	+	1.81949i	−0.453511	+	0.231075i
$63$	3.01272	−	2.53423i	0.379567	−	0.319283i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−6.84436	−	2.12183i	−0.848938	−	0.263181i
$66$	2.24781	+	3.40286i	0.276687	+	0.418863i
$67$	3.21747	+	12.0078i	0.393076	+	1.46698i	0.825032	+	0.565086i	$0.191157\pi$
$67$	3.21747	+	12.0078i	0.393076	+	1.46698i	−0.431955	+	0.901895i	$0.642176\pi$
$68$	2.44228	−	0.937504i	0.296170	−	0.113689i
$69$	2.58934	+	7.96917i	0.311720	+	0.959375i
$70$	−1.34634	+	5.76085i	−0.160918	+	0.688553i
$71$	2.64170	+	1.91931i	0.313512	+	0.227780i	0.733402	−	0.679795i	$-0.237931\pi$
$71$	2.64170	+	1.91931i	0.313512	+	0.227780i	−0.419890	+	0.907575i	$0.637931\pi$
$72$	−0.936422	−	1.15639i	−0.110358	−	0.136281i
$73$	−11.3434	−	0.594481i	−1.32764	−	0.0695787i	−0.624721	−	0.780848i	$-0.714787\pi$
$73$	−11.3434	−	0.594481i	−1.32764	−	0.0695787i	−0.702920	+	0.711269i	$0.748121\pi$
$74$	2.37237	−	11.1611i	0.275783	−	1.29746i
$75$	−5.89342	+	1.75152i	−0.680514	+	0.202248i
$76$			3.50693i			0.402272i
$77$	−6.36332	+	6.04220i	−0.725167	+	0.688573i
$78$	−2.78636	−	2.78636i	−0.315493	−	0.315493i
$79$	−0.395208	+	0.887651i	−0.0444644	+	0.0998686i	−0.934412	−	0.356194i	$-0.884074\pi$
$79$	−0.395208	+	0.887651i	−0.0444644	+	0.0998686i	0.889948	+	0.456063i	$0.150741\pi$
$80$	2.16752	+	0.549434i	0.242336	+	0.0614286i
$81$	1.55367	+	1.72552i	0.172630	+	0.191724i
$82$	5.14035	−	4.16258i	0.567657	−	0.459680i
$83$	1.04404	−	0.165360i	0.114599	−	0.0181506i	−0.0988717	−	0.995100i	$-0.531523\pi$
$83$	1.04404	−	0.165360i	0.114599	−	0.0181506i	0.213470	+	0.976950i	$0.431523\pi$
$84$	−2.13137	+	2.45791i	−0.232552	+	0.268180i
$85$	−2.85595	+	5.10508i	−0.309771	+	0.553723i
$86$	3.16928	+	1.41105i	0.341752	+	0.152158i
$87$	−5.29232	+	1.41807i	−0.567396	+	0.152033i
$88$	2.23843	+	2.44733i	0.238618	+	0.260886i
$89$	−1.35473	−	2.34645i	−0.143601	−	0.248724i	0.785249	−	0.619180i	$-0.212535\pi$
$89$	−1.35473	−	2.34645i	−0.143601	−	0.248724i	−0.928850	+	0.370456i	$0.879201\pi$
$90$	3.26361	+	0.647636i	0.344014	+	0.0682669i
$91$	4.85465	−	6.95117i	0.508905	−	0.728681i
$92$	3.09368	+	6.07170i	0.322539	+	0.633018i
$93$	3.82985	−	3.10136i	0.397137	−	0.321596i
$94$	−8.85817	+	3.94391i	−0.913650	+	0.406783i
$95$	−5.01704	−	6.02678i	−0.514737	−	0.618335i
$96$	0.913799	+	0.822789i	0.0932642	+	0.0839755i
$97$	0.117005	+	0.0185318i	0.0118801	+	0.00188162i	0.162372	−	0.986730i	$-0.448086\pi$
$97$	0.117005	+	0.0185318i	0.0118801	+	0.00188162i	−0.150492	+	0.988611i	$0.548086\pi$
$98$	−6.00894	−	3.59063i	−0.606995	−	0.362708i
$99$	3.51679	+	3.46229i	0.353451	+	0.347973i
$100$	−4.51098	+	2.15664i	−0.451098	+	0.215664i
$101$	9.06133	−	0.952385i	0.901637	−	0.0947658i	0.357646	−	0.933857i	$-0.383579\pi$
$101$	9.06133	−	0.952385i	0.901637	−	0.0947658i	0.543990	+	0.839091i	$0.316913\pi$
$102$	−2.69782	+	1.75198i	−0.267124	+	0.173472i
$103$	−4.00647	+	6.16942i	−0.394769	+	0.607891i	−0.979040	−	0.203667i	$-0.934714\pi$
$103$	−4.00647	+	6.16942i	−0.394769	+	0.607891i	0.584271	+	0.811559i	$0.301381\pi$
$104$	−2.59258	−	1.88362i	−0.254223	−	0.184704i
$105$	0.146538	−	7.27316i	0.0143007	−	0.709788i
$106$	−0.174951	+	0.538443i	−0.0169927	+	0.0522982i
$107$	−0.677317	−	12.9240i	−0.0654788	−	1.24941i	−0.811845	−	0.583873i	$-0.801536\pi$
$107$	−0.677317	−	12.9240i	−0.0654788	−	1.24941i	0.746366	−	0.665536i	$-0.231797\pi$
$108$	4.28876	+	3.47297i	0.412686	+	0.334187i
$109$	9.86589	+	5.69608i	0.944981	+	0.545585i	0.891518	−	0.452985i	$-0.149641\pi$
$109$	9.86589	+	5.69608i	0.944981	+	0.545585i	0.0534628	+	0.998570i	$0.482974\pi$
$110$	−7.34799	−	1.00350i	−0.700604	−	0.0956800i
$111$			14.0308i			1.33174i
$112$	−1.39930	+	2.24543i	−0.132221	+	0.212173i
$113$	−0.479626	+	0.941318i	−0.0451194	+	0.0885518i	−0.912465	−	0.409154i	$-0.865824\pi$
$113$	−0.479626	+	0.941318i	−0.0451194	+	0.0885518i	0.867346	+	0.497706i	$0.165824\pi$
$114$	−0.896568	−	4.21802i	−0.0839713	−	0.395054i
$115$	−14.0028	−	6.00858i	−1.30577	−	0.560303i
$116$	−4.07057	+	1.81233i	−0.377943	+	0.168271i
$117$	−3.99913	−	2.59707i	−0.369720	−	0.240099i
$118$	9.01936	+	4.59559i	0.830300	+	0.423059i
$119$	−4.72654	−	5.05622i	−0.433281	−	0.463503i
$120$	−2.74748	−	0.106703i	−0.250810	−	0.00974063i
$121$	−8.28854	−	7.23188i	−0.753504	−	0.657443i
$122$	−6.53763	+	1.75175i	−0.591889	+	0.158596i
$123$	−5.11846	+	6.32078i	−0.461516	+	0.569925i
$124$	2.68172	−	2.97835i	0.240825	−	0.267464i
$125$	4.66697	−	10.1597i	0.417426	−	0.908711i
$126$	−1.90443	+	3.44557i	−0.169660	+	0.306956i
$127$	−2.67538	+	0.423738i	−0.237401	+	0.0376007i	−0.274001	−	0.961729i	$-0.588347\pi$
$127$	−2.67538	+	0.423738i	−0.237401	+	0.0376007i	0.0366000	+	0.999330i	$0.488347\pi$
$128$	0.838671	+	0.544639i	0.0741287	+	0.0481397i
$129$	−4.17265	−	0.886925i	−0.367382	−	0.0780894i
$130$	7.15016	−	0.471897i	0.627110	−	0.0413881i
$131$	−0.926643	+	0.534997i	−0.0809611	+	0.0467429i	−0.539934	−	0.841707i	$-0.681551\pi$
$131$	−0.926643	+	0.534997i	−0.0809611	+	0.0467429i	0.458973	+	0.888450i	$0.348217\pi$
$132$	−3.31799	−	2.37130i	−0.288794	−	0.206395i
$133$	8.59860	−	3.48626i	0.745593	−	0.302297i
$134$	−7.30696	−	10.0572i	−0.631225	−	0.868807i
$135$	−12.3388	+	0.167111i	−1.06196	+	0.0143826i
$136$	−1.94409	+	1.75047i	−0.166705	+	0.150102i
$137$	3.63845	−	9.47849i	0.310854	−	0.809802i	−0.685779	−	0.727810i	$-0.740538\pi$
$137$	3.63845	−	9.47849i	0.310854	−	0.809802i	0.996633	−	0.0819922i	$-0.0261283\pi$
$138$	−5.27325	−	6.51192i	−0.448889	−	0.554331i
$139$	0.720651	−	2.21794i	0.0611249	−	0.188123i	−0.915831	−	0.401563i	$-0.868467\pi$
$139$	0.720651	−	2.21794i	0.0611249	−	0.188123i	0.976956	+	0.213440i	$0.0684669\pi$
$140$	−0.807586	−	5.86070i	−0.0682535	−	0.495320i
$141$	9.64603	−	7.00825i	0.812343	−	0.590201i
$142$	−3.15406	−	0.845128i	−0.264683	−	0.0709216i
$143$	9.24574	+	5.24220i	0.773168	+	0.438375i
$144$	1.28864	+	0.743995i	0.107386	+	0.0619996i
$145$	4.40268	−	8.93794i	0.365622	−	0.742256i
$146$	10.8030	−	3.51010i	0.894062	−	0.290498i
$147$	8.14533	+	2.78247i	0.671815	+	0.229494i
$148$	1.78499	+	11.2700i	0.146726	+	0.926389i
$149$	−6.99803	−	0.735523i	−0.573301	−	0.0602564i	−0.186558	−	0.982444i	$-0.559733\pi$
$149$	−6.99803	−	0.735523i	−0.573301	−	0.0602564i	−0.386743	+	0.922188i	$0.626400\pi$
$150$	4.87430	−	3.74720i	0.397985	−	0.305957i
$151$	6.06550	+	1.28926i	0.493604	+	0.104919i	0.447987	−	0.894040i	$-0.352141\pi$
$151$	6.06550	+	1.28926i	0.493604	+	0.104919i	0.0456171	+	0.998959i	$0.485475\pi$
$152$	−1.25677	−	3.27400i	−0.101938	−	0.265557i
$153$	−2.75251	+	2.75251i	−0.222527	+	0.222527i
$154$	3.77534	−	7.92129i	0.304225	−	0.638316i
$155$	−0.347779	+	8.95489i	−0.0279343	+	0.719274i
$156$	3.59983	+	1.60275i	0.288217	+	0.128322i
$157$	10.3752	+	15.9765i	0.828035	+	1.27506i	0.958924	+	0.283665i	$0.0915503\pi$
$157$	10.3752	+	15.9765i	0.828035	+	1.27506i	−0.130889	+	0.991397i	$0.541783\pi$
$158$	0.0508525	−	0.970324i	0.00404561	−	0.0771948i
$159$	0.0727688	−	0.692349i	0.00577094	−	0.0549068i
$160$	−2.22045	+	0.263827i	−0.175542	+	0.0208573i
$161$	11.8117	−	13.6213i	0.930890	−	1.07351i
$162$	−2.06884	−	1.05413i	−0.162544	−	0.0828201i
$163$	5.47483	+	14.2624i	0.428822	+	1.11712i	0.962464	+	0.271409i	$0.0874895\pi$
$163$	5.47483	+	14.2624i	0.428822	+	1.11712i	−0.533642	+	0.845710i	$0.679177\pi$
$164$	−3.30720	+	5.72824i	−0.258249	+	0.447300i
$165$	9.09448	−	0.671582i	0.708004	−	0.0522826i
$166$	−0.915438	+	0.528529i	−0.0710518	+	0.0410218i
$167$	−2.05922	−	0.326149i	−0.159348	−	0.0252382i	0.0762509	−	0.997089i	$-0.475705\pi$
$167$	−2.05922	−	0.326149i	−0.159348	−	0.0252382i	−0.235598	+	0.971850i	$0.575705\pi$
$168$	1.10897	−	3.05847i	0.0855591	−	0.235966i
$169$	2.59687	+	0.843775i	0.199759	+	0.0649058i
$170$	0.836759	−	5.78948i	0.0641765	−	0.444033i
$171$	−2.12246	−	4.76713i	−0.162309	−	0.364552i
$172$	−3.46446	−	0.181564i	−0.264162	−	0.0138442i
$173$	−0.870207	−	16.6045i	−0.0661606	−	1.26242i	−0.806925	−	0.590654i	$-0.798870\pi$
$173$	−0.870207	−	16.6045i	−0.0661606	−	1.26242i	0.740764	−	0.671765i	$-0.234464\pi$
$174$	4.43261	−	3.22048i	0.336036	−	0.244144i
$175$	9.77222	+	8.91648i	0.738711	+	0.674023i
$176$	−2.96680	−	1.48259i	−0.223631	−	0.111755i
$177$	−12.0231	−	3.22158i	−0.903711	−	0.242149i
$178$	2.10564	+	1.70511i	0.157824	+	0.127804i
$179$	2.63619	−	12.4023i	0.197038	−	0.926993i	−0.762842	−	0.646584i	$-0.776197\pi$
$179$	2.63619	−	12.4023i	0.197038	−	0.926993i	0.959881	−	0.280408i	$-0.0904698\pi$
$180$	−3.27893	+	0.564952i	−0.244397	+	0.0421090i
$181$	12.4308	−	17.1095i	0.923973	−	1.27174i	−0.0381908	−	0.999270i	$-0.512159\pi$
$181$	12.4308	−	17.1095i	0.923973	−	1.27174i	0.962164	−	0.272470i	$-0.0878405\pi$
$182$	−2.04113	+	8.22923i	−0.151298	+	0.609991i
$183$	7.41540	−	3.77834i	0.548162	−	0.279303i
$184$	−5.06410	−	4.55974i	−0.373331	−	0.336148i
$185$	−19.1905	−	16.8143i	−1.41092	−	1.23621i
$186$	−2.46405	+	4.26786i	−0.180673	+	0.312935i
$187$	5.75513	−	6.49297i	0.420857	−	0.474813i
$188$	6.85644	−	6.85644i	0.500057	−	0.500057i
$189$	4.25185	−	13.9681i	0.309277	−	1.01603i
$190$	6.84362	+	3.82854i	0.496488	+	0.277752i
$191$	12.8447	−	2.73022i	0.929409	−	0.197552i	0.281755	−	0.959486i	$-0.409084\pi$
$191$	12.8447	−	2.73022i	0.929409	−	0.197552i	0.647654	+	0.761934i	$0.275750\pi$
$192$	−1.14797	−	0.440663i	−0.0828473	−	0.0318021i
$193$	16.6108	+	6.37629i	1.19567	+	0.458975i	0.873086	−	0.487565i	$-0.162115\pi$
$193$	16.6108	+	6.37629i	1.19567	+	0.458975i	0.322585	+	0.946541i	$0.395448\pi$
$194$	−0.115875	+	0.0246300i	−0.00831934	+	0.00176833i
$195$	−8.47933	+	2.39556i	−0.607218	+	0.171550i
$196$	6.89660	+	1.19873i	0.492614	+	0.0856235i
$197$	−11.3580	+	11.3580i	−0.809225	+	0.809225i	−0.984517	−	0.175292i	$-0.943913\pi$
$197$	−11.3580	+	11.3580i	−0.809225	+	0.809225i	0.175292	+	0.984517i	$0.443913\pi$
$198$	−4.52398	−	1.97202i	−0.321505	−	0.140145i
$199$	2.46799	−	4.27468i	0.174951	−	0.303024i	−0.765193	−	0.643801i	$-0.777357\pi$
$199$	2.46799	−	4.27468i	0.174951	−	0.303024i	0.940144	+	0.340776i	$0.110690\pi$
$200$	3.43849	−	3.62999i	0.243138	−	0.256679i
$201$	11.3598	+	10.2284i	0.801255	+	0.721454i
$202$	−8.11818	+	4.13642i	−0.571193	+	0.291037i
$203$	8.49021	+	8.17893i	0.595896	+	0.574048i
$204$	1.89078	−	2.60243i	0.132381	−	0.182206i
$205$	−2.51132	−	14.5755i	−0.175398	−	1.01800i
$206$	1.52944	−	7.19544i	0.106561	−	0.501330i
$207$	−7.88010	−	6.38118i	−0.547705	−	0.443523i
$208$	3.09541	+	0.829413i	0.214628	+	0.0575094i
$209$	5.36120	+	10.3219i	0.370842	+	0.713981i
$210$	2.46966	+	6.84260i	0.170423	+	0.472184i
$211$	21.1297	−	15.3516i	1.45463	−	1.05685i	0.469904	−	0.882717i	$-0.344288\pi$
$211$	21.1297	−	15.3516i	1.45463	−	1.05685i	0.984722	−	0.174131i	$-0.0557116\pi$
$212$	−0.0296301	−	0.565376i	−0.00203501	−	0.0388302i
$213$	4.00967	+	0.210138i	0.274738	+	0.0143984i
$214$	5.26387	+	11.8229i	0.359831	+	0.808194i
$215$	6.21354	−	4.64425i	0.423760	−	0.316735i
$216$	−5.24850	−	1.70534i	−0.357115	−	0.116034i
$217$	−9.96849	−	3.61448i	−0.676705	−	0.245367i
$218$	−11.2519	−	1.78213i	−0.762074	−	0.120701i
$219$	−12.0961	+	6.98369i	−0.817379	+	0.471914i
$220$	7.21956	−	1.69644i	0.486743	−	0.114374i
$221$	−4.19168	+	7.26020i	−0.281963	+	0.488374i
$222$	−5.02818	−	13.0989i	−0.337469	−	0.879138i
$223$	−5.29655	−	2.69873i	−0.354683	−	0.180720i	0.267566	−	0.963540i	$-0.413781\pi$
$223$	−5.29655	−	2.69873i	−0.354683	−	0.180720i	−0.622249	+	0.782820i	$0.713781\pi$
$224$	0.501667	−	2.59775i	0.0335191	−	0.173570i
$225$	4.82674	−	5.66175i	0.321782	−	0.377450i
$226$	0.110431	−	1.05068i	0.00734575	−	0.0698901i
$227$	0.932967	−	17.8021i	0.0619232	−	1.18156i	−0.774170	−	0.632977i	$-0.781833\pi$
$227$	0.932967	−	17.8021i	0.0619232	−	1.18156i	0.836093	−	0.548587i	$-0.184834\pi$
$228$	2.34862	+	3.61656i	0.155541	+	0.239513i
$229$	−16.1545	−	7.19246i	−1.06752	−	0.475291i	−0.203671	−	0.979039i	$-0.565287\pi$
$229$	−16.1545	−	7.19246i	−1.06752	−	0.475291i	−0.863850	+	0.503748i	$0.831954\pi$
$230$	15.2260	+	0.591330i	1.00398	+	0.0389911i
$231$	−2.51573	+	10.4927i	−0.165523	+	0.690366i
$232$	3.15072	−	3.15072i	0.206855	−	0.206855i
$233$	4.83826	+	12.6041i	0.316965	+	0.825721i	0.995811	+	0.0914404i	$0.0291471\pi$
$233$	4.83826	+	12.6041i	0.316965	+	0.825721i	−0.678846	+	0.734281i	$0.737520\pi$
$234$	4.66422	+	0.991410i	0.304909	+	0.0648105i
$235$	−1.97416	+	21.5919i	−0.128780	+	1.40850i
$236$	−10.0672	−	1.05811i	−0.655320	−	0.0688769i
$237$	0.186905	+	1.18007i	0.0121408	+	0.0766541i
$238$	6.22459	+	3.02655i	0.403480	+	0.196182i
$239$	13.1739	−	4.28047i	0.852151	−	0.276881i	0.149804	−	0.988716i	$-0.452136\pi$
$239$	13.1739	−	4.28047i	0.852151	−	0.276881i	0.702347	+	0.711835i	$0.252136\pi$
$240$	2.60324	−	0.884994i	0.168038	−	0.0571261i
$241$	−23.2222	−	13.4073i	−1.49587	−	0.863642i	−0.495883	−	0.868389i	$-0.665156\pi$
$241$	−23.2222	−	13.4073i	−1.49587	−	0.863642i	−0.999989	+	0.00474735i	$0.998489\pi$
$242$	10.3297	+	3.78119i	0.664018	+	0.243064i
$243$	−13.2339	−	3.54600i	−0.848952	−	0.227476i
$244$	5.47563	−	3.97828i	0.350541	−	0.254683i
$245$	−13.5670	+	7.80626i	−0.866761	+	0.498724i
$246$	2.51333	−	7.73525i	0.160244	−	0.493181i
$247$	−7.07251	−	8.73382i	−0.450013	−	0.555719i
$248$	−1.43625	+	3.74157i	−0.0912023	+	0.237590i
$249$	0.965938	−	0.869734i	0.0612138	−	0.0551172i
$250$	−0.716078	+	11.1574i	−0.0452887	+	0.705655i
$251$	7.80339	+	10.7405i	0.492546	+	0.677931i	0.980855	−	0.194739i	$-0.0623861\pi$
$251$	7.80339	+	10.7405i	0.492546	+	0.677931i	−0.488309	+	0.872671i	$0.662386\pi$
$252$	0.543152	−	3.89920i	0.0342153	−	0.245627i
$253$	18.3877	+	13.1413i	1.15602	+	0.826186i
$254$	2.34583	−	1.35436i	0.147190	−	0.0849803i
$255$	0.473690	+	7.17732i	0.0296636	+	0.449461i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	20.6274	+	13.3956i	1.28670	+	0.835594i	0.992747	−	0.120226i	$-0.0383618\pi$
$257$	20.6274	+	13.3956i	1.28670	+	0.835594i	0.293955	+	0.955819i	$0.405028\pi$
$258$	4.21335	−	0.667330i	0.262312	−	0.0415461i
$259$	25.8583	−	15.5802i	1.60676	−	0.968105i
$260$	−6.50613	+	3.00294i	−0.403493	+	0.186234i
$261$	4.43645	−	4.92718i	0.274609	−	0.304985i
$262$	0.673370	−	0.831542i	0.0416009	−	0.0513728i
$263$	−10.9252	+	2.92741i	−0.673679	+	0.180512i	−0.579411	−	0.815035i	$-0.696718\pi$
$263$	−10.9252	+	2.92741i	−0.673679	+	0.180512i	−0.0942675	+	0.995547i	$0.530051\pi$
$264$	3.94741	+	1.02474i	0.242946	+	0.0630681i
$265$	0.859752	+	0.929230i	0.0528141	+	0.0570822i
$266$	−6.77812	+	6.33616i	−0.415593	+	0.388495i
$267$	−2.96852	−	1.51254i	−0.181670	−	0.0925657i
$268$	10.4258	+	6.77060i	0.636857	+	0.413580i
$269$	−5.23389	+	2.33028i	−0.319116	+	0.142080i	−0.560043	−	0.828464i	$-0.689215\pi$
$269$	−5.23389	+	2.33028i	−0.319116	+	0.142080i	0.240927	+	0.970543i	$0.422549\pi$
$270$	11.4594	−	4.57786i	0.697398	−	0.278599i
$271$	0.890556	+	4.18974i	0.0540974	+	0.254508i	0.996883	−	0.0788905i	$-0.0251377\pi$
$271$	0.890556	+	4.18974i	0.0540974	+	0.254508i	−0.942786	+	0.333399i	$0.891804\pi$
$272$	1.18766	−	2.33091i	0.0720122	−	0.141332i
$273$	0.351148	−	10.4197i	0.0212525	−	0.630628i
$274$			10.1528i			0.613355i
$275$	−9.98014	+	13.2437i	−0.601825	+	0.798628i
$276$	7.25667	+	4.18964i	0.436800	+	0.252187i
$277$	14.4602	+	11.7096i	0.868828	+	0.703563i	0.956232	−	0.292610i	$-0.0945237\pi$
$277$	14.4602	+	11.7096i	0.868828	+	0.703563i	−0.0874037	+	0.996173i	$0.527857\pi$
$278$	0.122051	+	2.32888i	0.00732016	+	0.139677i
$279$	−1.84283	+	5.67164i	−0.110327	+	0.339552i
$280$	2.85423	+	5.18202i	0.170573	+	0.309685i
$281$	−15.1439	−	11.0027i	−0.903408	−	0.656364i	0.0359309	−	0.999354i	$-0.488560\pi$
$281$	−15.1439	−	11.0027i	−0.903408	−	0.656364i	−0.939339	+	0.342990i	$0.888560\pi$
$282$	−6.49381	+	9.99960i	−0.386701	+	0.595467i
$283$	5.07875	−	3.29818i	0.301900	−	0.196056i	−0.384794	−	0.923002i	$-0.625728\pi$
$283$	5.07875	−	3.29818i	0.301900	−	0.196056i	0.686695	+	0.726946i	$0.259061\pi$
$284$	3.24744	−	0.341319i	0.192700	−	0.0202536i
$285$	−9.21007	−	2.85523i	−0.545557	−	0.169129i
$286$	−10.5103	−	1.58064i	−0.621486	−	0.0934650i
$287$	17.3327	+	2.41441i	1.02312	+	0.142518i
$288$	−1.46967	−	0.232773i	−0.0866011	−	0.0137163i
$289$	−7.54764	−	6.79593i	−0.443979	−	0.399760i
$290$	−0.907181	+	9.92207i	−0.0532715	+	0.582644i
$291$	0.133074	−	0.0592483i	0.00780093	−	0.00347320i
$292$	−8.82755	+	7.14841i	−0.516593	+	0.418329i
$293$	−10.2884	−	20.1921i	−0.601053	−	1.17963i	−0.968366	−	0.249535i	$-0.919722\pi$
$293$	−10.2884	−	20.1921i	−0.601053	−	1.17963i	0.367313	−	0.930098i	$-0.380278\pi$
$294$	−8.60147	+	0.321365i	−0.501648	+	0.0187424i
$295$	18.8146	−	12.5838i	1.09543	−	0.732659i
$296$	−5.70525	−	9.88177i	−0.331611	−	0.574366i
$297$	17.9323	+	3.66552i	1.04054	+	0.212695i
$298$	6.79682	−	1.82120i	0.393729	−	0.105499i
$299$	−19.9496	−	8.88212i	−1.15371	−	0.513666i
$300$	−3.20767	+	5.24510i	−0.185195	+	0.302826i
$301$	2.99886	+	8.67495i	0.172851	+	0.500016i
$302$	−6.12466	+	0.970052i	−0.352435	+	0.0558202i
$303$	8.70678	−	7.05061i	0.500192	−	0.405047i
$304$	2.34659	+	2.60616i	0.134586	+	0.149473i
$305$	−3.71871	+	14.6703i	−0.212933	+	0.840018i
$306$	1.58328	−	3.55610i	0.0905100	−	0.203289i
$307$	−14.4707	−	14.4707i	−0.825889	−	0.825889i	0.161057	−	0.986945i	$-0.448510\pi$
$307$	−14.4707	−	14.4707i	−0.825889	−	0.825889i	−0.986945	+	0.161057i	$0.948510\pi$
$308$	−0.685844	+	8.74812i	−0.0390796	+	0.498470i
$309$			9.04546i			0.514578i
$310$	−2.88447	−	8.48474i	−0.163827	−	0.481901i
$311$	−7.11730	+	33.4843i	−0.403585	+	1.89872i	0.0337677	+	0.999430i	$0.489249\pi$
$311$	−7.11730	+	33.4843i	−0.403585	+	1.89872i	−0.437353	+	0.899290i	$0.644084\pi$
$312$	−3.93510	−	0.206230i	−0.222781	−	0.0116755i
$313$	−14.5100	−	17.9183i	−0.820153	−	1.01280i	−0.999578	−	0.0290333i	$-0.990757\pi$
$313$	−14.5100	−	17.9183i	−0.820153	−	1.01280i	0.179425	−	0.983772i	$-0.442576\pi$
$314$	−15.4116	−	11.1972i	−0.869726	−	0.631893i
$315$	4.64480	+	7.47795i	0.261705	+	0.421335i
$316$	0.300258	+	0.924099i	0.0168908	+	0.0519846i
$317$	−17.3996	+	6.67907i	−0.977257	+	0.375134i	−0.793991	−	0.607929i	$-0.792000\pi$
$317$	−17.3996	+	6.67907i	−0.977257	+	0.375134i	−0.183266	+	0.983063i	$0.558667\pi$
$318$	0.180180	+	0.672441i	0.0101040	+	0.0377086i
$319$	−9.21025	+	11.5571i	−0.515675	+	0.647072i
$320$	1.97842	−	1.04204i	0.110597	−	0.0582519i
$321$	−9.35380	−	12.8744i	−0.522078	−	0.718579i
$322$	−6.14572	+	16.9495i	−0.342488	+	0.944557i
$323$	−8.17432	+	4.16503i	−0.454832	+	0.231748i
$324$	2.30920	+	0.242706i	0.128289	+	0.0134837i
$325$	6.88499	−	14.4684i	0.381911	−	0.802561i
$326$	−10.2224	−	11.3531i	−0.566166	−	0.628791i
$327$	13.9890	−	0.733134i	0.773595	−	0.0405424i
$328$	1.03472	−	6.53297i	0.0571329	−	0.360723i
$329$	−23.6273	−	9.99520i	−1.30261	−	0.551053i
$330$	−8.24975	+	3.88615i	−0.454134	+	0.213925i
$331$	−6.81925	−	11.8113i	−0.374820	−	0.649207i	0.615480	−	0.788152i	$-0.288962\pi$
$331$	−6.81925	−	11.8113i	−0.374820	−	0.649207i	−0.990300	+	0.138945i	$0.955629\pi$
$332$	0.665228	−	0.821488i	0.0365091	−	0.0450850i
$333$	−9.24726	−	14.2395i	−0.506747	−	0.780321i
$334$	2.03933	−	0.433474i	0.111587	−	0.0237186i
$335$	−27.6032	+	3.27972i	−1.50812	+	0.179190i
$336$	0.0607428	+	3.25275i	0.00331379	+	0.177452i
$337$	4.73420	+	9.29138i	0.257888	+	0.506134i	0.983256	−	0.182227i	$-0.0583306\pi$
$337$	4.73420	+	9.29138i	0.257888	+	0.506134i	−0.725368	+	0.688361i	$0.758331\pi$
$338$	−2.72677	+	0.142904i	−0.148317	+	0.00777296i
$339$	0.135790	+	1.29195i	0.00737510	+	0.0701693i
$340$	1.29358	+	5.70481i	0.0701543	+	0.309387i
$341$	3.33993	−	12.8658i	0.180867	−	0.696722i
$342$	3.68988	+	3.68988i	0.199526	+	0.199526i
$343$	−3.91679	−	18.1013i	−0.211487	−	0.977381i
$344$	3.29942	−	1.07204i	0.177893	−	0.0578008i
$345$	−18.4646	+	3.18140i	−0.994099	+	0.171281i
$346$	6.76294	+	15.1898i	0.363578	+	0.816609i
$347$	−6.82592	+	17.7821i	−0.366435	+	0.954595i	0.619129	+	0.785289i	$0.287486\pi$
$347$	−6.82592	+	17.7821i	−0.366435	+	0.954595i	−0.985564	+	0.169305i	$0.945848\pi$
$348$	−2.98408	+	4.59509i	−0.159964	+	0.246322i
$349$	7.65748	+	23.5673i	0.409895	+	1.26153i	0.916738	+	0.399490i	$0.130813\pi$
$349$	7.65748	+	23.5673i	0.409895	+	1.26153i	−0.506842	+	0.862039i	$0.669187\pi$
$350$	−12.3185	−	4.82220i	−0.658454	−	0.257757i
$351$	−17.6849			−0.943952
$352$	3.30106	+	0.320915i	0.175947	+	0.0171048i
$353$	−0.432525	−	1.61420i	−0.0230210	−	0.0859154i	0.953460	−	0.301521i	$-0.0974942\pi$
$353$	−0.432525	−	1.61420i	−0.0230210	−	0.0859154i	−0.976481	+	0.215605i	$0.930828\pi$
$354$	12.3790	−	1.30109i	0.657938	−	0.0691521i
$355$	−5.09254	+	5.23238i	−0.270284	+	0.277706i
$356$	−2.57684	−	0.837267i	−0.136572	−	0.0443750i
$357$	−8.26049	−	2.04888i	−0.437192	−	0.108438i
$358$	1.98349	+	12.5233i	0.104831	+	0.661876i
$359$	2.90533	+	13.6685i	0.153338	+	0.721397i	0.985882	+	0.167439i	$0.0535497\pi$
$359$	2.90533	+	13.6685i	0.153338	+	0.721397i	−0.832545	+	0.553958i	$0.813117\pi$
$360$	2.85869	−	1.70249i	0.150666	−	0.0897292i
$361$	0.700491	+	6.66473i	0.0368680	+	0.350775i
$362$	−5.47364	+	20.4279i	−0.287688	+	1.07367i
$363$	−13.3909	−	1.90705i	−0.702840	−	0.100094i
$364$	−1.04354	−	8.41412i	−0.0546961	−	0.441020i
$365$	4.94389	−	24.9136i	0.258775	−	1.30403i
$366$	−5.56884	+	6.18482i	−0.291088	+	0.323286i
$367$	−0.474622	+	9.05633i	−0.0247751	+	0.472736i	0.957866	+	0.287217i	$0.0927301\pi$
$367$	−0.474622	+	9.05633i	−0.0247751	+	0.472736i	−0.982641	+	0.185519i	$0.940603\pi$
$368$	6.36181	+	2.44207i	0.331632	+	0.127302i
$369$	1.02879	−	9.78824i	0.0535565	−	0.509556i
$370$	23.9416	+	8.82021i	1.24466	+	0.458541i
$371$	−1.35678	+	0.634693i	−0.0704407	+	0.0329516i
$372$	0.770925	−	4.86743i	0.0399706	−	0.252364i
$373$	−9.10913	+	33.9957i	−0.471653	+	1.76023i	0.162178	+	0.986762i	$0.448148\pi$
$373$	−9.10913	+	33.9957i	−0.471653	+	1.76023i	−0.633831	+	0.773472i	$0.718519\pi$
$374$	−3.04600	+	8.12416i	−0.157505	+	0.420090i
$375$	−1.99118	−	13.6028i	−0.102824	−	0.702446i
$376$	−3.94391	+	8.85817i	−0.203392	+	0.456825i
$377$	6.48255	−	12.7227i	0.333868	−	0.655254i
$378$	1.03626	+	14.5640i	0.0532993	+	0.749093i
$379$	−18.0119	+	24.7913i	−0.925210	+	1.27344i	0.0364890	+	0.999334i	$0.488383\pi$
$379$	−18.0119	+	24.7913i	−0.925210	+	1.27344i	−0.961699	+	0.274108i	$0.911617\pi$
$380$	−7.76109	−	1.12172i	−0.398136	−	0.0575429i
$381$	−2.47523	+	2.22871i	−0.126810	+	0.114180i
$382$	−11.0131	+	7.15201i	−0.563480	+	0.365929i
$383$	25.9761	−	9.97129i	1.32732	−	0.509509i	0.411611	−	0.911359i	$-0.364966\pi$
$383$	25.9761	−	9.97129i	1.32732	−	0.509509i	0.915705	+	0.401850i	$0.131633\pi$
$384$	1.22964			0.0627497
$385$	−11.3365	−	16.0151i	−0.577760	−	0.816206i
$386$	−17.7926			−0.905618
$387$	4.81928	−	1.84995i	0.244978	−	0.0940382i
$388$	0.0993521	−	0.0645200i	0.00504384	−	0.00327551i
$389$	5.94446	−	5.35241i	0.301396	−	0.271378i	−0.504530	−	0.863394i	$-0.668334\pi$
$389$	5.94446	−	5.35241i	0.301396	−	0.271378i	0.805926	+	0.592016i	$0.201668\pi$
$390$	7.05765	−	5.27517i	0.357378	−	0.267119i
$391$	−10.4783	+	14.4222i	−0.529911	+	0.729361i
$392$	−6.86811	+	1.35241i	−0.346892	+	0.0683070i
$393$	−0.597318	+	1.17230i	−0.0301307	+	0.0591349i
$394$	6.53327	−	14.6740i	0.329141	−	0.739264i
$395$	−1.83803	−	1.15855i	−0.0924812	−	0.0582928i
$396$	4.93021	+	0.219792i	0.247752	+	0.0110450i
$397$	7.27673	−	27.1571i	0.365209	−	1.36298i	−0.501929	−	0.864909i	$-0.667376\pi$
$397$	7.27673	−	27.1571i	0.365209	−	1.36298i	0.867137	−	0.498069i	$-0.165957\pi$
$398$	−0.772157	+	4.87521i	−0.0387048	+	0.244372i
$399$	6.53263	−	9.35380i	0.327040	−	0.468276i
$400$	−1.90923	+	4.62113i	−0.0954617	+	0.231056i
$401$	0.774111	−	7.36518i	0.0386573	−	0.367799i	−0.958043	−	0.286626i	$-0.907466\pi$
$401$	0.774111	−	7.36518i	0.0386573	−	0.367799i	0.996700	−	0.0811738i	$-0.0258669\pi$
$402$	−14.2708	−	5.47803i	−0.711761	−	0.273219i
$403$	−0.672167	+	12.8257i	−0.0334830	+	0.638894i
$404$	6.09661	−	6.77098i	0.303318	−	0.336869i
$405$	−4.31565	+	2.88645i	−0.214447	+	0.143429i
$406$	−10.8574	−	4.59307i	−0.538842	−	0.227950i
$407$	22.4827	+	30.4421i	1.11443	+	1.50896i
$408$	−0.832564	+	3.10717i	−0.0412180	+	0.153828i
$409$	1.36808	+	13.0164i	0.0676473	+	0.643621i	0.974840	+	0.222906i	$0.0715542\pi$
$409$	1.36808	+	13.0164i	0.0676473	+	0.643621i	−0.907193	+	0.420715i	$0.861779\pi$
$410$	7.56790	+	12.7074i	0.373752	+	0.627574i
$411$	−2.59563	−	12.2115i	−0.128033	−	0.602349i
$412$	1.15076	+	7.26563i	0.0566940	+	0.357952i
$413$	7.41351	+	25.7356i	0.364795	+	1.26636i
$414$	9.64352	+	3.13337i	0.473953	+	0.153997i
$415$	0.0320091	+	2.36343i	0.00157127	+	0.116016i
$416$	−3.18705	+	0.334972i	−0.156258	+	0.0164234i
$417$	−0.742192	−	2.76990i	−0.0363453	−	0.135643i
$418$	−8.70415	−	7.71504i	−0.425734	−	0.377355i
$419$	21.8410			1.06700			0.533502	−	0.845799i	$-0.320876\pi$
$419$	21.8410			1.06700			0.533502	+	0.845799i	$0.320876\pi$
$420$	−4.75780	−	5.50307i	−0.232157	−	0.268522i
$421$	11.0483	+	34.0033i	0.538463	+	1.65722i	0.736045	+	0.676932i	$0.236691\pi$
$421$	11.0483	+	34.0033i	0.538463	+	1.65722i	−0.197582	+	0.980286i	$0.563309\pi$
$422$	−14.2247	+	21.9042i	−0.692449	+	1.06628i
$423$	−5.17062	+	13.4699i	−0.251404	+	0.654931i
$424$	0.230275	+	0.517206i	0.0111831	+	0.0251177i
$425$	−10.3844	−	7.95331i	−0.503718	−	0.385792i
$426$	−3.81865	+	1.24076i	−0.185014	+	0.0601148i
$427$	−15.1976	−	9.47080i	−0.735465	−	0.458324i
$428$	−9.15118	−	9.15118i	−0.442339	−	0.442339i
$429$	13.0455	−	0.785879i	0.629844	−	0.0379426i
$430$	−4.13649	+	6.56251i	−0.199479	+	0.316473i
$431$	2.67693	+	25.4693i	0.128943	+	1.22681i	0.847291	+	0.531128i	$0.178232\pi$
$431$	2.67693	+	25.4693i	0.128943	+	1.22681i	−0.718348	+	0.695684i	$0.755102\pi$
$432$	5.51104	−	0.288821i	0.265150	−	0.0138959i
$433$	−4.05001	−	7.94859i	−0.194631	−	0.381985i	0.772980	−	0.634430i	$-0.218765\pi$
$433$	−4.05001	−	7.94859i	−0.194631	−	0.381985i	−0.967611	+	0.252445i	$0.918765\pi$
$434$	10.6017	−	0.197979i	0.508898	−	0.00950331i
$435$	−1.44551	−	12.1659i	−0.0693069	−	0.583309i
$436$	11.1432	−	2.36856i	0.533663	−	0.113434i
$437$	−13.0156	−	20.0423i	−0.622622	−	0.958753i
$438$	8.78996	−	10.8547i	0.420000	−	0.518657i
$439$	20.2579	+	35.0877i	0.966856	+	1.67464i	0.704544	+	0.709661i	$0.251152\pi$
$439$	20.2579	+	35.0877i	0.966856	+	1.67464i	0.262313	+	0.964983i	$0.415515\pi$
$440$	−6.13209	+	4.17102i	−0.292336	+	0.198846i
$441$	−10.1004	+	2.54447i	−0.480969	+	0.121165i
$442$	1.31145	−	8.28015i	0.0623792	−	0.393847i
$443$	14.4021	−	0.754780i	0.684263	−	0.0358607i	0.292963	−	0.956124i	$-0.405359\pi$
$443$	14.4021	−	0.754780i	0.684263	−	0.0358607i	0.391300	+	0.920263i	$0.372025\pi$
$444$	9.38842	+	10.4269i	0.445555	+	0.494839i
$445$	5.62619	−	2.24758i	0.266707	−	0.106545i
$446$	5.91189	+	0.621365i	0.279936	+	0.0294225i
$447$	−7.70939	+	3.92813i	−0.364642	+	0.185794i
$448$	0.462605	+	2.60499i	0.0218560	+	0.123074i
$449$	16.3039	+	22.4404i	0.769427	+	1.05903i	0.996371	+	0.0851178i	$0.0271267\pi$
$449$	16.3039	+	22.4404i	0.769427	+	1.05903i	−0.226944	+	0.973908i	$0.572873\pi$
$450$	−2.47716	+	7.01545i	−0.116774	+	0.330712i
$451$	−0.977017	+	21.9157i	−0.0460060	+	1.03197i
$452$	0.273434	+	1.02047i	0.0128612	+	0.0479988i
$453$	7.11855	−	2.73256i	0.334459	−	0.128387i
$454$	5.50869	+	16.9540i	0.258536	+	0.795691i
$455$	13.8307	+	12.9671i	0.648391	+	0.607906i
$456$	−3.48869	−	2.53468i	−0.163373	−	0.118697i
$457$	17.8245	+	22.0114i	0.833796	+	1.02965i	0.999058	+	0.0434020i	$0.0138196\pi$
$457$	17.8245	+	22.0114i	0.833796	+	1.02965i	−0.165262	+	0.986250i	$0.552847\pi$
$458$	17.6591	+	0.925474i	0.825156	+	0.0432446i
$459$	−3.00159	+	14.1214i	−0.140102	+	0.659130i
$460$	−14.4266	+	4.90447i	−0.672646	+	0.228672i
$461$		−	25.0633i		−	1.16731i	−0.812001	−	0.583656i	$-0.801622\pi$
$461$		−	25.0633i		−	1.16731i	0.812001	−	0.583656i	$-0.198378\pi$
$462$	−1.41160	−	10.6973i	−0.0656736	−	0.497683i
$463$	−26.8158	−	26.8158i	−1.24624	−	1.24624i	−0.957369	−	0.288868i	$-0.906721\pi$
$463$	−26.8158	−	26.8158i	−1.24624	−	1.24624i	−0.288868	−	0.957369i	$-0.593279\pi$
$464$	−1.81233	+	4.07057i	−0.0841355	+	0.188971i
$465$	5.63852	+	9.46774i	0.261480	+	0.439056i
$466$	−9.03380	−	10.0331i	−0.418483	−	0.464772i
$467$	14.0450	−	11.3734i	0.649924	−	0.526298i	−0.246700	−	0.969092i	$-0.579346\pi$
$467$	14.0450	−	11.3734i	0.649924	−	0.526298i	0.896623	+	0.442794i	$0.146013\pi$
$468$	−4.70971	+	0.745945i	−0.217706	+	0.0344813i
$469$	6.23640	−	32.2936i	0.287970	−	1.49118i
$470$	−5.89481	−	20.8653i	−0.271907	−	0.962443i
$471$	21.3992	+	9.52753i	0.986022	+	0.439005i
$472$	9.77775	−	2.61994i	0.450057	−	0.120592i
$473$	−10.4745	+	4.76188i	−0.481616	+	0.218951i
$474$	−0.597392	−	1.03471i	−0.0274391	−	0.0475260i
$475$	14.9424	−	9.17536i	0.685606	−	0.420994i
$476$	−6.89578	−	0.594834i	−0.316067	−	0.0272642i
$477$	0.382455	+	0.750610i	0.0175114	+	0.0343681i
$478$	−10.7649	+	8.71728i	−0.492377	+	0.398719i
$479$	4.81333	−	2.14303i	0.219927	−	0.0979177i	−0.293816	−	0.955862i	$-0.594925\pi$
$479$	4.81333	−	2.14303i	0.219927	−	0.0979177i	0.513743	+	0.857944i	$0.328259\pi$
$480$	−2.11318	+	1.75913i	−0.0964529	+	0.0802929i
$481$	−27.1739	−	24.4675i	−1.23902	−	1.11562i
$482$	26.4845	+	4.19474i	1.20634	+	0.191065i
$483$	3.05864	−	21.9575i	0.139173	−	0.999100i
$484$	−10.9987	+	0.171784i	−0.499939	+	0.00780838i
$485$	−0.0784373	+	0.253014i	−0.00356165	+	0.0114888i
$486$	13.6256	−	1.43211i	0.618072	−	0.0649619i
$487$	−25.3647	+	16.4720i	−1.14938	+	0.746418i	−0.971361	−	0.237608i	$-0.923637\pi$
$487$	−25.3647	+	16.4720i	−1.14938	+	0.746418i	−0.178022	+	0.984026i	$0.556970\pi$
$488$	−3.68625	+	5.67633i	−0.166869	+	0.256955i
$489$	15.1977	+	11.0417i	0.687262	+	0.499325i
$490$	9.86833	−	12.1497i	0.445806	−	0.548869i
$491$	−2.20241	+	6.77832i	−0.0993934	+	0.305902i	−0.988374	−	0.152044i	$-0.951414\pi$
$491$	−2.20241	+	6.77832i	−0.0993934	+	0.305902i	0.888980	+	0.457945i	$0.151414\pi$
$492$	0.425665	+	8.12217i	0.0191905	+	0.366176i
$493$	−9.05881	−	7.33568i	−0.407989	−	0.330383i
$494$	9.73267	+	5.61916i	0.437894	+	0.252818i
$495$	−8.78717	+	6.67547i	−0.394954	+	0.300040i
$496$		−	4.00777i		−	0.179954i
$497$	−4.06517	−	7.62304i	−0.182348	−	0.341940i
$498$	−0.590096	+	1.15813i	−0.0264428	+	0.0518970i
$499$	2.60401	+	12.2509i	0.116571	+	0.548425i	0.997211	+	0.0746379i	$0.0237801\pi$
$499$	2.60401	+	12.2509i	0.116571	+	0.548425i	−0.880639	+	0.473787i	$0.842887\pi$
$500$	−3.32993	−	10.6729i	−0.148919	−	0.477308i
$501$	−2.34202	+	1.04274i	−0.104634	+	0.0465860i
$502$	−11.1341	−	7.23059i	−0.496941	−	0.322717i
$503$	27.3098	+	13.9150i	1.21768	+	0.620441i	0.940309	−	0.340321i	$-0.110536\pi$
$503$	27.3098	+	13.9150i	1.21768	+	0.620441i	0.277374	+	0.960762i	$0.410536\pi$
$504$	0.890274	+	3.83487i	0.0396559	+	0.170819i
$505$	−0.790639	+	20.3580i	−0.0351830	+	0.905920i
$506$	−21.8758	−	5.67889i	−0.972498	−	0.252458i
$507$	3.24314	−	0.868996i	0.144033	−	0.0385935i
$508$	−1.70466	+	2.10508i	−0.0756319	+	0.0933976i
$509$	−2.14144	+	2.37832i	−0.0949179	+	0.105417i	−0.788732	−	0.614737i	$-0.789262\pi$
$509$	−2.14144	+	2.37832i	−0.0949179	+	0.105417i	0.693814	+	0.720154i	$0.255929\pi$
$510$	−3.01435	−	6.53085i	−0.133478	−	0.289191i
$511$	26.3026	+	14.5379i	1.16356	+	0.643119i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−16.2311	−	10.5406i	−0.716620	−	0.465379i
$514$	−24.0579	−	5.11366i	−1.06115	−	0.225554i
$515$	−12.3719	−	10.8399i	−0.545170	−	0.477665i
$516$	−3.69435	+	2.13294i	−0.162635	+	0.0938973i
$517$	9.69872	−	30.6622i	0.426549	−	1.34852i
$518$	−18.5574	+	23.8121i	−0.815365	+	1.04625i
$519$	−12.0176	−	16.5408i	−0.527515	−	0.726062i
$520$	4.99784	−	5.13508i	0.219170	−	0.225188i
$521$	3.49070	−	3.14304i	0.152930	−	0.137699i	−0.589114	−	0.808050i	$-0.700523\pi$
$521$	3.49070	−	3.14304i	0.152930	−	0.137699i	0.742044	+	0.670351i	$0.233856\pi$
$522$	−2.37604	+	6.18980i	−0.103997	+	0.270920i
$523$	14.0409	+	17.3390i	0.613964	+	0.758183i	0.985396	−	0.170277i	$-0.0544663\pi$
$523$	14.0409	+	17.3390i	0.613964	+	0.758183i	−0.371432	+	0.928460i	$0.621133\pi$
$524$	−0.330647	+	1.01763i	−0.0144444	+	0.0444552i
$525$	16.0492	+	2.65068i	0.700443	+	0.115685i
$526$	9.15050	−	6.64823i	0.398981	−	0.289876i
$527$	10.1272	+	2.71358i	0.441148	+	0.118205i
$528$	−4.05246	+	0.457951i	−0.176360	+	0.0199298i
$529$	−20.2965	−	11.7182i	−0.882456	−	0.509486i
$530$	−1.13565	−	0.559404i	−0.0493297	−	0.0242989i
$531$	14.3252	−	4.65455i	0.621661	−	0.201990i
$532$	4.05724	−	8.34438i	0.175904	−	0.361775i
$533$	−3.31587	−	20.9356i	−0.143626	−	0.906820i
$534$	3.31339	+	0.348252i	0.143385	+	0.0150703i
$535$	28.8184	+	2.63488i	1.24593	+	0.113916i
$536$	−12.1597	−	2.58462i	−0.525219	−	0.111639i
$537$	−5.58734	−	14.5555i	−0.241111	−	0.628117i
$538$	4.05116	−	4.05116i	0.174658	−	0.174658i
$539$	22.1312	−	7.01494i	0.953259	−	0.302155i
$540$	−9.05773	+	8.38048i	−0.389783	+	0.360639i
$541$	−7.95757	−	3.54294i	−0.342123	−	0.152323i	0.228481	−	0.973548i	$-0.426624\pi$
$541$	−7.95757	−	3.54294i	−0.342123	−	0.152323i	−0.570604	+	0.821226i	$0.693291\pi$
$542$	−2.33287	−	3.59231i	−0.100206	−	0.154303i
$543$	1.36100	−	25.9694i	0.0584060	−	1.11445i
$544$	−0.273450	+	2.60171i	−0.0117241	+	0.111547i
$545$	−15.7615	+	20.0120i	−0.675149	+	0.857220i
$546$	3.40625	+	9.85345i	0.145774	+	0.421689i
$547$	−40.2164	−	20.4913i	−1.71953	−	0.876144i	−0.978930	−	0.204198i	$-0.934541\pi$
$547$	−40.2164	−	20.4913i	−1.71953	−	0.876144i	−0.740600	−	0.671946i	$-0.765459\pi$
$548$	−3.63845	−	9.47849i	−0.155427	−	0.404901i
$549$	−5.03554	+	8.72182i	−0.214912	+	0.372238i
$550$	4.57113	−	15.9407i	0.194914	−	0.679712i
$551$	13.5326	−	7.81308i	0.576510	−	0.332848i
$552$	−8.27611	−	1.31081i	−0.352255	−	0.0557917i
$553$	1.96730	−	1.65485i	0.0836581	−	0.0703714i
$554$	−17.6961	−	5.74981i	−0.751835	−	0.244286i
$555$	−31.0511	−	4.48785i	−1.31805	−	0.190499i
$556$	−0.948541	−	2.13046i	−0.0402271	−	0.0903516i
$557$	−19.6954	−	1.03219i	−0.834522	−	0.0437354i	−0.369713	−	0.929146i	$-0.620544\pi$
$557$	−19.6954	−	1.03219i	−0.834522	−	0.0437354i	−0.464809	+	0.885411i	$0.653877\pi$
$558$	−0.312106	−	5.95534i	−0.0132125	−	0.252110i
$559$	8.99420	−	6.53467i	0.380414	−	0.276387i
$560$	−4.52173	−	3.81497i	−0.191078	−	0.161212i
$561$	1.58664	−	10.5502i	0.0669881	−	0.445430i
$562$	18.0810	+	4.84480i	0.762702	+	0.204366i
$563$	11.7399	+	9.50681i	0.494779	+	0.400664i	0.843972	−	0.536387i	$-0.180211\pi$
$563$	11.7399	+	9.50681i	0.494779	+	0.400664i	−0.349193	+	0.937051i	$0.613544\pi$
$564$	2.47896	−	11.6626i	0.104383	−	0.491084i
$565$	−1.92979	−	1.36253i	−0.0811870	−	0.0573222i
$566$	−3.55946	+	4.89918i	−0.149615	+	0.205928i
$567$	−1.70050	−	5.90317i	−0.0714141	−	0.247910i
$568$	−2.90943	+	1.48243i	−0.122077	+	0.0622012i
$569$	−0.323028	−	0.290856i	−0.0135420	−	0.0121933i	0.662332	−	0.749211i	$-0.269567\pi$
$569$	−0.323028	−	0.290856i	−0.0135420	−	0.0121933i	−0.675874	+	0.737017i	$0.736234\pi$
$570$	9.62156	−	0.635005i	0.403003	−	0.0265974i
$571$	−17.2441	+	29.8677i	−0.721644	+	1.24992i	0.238696	+	0.971094i	$0.423280\pi$
$571$	−17.2441	+	29.8677i	−0.721644	+	1.24992i	−0.960340	+	0.278830i	$0.910053\pi$
$572$	10.3786	−	2.29090i	0.433953	−	0.0957872i
$573$	11.4178	−	11.4178i	0.476984	−	0.476984i
$574$	−17.0467	+	3.95744i	−0.711516	+	0.165180i
$575$	17.7763	−	29.0674i	0.741324	−	1.21219i
$576$	1.45547	−	0.309370i	0.0606447	−	0.0128904i
$577$	9.54134	+	3.66258i	0.397211	+	0.152475i	0.548770	−	0.835973i	$-0.315096\pi$
$577$	9.54134	+	3.66258i	0.397211	+	0.152475i	−0.151559	+	0.988448i	$0.548429\pi$
$578$	9.48177	+	3.63971i	0.394390	+	0.151392i
$579$	21.4003	−	4.54878i	0.889367	−	0.189041i
$580$	−2.70883	−	9.58815i	−0.112478	−	0.398126i
$581$	−2.67550	−	0.814418i	−0.110999	−	0.0337878i
$582$	−0.103003	+	0.103003i	−0.00426959	+	0.00426959i
$583$	−0.951527	−	1.61877i	−0.0394082	−	0.0670425i
$584$	5.67947	−	9.83713i	0.235018	−	0.407063i
$585$	7.02665	−	8.01968i	0.290516	−	0.331573i
$586$	16.8412	+	15.1639i	0.695704	+	0.626415i
$587$	30.8507	−	15.7192i	1.27335	−	0.648802i	0.319070	−	0.947731i	$-0.396630\pi$
$587$	30.8507	−	15.7192i	1.27335	−	0.648802i	0.954275	+	0.298929i	$0.0966295\pi$
$588$	7.91499	−	3.38251i	0.326409	−	0.139492i
$589$	−8.26130	+	11.3707i	−0.340401	+	0.468521i
$590$	−13.0553	+	18.4906i	−0.537478	+	0.761245i
$591$	−4.10652	+	19.3196i	−0.168920	+	0.794704i
$592$	8.86762	+	7.18085i	0.364457	+	0.295131i
$593$	12.1038	+	3.24320i	0.497043	+	0.133182i	0.498627	−	0.866816i	$-0.333838\pi$
$593$	12.1038	+	3.24320i	0.497043	+	0.133182i	−0.00158436	+	0.999999i	$0.500504\pi$
$594$	−18.0549	+	3.00432i	−0.740801	+	0.123269i
$595$	12.7016	−	8.84290i	0.520715	−	0.362524i
$596$	−5.69271	+	4.13600i	−0.233183	+	0.169417i
$597$	−0.317651	−	6.06115i	−0.0130006	−	0.248066i
$598$	21.8076	+	1.14289i	0.891779	+	0.0467362i
$599$	−14.5287	−	32.6319i	−0.593626	−	1.33330i	−0.921425	−	0.388557i	$-0.872974\pi$
$599$	−14.5287	−	32.6319i	−0.593626	−	1.33330i	0.327799	−	0.944747i	$-0.393693\pi$
$600$	1.11495	−	6.04625i	0.0455175	−	0.246837i
$601$	32.9417	+	10.7034i	1.34372	+	0.436601i	0.890575	−	0.454836i	$-0.150302\pi$
$601$	32.9417	+	10.7034i	1.34372	+	0.436601i	0.453144	+	0.891437i	$0.350302\pi$
$602$	−5.90850	−	7.02407i	−0.240812	−	0.286280i
$603$	−18.2700	−	2.89368i	−0.744011	−	0.117840i
$604$	5.37023	−	3.10050i	0.218512	−	0.126158i
$605$	18.6558	−	16.0300i	0.758467	−	0.651711i
$606$	−5.60177	+	9.70255i	−0.227556	+	0.394139i
$607$	2.07387	+	5.40262i	0.0841759	+	0.219286i	0.969208	−	0.246245i	$-0.0791968\pi$
$607$	2.07387	+	5.40262i	0.0841759	+	0.219286i	−0.885032	+	0.465531i	$0.845863\pi$
$608$	−3.12470	−	1.59211i	−0.126723	−	0.0645687i
$609$	14.2331	+	2.74864i	0.576756	+	0.111381i
$610$	−1.78565	−	15.0286i	−0.0722987	−	0.608488i
$611$	−3.24805	+	30.9031i	−0.131402	+	1.25021i
$612$	−0.203725	+	3.88730i	−0.00823509	+	0.157135i
$613$	9.06938	+	13.9656i	0.366309	+	0.564066i	0.972981	−	0.230886i	$-0.0741625\pi$
$613$	9.06938	+	13.9656i	0.366309	+	0.564066i	−0.606672	+	0.794952i	$0.707496\pi$
$614$	18.6954	+	8.32375i	0.754487	+	0.335919i
$615$	−12.3512	−	13.3493i	−0.498047	−	0.538295i
$616$	−2.49476	−	8.41286i	−0.100517	−	0.338964i
$617$	28.4091	−	28.4091i	1.14371	−	1.14371i	0.155941	−	0.987766i	$-0.450159\pi$
$617$	28.4091	−	28.4091i	1.14371	−	1.14371i	0.987766	−	0.155941i	$-0.0498409\pi$
$618$	−3.24160	−	8.44466i	−0.130396	−	0.339694i
$619$	−28.8292	−	6.12784i	−1.15874	−	0.246299i	−0.411857	−	0.911249i	$-0.635120\pi$
$619$	−28.8292	−	6.12784i	−1.15874	−	0.246299i	−0.746888	+	0.664950i	$0.768453\pi$
$620$	5.73354	+	6.88749i	0.230264	+	0.276608i
$621$	−37.4001	−	3.93091i	−1.50081	−	0.157742i
$622$	−5.35512	−	33.8109i	−0.214721	−	1.35569i
$623$	0.508767	+	7.15046i	0.0203833	+	0.286477i
$624$	3.74764	−	1.21768i	0.150026	−	0.0487463i
$625$	20.9914	+	13.5780i	0.839655	+	0.543120i
$626$	19.9676	+	11.5283i	0.798066	+	0.460764i
$627$	12.4415	+	7.05413i	0.496865	+	0.281715i
$628$	18.4007	+	4.93044i	0.734266	+	0.196746i
$629$	−24.1494	+	17.5455i	−0.962898	+	0.699587i
$630$	−7.01616	−	5.31672i	−0.279530	−	0.211823i
$631$	−2.50988	+	7.72460i	−0.0999166	+	0.307512i	−0.988504	−	0.151196i	$-0.951688\pi$
$631$	−2.50988	+	7.72460i	−0.0999166	+	0.307512i	0.888587	+	0.458708i	$0.151688\pi$
$632$	−0.611483	−	0.755118i	−0.0243235	−	0.0300370i
$633$	11.5091	−	29.9823i	0.457446	−	1.19169i
$634$	13.8503	−	12.4709i	0.550067	−	0.495283i
$635$	−0.0820239	−	6.05634i	−0.00325502	−	0.240338i
$636$	−0.409194	−	0.563207i	−0.0162256	−	0.0223326i
$637$	−19.5931	+	10.9232i	−0.776307	+	0.432791i
$638$	4.45682	−	14.0901i	0.176447	−	0.557833i
$639$	−4.20782	+	2.42939i	−0.166459	+	0.0961050i
$640$	−1.47358	+	1.68183i	−0.0582484	+	0.0664803i
$641$	11.2425	+	2.38967i	0.444052	+	0.0943862i	0.424511	−	0.905423i	$-0.360446\pi$
$641$	11.2425	+	2.38967i	0.444052	+	0.0943862i	0.0195414	+	0.999809i	$0.493779\pi$
$642$	13.3463	+	8.66719i	0.526736	+	0.342067i
$643$	−43.1896	+	6.84057i	−1.70323	+	0.269766i	−0.930853	−	0.365395i	$-0.880934\pi$
$643$	−43.1896	+	6.84057i	−1.70323	+	0.269766i	−0.772380	+	0.635161i	$0.780934\pi$
$644$	−0.336625	−	18.0261i	−0.0132649	−	0.710329i
$645$	3.29748	−	8.95070i	0.129838	−	0.352433i
$646$	6.13878	−	6.81780i	0.241527	−	0.268243i
$647$	13.4413	−	16.5986i	0.528433	−	0.652560i	−0.441118	−	0.897449i	$-0.645418\pi$
$647$	13.4413	−	16.5986i	0.528433	−	0.652560i	0.969551	+	0.244889i	$0.0787514\pi$
$648$	−2.24280	+	0.600956i	−0.0881055	+	0.0236078i
$649$	−31.2483	+	12.2759i	−1.22660	+	0.481871i
$650$	−1.24269	+	15.9748i	−0.0487423	+	0.626582i
$651$	−12.7008	+	2.94851i	−0.497783	+	0.115561i
$652$	13.6120	+	6.93567i	0.533088	+	0.271622i
$653$	6.99967	+	4.54564i	0.273918	+	0.177885i	0.674287	−	0.738470i	$-0.264451\pi$
$653$	6.99967	+	4.54564i	0.273918	+	0.177885i	−0.400368	+	0.916354i	$0.631118\pi$
$654$	−12.7971	+	5.69766i	−0.500408	+	0.222796i
$655$	−0.887595	−	2.22185i	−0.0346812	−	0.0868149i
$656$	1.37521	+	6.46986i	0.0536930	+	0.252606i
$657$	7.67334	−	15.0598i	0.299365	−	0.587538i
$658$	25.6399	+	0.864077i	0.999547	+	0.0336852i
$659$			42.4945i			1.65535i	0.561208	+	0.827675i	$0.310337\pi$
$659$			42.4945i			1.65535i	−0.561208	+	0.827675i	$0.689663\pi$
$660$	6.30914	−	6.58448i	0.245583	−	0.256300i
$661$	−13.4561	−	7.76890i	−0.523383	−	0.302175i	0.214935	−	0.976628i	$-0.431046\pi$
$661$	−13.4561	−	7.76890i	−0.523383	−	0.302175i	−0.738318	+	0.674453i	$0.764379\pi$
$662$	10.5991	+	8.58298i	0.411946	+	0.333587i
$663$	0.539505	+	10.2944i	0.0209527	+	0.399800i
$664$	−0.326649	+	1.00532i	−0.0126764	+	0.0390140i
$665$	4.96501	+	20.1444i	0.192535	+	0.781168i
$666$	13.7361	+	9.97983i	0.532261	+	0.386710i
$667$	16.5372	−	25.4651i	0.640324	−	0.986013i
$668$	−1.74854	+	1.13551i	−0.0676530	+	0.0439344i
$669$	−7.26949	+	0.764054i	−0.281055	+	0.0295400i
$670$	24.5944	−	12.9540i	0.950166	−	0.500456i
$671$	10.0346	−	20.0801i	0.387380	−	0.775182i
$672$	−1.22239	−	3.01494i	−0.0471547	−	0.116304i
$673$	3.13258	+	0.496152i	0.120752	+	0.0191252i	0.216518	−	0.976279i	$-0.430530\pi$
$673$	3.13258	+	0.496152i	0.120752	+	0.0191252i	−0.0957659	+	0.995404i	$0.530530\pi$
$674$	−7.74949	−	6.97767i	−0.298499	−	0.268770i
$675$	3.57684	−	27.3602i	0.137673	−	1.05309i
$676$	2.49445	−	1.11060i	0.0959403	−	0.0427154i
$677$	−22.1316	+	17.9218i	−0.850585	+	0.688790i	−0.952015	−	0.306053i	$-0.900992\pi$
$677$	−22.1316	+	17.9218i	−0.850585	+	0.688790i	0.101430	+	0.994843i	$0.467658\pi$
$678$	−0.589766	−	1.15748i	−0.0226498	−	0.0444528i
$679$	−0.256962	−	0.179461i	−0.00986130	−	0.00688706i
$680$	−3.25209	−	4.86232i	−0.124712	−	0.186462i
$681$	−10.9601	−	18.9834i	−0.419991	−	0.727445i
$682$	1.49260	+	13.2082i	0.0571547	+	0.505768i
$683$	10.8293	−	2.90170i	0.414371	−	0.111030i	−0.0456094	−	0.998959i	$-0.514523\pi$
$683$	10.8293	−	2.90170i	0.414371	−	0.111030i	0.459981	+	0.887929i	$0.347856\pi$
$684$	−4.76713	−	2.12246i	−0.182276	−	0.0811545i
$685$	19.8128	+	11.0839i	0.757008	+	0.423495i
$686$	10.1436	+	15.4954i	0.387284	+	0.591617i
$687$	−21.4764	+	3.40153i	−0.819376	+	0.129776i
$688$	−2.69608	+	2.18324i	−0.102787	+	0.0832354i
$689$	1.21400	+	1.34828i	0.0462497	+	0.0513655i
$690$	16.0980	−	9.58720i	0.612842	−	0.364978i
$691$	−3.75935	+	8.44365i	−0.143013	+	0.321211i	−0.970823	−	0.239796i	$-0.922919\pi$
$691$	−3.75935	+	8.44365i	−0.143013	+	0.321211i	0.827811	+	0.561007i	$0.189586\pi$
$692$	−11.7573	−	11.7573i	−0.446945	−	0.446945i
$693$	−4.36224	−	12.3068i	−0.165708	−	0.467497i
$694$		−	19.0472i		−	0.723023i
$695$	4.67795	+	2.30428i	0.177445	+	0.0874062i
$696$	1.13915	−	5.35928i	0.0431794	−	0.203143i
$697$	−17.2798	−	0.905596i	−0.654519	−	0.0343019i
$698$	−15.5946	−	19.2578i	−0.590266	−	0.728917i
$699$	13.4306	+	9.75789i	0.507991	+	0.369077i
$700$	13.2285	+	0.0873417i	0.499989	+	0.00330121i
$701$	6.70016	+	20.6210i	0.253061	+	0.778843i	0.994205	+	0.107497i	$0.0342836\pi$
$701$	6.70016	+	20.6210i	0.253061	+	0.778843i	−0.741144	+	0.671346i	$0.765716\pi$
$702$	16.5103	−	6.33772i	0.623142	−	0.239202i
$703$	−10.3568	−	38.6523i	−0.390616	−	1.45780i
$704$	−3.19681	+	0.883395i	−0.120484	+	0.0332942i
$705$	12.4244	+	23.5890i	0.467931	+	0.888414i
$706$	0.982276	+	1.35199i	0.0369684	+	0.0508827i
$707$	−22.6624	−	8.21715i	−0.852305	−	0.309038i
$708$	−11.0906	+	5.65092i	−0.416808	+	0.212375i
$709$	17.7154	+	1.86197i	0.665317	+	0.0699276i	0.431166	−	0.902273i	$-0.358102\pi$
$709$	17.7154	+	1.86197i	0.665317	+	0.0699276i	0.234151	+	0.972200i	$0.424769\pi$
$710$	2.87918	−	6.70985i	0.108054	−	0.251816i
$711$	−0.967438	−	1.07445i	−0.0362818	−	0.0402950i
$712$	2.70574	−	0.141802i	0.101402	−	0.00531425i
$713$	−4.27232	+	26.9744i	−0.160000	+	1.01020i
$714$	8.44609	−	1.04750i	0.316087	−	0.0392017i
$715$	−14.5587	+	18.7847i	−0.544464	+	0.702509i
$716$	−6.33970	−	10.9807i	−0.236926	−	0.410367i
$717$	10.7191	−	13.2370i	0.400312	−	0.494344i
$718$	−7.61072	−	11.7195i	−0.284030	−	0.437367i
$719$	20.8202	−	4.42547i	0.776463	−	0.165042i	0.197398	−	0.980324i	$-0.436751\pi$
$719$	20.8202	−	4.42547i	0.776463	−	0.165042i	0.579065	+	0.815281i	$0.303418\pi$
$720$	−2.05870	+	2.61388i	−0.0767230	+	0.0974134i
$721$	16.6705	−	10.0443i	0.620843	−	0.374071i
$722$	−3.04239	−	5.97103i	−0.113226	−	0.222219i
$723$	−32.9271	+	1.72564i	−1.22457	+	0.0641772i
$724$	−2.21062	−	21.0327i	−0.0821572	−	0.781673i
$725$	18.3721	+	12.6023i	0.682322	+	0.468038i
$726$	13.1849	−	3.01849i	0.489338	−	0.112027i
$727$	−2.30098	−	2.30098i	−0.0853386	−	0.0853386i	0.663149	−	0.748487i	$-0.269220\pi$
$727$	−2.30098	−	2.30098i	−0.0853386	−	0.0853386i	−0.748487	+	0.663149i	$0.769220\pi$
$728$	3.98958	+	7.48129i	0.147864	+	0.277275i
$729$	−22.6472	+	7.35851i	−0.838784	+	0.272538i
$730$	4.31270	+	25.0305i	0.159620	+	0.926422i
$731$	−3.69137	−	8.29096i	−0.136530	−	0.306652i
$732$	2.98252	−	7.76972i	0.110237	−	0.287177i
$733$	−5.89493	+	9.07740i	−0.217734	+	0.335281i	−0.930612	−	0.366007i	$-0.880725\pi$
$733$	−5.89493	+	9.07740i	−0.217734	+	0.335281i	0.712878	+	0.701288i	$0.247391\pi$
$734$	−2.80240	−	8.62490i	−0.103438	−	0.318351i
$735$	−8.76315	+	17.1362i	−0.323234	+	0.632079i
$736$	−6.81442			−0.251183
$737$	41.0367	+	3.98940i	1.51160	+	0.146952i
$738$	2.54734	+	9.50680i	0.0937688	+	0.349950i
$739$	−29.5990	+	3.11098i	−1.08882	+	0.114439i	−0.631884	−	0.775063i	$-0.717718\pi$
$739$	−29.5990	+	3.11098i	−1.08882	+	0.114439i	−0.456932	+	0.889502i	$0.651052\pi$
$740$	−25.5123	+	0.345525i	−0.937850	+	0.0127018i
$741$	−13.1427	−	4.27033i	−0.482810	−	0.156874i
$742$	1.03921	−	1.07877i	0.0381507	−	0.0396027i
$743$	5.58189	+	35.2427i	0.204780	+	1.29293i	0.849124	+	0.528193i	$0.177130\pi$
$743$	5.58189	+	35.2427i	0.204780	+	1.29293i	−0.644344	+	0.764735i	$0.722870\pi$
$744$	1.02461	+	4.82041i	0.0375640	+	0.176725i
$745$	3.86614	−	15.2519i	0.141644	−	0.558786i
$746$	−3.67888	−	35.0022i	−0.134693	−	1.28152i
$747$	−0.407094	+	1.51930i	−0.0148948	+	0.0555881i
$748$	−0.0677508	−	8.67615i	−0.00247721	−	0.317231i
$749$	−13.3404	+	31.5349i	−0.487449	+	1.15226i
$750$	6.73374	+	11.9857i	0.245881	+	0.437657i
$751$	24.0112	−	26.6672i	0.876183	−	0.973100i	−0.123632	−	0.992328i	$-0.539454\pi$
$751$	24.0112	−	26.6672i	0.876183	−	0.973100i	0.999815	+	0.0192285i	$0.00612099\pi$
$752$	0.507474	−	9.68318i	0.0185057	−	0.353109i
$753$	15.2403	+	5.85021i	0.555388	+	0.213193i
$754$	−1.49257	+	14.2008i	−0.0543561	+	0.517164i
$755$	−4.79333	+	13.0110i	−0.174447	+	0.473519i
$756$	−6.18671	−	13.2253i	−0.225009	−	0.481001i
$757$	−8.26314	+	52.1714i	−0.300329	+	1.89620i	0.126663	+	0.991946i	$0.459573\pi$
$757$	−8.26314	+	52.1714i	−0.300329	+	1.89620i	−0.426991	+	0.904256i	$0.640427\pi$
$758$	7.93117	−	29.5995i	0.288073	−	1.07510i
$759$	27.7633	+	1.23771i	1.00775	+	0.0449260i
$760$	7.64759	−	1.73411i	0.277407	−	0.0629029i
$761$	−0.937751	+	2.10622i	−0.0339934	+	0.0763505i	−0.929744	−	0.368206i	$-0.879972\pi$
$761$	−0.937751	+	2.10622i	−0.0339934	+	0.0763505i	0.895751	+	0.444557i	$0.146639\pi$
$762$	1.51213	−	2.96772i	0.0547787	−	0.107509i
$763$	−16.8850	−	24.9673i	−0.611277	−	0.903877i
$764$	7.71859	−	10.6237i	0.279249	−	0.384353i
$765$	−5.21109	−	6.97191i	−0.188407	−	0.252070i
$766$	−20.6774	+	18.6180i	−0.747104	+	0.672696i
$767$	27.2057	−	17.6676i	0.982343	−	0.637941i
$768$	−1.14797	+	0.440663i	−0.0414237	+	0.0159011i
$769$	−36.4969			−1.31611			−0.658055	−	0.752970i	$-0.728621\pi$
$769$	−36.4969			−1.31611			−0.658055	+	0.752970i	$0.728621\pi$
$770$	16.3228	+	10.8888i	0.588234	+	0.392404i
$771$	30.2434			1.08919
$772$	16.6108	−	6.37629i	0.597836	−	0.229488i
$773$	−8.31819	+	5.40190i	−0.299185	+	0.194293i	−0.685497	−	0.728075i	$-0.740415\pi$
$773$	−8.31819	+	5.40190i	−0.299185	+	0.194293i	0.386313	+	0.922368i	$0.373749\pi$
$774$	−3.83622	+	3.45415i	−0.137890	+	0.124157i
$775$	−19.7066	−	3.63395i	−0.707881	−	0.130535i
$776$	−0.0696313	+	0.0958392i	−0.00249962	+	0.00344043i
$777$	16.2325	−	33.3848i	0.582338	−	1.19767i
$778$	−3.63150	+	7.12721i	−0.130195	+	0.255523i
$779$	9.43476	−	21.1908i	0.338035	−	0.759240i
$780$	−4.69843	+	7.45403i	−0.168231	+	0.266897i
$781$	9.03635	−	5.96911i	0.323346	−	0.213591i
$782$	4.61391	−	17.2194i	0.164993	−	0.615763i
$783$	3.84668	−	24.2870i	0.137469	−	0.867947i
$784$	5.92728	−	3.72389i	0.211688	−	0.132996i
$785$	−38.6757	+	17.8510i	−1.38040	+	0.637129i
$786$	0.137529	−	1.30850i	0.00490549	−	0.0466726i
$787$	−26.7941	−	10.2853i	−0.955108	−	0.366632i	−0.169621	−	0.985509i	$-0.554254\pi$
$787$	−26.7941	−	10.2853i	−0.955108	−	0.366632i	−0.785487	+	0.618878i	$0.787588\pi$
$788$	−0.840654	+	16.0406i	−0.0299471	+	0.571424i
$789$	−9.30626	+	10.3357i	−0.331312	+	0.367959i
$790$	2.13113	+	0.422906i	0.0758223	+	0.0150463i
$791$	2.23025	−	1.68488i	0.0792986	−	0.0599075i
$792$	−4.68151	+	1.56163i	−0.166350	+	0.0554903i
$793$	−5.61367	+	20.9505i	−0.199347	+	0.743974i
$794$	2.93883	+	27.9611i	0.104295	+	0.992303i
$795$	1.50894	+	0.382496i	0.0535167	+	0.0135657i
$796$	−1.02625	−	4.82812i	−0.0363744	−	0.171128i
$797$	−4.34822	−	27.4536i	−0.154022	−	0.972457i	−0.936726	−	0.350063i	$-0.886160\pi$
$797$	−4.34822	−	27.4536i	−0.154022	−	0.972457i	0.782704	−	0.622394i	$-0.213840\pi$
$798$	−2.74663	+	11.0736i	−0.0972296	+	0.392002i
$799$	24.1248	+	7.83863i	0.853475	+	0.277311i
$800$	0.126360	−	4.99840i	0.00446748	−	0.176720i
$801$	4.00955	−	0.421421i	0.141671	−	0.0148902i
$802$	1.91675	+	7.15340i	0.0676827	+	0.252595i
$803$	−15.0539	+	34.5349i	−0.531241	+	1.21871i
$804$	15.2861			0.539098
$805$	26.3668	+	30.4970i	0.929308	+	1.07488i
$806$	−3.96880	−	12.2147i	−0.139795	−	0.430245i
$807$	−3.83690	+	5.90831i	−0.135065	+	0.207982i
$808$	−3.26518	+	8.50608i	−0.114869	+	0.299243i
$809$	−10.2063	−	22.9238i	−0.358836	−	0.805959i	−0.999280	−	0.0379535i	$-0.987916\pi$
$809$	−10.2063	−	22.9238i	−0.358836	−	0.805959i	0.640444	−	0.768005i	$-0.278751\pi$
$810$	2.99460	−	4.24133i	0.105219	−	0.149025i
$811$	13.8955	−	4.51493i	0.487938	−	0.158541i	−0.0547078	−	0.998502i	$-0.517423\pi$
$811$	13.8955	−	4.51493i	0.487938	−	0.158541i	0.542645	+	0.839962i	$0.317423\pi$
$812$	11.7822	+	0.397067i	0.413475	+	0.0139343i
$813$	3.72430	+	3.72430i	0.130617	+	0.130617i
$814$	−31.8989	−	20.3630i	−1.11806	−	0.713724i
$815$	−33.3149	+	7.55426i	−1.16697	+	0.264614i
$816$	−0.336245	−	3.19916i	−0.0117709	−	0.111993i
$817$	12.1496	−	0.636734i	0.425061	−	0.0222765i
$818$	−5.94189	−	11.6616i	−0.207753	−	0.407739i
$819$	6.51092	+	10.8061i	0.227510	+	0.377597i
$820$	−11.6192	−	9.15129i	−0.405759	−	0.319577i
$821$	−30.8751	+	6.56271i	−1.07755	+	0.229040i	−0.712304	−	0.701871i	$-0.752348\pi$
$821$	−30.8751	+	6.56271i	−1.07755	+	0.229040i	−0.365245	+	0.930911i	$0.619015\pi$
$822$	6.79944	+	10.4702i	0.237158	+	0.365191i
$823$	10.9483	−	13.5201i	0.381635	−	0.471280i	−0.549743	−	0.835334i	$-0.685274\pi$
$823$	10.9483	−	13.5201i	0.381635	−	0.471280i	0.931378	+	0.364054i	$0.118608\pi$
$824$	−3.67810	−	6.37065i	−0.128133	−	0.221932i
$825$	−1.42268	+	20.3416i	−0.0495313	+	0.708202i
$826$	−16.1439	−	21.3694i	−0.561718	−	0.743538i
$827$	6.48803	−	40.9638i	0.225611	−	1.42445i	−0.571492	−	0.820607i	$-0.693635\pi$
$827$	6.48803	−	40.9638i	0.225611	−	1.42445i	0.797103	−	0.603843i	$-0.206365\pi$
$828$	−10.1259	+	0.530676i	−0.351899	+	0.0184423i
$829$	−14.2795	−	15.8590i	−0.495948	−	0.550806i	0.442256	−	0.896889i	$-0.354178\pi$
$829$	−14.2795	−	15.8590i	−0.495948	−	0.550806i	−0.938204	+	0.346083i	$0.887512\pi$
$830$	−0.876862	−	2.19499i	−0.0304363	−	0.0761890i
$831$	22.7543	+	2.39157i	0.789337	+	0.0829627i
$832$	2.85532	−	1.45486i	0.0989905	−	0.0504382i
$833$	5.39666	+	17.4990i	0.186983	+	0.606304i
$834$	1.68554	+	2.31995i	0.0583655	+	0.0803332i
$835$	1.38045	−	4.45289i	0.0477724	−	0.154099i
$836$	10.8909	+	4.08332i	0.376668	+	0.141225i
$837$	5.72437	+	21.3636i	0.197863	+	0.738436i
$838$	−20.3904	+	7.82713i	−0.704373	+	0.270384i
$839$	7.28369	+	22.4169i	0.251461	+	0.773917i	0.994506	+	0.104676i	$0.0333806\pi$
$839$	7.28369	+	22.4169i	0.251461	+	0.773917i	−0.743045	+	0.669241i	$0.766619\pi$
$840$	6.41391	+	3.43251i	0.221301	+	0.118433i
$841$	−7.39920	−	5.37583i	−0.255145	−	0.185374i
$842$	−22.5002	−	27.7854i	−0.775408	−	0.957549i
$843$	−22.9859	−	1.20464i	−0.791676	−	0.0414900i
$844$	5.43018	−	25.5470i	0.186914	−	0.879363i
$845$	−2.69797	+	5.47718i	−0.0928128	+	0.188421i
$846$		−	14.4283i		−	0.496054i
$847$	11.3550	+	26.7967i	0.390163	+	0.920746i
$848$	−0.400330	−	0.400330i	−0.0137474	−	0.0137474i
$849$	3.02870	−	6.80257i	0.103945	−	0.233464i
$850$	12.5449	+	3.70362i	0.430286	+	0.127033i
$851$	−52.0289	−	57.7839i	−1.78353	−	1.98081i
$852$	3.12037	−	2.52683i	0.106902	−	0.0865677i
$853$	−21.2537	+	3.36626i	−0.727714	+	0.115259i	−0.509290	−	0.860595i	$-0.670092\pi$
$853$	−21.2537	+	3.36626i	−0.727714	+	0.115259i	−0.218425	+	0.975854i	$0.570092\pi$
$854$	17.5823	+	3.39541i	0.601652	+	0.116189i
$855$	11.2289	−	3.17236i	0.384020	−	0.108493i
$856$	11.8229	+	5.26387i	0.404097	+	0.179915i
$857$	33.6327	−	9.01187i	1.14887	−	0.307839i	0.366359	−	0.930473i	$-0.380604\pi$
$857$	33.6327	−	9.01187i	1.14887	−	0.307839i	0.782513	+	0.622634i	$0.213937\pi$
$858$	−11.8974	+	5.40878i	−0.406171	+	0.184653i
$859$	11.2955	+	19.5644i	0.385398	+	0.667529i	0.991824	−	0.127611i	$-0.0407308\pi$
$859$	11.2955	+	19.5644i	0.385398	+	0.667529i	−0.606426	+	0.795140i	$0.707398\pi$
$860$	1.50995	−	7.60902i	0.0514888	−	0.259465i
$861$	19.4915	−	9.11798i	0.664269	−	0.310740i
$862$	−11.6265	−	22.8183i	−0.396000	−	0.777194i
$863$	44.1469	−	35.7495i	1.50278	−	1.21693i	0.590712	−	0.806882i	$-0.298847\pi$
$863$	44.1469	−	35.7495i	1.50278	−	1.21693i	0.912066	−	0.410044i	$-0.134487\pi$
$864$	−5.04150	+	2.24462i	−0.171515	+	0.0763635i
$865$	37.0254	+	3.38525i	1.25890	+	0.115102i
$866$	6.62953	+	5.96926i	0.225281	+	0.202844i
$867$	−12.3349	−	1.95365i	−0.418915	−	0.0663495i
$868$	−9.82659	+	3.98414i	−0.333536	+	0.135231i
$869$	2.29646	+	2.26087i	0.0779020	+	0.0766948i
$870$	5.70936	+	10.8398i	0.193565	+	0.367503i
$871$	−39.6193	+	4.16416i	−1.34245	+	0.141097i
$872$	−9.55426	+	6.20461i	−0.323548	+	0.210115i
$873$	−0.0960051	+	0.147835i	−0.00324928	+	0.00500345i
$874$	19.3337	+	14.0467i	0.653971	+	0.475137i
$875$	−22.8585	+	18.7746i	−0.772760	+	0.634699i
$876$	−4.31616	+	13.2838i	−0.145829	+	0.448817i
$877$	1.84315	+	35.1695i	0.0622389	+	1.18759i	0.834032	+	0.551715i	$0.186027\pi$
$877$	1.84315	+	35.1695i	0.0622389	+	1.18759i	−0.771794	+	0.635873i	$0.780640\pi$
$878$	−31.4867	−	25.4974i	−1.06262	−	0.860496i
$879$	−24.1328	−	13.9331i	−0.813979	−	0.469951i
$880$	4.23004	−	6.09153i	0.142595	−	0.205345i
$881$			8.89046i			0.299527i	0.988722	+	0.149764i	$0.0478512\pi$
$881$			8.89046i			0.299527i	−0.988722	+	0.149764i	$0.952149\pi$
$882$	8.51764	−	5.99511i	0.286804	−	0.201866i
$883$	13.3168	−	26.1358i	0.448148	−	0.879539i	−0.550843	−	0.834609i	$-0.685694\pi$
$883$	13.3168	−	26.1358i	0.448148	−	0.879539i	0.998990	−	0.0449300i	$-0.0143065\pi$
$884$	1.74300	+	8.20017i	0.0586234	+	0.275801i
$885$	10.9753	−	25.5775i	0.368929	−	0.859779i
$886$	−13.1750	+	5.86589i	−0.442623	+	0.197068i
$887$	24.8299	+	16.1247i	0.833706	+	0.541415i	0.889451	−	0.457030i	$-0.151087\pi$
$887$	24.8299	+	16.1247i	0.833706	+	0.541415i	−0.0557451	+	0.998445i	$0.517753\pi$
$888$	−12.5015	−	6.36984i	−0.419523	−	0.213758i
$889$	6.85602	+	2.08696i	0.229943	+	0.0699944i
$890$	−4.44704	+	4.11454i	−0.149065	+	0.137920i
$891$	7.16767	−	2.81582i	0.240126	−	0.0943335i
$892$	−5.74190	+	1.53854i	−0.192253	+	0.0515141i
$893$	−21.3999	+	26.4267i	−0.716122	+	0.884337i
$894$	5.78962	−	6.43002i	0.193634	−	0.215052i
$895$	26.6040	+	9.80106i	0.889274	+	0.327613i
$896$	−1.36543	−	2.26619i	−0.0456157	−	0.0757081i
$897$	−26.5217	+	4.20062i	−0.885533	+	0.140255i
$898$	−23.2629	−	15.1071i	−0.776292	−	0.504130i
$899$	−17.4675	−	3.71284i	−0.582575	−	0.123830i
$900$	−0.201489	−	7.43722i	−0.00671628	−	0.247907i
$901$	1.28265	−	0.740538i	0.0427312	−	0.0246709i
$902$	−6.94177	−	20.8102i	−0.231136	−	0.692904i
$903$	8.90230	+	6.93778i	0.296250	+	0.230875i
$904$	−0.620975	−	0.854699i	−0.0206533	−	0.0284269i
$905$	33.8885	+	32.9829i	1.12649	+	1.09639i
$906$	−5.66648	+	5.10212i	−0.188256	+	0.169507i
$907$	7.74008	−	20.1636i	0.257005	−	0.669521i	−0.742995	−	0.669297i	$-0.766595\pi$
$907$	7.74008	−	20.1636i	0.257005	−	0.669521i	1.00000		0.000223996i	$-7.13002e-5\pi$
$908$	−11.2186	−	13.8538i	−0.372302	−	0.459754i
$909$	−4.18948	+	12.8939i	−0.138956	+	0.427663i
$910$	−17.5590	−	7.14934i	−0.582076	−	0.236998i
$911$	6.78763	−	4.93151i	0.224884	−	0.163388i	−0.469638	−	0.882859i	$-0.655616\pi$
$911$	6.78763	−	4.93151i	0.224884	−	0.163388i	0.694523	+	0.719471i	$0.255616\pi$
$912$	4.16532	+	1.11609i	0.137927	+	0.0369576i
$913$	0.702110	−	3.43484i	0.0232364	−	0.113677i
$914$	−24.5288	−	14.1617i	−0.811341	−	0.468428i
$915$	5.98986	+	17.6194i	0.198019	+	0.582478i
$916$	−16.8179	+	5.46445i	−0.555677	+	0.180551i
$917$	2.82380	−	0.200918i	0.0932501	−	0.00663491i
$918$	−2.25842	−	14.2591i	−0.0745391	−	0.470621i
$919$	44.1506	+	4.64042i	1.45640	+	0.153073i	0.799390	−	0.600812i	$-0.205156\pi$
$919$	44.1506	+	4.64042i	1.45640	+	0.153073i	0.657005	+	0.753886i	$0.271823\pi$
$920$	11.7108	−	9.74876i	0.386095	−	0.321407i
$921$	−24.6143	−	5.23193i	−0.811069	−	0.172398i
$922$	8.98187	+	23.3986i	0.295802	+	0.770591i
$923$	−7.39922	+	7.39922i	−0.243548	+	0.243548i
$924$	5.15141	+	9.48091i	0.169469	+	0.311899i
$925$	43.3495	−	37.0919i	1.42532	−	1.21957i
$926$	34.6446	+	15.4248i	1.13849	+	0.506890i
$927$	−5.96159	−	9.18004i	−0.195804	−	0.301512i
$928$	0.233198	−	4.44969i	0.00765510	−	0.146068i
$929$	−5.25746	+	50.0214i	−0.172492	+	1.64115i	0.475653	+	0.879633i	$0.342212\pi$
$929$	−5.25746	+	50.0214i	−0.172492	+	1.64115i	−0.648145	+	0.761517i	$0.724455\pi$
$930$	−8.65694	−	6.81823i	−0.283872	−	0.223579i
$931$	−24.4928	−	1.65272i	−0.802720	−	0.0541656i
$932$	12.0293	+	6.12924i	0.394033	+	0.200770i
$933$	15.0849	+	39.2976i	0.493858	+	1.28654i
$934$	−9.03625	+	15.6512i	−0.295675	+	0.512124i
$935$	12.5286	+	14.8133i	0.409729	+	0.484448i
$936$	4.12957	−	2.38421i	0.134979	−	0.0779303i
$937$	39.1849	+	6.20628i	1.28012	+	0.202750i	0.759200	−	0.650858i	$-0.225591\pi$
$937$	39.1849	+	6.20628i	1.28012	+	0.202750i	0.520916	+	0.853608i	$0.325591\pi$
$938$	5.75081	+	32.3836i	0.187770	+	1.05736i
$939$	−26.9637	−	8.76103i	−0.879926	−	0.285905i
$940$	12.9807	+	17.3669i	0.423384	+	0.566445i
$941$	11.2527	+	25.2741i	0.366829	+	0.823911i	0.998803	+	0.0489215i	$0.0155784\pi$
$941$	11.2527	+	25.2741i	0.366829	+	0.823911i	−0.631974	+	0.774990i	$0.717755\pi$
$942$	−23.3922	−	1.22593i	−0.762160	−	0.0399431i
$943$	−2.35896	−	45.0116i	−0.0768182	−	1.46578i
$944$	−8.18941	+	5.94995i	−0.266543	+	0.193655i
$945$	29.5523	+	13.8775i	0.961338	+	0.451434i
$946$	8.07224	−	8.19930i	0.262451	−	0.266582i
$947$	−14.8783	−	3.98662i	−0.483479	−	0.129548i	0.00884327	−	0.999961i	$-0.497185\pi$
$947$	−14.8783	−	3.98662i	−0.483479	−	0.129548i	−0.492322	+	0.870413i	$0.663852\pi$
$948$	0.928522	+	0.751902i	0.0301570	+	0.0244207i
$949$	7.56817	−	35.6054i	0.245673	−	1.15580i
$950$	−10.6618	+	13.9208i	−0.345915	+	0.451651i
$951$	−13.4705	+	18.5405i	−0.436810	+	0.601217i
$952$	6.65093	−	1.91590i	0.215558	−	0.0620947i
$953$	−36.1594	+	18.4241i	−1.17132	+	0.596816i	−0.927799	−	0.373080i	$-0.878302\pi$
$953$	−36.1594	+	18.4241i	−1.17132	+	0.596816i	−0.243519	+	0.969896i	$0.578302\pi$
$954$	−0.626047	−	0.563695i	−0.0202690	−	0.0182503i
$955$	1.93371	+	29.2995i	0.0625734	+	0.948110i
$956$	6.92594	−	11.9961i	0.224001	−	0.387981i
$957$	−1.75830	+	18.0866i	−0.0568376	+	0.584656i
$958$	−3.72564	+	3.72564i	−0.120370	+	0.120370i
$959$	−19.6232	+	18.3437i	−0.633666	+	0.592349i
$960$	1.34240	−	2.39958i	0.0433259	−	0.0774462i
$961$	−14.6114	+	3.10575i	−0.471335	+	0.100185i
$962$	34.1374	+	13.1041i	1.10063	+	0.422494i
$963$	17.9781	+	6.90115i	0.579336	+	0.222386i
$964$	−26.2287	+	5.57508i	−0.844769	+	0.179561i
$965$	−19.4243	+	34.7214i	−0.625289	+	1.11772i
$966$	5.01337	+	21.5952i	0.161303	+	0.694814i
$967$	20.0335	−	20.0335i	0.644234	−	0.644234i	−0.307359	−	0.951594i	$-0.599445\pi$
$967$	20.0335	−	20.0335i	0.644234	−	0.644234i	0.951594	+	0.307359i	$0.0994453\pi$
$968$	10.2066	−	4.10194i	0.328052	−	0.131841i
$969$	−5.64051	+	9.76965i	−0.181199	+	0.313846i
$970$	−0.0174445	−	0.264318i	−0.000560109	−	0.00848674i
$971$	3.31392	+	2.98386i	0.106349	+	0.0957568i	0.720590	−	0.693362i	$-0.243871\pi$
$971$	3.31392	+	2.98386i	0.106349	+	0.0957568i	−0.614241	+	0.789118i	$0.710538\pi$
$972$	−12.2074	+	6.21998i	−0.391553	+	0.199506i
$973$	−4.28070	+	4.44362i	−0.137233	+	0.142456i
$974$	17.7769	−	24.4678i	0.569609	−	0.784000i
$975$	−2.58938	−	19.5316i	−0.0829265	−	0.625513i
$976$	1.40720	−	6.62035i	0.0450433	−	0.211912i
$977$	−16.1593	−	13.0856i	−0.516983	−	0.418645i	0.334997	−	0.942219i	$-0.391265\pi$
$977$	−16.1593	−	13.0856i	−0.516983	−	0.418645i	−0.851980	+	0.523575i	$0.824598\pi$
$978$	−18.1452	−	4.86200i	−0.580221	−	0.155470i
$979$	−8.86435	+	1.47502i	−0.283306	+	0.0471419i
$980$	−4.85880	+	14.8792i	−0.155209	+	0.475300i
$981$	−13.7140	+	9.96379i	−0.437854	+	0.318119i
$982$	−0.373006	−	7.11738i	−0.0119031	−	0.227125i
$983$	−44.6426	−	2.33962i	−1.42388	−	0.0746223i	−0.675239	−	0.737599i	$-0.735959\pi$
$983$	−44.6426	−	2.33962i	−1.42388	−	0.0746223i	−0.748640	+	0.662977i	$0.769293\pi$
$984$	−3.30812	−	7.43016i	−0.105459	−	0.236865i
$985$	−21.5032	−	28.7691i	−0.685148	−	0.916658i
$986$	11.0860	+	3.60206i	0.353050	+	0.114713i
$987$	−31.0597	+	5.51571i	−0.988643	+	0.175567i
$988$	−11.1000	−	1.75806i	−0.353137	−	0.0559314i
$989$	20.4734	−	11.8203i	0.651017	−	0.375865i
$990$	5.81126	−	9.38113i	0.184694	−	0.298152i
$991$	−18.8651	+	32.6753i	−0.599269	+	1.03796i	0.393660	+	0.919256i	$0.371209\pi$
$991$	−18.8651	+	32.6753i	−0.599269	+	1.03796i	−0.992929	+	0.118709i	$0.962125\pi$
$992$	1.43625	+	3.74157i	0.0456011	+	0.118795i
$993$	−14.9426	−	7.61361i	−0.474188	−	0.241611i
$994$	6.52702	+	5.65990i	0.207024	+	0.179521i
$995$	8.67078	+	6.82913i	0.274882	+	0.216498i
$996$	0.135866	−	1.29268i	0.00430507	−	0.0409600i
$997$	1.57702	−	30.0913i	0.0499447	−	0.953002i	−0.852642	−	0.522495i	$-0.825001\pi$
$997$	1.57702	−	30.0913i	0.0499447	−	0.953002i	0.902587	−	0.430507i	$-0.141665\pi$
$998$	−6.82138	−	10.5040i	−0.215927	−	0.332498i
$999$	−57.5259	−	25.6122i	−1.82004	−	0.810334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.3.17	✓	768
5.2	odd	4	inner	770.2.bv.a.157.8	yes	768
7.5	odd	6	inner	770.2.bv.a.663.32	yes	768
11.4	even	5	inner	770.2.bv.a.213.8	yes	768
35.12	even	12	inner	770.2.bv.a.47.8	yes	768
55.37	odd	20	inner	770.2.bv.a.367.32	yes	768
77.26	odd	30	inner	770.2.bv.a.103.8	yes	768
385.257	even	60	inner	770.2.bv.a.257.17	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.17	✓	768	1.1	even	1	trivial
770.2.bv.a.47.8	yes	768	35.12	even	12	inner
770.2.bv.a.103.8	yes	768	77.26	odd	30	inner
770.2.bv.a.157.8	yes	768	5.2	odd	4	inner
770.2.bv.a.213.8	yes	768	11.4	even	5	inner
770.2.bv.a.257.17	yes	768	385.257	even	60	inner
770.2.bv.a.367.32	yes	768	55.37	odd	20	inner
770.2.bv.a.663.32	yes	768	7.5	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-0.933580 + 0.358368i) q^{2} +(1.03126 - 0.669709i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.319857 + 2.21307i) q^{5} +(-0.722763 + 0.994798i) q^{6} +(-2.37940 - 1.15692i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.605220 + 1.35935i) q^{9} +O(q^{10})\)	\(q+(-0.933580 + 0.358368i) q^{2} +(1.03126 - 0.669709i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.319857 + 2.21307i) q^{5} +(-0.722763 + 0.994798i) q^{6} +(-2.37940 - 1.15692i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.605220 + 1.35935i) q^{9} +(-0.494482 - 2.18071i) q^{10} +(1.16436 - 3.10552i) q^{11} +(0.318254 - 1.18774i) q^{12} +(-0.501310 + 3.16515i) q^{13} +(2.63596 + 0.227380i) q^{14} +(1.15226 + 2.49647i) q^{15} +(0.104528 - 0.994522i) q^{16} +(2.44228 + 0.937504i) q^{17} +(0.0778754 - 1.48595i) q^{18} +(-2.34659 + 2.60616i) q^{19} +(1.24313 + 1.85866i) q^{20} +(-3.22858 + 0.400415i) q^{21} +(0.0258983 + 3.31652i) q^{22} +(-1.76370 + 6.58223i) q^{23} +(0.128532 + 1.22290i) q^{24} +(-4.79538 - 1.41574i) q^{25} +(-0.666275 - 3.13458i) q^{26} +(0.863300 + 5.45066i) q^{27} +(-2.54237 + 0.732367i) q^{28} +(-4.23771 - 1.37692i) q^{29} +(-1.97038 - 1.91772i) q^{30} +(3.98581 - 0.418926i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.879039 - 3.98239i) q^{33} -2.61604 q^{34} +(3.32142 - 4.89573i) q^{35} +(0.459814 + 1.41516i) q^{36} +(-6.21460 + 9.56964i) q^{37} +(1.25677 - 3.27400i) q^{38} +(1.60275 + 3.59983i) q^{39} +(-1.82665 - 1.28971i) q^{40} +(-6.29067 + 2.04396i) q^{41} +(2.87064 - 1.53084i) q^{42} +(-2.45310 - 2.45310i) q^{43} +(-1.21271 - 3.08696i) q^{44} +(-2.81475 - 1.77419i) q^{45} +(-0.712301 - 6.77709i) q^{46} +(9.68318 - 0.507474i) q^{47} +(-0.558244 - 1.09562i) q^{48} +(4.32306 + 5.50555i) q^{49} +(4.98423 - 0.396808i) q^{50} +(3.14648 - 0.668806i) q^{51} +(1.74535 + 2.68761i) q^{52} +(0.356291 - 0.439983i) q^{53} +(-2.75930 - 4.77925i) q^{54} +(6.50032 + 3.57013i) q^{55} +(2.11105 - 1.59483i) q^{56} +(-0.674585 + 4.25916i) q^{57} +(4.44969 - 0.233198i) q^{58} +(-6.77339 - 7.52261i) q^{59} +(2.52676 + 1.08423i) q^{60} +(6.73117 + 0.707475i) q^{61} +(-3.57095 + 1.81949i) q^{62} +(3.01272 - 2.53423i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-6.84436 - 2.12183i) q^{65} +(2.24781 + 3.40286i) q^{66} +(3.21747 + 12.0078i) q^{67} +(2.44228 - 0.937504i) q^{68} +(2.58934 + 7.96917i) q^{69} +(-1.34634 + 5.76085i) q^{70} +(2.64170 + 1.91931i) q^{71} +(-0.936422 - 1.15639i) q^{72} +(-11.3434 - 0.594481i) q^{73} +(2.37237 - 11.1611i) q^{74} +(-5.89342 + 1.75152i) q^{75} +3.50693i q^{76} +(-6.36332 + 6.04220i) q^{77} +(-2.78636 - 2.78636i) q^{78} +(-0.395208 + 0.887651i) q^{79} +(2.16752 + 0.549434i) q^{80} +(1.55367 + 1.72552i) q^{81} +(5.14035 - 4.16258i) q^{82} +(1.04404 - 0.165360i) q^{83} +(-2.13137 + 2.45791i) q^{84} +(-2.85595 + 5.10508i) q^{85} +(3.16928 + 1.41105i) q^{86} +(-5.29232 + 1.41807i) q^{87} +(2.23843 + 2.44733i) q^{88} +(-1.35473 - 2.34645i) q^{89} +(3.26361 + 0.647636i) q^{90} +(4.85465 - 6.95117i) q^{91} +(3.09368 + 6.07170i) q^{92} +(3.82985 - 3.10136i) q^{93} +(-8.85817 + 3.94391i) q^{94} +(-5.01704 - 6.02678i) q^{95} +(0.913799 + 0.822789i) q^{96} +(0.117005 + 0.0185318i) q^{97} +(-6.00894 - 3.59063i) q^{98} +(3.51679 + 3.46229i) 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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