LMFDB - Embedded newform 570.2.m.a.493.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(37,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("570.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 $ x^20 + 153x^16 + 6416x^12 + 78648x^8 + 19120x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.9
Root			$-2.19691 - 2.19691i$ of defining polynomial
Character	$\chi$	$=$	570.493
Dual form			570.2.m.a.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.25884 - 1.84806i) q^{5} +1.00000 q^{6} +(3.10690 - 3.10690i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.25884 - 1.84806i) q^{5} +1.00000 q^{6} +(3.10690 - 3.10690i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(2.19691 - 0.416642i) q^{10} -3.82217 q^{11} +(0.707107 + 0.707107i) q^{12} +(-0.0891314 + 0.0891314i) q^{13} +4.39382 q^{14} +(-0.416642 - 2.19691i) q^{15} -1.00000 q^{16} +(-1.83065 + 1.83065i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-2.70268 - 3.41987i) q^{19} +(1.84806 + 1.25884i) q^{20} -4.39382i q^{21} +(-2.70268 - 2.70268i) q^{22} +(2.58922 + 2.58922i) q^{23} +1.00000i q^{24} +(-1.83065 - 4.65282i) q^{25} -0.126051 q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.10690 + 3.10690i) q^{28} +3.60048 q^{29} +(1.25884 - 1.84806i) q^{30} +3.60048i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.70268 + 2.70268i) q^{33} -2.58893 q^{34} +(-1.83065 - 9.65282i) q^{35} +1.00000 q^{36} +(7.07188 + 7.07188i) q^{37} +(0.507128 - 4.32930i) q^{38} +0.126051i q^{39} +(0.416642 + 2.19691i) q^{40} +11.2134i q^{41} +(3.10690 - 3.10690i) q^{42} +(7.93755 + 7.93755i) q^{43} -3.82217i q^{44} +(-1.84806 - 1.25884i) q^{45} +3.66171i q^{46} +(-0.463170 + 0.463170i) q^{47} +(-0.707107 + 0.707107i) q^{48} -12.3056i q^{49} +(1.99558 - 4.58450i) q^{50} +2.58893i q^{51} +(-0.0891314 - 0.0891314i) q^{52} +(-3.21910 + 3.21910i) q^{53} -1.00000i q^{54} +(-4.81150 + 7.06360i) q^{55} +4.39382i q^{56} +(-4.32930 - 0.507128i) q^{57} +(2.54592 + 2.54592i) q^{58} +9.40851 q^{59} +(2.19691 - 0.416642i) q^{60} +8.21380 q^{61} +(-2.54592 + 2.54592i) q^{62} +(-3.10690 - 3.10690i) q^{63} -1.00000i q^{64} +(0.0525181 + 0.276922i) q^{65} -3.82217 q^{66} +(-8.78764 - 8.78764i) q^{67} +(-1.83065 - 1.83065i) q^{68} +3.66171 q^{69} +(5.53111 - 8.12004i) q^{70} +1.66657i q^{71} +(0.707107 + 0.707107i) q^{72} +(-3.64373 - 3.64373i) q^{73} +10.0011i q^{74} +(-4.58450 - 1.99558i) q^{75} +(3.41987 - 2.70268i) q^{76} +(-11.8751 + 11.8751i) q^{77} +(-0.0891314 + 0.0891314i) q^{78} -8.82758 q^{79} +(-1.25884 + 1.84806i) q^{80} -1.00000 q^{81} +(-7.92907 + 7.92907i) q^{82} +(-0.347181 - 0.347181i) q^{83} +4.39382 q^{84} +(1.07866 + 5.68764i) q^{85} +11.2254i q^{86} +(2.54592 - 2.54592i) q^{87} +(2.70268 - 2.70268i) q^{88} -9.79832 q^{89} +(-0.416642 - 2.19691i) q^{90} +0.553844i q^{91} +(-2.58922 + 2.58922i) q^{92} +(2.54592 + 2.54592i) q^{93} -0.655021 q^{94} +(-9.72236 + 0.689653i) q^{95} -1.00000 q^{96} +(-6.88409 - 6.88409i) q^{97} +(8.70140 - 8.70140i) q^{98} +3.82217i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7	$ 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} + 4 q^{17} + 44 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{30} + 4 q^{35} + 20 q^{36} - 4 q^{38} - 4 q^{42} + 52 q^{43} + 4 q^{47} + 16 q^{55} - 4 q^{57} + 8 q^{58} + 32 q^{61} - 8 q^{62} + 4 q^{63} - 8 q^{66} + 4 q^{68} - 20 q^{73} + 20 q^{76} - 24 q^{77} + 4 q^{80} - 20 q^{81} - 24 q^{82} - 116 q^{83} - 60 q^{85} + 8 q^{87} - 44 q^{92} + 8 q^{93} - 32 q^{95} - 20 q^{96}+O(q^{100}) $ 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 + 4 * q^17 + 44 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^30 + 4 * q^35 + 20 * q^36 - 4 * q^38 - 4 * q^42 + 52 * q^43 + 4 * q^47 + 16 * q^55 - 4 * q^57 + 8 * q^58 + 32 * q^61 - 8 * q^62 + 4 * q^63 - 8 * q^66 + 4 * q^68 - 20 * q^73 + 20 * q^76 - 24 * q^77 + 4 * q^80 - 20 * q^81 - 24 * q^82 - 116 * q^83 - 60 * q^85 + 8 * q^87 - 44 * q^92 + 8 * q^93 - 32 * q^95 - 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	1.25884	−	1.84806i	0.562970	−	0.826477i
$5$	1.25884	−	1.84806i	0.562970	−	0.826477i
$6$	1.00000			0.408248
$7$	3.10690	−	3.10690i	1.17430	−	1.17430i	0.193123	−	0.981175i	$-0.438138\pi$
$7$	3.10690	−	3.10690i	1.17430	−	1.17430i	0.981175	−	0.193123i	$-0.0618615\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	2.19691	−	0.416642i	0.694724	−	0.131754i
$11$	−3.82217			−1.15243			−0.576214	−	0.817299i	$-0.695470\pi$
$11$	−3.82217			−1.15243			−0.576214	+	0.817299i	$0.695470\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−0.0891314	+	0.0891314i	−0.0247206	+	0.0247206i	−0.719359	−	0.694638i	$-0.755564\pi$
$13$	−0.0891314	+	0.0891314i	−0.0247206	+	0.0247206i	0.694638	+	0.719359i	$0.255564\pi$
$14$	4.39382			1.17430
$15$	−0.416642	−	2.19691i	−0.107576	−	0.567239i
$16$	−1.00000			−0.250000
$17$	−1.83065	+	1.83065i	−0.443998	+	0.443998i	−0.893353	−	0.449355i	$-0.851654\pi$
$17$	−1.83065	+	1.83065i	−0.443998	+	0.443998i	0.449355	+	0.893353i	$0.351654\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−2.70268	−	3.41987i	−0.620038	−	0.784572i
$19$	−2.70268	−	3.41987i	−0.620038	−	0.784572i
$20$	1.84806	+	1.25884i	0.413239	+	0.281485i
$21$		−	4.39382i		−	0.958810i
$22$	−2.70268	−	2.70268i	−0.576214	−	0.576214i
$23$	2.58922	+	2.58922i	0.539890	+	0.539890i	0.923497	−	0.383607i	$-0.125318\pi$
$23$	2.58922	+	2.58922i	0.539890	+	0.539890i	−0.383607	+	0.923497i	$0.625318\pi$
$24$			1.00000i			0.204124i
$25$	−1.83065	−	4.65282i	−0.366130	−	0.930564i
$26$	−0.126051			−0.0247206
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	3.10690	+	3.10690i	0.587149	+	0.587149i
$29$	3.60048			0.668591			0.334296	−	0.942468i	$-0.391502\pi$
$29$	3.60048			0.668591			0.334296	+	0.942468i	$0.391502\pi$
$30$	1.25884	−	1.84806i	0.229832	−	0.337408i
$31$			3.60048i			0.646664i	0.946286	+	0.323332i	$0.104803\pi$
$31$			3.60048i			0.646664i	−0.946286	+	0.323332i	$0.895197\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.70268	+	2.70268i	−0.470477	+	0.470477i
$34$	−2.58893			−0.443998
$35$	−1.83065	−	9.65282i	−0.309436	−	1.63162i
$36$	1.00000			0.166667
$37$	7.07188	+	7.07188i	1.16261	+	1.16261i	0.983902	+	0.178707i	$0.0571915\pi$
$37$	7.07188	+	7.07188i	1.16261	+	1.16261i	0.178707	+	0.983902i	$0.442808\pi$
$38$	0.507128	−	4.32930i	0.0822670	−	0.702305i
$39$			0.126051i			0.0201843i
$40$	0.416642	+	2.19691i	0.0658769	+	0.347362i
$41$			11.2134i			1.75124i	0.483002	+	0.875619i	$0.339546\pi$
$41$			11.2134i			1.75124i	−0.483002	+	0.875619i	$0.660454\pi$
$42$	3.10690	−	3.10690i	0.479405	−	0.479405i
$43$	7.93755	+	7.93755i	1.21046	+	1.21046i	0.970874	+	0.239591i	$0.0770132\pi$
$43$	7.93755	+	7.93755i	1.21046	+	1.21046i	0.239591	+	0.970874i	$0.422987\pi$
$44$		−	3.82217i		−	0.576214i
$45$	−1.84806	−	1.25884i	−0.275492	−	0.187657i
$46$			3.66171i			0.539890i
$47$	−0.463170	+	0.463170i	−0.0675603	+	0.0675603i	−0.740080	−	0.672519i	$-0.765212\pi$
$47$	−0.463170	+	0.463170i	−0.0675603	+	0.0675603i	0.672519	+	0.740080i	$0.265212\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	12.3056i		−	1.75795i
$50$	1.99558	−	4.58450i	0.282217	−	0.648347i
$51$			2.58893i			0.362523i
$52$	−0.0891314	−	0.0891314i	−0.0123603	−	0.0123603i
$53$	−3.21910	+	3.21910i	−0.442178	+	0.442178i	−0.892743	−	0.450566i	$-0.851222\pi$
$53$	−3.21910	+	3.21910i	−0.442178	+	0.442178i	0.450566	+	0.892743i	$0.351222\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−4.81150	+	7.06360i	−0.648782	+	0.952455i
$56$			4.39382i			0.587149i
$57$	−4.32930	−	0.507128i	−0.573430	−	0.0671707i
$58$	2.54592	+	2.54592i	0.334296	+	0.334296i
$59$	9.40851			1.22488			0.612442	−	0.790516i	$-0.290187\pi$
$59$	9.40851			1.22488			0.612442	+	0.790516i	$0.290187\pi$
$60$	2.19691	−	0.416642i	0.283620	−	0.0537882i
$61$	8.21380			1.05167			0.525834	−	0.850587i	$-0.323753\pi$
$61$	8.21380			1.05167			0.525834	+	0.850587i	$0.323753\pi$
$62$	−2.54592	+	2.54592i	−0.323332	+	0.323332i
$63$	−3.10690	−	3.10690i	−0.391432	−	0.391432i
$64$		−	1.00000i		−	0.125000i
$65$	0.0525181	+	0.276922i	0.00651406	+	0.0343480i
$66$	−3.82217			−0.470477
$67$	−8.78764	−	8.78764i	−1.07358	−	1.07358i	−0.997069	−	0.0765120i	$-0.975622\pi$
$67$	−8.78764	−	8.78764i	−1.07358	−	1.07358i	−0.0765120	−	0.997069i	$-0.524378\pi$
$68$	−1.83065	−	1.83065i	−0.221999	−	0.221999i
$69$	3.66171			0.440818
$70$	5.53111	−	8.12004i	0.661094	−	0.970530i
$71$			1.66657i			0.197785i	0.995098	+	0.0988926i	$0.0315300\pi$
$71$			1.66657i			0.197785i	−0.995098	+	0.0988926i	$0.968470\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−3.64373	−	3.64373i	−0.426466	−	0.426466i	0.460957	−	0.887423i	$-0.347506\pi$
$73$	−3.64373	−	3.64373i	−0.426466	−	0.426466i	−0.887423	+	0.460957i	$0.847506\pi$
$74$			10.0011i			1.16261i
$75$	−4.58450	−	1.99558i	−0.529373	−	0.230429i
$76$	3.41987	−	2.70268i	0.392286	−	0.310019i
$77$	−11.8751	+	11.8751i	−1.35329	+	1.35329i
$78$	−0.0891314	+	0.0891314i	−0.0100921	+	0.0100921i
$79$	−8.82758			−0.993180			−0.496590	−	0.867985i	$-0.665415\pi$
$79$	−8.82758			−0.993180			−0.496590	+	0.867985i	$0.665415\pi$
$80$	−1.25884	+	1.84806i	−0.140742	+	0.206619i
$81$	−1.00000			−0.111111
$82$	−7.92907	+	7.92907i	−0.875619	+	0.875619i
$83$	−0.347181	−	0.347181i	−0.0381081	−	0.0381081i	0.687796	−	0.725904i	$-0.258578\pi$
$83$	−0.347181	−	0.347181i	−0.0381081	−	0.0381081i	−0.725904	+	0.687796i	$0.758578\pi$
$84$	4.39382			0.479405
$85$	1.07866	+	5.68764i	0.116997	+	0.616911i
$86$			11.2254i			1.21046i
$87$	2.54592	−	2.54592i	0.272951	−	0.272951i
$88$	2.70268	−	2.70268i	0.288107	−	0.288107i
$89$	−9.79832			−1.03862			−0.519310	−	0.854586i	$-0.673811\pi$
$89$	−9.79832			−1.03862			−0.519310	+	0.854586i	$0.673811\pi$
$90$	−0.416642	−	2.19691i	−0.0439179	−	0.231575i
$91$			0.553844i			0.0580587i
$92$	−2.58922	+	2.58922i	−0.269945	+	0.269945i
$93$	2.54592	+	2.54592i	0.264000	+	0.264000i
$94$	−0.655021			−0.0675603
$95$	−9.72236	+	0.689653i	−0.997494	+	0.0707569i
$96$	−1.00000			−0.102062
$97$	−6.88409	−	6.88409i	−0.698973	−	0.698973i	0.265216	−	0.964189i	$-0.414557\pi$
$97$	−6.88409	−	6.88409i	−0.698973	−	0.698973i	−0.964189	+	0.265216i	$0.914557\pi$
$98$	8.70140	−	8.70140i	0.878974	−	0.878974i
$99$			3.82217i			0.384143i
$100$	4.65282	−	1.83065i	0.465282	−	0.183065i
$101$	−3.89174			−0.387242			−0.193621	−	0.981076i	$-0.562023\pi$
$101$	−3.89174			−0.387242			−0.193621	+	0.981076i	$0.562023\pi$
$102$	−1.83065	+	1.83065i	−0.181261	+	0.181261i
$103$	9.40518	−	9.40518i	0.926720	−	0.926720i	−0.0707726	−	0.997492i	$-0.522546\pi$
$103$	9.40518	−	9.40518i	0.926720	−	0.926720i	0.997492	+	0.0707726i	$0.0225465\pi$
$104$		−	0.126051i		−	0.0123603i
$105$	−8.12004	−	5.53111i	−0.792435	−	0.539781i
$106$	−4.55250			−0.442178
$107$	−7.00983	−	7.00983i	−0.677666	−	0.677666i	0.281806	−	0.959472i	$-0.409067\pi$
$107$	−7.00983	−	7.00983i	−0.677666	−	0.677666i	−0.959472	+	0.281806i	$0.909067\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	17.7935			1.70431			0.852153	−	0.523293i	$-0.175297\pi$
$109$	17.7935			1.70431			0.852153	+	0.523293i	$0.175297\pi$
$110$	−8.39696	+	1.59248i	−0.800619	+	0.151837i
$111$	10.0011			0.949267
$112$	−3.10690	+	3.10690i	−0.293574	+	0.293574i
$113$	−12.4493	+	12.4493i	−1.17114	+	1.17114i	−0.189197	+	0.981939i	$0.560588\pi$
$113$	−12.4493	+	12.4493i	−1.17114	+	1.17114i	−0.981939	+	0.189197i	$0.939412\pi$
$114$	−2.70268	−	3.41987i	−0.253129	−	0.320300i
$115$	8.04445	−	1.52562i	0.750148	−	0.142265i
$116$			3.60048i			0.334296i
$117$	0.0891314	+	0.0891314i	0.00824020	+	0.00824020i
$118$	6.65282	+	6.65282i	0.612442	+	0.612442i
$119$			11.3753i			1.04277i
$120$	1.84806	+	1.25884i	0.168704	+	0.114916i
$121$	3.60898			0.328089
$122$	5.80803	+	5.80803i	0.525834	+	0.525834i
$123$	7.92907	+	7.92907i	0.714940	+	0.714940i
$124$	−3.60048			−0.323332
$125$	−10.9032	−	2.47400i	−0.975210	−	0.221281i
$126$		−	4.39382i		−	0.391432i
$127$	0.0636986	+	0.0636986i	0.00565234	+	0.00565234i	0.709927	−	0.704275i	$-0.248728\pi$
$127$	0.0636986	+	0.0636986i	0.00565234	+	0.00565234i	−0.704275	+	0.709927i	$0.748728\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	11.2254			0.988340
$130$	−0.158678	+	0.232949i	−0.0139170	+	0.0204310i
$131$	2.44811			0.213893			0.106946	−	0.994265i	$-0.465893\pi$
$131$	2.44811			0.213893			0.106946	+	0.994265i	$0.465893\pi$
$132$	−2.70268	−	2.70268i	−0.235238	−	0.235238i
$133$	−19.0221	−	2.22823i	−1.64943	−	0.193212i
$134$		−	12.4276i		−	1.07358i
$135$	−2.19691	+	0.416642i	−0.189080	+	0.0358588i
$136$		−	2.58893i		−	0.221999i
$137$	3.02688	−	3.02688i	0.258604	−	0.258604i	−0.565882	−	0.824486i	$-0.691464\pi$
$137$	3.02688	−	3.02688i	0.258604	−	0.258604i	0.824486	+	0.565882i	$0.191464\pi$
$138$	2.58922	+	2.58922i	0.220409	+	0.220409i
$139$		−	3.96170i		−	0.336027i	−0.985785	−	0.168013i	$-0.946265\pi$
$139$		−	3.96170i		−	0.336027i	0.985785	−	0.168013i	$-0.0537352\pi$
$140$	9.65282	−	1.83065i	0.815812	−	0.154718i
$141$			0.655021i			0.0551627i
$142$	−1.17844	+	1.17844i	−0.0988926	+	0.0988926i
$143$	0.340675	−	0.340675i	0.0284887	−	0.0284887i
$144$			1.00000i			0.0833333i
$145$	4.53242	−	6.65389i	0.376397	−	0.552576i
$146$		−	5.15301i		−	0.426466i
$147$	−8.70140	−	8.70140i	−0.717679	−	0.717679i
$148$	−7.07188	+	7.07188i	−0.581305	+	0.581305i
$149$			22.3940i			1.83459i	0.398211	+	0.917294i	$0.369631\pi$
$149$			22.3940i			1.83459i	−0.398211	+	0.917294i	$0.630369\pi$
$150$	−1.83065	−	4.65282i	−0.149472	−	0.379901i
$151$		−	11.2995i		−	0.919539i	−0.888038	−	0.459769i	$-0.847932\pi$
$151$		−	11.2995i		−	0.919539i	0.888038	−	0.459769i	$-0.152068\pi$
$152$	4.32930	+	0.507128i	0.351152	+	0.0411335i
$153$	1.83065	+	1.83065i	0.147999	+	0.147999i
$154$	−16.7939			−1.35329
$155$	6.65389	+	4.53242i	0.534454	+	0.364053i
$156$	−0.126051			−0.0100921
$157$	−4.57916	+	4.57916i	−0.365457	+	0.365457i	−0.865817	−	0.500361i	$-0.833201\pi$
$157$	−4.57916	+	4.57916i	−0.365457	+	0.365457i	0.500361	+	0.865817i	$0.333201\pi$
$158$	−6.24204	−	6.24204i	−0.496590	−	0.496590i
$159$			4.55250i			0.361037i
$160$	−2.19691	+	0.416642i	−0.173681	+	0.0329384i
$161$	16.0889			1.26798
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	7.54592	+	7.54592i	0.591042	+	0.591042i	0.937913	−	0.346871i	$-0.112756\pi$
$163$	7.54592	+	7.54592i	0.591042	+	0.591042i	−0.346871	+	0.937913i	$0.612756\pi$
$164$	−11.2134			−0.875619
$165$	1.59248	+	8.39696i	0.123974	+	0.653702i
$166$		−	0.490988i		−	0.0381081i
$167$	−15.1275	−	15.1275i	−1.17060	−	1.17060i	−0.982067	−	0.188531i	$-0.939627\pi$
$167$	−15.1275	−	15.1275i	−1.17060	−	1.17060i	−0.188531	−	0.982067i	$-0.560373\pi$
$168$	3.10690	+	3.10690i	0.239702	+	0.239702i
$169$			12.9841i			0.998778i
$170$	−3.25904	+	4.78449i	−0.249957	+	0.366954i
$171$	−3.41987	+	2.70268i	−0.261524	+	0.206679i
$172$	−7.93755	+	7.93755i	−0.605232	+	0.605232i
$173$	2.32458	−	2.32458i	0.176735	−	0.176735i	−0.613196	−	0.789931i	$-0.710116\pi$
$173$	2.32458	−	2.32458i	0.176735	−	0.176735i	0.789931	+	0.613196i	$0.210116\pi$
$174$	3.60048			0.272951
$175$	−20.1435	−	8.76820i	−1.52270	−	0.662813i
$176$	3.82217			0.288107
$177$	6.65282	−	6.65282i	0.500056	−	0.500056i
$178$	−6.92846	−	6.92846i	−0.519310	−	0.519310i
$179$	0.515834			0.0385553			0.0192776	−	0.999814i	$-0.493863\pi$
$179$	0.515834			0.0385553			0.0192776	+	0.999814i	$0.493863\pi$
$180$	1.25884	−	1.84806i	0.0938283	−	0.137746i
$181$		−	4.86127i		−	0.361336i	−0.983544	−	0.180668i	$-0.942174\pi$
$181$		−	4.86127i		−	0.361336i	0.983544	−	0.180668i	$-0.0578259\pi$
$182$	−0.391627	+	0.391627i	−0.0290293	+	0.0290293i
$183$	5.80803	−	5.80803i	0.429342	−	0.429342i
$184$	−3.66171			−0.269945
$185$	21.9716	−	4.16690i	1.61538	−	0.306356i
$186$			3.60048i			0.264000i
$187$	6.99705	−	6.99705i	0.511675	−	0.511675i
$188$	−0.463170	−	0.463170i	−0.0337801	−	0.0337801i
$189$	−4.39382			−0.319603
$190$	−7.36241	−	6.38709i	−0.534125	−	0.463368i
$191$	−15.3369			−1.10974			−0.554870	−	0.831937i	$-0.687232\pi$
$191$	−15.3369			−1.10974			−0.554870	+	0.831937i	$0.687232\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−17.1600	+	17.1600i	−1.23521	+	1.23521i	−0.273268	+	0.961938i	$0.588105\pi$
$193$	−17.1600	+	17.1600i	−1.23521	+	1.23521i	−0.961938	+	0.273268i	$0.911895\pi$
$194$		−	9.73557i		−	0.698973i
$195$	0.232949	+	0.158678i	0.0166819	+	0.0113631i
$196$	12.3056			0.878974
$197$	−6.25052	+	6.25052i	−0.445331	+	0.445331i	−0.893799	−	0.448468i	$-0.851970\pi$
$197$	−6.25052	+	6.25052i	−0.445331	+	0.445331i	0.448468	+	0.893799i	$0.351970\pi$
$198$	−2.70268	+	2.70268i	−0.192071	+	0.192071i
$199$		−	10.4094i		−	0.737904i	−0.929448	−	0.368952i	$-0.879717\pi$
$199$		−	10.4094i		−	0.737904i	0.929448	−	0.368952i	$-0.120283\pi$
$200$	4.58450	+	1.99558i	0.324173	+	0.141109i
$201$	−12.4276			−0.876575
$202$	−2.75187	−	2.75187i	−0.193621	−	0.193621i
$203$	11.1863	−	11.1863i	0.785125	−	0.785125i
$204$	−2.58893			−0.181261
$205$	20.7230	+	14.1159i	1.44736	+	0.985894i
$206$	13.3009			0.926720
$207$	2.58922	−	2.58922i	0.179963	−	0.179963i
$208$	0.0891314	−	0.0891314i	0.00618015	−	0.00618015i
$209$	10.3301	+	13.0713i	0.714549	+	0.904162i
$210$	−1.83065	−	9.65282i	−0.126327	−	0.666108i
$211$		−	13.0551i		−	0.898752i	−0.893343	−	0.449376i	$-0.851646\pi$
$211$		−	13.0551i		−	0.898752i	0.893343	−	0.449376i	$-0.148354\pi$
$212$	−3.21910	−	3.21910i	−0.221089	−	0.221089i
$213$	1.17844	+	1.17844i	0.0807455	+	0.0807455i
$214$		−	9.91340i		−	0.677666i
$215$	24.6612	−	4.67697i	1.68188	−	0.318967i
$216$	1.00000			0.0680414
$217$	11.1863	+	11.1863i	0.759376	+	0.759376i
$218$	12.5819	+	12.5819i	0.852153	+	0.852153i
$219$	−5.15301			−0.348208
$220$	−7.06360	−	4.81150i	−0.476228	−	0.324391i
$221$		−	0.326337i		−	0.0219518i
$222$	7.07188	+	7.07188i	0.474633	+	0.474633i
$223$	−11.5414	+	11.5414i	−0.772872	+	0.772872i	−0.978608	−	0.205736i	$-0.934041\pi$
$223$	−11.5414	+	11.5414i	−0.772872	+	0.772872i	0.205736	+	0.978608i	$0.434041\pi$
$224$	−4.39382			−0.293574
$225$	−4.65282	+	1.83065i	−0.310188	+	0.122043i
$226$	−17.6060			−1.17114
$227$	−16.4312	−	16.4312i	−1.09058	−	1.09058i	−0.995467	−	0.0951099i	$-0.969680\pi$
$227$	−16.4312	−	16.4312i	−1.09058	−	1.09058i	−0.0951099	−	0.995467i	$-0.530320\pi$
$228$	0.507128	−	4.32930i	0.0335854	−	0.286715i
$229$		−	15.5194i		−	1.02555i	−0.858522	−	0.512777i	$-0.828617\pi$
$229$		−	15.5194i		−	1.02555i	0.858522	−	0.512777i	$-0.171383\pi$
$230$	6.76706	+	4.60950i	0.446207	+	0.303942i
$231$			16.7939i			1.10496i
$232$	−2.54592	+	2.54592i	−0.167148	+	0.167148i
$233$	−1.69112	−	1.69112i	−0.110789	−	0.110789i	0.649539	−	0.760328i	$-0.274962\pi$
$233$	−1.69112	−	1.69112i	−0.110789	−	0.110789i	−0.760328	+	0.649539i	$0.774962\pi$
$234$			0.126051i			0.00824020i
$235$	0.272909	+	1.43902i	0.0178026	+	0.0938714i
$236$			9.40851i			0.612442i
$237$	−6.24204	+	6.24204i	−0.405464	+	0.405464i
$238$	−8.04354	+	8.04354i	−0.521385	+	0.521385i
$239$		−	12.9971i		−	0.840714i	−0.907359	−	0.420357i	$-0.861905\pi$
$239$		−	12.9971i		−	0.840714i	0.907359	−	0.420357i	$-0.138095\pi$
$240$	0.416642	+	2.19691i	0.0268941	+	0.141810i
$241$		−	8.64001i		−	0.556552i	−0.960501	−	0.278276i	$-0.910237\pi$
$241$		−	8.64001i		−	0.556552i	0.960501	−	0.278276i	$-0.0897630\pi$
$242$	2.55194	+	2.55194i	0.164045	+	0.164045i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$			8.21380i			0.525834i
$245$	−22.7416	−	15.4908i	−1.45290	−	0.989672i
$246$			11.2134i			0.714940i
$247$	0.545712	+	0.0639239i	0.0347228	+	0.00406738i
$248$	−2.54592	−	2.54592i	−0.161666	−	0.161666i
$249$	−0.490988			−0.0311151
$250$	−5.96033	−	9.45910i	−0.376964	−	0.598246i
$251$	23.6590			1.49334			0.746670	−	0.665194i	$-0.231651\pi$
$251$	23.6590			1.49334			0.746670	+	0.665194i	$0.231651\pi$
$252$	3.10690	−	3.10690i	0.195716	−	0.195716i
$253$	−9.89644	−	9.89644i	−0.622184	−	0.622184i
$254$			0.0900835i			0.00565234i
$255$	4.78449	+	3.25904i	0.299617	+	0.204089i
$256$	1.00000			0.0625000
$257$	−8.63732	−	8.63732i	−0.538781	−	0.538781i	0.384390	−	0.923171i	$-0.374412\pi$
$257$	−8.63732	−	8.63732i	−0.538781	−	0.538781i	−0.923171	+	0.384390i	$0.874412\pi$
$258$	7.93755	+	7.93755i	0.494170	+	0.494170i
$259$	43.9432			2.73050
$260$	−0.276922	+	0.0525181i	−0.0171740	+	0.00325703i
$261$		−	3.60048i		−	0.222864i
$262$	1.73108	+	1.73108i	0.106946	+	0.106946i
$263$	10.9291	+	10.9291i	0.673915	+	0.673915i	0.958616	−	0.284701i	$-0.0918943\pi$
$263$	10.9291	+	10.9291i	0.673915	+	0.673915i	−0.284701	+	0.958616i	$0.591894\pi$
$264$		−	3.82217i		−	0.235238i
$265$	1.89676	+	10.0014i	0.116517	+	0.614383i
$266$	−11.8751	−	15.0263i	−0.728109	−	0.921321i
$267$	−6.92846	+	6.92846i	−0.424015	+	0.424015i
$268$	8.78764	−	8.78764i	0.536790	−	0.536790i
$269$	13.8523			0.844591			0.422296	−	0.906458i	$-0.361224\pi$
$269$	13.8523			0.844591			0.422296	+	0.906458i	$0.361224\pi$
$270$	−1.84806	−	1.25884i	−0.112469	−	0.0766105i
$271$	14.8370			0.901284			0.450642	−	0.892705i	$-0.351195\pi$
$271$	14.8370			0.901284			0.450642	+	0.892705i	$0.351195\pi$
$272$	1.83065	−	1.83065i	0.110999	−	0.110999i
$273$	0.391627	+	0.391627i	0.0237024	+	0.0237024i
$274$	4.28065			0.258604
$275$	6.99705	+	17.7839i	0.421938	+	1.07241i
$276$			3.66171i			0.220409i
$277$	−8.95723	+	8.95723i	−0.538188	+	0.538188i	−0.922996	−	0.384808i	$-0.874268\pi$
$277$	−8.95723	+	8.95723i	−0.538188	+	0.538188i	0.384808	+	0.922996i	$0.374268\pi$
$278$	2.80134	−	2.80134i	0.168013	−	0.168013i
$279$	3.60048			0.215555
$280$	8.12004	+	5.53111i	0.485265	+	0.330547i
$281$		−	6.13940i		−	0.366246i	−0.983090	−	0.183123i	$-0.941379\pi$
$281$		−	6.13940i		−	0.366246i	0.983090	−	0.183123i	$-0.0586207\pi$
$282$	−0.463170	+	0.463170i	−0.0275814	+	0.0275814i
$283$	−22.7963	−	22.7963i	−1.35510	−	1.35510i	−0.879853	−	0.475246i	$-0.842359\pi$
$283$	−22.7963	−	22.7963i	−1.35510	−	1.35510i	−0.475246	−	0.879853i	$-0.657641\pi$
$284$	−1.66657			−0.0988926
$285$	−6.38709	+	7.36241i	−0.378339	+	0.436111i
$286$	0.481788			0.0284887
$287$	34.8389	+	34.8389i	2.05647	+	2.05647i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			10.2974i			0.605732i
$290$	7.90992	−	1.50011i	0.464486	−	0.0880894i
$291$	−9.73557			−0.570709
$292$	3.64373	−	3.64373i	0.213233	−	0.213233i
$293$	−0.341431	+	0.341431i	−0.0199466	+	0.0199466i	−0.717010	−	0.697063i	$-0.754490\pi$
$293$	−0.341431	+	0.341431i	−0.0199466	+	0.0199466i	0.697063	+	0.717010i	$0.254490\pi$
$294$		−	12.3056i		−	0.717679i
$295$	11.8438	−	17.3875i	0.689572	−	1.01234i
$296$	−10.0011			−0.581305
$297$	2.70268	+	2.70268i	0.156826	+	0.156826i
$298$	−15.8349	+	15.8349i	−0.917294	+	0.917294i
$299$	−0.461562			−0.0266928
$300$	1.99558	−	4.58450i	0.115215	−	0.264686i
$301$	49.3223			2.84289
$302$	7.98994	−	7.98994i	0.459769	−	0.459769i
$303$	−2.75187	+	2.75187i	−0.158091	+	0.158091i
$304$	2.70268	+	3.41987i	0.155009	+	0.196143i
$305$	10.3398	−	15.1796i	0.592058	−	0.869181i
$306$			2.58893i			0.147999i
$307$	18.0543	+	18.0543i	1.03041	+	1.03041i	0.999523	+	0.0308888i	$0.00983377\pi$
$307$	18.0543	+	18.0543i	1.03041	+	1.03041i	0.0308888	+	0.999523i	$0.490166\pi$
$308$	−11.8751	−	11.8751i	−0.676646	−	0.676646i
$309$		−	13.3009i		−	0.756664i
$310$	1.50011	+	7.90992i	0.0852005	+	0.449253i
$311$	5.73086			0.324967			0.162484	−	0.986711i	$-0.448049\pi$
$311$	5.73086			0.324967			0.162484	+	0.986711i	$0.448049\pi$
$312$	−0.0891314	−	0.0891314i	−0.00504607	−	0.00504607i
$313$	22.1761	+	22.1761i	1.25347	+	1.25347i	0.954155	+	0.299312i	$0.0967572\pi$
$313$	22.1761	+	22.1761i	1.25347	+	1.25347i	0.299312	+	0.954155i	$0.403243\pi$
$314$	−6.47591			−0.365457
$315$	−9.65282	+	1.83065i	−0.543875	+	0.103145i
$316$		−	8.82758i		−	0.496590i
$317$	−11.0630	−	11.0630i	−0.621359	−	0.621359i	0.324520	−	0.945879i	$-0.394797\pi$
$317$	−11.0630	−	11.0630i	−0.621359	−	0.621359i	−0.945879	+	0.324520i	$0.894797\pi$
$318$	−3.21910	+	3.21910i	−0.180518	+	0.180518i
$319$	−13.7616			−0.770503
$320$	−1.84806	−	1.25884i	−0.103310	−	0.0703712i
$321$	−9.91340			−0.553312
$322$	11.3766	+	11.3766i	0.633991	+	0.633991i
$323$	11.2082	+	1.31292i	0.623643	+	0.0730527i
$324$		−	1.00000i		−	0.0555556i
$325$	0.577881	+	0.251544i	0.0320550	+	0.0139531i
$326$			10.6715i			0.591042i
$327$	12.5819	−	12.5819i	0.695780	−	0.695780i
$328$	−7.92907	−	7.92907i	−0.437810	−	0.437810i
$329$			2.87804i			0.158672i
$330$	−4.81150	+	7.06360i	−0.264864	+	0.388838i
$331$		−	11.7959i		−	0.648364i	−0.945995	−	0.324182i	$-0.894911\pi$
$331$		−	11.7959i		−	0.648364i	0.945995	−	0.324182i	$-0.105089\pi$
$332$	0.347181	−	0.347181i	0.0190540	−	0.0190540i
$333$	7.07188	−	7.07188i	0.387537	−	0.387537i
$334$		−	21.3935i		−	1.17060i
$335$	−27.3023	+	5.17786i	−1.49168	+	0.282897i
$336$			4.39382i			0.239702i
$337$	10.9001	+	10.9001i	0.593765	+	0.593765i	0.938646	−	0.344881i	$-0.112081\pi$
$337$	10.9001	+	10.9001i	0.593765	+	0.593765i	−0.344881	+	0.938646i	$0.612081\pi$
$338$	−9.18115	+	9.18115i	−0.499389	+	0.499389i
$339$			17.6060i			0.956229i
$340$	−5.68764	+	1.07866i	−0.308456	+	0.0584983i
$341$		−	13.7616i		−	0.745234i
$342$	−4.32930	−	0.507128i	−0.234102	−	0.0274223i
$343$	−16.4841	−	16.4841i	−0.890057	−	0.890057i
$344$	−11.2254			−0.605232
$345$	4.60950	−	6.76706i	0.248167	−	0.364326i
$346$	3.28746			0.176735
$347$	15.9014	−	15.9014i	0.853630	−	0.853630i	−0.136948	−	0.990578i	$-0.543729\pi$
$347$	15.9014	−	15.9014i	0.853630	−	0.853630i	0.990578	+	0.136948i	$0.0437295\pi$
$348$	2.54592	+	2.54592i	0.136476	+	0.136476i
$349$			14.0170i			0.750311i	0.926962	+	0.375155i	$0.122411\pi$
$349$			14.0170i			0.750311i	−0.926962	+	0.375155i	$0.877589\pi$
$350$	−8.04354	−	20.4436i	−0.429945	−	1.09276i
$351$	0.126051			0.00672810
$352$	2.70268	+	2.70268i	0.144053	+	0.144053i
$353$	−1.70112	−	1.70112i	−0.0905412	−	0.0905412i	0.660386	−	0.750927i	$-0.270393\pi$
$353$	−1.70112	−	1.70112i	−0.0905412	−	0.0905412i	−0.750927	+	0.660386i	$0.770393\pi$
$354$	9.40851			0.500056
$355$	3.07992	+	2.09794i	0.163465	+	0.111347i
$356$		−	9.79832i		−	0.519310i
$357$	8.04354	+	8.04354i	0.425709	+	0.425709i
$358$	0.364750	+	0.364750i	0.0192776	+	0.0192776i
$359$		−	36.9693i		−	1.95117i	−0.219633	−	0.975583i	$-0.570486\pi$
$359$		−	36.9693i		−	1.95117i	0.219633	−	0.975583i	$-0.429514\pi$
$360$	2.19691	−	0.416642i	0.115787	−	0.0219590i
$361$	−4.39102	+	18.4856i	−0.231106	+	0.972929i
$362$	3.43744	−	3.43744i	0.180668	−	0.180668i
$363$	2.55194	−	2.55194i	0.133942	−	0.133942i
$364$	−0.553844			−0.0290293
$365$	−11.3207	+	2.14696i	−0.592552	+	0.112377i
$366$	8.21380			0.429342
$367$	−11.7866	+	11.7866i	−0.615255	+	0.615255i	−0.944311	−	0.329055i	$-0.893270\pi$
$367$	−11.7866	+	11.7866i	−0.615255	+	0.615255i	0.329055	+	0.944311i	$0.393270\pi$
$368$	−2.58922	−	2.58922i	−0.134972	−	0.134972i
$369$	11.2134			0.583746
$370$	18.4827	+	12.5898i	0.960871	+	0.654514i
$371$			20.0029i			1.03850i
$372$	−2.54592	+	2.54592i	−0.132000	+	0.132000i
$373$	−9.29229	+	9.29229i	−0.481137	+	0.481137i	−0.905495	−	0.424358i	$-0.860500\pi$
$373$	−9.29229	+	9.29229i	−0.481137	+	0.481137i	0.424358	+	0.905495i	$0.360500\pi$
$374$	9.89533			0.511675
$375$	−9.45910	+	5.96033i	−0.488466	+	0.307790i
$376$		−	0.655021i		−	0.0337801i
$377$	−0.320915	+	0.320915i	−0.0165280	+	0.0165280i
$378$	−3.10690	−	3.10690i	−0.159802	−	0.159802i
$379$	−9.08999			−0.466921			−0.233461	−	0.972366i	$-0.575005\pi$
$379$	−9.08999			−0.466921			−0.233461	+	0.972366i	$0.575005\pi$
$380$	−0.689653	−	9.72236i	−0.0353785	−	0.498747i
$381$	0.0900835			0.00461512
$382$	−10.8448	−	10.8448i	−0.554870	−	0.554870i
$383$	−2.91923	+	2.91923i	−0.149166	+	0.149166i	−0.777745	−	0.628579i	$-0.783637\pi$
$383$	−2.91923	+	2.91923i	−0.149166	+	0.149166i	0.628579	+	0.777745i	$0.283637\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	6.99705	+	36.8947i	0.356603	+	1.88033i
$386$	−24.2679			−1.23521
$387$	7.93755	−	7.93755i	0.403488	−	0.403488i
$388$	6.88409	−	6.88409i	0.349487	−	0.349487i
$389$		−	25.2850i		−	1.28200i	−0.767540	−	0.641001i	$-0.778519\pi$
$389$		−	25.2850i		−	1.28200i	0.767540	−	0.641001i	$-0.221481\pi$
$390$	0.0525181	+	0.276922i	0.00265936	+	0.0140225i
$391$	−9.47991			−0.479420
$392$	8.70140	+	8.70140i	0.439487	+	0.439487i
$393$	1.73108	−	1.73108i	0.0873213	−	0.0873213i
$394$	−8.83957			−0.445331
$395$	−11.1125	+	16.3139i	−0.559130	+	0.820841i
$396$	−3.82217			−0.192071
$397$	11.4572	−	11.4572i	0.575020	−	0.575020i	−0.358507	−	0.933527i	$-0.616714\pi$
$397$	11.4572	−	11.4572i	0.575020	−	0.575020i	0.933527	+	0.358507i	$0.116714\pi$
$398$	7.36057	−	7.36057i	0.368952	−	0.368952i
$399$	−15.0263	+	11.8751i	−0.752255	+	0.594498i
$400$	1.83065	+	4.65282i	0.0915324	+	0.232641i
$401$			7.22311i			0.360705i	0.983602	+	0.180352i	$0.0577238\pi$
$401$			7.22311i			0.360705i	−0.983602	+	0.180352i	$0.942276\pi$
$402$	−8.78764	−	8.78764i	−0.438287	−	0.438287i
$403$	−0.320915	−	0.320915i	−0.0159859	−	0.0159859i
$404$		−	3.89174i		−	0.193621i
$405$	−1.25884	+	1.84806i	−0.0625522	+	0.0918308i
$406$	15.8198			0.785125
$407$	−27.0299	−	27.0299i	−1.33982	−	1.33982i
$408$	−1.83065	−	1.83065i	−0.0906306	−	0.0906306i
$409$	−17.4019			−0.860470			−0.430235	−	0.902717i	$-0.641569\pi$
$409$	−17.4019			−0.860470			−0.430235	+	0.902717i	$0.641569\pi$
$410$	4.67197	+	24.6348i	0.230732	+	1.21663i
$411$		−	4.28065i		−	0.211149i
$412$	9.40518	+	9.40518i	0.463360	+	0.463360i
$413$	29.2313	−	29.2313i	1.43838	−	1.43838i
$414$	3.66171			0.179963
$415$	−1.07866	+	0.204566i	−0.0529491	+	0.0100418i
$416$	0.126051			0.00618015
$417$	−2.80134	−	2.80134i	−0.137182	−	0.137182i
$418$	−1.93833	+	16.5473i	−0.0948068	+	0.809356i
$419$		−	1.67485i		−	0.0818218i	−0.999163	−	0.0409109i	$-0.986974\pi$
$419$		−	1.67485i		−	0.0818218i	0.999163	−	0.0409109i	$-0.0130260\pi$
$420$	5.53111	−	8.12004i	0.269891	−	0.396217i
$421$		−	26.3045i		−	1.28200i	−0.767540	−	0.641001i	$-0.778520\pi$
$421$		−	26.3045i		−	1.28200i	0.767540	−	0.641001i	$-0.221480\pi$
$422$	9.23137	−	9.23137i	0.449376	−	0.449376i
$423$	0.463170	+	0.463170i	0.0225201	+	0.0225201i
$424$		−	4.55250i		−	0.221089i
$425$	11.8690	+	5.16640i	0.575729	+	0.250607i
$426$			1.66657i			0.0807455i
$427$	25.5194	−	25.5194i	1.23497	−	1.23497i
$428$	7.00983	−	7.00983i	0.338833	−	0.338833i
$429$		−	0.481788i		−	0.0232609i
$430$	20.7452	+	14.1310i	1.00042	+	0.681455i
$431$		−	9.18675i		−	0.442510i	−0.975216	−	0.221255i	$-0.928985\pi$
$431$		−	9.18675i		−	0.442510i	0.975216	−	0.221255i	$-0.0710154\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	7.28482	−	7.28482i	0.350086	−	0.350086i	−0.510055	−	0.860142i	$-0.670375\pi$
$433$	7.28482	−	7.28482i	0.350086	−	0.350086i	0.860142	+	0.510055i	$0.170375\pi$
$434$			15.8198i			0.759376i
$435$	−1.50011	−	7.90992i	−0.0719247	−	0.379251i
$436$			17.7935i			0.852153i
$437$	1.85696	−	15.8526i	0.0888302	−	0.758335i
$438$	−3.64373	−	3.64373i	−0.174104	−	0.174104i
$439$	11.5269			0.550148			0.275074	−	0.961423i	$-0.411298\pi$
$439$	11.5269			0.550148			0.275074	+	0.961423i	$0.411298\pi$
$440$	−1.59248	−	8.39696i	−0.0759183	−	0.400309i
$441$	−12.3056			−0.585983
$442$	0.230755	−	0.230755i	0.0109759	−	0.0109759i
$443$	1.68879	+	1.68879i	0.0802367	+	0.0802367i	0.746086	−	0.665849i	$-0.231931\pi$
$443$	1.68879	+	1.68879i	0.0802367	+	0.0802367i	−0.665849	+	0.746086i	$0.731931\pi$
$444$			10.0011i			0.474633i
$445$	−12.3345	+	18.1079i	−0.584712	+	0.858396i
$446$	−16.3221			−0.772872
$447$	15.8349	+	15.8349i	0.748967	+	0.748967i
$448$	−3.10690	−	3.10690i	−0.146787	−	0.146787i
$449$	−10.9876			−0.518538			−0.259269	−	0.965805i	$-0.583482\pi$
$449$	−10.9876			−0.518538			−0.259269	+	0.965805i	$0.583482\pi$
$450$	−4.58450	−	1.99558i	−0.216116	−	0.0940723i
$451$		−	42.8595i		−	2.01818i
$452$	−12.4493	−	12.4493i	−0.585568	−	0.585568i
$453$	−7.98994	−	7.98994i	−0.375400	−	0.375400i
$454$		−	23.2372i		−	1.09058i
$455$	1.02354	+	0.697201i	0.0479842	+	0.0326853i
$456$	3.41987	−	2.70268i	0.160150	−	0.126565i
$457$	−24.3188	+	24.3188i	−1.13759	+	1.13759i	−0.148703	+	0.988882i	$0.547510\pi$
$457$	−24.3188	+	24.3188i	−1.13759	+	1.13759i	−0.988882	+	0.148703i	$0.952490\pi$
$458$	10.9739	−	10.9739i	0.512777	−	0.512777i
$459$	2.58893			0.120841
$460$	1.52562	+	8.04445i	0.0711325	+	0.375074i
$461$	20.8769			0.972332			0.486166	−	0.873866i	$-0.338395\pi$
$461$	20.8769			0.972332			0.486166	+	0.873866i	$0.338395\pi$
$462$	−11.8751	+	11.8751i	−0.552479	+	0.552479i
$463$	−16.5161	−	16.5161i	−0.767568	−	0.767568i	0.210110	−	0.977678i	$-0.432618\pi$
$463$	−16.5161	−	16.5161i	−0.767568	−	0.767568i	−0.977678	+	0.210110i	$0.932618\pi$
$464$	−3.60048			−0.167148
$465$	7.90992	−	1.50011i	0.366814	−	0.0695659i
$466$		−	2.39161i		−	0.110789i
$467$	−14.6317	+	14.6317i	−0.677074	+	0.677074i	−0.959337	−	0.282263i	$-0.908915\pi$
$467$	−14.6317	+	14.6317i	−0.677074	+	0.677074i	0.282263	+	0.959337i	$0.408915\pi$
$468$	−0.0891314	+	0.0891314i	−0.00412010	+	0.00412010i
$469$	−54.6046			−2.52141
$470$	−0.824566	+	1.21052i	−0.0380344	+	0.0558370i
$471$			6.47591i			0.298394i
$472$	−6.65282	+	6.65282i	−0.306221	+	0.306221i
$473$	−30.3387	−	30.3387i	−1.39497	−	1.39497i
$474$	−8.82758			−0.405464
$475$	−10.9644	+	18.8357i	−0.503080	+	0.864240i
$476$	−11.3753			−0.521385
$477$	3.21910	+	3.21910i	0.147393	+	0.147393i
$478$	9.19036	−	9.19036i	0.420357	−	0.420357i
$479$			28.1296i			1.28527i	0.766171	+	0.642636i	$0.222159\pi$
$479$			28.1296i			1.28527i	−0.766171	+	0.642636i	$0.777841\pi$
$480$	−1.25884	+	1.84806i	−0.0574579	+	0.0843520i
$481$	−1.26065			−0.0574808
$482$	6.10941	−	6.10941i	0.278276	−	0.278276i
$483$	11.3766	−	11.3766i	0.517652	−	0.517652i
$484$			3.60898i			0.164045i
$485$	−21.3882	+	4.05625i	−0.971186	+	0.184185i
$486$	−1.00000			−0.0453609
$487$	−11.6398	−	11.6398i	−0.527451	−	0.527451i	0.392361	−	0.919811i	$-0.371658\pi$
$487$	−11.6398	−	11.6398i	−0.527451	−	0.527451i	−0.919811	+	0.392361i	$0.871658\pi$
$488$	−5.80803	+	5.80803i	−0.262917	+	0.262917i
$489$	10.6715			0.482584
$490$	−5.12704	−	27.0344i	−0.231616	−	1.22129i
$491$	5.55189			0.250553			0.125277	−	0.992122i	$-0.460018\pi$
$491$	5.55189			0.250553			0.125277	+	0.992122i	$0.460018\pi$
$492$	−7.92907	+	7.92907i	−0.357470	+	0.357470i
$493$	−6.59121	+	6.59121i	−0.296853	+	0.296853i
$494$	0.340675	+	0.431077i	0.0153277	+	0.0193951i
$495$	7.06360	+	4.81150i	0.317485	+	0.216261i
$496$		−	3.60048i		−	0.161666i
$497$	5.17786	+	5.17786i	0.232259	+	0.232259i
$498$	−0.347181	−	0.347181i	−0.0155576	−	0.0155576i
$499$			27.8562i			1.24701i	0.781818	+	0.623507i	$0.214293\pi$
$499$			27.8562i			1.24701i	−0.781818	+	0.623507i	$0.785707\pi$
$500$	2.47400	−	10.9032i	0.110641	−	0.487605i
$501$	−21.3935			−0.955789
$502$	16.7294	+	16.7294i	0.746670	+	0.746670i
$503$	20.5340	+	20.5340i	0.915564	+	0.915564i	0.996703	−	0.0811388i	$-0.0258557\pi$
$503$	20.5340	+	20.5340i	0.915564	+	0.915564i	−0.0811388	+	0.996703i	$0.525856\pi$
$504$	4.39382			0.195716
$505$	−4.89907	+	7.19216i	−0.218006	+	0.320047i
$506$		−	13.9957i		−	0.622184i
$507$	9.18115	+	9.18115i	0.407749	+	0.407749i
$508$	−0.0636986	+	0.0636986i	−0.00282617	+	0.00282617i
$509$	−27.6636			−1.22617			−0.613085	−	0.790017i	$-0.710072\pi$
$509$	−27.6636			−1.22617			−0.613085	+	0.790017i	$0.710072\pi$
$510$	1.07866	+	5.68764i	0.0477637	+	0.251853i
$511$	−22.6414			−1.00160
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.507128	+	4.32930i	−0.0223902	+	0.191143i
$514$		−	12.2150i		−	0.538781i
$515$	−5.54173	−	29.2209i	−0.244198	−	1.28763i
$516$			11.2254i			0.494170i
$517$	1.77031	−	1.77031i	0.0778583	−	0.0778583i
$518$	31.0725	+	31.0725i	1.36525	+	1.36525i
$519$		−	3.28746i		−	0.144303i
$520$	−0.232949	−	0.158678i	−0.0102155	−	0.00695848i
$521$			23.2591i			1.01900i	0.860471	+	0.509500i	$0.170170\pi$
$521$			23.2591i			1.01900i	−0.860471	+	0.509500i	$0.829830\pi$
$522$	2.54592	−	2.54592i	0.111432	−	0.111432i
$523$	−8.81162	+	8.81162i	−0.385305	+	0.385305i	−0.873009	−	0.487704i	$-0.837835\pi$
$523$	−8.81162	+	8.81162i	−0.385305	+	0.385305i	0.487704	+	0.873009i	$0.337835\pi$
$524$			2.44811i			0.106946i
$525$	−20.4436	+	8.04354i	−0.892234	+	0.351049i
$526$			15.4560i			0.673915i
$527$	−6.59121	−	6.59121i	−0.287117	−	0.287117i
$528$	2.70268	−	2.70268i	0.117619	−	0.117619i
$529$		−	9.59187i		−	0.417038i
$530$	−5.73086	+	8.41329i	−0.248933	+	0.365450i
$531$		−	9.40851i		−	0.408294i
$532$	2.22823	−	19.0221i	0.0966059	−	0.824715i
$533$	−0.999466	−	0.999466i	−0.0432917	−	0.0432917i
$534$	−9.79832			−0.424015
$535$	−21.7788	+	4.13034i	−0.941581	+	0.178570i
$536$	12.4276			0.536790
$537$	0.364750	−	0.364750i	0.0157401	−	0.0157401i
$538$	9.79507	+	9.79507i	0.422296	+	0.422296i
$539$			47.0342i			2.02591i
$540$	−0.416642	−	2.19691i	−0.0179294	−	0.0945399i
$541$	−16.3738			−0.703966			−0.351983	−	0.936006i	$-0.614493\pi$
$541$	−16.3738			−0.703966			−0.351983	+	0.936006i	$0.614493\pi$
$542$	10.4913	+	10.4913i	0.450642	+	0.450642i
$543$	−3.43744	−	3.43744i	−0.147515	−	0.147515i
$544$	2.58893			0.110999
$545$	22.3991	−	32.8834i	0.959473	−	1.40857i
$546$			0.553844i			0.0237024i
$547$	20.3289	+	20.3289i	0.869199	+	0.869199i	0.992384	−	0.123185i	$-0.0393108\pi$
$547$	20.3289	+	20.3289i	0.869199	+	0.869199i	−0.123185	+	0.992384i	$0.539311\pi$
$548$	3.02688	+	3.02688i	0.129302	+	0.129302i
$549$		−	8.21380i		−	0.350556i
$550$	−7.62743	+	17.5228i	−0.325235	+	0.747173i
$551$	−9.73094	−	12.3132i	−0.414552	−	0.524558i
$552$	−2.58922	+	2.58922i	−0.110205	+	0.110205i
$553$	−27.4264	+	27.4264i	−1.16629	+	1.16629i
$554$	−12.6674			−0.538188
$555$	12.5898	−	18.4827i	0.534409	−	0.784548i
$556$	3.96170			0.168013
$557$	−12.6433	+	12.6433i	−0.535713	+	0.535713i	−0.922267	−	0.386554i	$-0.873665\pi$
$557$	−12.6433	+	12.6433i	−0.535713	+	0.535713i	0.386554	+	0.922267i	$0.373665\pi$
$558$	2.54592	+	2.54592i	0.107777	+	0.107777i
$559$	−1.41497			−0.0598468
$560$	1.83065	+	9.65282i	0.0773590	+	0.407906i
$561$		−	9.89533i		−	0.417781i
$562$	4.34121	−	4.34121i	0.183123	−	0.183123i
$563$	20.5997	−	20.5997i	0.868176	−	0.868176i	−0.124095	−	0.992270i	$-0.539603\pi$
$563$	20.5997	−	20.5997i	0.868176	−	0.868176i	0.992270	+	0.124095i	$0.0396027\pi$
$564$	−0.655021			−0.0275814
$565$	7.33541	+	38.6789i	0.308603	+	1.62723i
$566$		−	32.2388i		−	1.35510i
$567$	−3.10690	+	3.10690i	−0.130477	+	0.130477i
$568$	−1.17844	−	1.17844i	−0.0494463	−	0.0494463i
$569$	39.5742			1.65904			0.829519	−	0.558478i	$-0.188614\pi$
$569$	39.5742			1.65904			0.829519	+	0.558478i	$0.188614\pi$
$570$	−9.72236	+	0.689653i	−0.407225	+	0.0288864i
$571$	−15.5508			−0.650780			−0.325390	−	0.945580i	$-0.605496\pi$
$571$	−15.5508			−0.650780			−0.325390	+	0.945580i	$0.605496\pi$
$572$	0.340675	+	0.340675i	0.0142444	+	0.0142444i
$573$	−10.8448	+	10.8448i	−0.453049	+	0.453049i
$574$			49.2696i			2.05647i
$575$	7.30722	−	16.7871i	0.304732	−	0.700072i
$576$	−1.00000			−0.0416667
$577$	2.21358	−	2.21358i	0.0921525	−	0.0921525i	−0.659528	−	0.751680i	$-0.729244\pi$
$577$	2.21358	−	2.21358i	0.0921525	−	0.0921525i	0.751680	+	0.659528i	$0.229244\pi$
$578$	−7.28140	+	7.28140i	−0.302866	+	0.302866i
$579$			24.2679i			1.00854i
$580$	6.65389	+	4.53242i	0.276288	+	0.188198i
$581$	−2.15731			−0.0895004
$582$	−6.88409	−	6.88409i	−0.285355	−	0.285355i
$583$	12.3040	−	12.3040i	0.509578	−	0.509578i
$584$	5.15301			0.213233
$585$	0.276922	−	0.0525181i	0.0114493	−	0.00217135i
$586$	−0.482856			−0.0199466
$587$	−0.773553	+	0.773553i	−0.0319279	+	0.0319279i	−0.722891	−	0.690963i	$-0.757187\pi$
$587$	−0.773553	+	0.773553i	−0.0319279	+	0.0319279i	0.690963	+	0.722891i	$0.257187\pi$
$588$	8.70140	−	8.70140i	0.358840	−	0.358840i
$589$	12.3132	−	9.73094i	0.507355	−	0.400956i
$590$	20.6696	−	3.91998i	0.850955	−	0.161383i
$591$			8.83957i			0.363611i
$592$	−7.07188	−	7.07188i	−0.290652	−	0.290652i
$593$	6.83126	+	6.83126i	0.280526	+	0.280526i	0.833319	−	0.552793i	$-0.186438\pi$
$593$	6.83126	+	6.83126i	0.280526	+	0.280526i	−0.552793	+	0.833319i	$0.686438\pi$
$594$			3.82217i			0.156826i
$595$	21.0222	+	14.3196i	0.861826	+	0.587048i
$596$	−22.3940			−0.917294
$597$	−7.36057	−	7.36057i	−0.301248	−	0.301248i
$598$	−0.326373	−	0.326373i	−0.0133464	−	0.0133464i
$599$	−4.89411			−0.199968			−0.0999840	−	0.994989i	$-0.531879\pi$
$599$	−4.89411			−0.199968			−0.0999840	+	0.994989i	$0.531879\pi$
$600$	4.65282	−	1.83065i	0.189951	−	0.0747359i
$601$			18.8596i			0.769299i	0.923063	+	0.384650i	$0.125678\pi$
$601$			18.8596i			0.769299i	−0.923063	+	0.384650i	$0.874322\pi$
$602$	34.8761	+	34.8761i	1.42145	+	1.42145i
$603$	−8.78764	+	8.78764i	−0.357860	+	0.357860i
$604$	11.2995			0.459769
$605$	4.54313	−	6.66962i	0.184705	−	0.271159i
$606$	−3.89174			−0.158091
$607$	−16.5646	−	16.5646i	−0.672335	−	0.672335i	0.285919	−	0.958254i	$-0.407701\pi$
$607$	−16.5646	−	16.5646i	−0.672335	−	0.672335i	−0.958254	+	0.285919i	$0.907701\pi$
$608$	−0.507128	+	4.32930i	−0.0205668	+	0.175576i
$609$		−	15.8198i		−	0.641052i
$610$	18.0450	−	3.42221i	0.730619	−	0.138561i
$611$		−	0.0825659i		−	0.00334026i
$612$	−1.83065	+	1.83065i	−0.0739996	+	0.0739996i
$613$	29.1371	+	29.1371i	1.17684	+	1.17684i	0.980546	+	0.196291i	$0.0628899\pi$
$613$	29.1371	+	29.1371i	1.17684	+	1.17684i	0.196291	+	0.980546i	$0.437110\pi$
$614$			25.5326i			1.03041i
$615$	24.6348	−	4.67197i	0.993372	−	0.188392i
$616$		−	16.7939i		−	0.676646i
$617$	18.0432	−	18.0432i	0.726393	−	0.726393i	−0.243506	−	0.969899i	$-0.578298\pi$
$617$	18.0432	−	18.0432i	0.726393	−	0.726393i	0.969899	+	0.243506i	$0.0782977\pi$
$618$	9.40518	−	9.40518i	0.378332	−	0.378332i
$619$		−	2.38578i		−	0.0958924i	−0.998850	−	0.0479462i	$-0.984732\pi$
$619$		−	2.38578i		−	0.0958924i	0.998850	−	0.0479462i	$-0.0152676\pi$
$620$	−4.53242	+	6.65389i	−0.182026	+	0.267227i
$621$		−	3.66171i		−	0.146939i
$622$	4.05233	+	4.05233i	0.162484	+	0.162484i
$623$	−30.4424	+	30.4424i	−1.21965	+	1.21965i
$624$		−	0.126051i		−	0.00504607i
$625$	−18.2974	+	17.0354i	−0.731898	+	0.681414i
$626$			31.3617i			1.25347i
$627$	16.5473	+	1.93833i	0.660836	+	0.0774094i
$628$	−4.57916	−	4.57916i	−0.182728	−	0.182728i
$629$	−25.8923			−1.03239
$630$	−8.12004	−	5.53111i	−0.323510	−	0.220365i
$631$	−14.5023			−0.577326			−0.288663	−	0.957431i	$-0.593211\pi$
$631$	−14.5023			−0.577326			−0.288663	+	0.957431i	$0.593211\pi$
$632$	6.24204	−	6.24204i	0.248295	−	0.248295i
$633$	−9.23137	−	9.23137i	−0.366914	−	0.366914i
$634$		−	15.6454i		−	0.621359i
$635$	0.197905	−	0.0375326i	0.00785363	−	0.00148943i
$636$	−4.55250			−0.180518
$637$	1.09682	+	1.09682i	0.0434575	+	0.0434575i
$638$	−9.73094	−	9.73094i	−0.385252	−	0.385252i
$639$	1.66657			0.0659284
$640$	−0.416642	−	2.19691i	−0.0164692	−	0.0868405i
$641$			12.7084i			0.501950i	0.967994	+	0.250975i	$0.0807512\pi$
$641$			12.7084i			0.501950i	−0.967994	+	0.250975i	$0.919249\pi$
$642$	−7.00983	−	7.00983i	−0.276656	−	0.276656i
$643$	−1.79680	−	1.79680i	−0.0708588	−	0.0708588i	0.670789	−	0.741648i	$-0.265956\pi$
$643$	−1.79680	−	1.79680i	−0.0708588	−	0.0708588i	−0.741648	+	0.670789i	$0.765956\pi$
$644$			16.0889i			0.633991i
$645$	14.1310	−	20.7452i	0.556406	−	0.816841i
$646$	6.99705	+	8.85380i	0.275295	+	0.348348i
$647$	7.42896	−	7.42896i	0.292063	−	0.292063i	−0.545832	−	0.837895i	$-0.683786\pi$
$647$	7.42896	−	7.42896i	0.292063	−	0.292063i	0.837895	+	0.545832i	$0.183786\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−35.9609			−1.41159
$650$	0.230755	+	0.586492i	0.00905095	+	0.0230041i
$651$	15.8198			0.620028
$652$	−7.54592	+	7.54592i	−0.295521	+	0.295521i
$653$	−32.4125	−	32.4125i	−1.26840	−	1.26840i	−0.946914	−	0.321486i	$-0.895818\pi$
$653$	−32.4125	−	32.4125i	−1.26840	−	1.26840i	−0.321486	−	0.946914i	$-0.604182\pi$
$654$	17.7935			0.695780
$655$	3.08178	−	4.52426i	0.120415	−	0.176777i
$656$		−	11.2134i		−	0.437810i
$657$	−3.64373	+	3.64373i	−0.142155	+	0.142155i
$658$	−2.03508	+	2.03508i	−0.0793358	+	0.0793358i
$659$	41.3365			1.61024			0.805122	−	0.593110i	$-0.202100\pi$
$659$	41.3365			1.61024			0.805122	+	0.593110i	$0.202100\pi$
$660$	−8.39696	+	1.59248i	−0.326851	+	0.0619871i
$661$		−	2.43023i		−	0.0945250i	−0.998883	−	0.0472625i	$-0.984950\pi$
$661$		−	2.43023i		−	0.0945250i	0.998883	−	0.0472625i	$-0.0150497\pi$
$662$	8.34099	−	8.34099i	0.324182	−	0.324182i
$663$	−0.230755	−	0.230755i	−0.00896177	−	0.00896177i
$664$	0.490988			0.0190540
$665$	−28.0637	+	32.3491i	−1.08826	+	1.25444i
$666$	10.0011			0.387537
$667$	9.32242	+	9.32242i	0.360966	+	0.360966i
$668$	15.1275	−	15.1275i	0.585299	−	0.585299i
$669$			16.3221i			0.631047i
$670$	−22.9669	−	15.6443i	−0.887290	−	0.604394i
$671$	−31.3945			−1.21197
$672$	−3.10690	+	3.10690i	−0.119851	+	0.119851i
$673$	19.4040	−	19.4040i	0.747968	−	0.747968i	−0.226129	−	0.974097i	$-0.572607\pi$
$673$	19.4040	−	19.4040i	0.747968	−	0.747968i	0.974097	+	0.226129i	$0.0726071\pi$
$674$			15.4150i			0.593765i
$675$	−1.99558	+	4.58450i	−0.0768097	+	0.176458i
$676$	−12.9841			−0.499389
$677$	18.9654	+	18.9654i	0.728899	+	0.728899i	0.970401	−	0.241501i	$-0.0776398\pi$
$677$	18.9654	+	18.9654i	0.728899	+	0.728899i	−0.241501	+	0.970401i	$0.577640\pi$
$678$	−12.4493	+	12.4493i	−0.478114	+	0.478114i
$679$	−42.7763			−1.64160
$680$	−4.78449	−	3.25904i	−0.183477	−	0.124979i
$681$	−23.2372			−0.890452
$682$	9.73094	−	9.73094i	0.372617	−	0.372617i
$683$	−11.9597	+	11.9597i	−0.457626	+	0.457626i	−0.897876	−	0.440249i	$-0.854890\pi$
$683$	−11.9597	+	11.9597i	−0.457626	+	0.457626i	0.440249	+	0.897876i	$0.354890\pi$
$684$	−2.70268	−	3.41987i	−0.103340	−	0.130762i
$685$	−1.78350	−	9.40420i	−0.0681440	−	0.359316i
$686$		−	23.3120i		−	0.890057i
$687$	−10.9739	−	10.9739i	−0.418680	−	0.418680i
$688$	−7.93755	−	7.93755i	−0.302616	−	0.302616i
$689$		−	0.573846i		−	0.0218618i
$690$	8.04445	−	1.52562i	0.306247	−	0.0580795i
$691$	3.66130			0.139282			0.0696412	−	0.997572i	$-0.477815\pi$
$691$	3.66130			0.139282			0.0696412	+	0.997572i	$0.477815\pi$
$692$	2.32458	+	2.32458i	0.0883674	+	0.0883674i
$693$	11.8751	+	11.8751i	0.451098	+	0.451098i
$694$	22.4879			0.853630
$695$	−7.32145	−	4.98714i	−0.277718	−	0.189173i
$696$			3.60048i			0.136476i
$697$	−20.5278	−	20.5278i	−0.777546	−	0.777546i
$698$	−9.91149	+	9.91149i	−0.375155	+	0.375155i
$699$	−2.39161			−0.0904590
$700$	8.76820	−	20.1435i	0.331407	−	0.761352i
$701$	−25.2380			−0.953225			−0.476612	−	0.879113i	$-0.658136\pi$
$701$	−25.2380			−0.953225			−0.476612	+	0.879113i	$0.658136\pi$
$702$	0.0891314	+	0.0891314i	0.00336405	+	0.00336405i
$703$	5.07186	−	43.2979i	0.191289	−	1.63301i
$704$			3.82217i			0.144053i
$705$	1.21052	+	0.824566i	0.0455907	+	0.0310550i
$706$		−	2.40574i		−	0.0905412i
$707$	−12.0912	+	12.0912i	−0.454737	+	0.454737i
$708$	6.65282	+	6.65282i	0.250028	+	0.250028i
$709$			7.14208i			0.268226i	0.990966	+	0.134113i	$0.0428186\pi$
$709$			7.14208i			0.268226i	−0.990966	+	0.134113i	$0.957181\pi$
$710$	0.694362	+	3.66130i	0.0260589	+	0.137406i
$711$			8.82758i			0.331060i
$712$	6.92846	−	6.92846i	0.259655	−	0.259655i
$713$	−9.32242	+	9.32242i	−0.349128	+	0.349128i
$714$			11.3753i			0.425709i
$715$	−0.200733	−	1.05844i	−0.00750699	−	0.0395836i
$716$			0.515834i			0.0192776i
$717$	−9.19036	−	9.19036i	−0.343220	−	0.343220i
$718$	26.1412	−	26.1412i	0.975583	−	0.975583i
$719$		−	30.1848i		−	1.12570i	−0.826558	−	0.562852i	$-0.809704\pi$
$719$		−	30.1848i		−	1.12570i	0.826558	−	0.562852i	$-0.190296\pi$
$720$	1.84806	+	1.25884i	0.0688731	+	0.0469142i
$721$		−	58.4419i		−	2.17649i
$722$	−16.1762	+	9.96641i	−0.602017	+	0.370911i
$723$	−6.10941	−	6.10941i	−0.227211	−	0.227211i
$724$	4.86127			0.180668
$725$	−6.59121	−	16.7524i	−0.244791	−	0.622167i
$726$	3.60898			0.133942
$727$	10.1806	−	10.1806i	0.377576	−	0.377576i	−0.492651	−	0.870227i	$-0.663972\pi$
$727$	10.1806	−	10.1806i	0.377576	−	0.377576i	0.870227	+	0.492651i	$0.163972\pi$
$728$	−0.391627	−	0.391627i	−0.0145147	−	0.0145147i
$729$			1.00000i			0.0370370i
$730$	−9.52307	−	6.48681i	−0.352465	−	0.240088i
$731$	−29.0617			−1.07489
$732$	5.80803	+	5.80803i	0.214671	+	0.214671i
$733$	−12.6028	−	12.6028i	−0.465495	−	0.465495i	0.434957	−	0.900451i	$-0.356764\pi$
$733$	−12.6028	−	12.6028i	−0.465495	−	0.465495i	−0.900451	+	0.434957i	$0.856764\pi$
$734$	−16.6688			−0.615255
$735$	−27.0344	+	5.12704i	−0.997178	+	0.189114i
$736$		−	3.66171i		−	0.134972i
$737$	33.5878	+	33.5878i	1.23722	+	1.23722i
$738$	7.92907	+	7.92907i	0.291873	+	0.291873i
$739$			30.9906i			1.14001i	0.821642	+	0.570003i	$0.193058\pi$
$739$			30.9906i			1.14001i	−0.821642	+	0.570003i	$0.806942\pi$
$740$	4.16690	+	21.9716i	0.153178	+	0.807692i
$741$	0.431077	−	0.340675i	0.0158360	−	0.0125150i
$742$	−14.1442	+	14.1442i	−0.519248	+	0.519248i
$743$	−33.1976	+	33.1976i	−1.21790	+	1.21790i	−0.249536	+	0.968366i	$0.580278\pi$
$743$	−33.1976	+	33.1976i	−1.21790	+	1.21790i	−0.968366	+	0.249536i	$0.919722\pi$
$744$	−3.60048			−0.132000
$745$	41.3854	+	28.1904i	1.51625	+	1.03282i
$746$	−13.1413			−0.481137
$747$	−0.347181	+	0.347181i	−0.0127027	+	0.0127027i
$748$	6.99705	+	6.99705i	0.255838	+	0.255838i
$749$	−43.5577			−1.59156
$750$	−10.9032	−	2.47400i	−0.398128	−	0.0903378i
$751$			11.6085i			0.423600i	0.977313	+	0.211800i	$0.0679325\pi$
$751$			11.6085i			0.423600i	−0.977313	+	0.211800i	$0.932067\pi$
$752$	0.463170	−	0.463170i	0.0168901	−	0.0168901i
$753$	16.7294	−	16.7294i	0.609654	−	0.609654i
$754$	−0.453843			−0.0165280
$755$	−20.8821	−	14.2242i	−0.759978	−	0.517673i
$756$		−	4.39382i		−	0.159802i
$757$	33.9555	−	33.9555i	1.23413	−	1.23413i	0.271772	−	0.962362i	$-0.412390\pi$
$757$	33.9555	−	33.9555i	1.23413	−	1.23413i	0.962362	−	0.271772i	$-0.0876098\pi$
$758$	−6.42759	−	6.42759i	−0.233461	−	0.233461i
$759$	−13.9957			−0.508011
$760$	6.38709	−	7.36241i	0.231684	−	0.267063i
$761$	−1.91340			−0.0693607			−0.0346803	−	0.999398i	$-0.511041\pi$
$761$	−1.91340			−0.0693607			−0.0346803	+	0.999398i	$0.511041\pi$
$762$	0.0636986	+	0.0636986i	0.00230756	+	0.00230756i
$763$	55.2825	−	55.2825i	2.00136	−	2.00136i
$764$		−	15.3369i		−	0.554870i
$765$	5.68764	−	1.07866i	0.205637	−	0.0389989i
$766$	−4.12842			−0.149166
$767$	−0.838593	+	0.838593i	−0.0302798	+	0.0302798i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$		−	17.5747i		−	0.633760i	−0.948466	−	0.316880i	$-0.897365\pi$
$769$		−	17.5747i		−	0.633760i	0.948466	−	0.316880i	$-0.102635\pi$
$770$	−21.1408	+	31.0362i	−0.761863	+	1.11847i
$771$	−12.2150			−0.439913
$772$	−17.1600	−	17.1600i	−0.617603	−	0.617603i
$773$	28.9882	−	28.9882i	1.04263	−	1.04263i	0.0435843	−	0.999050i	$-0.486122\pi$
$773$	28.9882	−	28.9882i	1.04263	−	1.04263i	0.999050	−	0.0435843i	$-0.0138777\pi$
$774$	11.2254			0.403488
$775$	16.7524	−	6.59121i	0.601763	−	0.236763i
$776$	9.73557			0.349487
$777$	31.0725	−	31.0725i	1.11472	−	1.11472i
$778$	17.8792	−	17.8792i	0.641001	−	0.641001i
$779$	38.3484	−	30.3062i	1.37397	−	1.08583i
$780$	−0.158678	+	0.232949i	−0.00568157	+	0.00834093i
$781$		−	6.36991i		−	0.227933i
$782$	−6.70331	−	6.70331i	−0.239710	−	0.239710i
$783$	−2.54592	−	2.54592i	−0.0909838	−	0.0909838i
$784$			12.3056i			0.439487i
$785$	2.69813	+	14.2270i	0.0963006	+	0.507783i
$786$	2.44811			0.0873213
$787$	−1.82074	−	1.82074i	−0.0649024	−	0.0649024i	0.673911	−	0.738813i	$-0.264613\pi$
$787$	−1.82074	−	1.82074i	−0.0649024	−	0.0649024i	−0.738813	+	0.673911i	$0.764613\pi$
$788$	−6.25052	−	6.25052i	−0.222666	−	0.222666i
$789$	15.4560			0.550249
$790$	−19.3934	+	3.67794i	−0.689986	+	0.130855i
$791$			77.3577i			2.75052i
$792$	−2.70268	−	2.70268i	−0.0960356	−	0.0960356i
$793$	−0.732107	+	0.732107i	−0.0259979	+	0.0259979i
$794$	16.2029			0.575020
$795$	8.41329	+	5.73086i	0.298389	+	0.203253i
$796$	10.4094			0.368952
$797$	−2.79855	−	2.79855i	−0.0991296	−	0.0991296i	0.655803	−	0.754932i	$-0.272330\pi$
$797$	−2.79855	−	2.79855i	−0.0991296	−	0.0991296i	−0.754932	+	0.655803i	$0.772330\pi$
$798$	−19.0221	−	2.22823i	−0.673377	−	0.0788784i
$799$		−	1.69580i		−	0.0599932i
$800$	−1.99558	+	4.58450i	−0.0705543	+	0.162087i
$801$			9.79832i			0.346207i
$802$	−5.10751	+	5.10751i	−0.180352	+	0.180352i
$803$	13.9270	+	13.9270i	0.491471	+	0.491471i
$804$		−	12.4276i		−	0.438287i
$805$	20.2533	−	29.7332i	0.713836	−	1.04796i
$806$		−	0.453843i		−	0.0159859i
$807$	9.79507	−	9.79507i	0.344803	−	0.344803i
$808$	2.75187	−	2.75187i	0.0968106	−	0.0968106i
$809$		−	45.2384i		−	1.59050i	−0.606282	−	0.795249i	$-0.707340\pi$
$809$		−	45.2384i		−	1.59050i	0.606282	−	0.795249i	$-0.292660\pi$
$810$	−2.19691	+	0.416642i	−0.0771915	+	0.0146393i
$811$			42.6013i			1.49593i	0.663737	+	0.747966i	$0.268970\pi$
$811$			42.6013i			1.49593i	−0.663737	+	0.747966i	$0.731030\pi$
$812$	11.1863	+	11.1863i	0.392563	+	0.392563i
$813$	10.4913	−	10.4913i	0.367948	−	0.367948i
$814$		−	38.2261i		−	1.33982i
$815$	23.4444	−	4.44621i	0.821222	−	0.155744i
$816$		−	2.58893i		−	0.0906306i
$817$	5.69271	−	48.5980i	0.199163	−	1.70023i
$818$	−12.3050	−	12.3050i	−0.430235	−	0.430235i
$819$	0.553844			0.0193529
$820$	−14.1159	+	20.7230i	−0.492947	+	0.723679i
$821$	52.7865			1.84226			0.921130	−	0.389255i	$-0.127268\pi$
$821$	52.7865			1.84226			0.921130	+	0.389255i	$0.127268\pi$
$822$	3.02688	−	3.02688i	0.105574	−	0.105574i
$823$	−24.2470	−	24.2470i	−0.845199	−	0.845199i	0.144331	−	0.989529i	$-0.453897\pi$
$823$	−24.2470	−	24.2470i	−0.845199	−	0.845199i	−0.989529	+	0.144331i	$0.953897\pi$
$824$			13.3009i			0.463360i
$825$	17.5228	+	7.62743i	0.610064	+	0.265553i
$826$	41.3393			1.43838
$827$	−8.09237	−	8.09237i	−0.281399	−	0.281399i	0.552268	−	0.833667i	$-0.313763\pi$
$827$	−8.09237	−	8.09237i	−0.281399	−	0.281399i	−0.833667	+	0.552268i	$0.813763\pi$
$828$	2.58922	+	2.58922i	0.0899816	+	0.0899816i
$829$	8.26535			0.287067			0.143534	−	0.989645i	$-0.454153\pi$
$829$	8.26535			0.287067			0.143534	+	0.989645i	$0.454153\pi$
$830$	−0.907375	−	0.618075i	−0.0314955	−	0.0214537i
$831$			12.6674i			0.439429i
$832$	0.0891314	+	0.0891314i	0.00309007	+	0.00309007i
$833$	22.5273	+	22.5273i	0.780525	+	0.780525i
$834$		−	3.96170i		−	0.137182i
$835$	−46.9995	+	8.91341i	−1.62648	+	0.308461i
$836$	−13.0713	+	10.3301i	−0.452081	+	0.357274i
$837$	2.54592	−	2.54592i	0.0879999	−	0.0879999i
$838$	1.18430	−	1.18430i	0.0409109	−	0.0409109i
$839$	36.8428			1.27196			0.635978	−	0.771707i	$-0.280597\pi$
$839$	36.8428			1.27196			0.635978	+	0.771707i	$0.280597\pi$
$840$	9.65282	−	1.83065i	0.333054	−	0.0631634i
$841$	−16.0366			−0.552985
$842$	18.6001	−	18.6001i	0.641001	−	0.641001i
$843$	−4.34121	−	4.34121i	−0.149519	−	0.149519i
$844$	13.0551			0.449376
$845$	23.9954	+	16.3449i	0.825467	+	0.562282i
$846$			0.655021i			0.0225201i
$847$	11.2127	−	11.2127i	0.385275	−	0.385275i
$848$	3.21910	−	3.21910i	0.110544	−	0.110544i
$849$	−32.2388			−1.10643
$850$	4.73942	+	12.0458i	0.162561	+	0.413168i
$851$			36.6213i			1.25536i
$852$	−1.17844	+	1.17844i	−0.0403727	+	0.0403727i
$853$	25.7405	+	25.7405i	0.881338	+	0.881338i	0.993671	−	0.112333i	$-0.0358324\pi$
$853$	25.7405	+	25.7405i	0.881338	+	0.881338i	−0.112333	+	0.993671i	$0.535832\pi$
$854$	36.0899			1.23497
$855$	0.689653	+	9.72236i	0.0235856	+	0.332498i
$856$	9.91340			0.338833
$857$	−4.80004	−	4.80004i	−0.163966	−	0.163966i	0.620355	−	0.784321i	$-0.286989\pi$
$857$	−4.80004	−	4.80004i	−0.163966	−	0.163966i	−0.784321	+	0.620355i	$0.786989\pi$
$858$	0.340675	−	0.340675i	0.0116305	−	0.0116305i
$859$			32.4106i			1.10584i	0.833235	+	0.552918i	$0.186486\pi$
$859$			32.4106i			1.10584i	−0.833235	+	0.552918i	$0.813514\pi$
$860$	4.67697	+	24.6612i	0.159483	+	0.840938i
$861$	49.2696			1.67910
$862$	6.49601	−	6.49601i	0.221255	−	0.221255i
$863$	−22.4852	+	22.4852i	−0.765406	+	0.765406i	−0.977294	−	0.211888i	$-0.932039\pi$
$863$	−22.4852	+	22.4852i	−0.765406	+	0.765406i	0.211888	+	0.977294i	$0.432039\pi$
$864$			1.00000i			0.0340207i
$865$	−1.36969	−	7.22225i	−0.0465709	−	0.245564i
$866$	10.3023			0.350086
$867$	7.28140	+	7.28140i	0.247289	+	0.247289i
$868$	−11.1863	+	11.1863i	−0.379688	+	0.379688i
$869$	33.7405			1.14457
$870$	4.53242	−	6.65389i	0.153663	−	0.225588i
$871$	1.56651			0.0530791
$872$	−12.5819	+	12.5819i	−0.426076	+	0.426076i
$873$	−6.88409	+	6.88409i	−0.232991	+	0.232991i
$874$	12.5226	−	9.89644i	0.423582	−	0.334752i
$875$	−41.5615	+	26.1886i	−1.40504	+	0.885336i
$876$		−	5.15301i		−	0.174104i
$877$	35.3194	+	35.3194i	1.19265	+	1.19265i	0.976320	+	0.216334i	$0.0694099\pi$
$877$	35.3194	+	35.3194i	1.19265	+	1.19265i	0.216334	+	0.976320i	$0.430590\pi$
$878$	8.15073	+	8.15073i	0.275074	+	0.275074i
$879$			0.482856i			0.0162863i
$880$	4.81150	−	7.06360i	0.162196	−	0.238114i
$881$	31.6981			1.06794			0.533968	−	0.845505i	$-0.320700\pi$
$881$	31.6981			1.06794			0.533968	+	0.845505i	$0.320700\pi$
$882$	−8.70140	−	8.70140i	−0.292991	−	0.292991i
$883$	5.19260	+	5.19260i	0.174745	+	0.174745i	0.789060	−	0.614316i	$-0.210568\pi$
$883$	5.19260	+	5.19260i	0.174745	+	0.174745i	−0.614316	+	0.789060i	$0.710568\pi$
$884$	0.326337			0.0109759
$885$	−3.91998	−	20.6696i	−0.131769	−	0.694802i
$886$			2.38830i			0.0802367i
$887$	38.1720	+	38.1720i	1.28169	+	1.28169i	0.939705	+	0.341986i	$0.111100\pi$
$887$	38.1720	+	38.1720i	1.28169	+	1.28169i	0.341986	+	0.939705i	$0.388900\pi$
$888$	−7.07188	+	7.07188i	−0.237317	+	0.237317i
$889$	0.395810			0.0132751
$890$	−21.5260	+	4.08239i	−0.721554	+	0.136842i
$891$	3.82217			0.128048
$892$	−11.5414	−	11.5414i	−0.386436	−	0.386436i
$893$	2.83578	+	0.332179i	0.0948958	+	0.0111160i
$894$			22.3940i			0.748967i
$895$	0.649352	−	0.953293i	0.0217055	−	0.0318651i
$896$		−	4.39382i		−	0.146787i
$897$	−0.326373	+	0.326373i	−0.0108973	+	0.0108973i
$898$	−7.76942	−	7.76942i	−0.259269	−	0.259269i
$899$			12.9634i			0.432354i
$900$	−1.83065	−	4.65282i	−0.0610216	−	0.155094i
$901$		−	11.7861i		−	0.392652i
$902$	30.3062	−	30.3062i	1.00909	−	1.00909i
$903$	34.8761	−	34.8761i	1.16061	−	1.16061i
$904$		−	17.6060i		−	0.585568i
$905$	−8.98392	−	6.11956i	−0.298636	−	0.203421i
$906$		−	11.2995i		−	0.375400i
$907$	2.04159	+	2.04159i	0.0677900	+	0.0677900i	0.740189	−	0.672399i	$-0.234736\pi$
$907$	2.04159	+	2.04159i	0.0677900	+	0.0677900i	−0.672399	+	0.740189i	$0.734736\pi$
$908$	16.4312	−	16.4312i	0.545288	−	0.545288i
$909$			3.89174i			0.129081i
$910$	0.230755	+	1.21675i	0.00764945	+	0.0403347i
$911$		−	52.8342i		−	1.75047i	−0.483695	−	0.875237i	$-0.660705\pi$
$911$		−	52.8342i		−	1.75047i	0.483695	−	0.875237i	$-0.339295\pi$
$912$	4.32930	+	0.507128i	0.143357	+	0.0167927i
$913$	1.32698	+	1.32698i	0.0439168	+	0.0439168i
$914$	−34.3920			−1.13759
$915$	−3.42221	−	18.0450i	−0.113135	−	0.596548i
$916$	15.5194			0.512777
$917$	7.60604	−	7.60604i	0.251173	−	0.251173i
$918$	1.83065	+	1.83065i	0.0604204	+	0.0604204i
$919$		−	3.57090i		−	0.117793i	−0.998264	−	0.0588965i	$-0.981242\pi$
$919$		−	3.57090i		−	0.117793i	0.998264	−	0.0588965i	$-0.0187582\pi$
$920$	−4.60950	+	6.76706i	−0.151971	+	0.223103i
$921$	25.5326			0.841328
$922$	14.7622	+	14.7622i	0.486166	+	0.486166i
$923$	−0.148543	−	0.148543i	−0.00488937	−	0.00488937i
$924$	−16.7939			−0.552479
$925$	19.9580	−	45.8503i	0.656216	−	1.50755i
$926$		−	23.3573i		−	0.767568i
$927$	−9.40518	−	9.40518i	−0.308907	−	0.308907i
$928$	−2.54592	−	2.54592i	−0.0835739	−	0.0835739i
$929$		−	14.0100i		−	0.459653i	−0.973232	−	0.229826i	$-0.926184\pi$
$929$		−	14.0100i		−	0.459653i	0.973232	−	0.229826i	$-0.0738159\pi$
$930$	6.65389	+	4.53242i	0.218190	+	0.148624i
$931$	−42.0837	+	33.2582i	−1.37924	+	1.08999i
$932$	1.69112	−	1.69112i	0.0553946	−	0.0553946i
$933$	4.05233	−	4.05233i	0.132667	−	0.132667i
$934$	−20.6923			−0.677074
$935$	−4.12281	−	21.7391i	−0.134830	−	0.710946i
$936$	−0.126051			−0.00412010
$937$	0.588249	−	0.588249i	0.0192173	−	0.0192173i	−0.697433	−	0.716650i	$-0.745674\pi$
$937$	0.588249	−	0.588249i	0.0192173	−	0.0192173i	0.716650	+	0.697433i	$0.245674\pi$
$938$	−38.6113	−	38.6113i	−1.26070	−	1.26070i
$939$	31.3617			1.02345
$940$	−1.43902	+	0.272909i	−0.0469357	+	0.00890132i
$941$		−	52.7538i		−	1.71972i	−0.510526	−	0.859862i	$-0.670549\pi$
$941$		−	52.7538i		−	1.71972i	0.510526	−	0.859862i	$-0.329451\pi$
$942$	−4.57916	+	4.57916i	−0.149197	+	0.149197i
$943$	−29.0340	+	29.0340i	−0.945476	+	0.945476i
$944$	−9.40851			−0.306221
$945$	−5.53111	+	8.12004i	−0.179927	+	0.264145i
$946$		−	42.9053i		−	1.39497i
$947$	−16.9932	+	16.9932i	−0.552205	+	0.552205i	−0.927077	−	0.374872i	$-0.877687\pi$
$947$	−16.9932	+	16.9932i	−0.552205	+	0.552205i	0.374872	+	0.927077i	$0.377687\pi$
$948$	−6.24204	−	6.24204i	−0.202732	−	0.202732i
$949$	0.649541			0.0210850
$950$	−21.0718	+	5.56585i	−0.683660	+	0.180580i
$951$	−15.6454			−0.507337
$952$	−8.04354	−	8.04354i	−0.260693	−	0.260693i
$953$	15.6870	−	15.6870i	0.508151	−	0.508151i	−0.405807	−	0.913959i	$-0.633010\pi$
$953$	15.6870	−	15.6870i	0.508151	−	0.508151i	0.913959	+	0.405807i	$0.133010\pi$
$954$			4.55250i			0.147393i
$955$	−19.3067	+	28.3435i	−0.624750	+	0.917174i
$956$	12.9971			0.420357
$957$	−9.73094	+	9.73094i	−0.314557	+	0.314557i
$958$	−19.8906	+	19.8906i	−0.642636	+	0.642636i
$959$		−	18.8084i		−	0.607355i
$960$	−2.19691	+	0.416642i	−0.0709049	+	0.0134471i
$961$	18.0366			0.581825
$962$	−0.891416	−	0.891416i	−0.0287404	−	0.0287404i
$963$	−7.00983	+	7.00983i	−0.225889	+	0.225889i
$964$	8.64001			0.278276
$965$	10.1110	+	53.3145i	0.325486	+	1.71625i
$966$	16.0889			0.517652
$967$	−33.2376	+	33.2376i	−1.06885	+	1.06885i	−0.0714018	+	0.997448i	$0.522747\pi$
$967$	−33.2376	+	33.2376i	−1.06885	+	1.06885i	−0.997448	+	0.0714018i	$0.977253\pi$
$968$	−2.55194	+	2.55194i	−0.0820224	+	0.0820224i
$969$	8.85380	−	6.99705i	0.284425	−	0.224778i
$970$	−17.9919	−	12.2555i	−0.577686	−	0.393501i
$971$			35.6664i			1.14459i	0.820048	+	0.572294i	$0.193946\pi$
$971$			35.6664i			1.14459i	−0.820048	+	0.572294i	$0.806054\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−12.3086	−	12.3086i	−0.394595	−	0.394595i
$974$		−	16.4612i		−	0.527451i
$975$	0.586492	−	0.230755i	0.0187828	−	0.00739007i
$976$	−8.21380			−0.262917
$977$	−31.4909	−	31.4909i	−1.00748	−	1.00748i	−0.999972	−	0.00751053i	$-0.997609\pi$
$977$	−31.4909	−	31.4909i	−1.00748	−	1.00748i	−0.00751053	−	0.999972i	$-0.502391\pi$
$978$	7.54592	+	7.54592i	0.241292	+	0.241292i
$979$	37.4508			1.19693
$980$	15.4908	−	22.7416i	0.494836	−	0.726452i
$981$		−	17.7935i		−	0.568102i
$982$	3.92578	+	3.92578i	0.125277	+	0.125277i
$983$	−5.10301	+	5.10301i	−0.162761	+	0.162761i	−0.783789	−	0.621028i	$-0.786715\pi$
$983$	−5.10301	+	5.10301i	−0.162761	+	0.162761i	0.621028	+	0.783789i	$0.286715\pi$
$984$	−11.2134			−0.357470
$985$	3.68293	+	19.4197i	0.117348	+	0.618764i
$986$	−9.32137			−0.296853
$987$	2.03508	+	2.03508i	0.0647774	+	0.0647774i
$988$	−0.0639239	+	0.545712i	−0.00203369	+	0.0173614i
$989$			41.1041i			1.30704i
$990$	1.59248	+	8.39696i	0.0506122	+	0.266873i
$991$			12.3920i			0.393644i	0.980439	+	0.196822i	$0.0630621\pi$
$991$			12.3920i			0.393644i	−0.980439	+	0.196822i	$0.936938\pi$
$992$	2.54592	−	2.54592i	0.0808331	−	0.0808331i
$993$	−8.34099	−	8.34099i	−0.264693	−	0.264693i
$994$			7.32260i			0.232259i
$995$	−19.2372	−	13.1038i	−0.609861	−	0.415418i
$996$		−	0.490988i		−	0.0155576i
$997$	−22.8719	+	22.8719i	−0.724359	+	0.724359i	−0.969490	−	0.245131i	$-0.921169\pi$
$997$	−22.8719	+	22.8719i	−0.724359	+	0.724359i	0.245131	+	0.969490i	$0.421169\pi$
$998$	−19.6973	+	19.6973i	−0.623507	+	0.623507i
$999$		−	10.0011i		−	0.316422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.a.493.9	yes	20
3.2	odd	2		1710.2.p.d.1063.2		20
5.2	odd	4	inner	570.2.m.a.37.4	✓	20
15.2	even	4		1710.2.p.d.37.7		20
19.18	odd	2	inner	570.2.m.a.493.4	yes	20
57.56	even	2		1710.2.p.d.1063.7		20
95.37	even	4	inner	570.2.m.a.37.9	yes	20
285.227	odd	4		1710.2.p.d.37.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.4	✓	20	5.2	odd	4	inner
570.2.m.a.37.9	yes	20	95.37	even	4	inner
570.2.m.a.493.4	yes	20	19.18	odd	2	inner
570.2.m.a.493.9	yes	20	1.1	even	1	trivial
1710.2.p.d.37.2		20	285.227	odd	4
1710.2.p.d.37.7		20	15.2	even	4
1710.2.p.d.1063.2		20	3.2	odd	2
1710.2.p.d.1063.7		20	57.56	even	2

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.25884 - 1.84806i) q^{5} +1.00000 q^{6} +(3.10690 - 3.10690i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.25884 - 1.84806i) q^{5} +1.00000 q^{6} +(3.10690 - 3.10690i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(2.19691 - 0.416642i) q^{10} -3.82217 q^{11} +(0.707107 + 0.707107i) q^{12} +(-0.0891314 + 0.0891314i) q^{13} +4.39382 q^{14} +(-0.416642 - 2.19691i) q^{15} -1.00000 q^{16} +(-1.83065 + 1.83065i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-2.70268 - 3.41987i) q^{19} +(1.84806 + 1.25884i) q^{20} -4.39382i q^{21} +(-2.70268 - 2.70268i) q^{22} +(2.58922 + 2.58922i) q^{23} +1.00000i q^{24} +(-1.83065 - 4.65282i) q^{25} -0.126051 q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.10690 + 3.10690i) q^{28} +3.60048 q^{29} +(1.25884 - 1.84806i) q^{30} +3.60048i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.70268 + 2.70268i) q^{33} -2.58893 q^{34} +(-1.83065 - 9.65282i) q^{35} +1.00000 q^{36} +(7.07188 + 7.07188i) q^{37} +(0.507128 - 4.32930i) q^{38} +0.126051i q^{39} +(0.416642 + 2.19691i) q^{40} +11.2134i q^{41} +(3.10690 - 3.10690i) q^{42} +(7.93755 + 7.93755i) q^{43} -3.82217i q^{44} +(-1.84806 - 1.25884i) q^{45} +3.66171i q^{46} +(-0.463170 + 0.463170i) q^{47} +(-0.707107 + 0.707107i) q^{48} -12.3056i q^{49} +(1.99558 - 4.58450i) q^{50} +2.58893i q^{51} +(-0.0891314 - 0.0891314i) q^{52} +(-3.21910 + 3.21910i) q^{53} -1.00000i q^{54} +(-4.81150 + 7.06360i) q^{55} +4.39382i q^{56} +(-4.32930 - 0.507128i) q^{57} +(2.54592 + 2.54592i) q^{58} +9.40851 q^{59} +(2.19691 - 0.416642i) q^{60} +8.21380 q^{61} +(-2.54592 + 2.54592i) q^{62} +(-3.10690 - 3.10690i) q^{63} -1.00000i q^{64} +(0.0525181 + 0.276922i) q^{65} -3.82217 q^{66} +(-8.78764 - 8.78764i) q^{67} +(-1.83065 - 1.83065i) q^{68} +3.66171 q^{69} +(5.53111 - 8.12004i) q^{70} +1.66657i q^{71} +(0.707107 + 0.707107i) q^{72} +(-3.64373 - 3.64373i) q^{73} +10.0011i q^{74} +(-4.58450 - 1.99558i) q^{75} +(3.41987 - 2.70268i) q^{76} +(-11.8751 + 11.8751i) q^{77} +(-0.0891314 + 0.0891314i) q^{78} -8.82758 q^{79} +(-1.25884 + 1.84806i) q^{80} -1.00000 q^{81} +(-7.92907 + 7.92907i) q^{82} +(-0.347181 - 0.347181i) q^{83} +4.39382 q^{84} +(1.07866 + 5.68764i) q^{85} +11.2254i q^{86} +(2.54592 - 2.54592i) q^{87} +(2.70268 - 2.70268i) q^{88} -9.79832 q^{89} +(-0.416642 - 2.19691i) q^{90} +0.553844i q^{91} +(-2.58922 + 2.58922i) q^{92} +(2.54592 + 2.54592i) q^{93} -0.655021 q^{94} +(-9.72236 + 0.689653i) q^{95} -1.00000 q^{96} +(-6.88409 - 6.88409i) q^{97} +(8.70140 - 8.70140i) q^{98} +3.82217i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7	\( 20 q - 4 q^{5} + 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} + 4 q^{17} + 44 q^{23} + 4 q^{25} - 8 q^{26} - 4 q^{28} - 4 q^{30} + 4 q^{35} + 20 q^{36} - 4 q^{38} - 4 q^{42} + 52 q^{43} + 4 q^{47} + 16 q^{55} - 4 q^{57} + 8 q^{58} + 32 q^{61} - 8 q^{62} + 4 q^{63} - 8 q^{66} + 4 q^{68} - 20 q^{73} + 20 q^{76} - 24 q^{77} + 4 q^{80} - 20 q^{81} - 24 q^{82} - 116 q^{83} - 60 q^{85} + 8 q^{87} - 44 q^{92} + 8 q^{93} - 32 q^{95} - 20 q^{96}+O(q^{100}) \) 20 * q - 4 * q^5 + 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 + 4 * q^17 + 44 * q^23 + 4 * q^25 - 8 * q^26 - 4 * q^28 - 4 * q^30 + 4 * q^35 + 20 * q^36 - 4 * q^38 - 4 * q^42 + 52 * q^43 + 4 * q^47 + 16 * q^55 - 4 * q^57 + 8 * q^58 + 32 * q^61 - 8 * q^62 + 4 * q^63 - 8 * q^66 + 4 * q^68 - 20 * q^73 + 20 * q^76 - 24 * q^77 + 4 * q^80 - 20 * q^81 - 24 * q^82 - 116 * q^83 - 60 * q^85 + 8 * q^87 - 44 * q^92 + 8 * q^93 - 32 * q^95 - 20 * q^96

Introduction

L-functions

Modular forms

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