LMFDB - Embedded newform 507.2.p.b.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			64.4
Character	$\chi$	$=$	507.64
Dual form			507.2.p.b.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61341 - 0.195904i) q^{2} +(0.748511 - 0.663123i) q^{3} +(0.622835 + 0.153515i) q^{4} +(-1.54944 - 2.95221i) q^{5} +(-1.33756 + 0.923254i) q^{6} +(-1.00058 - 0.379471i) q^{7} +(2.06448 + 0.782953i) q^{8} +(0.120537 - 0.992709i) q^{9} +O(q^{10})$	\(q+(-1.61341 - 0.195904i) q^{2} +(0.748511 - 0.663123i) q^{3} +(0.622835 + 0.153515i) q^{4} +(-1.54944 - 2.95221i) q^{5} +(-1.33756 + 0.923254i) q^{6} +(-1.00058 - 0.379471i) q^{7} +(2.06448 + 0.782953i) q^{8} +(0.120537 - 0.992709i) q^{9} +(1.92153 + 5.06666i) q^{10} +(4.69529 - 0.570112i) q^{11} +(0.567998 - 0.298108i) q^{12} +(-1.22711 - 3.39031i) q^{13} +(1.54001 + 0.808261i) q^{14} +(-3.11745 - 1.18229i) q^{15} +(-4.31346 - 2.26388i) q^{16} +(2.33208 - 6.14919i) q^{17} +(-0.388951 + 1.57803i) q^{18} +6.34907i q^{19} +(-0.511836 - 2.07660i) q^{20} +(-1.00058 + 0.379471i) q^{21} -7.68713 q^{22} -8.59360 q^{23} +(2.06448 - 0.782953i) q^{24} +(-3.47444 + 5.03360i) q^{25} +(1.31566 + 5.71036i) q^{26} +(-0.568065 - 0.822984i) q^{27} +(-0.564944 - 0.389953i) q^{28} +(0.573975 - 4.72711i) q^{29} +(4.79811 + 2.51824i) q^{30} +(-7.82885 + 5.40386i) q^{31} +(2.88166 + 1.98907i) q^{32} +(3.13642 - 3.54029i) q^{33} +(-4.96725 + 9.46431i) q^{34} +(0.430064 + 3.54190i) q^{35} +(0.227470 - 0.599789i) q^{36} +(2.46938 - 1.70449i) q^{37} +(1.24381 - 10.2437i) q^{38} +(-3.16670 - 1.72396i) q^{39} +(-0.887340 - 7.30790i) q^{40} +(4.53046 + 5.11383i) q^{41} +(1.68869 - 0.416225i) q^{42} +(-2.12214 + 3.07445i) q^{43} +(3.01191 + 0.365712i) q^{44} +(-3.11745 + 1.18229i) q^{45} +(13.8650 + 1.68352i) q^{46} +(-0.586369 - 2.37899i) q^{47} +(-4.72990 + 1.16582i) q^{48} +(-4.38241 - 3.88247i) q^{49} +(6.59181 - 7.44061i) q^{50} +(-2.33208 - 6.14919i) q^{51} +(-0.243826 - 2.29998i) q^{52} +(-2.26375 + 5.96901i) q^{53} +(0.755297 + 1.43910i) q^{54} +(-8.95815 - 12.9781i) q^{55} +(-1.76857 - 1.56682i) q^{56} +(4.21021 + 4.75234i) q^{57} +(-1.85212 + 7.51433i) q^{58} +(0.121083 + 0.230704i) q^{59} +(-1.76015 - 1.21495i) q^{60} +(-1.03138 - 2.71952i) q^{61} +(13.6898 - 7.18496i) q^{62} +(-0.497312 + 0.947548i) q^{63} +(3.03304 + 2.68704i) q^{64} +(-8.10756 + 8.87576i) q^{65} +(-5.75390 + 5.09751i) q^{66} +(-0.568943 - 2.30829i) q^{67} +(2.39649 - 3.47192i) q^{68} +(-6.43240 + 5.69861i) q^{69} -5.79879i q^{70} +(-6.72474 - 7.59066i) q^{71} +(1.02609 - 1.95505i) q^{72} +(6.68698 - 0.811946i) q^{73} +(-4.31804 + 2.26628i) q^{74} +(0.737236 + 6.07168i) q^{75} +(-0.974677 + 3.95442i) q^{76} +(-4.91437 - 1.21128i) q^{77} +(4.77146 + 3.40182i) q^{78} +(1.37301 - 0.338416i) q^{79} +16.2420i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-6.30767 - 9.13824i) q^{82} +(-7.84069 + 8.85031i) q^{83} +(-0.681453 + 0.0827434i) q^{84} +(-21.7671 + 2.64300i) q^{85} +(4.02618 - 4.54461i) q^{86} +(-2.70503 - 3.91891i) q^{87} +(10.1397 + 2.49921i) q^{88} -6.42759i q^{89} +(5.26134 - 1.29680i) q^{90} +(-0.0586956 + 3.85794i) q^{91} +(-5.35239 - 1.31925i) q^{92} +(-2.27655 + 9.23634i) q^{93} +(0.480001 + 3.95316i) q^{94} +(18.7438 - 9.83748i) q^{95} +(3.47595 - 0.422057i) q^{96} +(7.11346 - 13.5536i) q^{97} +(6.31003 + 7.12256i) q^{98} -4.72978i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{26}\right)$

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 $

$2$	−1.61341	−	0.195904i	−1.14085	−	0.138525i	−0.471777	−	0.881718i	$-0.656387\pi$
$2$	−1.61341	−	0.195904i	−1.14085	−	0.138525i	−0.669077	+	0.743193i	$0.733310\pi$
$3$	0.748511	−	0.663123i	0.432153	−	0.382854i
$3$	0.748511	−	0.663123i	0.432153	−	0.382854i
$4$	0.622835	+	0.153515i	0.311417	+	0.0767575i
$5$	−1.54944	−	2.95221i	−0.692929	−	1.32027i	−0.936597	−	0.350408i	$-0.886043\pi$
$5$	−1.54944	−	2.95221i	−0.692929	−	1.32027i	0.243668	−	0.969859i	$-0.421649\pi$
$6$	−1.33756	+	0.923254i	−0.546058	+	0.376917i
$7$	−1.00058	−	0.379471i	−0.378185	−	0.143427i	0.158185	−	0.987409i	$-0.449436\pi$
$7$	−1.00058	−	0.379471i	−0.378185	−	0.143427i	−0.536370	+	0.843983i	$0.680205\pi$
$8$	2.06448	+	0.782953i	0.729903	+	0.276816i
$9$	0.120537	−	0.992709i	0.0401789	−	0.330903i
$10$	1.92153	+	5.06666i	0.607642	+	1.60222i
$11$	4.69529	−	0.570112i	1.41568	−	0.171895i	0.623331	−	0.781958i	$-0.285779\pi$
$11$	4.69529	−	0.570112i	1.41568	−	0.171895i	0.792353	+	0.610063i	$0.208856\pi$
$12$	0.567998	−	0.298108i	0.163967	−	0.0860564i
$13$	−1.22711	−	3.39031i	−0.340340	−	0.940302i
$13$	−1.22711	−	3.39031i	−0.340340	−	0.940302i
$14$	1.54001	+	0.808261i	0.411586	+	0.216017i
$15$	−3.11745	−	1.18229i	−0.804921	−	0.305266i
$16$	−4.31346	−	2.26388i	−1.07837	−	0.565970i
$17$	2.33208	−	6.14919i	0.565613	−	1.49140i	−0.281276	−	0.959627i	$-0.590758\pi$
$17$	2.33208	−	6.14919i	0.565613	−	1.49140i	0.846888	−	0.531771i	$-0.178473\pi$
$18$	−0.388951	+	1.57803i	−0.0916765	+	0.371946i
$19$			6.34907i			1.45658i	0.685271	+	0.728288i	$0.259684\pi$
$19$			6.34907i			1.45658i	−0.685271	+	0.728288i	$0.740316\pi$
$20$	−0.511836	−	2.07660i	−0.114450	−	0.464342i
$21$	−1.00058	+	0.379471i	−0.218345	+	0.0828074i
$22$	−7.68713			−1.63890
$23$	−8.59360			−1.79189			−0.895945	−	0.444166i	$-0.853500\pi$
$23$	−8.59360			−1.79189			−0.895945	+	0.444166i	$0.853500\pi$
$24$	2.06448	−	0.782953i	0.421410	−	0.159820i
$25$	−3.47444	+	5.03360i	−0.694888	+	1.00672i
$26$	1.31566	+	5.71036i	0.258023	+	1.11989i
$27$	−0.568065	−	0.822984i	−0.109324	−	0.158383i
$28$	−0.564944	−	0.389953i	−0.106764	−	0.0736941i
$29$	0.573975	−	4.72711i	0.106584	−	0.877802i	−0.837122	−	0.547017i	$-0.815763\pi$
$29$	0.573975	−	4.72711i	0.106584	−	0.877802i	0.943706	−	0.330785i	$-0.107314\pi$
$30$	4.79811	+	2.51824i	0.876011	+	0.459766i
$31$	−7.82885	+	5.40386i	−1.40610	+	0.970563i	−0.407756	+	0.913091i	$0.633688\pi$
$31$	−7.82885	+	5.40386i	−1.40610	+	0.970563i	−0.998347	+	0.0574715i	$0.981696\pi$
$32$	2.88166	+	1.98907i	0.509410	+	0.351621i
$33$	3.13642	−	3.54029i	0.545981	−	0.616285i
$34$	−4.96725	+	9.46431i	−0.851877	+	1.62312i
$35$	0.430064	+	3.54190i	0.0726941	+	0.598690i
$36$	0.227470	−	0.599789i	0.0379117	−	0.0999649i
$37$	2.46938	−	1.70449i	0.405963	−	0.280216i	−0.347534	−	0.937667i	$-0.612981\pi$
$37$	2.46938	−	1.70449i	0.405963	−	0.280216i	0.753497	+	0.657451i	$0.228365\pi$
$38$	1.24381	−	10.2437i	0.201772	−	1.66174i
$39$	−3.16670	−	1.72396i	−0.507077	−	0.276054i
$40$	−0.887340	−	7.30790i	−0.140301	−	1.15548i
$41$	4.53046	+	5.11383i	0.707538	+	0.798646i	0.986864	−	0.161551i	$-0.0516495\pi$
$41$	4.53046	+	5.11383i	0.707538	+	0.798646i	−0.279326	+	0.960196i	$0.590111\pi$
$42$	1.68869	−	0.416225i	0.260571	−	0.0642250i
$43$	−2.12214	+	3.07445i	−0.323623	+	0.468849i	−0.950702	−	0.310107i	$-0.899635\pi$
$43$	−2.12214	+	3.07445i	−0.323623	+	0.468849i	0.627079	+	0.778956i	$0.284250\pi$
$44$	3.01191	+	0.365712i	0.454063	+	0.0551332i
$45$	−3.11745	+	1.18229i	−0.464721	+	0.176246i
$46$	13.8650	+	1.68352i	2.04428	+	0.248221i
$47$	−0.586369	−	2.37899i	−0.0855306	−	0.347011i	0.912548	−	0.408969i	$-0.134112\pi$
$47$	−0.586369	−	2.37899i	−0.0855306	−	0.347011i	−0.998079	+	0.0619579i	$0.980266\pi$
$48$	−4.72990	+	1.16582i	−0.682703	+	0.168271i
$49$	−4.38241	−	3.88247i	−0.626058	−	0.554639i
$50$	6.59181	−	7.44061i	0.932222	−	1.05226i
$51$	−2.33208	−	6.14919i	−0.326557	−	0.861059i
$52$	−0.243826	−	2.29998i	−0.0338125	−	0.318950i
$53$	−2.26375	+	5.96901i	−0.310950	+	0.819907i	0.684878	+	0.728657i	$0.259855\pi$
$53$	−2.26375	+	5.96901i	−0.310950	+	0.819907i	−0.995828	+	0.0912495i	$0.970914\pi$
$54$	0.755297	+	1.43910i	0.102783	+	0.195836i
$55$	−8.95815	−	12.9781i	−1.20792	−	1.74997i
$56$	−1.76857	−	1.56682i	−0.236336	−	0.209375i
$57$	4.21021	+	4.75234i	0.557656	+	0.629463i
$58$	−1.85212	+	7.51433i	−0.243195	+	0.986680i
$59$	0.121083	+	0.230704i	0.0157636	+	0.0300351i	0.893210	−	0.449639i	$-0.148447\pi$
$59$	0.121083	+	0.230704i	0.0157636	+	0.0300351i	−0.877447	+	0.479674i	$0.840755\pi$
$60$	−1.76015	−	1.21495i	−0.227235	−	0.156849i
$61$	−1.03138	−	2.71952i	−0.132054	−	0.348199i	0.852638	−	0.522503i	$-0.175002\pi$
$61$	−1.03138	−	2.71952i	−0.132054	−	0.348199i	−0.984692	+	0.174304i	$0.944232\pi$
$62$	13.6898	−	7.18496i	1.73861	−	0.912490i
$63$	−0.497312	+	0.947548i	−0.0626554	+	0.119380i
$64$	3.03304	+	2.68704i	0.379130	+	0.335880i
$65$	−8.10756	+	8.87576i	−1.00562	+	1.10090i
$66$	−5.75390	+	5.09751i	−0.708256	+	0.627460i
$67$	−0.568943	−	2.30829i	−0.0695075	−	0.282003i	0.925895	−	0.377780i	$-0.123312\pi$
$67$	−0.568943	−	2.30829i	−0.0695075	−	0.282003i	−0.995403	+	0.0957773i	$0.969466\pi$
$68$	2.39649	−	3.47192i	0.290618	−	0.421032i
$69$	−6.43240	+	5.69861i	−0.774370	+	0.686032i
$70$		−	5.79879i		−	0.693088i
$71$	−6.72474	−	7.59066i	−0.798079	−	0.900845i	0.198779	−	0.980044i	$-0.436302\pi$
$71$	−6.72474	−	7.59066i	−0.798079	−	0.900845i	−0.996859	+	0.0791988i	$0.974764\pi$
$72$	1.02609	−	1.95505i	0.120926	−	0.230405i
$73$	6.68698	−	0.811946i	0.782651	−	0.0950311i	0.280550	−	0.959840i	$-0.409483\pi$
$73$	6.68698	−	0.811946i	0.782651	−	0.0950311i	0.502102	+	0.864808i	$0.332560\pi$
$74$	−4.31804	+	2.26628i	−0.501962	+	0.263450i
$75$	0.737236	+	6.07168i	0.0851287	+	0.701098i
$76$	−0.974677	+	3.95442i	−0.111803	+	0.453603i
$77$	−4.91437	−	1.21128i	−0.560045	−	0.138039i
$78$	4.77146	+	3.40182i	0.540261	+	0.385180i
$79$	1.37301	−	0.338416i	0.154475	−	0.0380748i	−0.161320	−	0.986902i	$-0.551575\pi$
$79$	1.37301	−	0.338416i	0.154475	−	0.0380748i	0.315795	+	0.948827i	$0.397729\pi$
$80$			16.2420i			1.81591i
$81$	−0.970942	−	0.239316i	−0.107882	−	0.0265906i
$82$	−6.30767	−	9.13824i	−0.696566	−	1.00915i
$83$	−7.84069	+	8.85031i	−0.860628	+	0.971448i	−0.999823	−	0.0188171i	$-0.994010\pi$
$83$	−7.84069	+	8.85031i	−0.860628	+	0.971448i	0.139195	+	0.990265i	$0.455548\pi$
$84$	−0.681453	+	0.0827434i	−0.0743526	+	0.00902804i
$85$	−21.7671	+	2.64300i	−2.36097	+	0.286674i
$86$	4.02618	−	4.54461i	0.434154	−	0.490058i
$87$	−2.70503	−	3.91891i	−0.290009	−	0.420151i
$88$	10.1397	+	2.49921i	1.08089	+	0.266417i
$89$		−	6.42759i		−	0.681323i	−0.940186	−	0.340661i	$-0.889349\pi$
$89$		−	6.42759i		−	0.681323i	0.940186	−	0.340661i	$-0.110651\pi$
$90$	5.26134	−	1.29680i	0.554594	−	0.136695i
$91$	−0.0586956	+	3.85794i	−0.00615297	+	0.404422i
$92$	−5.35239	−	1.31925i	−0.558025	−	0.137541i
$93$	−2.27655	+	9.23634i	−0.236068	+	0.957764i
$94$	0.480001	+	3.95316i	0.0495083	+	0.407738i
$95$	18.7438	−	9.83748i	1.92307	−	1.00930i
$96$	3.47595	−	0.422057i	0.354763	−	0.0430760i
$97$	7.11346	−	13.5536i	0.722262	−	1.37616i	−0.196167	−	0.980570i	$-0.562849\pi$
$97$	7.11346	−	13.5536i	0.722262	−	1.37616i	0.918429	−	0.395585i	$-0.129458\pi$
$98$	6.31003	+	7.12256i	0.637410	+	0.719487i
$99$		−	4.72978i		−	0.475361i
$100$	−2.93674	+	2.60172i	−0.293674	+	0.260172i
$101$	7.00987	−	10.1555i	0.697508	−	1.01051i	−0.300875	−	0.953664i	$-0.597279\pi$
$101$	7.00987	−	10.1555i	0.697508	−	1.01051i	0.998383	−	0.0568510i	$-0.0181060\pi$
$102$	2.55796	+	10.3780i	0.253275	+	1.02758i
$103$	1.25453	−	1.11141i	0.123612	−	0.109511i	−0.599052	−	0.800710i	$-0.704456\pi$
$103$	1.25453	−	1.11141i	0.123612	−	0.109511i	0.722664	+	0.691199i	$0.242917\pi$
$104$	0.121105	−	7.95999i	0.0118753	−	0.780541i
$105$	2.67062	+	2.36596i	0.260626	+	0.230894i
$106$	4.82171	−	9.18700i	0.468326	−	0.892320i
$107$	16.8554	−	8.84640i	1.62947	−	0.855213i	0.632747	−	0.774359i	$-0.281927\pi$
$107$	16.8554	−	8.84640i	1.62947	−	0.855213i	0.996726	−	0.0808546i	$-0.0257650\pi$
$108$	−0.227470	−	0.599789i	−0.0218883	−	0.0577148i
$109$	15.0845	+	10.4121i	1.44483	+	0.997295i	0.994534	+	0.104417i	$0.0332975\pi$
$109$	15.0845	+	10.4121i	1.44483	+	0.997295i	0.450298	+	0.892878i	$0.351318\pi$
$110$	11.9107	+	22.6940i	1.13564	+	2.16379i
$111$	0.718071	−	2.91333i	0.0681563	−	0.276521i
$112$	3.45690	+	3.90204i	0.326647	+	0.368708i
$113$	−7.28821	−	6.45679i	−0.685617	−	0.607404i	0.246680	−	0.969097i	$-0.420660\pi$
$113$	−7.28821	−	6.45679i	−0.685617	−	0.607404i	−0.932297	+	0.361693i	$0.882199\pi$
$114$	−5.86180	−	8.49228i	−0.549008	−	0.795375i
$115$	13.3152	+	25.3701i	1.24165	+	2.36577i
$116$	1.08317	−	2.85609i	0.100570	−	0.265182i
$117$	−3.51350	+	0.809510i	−0.324823	+	0.0748392i
$118$	−0.150161	−	0.395941i	−0.0138234	−	0.0364493i
$119$	−4.66688	+	5.26782i	−0.427813	+	0.482901i
$120$	−5.51022	−	4.88163i	−0.503012	−	0.445629i
$121$	11.0404	−	2.72121i	1.00367	−	0.247383i
$122$	1.13127	+	4.58975i	0.102421	+	0.415537i
$123$	6.78219	+	0.823507i	0.611529	+	0.0742531i
$124$	−5.70565	+	2.16387i	−0.512383	+	0.194321i
$125$	3.69466	+	0.448613i	0.330460	+	0.0401251i
$126$	0.987996	−	1.43136i	0.0880177	−	0.127516i
$127$	−1.25732	+	0.309902i	−0.111569	+	0.0274993i	−0.294705	−	0.955588i	$-0.595221\pi$
$127$	−1.25732	+	0.309902i	−0.111569	+	0.0274993i	0.183136	+	0.983088i	$0.441375\pi$
$128$	−9.01096	−	10.1713i	−0.796464	−	0.899022i
$129$	0.450293	+	3.70849i	0.0396461	+	0.326515i
$130$	14.8196	−	12.7320i	1.29977	−	1.11667i
$131$	−0.717239	+	5.90699i	−0.0626655	+	0.516097i	0.927251	+	0.374441i	$0.122165\pi$
$131$	−0.717239	+	5.90699i	−0.0626655	+	0.516097i	−0.989916	+	0.141655i	$0.954758\pi$
$132$	2.49696	−	1.72353i	0.217333	−	0.150014i
$133$	2.40929	−	6.35277i	0.208912	−	0.550855i
$134$	0.465736	+	3.83568i	0.0402335	+	0.331353i
$135$	−1.54944	+	2.95221i	−0.133354	+	0.254085i
$136$	9.62905	−	10.8690i	0.825685	−	0.932005i
$137$	10.7905	+	7.44813i	0.921893	+	0.636337i	0.931549	−	0.363616i	$-0.118458\pi$
$137$	10.7905	+	7.44813i	0.921893	+	0.636337i	−0.00965537	+	0.999953i	$0.503073\pi$
$138$	11.4945	−	7.93407i	0.978476	−	0.675393i
$139$	−6.69754	−	3.51514i	−0.568078	−	0.298150i	0.156125	−	0.987737i	$-0.450100\pi$
$139$	−6.69754	−	3.51514i	−0.568078	−	0.298150i	−0.724203	+	0.689587i	$0.757792\pi$
$140$	−0.275875	+	2.27204i	−0.0233157	+	0.192022i
$141$	−2.01647	−	1.39187i	−0.169817	−	0.117216i
$142$	9.36273	+	13.5643i	0.785703	+	1.13829i
$143$	−7.69451	−	15.2189i	−0.643447	−	1.27267i
$144$	−2.76730	+	4.00913i	−0.230609	+	0.334094i
$145$	−14.8447	+	5.62987i	−1.23279	+	0.467535i
$146$	−10.9479			−0.906055
$147$	−5.85483			−0.482899
$148$	1.79968	−	0.682528i	0.147933	−	0.0561035i
$149$	−0.798152	−	3.23823i	−0.0653872	−	0.265286i	0.929145	−	0.369715i	$-0.120545\pi$
$149$	−0.798152	−	3.23823i	−0.0653872	−	0.265286i	−0.994532	+	0.104429i	$0.966699\pi$
$150$		−	9.94055i		−	0.811643i
$151$	−4.73734	+	19.2201i	−0.385519	+	1.56411i	0.382667	+	0.923887i	$0.375006\pi$
$151$	−4.73734	+	19.2201i	−0.385519	+	1.56411i	−0.768186	+	0.640227i	$0.778840\pi$
$152$	−4.97102	+	13.1075i	−0.403203	+	1.06316i
$153$	−5.82326	−	3.05628i	−0.470782	−	0.247086i
$154$	7.69161	+	2.91704i	0.619808	+	0.235062i
$155$	28.0836	+	14.7394i	2.25573	+	1.18390i
$156$	−1.70768	−	1.55988i	−0.136724	−	0.124890i
$157$	19.5786	−	10.2757i	1.56254	−	0.820087i	0.562567	−	0.826752i	$-0.309814\pi$
$157$	19.5786	−	10.2757i	1.56254	−	0.820087i	0.999978	+	0.00666515i	$0.00212160\pi$
$158$	−2.28152	+	0.277027i	−0.181508	+	0.0220391i
$159$	2.26375	+	5.96901i	0.179527	+	0.473374i
$160$	1.40718	−	11.5892i	0.111248	−	0.916206i
$161$	8.59862	+	3.26102i	0.677666	+	0.257005i
$162$	1.51965	+	0.576326i	0.119395	+	0.0452804i
$163$	−0.263892	+	0.182152i	−0.0206697	+	0.0142672i	−0.578355	−	0.815785i	$-0.696305\pi$
$163$	−0.263892	+	0.182152i	−0.0206697	+	0.0142672i	0.557685	+	0.830053i	$0.311690\pi$
$164$	2.03668	+	3.88056i	0.159038	+	0.303021i
$165$	−15.3114	−	3.77391i	−1.19199	−	0.293798i
$166$	14.3841	−	12.7432i	1.11642	−	0.989062i
$167$	8.02971	+	0.974983i	0.621358	+	0.0754465i	0.425160	−	0.905118i	$-0.360218\pi$
$167$	8.02971	+	0.974983i	0.621358	+	0.0754465i	0.196197	+	0.980564i	$0.437141\pi$
$168$	−2.36279			−0.182293
$169$	−9.98839	+	8.32058i	−0.768337	+	0.640045i
$170$	35.6371			2.73324
$171$	6.30277	+	0.765295i	0.481985	+	0.0585236i
$172$	−1.79371	+	1.58909i	−0.136769	+	0.121167i
$173$	−12.3485	−	3.04364i	−0.938842	−	0.231404i	−0.259934	−	0.965627i	$-0.583701\pi$
$173$	−12.3485	−	3.04364i	−0.938842	−	0.231404i	−0.678909	+	0.734223i	$0.737547\pi$
$174$	3.59659	+	6.85274i	0.272657	+	0.519505i
$175$	5.38658	−	3.71809i	0.407187	−	0.281061i
$176$	−21.5436	−	8.17042i	−1.62391	−	0.615869i
$177$	0.243617	+	0.0923917i	0.0183114	+	0.00694459i
$178$	−1.25919	+	10.3703i	−0.0943801	+	0.777290i
$179$	−3.23604	−	8.53275i	−0.241873	−	0.637768i	0.758022	−	0.652229i	$-0.226166\pi$
$179$	−3.23604	−	8.53275i	−0.241873	−	0.637768i	−0.999895	+	0.0144613i	$0.995397\pi$
$180$	−2.12315	+	0.257797i	−0.158250	+	0.0192151i
$181$	2.57715	−	1.35259i	0.191558	−	0.100538i	−0.366217	−	0.930529i	$-0.619347\pi$
$181$	2.57715	−	1.35259i	0.191558	−	0.100538i	0.557776	+	0.829992i	$0.311655\pi$
$182$	0.850485	−	6.21295i	0.0630421	−	0.460534i
$183$	−2.57537	−	1.35166i	−0.190377	−	0.0999175i
$184$	−17.7413	−	6.72838i	−1.30791	−	0.496023i
$185$	−8.85815	−	4.64912i	−0.651264	−	0.341810i
$186$	5.48245	−	14.4560i	0.401993	−	1.05997i
$187$	7.44407	−	30.2018i	0.544365	−	2.20857i
$188$		−	1.57173i		−	0.114631i
$189$	0.256098	+	1.03903i	0.0186284	+	0.0755782i
$190$	−32.1686	+	12.1999i	−2.33375	+	0.885076i
$191$	5.91276			0.427832			0.213916	−	0.976852i	$-0.431378\pi$
$191$	5.91276			0.427832			0.213916	+	0.976852i	$0.431378\pi$
$192$	4.05210			0.292435
$193$	5.73433	−	2.17474i	0.412766	−	0.156542i	−0.139476	−	0.990225i	$-0.544542\pi$
$193$	5.73433	−	2.17474i	0.412766	−	0.156542i	0.552242	+	0.833684i	$0.313773\pi$
$194$	−14.1321	+	20.4739i	−1.01463	+	1.46994i
$195$	−0.182874	+	12.0199i	−0.0130959	+	0.860763i
$196$	−2.13350	−	3.09090i	−0.152393	−	0.220779i
$197$	−19.8978	−	13.7345i	−1.41766	−	0.978541i	−0.997469	−	0.0711066i	$-0.977347\pi$
$197$	−19.8978	−	13.7345i	−1.41766	−	0.978541i	−0.420193	−	0.907435i	$-0.638038\pi$
$198$	−0.926581	+	7.63108i	−0.0658492	+	0.542317i
$199$	7.63991	+	4.00973i	0.541579	+	0.284242i	0.713247	−	0.700912i	$-0.247224\pi$
$199$	7.63991	+	4.00973i	0.541579	+	0.284242i	−0.171669	+	0.985155i	$0.554916\pi$
$200$	−11.1140	+	7.67142i	−0.785877	+	0.542452i
$201$	−1.95654	−	1.35050i	−0.138004	−	0.0952571i
$202$	−13.2993	+	15.0118i	−0.935736	+	1.05623i
$203$	−2.36811	+	4.51206i	−0.166209	+	0.316685i
$204$	−0.508508	−	4.18794i	−0.0356027	−	0.293214i
$205$	8.07742	−	21.2984i	0.564151	−	1.48754i
$206$	−2.24180	+	1.54740i	−0.156193	+	0.107813i
$207$	−1.03584	+	8.53094i	−0.0719961	+	0.592941i
$208$	−2.38215	+	17.4020i	−0.165172	+	1.20661i
$209$	3.61968	+	29.8107i	0.250378	+	2.06205i
$210$	−3.84531	−	4.34046i	−0.265351	−	0.299520i
$211$	−17.2514	+	4.25208i	−1.18763	+	0.292725i	−0.783157	−	0.621823i	$-0.786392\pi$
$211$	−17.2514	+	4.25208i	−1.18763	+	0.292725i	−0.404476	+	0.914549i	$0.632546\pi$
$212$	−2.32627	+	3.37019i	−0.159769	+	0.231466i
$213$	−10.0671	−	1.22236i	−0.689785	−	0.0837550i
$214$	−28.9277	+	10.9708i	−1.97746	+	0.749951i
$215$	12.3645	+	1.50132i	0.843253	+	0.102389i
$216$	−0.528399	−	2.14380i	−0.0359530	−	0.145867i
$217$	9.88403	−	2.43619i	0.670972	−	0.165380i
$218$	−22.2977	−	19.7541i	−1.51019	−	1.33791i
$219$	4.46685	−	5.04204i	0.301842	−	0.340709i
$220$	−3.58711	−	9.45843i	−0.241843	−	0.637687i
$221$	−23.7094	−	0.360720i	−1.59487	−	0.0242647i
$222$	−1.72928	+	4.55973i	−0.116061	+	0.306029i
$223$	2.69212	+	5.12941i	0.180278	+	0.343491i	0.958779	−	0.284152i	$-0.0917121\pi$
$223$	2.69212	+	5.12941i	0.180278	+	0.343491i	−0.778501	+	0.627643i	$0.784020\pi$
$224$	−2.12855	−	3.08374i	−0.142220	−	0.206041i
$225$	4.57810	+	4.05584i	0.305207	+	0.270390i
$226$	10.4940	+	11.8452i	0.698049	+	0.787934i
$227$	5.10663	−	20.7184i	0.338939	−	1.37513i	−0.516083	−	0.856539i	$-0.672610\pi$
$227$	5.10663	−	20.7184i	0.338939	−	1.37513i	0.855022	−	0.518592i	$-0.173544\pi$
$228$	1.89271	+	3.60626i	0.125348	+	0.238830i
$229$	15.0028	+	10.3557i	0.991411	+	0.684321i	0.949163	−	0.314786i	$-0.101933\pi$
$229$	15.0028	+	10.3557i	0.991411	+	0.684321i	0.0422480	+	0.999107i	$0.486548\pi$
$230$	−16.5129	−	43.5409i	−1.08883	−	2.87100i
$231$	−4.48169	+	2.35217i	−0.294874	+	0.154762i
$232$	4.88606	−	9.30961i	0.320786	−	0.611206i
$233$	−3.75569	−	3.32725i	−0.246043	−	0.217975i	0.531083	−	0.847320i	$-0.321785\pi$
$233$	−3.75569	−	3.32725i	−0.246043	−	0.217975i	−0.777127	+	0.629344i	$0.783324\pi$
$234$	5.82731	−	0.617764i	0.380943	−	0.0403845i
$235$	−6.11473	+	5.41718i	−0.398881	+	0.353378i
$236$	0.0399981	+	0.162279i	0.00260365	+	0.0105634i
$237$	0.803299	−	1.16378i	0.0521799	−	0.0755956i
$238$	8.56159	−	7.58491i	0.554965	−	0.491656i
$239$		−	16.2020i		−	1.04802i	−0.851711	−	0.524012i	$-0.824435\pi$
$239$		−	16.2020i		−	1.04802i	0.851711	−	0.524012i	$-0.175565\pi$
$240$	10.7704	+	12.1573i	0.695228	+	0.784750i
$241$	3.27560	−	6.24114i	0.211000	−	0.402027i	−0.756837	−	0.653603i	$-0.773257\pi$
$241$	3.27560	−	6.24114i	0.211000	−	0.402027i	0.967838	+	0.251576i	$0.0809488\pi$
$242$	−18.3458	+	2.22758i	−1.17931	+	0.143194i
$243$	−0.885456	+	0.464723i	−0.0568020	+	0.0298120i
$244$	−0.224891	−	1.85214i	−0.0143972	−	0.118571i
$245$	−4.67160	+	18.9534i	−0.298457	+	1.21089i
$246$	−10.7811	−	2.65731i	−0.687380	−	0.169424i
$247$	21.5253	−	7.79102i	1.36962	−	0.495731i
$248$	−20.3935	+	5.02653i	−1.29499	+	0.319185i
$249$			11.8239i			0.749309i
$250$	−5.87312	−	1.44759i	−0.371449	−	0.0915538i
$251$	7.48213	+	10.8397i	0.472268	+	0.684198i	0.984646	−	0.174562i	$-0.0558509\pi$
$251$	7.48213	+	10.8397i	0.472268	+	0.684198i	−0.512378	+	0.858760i	$0.671235\pi$
$252$	−0.455206	+	0.513821i	−0.0286753	+	0.0323677i
$253$	−40.3495	+	4.89931i	−2.53675	+	0.308017i
$254$	2.08929	−	0.253685i	0.131093	−	0.0159176i
$255$	−14.5403	+	16.4126i	−0.910547	+	1.02780i
$256$	7.94209	+	11.5061i	0.496381	+	0.719131i
$257$	12.0394	+	2.96746i	0.751000	+	0.185105i	0.596194	−	0.802840i	$-0.296679\pi$
$257$	12.0394	+	2.96746i	0.751000	+	0.185105i	0.154805	+	0.987945i	$0.450525\pi$
$258$		−	6.07154i		−	0.377998i
$259$	−3.11763	+	0.768426i	−0.193720	+	0.0477476i
$260$	−6.41223	+	4.28350i	−0.397670	+	0.265652i
$261$	−4.62346	−	1.13958i	−0.286185	−	0.0705382i
$262$	2.31440	−	9.38990i	0.142984	−	0.580110i
$263$	0.456549	+	3.76002i	0.0281520	+	0.231853i	0.999993	−	0.00378556i	$-0.00120498\pi$
$263$	0.456549	+	3.76002i	0.0281520	+	0.231853i	−0.971841	+	0.235638i	$0.924282\pi$
$264$	9.24695	−	4.85317i	0.569111	−	0.298692i
$265$	21.1293	−	2.56556i	1.29796	−	0.157601i
$266$	−5.13171	+	9.77765i	−0.314645	+	0.599506i
$267$	−4.26228	−	4.81112i	−0.260847	−	0.294436i
$268$		−	1.52503i		−	0.0931558i
$269$	−0.289054	+	0.256079i	−0.0176239	+	0.0156134i	−0.671889	−	0.740652i	$-0.734517\pi$
$269$	−0.289054	+	0.256079i	−0.0176239	+	0.0156134i	0.654265	+	0.756266i	$0.272978\pi$
$270$	3.07823	−	4.45958i	0.187335	−	0.271402i
$271$	−1.04590	−	4.24339i	−0.0635341	−	0.257768i	0.930583	−	0.366082i	$-0.119301\pi$
$271$	−1.04590	−	4.24339i	−0.0635341	−	0.257768i	−0.994117	+	0.108314i	$0.965455\pi$
$272$	−23.9804	+	21.2448i	−1.45402	+	1.28815i
$273$	2.51435	+	2.92663i	0.152176	+	0.177128i
$274$	−15.9504	−	14.1308i	−0.963598	−	0.853673i
$275$	−13.4438	+	25.6150i	−0.810692	+	1.54464i
$276$	−4.88115	+	2.56182i	−0.293810	+	0.154204i
$277$	−5.02506	−	13.2500i	−0.301926	−	0.796115i	−0.997016	−	0.0771917i	$-0.975405\pi$
$277$	−5.02506	−	13.2500i	−0.301926	−	0.796115i	0.695090	−	0.718923i	$-0.255365\pi$
$278$	10.1173	+	6.98344i	0.606793	+	0.418839i
$279$	4.42080	+	8.42313i	0.264666	+	0.504280i
$280$	−1.88528	+	7.64888i	−0.112667	+	0.457108i
$281$	−13.5367	−	15.2798i	−0.807532	−	0.911515i	0.189996	−	0.981785i	$-0.439152\pi$
$281$	−13.5367	−	15.2798i	−0.807532	−	0.911515i	−0.997528	+	0.0702701i	$0.977614\pi$
$282$	2.98072	+	2.64069i	0.177499	+	0.157251i
$283$	−12.2634	−	17.7666i	−0.728983	−	1.05611i	−0.995727	−	0.0923462i	$-0.970563\pi$
$283$	−12.2634	−	17.7666i	−0.728983	−	1.05611i	0.266744	−	0.963767i	$-0.414052\pi$
$284$	−3.02312	−	5.76007i	−0.179389	−	0.341798i
$285$	7.50644	−	19.7929i	0.444643	−	1.17243i
$286$	9.43297	+	26.0617i	0.557783	+	1.54106i
$287$	−2.59255	−	6.83599i	−0.153033	−	0.403516i
$288$	2.32191	−	2.62089i	0.136820	−	0.154438i
$289$	−19.6493	−	17.4077i	−1.15584	−	1.02398i
$290$	25.0536	−	6.17515i	1.47120	−	0.362618i
$291$	−3.66317	−	14.8621i	−0.214739	−	0.871231i
$292$	4.28953	+	0.520843i	0.251026	+	0.0304800i
$293$	1.45878	−	0.553241i	0.0852226	−	0.0323207i	−0.311625	−	0.950205i	$-0.600873\pi$
$293$	1.45878	−	0.553241i	0.0852226	−	0.0323207i	0.396848	+	0.917884i	$0.370104\pi$
$294$	9.44626	+	1.14698i	0.550917	+	0.0668934i
$295$	0.493476	−	0.714923i	0.0287313	−	0.0416244i
$296$	6.43251	−	1.58547i	0.373882	−	0.0921537i
$297$	−3.13642	−	3.54029i	−0.181994	−	0.205428i
$298$	0.653367	+	5.38096i	0.0378485	+	0.311711i
$299$	10.5453	+	29.1350i	0.609851	+	1.68492i
$300$	−0.472918	+	3.89483i	−0.0273040	+	0.224868i
$301$	3.29004	−	2.27095i	0.189635	−	0.130895i
$302$	11.4086	−	30.0819i	0.656490	−	1.73102i
$303$	−1.48741	−	12.2499i	−0.0854496	−	0.703741i
$304$	14.3735	−	27.3865i	0.824378	−	1.57072i
$305$	−6.43053	+	7.25856i	−0.368211	+	0.415624i
$306$	8.79657	+	6.07183i	0.502866	+	0.347104i
$307$	0.874657	−	0.603732i	0.0499193	−	0.0344568i	−0.542844	−	0.839834i	$-0.682652\pi$
$307$	0.874657	−	0.603732i	0.0499193	−	0.0344568i	0.592763	+	0.805377i	$0.298037\pi$
$308$	−2.87489	−	1.50886i	−0.163812	−	0.0859753i
$309$	0.202023	−	1.66381i	0.0114927	−	0.0946508i
$310$	−42.4229	−	29.2824i	−2.40946	−	1.66313i
$311$	7.92253	+	11.4778i	0.449245	+	0.650844i	0.980535	−	0.196346i	$-0.0629076\pi$
$311$	7.92253	+	11.4778i	0.449245	+	0.650844i	−0.531289	+	0.847190i	$0.678292\pi$
$312$	−5.18780	−	6.03844i	−0.293701	−	0.341860i
$313$	15.7580	−	22.8294i	0.890695	−	1.29039i	−0.0655569	−	0.997849i	$-0.520882\pi$
$313$	15.7580	−	22.8294i	0.890695	−	1.29039i	0.956252	−	0.292545i	$-0.0945022\pi$
$314$	−33.6014	+	12.7433i	−1.89624	+	0.719148i
$315$	3.56791			0.201029
$316$	0.907108			0.0510288
$317$	−1.88097	+	0.713356i	−0.105646	+	0.0400661i	−0.406861	−	0.913490i	$-0.633377\pi$
$317$	−1.88097	+	0.713356i	−0.105646	+	0.0400661i	0.301216	+	0.953556i	$0.402608\pi$
$318$	−2.48301	−	10.0740i	−0.139240	−	0.564919i
$319$		−	22.5224i		−	1.26101i
$320$	3.23319	−	13.1176i	0.180741	−	0.733294i
$321$	6.75020	−	17.7988i	0.376759	−	0.993433i
$322$	−13.2343	−	6.94587i	−0.737516	−	0.387078i
$323$	39.0416	+	14.8065i	2.17233	+	0.823858i
$324$	−0.567998	−	0.298108i	−0.0315554	−	0.0165616i
$325$	21.3290	+	5.60264i	1.18312	+	0.310778i
$326$	0.461451	−	0.242188i	0.0255574	−	0.0134136i
$327$	18.1954	−	2.20932i	1.00621	−	0.122176i
$328$	5.34914	+	14.1045i	0.295357	+	0.778791i
$329$	−0.316048	+	2.60289i	−0.0174243	+	0.143502i
$330$	23.9642	+	9.08842i	1.31919	+	0.500301i
$331$	−10.0492	−	3.81116i	−0.552355	−	0.209481i	0.0626059	−	0.998038i	$-0.480059\pi$
$331$	−10.0492	−	3.81116i	−0.552355	−	0.209481i	−0.614961	+	0.788558i	$0.710828\pi$
$332$	−6.24211	+	4.30862i	−0.342580	+	0.236466i
$333$	−1.39441	−	2.65683i	−0.0764132	−	0.145593i
$334$	−12.7642	−	3.14610i	−0.698427	−	0.172147i
$335$	−5.93301	+	5.25619i	−0.324155	+	0.287176i
$336$	5.17506	+	0.628366i	0.282323	+	0.0342802i
$337$	−1.78425			−0.0971945			−0.0485972	−	0.998818i	$-0.515475\pi$
$337$	−1.78425			−0.0971945			−0.0485972	+	0.998818i	$0.515475\pi$
$338$	17.7454	−	11.4678i	0.965223	−	0.623764i
$339$	−9.73695			−0.528838
$340$	−13.9630	−	1.69542i	−0.757252	−	0.0919471i
$341$	−33.6779	+	29.8360i	−1.82376	+	1.61571i
$342$	−10.0190	−	2.46947i	−0.541768	−	0.133534i
$343$	6.39286	+	12.1806i	0.345182	+	0.657689i
$344$	−6.78825	+	4.68559i	−0.365998	+	0.252630i
$345$	26.7901	+	10.1601i	1.44233	+	0.547003i
$346$	19.3270	+	7.32977i	1.03903	+	0.394051i
$347$	1.61913	−	13.3347i	0.0869195	−	0.715847i	−0.882479	−	0.470353i	$-0.844127\pi$
$347$	1.61913	−	13.3347i	0.0869195	−	0.715847i	0.969398	−	0.245494i	$-0.0789502\pi$
$348$	−1.08317	−	2.85609i	−0.0580642	−	0.153103i
$349$	1.69753	−	0.206117i	0.0908667	−	0.0110332i	−0.0749770	−	0.997185i	$-0.523888\pi$
$349$	1.69753	−	0.206117i	0.0908667	−	0.0110332i	0.165844	+	0.986152i	$0.446965\pi$
$350$	−9.41915	+	4.94355i	−0.503475	+	0.264244i
$351$	−2.09309	+	2.93581i	−0.111721	+	0.156702i
$352$	14.6642	+	7.69638i	0.781606	+	0.410218i
$353$	18.1669	+	6.88981i	0.966929	+	0.366708i	0.786987	−	0.616970i	$-0.211640\pi$
$353$	18.1669	+	6.88981i	0.966929	+	0.366708i	0.179942	+	0.983677i	$0.442409\pi$
$354$	−0.374955	−	0.196791i	−0.0199286	−	0.0104593i
$355$	−11.9896	+	31.6141i	−0.636344	+	1.67790i
$356$	0.986731	−	4.00333i	0.0522966	−	0.212176i
$357$			7.03774i			0.372477i
$358$	3.54948	+	14.4008i	0.187596	+	0.761105i
$359$	−17.5019	+	6.63759i	−0.923714	+	0.350319i	−0.770181	−	0.637825i	$-0.779834\pi$
$359$	−17.5019	+	6.63759i	−0.923714	+	0.350319i	−0.153533	+	0.988144i	$0.549065\pi$
$360$	−7.36157			−0.387989
$361$	−21.3106			−1.12161
$362$	−4.42299	+	1.67742i	−0.232467	+	0.0881631i
$363$	6.45935	−	9.35798i	0.339028	−	0.491167i
$364$	−0.628810	+	2.39385i	−0.0329586	+	0.125472i
$365$	−12.7581	−	18.4833i	−0.667789	−	0.967459i
$366$	3.89034	+	2.68531i	0.203351	+	0.140363i
$367$	0.768625	−	6.33020i	0.0401219	−	0.330434i	−0.958803	−	0.284072i	$-0.908314\pi$
$367$	0.768625	−	6.33020i	0.0401219	−	0.330434i	0.998925	−	0.0463612i	$-0.0147625\pi$
$368$	37.0682	+	19.4549i	1.93231	+	1.01416i
$369$	5.62263	−	3.88102i	0.292702	−	0.202038i
$370$	13.3811	+	9.23628i	0.695648	+	0.480171i
$371$	4.53014	−	5.11347i	0.235193	−	0.265478i
$372$	−2.83583	+	5.40323i	−0.147031	+	0.280144i
$373$	−0.0830999	−	0.684390i	−0.00430275	−	0.0354363i	0.990399	−	0.138236i	$-0.0441431\pi$
$373$	−0.0830999	−	0.684390i	−0.00430275	−	0.0354363i	−0.994702	+	0.102799i	$0.967220\pi$
$374$	−17.9270	+	47.2696i	−0.926983	+	2.44425i
$375$	3.06298	−	2.11422i	0.158171	−	0.109178i
$376$	0.652093	−	5.37047i	0.0336291	−	0.276961i
$377$	−16.7307	+	3.85475i	−0.861674	+	0.198529i
$378$	−0.209641	−	1.72655i	−0.0107828	−	0.0888042i
$379$	−3.85506	−	4.35147i	−0.198021	−	0.223520i	0.641110	−	0.767449i	$-0.278474\pi$
$379$	−3.85506	−	4.35147i	−0.198021	−	0.223520i	−0.839131	+	0.543929i	$0.816936\pi$
$380$	13.1845	−	3.24968i	0.676349	−	0.166705i
$381$	−0.735615	+	1.06572i	−0.0376867	+	0.0545986i
$382$	−9.53971	−	1.15833i	−0.488094	−	0.0592654i
$383$	34.8908	−	13.2323i	1.78284	−	0.676141i	0.784400	−	0.620256i	$-0.212971\pi$
$383$	34.8908	−	13.2323i	1.78284	−	0.676141i	0.998437	−	0.0558850i	$-0.0177980\pi$
$384$	−13.4896	−	1.63793i	−0.688388	−	0.0835855i
$385$	4.03855	+	16.3851i	0.205824	+	0.835060i
$386$	−9.67787	+	2.38538i	−0.492591	+	0.121413i
$387$	2.79623	+	2.47725i	0.142141	+	0.125926i
$388$	6.51118	−	7.34961i	0.330555	−	0.373120i
$389$	10.2056	+	26.9099i	0.517443	+	1.36438i	0.898150	+	0.439689i	$0.144911\pi$
$389$	10.2056	+	26.9099i	0.517443	+	1.36438i	−0.380708	+	0.924695i	$0.624320\pi$
$390$	2.64979	−	19.3572i	0.134178	−	0.980192i
$391$	−20.0410	+	52.8437i	−1.01352	+	2.67242i
$392$	−6.00758	−	11.4465i	−0.303429	−	0.578135i
$393$	3.38020	+	4.89707i	0.170509	+	0.247024i
$394$	29.4128	+	26.0574i	1.48179	+	1.31275i
$395$	−3.12646	−	3.52905i	−0.157309	−	0.177566i
$396$	0.726092	−	2.94587i	0.0364875	−	0.148036i
$397$	6.48866	+	12.3631i	0.325657	+	0.620487i	0.992154	−	0.125020i	$-0.0398996\pi$
$397$	6.48866	+	12.3631i	0.325657	+	0.620487i	−0.666498	+	0.745507i	$0.732207\pi$
$398$	−11.5408	−	7.96604i	−0.578488	−	0.399301i
$399$	−2.40929	−	6.35277i	−0.120615	−	0.318036i
$400$	26.3823	−	13.8465i	1.31912	−	0.692326i
$401$	14.2812	−	27.2105i	0.713168	−	1.35883i	−0.211244	−	0.977433i	$-0.567751\pi$
$401$	14.2812	−	27.2105i	0.713168	−	1.35883i	0.924412	−	0.381395i	$-0.124556\pi$
$402$	2.89214	+	2.56221i	0.144247	+	0.127791i
$403$	27.9277	+	19.9111i	1.39118	+	0.991841i
$404$	5.92502	−	5.24911i	0.294781	−	0.261153i
$405$	0.797904	+	3.23723i	0.0396482	+	0.160859i
$406$	4.70467	−	6.81589i	0.233489	−	0.338267i
$407$	10.6227	−	9.41090i	0.526548	−	0.466481i
$408$		−	14.5208i		−	0.718885i
$409$	−8.20601	−	9.26268i	−0.405761	−	0.458010i	0.509738	−	0.860330i	$-0.329742\pi$
$409$	−8.20601	−	9.26268i	−0.405761	−	0.458010i	−0.915499	+	0.402320i	$0.868204\pi$
$410$	−17.2046	+	32.7807i	−0.849676	+	1.61892i
$411$	13.0158	−	1.58041i	0.642023	−	0.0779557i
$412$	0.951981	−	0.499638i	0.0469008	−	0.0246154i
$413$	−0.0336079	−	0.276786i	−0.00165374	−	0.0136198i
$414$	3.34248	−	13.5610i	0.164274	−	0.666487i
$415$	38.2766	+	9.43434i	1.87892	+	0.463113i
$416$	3.20743	−	12.2105i	0.157257	−	0.598670i
$417$	−7.34415	+	1.81017i	−0.359644	+	0.0886444i
$418$		−	48.8061i		−	2.38718i
$419$	2.34856	+	0.578869i	0.114735	+	0.0282796i	0.296265	−	0.955106i	$-0.404259\pi$
$419$	2.34856	+	0.578869i	0.114735	+	0.0282796i	−0.181530	+	0.983385i	$0.558105\pi$
$420$	1.30014	+	1.88358i	0.0634405	+	0.0919095i
$421$	−6.06844	+	6.84985i	−0.295757	+	0.333841i	−0.877540	−	0.479503i	$-0.840817\pi$
$421$	−6.06844	+	6.84985i	−0.295757	+	0.333841i	0.581783	+	0.813344i	$0.302355\pi$
$422$	28.6666	−	3.48075i	1.39547	−	0.169440i
$423$	−2.43232	+	0.295338i	−0.118264	+	0.0143598i
$424$	−9.34691	+	10.5505i	−0.453926	+	0.512377i
$425$	22.8499	+	33.1038i	1.10838	+	1.60577i
$426$	16.0029	+	3.94435i	0.775342	+	0.191105i
$427$			3.11248i			0.150624i
$428$	11.8562	−	2.92229i	0.573090	−	0.141254i
$429$	−15.8514	−	6.28911i	−0.765314	−	0.303641i
$430$	−19.6549	−	4.84451i	−0.947845	−	0.233623i
$431$	9.69639	−	39.3398i	0.467059	−	1.89493i	0.0213123	−	0.999773i	$-0.493216\pi$
$431$	9.69639	−	39.3398i	0.467059	−	1.89493i	0.445747	−	0.895159i	$-0.352938\pi$
$432$	0.587190	+	4.83594i	0.0282512	+	0.232669i
$433$	−5.64710	+	2.96383i	−0.271382	+	0.142432i	−0.594925	−	0.803781i	$-0.702818\pi$
$433$	−5.64710	+	2.96383i	−0.271382	+	0.142432i	0.323543	+	0.946214i	$0.395126\pi$
$434$	−16.4243	+	1.99427i	−0.788390	+	0.0957279i
$435$	−7.37815	+	14.0579i	−0.353755	+	0.674025i
$436$	7.79673	+	8.80069i	0.373396	+	0.421477i
$437$		−	54.5613i		−	2.61002i
$438$	−8.19463	+	7.25981i	−0.391554	+	0.346887i
$439$	7.23959	−	10.4884i	0.345527	−	0.500582i	−0.611237	−	0.791447i	$-0.709328\pi$
$439$	7.23959	−	10.4884i	0.345527	−	0.500582i	0.956764	+	0.290866i	$0.0939433\pi$
$440$	−8.33264	−	33.8068i	−0.397243	−	1.61168i
$441$	−4.38241	+	3.88247i	−0.208686	+	0.184880i
$442$	38.1823	+	5.22674i	1.81615	+	0.248611i
$443$	−14.1914	−	12.5725i	−0.674256	−	0.597339i	0.254926	−	0.966961i	$-0.417949\pi$
$443$	−14.1914	−	12.5725i	−0.674256	−	0.597339i	−0.929182	+	0.369622i	$0.879487\pi$
$444$	0.894479	−	1.70429i	0.0424501	−	0.0808819i
$445$	−18.9756	+	9.95914i	−0.899528	+	0.472109i
$446$	−3.33863	−	8.80325i	−0.158089	−	0.416846i
$447$	−2.74477	−	1.89458i	−0.129823	−	0.0896105i
$448$	−2.01516	−	3.83956i	−0.0952072	−	0.181402i
$449$	−0.759341	+	3.08077i	−0.0358355	+	0.145390i	−0.986134	−	0.165949i	$-0.946931\pi$
$449$	−0.759341	+	3.08077i	−0.0358355	+	0.145390i	0.950299	+	0.311339i	$0.100778\pi$
$450$	−6.59181	−	7.44061i	−0.310741	−	0.350754i
$451$	24.1873	+	21.4280i	1.13893	+	1.00901i
$452$	−3.54814	−	5.14036i	−0.166890	−	0.241782i
$453$	9.19936	+	17.5279i	0.432224	+	0.823534i
$454$	−12.2979	+	32.4269i	−0.577170	+	1.52187i
$455$	11.4804	−	5.80436i	0.538209	−	0.272113i
$456$	4.97102	+	13.1075i	0.232789	+	0.613815i
$457$	−23.8133	+	26.8797i	−1.11394	+	1.25738i	−0.150744	+	0.988573i	$0.548167\pi$
$457$	−23.8133	+	26.8797i	−1.11394	+	1.25738i	−0.963195	+	0.268804i	$0.913372\pi$
$458$	−22.1769	−	19.6470i	−1.03626	−	0.918046i
$459$	−6.38546	+	1.57387i	−0.298048	+	0.0734621i
$460$	4.39851	+	17.8455i	0.205082	+	0.832049i
$461$	36.4883	+	4.43048i	1.69943	+	0.206348i	0.912038	−	0.410106i	$-0.134508\pi$
$461$	36.4883	+	4.43048i	1.69943	+	0.206348i	0.787391	+	0.616454i	$0.211431\pi$
$462$	7.69161	−	2.91704i	0.357846	−	0.135713i
$463$	10.6312	+	1.29086i	0.494075	+	0.0599916i	0.363782	−	0.931484i	$-0.381485\pi$
$463$	10.6312	+	1.29086i	0.494075	+	0.0599916i	0.130293	+	0.991476i	$0.458408\pi$
$464$	−13.1774	+	19.0908i	−0.611747	+	0.886268i
$465$	30.7949	−	7.59027i	1.42808	−	0.351990i
$466$	5.40765	+	6.10397i	0.250505	+	0.282761i
$467$	−3.00412	−	24.7412i	−0.139014	−	1.14489i	−0.880544	−	0.473965i	$-0.842822\pi$
$467$	−3.00412	−	24.7412i	−0.139014	−	1.14489i	0.741529	−	0.670920i	$-0.234101\pi$
$468$	−2.31260	−	0.0351845i	−0.106900	−	0.00162640i
$469$	−0.306656	+	2.52554i	−0.0141600	+	0.116618i
$470$	10.9268	−	7.54224i	0.504017	−	0.347898i
$471$	7.84079	−	20.6745i	0.361285	−	0.952629i
$472$	0.0693423	+	0.571086i	0.00319174	+	0.0262863i
$473$	−8.21128	+	15.6453i	−0.377555	+	0.719371i
$474$	−1.52404	+	1.72029i	−0.0700015	+	0.0790154i
$475$	−31.9587	−	22.0595i	−1.46636	−	1.01216i
$476$	−3.71539	+	2.56455i	−0.170294	+	0.117546i
$477$	5.65263	+	2.96673i	0.258816	+	0.135837i
$478$	−3.17404	+	26.1406i	−0.145177	+	1.19564i
$479$	19.6571	+	13.5683i	0.898155	+	0.619951i	0.925116	−	0.379685i	$-0.123968\pi$
$479$	19.6571	+	13.5683i	0.898155	+	0.619951i	−0.0269612	+	0.999636i	$0.508583\pi$
$480$	−6.63176	−	9.60777i	−0.302697	−	0.438533i
$481$	−8.80895	−	6.28036i	−0.401654	−	0.286360i
$482$	−6.50756	+	9.42783i	−0.296411	+	0.429426i
$483$	8.59862	−	3.26102i	0.391251	−	0.148382i
$484$	7.29408			0.331549
$485$	−51.0348			−2.31737
$486$	1.51965	−	0.576326i	0.0689325	−	0.0261427i
$487$	−0.408555	−	1.65757i	−0.0185134	−	0.0751118i	0.960959	−	0.276692i	$-0.0892383\pi$
$487$	−0.408555	−	1.65757i	−0.0185134	−	0.0751118i	−0.979472	+	0.201581i	$0.935392\pi$
$488$		−	6.42190i		−	0.290706i
$489$	−0.0767374	+	0.311336i	−0.00347018	+	0.0140791i
$490$	11.2503	−	29.6645i	0.508235	−	1.34010i
$491$	−15.8628	−	8.32546i	−0.715880	−	0.375723i	0.0671196	−	0.997745i	$-0.478619\pi$
$491$	−15.8628	−	8.32546i	−0.715880	−	0.375723i	−0.783000	+	0.622022i	$0.786311\pi$
$492$	4.09776	+	1.55408i	0.184741	+	0.0700632i
$493$	−27.7293	−	14.5535i	−1.24887	−	0.655456i
$494$	−36.2554	+	8.35324i	−1.63121	+	0.375830i
$495$	−13.9633	+	7.32849i	−0.627603	+	0.329391i
$496$	46.0032	−	5.58579i	2.06560	−	0.250810i
$497$	3.84822	+	10.1469i	0.172616	+	0.455152i
$498$	2.31634	−	19.0768i	0.103798	−	0.854852i
$499$	0.0732316	+	0.0277731i	0.00327830	+	0.00124329i	0.356243	−	0.934393i	$-0.384057\pi$
$499$	0.0732316	+	0.0277731i	0.00327830	+	0.00124329i	−0.352965	+	0.935636i	$0.614827\pi$
$500$	2.23229	+	0.846597i	0.0998311	+	0.0378610i
$501$	6.65686	−	4.59490i	0.297406	−	0.205285i
$502$	−9.94821	−	18.9547i	−0.444010	−	0.845991i
$503$	12.2680	+	3.02379i	0.547002	+	0.134824i	0.503126	−	0.864213i	$-0.332183\pi$
$503$	12.2680	+	3.02379i	0.547002	+	0.134824i	0.0438763	+	0.999037i	$0.486029\pi$
$504$	−1.76857	+	1.56682i	−0.0787785	+	0.0697917i
$505$	−40.8426	−	4.95919i	−1.81747	−	0.220681i
$506$	66.0601			2.93673
$507$	−1.95885	+	12.8516i	−0.0869954	+	0.570758i
$508$	−0.830677			−0.0368553
$509$	10.2338	+	1.24261i	0.453606	+	0.0550777i	0.344151	−	0.938914i	$-0.388167\pi$
$509$	10.2338	+	1.24261i	0.453606	+	0.0550777i	0.109454	+	0.993992i	$0.465090\pi$
$510$	26.6747	−	23.6317i	1.18118	−	1.04643i
$511$	−6.99899	−	1.72510i	−0.309617	−	0.0763138i
$512$	2.07018	+	3.94440i	0.0914899	+	0.174319i
$513$	5.22518	−	3.60668i	0.230697	−	0.159239i
$514$	−18.8432	−	7.14630i	−0.831140	−	0.315210i
$515$	−5.22493	−	1.98156i	−0.230238	−	0.0873178i
$516$	−0.288851	+	2.37891i	−0.0127160	+	0.104725i
$517$	−4.10946	−	10.8358i	−0.180734	−	0.476556i
$518$	5.18055	−	0.629033i	0.227620	−	0.0276381i
$519$	−11.2613	+	5.91040i	−0.494317	+	0.259438i
$520$	−23.6872	+	11.9760i	−1.03875	+	0.525181i
$521$	7.67921	+	4.03036i	0.336432	+	0.176573i	0.624476	−	0.781044i	$-0.285313\pi$
$521$	7.67921	+	4.03036i	0.336432	+	0.176573i	−0.288044	+	0.957617i	$0.593005\pi$
$522$	7.23629	+	2.74436i	0.316724	+	0.120118i
$523$	25.5471	+	13.4081i	1.11709	+	0.586297i	0.919147	−	0.393916i	$-0.128880\pi$
$523$	25.5471	+	13.4081i	1.11709	+	0.586297i	0.197948	+	0.980212i	$0.436572\pi$
$524$	−1.35353	+	3.56897i	−0.0591294	+	0.155911i
$525$	1.56636	−	6.35499i	0.0683617	−	0.277354i
$526$		−	6.15590i		−	0.268410i
$527$	14.9719	+	60.7433i	0.652186	+	2.64602i
$528$	−21.5436	+	8.17042i	−0.937566	+	0.355572i
$529$	50.8499			2.21087
$530$	−34.5928			−1.50262
$531$	0.243617	−	0.0923917i	0.0105721	−	0.00400946i
$532$	2.47583	−	3.58687i	0.107341	−	0.155510i
$533$	11.7781	−	21.6349i	0.510165	−	0.937111i
$534$	5.93429	+	8.59731i	0.256802	+	0.372042i
$535$	−52.2328	−	36.0537i	−2.25822	−	1.55874i
$536$	0.632715	−	5.21087i	0.0273291	−	0.225075i
$537$	−8.08047	−	4.24096i	−0.348698	−	0.183011i
$538$	0.516529	−	0.356534i	0.0222692	−	0.0153713i
$539$	−22.7901	−	15.7309i	−0.981640	−	0.677577i
$540$	−1.41825	+	1.60087i	−0.0610318	+	0.0688907i
$541$	−18.0472	+	34.3861i	−0.775910	+	1.47837i	0.0995231	+	0.995035i	$0.468268\pi$
$541$	−18.0472	+	34.3861i	−0.775910	+	1.47837i	−0.875434	+	0.483339i	$0.839424\pi$
$542$	0.856175	+	7.05124i	0.0367759	+	0.302877i
$543$	1.03209	−	2.72140i	0.0442913	−	0.116786i
$544$	18.9514	−	13.0812i	0.812535	−	0.560853i
$545$	7.36611	−	60.6653i	0.315529	−	2.59862i
$546$	−3.48335	−	5.21444i	−0.149074	−	0.223157i
$547$	−0.0967590	−	0.796882i	−0.00413712	−	0.0340722i	0.990494	−	0.137555i	$-0.0439244\pi$
$547$	−0.0967590	−	0.796882i	−0.00413712	−	0.0340722i	−0.994631	+	0.103483i	$0.967001\pi$
$548$	5.57729	+	6.29546i	0.238250	+	0.268929i
$549$	−2.82401	+	0.696056i	−0.120526	+	0.0297069i
$550$	26.7085	−	38.6939i	1.13885	−	1.64991i
$551$	30.0127	+	3.64420i	1.27859	+	0.155248i
$552$	−17.7413	+	6.72838i	−0.755119	+	0.286379i
$553$	−1.50223	−	0.182403i	−0.0638812	−	0.00775658i
$554$	5.51176	+	22.3621i	0.234172	+	0.950075i
$555$	−9.71336	+	2.39413i	−0.412309	+	0.101625i
$556$	−3.63183	−	3.21752i	−0.154024	−	0.136453i
$557$	−14.3994	+	16.2536i	−0.610123	+	0.688687i	−0.969664	−	0.244443i	$-0.921395\pi$
$557$	−14.3994	+	16.2536i	−0.610123	+	0.688687i	0.359540	+	0.933130i	$0.382933\pi$
$558$	−5.48245	−	14.4560i	−0.232091	−	0.611972i
$559$	13.0274	+	3.42201i	0.551001	+	0.144735i
$560$	6.16336	−	16.2515i	0.260450	−	0.686749i
$561$	−14.4555	−	27.5427i	−0.610313	−	1.16285i
$562$	18.8469	+	27.3044i	0.795008	+	1.15177i
$563$	−20.1835	−	17.8810i	−0.850634	−	0.753596i	0.120352	−	0.992731i	$-0.461598\pi$
$563$	−20.1835	−	17.8810i	−0.850634	−	0.753596i	−0.970986	+	0.239135i	$0.923136\pi$
$564$	−1.04225	−	1.17646i	−0.0438868	−	0.0495379i
$565$	−7.76915	+	31.5207i	−0.326851	+	1.32609i
$566$	16.3053	+	31.0672i	0.685365	+	1.30585i
$567$	0.880695	+	0.607900i	0.0369857	+	0.0255294i
$568$	−7.93994	−	20.9359i	−0.333152	−	0.878451i
$569$	−18.4385	+	9.67726i	−0.772981	+	0.405692i	−0.804607	−	0.593808i	$-0.797624\pi$
$569$	−18.4385	+	9.67726i	−0.772981	+	0.405692i	0.0316254	+	0.999500i	$0.489932\pi$
$570$	−15.9885	+	30.4635i	−0.669684	+	1.27598i
$571$	18.3510	+	16.2575i	0.767964	+	0.680357i	0.953201	−	0.302337i	$-0.0977668\pi$
$571$	18.3510	+	16.2575i	0.767964	+	0.680357i	−0.185237	+	0.982694i	$0.559305\pi$
$572$	−2.45608	−	10.6601i	−0.102694	−	0.445720i
$573$	4.42576	−	3.92088i	0.184889	−	0.163797i
$574$	2.84365	+	11.5372i	0.118692	+	0.481552i
$575$	29.8580	−	43.2567i	1.24516	−	1.80393i
$576$	3.03304	−	2.68704i	0.126377	−	0.111960i
$577$			2.38394i			0.0992445i	0.998768	+	0.0496223i	$0.0158017\pi$
$577$			2.38394i			0.0992445i	−0.998768	+	0.0496223i	$0.984198\pi$
$578$	28.2921	+	31.9352i	1.17680	+	1.32833i
$579$	2.85009	−	5.43038i	0.118445	−	0.225679i
$580$	−10.1101	+	1.22759i	−0.419799	+	0.0509728i
$581$	11.2037	−	5.88016i	0.464808	−	0.243950i
$582$	2.99867	+	24.6963i	0.124299	+	1.02369i
$583$	−7.22595	+	29.3168i	−0.299268	+	1.21418i
$584$	14.4408	+	3.55934i	0.597566	+	0.147287i
$585$	7.83379	+	9.11830i	0.323887	+	0.376995i
$586$	−2.46199	+	0.606826i	−0.101704	+	0.0250677i
$587$		−	3.45848i		−	0.142747i	−0.997450	−	0.0713734i	$-0.977262\pi$
$587$		−	3.45848i		−	0.142747i	0.997450	−	0.0713734i	$-0.0227382\pi$
$588$	−3.64659	−	0.898805i	−0.150383	−	0.0370661i
$589$	−34.3095	−	49.7059i	−1.41370	−	2.04810i
$590$	−0.936236	+	1.05679i	−0.0385442	+	0.0435074i
$591$	−24.0014	+	2.91430i	−0.987285	+	0.119878i
$592$	−14.5103	+	1.76187i	−0.596371	+	0.0724126i
$593$	−12.6018	+	14.2245i	−0.517495	+	0.584131i	−0.947925	−	0.318493i	$-0.896823\pi$
$593$	−12.6018	+	14.2245i	−0.517495	+	0.584131i	0.430431	+	0.902624i	$0.358362\pi$
$594$	4.36678	+	6.32638i	0.179171	+	0.259575i
$595$	22.7827	+	5.61544i	0.934001	+	0.230211i
$596$		−	2.13941i		−	0.0876337i
$597$	8.37750	−	2.06487i	0.342868	−	0.0845094i
$598$	−11.3063	−	49.0725i	−0.462349	−	2.00673i
$599$	21.9100	+	5.40034i	0.895220	+	0.220652i	0.659978	−	0.751285i	$-0.270566\pi$
$599$	21.9100	+	5.40034i	0.895220	+	0.220652i	0.235242	+	0.971937i	$0.424412\pi$
$600$	−3.23184	+	13.1121i	−0.131939	+	0.535298i
$601$	−1.50593	−	12.4024i	−0.0614280	−	0.505905i	−0.990655	−	0.136395i	$-0.956448\pi$
$601$	−1.50593	−	12.4024i	−0.0614280	−	0.505905i	0.929227	−	0.369510i	$-0.120475\pi$
$602$	−5.75308	+	3.01945i	−0.234478	+	0.123063i
$603$	−2.36004	+	0.286561i	−0.0961083	+	0.0116697i
$604$	−5.90116	+	11.2437i	−0.240115	+	0.457501i
$605$	−25.1399	−	28.3771i	−1.02208	−	1.15369i
$606$			20.0556i			0.814702i
$607$	0.496947	−	0.440256i	0.0201704	−	0.0178695i	−0.652977	−	0.757378i	$-0.726480\pi$
$607$	0.496947	−	0.440256i	0.0201704	−	0.0178695i	0.673148	+	0.739508i	$0.264942\pi$
$608$	−12.6287	+	18.2959i	−0.512162	+	0.741995i
$609$	1.21949	+	4.94768i	0.0494163	+	0.200490i
$610$	11.7971	−	10.4513i	0.477649	−	0.423160i
$611$	−7.34597	+	4.90726i	−0.297186	+	0.198527i
$612$	−3.15774	−	2.79751i	−0.127644	−	0.113083i
$613$	9.82857	−	18.7268i	0.396972	−	0.756368i	−0.602144	−	0.798387i	$-0.705687\pi$
$613$	9.82857	−	18.7268i	0.396972	−	0.756368i	0.999117	+	0.0420196i	$0.0133792\pi$
$614$	−1.52946	+	0.802720i	−0.0617238	+	0.0323952i
$615$	−8.07742	−	21.2984i	−0.325713	−	0.858834i
$616$	−9.19723	−	6.34839i	−0.370567	−	0.255784i
$617$	8.31507	+	15.8430i	0.334752	+	0.637817i	0.993409	−	0.114627i	$-0.0365673\pi$
$617$	8.31507	+	15.8430i	0.334752	+	0.637817i	−0.658657	+	0.752444i	$0.728875\pi$
$618$	−0.651893	+	2.64483i	−0.0262230	+	0.106391i
$619$	−8.20847	−	9.26545i	−0.329926	−	0.372410i	0.560017	−	0.828481i	$-0.310795\pi$
$619$	−8.20847	−	9.26545i	−0.329926	−	0.372410i	−0.889943	+	0.456071i	$0.849256\pi$
$620$	15.2287	+	13.4915i	0.611601	+	0.541831i
$621$	4.88172	+	7.07239i	0.195897	+	0.283805i
$622$	−10.5338	−	20.0704i	−0.422365	−	0.804750i
$623$	−2.43909	+	6.43134i	−0.0977199	+	0.257666i
$624$	9.75661	+	14.6052i	0.390577	+	0.584678i
$625$	6.44407	+	16.9916i	0.257763	+	0.679664i
$626$	−29.8965	+	33.7462i	−1.19490	+	1.34877i
$627$	22.4775	+	19.9134i	0.897666	+	0.795263i
$628$	13.7717	−	3.39442i	0.549551	−	0.135452i
$629$	−4.72244	−	19.1597i	−0.188296	−	0.763947i
$630$	−5.75651	−	0.698967i	−0.229345	−	0.0278475i
$631$	19.5705	−	7.42213i	0.779091	−	0.295470i	0.0671810	−	0.997741i	$-0.478600\pi$
$631$	19.5705	−	7.42213i	0.779091	−	0.295470i	0.711910	+	0.702270i	$0.247830\pi$
$632$	3.09951	+	0.376348i	0.123292	+	0.0149703i
$633$	−10.0932	+	14.6225i	−0.401168	+	0.581192i
$634$	3.17452	−	0.782449i	0.126076	−	0.0310750i
$635$	2.86303	+	3.23170i	0.113616	+	0.128246i
$636$	0.493608	+	4.06523i	0.0195728	+	0.161197i
$637$	−7.78507	+	19.6219i	−0.308456	+	0.777450i
$638$	−4.41222	+	36.3379i	−0.174681	+	1.43863i
$639$	−8.34589	+	5.76075i	−0.330158	+	0.227892i
$640$	−16.0658	+	42.3620i	−0.635056	+	1.67450i
$641$	0.450225	+	3.70794i	0.0177828	+	0.146455i	0.998896	−	0.0469809i	$-0.0149600\pi$
$641$	0.450225	+	3.70794i	0.0177828	+	0.146455i	−0.981113	+	0.193436i	$0.938037\pi$
$642$	−14.3777	+	27.3944i	−0.567443	+	1.08117i
$643$	0.802422	−	0.905748i	0.0316445	−	0.0357192i	−0.732475	−	0.680793i	$-0.761635\pi$
$643$	0.802422	−	0.905748i	0.0316445	−	0.0357192i	0.764120	+	0.645074i	$0.223174\pi$
$644$	4.85490	+	3.35110i	0.191310	+	0.132052i
$645$	10.2505	−	7.07543i	0.403614	−	0.278595i
$646$	−60.0896	−	31.5374i	−2.36419	−	1.24082i
$647$	−3.45241	+	28.4331i	−0.135728	+	1.11782i	0.752556	+	0.658528i	$0.228821\pi$
$647$	−3.45241	+	28.4331i	−0.135728	+	1.11782i	−0.888284	+	0.459294i	$0.848102\pi$
$648$	−1.81711	−	1.25426i	−0.0713830	−	0.0492721i
$649$	0.700047	+	1.01419i	0.0274792	+	0.0398105i
$650$	−33.3149	−	13.2178i	−1.30672	−	0.518444i
$651$	5.78281	−	8.37784i	0.226646	−	0.328354i
$652$	−0.192324	+	0.0729390i	−0.00753201	+	0.00285651i
$653$	−6.91537			−0.270619			−0.135310	−	0.990803i	$-0.543203\pi$
$653$	−6.91537			−0.270619			−0.135310	+	0.990803i	$0.543203\pi$
$654$	−29.7894			−1.16486
$655$	18.5500	−	7.03508i	0.724808	−	0.274883i
$656$	−7.96486	−	32.3147i	−0.310976	−	1.26168i
$657$		−	6.73609i		−	0.262800i
$658$	1.01983	−	4.13762i	0.0397572	−	0.161301i
$659$	−8.12451	+	21.4226i	−0.316486	+	0.834505i	0.678510	+	0.734591i	$0.262626\pi$
$659$	−8.12451	+	21.4226i	−0.316486	+	0.834505i	−0.994996	+	0.0999138i	$0.968143\pi$
$660$	−8.95709	−	4.70104i	−0.348654	−	0.182988i
$661$	−13.7233	−	5.20455i	−0.533774	−	0.202434i	0.0729658	−	0.997334i	$-0.476754\pi$
$661$	−13.7233	−	5.20455i	−0.533774	−	0.202434i	−0.606739	+	0.794901i	$0.707523\pi$
$662$	15.4669	+	8.11765i	0.601138	+	0.315502i
$663$	−17.9859	+	15.4522i	−0.698516	+	0.600115i
$664$	−23.1163	+	12.1324i	−0.897087	+	0.470827i
$665$	−22.4877	+	2.73051i	−0.872037	+	0.105884i
$666$	1.72928	+	4.55973i	0.0670081	+	0.176686i
$667$	−4.93251	+	40.6229i	−0.190988	+	1.57292i
$668$	4.85151	+	1.83993i	0.187710	+	0.0711892i
$669$	5.41651	+	2.05421i	0.209414	+	0.0794204i
$670$	10.6021	−	7.31810i	0.409595	−	0.282723i
$671$	−6.39305	−	12.1809i	−0.246801	−	0.470240i
$672$	−3.63814	−	0.896720i	−0.140344	−	0.0345917i
$673$	25.2847	−	22.4003i	0.974655	−	0.863469i	−0.0159988	−	0.999872i	$-0.505093\pi$
$673$	25.2847	−	22.4003i	0.974655	−	0.863469i	0.990653	+	0.136403i	$0.0435543\pi$
$674$	2.87873	+	0.349542i	0.110885	+	0.0134638i
$675$	6.11628			0.235416
$676$	−7.49845	+	3.64898i	−0.288402	+	0.140345i
$677$	−30.9158			−1.18819			−0.594096	−	0.804394i	$-0.702490\pi$
$677$	−30.9158			−1.18819			−0.594096	+	0.804394i	$0.702490\pi$
$678$	15.7097	+	1.90750i	0.603328	+	0.0732572i
$679$	−12.2608	+	10.8621i	−0.470526	+	0.416850i
$680$	−47.0070	−	11.5862i	−1.80264	−	0.444310i
$681$	−9.91649	−	18.8943i	−0.380001	−	0.724031i
$682$	60.1813	−	41.5402i	2.30446	−	1.59066i
$683$	−7.39741	−	2.80547i	−0.283054	−	0.107348i	0.208992	−	0.977917i	$-0.432982\pi$
$683$	−7.39741	−	2.80547i	−0.283054	−	0.107348i	−0.492046	+	0.870569i	$0.663751\pi$
$684$	3.80810	+	1.44422i	0.145606	+	0.0552212i
$685$	5.26925	−	43.3962i	0.201328	−	1.65808i
$686$	−7.92809	−	20.9047i	−0.302696	−	0.798144i
$687$	18.0968	−	2.19735i	0.690436	−	0.0838341i
$688$	16.1139	−	8.45725i	0.614338	−	0.322430i
$689$	23.0147	+	0.350151i	0.876789	+	0.0133397i
$690$	−41.2330	−	21.6408i	−1.56971	−	0.823849i
$691$	22.8385	+	8.66152i	0.868819	+	0.329500i	0.748419	−	0.663226i	$-0.230813\pi$
$691$	22.8385	+	8.66152i	0.868819	+	0.329500i	0.120400	+	0.992725i	$0.461582\pi$
$692$	−7.22386	−	3.79137i	−0.274610	−	0.144126i
$693$	−1.79482	+	4.73254i	−0.0681794	+	0.179774i
$694$	−5.22465	+	21.1972i	−0.198325	+	0.804636i
$695$			25.2190i			0.956611i
$696$	−2.51615	−	10.2084i	−0.0953742	−	0.386949i
$697$	42.0113	−	15.9328i	1.59129	−	0.603497i
$698$	−2.77919			−0.105194
$699$	−5.01755			−0.189781
$700$	3.92573	−	1.48883i	0.148379	−	0.0562726i
$701$	15.6444	−	22.6649i	0.590882	−	0.856041i	−0.407482	−	0.913213i	$-0.633593\pi$
$701$	15.6444	−	22.6649i	0.590882	−	0.856041i	0.998364	+	0.0571723i	$0.0182084\pi$
$702$	3.95215	−	4.32662i	0.149164	−	0.163298i
$703$	10.8219	+	15.6782i	0.408156	+	0.591316i
$704$	15.7729	+	10.8873i	0.594465	+	0.410329i
$705$	−0.984688	+	8.10963i	−0.0370855	+	0.305426i
$706$	−27.9610	−	14.6751i	−1.05233	−	0.552304i
$707$	−10.8677	+	7.50143i	−0.408722	+	0.282120i
$708$	0.137550	+	0.0949436i	0.00516943	+	0.00356820i
$709$	−12.1372	+	13.7000i	−0.455821	+	0.514516i	−0.930824	−	0.365469i	$-0.880909\pi$
$709$	−12.1372	+	13.7000i	−0.455821	+	0.514516i	0.475003	+	0.879984i	$0.342447\pi$
$710$	25.5375	−	48.6577i	0.958406	−	1.82609i
$711$	−0.170451	−	1.40379i	−0.00639240	−	0.0526462i
$712$	5.03250	−	13.2696i	0.188601	−	0.497300i
$713$	67.2780	−	46.4386i	2.51958	−	1.73914i
$714$	1.37872	−	11.3548i	0.0515972	−	0.424942i
$715$	−33.0072	+	46.2965i	−1.23440	+	1.73139i
$716$	−0.705616	−	5.81127i	−0.0263701	−	0.217178i
$717$	−10.7439	−	12.1274i	−0.401240	−	0.452906i
$718$	29.5381	−	7.28048i	1.10235	−	0.271705i
$719$	−19.2164	+	27.8398i	−0.716652	+	1.03825i	0.280276	+	0.959920i	$0.409574\pi$
$719$	−19.2164	+	27.8398i	−0.716652	+	1.03825i	−0.996928	+	0.0783298i	$0.975041\pi$
$720$	16.1236	+	1.95775i	0.600889	+	0.0729612i
$721$	−1.67701	+	0.636005i	−0.0624551	+	0.0236861i
$722$	34.3828	+	4.17483i	1.27960	+	0.155371i
$723$	−1.68682	−	6.84369i	−0.0627334	−	0.254520i
$724$	1.81278	−	0.446811i	0.0673716	−	0.0166056i
$725$	21.8001	+	19.3132i	0.809636	+	0.717275i
$726$	−12.2548	+	13.8329i	−0.454820	+	0.513386i
$727$	−9.31031	−	24.5493i	−0.345300	−	0.910482i	−0.989358	−	0.145505i	$-0.953519\pi$
$727$	−9.31031	−	24.5493i	−0.345300	−	0.910482i	0.644057	−	0.764977i	$-0.277250\pi$
$728$	−3.14176	+	7.91868i	−0.116441	+	0.293486i
$729$	−0.354605	+	0.935016i	−0.0131335	+	0.0346302i
$730$	16.9631	+	32.3205i	0.627832	+	1.19623i
$731$	13.9564	+	20.2193i	0.516195	+	0.747837i
$732$	−1.39653	−	1.23722i	−0.0516173	−	0.0457289i
$733$	31.6497	+	35.7251i	1.16901	+	1.31954i	0.938020	+	0.346582i	$0.112658\pi$
$733$	31.6497	+	35.7251i	1.16901	+	1.31954i	0.230990	+	0.972956i	$0.425804\pi$
$734$	−2.48022	+	10.0626i	−0.0915465	+	0.371419i
$735$	9.07170	+	17.2847i	0.334615	+	0.637555i
$736$	−24.7638	−	17.0932i	−0.912807	−	0.630065i
$737$	−3.98734	−	10.5137i	−0.146875	−	0.387279i
$738$	−9.83192	+	5.16019i	−0.361918	+	0.189949i
$739$	−2.68955	+	5.12450i	−0.0989365	+	0.188508i	−0.929893	−	0.367829i	$-0.880101\pi$
$739$	−2.68955	+	5.12450i	−0.0989365	+	0.188508i	0.830957	+	0.556337i	$0.187794\pi$
$740$	−4.80346	−	4.25549i	−0.176579	−	0.156435i
$741$	10.9455	−	20.1056i	0.402093	−	0.738597i
$742$	−8.31072	+	7.36266i	−0.305096	+	0.270292i
$743$	2.14702	+	8.71082i	0.0787666	+	0.319569i	0.997087	−	0.0762684i	$-0.0243006\pi$
$743$	2.14702	+	8.71082i	0.0787666	+	0.319569i	−0.918321	+	0.395837i	$0.870454\pi$
$744$	−11.9315	+	17.2858i	−0.437430	+	0.633727i
$745$	−8.32324	+	7.37375i	−0.304940	+	0.270153i
$746$			1.12048i			0.0410237i
$747$	7.84069	+	8.85031i	0.286876	+	0.323816i
$748$	9.27286	−	17.6680i	0.339049	−	0.646004i
$749$	−20.2222	+	2.45542i	−0.738903	+	0.0897190i
$750$	−5.35602	+	2.81106i	−0.195574	+	0.102645i
$751$	1.29105	+	10.6328i	0.0471113	+	0.387996i	0.997124	+	0.0757854i	$0.0241464\pi$
$751$	1.29105	+	10.6328i	0.0471113	+	0.387996i	−0.950013	+	0.312211i	$0.898931\pi$
$752$	−2.85647	+	11.5892i	−0.104165	+	0.422613i
$753$	12.7885	+	3.15209i	0.466040	+	0.114869i
$754$	27.7486	−	2.94169i	1.01055	−	0.107130i
$755$	64.0821	−	15.7948i	2.33218	−	0.574832i
$756$			0.686458i			0.0249662i
$757$	11.8558	+	2.92218i	0.430905	+	0.106209i	0.448802	−	0.893631i	$-0.351851\pi$
$757$	11.8558	+	2.92218i	0.430905	+	0.106209i	−0.0178969	+	0.999840i	$0.505697\pi$
$758$	5.36734	+	7.77593i	0.194950	+	0.282434i
$759$	−26.9532	+	30.4238i	−0.978338	+	1.10431i
$760$	46.3983	−	5.63378i	1.68304	−	0.204359i
$761$	22.6846	−	2.75441i	0.822316	−	0.0998472i	0.301446	−	0.953483i	$-0.402531\pi$
$761$	22.6846	−	2.75441i	0.822316	−	0.0998472i	0.520870	+	0.853636i	$0.325608\pi$
$762$	1.39563	−	1.57534i	0.0505583	−	0.0570685i
$763$	−11.1422	−	16.1423i	−0.403375	−	0.584390i
$764$	3.68267	+	0.907697i	0.133234	+	0.0328393i
$765$			21.9270i			0.792771i
$766$	−58.8855	+	14.5140i	−2.12762	+	0.524411i
$767$	0.633576	−	0.693608i	0.0228771	−	0.0250447i
$768$	13.5747	+	3.34586i	0.489835	+	0.120733i
$769$	−2.93233	+	11.8969i	−0.105743	+	0.429015i	−0.999821	−	0.0188948i	$-0.993985\pi$
$769$	−2.93233	+	11.8969i	−0.105743	+	0.429015i	0.894079	+	0.447910i	$0.147831\pi$
$770$	−3.30596	−	27.2270i	−0.119138	−	0.981193i
$771$	10.9794	−	5.76245i	0.395415	−	0.207530i
$772$	3.90540	−	0.474201i	0.140558	−	0.0170669i
$773$	10.1981	−	19.4309i	0.366802	−	0.698882i	−0.630186	−	0.776444i	$-0.717021\pi$
$773$	10.1981	−	19.4309i	0.366802	−	0.698882i	0.996988	+	0.0775621i	$0.0247136\pi$
$774$	−4.02618	−	4.54461i	−0.144718	−	0.163353i
$775$		−	58.1827i		−	2.08998i
$776$	25.2974	−	22.4115i	0.908123	−	0.804527i
$777$	−1.82402	+	2.64254i	−0.0654362	+	0.0948007i
$778$	−11.1940	−	45.4160i	−0.401326	−	1.62824i
$779$	−32.4680	+	28.7642i	−1.16329	+	1.03058i
$780$	−1.95914	+	7.45834i	−0.0701483	+	0.267052i
$781$	−35.9021	−	31.8065i	−1.28468	−	1.13813i
$782$	42.6866	−	81.3325i	1.52647	−	2.90844i
$783$	−4.21639	+	2.21293i	−0.150681	+	0.0790837i
$784$	10.1139	+	26.6681i	0.361211	+	0.952434i
$785$	−60.6717	−	41.8787i	−2.16547	−	1.49471i
$786$	−4.49430	−	8.56318i	−0.160306	−	0.305438i
$787$	−2.98568	+	12.1134i	−0.106428	+	0.431795i	−0.999848	−	0.0174270i	$-0.994453\pi$
$787$	−2.98568	+	12.1134i	−0.106428	+	0.431795i	0.893420	+	0.449222i	$0.148299\pi$
$788$	−10.2846	−	11.6089i	−0.366374	−	0.413551i
$789$	2.83509	+	2.51167i	0.100932	+	0.0894178i
$790$	4.35292	+	6.30629i	0.154870	+	0.224368i
$791$	4.84230	+	9.22623i	0.172172	+	0.328047i
$792$	3.70319	−	9.76452i	0.131587	−	0.346967i
$793$	−7.95439	+	6.83384i	−0.282469	+	0.242677i
$794$	−8.04690	−	21.2179i	−0.285574	−	0.752997i
$795$	14.1142	−	15.9317i	0.500580	−	0.565038i
$796$	4.14285	+	3.67024i	0.146839	+	0.130088i
$797$	20.6505	−	5.08989i	0.731478	−	0.180293i	0.144051	−	0.989570i	$-0.453987\pi$
$797$	20.6505	−	5.08989i	0.731478	−	0.180293i	0.587427	+	0.809277i	$0.300141\pi$
$798$	2.64264	+	10.7216i	0.0935486	+	0.379541i
$799$	−15.9963	−	1.94231i	−0.565909	−	0.0687138i
$800$	−20.0243	+	7.59422i	−0.707967	+	0.268496i
$801$	−6.38072	−	0.774760i	−0.225452	−	0.0273748i
$802$	−28.3721	+	41.1040i	−1.00185	+	1.45143i
$803$	30.9344	−	7.62465i	1.09165	−	0.269068i
$804$	−1.01128	−	1.14150i	−0.0356651	−	0.0402575i
$805$	−3.69580	−	30.4376i	−0.130260	−	1.07279i
$806$	−41.1581	−	37.5959i	−1.44973	−	1.32426i
$807$	−0.0465479	+	0.383356i	−0.00163856	+	0.0134948i
$808$	22.4230	−	15.4775i	0.788839	−	0.544496i
$809$	5.87442	−	15.4896i	0.206533	−	0.544584i	−0.791223	−	0.611527i	$-0.790555\pi$
$809$	5.87442	−	15.4896i	0.206533	−	0.544584i	0.997757	+	0.0669433i	$0.0213247\pi$
$810$	−0.653164	−	5.37929i	−0.0229498	−	0.189009i
$811$	13.3133	−	25.3663i	0.467492	−	0.890731i	−0.531553	−	0.847025i	$-0.678391\pi$
$811$	13.3133	−	25.3663i	0.467492	−	0.890731i	0.999044	−	0.0437058i	$-0.0139164\pi$
$812$	−2.16761	+	2.44673i	−0.0760683	+	0.0858633i
$813$	−3.59676	−	2.48266i	−0.126144	−	0.0870708i
$814$	−18.9824	+	13.1026i	−0.665334	+	0.459247i
$815$	0.946635	+	0.496832i	0.0331592	+	0.0174033i
$816$	−3.86169	+	31.8039i	−0.135186	+	1.11336i
$817$	−19.5199	−	13.4736i	−0.682914	−	0.471381i
$818$	11.4251	+	16.5521i	0.399469	+	0.578730i
$819$	3.82274	+	0.523291i	0.133577	+	0.0182853i
$820$	8.30052	−	12.0254i	0.289867	−	0.419944i
$821$	−29.1884	+	11.0697i	−1.01868	+	0.386336i	−0.806715	−	0.590941i	$-0.798757\pi$
$821$	−29.1884	+	11.0697i	−1.01868	+	0.386336i	−0.211969	+	0.977276i	$0.567987\pi$
$822$	−21.3095			−0.743254
$823$	11.7694			0.410254			0.205127	−	0.978735i	$-0.434239\pi$
$823$	11.7694			0.410254			0.205127	+	0.978735i	$0.434239\pi$
$824$	3.46013	−	1.31225i	0.120539	−	0.0457145i
$825$	6.92308	+	28.0880i	0.241031	+	0.977899i
$826$			0.453154i			0.0157672i
$827$	0.178335	−	0.723533i	0.00620131	−	0.0251597i	−0.967760	−	0.251875i	$-0.918953\pi$
$827$	0.178335	−	0.723533i	0.00620131	−	0.0251597i	0.973961	+	0.226716i	$0.0727988\pi$
$828$	−1.95479	+	5.15435i	−0.0679335	+	0.179126i
$829$	14.2817	+	7.49561i	0.496024	+	0.260333i	0.694133	−	0.719847i	$-0.255788\pi$
$829$	14.2817	+	7.49561i	0.496024	+	0.260333i	−0.198109	+	0.980180i	$0.563480\pi$
$830$	−59.9077	−	22.7200i	−2.07943	−	0.788622i
$831$	−12.5477	−	6.58553i	−0.435274	−	0.228449i
$832$	5.38801	−	13.5802i	0.186796	−	0.470810i
$833$	−34.0942	+	17.8940i	−1.18129	+	0.619991i
$834$	12.2038	−	1.48180i	0.422581	−	0.0513107i
$835$	−9.56318	−	25.2160i	−0.330948	−	0.872637i
$836$	−2.32193	+	19.1228i	−0.0803057	+	0.661377i
$837$	8.89459	+	3.37327i	0.307442	+	0.116597i
$838$	−3.67579	−	1.39404i	−0.126978	−	0.0481565i
$839$	−24.8669	+	17.1643i	−0.858499	+	0.592579i	−0.913925	−	0.405884i	$-0.866964\pi$
$839$	−24.8669	+	17.1643i	−0.858499	+	0.592579i	0.0554257	+	0.998463i	$0.482348\pi$
$840$	3.66100	+	6.97544i	0.126316	+	0.240676i
$841$	6.14120	+	1.51367i	0.211766	+	0.0521955i
$842$	11.1328	−	9.86279i	0.383661	−	0.339894i
$843$	−20.2647	−	2.46058i	−0.697954	−	0.0847470i
$844$	−11.3975			−0.392318
$845$	40.0405	+	16.5956i	1.37743	+	0.570904i
$846$	3.98220			0.136911
$847$	−12.0794	−	1.46671i	−0.415055	−	0.0503968i
$848$	23.2777	−	20.6223i	0.799360	−	0.708171i
$849$	−20.9607	−	5.16635i	−0.719369	−	0.177309i
$850$	−30.3811	−	57.8864i	−1.04206	−	1.98549i
$851$	−21.2209	+	14.6477i	−0.727441	+	0.502117i
$852$	−6.08247	−	2.30678i	−0.208382	−	0.0790289i
$853$	−29.8196	−	11.3091i	−1.02100	−	0.387216i	−0.213415	−	0.976962i	$-0.568459\pi$
$853$	−29.8196	−	11.3091i	−1.02100	−	0.387216i	−0.807589	+	0.589746i	$0.799228\pi$
$854$	0.609747	−	5.02172i	0.0208651	−	0.171840i
$855$	−7.50644	−	19.7929i	−0.256715	−	0.676902i
$856$	41.7239	−	5.06620i	1.42609	−	0.173159i
$857$	21.0465	−	11.0460i	0.718933	−	0.377325i	−0.0652379	−	0.997870i	$-0.520781\pi$
$857$	21.0465	−	11.0460i	0.718933	−	0.377325i	0.784171	+	0.620544i	$0.213088\pi$
$858$	24.3428	+	13.2523i	0.831050	+	0.452425i
$859$	−24.7695	−	13.0000i	−0.845124	−	0.443555i	−0.0141718	−	0.999900i	$-0.504511\pi$
$859$	−24.7695	−	13.0000i	−0.845124	−	0.443555i	−0.830952	+	0.556345i	$0.812203\pi$
$860$	7.47058	+	2.83322i	0.254745	+	0.0966119i
$861$	−6.47365	−	3.39763i	−0.220621	−	0.115791i
$862$	−23.3511	+	61.5717i	−0.795341	+	2.09714i
$863$	4.38368	−	17.7853i	0.149222	−	0.605419i	−0.847937	−	0.530097i	$-0.822155\pi$
$863$	4.38368	−	17.7853i	0.149222	−	0.605419i	0.997159	−	0.0753217i	$-0.0239984\pi$
$864$		−	3.50148i		−	0.119123i
$865$	10.1478	+	41.1714i	0.345037	+	1.39987i
$866$	9.69172	−	3.67558i	0.329338	−	0.124901i
$867$	−26.2512			−0.891536
$868$	6.53011			0.221646
$869$	6.25373	−	2.37173i	0.212143	−	0.0804554i
$870$	14.6580	−	21.2358i	0.496952	−	0.719960i
$871$	−7.12767	+	4.76143i	−0.241512	+	0.161335i
$872$	22.9894	+	33.3059i	0.778520	+	1.12788i
$873$	−12.5973	−	8.69529i	−0.426354	−	0.294291i
$874$	−10.6888	+	88.0299i	−0.361553	+	2.97765i
$875$	−3.52658	−	1.85089i	−0.119220	−	0.0625715i
$876$	3.55614	−	2.45463i	0.120151	−	0.0829341i
$877$	13.3187	+	9.19326i	0.449742	+	0.310434i	0.771319	−	0.636449i	$-0.219597\pi$
$877$	13.3187	+	9.19326i	0.449742	+	0.310434i	−0.321577	+	0.946883i	$0.604213\pi$
$878$	−13.7351	+	15.5038i	−0.463538	+	0.523227i
$879$	0.725043	−	1.38145i	0.0244551	−	0.0465953i
$880$	9.25974	+	76.2608i	0.312146	+	2.57075i
$881$	−14.1167	+	37.2227i	−0.475605	+	1.25407i	0.455801	+	0.890082i	$0.349353\pi$
$881$	−14.1167	+	37.2227i	−0.475605	+	1.25407i	−0.931405	+	0.363984i	$0.881416\pi$
$882$	7.83121	−	5.40550i	0.263691	−	0.182013i
$883$	−3.88528	+	31.9981i	−0.130750	+	1.07682i	0.768642	+	0.639680i	$0.220933\pi$
$883$	−3.88528	+	31.9981i	−0.130750	+	1.07682i	−0.899392	+	0.437144i	$0.855990\pi$
$884$	−14.7117	−	3.86441i	−0.494806	−	0.129974i
$885$	−0.104710	−	0.862363i	−0.00351978	−	0.0289880i
$886$	20.4336	+	23.0648i	0.686482	+	0.774878i
$887$	47.3193	−	11.6632i	1.58883	−	0.391610i	0.656818	−	0.754049i	$-0.271902\pi$
$887$	47.3193	−	11.6632i	1.58883	−	0.391610i	0.932008	+	0.362439i	$0.118056\pi$
$888$	3.76344	−	5.45229i	0.126293	−	0.182967i
$889$	1.37565	+	0.167034i	0.0461379	+	0.00560216i
$890$	32.5664	−	12.3508i	1.09163	−	0.414000i
$891$	−4.69529	−	0.570112i	−0.157298	−	0.0190995i
$892$	0.889306	+	3.60806i	0.0297762	+	0.120807i
$893$	15.1044	−	3.72289i	0.505448	−	0.124582i
$894$	4.05729	+	3.59444i	0.135696	+	0.120216i
$895$	−20.1764	+	22.7744i	−0.674422	+	0.761265i
$896$	5.15652	+	13.5966i	0.172267	+	0.454231i
$897$	27.2133	+	14.8150i	0.908627	+	0.494658i
$898$	1.82866	−	4.82179i	0.0610233	−	0.160905i
$899$	21.0511	+	40.1095i	0.702093	+	1.33773i
$900$	2.22877	+	3.22893i	0.0742922	+	0.107631i
$901$	31.4254	+	27.8404i	1.04693	+	0.927499i
$902$	−34.8262	−	39.3106i	−1.15958	−	1.30890i
$903$	0.956711	−	3.88153i	0.0318374	−	0.129169i
$904$	−9.99098	−	19.0362i	−0.332295	−	0.633135i
$905$	−7.98628	−	5.51253i	−0.265473	−	0.183243i
$906$	−11.4086	−	30.0819i	−0.379025	−	0.999406i
$907$	−41.0168	+	21.5273i	−1.36194	+	0.714801i	−0.978009	−	0.208561i	$-0.933122\pi$
$907$	−41.0168	+	21.5273i	−1.36194	+	0.714801i	−0.383931	+	0.923362i	$0.625430\pi$
$908$	6.36118	−	12.1202i	0.211103	−	0.402223i
$909$	−9.23656	−	8.18287i	−0.306357	−	0.271409i
$910$	−19.6597	+	7.11577i	−0.651712	+	0.235885i
$911$	−26.7387	+	23.6884i	−0.885893	+	0.784833i	−0.977494	−	0.210963i	$-0.932340\pi$
$911$	−26.7387	+	23.6884i	−0.885893	+	0.784833i	0.0916011	+	0.995796i	$0.470802\pi$
$912$	−7.40185	−	30.0305i	−0.245100	−	0.994408i
$913$	−31.7687	+	46.0249i	−1.05139	+	1.52320i
$914$	43.6865	−	38.7028i	1.44502	−	1.28018i
$915$			9.69734i			0.320584i
$916$	7.75450	+	8.75302i	0.256216	+	0.289208i
$917$	2.95919	−	5.63827i	0.0977212	−	0.186192i
$918$	10.6107	−	1.28837i	0.350205	−	0.0425226i
$919$	33.9209	−	17.8030i	1.11895	−	0.587268i	0.199270	−	0.979945i	$-0.436143\pi$
$919$	33.9209	−	17.8030i	1.11895	−	0.587268i	0.919677	+	0.392676i	$0.128451\pi$
$920$	7.62544	+	62.8012i	0.251403	+	2.07049i
$921$	0.254342	−	1.03191i	0.00838085	−	0.0340024i
$922$	−58.0027	−	14.2964i	−1.91022	−	0.470826i
$923$	−17.4827	+	32.1135i	−0.575449	+	1.05703i
$924$	−3.15245	+	0.777008i	−0.103708	+	0.0255617i
$925$			18.3520i			0.603410i
$926$	−16.8997	−	4.16539i	−0.555357	−	0.136883i
$927$	−0.952094	−	1.37935i	−0.0312709	−	0.0453037i
$928$	11.0565	−	12.4802i	0.362949	−	0.409684i
$929$	−0.522598	+	0.0634548i	−0.0171459	+	0.00208189i	−0.129105	−	0.991631i	$-0.541210\pi$
$929$	−0.522598	+	0.0634548i	−0.0171459	+	0.00208189i	0.111959	+	0.993713i	$0.464287\pi$
$930$	−51.1719	+	6.21339i	−1.67799	+	0.203745i
$931$	24.6501	−	27.8242i	0.807874	−	0.911901i
$932$	−1.82839	−	2.64888i	−0.0598909	−	0.0867670i
$933$	13.5413	+	3.33762i	0.443321	+	0.109269i
$934$			40.5062i			1.32540i
$935$	−100.696	+	24.8193i	−3.29311	+	0.811680i
$936$	−7.88735	−	1.07969i	−0.257806	−	0.0352909i
$937$	−11.5454	−	2.84569i	−0.377172	−	0.0929646i	0.0461720	−	0.998934i	$-0.485298\pi$
$937$	−11.5454	−	2.84569i	−0.377172	−	0.0929646i	−0.423344	+	0.905969i	$0.639144\pi$
$938$	0.989524	−	4.01466i	0.0323091	−	0.131083i
$939$	−3.34366	−	27.5375i	−0.109116	−	0.898654i
$940$	−4.64008	+	2.43530i	−0.151343	+	0.0794309i
$941$	−6.21330	+	0.754431i	−0.202548	+	0.0245938i	−0.221182	−	0.975233i	$-0.570991\pi$
$941$	−6.21330	+	0.754431i	−0.202548	+	0.0245938i	0.0186339	+	0.999826i	$0.494068\pi$
$942$	−16.7006	+	31.8204i	−0.544136	+	1.03676i
$943$	−38.9329	−	43.9462i	−1.26783	−	1.43108i
$944$		−	1.26925i		−	0.0413106i
$945$	2.67062	−	2.36596i	0.0868753	−	0.0769648i
$946$	16.3131	−	23.6337i	0.530386	−	0.768396i
$947$	−10.4488	−	42.3923i	−0.339539	−	1.37756i	−0.854100	−	0.520110i	$-0.825891\pi$
$947$	−10.4488	−	42.3923i	−0.339539	−	1.37756i	0.514561	−	0.857454i	$-0.327955\pi$
$948$	0.678980	−	0.601524i	0.0220523	−	0.0195366i
$949$	−10.9584	−	21.6746i	−0.355725	−	0.703586i
$950$	47.2409	+	41.8518i	1.53270	+	1.35785i
$951$	−0.934880	+	1.78127i	−0.0303156	+	0.0577615i
$952$	−13.7591	+	7.22135i	−0.445936	+	0.234045i
$953$	9.46784	+	24.9646i	0.306693	+	0.808684i	0.996414	+	0.0846087i	$0.0269640\pi$
$953$	9.46784	+	24.9646i	0.306693	+	0.808684i	−0.689721	+	0.724075i	$0.742267\pi$
$954$	−8.53882	−	5.89392i	−0.276455	−	0.190823i
$955$	−9.16145	−	17.4557i	−0.296458	−	0.564853i
$956$	2.48726	−	10.0912i	0.0804437	−	0.326373i
$957$	−14.9351	−	16.8582i	−0.482783	−	0.544950i
$958$	−29.0569	−	25.7421i	−0.938785	−	0.831691i
$959$	−7.97043	−	11.5472i	−0.257379	−	0.372877i
$960$	−6.27848	−	11.9626i	−0.202637	−	0.386092i
$961$	21.0964	−	55.6266i	0.680528	−	1.79441i
$962$	12.9821	+	11.8585i	0.418560	+	0.382333i
$963$	−6.75020	−	17.7988i	−0.217522	−	0.573559i
$964$	2.99827	−	3.38435i	0.0965677	−	0.109002i
$965$	−15.3053	−	13.5593i	−0.492694	−	0.436489i
$966$	−14.5120	+	3.57687i	−0.466914	+	0.115084i
$967$	0.224464	+	0.910687i	0.00721828	+	0.0292857i	0.974441	−	0.224646i	$-0.0721224\pi$
$967$	0.224464	+	0.910687i	0.00721828	+	0.0292857i	−0.967222	+	0.253931i	$0.918276\pi$
$968$	24.9232	+	3.02622i	0.801062	+	0.0972665i
$969$	39.0416	−	14.8065i	1.25420	−	0.475654i
$970$	82.3401	+	9.99790i	2.64378	+	0.321013i
$971$	11.2175	−	16.2514i	0.359987	−	0.521531i	−0.600586	−	0.799560i	$-0.705066\pi$
$971$	11.2175	−	16.2514i	0.359987	−	0.521531i	0.960573	+	0.278030i	$0.0896813\pi$
$972$	−0.622835	+	0.153515i	−0.0199774	+	0.00492400i
$973$	5.36755	+	6.05872i	0.172076	+	0.194233i
$974$	0.334443	+	2.75438i	0.0107162	+	0.0882562i
$975$	19.6802	−	9.95010i	0.630271	−	0.318658i
$976$	−1.70786	+	14.0655i	−0.0546671	+	0.450224i
$977$	−30.5673	+	21.0991i	−0.977936	+	0.675020i	−0.945897	−	0.324466i	$-0.894815\pi$
$977$	−30.5673	+	21.0991i	−0.977936	+	0.675020i	−0.0320386	+	0.999487i	$0.510200\pi$
$978$	0.184801	−	0.487279i	0.00590928	−	0.0155815i
$979$	−3.66444	−	30.1794i	−0.117116	−	0.964538i
$980$	−5.81927	+	11.0877i	−0.185890	+	0.354183i
$981$	12.1544	−	13.7195i	0.388060	−	0.438029i
$982$	23.9623	+	16.5400i	0.764668	+	0.527812i
$983$	13.5863	−	9.37794i	0.433336	−	0.299110i	−0.331357	−	0.943506i	$-0.607506\pi$
$983$	13.5863	−	9.37794i	0.433336	−	0.299110i	0.764692	+	0.644396i	$0.222891\pi$
$984$	13.3569	+	7.01025i	0.425803	+	0.223478i
$985$	−9.71658	+	80.0232i	−0.309596	+	2.54975i
$986$	41.8878	+	28.9130i	1.33398	+	0.920779i
$987$	1.48947	+	2.15787i	0.0474103	+	0.0686857i
$988$	14.6027	−	1.54806i	0.464575	−	0.0492505i
$989$	18.2368	−	26.4206i	0.579896	−	0.840125i
$990$	23.9642	−	9.08842i	0.761632	−	0.288849i
$991$	19.2056			0.610086			0.305043	−	0.952339i	$-0.401329\pi$
$991$	19.2056			0.610086			0.305043	+	0.952339i	$0.401329\pi$
$992$	−33.3087			−1.05755
$993$	−10.0492	+	3.81116i	−0.318902	+	0.120944i
$994$	−4.22095	−	17.1251i	−0.133880	−	0.543174i
$995$		−	28.7674i		−	0.911988i
$996$	−1.81514	+	7.36433i	−0.0575151	+	0.233348i
$997$	7.30908	−	19.2724i	0.231481	−	0.610365i	−0.768069	−	0.640367i	$-0.778782\pi$
$997$	7.30908	−	19.2724i	0.231481	−	0.610365i	0.999550	+	0.0300024i	$0.00955151\pi$
$998$	−0.112712	−	0.0591557i	−0.00356783	−	0.00187254i
$999$	−2.80553	−	1.06400i	−0.0887632	−	0.0336634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.64.4	✓	192
169.103	even	26	inner	507.2.p.b.103.4	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.64.4	✓	192	1.1	even	1	trivial
507.2.p.b.103.4	yes	192	169.103	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61341 - 0.195904i) q^{2} +(0.748511 - 0.663123i) q^{3} +(0.622835 + 0.153515i) q^{4} +(-1.54944 - 2.95221i) q^{5} +(-1.33756 + 0.923254i) q^{6} +(-1.00058 - 0.379471i) q^{7} +(2.06448 + 0.782953i) q^{8} +(0.120537 - 0.992709i) q^{9} +O(q^{10})\)	\(q+(-1.61341 - 0.195904i) q^{2} +(0.748511 - 0.663123i) q^{3} +(0.622835 + 0.153515i) q^{4} +(-1.54944 - 2.95221i) q^{5} +(-1.33756 + 0.923254i) q^{6} +(-1.00058 - 0.379471i) q^{7} +(2.06448 + 0.782953i) q^{8} +(0.120537 - 0.992709i) q^{9} +(1.92153 + 5.06666i) q^{10} +(4.69529 - 0.570112i) q^{11} +(0.567998 - 0.298108i) q^{12} +(-1.22711 - 3.39031i) q^{13} +(1.54001 + 0.808261i) q^{14} +(-3.11745 - 1.18229i) q^{15} +(-4.31346 - 2.26388i) q^{16} +(2.33208 - 6.14919i) q^{17} +(-0.388951 + 1.57803i) q^{18} +6.34907i q^{19} +(-0.511836 - 2.07660i) q^{20} +(-1.00058 + 0.379471i) q^{21} -7.68713 q^{22} -8.59360 q^{23} +(2.06448 - 0.782953i) q^{24} +(-3.47444 + 5.03360i) q^{25} +(1.31566 + 5.71036i) q^{26} +(-0.568065 - 0.822984i) q^{27} +(-0.564944 - 0.389953i) q^{28} +(0.573975 - 4.72711i) q^{29} +(4.79811 + 2.51824i) q^{30} +(-7.82885 + 5.40386i) q^{31} +(2.88166 + 1.98907i) q^{32} +(3.13642 - 3.54029i) q^{33} +(-4.96725 + 9.46431i) q^{34} +(0.430064 + 3.54190i) q^{35} +(0.227470 - 0.599789i) q^{36} +(2.46938 - 1.70449i) q^{37} +(1.24381 - 10.2437i) q^{38} +(-3.16670 - 1.72396i) q^{39} +(-0.887340 - 7.30790i) q^{40} +(4.53046 + 5.11383i) q^{41} +(1.68869 - 0.416225i) q^{42} +(-2.12214 + 3.07445i) q^{43} +(3.01191 + 0.365712i) q^{44} +(-3.11745 + 1.18229i) q^{45} +(13.8650 + 1.68352i) q^{46} +(-0.586369 - 2.37899i) q^{47} +(-4.72990 + 1.16582i) q^{48} +(-4.38241 - 3.88247i) q^{49} +(6.59181 - 7.44061i) q^{50} +(-2.33208 - 6.14919i) q^{51} +(-0.243826 - 2.29998i) q^{52} +(-2.26375 + 5.96901i) q^{53} +(0.755297 + 1.43910i) q^{54} +(-8.95815 - 12.9781i) q^{55} +(-1.76857 - 1.56682i) q^{56} +(4.21021 + 4.75234i) q^{57} +(-1.85212 + 7.51433i) q^{58} +(0.121083 + 0.230704i) q^{59} +(-1.76015 - 1.21495i) q^{60} +(-1.03138 - 2.71952i) q^{61} +(13.6898 - 7.18496i) q^{62} +(-0.497312 + 0.947548i) q^{63} +(3.03304 + 2.68704i) q^{64} +(-8.10756 + 8.87576i) q^{65} +(-5.75390 + 5.09751i) q^{66} +(-0.568943 - 2.30829i) q^{67} +(2.39649 - 3.47192i) q^{68} +(-6.43240 + 5.69861i) q^{69} -5.79879i q^{70} +(-6.72474 - 7.59066i) q^{71} +(1.02609 - 1.95505i) q^{72} +(6.68698 - 0.811946i) q^{73} +(-4.31804 + 2.26628i) q^{74} +(0.737236 + 6.07168i) q^{75} +(-0.974677 + 3.95442i) q^{76} +(-4.91437 - 1.21128i) q^{77} +(4.77146 + 3.40182i) q^{78} +(1.37301 - 0.338416i) q^{79} +16.2420i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-6.30767 - 9.13824i) q^{82} +(-7.84069 + 8.85031i) q^{83} +(-0.681453 + 0.0827434i) q^{84} +(-21.7671 + 2.64300i) q^{85} +(4.02618 - 4.54461i) q^{86} +(-2.70503 - 3.91891i) q^{87} +(10.1397 + 2.49921i) q^{88} -6.42759i q^{89} +(5.26134 - 1.29680i) q^{90} +(-0.0586956 + 3.85794i) q^{91} +(-5.35239 - 1.31925i) q^{92} +(-2.27655 + 9.23634i) q^{93} +(0.480001 + 3.95316i) q^{94} +(18.7438 - 9.83748i) q^{95} +(3.47595 - 0.422057i) q^{96} +(7.11346 - 13.5536i) q^{97} +(6.31003 + 7.12256i) q^{98} -4.72978i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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