LMFDB - Embedded newform 98.2.g.b.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			51.2
Character	$\chi$	$=$	98.51
Dual form			98.2.g.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.955573 + 0.294755i) q^{2} +(0.427316 - 1.08878i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0821245 + 0.0123783i) q^{5} +(0.729256 - 0.914459i) q^{6} +(-2.45519 - 0.985929i) q^{7} +(0.623490 + 0.781831i) q^{8} +(1.19630 + 1.11001i) q^{9} +O(q^{10})$	\(q+(0.955573 + 0.294755i) q^{2} +(0.427316 - 1.08878i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0821245 + 0.0123783i) q^{5} +(0.729256 - 0.914459i) q^{6} +(-2.45519 - 0.985929i) q^{7} +(0.623490 + 0.781831i) q^{8} +(1.19630 + 1.11001i) q^{9} +(-0.0821245 - 0.0123783i) q^{10} +(-2.81322 + 2.61029i) q^{11} +(0.966399 - 0.658880i) q^{12} +(-0.384222 - 1.68338i) q^{13} +(-2.05550 - 1.66581i) q^{14} +(-0.0216159 + 0.0947053i) q^{15} +(0.365341 + 0.930874i) q^{16} +(-0.107488 - 1.43433i) q^{17} +(0.815975 + 1.41331i) q^{18} +(-1.48321 + 2.56900i) q^{19} +(-0.0748274 - 0.0360350i) q^{20} +(-2.12260 + 2.25187i) q^{21} +(-3.45763 + 1.66511i) q^{22} +(0.117227 - 1.56428i) q^{23} +(1.11767 - 0.344756i) q^{24} +(-4.77127 + 1.47174i) q^{25} +(0.129035 - 1.72185i) q^{26} +(4.88118 - 2.35065i) q^{27} +(-1.47318 - 2.19767i) q^{28} +(4.85915 + 2.34005i) q^{29} +(-0.0485704 + 0.0841264i) q^{30} +(-5.30003 - 9.17993i) q^{31} +(0.0747301 + 0.997204i) q^{32} +(1.63990 + 4.17841i) q^{33} +(0.320064 - 1.40229i) q^{34} +(0.213835 + 0.0505779i) q^{35} +(0.363143 + 1.59103i) q^{36} +(6.91645 - 4.71556i) q^{37} +(-2.17454 + 2.01768i) q^{38} +(-1.99703 - 0.301003i) q^{39} +(-0.0608815 - 0.0564898i) q^{40} +(2.53433 + 3.17795i) q^{41} +(-2.69205 + 1.52617i) q^{42} +(-0.652186 + 0.817816i) q^{43} +(-3.79482 + 0.571977i) q^{44} +(-0.111986 - 0.0763507i) q^{45} +(0.573099 - 1.46023i) q^{46} +(8.15500 + 2.51548i) q^{47} +1.16964 q^{48} +(5.05589 + 4.84128i) q^{49} -4.99310 q^{50} +(-1.60761 - 0.495882i) q^{51} +(0.630826 - 1.60732i) q^{52} +(2.84982 + 1.94297i) q^{53} +(5.35719 - 0.807466i) q^{54} +(0.198723 - 0.249191i) q^{55} +(-0.759954 - 2.53426i) q^{56} +(2.16329 + 2.71267i) q^{57} +(3.95354 + 3.66834i) q^{58} +(3.45547 + 0.520829i) q^{59} +(-0.0712092 + 0.0660725i) q^{60} +(0.521887 - 0.355817i) q^{61} +(-2.35874 - 10.3343i) q^{62} +(-1.84276 - 3.90475i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(0.0523914 + 0.133491i) q^{65} +(0.335440 + 4.47614i) q^{66} +(-5.32626 - 9.22534i) q^{67} +(0.719177 - 1.24565i) q^{68} +(-1.65307 - 0.796078i) q^{69} +(0.189427 + 0.111360i) q^{70} +(-4.00735 + 1.92984i) q^{71} +(-0.121956 + 1.62739i) q^{72} +(-7.73648 + 2.38639i) q^{73} +(7.99911 - 2.46740i) q^{74} +(-0.436432 + 5.82378i) q^{75} +(-2.67266 + 1.28708i) q^{76} +(9.48054 - 3.63511i) q^{77} +(-1.81958 - 0.876264i) q^{78} +(6.16039 - 10.6701i) q^{79} +(-0.0415261 - 0.0719253i) q^{80} +(-0.107677 - 1.43686i) q^{81} +(1.48502 + 3.78377i) q^{82} +(-3.19663 + 14.0054i) q^{83} +(-3.02230 + 0.664873i) q^{84} +(0.0265820 + 0.116463i) q^{85} +(-0.864267 + 0.589247i) q^{86} +(4.62420 - 4.29063i) q^{87} +(-3.79482 - 0.571977i) q^{88} +(-11.3737 - 10.5532i) q^{89} +(-0.0845059 - 0.105967i) q^{90} +(-0.716361 + 4.51184i) q^{91} +(0.978050 - 1.22644i) q^{92} +(-12.2597 + 1.84786i) q^{93} +(7.05124 + 4.80746i) q^{94} +(0.0900084 - 0.229338i) q^{95} +(1.11767 + 0.344756i) q^{96} -12.3285 q^{97} +(3.40428 + 6.11644i) q^{98} -6.26291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{21}\right)$

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 $

$2$	0.955573	+	0.294755i	0.675692	+	0.208423i
$2$	0.955573	+	0.294755i	0.675692	+	0.208423i
$3$	0.427316	−	1.08878i	0.246711	−	0.628610i	−0.752851	−	0.658191i	$-0.771322\pi$
$3$	0.427316	−	1.08878i	0.246711	−	0.628610i	0.999562	+	0.0295810i	$0.00941731\pi$
$4$	0.826239	+	0.563320i	0.413119	+	0.281660i
$5$	−0.0821245	+	0.0123783i	−0.0367272	+	0.00553573i	−0.167380	−	0.985892i	$-0.553531\pi$
$5$	−0.0821245	+	0.0123783i	−0.0367272	+	0.00553573i	0.130653	+	0.991428i	$0.458293\pi$
$6$	0.729256	−	0.914459i	0.297718	−	0.373326i
$7$	−2.45519	−	0.985929i	−0.927974	−	0.372646i
$7$	−2.45519	−	0.985929i	−0.927974	−	0.372646i
$8$	0.623490	+	0.781831i	0.220437	+	0.276419i
$9$	1.19630	+	1.11001i	0.398768	+	0.370003i
$10$	−0.0821245	−	0.0123783i	−0.0259700	−	0.00391436i
$11$	−2.81322	+	2.61029i	−0.848218	+	0.787031i	−0.978889	−	0.204395i	$-0.934477\pi$
$11$	−2.81322	+	2.61029i	−0.848218	+	0.787031i	0.130671	+	0.991426i	$0.458287\pi$
$12$	0.966399	−	0.658880i	0.278975	−	0.190202i
$13$	−0.384222	−	1.68338i	−0.106564	−	0.466887i	−0.999849	−	0.0173958i	$-0.994462\pi$
$13$	−0.384222	−	1.68338i	−0.106564	−	0.466887i	0.893285	−	0.449491i	$-0.148395\pi$
$14$	−2.05550	−	1.66581i	−0.549356	−	0.445205i
$15$	−0.0216159	+	0.0947053i	−0.00558119	+	0.0244528i
$16$	0.365341	+	0.930874i	0.0913353	+	0.232718i
$17$	−0.107488	−	1.43433i	−0.0260698	−	0.347877i	−0.994952	−	0.100354i	$-0.968002\pi$
$17$	−0.107488	−	1.43433i	−0.0260698	−	0.347877i	0.968882	−	0.247523i	$-0.0796166\pi$
$18$	0.815975	+	1.41331i	0.192327	+	0.333121i
$19$	−1.48321	+	2.56900i	−0.340272	+	0.589369i	−0.984483	−	0.175479i	$-0.943853\pi$
$19$	−1.48321	+	2.56900i	−0.340272	+	0.589369i	0.644211	+	0.764848i	$0.277186\pi$
$20$	−0.0748274	−	0.0360350i	−0.0167319	−	0.00805766i
$21$	−2.12260	+	2.25187i	−0.463190	+	0.491397i
$22$	−3.45763	+	1.66511i	−0.737170	+	0.355002i
$23$	0.117227	−	1.56428i	0.0244435	−	0.326176i	−0.971556	−	0.236812i	$-0.923898\pi$
$23$	0.117227	−	1.56428i	0.0244435	−	0.326176i	0.995999	−	0.0893639i	$-0.0284834\pi$
$24$	1.11767	−	0.344756i	0.228144	−	0.0703731i
$25$	−4.77127	+	1.47174i	−0.954255	+	0.294349i
$26$	0.129035	−	1.72185i	0.0253058	−	0.337682i
$27$	4.88118	−	2.35065i	0.939383	−	0.452383i
$28$	−1.47318	−	2.19767i	−0.278404	−	0.415320i
$29$	4.85915	+	2.34005i	0.902322	+	0.434535i	0.826727	−	0.562603i	$-0.190200\pi$
$29$	4.85915	+	2.34005i	0.902322	+	0.434535i	0.0755951	+	0.997139i	$0.475914\pi$
$30$	−0.0485704	+	0.0841264i	−0.00886770	+	0.0153593i
$31$	−5.30003	−	9.17993i	−0.951914	−	1.64876i	−0.741277	−	0.671199i	$-0.765780\pi$
$31$	−5.30003	−	9.17993i	−0.951914	−	1.64876i	−0.210637	−	0.977564i	$-0.567554\pi$
$32$	0.0747301	+	0.997204i	0.0132105	+	0.176282i
$33$	1.63990	+	4.17841i	0.285471	+	0.727367i
$34$	0.320064	−	1.40229i	0.0548905	−	0.240491i
$35$	0.213835	+	0.0505779i	0.0361447	+	0.00854923i
$36$	0.363143	+	1.59103i	0.0605239	+	0.265172i
$37$	6.91645	−	4.71556i	1.13706	−	0.775233i	0.159771	−	0.987154i	$-0.448924\pi$
$37$	6.91645	−	4.71556i	1.13706	−	0.775233i	0.977287	+	0.211921i	$0.0679719\pi$
$38$	−2.17454	+	2.01768i	−0.352758	+	0.327311i
$39$	−1.99703	−	0.301003i	−0.319780	−	0.0481991i
$40$	−0.0608815	−	0.0564898i	−0.00962621	−	0.00893182i
$41$	2.53433	+	3.17795i	0.395796	+	0.496312i	0.939301	−	0.343093i	$-0.111475\pi$
$41$	2.53433	+	3.17795i	0.395796	+	0.496312i	−0.543505	+	0.839406i	$0.682903\pi$
$42$	−2.69205	+	1.52617i	−0.415393	+	0.235494i
$43$	−0.652186	+	0.817816i	−0.0994574	+	0.124716i	−0.829069	−	0.559146i	$-0.811129\pi$
$43$	−0.652186	+	0.817816i	−0.0994574	+	0.124716i	0.729612	+	0.683861i	$0.239701\pi$
$44$	−3.79482	+	0.571977i	−0.572090	+	0.0862287i
$45$	−0.111986	−	0.0763507i	−0.0166939	−	0.0113817i
$46$	0.573099	−	1.46023i	0.0844989	−	0.215300i
$47$	8.15500	+	2.51548i	1.18953	+	0.366921i	0.825465	−	0.564453i	$-0.190913\pi$
$47$	8.15500	+	2.51548i	1.18953	+	0.366921i	0.364064	+	0.931374i	$0.381389\pi$
$48$	1.16964			0.168822
$49$	5.05589	+	4.84128i	0.722270	+	0.691611i
$50$	−4.99310			−0.706131
$51$	−1.60761	−	0.495882i	−0.225110	−	0.0694374i
$52$	0.630826	−	1.60732i	0.0874798	−	0.222895i
$53$	2.84982	+	1.94297i	0.391452	+	0.266888i	0.743012	−	0.669278i	$-0.233396\pi$
$53$	2.84982	+	1.94297i	0.391452	+	0.266888i	−0.351560	+	0.936165i	$0.614349\pi$
$54$	5.35719	−	0.807466i	0.729021	−	0.109882i
$55$	0.198723	−	0.249191i	0.0267959	−	0.0336009i
$56$	−0.759954	−	2.53426i	−0.101553	−	0.338655i
$57$	2.16329	+	2.71267i	0.286534	+	0.359302i
$58$	3.95354	+	3.66834i	0.519125	+	0.481677i
$59$	3.45547	+	0.520829i	0.449864	+	0.0678061i	0.370067	−	0.929005i	$-0.379335\pi$
$59$	3.45547	+	0.520829i	0.449864	+	0.0678061i	0.0797971	+	0.996811i	$0.474573\pi$
$60$	−0.0712092	+	0.0660725i	−0.00919307	+	0.00852993i
$61$	0.521887	−	0.355817i	0.0668208	−	0.0455576i	−0.529449	−	0.848342i	$-0.677601\pi$
$61$	0.521887	−	0.355817i	0.0668208	−	0.0455576i	0.596270	+	0.802784i	$0.296649\pi$
$62$	−2.35874	−	10.3343i	−0.299560	−	1.31246i
$63$	−1.84276	−	3.90475i	−0.232166	−	0.491952i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	0.0523914	+	0.133491i	0.00649835	+	0.0165575i
$66$	0.335440	+	4.47614i	0.0412899	+	0.550975i
$67$	−5.32626	−	9.22534i	−0.650706	−	1.12706i	−0.982952	−	0.183863i	$-0.941140\pi$
$67$	−5.32626	−	9.22534i	−0.650706	−	1.12706i	0.332246	−	0.943193i	$-0.392193\pi$
$68$	0.719177	−	1.24565i	0.0872131	−	0.151057i
$69$	−1.65307	−	0.796078i	−0.199007	−	0.0958366i
$70$	0.189427	+	0.111360i	0.0226409	+	0.0133101i
$71$	−4.00735	+	1.92984i	−0.475585	+	0.229030i	−0.656292	−	0.754507i	$-0.727876\pi$
$71$	−4.00735	+	1.92984i	−0.475585	+	0.229030i	0.180706	+	0.983537i	$0.442162\pi$
$72$	−0.121956	+	1.62739i	−0.0143726	+	0.191789i
$73$	−7.73648	+	2.38639i	−0.905486	+	0.279306i	−0.712315	−	0.701860i	$-0.752353\pi$
$73$	−7.73648	+	2.38639i	−0.905486	+	0.279306i	−0.193171	+	0.981165i	$0.561877\pi$
$74$	7.99911	−	2.46740i	0.929878	−	0.286829i
$75$	−0.436432	+	5.82378i	−0.0503949	+	0.672473i
$76$	−2.67266	+	1.28708i	−0.306575	+	0.147639i
$77$	9.48054	−	3.63511i	1.08041	−	0.414259i
$78$	−1.81958	−	0.876264i	−0.206027	−	0.0992174i
$79$	6.16039	−	10.6701i	0.693098	−	1.20048i	−0.277720	−	0.960662i	$-0.589579\pi$
$79$	6.16039	−	10.6701i	0.693098	−	1.20048i	0.970818	−	0.239818i	$-0.0770879\pi$
$80$	−0.0415261	−	0.0719253i	−0.00464276	−	0.00804149i
$81$	−0.107677	−	1.43686i	−0.0119642	−	0.159651i
$82$	1.48502	+	3.78377i	0.163993	+	0.417847i
$83$	−3.19663	+	14.0054i	−0.350876	+	1.53729i	0.424288	+	0.905527i	$0.360524\pi$
$83$	−3.19663	+	14.0054i	−0.350876	+	1.53729i	−0.775164	+	0.631760i	$0.782333\pi$
$84$	−3.02230	+	0.664873i	−0.329760	+	0.0725436i
$85$	0.0265820	+	0.116463i	0.00288322	+	0.0126322i
$86$	−0.864267	+	0.589247i	−0.0931963	+	0.0635401i
$87$	4.62420	−	4.29063i	0.495766	−	0.460004i
$88$	−3.79482	−	0.571977i	−0.404529	−	0.0609729i
$89$	−11.3737	−	10.5532i	−1.20560	−	1.11864i	−0.989839	−	0.142193i	$-0.954585\pi$
$89$	−11.3737	−	10.5532i	−1.20560	−	1.11864i	−0.215766	−	0.976445i	$-0.569225\pi$
$90$	−0.0845059	−	0.105967i	−0.00890771	−	0.0111699i
$91$	−0.716361	+	4.51184i	−0.0750951	+	0.472969i
$92$	0.978050	−	1.22644i	0.101969	−	0.127865i
$93$	−12.2597	+	1.84786i	−1.27128	+	0.191614i
$94$	7.05124	+	4.80746i	0.727280	+	0.495851i
$95$	0.0900084	−	0.229338i	0.00923466	−	0.0235295i
$96$	1.11767	+	0.344756i	0.114072	+	0.0351866i
$97$	−12.3285			−1.25177			−0.625885	−	0.779915i	$-0.715262\pi$
$97$	−12.3285			−1.25177			−0.625885	+	0.779915i	$0.715262\pi$
$98$	3.40428	+	6.11644i	0.343884	+	0.617854i
$99$	−6.26291			−0.629446
$100$	−4.77127	−	1.47174i	−0.477127	−	0.147174i
$101$	−5.14955	+	13.1208i	−0.512400	+	1.30557i	0.407424	+	0.913239i	$0.366427\pi$
$101$	−5.14955	+	13.1208i	−0.512400	+	1.30557i	−0.919823	+	0.392333i	$0.871668\pi$
$102$	−1.39002	−	0.947703i	−0.137633	−	0.0938366i
$103$	−15.5066	+	2.33725i	−1.52791	+	0.230296i	−0.858585	−	0.512671i	$-0.828656\pi$
$103$	−15.5066	+	2.33725i	−1.52791	+	0.230296i	−0.669328	+	0.742967i	$0.733418\pi$
$104$	1.07656	−	1.34997i	0.105566	−	0.132375i
$105$	0.146444	−	0.211207i	0.0142914	−	0.0206117i
$106$	2.15051	+	2.69665i	0.208876	+	0.261922i
$107$	8.48455	+	7.87251i	0.820232	+	0.761065i	0.973881	−	0.227061i	$-0.0729117\pi$
$107$	8.48455	+	7.87251i	0.820232	+	0.761065i	−0.153648	+	0.988126i	$0.549102\pi$
$108$	5.35719	+	0.807466i	0.515496	+	0.0776985i
$109$	−3.06504	+	2.84394i	−0.293577	+	0.272400i	−0.813185	−	0.582005i	$-0.802268\pi$
$109$	−3.06504	+	2.84394i	−0.293577	+	0.272400i	0.519608	+	0.854405i	$0.326078\pi$
$110$	0.263345	−	0.179546i	0.0251090	−	0.0171190i
$111$	−2.17871	−	9.54556i	−0.206794	−	0.906024i
$112$	0.0207943	−	2.64567i	0.00196488	−	0.249992i
$113$	3.69142	−	16.1732i	0.347259	−	1.52144i	−0.436114	−	0.899892i	$-0.643646\pi$
$113$	3.69142	−	16.1732i	0.347259	−	1.52144i	0.783373	−	0.621552i	$-0.213497\pi$
$114$	1.26760	+	3.22980i	0.118722	+	0.302498i
$115$	0.00973594	+	0.129917i	0.000907881	+	0.0121148i
$116$	2.69663	+	4.67070i	0.250376	+	0.433663i
$117$	1.40893	−	2.44033i	0.130255	−	0.225609i
$118$	3.14844	+	1.51621i	0.289837	+	0.139578i
$119$	−1.15025	+	3.62753i	−0.105443	+	0.332535i
$120$	−0.0875208	+	0.0421478i	−0.00798952	+	0.00384755i
$121$	0.278579	−	3.71738i	0.0253253	−	0.337943i
$122$	0.603580	−	0.186180i	0.0546456	−	0.0168559i
$123$	4.54306	−	1.40135i	0.409634	−	0.126355i
$124$	0.792144	−	10.5704i	0.0711366	−	0.949252i
$125$	0.747758	−	0.360101i	0.0668815	−	0.0322084i
$126$	−0.609949	−	4.27444i	−0.0543386	−	0.380797i
$127$	2.18072	+	1.05018i	0.193507	+	0.0931882i	0.528128	−	0.849165i	$-0.322894\pi$
$127$	2.18072	+	1.05018i	0.193507	+	0.0931882i	−0.334621	+	0.942353i	$0.608608\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.611735	+	1.05956i	0.0538602	+	0.0932887i
$130$	0.0107166	+	0.143003i	0.000939908	+	0.0125422i
$131$	0.160095	+	0.407915i	0.0139876	+	0.0356397i	0.937697	−	0.347454i	$-0.112954\pi$
$131$	0.160095	+	0.407915i	0.0139876	+	0.0356397i	−0.923709	+	0.383094i	$0.874859\pi$
$132$	−0.998828	+	4.37615i	−0.0869368	+	0.380895i
$133$	6.17442	−	4.84504i	0.535390	−	0.420118i
$134$	−2.37041	−	10.3854i	−0.204772	−	0.897164i
$135$	−0.371767	+	0.253467i	−0.0319966	+	0.0218149i
$136$	1.05439	−	0.978330i	0.0904131	−	0.0838911i
$137$	16.6234	+	2.50558i	1.42023	+	0.214066i	0.813836	−	0.581095i	$-0.197376\pi$
$137$	16.6234	+	2.50558i	1.42023	+	0.214066i	0.606399	+	0.795161i	$0.292614\pi$
$138$	−1.34498	−	1.24796i	−0.114493	−	0.106234i
$139$	12.5175	+	15.6965i	1.06172	+	1.33136i	0.940899	+	0.338687i	$0.109983\pi$
$139$	12.5175	+	15.6965i	1.06172	+	1.33136i	0.120825	+	0.992674i	$0.461446\pi$
$140$	0.148187	+	0.162247i	0.0125241	+	0.0137124i
$141$	6.22358	−	7.80412i	0.524120	−	0.657226i
$142$	−4.39815	+	0.662914i	−0.369084	+	0.0556305i
$143$	5.47502	+	3.73280i	0.457844	+	0.312153i
$144$	−0.596219	+	1.51914i	−0.0496849	+	0.126595i
$145$	−0.428021	−	0.132027i	−0.0355452	−	0.0109643i
$146$	−8.09617			−0.670044
$147$	7.43157	−	3.43601i	0.612945	−	0.283398i
$148$	8.37101			0.688093
$149$	−18.6831	−	5.76298i	−1.53058	−	0.472122i	−0.588781	−	0.808293i	$-0.700392\pi$
$149$	−18.6831	−	5.76298i	−1.53058	−	0.472122i	−0.941801	+	0.336171i	$0.890868\pi$
$150$	−2.13363	+	5.43641i	−0.174210	+	0.443881i
$151$	1.03071	+	0.702723i	0.0838776	+	0.0571868i	0.604533	−	0.796580i	$-0.293360\pi$
$151$	1.03071	+	0.702723i	0.0838776	+	0.0571868i	−0.520655	+	0.853767i	$0.674312\pi$
$152$	−2.93329	+	0.442123i	−0.237922	+	0.0358609i
$153$	1.46353	−	1.83521i	0.118320	−	0.148368i
$154$	10.1308	−	0.679173i	0.816364	−	0.0547294i
$155$	0.548894	+	0.688292i	0.0440882	+	0.0552849i
$156$	−1.48046	−	1.37367i	−0.118532	−	0.109981i
$157$	9.19955	+	1.38661i	0.734204	+	0.110663i	0.505493	−	0.862831i	$-0.331311\pi$
$157$	9.19955	+	1.38661i	0.734204	+	0.110663i	0.228711	+	0.973494i	$0.426549\pi$
$158$	9.03177	−	8.38026i	0.718529	−	0.666697i
$159$	3.33325	−	2.27257i	0.264344	−	0.180227i
$160$	−0.0184808	−	0.0809698i	−0.00146104	−	0.00640123i
$161$	−1.83009	+	3.72503i	−0.144231	+	0.293574i
$162$	0.320627	−	1.40476i	0.0251908	−	0.110368i
$163$	6.29070	+	16.0284i	0.492725	+	1.25544i	0.933743	+	0.357945i	$0.116523\pi$
$163$	6.29070	+	16.0284i	0.492725	+	1.25544i	−0.441017	+	0.897499i	$0.645382\pi$
$164$	0.303759	+	4.05338i	0.0237196	+	0.316516i
$165$	−0.186398	−	0.322850i	−0.0145110	−	0.0251339i
$166$	−7.18277	+	12.4409i	−0.557491	+	0.965602i
$167$	−0.863130	−	0.415661i	−0.0667910	−	0.0321648i	0.400190	−	0.916432i	$-0.368944\pi$
$167$	−0.863130	−	0.415661i	−0.0667910	−	0.0321648i	−0.466981	+	0.884267i	$0.654658\pi$
$168$	−3.08400	−	0.255504i	−0.237936	−	0.0197126i
$169$	9.02644	−	4.34690i	0.694341	−	0.334377i
$170$	−0.00892714	+	0.119124i	−0.000684680	+	0.00913642i
$171$	−4.62599	+	1.42693i	−0.353758	+	0.109120i
$172$	−0.999553	+	0.308321i	−0.0762152	+	0.0235093i
$173$	1.35337	−	18.0595i	0.102895	−	1.37304i	−0.671813	−	0.740720i	$-0.734484\pi$
$173$	1.35337	−	18.0595i	0.102895	−	1.37304i	0.774709	−	0.632319i	$-0.217897\pi$
$174$	5.68344	−	2.73700i	0.430861	−	0.207492i
$175$	13.1654	+	1.09073i	0.995211	+	0.0824514i
$176$	−3.45763	−	1.66511i	−0.260629	−	0.125512i
$177$	2.04365	−	3.53970i	0.153610	−	0.266060i
$178$	−7.75774	−	13.4368i	−0.581467	−	1.00713i
$179$	0.172523	+	2.30216i	0.0128950	+	0.172071i	0.999933	+	0.0115842i	$0.00368745\pi$
$179$	0.172523	+	2.30216i	0.0128950	+	0.172071i	−0.987038	+	0.160487i	$0.948694\pi$
$180$	−0.0495172	−	0.126168i	−0.00369080	−	0.00940399i
$181$	−5.19876	+	22.7773i	−0.386421	+	1.69302i	0.290426	+	0.956897i	$0.406203\pi$
$181$	−5.19876	+	22.7773i	−0.386421	+	1.69302i	−0.676847	+	0.736124i	$0.736654\pi$
$182$	−2.01442	+	4.10024i	−0.149319	+	0.303930i
$183$	−0.164397	−	0.720268i	−0.0121525	−	0.0532438i
$184$	1.29610	−	0.883663i	0.0955494	−	0.0651445i
$185$	−0.509640	+	0.472877i	−0.0374695	+	0.0347666i
$186$	−12.2597	−	1.84786i	−0.898928	−	0.135492i
$187$	4.04641	+	3.75452i	0.295903	+	0.274558i
$188$	5.32095	+	6.67227i	0.388070	+	0.486625i
$189$	−14.3018	+	0.958797i	−1.04030	+	0.0697422i
$190$	0.153608	−	0.192618i	0.0111439	−	0.0139740i
$191$	−23.0712	+	3.47743i	−1.66938	+	0.251618i	−0.914598	−	0.404364i	$-0.867493\pi$
$191$	−23.0712	+	3.47743i	−1.66938	+	0.251618i	−0.754777	+	0.655982i	$0.772255\pi$
$192$	0.966399	+	0.658880i	0.0697438	+	0.0475505i
$193$	3.65095	−	9.30247i	0.262801	−	0.669607i	−0.737180	−	0.675696i	$-0.763843\pi$
$193$	3.65095	−	9.30247i	0.262801	−	0.669607i	0.999981	+	0.00608957i	$0.00193838\pi$
$194$	−11.7808	−	3.63389i	−0.845811	−	0.260898i
$195$	0.167731			0.0120114
$196$	1.45018	+	6.84814i	0.103584	+	0.489153i
$197$	−5.64688			−0.402324			−0.201162	−	0.979558i	$-0.564472\pi$
$197$	−5.64688			−0.402324			−0.201162	+	0.979558i	$0.564472\pi$
$198$	−5.98466	−	1.84602i	−0.425312	−	0.131191i
$199$	6.14835	−	15.6657i	0.435845	−	1.11051i	−0.529216	−	0.848487i	$-0.677514\pi$
$199$	6.14835	−	15.6657i	0.435845	−	1.11051i	0.965061	−	0.262027i	$-0.0843910\pi$
$200$	−4.12549	−	2.81271i	−0.291717	−	0.198889i
$201$	−12.3204	+	1.85700i	−0.869014	+	0.130983i
$202$	−8.78821	+	11.0201i	−0.618336	+	0.775369i
$203$	−9.62302	−	10.5360i	−0.675403	−	0.739484i
$204$	−1.04893	−	1.31532i	−0.0734397	−	0.0920905i
$205$	−0.247468	−	0.229617i	−0.0172839	−	0.0160371i
$206$	−15.5066	−	2.33725i	−1.08040	−	0.162844i
$207$	1.87661	−	1.74124i	0.130433	−	0.121024i
$208$	1.42665	−	0.972671i	0.0989202	−	0.0674426i
$209$	−2.53322	−	11.0988i	−0.175227	−	0.767718i
$210$	0.202192	−	0.158659i	0.0139526	−	0.0109485i
$211$	1.09599	−	4.80184i	0.0754510	−	0.330573i	−0.923089	−	0.384586i	$-0.874344\pi$
$211$	1.09599	−	4.80184i	0.0754510	−	0.330573i	0.998540	+	0.0540134i	$0.0172014\pi$
$212$	1.26011	+	3.21072i	0.0865449	+	0.220513i
$213$	0.388771	+	5.18779i	0.0266382	+	0.355462i
$214$	5.78714	+	10.0236i	0.395601	+	0.685201i
$215$	0.0434373	−	0.0752356i	0.00296240	−	0.00513103i
$216$	4.88118	+	2.35065i	0.332122	+	0.159942i
$217$	3.96182	+	27.7639i	0.268946	+	1.88474i
$218$	−3.76713	+	1.81415i	−0.255142	+	0.122870i
$219$	−0.707662	+	9.44309i	−0.0478194	+	0.638105i
$220$	0.304567	−	0.0939466i	0.0205339	−	0.00633388i
$221$	−2.37323	+	0.732046i	−0.159641	+	0.0492427i
$222$	0.731685	−	9.76366i	0.0491075	−	0.655294i
$223$	15.9307	−	7.67182i	1.06680	−	0.513743i	0.183725	−	0.982978i	$-0.441184\pi$
$223$	15.9307	−	7.67182i	1.06680	−	0.513743i	0.883074	+	0.469234i	$0.155470\pi$
$224$	0.799695	−	2.52200i	0.0534319	−	0.168508i
$225$	−7.34154	−	3.53550i	−0.489436	−	0.235700i
$226$	8.29454	−	14.3666i	0.551745	−	0.955650i
$227$	10.9356	+	18.9410i	0.725821	+	1.25716i	0.958635	+	0.284638i	$0.0918734\pi$
$227$	10.9356	+	18.9410i	0.725821	+	1.25716i	−0.232814	+	0.972521i	$0.574793\pi$
$228$	0.259287	+	3.45994i	0.0171717	+	0.229140i
$229$	−2.84980	−	7.26117i	−0.188320	−	0.479832i	0.805265	−	0.592914i	$-0.202023\pi$
$229$	−2.84980	−	7.26117i	−0.188320	−	0.479832i	−0.993586	+	0.113083i	$0.963928\pi$
$230$	−0.0289903	+	0.127015i	−0.00191157	+	0.00837512i
$231$	0.0933394	−	11.8756i	0.00614128	−	0.781357i
$232$	1.20011	+	5.25803i	0.0787912	+	0.345207i
$233$	−13.3974	+	9.13417i	−0.877691	+	0.598400i	−0.916139	−	0.400861i	$-0.868711\pi$
$233$	−13.3974	+	9.13417i	−0.877691	+	0.598400i	0.0384479	+	0.999261i	$0.487759\pi$
$234$	2.06563	−	1.91663i	0.135034	−	0.125294i
$235$	−0.700863	−	0.105638i	−0.0457192	−	0.00689107i
$236$	2.56165	+	2.37687i	0.166749	+	0.154721i
$237$	−8.98500	−	11.2668i	−0.583639	−	0.731860i
$238$	−2.16838	+	3.12733i	−0.140555	+	0.202715i
$239$	−9.49666	+	11.9084i	−0.614288	+	0.770292i	−0.987528	−	0.157442i	$-0.949675\pi$
$239$	−9.49666	+	11.9084i	−0.614288	+	0.770292i	0.373241	+	0.927735i	$0.378247\pi$
$240$	−0.0960558	+	0.0144781i	−0.00620038	+	0.000934556i
$241$	−9.25063	−	6.30697i	−0.595885	−	0.406268i	0.227477	−	0.973783i	$-0.426952\pi$
$241$	−9.25063	−	6.30697i	−0.595885	−	0.406268i	−0.823363	+	0.567516i	$0.807905\pi$
$242$	1.36192	−	3.47011i	0.0875474	−	0.223067i
$243$	13.9206	+	4.29393i	0.893005	+	0.275456i
$244$	0.631642			0.0404367
$245$	−0.475139	−	0.335004i	−0.0303555	−	0.0214026i
$246$	4.75428			0.303122
$247$	4.89450	+	1.50975i	0.311430	+	0.0960633i
$248$	3.87264	−	9.86732i	0.245913	−	0.626576i
$249$	13.8828	+	9.46516i	0.879789	+	0.599830i
$250$	0.820679	−	0.123697i	0.0519043	−	0.00782331i
$251$	4.87826	−	6.11715i	0.307913	−	0.386111i	−0.603665	−	0.797238i	$-0.706293\pi$
$251$	4.87826	−	6.11715i	0.307913	−	0.386111i	0.911578	+	0.411127i	$0.134865\pi$
$252$	0.677062	−	4.26432i	0.0426509	−	0.268627i
$253$	3.75344	+	4.70667i	0.235977	+	0.295906i
$254$	1.77429	+	1.64630i	0.111329	+	0.103298i
$255$	0.138162	+	0.0208246i	0.00865206	+	0.00130409i
$256$	−0.733052	+	0.680173i	−0.0458157	+	0.0425108i
$257$	22.7735	−	15.5267i	1.42057	−	0.968529i	0.422505	−	0.906361i	$-0.361151\pi$
$257$	22.7735	−	15.5267i	1.42057	−	0.968529i	0.998066	−	0.0621682i	$-0.0198015\pi$
$258$	0.272248	+	1.19279i	0.0169494	+	0.0742601i
$259$	−21.6304	+	4.75845i	−1.34405	+	0.295676i
$260$	−0.0319104	+	0.139809i	−0.00197900	+	0.00867057i
$261$	3.21556	+	8.19311i	0.199038	+	0.507141i
$262$	0.0327473	+	0.436982i	0.00202313	+	0.0269968i
$263$	−2.52644	−	4.37593i	−0.155787	−	0.269831i	0.777558	−	0.628811i	$-0.216458\pi$
$263$	−2.52644	−	4.37593i	−0.155787	−	0.269831i	−0.933345	+	0.358980i	$0.883125\pi$
$264$	−2.24435	+	3.88732i	−0.138130	+	0.239248i
$265$	−0.258090	−	0.124290i	−0.0158544	−	0.00763506i
$266$	7.32820	−	2.80984i	0.449321	−	0.172283i
$267$	−16.3503	+	7.87389i	−1.00062	+	0.481874i
$268$	0.796063	−	10.6227i	0.0486273	−	0.648886i
$269$	3.39173	−	1.04621i	0.206798	−	0.0637886i	−0.189626	−	0.981856i	$-0.560727\pi$
$269$	3.39173	−	1.04621i	0.206798	−	0.0637886i	0.396423	+	0.918068i	$0.370251\pi$
$270$	−0.429961	+	0.132625i	−0.0261666	+	0.00807133i
$271$	−1.11742	+	14.9109i	−0.0678784	+	0.905775i	0.854491	+	0.519466i	$0.173869\pi$
$271$	−1.11742	+	14.9109i	−0.0678784	+	0.905775i	−0.922370	+	0.386309i	$0.873750\pi$
$272$	1.29591	−	0.624079i	0.0785763	−	0.0378403i
$273$	4.60631	+	2.70794i	0.278786	+	0.163892i
$274$	15.1464	+	7.29410i	0.915025	+	0.440653i
$275$	9.58097	−	16.5947i	0.577754	−	1.00070i
$276$	−0.917387	−	1.58896i	−0.0552202	−	0.0956442i
$277$	−1.23674	−	16.5031i	−0.0743085	−	0.991578i	−0.902376	−	0.430949i	$-0.858179\pi$
$277$	−1.23674	−	16.5031i	−0.0743085	−	0.991578i	0.828068	−	0.560628i	$-0.189440\pi$
$278$	7.33480	+	18.6888i	0.439912	+	1.12088i
$279$	3.84934	−	16.8651i	0.230454	−	1.00969i
$280$	0.0937806	+	0.198718i	0.00560446	+	0.0118757i
$281$	−0.0748970	−	0.328145i	−0.00446798	−	0.0195755i	0.972645	−	0.232297i	$-0.0746243\pi$
$281$	−0.0748970	−	0.328145i	−0.00446798	−	0.0195755i	−0.977113	+	0.212722i	$0.931767\pi$
$282$	8.24739	−	5.62298i	0.491125	−	0.334843i
$283$	9.21985	−	8.55477i	0.548063	−	0.508529i	−0.356828	−	0.934170i	$-0.616142\pi$
$283$	9.21985	−	8.55477i	0.548063	−	0.508529i	0.904892	+	0.425641i	$0.139951\pi$
$284$	−4.39815	−	0.662914i	−0.260982	−	0.0393367i
$285$	−0.211237	−	0.195999i	−0.0125126	−	0.0116100i
$286$	4.13151	+	5.18075i	0.244302	+	0.306344i
$287$	−3.08902	−	10.3011i	−0.182339	−	0.608057i
$288$	−1.01750	+	1.27591i	−0.0599570	+	0.0751837i
$289$	14.7644	−	2.22537i	0.868492	−	0.130904i
$290$	−0.370090	−	0.252323i	−0.0217324	−	0.0148169i
$291$	−5.26817	+	13.4231i	−0.308826	+	0.786875i
$292$	−7.73648	−	2.38639i	−0.452743	−	0.139653i
$293$	−26.8234			−1.56704			−0.783519	−	0.621368i	$-0.786577\pi$
$293$	−26.8234			−1.56704			−0.783519	+	0.621368i	$0.786577\pi$
$294$	8.11419	−	1.09287i	0.473229	−	0.0637374i
$295$	−0.290226			−0.0168976
$296$	7.99911	+	2.46740i	0.464939	+	0.143415i
$297$	−7.59595	+	19.3542i	−0.440762	+	1.12304i
$298$	−16.1544	−	11.0139i	−0.935801	−	0.638018i
$299$	−2.67833	+	0.403694i	−0.154892	+	0.0233462i
$300$	−3.64125	+	4.56599i	−0.210228	+	0.263617i
$301$	2.40755	−	1.36488i	0.138769	−	0.0786705i
$302$	0.777783	+	0.975309i	0.0447564	+	0.0561227i
$303$	12.0853	+	11.2135i	0.694281	+	0.644199i
$304$	−2.93329	−	0.442123i	−0.168236	−	0.0253575i
$305$	−0.0384553	+	0.0356813i	−0.00220195	+	0.00204311i
$306$	1.93945	−	1.32229i	0.110871	−	0.0755906i
$307$	−4.14229	−	18.1486i	−0.236413	−	1.03579i	−0.944201	−	0.329369i	$-0.893164\pi$
$307$	−4.14229	−	18.1486i	−0.236413	−	1.03579i	0.707788	−	0.706425i	$-0.249693\pi$
$308$	9.88092	+	2.33711i	0.563017	+	0.133169i
$309$	−4.08147	+	17.8821i	−0.232187	+	1.01728i
$310$	0.321631	+	0.819502i	0.0182674	+	0.0465446i
$311$	−0.475170	−	6.34071i	−0.0269444	−	0.359548i	−0.994337	−	0.106269i	$-0.966110\pi$
$311$	−0.475170	−	6.34071i	−0.0269444	−	0.359548i	0.967393	−	0.253280i	$-0.0815094\pi$
$312$	−1.00979	−	1.74901i	−0.0571682	−	0.0990182i
$313$	−7.34703	+	12.7254i	−0.415278	+	0.719283i	−0.995458	−	0.0952055i	$-0.969649\pi$
$313$	−7.34703	+	12.7254i	−0.415278	+	0.719283i	0.580179	+	0.814489i	$0.302983\pi$
$314$	8.38213	+	4.03662i	0.473031	+	0.227800i
$315$	0.199670	+	0.297865i	0.0112501	+	0.0167828i
$316$	11.1006	−	5.34578i	0.624459	−	0.300724i
$317$	1.50898	−	20.1359i	0.0847527	−	1.13095i	−0.778998	−	0.627026i	$-0.784272\pi$
$317$	1.50898	−	20.1359i	0.0847527	−	1.13095i	0.863751	−	0.503919i	$-0.168109\pi$
$318$	3.85501	−	1.18911i	0.216178	−	0.0666822i
$319$	−19.7781	+	6.10072i	−1.10736	+	0.341575i
$320$	0.00620649	−	0.0828199i	0.000346954	−	0.00462977i
$321$	12.1970	−	5.87379i	0.680773	−	0.327843i
$322$	−2.84675	+	3.02011i	−0.158643	+	0.168304i
$323$	3.84423	+	1.85128i	0.213899	+	0.103008i
$324$	0.720442	−	1.24784i	0.0400246	−	0.0693246i
$325$	4.31074	+	7.46641i	0.239117	+	0.414162i
$326$	1.28675	+	17.1706i	0.0712668	+	0.950989i
$327$	1.78669	+	4.55242i	0.0988044	+	0.251750i
$328$	−0.904492	+	3.96284i	−0.0499422	+	0.218811i
$329$	−17.5420	−	14.2162i	−0.967120	−	0.783766i
$330$	−0.0829548	−	0.363449i	−0.00456651	−	0.0200072i
$331$	5.41808	−	3.69399i	0.297805	−	0.203040i	−0.405194	−	0.914231i	$-0.632796\pi$
$331$	5.41808	−	3.69399i	0.297805	−	0.203040i	0.702999	+	0.711191i	$0.251844\pi$
$332$	−10.5307	+	9.77104i	−0.577946	+	0.536256i
$333$	13.5085	+	2.03608i	0.740261	+	0.111576i
$334$	−0.702265	−	0.651607i	−0.0384262	−	0.0356543i
$335$	0.551610	+	0.691697i	0.0301377	+	0.0377914i
$336$	−2.87168	−	1.15318i	−0.156663	−	0.0629110i
$337$	−4.21499	+	5.28543i	−0.229605	+	0.287916i	−0.883266	−	0.468872i	$-0.844661\pi$
$337$	−4.21499	+	5.28543i	−0.229605	+	0.287916i	0.653661	+	0.756787i	$0.273232\pi$
$338$	9.90669	−	1.49319i	0.538853	−	0.0812190i
$339$	−16.0317	−	10.9302i	−0.870721	−	0.593648i
$340$	−0.0436431	+	0.111201i	−0.00236688	+	0.00603071i
$341$	38.8724	+	11.9905i	2.10506	+	0.649324i
$342$	−4.84106			−0.261775
$343$	−7.64000	−	16.8710i	−0.412521	−	0.910948i
$344$	−1.04603			−0.0563979
$345$	0.145612	+	0.0449153i	0.00783948	+	0.00241816i
$346$	6.61638	−	16.8583i	0.355699	−	0.906306i
$347$	−15.4713	−	10.5481i	−0.830542	−	0.566254i	0.0717289	−	0.997424i	$-0.477148\pi$
$347$	−15.4713	−	10.5481i	−0.830542	−	0.566254i	−0.902270	+	0.431171i	$0.858101\pi$
$348$	6.23769	−	0.940180i	0.334375	−	0.0503990i
$349$	0.330869	−	0.414897i	0.0177110	−	0.0222089i	−0.772897	−	0.634531i	$-0.781193\pi$
$349$	0.330869	−	0.414897i	0.0177110	−	0.0222089i	0.790608	+	0.612322i	$0.209765\pi$
$350$	12.2590	+	4.92284i	0.655271	+	0.263137i
$351$	−5.83250	−	7.31373i	−0.311316	−	0.390378i
$352$	−2.81322	−	2.61029i	−0.149945	−	0.139129i
$353$	0.927654	+	0.139821i	0.0493740	+	0.00744194i	0.173683	−	0.984802i	$-0.444433\pi$
$353$	0.927654	+	0.139821i	0.0493740	+	0.00744194i	−0.124309	+	0.992244i	$0.539671\pi$
$354$	2.99620	−	2.78007i	0.159246	−	0.147759i
$355$	0.305214	−	0.208091i	0.0161991	−	0.0110443i
$356$	−3.45252	−	15.1265i	−0.182983	−	0.801702i
$357$	3.45808	+	2.80247i	0.183021	+	0.148323i
$358$	−0.513715	+	2.25073i	−0.0271507	+	0.118955i
$359$	9.15965	+	23.3384i	0.483428	+	1.23175i	0.939727	+	0.341927i	$0.111080\pi$
$359$	9.15965	+	23.3384i	0.483428	+	1.23175i	−0.456299	+	0.889827i	$0.650825\pi$
$360$	−0.0101287	−	0.135158i	−0.000533829	−	0.00712345i
$361$	5.10016	+	8.83373i	0.268429	+	0.464933i
$362$	−11.6815	+	20.2330i	−0.613967	+	1.06342i
$363$	−3.92838	−	1.89181i	−0.206186	−	0.0992941i
$364$	−3.13350	+	3.32432i	−0.164240	+	0.174242i
$365$	0.605815	−	0.291745i	0.0317098	−	0.0152706i
$366$	0.0552100	−	0.736726i	0.00288587	−	0.0385093i
$367$	−9.88869	+	3.05026i	−0.516185	+	0.159222i	−0.541893	−	0.840447i	$-0.682292\pi$
$367$	−9.88869	+	3.05026i	−0.516185	+	0.159222i	0.0257078	+	0.999670i	$0.491816\pi$
$368$	1.49898	−	0.462374i	0.0781396	−	0.0241029i
$369$	−0.495720	+	6.61492i	−0.0258062	+	0.344359i
$370$	−0.626381	+	0.301649i	−0.0325640	+	0.0156820i
$371$	−5.08120	−	7.58007i	−0.263803	−	0.393538i
$372$	−11.1704	−	5.37939i	−0.579159	−	0.278908i
$373$	2.13722	−	3.70178i	0.110661	−	0.191671i	−0.805376	−	0.592764i	$-0.798037\pi$
$373$	2.13722	−	3.70178i	0.110661	−	0.191671i	0.916037	+	0.401094i	$0.131370\pi$
$374$	2.75997	+	4.78042i	0.142715	+	0.247189i
$375$	−0.0725433	−	0.968024i	−0.00374612	−	0.0499885i
$376$	3.11787	+	7.94421i	0.160792	+	0.409692i
$377$	2.07220	−	9.07892i	0.106724	−	0.467588i
$378$	−13.9490	−	3.29932i	−0.717459	−	0.169699i
$379$	1.68237	+	7.37095i	0.0864176	+	0.378620i	0.999580	−	0.0289753i	$-0.00922443\pi$
$379$	1.68237	+	7.37095i	0.0864176	+	0.378620i	−0.913163	+	0.407596i	$0.866367\pi$
$380$	0.203559	−	0.138784i	0.0104423	−	0.00711947i
$381$	2.07527	−	1.92557i	0.106319	−	0.0986499i
$382$	−23.0712	−	3.47743i	−1.18043	−	0.177921i
$383$	−7.53418	−	6.99070i	−0.384979	−	0.357208i	0.463815	−	0.885932i	$-0.346480\pi$
$383$	−7.53418	−	6.99070i	−0.384979	−	0.357208i	−0.848794	+	0.528724i	$0.822671\pi$
$384$	0.729256	+	0.914459i	0.0372147	+	0.0466658i
$385$	−0.733588	+	0.415884i	−0.0373871	+	0.0211954i
$386$	6.23070	−	7.81305i	0.317134	−	0.397674i
$387$	−1.68800	+	0.254424i	−0.0858056	+	0.0129331i
$388$	−10.1863	−	6.94490i	−0.517131	−	0.352574i
$389$	−11.5745	+	29.4913i	−0.586849	+	1.49527i	0.261165	+	0.965294i	$0.415893\pi$
$389$	−11.5745	+	29.4913i	−0.586849	+	1.49527i	−0.848014	+	0.529973i	$0.822202\pi$
$390$	0.160279	+	0.0494395i	0.00811604	+	0.00250347i
$391$	−2.25630			−0.114106
$392$	−0.632768	+	6.97134i	−0.0319596	+	0.352106i
$393$	0.512543			0.0258544
$394$	−5.39601	−	1.66445i	−0.271847	−	0.0838537i
$395$	−0.373841	+	0.952532i	−0.0188100	+	0.0479271i
$396$	−5.17466	−	3.52802i	−0.260036	−	0.177290i
$397$	−1.40551	+	0.211846i	−0.0705403	+	0.0106322i	−0.184218	−	0.982885i	$-0.558975\pi$
$397$	−1.40551	+	0.211846i	−0.0705403	+	0.0106322i	0.113677	+	0.993518i	$0.463737\pi$
$398$	10.4927	−	13.1575i	0.525954	−	0.659525i
$399$	−2.63677	−	8.79297i	−0.132004	−	0.440199i
$400$	−3.11315	−	3.90376i	−0.155657	−	0.195188i
$401$	−6.48599	−	6.01812i	−0.323895	−	0.300530i	0.501419	−	0.865204i	$-0.332811\pi$
$401$	−6.48599	−	6.01812i	−0.323895	−	0.300530i	−0.825314	+	0.564674i	$0.809002\pi$
$402$	−12.3204	−	1.85700i	−0.614486	−	0.0926188i
$403$	−13.4170	+	12.4491i	−0.668346	+	0.620135i
$404$	−11.6460	+	7.94010i	−0.579410	+	0.395035i
$405$	0.0266288	+	0.116668i	0.00132319	+	0.00579729i
$406$	−6.08994	−	12.9044i	−0.302239	−	0.640433i
$407$	−7.14855	+	31.3198i	−0.354340	+	1.55247i
$408$	−0.614632	−	1.56606i	−0.0304288	−	0.0775314i
$409$	−1.23131	−	16.4307i	−0.0608844	−	0.812446i	−0.941155	−	0.337975i	$-0.890258\pi$
$409$	−1.23131	−	16.4307i	−0.0608844	−	0.812446i	0.880271	−	0.474472i	$-0.157361\pi$
$410$	−0.168793	−	0.292358i	−0.00833610	−	0.0144385i
$411$	9.83149	−	17.0286i	0.484951	−	0.839960i
$412$	−14.1288	−	6.80407i	−0.696075	−	0.335212i
$413$	−7.97033	−	4.68558i	−0.392194	−	0.230562i
$414$	2.30647	−	1.11074i	0.113357	−	0.0545898i
$415$	0.0891596	−	1.18975i	0.00437667	−	0.0584026i
$416$	1.64996	−	0.508947i	0.0808962	−	0.0249532i
$417$	22.4391	−	6.92153i	1.09885	−	0.338949i
$418$	0.850742	−	11.3524i	0.0416112	−	0.555262i
$419$	19.8456	−	9.55716i	0.969523	−	0.466898i	0.119034	−	0.992890i	$-0.462020\pi$
$419$	19.8456	−	9.55716i	0.969523	−	0.466898i	0.850489	+	0.525992i	$0.176306\pi$
$420$	0.239975	−	0.0920132i	0.0117096	−	0.00448978i
$421$	5.78843	+	2.78756i	0.282111	+	0.135857i	0.569589	−	0.821930i	$-0.307103\pi$
$421$	5.78843	+	2.78756i	0.282111	+	0.135857i	−0.287478	+	0.957787i	$0.592817\pi$
$422$	2.46267	−	4.26546i	0.119881	−	0.207639i
$423$	6.96365	+	12.0614i	0.338584	+	0.586446i
$424$	0.257755	+	3.43950i	0.0125177	+	0.167037i
$425$	2.62383	+	6.68540i	0.127274	+	0.324289i
$426$	−1.15763	+	5.07190i	−0.0560873	+	0.245735i
$427$	−1.63214	+	0.359053i	−0.0789848	+	0.0173758i
$428$	2.57552	+	11.2841i	0.124492	+	0.545437i
$429$	6.40378	−	4.36602i	0.309177	−	0.210794i
$430$	0.0636836	−	0.0590898i	0.00307110	−	0.00284956i
$431$	10.0006	+	1.50735i	0.481712	+	0.0726063i	0.385409	−	0.922746i	$-0.374060\pi$
$431$	10.0006	+	1.50735i	0.481712	+	0.0726063i	0.0963025	+	0.995352i	$0.469298\pi$
$432$	3.97145	+	3.68497i	0.191077	+	0.177293i
$433$	−0.926528	−	1.16183i	−0.0445261	−	0.0558339i	0.759070	−	0.651009i	$-0.225654\pi$
$433$	−0.926528	−	1.16183i	−0.0445261	−	0.0558339i	−0.803596	+	0.595175i	$0.797083\pi$
$434$	−4.39774	+	27.6982i	−0.211098	+	1.32956i
$435$	−0.326649	+	0.409605i	−0.0156616	+	0.0196391i
$436$	−4.13450	+	0.623176i	−0.198007	+	0.0298447i
$437$	3.84477	+	2.62132i	0.183920	+	0.125395i
$438$	−3.45962	+	8.81498i	−0.165307	+	0.421196i
$439$	−11.1135	−	3.42806i	−0.530418	−	0.163612i	0.0179667	−	0.999839i	$-0.494281\pi$
$439$	−11.1135	−	3.42806i	−0.530418	−	0.163612i	−0.548384	+	0.836226i	$0.684757\pi$
$440$	0.318728			0.0151947
$441$	0.674524	+	11.4037i	0.0321202	+	0.543034i
$442$	−2.48357			−0.118132
$443$	13.2495	+	4.08693i	0.629503	+	0.194176i	0.593058	−	0.805160i	$-0.297920\pi$
$443$	13.2495	+	4.08693i	0.629503	+	0.194176i	0.0364449	+	0.999336i	$0.488397\pi$
$444$	3.57707	−	9.11422i	0.169760	−	0.432542i
$445$	1.06469	+	0.725891i	0.0504710	+	0.0344105i
$446$	17.4843	−	2.63533i	0.827904	−	0.124786i
$447$	−14.2582	+	17.8793i	−0.674392	+	0.845661i
$448$	1.50754	−	2.17424i	0.0712246	−	0.102723i
$449$	−11.5144	−	14.4386i	−0.543399	−	0.681401i	0.431993	−	0.901877i	$-0.357810\pi$
$449$	−11.5144	−	14.4386i	−0.543399	−	0.681401i	−0.975392	+	0.220476i	$0.929239\pi$
$450$	−5.97327	−	5.54239i	−0.281583	−	0.261271i
$451$	−15.4250	−	2.32494i	−0.726334	−	0.109477i
$452$	12.1607	−	11.2834i	0.571989	−	0.530729i
$453$	1.20555	−	0.821930i	0.0566417	−	0.0386177i
$454$	4.86680	+	21.3228i	0.228410	+	1.00073i
$455$	0.00298200	−	0.379400i	0.000139798	−	0.0177865i
$456$	−0.772068	+	3.38265i	−0.0361554	+	0.158407i
$457$	0.437853	+	1.11563i	0.0204819	+	0.0521871i	0.940749	−	0.339104i	$-0.110124\pi$
$457$	0.437853	+	1.11563i	0.0204819	+	0.0521871i	−0.920267	+	0.391291i	$0.872029\pi$
$458$	−0.582924	−	7.77857i	−0.0272382	−	0.363469i
$459$	−3.89629	−	6.74857i	−0.181863	−	0.314996i
$460$	−0.0651407	+	0.112827i	−0.00303720	+	0.00526058i
$461$	33.0565	+	15.9192i	1.53960	+	0.741430i	0.995243	−	0.0974256i	$-0.0310608\pi$
$461$	33.0565	+	15.9192i	1.53960	+	0.741430i	0.544353	+	0.838856i	$0.316775\pi$
$462$	3.58959	−	11.3205i	0.167003	−	0.526677i
$463$	14.3697	−	6.92010i	0.667818	−	0.321604i	−0.0690768	−	0.997611i	$-0.522005\pi$
$463$	14.3697	−	6.92010i	0.667818	−	0.321604i	0.736895	+	0.676007i	$0.236291\pi$
$464$	−0.403038	+	5.37817i	−0.0187106	+	0.249675i
$465$	0.983952	−	0.303509i	0.0456297	−	0.0140749i
$466$	−15.4945	+	4.77942i	−0.717769	+	0.221402i
$467$	−1.01568	+	13.5533i	−0.0469999	+	0.627170i	0.923115	+	0.384524i	$0.125634\pi$
$467$	−1.01568	+	13.5533i	−0.0469999	+	0.627170i	−0.970115	+	0.242646i	$0.921985\pi$
$468$	2.53880	−	1.22262i	0.117356	−	0.0565156i
$469$	3.98142	+	27.9013i	0.183845	+	1.28836i
$470$	−0.638588	−	0.307528i	−0.0294559	−	0.0141852i
$471$	5.44083	−	9.42380i	0.250700	−	0.434226i
$472$	1.74725	+	3.02633i	0.0804238	+	0.139298i
$473$	−0.299990	−	4.00309i	−0.0137936	−	0.184062i
$474$	−5.26487	−	13.4147i	−0.241823	−	0.616156i
$475$	3.29591	−	14.4403i	0.151227	−	0.662567i
$476$	−2.99384	+	2.34925i	−0.137222	+	0.107678i
$477$	1.25253	+	5.48770i	0.0573495	+	0.251265i
$478$	−12.5848	+	8.58018i	−0.575616	+	0.392448i
$479$	16.0154	−	14.8601i	0.731760	−	0.678974i	−0.223512	−	0.974701i	$-0.571752\pi$
$479$	16.0154	−	14.8601i	0.731760	−	0.678974i	0.955273	+	0.295727i	$0.0955618\pi$
$480$	−0.0960558	−	0.0144781i	−0.00438433	−	0.000660831i
$481$	−10.5956	−	9.83123i	−0.483116	−	0.448266i
$482$	−6.98063	−	8.75344i	−0.317959	−	0.398708i
$483$	3.27373	+	3.58433i	0.148960	+	0.163093i
$484$	2.32425	−	2.91451i	0.105648	−	0.132478i
$485$	1.01247	−	0.152606i	0.0459740	−	0.00692947i
$486$	12.0365	+	8.20632i	0.545985	+	0.372246i
$487$	8.64709	−	22.0324i	0.391837	−	0.998385i	−0.589787	−	0.807559i	$-0.700788\pi$
$487$	8.64709	−	22.0324i	0.391837	−	0.998385i	0.981624	−	0.190826i	$-0.0611165\pi$
$488$	0.603580	+	0.186180i	0.0273228	+	0.00842796i
$489$	20.1396			0.910745
$490$	−0.355286	−	0.460171i	−0.0160502	−	0.0207884i
$491$	15.4438			0.696970			0.348485	−	0.937314i	$-0.386696\pi$
$491$	15.4438			0.696970			0.348485	+	0.937314i	$0.386696\pi$
$492$	4.54306	+	1.40135i	0.204817	+	0.0631777i
$493$	2.83410	−	7.22117i	0.127642	−	0.325225i
$494$	4.23204	+	2.88536i	0.190409	+	0.129818i
$495$	0.514338	−	0.0775240i	0.0231178	−	0.00348444i
$496$	6.60903	−	8.28746i	0.296754	−	0.372118i
$497$	11.7415	−	0.787154i	0.526678	−	0.0353087i
$498$	10.4762	+	13.1367i	0.469448	+	0.588669i
$499$	−3.31579	−	3.07661i	−0.148435	−	0.137728i	0.602460	−	0.798149i	$-0.294187\pi$
$499$	−3.31579	−	3.07661i	−0.148435	−	0.137728i	−0.750895	+	0.660421i	$0.770378\pi$
$500$	0.820679	+	0.123697i	0.0367019	+	0.00553192i
$501$	−0.821395	+	0.762143i	−0.0366972	+	0.0340500i
$502$	6.46460	−	4.40749i	0.288529	−	0.196716i
$503$	1.74865	+	7.66134i	0.0779684	+	0.341602i	0.998834	−	0.0482784i	$-0.0153735\pi$
$503$	1.74865	+	7.66134i	0.0779684	+	0.341602i	−0.920865	+	0.389880i	$0.872516\pi$
$504$	1.90391	−	3.87530i	0.0848070	−	0.172620i
$505$	0.260491	−	1.14129i	0.0115917	−	0.0507865i
$506$	2.19937	+	5.60391i	0.0977741	+	0.249124i
$507$	−0.875695	−	11.6853i	−0.0388910	−	0.518964i
$508$	1.21021	+	2.09614i	0.0536942	+	0.0930011i
$509$	12.9947	−	22.5074i	0.575978	−	0.997624i	−0.419956	−	0.907544i	$-0.637955\pi$
$509$	12.9947	−	22.5074i	0.575978	−	0.997624i	0.995935	−	0.0900795i	$-0.0287121\pi$
$510$	0.125886	+	0.0606235i	0.00557433	+	0.00268445i
$511$	21.3473	+	1.76859i	0.944349	+	0.0782377i
$512$	−0.900969	+	0.433884i	−0.0398176	+	0.0191751i
$513$	−1.20100	+	16.0263i	−0.0530256	+	0.707577i
$514$	26.3383	−	8.12429i	1.16173	−	0.358347i
$515$	1.24454	−	0.383890i	0.0548411	−	0.0169162i
$516$	−0.0914300	+	1.22005i	−0.00402498	+	0.0537096i
$517$	−29.5079	+	14.2103i	−1.29776	+	0.624967i
$518$	−22.0720	−	1.82863i	−0.969788	−	0.0803452i
$519$	−19.0846	−	9.19065i	−0.837720	−	0.403425i
$520$	−0.0717021	+	0.124192i	−0.00314434	+	0.00544616i
$521$	−3.53052	−	6.11504i	−0.154675	−	0.267905i	0.778266	−	0.627935i	$-0.216100\pi$
$521$	−3.53052	−	6.11504i	−0.154675	−	0.267905i	−0.932941	+	0.360030i	$0.882766\pi$
$522$	0.657739	+	8.77691i	0.0287884	+	0.384155i
$523$	−6.63798	−	16.9133i	−0.290258	−	0.739566i	−0.999405	−	0.0345049i	$-0.989015\pi$
$523$	−6.63798	−	16.9133i	−0.290258	−	0.739566i	0.709146	−	0.705062i	$-0.249081\pi$
$524$	−0.0975102	+	0.427220i	−0.00425975	+	0.0186632i
$525$	6.81336	−	13.8682i	0.297359	−	0.605257i
$526$	−1.12437	−	4.92620i	−0.0490250	−	0.214793i
$527$	−12.5974	+	8.58875i	−0.548750	+	0.374132i
$528$	−3.29044	+	3.05309i	−0.143198	+	0.132869i
$529$	20.3099	+	3.06122i	0.883038	+	0.133097i
$530$	−0.209989	−	0.194841i	−0.00912134	−	0.00846337i
$531$	3.55567	+	4.45867i	0.154303	+	0.193490i
$532$	7.83085	−	0.524983i	0.339510	−	0.0227609i
$533$	4.37597	−	5.48729i	0.189544	−	0.237681i
$534$	−17.9448	+	2.70474i	−0.776546	+	0.117046i
$535$	−0.794238	−	0.541502i	−0.0343379	−	0.0234112i
$536$	3.89180	−	9.91614i	0.168100	−	0.428312i
$537$	2.58027	+	0.795909i	0.111347	+	0.0343460i
$538$	3.54942			0.153026
$539$	−26.8605	−	0.422260i	−1.15696	−	0.0181880i
$540$	−0.449951			−0.0193628
$541$	−25.9129	−	7.99306i	−1.11408	−	0.343648i	−0.317547	−	0.948242i	$-0.602859\pi$
$541$	−25.9129	−	7.99306i	−1.11408	−	0.343648i	−0.796534	+	0.604594i	$0.793335\pi$
$542$	−5.46285	+	13.9191i	−0.234649	+	0.597877i
$543$	22.5780	+	15.3934i	0.968915	+	0.660595i
$544$	1.42229	−	0.214376i	0.0609802	−	0.00919128i
$545$	0.216512	−	0.271497i	0.00927434	−	0.0116296i
$546$	3.60348	+	3.94537i	0.154215	+	0.168846i
$547$	−8.54320	−	10.7128i	−0.365281	−	0.458048i	0.564895	−	0.825163i	$-0.308917\pi$
$547$	−8.54320	−	10.7128i	−0.365281	−	0.458048i	−0.930175	+	0.367115i	$0.880345\pi$
$548$	12.3235	+	11.4345i	0.526433	+	0.488458i
$549$	1.01930	+	0.153634i	0.0435025	+	0.00655694i
$550$	14.0467	−	13.0334i	0.598953	−	0.555747i
$551$	−13.2187	+	9.01238i	−0.563137	+	0.383940i
$552$	−0.408275	−	1.78877i	−0.0173774	−	0.0761352i
$553$	−25.6449	+	20.1234i	−1.09053	+	0.855734i
$554$	3.68259	−	16.1345i	0.156458	−	0.685489i
$555$	0.297083	+	0.756956i	0.0126105	+	0.0321310i
$556$	1.50033	+	20.0204i	0.0636280	+	0.849056i
$557$	−4.99610	−	8.65349i	−0.211691	−	0.366660i	0.740553	−	0.671998i	$-0.234564\pi$
$557$	−4.99610	−	8.65349i	−0.211691	−	0.366660i	−0.952244	+	0.305338i	$0.901230\pi$
$558$	8.64939	−	14.9812i	0.366158	−	0.634204i
$559$	1.62728	+	0.783658i	0.0688267	+	0.0331452i
$560$	0.0310411	+	0.217532i	0.00131173	+	0.00919239i
$561$	5.81695	−	2.80130i	0.245592	−	0.118271i
$562$	0.0251529	−	0.335643i	0.00106101	−	0.0141582i
$563$	3.38307	−	1.04354i	0.142579	−	0.0439799i	−0.222644	−	0.974900i	$-0.571469\pi$
$563$	3.38307	−	1.04354i	0.142579	−	0.0439799i	0.365223	+	0.930920i	$0.380993\pi$
$564$	9.53838	−	2.94220i	0.401638	−	0.123889i
$565$	−0.102960	+	1.37391i	−0.00433156	+	0.0578007i
$566$	11.3318	−	5.45711i	0.476311	−	0.229379i
$567$	−1.15227	+	3.63391i	−0.0483907	+	0.152610i
$568$	−4.00735	−	1.92984i	−0.168145	−	0.0809742i
$569$	−22.4163	+	38.8262i	−0.939741	+	1.62768i	−0.173787	+	0.984783i	$0.555600\pi$
$569$	−22.4163	+	38.8262i	−0.939741	+	1.62768i	−0.765954	+	0.642896i	$0.777733\pi$
$570$	−0.144081	−	0.249555i	−0.00603487	−	0.0104527i
$571$	−2.27445	−	30.3505i	−0.0951829	−	1.27013i	−0.816428	−	0.577448i	$-0.804049\pi$
$571$	−2.27445	−	30.3505i	−0.0951829	−	1.27013i	0.721245	−	0.692680i	$-0.243570\pi$
$572$	2.42091	+	6.16837i	0.101223	+	0.257913i
$573$	−6.07254	+	26.6055i	−0.253684	+	1.11146i
$574$	0.0845238	−	10.7540i	0.00352796	−	0.448863i
$575$	1.74290	+	7.63615i	0.0726840	+	0.318450i
$576$	−1.34838	+	0.919311i	−0.0561825	+	0.0383046i
$577$	−23.4203	+	21.7308i	−0.974999	+	0.904666i	−0.995465	−	0.0951240i	$-0.969675\pi$
$577$	−23.4203	+	21.7308i	−0.974999	+	0.904666i	0.0204668	+	0.999791i	$0.493485\pi$
$578$	14.7644	+	2.22537i	0.614117	+	0.0925632i
$579$	−8.56827	−	7.95019i	−0.356085	−	0.330399i
$580$	−0.279274	−	0.350199i	−0.0115962	−	0.0145412i
$581$	21.6566	−	31.2341i	0.898468	−	1.29581i
$582$	−8.99064	+	11.2739i	−0.372674	+	0.467319i
$583$	−13.0889	+	1.97283i	−0.542085	+	0.0817062i
$584$	−6.68937	−	4.56073i	−0.276808	−	0.188725i
$585$	−0.0855002	+	0.217851i	−0.00353500	+	0.00900703i
$586$	−25.6317	−	7.90633i	−1.05884	−	0.326607i
$587$	−20.6997			−0.854367			−0.427183	−	0.904165i	$-0.640494\pi$
$587$	−20.6997			−0.854367			−0.427183	+	0.904165i	$0.640494\pi$
$588$	8.07583	+	1.34738i	0.333041	+	0.0555652i
$589$	31.4443			1.29564
$590$	−0.277332	−	0.0855456i	−0.0114176	−	0.00352186i
$591$	−2.41300	+	6.14824i	−0.0992578	+	0.252905i
$592$	6.91645	+	4.71556i	0.284265	+	0.193808i
$593$	−38.8954	+	5.86253i	−1.59724	+	0.240745i	−0.886507	−	0.462715i	$-0.846875\pi$
$593$	−38.8954	+	5.86253i	−1.59724	+	0.240745i	−0.710734	+	0.703461i	$0.751637\pi$
$594$	−12.9632	+	16.2554i	−0.531888	+	0.666966i
$595$	0.0495608	−	0.312147i	0.00203179	−	0.0127968i
$596$	−12.1903	−	15.2862i	−0.499335	−	0.626146i
$597$	−14.4293	−	13.3884i	−0.590552	−	0.547952i
$598$	−2.67833	−	0.403694i	−0.109525	−	0.0165083i
$599$	−28.1188	+	26.0905i	−1.14890	+	1.06603i	−0.151923	+	0.988392i	$0.548546\pi$
$599$	−28.1188	+	26.0905i	−1.14890	+	1.06603i	−0.996982	+	0.0776352i	$0.975263\pi$
$600$	−4.82533	+	3.28985i	−0.196993	+	0.134308i
$601$	3.75375	+	16.4463i	0.153119	+	0.670857i	0.991968	+	0.126493i	$0.0403720\pi$
$601$	3.75375	+	16.4463i	0.153119	+	0.670857i	−0.838849	+	0.544364i	$0.816771\pi$
$602$	2.70289	−	0.594607i	0.110162	−	0.0242344i
$603$	3.86839	−	16.9485i	0.157533	−	0.690197i
$604$	0.455751	+	1.16123i	0.0185442	+	0.0472499i
$605$	0.0231366	+	0.308736i	0.000940635	+	0.0125519i
$606$	8.24312	+	14.2775i	0.334854	+	0.579984i
$607$	−9.42596	+	16.3262i	−0.382588	+	0.662662i	−0.991431	−	0.130629i	$-0.958300\pi$
$607$	−9.42596	+	16.3262i	−0.382588	+	0.662662i	0.608843	+	0.793290i	$0.291634\pi$
$608$	−2.67266	−	1.28708i	−0.108391	−	0.0521982i
$609$	−15.5835	+	5.97517i	−0.631476	+	0.242126i
$610$	−0.0472641	+	0.0227612i	−0.00191367	+	0.000921574i
$611$	1.10120	−	14.6945i	0.0445498	−	0.594476i
$612$	2.24304	−	0.691886i	0.0906695	−	0.0279678i
$613$	−27.9608	+	8.62476i	−1.12933	+	0.348351i	−0.802452	−	0.596717i	$-0.796472\pi$
$613$	−27.9608	+	8.62476i	−1.12933	+	0.348351i	−0.326874	+	0.945068i	$0.605995\pi$
$614$	1.39112	−	18.5632i	0.0561411	−	0.749151i
$615$	−0.355750	+	0.171320i	−0.0143452	+	0.00690830i
$616$	8.75306	+	5.14573i	0.352671	+	0.207327i
$617$	−15.8721	−	7.64361i	−0.638988	−	0.307720i	0.0861933	−	0.996278i	$-0.472530\pi$
$617$	−15.8721	−	7.64361i	−0.638988	−	0.307720i	−0.725181	+	0.688558i	$0.758244\pi$
$618$	−9.17099	+	15.8846i	−0.368911	+	0.638973i
$619$	4.98078	+	8.62696i	0.200194	+	0.346747i	0.948591	−	0.316505i	$-0.102509\pi$
$619$	4.98078	+	8.62696i	0.200194	+	0.346747i	−0.748397	+	0.663251i	$0.769176\pi$
$620$	0.0657892	+	0.877896i	0.00264216	+	0.0352572i
$621$	−3.10488	−	7.91110i	−0.124595	−	0.317462i
$622$	1.41490	−	6.19906i	0.0567322	−	0.248560i
$623$	17.5197	+	37.1237i	0.701914	+	1.48733i
$624$	−0.449400	−	1.96895i	−0.0179904	−	0.0788210i
$625$	20.5705	−	14.0247i	0.822821	−	0.560990i
$626$	−10.7715	+	9.99449i	−0.430516	+	0.399460i
$627$	−13.1667	−	1.98455i	−0.525825	−	0.0792554i
$628$	6.81992	+	6.32796i	0.272144	+	0.252513i
$629$	−7.50712	−	9.41363i	−0.299328	−	0.375346i
$630$	0.103002	+	0.343486i	0.00410369	+	0.0136848i
$631$	10.9291	−	13.7046i	0.435080	−	0.545573i	−0.515159	−	0.857095i	$-0.672267\pi$
$631$	10.9291	−	13.7046i	0.435080	−	0.545573i	0.950239	+	0.311521i	$0.100839\pi$
$632$	12.1832	−	1.83632i	0.484620	−	0.0730447i
$633$	−4.75983	−	3.24520i	−0.189186	−	0.128985i
$634$	7.37710	−	18.7966i	0.292982	−	0.746507i
$635$	−0.192090	−	0.0592518i	−0.00762284	−	0.00235134i
$636$	4.03424			0.159968
$637$	6.20715	−	10.3711i	0.245936	−	0.410919i
$638$	−20.6976			−0.819426
$639$	−6.93615	−	2.13952i	−0.274390	−	0.0846381i
$640$	0.0303424	−	0.0773110i	0.00119939	−	0.00305599i
$641$	−4.15376	−	2.83199i	−0.164064	−	0.111857i	0.478505	−	0.878085i	$-0.341179\pi$
$641$	−4.15376	−	2.83199i	−0.164064	−	0.111857i	−0.642569	+	0.766228i	$0.722131\pi$
$642$	13.3865	−	2.01769i	0.528323	−	0.0796319i
$643$	−11.5953	+	14.5401i	−0.457276	+	0.573405i	−0.956004	−	0.293353i	$-0.905229\pi$
$643$	−11.5953	+	14.5401i	−0.457276	+	0.573405i	0.498729	+	0.866758i	$0.333800\pi$
$644$	−3.61047	+	2.04684i	−0.142273	+	0.0806569i
$645$	−0.0633539	−	0.0794432i	−0.00249456	−	0.00312807i
$646$	3.12777	+	2.90214i	0.123060	+	0.114183i
$647$	16.6892	+	2.51549i	0.656118	+	0.0988939i	0.468660	−	0.883379i	$-0.344737\pi$
$647$	16.6892	+	2.51549i	0.656118	+	0.0988939i	0.187458	+	0.982273i	$0.439975\pi$
$648$	1.05624	−	0.980050i	0.0414932	−	0.0385000i
$649$	−11.0805	+	7.55457i	−0.434948	+	0.296543i
$650$	1.91846	+	8.40531i	0.0752481	+	0.329683i
$651$	31.9218	+	7.55039i	1.25111	+	0.295923i
$652$	−3.83152	+	16.7870i	−0.150054	+	0.657429i
$653$	−18.0688	−	46.0385i	−0.707085	−	1.80162i	−0.588199	−	0.808716i	$-0.700163\pi$
$653$	−18.0688	−	46.0385i	−0.707085	−	1.80162i	−0.118886	−	0.992908i	$-0.537932\pi$
$654$	0.365466	+	4.87681i	0.0142909	+	0.190698i
$655$	−0.0181970	−	0.0315182i	−0.000711016	−	0.00123152i
$656$	−2.03238	+	3.52018i	−0.0793509	+	0.137440i
$657$	−11.9041	−	5.73271i	−0.464423	−	0.223654i
$658$	−12.5723	−	18.7552i	−0.490120	−	0.731155i
$659$	33.1760	−	15.9767i	1.29235	−	0.622365i	0.343818	−	0.939036i	$-0.388280\pi$
$659$	33.1760	−	15.9767i	1.29235	−	0.622365i	0.948535	+	0.316671i	$0.102565\pi$
$660$	0.0278590	−	0.371753i	0.00108441	−	0.0144705i
$661$	25.5354	−	7.87663i	0.993212	−	0.306365i	0.244781	−	0.969578i	$-0.421284\pi$
$661$	25.5354	−	7.87663i	0.993212	−	0.306365i	0.748431	+	0.663213i	$0.230808\pi$
$662$	6.26620	−	1.93287i	0.243543	−	0.0751230i
$663$	−0.217082	+	2.89675i	−0.00843076	+	0.112501i
$664$	−12.9429	+	6.23297i	−0.502282	+	0.241886i
$665$	−0.447098	+	0.474325i	−0.0173377	+	0.0183935i
$666$	12.3082	+	5.92732i	0.476933	+	0.229679i
$667$	4.23012	−	7.32678i	0.163791	−	0.283694i
$668$	−0.479001	−	0.829654i	−0.0185331	−	0.0321003i
$669$	−1.54551	−	20.6234i	−0.0597529	−	0.797346i
$670$	0.323222	+	0.823557i	0.0124872	+	0.0318168i
$671$	−0.539400	+	2.36327i	−0.0208233	+	0.0912328i
$672$	−2.40419	−	1.94839i	−0.0927437	−	0.0751607i
$673$	−8.43671	−	36.9636i	−0.325211	−	1.42484i	−0.828143	−	0.560517i	$-0.810602\pi$
$673$	−8.43671	−	36.9636i	−0.325211	−	1.42484i	0.502932	−	0.864326i	$-0.332255\pi$
$674$	−5.58564	+	3.80822i	−0.215151	+	0.146687i
$675$	−19.8299	+	18.3994i	−0.763252	+	0.708195i
$676$	9.90669	+	1.49319i	0.381027	+	0.0574305i
$677$	4.25489	+	3.94796i	0.163529	+	0.151733i	0.757693	−	0.652611i	$-0.226327\pi$
$677$	4.25489	+	3.94796i	0.163529	+	0.151733i	−0.594164	+	0.804344i	$0.702517\pi$
$678$	−12.0977	−	15.1700i	−0.464609	−	0.582601i
$679$	30.2688	+	12.1550i	1.16161	+	0.466467i
$680$	−0.0744811	+	0.0933964i	−0.00285622	+	0.00358159i
$681$	25.2956	−	3.81270i	0.969331	−	0.146103i
$682$	33.6111	+	22.9157i	1.28704	+	0.877487i
$683$	5.56942	−	14.1906i	0.213108	−	0.542990i	−0.783848	−	0.620952i	$-0.786746\pi$
$683$	5.56942	−	14.1906i	0.213108	−	0.542990i	0.996956	+	0.0779622i	$0.0248414\pi$
$684$	−4.62599	−	1.42693i	−0.176879	−	0.0545600i
$685$	−1.39620			−0.0533462
$686$	−2.32777	−	18.3734i	−0.0888745	−	0.701499i
$687$	−9.12362			−0.348088
$688$	−0.999553	−	0.308321i	−0.0381076	−	0.0117546i
$689$	2.17581	−	5.54387i	0.0828917	−	0.211205i
$690$	0.125904	+	0.0858397i	0.00479307	+	0.00326786i
$691$	17.1304	−	2.58199i	0.651669	−	0.0982234i	0.185116	−	0.982717i	$-0.440734\pi$
$691$	17.1304	−	2.58199i	0.651669	−	0.0982234i	0.466553	+	0.884493i	$0.345496\pi$
$692$	11.2915	−	14.1591i	0.429238	−	0.538248i
$693$	15.3766	+	6.17478i	0.584109	+	0.234560i
$694$	−11.6748	−	14.6398i	−0.443170	−	0.555717i
$695$	−1.22229	−	1.13412i	−0.0463642	−	0.0430197i
$696$	6.23769	+	0.940180i	0.236439	+	0.0356374i
$697$	4.28583	−	3.97667i	0.162337	−	0.150627i
$698$	0.438463	−	0.298939i	0.0165961	−	0.0113150i
$699$	4.22023	+	18.4900i	0.159624	+	0.699357i
$700$	10.2633	+	8.31754i	0.387918	+	0.314373i
$701$	−1.59733	+	6.99837i	−0.0603304	+	0.264325i	−0.996094	−	0.0883044i	$-0.971855\pi$
$701$	−1.59733	+	6.99837i	−0.0603304	+	0.264325i	0.935763	+	0.352629i	$0.114712\pi$
$702$	−3.41762	−	8.70796i	−0.128990	−	0.328661i
$703$	1.85570	+	24.7626i	0.0699889	+	0.933937i
$704$	−1.91884	−	3.32353i	−0.0723190	−	0.125260i
$705$	−0.414507	+	0.717947i	−0.0156112	+	0.0270395i
$706$	0.845228	+	0.407040i	0.0318106	+	0.0153192i
$707$	25.5793	−	27.1370i	0.962010	−	1.02059i
$708$	3.68253	−	1.77341i	0.138398	−	0.0666489i
$709$	−2.06236	+	27.5202i	−0.0774534	+	1.03354i	0.814129	+	0.580685i	$0.197215\pi$
$709$	−2.06236	+	27.5202i	−0.0774534	+	1.03354i	−0.891582	+	0.452859i	$0.850404\pi$
$710$	0.352990	−	0.108883i	0.0132475	−	0.00408630i
$711$	19.2136	−	5.92661i	0.720566	−	0.222265i
$712$	1.15947	−	15.4721i	0.0434531	−	0.579841i
$713$	−14.9813	+	7.21462i	−0.561055	+	0.270190i
$714$	2.47840	+	3.69725i	0.0927519	+	0.138366i
$715$	−0.495839	−	0.238783i	−0.0185433	−	0.00892999i
$716$	−1.15431	+	1.99932i	−0.0431384	+	0.0747180i
$717$	8.90763	+	15.4285i	0.332662	+	0.576187i
$718$	1.87360	+	25.0014i	0.0699220	+	0.933044i
$719$	−2.67930	−	6.82675i	−0.0999211	−	0.254595i	0.872168	−	0.489206i	$-0.162713\pi$
$719$	−2.67930	−	6.82675i	−0.0999211	−	0.254595i	−0.972089	+	0.234611i	$0.924618\pi$
$720$	0.0301598	−	0.132139i	0.00112399	−	0.00492452i
$721$	40.3760	+	9.55004i	1.50368	+	0.355662i
$722$	2.26978	+	9.94457i	0.0844726	+	0.370099i
$723$	−10.8199	+	7.37686i	−0.402395	+	0.274348i
$724$	−17.1263	+	15.8909i	−0.636494	+	0.590581i
$725$	−26.6283	−	4.01357i	−0.988950	−	0.149060i
$726$	−3.19623	−	2.96567i	−0.118623	−	0.110066i
$727$	6.05176	+	7.58866i	0.224447	+	0.281448i	0.881286	−	0.472583i	$-0.156678\pi$
$727$	6.05176	+	7.58866i	0.224447	+	0.281448i	−0.656839	+	0.754031i	$0.728107\pi$
$728$	−3.97414	+	2.25301i	−0.147292	+	0.0835022i
$729$	13.3188	−	16.7012i	0.493288	−	0.618564i
$730$	0.664894	−	0.100217i	0.0246088	−	0.00370918i
$731$	1.24312	+	0.847546i	0.0459785	+	0.0313476i
$732$	0.269911	−	0.687722i	0.00997619	−	0.0254189i
$733$	−17.2290	−	5.31444i	−0.636367	−	0.196293i	−0.0402485	−	0.999190i	$-0.512815\pi$
$733$	−17.2290	−	5.31444i	−0.636367	−	0.196293i	−0.596118	+	0.802896i	$0.703291\pi$
$734$	−10.3484			−0.381968
$735$	−0.567782	+	0.374171i	−0.0209430	+	0.0138015i
$736$	1.56867			0.0578219
$737$	39.0647	+	12.0499i	1.43897	+	0.443863i
$738$	−2.42348	+	6.17493i	−0.0892095	+	0.227302i
$739$	36.9062	+	25.1622i	1.35761	+	0.925606i	0.999966	−	0.00825002i	$-0.00262609\pi$
$739$	36.9062	+	25.1622i	1.35761	+	0.925606i	0.357649	+	0.933856i	$0.383578\pi$
$740$	−0.687465	+	0.103619i	−0.0252717	+	0.00380910i
$741$	3.73529	−	4.68391i	0.137219	−	0.172068i
$742$	−2.62119	−	8.74102i	−0.0962269	−	0.320893i
$743$	21.5315	+	26.9997i	0.789916	+	0.990523i	0.999918	+	0.0128219i	$0.00408145\pi$
$743$	21.5315	+	26.9997i	0.789916	+	0.990523i	−0.210002	+	0.977701i	$0.567347\pi$
$744$	−9.08854	−	8.43293i	−0.333202	−	0.309166i
$745$	1.60568	+	0.242017i	0.0588275	+	0.00886682i
$746$	3.13339	−	2.90736i	0.114721	−	0.106446i
$747$	−19.3702	+	13.2064i	−0.708719	+	0.483196i
$748$	1.22830	+	5.38155i	0.0449112	+	0.196769i
$749$	−13.0694	−	27.6937i	−0.477546	−	1.01190i
$750$	0.216010	−	0.946399i	0.00788755	−	0.0345576i
$751$	−9.36311	−	23.8568i	−0.341665	−	0.870547i	−0.993671	−	0.112334i	$-0.964167\pi$
$751$	−9.36311	−	23.8568i	−0.341665	−	0.870547i	0.652006	−	0.758214i	$-0.273928\pi$
$752$	0.637758	+	8.51028i	0.0232566	+	0.310338i
$753$	−4.57569	−	7.92533i	−0.166747	−	0.288815i
$754$	4.65620	−	8.06478i	0.169569	−	0.293702i
$755$	−0.0933447	−	0.0449524i	−0.00339716	−	0.00163599i
$756$	−12.3568	−	7.26428i	−0.449412	−	0.264199i
$757$	−24.4949	+	11.7961i	−0.890283	+	0.428738i	−0.822370	−	0.568954i	$-0.807348\pi$
$757$	−24.4949	+	11.7961i	−0.890283	+	0.428738i	−0.0679131	+	0.997691i	$0.521634\pi$
$758$	−0.564998	+	7.53937i	−0.0205216	+	0.273842i
$759$	6.72845	−	2.07545i	0.244227	−	0.0753341i
$760$	0.235423	−	0.0726183i	0.00853968	−	0.00263414i
$761$	−2.11552	+	28.2297i	−0.0766876	+	1.02332i	0.817587	+	0.575806i	$0.195311\pi$
$761$	−2.11552	+	28.2297i	−0.0766876	+	1.02332i	−0.894274	+	0.447519i	$0.852308\pi$
$762$	2.55064	−	1.22833i	0.0924001	−	0.0444975i
$763$	10.3292	−	3.96049i	0.373941	−	0.143380i
$764$	−21.0212	−	10.1233i	−0.760522	−	0.366248i
$765$	−0.0974751	+	0.168832i	−0.00352422	+	0.00610413i
$766$	−5.13891	−	8.90086i	−0.185676	−	0.321601i
$767$	−0.450912	−	6.01700i	−0.0162815	−	0.217261i
$768$	0.427316	+	1.08878i	0.0154194	+	0.0392881i
$769$	9.37984	−	41.0958i	0.338246	−	1.48195i	−0.464470	−	0.885589i	$-0.653755\pi$
$769$	9.37984	−	41.0958i	0.338246	−	1.48195i	0.802716	−	0.596362i	$-0.203388\pi$
$770$	−0.823581	+	0.181179i	−0.0296798	+	0.00652923i
$771$	−7.17374	−	31.4302i	−0.258356	−	1.13193i
$772$	8.25683	−	5.62941i	0.297170	−	0.202607i
$773$	9.04712	−	8.39450i	0.325402	−	0.301929i	−0.500507	−	0.865733i	$-0.666853\pi$
$773$	9.04712	−	8.39450i	0.325402	−	0.301929i	0.825909	+	0.563803i	$0.190662\pi$
$774$	−1.68800	−	0.254424i	−0.0606737	−	0.00914509i
$775$	38.7984	+	35.9996i	1.39368	+	1.29315i
$776$	−7.68670	−	9.63882i	−0.275936	−	0.346013i
$777$	−4.06209	+	25.5842i	−0.145727	+	0.917828i
$778$	−19.7530	+	24.7694i	−0.708178	+	0.888027i
$779$	−11.9231	+	1.79712i	−0.427190	+	0.0643885i
$780$	0.138586	+	0.0944861i	0.00496216	+	0.00338314i
$781$	6.23613	−	15.8894i	0.223146	−	0.568567i
$782$	−2.15606	−	0.665057i	−0.0771006	−	0.0237824i
$783$	29.2190			1.04420
$784$	−2.65950	+	6.47511i	−0.0949820	+	0.231254i
$785$	−0.772672			−0.0275779
$786$	0.489772	+	0.151075i	0.0174696	+	0.00538865i
$787$	−4.88599	+	12.4493i	−0.174167	+	0.443770i	−0.991126	−	0.132926i	$-0.957563\pi$
$787$	−4.88599	+	12.4493i	−0.174167	+	0.443770i	0.816959	+	0.576696i	$0.195658\pi$
$788$	−4.66567	−	3.18100i	−0.166208	−	0.113319i
$789$	−5.84403	+	0.880846i	−0.208053	+	0.0313590i
$790$	−0.637996	+	0.800022i	−0.0226989	+	0.0284635i
$791$	−25.0087	+	36.0687i	−0.889207	+	1.28245i
$792$	−3.90486	−	4.89654i	−0.138753	−	0.173991i
$793$	−0.799497	−	0.741824i	−0.0283910	−	0.0263430i
$794$	−1.40551	−	0.211846i	−0.0498796	−	0.00751813i
$795$	−0.245611	+	0.227894i	−0.00871092	+	0.00808255i
$796$	13.9048	−	9.48015i	0.492843	−	0.336015i
$797$	6.62245	+	29.0149i	0.234579	+	1.02776i	0.945790	+	0.324780i	$0.105290\pi$
$797$	6.62245	+	29.0149i	0.234579	+	1.02776i	−0.711210	+	0.702979i	$0.751853\pi$
$798$	0.0721489	−	9.17952i	0.00255404	−	0.324952i
$799$	2.73147	−	11.9674i	0.0966326	−	0.423375i
$800$	−1.82419	−	4.64795i	−0.0644947	−	0.164330i
$801$	−1.89220	−	25.2497i	−0.0668577	−	0.892154i
$802$	−4.42396	−	7.66253i	−0.156215	−	0.270573i
$803$	15.5353	−	26.9079i	0.548227	−	0.949558i
$804$	−11.2257	−	5.40600i	−0.395899	−	0.190655i
$805$	0.104185	−	0.328570i	0.00367205	−	0.0115806i
$806$	−16.4903	+	7.94132i	−0.580847	+	0.279721i
$807$	0.310245	−	4.13993i	0.0109211	−	0.145732i
$808$	−13.4690	+	4.15463i	−0.473837	+	0.146159i
$809$	8.34895	−	2.57531i	0.293533	−	0.0905430i	−0.144491	−	0.989506i	$-0.546155\pi$
$809$	8.34895	−	2.57531i	0.293533	−	0.0905430i	0.438024	+	0.898963i	$0.355678\pi$
$810$	−0.00894284	+	0.119334i	−0.000314219	+	0.00419297i
$811$	−33.1535	+	15.9659i	−1.16418	+	0.560638i	−0.913262	−	0.407372i	$-0.866445\pi$
$811$	−33.1535	+	15.9659i	−1.16418	+	0.560638i	−0.250914	+	0.968009i	$0.580731\pi$
$812$	−2.01575	−	14.1261i	−0.0707391	−	0.495729i
$813$	15.7573	+	7.58831i	0.552632	+	0.266134i
$814$	−16.0626	+	27.8213i	−0.562995	+	0.975136i
$815$	−0.715025	−	1.23846i	−0.0250462	−	0.0433813i
$816$	−0.125722	−	1.67765i	−0.00440116	−	0.0587294i
$817$	−1.13364	−	2.88846i	−0.0396610	−	0.101054i
$818$	3.66643	−	16.0637i	0.128194	−	0.561653i
$819$	−5.86517	+	4.60237i	−0.204945	+	0.160820i
$820$	−0.0751200	−	0.329122i	−0.00262330	−	0.0114934i
$821$	−2.88893	+	1.96964i	−0.100824	+	0.0687408i	−0.612683	−	0.790329i	$-0.709910\pi$
$821$	−2.88893	+	1.96964i	−0.100824	+	0.0687408i	0.511858	+	0.859070i	$0.328957\pi$
$822$	14.4140	−	13.3742i	0.502745	−	0.466479i
$823$	16.5010	+	2.48712i	0.575188	+	0.0866957i	0.430193	−	0.902737i	$-0.358445\pi$
$823$	16.5010	+	2.48712i	0.575188	+	0.0866957i	0.144995	+	0.989432i	$0.453683\pi$
$824$	−11.4956	−	10.6663i	−0.400467	−	0.371579i
$825$	−13.9740	−	17.5228i	−0.486511	−	0.610065i
$826$	−6.23513	−	6.82671i	−0.216948	−	0.237532i
$827$	−10.7751	+	13.5116i	−0.374687	+	0.469843i	−0.933046	−	0.359756i	$-0.882860\pi$
$827$	−10.7751	+	13.5116i	−0.374687	+	0.469843i	0.558359	+	0.829600i	$0.311431\pi$
$828$	2.53140	−	0.381547i	0.0879722	−	0.0132597i
$829$	−5.60046	−	3.81833i	−0.194512	−	0.132616i	0.462148	−	0.886803i	$-0.347079\pi$
$829$	−5.60046	−	3.81833i	−0.194512	−	0.132616i	−0.656660	+	0.754187i	$0.728031\pi$
$830$	0.435884	−	1.11061i	0.0151298	−	0.0385500i
$831$	−18.4968	−	5.70552i	−0.641648	−	0.197922i
$832$	1.72668			0.0598617
$833$	6.40056	−	7.77221i	0.221766	−	0.269291i
$834$	23.4823			0.813126
$835$	0.0760293	+	0.0234519i	0.00263110	+	0.000811587i
$836$	4.15912	−	10.5973i	0.143846	−	0.366514i
$837$	−47.4492	−	32.3503i	−1.64008	−	1.11819i
$838$	21.7810	−	3.28296i	0.752412	−	0.113408i
$839$	−22.9023	+	28.7186i	−0.790677	+	0.991477i	0.209231	+	0.977866i	$0.432904\pi$
$839$	−22.9023	+	28.7186i	−0.790677	+	0.991477i	−0.999907	+	0.0136110i	$0.995667\pi$
$840$	0.256435	−	0.0171915i	0.00884784	−	0.000593163i
$841$	0.0543621	+	0.0681679i	0.00187455	+	0.00235062i
$842$	4.70962	+	4.36989i	0.162304	+	0.150596i
$843$	−0.389284	−	0.0586751i	−0.0134076	−	0.00202088i
$844$	3.61052	−	3.35008i	0.124279	−	0.115314i
$845$	−0.687485	+	0.468719i	−0.0236502	+	0.0161244i
$846$	3.09912	+	13.5781i	0.106550	+	0.466825i
$847$	−4.34903	+	8.85220i	−0.149434	+	0.304165i
$848$	−0.767506	+	3.36267i	−0.0263563	+	0.115474i
$849$	−5.37451	−	13.6940i	−0.184453	−	0.469978i
$850$	0.536701	+	7.16177i	0.0184087	+	0.245647i
$851$	−6.56568	−	11.3721i	−0.225068	−	0.389830i
$852$	−2.60117	+	4.50536i	−0.0891146	+	0.154351i
$853$	5.80988	+	2.79789i	0.198926	+	0.0957980i	0.530695	−	0.847563i	$-0.321931\pi$
$853$	5.80988	+	2.79789i	0.198926	+	0.0957980i	−0.331768	+	0.943361i	$0.607645\pi$
$854$	−1.66546	−	0.137981i	−0.0569909	−	0.00472160i
$855$	0.362244	−	0.174448i	0.0123885	−	0.00596598i
$856$	−0.864947	+	11.5419i	−0.0295633	+	0.394495i
$857$	−28.9023	+	8.91518i	−0.987284	+	0.304537i	−0.746021	−	0.665923i	$-0.768038\pi$
$857$	−28.9023	+	8.91518i	−0.987284	+	0.304537i	−0.241263	+	0.970460i	$0.577562\pi$
$858$	7.40618	−	2.28451i	0.252843	−	0.0779917i
$859$	−0.614353	+	8.19797i	−0.0209614	+	0.279711i	0.976867	+	0.213847i	$0.0685994\pi$
$859$	−0.614353	+	8.19797i	−0.0209614	+	0.279711i	−0.997829	+	0.0658641i	$0.979020\pi$
$860$	0.0782713	−	0.0376935i	0.00266903	−	0.00128534i
$861$	−12.5357	−	1.03856i	−0.427215	−	0.0353940i
$862$	9.11200	+	4.38811i	0.310356	+	0.149459i
$863$	0.301118	−	0.521552i	0.0102502	−	0.0177538i	−0.860855	−	0.508851i	$-0.830071\pi$
$863$	0.301118	−	0.521552i	0.0102502	−	0.0177538i	0.871105	+	0.491097i	$0.163404\pi$
$864$	2.70885	+	4.69186i	0.0921569	+	0.159620i
$865$	0.112401	+	1.49988i	0.00382173	+	0.0509975i
$866$	−0.542909	−	1.38331i	−0.0184488	−	0.0470068i
$867$	3.88611	−	17.0261i	0.131979	−	0.578238i
$868$	−12.3665	+	25.1714i	−0.419748	+	0.854372i
$869$	10.5215	+	46.0977i	0.356918	+	1.56376i
$870$	−0.432871	+	0.295126i	−0.0146757	+	0.0100057i
$871$	−13.4833	+	12.5107i	−0.456866	+	0.423909i
$872$	−4.13450	−	0.623176i	−0.140012	−	0.0211034i
$873$	−14.7486	−	13.6847i	−0.499166	−	0.463159i
$874$	2.90131	+	3.63813i	0.0981384	+	0.123062i
$875$	−2.19092	+	0.146880i	−0.0740666	+	0.00496545i
$876$	−5.90418	+	7.40361i	−0.199484	+	0.250145i
$877$	49.8970	−	7.52076i	1.68490	−	0.253958i	0.764413	−	0.644726i	$-0.223029\pi$
$877$	49.8970	−	7.52076i	1.68490	−	0.253958i	0.920489	+	0.390768i	$0.127791\pi$
$878$	−9.60931	−	6.55151i	−0.324298	−	0.221103i
$879$	−11.4621	+	29.2049i	−0.386606	+	0.985055i
$880$	0.304567	+	0.0939466i	0.0102670	+	0.00316694i
$881$	32.6443			1.09981			0.549907	−	0.835226i	$-0.314663\pi$
$881$	32.6443			1.09981			0.549907	+	0.835226i	$0.314663\pi$
$882$	−2.71675	+	11.0959i	−0.0914777	+	0.373619i
$883$	−17.4014			−0.585604			−0.292802	−	0.956173i	$-0.594588\pi$
$883$	−17.4014			−0.585604			−0.292802	+	0.956173i	$0.594588\pi$
$884$	−2.37323	−	0.732046i	−0.0798205	−	0.0246214i
$885$	−0.124018	+	0.315993i	−0.00416883	+	0.0106220i
$886$	11.4562	+	7.81072i	0.384879	+	0.262406i
$887$	27.3578	−	4.12352i	0.918584	−	0.138454i	0.327303	−	0.944920i	$-0.393860\pi$
$887$	27.3578	−	4.12352i	0.918584	−	0.138454i	0.591281	+	0.806465i	$0.298622\pi$
$888$	6.10461	−	7.65494i	0.204857	−	0.256883i
$889$	−4.31867	−	4.72841i	−0.144843	−	0.158586i
$890$	0.803425	+	1.00746i	0.0269309	+	0.0337702i
$891$	4.05352	+	3.76112i	0.135798	+	0.126002i
$892$	17.4843	+	2.63533i	0.585416	+	0.0882373i
$893$	−18.5579	+	17.2192i	−0.621016	+	0.576219i
$894$	−18.8948	+	12.8823i	−0.631937	+	0.430847i
$895$	−0.0426651	−	0.186928i	−0.00142614	−	0.00624831i
$896$	2.08143	−	1.63329i	0.0695358	−	0.0545644i
$897$	−0.704959	+	3.08863i	−0.0235379	+	0.103126i
$898$	−6.74701	−	17.1911i	−0.225150	−	0.573674i
$899$	−4.27223	−	57.0090i	−0.142487	−	1.90136i
$900$	−4.07425	−	7.05681i	−0.135808	−	0.235227i
$901$	2.48055	−	4.29643i	0.0826389	−	0.143135i
$902$	−14.0544	−	6.76825i	−0.467961	−	0.225358i
$903$	−0.457277	−	3.20453i	−0.0152172	−	0.106640i
$904$	14.9462	−	7.19773i	0.497105	−	0.239393i
$905$	0.145003	−	1.93492i	0.00482005	−	0.0643190i
$906$	1.39426	−	0.430072i	0.0463212	−	0.0142882i
$907$	14.7456	−	4.54843i	0.489621	−	0.151028i	−0.0401075	−	0.999195i	$-0.512770\pi$
$907$	14.7456	−	4.54843i	0.489621	−	0.151028i	0.529728	+	0.848167i	$0.322294\pi$
$908$	−1.63444	+	21.8100i	−0.0542407	+	0.723792i
$909$	−20.7247	+	9.98048i	−0.687394	+	0.331032i
$910$	0.114680	−	0.361665i	0.00380159	−	0.0119891i
$911$	4.82602	+	2.32409i	0.159893	+	0.0770005i	0.512119	−	0.858915i	$-0.328861\pi$
$911$	4.82602	+	2.32409i	0.159893	+	0.0770005i	−0.352226	+	0.935915i	$0.614575\pi$
$912$	−1.73482	+	3.00480i	−0.0574456	+	0.0994988i
$913$	−27.5652	−	47.7443i	−0.912274	−	1.58010i
$914$	0.0895624	+	1.19513i	0.00296246	+	0.0395313i
$915$	0.0224167	+	0.0571167i	0.000741072	+	0.00188822i
$916$	1.73575	−	7.60481i	0.0573508	−	0.251270i
$917$	0.00911223	−	1.15935i	0.000300912	−	0.0382851i
$918$	−1.73401	−	7.59720i	−0.0572309	−	0.250745i
$919$	3.06629	−	2.09056i	0.101148	−	0.0689613i	−0.511690	−	0.859170i	$-0.670980\pi$
$919$	3.06629	−	2.09056i	0.101148	−	0.0689613i	0.612838	+	0.790209i	$0.290028\pi$
$920$	−0.0955030	+	0.0886138i	−0.00314864	+	0.00292151i
$921$	−21.5299	−	3.24511i	−0.709435	−	0.106930i
$922$	26.8957	+	24.9555i	0.885761	+	0.821866i
$923$	4.78837	+	6.00443i	0.157611	+	0.197638i
$924$	6.76688	−	9.75950i	0.222614	−	0.321064i
$925$	−26.0602	+	32.6785i	−0.856854	+	1.07446i
$926$	15.7711	−	2.37711i	0.518270	−	0.0781166i
$927$	−21.1450	−	14.4164i	−0.694493	−	0.473497i
$928$	−1.97038	+	5.02044i	−0.0646808	+	0.164804i
$929$	30.9114	+	9.53490i	1.01417	+	0.312830i	0.756915	−	0.653514i	$-0.226706\pi$
$929$	30.9114	+	9.53490i	1.01417	+	0.312830i	0.257255	+	0.966344i	$0.417182\pi$
$930$	1.02970			0.0337652
$931$	−19.9362	+	5.80794i	−0.653383	+	0.190347i
$932$	−16.2149			−0.531136
$933$	−7.10671	−	2.19213i	−0.232663	−	0.0717671i
$934$	−4.96545	+	12.6518i	−0.162474	+	0.413978i
$935$	−0.378784	−	0.258250i	−0.0123876	−	0.00844569i
$936$	2.78638	−	0.419979i	0.0910756	−	0.0137274i
$937$	32.7352	−	41.0487i	1.06941	−	1.34100i	0.132601	−	0.991170i	$-0.457667\pi$
$937$	32.7352	−	41.0487i	1.06941	−	1.34100i	0.936812	−	0.349832i	$-0.113761\pi$
$938$	−4.41950	+	27.8352i	−0.144302	+	0.908852i
$939$	10.7157	+	13.4371i	0.349695	+	0.438503i
$940$	−0.519572	−	0.482092i	−0.0169466	−	0.0157241i
$941$	41.4404	+	6.24613i	1.35092	+	0.203618i	0.784309	−	0.620370i	$-0.213017\pi$
$941$	41.4404	+	6.24613i	1.35092	+	0.203618i	0.566608	+	0.823988i	$0.308256\pi$
$942$	7.97683	−	7.40141i	0.259899	−	0.241151i
$943$	5.26831	−	3.59187i	0.171560	−	0.116967i
$944$	0.777600	+	3.40689i	0.0253087	+	0.110885i
$945$	1.16266	−	0.255772i	0.0378213	−	0.00832027i
$946$	0.893268	−	3.91366i	0.0290427	−	0.127244i
$947$	−16.3299	−	41.6079i	−0.530651	−	1.35208i	−0.905246	−	0.424888i	$-0.860314\pi$
$947$	−16.3299	−	41.6079i	−0.530651	−	1.35208i	0.374595	−	0.927188i	$-0.377782\pi$
$948$	−1.07692	−	14.3705i	−0.0349768	−	0.466733i
$949$	6.98973	+	12.1066i	0.226896	+	0.392996i
$950$	7.40584	−	12.8273i	0.240277	−	0.416172i
$951$	−21.2789	−	10.2474i	−0.690014	−	0.332293i
$952$	−3.55329	+	1.36243i	−0.115163	+	0.0441566i
$953$	1.03966	−	0.500672i	0.0336778	−	0.0162184i	−0.416969	−	0.908921i	$-0.636908\pi$
$953$	1.03966	−	0.500672i	0.0336778	−	0.0162184i	0.450647	+	0.892702i	$0.351193\pi$
$954$	−0.420643	+	5.61309i	−0.0136188	+	0.181731i
$955$	1.85167	−	0.571164i	0.0599186	−	0.0184824i
$956$	−14.5548	+	4.48955i	−0.470735	+	0.145202i
$957$	−1.80912	+	24.1410i	−0.0584804	+	0.780367i
$958$	19.6839	−	9.47928i	0.635959	−	0.306262i
$959$	−38.3433	−	22.5412i	−1.23817	−	0.727892i
$960$	−0.0875208	−	0.0421478i	−0.00282472	−	0.00136031i
$961$	−40.6807	+	70.4610i	−1.31228	+	2.27294i
$962$	−7.22701	−	12.5176i	−0.233008	−	0.403582i
$963$	1.41155	+	18.8358i	0.0454866	+	0.606977i
$964$	−4.09038	−	10.4221i	−0.131742	−	0.335674i
$965$	−0.184684	+	0.809153i	−0.00594519	+	0.0260476i
$966$	2.07179	+	4.39004i	0.0666586	+	0.141247i
$967$	3.95071	+	17.3092i	0.127046	+	0.556625i	0.997882	+	0.0650514i	$0.0207211\pi$
$967$	3.95071	+	17.3092i	0.127046	+	0.556625i	−0.870836	+	0.491574i	$0.836422\pi$
$968$	3.08005	−	2.09994i	0.0989966	−	0.0674948i
$969$	3.65835	−	3.39445i	0.117523	−	0.109046i
$970$	1.01247	+	0.152606i	0.0325085	+	0.00489987i
$971$	−16.3855	−	15.2035i	−0.525837	−	0.487905i	0.372001	−	0.928232i	$-0.378672\pi$
$971$	−16.3855	−	15.2035i	−0.525837	−	0.487905i	−0.897837	+	0.440327i	$0.854862\pi$
$972$	9.08286	+	11.3896i	0.291333	+	0.365320i
$973$	−15.2573	−	50.8793i	−0.489126	−	1.63111i
$974$	14.7571	−	18.5048i	0.472848	−	0.592932i
$975$	9.97136	−	1.50294i	0.319339	−	0.0481326i
$976$	0.521887	+	0.355817i	0.0167052	+	0.0113894i
$977$	−10.9643	+	27.9366i	−0.350780	+	0.893772i	0.641200	+	0.767374i	$0.278437\pi$
$977$	−10.9643	+	27.9366i	−0.350780	+	0.893772i	−0.991980	+	0.126398i	$0.959658\pi$
$978$	19.2449	+	5.93626i	0.615383	+	0.189821i
$979$	59.5435			1.90302
$980$	−0.203864	−	0.544449i	−0.00651219	−	0.0173918i
$981$	−6.82351			−0.217858
$982$	14.7577	+	4.55215i	0.470937	+	0.145265i
$983$	−1.56713	+	3.99298i	−0.0499836	+	0.127356i	−0.953685	−	0.300807i	$-0.902744\pi$
$983$	−1.56713	+	3.99298i	−0.0499836	+	0.127356i	0.903701	+	0.428163i	$0.140839\pi$
$984$	3.92817	+	2.67818i	0.125226	+	0.0853773i
$985$	0.463748	−	0.0698987i	0.0147762	−	0.00222716i
$986$	4.83667	−	6.06499i	0.154031	−	0.193149i
$987$	−22.9744	+	13.0246i	−0.731282	+	0.414577i
$988$	3.19355	+	4.00459i	0.101600	+	0.127403i
$989$	1.20284	+	1.11607i	0.0382481	+	0.0354891i
$990$	0.514338	+	0.0775240i	0.0163467	+	0.00246387i
$991$	−5.10151	+	4.73351i	−0.162055	+	0.150365i	−0.757032	−	0.653377i	$-0.773351\pi$
$991$	−5.10151	+	4.73351i	−0.162055	+	0.150365i	0.594977	+	0.803742i	$0.297161\pi$
$992$	8.75818	−	5.97123i	0.278073	−	0.189587i
$993$	−1.70672	−	7.47762i	−0.0541611	−	0.237295i
$994$	11.4519	+	2.70868i	0.363231	+	0.0859141i
$995$	−0.311015	+	1.36265i	−0.00985984	+	0.0431988i
$996$	6.13862	+	15.6410i	0.194510	+	0.495603i
$997$	1.64013	+	21.8861i	0.0519435	+	0.693138i	0.961015	+	0.276497i	$0.0891737\pi$
$997$	1.64013	+	21.8861i	0.0519435	+	0.693138i	−0.909071	+	0.416641i	$0.863207\pi$
$998$	−2.26164	−	3.91727i	−0.0715908	−	0.123999i
$999$	22.6758	−	39.2757i	0.717431	−	1.24263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.b.51.2	yes	24
3.2	odd	2		882.2.z.b.541.1		24
4.3	odd	2		784.2.bg.b.737.1		24
7.2	even	3		686.2.e.c.589.3		24
7.3	odd	6		686.2.g.d.655.2		24
7.4	even	3		686.2.g.f.655.1		24
7.5	odd	6		686.2.e.d.589.2		24
7.6	odd	2		686.2.g.e.471.1		24
49.5	odd	42		4802.2.a.l.1.6		12
49.9	even	21		686.2.e.c.99.3		24
49.15	even	7		686.2.g.f.177.1		24
49.24	odd	42		686.2.g.e.67.1		24
49.25	even	21	inner	98.2.g.b.25.2	✓	24
49.34	odd	14		686.2.g.d.177.2		24
49.40	odd	42		686.2.e.d.99.2		24
49.44	even	21		4802.2.a.o.1.7		12
147.74	odd	42		882.2.z.b.613.1		24
196.123	odd	42		784.2.bg.b.417.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.25.2	✓	24	49.25	even	21	inner
98.2.g.b.51.2	yes	24	1.1	even	1	trivial
686.2.e.c.99.3		24	49.9	even	21
686.2.e.c.589.3		24	7.2	even	3
686.2.e.d.99.2		24	49.40	odd	42
686.2.e.d.589.2		24	7.5	odd	6
686.2.g.d.177.2		24	49.34	odd	14
686.2.g.d.655.2		24	7.3	odd	6
686.2.g.e.67.1		24	49.24	odd	42
686.2.g.e.471.1		24	7.6	odd	2
686.2.g.f.177.1		24	49.15	even	7
686.2.g.f.655.1		24	7.4	even	3
784.2.bg.b.417.1		24	196.123	odd	42
784.2.bg.b.737.1		24	4.3	odd	2
882.2.z.b.541.1		24	3.2	odd	2
882.2.z.b.613.1		24	147.74	odd	42
4802.2.a.l.1.6		12	49.5	odd	42
4802.2.a.o.1.7		12	49.44	even	21

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.955573 + 0.294755i) q^{2} +(0.427316 - 1.08878i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0821245 + 0.0123783i) q^{5} +(0.729256 - 0.914459i) q^{6} +(-2.45519 - 0.985929i) q^{7} +(0.623490 + 0.781831i) q^{8} +(1.19630 + 1.11001i) q^{9} +O(q^{10})\)	\(q+(0.955573 + 0.294755i) q^{2} +(0.427316 - 1.08878i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0821245 + 0.0123783i) q^{5} +(0.729256 - 0.914459i) q^{6} +(-2.45519 - 0.985929i) q^{7} +(0.623490 + 0.781831i) q^{8} +(1.19630 + 1.11001i) q^{9} +(-0.0821245 - 0.0123783i) q^{10} +(-2.81322 + 2.61029i) q^{11} +(0.966399 - 0.658880i) q^{12} +(-0.384222 - 1.68338i) q^{13} +(-2.05550 - 1.66581i) q^{14} +(-0.0216159 + 0.0947053i) q^{15} +(0.365341 + 0.930874i) q^{16} +(-0.107488 - 1.43433i) q^{17} +(0.815975 + 1.41331i) q^{18} +(-1.48321 + 2.56900i) q^{19} +(-0.0748274 - 0.0360350i) q^{20} +(-2.12260 + 2.25187i) q^{21} +(-3.45763 + 1.66511i) q^{22} +(0.117227 - 1.56428i) q^{23} +(1.11767 - 0.344756i) q^{24} +(-4.77127 + 1.47174i) q^{25} +(0.129035 - 1.72185i) q^{26} +(4.88118 - 2.35065i) q^{27} +(-1.47318 - 2.19767i) q^{28} +(4.85915 + 2.34005i) q^{29} +(-0.0485704 + 0.0841264i) q^{30} +(-5.30003 - 9.17993i) q^{31} +(0.0747301 + 0.997204i) q^{32} +(1.63990 + 4.17841i) q^{33} +(0.320064 - 1.40229i) q^{34} +(0.213835 + 0.0505779i) q^{35} +(0.363143 + 1.59103i) q^{36} +(6.91645 - 4.71556i) q^{37} +(-2.17454 + 2.01768i) q^{38} +(-1.99703 - 0.301003i) q^{39} +(-0.0608815 - 0.0564898i) q^{40} +(2.53433 + 3.17795i) q^{41} +(-2.69205 + 1.52617i) q^{42} +(-0.652186 + 0.817816i) q^{43} +(-3.79482 + 0.571977i) q^{44} +(-0.111986 - 0.0763507i) q^{45} +(0.573099 - 1.46023i) q^{46} +(8.15500 + 2.51548i) q^{47} +1.16964 q^{48} +(5.05589 + 4.84128i) q^{49} -4.99310 q^{50} +(-1.60761 - 0.495882i) q^{51} +(0.630826 - 1.60732i) q^{52} +(2.84982 + 1.94297i) q^{53} +(5.35719 - 0.807466i) q^{54} +(0.198723 - 0.249191i) q^{55} +(-0.759954 - 2.53426i) q^{56} +(2.16329 + 2.71267i) q^{57} +(3.95354 + 3.66834i) q^{58} +(3.45547 + 0.520829i) q^{59} +(-0.0712092 + 0.0660725i) q^{60} +(0.521887 - 0.355817i) q^{61} +(-2.35874 - 10.3343i) q^{62} +(-1.84276 - 3.90475i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(0.0523914 + 0.133491i) q^{65} +(0.335440 + 4.47614i) q^{66} +(-5.32626 - 9.22534i) q^{67} +(0.719177 - 1.24565i) q^{68} +(-1.65307 - 0.796078i) q^{69} +(0.189427 + 0.111360i) q^{70} +(-4.00735 + 1.92984i) q^{71} +(-0.121956 + 1.62739i) q^{72} +(-7.73648 + 2.38639i) q^{73} +(7.99911 - 2.46740i) q^{74} +(-0.436432 + 5.82378i) q^{75} +(-2.67266 + 1.28708i) q^{76} +(9.48054 - 3.63511i) q^{77} +(-1.81958 - 0.876264i) q^{78} +(6.16039 - 10.6701i) q^{79} +(-0.0415261 - 0.0719253i) q^{80} +(-0.107677 - 1.43686i) q^{81} +(1.48502 + 3.78377i) q^{82} +(-3.19663 + 14.0054i) q^{83} +(-3.02230 + 0.664873i) q^{84} +(0.0265820 + 0.116463i) q^{85} +(-0.864267 + 0.589247i) q^{86} +(4.62420 - 4.29063i) q^{87} +(-3.79482 - 0.571977i) q^{88} +(-11.3737 - 10.5532i) q^{89} +(-0.0845059 - 0.105967i) q^{90} +(-0.716361 + 4.51184i) q^{91} +(0.978050 - 1.22644i) q^{92} +(-12.2597 + 1.84786i) q^{93} +(7.05124 + 4.80746i) q^{94} +(0.0900084 - 0.229338i) q^{95} +(1.11767 + 0.344756i) q^{96} -12.3285 q^{97} +(3.40428 + 6.11644i) q^{98} -6.26291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Introduction

L-functions

Modular forms

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