LMFDB - Embedded newform 507.2.p.b.493.9

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			493.9
Character	$\chi$	$=$	507.493
Dual form			507.2.p.b.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.168246 - 0.116132i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.694390 - 1.83096i) q^{4} +(-1.57986 + 1.78329i) q^{5} +(0.202943 + 0.0246418i) q^{6} +(-0.172035 + 0.697973i) q^{7} +(-0.193652 + 0.785677i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})$	\(q+(-0.168246 - 0.116132i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.694390 - 1.83096i) q^{4} +(-1.57986 + 1.78329i) q^{5} +(0.202943 + 0.0246418i) q^{6} +(-0.172035 + 0.697973i) q^{7} +(-0.193652 + 0.785677i) q^{8} +(0.568065 - 0.822984i) q^{9} +(0.472900 - 0.116559i) q^{10} +(2.94172 - 2.03052i) q^{11} +(1.46574 + 1.29853i) q^{12} +(-2.24044 - 2.82497i) q^{13} +(0.110001 - 0.0974522i) q^{14} +(0.570157 - 2.31322i) q^{15} +(-2.80765 + 2.48737i) q^{16} +(7.04646 + 1.73680i) q^{17} +(-0.191149 + 0.0724932i) q^{18} +4.66869i q^{19} +(4.36216 + 1.65435i) q^{20} +(-0.172035 - 0.697973i) q^{21} -0.730738 q^{22} +5.41784 q^{23} +(-0.193652 - 0.785677i) q^{24} +(-0.0814906 - 0.671136i) q^{25} +(0.0488756 + 0.735474i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(1.39742 - 0.169677i) q^{28} +(2.98264 - 4.32110i) q^{29} +(-0.364564 + 0.322976i) q^{30} +(5.52510 + 0.670868i) q^{31} +(2.36782 - 0.287505i) q^{32} +(-1.66113 + 3.16502i) q^{33} +(-0.983838 - 1.11052i) q^{34} +(-0.972897 - 1.40948i) q^{35} +(-1.90130 - 0.468630i) q^{36} +(6.65100 + 0.807577i) q^{37} +(0.542182 - 0.785487i) q^{38} +(3.29664 + 1.46020i) q^{39} +(-1.09515 - 1.58659i) q^{40} +(-1.60952 - 3.06668i) q^{41} +(-0.0521125 + 0.137409i) q^{42} +(-1.52309 - 12.5438i) q^{43} +(-5.76049 - 3.97618i) q^{44} +(0.570157 + 2.31322i) q^{45} +(-0.911528 - 0.629183i) q^{46} +(-0.217680 - 0.0825551i) q^{47} +(1.33012 - 3.50723i) q^{48} +(5.74062 + 3.01291i) q^{49} +(-0.0642296 + 0.122379i) q^{50} +(-7.04646 + 1.73680i) q^{51} +(-3.61665 + 6.06377i) q^{52} +(7.23049 + 1.78215i) q^{53} +(0.135565 - 0.153021i) q^{54} +(-1.02648 + 8.45386i) q^{55} +(-0.515066 - 0.270328i) q^{56} +(-2.16965 - 4.13392i) q^{57} +(-1.00363 + 0.380628i) q^{58} +(-7.91091 + 8.92957i) q^{59} +(-4.63131 + 0.562343i) q^{60} +(-11.4063 + 2.81141i) q^{61} +(-0.851665 - 0.754509i) q^{62} +(0.476693 + 0.538076i) q^{63} +(6.21091 + 3.25974i) q^{64} +(8.57730 + 0.467699i) q^{65} +(0.647037 - 0.339591i) q^{66} +(3.40627 + 1.29183i) q^{67} +(-1.71299 - 14.1078i) q^{68} +(-4.79726 + 2.51780i) q^{69} +0.350123i q^{70} +(1.58471 + 3.01941i) q^{71} +(0.536593 + 0.605688i) q^{72} +(-9.74228 + 6.72461i) q^{73} +(-1.02522 - 0.908262i) q^{74} +(0.384049 + 0.556390i) q^{75} +(8.54817 - 3.24189i) q^{76} +(0.911170 + 2.40256i) q^{77} +(-0.385069 - 0.628516i) q^{78} +(2.16010 - 5.69572i) q^{79} -8.93654i q^{80} +(-0.354605 - 0.935016i) q^{81} +(-0.0853441 + 0.702872i) q^{82} +(6.06034 - 11.5470i) q^{83} +(-1.15850 + 0.799653i) q^{84} +(-14.2296 + 9.82198i) q^{85} +(-1.20047 + 2.28731i) q^{86} +(-0.632882 + 5.21225i) q^{87} +(1.02566 + 2.70445i) q^{88} +18.7193i q^{89} +(0.172711 - 0.455402i) q^{90} +(2.35718 - 1.07777i) q^{91} +(-3.76209 - 9.91983i) q^{92} +(-5.20400 + 1.97362i) q^{93} +(0.0270364 + 0.0391690i) q^{94} +(-8.32563 - 7.37586i) q^{95} +(-1.96299 + 1.35495i) q^{96} +(-7.07746 - 7.98880i) q^{97} +(-0.615940 - 1.17358i) q^{98} -3.57445i 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{26}\right)$

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 $

$2$	−0.168246	−	0.116132i	−0.118968	−	0.0821174i	0.507095	−	0.861890i	$-0.330719\pi$
$2$	−0.168246	−	0.116132i	−0.118968	−	0.0821174i	−0.626063	+	0.779773i	$0.715335\pi$
$3$	−0.885456	+	0.464723i	−0.511218	+	0.268308i
$3$	−0.885456	+	0.464723i	−0.511218	+	0.268308i
$4$	−0.694390	−	1.83096i	−0.347195	−	0.915478i
$5$	−1.57986	+	1.78329i	−0.706533	+	0.797511i	−0.986719	−	0.162435i	$-0.948065\pi$
$5$	−1.57986	+	1.78329i	−0.706533	+	0.797511i	0.280186	+	0.959946i	$0.409604\pi$
$6$	0.202943	+	0.0246418i	0.0828512	+	0.0100600i
$7$	−0.172035	+	0.697973i	−0.0650230	+	0.263809i	−0.994452	−	0.105193i	$-0.966454\pi$
$7$	−0.172035	+	0.697973i	−0.0650230	+	0.263809i	0.929429	+	0.369001i	$0.120300\pi$
$8$	−0.193652	+	0.785677i	−0.0684663	+	0.277779i
$9$	0.568065	−	0.822984i	0.189355	−	0.274328i
$10$	0.472900	−	0.116559i	0.149544	−	0.0368593i
$11$	2.94172	−	2.03052i	0.886961	−	0.612225i	−0.0350513	−	0.999386i	$-0.511159\pi$
$11$	2.94172	−	2.03052i	0.886961	−	0.612225i	0.922012	+	0.387161i	$0.126544\pi$
$12$	1.46574	+	1.29853i	0.423122	+	0.374854i
$13$	−2.24044	−	2.82497i	−0.621385	−	0.783505i
$13$	−2.24044	−	2.82497i	−0.621385	−	0.783505i
$14$	0.110001	−	0.0974522i	0.0293989	−	0.0260452i
$15$	0.570157	−	2.31322i	0.147214	−	0.597271i
$16$	−2.80765	+	2.48737i	−0.701914	+	0.621841i
$17$	7.04646	+	1.73680i	1.70902	+	0.421235i	0.968141	−	0.250407i	$-0.0805645\pi$
$17$	7.04646	+	1.73680i	1.70902	+	0.421235i	0.740876	+	0.671642i	$0.234411\pi$
$18$	−0.191149	+	0.0724932i	−0.0450542	+	0.0170868i
$19$			4.66869i			1.07107i	0.844513	+	0.535536i	$0.179890\pi$
$19$			4.66869i			1.07107i	−0.844513	+	0.535536i	$0.820110\pi$
$20$	4.36216	+	1.65435i	0.975408	+	0.369924i
$21$	−0.172035	−	0.697973i	−0.0375411	−	0.152310i
$22$	−0.730738			−0.155794
$23$	5.41784			1.12970			0.564849	−	0.825194i	$-0.308934\pi$
$23$	5.41784			1.12970			0.564849	+	0.825194i	$0.308934\pi$
$24$	−0.193652	−	0.785677i	−0.0395290	−	0.160376i
$25$	−0.0814906	−	0.671136i	−0.0162981	−	0.134227i
$26$	0.0488756	+	0.735474i	0.00958529	+	0.144238i
$27$	−0.120537	+	0.992709i	−0.0231973	+	0.191047i
$28$	1.39742	−	0.169677i	0.264087	−	0.0320659i
$29$	2.98264	−	4.32110i	0.553863	−	0.802409i	−0.441635	−	0.897195i	$-0.645601\pi$
$29$	2.98264	−	4.32110i	0.553863	−	0.802409i	0.995498	+	0.0947861i	$0.0302167\pi$
$30$	−0.364564	+	0.322976i	−0.0665600	+	0.0589670i
$31$	5.52510	+	0.670868i	0.992337	+	0.120492i	0.600569	−	0.799573i	$-0.294941\pi$
$31$	5.52510	+	0.670868i	0.992337	+	0.120492i	0.391768	+	0.920064i	$0.371864\pi$
$32$	2.36782	−	0.287505i	0.418575	−	0.0508242i
$33$	−1.66113	+	3.16502i	−0.289166	+	0.550959i
$34$	−0.983838	−	1.11052i	−0.168727	−	0.190453i
$35$	−0.972897	−	1.40948i	−0.164450	−	0.238246i
$36$	−1.90130	−	0.468630i	−0.316884	−	0.0781049i
$37$	6.65100	+	0.807577i	1.09342	+	0.132765i	0.647319	−	0.762219i	$-0.275890\pi$
$37$	6.65100	+	0.807577i	1.09342	+	0.132765i	0.446098	+	0.894984i	$0.352813\pi$
$38$	0.542182	−	0.785487i	0.0879536	−	0.127423i
$39$	3.29664	+	1.46020i	0.527884	+	0.233820i
$40$	−1.09515	−	1.58659i	−0.173158	−	0.250863i
$41$	−1.60952	−	3.06668i	−0.251365	−	0.478936i	0.726777	−	0.686873i	$-0.241017\pi$
$41$	−1.60952	−	3.06668i	−0.251365	−	0.478936i	−0.978142	+	0.207938i	$0.933325\pi$
$42$	−0.0521125	+	0.137409i	−0.00804114	+	0.0212027i
$43$	−1.52309	−	12.5438i	−0.232269	−	1.91291i	−0.381968	−	0.924176i	$-0.624753\pi$
$43$	−1.52309	−	12.5438i	−0.232269	−	1.91291i	0.149699	−	0.988732i	$-0.452170\pi$
$44$	−5.76049	−	3.97618i	−0.868427	−	0.599432i
$45$	0.570157	+	2.31322i	0.0849941	+	0.344834i
$46$	−0.911528	−	0.629183i	−0.134398	−	0.0927679i
$47$	−0.217680	−	0.0825551i	−0.0317519	−	0.0120419i	0.338678	−	0.940902i	$-0.390020\pi$
$47$	−0.217680	−	0.0825551i	−0.0317519	−	0.0120419i	−0.370430	+	0.928861i	$0.620790\pi$
$48$	1.33012	−	3.50723i	0.191986	−	0.506226i
$49$	5.74062	+	3.01291i	0.820089	+	0.430416i
$50$	−0.0642296	+	0.122379i	−0.00908343	+	0.0173070i
$51$	−7.04646	+	1.73680i	−0.986701	+	0.243200i
$52$	−3.61665	+	6.06377i	−0.501540	+	0.840893i
$53$	7.23049	+	1.78215i	0.993184	+	0.244798i	0.702238	−	0.711942i	$-0.252184\pi$
$53$	7.23049	+	1.78215i	0.993184	+	0.244798i	0.290945	+	0.956740i	$0.406030\pi$
$54$	0.135565	−	0.153021i	0.0184480	−	0.0208235i
$55$	−1.02648	+	8.45386i	−0.138411	+	1.13992i
$56$	−0.515066	−	0.270328i	−0.0688286	−	0.0361240i
$57$	−2.16965	−	4.13392i	−0.287377	−	0.547551i
$58$	−1.00363	+	0.380628i	−0.131783	+	0.0499789i
$59$	−7.91091	+	8.92957i	−1.02991	+	1.16253i	−0.0433643	+	0.999059i	$0.513808\pi$
$59$	−7.91091	+	8.92957i	−1.02991	+	1.16253i	−0.986548	+	0.163471i	$0.947731\pi$
$60$	−4.63131	+	0.562343i	−0.597900	+	0.0725982i
$61$	−11.4063	+	2.81141i	−1.46043	+	0.359964i	−0.887945	−	0.459950i	$-0.847867\pi$
$61$	−11.4063	+	2.81141i	−1.46043	+	0.359964i	−0.572487	+	0.819914i	$0.694021\pi$
$62$	−0.851665	−	0.754509i	−0.108161	−	0.0958227i
$63$	0.476693	+	0.538076i	0.0600577	+	0.0677911i
$64$	6.21091	+	3.25974i	0.776363	+	0.407467i
$65$	8.57730	+	0.467699i	1.06388	+	0.0580109i
$66$	0.647037	−	0.339591i	0.0796447	−	0.0418008i
$67$	3.40627	+	1.29183i	0.416142	+	0.157822i	0.553784	−	0.832660i	$-0.313183\pi$
$67$	3.40627	+	1.29183i	0.416142	+	0.157822i	−0.137642	+	0.990482i	$0.543952\pi$
$68$	−1.71299	−	14.1078i	−0.207731	−	1.71082i
$69$	−4.79726	+	2.51780i	−0.577523	+	0.303107i
$70$			0.350123i			0.0418478i
$71$	1.58471	+	3.01941i	0.188070	+	0.358338i	0.961175	−	0.275941i	$-0.0889894\pi$
$71$	1.58471	+	3.01941i	0.188070	+	0.358338i	−0.773104	+	0.634279i	$0.781297\pi$
$72$	0.536593	+	0.605688i	0.0632381	+	0.0713810i
$73$	−9.74228	+	6.72461i	−1.14025	+	0.787056i	−0.979798	−	0.199988i	$-0.935910\pi$
$73$	−9.74228	+	6.72461i	−1.14025	+	0.787056i	−0.160450	+	0.987044i	$0.551294\pi$
$74$	−1.02522	−	0.908262i	−0.119179	−	0.105583i
$75$	0.384049	+	0.556390i	0.0443461	+	0.0642464i
$76$	8.54817	−	3.24189i	0.980542	−	0.371871i
$77$	0.911170	+	2.40256i	0.103837	+	0.273797i
$78$	−0.385069	−	0.628516i	−0.0436005	−	0.0711654i
$79$	2.16010	−	5.69572i	0.243030	−	0.640818i	−0.756889	−	0.653544i	$-0.773282\pi$
$79$	2.16010	−	5.69572i	0.243030	−	0.640818i	0.999919	+	0.0127254i	$0.00405074\pi$
$80$		−	8.93654i		−	0.999135i
$81$	−0.354605	−	0.935016i	−0.0394005	−	0.103891i
$82$	−0.0853441	+	0.702872i	−0.00942468	+	0.0776192i
$83$	6.06034	−	11.5470i	0.665208	−	1.26745i	−0.285802	−	0.958289i	$-0.592260\pi$
$83$	6.06034	−	11.5470i	0.665208	−	1.26745i	0.951010	−	0.309160i	$-0.100048\pi$
$84$	−1.15850	+	0.799653i	−0.126402	+	0.0872493i
$85$	−14.2296	+	9.82198i	−1.54342	+	1.06534i
$86$	−1.20047	+	2.28731i	−0.129450	+	0.246647i
$87$	−0.632882	+	5.21225i	−0.0678520	+	0.558812i
$88$	1.02566	+	2.70445i	0.109336	+	0.288296i
$89$			18.7193i			1.98424i	0.125294	+	0.992120i	$0.460013\pi$
$89$			18.7193i			1.98424i	−0.125294	+	0.992120i	$0.539987\pi$
$90$	0.172711	−	0.455402i	0.0182054	−	0.0480036i
$91$	2.35718	−	1.07777i	0.247100	−	0.112981i
$92$	−3.76209	−	9.91983i	−0.392226	−	1.03421i
$93$	−5.20400	+	1.97362i	−0.539630	+	0.204655i
$94$	0.0270364	+	0.0391690i	0.00278859	+	0.00403998i
$95$	−8.32563	−	7.37586i	−0.854191	−	0.756747i
$96$	−1.96299	+	1.35495i	−0.200347	+	0.138289i
$97$	−7.07746	−	7.98880i	−0.718607	−	0.811139i	0.269808	−	0.962914i	$-0.413040\pi$
$97$	−7.07746	−	7.98880i	−0.718607	−	0.811139i	−0.988415	+	0.151775i	$0.951501\pi$
$98$	−0.615940	−	1.17358i	−0.0622194	−	0.118549i
$99$		−	3.57445i		−	0.359246i
$100$	−1.17223	+	0.615235i	−0.117223	+	0.0615235i
$101$	−0.361155	−	2.97438i	−0.0359362	−	0.295962i	−0.999585	−	0.0287909i	$-0.990834\pi$
$101$	−0.361155	−	2.97438i	−0.0359362	−	0.295962i	0.963649	−	0.267171i	$-0.0860888\pi$
$102$	1.38723	+	0.526108i	0.137356	+	0.0520924i
$103$	−2.00943	+	1.05463i	−0.197995	+	0.103916i	−0.560807	−	0.827947i	$-0.689509\pi$
$103$	−2.00943	+	1.05463i	−0.197995	+	0.103916i	0.362812	+	0.931862i	$0.381817\pi$
$104$	2.65338	−	1.21320i	0.260185	−	0.118964i
$105$	1.51648	+	0.795909i	0.147993	+	0.0776727i
$106$	−1.00953	−	1.13953i	−0.0980545	−	0.110681i
$107$	4.10009	+	3.63236i	0.396371	+	0.351154i	0.837642	−	0.546220i	$-0.183934\pi$
$107$	4.10009	+	3.63236i	0.396371	+	0.351154i	−0.441271	+	0.897374i	$0.645472\pi$
$108$	1.90130	−	0.468630i	0.182953	−	0.0450939i
$109$	−6.30280	+	0.765298i	−0.603698	+	0.0733022i	−0.416679	−	0.909054i	$-0.636806\pi$
$109$	−6.30280	+	0.765298i	−0.603698	+	0.0733022i	−0.187020	+	0.982356i	$0.559883\pi$
$110$	1.15446	−	1.30312i	0.110074	−	0.124247i
$111$	−6.26447	+	2.37580i	−0.594597	+	0.225501i
$112$	−1.25310	−	2.38758i	−0.118407	−	0.225605i
$113$	2.27998	+	1.19662i	0.214482	+	0.112569i	0.568543	−	0.822653i	$-0.307507\pi$
$113$	2.27998	+	1.19662i	0.214482	+	0.112569i	−0.354061	+	0.935222i	$0.615200\pi$
$114$	−0.115045	+	0.947479i	−0.0107749	+	0.0887395i
$115$	−8.55941	+	9.66158i	−0.798169	+	0.900947i
$116$	−9.98286	−	2.46055i	−0.926886	−	0.228457i
$117$	−3.59762	+	0.239078i	−0.332600	+	0.0221028i
$118$	2.36798	−	0.583655i	0.217990	−	0.0537298i
$119$	−2.42447	+	4.61944i	−0.222251	+	0.423464i
$120$	1.70703	+	0.895919i	0.155830	+	0.0817859i
$121$	0.630031	−	1.66126i	0.0572756	−	0.151023i
$122$	2.24556	+	0.851628i	0.203303	+	0.0771028i
$123$	2.85032	+	1.96743i	0.257005	+	0.177397i
$124$	−2.60824	−	10.5821i	−0.234227	−	0.950296i
$125$	−8.47801	−	5.85195i	−0.758297	−	0.523414i
$126$	−0.0177140	−	0.145888i	−0.00157809	−	0.0129967i
$127$	2.85200	−	7.52010i	0.253074	−	0.667301i	−0.746923	−	0.664910i	$-0.768470\pi$
$127$	2.85200	−	7.52010i	0.253074	−	0.667301i	0.999997	−	0.00239096i	$-0.000761066\pi$
$128$	−2.88332	−	5.49371i	−0.254852	−	0.485580i
$129$	7.17801	+	10.3991i	0.631989	+	0.915594i
$130$	−1.38878	−	1.07478i	−0.121804	−	0.0942647i
$131$	3.59862	−	5.21350i	0.314413	−	0.455505i	−0.633636	−	0.773632i	$-0.718438\pi$
$131$	3.59862	−	5.21350i	0.314413	−	0.455505i	0.948048	+	0.318126i	$0.103054\pi$
$132$	6.94848	+	0.843699i	0.604788	+	0.0734345i
$133$	−3.25862	−	0.803178i	−0.282558	−	0.0696443i
$134$	−0.423068	−	0.612919i	−0.0365475	−	0.0529482i
$135$	−1.57986	−	1.78329i	−0.135972	−	0.153481i
$136$	−2.72912	+	5.19990i	−0.234020	+	0.445888i
$137$	21.0759	−	2.55908i	1.80064	−	0.218637i	0.849538	−	0.527528i	$-0.176881\pi$
$137$	21.0759	−	2.55908i	1.80064	−	0.218637i	0.951097	+	0.308891i	$0.0999578\pi$
$138$	1.09951	+	0.133505i	0.0935968	+	0.0113647i
$139$	11.7944	−	10.4489i	1.00039	−	0.886264i	0.00687174	−	0.999976i	$-0.497813\pi$
$139$	11.7944	−	10.4489i	1.00039	−	0.886264i	0.993514	+	0.113712i	$0.0362742\pi$
$140$	−1.90513	+	2.76006i	−0.161013	+	0.233268i
$141$	0.231111	−	0.0280620i	0.0194631	−	0.00236324i
$142$	0.0840286	−	0.692037i	0.00705152	−	0.0580745i
$143$	−12.3269	−	3.76101i	−1.03083	−	0.314511i
$144$	0.452132	+	3.72364i	0.0376776	+	0.310303i
$145$	2.99363	+	12.1456i	0.248607	+	1.00864i
$146$	2.42004			0.200284
$147$	−6.48324			−0.534728
$148$	−3.13975	−	12.7385i	−0.258086	−	1.04709i
$149$	3.95402	+	1.49956i	0.323926	+	0.122849i	0.511207	−	0.859457i	$-0.329198\pi$
$149$	3.95402	+	1.49956i	0.323926	+	0.122849i	−0.187281	+	0.982306i	$0.559968\pi$
$150$		−	0.138210i		−	0.0112848i
$151$	−7.04289	+	2.67102i	−0.573142	+	0.217364i	−0.624111	−	0.781336i	$-0.714539\pi$
$151$	−7.04289	+	2.67102i	−0.573142	+	0.217364i	0.0509682	+	0.998700i	$0.483769\pi$
$152$	−3.66808	−	0.904102i	−0.297521	−	0.0733323i
$153$	5.43220	−	4.81251i	0.439167	−	0.389068i
$154$	0.125712	−	0.510035i	0.0101302	−	0.0410998i
$155$	−9.92521	+	8.79297i	−0.797212	+	0.706268i
$156$	0.384416	−	7.04994i	0.0307779	−	0.564447i
$157$	−9.44433	−	8.36695i	−0.753740	−	0.667755i	0.196068	−	0.980590i	$-0.437183\pi$
$157$	−9.44433	−	8.36695i	−0.753740	−	0.667755i	−0.949807	+	0.312835i	$0.898721\pi$
$158$	−1.02488	+	0.707424i	−0.0815351	+	0.0562796i
$159$	−7.23049	+	1.78215i	−0.573415	+	0.141334i
$160$	−3.22811	+	4.67672i	−0.255204	+	0.369727i
$161$	−0.932058	+	3.78151i	−0.0734564	+	0.298024i
$162$	−0.0489242	+	0.198493i	−0.00384385	+	0.0155951i
$163$	17.4693	+	2.12116i	1.36830	+	0.166142i	0.771492	−	0.636239i	$-0.219511\pi$
$163$	17.4693	+	2.12116i	1.36830	+	0.166142i	0.596812	+	0.802381i	$0.296434\pi$
$164$	−4.49733	+	5.07643i	−0.351182	+	0.396403i
$165$	−3.01980	−	7.96255i	−0.235091	−	0.619884i
$166$	−2.36060	+	1.23894i	−0.183218	+	0.0961601i
$167$	15.6466	+	10.8001i	1.21077	+	0.835736i	0.990203	−	0.139636i	$-0.0445932\pi$
$167$	15.6466	+	10.8001i	1.21077	+	0.835736i	0.220569	+	0.975371i	$0.429209\pi$
$168$	0.581696			0.0448788
$169$	−2.96089	+	12.6583i	−0.227761	+	0.973717i
$170$	3.53471			0.271100
$171$	3.84226	+	2.65212i	0.293825	+	0.202813i
$172$	−21.9095	+	11.4990i	−1.67058	+	0.876789i
$173$	5.53595	+	14.5971i	0.420891	+	1.10980i	0.963003	+	0.269491i	$0.0868556\pi$
$173$	5.53595	+	14.5971i	0.420891	+	1.10980i	−0.542112	+	0.840306i	$0.682375\pi$
$174$	0.711786	−	0.803441i	0.0539604	−	0.0609087i
$175$	0.482453	+	0.0585805i	0.0364701	+	0.00442827i
$176$	−3.20868	+	13.0181i	−0.241863	+	0.981278i
$177$	2.85498	−	11.5831i	0.214594	−	0.870641i
$178$	2.17390	−	3.14944i	0.162941	−	0.236060i
$179$	15.6241	−	3.85100i	1.16780	−	0.287837i	0.392696	−	0.919668i	$-0.371542\pi$
$179$	15.6241	−	3.85100i	1.16780	−	0.287837i	0.775106	+	0.631831i	$0.217696\pi$
$180$	3.83949	−	2.65021i	0.286179	−	0.197535i
$181$	−16.1870	−	14.3404i	−1.20317	−	1.06591i	−0.996158	−	0.0875735i	$-0.972089\pi$
$181$	−16.1870	−	14.3404i	−1.20317	−	1.06591i	−0.207009	−	0.978339i	$-0.566373\pi$
$182$	−0.521749	−	0.0924133i	−0.0386746	−	0.00685013i
$183$	8.79328	−	7.79017i	0.650018	−	0.575866i
$184$	−1.04918	+	4.25668i	−0.0773463	+	0.313806i
$185$	−11.9478	+	10.5848i	−0.878417	+	0.778210i
$186$	1.10475	+	0.272296i	0.0810041	+	0.0199657i
$187$	24.2553	−	9.19881i	1.77372	−	0.672684i
$188$			0.455887i			0.0332490i
$189$	−0.672147	−	0.254912i	−0.0488915	−	0.0185421i
$190$	0.544180	+	2.20782i	0.0394790	+	0.160172i
$191$	−10.8106			−0.782229			−0.391115	−	0.920342i	$-0.627910\pi$
$191$	−10.8106			−0.782229			−0.391115	+	0.920342i	$0.627910\pi$
$192$	−7.01436			−0.506218
$193$	−0.847088	−	3.43677i	−0.0609747	−	0.247384i	0.932543	−	0.361058i	$-0.117584\pi$
$193$	−0.847088	−	3.43677i	−0.0609747	−	0.247384i	−0.993518	+	0.113674i	$0.963738\pi$
$194$	0.262999	+	2.16600i	0.0188823	+	0.155509i
$195$	−7.81217	+	3.57194i	−0.559441	+	0.255792i
$196$	1.53028	−	12.6030i	0.109305	−	0.900211i
$197$	−13.7810	+	1.67332i	−0.981857	+	0.119219i	−0.595694	−	0.803212i	$-0.703123\pi$
$197$	−13.7810	+	1.67332i	−0.981857	+	0.119219i	−0.386163	+	0.922431i	$0.626200\pi$
$198$	−0.415107	+	0.601386i	−0.0295004	+	0.0427386i
$199$	−3.09564	+	2.74250i	−0.219444	+	0.194411i	−0.765682	−	0.643220i	$-0.777598\pi$
$199$	−3.09564	+	2.74250i	−0.219444	+	0.194411i	0.546237	+	0.837630i	$0.316060\pi$
$200$	0.543077	+	0.0659414i	0.0384013	+	0.00466276i
$201$	−3.61644	+	0.439116i	−0.255084	+	0.0309728i
$202$	−0.284656	+	0.542367i	−0.0200284	+	0.0381608i
$203$	2.50289	+	2.82518i	0.175669	+	0.198289i
$204$	8.07298	+	11.6957i	0.565222	+	0.818865i
$205$	8.01159	+	1.97468i	0.559554	+	0.137918i
$206$	0.460553	+	0.0559213i	0.0320883	+	0.00389622i
$207$	3.07769	−	4.45880i	0.213914	−	0.309908i
$208$	13.3171	+	2.35875i	0.923375	+	0.163550i
$209$	9.47988	+	13.7340i	0.655737	+	0.949999i
$210$	−0.162710	−	0.310019i	−0.0112281	−	0.0213933i
$211$	−5.25882	+	13.8664i	−0.362032	+	0.954600i	0.622999	+	0.782223i	$0.285914\pi$
$211$	−5.25882	+	13.8664i	−0.362032	+	0.954600i	−0.985031	+	0.172377i	$0.944855\pi$
$212$	−1.75773	−	14.4762i	−0.120721	−	0.994230i
$213$	−2.80638	−	1.93711i	−0.192290	−	0.132728i
$214$	−0.267990	−	1.08728i	−0.0183194	−	0.0743249i
$215$	24.7754	+	17.1012i	1.68967	+	1.16630i
$216$	−0.756606	−	0.286943i	−0.0514805	−	0.0195240i
$217$	−1.41876	+	3.74096i	−0.0963115	+	0.253953i
$218$	1.14929	+	0.603195i	0.0778399	+	0.0408535i
$219$	5.50128	−	10.4818i	0.371742	−	0.708295i
$220$	16.1914	−	3.99083i	1.09163	−	0.269062i
$221$	−10.8807	−	23.7972i	−0.731918	−	1.60077i
$222$	1.32987	+	0.327784i	0.0892553	+	0.0219995i
$223$	17.2094	−	19.4254i	1.15242	−	1.30082i	0.205759	−	0.978603i	$-0.434034\pi$
$223$	17.2094	−	19.4254i	1.15242	−	1.30082i	0.946666	−	0.322216i	$-0.104428\pi$
$224$	−0.206676	+	1.70213i	−0.0138091	+	0.113729i
$225$	−0.598626	−	0.314183i	−0.0399084	−	0.0209455i
$226$	−0.244630	−	0.466104i	−0.0162726	−	0.0310048i
$227$	11.0615	−	4.19508i	0.734178	−	0.278437i	0.0409559	−	0.999161i	$-0.486960\pi$
$227$	11.0615	−	4.19508i	0.734178	−	0.278437i	0.693222	+	0.720724i	$0.256190\pi$
$228$	−6.06244	+	6.84308i	−0.401495	+	0.453194i
$229$	2.92887	−	0.355629i	0.193545	−	0.0235006i	−0.0231901	−	0.999731i	$-0.507382\pi$
$229$	2.92887	−	0.355629i	0.193545	−	0.0235006i	0.216735	+	0.976230i	$0.430459\pi$
$230$	2.56210	−	0.631500i	0.168940	−	0.0416399i
$231$	−1.92333	−	1.70392i	−0.126546	−	0.112110i
$232$	2.81740	+	3.18018i	0.184971	+	0.208789i
$233$	−21.4723	−	11.2695i	−1.40670	−	0.738291i	−0.421038	−	0.907043i	$-0.638334\pi$
$233$	−21.4723	−	11.2695i	−1.40670	−	0.738291i	−0.985659	+	0.168752i	$0.946026\pi$
$234$	0.633048	+	0.377573i	0.0413836	+	0.0246827i
$235$	0.491122	−	0.257761i	0.0320373	−	0.0168145i
$236$	21.8429	+	8.28392i	1.42185	+	0.539237i
$237$	0.734258	+	6.04716i	0.0476952	+	0.392805i
$238$	0.944370	−	0.495643i	0.0612144	−	0.0321278i
$239$			1.00209i			0.0648199i	0.999475	+	0.0324100i	$0.0103182\pi$
$239$			1.00209i			0.0648199i	−0.999475	+	0.0324100i	$0.989682\pi$
$240$	4.15302	+	7.91291i	0.268076	+	0.510776i
$241$	8.48944	+	9.58260i	0.546853	+	0.617269i	0.955345	−	0.295492i	$-0.0954837\pi$
$241$	8.48944	+	9.58260i	0.546853	+	0.617269i	−0.408492	+	0.912762i	$0.633945\pi$
$242$	−0.298924	+	0.206332i	−0.0192156	+	0.0132636i
$243$	0.748511	+	0.663123i	0.0480170	+	0.0425393i
$244$	13.0680	+	18.9323i	0.836594	+	1.21201i
$245$	−14.4422	+	5.47722i	−0.922681	+	0.349927i
$246$	−0.251072	−	0.662024i	−0.0160078	−	0.0422091i
$247$	13.1889	−	10.4599i	0.839190	−	0.665548i
$248$	−1.59703	+	4.21103i	−0.101412	+	0.267401i
$249$			13.0407i			0.826424i
$250$	0.746792	+	1.96913i	0.0472313	+	0.124539i
$251$	0.256040	−	2.10868i	0.0161611	−	0.133099i	−0.982395	−	0.186815i	$-0.940184\pi$
$251$	0.256040	−	2.10868i	0.0161611	−	0.133099i	0.998556	+	0.0537161i	$0.0171066\pi$
$252$	0.654181	−	1.24644i	0.0412095	−	0.0785182i
$253$	15.9378	−	11.0010i	1.00200	−	0.691630i
$254$	−1.35316	+	0.934017i	−0.0849047	+	0.0586055i
$255$	8.03518	−	15.3098i	0.503182	−	0.958734i
$256$	1.53809	−	12.6673i	0.0961305	−	0.791706i
$257$	3.55510	+	9.37404i	0.221761	+	0.584736i	0.999011	−	0.0444553i	$-0.0141552\pi$
$257$	3.55510	+	9.37404i	0.221761	+	0.584736i	−0.777250	+	0.629192i	$0.783386\pi$
$258$		−	2.58320i		−	0.160823i
$259$	−1.70787	+	4.50328i	−0.106122	+	0.279820i
$260$	−5.09965	−	16.0294i	−0.316267	−	0.994102i
$261$	−1.86186	−	4.90933i	−0.115247	−	0.303880i
$262$	−1.21090	+	0.459235i	−0.0748098	+	0.0283716i
$263$	−1.08738	−	1.57533i	−0.0670504	−	0.0971393i	0.788024	−	0.615644i	$-0.211104\pi$
$263$	−1.08738	−	1.57533i	−0.0670504	−	0.0971393i	−0.855075	+	0.518505i	$0.826489\pi$
$264$	−2.16500	−	1.91803i	−0.133247	−	0.118046i
$265$	−14.6012	+	10.0785i	−0.896946	+	0.619117i
$266$	0.454974	+	0.513560i	0.0278963	+	0.0314884i
$267$	−8.69928	−	16.5751i	−0.532387	−	1.01438i
$268$		−	7.13375i		−	0.435763i
$269$	3.46285	−	1.81744i	0.211134	−	0.110812i	−0.355842	−	0.934546i	$-0.615806\pi$
$269$	3.46285	−	1.81744i	0.211134	−	0.110812i	0.566975	+	0.823735i	$0.308113\pi$
$270$	0.0587077	+	0.483502i	0.00357284	+	0.0294250i
$271$	−16.6993	−	6.33321i	−1.01441	−	0.384715i	−0.209307	−	0.977850i	$-0.567121\pi$
$271$	−16.6993	−	6.33321i	−1.01441	−	0.384715i	−0.805103	+	0.593135i	$0.797890\pi$
$272$	−24.1041	+	12.6508i	−1.46152	+	0.767067i
$273$	−1.58632	+	2.04976i	−0.0960083	+	0.124057i
$274$	−3.84312	−	2.01702i	−0.232171	−	0.121853i
$275$	−1.60248	−	1.80882i	−0.0966330	−	0.109076i
$276$	7.94114	+	7.03524i	0.478001	+	0.423472i
$277$	−16.6183	+	4.09605i	−0.998499	+	0.246108i	−0.704505	−	0.709699i	$-0.748831\pi$
$277$	−16.6183	+	4.09605i	−0.998499	+	0.246108i	−0.293994	+	0.955807i	$0.594985\pi$
$278$	−3.19780	+	0.388283i	−0.191791	+	0.0232877i
$279$	3.69073	−	4.16597i	0.220958	−	0.249410i
$280$	1.29580	−	0.491433i	0.0774390	−	0.0293687i
$281$	−3.84569	−	7.32735i	−0.229415	−	0.437113i	0.743352	−	0.668901i	$-0.233235\pi$
$281$	−3.84569	−	7.32735i	−0.229415	−	0.437113i	−0.972766	+	0.231787i	$0.925543\pi$
$282$	−0.0421423	−	0.0221180i	−0.00250954	−	0.00131711i
$283$	2.83933	−	23.3839i	0.168780	−	1.39003i	−0.624429	−	0.781082i	$-0.714668\pi$
$283$	2.83933	−	23.3839i	0.168780	−	1.39003i	0.793209	−	0.608950i	$-0.208409\pi$
$284$	4.42800	−	4.99818i	0.262754	−	0.296587i
$285$	10.7997	+	2.66189i	0.639720	+	0.157677i
$286$	1.63717	+	2.06431i	0.0968081	+	0.122065i
$287$	2.41735	−	0.595824i	0.142692	−	0.0351704i
$288$	1.10846	−	2.11200i	0.0653168	−	0.124451i
$289$	31.5833	+	16.5762i	1.85784	+	0.975071i
$290$	0.906826	−	2.39110i	0.0532507	−	0.140410i
$291$	9.97935	+	3.78467i	0.585000	+	0.221861i
$292$	19.0774	+	13.1682i	1.11642	+	0.770610i
$293$	0.454634	+	1.84452i	0.0265600	+	0.107758i	0.982726	−	0.185068i	$-0.0592505\pi$
$293$	0.454634	+	1.84452i	0.0265600	+	0.107758i	−0.956166	+	0.292826i	$0.905404\pi$
$294$	1.09078	+	0.752908i	0.0636154	+	0.0439105i
$295$	−3.42590	−	28.2149i	−0.199464	−	1.64273i
$296$	−1.92247	+	5.06915i	−0.111742	+	0.294638i
$297$	1.66113	+	3.16502i	0.0963886	+	0.183653i
$298$	−0.491100	−	0.711481i	−0.0284487	−	0.0412150i
$299$	−12.1383	−	15.3052i	−0.701978	−	0.885125i
$300$	0.752047	−	1.08953i	0.0434194	−	0.0629039i
$301$	9.01723	+	1.09489i	0.519745	+	0.0631084i
$302$	1.49512	+	0.368515i	0.0860347	+	0.0212057i
$303$	1.70205	+	2.46584i	0.0977802	+	0.141659i
$304$	−11.6127	−	13.1081i	−0.666036	−	0.751800i
$305$	13.0068	−	24.7824i	0.744768	−	1.41904i
$306$	−1.47283	+	0.178834i	−0.0841959	+	0.0102232i
$307$	17.4993	+	2.12480i	0.998738	+	0.121269i	0.603545	−	0.797329i	$-0.293754\pi$
$307$	17.4993	+	2.12480i	0.998738	+	0.121269i	0.395193	+	0.918598i	$0.370678\pi$
$308$	3.76627	−	3.33662i	0.214603	−	0.190122i
$309$	1.28915	−	1.86766i	0.0733372	−	0.106247i
$310$	2.69101	−	0.326748i	0.152839	−	0.0185581i
$311$	−0.220540	+	1.81631i	−0.0125057	+	0.102994i	−0.997625	−	0.0688776i	$-0.978058\pi$
$311$	−0.220540	+	1.81631i	−0.0125057	+	0.102994i	0.985119	+	0.171871i	$0.0549813\pi$
$312$	−1.78565	+	2.30732i	−0.101092	+	0.130626i
$313$	3.97464	+	32.7341i	0.224660	+	1.85024i	0.472361	+	0.881405i	$0.343402\pi$
$313$	3.97464	+	32.7341i	0.224660	+	1.85024i	−0.247701	+	0.968837i	$0.579675\pi$
$314$	0.617301	+	2.50449i	0.0348363	+	0.141336i
$315$	−1.71265			−0.0964970
$316$	−11.9286			−0.671034
$317$	−1.88467	−	7.64640i	−0.105854	−	0.429465i	0.893972	−	0.448122i	$-0.147907\pi$
$317$	−1.88467	−	7.64640i	−0.105854	−	0.429465i	−0.999826	+	0.0186573i	$0.994061\pi$
$318$	1.42346	+	0.539848i	0.0798238	+	0.0302732i
$319$		−	18.7678i		−	1.05079i
$320$	−15.6254	+	5.92593i	−0.873486	+	0.331269i
$321$	−5.31850	−	1.31089i	−0.296849	−	0.0731668i
$322$	0.595967	−	0.527981i	0.0332119	−	0.0294232i
$323$	−8.10856	+	32.8977i	−0.451172	+	1.83048i
$324$	−1.46574	+	1.29853i	−0.0814299	+	0.0721406i
$325$	−1.71336	+	1.73384i	−0.0950402	+	0.0961764i
$326$	−2.69280	−	2.38562i	−0.149141	−	0.132127i
$327$	5.22520	−	3.60669i	0.288954	−	0.199451i
$328$	2.72111	−	0.670693i	0.150248	−	0.0370328i
$329$	0.0950697	−	0.137732i	0.00524136	−	0.00759342i
$330$	−0.416636	+	1.69036i	−0.0229351	+	0.0930512i
$331$	0.00726895	−	0.0294913i	0.000399538	−	0.00162099i	−0.970742	−	0.240126i	$-0.922811\pi$
$331$	0.00726895	−	0.0294913i	0.000399538	−	0.00162099i	0.971141	+	0.238505i	$0.0766574\pi$
$332$	−25.3503	−	3.07808i	−1.39128	−	0.168932i
$333$	4.44282	−	5.01491i	0.243465	−	0.274815i
$334$	−1.37824	−	3.63413i	−0.0754142	−	0.198851i
$335$	−7.68511	+	4.03346i	−0.419883	+	0.220371i
$336$	2.21913	+	1.53175i	0.121063	+	0.0835640i
$337$	−17.6205			−0.959850			−0.479925	−	0.877309i	$-0.659336\pi$
$337$	−17.6205			−0.959850			−0.479925	+	0.877309i	$0.659336\pi$
$338$	1.96819	−	1.78585i	0.107055	−	0.0971376i
$339$	−2.57492			−0.139850
$340$	27.8645	+	19.2335i	1.51116	+	1.04308i
$341$	17.6155	−	9.24532i	0.953932	−	0.500662i
$342$	−0.338448	−	0.892415i	−0.0183012	−	0.0482563i
$343$	−6.42737	+	7.25500i	−0.347045	+	0.391733i
$344$	10.1503	+	1.23247i	0.547268	+	0.0664503i
$345$	3.08902	−	12.5327i	0.166307	−	0.674736i
$346$	0.763785	−	3.09880i	0.0410613	−	0.166592i
$347$	−4.82892	+	6.99590i	−0.259230	+	0.375559i	−0.930890	−	0.365300i	$-0.880966\pi$
$347$	−4.82892	+	6.99590i	−0.259230	+	0.375559i	0.671660	+	0.740860i	$0.265582\pi$
$348$	9.98286	−	2.46055i	0.535138	−	0.131900i
$349$	−5.44633	+	3.75933i	−0.291535	+	0.201232i	−0.704851	−	0.709356i	$-0.748986\pi$
$349$	−5.44633	+	3.75933i	−0.291535	+	0.201232i	0.413316	+	0.910588i	$0.364371\pi$
$350$	−0.0743676	−	0.0658840i	−0.00397512	−	0.00352165i
$351$	3.07443	−	1.88359i	0.164101	−	0.100539i
$352$	6.38167	−	5.65366i	0.340144	−	0.301341i
$353$	−2.80307	+	11.3725i	−0.149193	+	0.605298i	0.847972	+	0.530042i	$0.177824\pi$
$353$	−2.80307	+	11.3725i	−0.149193	+	0.605298i	−0.997164	+	0.0752565i	$0.976022\pi$
$354$	−1.82550	+	1.61726i	−0.0970244	+	0.0859562i
$355$	−7.88810	−	1.94424i	−0.418657	−	0.103190i
$356$	34.2742	−	12.9985i	1.81653	−	0.688918i
$357$		−	5.21702i		−	0.276114i
$358$	−3.07591	−	1.16654i	−0.162567	−	0.0616536i
$359$	6.09355	+	24.7225i	0.321605	+	1.30480i	0.879899	+	0.475160i	$0.157610\pi$
$359$	6.09355	+	24.7225i	0.321605	+	1.30480i	−0.558294	+	0.829643i	$0.688544\pi$
$360$	−1.92786			−0.101607
$361$	−2.79669			−0.147194
$362$	1.05801	+	4.29252i	0.0556079	+	0.225610i
$363$	0.214159	+	1.76376i	0.0112404	+	0.0925733i
$364$	−3.61015	−	3.56751i	−0.189223	−	0.186988i
$365$	3.39948	−	27.9972i	0.177937	−	1.46544i
$366$	−2.38412	+	0.289484i	−0.124620	+	0.0151316i
$367$	−7.13592	+	10.3382i	−0.372492	+	0.539648i	−0.963740	−	0.266842i	$-0.914020\pi$
$367$	−7.13592	+	10.3382i	−0.372492	+	0.539648i	0.591248	+	0.806489i	$0.298635\pi$
$368$	−15.2114	+	13.4762i	−0.792951	+	0.702493i
$369$	−3.43814	−	0.417466i	−0.178983	−	0.0217324i
$370$	3.23939	−	0.393333i	0.168408	−	0.0204484i
$371$	−2.48779	+	4.74009i	−0.129160	+	0.246093i
$372$	7.22721	+	8.15783i	0.374713	+	0.422964i
$373$	−2.06566	−	2.99263i	−0.106956	−	0.154952i	0.765851	−	0.643018i	$-0.222318\pi$
$373$	−2.06566	−	2.99263i	−0.106956	−	0.154952i	−0.872807	+	0.488066i	$0.837703\pi$
$374$	−5.14912	−	1.26914i	−0.266254	−	0.0656258i
$375$	10.2264	+	1.24172i	0.528091	+	0.0641219i
$376$	0.107016	−	0.155039i	0.00551892	−	0.00799553i
$377$	−18.8894	+	1.25529i	−0.972854	+	0.0646505i
$378$	0.0834825	+	0.120945i	0.00429388	+	0.00622075i
$379$	11.3975	+	21.7161i	0.585449	+	1.11548i	0.980444	+	0.196796i	$0.0630538\pi$
$379$	11.3975	+	21.7161i	0.585449	+	1.11548i	−0.394996	+	0.918683i	$0.629254\pi$
$380$	−7.72364	+	20.3656i	−0.396215	+	1.04473i
$381$	0.969447	+	7.98411i	0.0496663	+	0.409038i
$382$	1.81884	+	1.25545i	0.0930600	+	0.0642346i
$383$	−0.582311	−	2.36253i	−0.0297547	−	0.120720i	0.954186	−	0.299213i	$-0.0967240\pi$
$383$	−0.582311	−	2.36253i	−0.0297547	−	0.120720i	−0.983941	+	0.178493i	$0.942878\pi$
$384$	5.10611	+	3.52450i	0.260570	+	0.179859i
$385$	−5.72397	−	2.17082i	−0.291721	−	0.110635i
$386$	−0.256599	+	0.676595i	−0.0130605	+	0.0344378i
$387$	−11.1885	−	5.87220i	−0.568745	−	0.298501i
$388$	−9.71262	+	18.5058i	−0.493083	+	0.939492i
$389$	−32.0230	+	7.89295i	−1.62363	+	0.400189i	−0.943094	−	0.332527i	$-0.892099\pi$
$389$	−32.0230	+	7.89295i	−1.62363	+	0.400189i	−0.680535	+	0.732716i	$0.738253\pi$
$390$	1.72918	+	0.306276i	0.0875604	+	0.0155089i
$391$	38.1766	+	9.40968i	1.93067	+	0.475868i
$392$	−3.47886	+	3.92682i	−0.175709	+	0.198334i
$393$	−0.763584	+	6.28868i	−0.0385177	+	0.317222i
$394$	2.51292	+	1.31888i	0.126599	+	0.0664443i
$395$	6.74446	+	12.8505i	0.339351	+	0.646579i
$396$	−6.54466	+	2.48206i	−0.328882	+	0.124728i
$397$	−7.12433	+	8.04171i	−0.357560	+	0.403602i	−0.899575	−	0.436767i	$-0.856123\pi$
$397$	−7.12433	+	8.04171i	−0.357560	+	0.403602i	0.542015	+	0.840369i	$0.317662\pi$
$398$	0.839318	−	0.101912i	0.0420712	−	0.00510837i
$399$	3.25862	−	0.803178i	0.163135	−	0.0402092i
$400$	1.89816	+	1.68162i	0.0949078	+	0.0840810i
$401$	−8.14596	−	9.19489i	−0.406790	−	0.459171i	0.509037	−	0.860745i	$-0.330002\pi$
$401$	−8.14596	−	9.19489i	−0.406790	−	0.459171i	−0.915827	+	0.401574i	$0.868463\pi$
$402$	0.659446	+	0.346104i	0.0328902	+	0.0172621i
$403$	−10.4834	−	17.1113i	−0.522218	−	0.852373i
$404$	−5.19517	+	2.72664i	−0.258469	+	0.135655i
$405$	2.22763	+	0.844828i	0.110692	+	0.0419798i
$406$	−0.0930080	−	0.765990i	−0.00461591	−	0.0380154i
$407$	21.2052	−	11.1293i	1.05110	−	0.551660i
$408$		−	5.87257i		−	0.290736i
$409$	2.38513	+	4.54449i	0.117937	+	0.224711i	0.937267	−	0.348611i	$-0.113347\pi$
$409$	2.38513	+	4.54449i	0.117937	+	0.224711i	−0.819330	+	0.573322i	$0.805654\pi$
$410$	−1.11859	−	1.26263i	−0.0552433	−	0.0623568i
$411$	−17.4725	+	12.0604i	−0.861856	+	0.594896i
$412$	3.32631	+	2.94685i	0.163875	+	0.145181i
$413$	−4.87164	−	7.05779i	−0.239718	−	0.347291i
$414$	−1.03561	+	0.392757i	−0.0508977	+	0.0193029i
$415$	11.0172	+	29.0499i	0.540813	+	1.42601i
$416$	−6.11714	−	6.04488i	−0.299917	−	0.296374i
$417$	−5.58755	+	14.7332i	−0.273624	+	0.721486i
$418$		−	3.41159i		−	0.166866i
$419$	−6.79870	−	17.9267i	−0.332138	−	0.875776i	−0.992210	−	0.124574i	$-0.960244\pi$
$419$	−6.79870	−	17.9267i	−0.332138	−	0.875776i	0.660072	−	0.751202i	$-0.270526\pi$
$420$	0.404247	−	3.32927i	0.0197252	−	0.162452i
$421$	−1.14581	+	2.18315i	−0.0558432	+	0.106400i	−0.911778	−	0.410683i	$-0.865290\pi$
$421$	−1.14581	+	2.18315i	−0.0558432	+	0.106400i	0.855935	+	0.517084i	$0.172982\pi$
$422$	2.49510	−	1.72224i	0.121459	−	0.0838373i
$423$	−0.191598	+	0.132250i	−0.00931580	+	0.00643023i
$424$	−2.80040	+	5.33571i	−0.135999	+	0.259125i
$425$	0.591405	−	4.87066i	0.0286874	−	0.236262i
$426$	0.247202	+	0.651819i	0.0119770	+	0.0315807i
$427$		−	8.44497i		−	0.408681i
$428$	3.80364	−	10.0294i	0.183856	−	0.484788i
$429$	12.6627	−	2.39838i	0.611363	−	0.115795i
$430$	−2.18236	−	5.75442i	−0.105243	−	0.277503i
$431$	11.7167	−	4.44355i	0.564372	−	0.214038i	−0.0558844	−	0.998437i	$-0.517798\pi$
$431$	11.7167	−	4.44355i	0.564372	−	0.214038i	0.620256	+	0.784399i	$0.287029\pi$
$432$	−2.13080	−	3.08700i	−0.102518	−	0.148523i
$433$	−13.8972	−	12.3118i	−0.667857	−	0.591670i	0.259547	−	0.965730i	$-0.416427\pi$
$433$	−13.8972	−	12.3118i	−0.667857	−	0.591670i	−0.927404	+	0.374061i	$0.877965\pi$
$434$	0.673143	−	0.464637i	0.0323119	−	0.0223033i
$435$	−8.29509	−	9.36322i	−0.397719	−	0.448932i
$436$	5.77782	+	11.0087i	0.276708	+	0.527222i
$437$			25.2942i			1.20999i
$438$	−2.14284	+	1.12465i	−0.102389	+	0.0537377i
$439$	−3.68539	−	30.3519i	−0.175894	−	1.44862i	−0.766804	−	0.641881i	$-0.778154\pi$
$439$	−3.68539	−	30.3519i	−0.175894	−	1.44862i	0.590910	−	0.806738i	$-0.298769\pi$
$440$	−6.44322	−	2.44359i	−0.307169	−	0.116494i
$441$	5.74062	−	3.01291i	0.273363	−	0.143472i
$442$	−0.932968	+	5.26737i	−0.0443768	+	0.250543i
$443$	−28.8745	−	15.1545i	−1.37187	−	0.720012i	−0.392058	−	0.919940i	$-0.628237\pi$
$443$	−28.8745	−	15.1545i	−1.37187	−	0.720012i	−0.979811	+	0.199928i	$0.935929\pi$
$444$	8.69996	+	9.82023i	0.412882	+	0.466047i
$445$	−33.3819	−	29.5738i	−1.58245	−	1.40193i
$446$	−5.15130	+	1.26968i	−0.243921	+	0.0601211i
$447$	−4.19799	+	0.509729i	−0.198558	+	0.0241093i
$448$	−3.34370	+	3.77425i	−0.157975	+	0.178317i
$449$	−5.84538	+	2.21686i	−0.275861	+	0.104620i	−0.488656	−	0.872477i	$-0.662513\pi$
$449$	−5.84538	+	2.21686i	−0.275861	+	0.104620i	0.212795	+	0.977097i	$0.431743\pi$
$450$	0.0642296	+	0.122379i	0.00302781	+	0.00576901i
$451$	−10.9617	−	5.75315i	−0.516167	−	0.270905i
$452$	0.607773	−	5.00546i	0.0285872	−	0.235437i
$453$	4.99489	−	5.63806i	0.234680	−	0.264899i
$454$	−2.34823	−	0.578787i	−0.110208	−	0.0271638i
$455$	−1.80204	+	5.90626i	−0.0844807	+	0.276890i
$456$	3.66808	−	0.904102i	0.171774	−	0.0423384i
$457$	−4.26223	+	8.12100i	−0.199379	+	0.379884i	−0.964533	−	0.263963i	$-0.914970\pi$
$457$	−4.26223	+	8.12100i	−0.199379	+	0.379884i	0.765154	+	0.643847i	$0.222663\pi$
$458$	−0.534069	−	0.280301i	−0.0249554	−	0.0130976i
$459$	−2.57349	+	6.78573i	−0.120120	+	0.316731i
$460$	23.6335	+	8.96300i	1.10192	+	0.417902i
$461$	25.2591	+	17.4351i	1.17643	+	0.812033i	0.985518	−	0.169574i	$-0.0542390\pi$
$461$	25.2591	+	17.4351i	1.17643	+	0.812033i	0.190915	+	0.981607i	$0.438854\pi$
$462$	0.125712	+	0.510035i	0.00584867	+	0.0237290i
$463$	−30.0745	−	20.7589i	−1.39768	−	0.964748i	−0.998861	−	0.0477176i	$-0.984805\pi$
$463$	−30.0745	−	20.7589i	−1.39768	−	0.964748i	−0.398818	−	0.917030i	$-0.630579\pi$
$464$	2.37393	+	19.5511i	0.110207	+	0.907636i
$465$	4.70204	−	12.3983i	0.218052	−	0.574956i
$466$	2.30387	+	4.38966i	0.106725	+	0.203347i
$467$	12.6354	+	18.3055i	0.584695	+	0.847077i	0.997980	−	0.0635244i	$-0.0202341\pi$
$467$	12.6354	+	18.3055i	0.584695	+	0.847077i	−0.413285	+	0.910602i	$0.635619\pi$
$468$	2.93589	+	6.42106i	0.135711	+	0.296814i
$469$	−1.48766	+	2.15524i	−0.0686936	+	0.0995198i
$470$	−0.112563	−	0.0136677i	−0.00519216	−	0.000630442i
$471$	12.2509	+	3.01956i	0.564490	+	0.139134i
$472$	−5.48379	−	7.94465i	−0.252412	−	0.365682i
$473$	−29.9509	−	33.8076i	−1.37714	−	1.55447i
$474$	0.578730	−	1.10268i	0.0265820	−	0.0506477i
$475$	3.13333	−	0.380455i	0.143767	−	0.0174565i
$476$	10.1415	+	1.23140i	0.464836	+	0.0564413i
$477$	5.57407	−	4.93819i	0.255219	−	0.226104i
$478$	0.116374	−	0.168597i	0.00532284	−	0.00771147i
$479$	−34.7194	+	4.21570i	−1.58637	+	0.192620i	−0.865665	−	0.500623i	$-0.833104\pi$
$479$	−34.7194	+	4.21570i	−1.58637	+	0.192620i	−0.720704	+	0.693243i	$0.756181\pi$
$480$	0.684967	−	5.64121i	0.0312643	−	0.257485i
$481$	−12.6198	−	20.5982i	−0.575411	−	0.939196i
$482$	−0.315469	−	2.59812i	−0.0143692	−	0.118341i
$483$	−0.932058	−	3.78151i	−0.0424101	−	0.172065i
$484$	−3.47917			−0.158144
$485$	25.4277			1.15461
$486$	−0.0489242	−	0.198493i	−0.00221925	−	0.00900383i
$487$	−23.9127	−	9.06889i	−1.08359	−	0.410951i	−0.252788	−	0.967522i	$-0.581348\pi$
$487$	−23.9127	−	9.06889i	−1.08359	−	0.410951i	−0.830800	+	0.556571i	$0.812117\pi$
$488$		−	9.50613i		−	0.430322i
$489$	−16.4541	+	6.24021i	−0.744079	+	0.282192i
$490$	3.06592	+	0.755682i	0.138504	+	0.0341382i
$491$	0.298825	−	0.264736i	0.0134858	−	0.0119474i	−0.656353	−	0.754454i	$-0.727902\pi$
$491$	0.298825	−	0.264736i	0.0134858	−	0.0119474i	0.669839	+	0.742507i	$0.266363\pi$
$492$	1.62305	−	6.58497i	0.0731727	−	0.296873i
$493$	28.5219	−	25.2682i	1.28456	−	1.13802i
$494$	−3.43370	+	0.228185i	−0.154489	+	0.0102665i
$495$	6.37428	+	5.64712i	0.286503	+	0.253819i
$496$	−17.1813	+	11.8594i	−0.771462	+	0.532501i
$497$	−2.38009	+	0.586640i	−0.106762	+	0.0263144i
$498$	1.51444	−	2.19405i	0.0678638	−	0.0983176i
$499$	0.0916698	−	0.371919i	0.00410370	−	0.0166494i	−0.968854	−	0.247632i	$-0.920348\pi$
$499$	0.0916698	−	0.371919i	0.00410370	−	0.0166494i	0.972958	+	0.230982i	$0.0741939\pi$
$500$	−4.82761	+	19.5864i	−0.215897	+	0.875930i
$501$	−18.8734	−	2.29165i	−0.843203	−	0.102383i
$502$	−0.287962	+	0.325042i	−0.0128524	+	0.0145073i
$503$	−11.5292	−	30.4001i	−0.514063	−	1.35547i	−0.901181	−	0.433444i	$-0.857298\pi$
$503$	−11.5292	−	30.4001i	−0.514063	−	1.35547i	0.387117	−	0.922030i	$-0.373471\pi$
$504$	−0.515066	+	0.270328i	−0.0229429	+	0.0120413i
$505$	5.87475	+	4.05505i	0.261423	+	0.180447i
$506$	−3.95903			−0.176000
$507$	−3.26088	−	12.5844i	−0.144821	−	0.558892i
$508$	−15.7494			−0.698765
$509$	−13.9673	−	9.64095i	−0.619091	−	0.427328i	0.216805	−	0.976215i	$-0.430436\pi$
$509$	−13.9673	−	9.64095i	−0.619091	−	0.427328i	−0.835896	+	0.548887i	$0.815052\pi$
$510$	−3.12983	+	1.64266i	−0.138591	+	0.0727382i
$511$	−3.01758	−	7.95671i	−0.133490	−	0.351984i
$512$	−9.95839	+	11.2407i	−0.440103	+	0.496773i
$513$	−4.63465	−	0.562749i	−0.204625	−	0.0248460i
$514$	0.490491	−	1.99000i	0.0216346	−	0.0877752i
$515$	1.29390	−	5.24956i	0.0570160	−	0.231323i
$516$	14.0560	−	20.3637i	0.618782	−	0.896461i
$517$	−0.807982	+	0.199150i	−0.0355350	+	0.00875859i
$518$	0.810315	−	0.559320i	0.0356032	−	0.0245751i
$519$	−11.6855	−	10.3524i	−0.512935	−	0.454420i
$520$	−2.02847	+	6.64842i	−0.0889544	+	0.291552i
$521$	−2.49916	+	2.21406i	−0.109490	+	0.0969998i	−0.716092	−	0.698006i	$-0.754071\pi$
$521$	−2.49916	+	2.21406i	−0.109490	+	0.0969998i	0.606602	+	0.795006i	$0.292532\pi$
$522$	−0.256878	+	1.04219i	−0.0112432	+	0.0456156i
$523$	−2.73195	+	2.42030i	−0.119460	+	0.105832i	−0.720738	−	0.693208i	$-0.756197\pi$
$523$	−2.73195	+	2.42030i	−0.119460	+	0.105832i	0.601278	+	0.799040i	$0.294658\pi$
$524$	−12.0445	−	2.96871i	−0.526167	−	0.129689i
$525$	−0.454415	+	0.172337i	−0.0198323	+	0.00752140i
$526$			0.391322i			0.0170624i
$527$	37.7672	+	14.3232i	1.64517	+	0.623929i
$528$	−3.20868	−	13.0181i	−0.139640	−	0.566541i
$529$	6.35303			0.276219
$530$	3.62702			0.157548
$531$	2.85498	+	11.5831i	0.123896	+	0.502665i
$532$	0.792170	+	6.52410i	0.0343449	+	0.282856i
$533$	−5.05726	+	11.4176i	−0.219054	+	0.494549i
$534$	−0.461276	+	3.79895i	−0.0199614	+	0.164397i
$535$	−12.9551	+	1.57304i	−0.560098	+	0.0680082i
$536$	−1.67459	+	2.42606i	−0.0723312	+	0.104790i
$537$	−12.0448	+	10.6708i	−0.519773	+	0.460479i
$538$	−0.793672	−	0.0963692i	−0.0342176	−	0.00415477i
$539$	23.0051	−	2.79332i	0.990898	−	0.120317i
$540$	−2.16809	+	4.13094i	−0.0932996	+	0.177767i
$541$	−19.4950	−	22.0053i	−0.838156	−	0.946083i	0.161008	−	0.986953i	$-0.448525\pi$
$541$	−19.4950	−	22.0053i	−0.838156	−	0.946083i	−0.999164	+	0.0408705i	$0.986987\pi$
$542$	2.07410	+	3.00485i	0.0890901	+	0.129069i
$543$	20.9971	+	5.17533i	0.901074	+	0.222095i
$544$	17.1841	+	2.08652i	0.736761	+	0.0894589i
$545$	8.59276	−	12.4488i	0.368073	−	0.533247i
$546$	0.504932	−	0.160641i	0.0216091	−	0.00687480i
$547$	−8.91961	−	12.9223i	−0.381375	−	0.552517i	0.584544	−	0.811362i	$-0.301273\pi$
$547$	−8.91961	−	12.9223i	−0.381375	−	0.552517i	−0.965919	+	0.258845i	$0.916658\pi$
$548$	−19.3204	−	36.8120i	−0.825328	−	1.57253i
$549$	−4.16579	+	10.9843i	−0.177792	+	0.468798i
$550$	0.0595483	+	0.490425i	0.00253915	+	0.0209118i
$551$	20.1739	+	13.9250i	0.859437	+	0.593227i
$552$	−1.04918	−	4.25668i	−0.0446559	−	0.181176i
$553$	3.60384	+	2.48755i	0.153251	+	0.105782i
$554$	3.27164	+	1.24077i	0.138999	+	0.0527153i
$555$	5.66022	−	14.9248i	0.240263	−	0.633521i
$556$	−27.3214	−	14.3394i	−1.15868	−	0.608124i
$557$	−8.14809	+	15.5249i	−0.345246	+	0.657811i	−0.994726	−	0.102568i	$-0.967294\pi$
$557$	−8.14809	+	15.5249i	−0.345246	+	0.657811i	0.649480	+	0.760378i	$0.274987\pi$
$558$	−1.10475	+	0.272296i	−0.0467678	+	0.0115272i
$559$	−32.0234	+	32.4062i	−1.35444	+	1.37064i
$560$	6.23746	+	1.53740i	0.263581	+	0.0649668i
$561$	−17.2021	+	19.4171i	−0.726272	+	0.819792i
$562$	−0.203916	+	1.67940i	−0.00860169	+	0.0708413i
$563$	−5.73324	−	3.00904i	−0.241627	−	0.126816i	0.339563	−	0.940583i	$-0.389721\pi$
$563$	−5.73324	−	3.00904i	−0.241627	−	0.126816i	−0.581191	+	0.813767i	$0.697413\pi$
$564$	−0.211861	−	0.403668i	−0.00892097	−	0.0169975i
$565$	−5.73596	+	2.17536i	−0.241314	+	0.0915182i
$566$	−3.19332	+	3.60451i	−0.134225	+	0.151509i
$567$	0.713620	−	0.0866492i	0.0299692	−	0.00363892i
$568$	−2.67916	+	0.660355i	−0.112415	+	0.0277079i
$569$	8.74712	+	7.74927i	0.366698	+	0.324866i	0.826270	−	0.563274i	$-0.190459\pi$
$569$	8.74712	+	7.74927i	0.366698	+	0.324866i	−0.459572	+	0.888141i	$0.651997\pi$
$570$	−1.50787	−	1.70204i	−0.0631579	−	0.0712905i
$571$	−24.9633	−	13.1018i	−1.04468	−	0.548292i	−0.147093	−	0.989123i	$-0.546992\pi$
$571$	−24.9633	−	13.1018i	−1.04468	−	0.548292i	−0.897590	+	0.440831i	$0.854684\pi$
$572$	1.67343	+	25.1816i	0.0699696	+	1.05289i
$573$	9.57233	−	5.02395i	0.399890	−	0.209878i
$574$	−0.475903	−	0.180486i	−0.0198638	−	0.00753335i
$575$	−0.441503	−	3.63611i	−0.0184120	−	0.151636i
$576$	6.21091	−	3.25974i	0.258788	−	0.135822i
$577$		−	12.2218i		−	0.508802i	−0.967099	−	0.254401i	$-0.918122\pi$
$577$		−	12.2218i		−	0.508802i	0.967099	−	0.254401i	$-0.0818782\pi$
$578$	−3.38873	−	6.45669i	−0.140953	−	0.268563i
$579$	2.34721	+	2.64945i	0.0975465	+	0.110107i
$580$	20.1594	−	13.9150i	0.837072	−	0.577789i
$581$	7.01691	+	6.21644i	0.291110	+	0.257901i
$582$	−1.23946	−	1.79567i	−0.0513774	−	0.0744330i
$583$	24.8887	−	9.43906i	1.03079	−	0.390926i
$584$	−3.39676	−	8.95652i	−0.140559	−	0.370624i
$585$	5.25737	−	6.79330i	0.217366	−	0.280868i
$586$	0.137717	−	0.363131i	0.00568905	−	0.0150008i
$587$			6.99380i			0.288665i	0.989529	+	0.144332i	$0.0461035\pi$
$587$			6.99380i			0.288665i	−0.989529	+	0.144332i	$0.953897\pi$
$588$	4.50189	+	11.8705i	0.185655	+	0.489532i
$589$	−3.13208	+	25.7950i	−0.129055	+	1.06286i
$590$	−2.70024	+	5.14488i	−0.111167	+	0.211811i
$591$	11.4249	−	7.88601i	0.469956	−	0.324387i
$592$	−20.6824	+	14.2761i	−0.850043	+	0.586742i
$593$	0.188992	−	0.360095i	0.00776099	−	0.0147873i	−0.881545	−	0.472101i	$-0.843496\pi$
$593$	0.188992	−	0.360095i	0.00776099	−	0.0147873i	0.889306	+	0.457313i	$0.151188\pi$
$594$	0.0880808	−	0.725411i	0.00361400	−	0.0297640i
$595$	−4.40749	−	11.6216i	−0.180689	−	0.476439i
$596$		−	8.28092i		−	0.339200i
$597$	1.46655	−	3.86698i	0.0600219	−	0.158265i
$598$	0.264800	+	3.98468i	0.0108285	+	0.162946i
$599$	−0.148630	−	0.391905i	−0.00607286	−	0.0160128i	0.931946	−	0.362598i	$-0.118110\pi$
$599$	−0.148630	−	0.391905i	−0.00607286	−	0.0160128i	−0.938018	+	0.346585i	$0.887341\pi$
$600$	−0.511515	+	0.193992i	−0.0208825	+	0.00791969i
$601$	14.6027	+	21.1557i	0.595657	+	0.862958i	0.998634	−	0.0522523i	$-0.0166400\pi$
$601$	14.6027	+	21.1557i	0.595657	+	0.862958i	−0.402977	+	0.915210i	$0.632025\pi$
$602$	−1.38996	−	1.23140i	−0.0566505	−	0.0501879i
$603$	2.99813	−	2.06946i	0.122093	−	0.0842750i
$604$	9.78102	+	11.0405i	0.397984	+	0.449231i
$605$	1.96714	+	3.74807i	0.0799756	+	0.152381i
$606$		−	0.612529i		−	0.0248823i
$607$	40.0842	−	21.0378i	1.62697	−	0.853898i	0.629955	−	0.776631i	$-0.283073\pi$
$607$	40.0842	−	21.0378i	1.62697	−	0.853898i	0.997011	−	0.0772661i	$-0.0246191\pi$
$608$	1.34227	+	11.0546i	0.0544364	+	0.448324i
$609$	−3.52913	−	1.33842i	−0.143008	−	0.0542356i
$610$	−5.06636	+	2.65903i	−0.205131	+	0.107661i
$611$	0.254482	+	0.799898i	0.0102952	+	0.0323604i
$612$	−12.5835	−	6.60435i	−0.508660	−	0.266965i
$613$	13.8190	+	15.5984i	0.558145	+	0.630015i	0.958071	−	0.286532i	$-0.0925025\pi$
$613$	13.8190	+	15.5984i	0.558145	+	0.630015i	−0.399926	+	0.916548i	$0.630964\pi$
$614$	−2.69742	−	2.38971i	−0.108859	−	0.0964408i
$615$	−8.01159	+	1.97468i	−0.323059	+	0.0796268i
$616$	−2.06408	+	0.250625i	−0.0831643	+	0.0100980i
$617$	3.69571	−	4.17160i	0.148784	−	0.167942i	−0.669394	−	0.742908i	$-0.733446\pi$
$617$	3.69571	−	4.17160i	0.148784	−	0.167942i	0.818178	+	0.574966i	$0.194985\pi$
$618$	−0.433788	+	0.164514i	−0.0174495	+	0.00661772i
$619$	20.1347	+	38.3635i	0.809283	+	1.54196i	0.840098	+	0.542434i	$0.182497\pi$
$619$	20.1347	+	38.3635i	0.809283	+	1.54196i	−0.0308159	+	0.999525i	$0.509811\pi$
$620$	22.9915	+	12.0669i	0.923361	+	0.484617i
$621$	−0.653049	+	5.37834i	−0.0262059	+	0.215825i
$622$	0.248036	−	0.279975i	0.00994534	−	0.0112260i
$623$	−13.0655	−	3.22037i	−0.523460	−	0.129021i
$624$	−12.8879	+	4.10019i	−0.515928	+	0.164139i
$625$	27.1119	−	6.68247i	1.08447	−	0.267299i
$626$	3.13275	−	5.96895i	0.125210	−	0.238567i
$627$	−14.7765	−	7.75531i	−0.590117	−	0.309717i
$628$	−8.76146	+	23.1021i	−0.349620	+	0.921873i
$629$	45.4634	+	17.2420i	1.81274	+	0.687483i
$630$	0.288146	+	0.198893i	0.0114800	+	0.00792408i
$631$	3.07306	+	12.4679i	0.122337	+	0.496339i	0.999859	+	0.0168032i	$0.00534887\pi$
$631$	3.07306	+	12.4679i	0.122337	+	0.496339i	−0.877522	+	0.479536i	$0.840805\pi$
$632$	4.05669	+	2.80013i	0.161366	+	0.111383i
$633$	−1.78757	−	14.7220i	−0.0710495	−	0.585145i
$634$	−0.570901	+	1.50534i	−0.0226734	+	0.0597848i
$635$	8.90477	+	16.9666i	0.353375	+	0.673300i
$636$	8.28382	+	12.0012i	0.328475	+	0.475878i
$637$	−4.35012	−	22.9673i	−0.172358	−	0.909998i
$638$	−2.17953	+	3.15760i	−0.0862885	+	0.125010i
$639$	3.38514	+	0.411031i	0.133914	+	0.0162601i
$640$	14.3521	+	3.53748i	0.567317	+	0.139831i
$641$	21.5177	+	31.1738i	0.849899	+	1.23129i	0.971102	+	0.238664i	$0.0767094\pi$
$641$	21.5177	+	31.1738i	0.849899	+	1.23129i	−0.121203	+	0.992628i	$0.538675\pi$
$642$	0.742578	+	0.838197i	0.0293072	+	0.0330810i
$643$	1.93082	−	3.67887i	0.0761442	−	0.145081i	−0.844408	−	0.535701i	$-0.820047\pi$
$643$	1.93082	−	3.67887i	0.0761442	−	0.145081i	0.920552	+	0.390621i	$0.127740\pi$
$644$	7.57098	−	0.919283i	0.298338	−	0.0362248i
$645$	−29.8849	−	3.62868i	−1.17672	−	0.142879i
$646$	5.18469	−	4.59324i	0.203989	−	0.180719i
$647$	−1.86913	+	2.70790i	−0.0734830	+	0.106459i	−0.858002	−	0.513646i	$-0.828294\pi$
$647$	−1.86913	+	2.70790i	−0.0734830	+	0.106459i	0.784519	+	0.620105i	$0.212910\pi$
$648$	0.803291	−	0.0975372i	0.0315562	−	0.00383162i
$649$	−5.13998	+	42.3315i	−0.201762	+	1.66166i
$650$	0.489620	−	0.0927363i	0.0192045	−	0.00363742i
$651$	−0.482261	−	3.97178i	−0.0189013	−	0.155666i
$652$	−8.24677	−	33.4585i	−0.322969	−	1.31034i
$653$	2.00649			0.0785200			0.0392600	−	0.999229i	$-0.487500\pi$
$653$	2.00649			0.0785200			0.0392600	+	0.999229i	$0.487500\pi$
$654$	−1.29797			−0.0507545
$655$	3.61187	+	14.6539i	0.141128	+	0.572577i
$656$	12.1469	+	4.60673i	0.474258	+	0.179862i
$657$			11.8378i			0.461835i
$658$	−0.0319901	+	0.0121322i	−0.00124710	+	0.000472964i
$659$	−25.7756	−	6.35312i	−1.00408	−	0.247482i	−0.297196	−	0.954817i	$-0.596051\pi$
$659$	−25.7756	−	6.35312i	−1.00408	−	0.247482i	−0.706879	+	0.707334i	$0.749898\pi$
$660$	−12.4822	+	11.0582i	−0.485868	+	0.430441i
$661$	8.35477	−	33.8966i	0.324963	−	1.31843i	−0.550376	−	0.834917i	$-0.685516\pi$
$661$	8.35477	−	33.8966i	0.324963	−	1.31843i	0.875339	−	0.483510i	$-0.160638\pi$
$662$	−0.00464784	+	0.00411762i	−0.000180643	+	0.000160036i
$663$	20.6935	+	16.0148i	0.803670	+	0.621965i
$664$	7.89862	+	6.99757i	0.306526	+	0.271558i
$665$	6.58045	−	4.54216i	0.255179	−	0.176137i
$666$	−1.32987	+	0.327784i	−0.0515316	+	0.0127014i
$667$	16.1595	−	23.4111i	0.625698	−	0.906480i
$668$	8.90962	−	36.1477i	0.344723	−	1.39860i
$669$	−6.21073	+	25.1979i	−0.240121	+	0.974207i
$670$	1.76140	+	0.213872i	0.0680487	+	0.00826261i
$671$	−27.8456	+	31.4312i	−1.07497	+	1.21339i
$672$	−0.608018	−	1.60321i	−0.0234548	−	0.0618452i
$673$	35.6668	−	18.7194i	1.37486	−	0.721580i	0.394515	−	0.918890i	$-0.370913\pi$
$673$	35.6668	−	18.7194i	1.37486	−	0.721580i	0.980341	+	0.197310i	$0.0632204\pi$
$674$	2.96457	+	2.04630i	0.114191	+	0.0788204i
$675$	0.676065			0.0260217
$676$	25.2328	−	3.36855i	0.970494	−	0.129560i
$677$	−38.1806			−1.46740			−0.733700	−	0.679473i	$-0.762208\pi$
$677$	−38.1806			−1.46740			−0.733700	+	0.679473i	$0.762208\pi$
$678$	0.433218	+	0.299029i	0.0166377	+	0.0114841i
$679$	6.79353	−	3.56552i	0.260712	−	0.136832i
$680$	−4.96131	−	13.0819i	−0.190258	−	0.501668i
$681$	−7.84493	+	8.85510i	−0.300618	+	0.339328i
$682$	−4.03740	−	0.490229i	−0.154600	−	0.0187719i
$683$	1.91253	−	7.75945i	0.0731811	−	0.296907i	−0.922935	−	0.384955i	$-0.874217\pi$
$683$	1.91253	−	7.75945i	0.0731811	−	0.296907i	0.996116	+	0.0880482i	$0.0280630\pi$
$684$	2.18789	−	8.87661i	0.0836560	−	0.339406i
$685$	−28.7333	+	41.6274i	−1.09784	+	1.59050i
$686$	1.92391	−	0.474201i	0.0734553	−	0.0181051i
$687$	−2.42811	+	1.67601i	−0.0926383	+	0.0639436i
$688$	35.4773	+	31.4301i	1.35256	+	1.19826i
$689$	−11.1649	−	24.4187i	−0.425349	−	0.930278i
$690$	−1.97515	+	1.74983i	−0.0751928	+	0.0666150i
$691$	0.410085	−	1.66378i	0.0156004	−	0.0632931i	−0.962626	−	0.270835i	$-0.912700\pi$
$691$	0.410085	−	1.66378i	0.0156004	−	0.0632931i	0.978226	+	0.207542i	$0.0665464\pi$
$692$	22.8825	−	20.2722i	0.869864	−	0.770632i
$693$	2.49487	+	0.614930i	0.0947723	+	0.0233593i
$694$	1.62489	−	0.616239i	0.0616799	−	0.0233921i
$695$			37.5405i			1.42399i
$696$	−3.97259	−	1.50660i	−0.150581	−	0.0571077i
$697$	−6.01521	−	24.4047i	−0.227842	−	0.924392i
$698$	1.35290			0.0512079
$699$	24.2500			0.917218
$700$	−0.227753	−	0.924028i	−0.00860824	−	0.0349250i
$701$	−2.12910	−	17.5347i	−0.0804151	−	0.662278i	−0.976059	−	0.217506i	$-0.930208\pi$
$701$	−2.12910	−	17.5347i	−0.0804151	−	0.662278i	0.895644	−	0.444772i	$-0.146715\pi$
$702$	−0.736003	−	0.0401324i	−0.0277786	−	0.00151470i
$703$	−3.77033	+	31.0515i	−0.142201	+	1.17113i
$704$	24.8897	−	3.02216i	0.938065	−	0.113902i
$705$	−0.315080	+	0.456472i	−0.0118666	+	0.0171917i
$706$	1.79231	−	1.58785i	0.0674546	−	0.0597596i
$707$	2.13817	+	0.259620i	0.0804140	+	0.00976403i
$708$	−23.1906	+	2.81585i	−0.871558	+	0.105826i
$709$	−1.95589	+	3.72664i	−0.0734551	+	0.139957i	−0.919414	−	0.393291i	$-0.871336\pi$
$709$	−1.95589	+	3.72664i	−0.0734551	+	0.139957i	0.845959	+	0.533248i	$0.179029\pi$
$710$	1.10135	+	1.24317i	0.0413329	+	0.0466552i
$711$	−3.46041	−	5.01327i	−0.129775	−	0.188012i
$712$	−14.7073	−	3.62503i	−0.551180	−	0.135854i
$713$	29.9341	+	3.63466i	1.12104	+	0.136119i
$714$	−0.605861	+	0.877741i	−0.0226738	+	0.0328486i
$715$	26.1817	−	16.0406i	0.979139	−	0.599883i
$716$	−17.9003	−	25.9330i	−0.668964	−	0.969161i
$717$	−0.465695	−	0.887308i	−0.0173917	−	0.0331371i
$718$	1.84585	−	4.86710i	0.0688865	−	0.181639i
$719$	−4.34566	−	35.7897i	−0.162066	−	1.33473i	−0.815944	−	0.578131i	$-0.803782\pi$
$719$	−4.34566	−	35.7897i	−0.162066	−	1.33473i	0.653878	−	0.756600i	$-0.273141\pi$
$720$	−7.35463	−	5.07653i	−0.274091	−	0.189191i
$721$	−0.390411	−	1.58396i	−0.0145397	−	0.0589897i
$722$	0.470530	+	0.324784i	0.0175113	+	0.0120872i
$723$	−11.9703	−	4.53973i	−0.445180	−	0.168834i
$724$	−15.0166	+	39.5954i	−0.558086	+	1.47155i
$725$	−3.14310	−	1.64963i	−0.116732	−	0.0612656i
$726$	0.168797	−	0.321615i	0.00626463	−	0.0119363i
$727$	14.1797	−	3.49498i	0.525895	−	0.129622i	0.0325750	−	0.999469i	$-0.489629\pi$
$727$	14.1797	−	3.49498i	0.525895	−	0.129622i	0.493320	+	0.869848i	$0.335783\pi$
$728$	0.390306	+	2.06070i	0.0144657	+	0.0763745i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−3.82331	+	4.31562i	−0.141507	+	0.159728i
$731$	11.0536	−	91.0344i	0.408831	−	3.36703i
$732$	−20.3694	−	10.6907i	−0.752875	−	0.395139i
$733$	−3.31249	−	6.31141i	−0.122349	−	0.233117i	0.816576	−	0.577238i	$-0.195869\pi$
$733$	−3.31249	−	6.31141i	−0.122349	−	0.233117i	−0.938926	+	0.344120i	$0.888177\pi$
$734$	2.40117	−	0.910645i	0.0886289	−	0.0336125i
$735$	10.2426	−	11.5615i	0.377803	−	0.426452i
$736$	12.8285	−	1.55766i	0.472864	−	0.0574160i
$737$	12.6434	−	3.11631i	0.465724	−	0.114791i
$738$	0.529971	+	0.469514i	0.0195085	+	0.0172830i
$739$	1.84235	+	2.07959i	0.0677721	+	0.0764989i	0.781419	−	0.624007i	$-0.214496\pi$
$739$	1.84235	+	2.07959i	0.0677721	+	0.0764989i	−0.713647	+	0.700506i	$0.752958\pi$
$740$	27.6767	+	14.5258i	1.01742	+	0.533981i
$741$	−6.81724	+	15.3910i	−0.250437	+	0.565402i
$742$	0.969034	−	0.508588i	0.0355743	−	0.0186709i
$743$	−6.03278	−	2.28793i	−0.221321	−	0.0839360i	0.241452	−	0.970413i	$-0.422376\pi$
$743$	−6.03278	−	2.28793i	−0.221321	−	0.0839360i	−0.462773	+	0.886477i	$0.653146\pi$
$744$	−0.542860	−	4.47086i	−0.0199022	−	0.163910i
$745$	−8.92094	+	4.68207i	−0.326838	+	0.171538i
$746$			0.743384i			0.0272172i
$747$	−6.06034	−	11.5470i	−0.221736	−	0.422483i
$748$	−33.6852	−	38.0228i	−1.23165	−	1.39025i
$749$	−3.24065	+	2.23686i	−0.118411	+	0.0817330i
$750$	−1.57635	−	1.39653i	−0.0575602	−	0.0509939i
$751$	7.62650	+	11.0489i	0.278295	+	0.403180i	0.937060	−	0.349169i	$-0.113536\pi$
$751$	7.62650	+	11.0489i	0.278295	+	0.403180i	−0.658765	+	0.752349i	$0.728921\pi$
$752$	0.816514	−	0.309663i	0.0297752	−	0.0112922i
$753$	0.753241	+	1.98613i	0.0274496	+	0.0723787i
$754$	3.32384	+	1.98246i	0.121047	+	0.0721969i
$755$	6.36356	−	16.7793i	0.231594	−	0.610662i
$756$			1.40768i			0.0511968i
$757$	−7.45836	−	19.6661i	−0.271079	−	0.714776i	−0.999559	−	0.0297086i	$-0.990542\pi$
$757$	−7.45836	−	19.6661i	−0.271079	−	0.714776i	0.728480	−	0.685067i	$-0.240227\pi$
$758$	0.604346	−	4.97724i	0.0219508	−	0.180781i
$759$	−8.99975	+	17.1476i	−0.326670	+	0.622418i
$760$	7.40732	−	5.11290i	0.268692	−	0.185465i
$761$	−19.1358	+	13.2085i	−0.693672	+	0.478807i	−0.861990	−	0.506925i	$-0.830782\pi$
$761$	−19.1358	+	13.2085i	−0.693672	+	0.478807i	0.168318	+	0.985733i	$0.446167\pi$
$762$	0.764102	−	1.45588i	0.0276805	−	0.0527408i
$763$	0.550143	−	4.53084i	0.0199165	−	0.164027i
$764$	7.50679	+	19.7938i	0.271586	+	0.716114i
$765$			17.2902i			0.625130i
$766$	−0.176393	+	0.465110i	−0.00637334	+	0.0168051i
$767$	42.9496	+	2.34193i	1.55082	+	0.0845624i
$768$	4.52488	+	11.9311i	0.163277	+	0.430527i
$769$	−40.9918	+	15.5461i	−1.47820	+	0.560608i	−0.956298	−	0.292395i	$-0.905548\pi$
$769$	−40.9918	+	15.5461i	−1.47820	+	0.560608i	−0.521905	+	0.853004i	$0.674779\pi$
$770$	0.710933	+	1.02996i	0.0256202	+	0.0371173i
$771$	−7.50422	−	6.64816i	−0.270258	−	0.239428i
$772$	−5.70436	+	3.93744i	−0.205304	+	0.141711i
$773$	−32.6467	−	36.8505i	−1.17422	−	1.32542i	−0.935081	−	0.354434i	$-0.884674\pi$
$773$	−32.6467	−	36.8505i	−1.17422	−	1.32542i	−0.239138	−	0.970986i	$-0.576865\pi$
$774$	1.20047	+	2.28731i	0.0431502	+	0.0822158i
$775$		−	3.76276i		−	0.135162i
$776$	7.64718	−	4.01355i	0.274518	−	0.144078i
$777$	−0.580536	−	4.78115i	−0.0208266	−	0.171523i
$778$	6.30434	+	2.39092i	0.226022	+	0.0857187i
$779$	14.3174	−	7.51435i	0.512974	−	0.269230i
$780$	11.9648	+	11.8234i	0.428407	+	0.423346i
$781$	10.7927	+	5.66447i	0.386195	+	0.202691i
$782$	−5.33028	−	6.01664i	−0.190610	−	0.215155i
$783$	3.93008	+	3.48175i	0.140450	+	0.124427i
$784$	−23.6119	+	5.81981i	−0.843282	+	0.207850i
$785$	29.8414	−	3.62340i	1.06508	−	0.129325i
$786$	0.858784	−	0.969367i	0.0306318	−	0.0345762i
$787$	−11.8873	+	4.50825i	−0.423736	+	0.160702i	−0.557249	−	0.830345i	$-0.688143\pi$
$787$	−11.8873	+	4.50825i	−0.423736	+	0.160702i	0.133513	+	0.991047i	$0.457374\pi$
$788$	12.6332	+	24.0705i	0.450038	+	0.857476i
$789$	1.69492	+	0.889561i	0.0603407	+	0.0316692i
$790$	0.357622	−	2.94528i	0.0127236	−	0.104789i
$791$	−1.22745	+	1.38550i	−0.0436430	+	0.0492627i
$792$	2.80837	+	0.692200i	0.0997909	+	0.0245963i
$793$	33.4973	+	25.9238i	1.18952	+	0.920580i
$794$	2.13253	−	0.525622i	0.0756808	−	0.0186536i
$795$	8.24503	−	15.7096i	0.292421	−	0.557162i
$796$	7.17097	+	3.76362i	0.254168	+	0.133398i
$797$	19.3586	−	51.0445i	0.685718	−	1.80809i	0.104198	−	0.994557i	$-0.466773\pi$
$797$	19.3586	−	51.0445i	0.685718	−	1.80809i	0.581520	−	0.813532i	$-0.302458\pi$
$798$	−0.641523	−	0.243297i	−0.0227097	−	0.00861264i
$799$	−1.39049	−	0.959786i	−0.0491920	−	0.0339548i
$800$	−0.385910	−	1.56570i	−0.0136440	−	0.0553558i
$801$	15.4057	+	10.6338i	0.544332	+	0.375725i
$802$	0.302705	+	2.49300i	0.0106889	+	0.0880310i
$803$	−15.0046	+	39.5638i	−0.529500	+	1.39618i
$804$	3.31522	+	6.31663i	0.116919	+	0.222770i
$805$	−5.27100	−	7.63636i	−0.185778	−	0.269146i
$806$	−0.223364	+	4.09635i	−0.00786766	+	0.144288i
$807$	−2.22159	+	3.21853i	−0.0782038	+	0.113298i
$808$	2.40684	+	0.292243i	0.0846723	+	0.0102811i
$809$	34.8475	+	8.58915i	1.22517	+	0.301978i	0.798259	−	0.602314i	$-0.205754\pi$
$809$	34.8475	+	8.58915i	1.22517	+	0.301978i	0.426915	+	0.904292i	$0.359601\pi$
$810$	−0.276678	−	0.400837i	−0.00972146	−	0.0140840i
$811$	−29.9095	−	33.7609i	−1.05026	−	1.18550i	−0.982203	−	0.187823i	$-0.939857\pi$
$811$	−29.9095	−	33.7609i	−1.05026	−	1.18550i	−0.0680621	−	0.997681i	$-0.521682\pi$
$812$	3.43480	−	6.54446i	0.120538	−	0.229666i
$813$	17.7297	−	2.15277i	0.621807	−	0.0755010i
$814$	−4.86014	−	0.590128i	−0.170348	−	0.0206840i
$815$	−31.3817	+	27.8017i	−1.09925	+	0.973852i
$816$	15.4640	−	22.4034i	0.541347	−	0.784277i
$817$	58.5630	−	7.11084i	2.04886	−	0.248777i
$818$	0.126471	−	1.04158i	0.00442194	−	0.0364180i
$819$	0.452045	−	2.55217i	0.0157957	−	0.0891799i
$820$	−1.94762	−	16.0401i	−0.0680137	−	0.560143i
$821$	−0.790729	−	3.20811i	−0.0275966	−	0.111964i	0.955528	−	0.294900i	$-0.0952862\pi$
$821$	−0.790729	−	3.20811i	−0.0275966	−	0.111964i	−0.983125	+	0.182936i	$0.941440\pi$
$822$	4.34027			0.151384
$823$	6.58108			0.229402			0.114701	−	0.993400i	$-0.463409\pi$
$823$	6.58108			0.229402			0.114701	+	0.993400i	$0.463409\pi$
$824$	−0.439468	−	1.78299i	−0.0153096	−	0.0621135i
$825$	2.25952	+	0.856925i	0.0786665	+	0.0298343i
$826$			1.75319i			0.0610014i
$827$	33.4447	−	12.6839i	1.16299	−	0.441063i	0.303806	−	0.952734i	$-0.401742\pi$
$827$	33.4447	−	12.6839i	1.16299	−	0.441063i	0.859182	+	0.511671i	$0.170973\pi$
$828$	−10.3010	−	2.53896i	−0.357984	−	0.0882350i
$829$	−27.6338	+	24.4814i	−0.959760	+	0.850273i	−0.988791	−	0.149305i	$-0.952296\pi$
$829$	−27.6338	+	24.4814i	−0.959760	+	0.850273i	0.0290308	+	0.999579i	$0.490758\pi$
$830$	1.52002	−	6.16697i	0.0527607	−	0.214059i
$831$	12.8113	−	11.3498i	0.444418	−	0.393720i
$832$	−4.70649	−	24.8488i	−0.163168	−	0.861479i
$833$	35.2182	+	31.2006i	1.22024	+	1.08104i
$834$	2.65107	−	1.82990i	0.0917989	−	0.0633642i
$835$	−43.9791	+	10.8399i	−1.52196	+	0.375129i
$836$	18.5636	−	26.8940i	0.642034	−	0.930147i
$837$	−1.33195	+	5.40395i	−0.0460391	+	0.186788i
$838$	−0.938003	+	3.80563i	−0.0324028	+	0.131463i
$839$	15.7418	+	1.91140i	0.543467	+	0.0659888i	0.387666	−	0.921800i	$-0.373281\pi$
$839$	15.7418	+	1.91140i	0.543467	+	0.0659888i	0.155800	+	0.987789i	$0.450204\pi$
$840$	−0.918996	+	1.03733i	−0.0317084	+	0.0357914i
$841$	0.507762	+	1.33886i	0.0175090	+	0.0461675i
$842$	0.446310	−	0.234241i	0.0153808	−	0.00807249i
$843$	6.81038	+	4.70087i	0.234562	+	0.161906i
$844$	29.0404			0.999610
$845$	−17.8957	−	25.2785i	−0.615629	−	0.869605i
$846$	0.0475939			0.00163631
$847$	1.05112	+	0.725538i	0.0361170	+	0.0249298i
$848$	−24.7336	+	12.9812i	−0.849354	+	0.445776i
$849$	8.35296	+	22.0250i	0.286673	+	0.755895i
$850$	−0.665138	+	0.750786i	−0.0228141	+	0.0257518i
$851$	36.0341	+	4.37533i	1.23523	+	0.149984i
$852$	−1.59803	+	6.48346i	−0.0547476	+	0.222120i
$853$	−5.20462	+	21.1160i	−0.178203	+	0.722997i	0.812035	+	0.583609i	$0.198360\pi$
$853$	−5.20462	+	21.1160i	−0.178203	+	0.722997i	−0.990238	+	0.139389i	$0.955486\pi$
$854$	−0.980728	+	1.42083i	−0.0335598	+	0.0486198i
$855$	−10.7997	+	2.66189i	−0.369342	+	0.0910347i
$856$	−3.64786	+	2.51793i	−0.124681	+	0.0860612i
$857$	10.3083	+	9.13237i	0.352125	+	0.311956i	0.820580	−	0.571532i	$-0.193651\pi$
$857$	10.3083	+	9.13237i	0.352125	+	0.311956i	−0.468455	+	0.883488i	$0.655189\pi$
$858$	−2.40898	−	1.06703i	−0.0822412	−	0.0364277i
$859$	−15.6121	+	13.8312i	−0.532679	+	0.471913i	−0.886062	−	0.463566i	$-0.846570\pi$
$859$	−15.6121	+	13.8312i	−0.532679	+	0.471913i	0.353383	+	0.935479i	$0.385031\pi$
$860$	14.1078	−	57.2376i	0.481072	−	1.95179i
$861$	−1.86357	+	1.65098i	−0.0635102	+	0.0562651i
$862$	−2.48731	−	0.613068i	−0.0847182	−	0.0208812i
$863$	−8.43572	+	3.19925i	−0.287155	+	0.108904i	−0.493977	−	0.869475i	$-0.664457\pi$
$863$	−8.43572	+	3.19925i	−0.287155	+	0.108904i	0.206822	+	0.978379i	$0.433688\pi$
$864$			2.38521i			0.0811465i
$865$	−34.7769	−	13.1891i	−1.18245	−	0.448444i
$866$	0.908349	+	3.68532i	0.0308670	+	0.125232i
$867$	−35.6690			−1.21138
$868$	7.83469			0.265927
$869$	−5.21087	−	21.1413i	−0.176767	−	0.717170i
$870$	0.308247	+	2.53864i	0.0104505	+	0.0860680i
$871$	−3.98215	−	12.5169i	−0.134930	−	0.424117i
$872$	0.619272	−	5.10016i	0.0209712	−	0.172713i
$873$	−10.5951	+	1.28648i	−0.358590	+	0.0435407i
$874$	2.93746	−	4.25565i	0.0993611	−	0.143949i
$875$	5.54302	−	4.91068i	0.187388	−	0.166011i
$876$	−23.0118	−	2.79413i	−0.777495	−	0.0944050i
$877$	−42.1402	+	5.11675i	−1.42297	+	0.172780i	−0.795546	−	0.605894i	$-0.792816\pi$
$877$	−42.1402	+	5.11675i	−1.42297	+	0.172780i	−0.627429	+	0.778674i	$0.715893\pi$
$878$	−2.90477	+	5.53457i	−0.0980311	+	0.186783i
$879$	−1.25975	−	1.42197i	−0.0424904	−	0.0479617i
$880$	−18.1458	−	26.2888i	−0.611696	−	0.886194i
$881$	14.5647	+	3.58988i	0.490698	+	0.120946i	0.476898	−	0.878959i	$-0.341761\pi$
$881$	14.5647	+	3.58988i	0.490698	+	0.120946i	0.0137997	+	0.999905i	$0.495607\pi$
$882$	−1.31573	−	0.159758i	−0.0443029	−	0.00537934i
$883$	−7.30242	+	10.5794i	−0.245746	+	0.356024i	−0.926374	−	0.376605i	$-0.877092\pi$
$883$	−7.30242	+	10.5794i	−0.245746	+	0.356024i	0.680628	+	0.732629i	$0.261707\pi$
$884$	−36.0161	+	36.4467i	−1.21135	+	1.22583i
$885$	16.1456	+	23.3909i	0.542728	+	0.786277i
$886$	3.09809	+	5.90292i	0.104082	+	0.198312i
$887$	−11.0504	+	29.1376i	−0.371037	+	0.978343i	0.611329	+	0.791376i	$0.290635\pi$
$887$	−11.0504	+	29.1376i	−0.371037	+	0.978343i	−0.982366	+	0.186967i	$0.940134\pi$
$888$	−0.653484	−	5.38192i	−0.0219295	−	0.180606i
$889$	4.75818	+	3.28434i	0.159584	+	0.110153i
$890$	2.18191	+	8.85234i	0.0731377	+	0.296731i
$891$	−2.94172	−	2.03052i	−0.0985512	−	0.0680250i
$892$	−47.5170	−	18.0208i	−1.59099	−	0.603382i
$893$	0.385424	−	1.01628i	0.0128977	−	0.0340085i
$894$	0.765489	+	0.401760i	0.0256018	+	0.0134369i
$895$	−17.8164	+	33.9464i	−0.595538	+	1.13470i
$896$	4.33049	−	1.06737i	0.144672	−	0.0356584i
$897$	17.8607	+	7.91115i	0.596350	+	0.264146i
$898$	1.24091	+	0.305856i	0.0414096	+	0.0102066i
$899$	19.3783	−	21.8736i	0.646302	−	0.729524i
$900$	−0.159575	+	1.31422i	−0.00531918	+	0.0438074i
$901$	47.8541	+	25.1157i	1.59425	+	0.836727i
$902$	1.17614	+	2.24094i	0.0391611	+	0.0746153i
$903$	−8.49319	+	3.22104i	−0.282636	+	0.107190i
$904$	−1.38168	+	1.55960i	−0.0459540	+	0.0518714i
$905$	51.1461	−	6.21026i	1.70015	−	0.206436i
$906$	−1.49512	+	0.368515i	−0.0496722	+	0.0122431i
$907$	29.3076	+	25.9643i	0.973144	+	0.862130i	0.990471	−	0.137720i	$-0.0439773\pi$
$907$	29.3076	+	25.9643i	0.973144	+	0.862130i	−0.0173274	+	0.999850i	$0.505516\pi$
$908$	−15.3620	−	17.3401i	−0.509806	−	0.575452i
$909$	−2.65302	−	1.39241i	−0.0879953	−	0.0461835i
$910$	0.989088	−	0.784429i	0.0327879	−	0.0260036i
$911$	−16.5430	+	8.68246i	−0.548095	+	0.287663i	−0.715953	−	0.698149i	$-0.754007\pi$
$911$	−16.5430	+	8.68246i	−0.548095	+	0.287663i	0.167857	+	0.985811i	$0.446315\pi$
$912$	16.3742	+	6.20991i	0.542204	+	0.205631i
$913$	−5.61864	−	46.2737i	−0.185950	−	1.53143i
$914$	1.66020	−	0.871343i	0.0549147	−	0.0288215i
$915$			27.9883i			0.925265i
$916$	−2.68492	−	5.11568i	−0.0887121	−	0.169027i
$917$	3.01979	+	3.40864i	0.0997223	+	0.112563i
$918$	1.22102	−	0.842806i	0.0402995	−	0.0278167i
$919$	−12.4337	−	11.0153i	−0.410150	−	0.363362i	0.432674	−	0.901551i	$-0.357570\pi$
$919$	−12.4337	−	11.0153i	−0.410150	−	0.363362i	−0.842824	+	0.538189i	$0.819109\pi$
$920$	−5.93333	−	8.59592i	−0.195616	−	0.283399i
$921$	−16.4823	+	6.25092i	−0.543111	+	0.205975i
$922$	−2.22497	−	5.86675i	−0.0732754	−	0.193211i
$923$	4.97930	−	11.2416i	0.163896	−	0.370020i
$924$	−1.78426	+	4.70471i	−0.0586978	+	0.154773i
$925$		−	4.52953i		−	0.148930i
$926$	2.64913	+	6.98519i	0.0870559	+	0.229547i
$927$	−0.273543	+	2.25283i	−0.00898432	+	0.0739925i
$928$	5.82002	−	11.0891i	0.191051	−	0.364018i
$929$	−21.1250	+	14.5816i	−0.693090	+	0.478406i	−0.861792	−	0.507262i	$-0.830658\pi$
$929$	−21.1250	+	14.5816i	−0.693090	+	0.478406i	0.168702	+	0.985667i	$0.446042\pi$
$930$	−2.23093	+	1.53990i	−0.0731550	+	0.0504953i
$931$	−14.0664	+	26.8012i	−0.461006	+	0.878374i
$932$	−5.72386	+	47.1402i	−0.187491	+	1.54413i
$933$	−0.648804	−	1.71075i	−0.0212409	−	0.0560076i
$934$		−	4.54718i		−	0.148788i
$935$	−21.9157	+	57.7870i	−0.716720	+	1.88984i
$936$	0.508848	−	2.87286i	0.0166322	−	0.0939024i
$937$	17.3883	+	45.8491i	0.568049	+	1.49782i	0.843834	+	0.536604i	$0.180293\pi$
$937$	17.3883	+	45.8491i	0.568049	+	1.49782i	−0.275785	+	0.961219i	$0.588938\pi$
$938$	0.500583	−	0.189846i	0.0163446	−	0.00619870i
$939$	−18.7317	−	27.1375i	−0.611285	−	0.885599i
$940$	−0.812979	−	0.720236i	−0.0265164	−	0.0234915i
$941$	−9.88656	+	6.82420i	−0.322293	+	0.222462i	−0.718215	−	0.695822i	$-0.755040\pi$
$941$	−9.88656	+	6.82420i	−0.322293	+	0.222462i	0.395922	+	0.918284i	$0.370425\pi$
$942$	−1.71049	−	1.93074i	−0.0557306	−	0.0629069i
$943$	−8.72013	−	16.6148i	−0.283966	−	0.541053i
$944$		−	44.7485i		−	1.45644i
$945$	1.51648	−	0.795909i	0.0493310	−	0.0258909i
$946$	1.11298	+	9.16622i	0.0361861	+	0.298019i
$947$	−39.0944	−	14.8266i	−1.27040	−	0.481798i	−0.374983	−	0.927032i	$-0.622352\pi$
$947$	−39.0944	−	14.8266i	−1.27040	−	0.481798i	−0.895415	+	0.445233i	$0.853121\pi$
$948$	10.5622	−	5.54348i	0.343045	−	0.180044i
$949$	40.8238	+	12.4556i	1.32520	+	0.404325i
$950$	−0.571351	−	0.299868i	−0.0185371	−	0.00972901i
$951$	5.22225	+	5.89470i	0.169343	+	0.191149i
$952$	−3.15989	−	2.79942i	−0.102413	−	0.0907296i
$953$	−6.00610	+	1.48037i	−0.194557	+	0.0479539i	−0.335390	−	0.942079i	$-0.608868\pi$
$953$	−6.00610	+	1.48037i	−0.194557	+	0.0479539i	0.140833	+	0.990033i	$0.455022\pi$
$954$	−1.51129	+	0.183504i	−0.0489299	+	0.00594117i
$955$	17.0792	−	19.2785i	0.552671	−	0.623837i
$956$	1.83478	−	0.695842i	0.0593412	−	0.0225051i
$957$	8.72182	+	16.6180i	0.281936	+	0.537185i
$958$	6.33096	+	3.32274i	0.204544	+	0.107353i
$959$	−1.83962	+	15.1506i	−0.0594045	+	0.489240i
$960$	11.0817	−	12.5086i	0.357660	−	0.403714i
$961$	−0.0225449	−	0.00555682i	−0.000727255	−	0.000179252i
$962$	−0.268881	+	4.93110i	−0.00866906	+	0.158985i
$963$	5.31850	−	1.31089i	0.171386	−	0.0422429i
$964$	11.6503	−	22.1978i	0.375232	−	0.714945i
$965$	7.46703	+	3.91900i	0.240372	+	0.126157i
$966$	−0.282338	+	0.744463i	−0.00908406	+	0.0239527i
$967$	−32.8997	−	12.4772i	−1.05798	−	0.401240i	−0.236594	−	0.971609i	$-0.576031\pi$
$967$	−32.8997	−	12.4772i	−1.05798	−	0.401240i	−0.821389	+	0.570368i	$0.806800\pi$
$968$	1.18320	+	0.816707i	0.0380296	+	0.0262499i
$969$	−8.10856	−	32.8977i	−0.260485	−	1.05683i
$970$	−4.27810	−	2.95296i	−0.137361	−	0.0948137i
$971$	2.12273	+	17.4823i	0.0681216	+	0.561032i	0.986312	+	0.164892i	$0.0527275\pi$
$971$	2.12273	+	17.4823i	0.0681216	+	0.561032i	−0.918190	+	0.396140i	$0.870349\pi$
$972$	0.694390	−	1.83096i	0.0222726	−	0.0587279i
$973$	5.26400	+	10.0297i	0.168756	+	0.321538i
$974$	2.97002	+	4.30282i	0.0951657	+	0.137871i
$975$	0.711349	−	2.33148i	0.0227814	−	0.0746672i
$976$	25.0321	−	36.2652i	0.801257	−	1.16082i
$977$	25.6335	+	3.11247i	0.820089	+	0.0995769i	0.519818	−	0.854277i	$-0.326000\pi$
$977$	25.6335	+	3.11247i	0.820089	+	0.0995769i	0.300271	+	0.953854i	$0.402923\pi$
$978$	3.49301	+	0.860950i	0.111694	+	0.0275301i
$979$	38.0099	+	55.0668i	1.21480	+	1.75994i
$980$	20.0571	+	22.6398i	0.640700	+	0.723201i
$981$	−2.95057	+	5.62184i	−0.0942044	+	0.179491i
$982$	−0.0810201	+	0.00983763i	−0.00258546	+	0.000313931i
$983$	2.50602	+	0.304286i	0.0799295	+	0.00970520i	0.160404	−	0.987051i	$-0.448720\pi$
$983$	2.50602	+	0.304286i	0.0799295	+	0.00970520i	−0.0804742	+	0.996757i	$0.525643\pi$
$984$	−2.09774	+	1.85843i	−0.0668734	+	0.0592447i
$985$	18.7880	−	27.2191i	0.598636	−	0.867274i
$986$	−7.73313	+	0.938972i	−0.246273	+	0.0299029i
$987$	−0.0201727	+	0.166137i	−0.000642103	+	0.00528820i
$988$	−28.3099	−	16.8850i	−0.900657	−	0.537185i
$989$	−8.25186	−	67.9602i	−0.262394	−	2.16101i
$990$	−0.416636	−	1.69036i	−0.0132416	−	0.0537231i
$991$	35.5594			1.12958			0.564790	−	0.825234i	$-0.308957\pi$
$991$	35.5594			1.12958			0.564790	+	0.825234i	$0.308957\pi$
$992$	13.2753			0.421491
$993$	0.00726895	+	0.0294913i	0.000230673	+	0.000935878i
$994$	0.468567	+	0.177704i	0.0148621	+	0.00563643i
$995$		−	9.85317i		−	0.312367i
$996$	23.8770	−	9.05536i	0.756572	−	0.286930i
$997$	21.8534	+	5.38637i	0.692104	+	0.170588i	0.569652	−	0.821886i	$-0.307078\pi$
$997$	21.8534	+	5.38637i	0.692104	+	0.170588i	0.122452	+	0.992474i	$0.460924\pi$
$998$	−0.0586146	+	0.0519280i	−0.00185541	+	0.00164375i
$999$	−1.60338	+	6.50516i	−0.0507286	+	0.205814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.493.9	yes	192
169.12	even	26	inner	507.2.p.b.181.9	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.181.9	✓	192	169.12	even	26	inner
507.2.p.b.493.9	yes	192	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.168246 - 0.116132i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.694390 - 1.83096i) q^{4} +(-1.57986 + 1.78329i) q^{5} +(0.202943 + 0.0246418i) q^{6} +(-0.172035 + 0.697973i) q^{7} +(-0.193652 + 0.785677i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})\)	\(q+(-0.168246 - 0.116132i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.694390 - 1.83096i) q^{4} +(-1.57986 + 1.78329i) q^{5} +(0.202943 + 0.0246418i) q^{6} +(-0.172035 + 0.697973i) q^{7} +(-0.193652 + 0.785677i) q^{8} +(0.568065 - 0.822984i) q^{9} +(0.472900 - 0.116559i) q^{10} +(2.94172 - 2.03052i) q^{11} +(1.46574 + 1.29853i) q^{12} +(-2.24044 - 2.82497i) q^{13} +(0.110001 - 0.0974522i) q^{14} +(0.570157 - 2.31322i) q^{15} +(-2.80765 + 2.48737i) q^{16} +(7.04646 + 1.73680i) q^{17} +(-0.191149 + 0.0724932i) q^{18} +4.66869i q^{19} +(4.36216 + 1.65435i) q^{20} +(-0.172035 - 0.697973i) q^{21} -0.730738 q^{22} +5.41784 q^{23} +(-0.193652 - 0.785677i) q^{24} +(-0.0814906 - 0.671136i) q^{25} +(0.0488756 + 0.735474i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(1.39742 - 0.169677i) q^{28} +(2.98264 - 4.32110i) q^{29} +(-0.364564 + 0.322976i) q^{30} +(5.52510 + 0.670868i) q^{31} +(2.36782 - 0.287505i) q^{32} +(-1.66113 + 3.16502i) q^{33} +(-0.983838 - 1.11052i) q^{34} +(-0.972897 - 1.40948i) q^{35} +(-1.90130 - 0.468630i) q^{36} +(6.65100 + 0.807577i) q^{37} +(0.542182 - 0.785487i) q^{38} +(3.29664 + 1.46020i) q^{39} +(-1.09515 - 1.58659i) q^{40} +(-1.60952 - 3.06668i) q^{41} +(-0.0521125 + 0.137409i) q^{42} +(-1.52309 - 12.5438i) q^{43} +(-5.76049 - 3.97618i) q^{44} +(0.570157 + 2.31322i) q^{45} +(-0.911528 - 0.629183i) q^{46} +(-0.217680 - 0.0825551i) q^{47} +(1.33012 - 3.50723i) q^{48} +(5.74062 + 3.01291i) q^{49} +(-0.0642296 + 0.122379i) q^{50} +(-7.04646 + 1.73680i) q^{51} +(-3.61665 + 6.06377i) q^{52} +(7.23049 + 1.78215i) q^{53} +(0.135565 - 0.153021i) q^{54} +(-1.02648 + 8.45386i) q^{55} +(-0.515066 - 0.270328i) q^{56} +(-2.16965 - 4.13392i) q^{57} +(-1.00363 + 0.380628i) q^{58} +(-7.91091 + 8.92957i) q^{59} +(-4.63131 + 0.562343i) q^{60} +(-11.4063 + 2.81141i) q^{61} +(-0.851665 - 0.754509i) q^{62} +(0.476693 + 0.538076i) q^{63} +(6.21091 + 3.25974i) q^{64} +(8.57730 + 0.467699i) q^{65} +(0.647037 - 0.339591i) q^{66} +(3.40627 + 1.29183i) q^{67} +(-1.71299 - 14.1078i) q^{68} +(-4.79726 + 2.51780i) q^{69} +0.350123i q^{70} +(1.58471 + 3.01941i) q^{71} +(0.536593 + 0.605688i) q^{72} +(-9.74228 + 6.72461i) q^{73} +(-1.02522 - 0.908262i) q^{74} +(0.384049 + 0.556390i) q^{75} +(8.54817 - 3.24189i) q^{76} +(0.911170 + 2.40256i) q^{77} +(-0.385069 - 0.628516i) q^{78} +(2.16010 - 5.69572i) q^{79} -8.93654i q^{80} +(-0.354605 - 0.935016i) q^{81} +(-0.0853441 + 0.702872i) q^{82} +(6.06034 - 11.5470i) q^{83} +(-1.15850 + 0.799653i) q^{84} +(-14.2296 + 9.82198i) q^{85} +(-1.20047 + 2.28731i) q^{86} +(-0.632882 + 5.21225i) q^{87} +(1.02566 + 2.70445i) q^{88} +18.7193i q^{89} +(0.172711 - 0.455402i) q^{90} +(2.35718 - 1.07777i) q^{91} +(-3.76209 - 9.91983i) q^{92} +(-5.20400 + 1.97362i) q^{93} +(0.0270364 + 0.0391690i) q^{94} +(-8.32563 - 7.37586i) q^{95} +(-1.96299 + 1.35495i) q^{96} +(-7.07746 - 7.98880i) q^{97} +(-0.615940 - 1.17358i) q^{98} -3.57445i 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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