LMFDB - Embedded newform 507.2.t.b.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			10.4
Character	$\chi$	$=$	507.10
Dual form			507.2.t.b.355.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49980 - 0.306186i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(0.315692 + 0.134504i) q^{4} +(-0.217058 + 0.880640i) q^{5} +(1.52949 + 0.0616365i) q^{6} +(0.786387 - 0.373145i) q^{7} +(2.08725 + 1.44072i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})$	\(q+(-1.49980 - 0.306186i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(0.315692 + 0.134504i) q^{4} +(-0.217058 + 0.880640i) q^{5} +(1.52949 + 0.0616365i) q^{6} +(0.786387 - 0.373145i) q^{7} +(2.08725 + 1.44072i) q^{8} +(0.948536 - 0.316668i) q^{9} +(0.595184 - 1.25432i) q^{10} +(-0.216875 + 0.649619i) q^{11} +(-0.333180 - 0.0821214i) q^{12} +(-2.69460 - 2.39565i) q^{13} +(-1.29368 + 0.318862i) q^{14} +(0.0729828 - 0.904054i) q^{15} +(-3.16475 - 3.29485i) q^{16} +(-1.35460 - 2.85477i) q^{17} +(-1.51957 + 0.184510i) q^{18} +(-2.27071 - 1.31100i) q^{19} +(-0.186973 + 0.248816i) q^{20} +(-0.716347 + 0.494459i) q^{21} +(0.524174 - 0.907895i) q^{22} +(4.63702 + 8.03156i) q^{23} +(-2.29133 - 1.08725i) q^{24} +(3.69887 + 1.94132i) q^{25} +(3.30785 + 4.41804i) q^{26} +(-0.885456 + 0.464723i) q^{27} +(0.298446 - 0.0120269i) q^{28} +(-1.59035 + 7.79004i) q^{29} +(-0.386269 + 1.33355i) q^{30} +(-0.146755 - 0.279618i) q^{31} +(1.02663 + 1.62348i) q^{32} +(0.109860 - 0.675996i) q^{33} +(1.15754 + 4.69634i) q^{34} +(0.157915 + 0.773518i) q^{35} +(0.342038 + 0.0276122i) q^{36} +(-2.64286 + 4.17935i) q^{37} +(3.00420 + 2.66149i) q^{38} +(3.04400 + 1.93238i) q^{39} +(-1.72181 + 1.52539i) q^{40} +(1.21950 + 7.50390i) q^{41} +(1.22577 - 0.522254i) q^{42} +(0.806242 - 0.509837i) q^{43} +(-0.155842 + 0.175909i) q^{44} +(0.0729828 + 0.904054i) q^{45} +(-4.49546 - 13.4655i) q^{46} +(-6.00539 - 0.729187i) q^{47} +(3.65229 + 2.74452i) q^{48} +(-3.94795 + 4.83536i) q^{49} +(-4.95316 - 4.04413i) q^{50} +(1.79500 + 2.60051i) q^{51} +(-0.528441 - 1.11872i) q^{52} +(0.296634 - 0.429748i) q^{53} +(1.47030 - 0.425877i) q^{54} +(-0.525006 - 0.331994i) q^{55} +(2.17899 + 0.354120i) q^{56} +(2.45160 + 0.929771i) q^{57} +(4.77041 - 11.1966i) q^{58} +(9.80531 + 9.41813i) q^{59} +(0.144639 - 0.275586i) q^{60} +(-6.60451 + 0.533171i) q^{61} +(0.134488 + 0.464306i) q^{62} +(0.627754 - 0.602966i) q^{63} +(2.19741 + 5.79410i) q^{64} +(2.69459 - 1.85298i) q^{65} +(-0.371749 + 0.980222i) q^{66} +(3.39819 + 7.97585i) q^{67} +(-0.0436606 - 1.08343i) q^{68} +(-5.86533 - 7.18373i) q^{69} -1.20847i q^{70} +(-2.47011 + 2.01678i) q^{71} +(2.43606 + 0.705614i) q^{72} +(0.513272 + 0.579364i) q^{73} +(5.24342 - 5.45898i) q^{74} +(-3.96238 - 1.32284i) q^{75} +(-0.540511 - 0.719290i) q^{76} +(0.0718549 + 0.591778i) q^{77} +(-3.97372 - 3.83021i) q^{78} +(1.41139 - 11.6238i) q^{79} +(3.58851 - 2.07183i) q^{80} +(0.799443 - 0.600742i) q^{81} +(0.468582 - 11.6277i) q^{82} +(-8.68714 + 3.29460i) q^{83} +(-0.292651 + 0.0597452i) q^{84} +(2.80805 - 0.573267i) q^{85} +(-1.36531 + 0.517793i) q^{86} +(0.320143 - 7.94427i) q^{87} +(-1.38859 + 1.04346i) q^{88} +(-15.1749 + 8.76121i) q^{89} +(0.167349 - 1.37825i) q^{90} +(-3.01293 - 0.878426i) q^{91} +(0.383596 + 3.15920i) q^{92} +(0.189708 + 0.252456i) q^{93} +(8.78362 + 2.93240i) q^{94} +(1.64739 - 1.71512i) q^{95} +(-1.27376 - 1.43777i) q^{96} +(6.54695 + 1.89635i) q^{97} +(7.40166 - 6.04327i) q^{98} +0.684865i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{78}\right)$

Coefficient data

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

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

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

$2$	−1.49980	−	0.306186i	−1.06052	−	0.216506i	−0.362059	−	0.932155i	$-0.617926\pi$
$2$	−1.49980	−	0.306186i	−1.06052	−	0.216506i	−0.698460	+	0.715649i	$0.746131\pi$
$3$	−0.987050	+	0.160411i	−0.569874	+	0.0926135i
$3$	−0.987050	+	0.160411i	−0.569874	+	0.0926135i
$4$	0.315692	+	0.134504i	0.157846	+	0.0672519i
$5$	−0.217058	+	0.880640i	−0.0970714	+	0.393834i	−0.999299	−	0.0374252i	$-0.988084\pi$
$5$	−0.217058	+	0.880640i	−0.0970714	+	0.393834i	0.902228	+	0.431259i	$0.141931\pi$
$6$	1.52949	+	0.0616365i	0.624413	+	0.0251630i
$7$	0.786387	−	0.373145i	0.297226	−	0.141036i	−0.274240	−	0.961661i	$-0.588426\pi$
$7$	0.786387	−	0.373145i	0.297226	−	0.141036i	0.571466	+	0.820626i	$0.306375\pi$
$8$	2.08725	+	1.44072i	0.737954	+	0.509373i
$9$	0.948536	−	0.316668i	0.316179	−	0.105556i
$10$	0.595184	−	1.25432i	0.188214	−	0.396652i
$11$	−0.216875	+	0.649619i	−0.0653902	+	0.195868i	−0.976162	−	0.217042i	$-0.930359\pi$
$11$	−0.216875	+	0.649619i	−0.0653902	+	0.195868i	0.910772	+	0.412909i	$0.135487\pi$
$12$	−0.333180	−	0.0821214i	−0.0961807	−	0.0237064i
$13$	−2.69460	−	2.39565i	−0.747348	−	0.664432i
$13$	−2.69460	−	2.39565i	−0.747348	−	0.664432i
$14$	−1.29368	+	0.318862i	−0.345749	+	0.0852196i
$15$	0.0729828	−	0.904054i	0.0188441	−	0.233426i
$16$	−3.16475	−	3.29485i	−0.791186	−	0.823712i
$17$	−1.35460	−	2.85477i	−0.328540	−	0.692383i	0.670221	−	0.742162i	$-0.266200\pi$
$17$	−1.35460	−	2.85477i	−0.328540	−	0.692383i	−0.998760	+	0.0497792i	$0.984148\pi$
$18$	−1.51957	+	0.184510i	−0.358167	+	0.0434894i
$19$	−2.27071	−	1.31100i	−0.520937	−	0.300763i	0.216381	−	0.976309i	$-0.430575\pi$
$19$	−2.27071	−	1.31100i	−0.520937	−	0.300763i	−0.737318	+	0.675546i	$0.763908\pi$
$20$	−0.186973	+	0.248816i	−0.0418084	+	0.0556369i
$21$	−0.716347	+	0.494459i	−0.156320	+	0.107900i
$22$	0.524174	−	0.907895i	0.111754	−	0.193564i
$23$	4.63702	+	8.03156i	0.966887	+	1.67470i	0.704459	+	0.709745i	$0.251190\pi$
$23$	4.63702	+	8.03156i	0.966887	+	1.67470i	0.262428	+	0.964952i	$0.415477\pi$
$24$	−2.29133	−	1.08725i	−0.467716	−	0.221934i
$25$	3.69887	+	1.94132i	0.739774	+	0.388263i
$26$	3.30785	+	4.41804i	0.648723	+	0.866449i
$27$	−0.885456	+	0.464723i	−0.170406	+	0.0894360i
$28$	0.298446	−	0.0120269i	0.0564009	−	0.00227288i
$29$	−1.59035	+	7.79004i	−0.295320	+	1.44657i	0.513283	+	0.858219i	$0.328429\pi$
$29$	−1.59035	+	7.79004i	−0.295320	+	1.44657i	−0.808603	+	0.588354i	$0.799776\pi$
$30$	−0.386269	+	1.33355i	−0.0705227	+	0.243473i
$31$	−0.146755	−	0.279618i	−0.0263580	−	0.0502209i	0.871921	−	0.489647i	$-0.162874\pi$
$31$	−0.146755	−	0.279618i	−0.0263580	−	0.0502209i	−0.898279	+	0.439426i	$0.855182\pi$
$32$	1.02663	+	1.62348i	0.181484	+	0.286993i
$33$	0.109860	−	0.675996i	0.0191242	−	0.117676i
$34$	1.15754	+	4.69634i	0.198517	+	0.805416i
$35$	0.157915	+	0.773518i	0.0266925	+	0.130748i
$36$	0.342038	+	0.0276122i	0.0570064	+	0.00460203i
$37$	−2.64286	+	4.17935i	−0.434483	+	0.687080i	−0.989463	−	0.144783i	$-0.953751\pi$
$37$	−2.64286	+	4.17935i	−0.434483	+	0.687080i	0.554980	+	0.831864i	$0.312726\pi$
$38$	3.00420	+	2.66149i	0.487346	+	0.431751i
$39$	3.04400	+	1.93238i	0.487430	+	0.309428i
$40$	−1.72181	+	1.52539i	−0.272243	+	0.241186i
$41$	1.21950	+	7.50390i	0.190454	+	1.17191i	0.889534	+	0.456869i	$0.151029\pi$
$41$	1.21950	+	7.50390i	0.190454	+	1.17191i	−0.699080	+	0.715044i	$0.746407\pi$
$42$	1.22577	−	0.522254i	0.189141	−	0.0805855i
$43$	0.806242	−	0.509837i	0.122951	−	0.0777494i	−0.471575	−	0.881826i	$-0.656314\pi$
$43$	0.806242	−	0.509837i	0.122951	−	0.0777494i	0.594526	+	0.804077i	$0.297340\pi$
$44$	−0.155842	+	0.175909i	−0.0234940	+	0.0265193i
$45$	0.0729828	+	0.904054i	0.0108796	+	0.134768i
$46$	−4.49546	−	13.4655i	−0.662819	−	1.98538i
$47$	−6.00539	−	0.729187i	−0.875977	−	0.106363i	−0.329818	−	0.944045i	$-0.606987\pi$
$47$	−6.00539	−	0.729187i	−0.875977	−	0.106363i	−0.546159	+	0.837682i	$0.683910\pi$
$48$	3.65229	+	2.74452i	0.527163	+	0.396137i
$49$	−3.94795	+	4.83536i	−0.563993	+	0.690766i
$50$	−4.95316	−	4.04413i	−0.700482	−	0.571926i
$51$	1.79500	+	2.60051i	0.251350	+	0.364144i
$52$	−0.528441	−	1.11872i	−0.0732816	−	0.155139i
$53$	0.296634	−	0.429748i	0.0407458	−	0.0590304i	−0.802082	−	0.597215i	$-0.796274\pi$
$53$	0.296634	−	0.429748i	0.0407458	−	0.0590304i	0.842827	+	0.538184i	$0.180889\pi$
$54$	1.47030	−	0.425877i	0.200082	−	0.0579546i
$55$	−0.525006	−	0.331994i	−0.0707918	−	0.0447660i
$56$	2.17899	+	0.354120i	0.291179	+	0.0473212i
$57$	2.45160	+	0.929771i	0.324723	+	0.123151i
$58$	4.77041	−	11.1966i	0.626385	−	1.47018i
$59$	9.80531	+	9.41813i	1.27654	+	1.22614i	0.960784	+	0.277297i	$0.0894384\pi$
$59$	9.80531	+	9.41813i	1.27654	+	1.22614i	0.315759	+	0.948840i	$0.397741\pi$
$60$	0.144639	−	0.275586i	0.0186728	−	0.0355780i
$61$	−6.60451	+	0.533171i	−0.845621	+	0.0682656i	−0.495679	−	0.868506i	$-0.665081\pi$
$61$	−6.60451	+	0.533171i	−0.845621	+	0.0682656i	−0.349942	+	0.936771i	$0.613799\pi$
$62$	0.134488	+	0.464306i	0.0170800	+	0.0589669i
$63$	0.627754	−	0.602966i	0.0790895	−	0.0759665i
$64$	2.19741	+	5.79410i	0.274677	+	0.724263i
$65$	2.69459	−	1.85298i	0.334222	−	0.229834i
$66$	−0.371749	+	0.980222i	−0.0457591	+	0.120657i
$67$	3.39819	+	7.97585i	0.415155	+	0.974405i	0.987959	+	0.154713i	$0.0494453\pi$
$67$	3.39819	+	7.97585i	0.415155	+	0.974405i	−0.572804	+	0.819692i	$0.694144\pi$
$68$	−0.0436606	−	1.08343i	−0.00529462	−	0.131385i
$69$	−5.86533	−	7.18373i	−0.706103	−	0.864819i
$70$		−	1.20847i		−	0.144440i
$71$	−2.47011	+	2.01678i	−0.293148	+	0.239348i	−0.767594	−	0.640937i	$-0.778546\pi$
$71$	−2.47011	+	2.01678i	−0.293148	+	0.239348i	0.474446	+	0.880285i	$0.342649\pi$
$72$	2.43606	+	0.705614i	0.287093	+	0.0831575i
$73$	0.513272	+	0.579364i	0.0600739	+	0.0678095i	0.777779	−	0.628537i	$-0.216346\pi$
$73$	0.513272	+	0.579364i	0.0600739	+	0.0678095i	−0.717706	+	0.696347i	$0.754808\pi$
$74$	5.24342	−	5.45898i	0.609535	−	0.634593i
$75$	−3.96238	−	1.32284i	−0.457536	−	0.152748i
$76$	−0.540511	−	0.719290i	−0.0620009	−	0.0825082i
$77$	0.0718549	+	0.591778i	0.00818862	+	0.0674394i
$78$	−3.97372	−	3.83021i	−0.449935	−	0.433686i
$79$	1.41139	−	11.6238i	0.158794	−	1.30778i	−0.667529	−	0.744584i	$-0.732648\pi$
$79$	1.41139	−	11.6238i	0.158794	−	1.30778i	0.826322	−	0.563198i	$-0.190429\pi$
$80$	3.58851	−	2.07183i	0.401207	−	0.231637i
$81$	0.799443	−	0.600742i	0.0888270	−	0.0667491i
$82$	0.468582	−	11.6277i	0.0517462	−	1.28407i
$83$	−8.68714	+	3.29460i	−0.953537	+	0.361629i	−0.781811	−	0.623516i	$-0.785704\pi$
$83$	−8.68714	+	3.29460i	−0.953537	+	0.361629i	−0.171726	+	0.985145i	$0.554934\pi$
$84$	−0.292651	+	0.0597452i	−0.0319309	+	0.00651874i
$85$	2.80805	−	0.573267i	0.304576	−	0.0621796i
$86$	−1.36531	+	0.517793i	−0.147225	+	0.0558350i
$87$	0.320143	−	7.94427i	0.0343229	−	0.851715i
$88$	−1.38859	+	1.04346i	−0.148025	+	0.111233i
$89$	−15.1749	+	8.76121i	−1.60853	+	0.928687i	−0.618833	+	0.785522i	$0.712394\pi$
$89$	−15.1749	+	8.76121i	−1.60853	+	0.928687i	−0.989699	+	0.143164i	$0.954272\pi$
$90$	0.167349	−	1.37825i	0.0176402	−	0.145280i
$91$	−3.01293	−	0.878426i	−0.315840	−	0.0920841i
$92$	0.383596	+	3.15920i	0.0399926	+	0.329369i
$93$	0.189708	+	0.252456i	0.0196718	+	0.0261785i
$94$	8.78362	+	2.93240i	0.905962	+	0.302454i
$95$	1.64739	−	1.71512i	0.169019	−	0.175967i
$96$	−1.27376	−	1.43777i	−0.130002	−	0.146742i
$97$	6.54695	+	1.89635i	0.664742	+	0.192545i	0.593401	−	0.804907i	$-0.297785\pi$
$97$	6.54695	+	1.89635i	0.664742	+	0.192545i	0.0713413	+	0.997452i	$0.477272\pi$
$98$	7.40166	−	6.04327i	0.747680	−	0.610462i
$99$			0.684865i			0.0688315i
$100$	0.906588	+	1.11037i	0.0906588	+	0.111037i
$101$	0.108610	+	2.69513i	0.0108071	+	0.268175i	0.995555	+	0.0941860i	$0.0300248\pi$
$101$	0.108610	+	2.69513i	0.0108071	+	0.268175i	−0.984748	+	0.173989i	$0.944334\pi$
$102$	−1.89590	−	4.44984i	−0.187722	−	0.440600i
$103$	3.47481	−	9.16233i	0.342384	−	0.902792i	−0.647647	−	0.761940i	$-0.724247\pi$
$103$	3.47481	−	9.16233i	0.342384	−	0.902792i	0.990031	−	0.140851i	$-0.0449839\pi$
$104$	−2.17284	−	8.88249i	−0.213065	−	0.871000i
$105$	−0.279951	−	0.738170i	−0.0273204	−	0.0720380i
$106$	−0.576474	+	0.553711i	−0.0559921	+	0.0537812i
$107$	−4.49331	−	15.5127i	−0.434385	−	1.49967i	−0.817478	−	0.575960i	$-0.804628\pi$
$107$	−4.49331	−	15.5127i	−0.434385	−	1.49967i	0.383093	−	0.923710i	$-0.374859\pi$
$108$	−0.342038	+	0.0276122i	−0.0329126	+	0.00265698i
$109$	−6.02566	+	11.4809i	−0.577153	+	1.09967i	0.405478	+	0.914105i	$0.367105\pi$
$109$	−6.02566	+	11.4809i	−0.577153	+	1.09967i	−0.982631	+	0.185569i	$0.940587\pi$
$110$	0.685752	+	0.658674i	0.0653839	+	0.0628021i
$111$	1.93822	−	4.54917i	0.183968	−	0.431788i
$112$	−3.71817	−	1.41012i	−0.351334	−	0.133244i
$113$	14.1973	+	2.30728i	1.33557	+	0.217051i	0.785910	−	0.618341i	$-0.212195\pi$
$113$	14.1973	+	2.30728i	1.33557	+	0.217051i	0.549656	+	0.835391i	$0.314759\pi$
$114$	−3.39223	−	2.14512i	−0.317712	−	0.200909i
$115$	−8.07942	+	2.34023i	−0.753410	+	0.218228i
$116$	−1.54985	+	2.24534i	−0.143900	+	0.208475i
$117$	−3.31455	−	1.41906i	−0.306431	−	0.131192i
$118$	−11.8223	−	17.1276i	−1.08833	−	1.57672i
$119$	−2.13049	−	1.73949i	−0.195301	−	0.159459i
$120$	1.45483	−	1.78184i	0.132807	−	0.162659i
$121$	8.41890	+	6.32639i	0.765355	+	0.575127i
$122$	10.0687	+	1.22256i	0.911577	+	0.110686i
$123$	−2.40742	−	7.21110i	−0.217070	−	0.650203i
$124$	−0.00871965	−	0.108012i	−0.000783047	−	0.00969978i
$125$	−5.51971	+	6.23047i	−0.493698	+	0.557270i
$126$	−1.12613	+	0.712118i	−0.100323	+	0.0634406i
$127$	19.0524	−	8.11749i	1.69063	−	0.720310i	0.690635	−	0.723204i	$-0.257331\pi$
$127$	19.0524	−	8.11749i	1.69063	−	0.720310i	0.999996	+	0.00289350i	$0.000921031\pi$
$128$	−2.13786	−	13.1548i	−0.188962	−	1.16273i
$129$	−0.714018	+	0.632565i	−0.0628658	+	0.0556942i
$130$	−4.60870	+	1.95405i	−0.404210	+	0.171382i
$131$	−5.70138	−	5.05098i	−0.498132	−	0.441307i	0.376269	−	0.926511i	$-0.377207\pi$
$131$	−5.70138	−	5.05098i	−0.498132	−	0.441307i	−0.874401	+	0.485204i	$0.838745\pi$
$132$	0.125606	−	0.198630i	0.0109326	−	0.0172885i
$133$	−2.27485	−	0.183645i	−0.197255	−	0.0159240i
$134$	−2.65451	−	13.0027i	−0.229315	−	1.12326i
$135$	−0.217058	−	0.880640i	−0.0186814	−	0.0757934i
$136$	1.28554	−	7.91022i	0.110234	−	0.678296i
$137$	−2.62380	−	4.14921i	−0.224167	−	0.354491i	0.714313	−	0.699827i	$-0.246739\pi$
$137$	−2.62380	−	4.14921i	−0.224167	−	0.354491i	−0.938479	+	0.345336i	$0.887765\pi$
$138$	6.59726	+	12.5700i	0.561596	+	1.07003i
$139$	−2.95745	+	10.2103i	−0.250848	+	0.866027i	0.731953	+	0.681355i	$0.238609\pi$
$139$	−2.95745	+	10.2103i	−0.250848	+	0.866027i	−0.982800	+	0.184671i	$0.940878\pi$
$140$	−0.0541886	+	0.265434i	−0.00457978	+	0.0224332i
$141$	6.04460	−	0.243589i	0.509047	−	0.0205139i
$142$	4.32218	−	2.26846i	0.362709	−	0.190365i
$143$	2.14065	−	1.23091i	0.179010	−	0.102934i
$144$	−4.04525	−	2.12311i	−0.337104	−	0.176926i
$145$	−6.51502	−	3.09141i	−0.541043	−	0.256728i
$146$	−0.592412	−	1.02609i	−0.0490284	−	0.0849196i
$147$	3.12118	−	5.40604i	0.257430	−	0.445883i
$148$	−1.39647	+	0.963911i	−0.114789	+	0.0792330i
$149$	0.620924	−	0.826300i	0.0508681	−	0.0676931i	−0.773292	−	0.634050i	$-0.781391\pi$
$149$	0.620924	−	0.826300i	0.0508681	−	0.0676931i	0.824160	+	0.566357i	$0.191648\pi$
$150$	5.53774	+	3.19722i	0.452155	+	0.261052i
$151$	−8.46301	+	1.02760i	−0.688710	+	0.0836246i	−0.457407	−	0.889257i	$-0.651222\pi$
$151$	−8.46301	+	1.02760i	−0.688710	+	0.0836246i	−0.231303	+	0.972882i	$0.574299\pi$
$152$	−2.85076	−	6.00784i	−0.231227	−	0.487300i
$153$	−2.18890	−	2.27889i	−0.176962	−	0.184237i
$154$	0.0734265	−	0.909550i	0.00591687	−	0.0732936i
$155$	0.278097	−	0.0685448i	0.0223373	−	0.00550565i
$156$	0.701053	+	1.01946i	0.0561292	+	0.0816225i
$157$	−17.3497	−	4.27632i	−1.38466	−	0.341288i	−0.524542	−	0.851385i	$-0.675763\pi$
$157$	−17.3497	−	4.27632i	−1.38466	−	0.341288i	−0.860117	+	0.510097i	$0.829609\pi$
$158$	−5.67586	+	17.0013i	−0.451547	+	1.35255i
$159$	−0.223856	+	0.471766i	−0.0177529	+	0.0374135i
$160$	−1.65254	+	0.551698i	−0.130645	+	0.0436156i
$161$	6.64344	+	4.58563i	0.523576	+	0.361399i
$162$	−1.38294	+	0.656215i	−0.108654	+	0.0515571i
$163$	5.75916	+	0.232086i	0.451093	+	0.0181784i	0.264773	−	0.964311i	$-0.414703\pi$
$163$	5.75916	+	0.232086i	0.451093	+	0.0181784i	0.186320	+	0.982489i	$0.440344\pi$
$164$	−0.624316	+	2.53295i	−0.0487509	+	0.197790i
$165$	0.571463	+	0.243478i	0.0444883	+	0.0189547i
$166$	14.0377	−	2.28135i	1.08954	−	0.177067i
$167$	13.8782	+	2.83326i	1.07393	+	0.219244i	0.704277	−	0.709926i	$-0.251271\pi$
$167$	13.8782	+	2.83326i	1.07393	+	0.219244i	0.369653	+	0.929170i	$0.379477\pi$
$168$	−2.20757			−0.170318
$169$	1.52177	+	12.9106i	0.117059	+	0.993125i
$170$	−4.38704			−0.336471
$171$	−2.56900	−	0.524466i	−0.196457	−	0.0401069i
$172$	0.323099	−	0.0525087i	0.0246361	−	0.00400375i
$173$	−20.2948	−	8.64681i	−1.54299	−	0.657405i	−0.557968	−	0.829862i	$-0.688419\pi$
$173$	−20.2948	−	8.64681i	−1.54299	−	0.657405i	−0.985017	+	0.172458i	$0.944829\pi$
$174$	−2.91258	+	11.8168i	−0.220802	+	0.895829i
$175$	3.63314	+	0.146410i	0.274639	+	0.0110676i
$176$	2.82675	−	1.34131i	0.213074	−	0.101105i
$177$	−11.1891	−	7.72329i	−0.841025	−	0.580518i
$178$	25.4418	−	8.49373i	1.90695	−	0.636632i
$179$	1.91005	−	4.02535i	0.142764	−	0.300868i	−0.819456	−	0.573142i	$-0.805724\pi$
$179$	1.91005	−	4.02535i	0.142764	−	0.300868i	0.962220	+	0.272274i	$0.0877756\pi$
$180$	−0.0985586	+	0.295219i	−0.00734612	+	0.0220043i
$181$	19.3412	+	4.76717i	1.43762	+	0.354341i	0.879690	−	0.475548i	$-0.157750\pi$
$181$	19.3412	+	4.76717i	1.43762	+	0.354341i	0.557928	+	0.829889i	$0.311597\pi$
$182$	4.24982	+	2.23998i	0.315018	+	0.166038i
$183$	6.43346	−	1.58571i	0.475575	−	0.117219i
$184$	−1.89264	+	23.4446i	−0.139527	+	1.72836i
$185$	−3.10684	−	3.23457i	−0.228420	−	0.237810i
$186$	−0.207226	−	0.436720i	−0.0151945	−	0.0320218i
$187$	2.14829	−	0.260850i	0.157099	−	0.0190752i
$188$	−1.79778	−	1.03795i	−0.131116	−	0.0757000i
$189$	−0.522902	+	0.695856i	−0.0380355	+	0.0506161i
$190$	−2.99590	+	2.06792i	−0.217346	+	0.150023i
$191$	2.98401	−	5.16845i	0.215915	−	0.373976i	−0.737640	−	0.675194i	$-0.764060\pi$
$191$	2.98401	−	5.16845i	0.215915	−	0.373976i	0.953555	+	0.301218i	$0.0973932\pi$
$192$	−3.09840	−	5.36658i	−0.223607	−	0.387300i
$193$	−8.15219	−	3.86826i	−0.586808	−	0.278444i	0.112052	−	0.993702i	$-0.464258\pi$
$193$	−8.15219	−	3.86826i	−0.586808	−	0.278444i	−0.698860	+	0.715259i	$0.746309\pi$
$194$	−9.23848	−	4.84873i	−0.663284	−	0.348119i
$195$	−2.36245	+	2.26123i	−0.169179	+	0.161930i
$196$	−1.89671	+	0.995470i	−0.135479	+	0.0711050i
$197$	1.34442	−	0.0541784i	0.0957862	−	0.00386005i	0.00767346	−	0.999971i	$-0.497557\pi$
$197$	1.34442	−	0.0541784i	0.0957862	−	0.00386005i	0.0881128	+	0.996111i	$0.471916\pi$
$198$	0.209696	−	1.02716i	0.0149025	−	0.0729971i
$199$	−3.89308	+	13.4405i	−0.275973	+	0.952770i	0.696071	+	0.717973i	$0.254930\pi$
$199$	−3.89308	+	13.4405i	−0.275973	+	0.952770i	−0.972044	+	0.234797i	$0.924557\pi$
$200$	4.92356	+	9.38106i	0.348148	+	0.663341i
$201$	−4.63360	−	7.32746i	−0.326829	−	0.516839i
$202$	0.662319	−	4.07541i	0.0466006	−	0.286745i
$203$	1.65619	+	6.71942i	0.116242	+	0.471611i
$204$	0.216889	+	1.06239i	0.0151853	+	0.0743823i
$205$	−6.87293	−	0.554841i	−0.480027	−	0.0387518i
$206$	−8.01691	+	12.6777i	−0.558565	+	0.883299i
$207$	6.94173	+	6.14983i	0.482483	+	0.427443i
$208$	0.634444	+	16.4599i	0.0439907	+	1.14129i
$209$	1.34411	−	1.19078i	0.0929739	−	0.0823677i
$210$	0.193853	+	1.19282i	0.0133771	+	0.0823127i
$211$	1.14480	−	0.487755i	0.0788115	−	0.0335784i	−0.352201	−	0.935924i	$-0.614567\pi$
$211$	1.14480	−	0.487755i	0.0788115	−	0.0335784i	0.431013	+	0.902346i	$0.358156\pi$
$212$	0.151448	−	0.0957697i	0.0104015	−	0.00657749i
$213$	2.11461	−	2.38690i	0.144891	−	0.163548i
$214$	1.98929	+	24.6418i	0.135985	+	1.68448i
$215$	0.273981	+	0.820673i	0.0186853	+	0.0559694i
$216$	−2.51771	−	0.305705i	−0.171308	−	0.0208006i
$217$	−0.219744	−	0.165127i	−0.0149172	−	0.0112096i
$218$	12.5526	−	15.3741i	0.850168	−	1.04127i
$219$	−0.599562	−	0.489527i	−0.0405146	−	0.0330792i
$220$	−0.121086	−	0.175423i	−0.00816360	−	0.0118270i
$221$	−3.18889	+	10.9376i	−0.214508	+	0.735744i
$222$	−4.29984	+	6.22939i	−0.288586	+	0.418089i
$223$	11.1149	−	3.21948i	0.744311	−	0.215592i	0.115670	−	0.993288i	$-0.463099\pi$
$223$	11.1149	−	3.21948i	0.744311	−	0.215592i	0.628641	+	0.777696i	$0.283611\pi$
$224$	1.41312	+	0.893603i	0.0944180	+	0.0597064i
$225$	4.12326	+	0.670096i	0.274884	+	0.0446730i
$226$	−20.5866	−	7.80747i	−1.36940	−	0.519345i
$227$	6.03208	−	14.1578i	0.400363	−	0.939687i	−0.590773	−	0.806838i	$-0.701177\pi$
$227$	6.03208	−	14.1578i	0.400363	−	0.939687i	0.991136	−	0.132849i	$-0.0424126\pi$
$228$	0.648894	+	0.623271i	0.0429741	+	0.0412771i
$229$	−1.53957	+	2.93341i	−0.101738	+	0.193845i	−0.931004	−	0.365008i	$-0.881066\pi$
$229$	−1.53957	+	2.93341i	−0.101738	+	0.193845i	0.829267	+	0.558853i	$0.188759\pi$
$230$	12.8341	−	1.03607i	0.846253	−	0.0683166i
$231$	−0.165852	−	0.572589i	−0.0109123	−	0.0376736i
$232$	−14.5427	+	13.9685i	−0.954778	+	0.917077i
$233$	6.03875	+	15.9229i	0.395612	+	1.04314i	0.973834	+	0.227262i	$0.0729775\pi$
$233$	6.03875	+	15.9229i	0.395612	+	1.04314i	−0.578222	+	0.815879i	$0.696253\pi$
$234$	4.53667	+	3.14318i	0.296571	+	0.205476i
$235$	1.94567	−	5.13031i	0.126922	−	0.334665i
$236$	1.82868	+	4.29208i	0.119037	+	0.279390i
$237$	0.471482	+	11.6997i	0.0306260	+	0.759977i
$238$	2.66270	+	3.26121i	0.172597	+	0.211393i
$239$			25.2733i			1.63479i	0.576077	+	0.817395i	$0.304583\pi$
$239$			25.2733i			1.63479i	−0.576077	+	0.817395i	$0.695417\pi$
$240$	−3.20969	+	2.62063i	−0.207185	+	0.169161i
$241$	−5.36483	−	1.55394i	−0.345579	−	0.100098i	0.100889	−	0.994898i	$-0.467831\pi$
$241$	−5.36483	−	1.55394i	−0.345579	−	0.100098i	−0.446468	+	0.894799i	$0.647318\pi$
$242$	−10.6896	−	12.0661i	−0.687154	−	0.775637i
$243$	−0.692724	+	0.721202i	−0.0444383	+	0.0462652i
$244$	−2.15670	−	0.720014i	−0.138069	−	0.0460942i
$245$	−3.40128	−	4.52628i	−0.217300	−	0.289173i
$246$	1.40271	+	11.5523i	0.0894334	+	0.736550i
$247$	2.97798	+	8.97243i	0.189485	+	0.570902i
$248$	0.0965385	−	0.795066i	0.00613020	−	0.0504867i
$249$	8.04615	−	4.64545i	0.509904	−	0.294393i
$250$	10.1862	−	7.65440i	0.644229	−	0.484107i
$251$	0.856857	−	21.2627i	0.0540844	−	1.34209i	−0.713280	−	0.700879i	$-0.752791\pi$
$251$	0.856857	−	21.2627i	0.0540844	−	1.34209i	0.767365	−	0.641211i	$-0.221568\pi$
$252$	0.279278	−	0.105916i	0.0175929	−	0.00667209i
$253$	−6.22311	+	1.27046i	−0.391244	+	0.0798730i
$254$	−31.0603	+	6.34101i	−1.94890	+	0.397870i
$255$	−2.67973	+	1.01629i	−0.167811	+	0.0636423i
$256$	−0.322411	+	8.00055i	−0.0201507	+	0.500035i
$257$	1.29196	−	0.970847i	0.0805904	−	0.0605598i	−0.559683	−	0.828706i	$-0.689077\pi$
$257$	1.29196	−	0.970847i	0.0805904	−	0.0605598i	0.640274	+	0.768147i	$0.278821\pi$
$258$	1.26457	−	0.730098i	0.0787285	−	0.0454539i
$259$	−0.518806	+	4.27275i	−0.0322371	+	0.265496i
$260$	1.09989	−	0.222539i	0.0682124	−	0.0138013i
$261$	0.958353	+	7.89275i	0.0593205	+	0.488549i
$262$	7.00439	+	9.32115i	0.432733	+	0.575863i
$263$	−7.51405	−	2.50856i	−0.463336	−	0.154684i	0.0754096	−	0.997153i	$-0.475974\pi$
$263$	−7.51405	−	2.50856i	−0.463336	−	0.154684i	−0.538746	+	0.842468i	$0.681102\pi$
$264$	1.20323	−	1.25269i	0.0740537	−	0.0770980i
$265$	0.314066	+	0.354508i	0.0192930	+	0.0217772i
$266$	3.35559	+	0.971959i	0.205745	+	0.0595946i
$267$	13.5730	−	11.0820i	0.830651	−	0.678206i
$268$			2.97498i			0.181726i
$269$	12.5384	+	15.3567i	0.764477	+	0.936314i	0.999362	−	0.0357089i	$-0.0113689\pi$
$269$	12.5384	+	15.3567i	0.764477	+	0.936314i	−0.234885	+	0.972023i	$0.575471\pi$
$270$	0.0559040	+	1.38724i	0.00340221	+	0.0844250i
$271$	1.07376	+	2.52022i	0.0652265	+	0.153092i	0.949403	−	0.314061i	$-0.101690\pi$
$271$	1.07376	+	2.52022i	0.0652265	+	0.153092i	−0.884176	+	0.467154i	$0.845280\pi$
$272$	−5.11905	+	13.4978i	−0.310388	+	0.818426i
$273$	3.11482	+	0.383743i	0.188517	+	0.0232252i
$274$	2.66475	+	7.02636i	0.160983	+	0.424478i
$275$	−2.06331	+	1.98183i	−0.124422	+	0.119509i
$276$	−0.885399	−	3.05675i	−0.0532948	−	0.183995i
$277$	5.36448	−	0.433065i	0.322320	−	0.0260204i	0.0817523	−	0.996653i	$-0.473948\pi$
$277$	5.36448	−	0.433065i	0.322320	−	0.0260204i	0.240568	+	0.970632i	$0.422666\pi$
$278$	7.56184	−	14.4079i	0.453529	−	0.864127i
$279$	−0.227748	−	0.218755i	−0.0136349	−	0.0130965i
$280$	−0.784819	+	1.84204i	−0.0469019	+	0.110083i
$281$	−16.3057	−	6.18394i	−0.972717	−	0.368903i	−0.183502	−	0.983019i	$-0.558743\pi$
$281$	−16.3057	−	6.18394i	−0.972717	−	0.368903i	−0.789215	+	0.614117i	$0.789512\pi$
$282$	−9.14027	−	1.48544i	−0.544295	−	0.0884566i
$283$	19.9709	+	12.6288i	1.18715	+	0.750706i	0.974052	−	0.226325i	$-0.0726712\pi$
$283$	19.9709	+	12.6288i	1.18715	+	0.750706i	0.213095	+	0.977031i	$0.431646\pi$
$284$	−1.05106	+	0.304443i	−0.0623688	+	0.0180654i
$285$	−1.35093	+	1.95717i	−0.0800224	+	0.115932i
$286$	−3.58743	+	1.19068i	−0.212129	+	0.0704066i
$287$	3.75905	+	5.44592i	0.221890	+	0.321462i
$288$	1.48790	+	1.21483i	0.0876751	+	0.0715845i
$289$	4.43683	−	5.43413i	0.260990	−	0.319654i
$290$	8.82468	+	6.63131i	0.518203	+	0.389404i
$291$	−6.76637	−	0.821586i	−0.396651	−	0.0481622i
$292$	0.0841091	+	0.251938i	0.00492211	+	0.0147435i
$293$	−1.01710	−	12.5991i	−0.0594197	−	0.736045i	−0.956038	−	0.293241i	$-0.905266\pi$
$293$	−1.01710	−	12.5991i	−0.0594197	−	0.736045i	0.896619	−	0.442803i	$-0.146016\pi$
$294$	−6.33640	+	7.15232i	−0.369546	+	0.417132i
$295$	−10.4223	+	6.59066i	−0.606810	+	0.383723i
$296$	−11.5376	+	4.91571i	−0.670609	+	0.285720i
$297$	−0.109860	−	0.675996i	−0.00637473	−	0.0392253i
$298$	−1.18426	+	1.04917i	−0.0686026	+	0.0607766i
$299$	6.74583	−	32.7505i	0.390122	−	1.89401i
$300$	−1.07296	−	0.950563i	−0.0619476	−	0.0548808i
$301$	0.443775	−	0.701775i	0.0255788	−	0.0404496i
$302$	13.0075	+	1.05007i	0.748496	+	0.0604248i
$303$	−0.539533	−	2.64281i	−0.0309954	−	0.151825i
$304$	2.86669	+	11.6306i	0.164416	+	0.667062i
$305$	0.964032	−	5.93192i	0.0552003	−	0.339661i
$306$	2.58515	+	4.08809i	0.147783	+	0.233701i
$307$	−2.06572	−	3.93590i	−0.117897	−	0.224634i	0.819355	−	0.573286i	$-0.194332\pi$
$307$	−2.06572	−	3.93590i	−0.117897	−	0.224634i	−0.937252	+	0.348652i	$0.886639\pi$
$308$	−0.0569124	+	0.196484i	−0.00324288	+	0.0111957i
$309$	−1.96008	+	9.60108i	−0.111505	+	0.546187i
$310$	−0.438078	+	0.0176539i	−0.0248811	+	0.00100268i
$311$	22.1549	−	11.6278i	1.25629	−	0.659352i	0.300606	−	0.953748i	$-0.402811\pi$
$311$	22.1549	−	11.6278i	1.25629	−	0.659352i	0.955683	+	0.294397i	$0.0951187\pi$
$312$	3.56956	+	8.41891i	0.202086	+	0.476627i
$313$	−17.8251	−	9.35533i	−1.00753	−	0.528794i	−0.121586	−	0.992581i	$-0.538798\pi$
$313$	−17.8251	−	9.35533i	−1.00753	−	0.528794i	−0.885947	+	0.463787i	$0.846490\pi$
$314$	24.7118	+	11.7259i	1.39457	+	0.661730i
$315$	0.394736	+	0.683704i	0.0222409	+	0.0385223i
$316$	2.00901	−	3.47971i	0.113016	−	0.195749i
$317$	−3.04951	+	2.10493i	−0.171278	+	0.118225i	−0.650620	−	0.759404i	$-0.725491\pi$
$317$	−3.04951	+	2.10493i	−0.171278	+	0.118225i	0.479342	+	0.877628i	$0.340875\pi$
$318$	0.480188	−	0.639014i	0.0269276	−	0.0358341i
$319$	−4.71565	−	2.72258i	−0.264026	−	0.152435i
$320$	−5.57948	+	0.677472i	−0.311903	+	0.0378718i
$321$	6.92354	+	14.5910i	0.386434	+	0.814393i
$322$	−8.55977	−	8.91167i	−0.477017	−	0.496628i
$323$	−0.666673	+	8.25823i	−0.0370947	+	0.459500i
$324$	0.333180	−	0.0821214i	0.0185100	−	0.00456230i
$325$	−5.31628	−	14.0923i	−0.294894	−	0.781697i
$326$	−8.56654	−	2.11146i	−0.474457	−	0.116943i
$327$	4.10595	−	12.2988i	0.227060	−	0.680127i
$328$	−8.26565	+	17.4195i	−0.456394	+	0.961830i
$329$	−4.99466	+	1.66746i	−0.275364	+	0.0919302i
$330$	−0.782531	−	0.540142i	−0.0430769	−	0.0297338i
$331$	31.3191	−	14.8611i	1.72145	−	0.816840i	0.730455	−	0.682960i	$-0.239308\pi$
$331$	31.3191	−	14.8611i	1.72145	−	0.816840i	0.990998	−	0.133879i	$-0.0427434\pi$
$332$	−3.18559	−	0.128375i	−0.174832	−	0.00704549i
$333$	−1.18338	+	4.80117i	−0.0648489	+	0.263102i
$334$	−19.9471	−	8.49865i	−1.09145	−	0.465025i
$335$	−7.76146	+	1.26136i	−0.424054	+	0.0689154i
$336$	3.89622	+	0.795420i	0.212556	+	0.0433937i
$337$	8.73626			0.475894			0.237947	−	0.971278i	$-0.423526\pi$
$337$	8.73626			0.475894			0.237947	+	0.971278i	$0.423526\pi$
$338$	1.67071	−	19.8293i	0.0908745	−	1.07857i
$339$	−14.3835			−0.781206
$340$	0.963585	+	0.196717i	0.0522577	+	0.0106685i
$341$	0.213473	−	0.0346927i	0.0115602	−	0.00187871i
$342$	3.69241	+	1.57319i	0.199662	+	0.0850682i
$343$	−2.75847	+	11.1916i	−0.148943	+	0.604288i
$344$	2.41736	+	0.0974164i	0.130335	+	0.00525234i
$345$	7.59939	−	3.60596i	0.409137	−	0.194138i
$346$	27.7906	+	19.1825i	1.49403	+	1.03126i
$347$	−4.08276	+	1.36303i	−0.219174	+	0.0731711i	−0.424135	−	0.905599i	$-0.639422\pi$
$347$	−4.08276	+	1.36303i	−0.219174	+	0.0731711i	0.204960	+	0.978770i	$0.434293\pi$
$348$	1.16960	−	2.46488i	0.0626971	−	0.132131i
$349$	−1.00189	+	3.00102i	−0.0536298	+	0.160641i	−0.971945	−	0.235210i	$-0.924422\pi$
$349$	−1.00189	+	3.00102i	−0.0536298	+	0.160641i	0.918315	+	0.395851i	$0.129550\pi$
$350$	−5.40415	−	1.33200i	−0.288864	−	0.0711986i
$351$	3.49926	+	0.868994i	0.186777	+	0.0463835i
$352$	−1.27729	+	0.314824i	−0.0680800	+	0.0167802i
$353$	0.0994830	−	1.23232i	0.00529495	−	0.0655897i	−0.993570	−	0.113218i	$-0.963884\pi$
$353$	0.0994830	−	1.23232i	0.00529495	−	0.0655897i	0.998865	+	0.0476282i	$0.0151663\pi$
$354$	14.4167	+	15.0093i	0.766237	+	0.797737i
$355$	−1.23990	−	2.61304i	−0.0658071	−	0.138686i
$356$	−5.96900	+	0.724767i	−0.316356	+	0.0384126i
$357$	2.38193	+	1.37521i	0.126065	+	0.0727838i
$358$	−4.09720	+	5.45238i	−0.216544	+	0.288167i
$359$	−29.1855	+	20.1453i	−1.54035	+	1.06323i	−0.569966	+	0.821668i	$0.693044\pi$
$359$	−29.1855	+	20.1453i	−1.54035	+	1.06323i	−0.970386	+	0.241560i	$0.922341\pi$
$360$	−1.15016	+	1.99213i	−0.0606187	+	0.104995i
$361$	−6.06258	−	10.5007i	−0.319083	−	0.552668i
$362$	−27.5482	−	13.0718i	−1.44790	−	0.687039i
$363$	−9.32470	−	4.89398i	−0.489420	−	0.256867i
$364$	−0.833004	−	0.682562i	−0.0436613	−	0.0357760i
$365$	−0.621621	+	0.326252i	−0.0325371	+	0.0170768i
$366$	−10.1344	+	0.408403i	−0.529735	+	0.0213476i
$367$	5.87509	−	28.7781i	0.306677	−	1.50220i	−0.475816	−	0.879545i	$-0.657847\pi$
$367$	5.87509	−	28.7781i	0.306677	−	1.50220i	0.782493	−	0.622659i	$-0.213948\pi$
$368$	11.7878	−	40.6961i	0.614481	−	2.12143i
$369$	3.53299	+	6.73154i	0.183920	+	0.350430i
$370$	3.66926	+	5.80248i	0.190756	+	0.301656i
$371$	0.0729104	−	0.448636i	0.00378532	−	0.0232920i
$372$	0.0259331	+	0.105215i	0.00134457	+	0.00545513i
$373$	−1.10947	−	5.43454i	−0.0574462	−	0.281390i	0.940913	−	0.338648i	$-0.109969\pi$
$373$	−1.10947	−	5.43454i	−0.0574462	−	0.281390i	−0.998359	+	0.0572577i	$0.981764\pi$
$374$	−3.30188	−	0.266555i	−0.170736	−	0.0137832i
$375$	4.44880	−	7.03521i	0.229735	−	0.363297i
$376$	−11.4842	−	10.1741i	−0.592252	−	0.524690i
$377$	22.9475	−	17.1811i	1.18186	−	0.884874i
$378$	0.997310	−	0.883540i	0.0512961	−	0.0454444i
$379$	−0.667343	−	4.10633i	−0.0342791	−	0.210928i	0.964260	−	0.264957i	$-0.0853577\pi$
$379$	−0.667343	−	4.10633i	−0.0342791	−	0.210928i	−0.998539	+	0.0540290i	$0.982794\pi$
$380$	0.750758	−	0.319868i	0.0385130	−	0.0164089i
$381$	−17.5036	+	11.0686i	−0.896735	+	0.567061i
$382$	−6.05793	+	6.83799i	−0.309950	+	0.349862i
$383$	2.76525	+	34.2538i	0.141298	+	1.75029i	0.547774	+	0.836626i	$0.315475\pi$
$383$	2.76525	+	34.2538i	0.141298	+	1.75029i	−0.406476	+	0.913661i	$0.633242\pi$
$384$	4.22034	+	12.6415i	0.215368	+	0.645107i
$385$	−0.536740	−	0.0651720i	−0.0273548	−	0.00332148i
$386$	11.0423	+	8.29771i	0.562036	+	0.422343i
$387$	0.603301	−	0.738910i	0.0306675	−	0.0375609i
$388$	1.81175	+	1.47925i	0.0919778	+	0.0750976i
$389$	−10.2705	−	14.8793i	−0.520733	−	0.754412i	0.471083	−	0.882089i	$-0.343863\pi$
$389$	−10.2705	−	14.8793i	−0.520733	−	0.754412i	−0.991816	+	0.127677i	$0.959248\pi$
$390$	4.23556	−	2.66804i	0.214476	−	0.135101i
$391$	16.6469	−	24.1172i	0.841870	−	1.21966i
$392$	−15.2068	+	4.40470i	−0.768058	+	0.222471i
$393$	6.43779	+	4.07101i	0.324743	+	0.205355i
$394$	−2.03296	−	0.330387i	−0.102419	−	0.0166447i
$395$	9.93005	+	3.76597i	0.499635	+	0.189486i
$396$	−0.0921169	+	0.216206i	−0.00462905	+	0.0108648i
$397$	−23.2067	−	22.2903i	−1.16471	−	1.11872i	−0.990992	−	0.133923i	$-0.957242\pi$
$397$	−23.2067	−	22.2903i	−1.16471	−	1.11872i	−0.173718	−	0.984795i	$-0.555578\pi$
$398$	9.95413	−	18.9660i	0.498956	−	0.950681i
$399$	2.27485	−	0.183645i	0.113885	−	0.00919374i
$400$	−5.30963	−	18.3310i	−0.265482	−	0.916549i
$401$	−2.62969	+	2.52585i	−0.131320	+	0.126135i	−0.755508	−	0.655140i	$-0.772610\pi$
$401$	−2.62969	+	2.52585i	−0.131320	+	0.126135i	0.624187	+	0.781275i	$0.285430\pi$
$402$	4.70591	+	12.4085i	0.234710	+	0.618878i
$403$	−0.274419	+	1.10503i	−0.0136698	+	0.0550456i
$404$	−0.328218	+	0.865439i	−0.0163294	+	0.0430572i
$405$	0.355512	+	0.834417i	0.0176655	+	0.0414625i
$406$	−0.426556	−	10.5849i	−0.0211696	−	0.525319i
$407$	−2.14181	−	2.62325i	−0.106166	−	0.130030i
$408$			8.01400i			0.396752i
$409$	−14.2896	+	11.6671i	−0.706574	+	0.576900i	−0.916122	−	0.400898i	$-0.868698\pi$
$409$	−14.2896	+	11.6671i	−0.706574	+	0.576900i	0.209549	+	0.977798i	$0.432801\pi$
$410$	10.1381	+	2.93655i	0.500687	+	0.145026i
$411$	3.25541	+	3.67459i	0.160577	+	0.181254i
$412$	2.32934	−	2.42510i	0.114758	−	0.119476i
$413$	11.2251	+	3.74749i	0.552351	+	0.184402i
$414$	−8.52821	−	11.3490i	−0.419139	−	0.557772i
$415$	−1.01574	−	8.36536i	−0.0498606	−	0.410639i
$416$	1.12293	−	6.83406i	0.0550562	−	0.335068i
$417$	1.28130	−	10.5525i	0.0627457	−	0.516758i
$418$	−2.38049	+	1.37438i	−0.116434	+	0.0672230i
$419$	−5.98613	+	4.49829i	−0.292442	+	0.219756i	−0.736829	−	0.676079i	$-0.763678\pi$
$419$	−5.98613	+	4.49829i	−0.292442	+	0.219756i	0.444387	+	0.895835i	$0.353421\pi$
$420$	0.0109084	−	0.270689i	0.000532275	−	0.0132083i
$421$	−27.5187	+	10.4365i	−1.34118	+	0.508642i	−0.917704	−	0.397265i	$-0.869959\pi$
$421$	−27.5187	+	10.4365i	−1.34118	+	0.508642i	−0.423475	+	0.905908i	$0.639190\pi$
$422$	−1.86632	+	0.381012i	−0.0908510	+	0.0185474i
$423$	−5.92725	+	1.21006i	−0.288193	+	0.0588349i
$424$	1.23830	−	0.469624i	0.0601370	−	0.0228070i
$425$	0.531503	−	13.1891i	0.0257817	−	0.639766i
$426$	−3.90232	+	2.93241i	−0.189068	+	0.142076i
$427$	−4.99475	+	2.88372i	−0.241713	+	0.139553i
$428$	0.668016	−	5.50160i	0.0322898	−	0.265930i
$429$	−1.91548	+	1.55836i	−0.0924801	+	0.0752381i
$430$	−0.159638	−	1.31473i	−0.00769841	−	0.0634021i
$431$	−10.2281	−	13.6111i	−0.492669	−	0.655624i	0.482808	−	0.875726i	$-0.339617\pi$
$431$	−10.2281	−	13.6111i	−0.492669	−	0.655624i	−0.975477	+	0.220103i	$0.929361\pi$
$432$	4.33344	+	1.44671i	0.208493	+	0.0696050i
$433$	−0.202323	+	0.210641i	−0.00972304	+	0.0101228i	−0.726046	−	0.687646i	$-0.758644\pi$
$433$	−0.202323	+	0.210641i	−0.00972304	+	0.0101228i	0.716323	+	0.697769i	$0.245824\pi$
$434$	0.279013	+	0.314940i	0.0133930	+	0.0151176i
$435$	6.92655	+	2.00630i	0.332103	+	0.0961947i
$436$	−3.44648	+	2.81396i	−0.165056	+	0.134764i
$437$		−	24.3165i		−	1.16321i
$438$	0.749336	+	0.917770i	0.0358047	+	0.0438528i
$439$	−0.618912	−	15.3581i	−0.0295390	−	0.733004i	−0.944315	−	0.329042i	$-0.893274\pi$
$439$	−0.618912	−	15.3581i	−0.0295390	−	0.733004i	0.914776	−	0.403961i	$-0.132367\pi$
$440$	−0.617507	−	1.44934i	−0.0294385	−	0.0690947i
$441$	−2.21357	+	5.83671i	−0.105408	+	0.277938i
$442$	8.13165	−	15.4278i	0.386783	−	0.733828i
$443$	5.18357	+	13.6680i	0.246279	+	0.649384i	0.999969	−	0.00784561i	$-0.00249736\pi$
$443$	5.18357	+	13.6680i	0.246279	+	0.649384i	−0.753690	+	0.657230i	$0.771728\pi$
$444$	1.22376	−	1.17544i	0.0580771	−	0.0557838i
$445$	−4.42164	−	15.2653i	−0.209606	−	0.723644i
$446$	−17.6559	+	1.42533i	−0.836033	+	0.0674915i
$447$	−0.480335	+	0.915203i	−0.0227191	+	0.0432876i
$448$	3.89006	+	3.73645i	0.183788	+	0.176531i
$449$	1.98577	−	4.66077i	0.0937142	−	0.219955i	−0.866525	−	0.499134i	$-0.833652\pi$
$449$	1.98577	−	4.66077i	0.0937142	−	0.219955i	0.960239	+	0.279178i	$0.0900620\pi$
$450$	−5.97890	−	2.26750i	−0.281848	−	0.106891i
$451$	−5.13916	−	0.835194i	−0.241993	−	0.0393278i
$452$	4.17162	+	2.63797i	0.196217	+	0.124080i
$453$	8.18858	−	2.37185i	0.384733	−	0.111439i
$454$	−13.3818	+	19.3870i	−0.628041	+	0.909875i
$455$	1.42756	−	2.46263i	0.0669249	−	0.115450i
$456$	3.77757	+	5.47275i	0.176901	+	0.256285i
$457$	20.5126	+	16.7480i	0.959537	+	0.783437i	0.976300	−	0.216422i	$-0.0694387\pi$
$457$	20.5126	+	16.7480i	0.959537	+	0.783437i	−0.0167632	+	0.999859i	$0.505336\pi$
$458$	3.20722	−	3.92813i	0.149864	−	0.183550i
$459$	2.52612	+	1.89826i	0.117909	+	0.0886030i
$460$	−2.86538	−	0.347920i	−0.133599	−	0.0162218i
$461$	8.16618	+	24.4607i	0.380337	+	1.13925i	0.948621	+	0.316416i	$0.102479\pi$
$461$	8.16618	+	24.4607i	0.380337	+	1.13925i	−0.568284	+	0.822833i	$0.692392\pi$
$462$	0.0734265	+	0.909550i	0.00341611	+	0.0423161i
$463$	15.2331	−	17.1946i	0.707940	−	0.799099i	−0.278982	−	0.960296i	$-0.589997\pi$
$463$	15.2331	−	17.1946i	0.707940	−	0.799099i	0.986922	+	0.161197i	$0.0515354\pi$
$464$	30.7000	−	19.4135i	1.42521	−	0.901250i
$465$	−0.263500	+	0.112267i	−0.0122195	+	0.00520626i
$466$	−4.18155	−	25.7301i	−0.193707	−	1.19192i
$467$	−5.75831	+	5.10142i	−0.266463	+	0.236065i	−0.785765	−	0.618525i	$-0.787730\pi$
$467$	−5.75831	+	5.10142i	−0.266463	+	0.236065i	0.519302	+	0.854591i	$0.326192\pi$
$468$	−0.855508	−	0.893806i	−0.0395459	−	0.0413162i
$469$	5.64845	+	5.00409i	0.260821	+	0.231067i
$470$	−4.48895	+	7.09871i	−0.207060	+	0.327439i
$471$	17.8110	+	1.43785i	0.820688	+	0.0662528i
$472$	6.89720	+	33.7847i	0.317470	+	1.55507i
$473$	0.156346	+	0.634321i	0.00718880	+	0.0291661i
$474$	2.87516	−	17.6916i	0.132060	−	0.812601i
$475$	−5.85400	−	9.25737i	−0.268600	−	0.424757i
$476$	−0.438610	−	0.835701i	−0.0201036	−	0.0383043i
$477$	0.145280	−	0.501566i	0.00665193	−	0.0229651i
$478$	7.73833	−	37.9048i	0.353943	−	1.73373i
$479$	10.3589	−	0.417449i	0.473309	−	0.0190737i	0.197534	−	0.980296i	$-0.436707\pi$
$479$	10.3589	−	0.417449i	0.473309	−	0.0190737i	0.275775	+	0.961222i	$0.411066\pi$
$480$	1.54264	−	0.809640i	0.0704115	−	0.0369548i
$481$	17.1337	−	4.93033i	0.781229	−	0.224804i
$482$	7.57038	+	3.97324i	0.344821	+	0.180976i
$483$	−7.29299	−	3.46057i	−0.331843	−	0.157461i
$484$	1.80685	+	3.12956i	0.0821298	+	0.142253i
$485$	−3.09107	+	5.35389i	−0.140358	+	0.243107i
$486$	1.25977	−	0.869557i	0.0571444	−	0.0394439i
$487$	22.5474	−	30.0051i	1.02172	−	1.35966i	0.0902203	−	0.995922i	$-0.471243\pi$
$487$	22.5474	−	30.0051i	1.02172	−	1.35966i	0.931500	−	0.363741i	$-0.118501\pi$
$488$	−14.5534	−	8.40242i	−0.658802	−	0.380360i
$489$	−5.72181	+	0.694754i	−0.258749	+	0.0314179i
$490$	3.71535	+	7.82993i	0.167842	+	0.353720i
$491$	−1.91854	−	1.99741i	−0.0865826	−	0.0901420i	0.676501	−	0.736441i	$-0.263495\pi$
$491$	−1.91854	−	1.99741i	−0.0865826	−	0.0901420i	−0.763084	+	0.646299i	$0.776316\pi$
$492$	0.209917	−	2.60029i	0.00946381	−	0.117230i
$493$	24.3930	−	6.01234i	1.09861	−	0.270782i
$494$	−1.71915	−	14.3687i	−0.0773480	−	0.646477i
$495$	−0.603119	−	0.148656i	−0.0271082	−	0.00668157i
$496$	−0.456857	+	1.36845i	−0.0205135	+	0.0614454i
$497$	−1.18991	+	2.50768i	−0.0533747	+	0.112485i
$498$	−13.4900	+	4.50362i	−0.604501	+	0.201812i
$499$	−3.85159	−	2.65856i	−0.172421	−	0.119014i	0.478729	−	0.877963i	$-0.341098\pi$
$499$	−3.85159	−	2.65856i	−0.172421	−	0.119014i	−0.651150	+	0.758949i	$0.725713\pi$
$500$	−2.58055	+	1.22449i	−0.115406	+	0.0547607i
$501$	−14.1530	−	0.570346i	−0.632309	−	0.0254812i
$502$	−7.79546	+	31.6274i	−0.347929	+	1.41160i
$503$	−11.8107	−	5.03206i	−0.526613	−	0.224369i	0.112263	−	0.993678i	$-0.464190\pi$
$503$	−11.8107	−	5.03206i	−0.526613	−	0.224369i	−0.638876	+	0.769310i	$0.720600\pi$
$504$	2.17899	−	0.354120i	0.0970598	−	0.0157737i
$505$	−2.39701	−	0.489354i	−0.106666	−	0.0217760i
$506$	9.72242			0.432214
$507$	−3.57307	−	12.4993i	−0.158686	−	0.555115i
$508$	7.10653			0.315301
$509$	−10.5399	−	2.15174i	−0.467173	−	0.0953740i	−0.0393282	−	0.999226i	$-0.512522\pi$
$509$	−10.5399	−	2.15174i	−0.467173	−	0.0953740i	−0.427844	+	0.903852i	$0.640727\pi$
$510$	4.33023	−	0.703731i	0.191746	−	0.0311617i
$511$	0.619818	+	0.264080i	0.0274191	+	0.0116822i
$512$	−3.44567	+	13.9796i	−0.152279	+	0.617818i
$513$	2.61986	+	0.105577i	0.115670	+	0.00466134i
$514$	−2.23495	+	1.06050i	−0.0985792	+	0.0467764i
$515$	7.31448	+	5.04882i	0.322314	+	0.222478i
$516$	−0.310492	+	0.103657i	−0.0136686	+	0.00456326i
$517$	1.77611	−	3.74308i	0.0781133	−	0.164620i
$518$	2.08637	−	6.24943i	0.0916696	−	0.274584i
$519$	21.4190	+	5.27932i	0.940191	+	0.231736i
$520$	8.29391	+	0.0145238i	0.363712	+	0.000636911i
$521$	4.15252	−	1.02350i	0.181925	−	0.0448405i	−0.147301	−	0.989092i	$-0.547058\pi$
$521$	4.15252	−	1.02350i	0.181925	−	0.0448405i	0.329226	+	0.944251i	$0.393212\pi$
$522$	0.979314	−	12.1310i	0.0428634	−	0.530958i
$523$	−25.3150	−	26.3557i	−1.10695	−	1.15246i	−0.987173	−	0.159655i	$-0.948962\pi$
$523$	−25.3150	−	26.3557i	−1.10695	−	1.15246i	−0.119776	−	0.992801i	$-0.538218\pi$
$524$	−1.12050	−	2.36141i	−0.0489494	−	0.103159i
$525$	−3.60957	+	0.438282i	−0.157535	+	0.0191282i
$526$	10.5015	+	6.06304i	0.457887	+	0.264361i
$527$	−0.599450	+	0.797723i	−0.0261124	+	0.0347493i
$528$	−2.57498	+	1.77738i	−0.112062	+	0.0773507i
$529$	−31.5040	+	54.5665i	−1.36974	+	2.37246i
$530$	−0.362492	−	0.627854i	−0.0157456	−	0.0272722i
$531$	12.2831	+	5.82841i	0.533042	+	0.252932i
$532$	−0.693451	−	0.363951i	−0.0300649	−	0.0157793i
$533$	14.6906	−	23.1415i	0.636321	−	1.00237i
$534$	−23.7499	+	12.4649i	−1.02776	+	0.539409i
$535$	14.6364	−	0.589827i	0.632787	−	0.0255005i
$536$	−4.39813	+	21.5434i	−0.189970	+	0.930535i
$537$	−1.23960	+	4.27961i	−0.0534929	+	0.184679i
$538$	−14.1030	−	26.8710i	−0.608024	−	1.15849i
$539$	−2.28493	−	3.61333i	−0.0984190	−	0.155637i
$540$	0.0499258	−	0.307206i	0.00214847	−	0.0132200i
$541$	−0.895271	−	3.63226i	−0.0384907	−	0.156163i	0.948552	−	0.316622i	$-0.102549\pi$
$541$	−0.895271	−	3.63226i	−0.0384907	−	0.156163i	−0.987042	+	0.160459i	$0.948703\pi$
$542$	−0.838775	−	4.10859i	−0.0360285	−	0.176479i
$543$	−19.8554	−	1.60289i	−0.852077	−	0.0687868i
$544$	3.24398	−	5.12995i	0.139085	−	0.219945i
$545$	−8.80264	−	7.79846i	−0.377064	−	0.334049i
$546$	−4.55411	−	1.52925i	−0.194898	−	0.0654460i
$547$	2.48847	−	2.20459i	0.106399	−	0.0942615i	−0.608246	−	0.793749i	$-0.708127\pi$
$547$	2.48847	−	2.20459i	0.106399	−	0.0942615i	0.714645	+	0.699487i	$0.246588\pi$
$548$	−0.270229	−	1.66278i	−0.0115436	−	0.0710306i
$549$	−6.09578	+	2.59717i	−0.260162	+	0.110845i
$550$	3.70136	−	2.34060i	0.157827	−	0.0998034i
$551$	13.8239	−	15.6040i	0.588919	−	0.664752i
$552$	−1.89264	−	23.4446i	−0.0805561	−	0.997866i
$553$	−3.22748	−	9.66748i	−0.137246	−	0.411103i
$554$	−8.17824	−	0.993018i	−0.347460	−	0.0421893i
$555$	3.58547	+	2.69431i	0.152195	+	0.114367i
$556$	−2.30697	+	2.82552i	−0.0978372	+	0.119829i
$557$	6.49450	+	5.30259i	0.275181	+	0.224678i	0.759979	−	0.649948i	$-0.225209\pi$
$557$	6.49450	+	5.30259i	0.275181	+	0.224678i	−0.484798	+	0.874626i	$0.661107\pi$
$558$	0.274597	+	0.397823i	0.0116246	+	0.0168412i
$559$	−3.39389	−	0.557663i	−0.143546	−	0.0235866i
$560$	2.04887	−	2.96829i	0.0865804	−	0.125433i
$561$	−2.07863	+	0.602082i	−0.0877598	+	0.0254199i
$562$	22.5619	+	14.2673i	0.951715	+	0.601828i
$563$	−10.4494	−	1.69820i	−0.440391	−	0.0715705i	−0.0638266	−	0.997961i	$-0.520330\pi$
$563$	−10.4494	−	1.69820i	−0.440391	−	0.0715705i	−0.376564	+	0.926391i	$0.622895\pi$
$564$	1.94099	+	0.736122i	0.0817306	+	0.0309963i
$565$	−5.11351	+	12.0019i	−0.215127	+	0.504922i
$566$	−26.0856	−	25.0556i	−1.09646	−	1.05316i
$567$	0.404507	−	0.770724i	0.0169877	−	0.0323674i
$568$	−8.06136	+	0.650780i	−0.338247	+	0.0273061i
$569$	1.90687	+	6.58328i	0.0799402	+	0.275986i	0.990524	−	0.137339i	$-0.0438548\pi$
$569$	1.90687	+	6.58328i	0.0799402	+	0.275986i	−0.910584	+	0.413324i	$0.864368\pi$
$570$	2.62539	−	2.52172i	0.109965	−	0.105623i
$571$	7.64200	+	20.1503i	0.319808	+	0.843264i	0.994459	+	0.105127i	$0.0335249\pi$
$571$	7.64200	+	20.1503i	0.319808	+	0.843264i	−0.674651	+	0.738137i	$0.735706\pi$
$572$	0.841348	−	0.100663i	0.0351785	−	0.00420895i
$573$	−2.11629	+	5.58019i	−0.0884092	+	0.233116i
$574$	−3.97035	−	9.31876i	−0.165719	−	0.388958i
$575$	1.55994	+	38.7096i	0.0650542	+	1.61430i
$576$	3.91913	+	4.80007i	0.163297	+	0.200003i
$577$		−	26.0731i		−	1.08544i	−0.839915	−	0.542718i	$-0.817395\pi$
$577$		−	26.0731i		−	1.08544i	0.839915	−	0.542718i	$-0.182605\pi$
$578$	−8.31821	+	6.79161i	−0.345992	+	0.282494i
$579$	8.66714	+	2.51047i	0.360194	+	0.104331i
$580$	−1.64093	−	1.85223i	−0.0681360	−	0.0769096i
$581$	−5.60209	+	5.83239i	−0.232414	+	0.241968i
$582$	9.89664	+	3.30398i	0.410229	+	0.136955i
$583$	0.214840	+	0.285901i	0.00889778	+	0.0118408i
$584$	0.236622	+	1.94876i	0.00979151	+	0.0806403i
$585$	1.96913	−	2.61091i	0.0814136	−	0.107948i
$586$	−2.33221	+	19.2075i	−0.0963428	+	0.793454i
$587$	−13.4478	+	7.76407i	−0.555049	+	0.320458i	−0.751156	−	0.660125i	$-0.770503\pi$
$587$	−13.4478	+	7.76407i	−0.555049	+	0.320458i	0.196107	+	0.980583i	$0.437170\pi$
$588$	1.71246	−	1.28683i	0.0706208	−	0.0530681i
$589$	−0.0333401	+	0.827327i	−0.00137376	+	0.0340894i
$590$	17.6493	−	6.69351i	0.726612	−	0.275568i
$591$	−1.31832	+	0.269138i	−0.0542286	+	0.0110708i
$592$	22.1343	−	4.51875i	0.909714	−	0.185719i
$593$	−5.34364	+	2.02658i	−0.219437	+	0.0832215i	−0.461874	−	0.886946i	$-0.652823\pi$
$593$	−5.34364	+	2.02658i	−0.219437	+	0.0832215i	0.242437	+	0.970167i	$0.422053\pi$
$594$	−0.0422127	+	1.04750i	−0.00173201	+	0.0429793i
$595$	1.99430	−	1.49862i	0.0817584	−	0.0614375i
$596$	0.307161	−	0.177340i	0.0125818	−	0.00726411i
$597$	1.68666	−	13.8909i	0.0690305	−	0.568517i
$598$	−20.1452	+	47.0538i	−0.823797	+	1.92417i
$599$	0.650266	+	5.35542i	0.0265691	+	0.218816i	0.999946	−	0.0103941i	$-0.00330862\pi$
$599$	0.650266	+	5.35542i	0.0265691	+	0.218816i	−0.973377	+	0.229211i	$0.926386\pi$
$600$	−6.36463	−	8.46978i	−0.259835	−	0.345777i
$601$	34.9892	+	11.6811i	1.42724	+	0.476482i	0.922233	−	0.386634i	$-0.126362\pi$
$601$	34.9892	+	11.6811i	1.42724	+	0.476482i	0.505005	+	0.863116i	$0.331491\pi$
$602$	−0.880448	+	0.916644i	−0.0358844	+	0.0373596i
$603$	5.74901	+	6.48929i	0.234118	+	0.264264i
$604$	−2.80992	−	0.813903i	−0.114334	−	0.0331173i
$605$	−7.39866	+	6.04082i	−0.300798	+	0.245594i
$606$			4.12888i			0.167724i
$607$	−8.53509	−	10.4536i	−0.346428	−	0.424298i	0.571773	−	0.820412i	$-0.306256\pi$
$607$	−8.53509	−	10.4536i	−0.346428	−	0.424298i	−0.918201	+	0.396114i	$0.870358\pi$
$608$	−0.202797	−	5.03236i	−0.00822450	−	0.204089i
$609$	−2.71261	−	6.36673i	−0.109921	−	0.257993i
$610$	−3.26213	+	8.60153i	−0.132080	+	0.348266i
$611$	14.4353	+	16.3517i	0.583989	+	0.661517i
$612$	−0.384500	−	1.01384i	−0.0155425	−	0.0409822i
$613$	−27.1663	+	26.0936i	−1.09724	+	1.05391i	−0.0989666	+	0.995091i	$0.531554\pi$
$613$	−27.1663	+	26.0936i	−1.09724	+	1.05391i	−0.998269	+	0.0588181i	$0.981267\pi$
$614$	1.89305	+	6.53556i	0.0763973	+	0.263754i
$615$	6.87293	−	0.554841i	0.277143	−	0.0223733i
$616$	−0.702610	+	1.33871i	−0.0283090	+	0.0539382i
$617$	24.6579	+	23.6842i	0.992688	+	0.953490i	0.998919	−	0.0464908i	$-0.0148038\pi$
$617$	24.6579	+	23.6842i	0.992688	+	0.953490i	−0.00623074	+	0.999981i	$0.501983\pi$
$618$	5.87944	−	13.7996i	0.236506	−	0.555100i
$619$	18.0300	+	6.83788i	0.724687	+	0.274838i	0.689239	−	0.724534i	$-0.257945\pi$
$619$	18.0300	+	6.83788i	0.724687	+	0.274838i	0.0354480	+	0.999372i	$0.488714\pi$
$620$	0.0970125	+	0.0157661i	0.00389612	+	0.000633180i
$621$	−7.83833	−	4.95666i	−0.314542	−	0.198904i
$622$	−36.7882	+	10.6558i	−1.47507	+	0.427260i
$623$	−8.66411	+	12.5521i	−0.347120	+	0.502891i
$624$	−3.26658	−	16.1450i	−0.130768	−	0.646317i
$625$	7.57635	+	10.9762i	0.303054	+	0.439050i
$626$	23.8696	+	19.4889i	0.954021	+	0.778934i
$627$	−1.13569	+	1.39097i	−0.0453550	+	0.0555498i
$628$	−4.90198	−	3.68360i	−0.195610	−	0.146992i
$629$	15.5111	+	1.88339i	0.618467	+	0.0750955i
$630$	−0.382685	−	1.14628i	−0.0152465	−	0.0456690i
$631$	−0.780081	−	9.66304i	−0.0310546	−	0.384680i	−0.993551	−	0.113386i	$-0.963830\pi$
$631$	−0.780081	−	9.66304i	−0.0310546	−	0.384680i	0.962497	−	0.271294i	$-0.0874516\pi$
$632$	19.6926	−	22.2284i	0.783331	−	0.884198i
$633$	−1.05174	+	0.665078i	−0.0418028	+	0.0264345i
$634$	5.21816	−	2.22325i	0.207240	−	0.0882966i
$635$	3.01309	+	18.5403i	0.119571	+	0.735749i
$636$	−0.134124	+	0.118823i	−0.00531836	+	0.00471165i
$637$	22.2220	−	3.57149i	0.880466	−	0.141508i
$638$	6.23892	+	5.52720i	0.247001	+	0.218824i
$639$	−1.70434	+	2.69520i	−0.0674226	+	0.106620i
$640$	12.0486	+	0.972667i	0.476264	+	0.0384480i
$641$	−1.28101	−	6.27478i	−0.0505967	−	0.247839i	0.946624	−	0.322339i	$-0.104469\pi$
$641$	−1.28101	−	6.27478i	−0.0505967	−	0.247839i	−0.997221	+	0.0745000i	$0.976264\pi$
$642$	−5.91634	−	24.0035i	−0.233499	−	0.947344i
$643$	−3.14338	+	19.3420i	−0.123963	+	0.762774i	0.848410	+	0.529340i	$0.177560\pi$
$643$	−3.14338	+	19.3420i	−0.123963	+	0.762774i	−0.972373	+	0.233434i	$0.925004\pi$
$644$	1.48049	+	2.34121i	0.0583397	+	0.0922568i
$645$	−0.402078	−	0.766096i	−0.0158318	−	0.0301650i
$646$	3.52844	−	12.1816i	0.138824	−	0.479278i
$647$	−6.94951	+	34.0410i	−0.273214	+	1.33829i	0.579100	+	0.815257i	$0.303404\pi$
$647$	−6.94951	+	34.0410i	−0.273214	+	1.33829i	−0.852313	+	0.523032i	$0.824801\pi$
$648$	2.53414	−	0.102122i	0.0995504	−	0.00401175i
$649$	−8.24473	+	4.32717i	−0.323634	+	0.169856i
$650$	3.65850	+	22.7633i	0.143498	+	0.892851i
$651$	0.243387	+	0.127739i	0.00953909	+	0.00500650i
$652$	1.78690	+	0.847897i	0.0699806	+	0.0332062i
$653$	−15.0506	−	26.0683i	−0.588974	−	1.02013i	−0.994367	−	0.105991i	$-0.966199\pi$
$653$	−15.0506	−	26.0683i	−0.588974	−	1.02013i	0.405393	−	0.914142i	$-0.367135\pi$
$654$	−9.92385	+	17.1886i	−0.388053	+	0.672128i
$655$	5.68563	−	3.92451i	0.222156	−	0.153343i
$656$	20.8648	−	27.7660i	0.814634	−	1.08408i
$657$	0.670323	+	0.387011i	0.0261518	+	0.0150987i
$658$	8.00154	−	0.971563i	0.311933	−	0.0378755i
$659$	12.6821	+	26.7270i	0.494025	+	1.04114i	0.985411	+	0.170194i	$0.0544395\pi$
$659$	12.6821	+	26.7270i	0.494025	+	1.04114i	−0.491385	+	0.870942i	$0.663509\pi$
$660$	0.147658	+	0.153728i	0.00574756	+	0.00598385i
$661$	−2.59019	+	32.0853i	−0.100747	+	1.24797i	0.726907	+	0.686736i	$0.240957\pi$
$661$	−2.59019	+	32.0853i	−0.100747	+	1.24797i	−0.827654	+	0.561238i	$0.810325\pi$
$662$	−51.5227	+	12.6992i	−2.00248	+	0.493568i
$663$	1.39308	−	11.3075i	0.0541026	−	0.439147i
$664$	−22.8788	−	5.63912i	−0.887871	−	0.218840i
$665$	0.655500	−	1.96346i	0.0254192	−	0.0761398i
$666$	3.24489	−	6.83846i	0.125737	−	0.264985i
$667$	−69.9406	+	23.3496i	−2.70811	+	0.904101i
$668$	4.00016	+	2.76111i	0.154771	+	0.106831i
$669$	−10.4546	+	4.96075i	−0.404196	+	0.191794i
$670$	12.0268	+	0.484665i	0.464638	+	0.0187243i
$671$	1.08599	−	4.40605i	0.0419243	−	0.170094i
$672$	−1.53816	−	0.655351i	−0.0593360	−	0.0252807i
$673$	31.5869	−	5.13338i	1.21759	−	0.197877i	0.482528	−	0.875880i	$-0.339719\pi$
$673$	31.5869	−	5.13338i	1.21759	−	0.197877i	0.735059	+	0.678003i	$0.237155\pi$
$674$	−13.1026	−	2.67492i	−0.504695	−	0.103034i
$675$	−4.17736			−0.160787
$676$	−1.25612	+	4.28046i	−0.0483122	+	0.164633i
$677$	45.5517			1.75069			0.875346	−	0.483497i	$-0.160633\pi$
$677$	45.5517			1.75069			0.875346	+	0.483497i	$0.160633\pi$
$678$	21.5724	+	4.40404i	0.828484	+	0.169136i
$679$	5.85605	−	0.951701i	0.224735	−	0.0365229i
$680$	6.68702	+	2.84907i	0.256436	+	0.109257i
$681$	−3.68289	+	14.9421i	−0.141129	+	0.572582i
$682$	−0.330789	−	0.0133303i	−0.0126666	−	0.000510445i
$683$	−32.8240	+	15.5752i	−1.25598	+	0.595968i	−0.936181	−	0.351519i	$-0.885665\pi$
$683$	−32.8240	+	15.5752i	−1.25598	+	0.595968i	−0.319795	+	0.947487i	$0.603614\pi$
$684$	−0.740471	−	0.511110i	−0.0283126	−	0.0195428i
$685$	4.22348	−	1.41000i	0.161371	−	0.0538735i
$686$	7.56386	−	15.9405i	0.288790	−	0.608611i
$687$	1.04908	−	3.14239i	0.0400250	−	0.119890i
$688$	−4.23139	−	1.04294i	−0.161320	−	0.0397618i
$689$	−1.82883	+	0.447371i	−0.0696730	+	0.0170435i
$690$	−12.5017	+	3.08138i	−0.475930	+	0.117306i
$691$	2.13038	−	26.3894i	0.0810433	−	1.00390i	−0.820623	−	0.571470i	$-0.806373\pi$
$691$	2.13038	−	26.3894i	0.0810433	−	1.00390i	0.901666	−	0.432432i	$-0.142344\pi$
$692$	−5.24388	−	5.45945i	−0.199342	−	0.207537i
$693$	0.255554	+	0.538569i	0.00970770	+	0.0204585i
$694$	6.54067	−	0.794181i	0.248280	−	0.0301467i
$695$	−8.34966	−	4.82068i	−0.316721	−	0.182859i
$696$	12.1137	−	16.1204i	0.459169	−	0.611043i
$697$	19.7699	−	13.6462i	0.748840	−	0.516887i
$698$	2.42150	−	4.19417i	0.0916553	−	0.158752i
$699$	−8.51476	−	14.7480i	−0.322058	−	0.557820i
$700$	1.12726	+	0.534891i	0.0426064	+	0.0202170i
$701$	−29.4661	−	15.4650i	−1.11292	−	0.584105i	−0.194972	−	0.980809i	$-0.562462\pi$
$701$	−29.4661	−	15.4650i	−1.11292	−	0.584105i	−0.917947	+	0.396704i	$0.870154\pi$
$702$	−4.98212	−	2.37474i	−0.188038	−	0.0896290i
$703$	11.4803	−	6.02531i	0.432987	−	0.227249i
$704$	−4.24052	+	0.170887i	−0.159821	+	0.00644056i
$705$	−1.09751	+	5.37598i	−0.0413348	+	0.202471i
$706$	−0.526524	+	1.81777i	−0.0198160	+	0.0684127i
$707$	1.09109	+	2.07889i	0.0410345	+	0.0781847i
$708$	−2.49350	−	3.94316i	−0.0937115	−	0.148193i
$709$	−6.06821	+	37.3392i	−0.227896	+	1.40230i	0.580786	+	0.814057i	$0.302745\pi$
$709$	−6.06821	+	37.3392i	−0.227896	+	1.40230i	−0.808682	+	0.588246i	$0.799819\pi$
$710$	1.05953	+	4.29867i	0.0397634	+	0.161326i
$711$	−2.34214	−	11.4726i	−0.0878371	−	0.430255i
$712$	−44.2962	−	3.57596i	−1.66007	−	0.134015i
$713$	1.56526	−	2.47527i	0.0586196	−	0.0926995i
$714$	−3.15135	−	2.79185i	−0.117936	−	0.104482i
$715$	0.619344	+	2.15232i	0.0231621	+	0.0804922i
$716$	1.14441	−	1.01386i	0.0427687	−	0.0378897i
$717$	−4.05411	−	24.9460i	−0.151404	−	0.931624i
$718$	49.9406	−	21.2777i	1.86377	−	0.794077i
$719$	−9.00648	+	5.69536i	−0.335885	+	0.212401i	−0.691751	−	0.722136i	$-0.743160\pi$
$719$	−9.00648	+	5.69536i	−0.335885	+	0.212401i	0.355866	+	0.934537i	$0.384186\pi$
$720$	2.74775	−	3.10157i	0.102403	−	0.115589i
$721$	−0.686333	−	8.50175i	−0.0255604	−	0.316622i
$722$	5.87749	+	17.6052i	0.218738	+	0.655199i
$723$	5.54463	+	0.673240i	0.206207	+	0.0250381i
$724$	5.46465	+	4.10642i	0.203092	+	0.152614i
$725$	−21.0054	+	25.7270i	−0.780121	+	0.955475i
$726$	12.4867	+	10.1951i	0.463426	+	0.378375i
$727$	9.93325	+	14.3908i	0.368404	+	0.533725i	0.962718	−	0.270508i	$-0.0871917\pi$
$727$	9.93325	+	14.3908i	0.368404	+	0.533725i	−0.594314	+	0.804233i	$0.702576\pi$
$728$	−5.02316	−	6.17429i	−0.186171	−	0.228834i
$729$	0.568065	−	0.822984i	0.0210394	−	0.0304809i
$730$	1.03220	−	0.298981i	0.0382035	−	0.0110658i
$731$	−2.54760	−	1.61101i	−0.0942265	−	0.0595852i
$732$	2.24427	+	0.364730i	0.0829508	+	0.0134808i
$733$	−25.4445	−	9.64982i	−0.939813	−	0.356424i	−0.163337	−	0.986570i	$-0.552226\pi$
$733$	−25.4445	−	9.64982i	−0.939813	−	0.356424i	−0.776477	+	0.630146i	$0.782995\pi$
$734$	−17.6229	+	41.3625i	−0.650474	+	1.52672i
$735$	4.08330	+	3.92206i	0.150615	+	0.144667i
$736$	−8.27859	+	15.7735i	−0.305153	+	0.581420i
$737$	−5.91825	+	0.477770i	−0.218002	+	0.0175989i
$738$	−3.23767	−	11.1777i	−0.119180	−	0.411458i
$739$	38.4461	−	36.9280i	1.41426	−	1.35842i	0.570959	−	0.820979i	$-0.306572\pi$
$739$	38.4461	−	36.9280i	1.41426	−	1.35842i	0.843303	−	0.537438i	$-0.180608\pi$
$740$	−0.545744	−	1.43901i	−0.0200619	−	0.0528990i
$741$	−4.37870	−	8.37854i	−0.160856	−	0.307793i
$742$	−0.246717	+	0.650540i	−0.00905728	+	0.0238821i
$743$	−2.48461	−	5.83160i	−0.0911516	−	0.213941i	0.868164	−	0.496278i	$-0.165300\pi$
$743$	−2.48461	−	5.83160i	−0.0911516	−	0.213941i	−0.959315	+	0.282338i	$0.908890\pi$
$744$	0.0322492	+	0.800256i	0.00118231	+	0.0293388i
$745$	0.592896	+	0.726165i	0.0217220	+	0.0266046i
$746$			8.49043i			0.310857i
$747$	−7.19677	+	5.87598i	−0.263316	+	0.214991i
$748$	0.713283	+	0.206605i	0.0260802	+	0.00755423i
$749$	−9.32198	−	10.5223i	−0.340618	−	0.384478i
$750$	−8.82640	+	9.18925i	−0.322294	+	0.335544i
$751$	−36.2079	−	12.0880i	−1.32124	−	0.441096i	−0.433384	−	0.901210i	$-0.642680\pi$
$751$	−36.2079	−	12.0880i	−1.32124	−	0.441096i	−0.887860	+	0.460114i	$0.847809\pi$
$752$	16.6030	+	22.0946i	0.605448	+	0.805706i
$753$	2.56501	+	21.1248i	0.0934743	+	0.769830i
$754$	−39.6773	+	18.7421i	−1.44496	+	0.682546i
$755$	0.932025	−	7.67591i	0.0339198	−	0.279355i
$756$	−0.258671	+	0.149344i	−0.00940778	+	0.00543158i
$757$	−4.41120	+	3.31480i	−0.160328	+	0.120479i	−0.677878	−	0.735174i	$-0.737100\pi$
$757$	−4.41120	+	3.31480i	−0.160328	+	0.120479i	0.517550	+	0.855653i	$0.326844\pi$
$758$	−0.256420	+	6.36300i	−0.00931360	+	0.231115i
$759$	5.93873	−	2.25226i	0.215562	−	0.0817520i
$760$	5.90953	−	1.20644i	0.214361	−	0.0437621i
$761$	44.4244	−	9.06930i	1.61038	−	0.328762i	0.691221	−	0.722643i	$-0.257073\pi$
$761$	44.4244	−	9.06930i	1.61038	−	0.328762i	0.919161	+	0.393881i	$0.128868\pi$
$762$	29.6409	−	11.2413i	1.07378	−	0.407230i
$763$	−0.454444	+	11.2769i	−0.0164520	+	0.408251i
$764$	1.63720	−	1.23028i	0.0592319	−	0.0445099i
$765$	2.48200	−	1.43298i	0.0897370	−	0.0518097i
$766$	6.34072	−	52.2206i	0.229100	−	1.88681i
$767$	−3.85893	−	48.8682i	−0.139338	−	1.76453i
$768$	−0.965143	−	7.94867i	−0.0348266	−	0.286823i
$769$	−3.76969	−	5.01655i	−0.135939	−	0.180901i	0.726340	−	0.687336i	$-0.241220\pi$
$769$	−3.76969	−	5.01655i	−0.135939	−	0.180901i	−0.862279	+	0.506434i	$0.830963\pi$
$770$	0.785048	+	0.262088i	0.0282912	+	0.00944498i
$771$	−1.11950	+	1.16552i	−0.0403177	+	0.0419752i
$772$	−2.05329	−	2.31768i	−0.0738994	−	0.0834151i
$773$	−8.87554	−	2.57083i	−0.319231	−	0.0924664i	0.114734	−	0.993396i	$-0.463399\pi$
$773$	−8.87554	−	2.57083i	−0.319231	−	0.0924664i	−0.433965	+	0.900930i	$0.642886\pi$
$774$	−1.13108	+	0.923494i	−0.0406557	+	0.0331943i
$775$		−	1.31917i		−	0.0473859i
$776$	10.9330	+	13.3905i	0.392472	+	0.480691i
$777$	−0.173310	−	4.30065i	−0.00621747	−	0.154285i
$778$	10.8478	+	25.4607i	0.388912	+	0.912810i
$779$	7.06844	−	18.6380i	0.253253	−	0.667774i
$780$	−1.04995	+	0.396092i	−0.0375943	+	0.0141824i
$781$	−0.774436	−	2.04202i	−0.0277115	−	0.0730692i
$782$	−32.3514	+	31.0739i	−1.15688	+	1.11120i
$783$	−2.21203	−	7.63681i	−0.0790514	−	0.272917i
$784$	28.4260	−	2.29479i	1.01522	−	0.0819567i
$785$	7.53180	−	14.3506i	0.268821	−	0.512196i
$786$	−8.40891	−	8.07686i	−0.299936	−	0.288092i
$787$	−1.59432	+	3.74201i	−0.0568314	+	0.133388i	−0.945974	−	0.324241i	$-0.894891\pi$
$787$	−1.59432	+	3.74201i	−0.0568314	+	0.133388i	0.889143	+	0.457629i	$0.151301\pi$
$788$	0.431711	+	0.163726i	0.0153791	+	0.00583251i
$789$	7.81915	+	1.27074i	0.278369	+	0.0452394i
$790$	−13.7400	−	8.68865i	−0.488847	−	0.309128i
$791$	12.0255	−	3.48323i	0.427577	−	0.123849i
$792$	−0.986702	+	1.42948i	−0.0350609	+	0.0507945i
$793$	19.0738	+	14.3854i	0.677331	+	0.510840i
$794$	27.9804	+	40.5366i	0.992987	+	1.43859i
$795$	−0.366866	−	0.299537i	−0.0130114	−	0.0106235i
$796$	−3.03681	+	3.71941i	−0.107637	+	0.131831i
$797$	21.5208	+	16.1718i	0.762305	+	0.572835i	0.909221	−	0.416314i	$-0.136678\pi$
$797$	21.5208	+	16.1718i	0.762305	+	0.572835i	−0.146916	+	0.989149i	$0.546935\pi$
$798$	−3.46805	−	0.421098i	−0.122768	−	0.0149067i
$799$	6.05327	+	18.1318i	0.214149	+	0.641456i
$800$	0.645669	+	7.99804i	0.0228278	+	0.282774i
$801$	−11.6195	+	13.1157i	−0.410555	+	0.463421i
$802$	4.71738	−	2.98309i	0.166577	−	0.105337i
$803$	−0.487682	+	0.207782i	−0.0172099	+	0.00733246i
$804$	−0.477220	−	2.93646i	−0.0168303	−	0.103561i
$805$	−5.48030	+	4.85513i	−0.193155	+	0.171121i
$806$	0.749920	−	1.57330i	0.0264148	−	0.0554173i
$807$	−14.8394	−	13.1465i	−0.522371	−	0.462780i
$808$	−3.65624	+	5.78189i	−0.128626	+	0.203406i
$809$	6.62689	+	0.534978i	0.232989	+	0.0188088i	0.196410	−	0.980522i	$-0.437072\pi$
$809$	6.62689	+	0.534978i	0.232989	+	0.0188088i	0.0365794	+	0.999331i	$0.488354\pi$
$810$	−0.277710	−	1.36031i	−0.00975772	−	0.0477965i
$811$	−11.9458	−	48.4659i	−0.419473	−	1.70187i	−0.677326	−	0.735683i	$-0.736861\pi$
$811$	−11.9458	−	48.4659i	−0.419473	−	1.70187i	0.257853	−	0.966184i	$-0.416985\pi$
$812$	−0.380942	+	2.34403i	−0.0133684	+	0.0822593i
$813$	−1.46413	−	2.31534i	−0.0513493	−	0.0812024i
$814$	2.40909	+	4.59014i	0.0844386	+	0.160884i
$815$	−1.45446	+	5.02137i	−0.0509475	+	0.175891i
$816$	2.88756	−	14.1442i	0.101085	−	0.495146i
$817$	−2.49914	+	0.100712i	−0.0874337	+	0.00352346i
$818$	25.0038	−	13.1230i	0.874238	−	0.458835i
$819$	−3.13604	+	0.120878i	−0.109582	+	0.00422381i
$820$	−2.09510	−	1.09959i	−0.0731641	−	0.0383995i
$821$	−45.0215	−	21.3630i	−1.57126	−	0.745573i	−0.573953	−	0.818888i	$-0.694591\pi$
$821$	−45.0215	−	21.3630i	−1.57126	−	0.745573i	−0.997309	+	0.0733155i	$0.976642\pi$
$822$	−3.75735	−	6.50792i	−0.131053	−	0.226990i
$823$	−12.0679	+	20.9022i	−0.420661	+	0.728606i	−0.996004	−	0.0893059i	$-0.971535\pi$
$823$	−12.0679	+	20.9022i	−0.420661	+	0.728606i	0.575343	+	0.817912i	$0.304868\pi$
$824$	20.4532	−	14.1178i	0.712521	−	0.491818i
$825$	1.71868	−	2.28715i	0.0598368	−	0.0796283i
$826$	−15.6880	−	9.05746i	−0.545855	−	0.315149i
$827$	−13.8666	+	1.68371i	−0.482188	+	0.0585483i	−0.358022	−	0.933713i	$-0.616549\pi$
$827$	−13.8666	+	1.68371i	−0.482188	+	0.0585483i	−0.124166	+	0.992261i	$0.539626\pi$
$828$	1.36427	+	2.87514i	0.0474117	+	0.0999180i
$829$	11.2789	+	11.7425i	0.391731	+	0.407835i	0.887639	−	0.460540i	$-0.152344\pi$
$829$	11.2789	+	11.7425i	0.391731	+	0.407835i	−0.495908	+	0.868375i	$0.665165\pi$
$830$	−1.03795	+	12.8574i	−0.0360279	+	0.446286i
$831$	−5.22554	+	1.28798i	−0.181272	+	0.0446795i
$832$	7.95946	−	20.8770i	0.275944	−	0.723781i
$833$	19.1517	+	4.72048i	0.663568	+	0.163555i
$834$	−5.15273	+	15.4343i	−0.178424	+	0.534446i
$835$	−5.50746	+	11.6067i	−0.190594	+	0.401668i
$836$	0.584488	−	0.195131i	0.0202149	−	0.00674874i
$837$	0.259890	+	0.179389i	0.00898311	+	0.00620059i
$838$	10.3553	−	4.91366i	0.357719	−	0.169740i
$839$	−22.3747	−	0.901668i	−0.772459	−	0.0311290i	−0.349093	−	0.937088i	$-0.613510\pi$
$839$	−22.3747	−	0.901668i	−0.772459	−	0.0311290i	−0.423365	+	0.905959i	$0.639151\pi$
$840$	0.479172	−	1.94408i	0.0165330	−	0.0670770i
$841$	−31.4761	−	13.4107i	−1.08538	−	0.462438i
$842$	44.4681	−	7.22676i	1.53247	−	0.249051i
$843$	17.0865	+	3.48824i	0.588491	+	0.120141i
$844$	0.427010			0.0146983
$845$	−11.6999	−	1.46223i	−0.402489	−	0.0503021i
$846$	9.26019			0.318372
$847$	8.98118	+	1.83352i	0.308597	+	0.0630005i
$848$	−2.35473	+	0.382680i	−0.0808616	+	0.0131413i
$849$	−21.7381	−	9.26174i	−0.746050	−	0.317862i
$850$	−4.83548	+	19.6183i	−0.165856	+	0.672902i
$851$	−45.8217	−	1.84655i	−1.57075	−	0.0632989i
$852$	0.988611	−	0.469102i	0.0338693	−	0.0160712i
$853$	13.5341	+	9.34191i	0.463398	+	0.319861i	0.776786	−	0.629764i	$-0.216849\pi$
$853$	13.5341	+	9.34191i	0.463398	+	0.319861i	−0.313388	+	0.949625i	$0.601464\pi$
$854$	8.37409	−	2.79568i	0.286555	−	0.0956663i
$855$	1.01949	−	2.14853i	0.0348658	−	0.0734780i
$856$	12.9709	−	38.8525i	0.443335	−	1.32795i
$857$	−14.6990	−	3.62298i	−0.502109	−	0.123759i	−0.0198773	−	0.999802i	$-0.506328\pi$
$857$	−14.6990	−	3.62298i	−0.502109	−	0.123759i	−0.482232	+	0.876044i	$0.660174\pi$
$858$	3.34998	−	1.75073i	0.114366	−	0.0597689i
$859$	−29.8874	+	7.36659i	−1.01975	+	0.251345i	−0.713536	−	0.700619i	$-0.752907\pi$
$859$	−29.8874	+	7.36659i	−1.01975	+	0.251345i	−0.306211	+	0.951964i	$0.599061\pi$
$860$	−0.0238900	+	0.295931i	−0.000814644	+	0.0100912i
$861$	−4.58396	−	4.77240i	−0.156221	−	0.162643i
$862$	11.1725	+	23.5456i	0.380538	+	0.801967i
$863$	−10.4957	+	1.27441i	−0.357279	+	0.0433816i	−0.297209	−	0.954813i	$-0.596056\pi$
$863$	−10.4957	+	1.27441i	−0.357279	+	0.0433816i	−0.0600707	+	0.998194i	$0.519133\pi$
$864$	−1.66350	−	0.960423i	−0.0565935	−	0.0326742i
$865$	12.0199	−	15.9955i	0.408688	−	0.543865i
$866$	0.367940	−	0.253971i	0.0125031	−	0.00863028i
$867$	−3.50768	+	6.07547i	−0.119127	+	0.206334i
$868$	−0.0471613	−	0.0816857i	−0.00160076	−	0.00277259i
$869$	7.24497	+	3.43778i	0.245769	+	0.116619i
$870$	−9.77414	−	5.12986i	−0.331374	−	0.173919i
$871$	9.95053	−	29.6326i	0.337161	−	1.00406i
$872$	−29.1179	+	15.2823i	−0.986056	+	0.517522i
$873$	6.81053	−	0.274455i	0.230502	−	0.00928890i
$874$	−7.44538	+	36.4699i	−0.251844	+	1.23361i
$875$	−2.01576	+	6.95922i	−0.0681452	+	0.235265i
$876$	−0.123434	−	0.235183i	−0.00417043	−	0.00794610i
$877$	7.70329	+	12.1818i	0.260122	+	0.411349i	0.949844	−	0.312725i	$-0.101242\pi$
$877$	7.70329	+	12.1818i	0.260122	+	0.411349i	−0.689722	+	0.724074i	$0.742267\pi$
$878$	−3.77421	+	23.2236i	−0.127373	+	0.783760i
$879$	3.02496	+	12.2727i	0.102029	+	0.413950i
$880$	0.567641	+	2.78049i	0.0191352	+	0.0937304i
$881$	12.3899	+	1.00021i	0.417426	+	0.0336981i	0.287396	−	0.957812i	$-0.407211\pi$
$881$	12.3899	+	1.00021i	0.417426	+	0.0336981i	0.130030	+	0.991510i	$0.458493\pi$
$882$	5.10703	−	8.07613i	0.171963	−	0.271937i
$883$	38.8667	+	34.4329i	1.30797	+	1.15876i	0.976554	+	0.215274i	$0.0690645\pi$
$883$	38.8667	+	34.4329i	1.30797	+	1.15876i	0.331415	+	0.943485i	$0.392474\pi$
$884$	−2.47786	+	3.02400i	−0.0833393	+	0.101708i
$885$	9.23012	−	8.17717i	0.310267	−	0.274873i
$886$	−3.58938	−	22.0863i	−0.120588	−	0.742005i
$887$	28.0834	−	11.9652i	0.942949	−	0.401753i	0.134894	−	0.990860i	$-0.456931\pi$
$887$	28.0834	−	11.9652i	0.942949	−	0.401753i	0.808055	+	0.589107i	$0.200520\pi$
$888$	10.5996	−	6.70281i	0.355701	−	0.224932i
$889$	11.9536	−	13.4928i	0.400911	−	0.452535i
$890$	1.95756	+	24.2487i	0.0656175	+	0.812819i
$891$	0.216875	+	0.649619i	0.00726558	+	0.0217631i
$892$	3.94192	+	0.478636i	0.131985	+	0.0160259i
$893$	12.6806	+	9.52882i	0.424339	+	0.318870i
$894$	1.00063	−	1.22555i	0.0334661	−	0.0409885i
$895$	3.13029	+	2.55580i	0.104634	+	0.0854310i
$896$	−6.58982	−	9.54700i	−0.220150	−	0.318943i
$897$	−1.40492	+	33.4085i	−0.0469089	+	1.11548i
$898$	−4.40532	+	6.38221i	−0.147008	+	0.212977i
$899$	2.41163	−	0.698536i	0.0804322	−	0.0232975i
$900$	1.21155	+	0.766138i	0.0403850	+	0.0255379i
$901$	−1.62865	−	0.264682i	−0.0542583	−	0.00881783i
$902$	7.45199	+	2.82617i	0.248124	+	0.0941010i
$903$	−0.325456	+	0.763873i	−0.0108305	+	0.0254201i
$904$	26.3091	+	25.2702i	0.875027	+	0.840475i
$905$	−8.39632	+	15.9978i	−0.279103	+	0.531786i
$906$	−13.0075	+	1.05007i	−0.432144	+	0.0348863i
$907$	10.1881	+	35.1734i	0.338290	+	1.16791i	0.931765	+	0.363061i	$0.118269\pi$
$907$	10.1881	+	35.1734i	0.338290	+	1.16791i	−0.593475	+	0.804853i	$0.702244\pi$
$908$	3.80856	−	3.65817i	0.126391	−	0.121401i
$909$	0.956482	+	2.52204i	0.0317245	+	0.0836506i
$910$	−2.89507	+	3.25636i	−0.0959708	+	0.107947i
$911$	−5.52918	+	14.5793i	−0.183190	+	0.483032i	−0.994881	−	0.101055i	$-0.967778\pi$
$911$	−5.52918	+	14.5793i	−0.183190	+	0.483032i	0.811691	+	0.584087i	$0.198547\pi$
$912$	−4.69525	−	11.0202i	−0.155475	−	0.364914i
$913$	−0.256212	−	6.35785i	−0.00847939	−	0.210414i
$914$	−25.6367	−	31.3993i	−0.847988	−	1.03860i
$915$			6.00975i			0.198676i
$916$	−0.880585	+	0.718976i	−0.0290954	+	0.0237556i
$917$	−6.36825	−	1.84459i	−0.210298	−	0.0609136i
$918$	−3.20745	−	3.62047i	−0.105862	−	0.119493i
$919$	−9.99054	+	10.4013i	−0.329557	+	0.343106i	−0.865280	−	0.501288i	$-0.832860\pi$
$919$	−9.99054	+	10.4013i	−0.329557	+	0.343106i	0.535723	+	0.844394i	$0.320039\pi$
$920$	−20.2354	−	6.75557i	−0.667141	−	0.222724i
$921$	2.67033	+	3.55357i	0.0879905	+	0.117094i
$922$	−4.75811	−	39.1865i	−0.156700	−	1.29054i
$923$	11.4875	+	0.483079i	0.378114	+	0.0159007i
$924$	0.0246571	−	0.203069i	0.000811158	−	0.00668049i
$925$	−17.8890	+	10.3282i	−0.588187	+	0.339590i
$926$	−28.1113	+	21.1243i	−0.923794	+	0.694186i
$927$	0.394571	−	9.79117i	0.0129594	−	0.321584i
$928$	−14.2797	+	5.41556i	−0.468753	+	0.177774i
$929$	21.4071	−	4.37030i	0.702345	−	0.143385i	0.164436	−	0.986388i	$-0.447420\pi$
$929$	21.4071	−	4.37030i	0.702345	−	0.143385i	0.537909	+	0.843003i	$0.319214\pi$
$930$	0.429573	−	0.0876979i	0.0140862	−	0.00287573i
$931$	15.3038	−	5.80396i	0.501562	−	0.190217i
$932$	−0.235302	+	5.83895i	−0.00770757	+	0.191261i
$933$	−20.0028	+	15.0311i	−0.654862	+	0.492097i
$934$	10.1983	−	5.88799i	0.333699	−	0.192661i
$935$	−0.236590	+	1.94849i	−0.00773731	+	0.0637225i
$936$	−4.87382	−	7.73729i	−0.159306	−	0.252901i
$937$	−3.26542	−	26.8931i	−0.106677	−	0.878560i	−0.943565	−	0.331187i	$-0.892551\pi$
$937$	−3.26542	−	26.8931i	−0.106677	−	0.878560i	0.836889	−	0.547373i	$-0.184372\pi$
$938$	−6.93936	−	9.23461i	−0.226578	−	0.301521i
$939$	19.0950	+	6.37483i	0.623140	+	0.208035i
$940$	1.30428	−	1.35790i	0.0425409	−	0.0442897i
$941$	0.541514	+	0.611243i	0.0176529	+	0.0199260i	0.757271	−	0.653101i	$-0.226532\pi$
$941$	0.541514	+	0.611243i	0.0176529	+	0.0199260i	−0.739618	+	0.673027i	$0.764994\pi$
$942$	−26.2727	−	7.60999i	−0.856011	−	0.247947i
$943$	−54.6132	+	44.5903i	−1.77845	+	1.45206i
$944$		−	62.1130i		−	2.02161i
$945$	−0.499298	−	0.611530i	−0.0162422	−	0.0198931i
$946$	−0.0402674	−	0.999226i	−0.00130921	−	0.0324876i
$947$	20.8318	+	48.8940i	0.676942	+	1.58884i	0.802430	+	0.596746i	$0.203540\pi$
$947$	20.8318	+	48.8940i	0.676942	+	1.58884i	−0.125488	+	0.992095i	$0.540050\pi$
$948$	−1.42481	+	3.75692i	−0.0462757	+	0.122019i
$949$	0.00488704	−	2.79077i	0.000158640	−	0.0905924i
$950$	5.94536	+	15.6766i	0.192893	+	0.508617i
$951$	2.67237	−	2.56685i	0.0866575	−	0.0832357i
$952$	−1.94073	−	6.70019i	−0.0628995	−	0.217154i
$953$	55.0399	−	4.44328i	1.78292	−	0.143932i	0.855463	−	0.517865i	$-0.173273\pi$
$953$	55.0399	−	4.44328i	1.78292	−	0.143932i	0.927456	+	0.373933i	$0.121991\pi$
$954$	−0.371464	+	0.707766i	−0.0120266	+	0.0229148i
$955$	3.90384	+	3.74969i	0.126325	+	0.121337i
$956$	−3.39935	+	7.97856i	−0.109943	+	0.258045i
$957$	5.09132	+	1.93088i	0.164579	+	0.0624166i
$958$	−15.6641	−	2.54566i	−0.506083	−	0.0822465i
$959$	−3.61159	−	2.28383i	−0.116624	−	0.0737487i
$960$	5.39856	−	1.56371i	0.174238	−	0.0504685i
$961$	17.5534	−	25.4304i	0.566237	−	0.820336i
$962$	−27.2067	+	2.14841i	−0.877179	+	0.0692674i
$963$	−9.17445	−	13.2915i	−0.295642	−	0.428312i
$964$	−1.48462	−	1.21216i	−0.0478165	−	0.0390409i
$965$	5.17605	−	6.33951i	0.166623	−	0.204076i
$966$	9.87846	+	7.42318i	0.317834	+	0.238837i
$967$	23.2593	+	2.82420i	0.747970	+	0.0908200i	0.485641	−	0.874158i	$-0.338586\pi$
$967$	23.2593	+	2.82420i	0.747970	+	0.0908200i	0.262329	+	0.964978i	$0.415509\pi$
$968$	8.45776	+	25.3341i	0.271843	+	0.814268i
$969$	−0.666673	−	8.25823i	−0.0214166	−	0.265293i
$970$	6.27527	−	7.08332i	0.201487	−	0.227432i
$971$	32.1275	−	20.3162i	1.03102	−	0.651978i	0.0919715	−	0.995762i	$-0.470683\pi$
$971$	32.1275	−	20.3162i	1.03102	−	0.651978i	0.939049	+	0.343784i	$0.111709\pi$
$972$	−0.315692	+	0.134504i	−0.0101258	+	0.00431421i
$973$	1.48423	+	9.13281i	0.0475821	+	0.292785i
$974$	−43.0038	+	38.0980i	−1.37793	+	1.22074i
$975$	7.50799	+	13.0570i	0.240448	+	0.418158i
$976$	22.6583	+	20.0735i	0.725275	+	0.642538i
$977$	1.73616	−	2.74551i	0.0555445	−	0.0878367i	−0.816276	−	0.577662i	$-0.803965\pi$
$977$	1.73616	−	2.74551i	0.0555445	−	0.0878367i	0.871821	+	0.489825i	$0.162939\pi$
$978$	8.79430	+	0.709950i	0.281211	+	0.0227017i
$979$	−2.40041	−	11.7580i	−0.0767173	−	0.375786i
$980$	−0.464954	−	1.88639i	−0.0148524	−	0.0602586i
$981$	−2.07991	+	12.7982i	−0.0664065	+	0.408615i
$982$	2.26585	+	3.58315i	0.0723061	+	0.114343i
$983$	3.69992	+	7.04961i	0.118009	+	0.224847i	0.937295	−	0.348538i	$-0.113322\pi$
$983$	3.69992	+	7.04961i	0.118009	+	0.224847i	−0.819285	+	0.573386i	$0.805630\pi$
$984$	5.36433	−	18.5198i	0.171008	−	0.590390i
$985$	−0.244107	+	1.19571i	−0.00777788	+	0.0380986i
$986$	−38.4256	+	1.54850i	−1.22372	+	0.0493142i
$987$	4.66250	−	2.44707i	0.148409	−	0.0778910i
$988$	−0.266700	+	3.23307i	−0.00848486	+	0.102858i
$989$	7.83335	+	4.11126i	0.249086	+	0.130730i
$990$	0.859042	+	0.407621i	0.0273022	+	0.0129550i
$991$	−10.5624	−	18.2947i	−0.335527	−	0.581150i	0.648059	−	0.761590i	$-0.275581\pi$
$991$	−10.5624	−	18.2947i	−0.335527	−	0.581150i	−0.983586	+	0.180440i	$0.942248\pi$
$992$	0.303292	−	0.525317i	0.00962952	−	0.0166788i
$993$	−28.5296	+	19.6926i	−0.905361	+	0.624925i
$994$	2.55244	−	3.39669i	0.0809586	−	0.107736i
$995$	−10.9912	−	6.34577i	−0.348444	−	0.201174i
$996$	3.16493	−	0.384293i	0.100285	−	0.0121768i
$997$	11.0385	+	23.2632i	0.349594	+	0.736753i	0.999734	−	0.0230612i	$-0.00734127\pi$
$997$	11.0385	+	23.2632i	0.349594	+	0.736753i	−0.650141	+	0.759814i	$0.725290\pi$
$998$	4.96260	+	5.16662i	0.157088	+	0.163546i
$999$	0.397896	−	4.92882i	0.0125889	−	0.155941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.10.4	✓	360
169.17	even	78	inner	507.2.t.b.355.4	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.10.4	✓	360	1.1	even	1	trivial
507.2.t.b.355.4	yes	360	169.17	even	78	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49980 - 0.306186i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(0.315692 + 0.134504i) q^{4} +(-0.217058 + 0.880640i) q^{5} +(1.52949 + 0.0616365i) q^{6} +(0.786387 - 0.373145i) q^{7} +(2.08725 + 1.44072i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})\)	\(q+(-1.49980 - 0.306186i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(0.315692 + 0.134504i) q^{4} +(-0.217058 + 0.880640i) q^{5} +(1.52949 + 0.0616365i) q^{6} +(0.786387 - 0.373145i) q^{7} +(2.08725 + 1.44072i) q^{8} +(0.948536 - 0.316668i) q^{9} +(0.595184 - 1.25432i) q^{10} +(-0.216875 + 0.649619i) q^{11} +(-0.333180 - 0.0821214i) q^{12} +(-2.69460 - 2.39565i) q^{13} +(-1.29368 + 0.318862i) q^{14} +(0.0729828 - 0.904054i) q^{15} +(-3.16475 - 3.29485i) q^{16} +(-1.35460 - 2.85477i) q^{17} +(-1.51957 + 0.184510i) q^{18} +(-2.27071 - 1.31100i) q^{19} +(-0.186973 + 0.248816i) q^{20} +(-0.716347 + 0.494459i) q^{21} +(0.524174 - 0.907895i) q^{22} +(4.63702 + 8.03156i) q^{23} +(-2.29133 - 1.08725i) q^{24} +(3.69887 + 1.94132i) q^{25} +(3.30785 + 4.41804i) q^{26} +(-0.885456 + 0.464723i) q^{27} +(0.298446 - 0.0120269i) q^{28} +(-1.59035 + 7.79004i) q^{29} +(-0.386269 + 1.33355i) q^{30} +(-0.146755 - 0.279618i) q^{31} +(1.02663 + 1.62348i) q^{32} +(0.109860 - 0.675996i) q^{33} +(1.15754 + 4.69634i) q^{34} +(0.157915 + 0.773518i) q^{35} +(0.342038 + 0.0276122i) q^{36} +(-2.64286 + 4.17935i) q^{37} +(3.00420 + 2.66149i) q^{38} +(3.04400 + 1.93238i) q^{39} +(-1.72181 + 1.52539i) q^{40} +(1.21950 + 7.50390i) q^{41} +(1.22577 - 0.522254i) q^{42} +(0.806242 - 0.509837i) q^{43} +(-0.155842 + 0.175909i) q^{44} +(0.0729828 + 0.904054i) q^{45} +(-4.49546 - 13.4655i) q^{46} +(-6.00539 - 0.729187i) q^{47} +(3.65229 + 2.74452i) q^{48} +(-3.94795 + 4.83536i) q^{49} +(-4.95316 - 4.04413i) q^{50} +(1.79500 + 2.60051i) q^{51} +(-0.528441 - 1.11872i) q^{52} +(0.296634 - 0.429748i) q^{53} +(1.47030 - 0.425877i) q^{54} +(-0.525006 - 0.331994i) q^{55} +(2.17899 + 0.354120i) q^{56} +(2.45160 + 0.929771i) q^{57} +(4.77041 - 11.1966i) q^{58} +(9.80531 + 9.41813i) q^{59} +(0.144639 - 0.275586i) q^{60} +(-6.60451 + 0.533171i) q^{61} +(0.134488 + 0.464306i) q^{62} +(0.627754 - 0.602966i) q^{63} +(2.19741 + 5.79410i) q^{64} +(2.69459 - 1.85298i) q^{65} +(-0.371749 + 0.980222i) q^{66} +(3.39819 + 7.97585i) q^{67} +(-0.0436606 - 1.08343i) q^{68} +(-5.86533 - 7.18373i) q^{69} -1.20847i q^{70} +(-2.47011 + 2.01678i) q^{71} +(2.43606 + 0.705614i) q^{72} +(0.513272 + 0.579364i) q^{73} +(5.24342 - 5.45898i) q^{74} +(-3.96238 - 1.32284i) q^{75} +(-0.540511 - 0.719290i) q^{76} +(0.0718549 + 0.591778i) q^{77} +(-3.97372 - 3.83021i) q^{78} +(1.41139 - 11.6238i) q^{79} +(3.58851 - 2.07183i) q^{80} +(0.799443 - 0.600742i) q^{81} +(0.468582 - 11.6277i) q^{82} +(-8.68714 + 3.29460i) q^{83} +(-0.292651 + 0.0597452i) q^{84} +(2.80805 - 0.573267i) q^{85} +(-1.36531 + 0.517793i) q^{86} +(0.320143 - 7.94427i) q^{87} +(-1.38859 + 1.04346i) q^{88} +(-15.1749 + 8.76121i) q^{89} +(0.167349 - 1.37825i) q^{90} +(-3.01293 - 0.878426i) q^{91} +(0.383596 + 3.15920i) q^{92} +(0.189708 + 0.252456i) q^{93} +(8.78362 + 2.93240i) q^{94} +(1.64739 - 1.71512i) q^{95} +(-1.27376 - 1.43777i) q^{96} +(6.54695 + 1.89635i) q^{97} +(7.40166 - 6.04327i) q^{98} +0.684865i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

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