LMFDB - Embedded newform 507.2.t.a.10.1

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:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	507.10
Dual form			507.2.t.a.355.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70648 - 0.552531i) q^{2} +(0.987050 - 0.160411i) q^{3} +(5.17976 + 2.20689i) q^{4} +(-0.330566 + 1.34116i) q^{5} +(-2.76006 - 0.111227i) q^{6} +(-2.19257 + 1.04039i) q^{7} +(-8.25286 - 5.69654i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})$	\(q+(-2.70648 - 0.552531i) q^{2} +(0.987050 - 0.160411i) q^{3} +(5.17976 + 2.20689i) q^{4} +(-0.330566 + 1.34116i) q^{5} +(-2.76006 - 0.111227i) q^{6} +(-2.19257 + 1.04039i) q^{7} +(-8.25286 - 5.69654i) q^{8} +(0.948536 - 0.316668i) q^{9} +(1.63570 - 3.44716i) q^{10} +(0.200014 - 0.599116i) q^{11} +(5.46669 + 1.34742i) q^{12} +(3.19315 - 1.67445i) q^{13} +(6.50898 - 1.60432i) q^{14} +(-0.111148 + 1.37682i) q^{15} +(11.3882 + 11.8563i) q^{16} +(0.810467 + 1.70802i) q^{17} +(-2.74216 + 0.332958i) q^{18} +(2.06266 + 1.19088i) q^{19} +(-4.67204 + 6.21735i) q^{20} +(-1.99729 + 1.37863i) q^{21} +(-0.872365 + 1.51098i) q^{22} +(-1.18337 - 2.04966i) q^{23} +(-9.05977 - 4.29892i) q^{24} +(2.73785 + 1.43693i) q^{25} +(-9.56737 + 2.76753i) q^{26} +(0.885456 - 0.464723i) q^{27} +(-13.6530 + 0.550197i) q^{28} +(-1.23682 + 6.05832i) q^{29} +(1.06155 - 3.66491i) q^{30} +(0.955788 + 1.82110i) q^{31} +(-13.5516 - 21.4301i) q^{32} +(0.101319 - 0.623443i) q^{33} +(-1.24977 - 5.07053i) q^{34} +(-0.670535 - 3.28450i) q^{35} +(5.61204 + 0.453051i) q^{36} +(-4.13797 + 6.54368i) q^{37} +(-4.92453 - 4.36276i) q^{38} +(2.88320 - 2.16498i) q^{39} +(10.3681 - 9.18530i) q^{40} +(0.997882 + 6.14021i) q^{41} +(6.16734 - 2.62766i) q^{42} +(-8.70030 + 5.50173i) q^{43} +(2.35821 - 2.66187i) q^{44} +(0.111148 + 1.37682i) q^{45} +(2.07027 + 6.20120i) q^{46} +(12.8572 + 1.56114i) q^{47} +(13.1426 + 9.87600i) q^{48} +(-0.702162 + 0.859992i) q^{49} +(-6.61597 - 5.40177i) q^{50} +(1.07396 + 1.55590i) q^{51} +(20.2351 - 1.62630i) q^{52} +(-2.73100 + 3.95653i) q^{53} +(-2.65324 + 0.768520i) q^{54} +(0.737392 + 0.466298i) q^{55} +(24.0216 + 3.90388i) q^{56} +(2.22698 + 0.844580i) q^{57} +(6.69482 - 15.7133i) q^{58} +(9.59097 + 9.21225i) q^{59} +(-3.61420 + 6.88629i) q^{60} +(5.67950 - 0.458497i) q^{61} +(-1.58060 - 5.45687i) q^{62} +(-1.75027 + 1.68116i) q^{63} +(13.1770 + 34.7449i) q^{64} +(1.19015 + 4.83604i) q^{65} +(-0.618689 + 1.63135i) q^{66} +(-2.73211 - 6.41249i) q^{67} +(0.428606 + 10.6358i) q^{68} +(-1.49684 - 1.83329i) q^{69} +9.25990i q^{70} +(-7.22763 + 5.90118i) q^{71} +(-9.63205 - 2.78996i) q^{72} +(-5.13228 - 5.79315i) q^{73} +(14.8149 - 15.4239i) q^{74} +(2.93290 + 0.979145i) q^{75} +(8.05593 + 10.7205i) q^{76} +(0.184767 + 1.52170i) q^{77} +(-8.99954 + 4.26641i) q^{78} +(1.67473 - 13.7926i) q^{79} +(-19.6657 + 11.3540i) q^{80} +(0.799443 - 0.600742i) q^{81} +(0.691915 - 17.1697i) q^{82} +(8.40285 - 3.18678i) q^{83} +(-13.3879 + 2.73317i) q^{84} +(-2.55864 + 0.522350i) q^{85} +(26.5870 - 10.0831i) q^{86} +(-0.248976 + 6.17827i) q^{87} +(-5.06358 + 3.80503i) q^{88} +(1.01750 - 0.587456i) q^{89} +(0.459914 - 3.78773i) q^{90} +(-5.25914 + 6.99346i) q^{91} +(-1.60621 - 13.2283i) q^{92} +(1.23554 + 1.64420i) q^{93} +(-33.9350 - 11.3292i) q^{94} +(-2.27899 + 2.37269i) q^{95} +(-16.8137 - 18.9787i) q^{96} +(5.86277 + 1.69817i) q^{97} +(2.37556 - 1.93958i) q^{98} -0.631622i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * 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 $

$2$	−2.70648	−	0.552531i	−1.91377	−	0.390698i	−0.913884	−	0.405976i	$-0.866932\pi$
$2$	−2.70648	−	0.552531i	−1.91377	−	0.390698i	−0.999883	+	0.0152779i	$0.995137\pi$
$3$	0.987050	−	0.160411i	0.569874	−	0.0926135i
$3$	0.987050	−	0.160411i	0.569874	−	0.0926135i
$4$	5.17976	+	2.20689i	2.58988	+	1.10344i
$5$	−0.330566	+	1.34116i	−0.147833	+	0.599784i	0.849551	+	0.527506i	$0.176873\pi$
$5$	−0.330566	+	1.34116i	−0.147833	+	0.599784i	−0.997385	+	0.0722776i	$0.976973\pi$
$6$	−2.76006	−	0.111227i	−1.12679	−	0.0454081i
$7$	−2.19257	+	1.04039i	−0.828713	+	0.393229i	−0.795303	−	0.606212i	$-0.792688\pi$
$7$	−2.19257	+	1.04039i	−0.828713	+	0.393229i	−0.0334106	+	0.999442i	$0.510637\pi$
$8$	−8.25286	−	5.69654i	−2.91783	−	2.01403i
$9$	0.948536	−	0.316668i	0.316179	−	0.105556i
$10$	1.63570	−	3.44716i	0.517253	−	1.09009i
$11$	0.200014	−	0.599116i	0.0603066	−	0.180640i	−0.914073	−	0.405549i	$-0.867080\pi$
$11$	0.200014	−	0.599116i	0.0603066	−	0.180640i	0.974380	+	0.224909i	$0.0722085\pi$
$12$	5.46669	+	1.34742i	1.57810	+	0.388966i
$13$	3.19315	−	1.67445i	0.885621	−	0.464408i
$13$	3.19315	−	1.67445i	0.885621	−	0.464408i
$14$	6.50898	−	1.60432i	1.73960	−	0.428772i
$15$	−0.111148	+	1.37682i	−0.0286983	+	0.355492i
$16$	11.3882	+	11.8563i	2.84704	+	2.96408i
$17$	0.810467	+	1.70802i	0.196567	+	0.414256i	0.977670	−	0.210146i	$-0.0673939\pi$
$17$	0.810467	+	1.70802i	0.196567	+	0.414256i	−0.781103	+	0.624402i	$0.785343\pi$
$18$	−2.74216	+	0.332958i	−0.646333	+	0.0784790i
$19$	2.06266	+	1.19088i	0.473206	+	0.273206i	0.717581	−	0.696475i	$-0.245249\pi$
$19$	2.06266	+	1.19088i	0.473206	+	0.273206i	−0.244375	+	0.969681i	$0.578583\pi$
$20$	−4.67204	+	6.21735i	−1.04470	+	1.39024i
$21$	−1.99729	+	1.37863i	−0.435844	+	0.300841i
$22$	−0.872365	+	1.51098i	−0.185989	+	0.322142i
$23$	−1.18337	−	2.04966i	−0.246750	−	0.427384i	0.715872	−	0.698231i	$-0.246029\pi$
$23$	−1.18337	−	2.04966i	−0.246750	−	0.427384i	−0.962622	+	0.270848i	$0.912696\pi$
$24$	−9.05977	−	4.29892i	−1.84932	−	0.877513i
$25$	2.73785	+	1.43693i	0.547570	+	0.287387i
$26$	−9.56737	+	2.76753i	−1.87632	+	0.542758i
$27$	0.885456	−	0.464723i	0.170406	−	0.0894360i
$28$	−13.6530	+	0.550197i	−2.58017	+	0.103977i
$29$	−1.23682	+	6.05832i	−0.229671	+	1.12500i	0.687400	+	0.726279i	$0.258752\pi$
$29$	−1.23682	+	6.05832i	−0.229671	+	1.12500i	−0.917071	+	0.398724i	$0.869453\pi$
$30$	1.06155	−	3.66491i	0.193812	−	0.669117i
$31$	0.955788	+	1.82110i	0.171665	+	0.327080i	0.956055	−	0.293188i	$-0.0947163\pi$
$31$	0.955788	+	1.82110i	0.171665	+	0.327080i	−0.784390	+	0.620268i	$0.787024\pi$
$32$	−13.5516	−	21.4301i	−2.39560	−	3.78834i
$33$	0.101319	−	0.623443i	0.0176374	−	0.108527i
$34$	−1.24977	−	5.07053i	−0.214334	−	0.869589i
$35$	−0.670535	−	3.28450i	−0.113341	−	0.555181i
$36$	5.61204	+	0.453051i	0.935340	+	0.0755085i
$37$	−4.13797	+	6.54368i	−0.680278	+	1.07577i	0.311799	+	0.950148i	$0.399068\pi$
$37$	−4.13797	+	6.54368i	−0.680278	+	1.07577i	−0.992078	+	0.125626i	$0.959906\pi$
$38$	−4.92453	−	4.36276i	−0.798865	−	0.707732i
$39$	2.88320	−	2.16498i	0.461682	−	0.346674i
$40$	10.3681	−	9.18530i	1.63933	−	1.45232i
$41$	0.997882	+	6.14021i	0.155843	+	0.958940i	0.940694	+	0.339256i	$0.110175\pi$
$41$	0.997882	+	6.14021i	0.155843	+	0.958940i	−0.784851	+	0.619684i	$0.787261\pi$
$42$	6.16734	−	2.62766i	0.951641	−	0.405456i
$43$	−8.70030	+	5.50173i	−1.32678	+	0.839007i	−0.994557	−	0.104193i	$-0.966774\pi$
$43$	−8.70030	+	5.50173i	−1.32678	+	0.839007i	−0.332226	+	0.943200i	$0.607800\pi$
$44$	2.35821	−	2.66187i	0.355514	−	0.401292i
$45$	0.111148	+	1.37682i	0.0165690	+	0.205244i
$46$	2.07027	+	6.20120i	0.305244	+	0.914317i
$47$	12.8572	+	1.56114i	1.87541	+	0.227716i	0.977271	−	0.211995i	$-0.0679961\pi$
$47$	12.8572	+	1.56114i	1.87541	+	0.227716i	0.898139	+	0.439711i	$0.144919\pi$
$48$	13.1426	+	9.87600i	1.89697	+	1.42548i
$49$	−0.702162	+	0.859992i	−0.100309	+	0.122856i
$50$	−6.61597	−	5.40177i	−0.935640	−	0.763926i
$51$	1.07396	+	1.55590i	0.150384	+	0.217869i
$52$	20.2351	−	1.62630i	2.80610	−	0.225527i
$53$	−2.73100	+	3.95653i	−0.375132	+	0.543472i	−0.964394	−	0.264470i	$-0.914803\pi$
$53$	−2.73100	+	3.95653i	−0.375132	+	0.543472i	0.589262	+	0.807942i	$0.299418\pi$
$54$	−2.65324	+	0.768520i	−0.361060	+	0.104582i
$55$	0.737392	+	0.466298i	0.0994299	+	0.0628756i
$56$	24.0216	+	3.90388i	3.21002	+	0.521679i
$57$	2.22698	+	0.844580i	0.294970	+	0.111867i
$58$	6.69482	−	15.7133i	0.879073	−	2.06326i
$59$	9.59097	+	9.21225i	1.24864	+	1.19933i	0.971115	+	0.238613i	$0.0766929\pi$
$59$	9.59097	+	9.21225i	1.24864	+	1.19933i	0.277523	+	0.960719i	$0.410487\pi$
$60$	−3.61420	+	6.88629i	−0.466591	+	0.889016i
$61$	5.67950	−	0.458497i	0.727185	−	0.0587045i	0.288671	−	0.957428i	$-0.406787\pi$
$61$	5.67950	−	0.458497i	0.727185	−	0.0587045i	0.438515	+	0.898724i	$0.355505\pi$
$62$	−1.58060	−	5.45687i	−0.200737	−	0.693023i
$63$	−1.75027	+	1.68116i	−0.220514	+	0.211806i
$64$	13.1770	+	34.7449i	1.64713	+	4.34311i
$65$	1.19015	+	4.83604i	0.147620	+	0.599837i
$66$	−0.618689	+	1.63135i	−0.0761554	+	0.200805i
$67$	−2.73211	−	6.41249i	−0.333780	−	0.783411i	−0.999314	−	0.0370427i	$-0.988206\pi$
$67$	−2.73211	−	6.41249i	−0.333780	−	0.783411i	0.665534	−	0.746368i	$-0.268204\pi$
$68$	0.428606	+	10.6358i	0.0519762	+	1.28977i
$69$	−1.49684	−	1.83329i	−0.180198	−	0.220702i
$70$			9.25990i			1.10677i
$71$	−7.22763	+	5.90118i	−0.857762	+	0.700341i	−0.955538	−	0.294867i	$-0.904725\pi$
$71$	−7.22763	+	5.90118i	−0.857762	+	0.700341i	0.0977760	+	0.995208i	$0.468827\pi$
$72$	−9.63205	−	2.78996i	−1.13515	−	0.328800i
$73$	−5.13228	−	5.79315i	−0.600688	−	0.678037i	0.366990	−	0.930225i	$-0.380388\pi$
$73$	−5.13228	−	5.79315i	−0.600688	−	0.678037i	−0.967678	+	0.252188i	$0.918850\pi$
$74$	14.8149	−	15.4239i	1.72220	−	1.79300i
$75$	2.93290	+	0.979145i	0.338662	+	0.113062i
$76$	8.05593	+	10.7205i	0.924079	+	1.22973i
$77$	0.184767	+	1.52170i	0.0210562	+	0.173413i
$78$	−8.99954	+	4.26641i	−1.01900	+	0.483076i
$79$	1.67473	−	13.7926i	0.188422	−	1.55179i	−0.525028	−	0.851085i	$-0.675945\pi$
$79$	1.67473	−	13.7926i	0.188422	−	1.55179i	0.713449	−	0.700707i	$-0.247132\pi$
$80$	−19.6657	+	11.3540i	−2.19870	+	1.26942i
$81$	0.799443	−	0.600742i	0.0888270	−	0.0667491i
$82$	0.691915	−	17.1697i	0.0764092	−	1.89608i
$83$	8.40285	−	3.18678i	0.922332	−	0.349795i	0.152693	−	0.988274i	$-0.451205\pi$
$83$	8.40285	−	3.18678i	0.922332	−	0.349795i	0.769639	+	0.638479i	$0.220436\pi$
$84$	−13.3879	+	2.73317i	−1.46074	+	0.298213i
$85$	−2.55864	+	0.522350i	−0.277524	+	0.0566568i
$86$	26.5870	−	10.0831i	2.86695	−	1.08729i
$87$	−0.248976	+	6.17827i	−0.0266930	+	0.662380i
$88$	−5.06358	+	3.80503i	−0.539779	+	0.405618i
$89$	1.01750	−	0.587456i	0.107855	−	0.0622702i	−0.445102	−	0.895480i	$-0.646833\pi$
$89$	1.01750	−	0.587456i	0.107855	−	0.0622702i	0.552957	+	0.833210i	$0.313499\pi$
$90$	0.459914	−	3.78773i	0.0484792	−	0.399262i
$91$	−5.25914	+	6.99346i	−0.551307	+	0.733113i
$92$	−1.60621	−	13.2283i	−0.167459	−	1.37915i
$93$	1.23554	+	1.64420i	0.128119	+	0.170496i
$94$	−33.9350	−	11.3292i	−3.50013	−	1.16851i
$95$	−2.27899	+	2.37269i	−0.233820	+	0.243432i
$96$	−16.8137	−	18.9787i	−1.71604	−	1.93701i
$97$	5.86277	+	1.69817i	0.595275	+	0.172423i	0.562160	−	0.827028i	$-0.309970\pi$
$97$	5.86277	+	1.69817i	0.595275	+	0.172423i	0.0331141	+	0.999452i	$0.489458\pi$
$98$	2.37556	−	1.93958i	0.239967	−	0.195927i
$99$		−	0.631622i		−	0.0634804i
$100$	11.0102	+	13.4851i	1.10102	+	1.34851i
$101$	0.179781	+	4.46121i	0.0178888	+	0.443907i	0.983170	+	0.182693i	$0.0584816\pi$
$101$	0.179781	+	4.46121i	0.0178888	+	0.443907i	−0.965281	+	0.261213i	$0.915877\pi$
$102$	−2.04696	−	4.80439i	−0.202679	−	0.475705i
$103$	−3.35664	+	8.85072i	−0.330739	+	0.872088i	0.661747	+	0.749728i	$0.269815\pi$
$103$	−3.35664	+	8.85072i	−0.330739	+	0.872088i	−0.992486	+	0.122360i	$0.960954\pi$
$104$	−35.8912	−	4.37094i	−3.51942	−	0.428606i
$105$	−1.18872	−	3.13440i	−0.116007	−	0.305886i
$106$	9.57749	−	9.19930i	0.930248	−	0.893515i
$107$	−5.73118	−	19.7863i	−0.554054	−	1.91282i	−0.365786	−	0.930699i	$-0.619200\pi$
$107$	−5.73118	−	19.7863i	−0.554054	−	1.91282i	−0.188268	−	0.982118i	$-0.560287\pi$
$108$	5.61204	−	0.453051i	0.540019	−	0.0435948i
$109$	3.04225	−	5.79653i	0.291395	−	0.555207i	−0.695117	−	0.718897i	$-0.744647\pi$
$109$	3.04225	−	5.79653i	0.291395	−	0.555207i	0.986512	+	0.163690i	$0.0523397\pi$
$110$	−1.73809	−	1.66946i	−0.165720	−	0.159176i
$111$	−3.03471	+	7.12272i	−0.288042	+	0.676058i
$112$	−37.3045	−	14.1477i	−3.52494	−	1.33683i
$113$	11.9454	+	1.94131i	1.12372	+	0.182623i	0.693748	−	0.720217i	$-0.255958\pi$
$113$	11.9454	+	1.94131i	1.12372	+	0.182623i	0.429976	+	0.902840i	$0.358522\pi$
$114$	−5.56060	−	3.51631i	−0.520798	−	0.329332i
$115$	3.14010	−	0.909541i	0.292816	−	0.0848151i
$116$	−19.7765	+	28.6511i	−1.83620	+	2.66019i
$117$	2.49858	−	2.59944i	0.230994	−	0.240319i
$118$	−20.8677	−	30.2320i	−1.92102	−	2.78308i
$119$	−3.55401	−	2.90176i	−0.325796	−	0.266004i
$120$	8.76037	−	10.7295i	0.799709	−	0.979466i
$121$	8.47494	+	6.36850i	0.770449	+	0.578955i
$122$	−15.6248	−	1.89719i	−1.41460	−	0.171763i
$123$	1.96992	+	5.90063i	0.177622	+	0.532042i
$124$	0.931782	+	11.5422i	0.0836765	+	1.03652i
$125$	−7.41204	+	8.36646i	−0.662953	+	0.748319i
$126$	5.66597	−	3.58294i	0.504765	−	0.319194i
$127$	−15.8477	+	6.75207i	−1.40626	+	0.599150i	−0.955898	−	0.293699i	$-0.905114\pi$
$127$	−15.8477	+	6.75207i	−1.40626	+	0.599150i	−0.450358	+	0.892848i	$0.648704\pi$
$128$	−8.33104	−	51.2629i	−0.736367	−	4.53105i
$129$	−7.70509	+	6.82611i	−0.678395	+	0.601006i
$130$	−0.549053	−	13.7462i	−0.0481551	−	1.20562i
$131$	6.08833	+	5.39379i	0.531940	+	0.471258i	0.885817	−	0.464034i	$-0.153599\pi$
$131$	6.08833	+	5.39379i	0.531940	+	0.471258i	−0.353877	+	0.935292i	$0.615137\pi$
$132$	1.90068	−	3.00568i	0.165433	−	0.261611i
$133$	−5.76149	−	0.465116i	−0.499585	−	0.0403306i
$134$	3.85128	+	18.8648i	0.332700	+	1.62967i
$135$	0.330566	+	1.34116i	0.0284506	+	0.115428i
$136$	3.04115	−	18.7129i	0.260776	−	1.60462i
$137$	−6.20147	−	9.80685i	−0.529828	−	0.837855i	0.469147	−	0.883120i	$-0.344561\pi$
$137$	−6.20147	−	9.80685i	−0.529828	−	0.837855i	−0.998975	+	0.0452645i	$0.985587\pi$
$138$	3.03820	+	5.78880i	0.258629	+	0.492776i
$139$	5.86455	−	20.2468i	0.497424	−	1.71731i	−0.181762	−	0.983343i	$-0.558180\pi$
$139$	5.86455	−	20.2468i	0.497424	−	1.71731i	0.679186	−	0.733966i	$-0.262333\pi$
$140$	3.77531	−	18.4927i	0.319072	−	1.56292i
$141$	12.9411	−	0.521508i	1.08984	−	0.0439189i
$142$	22.8220	−	11.9779i	1.91518	−	1.00516i
$143$	−0.364512	−	2.24798i	−0.0304820	−	0.187986i
$144$	14.5566	+	7.63989i	1.21305	+	0.636658i
$145$	−7.71632	−	3.66144i	−0.640805	−	0.304066i
$146$	10.6895	+	18.5148i	0.884669	+	1.53229i
$147$	−0.555116	+	0.961490i	−0.0457852	+	0.0793024i
$148$	−35.8749	+	24.7626i	−2.94890	+	2.03548i
$149$	5.53324	−	7.36340i	0.453301	−	0.603233i	−0.513712	−	0.857963i	$-0.671730\pi$
$149$	5.53324	−	7.36340i	0.453301	−	0.603233i	0.967012	+	0.254729i	$0.0819864\pi$
$150$	−7.39680	−	4.27055i	−0.603946	−	0.348689i
$151$	−14.4775	+	1.75789i	−1.17816	+	0.143055i	−0.686102	−	0.727505i	$-0.740680\pi$
$151$	−14.4775	+	1.75789i	−1.17816	+	0.143055i	−0.492062	+	0.870560i	$0.663757\pi$
$152$	−10.2389	−	21.5781i	−0.830488	−	1.75022i
$153$	1.30963	+	1.36347i	0.105878	+	0.110230i
$154$	0.340716	−	4.22053i	0.0274557	−	0.340100i
$155$	−2.75834	+	0.679869i	−0.221555	+	0.0546084i
$156$	19.7122	−	4.85117i	1.57824	−	0.388405i
$157$	6.42935	+	1.58469i	0.513118	+	0.126472i	0.487369	−	0.873196i	$-0.337957\pi$
$157$	6.42935	+	1.58469i	0.513118	+	0.126472i	0.0257493	+	0.999668i	$0.491803\pi$
$158$	−12.1535	+	36.4041i	−0.966878	+	2.89615i
$159$	−2.06096	+	4.34338i	−0.163445	+	0.344453i
$160$	33.2208	−	11.0907i	2.62633	−	0.876799i
$161$	4.72706	+	3.26286i	0.372545	+	0.257149i
$162$	−2.49560	+	1.18418i	−0.196073	+	0.0930377i
$163$	15.9721	+	0.643652i	1.25103	+	0.0504147i	0.656914	−	0.753966i	$-0.271862\pi$
$163$	15.9721	+	0.643652i	1.25103	+	0.0504147i	0.594114	+	0.804381i	$0.297503\pi$
$164$	−8.38198	+	34.0070i	−0.654523	+	2.65550i
$165$	0.802642	+	0.341974i	0.0624856	+	0.0266226i
$166$	−24.5029	+	3.98211i	−1.90179	+	0.309072i
$167$	−7.74902	−	1.58197i	−0.599637	−	0.122417i	−0.109388	−	0.993999i	$-0.534889\pi$
$167$	−7.74902	−	1.58197i	−0.599637	−	0.122417i	−0.490249	+	0.871582i	$0.663094\pi$
$168$	24.3367			1.87762
$169$	7.39246	−	10.6935i	0.568650	−	0.822579i
$170$	7.21351			0.553251
$171$	2.33362	+	0.476411i	0.178456	+	0.0364321i
$172$	−57.2071	+	9.29707i	−4.36200	+	0.708895i
$173$	3.92784	+	1.67350i	0.298628	+	0.127234i	0.536084	−	0.844165i	$-0.319903\pi$
$173$	3.92784	+	1.67350i	0.298628	+	0.127234i	−0.237455	+	0.971398i	$0.576313\pi$
$174$	4.08753	−	16.5838i	0.309875	−	1.25721i
$175$	−7.49790	−	0.302155i	−0.566788	−	0.0228408i
$176$	9.38111	−	4.45139i	0.707128	−	0.335536i
$177$	10.9445	+	7.55445i	0.822640	+	0.567827i
$178$	−3.07843	+	1.02773i	−0.230738	+	0.0770318i
$179$	5.64376	−	11.8940i	0.421834	−	0.888997i	−0.575622	−	0.817716i	$-0.695240\pi$
$179$	5.64376	−	11.8940i	0.421834	−	0.888997i	0.997456	−	0.0712809i	$-0.0227087\pi$
$180$	−2.46276	+	7.37687i	−0.183563	+	0.549839i
$181$	−5.24629	−	1.29309i	−0.389954	−	0.0961150i	0.0394639	−	0.999221i	$-0.487435\pi$
$181$	−5.24629	−	1.29309i	−0.389954	−	0.0961150i	−0.429418	+	0.903106i	$0.641281\pi$
$182$	18.0978	−	16.0218i	1.34150	−	1.18761i
$183$	5.53240	−	1.36361i	0.408967	−	0.100801i
$184$	−1.90976	+	23.6567i	−0.140790	+	1.74399i
$185$	−7.40823	−	7.71279i	−0.544664	−	0.567055i
$186$	−2.43548	−	5.13266i	−0.178578	−	0.376345i
$187$	1.18541	−	0.143935i	0.0866858	−	0.0105256i
$188$	63.1517	+	36.4607i	4.60581	+	2.65917i
$189$	−1.45793	+	1.94016i	−0.106049	+	0.141126i
$190$	7.47903	−	5.16240i	0.542586	−	0.374520i
$191$	0.770329	−	1.33425i	0.0557391	−	0.0965429i	−0.836810	−	0.547494i	$-0.815582\pi$
$191$	0.770329	−	1.33425i	0.0557391	−	0.0965429i	0.892549	+	0.450951i	$0.148915\pi$
$192$	18.5798	+	32.1812i	1.34088	+	2.32248i
$193$	−14.4278	−	6.84609i	−1.03854	−	0.492793i	−0.168461	−	0.985708i	$-0.553880\pi$
$193$	−14.4278	−	6.84609i	−1.03854	−	0.492793i	−0.870077	+	0.492916i	$0.835931\pi$
$194$	−14.9292	−	7.83543i	−1.07185	−	0.562551i
$195$	1.95049	+	4.58250i	0.139678	+	0.328159i
$196$	−5.53493	+	2.90496i	−0.395352	+	0.207497i
$197$	−1.80701	+	0.0728198i	−0.128744	+	0.00518820i	−0.104554	−	0.994519i	$-0.533342\pi$
$197$	−1.80701	+	0.0728198i	−0.128744	+	0.00518820i	−0.0241896	+	0.999707i	$0.507701\pi$
$198$	−0.348991	+	1.70947i	−0.0248017	+	0.121487i
$199$	−3.31214	+	11.4348i	−0.234792	+	0.810595i	0.753425	+	0.657534i	$0.228400\pi$
$199$	−3.31214	+	11.4348i	−0.234792	+	0.810595i	−0.988217	+	0.153061i	$0.951087\pi$
$200$	−14.4095	−	27.4551i	−1.01891	−	1.94137i
$201$	−3.72536	−	5.89119i	−0.262767	−	0.415533i
$202$	1.97838	−	12.1735i	0.139199	−	0.856523i
$203$	−3.59120	−	14.5701i	−0.252053	−	1.02262i
$204$	2.12915	+	10.4293i	0.149070	+	0.730195i
$205$	−8.56486	−	0.691427i	−0.598196	−	0.0482914i
$206$	13.9749	−	22.0996i	0.973681	−	1.53975i
$207$	−1.77153	−	1.56944i	−0.123130	−	0.109084i
$208$	56.2169	+	18.7902i	3.89794	+	1.30287i
$209$	1.12603	−	0.997579i	0.0778894	−	0.0690040i
$210$	1.48539	+	9.13999i	0.102502	+	0.630719i
$211$	−4.43479	+	1.88949i	−0.305303	+	0.130078i	−0.539185	−	0.842188i	$-0.681268\pi$
$211$	−4.43479	+	1.88949i	−0.305303	+	0.130078i	0.233881	+	0.972265i	$0.424857\pi$
$212$	−22.8775	+	14.4669i	−1.57124	+	0.993590i
$213$	−6.18742	+	6.98415i	−0.423955	+	0.478546i
$214$	4.57874	+	56.7179i	0.312996	+	3.87715i
$215$	−4.50267	−	13.4872i	−0.307080	−	0.919816i
$216$	−9.95485	−	1.20874i	−0.677342	−	0.0822442i
$217$	−3.99028	−	2.99850i	−0.270878	−	0.203552i
$218$	−11.4365	+	14.0072i	−0.774580	+	0.948689i
$219$	−5.99510	−	4.89485i	−0.405112	−	0.330763i
$220$	2.79044	+	4.04265i	0.188132	+	0.272556i
$221$	5.44794	+	4.09690i	0.366468	+	0.275587i
$222$	12.1489	−	17.6007i	0.815379	−	1.18128i
$223$	27.1440	−	7.86236i	1.81770	−	0.526503i	0.818829	−	0.574038i	$-0.194624\pi$
$223$	27.1440	−	7.86236i	1.81770	−	0.526503i	0.998870	+	0.0475352i	$0.0151366\pi$
$224$	52.0083	+	32.8881i	3.47495	+	2.19743i
$225$	3.05198	+	0.495995i	0.203465	+	0.0330664i
$226$	−31.2572	−	11.8543i	−2.07920	−	0.788535i
$227$	−2.32142	+	5.44858i	−0.154078	+	0.361635i	−0.979074	−	0.203504i	$-0.934767\pi$
$227$	−2.32142	+	5.44858i	−0.154078	+	0.361635i	0.824996	+	0.565139i	$0.191177\pi$
$228$	9.67130	+	9.28941i	0.640498	+	0.615206i
$229$	0.402059	−	0.766059i	0.0265688	−	0.0506226i	−0.871810	−	0.489845i	$-0.837054\pi$
$229$	0.402059	−	0.766059i	0.0265688	−	0.0506226i	0.898379	+	0.439222i	$0.144746\pi$
$230$	−9.00115	+	0.726648i	−0.593518	+	0.0479137i
$231$	0.426472	+	1.47235i	0.0280598	+	0.0968737i
$232$	44.7187	−	42.9529i	2.93593	−	2.82000i
$233$	2.64439	+	6.97269i	0.173240	+	0.456796i	0.993312	−	0.115465i	$-0.0368357\pi$
$233$	2.64439	+	6.97269i	0.173240	+	0.456796i	−0.820072	+	0.572261i	$0.806067\pi$
$234$	−8.19861	+	5.65479i	−0.535960	+	0.369665i
$235$	−6.34387	+	16.7274i	−0.413829	+	1.09118i
$236$	29.3485	+	68.8834i	1.91042	+	4.48393i
$237$	−0.559452	−	13.8827i	−0.0363403	−	0.901776i
$238$	8.01553	+	9.81724i	0.519570	+	0.636357i
$239$		−	1.64827i		−	0.106618i	−0.998578	−	0.0533089i	$-0.983023\pi$
$239$		−	1.64827i		−	0.106618i	0.998578	−	0.0533089i	$-0.0169768\pi$
$240$	−17.5898	+	14.3616i	−1.13541	+	0.927037i
$241$	4.66020	+	1.34984i	0.300190	+	0.0869511i	0.424895	−	0.905243i	$-0.360311\pi$
$241$	4.66020	+	1.34984i	0.300190	+	0.0869511i	−0.124705	+	0.992194i	$0.539798\pi$
$242$	−19.4184	−	21.9189i	−1.24826	−	1.40900i
$243$	0.692724	−	0.721202i	0.0444383	−	0.0462652i
$244$	30.4303	+	10.1591i	1.94810	+	0.650371i
$245$	−0.921274	−	1.22599i	−0.0588581	−	0.0783258i
$246$	−2.07126	−	17.0583i	−0.132059	−	1.08760i
$247$	8.58044	+	0.348839i	0.545960	+	0.0221961i
$248$	2.48599	−	20.4740i	0.157861	−	1.30010i
$249$	7.78284	−	4.49342i	0.493217	−	0.284759i
$250$	24.6832	−	18.5482i	1.56110	−	1.17309i
$251$	1.20987	−	30.0227i	0.0763666	−	1.89502i	−0.279000	−	0.960291i	$-0.590003\pi$
$251$	1.20987	−	30.0227i	0.0763666	−	1.89502i	0.355367	−	0.934727i	$-0.384356\pi$
$252$	−12.7761	+	4.84535i	−0.804821	+	0.305228i
$253$	−1.46468	+	0.299016i	−0.0920834	+	0.0187990i
$254$	46.6221	−	9.51798i	2.92533	−	0.597211i
$255$	−2.44172	+	0.926021i	−0.152906	+	0.0579897i
$256$	−2.78407	+	69.0860i	−0.174004	+	4.31787i
$257$	−17.7684	+	13.3521i	−1.10836	+	0.832879i	−0.987158	−	0.159749i	$-0.948931\pi$
$257$	−17.7684	+	13.3521i	−1.10836	+	0.832879i	−0.121203	+	0.992628i	$0.538675\pi$
$258$	24.6253	−	14.2174i	1.53310	−	0.885137i
$259$	2.26483	−	18.6526i	0.140730	−	1.15901i
$260$	−4.50790	+	27.6760i	−0.279568	+	1.71639i
$261$	0.745312	+	6.13820i	0.0461337	+	0.379945i
$262$	−13.4977	−	17.9622i	−0.833890	−	1.10971i
$263$	−15.2978	−	5.10717i	−0.943305	−	0.314922i	−0.196908	−	0.980422i	$-0.563090\pi$
$263$	−15.2978	−	5.10717i	−0.943305	−	0.314922i	−0.746398	+	0.665500i	$0.768218\pi$
$264$	−4.38764	+	4.56801i	−0.270040	+	0.281142i
$265$	−4.40356	−	4.97059i	−0.270509	−	0.305341i
$266$	15.3363	+	4.44222i	0.940331	+	0.272370i
$267$	0.910092	−	0.743067i	0.0556967	−	0.0454750i
$268$		−	39.2446i		−	2.39725i
$269$	−19.2319	−	23.5548i	−1.17259	−	1.43616i	−0.876763	−	0.480922i	$-0.840302\pi$
$269$	−19.2319	−	23.5548i	−1.17259	−	1.43616i	−0.295828	−	0.955241i	$-0.595595\pi$
$270$	−0.153637	−	3.81246i	−0.00935004	−	0.232019i
$271$	4.91289	+	11.5310i	0.298437	+	0.700457i	0.999925	−	0.0122240i	$-0.00389112\pi$
$271$	4.91289	+	11.5310i	0.298437	+	0.700457i	−0.701489	+	0.712681i	$0.747481\pi$
$272$	−11.0211	+	29.0604i	−0.668255	+	1.76204i
$273$	−4.06920	+	7.74652i	−0.246279	+	0.468841i
$274$	11.3655	+	29.9685i	0.686618	+	1.81046i
$275$	1.40850	−	1.35288i	0.0849358	−	0.0815819i
$276$	−3.70738	−	12.7994i	−0.223158	−	0.770431i
$277$	−22.1631	+	1.78919i	−1.33165	+	0.107502i	−0.725705	−	0.688006i	$-0.758486\pi$
$277$	−22.1631	+	1.78919i	−1.33165	+	0.107502i	−0.605944	+	0.795507i	$0.707204\pi$
$278$	−27.0592	+	51.5570i	−1.62290	+	3.09219i
$279$	1.48328	+	1.42471i	0.0888019	+	0.0852954i
$280$	−13.1764	+	30.9262i	−0.787442	+	1.84820i
$281$	−3.38456	−	1.28359i	−0.201906	−	0.0765727i	0.251579	−	0.967837i	$-0.419050\pi$
$281$	−3.38456	−	1.28359i	−0.201906	−	0.0765727i	−0.453485	+	0.891264i	$0.649819\pi$
$282$	−35.3129	−	5.73890i	−2.10285	−	0.341747i
$283$	2.78070	+	1.75841i	0.165296	+	0.104527i	0.614552	−	0.788876i	$-0.289337\pi$
$283$	2.78070	+	1.75841i	0.165296	+	0.104527i	−0.449257	+	0.893403i	$0.648311\pi$
$284$	−50.4606	+	14.6161i	−2.99429	+	0.867306i
$285$	−1.86888	+	2.70754i	−0.110703	+	0.160381i
$286$	−0.255539	+	6.28552i	−0.0151103	+	0.371670i
$287$	−8.57612	−	12.4247i	−0.506233	−	0.733405i
$288$	−19.6404	−	16.0359i	−1.15732	−	0.944922i
$289$	8.49109	−	10.3997i	0.499476	−	0.611747i
$290$	18.8610	+	14.1731i	1.10755	+	0.832273i
$291$	6.05926	+	0.735727i	0.355200	+	0.0431291i
$292$	−13.7991	−	41.3335i	−0.807534	−	2.41886i
$293$	0.418201	+	5.18035i	0.0244316	+	0.302639i	0.997420	+	0.0717857i	$0.0228698\pi$
$293$	0.418201	+	5.18035i	0.0244316	+	0.302639i	−0.972989	+	0.230854i	$0.925848\pi$
$294$	2.03366	−	2.29553i	0.118606	−	0.133878i
$295$	−15.5255	+	9.81774i	−0.903931	+	0.571611i
$296$	71.4264	−	30.4319i	4.15157	−	1.76882i
$297$	−0.101319	−	0.623443i	−0.00587914	−	0.0361758i
$298$	−19.0441	+	16.8716i	−1.10319	+	0.977344i
$299$	−7.21073	−	4.56339i	−0.417007	−	0.263907i
$300$	13.0308	+	11.5443i	0.752335	+	0.666511i
$301$	13.3521	−	21.1146i	0.769601	−	1.21703i
$302$	40.1543	+	3.24159i	2.31062	+	0.186533i
$303$	0.893080	+	4.37460i	0.0513061	+	0.251314i
$304$	9.37045	+	38.0174i	0.537432	+	2.18045i
$305$	−1.26253	+	7.76867i	−0.0722923	+	0.444833i
$306$	−2.79113	−	4.41382i	−0.159558	−	0.252321i
$307$	−5.71629	−	10.8915i	−0.326246	−	0.621610i	0.665993	−	0.745958i	$-0.268008\pi$
$307$	−5.71629	−	10.8915i	−0.326246	−	0.621610i	−0.992239	+	0.124349i	$0.960316\pi$
$308$	−2.40117	+	8.28978i	−0.136819	+	0.472354i
$309$	−1.89341	+	9.27455i	−0.107712	+	0.527611i
$310$	7.84101	−	0.315982i	0.445340	−	0.0179466i
$311$	−7.45269	+	3.91147i	−0.422603	+	0.221799i	−0.662599	−	0.748975i	$-0.730546\pi$
$311$	−7.45269	+	3.91147i	−0.422603	+	0.221799i	0.239995	+	0.970774i	$0.422854\pi$
$312$	−36.1276	+	1.44301i	−2.04532	+	0.0816944i
$313$	14.7579	+	7.74556i	0.834167	+	0.437805i	0.827022	−	0.562170i	$-0.190033\pi$
$313$	14.7579	+	7.74556i	0.834167	+	0.437805i	0.00714537	+	0.999974i	$0.497726\pi$
$314$	−16.5253	−	7.84135i	−0.932576	−	0.442513i
$315$	−1.67612	−	2.90313i	−0.0944388	−	0.163573i
$316$	39.1135	−	67.7466i	2.20031	−	3.81104i
$317$	5.08702	−	3.51132i	0.285716	−	0.197215i	−0.416583	−	0.909098i	$-0.636773\pi$
$317$	5.08702	−	3.51132i	0.285716	−	0.197215i	0.702299	+	0.711882i	$0.252157\pi$
$318$	7.97779	−	10.6165i	0.447372	−	0.595344i
$319$	3.38226	+	1.95275i	0.189370	+	0.109333i
$320$	−50.9542	+	6.18697i	−2.84843	+	0.345862i
$321$	−8.83091	−	18.6108i	−0.492893	−	1.03875i
$322$	−10.9909	−	11.4427i	−0.612496	−	0.637676i
$323$	−0.362327	+	4.48823i	−0.0201604	+	0.249732i
$324$	5.46669	−	1.34742i	0.303705	−	0.0748566i
$325$	11.1484	+	0.00396806i	0.618404	+	0.000220109i
$326$	−42.8723	−	10.5671i	−2.37448	−	0.585257i
$327$	2.07303	−	6.20948i	0.114639	−	0.343385i
$328$	26.7426	−	56.3588i	1.47661	−	3.11189i
$329$	−29.8144	+	9.95351i	−1.64372	+	0.548755i
$330$	−1.98338	−	1.36903i	−0.109181	−	0.0753625i
$331$	−10.9216	+	5.18238i	−0.600307	+	0.284849i	−0.704496	−	0.709708i	$-0.748827\pi$
$331$	−10.9216	+	5.18238i	−0.600307	+	0.284849i	0.104189	+	0.994558i	$0.466775\pi$
$332$	50.5576	+	2.03740i	2.77471	+	0.111817i
$333$	−1.85284	+	7.51728i	−0.101535	+	0.411944i
$334$	20.0984	+	8.56314i	1.09974	+	0.468554i
$335$	9.50330	−	1.54444i	0.519221	−	0.0843816i
$336$	−39.0909	−	7.98046i	−2.13258	−	0.435370i
$337$	21.5068			1.17155			0.585776	−	0.810473i	$-0.300790\pi$
$337$	21.5068			1.17155			0.585776	+	0.810473i	$0.300790\pi$
$338$	−25.9160	+	24.8572i	−1.40964	+	1.35205i
$339$	12.1021			0.657294
$340$	−14.4059	−	2.94099i	−0.781270	−	0.159497i
$341$	1.28222	−	0.208382i	0.0694363	−	0.0112845i
$342$	−6.05264	−	2.57879i	−0.327290	−	0.139445i
$343$	4.71035	−	19.1107i	0.254335	−	1.03188i
$344$	103.143	+	4.15653i	5.56111	+	0.224105i
$345$	2.95353	−	1.40147i	0.159013	−	0.0754526i
$346$	−9.70595	−	6.69954i	−0.521795	−	0.360169i
$347$	10.1912	−	3.40231i	0.547090	−	0.182646i	−0.0296688	−	0.999560i	$-0.509445\pi$
$347$	10.1912	−	3.40231i	0.547090	−	0.182646i	0.576759	+	0.816914i	$0.304317\pi$
$348$	−14.9244	+	31.4525i	−0.800031	+	1.68603i
$349$	−10.1029	+	30.2618i	−0.540795	+	1.61988i	0.223281	+	0.974754i	$0.428323\pi$
$349$	−10.1029	+	30.2618i	−0.540795	+	1.61988i	−0.764077	+	0.645126i	$0.776805\pi$
$350$	20.1259	+	4.96059i	1.07578	+	0.265155i
$351$	2.04924	−	2.96658i	0.109380	−	0.158344i
$352$	−15.5496	+	3.83264i	−0.828797	+	0.204280i
$353$	−0.622336	+	7.70902i	−0.0331236	+	0.410310i	0.958854	+	0.283899i	$0.0916279\pi$
$353$	−0.622336	+	7.70902i	−0.0331236	+	0.410310i	−0.991978	+	0.126411i	$0.959654\pi$
$354$	−25.4470	−	26.4931i	−1.35249	−	1.40809i
$355$	−5.52520	−	11.6441i	−0.293247	−	0.618006i
$356$	6.56687	−	0.797362i	0.348043	−	0.0422601i
$357$	−3.97346	−	2.29408i	−0.210298	−	0.121416i
$358$	−21.8465	+	29.0724i	−1.15462	+	1.53652i
$359$	13.3171	−	9.19211i	0.702848	−	0.485141i	−0.162246	−	0.986750i	$-0.551874\pi$
$359$	13.3171	−	9.19211i	0.702848	−	0.485141i	0.865094	+	0.501609i	$0.167259\pi$
$360$	6.92580	−	11.9958i	0.365021	−	0.632236i
$361$	−6.66363	−	11.5417i	−0.350717	−	0.607460i
$362$	13.4845	+	6.39847i	0.708729	+	0.336296i
$363$	9.38677	+	4.92656i	0.492677	+	0.258577i
$364$	−42.6748	+	24.6181i	−2.23677	+	1.29034i
$365$	9.46608	−	4.96818i	0.495477	−	0.260046i
$366$	−15.7267	+	0.633766i	−0.822050	+	0.0331275i
$367$	3.44533	−	16.8763i	0.179845	−	0.880937i	−0.785279	−	0.619142i	$-0.787480\pi$
$367$	3.44533	−	16.8763i	0.179845	−	0.880937i	0.965124	−	0.261795i	$-0.0843144\pi$
$368$	10.8250	−	37.3723i	0.564293	−	1.94816i
$369$	2.89094	+	5.50822i	0.150496	+	0.286746i
$370$	15.7886	+	24.9677i	0.820813	+	1.29801i
$371$	1.87158	−	11.5163i	0.0971674	−	0.597895i
$372$	2.77121	+	11.2432i	0.143681	+	0.582935i
$373$	6.97895	+	34.1851i	0.361356	+	1.77004i	0.601070	+	0.799196i	$0.294741\pi$
$373$	6.97895	+	34.1851i	0.361356	+	1.77004i	−0.239714	+	0.970844i	$0.577054\pi$
$374$	−3.28781	−	0.265420i	−0.170009	−	0.0137245i
$375$	−5.97398	+	9.44709i	−0.308495	+	0.487846i
$376$	−97.2152	−	86.1252i	−5.01349	−	4.44157i
$377$	6.19500	+	21.4161i	0.319059	+	1.10299i
$378$	5.01785	−	4.44543i	0.258090	−	0.228648i
$379$	−2.01313	−	12.3873i	−0.103408	−	0.636293i	−0.986076	−	0.166296i	$-0.946819\pi$
$379$	−2.01313	−	12.3873i	−0.103408	−	0.636293i	0.882668	−	0.469997i	$-0.155745\pi$
$380$	−17.0409	+	7.26045i	−0.874180	+	0.372453i
$381$	−14.5594	+	9.20679i	−0.745899	+	0.471678i
$382$	−2.82209	+	3.18548i	−0.144391	+	0.162983i
$383$	−2.35834	−	29.2133i	−0.120505	−	1.49273i	−0.720909	−	0.693030i	$-0.756275\pi$
$383$	−2.35834	−	29.2133i	−0.120505	−	1.49273i	0.600403	−	0.799697i	$-0.295007\pi$
$384$	−16.4463	−	49.2627i	−0.839272	−	2.51393i
$385$	−2.10191	−	0.255218i	−0.107123	−	0.0130071i
$386$	35.2659	+	26.5006i	1.79499	+	1.34885i
$387$	−6.51032	+	7.97370i	−0.330938	+	0.405326i
$388$	26.6201	+	21.7346i	1.35143	+	1.10341i
$389$	18.4601	+	26.7441i	0.935967	+	1.35598i	0.934492	+	0.355983i	$0.115854\pi$
$389$	18.4601	+	26.7441i	0.935967	+	1.35598i	0.00147415	+	0.999999i	$0.499531\pi$
$390$	−2.74699	−	13.4801i	−0.139099	−	0.682593i
$391$	2.54178	−	3.68241i	0.128543	−	0.186227i
$392$	10.6938	−	3.09750i	0.540119	−	0.156447i
$393$	6.87471	+	4.34731i	0.346783	+	0.219293i
$394$	4.93085	+	0.801341i	0.248413	+	0.0403710i
$395$	17.9445	+	6.80544i	0.902885	+	0.342419i
$396$	1.39392	−	3.27165i	0.0700471	−	0.164407i
$397$	−9.16792	−	8.80591i	−0.460125	−	0.441956i	0.426471	−	0.904501i	$-0.359757\pi$
$397$	−9.16792	−	8.80591i	−0.460125	−	0.441956i	−0.886596	+	0.462546i	$0.846936\pi$
$398$	15.2823	−	29.1181i	0.766034	−	1.45956i
$399$	−5.76149	+	0.465116i	−0.288435	+	0.0232849i
$400$	14.1423	+	48.8249i	0.707115	+	2.44124i
$401$	0.143540	−	0.137872i	0.00716804	−	0.00688499i	−0.689132	−	0.724636i	$-0.742008\pi$
$401$	0.143540	−	0.137872i	0.00716804	−	0.00688499i	0.696300	+	0.717751i	$0.254828\pi$
$402$	6.82754	+	18.0027i	0.340527	+	0.897895i
$403$	6.10132	+	4.21464i	0.303928	+	0.209946i
$404$	−8.91417	+	23.5047i	−0.443497	+	1.16940i
$405$	0.541422	+	1.27076i	0.0269035	+	0.0631447i
$406$	1.66908	+	41.4178i	0.0828350	+	2.05553i
$407$	3.09277	+	3.78796i	0.153303	+	0.187762i
$408$		−	18.9584i		−	0.938582i
$409$	11.1228	−	9.08150i	0.549988	−	0.449051i	−0.316255	−	0.948674i	$-0.602426\pi$
$409$	11.1228	−	9.08150i	0.549988	−	0.449051i	0.866243	+	0.499623i	$0.166528\pi$
$410$	22.7985	+	6.60368i	1.12594	+	0.326132i
$411$	−7.69430	−	8.68506i	−0.379532	−	0.428403i
$412$	−36.9191	+	38.4369i	−1.81887	+	1.89365i
$413$	−30.6132	−	10.2202i	−1.50638	−	0.502902i
$414$	3.92744	+	5.22648i	0.193023	+	0.256867i
$415$	1.49628	+	12.3230i	0.0734496	+	0.604912i
$416$	−79.1557	−	45.7381i	−3.88093	−	2.24250i
$417$	2.54079	−	20.9253i	0.124423	−	1.02472i
$418$	−3.59878	+	2.07775i	−0.176022	+	0.101626i
$419$	−2.01526	+	1.51437i	−0.0984518	+	0.0739817i	−0.648828	−	0.760935i	$-0.724741\pi$
$419$	−2.01526	+	1.51437i	−0.0984518	+	0.0739817i	0.550376	+	0.834917i	$0.314484\pi$
$420$	0.759985	−	18.8588i	0.0370835	−	0.920217i
$421$	−30.9978	+	11.7559i	−1.51074	+	0.572948i	−0.964361	−	0.264590i	$-0.914763\pi$
$421$	−30.9978	+	11.7559i	−1.51074	+	0.572948i	−0.546379	+	0.837538i	$0.683994\pi$
$422$	13.0466	−	2.66349i	0.635100	−	0.129657i
$423$	12.6899	−	2.59065i	0.617002	−	0.125962i
$424$	45.0771	−	17.0955i	2.18914	−	0.830230i
$425$	−0.235380	+	5.84090i	−0.0114176	+	0.283325i
$426$	20.6051	−	15.4837i	0.998319	−	0.750188i
$427$	−11.9757	+	6.91416i	−0.579544	+	0.334600i
$428$	13.9801	−	115.136i	0.675754	−	5.56533i
$429$	−0.720394	−	2.16040i	−0.0347809	−	0.104305i
$430$	4.73431	+	38.9905i	0.228308	+	1.88029i
$431$	−1.12783	−	1.50087i	−0.0543258	−	0.0722945i	0.771462	−	0.636275i	$-0.219526\pi$
$431$	−1.12783	−	1.50087i	−0.0543258	−	0.0722945i	−0.825788	+	0.563981i	$0.809269\pi$
$432$	15.5936	+	5.20591i	0.750248	+	0.250470i
$433$	0.249148	−	0.259391i	0.0119733	−	0.0124655i	−0.715189	−	0.698931i	$-0.753659\pi$
$433$	0.249148	−	0.259391i	0.0119733	−	0.0124655i	0.727162	+	0.686466i	$0.240839\pi$
$434$	9.14284	+	10.3201i	0.438870	+	0.495382i
$435$	−8.20373	−	2.37624i	−0.393339	−	0.113932i
$436$	28.5504	−	23.3107i	1.36732	−	1.11638i
$437$		−	5.63699i		−	0.269654i
$438$	13.5210	+	16.5603i	0.646061	+	0.791280i
$439$	−0.620222	−	15.3907i	−0.0296016	−	0.734556i	−0.944040	−	0.329831i	$-0.893008\pi$
$439$	−0.620222	−	15.3907i	−0.0296016	−	0.734556i	0.914438	−	0.404725i	$-0.132633\pi$
$440$	−3.42930	−	8.04887i	−0.163486	−	0.383715i
$441$	−0.393694	+	1.03809i	−0.0187473	+	0.0494327i
$442$	−12.4810	−	14.0983i	−0.593663	−	0.670588i
$443$	13.0856	+	34.5039i	0.621716	+	1.63933i	0.760753	+	0.649042i	$0.224830\pi$
$443$	13.0856	+	34.5039i	0.621716	+	1.63933i	−0.139037	+	0.990287i	$0.544401\pi$
$444$	−31.4381	+	30.1967i	−1.49199	+	1.43307i
$445$	0.451519	+	1.55882i	0.0214041	+	0.0738954i
$446$	−77.8088	+	6.28138i	−3.68435	+	0.297432i
$447$	4.28041	−	8.15564i	0.202457	−	0.385749i
$448$	−65.0396	−	62.4714i	−3.07283	−	2.95150i
$449$	7.22827	−	16.9654i	0.341123	−	0.800646i	−0.657752	−	0.753234i	$-0.728493\pi$
$449$	7.22827	−	16.9654i	0.341123	−	0.800646i	0.998875	−	0.0474113i	$-0.0150971\pi$
$450$	−7.98606	−	3.02871i	−0.376466	−	0.142775i
$451$	3.87829	+	0.630284i	0.182622	+	0.0296789i
$452$	57.5898	+	36.4176i	2.70880	+	1.71294i
$453$	−14.0081	+	4.05748i	−0.658156	+	0.190637i
$454$	9.29338	−	13.4638i	0.436160	−	0.631887i
$455$	−7.64084	−	9.36513i	−0.358208	−	0.439044i
$456$	−13.5677	−	19.6562i	−0.635367	−	0.920488i
$457$	12.0085	+	9.80462i	0.561733	+	0.458641i	0.870272	−	0.492571i	$-0.163943\pi$
$457$	12.0085	+	9.80462i	0.561733	+	0.458641i	−0.308539	+	0.951212i	$0.599840\pi$
$458$	−1.51143	+	1.85117i	−0.0706247	+	0.0864995i
$459$	1.51139	+	1.13574i	0.0705457	+	0.0530116i
$460$	18.2722	+	2.21865i	0.851946	+	0.103445i
$461$	0.795961	+	2.38420i	0.0370716	+	0.111043i	0.965446	−	0.260604i	$-0.0839215\pi$
$461$	0.795961	+	2.38420i	0.0370716	+	0.111043i	−0.928374	+	0.371647i	$0.878793\pi$
$462$	−0.340716	−	4.22053i	−0.0158515	−	0.196357i
$463$	12.3835	−	13.9781i	0.575510	−	0.649617i	−0.386610	−	0.922243i	$-0.626354\pi$
$463$	12.3835	−	13.9781i	0.575510	−	0.649617i	0.962120	+	0.272627i	$0.0878924\pi$
$464$	−85.9145	+	54.3290i	−3.98848	+	2.52216i
$465$	−2.61356	+	1.11353i	−0.121201	+	0.0516388i
$466$	−3.30436	−	20.3325i	−0.153071	−	0.941886i
$467$	−17.6245	+	15.6139i	−0.815563	+	0.722526i	−0.963858	−	0.266417i	$-0.914160\pi$
$467$	−17.6245	+	15.6139i	−0.815563	+	0.722526i	0.148295	+	0.988943i	$0.452622\pi$
$468$	18.6787	−	7.95040i	0.863424	−	0.367508i
$469$	12.6618	+	11.2174i	0.584668	+	0.517971i
$470$	26.4120	−	41.7672i	1.21829	−	1.92658i
$471$	6.60030	+	0.532831i	0.304126	+	0.0245516i
$472$	−26.6750	−	130.663i	−1.22782	−	6.01424i
$473$	1.55599	+	6.31292i	0.0715447	+	0.290268i
$474$	−6.15646	+	37.8822i	−0.282775	+	1.73999i
$475$	3.93603	+	6.22434i	0.180598	+	0.285592i
$476$	−12.0051	−	22.8737i	−0.550251	−	1.04842i
$477$	−1.33754	+	4.61774i	−0.0612419	+	0.211432i
$478$	−0.910721	+	4.46101i	−0.0416554	+	0.204042i
$479$	0.0198291		0.000799087i	0.000906016		3.65112e-5i	−0.0398129	−	0.999207i	$-0.512676\pi$
$479$	0.0198291		0.000799087i	0.000906016		3.65112e-5i	0.0407189	+	0.999171i	$0.487035\pi$
$480$	31.0115	−	16.2761i	1.41547	−	0.742898i
$481$	−2.25614	+	27.8238i	−0.102871	+	1.26866i
$482$	−11.8669	−	6.22822i	−0.540522	−	0.283688i
$483$	5.18925	+	2.46233i	0.236119	+	0.112040i
$484$	29.8435	+	51.6905i	1.35652	+	2.34957i
$485$	−4.21555	+	7.30155i	−0.191418	+	0.331546i
$486$	−2.27333	+	1.56916i	−0.103120	+	0.0711788i
$487$	5.48621	−	7.30081i	0.248604	−	0.330831i	−0.657840	−	0.753157i	$-0.728530\pi$
$487$	5.48621	−	7.30081i	0.248604	−	0.330831i	0.906444	+	0.422326i	$0.138786\pi$
$488$	−49.4839	−	28.5696i	−2.24003	−	1.29328i
$489$	15.8685	−	1.92678i	0.717597	−	0.0871321i
$490$	1.81601	+	3.82715i	0.0820388	+	0.172893i
$491$	−21.9861	−	22.8900i	−0.992220	−	1.03301i	−0.999454	−	0.0330366i	$-0.989482\pi$
$491$	−21.9861	−	22.8900i	−0.992220	−	1.03301i	0.00723415	−	0.999974i	$-0.497697\pi$
$492$	−2.81832	+	34.9112i	−0.127060	+	1.57392i
$493$	−11.3502	+	2.79756i	−0.511185	+	0.125996i
$494$	−23.0300	−	5.68508i	−1.03617	−	0.255784i
$495$	0.847105	+	0.208793i	0.0380745	+	0.00938453i
$496$	−10.7069	+	32.0711i	−0.480755	+	1.44004i
$497$	9.70758	−	20.4583i	0.435444	−	0.917679i
$498$	−23.5468	+	7.86108i	−1.05516	+	0.352264i
$499$	−0.830124	−	0.572993i	−0.0371615	−	0.0256507i	0.549339	−	0.835599i	$-0.314879\pi$
$499$	−0.830124	−	0.572993i	−0.0371615	−	0.0256507i	−0.586501	+	0.809949i	$0.699495\pi$
$500$	−56.8564	+	26.9787i	−2.54270	+	1.20652i
$501$	−7.90244	−	0.318457i	−0.353055	−	0.0142276i
$502$	−19.8630	+	80.5873i	−0.886528	+	3.59679i
$503$	−30.3583	−	12.9344i	−1.35361	−	0.576718i	−0.411310	−	0.911495i	$-0.634929\pi$
$503$	−30.3583	−	12.9344i	−1.35361	−	0.576718i	−0.942297	+	0.334777i	$0.891339\pi$
$504$	24.0216	−	3.90388i	1.07001	−	0.173893i
$505$	−6.04261	−	1.23361i	−0.268893	−	0.0548948i
$506$	4.12933			0.183571
$507$	5.58136	−	11.7409i	0.247877	−	0.521431i
$508$	−96.9883			−4.30316
$509$	−29.8031	−	6.08434i	−1.32100	−	0.269683i	−0.512756	−	0.858535i	$-0.671375\pi$
$509$	−29.8031	−	6.08434i	−1.32100	−	0.269683i	−0.808242	+	0.588851i	$0.799580\pi$
$510$	7.12010	−	1.15713i	0.315283	−	0.0512385i
$511$	17.2800	+	7.36232i	0.764422	+	0.325690i
$512$	20.8492	−	84.5885i	0.921413	−	3.73832i
$513$	2.37982	+	0.0959034i	0.105072	+	0.00423424i
$514$	55.4671	−	26.3195i	2.44655	−	1.16090i
$515$	−10.7606	−	7.42752i	−0.474170	−	0.327296i
$516$	−54.9750	+	18.3533i	−2.42014	+	0.807961i
$517$	3.50692	−	7.39069i	0.154234	−	0.325042i
$518$	−16.4358	+	49.2313i	−0.722149	+	2.16310i
$519$	4.14543	+	1.02176i	0.181964	+	0.0448501i
$520$	17.7265	−	46.6909i	0.777359	−	2.04753i
$521$	14.4072	−	3.55105i	0.631191	−	0.155574i	0.0892744	−	0.996007i	$-0.471545\pi$
$521$	14.4072	−	3.55105i	0.631191	−	0.155574i	0.541916	+	0.840433i	$0.317699\pi$
$522$	1.37438	−	17.0247i	0.0601548	−	0.745151i
$523$	9.21435	+	9.59316i	0.402916	+	0.419480i	0.891488	−	0.453044i	$-0.149662\pi$
$523$	9.21435	+	9.59316i	0.402916	+	0.419480i	−0.488573	+	0.872523i	$0.662482\pi$
$524$	19.6326	+	41.3748i	0.857654	+	1.80747i
$525$	−7.44927	+	0.904505i	−0.325113	+	0.0394758i
$526$	38.5814	+	22.2750i	1.68223	+	0.971234i
$527$	−2.33585	+	3.10845i	−0.101751	+	0.135406i
$528$	8.54558	−	5.89859i	0.371898	−	0.256703i
$529$	8.69926	−	15.0676i	0.378229	−	0.655112i
$530$	9.17172	+	15.8859i	0.398394	+	0.690039i
$531$	12.0146	+	5.70100i	0.521389	+	0.247402i
$532$	−28.8167	−	15.1242i	−1.24936	−	0.655715i
$533$	13.4679	+	17.9357i	0.583357	+	0.776883i
$534$	−2.87371	+	1.50824i	−0.124358	+	0.0652679i
$535$	28.4311	−	1.14573i	1.22918	−	0.0495344i
$536$	−13.9813	+	68.4849i	−0.603900	+	2.95810i
$537$	3.66275	−	12.6453i	0.158059	−	0.545683i
$538$	39.0360	+	74.3768i	1.68296	+	3.20661i
$539$	0.374793	+	0.592687i	0.0161435	+	0.0255289i
$540$	−1.24754	+	7.67639i	−0.0536854	+	0.330339i
$541$	7.48641	+	30.3736i	0.321866	+	1.30586i	0.879549	+	0.475808i	$0.157844\pi$
$541$	7.48641	+	30.3736i	0.321866	+	1.30586i	−0.557683	+	0.830054i	$0.688310\pi$
$542$	−6.92539	−	33.9228i	−0.297471	−	1.45711i
$543$	−5.38578	−	0.434785i	−0.231126	−	0.0186584i
$544$	25.6200	−	40.5147i	1.09845	−	1.73705i
$545$	6.76839	+	5.99627i	0.289926	+	0.256852i
$546$	15.2934	−	18.7174i	0.654497	−	0.801031i
$547$	26.2364	−	23.2434i	1.12179	−	0.993816i	0.121787	−	0.992556i	$-0.461137\pi$
$547$	26.2364	−	23.2434i	1.12179	−	0.993816i	0.999999	−	0.00125990i	$-0.000401038\pi$
$548$	−10.4795	−	64.4831i	−0.447663	−	2.75458i
$549$	5.24202	−	2.23342i	0.223724	−	0.0953199i
$550$	−4.55958	+	2.88331i	−0.194421	+	0.122945i
$551$	−9.76583	+	11.0233i	−0.416038	+	0.469610i
$552$	1.90976	+	23.6567i	0.0812849	+	1.00689i
$553$	10.6777	+	31.9837i	0.454063	+	1.36008i
$554$	60.9724	+	7.40338i	2.59047	+	0.314540i
$555$	−8.54952	−	6.42454i	−0.362907	−	0.272707i
$556$	75.0593	−	91.9310i	3.18322	−	3.89874i
$557$	22.3075	+	18.2135i	0.945199	+	0.771731i	0.973693	−	0.227863i	$-0.0731738\pi$
$557$	22.3075	+	18.2135i	0.945199	+	0.771731i	−0.0284943	+	0.999594i	$0.509071\pi$
$558$	−3.22727	−	4.67551i	−0.136621	−	0.197930i
$559$	−18.5690	+	32.1361i	−0.785386	+	1.35921i
$560$	31.3059	−	45.3544i	1.32292	−	1.91657i
$561$	1.14697	−	0.332224i	0.0484251	−	0.0140265i
$562$	8.45099	+	5.34408i	0.356484	+	0.225427i
$563$	16.2792	+	2.64562i	0.686084	+	0.111500i	0.493454	−	0.869772i	$-0.335734\pi$
$563$	16.2792	+	2.64562i	0.686084	+	0.111500i	0.192630	+	0.981271i	$0.438298\pi$
$564$	68.1826	+	25.8583i	2.87101	+	1.08883i
$565$	−6.55232	+	15.3789i	−0.275658	+	0.646994i
$566$	−6.55432	−	6.29551i	−0.275499	−	0.264620i
$567$	−1.12783	+	2.14890i	−0.0473644	+	0.0902453i
$568$	93.2649	−	7.52912i	3.91331	−	0.315915i
$569$	9.35504	+	32.2974i	0.392184	+	1.35398i	0.877475	+	0.479623i	$0.159226\pi$
$569$	9.35504	+	32.2974i	0.392184	+	1.35398i	−0.485291	+	0.874353i	$0.661286\pi$
$570$	6.55407	−	6.29527i	0.274520	−	0.263680i
$571$	10.0169	+	26.4125i	0.419196	+	1.10533i	0.963798	+	0.266635i	$0.0859117\pi$
$571$	10.0169	+	26.4125i	0.419196	+	1.10533i	−0.544602	+	0.838695i	$0.683319\pi$
$572$	3.07297	−	12.4485i	0.128487	−	0.520496i
$573$	0.546325	−	1.44054i	0.0228230	−	0.0601794i
$574$	16.3461	+	38.3656i	0.682271	+	1.60135i
$575$	−0.294667	−	7.31209i	−0.0122885	−	0.304935i
$576$	23.5015	+	28.7841i	0.979228	+	1.19934i
$577$			18.0683i			0.752194i	0.926580	+	0.376097i	$0.122734\pi$
$577$			18.0683i			0.752194i	−0.926580	+	0.376097i	$0.877266\pi$
$578$	−28.7271	+	23.4549i	−1.19489	+	0.975596i
$579$	−15.3392	−	4.44305i	−0.637475	−	0.184647i
$580$	−31.8883	−	35.9944i	−1.32409	−	1.49459i
$581$	−15.1083	+	15.7295i	−0.626800	+	0.652568i
$582$	−15.9927	−	5.33915i	−0.662920	−	0.221315i
$583$	1.82419	+	2.42755i	0.0755501	+	0.100539i
$584$	9.35511	+	77.0462i	0.387117	+	3.18820i
$585$	2.66032	+	4.21027i	0.109991	+	0.174073i
$586$	1.73045	−	14.2516i	0.0714843	−	0.588726i
$587$	32.8908	−	18.9895i	1.35755	−	0.783781i	0.368256	−	0.929725i	$-0.379955\pi$
$587$	32.8908	−	18.9895i	1.35755	−	0.783781i	0.989293	+	0.145943i	$0.0466218\pi$
$588$	−4.99727	+	3.75521i	−0.206084	+	0.154862i
$589$	−0.197243	+	4.89453i	−0.00812725	+	0.201676i
$590$	47.4440	−	17.9932i	1.95324	−	0.740766i
$591$	−1.77192	+	0.361741i	−0.0728872	+	0.0148800i
$592$	−124.708	+	25.4593i	−5.12546	+	1.04637i
$593$	42.0561	−	15.9498i	1.72704	−	0.654979i	0.727521	−	0.686085i	$-0.240672\pi$
$593$	42.0561	−	15.9498i	1.72704	−	0.654979i	0.999516	+	0.0311060i	$0.00990294\pi$
$594$	−0.0702532	+	1.74331i	−0.00288252	+	0.0715290i
$595$	5.06655	−	3.80727i	0.207708	−	0.156083i
$596$	44.9110	−	25.9294i	1.83963	−	1.06211i
$597$	−1.43497	+	11.8181i	−0.0587296	+	0.483682i
$598$	16.9943	+	16.3348i	0.694947	+	0.667981i
$599$	−0.0720033	−	0.593001i	−0.00294198	−	0.0242293i	0.991164	−	0.132642i	$-0.0423462\pi$
$599$	−0.0720033	−	0.593001i	−0.00294198	−	0.0242293i	−0.994106	+	0.108413i	$0.965423\pi$
$600$	−18.6270	−	24.7881i	−0.760446	−	1.01197i
$601$	−0.820156	−	0.273808i	−0.0334548	−	0.0111689i	0.299891	−	0.953973i	$-0.403050\pi$
$601$	−0.820156	−	0.273808i	−0.0334548	−	0.0111689i	−0.333346	+	0.942805i	$0.608178\pi$
$602$	−47.8035	+	49.7687i	−1.94833	+	2.02842i
$603$	−4.62213	−	5.21731i	−0.188228	−	0.212465i
$604$	−78.8695	−	22.8448i	−3.20916	−	0.929543i
$605$	−11.3427	+	9.26102i	−0.461146	+	0.376514i
$606$		−	12.3332i		−	0.501002i
$607$	11.1244	+	13.6249i	0.451526	+	0.553019i	0.949334	−	0.314268i	$-0.101759\pi$
$607$	11.1244	+	13.6249i	0.451526	+	0.553019i	−0.497808	+	0.867287i	$0.665862\pi$
$608$	−2.43166	−	60.3411i	−0.0986169	−	2.44715i
$609$	−5.88190	−	13.8053i	−0.238346	−	0.559420i
$610$	7.70944	−	20.3281i	0.312146	−	0.823061i
$611$	43.6689	−	16.5437i	1.76666	−	0.669285i
$612$	3.77455	+	9.95268i	0.152577	+	0.402313i
$613$	9.24641	−	8.88130i	0.373459	−	0.358712i	−0.482373	−	0.875966i	$-0.660225\pi$
$613$	9.24641	−	8.88130i	0.373459	−	0.358712i	0.855832	+	0.517254i	$0.173046\pi$
$614$	9.45312	+	32.6359i	0.381497	+	1.31708i
$615$	−8.56486	+	0.691427i	−0.345368	+	0.0278810i
$616$	7.14354	−	13.6109i	0.287822	−	0.548398i
$617$	−10.4898	−	10.0756i	−0.422303	−	0.405628i	0.451218	−	0.892414i	$-0.350990\pi$
$617$	−10.4898	−	10.0756i	−0.422303	−	0.405628i	−0.873521	+	0.486786i	$0.838169\pi$
$618$	10.2490	−	24.0552i	0.412273	−	0.967641i
$619$	−40.0554	−	15.1910i	−1.60996	−	0.610578i	−0.624583	−	0.780958i	$-0.714731\pi$
$619$	−40.0554	−	15.1910i	−1.60996	−	0.610578i	−0.985378	+	0.170380i	$0.945500\pi$
$620$	−15.7879	−	2.56578i	−0.634058	−	0.103044i
$621$	−2.00035	−	1.26494i	−0.0802712	−	0.0507604i
$622$	22.3317	−	6.46846i	0.895421	−	0.259362i
$623$	−1.61976	+	2.34663i	−0.0648945	+	0.0940159i
$624$	58.5031	+	9.52905i	2.34200	+	0.381467i
$625$	0.0117683	+	0.0170494i	0.000470734	+	0.000681975i
$626$	−35.6623	−	29.1174i	−1.42535	−	1.16376i
$627$	0.951429	−	1.16529i	0.0379964	−	0.0465372i
$628$	29.8053	+	22.3972i	1.18936	+	0.893745i
$629$	−14.5304	−	1.76431i	−0.579367	−	0.0703478i
$630$	2.93231	+	8.78336i	0.116826	+	0.349937i
$631$	−0.280549	−	3.47522i	−0.0111685	−	0.138346i	0.988770	−	0.149446i	$-0.0477489\pi$
$631$	−0.280549	−	3.47522i	−0.0111685	−	0.138346i	−0.999938	+	0.0110994i	$0.996467\pi$
$632$	−92.3915	+	104.288i	−3.67514	+	4.14837i
$633$	−4.07426	+	2.57641i	−0.161937	+	0.102403i
$634$	−15.7080	+	6.69256i	−0.623845	+	0.265795i
$635$	−3.81689	−	23.4863i	−0.151469	−	0.932024i
$636$	−20.2606	+	17.9494i	−0.803386	+	0.711738i
$637$	−0.802099	+	3.92182i	−0.0317803	+	0.155388i
$638$	−8.07505	−	7.15387i	−0.319694	−	0.283224i
$639$	−4.98696	+	7.88624i	−0.197281	+	0.311975i
$640$	71.5056	+	5.77253i	2.82651	+	0.228179i
$641$	−6.07228	−	29.7440i	−0.239841	−	1.17482i	−0.904102	−	0.427317i	$-0.859459\pi$
$641$	−6.07228	−	29.7440i	−0.239841	−	1.17482i	0.664261	−	0.747501i	$-0.268746\pi$
$642$	13.6176	+	55.2489i	0.537445	+	2.18050i
$643$	−2.88228	+	17.7354i	−0.113666	+	0.699416i	0.866191	+	0.499714i	$0.166562\pi$
$643$	−2.88228	+	17.7354i	−0.113666	+	0.699416i	−0.979857	+	0.199702i	$0.936003\pi$
$644$	17.2843	+	27.3329i	0.681096	+	1.07707i
$645$	−6.60786	−	12.5902i	−0.260184	−	0.495739i
$646$	3.46052	−	11.9471i	0.136152	−	0.470052i
$647$	2.71179	−	13.2832i	0.106611	−	0.522217i	−0.891052	−	0.453901i	$-0.850032\pi$
$647$	2.71179	−	13.2832i	0.106611	−	0.522217i	0.997664	−	0.0683164i	$-0.0217627\pi$
$648$	−10.0198	+	0.403786i	−0.393616	+	0.0158622i
$649$	7.43754	−	3.90352i	0.291949	−	0.153227i
$650$	−30.1708	−	6.17060i	−1.18340	−	0.242031i
$651$	−4.41960	−	2.31959i	−0.173218	−	0.0909118i
$652$	81.3109	+	38.5825i	3.18438	+	1.51101i
$653$	−12.1528	−	21.0493i	−0.475576	−	0.823722i	0.524033	−	0.851698i	$-0.324427\pi$
$653$	−12.1528	−	21.0493i	−0.475576	−	0.823722i	−0.999609	+	0.0279765i	$0.991094\pi$
$654$	−9.04153	+	15.6604i	−0.353552	+	0.612369i
$655$	−9.24652	+	6.38241i	−0.361291	+	0.249381i
$656$	−61.4363	+	81.7569i	−2.39869	+	3.19207i
$657$	−6.70266	−	3.86978i	−0.261496	−	0.150975i
$658$	86.1916	−	10.4656i	3.36010	−	0.407990i
$659$	−19.8475	−	41.8277i	−0.773148	−	1.62938i	−0.777095	−	0.629383i	$-0.783308\pi$
$659$	−19.8475	−	41.8277i	−0.773148	−	1.62938i	0.00394692	−	0.999992i	$-0.498744\pi$
$660$	3.40279	+	3.54268i	0.132454	+	0.137899i
$661$	−1.15171	+	14.2665i	−0.0447963	+	0.554902i	0.934966	+	0.354737i	$0.115430\pi$
$661$	−1.15171	+	14.2665i	−0.0447963	+	0.554902i	−0.979762	+	0.200165i	$0.935852\pi$
$662$	32.4225	−	7.99144i	1.26014	−	0.310596i
$663$	6.03458	+	3.16993i	0.234364	+	0.123110i
$664$	−87.5011	−	21.5671i	−3.39570	−	0.836965i
$665$	2.52834	−	7.57331i	0.0980450	−	0.293681i
$666$	9.16820	−	19.3216i	0.355261	−	0.748696i
$667$	13.8811	−	4.63420i	0.537479	−	0.179437i
$668$	−36.6468	−	25.2955i	−1.41791	−	0.978711i
$669$	25.5313	−	12.1148i	0.987097	−	0.468383i
$670$	−26.5738	−	1.07089i	−1.02664	−	0.0413720i
$671$	0.861289	−	3.49439i	0.0332497	−	0.134899i
$672$	56.6104	+	24.1194i	2.18379	+	0.930428i
$673$	−9.11056	+	1.48061i	−0.351186	+	0.0570733i	−0.333446	−	0.942769i	$-0.608211\pi$
$673$	−9.11056	+	1.48061i	−0.351186	+	0.0570733i	−0.0177405	+	0.999843i	$0.505647\pi$
$674$	−58.2077	−	11.8832i	−2.24208	−	0.457723i
$675$	3.09202			0.119012
$676$	61.8906	−	39.0756i	2.38041	−	1.50291i
$677$	2.71045			0.104171			0.0520856	−	0.998643i	$-0.483413\pi$
$677$	2.71045			0.104171			0.0520856	+	0.998643i	$0.483413\pi$
$678$	−32.7540	−	6.68677i	−1.25791	−	0.256804i
$679$	−14.6213	+	2.37619i	−0.561114	+	0.0911899i
$680$	24.0917	+	10.2645i	0.923874	+	0.393626i
$681$	−1.41735	+	5.75040i	−0.0543128	+	0.220356i
$682$	−3.58544	−	0.144488i	−0.137294	−	0.00553275i
$683$	−18.9517	+	8.99268i	−0.725165	+	0.344095i	−0.755236	−	0.655453i	$-0.772478\pi$
$683$	−18.9517	+	8.99268i	−0.725165	+	0.344095i	0.0300710	+	0.999548i	$0.490427\pi$
$684$	11.0362	+	7.61773i	0.421979	+	0.291271i
$685$	15.2025	−	5.07535i	0.580858	−	0.193919i
$686$	−23.3077	+	49.1199i	−0.889891	+	1.87541i
$687$	0.273968	−	0.820634i	0.0104525	−	0.0313091i
$688$	−164.311	−	40.4989i	−6.26428	−	1.54401i
$689$	−2.09549	+	17.2067i	−0.0798318	+	0.655524i
$690$	−8.76802	+	2.16112i	−0.333793	+	0.0822726i
$691$	2.10990	−	26.1359i	0.0802646	−	0.994255i	−0.823806	−	0.566872i	$-0.808153\pi$
$691$	2.10990	−	26.1359i	0.0802646	−	0.994255i	0.904071	−	0.427383i	$-0.140564\pi$
$692$	16.6521	+	17.3366i	0.633016	+	0.659040i
$693$	0.657131	+	1.38488i	0.0249624	+	0.0526071i
$694$	−29.4620	+	3.57734i	−1.11836	+	0.135794i
$695$	25.2155	+	14.5582i	0.956478	+	0.552223i
$696$	37.2495	−	49.5701i	1.41194	−	1.87895i
$697$	−9.67888	+	6.68085i	−0.366614	+	0.253055i
$698$	44.0638	−	76.3208i	1.66784	−	2.88878i
$699$	3.72865	+	6.45820i	0.141030	+	0.244272i
$700$	−38.1705	−	18.1121i	−1.44271	−	0.684573i
$701$	−6.31177	−	3.31267i	−0.238392	−	0.125118i	0.341297	−	0.939955i	$-0.389134\pi$
$701$	−6.31177	−	3.31267i	−0.238392	−	0.125118i	−0.579689	+	0.814838i	$0.696826\pi$
$702$	−7.18535	+	6.89671i	−0.271194	+	0.260300i
$703$	−16.3279	+	8.56955i	−0.615819	+	0.323207i
$704$	23.4518	−	0.945076i	0.883874	−	0.0356189i
$705$	−3.57846	+	17.5284i	−0.134772	+	0.660159i
$706$	5.94381	−	20.5204i	0.223698	−	0.772296i
$707$	−5.03556	−	9.59447i	−0.189382	−	0.360837i
$708$	40.0181	+	63.2836i	1.50397	+	2.37834i
$709$	6.78410	−	41.7443i	0.254782	−	1.56774i	−0.472456	−	0.881354i	$-0.656633\pi$
$709$	6.78410	−	41.7443i	0.254782	−	1.56774i	0.727239	−	0.686385i	$-0.240803\pi$
$710$	8.52009	+	34.5674i	0.319753	+	1.29729i
$711$	−2.77914	−	13.6131i	−0.104226	−	0.510533i
$712$	−11.7438	−	0.948055i	−0.440116	−	0.0355299i
$713$	2.60159	−	4.11408i	0.0974302	−	0.154074i
$714$	9.48653	+	8.40433i	0.355024	+	0.314524i
$715$	3.13540	+	0.254239i	0.117257	+	0.00950799i
$716$	55.4820	−	49.1527i	2.07346	−	1.83692i
$717$	−0.264401	−	1.62693i	−0.00987425	−	0.0607587i
$718$	−41.1212	+	17.5201i	−1.53463	+	0.653845i
$719$	−1.85296	+	1.17174i	−0.0691038	+	0.0436986i	−0.568571	−	0.822634i	$-0.692504\pi$
$719$	−1.85296	+	1.17174i	−0.0691038	+	0.0436986i	0.499467	+	0.866333i	$0.333529\pi$
$720$	−15.0582	+	16.9972i	−0.561186	+	0.633448i
$721$	−1.84852	−	22.8980i	−0.0688425	−	0.852767i
$722$	11.6578	+	34.9193i	0.433858	+	1.29956i
$723$	4.81638	+	0.584815i	0.179123	+	0.0217495i
$724$	−24.3208	−	18.2759i	−0.903876	−	0.679219i
$725$	−12.0916	+	14.8096i	−0.449072	+	0.550013i
$726$	−22.6830	−	18.5201i	−0.841844	−	0.687345i
$727$	2.63168	+	3.81265i	0.0976036	+	0.141403i	0.868743	−	0.495263i	$-0.164928\pi$
$727$	2.63168	+	3.81265i	0.0976036	+	0.141403i	−0.771139	+	0.636666i	$0.780313\pi$
$728$	83.2414	−	27.7571i	3.08513	−	1.02875i
$729$	0.568065	−	0.822984i	0.0210394	−	0.0304809i
$730$	−28.3648	+	8.21596i	−1.04983	+	0.304086i
$731$	−16.4484	−	10.4013i	−0.608366	−	0.384707i
$732$	31.6659	+	5.14620i	1.17040	+	0.190209i
$733$	−12.3049	−	4.66663i	−0.454492	−	0.172366i	0.116727	−	0.993164i	$-0.462760\pi$
$733$	−12.3049	−	4.66663i	−0.454492	−	0.172366i	−0.571219	+	0.820798i	$0.693529\pi$
$734$	−18.6494	+	43.7717i	−0.688361	+	1.61564i
$735$	−1.10601	−	1.06233i	−0.0407957	−	0.0391848i
$736$	−27.8878	+	53.1358i	−1.02796	+	1.95861i
$737$	−4.38829	+	0.354259i	−0.161645	+	0.0130493i
$738$	−4.78079	−	16.5052i	−0.175983	−	0.607564i
$739$	−5.25640	+	5.04884i	−0.193360	+	0.185725i	−0.783152	−	0.621831i	$-0.786389\pi$
$739$	−5.25640	+	5.04884i	−0.193360	+	0.185725i	0.589792	+	0.807555i	$0.299210\pi$
$740$	−21.3516	−	56.2995i	−0.784900	−	2.06961i
$741$	8.52528	−	1.03208i	0.313184	−	0.0379143i
$742$	−11.4285	+	30.1344i	−0.419552	+	1.10627i
$743$	−8.23925	−	19.3382i	−0.302269	−	0.709451i	0.697707	−	0.716383i	$-0.254204\pi$
$743$	−8.23925	−	19.3382i	−0.302269	−	0.709451i	−0.999976	+	0.00693220i	$0.997793\pi$
$744$	−0.830459	−	20.6076i	−0.0304461	−	0.755512i
$745$	8.04639	+	9.85503i	0.294797	+	0.361060i
$746$		−	96.3773i		−	3.52862i
$747$	6.96126	−	5.68369i	0.254699	−	0.207955i
$748$	6.45778	+	1.87052i	0.236120	+	0.0683930i
$749$	33.1515	+	37.4203i	1.21133	+	1.36731i
$750$	21.3882	−	22.2675i	0.780988	−	0.813094i
$751$	13.4002	+	4.47365i	0.488981	+	0.163246i	0.550458	−	0.834863i	$-0.314453\pi$
$751$	13.4002	+	4.47365i	0.488981	+	0.163246i	−0.0614776	+	0.998108i	$0.519581\pi$
$752$	127.910	+	170.217i	4.66440	+	6.20718i
$753$	−3.62178	−	29.8280i	−0.131985	−	1.08699i
$754$	−4.93353	−	61.3852i	−0.179669	−	2.23552i
$755$	2.42816	−	19.9977i	0.0883700	−	0.727792i
$756$	−11.8334	+	6.83204i	−0.430378	+	0.248479i
$757$	−22.1702	+	16.6598i	−0.805790	+	0.605512i	−0.921769	−	0.387740i	$-0.873256\pi$
$757$	−22.1702	+	16.6598i	−0.805790	+	0.605512i	0.115979	+	0.993252i	$0.462999\pi$
$758$	−1.39587	+	34.6382i	−0.0507004	+	1.25812i
$759$	−1.39774	+	0.530094i	−0.0507349	+	0.0192412i
$760$	32.3243	−	6.59905i	1.17253	−	0.239373i
$761$	26.3783	−	5.38517i	0.956212	−	0.195212i	0.303511	−	0.952828i	$-0.401841\pi$
$761$	26.3783	−	5.38517i	0.956212	−	0.195212i	0.652701	+	0.757616i	$0.273636\pi$
$762$	44.4916	−	16.8734i	1.61176	−	0.611260i
$763$	−0.639717	+	15.8744i	−0.0231593	+	0.574692i
$764$	6.93466	−	5.21106i	0.250887	−	0.188529i
$765$	−2.26155	+	1.30571i	−0.0817666	+	0.0472080i
$766$	−9.75844	+	80.3680i	−0.352587	+	2.90381i
$767$	46.0508	+	13.3566i	1.66280	+	0.482277i
$768$	8.33415	+	68.6379i	0.300733	+	2.47676i
$769$	−16.0008	−	21.2932i	−0.577004	−	0.767852i	0.412718	−	0.910859i	$-0.364579\pi$
$769$	−16.0008	−	21.2932i	−0.577004	−	0.767852i	−0.989722	+	0.143007i	$0.954323\pi$
$770$	5.54776	+	1.85211i	0.199927	+	0.0667456i
$771$	−15.3965	+	16.0294i	−0.554490	+	0.577285i
$772$	−59.6241	−	67.3017i	−2.14592	−	2.42224i
$773$	−34.8212	−	10.0861i	−1.25243	−	0.362771i	−0.415255	−	0.909705i	$-0.636308\pi$
$773$	−34.8212	−	10.0861i	−1.25243	−	0.362771i	−0.837176	+	0.546934i	$0.815795\pi$
$774$	22.0257	−	17.9835i	0.791699	−	0.646402i
$775$			6.35931i			0.228433i
$776$	−38.7109	−	47.4123i	−1.38964	−	1.70200i
$777$	−0.756579	−	18.7743i	−0.0271421	−	0.673525i
$778$	−35.1850	−	82.5822i	−1.26144	−	2.96071i
$779$	−5.25394	+	13.8535i	−0.188242	+	0.496353i
$780$	−0.00998054	+	28.0408i	−0.000357361	+	1.00402i
$781$	2.08986	+	5.51052i	0.0747812	+	0.197182i
$782$	−8.91391	+	8.56193i	−0.318761	+	0.306174i
$783$	1.72030	+	5.93916i	0.0614784	+	0.212248i
$784$	−18.1927	+	1.46866i	−0.649738	+	0.0524523i
$785$	−4.25065	+	8.09893i	−0.151712	+	0.289063i
$786$	−16.2042	−	15.5644i	−0.577985	−	0.555163i
$787$	−1.92473	+	4.51750i	−0.0686090	+	0.161031i	−0.950754	−	0.309947i	$-0.899689\pi$
$787$	−1.92473	+	4.51750i	−0.0686090	+	0.161031i	0.882145	+	0.470978i	$0.156099\pi$
$788$	−9.52056	−	3.61067i	−0.339156	−	0.128625i
$789$	−15.9190	−	2.58709i	−0.566731	−	0.0921028i
$790$	−44.8061	−	28.3336i	−1.59413	−	1.00807i
$791$	−28.2107	+	8.17134i	−1.00306	+	0.290539i
$792$	−3.59806	+	5.21269i	−0.127851	+	0.185225i
$793$	17.3678	−	10.9741i	0.616748	−	0.389701i
$794$	19.9472	+	28.8985i	0.707900	+	1.02557i
$795$	−5.14388	−	4.19985i	−0.182434	−	0.148953i
$796$	−42.3915	+	51.9202i	−1.50253	+	1.84026i
$797$	−9.40275	−	7.06571i	−0.333063	−	0.250280i	0.421033	−	0.907046i	$-0.361668\pi$
$797$	−9.40275	−	7.06571i	−0.333063	−	0.250280i	−0.754095	+	0.656765i	$0.771924\pi$
$798$	15.8503	+	1.92458i	0.561095	+	0.0681293i
$799$	7.75384	+	23.2256i	0.274311	+	0.821662i
$800$	−6.30852	−	78.1450i	−0.223040	−	2.76284i
$801$	0.779110	−	0.879434i	0.0275285	−	0.0310733i
$802$	−0.464665	+	0.293837i	−0.0164079	+	0.0103757i
$803$	−4.49730	+	1.91612i	−0.158706	+	0.0676184i
$804$	−6.29528	−	38.7364i	−0.222017	−	1.36613i
$805$	−5.93861	+	5.26115i	−0.209309	+	0.185431i
$806$	−14.1843	−	14.7780i	−0.499622	−	0.520532i
$807$	−22.7613	−	20.1648i	−0.801237	−	0.709834i
$808$	23.9297	−	37.8418i	0.841845	−	1.33127i
$809$	−23.0694	−	1.86236i	−0.811078	−	0.0654770i	−0.332033	−	0.943268i	$-0.607735\pi$
$809$	−23.0694	−	1.86236i	−0.811078	−	0.0654770i	−0.479044	+	0.877791i	$0.659017\pi$
$810$	−0.763208	−	3.73844i	−0.0268164	−	0.131355i
$811$	−7.00422	−	28.4173i	−0.245952	−	0.997865i	−0.955919	−	0.293630i	$-0.905137\pi$
$811$	−7.00422	−	28.4173i	−0.245952	−	0.997865i	0.709967	−	0.704234i	$-0.248710\pi$
$812$	13.5530	−	83.3948i	0.475616	−	2.92658i
$813$	6.69897	+	10.5936i	0.234943	+	0.371533i
$814$	−6.27755	−	11.9609i	−0.220028	−	0.419228i
$815$	−6.14305	+	21.2083i	−0.215182	+	0.742893i
$816$	−6.21682	+	30.4520i	−0.217632	+	1.06603i
$817$	−24.4976	+	0.987220i	−0.857063	+	0.0345384i
$818$	−35.1214	+	18.4331i	−1.22799	+	0.644500i
$819$	−2.77388	+	8.29895i	−0.0969272	+	0.289989i
$820$	−42.8380	−	22.4831i	−1.49597	−	0.785145i
$821$	30.3563	+	14.4042i	1.05944	+	0.502711i	0.876992	−	0.480505i	$-0.159546\pi$
$821$	30.3563	+	14.4042i	1.05944	+	0.502711i	0.182448	+	0.983215i	$0.441598\pi$
$822$	16.0257	+	27.7572i	0.558959	+	0.968145i
$823$	−3.81200	+	6.60258i	−0.132878	+	0.230151i	−0.924785	−	0.380490i	$-0.875755\pi$
$823$	−3.81200	+	6.60258i	−0.132878	+	0.230151i	0.791907	+	0.610642i	$0.209089\pi$
$824$	78.1203	−	53.9226i	2.72145	−	1.87848i
$825$	1.17324	−	1.56130i	0.0408471	−	0.0543576i
$826$	77.2068	+	44.5754i	2.68637	+	1.55098i
$827$	−8.91816	+	1.08286i	−0.310115	+	0.0376548i	−0.274115	−	0.961697i	$-0.588385\pi$
$827$	−8.91816	+	1.08286i	−0.310115	+	0.0376548i	−0.0360002	+	0.999352i	$0.511462\pi$
$828$	−5.71253	−	12.0389i	−0.198524	−	0.418381i
$829$	−19.3774	−	20.1740i	−0.673005	−	0.700672i	0.293892	−	0.955839i	$-0.405049\pi$
$829$	−19.3774	−	20.1740i	−0.673005	−	0.700672i	−0.966897	+	0.255166i	$0.917870\pi$
$830$	2.75918	−	34.1786i	0.0957726	−	1.18636i
$831$	−21.5890	+	5.32122i	−0.748916	+	0.184591i
$832$	100.255	+	88.8816i	3.47571	+	3.08141i
$833$	−2.03796	−	0.502313i	−0.0706113	−	0.0174041i
$834$	−18.4385	+	55.2300i	−0.638472	+	1.91246i
$835$	4.68324	−	9.86971i	0.162070	−	0.341555i
$836$	8.03413	−	2.68219i	0.277866	−	0.0927654i
$837$	1.69262	+	1.16833i	0.0585054	+	0.0403834i
$838$	6.29098	−	2.98511i	0.217318	−	0.103119i
$839$	−9.49988	−	0.382832i	−0.327972	−	0.0132168i	−0.124266	−	0.992249i	$-0.539658\pi$
$839$	−9.49988	−	0.382832i	−0.327972	−	0.0132168i	−0.203706	+	0.979032i	$0.565299\pi$
$840$	−8.04488	+	32.6394i	−0.277575	+	1.12617i
$841$	−8.49416	−	3.61902i	−0.292902	−	0.124794i
$842$	90.3902	−	14.6898i	3.11505	−	0.506245i
$843$	−3.54663	−	0.724050i	−0.122152	−	0.0249376i
$844$	−27.1410			−0.934232
$845$	11.8980	+	13.4494i	0.409304	+	0.462672i
$846$	−35.7762			−1.23001
$847$	−25.2076	−	5.14617i	−0.866143	−	0.176824i
$848$	−78.0110	+	12.6780i	−2.67891	+	0.435365i
$849$	3.02676	+	1.28958i	0.103878	+	0.0442583i
$850$	3.86433	−	15.6782i	0.132545	−	0.537758i
$851$	18.3091	+	0.737830i	0.627627	+	0.0252925i
$852$	−47.4626	+	22.5213i	−1.62604	+	0.771566i
$853$	16.8823	+	11.6530i	0.578038	+	0.398991i	0.820902	−	0.571070i	$-0.193471\pi$
$853$	16.8823	+	11.6530i	0.578038	+	0.398991i	−0.242864	+	0.970060i	$0.578087\pi$
$854$	36.2322	−	12.0961i	1.23984	−	0.413919i
$855$	−1.41036	+	2.97226i	−0.0482332	+	0.101649i
$856$	−65.4149	+	195.942i	−2.23584	+	6.69715i
$857$	−3.08172	−	0.759575i	−0.105269	−	0.0259466i	0.186329	−	0.982487i	$-0.440341\pi$
$857$	−3.08172	−	0.759575i	−0.105269	−	0.0259466i	−0.291598	+	0.956541i	$0.594187\pi$
$858$	0.756039	+	6.24511i	0.0258107	+	0.213205i
$859$	22.6704	−	5.58775i	0.773504	−	0.190652i	0.167241	−	0.985916i	$-0.446514\pi$
$859$	22.6704	−	5.58775i	0.773504	−	0.190652i	0.606263	+	0.795264i	$0.292668\pi$
$860$	6.44189	−	79.7971i	0.219667	−	2.72106i
$861$	−10.4581	−	10.8881i	−0.356412	−	0.371064i
$862$	2.22317	+	4.68524i	0.0757216	+	0.159580i
$863$	−24.4602	+	2.97001i	−0.832636	+	0.101100i	−0.525743	−	0.850644i	$-0.676213\pi$
$863$	−24.4602	+	2.97001i	−0.832636	+	0.101100i	−0.306893	+	0.951744i	$0.599290\pi$
$864$	−21.9584	−	12.6777i	−0.747038	−	0.431303i
$865$	−3.54283	+	4.71466i	−0.120460	+	0.160303i
$866$	−0.817635	+	0.564373i	−0.0277844	+	0.0191782i
$867$	6.71290	−	11.6271i	0.227982	−	0.394876i
$868$	−14.0513	−	24.3376i	−0.476934	−	0.826073i
$869$	−7.92842	−	3.76208i	−0.268953	−	0.127620i
$870$	20.8902	+	10.9640i	0.708246	+	0.371716i
$871$	−19.4614	−	15.9013i	−0.659425	−	0.538795i
$872$	−58.1274	+	30.5076i	−1.96844	+	1.03312i
$873$	6.09881	−	0.245774i	0.206414	−	0.00831818i
$874$	−3.11461	+	15.2564i	−0.105353	+	0.516055i
$875$	7.54705	−	26.0554i	0.255137	−	0.880834i
$876$	−20.2508	−	38.5847i	−0.684211	−	1.30366i
$877$	19.0494	+	30.1242i	0.643252	+	1.01722i	0.996653	+	0.0817492i	$0.0260507\pi$
$877$	19.0494	+	30.1242i	0.643252	+	1.01722i	−0.353401	+	0.935472i	$0.614975\pi$
$878$	−6.82520	+	41.9971i	−0.230339	+	1.41733i
$879$	1.24377	+	5.04618i	0.0419514	+	0.170203i
$880$	2.86895	+	14.0530i	0.0967122	+	0.473728i
$881$	−25.8481	−	2.08668i	−0.870845	−	0.0703019i	−0.363040	−	0.931774i	$-0.618261\pi$
$881$	−25.8481	−	2.08668i	−0.870845	−	0.0703019i	−0.507805	+	0.861472i	$0.669543\pi$
$882$	1.63910	−	2.59203i	0.0551913	−	0.0872780i
$883$	27.9428	+	24.7551i	0.940350	+	0.833077i	0.986147	−	0.165874i	$-0.0530444\pi$
$883$	27.9428	+	24.7551i	0.940350	+	0.833077i	−0.0457974	+	0.998951i	$0.514583\pi$
$884$	19.1776	+	33.2439i	0.645013	+	1.11811i
$885$	−13.7496	+	12.1811i	−0.462187	+	0.409462i
$886$	−16.3514	−	100.614i	−0.549335	−	3.38020i
$887$	11.5185	−	4.90759i	0.386755	−	0.164781i	−0.189832	−	0.981817i	$-0.560794\pi$
$887$	11.5185	−	4.90759i	0.386755	−	0.164781i	0.576587	+	0.817036i	$0.304384\pi$
$888$	65.6198	−	41.4955i	2.20206	−	1.39250i
$889$	27.7224	−	31.2921i	0.929780	−	1.04950i
$890$	−0.360726	−	4.46840i	−0.0120916	−	0.149781i
$891$	−0.200014	−	0.599116i	−0.00670074	−	0.0200712i
$892$	157.951	+	19.1787i	5.28859	+	0.642151i
$893$	24.6608	+	18.5314i	0.825242	+	0.620129i
$894$	−16.0911	+	19.7080i	−0.538166	+	0.659134i
$895$	14.0860	+	11.5009i	0.470845	+	0.384433i
$896$	71.5997	+	103.730i	2.39198	+	3.46538i
$897$	−7.84937	−	3.34761i	−0.262083	−	0.111773i
$898$	−28.9370	+	41.9225i	−0.965641	+	1.39897i
$899$	−12.2150	+	3.53811i	−0.407392	+	0.118002i
$900$	14.7139	+	9.30452i	0.490464	+	0.310151i
$901$	−8.97124	−	1.45797i	−0.298875	−	0.0485719i
$902$	−10.1483	−	3.84873i	−0.337900	−	0.128149i
$903$	9.79214	−	22.9830i	0.325862	−	0.764827i
$904$	−87.5246	−	84.0685i	−2.91102	−	2.79608i
$905$	3.46849	−	6.60865i	0.115296	−	0.219679i
$906$	40.1543	−	3.24159i	1.33404	−	0.107695i
$907$	−4.24636	−	14.6601i	−0.140998	−	0.486782i	0.858670	−	0.512528i	$-0.171291\pi$
$907$	−4.24636	−	14.6601i	−0.140998	−	0.486782i	−0.999669	+	0.0257461i	$0.991804\pi$
$908$	−24.0488	+	23.0992i	−0.798088	+	0.766574i
$909$	1.58325	+	4.17469i	0.0525131	+	0.138466i
$910$	15.5052	+	29.5683i	0.513993	+	0.980179i
$911$	16.4870	−	43.4726i	0.546238	−	1.44031i	−0.323228	−	0.946321i	$-0.604768\pi$
$911$	16.4870	−	43.4726i	0.546238	−	1.44031i	0.869467	−	0.493991i	$-0.164463\pi$
$912$	15.3475	+	36.0220i	0.508207	+	1.19281i
$913$	−0.228561	−	5.67169i	−0.00756427	−	0.187705i
$914$	−27.0833	−	33.1710i	−0.895836	−	1.09720i
$915$			7.87059i			0.260194i
$916$	3.77318	−	3.08070i	0.124669	−	0.101789i
$917$	−18.9607	−	5.49204i	−0.626138	−	0.181363i
$918$	−3.46301	−	3.90893i	−0.114296	−	0.129014i
$919$	20.0482	−	20.8724i	0.661328	−	0.688515i	−0.303071	−	0.952968i	$-0.598012\pi$
$919$	20.0482	−	20.8724i	0.661328	−	0.688515i	0.964399	+	0.264453i	$0.0851913\pi$
$920$	−31.0960	−	10.3814i	−1.02521	−	0.342264i
$921$	−7.38938	−	9.83348i	−0.243488	−	0.324024i
$922$	−0.836908	−	6.89256i	−0.0275621	−	0.226994i
$923$	−13.1977	+	30.9457i	−0.434409	+	1.01859i
$924$	−1.04030	+	8.56761i	−0.0342232	+	0.281854i
$925$	−20.7320	+	11.9696i	−0.681663	+	0.393559i
$926$	−41.2390	+	30.9891i	−1.35520	+	1.01836i
$927$	−0.381151	+	9.45817i	−0.0125187	+	0.310647i
$928$	146.591	−	55.5946i	4.81209	−	1.82498i
$929$	15.5321	−	3.17090i	0.509592	−	0.104034i	0.0616523	−	0.998098i	$-0.480363\pi$
$929$	15.5321	−	3.17090i	0.509592	−	0.104034i	0.447940	+	0.894064i	$0.352158\pi$
$930$	7.68879	−	1.56968i	0.252125	−	0.0514717i
$931$	−2.47246	+	0.937681i	−0.0810317	+	0.0307313i
$932$	−1.69064	+	41.9527i	−0.0553787	+	1.37421i
$933$	−6.72873	+	5.05632i	−0.220289	+	0.165536i
$934$	56.3273	−	32.5206i	1.84309	−	1.06411i
$935$	−0.198817	+	1.63740i	−0.00650200	+	0.0535487i
$936$	−35.4282	+	7.21959i	−1.15801	+	0.235980i
$937$	0.589906	+	4.85831i	0.0192714	+	0.158714i	0.999168	−	0.0407939i	$-0.0129887\pi$
$937$	0.589906	+	4.85831i	0.0192714	+	0.158714i	−0.979896	+	0.199508i	$0.936066\pi$
$938$	−28.0709	−	37.3556i	−0.916548	−	1.21970i
$939$	15.8093	+	5.27792i	0.515917	+	0.172238i
$940$	−69.7753	+	72.6438i	−2.27582	+	2.36938i
$941$	31.8525	+	35.9540i	1.03836	+	1.17207i	0.984834	+	0.173501i	$0.0555080\pi$
$941$	31.8525	+	35.9540i	1.03836	+	1.17207i	0.0535275	+	0.998566i	$0.482954\pi$
$942$	−17.5691	−	5.08896i	−0.572433	−	0.165807i
$943$	11.4045	−	9.31147i	0.371381	−	0.303223i
$944$			218.624i			7.11561i
$945$	−2.12011	−	2.59667i	−0.0689672	−	0.0844695i
$946$	−0.723178	−	17.9455i	−0.0235126	−	0.583458i
$947$	2.33890	+	5.48960i	0.0760040	+	0.178388i	0.953647	−	0.300926i	$-0.0972958\pi$
$947$	2.33890	+	5.48960i	0.0760040	+	0.178388i	−0.877643	+	0.479314i	$0.840885\pi$
$948$	27.7397	−	73.1435i	0.900943	−	2.37559i
$949$	−26.0885	−	9.90468i	−0.846868	−	0.321519i
$950$	−7.21364	−	19.0208i	−0.234041	−	0.617116i
$951$	4.45789	−	4.28186i	0.144557	−	0.138849i
$952$	12.8008	+	44.1934i	0.414875	+	1.43232i
$953$	−7.86288	+	0.634757i	−0.254704	+	0.0205618i	−0.207159	−	0.978307i	$-0.566422\pi$
$953$	−7.86288	+	0.634757i	−0.254704	+	0.0205618i	−0.0475447	+	0.998869i	$0.515140\pi$
$954$	6.17147	−	11.7588i	0.199809	−	0.380704i
$955$	1.53479	+	1.47419i	0.0496648	+	0.0477037i
$956$	3.63755	−	8.53765i	0.117647	−	0.276127i
$957$	3.65170	+	1.38491i	0.118043	+	0.0447677i
$958$	−0.0541086	−	0.00879350i	−0.00174817	−	0.000284105i
$959$	23.8001	+	15.0503i	0.768545	+	0.485998i
$960$	−49.3019	+	14.2805i	−1.59121	+	0.460901i
$961$	15.2071	−	22.0313i	0.490552	−	0.710688i
$962$	21.4797	−	74.0578i	0.692532	−	2.38772i
$963$	−11.7019	−	16.9532i	−0.377089	−	0.546308i
$964$	21.1598	+	17.2764i	0.681510	+	0.556436i
$965$	13.9510	−	17.0869i	0.449100	−	0.550047i
$966$	−12.6841	−	9.53145i	−0.408103	−	0.306670i
$967$	15.8259	+	1.92162i	0.508928	+	0.0617950i	0.370973	−	0.928644i	$-0.379024\pi$
$967$	15.8259	+	1.92162i	0.508928	+	0.0617950i	0.137954	+	0.990439i	$0.455947\pi$
$968$	−33.6640	−	100.836i	−1.08200	−	3.24100i
$969$	0.362327	+	4.48823i	0.0116396	+	0.144183i
$970$	15.4436	−	17.4322i	0.495864	−	0.559715i
$971$	−39.9848	+	25.2849i	−1.28317	+	0.811430i	−0.989508	−	0.144478i	$-0.953850\pi$
$971$	−39.9848	+	25.2849i	−1.28317	+	0.811430i	−0.293666	+	0.955908i	$0.594875\pi$
$972$	5.17976	−	2.20689i	0.166141	−	0.0707860i
$973$	8.20605	+	50.4938i	0.263074	+	1.61876i
$974$	−18.8822	+	16.7282i	−0.605025	+	0.536005i
$975$	11.0047	−	1.78442i	0.352433	−	0.0571472i
$976$	70.1151	+	62.1165i	2.24433	+	1.98830i
$977$	−14.3679	+	22.7210i	−0.459670	+	0.726910i	−0.992886	−	0.119069i	$-0.962009\pi$
$977$	−14.3679	+	22.7210i	−0.459670	+	0.726910i	0.533216	+	0.845979i	$0.320983\pi$
$978$	−44.0122	−	3.55303i	−1.40736	−	0.113614i
$979$	−0.148439	−	0.727102i	−0.00474413	−	0.0232383i
$980$	−2.06635	−	8.38350i	−0.0660070	−	0.267801i
$981$	1.05011	−	6.46160i	0.0335275	−	0.206303i
$982$	46.8575	+	74.0992i	1.49528	+	2.36460i
$983$	−2.89245	−	5.51110i	−0.0922547	−	0.175777i	0.834956	−	0.550317i	$-0.185493\pi$
$983$	−2.89245	−	5.51110i	−0.0922547	−	0.175777i	−0.927211	+	0.374540i	$0.877801\pi$
$984$	17.3557	−	59.9188i	0.553279	−	1.91014i
$985$	0.499671	−	2.44755i	0.0159208	−	0.0779855i
$986$	32.2646	−	1.30022i	1.02752	−	0.0414075i
$987$	−27.8317	+	14.6072i	−0.885892	+	0.464952i
$988$	43.6747	+	20.7430i	1.38948	+	0.659922i
$989$	21.5724	+	11.3221i	0.685961	+	0.360020i
$990$	−2.17730	−	1.03314i	−0.0691992	−	0.0328354i
$991$	2.52742	+	4.37761i	0.0802860	+	0.139059i	0.903373	−	0.428856i	$-0.141083\pi$
$991$	2.52742	+	4.37761i	0.0802860	+	0.139059i	−0.823087	+	0.567916i	$0.807750\pi$
$992$	26.0739	−	45.1614i	0.827848	−	1.43387i
$993$	−9.94888	+	6.86722i	−0.315718	+	0.217925i
$994$	−37.5771	+	50.0061i	−1.19187	+	1.58610i
$995$	−14.2410	−	8.22207i	−0.451472	−	0.260657i
$996$	50.2297	−	6.09899i	1.59159	−	0.193254i
$997$	−12.7577	−	26.8862i	−0.404040	−	0.851496i	−0.998865	−	0.0476403i	$-0.984830\pi$
$997$	−12.7577	−	26.8862i	−0.404040	−	0.851496i	0.594825	−	0.803855i	$-0.297221\pi$
$998$	1.93011	+	2.00946i	0.0610967	+	0.0636084i
$999$	−0.622993	+	7.71715i	−0.0197106	+	0.244160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.10.1	✓	336
169.17	even	78	inner	507.2.t.a.355.1	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.10.1	✓	336	1.1	even	1	trivial
507.2.t.a.355.1	yes	336	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)

\(f(q)\)	\(=\)	\(q+(-2.70648 - 0.552531i) q^{2} +(0.987050 - 0.160411i) q^{3} +(5.17976 + 2.20689i) q^{4} +(-0.330566 + 1.34116i) q^{5} +(-2.76006 - 0.111227i) q^{6} +(-2.19257 + 1.04039i) q^{7} +(-8.25286 - 5.69654i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})\)	\(q+(-2.70648 - 0.552531i) q^{2} +(0.987050 - 0.160411i) q^{3} +(5.17976 + 2.20689i) q^{4} +(-0.330566 + 1.34116i) q^{5} +(-2.76006 - 0.111227i) q^{6} +(-2.19257 + 1.04039i) q^{7} +(-8.25286 - 5.69654i) q^{8} +(0.948536 - 0.316668i) q^{9} +(1.63570 - 3.44716i) q^{10} +(0.200014 - 0.599116i) q^{11} +(5.46669 + 1.34742i) q^{12} +(3.19315 - 1.67445i) q^{13} +(6.50898 - 1.60432i) q^{14} +(-0.111148 + 1.37682i) q^{15} +(11.3882 + 11.8563i) q^{16} +(0.810467 + 1.70802i) q^{17} +(-2.74216 + 0.332958i) q^{18} +(2.06266 + 1.19088i) q^{19} +(-4.67204 + 6.21735i) q^{20} +(-1.99729 + 1.37863i) q^{21} +(-0.872365 + 1.51098i) q^{22} +(-1.18337 - 2.04966i) q^{23} +(-9.05977 - 4.29892i) q^{24} +(2.73785 + 1.43693i) q^{25} +(-9.56737 + 2.76753i) q^{26} +(0.885456 - 0.464723i) q^{27} +(-13.6530 + 0.550197i) q^{28} +(-1.23682 + 6.05832i) q^{29} +(1.06155 - 3.66491i) q^{30} +(0.955788 + 1.82110i) q^{31} +(-13.5516 - 21.4301i) q^{32} +(0.101319 - 0.623443i) q^{33} +(-1.24977 - 5.07053i) q^{34} +(-0.670535 - 3.28450i) q^{35} +(5.61204 + 0.453051i) q^{36} +(-4.13797 + 6.54368i) q^{37} +(-4.92453 - 4.36276i) q^{38} +(2.88320 - 2.16498i) q^{39} +(10.3681 - 9.18530i) q^{40} +(0.997882 + 6.14021i) q^{41} +(6.16734 - 2.62766i) q^{42} +(-8.70030 + 5.50173i) q^{43} +(2.35821 - 2.66187i) q^{44} +(0.111148 + 1.37682i) q^{45} +(2.07027 + 6.20120i) q^{46} +(12.8572 + 1.56114i) q^{47} +(13.1426 + 9.87600i) q^{48} +(-0.702162 + 0.859992i) q^{49} +(-6.61597 - 5.40177i) q^{50} +(1.07396 + 1.55590i) q^{51} +(20.2351 - 1.62630i) q^{52} +(-2.73100 + 3.95653i) q^{53} +(-2.65324 + 0.768520i) q^{54} +(0.737392 + 0.466298i) q^{55} +(24.0216 + 3.90388i) q^{56} +(2.22698 + 0.844580i) q^{57} +(6.69482 - 15.7133i) q^{58} +(9.59097 + 9.21225i) q^{59} +(-3.61420 + 6.88629i) q^{60} +(5.67950 - 0.458497i) q^{61} +(-1.58060 - 5.45687i) q^{62} +(-1.75027 + 1.68116i) q^{63} +(13.1770 + 34.7449i) q^{64} +(1.19015 + 4.83604i) q^{65} +(-0.618689 + 1.63135i) q^{66} +(-2.73211 - 6.41249i) q^{67} +(0.428606 + 10.6358i) q^{68} +(-1.49684 - 1.83329i) q^{69} +9.25990i q^{70} +(-7.22763 + 5.90118i) q^{71} +(-9.63205 - 2.78996i) q^{72} +(-5.13228 - 5.79315i) q^{73} +(14.8149 - 15.4239i) q^{74} +(2.93290 + 0.979145i) q^{75} +(8.05593 + 10.7205i) q^{76} +(0.184767 + 1.52170i) q^{77} +(-8.99954 + 4.26641i) q^{78} +(1.67473 - 13.7926i) q^{79} +(-19.6657 + 11.3540i) q^{80} +(0.799443 - 0.600742i) q^{81} +(0.691915 - 17.1697i) q^{82} +(8.40285 - 3.18678i) q^{83} +(-13.3879 + 2.73317i) q^{84} +(-2.55864 + 0.522350i) q^{85} +(26.5870 - 10.0831i) q^{86} +(-0.248976 + 6.17827i) q^{87} +(-5.06358 + 3.80503i) q^{88} +(1.01750 - 0.587456i) q^{89} +(0.459914 - 3.78773i) q^{90} +(-5.25914 + 6.99346i) q^{91} +(-1.60621 - 13.2283i) q^{92} +(1.23554 + 1.64420i) q^{93} +(-33.9350 - 11.3292i) q^{94} +(-2.27899 + 2.37269i) q^{95} +(-16.8137 - 18.9787i) q^{96} +(5.86277 + 1.69817i) q^{97} +(2.37556 - 1.93958i) q^{98} -0.631622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

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