LMFDB - Embedded newform 507.2.s.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, 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:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.250240 + 1.36552i) q^{2} +(0.0535762 + 1.73122i) q^{3} +(0.0680148 + 0.0257946i) q^{4} +(1.85720 + 0.112340i) q^{5} +(-2.37742 - 0.360062i) q^{6} +(3.00163 + 1.81455i) q^{7} +(-1.48864 + 2.46251i) q^{8} +(-2.99426 + 0.185505i) q^{9} +O(q^{10})$	\(q+(-0.250240 + 1.36552i) q^{2} +(0.0535762 + 1.73122i) q^{3} +(0.0680148 + 0.0257946i) q^{4} +(1.85720 + 0.112340i) q^{5} +(-2.37742 - 0.360062i) q^{6} +(3.00163 + 1.81455i) q^{7} +(-1.48864 + 2.46251i) q^{8} +(-2.99426 + 0.185505i) q^{9} +(-0.618149 + 2.50793i) q^{10} +(-0.461782 - 2.51986i) q^{11} +(-0.0410122 + 0.119131i) q^{12} +(3.38428 - 1.24364i) q^{13} +(-3.22893 + 3.64470i) q^{14} +(-0.0949836 + 3.22125i) q^{15} +(-2.88119 - 2.55251i) q^{16} +(1.99184 - 0.490945i) q^{17} +(0.495975 - 4.13513i) q^{18} +(-1.19628 + 1.19628i) q^{19} +(0.123419 + 0.0555465i) q^{20} +(-2.98057 + 5.29370i) q^{21} +3.55647 q^{22} +3.95522 q^{23} +(-4.34291 - 2.44523i) q^{24} +(-1.52697 - 0.185408i) q^{25} +(0.851322 + 4.93251i) q^{26} +(-0.481571 - 5.17379i) q^{27} +(0.157350 + 0.200842i) q^{28} +(0.668680 - 0.461557i) q^{29} +(-4.37490 - 0.935787i) q^{30} +(-4.58201 - 3.58977i) q^{31} +(-0.323755 + 0.253646i) q^{32} +(4.33770 - 0.934451i) q^{33} +(0.171955 + 2.84275i) q^{34} +(5.37078 + 3.70718i) q^{35} +(-0.208439 - 0.0646187i) q^{36} +(0.840849 - 1.07326i) q^{37} +(-1.33418 - 1.93290i) q^{38} +(2.33433 + 5.79232i) q^{39} +(-3.04134 + 4.40614i) q^{40} +(-2.50445 - 8.03706i) q^{41} +(-6.48278 - 5.39472i) q^{42} +(-6.71031 - 0.814779i) q^{43} +(0.0335908 - 0.183299i) q^{44} +(-5.58178 + 0.00814448i) q^{45} +(-0.989755 + 5.40092i) q^{46} +(-5.20943 - 2.34457i) q^{47} +(4.26460 - 5.12473i) q^{48} +(2.46413 + 4.69500i) q^{49} +(0.635287 - 2.03871i) q^{50} +(0.956650 + 3.42202i) q^{51} +(0.262260 + 0.00271062i) q^{52} +(-2.74908 - 11.1535i) q^{53} +(7.18541 + 0.637097i) q^{54} +(-0.574540 - 4.73177i) q^{55} +(-8.93668 + 4.69033i) q^{56} +(-2.13512 - 2.00693i) q^{57} +(0.462933 + 1.02859i) q^{58} +(-0.0608020 + 1.00518i) q^{59} +(-0.0895510 + 0.216642i) q^{60} +(-5.49462 - 1.35430i) q^{61} +(6.04850 - 5.35850i) q^{62} +(-9.32426 - 4.87641i) q^{63} +(-3.84299 - 7.32221i) q^{64} +(6.42500 - 1.92949i) q^{65} +(0.190542 + 6.15704i) q^{66} +(12.9553 + 5.83071i) q^{67} +(0.148138 + 0.0179873i) q^{68} +(0.211906 + 6.84736i) q^{69} +(-6.40621 + 6.40621i) q^{70} +(1.95880 + 6.28602i) q^{71} +(4.00056 - 7.64954i) q^{72} +(-7.57262 + 1.38773i) q^{73} +(1.25515 + 1.41677i) q^{74} +(0.239173 - 2.65346i) q^{75} +(-0.112222 + 0.0505071i) q^{76} +(3.18631 - 8.40161i) q^{77} +(-8.49365 + 1.73809i) q^{78} +(1.83996 + 4.85157i) q^{79} +(-5.06419 - 5.06419i) q^{80} +(8.93118 - 1.11090i) q^{81} +(11.6015 - 1.40867i) q^{82} +(5.49654 + 1.71279i) q^{83} +(-0.339272 + 0.283167i) q^{84} +(3.75440 - 0.688020i) q^{85} +(2.79179 - 8.95916i) q^{86} +(0.834882 + 1.13291i) q^{87} +(6.89261 + 2.61402i) q^{88} +(0.770403 - 0.770403i) q^{89} +(1.38567 - 7.62406i) q^{90} +(12.4150 + 2.40801i) q^{91} +(0.269013 + 0.102023i) q^{92} +(5.96921 - 8.12480i) q^{93} +(4.50516 - 6.52686i) q^{94} +(-2.35612 + 2.08734i) q^{95} +(-0.456463 - 0.546903i) q^{96} +(14.2515 - 0.862056i) q^{97} +(-7.02774 + 2.18993i) q^{98} +(1.85014 + 7.45946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9}+O(q^{10}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27} - 56 q^{28} + 78 q^{30} - 32 q^{31} - 10 q^{33} - 52 q^{34} - 26 q^{36} - 56 q^{37} + 70 q^{39} - 36 q^{40} - 10 q^{42} - 52 q^{43} - 140 q^{45} - 180 q^{46} - 2 q^{48} - 52 q^{49} - 26 q^{51} - 64 q^{52} - 22 q^{54} + 132 q^{55} - 22 q^{57} - 60 q^{58} - 18 q^{60} - 92 q^{61} + 108 q^{63} - 52 q^{64} - 124 q^{66} - 240 q^{67} - 104 q^{69} - 268 q^{70} - 2 q^{72} - 56 q^{73} + 104 q^{75} - 48 q^{76} - 22 q^{78} - 12 q^{79} + 2 q^{81} + 208 q^{82} - 22 q^{84} - 52 q^{85} - 26 q^{87} - 260 q^{88} - 26 q^{90} - 32 q^{91} - 176 q^{93} - 240 q^{94} + 292 q^{96} - 80 q^{97} - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

Coefficient data

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

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

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

$2$	−0.250240	+	1.36552i	−0.176947	+	0.965567i	0.768515	+	0.639832i	$0.220996\pi$
$2$	−0.250240	+	1.36552i	−0.176947	+	0.965567i	−0.945461	+	0.325734i	$0.894388\pi$
$3$	0.0535762	+	1.73122i	0.0309322	+	0.999521i
$3$	0.0535762	+	1.73122i	0.0309322	+	0.999521i
$4$	0.0680148	+	0.0257946i	0.0340074	+	0.0128973i
$5$	1.85720	+	0.112340i	0.830565	+	0.0502400i	0.470188	−	0.882566i	$-0.344186\pi$
$5$	1.85720	+	0.112340i	0.830565	+	0.0502400i	0.360378	+	0.932806i	$0.382648\pi$
$6$	−2.37742	−	0.360062i	−0.970578	−	0.146995i
$7$	3.00163	+	1.81455i	1.13451	+	0.685835i	0.954612	−	0.297851i	$-0.0962698\pi$
$7$	3.00163	+	1.81455i	1.13451	+	0.685835i	0.179897	+	0.983686i	$0.442424\pi$
$8$	−1.48864	+	2.46251i	−0.526313	+	0.870629i
$9$	−2.99426	+	0.185505i	−0.998086	+	0.0618349i
$10$	−0.618149	+	2.50793i	−0.195476	+	0.793076i
$11$	−0.461782	−	2.51986i	−0.139232	−	0.759767i	−0.976918	−	0.213614i	$-0.931476\pi$
$11$	−0.461782	−	2.51986i	−0.139232	−	0.759767i	0.837686	−	0.546153i	$-0.183908\pi$
$12$	−0.0410122	+	0.119131i	−0.0118392	+	0.0343901i
$13$	3.38428	−	1.24364i	0.938631	−	0.344923i
$13$	3.38428	−	1.24364i	0.938631	−	0.344923i
$14$	−3.22893	+	3.64470i	−0.862967	+	0.974088i
$15$	−0.0949836	+	3.22125i	−0.0245247	+	0.831722i
$16$	−2.88119	−	2.55251i	−0.720297	−	0.638127i
$17$	1.99184	−	0.490945i	0.483093	−	0.119072i	0.00975440	−	0.999952i	$-0.496895\pi$
$17$	1.99184	−	0.490945i	0.483093	−	0.119072i	0.473338	+	0.880881i	$0.343049\pi$
$18$	0.495975	−	4.13513i	0.116902	−	0.974660i
$19$	−1.19628	+	1.19628i	−0.274445	+	0.274445i	−0.830887	−	0.556442i	$-0.812166\pi$
$19$	−1.19628	+	1.19628i	−0.274445	+	0.274445i	0.556442	+	0.830887i	$0.312166\pi$
$20$	0.123419	+	0.0555465i	0.0275974	+	0.0124206i
$21$	−2.98057	+	5.29370i	−0.650413	+	1.15518i
$22$	3.55647			0.758242
$23$	3.95522			0.824720			0.412360	−	0.911021i	$-0.364705\pi$
$23$	3.95522			0.824720			0.412360	+	0.911021i	$0.364705\pi$
$24$	−4.34291	−	2.44523i	−0.886492	−	0.499131i
$25$	−1.52697	−	0.185408i	−0.305394	−	0.0370816i
$26$	0.851322	+	4.93251i	0.166958	+	0.967344i
$27$	−0.481571	−	5.17379i	−0.0926784	−	0.995696i
$28$	0.157350	+	0.200842i	0.0297363	+	0.0379555i
$29$	0.668680	−	0.461557i	0.124171	−	0.0857089i	−0.504361	−	0.863493i	$-0.668272\pi$
$29$	0.668680	−	0.461557i	0.124171	−	0.0857089i	0.628531	+	0.777784i	$0.283656\pi$
$30$	−4.37490	−	0.935787i	−0.798743	−	0.170851i
$31$	−4.58201	−	3.58977i	−0.822953	−	0.644742i	0.114279	−	0.993449i	$-0.463544\pi$
$31$	−4.58201	−	3.58977i	−0.822953	−	0.644742i	−0.937232	+	0.348706i	$0.886621\pi$
$32$	−0.323755	+	0.253646i	−0.0572324	+	0.0448387i
$33$	4.33770	−	0.934451i	0.755097	−	0.162667i
$34$	0.171955	+	2.84275i	0.0294900	+	0.487527i
$35$	5.37078	+	3.70718i	0.907828	+	0.626628i
$36$	−0.208439	−	0.0646187i	−0.0347398	−	0.0107698i
$37$	0.840849	−	1.07326i	0.138235	−	0.176444i	−0.713107	−	0.701055i	$-0.752713\pi$
$37$	0.840849	−	1.07326i	0.138235	−	0.176444i	0.851342	+	0.524612i	$0.175790\pi$
$38$	−1.33418	−	1.93290i	−0.216433	−	0.313557i
$39$	2.33433	+	5.79232i	0.373791	+	0.927513i
$40$	−3.04134	+	4.40614i	−0.480878	+	0.696672i
$41$	−2.50445	−	8.03706i	−0.391129	−	1.25518i	−0.915026	−	0.403396i	$-0.867830\pi$
$41$	−2.50445	−	8.03706i	−0.391129	−	1.25518i	0.523896	−	0.851782i	$-0.324478\pi$
$42$	−6.48278	−	5.39472i	−1.00032	−	0.832423i
$43$	−6.71031	−	0.814779i	−1.02331	−	0.124253i	−0.408364	−	0.912819i	$-0.633900\pi$
$43$	−6.71031	−	0.814779i	−1.02331	−	0.124253i	−0.614949	+	0.788567i	$0.710824\pi$
$44$	0.0335908	−	0.183299i	0.00506401	−	0.0276334i
$45$	−5.58178	+	0.00814448i	−0.832083	+	0.00121411i
$46$	−0.989755	+	5.40092i	−0.145931	+	0.796322i
$47$	−5.20943	−	2.34457i	−0.759873	−	0.341991i	−0.00684238	−	0.999977i	$-0.502178\pi$
$47$	−5.20943	−	2.34457i	−0.759873	−	0.341991i	−0.753031	+	0.657986i	$0.771409\pi$
$48$	4.26460	−	5.12473i	0.615541	−	0.739691i
$49$	2.46413	+	4.69500i	0.352018	+	0.670715i
$50$	0.635287	−	2.03871i	0.0898432	−	0.288317i
$51$	0.956650	+	3.42202i	0.133958	+	0.479178i
$52$	0.262260	+	0.00271062i	0.0363690	+	0.000375895i
$53$	−2.74908	−	11.1535i	−0.377615	−	1.53204i	−0.785413	−	0.618972i	$-0.787549\pi$
$53$	−2.74908	−	11.1535i	−0.377615	−	1.53204i	0.407798	−	0.913072i	$-0.366297\pi$
$54$	7.18541	+	0.637097i	0.977810	+	0.0866980i
$55$	−0.574540	−	4.73177i	−0.0774710	−	0.638031i
$56$	−8.93668	+	4.69033i	−1.19421	+	0.626772i
$57$	−2.13512	−	2.00693i	−0.282803	−	0.265825i
$58$	0.462933	+	1.02859i	0.0607861	+	0.135061i
$59$	−0.0608020	+	1.00518i	−0.00791574	+	0.130863i	0.992071	+	0.125680i	$0.0401113\pi$
$59$	−0.0608020	+	1.00518i	−0.00791574	+	0.130863i	−0.999987	+	0.00518279i	$0.998350\pi$
$60$	−0.0895510	+	0.216642i	−0.0115610	+	0.0279684i
$61$	−5.49462	−	1.35430i	−0.703513	−	0.173400i	−0.128698	−	0.991684i	$-0.541080\pi$
$61$	−5.49462	−	1.35430i	−0.703513	−	0.173400i	−0.574815	+	0.818283i	$0.694926\pi$
$62$	6.04850	−	5.35850i	0.768160	−	0.680531i
$63$	−9.32426	−	4.87641i	−1.17475	−	0.614370i
$64$	−3.84299	−	7.32221i	−0.480374	−	0.915276i
$65$	6.42500	−	1.92949i	0.796923	−	0.239324i
$66$	0.190542	+	6.15704i	0.0234541	+	0.757879i
$67$	12.9553	+	5.83071i	1.58274	+	0.712334i	0.995292	−	0.0969258i	$-0.0309009\pi$
$67$	12.9553	+	5.83071i	1.58274	+	0.712334i	0.587450	+	0.809260i	$0.300132\pi$
$68$	0.148138	+	0.0179873i	0.0179644	+	0.00218128i
$69$	0.211906	+	6.84736i	0.0255104	+	0.824325i
$70$	−6.40621	+	6.40621i	−0.765688	+	0.765688i
$71$	1.95880	+	6.28602i	0.232467	+	0.746013i	0.995073	+	0.0991491i	$0.0316121\pi$
$71$	1.95880	+	6.28602i	0.232467	+	0.746013i	−0.762606	+	0.646864i	$0.776080\pi$
$72$	4.00056	−	7.64954i	0.471471	−	0.901507i
$73$	−7.57262	+	1.38773i	−0.886308	+	0.162422i	−0.604079	−	0.796925i	$-0.706459\pi$
$73$	−7.57262	+	1.38773i	−0.886308	+	0.162422i	−0.282230	+	0.959347i	$0.591074\pi$
$74$	1.25515	+	1.41677i	0.145908	+	0.164696i
$75$	0.239173	−	2.65346i	0.0276173	−	0.306395i
$76$	−0.112222	+	0.0505071i	−0.0128728	+	0.00579356i
$77$	3.18631	−	8.40161i	0.363114	−	0.957453i
$78$	−8.49365	+	1.73809i	−0.961717	+	0.196800i
$79$	1.83996	+	4.85157i	0.207012	+	0.545845i	0.997804	−	0.0662402i	$-0.0211004\pi$
$79$	1.83996	+	4.85157i	0.207012	+	0.545845i	−0.790792	+	0.612085i	$0.790331\pi$
$80$	−5.06419	−	5.06419i	−0.566194	−	0.566194i
$81$	8.93118	−	1.11090i	0.992353	−	0.123433i
$82$	11.6015	−	1.40867i	1.28117	−	0.155562i
$83$	5.49654	+	1.71279i	0.603324	+	0.188003i	0.583924	−	0.811809i	$-0.301517\pi$
$83$	5.49654	+	1.71279i	0.603324	+	0.188003i	0.0193999	+	0.999812i	$0.493824\pi$
$84$	−0.339272	+	0.283167i	−0.0370176	+	0.0308961i
$85$	3.75440	−	0.688020i	0.407222	−	0.0746262i
$86$	2.79179	−	8.95916i	0.301046	−	0.966091i
$87$	0.834882	+	1.13291i	0.0895088	+	0.121460i
$88$	6.89261	+	2.61402i	0.734755	+	0.278656i
$89$	0.770403	−	0.770403i	0.0816626	−	0.0816626i	−0.665096	−	0.746758i	$-0.731609\pi$
$89$	0.770403	−	0.770403i	0.0816626	−	0.0816626i	0.746758	+	0.665096i	$0.231609\pi$
$90$	1.38567	−	7.62406i	0.146062	−	0.803646i
$91$	12.4150	+	2.40801i	1.30145	+	0.252428i
$92$	0.269013	+	0.102023i	0.0280466	+	0.0106367i
$93$	5.96921	−	8.12480i	0.618978	−	0.842502i
$94$	4.50516	−	6.52686i	0.464672	−	0.673194i
$95$	−2.35612	+	2.08734i	−0.241733	+	0.214157i
$96$	−0.456463	−	0.546903i	−0.0465876	−	0.0558181i
$97$	14.2515	−	0.862056i	1.44702	−	0.0875285i	0.681913	−	0.731433i	$-0.261148\pi$
$97$	14.2515	−	0.862056i	1.44702	−	0.0875285i	0.765106	+	0.643905i	$0.222687\pi$
$98$	−7.02774	+	2.18993i	−0.709908	+	0.221216i
$99$	1.85014	+	7.45946i	0.185946	+	0.749704i
$100$	−0.0990740	−	0.0519981i	−0.00990740	−	0.00519981i
$101$	−1.66332	+	13.6986i	−0.165506	+	1.36307i	0.639039	+	0.769175i	$0.279332\pi$
$101$	−1.66332	+	13.6986i	−0.165506	+	1.36307i	−0.804545	+	0.593892i	$0.797591\pi$
$102$	−4.91222	+	0.449995i	−0.486382	+	0.0445562i
$103$	−7.06447	+	13.4602i	−0.696083	+	1.32627i	0.238714	+	0.971090i	$0.423274\pi$
$103$	−7.06447	+	13.4602i	−0.696083	+	1.32627i	−0.934796	+	0.355185i	$0.884418\pi$
$104$	−1.97551	+	10.1852i	−0.193715	+	0.998736i
$105$	−6.13021	+	9.49663i	−0.598247	+	0.926776i
$106$	15.9182	−	0.962872i	1.54611	−	0.0935224i
$107$	2.16287	+	2.44138i	0.209093	+	0.236017i	0.843696	−	0.536821i	$-0.180375\pi$
$107$	2.16287	+	2.44138i	0.209093	+	0.236017i	−0.634603	+	0.772838i	$0.718836\pi$
$108$	0.100702	−	0.364316i	0.00969004	−	0.0350563i
$109$	3.17097	+	4.04745i	0.303724	+	0.387675i	0.914807	−	0.403892i	$-0.132343\pi$
$109$	3.17097	+	4.04745i	0.303724	+	0.387675i	−0.611083	+	0.791567i	$0.709266\pi$
$110$	6.60508	+	0.399534i	0.629770	+	0.0380941i
$111$	1.90311	+	1.39819i	0.180635	+	0.132711i
$112$	−4.01660	−	12.8897i	−0.379533	−	1.21797i
$113$	1.22778	+	2.33934i	0.115500	+	0.220066i	0.936342	−	0.351088i	$-0.114188\pi$
$113$	1.22778	+	2.33934i	0.115500	+	0.220066i	−0.820843	+	0.571154i	$0.806496\pi$
$114$	3.27479	−	2.41332i	0.306712	−	0.226028i
$115$	7.34563	+	0.444329i	0.684984	+	0.0414339i
$116$	0.0573858	−	0.0141443i	0.00532814	−	0.00131327i
$117$	−9.90272	+	4.35157i	−0.915507	+	0.402303i
$118$	−1.35737	−	0.334562i	−0.124956	−	0.0307989i
$119$	6.86961	+	2.14066i	0.629736	+	0.196234i
$120$	−7.79095	−	5.02917i	−0.711213	−	0.459098i
$121$	4.14872	−	1.57340i	0.377156	−	0.143036i
$122$	3.22430	−	7.16409i	0.291914	−	0.648606i
$123$	13.7798	−	4.76635i	1.24248	−	0.429768i
$124$	−0.219047	−	0.362349i	−0.0196710	−	0.0325399i
$125$	−11.9657	−	2.19279i	−1.07024	−	0.196129i
$126$	8.99213	−	11.5122i	0.801083	−	1.02559i
$127$	−11.8291	+	4.48618i	−1.04966	+	0.398084i	−0.818305	−	0.574785i	$-0.805086\pi$
$127$	−11.8291	+	4.48618i	−1.04966	+	0.398084i	−0.231357	+	0.972869i	$0.574317\pi$
$128$	10.1749	−	3.17064i	0.899347	−	0.280248i
$129$	1.05105	−	11.6607i	0.0925399	−	1.02667i
$130$	1.02696	+	9.25629i	0.0900703	+	0.811830i
$131$	5.23434	−	3.61300i	0.457326	−	0.315670i	−0.317034	−	0.948414i	$-0.602687\pi$
$131$	5.23434	−	3.61300i	0.457326	−	0.315670i	0.774361	+	0.632744i	$0.218072\pi$
$132$	0.319131	+	0.0483327i	0.0277768	+	0.00420682i
$133$	−5.76149	+	1.42008i	−0.499584	+	0.123136i
$134$	−11.2039	+	16.2316i	−0.967867	+	1.40220i
$135$	−0.313151	−	9.66286i	−0.0269517	−	0.831647i
$136$	−1.75618	+	5.63577i	−0.150591	+	0.483263i
$137$	−6.58953	−	8.41091i	−0.562981	−	0.718592i	0.418912	−	0.908027i	$-0.362411\pi$
$137$	−6.58953	−	8.41091i	−0.562981	−	0.718592i	−0.981893	+	0.189434i	$0.939335\pi$
$138$	−9.40322	−	1.42412i	−0.800455	−	0.121230i
$139$	5.04517	+	4.46963i	0.427926	+	0.379109i	0.849416	−	0.527724i	$-0.176954\pi$
$139$	5.04517	+	4.46963i	0.427926	+	0.379109i	−0.421490	+	0.906833i	$0.638493\pi$
$140$	0.269667	+	0.390680i	0.0227910	+	0.0330185i
$141$	3.77987	−	9.14429i	0.318323	−	0.770088i
$142$	−9.07384	+	1.10176i	−0.761459	+	0.0924579i
$143$	−4.69659	−	7.95364i	−0.392749	−	0.665116i
$144$	9.10052	+	7.10840i	0.758377	+	0.592366i
$145$	1.29372	−	0.782084i	0.107438	−	0.0649485i
$146$		−	10.6878i		−	0.884530i
$147$	−7.99608	+	4.51749i	−0.659505	+	0.372597i
$148$	0.0848746	−	0.0513085i	0.00697665	−	0.00421753i
$149$	9.25461	−	20.5629i	0.758167	−	1.68458i	0.0296406	−	0.999561i	$-0.490564\pi$
$149$	9.25461	−	20.5629i	0.758167	−	1.68458i	0.728527	−	0.685018i	$-0.240205\pi$
$150$	3.56349	+	0.990597i	0.290958	+	0.0808819i
$151$	2.04053	−	0.918366i	0.166056	−	0.0747356i	−0.325680	−	0.945480i	$-0.605593\pi$
$151$	2.04053	−	0.918366i	0.166056	−	0.0747356i	0.491736	+	0.870744i	$0.336363\pi$
$152$	−1.16502	−	4.72667i	−0.0944956	−	0.383384i
$153$	−5.87302	+	1.83951i	−0.474805	+	0.148716i
$154$	10.6752	+	6.45339i	0.860233	+	0.520029i
$155$	−8.10643	−	7.18167i	−0.651124	−	0.576846i
$156$	0.00935824	+	0.454176i	0.000749258	+	0.0363632i
$157$	−13.7669	+	12.1964i	−1.09872	+	0.973379i	−0.999764	−	0.0217127i	$-0.993088\pi$
$157$	−13.7669	+	12.1964i	−1.09872	+	0.973379i	−0.0989539	+	0.995092i	$0.531550\pi$
$158$	−7.08534	+	1.29844i	−0.563679	+	0.103298i
$159$	19.1618	−	5.35683i	1.51963	−	0.424824i
$160$	−0.629773	+	0.434701i	−0.0497879	+	0.0343661i
$161$	11.8721	+	7.17693i	0.935652	+	0.565621i
$162$	−0.717990	+	12.4737i	−0.0564106	+	0.980024i
$163$	10.2956	−	13.1414i	0.806415	−	1.02931i	−0.192432	−	0.981310i	$-0.561638\pi$
$163$	10.2956	−	13.1414i	0.806415	−	1.02931i	0.998847	−	0.0480023i	$-0.0152855\pi$
$164$	0.0369732	−	0.611240i	0.00288712	−	0.0477298i
$165$	8.16095	−	1.24817i	0.635329	−	0.0971697i
$166$	−3.71430	+	7.07701i	−0.288286	+	0.549283i
$167$	16.7587	+	3.07114i	1.29682	+	0.237652i	0.783956	−	0.620816i	$-0.213199\pi$
$167$	16.7587	+	3.07114i	1.29682	+	0.237652i	0.512868	+	0.858468i	$0.328583\pi$
$168$	−8.59880	−	15.2201i	−0.663412	−	1.17426i
$169$	9.90674	−	8.41763i	0.762057	−	0.647510i
$170$			5.29887i			0.406405i
$171$	3.36005	−	3.80388i	0.256950	−	0.290890i
$172$	−0.435383	−	0.228507i	−0.0331977	−	0.0174235i
$173$	−4.44659	+	11.7247i	−0.338068	+	0.891411i	0.652916	+	0.757430i	$0.273545\pi$
$173$	−4.44659	+	11.7247i	−0.338068	+	0.891411i	−0.990984	+	0.133981i	$0.957224\pi$
$174$	−1.75592	+	0.856548i	−0.133116	+	0.0649347i
$175$	−4.24697	−	3.32729i	−0.321040	−	0.251519i
$176$	−5.10149	+	8.43889i	−0.384539	+	0.636105i
$177$	−1.74344	−	0.0514082i	−0.131045	−	0.00386407i
$178$	0.859213	+	1.24478i	0.0644007	+	0.0933006i
$179$	−10.6236	−	2.61849i	−0.794046	−	0.195715i	−0.178629	−	0.983916i	$-0.557166\pi$
$179$	−10.6236	−	2.61849i	−0.794046	−	0.195715i	−0.615417	+	0.788202i	$0.711012\pi$
$180$	−0.379854	−	0.143426i	−0.0283126	−	0.0106903i
$181$	−11.3990	−	12.8668i	−0.847281	−	0.956383i	0.152208	−	0.988349i	$-0.451362\pi$
$181$	−11.3990	−	12.8668i	−0.847281	−	0.956383i	−0.999489	+	0.0319659i	$0.989823\pi$
$182$	−6.39491	+	16.3503i	−0.474022	+	1.21197i
$183$	2.05021	−	9.58496i	0.151556	−	0.708540i
$184$	−5.88789	+	9.73976i	−0.434061	+	0.718025i
$185$	1.68220	−	1.89881i	0.123677	−	0.139603i
$186$	9.60082	+	10.1842i	0.703966	+	0.746743i
$187$	−2.15691	−	4.79246i	−0.157729	−	0.350459i
$188$	−0.293841	−	0.293841i	−0.0214305	−	0.0214305i
$189$	7.94259	−	16.4036i	0.577738	−	1.19319i
$190$	−2.26070	−	3.73966i	−0.164009	−	0.271303i
$191$			21.9530i			1.58846i	0.607616	+	0.794231i	$0.292126\pi$
$191$			21.9530i			1.58846i	−0.607616	+	0.794231i	$0.707874\pi$
$192$	12.4705	−	7.04536i	0.899979	−	0.508455i
$193$	9.97414	+	16.4992i	0.717954	+	1.18764i	0.975206	+	0.221297i	$0.0710291\pi$
$193$	9.97414	+	16.4992i	0.717954	+	1.18764i	−0.257252	+	0.966344i	$0.582817\pi$
$194$	−2.38914	+	19.6764i	−0.171530	+	1.41268i
$195$	3.68460	+	11.0197i	0.263860	+	0.789139i
$196$	0.0464914	+	0.382891i	0.00332081	+	0.0273494i
$197$	−6.71391	+	5.26001i	−0.478346	+	0.374760i	−0.826737	−	0.562589i	$-0.809805\pi$
$197$	−6.71391	+	5.26001i	−0.478346	+	0.374760i	0.348390	+	0.937349i	$0.386728\pi$
$198$	−10.6490	+	0.659742i	−0.756791	+	0.0468858i
$199$	5.45866	−	6.16156i	0.386954	−	0.436781i	−0.522466	−	0.852660i	$-0.674988\pi$
$199$	5.45866	−	6.16156i	0.386954	−	0.436781i	0.909420	+	0.415879i	$0.136526\pi$
$200$	2.72968	−	3.48417i	0.193017	−	0.246368i
$201$	−9.40015	+	22.7409i	−0.663036	+	1.60402i
$202$	−18.2895	−	5.69924i	−1.28685	−	0.400997i
$203$	2.84465	−	0.172069i	0.199655	−	0.0120769i
$204$	−0.0232032	+	0.257424i	−0.00162455	+	0.0180233i
$205$	−3.74838	−	15.2078i	−0.261798	−	1.06216i
$206$	−16.6123	−	13.0149i	−1.15744	−	0.906794i
$207$	−11.8429	+	0.733711i	−0.823142	+	0.0509965i
$208$	−12.9251	−	5.05526i	−0.896197	−	0.350519i
$209$	3.56688	+	2.46204i	0.246726	+	0.170303i
$210$	−11.4338	−	10.7473i	−0.789006	−	0.741637i
$211$	1.47803	+	3.89725i	0.101752	+	0.268298i	0.976219	−	0.216787i	$-0.0695578\pi$
$211$	1.47803	+	3.89725i	0.101752	+	0.268298i	−0.874467	+	0.485085i	$0.838789\pi$
$212$	0.100721	−	0.829511i	0.00691754	−	0.0569710i
$213$	−10.7775	+	3.72790i	−0.738465	+	0.255432i
$214$	−3.87499	+	2.34251i	−0.264889	+	0.160131i
$215$	−12.3709	−	2.26704i	−0.843686	−	0.154611i
$216$	13.4574	+	6.51603i	0.915659	+	0.443360i
$217$	−7.23967	−	19.0894i	−0.491461	−	1.29588i
$218$	−6.32036	+	3.31718i	−0.428069	+	0.224668i
$219$	−2.80819	−	13.0355i	−0.189760	−	0.880860i
$220$	0.0829768	−	0.336650i	0.00559429	−	0.0226969i
$221$	6.13040	−	4.13862i	0.412375	−	0.278394i
$222$	−2.38549	+	2.24884i	−0.160104	+	0.150932i
$223$	0.980227	−	16.2051i	0.0656409	−	1.08517i	−0.805007	−	0.593266i	$-0.797838\pi$
$223$	0.980227	−	16.2051i	0.0656409	−	1.08517i	0.870648	−	0.491907i	$-0.163700\pi$
$224$	−1.43205	+	0.173882i	−0.0956826	+	0.0116180i
$225$	4.60654	+	0.271899i	0.307103	+	0.0181266i
$226$	−3.50164	+	1.09116i	−0.232926	+	0.0725826i
$227$	23.6995	−	10.6663i	1.57299	−	0.707947i	0.578792	−	0.815475i	$-0.303524\pi$
$227$	23.6995	−	10.6663i	1.57299	−	0.707947i	0.994202	+	0.107528i	$0.0342935\pi$
$228$	−0.0934514	−	0.191575i	−0.00618897	−	0.0126874i
$229$	−14.8041	+	11.5983i	−0.978284	+	0.766437i	−0.972346	−	0.233545i	$-0.924967\pi$
$229$	−14.8041	+	11.5983i	−0.978284	+	0.766437i	−0.00593852	+	0.999982i	$0.501890\pi$
$230$	−2.44491	+	9.91940i	−0.161213	+	0.654066i
$231$	14.7158	+	5.06609i	0.968227	+	0.333324i
$232$	0.141164	+	2.33372i	0.00926788	+	0.153216i
$233$	−24.5610	+	12.8906i	−1.60905	+	0.844493i	−0.610422	+	0.792076i	$0.709000\pi$
$233$	−24.5610	+	12.8906i	−1.60905	+	0.844493i	−0.998625	+	0.0524173i	$0.983307\pi$
$234$	−3.46408	−	14.6113i	−0.226454	−	0.955169i
$235$	−9.41156	−	4.93957i	−0.613943	−	0.322222i
$236$	−0.0300636	+	0.0667985i	−0.00195697	+	0.00434821i
$237$	−8.30057	+	3.44531i	−0.539180	+	0.223797i
$238$	−4.64216	+	8.84490i	−0.300907	+	0.573329i
$239$	8.85820	+	8.85820i	0.572989	+	0.572989i	0.932963	−	0.359974i	$-0.117214\pi$
$239$	8.85820	+	8.85820i	0.572989	+	0.572989i	−0.359974	+	0.932963i	$0.617214\pi$
$240$	8.49592	−	9.03856i	0.548409	−	0.583437i
$241$	−1.17477	−	19.4212i	−0.0756734	−	1.25103i	−0.815709	−	0.578463i	$-0.803653\pi$
$241$	−1.17477	−	19.4212i	−0.0756734	−	1.25103i	0.740036	−	0.672568i	$-0.234809\pi$
$242$	1.11033	+	6.05888i	0.0713747	+	0.389479i
$243$	2.40171	+	15.4023i	0.154070	+	0.988060i
$244$	−0.338781	−	0.233844i	−0.0216883	−	0.0149703i
$245$	4.04894	+	8.99639i	0.258678	+	0.574758i
$246$	3.06029	+	20.0092i	0.195117	+	1.27574i
$247$	−2.56081	+	5.53628i	−0.162940	+	0.352265i
$248$	15.6608	−	5.93936i	0.994462	−	0.377150i
$249$	−2.67074	+	9.60749i	−0.169251	+	0.608850i
$250$	5.98858	−	15.7906i	0.378751	−	0.998684i
$251$	2.90539	+	23.9280i	0.183386	+	1.51032i	0.736055	+	0.676922i	$0.236687\pi$
$251$	2.90539	+	23.9280i	0.183386	+	1.51032i	−0.552668	+	0.833401i	$0.686390\pi$
$252$	−0.508403	−	0.572184i	−0.0320263	−	0.0360442i
$253$	−1.82645	−	9.96660i	−0.114828	−	0.626595i
$254$	−3.16584	−	17.2754i	−0.198643	−	1.08396i
$255$	1.39226	+	6.46284i	0.0871868	+	0.404719i
$256$	−0.210152	−	1.73075i	−0.0131345	−	0.108172i
$257$	−0.230816	+	0.608611i	−0.0143979	+	0.0379641i	−0.942022	−	0.335550i	$-0.891078\pi$
$257$	−0.230816	+	0.608611i	−0.0143979	+	0.0379641i	0.927625	+	0.373514i	$0.121847\pi$
$258$	15.6599	+	4.35320i	0.974940	+	0.271019i
$259$	4.47141	−	1.69578i	0.277840	−	0.105371i
$260$	0.486766	+	0.0344965i	0.0301879	+	0.00213938i
$261$	−1.91658	+	1.50606i	−0.118633	+	0.0932230i
$262$	3.62378	+	8.05170i	0.223878	+	0.497436i
$263$	−9.37850	−	6.47351i	−0.578303	−	0.399174i	0.242697	−	0.970102i	$-0.421968\pi$
$263$	−9.37850	−	6.47351i	−0.578303	−	0.399174i	−0.821000	+	0.570929i	$0.806583\pi$
$264$	−4.15617	+	12.0727i	−0.255795	+	0.743023i
$265$	−3.85261	−	21.0230i	−0.236664	−	1.29143i
$266$	−0.497386	−	8.22277i	−0.0304967	−	0.504171i
$267$	1.37501	+	1.29246i	0.0841495	+	0.0790975i
$268$	0.730751	+	0.730751i	0.0446377	+	0.0446377i
$269$	6.77831	−	12.9150i	0.413281	−	0.787441i	−0.586465	−	0.809975i	$-0.699481\pi$
$269$	6.77831	−	12.9150i	0.413281	−	0.787441i	0.999746	+	0.0225332i	$0.00717314\pi$
$270$	13.2732	+	1.99043i	0.807780	+	0.121133i
$271$	−2.61621	+	5.81298i	−0.158923	+	0.353113i	−0.974106	−	0.226090i	$-0.927406\pi$
$271$	−2.61621	+	5.81298i	−0.158923	+	0.353113i	0.815183	+	0.579204i	$0.196636\pi$
$272$	−6.99201	−	3.66969i	−0.423953	−	0.222508i
$273$	−3.50365	+	21.6221i	−0.212051	+	1.30863i
$274$	13.1342	−	6.89336i	0.793466	−	0.416443i
$275$	0.237925	+	3.93337i	0.0143474	+	0.237191i
$276$	−0.162212	+	0.471188i	−0.00976403	+	0.0283622i
$277$	4.51262	−	18.3084i	0.271137	−	1.10005i	−0.664558	−	0.747237i	$-0.731380\pi$
$277$	4.51262	−	18.3084i	0.271137	−	1.10005i	0.935695	−	0.352810i	$-0.114774\pi$
$278$	−7.36587	+	5.77079i	−0.441776	+	0.346109i
$279$	14.3856	+	9.89873i	0.861246	+	0.592621i
$280$	−17.1241	+	7.70694i	−1.02336	+	0.460578i
$281$	−29.0379	+	9.04858i	−1.73226	+	0.539793i	−0.991284	−	0.131743i	$-0.957943\pi$
$281$	−29.0379	+	9.04858i	−1.73226	+	0.539793i	−0.740972	+	0.671536i	$0.765635\pi$
$282$	11.5408	+	7.44975i	0.687245	+	0.443626i
$283$	−12.6322	+	1.53383i	−0.750906	+	0.0911765i	−0.487036	−	0.873382i	$-0.661922\pi$
$283$	−12.6322	+	1.53383i	−0.750906	+	0.0911765i	−0.263870	+	0.964558i	$0.584999\pi$
$284$	−0.0289178	+	0.478069i	−0.00171596	+	0.0283681i
$285$	−3.73988	−	3.96713i	−0.221531	−	0.234993i
$286$	12.0361	−	4.42296i	0.711710	−	0.261535i
$287$	7.06620	−	28.6687i	0.417105	−	1.69226i
$288$	0.922355	−	0.819540i	0.0543503	−	0.0482919i
$289$	−11.3263	+	5.94453i	−0.666256	+	0.349678i
$290$	0.744207	+	1.96231i	0.0437013	+	0.115231i
$291$	2.25595	+	24.6263i	0.132246	+	1.44362i
$292$	−0.550846	−	0.100946i	−0.0322358	−	0.00590744i
$293$	4.37194	−	2.64293i	0.255412	−	0.154402i	−0.383839	−	0.923400i	$-0.625398\pi$
$293$	4.37194	−	2.64293i	0.255412	−	0.154402i	0.639251	+	0.768998i	$0.279245\pi$
$294$	−4.16778	−	12.0492i	−0.243070	−	0.702726i
$295$	−0.225843	+	1.85998i	−0.0131491	+	0.108292i
$296$	1.39120	+	3.66830i	0.0808621	+	0.213216i
$297$	−12.8149	+	3.60265i	−0.743593	+	0.209047i
$298$	25.7631	+	17.7830i	1.49242	+	1.03014i
$299$	13.3856	−	4.91885i	0.774108	−	0.284464i
$300$	0.0847122	−	0.174305i	0.00489086	−	0.0100635i
$301$	−18.6634	−	14.6218i	−1.07574	−	0.842789i
$302$	0.743423	+	3.01619i	0.0427792	+	0.173562i
$303$	−23.8045	−	2.14565i	−1.36753	−	0.123264i
$304$	6.50021	−	0.393190i	0.372813	−	0.0225510i
$305$	−10.0525	−	3.13247i	−0.575602	−	0.179365i
$306$	−1.04222	−	8.48003i	−0.0595797	−	0.484771i
$307$	−14.5568	+	18.5804i	−0.830800	+	1.06044i	0.166430	+	0.986053i	$0.446776\pi$
$307$	−14.5568	+	18.5804i	−0.830800	+	1.06044i	−0.997230	+	0.0743841i	$0.976301\pi$
$308$	0.433433	−	0.489244i	0.0246971	−	0.0278773i
$309$	−23.6811	−	11.5090i	−1.34717	−	0.654725i
$310$	11.8353	−	9.27233i	0.672197	−	0.526633i
$311$	−1.22802	−	10.1136i	−0.0696344	−	0.573491i	−0.985211	−	0.171347i	$-0.945188\pi$
$311$	−1.22802	−	10.1136i	−0.0696344	−	0.573491i	0.915576	−	0.402144i	$-0.131735\pi$
$312$	−17.7386	−	2.87436i	−1.00425	−	0.162729i
$313$	1.38931	−	11.4420i	0.0785283	−	0.646739i	−0.899300	−	0.437332i	$-0.855924\pi$
$313$	1.38931	−	11.4420i	0.0785283	−	0.646739i	0.977829	−	0.209407i	$-0.0671533\pi$
$314$	−13.2094	−	21.8510i	−0.745448	−	1.23312i
$315$	−16.7692	−	10.1040i	−0.944838	−	0.569294i
$316$			0.377440i			0.0212326i
$317$	10.5977	+	17.5308i	0.595228	+	0.984628i	0.997606	+	0.0691541i	$0.0220300\pi$
$317$	10.5977	+	17.5308i	0.595228	+	0.984628i	−0.402378	+	0.915474i	$0.631816\pi$
$318$	2.51978	+	27.5063i	0.141302	+	1.54248i
$319$	−1.47184	−	1.47184i	−0.0824074	−	0.0824074i
$320$	−6.31463	−	14.0305i	−0.352998	−	0.784330i
$321$	−4.11069	+	3.87522i	−0.229436	+	0.216293i
$322$	−12.7711	+	14.4156i	−0.711706	+	0.803350i
$323$	−1.79549	+	2.97010i	−0.0999038	+	0.165261i
$324$	0.636107	+	0.154819i	0.0353393	+	0.00860104i
$325$	−5.39828	+	1.27152i	−0.299443	+	0.0705314i
$326$	15.3684	+	17.3473i	0.851177	+	0.960781i
$327$	−6.83714	+	5.70650i	−0.378095	+	0.315570i
$328$	23.5196	+	5.79705i	1.29865	+	0.320089i
$329$	−11.3824	−	16.4903i	−0.627533	−	0.909139i
$330$	−0.337806	+	11.4563i	−0.0185956	+	0.630647i
$331$	−17.0982	+	28.2839i	−0.939803	+	1.55462i	−0.111924	+	0.993717i	$0.535701\pi$
$331$	−17.0982	+	28.2839i	−0.939803	+	1.55462i	−0.827879	+	0.560907i	$0.810452\pi$
$332$	0.329665	+	0.258276i	0.0180927	+	0.0141747i
$333$	−2.31862	+	3.36961i	−0.127060	+	0.184654i
$334$	−8.38739	+	22.1157i	−0.458937	+	1.21012i
$335$	23.4056	+	12.2842i	1.27878	+	0.671157i
$336$	22.0998	−	7.64421i	1.20564	−	0.417026i
$337$		−	25.0612i		−	1.36517i	−0.730807	−	0.682584i	$-0.760856\pi$
$337$		−	25.0612i		−	1.36517i	0.730807	−	0.682584i	$-0.239144\pi$
$338$	9.01536	+	15.6343i	0.490371	+	0.850391i
$339$	−3.98413	+	2.25089i	−0.216388	+	0.122252i
$340$	0.273102	+	0.0500478i	0.0148110	+	0.00271422i
$341$	−6.92985	+	13.2037i	−0.375272	+	0.715021i
$342$	4.35345	+	5.54010i	0.235408	+	0.299574i
$343$	0.359520	−	5.94357i	0.0194122	−	0.320923i
$344$	11.9956	−	15.3113i	0.646761	−	0.825530i
$345$	−0.375681	+	12.7407i	−0.0202260	+	0.685938i
$346$	−14.8975	−	9.00588i	−0.800897	−	0.484159i
$347$	−12.1381	+	8.37833i	−0.651608	+	0.449772i	−0.847459	−	0.530861i	$-0.821869\pi$
$347$	−12.1381	+	8.37833i	−0.651608	+	0.449772i	0.195851	+	0.980634i	$0.437253\pi$
$348$	0.0275615	+	0.0985898i	0.00147745	+	0.00528497i
$349$	8.06135	−	1.47730i	0.431514	−	0.0790779i	0.0398919	−	0.999204i	$-0.487299\pi$
$349$	8.06135	−	1.47730i	0.431514	−	0.0790779i	0.391622	+	0.920126i	$0.371914\pi$
$350$	5.60623	−	4.96669i	0.299666	−	0.265481i
$351$	−8.06408	−	16.9107i	−0.430429	−	0.902625i
$352$	0.788657	+	0.698690i	0.0420356	+	0.0372403i
$353$	16.4750	+	9.95949i	0.876876	+	0.530090i	0.882723	−	0.469893i	$-0.155707\pi$
$353$	16.4750	+	9.95949i	0.876876	+	0.530090i	−0.00584745	+	0.999983i	$0.501861\pi$
$354$	0.506478	−	2.36784i	0.0269190	−	0.125849i
$355$	2.93172	+	11.8944i	0.155599	+	0.631292i
$356$	0.0722710	−	0.0325266i	0.00383036	−	0.00172390i
$357$	−3.33791	+	12.0075i	−0.176661	+	0.635505i
$358$	6.23404	−	13.8515i	0.329479	−	0.732073i
$359$	−0.868614	+	0.525095i	−0.0458437	+	0.0277135i	−0.540074	−	0.841618i	$-0.681604\pi$
$359$	−0.868614	+	0.525095i	−0.0458437	+	0.0277135i	0.494230	+	0.869331i	$0.335450\pi$
$360$	8.28920	−	13.7573i	0.436879	−	0.725074i
$361$			16.1378i			0.849360i
$362$	20.4223	−	12.3457i	1.07337	−	0.648878i
$363$	2.94618	+	7.09805i	0.154634	+	0.372551i
$364$	0.782290	+	0.484020i	0.0410031	+	0.0253696i
$365$	−14.2198	+	1.72659i	−0.744297	+	0.0903740i
$366$	12.5754	+	5.19815i	0.657326	+	0.271712i
$367$	−8.43330	−	12.2177i	−0.440215	−	0.637761i	0.538587	−	0.842570i	$-0.318958\pi$
$367$	−8.43330	−	12.2177i	−0.440215	−	0.637761i	−0.978802	+	0.204809i	$0.934343\pi$
$368$	−11.3957	−	10.0957i	−0.594043	−	0.526276i
$369$	8.98988	+	23.6005i	0.467995	+	1.22859i
$370$	2.17190	+	2.77223i	0.112912	+	0.144121i
$371$	11.9868	−	38.4669i	0.622321	−	1.99710i
$372$	0.615570	−	0.398633i	0.0319158	−	0.0206682i
$373$	−15.6221	+	22.6326i	−0.808884	+	1.17187i	0.173470	+	0.984839i	$0.444502\pi$
$373$	−15.6221	+	22.6326i	−0.808884	+	1.17187i	−0.982354	+	0.187031i	$0.940113\pi$
$374$	7.08393	−	1.74603i	0.366301	−	0.0902851i
$375$	3.15513	−	20.8327i	0.162930	−	1.07580i
$376$	13.5285	−	9.33804i	0.697678	−	0.481573i
$377$	1.68899	−	2.39363i	0.0869876	−	0.123278i
$378$	20.4119	+	14.9506i	1.04987	+	0.768976i
$379$	28.5458	−	8.89522i	1.46630	−	0.456917i	0.542584	−	0.840002i	$-0.317446\pi$
$379$	28.5458	−	8.89522i	1.46630	−	0.456917i	0.923713	+	0.383085i	$0.125138\pi$
$380$	−0.214093	+	0.0811948i	−0.0109827	+	0.00416520i
$381$	−8.40033	−	20.2384i	−0.430362	−	1.03685i
$382$	−29.9772	−	5.49352i	−1.53377	−	0.281073i
$383$	2.67201	+	4.42005i	0.136534	+	0.225854i	0.916565	−	0.399887i	$-0.130951\pi$
$383$	2.67201	+	4.42005i	0.136534	+	0.225854i	−0.780031	+	0.625741i	$0.784797\pi$
$384$	6.03422	+	17.4452i	0.307933	+	0.890248i
$385$	6.86146	−	15.2455i	0.349692	−	0.776984i
$386$	−25.0259	+	9.49109i	−1.27379	+	0.483084i
$387$	20.2436	+	1.19487i	1.02904	+	0.0607385i
$388$	0.991548	+	0.308979i	0.0503382	+	0.0156860i
$389$	16.8998	+	4.16542i	0.856852	+	0.211195i	0.643184	−	0.765711i	$-0.277613\pi$
$389$	16.8998	+	4.16542i	0.856852	+	0.211195i	0.213668	+	0.976906i	$0.431459\pi$
$390$	−15.9697	+	2.27381i	−0.808656	+	0.115139i
$391$	7.87817	−	1.94179i	0.398416	−	0.0982007i
$392$	−15.2297	−	0.921227i	−0.769216	−	0.0465290i
$393$	6.53535	+	8.86824i	0.329665	+	0.447343i
$394$	−5.50254	−	10.4842i	−0.277214	−	0.528188i
$395$	2.87215	+	9.21704i	0.144513	+	0.463760i
$396$	−0.0665768	+	0.555077i	−0.00334561	+	0.0278937i
$397$	15.9699	+	0.966002i	0.801507	+	0.0484823i	0.456052	−	0.889953i	$-0.349263\pi$
$397$	15.9699	+	0.966002i	0.801507	+	0.0484823i	0.345455	+	0.938435i	$0.387725\pi$
$398$	7.04773	+	8.99577i	0.353271	+	0.450917i
$399$	−2.76715	−	9.89833i	−0.138531	−	0.495536i
$400$	3.92623	+	4.43180i	0.196312	+	0.221590i
$401$	−36.3735	+	2.20019i	−1.81641	+	0.109872i	−0.933255	−	0.359214i	$-0.883045\pi$
$401$	−36.3735	+	2.20019i	−1.81641	+	0.109872i	−0.883152	+	0.469087i	$0.844583\pi$
$402$	−28.7008	−	18.5268i	−1.43147	−	0.924031i
$403$	−19.9712	−	6.45046i	−0.994835	−	0.321320i
$404$	−0.466481	+	0.888806i	−0.0232083	+	0.0442198i
$405$	16.7118	−	1.05983i	0.830415	−	0.0526635i
$406$	−0.476881	+	3.92747i	−0.0236672	+	0.194917i
$407$	−3.09277	−	1.62321i	−0.153303	−	0.0804595i
$408$	−9.85086	−	2.73839i	−0.487690	−	0.135570i
$409$	27.4654	−	8.55857i	1.35808	−	0.423194i	0.469910	−	0.882714i	$-0.344286\pi$
$409$	27.4654	−	8.55857i	1.35808	−	0.423194i	0.888167	+	0.459520i	$0.151979\pi$
$410$	21.7045	−	1.31288i	1.07191	−	0.0648385i
$411$	14.2081	−	11.8586i	0.700834	−	0.584939i
$412$	−0.827689	+	0.733269i	−0.0407773	+	0.0361256i
$413$	−2.00645	+	2.90684i	−0.0987308	+	0.143036i
$414$	1.96169	−	16.3554i	0.0964117	−	0.803822i
$415$	10.0158	+	3.79848i	0.491654	+	0.186460i
$416$	−0.780236	+	1.26104i	−0.0382542	+	0.0618278i
$417$	−7.46763	+	8.97378i	−0.365691	+	0.439448i
$418$	−4.25453	+	4.25453i	−0.208096	+	0.208096i
$419$	−15.7706	−	5.98102i	−0.770446	−	0.292192i	−0.0621123	−	0.998069i	$-0.519784\pi$
$419$	−15.7706	−	5.98102i	−0.770446	−	0.292192i	−0.708334	+	0.705877i	$0.750553\pi$
$420$	−0.661907	+	0.487785i	−0.0322977	+	0.0238015i
$421$	0.777851	−	2.49621i	0.0379101	−	0.121658i	−0.933826	−	0.357728i	$-0.883552\pi$
$421$	0.777851	−	2.49621i	0.0379101	−	0.121658i	0.971736	+	0.236070i	$0.0758594\pi$
$422$	−5.69163	+	1.04303i	−0.277064	+	0.0507739i
$423$	16.0333	+	6.05388i	0.779566	+	0.294350i
$424$	31.5579	+	9.83383i	1.53259	+	0.477573i
$425$	−3.13251	+	0.380355i	−0.151949	+	0.0184499i
$426$	−2.39354	−	15.6498i	−0.115967	−	0.758235i
$427$	−14.0353	−	14.0353i	−0.679218	−	0.679218i
$428$	0.0841330	+	0.221840i	0.00406672	+	0.0107231i
$429$	13.5179	−	8.55697i	0.652650	−	0.413134i
$430$	6.19138	−	16.3253i	0.298575	−	0.787277i
$431$	14.5195	−	6.53470i	0.699380	−	0.314765i	−0.0293477	−	0.999569i	$-0.509343\pi$
$431$	14.5195	−	6.53470i	0.699380	−	0.314765i	0.728727	+	0.684804i	$0.240112\pi$
$432$	−11.8186	+	16.1359i	−0.568625	+	0.776337i
$433$	−20.5328	−	23.1767i	−0.986743	−	1.11380i	−0.993501	−	0.113826i	$-0.963689\pi$
$433$	−20.5328	−	23.1767i	−0.986743	−	1.11380i	0.00675758	−	0.999977i	$-0.497849\pi$
$434$	27.8786	−	5.10895i	1.33822	−	0.245237i
$435$	1.42327	+	2.19782i	0.0682407	+	0.105378i
$436$	0.111271	+	0.357080i	0.00532890	+	0.0171010i
$437$	−4.73154	+	4.73154i	−0.226340	+	0.226340i
$438$	18.5030	−	0.572613i	0.884107	−	0.0273605i
$439$	33.7014	+	4.09210i	1.60848	+	0.195305i	0.874903	−	0.484299i	$-0.160925\pi$
$439$	33.7014	+	4.09210i	1.60848	+	0.195305i	0.733579	+	0.679604i	$0.237848\pi$
$440$	12.5073	+	5.62908i	0.596262	+	0.268356i
$441$	−8.24918	−	13.6010i	−0.392818	−	0.647664i
$442$	4.11729	+	9.40682i	0.195839	+	0.447437i
$443$	−4.72138	−	8.99583i	−0.224319	−	0.427405i	0.747121	−	0.664688i	$-0.231435\pi$
$443$	−4.72138	−	8.99583i	−0.224319	−	0.427405i	−0.971441	+	0.237283i	$0.923743\pi$
$444$	0.0933736	+	0.144188i	0.00443132	+	0.00684285i
$445$	1.51734	−	1.34425i	0.0719288	−	0.0637234i
$446$	21.8830	+	5.39369i	1.03619	+	0.255398i
$447$	36.0948	+	14.9201i	1.70722	+	0.705697i
$448$	1.75126	−	28.9518i	0.0827394	−	1.36785i
$449$	−5.51271	−	12.2487i	−0.260161	−	0.578054i	0.734804	−	0.678280i	$-0.237274\pi$
$449$	−5.51271	−	12.2487i	−0.260161	−	0.578054i	−0.994965	+	0.100226i	$0.968043\pi$
$450$	−1.52402	+	6.22227i	−0.0718432	+	0.293321i
$451$	−19.0958	+	10.0222i	−0.899185	+	0.471929i
$452$	0.0231648	+	0.190779i	0.00108958	+	0.00897351i
$453$	1.69922	+	3.48340i	0.0798363	+	0.163664i
$454$	8.63444	+	35.0313i	0.405234	+	1.64410i
$455$	22.7866	+	5.86686i	1.06825	+	0.275043i
$456$	8.12050	−	2.27015i	0.380277	−	0.106309i
$457$	5.70981	−	18.3234i	0.267093	−	0.857133i	−0.719579	−	0.694411i	$-0.755665\pi$
$457$	5.70981	−	18.3234i	0.267093	−	0.857133i	0.986672	−	0.162722i	$-0.0520274\pi$
$458$	−12.1331	−	23.1177i	−0.566942	−	1.08022i
$459$	−3.49926	−	10.0689i	−0.163331	−	0.469978i
$460$	0.488150	+	0.219699i	0.0227601	+	0.0102435i
$461$	1.59518	−	8.70459i	0.0742947	−	0.405413i	−0.925359	−	0.379092i	$-0.876236\pi$
$461$	1.59518	−	8.70459i	0.0742947	−	0.405413i	0.999654	−	0.0263208i	$-0.00837914\pi$
$462$	−10.6003	+	18.8269i	−0.493171	+	0.875907i
$463$	2.72331	−	14.8606i	0.126563	−	0.690631i	−0.857732	−	0.514097i	$-0.828127\pi$
$463$	2.72331	−	14.8606i	0.126563	−	0.690631i	0.984295	−	0.176533i	$-0.0564883\pi$
$464$	−3.10472	−	0.376981i	−0.144133	−	0.0175009i
$465$	11.9988	−	14.4188i	0.556429	−	0.668656i
$466$	−11.4562	−	36.7643i	−0.530699	−	1.70307i
$467$	8.06651	−	11.6864i	0.373274	−	0.540780i	−0.590661	−	0.806920i	$-0.701133\pi$
$467$	8.06651	−	11.6864i	0.373274	−	0.540780i	0.963934	+	0.266140i	$0.0857483\pi$
$468$	−0.785778	+	0.0405342i	−0.0363226	+	0.00187370i
$469$	28.3069	+	41.0096i	1.30709	+	1.89365i
$470$	9.10022	−	11.6156i	0.419762	−	0.535786i
$471$	−21.8523	−	23.1801i	−1.00690	−	1.06808i
$472$	−2.38474	−	1.64607i	−0.109767	−	0.0757665i
$473$	1.04557	+	17.2853i	0.0480753	+	0.794779i
$474$	−2.62749	−	12.1967i	−0.120684	−	0.560214i
$475$	2.04848	−	1.60488i	0.0939908	−	0.0736371i
$476$	0.412018	+	0.322795i	0.0188848	+	0.0147953i
$477$	10.3005	+	32.8864i	0.471626	+	1.50576i
$478$	−14.3127	+	9.87934i	−0.654648	+	0.451871i
$479$	−1.97397	−	2.51959i	−0.0901932	−	0.115123i	0.739980	−	0.672629i	$-0.234835\pi$
$479$	−1.97397	−	2.51959i	−0.0901932	−	0.115123i	−0.830173	+	0.557506i	$0.811758\pi$
$480$	−0.786305	−	1.06699i	−0.0358897	−	0.0487011i
$481$	1.51092	−	4.67794i	0.0688920	−	0.213296i
$482$	26.8140	+	3.25581i	1.22134	+	0.148298i
$483$	−11.7888	+	20.9377i	−0.536409	+	0.952700i
$484$	0.322759			0.0146709
$485$	26.5647			1.20624
$486$	−21.6332	−	0.574708i	−0.981300	−	0.0260693i
$487$	−31.8251	−	14.3233i	−1.44213	−	0.649051i	−0.469826	−	0.882759i	$-0.655683\pi$
$487$	−31.8251	−	14.3233i	−1.44213	−	0.649051i	−0.972307	+	0.233708i	$0.924914\pi$
$488$	11.5145	−	11.5145i	0.521236	−	0.521236i
$489$	23.3023	+	17.1199i	1.05376	+	0.774190i
$490$	−13.2979	+	3.27765i	−0.600739	+	0.148069i
$491$	−22.5009	−	19.9340i	−1.01545	−	0.899610i	−0.0204800	−	0.999790i	$-0.506519\pi$
$491$	−22.5009	−	19.9340i	−1.01545	−	0.899610i	−0.994969	+	0.100181i	$0.968058\pi$
$492$	1.06017	+	0.0312609i	0.0477963	+	0.00140935i
$493$	1.10531	−	1.24763i	0.0497805	−	0.0561906i
$494$	−6.91907	−	4.88223i	−0.311304	−	0.219662i
$495$	2.59809	+	14.0616i	0.116775	+	0.632020i
$496$	4.03869	+	22.0384i	0.181343	+	0.989554i
$497$	−5.52668	+	22.4226i	−0.247906	+	1.00579i
$498$	−12.4509	−	6.05112i	−0.557937	−	0.271157i
$499$	−1.01787	+	1.68376i	−0.0455660	+	0.0753753i	−0.877734	−	0.479148i	$-0.840946\pi$
$499$	−1.01787	+	1.68376i	−0.0455660	+	0.0753753i	0.832168	+	0.554524i	$0.187099\pi$
$500$	−0.757279	−	0.457791i	−0.0338666	−	0.0204730i
$501$	−4.41896	+	29.1775i	−0.197424	+	1.30355i
$502$	−33.4012	−	2.02040i	−1.49077	−	0.0901748i
$503$	−22.8646	−	8.67139i	−1.01948	−	0.386638i	−0.212466	−	0.977168i	$-0.568149\pi$
$503$	−22.8646	−	8.67139i	−1.01948	−	0.386638i	−0.807016	+	0.590530i	$0.798919\pi$
$504$	25.8887	−	15.7019i	1.15317	−	0.699417i
$505$	−4.62802	+	25.2543i	−0.205944	+	1.12380i
$506$	14.0666			0.625337
$507$	15.1036	+	16.6998i	0.670772	+	0.741663i
$508$	−0.920272			−0.0408305
$509$	−1.77365	+	9.67848i	−0.0786155	+	0.428991i	0.920640	+	0.390413i	$0.127668\pi$
$509$	−1.77365	+	9.67848i	−0.0786155	+	0.428991i	−0.999256	+	0.0385786i	$0.987717\pi$
$510$	−9.17352	+	0.283894i	−0.406210	+	0.0125710i
$511$	−25.2483	−	9.57542i	−1.11692	−	0.423592i
$512$	23.6921	+	1.43311i	1.04705	+	0.0633350i
$513$	6.76539	+	5.61320i	0.298699	+	0.247829i
$514$	−0.773310	−	0.467482i	−0.0341092	−	0.0206198i
$515$	−14.6323	+	24.2047i	−0.644774	+	1.06659i
$516$	0.372270	−	0.765988i	0.0163883	−	0.0337207i
$517$	−3.50238	+	14.2097i	−0.154035	+	0.624943i
$518$	1.19669	+	6.53014i	0.0525796	+	0.286918i
$519$	−20.5363	−	7.06986i	−0.901442	−	0.310333i
$520$	−4.81312	+	18.6939i	−0.211069	+	0.819784i
$521$	−18.5724	+	20.9639i	−0.813673	+	0.918447i	−0.997922	−	0.0644325i	$-0.979476\pi$
$521$	−18.5724	+	20.9639i	−0.813673	+	0.918447i	0.184249	+	0.982880i	$0.441015\pi$
$522$	−1.57695	−	2.99400i	−0.0690212	−	0.131044i
$523$	7.30569	+	6.47228i	0.319456	+	0.283013i	0.807576	−	0.589763i	$-0.200779\pi$
$523$	7.30569	+	6.47228i	0.319456	+	0.283013i	−0.488121	+	0.872776i	$0.662317\pi$
$524$	0.449209	−	0.110720i	0.0196238	−	0.00483682i
$525$	5.53273	−	7.53071i	0.241468	−	0.328667i
$526$	11.1866	−	11.1866i	0.487758	−	0.487758i
$527$	−10.8890	−	4.90075i	−0.474333	−	0.213480i
$528$	−14.8829	−	8.37969i	−0.647696	−	0.364679i
$529$	−7.35626			−0.319837
$530$	29.6714			1.28884
$531$	−0.00440805	−	3.02104i	−0.000191293	−	0.131102i
$532$	−0.428497	−	0.0520289i	−0.0185777	−	0.00225574i
$533$	−18.4709	−	24.0851i	−0.800065	−	1.04324i
$534$	−2.10897	+	1.55418i	−0.0912639	+	0.0672559i
$535$	3.74263	+	4.77711i	0.161808	+	0.206532i
$536$	−33.6439	+	23.2227i	−1.45320	+	1.00307i
$537$	3.96401	−	18.5321i	0.171059	−	0.799720i
$538$	15.9394	+	12.4878i	0.687198	+	0.538386i
$539$	10.6929	−	8.37733i	0.460575	−	0.360837i
$540$	0.227951	−	0.665295i	0.00980944	−	0.0286297i
$541$	−0.107180	−	1.77190i	−0.00460804	−	0.0761799i	0.995145	−	0.0984245i	$-0.0313803\pi$
$541$	−0.107180	−	1.77190i	−0.00460804	−	0.0761799i	−0.999753	+	0.0222446i	$0.992919\pi$
$542$	−7.28304	−	5.02712i	−0.312833	−	0.215933i
$543$	21.6646	−	20.4236i	0.929717	−	0.876459i
$544$	−0.520343	+	0.664169i	−0.0223095	+	0.0284760i
$545$	5.43444	+	7.87315i	0.232786	+	0.337248i
$546$	−28.6486	−	10.1950i	−1.22605	−	0.436307i
$547$	12.7067	−	18.4088i	0.543299	−	0.787104i	−0.451136	−	0.892455i	$-0.648981\pi$
$547$	12.7067	−	18.4088i	0.543299	−	0.787104i	0.994435	+	0.105351i	$0.0335965\pi$
$548$	−0.231229	−	0.742040i	−0.00987762	−	0.0316984i
$549$	16.7035	+	3.03585i	0.712889	+	0.129567i
$550$	−5.43063	−	0.659397i	−0.231563	−	0.0281168i
$551$	−0.247777	+	1.35208i	−0.0105557	+	0.0576005i
$552$	−17.1771	−	9.67143i	−0.731108	−	0.411643i
$553$	−3.28054	+	17.9013i	−0.139503	+	0.761241i
$554$	23.8712	+	10.7436i	1.01419	+	0.456451i
$555$	3.37738	+	2.81052i	0.143362	+	0.119300i
$556$	0.227854	+	0.434140i	0.00966316	+	0.0184116i
$557$	5.32943	−	17.1027i	0.225815	−	0.724666i	−0.770386	−	0.637578i	$-0.779936\pi$
$557$	5.32943	−	17.1027i	0.225815	−	0.724666i	0.996201	−	0.0870876i	$-0.0277560\pi$
$558$	−17.1168	+	17.1668i	−0.724610	+	0.726728i
$559$	−23.7229	+	5.58774i	−1.00337	+	0.236336i
$560$	−6.01161	−	24.3900i	−0.254037	−	1.03067i
$561$	8.18125	−	3.99085i	0.345412	−	0.168494i
$562$	−5.08953	−	41.9161i	−0.214689	−	1.76812i
$563$	14.7627	−	7.74805i	0.622173	−	0.326541i	−0.124012	−	0.992281i	$-0.539576\pi$
$563$	14.7627	−	7.74805i	0.622173	−	0.326541i	0.746184	+	0.665739i	$0.231884\pi$
$564$	0.492961	−	0.524446i	0.0207574	−	0.0220832i
$565$	2.01743	+	4.48254i	0.0848739	+	0.188582i
$566$	1.06662	−	17.6333i	0.0448333	−	0.741184i
$567$	28.8239	+	12.8715i	1.21049	+	0.540554i
$568$	−18.3953	−	4.53404i	−0.771851	−	0.190244i
$569$	16.7664	−	14.8537i	0.702883	−	0.622700i	−0.234043	−	0.972226i	$-0.575196\pi$
$569$	16.7664	−	14.8537i	0.702883	−	0.622700i	0.936927	+	0.349526i	$0.113657\pi$
$570$	6.35306	−	4.11413i	0.266100	−	0.172322i
$571$	7.91680	+	15.0842i	0.331308	+	0.631254i	0.992946	−	0.118569i	$-0.0378307\pi$
$571$	7.91680	+	15.0842i	0.331308	+	0.631254i	−0.661638	+	0.749823i	$0.730138\pi$
$572$	−0.114277	−	0.662112i	−0.00477815	−	0.0276843i
$573$	−38.0055	+	1.17616i	−1.58770	+	0.0491347i
$574$	37.3794	+	16.8231i	1.56019	+	0.702182i
$575$	−6.03950	−	0.733328i	−0.251865	−	0.0305819i
$576$	12.8652	+	21.2117i	0.536050	+	0.883820i
$577$	2.23460	−	2.23460i	0.0930277	−	0.0930277i	−0.659061	−	0.752089i	$-0.729046\pi$
$577$	2.23460	−	2.23460i	0.0930277	−	0.0930277i	0.752089	+	0.659061i	$0.229046\pi$
$578$	−5.28304	−	16.9539i	−0.219746	−	0.705189i
$579$	−28.0295	+	18.1514i	−1.16487	+	0.754347i
$580$	0.108166	−	0.0198221i	0.00449135	−	0.000823070i
$581$	13.3906	+	15.1149i	0.555537	+	0.627072i
$582$	−34.1922	−	3.08195i	−1.41731	−	0.127751i
$583$	−26.8357	+	12.0778i	−1.11142	+	0.500210i
$584$	7.85559	−	20.7135i	0.325067	−	0.857130i
$585$	−18.8802	+	6.96926i	−0.780600	+	0.288144i
$586$	2.51493	+	6.63133i	0.103891	+	0.273938i
$587$	3.12024	+	3.12024i	0.128786	+	0.128786i	0.768562	−	0.639776i	$-0.220973\pi$
$587$	3.12024	+	3.12024i	0.128786	+	0.128786i	−0.639776	+	0.768562i	$0.720973\pi$
$588$	−0.660378	+	0.101001i	−0.0272335	+	0.00416520i
$589$	9.77573	−	1.18699i	0.402802	−	0.0489090i
$590$	−2.48333	−	0.773836i	−0.102237	−	0.0318583i
$591$	−9.46595	−	11.3415i	−0.389377	−	0.466525i
$592$	−5.16216	+	0.946001i	−0.212163	+	0.0388804i
$593$	4.11265	−	13.1980i	0.168886	−	0.541976i	−0.831012	−	0.556255i	$-0.812238\pi$
$593$	4.11265	−	13.1980i	0.168886	−	0.541976i	0.999898	+	0.0142793i	$0.00454541\pi$
$594$	−1.71269	−	18.4004i	−0.0702726	−	0.754979i
$595$	12.5178	+	4.74736i	0.513178	+	0.194623i
$596$	1.15986	−	1.15986i	0.0475098	−	0.0475098i
$597$	10.9595	+	9.12004i	0.448541	+	0.373259i
$598$	3.36716	+	19.5091i	0.137694	+	0.797788i
$599$	−8.83497	−	3.35066i	−0.360987	−	0.136904i	0.167442	−	0.985882i	$-0.446449\pi$
$599$	−8.83497	−	3.35066i	−0.360987	−	0.136904i	−0.528429	+	0.848978i	$0.677219\pi$
$600$	6.17812	+	4.53901i	0.252221	+	0.185304i
$601$	27.0658	−	39.2115i	1.10404	−	1.59947i	0.357787	−	0.933803i	$-0.383531\pi$
$601$	27.0658	−	39.2115i	1.10404	−	1.59947i	0.746248	−	0.665668i	$-0.231853\pi$
$602$	24.6367	−	21.8262i	1.00412	−	0.889571i
$603$	−39.8732	−	15.0554i	−1.62376	−	0.613103i
$604$	0.162475	−	0.00982791i	0.00661100	−	0.000399892i
$605$	7.88176	−	2.45605i	0.320439	−	0.0998528i
$606$	8.88677	−	31.9686i	0.361000	−	1.29863i
$607$	23.6470	+	12.4109i	0.959802	+	0.503743i	0.870450	−	0.492257i	$-0.163828\pi$
$607$	23.6470	+	12.4109i	0.959802	+	0.503743i	0.0893525	+	0.996000i	$0.471520\pi$
$608$	0.0838702	−	0.690733i	0.00340138	−	0.0280129i
$609$	0.450296	+	4.91549i	0.0182469	+	0.199186i
$610$	6.79298	−	12.9429i	0.275040	−	0.524044i
$611$	−20.5460	−	1.45607i	−0.831201	−	0.0589062i
$612$	−0.446901	−	0.0263781i	−0.0180649	−	0.00106627i
$613$	4.24859	−	0.256993i	0.171599	−	0.0103798i	0.0256445	−	0.999671i	$-0.491836\pi$
$613$	4.24859	−	0.256993i	0.171599	−	0.0103798i	0.145955	+	0.989291i	$0.453375\pi$
$614$	−21.7291	−	24.5271i	−0.876916	−	0.989833i
$615$	26.1272	−	7.30406i	1.05355	−	0.294528i
$616$	15.9458	+	20.3533i	0.642474	+	0.820058i
$617$	−43.8065	−	2.64980i	−1.76358	−	0.106677i	−0.853497	−	0.521098i	$-0.825523\pi$
$617$	−43.8065	−	2.64980i	−1.76358	−	0.106677i	−0.910085	+	0.414421i	$0.863984\pi$
$618$	21.6417	−	29.4570i	0.870558	−	1.18493i
$619$	1.65548	+	5.31263i	0.0665395	+	0.213533i	0.982002	−	0.188871i	$-0.0604827\pi$
$619$	1.65548	+	5.31263i	0.0665395	+	0.213533i	−0.915463	+	0.402403i	$0.868175\pi$
$620$	−0.366109	−	0.697562i	−0.0147033	−	0.0280148i
$621$	−1.90472	−	20.4635i	−0.0764337	−	0.821170i
$622$	14.1176	+	0.853960i	0.566066	+	0.0342407i
$623$	3.71040	−	0.914531i	0.148654	−	0.0366399i
$624$	8.05930	−	22.6471i	0.322630	−	0.906611i
$625$	−14.5088	−	3.57611i	−0.580354	−	0.143044i
$626$	15.2766	+	4.76037i	0.610574	+	0.190263i
$627$	−4.07123	+	6.30696i	−0.162589	+	0.251876i
$628$	−1.25095	+	0.474424i	−0.0499185	+	0.0189316i
$629$	1.14792	−	2.55058i	0.0457707	−	0.101698i
$630$	17.9935	−	20.3702i	0.716877	−	0.811569i
$631$	−14.3022	−	23.6587i	−0.569361	−	0.941837i	−0.999241	−	0.0389516i	$-0.987598\pi$
$631$	−14.3022	−	23.6587i	−0.569361	−	0.941837i	0.429881	−	0.902886i	$-0.358556\pi$
$632$	−14.6861	−	2.69132i	−0.584181	−	0.107055i
$633$	−6.66782	+	2.76760i	−0.265022	+	0.110002i
$634$	−26.5906	+	10.0845i	−1.05605	+	0.400506i
$635$	−22.4730	+	7.00286i	−0.891812	+	0.277900i
$636$	1.44146	+	0.129928i	0.0571578	+	0.00515199i
$637$	14.1782	+	12.8247i	0.561760	+	0.508135i
$638$	2.37814	−	1.64151i	0.0941515	−	0.0649881i
$639$	−7.03125	−	18.4586i	−0.278152	−	0.730211i
$640$	19.2531	−	4.74547i	0.761046	−	0.187581i
$641$	−12.0395	+	17.4423i	−0.475533	+	0.688929i	−0.985193	−	0.171447i	$-0.945156\pi$
$641$	−12.0395	+	17.4423i	−0.475533	+	0.688929i	0.509660	+	0.860376i	$0.329771\pi$
$642$	−4.26301	−	6.58296i	−0.168248	−	0.259809i
$643$	−0.992793	+	3.18598i	−0.0391519	+	0.125643i	−0.972228	−	0.234037i	$-0.924806\pi$
$643$	−0.992793	+	3.18598i	−0.0391519	+	0.125643i	0.933076	+	0.359680i	$0.117114\pi$
$644$	0.622352	+	0.794373i	0.0245241	+	0.0313027i
$645$	3.26197	−	21.5382i	0.128440	−	0.848065i
$646$	−3.60642	−	3.19501i	−0.141893	−	0.125706i
$647$	19.3413	+	28.0207i	0.760386	+	1.10161i	0.991680	+	0.128725i	$0.0410885\pi$
$647$	19.3413	+	28.0207i	0.760386	+	1.10161i	−0.231295	+	0.972884i	$0.574296\pi$
$648$	−10.5597	+	23.6468i	−0.414824	+	0.928935i
$649$	2.56098	−	0.310960i	0.100527	−	0.0122062i
$650$	−0.385419	−	7.68963i	−0.0151174	−	0.301612i
$651$	32.6602	−	13.5562i	1.28005	−	0.531310i
$652$	1.03923	−	0.628237i	0.0406994	−	0.0246037i
$653$			39.8772i			1.56051i	0.625459	+	0.780257i	$0.284912\pi$
$653$			39.8772i			1.56051i	−0.625459	+	0.780257i	$0.715088\pi$
$654$	−6.08140	−	10.7642i	−0.237802	−	0.420915i
$655$	10.1271	−	6.12205i	0.395699	−	0.239208i
$656$	−13.2989	+	29.5489i	−0.519234	+	1.15369i
$657$	22.4170	−	5.55999i	0.874569	−	0.216916i
$658$	25.3661	−	11.4164i	0.988874	−	0.445056i
$659$	5.41179	+	21.9565i	0.210813	+	0.855303i	0.977096	+	0.212799i	$0.0682581\pi$
$659$	5.41179	+	21.9565i	0.210813	+	0.855303i	−0.766283	+	0.642504i	$0.777896\pi$
$660$	0.587262	+	0.125615i	0.0228591	+	0.00488955i
$661$	−16.8660	−	10.1958i	−0.656011	−	0.396572i	0.149824	−	0.988713i	$-0.452129\pi$
$661$	−16.8660	−	10.1958i	−0.656011	−	0.396572i	−0.805835	+	0.592140i	$0.798283\pi$
$662$	−34.3435	−	30.4257i	−1.33480	−	1.18253i
$663$	7.49332	+	10.3913i	0.291016	+	0.403567i
$664$	−12.4001	+	10.9856i	−0.481218	+	0.426322i
$665$	−10.8598	+	1.99013i	−0.421124	+	0.0771738i
$666$	−4.02105	−	4.00933i	−0.155813	−	0.155359i
$667$	2.64478	−	1.82556i	0.102406	−	0.0706858i
$668$	1.06062	+	0.641166i	0.0410365	+	0.0248075i
$669$	28.1071	+	0.828784i	1.08668	+	0.0320426i
$670$	−22.6313	+	28.8867i	−0.874323	+	1.11599i
$671$	−0.875338	+	14.4711i	−0.0337920	+	0.558649i
$672$	−0.377752	−	2.46987i	−0.0145721	−	0.0952775i
$673$	21.0572	−	40.1212i	0.811696	−	1.54656i	−0.0255137	−	0.999674i	$-0.508122\pi$
$673$	21.0572	−	40.1212i	0.811696	−	1.54656i	0.837209	−	0.546882i	$-0.184186\pi$
$674$	34.2215	+	6.27131i	1.31816	+	0.241562i
$675$	−0.223916	+	7.98951i	−0.00861854	+	0.307516i
$676$	0.890934	−	0.316983i	0.0342667	−	0.0121916i
$677$			3.65082i			0.140313i	0.997536	+	0.0701563i	$0.0223498\pi$
$677$			3.65082i			0.140313i	−0.997536	+	0.0701563i	$0.977650\pi$
$678$	−2.07664	−	6.00366i	−0.0797528	−	0.230569i
$679$	44.3419	+	23.2724i	1.70169	+	0.893113i
$680$	−3.89469	+	10.2695i	−0.149355	+	0.393816i
$681$	19.7355	+	40.4577i	0.756265	+	1.55034i
$682$	−16.2958	−	12.7669i	−0.623998	−	0.488871i
$683$	−6.51319	+	10.7741i	−0.249220	+	0.412261i	−0.955195	−	0.295976i	$-0.904355\pi$
$683$	−6.51319	+	10.7741i	−0.249220	+	0.412261i	0.705975	+	0.708237i	$0.250509\pi$
$684$	0.326653	−	0.172049i	0.0124899	−	0.00657846i
$685$	−11.2932	−	16.3610i	−0.431491	−	0.625122i
$686$	8.02608	+	1.97825i	0.306437	+	0.0755300i
$687$	−20.8724	−	25.0078i	−0.796331	−	0.954109i
$688$	17.2539	+	19.4757i	0.657800	+	0.742502i
$689$	−23.1745	−	34.3276i	−0.882878	−	1.30778i
$690$	−17.3037	−	3.70124i	−0.658740	−	0.140904i
$691$	−21.0331	+	34.7930i	−0.800136	+	1.32359i	0.142510	+	0.989793i	$0.454483\pi$
$691$	−21.0331	+	34.7930i	−0.800136	+	1.32359i	−0.942646	+	0.333794i	$0.891671\pi$
$692$	−0.604867	+	0.682754i	−0.0229936	+	0.0259544i
$693$	−7.98211	+	25.7477i	−0.303215	+	0.978074i
$694$	−8.40331	−	18.6714i	−0.318985	−	0.708757i
$695$	8.86778	+	8.86778i	0.336374	+	0.336374i
$696$	−4.03263	+	0.369419i	−0.152856	+	0.0140028i
$697$	−8.93422	−	14.7790i	−0.338408	−	0.559795i
$698$			11.3776i			0.430648i
$699$	−23.6324	−	41.8300i	−0.893861	−	1.58216i
$700$	−0.203030	−	0.335853i	−0.00767383	−	0.0126941i
$701$	−5.18493	+	42.7017i	−0.195832	+	1.61282i	0.481024	+	0.876707i	$0.340265\pi$
$701$	−5.18493	+	42.7017i	−0.195832	+	1.61282i	−0.676857	+	0.736115i	$0.736658\pi$
$702$	25.1098	−	6.77991i	0.947707	−	0.255891i
$703$	0.278034	+	2.28981i	0.0104862	+	0.0863619i
$704$	−16.6763	+	13.0651i	−0.628513	+	0.492408i
$705$	8.04725	−	16.5581i	0.303077	−	0.623616i
$706$	−17.7226	+	20.0046i	−0.666998	+	0.752885i
$707$	−29.8495	+	38.1001i	−1.12261	+	1.43290i
$708$	−0.117254	−	0.0484679i	−0.00440667	−	0.00182154i
$709$	15.2864	+	4.76345i	0.574095	+	0.178895i	0.570785	−	0.821099i	$-0.306639\pi$
$709$	15.2864	+	4.76345i	0.574095	+	0.178895i	0.00330941	+	0.999995i	$0.498947\pi$
$710$	−16.9757	+	1.02684i	−0.637087	+	0.0385367i
$711$	−6.40930	−	14.1855i	−0.240368	−	0.531999i
$712$	0.750273	+	3.04398i	0.0281177	+	0.114078i
$713$	−18.1228	−	14.1983i	−0.678705	−	0.531732i
$714$	−15.5612	−	7.56273i	−0.582363	−	0.283028i
$715$	−7.82900	−	15.2991i	−0.292788	−	0.572154i
$716$	−0.655020	−	0.452128i	−0.0244792	−	0.0168968i
$717$	−14.8609	+	15.8101i	−0.554991	+	0.590439i
$718$	−0.499665	−	1.31751i	−0.0186473	−	0.0491689i
$719$	−1.27313	+	10.4852i	−0.0474798	+	0.391031i	0.949525	+	0.313691i	$0.101566\pi$
$719$	−1.27313	+	10.4852i	−0.0474798	+	0.391031i	−0.997005	+	0.0773398i	$0.975357\pi$
$720$	16.1029	+	14.2241i	0.600121	+	0.530100i
$721$	−45.6291	+	27.5838i	−1.69932	+	1.02727i
$722$	−22.0365	−	4.03834i	−0.820113	−	0.150291i
$723$	33.5595	−	3.07430i	1.24809	−	0.114334i
$724$	−0.443406	−	1.16917i	−0.0164791	−	0.0434517i
$725$	−1.10663	+	0.580805i	−0.0410992	+	0.0215705i
$726$	−10.4298	+	2.24684i	−0.387085	+	0.0833880i
$727$	−6.03289	+	24.4764i	−0.223748	+	0.907780i	0.746446	+	0.665447i	$0.231759\pi$
$727$	−6.03289	+	24.4764i	−0.223748	+	0.907780i	−0.970193	+	0.242333i	$0.922087\pi$
$728$	−24.4112	+	26.9874i	−0.904739	+	1.00022i
$729$	−26.5362	+	4.98309i	−0.982821	+	0.184559i
$730$	1.20067	−	19.8494i	0.0444387	−	0.734660i
$731$	−13.7659	+	1.67148i	−0.509150	+	0.0618220i
$732$	0.386685	−	0.599034i	0.0142923	−	0.0221409i
$733$	−7.25277	+	2.26006i	−0.267887	+	0.0834770i	−0.428504	−	0.903540i	$-0.640959\pi$
$733$	−7.25277	+	2.26006i	−0.267887	+	0.0834770i	0.160617	+	0.987017i	$0.448652\pi$
$734$	18.7939	−	8.45845i	0.693695	−	0.312207i
$735$	−15.3578	+	7.49161i	−0.566482	+	0.276332i
$736$	−1.28052	+	1.00323i	−0.0472007	+	0.0369794i
$737$	8.71006	−	35.3381i	0.320839	−	1.30170i
$738$	−34.4765	+	6.37005i	−1.26910	+	0.234485i
$739$	3.16399	+	52.3070i	0.116389	+	1.92414i	0.324227	+	0.945979i	$0.394896\pi$
$739$	3.16399	+	52.3070i	0.116389	+	1.92414i	−0.207838	+	0.978163i	$0.566643\pi$
$740$	0.163393	−	0.0857553i	0.00600645	−	0.00315243i
$741$	−9.72173	−	4.13672i	−0.357137	−	0.151966i
$742$	49.5276	+	25.9941i	1.81822	+	0.954273i
$743$	19.2962	−	42.8743i	0.707907	−	1.57291i	−0.107623	−	0.994192i	$-0.534324\pi$
$743$	19.2962	−	42.8743i	0.707907	−	1.57291i	0.815530	−	0.578714i	$-0.196445\pi$
$744$	11.1214	+	26.7941i	0.407730	+	0.982320i
$745$	19.4977	−	37.1498i	0.714340	−	1.36106i
$746$	−26.9959	−	26.9959i	−0.988390	−	0.988390i
$747$	−16.7758	−	4.10891i	−0.613794	−	0.150337i
$748$	−0.0230822	−	0.381594i	−0.000843969	−	0.0139525i
$749$	2.06214	+	11.2528i	0.0753491	+	0.411167i
$750$	27.6579	+	9.52156i	1.00992	+	0.347678i
$751$	22.3018	+	15.3938i	0.813805	+	0.561729i	0.900676	−	0.434491i	$-0.143072\pi$
$751$	22.3018	+	15.3938i	0.813805	+	0.561729i	−0.0868717	+	0.996220i	$0.527687\pi$
$752$	9.02479	+	20.0523i	0.329100	+	0.731230i
$753$	−41.2691	+	6.31184i	−1.50393	+	0.230016i
$754$	2.84589	+	2.90533i	0.103641	+	0.105806i
$755$	3.89283	−	1.47636i	0.141675	−	0.0537301i
$756$	0.963339	−	0.910813i	0.0350363	−	0.0331259i
$757$	−10.5400	+	27.7916i	−0.383082	+	1.01010i	0.595338	+	0.803475i	$0.297018\pi$
$757$	−10.5400	+	27.7916i	−0.383082	+	1.01010i	−0.978420	+	0.206628i	$0.933751\pi$
$758$	5.00327	+	41.2057i	0.181727	+	1.49666i
$759$	17.1565	−	3.69596i	0.622743	−	0.134155i
$760$	−1.63268	−	8.90926i	−0.0592236	−	0.323173i
$761$	7.67362	+	41.8736i	0.278169	+	1.51792i	0.764776	+	0.644296i	$0.222850\pi$
$761$	7.67362	+	41.8736i	0.278169	+	1.51792i	−0.486608	+	0.873621i	$0.661766\pi$
$762$	29.7380	−	6.40633i	1.07729	−	0.232077i
$763$	2.17379	+	17.9028i	0.0786966	+	0.648125i
$764$	−0.566268	+	1.49313i	−0.0204869	+	0.0540194i
$765$	−11.1140	+	2.75657i	−0.401828	+	0.0996639i
$766$	−6.70430	+	2.54261i	−0.242236	+	0.0918681i
$767$	1.04430	+	3.47742i	0.0377076	+	0.125562i
$768$	2.98506	−	0.456546i	0.107714	−	0.0164742i
$769$	−13.8247	−	30.7171i	−0.498530	−	1.10769i	−0.973708	−	0.227798i	$-0.926847\pi$
$769$	−13.8247	−	30.7171i	−0.498530	−	1.10769i	0.475179	−	0.879889i	$-0.342383\pi$
$770$	19.1010	+	13.1845i	0.688353	+	0.475136i
$771$	−1.06601	−	0.366986i	−0.0383913	−	0.0132167i
$772$	0.252798	+	1.37947i	0.00909838	+	0.0496483i
$773$	2.45760	+	40.6290i	0.0883938	+	1.46132i	0.724262	+	0.689525i	$0.242181\pi$
$773$	2.45760	+	40.6290i	0.0883938	+	1.46132i	−0.635868	+	0.771798i	$0.719358\pi$
$774$	−6.69737	+	27.3439i	−0.240732	+	0.982857i
$775$	6.33102	+	6.33102i	0.227417	+	0.227417i
$776$	−19.0925	+	36.3777i	−0.685380	+	1.30588i
$777$	3.17533	+	7.65014i	0.113914	+	0.274447i
$778$	−9.91695	+	22.0346i	−0.355540	+	0.789977i
$779$	12.6106	+	6.61854i	0.451821	+	0.237134i
$780$	−0.0336420	+	0.844547i	−0.00120458	+	0.0302397i
$781$	14.9354	−	7.83868i	0.534429	−	0.280490i
$782$	0.680118	+	11.2437i	0.0243210	+	0.402073i
$783$	−2.71001	−	3.23734i	−0.0968480	−	0.115693i
$784$	4.88443	−	19.8169i	0.174444	−	0.707746i
$785$	−26.9380	+	21.1046i	−0.961460	+	0.753256i
$786$	−13.7451	+	6.70494i	−0.490273	+	0.239157i
$787$	−14.2564	+	6.41626i	−0.508184	+	0.228715i	−0.648251	−	0.761427i	$-0.724499\pi$
$787$	−14.2564	+	6.41626i	−0.508184	+	0.228715i	0.140067	+	0.990142i	$0.455268\pi$
$788$	−0.592325	+	0.184576i	−0.0211007	+	0.00657524i
$789$	10.7046	−	16.5831i	0.381094	−	0.590373i
$790$	−13.3048	+	1.61549i	−0.473362	+	0.0574766i
$791$	−0.559502	+	9.24968i	−0.0198936	+	0.328881i
$792$	−21.1232	−	6.54845i	−0.750579	−	0.232689i
$793$	−20.2796	+	2.24996i	−0.720149	+	0.0798985i
$794$	−5.31541	+	21.5655i	−0.188637	+	0.765330i
$795$	36.1891	−	7.79606i	1.28350	−	0.276498i
$796$	0.530205	−	0.278273i	0.0187926	−	0.00986312i
$797$	−6.76416	−	17.8356i	−0.239599	−	0.631770i	0.760242	−	0.649640i	$-0.225081\pi$
$797$	−6.76416	−	17.8356i	−0.239599	−	0.631770i	−0.999840	+	0.0178706i	$0.994311\pi$
$798$	14.2088	−	1.30163i	0.502986	−	0.0460772i
$799$	−11.5274	−	2.11248i	−0.407810	−	0.0747340i
$800$	0.541393	−	0.327283i	0.0191411	−	0.0115712i
$801$	−2.16387	+	2.44970i	−0.0764567	+	0.0865559i
$802$	6.09772	−	50.2193i	0.215318	−	1.77330i
$803$	6.99380	+	18.4411i	0.246806	+	0.650773i
$804$	−1.22594	+	1.30424i	−0.0432356	+	0.0459971i
$805$	21.2426	+	14.6627i	0.748703	+	0.516793i
$806$	13.8058	−	25.6568i	0.486289	−	0.903723i
$807$	22.7219	+	11.0428i	0.799848	+	0.388726i
$808$	−31.2570	−	24.4883i	−1.09962	−	0.861495i
$809$	−7.59404	−	30.8102i	−0.266992	−	1.08323i	−0.939338	−	0.342993i	$-0.888559\pi$
$809$	−7.59404	−	30.8102i	−0.266992	−	1.08323i	0.672346	−	0.740237i	$-0.265287\pi$
$810$	−2.73474	+	23.0854i	−0.0960891	+	0.811140i
$811$	49.8514	−	3.01545i	1.75052	−	0.105887i	0.846232	−	0.532814i	$-0.178865\pi$
$811$	49.8514	−	3.01545i	1.75052	−	0.105887i	0.904286	+	0.426927i	$0.140404\pi$
$812$	0.197916	+	0.0616733i	0.00694551	+	0.00216431i
$813$	−10.2037	−	4.21780i	−0.357860	−	0.147925i
$814$	2.99046	−	3.81703i	0.104815	−	0.133787i
$815$	20.5973	−	23.2496i	0.721493	−	0.814397i
$816$	5.97844	−	12.3013i	0.209287	−	0.430633i
$817$	9.00210	−	7.05270i	0.314944	−	0.246743i
$818$	4.81392	+	39.6462i	0.168315	+	1.38620i
$819$	−37.6204	−	4.90717i	−1.31456	−	0.171470i
$820$	0.137333	−	1.13104i	0.00479589	−	0.0394977i
$821$	−19.1685	−	31.7085i	−0.668984	−	1.10663i	−0.987333	−	0.158661i	$-0.949282\pi$
$821$	−19.1685	−	31.7085i	−0.668984	−	1.10663i	0.318350	−	0.947973i	$-0.396871\pi$
$822$	12.6376	+	22.3689i	0.440788	+	0.780205i
$823$			5.13090i			0.178852i	0.995993	+	0.0894260i	$0.0285033\pi$
$823$			5.13090i			0.178852i	−0.995993	+	0.0894260i	$0.971497\pi$
$824$	−22.6295	−	37.4337i	−0.788335	−	1.30407i
$825$	−6.79679	+	0.622637i	−0.236634	+	0.0216774i
$826$	−3.46725	−	3.46725i	−0.120641	−	0.120641i
$827$	3.84125	+	8.53491i	0.133573	+	0.296788i	0.966531	−	0.256548i	$-0.0825853\pi$
$827$	3.84125	+	8.53491i	0.133573	+	0.296788i	−0.832958	+	0.553336i	$0.813355\pi$
$828$	−0.824421	−	0.255581i	−0.0286506	−	0.00888205i
$829$	25.5892	−	28.8843i	0.888751	−	1.00319i	−0.111205	−	0.993798i	$-0.535471\pi$
$829$	25.5892	−	28.8843i	0.888751	−	1.00319i	0.999956	−	0.00939526i	$-0.00299065\pi$
$830$	−7.69324	+	12.7262i	−0.267036	+	0.441732i
$831$	31.9377	+	6.83145i	1.10791	+	0.236981i
$832$	−22.1119	−	20.0011i	−0.766593	−	0.693415i
$833$	7.21314	+	8.14195i	0.249921	+	0.282102i
$834$	−10.3852	−	12.4428i	−0.359609	−	0.430858i
$835$	30.7792	+	7.58639i	1.06516	+	0.262538i
$836$	0.179093	+	0.259461i	0.00619406	+	0.00897365i
$837$	−16.3662	+	25.4351i	−0.565698	+	0.879165i
$838$	12.1136	−	20.0384i	0.418458	−	0.692215i
$839$	−8.52219	−	6.67671i	−0.294219	−	0.230506i	0.458744	−	0.888568i	$-0.348299\pi$
$839$	−8.52219	−	6.67671i	−0.294219	−	0.230506i	−0.752963	+	0.658063i	$0.771376\pi$
$840$	−14.2599	−	29.2328i	−0.492012	−	1.00863i
$841$	−10.0494	+	26.4982i	−0.346533	+	0.913731i
$842$	3.21397	+	1.68682i	0.110761	+	0.0581317i
$843$	−17.2208	−	49.7863i	−0.593117	−	1.71473i
$844$			0.303196i			0.0104364i
$845$	19.3444	−	14.5203i	0.665469	−	0.499514i
$846$	−12.2789	+	20.3788i	−0.422156	+	0.700639i
$847$	15.3079	+	2.80528i	0.525986	+	0.0963906i
$848$	−20.5487	+	39.1522i	−0.705644	+	1.34449i
$849$	−3.33218	−	21.7870i	−0.114360	−	0.747727i
$850$	0.264498	−	4.37267i	0.00907221	−	0.149982i
$851$	3.32574	−	4.24499i	0.114005	−	0.145516i
$852$	−0.829192	−	0.0244501i	−0.0284077	−	0.000837645i
$853$	−8.88489	−	5.37110i	−0.304213	−	0.183903i	0.356994	−	0.934107i	$-0.383802\pi$
$853$	−8.88489	−	5.37110i	−0.304213	−	0.183903i	−0.661207	+	0.750204i	$0.729955\pi$
$854$	22.6777	−	15.6533i	0.776016	−	0.535645i
$855$	6.66762	−	6.68711i	0.228028	−	0.228694i
$856$	−9.23166	+	1.69176i	−0.315532	+	0.0578233i
$857$	−4.73893	+	4.19833i	−0.161879	+	0.143412i	−0.740174	−	0.672416i	$-0.765257\pi$
$857$	−4.73893	+	4.19833i	−0.161879	+	0.143412i	0.578295	+	0.815828i	$0.303718\pi$
$858$	8.30197	+	20.6002i	0.283424	+	0.703279i
$859$	28.0989	+	24.8934i	0.958721	+	0.849353i	0.988656	−	0.150199i	$-0.0479915\pi$
$859$	28.0989	+	24.8934i	0.958721	+	0.849353i	−0.0299348	+	0.999552i	$0.509530\pi$
$860$	−0.782924	−	0.473294i	−0.0266975	−	0.0161392i
$861$	50.0105	+	10.6972i	1.70435	+	0.364560i
$862$	5.28988	+	21.4619i	0.180174	+	0.730994i
$863$	6.57521	−	2.95926i	0.223823	−	0.100735i	−0.295399	−	0.955374i	$-0.595453\pi$
$863$	6.57521	−	2.95926i	0.223823	−	0.100735i	0.519222	+	0.854639i	$0.326222\pi$
$864$	1.46822	+	1.55289i	0.0499499	+	0.0528305i
$865$	−9.57535	+	21.2756i	−0.325572	+	0.723391i
$866$	36.7864	−	22.2381i	1.25005	−	0.755683i
$867$	−10.8981	−	19.2899i	−0.370119	−	0.655121i
$868$		−	1.48511i		−	0.0504079i
$869$	11.3756	−	6.87681i	0.385892	−	0.233280i
$870$	−3.35733	+	1.39352i	−0.113824	+	0.0472448i
$871$	51.0957	+	3.62109i	1.73131	+	0.122696i
$872$	−14.6873	+	1.78336i	−0.497375	+	0.0603922i
$873$	−42.5127	+	5.22493i	−1.43884	+	0.176837i
$874$	−5.27698	−	7.64502i	−0.178496	−	0.258597i
$875$	−31.9375	−	28.2942i	−1.07969	−	0.956518i
$876$	0.145248	−	0.959046i	0.00490748	−	0.0324032i
$877$	28.6903	+	36.6204i	0.968802	+	1.23658i	0.971610	+	0.236588i	$0.0760292\pi$
$877$	28.6903	+	36.6204i	0.968802	+	1.23658i	−0.00280817	+	0.999996i	$0.500894\pi$
$878$	−14.0213	+	44.9959i	−0.473196	+	1.51854i
$879$	4.80973	+	7.42720i	0.162228	+	0.250513i
$880$	−10.4225	+	15.0996i	−0.351343	+	0.509008i
$881$	−39.0168	+	9.61677i	−1.31451	+	0.323997i	−0.833403	−	0.552666i	$-0.813611\pi$
$881$	−39.0168	+	9.61677i	−1.31451	+	0.323997i	−0.481105	+	0.876663i	$0.659764\pi$
$882$	20.6366	−	7.86090i	0.694871	−	0.264690i
$883$	−8.80295	+	6.07624i	−0.296243	+	0.204482i	−0.706910	−	0.707304i	$-0.749911\pi$
$883$	−8.80295	+	6.07624i	−0.296243	+	0.204482i	0.410667	+	0.911785i	$0.365296\pi$
$884$	0.523712	−	0.123356i	0.0176143	−	0.00414892i
$885$	−3.23215	−	0.291333i	−0.108647	−	0.00979307i
$886$	13.4654	−	4.19600i	0.452380	−	0.140967i
$887$	41.3878	−	15.6963i	1.38967	−	0.527031i	0.457547	−	0.889185i	$-0.348728\pi$
$887$	41.3878	−	15.6963i	1.38967	−	0.527031i	0.932118	+	0.362155i	$0.117959\pi$
$888$	−6.27611	+	2.60502i	−0.210612	+	0.0874186i
$889$	−43.6469	−	7.99859i	−1.46387	−	0.268264i
$890$	1.45589	+	2.40834i	0.0488016	+	0.0807277i
$891$	−6.92356	−	21.9923i	−0.231948	−	0.736771i
$892$	0.484674	−	1.07690i	0.0162281	−	0.0360573i
$893$	9.03669	−	3.42716i	0.302401	−	0.114686i
$894$	−29.4060	+	45.5544i	−0.983485	+	1.52357i
$895$	−19.4360	−	6.05651i	−0.649674	−	0.202447i
$896$	36.2947	+	8.94584i	1.21252	+	0.298860i
$897$	9.23277	+	22.9099i	0.308273	+	0.764938i
$898$	18.1054	−	4.46257i	0.604184	−	0.148918i
$899$	−4.72078	−	0.285555i	−0.157447	−	0.00952378i
$900$	0.306299	+	0.137317i	0.0102100	+	0.00457723i
$901$	−10.9515	−	20.8663i	−0.364846	−	0.695156i
$902$	−8.90700	−	28.5836i	−0.296571	−	0.951729i
$903$	24.3137	−	33.0939i	0.809111	−	1.10130i
$904$	−7.58835	−	0.459011i	−0.252385	−	0.0152665i
$905$	−19.7248	−	25.1768i	−0.655674	−	0.836906i
$906$	−5.18186	+	1.44863i	−0.172156	+	0.0481274i
$907$	−5.08352	−	5.73811i	−0.168796	−	0.190531i	0.658026	−	0.752995i	$-0.271392\pi$
$907$	−5.08352	−	5.73811i	−0.168796	−	0.190531i	−0.826821	+	0.562464i	$0.809853\pi$
$908$	1.88705	−	0.114146i	0.0626240	−	0.00378806i
$909$	2.43924	−	41.3259i	0.0809045	−	1.37069i
$910$	−13.7134	+	29.6474i	−0.454596	+	0.982802i
$911$	−5.84317	+	11.1332i	−0.193593	+	0.368860i	−0.962832	−	0.270100i	$-0.912943\pi$
$911$	−5.84317	+	11.1332i	−0.193593	+	0.368860i	0.769239	+	0.638961i	$0.220635\pi$
$912$	1.02896	+	11.2322i	0.0340722	+	0.371937i
$913$	1.77779	−	14.6415i	0.0588364	−	0.484561i
$914$	23.5921	+	12.3821i	0.780358	+	0.409563i
$915$	4.88443	−	17.5709i	0.161474	−	0.580875i
$916$	−1.30607	+	0.406989i	−0.0431539	+	0.0134473i
$917$	22.2675	−	1.34694i	0.735338	−	0.0444798i
$918$	14.6250	−	2.25864i	0.482696	−	0.0745463i
$919$	−27.7947	+	24.6240i	−0.916863	+	0.812270i	−0.982632	−	0.185565i	$-0.940589\pi$
$919$	−27.7947	+	24.6240i	−0.916863	+	0.812270i	0.0657687	+	0.997835i	$0.479050\pi$
$920$	−12.0292	+	17.4272i	−0.396590	+	0.574559i
$921$	−32.9466	−	24.2056i	−1.08563	−	0.797600i
$922$	11.4871	+	4.35648i	0.378307	+	0.143473i
$923$	14.4467	+	18.8376i	0.475517	+	0.620048i
$924$	0.870212	+	0.724156i	0.0286279	+	0.0238230i
$925$	−1.48294	+	1.48294i	−0.0487589	+	0.0487589i
$926$	19.6109	+	7.43744i	0.644455	+	0.244410i
$927$	18.6559	−	41.6139i	0.612741	−	1.36678i
$928$	−0.0994167	+	0.319040i	−0.00326351	+	0.0104730i
$929$	57.7484	−	10.5828i	1.89466	−	0.347210i	0.898822	−	0.438314i	$-0.144424\pi$
$929$	57.7484	−	10.5828i	1.89466	−	0.347210i	0.995841	+	0.0911043i	$0.0290397\pi$
$930$	16.6866	+	19.9927i	0.547174	+	0.655586i
$931$	−8.56432	−	2.66875i	−0.280684	−	0.0874647i
$932$	−2.00302	+	0.243211i	−0.0656112	+	0.00796664i
$933$	17.4431	−	2.66782i	0.571063	−	0.0873405i
$934$	13.9394	+	13.9394i	0.456110	+	0.456110i
$935$	−3.46743	−	9.14286i	−0.113397	−	0.299003i
$936$	4.02580	−	30.8635i	0.131587	−	1.00880i
$937$	15.2206	−	40.1333i	0.497234	−	1.31110i	−0.418100	−	0.908401i	$-0.637304\pi$
$937$	15.2206	−	40.1333i	0.497234	−	1.31110i	0.915334	−	0.402696i	$-0.131927\pi$
$938$	−63.0829	+	28.3913i	−2.05973	+	0.927009i
$939$	19.8830	+	1.79218i	0.648858	+	0.0584856i
$940$	−0.512711	−	0.578731i	−0.0167228	−	0.0188761i
$941$	25.5826	−	4.68818i	0.833969	−	0.152830i	0.253728	−	0.967276i	$-0.418343\pi$
$941$	25.5826	−	4.68818i	0.833969	−	0.152830i	0.580241	+	0.814445i	$0.302959\pi$
$942$	37.1212	−	24.0391i	1.20947	−	0.783235i
$943$	−9.90564	−	31.7883i	−0.322572	−	1.03517i
$944$	2.74090	−	2.74090i	0.0892088	−	0.0892088i
$945$	16.5938	−	29.5726i	0.539795	−	0.961995i
$946$	−23.8650	−	2.89774i	−0.775919	−	0.0942136i
$947$	−12.5668	−	5.65586i	−0.408366	−	0.183791i	0.195809	−	0.980642i	$-0.437267\pi$
$947$	−12.5668	−	5.65586i	−0.408366	−	0.183791i	−0.604175	+	0.796851i	$0.706497\pi$
$948$	−0.653432	+	0.0202218i	−0.0212225	+	0.000656773i
$949$	−23.9021	+	14.1141i	−0.775894	+	0.458162i
$950$	1.67888	+	3.19884i	0.0544701	+	0.103784i
$951$	−29.7819	+	19.2863i	−0.965745	+	0.625400i
$952$	−15.4978	+	13.7298i	−0.502285	+	0.444986i
$953$	23.0649	+	5.68499i	0.747146	+	0.184155i	0.594466	−	0.804121i	$-0.297364\pi$
$953$	23.0649	+	5.68499i	0.747146	+	0.184155i	0.152680	+	0.988276i	$0.451210\pi$
$954$	−47.4845	+	5.83598i	−1.53737	+	0.188947i
$955$	−2.46620	+	40.7711i	−0.0798042	+	1.31932i
$956$	0.373995	+	0.830982i	0.0120958	+	0.0268759i
$957$	2.46923	−	2.62694i	0.0798189	−	0.0849170i
$958$	3.93451	−	2.06499i	0.127118	−	0.0667169i
$959$	−4.51731	−	37.2034i	−0.145872	−	1.20136i
$960$	23.9516	−	11.6837i	0.773036	−	0.377091i
$961$	0.689532	+	2.79754i	0.0222430	+	0.0902433i
$962$	6.00972	+	3.23380i	0.193761	+	0.104262i
$963$	−6.92909	−	6.90890i	−0.223287	−	0.222636i
$964$	0.421061	−	1.35123i	0.0135615	−	0.0435203i
$965$	16.6705	+	31.7629i	0.536641	+	1.02248i
$966$	−25.6408	−	21.3373i	−0.824980	−	0.686516i
$967$	−8.88465	−	3.99865i	−0.285711	−	0.128588i	0.262490	−	0.964935i	$-0.415456\pi$
$967$	−8.88465	−	3.99865i	−0.285711	−	0.128588i	−0.548201	+	0.836347i	$0.684687\pi$
$968$	−2.30143	+	12.5585i	−0.0739707	+	0.403645i
$969$	−5.23811	−	2.94927i	−0.168272	−	0.0947441i
$970$	−6.64756	+	36.2746i	−0.213440	+	1.16471i
$971$	16.3797	+	1.98885i	0.525649	+	0.0638253i	0.379060	−	0.925372i	$-0.376247\pi$
$971$	16.3797	+	1.98885i	0.525649	+	0.0638253i	0.146589	+	0.989197i	$0.453171\pi$
$972$	−0.233945	+	1.10954i	−0.00750380	+	0.0355884i
$973$	7.03338	+	22.5709i	0.225480	+	0.723590i
$974$	27.5227	−	39.8734i	0.881883	−	1.27763i
$975$	−2.49051	−	9.27750i	−0.0797601	−	0.297118i
$976$	12.3741	+	17.9270i	0.396087	+	0.573831i
$977$	6.99831	−	8.93268i	0.223896	−	0.285782i	−0.662158	−	0.749364i	$-0.730359\pi$
$977$	6.99831	−	8.93268i	0.223896	−	0.285782i	0.886054	+	0.463582i	$0.153436\pi$
$978$	−29.2087	+	27.5355i	−0.933992	+	0.880489i
$979$	−2.29707	−	1.58555i	−0.0734146	−	0.0506744i
$980$	0.0433299	+	0.716328i	0.00138412	+	0.0228823i
$981$	−10.2455	−	11.5309i	−0.327115	−	0.368152i
$982$	32.8509	−	25.7370i	1.04831	−	0.821301i
$983$	−35.5919	−	27.8845i	−1.13521	−	0.889377i	−0.140292	−	0.990110i	$-0.544804\pi$
$983$	−35.5919	−	27.8845i	−1.13521	−	0.889377i	−0.994913	+	0.100733i	$0.967881\pi$
$984$	−8.77589	+	41.0282i	−0.279765	+	1.30793i
$985$	−13.0600	+	9.01465i	−0.416126	+	0.287231i
$986$	1.42707	+	1.82152i	0.0454472	+	0.0580091i
$987$	27.9385	−	20.5890i	0.889293	−	0.655355i
$988$	−0.316979	+	0.310494i	−0.0100844	+	0.00987812i
$989$	−26.5407	−	3.22263i	−0.843946	−	0.102474i
$990$	−19.8514	+	0.0289656i	−0.630920	+	0.000920587i
$991$	7.42834			0.235969			0.117984	−	0.993015i	$-0.462357\pi$
$991$	7.42834			0.235969			0.117984	+	0.993015i	$0.462357\pi$
$992$	2.39398			0.0760090
$993$	−49.8818	−	28.0855i	−1.58295	−	0.891265i
$994$	−29.2355	−	13.1578i	−0.927293	−	0.417341i
$995$	10.8300	−	10.8300i	0.343335	−	0.343335i
$996$	−0.429471	+	0.584561i	−0.0136083	+	0.0185225i
$997$	6.84698	−	1.68763i	0.216846	−	0.0534477i	−0.129396	−	0.991593i	$-0.541304\pi$
$997$	6.84698	−	1.68763i	0.216846	−	0.0534477i	0.346242	+	0.938145i	$0.387458\pi$
$998$	−2.04449	−	1.81126i	−0.0647171	−	0.0573344i
$999$	−5.95777	−	3.83352i	−0.188496	−	0.121287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.s.a.5.18	✓	1392
3.2	odd	2	inner	507.2.s.a.5.41	yes	1392
169.34	odd	52	inner	507.2.s.a.203.41	yes	1392
507.203	even	52	inner	507.2.s.a.203.18	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.s.a.5.18	✓	1392	1.1	even	1	trivial
507.2.s.a.5.41	yes	1392	3.2	odd	2	inner
507.2.s.a.203.18	yes	1392	507.203	even	52	inner
507.2.s.a.203.41	yes	1392	169.34	odd	52	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.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.250240 + 1.36552i) q^{2} +(0.0535762 + 1.73122i) q^{3} +(0.0680148 + 0.0257946i) q^{4} +(1.85720 + 0.112340i) q^{5} +(-2.37742 - 0.360062i) q^{6} +(3.00163 + 1.81455i) q^{7} +(-1.48864 + 2.46251i) q^{8} +(-2.99426 + 0.185505i) q^{9} +O(q^{10})\)	\(q+(-0.250240 + 1.36552i) q^{2} +(0.0535762 + 1.73122i) q^{3} +(0.0680148 + 0.0257946i) q^{4} +(1.85720 + 0.112340i) q^{5} +(-2.37742 - 0.360062i) q^{6} +(3.00163 + 1.81455i) q^{7} +(-1.48864 + 2.46251i) q^{8} +(-2.99426 + 0.185505i) q^{9} +(-0.618149 + 2.50793i) q^{10} +(-0.461782 - 2.51986i) q^{11} +(-0.0410122 + 0.119131i) q^{12} +(3.38428 - 1.24364i) q^{13} +(-3.22893 + 3.64470i) q^{14} +(-0.0949836 + 3.22125i) q^{15} +(-2.88119 - 2.55251i) q^{16} +(1.99184 - 0.490945i) q^{17} +(0.495975 - 4.13513i) q^{18} +(-1.19628 + 1.19628i) q^{19} +(0.123419 + 0.0555465i) q^{20} +(-2.98057 + 5.29370i) q^{21} +3.55647 q^{22} +3.95522 q^{23} +(-4.34291 - 2.44523i) q^{24} +(-1.52697 - 0.185408i) q^{25} +(0.851322 + 4.93251i) q^{26} +(-0.481571 - 5.17379i) q^{27} +(0.157350 + 0.200842i) q^{28} +(0.668680 - 0.461557i) q^{29} +(-4.37490 - 0.935787i) q^{30} +(-4.58201 - 3.58977i) q^{31} +(-0.323755 + 0.253646i) q^{32} +(4.33770 - 0.934451i) q^{33} +(0.171955 + 2.84275i) q^{34} +(5.37078 + 3.70718i) q^{35} +(-0.208439 - 0.0646187i) q^{36} +(0.840849 - 1.07326i) q^{37} +(-1.33418 - 1.93290i) q^{38} +(2.33433 + 5.79232i) q^{39} +(-3.04134 + 4.40614i) q^{40} +(-2.50445 - 8.03706i) q^{41} +(-6.48278 - 5.39472i) q^{42} +(-6.71031 - 0.814779i) q^{43} +(0.0335908 - 0.183299i) q^{44} +(-5.58178 + 0.00814448i) q^{45} +(-0.989755 + 5.40092i) q^{46} +(-5.20943 - 2.34457i) q^{47} +(4.26460 - 5.12473i) q^{48} +(2.46413 + 4.69500i) q^{49} +(0.635287 - 2.03871i) q^{50} +(0.956650 + 3.42202i) q^{51} +(0.262260 + 0.00271062i) q^{52} +(-2.74908 - 11.1535i) q^{53} +(7.18541 + 0.637097i) q^{54} +(-0.574540 - 4.73177i) q^{55} +(-8.93668 + 4.69033i) q^{56} +(-2.13512 - 2.00693i) q^{57} +(0.462933 + 1.02859i) q^{58} +(-0.0608020 + 1.00518i) q^{59} +(-0.0895510 + 0.216642i) q^{60} +(-5.49462 - 1.35430i) q^{61} +(6.04850 - 5.35850i) q^{62} +(-9.32426 - 4.87641i) q^{63} +(-3.84299 - 7.32221i) q^{64} +(6.42500 - 1.92949i) q^{65} +(0.190542 + 6.15704i) q^{66} +(12.9553 + 5.83071i) q^{67} +(0.148138 + 0.0179873i) q^{68} +(0.211906 + 6.84736i) q^{69} +(-6.40621 + 6.40621i) q^{70} +(1.95880 + 6.28602i) q^{71} +(4.00056 - 7.64954i) q^{72} +(-7.57262 + 1.38773i) q^{73} +(1.25515 + 1.41677i) q^{74} +(0.239173 - 2.65346i) q^{75} +(-0.112222 + 0.0505071i) q^{76} +(3.18631 - 8.40161i) q^{77} +(-8.49365 + 1.73809i) q^{78} +(1.83996 + 4.85157i) q^{79} +(-5.06419 - 5.06419i) q^{80} +(8.93118 - 1.11090i) q^{81} +(11.6015 - 1.40867i) q^{82} +(5.49654 + 1.71279i) q^{83} +(-0.339272 + 0.283167i) q^{84} +(3.75440 - 0.688020i) q^{85} +(2.79179 - 8.95916i) q^{86} +(0.834882 + 1.13291i) q^{87} +(6.89261 + 2.61402i) q^{88} +(0.770403 - 0.770403i) q^{89} +(1.38567 - 7.62406i) q^{90} +(12.4150 + 2.40801i) q^{91} +(0.269013 + 0.102023i) q^{92} +(5.96921 - 8.12480i) q^{93} +(4.50516 - 6.52686i) q^{94} +(-2.35612 + 2.08734i) q^{95} +(-0.456463 - 0.546903i) q^{96} +(14.2515 - 0.862056i) q^{97} +(-7.02774 + 2.18993i) q^{98} +(1.85014 + 7.45946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9}+O(q^{10}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27} - 56 q^{28} + 78 q^{30} - 32 q^{31} - 10 q^{33} - 52 q^{34} - 26 q^{36} - 56 q^{37} + 70 q^{39} - 36 q^{40} - 10 q^{42} - 52 q^{43} - 140 q^{45} - 180 q^{46} - 2 q^{48} - 52 q^{49} - 26 q^{51} - 64 q^{52} - 22 q^{54} + 132 q^{55} - 22 q^{57} - 60 q^{58} - 18 q^{60} - 92 q^{61} + 108 q^{63} - 52 q^{64} - 124 q^{66} - 240 q^{67} - 104 q^{69} - 268 q^{70} - 2 q^{72} - 56 q^{73} + 104 q^{75} - 48 q^{76} - 22 q^{78} - 12 q^{79} + 2 q^{81} + 208 q^{82} - 22 q^{84} - 52 q^{85} - 26 q^{87} - 260 q^{88} - 26 q^{90} - 32 q^{91} - 176 q^{93} - 240 q^{94} + 292 q^{96} - 80 q^{97} - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

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