LMFDB - Embedded newform 144.2.x.e.61.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(13,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("144.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.x (of order $12$, degree $4$, 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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			61.6
Character	$\chi$	$=$	144.61
Dual form			144.2.x.e.85.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.812713 + 1.15737i) q^{2} +(-0.460673 + 1.66966i) q^{3} +(-0.678997 - 1.88121i) q^{4} +(-2.69708 - 0.722679i) q^{5} +(-1.55802 - 1.89013i) q^{6} +(-2.89314 - 1.67035i) q^{7} +(2.72908 + 0.743037i) q^{8} +(-2.57556 - 1.53834i) q^{9} +O(q^{10})$	\(q+(-0.812713 + 1.15737i) q^{2} +(-0.460673 + 1.66966i) q^{3} +(-0.678997 - 1.88121i) q^{4} +(-2.69708 - 0.722679i) q^{5} +(-1.55802 - 1.89013i) q^{6} +(-2.89314 - 1.67035i) q^{7} +(2.72908 + 0.743037i) q^{8} +(-2.57556 - 1.53834i) q^{9} +(3.02835 - 2.53418i) q^{10} +(1.23365 + 4.60405i) q^{11} +(3.45379 - 0.267072i) q^{12} +(0.398486 - 1.48717i) q^{13} +(4.28450 - 1.99090i) q^{14} +(2.44910 - 4.17029i) q^{15} +(-3.07793 + 2.55468i) q^{16} -6.47719 q^{17} +(3.87361 - 1.73064i) q^{18} +(0.957336 + 0.957336i) q^{19} +(0.471792 + 5.56447i) q^{20} +(4.12172 - 4.06108i) q^{21} +(-6.33117 - 2.31398i) q^{22} +(-3.70277 + 2.13780i) q^{23} +(-2.49784 + 4.21436i) q^{24} +(2.42183 + 1.39824i) q^{25} +(1.39735 + 1.66984i) q^{26} +(3.75500 - 3.59165i) q^{27} +(-1.17786 + 6.57677i) q^{28} +(-1.07893 + 0.289099i) q^{29} +(2.83614 + 6.22376i) q^{30} +(1.89670 + 3.28518i) q^{31} +(-0.455227 - 5.63851i) q^{32} +(-8.25552 - 0.0611777i) q^{33} +(5.26409 - 7.49649i) q^{34} +(6.59588 + 6.59588i) q^{35} +(-1.14515 + 5.88971i) q^{36} +(-6.14639 + 6.14639i) q^{37} +(-1.88603 + 0.329950i) q^{38} +(2.29950 + 1.35044i) q^{39} +(-6.82357 - 3.97628i) q^{40} +(5.04156 - 2.91075i) q^{41} +(1.35039 + 8.07084i) q^{42} +(1.69287 + 6.31788i) q^{43} +(7.82355 - 5.44689i) q^{44} +(5.83476 + 6.01032i) q^{45} +(0.535074 - 6.02288i) q^{46} +(1.81739 - 3.14781i) q^{47} +(-2.84753 - 6.31598i) q^{48} +(2.08016 + 3.60295i) q^{49} +(-3.58653 + 1.66657i) q^{50} +(2.98387 - 10.8147i) q^{51} +(-3.06826 + 0.260146i) q^{52} +(0.762460 - 0.762460i) q^{53} +(1.10512 + 7.26490i) q^{54} -13.3090i q^{55} +(-6.65448 - 6.70824i) q^{56} +(-2.03945 + 1.15741i) q^{57} +(0.542268 - 1.48367i) q^{58} +(-8.11476 - 2.17434i) q^{59} +(-9.50814 - 1.77567i) q^{60} +(6.74711 - 1.80788i) q^{61} +(-5.34363 - 0.474729i) q^{62} +(4.88188 + 8.75272i) q^{63} +(6.89579 + 4.05562i) q^{64} +(-2.14950 + 3.72304i) q^{65} +(6.78017 - 9.50495i) q^{66} +(-0.487339 + 1.81878i) q^{67} +(4.39799 + 12.1850i) q^{68} +(-1.86364 - 7.16721i) q^{69} +(-12.9944 + 2.27330i) q^{70} -3.98472i q^{71} +(-5.88588 - 6.11199i) q^{72} -5.45461i q^{73} +(-2.11838 - 12.1089i) q^{74} +(-3.45027 + 3.39951i) q^{75} +(1.15092 - 2.45098i) q^{76} +(4.12126 - 15.3808i) q^{77} +(-3.43179 + 1.56385i) q^{78} +(-2.95225 + 5.11344i) q^{79} +(10.1476 - 4.66580i) q^{80} +(4.26702 + 7.92417i) q^{81} +(-0.728538 + 8.20053i) q^{82} +(-10.3428 + 2.77135i) q^{83} +(-10.4384 - 4.99638i) q^{84} +(17.4695 + 4.68093i) q^{85} +(-8.68792 - 3.17535i) q^{86} +(0.0143366 - 1.93463i) q^{87} +(-0.0542436 + 13.4815i) q^{88} -2.24307i q^{89} +(-11.6981 + 1.86829i) q^{90} +(-3.63698 + 3.63698i) q^{91} +(6.53582 + 5.51415i) q^{92} +(-6.35891 + 1.65346i) q^{93} +(2.16615 + 4.66165i) q^{94} +(-1.89016 - 3.27385i) q^{95} +(9.62413 + 1.83743i) q^{96} +(6.50191 - 11.2616i) q^{97} +(-5.86050 - 0.520649i) q^{98} +(3.90524 - 13.7558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8}+O(q^{10}) $ 72 * q + 4 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 28 * q^6 - 8 * q^8	$ 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22} - 40 q^{24} - 4 q^{26} + 8 q^{27} - 16 q^{28} + 4 q^{29} + 18 q^{30} + 28 q^{31} - 46 q^{32} - 32 q^{33} - 14 q^{34} - 16 q^{35} + 14 q^{36} + 16 q^{37} + 2 q^{38} - 10 q^{40} + 26 q^{42} - 10 q^{43} + 60 q^{44} + 40 q^{45} + 20 q^{46} - 56 q^{47} + 2 q^{48} + 4 q^{49} - 36 q^{50} - 54 q^{51} + 6 q^{52} - 8 q^{53} + 92 q^{54} + 52 q^{56} - 14 q^{58} - 14 q^{59} + 18 q^{60} - 32 q^{61} + 16 q^{62} - 108 q^{63} - 44 q^{64} - 64 q^{65} + 26 q^{66} - 18 q^{67} + 16 q^{68} + 32 q^{69} + 14 q^{70} + 114 q^{72} + 38 q^{74} + 86 q^{75} + 10 q^{76} - 36 q^{77} + 16 q^{78} + 44 q^{79} + 144 q^{80} - 44 q^{81} - 88 q^{82} + 20 q^{83} - 58 q^{84} - 8 q^{85} + 76 q^{86} - 42 q^{88} - 80 q^{91} - 68 q^{92} - 4 q^{93} + 20 q^{94} + 48 q^{95} + 94 q^{96} + 40 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) $ 72 * q + 4 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 28 * q^6 - 8 * q^8 - 20 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 20 * q^15 - 10 * q^16 - 16 * q^17 + 28 * q^19 + 12 * q^20 - 16 * q^21 - 8 * q^22 - 40 * q^24 - 4 * q^26 + 8 * q^27 - 16 * q^28 + 4 * q^29 + 18 * q^30 + 28 * q^31 - 46 * q^32 - 32 * q^33 - 14 * q^34 - 16 * q^35 + 14 * q^36 + 16 * q^37 + 2 * q^38 - 10 * q^40 + 26 * q^42 - 10 * q^43 + 60 * q^44 + 40 * q^45 + 20 * q^46 - 56 * q^47 + 2 * q^48 + 4 * q^49 - 36 * q^50 - 54 * q^51 + 6 * q^52 - 8 * q^53 + 92 * q^54 + 52 * q^56 - 14 * q^58 - 14 * q^59 + 18 * q^60 - 32 * q^61 + 16 * q^62 - 108 * q^63 - 44 * q^64 - 64 * q^65 + 26 * q^66 - 18 * q^67 + 16 * q^68 + 32 * q^69 + 14 * q^70 + 114 * q^72 + 38 * q^74 + 86 * q^75 + 10 * q^76 - 36 * q^77 + 16 * q^78 + 44 * q^79 + 144 * q^80 - 44 * q^81 - 88 * q^82 + 20 * q^83 - 58 * q^84 - 8 * q^85 + 76 * q^86 - 42 * q^88 - 80 * q^91 - 68 * q^92 - 4 * q^93 + 20 * q^94 + 48 * q^95 + 94 * q^96 + 40 * q^97 + 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.812713	+	1.15737i	−0.574675	+	0.818382i
$2$	−0.812713	+	1.15737i	−0.574675	+	0.818382i
$3$	−0.460673	+	1.66966i	−0.265970	+	0.963981i
$3$	−0.460673	+	1.66966i	−0.265970	+	0.963981i
$4$	−0.678997	−	1.88121i	−0.339498	−	0.940607i
$5$	−2.69708	−	0.722679i	−1.20617	−	0.323192i	−0.400911	−	0.916117i	$-0.631306\pi$
$5$	−2.69708	−	0.722679i	−1.20617	−	0.323192i	−0.805258	+	0.592925i	$0.797973\pi$
$6$	−1.55802	−	1.89013i	−0.636059	−	0.771640i
$7$	−2.89314	−	1.67035i	−1.09350	−	0.631334i	−0.158996	−	0.987279i	$-0.550826\pi$
$7$	−2.89314	−	1.67035i	−1.09350	−	0.631334i	−0.934507	+	0.355945i	$0.884159\pi$
$8$	2.72908	+	0.743037i	0.964877	+	0.262703i
$9$	−2.57556	−	1.53834i	−0.858520	−	0.512780i
$10$	3.02835	−	2.53418i	0.957649	−	0.801377i
$11$	1.23365	+	4.60405i	0.371960	+	1.38817i	0.857737	+	0.514089i	$0.171870\pi$
$11$	1.23365	+	4.60405i	0.371960	+	1.38817i	−0.485777	+	0.874083i	$0.661463\pi$
$12$	3.45379	−	0.267072i	0.997024	−	0.0770971i
$13$	0.398486	−	1.48717i	0.110520	−	0.412467i	−0.888393	−	0.459084i	$-0.848178\pi$
$13$	0.398486	−	1.48717i	0.110520	−	0.412467i	0.998913	+	0.0466175i	$0.0148442\pi$
$14$	4.28450	−	1.99090i	1.14508	−	0.532092i
$15$	2.44910	−	4.17029i	0.632356	−	1.07677i
$16$	−3.07793	+	2.55468i	−0.769482	+	0.638669i
$17$	−6.47719			−1.57095			−0.785475	−	0.618894i	$-0.787581\pi$
$17$	−6.47719			−1.57095			−0.785475	+	0.618894i	$0.787581\pi$
$18$	3.87361	−	1.73064i	0.913019	−	0.407916i
$19$	0.957336	+	0.957336i	0.219628	+	0.219628i	0.808342	−	0.588714i	$-0.200365\pi$
$19$	0.957336	+	0.957336i	0.219628	+	0.219628i	−0.588714	+	0.808342i	$0.700365\pi$
$20$	0.471792	+	5.56447i	0.105496	+	1.24425i
$21$	4.12172	−	4.06108i	0.899433	−	0.886201i
$22$	−6.33117	−	2.31398i	−1.34981	−	0.493342i
$23$	−3.70277	+	2.13780i	−0.772081	+	0.445761i	−0.833617	−	0.552343i	$-0.813734\pi$
$23$	−3.70277	+	2.13780i	−0.772081	+	0.445761i	0.0615352	+	0.998105i	$0.480400\pi$
$24$	−2.49784	+	4.21436i	−0.509869	+	0.860252i
$25$	2.42183	+	1.39824i	0.484365	+	0.279648i
$26$	1.39735	+	1.66984i	0.274042	+	0.327482i
$27$	3.75500	−	3.59165i	0.722651	−	0.691214i
$28$	−1.17786	+	6.57677i	−0.222595	+	1.24289i
$29$	−1.07893	+	0.289099i	−0.200353	+	0.0536843i	−0.357600	−	0.933875i	$-0.616405\pi$
$29$	−1.07893	+	0.289099i	−0.200353	+	0.0536843i	0.157247	+	0.987559i	$0.449738\pi$
$30$	2.83614	+	6.22376i	0.517807	+	1.13630i
$31$	1.89670	+	3.28518i	0.340657	+	0.590036i	0.984555	−	0.175076i	$-0.0560171\pi$
$31$	1.89670	+	3.28518i	0.340657	+	0.590036i	−0.643898	+	0.765112i	$0.722684\pi$
$32$	−0.455227	−	5.63851i	−0.0804734	−	0.996757i
$33$	−8.25552	−	0.0611777i	−1.43710	−	0.0106497i
$34$	5.26409	−	7.49649i	0.902785	−	1.28564i
$35$	6.59588	+	6.59588i	1.11491	+	1.11491i
$36$	−1.14515	+	5.88971i	−0.190858	+	0.981618i
$37$	−6.14639	+	6.14639i	−1.01046	+	1.01046i	−0.0105160	+	0.999945i	$0.503347\pi$
$37$	−6.14639	+	6.14639i	−1.01046	+	1.01046i	−0.999945	+	0.0105160i	$0.996653\pi$
$38$	−1.88603	+	0.329950i	−0.305954	+	0.0535249i
$39$	2.29950	+	1.35044i	0.368215	+	0.216243i
$40$	−6.82357	−	3.97628i	−1.07890	−	0.628705i
$41$	5.04156	−	2.91075i	0.787359	−	0.454582i	−0.0516729	−	0.998664i	$-0.516455\pi$
$41$	5.04156	−	2.91075i	0.787359	−	0.454582i	0.839032	+	0.544082i	$0.183122\pi$
$42$	1.35039	+	8.07084i	0.208369	+	1.24536i
$43$	1.69287	+	6.31788i	0.258160	+	0.963468i	0.966305	+	0.257400i	$0.0828659\pi$
$43$	1.69287	+	6.31788i	0.258160	+	0.963468i	−0.708144	+	0.706068i	$0.750467\pi$
$44$	7.82355	−	5.44689i	1.17944	−	0.821150i
$45$	5.83476	+	6.01032i	0.869794	+	0.895966i
$46$	0.535074	−	6.02288i	0.0788924	−	0.888025i
$47$	1.81739	−	3.14781i	0.265093	−	0.459155i	−0.702495	−	0.711689i	$-0.747931\pi$
$47$	1.81739	−	3.14781i	0.265093	−	0.459155i	0.967588	+	0.252534i	$0.0812639\pi$
$48$	−2.84753	−	6.31598i	−0.411006	−	0.911633i
$49$	2.08016	+	3.60295i	0.297166	+	0.514707i
$50$	−3.58653	+	1.66657i	−0.507212	+	0.235689i
$51$	2.98387	−	10.8147i	0.417825	−	1.51437i
$52$	−3.06826	+	0.260146i	−0.425491	+	0.0360758i
$53$	0.762460	−	0.762460i	0.104732	−	0.104732i	−0.652799	−	0.757531i	$-0.726405\pi$
$53$	0.762460	−	0.762460i	0.104732	−	0.104732i	0.757531	+	0.652799i	$0.226405\pi$
$54$	1.10512	+	7.26490i	0.150388	+	0.988627i
$55$		−	13.3090i		−	1.79458i
$56$	−6.65448	−	6.70824i	−0.889242	−	0.896427i
$57$	−2.03945	+	1.15741i	−0.270132	+	0.153303i
$58$	0.542268	−	1.48367i	0.0712033	−	0.194816i
$59$	−8.11476	−	2.17434i	−1.05645	−	0.283075i	−0.311536	−	0.950234i	$-0.600844\pi$
$59$	−8.11476	−	2.17434i	−1.05645	−	0.283075i	−0.744915	+	0.667159i	$0.767510\pi$
$60$	−9.50814	−	1.77567i	−1.22750	−	0.229238i
$61$	6.74711	−	1.80788i	0.863879	−	0.231476i	0.200440	−	0.979706i	$-0.435763\pi$
$61$	6.74711	−	1.80788i	0.863879	−	0.231476i	0.663439	+	0.748230i	$0.269096\pi$
$62$	−5.34363	−	0.474729i	−0.678641	−	0.0602907i
$63$	4.88188	+	8.75272i	0.615059	+	1.10274i
$64$	6.89579	+	4.05562i	0.861974	+	0.506953i
$65$	−2.14950	+	3.72304i	−0.266612	+	0.461786i
$66$	6.78017	−	9.50495i	0.834581	−	1.16998i
$67$	−0.487339	+	1.81878i	−0.0595380	+	0.222199i	−0.989284	−	0.146002i	$-0.953359\pi$
$67$	−0.487339	+	1.81878i	−0.0595380	+	0.222199i	0.929746	+	0.368201i	$0.120026\pi$
$68$	4.39799	+	12.1850i	0.533335	+	1.47765i
$69$	−1.86364	−	7.16721i	−0.224355	−	0.862831i
$70$	−12.9944	+	2.27330i	−1.55313	+	0.271711i
$71$		−	3.98472i		−	0.472899i	−0.971644	−	0.236450i	$-0.924016\pi$
$71$		−	3.98472i		−	0.472899i	0.971644	−	0.236450i	$-0.0759838\pi$
$72$	−5.88588	−	6.11199i	−0.693657	−	0.720305i
$73$		−	5.45461i		−	0.638414i	−0.947685	−	0.319207i	$-0.896583\pi$
$73$		−	5.45461i		−	0.638414i	0.947685	−	0.319207i	$-0.103417\pi$
$74$	−2.11838	−	12.1089i	−0.246257	−	1.40763i
$75$	−3.45027	+	3.39951i	−0.398402	+	0.392541i
$76$	1.15092	−	2.45098i	0.132020	−	0.281147i
$77$	4.12126	−	15.3808i	0.469662	−	1.75280i
$78$	−3.43179	+	1.56385i	−0.388574	+	0.177071i
$79$	−2.95225	+	5.11344i	−0.332154	+	0.575307i	−0.982934	−	0.183959i	$-0.941109\pi$
$79$	−2.95225	+	5.11344i	−0.332154	+	0.575307i	0.650780	+	0.759266i	$0.274442\pi$
$80$	10.1476	−	4.66580i	1.13454	−	0.521652i
$81$	4.26702	+	7.92417i	0.474114	+	0.880464i
$82$	−0.728538	+	8.20053i	−0.0804535	+	0.905597i
$83$	−10.3428	+	2.77135i	−1.13527	+	0.304195i	−0.777048	−	0.629441i	$-0.783284\pi$
$83$	−10.3428	+	2.77135i	−1.13527	+	0.304195i	−0.358223	+	0.933636i	$0.616617\pi$
$84$	−10.4384	−	4.99638i	−1.13892	−	0.545149i
$85$	17.4695	+	4.68093i	1.89483	+	0.507718i
$86$	−8.68792	−	3.17535i	−0.936843	−	0.342407i
$87$	0.0143366	−	1.93463i	0.00153705	−	0.207415i
$88$	−0.0542436	+	13.4815i	−0.00578239	+	1.43713i
$89$		−	2.24307i		−	0.237765i	−0.992908	−	0.118883i	$-0.962069\pi$
$89$		−	2.24307i		−	0.237765i	0.992908	−	0.118883i	$-0.0379312\pi$
$90$	−11.6981	+	1.86829i	−1.23309	+	0.196935i
$91$	−3.63698	+	3.63698i	−0.381259	+	0.381259i
$92$	6.53582	+	5.51415i	0.681407	+	0.574890i
$93$	−6.35891	+	1.65346i	−0.659388	+	0.171456i
$94$	2.16615	+	4.66165i	0.223422	+	0.480812i
$95$	−1.89016	−	3.27385i	−0.193926	−	0.335890i
$96$	9.62413	+	1.83743i	0.982258	+	0.187532i
$97$	6.50191	−	11.2616i	0.660169	−	1.14345i	−0.320402	−	0.947282i	$-0.603818\pi$
$97$	6.50191	−	11.2616i	0.660169	−	1.14345i	0.980571	−	0.196165i	$-0.0628488\pi$
$98$	−5.86050	−	0.520649i	−0.592000	−	0.0525935i
$99$	3.90524	−	13.7558i	0.392492	−	1.38251i
$100$	0.985980	−	5.50537i	0.0985980	−	0.550537i
$101$	−2.36072	−	8.81034i	−0.234901	−	0.876662i	−0.978194	−	0.207696i	$-0.933404\pi$
$101$	−2.36072	−	8.81034i	−0.234901	−	0.876662i	0.743293	−	0.668966i	$-0.233263\pi$
$102$	10.0916	+	12.2427i	0.999216	+	1.21221i
$103$	−3.73262	+	2.15503i	−0.367786	+	0.212342i	−0.672491	−	0.740105i	$-0.734776\pi$
$103$	−3.73262	+	2.15503i	−0.367786	+	0.212342i	0.304705	+	0.952447i	$0.401442\pi$
$104$	2.19253	−	3.76252i	0.214995	−	0.368946i
$105$	−14.0515	+	7.97436i	−1.37128	+	0.778218i
$106$	0.262785	+	1.50211i	0.0255239	+	0.145897i
$107$	0.0516852	−	0.0516852i	0.00499659	−	0.00499659i	−0.704604	−	0.709601i	$-0.748875\pi$
$107$	0.0516852	−	0.0516852i	0.00499659	−	0.00499659i	0.709601	+	0.704604i	$0.248875\pi$
$108$	−9.30630	−	4.62524i	−0.895499	−	0.445064i
$109$	5.73510	+	5.73510i	0.549323	+	0.549323i	0.926245	−	0.376922i	$-0.123018\pi$
$109$	5.73510	+	5.73510i	0.549323	+	0.549323i	−0.376922	+	0.926245i	$0.623018\pi$
$110$	15.4034	+	10.8164i	1.46866	+	1.03130i
$111$	−7.43094	−	13.0939i	−0.705313	−	1.24282i
$112$	13.1721	−	2.24980i	1.24464	−	0.212586i
$113$	7.13575	+	12.3595i	0.671275	+	1.16268i	0.977543	+	0.210737i	$0.0675862\pi$
$113$	7.13575	+	12.3595i	0.671275	+	1.16268i	−0.306268	+	0.951945i	$0.599080\pi$
$114$	0.317936	−	3.30103i	0.0297775	−	0.309170i
$115$	11.5316	−	3.08988i	1.07533	−	0.288133i
$116$	1.27645	+	1.83340i	0.118515	+	0.170227i
$117$	−3.31410	+	3.21729i	−0.306389	+	0.297439i
$118$	9.11148	−	7.62464i	0.838780	−	0.701905i
$119$	18.7394	+	10.8192i	1.71784	+	0.991794i
$120$	9.78249	−	9.56130i	0.893015	−	0.872824i
$121$	−10.1491	+	5.85956i	−0.922642	+	0.532688i
$122$	−3.39108	+	9.27818i	−0.307014	+	0.840007i
$123$	2.53746	+	9.75861i	0.228795	+	0.879905i
$124$	4.89227	−	5.79872i	0.439339	−	0.520740i
$125$	4.35061	+	4.35061i	0.389131	+	0.389131i
$126$	−14.0977	−	1.46332i	−1.25592	−	0.130363i
$127$	−16.2634			−1.44315			−0.721573	−	0.692338i	$-0.756581\pi$
$127$	−16.2634			−1.44315			−0.721573	+	0.692338i	$0.756581\pi$
$128$	−10.2981	+	4.68491i	−0.910235	+	0.414091i
$129$	−11.3286	−	0.0839508i	−0.997428	−	0.00739146i
$130$	−2.56200	−	5.51351i	−0.224702	−	0.483567i
$131$	−4.58345	+	17.1057i	−0.400458	+	1.49453i	0.411822	+	0.911264i	$0.364892\pi$
$131$	−4.58345	+	17.1057i	−0.400458	+	1.49453i	−0.812281	+	0.583267i	$0.801774\pi$
$132$	5.49038	+	15.5719i	0.477877	+	1.35536i
$133$	−1.17061	−	4.36879i	−0.101505	−	0.378822i
$134$	−1.70892	−	2.04217i	−0.147629	−	0.176417i
$135$	−12.7231	+	6.97329i	−1.09503	+	0.600166i
$136$	−17.6768	−	4.81279i	−1.51577	−	0.412694i
$137$	−9.62551	−	5.55729i	−0.822363	−	0.474791i	0.0288677	−	0.999583i	$-0.490810\pi$
$137$	−9.62551	−	5.55729i	−0.822363	−	0.474791i	−0.851231	+	0.524792i	$0.824143\pi$
$138$	9.80970	+	3.66797i	0.835057	+	0.312239i
$139$	6.50347	+	1.74260i	0.551617	+	0.147805i	0.523852	−	0.851809i	$-0.324494\pi$
$139$	6.50347	+	1.74260i	0.551617	+	0.147805i	0.0277649	+	0.999614i	$0.491161\pi$
$140$	7.92968	−	16.8868i	0.670180	−	1.42720i
$141$	4.41856	+	4.48454i	0.372110	+	0.377666i
$142$	4.61178	+	3.23843i	0.387012	+	0.271763i
$143$	7.33859			0.613684
$144$	11.8573	−	1.84482i	0.988112	−	0.153735i
$145$	3.11889			0.259009
$146$	6.31299	+	4.43303i	0.522467	+	0.366880i
$147$	−6.97399	+	1.81339i	−0.575205	+	0.149566i
$148$	15.7361	+	7.38930i	1.29350	+	0.607396i
$149$	−10.7583	−	2.88268i	−0.881354	−	0.236158i	−0.210363	−	0.977623i	$-0.567465\pi$
$149$	−10.7583	−	2.88268i	−0.881354	−	0.236158i	−0.670991	+	0.741465i	$0.734131\pi$
$150$	−1.13040	−	6.75605i	−0.0922969	−	0.551629i
$151$	−18.9045	−	10.9145i	−1.53842	−	0.888210i	−0.998931	−	0.0462196i	$-0.985283\pi$
$151$	−18.9045	−	10.9145i	−1.53842	−	0.888210i	−0.539493	−	0.841990i	$-0.681384\pi$
$152$	1.90131	+	3.32398i	0.154217	+	0.269611i
$153$	16.6824	+	9.96412i	1.34869	+	0.805551i
$154$	14.4518	+	17.2700i	1.16456	+	1.39165i
$155$	−2.74141	−	10.2311i	−0.220195	−	0.821780i
$156$	0.979106	−	5.24280i	0.0783912	−	0.419760i
$157$	−2.18429	+	8.15189i	−0.174326	+	0.650592i	0.822340	+	0.568996i	$0.192668\pi$
$157$	−2.18429	+	8.15189i	−0.174326	+	0.650592i	−0.996666	+	0.0815954i	$0.973998\pi$
$158$	−3.51880	−	7.57259i	−0.279941	−	0.602443i
$159$	0.921807	+	1.62430i	0.0731041	+	0.128815i
$160$	−2.84705	+	15.5365i	−0.225079	+	1.22827i
$161$	14.2835			1.12570
$162$	−12.6390	−	1.50156i	−0.993017	−	0.117974i
$163$	−6.93193	−	6.93193i	−0.542950	−	0.542950i	0.381442	−	0.924393i	$-0.375428\pi$
$163$	−6.93193	−	6.93193i	−0.542950	−	0.542950i	−0.924393	+	0.381442i	$0.875428\pi$
$164$	−8.89893	−	7.50786i	−0.694890	−	0.586265i
$165$	22.2216	+	6.13110i	1.72995	+	0.477305i
$166$	5.19827	−	14.2227i	0.403464	−	1.10390i
$167$	7.33544	−	4.23512i	0.567633	−	0.327723i	−0.188570	−	0.982060i	$-0.560385\pi$
$167$	7.33544	−	4.23512i	0.567633	−	0.327723i	0.756204	+	0.654336i	$0.227052\pi$
$168$	14.2661	−	8.02044i	1.10065	−	0.618790i
$169$	9.20544	+	5.31477i	0.708111	+	0.408828i
$170$	−19.6152	+	16.4143i	−1.50442	+	1.25892i
$171$	−0.992969	−	3.93838i	−0.0759342	−	0.301176i
$172$	10.7358	−	7.47447i	0.818599	−	0.569923i
$173$	−5.81815	+	1.55897i	−0.442346	+	0.118526i	−0.473116	−	0.881000i	$-0.656871\pi$
$173$	−5.81815	+	1.55897i	−0.442346	+	0.118526i	0.0307700	+	0.999526i	$0.490204\pi$
$174$	2.22743	+	1.58889i	0.168861	+	0.120454i
$175$	−4.67112	−	8.09061i	−0.353103	−	0.611593i
$176$	−15.5589	−	11.0193i	−1.17280	−	0.830614i
$177$	7.36868	−	12.5473i	0.553864	−	0.943110i
$178$	2.59606	+	1.82297i	0.194583	+	0.136638i
$179$	−8.34442	−	8.34442i	−0.623692	−	0.623692i	0.322782	−	0.946473i	$-0.395382\pi$
$179$	−8.34442	−	8.34442i	−0.623692	−	0.623692i	−0.946473	+	0.322782i	$0.895382\pi$
$180$	7.34492	−	15.0574i	0.547458	−	1.12231i
$181$	−13.3444	+	13.3444i	−0.991880	+	0.991880i	−0.999967	−	0.00808779i	$-0.997426\pi$
$181$	−13.3444	+	13.3444i	−0.991880	+	0.991880i	0.00808779	+	0.999967i	$0.497426\pi$
$182$	−1.25350	−	7.16513i	−0.0929156	−	0.531115i
$183$	−0.0896544	+	12.0983i	−0.00662744	+	0.894329i
$184$	−11.6936	+	3.08293i	−0.862066	+	0.227276i
$185$	21.0192	−	12.1354i	1.54536	−	0.892214i
$186$	3.25430	−	8.70337i	0.238617	−	0.638162i
$187$	−7.99059	−	29.8213i	−0.584330	−	2.18075i
$188$	−7.15570	−	1.28154i	−0.521883	−	0.0934661i
$189$	−16.8631	+	4.11896i	−1.22661	+	0.299610i
$190$	5.32521	+	0.473093i	0.386331	+	0.0343218i
$191$	−0.892527	+	1.54590i	−0.0645810	+	0.111858i	−0.896508	−	0.443027i	$-0.853904\pi$
$191$	−0.892527	+	1.54590i	−0.0645810	+	0.111858i	0.831927	+	0.554885i	$0.187238\pi$
$192$	−9.94823	+	9.64534i	−0.717952	+	0.696093i
$193$	−8.20588	−	14.2130i	−0.590672	−	1.02307i	−0.994142	−	0.108081i	$-0.965529\pi$
$193$	−8.20588	−	14.2130i	−0.590672	−	1.02307i	0.403470	−	0.914993i	$-0.367804\pi$
$194$	7.74967	+	16.6776i	0.556394	+	1.19738i
$195$	−5.22601	−	5.30404i	−0.374242	−	0.379830i
$196$	5.36549	−	6.35962i	0.383249	−	0.454258i
$197$	−3.44937	+	3.44937i	−0.245758	+	0.245758i	−0.819227	−	0.573469i	$-0.805597\pi$
$197$	−3.44937	+	3.44937i	−0.245758	+	0.245758i	0.573469	+	0.819227i	$0.305597\pi$
$198$	12.7466	+	15.6993i	0.905864	+	1.11570i
$199$			15.0093i			1.06398i	0.846751	+	0.531990i	$0.178556\pi$
$199$			15.0093i			1.06398i	−0.846751	+	0.531990i	$0.821444\pi$
$200$	5.57042	+	5.61543i	0.393888	+	0.397071i
$201$	−2.81224	−	1.65155i	−0.198360	−	0.116492i
$202$	12.1154	+	4.42805i	0.852436	+	0.311557i
$203$	3.60439	+	0.965795i	0.252979	+	0.0677855i
$204$	−22.3709	+	1.72988i	−1.56627	+	0.121116i
$205$	−15.7010	+	4.20707i	−1.09661	+	0.293835i
$206$	0.539388	−	6.07144i	0.0375809	−	0.423017i
$207$	12.8254	+	0.190096i	0.891425	+	0.0132126i
$208$	2.57273	+	5.59541i	0.178386	+	0.387972i
$209$	−3.22660	+	5.58863i	−0.223189	+	0.386574i
$210$	2.19053	−	22.7436i	0.151161	−	1.56945i
$211$	−3.18415	+	11.8834i	−0.219206	+	0.818089i	0.765437	+	0.643511i	$0.222523\pi$
$211$	−3.18415	+	11.8834i	−0.219206	+	0.818089i	−0.984643	+	0.174578i	$0.944144\pi$
$212$	−1.95206	−	0.916642i	−0.134068	−	0.0629552i
$213$	6.65314	+	1.83565i	0.455866	+	0.125777i
$214$	0.0178135	+	0.101824i	0.00121771	+	0.00696054i
$215$		−	18.2632i		−	1.24554i
$216$	12.9164	−	7.01181i	0.878853	−	0.477093i
$217$		−	12.6726i		−	0.860274i
$218$	−11.2986	+	1.97663i	−0.765238	+	0.133874i
$219$	9.10738	+	2.51279i	0.615419	+	0.169799i
$220$	−25.0371	+	9.03676i	−1.68800	+	0.609258i
$221$	−2.58107	+	9.63269i	−0.173622	+	0.647965i
$222$	21.1937	+	2.04125i	1.42242	+	0.137000i
$223$	0.258294	−	0.447379i	0.0172967	−	0.0299587i	−0.857248	−	0.514905i	$-0.827827\pi$
$223$	0.258294	−	0.447379i	0.0172967	−	0.0299587i	0.874544	+	0.484946i	$0.161161\pi$
$224$	−8.10127	+	17.0734i	−0.541289	+	1.14076i
$225$	−4.08659	−	7.32685i	−0.272439	−	0.488457i
$226$	−20.1038	−	1.78602i	−1.33728	−	0.118805i
$227$	9.84745	−	2.63862i	0.653598	−	0.175131i	0.0832432	−	0.996529i	$-0.473472\pi$
$227$	9.84745	−	2.63862i	0.653598	−	0.175131i	0.570355	+	0.821398i	$0.306806\pi$
$228$	3.56211	+	3.05076i	0.235907	+	0.202041i
$229$	−20.6838	−	5.54222i	−1.36683	−	0.366240i	−0.500508	−	0.865732i	$-0.666854\pi$
$229$	−20.6838	−	5.54222i	−1.36683	−	0.366240i	−0.866319	+	0.499491i	$0.833520\pi$
$230$	−5.79575	+	15.8575i	−0.382160	+	1.04561i
$231$	23.7822	+	13.9666i	1.56475	+	0.918937i
$232$	−3.15931	−	0.0127117i	−0.207419	−	0.000834563i
$233$			23.2468i			1.52295i	0.648194	+	0.761476i	$0.275525\pi$
$233$			23.2468i			1.52295i	−0.648194	+	0.761476i	$0.724475\pi$
$234$	−1.03018	−	6.45036i	−0.0673448	−	0.421673i
$235$	−7.17649	+	7.17649i	−0.468142	+	0.468142i
$236$	1.41949	+	16.7420i	0.0924010	+	1.08981i
$237$	−7.17771	−	7.28488i	−0.466242	−	0.473204i
$238$	−27.7515	+	12.8955i	−1.79886	+	0.835889i
$239$	0.219358	+	0.379939i	0.0141891	+	0.0245762i	0.873033	−	0.487662i	$-0.162150\pi$
$239$	0.219358	+	0.379939i	0.0141891	+	0.0245762i	−0.858844	+	0.512238i	$0.828817\pi$
$240$	3.11559	+	19.0925i	0.201110	+	1.23242i
$241$	7.67406	−	13.2919i	0.494330	−	0.856204i	−0.505649	−	0.862739i	$-0.668747\pi$
$241$	7.67406	−	13.2919i	0.494330	−	0.856204i	0.999979	+	0.00653501i	$0.00208017\pi$
$242$	1.46660	−	16.5083i	0.0942769	−	1.06120i
$243$	−15.1964	+	3.47405i	−0.974850	+	0.222860i
$244$	−7.98228	−	11.4652i	−0.511013	−	0.733985i
$245$	−3.00658	−	11.2207i	−0.192083	−	0.716865i
$246$	−13.3565	−	4.99418i	−0.851581	−	0.318417i
$247$	1.80521	−	1.04224i	0.114863	−	0.0663159i
$248$	2.73524	+	10.3748i	0.173688	+	0.658803i
$249$	0.137433	−	18.5457i	0.00870948	−	1.17529i
$250$	−8.57105	+	1.49946i	−0.542081	+	0.0948341i
$251$	8.02147	−	8.02147i	0.506310	−	0.506310i	−0.407081	−	0.913392i	$-0.633453\pi$
$251$	8.02147	−	8.02147i	0.506310	−	0.506310i	0.913392	+	0.407081i	$0.133453\pi$
$252$	13.1510	−	15.1269i	0.828433	−	0.952907i
$253$	−14.4104	−	14.4104i	−0.905977	−	0.905977i
$254$	13.2175	−	18.8228i	0.829339	−	1.18104i
$255$	−15.8633	+	27.0118i	−0.993399	+	1.69154i
$256$	2.94727	−	15.7262i	0.184204	−	0.982888i
$257$	4.72936	+	8.19149i	0.295009	+	0.510971i	0.974987	−	0.222262i	$-0.0713439\pi$
$257$	4.72936	+	8.19149i	0.295009	+	0.510971i	−0.679978	+	0.733233i	$0.738011\pi$
$258$	9.30406	−	13.0431i	0.579245	−	0.812029i
$259$	28.0490	−	7.51571i	1.74288	−	0.467003i
$260$	8.46332	+	1.51573i	0.524873	+	0.0940016i
$261$	3.22359	+	0.915171i	0.199535	+	0.0566477i
$262$	−16.0725	−	19.2067i	−0.992964	−	1.18660i
$263$	16.2413	+	9.37694i	1.00148	+	0.578207i	0.908687	−	0.417478i	$-0.137086\pi$
$263$	16.2413	+	9.37694i	1.00148	+	0.578207i	0.0927966	+	0.995685i	$0.470419\pi$
$264$	−22.4845	−	6.30112i	−1.38383	−	0.387807i
$265$	−2.60743	+	1.50540i	−0.160173	+	0.0924759i
$266$	6.00767	+	2.19574i	0.368354	+	0.134630i
$267$	3.74518	+	1.03332i	0.229201	+	0.0632384i
$268$	3.75241	−	0.318153i	0.229215	−	0.0194343i
$269$	−13.5606	−	13.5606i	−0.826805	−	0.826805i	0.160269	−	0.987073i	$-0.448764\pi$
$269$	−13.5606	−	13.5606i	−0.826805	−	0.826805i	−0.987073	+	0.160269i	$0.948764\pi$
$270$	2.26960	−	20.3926i	0.138123	−	1.24106i
$271$	30.6233			1.86023			0.930115	−	0.367268i	$-0.119707\pi$
$271$	30.6233			1.86023			0.930115	+	0.367268i	$0.119707\pi$
$272$	19.9363	−	16.5471i	1.20882	−	1.00332i
$273$	−4.39707	−	7.74799i	−0.266123	−	0.468930i
$274$	14.2546	−	6.62377i	0.861152	−	0.400156i
$275$	−3.44988	+	12.8751i	−0.208036	+	0.776400i
$276$	−12.2177	+	8.37241i	−0.735416	+	0.503960i
$277$	5.40521	+	20.1725i	0.324767	+	1.21205i	0.914545	+	0.404483i	$0.132549\pi$
$277$	5.40521	+	20.1725i	0.324767	+	1.21205i	−0.589778	+	0.807565i	$0.700785\pi$
$278$	−7.30228	+	6.11067i	−0.437962	+	0.366494i
$279$	0.168657	−	11.3789i	0.0100972	−	0.681240i
$280$	13.0997	+	22.9017i	0.782858	+	1.36864i
$281$	10.6538	+	6.15097i	0.635552	+	0.366936i	0.782899	−	0.622149i	$-0.213740\pi$
$281$	10.6538	+	6.15097i	0.635552	+	0.366936i	−0.147347	+	0.989085i	$0.547073\pi$
$282$	−8.78128	+	1.46926i	−0.522917	+	0.0874930i
$283$	12.8013	+	3.43009i	0.760957	+	0.203898i	0.618373	−	0.785885i	$-0.287792\pi$
$283$	12.8013	+	3.43009i	0.760957	+	0.203898i	0.142584	+	0.989783i	$0.454459\pi$
$284$	−7.49611	+	2.70561i	−0.444812	+	0.160548i
$285$	6.33698	−	1.64776i	0.375371	−	0.0976047i
$286$	−5.96417	+	8.49345i	−0.352669	+	0.502228i
$287$	−19.4479			−1.14797
$288$	−7.50147	+	15.2226i	−0.442029	+	0.897001i
$289$	24.9540			1.46788
$290$	−2.53476	+	3.60970i	−0.148846	+	0.211969i
$291$	15.8079	+	16.0440i	0.926676	+	0.940513i
$292$	−10.2613	+	3.70366i	−0.600497	+	0.216741i
$293$	21.3351	+	5.71672i	1.24641	+	0.333974i	0.820948	−	0.571003i	$-0.193446\pi$
$293$	21.3351	+	5.71672i	1.24641	+	0.333974i	0.425460	+	0.904977i	$0.360112\pi$
$294$	3.56909	−	9.54523i	0.208153	−	0.556689i
$295$	20.3148	+	11.7287i	1.18277	+	0.682874i
$296$	−21.3410	+	12.2070i	−1.24042	+	0.709518i
$297$	21.1685	+	12.8574i	1.22832	+	0.746060i
$298$	12.0797	−	10.1085i	0.699759	−	0.585570i
$299$	1.70377	+	6.35854i	0.0985313	+	0.367724i
$300$	8.73791	+	4.18243i	0.504484	+	0.241473i
$301$	5.65539	−	21.1062i	0.325971	−	1.21654i
$302$	27.9960	−	13.0091i	1.61099	−	0.748587i
$303$	15.7978	+	0.117070i	0.907562	+	0.00672551i
$304$	−5.39229	−	0.500928i	−0.309269	−	0.0287302i
$305$	−19.5040			−1.11680
$306$	−25.0901	+	11.2097i	−1.43431	+	0.640815i
$307$	−3.59225	−	3.59225i	−0.205021	−	0.205021i	0.597126	−	0.802147i	$-0.296309\pi$
$307$	−3.59225	−	3.59225i	−0.205021	−	0.205021i	−0.802147	+	0.597126i	$0.796309\pi$
$308$	−31.7328	+	2.69051i	−1.80815	+	0.153306i
$309$	−1.87866	−	7.22499i	−0.106873	−	0.411016i
$310$	14.0691	+	5.14211i	0.799071	+	0.292052i
$311$	−8.62665	+	4.98060i	−0.489173	+	0.282424i	−0.724231	−	0.689557i	$-0.757805\pi$
$311$	−8.62665	+	4.98060i	−0.489173	+	0.282424i	0.235058	+	0.971981i	$0.424472\pi$
$312$	5.27211	+	5.39408i	0.298475	+	0.305379i
$313$	−22.1588	−	12.7934i	−1.25249	−	0.723124i	−0.280885	−	0.959741i	$-0.590628\pi$
$313$	−22.1588	−	12.7934i	−1.25249	−	0.723124i	−0.971603	+	0.236617i	$0.923961\pi$
$314$	−7.65953	−	9.15317i	−0.432252	−	0.516543i
$315$	−6.84139	−	27.1348i	−0.385469	−	1.52887i
$316$	11.6240	+	2.08180i	0.653903	+	0.117110i
$317$	17.8781	−	4.79041i	1.00413	−	0.269056i	0.280957	−	0.959720i	$-0.409348\pi$
$317$	17.8781	−	4.79041i	1.00413	−	0.269056i	0.723176	+	0.690664i	$0.242682\pi$
$318$	−2.62907	−	0.253217i	−0.147431	−	0.0141997i
$319$	−2.66205	−	4.61080i	−0.149046	−	0.258155i
$320$	−15.6676	−	15.9218i	−0.875843	−	0.890054i
$321$	0.0624869	+	0.110107i	0.00348768	+	0.00614557i
$322$	−11.6084	+	16.5313i	−0.646910	+	0.921251i
$323$	−6.20084	−	6.20084i	−0.345024	−	0.345024i
$324$	12.0098	−	13.4077i	0.667209	−	0.744870i
$325$	3.04449	−	3.04449i	0.168878	−	0.168878i
$326$	13.6564	−	2.38912i	0.756361	−	0.132321i
$327$	−12.2177	+	6.93369i	−0.675641	+	0.383434i
$328$	15.9216	−	4.19760i	0.879125	−	0.231774i
$329$	−10.5159	+	6.07136i	−0.579760	+	0.334725i
$330$	−25.1557	+	20.7357i	−1.38477	+	1.14146i
$331$	5.10146	+	19.0389i	0.280402	+	1.04647i	0.952134	+	0.305680i	$0.0988836\pi$
$331$	5.10146	+	19.0389i	0.280402	+	1.04647i	−0.671733	+	0.740794i	$0.734450\pi$
$332$	12.2362	+	17.5753i	0.671550	+	0.964570i
$333$	25.2856	−	6.37517i	1.38564	−	0.349357i
$334$	−1.06002	+	11.9317i	−0.0580016	+	0.652875i
$335$	2.62878	−	4.55319i	0.143626	−	0.248767i
$336$	−2.31161	+	23.0294i	−0.126109	+	1.25636i
$337$	3.29609	+	5.70899i	0.179549	+	0.310988i	0.941726	−	0.336380i	$-0.109203\pi$
$337$	3.29609	+	5.70899i	0.179549	+	0.310988i	−0.762177	+	0.647369i	$0.775869\pi$
$338$	−13.6325	+	6.33470i	−0.741511	+	0.344562i
$339$	−23.9234	+	6.22063i	−1.29934	+	0.337858i
$340$	−3.05588	−	36.0421i	−0.165729	−	1.95466i
$341$	−12.7852	+	12.7852i	−0.692360	+	0.692360i
$342$	5.36515	+	2.05154i	0.290114	+	0.110935i
$343$			9.48653i			0.512224i
$344$	−0.0744356	+	18.4999i	−0.00401330	+	0.997447i
$345$	−0.153230	+	20.6773i	−0.00824961	+	1.11323i
$346$	2.92418	−	8.00073i	0.157205	−	0.430122i
$347$	−3.20074	−	0.857635i	−0.171825	−	0.0460403i	0.171881	−	0.985118i	$-0.445016\pi$
$347$	−3.20074	−	0.857635i	−0.171825	−	0.0460403i	−0.343706	+	0.939077i	$0.611682\pi$
$348$	−3.64919	+	1.28664i	−0.195617	+	0.0689711i
$349$	−22.0000	+	5.89488i	−1.17763	+	0.315546i	−0.793987	−	0.607935i	$-0.791998\pi$
$349$	−22.0000	+	5.89488i	−1.17763	+	0.315546i	−0.383645	+	0.923480i	$0.625331\pi$
$350$	13.1601	+	1.16915i	0.703436	+	0.0624935i
$351$	−3.84508	−	7.01555i	−0.205235	−	0.374463i
$352$	25.3984	−	9.05183i	1.35374	−	0.482464i
$353$	14.2071	−	24.6074i	0.756167	−	1.30972i	−0.188626	−	0.982049i	$-0.560403\pi$
$353$	14.2071	−	24.6074i	0.756167	−	1.30972i	0.944792	−	0.327670i	$-0.106263\pi$
$354$	8.53318	+	18.7256i	0.453533	+	0.995254i
$355$	−2.87967	+	10.7471i	−0.152837	+	0.570396i
$356$	−4.21970	+	1.52304i	−0.223644	+	0.0807209i
$357$	−26.6972	+	26.3044i	−1.41296	+	1.39218i
$358$	16.4392	−	2.87594i	0.868838	−	0.151998i
$359$			7.35521i			0.388193i	0.980982	+	0.194097i	$0.0621775\pi$
$359$			7.35521i			0.388193i	−0.980982	+	0.194097i	$0.937823\pi$
$360$	11.4576	+	20.7381i	0.603871	+	1.09299i
$361$		−	17.1670i		−	0.903527i
$362$	−4.59920	−	26.2895i	−0.241728	−	1.38174i
$363$	−5.10811	−	19.6449i	−0.268106	−	1.03109i
$364$	9.31142	+	4.37243i	0.488051	+	0.229178i
$365$	−3.94194	+	14.7115i	−0.206330	+	0.770035i
$366$	−13.9293	−	9.93617i	−0.728094	−	0.519372i
$367$	−17.0496	+	29.5308i	−0.889984	+	1.54150i	−0.0500906	+	0.998745i	$0.515951\pi$
$367$	−17.0496	+	29.5308i	−0.889984	+	1.54150i	−0.839893	+	0.542752i	$0.817382\pi$
$368$	5.93549	−	16.0394i	0.309409	−	0.836110i
$369$	−17.4626	−	0.258827i	−0.909064	−	0.0134740i
$370$	−3.03740	+	34.1895i	−0.157907	+	1.77743i
$371$	−3.47948	+	0.932323i	−0.180646	+	0.0484038i
$372$	7.42818	+	10.8398i	0.385133	+	0.562016i
$373$	23.8179	+	6.38198i	1.23324	+	0.330447i	0.815842	−	0.578275i	$-0.196274\pi$
$373$	23.8179	+	6.38198i	1.23324	+	0.330447i	0.417402	+	0.908722i	$0.362941\pi$
$374$	41.0082	+	14.9881i	2.12048	+	0.775015i
$375$	−9.26828	+	5.25986i	−0.478612	+	0.271618i
$376$	7.29874	−	7.24024i	0.376404	−	0.373387i
$377$			1.71976i			0.0885720i
$378$	8.93768	−	22.8643i	0.459705	−	1.17601i
$379$	−2.66916	+	2.66916i	−0.137106	+	0.137106i	−0.772329	−	0.635223i	$-0.780908\pi$
$379$	−2.66916	+	2.66916i	−0.137106	+	0.137106i	0.635223	+	0.772329i	$0.280908\pi$
$380$	−4.87540	+	5.77873i	−0.250103	+	0.296443i
$381$	7.49212	−	27.1545i	0.383833	−	1.39117i
$382$	−1.06381	−	2.28936i	−0.0544292	−	0.117134i
$383$	−3.14570	−	5.44851i	−0.160738	−	0.278406i	0.774396	−	0.632701i	$-0.218054\pi$
$383$	−3.14570	−	5.44851i	−0.160738	−	0.278406i	−0.935133	+	0.354296i	$0.884721\pi$
$384$	−3.07815	−	19.3526i	−0.157081	−	0.987586i
$385$	−22.2307	+	38.5047i	−1.13298	+	1.96238i
$386$	23.1187	+	2.05387i	1.17671	+	0.104539i
$387$	5.35895	−	18.8763i	0.272411	−	0.959536i
$388$	−25.6003	−	4.58487i	−1.29966	−	0.232761i
$389$	−0.724164	−	2.70262i	−0.0367166	−	0.137028i	0.945135	−	0.326681i	$-0.105930\pi$
$389$	−0.724164	−	2.70262i	−0.0367166	−	0.137028i	−0.981851	+	0.189653i	$0.939264\pi$
$390$	10.3860	−	1.73775i	0.525914	−	0.0879943i
$391$	23.9836	−	13.8469i	1.21290	−	0.700269i
$392$	2.99981	+	11.3784i	0.151513	+	0.574695i
$393$	−26.4493	−	15.5330i	−1.33419	−	0.783534i
$394$	−1.18884	−	6.79554i	−0.0598930	−	0.342354i
$395$	11.6578	−	11.6578i	0.586568	−	0.586568i
$396$	−28.5292	+	1.99353i	−1.43365	+	0.100178i
$397$	−4.29700	−	4.29700i	−0.215660	−	0.215660i	0.591007	−	0.806667i	$-0.298731\pi$
$397$	−4.29700	−	4.29700i	−0.215660	−	0.215660i	−0.806667	+	0.591007i	$0.798731\pi$
$398$	−17.3712	−	12.1982i	−0.870742	−	0.611442i
$399$	7.83369	+	0.0580517i	0.392175	+	0.00290622i
$400$	−11.0263	+	1.88329i	−0.551313	+	0.0941646i
$401$	−6.63116	−	11.4855i	−0.331145	−	0.573559i	0.651592	−	0.758570i	$-0.274101\pi$
$401$	−6.63116	−	11.4855i	−0.331145	−	0.573559i	−0.982737	+	0.185010i	$0.940768\pi$
$402$	4.19700	−	1.91256i	0.209327	−	0.0953896i
$403$	5.64143	−	1.51162i	0.281020	−	0.0752990i
$404$	−14.9712	+	10.4232i	−0.744846	+	0.518575i
$405$	−5.78185	−	24.4558i	−0.287303	−	1.21522i
$406$	−4.04712	+	3.38669i	−0.200855	+	0.168079i
$407$	−35.8808	−	20.7158i	−1.77854	−	1.02684i
$408$	16.1790	−	27.2972i	0.800979	−	1.35141i
$409$	−10.6538	+	6.15100i	−0.526799	+	0.304147i	−0.739712	−	0.672924i	$-0.765038\pi$
$409$	−10.6538	+	6.15100i	−0.526799	+	0.304147i	0.212913	+	0.977071i	$0.431705\pi$
$410$	7.89128	−	21.5910i	0.389722	−	1.06630i
$411$	13.7130	−	13.5113i	0.676414	−	0.666462i
$412$	6.58851	+	5.55860i	0.324593	+	0.273853i
$413$	19.8452	+	19.8452i	0.976518	+	0.976518i
$414$	−10.6434	+	14.6892i	−0.523092	+	0.721933i
$415$	29.8981			1.46764
$416$	−8.56683	−	1.56987i	−0.420023	−	0.0769691i
$417$	−5.90553	+	10.0558i	−0.289195	+	0.492437i
$418$	−3.84580	−	8.27631i	−0.188104	−	0.404808i
$419$	7.82317	−	29.1965i	0.382187	−	1.42634i	−0.460367	−	0.887729i	$-0.652282\pi$
$419$	7.82317	−	29.1965i	0.382187	−	1.42634i	0.842554	−	0.538612i	$-0.181051\pi$
$420$	24.5424	+	21.0192i	1.19755	+	1.02563i
$421$	−5.75964	−	21.4953i	−0.280708	−	1.04762i	−0.951919	−	0.306350i	$-0.900892\pi$
$421$	−5.75964	−	21.4953i	−0.280708	−	1.04762i	0.671211	−	0.741266i	$-0.265774\pi$
$422$	−11.1657	−	13.3430i	−0.543537	−	0.649529i
$423$	−9.52319	+	5.31161i	−0.463033	+	0.258259i
$424$	2.64735	−	1.51428i	0.128567	−	0.0735399i
$425$	−15.6866	−	9.05668i	−0.760913	−	0.439314i
$426$	−7.53162	+	6.20827i	−0.364908	+	0.300792i
$427$	−22.5401	−	6.03961i	−1.09079	−	0.292277i
$428$	−0.132325	−	0.0621368i	−0.00639616	−	0.00300349i
$429$	−3.38069	+	12.2530i	−0.163221	+	0.591580i
$430$	21.1372	+	14.8427i	1.01933	+	0.715780i
$431$	15.3940			0.741505			0.370752	−	0.928732i	$-0.379100\pi$
$431$	15.3940			0.741505			0.370752	+	0.928732i	$0.379100\pi$
$432$	−2.38212	+	20.6477i	−0.114610	+	0.993411i
$433$	−17.2454			−0.828763			−0.414382	−	0.910103i	$-0.636002\pi$
$433$	−17.2454			−0.828763			−0.414382	+	0.910103i	$0.636002\pi$
$434$	14.6669	+	10.2992i	0.704033	+	0.494378i
$435$	−1.43679	+	5.20749i	−0.0688887	+	0.249680i
$436$	6.89483	−	14.6831i	0.330203	−	0.703191i
$437$	−5.59138	−	1.49821i	−0.267472	−	0.0716690i
$438$	−10.3099	+	8.49840i	−0.492626	+	0.406069i
$439$	−4.55070	−	2.62735i	−0.217193	−	0.125397i	0.387457	−	0.921888i	$-0.373354\pi$
$439$	−4.55070	−	2.62735i	−0.217193	−	0.125397i	−0.604650	+	0.796491i	$0.706687\pi$
$440$	9.88908	−	36.3214i	0.471443	−	1.73155i
$441$	0.184971	−	12.4796i	0.00880813	−	0.594267i
$442$	−9.05089	−	10.8159i	−0.430507	−	0.514458i
$443$	3.35032	+	12.5036i	0.159179	+	0.594062i	0.998711	+	0.0507532i	$0.0161622\pi$
$443$	3.35032	+	12.5036i	0.159179	+	0.594062i	−0.839533	+	0.543309i	$0.817171\pi$
$444$	−19.5868	+	22.8699i	−0.929550	+	1.08536i
$445$	−1.62102	+	6.04974i	−0.0768438	+	0.286785i
$446$	0.307863	+	0.662532i	0.0145777	+	0.0313718i
$447$	9.76916	−	16.6348i	0.462066	−	0.786798i
$448$	−13.1761	−	23.2519i	−0.622514	−	1.09855i
$449$	27.9740			1.32018			0.660088	−	0.751189i	$-0.270519\pi$
$449$	27.9740			1.32018			0.660088	+	0.751189i	$0.270519\pi$
$450$	11.8011	+	1.22494i	0.556308	+	0.0577441i
$451$	19.6207	+	19.6207i	0.923904	+	0.923904i
$452$	18.4057	−	21.8159i	0.865730	−	1.02613i
$453$	26.9323	−	26.5361i	1.26539	−	1.24678i
$454$	−4.94930	+	13.5416i	−0.232282	+	0.635537i
$455$	12.4376	−	7.18083i	0.583082	−	0.336643i
$456$	−6.42582	+	1.64328i	−0.300917	+	0.0769538i
$457$	35.2732	+	20.3650i	1.65001	+	0.952635i	0.977064	+	0.212944i	$0.0683053\pi$
$457$	35.2732	+	20.3650i	1.65001	+	0.952635i	0.672947	+	0.739690i	$0.265028\pi$
$458$	23.2244	−	19.4346i	1.08521	−	0.908118i
$459$	−24.3219	+	23.2638i	−1.13525	+	1.08586i
$460$	−13.6426	−	19.5954i	−0.636092	−	0.913639i
$461$	−36.8721	+	9.87984i	−1.71730	+	0.460150i	−0.977196	−	0.212339i	$-0.931892\pi$
$461$	−36.8721	+	9.87984i	−1.71730	+	0.460150i	−0.740107	+	0.672489i	$0.765225\pi$
$462$	−35.4926	+	16.1738i	−1.65126	+	0.752475i
$463$	−17.7637	−	30.7676i	−0.825549	−	1.42989i	−0.901499	−	0.432781i	$-0.857532\pi$
$463$	−17.7637	−	30.7676i	−0.825549	−	1.42989i	0.0759497	−	0.997112i	$-0.475801\pi$
$464$	2.58232	−	3.64614i	0.119881	−	0.169268i
$465$	18.3454	+	0.135949i	0.850746	+	0.00630447i
$466$	−26.9051	−	18.8930i	−1.24636	−	0.875201i
$467$	−17.1010	−	17.1010i	−0.791341	−	0.791341i	0.190371	−	0.981712i	$-0.439031\pi$
$467$	−17.1010	−	17.1010i	−0.791341	−	0.791341i	−0.981712	+	0.190371i	$0.939031\pi$
$468$	8.30267	+	4.05000i	0.383791	+	0.187211i
$469$	4.44794	−	4.44794i	0.205387	−	0.205387i
$470$	−2.47341	−	14.1383i	−0.114090	−	0.652149i
$471$	−12.6047	−	7.40239i	−0.580793	−	0.341084i
$472$	−20.5302	−	11.9635i	−0.944981	−	0.550666i
$473$	−26.9994	+	15.5881i	−1.24143	+	0.716742i
$474$	14.2647	−	2.38673i	0.655199	−	0.109626i
$475$	0.979914	+	3.65709i	0.0449615	+	0.167799i
$476$	7.62923	−	42.5990i	0.349685	−	1.95252i
$477$	−3.13668	+	0.790839i	−0.143619	+	0.0362101i
$478$	−0.618004	−	0.0549036i	−0.0282668	−	0.00251123i
$479$	−6.76619	+	11.7194i	−0.309155	+	0.535473i	−0.978178	−	0.207769i	$-0.933380\pi$
$479$	−6.76619	+	11.7194i	−0.309155	+	0.535473i	0.669023	+	0.743242i	$0.266713\pi$
$480$	−24.6291	−	11.9109i	−1.12416	−	0.543654i
$481$	6.69148	+	11.5900i	0.305105	+	0.528458i
$482$	9.14676	+	19.6842i	0.416624	+	0.896590i
$483$	−6.58003	+	23.8487i	−0.299402	+	1.08515i
$484$	17.9143	+	15.1139i	0.814285	+	0.686997i
$485$	−25.6747	+	25.6747i	−1.16583	+	1.16583i
$486$	8.32957	−	20.4112i	0.377837	−	0.925872i
$487$		−	16.1436i		−	0.731536i	−0.930706	−	0.365768i	$-0.880806\pi$
$487$		−	16.1436i		−	0.731536i	0.930706	−	0.365768i	$-0.119194\pi$
$488$	19.7568	+	0.0794927i	0.894347	+	0.00359847i
$489$	14.7673	−	8.38064i	0.667802	−	0.378986i
$490$	15.4300	+	5.63950i	0.697055	+	0.254766i
$491$	−34.9555	−	9.36630i	−1.57752	−	0.422695i	−0.639363	−	0.768905i	$-0.720802\pi$
$491$	−34.9555	−	9.36630i	−1.57752	−	0.422695i	−0.938157	+	0.346209i	$0.887469\pi$
$492$	16.6351	−	11.3996i	0.749969	−	0.513932i
$493$	6.98844	−	1.87255i	0.314744	−	0.0843353i
$494$	−0.260864	+	2.93633i	−0.0117368	+	0.132112i
$495$	−20.4737	+	34.2781i	−0.920227	+	1.54069i
$496$	−14.2305	−	5.26609i	−0.638967	−	0.236454i
$497$	−6.65589	+	11.5283i	−0.298557	+	0.517117i
$498$	21.3525	+	15.2314i	0.956828	+	0.682535i
$499$	−1.70347	+	6.35742i	−0.0762576	+	0.284597i	−0.993516	−	0.113696i	$-0.963731\pi$
$499$	−1.70347	+	6.35742i	−0.0762576	+	0.284597i	0.917258	+	0.398294i	$0.130398\pi$
$500$	5.23038	−	11.1385i	0.233910	−	0.498128i
$501$	3.69199	+	14.1987i	0.164946	+	0.634352i
$502$	2.76463	+	15.8029i	0.123392	+	0.705319i
$503$			8.67964i			0.387006i	0.981100	+	0.193503i	$0.0619849\pi$
$503$			8.67964i			0.387006i	−0.981100	+	0.193503i	$0.938015\pi$
$504$	6.81945	+	27.5143i	0.303763	+	1.22559i
$505$			25.4682i			1.13332i
$506$	28.3897	−	4.96662i	1.26208	−	0.220793i
$507$	−13.1146	+	12.9216i	−0.582439	+	0.573870i
$508$	11.0428	+	30.5950i	0.489946	+	1.35743i
$509$	0.894794	−	3.33942i	0.0396611	−	0.148017i	−0.943256	−	0.332067i	$-0.892254\pi$
$509$	0.894794	−	3.33942i	0.0396611	−	0.148017i	0.982917	+	0.184050i	$0.0589207\pi$
$510$	−18.3702	−	40.3125i	−0.813448	−	1.78507i
$511$	−9.11113	+	15.7809i	−0.403053	+	0.698108i
$512$	15.8057	+	16.1920i	0.698520	+	0.715590i
$513$	7.03321	+	0.156382i	0.310524	+	0.00690444i
$514$	−13.3242	−	1.18372i	−0.587704	−	0.0522118i
$515$	11.6246	−	3.11479i	0.512240	−	0.137254i
$516$	7.53415	+	21.3685i	0.331673	+	0.940697i
$517$	16.7347	+	4.48404i	0.735990	+	0.197208i
$518$	−14.0973	+	38.5711i	−0.619402	+	1.69472i
$519$	0.0773105	−	10.4325i	0.00339355	−	0.457937i
$520$	−8.63251	+	8.56332i	−0.378560	+	0.375526i
$521$		−	15.7843i		−	0.691524i	−0.938322	−	0.345762i	$-0.887620\pi$
$521$		−	15.7843i		−	0.691524i	0.938322	−	0.345762i	$-0.112380\pi$
$522$	−3.67904	+	2.98710i	−0.161027	+	0.130742i
$523$	6.62449	−	6.62449i	0.289669	−	0.289669i	−0.547280	−	0.836949i	$-0.684337\pi$
$523$	6.62449	−	6.62449i	0.289669	−	0.289669i	0.836949	+	0.547280i	$0.184337\pi$
$524$	35.2916	−	2.99225i	1.54172	−	0.130717i
$525$	15.6605	−	4.07207i	0.683479	−	0.177720i
$526$	−24.0521	+	11.1764i	−1.04872	+	0.487315i
$527$	−12.2853	−	21.2787i	−0.535155	−	0.926916i
$528$	25.5662	−	20.9019i	1.11263	−	0.909637i
$529$	−2.35965	+	4.08703i	−0.102593	+	0.177697i
$530$	0.376790	−	4.24120i	0.0163667	−	0.184226i
$531$	17.5552	+	18.0834i	0.761830	+	0.784753i
$532$	−7.42379	+	5.16857i	−0.321862	+	0.224086i
$533$	−2.31978	−	8.65755i	−0.100481	−	0.375000i
$534$	−4.23969	+	3.49475i	−0.183469	+	0.151233i
$535$	−0.176751	+	0.102047i	−0.00764160	+	0.00441188i
$536$	−2.68141	+	4.60148i	−0.115819	+	0.198754i
$537$	17.7764	−	10.0883i	0.767110	−	0.435344i
$538$	26.7155	−	4.67372i	1.15179	−	0.201498i
$539$	−14.0219	+	14.0219i	−0.603967	+	0.603967i
$540$	21.7572	+	19.2001i	0.936282	+	0.826241i
$541$	32.2832	+	32.2832i	1.38796	+	1.38796i	0.829587	+	0.558377i	$0.188576\pi$
$541$	32.2832	+	32.2832i	1.38796	+	1.38796i	0.558377	+	0.829587i	$0.311424\pi$
$542$	−24.8879	+	35.4423i	−1.06903	+	1.52238i
$543$	−16.1332	−	28.4280i	−0.692343	−	1.21996i
$544$	2.94859	+	36.5217i	0.126420	+	1.56585i
$545$	−11.3234	−	19.6126i	−0.485040	−	0.840113i
$546$	12.5408	+	1.20786i	0.536698	+	0.0516916i
$547$	−7.43060	+	1.99102i	−0.317710	+	0.0851300i	−0.414150	−	0.910209i	$-0.635921\pi$
$547$	−7.43060	+	1.99102i	−0.317710	+	0.0851300i	0.0964402	+	0.995339i	$0.469254\pi$
$548$	−3.91876	+	21.8810i	−0.167401	+	0.934711i
$549$	−20.1587	−	5.72304i	−0.860354	−	0.244253i
$550$	−12.0975	−	14.4566i	−0.515839	−	0.616430i
$551$	−1.30966	−	0.756135i	−0.0557936	−	0.0322124i
$552$	0.239490	−	20.9447i	0.0101934	−	0.891465i
$553$	17.0825	−	9.86259i	0.726422	−	0.419400i
$554$	−27.7399	−	10.1386i	−1.17855	−	0.430750i
$555$	10.5791	+	40.6854i	0.449058	+	1.72700i
$556$	−1.13763	−	13.4176i	−0.0482464	−	0.569035i
$557$	24.4143	+	24.4143i	1.03447	+	1.03447i	0.999384	+	0.0350828i	$0.0111695\pi$
$557$	24.4143	+	24.4143i	1.03447	+	1.03447i	0.0350828	+	0.999384i	$0.488830\pi$
$558$	13.0325	+	9.44301i	0.551712	+	0.399754i
$559$	10.0704			0.425931
$560$	−37.1520	−	3.45131i	−1.56996	−	0.145844i
$561$	53.4726	+	0.396260i	2.25761	+	0.0167301i
$562$	−15.7774	+	7.33138i	−0.665530	+	0.309256i
$563$	3.30278	−	12.3261i	0.139196	−	0.519485i	−0.860750	−	0.509028i	$-0.830005\pi$
$563$	3.30278	−	12.3261i	0.139196	−	0.519485i	0.999945	−	0.0104567i	$-0.00332852\pi$
$564$	5.43618	−	11.3572i	0.228905	−	0.478226i
$565$	−10.3137	−	38.4913i	−0.433901	−	1.61934i
$566$	−14.3736	+	12.0281i	−0.604169	+	0.505578i
$567$	0.891083	−	30.0532i	0.0374220	−	1.26211i
$568$	2.96079	−	10.8746i	0.124232	−	0.456289i
$569$	22.2747	+	12.8603i	0.933803	+	0.539132i	0.888012	−	0.459819i	$-0.152086\pi$
$569$	22.2747	+	12.8603i	0.933803	+	0.539132i	0.0457910	+	0.998951i	$0.485419\pi$
$570$	−3.24309	+	8.67337i	−0.135838	+	0.363287i
$571$	33.6207	+	9.00865i	1.40698	+	0.377000i	0.880848	−	0.473400i	$-0.156973\pi$
$571$	33.6207	+	9.00865i	1.40698	+	0.377000i	0.526136	+	0.850400i	$0.323640\pi$
$572$	−4.98288	−	13.8055i	−0.208345	−	0.577235i
$573$	−2.16997	−	2.20238i	−0.0906520	−	0.0920056i
$574$	15.8055	−	22.5084i	0.659711	−	0.939480i
$575$	−11.9566			−0.498626
$576$	−11.5216	−	21.0536i	−0.480067	−	0.877232i
$577$	−26.7695			−1.11443			−0.557215	−	0.830369i	$-0.688130\pi$
$577$	−26.7695			−1.11443			−0.557215	+	0.830369i	$0.688130\pi$
$578$	−20.2804	+	28.8809i	−0.843554	+	1.20129i
$579$	27.5112	−	7.15352i	1.14333	−	0.297290i
$580$	−2.11771	−	5.86729i	−0.0879333	−	0.243626i
$581$	34.5523	+	9.25826i	1.43347	+	0.384097i
$582$	−31.4160	+	5.25643i	−1.30224	+	0.217886i
$583$	4.45101	+	2.56979i	0.184342	+	0.106430i
$584$	4.05298	−	14.8861i	0.167714	−	0.615991i
$585$	11.2634	−	6.28225i	0.465686	−	0.259739i
$586$	−23.9556	+	20.0465i	−0.989598	+	0.828112i
$587$	9.79668	+	36.5617i	0.404352	+	1.50906i	0.805247	+	0.592939i	$0.202033\pi$
$587$	9.79668	+	36.5617i	0.404352	+	1.50906i	−0.400895	+	0.916124i	$0.631301\pi$
$588$	8.14669	+	11.8883i	0.335964	+	0.490264i
$589$	−1.32924	+	4.96080i	−0.0547704	+	0.204406i
$590$	−30.0845	+	13.9796i	−1.23856	+	0.575529i
$591$	−4.17026	−	7.34833i	−0.171542	−	0.302270i
$592$	3.21611	−	34.6202i	0.132181	−	1.42288i
$593$	−7.98596			−0.327944			−0.163972	−	0.986465i	$-0.552431\pi$
$593$	−7.98596			−0.327944			−0.163972	+	0.986465i	$0.552431\pi$
$594$	−32.0846	+	14.0504i	−1.31645	+	0.576493i
$595$	−42.7228	−	42.7228i	−1.75146	−	1.75146i
$596$	1.88192	+	22.1960i	0.0770863	+	0.909183i
$597$	−25.0605	−	6.91437i	−1.02566	−	0.282986i
$598$	−8.74383	−	3.19578i	−0.357562	−	0.130685i
$599$	1.64879	−	0.951932i	0.0673679	−	0.0388949i	−0.465938	−	0.884818i	$-0.654283\pi$
$599$	1.64879	−	0.951932i	0.0673679	−	0.0388949i	0.533306	+	0.845923i	$0.320950\pi$
$600$	−11.9420	+	6.71386i	−0.487531	+	0.274092i
$601$	−11.7530	−	6.78561i	−0.479416	−	0.276791i	0.240757	−	0.970585i	$-0.422604\pi$
$601$	−11.7530	−	6.78561i	−0.479416	−	0.276791i	−0.720173	+	0.693794i	$0.755938\pi$
$602$	19.8314	+	23.6986i	0.808268	+	0.965884i
$603$	4.05307	−	3.93467i	0.165054	−	0.160232i
$604$	−7.69643	+	42.9743i	−0.313163	+	1.74860i
$605$	31.6074	−	8.46917i	1.28502	−	0.344321i
$606$	−12.9746	+	18.1888i	−0.527057	+	0.738868i
$607$	−3.16527	−	5.48241i	−0.128474	−	0.222524i	0.794611	−	0.607119i	$-0.207675\pi$
$607$	−3.16527	−	5.48241i	−0.128474	−	0.222524i	−0.923086	+	0.384594i	$0.874341\pi$
$608$	4.96214	−	5.83375i	0.201241	−	0.236590i
$609$	−3.27300	+	5.57321i	−0.132629	+	0.225838i
$610$	15.8511	−	22.5733i	0.641794	−	0.913966i
$611$	−3.95712	−	3.95712i	−0.160088	−	0.160088i
$612$	7.41734	−	38.1487i	0.299828	−	1.54207i
$613$	−1.83081	+	1.83081i	−0.0739458	+	0.0739458i	−0.743112	−	0.669167i	$-0.766651\pi$
$613$	−1.83081	+	1.83081i	−0.0739458	+	0.0739458i	0.669167	+	0.743112i	$0.266651\pi$
$614$	7.07703	−	1.23809i	0.285606	−	0.0499651i
$615$	0.208632	−	28.1535i	0.00841285	−	1.13526i
$616$	22.6758	−	38.9131i	0.913632	−	1.56786i
$617$	3.82758	−	2.20985i	0.154092	−	0.0889653i	−0.420971	−	0.907074i	$-0.638311\pi$
$617$	3.82758	−	2.20985i	0.154092	−	0.0889653i	0.575064	+	0.818109i	$0.304977\pi$
$618$	9.88878	+	3.69754i	0.397785	+	0.148737i
$619$	3.75899	+	14.0287i	0.151087	+	0.563863i	0.999409	+	0.0343824i	$0.0109464\pi$
$619$	3.75899	+	14.0287i	0.151087	+	0.563863i	−0.848322	+	0.529480i	$0.822387\pi$
$620$	−17.3854	+	12.1040i	−0.698216	+	0.486110i
$621$	−6.22570	+	21.3265i	−0.249829	+	0.855803i
$622$	1.24661	−	14.0320i	0.0499844	−	0.562632i
$623$	−3.74672	+	6.48952i	−0.150109	+	0.259997i
$624$	−10.5276	+	1.71794i	−0.421443	+	0.0687725i
$625$	−15.5810	−	26.9872i	−0.623242	−	1.07949i
$626$	32.8154	−	15.2485i	1.31157	−	0.609453i
$627$	−7.84474	−	7.96187i	−0.313289	−	0.317967i
$628$	16.8186	−	1.42599i	0.671134	−	0.0569031i
$629$	39.8114	−	39.8114i	1.58738	−	1.58738i
$630$	36.9650	+	14.1348i	1.47272	+	0.563144i
$631$			33.6255i			1.33861i	0.742987	+	0.669305i	$0.233408\pi$
$631$			33.6255i			1.33861i	−0.742987	+	0.669305i	$0.766592\pi$
$632$	−11.8564	+	11.7614i	−0.471622	+	0.467842i
$633$	−18.3745	−	10.7908i	−0.730320	−	0.428898i
$634$	−8.98546	+	24.5847i	−0.356858	+	0.976384i
$635$	43.8637	+	11.7532i	1.74068	+	0.466413i
$636$	2.42974	−	2.83701i	0.0963457	−	0.112495i
$637$	6.18711	−	1.65783i	0.245142	−	0.0656857i
$638$	7.49987	+	0.666291i	0.296923	+	0.0263787i
$639$	−6.12985	+	10.2629i	−0.242493	+	0.405993i
$640$	31.1605	−	5.19330i	1.23173	−	0.205283i
$641$	−22.9601	+	39.7681i	−0.906871	+	1.57075i	−0.0884843	+	0.996078i	$0.528202\pi$
$641$	−22.9601	+	39.7681i	−0.906871	+	1.57075i	−0.818386	+	0.574668i	$0.805131\pi$
$642$	−0.178218	−	0.0171649i	−0.00703370	−	0.000677445i
$643$	6.92565	−	25.8469i	0.273121	−	1.01930i	−0.683969	−	0.729511i	$-0.739748\pi$
$643$	6.92565	−	25.8469i	0.273121	−	1.01930i	0.957090	−	0.289790i	$-0.0935855\pi$
$644$	−9.69845	−	26.8703i	−0.382173	−	1.05884i
$645$	30.4934	+	8.41337i	1.20068	+	0.331276i
$646$	12.2162	−	2.13715i	0.480638	−	0.0840850i
$647$			11.4351i			0.449559i	0.974410	+	0.224780i	$0.0721662\pi$
$647$			11.4351i			0.449559i	−0.974410	+	0.224780i	$0.927834\pi$
$648$	5.75711	+	24.7963i	0.226161	+	0.974090i
$649$		−	40.0431i		−	1.57183i
$650$	1.04930	+	5.99789i	0.0411568	+	0.235256i
$651$	21.1590	+	5.83794i	0.829288	+	0.228807i
$652$	−8.33368	+	17.7472i	−0.326372	+	0.695034i
$653$	5.73613	−	21.4075i	0.224472	−	0.837741i	−0.758143	−	0.652088i	$-0.773893\pi$
$653$	5.73613	−	21.4075i	0.224472	−	0.837741i	0.982615	−	0.185653i	$-0.0594401\pi$
$654$	1.90466	−	19.7755i	0.0744780	−	0.773282i
$655$	24.7239	−	42.8230i	0.966041	−	1.67323i
$656$	−8.08154	+	21.8386i	−0.315531	+	0.852654i
$657$	−8.39105	+	14.0487i	−0.327366	+	0.548091i
$658$	1.51962	−	17.1050i	0.0592408	−	0.666823i
$659$	26.7345	−	7.16348i	1.04143	−	0.279050i	0.302723	−	0.953079i	$-0.402104\pi$
$659$	26.7345	−	7.16348i	1.04143	−	0.279050i	0.738705	+	0.674029i	$0.235438\pi$
$660$	−3.55446	−	45.9665i	−0.138357	−	1.78924i
$661$	9.68293	+	2.59453i	0.376622	+	0.100916i	0.442164	−	0.896934i	$-0.354211\pi$
$661$	9.68293	+	2.59453i	0.376622	+	0.100916i	−0.0655417	+	0.997850i	$0.520878\pi$
$662$	−26.1810	−	9.56890i	−1.01755	−	0.371906i
$663$	−14.8943	−	8.74704i	−0.578448	−	0.339707i
$664$	−30.2856	−	0.121856i	−1.17531	−	0.00472894i
$665$			12.6289i			0.489729i
$666$	−13.1716	+	34.4459i	−0.510387	+	1.33475i
$667$	3.37700	−	3.37700i	0.130758	−	0.130758i
$668$	−12.9479	−	10.9239i	−0.500969	−	0.422658i
$669$	0.627984	+	0.637360i	0.0242792	+	0.0246418i
$670$	3.13326	+	6.74290i	0.121048	+	0.260501i
$671$	16.6472	+	28.8337i	0.642656	+	1.11311i
$672$	−24.7748	−	21.3916i	−0.955707	−	0.825201i
$673$	−16.7789	+	29.0620i	−0.646781	+	1.12026i	0.337106	+	0.941467i	$0.390552\pi$
$673$	−16.7789	+	29.0620i	−0.646781	+	1.12026i	−0.983887	+	0.178791i	$0.942782\pi$
$674$	−9.28616	−	0.824985i	−0.357690	−	0.0317773i
$675$	14.1160	−	3.44795i	0.543324	−	0.132712i
$676$	3.74774	−	20.9261i	0.144144	−	0.804850i
$677$	6.92612	+	25.8486i	0.266192	+	0.993443i	0.961517	+	0.274747i	$0.0885941\pi$
$677$	6.92612	+	25.8486i	0.266192	+	0.993443i	−0.695324	+	0.718696i	$0.744739\pi$
$678$	12.2433	−	32.7438i	0.470202	−	1.25752i
$679$	−37.6218	+	21.7210i	−1.44379	+	0.833575i
$680$	44.1975	+	25.7551i	1.69490	+	0.987664i
$681$	−0.130851	+	17.6575i	−0.00501423	+	0.676636i
$682$	−4.40649	−	25.1880i	−0.168733	−	0.964497i
$683$	−9.62993	+	9.62993i	−0.368479	+	0.368479i	−0.866922	−	0.498443i	$-0.833905\pi$
$683$	−9.62993	+	9.62993i	−0.368479	+	0.368479i	0.498443	+	0.866922i	$0.333905\pi$
$684$	−6.73472	+	4.54213i	−0.257508	+	0.173673i
$685$	21.9446	+	21.9446i	0.838460	+	0.838460i
$686$	−10.9794	−	7.70982i	−0.419195	−	0.294362i
$687$	18.7821	−	31.9819i	0.716583	−	1.22019i
$688$	−21.3507	−	15.1212i	−0.813987	−	0.576492i
$689$	−0.830078	−	1.43774i	−0.0316235	−	0.0547734i
$690$	−23.8067	−	16.9821i	−0.906307	−	0.646496i
$691$	−36.8896	+	9.88454i	−1.40335	+	0.376025i	−0.879545	−	0.475815i	$-0.842153\pi$
$691$	−36.8896	+	9.88454i	−1.40335	+	0.376025i	−0.523801	+	0.851841i	$0.675486\pi$
$692$	6.88325	+	9.88664i	0.261662	+	0.375834i
$693$	−34.2754	+	33.2742i	−1.30201	+	1.26398i
$694$	3.59388	−	3.00742i	0.136422	−	0.114160i
$695$	−16.2810	−	9.39985i	−0.617574	−	0.356557i
$696$	1.47663	−	5.26913i	0.0559716	−	0.199726i
$697$	−32.6551	+	18.8534i	−1.23690	+	0.714125i
$698$	11.0571	−	30.2529i	0.418518	−	1.14509i
$699$	−38.8144	−	10.7092i	−1.46810	−	0.405059i
$700$	−12.0485	+	14.2809i	−0.455390	+	0.539766i
$701$	−24.7308	−	24.7308i	−0.934070	−	0.934070i	0.0638873	−	0.997957i	$-0.479650\pi$
$701$	−24.7308	−	24.7308i	−0.934070	−	0.934070i	−0.997957	+	0.0638873i	$0.979650\pi$
$702$	11.2445	+	1.25146i	0.424397	+	0.0472332i
$703$	−11.7683			−0.443851
$704$	−10.1653	+	36.7518i	−0.383118	+	1.38513i
$705$	−8.67631	−	15.2883i	−0.326769	−	0.575792i
$706$	16.9335	+	36.4415i	0.637301	+	1.37150i
$707$	−7.88649	+	29.4328i	−0.296602	+	1.10693i
$708$	−28.6074	−	5.34250i	−1.07513	−	0.200783i
$709$	−7.27509	−	27.1510i	−0.273222	−	1.01968i	−0.957024	−	0.290010i	$-0.906341\pi$
$709$	−7.27509	−	27.1510i	−0.273222	−	1.01968i	0.683802	−	0.729668i	$-0.260325\pi$
$710$	−10.0980	−	12.0671i	−0.378970	−	0.452871i
$711$	15.4699	−	8.62842i	0.580166	−	0.323591i
$712$	1.66669	−	6.12153i	0.0624617	−	0.229414i
$713$	−14.0461	−	8.10951i	−0.526030	−	0.303704i
$714$	−8.74672	−	52.2763i	−0.327338	−	1.95639i
$715$	−19.7927	−	5.30345i	−0.740207	−	0.198338i
$716$	−10.0318	+	21.3635i	−0.374906	+	0.798391i
$717$	−0.735423	+	0.191226i	−0.0274649	+	0.00714148i
$718$	−8.51267	−	5.97767i	−0.317690	−	0.223085i
$719$	12.7928			0.477091			0.238546	−	0.971131i	$-0.423329\pi$
$719$	12.7928			0.477091			0.238546	+	0.971131i	$0.423329\pi$
$720$	−33.3134	−	3.59343i	−1.24152	−	0.133919i
$721$	14.3987			0.536234
$722$	19.8685	+	13.9519i	0.739430	+	0.519234i
$723$	18.6577	+	18.9363i	0.693888	+	0.704249i
$724$	34.1644	+	16.0428i	1.26971	+	0.596227i
$725$	−3.01722	−	0.808460i	−0.112057	−	0.0300255i
$726$	26.8877	+	10.0537i	0.997898	+	0.373127i
$727$	3.44828	+	1.99086i	0.127890	+	0.0738371i	0.562580	−	0.826743i	$-0.309809\pi$
$727$	3.44828	+	1.99086i	0.127890	+	0.0738371i	−0.434690	+	0.900580i	$0.643142\pi$
$728$	−12.6280	+	7.22320i	−0.468026	+	0.267710i
$729$	1.20009	−	26.9733i	0.0444477	−	0.999012i
$730$	−13.8230	−	16.5185i	−0.511610	−	0.611377i
$731$	−10.9650	−	40.9221i	−0.405557	−	1.51356i
$732$	22.8203	−	8.04602i	0.843462	−	0.297389i
$733$	9.71206	−	36.2459i	0.358723	−	1.33877i	−0.517011	−	0.855979i	$-0.672955\pi$
$733$	9.71206	−	36.2459i	0.358723	−	1.33877i	0.875734	−	0.482794i	$-0.160378\pi$
$734$	−20.3216	−	43.7328i	−0.750082	−	1.61421i
$735$	20.1199	+	0.149099i	0.742133	+	0.00549959i
$736$	13.7396	+	19.9049i	0.506448	+	0.733705i
$737$	−8.97493			−0.330596
$738$	14.4916	−	20.0002i	0.533443	−	0.736219i
$739$	3.06425	+	3.06425i	0.112720	+	0.112720i	0.761217	−	0.648497i	$-0.224602\pi$
$739$	3.06425	+	3.06425i	0.112720	+	0.112720i	−0.648497	+	0.761217i	$0.724602\pi$
$740$	−37.1012	−	31.3016i	−1.36387	−	1.15067i
$741$	0.908575	+	3.49422i	0.0333774	+	0.128363i
$742$	1.74878	−	4.78474i	0.0641996	−	0.175653i
$743$	−30.1059	+	17.3817i	−1.10448	+	0.637671i	−0.937394	−	0.348272i	$-0.886769\pi$
$743$	−30.1059	+	17.3817i	−1.10448	+	0.637671i	−0.167085	+	0.985943i	$0.553435\pi$
$744$	−18.5826	−	0.212481i	−0.681270	−	0.00778993i
$745$	26.9327	+	15.5496i	0.986738	+	0.569693i
$746$	−26.7434	+	22.3793i	−0.979145	+	0.819365i
$747$	30.9018	+	8.77298i	1.13064	+	0.320986i
$748$	−50.6746	+	35.2805i	−1.85285	+	1.28998i
$749$	−0.235865	+	0.0631998i	−0.00861831	+	0.00230927i
$750$	1.44486	−	15.0015i	0.0527589	−	0.547779i
$751$	−7.10890	−	12.3130i	−0.259407	−	0.449307i	0.706676	−	0.707537i	$-0.250194\pi$
$751$	−7.10890	−	12.3130i	−0.259407	−	0.449307i	−0.966083	+	0.258231i	$0.916861\pi$
$752$	2.44784	+	14.3316i	0.0892635	+	0.522618i
$753$	9.69789	+	17.0884i	0.353411	+	0.622737i
$754$	−1.99039	−	1.39767i	−0.0724858	−	0.0509001i
$755$	43.0991	+	43.0991i	1.56854	+	1.56854i
$756$	19.1986	+	28.9263i	0.698246	+	1.05204i
$757$	2.11199	−	2.11199i	0.0767615	−	0.0767615i	−0.667684	−	0.744445i	$-0.732714\pi$
$757$	2.11199	−	2.11199i	0.0767615	−	0.0767615i	0.744445	+	0.667684i	$0.232714\pi$
$758$	−0.919938	−	5.25846i	−0.0334137	−	0.190996i
$759$	30.6991	−	17.4221i	1.11431	−	0.632382i
$760$	−2.72581	−	10.3391i	−0.0988755	−	0.375038i
$761$	−16.3519	+	9.44076i	−0.592755	+	0.342227i	−0.766186	−	0.642619i	$-0.777848\pi$
$761$	−16.3519	+	9.44076i	−0.592755	+	0.342227i	0.173431	+	0.984846i	$0.444515\pi$
$762$	25.3387	+	30.7399i	0.917926	+	1.11359i
$763$	−7.01279	−	26.1721i	−0.253880	−	0.947493i
$764$	3.51419	+	0.629371i	0.127139	+	0.0227699i
$765$	−37.7928	−	38.9300i	−1.36640	−	1.40752i
$766$	8.86247	+	0.787345i	0.320214	+	0.0284479i
$767$	−6.46724	+	11.2016i	−0.233519	+	0.404466i
$768$	24.8998	+	12.1656i	0.898493	+	0.438988i
$769$	3.50579	+	6.07221i	0.126422	+	0.218970i	0.922288	−	0.386503i	$-0.126317\pi$
$769$	3.50579	+	6.07221i	0.126422	+	0.218970i	−0.795866	+	0.605473i	$0.792984\pi$
$770$	−26.4969	−	57.0224i	−0.954883	−	2.05494i
$771$	−15.8557	+	4.12284i	−0.571030	+	0.148481i
$772$	−21.1659	+	25.0876i	−0.761778	+	0.902922i
$773$	8.54407	−	8.54407i	0.307309	−	0.307309i	−0.536556	−	0.843865i	$-0.680275\pi$
$773$	8.54407	−	8.54407i	0.307309	−	0.307309i	0.843865	+	0.536556i	$0.180275\pi$
$774$	17.4915	+	21.5433i	0.628719	+	0.774357i
$775$			10.6082i			0.381057i
$776$	26.1121	−	25.9028i	0.937369	−	0.929856i
$777$	−0.372710	+	50.2947i	−0.0133709	+	1.80431i
$778$	3.71646	+	1.35833i	0.133241	+	0.0486984i
$779$	7.61302	+	2.03990i	0.272765	+	0.0730871i
$780$	−6.42959	+	13.4327i	−0.230216	+	0.480966i
$781$	18.3458	−	4.91575i	0.656465	−	0.175899i
$782$	−3.46578	+	39.0113i	−0.123936	+	1.39504i
$783$	−3.01305	+	4.96071i	−0.107678	+	0.177281i
$784$	−15.6069	−	5.77547i	−0.557391	−	0.206267i
$785$	11.7824	−	20.4077i	0.420532	−	0.728383i
$786$	39.4730	−	17.9877i	1.40796	−	0.641600i
$787$	−6.16205	+	22.9971i	−0.219653	+	0.819758i	0.764823	+	0.644241i	$0.222826\pi$
$787$	−6.16205	+	22.9971i	−0.219653	+	0.819758i	−0.984476	+	0.175517i	$0.943840\pi$
$788$	8.83112	+	4.14689i	0.314596	+	0.147727i
$789$	−23.1383	+	22.7979i	−0.823745	+	0.811626i
$790$	4.01792	+	22.9668i	0.142951	+	0.817122i
$791$		−	47.6769i		−	1.69519i
$792$	20.8788	−	34.6389i	0.741895	−	1.23084i
$793$		−	10.7545i		−	0.381904i
$794$	8.46542	−	1.48098i	0.300427	−	0.0525580i
$795$	−1.31234	−	5.04702i	−0.0465439	−	0.178999i
$796$	28.2357	−	10.1912i	1.00079	−	0.361219i
$797$	1.78931	−	6.67778i	0.0633804	−	0.236539i	−0.926968	−	0.375141i	$-0.877594\pi$
$797$	1.78931	−	6.67778i	0.0633804	−	0.236539i	0.990348	+	0.138602i	$0.0442609\pi$
$798$	−6.43372	+	9.01927i	−0.227751	+	0.319279i
$799$	−11.7716	+	20.3889i	−0.416448	+	0.721309i
$800$	6.78152	−	14.2920i	0.239763	−	0.505299i
$801$	−3.45061	+	5.77717i	−0.121921	+	0.204126i
$802$	18.6822	+	1.65973i	0.659691	+	0.0586071i
$803$	25.1133	−	6.72909i	0.886229	−	0.237464i
$804$	−1.19742	+	6.41183i	−0.0422299	+	0.226128i
$805$	−38.5237	−	10.3224i	−1.35778	−	0.363817i
$806$	−2.83537	+	7.75772i	−0.0998715	+	0.273254i
$807$	28.8887	−	16.3947i	1.01693	−	0.577119i
$808$	0.103801	−	25.7983i	0.00365171	−	0.907580i
$809$		−	39.0505i		−	1.37294i	−0.727157	−	0.686471i	$-0.759159\pi$
$809$		−	39.0505i		−	1.37294i	0.727157	−	0.686471i	$-0.240841\pi$
$810$	33.0033	+	13.1838i	1.15962	+	0.463231i
$811$	−2.40853	+	2.40853i	−0.0845748	+	0.0845748i	−0.748129	−	0.663554i	$-0.769047\pi$
$811$	−2.40853	+	2.40853i	−0.0845748	+	0.0845748i	0.663554	+	0.748129i	$0.269047\pi$
$812$	−0.630506	−	7.43641i	−0.0221264	−	0.260967i
$813$	−14.1073	+	51.1306i	−0.494765	+	1.79323i
$814$	53.1365	−	24.6912i	1.86243	−	0.865428i
$815$	13.6864	+	23.7055i	0.479413	+	0.830367i
$816$	18.4440	+	40.9098i	0.645669	+	1.43213i
$817$	−4.42769	+	7.66898i	−0.154905	+	0.268304i
$818$	1.53955	−	17.3294i	0.0538291	−	0.605908i
$819$	14.9622	−	3.77235i	0.522820	−	0.131817i
$820$	18.5753	+	26.6803i	0.648678	+	0.931718i
$821$	7.66611	+	28.6103i	0.267549	+	0.998506i	0.960672	+	0.277687i	$0.0895677\pi$
$821$	7.66611	+	28.6103i	0.267549	+	0.998506i	−0.693123	+	0.720820i	$0.743766\pi$
$822$	4.49276	+	26.8518i	0.156703	+	0.936564i
$823$	22.1086	−	12.7644i	0.770659	−	0.444940i	−0.0624509	−	0.998048i	$-0.519892\pi$
$823$	22.1086	−	12.7644i	0.770659	−	0.444940i	0.833110	+	0.553108i	$0.186558\pi$
$824$	−11.7879	+	3.10778i	−0.410651	+	0.108265i
$825$	−19.9079	−	11.6914i	−0.693104	−	0.407042i
$826$	−39.0966	+	6.83973i	−1.36034	+	0.237985i
$827$	5.10050	−	5.10050i	0.177362	−	0.177362i	−0.612843	−	0.790205i	$-0.709974\pi$
$827$	5.10050	−	5.10050i	0.177362	−	0.177362i	0.790205	+	0.612843i	$0.209974\pi$
$828$	−8.35077	−	24.2563i	−0.290209	−	0.842966i
$829$	1.30033	+	1.30033i	0.0451624	+	0.0451624i	0.729327	−	0.684165i	$-0.239833\pi$
$829$	1.30033	+	1.30033i	0.0451624	+	0.0451624i	−0.684165	+	0.729327i	$0.739833\pi$
$830$	−24.2986	+	34.6031i	−0.843416	+	1.20109i
$831$	−36.1714	−	0.268049i	−1.25477	−	0.00929850i
$832$	8.77928	−	8.63911i	0.304367	−	0.299507i
$833$	−13.4736	−	23.3370i	−0.466833	−	0.808578i
$834$	−6.83881	−	15.0074i	−0.236808	−	0.519663i
$835$	−22.8449	+	6.12126i	−0.790579	+	0.211835i
$836$	12.7043	+	2.27526i	0.439386	+	0.0786914i
$837$	18.9213	+	5.52357i	0.654017	+	0.190923i
$838$	27.4330	+	32.7826i	0.947658	+	1.13246i
$839$	−28.6072	−	16.5164i	−0.987631	−	0.570209i	−0.0830657	−	0.996544i	$-0.526471\pi$
$839$	−28.6072	−	16.5164i	−0.987631	−	0.570209i	−0.904565	+	0.426335i	$0.859804\pi$
$840$	−44.2728	+	11.3219i	−1.52756	+	0.390644i
$841$	−24.0342	+	13.8762i	−0.828766	+	0.478488i
$842$	29.5589	+	10.8035i	1.01867	+	0.372312i
$843$	−15.1780	+	14.9547i	−0.522757	+	0.515067i
$844$	24.5173	−	2.07873i	0.843920	−	0.0715529i
$845$	−20.9869	−	20.9869i	−0.721972	−	0.721972i
$846$	1.59213	−	15.3386i	0.0547386	−	0.527353i
$847$	39.1502			1.34522
$848$	−0.398959	+	4.29463i	−0.0137003	+	0.147478i
$849$	−11.6243	+	19.7937i	−0.398945	+	0.679317i
$850$	23.2306	−	10.7947i	0.796804	−	0.370256i
$851$	9.61896	−	35.8984i	0.329734	−	1.23058i
$852$	−1.06421	−	13.7624i	−0.0364592	−	0.471492i
$853$	−4.12451	−	15.3929i	−0.141221	−	0.527043i	−0.999895	−	0.0145204i	$-0.995378\pi$
$853$	−4.12451	−	15.3929i	−0.141221	−	0.527043i	0.858674	−	0.512522i	$-0.171289\pi$
$854$	25.3087	−	21.1787i	0.866046	−	0.724721i
$855$	−0.168076	+	11.3397i	−0.00574806	+	0.387810i
$856$	0.179457	−	0.102649i	0.00613372	−	0.00350847i
$857$	−13.6603	−	7.88675i	−0.466625	−	0.269406i	0.248201	−	0.968709i	$-0.420161\pi$
$857$	−13.6603	−	7.88675i	−0.466625	−	0.269406i	−0.714826	+	0.699302i	$0.753494\pi$
$858$	−11.4337	−	13.8709i	−0.390339	−	0.473543i
$859$	−31.9956	−	8.57320i	−1.09168	−	0.292514i	−0.332306	−	0.943172i	$-0.607827\pi$
$859$	−31.9956	−	8.57320i	−1.09168	−	0.292514i	−0.759371	+	0.650658i	$0.774493\pi$
$860$	−34.3570	+	12.4007i	−1.17156	+	0.422859i
$861$	8.95912	−	32.4715i	0.305326	−	1.10662i
$862$	−12.5109	+	17.8166i	−0.426124	+	0.606834i
$863$	37.4407			1.27449			0.637247	−	0.770659i	$-0.280073\pi$
$863$	37.4407			1.27449			0.637247	+	0.770659i	$0.280073\pi$
$864$	−21.9609	−	19.5376i	−0.747126	−	0.664682i
$865$	16.8186			0.571850
$866$	14.0156	−	19.9593i	0.476269	−	0.678245i
$867$	−11.4956	+	41.6648i	−0.390412	+	1.41501i
$868$	−23.8399	+	8.60467i	−0.809180	+	0.292062i
$869$	−27.1845	−	7.28408i	−0.922173	−	0.247095i
$870$	−4.85929	−	5.89509i	−0.164745	−	0.199862i
$871$	2.51063	+	1.44951i	0.0850695	+	0.0491149i
$872$	11.3902	+	19.9130i	0.385720	+	0.674338i
$873$	−34.0703	+	19.0029i	−1.15310	+	0.643151i
$874$	6.27816	−	5.25367i	0.212362	−	0.177708i
$875$	−5.31986	−	19.8540i	−0.179844	−	0.671187i
$876$	−1.45678	−	18.8391i	−0.0492199	−	0.636514i
$877$	7.55790	−	28.2065i	0.255212	−	0.952465i	−0.712760	−	0.701408i	$-0.752555\pi$
$877$	7.55790	−	28.2065i	0.255212	−	0.952465i	0.967972	−	0.251057i	$-0.0807781\pi$
$878$	6.73922	−	3.13155i	0.227438	−	0.105685i
$879$	−19.3735	+	32.9889i	−0.653452	+	1.11269i
$880$	34.0002	+	40.9641i	1.14614	+	1.38090i
$881$	−11.5567			−0.389355			−0.194678	−	0.980867i	$-0.562366\pi$
$881$	−11.5567			−0.389355			−0.194678	+	0.980867i	$0.562366\pi$
$882$	14.2931	+	10.3564i	0.481275	+	0.348718i
$883$	−19.2632	−	19.2632i	−0.648260	−	0.648260i	0.304313	−	0.952572i	$-0.401573\pi$
$883$	−19.2632	−	19.2632i	−0.648260	−	0.648260i	−0.952572	+	0.304313i	$0.901573\pi$
$884$	19.8737	−	1.68502i	0.668424	−	0.0566733i
$885$	−28.9415	+	28.5157i	−0.972859	+	0.958546i
$886$	−17.1941	−	6.28426i	−0.577646	−	0.211124i
$887$	−19.8424	+	11.4560i	−0.666243	+	0.384656i	−0.794652	−	0.607066i	$-0.792347\pi$
$887$	−19.8424	+	11.4560i	−0.666243	+	0.384656i	0.128408	+	0.991721i	$0.459013\pi$
$888$	−10.5504	−	41.2558i	−0.354048	−	1.38445i
$889$	47.0523	+	27.1657i	1.57808	+	0.911107i
$890$	−5.68434	−	6.79281i	−0.190540	−	0.227696i
$891$	−31.2192	+	29.4212i	−1.04588	+	0.985648i
$892$	−1.01700	−	0.182138i	−0.0340515	−	0.00609843i
$893$	4.75336	−	1.27366i	0.159065	−	0.0426214i
$894$	11.3130	+	24.8258i	0.378364	+	0.830299i
$895$	16.4752	+	28.5359i	0.550705	+	0.953850i
$896$	37.6194	+	3.64746i	1.25678	+	0.121853i
$897$	−11.4015	−	0.0844911i	−0.380685	−	0.00282107i
$898$	−22.7348	+	32.3762i	−0.758671	+	1.08041i
$899$	−2.99615	−	2.99615i	−0.0999272	−	0.0999272i
$900$	−11.0086	+	12.6627i	−0.366953	+	0.422088i
$901$	−4.93860	+	4.93860i	−0.164529	+	0.164529i
$902$	−38.6544	+	6.76237i	−1.28705	+	0.225162i
$903$	32.6350	+	19.1657i	1.08602	+	0.637793i
$904$	10.2905	+	39.0322i	0.342257	+	1.29819i
$905$	45.6345	−	26.3471i	1.51694	−	0.875807i
$906$	8.82377	+	52.7368i	0.293150	+	1.75206i
$907$	−12.7169	−	47.4603i	−0.422259	−	1.57589i	−0.769836	−	0.638242i	$-0.779662\pi$
$907$	−12.7169	−	47.4603i	−0.422259	−	1.57589i	0.347577	−	0.937651i	$-0.387005\pi$
$908$	−11.6502	−	16.7335i	−0.386625	−	0.555322i
$909$	−7.47311	+	26.3232i	−0.247867	+	0.873084i
$910$	−1.79731	+	20.2308i	−0.0595802	+	0.670644i
$911$	6.47683	−	11.2182i	0.214587	−	0.371675i	−0.738558	−	0.674190i	$-0.764493\pi$
$911$	6.47683	−	11.2182i	0.214587	−	0.371675i	0.953145	+	0.302515i	$0.0978262\pi$
$912$	3.32046	−	8.77255i	0.109952	−	0.290488i
$913$	−25.5188	−	44.1999i	−0.844550	−	1.46280i
$914$	−52.2368	+	24.2732i	−1.72784	+	0.802885i
$915$	8.98497	−	32.5651i	0.297034	−	1.07657i
$916$	3.61816	+	42.6739i	0.119548	+	1.40998i
$917$	41.8331	−	41.8331i	1.38145	−	1.38145i
$918$	−7.15808	−	47.0561i	−0.236252	−	1.55308i
$919$			5.55214i			0.183148i	0.995798	+	0.0915740i	$0.0291898\pi$
$919$			5.55214i			0.183148i	−0.995798	+	0.0915740i	$0.970810\pi$
$920$	33.7666	+	0.135862i	1.11325	+	0.00447925i
$921$	7.65271	−	4.34300i	0.252166	−	0.143107i
$922$	18.5318	−	50.7040i	0.610312	−	1.66985i
$923$	−5.92596	−	1.58786i	−0.195055	−	0.0522649i
$924$	10.1262	−	54.2226i	0.333128	−	1.78379i
$925$	−23.4796	+	6.29135i	−0.772006	+	0.206858i
$926$	50.0462	+	4.44612i	1.64462	+	0.146109i
$927$	12.9288	+	0.191628i	0.424636	+	0.00629390i
$928$	2.12124	+	5.95196i	0.0696333	+	0.195383i
$929$	28.8356	−	49.9447i	0.946066	−	1.63863i	0.192462	−	0.981304i	$-0.438353\pi$
$929$	28.8356	−	49.9447i	0.946066	−	1.63863i	0.753603	−	0.657330i	$-0.228314\pi$
$930$	−15.0669	+	21.1218i	−0.494062	+	0.692612i
$931$	−1.45782	+	5.44064i	−0.0477780	+	0.178310i
$932$	43.7323	−	15.7845i	1.43250	−	0.517039i
$933$	−4.34187	−	16.6981i	−0.142146	−	0.546670i
$934$	33.6904	−	5.89394i	1.10238	−	0.192856i
$935$			86.2049i			2.81920i
$936$	−11.4350	+	6.31776i	−0.373765	+	0.206502i
$937$			44.7899i			1.46322i	0.681722	+	0.731612i	$0.261232\pi$
$937$			44.7899i			1.46322i	−0.681722	+	0.731612i	$0.738768\pi$
$938$	1.53300	+	8.76279i	0.0500543	+	0.286115i
$939$	31.5686	−	31.1042i	1.03020	−	1.01505i
$940$	18.3733	+	8.62769i	0.599271	+	0.281404i
$941$	−9.72682	+	36.3010i	−0.317085	+	1.18338i	0.604947	+	0.796266i	$0.293194\pi$
$941$	−9.72682	+	36.3010i	−0.317085	+	1.18338i	−0.922032	+	0.387113i	$0.873472\pi$
$942$	18.8113	−	8.57222i	0.612904	−	0.279298i
$943$	−12.4452	+	21.5557i	−0.405270	+	0.701949i
$944$	30.5314	−	14.0381i	0.993712	−	0.456901i
$945$	48.4577	+	1.07745i	1.57633	+	0.0350493i
$946$	3.90159	−	43.9169i	0.126852	−	1.42786i
$947$	−54.8652	+	14.7011i	−1.78288	+	0.477721i	−0.991104	−	0.133093i	$-0.957509\pi$
$947$	−54.8652	+	14.7011i	−1.78288	+	0.477721i	−0.791775	+	0.610813i	$0.790843\pi$
$948$	−8.83078	+	18.4492i	−0.286810	+	0.599203i
$949$	−8.11194	−	2.17359i	−0.263325	−	0.0705577i
$950$	−5.02898	−	1.83804i	−0.163162	−	0.0596339i
$951$	−0.237560	+	32.0572i	−0.00770343	+	1.03953i
$952$	43.1023	+	43.4506i	1.39695	+	1.40824i
$953$		−	7.26359i		−	0.235291i	−0.993056	−	0.117645i	$-0.962465\pi$
$953$		−	7.26359i		−	0.235291i	0.993056	−	0.117645i	$-0.0375346\pi$
$954$	1.63393	−	4.27302i	0.0529004	−	0.138344i
$955$	3.52440	−	3.52440i	0.114047	−	0.114047i
$956$	0.565803	−	0.670636i	0.0182994	−	0.0216899i
$957$	8.92483	−	2.32066i	0.288499	−	0.0750161i
$958$	−8.06467	−	17.3555i	−0.260558	−	0.560730i
$959$	18.5653	+	32.1560i	0.599504	+	1.03837i
$960$	33.8016	−	18.8248i	1.09094	−	0.607569i
$961$	8.30507	−	14.3848i	0.267905	−	0.464026i
$962$	−18.8521	−	1.67483i	−0.607817	−	0.0539986i
$963$	−0.212628	+	0.0536090i	−0.00685183	+	0.00172752i
$964$	−30.2155	−	5.41142i	−0.973176	−	0.174290i
$965$	11.8604	+	44.2638i	0.381801	+	1.42490i
$966$	−22.2540	−	26.9976i	−0.716010	−	0.868634i
$967$	4.17378	−	2.40973i	0.134220	−	0.0774917i	−0.431387	−	0.902167i	$-0.641976\pi$
$967$	4.17378	−	2.40973i	0.134220	−	0.0774917i	0.565606	+	0.824675i	$0.308642\pi$
$968$	−32.0515	+	8.45010i	−1.03017	+	0.271597i
$969$	13.2099	−	7.49677i	0.424363	−	0.240831i
$970$	−8.84890	−	50.5812i	−0.284121	−	1.62407i
$971$	2.69916	−	2.69916i	0.0866202	−	0.0866202i	−0.662469	−	0.749089i	$-0.730491\pi$
$971$	2.69916	−	2.69916i	0.0866202	−	0.0866202i	0.749089	+	0.662469i	$0.230491\pi$
$972$	16.8537	+	26.2288i	0.540584	+	0.841290i
$973$	−15.9047	−	15.9047i	−0.509881	−	0.509881i
$974$	18.6841	+	13.1201i	0.598676	+	0.420395i
$975$	3.68076	+	6.48579i	0.117879	+	0.207712i
$976$	−16.1486	+	22.8012i	−0.516903	+	0.729849i
$977$	−6.16168	−	10.6724i	−0.197130	−	0.341439i	0.750467	−	0.660908i	$-0.229829\pi$
$977$	−6.16168	−	10.6724i	−0.197130	−	0.341439i	−0.947597	+	0.319469i	$0.896495\pi$
$978$	−2.30213	+	23.9023i	−0.0736140	+	0.764311i
$979$	10.3272	−	2.76717i	0.330059	−	0.0884390i
$980$	−19.0671	+	13.2748i	−0.609076	+	0.424049i
$981$	−5.94857	−	23.5936i	−0.189923	−	0.753287i
$982$	39.2490	−	32.8443i	1.25249	−	1.04810i
$983$	42.5445	+	24.5631i	1.35696	+	0.783441i	0.989213	−	0.146485i	$-0.0467960\pi$
$983$	42.5445	+	24.5631i	1.35696	+	0.783441i	0.367747	+	0.929926i	$0.380129\pi$
$984$	−0.326081	+	28.5175i	−0.0103951	+	0.909105i
$985$	11.7960	−	6.81043i	0.375852	−	0.216998i
$986$	−3.51237	+	9.61004i	−0.111857	+	0.306046i
$987$	−5.29274	−	20.3549i	−0.168470	−	0.647905i
$988$	−3.18640	−	2.68830i	−0.101373	−	0.0855263i
$989$	−19.7747	−	19.7747i	−0.628798	−	0.628798i
$990$	−23.0331	−	51.5539i	−0.732040	−	1.63849i
$991$	−40.4968			−1.28642			−0.643212	−	0.765688i	$-0.722399\pi$
$991$	−40.4968			−1.28642			−0.643212	+	0.765688i	$0.722399\pi$
$992$	17.6601	−	12.1901i	0.560708	−	0.387035i
$993$	−34.1387	−	0.252986i	−1.08336	−	0.00802825i
$994$	−7.93319	−	17.0725i	−0.251626	−	0.541508i
$995$	10.8469	−	40.4812i	0.343870	−	1.28334i
$996$	−34.9818	+	12.3339i	−1.10844	+	0.390816i
$997$	6.26425	+	23.3785i	0.198391	+	0.740404i	0.991363	+	0.131147i	$0.0418659\pi$
$997$	6.26425	+	23.3785i	0.198391	+	0.740404i	−0.792972	+	0.609258i	$0.791467\pi$
$998$	−5.97344	−	7.13829i	−0.189086	−	0.225959i
$999$	−1.00402	+	45.1554i	−0.0317659	+	1.42865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.x.e.61.6	yes	72
3.2	odd	2		432.2.y.e.397.13		72
4.3	odd	2		576.2.bb.e.529.11		72
9.4	even	3	inner	144.2.x.e.13.6	✓	72
9.5	odd	6		432.2.y.e.253.13		72
12.11	even	2		1728.2.bc.e.721.17		72
16.5	even	4	inner	144.2.x.e.133.6	yes	72
16.11	odd	4		576.2.bb.e.241.3		72
36.23	even	6		1728.2.bc.e.145.2		72
36.31	odd	6		576.2.bb.e.337.3		72
48.5	odd	4		432.2.y.e.181.13		72
48.11	even	4		1728.2.bc.e.1585.2		72
144.5	odd	12		432.2.y.e.37.13		72
144.59	even	12		1728.2.bc.e.1009.17		72
144.85	even	12	inner	144.2.x.e.85.6	yes	72
144.139	odd	12		576.2.bb.e.49.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.6	✓	72	9.4	even	3	inner
144.2.x.e.61.6	yes	72	1.1	even	1	trivial
144.2.x.e.85.6	yes	72	144.85	even	12	inner
144.2.x.e.133.6	yes	72	16.5	even	4	inner
432.2.y.e.37.13		72	144.5	odd	12
432.2.y.e.181.13		72	48.5	odd	4
432.2.y.e.253.13		72	9.5	odd	6
432.2.y.e.397.13		72	3.2	odd	2
576.2.bb.e.49.11		72	144.139	odd	12
576.2.bb.e.241.3		72	16.11	odd	4
576.2.bb.e.337.3		72	36.31	odd	6
576.2.bb.e.529.11		72	4.3	odd	2
1728.2.bc.e.145.2		72	36.23	even	6
1728.2.bc.e.721.17		72	12.11	even	2
1728.2.bc.e.1009.17		72	144.59	even	12
1728.2.bc.e.1585.2		72	48.11	even	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.812713 + 1.15737i) q^{2} +(-0.460673 + 1.66966i) q^{3} +(-0.678997 - 1.88121i) q^{4} +(-2.69708 - 0.722679i) q^{5} +(-1.55802 - 1.89013i) q^{6} +(-2.89314 - 1.67035i) q^{7} +(2.72908 + 0.743037i) q^{8} +(-2.57556 - 1.53834i) q^{9} +O(q^{10})\)	\(q+(-0.812713 + 1.15737i) q^{2} +(-0.460673 + 1.66966i) q^{3} +(-0.678997 - 1.88121i) q^{4} +(-2.69708 - 0.722679i) q^{5} +(-1.55802 - 1.89013i) q^{6} +(-2.89314 - 1.67035i) q^{7} +(2.72908 + 0.743037i) q^{8} +(-2.57556 - 1.53834i) q^{9} +(3.02835 - 2.53418i) q^{10} +(1.23365 + 4.60405i) q^{11} +(3.45379 - 0.267072i) q^{12} +(0.398486 - 1.48717i) q^{13} +(4.28450 - 1.99090i) q^{14} +(2.44910 - 4.17029i) q^{15} +(-3.07793 + 2.55468i) q^{16} -6.47719 q^{17} +(3.87361 - 1.73064i) q^{18} +(0.957336 + 0.957336i) q^{19} +(0.471792 + 5.56447i) q^{20} +(4.12172 - 4.06108i) q^{21} +(-6.33117 - 2.31398i) q^{22} +(-3.70277 + 2.13780i) q^{23} +(-2.49784 + 4.21436i) q^{24} +(2.42183 + 1.39824i) q^{25} +(1.39735 + 1.66984i) q^{26} +(3.75500 - 3.59165i) q^{27} +(-1.17786 + 6.57677i) q^{28} +(-1.07893 + 0.289099i) q^{29} +(2.83614 + 6.22376i) q^{30} +(1.89670 + 3.28518i) q^{31} +(-0.455227 - 5.63851i) q^{32} +(-8.25552 - 0.0611777i) q^{33} +(5.26409 - 7.49649i) q^{34} +(6.59588 + 6.59588i) q^{35} +(-1.14515 + 5.88971i) q^{36} +(-6.14639 + 6.14639i) q^{37} +(-1.88603 + 0.329950i) q^{38} +(2.29950 + 1.35044i) q^{39} +(-6.82357 - 3.97628i) q^{40} +(5.04156 - 2.91075i) q^{41} +(1.35039 + 8.07084i) q^{42} +(1.69287 + 6.31788i) q^{43} +(7.82355 - 5.44689i) q^{44} +(5.83476 + 6.01032i) q^{45} +(0.535074 - 6.02288i) q^{46} +(1.81739 - 3.14781i) q^{47} +(-2.84753 - 6.31598i) q^{48} +(2.08016 + 3.60295i) q^{49} +(-3.58653 + 1.66657i) q^{50} +(2.98387 - 10.8147i) q^{51} +(-3.06826 + 0.260146i) q^{52} +(0.762460 - 0.762460i) q^{53} +(1.10512 + 7.26490i) q^{54} -13.3090i q^{55} +(-6.65448 - 6.70824i) q^{56} +(-2.03945 + 1.15741i) q^{57} +(0.542268 - 1.48367i) q^{58} +(-8.11476 - 2.17434i) q^{59} +(-9.50814 - 1.77567i) q^{60} +(6.74711 - 1.80788i) q^{61} +(-5.34363 - 0.474729i) q^{62} +(4.88188 + 8.75272i) q^{63} +(6.89579 + 4.05562i) q^{64} +(-2.14950 + 3.72304i) q^{65} +(6.78017 - 9.50495i) q^{66} +(-0.487339 + 1.81878i) q^{67} +(4.39799 + 12.1850i) q^{68} +(-1.86364 - 7.16721i) q^{69} +(-12.9944 + 2.27330i) q^{70} -3.98472i q^{71} +(-5.88588 - 6.11199i) q^{72} -5.45461i q^{73} +(-2.11838 - 12.1089i) q^{74} +(-3.45027 + 3.39951i) q^{75} +(1.15092 - 2.45098i) q^{76} +(4.12126 - 15.3808i) q^{77} +(-3.43179 + 1.56385i) q^{78} +(-2.95225 + 5.11344i) q^{79} +(10.1476 - 4.66580i) q^{80} +(4.26702 + 7.92417i) q^{81} +(-0.728538 + 8.20053i) q^{82} +(-10.3428 + 2.77135i) q^{83} +(-10.4384 - 4.99638i) q^{84} +(17.4695 + 4.68093i) q^{85} +(-8.68792 - 3.17535i) q^{86} +(0.0143366 - 1.93463i) q^{87} +(-0.0542436 + 13.4815i) q^{88} -2.24307i q^{89} +(-11.6981 + 1.86829i) q^{90} +(-3.63698 + 3.63698i) q^{91} +(6.53582 + 5.51415i) q^{92} +(-6.35891 + 1.65346i) q^{93} +(2.16615 + 4.66165i) q^{94} +(-1.89016 - 3.27385i) q^{95} +(9.62413 + 1.83743i) q^{96} +(6.50191 - 11.2616i) q^{97} +(-5.86050 - 0.520649i) q^{98} +(3.90524 - 13.7558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8}+O(q^{10}) \) 72 * q + 4 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 28 * q^6 - 8 * q^8	\( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22} - 40 q^{24} - 4 q^{26} + 8 q^{27} - 16 q^{28} + 4 q^{29} + 18 q^{30} + 28 q^{31} - 46 q^{32} - 32 q^{33} - 14 q^{34} - 16 q^{35} + 14 q^{36} + 16 q^{37} + 2 q^{38} - 10 q^{40} + 26 q^{42} - 10 q^{43} + 60 q^{44} + 40 q^{45} + 20 q^{46} - 56 q^{47} + 2 q^{48} + 4 q^{49} - 36 q^{50} - 54 q^{51} + 6 q^{52} - 8 q^{53} + 92 q^{54} + 52 q^{56} - 14 q^{58} - 14 q^{59} + 18 q^{60} - 32 q^{61} + 16 q^{62} - 108 q^{63} - 44 q^{64} - 64 q^{65} + 26 q^{66} - 18 q^{67} + 16 q^{68} + 32 q^{69} + 14 q^{70} + 114 q^{72} + 38 q^{74} + 86 q^{75} + 10 q^{76} - 36 q^{77} + 16 q^{78} + 44 q^{79} + 144 q^{80} - 44 q^{81} - 88 q^{82} + 20 q^{83} - 58 q^{84} - 8 q^{85} + 76 q^{86} - 42 q^{88} - 80 q^{91} - 68 q^{92} - 4 q^{93} + 20 q^{94} + 48 q^{95} + 94 q^{96} + 40 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) \) 72 * q + 4 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 28 * q^6 - 8 * q^8 - 20 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 20 * q^15 - 10 * q^16 - 16 * q^17 + 28 * q^19 + 12 * q^20 - 16 * q^21 - 8 * q^22 - 40 * q^24 - 4 * q^26 + 8 * q^27 - 16 * q^28 + 4 * q^29 + 18 * q^30 + 28 * q^31 - 46 * q^32 - 32 * q^33 - 14 * q^34 - 16 * q^35 + 14 * q^36 + 16 * q^37 + 2 * q^38 - 10 * q^40 + 26 * q^42 - 10 * q^43 + 60 * q^44 + 40 * q^45 + 20 * q^46 - 56 * q^47 + 2 * q^48 + 4 * q^49 - 36 * q^50 - 54 * q^51 + 6 * q^52 - 8 * q^53 + 92 * q^54 + 52 * q^56 - 14 * q^58 - 14 * q^59 + 18 * q^60 - 32 * q^61 + 16 * q^62 - 108 * q^63 - 44 * q^64 - 64 * q^65 + 26 * q^66 - 18 * q^67 + 16 * q^68 + 32 * q^69 + 14 * q^70 + 114 * q^72 + 38 * q^74 + 86 * q^75 + 10 * q^76 - 36 * q^77 + 16 * q^78 + 44 * q^79 + 144 * q^80 - 44 * q^81 - 88 * q^82 + 20 * q^83 - 58 * q^84 - 8 * q^85 + 76 * q^86 - 42 * q^88 - 80 * q^91 - 68 * q^92 - 4 * q^93 + 20 * q^94 + 48 * q^95 + 94 * q^96 + 40 * q^97 + 88 * q^98 + 28 * q^99

Introduction

L-functions

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