LMFDB - Embedded newform 140.2.w.b.123.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(23,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 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("140.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.w (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:	$1.11790562830$
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			123.17
Character	$\chi$	$=$	140.123
Dual form			140.2.w.b.107.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34344 - 0.441772i) q^{2} +(0.322645 + 1.20413i) q^{3} +(1.60968 - 1.18699i) q^{4} +(-0.381497 + 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-2.60693 - 0.451584i) q^{7} +(1.63813 - 2.30576i) q^{8} +(1.25225 - 0.722989i) q^{9} +O(q^{10})$	\(q+(1.34344 - 0.441772i) q^{2} +(0.322645 + 1.20413i) q^{3} +(1.60968 - 1.18699i) q^{4} +(-0.381497 + 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-2.60693 - 0.451584i) q^{7} +(1.63813 - 2.30576i) q^{8} +(1.25225 - 0.722989i) q^{9} +(0.460829 + 3.12852i) q^{10} +(-0.824629 - 0.476100i) q^{11} +(1.94864 + 1.55528i) q^{12} +(-3.15680 - 3.15680i) q^{13} +(-3.70175 + 0.544990i) q^{14} +(-2.77612 + 0.251508i) q^{15} +(1.18211 - 3.82134i) q^{16} +(-0.688322 - 2.56885i) q^{17} +(1.36293 - 1.52450i) q^{18} +(1.99048 + 3.44760i) q^{19} +(2.00119 + 3.99941i) q^{20} +(-0.297348 - 3.28477i) q^{21} +(-1.31817 - 0.275315i) q^{22} +(0.528392 + 0.141582i) q^{23} +(3.30496 + 1.22857i) q^{24} +(-4.70892 - 1.68109i) q^{25} +(-5.63557 - 2.84640i) q^{26} +(3.91905 + 3.91905i) q^{27} +(-4.73233 + 2.36749i) q^{28} +7.23080i q^{29} +(-3.61845 + 1.56430i) q^{30} +(-3.41863 - 1.97375i) q^{31} +(-0.100058 - 5.65597i) q^{32} +(0.307222 - 1.14657i) q^{33} +(-2.05957 - 3.14702i) q^{34} +(1.98950 - 5.57152i) q^{35} +(1.15754 - 2.65019i) q^{36} +(-1.00460 - 0.269180i) q^{37} +(4.19714 + 3.75232i) q^{38} +(2.78267 - 4.81972i) q^{39} +(4.45531 + 4.48890i) q^{40} +3.71449 q^{41} +(-1.85059 - 4.28155i) q^{42} +(-8.73324 + 8.73324i) q^{43} +(-1.89251 + 0.212459i) q^{44} +(1.11522 + 3.03489i) q^{45} +(0.772411 - 0.0432210i) q^{46} +(-0.830089 + 3.09794i) q^{47} +(4.98278 + 0.190479i) q^{48} +(6.59214 + 2.35449i) q^{49} +(-7.06882 - 0.178182i) q^{50} +(2.87114 - 1.65765i) q^{51} +(-8.82853 - 1.33434i) q^{52} +(2.83923 - 0.760768i) q^{53} +(6.99635 + 3.53369i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-5.31173 + 5.27120i) q^{56} +(-3.50914 + 3.50914i) q^{57} +(3.19436 + 9.71416i) q^{58} +(6.30084 - 10.9134i) q^{59} +(-4.17012 + 3.70007i) q^{60} +(3.01183 + 5.21665i) q^{61} +(-5.46468 - 1.14136i) q^{62} +(-3.59102 + 1.31928i) q^{63} +(-2.63307 - 7.55427i) q^{64} +(8.15965 - 5.75103i) q^{65} +(-0.0937861 - 1.67607i) q^{66} +(14.3910 - 3.85605i) q^{67} +(-4.15717 - 3.31799i) q^{68} +0.681932i q^{69} +(0.211440 - 8.36393i) q^{70} -7.60710i q^{71} +(0.384313 - 4.07174i) q^{72} +(-14.2178 + 3.80964i) q^{73} +(-1.46853 + 0.0821731i) q^{74} +(0.504938 - 6.21254i) q^{75} +(7.29629 + 3.18685i) q^{76} +(1.93475 + 1.61355i) q^{77} +(1.60914 - 7.70432i) q^{78} +(5.34864 + 9.26412i) q^{79} +(7.96852 + 4.06236i) q^{80} +(-1.28561 + 2.22674i) q^{81} +(4.99021 - 1.64096i) q^{82} +(5.72446 - 5.72446i) q^{83} +(-4.37763 - 4.93447i) q^{84} +(5.92250 - 0.536560i) q^{85} +(-7.87451 + 15.5907i) q^{86} +(-8.70680 + 2.33298i) q^{87} +(-2.44862 + 1.12148i) q^{88} +(1.83403 - 1.05888i) q^{89} +(2.83896 + 3.58452i) q^{90} +(6.80400 + 9.65512i) q^{91} +(1.01860 - 0.399294i) q^{92} +(1.27364 - 4.75329i) q^{93} +(0.253402 + 4.52861i) q^{94} +(-8.35541 + 3.07033i) q^{95} +(6.77823 - 1.94535i) q^{96} +(-3.08588 + 3.08588i) q^{97} +(9.89631 + 0.250904i) q^{98} -1.37686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.34344	−	0.441772i	0.949957	−	0.312380i
$2$	1.34344	−	0.441772i	0.949957	−	0.312380i
$3$	0.322645	+	1.20413i	0.186279	+	0.695203i	0.994353	+	0.106122i	$0.0338435\pi$
$3$	0.322645	+	1.20413i	0.186279	+	0.695203i	−0.808074	+	0.589081i	$0.799490\pi$
$4$	1.60968	−	1.18699i	0.804838	−	0.593495i
$5$	−0.381497	+	2.20328i	−0.170610	+	0.985339i
$5$	−0.381497	+	2.20328i	−0.170610	+	0.985339i
$6$	0.965404	+	1.47514i	0.394125	+	0.602224i
$7$	−2.60693	−	0.451584i	−0.985326	−	0.170683i
$7$	−2.60693	−	0.451584i	−0.985326	−	0.170683i
$8$	1.63813	−	2.30576i	0.579166	−	0.815210i
$9$	1.25225	−	0.722989i	0.417418	−	0.240996i
$10$	0.460829	+	3.12852i	0.145727	+	0.989325i
$11$	−0.824629	−	0.476100i	−0.248635	−	0.143549i	0.370504	−	0.928831i	$-0.379185\pi$
$11$	−0.824629	−	0.476100i	−0.248635	−	0.143549i	−0.619139	+	0.785281i	$0.712518\pi$
$12$	1.94864	+	1.55528i	0.562524	+	0.448970i
$13$	−3.15680	−	3.15680i	−0.875540	−	0.875540i	0.117529	−	0.993069i	$-0.462503\pi$
$13$	−3.15680	−	3.15680i	−0.875540	−	0.875540i	−0.993069	+	0.117529i	$0.962503\pi$
$14$	−3.70175	+	0.544990i	−0.989336	+	0.145655i
$15$	−2.77612	+	0.251508i	−0.716792	+	0.0649391i
$16$	1.18211	−	3.82134i	0.295528	−	0.955334i
$17$	−0.688322	−	2.56885i	−0.166943	−	0.623038i	−0.997784	−	0.0665295i	$-0.978807\pi$
$17$	−0.688322	−	2.56885i	−0.166943	−	0.623038i	0.830842	−	0.556508i	$-0.187859\pi$
$18$	1.36293	−	1.52450i	0.321247	−	0.359329i
$19$	1.99048	+	3.44760i	0.456646	+	0.790935i	0.998781	−	0.0493567i	$-0.0157171\pi$
$19$	1.99048	+	3.44760i	0.456646	+	0.790935i	−0.542135	+	0.840292i	$0.682384\pi$
$20$	2.00119	+	3.99941i	0.447479	+	0.894294i
$21$	−0.297348	−	3.28477i	−0.0648866	−	0.716797i
$22$	−1.31817	−	0.275315i	−0.281034	−	0.0586973i
$23$	0.528392	+	0.141582i	0.110177	+	0.0295219i	0.313486	−	0.949593i	$-0.398503\pi$
$23$	0.528392	+	0.141582i	0.110177	+	0.0295219i	−0.203309	+	0.979115i	$0.565170\pi$
$24$	3.30496	+	1.22857i	0.674623	+	0.250782i
$25$	−4.70892	−	1.68109i	−0.941784	−	0.336218i
$26$	−5.63557	−	2.84640i	−1.10523	−	0.558225i
$27$	3.91905	+	3.91905i	0.754222	+	0.754222i
$28$	−4.73233	+	2.36749i	−0.894327	+	0.447414i
$29$			7.23080i			1.34273i	0.741129	+	0.671363i	$0.234291\pi$
$29$			7.23080i			1.34273i	−0.741129	+	0.671363i	$0.765709\pi$
$30$	−3.61845	+	1.56430i	−0.660636	+	0.285601i
$31$	−3.41863	−	1.97375i	−0.614004	−	0.354495i	0.160527	−	0.987031i	$-0.448681\pi$
$31$	−3.41863	−	1.97375i	−0.614004	−	0.354495i	−0.774531	+	0.632536i	$0.782014\pi$
$32$	−0.100058	−	5.65597i	−0.0176879	−	0.999844i
$33$	0.307222	−	1.14657i	0.0534805	−	0.199592i
$34$	−2.05957	−	3.14702i	−0.353213	−	0.539710i
$35$	1.98950	−	5.57152i	0.336287	−	0.941760i
$36$	1.15754	−	2.65019i	0.192924	−	0.441698i
$37$	−1.00460	−	0.269180i	−0.165154	−	0.0442530i	0.175294	−	0.984516i	$-0.443912\pi$
$37$	−1.00460	−	0.269180i	−0.165154	−	0.0442530i	−0.340449	+	0.940263i	$0.610579\pi$
$38$	4.19714	+	3.75232i	0.680867	+	0.608707i
$39$	2.78267	−	4.81972i	0.445584	−	0.771773i
$40$	4.45531	+	4.48890i	0.704446	+	0.709758i
$41$	3.71449			0.580106			0.290053	−	0.957011i	$-0.406327\pi$
$41$	3.71449			0.580106			0.290053	+	0.957011i	$0.406327\pi$
$42$	−1.85059	−	4.28155i	−0.285552	−	0.660657i
$43$	−8.73324	+	8.73324i	−1.33181	+	1.33181i	−0.428052	+	0.903754i	$0.640800\pi$
$43$	−8.73324	+	8.73324i	−1.33181	+	1.33181i	−0.903754	+	0.428052i	$0.859200\pi$
$44$	−1.89251	+	0.212459i	−0.285307	+	0.0320295i
$45$	1.11522	+	3.03489i	0.166247	+	0.452414i
$46$	0.772411	−	0.0432210i	0.113886	−	0.00637258i
$47$	−0.830089	+	3.09794i	−0.121081	+	0.451880i	−0.999670	−	0.0256988i	$-0.991819\pi$
$47$	−0.830089	+	3.09794i	−0.121081	+	0.451880i	0.878589	+	0.477579i	$0.158486\pi$
$48$	4.98278	+	0.190479i	0.719202	+	0.0274933i
$49$	6.59214	+	2.35449i	0.941735	+	0.336356i
$50$	−7.06882	−	0.178182i	−0.999682	−	0.0251987i
$51$	2.87114	−	1.65765i	0.402040	−	0.232118i
$52$	−8.82853	−	1.33434i	−1.22430	−	0.185039i
$53$	2.83923	−	0.760768i	0.389998	−	0.104500i	−0.0584914	−	0.998288i	$-0.518629\pi$
$53$	2.83923	−	0.760768i	0.389998	−	0.104500i	0.448489	+	0.893788i	$0.351962\pi$
$54$	6.99635	+	3.53369i	0.952082	+	0.480875i
$55$	1.36358	−	1.63526i	0.183864	−	0.220498i
$56$	−5.31173	+	5.27120i	−0.709809	+	0.704394i
$57$	−3.50914	+	3.50914i	−0.464797	+	0.464797i
$58$	3.19436	+	9.71416i	0.419440	+	1.27553i
$59$	6.30084	−	10.9134i	0.820300	−	1.42080i	−0.0851594	−	0.996367i	$-0.527140\pi$
$59$	6.30084	−	10.9134i	0.820300	−	1.42080i	0.905459	−	0.424433i	$-0.139527\pi$
$60$	−4.17012	+	3.70007i	−0.538360	+	0.477678i
$61$	3.01183	+	5.21665i	0.385626	+	0.667923i	0.991856	−	0.127366i	$-0.0406523\pi$
$61$	3.01183	+	5.21665i	0.385626	+	0.667923i	−0.606230	+	0.795289i	$0.707319\pi$
$62$	−5.46468	−	1.14136i	−0.694015	−	0.144953i
$63$	−3.59102	+	1.31928i	−0.452426	+	0.166214i
$64$	−2.63307	−	7.55427i	−0.329134	−	0.944283i
$65$	8.15965	−	5.75103i	1.01208	−	0.713327i
$66$	−0.0937861	−	1.67607i	−0.0115443	−	0.206310i
$67$	14.3910	−	3.85605i	1.75814	−	0.471092i	0.771806	−	0.635858i	$-0.219353\pi$
$67$	14.3910	−	3.85605i	1.75814	−	0.471092i	0.986333	+	0.164766i	$0.0526868\pi$
$68$	−4.15717	−	3.31799i	−0.504131	−	0.402365i
$69$			0.681932i			0.0820949i
$70$	0.211440	−	8.36393i	0.0252719	−	0.999681i
$71$		−	7.60710i		−	0.902797i	−0.892322	−	0.451399i	$-0.850925\pi$
$71$		−	7.60710i		−	0.902797i	0.892322	−	0.451399i	$-0.149075\pi$
$72$	0.384313	−	4.07174i	0.0452917	−	0.479860i
$73$	−14.2178	+	3.80964i	−1.66406	+	0.445885i	−0.963501	−	0.267705i	$-0.913735\pi$
$73$	−14.2178	+	3.80964i	−1.66406	+	0.445885i	−0.700564	+	0.713590i	$0.747068\pi$
$74$	−1.46853	+	0.0821731i	−0.170713	+	0.00955243i
$75$	0.504938	−	6.21254i	0.0583052	−	0.717362i
$76$	7.29629	+	3.18685i	0.836942	+	0.365557i
$77$	1.93475	+	1.61355i	0.220485	+	0.183881i
$78$	1.60914	−	7.70432i	0.182199	−	0.872343i
$79$	5.34864	+	9.26412i	0.601769	+	1.04230i	0.992553	+	0.121813i	$0.0388707\pi$
$79$	5.34864	+	9.26412i	0.601769	+	1.04230i	−0.390784	+	0.920483i	$0.627796\pi$
$80$	7.96852	+	4.06236i	0.890907	+	0.454185i
$81$	−1.28561	+	2.22674i	−0.142846	+	0.247416i
$82$	4.99021	−	1.64096i	0.551076	−	0.181213i
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	−0.319309	−	0.947651i	$-0.603451\pi$
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	0.947651	+	0.319309i	$0.103451\pi$
$84$	−4.37763	−	4.93447i	−0.477638	−	0.538395i
$85$	5.92250	−	0.536560i	0.642386	−	0.0581981i
$86$	−7.87451	+	15.5907i	−0.849130	+	1.68119i
$87$	−8.70680	+	2.33298i	−0.933467	+	0.250122i
$88$	−2.44862	+	1.12148i	−0.261024	+	0.119551i
$89$	1.83403	−	1.05888i	0.194407	−	0.112241i	−0.399637	−	0.916673i	$-0.630864\pi$
$89$	1.83403	−	1.05888i	0.194407	−	0.112241i	0.594044	+	0.804433i	$0.297531\pi$
$90$	2.83896	+	3.58452i	0.299253	+	0.377842i
$91$	6.80400	+	9.65512i	0.713253	+	1.01213i
$92$	1.01860	−	0.399294i	0.106196	−	0.0416293i
$93$	1.27364	−	4.75329i	0.132070	−	0.492893i
$94$	0.253402	+	4.52861i	0.0261365	+	0.467090i
$95$	−8.35541	+	3.07033i	−0.857247	+	0.315010i
$96$	6.77823	−	1.94535i	0.691800	−	0.198547i
$97$	−3.08588	+	3.08588i	−0.313324	+	0.313324i	−0.846196	−	0.532872i	$-0.821113\pi$
$97$	−3.08588	+	3.08588i	−0.313324	+	0.313324i	0.532872	+	0.846196i	$0.321113\pi$
$98$	9.89631	+	0.250904i	0.999679	+	0.0253451i
$99$	−1.37686			−0.138379
$100$	−9.57527	+	2.88343i	−0.957527	+	0.288343i
$101$	0.715074	−	1.23854i	0.0711525	−	0.123240i	−0.828254	−	0.560353i	$-0.810666\pi$
$101$	0.715074	−	1.23854i	0.0711525	−	0.123240i	0.899407	+	0.437113i	$0.143999\pi$
$102$	3.12491	−	3.49535i	0.309412	−	0.346091i
$103$	−9.82894	−	2.63366i	−0.968474	−	0.259502i	−0.260291	−	0.965530i	$-0.583818\pi$
$103$	−9.82894	−	2.63366i	−0.968474	−	0.259502i	−0.708183	+	0.706028i	$0.750485\pi$
$104$	−12.4501	+	2.10758i	−1.22083	+	0.206666i
$105$	7.35073	+	0.597989i	0.717358	+	0.0583577i
$106$	3.47825	−	2.27634i	0.337838	−	0.221097i
$107$	0.0104111	−	0.0388547i	0.00100648	−	0.00375622i	−0.965421	−	0.260697i	$-0.916048\pi$
$107$	0.0104111	−	0.0388547i	0.00100648	−	0.00375622i	0.966427	+	0.256940i	$0.0827144\pi$
$108$	10.9603	+	1.65653i	1.05465	+	0.159400i
$109$	−5.44983	−	3.14646i	−0.521999	−	0.301376i	0.215753	−	0.976448i	$-0.430779\pi$
$109$	−5.44983	−	3.14646i	−0.521999	−	0.301376i	−0.737752	+	0.675072i	$0.764113\pi$
$110$	1.10947	−	2.79927i	0.105784	−	0.266900i
$111$		−	1.29651i		−	0.123059i
$112$	−4.80733	+	9.42812i	−0.454250	+	0.890874i
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.999779	+	0.0210265i	$0.00669344\pi$
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.0210265	+	0.999779i	$0.493307\pi$
$114$	−3.16409	+	6.26456i	−0.296344	+	0.586730i
$115$	−0.513525	+	1.11018i	−0.0478865	+	0.103525i
$116$	8.58288	+	11.6392i	0.796900	+	1.08068i
$117$	−6.23545	−	1.67078i	−0.576468	−	0.154464i
$118$	3.64360	−	17.4450i	0.335420	−	1.60595i
$119$	0.634353	+	7.00765i	0.0581511	+	0.642390i
$120$	−3.96773	+	6.81308i	−0.362202	+	0.621946i
$121$	−5.04666	−	8.74107i	−0.458787	−	0.794643i
$122$	6.35079	+	5.67772i	0.574974	+	0.514037i
$123$	1.19846	+	4.47272i	0.108062	+	0.403292i
$124$	−7.84570	+	0.880785i	−0.704565	+	0.0790968i
$125$	5.50036	−	9.73376i	0.491967	−	0.870614i
$126$	−4.24151	+	3.35879i	−0.377864	+	0.299225i
$127$	−1.22418	−	1.22418i	−0.108629	−	0.108629i	0.650703	−	0.759332i	$-0.274474\pi$
$127$	−1.22418	−	1.22418i	−0.108629	−	0.108629i	−0.759332	+	0.650703i	$0.774474\pi$
$128$	−6.87464	−	8.98551i	−0.607638	−	0.794214i
$129$	−13.3337	−	7.69820i	−1.17396	−	0.677788i
$130$	8.42138	−	11.3309i	0.738604	−	0.993783i
$131$	1.12982	−	0.652300i	0.0987126	−	0.0569918i	−0.449831	−	0.893114i	$-0.648516\pi$
$131$	1.12982	−	0.652300i	0.0987126	−	0.0569918i	0.548544	+	0.836122i	$0.315182\pi$
$132$	−0.866437	−	2.21027i	−0.0754137	−	0.192380i
$133$	−3.63214	−	9.88652i	−0.314947	−	0.857270i
$134$	17.6300	−	11.5379i	1.52300	−	0.996724i
$135$	−10.1299	+	7.13968i	−0.871842	+	0.614486i
$136$	−7.05072	−	2.62100i	−0.604594	−	0.224749i
$137$	0.300203	+	1.12037i	0.0256480	+	0.0957198i	0.977563	−	0.210641i	$-0.0675552\pi$
$137$	0.300203	+	1.12037i	0.0256480	+	0.0957198i	−0.951915	+	0.306361i	$0.900889\pi$
$138$	0.301258	+	0.916136i	0.0256448	+	0.0779867i
$139$	−17.4513			−1.48020			−0.740099	−	0.672498i	$-0.765221\pi$
$139$	−17.4513			−1.48020			−0.740099	+	0.672498i	$0.765221\pi$
$140$	−3.41089	−	11.3299i	−0.288273	−	0.957548i
$141$	−3.99813			−0.336704
$142$	−3.36060	−	10.2197i	−0.282015	−	0.857619i
$143$	1.10024	+	4.10614i	0.0920065	+	0.343373i
$144$	−1.28248	−	5.63993i	−0.106873	−	0.469994i
$145$	−15.9315	−	2.75852i	−1.32304	−	0.229083i
$146$	−17.4178	+	11.3990i	−1.44151	+	0.943392i
$147$	−0.708187	+	8.69745i	−0.0584103	+	0.717353i
$148$	−1.93659	+	0.759151i	−0.159186	+	0.0624018i
$149$	−9.70894	+	5.60546i	−0.795387	+	0.459217i	−0.841856	−	0.539703i	$-0.818537\pi$
$149$	−9.70894	+	5.60546i	−0.795387	+	0.459217i	0.0464684	+	0.998920i	$0.485203\pi$
$150$	−2.06617	−	8.56925i	−0.168702	−	0.699677i
$151$	−13.0081	−	7.51022i	−1.05858	−	0.611173i	−0.133543	−	0.991043i	$-0.542635\pi$
$151$	−13.0081	−	7.51022i	−1.05858	−	0.611173i	−0.925040	+	0.379870i	$0.875969\pi$
$152$	11.2100	+	1.05806i	0.909252	+	0.0858200i
$153$	−2.71920	−	2.71920i	−0.219835	−	0.219835i
$154$	3.31204	+	1.31299i	0.266892	+	0.105804i
$155$	5.65292	−	6.77924i	0.454054	−	0.544521i
$156$	−1.24177	−	11.0612i	−0.0994209	−	0.885604i
$157$	1.94845	+	7.27171i	0.155503	+	0.580345i	0.999062	+	0.0433084i	$0.0137898\pi$
$157$	1.94845	+	7.27171i	0.155503	+	0.580345i	−0.843559	+	0.537037i	$0.819544\pi$
$158$	11.2782	+	10.0829i	0.897247	+	0.802155i
$159$	1.83212	+	3.17333i	0.145297	+	0.251662i
$160$	12.4999	+	1.93728i	0.988202	+	0.153155i
$161$	−1.31354	−	0.607707i	−0.103522	−	0.0478941i
$162$	−0.743432	+	3.55944i	−0.0584095	+	0.279656i
$163$	6.42243	+	1.72089i	0.503044	+	0.134790i	0.501412	−	0.865208i	$-0.332814\pi$
$163$	6.42243	+	1.72089i	0.503044	+	0.134790i	0.00163153	+	0.999999i	$0.499481\pi$
$164$	5.97913	−	4.40906i	0.466891	−	0.344290i
$165$	2.40901	+	1.11431i	0.187541	+	0.0867489i
$166$	5.16158	−	10.2194i	0.400616	−	0.793179i
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	0.439276	−	0.898352i	$-0.355235\pi$
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	−0.898352	+	0.439276i	$0.855235\pi$
$168$	−8.06100	−	4.69527i	−0.621920	−	0.362248i
$169$			6.93083i			0.533141i
$170$	7.71950	−	3.33723i	0.592059	−	0.255954i
$171$	4.98516	+	2.87818i	0.381225	+	0.220100i
$172$	−3.69142	+	24.4239i	−0.281468	+	1.86231i
$173$	−0.572923	+	2.13818i	−0.0435585	+	0.162563i	−0.984279	−	0.176620i	$-0.943484\pi$
$173$	−0.572923	+	2.13818i	−0.0435585	+	0.162563i	0.940721	+	0.339182i	$0.110150\pi$
$174$	−10.6664	+	6.98064i	−0.808621	+	0.529201i
$175$	11.5167	+	6.50895i	0.870578	+	0.492031i
$176$	−2.79414	+	2.58838i	−0.210616	+	0.195106i
$177$	15.1740	+	4.06587i	1.14055	+	0.305610i
$178$	1.99613	−	2.23276i	0.149616	−	0.167353i
$179$	−8.23493	+	14.2633i	−0.615507	+	1.06609i	0.374788	+	0.927111i	$0.377716\pi$
$179$	−8.23493	+	14.2633i	−0.615507	+	1.06609i	−0.990295	+	0.138980i	$0.955618\pi$
$180$	5.39752	+	3.56143i	0.402307	+	0.265453i
$181$	−5.97636			−0.444219			−0.222110	−	0.975022i	$-0.571294\pi$
$181$	−5.97636			−0.444219			−0.222110	+	0.975022i	$0.571294\pi$
$182$	13.4061	+	9.96529i	0.993729	+	0.738676i
$183$	−5.30976	+	5.30976i	−0.392508	+	0.392508i
$184$	1.19203	−	0.986415i	0.0878775	−	0.0727195i
$185$	0.976331	−	2.11072i	0.0717813	−	0.155183i
$186$	−0.388806	−	6.94843i	−0.0285086	−	0.509483i
$187$	−0.655419	+	2.44606i	−0.0479290	+	0.178873i
$188$	2.34104	+	5.97198i	0.170738	+	0.435551i
$189$	−8.44690	−	11.9865i	−0.614422	−	0.871887i
$190$	−9.86863	+	7.81600i	−0.715946	+	0.567032i
$191$	6.96830	−	4.02315i	0.504209	−	0.291105i	−0.226241	−	0.974071i	$-0.572644\pi$
$191$	6.96830	−	4.02315i	0.504209	−	0.291105i	0.730450	+	0.682966i	$0.239310\pi$
$192$	8.24675	−	5.60790i	0.595158	−	0.404715i
$193$	14.0635	−	3.76831i	1.01231	−	0.271249i	0.285718	−	0.958314i	$-0.407768\pi$
$193$	14.0635	−	3.76831i	1.01231	−	0.271249i	0.726596	+	0.687065i	$0.241101\pi$
$194$	−2.78245	+	5.50896i	−0.199768	+	0.395520i
$195$	9.55764	+	7.96972i	0.684437	+	0.570723i
$196$	13.4060	−	4.03484i	0.957569	−	0.288203i
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.194001	−	0.981001i	$-0.437854\pi$
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.981001	−	0.194001i	$-0.0621465\pi$
$198$	−1.84973	+	0.608257i	−0.131455	+	0.0432269i
$199$	4.82793	−	8.36222i	0.342243	−	0.592782i	−0.642606	−	0.766197i	$-0.722147\pi$
$199$	4.82793	−	8.36222i	0.342243	−	0.592782i	0.984849	+	0.173415i	$0.0554801\pi$
$200$	−11.5900	+	8.10380i	−0.819538	+	0.573025i
$201$	9.28636	+	16.0844i	0.655009	+	1.13451i
$202$	0.413507	−	1.97981i	0.0290943	−	0.139299i
$203$	3.26531	−	18.8502i	0.229180	−	1.32302i
$204$	2.65399	−	6.07630i	0.185816	−	0.425426i
$205$	−1.41707	+	8.18408i	−0.0989722	+	0.571601i
$206$	−14.3681	+	0.803980i	−1.00107	+	0.0560159i
$207$	0.764042	−	0.204725i	0.0531046	−	0.0142293i
$208$	−15.7949	+	8.33151i	−1.09518	+	0.577687i
$209$		−	3.79066i		−	0.262205i
$210$	10.1395	−	2.44398i	0.699689	−	0.168651i
$211$			10.4344i			0.718333i	0.933274	+	0.359166i	$0.116939\pi$
$211$			10.4344i			0.718333i	−0.933274	+	0.359166i	$0.883061\pi$
$212$	3.66721	−	4.59472i	0.251865	−	0.315567i
$213$	9.15992	−	2.45439i	0.627628	−	0.168172i
$214$	−0.00317820	−	0.0567984i	−0.000217258	−	0.00388266i
$215$	−15.9101	−	22.5735i	−1.08506	−	1.53950i
$216$	15.4563	−	2.61649i	1.05167	−	0.178029i
$217$	8.02081	+	6.68921i	0.544488	+	0.454093i
$218$	−8.71155	−	1.81951i	−0.590020	−	0.123233i
$219$	−9.17459	−	15.8909i	−0.619961	−	1.07380i
$220$	0.253877	−	4.25079i	0.0171164	−	0.286588i
$221$	−5.93647	+	10.2823i	−0.399330	+	0.691660i
$222$	−0.572761	−	1.74179i	−0.0384412	−	0.116901i
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	−0.249973	−	0.968253i	$-0.580422\pi$
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	0.968253	+	0.249973i	$0.0804218\pi$
$224$	−2.29330	+	14.7899i	−0.153228	+	0.988191i
$225$	−7.11217	+	1.29934i	−0.474145	+	0.0866230i
$226$	19.3719	+	9.78431i	1.28860	+	0.650843i
$227$	9.68083	−	2.59397i	0.642539	−	0.172168i	0.0771860	−	0.997017i	$-0.475406\pi$
$227$	9.68083	−	2.59397i	0.642539	−	0.172168i	0.565353	+	0.824849i	$0.308740\pi$
$228$	−1.48327	+	9.81389i	−0.0982316	+	0.649941i
$229$	14.7989	−	8.54416i	0.977940	−	0.564614i	0.0762921	−	0.997086i	$-0.475692\pi$
$229$	14.7989	−	8.54416i	0.977940	−	0.564614i	0.901647	+	0.432472i	$0.142359\pi$
$230$	−0.199444	+	1.71833i	−0.0131510	+	0.113303i
$231$	−1.31868	+	2.85029i	−0.0867627	+	0.187535i
$232$	16.6725	+	11.8450i	1.09460	+	0.777661i
$233$	−0.485407	+	1.81156i	−0.0318001	+	0.118680i	−0.980001	−	0.198990i	$-0.936234\pi$
$233$	−0.485407	+	1.81156i	−0.0318001	+	0.118680i	0.948201	+	0.317670i	$0.102900\pi$
$234$	−9.11508	+	0.510043i	−0.595871	+	0.0333425i
$235$	−6.50895	−	3.01077i	−0.424597	−	0.196401i
$236$	−2.81175	−	25.0460i	−0.183029	−	1.63036i
$237$	−9.42947	+	9.42947i	−0.612510	+	0.612510i
$238$	3.94800	+	9.13413i	0.255911	+	0.592078i
$239$	15.2182			0.984385			0.492193	−	0.870486i	$-0.336196\pi$
$239$	15.2182			0.984385			0.492193	+	0.870486i	$0.336196\pi$
$240$	−2.32059	+	10.9058i	−0.149794	+	0.703967i
$241$	6.58780	−	11.4104i	0.424357	−	0.735008i	−0.572003	−	0.820252i	$-0.693833\pi$
$241$	6.58780	−	11.4104i	0.424357	−	0.735008i	0.996360	+	0.0852432i	$0.0271667\pi$
$242$	−10.6415	−	9.51365i	−0.684058	−	0.611561i
$243$	12.9645	+	3.47383i	0.831673	+	0.222846i
$244$	11.0402	+	4.82210i	0.706775	+	0.308703i
$245$	−7.70250	+	13.6261i	−0.492094	+	0.870542i
$246$	3.58599	+	5.47940i	0.228634	+	0.349354i
$247$	4.59987	−	17.1670i	0.292683	−	1.09231i
$248$	−10.1511	+	4.64929i	−0.644598	+	0.295230i
$249$	8.73995	+	5.04601i	0.553872	+	0.319778i
$250$	3.08932	−	15.5066i	0.195386	−	0.980727i
$251$			14.7048i			0.928161i	0.885793	+	0.464080i	$0.153615\pi$
$251$			14.7048i			0.928161i	−0.885793	+	0.464080i	$0.846385\pi$
$252$	−4.21441	+	6.38612i	−0.265483	+	0.402288i
$253$	−0.368320	−	0.368320i	−0.0231561	−	0.0231561i
$254$	−2.18543	−	1.10381i	−0.137126	−	0.0692592i
$255$	2.55695	+	6.95833i	0.160123	+	0.435747i
$256$	−13.2052	−	9.03450i	−0.825326	−	0.564656i
$257$	−12.7677	−	3.42109i	−0.796426	−	0.213402i	−0.162412	−	0.986723i	$-0.551927\pi$
$257$	−12.7677	−	3.42109i	−0.796426	−	0.213402i	−0.634014	+	0.773321i	$0.718594\pi$
$258$	−21.3139	−	4.45165i	−1.32694	−	0.277148i
$259$	2.49735	+	1.15539i	0.155178	+	0.0717926i
$260$	6.30798	−	18.9427i	0.391204	−	1.17478i
$261$	5.22778	+	9.05478i	0.323592	+	0.560477i
$262$	1.22968	−	1.37545i	0.0759697	−	0.0849755i
$263$	2.73529	+	10.2083i	0.168665	+	0.629468i	0.997544	+	0.0700398i	$0.0223126\pi$
$263$	2.73529	+	10.2083i	0.168665	+	0.629468i	−0.828879	+	0.559428i	$0.811021\pi$
$264$	−2.14044	−	2.58661i	−0.131735	−	0.159195i
$265$	0.593033	+	6.54585i	0.0364298	+	0.402108i
$266$	−9.24716	−	11.6774i	−0.566980	−	0.715987i
$267$	1.86676	+	1.86676i	0.114244	+	0.114244i
$268$	18.5877	−	23.2889i	1.13543	−	1.42260i
$269$	10.5625	+	6.09826i	0.644007	+	0.371818i	0.786156	−	0.618027i	$-0.212068\pi$
$269$	10.5625	+	6.09826i	0.644007	+	0.371818i	−0.142149	+	0.989845i	$0.545401\pi$
$270$	−10.4548	+	14.0668i	−0.636260	+	0.856081i
$271$	−5.70012	+	3.29096i	−0.346257	+	0.199912i	−0.663036	−	0.748588i	$-0.730732\pi$
$271$	−5.70012	+	3.29096i	−0.346257	+	0.199912i	0.316778	+	0.948500i	$0.397399\pi$
$272$	−10.6301	−	0.406362i	−0.644546	−	0.0246393i
$273$	−9.43072	+	11.3081i	−0.570773	+	0.684395i
$274$	0.898253	+	1.37253i	0.0542655	+	0.0829178i
$275$	3.08274	+	3.62819i	0.185896	+	0.218788i
$276$	0.809446	+	1.09769i	0.0487229	+	0.0660731i
$277$	−1.06292	−	3.96687i	−0.0638646	−	0.238346i	0.926614	−	0.376015i	$-0.122706\pi$
$277$	−1.06292	−	3.96687i	−0.0638646	−	0.238346i	−0.990478	+	0.137669i	$0.956039\pi$
$278$	−23.4448	+	7.70948i	−1.40613	+	0.462384i
$279$	−5.70799			−0.341728
$280$	−9.58754	−	13.7142i	−0.572965	−	0.819580i
$281$	−32.2773			−1.92550			−0.962752	−	0.270386i	$-0.912849\pi$
$281$	−32.2773			−1.92550			−0.962752	+	0.270386i	$0.912849\pi$
$282$	−5.37126	+	1.76626i	−0.319854	+	0.105179i
$283$	−5.05423	−	18.8626i	−0.300443	−	1.12127i	−0.936798	−	0.349872i	$-0.886225\pi$
$283$	−5.05423	−	18.8626i	−0.300443	−	1.12127i	0.636355	−	0.771396i	$-0.280441\pi$
$284$	−9.02955	−	12.2450i	−0.535805	−	0.726605i
$285$	−6.39291	−	9.07035i	−0.378683	−	0.537281i
$286$	3.29208	+	5.03032i	0.194665	+	0.297449i
$287$	−9.68341	−	1.67740i	−0.571594	−	0.0990140i
$288$	−4.21450	−	7.01036i	−0.248342	−	0.413090i
$289$	8.59722	−	4.96361i	0.505719	−	0.291977i
$290$	−22.6217	+	3.33216i	−1.32839	+	0.195671i
$291$	−4.71144	−	2.72015i	−0.276190	−	0.159458i
$292$	−18.3640	+	23.0086i	−1.07467	+	1.34648i
$293$	12.6859	+	12.6859i	0.741121	+	0.741121i	0.972794	−	0.231673i	$-0.0744200\pi$
$293$	12.6859	+	12.6859i	0.741121	+	0.741121i	−0.231673	+	0.972794i	$0.574420\pi$
$294$	2.89088	+	11.9974i	0.168599	+	0.699701i
$295$	21.6415	+	18.0460i	1.26002	+	1.05068i
$296$	−2.26632	+	1.87540i	−0.131727	+	0.109006i
$297$	−1.36590	−	5.09762i	−0.0792577	−	0.295794i
$298$	−10.5671	+	11.8197i	−0.612134	+	0.684699i
$299$	−1.22108	−	2.11498i	−0.0706170	−	0.122312i
$300$	−6.56143	−	10.5995i	−0.378824	−	0.611964i
$301$	26.7107	−	18.8231i	1.53958	−	1.08495i
$302$	−20.7934	−	4.34295i	−1.19653	−	0.249909i
$303$	1.72208	+	0.461430i	0.0989309	+	0.0265085i
$304$	15.5274	−	3.53082i	0.890559	−	0.202506i
$305$	−12.6428	+	4.64579i	−0.723922	+	0.266017i
$306$	−4.85436	−	2.45183i	−0.277505	−	0.140162i
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	0.362387	−	0.932028i	$-0.381962\pi$
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	−0.932028	+	0.362387i	$0.881962\pi$
$308$	5.02958	+	0.300760i	0.286587	+	0.0171374i
$309$		−	12.6850i		−	0.721626i
$310$	4.59950	−	11.6048i	0.261234	−	0.659109i
$311$	12.0711	+	6.96926i	0.684490	+	0.395190i	0.801544	−	0.597935i	$-0.204012\pi$
$311$	12.0711	+	6.96926i	0.684490	+	0.395190i	−0.117055	+	0.993125i	$0.537345\pi$
$312$	−6.55476	−	14.3115i	−0.371090	−	0.810229i
$313$	1.27037	−	4.74109i	0.0718056	−	0.267982i	−0.920684	−	0.390308i	$-0.872369\pi$
$313$	1.27037	−	4.74109i	0.0718056	−	0.267982i	0.992490	+	0.122326i	$0.0390353\pi$
$314$	5.83006	+	8.90835i	0.329009	+	0.502727i
$315$	−1.53679	−	8.41534i	−0.0865883	−	0.474151i
$316$	19.6060	+	8.56345i	1.10292	+	0.481732i
$317$	−33.2307	−	8.90414i	−1.86642	−	0.500106i	−1.00000		0.000794747i	$-0.999747\pi$
$317$	−33.2307	−	8.90414i	−1.86642	−	0.500106i	−0.866423	−	0.499312i	$-0.833586\pi$
$318$	3.86324	+	3.45381i	0.216640	+	0.193680i
$319$	3.44258	−	5.96272i	0.192747	−	0.333848i
$320$	17.6487	−	2.91947i	0.986592	−	0.163203i
$321$	0.0501451			0.00279883
$322$	−2.03314	−	0.236134i	−0.113302	−	0.0131592i
$323$	7.48630	−	7.48630i	0.416549	−	0.416549i
$324$	0.573704	+	5.11034i	0.0318724	+	0.283908i
$325$	9.55827	+	20.1720i	0.530197	+	1.11894i
$326$	9.38841	−	0.525337i	0.519976	−	0.0290957i
$327$	2.03038	−	7.57748i	0.112280	−	0.419035i
$328$	6.08482	−	8.56473i	0.335978	−	0.472908i
$329$	3.56296	−	7.70124i	0.196432	−	0.424583i
$330$	3.72864	+	0.432778i	0.205255	+	0.0238237i
$331$	−11.2201	+	6.47792i	−0.616712	+	0.356059i	−0.775588	−	0.631240i	$-0.782546\pi$
$331$	−11.2201	+	6.47792i	−0.616712	+	0.356059i	0.158876	+	0.987299i	$0.449213\pi$
$332$	2.41965	−	16.0094i	0.132796	−	0.878630i
$333$	−1.45262	+	0.389229i	−0.0796032	+	0.0213296i
$334$	−10.5909	−	5.34924i	−0.579510	−	0.292697i
$335$	3.00587	+	33.1785i	0.164228	+	1.81274i
$336$	−12.9037	−	2.74671i	−0.703956	−	0.149845i
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	−0.475136	−	0.879912i	$-0.657601\pi$
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	0.879912	+	0.475136i	$0.157601\pi$
$338$	3.06184	+	9.31117i	0.166542	+	0.506461i
$339$	−9.56524	+	16.5675i	−0.519513	+	0.899822i
$340$	8.89642	−	7.89363i	0.482476	−	0.428092i
$341$	1.87940	+	3.25522i	0.101775	+	0.176280i
$342$	7.96877	+	1.66437i	0.430902	+	0.0899989i
$343$	−16.1220	−	9.11490i	−0.870506	−	0.492158i
$344$	5.83059	+	34.4429i	0.314364	+	1.85704i
$345$	−1.50249	−	0.260155i	−0.0808913	−	0.0140063i
$346$	0.174897	+	3.12562i	0.00940251	+	0.168034i
$347$	−8.85066	+	2.37153i	−0.475128	+	0.127310i	−0.488433	−	0.872601i	$-0.662431\pi$
$347$	−8.85066	+	2.37153i	−0.475128	+	0.127310i	0.0133050	+	0.999911i	$0.495765\pi$
$348$	−11.2459	+	14.0902i	−0.602844	+	0.755315i
$349$			19.9513i			1.06797i	0.845495	+	0.533984i	$0.179306\pi$
$349$			19.9513i			1.06797i	−0.845495	+	0.533984i	$0.820694\pi$
$350$	18.3474	+	3.65667i	0.980712	+	0.195457i
$351$		−	24.7434i		−	1.32070i
$352$	−2.61029	+	4.71171i	−0.139129	+	0.251135i
$353$	−2.39430	+	0.641552i	−0.127436	+	0.0341464i	−0.321973	−	0.946749i	$-0.604346\pi$
$353$	−2.39430	+	0.641552i	−0.127436	+	0.0341464i	0.194537	+	0.980895i	$0.437679\pi$
$354$	22.1816	−	1.24119i	1.17894	−	0.0659687i
$355$	16.7606	+	2.90208i	0.889561	+	0.154027i
$356$	1.69532	−	3.88142i	0.0898516	−	0.205715i
$357$	−8.23343	+	3.02482i	−0.435759	+	0.160091i
$358$	−4.76203	+	22.7999i	−0.251681	+	1.20501i
$359$	−7.94645	−	13.7637i	−0.419398	−	0.726418i	0.576481	−	0.817110i	$-0.304425\pi$
$359$	−7.94645	−	13.7637i	−0.419398	−	0.726418i	−0.995879	+	0.0906921i	$0.971092\pi$
$360$	8.82459	+	2.40011i	0.465097	+	0.126497i
$361$	1.57601	−	2.72973i	0.0829481	−	0.143670i
$362$	−8.02889	+	2.64019i	−0.421989	+	0.138765i
$363$	8.89708	−	8.89708i	0.466976	−	0.466976i
$364$	22.4128	+	7.46534i	1.17475	+	0.391290i
$365$	−2.96969	−	32.7792i	−0.155441	−	1.71574i
$366$	−4.78765	+	9.47905i	−0.250255	+	0.495478i
$367$	−10.3988	+	2.78634i	−0.542812	+	0.145446i	−0.519798	−	0.854289i	$-0.673993\pi$
$367$	−10.3988	+	2.78634i	−0.542812	+	0.145446i	−0.0230136	+	0.999735i	$0.507326\pi$
$368$	1.16565	−	1.85180i	0.0607638	−	0.0965316i
$369$	4.65148	−	2.68553i	0.242147	−	0.139803i
$370$	0.379189	−	3.26694i	0.0197131	−	0.169840i
$371$	−7.74521	+	0.701119i	−0.402111	+	0.0364003i
$372$	−3.59195	−	9.16305i	−0.186234	−	0.475082i
$373$	−3.82144	+	14.2618i	−0.197867	+	0.738448i	0.793640	+	0.608388i	$0.208184\pi$
$373$	−3.82144	+	14.2618i	−0.197867	+	0.738448i	−0.991506	+	0.130060i	$0.958483\pi$
$374$	0.200081	+	3.57568i	0.0103459	+	0.184894i
$375$	13.4954	+	3.48258i	0.696897	+	0.179840i
$376$	5.78331	+	6.98880i	0.298251	+	0.360420i
$377$	22.8262	−	22.8262i	1.17561	−	1.17561i
$378$	−16.6432	−	12.3715i	−0.856034	−	0.636322i
$379$	−26.4563			−1.35897			−0.679483	−	0.733691i	$-0.737796\pi$
$379$	−26.4563			−1.35897			−0.679483	+	0.733691i	$0.737796\pi$
$380$	−9.80505	+	14.8600i	−0.502989	+	0.762303i
$381$	1.07909	−	1.86905i	0.0552837	−	0.0957542i
$382$	7.58420	−	8.48327i	0.388041	−	0.434042i
$383$	28.3799	+	7.60437i	1.45015	+	0.388565i	0.896074	−	0.443904i	$-0.146407\pi$
$383$	28.3799	+	7.60437i	1.45015	+	0.388565i	0.554071	+	0.832470i	$0.313074\pi$
$384$	8.60163	−	11.1771i	0.438950	−	0.570377i
$385$	−4.29320	+	3.64724i	−0.218802	+	0.185880i
$386$	17.2288	−	11.2754i	0.876922	−	0.573901i
$387$	−4.62219	+	17.2503i	−0.234959	+	0.876880i
$388$	−1.30436	+	8.63018i	−0.0662189	+	0.438131i
$389$	8.09963	+	4.67632i	0.410667	+	0.237099i	0.691076	−	0.722782i	$-0.257137\pi$
$389$	8.09963	+	4.67632i	0.410667	+	0.237099i	−0.280409	+	0.959881i	$0.590470\pi$
$390$	16.3609	+	6.48456i	0.828468	+	0.328359i
$391$		−	1.45481i		−	0.0735731i
$392$	16.2277	−	11.3429i	0.819622	−	0.572905i
$393$	1.14998	+	1.14998i	0.0580090	+	0.0580090i
$394$	14.8703	−	29.4416i	0.749155	−	1.48325i
$395$	−22.4520	+	8.25035i	−1.12968	+	0.415120i
$396$	−2.21629	+	1.63432i	−0.111373	+	0.0821275i
$397$	17.1641	+	4.59912i	0.861443	+	0.230823i	0.662384	−	0.749164i	$-0.269545\pi$
$397$	17.1641	+	4.59912i	0.861443	+	0.230823i	0.199059	+	0.979987i	$0.436211\pi$
$398$	2.79186	−	13.3670i	0.139943	−	0.670028i
$399$	10.7327	−	7.56340i	0.537309	−	0.378644i
$400$	−11.9905	+	16.0071i	−0.599524	+	0.800357i
$401$	−3.07671	−	5.32902i	−0.153644	−	0.266118i	0.778921	−	0.627122i	$-0.215767\pi$
$401$	−3.07671	−	5.32902i	−0.153644	−	0.266118i	−0.932564	+	0.361004i	$0.882434\pi$
$402$	19.5813	+	17.5061i	0.976629	+	0.873124i
$403$	4.56121	+	17.0227i	0.227210	+	0.847960i
$404$	−0.319102	−	2.84244i	−0.0158759	−	0.141417i
$405$	−4.41569	−	3.68206i	−0.219417	−	0.182963i
$406$	−3.94071	−	26.7666i	−0.195574	−	1.32841i
$407$	0.700261	+	0.700261i	0.0347107	+	0.0347107i
$408$	0.881145	−	9.33562i	0.0436232	−	0.462182i
$409$	−5.66917	−	3.27310i	−0.280322	−	0.161844i	0.353247	−	0.935530i	$-0.385078\pi$
$409$	−5.66917	−	3.27310i	−0.280322	−	0.161844i	−0.633569	+	0.773686i	$0.718411\pi$
$410$	1.71175	+	11.6209i	0.0845372	+	0.573913i
$411$	−1.25221	+	0.722965i	−0.0617670	+	0.0356612i
$412$	−18.9475	+	7.42751i	−0.933478	+	0.365927i
$413$	−21.3541	+	25.6050i	−1.05077	+	1.25994i
$414$	0.936005	−	0.612568i	0.0460022	−	0.0301061i
$415$	10.4288	+	14.7965i	0.511927	+	0.726331i
$416$	−17.5389	+	18.1707i	−0.859917	+	0.890890i
$417$	−5.63057	−	21.0136i	−0.275730	−	1.02904i
$418$	−1.67460	−	5.09253i	−0.0819076	−	0.249084i
$419$	−17.7908			−0.869139			−0.434569	−	0.900638i	$-0.643099\pi$
$419$	−17.7908			−0.869139			−0.434569	+	0.900638i	$0.643099\pi$
$420$	12.5421	−	7.76267i	0.611992	−	0.378779i
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	4.60961	+	14.0180i	0.224392	+	0.682385i
$423$	1.20029	+	4.47954i	0.0583601	+	0.217803i
$424$	2.89687	−	7.79281i	0.140684	−	0.378452i
$425$	−1.07722	+	13.2536i	−0.0522529	+	0.642896i
$426$	11.2215	−	7.34393i	0.543686	−	0.355815i
$427$	−5.49588	−	14.9595i	−0.265964	−	0.723942i
$428$	−0.0293616	−	0.0749013i	−0.00141925	−	0.00362049i
$429$	−4.58934	+	2.64965i	−0.221575	+	0.127926i
$430$	−31.3466	−	23.2976i	−1.51167	−	1.12351i
$431$	13.1055	+	7.56644i	0.631268	+	0.364463i	0.781243	−	0.624227i	$-0.214586\pi$
$431$	13.1055	+	7.56644i	0.631268	+	0.364463i	−0.149975	+	0.988690i	$0.547919\pi$
$432$	19.6088	−	10.3433i	0.943427	−	0.497640i
$433$	−5.45382	−	5.45382i	−0.262094	−	0.262094i	0.563811	−	0.825904i	$-0.309335\pi$
$433$	−5.45382	−	5.45382i	−0.262094	−	0.262094i	−0.825904	+	0.563811i	$0.809335\pi$
$434$	13.7306	+	5.44321i	0.659090	+	0.261282i
$435$	−1.81860	−	20.0736i	−0.0871953	−	0.962454i
$436$	−12.5073	+	1.40411i	−0.598990	+	0.0672446i
$437$	0.563632	+	2.10350i	0.0269622	+	0.100624i
$438$	−19.3457	−	17.2954i	−0.924371	−	0.826405i
$439$	12.8732	+	22.2970i	0.614402	+	1.06418i	0.990489	+	0.137592i	$0.0439362\pi$
$439$	12.8732	+	22.2970i	0.614402	+	1.06418i	−0.376087	+	0.926585i	$0.622730\pi$
$440$	−1.53681	−	5.82285i	−0.0732644	−	0.277593i
$441$	9.95730	−	1.81762i	0.474157	−	0.0865536i
$442$	−3.43289	+	16.4362i	−0.163286	+	0.781790i
$443$	−16.7002	−	4.47481i	−0.793452	−	0.212605i	−0.160745	−	0.986996i	$-0.551390\pi$
$443$	−16.7002	−	4.47481i	−0.793452	−	0.212605i	−0.632707	+	0.774391i	$0.718056\pi$
$444$	−1.53894	−	2.08696i	−0.0730351	−	0.0990428i
$445$	1.63333	+	4.44484i	0.0774273	+	0.210706i
$446$	9.67150	−	19.1486i	0.457959	−	0.906711i
$447$	−9.88223	−	9.88223i	−0.467413	−	0.467413i
$448$	3.45283	+	20.8825i	0.163131	+	0.986604i
$449$			11.0999i			0.523839i	0.965090	+	0.261919i	$0.0843555\pi$
$449$			11.0999i			0.523839i	−0.965090	+	0.261919i	$0.915645\pi$
$450$	−8.98078	+	4.88755i	−0.423358	+	0.230401i
$451$	−3.06308	−	1.76847i	−0.144235	−	0.0832739i
$452$	30.3475	+	4.58670i	1.42743	+	0.215740i
$453$	4.84627	−	18.0865i	0.227698	−	0.849779i
$454$	11.8597	−	7.76157i	0.556603	−	0.364268i
$455$	−23.8687	+	11.3077i	−1.11898	+	0.530115i
$456$	2.34281	+	13.8397i	0.109712	+	0.648101i
$457$	20.5140	+	5.49672i	0.959606	+	0.257126i	0.704434	−	0.709770i	$-0.251201\pi$
$457$	20.5140	+	5.49672i	0.959606	+	0.257126i	0.255172	+	0.966896i	$0.417868\pi$
$458$	16.1069	−	18.0163i	0.752627	−	0.841847i
$459$	7.36989	−	12.7650i	0.343997	−	0.595821i
$460$	0.491167	+	2.39659i	0.0229008	+	0.111741i
$461$	−8.61652			−0.401311			−0.200656	−	0.979662i	$-0.564307\pi$
$461$	−8.61652			−0.401311			−0.200656	+	0.979662i	$0.564307\pi$
$462$	−0.512393	+	4.41175i	−0.0238387	+	0.205253i
$463$	−1.63340	+	1.63340i	−0.0759103	+	0.0759103i	−0.744043	−	0.668132i	$-0.767094\pi$
$463$	−1.63340	+	1.63340i	−0.0759103	+	0.0759103i	0.668132	+	0.744043i	$0.267094\pi$
$464$	27.6313	+	8.54761i	1.28275	+	0.396813i
$465$	9.98695	+	4.61955i	0.463134	+	0.214227i
$466$	0.148181	+	2.64817i	0.00686435	+	0.122674i
$467$	−6.59489	+	24.6125i	−0.305175	+	1.13893i	0.627619	+	0.778521i	$0.284030\pi$
$467$	−6.59489	+	24.6125i	−0.305175	+	1.13893i	−0.932794	+	0.360409i	$0.882637\pi$
$468$	−12.0203	+	4.71199i	−0.555637	+	0.217812i
$469$	−39.2576	+	3.55372i	−1.81275	+	0.164095i
$470$	−10.0745	−	1.16933i	−0.464701	−	0.0539372i
$471$	−8.12741	+	4.69236i	−0.374491	+	0.216213i
$472$	−14.8421	−	32.4058i	−0.683161	−	1.49160i
$473$	11.3596	−	3.04379i	0.522313	−	0.139953i
$474$	−8.50228	+	16.8336i	−0.390523	+	0.773194i
$475$	−3.57726	−	19.5807i	−0.164136	−	0.898423i
$476$	9.33910	+	10.5271i	0.428057	+	0.482507i
$477$	3.00540	−	3.00540i	0.137608	−	0.137608i
$478$	20.4448	−	6.72298i	0.935124	−	0.307502i
$479$	−4.63924	+	8.03541i	−0.211972	+	0.367147i	−0.952332	−	0.305064i	$-0.901322\pi$
$479$	−4.63924	+	8.03541i	−0.211972	+	0.367147i	0.740359	+	0.672211i	$0.234655\pi$
$480$	1.70029	+	15.6765i	0.0776074	+	0.715531i
$481$	2.32156	+	4.02106i	0.105854	+	0.183345i
$482$	3.80954	−	18.2395i	0.173520	−	0.830787i
$483$	0.307949	−	1.77775i	0.0140122	−	0.0808903i
$484$	−18.4990	−	8.07996i	−0.840865	−	0.367271i
$485$	−5.62182	−	7.97633i	−0.255274	−	0.362186i
$486$	18.9517	−	1.06046i	0.859666	−	0.0481034i
$487$	17.2022	−	4.60932i	0.779506	−	0.208868i	0.152939	−	0.988236i	$-0.451126\pi$
$487$	17.2022	−	4.60932i	0.779506	−	0.208868i	0.626567	+	0.779368i	$0.284459\pi$
$488$	16.9621	+	1.60097i	0.767839	+	0.0724727i
$489$			8.28866i			0.374826i
$490$	−4.32822	+	21.7087i	−0.195529	+	0.980698i
$491$			2.49970i			0.112810i	0.998408	+	0.0564049i	$0.0179638\pi$
$491$			2.49970i			0.112810i	−0.998408	+	0.0564049i	$0.982036\pi$
$492$	7.23821	+	5.77707i	0.326324	+	0.260450i
$493$	18.5748	−	4.97711i	0.836569	−	0.224158i
$494$	−1.40421	−	25.0949i	−0.0631784	−	1.12907i
$495$	0.525267	−	3.03361i	0.0236090	−	0.136351i
$496$	−11.5836	+	10.7305i	−0.520117	+	0.481816i
$497$	−3.43524	+	19.8312i	−0.154092	+	0.889550i
$498$	13.9708	+	2.91797i	0.626047	+	0.130757i
$499$	−3.26199	−	5.64993i	−0.146027	−	0.252926i	0.783729	−	0.621103i	$-0.213315\pi$
$499$	−3.26199	−	5.64993i	−0.146027	−	0.252926i	−0.929756	+	0.368178i	$0.879982\pi$
$500$	−2.70008	−	22.1971i	−0.120751	−	0.992683i
$501$	5.22947	−	9.05770i	0.233635	−	0.404668i
$502$	6.49618	+	19.7551i	0.289938	+	0.881713i
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	−0.953313	−	0.301985i	$-0.902351\pi$
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	0.301985	+	0.953313i	$0.402351\pi$
$504$	−2.84061	+	10.4412i	−0.126531	+	0.465088i
$505$	2.45607	+	2.04801i	0.109294	+	0.0911353i
$506$	−0.657529	−	0.332103i	−0.0292308	−	0.0147638i
$507$	−8.34561	+	2.23620i	−0.370641	+	0.0993131i
$508$	−3.42363	−	0.517445i	−0.151899	−	0.0229579i
$509$	29.8459	−	17.2316i	1.32290	−	0.763775i	0.338708	−	0.940892i	$-0.390010\pi$
$509$	29.8459	−	17.2316i	1.32290	−	0.763775i	0.984190	+	0.177116i	$0.0566769\pi$
$510$	6.50911	+	8.21853i	0.288228	+	0.363922i
$511$	38.7851	−	3.51094i	1.71575	−	0.155315i
$512$	−21.7316	−	6.30364i	−0.960412	−	0.278584i
$513$	−5.71056	+	21.3121i	−0.252128	+	0.940953i
$514$	−18.6640	+	1.04436i	−0.823233	+	0.0460648i
$515$	9.55240	−	20.6512i	0.420929	−	0.910001i
$516$	−30.6006	+	3.43532i	−1.34711	+	0.151232i
$517$	2.15944	−	2.15944i	0.0949721	−	0.0949721i
$518$	3.86547	+	0.448946i	0.169839	+	0.0197256i
$519$	−2.75949			−0.121128
$520$	0.106060	−	28.2351i	0.00465102	−	1.23819i
$521$	16.9526	−	29.3627i	0.742705	−	1.28640i	−0.208555	−	0.978011i	$-0.566876\pi$
$521$	16.9526	−	29.3627i	0.742705	−	1.28640i	0.951259	−	0.308392i	$-0.0997908\pi$
$522$	11.0234	+	9.85510i	0.482480	+	0.431346i
$523$	−17.8250	−	4.77618i	−0.779431	−	0.208848i	−0.152897	−	0.988242i	$-0.548860\pi$
$523$	−17.8250	−	4.77618i	−0.779431	−	0.208848i	−0.626534	+	0.779394i	$0.715527\pi$
$524$	1.04437	−	2.39107i	0.0456233	−	0.104455i
$525$	−4.12182	+	15.9676i	−0.179891	+	0.696884i
$526$	8.18443	+	12.5058i	0.356858	+	0.545280i
$527$	−2.71715	+	10.1405i	−0.118361	+	0.441728i
$528$	−4.01825	−	2.52937i	−0.174872	−	0.110077i
$529$	−19.6594	−	11.3504i	−0.854758	−	0.493495i
$530$	3.68848	+	8.53199i	0.160217	+	0.370606i
$531$		−	18.2217i		−	0.790756i
$532$	−17.5818	−	11.6028i	−0.762267	−	0.503044i
$533$	−11.7259	−	11.7259i	−0.507906	−	0.507906i
$534$	3.33257	+	1.68321i	0.144214	+	0.0728394i
$535$	0.0816361	+	0.0377615i	0.00352944	+	0.00163257i
$536$	14.6832	−	39.4989i	0.634216	−	1.70609i
$537$	−19.8318	−	5.31392i	−0.855806	−	0.229312i
$538$	16.8842	+	3.52645i	0.727928	+	0.152036i
$539$	−4.31510	−	5.08010i	−0.185864	−	0.218815i
$540$	−7.83111	+	23.5166i	−0.336997	+	1.01199i
$541$	−1.59149	−	2.75655i	−0.0684236	−	0.118513i	0.829784	−	0.558085i	$-0.188464\pi$
$541$	−1.59149	−	2.75655i	−0.0684236	−	0.118513i	−0.898208	+	0.439572i	$0.855130\pi$
$542$	−6.20392	+	6.93937i	−0.266481	+	0.298071i
$543$	−1.92824	−	7.19630i	−0.0827488	−	0.308823i
$544$	−14.4605	+	4.15016i	−0.619988	+	0.177937i
$545$	9.01164	−	10.8072i	0.386016	−	0.462928i
$546$	−7.67406	+	19.3580i	−0.328419	+	0.828444i
$547$	15.6791	+	15.6791i	0.670391	+	0.670391i	0.957806	−	0.287415i	$-0.0927960\pi$
$547$	15.6791	+	15.6791i	0.670391	+	0.670391i	−0.287415	+	0.957806i	$0.592796\pi$
$548$	1.81310	+	1.44710i	0.0774517	+	0.0618169i
$549$	7.54315	+	4.35504i	0.321934	+	0.185869i
$550$	5.74432	+	3.51240i	0.244939	+	0.149769i
$551$	−24.9289	+	14.3927i	−1.06201	+	0.613151i
$552$	1.57237	+	1.11709i	0.0669246	+	0.0475466i
$553$	−9.76000	−	26.5663i	−0.415037	−	1.12971i
$554$	−3.18042	−	4.85969i	−0.135123	−	0.206469i
$555$	2.85658	+	0.494614i	0.121255	+	0.0209952i
$556$	−28.0909	+	20.7145i	−1.19132	+	0.878490i
$557$	5.52434	+	20.6171i	0.234074	+	0.873575i	0.978564	+	0.205942i	$0.0660258\pi$
$557$	5.52434	+	20.6171i	0.234074	+	0.873575i	−0.744491	+	0.667633i	$0.767308\pi$
$558$	−7.66835	+	2.52163i	−0.324627	+	0.106749i
$559$	55.1382			2.33210
$560$	−18.9389	−	14.1887i	−0.800313	−	0.599583i
$561$	−3.15683			−0.133282
$562$	−43.3627	+	14.2592i	−1.82915	+	0.601488i
$563$	3.52319	+	13.1487i	0.148485	+	0.554153i	0.999576	+	0.0291340i	$0.00927495\pi$
$563$	3.52319	+	13.1487i	0.148485	+	0.554153i	−0.851091	+	0.525019i	$0.824058\pi$
$564$	−6.43570	+	4.74574i	−0.270992	+	0.199832i
$565$	−28.0483	+	19.7688i	−1.18000	+	0.831679i
$566$	−15.1231	−	23.1081i	−0.635669	−	0.971305i
$567$	4.35705	−	5.22439i	0.182979	−	0.219404i
$568$	−17.5402	−	12.4614i	−0.735969	−	0.522869i
$569$	−20.3421	+	11.7445i	−0.852787	+	0.492357i	−0.861590	−	0.507605i	$-0.830531\pi$
$569$	−20.3421	+	11.7445i	−0.852787	+	0.492357i	0.00880335	+	0.999961i	$0.497198\pi$
$570$	−12.5955	−	9.36130i	−0.527569	−	0.392102i
$571$	−23.4830	−	13.5579i	−0.982734	−	0.567382i	−0.0796395	−	0.996824i	$-0.525377\pi$
$571$	−23.4830	−	13.5579i	−0.982734	−	0.567382i	−0.903094	+	0.429442i	$0.858710\pi$
$572$	6.64498	+	5.30359i	0.277840	+	0.221754i
$573$	7.09267	+	7.09267i	0.296301	+	0.296301i
$574$	−13.7501	+	2.02436i	−0.573920	+	0.0844951i
$575$	−2.25014	−	1.55497i	−0.0938374	−	0.0648469i
$576$	−8.75892	−	7.55617i	−0.364955	−	0.314841i
$577$	7.22183	+	26.9522i	0.300649	+	1.12204i	0.936627	+	0.350329i	$0.113930\pi$
$577$	7.22183	+	26.9522i	0.300649	+	1.12204i	−0.635978	+	0.771707i	$0.719403\pi$
$578$	9.35709	−	10.4663i	0.389204	−	0.435342i
$579$	9.07505	+	15.7184i	0.377146	+	0.653236i
$580$	−28.9189	+	14.4702i	−1.20079	+	0.600842i
$581$	−17.5083	+	12.3382i	−0.726368	+	0.511874i
$582$	−7.53124	−	1.57299i	−0.312180	−	0.0652024i
$583$	−2.70351	−	0.724403i	−0.111968	−	0.0300017i
$584$	−14.5064	+	39.0235i	−0.600280	+	1.61480i
$585$	6.06002	−	13.1011i	0.250551	−	0.541663i
$586$	22.6471	+	11.4385i	0.935544	+	0.472522i
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	0.998423	−	0.0561427i	$-0.0178802\pi$
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	−0.0561427	+	0.998423i	$0.517880\pi$
$588$	9.18383	+	14.8407i	0.378735	+	0.612019i
$589$		−	15.7148i		−	0.647516i
$590$	37.0463	+	14.6831i	1.52517	+	0.604494i
$591$	25.1794	+	14.5374i	1.03574	+	0.597987i
$592$	−2.21617	+	3.52069i	−0.0910842	+	0.144700i
$593$	9.88391	−	36.8872i	0.405883	−	1.51478i	−0.396537	−	0.918019i	$-0.629788\pi$
$593$	9.88391	−	36.8872i	0.405883	−	1.51478i	0.802421	−	0.596759i	$-0.203545\pi$
$594$	−4.08700	−	6.24494i	−0.167691	−	0.256233i
$595$	−15.6818	−	1.27573i	−0.642893	−	0.0522999i
$596$	−8.97462	+	20.5474i	−0.367615	+	0.841653i
$597$	11.6269	+	3.11542i	0.475857	+	0.127506i
$598$	−2.57479	−	2.30191i	−0.105291	−	0.0941321i
$599$	14.4801	−	25.0802i	0.591640	−	1.02475i	−0.402372	−	0.915476i	$-0.631814\pi$
$599$	14.4801	−	25.0802i	0.591640	−	1.02475i	0.994012	−	0.109274i	$-0.0348526\pi$
$600$	−13.4975	−	11.3412i	−0.551032	−	0.463003i
$601$	−8.88262			−0.362330			−0.181165	−	0.983453i	$-0.557987\pi$
$601$	−8.88262			−0.362330			−0.181165	+	0.983453i	$0.557987\pi$
$602$	27.5688	−	37.0878i	1.12362	−	1.51159i
$603$	15.2333	−	15.2333i	0.620347	−	0.620347i
$604$	−29.8534	+	3.35144i	−1.21472	+	0.136368i
$605$	21.1843	−	7.78453i	0.861266	−	0.316486i
$606$	2.51736	−	0.140861i	0.102261	−	0.00572210i
$607$	11.8891	−	44.3709i	0.482565	−	1.80096i	−0.108218	−	0.994127i	$-0.534515\pi$
$607$	11.8891	−	44.3709i	0.482565	−	1.80096i	0.590783	−	0.806830i	$-0.298819\pi$
$608$	19.3004	−	11.6030i	0.782734	−	0.470565i
$609$	23.7515	−	2.15006i	0.962461	−	0.0871249i
$610$	−14.9324	+	11.8266i	−0.604597	+	0.478844i
$611$	12.4000	−	7.15915i	0.501651	−	0.289628i
$612$	−7.60470	−	1.14937i	−0.307402	−	0.0464605i
$613$	−0.223941	+	0.0600047i	−0.00904487	+	0.00242357i	−0.263339	−	0.964703i	$-0.584824\pi$
$613$	−0.223941	+	0.0600047i	−0.00904487	+	0.00242357i	0.254294	+	0.967127i	$0.418157\pi$
$614$	−17.8181	−	8.99949i	−0.719078	−	0.363190i
$615$	−10.3119	+	0.934224i	−0.415815	+	0.0376716i
$616$	6.88982	−	1.81787i	0.277599	−	0.0732441i
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.0957517	+	0.995405i	$0.530525\pi$
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.995405	+	0.0957517i	$0.969475\pi$
$618$	−5.60389	−	17.0416i	−0.225421	−	0.685514i
$619$	−7.14970	+	12.3836i	−0.287371	+	0.497741i	−0.973181	−	0.230039i	$-0.926115\pi$
$619$	−7.14970	+	12.3836i	−0.287371	+	0.497741i	0.685811	+	0.727780i	$0.259448\pi$
$620$	1.05249	−	17.6223i	0.0422690	−	0.707730i
$621$	1.51593	+	2.62566i	0.0608320	+	0.105364i
$622$	19.2957	+	4.03012i	0.773685	+	0.161593i
$623$	−5.25935	+	1.93220i	−0.210711	+	0.0774119i
$624$	−15.1284	−	16.3310i	−0.605619	−	0.653762i
$625$	19.3479	+	15.8322i	0.773915	+	0.633290i
$626$	−0.387808	−	6.93059i	−0.0154999	−	0.277002i
$627$	4.56444	−	1.22304i	0.182286	−	0.0488434i
$628$	11.7678	+	9.39230i	0.469587	+	0.374794i
$629$			2.76594i			0.110285i
$630$	−5.78225	−	10.6266i	−0.230370	−	0.423375i
$631$		−	30.7128i		−	1.22266i	−0.791377	−	0.611328i	$-0.790636\pi$
$631$		−	30.7128i		−	1.22266i	0.791377	−	0.611328i	$-0.209364\pi$
$632$	30.1226	+	2.84313i	1.19821	+	0.113094i
$633$	−12.5643	+	3.36660i	−0.499387	+	0.133810i
$634$	−48.5771	+	2.71818i	−1.92924	+	0.107953i
$635$	3.16424	−	2.23020i	0.125569	−	0.0885027i
$636$	6.71584	+	2.93332i	0.266300	+	0.116314i
$637$	−13.3774	−	28.2428i	−0.530033	−	1.11902i
$638$	1.99075	−	9.53141i	0.0788144	−	0.377352i
$639$	−5.49985	−	9.52602i	−0.217571	−	0.376843i
$640$	22.4203	−	11.7188i	0.886239	−	0.463228i
$641$	−20.7752	+	35.9837i	−0.820572	+	1.42127i	0.0846851	+	0.996408i	$0.473012\pi$
$641$	−20.7752	+	35.9837i	−0.820572	+	1.42127i	−0.905257	+	0.424864i	$0.860322\pi$
$642$	0.0673670	−	0.0221527i	0.00265876	−	0.000874296i
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	−0.910090	−	0.414410i	$-0.863988\pi$
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	0.414410	+	0.910090i	$0.363988\pi$
$644$	−2.83572	+	0.580949i	−0.111743	+	0.0228926i
$645$	22.0481	−	26.4410i	0.868142	−	1.04111i
$646$	6.75018	−	13.3646i	0.265582	−	0.525825i
$647$	34.4127	−	9.22084i	1.35290	−	0.362509i	0.491696	−	0.870767i	$-0.336377\pi$
$647$	34.4127	−	9.22084i	1.35290	−	0.362509i	0.861205	+	0.508258i	$0.169710\pi$
$648$	3.02834	+	6.61200i	0.118964	+	0.259744i
$649$	−10.3917	+	5.99966i	−0.407910	+	0.235507i
$650$	21.7524	+	22.8774i	0.853200	+	0.897325i
$651$	−5.46679	+	11.8163i	−0.214261	+	0.463118i
$652$	12.3807	−	4.85329i	0.484866	−	0.190070i
$653$	3.40648	−	12.7132i	0.133306	−	0.497505i	−0.866693	−	0.498842i	$-0.833759\pi$
$653$	3.40648	−	12.7132i	0.133306	−	0.497505i	0.999999	+	0.00133684i	$0.000425528\pi$
$654$	−0.619816	−	11.0769i	−0.0242367	−	0.433140i
$655$	1.00618	+	2.73816i	0.0393148	+	0.106989i
$656$	4.39095	−	14.1943i	0.171438	−	0.554195i
$657$	−15.0499	+	15.0499i	−0.587153	+	0.587153i
$658$	1.38444	−	11.9202i	0.0539712	−	0.464697i
$659$	−10.3786			−0.404294			−0.202147	−	0.979355i	$-0.564792\pi$
$659$	−10.3786			−0.404294			−0.202147	+	0.979355i	$0.564792\pi$
$660$	5.20040	−	1.06579i	0.202425	−	0.0414860i
$661$	−11.5282	+	19.9675i	−0.448397	+	0.776646i	−0.998282	−	0.0585946i	$-0.981338\pi$
$661$	−11.5282	+	19.9675i	−0.448397	+	0.776646i	0.549885	+	0.835240i	$0.314671\pi$
$662$	−12.2118	+	13.6594i	−0.474624	+	0.530889i
$663$	−14.2965	−	3.83074i	−0.555231	−	0.148774i
$664$	−3.82184	−	22.5767i	−0.148316	−	0.876144i
$665$	23.1685	−	4.23097i	0.898435	−	0.164070i
$666$	−1.77956	+	1.16463i	−0.0689567	+	0.0451286i
$667$	−1.02375	+	3.82069i	−0.0396398	+	0.147938i
$668$	−16.5914	−	2.50762i	−0.641942	−	0.0970228i
$669$	16.3765	+	9.45496i	0.633151	+	0.365550i
$670$	18.6955	+	43.2455i	0.722271	+	1.67072i
$671$		−	5.73573i		−	0.221425i
$672$	−18.5488	+	2.01046i	−0.715537	+	0.0775551i
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.996700	+	0.0811716i	$0.0258662\pi$
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.0811716	+	0.996700i	$0.474134\pi$
$674$	6.70005	−	13.2654i	0.258076	−	0.510964i
$675$	−11.8662	−	25.0428i	−0.456731	−	0.963897i
$676$	8.22682	+	11.1564i	0.316416	+	0.429092i
$677$	33.0709	+	8.86132i	1.27102	+	0.340568i	0.830421	−	0.557137i	$-0.188100\pi$
$677$	33.0709	+	8.86132i	1.27102	+	0.340568i	0.440597	+	0.897705i	$0.354767\pi$
$678$	−5.53131	+	26.4831i	−0.212429	+	1.01708i
$679$	9.43821	−	6.65114i	0.362205	−	0.255247i
$680$	8.46464	−	14.5348i	0.324604	−	0.557385i
$681$	6.24694	+	10.8200i	0.239383	+	0.414624i
$682$	3.96293	+	3.54293i	0.151748	+	0.135666i
$683$	−0.498756	−	1.86138i	−0.0190844	−	0.0712239i	0.955727	−	0.294255i	$-0.0950715\pi$
$683$	−0.498756	−	1.86138i	−0.0190844	−	0.0712239i	−0.974811	+	0.223031i	$0.928405\pi$
$684$	11.4409	−	1.28439i	0.437452	−	0.0491099i
$685$	−2.58302	+	0.234014i	−0.0986922	+	0.00894120i
$686$	−25.6857	−	5.12310i	−0.980684	−	0.195601i
$687$	15.0630	+	15.0630i	0.574691	+	0.574691i
$688$	23.0490	+	43.6963i	0.878734	+	1.66591i
$689$	−11.3645	−	6.56128i	−0.432952	−	0.249965i
$690$	−2.13344	+	0.314254i	−0.0812186	+	0.0119635i
$691$	−30.8812	+	17.8293i	−1.17478	+	0.678257i	−0.954800	−	0.297248i	$-0.903931\pi$
$691$	−30.8812	+	17.8293i	−1.17478	+	0.678257i	−0.219976	+	0.975505i	$0.570598\pi$
$692$	1.61577	+	4.12182i	0.0614225	+	0.156688i
$693$	3.58937	+	0.621767i	0.136349	+	0.0236190i
$694$	−10.8427	+	7.09598i	−0.411582	+	0.269360i
$695$	6.65760	−	38.4501i	0.252537	−	1.45850i
$696$	−8.88357	+	23.8975i	−0.336731	+	0.905833i
$697$	−2.55677	−	9.54198i	−0.0968444	−	0.361428i
$698$	8.81390	+	26.8034i	0.333611	+	1.01452i
$699$	−2.33797			−0.0884301
$700$	26.2642	−	3.19285i	0.992692	−	0.120678i
$701$	33.6504			1.27096			0.635479	−	0.772119i	$-0.280803\pi$
$701$	33.6504			1.27096			0.635479	+	0.772119i	$0.280803\pi$
$702$	−10.9309	−	33.2413i	−0.412561	−	1.25461i
$703$	−1.07159	−	3.99924i	−0.0404159	−	0.150834i
$704$	−1.42528	+	7.48307i	−0.0537173	+	0.282029i
$705$	1.52527	−	8.80902i	0.0574452	−	0.331767i
$706$	−2.93319	+	1.91962i	−0.110392	+	0.0722460i
$707$	−2.42345	+	2.90588i	−0.0911433	+	0.109287i
$708$	29.2514	−	11.4667i	1.09934	−	0.430944i
$709$	−7.92917	+	4.57791i	−0.297786	+	0.171927i	−0.641448	−	0.767167i	$-0.721666\pi$
$709$	−7.92917	+	4.57791i	−0.297786	+	0.171927i	0.343662	+	0.939093i	$0.388333\pi$
$710$	23.7990	−	3.50558i	0.893160	−	0.131562i
$711$	13.3957	+	7.73401i	0.502378	+	0.290048i
$712$	0.562858	−	5.96341i	0.0210940	−	0.223488i
$713$	−1.52693	−	1.52693i	−0.0571839	−	0.0571839i
$714$	−9.72486	+	7.70097i	−0.363944	+	0.288202i
$715$	−9.46674	+	0.857657i	−0.354036	+	0.0320745i
$716$	3.67484	+	32.7341i	0.137335	+	1.22333i
$717$	4.91009	+	18.3247i	0.183370	+	0.684348i
$718$	−16.7560	−	14.9802i	−0.625328	−	0.559055i
$719$	6.67322	+	11.5584i	0.248869	+	0.431054i	0.963212	−	0.268742i	$-0.0866078\pi$
$719$	6.67322	+	11.5584i	0.248869	+	0.431054i	−0.714343	+	0.699796i	$0.753274\pi$
$720$	12.9156	−	0.674050i	0.481337	−	0.0251203i
$721$	24.4340	+	11.3043i	0.909970	+	0.420996i
$722$	0.911364	−	4.36348i	0.0339175	−	0.162392i
$723$	15.8651	+	4.25104i	0.590029	+	0.158098i
$724$	−9.62000	+	7.09387i	−0.357524	+	0.263642i
$725$	12.1556	−	34.0492i	0.451449	−	1.26456i
$726$	8.02224	−	15.8832i	0.297733	−	0.589481i
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	0.583602	−	0.812040i	$-0.301643\pi$
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	−0.812040	+	0.583602i	$0.801643\pi$
$728$	33.4082	+	0.127938i	1.23819	+	0.00474168i
$729$			24.4454i			0.905384i
$730$	−18.4705	−	42.7250i	−0.683624	−	1.58132i
$731$	28.4457	+	16.4231i	1.05210	+	0.607431i
$732$	−2.24436	+	14.8496i	−0.0829540	+	0.548857i
$733$	2.65865	−	9.92223i	0.0981996	−	0.366486i	−0.899286	−	0.437362i	$-0.855913\pi$
$733$	2.65865	−	9.92223i	0.0981996	−	0.366486i	0.997485	+	0.0708761i	$0.0225795\pi$
$734$	−12.7392	+	8.33717i	−0.470213	+	0.307731i
$735$	−18.8928	−	4.87838i	−0.696871	−	0.179942i
$736$	0.747914	−	3.00273i	0.0275685	−	0.110682i
$737$	−13.7031	−	3.67173i	−0.504760	−	0.135250i
$738$	5.06261	−	5.66275i	0.186357	−	0.208449i
$739$	−21.8583	+	37.8597i	−0.804070	+	1.39269i	0.112847	+	0.993612i	$0.464003\pi$
$739$	−21.8583	+	37.8597i	−0.804070	+	1.39269i	−0.916917	+	0.399078i	$0.869330\pi$
$740$	−0.933823	−	4.55646i	−0.0343280	−	0.167499i
$741$	22.1553			0.813897
$742$	−10.0955	+	4.36353i	−0.370618	+	0.160190i
$743$	−26.0186	+	26.0186i	−0.954529	+	0.954529i	−0.999010	−	0.0444813i	$-0.985836\pi$
$743$	−26.0186	+	26.0186i	−0.954529	+	0.954529i	0.0444813	+	0.999010i	$0.485836\pi$
$744$	−8.87356	−	10.7232i	−0.325320	−	0.393132i
$745$	−8.64649	−	23.5300i	−0.316783	−	0.862073i
$746$	1.16658	+	20.8481i	0.0427114	+	0.763304i
$747$	3.02975	−	11.3072i	0.110853	−	0.413709i
$748$	1.84843	+	4.71534i	0.0675854	+	0.172410i
$749$	−0.0446871	+	0.0965899i	−0.00163283	+	0.00352932i
$750$	19.6687	−	1.28321i	0.718201	−	0.0468562i
$751$	7.30460	−	4.21731i	0.266548	−	0.153892i	−0.360770	−	0.932655i	$-0.617486\pi$
$751$	7.30460	−	4.21731i	0.266548	−	0.153892i	0.627318	+	0.778763i	$0.284153\pi$
$752$	10.8570	+	6.83416i	0.395914	+	0.249216i
$753$	−17.7065	+	4.74444i	−0.645260	+	0.172897i
$754$	20.5817	−	40.7497i	0.749542	−	1.48402i
$755$	21.5097	−	25.7954i	0.782818	−	0.938790i
$756$	−27.8246	−	9.26793i	−1.01197	−	0.337072i
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	−0.643981	−	0.765041i	$-0.722718\pi$
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	0.765041	+	0.643981i	$0.222718\pi$
$758$	−35.5425	+	11.6876i	−1.29096	+	0.424514i
$759$	0.324667	−	0.562340i	0.0117847	−	0.0204117i
$760$	−6.60779	+	24.2952i	−0.239690	+	0.881279i
$761$	17.2317	+	29.8462i	0.624649	+	1.08192i	0.988609	+	0.150509i	$0.0480913\pi$
$761$	17.2317	+	29.8462i	0.624649	+	1.08192i	−0.363959	+	0.931415i	$0.618575\pi$
$762$	0.624010	−	2.98767i	0.0226055	−	0.108232i
$763$	12.7864	+	10.6636i	0.462899	+	0.386050i
$764$	6.44127	−	14.7473i	0.233037	−	0.533537i
$765$	7.02854	−	4.95381i	0.254118	−	0.179105i
$766$	41.4862	−	2.32140i	1.49896	−	0.0838755i
$767$	−54.3419	+	14.5609i	−1.96217	+	0.525763i
$768$	6.61809	−	18.8157i	0.238810	−	0.678953i
$769$		−	18.7498i		−	0.676135i	−0.941122	−	0.338067i	$-0.890227\pi$
$769$		−	18.7498i		−	0.676135i	0.941122	−	0.338067i	$-0.109773\pi$
$770$	−4.15642	+	6.79647i	−0.149787	+	0.244928i
$771$		−	16.4777i		−	0.593431i
$772$	18.1648	−	22.7590i	0.653764	−	0.819114i
$773$	−42.9466	+	11.5075i	−1.54468	+	0.413896i	−0.927775	−	0.373140i	$-0.878281\pi$
$773$	−42.9466	+	11.5075i	−1.54468	+	0.413896i	−0.616907	+	0.787036i	$0.711614\pi$
$774$	1.41102	+	25.2167i	0.0507181	+	0.906395i
$775$	12.7800	+	15.0412i	0.459072	+	0.540298i
$776$	2.06023	+	12.1704i	0.0739581	+	0.436891i
$777$	−0.585483	+	3.37991i	−0.0210041	+	0.121254i
$778$	12.9472	+	2.70418i	0.464181	+	0.0969497i
$779$	7.39361	+	12.8061i	0.264903	+	0.458826i
$780$	24.8447	+	1.48384i	0.889582	+	0.0531301i
$781$	−3.62174	+	6.27304i	−0.129596	+	0.224467i
$782$	−0.642695	−	1.95446i	−0.0229827	−	0.0698913i
$783$	−28.3379	+	28.3379i	−1.01271	+	1.01271i
$784$	16.7900	−	22.4075i	0.599641	−	0.800269i
$785$	−16.7650	+	1.51885i	−0.598367	+	0.0542102i
$786$	2.05297	+	1.03691i	0.0732269	+	0.0369852i
$787$	−1.04293	+	0.279451i	−0.0371763	+	0.00996136i	−0.277359	−	0.960766i	$-0.589459\pi$
$787$	−1.04293	+	0.279451i	−0.0371763	+	0.00996136i	0.240183	+	0.970728i	$0.422793\pi$
$788$	6.97092	−	46.1224i	0.248329	−	1.64304i
$789$	−11.4095	+	6.58729i	−0.406189	+	0.234514i
$790$	−26.5182	+	21.0025i	−0.943474	+	0.747236i
$791$	−23.3883	−	33.1889i	−0.831592	−	1.18006i
$792$	−2.25547	+	3.17471i	−0.0801447	+	0.112808i
$793$	6.96017	−	25.9757i	0.247163	−	0.922424i
$794$	25.0908	−	1.40398i	0.890439	−	0.0498253i
$795$	−7.69070	+	2.82607i	−0.272761	+	0.100230i
$796$	−2.15447	−	19.1912i	−0.0763630	−	0.680213i
$797$	−13.9414	+	13.9414i	−0.493829	+	0.493829i	−0.909510	−	0.415681i	$-0.863543\pi$
$797$	−13.9414	+	13.9414i	−0.493829	+	0.493829i	0.415681	+	0.909510i	$0.363543\pi$
$798$	11.0775	−	14.9024i	0.392140	−	0.527540i
$799$	8.52950			0.301752
$800$	−9.03703	+	26.8017i	−0.319507	+	0.947584i
$801$	1.53111	−	2.65196i	0.0540992	−	0.0937025i
$802$	−6.48759	−	5.80002i	−0.229085	−	0.204806i
$803$	13.5382	+	3.62754i	0.477751	+	0.128013i
$804$	34.0401	+	14.8679i	1.20050	+	0.524352i
$805$	1.84006	−	2.66227i	0.0648537	−	0.0938327i
$806$	13.6479	+	20.8540i	0.480726	+	0.734550i
$807$	−3.93515	+	14.6862i	−0.138524	+	0.516978i
$808$	−1.68440	−	3.67768i	−0.0592571	−	0.129380i
$809$	4.37439	+	2.52555i	0.153795	+	0.0887937i	0.574923	−	0.818208i	$-0.305032\pi$
$809$	4.37439	+	2.52555i	0.153795	+	0.0887937i	−0.421127	+	0.907001i	$0.638365\pi$
$810$	−7.55885	−	2.99591i	−0.265591	−	0.105265i
$811$			21.1629i			0.743131i	0.928407	+	0.371565i	$0.121179\pi$
$811$			21.1629i			0.743131i	−0.928407	+	0.371565i	$0.878821\pi$
$812$	−17.1189	−	34.2185i	−0.600754	−	1.20084i
$813$	−5.80185	−	5.80185i	−0.203480	−	0.203480i
$814$	1.25012	+	0.631405i	0.0438165	+	0.0221307i
$815$	−6.24174	+	13.4939i	−0.218639	+	0.472672i
$816$	−2.94044	−	12.9311i	−0.102936	−	0.452680i
$817$	−47.4920	−	12.7255i	−1.66154	−	0.445207i
$818$	−9.06216	−	1.89274i	−0.316851	−	0.0661781i
$819$	15.5009	+	7.17144i	0.541644	+	0.250590i
$820$	7.43340	+	14.8558i	0.259586	+	0.518786i
$821$	−21.3620	−	37.0001i	−0.745540	−	1.29131i	−0.949942	−	0.312426i	$-0.898858\pi$
$821$	−21.3620	−	37.0001i	−0.745540	−	1.29131i	0.204402	−	0.978887i	$-0.434475\pi$
$822$	−1.36289	+	1.52445i	−0.0475362	+	0.0531714i
$823$	1.23565	+	4.61152i	0.0430722	+	0.160748i	0.984112	−	0.177548i	$-0.0568164\pi$
$823$	1.23565	+	4.61152i	0.0430722	+	0.160748i	−0.941040	+	0.338295i	$0.890150\pi$
$824$	−22.1736	+	18.3489i	−0.772456	+	0.639215i
$825$	−3.37417	+	4.88263i	−0.117474	+	0.169992i
$826$	−17.3765	+	43.8325i	−0.604605	+	1.52513i
$827$	6.21884	+	6.21884i	0.216250	+	0.216250i	0.806916	−	0.590666i	$-0.201135\pi$
$827$	6.21884	+	6.21884i	0.216250	+	0.216250i	−0.590666	+	0.806916i	$0.701135\pi$
$828$	0.986854	−	1.23645i	0.0342956	−	0.0429696i
$829$	−33.7077	−	19.4612i	−1.17072	−	0.675915i	−0.216869	−	0.976201i	$-0.569585\pi$
$829$	−33.7077	−	19.4612i	−1.17072	−	0.675915i	−0.953849	+	0.300286i	$0.902918\pi$
$830$	20.5471	+	15.2711i	0.713200	+	0.530067i
$831$	4.43367	−	2.55978i	0.153802	−	0.0887978i
$832$	−15.5353	+	32.1594i	−0.538588	+	1.11493i
$833$	1.51083	−	18.5549i	0.0523470	−	0.642889i
$834$	−16.8475	−	25.7431i	−0.583383	−	0.891410i
$835$	15.3344	−	10.8079i	0.530669	−	0.374023i
$836$	−4.49947	−	6.10173i	−0.155617	−	0.211033i
$837$	−5.66257	−	21.1330i	−0.195727	−	0.730464i
$838$	−23.9009	+	7.85948i	−0.825645	+	0.271501i
$839$	15.0742			0.520418			0.260209	−	0.965552i	$-0.416209\pi$
$839$	15.0742			0.520418			0.260209	+	0.965552i	$0.416209\pi$
$840$	13.4203	−	15.9694i	0.463043	−	0.550998i
$841$	−23.2844			−0.802910
$842$	−22.1235	+	7.27500i	−0.762427	+	0.250713i
$843$	−10.4141	−	38.8660i	−0.358681	−	1.33862i
$844$	12.3855	+	16.7960i	0.426327	+	0.578141i
$845$	−15.2706	−	2.64409i	−0.525324	−	0.0909594i
$846$	3.59146	+	5.48776i	0.123477	+	0.188673i
$847$	9.20895	+	25.0663i	0.316423	+	0.861289i
$848$	0.449132	−	11.7489i	0.0154233	−	0.403461i
$849$	21.0823	−	12.1719i	0.723543	−	0.417738i
$850$	4.40790	+	18.2814i	0.151190	+	0.627047i
$851$	−0.492709	−	0.284465i	−0.0168898	−	0.00975135i
$852$	11.8312	−	14.8235i	0.405329	−	0.507845i
$853$	−14.0097	−	14.0097i	−0.479684	−	0.479684i	0.425346	−	0.905031i	$-0.360152\pi$
$853$	−14.0097	−	14.0097i	−0.479684	−	0.479684i	−0.905031	+	0.425346i	$0.860152\pi$
$854$	−13.9921	−	17.6693i	−0.478799	−	0.604632i
$855$	−8.24327	+	9.88570i	−0.281914	+	0.338084i
$856$	−0.0725349	−	0.0876544i	−0.00247919	−	0.00299597i
$857$	−9.22615	−	34.4324i	−0.315159	−	1.17619i	−0.923841	−	0.382776i	$-0.874968\pi$
$857$	−9.22615	−	34.4324i	−0.315159	−	1.17619i	0.608682	−	0.793414i	$-0.291698\pi$
$858$	−4.99497	+	5.58710i	−0.170525	+	0.190740i
$859$	−26.2004	−	45.3805i	−0.893947	−	1.54836i	−0.835103	−	0.550094i	$-0.814592\pi$
$859$	−26.2004	−	45.3805i	−0.893947	−	1.54836i	−0.0588442	−	0.998267i	$-0.518742\pi$
$860$	−52.4046	−	17.4509i	−1.78698	−	0.595071i
$861$	−1.10450	−	12.2013i	−0.0376411	−	0.415818i
$862$	20.9491	+	4.37546i	0.713528	+	0.149029i
$863$	−5.09743	−	1.36585i	−0.173518	−	0.0464941i	0.171014	−	0.985269i	$-0.445296\pi$
$863$	−5.09743	−	1.36585i	−0.173518	−	0.0464941i	−0.344532	+	0.938775i	$0.611962\pi$
$864$	21.7739	−	22.5582i	0.740763	−	0.767444i
$865$	−4.49244	−	2.07802i	−0.152748	−	0.0706547i
$866$	−9.73623	−	4.91755i	−0.330851	−	0.167105i
$867$	8.75067	+	8.75067i	0.297188	+	0.297188i
$868$	20.8509	+	1.24685i	0.707727	+	0.0423208i
$869$		−	10.1859i		−	0.345535i
$870$	−11.3111	−	26.1643i	−0.383483	−	0.887053i
$871$	−57.6023	−	33.2567i	−1.95178	−	1.12686i
$872$	−16.1825	+	7.41169i	−0.548009	+	0.250992i
$873$	−1.63325	+	6.09536i	−0.0552771	+	0.206297i
$874$	1.68647	+	2.57694i	0.0570458	+	0.0871662i
$875$	−18.7346	+	22.8913i	−0.633347	+	0.773868i
$876$	−33.6304	−	14.6890i	−1.13627	−	0.496295i
$877$	10.7858	+	2.89005i	0.364211	+	0.0975901i	0.436283	−	0.899809i	$-0.356295\pi$
$877$	10.7858	+	2.89005i	0.364211	+	0.0975901i	−0.0720722	+	0.997399i	$0.522961\pi$
$878$	27.1445	+	24.2677i	0.916083	+	0.818995i
$879$	−11.1824	+	19.3685i	−0.377174	+	0.653285i
$880$	−4.63698	−	7.14374i	−0.156313	−	0.240815i
$881$	22.0701			0.743561			0.371781	−	0.928321i	$-0.378747\pi$
$881$	22.0701			0.743561			0.371781	+	0.928321i	$0.378747\pi$
$882$	12.5741	−	6.84073i	0.423392	−	0.230339i
$883$	−5.32169	+	5.32169i	−0.179089	+	0.179089i	−0.790959	−	0.611869i	$-0.790418\pi$
$883$	−5.32169	+	5.32169i	−0.179089	+	0.179089i	0.611869	+	0.790959i	$0.290418\pi$
$884$	2.64915	+	23.5976i	0.0891005	+	0.793674i
$885$	−14.7471	+	31.8816i	−0.495719	+	1.07169i
$886$	−24.4127	+	1.36603i	−0.820159	+	0.0458928i
$887$	−1.31079	+	4.89193i	−0.0440120	+	0.164255i	−0.984434	−	0.175754i	$-0.943764\pi$
$887$	−1.31079	+	4.89193i	−0.0440120	+	0.164255i	0.940422	+	0.340009i	$0.110430\pi$
$888$	−2.98944	−	2.12385i	−0.100319	−	0.0712718i
$889$	2.63853	+	3.74417i	0.0884936	+	0.125576i
$890$	4.15789	+	5.24983i	0.139373	+	0.175975i
$891$	2.12030	−	1.22416i	0.0710327	−	0.0410108i
$892$	4.53382	−	29.9976i	0.151803	−	1.00439i
$893$	−12.3327	+	3.30454i	−0.412699	+	0.110582i
$894$	−17.6419	−	8.91052i	−0.590033	−	0.298012i
$895$	−28.2845	−	23.5853i	−0.945448	−	0.788369i
$896$	13.8640	+	26.5290i	0.463163	+	0.886273i
$897$	2.15273	−	2.15273i	0.0718774	−	0.0718774i
$898$	4.90364	+	14.9121i	0.163637	+	0.497625i
$899$	14.2718	−	24.7194i	0.475990	−	0.824439i
$900$	−9.90598	+	10.5336i	−0.330199	+	0.351120i
$901$	−3.90860	−	6.76989i	−0.130214	−	0.225538i
$902$	−4.89633	−	1.02265i	−0.163030	−	0.0340507i
$903$	31.2835	+	26.0899i	1.04105	+	0.868218i
$904$	42.7964	−	7.24469i	1.42339	−	0.240955i
$905$	2.27996	−	13.1676i	0.0757885	−	0.437706i
$906$	−1.47943	−	26.4392i	−0.0491507	−	0.878382i
$907$	3.27202	−	0.876735i	0.108646	−	0.0291115i	−0.204087	−	0.978953i	$-0.565422\pi$
$907$	3.27202	−	0.876735i	0.108646	−	0.0291115i	0.312732	+	0.949841i	$0.398756\pi$
$908$	12.5040	−	15.6665i	0.414959	−	0.519911i
$909$		−	2.06796i		−	0.0685899i
$910$	−27.0708	+	25.7358i	−0.897387	+	0.853134i
$911$			31.5983i			1.04690i	0.852057	+	0.523449i	$0.175355\pi$
$911$			31.5983i			1.04690i	−0.852057	+	0.523449i	$0.824645\pi$
$912$	9.26140	+	17.5578i	0.306676	+	0.581397i
$913$	−7.44597	+	1.99514i	−0.246426	+	0.0660295i
$914$	29.9877	−	1.67799i	0.991905	−	0.0555030i
$915$	−9.67325	−	13.7246i	−0.319788	−	0.453720i
$916$	13.6796	−	31.3195i	0.451988	−	1.03482i
$917$	−3.23992	+	1.19029i	−0.106992	+	0.0393069i
$918$	4.26180	−	20.4049i	0.140660	−	0.673462i
$919$	23.1351	+	40.0712i	0.763157	+	1.32183i	0.941215	+	0.337807i	$0.109685\pi$
$919$	23.1351	+	40.0712i	0.763157	+	1.32183i	−0.178058	+	0.984020i	$0.556982\pi$
$920$	1.71860	+	3.00269i	0.0566605	+	0.0989958i
$921$	8.79800	−	15.2386i	0.289904	−	0.502128i
$922$	−11.5758	+	3.80653i	−0.381229	+	0.125362i
$923$	−24.0141	+	24.0141i	−0.790435	+	0.790435i
$924$	1.26062	+	6.15329i	0.0414712	+	0.202428i
$925$	4.27804	+	2.95637i	0.140661	+	0.0972047i
$926$	−1.47279	+	2.91596i	−0.0483987	+	0.0958244i
$927$	−14.2124	+	3.80821i	−0.466797	+	0.125078i
$928$	40.8972	−	0.723497i	1.34251	−	0.0237499i
$929$	−37.0594	+	21.3962i	−1.21588	+	0.701987i	−0.964034	−	0.265780i	$-0.914370\pi$
$929$	−37.0594	+	21.3962i	−1.21588	+	0.701987i	−0.251844	+	0.967768i	$0.581037\pi$
$930$	15.4577	+	1.79415i	0.506877	+	0.0588326i
$931$	5.00414	+	27.4137i	0.164004	+	0.898447i
$932$	1.36896	+	3.49220i	0.0448418	+	0.114391i
$933$	−4.49719	+	16.7837i	−0.147231	+	0.549475i
$934$	2.01323	+	35.9789i	0.0658750	+	1.17727i
$935$	−5.13932	−	2.37724i	−0.168074	−	0.0777440i
$936$	−14.0669	+	11.6405i	−0.459791	+	0.380482i
$937$	18.9957	−	18.9957i	0.620561	−	0.620561i	−0.325114	−	0.945675i	$-0.605403\pi$
$937$	18.9957	−	18.9957i	0.620561	−	0.620561i	0.945675	+	0.325114i	$0.105403\pi$
$938$	−51.1704	+	22.1171i	−1.67077	+	0.722149i
$939$	6.11875			0.199678
$940$	−14.0511	+	2.87969i	−0.458295	+	0.0939251i
$941$	10.8404	−	18.7762i	0.353388	−	0.612086i	−0.633453	−	0.773781i	$-0.718363\pi$
$941$	10.8404	−	18.7762i	0.353388	−	0.612086i	0.986841	+	0.161696i	$0.0516963\pi$
$942$	−8.84575	+	9.89437i	−0.288210	+	0.322376i
$943$	1.96271	+	0.525906i	0.0639145	+	0.0171258i
$944$	−34.2554	−	36.9785i	−1.11492	−	1.20355i
$945$	29.6320	−	14.0381i	0.963931	−	0.456660i
$946$	13.9163	−	9.10749i	0.452457	−	0.296110i
$947$	3.97536	−	14.8363i	0.129182	−	0.482114i	−0.870772	−	0.491687i	$-0.836381\pi$
$947$	3.97536	−	14.8363i	0.129182	−	0.482114i	0.999954	+	0.00957300i	$0.00304723\pi$
$948$	−3.98571	+	26.3711i	−0.129450	+	0.856493i
$949$	56.9090	+	32.8564i	1.84735	+	1.06657i
$950$	−13.4560	−	24.7252i	−0.436571	−	0.802191i
$951$		−	42.8869i		−	1.39070i
$952$	17.1971	+	10.0168i	0.557361	+	0.324645i
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	0.967147	−	0.254216i	$-0.0818174\pi$
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	−0.254216	+	0.967147i	$0.581817\pi$
$954$	2.70988	−	5.36528i	0.0877357	−	0.173708i
$955$	6.20576	+	16.8880i	0.200814	+	0.546482i
$956$	24.4964	−	18.0639i	0.792271	−	0.584228i
$957$	8.29061	+	2.22146i	0.267997	+	0.0718096i
$958$	−2.68274	+	12.8446i	−0.0866755	+	0.414990i
$959$	−0.276665	−	3.05629i	−0.00893398	−	0.0986929i
$960$	9.20968	+	20.3093i	0.297241	+	0.655481i
$961$	−7.70864	−	13.3518i	−0.248666	−	0.430702i
$962$	4.89527	+	4.37647i	0.157830	+	0.141103i
$963$	−0.0150542	−	0.0561830i	−0.000485114	−	0.00181047i
$964$	−2.93981	−	26.1867i	−0.0946848	−	0.843417i
$965$	2.93747	+	32.4235i	0.0945604	+	1.04375i
$966$	−0.371646	−	2.52434i	−0.0119575	−	0.0812194i
$967$	−16.9281	−	16.9281i	−0.544372	−	0.544372i	0.380435	−	0.924807i	$-0.375774\pi$
$967$	−16.9281	−	16.9281i	−0.544372	−	0.544372i	−0.924807	+	0.380435i	$0.875774\pi$
$968$	−28.4219	−	2.68261i	−0.913514	−	0.0862223i
$969$	11.4299	+	6.59904i	0.367180	+	0.211992i
$970$	−11.0763	−	8.23218i	−0.355639	−	0.264319i
$971$	32.1198	−	18.5444i	1.03077	−	0.595118i	0.113568	−	0.993530i	$-0.463772\pi$
$971$	32.1198	−	18.5444i	1.03077	−	0.595118i	0.917206	+	0.398412i	$0.130439\pi$
$972$	24.9920	−	9.79698i	0.801620	−	0.314238i
$973$	45.4942	+	7.88071i	1.45848	+	0.252644i
$974$	21.0739	−	13.7918i	0.675251	−	0.441918i
$975$	−21.2058	+	18.0178i	−0.679128	+	0.577031i
$976$	23.4949	−	5.34256i	0.752053	−	0.171011i
$977$	6.04928	+	22.5762i	0.193534	+	0.722277i	0.992642	+	0.121090i	$0.0386389\pi$
$977$	6.04928	+	22.5762i	0.193534	+	0.722277i	−0.799108	+	0.601188i	$0.794694\pi$
$978$	3.66170	+	11.1353i	0.117088	+	0.356069i
$979$	−2.01652			−0.0644484
$980$	3.77556	+	31.0764i	0.120606	+	0.992700i
$981$	−9.09942			−0.290522
$982$	1.10430	+	3.35820i	0.0352395	+	0.107165i
$983$	−5.14648	−	19.2069i	−0.164147	−	0.612606i	−0.998147	−	0.0608417i	$-0.980622\pi$
$983$	−5.14648	−	19.2069i	−0.164147	−	0.612606i	0.834000	−	0.551764i	$-0.186045\pi$
$984$	12.2763	+	4.56353i	0.391353	+	0.145480i
$985$	30.0448	+	42.6281i	0.957307	+	1.35824i
$986$	22.7555	−	14.8923i	0.724682	−	0.474268i
$987$	10.4228	+	1.80549i	0.331763	+	0.0574694i
$988$	−12.9727	−	33.0932i	−0.412716	−	1.05284i
$989$	−5.85104	+	3.37810i	−0.186052	+	0.107417i
$990$	−0.634497	−	4.30753i	−0.0201656	−	0.136902i
$991$	19.5362	+	11.2792i	0.620586	+	0.358296i	0.777097	−	0.629380i	$-0.216691\pi$
$991$	19.5362	+	11.2792i	0.620586	+	0.358296i	−0.156511	+	0.987676i	$0.550025\pi$
$992$	−10.8214	+	19.5332i	−0.343580	+	0.620178i
$993$	−11.4204	−	11.4204i	−0.362414	−	0.362414i
$994$	4.14579	+	28.1596i	0.131497	+	0.893169i
$995$	16.5825	+	13.8275i	0.525701	+	0.438360i
$996$	20.0581	−	2.25178i	0.635564	−	0.0713505i
$997$	4.45792	+	16.6372i	0.141184	+	0.526905i	0.999896	+	0.0144466i	$0.00459864\pi$
$997$	4.45792	+	16.6372i	0.141184	+	0.526905i	−0.858712	+	0.512459i	$0.828735\pi$
$998$	−6.87827	−	6.14930i	−0.217728	−	0.194653i
$999$	−2.88213	−	4.99199i	−0.0911865	−	0.157940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.123.17	yes	72
4.3	odd	2	inner	140.2.w.b.123.14	yes	72
5.2	odd	4	inner	140.2.w.b.67.11	yes	72
5.3	odd	4		700.2.be.e.207.8		72
5.4	even	2		700.2.be.e.543.2		72
7.2	even	3	inner	140.2.w.b.23.5	✓	72
7.3	odd	6		980.2.k.j.883.8		36
7.4	even	3		980.2.k.k.883.8		36
7.5	odd	6		980.2.x.m.863.5		72
7.6	odd	2		980.2.x.m.263.17		72
20.3	even	4		700.2.be.e.207.14		72
20.7	even	4	inner	140.2.w.b.67.5	yes	72
20.19	odd	2		700.2.be.e.543.5		72
28.3	even	6		980.2.k.j.883.1		36
28.11	odd	6		980.2.k.k.883.1		36
28.19	even	6		980.2.x.m.863.11		72
28.23	odd	6	inner	140.2.w.b.23.11	yes	72
28.27	even	2		980.2.x.m.263.14		72
35.2	odd	12	inner	140.2.w.b.107.14	yes	72
35.9	even	6		700.2.be.e.443.14		72
35.12	even	12		980.2.x.m.667.14		72
35.17	even	12		980.2.k.j.687.1		36
35.23	odd	12		700.2.be.e.107.5		72
35.27	even	4		980.2.x.m.67.11		72
35.32	odd	12		980.2.k.k.687.1		36
140.23	even	12		700.2.be.e.107.2		72
140.27	odd	4		980.2.x.m.67.5		72
140.47	odd	12		980.2.x.m.667.17		72
140.67	even	12		980.2.k.k.687.8		36
140.79	odd	6		700.2.be.e.443.8		72
140.87	odd	12		980.2.k.j.687.8		36
140.107	even	12	inner	140.2.w.b.107.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	7.2	even	3	inner
140.2.w.b.23.11	yes	72	28.23	odd	6	inner
140.2.w.b.67.5	yes	72	20.7	even	4	inner
140.2.w.b.67.11	yes	72	5.2	odd	4	inner
140.2.w.b.107.14	yes	72	35.2	odd	12	inner
140.2.w.b.107.17	yes	72	140.107	even	12	inner
140.2.w.b.123.14	yes	72	4.3	odd	2	inner
140.2.w.b.123.17	yes	72	1.1	even	1	trivial
700.2.be.e.107.2		72	140.23	even	12
700.2.be.e.107.5		72	35.23	odd	12
700.2.be.e.207.8		72	5.3	odd	4
700.2.be.e.207.14		72	20.3	even	4
700.2.be.e.443.8		72	140.79	odd	6
700.2.be.e.443.14		72	35.9	even	6
700.2.be.e.543.2		72	5.4	even	2
700.2.be.e.543.5		72	20.19	odd	2
980.2.k.j.687.1		36	35.17	even	12
980.2.k.j.687.8		36	140.87	odd	12
980.2.k.j.883.1		36	28.3	even	6
980.2.k.j.883.8		36	7.3	odd	6
980.2.k.k.687.1		36	35.32	odd	12
980.2.k.k.687.8		36	140.67	even	12
980.2.k.k.883.1		36	28.11	odd	6
980.2.k.k.883.8		36	7.4	even	3
980.2.x.m.67.5		72	140.27	odd	4
980.2.x.m.67.11		72	35.27	even	4
980.2.x.m.263.14		72	28.27	even	2
980.2.x.m.263.17		72	7.6	odd	2
980.2.x.m.667.14		72	35.12	even	12
980.2.x.m.667.17		72	140.47	odd	12
980.2.x.m.863.5		72	7.5	odd	6
980.2.x.m.863.11		72	28.19	even	6

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34344 - 0.441772i) q^{2} +(0.322645 + 1.20413i) q^{3} +(1.60968 - 1.18699i) q^{4} +(-0.381497 + 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-2.60693 - 0.451584i) q^{7} +(1.63813 - 2.30576i) q^{8} +(1.25225 - 0.722989i) q^{9} +O(q^{10})\)	\(q+(1.34344 - 0.441772i) q^{2} +(0.322645 + 1.20413i) q^{3} +(1.60968 - 1.18699i) q^{4} +(-0.381497 + 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-2.60693 - 0.451584i) q^{7} +(1.63813 - 2.30576i) q^{8} +(1.25225 - 0.722989i) q^{9} +(0.460829 + 3.12852i) q^{10} +(-0.824629 - 0.476100i) q^{11} +(1.94864 + 1.55528i) q^{12} +(-3.15680 - 3.15680i) q^{13} +(-3.70175 + 0.544990i) q^{14} +(-2.77612 + 0.251508i) q^{15} +(1.18211 - 3.82134i) q^{16} +(-0.688322 - 2.56885i) q^{17} +(1.36293 - 1.52450i) q^{18} +(1.99048 + 3.44760i) q^{19} +(2.00119 + 3.99941i) q^{20} +(-0.297348 - 3.28477i) q^{21} +(-1.31817 - 0.275315i) q^{22} +(0.528392 + 0.141582i) q^{23} +(3.30496 + 1.22857i) q^{24} +(-4.70892 - 1.68109i) q^{25} +(-5.63557 - 2.84640i) q^{26} +(3.91905 + 3.91905i) q^{27} +(-4.73233 + 2.36749i) q^{28} +7.23080i q^{29} +(-3.61845 + 1.56430i) q^{30} +(-3.41863 - 1.97375i) q^{31} +(-0.100058 - 5.65597i) q^{32} +(0.307222 - 1.14657i) q^{33} +(-2.05957 - 3.14702i) q^{34} +(1.98950 - 5.57152i) q^{35} +(1.15754 - 2.65019i) q^{36} +(-1.00460 - 0.269180i) q^{37} +(4.19714 + 3.75232i) q^{38} +(2.78267 - 4.81972i) q^{39} +(4.45531 + 4.48890i) q^{40} +3.71449 q^{41} +(-1.85059 - 4.28155i) q^{42} +(-8.73324 + 8.73324i) q^{43} +(-1.89251 + 0.212459i) q^{44} +(1.11522 + 3.03489i) q^{45} +(0.772411 - 0.0432210i) q^{46} +(-0.830089 + 3.09794i) q^{47} +(4.98278 + 0.190479i) q^{48} +(6.59214 + 2.35449i) q^{49} +(-7.06882 - 0.178182i) q^{50} +(2.87114 - 1.65765i) q^{51} +(-8.82853 - 1.33434i) q^{52} +(2.83923 - 0.760768i) q^{53} +(6.99635 + 3.53369i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-5.31173 + 5.27120i) q^{56} +(-3.50914 + 3.50914i) q^{57} +(3.19436 + 9.71416i) q^{58} +(6.30084 - 10.9134i) q^{59} +(-4.17012 + 3.70007i) q^{60} +(3.01183 + 5.21665i) q^{61} +(-5.46468 - 1.14136i) q^{62} +(-3.59102 + 1.31928i) q^{63} +(-2.63307 - 7.55427i) q^{64} +(8.15965 - 5.75103i) q^{65} +(-0.0937861 - 1.67607i) q^{66} +(14.3910 - 3.85605i) q^{67} +(-4.15717 - 3.31799i) q^{68} +0.681932i q^{69} +(0.211440 - 8.36393i) q^{70} -7.60710i q^{71} +(0.384313 - 4.07174i) q^{72} +(-14.2178 + 3.80964i) q^{73} +(-1.46853 + 0.0821731i) q^{74} +(0.504938 - 6.21254i) q^{75} +(7.29629 + 3.18685i) q^{76} +(1.93475 + 1.61355i) q^{77} +(1.60914 - 7.70432i) q^{78} +(5.34864 + 9.26412i) q^{79} +(7.96852 + 4.06236i) q^{80} +(-1.28561 + 2.22674i) q^{81} +(4.99021 - 1.64096i) q^{82} +(5.72446 - 5.72446i) q^{83} +(-4.37763 - 4.93447i) q^{84} +(5.92250 - 0.536560i) q^{85} +(-7.87451 + 15.5907i) q^{86} +(-8.70680 + 2.33298i) q^{87} +(-2.44862 + 1.12148i) q^{88} +(1.83403 - 1.05888i) q^{89} +(2.83896 + 3.58452i) q^{90} +(6.80400 + 9.65512i) q^{91} +(1.01860 - 0.399294i) q^{92} +(1.27364 - 4.75329i) q^{93} +(0.253402 + 4.52861i) q^{94} +(-8.35541 + 3.07033i) q^{95} +(6.77823 - 1.94535i) q^{96} +(-3.08588 + 3.08588i) q^{97} +(9.89631 + 0.250904i) q^{98} -1.37686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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