LMFDB - Embedded newform 140.2.w.b.107.14

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			107.14
Character	$\chi$	$=$	140.107
Dual form			140.2.w.b.123.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.942570 - 1.05431i) q^{2} +(-0.322645 + 1.20413i) q^{3} +(-0.223125 - 1.98751i) q^{4} +(-0.381497 - 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(2.60693 - 0.451584i) q^{7} +(-2.30576 - 1.63813i) q^{8} +(1.25225 + 0.722989i) q^{9} +O(q^{10})$	\(q+(0.942570 - 1.05431i) q^{2} +(-0.322645 + 1.20413i) q^{3} +(-0.223125 - 1.98751i) q^{4} +(-0.381497 - 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(2.60693 - 0.451584i) q^{7} +(-2.30576 - 1.63813i) q^{8} +(1.25225 + 0.722989i) q^{9} +(-2.68252 - 1.67453i) q^{10} +(0.824629 - 0.476100i) q^{11} +(2.46521 + 0.372591i) q^{12} +(-3.15680 + 3.15680i) q^{13} +(1.98110 - 3.17415i) q^{14} +(2.77612 + 0.251508i) q^{15} +(-3.90043 + 0.886929i) q^{16} +(-0.688322 + 2.56885i) q^{17} +(1.94259 - 0.638792i) q^{18} +(-1.99048 + 3.44760i) q^{19} +(-4.29394 + 1.24984i) q^{20} +(-0.297348 + 3.28477i) q^{21} +(0.275315 - 1.31817i) q^{22} +(-0.528392 + 0.141582i) q^{23} +(2.71646 - 2.24790i) q^{24} +(-4.70892 + 1.68109i) q^{25} +(0.352732 + 6.30375i) q^{26} +(-3.91905 + 3.91905i) q^{27} +(-1.47920 - 5.08055i) q^{28} -7.23080i q^{29} +(2.88186 - 2.68982i) q^{30} +(3.41863 - 1.97375i) q^{31} +(-2.74133 + 4.94824i) 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} +(1.75867 + 5.34818i) q^{38} +(-2.78267 - 4.81972i) q^{39} +(-2.72962 + 5.70519i) q^{40} +3.71449 q^{41} +(3.18289 + 3.40962i) q^{42} +(8.73324 + 8.73324i) q^{43} +(-1.13025 - 1.53273i) q^{44} +(1.11522 - 3.03489i) q^{45} +(-0.348775 + 0.690538i) q^{46} +(0.830089 + 3.09794i) q^{47} +(0.190479 - 4.98278i) q^{48} +(6.59214 - 2.35449i) q^{49} +(-2.66610 + 6.54919i) q^{50} +(-2.87114 - 1.65765i) q^{51} +(6.97856 + 5.56983i) q^{52} +(2.83923 + 0.760768i) q^{53} +(0.437903 + 7.82586i) q^{54} +(-1.36358 - 1.63526i) q^{55} +(-6.75070 - 3.22924i) q^{56} +(-3.50914 - 3.50914i) q^{57} +(-7.62348 - 6.81553i) q^{58} +(-6.30084 - 10.9134i) q^{59} +(-0.119547 - 5.57370i) q^{60} +(3.01183 - 5.21665i) q^{61} +(1.14136 - 5.46468i) q^{62} +(3.59102 + 1.31928i) q^{63} +(2.63307 + 7.55427i) q^{64} +(8.15965 + 5.75103i) q^{65} +(1.49841 + 0.756815i) q^{66} +(-14.3910 - 3.85605i) q^{67} +(5.25921 + 0.794874i) q^{68} -0.681932i q^{69} +(-7.74934 - 3.15400i) q^{70} -7.60710i q^{71} +(-1.70305 - 3.71839i) q^{72} +(-14.2178 - 3.80964i) q^{73} +(-0.663102 + 1.31287i) q^{74} +(-0.504938 - 6.21254i) q^{75} +(7.29629 + 3.18685i) q^{76} +(1.93475 - 1.61355i) q^{77} +(-7.70432 - 1.60914i) q^{78} +(-5.34864 + 9.26412i) q^{79} +(3.44216 + 8.25540i) q^{80} +(-1.28561 - 2.22674i) q^{81} +(3.50117 - 3.91621i) q^{82} +(-5.72446 - 5.72446i) q^{83} +(6.59488 - 0.141933i) q^{84} +(5.92250 + 0.536560i) q^{85} +(17.4392 - 0.975826i) q^{86} +(8.70680 + 2.33298i) q^{87} +(-2.68131 - 0.253076i) q^{88} +(1.83403 + 1.05888i) q^{89} +(-2.14853 - 4.03637i) q^{90} +(-6.80400 + 9.65512i) q^{91} +(0.399294 + 1.01860i) q^{92} +(1.27364 + 4.75329i) q^{93} +(4.04859 + 2.04485i) q^{94} +(8.35541 + 3.07033i) q^{95} +(-5.07384 - 4.89744i) q^{96} +(-3.08588 - 3.08588i) q^{97} +(3.73120 - 9.16941i) 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 $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.942570	−	1.05431i	0.666497	−	0.745507i
$2$	0.942570	−	1.05431i	0.666497	−	0.745507i
$3$	−0.322645	+	1.20413i	−0.186279	+	0.695203i	0.808074	+	0.589081i	$0.200510\pi$
$3$	−0.322645	+	1.20413i	−0.186279	+	0.695203i	−0.994353	+	0.106122i	$0.966157\pi$
$4$	−0.223125	−	1.98751i	−0.111563	−	0.993757i
$5$	−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
$8$	−2.30576	−	1.63813i	−0.815210	−	0.579166i
$9$	1.25225	+	0.722989i	0.417418	+	0.240996i
$10$	−2.68252	−	1.67453i	−0.848289	−	0.529534i
$11$	0.824629	−	0.476100i	0.248635	−	0.143549i	−0.370504	−	0.928831i	$-0.620815\pi$
$11$	0.824629	−	0.476100i	0.248635	−	0.143549i	0.619139	+	0.785281i	$0.287482\pi$
$12$	2.46521	+	0.372591i	0.711645	+	0.107558i
$13$	−3.15680	+	3.15680i	−0.875540	+	0.875540i	−0.993069	−	0.117529i	$-0.962503\pi$
$13$	−3.15680	+	3.15680i	−0.875540	+	0.875540i	0.117529	+	0.993069i	$0.462503\pi$
$14$	1.98110	−	3.17415i	0.529472	−	0.848327i
$15$	2.77612	+	0.251508i	0.716792	+	0.0649391i
$16$	−3.90043	+	0.886929i	−0.975108	+	0.221732i
$17$	−0.688322	+	2.56885i	−0.166943	+	0.623038i	0.830842	+	0.556508i	$0.187859\pi$
$17$	−0.688322	+	2.56885i	−0.166943	+	0.623038i	−0.997784	+	0.0665295i	$0.978807\pi$
$18$	1.94259	−	0.638792i	0.457872	−	0.150565i
$19$	−1.99048	+	3.44760i	−0.456646	+	0.790935i	−0.998781	−	0.0493567i	$-0.984283\pi$
$19$	−1.99048	+	3.44760i	−0.456646	+	0.790935i	0.542135	+	0.840292i	$0.317616\pi$
$20$	−4.29394	+	1.24984i	−0.960154	+	0.279472i
$21$	−0.297348	+	3.28477i	−0.0648866	+	0.716797i
$22$	0.275315	−	1.31817i	0.0586973	−	0.281034i
$23$	−0.528392	+	0.141582i	−0.110177	+	0.0295219i	−0.313486	−	0.949593i	$-0.601497\pi$
$23$	−0.528392	+	0.141582i	−0.110177	+	0.0295219i	0.203309	+	0.979115i	$0.434830\pi$
$24$	2.71646	−	2.24790i	0.554495	−	0.458850i
$25$	−4.70892	+	1.68109i	−0.941784	+	0.336218i
$26$	0.352732	+	6.30375i	0.0691765	+	1.23627i
$27$	−3.91905	+	3.91905i	−0.754222	+	0.754222i
$28$	−1.47920	−	5.08055i	−0.279543	−	0.960133i
$29$		−	7.23080i		−	1.34273i	−0.741129	−	0.671363i	$-0.765709\pi$
$29$		−	7.23080i		−	1.34273i	0.741129	−	0.671363i	$-0.234291\pi$
$30$	2.88186	−	2.68982i	0.526152	−	0.491092i
$31$	3.41863	−	1.97375i	0.614004	−	0.354495i	−0.160527	−	0.987031i	$-0.551319\pi$
$31$	3.41863	−	1.97375i	0.614004	−	0.354495i	0.774531	+	0.632536i	$0.217986\pi$
$32$	−2.74133	+	4.94824i	−0.484604	+	0.874734i
$33$	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	−0.340449	−	0.940263i	$-0.610579\pi$
$37$	−1.00460	+	0.269180i	−0.165154	+	0.0442530i	0.175294	+	0.984516i	$0.443912\pi$
$38$	1.75867	+	5.34818i	0.285294	+	0.867589i
$39$	−2.78267	−	4.81972i	−0.445584	−	0.771773i
$40$	−2.72962	+	5.70519i	−0.431591	+	0.902069i
$41$	3.71449			0.580106			0.290053	−	0.957011i	$-0.406327\pi$
$41$	3.71449			0.580106			0.290053	+	0.957011i	$0.406327\pi$
$42$	3.18289	+	3.40962i	0.491130	+	0.526116i
$43$	8.73324	+	8.73324i	1.33181	+	1.33181i	0.903754	+	0.428052i	$0.140800\pi$
$43$	8.73324	+	8.73324i	1.33181	+	1.33181i	0.428052	+	0.903754i	$0.359200\pi$
$44$	−1.13025	−	1.53273i	−0.170392	−	0.231068i
$45$	1.11522	−	3.03489i	0.166247	−	0.452414i
$46$	−0.348775	+	0.690538i	−0.0514241	+	0.101814i
$47$	0.830089	+	3.09794i	0.121081	+	0.451880i	0.999670	−	0.0256988i	$-0.00818107\pi$
$47$	0.830089	+	3.09794i	0.121081	+	0.451880i	−0.878589	+	0.477579i	$0.841514\pi$
$48$	0.190479	−	4.98278i	0.0274933	−	0.719202i
$49$	6.59214	−	2.35449i	0.941735	−	0.336356i
$50$	−2.66610	+	6.54919i	−0.377044	+	0.926196i
$51$	−2.87114	−	1.65765i	−0.402040	−	0.232118i
$52$	6.97856	+	5.56983i	0.967752	+	0.772397i
$53$	2.83923	+	0.760768i	0.389998	+	0.104500i	0.448489	−	0.893788i	$-0.351962\pi$
$53$	2.83923	+	0.760768i	0.389998	+	0.104500i	−0.0584914	+	0.998288i	$0.518629\pi$
$54$	0.437903	+	7.82586i	0.0595911	+	1.06496i
$55$	−1.36358	−	1.63526i	−0.183864	−	0.220498i
$56$	−6.75070	−	3.22924i	−0.902101	−	0.431525i
$57$	−3.50914	−	3.50914i	−0.464797	−	0.464797i
$58$	−7.62348	−	6.81553i	−1.00101	−	0.894923i
$59$	−6.30084	−	10.9134i	−0.820300	−	1.42080i	−0.905459	−	0.424433i	$-0.860473\pi$
$59$	−6.30084	−	10.9134i	−0.820300	−	1.42080i	0.0851594	−	0.996367i	$-0.472860\pi$
$60$	−0.119547	−	5.57370i	−0.0154334	−	0.719562i
$61$	3.01183	−	5.21665i	0.385626	−	0.667923i	−0.606230	−	0.795289i	$-0.707319\pi$
$61$	3.01183	−	5.21665i	0.385626	−	0.667923i	0.991856	+	0.127366i	$0.0406523\pi$
$62$	1.14136	−	5.46468i	0.144953	−	0.694015i
$63$	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
$66$	1.49841	+	0.756815i	0.184442	+	0.0931574i
$67$	−14.3910	−	3.85605i	−1.75814	−	0.471092i	−0.771806	−	0.635858i	$-0.780647\pi$
$67$	−14.3910	−	3.85605i	−1.75814	−	0.471092i	−0.986333	+	0.164766i	$0.947313\pi$
$68$	5.25921	+	0.794874i	0.637773	+	0.0963927i
$69$		−	0.681932i		−	0.0820949i
$70$	−7.74934	−	3.15400i	−0.926223	−	0.376976i
$71$		−	7.60710i		−	0.902797i	−0.892322	−	0.451399i	$-0.850925\pi$
$71$		−	7.60710i		−	0.902797i	0.892322	−	0.451399i	$-0.149075\pi$
$72$	−1.70305	−	3.71839i	−0.200706	−	0.438216i
$73$	−14.2178	−	3.80964i	−1.66406	−	0.445885i	−0.700564	−	0.713590i	$-0.747068\pi$
$73$	−14.2178	−	3.80964i	−1.66406	−	0.445885i	−0.963501	+	0.267705i	$0.913735\pi$
$74$	−0.663102	+	1.31287i	−0.0770841	+	0.152618i
$75$	−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
$78$	−7.70432	−	1.60914i	−0.872343	−	0.182199i
$79$	−5.34864	+	9.26412i	−0.601769	+	1.04230i	0.390784	+	0.920483i	$0.372204\pi$
$79$	−5.34864	+	9.26412i	−0.601769	+	1.04230i	−0.992553	+	0.121813i	$0.961129\pi$
$80$	3.44216	+	8.25540i	0.384845	+	0.922981i
$81$	−1.28561	−	2.22674i	−0.142846	−	0.247416i
$82$	3.50117	−	3.91621i	0.386639	−	0.432473i
$83$	−5.72446	−	5.72446i	−0.628341	−	0.628341i	0.319309	−	0.947651i	$-0.396549\pi$
$83$	−5.72446	−	5.72446i	−0.628341	−	0.628341i	−0.947651	+	0.319309i	$0.896549\pi$
$84$	6.59488	−	0.141933i	0.719561	−	0.0154861i
$85$	5.92250	+	0.536560i	0.642386	+	0.0581981i
$86$	17.4392	−	0.975826i	1.88052	−	0.105226i
$87$	8.70680	+	2.33298i	0.933467	+	0.250122i
$88$	−2.68131	−	0.253076i	−0.285828	−	0.0269780i
$89$	1.83403	+	1.05888i	0.194407	+	0.112241i	0.594044	−	0.804433i	$-0.297531\pi$
$89$	1.83403	+	1.05888i	0.194407	+	0.112241i	−0.399637	+	0.916673i	$0.630864\pi$
$90$	−2.14853	−	4.03637i	−0.226475	−	0.425471i
$91$	−6.80400	+	9.65512i	−0.713253	+	1.01213i
$92$	0.399294	+	1.01860i	0.0416293	+	0.106196i
$93$	1.27364	+	4.75329i	0.132070	+	0.492893i
$94$	4.04859	+	2.04485i	0.417580	+	0.210910i
$95$	8.35541	+	3.07033i	0.857247	+	0.315010i
$96$	−5.07384	−	4.89744i	−0.517846	−	0.499843i
$97$	−3.08588	−	3.08588i	−0.313324	−	0.313324i	0.532872	−	0.846196i	$-0.321113\pi$
$97$	−3.08588	−	3.08588i	−0.313324	−	0.313324i	−0.846196	+	0.532872i	$0.821113\pi$
$98$	3.73120	−	9.16941i	0.376908	−	0.926251i
$99$	1.37686			0.138379
$100$	4.39187	+	8.98396i	0.439187	+	0.898396i
$101$	0.715074	+	1.23854i	0.0711525	+	0.123240i	0.899407	−	0.437113i	$-0.143999\pi$
$101$	0.715074	+	1.23854i	0.0711525	+	0.123240i	−0.828254	+	0.560353i	$0.810666\pi$
$102$	−4.45393	+	1.46461i	−0.441004	+	0.145018i
$103$	9.82894	−	2.63366i	0.968474	−	0.259502i	0.260291	−	0.965530i	$-0.416182\pi$
$103$	9.82894	−	2.63366i	0.968474	−	0.259502i	0.708183	+	0.706028i	$0.249515\pi$
$104$	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	$-0.0839522\pi$
$107$	−0.0104111	−	0.0388547i	−0.00100648	−	0.00375622i	−0.966427	+	0.256940i	$0.917286\pi$
$108$	8.66361	+	6.91473i	0.833656	+	0.665371i
$109$	−5.44983	+	3.14646i	−0.521999	+	0.301376i	−0.737752	−	0.675072i	$-0.764113\pi$
$109$	−5.44983	+	3.14646i	−0.521999	+	0.301376i	0.215753	+	0.976448i	$0.430779\pi$
$110$	−3.00933	−	0.103720i	−0.286928	−	0.00988933i
$111$		−	1.29651i		−	0.123059i
$112$	−9.76762	+	4.07353i	−0.922953	+	0.384912i
$113$	10.8513	−	10.8513i	1.02081	−	1.02081i	0.0210265	−	0.999779i	$-0.493307\pi$
$113$	10.8513	−	10.8513i	1.02081	−	1.02081i	0.999779	−	0.0210265i	$-0.00669344\pi$
$114$	−7.00732	+	0.392101i	−0.656295	+	0.0367236i
$115$	0.513525	+	1.11018i	0.0478865	+	0.103525i
$116$	−14.3713	+	1.61337i	−1.33434	+	0.149798i
$117$	−6.23545	+	1.67078i	−0.576468	+	0.154464i
$118$	−17.4450	−	3.64360i	−1.60595	−	0.335420i
$119$	−0.634353	+	7.00765i	−0.0581511	+	0.642390i
$120$	−5.98907	−	5.12756i	−0.546725	−	0.468080i
$121$	−5.04666	+	8.74107i	−0.458787	+	0.794643i
$122$	−2.66108	−	8.09245i	−0.240923	−	0.732656i
$123$	−1.19846	+	4.47272i	−0.108062	+	0.403292i
$124$	−4.68563	−	6.35419i	−0.420782	−	0.570623i
$125$	5.50036	+	9.73376i	0.491967	+	0.870614i
$126$	4.77572	−	2.54252i	0.425455	−	0.226506i
$127$	1.22418	−	1.22418i	0.108629	−	0.108629i	−0.650703	−	0.759332i	$-0.725526\pi$
$127$	1.22418	−	1.22418i	0.108629	−	0.108629i	0.759332	+	0.650703i	$0.225526\pi$
$128$	10.4464	+	4.34436i	0.923337	+	0.383991i
$129$	−13.3337	+	7.69820i	−1.17396	+	0.677788i
$130$	13.7544	−	3.18203i	1.20634	−	0.279082i
$131$	−1.12982	−	0.652300i	−0.0987126	−	0.0569918i	0.449831	−	0.893114i	$-0.351484\pi$
$131$	−1.12982	−	0.652300i	−0.0987126	−	0.0569918i	−0.548544	+	0.836122i	$0.684818\pi$
$132$	2.21027	−	0.866437i	0.192380	−	0.0754137i
$133$	−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
$136$	5.79522	−	4.79560i	0.496936	−	0.411219i
$137$	0.300203	−	1.12037i	0.0256480	−	0.0957198i	−0.951915	−	0.306361i	$-0.900889\pi$
$137$	0.300203	−	1.12037i	0.0256480	−	0.0957198i	0.977563	+	0.210641i	$0.0675552\pi$
$138$	−0.718965	−	0.642768i	−0.0612024	−	0.0547161i
$139$	17.4513			1.48020			0.740099	−	0.672498i	$-0.234779\pi$
$139$	17.4513			1.48020			0.740099	+	0.672498i	$0.234779\pi$
$140$	−10.6296	+	5.19731i	−0.898363	+	0.439253i
$141$	−3.99813			−0.336704
$142$	−8.02022	−	7.17023i	−0.673042	−	0.601712i
$143$	−1.10024	+	4.10614i	−0.0920065	+	0.343373i
$144$	−5.52556	−	1.70931i	−0.460464	−	0.142442i
$145$	−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
$148$	0.759151	+	1.93659i	0.0624018	+	0.159186i
$149$	−9.70894	−	5.60546i	−0.795387	−	0.459217i	0.0464684	−	0.998920i	$-0.485203\pi$
$149$	−9.70894	−	5.60546i	−0.795387	−	0.459217i	−0.841856	+	0.539703i	$0.818537\pi$
$150$	−7.02586	−	5.32339i	−0.573659	−	0.434653i
$151$	13.0081	−	7.51022i	1.05858	−	0.611173i	0.133543	−	0.991043i	$-0.457365\pi$
$151$	13.0081	−	7.51022i	1.05858	−	0.611173i	0.925040	+	0.379870i	$0.124031\pi$
$152$	10.2372	−	4.68870i	0.830345	−	0.380304i
$153$	−2.71920	+	2.71920i	−0.219835	+	0.219835i
$154$	0.122463	−	3.56070i	0.00986832	−	0.286929i
$155$	−5.65292	−	6.77924i	−0.454054	−	0.544521i
$156$	−8.95839	+	6.60600i	−0.717245	+	0.528903i
$157$	1.94845	−	7.27171i	0.155503	−	0.580345i	−0.843559	−	0.537037i	$-0.819544\pi$
$157$	1.94845	−	7.27171i	0.155503	−	0.580345i	0.999062	−	0.0433084i	$-0.0137898\pi$
$158$	4.72576	+	14.3712i	0.375961	+	1.14331i
$159$	−1.83212	+	3.17333i	−0.145297	+	0.251662i
$160$	11.9482	+	4.15220i	0.944587	+	0.328260i
$161$	−1.31354	+	0.607707i	−0.103522	+	0.0478941i
$162$	−3.55944	−	0.743432i	−0.279656	−	0.0584095i
$163$	−6.42243	+	1.72089i	−0.503044	+	0.134790i	−0.501412	−	0.865208i	$-0.667186\pi$
$163$	−6.42243	+	1.72089i	−0.503044	+	0.134790i	−0.00163153	+	0.999999i	$0.500519\pi$
$164$	−0.828796	−	7.38261i	−0.0647181	−	0.576485i
$165$	2.40901	−	1.11431i	0.187541	−	0.0867489i
$166$	−11.4310	+	0.639635i	−0.887221	+	0.0496453i
$167$	5.93258	−	5.93258i	0.459077	−	0.459077i	−0.439276	−	0.898352i	$-0.644765\pi$
$167$	5.93258	−	5.93258i	0.459077	−	0.459077i	0.898352	+	0.439276i	$0.144765\pi$
$168$	6.06650	−	7.08681i	0.468040	−	0.546759i
$169$		−	6.93083i		−	0.533141i
$170$	6.14807	−	5.73839i	0.471535	−	0.440114i
$171$	−4.98516	+	2.87818i	−0.381225	+	0.220100i
$172$	15.4088	−	19.3060i	1.17491	−	1.47207i
$173$	−0.572923	−	2.13818i	−0.0435585	−	0.162563i	0.940721	−	0.339182i	$-0.110150\pi$
$173$	−0.572923	−	2.13818i	−0.0435585	−	0.162563i	−0.984279	+	0.176620i	$0.943484\pi$
$174$	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
$178$	2.84508	−	0.935563i	0.213248	−	0.0701234i
$179$	8.23493	+	14.2633i	0.615507	+	1.06609i	0.990295	+	0.138980i	$0.0443822\pi$
$179$	8.23493	+	14.2633i	0.615507	+	1.06609i	−0.374788	+	0.927111i	$0.622284\pi$
$180$	−6.28071	−	1.53935i	−0.468137	−	0.114737i
$181$	−5.97636			−0.444219			−0.222110	−	0.975022i	$-0.571294\pi$
$181$	−5.97636			−0.444219			−0.222110	+	0.975022i	$0.571294\pi$
$182$	3.76622	+	16.2741i	0.279171	+	1.20632i
$183$	5.30976	+	5.30976i	0.392508	+	0.392508i
$184$	1.45027	+	0.539119i	0.106916	+	0.0397444i
$185$	0.976331	+	2.11072i	0.0717813	+	0.155183i
$186$	6.21192	+	3.13750i	0.455480	+	0.230052i
$187$	0.655419	+	2.44606i	0.0479290	+	0.178873i
$188$	5.97198	−	2.34104i	0.435551	−	0.170738i
$189$	−8.44690	+	11.9865i	−0.614422	+	0.871887i
$190$	11.1126	−	5.91516i	0.806195	−	0.429131i
$191$	−6.96830	−	4.02315i	−0.504209	−	0.291105i	0.226241	−	0.974071i	$-0.427356\pi$
$191$	−6.96830	−	4.02315i	−0.504209	−	0.291105i	−0.730450	+	0.682966i	$0.760690\pi$
$192$	−9.94585	+	0.733203i	−0.717780	+	0.0529144i
$193$	14.0635	+	3.76831i	1.01231	+	0.271249i	0.726596	−	0.687065i	$-0.241101\pi$
$193$	14.0635	+	3.76831i	1.01231	+	0.271249i	0.285718	+	0.958314i	$0.407768\pi$
$194$	−6.16213	+	0.344807i	−0.442415	+	0.0247557i
$195$	−9.55764	+	7.96972i	−0.684437	+	0.570723i
$196$	−6.15046	−	12.5766i	−0.439319	−	0.898331i
$197$	16.4919	+	16.4919i	1.17500	+	1.17500i	0.981001	+	0.194001i	$0.0621465\pi$
$197$	16.4919	+	16.4919i	1.17500	+	1.17500i	0.194001	+	0.981001i	$0.437854\pi$
$198$	1.29778	−	1.45163i	0.0922295	−	0.103163i
$199$	−4.82793	−	8.36222i	−0.342243	−	0.592782i	0.642606	−	0.766197i	$-0.277853\pi$
$199$	−4.82793	−	8.36222i	−0.342243	−	0.592782i	−0.984849	+	0.173415i	$0.944520\pi$
$200$	13.6115	+	3.83762i	0.962478	+	0.271361i
$201$	9.28636	−	16.0844i	0.655009	−	1.13451i
$202$	1.97981	+	0.413507i	0.139299	+	0.0290943i
$203$	−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
$206$	6.48778	−	12.8451i	0.452025	−	0.894962i
$207$	−0.764042	−	0.204725i	−0.0531046	−	0.0142293i
$208$	9.51304	−	15.1128i	0.659610	−	1.04788i
$209$			3.79066i			0.262205i
$210$	6.29811	−	8.31357i	0.434611	−	0.573691i
$211$			10.4344i			0.718333i	0.933274	+	0.359166i	$0.116939\pi$
$211$			10.4344i			0.718333i	−0.933274	+	0.359166i	$0.883061\pi$
$212$	0.878535	−	5.81275i	0.0603381	−	0.399221i
$213$	9.15992	+	2.45439i	0.627628	+	0.168172i
$214$	−0.0507779	−	0.0256468i	−0.00347111	−	0.00175318i
$215$	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
$218$	−1.81951	+	8.71155i	−0.123233	+	0.590020i
$219$	9.17459	−	15.8909i	0.619961	−	1.07380i
$220$	−2.94586	+	3.07499i	−0.198610	+	0.207316i
$221$	−5.93647	−	10.2823i	−0.399330	−	0.691660i
$222$	−1.36692	−	1.22205i	−0.0917416	−	0.0820187i
$223$	−10.7262	−	10.7262i	−0.718279	−	0.718279i	0.249973	−	0.968253i	$-0.419578\pi$
$223$	−10.7262	−	10.7262i	−0.718279	−	0.718279i	−0.968253	+	0.249973i	$0.919578\pi$
$224$	−4.91191	+	14.1377i	−0.328191	+	0.944611i
$225$	−7.11217	−	1.29934i	−0.474145	−	0.0866230i
$226$	−1.21249	−	21.6687i	−0.0806539	−	1.44138i
$227$	−9.68083	−	2.59397i	−0.642539	−	0.172168i	−0.0771860	−	0.997017i	$-0.524594\pi$
$227$	−9.68083	−	2.59397i	−0.642539	−	0.172168i	−0.565353	+	0.824849i	$0.691260\pi$
$228$	−6.19149	+	7.75744i	−0.410041	+	0.513749i
$229$	14.7989	+	8.54416i	0.977940	+	0.564614i	0.901647	−	0.432472i	$-0.142359\pi$
$229$	14.7989	+	8.54416i	0.977940	+	0.564614i	0.0762921	+	0.997086i	$0.475692\pi$
$230$	1.65451	+	0.505012i	0.109095	+	0.0332995i
$231$	1.31868	+	2.85029i	0.0867627	+	0.187535i
$232$	−11.8450	+	16.6725i	−0.777661	+	1.09460i
$233$	−0.485407	−	1.81156i	−0.0318001	−	0.118680i	0.948201	−	0.317670i	$-0.102900\pi$
$233$	−0.485407	−	1.81156i	−0.0318001	−	0.118680i	−0.980001	+	0.198990i	$0.936234\pi$
$234$	−4.11583	+	8.14891i	−0.269060	+	0.532711i
$235$	6.50895	−	3.01077i	0.424597	−	0.196401i
$236$	−20.2846	+	14.9581i	−1.32042	+	0.973687i
$237$	−9.42947	−	9.42947i	−0.612510	−	0.612510i
$238$	6.79029	+	7.27400i	0.440149	+	0.471503i
$239$	−15.2182			−0.984385			−0.492193	−	0.870486i	$-0.663804\pi$
$239$	−15.2182			−0.984385			−0.492193	+	0.870486i	$0.663804\pi$
$240$	−11.0511	+	1.48123i	−0.713348	+	0.0956132i
$241$	6.58780	+	11.4104i	0.424357	+	0.735008i	0.996360	−	0.0852432i	$-0.0271667\pi$
$241$	6.58780	+	11.4104i	0.424357	+	0.735008i	−0.572003	+	0.820252i	$0.693833\pi$
$242$	4.45894	+	13.5598i	0.286632	+	0.871656i
$243$	−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
$248$	−11.1158	−	1.04917i	−0.705854	−	0.0666222i
$249$	8.73995	−	5.04601i	0.553872	−	0.319778i
$250$	15.4468	+	3.37568i	0.976944	+	0.213497i
$251$			14.7048i			0.928161i	0.885793	+	0.464080i	$0.153615\pi$
$251$			14.7048i			0.928161i	−0.885793	+	0.464080i	$0.846385\pi$
$252$	1.82084	−	7.43158i	0.114702	−	0.468145i
$253$	−0.368320	+	0.368320i	−0.0231561	+	0.0231561i
$254$	−0.136786	−	2.44454i	−0.00858275	−	0.153384i
$255$	−2.55695	+	6.95833i	−0.160123	+	0.435747i
$256$	14.4267	−	6.91881i	0.901670	−	0.432426i
$257$	−12.7677	+	3.42109i	−0.796426	+	0.213402i	−0.634014	−	0.773321i	$-0.718594\pi$
$257$	−12.7677	+	3.42109i	−0.796426	+	0.213402i	−0.162412	+	0.986723i	$0.551927\pi$
$258$	−4.45165	+	21.3139i	−0.277148	+	1.32694i
$259$	−2.49735	+	1.15539i	−0.155178	+	0.0717926i
$260$	9.60963	−	17.5006i	0.595964	−	1.08534i
$261$	5.22778	−	9.05478i	0.323592	−	0.560477i
$262$	−1.75266	+	0.576336i	−0.108279	+	0.0356061i
$263$	−2.73529	+	10.2083i	−0.168665	+	0.629468i	0.828879	+	0.559428i	$0.188979\pi$
$263$	−2.73529	+	10.2083i	−0.168665	+	0.629468i	−0.997544	+	0.0700398i	$0.977687\pi$
$264$	1.16985	−	3.14698i	0.0719991	−	0.193683i
$265$	0.593033	−	6.54585i	0.0364298	−	0.402108i
$266$	6.99988	+	13.1481i	0.429190	+	0.806164i
$267$	−1.86676	+	1.86676i	−0.114244	+	0.114244i
$268$	−4.45297	+	29.4627i	−0.272009	+	1.79972i
$269$	10.5625	−	6.09826i	0.644007	−	0.371818i	−0.142149	−	0.989845i	$-0.545401\pi$
$269$	10.5625	−	6.09826i	0.644007	−	0.371818i	0.786156	+	0.618027i	$0.212068\pi$
$270$	17.0755	−	3.95036i	1.03918	−	0.240412i
$271$	5.70012	+	3.29096i	0.346257	+	0.199912i	0.663036	−	0.748588i	$-0.269268\pi$
$271$	5.70012	+	3.29096i	0.346257	+	0.199912i	−0.316778	+	0.948500i	$0.602601\pi$
$272$	0.406362	−	10.6301i	0.0246393	−	0.644546i
$273$	−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
$276$	−1.35535	+	0.152156i	−0.0815824	+	0.00915872i
$277$	−1.06292	+	3.96687i	−0.0638646	+	0.238346i	−0.990478	−	0.137669i	$-0.956039\pi$
$277$	−1.06292	+	3.96687i	−0.0638646	+	0.238346i	0.926614	+	0.376015i	$0.122706\pi$
$278$	16.4490	−	18.3990i	0.986548	−	1.10350i
$279$	5.70799			0.341728
$280$	−4.53956	+	16.1057i	−0.271291	+	0.962497i
$281$	−32.2773			−1.92550			−0.962752	−	0.270386i	$-0.912849\pi$
$281$	−32.2773			−1.92550			−0.962752	+	0.270386i	$0.912849\pi$
$282$	−3.76852	+	4.21526i	−0.224412	+	0.251015i
$283$	5.05423	−	18.8626i	0.300443	−	1.12127i	−0.636355	−	0.771396i	$-0.719559\pi$
$283$	5.05423	−	18.8626i	0.300443	−	1.12127i	0.936798	−	0.349872i	$-0.113775\pi$
$284$	−15.1192	+	1.69734i	−0.897161	+	0.100718i
$285$	−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
$288$	−7.01036	+	4.21450i	−0.413090	+	0.248342i
$289$	8.59722	+	4.96361i	0.505719	+	0.291977i
$290$	−12.1082	+	19.3968i	−0.711019	+	1.13902i
$291$	4.71144	−	2.72015i	0.276190	−	0.159458i
$292$	−4.39938	+	29.1081i	−0.257454	+	1.70342i
$293$	12.6859	−	12.6859i	0.741121	−	0.741121i	−0.231673	−	0.972794i	$-0.574420\pi$
$293$	12.6859	−	12.6859i	0.741121	−	0.741121i	0.972794	+	0.231673i	$0.0744200\pi$
$294$	9.83729	+	7.45130i	0.573723	+	0.434569i
$295$	−21.6415	+	18.0460i	−1.26002	+	1.05068i
$296$	2.75731	+	1.02499i	0.160265	+	0.0595764i
$297$	−1.36590	+	5.09762i	−0.0792577	+	0.295794i
$298$	−15.0612	+	4.95266i	−0.872473	+	0.286900i
$299$	1.22108	−	2.11498i	0.0706170	−	0.122312i
$300$	−12.2348	+	2.38974i	−0.706379	+	0.137972i
$301$	26.7107	+	18.8231i	1.53958	+	1.08495i
$302$	4.34295	−	20.7934i	0.249909	−	1.19653i
$303$	−1.72208	+	0.461430i	−0.0989309	+	0.0265085i
$304$	4.70593	−	15.2126i	0.269904	−	0.872500i
$305$	−12.6428	−	4.64579i	−0.723922	−	0.266017i
$306$	0.303836	+	5.42991i	0.0173691	+	0.310407i
$307$	9.98091	−	9.98091i	0.569640	−	0.569640i	−0.362387	−	0.932028i	$-0.618038\pi$
$307$	9.98091	−	9.98091i	0.569640	−	0.569640i	0.932028	+	0.362387i	$0.118038\pi$
$308$	−3.63864	−	3.48532i	−0.207331	−	0.198594i
$309$			12.6850i			0.721626i
$310$	−12.4757	−	0.429989i	−0.708570	−	0.0244217i
$311$	−12.0711	+	6.96926i	−0.684490	+	0.395190i	−0.801544	−	0.597935i	$-0.795988\pi$
$311$	−12.0711	+	6.96926i	−0.684490	+	0.395190i	0.117055	+	0.993125i	$0.462655\pi$
$312$	−1.47916	+	15.6715i	−0.0837409	+	0.887224i
$313$	1.27037	+	4.74109i	0.0718056	+	0.267982i	0.992490	−	0.122326i	$-0.0390353\pi$
$313$	1.27037	+	4.74109i	0.0718056	+	0.267982i	−0.920684	+	0.390308i	$0.872369\pi$
$314$	−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	−0.866423	+	0.499312i	$0.833586\pi$
$317$	−33.2307	+	8.90414i	−1.86642	+	0.500106i	−1.00000		0.000794747i	$0.999747\pi$
$318$	1.61876	+	4.92271i	0.0907756	+	0.276052i
$319$	−3.44258	−	5.96272i	−0.192747	−	0.333848i
$320$	15.6397	−	8.68332i	0.874285	−	0.485413i
$321$	0.0501451			0.00279883
$322$	−0.597395	+	1.95768i	−0.0332915	+	0.109097i
$323$	−7.48630	−	7.48630i	−0.416549	−	0.416549i
$324$	−4.13883	+	3.05201i	−0.229935	+	0.169556i
$325$	9.55827	−	20.1720i	0.530197	−	1.11894i
$326$	−4.23925	+	8.39327i	−0.234790	+	0.464860i
$327$	−2.03038	−	7.57748i	−0.112280	−	0.419035i
$328$	−8.56473	−	6.08482i	−0.472908	−	0.335978i
$329$	3.56296	+	7.70124i	0.196432	+	0.424583i
$330$	1.09584	−	3.59015i	0.0603239	−	0.197631i
$331$	11.2201	+	6.47792i	0.616712	+	0.356059i	0.775588	−	0.631240i	$-0.217454\pi$
$331$	11.2201	+	6.47792i	0.616712	+	0.356059i	−0.158876	+	0.987299i	$0.550787\pi$
$332$	−10.1002	+	12.6547i	−0.554320	+	0.694518i
$333$	−1.45262	−	0.389229i	−0.0796032	−	0.0213296i
$334$	−0.662889	−	11.8466i	−0.0362717	−	0.648219i
$335$	−3.00587	+	33.1785i	−0.164228	+	1.81274i
$336$	−1.75358	−	13.0758i	−0.0956655	−	0.713341i
$337$	7.43071	+	7.43071i	0.404776	+	0.404776i	0.879912	−	0.475136i	$-0.157601\pi$
$337$	7.43071	+	7.43071i	0.404776	+	0.404776i	−0.475136	+	0.879912i	$0.657601\pi$
$338$	−7.30722	−	6.53279i	−0.397461	−	0.355337i
$339$	9.56524	+	16.5675i	0.519513	+	0.899822i
$340$	−0.255038	−	11.8908i	−0.0138314	−	0.644868i
$341$	1.87940	−	3.25522i	0.101775	−	0.176280i
$342$	−1.66437	+	7.96877i	−0.0899989	+	0.430902i
$343$	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
$346$	−2.79431	−	1.41134i	−0.150223	−	0.0758743i
$347$	8.85066	+	2.37153i	0.475128	+	0.127310i	0.488433	−	0.872601i	$-0.337569\pi$
$347$	8.85066	+	2.37153i	0.475128	+	0.127310i	−0.0133050	+	0.999911i	$0.504235\pi$
$348$	2.69413	−	17.8254i	0.144420	−	0.955544i
$349$		−	19.9513i		−	1.06797i	−0.845495	−	0.533984i	$-0.820694\pi$
$349$		−	19.9513i		−	1.06797i	0.845495	−	0.533984i	$-0.179306\pi$
$350$	−3.99282	+	18.2772i	−0.213425	+	0.976959i
$351$		−	24.7434i		−	1.32070i
$352$	0.0952748	+	5.38561i	0.00507817	+	0.287054i
$353$	−2.39430	−	0.641552i	−0.127436	−	0.0341464i	0.194537	−	0.980895i	$-0.437679\pi$
$353$	−2.39430	−	0.641552i	−0.127436	−	0.0341464i	−0.321973	+	0.946749i	$0.604346\pi$
$354$	10.0159	−	19.8305i	0.532340	−	1.05398i
$355$	−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
$358$	22.7999	+	4.76203i	1.20501	+	0.251681i
$359$	7.94645	−	13.7637i	0.419398	−	0.726418i	−0.576481	−	0.817110i	$-0.695575\pi$
$359$	7.94645	−	13.7637i	0.419398	−	0.726418i	0.995879	+	0.0906921i	$0.0289079\pi$
$360$	−7.54296	+	5.17085i	−0.397549	+	0.272528i
$361$	1.57601	+	2.72973i	0.0829481	+	0.143670i
$362$	−5.63313	+	6.30091i	−0.296071	+	0.331169i
$363$	−8.89708	−	8.89708i	−0.466976	−	0.466976i
$364$	20.7078	+	11.3688i	1.08539	+	0.595884i
$365$	−2.96969	+	32.7792i	−0.155441	+	1.71574i
$366$	10.6029	−	0.593297i	0.554224	−	0.0310121i
$367$	10.3988	+	2.78634i	0.542812	+	0.145446i	0.519798	−	0.854289i	$-0.326007\pi$
$367$	10.3988	+	2.78634i	0.542812	+	0.145446i	0.0230136	+	0.999735i	$0.492674\pi$
$368$	1.93538	−	1.02088i	0.100889	−	0.0532169i
$369$	4.65148	+	2.68553i	0.242147	+	0.139803i
$370$	3.14560	+	0.960146i	0.163532	+	0.0499156i
$371$	7.74521	+	0.701119i	0.402111	+	0.0364003i
$372$	9.16305	−	3.59195i	0.475082	−	0.186234i
$373$	−3.82144	−	14.2618i	−0.197867	−	0.738448i	−0.991506	−	0.130060i	$-0.958483\pi$
$373$	−3.82144	−	14.2618i	−0.197867	−	0.738448i	0.793640	−	0.608388i	$-0.208184\pi$
$374$	3.19667	+	1.61457i	0.165296	+	0.0834873i
$375$	−13.4954	+	3.48258i	−0.696897	+	0.179840i
$376$	3.16083	−	8.50289i	0.163007	−	0.438503i
$377$	22.8262	+	22.8262i	1.17561	+	1.17561i
$378$	4.67561	+	20.2037i	0.240488	+	1.03917i
$379$	26.4563			1.35897			0.679483	−	0.733691i	$-0.262204\pi$
$379$	26.4563			1.35897			0.679483	+	0.733691i	$0.262204\pi$
$380$	4.23803	−	17.2916i	0.217406	−	0.887039i
$381$	1.07909	+	1.86905i	0.0552837	+	0.0957542i
$382$	−10.8097	+	3.55463i	−0.553075	+	0.181871i
$383$	−28.3799	+	7.60437i	−1.45015	+	0.388565i	−0.896074	−	0.443904i	$-0.853593\pi$
$383$	−28.3799	+	7.60437i	−1.45015	+	0.388565i	−0.554071	+	0.832470i	$0.686926\pi$
$384$	−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
$388$	−5.44470	+	6.82177i	−0.276413	+	0.346323i
$389$	8.09963	−	4.67632i	0.410667	−	0.237099i	−0.280409	−	0.959881i	$-0.590470\pi$
$389$	8.09963	−	4.67632i	0.410667	−	0.237099i	0.691076	+	0.722782i	$0.257137\pi$
$390$	−0.606215	+	17.5887i	−0.0306969	+	0.890638i
$391$		−	1.45481i		−	0.0735731i
$392$	−19.0569	−	5.36988i	−0.962517	−	0.271220i
$393$	1.14998	−	1.14998i	0.0580090	−	0.0580090i
$394$	32.9324	−	1.84276i	1.65911	−	0.0928370i
$395$	22.4520	+	8.25035i	1.12968	+	0.415120i
$396$	−0.307212	−	2.73653i	−0.0154380	−	0.137516i
$397$	17.1641	−	4.59912i	0.861443	−	0.230823i	0.199059	−	0.979987i	$-0.436211\pi$
$397$	17.1641	−	4.59912i	0.861443	−	0.230823i	0.662384	+	0.749164i	$0.269545\pi$
$398$	−13.3670	−	2.79186i	−0.670028	−	0.139943i
$399$	−10.7327	−	7.56340i	−0.537309	−	0.378644i
$400$	16.8758	−	10.7335i	0.843790	−	0.536673i
$401$	−3.07671	+	5.32902i	−0.153644	+	0.266118i	−0.932564	−	0.361004i	$-0.882434\pi$
$401$	−3.07671	+	5.32902i	−0.153644	+	0.266118i	0.778921	+	0.627122i	$0.215767\pi$
$402$	−8.20490	−	24.9514i	−0.409223	−	1.24446i
$403$	−4.56121	+	17.0227i	−0.227210	+	0.847960i
$404$	2.30207	−	1.69757i	0.114532	−	0.0844573i
$405$	−4.41569	+	3.68206i	−0.219417	+	0.182963i
$406$	−22.9516	−	14.3250i	−1.13907	−	0.710935i
$407$	−0.700261	+	0.700261i	−0.0347107	+	0.0347107i
$408$	3.90471	+	8.52545i	0.193312	+	0.422073i
$409$	−5.66917	+	3.27310i	−0.280322	+	0.161844i	−0.633569	−	0.773686i	$-0.718411\pi$
$409$	−5.66917	+	3.27310i	−0.280322	+	0.161844i	0.353247	+	0.935530i	$0.385078\pi$
$410$	−9.96421	−	6.22004i	−0.492097	−	0.307186i
$411$	1.25221	+	0.722965i	0.0617670	+	0.0356612i
$412$	−7.42751	−	18.9475i	−0.365927	−	0.933478i
$413$	−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
$416$	−6.96678	−	24.2745i	−0.341575	−	1.19015i
$417$	−5.63057	+	21.0136i	−0.275730	+	1.02904i
$418$	3.99652	+	3.57296i	0.195476	+	0.174759i
$419$	17.7908			0.869139			0.434569	−	0.900638i	$-0.356901\pi$
$419$	17.7908			0.869139			0.434569	+	0.900638i	$0.356901\pi$
$420$	−2.82864	−	14.4763i	−0.138024	−	0.706369i
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	11.0010	+	9.83513i	0.535522	+	0.478767i
$423$	−1.20029	+	4.47954i	−0.0583601	+	0.217803i
$424$	−5.30034	−	6.40517i	−0.257407	−	0.311062i
$425$	−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
$428$	−0.0749013	+	0.0293616i	−0.00362049	+	0.00141925i
$429$	−4.58934	−	2.64965i	−0.221575	−	0.127926i
$430$	−8.80302	−	38.0512i	−0.424519	−	1.83499i
$431$	−13.1055	+	7.56644i	−0.631268	+	0.364463i	−0.781243	−	0.624227i	$-0.785414\pi$
$431$	−13.1055	+	7.56644i	−0.631268	+	0.364463i	0.149975	+	0.988690i	$0.452081\pi$
$432$	11.8101	−	18.7619i	0.568212	−	0.902683i
$433$	−5.45382	+	5.45382i	−0.262094	+	0.262094i	−0.825904	−	0.563811i	$-0.809335\pi$
$433$	−5.45382	+	5.45382i	−0.262094	+	0.262094i	0.563811	+	0.825904i	$0.309335\pi$
$434$	0.507689	−	14.7614i	0.0243698	−	0.708572i
$435$	1.81860	−	20.0736i	0.0871953	−	0.962454i
$436$	7.46963	+	10.1296i	0.357730	+	0.485118i
$437$	0.563632	−	2.10350i	0.0269622	−	0.100624i
$438$	−8.10614	−	24.6511i	−0.387327	−	1.17787i
$439$	−12.8732	+	22.2970i	−0.614402	+	1.06418i	0.376087	+	0.926585i	$0.377270\pi$
$439$	−12.8732	+	22.2970i	−0.614402	+	1.06418i	−0.990489	+	0.137592i	$0.956064\pi$
$440$	0.465312	+	6.00423i	0.0221829	+	0.286241i
$441$	9.95730	+	1.81762i	0.474157	+	0.0865536i
$442$	−16.4362	−	3.43289i	−0.781790	−	0.163286i
$443$	16.7002	−	4.47481i	0.793452	−	0.212605i	0.160745	−	0.986996i	$-0.448610\pi$
$443$	16.7002	−	4.47481i	0.793452	−	0.212605i	0.632707	+	0.774391i	$0.281944\pi$
$444$	−2.57683	+	0.289284i	−0.122291	+	0.0137288i
$445$	1.63333	−	4.44484i	0.0774273	−	0.210706i
$446$	−21.4189	+	1.19851i	−1.01421	+	0.0567513i
$447$	9.88223	−	9.88223i	0.467413	−	0.467413i
$448$	10.2756	+	18.5044i	0.485477	+	0.874250i
$449$		−	11.0999i		−	0.523839i	−0.965090	−	0.261919i	$-0.915645\pi$
$449$		−	11.0999i		−	0.523839i	0.965090	−	0.261919i	$-0.0843555\pi$
$450$	−8.07362	+	6.27368i	−0.380594	+	0.295744i
$451$	3.06308	−	1.76847i	0.144235	−	0.0832739i
$452$	−23.9883	−	19.1459i	−1.12832	−	0.900549i
$453$	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	0.255172	−	0.966896i	$-0.417868\pi$
$457$	20.5140	−	5.49672i	0.959606	−	0.257126i	0.704434	+	0.709770i	$0.251201\pi$
$458$	22.9572	−	7.54913i	1.07272	−	0.352748i
$459$	−7.36989	−	12.7650i	−0.343997	−	0.595821i
$460$	2.09193	−	1.26835i	0.0975366	−	0.0591371i
$461$	−8.61652			−0.401311			−0.200656	−	0.979662i	$-0.564307\pi$
$461$	−8.61652			−0.401311			−0.200656	+	0.979662i	$0.564307\pi$
$462$	4.24802	+	1.29630i	0.197636	+	0.0603094i
$463$	1.63340	+	1.63340i	0.0759103	+	0.0759103i	0.744043	−	0.668132i	$-0.232906\pi$
$463$	1.63340	+	1.63340i	0.0759103	+	0.0759103i	−0.668132	+	0.744043i	$0.732906\pi$
$464$	6.41320	+	28.2032i	0.297725	+	1.30930i
$465$	9.98695	−	4.61955i	0.463134	−	0.214227i
$466$	−2.36747	−	1.19576i	−0.109671	−	0.0553924i
$467$	6.59489	+	24.6125i	0.305175	+	1.13893i	0.932794	+	0.360409i	$0.117363\pi$
$467$	6.59489	+	24.6125i	0.305175	+	1.13893i	−0.627619	+	0.778521i	$0.715970\pi$
$468$	4.71199	+	12.0203i	0.217812	+	0.555637i
$469$	−39.2576	−	3.55372i	−1.81275	−	0.164095i
$470$	2.96086	−	9.70030i	0.136574	−	0.447441i
$471$	8.12741	+	4.69236i	0.374491	+	0.216213i
$472$	−3.34928	+	35.4852i	−0.154163	+	1.63334i
$473$	11.3596	+	3.04379i	0.522313	+	0.139953i
$474$	−18.8295	+	1.05362i	−0.864867	+	0.0483944i
$475$	3.57726	−	19.5807i	0.164136	−	0.898423i
$476$	14.0693	−	0.302795i	0.644867	−	0.0138786i
$477$	3.00540	+	3.00540i	0.137608	+	0.137608i
$478$	−14.3442	+	16.0447i	−0.656090	+	0.733867i
$479$	4.63924	+	8.03541i	0.211972	+	0.367147i	0.952332	−	0.305064i	$-0.0986780\pi$
$479$	4.63924	+	8.03541i	0.211972	+	0.367147i	−0.740359	+	0.672211i	$0.765345\pi$
$480$	−8.85480	+	13.0475i	−0.404164	+	0.595532i
$481$	2.32156	−	4.02106i	0.105854	−	0.183345i
$482$	18.2395	+	3.80954i	0.830787	+	0.173520i
$483$	−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
$486$	−8.55746	+	16.9429i	−0.388174	+	0.768544i
$487$	−17.2022	−	4.60932i	−0.779506	−	0.208868i	−0.152939	−	0.988236i	$-0.548874\pi$
$487$	−17.2022	−	4.60932i	−0.779506	−	0.208868i	−0.626567	+	0.779368i	$0.715541\pi$
$488$	−15.4901	+	7.09457i	−0.701204	+	0.321156i
$489$		−	8.28866i		−	0.374826i
$490$	−21.6263	−	4.72279i	−0.976975	−	0.213354i
$491$			2.49970i			0.112810i	0.998408	+	0.0564049i	$0.0179638\pi$
$491$			2.49970i			0.112810i	−0.998408	+	0.0564049i	$0.982036\pi$
$492$	9.15701	+	1.38398i	0.412830	+	0.0623949i
$493$	18.5748	+	4.97711i	0.836569	+	0.224158i
$494$	−22.4349	−	11.3314i	−1.00940	−	0.509823i
$495$	−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
$498$	2.91797	−	13.9708i	0.130757	−	0.626047i
$499$	3.26199	−	5.64993i	0.146027	−	0.252926i	−0.783729	−	0.621103i	$-0.786685\pi$
$499$	3.26199	−	5.64993i	0.146027	−	0.252926i	0.929756	+	0.368178i	$0.120018\pi$
$500$	18.1187	−	13.1039i	0.810294	−	0.586024i
$501$	5.22947	+	9.05770i	0.233635	+	0.404668i
$502$	15.5034	+	13.8603i	0.691951	+	0.618617i
$503$	14.6078	+	14.6078i	0.651327	+	0.651327i	0.953313	−	0.301985i	$-0.0976493\pi$
$503$	14.6078	+	14.6078i	0.651327	+	0.651327i	−0.301985	+	0.953313i	$0.597649\pi$
$504$	−6.11889	−	8.92451i	−0.272557	−	0.397529i
$505$	2.45607	−	2.04801i	0.109294	−	0.0911353i
$506$	0.0411550	+	0.735489i	0.00182956	+	0.0326965i
$507$	8.34561	+	2.23620i	0.370641	+	0.0993131i
$508$	−2.70623	−	2.15993i	−0.120069	−	0.0958316i
$509$	29.8459	+	17.2316i	1.32290	+	0.763775i	0.984190	−	0.177116i	$-0.0566769\pi$
$509$	29.8459	+	17.2316i	1.32290	+	0.763775i	0.338708	+	0.940892i	$0.390010\pi$
$510$	4.92611	+	9.25452i	0.218132	+	0.409797i
$511$	−38.7851	−	3.51094i	−1.71575	−	0.155315i
$512$	6.30364	−	21.7316i	0.278584	−	0.960412i
$513$	−5.71056	−	21.3121i	−0.252128	−	0.940953i
$514$	−8.42755	+	16.6857i	−0.371723	+	0.735973i
$515$	−9.55240	−	20.6512i	−0.420929	−	0.910001i
$516$	18.2754	+	24.7832i	0.804528	+	1.09102i
$517$	2.15944	+	2.15944i	0.0949721	+	0.0949721i
$518$	−1.13579	+	3.72201i	−0.0499036	+	0.163536i
$519$	2.75949			0.121128
$520$	−9.39327	−	26.6270i	−0.411922	−	1.16767i
$521$	16.9526	+	29.3627i	0.742705	+	1.28640i	0.951259	+	0.308392i	$0.0997908\pi$
$521$	16.9526	+	29.3627i	0.742705	+	1.28640i	−0.208555	+	0.978011i	$0.566876\pi$
$522$	−4.61897	−	14.0465i	−0.202167	−	0.614796i
$523$	17.8250	−	4.77618i	0.779431	−	0.208848i	0.152897	−	0.988242i	$-0.451140\pi$
$523$	17.8250	−	4.77618i	0.779431	−	0.208848i	0.626534	+	0.779394i	$0.284473\pi$
$524$	−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
$528$	−2.21522	−	4.19963i	−0.0964053	−	0.182765i
$529$	−19.6594	+	11.3504i	−0.854758	+	0.493495i
$530$	−6.34236	−	6.79516i	−0.275494	−	0.295163i
$531$		−	18.2217i		−	0.790756i
$532$	20.4600	+	5.01301i	0.887055	+	0.217341i
$533$	−11.7259	+	11.7259i	−0.507906	+	0.507906i
$534$	0.208587	+	3.72769i	0.00902643	+	0.161313i
$535$	−0.0816361	+	0.0377615i	−0.00352944	+	0.00163257i
$536$	26.8655	+	32.4654i	1.16041	+	1.40229i
$537$	−19.8318	+	5.31392i	−0.855806	+	0.229312i
$538$	3.52645	−	16.8842i	0.152036	−	0.727928i
$539$	4.31510	−	5.08010i	0.185864	−	0.218815i
$540$	11.9300	−	21.7263i	0.513385	−	0.934953i
$541$	−1.59149	+	2.75655i	−0.0684236	+	0.118513i	−0.898208	−	0.439572i	$-0.855130\pi$
$541$	−1.59149	+	2.75655i	−0.0684236	+	0.118513i	0.829784	+	0.558085i	$0.188464\pi$
$542$	8.84244	−	2.90771i	0.379815	−	0.124897i
$543$	1.92824	−	7.19630i	0.0827488	−	0.308823i
$544$	−10.8244	−	10.4481i	−0.464092	−	0.447957i
$545$	9.01164	+	10.8072i	0.386016	+	0.462928i
$546$	−20.8113	−	0.715760i	−0.890640	−	0.0306317i
$547$	−15.6791	+	15.6791i	−0.670391	+	0.670391i	−0.957806	−	0.287415i	$-0.907204\pi$
$547$	−15.6791	+	15.6791i	−0.670391	+	0.670391i	0.287415	+	0.957806i	$0.407204\pi$
$548$	−2.29374	−	0.346674i	−0.0979836	−	0.0148092i
$549$	7.54315	−	4.35504i	0.321934	−	0.185869i
$550$	0.919524	+	6.66998i	0.0392087	+	0.284409i
$551$	24.9289	+	14.3927i	1.06201	+	0.613151i
$552$	−1.11709	+	1.57237i	−0.0475466	+	0.0669246i
$553$	−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
$556$	−3.89382	−	34.6847i	−0.165135	−	1.47096i
$557$	5.52434	−	20.6171i	0.234074	−	0.873575i	−0.744491	−	0.667633i	$-0.767308\pi$
$557$	5.52434	−	20.6171i	0.234074	−	0.873575i	0.978564	−	0.205942i	$-0.0660258\pi$
$558$	5.38017	−	6.01797i	0.227761	−	0.254761i
$559$	−55.1382			−2.33210
$560$	12.7015	+	19.9668i	0.536735	+	0.843751i
$561$	−3.15683			−0.133282
$562$	−30.4236	+	34.0302i	−1.28334	+	1.43548i
$563$	−3.52319	+	13.1487i	−0.148485	+	0.554153i	0.851091	+	0.525019i	$0.175942\pi$
$563$	−3.52319	+	13.1487i	−0.148485	+	0.554153i	−0.999576	+	0.0291340i	$0.990725\pi$
$564$	0.892084	+	7.94635i	0.0375635	+	0.334602i
$565$	−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
$568$	−12.4614	+	17.5402i	−0.522869	+	0.735969i
$569$	−20.3421	−	11.7445i	−0.852787	−	0.492357i	0.00880335	−	0.999961i	$-0.497198\pi$
$569$	−20.3421	−	11.7445i	−0.852787	−	0.492357i	−0.861590	+	0.507605i	$0.830531\pi$
$570$	3.53718	+	15.2895i	0.148156	+	0.640408i
$571$	23.4830	−	13.5579i	0.982734	−	0.567382i	0.0796395	−	0.996824i	$-0.474623\pi$
$571$	23.4830	−	13.5579i	0.982734	−	0.567382i	0.903094	+	0.429442i	$0.141290\pi$
$572$	8.40651	+	1.27056i	0.351494	+	0.0531246i
$573$	7.09267	−	7.09267i	0.296301	−	0.296301i
$574$	7.35879	−	11.7904i	0.307150	−	0.492120i
$575$	2.25014	−	1.55497i	0.0938374	−	0.0648469i
$576$	−2.16438	+	11.3635i	−0.0901826	+	0.473480i
$577$	7.22183	−	26.9522i	0.300649	−	1.12204i	−0.635978	−	0.771707i	$-0.719403\pi$
$577$	7.22183	−	26.9522i	0.300649	−	1.12204i	0.936627	−	0.350329i	$-0.113930\pi$
$578$	13.3366	−	4.38556i	0.554731	−	0.182415i
$579$	−9.07505	+	15.7184i	−0.377146	+	0.653236i
$580$	9.03732	+	31.0486i	0.375254	+	1.28922i
$581$	−17.5083	−	12.3382i	−0.726368	−	0.511874i
$582$	1.57299	−	7.53124i	0.0652024	−	0.312180i
$583$	2.70351	−	0.724403i	0.111968	−	0.0300017i
$584$	26.5421	+	32.0747i	1.09832	+	1.32726i
$585$	6.06002	+	13.1011i	0.250551	+	0.541663i
$586$	−1.41749	−	25.3323i	−0.0585560	−	1.04647i
$587$	−22.8296	+	22.8296i	−0.942280	+	0.942280i	−0.998423	−	0.0561427i	$-0.982120\pi$
$587$	−22.8296	+	22.8296i	−0.942280	+	0.942280i	0.0561427	+	0.998423i	$0.482120\pi$
$588$	17.1283	−	3.34815i	0.706359	−	0.138075i
$589$			15.7148i			0.647516i
$590$	−1.37266	+	39.8264i	−0.0565117	+	1.63963i
$591$	−25.1794	+	14.5374i	−1.03574	+	0.597987i
$592$	3.67961	−	1.94092i	0.151231	−	0.0797715i
$593$	9.88391	+	36.8872i	0.405883	+	1.51478i	0.802421	+	0.596759i	$0.203545\pi$
$593$	9.88391	+	36.8872i	0.405883	+	1.51478i	−0.396537	+	0.918019i	$0.629788\pi$
$594$	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
$598$	−1.07888	−	3.28091i	−0.0441186	−	0.134166i
$599$	−14.4801	−	25.0802i	−0.591640	−	1.02475i	−0.994012	−	0.109274i	$-0.965147\pi$
$599$	−14.4801	−	25.0802i	−0.591640	−	1.02475i	0.402372	−	0.915476i	$-0.368186\pi$
$600$	−9.01267	+	15.1518i	−0.367941	+	0.618569i
$601$	−8.88262			−0.362330			−0.181165	−	0.983453i	$-0.557987\pi$
$601$	−8.88262			−0.362330			−0.181165	+	0.983453i	$0.557987\pi$
$602$	45.0220	−	10.4192i	1.83496	−	0.424653i
$603$	−15.2333	−	15.2333i	−0.620347	−	0.620347i
$604$	−17.8291	−	24.1780i	−0.725456	−	0.983791i
$605$	21.1843	+	7.78453i	0.861266	+	0.316486i
$606$	−1.13669	+	2.25053i	−0.0461749	+	0.0914215i
$607$	−11.8891	−	44.3709i	−0.482565	−	1.80096i	−0.590783	−	0.806830i	$-0.701181\pi$
$607$	−11.8891	−	44.3709i	−0.482565	−	1.80096i	0.108218	−	0.994127i	$-0.465485\pi$
$608$	−11.6030	−	19.3004i	−0.470565	−	0.782734i
$609$	23.7515	+	2.15006i	0.962461	+	0.0871249i
$610$	−16.8148	+	8.95037i	−0.680810	+	0.362390i
$611$	−12.4000	−	7.15915i	−0.501651	−	0.289628i
$612$	6.01118	+	4.79773i	0.242988	+	0.193937i
$613$	−0.223941	−	0.0600047i	−0.00904487	−	0.00242357i	0.254294	−	0.967127i	$-0.418157\pi$
$613$	−0.223941	−	0.0600047i	−0.00904487	−	0.00242357i	−0.263339	+	0.964703i	$0.584824\pi$
$614$	−1.11524	−	19.9306i	−0.0450073	−	0.804335i
$615$	10.3119	+	0.934224i	0.415815	+	0.0376716i
$616$	−7.10426	+	0.551085i	−0.286239	+	0.0222038i
$617$	−27.1038	−	27.1038i	−1.09116	−	1.09116i	−0.995405	−	0.0957517i	$-0.969475\pi$
$617$	−27.1038	−	27.1038i	−1.09116	−	1.09116i	−0.0957517	−	0.995405i	$-0.530525\pi$
$618$	13.3739	+	11.9565i	0.537978	+	0.480962i
$619$	7.14970	+	12.3836i	0.287371	+	0.497741i	0.973181	−	0.230039i	$-0.0738855\pi$
$619$	7.14970	+	12.3836i	0.287371	+	0.497741i	−0.685811	+	0.727780i	$0.740552\pi$
$620$	−12.2125	+	12.7479i	−0.490467	+	0.511967i
$621$	1.51593	−	2.62566i	0.0608320	−	0.105364i
$622$	−4.03012	+	19.2957i	−0.161593	+	0.773685i
$623$	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
$626$	6.19597	+	3.12944i	0.247641	+	0.125078i
$627$	−4.56444	−	1.22304i	−0.182286	−	0.0488434i
$628$	−14.8874	−	2.25007i	−0.594071	−	0.0897875i
$629$		−	2.76594i		−	0.110285i
$630$	−7.42382	−	9.55229i	−0.295772	−	0.380573i
$631$		−	30.7128i		−	1.22266i	−0.791377	−	0.611328i	$-0.790636\pi$
$631$		−	30.7128i		−	1.22266i	0.791377	−	0.611328i	$-0.209364\pi$
$632$	27.5085	−	12.5991i	1.09423	−	0.501165i
$633$	−12.5643	−	3.36660i	−0.499387	−	0.133810i
$634$	−21.9346	+	43.4281i	−0.871132	+	1.72475i
$635$	−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
$638$	−9.53141	−	1.99075i	−0.377352	−	0.0788144i
$639$	5.49985	−	9.52602i	0.217571	−	0.376843i
$640$	5.58661	−	24.6737i	0.220830	−	0.975312i
$641$	−20.7752	−	35.9837i	−0.820572	−	1.42127i	−0.905257	−	0.424864i	$-0.860322\pi$
$641$	−20.7752	−	35.9837i	−0.820572	−	1.42127i	0.0846851	−	0.996408i	$-0.473012\pi$
$642$	0.0472652	−	0.0528683i	0.00186541	−	0.00208655i
$643$	12.5692	+	12.5692i	0.495681	+	0.495681i	0.910090	−	0.414410i	$-0.136012\pi$
$643$	12.5692	+	12.5692i	0.495681	+	0.495681i	−0.414410	+	0.910090i	$0.636012\pi$
$644$	1.50091	+	2.47509i	0.0591442	+	0.0975322i
$645$	22.0481	+	26.4410i	0.868142	+	1.04111i
$646$	−14.9492	+	0.836497i	−0.588169	+	0.0329115i
$647$	−34.4127	−	9.22084i	−1.35290	−	0.362509i	−0.491696	−	0.870767i	$-0.663623\pi$
$647$	−34.4127	−	9.22084i	−1.35290	−	0.362509i	−0.861205	+	0.508258i	$0.830290\pi$
$648$	−0.683380	+	7.24033i	−0.0268457	+	0.284427i
$649$	−10.3917	−	5.99966i	−0.407910	−	0.235507i
$650$	−12.2582	−	29.0909i	−0.480805	−	1.14104i
$651$	5.46679	+	11.8163i	0.214261	+	0.463118i
$652$	4.85329	+	12.3807i	0.190070	+	0.484866i
$653$	3.40648	+	12.7132i	0.133306	+	0.497505i	0.999999	−	0.00133684i	$-0.000425528\pi$
$653$	3.40648	+	12.7132i	0.133306	+	0.497505i	−0.866693	+	0.498842i	$0.833759\pi$
$654$	−9.90276	−	5.00166i	−0.387229	−	0.195580i
$655$	−1.00618	+	2.73816i	−0.0393148	+	0.106989i
$656$	−14.4881	+	3.29449i	−0.565666	+	0.128628i
$657$	−15.0499	−	15.0499i	−0.587153	−	0.587153i
$658$	11.4778	+	3.50250i	0.447451	+	0.136542i
$659$	10.3786			0.404294			0.202147	−	0.979355i	$-0.435208\pi$
$659$	10.3786			0.404294			0.202147	+	0.979355i	$0.435208\pi$
$660$	−2.75222	−	4.53932i	−0.107130	−	0.176693i
$661$	−11.5282	−	19.9675i	−0.448397	−	0.776646i	0.549885	−	0.835240i	$-0.314671\pi$
$661$	−11.5282	−	19.9675i	−0.448397	−	0.776646i	−0.998282	+	0.0585946i	$0.981338\pi$
$662$	17.4054	−	5.72352i	0.676481	−	0.222451i
$663$	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
$668$	−13.1148	−	10.4674i	−0.507427	−	0.404995i
$669$	16.3765	−	9.45496i	0.633151	−	0.365550i
$670$	32.1471	+	34.4422i	1.24195	+	1.33062i
$671$		−	5.73573i		−	0.221425i
$672$	−15.4387	−	10.4760i	−0.595562	−	0.404121i
$673$	27.9624	−	27.9624i	1.07787	−	1.07787i	0.0811716	−	0.996700i	$-0.474134\pi$
$673$	27.9624	−	27.9624i	1.07787	−	1.07787i	0.996700	−	0.0811716i	$-0.0258662\pi$
$674$	14.8382	−	0.830285i	0.571546	−	0.0319814i
$675$	11.8662	−	25.0428i	0.456731	−	0.963897i
$676$	−13.7751	+	1.54644i	−0.529813	+	0.0594786i
$677$	33.0709	−	8.86132i	1.27102	−	0.340568i	0.440597	−	0.897705i	$-0.354767\pi$
$677$	33.0709	−	8.86132i	1.27102	−	0.340568i	0.830421	+	0.557137i	$0.188100\pi$
$678$	26.4831	+	5.53131i	1.01708	+	0.212429i
$679$	−9.43821	−	6.65114i	−0.362205	−	0.255247i
$680$	−12.7769	−	10.9390i	−0.489973	−	0.419492i
$681$	6.24694	−	10.8200i	0.239383	−	0.414624i
$682$	−1.66053	−	5.04973i	−0.0635850	−	0.193364i
$683$	0.498756	−	1.86138i	0.0190844	−	0.0712239i	−0.955727	−	0.294255i	$-0.904928\pi$
$683$	0.498756	−	1.86138i	0.0190844	−	0.0712239i	0.974811	+	0.223031i	$0.0715952\pi$
$684$	6.83274	+	9.26588i	0.261256	+	0.354290i
$685$	−2.58302	−	0.234014i	−0.0986922	−	0.00894120i
$686$	5.58620	−	25.5889i	0.213282	−	0.976991i
$687$	−15.0630	+	15.0630i	−0.574691	+	0.574691i
$688$	−41.8091	−	26.3176i	−1.59396	−	1.00335i
$689$	−11.3645	+	6.56128i	−0.432952	+	0.249965i
$690$	−1.14192	+	1.82930i	−0.0434721	+	0.0696402i
$691$	30.8812	+	17.8293i	1.17478	+	0.678257i	0.954800	−	0.297248i	$-0.0960688\pi$
$691$	30.8812	+	17.8293i	1.17478	+	0.678257i	0.219976	+	0.975505i	$0.429402\pi$
$692$	−4.12182	+	1.61577i	−0.156688	+	0.0614225i
$693$	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
$696$	−16.2541	−	19.6422i	−0.616109	−	0.744534i
$697$	−2.55677	+	9.54198i	−0.0968444	+	0.361428i
$698$	−21.0348	−	18.8055i	−0.796177	−	0.711797i
$699$	2.33797			0.0884301
$700$	15.5063	+	21.4372i	0.586083	+	0.810251i
$701$	33.6504			1.27096			0.635479	−	0.772119i	$-0.280803\pi$
$701$	33.6504			1.27096			0.635479	+	0.772119i	$0.280803\pi$
$702$	−26.0871	−	23.3223i	−0.984594	−	0.880245i
$703$	1.07159	−	3.99924i	0.0404159	−	0.150834i
$704$	5.76789	+	4.97586i	0.217385	+	0.187535i
$705$	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
$708$	−11.4667	−	29.2514i	−0.430944	−	1.09934i
$709$	−7.92917	−	4.57791i	−0.297786	−	0.171927i	0.343662	−	0.939093i	$-0.388333\pi$
$709$	−7.92917	−	4.57791i	−0.297786	−	0.171927i	−0.641448	+	0.767167i	$0.721666\pi$
$710$	−12.7384	+	20.4062i	−0.478062	+	0.765833i
$711$	−13.3957	+	7.73401i	−0.502378	+	0.290048i
$712$	−2.49425	−	5.44589i	−0.0934762	−	0.204093i
$713$	−1.52693	+	1.52693i	−0.0571839	+	0.0571839i
$714$	−10.9497	+	5.82945i	−0.409781	+	0.218162i
$715$	9.46674	+	0.857657i	0.354036	+	0.0320745i
$716$	26.5111	−	19.5495i	0.990767	−	0.730601i
$717$	4.91009	−	18.3247i	0.183370	−	0.684348i
$718$	−7.02104	−	21.3512i	−0.262023	−	0.796820i
$719$	−6.67322	+	11.5584i	−0.248869	+	0.431054i	−0.963212	−	0.268742i	$-0.913392\pi$
$719$	−6.67322	+	11.5584i	−0.248869	+	0.431054i	0.714343	+	0.699796i	$0.246726\pi$
$720$	−1.65811	+	12.8265i	−0.0617939	+	0.478015i
$721$	24.4340	−	11.3043i	0.909970	−	0.420996i
$722$	4.36348	+	0.911364i	0.162392	+	0.0339175i
$723$	−15.8651	+	4.25104i	−0.590029	+	0.158098i
$724$	1.33348	+	11.8781i	0.0495582	+	0.441446i
$725$	12.1556	+	34.0492i	0.451449	+	1.26456i
$726$	−17.7664	+	0.994134i	−0.659372	+	0.0368958i
$727$	6.15934	−	6.15934i	0.228437	−	0.228437i	−0.583602	−	0.812040i	$-0.698357\pi$
$727$	6.15934	−	6.15934i	0.228437	−	0.228437i	0.812040	+	0.583602i	$0.198357\pi$
$728$	31.5047	−	11.1166i	1.16764	−	0.412008i
$729$		−	24.4454i		−	0.905384i
$730$	31.7602	+	34.0276i	1.17550	+	1.25942i
$731$	−28.4457	+	16.4231i	−1.05210	+	0.607431i
$732$	9.36848	−	11.7380i	0.346269	−	0.433847i
$733$	2.65865	+	9.92223i	0.0981996	+	0.366486i	0.997485	−	0.0708761i	$-0.0225795\pi$
$733$	2.65865	+	9.92223i	0.0981996	+	0.366486i	−0.899286	+	0.437362i	$0.855913\pi$
$734$	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
$738$	7.21572	−	2.37279i	0.265614	−	0.0873435i
$739$	21.8583	+	37.8597i	0.804070	+	1.39269i	0.916917	+	0.399078i	$0.130670\pi$
$739$	21.8583	+	37.8597i	0.804070	+	1.39269i	−0.112847	+	0.993612i	$0.535997\pi$
$740$	3.97724	−	2.41143i	0.146206	−	0.0886458i
$741$	22.1553			0.813897
$742$	8.03959	−	7.50497i	0.295143	−	0.275516i
$743$	26.0186	+	26.0186i	0.954529	+	0.954529i	0.999010	−	0.0444813i	$-0.0141635\pi$
$743$	26.0186	+	26.0186i	0.954529	+	0.954529i	−0.0444813	+	0.999010i	$0.514164\pi$
$744$	4.84979	−	13.0463i	0.177802	−	0.478302i
$745$	−8.64649	+	23.5300i	−0.316783	+	0.862073i
$746$	−18.6383	−	9.41377i	−0.682396	−	0.344663i
$747$	−3.02975	−	11.3072i	−0.110853	−	0.413709i
$748$	4.71534	−	1.84843i	0.172410	−	0.0675854i
$749$	−0.0446871	−	0.0965899i	−0.00163283	−	0.00352932i
$750$	−9.04860	+	17.5108i	−0.330408	+	0.639405i
$751$	−7.30460	−	4.21731i	−0.266548	−	0.153892i	0.360770	−	0.932655i	$-0.382514\pi$
$751$	−7.30460	−	4.21731i	−0.266548	−	0.153892i	−0.627318	+	0.778763i	$0.715847\pi$
$752$	−5.98535	−	11.3471i	−0.218263	−	0.413784i
$753$	−17.7065	−	4.74444i	−0.645260	−	0.172897i
$754$	45.5811	−	2.55053i	1.65997	−	0.0928850i
$755$	−21.5097	−	25.7954i	−0.782818	−	0.938790i
$756$	25.7080	+	14.1139i	0.934991	+	0.513316i
$757$	3.33081	+	3.33081i	0.121060	+	0.121060i	0.765041	−	0.643981i	$-0.222718\pi$
$757$	3.33081	+	3.33081i	0.121060	+	0.121060i	−0.643981	+	0.765041i	$0.722718\pi$
$758$	24.9369	−	27.8930i	0.905748	−	1.01312i
$759$	−0.324667	−	0.562340i	−0.0117847	−	0.0204117i
$760$	−14.2360	−	20.7667i	−0.516393	−	0.753287i
$761$	17.2317	−	29.8462i	0.624649	−	1.08192i	−0.363959	−	0.931415i	$-0.618575\pi$
$761$	17.2317	−	29.8462i	0.624649	−	1.08192i	0.988609	−	0.150509i	$-0.0480913\pi$
$762$	2.98767	+	0.624010i	0.108232	+	0.0226055i
$763$	−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
$766$	−18.7327	+	37.0888i	−0.676840	+	1.34007i
$767$	54.3419	+	14.5609i	1.96217	+	0.525763i
$768$	3.67642	+	19.6039i	0.132661	+	0.707396i
$769$			18.7498i			0.676135i	0.941122	+	0.338067i	$0.109773\pi$
$769$			18.7498i			0.676135i	−0.941122	+	0.338067i	$0.890227\pi$
$770$	−7.89195	+	1.08857i	−0.284406	+	0.0392295i
$771$		−	16.4777i		−	0.593431i
$772$	4.35164	−	28.7922i	0.156619	−	1.03626i
$773$	−42.9466	−	11.5075i	−1.54468	−	0.413896i	−0.616907	−	0.787036i	$-0.711614\pi$
$773$	−42.9466	−	11.5075i	−1.54468	−	0.413896i	−0.927775	+	0.373140i	$0.878281\pi$
$774$	22.5438	+	11.3864i	0.810320	+	0.409274i
$775$	−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
$778$	2.70418	−	12.9472i	0.0969497	−	0.464181i
$779$	−7.39361	+	12.8061i	−0.264903	+	0.458826i
$780$	17.9725	+	17.2177i	0.643518	+	0.616493i
$781$	−3.62174	−	6.27304i	−0.129596	−	0.224467i
$782$	−1.53382	−	1.37126i	−0.0548493	−	0.0490363i
$783$	28.3379	+	28.3379i	1.01271	+	1.01271i
$784$	−23.6239	+	15.0303i	−0.843712	+	0.536796i
$785$	−16.7650	−	1.51885i	−0.598367	−	0.0542102i
$786$	−0.128496	−	2.29637i	−0.00458329	−	0.0819089i
$787$	1.04293	+	0.279451i	0.0371763	+	0.00996136i	0.277359	−	0.960766i	$-0.410541\pi$
$787$	1.04293	+	0.279451i	0.0371763	+	0.00996136i	−0.240183	+	0.970728i	$0.577207\pi$
$788$	29.0982	−	36.4577i	1.03658	−	1.29875i
$789$	−11.4095	−	6.58729i	−0.406189	−	0.234514i
$790$	29.8610	−	15.8947i	1.06240	−	0.565510i
$791$	23.3883	−	33.1889i	0.831592	−	1.18006i
$792$	−3.17471	−	2.25547i	−0.112808	−	0.0801447i
$793$	6.96017	+	25.9757i	0.247163	+	0.922424i
$794$	11.3295	−	22.4312i	0.402069	−	0.796055i
$795$	7.69070	+	2.82607i	0.272761	+	0.100230i
$796$	−15.5428	+	11.4614i	−0.550900	+	0.406239i
$797$	−13.9414	−	13.9414i	−0.493829	−	0.493829i	0.415681	−	0.909510i	$-0.363543\pi$
$797$	−13.9414	−	13.9414i	−0.493829	−	0.493829i	−0.909510	+	0.415681i	$0.863543\pi$
$798$	−18.0905	+	4.18657i	−0.640397	+	0.148203i
$799$	−8.52950			−0.301752
$800$	4.59027	−	27.9093i	0.162291	−	0.986743i
$801$	1.53111	+	2.65196i	0.0540992	+	0.0937025i
$802$	2.71841	+	8.26676i	0.0959902	+	0.291910i
$803$	−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
$808$	0.380106	−	4.02717i	0.0133721	−	0.141675i
$809$	4.37439	−	2.52555i	0.153795	−	0.0887937i	−0.421127	−	0.907001i	$-0.638365\pi$
$809$	4.37439	−	2.52555i	0.153795	−	0.0887937i	0.574923	+	0.818208i	$0.305032\pi$
$810$	−0.280075	+	8.12608i	−0.00984084	+	0.285521i
$811$			21.1629i			0.743131i	0.928407	+	0.371565i	$0.121179\pi$
$811$			21.1629i			0.743131i	−0.928407	+	0.371565i	$0.878821\pi$
$812$	−36.7364	+	10.6958i	−1.28919	+	0.375349i
$813$	−5.80185	+	5.80185i	−0.203480	+	0.203480i
$814$	0.0782451	+	1.39833i	0.00274249	+	0.0490116i
$815$	6.24174	+	13.4939i	0.218639	+	0.472672i
$816$	12.6689	+	3.91907i	0.443501	+	0.137195i
$817$	−47.4920	+	12.7255i	−1.66154	+	0.445207i
$818$	−1.89274	+	9.06216i	−0.0661781	+	0.316851i
$819$	−15.5009	+	7.17144i	−0.541644	+	0.250590i
$820$	−15.9498	+	4.64251i	−0.556991	+	0.162124i
$821$	−21.3620	+	37.0001i	−0.745540	+	1.29131i	0.204402	+	0.978887i	$0.434475\pi$
$821$	−21.3620	+	37.0001i	−0.745540	+	1.29131i	−0.949942	+	0.312426i	$0.898858\pi$
$822$	1.94252	−	0.638770i	0.0677533	−	0.0222797i
$823$	−1.23565	+	4.61152i	−0.0430722	+	0.160748i	−0.984112	−	0.177548i	$-0.943184\pi$
$823$	−1.23565	+	4.61152i	−0.0430722	+	0.160748i	0.941040	+	0.338295i	$0.109850\pi$
$824$	−26.9775	−	10.0285i	−0.939804	−	0.349359i
$825$	−3.37417	−	4.88263i	−0.117474	−	0.169992i
$826$	−47.1233	−	1.62071i	−1.63963	−	0.0563916i
$827$	−6.21884	+	6.21884i	−0.216250	+	0.216250i	−0.806916	−	0.590666i	$-0.798865\pi$
$827$	−6.21884	+	6.21884i	−0.216250	+	0.216250i	0.590666	+	0.806916i	$0.298865\pi$
$828$	−0.236416	+	1.56422i	−0.00821602	+	0.0543606i
$829$	−33.7077	+	19.4612i	−1.17072	+	0.675915i	−0.953849	−	0.300286i	$-0.902918\pi$
$829$	−33.7077	+	19.4612i	−1.17072	+	0.675915i	−0.216869	+	0.976201i	$0.569585\pi$
$830$	5.77020	+	24.9418i	0.200287	+	0.865743i
$831$	−4.43367	−	2.55978i	−0.153802	−	0.0887978i
$832$	−32.1594	−	15.5353i	−1.11493	−	0.538588i
$833$	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
$836$	7.53399	−	0.845791i	0.260568	−	0.0292523i
$837$	−5.66257	+	21.1330i	−0.195727	+	0.730464i
$838$	16.7691	−	18.7570i	0.579279	−	0.647949i
$839$	−15.0742			−0.520418			−0.260209	−	0.965552i	$-0.583791\pi$
$839$	−15.0742			−0.520418			−0.260209	+	0.965552i	$0.583791\pi$
$840$	−17.9286	−	10.6626i	−0.618596	−	0.367895i
$841$	−23.2844			−0.802910
$842$	−15.5220	+	17.3621i	−0.534925	+	0.598337i
$843$	10.4141	−	38.8660i	0.358681	−	1.33862i
$844$	20.7385	−	2.32817i	0.713848	−	0.0801390i
$845$	−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
$848$	−11.7489	−	0.449132i	−0.403461	−	0.0154233i
$849$	21.0823	+	12.1719i	0.723543	+	0.417738i
$850$	−14.9888	−	11.3568i	−0.514110	−	0.389534i
$851$	0.492709	−	0.284465i	0.0168898	−	0.00975135i
$852$	2.83434	−	18.7531i	0.0971028	−	0.642471i
$853$	−14.0097	+	14.0097i	−0.479684	+	0.479684i	−0.905031	−	0.425346i	$-0.860152\pi$
$853$	−14.0097	+	14.0097i	−0.479684	+	0.479684i	0.425346	+	0.905031i	$0.360152\pi$
$854$	−10.5917	−	19.8947i	−0.362440	−	0.680784i
$855$	8.24327	+	9.88570i	0.281914	+	0.338084i
$856$	−0.0396435	+	0.106644i	−0.00135499	+	0.00364503i
$857$	−9.22615	+	34.4324i	−0.315159	+	1.17619i	0.608682	+	0.793414i	$0.291698\pi$
$857$	−9.22615	+	34.4324i	−0.315159	+	1.17619i	−0.923841	+	0.382776i	$0.874968\pi$
$858$	−7.11932	+	2.34108i	−0.243049	+	0.0799233i
$859$	26.2004	−	45.3805i	0.893947	−	1.54836i	0.0588442	−	0.998267i	$-0.481258\pi$
$859$	26.2004	−	45.3805i	0.893947	−	1.54836i	0.835103	−	0.550094i	$-0.185408\pi$
$860$	−48.4151	−	26.5848i	−1.65094	−	0.906536i
$861$	−1.10450	+	12.2013i	−0.0376411	+	0.415818i
$862$	−4.37546	+	20.9491i	−0.149029	+	0.713528i
$863$	5.09743	−	1.36585i	0.173518	−	0.0464941i	−0.171014	−	0.985269i	$-0.554704\pi$
$863$	5.09743	−	1.36585i	0.173518	−	0.0464941i	0.344532	+	0.938775i	$0.388038\pi$
$864$	−8.64899	−	30.1358i	−0.294245	−	1.02524i
$865$	−4.49244	+	2.07802i	−0.152748	+	0.0706547i
$866$	0.609393	+	10.8906i	0.0207080	+	0.370077i
$867$	−8.75067	+	8.75067i	−0.297188	+	0.297188i
$868$	−15.0846	−	14.4489i	−0.512003	−	0.490429i
$869$			10.1859i			0.345535i
$870$	−19.4495	−	20.8381i	−0.659401	−	0.706478i
$871$	57.6023	−	33.2567i	1.95178	−	1.12686i
$872$	17.7203	+	1.67254i	0.600085	+	0.0566392i
$873$	−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	−0.0720722	−	0.997399i	$-0.522961\pi$
$877$	10.7858	−	2.89005i	0.364211	−	0.0975901i	0.436283	+	0.899809i	$0.356295\pi$
$878$	11.3740	+	34.5887i	0.383854	+	1.16731i
$879$	11.1824	+	19.3685i	0.377174	+	0.653285i
$880$	6.76889	+	5.16883i	0.228179	+	0.174241i
$881$	22.0701			0.743561			0.371781	−	0.928321i	$-0.378747\pi$
$881$	22.0701			0.743561			0.371781	+	0.928321i	$0.378747\pi$
$882$	11.3018	−	8.78481i	0.380551	−	0.295800i
$883$	5.32169	+	5.32169i	0.179089	+	0.179089i	0.790959	−	0.611869i	$-0.209582\pi$
$883$	5.32169	+	5.32169i	0.179089	+	0.179089i	−0.611869	+	0.790959i	$0.709582\pi$
$884$	−19.1116	+	14.0930i	−0.642792	+	0.474000i
$885$	−14.7471	−	31.8816i	−0.495719	−	1.07169i
$886$	11.0233	−	21.8250i	0.370335	−	0.733225i
$887$	1.31079	+	4.89193i	0.0440120	+	0.164255i	0.984434	−	0.175754i	$-0.0562364\pi$
$887$	1.31079	+	4.89193i	0.0440120	+	0.164255i	−0.940422	+	0.340009i	$0.889570\pi$
$888$	−2.12385	+	2.98944i	−0.0712718	+	0.100319i
$889$	2.63853	−	3.74417i	0.0884936	−	0.125576i
$890$	−3.14670	−	5.91161i	−0.105478	−	0.198157i
$891$	−2.12030	−	1.22416i	−0.0710327	−	0.0410108i
$892$	−18.9252	+	23.7118i	−0.633662	+	0.793929i
$893$	−12.3327	−	3.30454i	−0.412699	−	0.110582i
$894$	−1.10421	−	19.7336i	−0.0369303	−	0.659990i
$895$	28.2845	−	23.5853i	0.945448	−	0.788369i
$896$	29.1948	+	6.60803i	0.975328	+	0.220759i
$897$	2.15273	+	2.15273i	0.0718774	+	0.0718774i
$898$	−11.7028	−	10.4625i	−0.390526	−	0.349137i
$899$	−14.2718	−	24.7194i	−0.475990	−	0.824439i
$900$	−0.995564	+	14.4255i	−0.0331855	+	0.480849i
$901$	−3.90860	+	6.76989i	−0.130214	+	0.225538i
$902$	1.02265	−	4.89633i	0.0340507	−	0.163030i
$903$	−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
$906$	23.6367	+	11.9384i	0.785277	+	0.396625i
$907$	−3.27202	−	0.876735i	−0.108646	−	0.0291115i	0.204087	−	0.978953i	$-0.434578\pi$
$907$	−3.27202	−	0.876735i	−0.108646	−	0.0291115i	−0.312732	+	0.949841i	$0.601244\pi$
$908$	−2.99552	+	19.8196i	−0.0994098	+	0.657736i
$909$			2.06796i			0.0685899i
$910$	34.4197	−	14.5066i	1.14100	−	0.480888i
$911$			31.5983i			1.04690i	0.852057	+	0.523449i	$0.175355\pi$
$911$			31.5983i			1.04690i	−0.852057	+	0.523449i	$0.824645\pi$
$912$	16.7995	+	10.5748i	0.556287	+	0.350166i
$913$	−7.44597	−	1.99514i	−0.246426	−	0.0660295i
$914$	13.5407	−	26.8091i	0.447886	−	0.886767i
$915$	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
$918$	−20.4049	−	4.26180i	−0.673462	−	0.140660i
$919$	−23.1351	+	40.0712i	−0.763157	+	1.32183i	0.178058	+	0.984020i	$0.443018\pi$
$919$	−23.1351	+	40.0712i	−0.763157	+	1.32183i	−0.941215	+	0.337807i	$0.890315\pi$
$920$	0.634558	−	3.40104i	0.0209207	−	0.112129i
$921$	8.79800	+	15.2386i	0.289904	+	0.502128i
$922$	−8.12167	+	9.08446i	−0.267473	+	0.299181i
$923$	24.0141	+	24.0141i	0.790435	+	0.790435i
$924$	5.37076	−	3.25686i	0.176685	−	0.107143i
$925$	4.27804	−	2.95637i	0.140661	−	0.0972047i
$926$	3.26169	−	0.182511i	0.107186	−	0.00599768i
$927$	14.2124	+	3.80821i	0.466797	+	0.125078i
$928$	35.7797	+	19.8220i	1.17453	+	0.650689i
$929$	−37.0594	−	21.3962i	−1.21588	−	0.701987i	−0.251844	−	0.967768i	$-0.581037\pi$
$929$	−37.0594	−	21.3962i	−1.21588	−	0.701987i	−0.964034	+	0.265780i	$0.914370\pi$
$930$	4.54297	−	14.8836i	0.148970	−	0.488051i
$931$	−5.00414	+	27.4137i	−0.164004	+	0.898447i
$932$	−3.49220	+	1.36896i	−0.114391	+	0.0448418i
$933$	−4.49719	−	16.7837i	−0.147231	−	0.549475i
$934$	32.1652	+	16.2459i	1.05248	+	0.531583i
$935$	5.13932	−	2.37724i	0.168074	−	0.0777440i
$936$	17.1144	+	6.36204i	0.559402	+	0.207950i
$937$	18.9957	+	18.9957i	0.620561	+	0.620561i	0.945675	−	0.325114i	$-0.105403\pi$
$937$	18.9957	+	18.9957i	0.620561	+	0.620561i	−0.325114	+	0.945675i	$0.605403\pi$
$938$	−40.7497	+	38.0399i	−1.33053	+	1.24205i
$939$	−6.11875			−0.199678
$940$	−7.43627	−	12.2649i	−0.242544	−	0.400036i
$941$	10.8404	+	18.7762i	0.353388	+	0.612086i	0.986841	−	0.161696i	$-0.0516963\pi$
$941$	10.8404	+	18.7762i	0.353388	+	0.612086i	−0.633453	+	0.773781i	$0.718363\pi$
$942$	12.6078	−	4.14590i	0.410785	−	0.135081i
$943$	−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	$-0.163619\pi$
$947$	−3.97536	−	14.8363i	−0.129182	−	0.482114i	−0.999954	+	0.00957300i	$0.996953\pi$
$948$	−16.6373	+	20.8452i	−0.540353	+	0.677019i
$949$	56.9090	−	32.8564i	1.84735	−	1.06657i
$950$	−17.2722	−	22.2277i	−0.560385	−	0.721161i
$951$		−	42.8869i		−	1.39070i
$952$	12.9421	−	15.1188i	0.419456	−	0.490003i
$953$	22.0087	−	22.0087i	0.712931	−	0.712931i	−0.254216	−	0.967147i	$-0.581817\pi$
$953$	22.0087	−	22.0087i	0.712931	−	0.712931i	0.967147	+	0.254216i	$0.0818174\pi$
$954$	6.00141	−	0.335815i	0.194303	−	0.0108724i
$955$	−6.20576	+	16.8880i	−0.200814	+	0.546482i
$956$	3.39557	+	30.2465i	0.109821	+	0.978240i
$957$	8.29061	−	2.22146i	0.267997	−	0.0718096i
$958$	12.8446	+	2.68274i	0.414990	+	0.0866755i
$959$	0.276665	−	3.05629i	0.00893398	−	0.0986929i
$960$	5.40976	+	21.6338i	0.174599	+	0.698228i
$961$	−7.70864	+	13.3518i	−0.248666	+	0.430702i
$962$	−2.05120	−	6.23777i	−0.0661333	−	0.201114i
$963$	0.0150542	−	0.0561830i	0.000485114	−	0.00181047i
$964$	21.2084	−	15.6393i	0.683078	−	0.503708i
$965$	2.93747	−	32.4235i	0.0945604	−	1.04375i
$966$	−2.16455	−	1.35098i	−0.0696434	−	0.0434670i
$967$	16.9281	−	16.9281i	0.544372	−	0.544372i	−0.380435	−	0.924807i	$-0.624226\pi$
$967$	16.9281	−	16.9281i	0.544372	−	0.544372i	0.924807	+	0.380435i	$0.124226\pi$
$968$	25.9554	−	11.8877i	0.834238	−	0.382086i
$969$	11.4299	−	6.59904i	0.367180	−	0.211992i
$970$	3.11054	+	13.4454i	0.0998734	+	0.431705i
$971$	−32.1198	−	18.5444i	−1.03077	−	0.595118i	−0.113568	−	0.993530i	$-0.536228\pi$
$971$	−32.1198	−	18.5444i	−1.03077	−	0.595118i	−0.917206	+	0.398412i	$0.869561\pi$
$972$	9.79698	+	24.9920i	0.314238	+	0.801620i
$973$	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
$976$	−7.12065	+	23.0185i	−0.227926	+	0.736803i
$977$	6.04928	−	22.5762i	0.193534	−	0.722277i	−0.799108	−	0.601188i	$-0.794694\pi$
$977$	6.04928	−	22.5762i	0.193534	−	0.722277i	0.992642	−	0.121090i	$-0.0386389\pi$
$978$	−8.73879	−	7.81264i	−0.279436	−	0.249821i
$979$	2.01652			0.0644484
$980$	−25.3635	+	18.3492i	−0.810208	+	0.586142i
$981$	−9.09942			−0.290522
$982$	2.63545	+	2.35614i	0.0841006	+	0.0751875i
$983$	5.14648	−	19.2069i	0.164147	−	0.612606i	−0.834000	−	0.551764i	$-0.813955\pi$
$983$	5.14648	−	19.2069i	0.164147	−	0.612606i	0.998147	−	0.0608417i	$-0.0193785\pi$
$984$	10.0903	−	8.34979i	0.321666	−	0.266182i
$985$	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
$988$	−33.0932	+	12.9727i	−1.05284	+	0.412716i
$989$	−5.85104	−	3.37810i	−0.186052	−	0.107417i
$990$	−3.69345	−	2.30560i	−0.117386	−	0.0732766i
$991$	−19.5362	+	11.2792i	−0.620586	+	0.358296i	−0.777097	−	0.629380i	$-0.783309\pi$
$991$	−19.5362	+	11.2792i	−0.620586	+	0.358296i	0.156511	+	0.987676i	$0.449975\pi$
$992$	0.394977	+	22.3269i	0.0125405	+	0.708880i
$993$	−11.4204	+	11.4204i	−0.362414	+	0.362414i
$994$	−24.1461	−	15.0705i	−0.765868	−	0.478006i
$995$	−16.5825	+	13.8275i	−0.525701	+	0.438360i
$996$	−11.9791	−	16.2449i	−0.379573	−	0.514739i
$997$	4.45792	−	16.6372i	0.141184	−	0.526905i	−0.858712	−	0.512459i	$-0.828735\pi$
$997$	4.45792	−	16.6372i	0.141184	−	0.526905i	0.999896	−	0.0144466i	$-0.00459864\pi$
$998$	−2.88211	−	8.76459i	−0.0912315	−	0.277438i
$999$	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.107.14	yes	72
4.3	odd	2	inner	140.2.w.b.107.17	yes	72
5.2	odd	4		700.2.be.e.443.14		72
5.3	odd	4	inner	140.2.w.b.23.5	✓	72
5.4	even	2		700.2.be.e.107.5		72
7.2	even	3		980.2.k.k.687.1		36
7.3	odd	6		980.2.x.m.67.11		72
7.4	even	3	inner	140.2.w.b.67.11	yes	72
7.5	odd	6		980.2.k.j.687.1		36
7.6	odd	2		980.2.x.m.667.14		72
20.3	even	4	inner	140.2.w.b.23.11	yes	72
20.7	even	4		700.2.be.e.443.8		72
20.19	odd	2		700.2.be.e.107.2		72
28.3	even	6		980.2.x.m.67.5		72
28.11	odd	6	inner	140.2.w.b.67.5	yes	72
28.19	even	6		980.2.k.j.687.8		36
28.23	odd	6		980.2.k.k.687.8		36
28.27	even	2		980.2.x.m.667.17		72
35.3	even	12		980.2.x.m.263.17		72
35.4	even	6		700.2.be.e.207.8		72
35.13	even	4		980.2.x.m.863.5		72
35.18	odd	12	inner	140.2.w.b.123.17	yes	72
35.23	odd	12		980.2.k.k.883.8		36
35.32	odd	12		700.2.be.e.543.2		72
35.33	even	12		980.2.k.j.883.8		36
140.3	odd	12		980.2.x.m.263.14		72
140.23	even	12		980.2.k.k.883.1		36
140.39	odd	6		700.2.be.e.207.14		72
140.67	even	12		700.2.be.e.543.5		72
140.83	odd	4		980.2.x.m.863.11		72
140.103	odd	12		980.2.k.j.883.1		36
140.123	even	12	inner	140.2.w.b.123.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	5.3	odd	4	inner
140.2.w.b.23.11	yes	72	20.3	even	4	inner
140.2.w.b.67.5	yes	72	28.11	odd	6	inner
140.2.w.b.67.11	yes	72	7.4	even	3	inner
140.2.w.b.107.14	yes	72	1.1	even	1	trivial
140.2.w.b.107.17	yes	72	4.3	odd	2	inner
140.2.w.b.123.14	yes	72	140.123	even	12	inner
140.2.w.b.123.17	yes	72	35.18	odd	12	inner
700.2.be.e.107.2		72	20.19	odd	2
700.2.be.e.107.5		72	5.4	even	2
700.2.be.e.207.8		72	35.4	even	6
700.2.be.e.207.14		72	140.39	odd	6
700.2.be.e.443.8		72	20.7	even	4
700.2.be.e.443.14		72	5.2	odd	4
700.2.be.e.543.2		72	35.32	odd	12
700.2.be.e.543.5		72	140.67	even	12
980.2.k.j.687.1		36	7.5	odd	6
980.2.k.j.687.8		36	28.19	even	6
980.2.k.j.883.1		36	140.103	odd	12
980.2.k.j.883.8		36	35.33	even	12
980.2.k.k.687.1		36	7.2	even	3
980.2.k.k.687.8		36	28.23	odd	6
980.2.k.k.883.1		36	140.23	even	12
980.2.k.k.883.8		36	35.23	odd	12
980.2.x.m.67.5		72	28.3	even	6
980.2.x.m.67.11		72	7.3	odd	6
980.2.x.m.263.14		72	140.3	odd	12
980.2.x.m.263.17		72	35.3	even	12
980.2.x.m.667.14		72	7.6	odd	2
980.2.x.m.667.17		72	28.27	even	2
980.2.x.m.863.5		72	35.13	even	4
980.2.x.m.863.11		72	140.83	odd	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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.942570 - 1.05431i) q^{2} +(-0.322645 + 1.20413i) q^{3} +(-0.223125 - 1.98751i) q^{4} +(-0.381497 - 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(2.60693 - 0.451584i) q^{7} +(-2.30576 - 1.63813i) q^{8} +(1.25225 + 0.722989i) q^{9} +O(q^{10})\)	\(q+(0.942570 - 1.05431i) q^{2} +(-0.322645 + 1.20413i) q^{3} +(-0.223125 - 1.98751i) q^{4} +(-0.381497 - 2.20328i) q^{5} +(0.965404 + 1.47514i) q^{6} +(2.60693 - 0.451584i) q^{7} +(-2.30576 - 1.63813i) q^{8} +(1.25225 + 0.722989i) q^{9} +(-2.68252 - 1.67453i) q^{10} +(0.824629 - 0.476100i) q^{11} +(2.46521 + 0.372591i) q^{12} +(-3.15680 + 3.15680i) q^{13} +(1.98110 - 3.17415i) q^{14} +(2.77612 + 0.251508i) q^{15} +(-3.90043 + 0.886929i) q^{16} +(-0.688322 + 2.56885i) q^{17} +(1.94259 - 0.638792i) q^{18} +(-1.99048 + 3.44760i) q^{19} +(-4.29394 + 1.24984i) q^{20} +(-0.297348 + 3.28477i) q^{21} +(0.275315 - 1.31817i) q^{22} +(-0.528392 + 0.141582i) q^{23} +(2.71646 - 2.24790i) q^{24} +(-4.70892 + 1.68109i) q^{25} +(0.352732 + 6.30375i) q^{26} +(-3.91905 + 3.91905i) q^{27} +(-1.47920 - 5.08055i) q^{28} -7.23080i q^{29} +(2.88186 - 2.68982i) q^{30} +(3.41863 - 1.97375i) q^{31} +(-2.74133 + 4.94824i) 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} +(1.75867 + 5.34818i) q^{38} +(-2.78267 - 4.81972i) q^{39} +(-2.72962 + 5.70519i) q^{40} +3.71449 q^{41} +(3.18289 + 3.40962i) q^{42} +(8.73324 + 8.73324i) q^{43} +(-1.13025 - 1.53273i) q^{44} +(1.11522 - 3.03489i) q^{45} +(-0.348775 + 0.690538i) q^{46} +(0.830089 + 3.09794i) q^{47} +(0.190479 - 4.98278i) q^{48} +(6.59214 - 2.35449i) q^{49} +(-2.66610 + 6.54919i) q^{50} +(-2.87114 - 1.65765i) q^{51} +(6.97856 + 5.56983i) q^{52} +(2.83923 + 0.760768i) q^{53} +(0.437903 + 7.82586i) q^{54} +(-1.36358 - 1.63526i) q^{55} +(-6.75070 - 3.22924i) q^{56} +(-3.50914 - 3.50914i) q^{57} +(-7.62348 - 6.81553i) q^{58} +(-6.30084 - 10.9134i) q^{59} +(-0.119547 - 5.57370i) q^{60} +(3.01183 - 5.21665i) q^{61} +(1.14136 - 5.46468i) q^{62} +(3.59102 + 1.31928i) q^{63} +(2.63307 + 7.55427i) q^{64} +(8.15965 + 5.75103i) q^{65} +(1.49841 + 0.756815i) q^{66} +(-14.3910 - 3.85605i) q^{67} +(5.25921 + 0.794874i) q^{68} -0.681932i q^{69} +(-7.74934 - 3.15400i) q^{70} -7.60710i q^{71} +(-1.70305 - 3.71839i) q^{72} +(-14.2178 - 3.80964i) q^{73} +(-0.663102 + 1.31287i) q^{74} +(-0.504938 - 6.21254i) q^{75} +(7.29629 + 3.18685i) q^{76} +(1.93475 - 1.61355i) q^{77} +(-7.70432 - 1.60914i) q^{78} +(-5.34864 + 9.26412i) q^{79} +(3.44216 + 8.25540i) q^{80} +(-1.28561 - 2.22674i) q^{81} +(3.50117 - 3.91621i) q^{82} +(-5.72446 - 5.72446i) q^{83} +(6.59488 - 0.141933i) q^{84} +(5.92250 + 0.536560i) q^{85} +(17.4392 - 0.975826i) q^{86} +(8.70680 + 2.33298i) q^{87} +(-2.68131 - 0.253076i) q^{88} +(1.83403 + 1.05888i) q^{89} +(-2.14853 - 4.03637i) q^{90} +(-6.80400 + 9.65512i) q^{91} +(0.399294 + 1.01860i) q^{92} +(1.27364 + 4.75329i) q^{93} +(4.04859 + 2.04485i) q^{94} +(8.35541 + 3.07033i) q^{95} +(-5.07384 - 4.89744i) q^{96} +(-3.08588 - 3.08588i) q^{97} +(3.73120 - 9.16941i) 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

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